[gsw] 01/08: New upstream 3.1.1
Alastair McKinstry
mckinstry at moszumanska.debian.org
Wed May 3 10:36:16 UTC 2017
This is an automated email from the git hooks/post-receive script.
mckinstry pushed a commit to branch debian/master
in repository gsw.
commit f4598566be8de7d96e0c116e4264c3b2b1c53824
Author: Alastair McKinstry <mckinstry at debian.org>
Date: Tue May 2 16:52:50 2017 +0100
New upstream 3.1.1
---
CHANGES.txt | 10 -
LICENSE.txt => LICENSE | 12 +-
MANIFEST.in | 7 +-
PKG-INFO | 201 +-
README.rst | 157 +-
gsw.egg-info/PKG-INFO | 201 +-
gsw.egg-info/SOURCES.txt | 65 +-
gsw.egg-info/requires.txt | 1 -
gsw.egg-info/top_level.txt | 3 -
gsw/__init__.py | 54 +-
gsw/_utilities.py | 252 +
gsw/_wrapped_ufuncs.py | 4330 +
gsw/conversions.py | 89 +
gsw/density.py | 27 +
gsw/energy.py | 10 +
gsw/freezing.py | 22 +
gsw/geostrophy.py | 269 +
gsw/gibbs/__init__.py | 20 -
gsw/gibbs/constants.py | 171 -
gsw/gibbs/conversions.py | 1545 -
gsw/gibbs/density_enthalpy_48.py | 1341 -
gsw/gibbs/density_enthalpy_48_ct.py | 107 -
gsw/gibbs/density_enthalpy_75.py | 447 -
gsw/gibbs/density_enthalpy_ct_exact.py | 758 -
gsw/gibbs/derivatives.py | 608 -
gsw/gibbs/earth.py | 198 -
gsw/gibbs/freezing.py | 525 -
gsw/gibbs/geostrophic.py | 17 -
gsw/gibbs/geostrophic_48.py | 42 -
gsw/gibbs/isobaric.py | 57 -
gsw/gibbs/library.py | 1780 -
gsw/gibbs/neutral_nonlinear_48.py | 36 -
gsw/gibbs/practical_salinity.py | 695 -
gsw/gibbs/steric.py | 125 -
gsw/gibbs/thermodynamics_from_t.py | 1709 -
gsw/gibbs/water_column_48.py | 326 -
gsw/ice.py | 39 +
gsw/stability.py | 202 +
gsw/test/__init__.py | 1 -
gsw/test/check_functions.py | 308 -
gsw/test/signatures.py | 178 -
gsw/test/test_octave.py | 245 -
gsw/test/test_profiles.py | 344 -
gsw/utilities/__init__.py | 3 -
gsw/utilities/data/gsw_cf.npz | Bin 266964 -> 0 bytes
gsw/utilities/data/gsw_cv_v3_0.npz | Bin 285644 -> 0 bytes
gsw/utilities/data/gsw_data_v3_0.npz | Bin 4492826 -> 0 bytes
gsw/utilities/data/gsw_demo_data_v3_0.npz | Bin 4456 -> 0 bytes
gsw/utilities/list_npz.py | 27 -
gsw/utilities/mat2npz.py | 51 -
gsw/utilities/utilities.py | 405 -
requirements-dev.txt | 6 -
setup.cfg | 1 -
setup.py | 141 +-
src/_ufuncs.c | 2751 +
src/c_gsw/LICENSE | 34 +
src/c_gsw/gsw_internal_const.h | 499 +
src/c_gsw/gsw_oceanographic_toolbox.c | 10704 +++
src/c_gsw/gsw_saar.c | 272 +
src/c_gsw/gsw_saar_data.c | 122859 +++++++++++++++++++++++++++
src/c_gsw/gswteos-10.h | 294 +
src/method_bodies.c | 69 +
src/method_def_entries.c | 3 +
src2/_ufuncs.c | 2751 +
src2/c_gsw/LICENSE | 34 +
src2/c_gsw/gsw_internal_const.h | 500 +
src2/c_gsw/gsw_oceanographic_toolbox.cpp | 10704 +++
src2/c_gsw/gsw_saar.cpp | 267 +
src2/c_gsw/gsw_saar_data.c | 122859 +++++++++++++++++++++++++++
src2/c_gsw/gswteos-10.h | 294 +
src2/c_gsw/gswteos-10_cpp.h | 294 +
src2/method_bodies.c | 69 +
src2/method_def_entries.c | 3 +
73 files changed, 280870 insertions(+), 12558 deletions(-)
diff --git a/CHANGES.txt b/CHANGES.txt
deleted file mode 100644
index 0962080..0000000
--- a/CHANGES.txt
+++ /dev/null
@@ -1,10 +0,0 @@
-Changelog
----------
-
-Version 3.0.3
-
-* Fixed NumPy 1.8.1 indexing bug.
-
-Version 3.0
-
-* New repository with TEOS-10 code (version 3 only).
diff --git a/LICENSE.txt b/LICENSE
similarity index 65%
rename from LICENSE.txt
rename to LICENSE
index eb056c7..bc55c7d 100644
--- a/LICENSE.txt
+++ b/LICENSE
@@ -1,4 +1,14 @@
-Copyright Notice and Statement for the gsw project:
+The src/c_gsw subdirectory contents are derived from the GSW-C
+project, and are subject to src/c_gsw/LICENSE.
+
+Sections of documentation text, as well as the function names and the
+names of their inputs and outputs, and the algorithms, are ultimately
+derived from the GSW-Matlab implementation and other work of the
+TEOS-10 developers, and may be subject to additional restrictions.
+See http://teos-10.org/ for more information.
+
+Copyright Notice and Statement for the remainder of the gsw project,
+which is this specific Python implementation:
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
diff --git a/MANIFEST.in b/MANIFEST.in
index 64d74b2..82b4fcd 100644
--- a/MANIFEST.in
+++ b/MANIFEST.in
@@ -1,4 +1,5 @@
-include *.txt
+include LICENSE
include README.rst
-recursive-include gsw *.py
-include gsw/utilities/data/*.npz
+recursive-include src *
+recursive-include src2 *
+# recursive-include docs *
diff --git a/PKG-INFO b/PKG-INFO
index 90ff9cf..b160b6d 100644
--- a/PKG-INFO
+++ b/PKG-INFO
@@ -1,11 +1,21 @@
-Metadata-Version: 1.1
+Metadata-Version: 1.2
Name: gsw
-Version: 3.0.6
+Version: 3.1.1
Summary: Gibbs Seawater Oceanographic Package of TEOS-10
-Home-page: https://github.com/TEOS-10/python-gsw
-Author: Filipe Fernandes
-Author-email: ocefpaf at gmail.com
-License: Copyright Notice and Statement for the gsw project:
+Home-page: https://github.com/TEOS-10/GSW-python
+Author: ['Eric Firing', 'Filipe Fernandes']
+Author-email: efiring at hawaii.edu
+License: The src/c_gsw subdirectory contents are derived from the GSW-C
+project, and are subject to src/c_gsw/LICENSE.
+
+Sections of documentation text, as well as the function names and the
+names of their inputs and outputs, and the algorithms, are ultimately
+derived from the GSW-Matlab implementation and other work of the
+TEOS-10 developers, and may be subject to additional restrictions.
+See http://teos-10.org/ for more information.
+
+Copyright Notice and Statement for the remainder of the gsw project,
+which is this specific Python implementation:
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
@@ -26,132 +36,69 @@ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
Download-URL: https://pypi.python.org/pypi/gsw/
-Description: python gsw
- ==========
-
- (This python module is incomplete and should be used with caution!)
-
- .. image:: http://img.shields.io/pypi/v/gsw.svg?style=flat
- :target: https://pypi.python.org/pypi/gsw
- :alt: Version_status
- .. image:: http://img.shields.io/travis/TEOS-10/python-gsw/master.svg?style=flat
- :target: https://travis-ci.org/TEOS-10/python-gsw
- :alt: Build_status
- .. image:: http://img.shields.io/badge/license-MIT-blue.svg?style=flat
- :target: https://github.com/TEOS-10/python-gsw/blob/master/LICENSE.txt
- :alt: license
-
- Python implementation of the Thermodynamic Equation Of Seawater - 2010 (`TEOS-10 <http://www.teos-10.org/>`__)
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
- This module is an python alternative to the gsw MatlabTM toolbox. The
- table below shows some function names in the gibbs library and the
- corresponding function names in the seawater library.
-
- TEOS-10 vs. EOS-80
- ~~~~~~~~~~~~~~~~~~
-
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | **Variable** | **SeaWater (EOS 80)** | **Gibbs SeaWater (GSW TEOS 10)** |
- +===================================================================+==================================================================+==============================================================+
- | Absolute Salinity | NA | gsw.SA\_from\_SP(SP,p,long,lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | Conservative Temperature | NA | gsw.CT\_from\_t(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | density (i.e. in situ density) | sw.dens(SP,t,p) | gsw.rho\_CT(SA,CT,p), or gsw.rho(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | potential density | sw.pden(SP,t,p,pr) | gsw.rho\_CT(SA,CT,pr) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | potential temperature | sw.ptmp(SP,t,p,pr) | gsw.pt\_from\_t(SA,t,p,pr) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | :math:`\sigma_0`, using :math:`\theta_o` = sw.ptmp(SP,t,p,0) | sw.dens(SP, :math:`\theta_o`, 0) -1000 kg m\ :math:`^{-3}` | gsw.sigma0\_CT(SA,CT) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | :math:`\sigma_2`, using :math:`\theta_2` = sw.ptmp(SP,t,p,2000) | sw.dens(SP,\ :math:`\theta_2`, 2000) -1000 kg m\ :math:`^{-3}` | gsw.sigma2\_CT(SA,CT) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | :math:`\sigma_4`, using :math:`\theta_4` = sw.ptmp(SP,t,p,2000) | sw.dens(SP,\ :math:`\theta_4`, 4000) -1000 kg m\ :math:`^{-3}` | gsw.sigma2\_CT(SA,CT) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | specific volume anomaly | sw.svan(SP,t,p) | gsw.specvol\_anom\_CT(SA,CT,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | dynamic height anomaly | -sw.gpan(SP,t,p) | gsw.geo\_strf\_dyn\_height(SA,CT,p,delta\_p,interp\_style) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | geostrophic velocity | sw.gvel(ga,lat,long) | gsw.geostrophic\_velocity(geo\_str,long,lat,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | N\ :math:`^2` | sw.bfrq(SP,t,p,lat) | gsw.Nsquared(SA,CT,p,lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | pressure from height (SW uses depth, not height) | sw.pres(-z,lat) | gsw.p\_from\_z(z,lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | height from pressure (SW outputs depth, not height) | z = -sw.dpth(p,lat) | gsw.z\_from\_p(p,lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | in situ temperature from pt | sw.temp(SP,pt,p,pr) | gsw.pt\_from\_t(SA,pt,pr,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | sound speed | sw.svel(SP,t,p) | gsw.sound\_speed(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | isobaric heat capacity | sw.cp(SP,t,p) | gsw.cp(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | adiabatic lapse rate\* | sw.adtg(SP,t,p) | gsw.adiabatic\_lapse\_rate(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | SP from cndr, (PSS 78) | sw.salt(cndr,t,p) | gsw.SP\_from\_cndr(cndr,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | cndr from SP, (PSS 78) | sw.cndr(SP,t,p) | gsw.cndr\_from\_SP(SP,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | distance | sw.dist(lat,long,units) | gsw.distance(long,lat,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | gravitational acceleration | sw.g(lat,z) | gsw.grav(lat,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | Coriolis parameter | sw.f(lat) | gsw.f(lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-
- Note that the SW and GSW functions output the adiabatic lapse rate in
- different units, being K (dbar):math:`^{-1}` and K Pa\ :math:`^{-1}`
- respectively.
-
- Authors
- ~~~~~~~
-
- - Bjørn Ådlandsvik
- - Eric Firing
- - Filipe Fernandes
-
- Thanks
- ~~~~~~
-
- - Bjørn Ådlandsvik - Testing unit and several bug fixes.
- - Eric Firing - Support for masked arrays, re-write of *delta*\ SA.
- - Trevor J. McDougall (and all of SCOR/IAPSO WG127) for making
- available the Matlab version of this software.
-
- Acknowledgments
- ~~~~~~~~~~~~~~~
-
- - SCOR/IAPSO WG127 for the original MatlabTM code.
-
- Caveats
- ~~~~~~~
-
- - This python module is incomplete and should be used with caution.
- - The database used in ``_delta_SA`` comes from the MatlabTM gsw
- version.
-
- Changelog
- ---------
-
- Version 3.0.3
-
- * Fixed NumPy 1.8.1 indexing bug.
-
- Version 3.0
-
- * New repository with TEOS-10 code (version 3 only).
-
-Keywords: oceanography,seawater,TEOS-10,gibbs
+Description: gsw Python package
+ ==================
+
+ .. image:: https://travis-ci.org/TEOS-10/GSW-Python.svg?branch=master
+ :target: https://travis-ci.org/TEOS-10/GSW-Python
+
+ This Python implementation of the Thermodynamic Equation of
+ Seawater 2010 (TEOS-10) is based primarily on numpy ufunc wrappers of
+ the GSW-C implementation. We expect it to replace the original
+ `python-gsw <https://github.com/TEOS-10/python-gsw/>`__
+ pure-python implementation after a brief overlap period.
+ The primary reasons for this change are that by building on the
+ C implementation we reduce code duplication and we gain an immediate
+ update to the 75-term equation. Additional benefits include a
+ major increase in speed, a reduction in memory usage, and the
+ inclusion of more functions. The penalty is that a C (or MSVC C++ for
+ Windows) compiler is required to build the package from source.
+
+ **Warning: this is for Python >=3.5 only.**
+
+ **Warning:** the only *official* TEOS-10 implementations are
+ provided as zipfiles at <http://www.teos-10.org/software.htm>.
+
+ Documentation is provided at <https://teos-10.github.io/GSW-Python/>.
+
+ For the core functionality, we use an auto-generated C extension
+ module to wrap the C functions as numpy
+ `ufuncs <https://docs.scipy.org/doc/numpy/reference/ufuncs.html>`__,
+ and then use an
+ autogenerated Python module to add docstrings and handle masked
+ arrays. 161 scalar C functions with only double-precision
+ arguments and return values are wrapped as ufuncs, and 155 of
+ these are exposed in the ``gsw`` namespace with an additional
+ wrapper in Python.
+
+ A hand-written wrapper is used for one C function, and others
+ are re-implemented directly in Python instead of being wrapped.
+ Additional functions present in GSW-Matlab but not in GSW-C may
+ be re-implemented in Python, but there is no expectation that
+ all such functions will be provided.
+
+ The package can be installed from a clone of the repo using
+ ``pip install .``. It is neither necessary nor recommended
+ to run the code generators, and no instructions are provided
+ for them; their output is
+ included in the repo. You will need a suitable compiler: gcc or
+ clang for unix-like systems, or the MSVC compiler set used for Python
+ itself on Windows. For Windows, some of the source code has been
+ modified to C++ because the MSVC C compiler does not support the
+ C99 complex data type used in original GSW-C.
+
+ To test, after installation, run "py.test" from the source directory.
+
+Keywords: oceanography,seawater,TEOS-10
Platform: any
Classifier: Development Status :: 4 - Beta
Classifier: Environment :: Console
Classifier: Intended Audience :: Science/Research
-Classifier: Intended Audience :: Developers
-Classifier: Intended Audience :: Education
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python
-Classifier: Topic :: Education
+Classifier: Programming Language :: Python :: 3 :: Only
+Classifier: Programming Language :: Python :: 3.5
+Classifier: Programming Language :: Python :: 3.6
Classifier: Topic :: Scientific/Engineering
+Requires-Python: >=3.5
diff --git a/README.rst b/README.rst
index 2722859..22e2ca3 100644
--- a/README.rst
+++ b/README.rst
@@ -1,105 +1,52 @@
-python gsw
-==========
-
-(This python module is incomplete and should be used with caution!)
-
-.. image:: http://img.shields.io/pypi/v/gsw.svg?style=flat
- :target: https://pypi.python.org/pypi/gsw
- :alt: Version_status
-.. image:: http://img.shields.io/travis/TEOS-10/python-gsw/master.svg?style=flat
- :target: https://travis-ci.org/TEOS-10/python-gsw
- :alt: Build_status
-.. image:: http://img.shields.io/badge/license-MIT-blue.svg?style=flat
- :target: https://github.com/TEOS-10/python-gsw/blob/master/LICENSE.txt
- :alt: license
-
-Python implementation of the Thermodynamic Equation Of Seawater - 2010 (`TEOS-10 <http://www.teos-10.org/>`__)
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-This module is an python alternative to the gsw MatlabTM toolbox. The
-table below shows some function names in the gibbs library and the
-corresponding function names in the seawater library.
-
-TEOS-10 vs. EOS-80
-~~~~~~~~~~~~~~~~~~
-
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| **Variable** | **SeaWater (EOS 80)** | **Gibbs SeaWater (GSW TEOS 10)** |
-+===================================================================+==================================================================+==============================================================+
-| Absolute Salinity | NA | gsw.SA\_from\_SP(SP,p,long,lat) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| Conservative Temperature | NA | gsw.CT\_from\_t(SA,t,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| density (i.e. in situ density) | sw.dens(SP,t,p) | gsw.rho\_CT(SA,CT,p), or gsw.rho(SA,t,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| potential density | sw.pden(SP,t,p,pr) | gsw.rho\_CT(SA,CT,pr) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| potential temperature | sw.ptmp(SP,t,p,pr) | gsw.pt\_from\_t(SA,t,p,pr) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| :math:`\sigma_0`, using :math:`\theta_o` = sw.ptmp(SP,t,p,0) | sw.dens(SP, :math:`\theta_o`, 0) -1000 kg m\ :math:`^{-3}` | gsw.sigma0\_CT(SA,CT) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| :math:`\sigma_2`, using :math:`\theta_2` = sw.ptmp(SP,t,p,2000) | sw.dens(SP,\ :math:`\theta_2`, 2000) -1000 kg m\ :math:`^{-3}` | gsw.sigma2\_CT(SA,CT) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| :math:`\sigma_4`, using :math:`\theta_4` = sw.ptmp(SP,t,p,2000) | sw.dens(SP,\ :math:`\theta_4`, 4000) -1000 kg m\ :math:`^{-3}` | gsw.sigma2\_CT(SA,CT) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| specific volume anomaly | sw.svan(SP,t,p) | gsw.specvol\_anom\_CT(SA,CT,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| dynamic height anomaly | -sw.gpan(SP,t,p) | gsw.geo\_strf\_dyn\_height(SA,CT,p,delta\_p,interp\_style) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| geostrophic velocity | sw.gvel(ga,lat,long) | gsw.geostrophic\_velocity(geo\_str,long,lat,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| N\ :math:`^2` | sw.bfrq(SP,t,p,lat) | gsw.Nsquared(SA,CT,p,lat) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| pressure from height (SW uses depth, not height) | sw.pres(-z,lat) | gsw.p\_from\_z(z,lat) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| height from pressure (SW outputs depth, not height) | z = -sw.dpth(p,lat) | gsw.z\_from\_p(p,lat) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| in situ temperature from pt | sw.temp(SP,pt,p,pr) | gsw.pt\_from\_t(SA,pt,pr,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| sound speed | sw.svel(SP,t,p) | gsw.sound\_speed(SA,t,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| isobaric heat capacity | sw.cp(SP,t,p) | gsw.cp(SA,t,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| adiabatic lapse rate\* | sw.adtg(SP,t,p) | gsw.adiabatic\_lapse\_rate(SA,t,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| SP from cndr, (PSS 78) | sw.salt(cndr,t,p) | gsw.SP\_from\_cndr(cndr,t,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| cndr from SP, (PSS 78) | sw.cndr(SP,t,p) | gsw.cndr\_from\_SP(SP,t,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| distance | sw.dist(lat,long,units) | gsw.distance(long,lat,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| gravitational acceleration | sw.g(lat,z) | gsw.grav(lat,p) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-| Coriolis parameter | sw.f(lat) | gsw.f(lat) |
-+-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-
-Note that the SW and GSW functions output the adiabatic lapse rate in
-different units, being K (dbar):math:`^{-1}` and K Pa\ :math:`^{-1}`
-respectively.
-
-Authors
-~~~~~~~
-
-- Bjørn Ådlandsvik
-- Eric Firing
-- Filipe Fernandes
-
-Thanks
-~~~~~~
-
-- Bjørn Ådlandsvik - Testing unit and several bug fixes.
-- Eric Firing - Support for masked arrays, re-write of *delta*\ SA.
-- Trevor J. McDougall (and all of SCOR/IAPSO WG127) for making
- available the Matlab version of this software.
-
-Acknowledgments
-~~~~~~~~~~~~~~~
-
-- SCOR/IAPSO WG127 for the original MatlabTM code.
-
-Caveats
-~~~~~~~
-
-- This python module is incomplete and should be used with caution.
-- The database used in ``_delta_SA`` comes from the MatlabTM gsw
- version.
+gsw Python package
+==================
+
+.. image:: https://travis-ci.org/TEOS-10/GSW-Python.svg?branch=master
+ :target: https://travis-ci.org/TEOS-10/GSW-Python
+
+This Python implementation of the Thermodynamic Equation of
+Seawater 2010 (TEOS-10) is based primarily on numpy ufunc wrappers of
+the GSW-C implementation. We expect it to replace the original
+`python-gsw <https://github.com/TEOS-10/python-gsw/>`__
+pure-python implementation after a brief overlap period.
+The primary reasons for this change are that by building on the
+C implementation we reduce code duplication and we gain an immediate
+update to the 75-term equation. Additional benefits include a
+major increase in speed, a reduction in memory usage, and the
+inclusion of more functions. The penalty is that a C (or MSVC C++ for
+Windows) compiler is required to build the package from source.
+
+**Warning: this is for Python >=3.5 only.**
+
+**Warning:** the only *official* TEOS-10 implementations are
+provided as zipfiles at <http://www.teos-10.org/software.htm>.
+
+Documentation is provided at <https://teos-10.github.io/GSW-Python/>.
+
+For the core functionality, we use an auto-generated C extension
+module to wrap the C functions as numpy
+`ufuncs <https://docs.scipy.org/doc/numpy/reference/ufuncs.html>`__,
+and then use an
+autogenerated Python module to add docstrings and handle masked
+arrays. 161 scalar C functions with only double-precision
+arguments and return values are wrapped as ufuncs, and 155 of
+these are exposed in the ``gsw`` namespace with an additional
+wrapper in Python.
+
+A hand-written wrapper is used for one C function, and others
+are re-implemented directly in Python instead of being wrapped.
+Additional functions present in GSW-Matlab but not in GSW-C may
+be re-implemented in Python, but there is no expectation that
+all such functions will be provided.
+
+The package can be installed from a clone of the repo using
+``pip install .``. It is neither necessary nor recommended
+to run the code generators, and no instructions are provided
+for them; their output is
+included in the repo. You will need a suitable compiler: gcc or
+clang for unix-like systems, or the MSVC compiler set used for Python
+itself on Windows. For Windows, some of the source code has been
+modified to C++ because the MSVC C compiler does not support the
+C99 complex data type used in original GSW-C.
+
+To test, after installation, run "py.test" from the source directory.
diff --git a/gsw.egg-info/PKG-INFO b/gsw.egg-info/PKG-INFO
index 90ff9cf..b160b6d 100644
--- a/gsw.egg-info/PKG-INFO
+++ b/gsw.egg-info/PKG-INFO
@@ -1,11 +1,21 @@
-Metadata-Version: 1.1
+Metadata-Version: 1.2
Name: gsw
-Version: 3.0.6
+Version: 3.1.1
Summary: Gibbs Seawater Oceanographic Package of TEOS-10
-Home-page: https://github.com/TEOS-10/python-gsw
-Author: Filipe Fernandes
-Author-email: ocefpaf at gmail.com
-License: Copyright Notice and Statement for the gsw project:
+Home-page: https://github.com/TEOS-10/GSW-python
+Author: ['Eric Firing', 'Filipe Fernandes']
+Author-email: efiring at hawaii.edu
+License: The src/c_gsw subdirectory contents are derived from the GSW-C
+project, and are subject to src/c_gsw/LICENSE.
+
+Sections of documentation text, as well as the function names and the
+names of their inputs and outputs, and the algorithms, are ultimately
+derived from the GSW-Matlab implementation and other work of the
+TEOS-10 developers, and may be subject to additional restrictions.
+See http://teos-10.org/ for more information.
+
+Copyright Notice and Statement for the remainder of the gsw project,
+which is this specific Python implementation:
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
@@ -26,132 +36,69 @@ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
Download-URL: https://pypi.python.org/pypi/gsw/
-Description: python gsw
- ==========
-
- (This python module is incomplete and should be used with caution!)
-
- .. image:: http://img.shields.io/pypi/v/gsw.svg?style=flat
- :target: https://pypi.python.org/pypi/gsw
- :alt: Version_status
- .. image:: http://img.shields.io/travis/TEOS-10/python-gsw/master.svg?style=flat
- :target: https://travis-ci.org/TEOS-10/python-gsw
- :alt: Build_status
- .. image:: http://img.shields.io/badge/license-MIT-blue.svg?style=flat
- :target: https://github.com/TEOS-10/python-gsw/blob/master/LICENSE.txt
- :alt: license
-
- Python implementation of the Thermodynamic Equation Of Seawater - 2010 (`TEOS-10 <http://www.teos-10.org/>`__)
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
- This module is an python alternative to the gsw MatlabTM toolbox. The
- table below shows some function names in the gibbs library and the
- corresponding function names in the seawater library.
-
- TEOS-10 vs. EOS-80
- ~~~~~~~~~~~~~~~~~~
-
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | **Variable** | **SeaWater (EOS 80)** | **Gibbs SeaWater (GSW TEOS 10)** |
- +===================================================================+==================================================================+==============================================================+
- | Absolute Salinity | NA | gsw.SA\_from\_SP(SP,p,long,lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | Conservative Temperature | NA | gsw.CT\_from\_t(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | density (i.e. in situ density) | sw.dens(SP,t,p) | gsw.rho\_CT(SA,CT,p), or gsw.rho(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | potential density | sw.pden(SP,t,p,pr) | gsw.rho\_CT(SA,CT,pr) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | potential temperature | sw.ptmp(SP,t,p,pr) | gsw.pt\_from\_t(SA,t,p,pr) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | :math:`\sigma_0`, using :math:`\theta_o` = sw.ptmp(SP,t,p,0) | sw.dens(SP, :math:`\theta_o`, 0) -1000 kg m\ :math:`^{-3}` | gsw.sigma0\_CT(SA,CT) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | :math:`\sigma_2`, using :math:`\theta_2` = sw.ptmp(SP,t,p,2000) | sw.dens(SP,\ :math:`\theta_2`, 2000) -1000 kg m\ :math:`^{-3}` | gsw.sigma2\_CT(SA,CT) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | :math:`\sigma_4`, using :math:`\theta_4` = sw.ptmp(SP,t,p,2000) | sw.dens(SP,\ :math:`\theta_4`, 4000) -1000 kg m\ :math:`^{-3}` | gsw.sigma2\_CT(SA,CT) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | specific volume anomaly | sw.svan(SP,t,p) | gsw.specvol\_anom\_CT(SA,CT,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | dynamic height anomaly | -sw.gpan(SP,t,p) | gsw.geo\_strf\_dyn\_height(SA,CT,p,delta\_p,interp\_style) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | geostrophic velocity | sw.gvel(ga,lat,long) | gsw.geostrophic\_velocity(geo\_str,long,lat,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | N\ :math:`^2` | sw.bfrq(SP,t,p,lat) | gsw.Nsquared(SA,CT,p,lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | pressure from height (SW uses depth, not height) | sw.pres(-z,lat) | gsw.p\_from\_z(z,lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | height from pressure (SW outputs depth, not height) | z = -sw.dpth(p,lat) | gsw.z\_from\_p(p,lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | in situ temperature from pt | sw.temp(SP,pt,p,pr) | gsw.pt\_from\_t(SA,pt,pr,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | sound speed | sw.svel(SP,t,p) | gsw.sound\_speed(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | isobaric heat capacity | sw.cp(SP,t,p) | gsw.cp(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | adiabatic lapse rate\* | sw.adtg(SP,t,p) | gsw.adiabatic\_lapse\_rate(SA,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | SP from cndr, (PSS 78) | sw.salt(cndr,t,p) | gsw.SP\_from\_cndr(cndr,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | cndr from SP, (PSS 78) | sw.cndr(SP,t,p) | gsw.cndr\_from\_SP(SP,t,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | distance | sw.dist(lat,long,units) | gsw.distance(long,lat,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | gravitational acceleration | sw.g(lat,z) | gsw.grav(lat,p) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
- | Coriolis parameter | sw.f(lat) | gsw.f(lat) |
- +-------------------------------------------------------------------+------------------------------------------------------------------+--------------------------------------------------------------+
-
- Note that the SW and GSW functions output the adiabatic lapse rate in
- different units, being K (dbar):math:`^{-1}` and K Pa\ :math:`^{-1}`
- respectively.
-
- Authors
- ~~~~~~~
-
- - Bjørn Ådlandsvik
- - Eric Firing
- - Filipe Fernandes
-
- Thanks
- ~~~~~~
-
- - Bjørn Ådlandsvik - Testing unit and several bug fixes.
- - Eric Firing - Support for masked arrays, re-write of *delta*\ SA.
- - Trevor J. McDougall (and all of SCOR/IAPSO WG127) for making
- available the Matlab version of this software.
-
- Acknowledgments
- ~~~~~~~~~~~~~~~
-
- - SCOR/IAPSO WG127 for the original MatlabTM code.
-
- Caveats
- ~~~~~~~
-
- - This python module is incomplete and should be used with caution.
- - The database used in ``_delta_SA`` comes from the MatlabTM gsw
- version.
-
- Changelog
- ---------
-
- Version 3.0.3
-
- * Fixed NumPy 1.8.1 indexing bug.
-
- Version 3.0
-
- * New repository with TEOS-10 code (version 3 only).
-
-Keywords: oceanography,seawater,TEOS-10,gibbs
+Description: gsw Python package
+ ==================
+
+ .. image:: https://travis-ci.org/TEOS-10/GSW-Python.svg?branch=master
+ :target: https://travis-ci.org/TEOS-10/GSW-Python
+
+ This Python implementation of the Thermodynamic Equation of
+ Seawater 2010 (TEOS-10) is based primarily on numpy ufunc wrappers of
+ the GSW-C implementation. We expect it to replace the original
+ `python-gsw <https://github.com/TEOS-10/python-gsw/>`__
+ pure-python implementation after a brief overlap period.
+ The primary reasons for this change are that by building on the
+ C implementation we reduce code duplication and we gain an immediate
+ update to the 75-term equation. Additional benefits include a
+ major increase in speed, a reduction in memory usage, and the
+ inclusion of more functions. The penalty is that a C (or MSVC C++ for
+ Windows) compiler is required to build the package from source.
+
+ **Warning: this is for Python >=3.5 only.**
+
+ **Warning:** the only *official* TEOS-10 implementations are
+ provided as zipfiles at <http://www.teos-10.org/software.htm>.
+
+ Documentation is provided at <https://teos-10.github.io/GSW-Python/>.
+
+ For the core functionality, we use an auto-generated C extension
+ module to wrap the C functions as numpy
+ `ufuncs <https://docs.scipy.org/doc/numpy/reference/ufuncs.html>`__,
+ and then use an
+ autogenerated Python module to add docstrings and handle masked
+ arrays. 161 scalar C functions with only double-precision
+ arguments and return values are wrapped as ufuncs, and 155 of
+ these are exposed in the ``gsw`` namespace with an additional
+ wrapper in Python.
+
+ A hand-written wrapper is used for one C function, and others
+ are re-implemented directly in Python instead of being wrapped.
+ Additional functions present in GSW-Matlab but not in GSW-C may
+ be re-implemented in Python, but there is no expectation that
+ all such functions will be provided.
+
+ The package can be installed from a clone of the repo using
+ ``pip install .``. It is neither necessary nor recommended
+ to run the code generators, and no instructions are provided
+ for them; their output is
+ included in the repo. You will need a suitable compiler: gcc or
+ clang for unix-like systems, or the MSVC compiler set used for Python
+ itself on Windows. For Windows, some of the source code has been
+ modified to C++ because the MSVC C compiler does not support the
+ C99 complex data type used in original GSW-C.
+
+ To test, after installation, run "py.test" from the source directory.
+
+Keywords: oceanography,seawater,TEOS-10
Platform: any
Classifier: Development Status :: 4 - Beta
Classifier: Environment :: Console
Classifier: Intended Audience :: Science/Research
-Classifier: Intended Audience :: Developers
-Classifier: Intended Audience :: Education
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python
-Classifier: Topic :: Education
+Classifier: Programming Language :: Python :: 3 :: Only
+Classifier: Programming Language :: Python :: 3.5
+Classifier: Programming Language :: Python :: 3.6
Classifier: Topic :: Scientific/Engineering
+Requires-Python: >=3.5
diff --git a/gsw.egg-info/SOURCES.txt b/gsw.egg-info/SOURCES.txt
index 3b35499..909ba26 100644
--- a/gsw.egg-info/SOURCES.txt
+++ b/gsw.egg-info/SOURCES.txt
@@ -1,44 +1,37 @@
-CHANGES.txt
-LICENSE.txt
+LICENSE
MANIFEST.in
README.rst
-requirements-dev.txt
setup.py
gsw/__init__.py
+gsw/_utilities.py
+gsw/_wrapped_ufuncs.py
+gsw/conversions.py
+gsw/density.py
+gsw/energy.py
+gsw/freezing.py
+gsw/geostrophy.py
+gsw/ice.py
+gsw/stability.py
gsw.egg-info/PKG-INFO
gsw.egg-info/SOURCES.txt
gsw.egg-info/dependency_links.txt
-gsw.egg-info/requires.txt
gsw.egg-info/top_level.txt
-gsw/gibbs/__init__.py
-gsw/gibbs/constants.py
-gsw/gibbs/conversions.py
-gsw/gibbs/density_enthalpy_48.py
-gsw/gibbs/density_enthalpy_48_ct.py
-gsw/gibbs/density_enthalpy_75.py
-gsw/gibbs/density_enthalpy_ct_exact.py
-gsw/gibbs/derivatives.py
-gsw/gibbs/earth.py
-gsw/gibbs/freezing.py
-gsw/gibbs/geostrophic.py
-gsw/gibbs/geostrophic_48.py
-gsw/gibbs/isobaric.py
-gsw/gibbs/library.py
-gsw/gibbs/neutral_nonlinear_48.py
-gsw/gibbs/practical_salinity.py
-gsw/gibbs/steric.py
-gsw/gibbs/thermodynamics_from_t.py
-gsw/gibbs/water_column_48.py
-gsw/test/__init__.py
-gsw/test/check_functions.py
-gsw/test/signatures.py
-gsw/test/test_octave.py
-gsw/test/test_profiles.py
-gsw/utilities/__init__.py
-gsw/utilities/list_npz.py
-gsw/utilities/mat2npz.py
-gsw/utilities/utilities.py
-gsw/utilities/data/gsw_cf.npz
-gsw/utilities/data/gsw_cv_v3_0.npz
-gsw/utilities/data/gsw_data_v3_0.npz
-gsw/utilities/data/gsw_demo_data_v3_0.npz
\ No newline at end of file
+src/_ufuncs.c
+src/method_bodies.c
+src/method_def_entries.c
+src/c_gsw/LICENSE
+src/c_gsw/gsw_internal_const.h
+src/c_gsw/gsw_oceanographic_toolbox.c
+src/c_gsw/gsw_saar.c
+src/c_gsw/gsw_saar_data.c
+src/c_gsw/gswteos-10.h
+src2/_ufuncs.c
+src2/method_bodies.c
+src2/method_def_entries.c
+src2/c_gsw/LICENSE
+src2/c_gsw/gsw_internal_const.h
+src2/c_gsw/gsw_oceanographic_toolbox.cpp
+src2/c_gsw/gsw_saar.cpp
+src2/c_gsw/gsw_saar_data.c
+src2/c_gsw/gswteos-10.h
+src2/c_gsw/gswteos-10_cpp.h
\ No newline at end of file
diff --git a/gsw.egg-info/requires.txt b/gsw.egg-info/requires.txt
deleted file mode 100644
index 24ce15a..0000000
--- a/gsw.egg-info/requires.txt
+++ /dev/null
@@ -1 +0,0 @@
-numpy
diff --git a/gsw.egg-info/top_level.txt b/gsw.egg-info/top_level.txt
index d9a3fb5..7b1b7b2 100644
--- a/gsw.egg-info/top_level.txt
+++ b/gsw.egg-info/top_level.txt
@@ -1,4 +1 @@
-gsw/utilities
-gsw/gibbs
-gsw/test
gsw
diff --git a/gsw/__init__.py b/gsw/__init__.py
index 9b5a5e2..be9225c 100644
--- a/gsw/__init__.py
+++ b/gsw/__init__.py
@@ -1,12 +1,48 @@
-# -*- coding: utf-8 -*-
+"""
+This is a Python implementation of the Gibbs SeaWater (GSW) Oceanographic
+Toolbox of TEOS-10. Extensive documentation is available from
+http://www.teos-10.org/; users of this Python package are strongly
+encouraged to study the documents posted there.
-from .gibbs import *
-from .utilities import (Bunch, match_args_return, read_data, strip_mask,
- loadmatbunch)
+This implementation is based on GSW-C for core functions, with
+additional functions written in Python. GSW-C is the
+work of Frank Delahoyde and Glenn Hyland (author of GSW-Fortran,
+on which GSW-C is based), who translated and re-implemented the
+algorithms originally written in Matlab by David Jackett,
+Trevor McDougall, and Paul Barker.
-data = read_data('gsw_data_v3_0.npz')
+The present Python library has an interface that is similar to the
+original Matlab code, but with a few important differences:
-__version__ = '3.0.6'
-__all__ = ['gibbs', 'utilities']
-__data_date__ = str(data['version_date'])
-__data_version__ = str(data['version_number'])
+- Many functions in the GSW-Matlab toolbox are not yet available here.
+- Taking advantage of Python namespaces, we omit the "gsw" prefix
+ from the function names.
+- Missing values may be handled using `numpy.ma` masked arrays, or
+ using `nan` values.
+- All functions follow numpy broadcasting rules; function arguments
+ must be broadcastable to the dimensions of the highest-dimensioned
+ argument. Recall that with numpy broadcasting, extra dimensions
+ are automatically added as needed on the left, but must be added
+ explicitly as needed on the right.
+- Functions such as `Nsquared` that operate on profiles rather than
+ scalars have an `axis` keyword argument to specify the index that
+ is incremented along the pressure (depth) axis.
+
+"""
+
+
+from ._wrapped_ufuncs import *
+
+from .stability import *
+from .geostrophy import *
+from . import geostrophy
+from . import stability
+from . import density
+from . import energy
+from . import conversions
+
+from . import ice
+
+from .conversions import t90_from_t68
+
+__version__ = "3.1.1"
diff --git a/gsw/_utilities.py b/gsw/_utilities.py
new file mode 100644
index 0000000..09af840
--- /dev/null
+++ b/gsw/_utilities.py
@@ -0,0 +1,252 @@
+from functools import wraps
+
+import numpy as np
+
+def masked_to_nan(arg):
+ """
+ Convert a masked array to a float ndarray with nans; ensure
+ other arguments are float arrays or scalars.
+ """
+ if np.ma.isMaskedArray(arg):
+ if arg.dtype.kind == 'f':
+ return arg.filled(np.nan)
+ else:
+ return arg.astype(float).filled(np.nan)
+ else:
+ return np.asarray(arg, dtype=float)
+
+def match_args_return(f):
+ """
+ Decorator for most functions that operate on profile data.
+ """
+ @wraps(f)
+ def wrapper(*args, **kw):
+ p = kw.get('p', None)
+ if p is not None:
+ args = list(args)
+ args.append(p)
+
+ isarray = np.any([hasattr(a, '__iter__') for a in args])
+ ismasked = np.any([np.ma.isMaskedArray(a) for a in args])
+
+ def fixup(ret):
+ if ismasked:
+ ret = np.ma.masked_invalid(ret)
+ if not isarray and isinstance(ret, np.ndarray):
+ ret = ret[0]
+ return ret
+
+ if ismasked:
+ newargs = [masked_to_nan(a) for a in args]
+ else:
+ newargs = [np.asarray(a, dtype=float) for a in args]
+
+ if p is not None:
+ kw['p'] = newargs.pop()
+
+ ret = f(*newargs, **kw)
+
+ if isinstance(ret, tuple):
+ retlist = [fixup(arg) for arg in ret]
+ ret = tuple(retlist)
+ else:
+ ret = fixup(ret)
+ return ret
+ wrapper.__wrapped__ = f
+ return wrapper
+
+
+def axis_slicer(n, sl, axis):
+ """
+ Return an indexing tuple for an array with `n` dimensions,
+ with slice `sl` taken on `axis`.
+ """
+ itup = [slice(None)] * n
+ itup[axis] = sl
+ return tuple(itup)
+
+
+def indexer(shape, axis, order='C'):
+ """
+ Generator of indexing tuples for "apply_along_axis" usage.
+
+ The generator cycles through all axes other than `axis`.
+ The numpy np.apply_along_axis function only works with functions
+ of a single array; this generator allows us work with a function
+ of more than one array.
+ """
+
+ ndim = len(shape)
+ ind_shape = list(shape)
+ ind_shape[axis] = 1 # "axis" and any dim of 1 will not be incremented
+ # list of indices, with a slice at "axis"
+ inds = [0] * ndim
+ inds[axis] = slice(None)
+ kmax = np.prod(ind_shape)
+
+ if order == 'C':
+ index_position = list(reversed(range(ndim)))
+ else:
+ index_position = list(range(ndim))
+
+ for k in range(kmax):
+ yield tuple(inds)
+
+ for i in index_position:
+ if ind_shape[i] == 1:
+ continue
+ inds[i] += 1
+ if inds[i] == ind_shape[i]:
+ inds[i] = 0
+ else:
+ break
+
+
+# This is straight from pycurrents.system. We can trim out
+# the parts we don't need, but there is no rush to do so.
+class Bunch(dict):
+ """
+ A dictionary that also provides access via attributes.
+
+ Additional methods update_values and update_None provide
+ control over whether new keys are added to the dictionary
+ when updating, and whether an attempt to add a new key is
+ ignored or raises a KeyError.
+
+ The Bunch also prints differently than a normal
+ dictionary, using str() instead of repr() for its
+ keys and values, and in key-sorted order. The printing
+ format can be customized by subclassing with a different
+ str_ftm class attribute. Do not assign directly to this
+ class attribute, because that would substitute an instance
+ attribute which would then become part of the Bunch, and
+ would be reported as such by the keys() method.
+
+ To output a string representation with
+ a particular format, without subclassing, use the
+ formatted() method.
+ """
+
+ str_fmt = "{0!s:<{klen}} : {1!s:>{vlen}}\n"
+
+ def __init__(self, *args, **kwargs):
+ """
+ *args* can be dictionaries, bunches, or sequences of
+ key,value tuples. *kwargs* can be used to initialize
+ or add key, value pairs.
+ """
+ dict.__init__(self)
+ for arg in args:
+ self.update(arg)
+ self.update(kwargs)
+
+ def __getattr__(self, name):
+ try:
+ return self[name]
+ except KeyError:
+ raise AttributeError("'Bunch' object has no attribute '%s'" % name)
+
+ def __setattr__(self, name, value):
+ self[name] = value
+
+ def __str__(self):
+ return self.formatted()
+
+ def formatted(self, fmt=None, types=False):
+ """
+ Return a string with keys and/or values or types.
+
+ *fmt* is a format string as used in the str.format() method.
+
+ The str.format() method is called with key, value as positional
+ arguments, and klen, vlen as kwargs. The latter are the maxima
+ of the string lengths for the keys and values, respectively,
+ up to respective maxima of 20 and 40.
+ """
+ if fmt is None:
+ fmt = self.str_fmt
+
+ items = list(self.items())
+ items.sort()
+
+ klens = []
+ vlens = []
+ for i, (k, v) in enumerate(items):
+ lenk = len(str(k))
+ if types:
+ v = type(v).__name__
+ lenv = len(str(v))
+ items[i] = (k, v)
+ klens.append(lenk)
+ vlens.append(lenv)
+
+ klen = min(20, max(klens))
+ vlen = min(40, max(vlens))
+ slist = [fmt.format(k, v, klen=klen, vlen=vlen) for k, v in items]
+ return ''.join(slist)
+
+ def from_pyfile(self, filename):
+ """
+ Read in variables from a python code file.
+ """
+ # We can't simply exec the code directly, because in
+ # Python 3 the scoping for list comprehensions would
+ # lead to a NameError. Wrapping the code in a function
+ # fixes this.
+ d = dict()
+ lines = ["def _temp_func():\n"]
+ with open(filename) as f:
+ lines.extend([" " + line for line in f])
+ lines.extend(["\n return(locals())\n",
+ "_temp_out = _temp_func()\n",
+ "del(_temp_func)\n"])
+ codetext = "".join(lines)
+ code = compile(codetext, filename, 'exec')
+ exec(code, globals(), d)
+ self.update(d["_temp_out"])
+ return self
+
+ def update_values(self, *args, **kw):
+ """
+ arguments are dictionary-like; if present, they act as
+ additional sources of kwargs, with the actual kwargs
+ taking precedence.
+
+ One reserved optional kwarg is "strict". If present and
+ True, then any attempt to update with keys that are not
+ already in the Bunch instance will raise a KeyError.
+ """
+ strict = kw.pop("strict", False)
+ newkw = dict()
+ for d in args:
+ newkw.update(d)
+ newkw.update(kw)
+ self._check_strict(strict, newkw)
+ dsub = dict([(k, v) for (k, v) in newkw.items() if k in self])
+ self.update(dsub)
+
+ def update_None(self, *args, **kw):
+ """
+ Similar to update_values, except that an existing value
+ will be updated only if it is None.
+ """
+ strict = kw.pop("strict", False)
+ newkw = dict()
+ for d in args:
+ newkw.update(d)
+ newkw.update(kw)
+ self._check_strict(strict, newkw)
+ dsub = dict([(k, v) for (k, v) in newkw.items()
+ if k in self and self[k] is None])
+ self.update(dsub)
+
+ def _check_strict(self, strict, kw):
+ if strict:
+ bad = set(kw.keys()) - set(self.keys())
+ if bad:
+ bk = list(bad)
+ bk.sort()
+ ek = list(self.keys())
+ ek.sort()
+ raise KeyError(
+ "Update keys %s don't match existing keys %s" % (bk, ek))
diff --git a/gsw/_wrapped_ufuncs.py b/gsw/_wrapped_ufuncs.py
new file mode 100644
index 0000000..3bd3c21
--- /dev/null
+++ b/gsw/_wrapped_ufuncs.py
@@ -0,0 +1,4330 @@
+
+"""
+Auto-generated wrapper for C ufunc extension; do not edit!
+"""
+
+from . import _gsw_ufuncs
+from ._utilities import match_args_return
+
+
+ at match_args_return
+def adiabatic_lapse_rate_from_CT(SA, CT, p):
+ """
+ Calculates the adiabatic lapse rate of sea water from Conservative
+ Temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ adiabatic_lapse_rate : array-like, K/Pa
+ adiabatic lapse rate
+
+
+ """
+ return _gsw_ufuncs.adiabatic_lapse_rate_from_ct(SA, CT, p)
+
+ at match_args_return
+def adiabatic_lapse_rate_ice(t, p):
+ """
+ Calculates the adiabatic lapse rate of ice.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ adiabatic_lapse_rate_ice : array-like, K/Pa
+ adiabatic lapse rate
+
+
+ """
+ return _gsw_ufuncs.adiabatic_lapse_rate_ice(t, p)
+
+ at match_args_return
+def alpha(SA, CT, p):
+ """
+ Calculates the thermal expansion coefficient of seawater with respect to
+ Conservative Temperature using the computationally-efficient expression
+ for specific volume in terms of SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ alpha : array-like, 1/K
+ thermal expansion coefficient
+ with respect to Conservative Temperature
+
+
+ """
+ return _gsw_ufuncs.alpha(SA, CT, p)
+
+ at match_args_return
+def alpha_on_beta(SA, CT, p):
+ """
+ Calculates alpha divided by beta, where alpha is the thermal expansion
+ coefficient and beta is the saline contraction coefficient of seawater
+ from Absolute Salinity and Conservative Temperature. This function uses
+ the computationally-efficient expression for specific volume in terms of
+ SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ alpha_on_beta : array-like, kg g^-1 K^-1
+ thermal expansion coefficient with respect to
+ Conservative Temperature divided by the saline
+ contraction coefficient at constant Conservative
+ Temperature
+
+
+ """
+ return _gsw_ufuncs.alpha_on_beta(SA, CT, p)
+
+ at match_args_return
+def alpha_wrt_t_exact(SA, t, p):
+ """
+ Calculates the thermal expansion coefficient of seawater with respect to
+ in-situ temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ alpha_wrt_t_exact : array-like, 1/K
+ thermal expansion coefficient
+ with respect to in-situ temperature
+
+
+ """
+ return _gsw_ufuncs.alpha_wrt_t_exact(SA, t, p)
+
+ at match_args_return
+def alpha_wrt_t_ice(t, p):
+ """
+ Calculates the thermal expansion coefficient of ice with respect to
+ in-situ temperature.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ alpha_wrt_t_ice : array-like, 1/K
+ thermal expansion coefficient of ice with respect
+ to in-situ temperature
+
+
+ """
+ return _gsw_ufuncs.alpha_wrt_t_ice(t, p)
+
+ at match_args_return
+def beta(SA, CT, p):
+ """
+ Calculates the saline (i.e. haline) contraction coefficient of seawater
+ at constant Conservative Temperature using the computationally-efficient
+ 75-term expression for specific volume in terms of SA, CT and p
+ (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ beta : array-like, kg/g
+ saline contraction coefficient
+ at constant Conservative Temperature
+
+
+ """
+ return _gsw_ufuncs.beta(SA, CT, p)
+
+ at match_args_return
+def beta_const_t_exact(SA, t, p):
+ """
+ Calculates the saline (i.e. haline) contraction coefficient of seawater
+ at constant in-situ temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ beta_const_t_exact : array-like, kg/g
+ saline contraction coefficient
+ at constant in-situ temperature
+
+
+ """
+ return _gsw_ufuncs.beta_const_t_exact(SA, t, p)
+
+ at match_args_return
+def C_from_SP(SP, t, p):
+ """
+ Calculates conductivity, C, from (SP,t,p) using PSS-78 in the range
+ 2 < SP < 42. If the input Practical Salinity is less than 2 then a
+ modified form of the Hill et al. (1986) fomula is used for Practical
+ Salinity. The modification of the Hill et al. (1986) expression is to
+ ensure that it is exactly consistent with PSS-78 at SP = 2.
+
+ Parameters
+ ----------
+ SP : array-like
+ Practical Salinity (PSS-78), unitless
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ C : array-like, mS/cm
+ conductivity
+
+
+ """
+ return _gsw_ufuncs.c_from_sp(SP, t, p)
+
+ at match_args_return
+def cabbeling(SA, CT, p):
+ """
+ Calculates the cabbeling coefficient of seawater with respect to
+ Conservative Temperature. This function uses the computationally-
+ efficient expression for specific volume in terms of SA, CT and p
+ (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ cabbeling : array-like, 1/K^2
+ cabbeling coefficient with respect to
+ Conservative Temperature.
+
+
+ """
+ return _gsw_ufuncs.cabbeling(SA, CT, p)
+
+ at match_args_return
+def chem_potential_water_ice(t, p):
+ """
+ Calculates the chemical potential of water in ice from in-situ
+ temperature and pressure.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ chem_potential_water_ice : array-like, J/kg
+ chemical potential of ice
+
+
+ """
+ return _gsw_ufuncs.chem_potential_water_ice(t, p)
+
+ at match_args_return
+def chem_potential_water_t_exact(SA, t, p):
+ """
+ Calculates the chemical potential of water in seawater.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ chem_potential_water_t_exact : array-like, J/g
+ chemical potential of water in seawater
+
+
+ """
+ return _gsw_ufuncs.chem_potential_water_t_exact(SA, t, p)
+
+ at match_args_return
+def cp_ice(t, p):
+ """
+ Calculates the isobaric heat capacity of seawater.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ cp_ice : array-like, J kg^-1 K^-1
+ heat capacity of ice
+
+
+ """
+ return _gsw_ufuncs.cp_ice(t, p)
+
+ at match_args_return
+def cp_t_exact(SA, t, p):
+ """
+ Calculates the isobaric heat capacity of seawater.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ cp_t_exact : array-like, J/(kg*K)
+ heat capacity of seawater
+
+
+ """
+ return _gsw_ufuncs.cp_t_exact(SA, t, p)
+
+ at match_args_return
+def CT_first_derivatives(SA, pt):
+ """
+ Calculates the following two derivatives of Conservative Temperature
+ (1) CT_SA, the derivative with respect to Absolute Salinity at
+ constant potential temperature (with pr = 0 dbar), and
+ 2) CT_pt, the derivative with respect to potential temperature
+ (the regular potential temperature which is referenced to 0 dbar)
+ at constant Absolute Salinity.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ pt : array-like
+ Potential temperature referenced to a sea pressure, degrees C
+
+ Returns
+ -------
+ CT_SA : array-like, K/(g/kg)
+ The derivative of Conservative Temperature with respect to
+ Absolute Salinity at constant potential temperature
+ (the regular potential temperature which has reference
+ sea pressure of 0 dbar).
+ CT_pt : array-like, unitless
+ The derivative of Conservative Temperature with respect to
+ potential temperature (the regular one with pr = 0 dbar)
+ at constant SA. CT_pt is dimensionless.
+
+
+ """
+ return _gsw_ufuncs.ct_first_derivatives(SA, pt)
+
+ at match_args_return
+def CT_first_derivatives_wrt_t_exact(SA, t, p):
+ """
+ Calculates the following three derivatives of Conservative Temperature.
+ These derivatives are done with respect to in-situ temperature t (in the
+ case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of
+ CT_SA_wrt_t and CT_P_wrt_t).
+ (1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity
+ at constant t and p, and
+ (2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t
+ at constant SA and p.
+ (3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at
+ constant SA and t.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ CT_SA_wrt_t : array-like, K kg/g
+ The first derivative of Conservative Temperature with
+ respect to Absolute Salinity at constant t and p.
+ [ K/(g/kg)] i.e.
+ CT_T_wrt_t : array-like, unitless
+ The first derivative of Conservative Temperature with
+ respect to in-situ temperature, t, at constant SA and p.
+ CT_P_wrt_t : array-like, K/Pa
+ The first derivative of Conservative Temperature with
+ respect to pressure P (in Pa) at constant SA and t.
+
+
+ """
+ return _gsw_ufuncs.ct_first_derivatives_wrt_t_exact(SA, t, p)
+
+ at match_args_return
+def CT_freezing(SA, p, saturation_fraction):
+ """
+ Calculates the Conservative Temperature at which seawater freezes. The
+ Conservative Temperature freezing point is calculated from the exact
+ in-situ freezing temperature which is found by a modified Newton-Raphson
+ iteration (McDougall and Wotherspoon, 2014) of the equality of the
+ chemical potentials of water in seawater and in ice.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ CT_freezing : array-like, deg C
+ Conservative Temperature at freezing of seawater
+ That is, the freezing temperature expressed in terms of
+ Conservative Temperature (ITS-90).
+
+
+ """
+ return _gsw_ufuncs.ct_freezing(SA, p, saturation_fraction)
+
+ at match_args_return
+def CT_freezing_first_derivatives(SA, p, saturation_fraction):
+ """
+ Calculates the first derivatives of the Conservative Temperature at
+ which seawater freezes, with respect to Absolute Salinity SA and
+ pressure P (in Pa).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ CTfreezing_SA : array-like, K kg/g
+ the derivative of the Conservative Temperature at
+ freezing (ITS-90) with respect to Absolute Salinity at
+ fixed pressure [ K/(g/kg) ] i.e.
+ CTfreezing_P : array-like, K/Pa
+ the derivative of the Conservative Temperature at
+ freezing (ITS-90) with respect to pressure (in Pa) at
+ fixed Absolute Salinity
+
+
+ """
+ return _gsw_ufuncs.ct_freezing_first_derivatives(SA, p, saturation_fraction)
+
+ at match_args_return
+def CT_freezing_first_derivatives_poly(SA, p, saturation_fraction):
+ """
+ Calculates the first derivatives of the Conservative Temperature at
+ which seawater freezes, with respect to Absolute Salinity SA and
+ pressure P (in Pa) of the comptationally efficient polynomial fit of the
+ freezing temperature (McDougall et al., 2014).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ CTfreezing_SA : array-like, K kg/g
+ the derivative of the Conservative Temperature at
+ freezing (ITS-90) with respect to Absolute Salinity at
+ fixed pressure [ K/(g/kg) ] i.e.
+ CTfreezing_P : array-like, K/Pa
+ the derivative of the Conservative Temperature at
+ freezing (ITS-90) with respect to pressure (in Pa) at
+ fixed Absolute Salinity
+
+
+ """
+ return _gsw_ufuncs.ct_freezing_first_derivatives_poly(SA, p, saturation_fraction)
+
+ at match_args_return
+def CT_freezing_poly(SA, p, saturation_fraction):
+ """
+ Calculates the Conservative Temperature at which seawater freezes.
+ The error of this fit ranges between -5e-4 K and 6e-4 K when compared
+ with the Conservative Temperature calculated from the exact in-situ
+ freezing temperature which is found by a Newton-Raphson iteration of the
+ equality of the chemical potentials of water in seawater and in ice.
+ Note that the Conservative Temperature freezing temperature can be found
+ by this exact method using the function gsw_CT_freezing.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ CT_freezing : array-like, deg C
+ Conservative Temperature at freezing of seawater
+ That is, the freezing temperature expressed in
+ terms of Conservative Temperature (ITS-90).
+
+
+ """
+ return _gsw_ufuncs.ct_freezing_poly(SA, p, saturation_fraction)
+
+ at match_args_return
+def CT_from_enthalpy(SA, h, p):
+ """
+ Calculates the Conservative Temperature of seawater, given the Absolute
+ Salinity, specific enthalpy, h, and pressure p. The specific enthalpy
+ input is the one calculated from the computationally-efficient
+ expression for specific volume in terms of SA, CT and p (Roquet et al.,
+ 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ h : array-like
+ Specific enthalpy, J/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ CT : array-like, deg C
+ Conservative Temperature ( ITS-90)
+
+
+ """
+ return _gsw_ufuncs.ct_from_enthalpy(SA, h, p)
+
+ at match_args_return
+def CT_from_enthalpy_exact(SA, h, p):
+ """
+ Calculates the Conservative Temperature of seawater, given the Absolute
+ Salinity, SA, specific enthalpy, h, and pressure p. The specific
+ enthalpy input is calculated from the full Gibbs function of seawater,
+ gsw_enthalpy_t_exact.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ h : array-like
+ Specific enthalpy, J/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ CT : array-like, deg C
+ Conservative Temperature ( ITS-90)
+
+
+ """
+ return _gsw_ufuncs.ct_from_enthalpy_exact(SA, h, p)
+
+ at match_args_return
+def CT_from_entropy(SA, entropy):
+ """
+ Calculates Conservative Temperature with entropy as an input variable.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ entropy : array-like
+ Specific entropy, J/(kg*K)
+
+ Returns
+ -------
+ CT : array-like, deg C
+ Conservative Temperature (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.ct_from_entropy(SA, entropy)
+
+ at match_args_return
+def CT_from_pt(SA, pt):
+ """
+ Calculates Conservative Temperature of seawater from potential
+ temperature (whose reference sea pressure is zero dbar).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ pt : array-like
+ Potential temperature referenced to a sea pressure, degrees C
+
+ Returns
+ -------
+ CT : array-like, deg C
+ Conservative Temperature (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.ct_from_pt(SA, pt)
+
+ at match_args_return
+def CT_from_rho(rho, SA, p):
+ """
+ Calculates the Conservative Temperature of a seawater sample, for given
+ values of its density, Absolute Salinity and sea pressure (in dbar),
+ using the computationally-efficient expression for specific volume in
+ terms of SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ rho : array-like
+ Seawater density (not anomaly) in-situ, e.g., 1026 kg/m^3.
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ CT : array-like, deg C
+ Conservative Temperature (ITS-90)
+ CT_multiple : array-like, deg C
+ Conservative Temperature (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.ct_from_rho(rho, SA, p)
+
+ at match_args_return
+def CT_from_t(SA, t, p):
+ """
+ Calculates Conservative Temperature of seawater from in-situ
+ temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ CT : array-like, deg C
+ Conservative Temperature (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.ct_from_t(SA, t, p)
+
+ at match_args_return
+def CT_maxdensity(SA, p):
+ """
+ Calculates the Conservative Temperature of maximum density of seawater.
+ This function returns the Conservative temperature at which the density
+ of seawater is a maximum, at given Absolute Salinity, SA, and sea
+ pressure, p (in dbar). This function uses the computationally-efficient
+ expression for specific volume in terms of SA, CT and p
+ (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ CT_maxdensity : array-like, deg C
+ Conservative Temperature at which
+ the density of seawater is a maximum for
+ given Absolute Salinity and pressure.
+
+
+ """
+ return _gsw_ufuncs.ct_maxdensity(SA, p)
+
+ at match_args_return
+def CT_second_derivatives(SA, pt):
+ """
+ Calculates the following three, second-order derivatives of Conservative
+ Temperature
+ (1) CT_SA_SA, the second derivative with respect to Absolute Salinity
+ at constant potential temperature (with p_ref = 0 dbar),
+ (2) CT_SA_pt, the derivative with respect to potential temperature
+ (the regular potential temperature which is referenced to 0 dbar)
+ and Absolute Salinity, and
+ (3) CT_pt_pt, the second derivative with respect to potential
+ temperature (the regular potential temperature which is referenced
+ to 0 dbar) at constant Absolute Salinity.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ pt : array-like
+ Potential temperature referenced to a sea pressure, degrees C
+
+ Returns
+ -------
+ CT_SA_SA : array-like, K/((g/kg)^2)
+ The second derivative of Conservative Temperature with
+ respect to Absolute Salinity at constant potential
+ temperature (the regular potential temperature which
+ has reference sea pressure of 0 dbar).
+ CT_SA_pt : array-like,
+ The derivative of Conservative Temperature with
+ respect to potential temperature (the regular one with
+ p_ref : array-like, 1/(g/kg)
+ 0 dbar) and Absolute Salinity.
+ CT_pt_pt : array-like,
+ The second derivative of Conservative Temperature with
+ respect to potential temperature (the regular one with
+ p_ref : array-like, 1/K
+ 0 dbar) at constant SA.
+
+
+ """
+ return _gsw_ufuncs.ct_second_derivatives(SA, pt)
+
+ at match_args_return
+def deltaSA_atlas(p, lon, lat):
+ """
+ Calculates the Absolute Salinity Anomaly atlas value, SA - SR, in
+ the open ocean by spatially interpolating the global reference data set
+ of deltaSA_atlas to the location of the seawater sample.
+
+ Parameters
+ ----------
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ deltaSA_atlas : array-like, g/kg
+ Absolute Salinity Anomaly atlas value
+
+
+ """
+ return _gsw_ufuncs.deltasa_atlas(p, lon, lat)
+
+ at match_args_return
+def deltaSA_from_SP(SP, p, lon, lat):
+ """
+ Calculates Absolute Salinity Anomaly from Practical Salinity. Since SP
+ is non-negative by definition, this function changes any negative input
+ values of SP to be zero.
+
+ Parameters
+ ----------
+ SP : array-like
+ Practical Salinity (PSS-78), unitless
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ deltaSA : array-like, g/kg
+ Absolute Salinity Anomaly
+
+
+ """
+ return _gsw_ufuncs.deltasa_from_sp(SP, p, lon, lat)
+
+ at match_args_return
+def dilution_coefficient_t_exact(SA, t, p):
+ """
+ Calculates the dilution coefficient of seawater. The dilution
+ coefficient of seawater is defined as the Absolute Salinity times the
+ second derivative of the Gibbs function with respect to Absolute
+ Salinity, that is, SA.*g_SA_SA.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ dilution_coefficient_t_exact : array-like, (J/kg)(kg/g)
+ dilution coefficient
+
+
+ """
+ return _gsw_ufuncs.dilution_coefficient_t_exact(SA, t, p)
+
+ at match_args_return
+def dynamic_enthalpy(SA, CT, p):
+ """
+ Calculates dynamic enthalpy of seawater using the computationally-
+ efficient expression for specific volume in terms of SA, CT and p
+ (Roquet et al., 2015). Dynamic enthalpy is defined as enthalpy minus
+ potential enthalpy (Young, 2010).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ dynamic_enthalpy : array-like, J/kg
+ dynamic enthalpy
+
+
+ """
+ return _gsw_ufuncs.dynamic_enthalpy(SA, CT, p)
+
+ at match_args_return
+def enthalpy(SA, CT, p):
+ """
+ Calculates specific enthalpy of seawater using the computationally-
+ efficient expression for specific volume in terms of SA, CT and p
+ (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ enthalpy : array-like, J/kg
+ specific enthalpy
+
+
+ """
+ return _gsw_ufuncs.enthalpy(SA, CT, p)
+
+ at match_args_return
+def enthalpy_CT_exact(SA, CT, p):
+ """
+ Calculates specific enthalpy of seawater from Absolute Salinity and
+ Conservative Temperature and pressure.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ enthalpy_CT_exact : array-like, J/kg
+ specific enthalpy
+
+
+ """
+ return _gsw_ufuncs.enthalpy_ct_exact(SA, CT, p)
+
+ at match_args_return
+def enthalpy_diff(SA, CT, p_shallow, p_deep):
+ """
+ Calculates the difference of the specific enthalpy of seawater between
+ two different pressures, p_deep (the deeper pressure) and p_shallow
+ (the shallower pressure), at the same values of SA and CT. This
+ function uses the computationally-efficient expression for specific
+ volume in terms of SA, CT and p (Roquet et al., 2015). The output
+ (enthalpy_diff) is the specific enthalpy evaluated at (SA,CT,p_deep)
+ minus the specific enthalpy at (SA,CT,p_shallow).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p_shallow : array-like
+ Upper sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ p_deep : array-like
+ Lower sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ enthalpy_diff : array-like, J/kg
+ difference of specific enthalpy
+ (deep minus shallow)
+
+
+ """
+ return _gsw_ufuncs.enthalpy_diff(SA, CT, p_shallow, p_deep)
+
+ at match_args_return
+def enthalpy_first_derivatives(SA, CT, p):
+ """
+ Calculates the following two derivatives of specific enthalpy (h) of
+ seawater using the computationally-efficient expression for
+ specific volume in terms of SA, CT and p (Roquet et al., 2015).
+ (1) h_SA, the derivative with respect to Absolute Salinity at
+ constant CT and p, and
+ (2) h_CT, derivative with respect to CT at constant SA and p.
+ Note that h_P is specific volume (1/rho) it can be caclulated by calling
+ gsw_specvol(SA,CT,p).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ h_SA : array-like, J/g
+ The first derivative of specific enthalpy with respect to
+ Absolute Salinity at constant CT and p.
+ [ J/(kg (g/kg))] i.e.
+ h_CT : array-like, J/(kg K)
+ The first derivative of specific enthalpy with respect to
+ CT at constant SA and p.
+
+
+ """
+ return _gsw_ufuncs.enthalpy_first_derivatives(SA, CT, p)
+
+ at match_args_return
+def enthalpy_first_derivatives_CT_exact(SA, CT, p):
+ """
+ Calculates the following two derivatives of specific enthalpy, h,
+ (1) h_SA, the derivative with respect to Absolute Salinity at
+ constant CT and p, and
+ (2) h_CT, derivative with respect to CT at constant SA and p.
+ Note that h_P is specific volume, v, it can be calulated by calling
+ gsw_specvol_CT_exact(SA,CT,p).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ h_SA : array-like, J/g
+ The first derivative of specific enthalpy with respect to
+ Absolute Salinity at constant CT and p.
+ [ J/(kg (g/kg))] i.e.
+ h_CT : array-like, J/(kg K)
+ The first derivative of specific enthalpy with respect to
+ CT at constant SA and p.
+
+
+ """
+ return _gsw_ufuncs.enthalpy_first_derivatives_ct_exact(SA, CT, p)
+
+ at match_args_return
+def enthalpy_ice(t, p):
+ """
+ Calculates the specific enthalpy of ice (h_Ih).
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ enthalpy_ice : array-like, J/kg
+ specific enthalpy of ice
+
+
+ """
+ return _gsw_ufuncs.enthalpy_ice(t, p)
+
+ at match_args_return
+def enthalpy_second_derivatives(SA, CT, p):
+ """
+ Calculates the following three second-order derivatives of specific
+ enthalpy (h),using the computationally-efficient expression for
+ specific volume in terms of SA, CT and p (Roquet et al., 2015).
+ (1) h_SA_SA, second-order derivative with respect to Absolute Salinity
+ at constant CT & p.
+ (2) h_SA_CT, second-order derivative with respect to SA & CT at
+ constant p.
+ (3) h_CT_CT, second-order derivative with respect to CT at constant SA
+ and p.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ h_SA_SA : array-like, J/(kg (g/kg)^2)
+ The second derivative of specific enthalpy with respect to
+ Absolute Salinity at constant CT & p.
+ h_SA_CT : array-like, J/(kg K(g/kg))
+ The second derivative of specific enthalpy with respect to
+ SA and CT at constant p.
+ h_CT_CT : array-like, J/(kg K^2)
+ The second derivative of specific enthalpy with respect to
+ CT at constant SA and p.
+
+
+ """
+ return _gsw_ufuncs.enthalpy_second_derivatives(SA, CT, p)
+
+ at match_args_return
+def enthalpy_second_derivatives_CT_exact(SA, CT, p):
+ """
+ Calculates the following three second-order derivatives of specific
+ enthalpy (h),
+ (1) h_SA_SA, second-order derivative with respect to Absolute Salinity
+ at constant CT & p.
+ (2) h_SA_CT, second-order derivative with respect to SA & CT at
+ constant p.
+ (3) h_CT_CT, second-order derivative with respect to CT at constant SA
+ and p.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ h_SA_SA : array-like, J/(kg (g/kg)^2)
+ The second derivative of specific enthalpy with respect to
+ Absolute Salinity at constant CT & p.
+ h_SA_CT : array-like, J/(kg K(g/kg))
+ The second derivative of specific enthalpy with respect to
+ SA and CT at constant p.
+ h_CT_CT : array-like, J/(kg K^2)
+ The second derivative of specific enthalpy with respect to
+ CT at constant SA and p.
+
+
+ """
+ return _gsw_ufuncs.enthalpy_second_derivatives_ct_exact(SA, CT, p)
+
+ at match_args_return
+def enthalpy_t_exact(SA, t, p):
+ """
+ Calculates the specific enthalpy of seawater.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ enthalpy_t_exact : array-like, J/kg
+ specific enthalpy
+
+
+ """
+ return _gsw_ufuncs.enthalpy_t_exact(SA, t, p)
+
+ at match_args_return
+def entropy_first_derivatives(SA, CT):
+ """
+ Calculates the following two partial derivatives of specific entropy
+ (eta)
+ (1) eta_SA, the derivative with respect to Absolute Salinity at
+ constant Conservative Temperature, and
+ (2) eta_CT, the derivative with respect to Conservative Temperature at
+ constant Absolute Salinity.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ eta_SA : array-like, J/(g K)
+ The derivative of specific entropy with respect to
+ Absolute Salinity (in units of g kg^-1) at constant
+ Conservative Temperature.
+ eta_CT : array-like, J/(kg K^2)
+ The derivative of specific entropy with respect to
+ Conservative Temperature at constant Absolute Salinity.
+
+
+ """
+ return _gsw_ufuncs.entropy_first_derivatives(SA, CT)
+
+ at match_args_return
+def entropy_from_CT(SA, CT):
+ """
+ Calculates specific entropy of seawater from Conservative Temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ entropy : array-like, J/(kg*K)
+ specific entropy
+
+
+ """
+ return _gsw_ufuncs.entropy_from_ct(SA, CT)
+
+ at match_args_return
+def entropy_from_pt(SA, pt):
+ """
+ Calculates specific entropy of seawater as a function of potential
+ temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ pt : array-like
+ Potential temperature referenced to a sea pressure, degrees C
+
+ Returns
+ -------
+ entropy : array-like, J/(kg*K)
+ specific entropy
+
+
+ """
+ return _gsw_ufuncs.entropy_from_pt(SA, pt)
+
+ at match_args_return
+def entropy_from_t(SA, t, p):
+ """
+ Calculates specific entropy of seawater from in-situ temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ entropy : array-like, J/(kg*K)
+ specific entropy
+
+
+ """
+ return _gsw_ufuncs.entropy_from_t(SA, t, p)
+
+ at match_args_return
+def entropy_ice(t, p):
+ """
+ Calculates specific entropy of ice.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ ice_entropy : array-like, J kg^-1 K^-1
+ specific entropy of ice
+
+
+ """
+ return _gsw_ufuncs.entropy_ice(t, p)
+
+ at match_args_return
+def entropy_second_derivatives(SA, CT):
+ """
+ Calculates the following three second-order partial derivatives of
+ specific entropy (eta)
+ (1) eta_SA_SA, the second derivative with respect to Absolute
+ Salinity at constant Conservative Temperature, and
+ (2) eta_SA_CT, the derivative with respect to Absolute Salinity and
+ Conservative Temperature.
+ (3) eta_CT_CT, the second derivative with respect to Conservative
+ Temperature at constant Absolute Salinity.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ eta_SA_SA : array-like, J/(kg K(g/kg)^2)
+ The second derivative of specific entropy with respect
+ to Absolute Salinity (in units of g kg^-1) at constant
+ Conservative Temperature.
+ eta_SA_CT : array-like, J/(kg (g/kg) K^2)
+ The second derivative of specific entropy with respect
+ to Conservative Temperature at constant Absolute
+ eta_CT_CT : array-like, J/(kg K^3)
+ The second derivative of specific entropy with respect
+ to Conservative Temperature at constant Absolute
+
+
+ """
+ return _gsw_ufuncs.entropy_second_derivatives(SA, CT)
+
+ at match_args_return
+def Fdelta(p, lon, lat):
+ """
+ Calculates Fdelta from the Absolute Salinity Anomaly Ratio (SAAR). It
+ finds SAAR by calling the function "gsw_SAAR(p,long,lat)" and then
+ simply calculates Fdelta from
+
+ Parameters
+ ----------
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ Fdelta : array-like, unitless
+ ratio of SA to Sstar, minus 1
+
+
+ """
+ return _gsw_ufuncs.fdelta(p, lon, lat)
+
+ at match_args_return
+def frazil_properties(SA_bulk, h_bulk, p):
+ """
+ Calculates the mass fraction of ice (mass of ice divided by mass of ice
+ plus seawater), w_Ih_final, which results from given values of the bulk
+ Absolute Salinity, SA_bulk, bulk enthalpy, h_bulk, occuring at pressure
+ p. The final values of Absolute Salinity, SA_final, and Conservative
+ Temperature, CT_final, of the interstitial seawater phase are also
+ returned. This code assumes that there is no dissolved air in the
+ seawater (that is, saturation_fraction is assumed to be zero
+ throughout the code).
+
+ Parameters
+ ----------
+ SA_bulk : array-like
+ bulk Absolute Salinity of the seawater and ice mixture, g/kg
+ h_bulk : array-like
+ bulk enthalpy of the seawater and ice mixture, J/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ SA_final : array-like, g/kg
+ Absolute Salinity of the seawater in the final state,
+ whether or not any ice is present.
+ CT_final : array-like, deg C
+ Conservative Temperature of the seawater in the the final
+ state, whether or not any ice is present.
+ w_Ih_final : array-like, unitless
+ mass fraction of ice in the final seawater-ice mixture.
+ If this ice mass fraction is positive, the system is at
+ thermodynamic equilibrium. If this ice mass fraction is
+ zero there is no ice in the final state which consists
+ only of seawater which is warmer than the freezing
+ temperature.
+
+
+ """
+ return _gsw_ufuncs.frazil_properties(SA_bulk, h_bulk, p)
+
+ at match_args_return
+def frazil_properties_potential(SA_bulk, h_pot_bulk, p):
+ """
+ Calculates the mass fraction of ice (mass of ice divided by mass of ice
+ plus seawater), w_Ih_eq, which results from given values of the bulk
+ Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk,
+ occuring at pressure p. The final equilibrium values of Absolute
+ Salinity, SA_eq, and Conservative Temperature, CT_eq, of the
+ interstitial seawater phase are also returned. This code assumes that
+ there is no dissolved air in the seawater (that is, saturation_fraction
+ is assumed to be zero thoughout the code).
+
+ Parameters
+ ----------
+ SA_bulk : array-like
+ bulk Absolute Salinity of the seawater and ice mixture, g/kg
+ h_pot_bulk : array-like
+ bulk enthalpy of the seawater and ice mixture, J/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ SA_final : array-like, g/kg
+ Absolute Salinity of the seawater in the final state,
+ whether or not any ice is present.
+ CT_final : array-like, deg C
+ Conservative Temperature of the seawater in the the final
+ state, whether or not any ice is present.
+ w_Ih_final : array-like, unitless
+ mass fraction of ice in the final seawater-ice mixture.
+ If this ice mass fraction is positive, the system is at
+ thermodynamic equilibrium. If this ice mass fraction is
+ zero there is no ice in the final state which consists
+ only of seawater which is warmer than the freezing
+ temperature.
+
+
+ """
+ return _gsw_ufuncs.frazil_properties_potential(SA_bulk, h_pot_bulk, p)
+
+ at match_args_return
+def frazil_properties_potential_poly(SA_bulk, h_pot_bulk, p):
+ """
+ Calculates the mass fraction of ice (mass of ice divided by mass of ice
+ plus seawater), w_Ih_eq, which results from given values of the bulk
+ Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk,
+ occuring at pressure p. The final equilibrium values of Absolute
+ Salinity, SA_eq, and Conservative Temperature, CT_eq, of the
+ interstitial seawater phase are also returned. This code assumes that
+ there is no dissolved air in the seawater (that is, saturation_fraction
+ is assumed to be zero thoughout the code).
+
+ Parameters
+ ----------
+ SA_bulk : array-like
+ bulk Absolute Salinity of the seawater and ice mixture, g/kg
+ h_pot_bulk : array-like
+ bulk enthalpy of the seawater and ice mixture, J/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ SA_final : array-like, g/kg
+ Absolute Salinity of the seawater in the final state,
+ whether or not any ice is present.
+ CT_final : array-like, deg C
+ Conservative Temperature of the seawater in the the final
+ state, whether or not any ice is present.
+ w_Ih_final : array-like, unitless
+ mass fraction of ice in the final seawater-ice mixture.
+ If this ice mass fraction is positive, the system is at
+ thermodynamic equilibrium. If this ice mass fraction is
+ zero there is no ice in the final state which consists
+ only of seawater which is warmer than the freezing
+ temperature.
+
+
+ """
+ return _gsw_ufuncs.frazil_properties_potential_poly(SA_bulk, h_pot_bulk, p)
+
+ at match_args_return
+def frazil_ratios_adiabatic(SA, p, w_Ih):
+ """
+ Calculates the ratios of SA, CT and P changes when frazil ice forms or
+ melts in response to an adiabatic change in pressure of a mixture of
+ seawater and frazil ice crystals.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ w_Ih : array-like
+ mass fraction of ice: the mass of ice divided by the
+ sum of the masses of ice and seawater. 0 <= wIh <= 1. unitless.
+
+ Returns
+ -------
+ dSA_dCT_frazil : array-like, g/(kg K)
+ the ratio of the changes in Absolute Salinity
+ to that of Conservative Temperature
+ dSA_dP_frazil : array-like, g/(kg Pa)
+ the ratio of the changes in Absolute Salinity
+ to that of pressure (in Pa)
+ dCT_dP_frazil : array-like, K/Pa
+ the ratio of the changes in Conservative Temperature
+ to that of pressure (in Pa)
+
+
+ """
+ return _gsw_ufuncs.frazil_ratios_adiabatic(SA, p, w_Ih)
+
+ at match_args_return
+def frazil_ratios_adiabatic_poly(SA, p, w_Ih):
+ """
+ Calculates the ratios of SA, CT and P changes when frazil ice forms or
+ melts in response to an adiabatic change in pressure of a mixture of
+ seawater and frazil ice crystals.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ w_Ih : array-like
+ mass fraction of ice: the mass of ice divided by the
+ sum of the masses of ice and seawater. 0 <= wIh <= 1. unitless.
+
+ Returns
+ -------
+ dSA_dCT_frazil : array-like, g/(kg K)
+ the ratio of the changes in Absolute Salinity
+ to that of Conservative Temperature
+ dSA_dP_frazil : array-like, g/(kg Pa)
+ the ratio of the changes in Absolute Salinity
+ to that of pressure (in Pa)
+ dCT_dP_frazil : array-like, K/Pa
+ the ratio of the changes in Conservative Temperature
+ to that of pressure (in Pa)
+
+
+ """
+ return _gsw_ufuncs.frazil_ratios_adiabatic_poly(SA, p, w_Ih)
+
+ at match_args_return
+def gibbs_ice_part_t(t, p):
+ """
+ part of the the first temperature derivative of Gibbs energy of ice
+ that is the outout is gibbs_ice(1,0,t,p) + S0
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ gibbs_ice_part_t : array-like, J kg^-1 K^-1
+ part of temperature derivative
+
+
+ """
+ return _gsw_ufuncs.gibbs_ice_part_t(t, p)
+
+ at match_args_return
+def gibbs_ice_pt0(pt0):
+ """
+ part of the the first temperature derivative of Gibbs energy of ice
+ that is the outout is "gibbs_ice(1,0,pt0,0) + s0"
+
+ Parameters
+ ----------
+ pt0 : array-like
+ Potential temperature with reference pressure of 0 dbar, degrees C
+
+ Returns
+ -------
+ gibbs_ice_part_pt0 : array-like, J kg^-1 K^-1
+ part of temperature derivative
+
+
+ """
+ return _gsw_ufuncs.gibbs_ice_pt0(pt0)
+
+ at match_args_return
+def gibbs_ice_pt0_pt0(pt0):
+ """
+ The second temperature derivative of Gibbs energy of ice at the
+ potential temperature with reference sea pressure of zero dbar. That is
+ the output is gibbs_ice(2,0,pt0,0).
+
+ Parameters
+ ----------
+ pt0 : array-like
+ Potential temperature with reference pressure of 0 dbar, degrees C
+
+ Returns
+ -------
+ gibbs_ice_pt0_pt0 : array-like, J kg^-1 K^-2
+ temperature second derivative at pt0
+
+
+ """
+ return _gsw_ufuncs.gibbs_ice_pt0_pt0(pt0)
+
+ at match_args_return
+def grav(lat, p):
+ """
+ Calculates acceleration due to gravity as a function of latitude and as
+ a function of pressure in the ocean.
+
+ Parameters
+ ----------
+ lat : array-like
+ Latitude, -90 to 90 degrees
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ grav : array-like, m s^-2
+ gravitational acceleration
+
+
+ """
+ return _gsw_ufuncs.grav(lat, p)
+
+ at match_args_return
+def Helmholtz_energy_ice(t, p):
+ """
+ Calculates the Helmholtz energy of ice.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ Helmholtz_energy_ice : array-like, J/kg
+ Helmholtz energy of ice
+
+
+ """
+ return _gsw_ufuncs.helmholtz_energy_ice(t, p)
+
+ at match_args_return
+def Hill_ratio_at_SP2(t):
+ """
+ Calculates the Hill ratio, which is the adjustment needed to apply for
+ Practical Salinities smaller than 2. This ratio is defined at a
+ Practical Salinity = 2 and in-situ temperature, t using PSS-78. The Hill
+ ratio is the ratio of 2 to the output of the Hill et al. (1986) formula
+ for Practical Salinity at the conductivity ratio, Rt, at which Practical
+ Salinity on the PSS-78 scale is exactly 2.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ Hill_ratio : array-like, unitless
+ Hill ratio at SP of 2
+
+
+ """
+ return _gsw_ufuncs.hill_ratio_at_sp2(t)
+
+ at match_args_return
+def ice_fraction_to_freeze_seawater(SA, CT, p, t_Ih):
+ """
+ Calculates the mass fraction of ice (mass of ice divided by mass of ice
+ plus seawater), which, when melted into seawater having (SA,CT,p) causes
+ the final dilute seawater to be at the freezing temperature. The other
+ outputs are the Absolute Salinity and Conservative Temperature of the
+ final diluted seawater.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ t_Ih : array-like
+ In-situ temperature of ice (ITS-90), degrees C
+
+ Returns
+ -------
+ SA_freeze : array-like, g/kg
+ Absolute Salinity of seawater after the mass fraction of
+ ice, ice_fraction, at temperature t_Ih has melted into the
+ original seawater, and the final mixture is at the freezing
+ temperature of seawater.
+ CT_freeze : array-like, deg C
+ Conservative Temperature of seawater after the mass
+ fraction, w_Ih, of ice at temperature t_Ih has melted into
+ the original seawater, and the final mixture is at the
+ freezing temperature of seawater.
+ w_Ih : array-like, unitless
+ mass fraction of ice, having in-situ temperature t_Ih,
+ which, when melted into seawater at (SA,CT,p) leads to the
+ final diluted seawater being at the freezing temperature.
+ This output must be between 0 and 1.
+
+
+ """
+ return _gsw_ufuncs.ice_fraction_to_freeze_seawater(SA, CT, p, t_Ih)
+
+ at match_args_return
+def internal_energy(SA, CT, p):
+ """
+ Calculates specific internal energy of seawater using the
+ computationally-efficient expression for specific volume in terms of SA,
+ CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ internal_energy : array-like, J/kg
+ specific internal energy
+
+
+ """
+ return _gsw_ufuncs.internal_energy(SA, CT, p)
+
+ at match_args_return
+def internal_energy_ice(t, p):
+ """
+ Calculates the specific internal energy of ice.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ internal_energy_ice : array-like, J/kg
+ specific internal energy (u)
+
+
+ """
+ return _gsw_ufuncs.internal_energy_ice(t, p)
+
+ at match_args_return
+def kappa(SA, CT, p):
+ """
+ Calculates the isentropic compressibility of seawater. This function
+ has inputs of Absolute Salinity and Conservative Temperature. This
+ function uses the computationally-efficient expression for
+ specific volume in terms of SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ kappa : array-like, 1/Pa
+ isentropic compressibility of seawater
+
+
+ """
+ return _gsw_ufuncs.kappa(SA, CT, p)
+
+ at match_args_return
+def kappa_const_t_ice(t, p):
+ """
+ Calculates isothermal compressibility of ice.
+ Note. This is the compressibility of ice AT CONSTANT IN-SITU
+ TEMPERATURE
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ kappa_const_t_ice : array-like, 1/Pa
+ isothermal compressibility
+
+
+ """
+ return _gsw_ufuncs.kappa_const_t_ice(t, p)
+
+ at match_args_return
+def kappa_ice(t, p):
+ """
+ Calculates the isentropic compressibility of ice.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ kappa_ice : array-like, 1/Pa
+ isentropic compressibility
+
+
+ """
+ return _gsw_ufuncs.kappa_ice(t, p)
+
+ at match_args_return
+def kappa_t_exact(SA, t, p):
+ """
+ Calculates the isentropic compressibility of seawater.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ kappa_t_exact : array-like, 1/Pa
+ isentropic compressibility
+
+
+ """
+ return _gsw_ufuncs.kappa_t_exact(SA, t, p)
+
+ at match_args_return
+def latentheat_evap_CT(SA, CT):
+ """
+ Calculates latent heat, or enthalpy, of evaporation at p = 0 (the
+ surface). It is defined as a function of Absolute Salinity, SA, and
+ Conservative Temperature, CT, and is valid in the ranges
+ 0 < SA < 42 g/kg and 0 < CT < 40 deg C. The errors range between
+ -0.4 and 0.6 J/kg.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ latentheat_evap : array-like, J/kg
+ latent heat of evaporation
+
+
+ """
+ return _gsw_ufuncs.latentheat_evap_ct(SA, CT)
+
+ at match_args_return
+def latentheat_evap_t(SA, t):
+ """
+ Calculates latent heat, or enthalpy, of evaporation at p = 0 (the
+ surface). It is defined as a function of Absolute Salinity, SA, and
+ in-situ temperature, t, and is valid in the ranges 0 < SA < 40 g/kg
+ and 0 < CT < 42 deg C. The errors range between -0.4 and 0.6 J/kg.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ latentheat_evap : array-like, J/kg
+ latent heat of evaporation
+
+
+ """
+ return _gsw_ufuncs.latentheat_evap_t(SA, t)
+
+ at match_args_return
+def latentheat_melting(SA, p):
+ """
+ Calculates latent heat, or enthalpy, of melting. It is defined in terms
+ of Absolute Salinity, SA, and sea pressure, p, and is valid in the
+ ranges 0 < SA < 42 g kg^-1 and 0 < p < 10,000 dbar. This is based on
+ the IAPWS Releases IAPWS-09 (for pure water), IAPWS-08 (for the saline
+ compoonent of seawater and IAPWS-06 for ice Ih.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ latentheat_melting : array-like, J/kg
+ latent heat of melting
+
+
+ """
+ return _gsw_ufuncs.latentheat_melting(SA, p)
+
+ at match_args_return
+def melting_ice_equilibrium_SA_CT_ratio(SA, p):
+ """
+ Calculates the ratio of SA to CT changes when ice melts into seawater
+ with both the seawater and the seaice temperatures being almost equal to
+ the equilibrium freezing temperature. It is assumed that a small mass
+ of ice melts into an infinite mass of seawater. If indeed the
+ temperature of the seawater and the ice were both equal to the freezing
+ temperature, then no melting or freezing would occur; an imbalance
+ between these three temperatures is needed for freezing or melting to
+ occur (the three temperatures being (1) the seawater temperature,
+ (2) the ice temperature, and (3) the freezing temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ melting_ice_equilibrium_SA_CT_ratio : array-like, g/(kg K)
+ the ratio dSA/dCT of SA to CT
+ changes when ice melts into seawater, with
+ the seawater and seaice being close to the
+ freezing temperature.
+
+
+ """
+ return _gsw_ufuncs.melting_ice_equilibrium_sa_ct_ratio(SA, p)
+
+ at match_args_return
+def melting_ice_equilibrium_SA_CT_ratio_poly(SA, p):
+ """
+ Calculates the ratio of SA to CT changes when ice melts into seawater
+ with both the seawater and the seaice temperatures being almost equal to
+ the equilibrium freezing temperature. It is assumed that a small mass
+ of ice melts into an infinite mass of seawater. If indeed the
+ temperature of the seawater and the ice were both equal to the freezing
+ temperature, then no melting or freezing would occur; an imbalance
+ between these three temperatures is needed for freezing or melting to
+ occur (the three temperatures being (1) the seawater temperature,
+ (2) the ice temperature, and (3) the freezing temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ melting_ice_equilibrium_SA_CT_ratio : array-like, g/(kg K)
+ the ratio dSA/dCT of SA to CT
+ changes when ice melts into seawater, with
+ the seawater and seaice being close to the
+ freezing temperature.
+
+
+ """
+ return _gsw_ufuncs.melting_ice_equilibrium_sa_ct_ratio_poly(SA, p)
+
+ at match_args_return
+def melting_ice_into_seawater(SA, CT, p, w_Ih, t_Ih):
+ """
+ Calculates the final Absolute Salinity, final Conservative Temperature
+ and final ice mass fraction that results when a given mass fraction of
+ ice melts and is mixed into seawater whose properties are (SA,CT,p).
+ This code takes the seawater to contain no dissolved air.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ w_Ih : array-like
+ mass fraction of ice: the mass of ice divided by the
+ sum of the masses of ice and seawater. 0 <= wIh <= 1. unitless.
+ t_Ih : array-like
+ In-situ temperature of ice (ITS-90), degrees C
+
+ Returns
+ -------
+ SA_final : array-like, g/kg
+ Absolute Salinity of the seawater in the final state,
+ whether or not any ice is present.
+ CT_final : array-like, deg C
+ Conservative Temperature of the seawater in the the final
+ state, whether or not any ice is present.
+ w_Ih_final : array-like, unitless
+ mass fraction of ice in the final seawater-ice mixture.
+ If this ice mass fraction is positive, the system is at
+ thermodynamic equilibrium. If this ice mass fraction is
+ zero there is no ice in the final state which consists
+ only of seawater which is warmer than the freezing
+ temperature.
+
+
+ """
+ return _gsw_ufuncs.melting_ice_into_seawater(SA, CT, p, w_Ih, t_Ih)
+
+ at match_args_return
+def melting_ice_SA_CT_ratio(SA, CT, p, t_Ih):
+ """
+ Calculates the ratio of SA to CT changes when ice melts into seawater.
+ It is assumed that a small mass of ice melts into an infinite mass of
+ seawater. Because of the infinite mass of seawater, the ice will always
+ melt.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ t_Ih : array-like
+ In-situ temperature of ice (ITS-90), degrees C
+
+ Returns
+ -------
+ melting_ice_SA_CT_ratio : array-like, g kg^-1 K^-1
+ the ratio of SA to CT changes when ice melts
+ into a large mass of seawater
+
+
+ """
+ return _gsw_ufuncs.melting_ice_sa_ct_ratio(SA, CT, p, t_Ih)
+
+ at match_args_return
+def melting_ice_SA_CT_ratio_poly(SA, CT, p, t_Ih):
+ """
+ Calculates the ratio of SA to CT changes when ice melts into seawater.
+ It is assumed that a small mass of ice melts into an infinite mass of
+ seawater. Because of the infinite mass of seawater, the ice will always
+ melt.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ t_Ih : array-like
+ In-situ temperature of ice (ITS-90), degrees C
+
+ Returns
+ -------
+ melting_ice_SA_CT_ratio : array-like, g kg^-1 K^-1
+ the ratio of SA to CT changes when ice melts
+ into a large mass of seawater
+
+
+ """
+ return _gsw_ufuncs.melting_ice_sa_ct_ratio_poly(SA, CT, p, t_Ih)
+
+ at match_args_return
+def melting_seaice_equilibrium_SA_CT_ratio(SA, p):
+ """
+ Calculates the ratio of SA to CT changes when sea ice melts into
+ seawater with both the seawater and the sea ice temperatures being
+ almost equal to the equilibrium freezing temperature. It is assumed
+ that a small mass of seaice melts into an infinite mass of seawater. If
+ indeed the temperature of the seawater and the sea ice were both equal
+ to the freezing temperature, then no melting or freezing would occur; an
+ imbalance between these three temperatures is needed for freezing or
+ melting to occur (the three temperatures being (1) the seawater
+ temperature, (2) the sea ice temperature, and (3) the freezing
+ temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ melting_seaice_equilibrium_SA_CT_ratio : array-like, g/(kg K)
+ the ratio dSA/dCT of SA to CT
+ changes when sea ice melts into seawater, with
+ the seawater and sea ice being close to the
+ freezing temperature.
+
+
+ """
+ return _gsw_ufuncs.melting_seaice_equilibrium_sa_ct_ratio(SA, p)
+
+ at match_args_return
+def melting_seaice_equilibrium_SA_CT_ratio_poly(SA, p):
+ """
+ Calculates the ratio of SA to CT changes when sea ice melts into
+ seawater with both the seawater and the sea ice temperatures being
+ almost equal to the equilibrium freezing temperature. It is assumed
+ that a small mass of seaice melts into an infinite mass of seawater. If
+ indeed the temperature of the seawater and the sea ice were both equal
+ to the freezing temperature, then no melting or freezing would occur; an
+ imbalance between these three temperatures is needed for freezing or
+ melting to occur (the three temperatures being (1) the seawater
+ temperature, (2) the sea ice temperature, and (3) the freezing
+ temperature.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ melting_seaice_equilibrium_SA_CT_ratio : array-like, g/(kg K)
+ the ratio dSA/dCT of SA to CT
+ changes when sea ice melts into seawater, with
+ the seawater and sea ice being close to the
+ freezing temperature.
+
+
+ """
+ return _gsw_ufuncs.melting_seaice_equilibrium_sa_ct_ratio_poly(SA, p)
+
+ at match_args_return
+def melting_seaice_into_seawater(SA, CT, p, w_seaice, SA_seaice, t_seaice):
+ """
+ Calculates the Absolute Salinity and Conservative Temperature that
+ results when a given mass of sea ice (or ice) melts and is mixed into a
+ known mass of seawater (whose properties are (SA,CT,p)).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ w_seaice : array-like
+ mass fraction of ice: the mass of sea-ice divided by the sum
+ of the masses of sea-ice and seawater. 0 <= wIh <= 1. unitless.
+ SA_seaice : array-like
+ Absolute Salinity of sea ice: the mass fraction of salt
+ in sea ice, expressed in g of salt per kg of sea ice.
+ t_seaice : array-like
+ In-situ temperature of the sea ice at pressure p (ITS-90), degrees C
+
+ Returns
+ -------
+ SA_final : array-like, g/kg
+ Absolute Salinity of the mixture of the melted sea ice
+ (or ice) and the orignal seawater
+ CT_final : array-like, deg C
+ Conservative Temperature of the mixture of the melted
+ sea ice (or ice) and the orignal seawater
+
+
+ """
+ return _gsw_ufuncs.melting_seaice_into_seawater(SA, CT, p, w_seaice, SA_seaice, t_seaice)
+
+ at match_args_return
+def melting_seaice_SA_CT_ratio(SA, CT, p, SA_seaice, t_seaice):
+ """
+ Calculates the ratio of SA to CT changes when sea ice melts into
+ seawater. It is assumed that a small mass of sea ice melts into an
+ infinite mass of seawater. Because of the infinite mass of seawater,
+ the sea ice will always melt.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ SA_seaice : array-like
+ Absolute Salinity of sea ice: the mass fraction of salt
+ in sea ice, expressed in g of salt per kg of sea ice.
+ t_seaice : array-like
+ In-situ temperature of the sea ice at pressure p (ITS-90), degrees C
+
+ Returns
+ -------
+ melting_seaice_SA_CT_ratio : array-like, g/(kg K)
+ the ratio dSA/dCT of SA to CT changes when
+ sea ice melts into a large mass of seawater
+
+
+ """
+ return _gsw_ufuncs.melting_seaice_sa_ct_ratio(SA, CT, p, SA_seaice, t_seaice)
+
+ at match_args_return
+def melting_seaice_SA_CT_ratio_poly(SA, CT, p, SA_seaice, t_seaice):
+ """
+ Calculates the ratio of SA to CT changes when sea ice melts into
+ seawater. It is assumed that a small mass of sea ice melts into an
+ infinite mass of seawater. Because of the infinite mass of seawater,
+ the sea ice will always melt.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ SA_seaice : array-like
+ Absolute Salinity of sea ice: the mass fraction of salt
+ in sea ice, expressed in g of salt per kg of sea ice.
+ t_seaice : array-like
+ In-situ temperature of the sea ice at pressure p (ITS-90), degrees C
+
+ Returns
+ -------
+ melting_seaice_SA_CT_ratio : array-like, g/(kg K)
+ the ratio dSA/dCT of SA to CT changes when
+ sea ice melts into a large mass of seawater
+
+
+ """
+ return _gsw_ufuncs.melting_seaice_sa_ct_ratio_poly(SA, CT, p, SA_seaice, t_seaice)
+
+ at match_args_return
+def p_from_z(z, lat):
+ """
+ Calculates sea pressure from height using computationally-efficient
+ 75-term expression for density, in terms of SA, CT and p (Roquet et al.,
+ 2015). Dynamic height anomaly, geo_strf_dyn_height, if provided,
+ must be computed with its p_ref = 0 (the surface). Also if provided,
+ sea_surface_geopotental is the geopotential at zero sea pressure. This
+ function solves Eqn.(3.32.3) of IOC et al. (2010) iteratively for p.
+
+ Parameters
+ ----------
+ z : array-like
+ Depth, positive up, m
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ p : array-like, dbar
+ sea pressure
+ ( i.e. absolute pressure - 10.1325 dbar )
+
+
+ """
+ return _gsw_ufuncs.p_from_z(z, lat)
+
+ at match_args_return
+def pot_enthalpy_from_pt_ice(pt0_ice):
+ """
+ Calculates the potential enthalpy of ice from potential temperature of
+ ice (whose reference sea pressure is zero dbar).
+
+ Parameters
+ ----------
+ pt0_ice : array-like
+ Potential temperature of ice (ITS-90), degrees C
+
+ Returns
+ -------
+ pot_enthalpy_ice : array-like, J/kg
+ potential enthalpy of ice
+
+
+ """
+ return _gsw_ufuncs.pot_enthalpy_from_pt_ice(pt0_ice)
+
+ at match_args_return
+def pot_enthalpy_from_pt_ice_poly(pt0_ice):
+ """
+ Calculates the potential enthalpy of ice from potential temperature of
+ ice (whose reference sea pressure is zero dbar). This is a
+ compuationally efficient polynomial fit to the potential enthalpy of
+ ice.
+
+ Parameters
+ ----------
+ pt0_ice : array-like
+ Potential temperature of ice (ITS-90), degrees C
+
+ Returns
+ -------
+ pot_enthalpy_ice : array-like, J/kg
+ potential enthalpy of ice
+
+
+ """
+ return _gsw_ufuncs.pot_enthalpy_from_pt_ice_poly(pt0_ice)
+
+ at match_args_return
+def pot_enthalpy_ice_freezing(SA, p):
+ """
+ Calculates the potential enthalpy of ice at which seawater freezes.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ pot_enthalpy_ice_freezing : array-like, J/kg
+ potential enthalpy of ice at freezing
+ of seawater
+
+
+ """
+ return _gsw_ufuncs.pot_enthalpy_ice_freezing(SA, p)
+
+ at match_args_return
+def pot_enthalpy_ice_freezing_first_derivatives(SA, p):
+ """
+ Calculates the first derivatives of the potential enthalpy of ice at
+ which seawater freezes, with respect to Absolute Salinity SA and
+ pressure P (in Pa).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ pot_enthalpy_ice_freezing_SA : array-like, K kg/g
+ the derivative of the potential enthalpy
+ of ice at freezing (ITS-90) with respect to Absolute
+ salinity at fixed pressure [ K/(g/kg) ] i.e.
+ pot_enthalpy_ice_freezing_P : array-like, K/Pa
+ the derivative of the potential enthalpy
+ of ice at freezing (ITS-90) with respect to pressure
+ (in Pa) at fixed Absolute Salinity
+
+
+ """
+ return _gsw_ufuncs.pot_enthalpy_ice_freezing_first_derivatives(SA, p)
+
+ at match_args_return
+def pot_enthalpy_ice_freezing_first_derivatives_poly(SA, p):
+ """
+ Calculates the first derivatives of the potential enthalpy of ice Ih at
+ which ice melts into seawater with Absolute Salinity SA and at pressure
+ p. This code uses the comptationally efficient polynomial fit of the
+ freezing potential enthalpy of ice Ih (McDougall et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ pot_enthalpy_ice_freezing_SA : array-like, J/g
+ the derivative of the potential enthalpy
+ of ice at freezing (ITS-90) with respect to Absolute
+ salinity at fixed pressure [ (J/kg)/(g/kg) ] i.e.
+ pot_enthalpy_ice_freezing_P : array-like, (J/kg)/Pa
+ the derivative of the potential enthalpy
+ of ice at freezing (ITS-90) with respect to pressure
+ (in Pa) at fixed Absolute Salinity
+
+
+ """
+ return _gsw_ufuncs.pot_enthalpy_ice_freezing_first_derivatives_poly(SA, p)
+
+ at match_args_return
+def pot_enthalpy_ice_freezing_poly(SA, p):
+ """
+ Calculates the potential enthalpy of ice at which seawater freezes.
+ The error of this fit ranges between -2.5 and 1 J/kg with an rms of
+ 1.07, between SA of 0 and 120 g/kg and p between 0 and 10,000 dbar (the
+ error in the fit is between -0.7 and 0.7 with an rms of
+ 0.3, between SA of 0 and 120 g/kg and p between 0 and 5,000 dbar) when
+ compared with the potential enthalpy calculated from the exact in-situ
+ freezing temperature which is found by a Newton-Raphson iteration of the
+ equality of the chemical potentials of water in seawater and in ice.
+ Note that the potential enthalpy at freezing can be found
+ by this exact method using the function gsw_pot_enthalpy_ice_freezing.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ pot_enthalpy_ice_freezing : array-like, J/kg
+ potential enthalpy of ice at freezing
+ of seawater
+
+
+ """
+ return _gsw_ufuncs.pot_enthalpy_ice_freezing_poly(SA, p)
+
+ at match_args_return
+def pot_rho_t_exact(SA, t, p, p_ref):
+ """
+ Calculates potential density of seawater. Note. This function outputs
+ potential density, not potential density anomaly; that is, 1000 kg/m^3
+ is not subtracted.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ p_ref : array-like
+ Reference pressure, dbar
+
+ Returns
+ -------
+ pot_rho_t_exact : array-like, kg/m^3
+ potential density (not potential density anomaly)
+
+
+ """
+ return _gsw_ufuncs.pot_rho_t_exact(SA, t, p, p_ref)
+
+ at match_args_return
+def pressure_coefficient_ice(t, p):
+ """
+ Calculates pressure coefficient of ice.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ pressure_coefficient_ice : array-like, Pa/K
+ pressure coefficient of ice
+
+
+ """
+ return _gsw_ufuncs.pressure_coefficient_ice(t, p)
+
+ at match_args_return
+def pressure_freezing_CT(SA, CT, saturation_fraction):
+ """
+ Calculates the pressure (in dbar) of seawater at the freezing
+ temperature. That is, the output is the pressure at which seawater,
+ with Absolute Salinity SA, Conservative Temperature CT, and with
+ saturation_fraction of dissolved air, freezes. If the input values are
+ such that there is no value of pressure in the range between 0 dbar and
+ 10,000 dbar for which seawater is at the freezing temperature, the
+ output, pressure_freezing, is put equal to NaN.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ pressure_freezing : array-like, dbar
+ sea pressure at which the seawater freezes
+ ( i.e. absolute pressure - 10.1325 dbar )
+
+
+ """
+ return _gsw_ufuncs.pressure_freezing_ct(SA, CT, saturation_fraction)
+
+ at match_args_return
+def pt0_from_t(SA, t, p):
+ """
+ Calculates potential temperature with reference pressure, p_ref = 0 dbar.
+ The present routine is computationally faster than the more general
+ function "gsw_pt_from_t(SA,t,p,p_ref)" which can be used for any
+ reference pressure value.
+ This subroutine calls "gsw_entropy_part(SA,t,p)",
+ "gsw_entropy_part_zerop(SA,pt0)" and "gsw_gibbs_pt0_pt0(SA,pt0)".
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ pt0 : array-like, deg C
+ potential temperature
+ with reference sea pressure (p_ref) = 0 dbar.
+
+
+ """
+ return _gsw_ufuncs.pt0_from_t(SA, t, p)
+
+ at match_args_return
+def pt0_from_t_ice(t, p):
+ """
+ Calculates potential temperature of ice Ih with a reference pressure of
+ 0 dbar, from in-situ temperature, t.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ pt0_ice : array-like, deg C
+ potential temperature of ice Ih with reference pressure of
+ zero dbar (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.pt0_from_t_ice(t, p)
+
+ at match_args_return
+def pt_first_derivatives(SA, CT):
+ """
+ Calculates the following two partial derivatives of potential
+ temperature (the regular potential temperature whose reference sea
+ pressure is 0 dbar)
+ (1) pt_SA, the derivative with respect to Absolute Salinity at
+ constant Conservative Temperature, and
+ (2) pt_CT, the derivative with respect to Conservative Temperature at
+ constant Absolute Salinity.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ pt_SA : array-like, K/(g/kg)
+ The derivative of potential temperature with respect to
+ Absolute Salinity at constant Conservative Temperature.
+ pt_CT : array-like, unitless
+ The derivative of potential temperature with respect to
+ Conservative Temperature at constant Absolute Salinity.
+ pt_CT is dimensionless.
+
+
+ """
+ return _gsw_ufuncs.pt_first_derivatives(SA, CT)
+
+ at match_args_return
+def pt_from_CT(SA, CT):
+ """
+ Calculates potential temperature (with a reference sea pressure of
+ zero dbar) from Conservative Temperature. This function uses 1.5
+ iterations through a modified Newton-Raphson (N-R) iterative solution
+ proceedure, starting from a rational-function-based initial condition
+ for both pt and dCT_dpt.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ pt : array-like, deg C
+ potential temperature referenced to a sea pressure
+ of zero dbar (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.pt_from_ct(SA, CT)
+
+ at match_args_return
+def pt_from_entropy(SA, entropy):
+ """
+ Calculates potential temperature with reference pressure p_ref = 0 dbar
+ and with entropy as an input variable.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ entropy : array-like
+ Specific entropy, J/(kg*K)
+
+ Returns
+ -------
+ pt : array-like, deg C
+ potential temperature
+ with reference sea pressure (p_ref) = 0 dbar.
+
+
+ """
+ return _gsw_ufuncs.pt_from_entropy(SA, entropy)
+
+ at match_args_return
+def pt_from_pot_enthalpy_ice(pot_enthalpy_ice):
+ """
+ Calculates the potential temperature of ice from the potential enthalpy
+ of ice. The reference sea pressure of both the potential temperature
+ and the potential enthalpy is zero dbar.
+
+ Parameters
+ ----------
+ pot_enthalpy_ice : array-like
+ Potential enthalpy of ice, J/kg
+
+ Returns
+ -------
+ pt0_ice : array-like, deg C
+ potential temperature of ice (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.pt_from_pot_enthalpy_ice(pot_enthalpy_ice)
+
+ at match_args_return
+def pt_from_pot_enthalpy_ice_poly(pot_enthalpy_ice):
+ """
+ Calculates the potential temperature of ice (whose reference sea
+ pressure is zero dbar) from the potential enthalpy of ice. This is a
+ compuationally efficient polynomial fit to the potential enthalpy of
+ ice.
+
+ Parameters
+ ----------
+ pot_enthalpy_ice : array-like
+ Potential enthalpy of ice, J/kg
+
+ Returns
+ -------
+ pt0_ice : array-like, deg C
+ potential temperature of ice (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.pt_from_pot_enthalpy_ice_poly(pot_enthalpy_ice)
+
+ at match_args_return
+def pt_from_t(SA, t, p, p_ref):
+ """
+ Calculates potential temperature with the general reference pressure,
+ p_ref, from in-situ temperature, t. This function calls
+ "gsw_entropy_part" which evaluates entropy except for the parts which
+ are a function of Absolute Salinity alone.
+ A faster gsw routine exists if p_ref is indeed zero dbar. This routine
+ is "gsw_pt0_from_t(SA,t,p)".
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ p_ref : array-like
+ Reference pressure, dbar
+
+ Returns
+ -------
+ pt : array-like, deg C
+ potential temperature with reference pressure, p_ref, on the
+ ITS-90 temperature scale
+
+
+ """
+ return _gsw_ufuncs.pt_from_t(SA, t, p, p_ref)
+
+ at match_args_return
+def pt_from_t_ice(t, p, p_ref):
+ """
+ Calculates potential temperature of ice Ih with the general reference
+ pressure, p_ref, from in-situ temperature, t.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ p_ref : array-like
+ Reference pressure, dbar
+
+ Returns
+ -------
+ pt_ice : array-like, deg C
+ potential temperature of ice Ih with reference pressure,
+ p_ref, on the ITS-90 temperature scale
+
+
+ """
+ return _gsw_ufuncs.pt_from_t_ice(t, p, p_ref)
+
+ at match_args_return
+def pt_second_derivatives(SA, CT):
+ """
+ Calculates the following three second-order derivatives of potential
+ temperature (the regular potential temperature which has a reference
+ sea pressure of 0 dbar),
+ (1) pt_SA_SA, the second derivative with respect to Absolute Salinity
+ at constant Conservative Temperature,
+ (2) pt_SA_CT, the derivative with respect to Conservative Temperature
+ and Absolute Salinity, and
+ (3) pt_CT_CT, the second derivative with respect to Conservative
+ Temperature at constant Absolute Salinity.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ pt_SA_SA : array-like, K/((g/kg)^2)
+ The second derivative of potential temperature (the
+ regular potential temperature which has reference sea
+ pressure of 0 dbar) with respect to Absolute Salinity
+ at constant Conservative Temperature.
+ pt_SA_CT : array-like, 1/(g/kg)
+ The derivative of potential temperature with respect
+ to Absolute Salinity and Conservative Temperature.
+ pt_CT_CT : array-like, 1/K
+ The second derivative of potential temperature (the
+ regular one with p_ref = 0 dbar) with respect to
+ Conservative Temperature at constant SA.
+
+
+ """
+ return _gsw_ufuncs.pt_second_derivatives(SA, CT)
+
+ at match_args_return
+def rho(SA, CT, p):
+ """
+ Calculates in-situ density from Absolute Salinity and Conservative
+ Temperature, using the computationally-efficient expression for
+ specific volume in terms of SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ rho : array-like, kg/m
+ in-situ density
+
+
+ """
+ return _gsw_ufuncs.rho(SA, CT, p)
+
+ at match_args_return
+def rho_alpha_beta(SA, CT, p):
+ """
+ Calculates in-situ density, the appropiate thermal expansion coefficient
+ and the appropriate saline contraction coefficient of seawater from
+ Absolute Salinity and Conservative Temperature. This function uses the
+ computationally-efficient expression for specific volume in terms of
+ SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ rho : array-like, kg/m
+ in-situ density
+ alpha : array-like, 1/K
+ thermal expansion coefficient
+ with respect to Conservative Temperature
+ beta : array-like, kg/g
+ saline (i.e. haline) contraction
+ coefficient at constant Conservative Temperature
+
+
+ """
+ return _gsw_ufuncs.rho_alpha_beta(SA, CT, p)
+
+ at match_args_return
+def rho_first_derivatives(SA, CT, p):
+ """
+ Calculates the three (3) partial derivatives of in-situ density with
+ respect to Absolute Salinity, Conservative Temperature and pressure.
+ Note that the pressure derivative is done with respect to pressure in
+ Pa, not dbar. This function uses the computationally-efficient
+ expression for specific volume in terms of SA, CT and p (Roquet et al.,
+ 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ rho_SA : array-like, (kg/m^3)(g/kg)^-1
+ partial derivative of density
+ with respect to Absolute Salinity
+ rho_CT : array-like, kg/(m^3 K)
+ partial derivative of density
+ with respect to Conservative Temperature
+ rho_P : array-like, kg/(m^3 Pa)
+ partial derivative of density
+ with respect to pressure in Pa
+
+
+ """
+ return _gsw_ufuncs.rho_first_derivatives(SA, CT, p)
+
+ at match_args_return
+def rho_first_derivatives_wrt_enthalpy(SA, CT, p):
+ """
+ Calculates the following two first-order derivatives of specific
+ volume (v),
+ (1) rho_SA, first-order derivative with respect to Absolute Salinity
+ at constant CT & p.
+ (2) rho_h, first-order derivative with respect to SA & CT at
+ constant p.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ rho_SA : array-like, J/(kg (g/kg)^2)
+ The first derivative of rho with respect to
+ Absolute Salinity at constant CT & p.
+ rho_h : array-like, J/(kg K(g/kg))
+ The first derivative of rho with respect to
+ SA and CT at constant p.
+
+
+ """
+ return _gsw_ufuncs.rho_first_derivatives_wrt_enthalpy(SA, CT, p)
+
+ at match_args_return
+def rho_ice(t, p):
+ """
+ Calculates in-situ density of ice from in-situ temperature and pressure.
+ Note that the output, rho_ice, is density, not density anomaly; that
+ is, 1000 kg/m^3 is not subracted from it.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ rho_ice : array-like, kg/m^3
+ in-situ density of ice (not density anomaly)
+
+
+ """
+ return _gsw_ufuncs.rho_ice(t, p)
+
+ at match_args_return
+def rho_second_derivatives(SA, CT, p):
+ """
+ Calculates the following five second-order derivatives of rho,
+ (1) rho_SA_SA, second-order derivative with respect to Absolute
+ Salinity at constant CT & p.
+ (2) rho_SA_CT, second-order derivative with respect to SA & CT at
+ constant p.
+ (3) rho_CT_CT, second-order derivative with respect to CT at
+ constant SA & p.
+ (4) rho_SA_P, second-order derivative with respect to SA & P at
+ constant CT.
+ (5) rho_CT_P, second-order derivative with respect to CT & P at
+ constant SA.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ rho_SA_SA : array-like, (kg/m^3)(g/kg)^-2
+ The second-order derivative of rho with respect to
+ Absolute Salinity at constant CT & p.
+ rho_SA_CT : array-like, (kg/m^3)(g/kg)^-1 K^-1
+ The second-order derivative of rho with respect to
+ SA and CT at constant p.
+ rho_CT_CT : array-like, (kg/m^3) K^-2
+ The second-order derivative of rho with respect to CT at
+ constant SA & p
+ rho_SA_P : array-like, (kg/m^3)(g/kg)^-1 Pa^-1
+ The second-order derivative with respect to SA & P at
+ constant CT.
+ rho_CT_P : array-like, (kg/m^3) K^-1 Pa^-1
+ The second-order derivative with respect to CT & P at
+ constant SA.
+
+
+ """
+ return _gsw_ufuncs.rho_second_derivatives(SA, CT, p)
+
+ at match_args_return
+def rho_second_derivatives_wrt_enthalpy(SA, CT, p):
+ """
+ Calculates the following three second-order derivatives of rho with
+ respect to enthalpy,
+ (1) rho_SA_SA, second-order derivative with respect to Absolute Salinity
+ at constant h & p.
+ (2) rho_SA_h, second-order derivative with respect to SA & h at
+ constant p.
+ (3) rho_h_h, second-order derivative with respect to h at
+ constant SA & p.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ rho_SA_SA : array-like, J/(kg (g/kg)^2)
+ The second-order derivative of rho with respect to
+ Absolute Salinity at constant h & p.
+ rho_SA_h : array-like, J/(kg K(g/kg))
+ The second-order derivative of rho with respect to
+ SA and h at constant p.
+ rho_h_h : array-like,
+ The second-order derivative of rho with respect to h at
+ constant SA & p
+
+
+ """
+ return _gsw_ufuncs.rho_second_derivatives_wrt_enthalpy(SA, CT, p)
+
+ at match_args_return
+def rho_t_exact(SA, t, p):
+ """
+ Calculates in-situ density of seawater from Absolute Salinity and
+ in-situ temperature. Note that the output, rho, is density,
+ not density anomaly; that is, 1000 kg/m^3 is not subracted from it.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ rho_t_exact : array-like, kg/m^3
+ in-situ density (not density anomaly)
+
+
+ """
+ return _gsw_ufuncs.rho_t_exact(SA, t, p)
+
+ at match_args_return
+def SA_freezing_from_CT(CT, p, saturation_fraction):
+ """
+ Calculates the Absolute Salinity of seawater at the freezing temperature.
+ That is, the output is the Absolute Salinity of seawater, with
+ Conservative Temperature CT, pressure p and the fraction
+ saturation_fraction of dissolved air, that is in equilibrium
+ with ice at the same in situ temperature and pressure. If the input
+ values are such that there is no positive value of Absolute Salinity for
+ which seawater is frozen, the output, SA_freezing, is made a NaN.
+
+ Parameters
+ ----------
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ SA_freezing : array-like, g/kg
+ Absolute Salinity of seawater when it freezes, for
+ given input values of its Conservative Temperature,
+ pressure and air saturation fraction.
+
+
+ """
+ return _gsw_ufuncs.sa_freezing_from_ct(CT, p, saturation_fraction)
+
+ at match_args_return
+def SA_freezing_from_CT_poly(CT, p, saturation_fraction):
+ """
+ Calculates the Absolute Salinity of seawater at the freezing temperature.
+ That is, the output is the Absolute Salinity of seawater, with the
+ fraction saturation_fraction of dissolved air, that is in equilibrium
+ with ice at Conservative Temperature CT and pressure p. If the input
+ values are such that there is no positive value of Absolute Salinity for
+ which seawater is frozen, the output, SA_freezing, is put equal to NaN.
+
+ Parameters
+ ----------
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ SA_freezing : array-like, g/kg
+ Absolute Salinity of seawater when it freezes, for
+ given input values of Conservative Temperature
+ pressure and air saturation fraction.
+
+
+ """
+ return _gsw_ufuncs.sa_freezing_from_ct_poly(CT, p, saturation_fraction)
+
+ at match_args_return
+def SA_freezing_from_t(t, p, saturation_fraction):
+ """
+ Calculates the Absolute Salinity of seawater at the freezing temperature.
+ That is, the output is the Absolute Salinity of seawater, with the
+ fraction saturation_fraction of dissolved air, that is in equilibrium
+ with ice at in-situ temperature t and pressure p. If the input values
+ are such that there is no positive value of Absolute Salinity for which
+ seawater is frozen, the output, SA_freezing, is set to NaN.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ SA_freezing : array-like, g/kg
+ Absolute Salinity of seawater when it freezes, for
+ given input values of in situ temperature, pressure and
+ air saturation fraction.
+
+
+ """
+ return _gsw_ufuncs.sa_freezing_from_t(t, p, saturation_fraction)
+
+ at match_args_return
+def SA_freezing_from_t_poly(t, p, saturation_fraction):
+ """
+ Calculates the Absolute Salinity of seawater at the freezing temperature.
+ That is, the output is the Absolute Salinity of seawater, with the
+ fraction saturation_fraction of dissolved air, that is in equilibrium
+ with ice at in-situ temperature t and pressure p. If the input values
+ are such that there is no positive value of Absolute Salinity for which
+ seawater is frozen, the output, SA_freezing, is put equal to NaN.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ SA_freezing : array-like, g/kg
+ Absolute Salinity of seawater when it freezes, for
+ given input values of in situ temperature, pressure and
+ air saturation fraction.
+
+
+ """
+ return _gsw_ufuncs.sa_freezing_from_t_poly(t, p, saturation_fraction)
+
+ at match_args_return
+def SA_from_rho(rho, CT, p):
+ """
+ Calculates the Absolute Salinity of a seawater sample, for given values
+ of its density, Conservative Temperature and sea pressure (in dbar).
+ This function uses the computationally-efficient 75-term expression for
+ specific volume in terms of SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ rho : array-like
+ Seawater density (not anomaly) in-situ, e.g., 1026 kg/m^3.
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ SA : array-like, g/kg
+ Absolute Salinity.
+
+
+ """
+ return _gsw_ufuncs.sa_from_rho(rho, CT, p)
+
+ at match_args_return
+def SA_from_SP(SP, p, lon, lat):
+ """
+ Calculates Absolute Salinity from Practical Salinity. Since SP is
+ non-negative by definition, this function changes any negative input
+ values of SP to be zero.
+
+ Parameters
+ ----------
+ SP : array-like
+ Practical Salinity (PSS-78), unitless
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ SA : array-like, g/kg
+ Absolute Salinity
+
+
+ """
+ return _gsw_ufuncs.sa_from_sp(SP, p, lon, lat)
+
+ at match_args_return
+def SA_from_SP_Baltic(SP, lon, lat):
+ """
+ Calculates Absolute Salinity in the Baltic Sea, from Practical Salinity.
+ Since SP is non-negative by definition, this function changes any
+ negative input values of SP to be zero.
+ Note. This programme will only produce Absolute Salinity values for the
+ Baltic Sea.
+
+ Parameters
+ ----------
+ SP : array-like
+ Practical Salinity (PSS-78), unitless
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ SA_baltic : array-like, g kg^-1
+ Absolute Salinity in the Baltic Sea
+
+
+ """
+ return _gsw_ufuncs.sa_from_sp_baltic(SP, lon, lat)
+
+ at match_args_return
+def SA_from_Sstar(Sstar, p, lon, lat):
+ """
+ Calculates Absolute Salinity from Preformed Salinity.
+
+ Parameters
+ ----------
+ Sstar : array-like
+ Preformed Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ SA : array-like, g/kg
+ Absolute Salinity
+
+
+ """
+ return _gsw_ufuncs.sa_from_sstar(Sstar, p, lon, lat)
+
+ at match_args_return
+def SAAR(p, lon, lat):
+ """
+ Calculates the Absolute Salinity Anomaly Ratio, SAAR, in the open ocean
+ by spatially interpolating the global reference data set of SAAR to the
+ location of the seawater sample.
+
+ Parameters
+ ----------
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ SAAR : array-like, unitless
+ Absolute Salinity Anomaly Ratio
+
+
+ """
+ return _gsw_ufuncs.saar(p, lon, lat)
+
+ at match_args_return
+def seaice_fraction_to_freeze_seawater(SA, CT, p, SA_seaice, t_seaice):
+ """
+ Calculates the mass fraction of sea ice (mass of sea ice divided by mass
+ of sea ice plus seawater), which, when melted into seawater having the
+ properties (SA,CT,p) causes the final seawater to be at the freezing
+ temperature. The other outputs are the Absolute Salinity and
+ Conservative Temperature of the final seawater.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ SA_seaice : array-like
+ Absolute Salinity of sea ice: the mass fraction of salt
+ in sea ice, expressed in g of salt per kg of sea ice.
+ t_seaice : array-like
+ In-situ temperature of the sea ice at pressure p (ITS-90), degrees C
+
+ Returns
+ -------
+ SA_freeze : array-like, g/kg
+ Absolute Salinity of seawater after the mass fraction of
+ sea ice, w_seaice, at temperature t_seaice has melted into
+ the original seawater, and the final mixture is at the
+ freezing temperature of seawater.
+ CT_freeze : array-like, deg C
+ Conservative Temperature of seawater after the mass
+ fraction, w_seaice, of sea ice at temperature t_seaice has
+ melted into the original seawater, and the final mixture
+ is at the freezing temperature of seawater.
+ w_seaice : array-like, unitless
+ mass fraction of sea ice, at SA_seaice and t_seaice,
+ which, when melted into seawater at (SA,CT,p) leads to the
+ final mixed seawater being at the freezing temperature.
+ This output is between 0 and 1.
+
+
+ """
+ return _gsw_ufuncs.seaice_fraction_to_freeze_seawater(SA, CT, p, SA_seaice, t_seaice)
+
+ at match_args_return
+def sigma0(SA, CT):
+ """
+ Calculates potential density anomaly with reference pressure of 0 dbar,
+ this being this particular potential density minus 1000 kg/m^3. This
+ function has inputs of Absolute Salinity and Conservative Temperature.
+ This function uses the computationally-efficient expression for
+ specific volume in terms of SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ sigma0 : array-like, kg/m^3
+ potential density anomaly with
+ respect to a reference pressure of 0 dbar,
+ that is, this potential density - 1000 kg/m^3.
+
+
+ """
+ return _gsw_ufuncs.sigma0(SA, CT)
+
+ at match_args_return
+def sigma1(SA, CT):
+ """
+ Calculates potential density anomaly with reference pressure of 1000
+ dbar, this being this particular potential density minus 1000 kg/m^3.
+ This function has inputs of Absolute Salinity and Conservative
+ Temperature. This function uses the computationally-efficient
+ expression for specific volume in terms of SA, CT and p (Roquet et al.,
+ 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ sigma1 : array-like, kg/m^3
+ potential density anomaly with
+ respect to a reference pressure of 1000 dbar,
+ that is, this potential density - 1000 kg/m^3.
+
+
+ """
+ return _gsw_ufuncs.sigma1(SA, CT)
+
+ at match_args_return
+def sigma2(SA, CT):
+ """
+ Calculates potential density anomaly with reference pressure of 2000
+ dbar, this being this particular potential density minus 1000 kg/m^3.
+ Temperature. This function uses the computationally-efficient
+ expression for specific volume in terms of SA, CT and p (Roquet et al.,
+ 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ sigma2 : array-like, kg/m^3
+ potential density anomaly with
+ respect to a reference pressure of 2000 dbar,
+ that is, this potential density - 1000 kg/m^3.
+
+
+ """
+ return _gsw_ufuncs.sigma2(SA, CT)
+
+ at match_args_return
+def sigma3(SA, CT):
+ """
+ Calculates potential density anomaly with reference pressure of 3000
+ dbar, this being this particular potential density minus 1000 kg/m^3.
+ Temperature. This function uses the computationally-efficient
+ expression for specific volume in terms of SA, CT and p (Roquet et al.,
+ 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ sigma3 : array-like, kg/m^3
+ potential density anomaly with
+ respect to a reference pressure of 3000 dbar,
+ that is, this potential density - 1000 kg/m^3.
+
+
+ """
+ return _gsw_ufuncs.sigma3(SA, CT)
+
+ at match_args_return
+def sigma4(SA, CT):
+ """
+ Calculates potential density anomaly with reference pressure of 4000
+ dbar, this being this particular potential density minus 1000 kg/m^3.
+ Temperature. This function uses the computationally-efficient
+ expression for specific volume in terms of SA, CT and p (Roquet et al.,
+ 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ sigma4 : array-like, kg/m^3
+ potential density anomaly with
+ respect to a reference pressure of 4000 dbar,
+ that is, this potential density - 1000 kg/m^3.
+
+
+ """
+ return _gsw_ufuncs.sigma4(SA, CT)
+
+ at match_args_return
+def sound_speed(SA, CT, p):
+ """
+ Calculates the speed of sound in seawater. This function has inputs of
+ Absolute Salinity and Conservative Temperature. This function uses the
+ computationally-efficient expression for specific volume in terms of SA,
+ CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ sound_speed : array-like, m/s
+ speed of sound in seawater
+
+
+ """
+ return _gsw_ufuncs.sound_speed(SA, CT, p)
+
+ at match_args_return
+def sound_speed_ice(t, p):
+ """
+ Calculates the compression speed of sound in ice.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ sound_speed_ice : array-like, m/s
+ compression speed of sound in ice
+
+
+ """
+ return _gsw_ufuncs.sound_speed_ice(t, p)
+
+ at match_args_return
+def sound_speed_t_exact(SA, t, p):
+ """
+ Calculates the speed of sound in seawater.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ sound_speed_t_exact : array-like, m/s
+ speed of sound in seawater
+
+
+ """
+ return _gsw_ufuncs.sound_speed_t_exact(SA, t, p)
+
+ at match_args_return
+def SP_from_C(C, t, p):
+ """
+ Calculates Practical Salinity, SP, from conductivity, C, primarily using
+ the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical
+ Salinity is only valid in the range 2 < SP < 42. If the PSS-78
+ algorithm produces a Practical Salinity that is less than 2 then the
+ Practical Salinity is recalculated with a modified form of the Hill et
+ al. (1986) formula. The modification of the Hill et al. (1986)
+ expression is to ensure that it is exactly consistent with PSS-78
+ at SP = 2. Note that the input values of conductivity need to be in
+ units of mS/cm (not S/m).
+
+ Parameters
+ ----------
+ C : array-like
+ Conductivity, mS/cm
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ SP : array-like, unitless
+ Practical Salinity on the PSS-78 scale
+
+
+ """
+ return _gsw_ufuncs.sp_from_c(C, t, p)
+
+ at match_args_return
+def SP_from_SA(SA, p, lon, lat):
+ """
+ Calculates Practical Salinity from Absolute Salinity.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ SP : array-like, unitless
+ Practical Salinity (PSS-78)
+
+
+ """
+ return _gsw_ufuncs.sp_from_sa(SA, p, lon, lat)
+
+ at match_args_return
+def SP_from_SA_Baltic(SA, lon, lat):
+ """
+ Calculates Practical Salinity for the Baltic Sea, from a value computed
+ analytically from Absolute Salinity.
+ Note. This programme will only produce Practical Salinty values for the
+ Baltic Sea.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ SP_baltic : array-like, unitless
+ Practical Salinity
+
+
+ """
+ return _gsw_ufuncs.sp_from_sa_baltic(SA, lon, lat)
+
+ at match_args_return
+def SP_from_SK(SK):
+ """
+ Calculates Practical Salinity from Knudsen Salinity.
+
+ Parameters
+ ----------
+ SK : array-like
+ Knudsen Salinity, ppt
+
+ Returns
+ -------
+ SP : array-like, unitless
+ Practical Salinity (PSS-78)
+
+
+ """
+ return _gsw_ufuncs.sp_from_sk(SK)
+
+ at match_args_return
+def SP_from_SR(SR):
+ """
+ Calculates Practical Salinity from Reference Salinity.
+
+ Parameters
+ ----------
+ SR : array-like
+ Reference Salinity, g/kg
+
+ Returns
+ -------
+ SP : array-like, unitless
+ Practical Salinity (PSS-78)
+
+
+ """
+ return _gsw_ufuncs.sp_from_sr(SR)
+
+ at match_args_return
+def SP_from_Sstar(Sstar, p, lon, lat):
+ """
+ Calculates Practical Salinity from Preformed Salinity.
+
+ Parameters
+ ----------
+ Sstar : array-like
+ Preformed Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ SP : array-like, unitless
+ Practical Salinity (PSS-78)
+
+
+ """
+ return _gsw_ufuncs.sp_from_sstar(Sstar, p, lon, lat)
+
+ at match_args_return
+def specvol(SA, CT, p):
+ """
+ Calculates specific volume from Absolute Salinity, Conservative
+ Temperature and pressure, using the computationally-efficient 75-term
+ polynomial expression for specific volume (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ specvol : array-like, m^3/kg
+ specific volume
+
+
+ """
+ return _gsw_ufuncs.specvol(SA, CT, p)
+
+ at match_args_return
+def specvol_alpha_beta(SA, CT, p):
+ """
+ Calculates specific volume, the appropiate thermal expansion coefficient
+ and the appropriate saline contraction coefficient of seawater from
+ Absolute Salinity and Conservative Temperature. This function uses the
+ computationally-efficient expression for specific volume in terms of
+ SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ specvol : array-like, m/kg
+ specific volume
+ alpha : array-like, 1/K
+ thermal expansion coefficient
+ with respect to Conservative Temperature
+ beta : array-like, kg/g
+ saline (i.e. haline) contraction
+ coefficient at constant Conservative Temperature
+
+
+ """
+ return _gsw_ufuncs.specvol_alpha_beta(SA, CT, p)
+
+ at match_args_return
+def specvol_anom_standard(SA, CT, p):
+ """
+ Calculates specific volume anomaly from Absolute Salinity, Conservative
+ Temperature and pressure. It uses the computationally-efficient
+ expression for specific volume as a function of SA, CT and p (Roquet
+ et al., 2015). The reference value to which the anomally is calculated
+ has an Absolute Salinity of SSO and Conservative Temperature equal to
+ 0 degress C.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ specvol_anom : array-like, m^3/kg
+ specific volume anomaly
+
+
+ """
+ return _gsw_ufuncs.specvol_anom_standard(SA, CT, p)
+
+ at match_args_return
+def specvol_first_derivatives(SA, CT, p):
+ """
+ Calculates the following three first-order derivatives of specific
+ volume (v),
+ (1) v_SA, first-order derivative with respect to Absolute Salinity
+ at constant CT & p.
+ (2) v_CT, first-order derivative with respect to CT at
+ constant SA & p.
+ (3) v_P, first-order derivative with respect to P at constant SA
+ and CT.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ v_SA : array-like, (m^3/kg)(g/kg)^-1
+ The first derivative of specific volume with respect to
+ Absolute Salinity at constant CT & p.
+ v_CT : array-like, m^3/(K kg)
+ The first derivative of specific volume with respect to
+ CT at constant SA and p.
+ v_P : array-like, m^3/(Pa kg)
+ The first derivative of specific volume with respect to
+ P at constant SA and CT.
+
+
+ """
+ return _gsw_ufuncs.specvol_first_derivatives(SA, CT, p)
+
+ at match_args_return
+def specvol_first_derivatives_wrt_enthalpy(SA, CT, p):
+ """
+ Calculates the following two first-order derivatives of specific
+ volume (v),
+ (1) v_SA_wrt_h, first-order derivative with respect to Absolute Salinity
+ at constant h & p.
+ (2) v_h, first-order derivative with respect to h at
+ constant SA & p.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ v_SA_wrt_h : array-like, (m^3/kg)(g/kg)^-1 (J/kg)^-1
+ The first derivative of specific volume with respect to
+ Absolute Salinity at constant CT & p.
+ v_h : array-like, (m^3/kg)(J/kg)^-1
+ The first derivative of specific volume with respect to
+ SA and CT at constant p.
+
+
+ """
+ return _gsw_ufuncs.specvol_first_derivatives_wrt_enthalpy(SA, CT, p)
+
+ at match_args_return
+def specvol_ice(t, p):
+ """
+ Calculates the specific volume of ice.
+
+ Parameters
+ ----------
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ specvol_ice : array-like, m^3/kg
+ specific volume
+
+
+ """
+ return _gsw_ufuncs.specvol_ice(t, p)
+
+ at match_args_return
+def specvol_second_derivatives(SA, CT, p):
+ """
+ Calculates the following five second-order derivatives of specific
+ volume (v),
+ (1) v_SA_SA, second-order derivative with respect to Absolute Salinity
+ at constant CT & p.
+ (2) v_SA_CT, second-order derivative with respect to SA & CT at
+ constant p.
+ (3) v_CT_CT, second-order derivative with respect to CT at constant SA
+ and p.
+ (4) v_SA_P, second-order derivative with respect to SA & P at
+ constant CT.
+ (5) v_CT_P, second-order derivative with respect to CT & P at
+ constant SA.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ v_SA_SA : array-like, (m^3/kg)(g/kg)^-2
+ The second derivative of specific volume with respect to
+ Absolute Salinity at constant CT & p.
+ v_SA_CT : array-like, (m^3/kg)(g/kg)^-1 K^-1
+ The second derivative of specific volume with respect to
+ SA and CT at constant p.
+ v_CT_CT : array-like, (m^3/kg) K^-2)
+ The second derivative of specific volume with respect to
+ CT at constant SA and p.
+ v_SA_P : array-like, (m^3/kg) Pa^-1
+ The second derivative of specific volume with respect to
+ SA and P at constant CT.
+ v_CT_P : array-like, (m^3/kg) K^-1 Pa^-1
+ The second derivative of specific volume with respect to
+ CT and P at constant SA.
+
+
+ """
+ return _gsw_ufuncs.specvol_second_derivatives(SA, CT, p)
+
+ at match_args_return
+def specvol_second_derivatives_wrt_enthalpy(SA, CT, p):
+ """
+ Calculates the following three first-order derivatives of specific
+ volume (v) with respect to enthalpy,
+ (1) v_SA_SA_wrt_h, second-order derivative with respect to Absolute Salinity
+ at constant h & p.
+ (2) v_SA_h, second-order derivative with respect to SA & h at
+ constant p.
+ (3) v_h_h, second-order derivative with respect to h at
+ constant SA & p.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ v_SA_SA_wrt_h : array-like, (m^3/kg)(g/kg)^-2 (J/kg)^-1
+ The second-order derivative of specific volume with
+ respect to Absolute Salinity at constant h & p.
+ v_SA_h : array-like, (m^3/kg)(g/kg)^-1 (J/kg)^-1
+ The second-order derivative of specific volume with respect to
+ SA and h at constant p.
+ v_h_h : array-like, (m^3/kg)(J/kg)^-2
+ The second-order derivative with respect to h at
+ constant SA & p.
+
+
+ """
+ return _gsw_ufuncs.specvol_second_derivatives_wrt_enthalpy(SA, CT, p)
+
+ at match_args_return
+def specvol_t_exact(SA, t, p):
+ """
+ Calculates the specific volume of seawater.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ specvol_t_exact : array-like, m^3/kg
+ specific volume
+
+
+ """
+ return _gsw_ufuncs.specvol_t_exact(SA, t, p)
+
+ at match_args_return
+def spiciness0(SA, CT):
+ """
+ Calculates spiciness from Absolute Salinity and Conservative
+ Temperature at a pressure of 0 dbar, as described by McDougall and
+ Krzysik (2015). This routine is based on the computationally-efficient
+ expression for specific volume in terms of SA, CT and p (Roquet et al.,
+ 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ spiciness0 : array-like, kg/m^3
+ spiciness referenced to a pressure of 0 dbar,
+ i.e. the surface
+
+
+ """
+ return _gsw_ufuncs.spiciness0(SA, CT)
+
+ at match_args_return
+def spiciness1(SA, CT):
+ """
+ Calculates spiciness from Absolute Salinity and Conservative
+ Temperature at a pressure of 1000 dbar, as described by McDougall and
+ Krzysik (2015). This routine is based on the computationally-efficient
+ expression for specific volume in terms of SA, CT and p (Roquet et al.,
+ 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ spiciness1 : array-like, kg/m^3
+ spiciness referenced to a pressure of 1000 dbar
+
+
+ """
+ return _gsw_ufuncs.spiciness1(SA, CT)
+
+ at match_args_return
+def spiciness2(SA, CT):
+ """
+ Calculates spiciness from Absolute Salinity and Conservative
+ Temperature at a pressure of 2000 dbar, as described by McDougall and
+ Krzysik (2015). This routine is based on the computationally-efficient
+ expression for specific volume in terms of SA, CT and p (Roquet et al.,
+ 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+
+ Returns
+ -------
+ spiciness2 : array-like, kg/m^3
+ spiciness referenced to a pressure of 2000 dbar
+
+
+ """
+ return _gsw_ufuncs.spiciness2(SA, CT)
+
+ at match_args_return
+def SR_from_SP(SP):
+ """
+ Calculates Reference Salinity from Practical Salinity.
+
+ Parameters
+ ----------
+ SP : array-like
+ Practical Salinity (PSS-78), unitless
+
+ Returns
+ -------
+ SR : array-like, g/kg
+ Reference Salinity
+
+
+ """
+ return _gsw_ufuncs.sr_from_sp(SP)
+
+ at match_args_return
+def Sstar_from_SA(SA, p, lon, lat):
+ """
+ Converts Preformed Salinity from Absolute Salinity.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ Sstar : array-like, g/kg
+ Preformed Salinity
+
+
+ """
+ return _gsw_ufuncs.sstar_from_sa(SA, p, lon, lat)
+
+ at match_args_return
+def Sstar_from_SP(SP, p, lon, lat):
+ """
+ Calculates Preformed Salinity from Absolute Salinity.
+ Since SP is non-negative by definition, this function changes any
+ negative input values of SP to be zero.
+
+ Parameters
+ ----------
+ SP : array-like
+ Practical Salinity (PSS-78), unitless
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lon : array-like
+ Longitude, -360 to 360 degrees
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ Sstar : array-like, g/kg
+ Preformed Salinity
+
+
+ """
+ return _gsw_ufuncs.sstar_from_sp(SP, p, lon, lat)
+
+ at match_args_return
+def t_deriv_chem_potential_water_t_exact(SA, t, p):
+ """
+ Calculates the temperature derivative of the chemical potential of water
+ in seawater so that it is valid at exactly SA = 0.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ chem_potential_water_dt : array-like, J g^-1 K^-1
+ temperature derivative of the chemical
+ potential of water in seawater
+
+
+ """
+ return _gsw_ufuncs.t_deriv_chem_potential_water_t_exact(SA, t, p)
+
+ at match_args_return
+def t_freezing(SA, p, saturation_fraction):
+ """
+ Calculates the in-situ temperature at which seawater freezes. The
+ in-situ temperature freezing point is calculated from the exact
+ in-situ freezing temperature which is found by a modified Newton-Raphson
+ iteration (McDougall and Wotherspoon, 2013) of the equality of the
+ chemical potentials of water in seawater and in ice.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ t_freezing : array-like, deg C
+ in-situ temperature at which seawater freezes.
+ (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.t_freezing(SA, p, saturation_fraction)
+
+ at match_args_return
+def t_freezing_first_derivatives(SA, p, saturation_fraction):
+ """
+ Calculates the frist derivatives of the in-situ temperature at which
+ seawater freezes with respect to Absolute Salinity SA and pressure P (in
+ Pa). These expressions come from differentiating the expression that
+ defines the freezing temperature, namely the equality between the
+ chemical potentials of water in seawater and in ice.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ tfreezing_SA : array-like, K kg/g
+ the derivative of the in-situ freezing temperature
+ (ITS-90) with respect to Absolute Salinity at fixed
+ pressure [ K/(g/kg) ] i.e.
+ tfreezing_P : array-like, K/Pa
+ the derivative of the in-situ freezing temperature
+ (ITS-90) with respect to pressure (in Pa) at fixed
+ Absolute Salinity
+
+
+ """
+ return _gsw_ufuncs.t_freezing_first_derivatives(SA, p, saturation_fraction)
+
+ at match_args_return
+def t_freezing_first_derivatives_poly(SA, p, saturation_fraction):
+ """
+ Calculates the frist derivatives of the in-situ temperature at which
+ seawater freezes with respect to Absolute Salinity SA and pressure P (in
+ Pa). These expressions come from differentiating the expression that
+ defines the freezing temperature, namely the equality between the
+ chemical potentials of water in seawater and in ice.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ tfreezing_SA : array-like, K kg/g
+ the derivative of the in-situ freezing temperature
+ (ITS-90) with respect to Absolute Salinity at fixed
+ pressure [ K/(g/kg) ] i.e.
+ tfreezing_P : array-like, K/Pa
+ the derivative of the in-situ freezing temperature
+ (ITS-90) with respect to pressure (in Pa) at fixed
+ Absolute Salinity
+
+
+ """
+ return _gsw_ufuncs.t_freezing_first_derivatives_poly(SA, p, saturation_fraction)
+
+ at match_args_return
+def t_freezing_poly(SA, p, saturation_fraction):
+ """
+ Calculates the in-situ temperature at which seawater freezes from a
+ comptationally efficient polynomial.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ saturation_fraction : array-like
+ Saturation fraction of dissolved air in seawater. (0..1)
+
+ Returns
+ -------
+ t_freezing : array-like, deg C
+ in-situ temperature at which seawater freezes.
+ (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.t_freezing_poly(SA, p, saturation_fraction)
+
+ at match_args_return
+def t_from_CT(SA, CT, p):
+ """
+ Calculates in-situ temperature from the Conservative Temperature of
+ seawater.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ t : array-like, deg C
+ in-situ temperature (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.t_from_ct(SA, CT, p)
+
+ at match_args_return
+def t_from_pt0_ice(pt0_ice, p):
+ """
+ Calculates in-situ temperature from the potential temperature of ice Ih
+ with reference pressure, p_ref, of 0 dbar (the surface), and the
+ in-situ pressure.
+
+ Parameters
+ ----------
+ pt0_ice : array-like
+ Potential temperature of ice (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ t : array-like, deg C
+ in-situ temperature (ITS-90)
+
+
+ """
+ return _gsw_ufuncs.t_from_pt0_ice(pt0_ice, p)
+
+ at match_args_return
+def thermobaric(SA, CT, p):
+ """
+ Calculates the thermobaric coefficient of seawater with respect to
+ Conservative Temperature. This routine is based on the
+ computationally-efficient expression for specific volume in terms of
+ SA, CT and p (Roquet et al., 2015).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+
+ Returns
+ -------
+ thermobaric : array-like, 1/(K Pa)
+ thermobaric coefficient with
+ respect to Conservative Temperature.
+
+
+ """
+ return _gsw_ufuncs.thermobaric(SA, CT, p)
+
+ at match_args_return
+def z_from_p(p, lat):
+ """
+ Calculates height from sea pressure using the computationally-efficient
+ 75-term expression for specific volume in terms of SA, CT and p
+ (Roquet et al., 2015). Dynamic height anomaly, geo_strf_dyn_height, if
+ provided, must be computed with its p_ref = 0 (the surface). Also if
+ provided, sea_surface_geopotental is the geopotential at zero sea
+ pressure. This function solves Eqn.(3.32.3) of IOC et al. (2010).
+
+ Parameters
+ ----------
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lat : array-like
+ Latitude, -90 to 90 degrees
+
+ Returns
+ -------
+ z : array-like, m
+ height
+
+
+ """
+ return _gsw_ufuncs.z_from_p(p, lat)
diff --git a/gsw/conversions.py b/gsw/conversions.py
new file mode 100644
index 0000000..99be562
--- /dev/null
+++ b/gsw/conversions.py
@@ -0,0 +1,89 @@
+"""
+Conversions involving temperature, salinity, entropy, pressure,
+and height.
+
+Those most commonly used probably include:
+
+- :func:`gsw.CT_from_t`
+- :func:`gsw.SA_from_SP`
+- :func:`gsw.SP_from_C`
+- :func:`gsw.p_from_z`
+- :func:`gsw.z_from_p`
+
+"""
+
+__all__ = ['t90_from_t68',
+ 'adiabatic_lapse_rate_from_CT',
+ 'C_from_SP',
+ 'CT_from_enthalpy',
+ 'CT_from_entropy',
+ 'CT_from_pt',
+ 'CT_from_rho',
+ 'CT_from_t',
+ 'deltaSA_from_SP',
+ 'entropy_from_pt',
+ 'entropy_from_t',
+ 'pt0_from_t',
+ 'pt_from_CT',
+ 'pt_from_entropy',
+ 'pt_from_t',
+ 'SA_from_rho',
+ 'SA_from_SP',
+ 'SA_from_Sstar',
+ 'SP_from_C',
+ 'SP_from_SA',
+ 'SP_from_SK',
+ 'SP_from_SR',
+ 'SP_from_Sstar',
+ 'SR_from_SP',
+ 'Sstar_from_SA',
+ 'Sstar_from_SP',
+ 't_from_CT',
+ 'p_from_z',
+ 'z_from_p',
+ ]
+
+from ._utilities import match_args_return
+
+from ._wrapped_ufuncs import (
+adiabatic_lapse_rate_from_CT,
+C_from_SP,
+CT_from_enthalpy,
+CT_from_entropy,
+CT_from_pt,
+CT_from_rho,
+CT_from_t,
+deltaSA_from_SP,
+entropy_from_pt,
+entropy_from_t,
+pt0_from_t,
+pt_from_CT,
+pt_from_entropy,
+pt_from_t,
+SA_from_rho,
+SA_from_SP,
+SA_from_Sstar,
+SP_from_C,
+SP_from_SA,
+SP_from_SK,
+SP_from_SR,
+SP_from_Sstar,
+SR_from_SP,
+Sstar_from_SA,
+Sstar_from_SP,
+t_from_CT,
+p_from_z,
+z_from_p,
+)
+
+
+ at match_args_return
+def t90_from_t68(t68):
+ """
+ ITS-90 temperature from IPTS-68 temperature
+
+ This conversion should be applied to all in-situ
+ data collected between 1/1/1968 and 31/12/1989.
+
+ """
+ return t68 / 1.00024
diff --git a/gsw/density.py b/gsw/density.py
new file mode 100644
index 0000000..35458d1
--- /dev/null
+++ b/gsw/density.py
@@ -0,0 +1,27 @@
+"""
+Functions related to density and specific volume.
+
+These are a subset of the TEOS-10 table category
+"specific volume, density, and enthalpy".
+
+We are grouping the functions related to enthalpy and internal energy
+in their own "energy" module.
+"""
+from ._wrapped_ufuncs import (
+specvol,
+alpha,
+beta,
+alpha_on_beta,
+specvol_alpha_beta,
+specvol_anom_standard,
+rho,
+rho_alpha_beta,
+rho_t_exact,
+sigma0,
+sigma1,
+sigma2,
+sigma3,
+sigma4,
+sound_speed,
+kappa,
+)
diff --git a/gsw/energy.py b/gsw/energy.py
new file mode 100644
index 0000000..bdae24e
--- /dev/null
+++ b/gsw/energy.py
@@ -0,0 +1,10 @@
+"""
+Functions involving internal energy, enthalpy, latent heat.
+"""
+from ._wrapped_ufuncs import (
+enthalpy,
+enthalpy_diff,
+internal_energy,
+latentheat_evap_CT,
+latentheat_evap_t,
+)
diff --git a/gsw/freezing.py b/gsw/freezing.py
new file mode 100644
index 0000000..27220cb
--- /dev/null
+++ b/gsw/freezing.py
@@ -0,0 +1,22 @@
+"""
+Freezing-point functions.
+"""
+
+from ._wrapped_ufuncs import (
+CT_freezing,
+CT_freezing_first_derivatives,
+CT_freezing_first_derivatives_poly,
+CT_freezing_poly,
+pot_enthalpy_ice_freezing,
+pot_enthalpy_ice_freezing_first_derivatives,
+pot_enthalpy_ice_freezing_first_derivatives_poly,
+pot_enthalpy_ice_freezing_poly,
+pressure_freezing_CT,
+SA_freezing_from_CT,
+SA_freezing_from_CT_poly,
+SA_freezing_from_t,
+SA_freezing_from_t_poly,
+t_freezing,
+t_freezing_first_derivatives,
+t_freezing_first_derivatives_poly,
+)
diff --git a/gsw/geostrophy.py b/gsw/geostrophy.py
new file mode 100644
index 0000000..47d882d
--- /dev/null
+++ b/gsw/geostrophy.py
@@ -0,0 +1,269 @@
+"""
+Functions for calculating geostrophic currents.
+"""
+
+import numpy as np
+
+from . import _gsw_ufuncs
+from ._utilities import match_args_return, indexer
+from .conversions import z_from_p
+
+__all__ = ['geo_strf_dyn_height',
+ 'distance',
+ 'f',
+ 'geostrophic_velocity',
+ ]
+
+ at match_args_return
+def geo_strf_dyn_height(SA, CT, p, p_ref=0, axis=0):
+ """
+ Dynamic height anomaly as a function of pressure.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ p_ref : float or array-like, optional
+ Reference pressure, dbar
+ axis : int, optional
+ The index of the pressure dimension in SA and CT.
+
+ Returns
+ -------
+ dynamic_height : array
+ This is the integral of specific volume anomaly with respect
+ to pressure, from each pressure in p to the specified
+ reference pressure. It is the geostrophic streamfunction
+ in an isobaric surface, relative to the reference surface.
+
+ """
+ if SA.shape != CT.shape:
+ raise ValueError('Shapes of SA and CT must match; found %s and %s'
+ % (SA.shape, CT.shape))
+ if p.ndim == 1 and SA.ndim > 1:
+ if len(p) != SA.shape[axis]:
+ raise ValueError('With 1-D p, len(p) must be SA.shape[axis];\n'
+ ' found %d versus %d on specified axis, %d'
+ % (len(p), SA.shape[axis], axis))
+ ind = [np.newaxis] * SA.ndim
+ ind[axis] = slice(None)
+ p = p[tuple(ind)]
+ p_ref = float(p_ref)
+ with np.errstate(invalid='ignore'):
+ # The need for this context seems to be a bug in np.ma.any.
+ if np.ma.any(np.ma.diff(np.ma.masked_invalid(p), axis=axis) <= 0):
+ raise ValueError('p must be increasing along the specified axis')
+ p = np.broadcast_to(p, SA.shape)
+ goodmask = ~(np.isnan(SA) | np.isnan(CT) | np.isnan(p))
+ dh = np.empty(SA.shape, dtype=float)
+ dh.fill(np.nan)
+
+ order = 'F' if SA.flags.fortran else 'C'
+ for ind in indexer(SA.shape, axis, order=order):
+ igood = goodmask[ind]
+ # If p_ref is below the deepest value, skip the profile.
+ pgood = p[ind][igood]
+ # The C function calls the rr68 interpolation, which
+ # requires at least 4 "bottles"; but the C function is
+ # not checking this, so we need to do so.
+ if pgood[-1] >= p_ref and len(pgood) > 3:
+ dh[ind][igood] = _gsw_ufuncs.geo_strf_dyn_height(
+ SA[ind][igood],
+ CT[ind][igood],
+ pgood, p_ref)
+ return dh
+
+
+def unwrap(lon, centered=True, copy=True):
+ """
+ Unwrap a sequence of longitudes or headings in degrees.
+
+ Optionally center it as close to zero as possible
+
+ By default, return a copy; if *copy* is False, avoid a
+ copy when possible.
+
+ Returns a masked array only if the input is a masked array.
+ """
+ # From pycurrents.data.ocean. It could probably be simplified
+ # for use here.
+
+ masked_input = np.ma.isMaskedArray(lon)
+ if masked_input:
+ fill_value = lon.fill_value
+ # masked_invalid loses the original fill_value (ma bug, 2011/01/20)
+ lon = np.ma.masked_invalid(lon).astype(float)
+ if lon.ndim != 1:
+ raise ValueError("Only 1-D sequences are supported")
+ if lon.shape[0] < 2:
+ return lon
+ x = lon.compressed()
+ if len(x) < 2:
+ return lon
+ w = np.zeros(x.shape[0]-1, int)
+ ld = np.diff(x)
+ np.putmask(w, ld > 180, -1)
+ np.putmask(w, ld < -180, 1)
+ x[1:] += (w.cumsum() * 360.0)
+
+ if centered:
+ x -= 360 * np.round(x.mean() / 360.0)
+
+ if lon.mask is np.ma.nomask:
+ lon[:] = x
+ else:
+ lon[~lon.mask] = x
+ if masked_input:
+ lon.fill_value = fill_value
+ return lon
+ else:
+ return lon.filled(np.nan)
+
+
+ at match_args_return
+def distance(lon, lat, p=0, axis=-1):
+ """
+ Great-circle distance in m between lon, lat points.
+
+ Parameters
+ ----------
+ lon, lat : array-like, 1-D or 2-D (shapes must match)
+ Longitude, latitude, in degrees.
+ p : array-like, scalar, 1-D or 2-D, optional, default is 0
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ axis : int, -1, 0, 1, optional
+ The axis or dimension along which *lat and lon* vary.
+ This differs from most functions, for which axis is the
+ dimension along which p increases.
+
+ Returns
+ -------
+ distance : 1-D or 2-D array
+ distance in meters between adjacent points.
+
+ """
+ earth_radius = 6371e3
+
+ if not lon.shape == lat.shape:
+ raise ValueError('lon, lat shapes must match; found %s, %s'
+ % (lon.shape, lat.shape))
+ if not (lon.ndim in (1, 2) and lon.shape[axis] > 1):
+ raise ValueError('lon, lat must be 1-D or 2-D with more than one point'
+ ' along axis; found shape %s and axis %s'
+ % (lon.shape, axis))
+
+ if np.all(p == 0):
+ z = 0
+ else:
+ lon, lat, p = np.broadcast_arrays(lon, lat, p)
+ if axis == 0:
+ indm = (slice(0, -1), slice(None))
+ indp = (slice(1, None), slice(None))
+ else:
+ indm = (slice(None), slice(0, -1))
+ indp = (slice(None), slice(1, None))
+
+ p_mid = 0.5 * (p[indm] + p[indp])
+ lat_mid = 0.5 * (lat[indm] + lat[indp])
+
+ z = z_from_p(p_mid, lat_mid)
+
+ lon = np.radians(lon)
+ lat = np.radians(lat)
+
+ dlon = np.diff(lon, axis=axis)
+ dlat = np.diff(lat, axis=axis)
+
+ a = ((np.sin(dlat / 2)) ** 2 + np.cos(lat[:, :-1]) *
+ np.cos(lat[:, 1:]) * (np.sin(dlon / 2)) ** 2)
+
+ angles = 2 * np.arctan2(np.sqrt(a), np.sqrt(1 - a))
+
+ distance = (earth_radius + z) * angles
+
+ return distance
+
+
+ at match_args_return
+def f(lat):
+ """
+ Coriolis parameter in 1/s for latitude in degrees.
+ """
+ omega = 7.292115e-5 # (1/s) (Groten, 2004).
+ f = 2 * omega * np.sin(np.radians(lat))
+ return f
+
+ at match_args_return
+def geostrophic_velocity(geo_strf, lon, lat, p=0, axis=0):
+ """
+ Calculate geostrophic velocity from a streamfunction.
+
+ Calculates geostrophic velocity relative to the sea surface, given a
+ geostrophic streamfunction and the position of each station in
+ sequence along an ocean section. The data can be from a single
+ isobaric or "density" surface, or from a series of such surfaces.
+
+ Parameters
+ ----------
+ geo_strf : array-like, 1-D or 2-D
+ geostrophic streamfunction; see Notes below.
+ lon : array-like, 1-D
+ Longitude, -360 to 360 degrees
+ lat : array-like, 1-D
+ Latitude, degrees
+ p : float or array-like, optional
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar.
+ This used only for a tiny correction in the distance calculation;
+ it is safe to omit it.
+ axis : int, 0 or 1, optional
+ The axis or dimension along which pressure increases in geo_strf.
+ If geo_strf is 1-D, it is ignored.
+
+ Returns
+ -------
+ velocity : array, 2-D or 1-D
+ Geostrophic velocity in m/s relative to the sea surface,
+ averaged between each successive pair of positions.
+ mid_lon, mid_lat : array, 1-D
+ Midpoints of input lon and lat.
+
+ Notes
+ -----
+ The geostrophic streamfunction can be:
+
+ - geo_strf_dyn_height (in an isobaric surface)
+ - geo_strf_Montgomery (in a specific volume anomaly surface)
+ - geo_strf_Cunninhgam (in an approximately neutral surface
+ such as a potential density surface).
+ - geo_strf_isopycnal (in an approximately neutral surface
+ such as a potential density surface, a Neutral Density
+ surface, or an omega surface (Klocker et al., 2009)).
+
+ Only :func:`geo_strf_dyn_height` is presently implemented
+ in GSW-Python.
+
+ """
+ lon = unwrap(lon)
+
+ if lon.shape != lat.shape or lon.ndim != 1:
+ raise ValueError('lon, lat must be 1-D and matching; found shapes'
+ ' %s and %s' % (lon.shape, lat.shape))
+
+ if geo_strf.ndim not in (1, 2):
+ raise ValueError('geo_strf must be 1-D or 2-d; found shape %s'
+ % (geo_strf.shape,))
+
+ laxis = 0 if axis else -1
+
+ ds = distance(lon, lat, p)
+
+ mid_lon = 0.5 * (lon[:-1] + lon[1:])
+ mid_lat = 0.5 * (lat[:-1] + lat[1:])
+
+ u = np.diff(geo_strf, axis=laxis) / (ds * f(mid_lat))
+
+ return u, mid_lat, mid_lon
diff --git a/gsw/gibbs/__init__.py b/gsw/gibbs/__init__.py
deleted file mode 100644
index 04144b7..0000000
--- a/gsw/gibbs/__init__.py
+++ /dev/null
@@ -1,20 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from .earth import *
-from .steric import *
-from .library import *
-from .freezing import *
-from .isobaric import *
-from .constants import *
-from .derivatives import *
-from .conversions import *
-from .geostrophic import *
-from .geostrophic_48 import *
-from .water_column_48 import *
-from .practical_salinity import *
-from .density_enthalpy_48 import *
-from .density_enthalpy_75 import *
-from .neutral_nonlinear_48 import *
-from .thermodynamics_from_t import *
-from .density_enthalpy_48_ct import *
-from .density_enthalpy_ct_exact import *
diff --git a/gsw/gibbs/constants.py b/gsw/gibbs/constants.py
deleted file mode 100644
index d5f2f19..0000000
--- a/gsw/gibbs/constants.py
+++ /dev/null
@@ -1,171 +0,0 @@
-# -*- coding: utf-8 -*-
-
-"""Constants"""
-
-from __future__ import division
-
-C3515 = 42.9140
-"""
-Conductivity of 42.914 [mmho cm :sup:`-1` == mS cm :sup:`-1`] at Salinity
-35 psu, Temperature 15 :math:`^\\circ` C [ITPS 68] and Pressure 0 db.
-
-References
-----------
-.. [1] Culkin and Smith, 1980: Determination of the Concentration of Potassium
- Chloride Solution Having the Same Electrical Conductivity, at 15C and
- Infinite Frequency, as Standard Seawater of Salinity 35.0000 (Chlorinity
- 19.37394), IEEE J. Oceanic Eng, 5, 22-23.
-
-.. [2] Unesco, 1983: Algorithms for computation of fundamental properties of
- seawater. Unesco Technical Papers in Marine Science, 44, 53 pp.
-"""
-
-earth_radius = 6371000.
-"""Mean radius of earth A.E. Gill."""
-
-OMEGA = 7.292115e-5
-"""
-:math:`\\Omega = \\frac{2\\pi}{\\textrm{sidereal day}}` =
- 7.292e-5.radians sec :sup:`-1`
-
-1 sidereal day = 23.9344696 hours
-
-Changed to a more precise value at Groten 2004
-
-References
-----------
-.. [1] A.E. Gill 1982. p.54 eqn 3.7.15 "Atmosphere-Ocean Dynamics" Academic
- Press: New York. ISBN: 0-12-283522-0. page: 597
-.. [2] Groten, E., 2004: Fundamental Parameters and Current (2004) Best
- Estimates of the Parameters of Common Relevance to Astronomy, Geodesy, and
- Geodynamics. Journal of Geodesy, 77, pp. 724-797.
-"""
-
-T0 = Kelvin = 273.15
-"""
-The Celsius zero point; 273.15 K. That is T = t + T0 where T is the
-Absolute Temperature (in degrees K) and t is temperature in degrees C.
-"""
-
-db2Pascal = 1e4
-"""
-Decibar to pascal.
-"""
-
-gamma = 2.26e-7
-"""
-Gamma (A.E. Gill).
-"""
-
-M_S = 0.0314038218
-"""
-Mole-weighted average atomic weight of the elements of
-Reference-Composition sea salt, in units of kg mol :sup:`-1`. Strictly
-speaking, the formula below applies only to seawater of Reference Composition.
-If molality is required to an accuracy of better than 0.1% we suggest you
-contact the authors for further guidance.
-"""
-
-cp0 = 3991.86795711963
-"""
-The "specific heat" for use with Conservative Temperature. cp0 is the ratio
-of potential enthalpy to Conservative Temperature.
-See Eqn. (3.3.3) and Table D.5 from IOC et al. (2010).
-"""
-
-SSO = 35.16504
-"""
-SSO is the Standard Ocean Reference Salinity (35.16504 g/kg.)
-
-SSO is the best estimate of the Absolute Salinity of Standard Seawater
-when the seawater sample has a Practical Salinity, SP, of 35
-(Millero et al., 2008), and this number is a fundamental part of the
-TEOS-10 definition of seawater.
-
-References:
------------
-.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
- seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendices A.3, A.5 and Table D.4.
-
-.. [2] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
- The composition of Standard Seawater and the definition of the
- Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.
- See Table 4 and section 5.
-"""
-
-sfac = 0.0248826675584615
-"""
-sfac = 1 / (40 * uPS) = 1 / (40. * (SSO / 35.))
-"""
-
-soffset = 5.971840214030754e-1
-"""
-soffset = deltaS * sfac.
-"""
-
-R = 8.314472
-"""
-The molar gas constant = 8.314472 m :sup:`2` kg s:sup:`-21 K :sup:`-1`
-mol :sup:`-1`.
-"""
-
-r1 = 0.35
-""" TODO """
-
-uPS = SSO / 35.0
-"""
-The unit conversion factor for salinities (35.16504/35) g/kg (Millero et
-al., 2008). Reference Salinity SR is uPS times Practical Salinity SP.
-
-Ratio, unit conversion factor for salinities [g kg :sup:`-1`]
-
-References
-----------
-.. [1] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008: The
- composition of Standard Seawater and the definition of the
- Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72. See
- section 6, Eqn.(6.1).
-"""
-
-
-P0 = 101325
-"""Absolute Pressure of one standard atmosphere in Pa, 101325 Pa."""
-
-SonCl = 1.80655
-"""
-The ratio of Practical Salinity, SP, to Chlorinity, 1.80655 kg/g for
-Reference Seawater (Millero et al., 2008). This is the ratio that was used by
-the JPOTS committee in their construction of the 1978 Practical Salinity Scale
-(PSS-78) to convert between the laboratory measurements of seawater samples
-(which were measured in Chlorinity) to Practical Salinity.
-
-References:
------------
-.. [1] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
- The composition of Standard Seawater and the definition of the
- Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72. See
- section 5 below Eqn. (5.5).
-"""
-
-valence_factor = 1.2452898
-"""
-This function returns the valence factor of sea salt of Reference
-Composition, 1.2452898. This valence factor is exact, and follows from
-the definition of the Reference-Composition Salinity Scale 2008 of
-Millero et al. (2008). The valence factor is the mole-weighted square
-of the charges, Z, of the ions comprising Reference Composition sea salt.
-
-References:
------------
-.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
- seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Table D.4 of this TEOS-10 Manual.
-
-.. [2] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
- The composition of Standard Seawater and the definition of the
- Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.
- See Eqn. (5.9).
-"""
diff --git a/gsw/gibbs/conversions.py b/gsw/gibbs/conversions.py
deleted file mode 100644
index 42edb23..0000000
--- a/gsw/gibbs/conversions.py
+++ /dev/null
@@ -1,1545 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from ..utilities import match_args_return, strip_mask
-from .constants import SSO, cp0, r1, Kelvin, sfac, uPS
-from .constants import db2Pascal, gamma, P0, M_S, valence_factor
-from .library import (entropy_part, entropy_part_zerop, gibbs, gibbs_pt0_pt0,
- enthalpy_SSO_0_p, specvol_SSO_0_p)
-
-from .library import SA_from_SP_Baltic, SP_from_SA_Baltic, SAAR
-
-# This first set is moved over from absolute_salinity_sstar_ct,
-# which is being absorbed into this module.
-__all__ = ['CT_from_t',
- 'SA_from_SP',
- 'Sstar_from_SP',
- 'Abs_Pressure_from_p',
- 'CT_from_entropy',
- 'CT_from_pt',
- 'SA_Sstar_from_SP',
- 'SA_from_Sstar',
- 'SP_from_SA',
- 'SP_from_SR',
- #'SP_from_Sstar', # TODO
- 'SR_from_SP',
- 'Sstar_from_SA',
- 'deltaSA_from_SP', # TODO
- 'depth_from_z',
- 'entropy_from_CT',
- 'entropy_from_pt',
- 'entropy_from_t',
- 'ionic_strength_from_SA',
- 'molality_from_SA',
- 'p_from_Abs_Pressure',
- 'p_from_z',
- 'pot_enthalpy_from_pt',
- 'pt0_from_t',
- 'pt_from_CT',
- 'pt_from_entropy',
- 'pt_from_t',
- 't90_from_t48',
- 't90_from_t68',
- 't_from_CT',
- 't_from_entropy',
- 'z_from_depth',
- 'z_from_p'] # TODO: Test with geo_strf_dyn_height != None
-
-DEG2RAD = np.pi / 180.0
-n0, n1, n2 = 0, 1, 2 # constants used as arguments to gibbs()
-
-
-def check_input(SP, p, lon, lat):
- """
- Check for out of range values.
- """
-
- # Helper for the "from_SP" functions.
- lon, lat, p, SP = np.broadcast_arrays(lon, lat, p, SP, subok=True)
-
- cond1 = ((p < 100) & (SP > 120))
- cond2 = ((p >= 100) & (SP > 42))
- if cond1.any() or cond2.any(): # don't modify input array
- mask = np.ma.filled(cond1, False) | np.ma.filled(cond2, False)
- SP = np.ma.array(SP, mask=mask)
-
- lon = lon % 360
-
- # FIXME: If we do keep the checks below, they need to
- # be reformulated with ValueError('pressure out of range') etc.
- # The original also checks for 9999s--a fossil from old-time
- # Fortran days.
-
- # I don't think we need these here; if any such checking is
- # needed, it should not just be for the "from_SP" functions.
- if False:
- if ((p < -1.5) | (p > 12000)).any():
- raise Exception('Sstar_from_SP: pressure is out of range')
- if ((lon < 0) | (lon > 360)).any():
- raise Exception('Sstar_from_SP: longitude is out of range')
- if (np.abs(lat) > 90).any():
- raise Exception('Sstar_from_SP: latitude is out of range')
-
- SP = np.maximum(SP, 0) # Works on masked array also.
-
- return SP, p, lon, lat
-
-
- at match_args_return
-def Abs_Pressure_from_p(p):
- """
- Calculates Absolute Pressure from sea pressure. Note that Absolute
- Pressure is in Pa NOT dbar.
-
- Parameters
- ---------
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- Absolute_Pressure : array_like
- Absolute Pressure [Pa]
-
-
- Examples
- --------
- >>> import gsw
- >>> gsw.Abs_Pressure_from_p([0, 500, 1000])
- array([ 101325., 5101325., 10101325.])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.2.1).
- """
-
- return p * db2Pascal + P0
-
-
- at match_args_return
-def CT_from_entropy(SA, entropy):
- """
- Calculates Conservative Temperature with entropy as an input variable.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- entropy : array_like
- specific entropy [J kg :sup:`-1` K :sup:`-1`]
-
- Returns
- -------
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> entropy = [400.3892, 395.4378, 319.8668, 146.7910, 98.6471, 62.7919]
- >>> gsw.CT_from_entropy(SA, entropy)
- array([ 28.80990279, 28.43919923, 22.78619927, 10.22619767,
- 6.82719674, 4.32360295])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix A.10.
- """
-
- SA = np.maximum(SA, 0)
- pt = pt_from_entropy(SA, entropy)
- return CT_from_pt(SA, pt)
-
-
- at match_args_return
-def CT_from_pt(SA, pt):
- """
- Calculates Conservative Temperature of seawater from potential
- temperature (whose reference sea pressure is zero dbar).
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- pt : array_like
- potential temperature referenced to a sea pressure of zero dbar
- [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> pt = [28.7832, 28.4209, 22.7850, 10.2305, 6.8292, 4.3245]
- >>> gsw.CT_from_pt(SA, pt)
- array([ 28.80992302, 28.43914426, 22.78624661, 10.22616561,
- 6.82718342, 4.32356518])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.3.
- """
-
- SA, pt, mask = strip_mask(SA, pt)
-
- pot_enthalpy = pot_enthalpy_from_pt(SA, pt)
-
- CT = pot_enthalpy / cp0
-
- return np.ma.array(CT, mask=mask, copy=False)
-
-
- at match_args_return
-def SA_Sstar_from_SP(SP, p, lon, lat):
- """
- TODO: docstring
- """
-
- # Note: with match_args_return, the variables inside
- # this function are masked arrays, so the outputs of
- # other functions called here are also masked arrays.
-
- SP, p, lon, lat = check_input(SP, p, lon, lat)
-
- saar, in_ocean = SAAR(p, lon, lat)
- SA = uPS * SP * (1 + saar)
- Sstar = uPS * SP * (1 - r1 * saar)
-
- SA_baltic = SA_from_SP_Baltic(SP, lon, lat)
- bmask = SA_baltic.mask
- if bmask is not np.ma.nomask and not bmask.all():
- inbaltic = ~bmask
- SA[inbaltic] = SA_baltic[inbaltic]
- Sstar[inbaltic] = SA_baltic[inbaltic]
-
- return SA, Sstar
-
-
- at match_args_return
-def SA_from_Sstar(Sstar, p, lon, lat):
- """
- TODO: docstring
- """
- # maybe add some input checking...
-
- saar, in_ocean = SAAR(p, lon, lat)
- SA = Sstar * (1 + saar) / (1.0 - r1 * saar)
-
- # In the Baltic Sea, SA = Sstar, and note that gsw_delta_SA returns zero
- # for dSA in the Baltic.
-
- return SA, in_ocean
-
-
- at match_args_return
-def SP_from_SA(SA, p, lon, lat):
- """
- TODO: docstring
- """
- # maybe add input checking...
-
- saar, in_ocean = SAAR(p, lon, lat)
- SP = (35 / 35.16504) * SA / (1.0 + saar)
-
- SP_baltic = SP_from_SA_Baltic(SA, lon, lat)
- bmask = SP_baltic.mask
- if bmask is not np.ma.nomask and not bmask.all():
- inbaltic = ~bmask
- SP[inbaltic] = SP_baltic[inbaltic]
-
- return SP, in_ocean
-
-
- at match_args_return
-def SP_from_SR(SR):
- """
- Calculates Practical Salinity from Reference Salinity.
-
- Parameters
- ---------
- SR : array_like
- Reference Salinity [g kg :sup:`-1`]
-
- Returns
- -------
- SP : array_like
- Practical Salinity (PSS-78) [unitless]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- return 1. / uPS * SR
-
-
-#def SP_from_Sstar():
-# pass
-
-
- at match_args_return
-def SR_from_SP(SP):
- """
- Calculates Reference Salinity from Practical Salinity.
-
- Parameters
- ---------
- SP : array_like
- Practical Salinity (PSS-78) [unitless]
-
- Returns
- -------
- SR : array_like
- Reference Salinity [g kg :sup:`-1`]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- return uPS * SP
-
-
- at match_args_return
-def Sstar_from_SA(SA, p, lon, lat):
- """
- TODO: docstring
- """
-
- saar, in_ocean = SAAR(p, lon, lat)
- Sstar = SA * (1 - r1 * saar) / (1 + saar)
- # dSA is zero in Baltic
- return Sstar, in_ocean
-
-
- at match_args_return
-def CT_from_t(SA, t, p):
- """
- Calculates Conservative Temperature of seawater from in situ
- temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- TODO
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.3.
- """
-
- # Find values that are out of range, set them to NaN.
- invalid = np.logical_and(p < 100, np.logical_or(t > 80, t < -12))
- t[invalid] = np.ma.masked
-
- invalid = np.logical_and(p >= 100, np.logical_or(t > 40, t < -12))
- t[invalid] = np.ma.masked
-
- pt0 = pt0_from_t(SA, t, p)
- CT = CT_from_pt(SA, pt0)
-
- return CT
-
-
- at match_args_return
-def SA_from_SP(SP, p, lon, lat):
- """Calculates Absolute Salinity from Practical Salinity.
-
- Parameters
- ----------
- SP : array_like
- salinity (PSS-78) [unitless]
- p : array_like
- pressure [dbar]
- lon : array_like
- decimal degrees east [0..+360] or [-180..+180]
- lat : array_like
- decimal degrees (+ve N, -ve S) [-90..+90]
-
- Returns
- -------
- SA : masked array
- Absolute salinity [g kg :sup:`-1`]
-
- Notes
- -----
- The mask is only set when the observation is well and truly on dry
- land; often the warning flag is not set until one is several hundred
- kilometers inland from the coast.
-
- Since SP is non-negative by definition, this function changes any negative
- input values of SP to be zero.
-
- Examples
- --------
- >>> import gsw
- >>> SP = [34.5487, 34.7275, 34.8605, 34.6810, 34.5680, 34.5600]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> lon = 188
- >>> lat = 4
- >>> gsw.SA_from_SP(SP, p, lon, lat)
- array([ 34.71177834, 34.89152262, 35.02554486, 34.84722903,
- 34.73662847, 34.73236307])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.5 and appendices A.4 and A.5.
-
- .. [2] McDougall, T.J., D.R. Jackett and F.J. Millero, 2010: An algorithm
- for estimating Absolute Salinity in the global ocean. Submitted to Ocean
- Science. A preliminary version is available at Ocean Sci. Discuss.,
- 6, 215-242.
- http://www.ocean-sci-discuss.net/6/215/2009/osd-6-215-2009-print.pdf
- """
-
- SP, p, lon, lat = check_input(SP, p, lon, lat)
-
- SA = (SSO / 35) * SP * (1 + SAAR(p, lon, lat)[0])
- SA_baltic = SA_from_SP_Baltic(SP, lon, lat)
-
- # The following function (SAAR) finds SAAR in the non-Baltic parts of
- # the world ocean. (Actually, this SAAR look-up table returns values
- # of zero in the Baltic Sea since SAAR in the Baltic is a function of SP,
- # not space.
- if SA_baltic is not None:
- SA[~SA_baltic.mask] = SA_baltic[~SA_baltic.mask]
-
- return SA
-
-
- at match_args_return
-def Sstar_from_SP(SP, p, lon, lat):
- """
- Calculates Preformed Salinity from Absolute Salinity.
-
- Parameters
- ----------
- SP : array_like
- salinity (PSS-78) [unitless]
- p : array_like
- pressure [dbar]
- lon : array_like
- decimal degrees east [0..+360] or [-180..+180]
- lat : array_like
- decimal degrees (+ve N, -ve S) [-90..+90]
-
- Returns
- -------
- Sstar : masked array
- Preformed Salinity [g kg :sup:`-1`]
-
- Notes
- -----
- The mask is only set when the observation is well and truly on dry
- land; often the warning flag is not set until one is several hundred
- kilometers inland from the coast.
-
- Since SP is non-negative by definition, this function changes any negative
- input values of SP to be zero.
-
- Examples
- --------
- >>> import gsw
- >>> SP = [34.5487, 34.7275, 34.8605, 34.6810, 34.5680, 34.5600]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> lon = 188
- >>> lat = 4
- >>> gsw.Sstar_from_SP(SP, p, lon, lat)
- array([ 34.71155368, 34.8911614 , 35.02465027, 34.84359314,
- 34.729034 , 34.71967596])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.5 and appendices A.4 and A.5.
-
- .. [2] McDougall, T.J., D.R. Jackett and F.J. Millero, 2010: An algorithm
- for estimating Absolute Salinity in the global ocean. Submitted to Ocean
- Science. A preliminary version is available at Ocean Sci. Discuss.,
- 6, 215-242.
- """
-
- SP, p, lon, lat = check_input(SP, p, lon, lat)
-
- Sstar = (SSO / 35.0) * SP * (1.0 - r1 * SAAR(p, lon, lat)[0])
-
- # In the Baltic Sea, Sstar==SA.
- Sstar_baltic = SA_from_SP_Baltic(SP, lon, lat)
-
- # TODO: Create Baltic and non-Baltic test cases.
- if Sstar_baltic is not None:
- Sstar[~Sstar_baltic.mask] = Sstar_baltic[~Sstar_baltic.mask]
-
- return Sstar
-
-
- at match_args_return
-def deltaSA_from_SP(SP, p, lon, lat):
- """
- gsw_deltaSA_from_SP Absolute Salinity Anomaly
- from Practical Salinity
- ==========================================================================
-
- USAGE:
- deltaSA = gsw_deltaSA_from_SP(SP,p,long,lat)
-
- DESCRIPTION:
- Calculates Absolute Salinity Anomaly from Practical Salinity. Since SP
- is non-negative by definition, this function changes any negative input
- values of SP to be zero.
-
- INPUT:
- SP = Practical Salinity (PSS-78) [ unitless ]
- p = sea pressure [ dbar ]
- ( i.e. absolute pressure - 10.1325 dbar )
- long = longitude in decimal degrees [ 0 ... +360 ]
- or [ -180 ... +180 ]
- lat = latitude in decimal degrees north [ -90 ... +90 ]
-
- p, lat & long may have dimensions 1x1 or Mx1 or 1xN or MxN,
- where SP is MxN.
-
- OUTPUT:
- deltaSA = Absolute Salinity Anomaly [ g/kg ]
-
- AUTHOR:
- Trevor McDougall & Paul Barker [ help at teos-10.org ]
-
- VERSION NUMBER: 3.03 (29th April, 2013)
-
- REFERENCES:
- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
- seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Available from http://www.TEOS-10.org
- See section 2.5 and appendices A.4 and A.5 of this TEOS-10 Manual.
-
- McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and
- P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity.
- Ocean Science, 8, 1117-1128.
- http://www.ocean-sci.net/8/1117/2012/os-8-1117-2012.pdf
-
- """
- return SA_from_SP(SP, p, lon, lat) - SR_from_SP(SP)
-
-
-def depth_from_z(z):
- """
- Calculates depth from height, z. Note that in general height is
- negative in the ocean.
-
- Parameters
- ---------
- z : array_like
- height [m]
-
- Returns
- -------
- depth : array_like
- depth [m]
- """
-
- return -z
-
-
- at match_args_return
-def entropy_from_CT(SA, CT):
- """
- Calculates specific entropy of seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- entropy : array_like
- specific entropy [J kg :sup:`-1` K :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> CT = [28.8099, 28.4392, 22.7862, 10.2262, 6.8272, 4.3236]
- >>> gsw.entropy_from_CT(SA, CT)
- array([ 400.38916315, 395.43781023, 319.86680989, 146.79103279,
- 98.64714648, 62.79185763])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix A.10.
- """
-
- SA = np.maximum(SA, 0)
- pt0 = pt_from_CT(SA, CT)
- return -gibbs(n0, n1, n0, SA, pt0, 0)
-
-
- at match_args_return
-def entropy_from_pt(SA, pt):
- """
- Calculates specific entropy of seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- pt : array_like
- potential temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- entropy : array_like
- specific entropy [J kg :sup:`-1` K :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> pt = [28.7832, 28.4210, 22.7850, 10.2305, 6.8292, 4.3245]
- >>> gsw.entropy_from_pt(SA, pt)
- array([ 400.38946744, 395.43839949, 319.86743859, 146.79054828,
- 98.64691006, 62.79135672])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix A.10.
- """
-
- SA = np.maximum(SA, 0)
- return -gibbs(n0, n1, n0, SA, pt, 0)
-
-
- at match_args_return
-def entropy_from_t(SA, t, p):
- """
- gsw_entropy_from_t specific entropy of seawater
- ==========================================================================
-
- USAGE:
- entropy = gsw_entropy_from_t(SA,t,p)
-
- DESCRIPTION:
- Calculates specific entropy of seawater.
-
- INPUT:
- SA = Absolute Salinity [ g/kg ]
- t = in-situ temperature (ITS-90) [ deg C ]
- p = sea pressure [ dbar ]
- ( i.e. absolute pressure - 10.1325 dbar )
-
- SA & t need to have the same dimensions.
- p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & t are MxN.
-
- OUTPUT:
- entropy = specific entropy [ J/(kg*K) ]
-
- AUTHOR:
- David Jackett, Trevor McDougall and Paul Barker [ help at teos-10.org ]
-
- VERSION NUMBER: 3.03 (29th April, 2013)
-
- REFERENCES:
- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
- seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Available from http://www.TEOS-10.org
- """
-
- return -gibbs(n0, n1, n0, SA, t, p)
-
-
- at match_args_return
-def ionic_strength_from_SA(SA):
- """
- Calculates the ionic strength of seawater from Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
-
- Returns
- -------
- ionic_strength : array_like
- ionic strength of seawater [mol kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> gsw.ionic_strength_from_SA(SA)
- array([ 0.71298118, 0.71680567, 0.71966059, 0.71586272, 0.71350891,
- 0.71341953])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Table L.1.
-
- .. [2] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
- The composition of Standard Seawater and the definition of the
- Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.
- See Eqns. 5.9 and 5.12.
- """
-
- # Molality of seawater in mol kg :sup:`-1`
- molality = molality_from_SA(SA)
-
- return 0.5 * valence_factor * molality
-
-
- at match_args_return
-def molality_from_SA(SA):
- """
- Calculates the molality of seawater from Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
-
- Returns
- -------
- molality : array_like
- seawater molality [mol kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> gsw.molality_from_SA(SA)
- array([ 1.14508476, 1.15122708, 1.15581223, 1.14971265, 1.14593231,
- 1.14578877])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- # Molality of seawater in mol kg :sup:`-1`.
- SA = np.maximum(SA, 0)
- molality = SA / (M_S * (1000 - SA))
-
- return molality
-
-
- at match_args_return
-def p_from_Abs_Pressure(Absolute_Pressure):
- """
- Calculates sea pressure from Absolute Pressure. Note that Absolute
- Pressure is in Pa NOT dbar.
-
- Parameters
- ---------
- Absolute_Pressure : array_like
- Absolute Pressure [Pa]
-
- Returns
- -------
- p : array_like
- sea pressure [dbar]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.2.1).
- """
-
- return (Absolute_Pressure - P0) * 1. / db2Pascal
-
-
- at match_args_return
-def p_from_z(z, lat, geo_strf_dyn_height=0):
- """
- Calculates sea pressure from height using computationally-efficient
- 48-term expression for density, in terms of SA, CT and p (McDougall et al.,
- 2011). Dynamic height anomaly, geo_strf_dyn_height, if provided, must be
- computed with its pr=0 (the surface.)
-
- Parameters
- ----------
- z : array_like
- height [m]
- lat : array_like
- latitude in decimal degrees north [-90..+90]
- geo_strf_dyn_height : float, optional
- dynamic height anomaly [ m :sup:`2` s :sup:`-2` ]
- The reference pressure (p_ref) of geo_strf_dyn_height
- must be zero (0) dbar.
-
- Returns
- -------
- p : array_like
- pressure [dbar]
-
- Examples
- --------
- >>> import gsw
- >>> z = [-10., -50., -125., -250., -600., -1000.]
- >>> lat = 4.
- >>> gsw.p_from_z(z, lat)
- array([ 10.05572704, 50.28354425, 125.73185732, 251.54028663,
- 604.2099135 , 1007.9900587 ])
- >>> -gsw.z_from_p(gsw.p_from_z(z, lat), lat)
- array([ 10., 50., 125., 250., 600., 1000.])
-
- Notes
- -----
- Height (z) is NEGATIVE in the ocean. Depth is -z. Depth is not used in the
- gibbs library.
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of seawater
- in terms of Conservative Temperature, and related properties of seawater.
-
- .. [3] Moritz (2000) Goedetic reference system 1980. J. Geodesy, 74,
- 128-133.
-
- .. [4] Saunders, P. M., 1981: Practical conversion of pressure to depth.
- Journal of Physical Oceanography, 11, 573-574.
- """
-
- X = np.sin(lat * DEG2RAD)
- sin2 = X ** 2
- gs = 9.780327 * (1.0 + (5.2792e-3 + (2.32e-5 * sin2)) * sin2)
-
- # get the first estimate of p from Saunders (1981)
- c1 = 5.25e-3 * sin2 + 5.92e-3
- p = -2 * z / ((1 - c1) + np.sqrt((1 - c1) * (1 - c1) + 8.84e-6 * z))
-
- df_dp = db2Pascal * specvol_SSO_0_p(p) # Initial value for f derivative.
-
- f = (enthalpy_SSO_0_p(p) + gs *
- (z - 0.5 * gamma * (z ** 2)) - geo_strf_dyn_height)
-
- p_old = p
- p = p_old - f / df_dp
- p_mid = 0.5 * (p + p_old)
- df_dp = db2Pascal * specvol_SSO_0_p(p_mid)
- p = p_old - f / df_dp
-
- # After this one iteration through this modified Newton-Raphson iterative
- # procedure, the remaining error in p is at computer machine precision,
- # being no more than 1.6e-10 dbar.
-
- return p
-
-
- at match_args_return
-def pot_enthalpy_from_pt(SA, pt):
- """
- Calculates the potential enthalpy of seawater from potential
- temperature (whose reference sea pressure is zero dbar).
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- pt : array_like
- potential temperature referenced to a sea pressure of zero dbar
- [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- pot_enthalpy : array_like
- potential enthalpy [J kg :sup:`-1`]
-
- Notes
- -----
- TODO
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> pt = [28.7832, 28.4209, 22.7850, 10.2305, 6.8292, 4.3245]
- >>> gsw.pot_enthalpy_from_pt(SA, pt)
- array([ 115005.40853458, 113525.30870246, 90959.68769935,
- 40821.50280454, 27253.21472227, 17259.10131183])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.2.
- """
-
- SA, pt, mask = strip_mask(SA, pt)
-
- SA = np.maximum(SA, 0)
-
- x2 = sfac * SA
- x = np.sqrt(x2)
- y = pt * 0.025 # Normalize for F03 and F08
-
- pot_enthalpy = (61.01362420681071 + y * (168776.46138048015 +
- y * (-2735.2785605119625 + y * (2574.2164453821433 +
- y * (-1536.6644434977543 + y * (545.7340497931629 +
- (-50.91091728474331 - 18.30489878927802 * y) * y))))) +
- x2 * (268.5520265845071 + y * (-12019.028203559312 +
- y * (3734.858026725145 + y * (-2046.7671145057618 +
- y * (465.28655623826234 + (-0.6370820302376359 -
- 10.650848542359153 * y) * y)))) +
- x * (937.2099110620707 + y * (588.1802812170108 +
- y * (248.39476522971285 + (-3.871557904936333 -
- 2.6268019854268356 * y) * y)) +
- x * (-1687.914374187449 + x * (246.9598888781377 +
- x * (123.59576582457964 - 48.5891069025409 * x)) +
- y * (936.3206544460336 +
- y * (-942.7827304544439 + y * (369.4389437509002 +
- (-33.83664947895248 - 9.987880382780322 * y) * y)))))))
-
- # The above polynomial for pot_enthalpy is the full expression for
- # potential enthalpy in terms of SA and pt, obtained from the Gibbs function
- # as below. It has simply collected like powers of x and y so that it is
- # computationally faster than calling the Gibbs function twice as is done in
- # the commented code below. When this code below is run, the results are
- # identical to calculating pot_enthalpy as above, to machine precision.
-
- # g000 = gibbs(n0, n0, n0, SA, pt, 0)
- # g010 = gibbs(n0, n1, n0, SA, pt, 0)
- # pot_enthalpy = g000 - (Kelvin + pt) * g010
-
- # This is the end of the alternative code
- # %timeit gsw.CT_from_pt(SA, pt)
- # 1000 loops, best of 3: 1.34 ms per loop <- calling gibbs
- # 1000 loops, best of 3: 254 us per loop <- standard
-
- return np.ma.array(pot_enthalpy, mask=mask, copy=False)
-
-
- at match_args_return
-def pt0_from_t(SA, t, p):
- """
- Calculates potential temperature with reference pressure, pr = 0 dbar.
- The present routine is computationally faster than the more general
- function "pt_from_t(SA, t, p, pr)" which can be used for any reference
- pressure value.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- pt0 : array_like
- potential temperature relative to 0 dbar [:math:`^\circ` C (ITS-90)]
-
- See Also
- --------
- entropy_part, gibbs_pt0_pt0, entropy_part_zerop
-
- Notes
- -----
- pt_from_t has the same result (only slower)
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.pt0_from_t(SA, t, p)
- array([ 28.78319682, 28.42098334, 22.7849304 , 10.23052366,
- 6.82923022, 4.32451057])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.1.
-
- .. [2] McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson,
- R. Feistel and R. W. Hallberg, 2010: A computationally efficient 25-term
- expression for the density of seawater in terms of Conservative
- Temperature, and related properties of seawater.
- """
-
- SA = np.maximum(SA, 0)
-
- s1 = SA * (35. / SSO)
-
- pt0 = t + p * (8.65483913395442e-6 -
- s1 * 1.41636299744881e-6 -
- p * 7.38286467135737e-9 +
- t * (-8.38241357039698e-6 +
- s1 * 2.83933368585534e-8 +
- t * 1.77803965218656e-8 +
- p * 1.71155619208233e-10))
-
- dentropy_dt = cp0 / ((Kelvin + pt0) * (1 - 0.05 * (1 - SA / SSO)))
-
- true_entropy_part = entropy_part(SA, t, p)
-
- for Number_of_iterations in range(0, 2, 1):
- pt0_old = pt0
- dentropy = entropy_part_zerop(SA, pt0_old) - true_entropy_part
- # Half way the mod. method (McDougall and Wotherspoon, 2012).
- pt0 = pt0_old - dentropy / dentropy_dt
- pt0m = 0.5 * (pt0 + pt0_old)
- dentropy_dt = -gibbs_pt0_pt0(SA, pt0m)
- pt0 = pt0_old - dentropy / dentropy_dt
-
- # maximum error of 6.3x10^-9 degrees C for one iteration. maximum error is
- # 1.8x10^-14 degrees C for two iterations (two iterations is the default,
- # "for Number_of_iterations = 1:2"). These errors are over the full
- # "oceanographic funnel" of McDougall et al. (2010), which reaches down to
- # p = 8000 dbar.
-
- return pt0
-
-
- at match_args_return
-def pt_from_CT(SA, CT):
- """
- Calculates potential temperature (with a reference sea pressure of zero
- dbar) from Conservative Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- pt : array_like
- potential temperature referenced to a sea pressure of zero dbar
- [:math:`^\circ` C (ITS-90)]
-
- See Also
- --------
- specvol_anom
-
- Notes
- -----
- This function uses 1.5 iterations through a modified Newton-Raphson (N-R)
- iterative solution procedure, starting from a rational-function-based
- initial condition for both pt and dCT_dpt.
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> CT = [28.8099, 28.4392, 22.7862, 10.2262, 6.8272, 4.3236]
- >>> gsw.pt_from_CT(SA, CT)
- array([ 28.78317705, 28.4209556 , 22.78495347, 10.23053439,
- 6.82921659, 4.32453484])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See sections 3.1 and 3.3.
-
- .. [2] McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson,
- R. Feistel and R. W. Hallberg, 2010: A computationally efficient
- 25-term expression for the density of seawater in terms of Conservative
- Temperature, and related properties of seawater.
- """
-
- SA, CT, mask = strip_mask(SA, CT)
- SA = np.maximum(SA, 0)
-
- s1 = SA * 35. / SSO
-
- a0 = -1.446013646344788e-2
- a1 = -3.305308995852924e-3
- a2 = 1.062415929128982e-4
- a3 = 9.477566673794488e-1
- a4 = 2.166591947736613e-3
- a5 = 3.828842955039902e-3
-
- b0 = 1.000000000000000e+0
- b1 = 6.506097115635800e-4
- b2 = 3.830289486850898e-3
- b3 = 1.247811760368034e-6
-
- a5CT = a5 * CT
- b3CT = b3 * CT
- CT_factor = (a3 + a4 * s1 + a5CT)
- pt_num = a0 + s1 * (a1 + a2 * s1) + CT * CT_factor
- pt_den = b0 + b1 * s1 + CT * (b2 + b3CT)
- pt = pt_num / pt_den
-
- dCT_dpt = pt_den / (CT_factor + a5CT - (b2 + b3CT + b3CT) * pt)
-
- # 1.5 iterations through the modified Newton-Rapshon iterative method
- CT_diff = CT_from_pt(SA, pt) - CT
- pt_old = pt
- pt = pt_old - CT_diff / dCT_dpt # 1/2-way through the 1st modified N-R.
- ptm = 0.5 * (pt + pt_old)
-
- # This routine calls gibbs_pt0_pt0(SA, pt0) to get the second derivative of
- # the Gibbs function with respect to temperature at zero sea pressure.
-
- dCT_dpt = -(ptm + Kelvin) * gibbs_pt0_pt0(SA, ptm) / cp0
- pt = pt_old - CT_diff / dCT_dpt # End of 1st full modified N-R iteration.
- CT_diff = CT_from_pt(SA, pt) - CT
- pt_old = pt
- pt = pt_old - CT_diff / dCT_dpt # 1.5 iterations of the modified N-R.
- # Abs max error of result is 1.42e-14 deg C.
- return np.ma.array(pt, mask=mask, copy=False)
-
-
- at match_args_return
-def pt_from_entropy(SA, entropy):
- """
- Calculates potential temperature with reference pressure p_ref = 0 dbar
- and with entropy as an input variable.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- entropy : array_like
- specific entropy [J kg :sup:`-1` K :sup:`-1`]
-
- Returns
- -------
- pt : array_like
- potential temperature [:math:`^\circ` C (ITS-90)]
- with reference sea pressure (p_ref) = 0 dbar.
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> entropy = [400.3892, 395.4378, 319.8668, 146.7910, 98.6471, 62.7919]
- >>> gsw.pt_from_entropy(SA, entropy)
- array([ 28.78317983, 28.42095483, 22.78495274, 10.23053207,
- 6.82921333, 4.32453778])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix A.10.
- """
-
- SA = np.maximum(SA, 0)
-
- part1 = 1 - SA / SSO
- part2 = 1 - 0.05 * part1
- ent_SA = (cp0 / Kelvin) * part1 * (1 - 1.01 * part1)
- c = (entropy - ent_SA) * part2 / cp0
- pt = Kelvin * (np.exp(c) - 1)
- dentropy_dt = cp0 / ((Kelvin + pt) * part2) # Initial dentropy_dt.
-
- for Number_of_iterations in range(0, 3):
- pt_old = pt
- dentropy = entropy_from_pt(SA, pt_old) - entropy
- # This is half way through the modified method
- # (McDougall and Wotherspoon, 2012)
- pt = pt_old - dentropy / dentropy_dt
- ptm = 0.5 * (pt + pt_old)
- dentropy_dt = -gibbs_pt0_pt0(SA, ptm)
- pt = pt_old - dentropy / dentropy_dt
-
- # maximum error of 2.2x10^-6 degrees C for one iteration. maximum error is
- # 1.4x10^-14 degrees C for two iterations (two iterations is the default,
- # "for Number_of_iterations = 1:2").
-
- return pt
-
-
- at match_args_return
-def pt_from_t(SA, t, p, p_ref=0):
- """
- Calculates potential temperature with the general reference pressure,
- pr, from in situ temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
- p_ref : int, float, optional
- reference pressure, default = 0
-
- Returns
- -------
- pt : array_like
- potential temperature [:math:`^\circ` C (ITS-90)]
-
- Notes
- -----
- This function calls `entropy_part` which evaluates entropy except for the
- parts which are a function of Absolute Salinity alone. A faster routine
- exists pt0_from_t(SA,t,p) if p_ref is indeed zero dbar.
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.pt_from_t(SA, t, p)
- array([ 28.78319682, 28.42098334, 22.7849304 , 10.23052366,
- 6.82923022, 4.32451057])
- >>> gsw.pt_from_t(SA, t, p, p_ref=1000)
- array([ 29.02665528, 28.662375 , 22.99149634, 10.35341725,
- 6.92732954, 4.4036 ])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.1.
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of seawater
- in terms of Conservative Temperature, and related properties of seawater.
- """
-
- p_ref = np.asanyarray(p_ref)
-
- SA = np.maximum(SA, 0)
-
- s1 = SA * 35. / SSO
-
- pt = (t + (p - p_ref) * (8.65483913395442e-6 -
- s1 * 1.41636299744881e-6 -
- (p + p_ref) * 7.38286467135737e-9 +
- t * (-8.38241357039698e-6 +
- s1 * 2.83933368585534e-8 +
- t * 1.77803965218656e-8 +
- (p + p_ref) * 1.71155619208233e-10)))
-
- dentropy_dt = cp0 / ((Kelvin + pt) *
- (1 - 0.05 * (1 - SA / SSO)))
-
- true_entropy_part = entropy_part(SA, t, p)
-
- for Number_of_iterations in range(0, 2, 1):
- pt_old = pt
- dentropy = entropy_part(SA, pt_old, p_ref) - true_entropy_part
- pt = pt_old - dentropy / dentropy_dt # half way through the method
- ptm = 0.5 * (pt + pt_old)
- dentropy_dt = -gibbs(n0, n2, n0, SA, ptm, p_ref)
- pt = pt_old - dentropy / dentropy_dt
-
- # maximum error of 6.3x10^-9 degrees C for one iteration. maximum error
- # is 1.8x10^-14 degrees C for two iterations (two iterations is the default,
- # "for Number_of_iterations = 1:2). These errors are over the full
- # "oceanographic funnel" of McDougall et al. (2010), which reaches down to
- # p = 8000 dbar.
-
- return pt
-
-
- at match_args_return
-def t90_from_t48(t48):
- """
- Converts IPTS-48 temperature to International Temperature Scale 1990
- (ITS-90) temperature. This conversion should be applied to all in-situ
- data collected prior to 31/12/1967.
-
- Parameters
- ---------
- t48 : array_like
- in-situ temperature [:math:`^\circ` C (ITPS-48)]
-
- Returns
- -------
- t90 : array_like
- in-situ temperature [:math:`^\circ` C (ITS-90)]
-
- References
- ----------
- .. [1] International Temperature Scales of 1948, 1968 and 1990, an ICES
- note, available from http://www.ices.dk/ocean/procedures/its.htm
- """
-
- return (t48 - (4.4e-6) * t48 * (100 - t48)) / 1.00024
-
-
- at match_args_return
-def t90_from_t68(t68):
- """
- Converts IPTS-68 temperature to International Temperature Scale 1990
- (ITS-90) temperature. This conversion should be applied to all in-situ
- data collected between 1/1/1968 and 31/12/1989.
-
- Parameters
- ---------
- t68 : array_like
- in-situ temperature [:math:`^\circ` C (ITPS-68)]
-
- Returns
- -------
- t90 : array_like
- in-situ temperature [:math:`^\circ` C (ITS-90)]
-
- References
- ----------
- .. [1] International Temperature Scales of 1948, 1968 and 1990, an ICES
- note, available from http://www.ices.dk/ocean/procedures/its.htm
- """
-
- return t68 * 0.999760057586179
-
-
- at match_args_return
-def t_from_CT(SA, CT, p):
- """
- Calculates *in-situ* temperature from Conservative Temperature of
- seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> CT = [28.8099, 28.4392, 22.7862, 10.2262, 6.8272, 4.3236]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.t_from_CT(SA, CT, p)
- array([ 28.78558023, 28.43287225, 22.81032309, 10.26001075,
- 6.8862863 , 4.40362445])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See sections 3.1 and 3.3.
- """
-
- pt0 = pt_from_CT(SA, CT)
- return pt_from_t(SA, pt0, 0, p)
-
-
- at match_args_return
-def t_from_entropy(SA, entropy, p):
- """
- gsw_t_from_entropy in-situ temperature
- as a function of entropy
- =========================================================================
-
- USAGE:
- t = gsw_t_from_entropy(SA,entropy,p)
-
- DESCRIPTION:
- Calculates in-situ temperature with entropy as an input variable.
-
- INPUT:
- SA = Absolute Salinity [ g/kg ]
- entropy = specific entropy [ J/(kg*K) ]
- p = sea pressure [ dbar ]
- ( i.e. absolute pressure - 10.1325 dbar )
-
- SA & entropy need to have the same dimensions.
- p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & entropy are
- MxN.
-
- OUTPUT:
- t = in-situ temperature (ITS-90) [ deg C ]
-
- AUTHOR:
- Trevor McDougall and Paul Barker [ help at teos-10.org ]
-
- VERSION NUMBER: 3.03 (29th April, 2013)
-
- REFERENCES:
- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
- seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Available from http://www.TEOS-10.org
- See appendix A.10 of this TEOS-10 Manual.
- """
-
- pt = pt_from_entropy(SA, entropy)
- # Note that pt is potential temperature with a reference pressure of zero.
- p0 = 0
- return pt_from_t(SA, pt, p0, p)
-
-
-def z_from_depth(depth):
- """
- Calculates height, z, from depth. Note that in general height is
- negative in the ocean.
-
- Parameters
- ---------
- depth : array_like
- depth [m]
-
- Returns
- -------
- z : array_like
- height [m]
- """
-
- return -depth
-
-
- at match_args_return
-def z_from_p(p, lat, geo_strf_dyn_height=0):
- """
- Calculates height from sea pressure using the computationally-efficient
- 48-term expression for density in terms of SA, CT and p (McDougall et
- al., 2011). Dynamic height anomaly, geo_strf_dyn_height, if provided, must
- be computed with its pr=0 (the surface).
-
- Parameters
- ----------
- p : array_like
- pressure [dbar]
- lat : array_like
- latitude in decimal degrees north [-90..+90]
- geo_strf_dyn_height : float, optional
- dynamic height anomaly [ m :sup:`2` s :sup:`-2` ]
-
- Returns
- -------
- z : array_like
- height [m]
-
- Examples
- --------
- >>> import gsw
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> lat = 4
- >>> gsw.z_from_p(p, lat)
- array([ -9.94458313, -49.71808883, -124.27262301, -248.47007032,
- -595.82544461, -992.09217796])
-
- Notes
- -----
- At sea level z = 0, and since z (HEIGHT) is defined to be positive upwards,
- it follows that while z is positive in the atmosphere, it is NEGATIVE in
- the ocean.
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of seawater
- in terms of Conservative Temperature, and related properties of seawater.
-
- .. [3] Moritz (2000) Goedetic reference system 1980. J. Geodesy, 74,
- 128-133.
- """
-
- X = np.sin(lat * DEG2RAD)
- sin2 = X ** 2
- B = 9.780327 * (1.0 + (5.2792e-3 + (2.32e-5 * sin2)) * sin2)
- A = -0.5 * gamma * B
- C = enthalpy_SSO_0_p(p) - geo_strf_dyn_height
-
- return -2 * C / (B + np.sqrt(B ** 2 - 4 * A * C))
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/density_enthalpy_48.py b/gsw/gibbs/density_enthalpy_48.py
deleted file mode 100644
index 659c685..0000000
--- a/gsw/gibbs/density_enthalpy_48.py
+++ /dev/null
@@ -1,1341 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from .library import specvol_SSO_0_p
-from .constants import P0, db2Pascal, cp0
-from ..utilities import match_args_return
-
-__all__ = ['alpha',
- 'alpha_on_beta',
- 'alpha_on_beta_CT',
- 'beta',
- 'dynamic_enthalpy',
- 'enthalpy',
- 'enthalpy_diff',
- 'internal_energy',
- 'rho',
- 'rho_alpha_beta',
- 'SA_from_rho',
- 'sigma0',
- 'sigma1',
- 'sigma2',
- 'sigma3',
- 'sigma4',
- 'sound_speed',
- 'specvol',
- 'specvol_anom']
-
-
-# NOTE: these are from gsw_rho_alpha_beta.m
-v01 = 9.998420897506056e+2
-v02 = 2.839940833161907
-v03 = -3.147759265588511e-2
-v04 = 1.181805545074306e-3
-v05 = -6.698001071123802
-v06 = -2.986498947203215e-2
-v07 = 2.327859407479162e-4
-v08 = -3.988822378968490e-2
-v09 = 5.095422573880500e-4
-v10 = -1.426984671633621e-5
-v11 = 1.645039373682922e-7
-v12 = -2.233269627352527e-2
-v13 = -3.436090079851880e-4
-v14 = 3.726050720345733e-6
-v15 = -1.806789763745328e-4
-v16 = 6.876837219536232e-7
-v17 = -3.087032500374211e-7
-v18 = -1.988366587925593e-8
-v19 = -1.061519070296458e-11
-v20 = 1.550932729220080e-10
-v21 = 1.0
-v22 = 2.775927747785646e-3
-v23 = -2.349607444135925e-5
-v24 = 1.119513357486743e-6
-v25 = 6.743689325042773e-10
-v26 = -7.521448093615448e-3
-v27 = -2.764306979894411e-5
-v28 = 1.262937315098546e-7
-v29 = 9.527875081696435e-10
-v30 = -1.811147201949891e-11
-v31 = -3.303308871386421e-5
-v32 = 3.801564588876298e-7
-v33 = -7.672876869259043e-9
-v34 = -4.634182341116144e-11
-v35 = 2.681097235569143e-12
-v36 = 5.419326551148740e-6
-v37 = -2.742185394906099e-5
-v38 = -3.212746477974189e-7
-v39 = 3.191413910561627e-9
-v40 = -1.931012931541776e-12
-v41 = -1.105097577149576e-7
-v42 = 6.211426728363857e-10
-v43 = -1.119011592875110e-10
-v44 = -1.941660213148725e-11
-v45 = -1.864826425365600e-14
-v46 = 1.119522344879478e-14
-v47 = -1.200507748551599e-15
-v48 = 6.057902487546866e-17
-
-a01 = 2.839940833161907
-a02 = -6.295518531177023e-2
-a03 = 3.545416635222918e-3
-a04 = -2.986498947203215e-2
-a05 = 4.655718814958324e-4
-a06 = 5.095422573880500e-4
-a07 = -2.853969343267241e-5
-a08 = 4.935118121048767e-7
-a09 = -3.436090079851880e-4
-a10 = 7.452101440691467e-6
-a11 = 6.876837219536232e-7
-a12 = -1.988366587925593e-8
-a13 = -2.123038140592916e-11
-
-a14 = 2.775927747785646e-3
-a15 = -4.699214888271850e-5
-a16 = 3.358540072460230e-6
-a17 = 2.697475730017109e-9
-a18 = -2.764306979894411e-5
-a19 = 2.525874630197091e-7
-a20 = 2.858362524508931e-9
-a21 = -7.244588807799565e-11
-a22 = 3.801564588876298e-7
-a23 = -1.534575373851809e-8
-a24 = -1.390254702334843e-10
-a25 = 1.072438894227657e-11
-a26 = -3.212746477974189e-7
-a27 = 6.382827821123254e-9
-a28 = -5.793038794625329e-12
-a29 = 6.211426728363857e-10
-a30 = -1.941660213148725e-11
-a31 = -3.729652850731201e-14
-a32 = 1.119522344879478e-14
-a33 = 6.057902487546866e-17
-
-b01 = -6.698001071123802
-b02 = -2.986498947203215e-2
-b03 = 2.327859407479162e-4
-b04 = -5.983233568452735e-2
-b05 = 7.643133860820750e-4
-b06 = -2.140477007450431e-5
-b07 = 2.467559060524383e-7
-b08 = -1.806789763745328e-4
-b09 = 6.876837219536232e-7
-b10 = 1.550932729220080e-10
-b11 = -7.521448093615448e-3
-b12 = -2.764306979894411e-5
-b13 = 1.262937315098546e-7
-b14 = 9.527875081696435e-10
-b15 = -1.811147201949891e-11
-b16 = -4.954963307079632e-5
-b17 = 5.702346883314446e-7
-b18 = -1.150931530388857e-8
-b19 = -6.951273511674217e-11
-b20 = 4.021645853353715e-12
-b21 = 1.083865310229748e-5
-b22 = -1.105097577149576e-7
-b23 = 6.211426728363857e-10
-b24 = 1.119522344879478e-14
-
-c01 = -2.233269627352527e-2
-c02 = -3.436090079851880e-4
-c03 = 3.726050720345733e-6
-c04 = -1.806789763745328e-4
-c05 = 6.876837219536232e-7
-c06 = -6.174065000748422e-7
-c07 = -3.976733175851186e-8
-c08 = -2.123038140592916e-11
-c09 = 3.101865458440160e-10
-c10 = -2.742185394906099e-5
-c11 = -3.212746477974189e-7
-c12 = 3.191413910561627e-9
-c13 = -1.931012931541776e-12
-c14 = -1.105097577149576e-7
-c15 = 6.211426728363857e-10
-c16 = -2.238023185750219e-10
-c17 = -3.883320426297450e-11
-c18 = -3.729652850731201e-14
-c19 = 2.239044689758956e-14
-c20 = -3.601523245654798e-15
-c21 = 1.817370746264060e-16
-
-# Helper functions that are used by more than one user function.
-# FIXME: arrange all these things so that inputs to these
-# functions are done with ordinary ndarrays with nans, not
-# masked arrays. We might need a different decorator for this.
-
-
-def v_hat_denominator(SA, CT, p, sqrtSA):
- return (v01 + CT * (v02 + CT * (v03 + v04*CT)) +
- SA *
- (v05 + CT * (v06 + v07 * CT) + sqrtSA *
- (v08 + CT * (v09 + CT * (v10 + v11 * CT)))) +
- p *
- (v12 + CT * (v13 + v14 * CT) + SA * (v15 + v16 * CT) +
- p * (v17 + CT * (v18 + v19 * CT) + v20 * SA)))
-
-
-def v_hat_numerator(SA, CT, p, sqrtSA):
- return (v21 + CT * (v22 + CT * (v23 + CT * (v24 + v25 * CT))) +
- SA *
- (v26 + CT * (v27 + CT * (v28 + CT * (v29 + v30 * CT))) +
- v36 * SA + sqrtSA *
- (v31 + CT * (v32 + CT * (v33 + CT * (v34 + v35 * CT))))) +
- p *
- (v37 + CT * (v38 + CT * (v39 + v40 * CT)) + SA *
- (v41 + v42 * CT) + p *
- (v43 + CT * (v44 + v45 * CT + v46 * SA) + p * (v47 + v48 * CT))))
-
-
-# Next 4 are from alpha on beta:
-def dvhatden_dCT(SA, CT, p, sqrtSA):
- return (a01 + CT * (a02 + a03 * CT) + SA *
- (a04 + a05 * CT + sqrtSA * (a06 + CT * (a07 + a08 * CT))) +
- p * (a09 + a10 * CT + a11 * SA + p * (a12 + a13 * CT)))
-
-
-def dvhatnum_dCT(SA, CT, p, sqrtSA):
- return (a14 + CT * (a15 + CT * (a16 + a17 * CT)) + SA *
- (a18 + CT * (a19 + CT * (a20 + a21 * CT)) + sqrtSA *
- (a22 + CT * (a23 + CT * (a24 + a25 * CT)))) + p *
- (a26 + CT * (a27 + a28 * CT) + a29 * SA + p *
- (a30 + a31 * CT + a32 * SA + a33 * p)))
-
-
-def dvhatden_dSA(SA, CT, p, sqrtSA):
- return (b01 + CT * (b02 + b03 * CT) + sqrtSA *
- (b04 + CT * (b05 + CT * (b06 + b07 * CT))) +
- p * (b08 + b09 * CT + b10 * p))
-
-
-def dvhatnum_dSA(SA, CT, p, sqrtSA):
- return(b11 + CT * (b12 + CT * (b13 + CT * (b14 + b15*CT)))
- + sqrtSA * (b16 + CT * (b17 + CT * (b18 + CT * (b19 + b20*CT))))
- + b21*SA
- + p * (b22 + CT * (b23 + b24*p)))
-
-
- at match_args_return
-def alpha_on_beta(SA, CT, p):
- """
- gsw_alpha_on_beta alpha/beta (48-term equation)
- ==========================================================================
-
- USAGE:
- alpha_on_beta = gsw_alpha_on_beta(SA,CT,p)
-
- DESCRIPTION:
- Calculates alpha divided by beta, where alpha is the thermal expansion
- coefficient and beta is the saline contraction coefficient of seawater
- from Absolute Salinity and Conservative Temperature. This function uses
- the computationally-efficient 48-term expression for density in terms of
- SA, CT and p (IOC et al., 2010).
-
- Note that the 48-term equation has been fitted in a restricted range of
- parameter space, and is most accurate inside the "oceanographic funnel"
- described in IOC et al. (2010). The GSW library function
- "gsw_infunnel(SA,CT,p)" is avaialble to be used if one wants to test if
- some of one's data lies outside this "funnel".
-
- INPUT:
- SA = Absolute Salinity [ g/kg ]
- CT = Conservative Temperature (ITS-90) [ deg C ]
- p = sea pressure [ dbar ]
- ( i.e. absolute pressure - 10.1325 dbar )
-
- SA & CT need to have the same dimensions.
- p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN.
-
- OUTPUT:
- alpha_on_beta = thermal expansion coefficient with respect to
- Conservative Temperature divided by the saline
- contraction coefficient at constant Conservative
- Temperature [ kg g^-1 K^-1 ]
-
- AUTHOR:
- Paul Barker and Trevor McDougall [ help at teos-10.org ]
-
- VERSION NUMBER: 3.03 (10th May, 2013)
-
- REFERENCES:
- IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
- seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Available from http://www.TEOS-10.org
- """
-
- SA = np.maximum(SA, 0)
- sqrtSA = np.sqrt(SA)
- args = SA, CT, p, sqrtSA
-
- num = (dvhatnum_dCT(*args) * v_hat_denominator(*args) -
- dvhatden_dCT(*args) * v_hat_numerator(*args))
- denom = (dvhatden_dSA(*args) * v_hat_numerator(*args) -
- dvhatnum_dSA(*args) * v_hat_denominator(*args))
- return num / denom
-
-alpha_on_beta_CT = alpha_on_beta
-
-
- at match_args_return
-def alpha(SA, CT, p):
- """
- Calculates the thermal expansion coefficient of seawater with respect
- to Conservative Temperature using the computationally-efficient 48-term
- expression for density in terms of SA, CT and p (McDougall et al., 2011)
-
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- alpha : array_like
- thermal expansion coefficient [K :math:`-1`]
- with respect to Conservative Temperature
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel"
- described in McDougall et al. (2011). The GSW library function
- "infunnel(SA, CT, p)" is available to be used if one wants to test if
- some of one's data lies outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.18.3).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- SA = np.maximum(SA, 0)
- sqrtSA = np.sqrt(SA)
- args = SA, CT, p, sqrtSA
-
- spec_vol = v_hat_numerator(*args) / v_hat_denominator(*args)
-
- return ((dvhatnum_dCT(*args) - dvhatden_dCT(*args) * spec_vol) /
- v_hat_numerator(*args))
-
-
- at match_args_return
-def beta(SA, CT, p):
- """
- Calculates the saline (i.e. haline) contraction coefficient of seawater
- at constant Conservative Temperature using the computationally-efficient
- 48-term expression for density in terms of SA, CT and p (McDougall et al.,
- 2011).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- beta : array_like
- saline contraction coefficient [kg g :math:`-1`]
- at constant Conservative Temperature.
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel"
- described in McDougall et al. (2011). The GSW library function
- "infunnel(SA, CT, p)" is available to be used if one wants to test if some
- of one's data lies outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.19.3).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- SA = np.maximum(SA, 0)
- sqrtSA = np.sqrt(SA)
- args = SA, CT, p, sqrtSA
-
- spec_vol = v_hat_numerator(*args) / v_hat_denominator(*args)
-
- return ((dvhatden_dSA(*args) * spec_vol - dvhatnum_dSA(*args)) /
- v_hat_numerator(*args))
-
-
- at match_args_return
-def dynamic_enthalpy(SA, CT, p):
- """
- Calculates dynamic enthalpy of seawater using the computationally-
- efficient 48-term expression for density in terms of SA, CT and p
- (McDougall et al., 2011). Dynamic enthalpy is defined as enthalpy minus
- potential enthalpy (Young, 2010).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- dynamic_enthalpy : array_like
- dynamic enthalpy [J/kg]
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA, CT, p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.2
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
-
- .. [3] Young, W.R., 2010: Dynamic enthalpy, Conservative Temperature, and
- the seawater Boussinesq approximation. Journal of Physical Oceanography,
- 40, 394-400.
- """
-
- SA = np.maximum(SA, 0)
-
- sqrtSA = np.sqrt(SA)
-
- a0 = (v21 + CT * (v22 + CT * (v23 + CT * (v24 + v25 * CT))) + SA *
- (v26 + CT * (v27 + CT * (v28 + CT * (v29 + v30 * CT))) + v36 * SA +
- sqrtSA * (v31 + CT * (v32 + CT * (v33 + CT * (v34 + v35 * CT))))))
-
- a1 = v37 + CT * (v38 + CT * (v39 + v40 * CT)) + SA * (v41 + v42 * CT)
-
- a2 = v43 + CT * (v44 + v45 * CT + v46 * SA)
-
- a3 = v47 + v48 * CT
-
- b0 = (v01 + CT * (v02 + CT * (v03 + v04 * CT)) + SA * (v05 + CT * (v06 +
- v07 * CT) + sqrtSA * (v08 + CT * (v09 + CT * (v10 + v11 * CT)))))
-
- b1 = 0.5 * (v12 + CT * (v13 + v14 * CT) + SA * (v15 + v16 * CT))
-
- b2 = v17 + CT * (v18 + v19 * CT) + v20 * SA
-
- b1sq = b1 * b1
-
- sqrt_disc = np.sqrt(b1sq - b0 * b2)
-
- N = a0 + (2 * a3 * b0 * b1 / b2 - a2 * b0) / b2
- M = a1 + (4 * a3 * b1sq / b2 - a3 * b0 - 2 * a2 * b1) / b2
-
- A = b1 - sqrt_disc
- B = b1 + sqrt_disc
-
- part = (N * b2 - M * b1) / (b2 * (B - A))
-
- """This function calculates dynamic_enthalpy using the computationally-
- efficient 48-term expression for density in terms of SA, CT and p. If one
- wanted to compute dynamic_enthalpy from SA, CT, and p with the full TEOS-10
- Gibbs function, the following lines of code will enable this.
-
- dynamic_enthalpy = dynamic_enthalpy_CT_exact(SA, CT, p)
- """
-
- return db2Pascal * (p * (a2 - 2 * a3 * b1 / b2 + 0.5 * a3 * p) / b2 +
- (M / (2 * b2)) *
- np.log(1 + p * (2 * b1 + b2 * p) / b0) + part *
- np.log(1 + (b2 * p * (B - A)) / (A * (B + b2 * p))))
-
-
- at match_args_return
-def enthalpy(SA, CT, p):
- """
- Calculates specific enthalpy of seawater using the computationally-
- efficient 48-term expression for density in terms of SA, CT and p
- (McDougall et al., 2011)
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- enthalpy : array_like
- specific enthalpy [J/kg]
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA, CT, p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (A.30.6).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- SA = np.maximum(SA, 0)
-
- sqrtSA = np.sqrt(SA)
-
- a0 = (v21 + CT * (v22 + CT * (v23 + CT * (v24 + v25 * CT))) + SA *
- (v26 + CT * (v27 + CT * (v28 + CT * (v29 + v30 * CT))) + v36 * SA +
- sqrtSA * (v31 + CT * (v32 + CT * (v33 + CT * (v34 + v35 * CT))))))
-
- a1 = v37 + CT * (v38 + CT * (v39 + v40 * CT)) + SA * (v41 + v42 * CT)
-
- a2 = v43 + CT * (v44 + v45 * CT + v46 * SA)
-
- a3 = v47 + v48 * CT
-
- b0 = (v01 + CT * (v02 + CT * (v03 + v04 * CT)) + SA * (v05 + CT * (v06 +
- v07 * CT) + sqrtSA * (v08 + CT * (v09 + CT * (v10 + v11 * CT)))))
-
- b1 = 0.5 * (v12 + CT * (v13 + v14 * CT) + SA * (v15 + v16 * CT))
-
- b2 = v17 + CT * (v18 + v19 * CT) + v20 * SA
-
- b1sq = b1 * b1
-
- sqrt_disc = np.sqrt(b1sq - b0 * b2)
-
- N = a0 + (2 * a3 * b0 * b1 / b2 - a2 * b0) / b2
- M = a1 + (4 * a3 * b1sq / b2 - a3 * b0 - 2 * a2 * b1) / b2
-
- A = b1 - sqrt_disc
- B = b1 + sqrt_disc
-
- part = (N * b2 - M * b1) / (b2 * (B - A))
-
- # This function calculates enthalpy using the computationally-efficient
- # 48-term expression for density in terms of SA, CT and p. If one wanted to
- # compute enthalpy from SA, CT, and p with the full TEOS-10 Gibbs function,
- # the following lines of code will enable this.
-
- # pt = pt_from_CT(SA, CT)
- # t = pt_from_t(SA, pt, 0, p)
- # enthalpy = enthalpy_t_exact(SA, t, p)
-
- # or call the following, it is identical to the lines above.
-
- # enthalpy = enthalpy_CT_exact(SA, CT, p)
-
- return (cp0 * CT + db2Pascal *
- (p * (a2 - 2 * a3 * b1 / b2 + 0.5 * a3 * p) / b2 + (M / (2 * b2)) *
- np.log(1 + p * (2 * b1 + b2 * p) / b0) + part *
- np.log(1 + (b2 * p * (B - A)) / (A * (B + b2 * p)))))
-
-
- at match_args_return
-def enthalpy_diff(SA, CT, p_shallow, p_deep):
- """
- Calculates the difference of the specific enthalpy of seawater between
- two different pressures, p_deep (the deeper pressure) and p_shallow (the
- shallower pressure), at the same values of SA and CT. This function uses
- the computationally-efficient 48-term expression for density in terms of
- SA, CT and p (McDougall et al., 2011). The output (enthalpy_diff_CT) is
- the specific enthalpy evaluated at (SA, CT, p_deep) minus the specific
- enthalpy at (SA, CT, p_shallow).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p_shallow : array_like
- lower sea pressure [dbar]
- p_deep : array_like
- upper sea pressure [dbar]
-
- Returns
- -------
- enthalpy_diff : array_like
- difference of specific enthalpy [J/kg]
- (deep minus shallow)
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA, CT, p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (3.32.2) and (A.30.6).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- SA = np.maximum(SA, 0)
-
- sqrtSA = np.sqrt(SA)
-
- a0 = (v21 + CT * (v22 + CT * (v23 + CT * (v24 + v25 * CT))) + SA *
- (v26 + CT * (v27 + CT * (v28 + CT * (v29 + v30 * CT))) + v36 * SA +
- sqrtSA * (v31 + CT * (v32 + CT * (v33 + CT * (v34 + v35 * CT))))))
-
- a1 = v37 + CT * (v38 + CT * (v39 + v40 * CT)) + SA * (v41 + v42 * CT)
-
- a2 = v43 + CT * (v44 + v45 * CT + v46 * SA)
-
- a3 = v47 + v48 * CT
-
- b0 = (v01 + CT * (v02 + CT * (v03 + v04 * CT)) + SA * (v05 + CT * (v06 +
- v07 * CT) + sqrtSA * (v08 + CT * (v09 + CT * (v10 + v11 * CT)))))
-
- b1 = 0.5 * (v12 + CT * (v13 + v14 * CT) + SA * (v15 + v16 * CT))
-
- b2 = v17 + CT * (v18 + v19 * CT) + v20 * SA
-
- b1sq = b1 * b1
-
- sqrt_disc = np.sqrt(b1sq - b0 * b2)
-
- N = a0 + (2 * a3 * b0 * b1 / b2 - a2 * b0) / b2
- M = a1 + (4 * a3 * b1sq / b2 - a3 * b0 - 2 * a2 * b1) / b2
-
- A = b1 - sqrt_disc
- B = b1 + sqrt_disc
-
- delta_p = p_deep - p_shallow
- p_sum = p_deep + p_shallow
-
- part1 = b0 + p_shallow * (2 * b1 + b2 * p_shallow)
- part2 = (B + b2 * p_deep) * (A + b2 * p_shallow)
- part3 = (N * b2 - M * b1) / (b2 * (B - A))
-
- # This function calculates enthalpy_diff using the computationally
- # efficient 48-term expression for density in terms of SA, CT and p. If one
- # wanted to compute the enthalpy difference using the full TEOS-10 Gibbs
- # function, the following lines of code will enable this.
-
- # pt = pt_from_CT(SA, CT)
- # t_shallow = pt_from_t(SA, pt, 0, p_shallow)
- # t_deep = pt_from_t(SA, pt, 0, p_deep)
- # enthalpy_diff = (enthalpy_t_exact(SA, t_deep, p_deep) -
- # enthalpy_t_exact(SA, t_shallow, p_shallow))
-
- # or call the following, it is identical to the lines above.
-
- # enthalpy_diff = enthalpy_diff_CT_exact(SA, CT, p_shallow, p_deep)
-
- return db2Pascal * (delta_p * (a2 - 2 * a3 * b1 / b2 + 0.5 * a3 * p_sum) /
- b2 + (M / (2 * b2)) *
- np.log(1 + delta_p * (2 * b1 + b2 * p_sum) / part1) +
- part3 * np.log(1 + delta_p * b2 * (B - A) / part2))
-
-
- at match_args_return
-def internal_energy(SA, CT, p):
- """
- Calculates specific internal energy of seawater using the
- computationally-efficient 48-term expression for density in terms of SA,
- CT and p (McDougall et al., 2011).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- internal_energy : array_like
- specific internal energy [J/kg]
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel"
- described in McDougall et al. (2011). The GSW library function
- "infunnel(SA, CT, p)" is available to be used if one wants to test if
- some of one's data lies outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- SA = np.maximum(SA, 0)
-
- # This function calculates enthalpy using the computationally-efficient
- # 48-term expression for density in terms of SA, CT and p. If one wanted to
- # compute enthalpy from SA, CT, and p with the full TEOS-10 Gibbs function,
- # the following line of code will enable this.
-
- # internal_energy = internal_energy_CT_exact(SA, CT, p)
-
- return (enthalpy(SA, CT, p) - (P0 + db2Pascal * p) * specvol(SA, CT, p))
-
-
- at match_args_return
-def rho(SA, CT, p):
- """
- Calculates in-situ density from Absolute Salinity and Conservative
- Temperature, using the computationally-efficient 48-term expression for
- density in terms of SA, CT and p (McDougall et al., 2011).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- rho : array_like
- in-situ density [kg/m**3]
-
- Notes
- -----
- The potential density with respect to reference pressure, pr, is obtained
- by calling this function with the pressure argument being pr (i.e.
- "rho(SA,CT,pr)").
-
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA,CT,p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix A.20 and appendix K.
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- SA = np.maximum(SA, 0)
- sqrtSA = np.sqrt(SA)
- args = SA, CT, p, sqrtSA
-
- # This function calculates rho using the computationally-efficient 48-term
- # expression for density in terms of SA, CT and p. If one wanted to compute
- # rho from SA, CT, and p with the full TEOS-10 Gibbs function, the following
- # lines of code will enable this.
- #
- # pt0 = pt_from_CT(SA, CT)
- # t = pt_from_t(SA, pt0, 0, p)
- # rho = rho_t_exact(SA, t, p)
- #
- # or call the following, it is identical to the lines above.
- #
- # rho = rho_CT_exact(SA, CT, p)
- #
- # or call the following, it is identical to the lines above.
- #
- # rho,_ ,_ = rho_alpha_beta_CT_exact(SA, CT, p)
-
- return v_hat_denominator(*args) / v_hat_numerator(*args)
-
-
-def rho_alpha_beta(SA, CT, p):
- """
- Calculates in-situ density, the appropriate thermal expansion
- coefficient and the appropriate saline contraction coefficient of seawater
- from Absolute Salinity and Conservative Temperature. This function uses
- the computationally-efficient 48-term expression for density in terms of
- SA, CT and p (McDougall et al., 2011).
-
- The potential density (pot_rho) with respect to reference pressure p_ref is
- obtained by calling this function with the pressure argument being p_ref as
- in pot_rho, _, _] = rho_alpha_beta(SA, CT, p_ref).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- rho : array_like
- in-situ density [kg/m**3]
- alpha : array_like
- thermal expansion coefficient [K :math:`-1`]
- with respect to Conservative Temperature
- beta : array_like
- saline contraction coefficient [kg g :math:`-1`]
- at constant Conservative Temperature.
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA, CT, p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix A.20 and appendix K.
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- return rho(SA, CT, p), alpha(SA, CT, p), beta(SA, CT, p)
-
-
- at match_args_return
-def SA_from_rho(rho, CT, p):
- """
- Calculates the Absolute Salinity of a seawater sample, for given values
- of its density, Conservative Temperature and sea pressure (in dbar). This
- function uses the computationally-efficient 48-term expression for density
- in terms of SA, CT and p (McDougall et al., 2011).
-
- Parameters
- ----------
- rho : array_like
- density of a seawater sample [kg/m**3]
- This input has not had 1000 kg/m^3 subtracted from it
- (e.g. 1026 kg m**-3), that is, it is density, NOT density anomaly.
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- SA : array_like
- Absolute Salinity [g/kg]
-
- Notes
- -----
- This is expressed on the Reference-Composition Salinity Scale of
- Millero et al. (2008).
-
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA, CT, p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.5
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
-
- .. [3] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
- The composition of Standard Seawater and the definition of the
- Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.
- """
-
- v_lab = 1. / rho
- v_0 = specvol(np.zeros_like(rho), CT, p)
- v_50 = specvol(50 * np.ones_like(rho), CT, p)
-
- SA = 50 * (v_lab - v_0) / (v_50 - v_0) # Initial estimate of SA.
-
- SA[np.logical_or(SA < 0, SA > 50)] = np.ma.masked
-
- v_SA = (v_50 - v_0) / 50. # Initial v_SA estimate (SA derivative of v).
-
- # Begin the modified Newton-Raphson iterative procedure.
- for Number_of_iterations in range(0, 3):
- SA_old = SA
- delta_v = specvol(SA_old, CT, p) - v_lab
- # Half way the mod. N-R method (McDougall and Wotherspoon, 2012)
- SA = SA_old - delta_v / v_SA # Half way through the mod. N-R method.
- SA_mean = 0.5 * (SA + SA_old)
- rho, alpha, beta = rho_alpha_beta(SA_mean, CT, p)
- v_SA = -beta / rho
- SA = SA_old - delta_v / v_SA
- SA[np.logical_or(SA < 0, SA > 50)] = np.ma.masked
-
- # After two iterations of this modified Newton-Raphson iteration,
- # the error in SA is no larger than 8x10^-13 g kg^-1, which
- # is machine precision for this calculation.
- return SA
-
-
-def sigma0(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of 0 dbar,
- this being this particular potential density minus 1000 kg/m^3. This
- function has inputs of Absolute Salinity and Conservative Temperature.
- This function uses the computationally-efficient 48-term expression for
- density in terms of SA, CT and p (McDougall et al., 2011).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- sigma0 : array_like
- potential density anomaly with [kg/m**3]
- respect to a reference pressure of 0 dbar
- """
-
- # This function calculates sigma0 using the computationally-efficient
- # 48-term expression for density in terms of SA, CT and p. If one wanted
- # to compute sigma0 with the full TEOS-10 Gibbs function expression for
- # density, the following lines of code will enable this.
- #
- # sigma0 = rho_CT_exact(SA, CT, 0) - 1000
-
- return rho(SA, CT, 0.) - 1000
-
-
-def sigma1(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of 1000
- dbar, this being this particular potential density minus 1000 kg/m^3.
- This function has inputs of Absolute Salinity and Conservative Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- sigma1 : array_like
- potential density anomaly with [kg/m**3]
- respect to a reference pressure of 1000 dbar
- """
-
- # This function calculates sigma1 using the computationally-efficient
- # 48-term expression for density in terms of SA, CT and p. If one wanted
- # to compute sigma1 with the full TEOS-10 Gibbs function expression for
- # density, the following lines of code will enable this.
- #
- # rho1 = rho_CT_exact(SA, CT, 1000)
-
- return rho(SA, CT, 1000.) - 1000
-
-
-def sigma2(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of 2000
- dbar, this being this particular potential density minus 1000 kg/m^3.
- This function has inputs of Absolute Salinity and Conservative Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- sigma2 : array_like
- potential density anomaly with [kg/m**3]
- respect to a reference pressure of 2000 dbar
- """
-
- # This function calculates sigma2 using the computationally-efficient
- # 48-term expression for density in terms of SA, CT and p. If one wanted
- # to compute sigma2 with the full TEOS-10 Gibbs function expression for
- # density, the following lines of code will enable this.
- #
- # rho2 = rho_CT_exact(SA, CT, 2000.)
-
- return rho(SA, CT, 2000.) - 1000
-
-
-def sigma3(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of 3000
- dbar, this being this particular potential density minus 1000 kg/m^3.
- This function has inputs of Absolute Salinity and Conservative Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- sigma1 : array_like
- potential density anomaly with [kg/m**3]
- respect to a reference pressure of 3000 dbar
- """
-
- # This function calculates sigma3 using the computationally-efficient
- # 48-term expression for density in terms of SA, CT and p. If one wanted
- # to compute sigma3 with the full TEOS-10 Gibbs function expression for
- # density, the following lines of code will enable this.
- #
- # rho3 = rho_CT_exact(SA, CT, 3000.)
-
- return rho(SA, CT, 3000.) - 1000
-
-
-def sigma4(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of 4000
- dbar, this being this particular potential density minus 1000 kg/m^3.
- This function has inputs of Absolute Salinity and Conservative Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- sigma1 : array_like
- potential density anomaly with [kg/m**3]
- respect to a reference pressure of 4000 dbar
- """
-
- # This function calculates sigma3 using the computationally-efficient
- # 48-term expression for density in terms of SA, CT and p. If one wanted
- # to compute sigma3 with the full TEOS-10 Gibbs function expression for
- # density, the following lines of code will enable this.
- #
- # rho4 = rho_CT_exact(SA, CT, 4000.)
-
- return rho(SA, CT, 4000.) - 1000
-
-
- at match_args_return
-def sound_speed(SA, CT, p):
- """
- Calculates the speed of sound in seawater. This function has inputs of
- Absolute Salinity and Conservative Temperature. This function uses the
- computationally-efficient 48-term expression for density in terms of SA,
- CT and p (McDougall et al., 2011).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- sound_speed : array_like
- speed of sound in seawater [m/s]
-
- Notes
- -----
- Approximate with a r.m.s. of 6.7 cm s^-1.
-
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel"
- described in McDougall et al. (2011). The GSW library function
- "infunnel(SA, CT, p)" is available to be used if one wants to test if
- some of one's data lies outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.17.1).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- SA = np.maximum(SA, 0)
- sqrtSA = np.sqrt(SA)
- args = SA, CT, p, sqrtSA
-
- dvden_dp = (c01 + CT * (c02 + c03 * CT) + SA * (c04 + c05 * CT) + p *
- (c06 + CT * (c07 + c08 * CT) + c09 * SA))
-
- dvnum_dp = (c10 + CT * (c11 + CT * (c12 + c13 * CT)) + SA *
- (c14 + c15 * CT) + p *
- (c16 + CT * (c17 + c18 * CT + c19 * SA) + p *
- (c20 + c21 * CT)))
-
- drho_dp = ((dvden_dp * v_hat_numerator(*args) - dvnum_dp *
- v_hat_denominator(*args)) / (v_hat_numerator(*args) *
- v_hat_numerator(*args)))
-
- return 100 * np.sqrt(1. / drho_dp)
-
-
- at match_args_return
-def specvol(SA, CT, p):
- """
- Calculates specific volume from Absolute Salinity, Conservative
- Temperature and pressure, using the computationally-efficient 48-term
- expression for density (McDougall et al., 2011).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- specvol : array_like
- specific volume [m**3/kg]
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA,CT,p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.7.2).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- SA = np.maximum(SA, 0)
-
- # This function calculates specvol using the computationally-efficient
- # 48-term expression for density in terms of SA, CT and p. If one wanted to
- # compute specvol from SA, CT, and p with the full TEOS-10 Gibbs function,
- # the following lines of code will enable this.
- #
- # pt = pt_from_CT(SA, CT)
- # t = pt_from_t(SA, pt, 0, p)
- # specvol = specvol_t_exact(SA, t, p)
- #
- # or call the following, it is identical to the lines above.
- #
- # specvol = specvol_CT_exact(SA, CT, p)
-
- SA = np.maximum(SA, 0)
- sqrtSA = np.sqrt(SA)
- args = SA, CT, p, sqrtSA
-
- return v_hat_numerator(*args) / v_hat_denominator(*args)
-
-
- at match_args_return
-def specvol_anom(SA, CT, p):
- """
- Calculates specific volume anomaly from Absolute Salinity, Conservative
- Temperature and pressure. It uses the computationally-efficient 48-term
- expression for density as a function of SA, CT and p (McDougall et al.,
- 2011). The reference value of Absolute Salinity is SSO and the reference
- value of Conservative Temperature is equal to 0 degrees C.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- specvol_anom : array_like
- specific volume anomaly [m**3/kg]
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA,CT,p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (3.7.3).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- SA = np.maximum(SA, 0)
- sqrtSA = np.sqrt(SA)
- args = SA, CT, p, sqrtSA
-
- # This function calculates specvol_anom using the computationally-
- # efficient 48-term expression for density in terms of SA, CT and p. If
- # one wanted to compute specvol_anom from SA, CT, and p with the full
- # TEOS-10 Gibbs function, the following lines of code will enable this.
- #
- # pt = pt_from_CT(SA, CT)
- # t = pt_from_t(SA, pt, 0, p)
- # specvol_anom = specvol_anom_t_exact(SA, t, p)
- #
- # or call the following, it is identical to the lines above.
- #
- # specvol_anom = specvol_anom_CT_exact(SA, CT, p)
-
- return (v_hat_numerator(*args) / v_hat_denominator(*args) -
- specvol_SSO_0_p(p))
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/density_enthalpy_48_ct.py b/gsw/gibbs/density_enthalpy_48_ct.py
deleted file mode 100644
index ea2ea27..0000000
--- a/gsw/gibbs/density_enthalpy_48_ct.py
+++ /dev/null
@@ -1,107 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-__all__ = []
-# 'alpha_CT', # TODO
-# 'beta_CT', # TODO
-# 'CT_from_rho', # TODO
-# 'CT_maxdensity', # TODO
-# 'dynamic_enthalpy_CT', # TODO
-# 'enthalpy_CT', # TODO
-# 'enthalpy_diff_CT', # TODO
-# 'internal_energy_CT', # TODO
-# 'rho_CT', # TODO
-# 'rho_alpha_beta_CT', # TODO
-# 'SA_from_rho_CT', # TODO
-# 'sigma0_CT', # TODO
-# 'sigma1_CT', # TODO
-# 'sigma2_CT', # TODO
-# 'sigma3_CT', # TODO
-# 'sigma4_CT', # TODO
-# 'sound_speed_CT', # TODO
-# 'specvol_CT', # TODO
-# 'specvol_anom_CT'] # TODO
-
-
-#def alpha_CT():
-# pass
-
-
-#def beta_CT():
-# pass
-
-
-#def CT_from_rho():
-# pass
-
-
-#def CT_maxdensity():
-# pass
-
-
-#def dynamic_enthalpy_CT():
-# pass
-
-
-#def enthalpy_CT():
-# pass
-
-
-#def enthalpy_diff_CT():
-# pass
-
-
-#def internal_energy_CT():
-# pass
-
-
-#def rho_CT():
-# pass
-
-
-#def rho_alpha_beta_CT():
-# pass
-
-
-#def SA_from_rho_CT():
-# pass
-
-
-#def sigma0_CT():
-# pass
-
-
-#def sigma1_CT():
-# pass
-
-
-#def sigma2_CT():
-# pass
-
-
-#def sigma3_CT():
-# pass
-
-
-#def sigma4_CT():
-# pass
-
-
-#def sound_speed_CT():
-# pass
-
-
-#def specvol_CT():
-# pass
-
-
-#def specvol_anom_CT():
-# pass
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/density_enthalpy_75.py b/gsw/gibbs/density_enthalpy_75.py
deleted file mode 100644
index e9d02f3..0000000
--- a/gsw/gibbs/density_enthalpy_75.py
+++ /dev/null
@@ -1,447 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from .constants import sfac, soffset
-from ..utilities import match_args_return
-
-__all__ = ['alpha',
- 'rho',
- 'specvol']
-
-
-a000 = -1.5649734675e-5
-a001 = 1.8505765429e-5
-a002 = -1.1736386731e-6
-a003 = -3.6527006553e-7
-a004 = 3.1454099902e-7
-a010 = 5.5524212968e-5
-a011 = -2.3433213706e-5
-a012 = 4.2610057480e-6
-a013 = 5.7391810318e-7
-a020 = -4.9563477777e-5
-a021 = 2.37838968519e-5
-a022 = -1.38397620111e-6
-a030 = 2.76445290808e-5
-a031 = -1.36408749928e-5
-a032 = -2.53411666056e-7
-a040 = -4.0269807770e-6
-a041 = 2.5368383407e-6
-a050 = 1.23258565608e-6
-a100 = 3.5009599764e-5
-a101 = -9.5677088156e-6
-a102 = -5.5699154557e-6
-a103 = -2.7295696237e-7
-a110 = -7.4871684688e-5
-a111 = -4.7356616722e-7
-a112 = 7.8274774160e-7
-a120 = 7.2424438449e-5
-a121 = -1.03676320965e-5
-a122 = 2.32856664276e-8
-a130 = -3.50383492616e-5
-a131 = 5.1826871132e-6
-a140 = -1.6526379450e-6
-a200 = -4.3592678561e-5
-a201 = 1.1100834765e-5
-a202 = 5.4620748834e-6
-a210 = 7.1815645520e-5
-a211 = 5.8566692590e-6
-a212 = -1.31462208134e-6
-a220 = -4.3060899144e-5
-a221 = 9.4965918234e-7
-a230 = 1.74814722392e-5
-a300 = 3.4532461828e-5
-a301 = -9.8447117844e-6
-a302 = -1.3544185627e-6
-a310 = -3.7397168374e-5
-a311 = -9.7652278400e-7
-a320 = 6.8589973668e-6
-a400 = -1.1959409788e-5
-a401 = 2.5909225260e-6
-a410 = 7.7190678488e-6
-a500 = 1.3864594581e-6
-
-v000 = 1.0769995862e-3
-v001 = -6.0799143809e-5
-v002 = 9.9856169219e-6
-v003 = -1.1309361437e-6
-v004 = 1.0531153080e-7
-v005 = -1.2647261286e-8
-v006 = 1.9613503930e-9
-v010 = -1.5649734675e-5
-v011 = 1.8505765429e-5
-v012 = -1.1736386731e-6
-v013 = -3.6527006553e-7
-v014 = 3.1454099902e-7
-v020 = 2.7762106484e-5
-v021 = -1.1716606853e-5
-v022 = 2.1305028740e-6
-v023 = 2.8695905159e-7
-v030 = -1.6521159259e-5
-v031 = 7.9279656173e-6
-v032 = -4.6132540037e-7
-v040 = 6.9111322702e-6
-v041 = -3.4102187482e-6
-v042 = -6.3352916514e-8
-v050 = -8.0539615540e-7
-v051 = 5.0736766814e-7
-v060 = 2.0543094268e-7
-v100 = -3.1038981976e-4
-v101 = 2.4262468747e-5
-v102 = -5.8484432984e-7
-v103 = 3.6310188515e-7
-v104 = -1.1147125423e-7
-v110 = 3.5009599764e-5
-v111 = -9.5677088156e-6
-v112 = -5.5699154557e-6
-v113 = -2.7295696237e-7
-v120 = -3.7435842344e-5
-v121 = -2.3678308361e-7
-v122 = 3.9137387080e-7
-v130 = 2.4141479483e-5
-v131 = -3.4558773655e-6
-v132 = 7.7618888092e-9
-v140 = -8.7595873154e-6
-v141 = 1.2956717783e-6
-v150 = -3.3052758900e-7
-v200 = 6.6928067038e-4
-v201 = -3.4792460974e-5
-v202 = -4.8122251597e-6
-v203 = 1.6746303780e-8
-v210 = -4.3592678561e-5
-v211 = 1.1100834765e-5
-v212 = 5.4620748834e-6
-v220 = 3.5907822760e-5
-v221 = 2.9283346295e-6
-v222 = -6.5731104067e-7
-v230 = -1.4353633048e-5
-v231 = 3.1655306078e-7
-v240 = 4.3703680598e-6
-v300 = -8.5047933937e-4
-v301 = 3.7470777305e-5
-v302 = 4.9263106998e-6
-v310 = 3.4532461828e-5
-v311 = -9.8447117844e-6
-v312 = -1.3544185627e-6
-v320 = -1.8698584187e-5
-v321 = -4.8826139200e-7
-v330 = 2.2863324556e-6
-v400 = 5.8086069943e-4
-v401 = -1.7322218612e-5
-v402 = -1.7811974727e-6
-v410 = -1.1959409788e-5
-v411 = 2.5909225260e-6
-v420 = 3.8595339244e-6
-v500 = -2.1092370507e-4
-v501 = 3.0927427253e-6
-v510 = 1.3864594581e-6
-v600 = 3.1932457305e-5
-
-
- at match_args_return
-def alpha(SA, CT, p):
- """
- Thermal expansion coefficient from CT (75-term equation)
-
- Calculates the thermal expansion coefficient of seawater with respect to
- Conservative Temperature using the computationally-efficient expression
- for specific volume in terms of SA, CT and p (Roquet et al., 2015).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure ( i.e. absolute pressure - 10.1325 dbar ) [dbar]
-
- Returns
- -------
- alpha : array_like
- thermal expansion coefficient [K :math:`-1`]
- with respect to Conservative Temperature
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> CT = [28.8099, 28.4392, 22.7861, 10.2261, 6.8272, 4.3235]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.alpha(SA, CT, p)
- array([ 0.00032464, 0.00032266, 0.00028114, 0.0001732 , 0.00014629,
- 0.00012941])
-
- Notes
- -----
- Note that this 75-term equation has been fitted in a restricted range of
- parameter space, and is most accurate inside the "oceanographic funnel"
- described in McDougall et al. (2003). The GSW library function
- "infunnel(SA,CT,p)" is avaialble to be used if one wants to test if some of
- one's data lies outside this "funnel".
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Available from http://www.TEOS-10.org
- See Eqn. (2.18.3) of this TEOS-10 manual.
-
- .. [2] McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003:
- Accurate and computationally efficient algorithms for potential
- temperature and density of seawater. J. Atmosph. Ocean. Tech., 20,
- pp. 730-741.
-
- .. [3] Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
- polynomial expressions for the density and specifc volume of seawater
- using the TEOS-10 standard. Ocean Modelling.
- """
-
- SA = np.maximum(SA, 0)
-
- xs = np.sqrt(sfac * SA + soffset)
- ys = CT * 0.025
- z = p * 1e-4
-
- v_CT_part = (a000
- + xs * (a100 + xs * (a200 + xs * (a300 + xs * (a400 + a500 * xs))))
- + ys * (a010 + xs * (a110 + xs * (a210 + xs * (a310 + a410 * xs)))
- + ys * (a020 + xs * (a120 + xs * (a220 + a320 * xs))
- + ys * (a030 + xs * (a130 + a230 * xs)
- + ys * (a040 + a140 * xs + a050 * ys))))
- + z * (a001 + xs * (a101 + xs * (a201 + xs * (a301 + a401 * xs)))
- + ys * (a011 + xs * (a111 + xs * (a211 + a311 * xs))
- + ys * (a021 + xs * (a121 + a221 * xs)
- + ys * (a031 + a131 * xs + a041 * ys)))
- + z * (a002 + xs * (a102 + xs * (a202 + a302 * xs))
- + ys * (a012 + xs * (a112 + a212 * xs)
- + ys * (a022 + a122 * xs + a032 * ys))
- + z * (a003 + a103 * xs + a013 * ys + a004 * z))))
-
- specific_volume = (v000
- + xs * (v100 + xs * (v200 + xs * (v300 + xs * (v400 + xs * (v500
- + xs * v600)))))
- + ys * (v010
- + xs * (v110 + xs * (v210 + xs * (v310 + xs * (v410 + xs * v510))))
- + ys * (v020 + xs * (v120 + xs * (v220 + xs * (v320 + xs * v420)))
- + ys * (v030 + xs * (v130 + xs * (v230 + xs * v330))
- + ys * (v040 + xs * (v140 + xs * v240)
- + ys * (v050 + xs * v150 + ys * v060)))))
- + z * (v001
- + xs * (v101 + xs * (v201 + xs * (v301 + xs * (v401 + xs * v501))))
- + ys * (v011 + xs * (v111 + xs * (v211 + xs * (v311 + xs * v411)))
- + ys * (v021 + xs * (v121 + xs * (v221 + xs * v321))
- + ys * (v031 + xs * (v131 + xs * v231)
- + ys * (v041 + xs * v141 + ys * v051))))
- + z * (v002
- + xs * (v102 + xs * (v202 + xs * (v302 + xs * v402)))
- + ys * (v012 + xs * (v112 + xs * (v212 + xs * v312))
- + ys * (v022 + xs * (v122 + xs * v222)
- + ys * (v032 + xs * v132 + ys * v042)))
- + z * (v003
- + xs * (v103 + xs * v203)
- + ys * (v013 + xs * v113 + ys * v023)
- + z * (v004 + xs * v104 + ys * v014
- + z * (v005 + z * v006))))))
-
- return 0.025 * v_CT_part / specific_volume
-
-
- at match_args_return
-def rho(SA, CT, p):
- """
- In-situ density from SA, CT & p (75-term equation)
-
- Calculates in-situ density from Absolute Salinity and Conservative
- Temperature, using the computationally-efficient expression for
- specific volume in terms of SA, CT and p (Roquet et al., 2015).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure ( i.e. absolute pressure - 10.1325 dbar ) [dbar]
-
- Returns
- -------
- rho : array_like
- in-situ density [kg/m**3]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> CT = [28.8099, 28.4392, 22.7861, 10.2261, 6.8272, 4.3235]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.rho(SA, CT, p)
- array([ 1021.83993574, 1022.26245797, 1024.42722421, 1027.79017056,
- 1029.837779 , 1032.00246658])
-
- Notes
- -----
- The potential density with respect to reference pressure, pr, is obtained
- by calling this function with the pressure argument being pr (i.e.
- "rho(SA,CT,pr)").
-
- Note that this 75-term equation has been fitted in a restricted range of
- parameter space, and is most accurate inside the "oceanographic funnel"
- described in McDougall et al. (2003). The GSW library function
- "infunnel(SA,CT,p)" is avaialble to be used if one wants to test if some of
- one's data lies outside this "funnel".
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Available from http://www.TEOS-10.org
- See Eqn. (2.18.3) of this TEOS-10 manual.
-
- .. [2] McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003:
- Accurate and computationally efficient algorithms for potential
- temperature and density of seawater. J. Atmosph. Ocean. Tech., 20,
- pp. 730-741.
-
- .. [3] Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
- polynomial expressions for the density and specifc volume of seawater
- using the TEOS-10 standard. Ocean Modelling.
- """
-
- SA = np.maximum(SA, 0)
-
- xs = np.sqrt(sfac * SA + soffset)
- ys = CT * 0.025
- z = p * 1e-4
-
- specific_volume = (v000
- + xs * (v100 + xs * (v200 + xs * (v300 + xs * (v400 + xs * (v500
- + xs * v600)))))
- + ys * (v010
- + xs * (v110 + xs * (v210 + xs * (v310 + xs * (v410 + xs * v510))))
- + ys * (v020 + xs * (v120 + xs * (v220 + xs * (v320 + xs * v420)))
- + ys * (v030 + xs * (v130 + xs * (v230 + xs * v330))
- + ys * (v040 + xs * (v140 + xs * v240)
- + ys * (v050 + xs * v150 + ys * v060)))))
- + z * (v001
- + xs * (v101 + xs * (v201 + xs * (v301 + xs * (v401 + xs * v501))))
- + ys * (v011 + xs * (v111 + xs * (v211 + xs * (v311 + xs * v411)))
- + ys * (v021 + xs * (v121 + xs * (v221 + xs * v321))
- + ys * (v031 + xs * (v131 + xs * v231)
- + ys * (v041 + xs * v141 + ys * v051))))
- + z * (v002
- + xs * (v102 + xs * (v202 + xs * (v302 + xs * v402)))
- + ys * (v012 + xs * (v112 + xs * (v212 + xs * v312))
- + ys * (v022 + xs * (v122 + xs * v222)
- + ys * (v032 + xs * v132 + ys * v042)))
- + z * (v003
- + xs * (v103 + xs * v203)
- + ys * (v013 + xs * v113 + ys * v023)
- + z * (v004 + xs * v104 + ys * v014
- + z * (v005 + z * v006))))))
-
- return 1. / specific_volume
-
-
- at match_args_return
-def specvol(SA, CT, p):
- """
- Specific volume from SA, CT & p (75-term equation)
-
- Calculates specific volume from Absolute Salinity, Conservative
- Temperature and pressure, using the computationally-efficient 75-term
- polynomial expression for specific volume (Roquet et al., 2015).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure ( i.e. absolute pressure - 10.1325 dbar ) [dbar]
-
- Returns
- -------
- specvol : array_like
- in-situ density [m**3/kg]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> CT = [28.8099, 28.4392, 22.7861, 10.2261, 6.8272, 4.3235]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.specvol(SA, CT, p)
- array([ 0.00097863, 0.00097822, 0.00097616, 0.00097296, 0.00097103,
- 0.00096899])
-
- Notes
- -----
- Note that this 75-term equation has been fitted in a restricted range of
- parameter space, and is most accurate inside the "oceanographic funnel"
- described in McDougall et al. (2003). The GSW library function
- "infunnel(SA,CT,p)" is avaialble to be used if one wants to test if some of
- one's data lies outside this "funnel".
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Available from http://www.TEOS-10.org
- See Eqn. (2.18.3) of this TEOS-10 manual.
-
- .. [2] McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003:
- Accurate and computationally efficient algorithms for potential
- temperature and density of seawater. J. Atmosph. Ocean. Tech., 20,
- pp. 730-741.
-
- .. [3] Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
- polynomial expressions for the density and specifc volume of seawater
- using the TEOS-10 standard. Ocean Modelling.
- """
-
- SA = np.maximum(SA, 0)
-
- xs = np.sqrt(sfac * SA + soffset)
- ys = CT * 0.025
- z = p * 1e-4
-
- specific_volume = (v000
- + xs * (v100 + xs * (v200 + xs * (v300 + xs * (v400 + xs * (v500
- + xs * v600)))))
- + ys * (v010
- + xs * (v110 + xs * (v210 + xs * (v310 + xs * (v410 + xs * v510))))
- + ys * (v020 + xs * (v120 + xs * (v220 + xs * (v320 + xs * v420)))
- + ys * (v030 + xs * (v130 + xs * (v230 + xs * v330))
- + ys * (v040 + xs * (v140 + xs * v240)
- + ys * (v050 + xs * v150 + ys * v060)))))
- + z * (v001
- + xs * (v101 + xs * (v201 + xs * (v301 + xs * (v401 + xs * v501))))
- + ys * (v011 + xs * (v111 + xs * (v211 + xs * (v311 + xs * v411)))
- + ys * (v021 + xs * (v121 + xs * (v221 + xs * v321))
- + ys * (v031 + xs * (v131 + xs * v231)
- + ys * (v041 + xs * v141 + ys * v051))))
- + z * (v002
- + xs * (v102 + xs * (v202 + xs * (v302 + xs * v402)))
- + ys * (v012 + xs * (v112 + xs * (v212 + xs * v312))
- + ys * (v022 + xs * (v122 + xs * v222)
- + ys * (v032 + xs * v132 + ys * v042)))
- + z * (v003
- + xs * (v103 + xs * v203)
- + ys * (v013 + xs * v113 + ys * v023)
- + z * (v004 + xs * v104 + ys * v014
- + z * (v005 + z * v006))))))
-
- return specific_volume
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/density_enthalpy_ct_exact.py b/gsw/gibbs/density_enthalpy_ct_exact.py
deleted file mode 100644
index 2c6b623..0000000
--- a/gsw/gibbs/density_enthalpy_ct_exact.py
+++ /dev/null
@@ -1,758 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from .constants import cp0
-from ..utilities import match_args_return
-from .conversions import t_from_CT, CT_from_t, pt_from_CT
-from .thermodynamics_from_t import (t_from_rho_exact, rho_t_exact,
- alpha_wrt_CT_t_exact, t_maxdensity_exact,
- enthalpy_t_exact, beta_const_CT_t_exact,
- specvol_t_exact, internal_energy_t_exact,
- sigma0_pt0_exact, specvol_anom_t_exact,
- sound_speed_t_exact)
-
-__all__ = ['alpha_CT_exact',
- 'beta_CT_exact',
- 'CT_from_rho_exact',
- 'CT_maxdensity_exact',
- 'dynamic_enthalpy_CT_exact',
- 'enthalpy_CT_exact',
- 'enthalpy_diff_CT_exact',
- 'internal_energy_CT_exact',
- 'rho_CT_exact',
- 'rho_alpha_beta_CT_exact',
- 'SA_from_rho_CT_exact',
- 'sigma0_CT_exact',
- 'sigma1_CT_exact',
- 'sigma2_CT_exact',
- 'sigma3_CT_exact',
- 'sigma4_CT_exact',
- 'sound_speed_CT_exact',
- 'specvol_CT_exact',
- 'specvol_anom_CT_exact']
-
-
-def alpha_CT_exact(SA, CT, p):
- """
- Calculates the thermal expansion coefficient of seawater with respect
- to Conservative Temperature from Absolute Salinity and Conservative
- Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- alpha_CT_exact : array_like
- thermal expansion coefficient [K :sup:`-1`]
- with respect to Conservative Temperature
-
- Notes
- -----
- This function uses the full Gibbs function. There is an alternative to
- calling this function, namely alpha_wrt_CT(SA, CT, p) which uses the
- computationally efficient 48-term expression for density in terms of SA,
- CT and p (McDougall et al., (2011)).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.18.3).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- t = t_from_CT(SA, CT, p)
- return alpha_wrt_CT_t_exact(SA, t, p)
-
-
-def beta_CT_exact(SA, CT, p):
- """
- Calculates the saline (i.e. haline) contraction coefficient of seawater
- at constant Conservative Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- beta_CT_exact : array_like
- thermal expansion coefficient [K :sup:`-1`]
-
- Notes
- -----
- This function uses the full Gibbs function. There is an alternative to
- calling this function, namely beta_const_CT(SA, CT, p) which uses the
- computationally efficient 48-term expression for density in terms of SA, CT
- and p (McDougall et al., (2011)).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.19.3).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- t = t_from_CT(SA, CT, p)
- return beta_const_CT_t_exact(SA, t, p)
-
-
-def CT_from_rho_exact(rho, SA, p):
- """
- Calculates the in-situ temperature of a seawater sample, for given
- values of its density, Absolute Salinity and sea pressure (in dbar).
-
- Parameters
- ----------
- rho : array_like
- density of a seawater sample [kg/m**3]
- This input has not had 1000 kg/m^3 subtracted from it
- (e.g. 1026 kg m**-3), that is, it is density, NOT density anomaly.
- SA : array_like
- Absolute Salinity [g/kg]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- CT_multiple : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Notes
- -----
- At low salinities, in brackish water, there are two possible temperatures
- for a single density. This program will output both valid solutions
- (t, t_multiple), if there is only one possible solution the second variable
- will be set to NaN.
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.5.
- """
-
- t, t_multiple = t_from_rho_exact(rho, SA, p)
- return CT_from_t(SA, t, p), CT_from_t(SA, t_multiple, p)
-
-
-def CT_maxdensity_exact(SA, p):
- """
- Calculates the Conservative Temperature of maximum density of seawater.
- This function returns the Conservative temperature at which the density of
- seawater is a maximum, at given Absolute Salinity, SA, and sea pressure,
- p (in dbar).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- CT_maxdensity_exact : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- at which the density of seawater is a maximum for given SA and p.
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.42.
- """
-
- t_max_exact = t_maxdensity_exact(SA, p)
- return CT_from_t(SA, t_max_exact, p)
-
-
-def dynamic_enthalpy_CT_exact(SA, CT, p):
- """
- Calculates the dynamic enthalpy of seawater from Absolute Salinity and
- Conservative Temperature and pressure. Dynamic enthalpy is defined as
- enthalpy minus potential enthalpy (Young, 2010).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- dynamic_enthalpy_CT_exact : array_like
- dynamic enthalpy [J/kg]
-
- See Also
- --------
- TODO
-
- Notes
- -----
- This function uses the full Gibbs function. There is an alternative to
- calling this function, namely dynamic_enthalpy(SA, CT, p), which uses the
- computationally efficient 48-term expression for density in terms of SA, CT
- and p (McDougall et al., 2011).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See apendix A.30.
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
-
- .. [3] Young, W.R., 2010: Dynamic enthalpy, Conservative Temperature, and
- the seawater Boussinesq approximation. Journal of Physical Oceanography,
- 40, 394-400.
- """
-
- t = t_from_CT(SA, CT, p)
- return enthalpy_t_exact(SA, t, p) - cp0 * CT
-
-
- at match_args_return
-def enthalpy_CT_exact(SA, CT, p):
- """
- Calculates specific enthalpy of seawater from Absolute Salinity and
- Conservative Temperature and pressure.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- enthalpy_CT_exact : array_like
- specific enthalpy [J/kg]
-
- Notes
- -----
- This function uses the full Gibbs function. There is an alternative to
- calling this function, namely enthalpy_CT(SA, CT, p), which uses the
- computationally-efficient 48-term expression for density in terms of SA, CT
- and p (McDougall et al., 2011).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix A.11.
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- t = t_from_CT(SA, CT, p)
- return enthalpy_t_exact(SA, t, p)
-
-
-def enthalpy_diff_CT_exact(SA, CT, p_shallow, p_deep):
- """
- Calculates the difference of the specific enthalpy of seawater between
- two different pressures, p_deep (the deeper pressure) and p_shallow (the
- shallower pressure), at the same values of SA and CT. The output
- (enthalpy_diff_CT_exact) is the specific enthalpy evaluated at
- (SA, CT, p_deep) minus the specific enthalpy at (SA,CT,p_shallow).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p_shallow : array_like
- lower sea pressure [dbar]
- p_deep : array_like
- upper sea pressure [dbar]
-
- Returns
- -------
- enthalpy_diff_CT_exact : array_like
- difference of specific enthalpy [J/kg]
- (deep minus shallow)
-
- Notes
- -----
- This function uses the full Gibbs function. There is an alternative to
- calling this function, namely enthalpy_diff_CT(SA, CT, p), which uses the
- computationally efficient 48-term expression for density in terms of SA, CT
- and p (McDougall et al., 2011).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns (3.32.2).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- t_shallow = t_from_CT(SA, CT, p_shallow)
- t_deep = t_from_CT(SA, CT, p_deep)
- return (enthalpy_t_exact(SA, t_deep, p_deep) -
- enthalpy_t_exact(SA, t_shallow, p_shallow))
-
-
-def internal_energy_CT_exact(SA, CT, p):
- """
- Calculates the specific internal energy of seawater from Absolute
- Salinity, Conservative Temperature and pressure.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- internal_energy_CT_exact: array_like
- specific internal energy (u) [J/kg]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.11.1).
- """
-
- t = t_from_CT(SA, CT, p)
- return internal_energy_t_exact(SA, t, p)
-
-
-def rho_CT_exact(SA, CT, p):
- """
- Calculates in-situ density from Absolute Salinity and Conservative
- Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- rho_CT_exact : array_like
- in-situ density [kg/m**3]
-
- Notes
- -----
- The potential density with respect to reference pressure, p_ref, is
- obtained by calling this function with the pressure argument being p_ref
- (i.e. "rho_CT_exact(SA, CT, p_ref)"). This function uses the full Gibbs
- function. There is an alternative to calling this function, namely
- rho_CT(SA, CT, p), which uses the computationally efficient 48-term
- expression for density in terms of SA, CT and p (McDougall et al., 2011).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.8.2).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- t = t_from_CT(SA, CT, p)
- return rho_t_exact(SA, t, p)
-
-
-def rho_alpha_beta_CT_exact(SA, CT, p):
- """
- Calculates in-situ density, the appropriate thermal expansion
- coefficient and the appropriate saline contraction coefficient of seawater
- from Absolute Salinity and Conservative Temperature.
- See the individual functions rho_CT_exact, alpha_CT_exact, and
- beta_CT_exact. Retained for compatibility with the Matlab GSW toolbox.
- """
-
- t = t_from_CT(SA, CT, p)
- rho_CT_exact = rho_t_exact(SA, t, p)
- alpha_CT_exact = alpha_wrt_CT_t_exact(SA, t, p)
- beta_CT_exact = beta_const_CT_t_exact(SA, t, p)
- return rho_CT_exact, alpha_CT_exact, beta_CT_exact
-
-
-def SA_from_rho_CT_exact(rho, CT, p):
- """
- Calculates the Absolute Salinity of a seawater sample, for given values
- of its density, Conservative Temperature and sea pressure (in dbar).
-
- Parameters
- ----------
- rho : array_like
- density of a seawater sample [kg/m**3]
- This input has not had 1000 kg/m^3 subtracted from it
- (e.g. 1026 kg m**-3), that is, it is density, NOT density anomaly.
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- SA : array_like
- Absolute Salinity [g/kg]
-
- Notes
- -----
- This function uses the full Gibbs function. There is an alternative to
- calling this function, namely SA_from_rho_CT(rho, CT, p), which uses the
- computationally efficient 48-term expression for density in terms of SA, CT
- and p (McDougall et al., 2011).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.5.
-
- .. [2] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
- The composition of Standard Seawater and the definition of the
- Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.
- """
-
- v_lab = 1. / rho
- v_0 = specvol_CT_exact(np.zeros_like(rho), CT, p)
- v_120 = specvol_CT_exact(120 * np.ones_like(rho), CT, p)
- SA = 120 * (v_lab - v_0) / (v_120 - v_0) # Initial estimate of SA.
- SA[np.logical_or(SA < 0, SA > 120)] = np.ma.masked
- v_SA = (v_120 - v_0) / 120 # Initial v_SA estimate (SA derivative of v).
- # Begin the modified Newton-Raphson iterative procedure.
- for Number_of_iterations in range(0, 3):
- SA_old = SA
- delta_v = specvol_CT_exact(SA_old, CT, p) - v_lab
- # Half way the mod. N-R method (McDougall and Wotherspoon, 2012).
- SA = SA_old - delta_v / v_SA
- SA_mean = 0.5 * (SA + SA_old)
- rho, alpha, beta = rho_alpha_beta_CT_exact(SA_mean, CT, p)
- v_SA = -beta / rho
- SA = SA_old - delta_v / v_SA
- SA[np.logical_or(SA < 0, SA > 120)] = np.ma.masked
-
- # After two iterations of this modified Newton-Raphson iteration, the
- # error in SA is no larger than 8x10^-13 g kg^-1, which is machine precision
- # for this calculation.
- return SA
-
-
-def sigma0_CT_exact(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of 0 dbar,
- this being this particular potential density minus 1000 kg/m^3. This
- function has inputs of Absolute Salinity and Conservative Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- sigma0_CT_exact: array_like
- Potential density anomaly with [kg/m**3]
- respect to a reference pressure of 0 dbar
- that is, this potential density - 1000 kg/m**3.
-
- Notes
- -----
- Note that this function uses the full Gibbs function. There is an
- alternative to calling this function, namely gsw_sigma0_CT(SA,CT,p), which
- uses the computationally efficient 48-term expression for density in terms
- of SA, CT and p (McDougall et al., 2011).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (A.30.1).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- pt0 = pt_from_CT(SA, CT)
- return sigma0_pt0_exact(SA, pt0)
-
-
-def sigma1_CT_exact(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of
- 1000 dbar.
- """
-
- t = t_from_CT(SA, CT, 1000.)
- return rho_t_exact(SA, t, 1000.) - 1000
-
-
-def sigma2_CT_exact(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of
- 2000 dbar.
- """
-
- t = t_from_CT(SA, CT, 2000.)
- return rho_t_exact(SA, t, 2000.) - 1000
-
-
-def sigma3_CT_exact(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of
- 3000 dbar.
- """
-
- t = t_from_CT(SA, CT, 3000.)
- return rho_t_exact(SA, t, 3000.) - 1000
-
-
-def sigma4_CT_exact(SA, CT):
- """
- Calculates potential density anomaly with reference pressure of
- 4000 dbar.
- """
-
- t = t_from_CT(SA, CT, 4000.)
- return rho_t_exact(SA, t, 4000.) - 1000
-
-
-def sound_speed_CT_exact(SA, CT, p):
- """
- Calculates the speed of sound in seawater from Absolute Salinity and
- Conservative Temperature and pressure.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- sound_speed_CT_exact : array_like
- Speed of sound in seawater [m s :sup:`-1`]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.17.1).
- """
-
- t = t_from_CT(SA, CT, p)
- return sound_speed_t_exact(SA, t, p)
-
-
-def specvol_CT_exact(SA, CT, p):
- """
- Calculates specific volume from Absolute Salinity, Conservative
- Temperature and pressure.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- specvol_CT_exact : array_like
- specific volume [m**3/kg]
-
- Notes
- -----
- This function uses the full Gibbs function. There is an alternative to
- calling this function, namely specvol_CT(SA, CT, p), which uses the
- computationally efficient 48-term expression for density in terms of SA, CT
- and p (McDougall et al., 2011).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.7.2).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- t = t_from_CT(SA, CT, p)
- return specvol_t_exact(SA, t, p)
-
-
-def specvol_anom_CT_exact(SA, CT, p):
- """
- Calculates specific volume anomaly from Absolute Salinity, Conservative
- Temperature and pressure. The reference value of Absolute Salinity is SSO
- and the reference value of Conservative Temperature is equal to 0 deg C.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- specvol_anom_CT_exact : array_like
- specific volume anomaly [m**3/kg]
-
- Notes
- -----
- This function uses the full Gibbs function. There is an alternative to
- calling this function, namely specvol_anom_CT(SA, CT, p), which uses the
- computationally efficient 48-term expression for density in terms of SA, CT
- and p (McDougall et al., 2011).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (3.7.3).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
- t = t_from_CT(SA, CT, p)
- return specvol_anom_t_exact(SA, t, p)
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/derivatives.py b/gsw/gibbs/derivatives.py
deleted file mode 100644
index 8e0d8c5..0000000
--- a/gsw/gibbs/derivatives.py
+++ /dev/null
@@ -1,608 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from .library import gibbs
-from .constants import Kelvin, cp0, sfac
-from ..utilities import match_args_return
-from .conversions import pt_from_CT, pt_from_t
-
-__all__ = ['CT_first_derivatives',
- 'CT_second_derivatives',
- 'enthalpy_first_derivatives',
- 'enthalpy_second_derivatives',
- 'entropy_first_derivatives',
- 'entropy_second_derivatives',
- 'pt_first_derivatives',
- 'pt_second_derivatives']
-
-n0, n1, n2 = 0, 1, 2
-
-
- at match_args_return
-def CT_first_derivatives(SA, pt):
- """
- Calculates the following two derivatives of Conservative Temperature
- (1) CT_SA, the derivative with respect to Absolute Salinity at constant
- potential temperature (with pr = 0 dbar), and
- (2) CT_pt, the derivative with respect to potential temperature (the
- regular potential temperature which is referenced to 0 dbar) at
- constant Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- pt : array_like
- potential temperature referenced to a sea pressure of zero dbar
- [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- CT_SA : array_like
- The derivative of CT with respect to SA at constant potential
- temperature reference sea pressure of 0 dbar.
- [K (g kg :sup:`-1`) :sup:`-1`]
-
- CT_pt : array_like
- The derivative of CT with respect to pt at constant SA.
- [ unitless ]
-
- Examples
- --------
- >>> import gsw
- >>> SA = 34.7118
- >>> pt = 28.7832
- >>> gsw.CT_first_derivatives(SA, pt)
- (-0.041981092877805957, 1.0028149372966355)
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (A.12.3) and (A.12.9a,b).
-
- .. [2] McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson, R.
- Feistel and R. W. Hallberg, 2010: A computationally efficient 25-term
- expression for the density of seawater in terms of Conservative
- Temperature, and related properties of seawater.
- """
-
- # FIXME: Matlab version 3.0 has a copy-and-paste of the gibbs function here
- # instead of a call. Why?
-
- abs_pt = Kelvin + pt
-
- CT_pt = -(abs_pt * gibbs(n0, n2, n0, SA, pt, 0)) / cp0
-
- x2 = sfac * SA
- x = np.sqrt(x2)
- y_pt = 0.025 * pt
-
- g_SA_T_mod = (1187.3715515697959 + x * (-1480.222530425046 + x *
- (2175.341332000392 + x * (-980.14153344888 +
- 220.542973797483 * x) + y_pt * (-548.4580073635929 + y_pt *
- (592.4012338275047 + y_pt * (-274.2361238716608 +
- 49.9394019139016 * y_pt)))) + y_pt * (-258.3988055868252 +
- y_pt * (-90.2046337756875 + y_pt * 10.50720794170734))) +
- y_pt * (3520.125411988816 + y_pt * (-1351.605895580406 +
- y_pt * (731.4083582010072 + y_pt * (-216.60324087531103 +
- 25.56203650166196 * y_pt)))))
-
- g_SA_T_mod *= 0.5 * sfac * 0.025
-
- g_SA_mod = (8645.36753595126 + x * (-7296.43987145382 + x *
- (8103.20462414788 + y_pt * (2175.341332000392 + y_pt *
- (-274.2290036817964 + y_pt * (197.4670779425016 + y_pt *
- (-68.5590309679152 + 9.98788038278032 * y_pt)))) + x *
- (-5458.34205214835 - 980.14153344888 * y_pt + x *
- (2247.60742726704 - 340.1237483177863 * x + 220.542973797483 *
- y_pt))) + y_pt * (-1480.222530425046 + y_pt *
- (-129.1994027934126 + y_pt * (-30.0682112585625 + y_pt *
- (2.626801985426835))))) + y_pt * (1187.3715515697959 + y_pt *
- (1760.062705994408 + y_pt * (-450.535298526802 + y_pt *
- (182.8520895502518 + y_pt * (-43.3206481750622 +
- 4.26033941694366 * y_pt))))))
-
- g_SA_mod *= 0.5 * sfac
-
- CT_SA = (g_SA_mod - abs_pt * g_SA_T_mod) / cp0
-
- return CT_SA, CT_pt
-
-
- at match_args_return
-def CT_second_derivatives(SA, pt):
- """
- Calculates the following three, second-order derivatives of Conservative
- Temperature
- (1) CT_SA_SA, the second derivative with respect to Absolute Salinity at
- constant potential temperature (with p_ref = 0 dbar),
- (2) CT_SA_pt, the derivative with respect to potential temperature (the
- regular potential temperature which is referenced to 0 dbar) and
- Absolute Salinity, and
- (3) CT_pt_pt, the second derivative with respect to potential temperature
- (the regular potential temperature which is referenced to 0 dbar) at
- constant Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- pt : array_like
- potential temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- CT_SA_SA : array_like
- The second derivative of Conservative Temperature with respect
- to Absolute Salinity at constant potential temperature (the
- regular potential temperature which has reference sea pressure
- of 0 dbar). [K/((g/kg)^2)]
- CT_SA_pt : array_like
- The derivative of Conservative Temperature with respect to
- potential temperature (the regular one with p_ref = 0 dbar) and
- Absolute Salinity. [1/(g/kg)]
- CT_pt_pt : array_like
- The second derivative of Conservative Temperature with respect
- to potential temperature (the regular one with p_ref = 0 dbar)
- at constant SA. [1/K]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix A.12.
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of seawater
- in terms of Conservative Temperature, and related properties of
- seawater. To be submitted to Ocean Science Discussions.
- """
-
- dSA = 1e-3
- SA_l = SA - dSA
- SA_l = np.maximum(SA_l, 0)
- SA_u = SA + dSA
-
- CT_SA_l, _ = CT_first_derivatives(SA_l, pt)
- CT_SA_u, _ = CT_first_derivatives(SA_u, pt)
-
- CT_SA_SA = np.zeros_like(SA) * np.NaN
- CT_SA_SA[SA_u != SA_l] = ((CT_SA_u[SA_u != SA_l] - CT_SA_l[SA_u != SA_l]) /
- (SA_u[SA_u != SA_l] - SA_l[SA_u != SA_l]))
-
- # Increment of potential temperature is 0.01 degrees C.
- dpt = 1e-2
- pt_l = pt - dpt
- pt_u = pt + dpt
-
- CT_SA_l, CT_pt_l = CT_first_derivatives(SA, pt_l)
- CT_SA_u, CT_pt_u = CT_first_derivatives(SA, pt_u)
-
- CT_SA_pt = (CT_SA_u - CT_SA_l) / (pt_u - pt_l)
- CT_pt_pt = (CT_pt_u - CT_pt_l) / (pt_u - pt_l)
-
- return CT_SA_SA, CT_SA_pt, CT_pt_pt
-
-
- at match_args_return
-def enthalpy_first_derivatives(SA, CT, p):
- """
- Calculates the following three derivatives of specific enthalpy (h)
- (1) h_SA, the derivative with respect to Absolute Salinity at
- constant CT and p, and
- (2) h_CT, derivative with respect to CT at constant SA and p.
- (3) h_P, derivative with respect to pressure (in Pa) at constant SA and CT.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- h_SA : array_like
- The first derivative of specific enthalpy with respect to Absolute
- Salinity at constant CT and p. [J/(kg (g/kg))] i.e. [J/g]
- h_CT : array_like
- The first derivative of specific enthalpy with respect to CT at
- constant SA and p. [J/(kg K)]
- h_P : array_like
- The first partial derivative of specific enthalpy with respect to
- pressure (in Pa) at fixed SA and CT. Note that h_P is specific
- volume (1/rho.)
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (A.11.18), (A.11.15) and (A.11.12.)
- """
-
- # FIXME: The gsw 3.0 has the gibbs derivatives "copy-and-pasted" here
- # instead of the calls to the library! Why?
-
- pt0 = pt_from_CT(SA, CT)
- t = pt_from_t(SA, pt0, 0, p)
- temp_ratio = (Kelvin + t) / (Kelvin + pt0)
-
- def enthalpy_derivative_SA(SA, CT, p):
- return (gibbs(n1, n0, n0, SA, t, p) -
- temp_ratio * gibbs(n1, n0, n0, SA, pt0, 0))
-
- def enthalpy_derivative_CT(SA, CT, p):
- return cp0 * temp_ratio
-
- def enthalpy_derivative_p(SA, CT, p):
- return gibbs(n0, n0, n1, SA, t, p)
-
- return (enthalpy_derivative_SA(SA, CT, p),
- enthalpy_derivative_CT(SA, CT, p),
- enthalpy_derivative_p(SA, CT, p),)
-
-
- at match_args_return
-def enthalpy_second_derivatives(SA, CT, p):
- """
- Calculates the following three second-order derivatives of specific
- enthalpy (h)
- (1) h_SA_SA, second-order derivative with respect to Absolute Salinity
- at constant CT & p.
- (2) h_SA_CT, second-order derivative with respect to SA & CT at
- constant p.
- (3) h_CT_CT, second-order derivative with respect to CT at constant SA
- and p.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- h_SA_SA : array_like
- The second derivative of specific enthalpy with respect to
- Absolute Salinity at constant CT & p. [J/(kg (g/kg)^2)]
- h_SA_CT : array_like
- The second derivative of specific enthalpy with respect to SA and
- CT at constant p. [J/(kg K(g/kg))]
- h_CT_CT : array_like
- The second derivative of specific enthalpy with respect to CT at
- constant SA and p. [J/(kg K^2)]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (A.11.18), (A.11.15) and (A.11.12.)
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of seawater
- in terms of Conservative Temperature, and related properties of
- seawater. To be submitted to Ocean Science Discussions.
- """
-
- # NOTE: The Matlab version 3.0 mentions that this function is unchanged,
- # but that's not true!
-
- pt0 = pt_from_CT(SA, CT)
- abs_pt0 = Kelvin + pt0
- t = pt_from_t(SA, pt0, 0, p)
- temp_ratio = (Kelvin + t) / abs_pt0
-
- rec_gTT_pt0 = 1 / gibbs(n0, n2, n0, SA, pt0, 0)
- rec_gTT_t = 1 / gibbs(n0, n2, n0, SA, t, p)
- gST_pt0 = gibbs(n1, n1, n0, SA, pt0, 0)
- gST_t = gibbs(n1, n1, n0, SA, t, p)
- gS_pt0 = gibbs(n1, n0, n0, SA, pt0, 0)
-
- part = ((temp_ratio * gST_pt0 * rec_gTT_pt0 - gST_t * rec_gTT_t) /
- (abs_pt0))
-
- factor = gS_pt0 / cp0
-
- # h_CT_CT is naturally well-behaved as SA approaches zero.
- def enthalpy_derivative_CT_CT(SA, CT, p):
- return (cp0 ** 2 * ((temp_ratio * rec_gTT_pt0 - rec_gTT_t) /
- (abs_pt0 * abs_pt0)))
-
- # h_SA_SA has a singularity at SA = 0, and blows up as SA approaches zero.
- def enthalpy_derivative_SA_SA(SA, CT, p):
- SA[SA < 1e-100] = 1e-100 # NOTE: Here is the changes from 2.0 to 3.0.
- h_CT_CT = enthalpy_derivative_CT_CT(SA, CT, p)
- return (gibbs(n2, n0, n0, SA, t, p) -
- temp_ratio * gibbs(n2, n0, n0, SA, pt0, 0) +
- temp_ratio * gST_pt0 ** 2 * rec_gTT_pt0 -
- gST_t ** 2 * rec_gTT_t - 2.0 * gS_pt0 * part +
- factor ** 2 * h_CT_CT)
-
- # h_SA_CT should not blow up as SA approaches zero. The following lines of
- # code ensure that the h_SA_CT output of this function does not blow up in
- # this limit. That is, when SA < 1e-100 g/kg, we force the h_SA_CT output
- # to be the same as if SA = 1e-100 g/kg.
-
- def enthalpy_derivative_SA_CT(SA, CT, p):
- h_CT_CT = enthalpy_derivative_CT_CT(SA, CT, p)
- return cp0 * part - factor * h_CT_CT
-
- return (enthalpy_derivative_SA_SA(SA, CT, p),
- enthalpy_derivative_SA_CT(SA, CT, p),
- enthalpy_derivative_CT_CT(SA, CT, p))
-
-
- at match_args_return
-def entropy_first_derivatives(SA, CT):
- """
- Calculates the following two partial derivatives of specific entropy
- (eta)
- (1) eta_SA, the derivative with respect to Absolute Salinity at constant
- Conservative Temperature, and
- (2) eta_CT, the derivative with respect to Conservative Temperature at
- constant Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- eta_SA : array_like
- The derivative of specific entropy with respect to SA at constant
- CT [J g :sup:`-1` K :sup:`-1`]
- eta_CT : array_like
- The derivative of specific entropy with respect to CT at constant
- SA [ J (kg K :sup:`-2`) :sup:`-1` ]
-
- Examples
- --------
- >>> import gsw
- >>> SA = 34.7118
- >>> CT = 28.8099
- >>> gsw.entropy_first_derivatives(SA, CT)
- (-0.26328680071165517, 13.221031210083824)
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (A.12.8) and (P.14a,c).
- """
- pt = pt_from_CT(SA, CT)
-
- eta_SA = -(gibbs(n1, n0, n0, SA, pt, 0)) / (Kelvin + pt)
- eta_CT = cp0 / (Kelvin + pt)
- return eta_SA, eta_CT
-
-
- at match_args_return
-def entropy_second_derivatives(SA, CT):
- """
- Calculates the following three second-order partial derivatives of
- specific entropy (eta)
- (1) eta_SA_SA, the second derivative with respect to Absolute Salinity at
- constant Conservative Temperature, and
- (2) eta_SA_CT, the derivative with respect to Absolute Salinity and
- Conservative Temperature.
- (3) eta_CT_CT, the second derivative with respect to Conservative
- Temperature at constant Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- eta_SA_SA : array_like
- The second derivative of specific entropy with respect to SA at
- constant CT [J (kg K (g kg :sup:`-1` ) :sup:`2`) :sup:`-1`]
- eta_SA_CT : array_like
- The second derivative of specific entropy with respect to
- SA and CT [J (kg (g kg :sup:`-1` ) K :sup:`2`) :sup:`-1` ]
- eta_CT_CT : array_like
- The second derivative of specific entropy with respect to CT at
- constant SA [J (kg K :sup:`3`) :sup:`-1` ]
-
- Examples
- --------
- >>> import gsw
- >>> SA = 34.7118
- >>> CT = 28.8099
- >>> gsw.entropy_second_derivatives(SA, CT)
- (-0.0076277189296690626, -0.0018331042167510211, -0.043665023731108685)
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (P.14b) and (P.15a,b).
- """
-
- pt = pt_from_CT(SA, CT)
- abs_pt = Kelvin + pt
-
- CT_SA = ((gibbs(n1, n0, n0, SA, pt, 0) -
- (abs_pt * gibbs(n1, n1, n0, SA, pt, 0))) / cp0)
-
- CT_pt = -(abs_pt * gibbs(n0, n2, n0, SA, pt, 0)) / cp0
-
- eta_CT_CT = - cp0 / (CT_pt * abs_pt ** 2)
-
- eta_SA_CT = - CT_SA * eta_CT_CT
-
- eta_SA_SA = -gibbs(n2, n0, n0, SA, pt, 0) / abs_pt - CT_SA * eta_SA_CT
-
- return eta_SA_SA, eta_SA_CT, eta_CT_CT
-
-
- at match_args_return
-def pt_first_derivatives(SA, CT):
- """
- Calculates the following two partial derivatives of potential
- temperature (the regular potential temperature whose reference sea
- pressure is 0 dbar)
- (1) pt_SA, the derivative with respect to Absolute Salinity at
- constant Conservative Temperature, and
- (2) pt_CT, the derivative with respect to Conservative Temperature at
- constant Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- pt_SA : array_like
- The derivative of potential temperature with respect to Absolute
- Salinity at constant Conservative Temperature. [K/(g/kg)]
- pt_CT : array_like
- The derivative of potential temperature with respect to
- Conservative Temperature at constant Absolute Salinity. [unitless]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (A.12.6), (A.12.3), (P.6) and (P.8).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of seawater
- in terms of Conservative Temperature, and related properties of
- seawater. To be submitted to Ocean Science Discussions.
- """
-
- pt = pt_from_CT(SA, CT)
- abs_pt = Kelvin + pt
-
- CT_SA = ((gibbs(n1, n0, n0, SA, pt, 0) - abs_pt *
- gibbs(n1, n1, n0, SA, pt, 0)) / cp0)
-
- CT_pt = - (abs_pt * gibbs(n0, n2, n0, SA, pt, 0)) / cp0
-
- pt_SA = - CT_SA / CT_pt
-
- pt_CT = 1.0 / CT_pt
-
- return pt_SA, pt_CT
-
-
- at match_args_return
-def pt_second_derivatives(SA, CT):
- """
- Calculates the following three second-order derivatives of potential
- temperature (the regular potential temperature which has a reference
- sea pressure of 0 dbar),
- (1) pt_SA_SA, the second derivative with respect to Absolute Salinity at
- constant Conservative Temperature,
- (2) pt_SA_CT, the derivative with respect to Conservative Temperature and
- Absolute Salinity, and
- (3) pt_CT_CT, the second derivative with respect to Conservative
- Temperature at constant Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- pt_SA_SA : array_like
- The second derivative of potential temperature (the regular
- potential temperature which has reference sea pressure of 0
- dbar) with respect to Absolute Salinity at constant Conservative
- Temperature. [K/((g/kg)^2)]
- pt_SA_CT : array_like
- The derivative of potential temperature with respect to Absolute
- Salinity and Conservative Temperature. [1/(g/kg)]
- pt_CT_CT : array_like
- The second derivative of potential temperature (the regular one
- with p_ref = 0 dbar) with respect to Conservative Temperature at
- constant SA. [1/K]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (A.12.9) and (A.12.10).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of seawater
- in
- terms of Conservative Temperature, and related properties of seawater.
- To be submitted to Ocean Science Discussions.
- """
-
- # Increment of Absolute Salinity is 0.001 g/kg.
- dSA = 1e-3
- SA_l = SA - dSA
- SA_l = np.maximum(SA_l, 0)
- SA_u = SA + dSA
- pt_SA_l, pt_CT_l = pt_first_derivatives(SA_l, CT)
- pt_SA_u, pt_CT_u = pt_first_derivatives(SA_u, CT)
- pt_SA_SA = (pt_SA_u - pt_SA_l) / (SA_u - SA_l)
- # Can calculate this either way.
- # pt_SA_CT = (pt_CT_u - pt_CT_l) / (SA_u - SA_l)
-
- dCT = 1e-2
- CT_l = CT - dCT
- CT_u = CT + dCT
- pt_SA_l, pt_CT_l = pt_first_derivatives(SA, CT_l)
- pt_SA_u, pt_CT_u = pt_first_derivatives(SA, CT_u)
-
- pt_SA_CT = (pt_SA_u - pt_SA_l) / (CT_u - CT_l)
- pt_CT_CT = (pt_CT_u - pt_CT_l) / (CT_u - CT_l)
-
- return pt_SA_SA, pt_SA_CT, pt_CT_CT
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/earth.py b/gsw/gibbs/earth.py
deleted file mode 100644
index 7088ac6..0000000
--- a/gsw/gibbs/earth.py
+++ /dev/null
@@ -1,198 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from .conversions import z_from_p
-from ..utilities import match_args_return
-from .constants import gamma, earth_radius, OMEGA
-
-
-__all__ = ['distance',
- 'f',
- 'grav']
-
-DEG2RAD = np.pi / 180
-
-
- at match_args_return
-def distance(lon, lat, p=0):
- """
- Calculates the distance in met res between successive points in the
- vectors lon and lat, computed using the Haversine formula on a spherical
- earth of radius 6,371 km, being the radius of a sphere having the same
- volume as Earth. For a spherical Earth of radius 6,371,000 m, one nautical
- mile is 1,853.2488 m, thus one degree of latitude is 111,194.93 m.
-
- Haversine formula:
- R = earth's radius (mean radius = 6,371 km)
-
- .. math::
- a = \sin^2(\delta \text{lat}/2) +
- \cos(\text{lat}_1) \cos(\text{lat}_2) \sin^2(\delta \text{lon}/2)
-
- c = 2 \times \text{atan2}(\sqrt{a}, \sqrt{(1-a)})
-
- d = R \times c
-
- Parameters
- ----------
- lon : array_like
- decimal degrees east [0..+360] or [-180 ... +180]
- lat : array_like
- latitude in decimal degrees north [-90..+90]
- p : number or array_like. Default p = 0
- pressure [dbar]
-
- Returns
- -------
- dist: array_like
- distance between points on a spherical Earth at pressure (p) [m]
-
- Notes
- -----
- z is height and is negative in the oceanographic.
-
- Distances are probably good to better than 1\% of the "true" distance on
- the ellipsoidal earth.
-
- Examples
- --------
- >>> import gsw
- >>> lon = [159, 220]
- >>> lat = [-35, 35]
- >>> gsw.distance(lon, lat)
- array([[ 10030974.652916]])
- >>> p = [200, 1000]
- >>> gsw.distance(lon, lat, p)
- array([[ 10030661.63927133]])
- >>> p = [[200], [1000]]
- >>> gsw.distance(lon, lat, p)
- array([[ 10030661.63927133],
- [ 10029412.58932955]])
-
- References
- ----------
- .. [1] http://www.eos.ubc.ca/~rich/map.html
-
- """
- lon, lat, = np.atleast_2d(lon), np.atleast_2d(lat)
-
- if (lon.size == 1) & (lat.size == 1):
- raise ValueError('more than one point is needed to compute distance')
- elif lon.ndim != lat.ndim:
- raise ValueError('lon, lat must have the same dimension')
-
- lon, lat, p = np.broadcast_arrays(lon, lat, p, subok=True)
-
- dlon = np.diff(lon * DEG2RAD)
- dlat = np.diff(lat * DEG2RAD)
-
- a = ((np.sin(dlat / 2)) ** 2 + np.cos(lat[:, :-1] * DEG2RAD) *
- np.cos(lat[:, 1:] * DEG2RAD) * (np.sin(dlon / 2)) ** 2)
-
- angles = 2 * np.arctan2(np.sqrt(a), np.sqrt(1 - a))
-
- p_mid = 0.5 * (p[:, 0:-1] + p[:, 0:-1])
- lat_mid = 0.5 * (lat[:, :-1] + lat[:, 1:])
-
- z = z_from_p(p_mid, lat_mid)
-
- distance = (earth_radius + z) * angles
-
- return distance
-
-
-def f(lat):
- """
- Calculates the Coriolis parameter (f) defined by:
- f = 2*omega*sin(lat)
- where,
- omega = 7.292115e-5 (Groten, 2004) [radians s :sup:`-1`]
-
- Parameters
- ----------
- lat : array_like
- latitude [degrees north]
-
- Returns
- -------
- f : array_like
- Coriolis paramter [s :sup:`-1`]
-
- References
- ----------
- .. [1] Groten, E., 2004: Fundamental Parameters and Current (2004) Best
- Estimates of the Parameters of Common Relevance to Astronomy, Geodesy,
- and Geodynamics. Journal of Geodesy, 77, pp. 724-797.
-
- .. [2] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- lat = np.asanyarray(lat)
- return 2 * OMEGA * np.sin(lat * DEG2RAD)
-
-
- at match_args_return
-def grav(lat, p=0):
- """
- Calculates acceleration due to gravity as a function of latitude and as
- a function of pressure in the ocean.
-
- Parameters
- ----------
- lat : array_like
- latitude in decimal degrees north [-90...+90]
- p : number or array_like. Default p = 0
- pressure [dbar]
-
- Returns
- -------
- g : array_like
- gravity [m s :sup:`2`]
-
- Notes
- -----
- In the ocean z is negative.
-
- Examples
- --------
- >>> import gsw
- >>> lat = [-90, -60, -30, 0]
- >>> p = 0
- >>> gsw.grav(lat, p)
- array([ 9.83218621, 9.81917886, 9.79324926, 9.780327 ])
- >>> gsw.grav(45)
- 9.8061998770458008
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
-
- .. [2] Moritz (2000) Goedetic reference system 1980. J. Geodesy, 74,
- 128-133.
-
- .. [3] Saunders, P.M., and N.P. Fofonoff (1976) Conversion of pressure to
- depth in the ocean. Deep-Sea Res.,pp. 109 - 111.
- """
-
- X = np.sin(lat * DEG2RAD)
- sin2 = X ** 2
- gs = 9.780327 * (1.0 + (5.2792e-3 + (2.32e-5 * sin2)) * sin2)
- z = z_from_p(p, lat)
- # z is the height corresponding to p.
- grav = gs * (1 - gamma * z)
-
- return grav
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/freezing.py b/gsw/gibbs/freezing.py
deleted file mode 100644
index 33082ac..0000000
--- a/gsw/gibbs/freezing.py
+++ /dev/null
@@ -1,525 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from .constants import SSO
-from .conversions import t_from_CT, CT_from_t
-from ..utilities import match_args_return
-
-__all__ = ['brineSA_CT',
- 'brineSA_t',
- 'CT_freezing',
- 't_freezing']
-
-# Constants:
-c = (0.017947064327968736, -6.076099099929818, 4.883198653547851,
- -11.88081601230542, 13.34658511480257, -8.722761043208607,
- 2.082038908808201, -7.389420998107497, -2.110913185058476,
- 0.2295491578006229, -0.9891538123307282, -0.08987150128406496,
- 0.3831132432071728, 1.054318231187074, 1.065556599652796,
- -0.7997496801694032, 0.3850133554097069, -2.078616693017569,
- 0.8756340772729538, -2.079022768390933, 1.596435439942262,
- 0.1338002171109174, 1.242891021876471)
-
-T = (0.002519, -5.946302841607319, 4.136051661346983,
- -1.115150523403847e1, 1.476878746184548e1, -1.088873263630961e1,
- 2.961018839640730, -7.433320943962606, -1.561578562479883,
- 4.073774363480365e-2, 1.158414435887717e-2, -4.122639292422863e-1,
- -1.123186915628260e-1, 5.715012685553502e-1, 2.021682115652684e-1,
- 4.140574258089767e-2, -6.034228641903586e-1, -1.205825928146808e-2,
- -2.812172968619369e-1, 1.877244474023750e-2, -1.204395563789007e-1,
- 2.349147739749606e-1, 2.748444541144219e-3)
-
-# Adjust for the effects of dissolved air. Note that
-# a = 0.502500117621 / 35.16504
-a, b = 0.014289763856964, 0.057000649899720
-
-P = (2.570124672768757e-1, -1.917742353032266e+1, -1.413382858617969e-2,
- -5.427484830917552e-1, -4.126621135193472e-4, -4.176407833276121e-7,
- 4.688217641883641e-5, -3.039808885885726e-8, -4.990118091261456e-11,
- -9.733920711119464e-9, -7.723324202726337e-12, 7.121854166249257e-16,
- 1.256474634100811e-12, 2.105103897918125e-15, 8.663811778227171e-19)
-
-
- at match_args_return
-def brineSA_CT(CT, p, saturation_fraction=1):
- """
- Calculates the Absolute Salinity of seawater at the freezing
- temperature. That is, the output is the Absolute Salinity of seawater,
- with the fraction saturation_fraction of dissolved air, that is in
- equilibrium with ice at Conservative Temperature CT and pressure p. If the
- input values are such that there is no positive value of Absolute Salinity
- for which seawater is frozen, the output, brineSA_CT, is put equal to -99.
-
- Parameters
- ----------
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
- saturation_fraction : fraction between 0, 1. The saturation fraction of
- dissolved air in seawater. Default is 0 or
- completely saturated.
-
- Returns
- -------
- brine_SA_CT : array_like
- Absolute Salinity of seawater when it freezes [ g/kg ]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See sections 3.33.
- """
-
- CT, p, saturation_fraction = np.broadcast_arrays(CT, p,
- saturation_fraction,
- subok=True)
-
- if np.logical_or(saturation_fraction < 0, saturation_fraction > 1).any():
- raise ValueError('Saturation_fraction MUST be between zero and one.')
-
- p_r = p * 1e-4
- # Form the first estimate of brine_SA_CT from a polynomial in CT and p_r.
- SA = -(CT + 9 * p_r) / 0.06 # A rough estimate to get the saturated CT.
-
- SA = np.maximum(SA, 0)
-
- CTsat = (CT - (1 - saturation_fraction) * 1e-3 * (2.4 - a * SA) *
- (1 + b * (1 - SA / SSO)))
-
- SA = (P[0] + p * (P[2] + P[4] * CTsat + p * (P[5] + CTsat * (P[7] + P[9] *
- CTsat) + p * (P[8] + CTsat * (P[10] + P[12] * CTsat) + p * (P[11] +
- P[13] * CTsat + P[14] * p)))) + CTsat * (P[1] + CTsat *
- (P[3] + P[6] * p)))
-
- CT_freezing_zero_SA = (c[0] + p_r * (c[7] + p_r * (c[8] + c[9] * p_r)) -
- saturation_fraction * 2.4e-3 * (1 + b))
-
- # Find CT > CT_freezing_zero_SA. If this is the case, the input values
- # represent seawater that is not frozen (at any positive SA).
- Itw = (CT > CT_freezing_zero_SA) # tw stands for "too warm"
- SA[Itw] = np.ma.masked
-
- # Find -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
- # with one based on (CT_freezing_zero_SA - CT).
- SA_cut_off = 2.5 # This is the band of SA within +- 2.5 g/kg of SA = 0,
- # which we treat differently in calculating the initial
- # values of both SA and dCT_dSA.
-
- Ico = (np.abs(SA) < SA_cut_off)
- Icoa = np.logical_and(SA < 0, SA >= -SA_cut_off)
-
- SA[Icoa] = 0
-
- # Find SA < -SA_cut_off, set them to NaN.
- SA[SA < -SA_cut_off] = np.ma.masked
-
- # Form the first estimate of dCT_dSA, the derivative of CT with respect
- # to SA at fixed p.
- SA_r = 0.01 * SA
- x = np.sqrt(SA_r)
-
- dCT_dSA_part = (2 * c[1] + x * (3 * c[2] + x * (4 * c[3] + x * (5 * c[4] +
- x * (6 * c[5] + 7 * c[6] * x)))) + p_r * (2 * c[10] + p_r *
- (2 * c[12] + p_r * (2 * c[15] + 4 * c[21] * x * x)) + x *
- x * (4 * c[13] + 4 * c[17] * p_r + 6 * c[19] * x * x) + x *
- (3 * c[11] + 3 * p_r * (c[14] + c[18] * p_r) + x * x * (5 *
- c[16] + 5 * c[20] * p_r + 7 * c[22] * x * x))))
-
- dCT_dSA = 0.5 * 0.01 * dCT_dSA_part - saturation_fraction * 1e-3 * (-a *
- (1 + b * (1 - SA / SSO)) - b * (2.4 - a * SA) / SSO)
-
- # Now replace the estimate of SA with the one based on
- # (CT_freezing_zero_SA - CT) when (np.abs(SA) < SA_cut_off).
- SA[Ico] = (CT[Ico] - CT_freezing_zero_SA[Ico]) / dCT_dSA[Ico]
-
- # Begin the modified Newton-Raphson method to solve the root of
- # CT_freezing = CT for SA.
- Number_of_Iterations = 2
- for I_iter in range(0, Number_of_Iterations):
- # CT_freezing temperature function evaluation (the forward function
- # evaluation), the same as CT_freezing(SA, p, saturation_fraction).
-
- SA_r = 0.01 * SA
- x = np.sqrt(SA_r)
- SA_old = SA
- CT_freeze = (c[0] + SA_r * (c[1] + x * (c[2] + x * (c[3] + x * (c[4] +
- x * (c[5] + c[6] * x))))) + p_r * (c[7] + p_r * (c[8] +
- c[9] * p_r)) + SA_r * p_r * (c[10] + p_r * (c[12] + p_r *
- (c[15] + c[21] * SA_r)) + SA_r * (c[13] + c[17] * p_r +
- c[19] * SA_r) + x * (c[11] + p_r * (c[14] + c[18] * p_r) +
- SA_r * (c[16] + c[20] * p_r + c[22] * SA_r))) -
- saturation_fraction * 1e-3 * (2.4 - a * SA) * (1 + b *
- (1 - SA / SSO)))
-
- SA = SA_old - (CT_freeze - CT) / dCT_dSA
-
- # Half-way point of the modified Newton-Raphson solution method.
- SA_r = 0.5 * 0.01 * (SA + SA_old) # The mean value of SA and SA_old.
- x = np.sqrt(SA_r)
-
- dCT_dSA_part = 2 * c[1] + x * (3 * c[2] + x * (4 * c[3] + x * (5 *
- c[4] + x * (6 * c[5] + 7 * c[6] * x)))) + p_r * (2 *
- c[10] + p_r * (2 * c[12] + p_r * (2 * c[15] + 4 *
- c[21] * x * x)) + x * x * (4 * c[13] + 4 * c[17] *
- p_r + 6 * c[19] * x * x) + x * (3 * c[11] + 3 * p_r *
- (c[14] + c[18] * p_r) + x * x * (5 * c[16] + 5 * c[20] *
- p_r + 7 * c[22] * x * x)))
-
- dCT_dSA = (0.5 * 0.01 * dCT_dSA_part - saturation_fraction * 1e-3 *
- (-a * (1 + b * (1 - SA / SSO)) - b * (2.4 - a * SA) / SSO))
-
- SA = SA_old - (CT_freeze - CT) / dCT_dSA
-
- # The following lines of code, if implemented, calculates the error of
- # this function in terms of Conservative Temperature, CT_error. With
- # Number_of_Iterations = 1, the maximum error in CT is 2x10^-7 C. With
- # Number_of_Iterations = 2, the maximum error in CT is 7x10^-15 C, which is
- # the machine precision of the computer. Number_of_Iterations = 2 is what
- # we recommend.
- #
- # SA_r = 0.01 * SA
- # x = np.sqrt(SA_r)
- # CT_freeze = c[0] + SA_r * (c[1] + x * (c[2] + x * (c[3] + x * (c[4] + x *
- # (c[5] + c[6] * x))))) + p_r * (c[7] + p_r * (c[8] + c[9] *
- # p_r)) + SA_r * p_r * (c[10] + p_r * (c[12] + p_r * (c[15] +
- # c[21] * SA_r)) + SA_r * (c[13] + c[17] * p_r + c[19] * SA_r)
- # + x * (c[11] + p_r * (c[14] + c[18] * p_r) + SA_r * (c[16] +
- # c[20] * p_r + c[22] * SA_r))) - saturation_fraction * 1e-3 *
- # (2.4 - a * SA) * (1 + b * (1 - SA / SSO))
- #
- # CT_error = np.abs(CT_freeze - CT)
- #
- # tmp = np.logical_or(p > 10000, SA > 120
- # out = np.logical_and(tmp, p + SA * 71.428571428571402 > 13571.42857142857)
- # CT_error[out] = np.ma.masked
-
- brine_SA_CT = SA
-
- tmp = np.logical_or(p > 10000, SA > 120)
- out = np.logical_and(tmp, p + SA * 71.428571428571402 > 13571.42857142857)
-
- brine_SA_CT[out] = np.ma.masked
-
- # If the CT input is too warm, then there is no (positive) value of SA
- # that represents frozen seawater.
- brine_SA_CT[Itw] = -99 # NOTE: Mask these?
-
- return brine_SA_CT
-
-
- at match_args_return
-def brineSA_t(t, p, saturation_fraction=1):
- """
- Calculates the Absolute Salinity of seawater at the freezing temperature.
- That is, the output is the Absolute Salinity of seawater, with the fraction
- saturation_fraction of dissolved air, that is in equilibrium with ice at
- in-situ temperature t and pressure p. If the input values are such that
- there is no positive value of Absolute Salinity for which seawater is
- frozen, the output, brineSA_t, is put equal to -99.
-
- Parameters
- ----------
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
- saturation_fraction : fraction between 0, 1. The saturation fraction of
- dissolved air in seawater. Default is 0 or
- completely saturated.
-
- Returns
- -------
- brine_SA_t : array_like
- Absolute Salinity of seawater when it freezes [ g/kg ]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See sections 3.33.
- """
-
- t, p, saturation_fraction = np.broadcast_arrays(t, p, saturation_fraction,
- subok=True)
-
- if np.logical_or(saturation_fraction < 0, saturation_fraction > 1).any():
- raise ValueError('Saturation_fraction MUST be between zero and one.')
-
- p_r = p * 1e-4
-
- # Form the first estimate of brine_SA_t, called SA here, from a polynomial
- # in CT and p_r.
- SA = -(t + 9 * p_r) / 0.06 # A rough estimate to get the saturated CT.
-
- SA = np.maximum(SA, 0)
-
- CT = CT_from_t(SA, t, p)
- CTsat = CT - (1 - saturation_fraction) * 1e-3 * (2.4 - a * SA) * (1 + b *
- (1 - SA / SSO))
-
- SA = P[0] + p * (P[2] + P[4] * CTsat + p * (P[5] + CTsat * (P[7] +
- P[9] * CTsat) + p * (P[8] + CTsat * (P[10] + P[12] * CTsat) + p *
- (P[11] + P[13] * CTsat + P[14] * p)))) + CTsat * (P[1] + CTsat *
- (P[3] + P[6] * p))
-
- t_freezing_zero_SA = t_freezing(np.zeros_like(t), p, saturation_fraction)
-
- # Find t > t_freezing_zero_SA. If this is the case, the input values
- # represent seawater that is not frozen (at any positive SA).
- Itw = (t > t_freezing_zero_SA) # Itw stands for "I_too_warm"
- SA[Itw] = np.ma.masked
-
- # Find -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
- # with one based on (t_freezing_zero_SA - t).
- SA_cut_off = 2.5 # This is the band of SA within +- 2.5 g/kg of SA = 0,
- # which we treat differently in calculating the initial
- # values of both SA and dCT_dSA.
-
- Ico = (np.abs(SA) < SA_cut_off)
- Icoa = np.logical_and(SA < 0, SA >= -SA_cut_off)
- SA[Icoa] = 0
-
- # Find SA < -SA_cut_off, set them to masked.
- SA[SA < -SA_cut_off] = np.ma.masked
-
- # Form the first estimate of dt_dSA, the derivative of t with respect
- # to SA at fixed p, using the coefficients, t0 ... t22 from t_freezing.
- SA_r = 0.01 * SA
- x = np.sqrt(SA_r)
- dt_dSA_part = 2 * T[1] + x * (3 * T[2] + x * (4 * T[3] + x * (5 * T[4] +
- x * (6 * T[5] + 7 * T[6] * x)))) + p_r * (2 * T[10] + p_r * (2 * T[12] +
- p_r * (2 * T[15] + 4 * T[21] * x * x)) + x * x * (4 * T[13] + 4 * T[17] *
- p_r + 6 * T[19] * x * x) + x * (3 * T[11] + 3 * p_r * (T[14] + T[18] *
- p_r) + x * x * (5 * T[16] + 5 * T[20] * p_r + 7 * T[22] * x * x)))
-
- dt_dSA = 0.5 * 0.01 * dt_dSA_part + saturation_fraction * 1e-3 / 70.33008
-
- # Now replace the estimate of SA with the one based on
- # (t_freezing_zero_SA - t) when (abs(SA) < SA_cut_off).
- SA[Ico] = (t[Ico] - t_freezing_zero_SA[Ico]) / dt_dSA[Ico]
-
- # Begin the modified Newton-Raphson method to find the root of
- # t_freeze = t for SA.
- Number_of_Iterations = 5
- for I_iter in range(0, Number_of_Iterations):
- SA_old = SA
- t_freeze = t_freezing(SA_old, p, saturation_fraction)
- SA = SA_old - (t_freeze - t) / dt_dSA
- # Half-way point of the modified Newton-Raphson solution method.
- SA_r = 0.5 * 0.01 * (SA + SA_old) # Mean value of SA and SA_old.
- x = np.sqrt(SA_r)
- dt_dSA_part = (2 * T[1] + x * (3 * T[2] + x * (4 * T[3] + x * (5 *
- T[4] + x * (6 * T[5] + 7 * T[6] * x)))) + p_r *
- (2 * T[10] + p_r * (2 * T[12] + p_r * (2 * T[15] + 4 *
- T[21] * x * x)) + x * x * (4 * T[13] + 4 * T[17] * p_r +
- 6 * T[19] * x * x) + x * (3 * T[11] + 3 * p_r * (T[14] +
- T[18] * p_r) + x * x * (5 * T[16] + 5 * T[20] * p_r +
- 7 * T[22] * x * x))))
-
- dt_dSA = (0.5 * 0.01 * dt_dSA_part + saturation_fraction * 1e-3 /
- 70.33008)
-
- SA = SA_old - (t_freeze - t) / dt_dSA
-
- # The following lines of code, if implemented, calculate the error of this
- # function in terms of in-situ temperature. With Number_of_Iterations = 4,
- # the max error in t is 3x10^-13 C. With Number_of_Iterations = 5, the max
- # error in t is 2x10^-14 C, which is the machine precision of the computer.
- # Number_of_Iterations = 5 is what we recommend.
- #
- # SA[SA < 0] = np.ma.masked
- #
- # t_freeze = t_freezing(SA, p, saturation_fraction)
- # t_error = np.abs(t_freeze - t)
- # tmp = np.logical_or(p > 10000, SA > 120)
- # out = np.logical_and(tmp, p + SA * 71.428571428571402 > 13571.42857142857)
- # t_error[out] = np.ma.masked
-
- brine_SA_t = SA
- tmp = np.logical_or(p > 10000, SA > 120)
- out = np.logical_and(tmp, p + SA * 71.428571428571402 > 13571.42857142857)
- brine_SA_t[out] = np.ma.masked
-
- brine_SA_t[Itw] = -99 # If the t input is too warm, then there is no
- # (positive) value of SA that represents frozen
- # seawater.
-
- return brine_SA_t
-
-
- at match_args_return
-def CT_freezing(SA, p, saturation_fraction=1):
- """
- Calculates the Conservative Temperature at which seawater freezes.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- p : array_like
- sea pressure [dbar]
- saturation_fraction : fraction between 0, 1. The saturation fraction of
- dissolved air in seawater. Default is 0 or
- completely saturated.
-
- Returns
- -------
- CT_freezing : array_like
- Conservative Temperature at freezing of
- seawater [:math:`^\circ` C (ITS-90)]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See sections 3.33 and 3.34.
- """
-
- SA, p, saturation_fraction = np.broadcast_arrays(SA, p,
- saturation_fraction,
- subok=True)
- if (SA < 0).any():
- raise ValueError('SA must be non-negative!')
-
- if np.logical_or(saturation_fraction < 0, saturation_fraction > 1).any():
- raise ValueError('Saturation_fraction MUST be between zero and one.')
-
- SA_r = SA * 1e-2
- x = np.sqrt(SA_r)
- p_r = p * 1e-4
-
- CT_freeze = (c[0] + SA_r * (c[1] + x * (c[2] + x * (c[3] + x * (c[4] +
- x * (c[5] + c[6] * x))))) + p_r * (c[7] + p_r * (c[8] +
- c[9] * p_r)) + SA_r * p_r * (c[10] + p_r * (c[12] + p_r *
- (c[15] + c[21] * SA_r)) + SA_r * (c[13] + c[17] * p_r +
- c[19] * SA_r) + x * (c[11] + p_r * (c[14] + c[18] * p_r) +
- SA_r * (c[16] + c[20] * p_r + c[22] * SA_r))))
-
- # The error of this fit ranges between -5e-4 K and 6e-4 K when compared
- # with the Conservative Temperature calculated from the exact in-situ
- # freezing temperature which is found by a Newton-Raphson iteration of the
- # equality of the chemical potentials of water in seawater and in ice.
- # (Note that the in-situ freezing temperature can be found by this exact
- # method using the function sea_ice_freezingtemperature_si in the SIA
- # library).
-
- # Adjust for the effects of dissolved air.
- a, b = 0.014289763856964, 0.057000649899720
- # Note that a = 0.502500117621 / 35.16504
-
- CT_freeze = (CT_freeze - saturation_fraction * (1e-3) *
- (2.4 - a * SA) * (1 + b * (1 - SA / 35.16504)))
-
- tmp = np.logical_or(p > 10000, SA > 120)
- out = np.logical_or(tmp, p + SA * 71.428571428571402 > 13571.42857142857)
-
- CT_freeze[out] = np.ma.masked
-
- return CT_freeze
-
-
- at match_args_return
-def t_freezing(SA, p, saturation_fraction=1):
- """
- Calculates the in-situ temperature at which seawater freezes.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- p : array_like
- sea pressure [dbar]
- saturation_fraction : fraction between 0, 1. The saturation fraction of
- dissolved air in seawater. Default is 0 or
- completely saturated.
-
- Returns
- -------
- t_freezing : array_like
- in-situ temperature at which seawater freezes
- [:math:`^\circ` C (ITS-90)]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See sections 3.33 and 3.34.
- """
-
- # This function, t_freezing, calculates the in-situ freezing temperature,
- # t_freezing, of seawater by first evaluating a polynomial of the
- # Conservative Temperature at which seawater freezes, CT_freezing, using
- # the GSW function CT_freezing. The in-situ freezing temperature is then
- # calculated using the GSW function t_from_CT. However, if one wanted to
- # compute the in-situ freezing temperature directly from a single polynomial
- # expression without first calculating the Conservative Temperature at the
- # freezing point, the following lines of code achieve this. The error of the
- # following fit is similar to that of the present function, t_freezing, and
- # ranges between -8e-4 K and 3e-4 K when compared with the in-situ freezing
- # temperature evaluated by Newton-Raphson iteration of the equality of the
- # chemical potentials of water in seawater and in ice. (Note that the
- # in-situ freezing temperature can be found by this exact method using the
- # function sea_ice_freezingtemperature_si in the SIA library).
- #
- # SA_r = SA * 1e-2
- # x = np.sqrt(SA_r)
- # p_r = p * 1e-4
- #
- # t_freeze = T[0] + SA_r * (T[1] + x * (T[2] + x * (T[3] + x * (T[4] + x *
- # (T[5] + T[6] * x))))) + p_r * (T[7] + p_r * (T[8] + T[9] *
- # p_r)) + SA_r * p_r * (T[10] + p_r * (T[12] + p_r * (T[15] +
- # T[21] * SA_r)) + SA_r * (T[13] + T[17] * p_r + T[19] * SA_r) +
- # x * (T[11] + p_r * (T[14] + T[18] * p_r) + SA_r * (T[16] +
- # T[20] * p_r + T[22] * SA_r)))
- #
- # Adjust for the effects of dissolved air
- # t_freezing -= saturation_fraction * (1e-3) * (2.4 - SA / 70.33008)
-
- SA, p, saturation_fraction = np.broadcast_arrays(SA, p,
- saturation_fraction,
- subok=True)
- if (SA < 0).any():
- raise ValueError('SA must be non-negative!')
-
- if np.logical_or(saturation_fraction < 0, saturation_fraction > 1).any():
- raise ValueError('Saturation_fraction MUST be between zero and one.')
-
- CT_freeze = CT_freezing(SA, p, saturation_fraction)
-
- t_freeze = t_from_CT(SA, CT_freeze, p)
-
- tmp = np.logical_or(p > 10000, SA > 120)
- out = np.logical_or(tmp, p + SA * 71.428571428571402 > 13571.42857142857)
-
- t_freeze[out] = np.ma.masked
-
- return t_freeze
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/geostrophic.py b/gsw/gibbs/geostrophic.py
deleted file mode 100644
index 63ebcc1..0000000
--- a/gsw/gibbs/geostrophic.py
+++ /dev/null
@@ -1,17 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-__all__ = []
-#__all__ = ['geostrophic_velocity'] # TODO
-
-
-#def geostrophic_velocity():
-# pass
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/geostrophic_48.py b/gsw/gibbs/geostrophic_48.py
deleted file mode 100644
index cf83a24..0000000
--- a/gsw/gibbs/geostrophic_48.py
+++ /dev/null
@@ -1,42 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-__all__ = []
-# 'geo_strf_Cunningham', # TODO
-# 'geo_strf_dyn_height', # TODO
-# 'geo_strf_dyn_height_pc', # TODO
-# 'geo_strf_isopycnal', # TODO
-# 'geof_str_isopycnal_pc', # TODO
-# 'geo_strf_Montgomery'] # TODO
-
-
-#def geo_strf_Cunningham():
-# pass
-
-
-#def geo_strf_dyn_height():
-# pass
-
-
-#def geo_strf_dyn_height_pc():
-# pass
-
-
-#def geo_strf_isopycnal():
-# pass
-
-
-#def geof_str_isopycnal_pc():
-# pass
-
-
-#def geo_strf_Montgomery():
-# pass
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/isobaric.py b/gsw/gibbs/isobaric.py
deleted file mode 100644
index 132edaa..0000000
--- a/gsw/gibbs/isobaric.py
+++ /dev/null
@@ -1,57 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-from .conversions import CT_from_pt
-from ..utilities import match_args_return
-
-
-__all__ = ['latentheat_evap_t']
-# 'latentheat_evap_CT',
-# 'latentheat_melting',
-
-
-#@match_args_return
-#def latentheat_evap_CT(SA, CT):
-# pass
-
-
-#@match_args_return
-#def latentheat_melting(SA, p):
-# pass
-
-
- at match_args_return
-def latentheat_evap_t(SA, t):
- """
- Calculates latent heat, or enthalpy, of evaporation at p = 0 (the
- surface). It is defined as a function of Absolute Salinity, SA, and
- in-situ temperature, t, and is valid in the ranges 0 < SA < 40 g/kg and
- 0 < CT < 42 deg C. The errors range between -0.4 and 0.6 J/kg.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- latentheat_evap_t : array_like
- latent heat of evaporation [J kg :sup:`-1`]
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.39.
- """
-
- CT = CT_from_pt(SA, t)
- return latentheat_evap_CT(SA, CT)
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/library.py b/gsw/gibbs/library.py
deleted file mode 100644
index 2268414..0000000
--- a/gsw/gibbs/library.py
+++ /dev/null
@@ -1,1780 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from .constants import sfac, SSO, db2Pascal
-from ..utilities import match_args_return, strip_mask, read_data
-
-__all__ = ['deltaSA_atlas',
- 'enthalpy_SSO_0',
- 'enthalpy_SSO_0_p',
- 'entropy_part',
- 'entropy_part_zerop',
- 'Fdelta', # Seems to be new in V3.
- 'gibbs',
- 'gibbs_pt0_pt0',
- 'Hill_ratio_at_SP2',
- 'infunnel',
- 'interp_ref_cast',
- 'interp_SA_CT',
- 'SAAR', # New in V3.
- 'SA_from_SP_Baltic',
- 'specvol_SSO_0_p',
- 'SP_from_SA_Baltic']
-
-
-h006 = -2.1078768810e-9
-h007 = 2.8019291329e-10
-
-
-class SA_table(object):
- """
- TODO: Write docstring.
- """
- # Central America barrier
- x_ca = np.array([260.0, 272.59, 276.5, 278.65, 280.73, 295.217])
- y_ca = np.array([19.55, 13.97, 9.6, 8.1, 9.33, 0.0])
-
- def __init__(self, fname="gsw_data_v3_0.npz", max_p_fudge=10000,
- min_frac=0):
- self.fname = fname
- self.max_p_fudge = max_p_fudge
- self.min_frac = min_frac
- data = read_data(fname)
- self.lon = data.longs_ref.astype(np.float)
- self.lat = data.lats_ref.astype(np.float)
- self.p = data.p_ref # Depth levels
- self.dlon = self.lon[1] - self.lon[0]
- self.dlat = self.lat[1] - self.lat[0]
- self.i_ca, self.j_ca = self.xy_to_ij(self.x_ca, self.y_ca)
- # Make the order x, y, z:
- # Start with deltaSA_ref (was delta_SA_ref in V2):
- temp = data.deltaSA_ref.transpose((2, 1, 0)).copy()
- self.dsa_ref = np.ma.masked_invalid(temp)
- self.dsa_ref.data[self.dsa_ref.mask] = 0
- # Now SAAR_ref, which did not exist in V2:
- temp = data.SAAR_ref.transpose((2, 1, 0)).copy()
- self.SAAR_ref = np.ma.masked_invalid(temp)
- self.SAAR_ref.data[self.SAAR_ref.mask] = 0
-
- def xy_to_ij(self, x, y):
- """
- Convert from lat/lon to grid index coordinates,
- without truncation or rounding.
- """
- i = (x - self.lon[0]) / self.dlon
- j = (y - self.lat[0]) / self.dlat
- return i, j
-
- def _central_america(self, di, dj, ii, jj, gm):
- """
- Use a line running through Central America to zero
- the goodmask for grid points in the Pacific forming
- the grid box around input locations in the Atlantic,
- and vice-versa.
- """
- ix, jy = ii[0] + di, jj[0] + dj # Reconstruction: minor inefficiency.
- inear = ((ix >= self.i_ca[0]) & (ix <= self.i_ca[-1])
- & (jy >= self.j_ca[-1]) & (jy <= self.j_ca[0]))
- if not inear.any():
- return gm
- inear_ind = inear.nonzero()[0]
- ix = ix[inear]
- jy = jy[inear]
- ii = ii[:, inear]
- jj = jj[:, inear]
- jy_ca = np.interp(ix, self.i_ca, self.j_ca)
- above = jy - jy_ca # > 0 if input point is above dividing line
- # Intersections of left and right grid lines with dividing line
- jleft_ca = np.interp(ii[0], self.i_ca, self.j_ca)
- jright_ca = np.interp(ii[1], self.i_ca, self.j_ca)
- jgrid_ca = [jleft_ca, jright_ca, jright_ca, jleft_ca]
- # Zero the goodmask for grid points on opposite side of divider
- for i in range(4):
- opposite = (above * (jj[i] - jgrid_ca[i])) < 0
- gm[i, inear_ind[opposite]] = 0
- return gm
-
- def xy_interp(self, di, dj, ii, jj, k):
- """
- 2-D interpolation, bilinear if all 4 surrounding
- grid points are present, but treating missing points
- as having the average value of the remaining grid
- points. This matches the matlab V2 behavior.
- """
- # Array of weights, CCW around the grid box
- w = np.vstack(((1 - di) * (1 - dj), # lower left
- di * (1 - dj), # lower right
- di * dj, # upper right
- (1 - di) * dj)) # upper left
- gm = ~self.dsa.mask[ii, jj, k] # gm is "goodmask"
- gm = self._central_america(di, dj, ii, jj, gm)
- # Save a measure of real interpolation quality.
- frac = (w * gm).sum(axis=0)
- # Now loosen the interpolation, allowing a value to
- # be calculated on a grid point that is masked.
- # This matches the matlab gsw version 2 behavior.
- jm_partial = gm.any(axis=0) & (~(gm.all(axis=0)))
- # The weights of the unmasked points will be increased
- # by the sum of the weights of the masked points divided
- # by the number of unmasked points in the grid square.
- # This is equivalent to setting the masked data values
- # to the average of the unmasked values, and then
- # unmasking, which is the matlab v2 implementation.
- if jm_partial.any():
- w_bad = w * (~gm)
- w[:, jm_partial] += (w_bad[:, jm_partial].sum(axis=0) /
- gm[:, jm_partial].sum(axis=0))
- w *= gm
- wsum = w.sum(axis=0)
- valid = wsum > 0 # Only need to prevent division by zero here.
- w[:, valid] /= wsum[valid]
- w[:, ~valid] = 0
- vv = self.dsa.data[ii, jj, k]
- vv *= w
- dsa = vv.sum(axis=0)
- return dsa, frac
-
- def _delta_SA(self, p, lon, lat):
- """
- Table lookup engine--to be called only from SAAR or SA_ref.
- """
- p = np.ma.masked_less(p, 0)
- mask_in = np.ma.mask_or(np.ma.getmask(p), np.ma.getmask(lon))
- mask_in = np.ma.mask_or(mask_in, np.ma.getmask(lat))
- p, lon, lat = [np.ma.filled(a, 0).astype(float) for a in (p, lon, lat)]
- p, lon, lat = np.broadcast_arrays(p, lon, lat)
- if p.ndim > 1:
- shape_in = p.shape
- p, lon, lat = list(map(np.ravel, (p, lon, lat)))
- reshaped = True
- else:
- reshaped = False
- p_orig = p.copy() # Save for comparison to clipped p.
- ix0, iy0 = self.xy_to_ij(lon, lat)
- i0raw = np.floor(ix0).astype(int)
- i0 = np.clip(i0raw, 0, len(self.lon) - 2)
- di = ix0 - i0
- j0raw = np.floor(iy0).astype(int)
- j0 = np.clip(j0raw, 0, len(self.lat) - 2)
- dj = iy0 - j0
- # Start at lower left and go CCW; match order in _xy_interp.
- ii = np.vstack((i0, i0 + 1, i0 + 1, i0))
- jj = np.vstack((j0, j0, j0 + 1, j0 + 1))
- k1 = np.searchsorted(self.p, p, side='right')
- # Clip p and k1 at max p of grid cell.
- kmax = (self.ndepth[ii, jj].max(axis=0) - 1)
- mask_out = kmax.mask
- kmax = kmax.filled(1)
- clip_p = (p >= self.p[kmax])
- p[clip_p] = self.p[kmax[clip_p]]
- k1[clip_p] = kmax[clip_p]
- k0 = k1 - 1
- dsa0, frac0 = self.xy_interp(di, dj, ii, jj, k0)
- dsa1, frac1 = self.xy_interp(di, dj, ii, jj, k1)
- dp = np.diff(self.p)
- pfrac = (p - self.p[k0]) / dp[k0]
- delta_SA = dsa0 * (1 - pfrac) + dsa1 * pfrac
- # Save intermediate results in case we are curious about
- # them; the frac values are most likely to be useful.
- # We won't bother to reshape them, though, and we may
- # delete them later.
- self.dsa0 = dsa0
- self.frac0 = frac0
- self.dsa1 = dsa1
- self.frac1 = frac1
- self.pfrac = pfrac
- self.p_fudge = p_orig - p
- # Editing options, in case we don't want to use
- # values calculated from the wrong pressure, or from
- # an incomplete SA table grid square.
- # mask_out |= self.p_fudge > self.max_p_fudge
- # mask_out |= self.frac1 < self.min_frac
- # delta_SA = np.ma.array(delta_SA, mask=mask_out, copy=False)
- # Later on, it is expected to be a masked array.
- delta_SA = np.ma.array(delta_SA, copy=False)
- if reshaped:
- delta_SA.shape = shape_in
- self.p_fudge.shape = shape_in
- if mask_in is not np.ma.nomask:
- delta_SA = np.ma.array(delta_SA, mask=mask_in, copy=False)
- return delta_SA
-
- def SAAR(self, p, lon, lat):
- """
- Table lookup of salinity anomaly ratio, given pressure, lon, and lat.
- """
- self.dsa = self.SAAR_ref
- # In V2,
- # ndepth from the file disagrees with the unmasked count from
- # SAAR_ref in a few places; this should be fixed in the
- # file, but for now we will simply calculate ndepth directly from
- # SAAR_ref.
- # TODO: check to see whether this discrepancy is also found in V3.
- # TODO: check: do we even need to calculate ndepth? It doesn't
- # appear to be used for anything.
- # self.ndepth = np.ma.masked_invalid(data.ndepth_ref.T).astype(np.int8)
- ndepth = self.dsa.count(axis=-1)
- self.ndepth = np.ma.masked_equal(ndepth, 0)
- return self._delta_SA(p, lon, lat)
-
- def delta_SA_ref(self, p, lon, lat):
- """
- Table lookup of salinity anomaly reference value, given pressure,
- lon, and lat.
- """
- self.dsa = self.dsa_ref
- # See comment in previous method.
- ndepth = self.dsa.count(axis=-1)
- self.ndepth = np.ma.masked_equal(ndepth, 0)
- return self._delta_SA(p, lon, lat)
-
-
-def Fdelta(p, lon, lat):
- """
- Fdelta from the Absolute Salinity Anomaly Ratio (SAAR):
- Fdelta = (1 + r1)SAAR/(1 - r1*SAAR)
- = (SA/Sstar) - 1
- with r1 being the constant 0.35 based on the work of Pawlowicz et al.
- (2011). Note that since SAAR is everywhere less than 0.001 in the global
- ocean, Fdelta is only slightly different to 1.35*SAAR.
-
- Parameters
- ----------
- p : array_like
- pressure [dbar]
- lon : array_like
- decimal degrees east (will be treated modulo 360)
- lat : array_like
- decimal degrees (+ve N, -ve S) [-90..+90]
-
- Returns
- -------
- Fdelta : masked array; masked where no nearby ocean is found in data
- Ratio of SA to Sstar, minus 1 [unitless]
-
- Notes
- -----
- The mask is only set when the observation is well and truly on dry
- land; often the warning flag is not set until one is several hundred
- kilometers inland from the coast.
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Available from http://www.TEOS-10.org
- See section 2.5 and appendices A.4 and A.5 of this TEOS-10 Manual.
-
- .. [2] McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and
- P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity.
- Ocean Science, 8, 1123-1134.
- http://www.ocean-sci.net/8/1123/2012/os-8-1123-2012.pdf
-
- .. [3] Pawlowicz, R., D.G. Wright and F.J. Millero, 2011; The effects of
- biogeochemical processes on oceanic conductivity/salinty/density
- relationships and the characterization of real seawater. Ocean Science,
- 7, 363-387. http://www.ocean-sci.net/7/363/2011/os-7-363-2011.pdf
- """
-
- r = 0.35
- saar, _ = SAAR(p, lon, lat)
- Fdelta = ((1 + r) * saar) / (1 - r * saar)
- return Fdelta
-
-
- at match_args_return
-def Hill_ratio_at_SP2(t):
- """
- USAGE:
- Hill_ratio = Hill_ratio_at_SP2(t)
-
- DESCRIPTION:
- Calculates the Hill ratio, which is the adjustment needed to apply for
- Practical Salinities smaller than 2. This ratio is defined at a
- Practical Salinity = 2 and in-situ temperature, t using PSS-78. The Hill
- ratio is the ratio of 2 to the output of the Hill et al. (1986) formula
- for Practical Salinity at the conductivity ratio, Rt, at which Practical
- Salinity on the PSS-78 scale is exactly 2.
-
- INPUT:
- t = in-situ temperature (ITS-90) [ deg C ]
-
- OUTPUT:
- Hill_ratio = Hill ratio at SP of 2 [ unitless ]
-
- AUTHOR:
- Trevor McDougall and Paul Barker
-
- VERSION NUMBER: 3.0 (26th March, 2011)
- """
-
- SP2 = 2 * np.ones_like(t)
-
- a0 = 0.0080
- a1 = -0.1692
- a2 = 25.3851
- a3 = 14.0941
- a4 = -7.0261
- a5 = 2.7081
- b0 = 0.0005
- b1 = -0.0056
- b2 = -0.0066
- b3 = -0.0375
- b4 = 0.0636
- b5 = -0.0144
- g0 = 2.641463563366498e-1
- g1 = 2.007883247811176e-4
- g2 = -4.107694432853053e-6
- g3 = 8.401670882091225e-8
- g4 = -1.711392021989210e-9
- g5 = 3.374193893377380e-11
- g6 = -5.923731174730784e-13
- g7 = 8.057771569962299e-15
- g8 = -7.054313817447962e-17
- g9 = 2.859992717347235e-19
- k = 0.0162
- t68 = t * 1.00024
- ft68 = (t68 - 15) / (1 + k * (t68 - 15))
- # -------------------------------------------------------------------------
- # Find the initial estimates of Rtx (Rtx0) and of the derivative dSP_dRtx
- # at SP = 2.
- # -------------------------------------------------------------------------
- Rtx0 = g0 + t68 * (g1 + t68 * (g2 + t68 * (g3 + t68 * (g4 + t68 * (g5
- + t68 * (g6 + t68 * (g7 + t68 * (g8 + t68 * g9))))))))
- dSP_dRtx = (a1 + (2 * a2 + (3 * a3 + (4 * a4 + 5 * a5 * Rtx0) * Rtx0) *
- Rtx0) * Rtx0 + ft68 * (b1 + (2 * b2 + (3 * b3 + (4 * b4 + 5 *
- b5 * Rtx0) * Rtx0) * Rtx0) * Rtx0))
- # -------------------------------------------------------------------------
- # Begin a single modified Newton-Raphson iteration to find Rt at SP = 2.
- # -------------------------------------------------------------------------
- SP_est = (a0 + (a1 + (a2 + (a3 + (a4 + a5 * Rtx0) * Rtx0) * Rtx0) * Rtx0) *
- Rtx0 + ft68 * (b0 + (b1 + (b2 + (b3 + (b4 + b5 * Rtx0) * Rtx0) *
- Rtx0) * Rtx0) * Rtx0))
- Rtx = Rtx0 - (SP_est - SP2) / dSP_dRtx
- Rtxm = 0.5 * (Rtx + Rtx0)
- dSP_dRtx = (a1 + (2 * a2 + (3 * a3 + (4 * a4 + 5 * a5 * Rtxm) * Rtxm) *
- Rtxm) * Rtxm + ft68 * (b1 + (2 * b2 + (3 * b3 + (4 * b4 + 5 *
- b5 * Rtxm) * Rtxm) * Rtxm) * Rtxm))
- Rtx = Rtx0 - (SP_est - SP2) / dSP_dRtx
- # This is the end of one full iteration of the modified Newton-Raphson
- # iterative equation solver. The error in Rtx at this point is equivalent
- # to an error in SP of 9e-16 psu.
- x = 400 * Rtx * Rtx
- sqrty = 10 * Rtx
- part1 = 1 + x * (1.5 + x)
- part2 = 1 + sqrty * (1 + sqrty * (1 + sqrty))
- SP_Hill_raw_at_SP2 = SP2 - a0 / part1 - b0 * ft68 / part2
- return 2. / SP_Hill_raw_at_SP2
-
-
- at match_args_return
-def SAAR(p, lon, lat):
- """
- Absolute Salinity Anomaly Ratio (excluding the Baltic Sea).
- Calculates the Absolute Salinity Anomaly Ratio, SAAR, in the open ocean
- by spatially interpolating the global reference data set of SAAR to the
- location of the seawater sample.
- This function uses version 3.0 of the SAAR look up table.
-
- Parameters
- ----------
- p : array_like
- pressure [dbar]
- lon : array_like
- decimal degrees east (will be treated modulo 360)
- lat : array_like
- decimal degrees (+ve N, -ve S) [-90..+90]
-
- Returns
- -------
- SAAR : array
- Absolute Salinity Anomaly Ratio [unitless]
- in_ocean : boolean array
-
- Notes
- -----
- The Absolute Salinity Anomaly Ratio in the Baltic Sea is evaluated
- separately, since it is a function of Practical Salinity, not of space.
- The present function returns a SAAR of zero for data in the Baltic Sea.
- The correct way of calculating Absolute Salinity in the Baltic Sea is by
- calling SA_from_SP.
- The in_ocean flag is only set when the observation is well and truly on dry
- land; often the warning flag is not set until one is several hundred
- kilometers inland from the coast.
-
- The algorithm is taken from the matlab implementation of the references,
- but the numpy implementation here differs substantially from the
- matlab implementation.
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
-
- .. [2] McDougall, T.J., D.R. Jackett and F.J. Millero, 2010: An algorithm
- for estimating Absolute Salinity in the global ocean. Submitted to
- Ocean Science. A preliminary version is available at Ocean Sci.
- Discuss., 6, 215-242.
- http://www.ocean-sci-discuss.net/6/215/2009/osd-6-215-2009-print.pdf
- """
-
- saar = SA_table().SAAR(p, lon, lat)
- return saar, ~saar.mask
-
-
-def SA_from_SP_Baltic(SP, lon, lat):
- """
- Computes absolute salinity from practical in the Baltic Sea.
-
- Parameters
- ----------
- SP : array_like or masked array
- Practical salinity (PSS-78)
- lon, lat : array_like or masked arrays
- geographical position
-
- Returns
- -------
- SA : masked array, at least 1D
- Absolute salinity [g/kg]
- masked where inputs are masked or position outside the Baltic
- """
-
- # Handle masked array input
- input_mask = False
- if np.ma.is_masked(SP):
- input_mask = input_mask | SP.mask
- if np.ma.is_masked(lon):
- input_mask = input_mask | lon.mask
- if np.ma.is_masked(lat):
- input_mask = input_mask | lat.mask
- SP, lon, lat = list(map(np.atleast_1d, (SP, lon, lat)))
- SP, lon, lat = np.broadcast_arrays(SP, lon, lat)
- inds_baltic = in_Baltic(lon, lat)
- # SA_baltic = np.ma.masked_all(SP.shape, dtype=np.float)
- all_nans = np.nan + np.zeros_like(SP)
- SA_baltic = np.ma.MaskedArray(all_nans, mask=~inds_baltic)
- if np.any(inds_baltic):
- SA_baltic[inds_baltic] = (((SSO - 0.087) / 35) *
- SP[inds_baltic] + 0.087)
- SA_baltic.mask = SA_baltic.mask | input_mask | np.isnan(SP)
- return SA_baltic
-
-
-def SP_from_SA_Baltic(SA, lon, lat):
- """
- Calculates Practical Salinity (SP) for the Baltic Sea, from a value
- computed analytically from Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- lon : array_like
- decimal degrees east [0..+360]
- lat : array_like
- decimal degrees (+ve N, -ve S) [-90..+90]
-
- Returns
- -------
- SP_baltic : array_like
- salinity [psu (PSS-78)], unitless
-
- See Also
- --------
- SP_from_SA, SP_from_Sstar
-
- Notes
- -----
- This program will only produce Practical Salinity values for the Baltic
- Sea.
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] Feistel, R., S. Weinreben, H. Wolf, S. Seitz, P. Spitzer, B. Adel,
- G. Nausch, B. Schneider and D. G. Wright, 2010c: Density and Absolute
- Salinity of the Baltic Sea 2006-2009. Ocean Science, 6, 3-24.
- http://www.ocean-sci.net/6/3/2010/os-6-3-2010.pdf
-
- .. [2] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
-
- .. [3] McDougall, T.J., D.R. Jackett and F.J. Millero, 2010: An algorithm
- for estimating Absolute Salinity in the global ocean. Submitted to Ocean
- Science. A preliminary version is available at Ocean Sci. Discuss.,
- 6, 215-242.
- http://www.ocean-sci-discuss.net/6/215/2009/osd-6-215-2009-print.pdf
- """
-
- SA, lon, lat = list(map(np.ma.masked_invalid, (SA, lon, lat)))
- lon, lat, SA = np.broadcast_arrays(lon, lat, SA)
- inds_baltic = in_Baltic(lon, lat)
- if not inds_baltic.sum():
- return None
- SP_baltic = np.ma.masked_all(SA.shape, dtype=np.float)
- SP_baltic[inds_baltic] = ((35 / (SSO - 0.087)) *
- (SA[inds_baltic] - 0.087))
- return SP_baltic
-
-
-# FIXME: Check if this is still used and remove it.
-def SP_from_SA_Baltic_old(SA, lon, lat):
- """
- Calculates Practical Salinity (SP) for the Baltic Sea, from a value
- computed analytically from Absolute Salinity.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- lon : array_like
- decimal degrees east [0..+360]
- lat : array_like
- decimal degrees (+ve N, -ve S) [-90..+90]
-
- Returns
- -------
- SP_baltic : array_like
- salinity [psu (PSS-78)], unitless
-
- See Also
- --------
- SP_from_SA, SP_from_Sstar
-
- Notes
- -----
- This program will only produce Practical Salinity values for the Baltic
- Sea.
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] Feistel, R., S. Weinreben, H. Wolf, S. Seitz, P. Spitzer, B. Adel,
- G. Nausch, B. Schneider and D. G. Wright, 2010c: Density and Absolute
- Salinity of the Baltic Sea 2006-2009. Ocean Science, 6, 3-24.
- http://www.ocean-sci.net/6/3/2010/os-6-3-2010.pdf
-
- .. [2] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
-
- .. [3] McDougall, T.J., D.R. Jackett and F.J. Millero, 2010: An algorithm
- for estimating Absolute Salinity in the global ocean. Submitted to Ocean
- Science. A preliminary version is available at Ocean Sci. Discuss.,
- 6, 215-242.
- http://www.ocean-sci-discuss.net/6/215/2009/osd-6-215-2009-print.pdf
- """
-
- SA, lon, lat = list(map(np.ma.masked_invalid, (SA, lon, lat)))
- lon, lat, SA = np.broadcast_arrays(lon, lat, SA, subok=True)
- xb1, xb2, xb3 = 12.6, 7., 26.
- xb1a, xb3a = 45., 26.
- yb1, yb2, yb3 = 50., 59., 69.
- inds_baltic = (xb2 < lon) & (lon < xb1a) & (yb1 < lat) & (lat < yb3)
- if not inds_baltic.sum():
- return None
- SP_baltic = np.ma.masked_all(SA.shape, dtype=np.float)
- xx_left = np.interp(lat[inds_baltic], [yb1, yb2, yb3], [xb1, xb2, xb3])
- xx_right = np.interp(lat[inds_baltic], [yb1, yb3], [xb1a, xb3a])
- inds_baltic1 = ((xx_left <= lon[inds_baltic]) &
- (lon[inds_baltic] <= xx_right))
- if not inds_baltic1.sum():
- return None
- SP_baltic[inds_baltic[inds_baltic1]] = ((35 / (SSO - 0.087)) *
- (SA[inds_baltic[inds_baltic1]] -
- 0.087))
- return SP_baltic
-
-
- at match_args_return
-def deltaSA_atlas(p, lon, lat):
- """
- Absolute Salinity anomaly atlas value (excluding the Baltic Sea).
- Calculates the Absolute Salinity anomaly atlas value, SA - SR,
- in the open ocean by spatially interpolating the global reference
- data set of deltaSA_atlas to the location of the seawater sample.
- This function uses version 3.0 of the deltaSA_ref look up table.
-
- Parameters
- ----------
- p : array_like
- sea pressure (absolute pressure - 10.1325 dbar) [dbar]
- lon : array_like
- decimal degrees east (will be treated modulo 360)
- lat : array_like
- decimal degrees (+ve N, -ve S) [-90..+90]
-
- Returns
- -------
- deltaSA_atlas : masked array; masked where no nearby ocean is found in data
- Absolute Salinity anomaly atlas value [g/kg]
-
- Notes
- -----
- The Absolute Salinity anomaly atlas value in the Baltic Sea is
- evaluated separately, since it is a function of Practical Salinity,
- not of space. The present function returns a deltaSA_atlas of zero
- for data in the Baltic Sea. The correct way of calculating Absolute
- Salinity in the Baltic Sea is by calling SA_from_SP.
- The mask is only set when the observation is well and truly on dry
- land; often the warning flag is not set until one is several hundred
- kilometers inland from the coast.
-
- The algorithm is taken from the Matlab implementation of the references,
- but the numpy implementation here differs substantially from the
- Matlab implementation.
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
-
- .. [2] McDougall, T.J., D.R. Jackett and F.J. Millero, 2010: An algorithm
- for estimating Absolute Salinity in the global ocean. Submitted to Ocean
- Science. A preliminary version is available at Ocean Sci. Discuss.,
- 6, 215-242.
- http://www.ocean-sci-discuss.net/6/215/2009/osd-6-215-2009-print.pdf
- """
- return SA_table().delta_SA_ref(p, lon, lat)
-
-
-def enthalpy_SSO_0_CT25(p):
- """
- Calculates enthalpy at the Standard Ocean Salinity (SSO) and at a
- Conservative Temperature of zero degrees C (CT=0), as a function of
- pressure (p [dbar]) or enthalpy_CT25(35.16504,0,p).
-
- Parameters
- ----------
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- enthalpy_CT25 : array_like
- enthalpy_CT25 at (SSO, CT = 0, p), 25-term equation.
- [J kg :sup:`-1`]
-
- Notes
- -----
- Uses a streamlined version of the 25-term CT version of the Gibbs function,
- that is, a streamlined version of the code "enthalpy_CT25(SA,CT,p)"
- """
-
- p = np.asanyarray(p)
- mask = np.ma.getmask(p)
- p = np.ma.filled(p, 0)
- a0 = 1 + SSO * (2.0777716085618458e-3 + np.sqrt(SSO) *
- 3.4688210757917340e-6)
- a1 = 6.8314629554123324e-6
- b0 = 9.9984380290708214e2 + SSO * (2.8925731541277653e0 + SSO *
- 1.9457531751183059e-3)
- b1 = 0.5 * (1.1930681818531748e-2 + SSO * 5.9355685925035653e-6)
- b2 = -2.5943389807429039e-8
- A = b1 - np.sqrt(b1 ** 2 - b0 * b2)
- B = b1 + np.sqrt(b1 ** 2 - b0 * b2)
- part = (a0 * b2 - a1 * b1) / (b2 * (B - A))
- enthalpy_SSO_0_CT25 = (db2Pascal * ((a1 / (2 * b2)) *
- np.log(1 + p * (2 * b1 + b2 * p) / b0) + part *
- np.log(1 + (b2 * p * (B - A)) /
- (A * (B + b2 * p)))))
- return np.ma.array(enthalpy_SSO_0_CT25, mask=mask, copy=False)
-
-
-def enthalpy_SSO_0(p):
- """
- Enthalpy at SSO and CT(T=0) (75-term equation)
-
- This function calculates enthalpy at the Standard Ocean Salinty, SSO,
- and at a Conservative Temperature of zero degrees C, as a function of
- pressure, p, in dbar, using a streamlined version of the 75-term
- computationally-efficient expression for specific volume, that is, a
- streamlined version of the code "enthalpy(SA,CT,p)".
-
- Parameters
- ----------
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- enthalpy_SSO_0 : array_like
- enthalpy at (SSO, CT=0, p)
- [J kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> p = np.array([10, 50, 125, 250, 600, 1000])
- >>> gsw.library.enthalpy_SSO_0(p)
- array([ 97.26388583, 486.27439853, 1215.47517122, 2430.24907325,
- 5827.90879421, 9704.32030926])
-
- References
- ----------
- .. [1] Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
- polynomial expressions for the density and specifc volume of
- seawater using the TEOS-10 standard. Ocean Modelling.
- """
-
- z = p * 1e-4
-
- dynamic_enthalpy_SSO_0_p = z * (9.726613854843870e-4 + z * (
- -2.252956605630465e-5 + z * (2.376909655387404e-6 + z * (
- -1.664294869986011e-7 + z * (-5.988108894465758e-9 + z * (
- h006 + h007 * z))))))
-
- return dynamic_enthalpy_SSO_0_p * db2Pascal * 1e4
-
-
-# FIXME: Check if this is still used and remove it.
-def enthalpy_SSO_0_p(p):
- """
- This function calculates enthalpy at the Standard Ocean Salinty, SSO,
- and at a Conservative Temperature of zero degrees C, as a function of
- pressure, p, in dbar, using a streamlined version of the 48-term CT
- version of the Gibbs function, that is, a streamlined version of the
- code "enthalpy(SA,CT,p).
-
- Examples
- --------
- >>> import gsw
- >>> p = np.array([10, 50, 125, 250, 600, 1000])
- >>> gsw.library.enthalpy_SSO_0_p(p)
- array([ 97.26388276, 486.27439004, 1215.47518168, 2430.24919716,
- 5827.90973888, 9704.32296903])
-
- References
- ----------
- .. [1] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2013: A
- computationally efficient 48-term expression for the density of seawater
- in terms of Conservative Temperature, and related properties of
- seawater. To be submitted to J. Atm. Ocean. Technol., xx, yyy-zzz.
- """
-
- v01 = 9.998420897506056e+2
- v05 = -6.698001071123802
- v08 = -3.988822378968490e-2
- v12 = -2.233269627352527e-2
- v15 = -1.806789763745328e-4
- v17 = -3.087032500374211e-7
- v20 = 1.550932729220080e-10
- v21 = 1.0
- v26 = -7.521448093615448e-3
- v31 = -3.303308871386421e-5
- v36 = 5.419326551148740e-6
- v37 = -2.742185394906099e-5
- v41 = -1.105097577149576e-7
- v43 = -1.119011592875110e-10
- v47 = -1.200507748551599e-15
- a0 = v21 + SSO * (v26 + v36 * SSO + v31 * np.sqrt(SSO))
- a1 = v37 + v41 * SSO
- a2 = v43
- a3 = v47
- b0 = v01 + SSO * (v05 + v08 * np.sqrt(SSO))
- b1 = 0.5 * (v12 + v15 * SSO)
- b2 = v17 + v20 * SSO
- b1sq = b1 ** 2
- sqrt_disc = np.sqrt(b1sq - b0 * b2)
- N = a0 + (2 * a3 * b0 * b1 / b2 - a2 * b0) / b2
- M = a1 + (4 * a3 * b1sq / b2 - a3 * b0 - 2 * a2 * b1) / b2
- A = b1 - sqrt_disc
- B = b1 + sqrt_disc
- part = (N * b2 - M * b1) / (b2 * (B - A))
- return (db2Pascal * (p * (a2 - 2 * a3 * b1 / b2 + 0.5 * a3 * p) / b2 +
- (M / (2 * b2)) * np.log(1 + p * (2 * b1 + b2 * p) / b0) + part *
- np.log(1 + (b2 * p * (B - A)) / (A * (B + b2 * p)))))
-
-
-def entropy_part(SA, t, p):
- """
- Calculates entropy, except that it does not evaluate any terms that are
- functions of Absolute Salinity alone.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- entropy_part : array_like
- entropy minus the terms that due to SA alone
- [J kg :sup:`-1` K :sup:`-1`]
-
- Notes
- -----
- By not calculating these terms, which are a function only of Absolute
- Salinity, several unnecessary computations are avoided (including saving
- the computation of a natural logarithm). These terms are a necessary part
- of entropy, but are not needed when calculating potential temperature from
- in situ temperature.
- """
-
- SA, t, p, mask = strip_mask(SA, t, p)
- x2 = sfac * SA
- x = np.sqrt(x2)
- y = t * 0.025
- z = p * 1e-4
- g03 = (z * (-270.983805184062 + z * (776.153611613101 + z *
- (-196.51255088122 + (28.9796526294175 - 2.13290083518327 * z) *
- z))) + y * (-24715.571866078 + z * (2910.0729080936 + z *
- (-1513.116771538718 + z * (546.959324647056 + z *
- (-111.1208127634436 + 8.68841343834394 * z)))) + y *
- (2210.2236124548363 + z * (-2017.52334943521 + z *
- (1498.081172457456 + z * (-718.6359919632359 +
- (146.4037555781616 - 4.9892131862671505 * z) * z))) + y *
- (-592.743745734632 + z * (1591.873781627888 + z *
- (-1207.261522487504 + (608.785486935364 - 105.4993508931208 * z) *
- z)) + y * (290.12956292128547 + z * (-973.091553087975 + z *
- (602.603274510125 + z * (-276.361526170076 + 32.40953340386105 *
- z))) + y * (-113.90630790850321 + y * (21.35571525415769 -
- 67.41756835751434 * z) + z * (381.06836198507096 + z *
- (-133.7383902842754 + 49.023632509086724 * z))))))))
-
- g08 = (x2 * (z * (729.116529735046 + z * (-343.956902961561 + z *
- (124.687671116248 + z * (-31.656964386073 + 7.04658803315449 *
- z)))) + x * (x * (y * (-137.1145018408982 + y *
- (148.10030845687618 + y * (-68.5590309679152 + 12.4848504784754 *
- y))) - 22.6683558512829 * z) + z * (-175.292041186547 +
- (83.1923927801819 - 29.483064349429 * z) * z) + y *
- (-86.1329351956084 + z * (766.116132004952 + z *
- (-108.3834525034224 + 51.2796974779828 * z)) + y *
- (-30.0682112585625 - 1380.9597954037708 * z + y *
- (3.50240264723578 + 938.26075044542 * z)))) + y *
- (1760.062705994408 + y * (-675.802947790203 + y *
- (365.7041791005036 + y * (-108.30162043765552 + 12.78101825083098 *
- y) + z * (-1190.914967948748 + (298.904564555024 -
- 145.9491676006352 * z) * z)) + z * (2082.7344423998043 + z *
- (-614.668925894709 + (340.685093521782 - 33.3848202979239 * z) *
- z))) + z * (-1721.528607567954 + z * (674.819060538734 + z *
- (-356.629112415276 + (88.4080716616 - 15.84003094423364 * z) *
- z))))))
-
- entropy_part = -(g03 + g08) * 0.025
- return np.ma.array(entropy_part, mask=mask, copy=False)
-
-
-def entropy_part_zerop(SA, pt0):
- """
- Calculates entropy at a sea surface (p = 0 dbar), except that it does
- not evaluate any terms that are functions of Absolute Salinity alone.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- pt0 : array_like
- potential temperature relative to 0 dbar [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- entropy_part_zerop : array_like
- [J kg :sup:`-1` K :sup:`-1`]
-
- Notes
- -----
- By not calculating these terms, which are a function only of Absolute
- Salinity, several unnecessary computations are avoided (including saving
- the computation of a natural logarithm). These terms are a necessary part
- of entropy, but are not needed when calculating potential temperature from
- in situ temperature.
- """
-
- SA, pt0, mask = strip_mask(SA, pt0)
- x2 = sfac * SA
- x = np.sqrt(x2)
- y = pt0 * 0.025
- g03 = y * (-24715.571866078 + y * (2210.2236124548363 +
- y * (-592.743745734632 + y * (290.12956292128547 +
- y * (-113.90630790850321 + y * 21.35571525415769)))))
- g08 = x2 * (x * (x * (y * (-137.1145018408982 + y *
- (148.10030845687618 +
- y * (-68.5590309679152 + 12.4848504784754 * y)))) +
- y * (-86.1329351956084 + y * (-30.0682112585625 + y *
- 3.50240264723578))) +
- y * (1760.062705994408 + y * (-675.802947790203 +
- y * (365.7041791005036 + y * (-108.30162043765552 +
- 12.78101825083098 * y)))))
- entropy_part_zerop = -(g03 + g08) * 0.025
- return np.ma.array(entropy_part_zerop, mask=mask, copy=False)
-
-
-# FIXME: Check if this is still used and remove it.
-def gibbs(ns, nt, npr, SA, t, p):
- """
- Calculates specific Gibbs energy and its derivatives up to order 2 for
- seawater.
- The Gibbs function approach allows the calculation of internal energy,
- entropy, enthalpy, potential enthalpy and the chemical potentials of
- seawater as well as the freezing temperature, and the latent heats of
- freezing and of evaporation. These quantities were not available from
- EOS-80 but are essential for the accurate accounting of heat in the ocean
- and for the consistent and accurate treatment of air-sea and ice-sea heat
- fluxes.
-
- Parameters
- ----------
- ns : int
- order of SA derivative [0, 1 or 2 ]
- nt : int
- order of t derivative [0, 1 or 2 ]
- npr : int
- order of p derivative [0, 1 or 2 ]
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- gibbs : array_like
- Specific Gibbs energy or its derivatives.
- Gibbs energy (ns=nt=npr=0) has units of:
- [J kg :sup:`-1`]
- Absolute Salinity derivatives are output in units of:
- [(J kg :sup:`-1`) (g kg :sup:`-1`) :sup:`-ns`]
- Temperature derivatives are output in units of:
- [(J kg :sup:`-1`) K :sup:`-nt`]
- Pressure derivatives are output in units of:
- [(J kg :sup:`-1`) Pa :sup:`-npr`]
- The mixed derivatives are output in units of:
- [(J kg :sup:`-1`) (g kg :sup:`-1`) :sup:`-ns` K :sup:`-nt`
- Pa :sup:`-npr`]
-
- Notes
- -----
- The Gibbs function for seawater is that of TEOS-10 (IOC et al., 2010),
- being the sum of IAPWS-08 for the saline part and IAPWS-09 for the pure
- water part. These IAPWS releases are the officially blessed IAPWS
- descriptions of Feistel (2008) and the pure water part of Feistel (2003).
- Absolute Salinity, SA, in all of the GSW routines is expressed on the
- Reference-Composition Salinity Scale of 2008 (RCSS-08) of Millero et al.
- (2008).
- The derivatives are taken with respect to pressure in Pa, not withstanding
- that the pressure input into this routine is in dbar.
-
- References
- ----------
- .. [1] Feistel, R., 2003: A new extended Gibbs thermodynamic potential of
- seawater Progr. Oceanogr., 58, 43-114.
-
- .. [2] Feistel, R., 2008: A Gibbs function for seawater thermodynamics
- for -6 to 80 :math:`^\circ` C and salinity up to 120 g kg :sup:`-1`,
- Deep-Sea Res. I, 55, 1639-1671.
-
- .. [3] IAPWS, 2008: Release on the IAPWS Formulation 2008 for the
- Thermodynamic Properties of Seawater. The International Association for
- the Properties of Water and Steam. Berlin, Germany, September 2008,
- available from http://www.iapws.org. This Release is referred to as
- IAPWS-08.
-
- .. [4] IAPWS, 2009: Supplementary Release on a Computationally Efficient
- Thermodynamic Formulation for Liquid Water for Oceanographic Use. The
- International Association for the Properties of Water and Steam.
- Doorwerth, The Netherlands, September 2009, available from
- http://www.iapws.org. This Release is referred to as IAPWS-09.
-
- .. [5] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.6 and appendices A.6, G and H.
-
- .. [6] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
- The composition of Standard Seawater and the definition of the
- Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.
- """
-
- SA, t, p = np.asanyarray(SA), np.asanyarray(t), np.asanyarray(p)
- SA = np.atleast_1d(SA)
- nonzero_SA = np.any(SA > 0)
- _SA = SA
- _t = t
- _p = p
- SA = np.ma.filled(SA, 0)
- t = np.ma.filled(t, 20)
- p = np.ma.filled(p, 10)
- SA, t, p = np.broadcast_arrays(SA, t, p)
- gibbs = np.zeros(SA.shape, dtype=np.float) # Use if all_masked is True
- all_masked = False
- # Ensure a full mask, so we can set elements if necessary.
- mask = np.ma.mask_or(np.ma.getmaskarray(_SA), np.ma.getmask(_t))
- mask = np.ma.mask_or(mask, np.ma.getmask(_p))
- mask = np.ma.mask_or(mask, SA < 0)
- ipos = (SA > 0)
- # inpos = ~ipos # FIXME: Assigned but never used.
- if np.all(ipos):
- ipos = slice(None) # More efficient for usual case.
- x2 = sfac * SA
- x = np.sqrt(x2)
- y = t * 0.025
- z = p * 1e-4 # The input pressure (p) is sea pressure in units of dbar.
- if (ns == 0) & (nt == 0) & (npr == 0):
- g03 = (101.342743139674 + z * (100015.695367145 +
- z * (-2544.5765420363 + z * (284.517778446287 +
- z * (-33.3146754253611 + (4.20263108803084 - 0.546428511471039 * z)
- * z)))) +
- y * (5.90578347909402 + z * (-270.983805184062 +
- z * (776.153611613101 + z * (-196.51255088122 + (28.9796526294175 -
- 2.13290083518327 * z) * z))) +
- y * (-12357.785933039 + z * (1455.0364540468 +
- z * (-756.558385769359 + z * (273.479662323528 + z *
- (-55.5604063817218 + 4.34420671917197 * z)))) +
- y * (736.741204151612 + z * (-672.50778314507 +
- z * (499.360390819152 + z * (-239.545330654412 + (48.8012518593872 -
- 1.66307106208905 * z) * z))) +
- y * (-148.185936433658 + z * (397.968445406972 +
- z * (-301.815380621876 + (152.196371733841 - 26.3748377232802 * z) *
- z)) +
- y * (58.0259125842571 + z * (-194.618310617595 +
- z * (120.520654902025 + z * (-55.2723052340152 +
- 6.48190668077221 * z))) +
- y * (-18.9843846514172 + y * (3.05081646487967 -
- 9.63108119393062 * z) +
- z * (63.5113936641785 + z * (-22.2897317140459 +
- 8.17060541818112 * z)))))))))
- if nonzero_SA:
- g08 = x2 * (1416.27648484197 + z * (-3310.49154044839 +
- z * (384.794152978599 + z * (-96.5324320107458 +
- (15.8408172766824 - 2.62480156590992 * z) * z))) +
- x * (-2432.14662381794 + x * (2025.80115603697 +
- y * (543.835333000098 + y * (-68.5572509204491 +
- y * (49.3667694856254 + y * (-17.1397577419788 +
- 2.49697009569508 * y))) - 22.6683558512829 * z) +
- x * (-1091.66841042967 - 196.028306689776 * y +
- x * (374.60123787784 - 48.5891069025409 * x +
- 36.7571622995805 * y) + 36.0284195611086 * z) +
- z * (-54.7919133532887 + (-4.08193978912261 -
- 30.1755111971161 * z) * z)) +
- z * (199.459603073901 + z * (-52.2940909281335 +
- (68.0444942726459 - 3.41251932441282 * z) * z)) +
- y * (-493.407510141682 + z * (-175.292041186547 +
- (83.1923927801819 - 29.483064349429 * z) * z) +
- y * (-43.0664675978042 + z * (383.058066002476 + z *
- (-54.1917262517112 + 25.6398487389914 * z)) +
- y * (-10.0227370861875 - 460.319931801257 * z + y *
- (0.875600661808945 + 234.565187611355 * z))))) +
- y * (168.072408311545 + z * (729.116529735046 +
- z * (-343.956902961561 + z * (124.687671116248 + z *
- (-31.656964386073 + 7.04658803315449 * z)))) +
- y * (880.031352997204 + y * (-225.267649263401 +
- y * (91.4260447751259 + y * (-21.6603240875311 +
- 2.13016970847183 * y) +
- z * (-297.728741987187 + (74.726141138756 -
- 36.4872919001588 * z) * z)) +
- z * (694.244814133268 + z * (-204.889641964903 +
- (113.561697840594 - 11.1282734326413 * z) * z))) +
- z * (-860.764303783977 + z * (337.409530269367 +
- z * (-178.314556207638 + (44.2040358308 -
- 7.92001547211682 * z) * z))))))
- g08[ipos] += x2[ipos] * (5812.81456626732 + 851.226734946706 *
- y[ipos]) * np.log(x[ipos])
- else:
- g08 = 0
- gibbs = g03 + g08
- elif (ns == 1) & (nt == 0) & (npr == 0):
- if nonzero_SA:
- g08 = (8645.36753595126 + z * (-6620.98308089678 +
- z * (769.588305957198 + z * (-193.0648640214916 +
- (31.6816345533648 - 5.24960313181984 * z) * z))) +
- x * (-7296.43987145382 + x * (8103.20462414788 +
- y * (2175.341332000392 + y * (-274.2290036817964 +
- y * (197.4670779425016 + y * (-68.5590309679152 +
- 9.98788038278032 * y))) - 90.6734234051316 * z) +
- x * (-5458.34205214835 - 980.14153344888 * y +
- x * (2247.60742726704 - 340.1237483177863 * x +
- 220.542973797483 * y) + 180.142097805543 * z) +
- z * (-219.1676534131548 + (-16.32775915649044 -
- 120.7020447884644 * z) * z)) +
- z * (598.378809221703 + z * (-156.8822727844005 +
- (204.1334828179377 - 10.23755797323846 * z) * z)) +
- y * (-1480.222530425046 + z * (-525.876123559641 +
- (249.57717834054571 - 88.449193048287 * z) * z) +
- y * (-129.1994027934126 + z * (1149.174198007428 +
- z * (-162.5751787551336 + 76.9195462169742 * z)) +
- y * (-30.0682112585625 - 1380.9597954037708 * z + y *
- (2.626801985426835 + 703.695562834065 * z))))) +
- y * (1187.3715515697959 + z * (1458.233059470092 +
- z * (-687.913805923122 + z * (249.375342232496 + z *
- (-63.313928772146 + 14.09317606630898 * z)))) +
- y * (1760.062705994408 + y * (-450.535298526802 +
- y * (182.8520895502518 + y * (-43.3206481750622 +
- 4.26033941694366 * y) +
- z * (-595.457483974374 + (149.452282277512 -
- 72.9745838003176 * z) * z)) +
- z * (1388.489628266536 + z * (-409.779283929806 +
- (227.123395681188 - 22.2565468652826 * z) * z))) +
- z * (-1721.528607567954 + z * (674.819060538734 +
- z * (-356.629112415276 + (88.4080716616 -
- 15.84003094423364 * z) * z))))))
- g08[ipos] = g08[ipos] + (11625.62913253464 + 1702.453469893412 *
- y[ipos]) * np.log(x[ipos])
- gibbs = 0.5 * sfac * g08
- else:
- all_masked = True
- elif (ns == 0) & (nt == 1) & (npr == 0):
- g03 = (5.90578347909402 + z * (-270.983805184062 +
- z * (776.153611613101 + z * (-196.51255088122 +
- (28.9796526294175 - 2.13290083518327 * z) * z))) +
- y * (-24715.571866078 + z * (2910.0729080936 +
- z * (-1513.116771538718 + z * (546.959324647056 + z *
- (-111.1208127634436 + 8.68841343834394 * z)))) +
- y * (2210.2236124548363 + z * (-2017.52334943521 +
- z * (1498.081172457456 + z * (-718.6359919632359 +
- (146.4037555781616 - 4.9892131862671505 * z) * z))) +
- y * (-592.743745734632 + z * (1591.873781627888 +
- z * (-1207.261522487504 + (608.785486935364 -
- 105.4993508931208 * z) * z)) +
- y * (290.12956292128547 + z * (-973.091553087975 +
- z * (602.603274510125 + z * (-276.361526170076 +
- 32.40953340386105 * z))) +
- y * (-113.90630790850321 + y * (21.35571525415769 -
- 67.41756835751434 * z) +
- z * (381.06836198507096 + z * (-133.7383902842754 +
- 49.023632509086724 * z))))))))
- if nonzero_SA:
- g08 = x2 * (168.072408311545 + z * (729.116529735046 +
- z * (-343.956902961561 + z * (124.687671116248 + z *
- (-31.656964386073 + 7.04658803315449 * z)))) +
- x * (-493.407510141682 + x * (543.835333000098 + x *
- (-196.028306689776 + 36.7571622995805 * x) +
- y * (-137.1145018408982 + y * (148.10030845687618 + y *
- (-68.5590309679152 + 12.4848504784754 * y))) -
- 22.6683558512829 * z) + z * (-175.292041186547 +
- (83.1923927801819 - 29.483064349429 * z) * z) +
- y * (-86.1329351956084 + z * (766.116132004952 + z *
- (-108.3834525034224 + 51.2796974779828 * z)) +
- y * (-30.0682112585625 - 1380.9597954037708 * z + y *
- (3.50240264723578 + 938.26075044542 * z)))) +
- y * (1760.062705994408 + y * (-675.802947790203 +
- y * (365.7041791005036 + y * (-108.30162043765552 +
- 12.78101825083098 * y) +
- z * (-1190.914967948748 + (298.904564555024 -
- 145.9491676006352 * z) * z)) +
- z * (2082.7344423998043 + z * (-614.668925894709 +
- (340.685093521782 - 33.3848202979239 * z) * z))) +
- z * (-1721.528607567954 + z * (674.819060538734 +
- z * (-356.629112415276 + (88.4080716616 -
- 15.84003094423364 * z) * z)))))
- g08[ipos] += 851.226734946706 * x2[ipos] * np.log(x[ipos])
- gibbs = (g03 + g08) * 0.025
- else:
- gibbs = g03
- elif (ns == 0) & (nt == 0) & (npr == 1):
- g03 = (100015.695367145 + z * (-5089.1530840726 +
- z * (853.5533353388611 + z * (-133.2587017014444 +
- (21.0131554401542 - 3.278571068826234 * z) * z))) +
- y * (-270.983805184062 + z * (1552.307223226202 +
- z * (-589.53765264366 + (115.91861051767 -
- 10.664504175916349 * z) * z)) +
- y * (1455.0364540468 + z * (-1513.116771538718 +
- z * (820.438986970584 + z * (-222.2416255268872 +
- 21.72103359585985 * z))) +
- y * (-672.50778314507 + z * (998.720781638304 +
- z * (-718.6359919632359 + (195.2050074375488 -
- 8.31535531044525 * z) * z)) +
- y * (397.968445406972 + z * (-603.630761243752 +
- (456.589115201523 - 105.4993508931208 * z) * z) +
- y * (-194.618310617595 + y * (63.5113936641785 -
- 9.63108119393062 * y +
- z * (-44.5794634280918 + 24.511816254543362 * z)) +
- z * (241.04130980405 + z * (-165.8169157020456 +
- 25.92762672308884 * z))))))))
- if nonzero_SA:
- g08 = x2 * (-3310.49154044839 + z * (769.588305957198 +
- z * (-289.5972960322374 + (63.3632691067296 -
- 13.1240078295496 * z) * z)) +
- x * (199.459603073901 + x * (-54.7919133532887 +
- 36.0284195611086 * x - 22.6683558512829 * y +
- (-8.16387957824522 - 90.52653359134831 * z) * z) +
- z * (-104.588181856267 + (204.1334828179377 -
- 13.65007729765128 * z) * z) +
- y * (-175.292041186547 + (166.3847855603638 -
- 88.449193048287 * z) * z +
- y * (383.058066002476 + y * (-460.319931801257 +
- 234.565187611355 * y) +
- z * (-108.3834525034224 + 76.9195462169742 * z)))) +
- y * (729.116529735046 + z * (-687.913805923122 +
- z * (374.063013348744 + z * (-126.627857544292 +
- 35.23294016577245 * z))) +
- y * (-860.764303783977 + y * (694.244814133268 +
- y * (-297.728741987187 + (149.452282277512 -
- 109.46187570047641 * z) * z) +
- z * (-409.779283929806 + (340.685093521782 -
- 44.5130937305652 * z) * z)) +
- z * (674.819060538734 + z * (-534.943668622914 +
- (176.8161433232 - 39.600077360584095 * z) * z)))))
- else:
- g08 = 0
- # Pressure derivative of the Gibbs function
- # in units of (J kg :sup:`-1`) (Pa :sup:`-1`) = m :sup:`3` kg :sup:`-1`
- gibbs = (g03 + g08) * 1e-8
- elif (ns == 1) & (nt == 1) & (npr == 0):
- if nonzero_SA:
- g08 = (1187.3715515697959 + z * (1458.233059470092 +
- z * (-687.913805923122 + z * (249.375342232496 + z *
- (-63.313928772146 + 14.09317606630898 * z)))) +
- x * (-1480.222530425046 + x * (2175.341332000392 + x *
- (-980.14153344888 + 220.542973797483 * x) +
- y * (-548.4580073635929 + y * (592.4012338275047 + y *
- (-274.2361238716608 + 49.9394019139016 * y))) -
- 90.6734234051316 * z) + z * (-525.876123559641 +
- (249.57717834054571 - 88.449193048287 * z) * z) +
- y * (-258.3988055868252 + z * (2298.348396014856 +
- z * (-325.1503575102672 + 153.8390924339484 * z)) +
- y * (-90.2046337756875 - 4142.8793862113125 * z + y *
- (10.50720794170734 + 2814.78225133626 * z)))) +
- y * (3520.125411988816 + y * (-1351.605895580406 +
- y * (731.4083582010072 + y * (-216.60324087531103 +
- 25.56203650166196 * y) +
- z * (-2381.829935897496 + (597.809129110048 -
- 291.8983352012704 * z) * z)) +
- z * (4165.4688847996085 + z * (-1229.337851789418 +
- (681.370187043564 - 66.7696405958478 * z) * z))) +
- z * (-3443.057215135908 + z * (1349.638121077468 +
- z * (-713.258224830552 + (176.8161433232 -
- 31.68006188846728 * z) * z)))))
- g08[ipos] = g08[ipos] + 1702.453469893412 * np.log(x[ipos])
- gibbs = 0.5 * sfac * 0.025 * g08
- # FIXME: commented by FF, g110 without nan did not pass
- # mask[inpos] = True
- else:
- all_masked = True
- elif (ns == 1) & (nt == 0) & (npr == 1):
- g08 = (-6620.98308089678 + z * (1539.176611914396 +
- z * (-579.1945920644748 + (126.7265382134592 -
- 26.2480156590992 * z) * z)) +
- x * (598.378809221703 + x * (-219.1676534131548 +
- 180.142097805543 * x - 90.6734234051316 * y +
- (-32.65551831298088 - 362.10613436539325 * z) * z) +
- z * (-313.764545568801 + (612.4004484538132 -
- 40.95023189295384 * z) * z) +
- y * (-525.876123559641 + (499.15435668109143 -
- 265.347579144861 * z) * z +
- y * (1149.174198007428 + y * (-1380.9597954037708 +
- 703.695562834065 * y) +
- z * (-325.1503575102672 + 230.7586386509226 * z)))) +
- y * (1458.233059470092 + z * (-1375.827611846244 +
- z * (748.126026697488 + z * (-253.255715088584 +
- 70.4658803315449 * z))) +
- y * (-1721.528607567954 + y * (1388.489628266536 +
- y * (-595.457483974374 + (298.904564555024 -
- 218.92375140095282 * z) * z) +
- z * (-819.558567859612 + (681.370187043564 -
- 89.0261874611304 * z) * z)) +
- z * (1349.638121077468 + z * (-1069.887337245828 +
- (353.6322866464 - 79.20015472116819 * z) * z)))))
- # Derivative of the Gibbs function is in units of
- # (m :sup:`3` kg :sup:`-1`) / (g kg :sup:`-1`) = m :sup:`3` g :sup:`-1`
- # that is, it is the derivative of specific volume with respect to
- # Absolute Salinity measured in g kg :sup:`-1`
- gibbs = g08 * sfac * 0.5e-8
- elif (ns == 0) & (nt == 1) & (npr == 1):
- g03 = (-270.983805184062 + z * (1552.307223226202 + z *
- (-589.53765264366 +
- (115.91861051767 - 10.664504175916349 * z) * z)) +
- y * (2910.0729080936 + z * (-3026.233543077436 +
- z * (1640.877973941168 + z * (-444.4832510537744 +
- 43.4420671917197 * z))) +
- y * (-2017.52334943521 + z * (2996.162344914912 +
- z * (-2155.907975889708 + (585.6150223126464 -
- 24.946065931335752 * z) * z)) +
- y * (1591.873781627888 + z * (-2414.523044975008 +
- (1826.356460806092 - 421.9974035724832 * z) * z) +
- y * (-973.091553087975 + z * (1205.20654902025 + z *
- (-829.084578510228 + 129.6381336154442 * z)) +
- y * (381.06836198507096 - 67.41756835751434 * y + z *
- (-267.4767805685508 + 147.07089752726017 * z)))))))
- if nonzero_SA:
- g08 = x2 * (729.116529735046 + z * (-687.913805923122 +
- z * (374.063013348744 + z * (-126.627857544292 +
- 35.23294016577245 * z))) +
- x * (-175.292041186547 - 22.6683558512829 * x +
- (166.3847855603638 - 88.449193048287 * z) * z +
- y * (766.116132004952 + y * (-1380.9597954037708 +
- 938.26075044542 * y) +
- z * (-216.7669050068448 + 153.8390924339484 * z))) +
- y * (-1721.528607567954 + y * (2082.7344423998043 +
- y * (-1190.914967948748 + (597.809129110048 -
- 437.84750280190565 * z) * z) +
- z * (-1229.337851789418 + (1022.055280565346 -
- 133.5392811916956 * z) * z)) +
- z * (1349.638121077468 + z * (-1069.887337245828 +
- (353.6322866464 - 79.20015472116819 * z) * z))))
- else:
- g08 = 0
- # Derivative of the Gibbs function is in units of (m :sup:`3` (K kg))
- # that is, the pressure of the derivative in Pa.
- gibbs = (g03 + g08) * 2.5e-10
- elif (ns == 2) & (nt == 0) & (npr == 0):
- g08 = 2.0 * (8103.20462414788 +
- y * (2175.341332000392 + y * (-274.2290036817964 +
- y * (197.4670779425016 + y * (-68.5590309679152 +
- 9.98788038278032 * y))) - 90.6734234051316 * z) +
- 1.5 * x * (-5458.34205214835 - 980.14153344888 * y +
- (4.0 / 3.0) * x * (2247.60742726704 - 340.1237483177863 * 1.25 *
- x + 220.542973797483 * y) +
- 180.142097805543 * z) +
- z * (-219.1676534131548 + (-16.32775915649044 -
- 120.7020447884644 * z) * z))
- if nonzero_SA:
- tmp = ((-7296.43987145382 + z * (598.378809221703 +
- z * (-156.8822727844005 + (204.1334828179377 -
- 10.23755797323846 * z) * z)) +
- y * (-1480.222530425046 + z * (-525.876123559641 +
- (249.57717834054571 - 88.449193048287 * z) * z) +
- y * (-129.1994027934126 + z * (1149.174198007428 +
- z * (-162.5751787551336 + 76.9195462169742 * z)) +
- y * (-30.0682112585625 - 1380.9597954037708 * z +
- y * (2.626801985426835 + 703.695562834065 * z))))) / x +
- (11625.62913253464 + 1702.453469893412 * y) / x2)
- g08[ipos] += tmp[ipos]
- gibbs = 0.25 * sfac ** 2 * g08
- elif (ns == 0) & (nt == 2) & (npr == 0):
- g03 = (-24715.571866078 + z * (2910.0729080936 + z *
- (-1513.116771538718 + z * (546.959324647056 + z *
- (-111.1208127634436 + 8.68841343834394 * z)))) +
- y * (4420.4472249096725 + z * (-4035.04669887042 +
- z * (2996.162344914912 + z * (-1437.2719839264719 +
- (292.8075111563232 - 9.978426372534301 * z) * z))) +
- y * (-1778.231237203896 + z * (4775.621344883664 +
- z * (-3621.784567462512 + (1826.356460806092 -
- 316.49805267936244 * z) * z)) +
- y * (1160.5182516851419 + z * (-3892.3662123519 +
- z * (2410.4130980405 + z * (-1105.446104680304 +
- 129.6381336154442 * z))) +
- y * (-569.531539542516 + y * (128.13429152494615 -
- 404.50541014508605 * z) +
- z * (1905.341809925355 + z * (-668.691951421377 +
- 245.11816254543362 * z)))))))
- if nonzero_SA:
- g08 = x2 * (1760.062705994408 + x * (-86.1329351956084 +
- x * (-137.1145018408982 + y * (296.20061691375236 +
- y * (-205.67709290374563 + 49.9394019139016 * y))) +
- z * (766.116132004952 + z * (-108.3834525034224 +
- 51.2796974779828 * z)) +
- y * (-60.136422517125 - 2761.9195908075417 * z +
- y * (10.50720794170734 + 2814.78225133626 * z))) +
- y * (-1351.605895580406 + y * (1097.1125373015109 +
- y * (-433.20648175062206 + 63.905091254154904 * y) +
- z * (-3572.7449038462437 + (896.713693665072 -
- 437.84750280190565 * z) * z)) +
- z * (4165.4688847996085 + z * (-1229.337851789418 +
- (681.370187043564 - 66.7696405958478 * z) * z))) +
- z * (-1721.528607567954 + z * (674.819060538734 +
- z * (-356.629112415276 + (88.4080716616 -
- 15.84003094423364 * z) * z))))
- else:
- g08 = 0
- gibbs = (g03 + g08) * 0.000625
- elif (ns == 0) & (nt == 0) & (npr == 2):
- g03 = (-5089.1530840726 + z * (1707.1066706777221 +
- z * (-399.7761051043332 + (84.0526217606168 -
- 16.39285534413117 * z) * z)) +
- y * (1552.307223226202 + z * (-1179.07530528732 +
- (347.75583155301 - 42.658016703665396 * z) * z) +
- y * (-1513.116771538718 + z * (1640.877973941168 +
- z * (-666.7248765806615 + 86.8841343834394 * z)) +
- y * (998.720781638304 + z * (-1437.2719839264719 +
- (585.6150223126464 - 33.261421241781 * z) * z) +
- y * (-603.630761243752 + (913.178230403046 -
- 316.49805267936244 * z) * z +
- y * (241.04130980405 + y * (-44.5794634280918 +
- 49.023632509086724 * z) +
- z * (-331.6338314040912 + 77.78288016926652 * z)))))))
- if nonzero_SA:
- g08 = x2 * (769.588305957198 + z * (-579.1945920644748 +
- (190.08980732018878 - 52.4960313181984 * z) * z) +
- x * (-104.588181856267 + x * (-8.16387957824522 -
- 181.05306718269662 * z) +
- (408.2669656358754 - 40.95023189295384 * z) * z +
- y * (166.3847855603638 - 176.898386096574 * z + y *
- (-108.3834525034224 + 153.8390924339484 * z))) +
- y * (-687.913805923122 + z * (748.126026697488 +
- z * (-379.883572632876 + 140.9317606630898 * z)) +
- y * (674.819060538734 + z * (-1069.887337245828 +
- (530.4484299696 - 158.40030944233638 * z) * z) +
- y * (-409.779283929806 + y * (149.452282277512 -
- 218.92375140095282 * z) +
- (681.370187043564 - 133.5392811916956 * z) * z))))
- else:
- g08 = 0
- # Second derivative of the Gibbs function with respect to pressure,
- # measured in Pa; units of (J kg :sup:`-1`) (Pa :sup:`-2`).
- gibbs = (g03 + g08) * 1e-16
- else:
- raise ValueError('Illegal derivative of the Gibbs function')
- gibbs = np.ma.array(gibbs, mask=mask, copy=False)
- # BÅ: Code below is not needed? EF: it is needed.
- if all_masked:
- gibbs[:] = np.ma.masked
- # Do not allow zero salinity with salinity derivatives
- if ns > 0:
- gibbs = np.ma.masked_where(SA == 0, gibbs)
- return gibbs
-
-
-def gibbs_pt0_pt0(SA, pt0):
- """
- Calculates the second derivative of the specific Gibbs function with
- respect to temperature at zero sea pressure or _gibbs(0,2,0,SA,t,0).
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- pt0 : array_like
- potential temperature relative to 0 dbar [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- gibbs_pt0_pt0 : array_like
- TODO: write the eq. for the second derivative of the
- specific Gibbs function. FIXME: [units]
-
- Notes
- -----
- This library function is called by both "pt_from_CT(SA,CT)"
- and "pt0_from_t(SA,t,p)".
- """
-
- SA, pt0, mask = strip_mask(SA, pt0)
- x2 = sfac * SA
- x = np.sqrt(x2)
- y = pt0 * 0.025
- g03 = (-24715.571866078 +
- y * (4420.4472249096725 +
- y * (-1778.231237203896 +
- y * (1160.5182516851419 +
- y * (-569.531539542516 + y * 128.13429152494615)))))
-
- g08 = (x2 * (1760.062705994408 + x * (-86.1329351956084 +
- x * (-137.1145018408982 + y * (296.20061691375236 +
- y * (-205.67709290374563 + 49.9394019139016 * y))) +
- y * (-60.136422517125 + y * 10.50720794170734)) +
- y * (-1351.605895580406 + y * (1097.1125373015109 +
- y * (-433.20648175062206 + 63.905091254154904 * y)))))
- gibbs_pt0_pt0 = (g03 + g08) * 0.000625
- return np.ma.array(gibbs_pt0_pt0, mask=mask, copy=False)
-
-
-def in_Baltic(lon, lat):
- """
- Check if positions are in the Baltic Sea
-
- Parameters
- ----------
- lon, lat : array_like or masked arrays
-
- Returns
- -------
- in_Baltic : boolean array (at least 1D)
- True for points in the Baltic Sea
- False for points outside, masked or NaN
- """
-
- lon, lat = np.atleast_1d(lon, lat)
- # Polygon bounding the Baltic, (xb, yb)
- # Effective boundary is the intersection of this polygon
- # with rectangle defined by xmin, xmax, ymin, ymax
-
- # start with southwestern point and go round cyclonically
- xb = np.array([12.6, 45.0, 26.0, 7.0, 12.6])
- yb = np.array([50.0, 50.0, 69.0, 59.0, 50.0])
- # Enclosing rectangle
- # xmin, xmax = xb.min(), xb.max()
- # ymin, ymax = yb.min(), yb.max()
- xmin, xmax = 7.0, 32.0
- ymin, ymax = 52.0, 67.0
- # First check if outside the rectangle
- in_rectangle = ((xmin < lon) & (lon < xmax) &
- (ymin < lat) & (lat < ymax))
- # Masked values are also considered outside the rectangle
- if np.ma.is_masked(in_rectangle):
- in_rectangle = in_rectangle.data & ~in_rectangle.mask
- # Closer check for points in the rectangle
- if np.any(in_rectangle):
- lon, lat = np.broadcast_arrays(lon, lat, subok=True)
- in_baltic = np.zeros(lon.shape, dtype='bool')
- lon1 = lon[in_rectangle]
- lat1 = lat[in_rectangle]
- # There are general ways of testing for point in polygon
- # This works for this special configuration of points
- xx_right = np.interp(lat1, yb[1:3], xb[1:3])
- xx_left = np.interp(lat1, yb[-1:1:-1], xb[-1:1:-1])
- in_baltic[in_rectangle] = (xx_left <= lon1) & (lon1 <= xx_right)
- return in_baltic
- else: # Nothing inside the rectangle, return the False array.
- return in_rectangle
-
-
-def infunnel(SA, CT, p):
- """
- Oceanographic funnel check for the 25-term equation
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [°C]
- p : array_like
- sea pressure [dbar]
- (ie. absolute pressure - 10.1325 dbar)
-
- Returns
- -------
- in_funnel : boolean ndarray or scalar
- True, if SA, CT and p are inside the "funnel"
- False, if SA, CT and p are outside the "funnel",
- or one of the values are NaN or masked
- Note. The term "funnel" describes the range of SA, CT and p over which
- the error in the fit of the computationally-efficient 25-term
- expression for density in terms of SA, CT and p was calculated
- (McDougall et al., 2010).
- """
-
- # Check variables and re-size if necessary.
- scalar = np.isscalar(SA) and np.isscalar(CT) and np.isscalar(p)
- SA, CT, p = np.broadcast_arrays(SA, CT, p, subok=True)
- input_nan = np.isnan(SA) | np.isnan(CT) | np.isnan(p)
- infunnel = ((p <= 8000) &
- (SA >= 0) &
- (SA <= 42.2) &
- (CT >= (-0.3595467 - 0.0553734 * SA)) &
- ((p >= 5500) | (SA >= 0.006028 * (p - 500))) &
- ((p >= 5500) | (CT <= (33.0 - 0.003818181818182 * p))) &
- ((p <= 5500) | (SA >= 30.14)) &
- ((p <= 5500) | (CT <= 12.0)))
- infunnel = infunnel & np.logical_not(input_nan)
- if scalar:
- infunnel = bool(infunnel)
- return infunnel
-
-
-def interp_SA_CT(SA, CT, p, p_i):
- """
- function [SA_i, CT_i] = interp_SA_CT(SA,CT,p,p_i)
- interp_SA_CT linear interpolation to p_i on a cast
- ==========================================================================
- This function interpolates the cast with respect to the interpolating
- variable p. This function finds the values of SA, CT at p_i on this cast.
- """
- return interp_S_T(SA, CT, p, p_i)
-
-
-def interp_S_T(S, T, z, znew, P=None):
- """
- Linear interpolation of ndarrays *S* and *T* from *z* to *znew*.
- Optionally interpolate a third ndarray, *P*.
- *z* must be strictly increasing or strictly decreasing. It must
- be a 1-D array, and its length must match the last dimension
- of *S* and *T*.
- *znew* may be a scalar or a sequence.
- It is assumed, but not checked, that *S*, *T*, and *z* are
- all plain ndarrays, not masked arrays or other sequences.
- Out-of-range values of *znew*, and *nan* in *S* and *T*,
- yield corresponding *nan* in the output.
- The basic algorithm is from scipy.interpolate.
- """
-
- isscalar = False
- if not np.iterable(znew):
- isscalar = True
- znew = [znew]
- znew = np.asarray(znew)
- inverted = False
- if z[1] - z[0] < 0:
- inverted = True
- z = z[::-1]
- S = S[..., ::-1]
- T = T[..., ::-1]
- if P is not None:
- P = P[..., ::-1]
- if (np.diff(z) <= 0).any():
- raise ValueError("z must be strictly increasing or decreasing")
- hi = np.searchsorted(z, znew)
- hi = hi.clip(1, len(z) - 1).astype(int)
- lo = hi - 1
- z_lo = z[lo]
- z_hi = z[hi]
- S_lo = S[lo]
- S_hi = S[hi]
- T_lo = T[lo]
- T_hi = T[hi]
- zratio = (znew - z_lo) / (z_hi - z_lo)
- Si = S_lo + (S_hi - S_lo) * zratio
- Ti = T_lo + (T_hi - T_lo) * zratio
- if P is not None:
- Pi = P[lo] + (P[hi] - P[lo]) * zratio
- if inverted:
- Si = Si[..., ::-1]
- Ti = Ti[..., ::-1]
- if P is not None:
- Pi = Pi[..., ::-1]
- outside = (znew < z.min()) | (znew > z.max())
- if np.any(outside):
- Si[..., outside] = np.nan
- Ti[..., outside] = np.nan
- if P is not None:
- Pi[..., outside] = np.nan
- if isscalar:
- Si = Si[0]
- Ti = Ti[0]
- if P is not None:
- Pi = Pi[0]
- if P is None:
- return Si, Ti
- return Si, Ti, Pi
-
-
-def interp_ref_cast(spycnl, A="gn"):
- """
- Translation of:
- [SA_iref_cast, CT_iref_cast, p_iref_cast] = interp_ref_cast(spycnl, A)
- interp_ref_cast linear interpolation of the reference cast
- ==========================================================================
- This function interpolates the reference cast with respect to the
- interpolating variable "spycnl". This reference cast is at the location
- 188E,4N from the reference data set which underlies the Jackett &
- McDougall (1997) Neutral Density computer code. This function finds the
- values of SA, CT and p on this reference cast which correspond to the
- value of isopycnal which is passed to this function from the function
- "geo_strf_isopycnal_CT". The isopycnal could be either gamma_n or
- sigma_2. If A is set to any of the following 's2','S2','sigma2','sigma_2'
- the interpolation will take place in sigma 2 space, any other input
- will result in the programme working in gamma_n space.
- VERSION NUMBER: 3.0 (14th April, 2011)
- REFERENCE:
- Jackett, D. R. and T. J. McDougall, 1997: A neutral density variable
- for the world<92>s oceans. Journal of Physical Oceanography, 27, 237-263.
- FIXME? Do we need argument checking here to handle masked arrays,
- etc.? I suspect not, since I don't think this is intended to be
- user-callable, but is instead used internally by user-callable
- functions.
- Note: The v3.03 matlab code is incorrectly using approximate numbers
- for the gamma_n case, even when the sigma_2 case is in effect.
- That bug is fixed here.
- """
-
- if A.lower() in ["s2", "sigma2", "sigma_2"]:
- A = "s2"
- gsw_data = read_data("gsw_data_v3_0.npz")
- SA_ref = gsw_data.SA_ref_cast
- CT_ref = gsw_data.CT_ref_cast
- p_ref = gsw_data.p_ref_cast
- if A == "s2":
- zvar_ref = gsw_data.sigma_2_ref_cast
- else:
- zvar_ref = gsw_data.gamma_n_ref_cast
- zvar_new = spycnl
- Si, Ci, Pi = interp_S_T(SA_ref, CT_ref, zvar_ref, zvar_new, P=p_ref)
- shallower = spycnl <= zvar_ref[0]
- deeper = spycnl >= zvar_ref[-1]
- if shallower.any():
- Si[shallower] = SA_ref[0]
- Ci[shallower] = CT_ref[0]
- Pi[shallower] = p_ref[0]
- if deeper.any():
- Si[deeper] = SA_ref[-1]
- Ci[deeper] = CT_ref[-1]
- Pi[deeper] = p_ref[-1]
- return Si, Ci, Pi
-
-
-def specvol_SSO_0_CT25(p):
- """
- Calculates specific volume at the Standard Ocean Salinity (SSO) and
- Conservative Temperature of zero degrees C (CT=0), as a function of
- pressure (p [dbar]) or spec_vol_CT25(35.16504,0,p).
-
- Parameters
- ----------
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- specvol_SSO_0_CT25 : array_like
- Specific volume at (SSO, CT=0, p), 25-term equation.
- [m :sup:`3` kg :sup:`-1`]
-
- Notes
- -----
- It uses a streamlined version of the 25-term CT version of specific volume
- that is, a streamlined version of the code "rho_alpha_beta_CT25(SA,CT,p)"
- Modifications
- """
-
- p = np.asanyarray(p)
- # No need to strip mask and replace it here; the calculation is simple.
- specvol_SSO_0_CT25 = ((1. + SSO * (2.0777716085618458e-003 + np.sqrt(SSO) *
- 3.4688210757917340e-006) + p *
- 6.8314629554123324e-006) /
- (9.9984380290708214e+002 + SSO *
- (2.8925731541277653e+000 + SSO *
- 1.9457531751183059e-003) + p *
- (1.1930681818531748e-002 + SSO *
- 5.9355685925035653e-006 + p *
- -2.5943389807429039e-008)))
- return specvol_SSO_0_CT25
-
-
-# Salinity lib functions.
-def specvol_SSO_0_p(p):
- """
- This function calculates specific volume at the Standard Ocean
- Salinity, SSO, and at a Conservative Temperature of zero degrees C, as a
- function of pressure, p, in dbar, using a streamlined version of the
- 48-term CT version of specific volume, that is, a streamlined version of
- the code "specvol(SA, CT, p)".
- """
-
- v01 = 9.998420897506056e+2
- v05 = -6.698001071123802
- v08 = -3.988822378968490e-2
- v12 = -2.233269627352527e-2
- v15 = -1.806789763745328e-4
- v17 = -3.087032500374211e-7
- v20 = 1.550932729220080e-10
- v21 = 1.0
- v26 = -7.521448093615448e-3
- v31 = -3.303308871386421e-5
- v36 = 5.419326551148740e-6
- v37 = -2.742185394906099e-5
- v41 = -1.105097577149576e-7
- v43 = -1.119011592875110e-10
- v47 = -1.200507748551599e-15
- return ((v21 + SSO * (v26 + v36 * SSO + v31 * np.sqrt(SSO)) + p *
- (v37 + v41 * SSO + p * (v43 + v47 * p))) / (v01 + SSO *
- (v05 + v08 * np.sqrt(SSO)) + p * (v12 + v15 * SSO + p *
- (v17 + v20 * SSO))))
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/neutral_nonlinear_48.py b/gsw/gibbs/neutral_nonlinear_48.py
deleted file mode 100644
index 8203ba9..0000000
--- a/gsw/gibbs/neutral_nonlinear_48.py
+++ /dev/null
@@ -1,36 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-__all__ = []
-# 'cabbeling', # TODO
-# 'isopycnal_slope_ratio', # TODO
-# 'isopycnal_vs_ntp_CT_ratio', # TODO
-# 'ntp_pt_vs_CT_ratio', # TODO
-# 'thermobaric'] # TODO
-
-
-#def cabbeling():
-# pass
-
-
-#def isopycnal_slope_ratio():
-# pass
-
-
-#def isopycnal_vs_ntp_CT_ratio():
-# pass
-
-
-#def ntp_pt_vs_CT_ratio():
-# pass
-
-
-#def thermobaric():
-# pass
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/practical_salinity.py b/gsw/gibbs/practical_salinity.py
deleted file mode 100644
index a6963a9..0000000
--- a/gsw/gibbs/practical_salinity.py
+++ /dev/null
@@ -1,695 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from .library import Hill_ratio_at_SP2
-from ..utilities import match_args_return
-
-__all__ = ['C_from_SP',
- 'R_from_SP',
- 'SK_from_SP',
- 'SP_from_C',
- 'SP_from_R',
- 'SP_from_SK',
- 'SP_salinometer']
-
-# Constants.
-a = (0.0080, -0.1692, 25.3851, 14.0941, -7.0261, 2.7081)
-b = (0.0005, -0.0056, -0.0066, -0.0375, 0.0636, -0.0144)
-c = (0.6766097, 2.00564e-2, 1.104259e-4, -6.9698e-7, 1.0031e-9)
-d = (3.426e-2, 4.464e-4, 4.215e-1, -3.107e-3)
-e = (2.070e-5, -6.370e-10, 3.989e-15)
-P = (4.577801212923119e-3, 1.924049429136640e-1, 2.183871685127932e-5,
- -7.292156330457999e-3, 1.568129536470258e-4, -1.478995271680869e-6,
- 9.086442524716395e-4, -1.949560839540487e-5, -3.223058111118377e-6,
- 1.175871639741131e-7, -7.522895856600089e-5, -2.254458513439107e-6,
- 6.179992190192848e-7, 1.005054226996868e-8, -1.923745566122602e-9,
- 2.259550611212616e-6, 1.631749165091437e-7, -5.931857989915256e-9,
- -4.693392029005252e-9, 2.571854839274148e-10, 4.198786822861038e-12)
-q = (5.540896868127855e-5, 2.015419291097848e-1, -1.445310045430192e-5,
- -1.567047628411722e-2, 2.464756294660119e-4, -2.575458304732166e-7,
- 5.071449842454419e-3, -9.081985795339206e-5, -3.635420818812898e-6,
- 2.249490528450555e-8, -1.143810377431888e-3, 2.066112484281530e-5,
- 7.482907137737503e-7, 4.019321577844724e-8, -5.755568141370501e-10,
- 1.120748754429459e-4, -2.420274029674485e-6, -4.774829347564670e-8,
- -4.279037686797859e-9, -2.045829202713288e-10, 5.025109163112005e-12)
-r = (3.432285006604888e-3, 1.672940491817403e-1, 2.640304401023995e-5,
- 1.082267090441036e-1, -6.296778883666940e-5, -4.542775152303671e-7,
- -1.859711038699727e-1, 7.659006320303959e-4, -4.794661268817618e-7,
- 8.093368602891911e-9, 1.001140606840692e-1, -1.038712945546608e-3,
- -6.227915160991074e-6, 2.798564479737090e-8, -1.343623657549961e-10,
- 1.024345179842964e-2, 4.981135430579384e-4, 4.466087528793912e-6,
- 1.960872795577774e-8, -2.723159418888634e-10, 1.122200786423241e-12)
-u = (5.180529787390576e-3, 1.052097167201052e-3, 3.666193708310848e-5,
- 7.112223828976632, -3.631366777096209e-4, -7.336295318742821e-7,
- -1.576886793288888e+2, -1.840239113483083e-3, 8.624279120240952e-6,
- 1.233529799729501e-8, 1.826482800939545e+3, 1.633903983457674e-1,
- -9.201096427222349e-5, -9.187900959754842e-8, -1.442010369809705e-10,
- -8.542357182595853e+3, -1.408635241899082, 1.660164829963661e-4,
- 6.797409608973845e-7, 3.345074990451475e-10, 8.285687652694768e-13)
-k = 0.0162
-
-a, b, c, d, e, P, q, r, u, k = (np.asarray(x)
- for x in (a, b, c, d, e, P, q, r, u, k))
-
-
-def C_from_SP(SP, t, p):
- """
- Calculates conductivity, C, from (SP, t, p) using PSS-78 in the range
- 2 < SP < 42. If the input Practical Salinity is less than 2 then a modified
- form of the Hill et al. (1986) fomula is used for Practical Salinity. The
- modification of the Hill et al. (1986) expression is to ensure that it is
- exactly consistent with PSS-78 at SP = 2.
-
- The conductivity ratio returned by this function is consistent with the
- input value of Practical Salinity, SP, to 2x10^-14 psu over the full range
- of input parameters (from pure fresh water up to SP = 42 psu). This error
- of 2x10^-14 psu is machine precision at typical seawater salinities. This
- accuracy is achieved by having four different polynomials for the starting
- value of Rtx (the square root of Rt) in four different ranges of SP, and by
- using one and a half iterations of a computationally efficient modified
- Newton-Raphson technique to find the root of the equation.
-
- Parameters
- ----------
- SP : array
- Practical Salinity [psu (PSS-78), unitless]
- t : array
- in-situ temperature [:math:`^\circ` C (ITS-90)]
- p : array
- sea pressure [dbar]
- (i.e. absolute pressure - 10.1325 dbar)
-
- Returns
- -------
- C : array
- conductivity [mS cm :sup:`-1`]
-
- Notes
- -----
- Note that strictly speaking PSS-78 (Unesco, 1983) defines Practical
- Salinity in terms of the conductivity ratio, R, without actually
- specifying the value of C(35,15,0) (which we currently take to be
- 42.9140 mS/cm).
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] Hill, K.D., T.M. Dauphinee and D.J. Woods, 1986: The extension of
- the Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic
- Eng., OE-11, 1, 109 - 112.
-
- .. [2] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix E.
-
- .. [3] Unesco, 1983: Algorithms for computation of fundamental properties
- of seawater. Unesco Technical Papers in Marine Science, 44, 53 pp.
- """
-
- C = 42.9140 * R_from_SP(SP, t, p)
-
- return C
-
-
- at match_args_return
-def R_from_SP(SP, t, p):
- """
- Calculates conductivity ratio from (SP, t, p) using PSS-78 in the range
- 2 < SP < 42. If the input Practical Salinity is less than 2 then a
- modified form of the Hill et al. (1986) formula is used for Practical
- Salinity. The modification of the Hill et al. (1986) expression is to
- ensure that it is exactly consistent with PSS-78 at SP = 2.
-
- The conductivity ratio returned by this function is consistent with the
- input value of Practical Salinity, SP, to 2x10^-14 psu over the full range
- of input parameters (from pure fresh water up to SP = 42 psu). This error
- of 2x10^-14 psu is machine precision at typical seawater salinities. This
- accuracy is achieved by having four different polynomials for the starting
- value of Rtx (the square root of Rt) in four different ranges of SP, and by
- using one and a half iterations of a computationally efficient modified
- Newton-Raphson technique to find the root of the equation.
-
- Parameters
- ----------
- SP : array
- Practical Salinity [psu (PSS-78), unitless]
- t : array_like
- in-situ temperature [:math:`^\circ` C (ITS-90)]
- p : array
- sea pressure [dbar]
- (i.e. absolute pressure - 10.1325 dbar)
-
- Returns
- -------
- R : array_like
- conductivity ratio [unitless]
-
- Examples
- --------
- TODO
-
- Notes
- -----
- Strictly speaking PSS-78 (Unesco, 1983) defines Practical Salinity in terms
- of the conductivity ratio, R, without actually specifying the value of
- C(35, 15, 0) (which we currently take to be 42.9140 mS cm^-1.
- Culkin and Smith, 1980).
-
- References
- ----------
- .. [1] Culkin and Smith, 1980: Determination of the Concentration of
- Potassium Chloride Solution Having the Same Electrical Conductivity, at
- 15C and Infinite Frequency, as Standard Seawater of Salinity 35.0000
- (Chlorinity 19.37394), IEEE J. Oceanic Eng, 5, 22-23.
-
- .. [2] Hill, K.D., T.M. Dauphinee & D.J. Woods, 1986: The extension of the
- Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng.,
- 11, 109 - 112.
-
- .. [3] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Appendix E.
-
- .. [4] Unesco, 1983: Algorithms for computation of fundamental properties
- of seawater. Unesco Technical Papers in Marine Science, 44, 53 pp.
- """
-
- # These few lines ensure that SP is non-negative.
- if (SP < 0).any():
- raise ValueError('R_from_SP: SP must be non-negative!')
-
- SP, t, p = np.broadcast_arrays(SP, t, p, subok=True)
-
- # Setting up the constants
- t68 = t * 1.00024
- ft68 = (t68 - 15) / (1 + k * (t68 - 15))
-
- x = np.sqrt(SP)
- Rtx = np.zeros_like(SP) * np.NaN
-
- # Finding the starting value of Rtx, the square root of Rt, using four
- # different polynomials of SP and t68.
- # TODO: Test case that cover all those "ifs"
- I = SP >= 9
- if I.any():
- Rtx[I] = (P[0] + x[I] * (P[1] + P[4] * t68[I] + x[I] * (P[3] + P[7] *
- t68[I] + x[I] * (P[6] + P[11] * t68[I] + x[I] * (P[10] +
- P[16] * t68[I] + x[I] * P[15])))) + t68[I] * (P[2] +
- t68[I] * (P[5] + x[I] * x[I] * (P[12] + x[I] * P[17]) +
- P[8] * x[I] + t68[I] * (P[9] + x[I] * (P[13] + x[I] *
- P[18]) + t68[I] * (P[14] + P[19] * x[I] + P[20] * t68[I])))))
-
- I = np.logical_and(SP >= 0.25, SP < 9)
- if I.any():
- Rtx[I] = (q[0] + x[I] * (q[1] + q[4] * t68[I] + x[I] * (q[3] + q[7] *
- t68[I] + x[I] * (q[6] + q[11] * t68[I] + x[I] * (q[10] +
- q[16] * t68[I] + x[I] * q[15])))) + t68[I] * (q[2] +
- t68[I] * (q[5] + x[I] * x[I] * (q[12] + x[I] * q[17]) +
- q[8] * x[I] + t68[I] * (q[9] + x[I] * (q[13] + x[I] *
- q[18]) + t68[I] * (q[14] + q[19] * x[I] + q[20] * t68[I])))))
-
- I = np.logical_and(SP >= 0.003, SP < 0.25)
- if I.any():
- Rtx[I] = (r[0] + x[I] * (r[1] + r[4] * t68[I] + x[I] * (r[3] + r[7] *
- t68[I] + x[I] * (r[6] + r[11] * t68[I] + x[I] * (r[10] +
- r[16] * t68[I] + x[I] * r[15])))) + t68[I] * (r[2] +
- t68[I] * (r[5] + x[I] * x[I] * (r[12] + x[I] * r[17]) +
- r[8] * x[I] + t68[I] * (r[9] + x[I] * (r[13] + x[I] *
- r[18]) + t68[I] * (r[14] + r[19] * x[I] + r[20] * t68[I])))))
-
- I = SP < 0.003
- if I.any():
- Rtx[I] = (u[0] + x[I] * (u[1] + u[4] * t68[I] + x[I] * (u[3] + u[7] *
- t68[I] + x[I] * (u[6] + u[11] * t68[I] + x[I] * (u[10] +
- u[16] * t68[I] + x[I] * u[15])))) + t68[I] * (u[2] +
- t68[I] * (u[5] + x[I] * x[I] * (u[12] + x[I] * u[17]) +
- u[8] * x[I] + t68[I] * (u[9] + x[I] * (u[13] + x[I] *
- u[18]) + t68[I] * (u[14] + u[19] * x[I] + u[20] * t68[I])))))
-
- # Finding the starting value of dSP_dRtx, the derivative of SP with
- # respect to Rtx.
- dSP_dRtx = (a[1] + (2 * a[2] + (3 * a[3] + (4 * a[4] + 5 * a[5] * Rtx) *
- Rtx) * Rtx) * Rtx + ft68 * (b[1] + (2 * b[2] + (3 * b[3] +
- (4 * b[4] + 5 * b[5] * Rtx) * Rtx) * Rtx) * Rtx))
-
- # TODO: Test case that cover all those "ifs"
- I2 = SP < 2
- if I2.any():
- x = 400 * (Rtx[I2] ** 2)
- sqrty = 10 * Rtx[I2]
- part1 = 1 + x * (1.5 + x)
- part2 = 1 + sqrty * (1 + sqrty * (1 + sqrty))
- Hill_ratio = Hill_ratio_at_SP2(t[I2])
- dSP_dRtx[I2] = (dSP_dRtx[I2] + a[0] * 800 * Rtx[I2] * (1.5 + 2 * x) /
- (part1 ** 2) + b[0] * ft68[I2] * (10 + sqrty * (20 +
- 30 * sqrty)) / (part2 ** 2))
-
- dSP_dRtx[I2] = Hill_ratio * dSP_dRtx[I2]
-
- """One iteration through the modified Newton-Raphson method achieves an
- error in Practical Salinity of about 10^-12 for all combinations of the
- inputs. One and a half iterations of the modified Newton-Raphson method
- achieves a maximum error in terms of Practical Salinity of better than
- 2x10^-14 everywhere.
-
- We recommend one and a half iterations of the modified Newton-Raphson
- method."""
-
- # Begin the modified Newton-Raphson method.
- SP_est = (a[0] + (a[1] + (a[2] + (a[3] + (a[4] + a[5] * Rtx) * Rtx) *
- Rtx) * Rtx) * Rtx + ft68 * (b[0] + (b[1] + (b[2] + (b[3] +
- (b[4] + b[5] * Rtx) * Rtx) * Rtx) * Rtx) * Rtx))
-
- # TODO: Test case that cover all those "ifs"
- I2 = SP_est < 2
- if I2.any():
- x = 400 * (Rtx[I2] ** 2)
- sqrty = 10 * Rtx[I2]
- part1 = 1 + x * (1.5 + x)
- part2 = 1 + sqrty * (1 + sqrty * (1 + sqrty))
- SP_Hill_raw = SP_est[I2] - a[0] / part1 - b[0] * ft68[I2] / part2
- Hill_ratio = Hill_ratio_at_SP2(t[I2])
- SP_est[I2] = Hill_ratio * SP_Hill_raw
-
- Rtx_old = Rtx
- Rtx = Rtx_old - (SP_est - SP) / dSP_dRtx
-
- # This mean value of Rtx, Rtxm, is the value of Rtx at which the
- # derivative dSP_dRtx is evaluated.
- Rtxm = 0.5 * (Rtx + Rtx_old)
-
- dSP_dRtx = (a[1] +
- (2 * a[2] + (3 * a[3] + (4 * a[4] + 5 * a[5] * Rtxm) * Rtxm) *
- Rtxm) * Rtxm + ft68 *
- (b[1] + (2 * b[2] + (3 * b[3] + (4 * b[4] + 5 * b[5] * Rtxm) *
- Rtxm) * Rtxm) * Rtxm))
-
- # TODO: Test case that cover all those "ifs"
- I2 = SP_est < 2
- if I2.any():
- x = 400 * (Rtxm[I2] ** 2)
- sqrty = 10 * Rtxm[I2]
- part1 = 1 + x * (1.5 + x)
- part2 = 1 + sqrty * (1 + sqrty * (1 + sqrty))
- dSP_dRtx[I2] = (dSP_dRtx[I2] + a[0] * 800 * Rtxm[I2] * (1.5 + 2 *
- x) / (part1 ** 2) + b[0] * ft68[I2] * (10 + sqrty *
- (20 + 30 * sqrty)) / (part2 ** 2))
- Hill_ratio = Hill_ratio_at_SP2(t[I2])
- dSP_dRtx[I2] = Hill_ratio * dSP_dRtx[I2]
-
- # End of the one full iteration of the modified Newton-Raphson technique.
- Rtx = Rtx_old - (SP_est - SP) / dSP_dRtx # Updated Rtx
-
- # Now we do another half iteration of the modified Newton-Raphson
- # technique, making a total of one and a half modified N-R iterations.
- SP_est = (a[0] + (a[1] + (a[2] + (a[3] + (a[4] + a[5] * Rtx) * Rtx) *
- Rtx) * Rtx) * Rtx + ft68 *
- (b[0] + (b[1] + (b[2] + (b[3] + (b[4] + b[5] * Rtx) * Rtx) *
- Rtx) * Rtx) * Rtx))
-
- # TODO: Test case that cover all those "ifs"
- I2 = SP_est < 2
- if I2.any():
- x = 400 * (Rtx[I2] ** 2)
- sqrty = 10 * Rtx[I2]
- part1 = 1 + x * (1.5 + x)
- part2 = 1 + sqrty * (1 + sqrty * (1 + sqrty))
- SP_Hill_raw = SP_est[I2] - a[0] / part1 - b[0] * ft68[I2] / part2
- Hill_ratio = Hill_ratio_at_SP2(t[I2])
- SP_est[I2] = Hill_ratio * SP_Hill_raw
-
- Rtx = Rtx - (SP_est - SP) / dSP_dRtx
-
- """ TODO: add this as a kw.
- Return the error, SP_error, in Rtx (in terms of psu).
-
- SP_est = (a[0] + (a[1] + (a[2] + (a[3] + (a[4] + a[5] * Rtx) * Rtx) *
- Rtx) * Rtx) * Rtx + ft68 * (b[0] + (b[1] + (b[2] + (b[3] +
- (b[4] + b[5] * Rtx) * Rtx) * Rtx) * Rtx) * Rtx))
- I2 = SP_est < 2
- if I2.any():
- x = 400 * (Rtx[I2] ** 2)
- sqrty = 10 * Rtx[I2]
- part1 = 1 + x * (1.5 + x)
- part2 = 1 + sqrty * (1 + sqrty * (1 + sqrty))
- SP_Hill_raw = SP_est[I2] - a[0] / part1 - b[0] * ft68[I2] / part2
- Hill_ratio = Hill_ratio_at_SP2(t[I2])
- SP_est[I2] = Hill_ratio * SP_Hill_raw
-
- SP_error = np.abs(SP - SP_est)
-
- This is the end of the error testing
- """
-
- # Now go from Rtx to Rt and then to the conductivity ratio R at pressure p.
- Rt = Rtx ** 2
- A = d[2] + d[3] * t68
- B = 1 + d[0] * t68 + d[1] * t68 ** 2
- C = p * (e[0] + e[1] * p + e[2] * p ** 2)
- # rt_lc (i.e. rt_lower_case) corresponds to rt as defined in the
- # UNESCO 44 (1983) routines.
- rt_lc = c[0] + (c[1] + (c[2] + (c[3] + c[4] * t68) * t68) * t68) * t68
-
- D = B - A * rt_lc * Rt
- E = rt_lc * Rt * A * (B + C)
- Ra = np.sqrt(D ** 2 + 4 * E) - D
-
- return 0.5 * Ra / A
-
-
- at match_args_return
-def SK_from_SP(SP):
- """
- Calculates Knudsen Salinity from Practical Salinity.
-
- Parameters
- ----------
- SP : array
- Practical Salinity [psu (PSS-78), unitless]
-
- Returns
- -------
- SK : array_like
- Knudsen Salinity [parts per thousand, ppt]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Appendix A.3.
- """
- SP = np.maximum(SP, 0) # Ensure that SP is non-negative.
-
- return 0.03 + SP * (1.805 / 1.80655)
-
-
- at match_args_return
-def SP_from_C(C, t, p):
- """
- Calculates Practical Salinity, SP, from conductivity, C, primarily
- using the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical
- Salinity is only valid in the range 2 < SP < 42. If the PSS-78 algorithm
- produces a Practical Salinity that is less than 2 then the Practical
- Salinity is recalculated with a modified form of the Hill et al. (1986)
- formula. The modification of the Hill et al. (1986) expression is to ensure
- that it is exactly consistent with PSS-78 at SP = 2. Note that the input
- values of conductivity need to be in units of mS/cm (not S/m).
-
- Parameters
- ----------
- C : array
- conductivity [mS cm :sup:`-1`]
- t : array
- in-situ temperature [:math:`^\circ` C (ITS-90)]
- p : array
- sea pressure [dbar]
- (i.e. absolute pressure - 10.1325 dbar)
-
- Returns
- -------
- SP : array
- Practical Salinity [psu (PSS-78), unitless]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] Culkin and Smith, 1980: Determination of the Concentration of
- Potassium Chloride Solution Having the Same Electrical Conductivity, at
- 15C and Infinite Frequency, as Standard Seawater of Salinity 35.0000
- (Chlorinity 19.37394), IEEE J. Oceanic Eng, 5, 22-23.
-
- .. [2] Hill, K.D., T.M. Dauphinee & D.J. Woods, 1986: The extension of the
- Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng.,
- 11, 109 - 112.
-
- .. [3] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Appendix E.
-
- .. [4] Unesco, 1983: Algorithms for computation of fundamental properties
- of seawater. Unesco Technical Papers in Marine Science, 44, 53 pp.
- """
-
- C, t, p = np.broadcast_arrays(C, t, p, subok=True)
-
- t68 = t * 1.00024
- ft68 = (t68 - 15) / (1 + k * (t68 - 15))
-
- # The dimensionless conductivity ratio, R, is the conductivity input, C,
- # divided by the present estimate of C(SP=35, t_68=15, p=0) which is
- # 42.9140 mS/cm (=4.29140 S/m), (Culkin and Smith, 1980).
-
- R = 0.023302418791070513 * C # 0.023302418791070513 = 1./42.9140
-
- # rt_lc corresponds to rt as defined in the UNESCO 44 (1983) routines.
- rt_lc = c[0] + (c[1] + (c[2] + (c[3] + c[4] * t68) * t68) * t68) * t68
- Rp = (1 + (p * (e[0] + e[1] * p + e[2] * p ** 2)) /
- (1 + d[0] * t68 + d[1] * t68 ** 2 + (d[2] + d[3] * t68) * R))
- Rt = R / (Rp * rt_lc)
-
- Rt[Rt < 0] = np.ma.masked
- Rtx = np.sqrt(Rt)
-
- SP = (a[0] + (a[1] + (a[2] + (a[3] + (a[4] + a[5] * Rtx) * Rtx) * Rtx) *
- Rtx) * Rtx + ft68 *
- (b[0] + (b[1] + (b[2] + (b[3] + (b[4] + b[5] * Rtx) * Rtx) * Rtx) *
- Rtx) * Rtx))
-
- # The following section of the code is designed for SP < 2 based on the
- # Hill et al. (1986) algorithm. This algorithm is adjusted so that it is
- # exactly equal to the PSS-78 algorithm at SP = 2.
-
- I2, = np.nonzero(np.ravel(SP) < 2)
- if len(I2) > 0:
- Hill_ratio = Hill_ratio_at_SP2(t[I2])
- x = 400 * Rt[I2]
- sqrty = 10 * Rtx[I2]
- part1 = 1 + x * (1.5 + x)
- part2 = 1 + sqrty * (1 + sqrty * (1 + sqrty))
- SP_Hill_raw = SP[I2] - a[0] / part1 - b[0] * ft68[I2] / part2
- SP[I2] = Hill_ratio * SP_Hill_raw
-
- SP = np.maximum(SP, 0) # Ensure that SP is non-negative.
-
- return SP
-
-
- at match_args_return
-def SP_from_R(R, t, p):
- """
- Calculates Practical Salinity, SP, from the conductivity ratio, R,
- primarily using the PSS-78 algorithm. Note that the PSS-78 algorithm for
- Practical Salinity is only valid in the range 2 < SP < 42. If the PSS-78
- algorithm produces a Practical Salinity that is less than 2 then the
- Practical Salinity is recalculated with a modified form of the Hill et al.
- (1986) formula. The modification of the Hill et al. (1986) expression are
- to ensure that it is exactly consistent with PSS-78 at SP = 2.
-
- Parameters
- ----------
- R : array_like
- conductivity ratio [unitless]
- t : array_like
- in-situ temperature [:math:`^\circ` C (ITS-90)]
- p : array
- sea pressure [dbar]
- (i.e. absolute pressure - 10.1325 dbar)
-
- Returns
- -------
- SP : array
- Practical Salinity [psu (PSS-78), unitless]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] Culkin and Smith, 1980: Determination of the Concentration of
- Potassium Chloride Solution Having the Same Electrical Conductivity, at
- 15C and Infinite Frequency, as Standard Seawater of Salinity 35.0000
- (Chlorinity 19.37394), IEEE J. Oceanic Eng, 5, 22-23.
-
- .. [2] Hill, K.D., T.M. Dauphinee & D.J. Woods, 1986: The extension of the
- Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng.,
- 11, 109 - 112.
-
- .. [3] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. Appendix E.
-
- .. [4] Unesco, 1983: Algorithms for computation of fundamental properties
- of seawater. Unesco Technical Papers in Marine Science, 44, 53 pp.
- """
-
- R, t, p = np.broadcast_arrays(R, t, p, subok=True)
-
- t68 = t * 1.00024
- ft68 = (t68 - 15) / (1 + k * (t68 - 15))
-
- # rt_lc corresponds to rt as defined in the UNESCO 44 (1983) routines.
- rt_lc = c[0] + (c[1] + (c[2] + (c[3] + c[4] * t68) * t68) * t68) * t68
- Rp = (1 + (p * (e[0] + e[1] * p + e[2] * p ** 2)) /
- (1 + d[0] * t68 + d[1] * t68 ** 2 + (d[2] + d[3] * t68) * R))
- Rt = R / (Rp * rt_lc)
-
- Rt[Rt < 0] = np.ma.masked
- Rtx = np.sqrt(Rt)
-
- SP = (a[0] + (a[1] + (a[2] + (a[3] + (a[4] + a[5] * Rtx) * Rtx) * Rtx) *
- Rtx) * Rtx + ft68 *
- (b[0] + (b[1] + (b[2] + (b[3] + (b[4] + b[5] * Rtx) * Rtx) * Rtx) *
- Rtx) * Rtx))
-
- # The following section of the code is designed for SP < 2 based on the
- # Hill et al. (1986) algorithm. This algorithm is adjusted so that it is
- # exactly equal to the PSS-78 algorithm at SP = 2.
-
- I2 = SP < 2
- if I2.any():
- Hill_ratio = Hill_ratio_at_SP2(t[I2])
- x = 400 * Rt[I2]
- sqrty = 10 * Rtx[I2]
- part1 = 1 + x * (1.5 + x)
- part2 = 1 + sqrty * (1 + sqrty * (1 + sqrty))
- SP_Hill_raw = SP[I2] - a[0] / part1 - b[0] * ft68[I2] / part2
- SP[I2] = Hill_ratio * SP_Hill_raw
-
- SP = np.maximum(SP, 0) # Ensure that SP is non-negative.
-
- return SP
-
-
- at match_args_return
-def SP_from_SK(SK):
- """Calculates Practical Salinity from Knudsen Salinity.
-
- Parameters
- ----------
- SK : array_like
- Knudsen Salinity [parts per thousand, ppt]
-
- Returns
- -------
- SP : array
- Practical Salinity [psu (PSS-78), unitless]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Appendix A.3.
- """
-
- SP = (SK - 0.03) * (1.80655 / 1.805)
- return np.maximum(SP, 0) # Ensure that SP is non-negative.
-
-
- at match_args_return
-def SP_salinometer(Rt, t):
- """
- Calculates Practical Salinity SP from a salinometer, primarily using
- the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical
- Salinity is only valid in the range 2 < SP < 42. If the PSS-78 algorithm
- produces a Practical Salinity that is less than 2 then the Practical
- Salinity is recalculated with a modified form of the Hill et al. (1986)
- formula. The modification of the Hill et al. (1986) expression is to
- ensure that it is exactly consistent with PSS-78 at SP = 2.
-
- A laboratory salinometer has the ratio of conductivities, Rt, as an output,
- and the present function uses this conductivity ratio and the temperature t
- of the salinometer bath as the two input variables.
-
- Parameters
- ----------
- Rt : array
- C(SP,t_68,0)/C(SP=35,t_68,0) [unitless]
- conductivity ratio
- :math:`R = \frac{C(S, t_68, 0)}{C(35, 15(IPTS-68),0)} [unitless]
-
- t : array
- Temperature of the bath of the salinometer [:math:`^\circ` C (ITS-90)]
-
- Returns
- -------
- SP : array
- Practical Salinity [psu (PSS-78), unitless]
-
- Examples
- --------
- TODO
-
- References
- -----------
- .. [1] Fofonoff, P. and R.C. Millard Jr. 1983: Algorithms for computation
- of fundamental properties of seawater. Unesco Tech. Pap. in Mar. Sci.,
- 44, 53 pp.
-
- .. [2] Hill, K.D., T.M. Dauphinee & D.J. Woods, 1986: The extension of the
- Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng.,
- 11, 109 - 112.
-
- .. [3] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix E of this TEOS-10 Manual, and in
- particular, Eqns. (E.2.1) and (E.2.6).
- """
-
- Rt, t = np.broadcast_arrays(Rt, t, subok=True)
-
- t68 = t * 1.00024
- ft68 = (t68 - 15) / (1 + k * (t68 - 15))
-
- Rt[Rt < 0] = np.ma.masked
- Rtx = np.sqrt(Rt)
-
- SP = (a[0] + (a[1] + (a[2] + (a[3] + (a[4] + a[5] * Rtx) * Rtx) * Rtx) *
- Rtx) * Rtx + ft68 *
- (b[0] + (b[1] + (b[2] + (b[3] + (b[4] + b[5] * Rtx) * Rtx) * Rtx) *
- Rtx) * Rtx))
-
- """The following section of the code is designed for SP < 2 based on the
- Hill et al. (1986) algorithm. This algorithm is adjusted so that it is
- exactly equal to the PSS-78 algorithm at SP = 2."""
-
- I2 = SP < 2
- if I2.any():
- Hill_ratio = Hill_ratio_at_SP2(t[I2])
- x = 400 * Rt[I2]
- sqrty = 10 * Rtx[I2]
- part1 = 1 + x * (1.5 + x)
- part2 = 1 + sqrty * (1 + sqrty * (1 + sqrty))
- SP_Hill_raw = SP[I2] - a[0] / part1 - b[0] * ft68[I2] / part2
- SP[I2] = Hill_ratio * SP_Hill_raw
- # Ensure that SP is non-negative.
- SP = np.maximum(SP, 0)
- return SP
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/steric.py b/gsw/gibbs/steric.py
deleted file mode 100644
index 2277f8b..0000000
--- a/gsw/gibbs/steric.py
+++ /dev/null
@@ -1,125 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-from ..utilities import match_args_return
-#from .geostrophic_48 import geo_strf_dyn_height
-
-__all__ = []
-
-# Depends on geo_strf_dyn_height(), which was not implemented yet.
-#@match_args_return
-#def steric_height(SA, CT, p, p_ref):
-# """
-# Calculates steric height anomaly as the pressure integral of specific
-# volume anomaly from the pressure p of the "bottle" to the reference
-# pressure p_ref, divided by the constant value of the gravitational
-# acceleration, 9.7963 m s^-2. That is, this function returns the dynamic
-# height anomaly divided by 9.7963 m s^-2; this being the gravitational
-# acceleration averaged over the surface of the global ocean (see page 46 of
-# Griffies, 2004). Hence, steric_height is the steric height anomaly with
-# respect to a given reference pressure p_ref.
-#
-# Dynamic height anomaly is the geostrophic streamfunction for the difference
-# between the horizontal velocity at the pressure concerned, p, and the
-# horizontal velocity at p_ref. Dynamic height anomaly is the exact
-# geostrophic streamfunction in isobaric surfaces even though the
-# gravitational acceleration varies with latitude and pressure. Steric
-# height anomaly, being simply proportional to dynamic height anomaly, is
-# also an exact geostrophic streamfunction in an isobaric surface (up to the
-# constant of proportionality, 9.7963 m s^-2).
-#
-# Note however that steric_height is not exactly the height (in meters) of an
-# isobaric surface above a geopotential surface. It is tempting to divide
-# dynamic height anomaly by the local value of the gravitational
-# acceleration, but doing so robs the resulting quantity of either being
-#
-# (i) an exact geostrophic streamfunction, or
-# (ii) exactly the height of an isobaric surface above a geopotential
-# surface.
-#
-# By using a constant value of the gravitational acceleration, we have
-# retained the first of these two properties. So it should be noted that
-# because of the variation of the gravitational acceleration with latitude,
-# steric_height does not exactly represent the height of an isobaric surface
-# above a geopotential surface under the assumption of geostropy.
-#
-# The reference values used for the specific volume anomaly are
-# SSO = 35.16504 g/kg and CT = 0 deg C. This function calculates specific
-# volume anomaly using the computationally efficient 48-term expression for
-# specific volume of McDougall et al. (2011). Note that the 48-term equation
-# has been fitted in a restricted range of parameter space, and is most
-# accurate inside the "oceanographic funnel" described in McDougall et al.
-# (2011) and IOC et al. (2010). For dynamical oceanography we may take the
-# 48-term rational function expression for density as essentially reflecting
-# the full accuracy of TEOS-10. The GSW internal library function
-# "infunnel(SA,CT,p)" is available to be used if one wants to test if some of
-# one's data lies outside this "funnel".
-#
-# Parameters
-# ----------
-# SA : array_like
-# Absolute salinity [g kg :sup:`-1`]
-# CT : array_like
-# Conservative Temperature [:math:`^\circ` C (ITS-90)]
-# p : array_like
-# pressure [dbar]
-# p_ref : int, float, optional
-# reference pressure, default = 0
-#
-# Returns
-# -------
-# steric_height : array_like
-# dynamic height anomaly divided by 9.7963 m s^-2 [m]
-#
-# Notes
-# -----
-# If p_ref exceeds the pressure of the deepest "bottle" on a vertical
-# profile, the steric height anomaly for each "bottle" on the whole vertical
-# profile is returned as NaN.
-#
-# Examples
-# --------
-# TODO
-#
-# References
-# ----------
-# .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
-# of seawater - 2010: Calculation and use of thermodynamic properties.
-# Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
-# UNESCO (English), 196 pp. See section 3.27.
-#
-# .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
-# computationally efficient 48-term expression for the density of seawater
-# in terms of Conservative Temperature, and related properties of seawater.
-#
-# .. [3] Griffies, S. M., 2004: Fundamentals of Ocean Climate Models.
-# Princeton, NJ: Princeton University Press, 518 pp + xxxiv.
-# """
-#
-# p_ref = np.asanyarray(p_ref)
-#
-# p_ref = np.unique(p_ref)
-#
-# if not np.isscalar(p_ref):
-# raise ValueError('The reference pressure p_ref must be unique')
-#
-# if (p_ref < 0).any():
-# raise ValueError('The reference pressure p_ref must be positive')
-#
-# if (SA < 0).any():
-# raise ValueError('The Absolute Salinity must be positive!')
-#
-# # Start of the calculation.
-# if p.max() < p_ref.max():
-# raise ValueError('The reference pressure p_ref is deeper than bottles')
-#
-# dynamic_height_anomaly = geo_strf_dyn_height(SA, CT, p, p_ref)
-# const_grav = 9.7963 # Griffies, 2004.
-#
-# return dynamic_height_anomaly / const_grav
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/thermodynamics_from_t.py b/gsw/gibbs/thermodynamics_from_t.py
deleted file mode 100644
index 4aa9b97..0000000
--- a/gsw/gibbs/thermodynamics_from_t.py
+++ /dev/null
@@ -1,1709 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-import numpy.ma as ma
-
-from .library import gibbs
-from .freezing import t_freezing
-from ..utilities import match_args_return, strip_mask
-from .conversions import (pt_from_CT, pt_from_t, pt0_from_t, CT_from_t,
- t_from_CT)
-from .constants import Kelvin, db2Pascal, P0, SSO, cp0, R, sfac, M_S
-
-__all__ = ['adiabatic_lapse_rate_from_t',
- 'adiabatic_lapse_rate_from_CT',
- 'alpha_wrt_CT_t_exact',
- 'alpha_wrt_pt_t_exact',
- 'alpha_wrt_t_exact',
- 'beta_const_CT_t_exact',
- 'beta_const_pt_t_exact',
- 'beta_const_t_exact',
- 'chem_potential_relative_t_exact',
- 'chem_potential_salt_t_exact',
- 'chem_potential_water_t_exact',
- 'cp_t_exact',
-# 'deltaSA_from_rho_t_exact',
- 'dynamic_enthalpy_t_exact',
- 'enthalpy_t_exact',
- 'entropy_t_exact',
- 'Helmholtz_energy_t_exact',
- 'internal_energy_t_exact',
- 'isochoric_heat_cap_t_exact',
- 'kappa_const_t_exact',
- 'kappa_t_exact',
- 'osmotic_coefficient_t_exact',
- 'osmotic_pressure_t_exact',
- 'pot_rho_t_exact',
- 'rho_t_exact',
- 'SA_from_rho_t',
- 'SA_from_rho_t_exact',
- 'sigma0_pt0_exact',
- 'sound_speed_t_exact',
- 'specvol_anom_t_exact',
- 'specvol_t_exact',
- 't_from_rho_exact',
- 't_maxdensity_exact']
-
-n0, n1, n2 = 0, 1, 2
-
-
- at match_args_return
-def adiabatic_lapse_rate_from_t(SA, t, p):
- """
- Calculates the adiabatic lapse rate of sea water
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- SA & t need to have the same dimensions.
- p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & t are MxN.
-
- Returns
- -------
- adiabatic_lapse_rate : array_like
- adiabatic lapse rate [K Pa:sup:`-1`]
- Note. The output is in unit of degress Celsius per Pa,
- (or equivilently K/Pa) not in units of K/dbar.
-
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- return -gibbs(n0, n1, n1, SA, t, p) / (gibbs(n0, n2, n0, SA, t, p))
-
-
- at match_args_return
-def adiabatic_lapse_rate_from_CT(SA, CT, p):
- """
- Calculates the adiabatic lapse rate of sea water from Conservative
- Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- CT : array_like
- Conservative temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- adiabatic_lapse_rate : array_like
- adiabatic lapse rate [K Pa:sup:`-1`]
- Note. The output is in unit of degress Celsius per Pa,
- (or equivilently K/Pa) not in units of K/dbar.
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- t = t_from_CT(SA, CT, p)
- return -gibbs(n0, n1, n1, SA, t, p) / gibbs(n0, n2, n0, SA, t, p)
-
-
- at match_args_return
-def alpha_wrt_CT_t_exact(SA, t, p):
- """
- Calculates the thermal expansion coefficient of seawater with respect
- to Conservative Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- alpha_wrt_CT : array_like
- thermal expansion coefficient [K :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.alpha_wrt_CT_t_exact(SA, t, p)
- array([ 0.00032471, 0.00032272, 0.00028118, 0.00017314, 0.00014627,
- 0.00012943])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.18.3).
- """
-
- pt0 = pt0_from_t(SA, t, p)
- factor = -cp0 / ((Kelvin + pt0) * gibbs(n0, n2, n0, SA, t, p))
- return factor * (gibbs(n0, n1, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p))
-
-
- at match_args_return
-def alpha_wrt_pt_t_exact(SA, t, p):
- """
- Calculates the thermal expansion coefficient of seawater with respect
- to potential temperature, with a reference pressure of zero.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- alpha_wrt_pt : array_like
- thermal expansion coefficient [K :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.alpha_wrt_pt_t_exact(SA, t, p)
- array([ 0.00032562, 0.00032355, 0.00028164, 0.00017314, 0.00014623,
- 0.00012936])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.18.2).
- """
-
- pt0 = pt0_from_t(SA, t, p)
- factor = gibbs(n0, n2, n0, SA, pt0, 0) / gibbs(n0, n2, n0, SA, t, p)
- return factor * (gibbs(n0, n1, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p))
-
-
- at match_args_return
-def alpha_wrt_t_exact(SA, t, p):
- """
- Calculates the thermal expansion coefficient of seawater with respect
- to in situ temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- alpha_wrt_t : array_like
- thermal expansion coefficient [K :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.alpha_wrt_t_exact(SA, t, p)
- array([ 0.0003256 , 0.00032345, 0.00028141, 0.00017283, 0.00014557,
- 0.00012836])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.18.1)
-
- .. [2] McDougall, T.J., D.R. Jackett and F.J. Millero, 2010: An algorithm
- for estimating Absolute Salinity in the global ocean. Submitted to Ocean
- Science. A preliminary version is available at Ocean Sci. Discuss.,
- 6, 215-242.
- """
-
- return gibbs(n0, n1, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p)
-
-
- at match_args_return
-def beta_const_CT_t_exact(SA, t, p):
- """
- Calculates the saline (i.e. haline) contraction coefficient of seawater
- at constant Conservative Temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- beta_const_CT : array_like
- saline contraction coefficient [kg g :sup:`-1`]
- See Also
- --------
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.beta_const_CT_t_exact(SA, t, p)
- array([ 0.00071749, 0.00071765, 0.00072622, 0.00075051, 0.00075506,
- 0.00075707])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.19.3)
- """
-
- # TODO: gsw-v3.04 implements a shorter gibbs. The results seems similar.
- pt0 = pt0_from_t(SA, t, p)
- factora = (gibbs(n1, n1, n0, SA, t, p) - gibbs(n1, n0, n0, SA, pt0, 0) /
- (Kelvin + pt0))
- factor = (factora / (gibbs(n0, n0, n1, SA, t, p) *
- gibbs(n0, n2, n0, SA, t, p)))
- return (gibbs(n0, n1, n1, SA, t, p) * factor -
- gibbs(n1, n0, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p))
-
-
- at match_args_return
-def beta_const_pt_t_exact(SA, t, p):
- """
- Calculates the saline (i.e. haline) contraction coefficient of seawater
- at constant potential temperature with a reference pressure of 0 dbar.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- beta_const_pt : array_like
- saline contraction coefficient [kg g :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.beta_const_pt_t_exact(SA, t, p)
- array([ 0.00073112, 0.00073106, 0.00073599, 0.00075375, 0.00075712,
- 0.00075843])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.19.2)
- """
-
- # NOTE: The original Matlab toolbox re-implement some code here. Why?
- pt0 = pt0_from_t(SA, t, p)
- factora = gibbs(n1, n1, n0, SA, t, p) - gibbs(n1, n1, n0, SA, pt0, 0)
- factor = (factora / (gibbs(n0, n0, n1, SA, t, p) *
- gibbs(n0, n2, n0, SA, t, p)))
- return (gibbs(n0, n1, n1, SA, t, p) * factor -
- gibbs(n1, n0, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p))
-
-
- at match_args_return
-def beta_const_t_exact(SA, t, p):
- """
- Calculates the saline (i.e. haline) contraction coefficient of seawater
- at constant in situ temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- beta_const_t : array_like
- saline contraction coefficient [kg g :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.beta_const_t_exact(SA, t, p)
- array([ 0.00073112, 0.00073107, 0.00073602, 0.00075381, 0.00075726,
- 0.00075865])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.19.1)
- """
-
- return -gibbs(n1, n0, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p)
-
-
- at match_args_return
-def chem_potential_relative_t_exact(SA, t, p):
- """
- Calculates the chemical potential of water in seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- chem_potential_relative : array_like
- relative chemical potential [J g:sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.chem_potential_relative_t_exact(SA, t, p)
- array([ 79.4254481 , 79.25989214, 74.69154859, 65.64063719,
- 61.22685656, 57.21298557])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- return gibbs(n1, n0, n0, SA, t, p)
-
-
- at match_args_return
-def chem_potential_salt_t_exact(SA, t, p):
- """
- Calculates the chemical potential of salt in seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- chem_potential_salt : array_like
- chemical potential of salt in seawater [J kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.chem_potential_salt_t_exact(SA, t, p)
- array([ 70.87988696, 71.25180659, 69.58756845, 65.00656941,
- 64.56242337, 64.76842002])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.9.
- """
-
- return (chem_potential_relative_t_exact(SA, t, p) +
- chem_potential_water_t_exact(SA, t, p))
-
-
- at match_args_return
-def chem_potential_water_t_exact(SA, t, p):
- """
- Calculates the chemical potential of water in seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- chem_potential_water : array_like
- chemical potential of water in seawater [J/g]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.chem_potential_water_t_exact(SA, t, p)
- array([-8.54556115, -8.00808555, -5.10398014, -0.63406778, 3.3355668 ,
- 7.55543445])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- SA, t, p, mask = strip_mask(SA, t, p)
- # FIXME: Copy from gibbs.
- x2 = sfac * SA
- x = np.sqrt(x2)
- y = t * 0.025
- z = p * 1e-4 # Pressure (p) is sea pressure in units of dbar.
- g03_g = (101.342743139674 + z * (100015.695367145 +
- z * (-2544.5765420363 + z * (284.517778446287 +
- z * (-33.3146754253611 + (4.20263108803084 -
- 0.546428511471039 * z) * z)))) +
- y * (5.90578347909402 + z * (-270.983805184062 +
- z * (776.153611613101 + z * (-196.51255088122 +
- (28.9796526294175 - 2.13290083518327 * z) * z))) +
- y * (-12357.785933039 + z * (1455.0364540468 +
- z * (-756.558385769359 + z * (273.479662323528 +
- z * (-55.5604063817218 + 4.34420671917197 * z)))) +
- y * (736.741204151612 + z * (-672.50778314507 +
- z * (499.360390819152 + z * (-239.545330654412 +
- (48.8012518593872 - 1.66307106208905 * z) * z))) +
- y * (-148.185936433658 + z * (397.968445406972 +
- z * (-301.815380621876 + (152.196371733841 -
- 26.3748377232802 * z) * z)) +
- y * (58.0259125842571 + z * (-194.618310617595 +
- z * (120.520654902025 + z * (-55.2723052340152 +
- 6.48190668077221 * z))) +
- y * (-18.9843846514172 + y * (3.05081646487967 -
- 9.63108119393062 * z) +
- z * (63.5113936641785 + z * (-22.2897317140459 +
- 8.17060541818112 * z)))))))))
- g08_g = x2 * (1416.27648484197 +
- x * (-2432.14662381794 + x * (2025.80115603697 +
- y * (543.835333000098 + y * (-68.5572509204491 +
- y * (49.3667694856254 + y * (-17.1397577419788 +
- 2.49697009569508 * y))) - 22.6683558512829 * z) +
- x * (-1091.66841042967 - 196.028306689776 * y +
- x * (374.60123787784 - 48.5891069025409 * x +
- 36.7571622995805 * y) + 36.0284195611086 * z) +
- z * (-54.7919133532887 + (-4.08193978912261 -
- 30.1755111971161 * z) * z)) +
- z * (199.459603073901 + z * (-52.2940909281335 +
- (68.0444942726459 - 3.41251932441282 * z) * z)) +
- y * (-493.407510141682 + z * (-175.292041186547 +
- (83.1923927801819 - 29.483064349429 * z) * z) +
- y * (-43.0664675978042 + z * (383.058066002476 +
- z * (-54.1917262517112 + 25.6398487389914 * z)) +
- y * (-10.0227370861875 - 460.319931801257 * z + y *
- (0.875600661808945 + 234.565187611355 * z))))) +
- y * (168.072408311545))
- g_SA_part = (8645.36753595126 +
- x * (-7296.43987145382 + x * (8103.20462414788 +
- y * (2175.341332000392 + y * (-274.2290036817964 +
- y * (197.4670779425016 + y * (-68.5590309679152 +
- 9.98788038278032 * y))) - 90.6734234051316 * z) +
- x * (-5458.34205214835 - 980.14153344888 * y +
- x * (2247.60742726704 - 340.1237483177863 * x +
- 220.542973797483 * y) + 180.142097805543 * z) +
- z * (-219.1676534131548 + (-16.32775915649044 -
- 120.7020447884644 * z) * z)) +
- z * (598.378809221703 + z * (-156.8822727844005 +
- (204.1334828179377 - 10.23755797323846 * z) * z)) +
- y * (-1480.222530425046 + z * (-525.876123559641 +
- (249.57717834054571 - 88.449193048287 * z) * z) +
- y * (-129.1994027934126 + z * (1149.174198007428 +
- z * (-162.5751787551336 + 76.9195462169742 * z)) +
- y * (-30.0682112585625 - 1380.9597954037708 * z + y *
- (2.626801985426835 + 703.695562834065 * z))))) +
- y * (1187.3715515697959))
- chem_potential_water = g03_g + g08_g - 0.5 * sfac * SA * g_SA_part
- # V3.03: convert from J/kg to J/g.
- # See section 2.9 of TEOS-10 manual.
- chem_potential_water *= 1e-3
- return ma.array(chem_potential_water, mask=mask, copy=False)
-
-
- at match_args_return
-def cp_t_exact(SA, t, p):
- """
- Calculates the isobaric heat capacity of seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- cp_t_exact : array_like
- heat capacity of seawater [J kg :sup:`-1` K :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.cp_t_exact(SA, t, p)
- array([ 4002.88800396, 4000.98028393, 3995.54646889, 3985.07676902,
- 3973.59384348, 3960.18408479])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- return -(t + Kelvin) * gibbs(n0, n2, n0, SA, t, p)
-
-
-#@match_args_return
-#def deltaSA_from_rho_t_exact(rho, SP, t, p):
-# pass
-
-
- at match_args_return
-def dynamic_enthalpy_t_exact(SA, t, p):
- """
- Calculates the dynamic enthalpy of seawater from Absolute Salinity, in
- situ temperature and pressure. Dynamic enthalpy was defined by Young
- (2010) as the difference between enthalpy and potential enthalpy. Note that
- this function uses the full TEOS-10 Gibbs function (i.e. the sum of the
- IAPWS-09 and IAPWS-08 Gibbs functions, see the TEOS-10 Manual, IOC et al.
- (2010)).
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- dynamic_enthalpy_t_exact : array_like
- dynamic enthalpy [J :sup:`-1`]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
-
- .. [2] Young, W.R., 2010: Dynamic enthalpy, Conservative Temperature, and
- the seawater. Boussinesq approximation. Journal of Physical
- Oceanography, 40, 394-400.
- """
-
- CT = CT_from_t(SA, t, p)
- return enthalpy_t_exact(SA, t, p) - cp0 * CT
-
-
- at match_args_return
-def enthalpy_t_exact(SA, t, p):
- """
- Calculates the specific enthalpy of seawater.
- The specific enthalpy of seawater :math:`h` is given by:
-
- .. math::
- h(SA, t, p) = g + (T_0 + t)\eta =
- g - (T_0 + t) \frac{\partial g}{\partial T}\Big|_{SA,p}
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- enthalpy : array_like
- specific enthalpy [J kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.enthalpy(SA, t, p)
- array([ 115006.17814391, 113989.54266878, 92276.22539967,
- 43390.30953352, 33323.12790127, 27290.12626901])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See appendix A.11.
- """
-
- return (gibbs(n0, n0, n0, SA, t, p) -
- (t + Kelvin) * gibbs(n0, n1, n0, SA, t, p))
-
-
- at match_args_return
-def entropy_t_exact(SA, t, p):
- """
- Calculates specific entropy of seawater.
- The specific entropy of seawater :math:`\eta` is given by:
-
- .. math::
- \eta(SA, t, p) = -g_T = \frac{\partial g}{\partial T}\Big|_{SA,p}
-
- When taking derivatives with respect to *in situ* temperature, the symbol
- :math:`T` will be used for temperature in order that these derivatives not
- be confused with time derivatives.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- entropy : array_like
- specific entropy [J kg :sup:`-1` K :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.entropy_t_exact(SA, t, p)
- array([ 400.38942528, 395.43817843, 319.8664982 , 146.79088159,
- 98.64734087, 62.79150873])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- return -gibbs(n0, n1, n0, SA, t, p)
-
-
- at match_args_return
-def Helmholtz_energy_t_exact(SA, t, p):
- """
- Calculates the Helmholtz energy of seawater.
- The specific Helmholtz energy of seawater :math:`f` is given by:
-
- .. math::
- f(SA, t, p) = g - (p + P_0) \nu =
- g - (p + P_0) \frac{\partial g}{\partial P}\Big|_{SA,T}
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- Helmholtz_energy : array_like
- Helmholtz energy [J kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.Helmholtz_energy_t_exact(SA, t, p)
- array([-5985.58288209, -5830.81845224, -3806.96617841, -877.66369421,
- -462.17033905, -245.50407205])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.13.
- """
-
- return (gibbs(n0, n0, n0, SA, t, p) -
- (db2Pascal * p + P0) * gibbs(n0, n0, n1, SA, t, p))
-
-
- at match_args_return
-def internal_energy_t_exact(SA, t, p):
- """
- Calculates the Helmholtz energy of seawater.
- The specific internal energy of seawater :math:`u` is given by:
-
- .. math::
- u(SA, t, p) = g + (T_0 + t)\eta - (p + P_0)\nu =
- g - (T_0 + t)\frac{\partial g}{\partial T}\Big|_{SA,p} -
- (p + P_0)\frac{\partial g}{\partial P}\Big|_{SA,T}
-
- where :math:`T_0` is the Celsius zero point, 273.15 K and
- :math:`P_0` = 101 325 Pa is the standard atmosphere pressure.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- internal_energy (u) : array_like
- specific internal energy [J kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.internal_energy_t_exact(SA, t, p)
- array([ 114906.23847309, 113426.57417062, 90860.81858842,
- 40724.34005719, 27162.66600185, 17182.50522667])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.11.1)
- """
-
- return (gibbs(n0, n0, n0, SA, t, p) -
- (Kelvin + t) * gibbs(n0, n1, n0, SA, t, p) -
- (db2Pascal * p + P0) * gibbs(n0, n0, n1, SA, t, p))
-
-
- at match_args_return
-def isochoric_heat_cap_t_exact(SA, t, p):
- """
- Calculates the isochoric heat capacity of seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- isochoric_heat_cap : array_like
- isochoric heat capacity [J kg :sup:`-1` K :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.isochoric_heat_cap_t_exact(SA, t, p)
- array([ 3928.13708702, 3927.27381633, 3941.36418525, 3966.26126146,
- 3960.50903222, 3950.13901342])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.21.
- """
-
- return (-(Kelvin + t) * (gibbs(n0, n2, n0, SA, t, p) -
- gibbs(n0, n1, n1, SA, t, p) ** 2 / gibbs(n0, n0, n2, SA, t, p)))
-
-
- at match_args_return
-def kappa_const_t_exact(SA, t, p):
- """
- Calculates isothermal compressibility of seawater at constant in situ
- temperature.
-
- .. math::
- \kappa^t(SA, t, p) =
- \rho^{-1}\frac{\partial \rho}{\partial P}\Big|_{SA,T} =
- -\nu^{-1}\frac{\partial \nu}{\partial P}\Big|_{SA,T} =
- -\frac{g_{PP}}{g_P}
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- kappa : array_like
- Isothermal compressibility [Pa :sup:`-1`]
-
- Notes
- -----
- This is the compressibility of seawater at constant in situ temperature.
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.kappa_const_t_exact(SA, t, p)
- array([ 4.19071646e-10, 4.18743202e-10, 4.22265764e-10,
- 4.37735100e-10, 4.40373818e-10, 4.41156577e-10])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.15.1)
- """
-
- return -gibbs(n0, n0, n2, SA, t, p) / gibbs(n0, n0, n1, SA, t, p)
-
-
- at match_args_return
-def kappa_t_exact(SA, t, p):
- """
- Calculates the isentropic compressibility of seawater.
- When the entropy and Absolute Salinity are held constant while the pressure
- is changed, the isentropic and isohaline compressibility
- :math:`kappa` is obtained:
-
- .. math::
- \kappa(SA, t, p) =
- \rho^{-1}\frac{\partial \rho}{\partial P}\Big|_{SA,\eta} =
- -\nu^{-1}\frac{\partial \nu}{\partial P}\Big|_{SA,\eta} =
- \rho^{-1}\frac{\partial \rho}{\partial P}\Big|_{SA,\theta} =
- -\nu^{-1}\frac{\partial \nu}{\partial P}\Big|_{SA,\theta} =
- -\frac{ (g_{TP}^2 - g_{TT} g_{PP} ) }{g_P g_{TT}}
-
- The isentropic and isohaline compressibility is sometimes called simply the
- isentropic compressibility (or sometimes the "adiabatic compressibility"),
- on the unstated understanding that there is also no transfer of salt during
- the isentropic or adiabatic change in pressure.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- kappa : array_like
- Isentropic compressibility [Pa :sup:`-1`]
-
- Notes
- -----
- The output is Pascal and not dbar.
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.kappa_t_exact(SA, t, p)
- array([ 4.11245799e-10, 4.11029072e-10, 4.16539558e-10,
- 4.35668338e-10, 4.38923693e-10, 4.40037576e-10])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (2.16.1) and the row for kappa in
- Table P.1 of appendix P
- """
-
- return ((gibbs(n0, n1, n1, SA, t, p) ** 2 - gibbs(n0, n2, n0, SA, t, p) *
- gibbs(n0, n0, n2, SA, t, p)) / (gibbs(n0, n0, n1, SA, t, p) *
- gibbs(n0, n2, n0, SA, t, p)))
-
-
- at match_args_return
-def osmotic_coefficient_t_exact(SA, t, p):
- """
- Calculates the osmotic coefficient of seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- osmotic_coefficient : array_like
- osmotic coefficient of seawater [unitless]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.osmotic_coefficient_t_exact(SA,t , p)
- array([ 0.90284718, 0.90298624, 0.90238866, 0.89880927, 0.89801054,
- 0.89767912])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- SA = np.maximum(SA, 0)
- k = M_S / R
- part = k * (1000 - SA) / (Kelvin + t)
- x2 = sfac * SA
- x = np.sqrt(x2)
- y = t * 0.025
- # Note that the input pressure (p) is sea pressure in units of dbar.
- z = p / db2Pascal
- oc = (7.231916621570606e1, 1.059039593127674e1, -3.025914794694813e1,
- 5.040733670521486e1, -4.074543321119333e1, 1.864215613820487e1,
- -3.022566485046178, -6.138647522851840, 1.353207379758663e1,
- -7.316560781114737, 1.829232499785750, -5.358042980767074e-1,
- -1.705887283375562, -1.246962174707332e-1, 1.228376913546017,
- 1.089364009088042e-2, -4.264828939262248e-1, 6.213127679460041e-2,
- 2.481543497315280, -1.363368964861909, -5.640491627443773e-1,
- 1.344724779893754, -2.180866793244492, 4.765753255963401,
- -5.726993916772165, 2.918303792060746, -6.506082399183509e-1,
- -1.015695507663942e-1, 1.035024326471108, -6.742173543702397e-1,
- 8.465642650849419e-1, -7.508472135244717e-1, -3.668086444057845e-1,
- 3.189939162107803e-1, -4.245629194309487e-2)
- tl = (oc[0] + oc[1] * y + x * (oc[2] + x * (oc[3] + x * (oc[4] + x *
- (oc[5] + oc[6] * x))) + y * (oc[7] + x * (oc[8] + x *
- (oc[9] + oc[10] * x)) + y * (oc[11] + oc[12] * x + y * (oc[13] +
- oc[14] * x + y * (oc[15] + x * (oc[16] + oc[17] * y))))) + z *
- (oc[18] + x * (oc[19] + oc[20] * y + oc[21] * x) + y * (oc[22] + y *
- (oc[23] + y * (oc[24] + oc[25] * y))) + z * (oc[26] + oc[27] * x + y *
- (oc[28] + oc[29] * y) + z * (oc[30] + oc[31] * x + y * (oc[32] +
- oc[33] * y) + oc[34] * z)))))
- return tl * part
-
-
- at match_args_return
-def osmotic_pressure_t_exact(SA, t, pw):
- """
- Calculates the osmotic pressure of seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- pw : array_like
- sea pressure of the pure water side [dbar]
-
- Returns
- -------
- osmotic_pressure_t_exact : array_like
- dynamic osmotic pressure of seawater [dbar]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.41.
- """
-
- SA = np.maximum(SA, 0)
- gibbs_pure_water = gibbs(0, 0, 0, 0, t, pw)
- # Initial guess of p, in dbar.
- p = pw + 235.4684
- # Initial guess of df/dp.
- df_dp = -db2Pascal * (gibbs(n0, n0, n1, SA, t, p) -
- SA * gibbs(n1, n0, n1, SA, t, p))
- for Number_of_iterations in range(0, 2):
- p_old = p
- f = gibbs_pure_water - chem_potential_water_t_exact(SA, t, p_old)
- # This is half way through the modified N-R method.
- p = p_old - f / df_dp
- p_mean = 0.5 * (p + p_old)
- df_dp = -db2Pascal * (gibbs(0, 0, 1, SA, t, p_mean) -
- SA * gibbs(1, 0, 1, SA, t, p_mean))
- p = p_old - f / df_dp
- # After two iterations though the modified Newton-Raphson technique the
- # maximum error is 6x10^-12 dbar.
- # Osmotic pressure of seawater in dbar.
- return p - pw
-
-
- at match_args_return
-def pot_rho_t_exact(SA, t, p, p_ref=0):
- """
- Calculates potential density of seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
- p_ref : int, float, optional
- reference pressure, default = 0
-
- Returns
- -------
- pot_rho : array_like
- potential density [kg m :sup:`-3`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.pot_rho_t_exact(SA, t, p)
- array([ 1021.79814581, 1022.05248442, 1023.89358365, 1026.66762112,
- 1027.10723087, 1027.40963126])
- >>> gsw.pot_rho_t_exact(SA, t, p, p_ref=1000)
- array([ 1025.95554512, 1026.21306986, 1028.12563226, 1031.1204547 ,
- 1031.63768355, 1032.00240412])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.4.
- """
-
- pt = pt_from_t(SA, t, p, p_ref=p_ref)
- return rho_t_exact(SA, pt, p_ref)
-
-
- at match_args_return
-def rho_t_exact(SA, t, p):
- """
- Calculates in situ density of seawater from Absolute Salinity and in
- situ temperature.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- rho_t_exact : array_like
- in situ density [kg m :sup:`-3`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.rho_t_exact(SA, t, p)
- array([ 1021.84017319, 1022.26268993, 1024.42771594, 1027.79020181,
- 1029.83771473, 1032.00240412])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.8.
- """
-
- return 1. / gibbs(n0, n0, n1, SA, t, p)
-
-
- at match_args_return
-def SA_from_rho_t(rho, t, p):
- return None
-
-
- at match_args_return
-def SA_from_rho_t_exact(rho, t, p):
- """
- Calculates the Absolute Salinity of a seawater sample, for given values
- of its density, in situ temperature and sea pressure (in dbar).
- One use for this function is in the laboratory where a measured value of
- the in situ density :math:`\rho` of a seawater sample may have been made at
- the laboratory temperature :math:`t` and at atmospheric pressure :math:`p`.
- The present function will return the Absolute Salinity SA of this seawater
- sample.
-
- Parameters
- ----------
- rho : array_like
- in situ density [kg m :sup:`-3`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
-
- Notes
- -----
- This is expressed on the Reference-Composition Salinity Scale of
- Millero et al. (2008).
- After two iterations of a modified Newton-Raphson iteration,
- the error in SA is typically no larger than
-
- 2 :math:`^\times` 10 :sup:`-13` [g kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> rho = [1021.839, 1022.262, 1024.426, 1027.792, 1029.839, 1032.002]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.SA_from_rho_t_exact(rho, t, p)
- array([ 34.71022966, 34.89057683, 35.02332421, 34.84952096,
- 34.73824809, 34.73188384])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.5.
-
- .. [2] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
- The composition of Standard Seawater and the definition of the
- Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.
- """
-
- v_lab = np.ones_like(rho) / rho
- v_0 = gibbs(n0, n0, n1, 0, t, p)
- v_120 = gibbs(n0, n0, n1, 120, t, p)
- # Initial estimate of SA.
- SA = 120 * (v_lab - v_0) / (v_120 - v_0)
- Ior = np.logical_or(SA < 0, SA > 120)
- # Initial estimate of v_SA, SA derivative of v
- v_SA = (v_120 - v_0) / 120
- for k in range(0, 2):
- SA_old = SA
- delta_v = gibbs(n0, n0, n1, SA_old, t, p) - v_lab
- # Half way the mod. N-R method (McDougall and Wotherspoon, 2012)
- SA = SA_old - delta_v / v_SA
- SA_mean = 0.5 * (SA + SA_old)
- v_SA = gibbs(n1, n0, n1, SA_mean, t, p)
- SA = SA_old - delta_v / v_SA
- SA[Ior] = ma.masked
- return SA
-
-
- at match_args_return
-def sigma0_pt0_exact(SA, pt0):
- """
- Calculates potential density anomaly with reference sea pressure of
- zero (0) dbar. The temperature input to this function is potential
- temperature referenced to zero dbar.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- pt0 : array_like
- potential temperature [:math:`^\circ` C (ITS-90)]
- with respect to a reference sea pressure of 0 dbar
-
- Returns
- -------
- sigma0_pt0_exact : array_like
- potential density anomaly [kg m :sup:`-3`]
- respect to a reference pressure of 0 dbar
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> pt0 = [28.7832, 28.4209, 22.7850, 10.2305, 6.8292, 4.3245]
- >>> gsw.sigma0_pt0_exact(SA, pt0)
- array([ 21.79814475, 22.05251193, 23.89356369, 26.66762521,
- 27.10723499, 27.4096324 ])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (3.6.1).
- """
-
- SA = np.maximum(SA, 0) # Ensure that SA is non-negative.
- x2 = sfac * SA
- x = np.sqrt(x2)
- y = pt0 * 0.025
- g03 = (100015.695367145 +
- y * (-270.983805184062 +
- y * (1455.0364540468 +
- y * (-672.50778314507 +
- y * (397.968445406972 +
- y * (-194.618310617595 +
- y * (63.5113936641785 -
- y * 9.63108119393062)))))))
- g08 = x2 * (-3310.49154044839 +
- x * (199.459603073901 +
- x * (-54.7919133532887 +
- x * 36.0284195611086 -
- y * 22.6683558512829) +
- y * (-175.292041186547 +
- y * (383.058066002476 +
- y * (-460.319931801257 +
- y * 234.565187611355)))) +
- y * (729.116529735046 +
- y * (-860.764303783977 +
- y * (694.244814133268 +
- y * (-297.728741987187)))))
-
- # The above code is exactly the same as the following two lines of code.
- # sigma0_pt_exact = rho_t_exact(SA, pt0, 0.) - 1000
-
- return 100000000. / (g03 + g08) - 1000.0
-
-
- at match_args_return
-def sound_speed_t_exact(SA, t, p):
- """
- Calculates the speed of sound in seawater.
- The speed of sound in seawater :math:`c` is given by:
- .. math::
- c(SA, t, p) = \sqrt{ \partial P / \partial \rho |_{SA,\eta}} =
- \sqrt{(\rho\kappa)^{-1}} =
- g_P \sqrt{g_{TT}/(g^2_{TP} - g_{TT}g_{PP})}
- Note that in these expressions, since sound speed is in m s :sup`-1` and
- density has units of kg m :sup:`-3` it follows that the pressure of the
- partial derivatives must be in Pa and the isentropic compressibility
- :math:`kappa` must have units of Pa :sup:`-1`. The sound speed c produced
- by both the SIA and the GSW software libraries (appendices M and N) has
- units of m s :sup:`-1`.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- sound_speed : array_like
- speed of sound in seawater [m s :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.sound_speed_t_exact(SA, t, p)
- array([ 1542.61580359, 1542.70353407, 1530.84497914, 1494.40999692,
- 1487.37710252, 1483.93460908])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (2.17.1)
- """
-
- return (gibbs(n0, n0, n1, SA, t, p) * np.sqrt(gibbs(n0, n2, n0, SA, t, p) /
- (gibbs(n0, n1, n1, SA, t, p) ** 2 - gibbs(n0, n2, n0, SA, t, p) *
- gibbs(n0, n0, n2, SA, t, p))))
-
-
- at match_args_return
-def specvol_anom_t_exact(SA, t, p):
- """
- Calculates specific volume anomaly from Absolute Salinity, in situ
- temperature and pressure, using the full TEOS-10 Gibbs function.
- The reference value of Absolute Salinity is SSO and the reference value of
- Conservative Temperature is equal to 0 :math:`^\circ` C.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- specvol_anom_t_exact : array_like
- specific volume anomaly [m :sup:`3` kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.specvol_anom_t_exact(SA, t, p)
- array([ 6.01044463e-06, 5.78602432e-06, 4.05564999e-06,
- 1.42198662e-06, 1.04351837e-06, 7.63964850e-07])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (3.7.3)
- """
-
- pt_zero = pt_from_CT(SSO, 0)
- t_zero = pt_from_t(SSO, pt_zero, 0, p)
- return (gibbs(n0, n0, n1, SA, t, p) -
- gibbs(n0, n0, n1, SSO, t_zero, p))
-
-
- at match_args_return
-def specvol_t_exact(SA, t, p):
- """
- Calculates the specific volume of seawater.
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- specvol : array_like
- specific volume [m :sup:`3` kg :sup:`-1`]
-
- Examples
- --------
- >>> import gsw
- >>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
- >>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
- >>> p = [10, 50, 125, 250, 600, 1000]
- >>> gsw.specvol(SA, t, p)
- array([ 0.00097862, 0.00097822, 0.00097616, 0.00097297, 0.00097104,
- 0.000969 ])
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 2.7.
- """
-
- return gibbs(n0, n0, n1, SA, t, p)
-
-
- at match_args_return
-def t_from_rho_exact(rho, SA, p):
- """
- Calculates the in-situ temperature of a seawater sample, for given
- values of its density, Absolute Salinity and sea pressure (in dbar).
-
- Parameters
- ----------
- rho : array_like
- in situ density [kg m :sup:`-3`]
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- t : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
- t_multiple : array_like
- in situ temperature [:math:`^\circ` C (ITS-90)]
-
- Notes
- -----
- At low salinities, in brackish water, there are two possible temperatures
- for a single density. This program will output both valid solutions
- (t, t_multiple), if there is only one possible solution the second variable
- will be set to NaN.
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp.
- """
-
- # alpha_limit is the positive value of the thermal expansion coefficient
- # which is used at the freezing temperature to distinguish between I_salty
- # and I_fresh.
- alpha_limit = 1e-5
-
- # rec_half_rho_TT is a constant representing the reciprocal of half the
- # second derivative of density with respect to temperature near the
- # temperature of maximum density.
- rec_half_rho_TT = -110.0
- t_a, t_b = None, None
- t = np.zeros_like(SA) * np.NaN
- t_multiple = np.zeros_like(SA) * np.NaN
- I_SA = np.logical_or(SA < 0, SA > 42)
- I_p = np.logical_or(p < -1.5, p > 12000)
- I_SA_p = np.logical_or(I_SA, I_p)
- SA[I_SA_p] = ma.masked
- rho_40 = rho_t_exact(SA, 40 * np.ones_like(SA), p)
- SA[(rho - rho_40) < 0] = ma.masked
- t_max_rho = t_maxdensity_exact(SA, p)
- rho_max = rho_t_exact(SA, t_max_rho, p)
- rho_extreme = rho_max.copy()
- t_freeze = t_freezing(SA, p) # Assumes seawater is saturated with air.
- rho_freezing = rho_t_exact(SA, t_freeze, p)
- # Set rhos greater than those at the freezing point to be equal to the
- # freezing point.
- I_fr_gr_max = (t_freeze - t_max_rho) > 0
- rho_extreme[I_fr_gr_max] = rho_freezing[I_fr_gr_max]
- SA[rho > rho_extreme] = ma.masked
- SA[np.isnan(SA * p * rho)] = ma.masked
- alpha_freezing = alpha_wrt_t_exact(SA, t_freeze, p)
- I_salty = alpha_freezing > alpha_limit
- if I_salty.any():
- t_diff = 40. * np.ones_like(I_salty) - t_freeze[I_salty]
- top = (rho_40[I_salty] - rho_freezing[I_salty] +
- rho_freezing[I_salty] * alpha_freezing[I_salty] * t_diff)
- a = top / (t_diff ** 2)
- b = -rho_freezing[I_salty] * alpha_freezing[I_salty]
- c = rho_freezing[I_salty] - rho[I_salty]
- sqrt_disc = np.sqrt(b ** 2 - 4 * a * c)
- # The value of t[I_salty] is the initial guess `t` in the range of
- # I_salty.
- t[I_salty] = t_freeze[I_salty] + 0.5 * (-b - sqrt_disc) / a
- I_fresh = alpha_freezing <= alpha_limit
- if I_fresh.any():
- t_diff = 40 * np.ones_like[I_fresh] - t_max_rho[I_fresh]
- factor = ((rho_max[I_fresh] - rho[I_fresh]) / (rho_max[I_fresh] -
- rho_40[I_fresh]))
- delta_t = t_diff * np.sqrt(factor)
- I_fresh_NR = delta_t > 5
- if I_fresh_NR.any():
- t[I_fresh[I_fresh_NR]] = (t_max_rho[I_fresh[I_fresh_NR]] +
- delta_t[I_fresh_NR])
- I_quad = delta_t <= 5
- if I_quad.any():
- t_a = np.zeros_like(SA) * np.NaN
- # Set the initial value of the quadratic solution roots.
- t_a[I_fresh[I_quad]] = (t_max_rho[I_fresh[I_quad]] +
- np.sqrt(rec_half_rho_TT *
- (rho[I_fresh[I_quad]] -
- rho_max[I_fresh[I_quad]])))
- for Number_of_iterations in range(0, 6):
- t_old = t_a
- rho_old = rho_t_exact(SA, t_old, p)
- factorqa = (rho_max - rho) / (rho_max - rho_old)
- t_a = t_max_rho + (t_old - t_max_rho) * np.sqrt(factorqa)
- t_a[t_freezing - t_a < 0] = ma.masked
- t_b = np.zeros_like(SA) * np.NaN
- # Set the initial value of the quadratic solution routes.
- t_b[I_fresh[I_quad]] = (t_max_rho[I_fresh[I_quad]] -
- np.sqrt(rec_half_rho_TT *
- (rho[I_fresh[I_quad]] -
- rho_max[I_fresh[I_quad]])))
- for Number_of_iterations in range(0, 6):
- t_old = t_b.copy()
- rho_old = rho_t_exact(SA, t_old, p)
- factorqb = (rho_max - rho) / (rho_max - rho_old)
- t_b = t_max_rho + (t_old - t_max_rho) * np.sqrt(factorqb)
- # After seven iterations of this quadratic iterative procedure,
- # the error in rho is no larger than 4.6x10^-13 kg/m^3.
- t_b[t_freezing - t_b < 0] = ma.masked
- # Begin the modified Newton-Raphson iterative method, which will
- # only operate on non-masked data.
- v_lab = np.ones_like(rho) / rho
- v_t = gibbs(0, 1, 1, SA, t, p)
- for Number_of_iterations in range(0, 3):
- t_old = t.copy()
- delta_v = gibbs(0, 0, 1, SA, t_old, p) - v_lab
- t = t_old - delta_v / v_t # Half way through the modified N-R method.
- t_mean = 0.5 * (t + t_old)
- v_t = gibbs(0, 1, 1, SA, t_mean, p)
- t = t_old - delta_v / v_t
- if t_a:
- t[~np.isnan(t_a)] = t_a[~np.isnan(t_a)]
- if t_b:
- t_multiple[~np.isnan(t_b)] = t_b[~np.isnan(t_b)]
- # After three iterations of this modified Newton-Raphson iteration,
- # the error in rho is no larger than 4.6x10^-13 kg/m^3.
- return t, t_multiple
-
-
- at match_args_return
-def t_maxdensity_exact(SA, p):
- """
- Calculates the in-situ temperature of maximum density of seawater.
- This function returns the in-situ temperature at which the density of
- seawater is a maximum, at given Absolute Salinity, SA, and sea pressure, p
- (in dbar).
-
- Parameters
- ----------
- SA : array_like
- Absolute salinity [g kg :sup:`-1`]
- p : array_like
- pressure [dbar]
-
- Returns
- -------
- t_maxdensity_exact : array_like
- max in-situ temperature [:math:`^\circ` C]
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.42.
- """
- # The temperature increment for calculating the gibbs_PTT derivative.
- dt = 0.001
- t = 3.978 - 0.22072 * SA # The initial guess of t_maxden.
- gibbs_PTT = 1.1e-8 # The initial guess for g_PTT.
- for Number_of_iterations in range(0, 3):
- t_old = t
- gibbs_PT = gibbs(n0, n1, n1, SA, t_old, p)
- # Half way through the mod. method (McDougall and Wotherspoon, 2012)
- t = t_old - gibbs_PT / gibbs_PTT
- t_mean = 0.5 * (t + t_old)
- gibbs_PTT = (gibbs(n0, n1, n1, SA, t_mean + dt, p) -
- gibbs(n0, n1, n1, SA, t_mean - dt, p)) / (dt + dt)
- t = t_old - gibbs_PT / gibbs_PTT
- # After three iterations of this modified Newton-Raphson iteration, the
- # error in t_maxdensity_exact is typically no larger than 1x10^-15 deg C.
- return t
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/gibbs/water_column_48.py b/gsw/gibbs/water_column_48.py
deleted file mode 100644
index 0f641fe..0000000
--- a/gsw/gibbs/water_column_48.py
+++ /dev/null
@@ -1,326 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import numpy as np
-
-from .earth import grav
-from .constants import db2Pascal
-from ..utilities import match_args_return
-from .density_enthalpy_48 import rho_alpha_beta
-
-__all__ = ['IPV_vs_fNsquared_ratio',
- 'Nsquared',
- 'Turner_Rsubrho']
-
-
-def IPV_vs_fNsquared_ratio(SA, CT, p, p_ref=0):
- """
- Calculates the ratio of the vertical gradient of potential density to
- the vertical gradient of locally-referenced potential density. This
- ratio is also the ratio of the planetary Isopycnal Potential Vorticity
- (IPV) to f times N^2, hence the name for this variable,
- IPV_vs_fNsquared_ratio (see Eqn. (3.20.5) of IOC et al. (2010)). The
- reference sea pressure, p_ref, of the potential density surface must
- have a constant value.
-
- IPV_vs_fNsquared_ratio is evaluated at the mid pressure between the
- individual data points in the vertical. This function uses the
- computationally-efficient 48-term expression for density in terms of
- SA, CT and p (McDougall et al., 2011).
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
- p_ref : int, float, optional
- reference pressure, default = 0
-
- Returns
- -------
- IPV_vs_fNsquared_ratio : array_like
- The ratio of the vertical gradient of potential density,
- on the same (M-1)xN grid as p_mid. [unitless]
- referenced to p_ref, to the vertical gradient of locally-
- referenced potential density.
-
- p_mid : array_like
- Mid pressure between p grid [dbar]
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA, CT, p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqn. (3.20.5).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
- p_ref = np.unique(np.asanyarray(p_ref))
-
- # BUG
- # if not np.isscalar(p_ref):
- # raise ValueError('The reference pressure p_ref must be unique')
-
- if SA.ndim == 1:
- raise ValueError('There must be at least 2 columns.')
-
- SA = np.maximum(SA, 0)
-
- SA, CT, p, p_ref = np.broadcast_arrays(SA, CT, p, p_ref, subok=True)
-
- p_ref = p_ref[:-1, ...]
-
- p_mid = 0.5 * (p[0:-1, ...] + p[1:, ...])
- SA_mid = 0.5 * (SA[0:-1, ...] + SA[1:, ...])
- CT_mid = 0.5 * (CT[0:-1, ...] + CT[1:, ...])
-
- dSA = SA[0:-1, ...] - SA[1:, ...]
- dCT = CT[0:-1, ...] - CT[1:, ...]
-
- [dummy, alpha, beta] = rho_alpha_beta(SA_mid, CT_mid, p_mid)
-
- _, alpha, beta = rho_alpha_beta(SA_mid, CT_mid, p_mid)
- _, alpha_pref, beta_pref = rho_alpha_beta(SA_mid, CT_mid, p_ref)
-
- # This function calculates IPV_vs_fNsquared_ratio using the
- # computationally efficient 48-term expression for density in terms of SA,
- # CT and p. If one wanted to compute this with the full TEOS-10 Gibbs
- # function expression for density, the following lines of code will enable
- # this.
- #
- # pt_mid = pt_from_CT(SA_mid, CT_mid)
- # pr0 = np.zeros_like(SA_mid)
- # t_mid = pt_from_t(SA_mid, pt_mid, pr0, p_mid)
- # beta = beta_const_CT_t_exact(SA_mid, t_mid, p_mid)
- # alpha = alpha_wrt_CT_t_exact(SA_mid, t_mid, p_mid)
- # beta_pref = beta_const_CT_t_exact(SA_mid, t_mid, p_ref)
- # alpha_pref = alpha_wrt_CT_t_exact(SA_mid, t_mid, p_ref)
-
- numerator = dCT * alpha_pref - dSA * beta_pref
- denominator = dCT * alpha - dSA * beta
-
- # IPV_vs_fNsquared_ratio = np.zeros_like(SA_mid) * np.NaN
- # I = denominator != 0.
- # IPV_vs_fNsquared_ratio[I] = numerator[I] / denominator[I]
-
- IPV_vs_fNsquared_ratio = numerator / denominator
-
- return IPV_vs_fNsquared_ratio, p_mid
-
-
-# In the following, we are assuming the p dimension comes
-# first. This follows the matlab code, (Fortran order)
-# but is unnatural in Python (C order).
-# We might need to deal with this in a better way.
-
- at match_args_return
-def Nsquared(SA, CT, p, lat=None):
- """
- Calculates the buoyancy frequency squared (N^2)
- (i.e. the Brunt-Väisälä frequency squared) at the
- mid pressure from the equation::
-
- 2 2 beta.d(SA) - alpha.d(CT)
- N = g rho_local ------------------------
- dP
-
- dP in the above formula is in Pascals
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
- lat : array_like, optional
- latitude in decimal degrees north [-90..+90]
- If lat is not supplied, a default gravitational acceleration of
- 9.7963 m/s^2 (Griffies, 2004) will be used.
-
- Returns
- -------
- N2 : array_like
- Brunt-Väisälä frequency squared [1 s :math:`-2`]
- p_mid : array_like
- Mid pressure between p grid [dbar]
-
- Notes
- -----
- This routine uses rho from the computationally efficient 48-term expression
- for density in terms of SA, CT and p.
-
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- IOC et al. (2010). The GSW library function "infunnel(SA, CT, p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See section 3.10 and Eqn. (3.10.2).
-
- .. [2] Griffies, S. M., 2004: Fundamentals of Ocean Climate Models.
- Princeton, NJ: Princeton University Press, 518 pp + xxxiv.
- """
-
- if lat is not None:
- g = grav(lat, p)
- SA, CT, p, g = np.broadcast_arrays(SA, CT, p, g, subok=True)
- else:
- g = 9.7963 # Standard value from Griffies (2004).
- SA, CT, p = np.broadcast_arrays(SA, CT, p, subok=True)
-
- ishallow = (slice(0, -1), Ellipsis)
- ideep = (slice(1, None), Ellipsis)
-
- def mid(x):
- return 0.5 * (x[ideep] + x[ishallow])
-
- def delta(x):
- return x[ideep] - x[ishallow]
-
- vars = SA, CT, p
- SA_mid, CT_mid, p_mid = [mid(x) for x in vars]
- dSA, dCT, dp = [delta(x) for x in vars]
-
- rho_mid, alpha_mid, beta_mid = rho_alpha_beta(SA_mid, CT_mid, p_mid)
-
- if lat is not None:
- grav_mid = mid(g)
- else:
- grav_mid = g
-
- N2 = (grav_mid ** 2 / db2Pascal) * (rho_mid / dp)
- N2 *= (beta_mid * dSA - alpha_mid * dCT)
-
- return N2, p_mid
-
-
-def Turner_Rsubrho(SA, CT, p):
- """
- Calculates the Turner angle and the Rsubrho as a function of pressure
- down a vertical water column. These quantities express the relative
- contributions of the vertical gradients of Conservative Temperature and
- Absolute Salinity to the vertical stability (the square of the
- Brunt-Väisälä Frequency squared, N^2). `Tu` and `Rsubrho` are evaluated at
- the mid pressure between the individual data points in the vertical. This
- function uses computationally-efficient 48-term expression for density in
- terms of SA, CT and p (McDougall et al., 2011). Note that in the
- double-diffusive literature, papers concerned with the "diffusive" form of
- double-diffusive convection often define the stability ratio as the
- reciprocal of what is defined here as the stability ratio.
-
- Parameters
- ----------
- SA : array_like
- Absolute Salinity [g/kg]
- CT : array_like
- Conservative Temperature [:math:`^\circ` C (ITS-90)]
- p : array_like
- sea pressure [dbar]
-
- Returns
- -------
- Tu : array_like
- Turner angle, on the same (M-1)xN grid as p_mid. [degrees of rotation]
- Rsubrho : array_like
- Stability Ratio, on the same (M-1)xN grid as p_mid. [unitless]
- p_mid : array_like
- Mid pressure between p grid [dbar]
-
- Notes
- -----
- The 48-term equation has been fitted in a restricted range of parameter
- space, and is most accurate inside the "oceanographic funnel" described in
- McDougall et al. (2011). The GSW library function "infunnel(SA, CT, p)" is
- available to be used if one wants to test if some of one's data lies
- outside this "funnel".
-
- Examples
- --------
- TODO
-
- References
- ----------
- .. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
- of seawater - 2010: Calculation and use of thermodynamic properties.
- Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
- UNESCO (English), 196 pp. See Eqns. (3.15.1) and (3.16.1).
-
- .. [2] McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
- computationally efficient 48-term expression for the density of
- seawater in terms of Conservative Temperature, and related properties
- of seawater.
- """
-
- if SA.ndim == 1:
- raise ValueError('There must be at least 2 columns.')
-
- SA = np.maximum(SA, 0)
-
- SA, CT, p = np.broadcast_arrays(SA, CT, p, subok=True)
-
- p_mid = 0.5 * (p[0:-1, ...] + p[1:, ...])
- SA_mid = 0.5 * (SA[0:-1, ...] + SA[1:, ...])
- CT_mid = 0.5 * (CT[0:-1, ...] + CT[1:, ...])
-
- dSA = SA[0:-1, ...] - SA[1:, ...]
- dCT = CT[0:-1, ...] - CT[1:, ...]
-
- [dummy, alpha, beta] = rho_alpha_beta(SA_mid, CT_mid, p_mid)
-
- # This function evaluates Tu and Rsubrho using the computationally
- # efficient 48-term expression for density in terms of SA, CT and p. If one
- # wanted to compute Tu and Rsubrho using the full TEOS-10 Gibbs function
- # expression for density, the following lines of code would do that.
- #
- # pt_mid = pt_from_CT(SA_mid, CT_mid)
- # pr0 = np.zeros_like(SA_mid)
- # t_mid = pt_from_t(SA_mid, pt_mid, pr0, p_mid)
- # beta = beta_const_CT_t_exact(SA_mid, t_mid, p_mid)
- # alpha = alpha_wrt_CT_t_exact(SA_mid, t_mid, p_mid)
-
- Tu = np.arctan2((alpha * dCT + beta * dSA), (alpha * dCT - beta * dSA))
-
- Tu = Tu * (180 / np.pi)
-
- Rsubrho = np.zeros_like(dSA) + np.NaN
-
- Inz = dSA != 0
- Rsubrho[Inz] = (alpha[Inz] * dCT[Inz]) / (beta[Inz] * dSA[Inz])
-
- return Tu, Rsubrho, p_mid
-
-
-if __name__ == '__main__':
- import doctest
- doctest.testmod()
diff --git a/gsw/ice.py b/gsw/ice.py
new file mode 100644
index 0000000..aac1754
--- /dev/null
+++ b/gsw/ice.py
@@ -0,0 +1,39 @@
+"""
+Functions about ice and melting, but not the freezing point.
+"""
+
+from ._wrapped_ufuncs import (
+adiabatic_lapse_rate_ice,
+alpha_wrt_t_ice,
+chem_potential_water_ice,
+cp_ice,
+enthalpy_ice,
+entropy_ice,
+Helmholtz_energy_ice,
+ice_fraction_to_freeze_seawater,
+internal_energy_ice,
+kappa_const_t_ice,
+kappa_ice,
+melting_ice_equilibrium_SA_CT_ratio,
+melting_ice_equilibrium_SA_CT_ratio_poly,
+melting_ice_into_seawater,
+melting_ice_SA_CT_ratio,
+melting_ice_SA_CT_ratio_poly,
+melting_seaice_equilibrium_SA_CT_ratio,
+melting_seaice_equilibrium_SA_CT_ratio_poly,
+melting_seaice_into_seawater,
+melting_seaice_SA_CT_ratio,
+melting_seaice_SA_CT_ratio_poly,
+pot_enthalpy_from_pt_ice,
+pot_enthalpy_from_pt_ice_poly,
+pressure_coefficient_ice,
+pt0_from_t_ice,
+pt_from_pot_enthalpy_ice,
+pt_from_pot_enthalpy_ice_poly,
+pt_from_t_ice,
+rho_ice,
+seaice_fraction_to_freeze_seawater,
+sound_speed_ice,
+specvol_ice,
+t_from_pt0_ice,
+)
diff --git a/gsw/stability.py b/gsw/stability.py
new file mode 100644
index 0000000..76189a2
--- /dev/null
+++ b/gsw/stability.py
@@ -0,0 +1,202 @@
+"""
+Vertical stability functions.
+
+These work with ndarrays of profiles; use the `axis` keyword
+argument to specify the axis along which pressure varies.
+For example, the default, following the Matlab versions, is
+`axis=0`, meaning the pressure varies along the first dimension.
+Use `axis=-1` if pressure varies along the last dimension--that
+is, along a row, as the column index increases, in the 2-D case.
+
+Docstrings will be added later, either manually or via
+an automated mechanism.
+
+"""
+
+
+import numpy as np
+
+from ._utilities import match_args_return, axis_slicer
+from ._gsw_ufuncs import grav, specvol_alpha_beta
+
+__all__ = ['Nsquared',
+ 'Turner_Rsubrho',
+ 'IPV_vs_fNsquared_ratio',
+ ]
+
+# In the following, axis=0 matches the Matlab behavior.
+
+ at match_args_return
+def Nsquared(SA, CT, p, lat=None, axis=0):
+ """
+ Calculate the square of the buoyancy frequency.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ lat : array-like, 1-D, optional
+ Latitude, degrees.
+ axis : int, optional
+ The dimension along which pressure increases.
+
+ Returns
+ -------
+ N2 : array
+ Buoyancy frequency-squared at pressure midpoints, 1/s.
+ The shape along the pressure axis dimension is one
+ less than that of the inputs.
+ p_mid : array
+ Pressure at midpoints of p, dbar.
+ The array shape matches N2.
+
+ """
+ if lat is not None:
+ if np.any((lat < -90) | (lat > 90)):
+ raise ValueError('lat is out of range')
+ SA, CT, p, lat = np.broadcast_arrays(SA, CT, p, lat)
+ g = grav(lat, p)
+ else:
+ SA, CT, p = np.broadcast_arrays(SA, CT, p)
+ g = 9.7963 # (Griffies, 2004)
+
+ db_to_pa = 1e4
+ shallow = axis_slicer(SA.ndim, slice(-1), axis)
+ deep = axis_slicer(SA.ndim, slice(1, None), axis)
+ if lat is not None:
+ g_local = 0.5 * (g[shallow] + g[deep])
+ else:
+ g_local = g
+
+ dSA = SA[deep] - SA[shallow]
+ dCT = CT[deep] - CT[shallow]
+ dp = p[deep] - p[shallow]
+ SA_mid = 0.5 * (SA[shallow] + SA[deep])
+ CT_mid = 0.5 * (CT[shallow] + CT[deep])
+ p_mid = 0.5 * (p[shallow] + p[deep])
+
+ specvol_mid, alpha_mid, beta_mid = specvol_alpha_beta(SA_mid,
+ CT_mid, p_mid)
+
+ N2 = ((g_local**2) / (specvol_mid * db_to_pa * dp))
+ N2 *= (beta_mid*dSA - alpha_mid*dCT)
+
+ return N2, p_mid
+
+
+ at match_args_return
+def Turner_Rsubrho(SA, CT, p, axis=0):
+ """
+ Calculate the Turner Angle and the Stability Ratio.
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ CT : array-like
+ Conservative Temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ axis : int, optional
+ The dimension along which pressure increases.
+
+ Returns
+ -------
+ Tu : array
+ Turner Angle at pressure midpoints, degrees.
+ The shape along the pressure axis dimension is one
+ less than that of the inputs.
+ Rsubrho : array
+ Stability Ratio, dimensionless.
+ The shape matches Tu.
+ p_mid : array
+ Pressure at midpoints of p, dbar.
+ The array shape matches Tu.
+
+ """
+
+ SA = np.clip(SA, 0, 50)
+ SA, CT, p = np.broadcast_arrays(SA, CT, p)
+ shallow = axis_slicer(SA.ndim, slice(-1), axis)
+ deep = axis_slicer(SA.ndim, slice(1, None), axis)
+
+ dSA = -SA[deep] + SA[shallow]
+ dCT = -CT[deep] + CT[shallow]
+
+ SA_mid = 0.5 * (SA[shallow] + SA[deep])
+ CT_mid = 0.5 * (CT[shallow] + CT[deep])
+ p_mid = 0.5 * (p[shallow] + p[deep])
+
+ _, alpha, beta = specvol_alpha_beta(SA_mid, CT_mid, p_mid)
+
+ Tu = np.arctan2((alpha*dCT + beta*dSA), (alpha*dCT - beta*dSA))
+ Tu = np.degrees(Tu)
+
+ igood = (dSA != 0)
+ Rsubrho = np.zeros_like(dSA)
+ Rsubrho.fill(np.nan)
+ Rsubrho[igood] = (alpha[igood]*dCT[igood])/(beta[igood]*dSA[igood])
+
+ return Tu, Rsubrho, p_mid
+
+
+ at match_args_return
+def IPV_vs_fNsquared_ratio(SA, CT, p, p_ref=0, axis=0):
+ """
+ Calculates the ratio of the vertical gradient of potential density to
+ the vertical gradient of locally-referenced potential density. This
+ is also the ratio of the planetary Isopycnal Potential Vorticity
+ (IPV) to f times N^2, hence the name for this variable,
+ IPV_vs_fNsquared_ratio (see Eqn. (3.20.17) of IOC et al. (2010)).
+
+ Parameters
+ ----------
+ SA : array-like
+ Absolute Salinity, g/kg
+ t : array-like
+ In-situ temperature (ITS-90), degrees C
+ p : array-like
+ Sea pressure (absolute pressure minus 10.1325 dbar), dbar
+ p_ref : float
+ Reference pressure, dbar
+
+ Returns
+ -------
+ IPV_vs_fNsquared_ratio : array
+ The ratio of the vertical gradient of
+ potential density referenced to p_ref, to the vertical
+ gradient of locally-referenced potential density, dimensionless.
+ p_mid : array
+ Pressure at midpoints of p, dbar.
+ The array shape matches IPV_vs_fNsquared_ratio.
+
+ """
+
+ SA = np.clip(SA, 0, 50)
+ SA, CT, p = np.broadcast_arrays(SA, CT, p)
+ shallow = axis_slicer(SA.ndim, slice(-1), axis)
+ deep = axis_slicer(SA.ndim, slice(1, None), axis)
+
+ dSA = -SA[deep] + SA[shallow]
+ dCT = -CT[deep] + CT[shallow]
+
+ SA_mid = 0.5 * (SA[shallow] + SA[deep])
+ CT_mid = 0.5 * (CT[shallow] + CT[deep])
+ p_mid = 0.5 * (p[shallow] + p[deep])
+
+ _, alpha, beta = specvol_alpha_beta(SA_mid, CT_mid, p_mid)
+ _, alpha_pref, beta_pref = specvol_alpha_beta(SA_mid, CT_mid, p_ref)
+
+ num = dCT*alpha_pref - dSA*beta_pref
+ den = dCT*alpha - dSA*beta
+
+ igood = (den != 0)
+ IPV_vs_fNsquared_ratio = np.zeros_like(dSA)
+ IPV_vs_fNsquared_ratio.fill(np.nan)
+ IPV_vs_fNsquared_ratio[igood] = num[igood] / den[igood]
+
+ return IPV_vs_fNsquared_ratio, p_mid
diff --git a/gsw/test/__init__.py b/gsw/test/__init__.py
deleted file mode 100644
index 026fed5..0000000
--- a/gsw/test/__init__.py
+++ /dev/null
@@ -1 +0,0 @@
-# dummy--just to make it a sub-package
diff --git a/gsw/test/check_functions.py b/gsw/test/check_functions.py
deleted file mode 100644
index 7fa3b72..0000000
--- a/gsw/test/check_functions.py
+++ /dev/null
@@ -1,308 +0,0 @@
-"""
-Script to generate tests directly from gsw_check_functions.m.
-
-Usage (run from this test directory):
- python check_functions.py [gsw_matlab_dir]
-
-At present, this assumes by default that the matlab code resides
-in a "gsw_matlab_v3_04" directory which has been symlinked into
-the test directory. Alternatively, you may specify the directory
-as an optional argument.
-
-A primary use for this script is to see which functions are
-missing from python-gsw.
-
-The results are summarized at the end. The NameError category
-includes functions that are missing entirely from python-gsw;
-the TypeError category can include functions that are incomplete
-or otherwise not functioning.
-
-For functions that run but yield results that fail the check,
-the error arrays are printed.
-"""
-
-from __future__ import print_function
-import os
-import sys
-
-import numpy as np
-
-import gsw
-from gsw.gibbs import *
-from gsw.utilities import Bunch
-
-# If we switch to using the logging module, uncomment:
-# import logging
-# log = logging.getLogger()
-# logging.basicConfig()
-
-# There is probably a better way to handle the "invalid value"
-# problem, but for now we will ignore it. (Nans in the test arrays...)
-np.seterr(invalid='ignore')
-
-# There are also divide-by-zero warnings, which we will leave in
-# place. (library.py lines 1238, 1239; maybe something should be
-# done to block this, so we don't get inf values.)
-
-
-def find(x):
- """
- Numpy equivalent to Matlab find.
- """
- return np.nonzero(x.flatten())[0]
-
-
-def group_or(line):
- """
- Translate matlab 'find' functions including logical or operators.
-
- Example: the test for gsw_rho_alpha_beta
-
- Numpy wart: using bitwise or as a fake elementwise logical or,
- we need to add parentheses.
- """
- if not ('find(' in line and '|' in line):
- return line
- i0 = line.index('find(') + 5
- head = line[:i0]
- tail = line[i0:]
- parts = tail.replace('|', ') | (')
- new = head + '(' + parts + ')'
- return new
-
-
-class FunctionCheck(object):
- """
- Parse the line-pair for checks in gsw_check_functions.
- """
- def __init__(self, linepair):
- """
- *linepair* is the sequence of two lines; the first runs
- the function and assigns the output, and the second
- generates an array of indices where the output error
- exceeds a tolerance.
- """
-
- self.linepair = linepair
- self.runline = linepair[0]
- self.testline = linepair[1]
-
- # parse the line that runs the function
- head, tail = self.runline.split('=')
- self.outstrings = [s.strip() for s in head.split(',')]
- self.outstr = ','.join(self.outstrings)
- funcstr, argpart = tail.split('(', 1)
- self.name = funcstr.strip()
- self.argstrings = [s.strip() for s in argpart[:-1].split(',')]
- self.argstr = ','.join(self.argstrings)
-
- # parse the line that checks the results
- head, tail = self.testline.split('=', 1)
- self.resultstr = head.strip() # cv.I*
- head, tail = tail.split('(', 1)
- self.teststr = tail.strip()[:-1] # argument of "find()"
- self.teststr = self.teststr.replace('abs(', 'np.abs(')
-
- # To be set when run() is successful
- self.outlist = None
- self.result = None # will be a reference to the cv.I* array
- self.passed = None # will be set to True or False
-
- # To be set if run() is not successful
- self.exception = None
-
- def __str__(self):
- return self.runline
-
- def record_details(self):
- tline = self.testline
- i0 = 5 + tline.index('find(')
- tline = tline[i0:-1]
- checks = tline.split('|')
- parts = []
- for check in checks:
- check = check.strip()
- if check.startswith('('):
- check = check[1:-1].strip()
- part = Bunch(check=check)
- LHS, RHS = check.split('>=')
- part.tolerance = eval(RHS)
- LHS = LHS.strip()[4:-1] # chop off abs(...)
- target, calculated = LHS.split('-')
- part.checkval = eval(target)
- part.val = eval(calculated)
- parts.append(part)
-
- self.details = parts
-
- def run(self):
- try:
- exec(self.runline)
- # In Matlab, the number of output arguments varies
- # depending on the LHS of the assignment, but Python
- # always returns the full set. Here we handle the
- # case where Python is returning 2 (or more) but
- # the LHS is assigning only the first.
- if len(self.outstrings) == 1:
- if isinstance(eval(self.outstr), tuple):
- exec("%s = %s[0]" % (self.outstr, self.outstr))
- self.outlist = [eval(s) for s in self.outstrings]
- exec(self.testline)
- self.result = eval(self.resultstr)
- self.passed = len(self.result) == 0
- self.record_details()
-
- except Exception as e:
- self.exception = e
-
-
-def find_arguments(checks):
- """
- For a sequence of FunctionCheck instances, return the
- set of unique arguments as a sorted list.
- """
- argset = set()
- for c in checks:
- argset.update(c.argstrings)
- argsetlist = list(argset)
- argsetlist.sort()
- return argsetlist
-
-
-def find_arglists(checks):
- """
- For a sequence of FunctionCheck instances, return the
- set of unique argument lists as a sorted list.
- """
- alset = set()
- for c in checks:
- alset.update([c.argstr])
- arglists = list(alset)
- arglists.sort()
- return arglists
-
-def parse_check_functions(mfile):
- """
- Return a list of FunctionCheck instances from gsw_check_functions.m
- """
-
- with open(mfile, 'rt') as fid:
- mfilelines = fid.readlines()
-
- first_pass = []
-
- concat = False
- for line in mfilelines:
- line = line.strip()
- if concat:
- if line.endswith('...'):
- line = line[:-3]
- first_pass[-1] += line
- if line.endswith(';'):
- concat = False
- continue
- if '=' in line and (line.startswith('gsw_') or line.startswith('[gsw_')):
- if line.endswith('...'):
- line = line[:-3]
- concat = True
- first_pass.append(line)
-
- second_pass = []
-
- for line in first_pass:
- if not '(' in line:
- continue
- if 'which' in line:
- continue
- line = line.replace('gsw_', '')
- if line.startswith('['):
- line = line[1:].replace(']', '')
- if line.endswith(';'):
- line = line[:-1]
- line = line.replace('(I)', '') # For deltaSA_atlas.
- second_pass.append(line)
-
- pairs = []
-
- for i in range(len(second_pass)):
- if 'find(' in second_pass[i] and not 'find(' in second_pass[i-1]:
- pairs.extend(second_pass[i-1:i+1])
-
- final = [group_or(line) for line in pairs]
-
- checks = []
- for i in range(0, len(final), 2):
- pair = final[i:i+2]
- checks.append(FunctionCheck(pair))
-
- return checks
-
-if __name__ == '__main__':
- import argparse
-
- parser = argparse.ArgumentParser(
- description='Run checks from gsw_check_functions.m')
-
- parser.add_argument('--path', dest='mfiledir',
- default="gsw_matlab_v3_04",
- help='location of gsw_check_functions.m')
- parser.add_argument('-v', '--verbose',
- action='store_true',
- help='print output mismatch arrays')
- parser.add_argument('--find',
- help='run functions with this substring')
-
- args = parser.parse_args()
-
- mfile = os.path.join(args.mfiledir, "gsw_check_functions.m")
- checks = parse_check_functions(mfile)
-
- datadir = os.path.join(os.path.dirname(gsw.utilities.__file__), 'data')
- cv = Bunch(np.load(os.path.join(datadir, 'gsw_cv_v3_0.npz')))
- cf = Bunch()
-
- if args.find:
- checks = [c for c in checks if args.find in c.runline]
-
- for fc in checks:
- fc.run()
-
- passes = [f for f in checks if f.passed]
- failures = [f for f in checks if f.passed is False]
-
- run_problems = [f for f in checks if f.exception is not None]
-
- etypes = [NameError, UnboundLocalError, TypeError, AttributeError]
- ex_dict = dict()
- for exc in etypes:
- elist = [(f.name, f.exception) for f in checks if
- isinstance(f.exception, exc)]
- ex_dict[exc] = elist
-
- print("\n%s tests were translated from gsw_check_functions.m" % len(checks))
- print("\n%s tests ran with no error and with correct output" % len(passes))
- print("\n%s tests had an output mismatch:" % len(failures))
- for f in failures:
- print(f.name)
- print(f.runline)
- print(f.testline)
- if args.verbose:
- print(f.result)
- for part in f.details:
- print("tolerance: ", part.tolerance)
- print("error:")
- print(part.checkval - part.val)
- print('')
-
- print('')
-
- print("\n%s exceptions were raised as follows:" % len(run_problems))
- for exc in etypes:
- print(" ", exc.__name__)
- strings = [" %s : %s" % e for e in ex_dict[exc]]
- print("\n".join(strings))
- print("")
-
- checkbunch = Bunch([(c.name, c) for c in checks])
-
-
diff --git a/gsw/test/signatures.py b/gsw/test/signatures.py
deleted file mode 100644
index ea19f2b..0000000
--- a/gsw/test/signatures.py
+++ /dev/null
@@ -1,178 +0,0 @@
-"""
-Functions for parsing gsw mfiles.
-
-These might become useful in a scheme for automating docstring
-generation.
-"""
-
-import os
-import sys
-import glob
-from collections import OrderedDict
-
-import logging
-
-from gsw.gibbs import *
-
-log = logging.getLogger()
-logging.basicConfig()
-
-try:
- mfiledir = sys.argv[1]
-except IndexError:
- mfiledir = "../../../../TEOS-10/matlab_gsw_V3_03"
-
-subdirs = ['./', 'library', 'thermodynamics_from_t']
-
-mfile = os.path.join(mfiledir, "gsw_check_functions.m")
-mfilelines = open(mfile, 'rt').readlines()
-
-
-def funcline_parts(base, topline):
- """
- Parse the m-file function declaration.
-
- Returns [base, arguments, outputs] where base is the
- function name without the gsw_ prefix, arguments is a
- tuple of strings, and outputs is a tuple of strings.
- """
-
- cmd = topline.split(None, 1)[1]
-
- parts = cmd.split('=')
- if len(parts) == 1:
- out = ''
- func_call = parts[0].strip()
- else:
- out = parts[0].strip()
- if out.startswith('['):
- out = out[1:-1]
- func_call = parts[1].strip()
- out = [a.strip() for a in out.split(',')]
-
- parts = func_call.split('(')
- if len(parts) == 1:
- argstring = ''
- else:
- argstring = parts[1][:-1]
-
- args = [a.strip() for a in argstring.split(',')]
-
- parts = [base[4:], tuple(args), tuple(out)]
- return parts
-
-help_sections = ['USAGE:',
- 'DESCRIPTION:',
- 'INPUT:',
- 'OPTIONAL:',
- 'OUTPUT:',
- 'AUTHOR:',
- 'VERSION NUMBER:',
- 'REFERENCES:',
- ]
-
-
-def helptext_parts(lines):
- """
- Parse the help text from gsw m-files.
-
- Returns [lines, indexdict], where lines are the lines of
- text with extraneous material removed, and indexdict is
- a dictionary in which the keys are the help sections and
- the values are the indices into lines where the section
- titles are found.
- """
- helplines = []
- parts = OrderedDict()
- for line in lines[2:]:
- line = line.rstrip()
- if line.startswith('%'):
- if line.endswith('=========================='):
- continue
- helplines.append(line[1:])
- else:
- break
- for i, line in enumerate(helplines):
- for section in help_sections:
- if section in line:
- parts[section] = i
-
- return helplines, parts
-
-
-def function_parts(subdir='./'):
- """
- Parse the gsw m-files in a given subdirectory.
-
- Returns a list of parts: function base name, arguments,
- inputs, and the help lines with a section index dictionary.
- """
-
- d = os.path.join(mfiledir, subdir)
- mfilelist = glob.glob(os.path.join(d, '*.m'))
- partslist = []
- for fpath in mfilelist:
- base = os.path.basename(fpath)[:-2]
- if not base.startswith('gsw_') or base == 'gsw_check_functions':
- continue
- lines = open(fpath).readlines()
- topline = lines[0].strip()
- if not topline.startswith('function'):
- log.warn("path %s, topline is\n%s", fpath, topline)
- continue
-
- parts = funcline_parts(base, topline)
-
- parts.append(helptext_parts(lines))
-
- partslist.append(parts)
-
- return partslist
-
-
-def arguments(partslist):
- args = set()
- for entry in partslist:
- args.update(entry[1])
-
- arglist = list(args)
- arglist.sort()
- return arglist
-
-
-def arglists(partslist):
- args = set()
- for entry in partslist:
- args.update([', '.join(entry[1])])
-
- arglist = list(args)
- arglist.sort()
- return arglist
-
-
-def funclist_by_arg(partslist):
- out = dict()
- for entry in partslist:
- if entry[1] not in out:
- out[entry[1]] = []
- out[entry[1]].append(entry[0])
- return out
-
-
-def help_chunk(helptuple, sect):
- lines, secdict = helptuple
- sections = list(secdict.keys())
- ind = list(secdict.values())
- try:
- i0 = sections.index(sect)
- except ValueError:
- return [] # or None?
- # Assuming the sections are always in the expected order, this will
- # work; otherwise we would have to look for the nearest section index
- # after the one found.
- return lines[ind[i0]:ind[i0 + 1]]
-
-
-def funcs_with_descriptions(partslist):
- fdlist = [(p[0], help_chunk(p[3], 'DESCRIPTION:')) for p in partslist]
- return OrderedDict(fdlist)
diff --git a/gsw/test/test_octave.py b/gsw/test/test_octave.py
deleted file mode 100644
index 4bf152a..0000000
--- a/gsw/test/test_octave.py
+++ /dev/null
@@ -1,245 +0,0 @@
-# -*- coding: utf-8 -*-
-"""
-Script to test by comparing output from python with that from octave.
-
-Usage (run from this test directory):
- python test_octave.py [gsw_matlab_dir]
-
-At present, this assumes by default that the matlab code resides
-in a "gsw_matlab_v3_04" directory which has been symlinked into
-the test directory. Alternatively, you may specify the directory
-as an optional argument.
-
-For functions that return more than one variable, only the
-first is tested.
-
-"""
-
-#
-# test_octave.py
-#
-# purpose: Quick "compare test" with octave results.
-# author: Filipe P. A. Fernandes
-# e-mail: ocefpaf at gmail
-# web: http://ocefpaf.tiddlyspot.com/
-# created: 13-Jun-2013
-# modified: Tue 02 Jul 2013 07:45:17 PM BRT
-#
-# obs: This is different from `test_check_values.py`, that tests
-# against the results in the docs, `test_octave.py` uses same input values to
-# run both python and Matlab versions (using Octave).
-#
-# This is not a thorough test, just an "ad hoc" test to compare when a new
-# Matlab version is released.
-#
-
-from __future__ import print_function
-
-import os
-import sys
-from collections import OrderedDict
-
-import numpy as np
-
-from oct2py import Oct2Py
-from oct2py import Oct2PyError
-
-import gsw
-
-
-def get_octave(path):
- """
- Return an Oct2Py instance with a suitable path.
-
- It can be useful to have this as a function because
- an exception in oct2py kills the module-level instance.
- """
- engine = Oct2Py(oned_as='column') # 'column' makes interp_SA_CT work
- _ = engine.addpath(engine.genpath(path))
- _ = engine.addpath('./')
- return engine
-
-
-def compare_results(name, function, args, octave):
- args = [values.get(arg) for arg in args]
- print(name)
-
- try: # Python.
- res = function(*args)
- except:
- print('%s: python runtime error' % name)
- raise
- return 'no_python'
-
- if isinstance(res, tuple):
- res = res[0]
-
- try: # Octave.
- ocmd = octave.__getattr__('gsw_%s' % (name,))
- val = ocmd(*args)
- except Exception as err: #Oct2PyError as err:
- print('%s: Octave runtime error; %s' % (name, err))
- print("python:\n%s" % res)
- return 'no_octave'
-
- if isinstance(val, tuple):
- val = val[0]
-
- try:
- val = val.flatten()
- perfect = (val == res).all()
- except:
- print('%s: Comparison failed' % name)
- print("octave:\n%s" % val)
- print("python:\n%s" % res)
- return 'no_comparison'
- if (np.allclose(val, res, rtol=1e-15, atol=0) or
- (np.all(np.isnan(val)) and np.all(np.isnan(res)))):
- print('%s: Passed' % name)
- return 'passed'
- else:
- print('%s: Failed' % name)
- print("octave:\n%s" % val)
- print("python:\n%s" % res)
- print("python - octave:\n%s" % (res -val))
- return 'failed'
- print('')
-
-#############################################################################
-
-values = dict(C=np.array([34.5487, 34.7275, 34.8605, 34.6810, 34.568, 34.56]),
- t=np.array([28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]),
- p=np.array([10., 50., 125., 250., 600., 1000.]),
- SP=np.array([34.5487, 34.7275, 34.8605, 34.6810, 34.5680,
- 34.5600]),
- SA=np.array([34.7118, 34.8915, 35.0256, 34.8472, 34.7366,
- 34.7324]),
- CT=np.array([28.7856, 28.4329, 22.8103, 10.2600, 6.8863,
- 4.4036]),
- rho=np.array([1021.8484, 1022.2647, 1024.4207, 1027.7841,
- 1029.8287, 1031.9916]),
- ps=0, pt=0, pp=0,
- lat=np.array([4., 4., 4., 4., 4., 4.]),
- lon=np.array([188., 188., 188., 188., 188., 188.]),
- pt0=np.array([28.8099, 28.4392, 22.7862, 10.2262, 6.8272,
- 4.3236]),
- spycnl=np.array([21.8482, 22.2647, 24.4207, 27.7841, 29.8287,
- 31.9916]),
- A='gn', # or s2 for sigma2; but then spycnl would need to change
- # Also, the matlab code is incorrect for the s2 case.
- p_i=np.array([500.0, 600.0, 700.0]),
- # Baltic.
- SAb=np.array([6.6699, 6.7738, 6.9130, 7.3661, 7.5862, 10.3895]),
- SPb=np.array([6.5683, 6.6719, 6.8108, 7.2629, 7.4825, 10.2796]),
- latb=np.array([59., 59., 59., 59., 59., 59.]),
- lonb=np.array([20., 20., 20., 20., 20., 20.])
- )
-# Functions.
-library = OrderedDict({
- # library.py
- 'deltaSA_atlas': (gsw.library.deltaSA_atlas, ('p', 'lon', 'lat')),
- 'enthalpy_SSO_0_p': (gsw.library.enthalpy_SSO_0_p, ('p')),
- 'entropy_part': (gsw.library.entropy_part, ('SA', 't', 'p')),
- 'entropy_part_zerop': (gsw.library.entropy_part_zerop, ('SA', 'pt0')),
- 'Fdelta': (gsw.library.Fdelta, ('p', 'lon', 'lat')),
- 'gibbs': (gsw.library.gibbs, ('ps', 'pt', 'pp', 'SA', 't', 'p')),
- 'gibbs_pt0_pt0': (gsw.library.gibbs_pt0_pt0, ('SA', 'pt0')),
- 'Hill_ratio_at_SP2': (gsw.library.Hill_ratio_at_SP2, ('t')),
- 'infunnel': (gsw.library.infunnel, ('SA', 'CT', 'p')),
- 'interp_ref_cast': (gsw.library.interp_ref_cast, ('spycnl', 'A')),
- 'interp_SA_CT': (gsw.library.interp_SA_CT, ('SA', 'CT', 'p', 'p_i')),
- 'SAAR': (gsw.library.SAAR, ('p', 'lon', 'lat')),
- 'SA_from_SP_Baltic': (gsw.library.SA_from_SP_Baltic, ('SPb', 'lonb',
- 'latb')),
- 'specvol_SSO_0_p': (gsw.library.specvol_SSO_0_p, ('p')),
- 'SP_from_SA_Baltic': (gsw.library.SP_from_SA_Baltic, ('SAb', 'lonb',
- 'latb')),
- # thermodynamics_from_t.py
- #'adiabatic_lapse_rate_from_t': (gsw.adiabatic_lapse_rate_from_t,
- #('SA', 't', 'p')),
- 'alpha_wrt_CT_t_exact': (gsw.alpha_wrt_CT_t_exact, ('SA', 't', 'p')),
- 'alpha_wrt_pt_t_exact': (gsw.alpha_wrt_pt_t_exact, ('SA', 't', 'p')),
- 'alpha_wrt_t_exact': (gsw.alpha_wrt_t_exact, ('SA', 't', 'p')),
- 'beta_const_CT_t_exact': (gsw.beta_const_CT_t_exact, ('SA', 't', 'p')),
- 'beta_const_pt_t_exact': (gsw.beta_const_pt_t_exact, ('SA', 't', 'p')),
- 'beta_const_t_exact': (gsw.beta_const_t_exact, ('SA', 't', 'p')),
- 'chem_potential_relative_t_exact': (gsw.chem_potential_relative_t_exact,
- ('SA', 't', 'p')),
- 'chem_potential_salt_t_exact': (gsw.chem_potential_salt_t_exact,
- ('SA', 't', 'p')),
- 'chem_potential_water_t_exact': (gsw.chem_potential_water_t_exact,
- ('SA', 't', 'p')),
- 'cp_t_exact': (gsw.cp_t_exact, ('SA', 't', 'p')),
- #'deltaSA_from_rho_t_exact': (gsw.deltaSA_from_rho_t_exact,
- #('rho', 'SP', 't', 'p')),
- 'dynamic_enthalpy_t_exact': (gsw.dynamic_enthalpy_t_exact,
- ('SA', 't', 'p')),
- 'enthalpy_t_exact': (gsw.enthalpy_t_exact, ('SA', 't', 'p')),
- 'entropy_t_exact': (gsw.entropy_t_exact, ('SA', 't', 'p')),
- 'Helmholtz_energy_t_exact': (gsw.Helmholtz_energy_t_exact,
- ('SA', 't', 'p')),
- 'internal_energy_t_exact': (gsw.internal_energy_t_exact, ('SA', 't', 'p')),
- 'isochoric_heat_cap_t_exact': (gsw.isochoric_heat_cap_t_exact,
- ('SA', 't', 'p')),
- 'kappa_const_t_exact': (gsw.kappa_const_t_exact, ('SA', 't', 'p')),
- 'kappa_t_exact': (gsw.kappa_t_exact, ('SA', 't', 'p')),
- 'osmotic_coefficient_t_exact': (gsw.osmotic_coefficient_t_exact,
- ('SA', 't', 'p')),
- 'osmotic_pressure_t_exact': (gsw.osmotic_pressure_t_exact,
- ('SA', 't', 'pw')),
- 'pot_rho_t_exact': (gsw.pot_rho_t_exact, ('SA', 't', 'p', 'p_ref')),
- 'rho_t_exact': (gsw.rho_t_exact, ('SA', 't', 'p')),
- 'SA_from_rho_t_exact': (gsw.SA_from_rho_t_exact, ('rho', 't', 'p')),
- #'SA_from_rho_t': (gsw.SA_from_rho_t, ('rho', 't', 'p')),
- 'sigma0_pt0_exact': (gsw.sigma0_pt0_exact, ('SA', 'pt0')),
- 'sound_speed_t_exact': (gsw.sound_speed_t_exact, ('SA', 't', 'p')),
- 'specvol_anom_t_exact': (gsw.specvol_anom_t_exact, ('SA', 't', 'p')),
- 'specvol_t_exact': (gsw.specvol_t_exact, ('SA', 't', 'p')),
- 't_from_rho_exact': (gsw.t_from_rho_exact, ('rho', 'SA', 'p')),
- 't_maxdensity_exact': (gsw.t_maxdensity_exact, ('SA', 'p')),
- # absolute_salinity_sstar_ct.py
- 'SA_from_SP': (gsw.SA_from_SP, ('SP', 'p', 'lon', 'lat'))})
-
-
-if __name__ == '__main__':
- try:
- path = sys.argv[1]
- except IndexError:
- path = "gsw_matlab_v3_04"
-
- if not os.path.exists(path):
- raise ValueError("matlab gsw path %s not found" % path)
-
- octave = get_octave(path)
- #print('\n'.join(octave.path().split(':')))
-
-
- # We have to supply a fake superiorfloat function for octave.
- # We are writing it in the local directory, which is not a nice
- # thing to do; maybe this can be improved later.
-
- _sfloat = """function out = superiorfloat(varargin)
- out = 'double';
- """
- open('superiorfloat.m', 'wt').write(_sfloat)
-
-
-
-
-
- outcomes = ['passed', 'no_octave', 'no_python', 'failed', 'no_comparison']
- results = dict([(k, list()) for k in outcomes])
-
- for name, (function, args) in library.items():
- ret = compare_results(name, function, args, octave)
- results[ret].append(name)
-
- #os.remove('superiorfloat.m')
-
- print('\nSummary:')
- print('passed:\n %s' % '\n '.join(results['passed']))
- print('octave call failed:\n %s' % '\n '.join(results['no_octave']))
- print('python call failed:\n %s' % '\n '.join(results['no_python']))
- print('results did not match:\n %s' % '\n '.join(results['failed']))
- print('comparison failed:\n %s' % '\n '.join(results['no_comparison']))
- print('')
diff --git a/gsw/test/test_profiles.py b/gsw/test/test_profiles.py
deleted file mode 100644
index 5da9d15..0000000
--- a/gsw/test/test_profiles.py
+++ /dev/null
@@ -1,344 +0,0 @@
-# -*- coding: utf-8 -*-
-
-
-"""
-Unit check for standard profiles for the Gibbs Sea Water python package.
-"""
-
-from __future__ import print_function
-
-# Auto generates and perform a set of test methods like:
-#
-# def test_funct(self):
-# out = gsw.func(arg1_chck_cast, arg2_chck_cast, ...)
-# maxdiff = np.nanmax(abs(out - cv.func)
-# self.assertTrue(maxdiff < cv.func_ca)
-#
-# cv is a Bunch instance with all the check values from
-# the profile-file
-# The func, args are taken from the main dictionary below
-# giving a alphabetical table of all functions and their arguments
-#
-# Extra aliasing attributes are added to cv if the naming
-# convention is broken, if the targets or the attributes
-# in the check file has "wrong" names
-#
-
-
-# Bjørn Ådlandsvik <bjorn at imr.no>
-# 2011-03-03
-
-import os
-import unittest
-import functools # Requires python 2.5.
-import numpy as np
-
-import gsw
-from gsw.utilities import Bunch
-
-
-# Read data file with check value profiles.
-datadir = os.path.join(os.path.dirname(gsw.utilities.__file__), 'data')
-cv = Bunch(np.load(os.path.join(datadir, 'gsw_cv_v3_0.npz')))
-cf = Bunch(np.load(os.path.join(datadir, 'gsw_cf.npz')))
-
-# Main dictionary of functions with arguments. Could perhaps be auto-generated.
-function_arguments = dict(
- # absolute_salinity_sstar_ct.py
- SA_from_SP=('SP', 'p', 'long', 'lat'), # uses SAAR
- # Sstar_from_SP TODO
- CT_from_t=('SA', 't', 'p'),
- #
- # thermodynamics_from_t.py
- rho_t_exact=('SA', 't', 'p'),
- pot_rho_t_exact=('SA', 't', 'p', 'pr'),
- sigma0_pt0_exact=('SA', 'pt0'),
- alpha_wrt_CT_t_exact=('SA', 't', 'p'),
- alpha_wrt_pt_t_exact=('SA', 't', 'p'),
- alpha_wrt_t_exact=('SA', 't', 'p'),
- beta_const_CT_t_exact=('SA', 't', 'p'),
- beta_const_pt_t_exact=('SA', 't', 'p'),
- beta_const_t_exact=('SA', 't', 'p'),
- specvol_t_exact=('SA', 't', 'p'),
- specvol_anom_t_exact=('SA', 't', 'p'),
- sound_speed_t_exact=('SA', 't', 'p'),
- kappa_t_exact=('SA', 't', 'p'),
- kappa_const_t_exact=('SA', 't', 'p'),
- internal_energy_t_exact=('SA', 't', 'p'),
- enthalpy_t_exact=('SA', 't', 'p'),
- dynamic_enthalpy_t_exact=('SA', 't', 'p'),
- SA_from_rho_t_exact=('rho', 't', 'p'),
- # t_from_rho_exact=('rho', 'SA', 'p'),
- t_maxdensity_exact=('SA', 'p'),
- # entropy_t_exact=('SA', 't', 'p'), # Not in V3.03
- cp_t_exact=('SA', 't', 'p'),
- isochoric_heat_cap_t_exact=('SA', 't', 'p'),
- chem_potential_relative_t_exact=('SA', 't', 'p'),
- chem_potential_water_t_exact=('SA', 't', 'p'),
- chem_potential_salt_t_exact=('SA', 't', 'p'),
- Helmholtz_energy_t_exact=('SA', 't', 'p'),
- # adiabatic_lapse_rate_t_exact=('SA', 't', 'p'), # Not in V3.03
- osmotic_coefficient_t_exact=('SA', 't', 'p'),
- osmotic_pressure_t_exact=('SA', 't', 'p'),
- #
- # conversion.py
- # deltaSA_from_SP TODO
- # SA_Sstar_from_SP TODO
- SR_from_SP=('SP',),
- SP_from_SR=('SR',),
- # SP_from_SA=('SA', 'p', 'long', 'lat'), TODO
- # Sstar_from_SA=('SA', 'p', 'long', 'lat'), TODO
- # SA_from_Sstar=('Sstar', 'p', 'long', 'lat'), TODO
- # SP_from_Sstar=('Sstar', 'p', 'long', 'lat'), TODO
- pt_from_CT=('SA', 'CT'),
- t_from_CT=('SA', 'CT', 'p'),
- CT_from_pt=('SA', 'pt'),
- pot_enthalpy_from_pt=('SA', 'pt'),
- pt0_from_t=('SA', 't', 'p'),
- pt_from_t=('SA', 't', 'p', 'pr'),
- t90_from_t48=('t',),
- t90_from_t68=('t',),
- z_from_p=('p', 'lat'),
- p_from_z=('z', 'lat'),
- depth_from_z=('z'),
- z_from_depth=('depth',),
- Abs_Pressure_from_p=('p',),
- p_from_Abs_Pressure=('Abs_Pressure_from_p',),
- entropy_from_CT=('SA', 'CT'),
- CT_from_entropy=('SA', 'entropy'),
- entropy_from_pt=('SA', 'pt'),
- pt_from_entropy=('SA', 'entropy'),
- molality_from_SA=('SA',),
- ionic_strength_from_SA=('SA',),
- #
- # density_enthalpy_48_ct.py
- # rho_CT TODO
- # alpha_CT TODO
- # beta_CT TODO
- # rho_alpha_beta_CT TODO
- # specvol_CT TODO
- # specvol_anom_CT TODO
- # sigma0_CT TODO
- # sigma1_CT TODO
- # sigma2_CT TODO
- # sigma3_CT TODO
- # sigma4_CT TODO
- # sound_speed_CT TODO
- # internal_energy_CT TODO
- # enthalpy_CT TODO
- # enthalpy_diff_CT TODO
- # dynamic_enthalpy_CT TODO
- # SA_from_rho_CT TODO
- # CT_from_rho TODO
- # CT_maxdensity TODO
- #
- # density_enthalpy_48.py NOTE: None are tested on Matlab.
- #rho=('SA', 'CT', 'p'),
- #alpha=('SA', 'CT', 'p'),
- beta=('SA', 'CT', 'p'),
- rho_alpha_beta=('SA', 'CT', 'p'),
- #specvol=('SA', 'CT', 'p'),
- specvol_anom=('SA', 'CT', 'p'),
- sigma0=('SA', 'CT'),
- sigma1=('SA', 'CT'),
- sigma2=('SA', 'CT'),
- sigma3=('SA', 'CT'),
- sigma4=('SA', 'CT'),
- sound_speed=('SA', 'CT', 'p'),
- internal_energy=('SA', 'CT', 'p'),
- enthalpy=('SA', 'CT', 'p'),
- enthalpy_diff=('SA', 'CT', 'p_shallow', 'p_deep'),
- dynamic_enthalpy=('SA', 'CT', 'p'),
- SA_from_rho=('rho_cf', 'CT', 'p'),
- #
- # density_enthalpy_ct_exact.py
- rho_CT_exact=('SA', 'CT', 'p'),
- alpha_CT_exact=('SA', 'CT', 'p'),
- beta_CT_exact=('SA', 'CT', 'p'),
- rho_alpha_beta_CT_exact=('SA', 'CT', 'p'),
- specvol_CT_exact=('SA', 'CT', 'p'),
- specvol_anom_CT_exact=('SA', 'CT', 'p'),
- sigma0_CT_exact=('SA', 'CT'),
- sigma1_CT_exact=('SA', 'CT'),
- sigma2_CT_exact=('SA', 'CT'),
- sigma3_CT_exact=('SA', 'CT'),
- sigma4_CT_exact=('SA', 'CT'),
- sound_speed_CT_exact=('SA', 'CT', 'p'),
- internal_energy_CT_exact=('SA', 'CT', 'p'),
- enthalpy_CT_exact=('SA', 'CT', 'p'),
- enthalpy_diff_CT_exact=('SA', 'CT', 'p_shallow', 'p_deep'),
- dynamic_enthalpy_CT_exact=('SA', 'CT', 'p'),
- SA_from_rho_CT_exact=('rho', 'CT', 'p'),
- # FIXME: NameError: 't_from_rho_exact' not defined
- # CT_from_rho_exact=('rho', 'SA', 'p'),
- CT_maxdensity_exact=('SA', 'p'),
- #
- # derivatives.py
- # CT_first_derivatives=('SA', 'pt'), FIXME: out should tuple.
- # CT_second_derivatives=('SA', 'pt'), FIXME: out should tuple.
- # enthalpy_first_derivatives=('SA', 'CT', 'p'), FIXME: out should tuple.
- # enthalpy_second_derivatives=('SA', 'CT', 'p'), FIXME: out should tuple.
- # entropy_first_derivatives=('SA', 'CT'), FIXME: out should tuple.
- # entropy_second_derivatives=('SA', 'CT'), FIXME: out should tuple.
- # pt_first_derivatives=('SA', 'CT'), FIXME: out should tuple.
- # pt_second_derivatives=('SA', 'CT'), FIXME: out should tuple.
- #
- # earth.py
- f=('lat',),
- grav=('lat', 'p'),
- distance=('long', 'lat', 'p'),
- #
- # freezing.py
- # NOTE: The matlab test does not use saturation_fraction=1 which is the
- # default! It uses saturation_fraction=0.
- CT_freezing=('SA', 'p', 'sat0'),
- t_freezing=('SA', 'p', 'sat0'),
- brineSA_CT=('CT_freezing', 'p', 'sat05'),
- brineSA_t=('t_freezing', 'p', 'sat05'),
- #
- # geostrophic.py
- # geostrophic_velocity TODO
- #
- # geostrophic_48.py
- # geo_strf_dyn_height TODO
- # geo_strf_dyn_height_pc TODO
- # geo_strf_isopycnal TODO
- # geof_str_isopycnal_pc TODO
- # geo_strf_Montgomery TODO
- # geo_strf_Cunningham TODO
- #
- # isobaric.py
- # latentheat_melting TODO
- # latentheat_evap_CT TODO
- # latentheat_evap_t=('SA', 't'),
- #
- # library.py
- # gibbs
- # SAAR=('p', 'long', 'lat'), # not directly tested on Matlab
- Fdelta=('p', 'long', 'lat'),
- deltaSA_atlas=('p', 'long', 'lat'),
- # SA_from_SP_Baltic=('SP', 'long', 'lat'), NOTE: Not tested on Matlab.
- # SP_from_SA_Baltic=('SA', 'long', 'lat'), NOTE: Not tested on Matlab.
- # infunnel=('SA', 'CT', 'p'), NOTE: Not tested on Matlab.
- # entropy_part=('SA', 'CT', 'p'), NOTE: Not tested on Matlab.
- # entropy_part_zerop=('SA', 'pt0'), NOTE: Not tested on Matlab.
- # interp_ref_cast=('spycnl', 'gn'), NOTE: Not tested on Matlab.
- # interp_SA_CT=('SA', 'CT', 'p', 'p_i'), NOTE: Not tested on Matlab.
- # gibbs_pt0_pt0=('SA', 'pt0'), NOTE: Not tested on Matlab.
- # specvol_SSO_0_p=('p'), NOTE: Not tested on Matlab.
- # enthalpy_SSO_0_p=('p',), FIXME: No enthalpy_SSO_0_p.
- # Hill_ratio_at_SP2= ('t'), FIXME: No Hill_ratio_at_SP2.
- #
- # neutral_nonlinear_48.py
- # cabbeling, TODO
- # thermobaric, TODO
- # isopycnal_slope_ratio, TODO
- # isopycnal_vs_ntp_CT_ratio, TODO
- # ntp_pt_vs_CT_ratio TODO
- #
- # practical_salinity.py
- SP_from_C=('C', 't', 'p'),
- C_from_SP=('SP', 't', 'p'),
- SP_from_R=('R_cf', 't', 'p'),
- R_from_SP=('SP', 't', 'p'),
- SP_salinometer=('Rt', 't'),
- # SP_from_SK=('SK',), NOTE: Not tested on Matlab.
- # SK_from_SP=('SP',), NOTE: Not tested on Matlab.
- #
- # steric.py
- # steric_height=TODO
- #
- # water_column_48.py
- Nsquared=('SA', 'CT', 'p', 'lat'),
- Turner_Rsubrho=('SA', 'CT', 'p'),
- IPV_vs_fNsquared_ratio=('SA', 'CT', 'p'))
-
-
-# Make aliases for some values to be used as arguments.
-cv.entropy_chck_cast = cv.entropy_from_CT
-cv.Abs_Pressure_from_p_chck_cast = cv.Abs_Pressure_from_p
-cv.depth_chck_cast = cv.depth_from_z
-cv.C_chck_cast = cv.C_from_SP
-cv.pt_chck_cast = cv.pt_from_t
-cv.z_chck_cast = cv.z_from_p
-cv.SR_chck_cast = cv.SR_from_SP
-cv.pr_chck_cast = cv.pr
-cv.p_shallow_chck_cast = cv.p_chck_cast_shallow
-cv.p_deep_chck_cast = cv.p_chck_cast_deep
-cv.rho_chck_cast = cv.rho_CT_exact
-cv.rho_CTrab_exact_ca = cv.rho_CT_exact_rab_ca
-cv.CT_freezing_chck_cast = cv.CT_freezing
-cv.t_freezing_chck_cast = cv.t_freezing
-cv.sat0_chck_cast = 0
-cv.sat05_chck_cast = 0.5
-
-# Aliases from computed values.
-cv.R_cf_chck_cast = cf.R
-cv.rho_cf_chck_cast = cf.rho
-cv.pt0_chck_cast = cf.pt0_from_t
-
-# Functions and targets which does not follow the naming convention.
-not_match = {
- 'CT_first_derivatives': 'CT_SA',
- 'CT_second_derivatives': 'CT_SA_SA',
- 'enthalpy_first_derivatives': 'h_SA',
- 'enthalpy_second_derivatives': 'h_SA_SA',
- 'entropy_first_derivatives': 'eta_SA',
- 'entropy_second_derivatives': 'eta_SA_SA',
- 'pt_first_derivatives': 'pt_SA',
- 'pt_second_derivatives': 'pt_SA_SA',
- 'Turner_Rsubrho': 'Tu',
- 'IPV_vs_fNsquared_ratio': 'IPVfN2',
- 'Nsquared': 'n2',
- # 'chem_potential_relative_t_exact': 'chem_potential_t_exact',
- 'rho_alpha_beta_CT_exact': 'rho_CTrab_exact',
- 'rho_alpha_beta': 'rho_rab'}
-
-# Add target aliases to cv.
-for f in not_match:
- setattr(cv, f, getattr(cv, not_match[f]))
- setattr(cv, f + '_ca', getattr(cv, not_match[f] + '_ca'))
-
-
-# Generic test method.
-def generic_test(self, func=None, argnames=None):
- """Generic test function, to be specialized by functools.partial."""
- # Transform argument names to name convention in cv dataset.
- args = [getattr(cv, a + '_chck_cast') for a in argnames]
- # Perform the function call
- out = getattr(gsw, func)(*args)
- # FIXME: Testing just the first output!
- # Check that the maximal error is less than the given tolerance
- if isinstance(out, tuple):
- out = out[0]
- # print("""%s returns a tuple.""" % func)
- target = getattr(cv, func)
- maxdiff = np.nanmax(abs(out - target))
- maxallowed = getattr(cv, func + '_ca')
- try:
- self.assertTrue(maxdiff < maxallowed)
- except AssertionError as e:
- print(out)
- print(target)
- raise AssertionError("Error in %s %s, maxdiff is %s vs %s allowed" %
- (func, e.args, maxdiff, maxallowed))
-
-
-# Dictionary of functions with corresponding test methods.
-function_test = {}
-for f in function_arguments:
- function_test[f] = functools.partial(generic_test, func=f,
- argnames=function_arguments[f])
-
-
-# Auto-generated TestCase.
-class Test_profiles(unittest.TestCase):
-
- for f in function_test:
- method_def = ("test_" + f +
- " = lambda self: function_test['" + f + "'](self)")
- exec(method_def)
-
-
-if __name__ == '__main__':
- unittest.main(verbosity=2)
diff --git a/gsw/utilities/__init__.py b/gsw/utilities/__init__.py
deleted file mode 100644
index c1de93c..0000000
--- a/gsw/utilities/__init__.py
+++ /dev/null
@@ -1,3 +0,0 @@
-# -*- coding: utf-8 -*-
-from .utilities import (Bunch, match_args_return, read_data, strip_mask,
- loadmatbunch)
diff --git a/gsw/utilities/data/gsw_cf.npz b/gsw/utilities/data/gsw_cf.npz
deleted file mode 100644
index f387803..0000000
Binary files a/gsw/utilities/data/gsw_cf.npz and /dev/null differ
diff --git a/gsw/utilities/data/gsw_cv_v3_0.npz b/gsw/utilities/data/gsw_cv_v3_0.npz
deleted file mode 100644
index 7668c3e..0000000
Binary files a/gsw/utilities/data/gsw_cv_v3_0.npz and /dev/null differ
diff --git a/gsw/utilities/data/gsw_data_v3_0.npz b/gsw/utilities/data/gsw_data_v3_0.npz
deleted file mode 100644
index b963c5b..0000000
Binary files a/gsw/utilities/data/gsw_data_v3_0.npz and /dev/null differ
diff --git a/gsw/utilities/data/gsw_demo_data_v3_0.npz b/gsw/utilities/data/gsw_demo_data_v3_0.npz
deleted file mode 100644
index ea4ae9c..0000000
Binary files a/gsw/utilities/data/gsw_demo_data_v3_0.npz and /dev/null differ
diff --git a/gsw/utilities/list_npz.py b/gsw/utilities/list_npz.py
deleted file mode 100644
index 60b608b..0000000
--- a/gsw/utilities/list_npz.py
+++ /dev/null
@@ -1,27 +0,0 @@
-#!/usr/bin/env python
-"""
-List to stdout the contents of an npz file used in testing.
-
-The filename is the sole command-line argument.
-"""
-from __future__ import print_function
-
-import sys
-import numpy as np
-
-fname = sys.argv[1]
-
-dat = np.load(fname)
-keys = list(dat.keys())
-keys.sort()
-klens = [len(str(k)) for k in keys]
-klen = max(klens)
-
-str_fmt = "{0!s:<{klen}} : {1!s:>10} {2!s:>12}\n"
-
-slist = [str_fmt.format(k, dat[k].dtype, dat[k].shape, klen=klen)
- for k in keys]
-
-print(''.join(slist))
-
-
diff --git a/gsw/utilities/mat2npz.py b/gsw/utilities/mat2npz.py
deleted file mode 100644
index 90b03a3..0000000
--- a/gsw/utilities/mat2npz.py
+++ /dev/null
@@ -1,51 +0,0 @@
-#!/usr/bin/env python
-# -*- coding: utf-8 -*-
-#
-# mat2npz.py
-#
-# purpose: Convert matlab file from TEOS-10 group to a npz file
-# author: Filipe P. A. Fernandes
-# e-mail: ocefpaf at gmail
-# web: http://ocefpaf.tiddlyspot.com/
-# created: 06-Jun-2011
-# modified: Mon 16 Sep 2013 01:40:54 PM BRT
-#
-# obs:
-#
-
-from __future__ import print_function
-import numpy as np
-
-from gsw.utilities import loadmatbunch
-
-data_ver = 'v3_0'
-gsw_data = loadmatbunch('gsw_data_%s.mat' % data_ver, masked=False)
-
-print('Data version number: %s' % gsw_data.version_number)
-print('Data version date: %s' % gsw_data.version_date)
-
-# Delta SA Atlas.
-ref_table = dict()
-for k in gsw_data:
- if k == u'gsw_cv' or k == u'#refs#' or k == 'gsw_demo_data':
- pass
- else:
- ref_table[k] = gsw_data[k]
-np.savez("data/gsw_data_%s" % data_ver, **ref_table)
-
-# Save demo data values gsw_demo_data in a separate file.
-gsw_demo_data = gsw_data['gsw_demo_data']
-
-np.savez("data/gsw_demo_data_%s" % data_ver, **gsw_data['gsw_demo_data'])
-
-# Save compare values `gsw_cv` in a separate file.
-cv_vars = gsw_data['gsw_cv']
-
-np.savez("data/gsw_cv_%s" % data_ver, **cv_vars)
-
-# NOTE: The matfile gsw_cf.mat contains the results from
-# `gsw_check_functions.m.` and is used later for tests. Remember to save it as
-# MatlabTM '-v6' otherwise will have to use hdf5 instead of loadmat to read it.
-if True:
- gsw_cf = loadmatbunch('gsw_cf.mat', masked=False)
- np.savez("data/gsw_cf", **gsw_cf)
diff --git a/gsw/utilities/utilities.py b/gsw/utilities/utilities.py
deleted file mode 100644
index e54e0a2..0000000
--- a/gsw/utilities/utilities.py
+++ /dev/null
@@ -1,405 +0,0 @@
-# -*- coding: utf-8 -*-
-
-from __future__ import division
-
-import os
-from functools import wraps
-
-import numpy as np
-
-__all__ = ['Bunch',
- 'Cache_npz',
- 'match_args_return',
- 'read_data',
- 'strip_mask']
-
-
-# Based on Robert Kern's Bunch; taken from
-# http://currents.soest.hawaii.edu/hgstage/pycurrents/
-# pycurrents/system/utilities.py
-
-class Bunch(dict):
- """
- A dictionary that also provides access via attributes.
-
- Additional methods update_values and update_None provide
- control over whether new keys are added to the dictionary
- when updating, and whether an attempt to add a new key is
- ignored or raises a KeyError.
-
- The Bunch also prints differently than a normal
- dictionary, using str() instead of repr() for its
- keys and values, and in key-sorted order. The printing
- format can be customized by subclassing with a different
- str_ftm class attribute. Do not assign directly to this
- class attribute, because that would substitute an instance
- attribute which would then become part of the Bunch, and
- would be reported as such by the keys() method.
-
- To output a string representation with
- a particular format, without subclassing, use the
- formatted() method.
- """
-
- str_fmt = "{0!s:<{klen}} : {1!s:>{vlen}}\n"
-
- def __init__(self, *args, **kwargs):
- """
- *args* can be dictionaries, bunches, or sequences of
- key,value tuples. *kwargs* can be used to initialize
- or add key, value pairs.
- """
- dict.__init__(self)
- self.__dict__ = self
- for arg in args:
- self.update(arg)
- self.update(kwargs)
-
- def __str__(self):
- return self.formatted()
-
- def formatted(self, fmt=None, types=False):
- """
- Return a string with keys and/or values or types.
-
- *fmt* is a format string as used in the str.format() method.
-
- The str.format() method is called with key, value as positional
- arguments, and klen, vlen as kwargs. The latter are the maxima
- of the string lengths for the keys and values, respectively,
- up to respective maxima of 20 and 40.
- """
- if fmt is None:
- fmt = self.str_fmt
-
- items = list(self.items())
- items.sort()
-
- klens = []
- vlens = []
- for i, (k, v) in enumerate(items):
- lenk = len(str(k))
- if types:
- v = type(v).__name__
- lenv = len(str(v))
- items[i] = (k, v)
- klens.append(lenk)
- vlens.append(lenv)
-
- klen = min(20, max(klens))
- vlen = min(40, max(vlens))
- slist = [fmt.format(k, v, klen=klen, vlen=vlen) for k, v in items]
- return ''.join(slist)
-
- def from_pyfile(self, filename):
- """
- Read in variables from a python code file.
- """
- # We can't simply exec the code directly, because in
- # Python 3 the scoping for list comprehensions would
- # lead to a NameError. Wrapping the code in a function
- # fixes this.
- d = dict()
- lines = ["def _temp_func():\n"]
- with open(filename) as f:
- lines.extend([" " + line for line in f])
- lines.extend(["\n return(locals())\n",
- "_temp_out = _temp_func()\n",
- "del(_temp_func)\n"])
- codetext = "".join(lines)
- code = compile(codetext, filename, 'exec')
- exec(code, globals(), d)
- self.update(d["_temp_out"])
- return self
-
- def update_values(self, *args, **kw):
- """
- arguments are dictionary-like; if present, they act as
- additional sources of kwargs, with the actual kwargs
- taking precedence.
-
- One reserved optional kwarg is "strict". If present and
- True, then any attempt to update with keys that are not
- already in the Bunch instance will raise a KeyError.
- """
- strict = kw.pop("strict", False)
- newkw = dict()
- for d in args:
- newkw.update(d)
- newkw.update(kw)
- self._check_strict(strict, newkw)
- dsub = dict([(k, v) for (k, v) in newkw.items() if k in self])
- self.update(dsub)
-
- def update_None(self, *args, **kw):
- """
- Similar to update_values, except that an existing value
- will be updated only if it is None.
- """
- strict = kw.pop("strict", False)
- newkw = dict()
- for d in args:
- newkw.update(d)
- newkw.update(kw)
- self._check_strict(strict, newkw)
- dsub = dict([(k, v) for (k, v) in newkw.items()
- if k in self and self[k] is None])
- self.update(dsub)
-
- def _check_strict(self, strict, kw):
- if strict:
- bad = set(kw.keys()) - set(self.keys())
- if bad:
- bk = list(bad)
- bk.sort()
- ek = list(self.keys())
- ek.sort()
- raise KeyError(
- "Update keys %s don't match existing keys %s" % (bk, ek))
-
-
-class Cache_npz(object):
- def __init__(self):
- self._cache = dict()
- self._default_path = os.path.join(os.path.dirname(__file__), 'data')
-
- def __call__(self, fname, datadir=None):
- if datadir is None:
- datadir = self._default_path
- fpath = os.path.join(datadir, fname)
- try:
- return self._cache[fpath]
- except KeyError:
- pass
- d = np.load(fpath)
- ret = Bunch(d)
- self._cache[fpath] = ret
- return ret
-
-_npz_cache = Cache_npz()
-
-
-def repair_npzfile_with_objects(infile, outfile):
- """
- Read an npz file written based on scipy.io.loadmat,
- and write out a new npz file in which arrays have been
- extracted from object arrays.
-
- This might be needed only during the development process.
- It is motivated by the need to fix gsw_cf.npz so that
- the special object array handling in to_masked is not needed
- for the tests.
- """
- dat = np.load(infile)
- out = dict()
- for k, v in dat.items():
- if v.dtype.kind == 'O':
- v = v.item()
- out[k] = v
- np.savez(outfile, **out)
-
-
-def to_masked(arg):
- r"""
- Ensure an argument is a floating-point masked array.
-
- This is a helper for match_args_return.
- """
- if not np.iterable(arg):
- arg = [arg]
- try:
- arg = np.ma.array(arg, copy=False, dtype=float)
- except ValueError:
- # We might not want to keep this here. It handles the
- # case where reading a matfile with scipy has yielded
- # an object array containing a single object, which is
- # the array one actually wants.
- if arg.dtype.kind == 'O':
- arg = np.ma.array(arg.item(), copy=False, dtype=float)
- else:
- raise
- return np.ma.masked_invalid(arg)
-
-
-def match_args_return(f):
- """
- Decorator for most functions that operate on profile data.
- """
- @wraps(f)
- def wrapper(*args, **kw):
- p = kw.get('p', None)
- if p is not None:
- args = list(args)
- args.append(p)
-
- isarray = np.any([hasattr(a, '__iter__') for a in args])
- ismasked = np.any([np.ma.isMaskedArray(a) for a in args])
-
- def fixup(ret):
- if not ismasked:
- ret = np.ma.filled(ret, np.nan)
- if not isarray:
- ret = ret[0]
- return ret
-
- newargs = [to_masked(a) for a in args]
- if p is not None:
- kw['p'] = newargs.pop()
-
- ret = f(*newargs, **kw)
-
- if isinstance(ret, tuple):
- retlist = [fixup(arg) for arg in ret]
- ret = tuple(retlist)
- else:
- ret = fixup(ret)
- return ret
- wrapper.__wrapped__ = f
- return wrapper
-
-
-def read_data(fname, datadir=None):
- """
- Read variables from a numpy '.npz' file into a minimal class providing
- attribute access. A cache is used to avoid re-reading the same file.
- """
- return _npz_cache(fname, datadir=datadir)
-
-
-def strip_mask(*args):
- """
- Process the standard arguments for efficient calculation.
-
- Return unmasked arguments, plus a mask.
-
- The first argument, SA, is handled specially so that it can be
-
- This could be absorbed into a decorator, but it would
- require redefining functions to take the additional
- mask argument or kwarg.
- """
- mask = np.ma.getmaskarray(args[-1])
- SA = args[0]
- if SA.shape:
- SA = np.ma.asarray(SA)
- SA[SA < 0] = np.ma.masked
- for a in args[:-1]:
- mask = np.ma.mask_or(mask, np.ma.getmask(a))
- newargs = [SA.filled(0)]
- elif SA < 0:
- SA = 0
- for a in args[1:-1]:
- mask = np.ma.mask_or(mask, np.ma.getmask(a))
- newargs = [SA]
- newargs.extend([np.ma.filled(a, 0) for a in args[1:]])
- newargs.append(mask)
- return newargs
-
-# The following functions ending with loadmatbunch() and showmatbunch()
-# are taken from the repo
-# http://currents.soest.hawaii.edu/hgstage/pycurrents/,
-# pycurrents/file/matfile.py.
-
-def _crunch(arr, masked=True):
- """
- Handle all arrays that are not Matlab structures.
- """
- if arr.size == 1:
- arr = arr.item() # Returns the contents.
- return arr
-
- # The following squeeze is discarding some information;
- # we might want to make it optional.
- arr = arr.squeeze()
-
- if masked and arr.dtype.kind == 'f': # check for complex also
- arrm = np.ma.masked_invalid(arr)
- if arrm.count() < arrm.size:
- arr = arrm
- else:
- arr = np.array(arr) # copy to force a read
- else:
- arr = np.array(arr)
- return arr
-
-def _structured_to_bunch(arr, masked=True):
- """
- Recursively move through the structure tree, creating
- a Bunch for each structure. When a non-structure is
- encountered, process it with crunch().
- """
- # A single "void" object comes from a Matlab structure.
- # Each Matlab structure field corresponds to a field in
- # a numpy structured dtype.
- if arr.dtype.kind == 'V' and arr.shape == (1,1):
- b = Bunch()
- x = arr[0,0]
- for name in x.dtype.names:
- b[name] = _structured_to_bunch(x[name], masked=masked)
- return b
-
- return _crunch(arr, masked=masked)
-
-def _showmatbunch(b, elements=None, origin=None):
- if elements is None:
- elements = []
- if origin is None:
- origin = ''
- items = list(b.items())
- for k, v in items:
- _origin = "%s.%s" % (origin, k)
- if isinstance(v, Bunch):
- _showmatbunch(v, elements, _origin)
- else:
- if isinstance(v, str):
- slen = len(v)
- if slen < 50:
- entry = v
- else:
- entry = 'string, %d characters' % slen
- elif isinstance(v, np.ndarray):
- if np.ma.isMA(v):
- entry = 'masked array, shape %s, dtype %s' % (v.shape, v.dtype)
- else:
- entry = 'ndarray, shape %s, dtype %s' % (v.shape, v.dtype)
- else:
- entry = '%s %s' % (type(v).__name__, v)
- elements.append((_origin, entry))
- elements.sort()
- return elements
-
-def showmatbunch(b):
- """
- Show the contents of a matfile as it has been, or would be, loaded
- by loadmatbunch.
-
- *b* can be either the name of a matfile or the output of loadmatbunch.
-
- Returns a multi-line string suitable for printing.
- """
- if isinstance(b, str):
- b = loadmatbunch(b)
- elist = _showmatbunch(b)
- names = [n for n, v in elist]
- namelen = min(40, max([len(n) for n in names]))
- str_fmt = "{0!s:<{namelen}} : {1!s}\n"
- strlist = [str_fmt.format(n[1:], v, namelen=namelen) for (n, v) in elist]
- return ''.join(strlist)
-
-
-def loadmatbunch(fname, masked=True):
- """
- Wrapper for loadmat that dereferences (1,1) object arrays,
- converts floating point arrays to masked arrays, and uses
- nested Bunch objects in place of the matlab structures.
- """
- from scipy.io import loadmat
- out = Bunch()
- fobj = open(fname, 'rb')
- xx = loadmat(fobj)
- keys = [k for k in xx.keys() if not k.startswith("__")]
- for k in keys:
- out[k] = _structured_to_bunch(xx[k], masked=masked)
- fobj.close()
- return out
-
diff --git a/requirements-dev.txt b/requirements-dev.txt
deleted file mode 100644
index 83f11de..0000000
--- a/requirements-dev.txt
+++ /dev/null
@@ -1,6 +0,0 @@
-scipy
-oct2py
-pytest
-sphinx
-matplotlib
-numpydoc
diff --git a/setup.cfg b/setup.cfg
index 861a9f5..8bfd5a1 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -1,5 +1,4 @@
[egg_info]
tag_build =
tag_date = 0
-tag_svn_revision = 0
diff --git a/setup.py b/setup.py
index 31f1600..54056b4 100644
--- a/setup.py
+++ b/setup.py
@@ -1,28 +1,53 @@
-# -*- coding: utf-8 -*-
+'''
+Minimal setup.py for building gswc.
+'''
-from __future__ import absolute_import
+from __future__ import print_function
-import io
import os
-import re
import sys
-import codecs
-from setuptools import setup
-from setuptools.command.test import test as TestCommand
+from setuptools import Extension, setup
+
+import numpy as np
+
+# Check Python version.
+if sys.version_info < (3, 5):
+ pip_message = ('This may be due to an out of date pip. '
+ 'Make sure you have pip >= 9.0.1.')
+ try:
+ import pip
+ pip_version = tuple([int(x) for x in pip.__version__.split('.')[:3]])
+ if pip_version < (9, 0, 1):
+ pip_message = ('Your pip version is out of date, '
+ 'please install pip >= 9.0.1. '
+ 'pip {} detected.').format(pip.__version__)
+ else:
+ # pip is new enough - it must be something else.
+ pip_message = ''
+ except Exception:
+ pass
+
+ error = """
+Latest gsw does not support Python < 3.5.
+When using Python 2.7 please install the last pure Python version
+of gsw available at PyPI (3.0.6).
+Python {py} detected.
+{pip}
+""".format(py=sys.version_info, pip=pip_message)
+
+ print(error, file=sys.stderr)
+ sys.exit(1)
+
+if os.name in ('nt', 'dos'):
+ srcdir = 'src2'
+ c_ext = 'cpp'
+else:
+ srcdir = 'src'
+ c_ext = 'c'
-rootpath = os.path.abspath(os.path.dirname(__file__))
-
-
-class PyTest(TestCommand):
- def finalize_options(self):
- TestCommand.finalize_options(self)
- self.verbose = True
- def run_tests(self):
- import pytest
- errno = pytest.main(self.test_args)
- sys.exit(errno)
+rootpath = os.path.abspath(os.path.dirname(__file__))
def read(*parts):
@@ -40,47 +65,43 @@ def extract_version():
break
return version
-
-email = "ocefpaf at gmail.com"
-maintainer = "Filipe Fernandes"
-authors = ['Eric Firing', u'Bjørn Ådlandsvik', 'Filipe Fernandes']
-
-LICENSE = read('LICENSE.txt')
-long_description = '{}\n{}'.format(read('README.rst'), read('CHANGES.txt'))
-
-with open('requirements-dev.txt') as f:
- tests_require = f.readlines()
-tests_require = [t.strip() for t in tests_require]
-
-config = dict(name='gsw',
- version=extract_version(),
- packages=['gsw', 'gsw/gibbs', 'gsw/utilities', 'gsw/test'],
- package_data={'gsw': ['utilities/data/*.npz']},
- cmdclass=dict(test=PyTest),
- license=LICENSE,
- long_description=long_description,
- classifiers=['Development Status :: 4 - Beta',
- 'Environment :: Console',
- 'Intended Audience :: Science/Research',
- 'Intended Audience :: Developers',
- 'Intended Audience :: Education',
- 'License :: OSI Approved :: MIT License',
- 'Operating System :: OS Independent',
- 'Programming Language :: Python',
- 'Topic :: Education',
- 'Topic :: Scientific/Engineering',
- ],
- description='Gibbs Seawater Oceanographic Package of TEOS-10',
- author=authors,
- author_email=email,
- maintainer=maintainer,
- maintainer_email=email,
- url='https://github.com/TEOS-10/python-gsw',
- download_url='https://pypi.python.org/pypi/gsw/',
- platforms='any',
- keywords=['oceanography', 'seawater', 'TEOS-10', 'gibbs'],
- install_requires=['numpy'],
- tests_require=tests_require,
- )
+LICENSE = read('LICENSE')
+long_description = read('README.rst')
+
+config = dict(
+ name='gsw',
+ version=extract_version(),
+ packages=['gsw'],
+ author=['Eric Firing', 'Filipe Fernandes'],
+ author_email='efiring at hawaii.edu',
+ description='Gibbs Seawater Oceanographic Package of TEOS-10',
+ long_description=long_description,
+ license=LICENSE,
+ url='https://github.com/TEOS-10/GSW-python',
+ download_url='https://pypi.python.org/pypi/gsw/',
+ classifiers=[
+ 'Development Status :: 4 - Beta',
+ 'Environment :: Console',
+ 'Intended Audience :: Science/Research',
+ 'License :: OSI Approved :: MIT License',
+ 'Operating System :: OS Independent',
+ 'Programming Language :: Python',
+ 'Programming Language :: Python :: 3 :: Only',
+ 'Programming Language :: Python :: 3.5',
+ 'Programming Language :: Python :: 3.6',
+ 'Topic :: Scientific/Engineering',
+ ],
+ python_requires='>=3.5',
+ platforms='any',
+ keywords=['oceanography', 'seawater', 'TEOS-10'],
+ setup_requires=['numpy'],
+ ext_modules=[
+ Extension('gsw._gsw_ufuncs',
+ [srcdir + '/_ufuncs.c',
+ srcdir + '/c_gsw/gsw_oceanographic_toolbox.' + c_ext,
+ srcdir + '/c_gsw/gsw_saar.' + c_ext])],
+ include_dirs=[np.get_include(),
+ os.path.join(rootpath, srcdir, 'c_gsw')],
+)
setup(**config)
diff --git a/src/_ufuncs.c b/src/_ufuncs.c
new file mode 100644
index 0000000..c0a32ac
--- /dev/null
+++ b/src/_ufuncs.c
@@ -0,0 +1,2751 @@
+
+/*
+This file is auto-generated--do not edit it.
+
+This is python 3-only (for simplicity) to begin with.
+*/
+
+#include "Python.h"
+#include "math.h"
+#include "numpy/ndarraytypes.h"
+#include "numpy/ufuncobject.h"
+#include "numpy/npy_3kcompat.h"
+#include "gswteos-10.h"
+
+/* possible hack for MSVC: */
+#ifndef NAN
+ static double NAN = 0.0/0.0;
+#endif
+
+#ifndef isnan
+# define isnan(x) ((x) != (x))
+#endif
+
+#define CONVERT_INVALID(x) ((x == GSW_INVALID_VALUE)? NAN: x)
+
+
+/* 1 in, 1 out */
+static void loop1d_d_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *out0 = args[1];
+ npy_intp out_step0 = steps[1];
+ double (*func)(double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_d_d[] = {&loop1d_d_d};
+
+static char types_d_d[] = {
+ NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 2 in, 1 out */
+static void loop1d_dd_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *out0 = args[2];
+ npy_intp out_step0 = steps[2];
+ double (*func)(double, double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0, *(double *)in1);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dd_d[] = {&loop1d_dd_d};
+
+static char types_dd_d[] = {
+ NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 3 in, 1 out */
+static void loop1d_ddd_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *out0 = args[3];
+ npy_intp out_step0 = steps[3];
+ double (*func)(double, double, double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddd_d[] = {&loop1d_ddd_d};
+
+static char types_ddd_d[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 4 in, 1 out */
+static void loop1d_dddd_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *out0 = args[4];
+ npy_intp out_step0 = steps[4];
+ double (*func)(double, double, double, double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dddd_d[] = {&loop1d_dddd_d};
+
+static char types_dddd_d[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 5 in, 1 out */
+static void loop1d_ddddd_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *in4 = args[4];
+ npy_intp in_step4 = steps[4];
+ char *out0 = args[5];
+ npy_intp out_step0 = steps[5];
+ double (*func)(double, double, double, double, double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)||isnan(*(double *)in4)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, *(double *)in4);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ in4 += in_step4;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddddd_d[] = {&loop1d_ddddd_d};
+
+static char types_ddddd_d[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 2 in, 2 out */
+static void loop1d_dd_dd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *out0 = args[2];
+ npy_intp out_step0 = steps[2];
+ char *out1 = args[3];
+ npy_intp out_step1 = steps[3];
+ void (*func)(double, double, double *, double *);
+ double outd0, outd1;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, &outd0, &outd1);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ out0 += out_step0;
+ out1 += out_step1;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dd_dd[] = {&loop1d_dd_dd};
+
+static char types_dd_dd[] = {
+ NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 3 in, 2 out */
+static void loop1d_ddd_dd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *out0 = args[3];
+ npy_intp out_step0 = steps[3];
+ char *out1 = args[4];
+ npy_intp out_step1 = steps[4];
+ void (*func)(double, double, double, double *, double *);
+ double outd0, outd1;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, &outd0, &outd1);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ out0 += out_step0;
+ out1 += out_step1;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddd_dd[] = {&loop1d_ddd_dd};
+
+static char types_ddd_dd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 3 in, 3 out */
+static void loop1d_ddd_ddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *out0 = args[3];
+ npy_intp out_step0 = steps[3];
+ char *out1 = args[4];
+ npy_intp out_step1 = steps[4];
+ char *out2 = args[5];
+ npy_intp out_step2 = steps[5];
+ void (*func)(double, double, double, double *, double *, double *);
+ double outd0, outd1, outd2;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, &outd0, &outd1, &outd2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddd_ddd[] = {&loop1d_ddd_ddd};
+
+static char types_ddd_ddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 6 in, 2 out */
+static void loop1d_dddddd_dd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *in4 = args[4];
+ npy_intp in_step4 = steps[4];
+ char *in5 = args[5];
+ npy_intp in_step5 = steps[5];
+ char *out0 = args[6];
+ npy_intp out_step0 = steps[6];
+ char *out1 = args[7];
+ npy_intp out_step1 = steps[7];
+ void (*func)(double, double, double, double, double, double, double *, double *);
+ double outd0, outd1;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)||isnan(*(double *)in4)||isnan(*(double *)in5)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, *(double *)in4, *(double *)in5, &outd0, &outd1);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ in4 += in_step4;
+ in5 += in_step5;
+ out0 += out_step0;
+ out1 += out_step1;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dddddd_dd[] = {&loop1d_dddddd_dd};
+
+static char types_dddddd_dd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 2 in, 3 out */
+static void loop1d_dd_ddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *out0 = args[2];
+ npy_intp out_step0 = steps[2];
+ char *out1 = args[3];
+ npy_intp out_step1 = steps[3];
+ char *out2 = args[4];
+ npy_intp out_step2 = steps[4];
+ void (*func)(double, double, double *, double *, double *);
+ double outd0, outd1, outd2;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, &outd0, &outd1, &outd2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dd_ddd[] = {&loop1d_dd_ddd};
+
+static char types_dd_ddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 4 in, 3 out */
+static void loop1d_dddd_ddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *out0 = args[4];
+ npy_intp out_step0 = steps[4];
+ char *out1 = args[5];
+ npy_intp out_step1 = steps[5];
+ char *out2 = args[6];
+ npy_intp out_step2 = steps[6];
+ void (*func)(double, double, double, double, double *, double *, double *);
+ double outd0, outd1, outd2;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, &outd0, &outd1, &outd2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dddd_ddd[] = {&loop1d_dddd_ddd};
+
+static char types_dddd_ddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 5 in, 3 out */
+static void loop1d_ddddd_ddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *in4 = args[4];
+ npy_intp in_step4 = steps[4];
+ char *out0 = args[5];
+ npy_intp out_step0 = steps[5];
+ char *out1 = args[6];
+ npy_intp out_step1 = steps[6];
+ char *out2 = args[7];
+ npy_intp out_step2 = steps[7];
+ void (*func)(double, double, double, double, double, double *, double *, double *);
+ double outd0, outd1, outd2;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)||isnan(*(double *)in4)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, *(double *)in4, &outd0, &outd1, &outd2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ in4 += in_step4;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddddd_ddd[] = {&loop1d_ddddd_ddd};
+
+static char types_ddddd_ddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 3 in, 5 out */
+static void loop1d_ddd_ddddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *out0 = args[3];
+ npy_intp out_step0 = steps[3];
+ char *out1 = args[4];
+ npy_intp out_step1 = steps[4];
+ char *out2 = args[5];
+ npy_intp out_step2 = steps[5];
+ char *out3 = args[6];
+ npy_intp out_step3 = steps[6];
+ char *out4 = args[7];
+ npy_intp out_step4 = steps[7];
+ void (*func)(double, double, double, double *, double *, double *, double *, double *);
+ double outd0, outd1, outd2, outd3, outd4;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;*((double *)out3) = NAN;*((double *)out4) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, &outd0, &outd1, &outd2, &outd3, &outd4);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ *((double *)out3) = CONVERT_INVALID(outd3);
+ *((double *)out4) = CONVERT_INVALID(outd4);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ out3 += out_step3;
+ out4 += out_step4;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddd_ddddd[] = {&loop1d_ddd_ddddd};
+
+static char types_ddd_ddddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+static void *data_enthalpy_sso_0[] = {&gsw_enthalpy_sso_0};
+static void *data_gibbs_ice_pt0[] = {&gsw_gibbs_ice_pt0};
+static void *data_gibbs_ice_pt0_pt0[] = {&gsw_gibbs_ice_pt0_pt0};
+static void *data_hill_ratio_at_sp2[] = {&gsw_hill_ratio_at_sp2};
+static void *data_pot_enthalpy_from_pt_ice[] = {&gsw_pot_enthalpy_from_pt_ice};
+static void *data_pot_enthalpy_from_pt_ice_poly[] = {&gsw_pot_enthalpy_from_pt_ice_poly};
+static void *data_pt0_cold_ice_poly[] = {&gsw_pt0_cold_ice_poly};
+static void *data_pt_from_pot_enthalpy_ice[] = {&gsw_pt_from_pot_enthalpy_ice};
+static void *data_pt_from_pot_enthalpy_ice_poly[] = {&gsw_pt_from_pot_enthalpy_ice_poly};
+static void *data_pt_from_pot_enthalpy_ice_poly_dh[] = {&gsw_pt_from_pot_enthalpy_ice_poly_dh};
+static void *data_sp_from_sk[] = {&gsw_sp_from_sk};
+static void *data_sp_from_sr[] = {&gsw_sp_from_sr};
+static void *data_specvol_sso_0[] = {&gsw_specvol_sso_0};
+static void *data_sr_from_sp[] = {&gsw_sr_from_sp};
+static void *data_adiabatic_lapse_rate_ice[] = {&gsw_adiabatic_lapse_rate_ice};
+static void *data_alpha_wrt_t_ice[] = {&gsw_alpha_wrt_t_ice};
+static void *data_chem_potential_water_ice[] = {&gsw_chem_potential_water_ice};
+static void *data_cp_ice[] = {&gsw_cp_ice};
+static void *data_ct_from_entropy[] = {&gsw_ct_from_entropy};
+static void *data_ct_from_pt[] = {&gsw_ct_from_pt};
+static void *data_ct_maxdensity[] = {&gsw_ct_maxdensity};
+static void *data_enthalpy_ice[] = {&gsw_enthalpy_ice};
+static void *data_entropy_from_ct[] = {&gsw_entropy_from_ct};
+static void *data_entropy_from_pt[] = {&gsw_entropy_from_pt};
+static void *data_entropy_ice[] = {&gsw_entropy_ice};
+static void *data_entropy_part_zerop[] = {&gsw_entropy_part_zerop};
+static void *data_gibbs_ice_part_t[] = {&gsw_gibbs_ice_part_t};
+static void *data_gibbs_pt0_pt0[] = {&gsw_gibbs_pt0_pt0};
+static void *data_grav[] = {&gsw_grav};
+static void *data_helmholtz_energy_ice[] = {&gsw_helmholtz_energy_ice};
+static void *data_internal_energy_ice[] = {&gsw_internal_energy_ice};
+static void *data_kappa_const_t_ice[] = {&gsw_kappa_const_t_ice};
+static void *data_kappa_ice[] = {&gsw_kappa_ice};
+static void *data_latentheat_evap_ct[] = {&gsw_latentheat_evap_ct};
+static void *data_latentheat_evap_t[] = {&gsw_latentheat_evap_t};
+static void *data_latentheat_melting[] = {&gsw_latentheat_melting};
+static void *data_melting_ice_equilibrium_sa_ct_ratio[] = {&gsw_melting_ice_equilibrium_sa_ct_ratio};
+static void *data_melting_ice_equilibrium_sa_ct_ratio_poly[] = {&gsw_melting_ice_equilibrium_sa_ct_ratio_poly};
+static void *data_melting_seaice_equilibrium_sa_ct_ratio[] = {&gsw_melting_seaice_equilibrium_sa_ct_ratio};
+static void *data_melting_seaice_equilibrium_sa_ct_ratio_poly[] = {&gsw_melting_seaice_equilibrium_sa_ct_ratio_poly};
+static void *data_p_from_z[] = {&gsw_p_from_z};
+static void *data_pot_enthalpy_ice_freezing[] = {&gsw_pot_enthalpy_ice_freezing};
+static void *data_pot_enthalpy_ice_freezing_poly[] = {&gsw_pot_enthalpy_ice_freezing_poly};
+static void *data_pressure_coefficient_ice[] = {&gsw_pressure_coefficient_ice};
+static void *data_pt0_from_t_ice[] = {&gsw_pt0_from_t_ice};
+static void *data_pt_from_ct[] = {&gsw_pt_from_ct};
+static void *data_pt_from_entropy[] = {&gsw_pt_from_entropy};
+static void *data_rho_ice[] = {&gsw_rho_ice};
+static void *data_sigma0[] = {&gsw_sigma0};
+static void *data_sigma1[] = {&gsw_sigma1};
+static void *data_sigma2[] = {&gsw_sigma2};
+static void *data_sigma3[] = {&gsw_sigma3};
+static void *data_sigma4[] = {&gsw_sigma4};
+static void *data_sound_speed_ice[] = {&gsw_sound_speed_ice};
+static void *data_specvol_ice[] = {&gsw_specvol_ice};
+static void *data_spiciness0[] = {&gsw_spiciness0};
+static void *data_spiciness1[] = {&gsw_spiciness1};
+static void *data_spiciness2[] = {&gsw_spiciness2};
+static void *data_t_from_pt0_ice[] = {&gsw_t_from_pt0_ice};
+static void *data_z_from_p[] = {&gsw_z_from_p};
+static void *data_adiabatic_lapse_rate_from_ct[] = {&gsw_adiabatic_lapse_rate_from_ct};
+static void *data_alpha[] = {&gsw_alpha};
+static void *data_alpha_on_beta[] = {&gsw_alpha_on_beta};
+static void *data_alpha_wrt_t_exact[] = {&gsw_alpha_wrt_t_exact};
+static void *data_beta[] = {&gsw_beta};
+static void *data_beta_const_t_exact[] = {&gsw_beta_const_t_exact};
+static void *data_c_from_sp[] = {&gsw_c_from_sp};
+static void *data_cabbeling[] = {&gsw_cabbeling};
+static void *data_chem_potential_water_t_exact[] = {&gsw_chem_potential_water_t_exact};
+static void *data_cp_t_exact[] = {&gsw_cp_t_exact};
+static void *data_ct_freezing[] = {&gsw_ct_freezing};
+static void *data_ct_freezing_poly[] = {&gsw_ct_freezing_poly};
+static void *data_ct_from_enthalpy[] = {&gsw_ct_from_enthalpy};
+static void *data_ct_from_enthalpy_exact[] = {&gsw_ct_from_enthalpy_exact};
+static void *data_ct_from_t[] = {&gsw_ct_from_t};
+static void *data_deltasa_atlas[] = {&gsw_deltasa_atlas};
+static void *data_dilution_coefficient_t_exact[] = {&gsw_dilution_coefficient_t_exact};
+static void *data_dynamic_enthalpy[] = {&gsw_dynamic_enthalpy};
+static void *data_enthalpy[] = {&gsw_enthalpy};
+static void *data_enthalpy_ct_exact[] = {&gsw_enthalpy_ct_exact};
+static void *data_enthalpy_t_exact[] = {&gsw_enthalpy_t_exact};
+static void *data_entropy_from_t[] = {&gsw_entropy_from_t};
+static void *data_entropy_part[] = {&gsw_entropy_part};
+static void *data_fdelta[] = {&gsw_fdelta};
+static void *data_internal_energy[] = {&gsw_internal_energy};
+static void *data_kappa[] = {&gsw_kappa};
+static void *data_kappa_t_exact[] = {&gsw_kappa_t_exact};
+static void *data_pressure_freezing_ct[] = {&gsw_pressure_freezing_ct};
+static void *data_pt0_from_t[] = {&gsw_pt0_from_t};
+static void *data_pt_from_t_ice[] = {&gsw_pt_from_t_ice};
+static void *data_rho[] = {&gsw_rho};
+static void *data_rho_t_exact[] = {&gsw_rho_t_exact};
+static void *data_sa_freezing_from_ct[] = {&gsw_sa_freezing_from_ct};
+static void *data_sa_freezing_from_ct_poly[] = {&gsw_sa_freezing_from_ct_poly};
+static void *data_sa_freezing_from_t[] = {&gsw_sa_freezing_from_t};
+static void *data_sa_freezing_from_t_poly[] = {&gsw_sa_freezing_from_t_poly};
+static void *data_sa_from_rho[] = {&gsw_sa_from_rho};
+static void *data_sa_from_sp_baltic[] = {&gsw_sa_from_sp_baltic};
+static void *data_saar[] = {&gsw_saar};
+static void *data_sound_speed[] = {&gsw_sound_speed};
+static void *data_sound_speed_t_exact[] = {&gsw_sound_speed_t_exact};
+static void *data_sp_from_c[] = {&gsw_sp_from_c};
+static void *data_sp_from_sa_baltic[] = {&gsw_sp_from_sa_baltic};
+static void *data_specvol[] = {&gsw_specvol};
+static void *data_specvol_anom_standard[] = {&gsw_specvol_anom_standard};
+static void *data_specvol_t_exact[] = {&gsw_specvol_t_exact};
+static void *data_t_deriv_chem_potential_water_t_exact[] = {&gsw_t_deriv_chem_potential_water_t_exact};
+static void *data_t_freezing[] = {&gsw_t_freezing};
+static void *data_t_freezing_poly[] = {&gsw_t_freezing_poly};
+static void *data_t_from_ct[] = {&gsw_t_from_ct};
+static void *data_thermobaric[] = {&gsw_thermobaric};
+static void *data_deltasa_from_sp[] = {&gsw_deltasa_from_sp};
+static void *data_enthalpy_diff[] = {&gsw_enthalpy_diff};
+static void *data_melting_ice_sa_ct_ratio[] = {&gsw_melting_ice_sa_ct_ratio};
+static void *data_melting_ice_sa_ct_ratio_poly[] = {&gsw_melting_ice_sa_ct_ratio_poly};
+static void *data_pot_rho_t_exact[] = {&gsw_pot_rho_t_exact};
+static void *data_pt_from_t[] = {&gsw_pt_from_t};
+static void *data_sa_from_sp[] = {&gsw_sa_from_sp};
+static void *data_sa_from_sstar[] = {&gsw_sa_from_sstar};
+static void *data_sp_from_sa[] = {&gsw_sp_from_sa};
+static void *data_sp_from_sstar[] = {&gsw_sp_from_sstar};
+static void *data_sstar_from_sa[] = {&gsw_sstar_from_sa};
+static void *data_sstar_from_sp[] = {&gsw_sstar_from_sp};
+static void *data_melting_seaice_sa_ct_ratio[] = {&gsw_melting_seaice_sa_ct_ratio};
+static void *data_melting_seaice_sa_ct_ratio_poly[] = {&gsw_melting_seaice_sa_ct_ratio_poly};
+static void *data_ct_first_derivatives[] = {&gsw_ct_first_derivatives};
+static void *data_entropy_first_derivatives[] = {&gsw_entropy_first_derivatives};
+static void *data_pot_enthalpy_ice_freezing_first_derivatives[] = {&gsw_pot_enthalpy_ice_freezing_first_derivatives};
+static void *data_pot_enthalpy_ice_freezing_first_derivatives_poly[] = {&gsw_pot_enthalpy_ice_freezing_first_derivatives_poly};
+static void *data_pt_first_derivatives[] = {&gsw_pt_first_derivatives};
+static void *data_ct_freezing_first_derivatives[] = {&gsw_ct_freezing_first_derivatives};
+static void *data_ct_freezing_first_derivatives_poly[] = {&gsw_ct_freezing_first_derivatives_poly};
+static void *data_ct_from_rho[] = {&gsw_ct_from_rho};
+static void *data_enthalpy_first_derivatives[] = {&gsw_enthalpy_first_derivatives};
+static void *data_enthalpy_first_derivatives_ct_exact[] = {&gsw_enthalpy_first_derivatives_ct_exact};
+static void *data_rho_first_derivatives_wrt_enthalpy[] = {&gsw_rho_first_derivatives_wrt_enthalpy};
+static void *data_specvol_first_derivatives_wrt_enthalpy[] = {&gsw_specvol_first_derivatives_wrt_enthalpy};
+static void *data_t_freezing_first_derivatives[] = {&gsw_t_freezing_first_derivatives};
+static void *data_t_freezing_first_derivatives_poly[] = {&gsw_t_freezing_first_derivatives_poly};
+static void *data_ct_first_derivatives_wrt_t_exact[] = {&gsw_ct_first_derivatives_wrt_t_exact};
+static void *data_enthalpy_second_derivatives[] = {&gsw_enthalpy_second_derivatives};
+static void *data_enthalpy_second_derivatives_ct_exact[] = {&gsw_enthalpy_second_derivatives_ct_exact};
+static void *data_frazil_properties[] = {&gsw_frazil_properties};
+static void *data_frazil_properties_potential[] = {&gsw_frazil_properties_potential};
+static void *data_frazil_properties_potential_poly[] = {&gsw_frazil_properties_potential_poly};
+static void *data_frazil_ratios_adiabatic[] = {&gsw_frazil_ratios_adiabatic};
+static void *data_frazil_ratios_adiabatic_poly[] = {&gsw_frazil_ratios_adiabatic_poly};
+static void *data_rho_alpha_beta[] = {&gsw_rho_alpha_beta};
+static void *data_rho_first_derivatives[] = {&gsw_rho_first_derivatives};
+static void *data_rho_second_derivatives_wrt_enthalpy[] = {&gsw_rho_second_derivatives_wrt_enthalpy};
+static void *data_specvol_alpha_beta[] = {&gsw_specvol_alpha_beta};
+static void *data_specvol_first_derivatives[] = {&gsw_specvol_first_derivatives};
+static void *data_specvol_second_derivatives_wrt_enthalpy[] = {&gsw_specvol_second_derivatives_wrt_enthalpy};
+static void *data_melting_seaice_into_seawater[] = {&gsw_melting_seaice_into_seawater};
+static void *data_ct_second_derivatives[] = {&gsw_ct_second_derivatives};
+static void *data_entropy_second_derivatives[] = {&gsw_entropy_second_derivatives};
+static void *data_pt_second_derivatives[] = {&gsw_pt_second_derivatives};
+static void *data_ice_fraction_to_freeze_seawater[] = {&gsw_ice_fraction_to_freeze_seawater};
+static void *data_melting_ice_into_seawater[] = {&gsw_melting_ice_into_seawater};
+static void *data_seaice_fraction_to_freeze_seawater[] = {&gsw_seaice_fraction_to_freeze_seawater};
+static void *data_rho_second_derivatives[] = {&gsw_rho_second_derivatives};
+static void *data_specvol_second_derivatives[] = {&gsw_specvol_second_derivatives};
+
+
+#include "method_bodies.c"
+
+static PyMethodDef GswMethods[] = {
+# include "method_def_entries.c"
+ {NULL, NULL, 0, NULL}
+};
+
+static struct PyModuleDef moduledef = {
+ PyModuleDef_HEAD_INIT,
+ "npufunc",
+ NULL,
+ -1,
+ GswMethods,
+ NULL,
+ NULL,
+ NULL,
+ NULL
+};
+
+
+PyMODINIT_FUNC PyInit__gsw_ufuncs(void)
+{
+ PyObject *m, *d;
+
+ PyObject *ufunc_ptr;
+
+ m = PyModule_Create(&moduledef);
+ if (!m) {
+ return NULL;
+ }
+
+ d = PyModule_GetDict(m);
+
+ import_array();
+ import_umath();
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_enthalpy_sso_0,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_sso_0",
+ "enthalpy_sso_0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_sso_0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_gibbs_ice_pt0,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "gibbs_ice_pt0",
+ "gibbs_ice_pt0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "gibbs_ice_pt0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_gibbs_ice_pt0_pt0,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "gibbs_ice_pt0_pt0",
+ "gibbs_ice_pt0_pt0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "gibbs_ice_pt0_pt0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_hill_ratio_at_sp2,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "hill_ratio_at_sp2",
+ "hill_ratio_at_sp2_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "hill_ratio_at_sp2", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pot_enthalpy_from_pt_ice,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_from_pt_ice",
+ "pot_enthalpy_from_pt_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_from_pt_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pot_enthalpy_from_pt_ice_poly,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_from_pt_ice_poly",
+ "pot_enthalpy_from_pt_ice_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_from_pt_ice_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pt0_cold_ice_poly,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt0_cold_ice_poly",
+ "pt0_cold_ice_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt0_cold_ice_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pt_from_pot_enthalpy_ice,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_pot_enthalpy_ice",
+ "pt_from_pot_enthalpy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_pot_enthalpy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pt_from_pot_enthalpy_ice_poly,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_pot_enthalpy_ice_poly",
+ "pt_from_pot_enthalpy_ice_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_pot_enthalpy_ice_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pt_from_pot_enthalpy_ice_poly_dh,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_pot_enthalpy_ice_poly_dh",
+ "pt_from_pot_enthalpy_ice_poly_dh_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_pot_enthalpy_ice_poly_dh", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_sp_from_sk,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sk",
+ "sp_from_sk_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sk", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_sp_from_sr,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sr",
+ "sp_from_sr_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sr", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_specvol_sso_0,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_sso_0",
+ "specvol_sso_0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_sso_0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_sr_from_sp,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sr_from_sp",
+ "sr_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sr_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_adiabatic_lapse_rate_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "adiabatic_lapse_rate_ice",
+ "adiabatic_lapse_rate_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "adiabatic_lapse_rate_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_alpha_wrt_t_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "alpha_wrt_t_ice",
+ "alpha_wrt_t_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "alpha_wrt_t_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_chem_potential_water_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "chem_potential_water_ice",
+ "chem_potential_water_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "chem_potential_water_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_cp_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "cp_ice",
+ "cp_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "cp_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_ct_from_entropy,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_entropy",
+ "ct_from_entropy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_entropy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_ct_from_pt,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_pt",
+ "ct_from_pt_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_pt", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_ct_maxdensity,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_maxdensity",
+ "ct_maxdensity_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_maxdensity", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_enthalpy_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_ice",
+ "enthalpy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_entropy_from_ct,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_from_ct",
+ "entropy_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_entropy_from_pt,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_from_pt",
+ "entropy_from_pt_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_from_pt", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_entropy_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_ice",
+ "entropy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_entropy_part_zerop,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_part_zerop",
+ "entropy_part_zerop_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_part_zerop", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_gibbs_ice_part_t,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "gibbs_ice_part_t",
+ "gibbs_ice_part_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "gibbs_ice_part_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_gibbs_pt0_pt0,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "gibbs_pt0_pt0",
+ "gibbs_pt0_pt0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "gibbs_pt0_pt0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_grav,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "grav",
+ "grav_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "grav", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_helmholtz_energy_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "helmholtz_energy_ice",
+ "helmholtz_energy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "helmholtz_energy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_internal_energy_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "internal_energy_ice",
+ "internal_energy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "internal_energy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_kappa_const_t_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "kappa_const_t_ice",
+ "kappa_const_t_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "kappa_const_t_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_kappa_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "kappa_ice",
+ "kappa_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "kappa_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_latentheat_evap_ct,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "latentheat_evap_ct",
+ "latentheat_evap_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "latentheat_evap_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_latentheat_evap_t,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "latentheat_evap_t",
+ "latentheat_evap_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "latentheat_evap_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_latentheat_melting,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "latentheat_melting",
+ "latentheat_melting_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "latentheat_melting", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_melting_ice_equilibrium_sa_ct_ratio,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_equilibrium_sa_ct_ratio",
+ "melting_ice_equilibrium_sa_ct_ratio_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_equilibrium_sa_ct_ratio", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_melting_ice_equilibrium_sa_ct_ratio_poly,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_equilibrium_sa_ct_ratio_poly",
+ "melting_ice_equilibrium_sa_ct_ratio_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_equilibrium_sa_ct_ratio_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_melting_seaice_equilibrium_sa_ct_ratio,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_equilibrium_sa_ct_ratio",
+ "melting_seaice_equilibrium_sa_ct_ratio_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_equilibrium_sa_ct_ratio", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_melting_seaice_equilibrium_sa_ct_ratio_poly,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_equilibrium_sa_ct_ratio_poly",
+ "melting_seaice_equilibrium_sa_ct_ratio_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_equilibrium_sa_ct_ratio_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_p_from_z,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "p_from_z",
+ "p_from_z_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "p_from_z", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pot_enthalpy_ice_freezing,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_ice_freezing",
+ "pot_enthalpy_ice_freezing_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_ice_freezing", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pot_enthalpy_ice_freezing_poly,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_ice_freezing_poly",
+ "pot_enthalpy_ice_freezing_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_ice_freezing_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pressure_coefficient_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pressure_coefficient_ice",
+ "pressure_coefficient_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pressure_coefficient_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pt0_from_t_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt0_from_t_ice",
+ "pt0_from_t_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt0_from_t_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pt_from_ct,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_ct",
+ "pt_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pt_from_entropy,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_entropy",
+ "pt_from_entropy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_entropy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_rho_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_ice",
+ "rho_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma0,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma0",
+ "sigma0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma1,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma1",
+ "sigma1_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma1", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma2,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma2",
+ "sigma2_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma2", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma3,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma3",
+ "sigma3_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma3", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma4,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma4",
+ "sigma4_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma4", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sound_speed_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sound_speed_ice",
+ "sound_speed_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sound_speed_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_specvol_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_ice",
+ "specvol_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_spiciness0,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "spiciness0",
+ "spiciness0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "spiciness0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_spiciness1,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "spiciness1",
+ "spiciness1_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "spiciness1", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_spiciness2,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "spiciness2",
+ "spiciness2_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "spiciness2", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_t_from_pt0_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_from_pt0_ice",
+ "t_from_pt0_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_from_pt0_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_z_from_p,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "z_from_p",
+ "z_from_p_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "z_from_p", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_adiabatic_lapse_rate_from_ct,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "adiabatic_lapse_rate_from_ct",
+ "adiabatic_lapse_rate_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "adiabatic_lapse_rate_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_alpha,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "alpha",
+ "alpha_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "alpha", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_alpha_on_beta,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "alpha_on_beta",
+ "alpha_on_beta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "alpha_on_beta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_alpha_wrt_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "alpha_wrt_t_exact",
+ "alpha_wrt_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "alpha_wrt_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_beta,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "beta",
+ "beta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "beta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_beta_const_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "beta_const_t_exact",
+ "beta_const_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "beta_const_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_c_from_sp,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "c_from_sp",
+ "c_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "c_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_cabbeling,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "cabbeling",
+ "cabbeling_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "cabbeling", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_chem_potential_water_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "chem_potential_water_t_exact",
+ "chem_potential_water_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "chem_potential_water_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_cp_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "cp_t_exact",
+ "cp_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "cp_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_freezing,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_freezing",
+ "ct_freezing_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_freezing", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_freezing_poly,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_freezing_poly",
+ "ct_freezing_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_freezing_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_from_enthalpy,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_enthalpy",
+ "ct_from_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_from_enthalpy_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_enthalpy_exact",
+ "ct_from_enthalpy_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_enthalpy_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_from_t,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_t",
+ "ct_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_deltasa_atlas,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "deltasa_atlas",
+ "deltasa_atlas_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "deltasa_atlas", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_dilution_coefficient_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "dilution_coefficient_t_exact",
+ "dilution_coefficient_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "dilution_coefficient_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_dynamic_enthalpy,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "dynamic_enthalpy",
+ "dynamic_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "dynamic_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_enthalpy,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy",
+ "enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_enthalpy_ct_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_ct_exact",
+ "enthalpy_ct_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_ct_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_enthalpy_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_t_exact",
+ "enthalpy_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_entropy_from_t,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_from_t",
+ "entropy_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_entropy_part,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_part",
+ "entropy_part_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_part", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_fdelta,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "fdelta",
+ "fdelta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "fdelta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_internal_energy,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "internal_energy",
+ "internal_energy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "internal_energy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_kappa,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "kappa",
+ "kappa_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "kappa", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_kappa_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "kappa_t_exact",
+ "kappa_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "kappa_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_pressure_freezing_ct,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pressure_freezing_ct",
+ "pressure_freezing_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pressure_freezing_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_pt0_from_t,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt0_from_t",
+ "pt0_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt0_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_pt_from_t_ice,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_t_ice",
+ "pt_from_t_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_t_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_rho,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho",
+ "rho_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_rho_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_t_exact",
+ "rho_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_freezing_from_ct,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_freezing_from_ct",
+ "sa_freezing_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_freezing_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_freezing_from_ct_poly,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_freezing_from_ct_poly",
+ "sa_freezing_from_ct_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_freezing_from_ct_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_freezing_from_t,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_freezing_from_t",
+ "sa_freezing_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_freezing_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_freezing_from_t_poly,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_freezing_from_t_poly",
+ "sa_freezing_from_t_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_freezing_from_t_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_from_rho,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_from_rho",
+ "sa_from_rho_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_from_rho", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_from_sp_baltic,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_from_sp_baltic",
+ "sa_from_sp_baltic_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_from_sp_baltic", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_saar,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "saar",
+ "saar_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "saar", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sound_speed,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sound_speed",
+ "sound_speed_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sound_speed", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sound_speed_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sound_speed_t_exact",
+ "sound_speed_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sound_speed_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sp_from_c,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_c",
+ "sp_from_c_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_c", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sp_from_sa_baltic,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sa_baltic",
+ "sp_from_sa_baltic_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sa_baltic", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_specvol,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol",
+ "specvol_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_specvol_anom_standard,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_anom_standard",
+ "specvol_anom_standard_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_anom_standard", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_specvol_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_t_exact",
+ "specvol_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_t_deriv_chem_potential_water_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_deriv_chem_potential_water_t_exact",
+ "t_deriv_chem_potential_water_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_deriv_chem_potential_water_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_t_freezing,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_freezing",
+ "t_freezing_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_freezing", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_t_freezing_poly,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_freezing_poly",
+ "t_freezing_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_freezing_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_t_from_ct,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_from_ct",
+ "t_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_thermobaric,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "thermobaric",
+ "thermobaric_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "thermobaric", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_deltasa_from_sp,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "deltasa_from_sp",
+ "deltasa_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "deltasa_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_enthalpy_diff,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_diff",
+ "enthalpy_diff_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_diff", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_melting_ice_sa_ct_ratio,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_sa_ct_ratio",
+ "melting_ice_sa_ct_ratio_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_sa_ct_ratio", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_melting_ice_sa_ct_ratio_poly,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_sa_ct_ratio_poly",
+ "melting_ice_sa_ct_ratio_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_sa_ct_ratio_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_pot_rho_t_exact,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_rho_t_exact",
+ "pot_rho_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_rho_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_pt_from_t,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_t",
+ "pt_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sa_from_sp,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_from_sp",
+ "sa_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sa_from_sstar,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_from_sstar",
+ "sa_from_sstar_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_from_sstar", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sp_from_sa,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sa",
+ "sp_from_sa_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sa", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sp_from_sstar,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sstar",
+ "sp_from_sstar_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sstar", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sstar_from_sa,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sstar_from_sa",
+ "sstar_from_sa_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sstar_from_sa", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sstar_from_sp,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sstar_from_sp",
+ "sstar_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sstar_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_d,
+ data_melting_seaice_sa_ct_ratio,
+ types_ddddd_d,
+ 1, 5, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_sa_ct_ratio",
+ "melting_seaice_sa_ct_ratio_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_sa_ct_ratio", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_d,
+ data_melting_seaice_sa_ct_ratio_poly,
+ types_ddddd_d,
+ 1, 5, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_sa_ct_ratio_poly",
+ "melting_seaice_sa_ct_ratio_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_sa_ct_ratio_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_ct_first_derivatives,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_first_derivatives",
+ "ct_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_entropy_first_derivatives,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_first_derivatives",
+ "entropy_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_pot_enthalpy_ice_freezing_first_derivatives,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_ice_freezing_first_derivatives",
+ "pot_enthalpy_ice_freezing_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_ice_freezing_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_pot_enthalpy_ice_freezing_first_derivatives_poly,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_ice_freezing_first_derivatives_poly",
+ "pot_enthalpy_ice_freezing_first_derivatives_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_ice_freezing_first_derivatives_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_pt_first_derivatives,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_first_derivatives",
+ "pt_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_ct_freezing_first_derivatives,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_freezing_first_derivatives",
+ "ct_freezing_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_freezing_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_ct_freezing_first_derivatives_poly,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_freezing_first_derivatives_poly",
+ "ct_freezing_first_derivatives_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_freezing_first_derivatives_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_ct_from_rho,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_rho",
+ "ct_from_rho_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_rho", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_enthalpy_first_derivatives,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_first_derivatives",
+ "enthalpy_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_enthalpy_first_derivatives_ct_exact,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_first_derivatives_ct_exact",
+ "enthalpy_first_derivatives_ct_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_first_derivatives_ct_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_rho_first_derivatives_wrt_enthalpy,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_first_derivatives_wrt_enthalpy",
+ "rho_first_derivatives_wrt_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_first_derivatives_wrt_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_specvol_first_derivatives_wrt_enthalpy,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_first_derivatives_wrt_enthalpy",
+ "specvol_first_derivatives_wrt_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_first_derivatives_wrt_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_t_freezing_first_derivatives,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_freezing_first_derivatives",
+ "t_freezing_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_freezing_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_t_freezing_first_derivatives_poly,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_freezing_first_derivatives_poly",
+ "t_freezing_first_derivatives_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_freezing_first_derivatives_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_ct_first_derivatives_wrt_t_exact,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_first_derivatives_wrt_t_exact",
+ "ct_first_derivatives_wrt_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_first_derivatives_wrt_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_enthalpy_second_derivatives,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_second_derivatives",
+ "enthalpy_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_enthalpy_second_derivatives_ct_exact,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_second_derivatives_ct_exact",
+ "enthalpy_second_derivatives_ct_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_second_derivatives_ct_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_properties,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_properties",
+ "frazil_properties_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_properties", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_properties_potential,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_properties_potential",
+ "frazil_properties_potential_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_properties_potential", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_properties_potential_poly,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_properties_potential_poly",
+ "frazil_properties_potential_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_properties_potential_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_ratios_adiabatic,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_ratios_adiabatic",
+ "frazil_ratios_adiabatic_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_ratios_adiabatic", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_ratios_adiabatic_poly,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_ratios_adiabatic_poly",
+ "frazil_ratios_adiabatic_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_ratios_adiabatic_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_rho_alpha_beta,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_alpha_beta",
+ "rho_alpha_beta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_alpha_beta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_rho_first_derivatives,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_first_derivatives",
+ "rho_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_rho_second_derivatives_wrt_enthalpy,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_second_derivatives_wrt_enthalpy",
+ "rho_second_derivatives_wrt_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_second_derivatives_wrt_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_specvol_alpha_beta,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_alpha_beta",
+ "specvol_alpha_beta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_alpha_beta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_specvol_first_derivatives,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_first_derivatives",
+ "specvol_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_specvol_second_derivatives_wrt_enthalpy,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_second_derivatives_wrt_enthalpy",
+ "specvol_second_derivatives_wrt_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_second_derivatives_wrt_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddddd_dd,
+ data_melting_seaice_into_seawater,
+ types_dddddd_dd,
+ 1, 6, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_into_seawater",
+ "melting_seaice_into_seawater_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_into_seawater", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_ddd,
+ data_ct_second_derivatives,
+ types_dd_ddd,
+ 1, 2, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_second_derivatives",
+ "ct_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_ddd,
+ data_entropy_second_derivatives,
+ types_dd_ddd,
+ 1, 2, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_second_derivatives",
+ "entropy_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_ddd,
+ data_pt_second_derivatives,
+ types_dd_ddd,
+ 1, 2, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_second_derivatives",
+ "pt_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_ddd,
+ data_ice_fraction_to_freeze_seawater,
+ types_dddd_ddd,
+ 1, 4, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ice_fraction_to_freeze_seawater",
+ "ice_fraction_to_freeze_seawater_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ice_fraction_to_freeze_seawater", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_ddd,
+ data_melting_ice_into_seawater,
+ types_ddddd_ddd,
+ 1, 5, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_into_seawater",
+ "melting_ice_into_seawater_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_into_seawater", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_ddd,
+ data_seaice_fraction_to_freeze_seawater,
+ types_ddddd_ddd,
+ 1, 5, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "seaice_fraction_to_freeze_seawater",
+ "seaice_fraction_to_freeze_seawater_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "seaice_fraction_to_freeze_seawater", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddddd,
+ data_rho_second_derivatives,
+ types_ddd_ddddd,
+ 1, 3, 5, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_second_derivatives",
+ "rho_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddddd,
+ data_specvol_second_derivatives,
+ types_ddd_ddddd,
+ 1, 3, 5, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_second_derivatives",
+ "specvol_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+
+ return m;
+}
diff --git a/src/c_gsw/LICENSE b/src/c_gsw/LICENSE
new file mode 100644
index 0000000..6119a6f
--- /dev/null
+++ b/src/c_gsw/LICENSE
@@ -0,0 +1,34 @@
+Licence for the use of the Gibbs SeaWater (GSW) Oceanographic Toolbox
+
+Copyright (c) 2011, SCOR/IAPSO WG127 (Scientific Committee on Oceanic Research/
+International Association for the Physical Sciences of the Oceans, Working Group 127).
+
+All rights reserved.
+
+Redistribution and use, in source and binary forms, without modification, is permitted
+provided that the following conditions are met:
+
+• Redistributions of source code must retain the above copyright notice, this list
+ of conditions and the following disclaimer.
+
+• Redistributions in binary form must reproduce the above copyright notice, this
+ list of conditions and the following disclaimer in the documentation and/or other
+ materials provided with the distribution.
+
+• Neither the name of SCOR/IAPSO WG127 nor the names of its contributors may be used
+ to endorse or promote products derived from this software without specific prior
+ written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
+EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
+SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
+BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
+DAMAGE.
+
+The software is available from http://www.TEOS-10.org
+
diff --git a/src/c_gsw/gsw_internal_const.h b/src/c_gsw/gsw_internal_const.h
new file mode 100644
index 0000000..3d39c0a
--- /dev/null
+++ b/src/c_gsw/gsw_internal_const.h
@@ -0,0 +1,499 @@
+/*
+** $Id: gsw_internal_const.h,v a1406e71e2a9 2016/01/08 08:01:43 fdelahoyde $
+**
+** Internal constants for GSW-TEOS-10 V3.05.
+*/
+#ifndef GSW_INTERNAL_CONST_H
+#define GSW_INTERNAL_CONST_H
+
+/*
+** The following hack is used to ensure that gcc (and gcc emulating compilers
+** such as Macosx clang) do not emit unused variable warning messages.
+*/
+#ifdef __GNUC__
+#define UNUSED __attribute__ ((unused))
+#else
+#define UNUSED
+#endif
+
+#define GSW_TEOS10_CONSTANTS \
+UNUSED double db2pa = 1.0e4, \
+ rec_db2pa = 1.0e-4, \
+ pa2db = 1.0e-4, \
+ rec_pa2db = 1.0e4, \
+ pi = 3.141592653589793, \
+ deg2rad = pi/180.0, \
+ rad2deg = 180.0/pi, \
+ gamma = 2.26e-7, \
+/*\
+! cp0 = The "specific heat" for use [ J/(kg K) ]\
+! with Conservative Temperature \
+*/\
+ gsw_cp0 = 3991.86795711963, \
+/*\
+! T0 = the Celsius zero point. [ K ]\
+*/\
+ gsw_t0 = 273.15, \
+/*\
+! P0 = Absolute Pressure of one standard atmosphere. [ Pa ]\
+*/\
+ gsw_p0 = 101325.0, \
+/*\
+! SSO = Standard Ocean Reference Salinity. [ g/kg ]\
+*/\
+ gsw_sso = 35.16504, \
+ gsw_sqrtsso = 5.930011804372737, \
+/*\
+! uPS = unit conversion factor for salinities [ g/kg ]\
+*/\
+ gsw_ups = gsw_sso/35.0, \
+/*\
+! sfac = 1/(40*gsw_ups)\
+*/\
+ gsw_sfac = 0.0248826675584615, \
+/*\
+! deltaS = 24, offset = deltaS*gsw_sfac\
+*/\
+ offset = 5.971840214030754e-1, \
+/*\
+! C3515 = Conductivity at (SP=35, t_68=15, p=0) [ mS/cm ]\
+*/\
+ gsw_c3515 = 42.9140, \
+/*\
+! SonCl = SP to Chlorinity ratio [ (g/kg)^-1 ]\
+*/\
+ gsw_soncl = 1.80655, \
+/*\
+! valence_factor = valence factor of sea salt of Reference Composition\
+! [ unitless ]\
+*/\
+ gsw_valence_factor = 1.2452898, \
+/*\
+! atomic_weight = mole-weighted atomic weight of sea salt of Reference \
+! Composition [ g/mol ]\
+*/\
+ gsw_atomic_weight = 31.4038218
+
+
+#define GSW_SPECVOL_COEFFICIENTS \
+UNUSED double a000 = -1.56497346750e-5, \
+ a001 = 1.85057654290e-5, \
+ a002 = -1.17363867310e-6, \
+ a003 = -3.65270065530e-7, \
+ a004 = 3.14540999020e-7, \
+ a010 = 5.55242129680e-5, \
+ a011 = -2.34332137060e-5, \
+ a012 = 4.26100574800e-6, \
+ a013 = 5.73918103180e-7, \
+ a020 = -4.95634777770e-5, \
+ a021 = 2.37838968519e-5, \
+ a022 = -1.38397620111e-6, \
+ a030 = 2.76445290808e-5, \
+ a031 = -1.36408749928e-5, \
+ a032 = -2.53411666056e-7, \
+ a040 = -4.02698077700e-6, \
+ a041 = 2.53683834070e-6, \
+ a050 = 1.23258565608e-6, \
+ a100 = 3.50095997640e-5, \
+ a101 = -9.56770881560e-6, \
+ a102 = -5.56991545570e-6, \
+ a103 = -2.72956962370e-7, \
+ a110 = -7.48716846880e-5, \
+ a111 = -4.73566167220e-7, \
+ a112 = 7.82747741600e-7, \
+ a120 = 7.24244384490e-5, \
+ a121 = -1.03676320965e-5, \
+ a122 = 2.32856664276e-8, \
+ a130 = -3.50383492616e-5, \
+ a131 = 5.18268711320e-6, \
+ a140 = -1.65263794500e-6, \
+ a200 = -4.35926785610e-5, \
+ a201 = 1.11008347650e-5, \
+ a202 = 5.46207488340e-6, \
+ a210 = 7.18156455200e-5, \
+ a211 = 5.85666925900e-6, \
+ a212 = -1.31462208134e-6, \
+ a220 = -4.30608991440e-5, \
+ a221 = 9.49659182340e-7, \
+ a230 = 1.74814722392e-5, \
+ a300 = 3.45324618280e-5, \
+ a301 = -9.84471178440e-6, \
+ a302 = -1.35441856270e-6, \
+ a310 = -3.73971683740e-5, \
+ a311 = -9.76522784000e-7, \
+ a320 = 6.85899736680e-6, \
+ a400 = -1.19594097880e-5, \
+ a401 = 2.59092252600e-6, \
+ a410 = 7.71906784880e-6, \
+ a500 = 1.38645945810e-6, \
+ b000 = -3.10389819760e-4, \
+ b003 = 3.63101885150e-7, \
+ b004 = -1.11471254230e-7, \
+ b010 = 3.50095997640e-5, \
+ b013 = -2.72956962370e-7, \
+ b020 = -3.74358423440e-5, \
+ b030 = 2.41414794830e-5, \
+ b040 = -8.75958731540e-6, \
+ b050 = -3.30527589000e-7, \
+ b100 = 1.33856134076e-3, \
+ b103 = 3.34926075600e-8, \
+ b110 = -8.71853571220e-5, \
+ b120 = 7.18156455200e-5, \
+ b130 = -2.87072660960e-5, \
+ b140 = 8.74073611960e-6, \
+ b200 = -2.55143801811e-3, \
+ b210 = 1.03597385484e-4, \
+ b220 = -5.60957525610e-5, \
+ b230 = 6.85899736680e-6, \
+ b300 = 2.32344279772e-3, \
+ b310 = -4.78376391520e-5, \
+ b320 = 1.54381356976e-5, \
+ b400 = -1.05461852535e-3, \
+ b410 = 6.93229729050e-6, \
+ b500 = 1.91594743830e-4, \
+ b001 = 2.42624687470e-5, \
+ b011 = -9.56770881560e-6, \
+ b021 = -2.36783083610e-7, \
+ b031 = -3.45587736550e-6, \
+ b041 = 1.29567177830e-6, \
+ b101 = -6.95849219480e-5, \
+ b111 = 2.22016695300e-5, \
+ b121 = 5.85666925900e-6, \
+ b131 = 6.33106121560e-7, \
+ b201 = 1.12412331915e-4, \
+ b211 = -2.95341353532e-5, \
+ b221 = -1.46478417600e-6, \
+ b301 = -6.92888744480e-5, \
+ b311 = 1.03636901040e-5, \
+ b401 = 1.54637136265e-5, \
+ b002 = -5.84844329840e-7, \
+ b012 = -5.56991545570e-6, \
+ b022 = 3.91373870800e-7, \
+ b032 = 7.76188880920e-9, \
+ b102 = -9.62445031940e-6, \
+ b112 = 1.09241497668e-5, \
+ b122 = -1.31462208134e-6, \
+ b202 = 1.47789320994e-5, \
+ b212 = -4.06325568810e-6, \
+ b302 = -7.12478989080e-6, \
+ c000 = -6.07991438090e-5, \
+ c001 = 1.99712338438e-5, \
+ c002 = -3.39280843110e-6, \
+ c003 = 4.21246123200e-7, \
+ c004 = -6.32363064300e-8, \
+ c005 = 1.17681023580e-8, \
+ c010 = 1.85057654290e-5, \
+ c011 = -2.34727734620e-6, \
+ c012 = -1.09581019659e-6, \
+ c013 = 1.25816399608e-6, \
+ c020 = -1.17166068530e-5, \
+ c021 = 4.26100574800e-6, \
+ c022 = 8.60877154770e-7, \
+ c030 = 7.92796561730e-6, \
+ c031 = -9.22650800740e-7, \
+ c040 = -3.41021874820e-6, \
+ c041 = -1.26705833028e-7, \
+ c050 = 5.07367668140e-7, \
+ c100 = 2.42624687470e-5, \
+ c101 = -1.16968865968e-6, \
+ c102 = 1.08930565545e-6, \
+ c103 = -4.45885016920e-7, \
+ c110 = -9.56770881560e-6, \
+ c111 = -1.11398309114e-5, \
+ c112 = -8.18870887110e-7, \
+ c120 = -2.36783083610e-7, \
+ c121 = 7.82747741600e-7, \
+ c130 = -3.45587736550e-6, \
+ c131 = 1.55237776184e-8, \
+ c140 = 1.29567177830e-6, \
+ c200 = -3.47924609740e-5, \
+ c201 = -9.62445031940e-6, \
+ c202 = 5.02389113400e-8, \
+ c210 = 1.11008347650e-5, \
+ c211 = 1.09241497668e-5, \
+ c220 = 2.92833462950e-6, \
+ c221 = -1.31462208134e-6, \
+ c230 = 3.16553060780e-7, \
+ c300 = 3.74707773050e-5, \
+ c301 = 9.85262139960e-6, \
+ c310 = -9.84471178440e-6, \
+ c311 = -2.70883712540e-6, \
+ c320 = -4.88261392000e-7, \
+ c400 = -1.73222186120e-5, \
+ c401 = -3.56239494540e-6, \
+ c410 = 2.59092252600e-6, \
+ c500 = 3.09274272530e-6, \
+ h001 = 1.07699958620e-3, \
+ h002 = -3.03995719050e-5, \
+ h003 = 3.32853897400e-6, \
+ h004 = -2.82734035930e-7, \
+ h005 = 2.10623061600e-8, \
+ h006 = -2.10787688100e-9, \
+ h007 = 2.80192913290e-10, \
+ h011 = -1.56497346750e-5, \
+ h012 = 9.25288271450e-6, \
+ h013 = -3.91212891030e-7, \
+ h014 = -9.13175163830e-8, \
+ h015 = 6.29081998040e-8, \
+ h021 = 2.77621064840e-5, \
+ h022 = -5.85830342650e-6, \
+ h023 = 7.10167624670e-7, \
+ h024 = 7.17397628980e-8, \
+ h031 = -1.65211592590e-5, \
+ h032 = 3.96398280870e-6, \
+ h033 = -1.53775133460e-7, \
+ h042 = -1.70510937410e-6, \
+ h043 = -2.11176388380e-8, \
+ h041 = 6.91113227020e-6, \
+ h051 = -8.05396155400e-7, \
+ h052 = 2.53683834070e-7, \
+ h061 = 2.05430942680e-7, \
+ h101 = -3.10389819760e-4, \
+ h102 = 1.21312343735e-5, \
+ h103 = -1.94948109950e-7, \
+ h104 = 9.07754712880e-8, \
+ h105 = -2.22942508460e-8, \
+ h111 = 3.50095997640e-5, \
+ h112 = -4.78385440780e-6, \
+ h113 = -1.85663848520e-6, \
+ h114 = -6.82392405930e-8, \
+ h121 = -3.74358423440e-5, \
+ h122 = -1.18391541805e-7, \
+ h123 = 1.30457956930e-7, \
+ h131 = 2.41414794830e-5, \
+ h132 = -1.72793868275e-6, \
+ h133 = 2.58729626970e-9, \
+ h141 = -8.75958731540e-6, \
+ h142 = 6.47835889150e-7, \
+ h151 = -3.30527589000e-7, \
+ h201 = 6.69280670380e-4, \
+ h202 = -1.73962304870e-5, \
+ h203 = -1.60407505320e-6, \
+ h204 = 4.18657594500e-9, \
+ h211 = -4.35926785610e-5, \
+ h212 = 5.55041738250e-6, \
+ h213 = 1.82069162780e-6, \
+ h221 = 3.59078227600e-5, \
+ h222 = 1.46416731475e-6, \
+ h223 = -2.19103680220e-7, \
+ h231 = -1.43536330480e-5, \
+ h232 = 1.58276530390e-7, \
+ h241 = 4.37036805980e-6, \
+ h301 = -8.50479339370e-4, \
+ h302 = 1.87353886525e-5, \
+ h303 = 1.64210356660e-6, \
+ h311 = 3.45324618280e-5, \
+ h312 = -4.92235589220e-6, \
+ h313 = -4.51472854230e-7, \
+ h321 = -1.86985841870e-5, \
+ h322 = -2.44130696000e-7, \
+ h331 = 2.28633245560e-6, \
+ h401 = 5.80860699430e-4, \
+ h402 = -8.66110930600e-6, \
+ h403 = -5.93732490900e-7, \
+ h411 = -1.19594097880e-5, \
+ h421 = 3.85953392440e-6, \
+ h412 = 1.29546126300e-6, \
+ h501 = -2.10923705070e-4, \
+ h502 = 1.54637136265e-6, \
+ h511 = 1.38645945810e-6, \
+ h601 = 3.19324573050e-5, \
+ v000 = 1.0769995862e-3, \
+ v001 = -6.0799143809e-5, \
+ v002 = 9.9856169219e-6, \
+ v003 = -1.1309361437e-6, \
+ v004 = 1.0531153080e-7, \
+ v005 = -1.2647261286e-8, \
+ v006 = 1.9613503930e-9, \
+ v010 = -3.1038981976e-4, \
+ v011 = 2.4262468747e-5, \
+ v012 = -5.8484432984e-7, \
+ v013 = 3.6310188515e-7, \
+ v014 = -1.1147125423e-7, \
+ v020 = 6.6928067038e-4, \
+ v021 = -3.4792460974e-5, \
+ v022 = -4.8122251597e-6, \
+ v023 = 1.6746303780e-8, \
+ v030 = -8.5047933937e-4, \
+ v031 = 3.7470777305e-5, \
+ v032 = 4.9263106998e-6, \
+ v040 = 5.8086069943e-4, \
+ v041 = -1.7322218612e-5, \
+ v042 = -1.7811974727e-6, \
+ v050 = -2.1092370507e-4, \
+ v051 = 3.0927427253e-6, \
+ v060 = 3.1932457305e-5, \
+ v100 = -1.5649734675e-5, \
+ v101 = 1.8505765429e-5, \
+ v102 = -1.1736386731e-6, \
+ v103 = -3.6527006553e-7, \
+ v104 = 3.1454099902e-7, \
+ v110 = 3.5009599764e-5, \
+ v111 = -9.5677088156e-6, \
+ v112 = -5.5699154557e-6, \
+ v113 = -2.7295696237e-7, \
+ v120 = -4.3592678561e-5, \
+ v121 = 1.1100834765e-5, \
+ v122 = 5.4620748834e-6, \
+ v130 = 3.4532461828e-5, \
+ v131 = -9.8447117844e-6, \
+ v132 = -1.3544185627e-6, \
+ v140 = -1.1959409788e-5, \
+ v141 = 2.5909225260e-6, \
+ v150 = 1.3864594581e-6, \
+ v200 = 2.7762106484e-5, \
+ v201 = -1.1716606853e-5, \
+ v202 = 2.1305028740e-6, \
+ v203 = 2.8695905159e-7, \
+ v210 = -3.7435842344e-5, \
+ v211 = -2.3678308361e-7, \
+ v212 = 3.9137387080e-7, \
+ v220 = 3.5907822760e-5, \
+ v221 = 2.9283346295e-6, \
+ v222 = -6.5731104067e-7, \
+ v230 = -1.8698584187e-5, \
+ v231 = -4.8826139200e-7, \
+ v240 = 3.8595339244e-6, \
+ v300 = -1.6521159259e-5, \
+ v301 = 7.9279656173e-6, \
+ v302 = -4.6132540037e-7, \
+ v310 = 2.4141479483e-5, \
+ v311 = -3.4558773655e-6, \
+ v312 = 7.7618888092e-9, \
+ v320 = -1.4353633048e-5, \
+ v321 = 3.1655306078e-7, \
+ v330 = 2.2863324556e-6, \
+ v400 = 6.9111322702e-6, \
+ v401 = -3.4102187482e-6, \
+ v402 = -6.3352916514e-8, \
+ v410 = -8.7595873154e-6, \
+ v411 = 1.2956717783e-6, \
+ v420 = 4.3703680598e-6, \
+ v500 = -8.0539615540e-7, \
+ v501 = 5.0736766814e-7, \
+ v510 = -3.3052758900e-7, \
+ v600 = 2.0543094268e-7
+
+#define GSW_SP_COEFFICIENTS \
+UNUSED double a0 = 0.0080, \
+ a1 = -0.1692, \
+ a2 = 25.3851, \
+ a3 = 14.0941, \
+ a4 = -7.0261, \
+ a5 = 2.7081, \
+ b0 = 0.0005, \
+ b1 = -0.0056, \
+ b2 = -0.0066, \
+ b3 = -0.0375, \
+ b4 = 0.0636, \
+ b5 = -0.0144, \
+ c0 = 0.6766097, \
+ c1 = 2.00564e-2, \
+ c2 = 1.104259e-4, \
+ c3 = -6.9698e-7, \
+ c4 = 1.0031e-9, \
+ d1 = 3.426e-2, \
+ d2 = 4.464e-4, \
+ d3 = 4.215e-1, \
+ d4 = -3.107e-3, \
+ e1 = 2.070e-5, \
+ e2 = -6.370e-10, \
+ e3 = 3.989e-15, \
+ k = 0.0162
+
+#define GSW_SAAR_DATA \
+UNUSED int deli[4] = {0,1,1,0}, delj[4] = {0,0,1,1}, npan = 6; \
+UNUSED double longs_pan[6] = {260.00, 272.59, 276.50, 278.65, 280.73, 292.0},\
+ lats_pan[6] = { 19.55, 13.97, 9.60, 8.10, 9.33, 3.4}
+
+#define GSW_GIBBS_ICE_COEFFICIENTS \
+UNUSED double complex t1 =( 3.68017112855051e-2+ 5.10878114959572e-2*I), \
+ t2 =( 3.37315741065416e-1+ 3.35449415919309e-1*I), \
+ r1 =( 4.47050716285388e1+ 6.56876847463481e1*I), \
+ r20 =(-7.25974574329220e1+ -7.81008427112870e1*I), \
+ r21 =(-5.57107698030123e-5+ 4.64578634580806e-5*I), \
+ r22 =(2.34801409215913e-11+-2.85651142904972e-11*I); \
+/*\
+! 1./Pt, where Pt = 611.657; Experimental triple-point pressure in Pa.\
+*/\
+UNUSED double rec_pt = 1.634903221903779e-3, \
+ tt = 273.16, /*Triple-point temperature, kelvin (K).*/ \
+ rec_tt = 3.660858105139845e-3, /*= 1/tt */ \
+ g00 = -6.32020233335886e5, \
+ g01 = 6.55022213658955e-1, \
+ g02 = -1.89369929326131e-8, \
+ g03 = 3.3974612327105304e-15, \
+ g04 = -5.564648690589909e-22
+
+
+#define GSW_FREEZING_POLY_COEFFICIENTS \
+UNUSED double c0 = 0.017947064327968736, \
+ c1 = -6.076099099929818, \
+ c2 = 4.883198653547851, \
+ c3 = -11.88081601230542, \
+ c4 = 13.34658511480257, \
+ c5 = -8.722761043208607, \
+ c6 = 2.082038908808201, \
+ c7 = -7.389420998107497, \
+ c8 = -2.110913185058476, \
+ c9 = 0.2295491578006229, \
+ c10 = -0.9891538123307282, \
+ c11 = -0.08987150128406496, \
+ c12 = 0.3831132432071728, \
+ c13 = 1.054318231187074, \
+ c14 = 1.065556599652796, \
+ c15 = -0.7997496801694032, \
+ c16 = 0.3850133554097069, \
+ c17 = -2.078616693017569, \
+ c18 = 0.8756340772729538, \
+ c19 = -2.079022768390933, \
+ c20 = 1.596435439942262, \
+ c21 = 0.1338002171109174, \
+ c22 = 1.242891021876471, \
+/* \
+! Note that a = 0.502500117621,/gsw_sso \
+*/ \
+ a = 0.014289763856964, \
+ b = 0.057000649899720, \
+ t0 = 0.002519, \
+ t1 = -5.946302841607319, \
+ t2 = 4.136051661346983, \
+ t3 = -1.115150523403847e1, \
+ t4 = 1.476878746184548e1, \
+ t5 = -1.088873263630961e1, \
+ t6 = 2.961018839640730, \
+ t7 = -7.433320943962606, \
+ t8 = -1.561578562479883, \
+ t9 = 4.073774363480365e-2, \
+ t10 = 1.158414435887717e-2, \
+ t11 = -4.122639292422863e-1, \
+ t12 = -1.123186915628260e-1, \
+ t13 = 5.715012685553502e-1, \
+ t14 = 2.021682115652684e-1, \
+ t15 = 4.140574258089767e-2, \
+ t16 = -6.034228641903586e-1, \
+ t17 = -1.205825928146808e-2, \
+ t18 = -2.812172968619369e-1, \
+ t19 = 1.877244474023750e-2, \
+ t20 = -1.204395563789007e-1, \
+ t21 = 2.349147739749606e-1, \
+ t22 = 2.748444541144219e-3
+
+
+#define GSW_BALTIC_DATA \
+/*\
+! Coordinate data for the Baltic Sea\
+*/\
+UNUSED double xb_left[3]={12.6, 7.0, 26.0},\
+ yb_left[3]={50.0, 59.0, 69.0},\
+ xb_right[2]={45.0, 26.0},\
+ yb_right[2]={50.0, 69.0}
+
+#ifndef max
+#define max(a,b) (((a)>(b))?(a):(b))
+#endif
+#ifndef min
+#define min(a,b) (((a)<(b))?(a):(b))
+#endif
+
+#endif /* GSW_INTERNAL_CONST_H */
diff --git a/src/c_gsw/gsw_oceanographic_toolbox.c b/src/c_gsw/gsw_oceanographic_toolbox.c
new file mode 100644
index 0000000..eeee4c9
--- /dev/null
+++ b/src/c_gsw/gsw_oceanographic_toolbox.c
@@ -0,0 +1,10704 @@
+/*
+** $Id: gsw_oceanographic_toolbox-head,v c61271a7810d 2016/08/19 20:04:03 fdelahoyde $
+** Version: 3.05.0-3
+**
+** This is a translation of the original f90 source code into C
+** by the Shipboard Technical Support Computing Resources group
+** at Scripps Institution of Oceanography -- sts-cr at sio.ucsd.edu.
+** The original notices follow.
+**
+==========================================================================
+ Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS-10 (Fortran)
+==========================================================================
+
+ This is a subset of functions contained in the Gibbs SeaWater (GSW)
+ Oceanographic Toolbox of TEOS-10.
+
+ Version 1.0 written by David Jackett
+ Modified by Paul Barker (version 3.02)
+ Modified by Glenn Hyland (version 3.04+)
+
+ For help with this Oceanographic Toolbox email: help at teos-10.org
+
+ This software is available from http://www.teos-10.org
+
+==========================================================================
+
+ gsw_data_v3_0.nc
+ NetCDF file that contains the global data set of Absolute Salinity Anomaly
+ Ratio, the global data set of Absolute Salinity Anomaly atlas, and check
+ values and computation accuracy values for use in gsw_check_function.
+ The data set gsw_data_v3_0.nc must not be tampered with.
+
+ gsw_check_function.f90
+ Contains the check functions. We suggest that after downloading, unzipping
+ and installing the toolbox the user runs this program to ensure that the
+ toolbox is installed correctly and there are no conflicts. This toolbox has
+ been tested to compile and run with gfortran.
+
+ cd test
+ make
+ ./gsw_check
+
+ Note that gfortran is the name of the GNU Fortran project, developing a
+ free Fortran 95/2003/2008 compiler for GCC, the GNU Compiler Collection.
+ It is available from http://gcc.gnu.org/fortran/
+
+==========================================================================
+*/
+#include "gswteos-10.h"
+#include "gsw_internal_const.h"
+
+/*
+!==========================================================================
+subroutine gsw_add_barrier(input_data,lon,lat,long_grid,lat_grid,dlong_grid,dlat_grid,output_data)
+!==========================================================================
+
+! Adds a barrier through Central America (Panama) and then averages
+! over the appropriate side of the barrier
+!
+! data_in : data [unitless]
+! lon : Longitudes of data degrees east [0 ... +360]
+! lat : Latitudes of data degrees north [-90 ... +90]
+! longs_grid : Longitudes of regular grid degrees east [0 ... +360]
+! lats_grid : Latitudes of regular grid degrees north [-90 ... +90]
+! dlongs_grid : Longitude difference of regular grid degrees [deg longitude]
+! dlats_grid : Latitude difference of regular grid degrees [deg latitude]
+!
+! output_data : average of data depending on which side of the
+! Panama canal it is on [unitless]
+*/
+void
+gsw_add_barrier(double *input_data, double lon, double lat,
+ double long_grid, double lat_grid, double dlong_grid,
+ double dlat_grid, double *output_data)
+{
+ GSW_SAAR_DATA;
+ int above_line[4];
+ int k, nmean, above_line0, kk;
+ double r, lats_line, data_mean;
+
+ k = gsw_util_indx(longs_pan,npan,lon);
+ /* the lon/lat point */
+ r = (lon-longs_pan[k])/(longs_pan[k+1]-longs_pan[k]);
+ lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]);
+
+ above_line0 = (lats_line <= lat);
+
+ k = gsw_util_indx(longs_pan,npan,long_grid);
+ /*the 1 & 4 lon/lat points*/
+ r = (long_grid-longs_pan[k])/
+ (longs_pan[k+1]-longs_pan[k]);
+ lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]);
+
+ above_line[0] = (lats_line <= lat_grid);
+ above_line[3] = (lats_line <= lat_grid+dlat_grid);
+
+ k = gsw_util_indx(longs_pan,6,long_grid+dlong_grid);
+ /*the 2 & 3 lon/lat points */
+ r = (long_grid+dlong_grid-longs_pan[k])/
+ (longs_pan[k+1]-longs_pan[k]);
+ lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]);
+
+ above_line[1] = (lats_line <= lat_grid);
+ above_line[2] = (lats_line <= lat_grid+dlat_grid);
+
+ nmean = 0;
+ data_mean = 0.0;
+
+ for (kk=0; kk<4; kk++) {
+ if ((fabs(input_data[kk]) <= 100.0) &&
+ above_line0 == above_line[kk]) {
+ nmean = nmean+1;
+ data_mean = data_mean+input_data[kk];
+ }
+ }
+ if (nmean == 0)
+ data_mean = 0.0; /*errorreturn*/
+ else
+ data_mean = data_mean/nmean;
+
+ for (kk=0; kk<4; kk++) {
+ if ((fabs(input_data[kk]) >= 1.0e10) ||
+ above_line0 != above_line[kk])
+ output_data[kk] = data_mean;
+ else
+ output_data[kk] = input_data[kk];
+ }
+
+ return;
+}
+/*
+!==========================================================================
+subroutine gsw_add_mean(data_in,data_out)
+!==========================================================================
+
+! Replaces NaN's with non-nan mean of the 4 adjacent neighbours
+!
+! data_in : data set of the 4 adjacent neighbours
+!
+! data_out : non-nan mean of the 4 adjacent neighbours [unitless]
+*/
+void
+gsw_add_mean(double *data_in, double *data_out)
+{
+ int k, nmean;
+ double data_mean;
+
+ nmean = 0;
+ data_mean = 0.0;
+
+ for (k=0; k<4; k++) {
+ if (fabs(data_in[k]) <= 100.0) {
+ nmean++;
+ data_mean = data_mean+data_in[k];
+ }
+ }
+
+ if (nmean == 0.0)
+ data_mean = 0.0; /*errorreturn*/
+ else
+ data_mean = data_mean/nmean;
+
+ for (k=0; k<4; k++) {
+ if (fabs(data_in[k]) >= 100.0)
+ data_out[k] = data_mean;
+ else
+ data_out[k] = data_in[k];
+ }
+ return;
+}
+/*
+!==========================================================================
+function gsw_adiabatic_lapse_rate_from_ct(sa,ct,p)
+!==========================================================================
+
+! Calculates the adiabatic lapse rate from Conservative Temperature
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_adiabatic_lapse_rate_from_ct : adiabatic lapse rate [K/Pa]
+*/
+double
+gsw_adiabatic_lapse_rate_from_ct(double sa, double ct, double p)
+{
+ int n0=0, n1=1, n2=2;
+ double pt0, pr0=0.0, t;
+
+ pt0 = gsw_pt_from_ct(sa,ct);
+ t = gsw_pt_from_t(sa,pt0,pr0,p);
+
+ return (-gsw_gibbs(n0,n1,n1,sa,t,p)/gsw_gibbs(n0,n2,n0,sa,t,p));
+
+}
+/*
+!==========================================================================
+elemental function gsw_adiabatic_lapse_rate_ice (t, p)
+!==========================================================================
+!
+! Calculates the adiabatic lapse rate of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! Note. The output is in unit of degress Celsius per Pa,
+! (or equivilently K/Pa) not in units of K/dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_adiabatic_lapse_rate_ice(double t, double p)
+{
+ return (-gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(2,0,t,p));
+}
+/*
+!==========================================================================
+function gsw_alpha(sa,ct,p)
+!==========================================================================
+
+! Calculates the thermal expansion coefficient of seawater with respect to
+! Conservative Temperature using the computationally-efficient 48-term
+! expression for density in terms of SA, CT and p (IOC et al., 2010)
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_alpha : thermal expansion coefficient of seawater (48 term equation)
+*/
+double
+gsw_alpha(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double xs, ys, z, v_ct_part;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v_ct_part = a000
+ + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ return (0.025*v_ct_part/gsw_specvol(sa,ct,p));
+}
+/*
+!==========================================================================
+function gsw_alpha_on_beta(sa,ct,p)
+!==========================================================================
+
+! Calculates alpha divided by beta, where alpha is the thermal expansion
+! coefficient and beta is the saline contraction coefficient of seawater
+! from Absolute Salinity and Conservative Temperature. This function uses
+! the computationally-efficient expression for specific volume in terms of
+! SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+!
+! alpha_on_beta
+! : thermal expansion coefficient with respect to [kg g^-1 K^-1]
+! Conservative Temperature divided by the saline
+! contraction coefficient at constant Conservative
+! Temperature
+*/
+double
+gsw_alpha_on_beta(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double xs, ys, z, v_ct_part, v_sa_part;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v_ct_part = a000
+ + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ v_sa_part = b000
+ + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ return (-(v_ct_part*xs)/(20.0*gsw_sfac*v_sa_part));
+}
+/*
+!==========================================================================
+function gsw_alpha_wrt_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates thermal expansion coefficient of seawater with respect to
+! in-situ temperature
+!
+! sa : Absolute Salinity [g/kg]
+! t : insitu temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_alpha_wrt_t_exact : thermal expansion coefficient [1/K]
+! wrt (in-situ) temperature
+*/
+double
+gsw_alpha_wrt_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (gsw_gibbs(n0,n1,n1,sa,t,p)/gsw_gibbs(n0,n0,n1,sa,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_alpha_wrt_t_ice (t, p)
+!==========================================================================
+!
+! Calculates the thermal expansion coefficient of ice with respect to
+! in-situ temperature.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! alpha_wrt_t_ice = thermal expansion coefficient of ice with respect
+! to in-situ temperature [ 1/K ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_alpha_wrt_t_ice(double t, double p)
+{
+ return (gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+function gsw_beta(sa,ct,p)
+!==========================================================================
+
+! Calculates the saline (i.e. haline) contraction coefficient of seawater
+! at constant Conservative Temperature using the computationally-efficient
+! expression for specific volume in terms of SA, CT and p
+! (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! beta : saline contraction coefficient of seawater [kg/g]
+! at constant Conservative Temperature
+*/
+double
+gsw_beta(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double xs, ys, z, v_sa_part;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v_sa_part = b000
+ + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ return (-v_sa_part*0.5*gsw_sfac/(gsw_specvol(sa,ct,p)*xs));
+}
+/*
+!==========================================================================
+function gsw_beta_const_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates saline (haline) contraction coefficient of seawater at
+! constant in-situ temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! beta_const_t_exact : haline contraction coefficient [kg/g]
+*/
+double
+gsw_beta_const_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (-gsw_gibbs(n1,n0,n1,sa,t,p)/gsw_gibbs(n0,n0,n1,sa,t,p));
+}
+/*
+!==========================================================================
+function gsw_c_from_sp(sp,t,p)
+!==========================================================================
+
+! Calculates conductivity, C, from (SP,t,p) using PSS-78 in the range
+! 2 < SP < 42. If the input Practical Salinity is less than 2 then a
+! modified form of the Hill et al. (1986) fomula is used for Practical
+! Salinity. The modification of the Hill et al. (1986) expression is to
+! ensure that it is exactly consistent with PSS-78 at SP = 2.
+!
+! The conductivity ratio returned by this function is consistent with the
+! input value of Practical Salinity, SP, to 2x10^-14 psu over the full
+! range of input parameters (from pure fresh water up to SP = 42 psu).
+! This error of 2x10^-14 psu is machine precision at typical seawater
+! salinities. This accuracy is achieved by having four different
+! polynomials for the starting value of Rtx (the square root of Rt) in
+! four different ranges of SP, and by using one and a half iterations of
+! a computationally efficient modified Newton-Raphson technique (McDougall
+! and Wotherspoon, 2012) to find the root of the equation.
+!
+! Note that strictly speaking PSS-78 (Unesco, 1983) defines Practical
+! Salinity in terms of the conductivity ratio, R, without actually
+! specifying the value of C(35,15,0) (which we currently take to be
+! 42.9140 mS/cm).
+!
+! sp : Practical Salinity [unitless]
+! t : in-situ temperature [ITS-90] [deg C]
+! p : sea pressure [dbar]
+!
+! c : conductivity [ mS/cm ]
+*/
+double
+gsw_c_from_sp(double sp, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SP_COEFFICIENTS;
+ double p0 = 4.577801212923119e-3, p1 = 1.924049429136640e-1,
+ p2 = 2.183871685127932e-5, p3 = -7.292156330457999e-3,
+ p4 = 1.568129536470258e-4, p5 = -1.478995271680869e-6,
+ p6 = 9.086442524716395e-4, p7 = -1.949560839540487e-5,
+ p8 = -3.223058111118377e-6, p9 = 1.175871639741131e-7,
+ p10 = -7.522895856600089e-5, p11 = -2.254458513439107e-6,
+ p12 = 6.179992190192848e-7, p13 = 1.005054226996868e-8,
+ p14 = -1.923745566122602e-9, p15 = 2.259550611212616e-6,
+ p16 = 1.631749165091437e-7, p17 = -5.931857989915256e-9,
+ p18 = -4.693392029005252e-9, p19 = 2.571854839274148e-10,
+ p20 = 4.198786822861038e-12,
+ q0 = 5.540896868127855e-5, q1 = 2.015419291097848e-1,
+ q2 = -1.445310045430192e-5, q3 = -1.567047628411722e-2,
+ q4 = 2.464756294660119e-4, q5 = -2.575458304732166e-7,
+ q6 = 5.071449842454419e-3, q7 = 9.081985795339206e-5,
+ q8 = -3.635420818812898e-6, q9 = 2.249490528450555e-8,
+ q10 = -1.143810377431888e-3, q11 = 2.066112484281530e-5,
+ q12 = 7.482907137737503e-7, q13 = 4.019321577844724e-8,
+ q14 = -5.755568141370501e-10, q15 = 1.120748754429459e-4,
+ q16 = -2.420274029674485e-6, q17 = -4.774829347564670e-8,
+ q18 = -4.279037686797859e-9, q19 = -2.045829202713288e-10,
+ q20 = 5.025109163112005e-12,
+ s0 = 3.432285006604888e-3, s1 = 1.672940491817403e-1,
+ s2 = 2.640304401023995e-5, s3 = 1.082267090441036e-1,
+ s4 = -6.296778883666940e-5, s5 = -4.542775152303671e-7,
+ s6 = -1.859711038699727e-1, s7 = 7.659006320303959e-4,
+ s8 = -4.794661268817618e-7, s9 = 8.093368602891911e-9,
+ s10 = 1.001140606840692e-1, s11 = -1.038712945546608e-3,
+ s12 = -6.227915160991074e-6, s13 = 2.798564479737090e-8,
+ s14 = -1.343623657549961e-10, s15 = 1.024345179842964e-2,
+ s16 = 4.981135430579384e-4, s17 = 4.466087528793912e-6,
+ s18 = 1.960872795577774e-8, s19 = -2.723159418888634e-10,
+ s20 = 1.122200786423241e-12,
+ u0 = 5.180529787390576e-3, u1 = 1.052097167201052e-3,
+ u2 = 3.666193708310848e-5, u3 = 7.112223828976632e0,
+ u4 = -3.631366777096209e-4, u5 = -7.336295318742821e-7,
+ u6 = -1.576886793288888e+2, u7 = -1.840239113483083e-3,
+ u8 = 8.624279120240952e-6, u9 = 1.233529799729501e-8,
+ u10 = 1.826482800939545e+3, u11 = 1.633903983457674e-1,
+ u12 = -9.201096427222349e-5, u13 = -9.187900959754842e-8,
+ u14 = -1.442010369809705e-10, u15 = -8.542357182595853e+3,
+ u16 = -1.408635241899082e0, u17 = 1.660164829963661e-4,
+ u18 = 6.797409608973845e-7, u19 = 3.345074990451475e-10,
+ u20 = 8.285687652694768e-13;
+
+ double t68, ft68, x, rtx=0.0, dsp_drtx, sqrty,
+ part1, part2, hill_ratio, sp_est,
+ rtx_old, rt, aa, bb, cc, dd, ee, ra,r, rt_lc, rtxm,
+ sp_hill_raw;
+
+ t68 = t*1.00024e0;
+ ft68 = (t68 - 15e0)/(1e0 + k*(t68 - 15e0));
+
+ x = sqrt(sp);
+
+ /*
+ |--------------------------------------------------------------------------
+ ! Finding the starting value of Rtx, the square root of Rt, using four
+ ! different polynomials of SP and t68.
+ !--------------------------------------------------------------------------
+ */
+
+ if (sp >= 9.0) {
+ rtx = p0 + x*(p1 + p4*t68 + x*(p3 + p7*t68 + x*(p6
+ + p11*t68 + x*(p10 + p16*t68 + x*p15))))
+ + t68*(p2+ t68*(p5 + x*x*(p12 + x*p17) + p8*x
+ + t68*(p9 + x*(p13 + x*p18)+ t68*(p14 + p19*x + p20*t68))));
+ } else if (sp >= 0.25 && sp < 9.0) {
+ rtx = q0 + x*(q1 + q4*t68 + x*(q3 + q7*t68 + x*(q6
+ + q11*t68 + x*(q10 + q16*t68 + x*q15))))
+ + t68*(q2+ t68*(q5 + x*x*(q12 + x*q17) + q8*x
+ + t68*(q9 + x*(q13 + x*q18)+ t68*(q14 + q19*x + q20*t68))));
+ } else if (sp >= 0.003 && sp < 0.25) {
+ rtx = s0 + x*(s1 + s4*t68 + x*(s3 + s7*t68 + x*(s6
+ + s11*t68 + x*(s10 + s16*t68 + x*s15))))
+ + t68*(s2+ t68*(s5 + x*x*(s12 + x*s17) + s8*x
+ + t68*(s9 + x*(s13 + x*s18)+ t68*(s14 + s19*x + s20*t68))));
+ } else if (sp < 0.003) {
+ rtx = u0 + x*(u1 + u4*t68 + x*(u3 + u7*t68 + x*(u6
+ + u11*t68 + x*(u10 + u16*t68 + x*u15))))
+ + t68*(u2+ t68*(u5 + x*x*(u12 + x*u17) + u8*x
+ + t68*(u9 + x*(u13 + x*u18)+ t68*(u14 + u19*x + u20*t68))));
+ }
+
+ /*
+ !--------------------------------------------------------------------------
+ ! Finding the starting value of dSP_dRtx, the derivative of SP with respect
+ ! to Rtx.
+ !--------------------------------------------------------------------------
+ */
+ dsp_drtx = a1 + (2e0*a2 + (3e0*a3 +
+ (4e0*a4 + 5e0*a5*rtx)*rtx)*rtx)*rtx
+ + ft68*(b1 + (2e0*b2 + (3e0*b3 + (4e0*b4 +
+ 5e0*b5*rtx)*rtx)*rtx)*rtx);
+
+ if (sp < 2.0) {
+ x = 400e0*(rtx*rtx);
+ sqrty = 10.0*rtx;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ dsp_drtx = dsp_drtx
+ + a0*800e0*rtx*(1.5e0 + 2e0*x)/(part1*part1)
+ + b0*ft68*(10e0 + sqrty*(20e0 + 30e0*sqrty))/
+ (part2*part2);
+ dsp_drtx = hill_ratio*dsp_drtx;
+ }
+
+ /*
+ !--------------------------------------------------------------------------
+ ! One iteration through the modified Newton-Raphson method (McDougall and
+ ! Wotherspoon, 2012) achieves an error in Practical Salinity of about
+ ! 10^-12 for all combinations of the inputs. One and a half iterations of
+ ! the modified Newton-Raphson method achevies a maximum error in terms of
+ ! Practical Salinity of better than 2x10^-14 everywhere.
+ !
+ ! We recommend one and a half iterations of the modified Newton-Raphson
+ ! method.
+ !
+ ! Begin the modified Newton-Raphson method.
+ !--------------------------------------------------------------------------
+ */
+ sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx
+ + ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx);
+ if (sp_est < 2.0) {
+ x = 400e0*(rtx*rtx);
+ sqrty = 10e0*rtx;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ sp_hill_raw = sp_est - a0/part1 - b0*ft68/part2;
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ sp_est = hill_ratio*sp_hill_raw;
+ }
+
+ rtx_old = rtx;
+ rtx = rtx_old - (sp_est - sp)/dsp_drtx;
+
+ rtxm = 0.5e0*(rtx + rtx_old); /*This mean value of Rtx, Rtxm, is the
+ value of Rtx at which the derivative dSP_dRtx is evaluated.*/
+
+ dsp_drtx= a1 + (2e0*a2 + (3e0*a3 + (4e0*a4 +
+ 5e0*a5*rtxm)*rtxm)*rtxm)*rtxm
+ + ft68*(b1 + (2e0*b2 + (3e0*b3 + (4e0*b4 +
+ 5e0*b5*rtxm)*rtxm)*rtxm)*rtxm);
+ if (sp_est < 2.0) {
+ x = 400e0*(rtxm*rtxm);
+ sqrty = 10e0*rtxm;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ dsp_drtx = dsp_drtx
+ + a0*800e0*rtxm*(1.5e0 + 2e0*x)/(part1*part1)
+ + b0*ft68*(10e0 + sqrty*(20e0 + 30e0*sqrty))/
+ (part2*part2);
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ dsp_drtx = hill_ratio*dsp_drtx;
+ }
+
+ /*
+ !--------------------------------------------------------------------------
+ ! The line below is where Rtx is updated at the end of the one full
+ ! iteration of the modified Newton-Raphson technique.
+ !--------------------------------------------------------------------------
+ */
+ rtx = rtx_old - (sp_est - sp)/dsp_drtx;
+ /*
+ !--------------------------------------------------------------------------
+ ! Now we do another half iteration of the modified Newton-Raphson
+ ! technique, making a total of one and a half modified N-R iterations.
+ !--------------------------------------------------------------------------
+ */
+ sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx
+ + ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx);
+ if (sp_est < 2.0) {
+ x = 400e0*(rtx*rtx);
+ sqrty = 10e0*rtx;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ sp_hill_raw = sp_est - a0/part1 - b0*ft68/part2;
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ sp_est = hill_ratio*sp_hill_raw;
+ }
+ rtx = rtx - (sp_est - sp)/dsp_drtx;
+
+ /*
+ !--------------------------------------------------------------------------
+ ! Now go from Rtx to Rt and then to the conductivity ratio R at pressure p.
+ !--------------------------------------------------------------------------
+ */
+ rt = rtx*rtx;
+
+ aa = d3 + d4*t68;
+ bb = 1e0 + t68*(d1 + d2*t68);
+ cc = p*(e1 + p*(e2 + e3*p));
+ /* rt_lc (i.e. rt_lower_case) corresponds to rt as defined in
+ the UNESCO 44 (1983) routines. */
+ rt_lc = c0 + (c1 + (c2 + (c3 + c4*t68)*t68)*t68)*t68;
+
+ dd = bb - aa*rt_lc*rt;
+ ee = rt_lc*rt*aa*(bb + cc);
+ ra = sqrt(dd*dd + 4e0*ee) - dd;
+ r = 0.5e0*ra/aa;
+
+ /*
+ ! The dimensionless conductivity ratio, R, is the conductivity input, C,
+ ! divided by the present estimate of C(SP=35, t_68=15, p=0) which is
+ ! 42.9140 mS/cm (=4.29140 S/m^).
+ */
+ return (gsw_c3515*r);
+}
+/*
+!==========================================================================
+function gsw_cabbeling(sa,ct,p)
+!==========================================================================
+
+! Calculates the cabbeling coefficient of seawater with respect to
+! Conservative Temperature. This function uses the computationally-
+! efficient expression for specific volume in terms of SA, CT and p
+! (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! cabbeling : cabbeling coefficient with respect to [1/K^2]
+! Conservative Temperature.
+*/
+double
+gsw_cabbeling(double sa, double ct, double p)
+{
+ double alpha_ct, alpha_on_beta, alpha_sa, beta_sa, rho,
+ v_sa, v_ct, v_sa_sa, v_sa_ct, v_ct_ct;
+
+ gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct, NULL);
+
+ gsw_specvol_second_derivatives(sa,ct,p,&v_sa_sa,&v_sa_ct,&v_ct_ct,
+ NULL, NULL);
+
+ rho = gsw_rho(sa,ct,p);
+
+ alpha_ct = rho*(v_ct_ct - rho*v_ct*v_ct);
+
+ alpha_sa = rho*(v_sa_ct - rho*v_sa*v_ct);
+
+ beta_sa = -rho*(v_sa_sa - rho*v_sa*v_sa);
+
+ alpha_on_beta = gsw_alpha_on_beta(sa,ct,p);
+
+ return (alpha_ct +
+ alpha_on_beta*(2.0*alpha_sa - alpha_on_beta*beta_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_chem_potential_water_ice (t, p)
+!==========================================================================
+!
+! Calculates the chemical potential of water in ice from in-situ
+! temperature and pressure.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! chem_potential_water_ice = chemical potential of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_chem_potential_water_ice(double t, double p)
+{
+ return (gsw_gibbs_ice(0,0,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_chem_potential_water_t_exact (sa, t, p)
+!==========================================================================
+!
+! Calculates the chemical potential of water in seawater.
+!
+! SA = Absolute Salinity [ g/kg ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! chem_potential_water_t_exact = chemical potential of water in seawater
+! [ J/g ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_chem_potential_water_t_exact(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g03_g, g08_g, g_sa_part, x, x2, y, z, kg2g = 1e-3;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*1e-4;
+
+ g03_g = 101.342743139674 + z*(100015.695367145 +
+ z*(-2544.5765420363 + z*(284.517778446287 +
+ z*(-33.3146754253611 + (4.20263108803084 - 0.546428511471039*z)*z)))) +
+ y*(5.90578347909402 + z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 +
+ (28.9796526294175 - 2.13290083518327*z)*z))) +
+ y*(-12357.785933039 + z*(1455.0364540468 +
+ z*(-756.558385769359 + z*(273.479662323528 +
+ z*(-55.5604063817218 + 4.34420671917197*z)))) +
+ y*(736.741204151612 + z*(-672.50778314507 +
+ z*(499.360390819152 + z*(-239.545330654412 +
+ (48.8012518593872 - 1.66307106208905*z)*z))) +
+ y*(-148.185936433658 + z*(397.968445406972 +
+ z*(-301.815380621876 + (152.196371733841 - 26.3748377232802*z)*z)) +
+ y*(58.0259125842571 + z*(-194.618310617595 +
+ z*(120.520654902025 + z*(-55.2723052340152 + 6.48190668077221*z))) +
+ y*(-18.9843846514172 + y*(3.05081646487967 - 9.63108119393062*z) +
+ z*(63.5113936641785 + z*(-22.2897317140459 + 8.17060541818112*z))))))));
+
+ g08_g = x2*(1416.27648484197 +
+ x*(-2432.14662381794 + x*(2025.80115603697 +
+ y*(543.835333000098 + y*(-68.5572509204491 +
+ y*(49.3667694856254 + y*(-17.1397577419788 +
+ 2.49697009569508*y))) - 22.6683558512829*z) +
+ x*(-1091.66841042967 - 196.028306689776*y +
+ x*(374.60123787784 - 48.5891069025409*x +
+ 36.7571622995805*y) + 36.0284195611086*z) +
+ z*(-54.7919133532887 + (-4.08193978912261 -
+ 30.1755111971161*z)*z)) +
+ z*(199.459603073901 + z*(-52.2940909281335 +
+ (68.0444942726459 - 3.41251932441282*z)*z)) +
+ y*(-493.407510141682 + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-43.0664675978042 + z*(383.058066002476 +
+ z*(-54.1917262517112 + 25.6398487389914*z)) +
+ y*(-10.0227370861875 - 460.319931801257*z +
+ y*(0.875600661808945 + 234.565187611355*z))))) +
+ y*(168.072408311545));
+
+ g_sa_part = 8645.36753595126 +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y*(2175.341332000392 + y*(-274.2290036817964 +
+ y*(197.4670779425016 + y*(-68.5590309679152 +
+ 9.98788038278032*y))) - 90.6734234051316*z) +
+ x*(-5458.34205214835 - 980.14153344888*y +
+ x*(2247.60742726704 - 340.1237483177863*x +
+ 220.542973797483*y) + 180.142097805543*z) +
+ z*(-219.1676534131548 + (-16.32775915649044 -
+ 120.7020447884644*z)*z)) +
+ z*(598.378809221703 + z*(-156.8822727844005 +
+ (204.1334828179377 - 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 + z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(2.626801985426835 + 703.695562834065*z))))) +
+ y*(1187.3715515697959);
+
+ return (kg2g*(g03_g + g08_g - 0.5*x2*g_sa_part));
+}
+/*
+!==========================================================================
+elemental function gsw_cp_ice (t, p)
+!==========================================================================
+!
+! Calculates the isobaric heat capacity of seawater.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! gsw_cp_ice = heat capacity of ice [J kg^-1 K^-1]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_cp_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (-(t + gsw_t0)*gsw_gibbs_ice(2,0,t,p));
+}
+/*
+!==========================================================================
+function gsw_cp_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates isobaric heat capacity of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_cp_t_exact : heat capacity [J/(kg K)]
+*/
+double
+gsw_cp_t_exact(double sa, double t, double p)
+{
+ int n0, n2;
+
+ n0 = 0;
+ n2 = 2;
+
+ return (-(t+273.15e0)*gsw_gibbs(n0,n2,n0,sa,t,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_first_derivatives (sa, pt, ct_sa, ct_pt)
+!==========================================================================
+!
+! Calculates the following two derivatives of Conservative Temperature
+! (1) CT_SA, the derivative with respect to Absolute Salinity at
+! constant potential temperature (with pr = 0 dbar), and
+! 2) CT_pt, the derivative with respect to potential temperature
+! (the regular potential temperature which is referenced to 0 dbar)
+! at constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! pt = potential temperature (ITS-90) [ deg C ]
+! (whose reference pressure is 0 dbar)
+!
+! CT_SA = The derivative of Conservative Temperature with respect to
+! Absolute Salinity at constant potential temperature
+! (the regular potential temperature which has reference
+! sea pressure of 0 dbar).
+! The CT_SA output has units of: [ K/(g/kg)]
+! CT_pt = The derivative of Conservative Temperature with respect to
+! potential temperature (the regular one with pr = 0 dbar)
+! at constant SA. CT_pt is dimensionless. [ unitless ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_first_derivatives(double sa, double pt, double *ct_sa, double *ct_pt)
+{
+ GSW_TEOS10_CONSTANTS;
+ double abs_pt, g_sa_mod, g_sa_t_mod, x, y_pt;
+
+ abs_pt = gsw_t0 + pt ;
+
+ if (ct_pt != NULL)
+ *ct_pt = -(abs_pt*gsw_gibbs_pt0_pt0(sa,pt))/gsw_cp0;
+
+ if (ct_sa == NULL)
+ return;
+
+ x = sqrt(gsw_sfac*sa);
+ y_pt = 0.025*pt;
+
+ g_sa_t_mod = 1187.3715515697959 + x*(-1480.222530425046
+ + x*(2175.341332000392 + x*(-980.14153344888
+ + 220.542973797483*x) + y_pt*(-548.4580073635929
+ + y_pt*(592.4012338275047 + y_pt*(-274.2361238716608
+ + 49.9394019139016*y_pt)))) + y_pt*(-258.3988055868252
+ + y_pt*(-90.2046337756875 + y_pt*10.50720794170734)))
+ + y_pt*(3520.125411988816 + y_pt*(-1351.605895580406
+ + y_pt*(731.4083582010072 + y_pt*(-216.60324087531103
+ + 25.56203650166196*y_pt))));
+ g_sa_t_mod = 0.5*gsw_sfac*0.025*g_sa_t_mod;
+
+ g_sa_mod = 8645.36753595126 + x*(-7296.43987145382
+ + x*(8103.20462414788 + y_pt*(2175.341332000392
+ + y_pt*(-274.2290036817964 + y_pt*(197.4670779425016
+ + y_pt*(-68.5590309679152 + 9.98788038278032*y_pt))))
+ + x*(-5458.34205214835 - 980.14153344888*y_pt
+ + x*(2247.60742726704 - 340.1237483177863*x
+ + 220.542973797483*y_pt))) + y_pt*(-1480.222530425046
+ + y_pt*(-129.1994027934126 + y_pt*(-30.0682112585625
+ + y_pt*(2.626801985426835 ))))) + y_pt*(1187.3715515697959
+ + y_pt*(1760.062705994408 + y_pt*(-450.535298526802
+ + y_pt*(182.8520895502518 + y_pt*(-43.3206481750622
+ + 4.26033941694366*y_pt)))));
+ g_sa_mod = 0.5*gsw_sfac*g_sa_mod;
+
+ *ct_sa = (g_sa_mod - abs_pt*g_sa_t_mod)/gsw_cp0;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_first_derivatives_wrt_t_exact (sa, t, p, &
+ ct_sa_wrt_t, ct_t_wrt_t, ct_p_wrt_t)
+!==========================================================================
+!
+! Calculates the following three derivatives of Conservative Temperature.
+! These derivatives are done with respect to in-situ temperature t (in the
+! case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of
+! CT_SA_wrt_t and CT_P_wrt_t).
+! (1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity
+! at constant t and p, and
+! (2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t
+! at constant SA and p.
+! (3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at
+! constant SA and t.
+!
+! This function uses the full Gibbs function. Note that this function
+! avoids the NaN that would exist in CT_SA_wrt_t at SA = 0 if it were
+! evaluated in the straightforward way from the derivatives of the Gibbs
+! function function.
+!
+! SA = Absolute Salinity [ g/kg ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar)
+!
+! CT_SA_wrt_t = The first derivative of Conservative Temperature with
+! respect to Absolute Salinity at constant t and p.
+! [ K/(g/kg)] i.e. [ K kg/g ]
+! CT_T_wrt_t = The first derivative of Conservative Temperature with
+! respect to in-situ temperature, t, at constant SA and p.
+! [ unitless ]
+! CT_P_wrt_t = The first derivative of Conservative Temperature with
+! respect to pressure P (in Pa) at constant SA and t.
+! [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_first_derivatives_wrt_t_exact(double sa, double t, double p,
+ double *ct_sa_wrt_t, double *ct_t_wrt_t, double *ct_p_wrt_t)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g_sa_mod, g_sa_t_mod, pt0, x, y, y_pt, z;
+
+ pt0 = gsw_pt0_from_t(sa,t,p);
+
+ if (ct_sa_wrt_t != NULL) {
+
+ x = sqrt(gsw_sfac*sa);
+ y = 0.025*t;
+ y_pt = 0.025*pt0;
+ z = rec_db2pa*p;
+ /* the input pressure (p) is sea pressure in units of dbar */
+
+ g_sa_t_mod = 1187.3715515697959 + z*(1458.233059470092 +
+ z*(-687.913805923122 + z*(249.375342232496 +
+ z*(-63.313928772146 + 14.09317606630898*z)))) +
+ x*(-1480.222530425046 + x*(2175.341332000392 +
+ x*(-980.14153344888 + 220.542973797483*x) +
+ y*(-548.4580073635929 + y*(592.4012338275047 +
+ y*(-274.2361238716608 + 49.9394019139016*y))) -
+ 90.6734234051316*z) + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-258.3988055868252 + z*(2298.348396014856 +
+ z*(-325.1503575102672 + 153.8390924339484*z)) +
+ y*(-90.2046337756875 - 4142.8793862113125*z +
+ y*(10.50720794170734 + 2814.78225133626*z)))) +
+ y*(3520.125411988816 + y*(-1351.605895580406 +
+ y*(731.4083582010072 + y*(-216.60324087531103 +
+ 25.56203650166196*y) + z*(-2381.829935897496 +
+ (597.809129110048 - 291.8983352012704*z)*z)) +
+ z*(4165.4688847996085 + z*(-1229.337851789418 +
+ (681.370187043564 - 66.7696405958478*z)*z))) +
+ z*(-3443.057215135908 + z*(1349.638121077468 +
+ z*(-713.258224830552 +
+ (176.8161433232 - 31.68006188846728*z)*z))));
+ g_sa_t_mod = 0.5*gsw_sfac*0.025*g_sa_t_mod;
+
+ g_sa_mod = 8645.36753595126 +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y_pt*(2175.341332000392 + y_pt*(-274.2290036817964 +
+ y_pt*(197.4670779425016 + y_pt*(-68.5590309679152 +
+ 9.98788038278032*y_pt)))) +
+ x*(-5458.34205214835 - 980.14153344888*y_pt +
+ x*(2247.60742726704 - 340.1237483177863*x +
+ 220.542973797483*y_pt))) +
+ y_pt*(-1480.222530425046 +
+ y_pt*(-129.1994027934126 +
+ y_pt*(-30.0682112585625 + y_pt*(2.626801985426835 ))))) +
+ y_pt*(1187.3715515697959 +
+ y_pt*(1760.062705994408 + y_pt*(-450.535298526802 +
+ y_pt*(182.8520895502518 + y_pt*(-43.3206481750622 +
+ 4.26033941694366*y_pt)))));
+ g_sa_mod = 0.5*gsw_sfac*g_sa_mod;
+
+ *ct_sa_wrt_t = (g_sa_mod - (gsw_t0+pt0)*g_sa_t_mod)/gsw_cp0;
+
+ }
+
+ if (ct_t_wrt_t != NULL)
+ *ct_t_wrt_t = -(gsw_t0+pt0)*gsw_gibbs(0,2,0,sa,t,p)/gsw_cp0;
+
+ if (ct_p_wrt_t != NULL)
+ *ct_p_wrt_t = -(gsw_t0+pt0)*gsw_gibbs(0,1,1,sa,t,p)/gsw_cp0;
+}
+/*
+!==========================================================================
+elemental function gsw_ct_freezing (sa, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Conservative Temperature at which seawater freezes. The
+! Conservative Temperature freezing point is calculated from the exact
+! in-situ freezing temperature which is found by a modified Newton-Raphson
+! iteration (McDougall and Wotherspoon, 2013) of the equality of the
+! chemical potentials of water in seawater and in ice.
+!
+! An alternative GSW function, gsw_CT_freezing_poly, it is based on a
+! computationally-efficient polynomial, and is accurate to within -5e-4 K
+! and 6e-4 K, when compared with this function.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! CT_freezing = Conservative Temperature at freezing of seawater [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_freezing(double sa, double p, double saturation_fraction)
+{
+ double t_freezing;
+
+ t_freezing = gsw_t_freezing(sa,p,saturation_fraction);
+ return (gsw_ct_from_t(sa,t_freezing,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_freezing_first_derivatives (sa, p, &
+ saturation_fraction, ctfreezing_sa, ctfreezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the Conservative Temperature at
+! which seawater freezes, with respect to Absolute Salinity SA and
+! pressure P (in Pa).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! CTfreezing_SA = the derivative of the Conservative Temperature at
+! freezing (ITS-90) with respect to Absolute Salinity at
+! fixed pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! CTfreezing_P = the derivative of the Conservative Temperature at
+! freezing (ITS-90) with respect to pressure (in Pa) at
+! fixed Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa, double *ctfreezing_p)
+{
+ double tf_sa, tf_p, ct_sa_wrt_t, ct_t_wrt_t, ct_p_wrt_t, tf;
+
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+
+ if (ctfreezing_sa != NULL && ctfreezing_p != NULL) {
+
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tf_sa,&tf_p);
+ gsw_ct_first_derivatives_wrt_t_exact(sa,tf,p,
+ &ct_sa_wrt_t,&ct_t_wrt_t,&ct_p_wrt_t);
+
+ *ctfreezing_sa = ct_sa_wrt_t + ct_t_wrt_t*tf_sa;
+ *ctfreezing_p = ct_p_wrt_t + ct_t_wrt_t*tf_p;
+
+ } else if (ctfreezing_sa != NULL && ctfreezing_p == NULL) {
+
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tf_sa, NULL);
+ gsw_ct_first_derivatives_wrt_t_exact(sa,tf,p,
+ &ct_sa_wrt_t,&ct_t_wrt_t,NULL);
+
+ *ctfreezing_sa = ct_sa_wrt_t + ct_t_wrt_t*tf_sa;
+
+ } else if (ctfreezing_sa == NULL && ctfreezing_p != NULL) {
+
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ NULL, &tf_p);
+ gsw_ct_first_derivatives_wrt_t_exact(sa,tf,p,
+ NULL,&ct_t_wrt_t,&ct_p_wrt_t);
+
+ *ctfreezing_p = ct_p_wrt_t + ct_t_wrt_t*tf_p;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_freezing_first_derivatives_poly (sa, p, &
+ saturation_fraction, ctfreezing_sa, ctfreezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the Conservative Temperature at
+! which seawater freezes, with respect to Absolute Salinity SA and
+! pressure P (in Pa) of the comptationally efficient polynomial fit of the
+! freezing temperature (McDougall et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! CTfreezing_SA = the derivative of the Conservative Temperature at
+! freezing (ITS-90) with respect to Absolute Salinity at
+! fixed pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! CTfreezing_P = the derivative of the Conservative Temperature at
+! freezing (ITS-90) with respect to pressure (in Pa) at
+! fixed Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa,
+ double *ctfreezing_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_FREEZING_POLY_COEFFICIENTS;
+ double p_r, sa_r, x, d = -a - a*b - 2.4*b/gsw_sso,
+ e = 2.0*a*b/gsw_sso;
+
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ if (ctfreezing_sa != NULL) *ctfreezing_sa =
+ (c1 + x*(1.5*c2 + x*(2.0*c3 + x*(2.5*c4 + x*(3.0*c5
+ + 3.5*c6*x)))) + p_r*(c10 + x*(1.5*c11 + x*(2.0*c13
+ + x*(2.5*c16 + x*(3.0*c19 + 3.5*c22*x))))
+ + p_r*(c12 + x*(1.5*c14 + x*(2.0*c17 + 2.5*c20*x))
+ + p_r*(c15 + x*(1.5*c18 + 2.0*c21*x)))))*1e-2
+ - saturation_fraction*1e-3*(d - sa*e);
+
+ if (ctfreezing_p != NULL) *ctfreezing_p =
+ (c7 + sa_r*(c10 + x*(c11 + x*(c13 + x*(c16 + x*(c19 + c22*x)))))
+ + p_r*(2.0*c8 + sa_r*(2.0*c12 + x*(2.0*c14 + x*(2.0*c17
+ + 2.0*c20*x))) + p_r*(3.0*c9 + sa_r*(3.0*c15 + x*(3.0*c18
+ + 3.0*c21*x)))))*1e-8;
+}
+/*
+!==========================================================================
+elemental function gsw_ct_freezing_poly (sa, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Conservative Temperature at which seawater freezes.
+! The error of this fit ranges between -5e-4 K and 6e-4 K when compared
+! with the Conservative Temperature calculated from the exact in-situ
+! freezing temperature which is found by a Newton-Raphson iteration of the
+! equality of the chemical potentials of water in seawater and in ice.
+! Note that the Conservative temperature freezing temperature can be found
+! by this exact method using the function gsw_CT_freezing.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! CT_freezing = Conservative Temperature at freezing of seawater [ deg C ]
+! That is, the freezing temperature expressed in
+! terms of Conservative Temperature (ITS-90).
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_freezing_poly(double sa, double p, double saturation_fraction)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_FREEZING_POLY_COEFFICIENTS;
+ double p_r, sa_r, x, return_value;
+
+ sa_r = sa*1.0e-2;
+ x = sqrt(sa_r);
+ p_r = p*1.0e-4;
+
+ return_value = c0
+ + sa_r*(c1 + x*(c2 + x*(c3 + x*(c4 + x*(c5 + c6*x)))))
+ + p_r*(c7 + p_r*(c8 + c9*p_r)) + sa_r*p_r*(c10 + p_r*(c12
+ + p_r*(c15 + c21*sa_r)) + sa_r*(c13 + c17*p_r + c19*sa_r)
+ + x*(c11 + p_r*(c14 + c18*p_r) + sa_r*(c16 + c20*p_r + c22*sa_r)));
+
+ /* Adjust for the effects of dissolved air */
+ return_value = return_value - saturation_fraction*
+ (1e-3)*(2.4 - a*sa)*(1.0 + b*(1.0 - sa/gsw_sso));
+
+ return (return_value);
+}
+/*
+!==========================================================================
+elemental function gsw_ct_from_enthalpy (sa, h, p)
+!==========================================================================
+!
+! Calculates the Conservative Temperature of seawater, given the Absolute
+! Salinity, specific enthalpy, h, and pressure p.
+!
+! SA = Absolute Salinity [ g/kg ]
+! h = specific enthalpy [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+!
+! CT = Conservative Temperature ( ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_from_enthalpy(double sa, double h, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double ct, ct_freezing, ct_mean, ct_old, f, h_freezing, h_ct, h_40,
+ ct_40 = 40.0;
+
+ ct_freezing = gsw_ct_freezing(sa,p,0.0);
+
+ h_freezing = gsw_enthalpy(sa,ct_freezing,p);
+ if (h < (h_freezing - gsw_cp0)) {
+ /*
+ ! The input, seawater enthalpy h, is less than the enthalpy at the
+ ! freezing temperature, i.e. the water is frozen.
+ */
+ return (GSW_INVALID_VALUE);
+ }
+
+ h_40 = gsw_enthalpy(sa,ct_40,p);
+ if (h > h_40) {
+ /*
+ ! The input seawater enthalpy is greater than the enthalpy
+ ! when CT is 40C
+ */
+ return (GSW_INVALID_VALUE);
+ }
+
+ /* first guess of ct */
+ ct = ct_freezing + (ct_40 - ct_freezing)*(h - h_freezing)/
+ (h_40 - h_freezing);
+ gsw_enthalpy_first_derivatives(sa,ct,p,NULL,&h_ct);
+
+ /*
+ !------------------------------------------------------
+ ! Begin the modified Newton-Raphson iterative procedure
+ !------------------------------------------------------
+ */
+
+ ct_old = ct;
+ f = gsw_enthalpy(sa,ct_old,p) - h;
+ ct = ct_old - f/h_ct;
+ ct_mean = 0.5*(ct + ct_old);
+ gsw_enthalpy_first_derivatives(sa,ct_mean,p,NULL,&h_ct);
+ ct = ct_old - f/h_ct;
+
+ ct_old = ct;
+ f = gsw_enthalpy(sa,ct_old,p) - h;
+ ct = ct_old - f/h_ct;
+ /*
+ ! After 1.5d0 iterations of this modified Newton-Raphson iteration,
+ ! the error in CT is no larger than 4x10^-13 degrees C, which
+ ! is machine precision for this calculation.
+ */
+ return (ct);
+}
+/*
+!==========================================================================
+elemental function gsw_ct_from_enthalpy_exact (sa, h, p)
+!==========================================================================
+!
+! Calculates the Conservative Temperature of seawater, given the Absolute
+! Salinity, specific enthalpy, h, and pressure p.
+!
+! SA = Absolute Salinity [ g/kg ]
+! h = specific enthalpy [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+!
+! CT = Conservative Temperature ( ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_from_enthalpy_exact(double sa, double h, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double ct, ct_freezing, ct_mean, ct_old, f, h_freezing, h_ct, h_40,
+ ct_40 = 40.0;
+
+ ct_freezing = gsw_ct_freezing(sa,p,0.0);
+
+ h_freezing = gsw_enthalpy_ct_exact(sa,ct_freezing,p);
+ if (h < (h_freezing - gsw_cp0)) {
+ /*
+ ! The input, seawater enthalpy h, is less than the enthalpy at the
+ ! freezing temperature, i.e. the water is frozen.
+ */
+ return (GSW_INVALID_VALUE);
+ }
+
+ h_40 = gsw_enthalpy_ct_exact(sa,ct_40,p);
+ if (h > h_40) {
+ /*
+ ! The input seawater enthalpy is greater than the enthalpy
+ ! when CT is 40C
+ */
+ return (GSW_INVALID_VALUE);
+ }
+
+ /* First guess of ct */
+ ct = ct_freezing + (ct_40 - ct_freezing)*(h - h_freezing)/
+ (h_40 - h_freezing);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ct,p,NULL,&h_ct);
+ /*
+ !------------------------------------------------------
+ ! Begin the modified Newton-Raphson iterative procedure
+ !------------------------------------------------------
+ */
+ ct_old = ct;
+ f = gsw_enthalpy_ct_exact(sa,ct_old,p) - h;
+ ct = ct_old - f/h_ct;
+ ct_mean = 0.5*(ct + ct_old);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ct_mean,p,NULL,&h_ct);
+ ct = ct_old - f/h_ct;
+ /*
+ ! After 1 iteration of this modified Newton-Raphson iteration,
+ ! the error in CT is no larger than 5x10^-14 degrees C, which
+ ! is machine precision for this calculation.
+ */
+ return (ct);
+}
+/*
+!=========================================================================
+elemental function gsw_ct_from_entropy (sa, entropy)
+!=========================================================================
+!
+! Calculates Conservative Temperature with entropy as an input variable.
+!
+! SA = Absolute Salinity [ g/kg ]
+! entropy = specific entropy [ deg C ]
+!
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_from_entropy(double sa, double entropy)
+{
+ double pt;
+
+ pt = gsw_pt_from_entropy(sa,entropy);
+ return (gsw_ct_from_pt(sa,pt));
+}
+/*
+!==========================================================================
+function gsw_ct_from_pt(sa,pt)
+!==========================================================================
+
+! Calculates Conservative Temperature from potential temperature of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! pt : potential temperature with [deg C]
+! reference pressure of 0 dbar
+!
+! gsw_ct_from_pt : Conservative Temperature [deg C]
+*/
+double
+gsw_ct_from_pt(double sa, double pt)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, pot_enthalpy;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = pt*0.025e0; /*! normalize for F03 and F08 */
+ pot_enthalpy = 61.01362420681071e0 + y*(168776.46138048015e0 +
+ y*(-2735.2785605119625e0 + y*(2574.2164453821433e0 +
+ y*(-1536.6644434977543e0 + y*(545.7340497931629e0 +
+ (-50.91091728474331e0 - 18.30489878927802e0*y)*y))))) +
+ x2*(268.5520265845071e0 + y*(-12019.028203559312e0 +
+ y*(3734.858026725145e0 + y*(-2046.7671145057618e0 +
+ y*(465.28655623826234e0 + (-0.6370820302376359e0 -
+ 10.650848542359153e0*y)*y)))) +
+ x*(937.2099110620707e0 + y*(588.1802812170108e0+
+ y*(248.39476522971285e0 + (-3.871557904936333e0-
+ 2.6268019854268356e0*y)*y)) +
+ x*(-1687.914374187449e0 + x*(246.9598888781377e0 +
+ x*(123.59576582457964e0 - 48.5891069025409e0*x)) +
+ y*(936.3206544460336e0 +
+ y*(-942.7827304544439e0 + y*(369.4389437509002e0 +
+ (-33.83664947895248e0 - 9.987880382780322e0*y)*y))))));
+
+ return (pot_enthalpy/gsw_cp0);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_from_rho (rho, sa, p, ct, ct_multiple)
+! =========================================================================
+!
+! Calculates the Conservative Temperature of a seawater sample, for given
+! values of its density, Absolute Salinity and sea pressure (in dbar).
+!
+! rho = density of a seawater sample (e.g. 1026 kg/m^3) [ kg/m^3 ]
+! Note. This input has not had 1000 kg/m^3 subtracted from it.
+! That is, it is 'density', not 'density anomaly'.
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! CT_multiple = Conservative Temperature (ITS-90) [ deg C ]
+! Note that at low salinities, in brackish water, there are two possible
+! Conservative Temperatures for a single density. This programme will
+! output both valid solutions. To see this second solution the user
+! must call the programme with two outputs (i.e. [CT,CT_multiple]), if
+! there is only one possible solution and the programme has been
+! called with two outputs the second variable will be set to NaN.
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_from_rho(double rho, double sa, double p, double *ct,
+ double *ct_multiple)
+{
+ int number_of_iterations;
+ double a, alpha_freezing, alpha_mean, b, c, ct_a, ct_b, ct_diff,
+ ct_freezing, ct_max_rho, ct_mean, ct_old,
+ delta_ct, delta_v, factor, factorqa, factorqb,
+ rho_40, rho_extreme, rho_freezing, rho_max, rho_mean,
+ rho_old, sqrt_disc, top, v_ct, v_lab;
+
+ /*alpha_limit is the positive value of the thermal expansion coefficient
+ ! which is used at the freezing temperature to distinguish between
+ ! salty and fresh water.*/
+ double alpha_limit = 1e-5;
+
+ /*rec_half_rho_TT is a constant representing the reciprocal of half the
+ ! second derivative of density with respect to temperature near the
+ ! temperature of maximum density.*/
+ double rec_half_rho_tt = -110.0;
+
+ rho_40 = gsw_rho(sa,40.0,p);
+ if (rho < rho_40) {
+ *ct = GSW_INVALID_VALUE;
+ if (ct_multiple != NULL) *ct_multiple = *ct;
+ return;
+ }
+
+ ct_max_rho = gsw_ct_maxdensity(sa,p);
+ rho_max = gsw_rho(sa,ct_max_rho,p);
+ rho_extreme = rho_max;
+
+ /*Assumes that the seawater is always unsaturated with air*/
+ ct_freezing = gsw_ct_freezing_poly(sa,p,0.0);
+
+ gsw_rho_alpha_beta(sa,ct_freezing,p,&rho_freezing,&alpha_freezing,NULL);
+
+ /*reset the extreme values*/
+ if (ct_freezing > ct_max_rho) rho_extreme = rho_freezing;
+
+ if (rho > rho_extreme) {
+ *ct = GSW_INVALID_VALUE;
+ if (ct_multiple != NULL) *ct_multiple = *ct;
+ return;
+ }
+
+ if (alpha_freezing > alpha_limit) {
+
+ ct_diff = 40.0 - ct_freezing;
+ top = rho_40 - rho_freezing + rho_freezing*alpha_freezing*ct_diff;
+ a = top/(ct_diff*ct_diff);
+ b = -rho_freezing*alpha_freezing;
+ c = rho_freezing - rho;
+ sqrt_disc = sqrt(b*b - 4*a*c);
+ *ct = ct_freezing + 0.5*(-b - sqrt_disc)/a;
+
+ } else {
+
+ ct_diff = 40.0 - ct_max_rho;
+ factor = (rho_max - rho)/(rho_max - rho_40);
+ delta_ct = ct_diff*sqrt(factor);
+
+ if (delta_ct > 5.0)
+ *ct = ct_max_rho + delta_ct;
+ else {
+ /*Set the initial value of the quadratic solution roots.*/
+ ct_a = ct_max_rho + sqrt(rec_half_rho_tt*(rho - rho_max));
+ for (number_of_iterations = 1; number_of_iterations <= 7;
+ number_of_iterations++) {
+ ct_old = ct_a;
+ rho_old = gsw_rho(sa,ct_old,p);
+ factorqa = (rho_max - rho)/(rho_max - rho_old);
+ ct_a = ct_max_rho + (ct_old - ct_max_rho)*sqrt(factorqa);
+ }
+
+ if ((ct_freezing - ct_a) < 0.0) {
+ *ct = GSW_INVALID_VALUE;
+ if (ct_multiple != NULL) *ct_multiple = *ct;
+ return;
+ }
+
+ *ct = ct_a;
+ if (ct_multiple == NULL) return;
+
+ /*Set the initial value of the quadratic solution roots.*/
+ ct_b = ct_max_rho - sqrt(rec_half_rho_tt*(rho - rho_max));
+ for (number_of_iterations = 1; number_of_iterations <= 7;
+ number_of_iterations++) {
+ ct_old = ct_b;
+ rho_old = gsw_rho(sa,ct_old,p);
+ factorqb = (rho_max - rho)/(rho_max - rho_old);
+ ct_b = ct_max_rho + (ct_old - ct_max_rho)*sqrt(factorqb);
+ }
+ /*
+ ! After seven iterations of this quadratic iterative procedure,
+ ! the error in rho is no larger than 4.6x10^-13 kg/m^3.
+ */
+ if ((ct_freezing - ct_b) < 0.0) {
+ *ct = GSW_INVALID_VALUE;
+ *ct_multiple = *ct;
+ return;
+ }
+ *ct_multiple = ct_b;
+ return;
+ }
+ }
+
+ /*Begin the modified Newton-Raphson iterative method*/
+
+ v_lab = 1.0/rho;
+ gsw_rho_alpha_beta(sa,*ct,p,&rho_mean,&alpha_mean,NULL);
+ v_ct = alpha_mean/rho_mean;
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ ct_old = *ct;
+ delta_v = gsw_specvol(sa,ct_old,p) - v_lab;
+ *ct = ct_old - delta_v/v_ct;
+ ct_mean = 0.5*(*ct + ct_old);
+ gsw_rho_alpha_beta(sa,ct_mean,p,&rho_mean,&alpha_mean,NULL);
+ v_ct = alpha_mean/rho_mean;
+ *ct = ct_old - delta_v/v_ct ;
+ }
+ /*
+ ! After three iterations of this modified Newton-Raphson iteration,
+ ! the error in rho is no larger than 1.6x10^-12 kg/m^3.
+ */
+ if (ct_multiple != NULL) *ct_multiple = GSW_INVALID_VALUE;
+ return;
+}
+/*
+!==========================================================================
+function gsw_ct_from_t(sa,t,p)
+!==========================================================================
+
+! Calculates Conservative Temperature from in-situ temperature
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_ct_from_t : Conservative Temperature [deg C]
+*/
+double
+gsw_ct_from_t(double sa, double t, double p)
+{
+ double pt0;
+
+ pt0 = gsw_pt0_from_t(sa,t,p);
+ return (gsw_ct_from_pt(sa,pt0));
+}
+/*
+!==========================================================================
+elemental function gsw_ct_maxdensity (sa, p)
+!==========================================================================
+!
+! Calculates the Conservative Temperature of maximum density of seawater.
+! This function returns the Conservative temperature at which the density
+! of seawater is a maximum, at given Absolute Salinity, SA, and sea
+! pressure, p (in dbar).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! CT_maxdensity = Conservative Temperature at which [ deg C ]
+! the density of seawater is a maximum for
+! given Absolute Salinity and pressure.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_maxdensity(double sa, double p)
+{
+ int number_of_iterations;
+ double alpha, ct, ct_mean, ct_old, dalpha_dct,
+ dct = 0.001;
+
+ ct = 3.978 - 0.22072*sa; /*the initial guess of ct.*/
+
+ dalpha_dct = 1.1e-5; /*the initial guess for dalpha_dct.*/
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ ct_old = ct;
+ alpha = gsw_alpha(sa,ct_old,p);
+ ct = ct_old - alpha/dalpha_dct;
+ ct_mean = 0.5*(ct + ct_old);
+ dalpha_dct = (gsw_alpha(sa,ct_mean+dct,p)
+ - gsw_alpha(sa,ct_mean-dct,p))/(dct + dct);
+ ct = ct_old - alpha/dalpha_dct;
+ }
+ /*
+ ! After three iterations of this modified Newton-Raphson (McDougall and
+ ! Wotherspoon, 2012) iteration, the error in CT_maxdensity is typically
+ ! no larger than 1x10^-15 degress C.
+ */
+ return (ct);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_second_derivatives (sa, pt, ct_sa_sa, ct_sa_pt, &
+ ct_pt_pt)
+!==========================================================================
+!
+! Calculates the following three, second-order derivatives of Conservative
+! Temperature
+! (1) CT_SA_SA, the second derivative with respect to Absolute Salinity
+! at constant potential temperature (with p_ref = 0 dbar),
+! (2) CT_SA_pt, the derivative with respect to potential temperature
+! (the regular potential temperature which is referenced to 0 dbar)
+! and Absolute Salinity, and
+! (3) CT_pt_pt, the second derivative with respect to potential
+! temperature (the regular potential temperature which is referenced
+! to 0 dbar) at constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! pt = potential temperature (ITS-90) [ deg C ]
+! (whose reference pressure is 0 dbar)
+!
+! CT_SA_SA = The second derivative of Conservative Temperature with
+! respect to Absolute Salinity at constant potential
+! temperature (the regular potential temperature which
+! has reference sea pressure of 0 dbar).
+! CT_SA_SA has units of: [ K/((g/kg)^2) ]
+! CT_SA_pt = The derivative of Conservative Temperature with
+! respect to potential temperature (the regular one with
+! p_ref = 0 dbar) and Absolute Salinity.
+! CT_SA_pt has units of: [ 1/(g/kg) ]
+! CT_pt_pt = The second derivative of Conservative Temperature with
+! respect to potential temperature (the regular one with
+! p_ref = 0 dbar) at constant SA.
+! CT_pt_pt has units of: [ 1/K ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_second_derivatives(double sa, double pt, double *ct_sa_sa,
+ double *ct_sa_pt, double *ct_pt_pt)
+{
+ double ct_pt_l, ct_pt_u, ct_sa_l, ct_sa_u, pt_l, pt_u, sa_l, sa_u,
+ dsa = 1e-3, dpt = 1e-2;
+
+ if ((ct_sa_sa != NULL)) {
+
+ if ((sa_l = sa - dsa) < 0.0)
+ sa_l = 0.0;
+ sa_u = sa + dsa;
+
+ gsw_ct_first_derivatives(sa_l,pt,&ct_sa_l,NULL);
+ gsw_ct_first_derivatives(sa_u,pt,&ct_sa_u,NULL);
+
+ *ct_sa_sa = (ct_sa_u - ct_sa_l)/(sa_u - sa_l);
+
+ }
+
+ if ((ct_sa_pt != NULL) || (ct_pt_pt != NULL)) {
+
+ pt_l = pt - dpt;
+ pt_u = pt + dpt;
+
+ if ((ct_sa_pt != NULL) && (ct_pt_pt != NULL)) {
+
+ gsw_ct_first_derivatives(sa,pt_l,&ct_sa_l,&ct_pt_l);
+ gsw_ct_first_derivatives(sa,pt_u,&ct_sa_u,&ct_pt_u);
+
+ *ct_sa_pt = (ct_sa_u - ct_sa_l)/(pt_u - pt_l);
+ *ct_pt_pt = (ct_pt_u - ct_pt_l)/(pt_u - pt_l);
+
+ } else if ((ct_sa_pt != NULL) && (ct_pt_pt == NULL)) {
+
+ gsw_ct_first_derivatives(sa,pt_l,&ct_sa_l,NULL);
+ gsw_ct_first_derivatives(sa,pt_u,&ct_sa_u,NULL);
+
+ *ct_sa_pt = (ct_sa_u - ct_sa_l)/(pt_u - pt_l);
+
+ } else if ((ct_sa_pt == NULL) && (ct_pt_pt != NULL)) {
+
+ gsw_ct_first_derivatives(sa,pt_l,NULL,&ct_pt_l);
+ gsw_ct_first_derivatives(sa,pt_u,NULL,&ct_pt_u);
+
+ *ct_pt_pt = (ct_pt_u - ct_pt_l)/(pt_u - pt_l);
+
+ }
+ }
+}
+/*
+!==========================================================================
+function gsw_deltasa_from_sp(sp,p,lon,lat)
+!==========================================================================
+
+! Calculates Absolute Salinity Anomaly, deltaSA, from Practical Salinity, SP.
+!
+! sp : Practical Salinity [unitless]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_deltasa_from_sp : Absolute Salinty Anomaly [g/kg]
+*/
+double
+gsw_deltasa_from_sp(double sp, double p, double lon, double lat)
+{
+ double res;
+
+ res = gsw_sa_from_sp(sp,p,lon,lat) - gsw_sr_from_sp(sp);
+ if (res > GSW_ERROR_LIMIT)
+ res = GSW_INVALID_VALUE;
+ return (res);
+}
+/*
+!==========================================================================
+elemental function gsw_dilution_coefficient_t_exact (sa, t, p)
+!==========================================================================
+!
+! Calculates the dilution coefficient of seawater. The dilution
+! coefficient of seawater is defined as the Absolute Salinity times the
+! second derivative of the Gibbs function with respect to Absolute
+! Salinity, that is, SA.*g_SA_SA.
+!
+! SA = Absolute Salinity [ g/kg ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! dilution_coefficient_t_exact = dilution coefficient [ (J/kg)(kg/g) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_dilution_coefficient_t_exact(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g08, x, x2, y, z;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*1e-4;
+ /*note.the input pressure (p) is sea pressure in units of dbar.*/
+
+ g08 = 2.0*(8103.20462414788 +
+ y*(2175.341332000392 +
+ y*(-274.2290036817964 +
+ y*(197.4670779425016 +
+ y*(-68.5590309679152 + 9.98788038278032*y))) -
+ 90.6734234051316*z) +
+ 1.5*x*(-5458.34205214835 - 980.14153344888*y +
+ (4.0/3.0)*x*(2247.60742726704 -
+ 340.1237483177863*1.25*x + 220.542973797483*y) +
+ 180.142097805543*z) +
+ z*(-219.1676534131548 +
+ (-16.32775915649044 - 120.7020447884644*z)*z));
+
+ g08 = x2*g08 +
+ x*(-7296.43987145382 +
+ z*(598.378809221703 +
+ z*(-156.8822727844005 +
+ (204.1334828179377 - 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 +
+ z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 +
+ z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(2.626801985426835 + 703.695562834065*z))))) +
+ 11625.62913253464 + 1702.453469893412*y;
+
+ return (0.25*gsw_sfac*g08);
+/*
+! Note that this function avoids the singularity that occurs at SA = 0 if
+! the straightforward expression for the dilution coefficient of seawater,
+! SA*g_SA_SA is simply evaluated as SA.*gsw_gibbs(2,0,0,SA,t,p).
+*/
+}
+/*
+!==========================================================================
+function gsw_dynamic_enthalpy(sa,ct,p)
+!==========================================================================
+
+! Calculates dynamic enthalpy of seawater using the computationally-
+! efficient expression for specific volume in terms of SA, CT and p
+! (Roquet et al., 2014). Dynamic enthalpy is defined as enthalpy minus
+| potential enthalpy (Young, 2010).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! dynamic_enthalpy : dynamic enthalpy [J/kg]
+*/
+double
+gsw_dynamic_enthalpy(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_enthalpy_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ dynamic_enthalpy_part =
+ z*(h001 + xs*(h101 + xs*(h201 + xs*(h301 + xs*(h401
+ + xs*(h501 + h601*xs))))) + ys*(h011 + xs*(h111 + xs*(h211 + xs*(h311
+ + xs*(h411 + h511*xs)))) + ys*(h021 + xs*(h121 + xs*(h221 + xs*(h321
+ + h421*xs))) + ys*(h031 + xs*(h131 + xs*(h231 + h331*xs)) + ys*(h041
+ + xs*(h141 + h241*xs) + ys*(h051 + h151*xs + h061*ys))))) + z*(h002
+ + xs*(h102 + xs*(h202 + xs*(h302 + xs*(h402 + h502*xs)))) + ys*(h012
+ + xs*(h112 + xs*(h212 + xs*(h312 + h412*xs))) + ys*(h022 + xs*(h122
+ + xs*(h222 + h322*xs)) + ys*(h032 + xs*(h132 + h232*xs) + ys*(h042
+ + h142*xs + h052*ys)))) + z*(h003 + xs*(h103 + xs*(h203 + xs*(h303
+ + h403*xs))) + ys*(h013 + xs*(h113 + xs*(h213 + h313*xs)) + ys*(h023
+ + xs*(h123 + h223*xs) + ys*(h033 + h133*xs + h043*ys))) + z*(h004
+ + xs*(h104 + h204*xs) + ys*(h014 + h114*xs + h024*ys) + z*(h005
+ + h105*xs + h015*ys + z*(h006 + h007*z))))));
+
+ return (dynamic_enthalpy_part*db2pa*1e4);
+}
+/*
+!==========================================================================
+function gsw_enthalpy(sa,ct,p)
+!==========================================================================
+
+! Calculates specific enthalpy of seawater using the computationally-
+! efficient expression for specific volume in terms of SA, CT and p
+! (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! enthalpy : specific enthalpy of seawater [J/kg]
+*/
+double
+gsw_enthalpy(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ return (gsw_cp0*ct + gsw_dynamic_enthalpy(sa,ct,p));
+}
+/*
+!==========================================================================
+elemental function gsw_enthalpy_ct_exact (sa, ct, p)
+!==========================================================================
+!
+! Calculates specific enthalpy of seawater from Absolute Salinity and
+! Conservative Temperature and pressure.
+!
+! Note that this function uses the full Gibbs function.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! enthalpy_CT_exact = specific enthalpy [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_enthalpy_ct_exact(double sa, double ct, double p)
+{
+ double t;
+
+ t = gsw_t_from_ct(sa,ct,p);
+ return (gsw_enthalpy_t_exact(sa,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_enthalpy_diff (sa, ct, p_shallow, p_deep)
+!==========================================================================
+!
+! Calculates the difference of the specific enthalpy of seawater between
+! two different pressures, p_deep (the deeper pressure) and p_shallow
+! (the shallower pressure), at the same values of SA and CT. This
+! function uses the computationally-efficient expression for specific
+! volume in terms of SA, CT and p (Roquet et al., 2014). The output
+! (enthalpy_diff_CT) is the specific enthalpy evaluated at (SA,CT,p_deep)
+! minus the specific enthalpy at (SA,CT,p_shallow).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p_shallow = upper sea pressure [ dbar ]
+! ( i.e. shallower absolute pressure - 10.1325 dbar )
+! p_deep = lower sea pressure [ dbar ]
+! ( i.e. deeper absolute pressure - 10.1325 dbar )
+!
+! enthalpy_diff_CT = difference of specific enthalpy [ J/kg ]
+! (deep minus shallow)
+!--------------------------------------------------------------------------
+*/
+double
+gsw_enthalpy_diff(double sa, double ct, double p_shallow, double p_deep)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_enthalpy_shallow, dynamic_enthalpy_deep,
+ part_1, part_2, part_3, part_4, part_5, xs, ys,
+ z_deep, z_shallow;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z_shallow = p_shallow*1e-4;
+ z_deep = p_deep*1e-4;
+
+ part_1 = h001 + xs*(h101 + xs*(h201 + xs*(h301 + xs*(h401
+ + xs*(h501 + h601*xs))))) + ys*(h011 + xs*(h111 + xs*(h211+ xs*(h311
+ + xs*(h411 + h511*xs)))) + ys*(h021 + xs*(h121 + xs*(h221 + xs*(h321
+ + h421*xs))) + ys*(h031 + xs*(h131 + xs*(h231 + h331*xs)) + ys*(h041
+ + xs*(h141 + h241*xs) + ys*(h051 + h151*xs + h061*ys)))));
+
+ part_2 = h002 + xs*(h102 + xs*(h202 + xs*(h302 + xs*(h402 + h502*xs))))
+ + ys*(h012 + xs*(h112 + xs*(h212 + xs*(h312 + h412*xs))) + ys*(h022
+ + xs*(h122 + xs*(h222 + h322*xs)) + ys*(h032 + xs*(h132 + h232*xs)
+ + ys*(h042 + h142*xs + h052*ys))));
+
+ part_3 = h003 + xs*(h103 + xs*(h203 + xs*(h303 + h403*xs))) + ys*(h013
+ + xs*(h113 + xs*(h213 + h313*xs)) + ys*(h023 + xs*(h123 + h223*xs)
+ + ys*(h033 + h133*xs + h043*ys)));
+
+ part_4 = h004 + xs*(h104 + h204*xs) + ys*(h014 + h114*xs + h024*ys);
+
+ part_5 = h005 + h105*xs + h015*ys;
+
+ dynamic_enthalpy_shallow = z_shallow*(part_1 + z_shallow*(part_2
+ + z_shallow*(part_3 + z_shallow*(part_4 + z_shallow*(part_5
+ + z_shallow*(h006 + h007*z_shallow))))));
+
+ dynamic_enthalpy_deep = z_deep*(part_1 + z_deep*(part_2 + z_deep*(part_3
+ + z_deep*(part_4+z_deep*(part_5 + z_deep*(h006 + h007*z_deep))))));
+
+ return ((dynamic_enthalpy_deep - dynamic_enthalpy_shallow)*db2pa*1e4);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_enthalpy_first_derivatives (sa, ct, p, h_sa, h_ct)
+!==========================================================================
+!
+! Calculates the following two derivatives of specific enthalpy (h) of
+! seawater using the computationally-efficient expression for
+! specific volume in terms of SA, CT and p (Roquet et al., 2014).
+! (1) h_SA, the derivative with respect to Absolute Salinity at
+! constant CT and p, and
+! (2) h_CT, derivative with respect to CT at constant SA and p.
+! Note that h_P is specific volume (1/rho) it can be caclulated by calling
+! gsw_specvol(SA,CT,p).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! h_SA = The first derivative of specific enthalpy with respect to
+! Absolute Salinity at constant CT and p.
+! [ J/(kg (g/kg))] i.e. [ J/g ]
+! h_CT = The first derivative of specific enthalpy with respect to
+! CT at constant SA and p. [ J/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_enthalpy_first_derivatives(double sa, double ct, double p, double *h_sa,
+ double *h_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_h_ct_part, dynamic_h_sa_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ if (h_sa != NULL) {
+
+ dynamic_h_sa_part = z*(h101 + xs*(2.0*h201 + xs*(3.0*h301
+ + xs*(4.0*h401 + xs*(5.0*h501 + 6.0*h601*xs)))) + ys*(h111
+ + xs*(2.0*h211 + xs*(3.0*h311 + xs*(4.0*h411
+ + 5.0*h511*xs))) + ys*(h121 + xs*(2.0*h221 + xs*(3.0*h321
+ + 4.0*h421*xs)) + ys*(h131 + xs*(2.0*h231 + 3.0*h331*xs)
+ + ys*(h141 + 2.0*h241*xs + h151*ys)))) + z*(h102
+ + xs*(2.0*h202 + xs*(3.0*h302 + xs*(4.0*h402
+ + 5.0*h502*xs))) + ys*(h112 + xs*(2.0*h212 + xs*(3.0*h312
+ + 4.0*h412*xs)) + ys*(h122 + xs*(2.0*h222 + 3.0*h322*xs)
+ + ys*(h132 + 2.0*h232*xs + h142*ys ))) + z*(h103 + xs*(2.0*h203
+ + xs*(3.0*h303 + 4.0*h403*xs)) + ys*(h113 + xs*(2.0*h213
+ + 3.0*h313*xs) + ys*(h123 + 2.0*h223*xs + h133*ys))
+ + z*(h104 + 2.0*h204*xs + h114*ys + h105*z))));
+
+ *h_sa = 1e8*0.5*gsw_sfac*dynamic_h_sa_part/xs;
+
+ }
+
+ if (h_ct != NULL) {
+
+ dynamic_h_ct_part = z*(h011 + xs*(h111
+ + xs*(h211 + xs*(h311 + xs*(h411
+ + h511*xs)))) + ys*(2.0*(h021 + xs*(h121 + xs*(h221 + xs*(h321
+ + h421*xs)))) + ys*(3.0*(h031 + xs*(h131 + xs*(h231 + h331*xs)))
+ + ys*(4.0*(h041 + xs*(h141 + h241*xs)) + ys*(5.0*(h051
+ + h151*xs) + 6.0*h061*ys)))) + z*(h012 + xs*(h112 + xs*(h212
+ + xs*(h312 + h412*xs))) + ys*(2.0*(h022 + xs*(h122 + xs*(h222
+ + h322*xs))) + ys*(3.0*(h032 + xs*(h132 + h232*xs))
+ + ys*(4.0*(h042 + h142*xs) + 5.0*h052*ys))) + z*(h013
+ + xs*(h113 + xs*(h213 + h313*xs)) + ys*(2.0*(h023 + xs*(h123
+ + h223*xs)) + ys*(3.0*(h033 + h133*xs) + 4.0*h043*ys))
+ + z*(h014 + h114*xs + 2.0*h024*ys + h015*z ))));
+
+ *h_ct = gsw_cp0 + 1e8*0.025*dynamic_h_ct_part;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_enthalpy_first_derivatives_ct_exact (sa, ct, p, &
+ h_sa, h_ct)
+!==========================================================================
+!
+! Calculates the following two derivatives of specific enthalpy (h)
+! (1) h_SA, the derivative with respect to Absolute Salinity at
+! constant CT and p, and
+! (2) h_CT, derivative with respect to CT at constant SA and p.
+! Note that h_P is specific volume (1/rho) it can be calulated by calling
+! gsw_specvol_CT_exact(SA,CT,p). This function uses the full Gibbs function.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! h_SA = The first derivative of specific enthalpy with respect to
+! Absolute Salinity at constant CT and p.
+! [ J/(kg (g/kg))] i.e. [ J/g ]
+! h_CT = The first derivative of specific enthalpy with respect to
+! CT at constant SA and p. [ J/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_enthalpy_first_derivatives_ct_exact(double sa, double ct, double p,
+ double *h_sa, double *h_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g_sa_mod_pt, g_sa_mod_t, pt0, t, temp_ratio, x, y, y_pt, z;
+
+ t = gsw_t_from_ct(sa,ct,p);
+ pt0 = gsw_pt_from_ct(sa,ct);
+
+ temp_ratio = (gsw_t0 + t)/(gsw_t0 + pt0);
+
+ if (h_ct != NULL) *h_ct = gsw_cp0*temp_ratio;
+
+ if (h_sa == NULL) return;
+
+ x = sqrt(gsw_sfac*sa);
+ y = 0.025*t;
+ z = rec_db2pa*p;
+ /*note.the input pressure (p) is sea pressure in units of dbar.*/
+
+ g_sa_mod_t = 8645.36753595126 + z*(-6620.98308089678 +
+ z*(769.588305957198 + z*(-193.0648640214916 +
+ (31.6816345533648 - 5.24960313181984*z)*z))) +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y*(2175.341332000392 + y*(-274.2290036817964 +
+ y*(197.4670779425016 + y*(-68.5590309679152 + 9.98788038278032*y)))
+ - 90.6734234051316*z) +
+ x*(-5458.34205214835 - 980.14153344888*y +
+ x*(2247.60742726704 - 340.1237483177863*x + 220.542973797483*y)
+ + 180.142097805543*z) +
+ z*(-219.1676534131548 + (-16.32775915649044
+ - 120.7020447884644*z)*z)) +
+ z*(598.378809221703 + z*(-156.8822727844005 + (204.1334828179377
+ - 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 + z*(-525.876123559641 + (249.57717834054571
+ - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 + z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z + y*(2.626801985426835
+ + 703.695562834065*z))))) +
+ y*(1187.3715515697959 + z*(1458.233059470092 +
+ z*(-687.913805923122 + z*(249.375342232496 + z*(-63.313928772146
+ + 14.09317606630898*z)))) +
+ y*(1760.062705994408 + y*(-450.535298526802 +
+ y*(182.8520895502518 + y*(-43.3206481750622 + 4.26033941694366*y) +
+ z*(-595.457483974374 + (149.452282277512 - 72.9745838003176*z)*z)) +
+ z*(1388.489628266536 + z*(-409.779283929806 + (227.123395681188
+ - 22.2565468652826*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 - 15.84003094423364*z)*z)))));
+
+ g_sa_mod_t = 0.5*gsw_sfac*g_sa_mod_t;
+
+ y_pt = 0.025*pt0;
+
+ g_sa_mod_pt = 8645.36753595126 +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y_pt*(2175.341332000392 + y_pt*(-274.2290036817964 +
+ y_pt*(197.4670779425016 + y_pt*(-68.5590309679152
+ + 9.98788038278032*y_pt)))) +
+ x*(-5458.34205214835 - 980.14153344888*y_pt +
+ x*(2247.60742726704 - 340.1237483177863*x
+ + 220.542973797483*y_pt))) +
+ y_pt*(-1480.222530425046 + y_pt*(-129.1994027934126 +
+ y_pt*(-30.0682112585625 + y_pt*2.626801985426835)))) +
+ y_pt*(1187.3715515697959 + y_pt*(1760.062705994408
+ + y_pt*(-450.535298526802 +
+ y_pt*(182.8520895502518 + y_pt*(-43.3206481750622
+ + 4.26033941694366*y_pt)))));
+
+ g_sa_mod_pt = 0.5*gsw_sfac*g_sa_mod_pt;
+
+ *h_sa = g_sa_mod_t - temp_ratio*g_sa_mod_pt;
+}
+/*
+!==========================================================================
+elemental function gsw_enthalpy_ice (t, p)
+!==========================================================================
+!
+! Calculates the specific enthalpy of ice (h_Ih).
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! gsw_enthalpy_ice : specific enthalpy of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_enthalpy_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double tau, dzi, g0;
+ double complex r2, sqtau_t1, sqtau_t2, g;
+
+ tau = (t + gsw_t0)*rec_tt;
+
+ dzi = db2pa*p*rec_pt;
+
+ g0 = g00 + dzi*(g01 + dzi*(g02 + dzi*(g03 + g04*dzi)));
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ sqtau_t1 = (tau*tau)/(t1*t1);
+ sqtau_t2 = (tau*tau)/(t2*t2);
+
+ g = r1*t1*(clog(1.0 - sqtau_t1) + sqtau_t1)
+ + r2*t2*(clog(1.0 - sqtau_t2) + sqtau_t2);
+
+ return (g0 + tt*creal(g));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_enthalpy_second_derivatives (sa, ct, p, h_sa_sa, &
+ h_sa_ct, h_ct_ct)
+! =========================================================================
+!
+! Calculates the following three second-order derivatives of specific
+! enthalpy (h),using the computationally-efficient expression for
+! specific volume in terms of SA, CT and p (Roquet et al., 2014).
+! (1) h_SA_SA, second-order derivative with respect to Absolute Salinity
+! at constant CT & p.
+! (2) h_SA_CT, second-order derivative with respect to SA & CT at
+! constant p.
+! (3) h_CT_CT, second-order derivative with respect to CT at constant SA
+! and p.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! h_SA_SA = The second derivative of specific enthalpy with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! h_SA_CT = The second derivative of specific enthalpy with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+! h_CT_CT = The second derivative of specific enthalpy with respect to
+! CT at constant SA and p. [ J/(kg K^2) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_enthalpy_second_derivatives(double sa, double ct, double p,
+ double *h_sa_sa, double *h_sa_ct, double *h_ct_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_h_ct_ct_part, dynamic_h_sa_ct_part,
+ dynamic_h_sa_sa_part, xs, xs2, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ if (h_sa_sa != NULL) {
+
+ xs2 = pow(xs,2);
+ dynamic_h_sa_sa_part = z*(-h101 + xs2*(3.0*h301 + xs*(8.0*h401
+ + xs*(15.0*h501 + 24.0*h601*xs))) + ys*(- h111
+ + xs2*(3.0*h311 + xs*(8.0*h411 + 15.0*h511*xs)) + ys*(-h121
+ + xs2*(3.0*h321 + 8.0*h421*xs) + ys*(-h131 + 3.0*h331*xs2
+ + ys*(-h141 - h151*ys)))) + z*(-h102 + xs2*(3.0*h302
+ + xs*(8.0*h402 + 15.0*h502*xs)) + ys*(-h112 + xs2*(3.0*h312
+ + 8.0*h412*xs) + ys*(-h122 + 3.0*h322*xs2 + ys*(-h132
+ - h142*ys ))) + z*(xs2*(8.0*h403*xs + 3.0*h313*ys)
+ + z*(-h103 + 3.0*h303*xs2 + ys*(-h113 + ys*(-h123 - h133*ys))
+ + z*(-h104 - h114*ys - h105*z)))));
+
+ *h_sa_sa = 1e8*0.25*gsw_sfac*gsw_sfac*dynamic_h_sa_sa_part/
+ pow(xs,3);
+
+ }
+
+ if (h_sa_ct != NULL) {
+
+ dynamic_h_sa_ct_part = z*(h111 + xs*(2.0*h211 + xs*(3.0*h311
+ + xs*(4.0*h411 + 5.0*h511*xs))) + ys*(2.0*h121
+ + xs*(4.0*h221 + xs*(6.0*h321 + 8.0*h421*xs))
+ + ys*(3.0*h131 + xs*(6.0*h231 + 9.0*h331*xs)
+ + ys*(4.0*h141 + 8.0*h241*xs + 5.0*h151*ys ))) + z*(h112
+ + xs*(2.0*h212 + xs*(3.0*h312 + 4.0*h412*xs))
+ + ys*(2.0*h122 + xs*(4.0*h222 + 6.0*h322*xs)
+ + ys*(3.0*h132 + 6.0*h232*xs + 4.0*h142*ys)) + z*(h113
+ + xs*(2.0*h213 + 3.0*h313*xs) + ys*(2.0*h123
+ + 4.0*h223*xs + 3.0*h133*ys) + h114*z)));
+
+ *h_sa_ct = 1e8*0.025*0.5*gsw_sfac*dynamic_h_sa_ct_part/xs;
+
+ }
+
+ if (h_ct_ct != NULL) {
+
+ dynamic_h_ct_ct_part = z*(2.0*h021 + xs*(2.0*h121 + xs*(2.0*h221
+ + xs*(2.0*h321 + 2.0*h421*xs))) + ys*(6.0*h031
+ + xs*(6.0*h131 + xs*(6.0*h231 + 6.0*h331*xs))
+ + ys*(12.0*h041 + xs*(12.0*h141 + 12.0*h241*xs)
+ + ys*(20.0*h051 + 20.0*h151*xs + 30.0*h061*ys)))
+ + z*(2.0*h022 + xs*(2.0*h122 + xs*(2.0*h222
+ + 2.0*h322*xs)) + ys*(6.0*h032 + xs*(6.0*h132
+ + 6.0*h232*xs) + ys*(12.0*h042 + 12.0*h142*xs
+ + 20.0*h052*ys)) + z*(2.0*h023 + xs*(2.0*h123
+ + 2.0*h223*xs) + ys*(6.0*h133*xs + 6.0*h033
+ + 12.0*h043*ys) + 2.0*h024*z)));
+
+ *h_ct_ct = 1e8*6.25e-4*dynamic_h_ct_ct_part;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_enthalpy_second_derivatives_ct_exact (sa, ct, p, &
+ h_sa_sa, h_sa_ct, h_ct_ct)
+!==========================================================================
+!
+! Calculates three second-order derivatives of specific enthalpy (h).
+! Note that this function uses the full Gibbs function.
+!
+! sa = Absolute Salinity [ g/kg ]
+! ct = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! h_sa_sa = The second derivative of specific enthalpy with respect to
+! Absolute Salinity at constant ct & p. [ J/(kg (g/kg)^2) ]
+! h_sa_ct = The second derivative of specific enthalpy with respect to
+! sa and ct at constant p. [ J/(kg K(g/kg)) ]
+! h_ct_ct = The second derivative of specific enthalpy with respect to
+! ct at constant sa and p. [ J/(kg K^2) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_enthalpy_second_derivatives_ct_exact(double sa, double ct, double p,
+ double *h_sa_sa, double *h_sa_ct, double *h_ct_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double factor, gsa_pt0, gsat_pt0, gsat, part_b, pt0, h_ct_ct_val,
+ rec_abs_pt0, rec_gtt_pt0, rec_gtt, t, temp_ratio,
+ gsasa, gsasa_pt0, pr0 = 0.0, sa_small = 1e-100;
+ int n0=0, n1=1, n2=2;
+
+ pt0 = gsw_pt_from_ct(sa,ct);
+ rec_abs_pt0 = 1.0/(gsw_t0 + pt0);
+ t = gsw_pt_from_t(sa,pt0,pr0,p);
+ temp_ratio = (gsw_t0 + t)*rec_abs_pt0;
+
+ rec_gtt_pt0 = 1.0/gsw_gibbs(n0,n2,n0,sa,pt0,pr0);
+ rec_gtt = 1.0/gsw_gibbs(n0,n2,n0,sa,t,p);
+
+ /*h_ct_ct is naturally well-behaved as sa approaches zero.*/
+ h_ct_ct_val = gsw_cp0*gsw_cp0*
+ (temp_ratio*rec_gtt_pt0 - rec_gtt)*(rec_abs_pt0*rec_abs_pt0);
+
+ if (h_ct_ct != NULL) *h_ct_ct = h_ct_ct_val;
+
+ if ((h_sa_sa == NULL) && (h_sa_ct == NULL)) return;
+
+ gsat_pt0 = gsw_gibbs(n1,n1,n0,sa,pt0,pr0);
+ gsat = gsw_gibbs(n1,n1,n0,sa,t,p);
+ gsa_pt0 = gsw_gibbs(n1,n0,n0,sa,pt0,pr0);
+
+ part_b = (temp_ratio*gsat_pt0*rec_gtt_pt0 - gsat*rec_gtt)*rec_abs_pt0;
+ factor = gsa_pt0/gsw_cp0;
+
+ if (h_sa_sa != NULL) {
+
+ gsasa = gsw_gibbs(n2,n0,n0,sa,t,p);
+ gsasa_pt0 = gsw_gibbs(n2,n0,n0,sa,pt0,pr0);
+ /*
+ ! h_sa_sa has a singularity at sa = 0, and blows up as sa
+ ! approaches zero.
+ */
+ *h_sa_sa = gsasa - temp_ratio*gsasa_pt0
+ + temp_ratio*gsat_pt0*gsat_pt0*rec_gtt_pt0
+ - gsat*gsat*rec_gtt
+ - 2.0*gsa_pt0*part_b + (factor*factor)*h_ct_ct_val;
+
+ }
+ if (h_sa_ct == NULL) return;
+
+ /*
+ ! h_sa_ct should not blow up as sa approaches zero.
+ ! The following lines of code ensure that the h_sa_ct output
+ ! of this function does not blow up in this limit.
+ ! That is, when sa < 1e-100 g/kg, we force the h_sa_ct
+ ! output to be the same as if sa = 1e-100 g/kg.
+ */
+ if (sa < sa_small) {
+ rec_gtt_pt0 = 1.0/gsw_gibbs(n0,n2,n0,sa_small,pt0,pr0);
+ rec_gtt = 1.0/gsw_gibbs(n0,n2,n0,sa_small,t,p);
+ gsat_pt0 = gsw_gibbs(n1,n1,n0,sa_small,pt0,pr0);
+ gsat = gsw_gibbs(n1,n1,n0,sa_small,t,p);
+ gsa_pt0 = gsw_gibbs(n1,n0,n0,sa_small,pt0,pr0);
+ part_b = (temp_ratio*gsat_pt0*rec_gtt_pt0
+ - gsat*rec_gtt)*rec_abs_pt0;
+ factor = gsa_pt0/gsw_cp0;
+ }
+
+ *h_sa_ct = gsw_cp0*part_b - factor*h_ct_ct_val;
+}
+/*
+!==========================================================================
+function gsw_enthalpy_sso_0(p)
+!==========================================================================
+
+! This function calculates enthalpy at the Standard Ocean Salinity, SSO,
+! and at a Conservative Temperature of zero degrees C, as a function of
+! pressure, p, in dbar, using a streamlined version of the
+! computationally-efficient expression for specific volume, that is, a
+! streamlined version of the code "gsw_enthalpy(SA,CT,p)".
+!
+! p : sea pressure [dbar]
+!
+! enthalpy_sso_0 : enthalpy(sso,0,p)
+*/
+double
+gsw_enthalpy_sso_0(double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_enthalpy_sso_0_p, z;
+
+ z = p*1.0e-4;
+
+ dynamic_enthalpy_sso_0_p =
+ z*( 9.726613854843870e-4 + z*(-2.252956605630465e-5
+ + z*( 2.376909655387404e-6 + z*(-1.664294869986011e-7
+ + z*(-5.988108894465758e-9 + z*(h006 + h007*z))))));
+ return (dynamic_enthalpy_sso_0_p*db2pa*1.0e4);
+}
+/*
+!==========================================================================
+function gsw_enthalpy_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates the specific enthalpy of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_enthalpy_t_exact : specific enthalpy [J/kg]
+*/
+double
+gsw_enthalpy_t_exact(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ int n0=0, n1=1;
+
+ return (gsw_gibbs(n0,n0,n0,sa,t,p) -
+ (t+gsw_t0)*gsw_gibbs(n0,n1,n0,sa,t,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_entropy_first_derivatives (sa, ct, eta_sa, eta_ct)
+! =========================================================================
+!
+! Calculates the following two partial derivatives of specific entropy
+! (eta)
+! (1) eta_SA, the derivative with respect to Absolute Salinity at
+! constant Conservative Temperature, and
+! (2) eta_CT, the derivative with respect to Conservative Temperature at
+! constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! eta_SA = The derivative of specific entropy with respect to
+! Absolute Salinity (in units of g kg^-1) at constant
+! Conservative Temperature.
+! eta_SA has units of: [ J/(kg K(g/kg))] or [ J/(g K) ]
+! eta_CT = The derivative of specific entropy with respect to
+! Conservative Temperature at constant Absolute Salinity.
+! eta_CT has units of: [ J/(kg K^2) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_entropy_first_derivatives(double sa, double ct, double *eta_sa,
+ double *eta_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double pt, pr0 = 0.0;
+ int n0=0, n1=1;
+
+ pt = gsw_pt_from_ct(sa,ct);
+
+ if (eta_sa != NULL)
+ *eta_sa = -(gsw_gibbs(n1,n0,n0,sa,pt,pr0))/(gsw_t0 + pt);
+
+ if (eta_ct != NULL)
+ *eta_ct = gsw_cp0/(gsw_t0 + pt);
+}
+/*
+!=========================================================================
+elemental function gsw_entropy_from_ct (sa, ct)
+!=========================================================================
+!
+! Calculates specific entropy of seawater from Conservative Temperature.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! entropy = specific entropy [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_entropy_from_ct(double sa, double ct)
+{
+ double pt0;
+
+ pt0 = gsw_pt_from_ct(sa, ct);
+ return (-gsw_gibbs(0,1,0,sa,pt0,0));
+}
+/*
+!==========================================================================
+elemental function gsw_entropy_from_pt (sa, pt)
+!==========================================================================
+!
+! Calculates specific entropy of seawater.
+!
+! SA = Absolute Salinity [ g/kg ]
+! pt = potential temperature (ITS-90) [ deg C ]
+!
+! entropy = specific entropy [ J/(kg*K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_entropy_from_pt(double sa, double pt)
+{
+ int n0 = 0, n1 = 1;
+ double pr0 = 0.0;
+
+ return (-gsw_gibbs(n0,n1,n0,sa,pt,pr0));
+}
+/*
+!==========================================================================
+function gsw_entropy_from_t(sa,t,p)
+!==========================================================================
+
+! Calculates the specific entropy of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_entropy_from_t : specific entropy [J/(kg K)]
+*/
+double
+gsw_entropy_from_t(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (-gsw_gibbs(n0,n1,n0,sa,t,p));
+
+}
+/*
+!==========================================================================
+elemental function gsw_entropy_ice (t, p)
+!==========================================================================
+!
+! Calculates specific entropy of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! ice_entropy = specific entropy of ice [ J kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_entropy_ice(double t, double p)
+{
+ return (-gsw_gibbs_ice(1,0,t,p));
+}
+/*
+!==========================================================================
+function gsw_entropy_part(sa,t,p)
+!==========================================================================
+
+! entropy minus the terms that are a function of only SA
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! entropy_part : entropy part
+*/
+double
+gsw_entropy_part(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, z, g03, g08;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*1e-4;
+
+ g03 = z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 +
+ (28.9796526294175 - 2.13290083518327*z)*z))) +
+ y*(-24715.571866078 + z*(2910.0729080936 +
+ z*(-1513.116771538718 + z*(546.959324647056 +
+ z*(-111.1208127634436 + 8.68841343834394*z)))) +
+ y*(2210.2236124548363 + z*(-2017.52334943521 +
+ z*(1498.081172457456 + z*(-718.6359919632359 +
+ (146.4037555781616 - 4.9892131862671505*z)*z))) +
+ y*(-592.743745734632 + z*(1591.873781627888 +
+ z*(-1207.261522487504 + (608.785486935364 -
+ 105.4993508931208*z)*z)) +
+ y*(290.12956292128547 + z*(-973.091553087975 +
+ z*(602.603274510125 + z*(-276.361526170076 +
+ 32.40953340386105*z))) +
+ y*(-113.90630790850321 + y*(21.35571525415769 -
+ 67.41756835751434*z) +
+ z*(381.06836198507096 + z*(-133.7383902842754 +
+ 49.023632509086724*z)))))));
+
+ g08 = x2*(z*(729.116529735046 +
+ z*(-343.956902961561 + z*(124.687671116248 +
+ z*(-31.656964386073 + 7.04658803315449*z)))) +
+ x*( x*(y*(-137.1145018408982 + y*(148.10030845687618 +
+ y*(-68.5590309679152 + 12.4848504784754*y))) -
+ 22.6683558512829*z) + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-86.1329351956084 + z*(766.116132004952 +
+ z*(-108.3834525034224 + 51.2796974779828*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(3.50240264723578 + 938.26075044542*z)))) +
+ y*(1760.062705994408 + y*(-675.802947790203 +
+ y*(365.7041791005036 + y*(-108.30162043765552 +
+ 12.78101825083098*y) +
+ z*(-1190.914967948748 + (298.904564555024 -
+ 145.9491676006352*z)*z)) +
+ z*(2082.7344423998043 + z*(-614.668925894709 +
+ (340.685093521782 - 33.3848202979239*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 -
+ 15.84003094423364*z)*z)))));
+
+ return (-(g03 + g08)*0.025);
+}
+
+/*
+!==========================================================================
+function gsw_entropy_part_zerop(sa,pt0)
+!==========================================================================
+
+! entropy part evaluated at the sea surface
+!
+! sa : Absolute Salinity [g/kg]
+! pt0 : insitu temperature [deg C]
+!
+! entropy_part_zerop : entropy part at the sea surface
+*/
+double
+gsw_entropy_part_zerop(double sa, double pt0)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, g03, g08;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = pt0*0.025;
+
+ g03 = y*(-24715.571866078 + y*(2210.2236124548363 +
+ y*(-592.743745734632 + y*(290.12956292128547 +
+ y*(-113.90630790850321 + y*21.35571525415769)))));
+
+ g08 = x2*(x*(x*(y*(-137.1145018408982 + y*(148.10030845687618 +
+ y*(-68.5590309679152 + 12.4848504784754*y)))) +
+ y*(-86.1329351956084 + y*(-30.0682112585625 +
+ y*3.50240264723578))) +
+ y*(1760.062705994408 + y*(-675.802947790203 +
+ y*(365.7041791005036 + y*(-108.30162043765552 +
+ 12.78101825083098*y)))));
+
+ return (-(g03 + g08)*0.025);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_entropy_second_derivatives (sa, ct, eta_sa_sa, &
+ eta_sa_ct, eta_ct_ct)
+! =========================================================================
+!
+! Calculates the following three second-order partial derivatives of
+! specific entropy (eta)
+! (1) eta_SA_SA, the second derivative with respect to Absolute
+! Salinity at constant Conservative Temperature, and
+! (2) eta_SA_CT, the derivative with respect to Absolute Salinity and
+! Conservative Temperature.
+! (3) eta_CT_CT, the second derivative with respect to Conservative
+! Temperature at constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! eta_SA_SA = The second derivative of specific entropy with respect
+! to Absolute Salinity (in units of g kg^-1) at constant
+! Conservative Temperature.
+! eta_SA_SA has units of: [ J/(kg K(g/kg)^2)]
+! eta_SA_CT = The second derivative of specific entropy with respect
+! to Conservative Temperature at constant Absolute
+! Salinity. eta_SA_CT has units of: [ J/(kg (g/kg) K^2) ]
+! eta_CT_CT = The second derivative of specific entropy with respect
+! to Conservative Temperature at constant Absolute
+! Salinity. eta_CT_CT has units of: [ J/(kg K^3) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_entropy_second_derivatives(double sa, double ct,
+ double *eta_sa_sa, double *eta_sa_ct, double *eta_ct_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double abs_pt, ct_pt, ct_sa, pt, ct_ct, pr0 = 0.0;
+ int n0=0, n1=1, n2=2;
+
+ pt = gsw_pt_from_ct(sa,ct);
+ abs_pt = gsw_t0 + pt;
+
+ ct_pt = -(abs_pt*gsw_gibbs(n0,n2,n0,sa,pt,pr0))/gsw_cp0;
+
+ ct_ct = -gsw_cp0/(ct_pt*abs_pt*abs_pt);
+
+ if ((eta_sa_ct != NULL) || (eta_sa_sa != NULL)) {
+
+ ct_sa = (gsw_gibbs(n1,n0,n0,sa,pt,pr0) -
+ (abs_pt*gsw_gibbs(n1,n1,n0,sa,pt,pr0)))/gsw_cp0;
+
+ if (eta_sa_ct != NULL) *eta_sa_ct = -ct_sa*ct_ct;
+
+ if (eta_sa_sa != NULL)
+ *eta_sa_sa = -gsw_gibbs(n2,n0,n0,sa,pt,pr0)/abs_pt +
+ ct_sa*ct_sa*ct_ct;
+ }
+
+ if (eta_ct_ct != NULL) *eta_ct_ct = ct_ct;
+}
+/*
+!==========================================================================
+function gsw_fdelta(p,lon,lat)
+!==========================================================================
+
+! Calculates fdelta.
+!
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_fdelta : Absolute Salinty Anomaly [unitless]
+*/
+double
+gsw_fdelta(double p, double lon, double lat)
+{
+ double sa, saar;
+
+ saar = gsw_saar(p,lon,lat);
+ if (saar >= GSW_ERROR_LIMIT)
+ sa = GSW_INVALID_VALUE;
+ else
+ sa = ((1.0 + 0.35)*saar)/(1.0 - 0.35*saar);
+ return (sa);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_properties (sa_bulk, h_bulk, p, &
+ sa_final, ct_final, w_ih_final)
+!==========================================================================
+!
+! Calculates the mass fraction of ice (mass of ice divided by mass of ice
+! plus seawater), w_Ih_final, which results from given values of the bulk
+! Absolute Salinity, SA_bulk, bulk enthalpy, h_bulk, occuring at pressure
+! p. The final values of Absolute Salinity, SA_final, and Conservative
+! Temperature, CT_final, of the interstitial seawater phase are also
+! returned. This code assumes that there is no dissolved air in the
+! seawater (that is, saturation_fraction is assumed to be zero
+! throughout the code).
+!
+! When the mass fraction w_Ih_final is calculated as being a positive
+! value, the seawater-ice mixture is at thermodynamic equlibrium.
+!
+! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk,
+! is sufficiently large (i.e. sufficiently "warm") so that there is no ice
+! present in the final state. In this case the final state consists of
+! only seawater rather than being an equlibrium mixture of seawater and
+! ice which occurs when w_Ih_final is positive. Note that when
+! w_Ih_final = 0, the final seawater is not at the freezing temperature.
+!
+! SA_bulk = bulk Absolute Salinity of the seawater and ice mixture
+! [ g/kg ]
+! h_bulk = bulk enthalpy of the seawater and ice mixture [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! SA_final = Absolute Salinity of the seawater in the final state,
+! whether or not any ice is present. [ g/kg ]
+! CT_final = Conservative Temperature of the seawater in the the final
+! state, whether or not any ice is present. [ deg C ]
+! w_Ih_final = mass fraction of ice in the final seawater-ice mixture.
+! If this ice mass fraction is positive, the system is at
+! thermodynamic equilibrium. If this ice mass fraction is
+! zero there is no ice in the final state which consists
+! only of seawater which is warmer than the freezing
+! temperature. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_properties(double sa_bulk, double h_bulk, double p,
+ double *sa_final, double *ct_final, double *w_ih_final)
+{
+ int number_of_iterations;
+ double cp_ih, ctf_sa, ctf, dfunc_dw_ih, dfunc_dw_ih_mean_poly,
+ func, func0, hf, h_hat_ct, h_hat_sa,
+ h_ihf, sa, tf_sa, tf, w_ih_mean, w_ih_old, w_ih,
+ /*
+ ! Throughout this code seawater is taken to contain
+ ! no dissolved air.
+ */
+ saturation_fraction = 0.0,
+ num_f = 5.0e-2, num_f2 = 6.9e-7, num_p = 2.21;
+ /*
+ !---------------
+ ! Finding func0
+ !--------------
+ */
+ ctf = gsw_ct_freezing(sa_bulk,p,saturation_fraction);
+ func0 = h_bulk - gsw_enthalpy_ct_exact(sa_bulk,ctf,p);
+ /*
+ !-----------------------------------------------------------------------
+ ! When func0 is zero or positive we can immediately calculate the three
+ ! outputs, as the bulk enthalpy, h_bulk, is too large to allow any ice
+ ! at thermodynamic equilibrium. The result will be (warm) seawater with
+ ! no frazil ice being present. The three outputs can be set and the rest
+ ! of this code does not need to be performed.
+ !-----------------------------------------------------------------------
+ */
+ if (func0 >= 0.0) {
+ *sa_final = sa_bulk;
+ *ct_final = gsw_ct_from_enthalpy_exact(sa_bulk,h_bulk,p);
+ *w_ih_final = 0.0;
+ return;
+ }
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin to find the solution for those data points that have func0 < 0,
+ ! implying that the output will be a positive ice mass fraction
+ ! w_Ih_final.
+ !
+ ! Do a quasi-Newton step with a separate polynomial estimate of the
+ ! derivative of func with respect to the ice mass fraction. This
+ ! section of the code delivers initial values of both w_Ih and SA to
+ ! the rest of the more formal modified Newtons Method approach of
+ ! McDougall and Wotherspoon (2014).
+ !-----------------------------------------------------------------------
+ */
+ dfunc_dw_ih_mean_poly = 3.347814e+05
+ - num_f*func0*(1.0 + num_f2*func0) - num_p*p;
+ w_ih = min(-func0/dfunc_dw_ih_mean_poly, 0.95);
+ sa = sa_bulk/(1.0 - w_ih);
+ if (sa < 0.0 || sa > 120.0) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+ /*
+ !-----------------------------------------------------------------------
+ ! Calculating the estimate of the derivative of func, dfunc_dw_Ih, to be
+ ! fed into the iterative Newton's Method.
+ !-----------------------------------------------------------------------
+ */
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ hf = gsw_enthalpy_ct_exact(sa,ctf,p);
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ h_ihf = gsw_enthalpy_ice(tf,p);
+ cp_ih = gsw_cp_ice(tf,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,
+ &h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,&ctf_sa,
+ NULL);
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,&tf_sa,NULL);
+
+ dfunc_dw_ih = hf - h_ihf
+ - sa*(h_hat_sa + h_hat_ct*ctf_sa + w_ih*cp_ih*tf_sa/
+ (1.0 - w_ih));
+ /*
+ !-----------------------------------------------------------------------
+ ! Enter the main McDougall-Wotherspoon (2014) modified Newton-Raphson
+ | loop
+ !-----------------------------------------------------------------------
+ */
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+
+ if (number_of_iterations > 1) {
+ /* on the first iteration these values are already known */
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ hf = gsw_enthalpy_ct_exact(sa,ctf,p);
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ h_ihf = gsw_enthalpy_ice(tf,p);
+ }
+
+ func = h_bulk - (1.0 - w_ih)*hf - w_ih*h_ihf;
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih;
+ w_ih_mean = 0.5*(w_ih + w_ih_old);
+
+ if (w_ih_mean > 0.9) {
+ /*This ensures that the mass fraction of ice never exceeds 0.9*/
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa = sa_bulk/(1.0 - w_ih_mean);
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ hf = gsw_enthalpy_ct_exact(sa,ctf,p);
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ h_ihf = gsw_enthalpy_ice(tf,p);
+ cp_ih = gsw_cp_ice(tf,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,
+ &h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,&ctf_sa,
+ NULL);
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,&tf_sa,
+ NULL);
+
+ dfunc_dw_ih = hf - h_ihf - sa*(h_hat_sa + h_hat_ct*ctf_sa
+ + w_ih_mean*cp_ih*tf_sa/
+ (1.0 - w_ih_mean));
+
+ w_ih = w_ih_old - func/dfunc_dw_ih;
+
+ if (w_ih > 0.9) {
+ /*This ensures that the mass fraction of ice never exceeds 0.9*/
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa = sa_bulk/(1.0 - w_ih);
+ }
+
+ *sa_final = sa;
+ *ct_final = gsw_ct_freezing(sa,p,saturation_fraction);
+ *w_ih_final = w_ih;
+
+ if (*w_ih_final < 0.0) {
+ /*
+ ! This will only trap cases that are smaller than zero by just
+ ! machine precision
+ */
+ *sa_final = sa_bulk;
+ *ct_final = gsw_ct_from_enthalpy_exact(*sa_final,h_bulk,p);
+ *w_ih_final = 0.0;
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_properties_potential (sa_bulk, h_pot_bulk,&
+ p, sa_final, ct_final, w_ih_final)
+!==========================================================================
+!
+! Calculates the mass fraction of ice (mass of ice divided by mass of ice
+! plus seawater), w_Ih_final, which results from given values of the bulk
+! Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk,
+! occuring at pressure p. The final equilibrium values of Absolute
+! Salinity, SA_final, and Conservative Temperature, CT_final, of the
+! interstitial seawater phase are also returned. This code assumes that
+! there is no dissolved air in the seawater (that is, saturation_fraction
+! is assumed to be zero thoughout the code).
+!
+! When the mass fraction w_Ih_final is calculated as being a positive
+! value, the seawater-ice mixture is at thermodynamic equlibrium.
+!
+! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk,
+! is sufficiently large (i.e. sufficiently "warm") so that there is no ice
+! present in the final state. In this case the final state consists of
+! only seawater rather than being an equlibrium mixture of seawater and
+! ice which occurs when w_Ih_final is positive. Note that when
+! w_Ih_final = 0, the final seawater is not at the freezing temperature.
+!
+! Note that this code uses the exact forms of CT_freezing and
+! pot_enthalpy_ice_freezing.
+!
+! SA_bulk = bulk Absolute Salinity of the seawater and ice mixture
+! [ g/kg ]
+! h_pot_bulk = bulk potential enthalpy of the seawater and ice mixture
+! [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! SA_final = Absolute Salinity of the seawater in the final state,
+! whether or not any ice is present. [ g/kg ]
+! CT_final = Conservative Temperature of the seawater in the the final
+! state, whether or not any ice is present. [ deg C ]
+! w_Ih_final = mass fraction of ice in the final seawater-ice mixture.
+! If this ice mass fraction is positive, the system is at
+! thermodynamic equilibrium. If this ice mass fraction is
+! zero there is no ice in the final state which consists
+! only of seawater which is warmer than the freezing
+! temperature. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_properties_potential(double sa_bulk, double h_pot_bulk, double p,
+ double *sa_final, double *ct_final, double *w_ih_final)
+{
+ GSW_TEOS10_CONSTANTS;
+ int iterations, max_iterations;
+ double ctf_sa, ctf, dfunc_dw_ih, dfunc_dw_ih_mean_poly,
+ dpot_h_ihf_dsa, func, func0, h_pot_ihf, sa, w_ih_old, w_ih,
+ x, xa, y, z;
+
+ double f01 = -9.041191886754806e-1,
+ f02 = 4.169608567309818e-2,
+ f03 = -9.325971761333677e-3,
+ f04 = 4.699055851002199e-2,
+ f05 = -3.086923404061666e-2,
+ f06 = 1.057761186019000e-2,
+ f07 = -7.349302346007727e-2,
+ f08 = 1.444842576424337e-1,
+ f09 = -1.408425967872030e-1,
+ f10 = 1.070981398567760e-1,
+ f11 = -1.768451760854797e-2,
+ f12 = -4.013688314067293e-1,
+ f13 = 7.209753205388577e-1,
+ f14 = -1.807444462285120e-1,
+ f15 = 1.362305015808993e-1,
+ f16 = -9.500974920072897e-1,
+ f17 = 1.192134856624248,
+ f18 = -9.191161283559850e-2,
+ f19 = -1.008594411490973,
+ f20 = 8.020279271484482e-1,
+ f21 = -3.930534388853466e-1,
+ f22 = -2.026853316399942e-2,
+ f23 = -2.722731069001690e-2,
+ f24 = 5.032098120548072e-2,
+ f25 = -2.354888890484222e-2,
+ f26 = -2.454090179215001e-2,
+ f27 = 4.125987229048937e-2,
+ f28 = -3.533404753585094e-2,
+ f29 = 3.766063025852511e-2,
+ f30 = -3.358409746243470e-2,
+ f31 = -2.242158862056258e-2,
+ f32 = 2.102254738058931e-2,
+ f33 = -3.048635435546108e-2,
+ f34 = -1.996293091714222e-2,
+ f35 = 2.577703068234217e-2,
+ f36 = -1.292053030649309e-2,
+
+ g01 = 3.332286683867741e5,
+ g02 = 1.416532517833479e4,
+ g03 = -1.021129089258645e4,
+ g04 = 2.356370992641009e4,
+ g05 = -8.483432350173174e3,
+ g06 = 2.279927781684362e4,
+ g07 = 1.506238790315354e4,
+ g08 = 4.194030718568807e3,
+ g09 = -3.146939594885272e5,
+ g10 = -7.549939721380912e4,
+ g11 = 2.790535212869292e6,
+ g12 = 1.078851928118102e5,
+ g13 = -1.062493860205067e7,
+ g14 = 2.082909703458225e7,
+ g15 = -2.046810820868635e7,
+ g16 = 8.039606992745191e6,
+ g17 = -2.023984705844567e4,
+ g18 = 2.871769638352535e4,
+ g19 = -1.444841553038544e4,
+ g20 = 2.261532522236573e4,
+ g21 = -2.090579366221046e4,
+ g22 = -1.128417003723530e4,
+ g23 = 3.222965226084112e3,
+ g24 = -1.226388046175992e4,
+ g25 = 1.506847628109789e4,
+ g26 = -4.584670946447444e4,
+ g27 = 1.596119496322347e4,
+ g28 = -6.338852410446789e4,
+ g29 = 8.951570926106525e4,
+
+ saturation_fraction = 0.0;
+ /*
+ !-----------------------------------------------------------------------
+ ! Finding func0. This is the value of the function, func, that would
+ ! result in the output w_Ih_final being exactly zero.
+ !-----------------------------------------------------------------------
+ */
+ func0 = h_pot_bulk - gsw_cp0
+ *gsw_ct_freezing(sa_bulk,p,saturation_fraction);
+ /*
+ !-----------------------------------------------------------------------
+ ! Setting the three outputs for data points that have func0 non-negative
+ !-----------------------------------------------------------------------
+ */
+ if (func0 >= 0.0) {
+ /*
+ ! When func0 is zero or positive then the final answer will contain
+ ! no frazil ice; that is, it will be pure seawater that is warmer
+ ! than the freezing temperature. If func0 >= 0 we do not need to go
+ ! through the modified Newton-Raphson procedure and we can simply
+ ! write down the answer, as in the following 4 lines of code.
+ */
+ *sa_final = sa_bulk;
+ *ct_final = h_pot_bulk/gsw_cp0;
+ *w_ih_final = 0.0;
+ return;
+ }
+ /*
+ !-----------------------------------------------------------------------
+ !Begin finding the solution for data points that have func0 < 0, so that
+ !the output will have a positive ice mass fraction w_Ih_final.
+ !-----------------------------------------------------------------------
+ */
+
+ /*Evalaute a polynomial for w_Ih in terms of SA_bulk, func0 and p*/
+ x = sa_bulk*1e-2;
+ y = func0/3e5;
+ z = p*1e-4;
+
+ w_ih = y*(f01 + x*(f02 + x*(f03 + x*(f04 + x*(f05 + f06*x))))
+ + y*(f07 + x*(f08 + x*(f09 + x*(f10 + f11*x))) + y*(f12 + x*(f13
+ + x*(f14 + f15*x)) + y*(f16 + x*(f17 + f18*x) + y*(f19 + f20*x
+ + f21*y)))) + z*(f22 + x*(f23 + x*(f24 + f25*x)) + y*(x*(f26
+ + f27*x)
+ + y*(f28 + f29*x + f30*y)) + z*(f31 + x*(f32 + f33*x) + y*(f34
+ + f35*x + f36*y))));
+
+ if (w_ih > 0.9) {
+ /*
+ ! The ice mass fraction out of this code is restricted to be
+ !less than 0.9.
+ */
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ /*
+ !The initial guess at the absolute salinity of the interstitial seawater
+ */
+ sa = sa_bulk/(1.0 - w_ih);
+ /*
+ !-----------------------------------------------------------------------
+ ! Doing a Newton step with a separate polynomial estimate of the mean
+ ! derivative dfunc_dw_Ih_mean_poly.
+ !-----------------------------------------------------------------------' */
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing(sa,p);
+ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf;
+
+ xa = sa*1e-2;
+
+ dfunc_dw_ih_mean_poly = g01 + xa*(g02 + xa*(g03 + xa*(g04 + g05*xa)))
+ + w_ih*(xa*(g06 + xa*(g07 + g08*xa)) + w_ih*(xa*(g09 + g10*xa)
+ + w_ih*xa*(g11 + g12*xa + w_ih*(g13 + w_ih*(g14 + w_ih*(g15
+ + g16*w_ih)))))) + z*(g17 + xa*(g18 + g19*xa) + w_ih*(g20
+ + w_ih*(g21 + g22*w_ih) + xa*(g23 + g24*xa*w_ih))
+ + z*(g25 + xa*(g26 + g27*xa) + w_ih*(g28 + g29*w_ih)));
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih_mean_poly;
+
+ sa = sa_bulk/(1.0 - w_ih);
+ /*
+ !-----------------------------------------------------------------------
+ ! Calculating the estimate of the derivative of func, dfunc_dw_Ih, to be
+ ! fed into Newton's Method.
+ !-----------------------------------------------------------------------
+ */
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing(sa,p);
+
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,&ctf_sa,
+ NULL);
+ gsw_pot_enthalpy_ice_freezing_first_derivatives(sa,p,&dpot_h_ihf_dsa,
+ NULL);
+
+ dfunc_dw_ih = gsw_cp0*ctf - h_pot_ihf -
+ sa*(gsw_cp0*ctf_sa + w_ih*dpot_h_ihf_dsa/(1.0 - w_ih));
+
+ if (w_ih >= 0.0 && w_ih <= 0.20 && sa > 15.0
+ && sa < 60.0 && p <= 3000.0) {
+ max_iterations = 1;
+ } else if (w_ih >= 0.0 && w_ih <= 0.85 && sa > 0.0
+ && sa < 120.0 && p <= 3500.0) {
+ max_iterations = 2;
+ } else {
+ max_iterations = 3;
+ }
+
+ for (iterations = 1; iterations <= max_iterations; iterations++) {
+
+ if (iterations > 1) {
+ /*On the first iteration ctf and h_pot_ihf are both known*/
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing(sa,p);
+ }
+
+ /*This is the function, func, whose zero we seek ...*/
+ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf;
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih;
+
+ if (w_ih > 0.9) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa = sa_bulk/(1.0 - w_ih);
+
+ }
+
+ if (w_ih < 0.0) {
+ *sa_final = sa_bulk;
+ *ct_final = h_pot_bulk/gsw_cp0;
+ *w_ih_final = 0.0;
+ } else {
+ *sa_final = sa;
+ *ct_final = gsw_ct_freezing(sa,p,saturation_fraction);
+ *w_ih_final = w_ih;
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_properties_potential_poly (sa_bulk, &
+ h_pot_bulk, p, sa_final, ct_final, w_ih_final)
+!==========================================================================
+!
+! Calculates the mass fraction of ice (mass of ice divided by mass of ice
+! plus seawater), w_Ih_final, which results from given values of the bulk
+! Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk,
+! occuring at pressure p. The final equilibrium values of Absolute
+! Salinity, SA_final, and Conservative Temperature, CT_final, of the
+! interstitial seawater phase are also returned. This code assumes that
+! there is no dissolved air in the seawater (that is, saturation_fraction
+! is assumed to be zero thoughout the code).
+!
+! When the mass fraction w_Ih_final is calculated as being a positive
+! value, the seawater-ice mixture is at thermodynamic equlibrium.
+!
+! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk,
+! is sufficiently large (i.e. sufficiently "warm") so that there is no ice
+! present in the final state. In this case the final state consists of
+! only seawater rather than being an equlibrium mixture of seawater and
+! ice which occurs when w_Ih_final is positive. Note that when
+! w_Ih_final = 0, the final seawater is not at the freezing temperature.
+!
+! Note that this code uses the polynomial forms of CT_freezing and
+! pot_enthalpy_ice_freezing. This code is intended to be used in ocean
+! models where the model prognostic variables are SA_bulk and h_pot_bulk.
+!
+! SA_bulk = bulk Absolute Salinity of the seawater and ice mixture
+! [ g/kg ]
+! h_pot_bulk = bulk potential enthalpy of the seawater and ice mixture
+! [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! SA_final = Absolute Salinity of the seawater in the final state,
+! whether or not any ice is present. [ g/kg ]
+! CT_final = Conservative Temperature of the seawater in the the final
+! state, whether or not any ice is present. [ deg C ]
+! w_Ih_final = mass fraction of ice in the final seawater-ice mixture.
+! If this ice mass fraction is positive, the system is at
+! thermodynamic equilibrium. If this ice mass fraction is
+! zero there is no ice in the final state which consists
+! only of seawater which is warmer than the freezing
+! temperature. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_properties_potential_poly(double sa_bulk, double h_pot_bulk,
+ double p, double *sa_final, double *ct_final, double *w_ih_final)
+{
+ GSW_TEOS10_CONSTANTS;
+ int iterations, max_iterations;
+ double ctf_sa, ctf, dfunc_dw_ih, dfunc_dw_ih_mean_poly, dpot_h_ihf_dsa,
+ func, func0, h_pot_ihf, sa, w_ih_old, w_ih, x, xa, y, z;
+
+ double f01 = -9.041191886754806e-1,
+ f02 = 4.169608567309818e-2,
+ f03 = -9.325971761333677e-3,
+ f04 = 4.699055851002199e-2,
+ f05 = -3.086923404061666e-2,
+ f06 = 1.057761186019000e-2,
+ f07 = -7.349302346007727e-2,
+ f08 = 1.444842576424337e-1,
+ f09 = -1.408425967872030e-1,
+ f10 = 1.070981398567760e-1,
+ f11 = -1.768451760854797e-2,
+ f12 = -4.013688314067293e-1,
+ f13 = 7.209753205388577e-1,
+ f14 = -1.807444462285120e-1,
+ f15 = 1.362305015808993e-1,
+ f16 = -9.500974920072897e-1,
+ f17 = 1.192134856624248,
+ f18 = -9.191161283559850e-2,
+ f19 = -1.008594411490973,
+ f20 = 8.020279271484482e-1,
+ f21 = -3.930534388853466e-1,
+ f22 = -2.026853316399942e-2,
+ f23 = -2.722731069001690e-2,
+ f24 = 5.032098120548072e-2,
+ f25 = -2.354888890484222e-2,
+ f26 = -2.454090179215001e-2,
+ f27 = 4.125987229048937e-2,
+ f28 = -3.533404753585094e-2,
+ f29 = 3.766063025852511e-2,
+ f30 = -3.358409746243470e-2,
+ f31 = -2.242158862056258e-2,
+ f32 = 2.102254738058931e-2,
+ f33 = -3.048635435546108e-2,
+ f34 = -1.996293091714222e-2,
+ f35 = 2.577703068234217e-2,
+ f36 = -1.292053030649309e-2,
+
+ g01 = 3.332286683867741e5,
+ g02 = 1.416532517833479e4,
+ g03 = -1.021129089258645e4,
+ g04 = 2.356370992641009e4,
+ g05 = -8.483432350173174e3,
+ g06 = 2.279927781684362e4,
+ g07 = 1.506238790315354e4,
+ g08 = 4.194030718568807e3,
+ g09 = -3.146939594885272e5,
+ g10 = -7.549939721380912e4,
+ g11 = 2.790535212869292e6,
+ g12 = 1.078851928118102e5,
+ g13 = -1.062493860205067e7,
+ g14 = 2.082909703458225e7,
+ g15 = -2.046810820868635e7,
+ g16 = 8.039606992745191e6,
+ g17 = -2.023984705844567e4,
+ g18 = 2.871769638352535e4,
+ g19 = -1.444841553038544e4,
+ g20 = 2.261532522236573e4,
+ g21 = -2.090579366221046e4,
+ g22 = -1.128417003723530e4,
+ g23 = 3.222965226084112e3,
+ g24 = -1.226388046175992e4,
+ g25 = 1.506847628109789e4,
+ g26 = -4.584670946447444e4,
+ g27 = 1.596119496322347e4,
+ g28 = -6.338852410446789e4,
+ g29 = 8.951570926106525e4,
+
+ saturation_fraction = 0.0;
+ /*
+ !-----------------------------------------------------------------------
+ ! Finding func0. This is the value of the function, func, that would
+ ! result in the output w_Ih_final being exactly zero.
+ !-----------------------------------------------------------------------
+ */
+ func0 = h_pot_bulk - gsw_cp0
+ *gsw_ct_freezing_poly(sa_bulk,p,saturation_fraction);
+ /*
+ !-----------------------------------------------------------------------
+ ! Setting the three outputs for data points that have func0 non-negative
+ !-----------------------------------------------------------------------
+ */
+ if (func0 >= 0.0) {
+ /*
+ ! When func0 is zero or positive then the final answer will contain
+ ! no frazil ice; that is, it will be pure seawater that is warmer
+ ! han the freezing temperature. If func0 >= 0 we do not need to go
+ ! through the modified Newton-Raphson procedure and we can simply
+ ! write down the answer, as in the following 4 lines of code.
+ */
+ *sa_final = sa_bulk;
+ *ct_final = h_pot_bulk/gsw_cp0;
+ *w_ih_final = 0.0;
+ return;
+ }
+ /*
+ !-----------------------------------------------------------------------
+ !Begin finding the solution for data points that have func0 < 0, so that
+ !the output will have a positive ice mass fraction w_Ih_final.
+ !-----------------------------------------------------------------------
+ */
+
+ /*Evalaute a polynomial for w_Ih in terms of SA_bulk, func0 and p*/
+ x = sa_bulk*1e-2;
+ y = func0/3e5;
+ z = p*1e-4;
+
+ w_ih = y*(f01 + x*(f02 + x*(f03 + x*(f04 + x*(f05 + f06*x))))
+ + y*(f07 + x*(f08 + x*(f09 + x*(f10 + f11*x))) + y*(f12 + x*(f13
+ + x*(f14 + f15*x)) + y*(f16 + x*(f17 + f18*x) + y*(f19 + f20*x
+ + f21*y)))) + z*(f22 + x*(f23 + x*(f24 + f25*x)) + y*(x*(f26
+ + f27*x)
+ + y*(f28 + f29*x + f30*y)) + z*(f31 + x*(f32 + f33*x) + y*(f34
+ + f35*x + f36*y))));
+
+ if (w_ih > 0.9) {
+ /*
+ ! The ice mass fraction out of this code is restricted to be
+ ! less than 0.9.
+ */
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+ /*
+ ! The initial guess at the absolute salinity of the interstitial
+ ! seawater
+ */
+ sa = sa_bulk/(1.0 - w_ih);
+ /*
+ !-----------------------------------------------------------------------
+ ! Doing a Newton step with a separate polynomial estimate of the mean
+ ! derivative dfunc_dw_Ih_mean_poly.
+ !-----------------------------------------------------------------------
+ */
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing_poly(sa,p);
+ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf;
+
+ xa = sa*1e-2;
+
+ dfunc_dw_ih_mean_poly = g01 + xa*(g02 + xa*(g03 + xa*(g04 + g05*xa)))
+ + w_ih*(xa*(g06 + xa*(g07 + g08*xa)) + w_ih*(xa*(g09 + g10*xa)
+ + w_ih*xa*(g11 + g12*xa + w_ih*(g13 + w_ih*(g14 + w_ih*(g15
+ + g16*w_ih)))))) + z*(g17 + xa*(g18 + g19*xa) + w_ih*(g20
+ + w_ih*(g21 + g22*w_ih) + xa*(g23 + g24*xa*w_ih))
+ + z*(g25 + xa*(g26 + g27*xa) + w_ih*(g28 + g29*w_ih)));
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih_mean_poly;
+
+ sa = sa_bulk/(1.0 - w_ih);
+ /*
+ !-----------------------------------------------------------------------
+ ! Calculating the estimate of the derivative of func, dfunc_dw_Ih, to be
+ ! fed into Newton's Method.
+ !-----------------------------------------------------------------------
+ */
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing_poly(sa,p);
+
+ gsw_ct_freezing_first_derivatives_poly(sa,p,saturation_fraction,&ctf_sa,
+ NULL);
+ gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(sa,p,
+ &dpot_h_ihf_dsa, NULL);
+
+ dfunc_dw_ih = gsw_cp0*ctf - h_pot_ihf -
+ sa*(gsw_cp0*ctf_sa + w_ih*dpot_h_ihf_dsa/(1.0 - w_ih));
+
+ if (w_ih >= 0.0 && w_ih <= 0.20 && sa > 15.0
+ && sa < 60.0 && p <= 3000.0) {
+ max_iterations = 1;
+ } else if (w_ih >= 0.0 && w_ih <= 0.85 && sa > 0.0
+ && sa < 120.0 && p <= 3500.0) {
+ max_iterations = 2;
+ } else {
+ max_iterations = 3;
+ }
+
+ for (iterations = 1; iterations <= max_iterations; iterations++) {
+
+ if (iterations > 1) {
+ /*On the first iteration ctf and h_pot_ihf are both known*/
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing_poly(sa,p);
+ }
+
+ /*This is the function, func, whose zero we seek ...*/
+ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf;
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih;
+
+ if (w_ih > 0.9) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa = sa_bulk/(1.0 - w_ih);
+
+ }
+
+ if (w_ih < 0.0) {
+ *sa_final = sa_bulk;
+ *ct_final = h_pot_bulk/gsw_cp0;
+ *w_ih_final = 0.0;
+ } else {
+ *sa_final = sa;
+ *ct_final = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ *w_ih_final = w_ih;
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_ratios_adiabatic (sa, p, w_ih, &
+ dsa_dct_frazil, dsa_dp_frazil, dct_dp_frazil)
+!==========================================================================
+!
+! Calculates the ratios of SA, CT and P changes when frazil ice forms or
+! melts in response to an adiabatic change in pressure of a mixture of
+! seawater and frazil ice crystals.
+!
+! Note that the first output, dSA_dCT_frazil, is dSA/dCT rather than
+! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT, is zero
+! whereas dCT/dSA would then be infinite.
+!
+! Also note that both dSA_dP_frazil and dCT_dP_frazil are the pressure
+! derivatives with the pressure measured in Pa not dbar.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure of seawater at which melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! w_Ih = mass fraction of ice, that is the mass of ice divided by the
+! sum of the masses of ice and seawater. That is, the mass of
+! ice divided by the mass of the final mixed fluid.
+! w_Ih must be between 0 and 1. [ unitless ]
+!
+! dSA_dCT_frazil = the ratio of the changes in Absolute Salinity
+! to that of Conservative Temperature [ g/(kg K) ]
+! dSA_dP_frazil = the ratio of the changes in Absolute Salinity
+! to that of pressure (in Pa) [ g/(kg Pa) ]
+! dCT_dP_frazil = the ratio of the changes in Conservative Temperature
+! to that of pressure (in Pa) [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_ratios_adiabatic (double sa, double p, double w_ih,
+ double *dsa_dct_frazil, double *dsa_dp_frazil, double *dct_dp_frazil)
+{
+ double bracket1, bracket2, cp_ih, gamma_ih, h, h_ih, part,
+ rec_bracket3, tf, wcp, h_hat_sa, h_hat_ct, tf_sa, tf_p,
+ ctf, ctf_sa, ctf_p;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ h = gsw_enthalpy_ct_exact(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(tf,p);
+ cp_ih = gsw_cp_ice(tf,p);
+ gamma_ih = gsw_adiabatic_lapse_rate_ice(tf,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,&tf_sa,&tf_p);
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,
+ &ctf_sa,&ctf_p);
+
+ wcp = cp_ih*w_ih/(1.0 - w_ih);
+ part = (tf_p - gamma_ih)/ctf_p;
+
+ bracket1 = h_hat_ct + wcp*part;
+ bracket2 = h - h_ih - sa*(h_hat_sa + wcp*(tf_sa - part*ctf_sa));
+ rec_bracket3 = 1.0/(h - h_ih - sa*(h_hat_sa + h_hat_ct*ctf_sa
+ + wcp*tf_sa));
+
+ *dsa_dct_frazil = sa*(bracket1/bracket2);
+ *dsa_dp_frazil = sa*ctf_p*bracket1*rec_bracket3;
+ *dct_dp_frazil = ctf_p*bracket2*rec_bracket3;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_ratios_adiabatic_poly (sa, p, w_ih, &
+ dsa_dct_frazil, dsa_dp_frazil, dct_dp_frazil)
+!==========================================================================
+!
+! Calculates the ratios of SA, CT and P changes when frazil ice forms or
+! melts in response to an adiabatic change in pressure of a mixture of
+! seawater and frazil ice crystals.
+!
+! Note that the first output, dSA_dCT_frazil, is dSA/dCT rather than
+! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT, is zero
+! whereas dCT/dSA would then be infinite.
+!
+! Also note that both dSA_dP_frazil and dCT_dP_frazil are the pressure
+! derivatives with the pressure measured in Pa not dbar.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure of seawater at which melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! w_Ih = mass fraction of ice, that is the mass of ice divided by the
+! sum of the masses of ice and seawater. That is, the mass of
+! ice divided by the mass of the final mixed fluid.
+! w_Ih must be between 0 and 1. [ unitless ]
+!
+! dSA_dCT_frazil = the ratio of the changes in Absolute Salinity
+! to that of Conservative Temperature [ g/(kg K) ]
+! dSA_dP_frazil = the ratio of the changes in Absolute Salinity
+! to that of pressure (in Pa) [ g/(kg Pa) ]
+! dCT_dP_frazil = the ratio of the changes in Conservative Temperature
+! to that of pressure (in Pa) [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_ratios_adiabatic_poly(double sa, double p, double w_ih,
+ double *dsa_dct_frazil, double *dsa_dp_frazil, double *dct_dp_frazil)
+{
+ double bracket1, bracket2, cp_ih, gamma_ih, h, h_ih, part,
+ rec_bracket3, tf, wcp, h_hat_sa, h_hat_ct, tf_sa, tf_p,
+ ctf, ctf_sa, ctf_p;
+ double saturation_fraction = 0.0;
+
+ tf = gsw_t_freezing_poly(sa,p,saturation_fraction);
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ h = gsw_enthalpy(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(tf,p);
+ cp_ih = gsw_cp_ice(tf,p);
+ gamma_ih = gsw_adiabatic_lapse_rate_ice(tf,p);
+ gsw_enthalpy_first_derivatives(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+ gsw_t_freezing_first_derivatives_poly(sa,p,saturation_fraction,
+ &tf_sa,&tf_p);
+ gsw_ct_freezing_first_derivatives_poly(sa,p,saturation_fraction,
+ &ctf_sa,&ctf_p);
+
+ wcp = cp_ih*w_ih/(1.0 - w_ih);
+ part = (tf_p - gamma_ih)/ctf_p;
+
+ bracket1 = h_hat_ct + wcp*part;
+ bracket2 = h - h_ih - sa*(h_hat_sa + wcp*(tf_sa - part*ctf_sa));
+ rec_bracket3 = 1.0/(h - h_ih - sa*(h_hat_sa + h_hat_ct*ctf_sa
+ + wcp*tf_sa));
+
+ *dsa_dct_frazil = sa*(bracket1/bracket2);
+ *dsa_dp_frazil = sa*ctf_p*bracket1*rec_bracket3;
+ *dct_dp_frazil = ctf_p*bracket2*rec_bracket3;
+}
+/*
+!==========================================================================
+pure function gsw_geo_strf_dyn_height (sa, ct, p, p_ref)
+!==========================================================================
+!
+! Calculates dynamic height anomaly as the integral of specific volume
+! anomaly from the pressure p of the bottle to the reference pressure
+! p_ref.
+!
+! Hence, geo_strf_dyn_height is the dynamic height anomaly with respect
+! to a given reference pressure. This is the geostrophic streamfunction
+! for the difference between the horizontal velocity at the pressure
+! concerned, p, and the horizontal velocity at p_ref. Dynamic height
+! anomaly is the geostrophic streamfunction in an isobaric surface. The
+! reference values used for the specific volume anomaly are
+! SSO = 35.16504 g/kg and CT = 0 deg C. This function calculates
+! specific volume anomaly using the computationally efficient
+! expression for specific volume of Roquet et al. (2015).
+!
+! This function evaluates the pressure integral of specific volume using
+! SA and CT interpolated with respect to pressure using the method of
+! Reiniger and Ross (1968). It uses a weighted mean of (i) values
+! obtained from linear interpolation of the two nearest data points, and
+! (ii) a linear extrapolation of the pairs of data above and below. This
+! "curve fitting" method resembles the use of cubic splines.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! p_ref = reference pressure [ dbar ]
+! ( i.e. reference absolute pressure - 10.1325 dbar )
+!
+! geo_strf_dyn_height = dynamic height anomaly [ m^2/s^2 ]
+! Note. If p_ref exceeds the pressure of the deepest bottle on a
+! vertical profile, the dynamic height anomaly for each bottle
+! on the whole vertical profile is returned as NaN.
+!--------------------------------------------------------------------------
+*/
+static void p_sequence(double p1,double p2,double max_dp_i,double *pseq,
+ int *nps); /* forward reference */
+
+double * /* Returns NULL on error, dyn_height if okay */
+gsw_geo_strf_dyn_height(double *sa, double *ct, double *p, double p_ref,
+ int n_levels, double *dyn_height)
+{
+ GSW_TEOS10_CONSTANTS;
+ int m_levels = (n_levels <= 0) ? 1 : n_levels,
+ p_cnt, top_pad, i, nz, ibottle, ipref, np_max, np, ibpr=0,
+ *iidata;
+ double dp_min, dp_max, p_min, p_max, max_dp_i,
+ *b, *b_av, *dp, *dp_i, *sa_i=NULL, *ct_i, *p_i=NULL,
+ *geo_strf_dyn_height0;
+
+/*
+!--------------------------------------------------------------------------
+! This max_dp_i is the limit we choose for the evaluation of specific
+! volume in the pressure integration. That is, the vertical integration
+! of specific volume with respect to pressure is perfomed with the pressure
+! increment being no more than max_dp_i (the default value being 1 dbar).
+!--------------------------------------------------------------------------
+*/
+ max_dp_i = 1.0;
+
+ if ((nz = m_levels) <= 1)
+ return (NULL);
+
+ dp = malloc(nz*sizeof (double));
+ dp_min = 11000.0;
+ dp_max = -11000.0;
+ for (i=0; i<nz-1; i++) {
+ if ((dp[i] = p[i+1] - p[i]) < dp_min)
+ dp_min = dp[i];
+ if (dp[i] > dp_max)
+ dp_max = dp[i];
+ }
+
+ if (dp_min <= 0.0) {
+ /* pressure must be monotonic */
+ free(dp);
+ return (NULL);
+ }
+ p_min = p[0];
+ p_max = p[nz-1];
+
+ if (p_ref > p_max) {
+ /*the reference pressure p_ref is deeper than all bottles*/
+ free(dp);
+ return (NULL);
+ }
+
+ /* Determine if there is a "bottle" at exactly p_ref */
+ ipref = -1;
+ for (ibottle = 0; ibottle < nz; ibottle++) {
+ if (p[ibottle] == p_ref) {
+ ipref = ibottle;
+ break;
+ }
+ }
+ if ((dp_max <= max_dp_i) && (p[0] == 0.0) && (ipref >= 0)) {
+ /*
+ !vertical resolution is good (bottle gap is no larger than max_dp_i)
+ ! & the vertical profile begins at the surface (i.e. at p = 0 dbar)
+ ! & the profile contains a "bottle" at exactly p_ref.
+ */
+ b = malloc(3*nz*sizeof (double));
+ b_av = b+nz; geo_strf_dyn_height0 = b_av+nz;
+ for (i=0; i<nz; i++) {
+ b[i] = gsw_specvol_anom_standard(sa[i],ct[i],p[i]);
+ if (i > 0)
+ b_av[i-1] = 0.5*(b[i] + b[i-1]);
+ }
+ /*
+ ! "geo_strf_dyn_height0" is the dynamic height anomaly with respect
+ ! to p_ref = 0 (the surface).
+ */
+ geo_strf_dyn_height0[0] = 0.0;
+ for (i=1; i<nz; i++)
+ geo_strf_dyn_height0[i] = b_av[i]*dp[i]*db2pa;
+ for (i=1; i<nz; i++) /* cumulative sum */
+ geo_strf_dyn_height0[i] = geo_strf_dyn_height0[i-1]
+ - geo_strf_dyn_height0[i];
+ for (i=0; i<nz; i++)
+ dyn_height[i] = geo_strf_dyn_height0[i]
+ - geo_strf_dyn_height0[ipref];
+ free(b);
+ } else {
+ /*
+ ! Test if there are vertical gaps between adjacent "bottles" which are
+ ! greater than max_dp_i, and that there is a "bottle" exactly at the
+ ! reference pressure.
+ */
+ iidata = malloc((nz+1)*sizeof (int));
+
+ if ((dp_max <= max_dp_i) && (ipref >= 0)) {
+ /*
+ ! Vertical resolution is already good (no larger than max_dp_i), and
+ ! there is a "bottle" at exactly p_ref.
+ */
+ sa_i = malloc(2*(nz+1)*sizeof (double));
+ ct_i = sa_i+nz+1;
+ p_i = malloc((nz+1)*sizeof (double));;
+
+ if (p_min > 0.0) {
+ /*
+ ! resolution is fine and there is a bottle at p_ref, but
+ ! there is not a bottle at p = 0. So add an extra bottle.
+ */
+ for (i=0; i<nz; i++) {
+ sa_i[i+1] = sa[i];
+ ct_i[i+1] = ct[i];
+ p_i[i+1] = p[i];
+ }
+ sa_i[0] = sa[0];
+ ct_i[0] = ct[0];
+ p_i[0] = 0.0;
+ ibpr = ipref+1;
+ p_cnt = nz+1;
+ for (i=0; i<p_cnt; i++)
+ iidata[i] = i;
+ } else {
+ /*
+ ! resolution is fine, there is a bottle at p_ref, and
+ ! there is a bottle at p = 0
+ */
+ memmove(sa_i, sa, nz*sizeof (double));
+ memmove(ct_i, ct, nz*sizeof (double));
+ memmove(p_i, p, nz*sizeof (double));
+ ibpr = ipref;
+ for (i=0; i<nz; i++)
+ iidata[i] = i;
+ p_cnt = nz;
+ }
+
+ } else {
+ /*
+ ! interpolation is needed.
+ */
+ np_max = 2*rint(p[nz-1]/max_dp_i+0.5);
+ p_i = malloc(np_max*sizeof (double));
+ /* sa_i is allocated below, when its size is known */
+
+ if (p_min > 0.0) {
+ /*
+ ! there is not a bottle at p = 0.
+ */
+ if (p_ref < p_min) {
+ /*
+ ! p_ref is shallower than the minimum bottle pressure.
+ */
+ p_i[0] = 0.0;
+ p_sequence(p_i[0],p_ref,max_dp_i, p_i+1,&np);
+ ibpr = p_cnt = np;
+ p_cnt++;
+ p_sequence(p_ref,p_min,max_dp_i, p_i+p_cnt,&np);
+ p_cnt += np;
+ top_pad = p_cnt;
+ } else {
+ /*
+ ! p_ref is deeper than the minimum bottle pressure.
+ */
+ p_i[0] = 0.0;
+ p_i[1] = p_min;
+ top_pad = 2;
+ p_cnt = 2;
+ }
+ } else {
+ /*
+ ! there is a bottle at p = 0.
+ */
+ p_i[0] = p_min;
+ top_pad = 1;
+ p_cnt = 1;
+ }
+
+ for (ibottle=0; ibottle < nz-1; ibottle++) {
+
+ iidata[ibottle] = p_cnt-1;
+ if (p[ibottle] == p_ref) ibpr = p_cnt-1;
+
+ if (p[ibottle] < p_ref && p[ibottle+1] > p_ref) {
+ /*
+ ! ... reference pressure is spanned by bottle pairs -
+ ! need to include p_ref as an interpolated pressure.
+ */
+ p_sequence(p[ibottle],p_ref,max_dp_i, p_i+p_cnt,&np);
+ p_cnt += np;
+ ibpr = p_cnt-1;
+ p_sequence(p_ref,p[ibottle+1],max_dp_i,p_i+p_cnt,&np);
+ p_cnt += np;
+ } else {
+ /*
+ ! ... reference pressure is not spanned by bottle pairs.
+ */
+ p_sequence(p[ibottle],p[ibottle+1],max_dp_i,
+ p_i+p_cnt,&np);
+ p_cnt += np;
+ }
+
+ }
+
+ iidata[nz-1] = p_cnt-1;
+ if (p[nz-1] == p_ref) ibpr = p_cnt-1;
+
+ sa_i = malloc(2*p_cnt*sizeof (double));
+ ct_i = sa_i+p_cnt;
+
+ if (top_pad > 1) {
+ gsw_linear_interp_sa_ct(sa,ct,p,nz,
+ p_i,top_pad-1,sa_i,ct_i);
+ }
+ gsw_rr68_interp_sa_ct(sa,ct,p,nz,p_i+top_pad-1,p_cnt-top_pad+1,
+ sa_i+top_pad-1,ct_i+top_pad-1);
+ }
+
+ b = malloc(4*p_cnt*sizeof (double));
+ b_av = b+p_cnt; dp_i = b_av+p_cnt;
+ geo_strf_dyn_height0 = dp_i+p_cnt;
+ for (i=0; i<p_cnt; i++) {
+ b[i] = gsw_specvol_anom_standard(sa_i[i],ct_i[i],p_i[i]);
+ if (i > 0) {
+ dp_i[i-1] = p_i[i]-p_i[i-1];
+ b_av[i-1] = 0.5*(b[i] + b[i-1]);
+ }
+ }
+ /*
+ ! "geo_strf_dyn_height0" is the dynamic height anomaly with respect
+ ! to p_ref = 0 (the surface).
+ */
+ geo_strf_dyn_height0[0] = 0.0;
+ for (i=1; i<p_cnt; i++)
+ geo_strf_dyn_height0[i] = b_av[i-1]*dp_i[i-1];
+ for (i=1; i<p_cnt; i++) /* cumulative sum */
+ geo_strf_dyn_height0[i] = geo_strf_dyn_height0[i-1]
+ - geo_strf_dyn_height0[i];
+ for (i=0; i<nz; i++)
+ dyn_height[i] = (geo_strf_dyn_height0[iidata[i]]
+ - geo_strf_dyn_height0[ibpr])*db2pa;
+
+ free(b);
+ free(iidata);
+ if (sa_i != NULL)
+ free(sa_i);
+ if (p_i != NULL)
+ free(p_i);
+
+ }
+ free(dp);
+ return (dyn_height);
+}
+
+static void
+p_sequence(double p1, double p2, double max_dp_i, double *pseq, int *nps)
+{
+ double dp, pstep;
+ int n, i;
+
+ dp = p2 - p1;
+ n = ceil(dp/max_dp_i);
+ pstep = dp/n;
+
+ if (nps != NULL) *nps = n;
+
+ for (i=1; i<=n; i++)
+ pseq[i-1] = p1+pstep*i;
+}
+/*
+!==========================================================================
+pure subroutine gsw_geo_strf_dyn_height_pc (sa, ct, delta_p, &
+ geo_strf_dyn_height_pc, p_mid)
+!==========================================================================
+!
+! Calculates dynamic height anomaly as the integral of specific volume
+! anomaly from the the sea surface pressure (0 Pa) to the pressure p.
+! This function, gsw_geo_strf_dyn_height_pc, is to used when the
+! Absolute Salinity and Conservative Temperature are piecewise constant in
+! the vertical over sucessive pressure intervals of delta_p (such as in
+! a forward "z-coordinate" ocean model). "geo_strf_dyn_height_pc" is
+! the dynamic height anomaly with respect to the sea surface. That is,
+! "geo_strf_dyn_height_pc" is the geostrophic streamfunction for the
+! difference between the horizontal velocity at the pressure concerned, p,
+! and the horizontal velocity at the sea surface. Dynamic height anomaly
+! is the geostrophic streamfunction in an isobaric surface. The reference
+! values used for the specific volume anomaly are SA = SSO = 35.16504 g/kg
+! and CT = 0 deg C. The output values of geo_strf_dyn_height_pc are
+! given at the mid-point pressures, p_mid, of each layer in which SA and
+! CT are vertically piecewice constant (pc). This function calculates
+! enthalpy using the computationally-efficient 75-term expression for
+! specific volume of Roquet et al., (2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! delta_p = difference in sea pressure between the deep and [ dbar ]
+! shallow extents of each layer in which SA and CT
+! are vertically constant. delta_p must be positive.
+!
+! Note. sea pressure is absolute pressure minus 10.1325 dbar.
+!
+! geo_strf_dyn_height_pc = dynamic height anomaly [ m^2/s^2 ]
+! p_mid = mid-point pressure in each layer [ dbar ]
+!--------------------------------------------------------------------------
+*/
+double *
+gsw_geo_strf_dyn_height_pc(double *sa, double *ct, double *delta_p, int n_levels,
+ double *geo_strf_dyn_height_pc, double *p_mid)
+{
+ int i, np;
+ double *delta_h, delta_h_half, dyn_height_deep=0.0,
+ *p_deep, *p_shallow;
+
+ for (i=0; i<n_levels; i++)
+ if (delta_p[i] < 0.0)
+ return (NULL);
+
+ np = n_levels;
+ delta_h = malloc(3*np*sizeof (double));
+ p_deep = delta_h+np; p_shallow = p_deep+np;
+
+ for (i=0; i<np; i++) {
+ p_deep[i] = (i==0)? delta_p[0] : p_deep[i-1] + delta_p[i];
+ p_shallow[i] = p_deep[i] - delta_p[i];
+ delta_h[i] = gsw_enthalpy_diff(sa[i],ct[i],p_shallow[i],p_deep[i]);
+ }
+
+ for (i=0; i<np; i++) {
+ dyn_height_deep = dyn_height_deep - delta_h[i];
+ /* This is Phi minus Phi_0 of Eqn. (3.32.2) of IOC et al. (2010).*/
+ p_mid[i] = 0.5*(p_shallow[i] + p_deep[i]);
+ delta_h_half = gsw_enthalpy_diff(sa[i],ct[i],p_mid[i],p_deep[i]);
+
+ geo_strf_dyn_height_pc[i] = gsw_enthalpy_sso_0(p_mid[i]) +
+ dyn_height_deep + delta_h_half;
+ }
+ free(delta_h);
+ return (geo_strf_dyn_height_pc);
+}
+/*
+!==========================================================================
+function gsw_gibbs(ns,nt,np,sa,t,p)
+!==========================================================================
+!
+! seawater specific Gibbs free energy and derivatives up to order 2
+!
+! ns : order of s derivative
+! nt : order of t derivative
+! np : order of p derivative
+! sa : Absolute Salinity [g/kg]
+! t : temperature [deg C]
+! p : sea pressure [dbar]
+! -1
+! gsw_gibbs : specific Gibbs energy or its derivative [J kg ]
+*/
+double
+gsw_gibbs(int ns, int nt, int np, double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, z, g03, g08, return_value = 0.0;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*1e-4;
+
+ if (ns == 0 && nt == 0 && np == 0) {
+ g03 = 101.342743139674 + z*(100015.695367145 +
+ z*(-2544.5765420363 + z*(284.517778446287 +
+ z*(-33.3146754253611 + (4.20263108803084 -
+ 0.546428511471039*z)*z)))) +
+ y*(5.90578347909402 + z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 +
+ (28.9796526294175 - 2.13290083518327*z)*z))) +
+ y*(-12357.785933039 + z*(1455.0364540468 +
+ z*(-756.558385769359 + z*(273.479662323528 +
+ z*(-55.5604063817218 + 4.34420671917197*z)))) +
+ y*(736.741204151612 + z*(-672.50778314507 +
+ z*(499.360390819152 + z*(-239.545330654412 +
+ (48.8012518593872 - 1.66307106208905*z)*z))) +
+ y*(-148.185936433658 + z*(397.968445406972 +
+ z*(-301.815380621876 + (152.196371733841 -
+ 26.3748377232802*z)*z)) +
+ y*(58.0259125842571 + z*(-194.618310617595 +
+ z*(120.520654902025 + z*(-55.2723052340152 +
+ 6.48190668077221*z))) +
+ y*(-18.9843846514172 + y*(3.05081646487967 -
+ 9.63108119393062*z) +
+ z*(63.5113936641785 + z*(-22.2897317140459 +
+ 8.17060541818112*z))))))));
+
+ g08 = x2*(1416.27648484197 + z*(-3310.49154044839 +
+ z*(384.794152978599 + z*(-96.5324320107458 +
+ (15.8408172766824 - 2.62480156590992*z)*z))) +
+ x*(-2432.14662381794 + x*(2025.80115603697 +
+ y*(543.835333000098 + y*(-68.5572509204491 +
+ y*(49.3667694856254 + y*(-17.1397577419788 +
+ 2.49697009569508*y))) - 22.6683558512829*z) +
+ x*(-1091.66841042967 - 196.028306689776*y +
+ x*(374.60123787784 - 48.5891069025409*x +
+ 36.7571622995805*y) + 36.0284195611086*z) +
+ z*(-54.7919133532887 + (-4.08193978912261 -
+ 30.1755111971161*z)*z)) +
+ z*(199.459603073901 + z*(-52.2940909281335 +
+ (68.0444942726459 - 3.41251932441282*z)*z)) +
+ y*(-493.407510141682 + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-43.0664675978042 + z*(383.058066002476 +
+ z*(-54.1917262517112 + 25.6398487389914*z)) +
+ y*(-10.0227370861875 - 460.319931801257*z +
+ y*(0.875600661808945 + 234.565187611355*z))))) +
+ y*(168.072408311545 + z*(729.116529735046 +
+ z*(-343.956902961561 + z*(124.687671116248 +
+ z*(-31.656964386073 + 7.04658803315449*z)))) +
+ y*(880.031352997204 + y*(-225.267649263401 +
+ y*(91.4260447751259 + y*(-21.6603240875311 +
+ 2.13016970847183*y) +
+ z*(-297.728741987187 + (74.726141138756 -
+ 36.4872919001588*z)*z)) +
+ z*(694.244814133268 + z*(-204.889641964903 +
+ (113.561697840594 - 11.1282734326413*z)*z))) +
+ z*(-860.764303783977 + z*(337.409530269367 +
+ z*(-178.314556207638 + (44.2040358308 -
+ 7.92001547211682*z)*z))))));
+
+ if (sa > 0.0)
+ g08 = g08 + x2*(5812.81456626732 +
+ 851.226734946706*y)*log(x);
+
+ return_value = g03 + g08;
+
+ } else if (ns == 1 && nt == 0 && np == 0) {
+
+ g08 = 8645.36753595126 + z*(-6620.98308089678 +
+ z*(769.588305957198 + z*(-193.0648640214916 +
+ (31.6816345533648 - 5.24960313181984*z)*z))) +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y*(2175.341332000392 + y*(-274.2290036817964 +
+ y*(197.4670779425016 + y*(-68.5590309679152 +
+ 9.98788038278032*y))) - 90.6734234051316*z) +
+ x*(-5458.34205214835 - 980.14153344888*y +
+ x*(2247.60742726704 - 340.1237483177863*x +
+ 220.542973797483*y) + 180.142097805543*z) +
+ z*(-219.1676534131548 + (-16.32775915649044 -
+ 120.7020447884644*z)*z)) +
+ z*(598.378809221703 + z*(-156.8822727844005 +
+ (204.1334828179377 - 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 + z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(2.626801985426835 + 703.695562834065*z))))) +
+ y*(1187.3715515697959 + z*(1458.233059470092 +
+ z*(-687.913805923122 + z*(249.375342232496 +
+ z*(-63.313928772146 + 14.09317606630898*z)))) +
+ y*(1760.062705994408 + y*(-450.535298526802 +
+ y*(182.8520895502518 + y*(-43.3206481750622 +
+ 4.26033941694366*y) +
+ z*(-595.457483974374 + (149.452282277512 -
+ 72.9745838003176*z)*z)) +
+ z*(1388.489628266536 + z*(-409.779283929806 +
+ (227.123395681188 - 22.2565468652826*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 -
+ 15.84003094423364*z)*z)))));
+
+ if (sa > 0.0)
+ g08 = g08 + (11625.62913253464 + 1702.453469893412*y)*
+ log(x);
+ else
+ g08 = 0.0;
+
+ return_value = 0.5*gsw_sfac*g08;
+
+ } else if (ns == 0 && nt == 1 && np == 0) {
+
+ g03 = 5.90578347909402 + z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 +
+ (28.9796526294175 - 2.13290083518327*z)*z))) +
+ y*(-24715.571866078 + z*(2910.0729080936 +
+ z*(-1513.116771538718 + z*(546.959324647056 +
+ z*(-111.1208127634436 + 8.68841343834394*z)))) +
+ y*(2210.2236124548363 + z*(-2017.52334943521 +
+ z*(1498.081172457456 + z*(-718.6359919632359 +
+ (146.4037555781616 - 4.9892131862671505*z)*z))) +
+ y*(-592.743745734632 + z*(1591.873781627888 +
+ z*(-1207.261522487504 + (608.785486935364 -
+ 105.4993508931208*z)*z)) +
+ y*(290.12956292128547 + z*(-973.091553087975 +
+ z*(602.603274510125 + z*(-276.361526170076 +
+ 32.40953340386105*z))) +
+ y*(-113.90630790850321 + y*(21.35571525415769 -
+ 67.41756835751434*z) +
+ z*(381.06836198507096 + z*(-133.7383902842754 +
+ 49.023632509086724*z)))))));
+
+ g08 = x2*(168.072408311545 + z*(729.116529735046 +
+ z*(-343.956902961561 + z*(124.687671116248 +
+ z*(-31.656964386073 + 7.04658803315449*z)))) +
+ x*(-493.407510141682 + x*(543.835333000098 +
+ x*(-196.028306689776 + 36.7571622995805*x) +
+ y*(-137.1145018408982 + y*(148.10030845687618 +
+ y*(-68.5590309679152 + 12.4848504784754*y))) -
+ 22.6683558512829*z) + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-86.1329351956084 + z*(766.116132004952 +
+ z*(-108.3834525034224 + 51.2796974779828*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(3.50240264723578 + 938.26075044542*z)))) +
+ y*(1760.062705994408 + y*(-675.802947790203 +
+ y*(365.7041791005036 + y*(-108.30162043765552 +
+ 12.78101825083098*y) +
+ z*(-1190.914967948748 + (298.904564555024 -
+ 145.9491676006352*z)*z)) +
+ z*(2082.7344423998043 + z*(-614.668925894709 +
+ (340.685093521782 - 33.3848202979239*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 -
+ 15.84003094423364*z)*z)))));
+
+ if (sa > 0.0)
+ g08 = g08 + 851.226734946706*x2*log(x);
+
+ return_value = (g03 + g08)*0.025;
+
+ } else if (ns == 0 && nt == 0 && np == 1) {
+
+ g03 = 100015.695367145 + z*(-5089.1530840726 +
+ z*(853.5533353388611 + z*(-133.2587017014444 +
+ (21.0131554401542 - 3.278571068826234*z)*z))) +
+ y*(-270.983805184062 + z*(1552.307223226202 +
+ z*(-589.53765264366 + (115.91861051767 -
+ 10.664504175916349*z)*z)) +
+ y*(1455.0364540468 + z*(-1513.116771538718 +
+ z*(820.438986970584 + z*(-222.2416255268872 +
+ 21.72103359585985*z))) +
+ y*(-672.50778314507 + z*(998.720781638304 +
+ z*(-718.6359919632359 + (195.2050074375488 -
+ 8.31535531044525*z)*z)) +
+ y*(397.968445406972 + z*(-603.630761243752 +
+ (456.589115201523 - 105.4993508931208*z)*z) +
+ y*(-194.618310617595 + y*(63.5113936641785 -
+ 9.63108119393062*y +
+ z*(-44.5794634280918 + 24.511816254543362*z)) +
+ z*(241.04130980405 + z*(-165.8169157020456 +
+ 25.92762672308884*z)))))));
+
+ g08 = x2*(-3310.49154044839 + z*(769.588305957198 +
+ z*(-289.5972960322374 + (63.3632691067296 -
+ 13.1240078295496*z)*z)) +
+ x*(199.459603073901 + x*(-54.7919133532887 +
+ 36.0284195611086*x - 22.6683558512829*y +
+ (-8.16387957824522 - 90.52653359134831*z)*z) +
+ z*(-104.588181856267 + (204.1334828179377 -
+ 13.65007729765128*z)*z) +
+ y*(-175.292041186547 + (166.3847855603638 -
+ 88.449193048287*z)*z +
+ y*(383.058066002476 + y*(-460.319931801257 +
+ 234.565187611355*y) +
+ z*(-108.3834525034224 + 76.9195462169742*z)))) +
+ y*(729.116529735046 + z*(-687.913805923122 +
+ z*(374.063013348744 + z*(-126.627857544292 +
+ 35.23294016577245*z))) +
+ y*(-860.764303783977 + y*(694.244814133268 +
+ y*(-297.728741987187 + (149.452282277512 -
+ 109.46187570047641*z)*z) +
+ z*(-409.779283929806 + (340.685093521782 -
+ 44.5130937305652*z)*z)) +
+ z*(674.819060538734 + z*(-534.943668622914 +
+ (176.8161433232 - 39.600077360584095*z)*z)))));
+
+ return_value = (g03 + g08)*1.0e-8;
+
+ } else if (ns == 0 && nt == 2 && np == 0) {
+
+ g03 = -24715.571866078 + z*(2910.0729080936 + z*
+ (-1513.116771538718 + z*(546.959324647056 +
+ z*(-111.1208127634436 + 8.68841343834394*z)))) +
+ y*(4420.4472249096725 + z*(-4035.04669887042 +
+ z*(2996.162344914912 + z*(-1437.2719839264719 +
+ (292.8075111563232 - 9.978426372534301*z)*z))) +
+ y*(-1778.231237203896 + z*(4775.621344883664 +
+ z*(-3621.784567462512 + (1826.356460806092 -
+ 316.49805267936244*z)*z)) +
+ y*(1160.5182516851419 + z*(-3892.3662123519 +
+ z*(2410.4130980405 + z*(-1105.446104680304 +
+ 129.6381336154442*z))) +
+ y*(-569.531539542516 + y*(128.13429152494615 -
+ 404.50541014508605*z) +
+ z*(1905.341809925355 + z*(-668.691951421377 +
+ 245.11816254543362*z))))));
+
+ g08 = x2*(1760.062705994408 + x*(-86.1329351956084 +
+ x*(-137.1145018408982 + y*(296.20061691375236 +
+ y*(-205.67709290374563 + 49.9394019139016*y))) +
+ z*(766.116132004952 + z*(-108.3834525034224 +
+ 51.2796974779828*z)) +
+ y*(-60.136422517125 - 2761.9195908075417*z +
+ y*(10.50720794170734 + 2814.78225133626*z))) +
+ y*(-1351.605895580406 + y*(1097.1125373015109 +
+ y*(-433.20648175062206 + 63.905091254154904*y) +
+ z*(-3572.7449038462437 + (896.713693665072 -
+ 437.84750280190565*z)*z)) +
+ z*(4165.4688847996085 + z*(-1229.337851789418 +
+ (681.370187043564 - 66.7696405958478*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 -
+ 15.84003094423364*z)*z))));
+
+ return_value = (g03 + g08)*0.000625;
+
+ } else if (ns == 1 && nt == 0 && np == 1) {
+
+ g08 = -6620.98308089678 + z*(1539.176611914396 +
+ z*(-579.1945920644748 + (126.7265382134592 -
+ 26.2480156590992*z)*z)) +
+ x*(598.378809221703 + x*(-219.1676534131548 +
+ 180.142097805543*x - 90.6734234051316*y +
+ (-32.65551831298088 - 362.10613436539325*z)*z) +
+ z*(-313.764545568801 + (612.4004484538132 -
+ 40.95023189295384*z)*z) +
+ y*(-525.876123559641 + (499.15435668109143 -
+ 265.347579144861*z)*z +
+ y*(1149.174198007428 + y*(-1380.9597954037708 +
+ 703.695562834065*y) +
+ z*(-325.1503575102672 + 230.7586386509226*z)))) +
+ y*(1458.233059470092 + z*(-1375.827611846244 +
+ z*(748.126026697488 + z*(-253.255715088584 +
+ 70.4658803315449*z))) +
+ y*(-1721.528607567954 + y*(1388.489628266536 +
+ y*(-595.457483974374 + (298.904564555024 -
+ 218.92375140095282*z)*z) +
+ z*(-819.558567859612 + (681.370187043564 -
+ 89.0261874611304*z)*z)) +
+ z*(1349.638121077468 + z*(-1069.887337245828 +
+ (353.6322866464 - 79.20015472116819*z)*z))));
+
+ return_value = g08*gsw_sfac*0.5e-8;
+
+ } else if (ns == 0 && nt == 1 && np == 1) {
+
+ g03 = -270.983805184062 + z*(1552.307223226202 +
+ z*(-589.53765264366 + (115.91861051767 -
+ 10.664504175916349*z)*z)) +
+ y*(2910.0729080936 + z*(-3026.233543077436 +
+ z*(1640.877973941168 + z*(-444.4832510537744 +
+ 43.4420671917197*z))) +
+ y*(-2017.52334943521 + z*(2996.162344914912 +
+ z*(-2155.907975889708 + (585.6150223126464 -
+ 24.946065931335752*z)*z)) +
+ y*(1591.873781627888 + z*(-2414.523044975008 +
+ (1826.356460806092 - 421.9974035724832*z)*z) +
+ y*(-973.091553087975 + z*(1205.20654902025 +
+ z*(-829.084578510228 + 129.6381336154442*z)) +
+ y*(381.06836198507096 - 67.41756835751434*y +
+ z*(-267.4767805685508 + 147.07089752726017*z))))));
+
+ g08 = x2*(729.116529735046 + z*(-687.913805923122 +
+ z*(374.063013348744 + z*(-126.627857544292 +
+ 35.23294016577245*z))) +
+ x*(-175.292041186547 - 22.6683558512829*x +
+ (166.3847855603638 - 88.449193048287*z)*z +
+ y*(766.116132004952 + y*(-1380.9597954037708 +
+ 938.26075044542*y) +
+ z*(-216.7669050068448 + 153.8390924339484*z))) +
+ y*(-1721.528607567954 + y*(2082.7344423998043 +
+ y*(-1190.914967948748 + (597.809129110048 -
+ 437.84750280190565*z)*z) +
+ z*(-1229.337851789418 + (1022.055280565346 -
+ 133.5392811916956*z)*z)) +
+ z*(1349.638121077468 + z*(-1069.887337245828 +
+ (353.6322866464 - 79.20015472116819*z)*z))));
+
+ return_value = (g03 + g08)*2.5e-10;
+
+ } else if (ns == 1 && nt == 1 && np == 0) {
+
+ g08 = 1187.3715515697959 + z*(1458.233059470092 +
+ z*(-687.913805923122 + z*(249.375342232496 +
+ z*(-63.313928772146 + 14.09317606630898*z)))) +
+ x*(-1480.222530425046 + x*(2175.341332000392 +
+ x*(-980.14153344888 + 220.542973797483*x) +
+ y*(-548.4580073635929 + y*(592.4012338275047 +
+ y*(-274.2361238716608 + 49.9394019139016*y))) -
+ 90.6734234051316*z) +
+ z*(-525.876123559641 + (249.57717834054571 -
+ 88.449193048287*z)*z) +
+ y*(-258.3988055868252 + z*(2298.348396014856 +
+ z*(-325.1503575102672 + 153.8390924339484*z)) +
+ y*(-90.2046337756875 - 4142.8793862113125*z +
+ y*(10.50720794170734 + 2814.78225133626*z)))) +
+ y*(3520.125411988816 + y*(-1351.605895580406 +
+ y*(731.4083582010072 + y*(-216.60324087531103 +
+ 25.56203650166196*y) +
+ z*(-2381.829935897496 + (597.809129110048 -
+ 291.8983352012704*z)*z)) +
+ z*(4165.4688847996085 + z*(-1229.337851789418 +
+ (681.370187043564 - 66.7696405958478*z)*z))) +
+ z*(-3443.057215135908 + z*(1349.638121077468 +
+ z*(-713.258224830552 + (176.8161433232 -
+ 31.68006188846728*z)*z))));
+
+ if (sa > 0.0)
+ g08 = g08 + 1702.453469893412*log(x);
+
+ return_value = 0.5*gsw_sfac*0.025*g08;
+
+ } else if (ns == 2 && nt == 0 && np == 0) {
+
+ g08 = 2.0*(8103.20462414788 +
+ y*(2175.341332000392 + y*(-274.2290036817964 +
+ y*(197.4670779425016 + y*(-68.5590309679152 +
+ 9.98788038278032*y))) - 90.6734234051316*z) +
+ 1.5*x*(-5458.34205214835 - 980.14153344888*y +
+ (4.0/3.0)*x*(2247.60742726704 - 340.1237483177863*1.25*x +
+ 220.542973797483*y) + 180.142097805543*z) +
+ z*(-219.1676534131548 + (-16.32775915649044 -
+ 120.7020447884644*z)*z));
+
+ if (x > 0.0) {
+ g08 += (-7296.43987145382 + z*(598.378809221703 +
+ z*(-156.8822727844005 + (204.1334828179377 -
+ 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 + z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(2.626801985426835 + 703.695562834065*z)))))/x +
+ (11625.62913253464 + 1702.453469893412*y)/x2;
+ } else
+ g08 = 0.0;
+
+ return_value = 0.25*gsw_sfac*gsw_sfac*g08;
+
+ } else if (ns == 0 && nt == 0 && np == 2) {
+
+ g03 = -5089.1530840726 + z*(1707.1066706777221 +
+ z*(-399.7761051043332 + (84.0526217606168 -
+ 16.39285534413117*z)*z)) +
+ y*(1552.307223226202 + z*(-1179.07530528732 +
+ (347.75583155301 - 42.658016703665396*z)*z) +
+ y*(-1513.116771538718 + z*(1640.877973941168 +
+ z*(-666.7248765806615 + 86.8841343834394*z)) +
+ y*(998.720781638304 + z*(-1437.2719839264719 +
+ (585.6150223126464 - 33.261421241781*z)*z) +
+ y*(-603.630761243752 + (913.178230403046 -
+ 316.49805267936244*z)*z +
+ y*(241.04130980405 + y*(-44.5794634280918 +
+ 49.023632509086724*z) +
+ z*(-331.6338314040912 + 77.78288016926652*z))))));
+
+ g08 = x2*(769.588305957198 + z*(-579.1945920644748 +
+ (190.08980732018878 - 52.4960313181984*z)*z) +
+ x*(-104.588181856267 + x*(-8.16387957824522 -
+ 181.05306718269662*z) +
+ (408.2669656358754 - 40.95023189295384*z)*z +
+ y*(166.3847855603638 - 176.898386096574*z +
+ y*(-108.3834525034224 + 153.8390924339484*z))) +
+ y*(-687.913805923122 + z*(748.126026697488 +
+ z*(-379.883572632876 + 140.9317606630898*z)) +
+ y*(674.819060538734 + z*(-1069.887337245828 +
+ (530.4484299696 - 158.40030944233638*z)*z) +
+ y*(-409.779283929806 + y*(149.452282277512 -
+ 218.92375140095282*z) +
+ (681.370187043564 - 133.5392811916956*z)*z))));
+
+ return_value = (g03 + g08)*1e-16 ;
+
+ } else
+ return_value = GSW_INVALID_VALUE;
+
+ return (return_value);
+}
+/*
+! =========================================================================
+elemental function gsw_gibbs_ice (nt, np, t, p)
+! =========================================================================
+!
+! Ice specific Gibbs energy and derivatives up to order 2.
+!
+! nt = order of t derivative [ integers 0, 1 or 2 ]
+! np = order of p derivative [ integers 0, 1 or 2 ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+!
+! gibbs_ice = Specific Gibbs energy of ice or its derivatives.
+! The Gibbs energy (when nt = np = 0) has units of: [ J/kg ]
+! The temperature derivatives are output in units of:
+! [ (J/kg) (K)^(-nt) ]
+! The pressure derivatives are output in units of:
+! [ (J/kg) (Pa)^(-np) ]
+! The mixed derivatives are output in units of:
+! [ (J/kg) (K)^(-nt) (Pa)^(-np) ]
+! Note. The derivatives are taken with respect to pressure in Pa, not
+! withstanding that the pressure input into this routine is in dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_gibbs_ice (int nt, int np, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double dzi, g0, g0p, g0pp, sqrec_pt;
+ double complex r2, r2p, r2pp, g, sqtau_t1, sqtau_t2, tau,
+ tau_t1, tau_t2;
+ double s0 = -3.32733756492168e3;
+
+ tau = (t + gsw_t0)*rec_tt;
+
+ dzi = db2pa*p*rec_pt;
+
+ if (nt == 0 && np == 0) {
+
+ tau_t1 = tau/t1;
+ sqtau_t1 = tau_t1*tau_t1;
+ tau_t2 = tau/t2;
+ sqtau_t2 = tau_t2*tau_t2;
+
+ g0 = g00 + dzi*(g01 + dzi*(g02 + dzi*(g03 + g04*dzi)));
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ g = r1*(tau*clog((1.0 + tau_t1)/(1.0 - tau_t1))
+ + t1*(clog(1.0 - sqtau_t1) - sqtau_t1))
+ + r2*(tau*clog((1.0 + tau_t2)/(1.0 - tau_t2))
+ + t2*(clog(1.0 - sqtau_t2) - sqtau_t2));
+
+ return (g0 - tt*(s0*tau - creal(g)));
+
+ } else if (nt == 1 && np == 0) {
+
+ tau_t1 = tau/t1;
+ tau_t2 = tau/t2;
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ g = r1*(clog((1.0 + tau_t1)/(1.0 - tau_t1)) - 2.0*tau_t1)
+ + r2*(clog((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2);
+
+ return (-s0 + creal(g));
+
+ } else if (nt == 0 && np == 1) {
+
+ tau_t2 = tau/t2;
+ sqtau_t2 = tau_t2*tau_t2;
+
+ g0p = rec_pt*(g01 + dzi*(2.0*g02 + dzi*(3.0*g03 + 4.0*g04*dzi)));
+
+ r2p = rec_pt*(r21 + 2.0*r22*dzi);
+
+ g = r2p*(tau*clog((1.0 + tau_t2)/(1.0 - tau_t2))
+ + t2*(clog(1.0 - sqtau_t2) - sqtau_t2));
+
+ return (g0p + tt*creal(g));
+
+ } else if (nt == 1 && np == 1) {
+
+ tau_t2 = tau/t2;
+
+ r2p = rec_pt*(r21 + 2.0*r22*dzi) ;
+
+ g = r2p*(clog((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2);
+
+ return (creal(g));
+
+ } else if (nt == 2 && np == 0) {
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ g = r1*(1.0/(t1 - tau) + 1.0/(t1 + tau) - 2.0/t1)
+ + r2*(1.0/(t2 - tau) + 1.0/(t2 + tau) - 2.0/t2);
+
+ return (rec_tt*creal(g));
+
+ } else if (nt == 0 && np == 2) {
+
+ sqrec_pt = rec_pt*rec_pt;
+
+ tau_t2 = tau/t2;
+ sqtau_t2 = tau_t2*tau_t2;
+
+ g0pp = sqrec_pt*(2.0*g02 + dzi*(6.0*g03 + 12.0*g04*dzi));
+
+ r2pp = 2.0*r22*sqrec_pt;
+
+ g = r2pp*(tau*clog((1.0 + tau_t2)/(1.0 - tau_t2))
+ + t2*(clog(1.0 - sqtau_t2) - sqtau_t2));
+
+ return (g0pp + tt*creal(g));
+
+ } else
+ return (GSW_INVALID_VALUE);
+}
+/*
+! =========================================================================
+elemental function gsw_gibbs_ice_part_t (t, p)
+! =========================================================================
+!
+! part of the the first temperature derivative of Gibbs energy of ice
+! that is the outout is gibbs_ice(1,0,t,p) + S0
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+!
+! gibbs_ice_part_t = part of temperature derivative [ J kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_gibbs_ice_part_t(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double dzi, tau;
+ double complex g, tau_t1, tau_t2, r2;
+
+ tau = (t + gsw_t0)*rec_tt;
+
+ dzi = db2pa*p*rec_pt;
+
+ tau_t1 = tau/t1;
+ tau_t2 = tau/t2;
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ g = r1*(clog((1.0 + tau_t1)/(1.0 - tau_t1)) - 2.0*tau_t1)
+ + r2*(clog((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2);
+
+ return (creal(g));
+}
+/*
+! =========================================================================
+elemental function gsw_gibbs_ice_pt0 (pt0)
+! =========================================================================
+!
+! Part of the the first temperature derivative of Gibbs energy of ice
+! that is the outout is "gibbs_ice(1,0,pt0,0) + s0"
+!
+! pt0 = potential temperature with reference sea pressure of zero dbar
+! [ deg C ]
+!
+! gsw_gibbs_ice_pt0 = part of temperature derivative [ J kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_gibbs_ice_pt0(double pt0)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double tau;
+ double complex g, tau_t1, tau_t2;
+
+ tau = (pt0 + gsw_t0)*rec_tt;
+
+ tau_t1 = tau/t1;
+ tau_t2 = tau/t2;
+
+ g = r1*(clog((1.0 + tau_t1)/(1.0 - tau_t1)) - 2.0*tau_t1)
+ + r20*(clog((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2);
+
+ return (creal(g));
+}
+/*
+! =========================================================================
+elemental function gsw_gibbs_ice_pt0_pt0 (pt0)
+! =========================================================================
+!
+! The second temperature derivative of Gibbs energy of ice at the
+! potential temperature with reference sea pressure of zero dbar. That is
+! the output is gibbs_ice(2,0,pt0,0).
+!
+! pt0 = potential temperature with reference sea pressure of zero dbar
+! [ deg C ]
+!
+! gsw_gibbs_ice_pt0_pt0 = temperature second derivative at pt0
+!--------------------------------------------------------------------------
+*/
+double
+gsw_gibbs_ice_pt0_pt0(double pt0)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double tau;
+ double complex g;
+
+ tau = (pt0 + gsw_t0)*rec_tt;
+
+ g = r1*(1.0/(t1 - tau) + 1.0/(t1 + tau) - 2.0/t1)
+ + r20*(1.0/(t2 - tau) + 1.0/(t2 + tau) - 2.0/t2);
+
+ return (rec_tt*creal(g));
+}
+/*
+!==========================================================================
+function gsw_gibbs_pt0_pt0(sa,pt0)
+!==========================================================================
+
+! gibbs_tt at (sa,pt,0)
+!
+! sa : Absolute Salinity [g/kg]
+! pt0 : potential temperature [deg C]
+!
+! gibbs_pt0_pt0 : gibbs_tt at (sa,pt,0)
+*/
+double
+gsw_gibbs_pt0_pt0(double sa, double pt0)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, g03, g08;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = pt0*0.025;
+
+ g03 = -24715.571866078 +
+ y*(4420.4472249096725 +
+ y*(-1778.231237203896 +
+ y*(1160.5182516851419 +
+ y*(-569.531539542516 + y*128.13429152494615))));
+
+ g08 = x2*(1760.062705994408 + x*(-86.1329351956084 +
+ x*(-137.1145018408982 + y*(296.20061691375236 +
+ y*(-205.67709290374563 + 49.9394019139016*y))) +
+ y*(-60.136422517125 + y*10.50720794170734)) +
+ y*(-1351.605895580406 + y*(1097.1125373015109 +
+ y*(-433.20648175062206 + 63.905091254154904*y))));
+
+ return ((g03 + g08)*0.000625);
+}
+/*
+!==========================================================================
+function gsw_grav(lat,p)
+!==========================================================================
+
+! Calculates acceleration due to gravity as a function of latitude and as
+! a function of pressure in the ocean.
+!
+! lat = latitude in decimal degress north [ -90 ... +90 ]
+! p = sea pressure [ dbar ]
+!
+! grav : grav = gravitational acceleration [ m s^-2 ]
+*/
+double
+gsw_grav(double lat, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x, sin2, gs, z;
+
+ x = sin(lat*deg2rad); /* convert to radians */
+ sin2 = x*x;
+ gs = 9.780327*(1.0 + (5.2792e-3 + (2.32e-5*sin2))*sin2);
+
+ z = gsw_z_from_p(p,lat);
+
+ return (gs*(1.0 - gamma*z)); /* z is the height corresponding to p.
+ Note. In the ocean z is negative. */
+}
+/*
+!==========================================================================
+elemental function gsw_helmholtz_energy_ice (t, p)
+!==========================================================================
+!
+! Calculates the Helmholtz energy of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! Helmholtz_energy_ice = Helmholtz energy of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_helmholtz_energy_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (gsw_gibbs_ice(0,0,t,p)
+ - (db2pa*p + gsw_p0)*gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+function gsw_hill_ratio_at_sp2(t)
+!==========================================================================
+
+! Calculates the Hill ratio, which is the adjustment needed to apply for
+! Practical Salinities smaller than 2. This ratio is defined at a
+! Practical Salinity = 2 and in-situ temperature, t using PSS-78. The Hill
+! ratio is the ratio of 2 to the output of the Hill et al. (1986) formula
+! for Practical Salinity at the conductivity ratio, Rt, at which Practical
+! Salinity on the PSS-78 scale is exactly 2.
+!
+! t : in-situ temperature (ITS-90) [deg C]
+! hill_ratio_at_sp2 : Hill ratio [dimensionless]
+*/
+double
+gsw_hill_ratio_at_sp2(double t)
+{
+ GSW_SP_COEFFICIENTS;
+ double g0 = 2.641463563366498e-1, g1 = 2.007883247811176e-4,
+ g2 = -4.107694432853053e-6, g3 = 8.401670882091225e-8,
+ g4 = -1.711392021989210e-9, g5 = 3.374193893377380e-11,
+ g6 = -5.923731174730784e-13, g7 = 8.057771569962299e-15,
+ g8 = -7.054313817447962e-17, g9 = 2.859992717347235e-19,
+ sp2 = 2.0;
+ double t68, ft68, rtx0, dsp_drtx, sp_est, rtx, rtxm, x, part1, part2;
+ double sqrty, sp_hill_raw_at_sp2;
+
+ t68 = t*1.00024;
+ ft68 = (t68 - 15.0)/(1.0 + k*(t68 - 15.0));
+
+ /*!------------------------------------------------------------------------
+ **! Find the initial estimates of Rtx (Rtx0) and of the derivative dSP_dRtx
+ **! at SP = 2.
+ **!------------------------------------------------------------------------
+ */
+ rtx0 = g0 + t68*(g1 + t68*(g2 + t68*(g3 + t68*(g4 + t68*(g5
+ + t68*(g6 + t68*(g7 + t68*(g8 + t68*g9))))))));
+
+ dsp_drtx= a1 + (2*a2 + (3*a3 + (4*a4 + 5*a5*rtx0)*rtx0)*rtx0)*rtx0 +
+ ft68*(b1 + (2*b2 + (3*b3 + (4*b4 + 5*b5*rtx0)*rtx0)*rtx0)*rtx0);
+
+ /*!-------------------------------------------------------------------------
+ **! Begin a single modified Newton-Raphson iteration to find Rt at SP = 2.
+ **!-------------------------------------------------------------------------
+ */
+ sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx0)*rtx0)*rtx0)*rtx0)*rtx0
+ + ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx0)*rtx0)*rtx0)*
+ rtx0)*rtx0);
+ rtx = rtx0 - (sp_est - sp2)/dsp_drtx;
+ rtxm = 0.5*(rtx + rtx0);
+ dsp_drtx= a1 + (2*a2 + (3*a3 + (4*a4 + 5*a5*rtxm)*rtxm)*rtxm)*rtxm
+ + ft68*(b1 + (2*b2 + (3*b3 + (4*b4 + 5*b5*rtxm)*
+ rtxm)*rtxm)*rtxm);
+ rtx = rtx0 - (sp_est - sp2)/dsp_drtx;
+ /*
+ **! This is the end of one full iteration of the modified Newton-Raphson
+ **! iterative equation solver. The error in Rtx at this point is equivalent
+ **! to an error in SP of 9e-16 psu.
+ */
+
+ x = 400.0*rtx*rtx;
+ sqrty = 10.0*rtx;
+ part1 = 1.0 + x*(1.5 + x);
+ part2 = 1.0 + sqrty*(1.0 + sqrty*(1.0 + sqrty));
+ sp_hill_raw_at_sp2 = sp2 - a0/part1 - b0*ft68/part2;
+
+ return (2.0/sp_hill_raw_at_sp2);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ice_fraction_to_freeze_seawater (sa, ct, p, &
+ t_ih, sa_freeze, ct_freeze, w_ih)
+!==========================================================================
+!
+! Calculates the mass fraction of ice (mass of ice divided by mass of ice
+! plus seawater), which, when melted into seawater having (SA,CT,p) causes
+! the final dilute seawater to be at the freezing temperature. The other
+! outputs are the Absolute Salinity and Conservative Temperature of the
+! final diluted seawater.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! t_Ih = in-situ temperature of the ice at pressure p (ITS-90) [ deg C ]
+!
+! SA_freeze = Absolute Salinity of seawater after the mass fraction of
+! ice, ice_fraction, at temperature t_Ih has melted into the
+! original seawater, and the final mixture is at the freezing
+! temperature of seawater. [ g/kg ]
+!
+! CT_freeze = Conservative Temperature of seawater after the mass
+! fraction, w_Ih, of ice at temperature t_Ih has melted into
+! the original seawater, and the final mixture is at the
+! freezing temperature of seawater. [ deg C ]
+!
+! w_Ih = mass fraction of ice, having in-situ temperature t_Ih,
+! which, when melted into seawater at (SA,CT,p) leads to the
+! final diluted seawater being at the freezing temperature.
+! This output must be between 0 and 1. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ice_fraction_to_freeze_seawater(double sa, double ct, double p, double t_ih,
+ double *sa_freeze, double *ct_freeze, double *w_ih)
+{
+ int no_iter;
+ double ctf, ctf_mean, ctf_old, ctf_plus1, ctf_zero,
+ dfunc_dsaf, func, func_plus1, func_zero, h, h_ih,
+ saf, saf_mean, saf_old, tf, h_hat_sa, h_hat_ct, ctf_sa;
+ double sa0 = 0.0, saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*The seawater ct input is below the freezing temp*/
+ *sa_freeze = GSW_INVALID_VALUE;
+ *ct_freeze = *sa_freeze;
+ *w_ih = *sa_freeze;
+ return;
+ }
+
+ tf = gsw_t_freezing(sa0,p,saturation_fraction);
+ if (t_ih > tf) {
+ /*The input, t_Ih, exceeds the freezing temperature at sa = 0*/
+ *sa_freeze = GSW_INVALID_VALUE;
+ *ct_freeze = *sa_freeze;
+ *w_ih = *sa_freeze;
+ return;
+ }
+
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_ih,p);
+
+ ctf_zero = gsw_ct_freezing(sa0,p,saturation_fraction);
+ func_zero = sa*(gsw_enthalpy_ct_exact(sa0,ctf_zero,p) - h_ih);
+
+ ctf_plus1 = gsw_ct_freezing(sa+1.0,p,saturation_fraction);
+ func_plus1 = sa*(gsw_enthalpy_ct_exact(sa+1.0,ctf_plus1,p) - h)
+ - (h - h_ih);
+
+ saf = -(sa+1.0)*func_zero/(func_plus1 - func_zero); /*initial guess*/
+ ctf = gsw_ct_freezing(saf,p,saturation_fraction);
+ gsw_enthalpy_first_derivatives_ct_exact(saf,ctf,p,&h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(saf,p,1.0,&ctf_sa,NULL);
+
+ dfunc_dsaf = sa*(h_hat_sa + h_hat_ct*ctf_sa) - (h - h_ih);
+
+ for (no_iter = 1; no_iter <= 2; no_iter++) {
+ saf_old = saf;
+ ctf_old = ctf;
+ func = sa*(gsw_enthalpy_ct_exact(saf_old,ctf_old,p) - h)
+ - (saf_old - sa)*(h - h_ih);
+ saf = saf_old - func/dfunc_dsaf;
+ saf_mean = 0.5*(saf + saf_old);
+ ctf_mean = gsw_ct_freezing(saf_mean,p,saturation_fraction);
+ gsw_enthalpy_first_derivatives_ct_exact(saf_mean,ctf_mean,p,
+ &h_hat_sa, &h_hat_ct);
+ gsw_ct_freezing_first_derivatives(saf_mean,p,saturation_fraction,
+ &ctf_sa, NULL);
+ dfunc_dsaf = sa*(h_hat_sa + h_hat_ct*ctf_sa) - (h - h_ih);
+ saf = saf_old - func/dfunc_dsaf;
+ ctf = gsw_ct_freezing(saf,p,saturation_fraction);
+ }
+ /*
+ ! After these 2 iterations of this modified Newton-Raphson method, the
+ ! error in SA_freeze is less than 1.3d0x10^-13 g/kg, in CT_freeze is
+ ! less than ! 4x10^-13 deg C and in w_Ih is less than 3.8d0x10^-15
+ ! which represent machine precision for these calculations.
+ */
+
+ *sa_freeze = saf;
+ *ct_freeze = ctf;
+ *w_ih = (h - gsw_enthalpy_ct_exact(*sa_freeze,*ct_freeze,p))/(h - h_ih);
+}
+/*
+!==========================================================================
+function gsw_internal_energy(sa,ct,p)
+!==========================================================================
+
+! Calculates internal energy of seawater.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! internal_energy : internal_energy of seawater [J/kg]
+*/
+double
+gsw_internal_energy(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (gsw_enthalpy(sa,ct,p) - (gsw_p0 + db2pa*p)
+ *gsw_specvol(sa,ct,p));
+}
+/*
+!==========================================================================
+elemental function gsw_internal_energy_ice (t, p)
+!==========================================================================
+!
+! Calculates the specific internal energy of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! internal_energy_ice = specific internal energy (u) [J/kg]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_internal_energy_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (gsw_gibbs_ice(0,0,t,p)
+ - (gsw_t0 + t)*gsw_gibbs_ice(1,0,t,p)
+ - (db2pa*p + gsw_p0)*gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+subroutine gsw_ipv_vs_fnsquared_ratio(sa,ct,p,pref,nz,ipv_vs_fnsquared_ratio,p_mid)
+!==========================================================================
+
+! Calculates the ratio of the vertical gradient of potential density to
+! the vertical gradient of locally-referenced potential density. This
+! ratio is also the ratio of the planetary Isopycnal Potential Vorticity
+! (IPV) to f times N^2, hence the name for this variable,
+! IPV_vs_fNsquared_ratio (see Eqn. (3.20.5) of IOC et al. (2010)).
+! The reference sea pressure, p_ref, of the potential density surface must
+! have a constant value.
+!
+! IPV_vs_fNsquared_ratio is evaluated at the mid pressure between the
+! individual data points in the vertical.
+
+! sa : Absolute Salinity (a profile (length nz)) [g/kg]
+! ct : Conservative Temperature (a profile (length nz)) [deg C]
+! p : sea pressure (a profile (length nz)) [dbar]
+! p_ref : reference sea pressure of the potential density surface
+! ( i.e. absolute reference pressure - 10.1325 dbar ) [dbar]
+! nz : number of bottles
+! IPV_vs_fNsquared_ratio
+! : The ratio of the vertical gradient of potential density
+! referenced to p_ref, to the vertical gradient of locally-
+! referenced potential density. It is ouput on the same
+! vertical (M-1)xN grid as p_mid.
+! IPV_vs_fNsquared_ratio is dimensionless. [ unitless ]
+! p_mid : Mid pressure between p grid (length nz-1) [dbar]
+*/
+void
+gsw_ipv_vs_fnsquared_ratio(double *sa, double *ct, double *p, double p_ref,
+ int nz, double *ipv_vs_fnsquared_ratio, double *p_mid)
+{
+ int k;
+ double dsa, sa_mid, dct, ct_mid;
+ double alpha_mid, beta_mid;
+ double alpha_pref, beta_pref, numerator, denominator;
+
+ if (nz < 2) {
+ *p_mid = *ipv_vs_fnsquared_ratio = GSW_INVALID_VALUE;
+ return;
+ }
+ for (k = 0; k < nz-1; k++) {
+ dsa = (sa[k] - sa[k+1]);
+ dct = (ct[k] - ct[k+1]);
+ sa_mid = 0.5*(sa[k] + sa[k+1]);
+ ct_mid = 0.5*(ct[k] + ct[k+1]);
+ p_mid[k] = 0.5*(p[k] + p[k+1]);
+
+ alpha_mid = gsw_alpha(sa_mid,ct_mid,p_mid[k]);
+ beta_mid = gsw_beta(sa_mid,ct_mid,p_mid[k]);
+ alpha_pref = gsw_alpha(sa_mid,ct_mid,p_ref);
+ beta_pref = gsw_beta(sa_mid,ct_mid,p_ref);
+
+ numerator = dct*alpha_pref - dsa*beta_pref;
+ denominator = dct*alpha_mid - dsa*beta_mid;
+
+ if (denominator == 0.0)
+ ipv_vs_fnsquared_ratio[k] = GSW_INVALID_VALUE;
+ else
+ ipv_vs_fnsquared_ratio[k] = numerator/denominator;
+ }
+}
+/*
+!==========================================================================
+function gsw_kappa(sa,ct,p)
+!==========================================================================
+
+! Calculates isentropic compressibility of seawater. This function
+! has inputs of Absolute Salinity and Conservative Temperature. This
+! function uses the computationally-efficient expression for
+! specific volume in terms of SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! kappa : isentropic compressibility [1.0/Pa]
+*/
+double
+gsw_kappa(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v, v_p, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ v_p = c000
+ + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs))))
+ + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020
+ + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs)
+ + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201
+ + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs))
+ + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys)))
+ + z*( c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys)
+ + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z))));
+
+ return (-1e-8*v_p/v);
+}
+/*
+!==========================================================================
+elemental function gsw_kappa_const_t_ice (t, p)
+!==========================================================================
+!
+! Calculates isothermal compressibility of ice.
+! Note. This is the compressibility of ice AT CONSTANT IN-SITU
+! TEMPERATURE
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! kappa_const_t_ice = isothermal compressibility [ 1/Pa ]
+! Note. The output units are 1/Pa not 1/dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_kappa_const_t_ice(double t, double p)
+{
+ return (-gsw_gibbs_ice(0,2,t,p)/gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_kappa_ice (t, p)
+!==========================================================================
+!
+! Calculates the isentropic compressibility of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! kappa_ice = isentropic compressibility [ 1/Pa ]
+! Note. The output units are 1/Pa not 1/dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_kappa_ice(double t, double p)
+{
+ double gi_tp, gi_tt;
+
+ gi_tt = gsw_gibbs_ice(2,0,t,p);
+ gi_tp = gsw_gibbs_ice(1,1,t,p);
+
+ return ((gi_tp*gi_tp - gi_tt*gsw_gibbs_ice(0,2,t,p))/
+ (gsw_gibbs_ice(0,1,t,p)*gi_tt));
+}
+/*
+!==========================================================================
+function gsw_kappa_t_exact(sa,t,p)
+!==========================================================================
+
+! isentropic compressibility of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_kappa_t_exact : isentropic compressibility [1/Pa]
+*/
+double
+gsw_kappa_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1, n2=2;
+ double g_tt, g_tp;
+
+ g_tt = gsw_gibbs(n0,n2,n0,sa,t,p);
+ g_tp = gsw_gibbs(n0,n1,n1,sa,t,p);
+
+ return ((g_tp*g_tp - g_tt*gsw_gibbs(n0,n0,n2,sa,t,p)) /
+ (gsw_gibbs(n0,n0,n1,sa,t,p)*g_tt));
+}
+/*
+!==========================================================================
+function gsw_latentheat_evap_ct(sa,ct)
+!==========================================================================
+
+! Calculates latent heat, or enthalpy, of evaporation.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! latentheat_evaporation : latent heat of evaporation [J/kg]
+*/
+double
+gsw_latentheat_evap_ct(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double c0 = 2.499065844825125e6, c1 = -1.544590633515099e-1,
+ c2 = -9.096800915831875e4, c3 = 1.665513670736000e2,
+ c4 = 4.589984751248335e1, c5 = 1.894281502222415e1,
+ c6 = 1.192559661490269e3, c7 = -6.631757848479068e3,
+ c8 = -1.104989199195898e2, c9 = -1.207006482532330e3,
+ c10 = -3.148710097513822e3, c11 = 7.437431482069087e2,
+ c12 = 2.519335841663499e3, c13 = 1.186568375570869e1,
+ c14 = 5.731307337366114e2, c15 = 1.213387273240204e3,
+ c16 = 1.062383995581363e3, c17 = -6.399956483223386e2,
+ c18 = -1.541083032068263e3, c19 = 8.460780175632090e1,
+ c20 = -3.233571307223379e2, c21 = -2.031538422351553e2,
+ c22 = 4.351585544019463e1, c23 = -8.062279018001309e2,
+ c24 = 7.510134932437941e2, c25 = 1.797443329095446e2,
+ c26 = -2.389853928747630e1, c27 = 1.021046205356775e2;
+
+ double x, y;
+
+ x = sqrt(gsw_sfac*sa);
+ y = ct/40.0;
+
+ return (c0 + x*(c1 + c4*y + x*(c3
+ + y*(c7 + c12*y) + x*(c6 + y*(c11 + y*(c17 + c24*y))
+ + x*(c10 + y*(c16 + c23*y) + x*(c15 + c22*y + c21*x)))))
+ + y*(c2 + y*(c5 + c8*x + y*(c9 + x*(c13 + c18*x)
+ + y*(c14 + x*(c19 + c25*x) + y*(c20 + c26*x + c27*y))))));
+}
+/*
+!==========================================================================
+function gsw_latentheat_evap_t(sa,t)
+!==========================================================================
+!
+! Calculates latent heat, or enthalpy, of evaporation.
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+!
+! gsw_latentheat_evap_t : latent heat of evaporation [J/kg]
+*/
+double
+gsw_latentheat_evap_t(double sa, double t)
+{
+
+ double ct = gsw_ct_from_pt(sa,t);
+
+ return (gsw_latentheat_evap_ct(sa,ct));
+}
+/*
+!--------------------------------------------------------------------------
+! isobaric melting enthalpy and isobaric evaporation enthalpy
+!--------------------------------------------------------------------------
+
+!==========================================================================
+function gsw_latentheat_melting(sa,p)
+!==========================================================================
+
+! Calculates latent heat, or enthalpy, of melting.
+!
+! sa : Absolute Salinity [g/kg]
+! p : sea pressure [dbar]
+!
+! latentheat_melting : latent heat of melting [kg/m^3]
+*/
+double
+gsw_latentheat_melting(double sa, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double tf = gsw_t_freezing(sa,p,0.0);
+
+ return (1000.0*(gsw_chem_potential_water_t_exact(sa,tf,p)
+ - (gsw_t0 + tf)*gsw_t_deriv_chem_potential_water_t_exact(sa,tf,p))
+ - gsw_enthalpy_ice(tf,p));
+}
+/*
+!==========================================================================
+pure subroutine gsw_linear_interp_sa_ct (sa, ct, p, p_i, sa_i, ct_i)
+!==========================================================================
+! This function interpolates the cast with respect to the interpolating
+! variable p. This function finds the values of SA, CT at p_i on this cast.
+!
+! VERSION NUMBER: 3.05 (27th January 2015)
+!
+! This function was adapted from Matlab's interp1q.
+!==========================================================================
+*/
+void
+gsw_linear_interp_sa_ct(double *sa, double *ct, double *p, int np,
+ double *p_i, int npi, double *sa_i, double *ct_i)
+{
+ char *in_rng;
+ int *j, *k, *r, *jrev, *ki, imax_p, imin_p, i, n, m, ii;
+ double *xi, *xxi, u, max_p, min_p;
+
+ min_p = max_p = p[0];
+ imin_p = imax_p = 0;
+ for (i=1; i<np; i++) {
+ if (p[i] < min_p) {
+ min_p = p[i];
+ imin_p = i;
+ } else if (p[i] > max_p) {
+ max_p = p[i];
+ imax_p = i;
+ }
+ }
+ in_rng = malloc(npi*sizeof (char));
+ memset(in_rng, 0, npi*sizeof (char));
+ for (i=n=0; i<npi; i++) {
+ if (p_i[i] <= min_p) {
+ sa_i[i] = sa[imin_p];
+ ct_i[i] = ct[imin_p];
+ } else if (p_i[i] >= max_p) {
+ sa_i[i] = sa[imax_p];
+ ct_i[i] = ct[imax_p];
+ } else {
+ in_rng[i] = 1;
+ n++;
+ }
+ }
+ if (n==0)
+ return;
+
+ xi = malloc(n*sizeof (double));
+ k = malloc(3*n*sizeof (int)); ki = k+n; r = ki+n;
+ m = np + n;
+ xxi = malloc(m*sizeof (double));
+ j = malloc(2*m*sizeof (int)); jrev = j+m;
+
+ ii = 0;
+ for (i = 0; i<npi; i++) {
+ if (in_rng[i]) {
+ xi[ii] = p_i[i];
+ ki[ii] = i;
+ ii++;
+ }
+ }
+ free(in_rng);
+ /*
+ ** Note that the following operations on the index
+ ** vectors jrev and r depend on the sort utility
+ ** gsw_util_sort_real() consistently ordering the
+ ** sorting indexes either in ascending or descending
+ ** sequence for replicate values in the real vector.
+ */
+ gsw_util_sort_real(xi, n, k);
+ for (i = 0; i<np; i++)
+ xxi[i] = p[i];
+ for (i = 0; i<n; i++)
+ xxi[np+i] = xi[k[i]];
+ gsw_util_sort_real(xxi, m, j);
+
+ for (i = 0; i<m; i++)
+ jrev[j[i]] = i;
+ for (i = 0; i<n; i++)
+ r[k[i]] = jrev[np+i]-i-1;
+
+ for (i = 0; i<n; i++) {
+ u = (xi[i]-p[r[i]])/(p[r[i]+1]-p[r[i]]);
+ sa_i[ki[i]] = sa[r[i]] + (sa[r[i]+1]-sa[r[i]])*u;
+ ct_i[ki[i]] = ct[r[i]] + (ct[r[i]+1]-ct[r[i]])*u;
+ }
+ free(j); free(xxi); free(k); free(xi);
+}
+/*
+!==========================================================================
+elemental function gsw_melting_ice_equilibrium_sa_ct_ratio (sa, p)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when ice melts into seawater
+! with both the seawater and the seaice temperatures being almost equal to
+! the equilibrium freezing temperature. It is assumed that a small mass
+! of ice melts into an infinite mass of seawater. If indeed the
+! temperature of the seawater and the ice were both equal to the freezing
+! temperature, then no melting or freezing would occur an imbalance
+! between these three temperatures is needed for freezing or melting to
+! occur (the three temperatures being (1) the seawater temperature,
+! (2) the ice temperature, and (3) the freezing temperature.
+!
+! The output, melting_ice_equilibrium_SA_CT_ratio, is dSA/dCT rather than
+! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero
+! whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+!
+! melting_ice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT
+! changes when ice melts into seawater, with
+! the seawater and seaice being close to the
+! freezing temperature. [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_ice_equilibrium_sa_ct_ratio(double sa, double p)
+{
+ double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ t_seaice = gsw_t_freezing(sa,p,saturation_fraction);
+
+ h = gsw_enthalpy_ct_exact(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+ /*note that h_hat_ct is equal to cp0*(273.15 + t)/(273.15 + pt0)*/
+
+ return (sa*h_hat_ct/(h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_ice_equilibrium_sa_ct_ratio_poly (sa, p)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when ice melts into seawater
+! with both the seawater and the seaice temperatures being almost equal to
+! the equilibrium freezing temperature. It is assumed that a small mass
+! of ice melts into an infinite mass of seawater. If indeed the
+! temperature of the seawater and the ice were both equal to the freezing
+! temperature, then no melting or freezing would occur an imbalance
+! between these three temperatures is needed for freezing or melting to
+! occur (the three temperatures being (1) the seawater temperature,
+! (2) the ice temperature, and (3) the freezing temperature.
+!
+! The output, melting_ice_equilibrium_SA_CT_ratio, is dSA/dCT rather than
+! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero
+! whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+!
+! melting_ice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT
+! changes when ice melts into seawater, with
+! the seawater and seaice being close to the
+! freezing temperature. [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_ice_equilibrium_sa_ct_ratio_poly(double sa, double p)
+{
+ double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ t_seaice = gsw_t_freezing_poly(sa,p,saturation_fraction);
+
+ h = gsw_enthalpy(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+ /*note that h_hat_ct is equal to cp0*(273.15 + t)/(273.15 + pt0)*/
+
+ return (sa*h_hat_ct / (h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_melting_ice_into_seawater (sa, ct, p, w_ih, t_ih,&
+ sa_final, ct_final, w_ih_final)
+!==========================================================================
+!
+! Calculates the final Absolute Salinity, final Conservative Temperature
+! and final ice mass fraction that results when a given mass fraction of
+! ice melts and is mixed into seawater whose properties are (SA,CT,p).
+! This code takes the seawater to contain no dissolved air.
+!
+! When the mass fraction w_Ih_final is calculated as being a positive
+! value, the seawater-ice mixture is at thermodynamic equlibrium.
+!
+! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk,
+! is sufficiently large (i.e. sufficiently "warm") so that there is no ice
+! present in the final state. In this case the final state consists of
+! only seawater rather than being an equlibrium mixture of seawater and
+! ice which occurs when w_Ih_final is positive. Note that when
+! w_Ih_final = 0, the final seawater is not at the freezing temperature.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! w_Ih = mass fraction of ice, that is the mass of ice divided by the
+! sum of the masses of ice and seawater. That is, the mass of
+! ice divided by the mass of the final mixed fluid.
+! w_Ih must be between 0 and 1. [ unitless ]
+! t_Ih = the in-situ temperature of the ice (ITS-90) [ deg C ]
+!
+! SA_final = Absolute Salinity of the seawater in the final state,
+! whether or not any ice is present. [ g/kg ]
+! CT_final = Conservative Temperature of the seawater in the the final
+! state, whether or not any ice is present. [ deg C ]
+! w_Ih_final = mass fraction of ice in the final seawater-ice mixture.
+! If this ice mass fraction is positive, the system is at
+! thermodynamic equilibrium. If this ice mass fraction is
+! zero there is no ice in the final state which consists
+! only of seawater which is warmer than the freezing
+! temperature. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_melting_ice_into_seawater(double sa, double ct, double p, double w_ih,
+ double t_ih, double *sa_final, double *ct_final, double *w_ih_final)
+{
+ double ctf, h_bulk, sa_bulk, tf_ih;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*The seawater ct input is below the freezing temp*/
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ tf_ih = gsw_t_freezing(0.0,p,saturation_fraction) - 1e-6;
+ if (t_ih > tf_ih) {
+ /*
+ ! t_ih input exceeds the freezing temp.
+ ! The 1e-6 C buffer in the allowable
+ ! t_Ih is to ensure that there is some ice Ih in the sea ice.
+ */
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa_bulk = (1.0 - w_ih)*sa;
+ h_bulk = (1.0 - w_ih)*gsw_enthalpy_ct_exact(sa,ct,p)
+ + w_ih*gsw_enthalpy_ice(t_ih,p);
+ gsw_frazil_properties(sa_bulk,h_bulk,p,sa_final,ct_final,w_ih_final);
+ if (*sa_final > GSW_ERROR_LIMIT) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+}
+/*
+!==========================================================================
+elemental function gsw_melting_ice_sa_ct_ratio (sa, ct, p, t_ih)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when ice melts into seawater.
+! It is assumed that a small mass of ice melts into an infinite mass of
+! seawater. Because of the infinite mass of seawater, the ice will always
+! melt.
+!
+! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA.
+! This is done so that when SA = 0, the output, dSA/dCT is zero whereas
+! dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! t_Ih = the in-situ temperature of the ice (ITS-90) [ deg C ]
+!
+! melting_ice_SA_CT_ratio = the ratio of SA to CT changes when ice melts
+! into a large mass of seawater
+! [ g kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_ice_sa_ct_ratio(double sa, double ct, double p, double t_ih)
+{
+ double ctf, h, h_ih, tf, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*the seawater ct input is below the freezing temperature*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ tf = gsw_t_freezing(0.0,p,saturation_fraction);
+ if (t_ih > tf) {
+ /*t_ih exceeds the freezing temperature at sa = 0*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_ih,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ct,p,&h_hat_sa,&h_hat_ct);
+ /*Note that h_hat_CT is equal to cp0*(273.15 + t)/(273.15 + pt0)*/
+
+ return (sa*h_hat_ct/(h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_ice_sa_ct_ratio_poly (sa, ct, p, t_ih)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when ice melts into seawater.
+! It is assumed that a small mass of ice melts into an infinite mass of
+! seawater. Because of the infinite mass of seawater, the ice will always
+! melt.
+!
+! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA.
+! This is done so that when SA = 0, the output, dSA/dCT is zero whereas
+! dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! t_Ih = the in-situ temperature of the ice (ITS-90) [ deg C ]
+!
+! melting_ice_SA_CT_ratio = the ratio of SA to CT changes when ice melts
+! into a large mass of seawater
+! [ g kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_ice_sa_ct_ratio_poly(double sa, double ct, double p, double t_ih)
+{
+ double ctf, h, h_ih, tf, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*the seawater ct input is below the freezing temperature*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ tf = gsw_t_freezing_poly(0.0,p,saturation_fraction);
+ if (t_ih > tf) {
+ /*t_ih exceeds the freezing temperature at sa = 0*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ h = gsw_enthalpy(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_ih,p);
+ gsw_enthalpy_first_derivatives(sa,ct,p,&h_hat_sa,&h_hat_ct);
+ /*Note that h_hat_CT is equal to cp0*(273.15 + t)/(273.15 + pt0)*/
+
+ return (sa*h_hat_ct/(h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_seaice_equilibrium_sa_ct_ratio (sa, p)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when sea ice melts into
+! seawater with both the seawater and the sea ice temperatures being
+! almost equal to the equilibrium freezing temperature. It is assumed
+! that a small mass of seaice melts into an infinite mass of seawater. If
+! indeed the temperature of the seawater and the sea ice were both equal
+! to the freezing temperature, then no melting or freezing would occur; an
+! imbalance between these three temperatures is needed for freezing or
+! melting to occur (the three temperatures being (1) the seawater
+! temperature, (2) the sea ice temperature, and (3) the freezing
+! temperature.
+!
+! Note that the output of this function, dSA/dCT is independent of the
+! sea ice salinity, SA_seaice. That is, the output applies equally to
+! pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result
+! is proven in the manuscript, McDougall et al. (2013).
+!
+! The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather
+! than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is
+! zero whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! melting_seaice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT
+! changes when sea ice melts into seawater, with
+! the seawater and sea ice being close to the
+! freezing temperature. [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_seaice_equilibrium_sa_ct_ratio(double sa, double p)
+{
+ double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ t_seaice = gsw_t_freezing(sa,p,saturation_fraction);
+
+ h = gsw_enthalpy_ct_exact(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+
+ return (sa*h_hat_ct / (h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_seaice_equilibrium_sa_ct_ratio_poly (sa, p)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when sea ice melts into
+! seawater with both the seawater and the sea ice temperatures being
+! almost equal to the equilibrium freezing temperature. It is assumed
+! that a small mass of seaice melts into an infinite mass of seawater. If
+! indeed the temperature of the seawater and the sea ice were both equal
+! to the freezing temperature, then no melting or freezing would occur; an
+! imbalance between these three temperatures is needed for freezing or
+! melting to occur (the three temperatures being (1) the seawater
+! temperature, (2) the sea ice temperature, and (3) the freezing
+! temperature.
+!
+! Note that the output of this function, dSA/dCT is independent of the
+! sea ice salinity, SA_seaice. That is, the output applies equally to
+! pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result
+! is proven in the manuscript, McDougall et al. (2013).
+!
+! The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather
+! than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is
+! zero whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! melting_seaice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT
+! changes when sea ice melts into seawater, with
+! the seawater and sea ice being close to the
+! freezing temperature. [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_seaice_equilibrium_sa_ct_ratio_poly(double sa, double p)
+{
+ double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ t_seaice = gsw_t_freezing_poly(sa,p,saturation_fraction);
+
+ h = gsw_enthalpy(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+
+ return (sa*h_hat_ct / (h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_melting_seaice_into_seawater (sa, ct, p, &
+ w_seaice, sa_seaice, t_seaice, sa_final, ct_final)
+!==========================================================================
+!
+! Calculates the Absolute Salinity and Conservative Temperature that
+! results when a given mass of sea ice (or ice) melts and is mixed into a
+! known mass of seawater (whose properties are (SA,CT,p)).
+!
+! If the ice contains no salt (e.g. if it is of glacial origin), then the
+! input 'SA_seaice' should be set to zero.
+!
+! Ice formed at the sea surface (sea ice) typically contains between 2 g/kg
+! and 12 g/kg of salt (defined as the mass of salt divided by the mass of
+! ice Ih plus brine) and this programme returns NaN's if the input
+! SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero,
+! usually this would imply that the pressure p should be zero, as sea ice
+! only occurs near the sea surface. The code does not impose that p = 0
+! if SA_seaice is non-zero. Rather, this is left to the user.
+!
+! The Absolute Salinity, SA_brine, of the brine trapped in little pockets
+! in the sea ice, is in thermodynamic equilibrium with the ice Ih that
+! surrounds these pockets. As the sea ice temperature, t_seaice, may be
+! less than the freezing temperature, SA_brine is usually greater than the
+! Absolute Salinity of the seawater at the time and place when and where
+! the sea ice was formed. So usually SA_brine will be larger than SA.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! w_seaice = mass fraction of sea ice, that is the mass of sea ice
+! divided by the sum of the masses of sea ice and seawater.
+! That is, the mass of sea ice divided by the mass of the
+! final mixed fluid. w_seaice must be between 0 and 1.
+! [ unitless ]
+! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction of
+! salt in sea ice, expressed in g of salt per kg of sea ice.
+! [ g/kg ]
+! t_seaice = the in-situ temperature of the sea ice (or ice) (ITS-90)
+! [ deg C ]
+!
+! SA_final = Absolute Salinity of the mixture of the melted sea ice
+! (or ice) and the orignal seawater [ g/kg ]
+! CT_final = Conservative Temperature of the mixture of the melted
+! sea ice (or ice) and the orignal seawater [ deg C ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_melting_seaice_into_seawater(double sa, double ct, double p,
+ double w_seaice, double sa_seaice, double t_seaice,
+ double *sa_final, double *ct_final)
+{
+ double ctf, h, h_brine, h_final, h_ih, sa_brine, tf_sa_seaice;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*The seawater ct input is below the freezing temp*/
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ return;
+ }
+
+ tf_sa_seaice = gsw_t_freezing(sa_seaice,p,saturation_fraction)
+ - 1e-6;
+ if (t_seaice > tf_sa_seaice) {
+ /*
+ ! The 1e-6 C buffer in the allowable t_seaice is to ensure that there is
+ ! some ice Ih in the sea ice. Without this buffer, that is if t_seaice
+ ! is allowed to be exactly equal to tf_sa_seaice, the seaice is
+ ! actually 100% brine at Absolute Salinity of SA_seaice.
+ */
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ return;
+ }
+
+ sa_brine = gsw_sa_freezing_from_t(t_seaice,p,saturation_fraction);
+ if (sa_brine >= GSW_ERROR_LIMIT) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ return;
+ }
+ h_brine = gsw_enthalpy_t_exact(sa_brine,t_seaice,p);
+
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+
+ h_final = h - w_seaice*(h - h_ih - (h_brine - h_ih)*sa_seaice/sa_brine);
+
+ *sa_final = sa - w_seaice*(sa - sa_seaice);
+ /*
+ !ctf = gsw_ct_freezing(sa_final,p,saturation_fraction)
+ !
+ !if (h_final .lt. gsw_enthalpy_ct_exact(sa_final,ctf,p)) then
+ ! ! Melting this much seaice is not possible as it would result in
+ ! ! frozen seawater
+ ! sa_final = gsw_error_code(4,func_name)
+ ! ct_final = sa_final
+ ! return
+ !end if
+ */
+ *ct_final = gsw_ct_from_enthalpy_exact(*sa_final,h_final,p);
+ if (*ct_final > GSW_ERROR_LIMIT) {
+ *sa_final = *ct_final;
+ return;
+ }
+}
+/*
+!==========================================================================
+elemental function gsw_melting_seaice_sa_ct_ratio (sa, ct, p, sa_seaice, &
+ t_seaice)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when sea ice melts into seawater.
+! It is assumed that a small mass of sea ice melts into an infinite mass of
+! seawater. Because of the infinite mass of seawater, the sea ice will
+! always melt.
+!
+! Ice formed at the sea surface (sea ice) typically contains between 2 g/kg
+! and 12 g/kg of salt (defined as the mass of salt divided by the mass of
+! ice Ih plus brine) and this programme returns NaN's if the input
+! SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero,
+! usually this would imply that the pressure p should be zero, as sea ice
+! only occurs near the sea surface. The code does not impose that p = 0 if
+! SA_seaice is non-zero. Rather, this is left to the user.
+!
+! The Absolute Salinity, SA_brine, of the brine trapped in little pockets
+! in the sea ice, is in thermodynamic equilibrium with the ice Ih that
+! surrounds these pockets. As the seaice temperature, t_seaice, may be
+! less than the freezing temperature, SA_brine is usually greater than the
+! Absolute Salinity of the seawater at the time and place when and where
+! the sea ice was formed. So usually SA_brine will be larger than SA.
+!
+! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA.
+! This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is
+! zero whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction
+! of salt in sea ice expressed in g of salt per kg of
+! sea ice [ g/kg ]
+! t_seaice = the in-situ temperature of the sea ice (ITS-90) [ deg C ]
+!
+! melting_seaice_SA_CT_ratio = the ratio dSA/dCT of SA to CT changes when
+! sea ice melts into a large mass of seawater [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_seaice_sa_ct_ratio(double sa, double ct, double p,
+ double sa_seaice, double t_seaice)
+{
+ double ctf, delsa, h, h_brine, h_ih, sa_brine,
+ tf_sa_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ if (sa_seaice < 0.0 || sa_seaice > 15.0) {
+ return (GSW_INVALID_VALUE);
+ }
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) { /*the seawater ct input is below the freezing temp*/
+ return (GSW_INVALID_VALUE);
+ }
+ tf_sa_seaice = gsw_t_freezing(sa_seaice,p,saturation_fraction) - 1e-6;
+ if (t_seaice > tf_sa_seaice) { /*t_seaice exceeds the freezing sa*/
+ return (GSW_INVALID_VALUE);
+ }
+ /*
+ !-----------------------------------------------------------------------
+ !The 1e-6 C buffer in the allowable t_seaice is to ensure that there is
+ !some ice Ih in the sea ice. Without this buffer, that is if t_seaice
+ !is allowed to be exactly equal to tf_sa_seaice, the sea ice is actually
+ !100% brine at Absolute Salinity of SA_seaice.
+ !-----------------------------------------------------------------------
+ */
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ct,p,&h_hat_sa,&h_hat_ct);
+
+ sa_brine = gsw_sa_freezing_from_t(t_seaice,p,saturation_fraction);
+ if (sa_brine > GSW_ERROR_LIMIT) {
+ return (GSW_INVALID_VALUE);
+ }
+ h_brine = gsw_enthalpy_t_exact(sa_brine,t_seaice,p);
+ delsa = sa - sa_seaice;
+
+ return (h_hat_ct*delsa /
+ (h - h_ih - delsa*h_hat_sa - sa_seaice*(h_brine - h_ih)/sa_brine));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_seaice_sa_ct_ratio_poly (sa, ct, p, &
+ sa_seaice, t_seaice)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when sea ice melts into seawater.
+! It is assumed that a small mass of sea ice melts into an infinite mass of
+! seawater. Because of the infinite mass of seawater, the sea ice will
+! always melt.
+!
+! Ice formed at the sea surface (sea ice) typically contains between 2 g/kg
+! and 12 g/kg of salt (defined as the mass of salt divided by the mass of
+! ice Ih plus brine) and this programme returns NaN's if the input
+! SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero,
+! usually this would imply that the pressure p should be zero, as sea ice
+! only occurs near the sea surface. The code does not impose that p = 0 if
+! SA_seaice is non-zero. Rather, this is left to the user.
+!
+! The Absolute Salinity, SA_brine, of the brine trapped in little pockets
+! in the sea ice, is in thermodynamic equilibrium with the ice Ih that
+! surrounds these pockets. As the seaice temperature, t_seaice, may be
+! less than the freezing temperature, SA_brine is usually greater than the
+! Absolute Salinity of the seawater at the time and place when and where
+! the sea ice was formed. So usually SA_brine will be larger than SA.
+!
+! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA.
+! This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is
+! zero whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction
+! of salt in sea ice expressed in g of salt per kg of
+! sea ice [ g/kg ]
+! t_seaice = the in-situ temperature of the sea ice (ITS-90) [ deg C ]
+!
+! melting_seaice_SA_CT_ratio = the ratio dSA/dCT of SA to CT changes when
+! sea ice melts into a large mass of seawater [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_seaice_sa_ct_ratio_poly(double sa, double ct, double p,
+ double sa_seaice, double t_seaice)
+{
+ double ctf, delsa, h, h_brine, h_ih, sa_brine, ct_brine,
+ tf_sa_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ if (sa_seaice < 0.0 || sa_seaice > 15.0) {
+ return (GSW_INVALID_VALUE);
+ }
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ if (ct < ctf) { /*the seawater ct input is below the freezing temp*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ tf_sa_seaice = gsw_t_freezing_poly(sa_seaice,p,saturation_fraction)
+ - 1e-6;
+ if (t_seaice > tf_sa_seaice) { /*t_seaice exceeds the freezing sa*/
+ return (GSW_INVALID_VALUE);
+ }
+ /*
+ !-----------------------------------------------------------------------
+ !The 1e-6 C buffer in the allowable t_seaice is to ensure that there is
+ !some ice Ih in the sea ice. Without this buffer, that is if t_seaice
+ !is allowed to be exactly equal to tf_sa_seaice, the sea ice is actually
+ !100% brine at Absolute Salinity of SA_seaice.
+ !-----------------------------------------------------------------------
+ */
+ h = gsw_enthalpy(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives(sa,ct,p,&h_hat_sa,&h_hat_ct);
+
+ sa_brine = gsw_sa_freezing_from_t_poly(t_seaice,p,saturation_fraction);
+ if (sa_brine > GSW_ERROR_LIMIT) {
+ return (GSW_INVALID_VALUE);
+ }
+ ct_brine = gsw_ct_from_t(sa_brine,t_seaice,p);
+ h_brine = gsw_enthalpy(sa_brine,ct_brine,p);
+ delsa = sa - sa_seaice;
+
+ return (h_hat_ct*delsa /
+ (h - h_ih - delsa*h_hat_sa - sa_seaice*(h_brine - h_ih)/sa_brine));
+}
+/*
+!--------------------------------------------------------------------------
+! water column properties, based on the 48-term expression for density
+!--------------------------------------------------------------------------
+
+!==========================================================================
+subroutine gsw_nsquared(sa,ct,p,lat,nz,n2,p_mid)
+!==========================================================================
+
+! Calculates the buoyancy frequency squared (N^2)(i.e. the Brunt-Vaisala
+! frequency squared) at the mid pressure from the equation,
+!
+!
+! 2 2 beta.d(SA) - alpha.d(CT)
+! N = g .rho_local. -------------------------
+! dP
+!
+! The pressure increment, dP, in the above formula is in Pa, so that it is
+! 10^4 times the pressure increment dp in dbar.
+!
+! sa : Absolute Salinity (a profile (length nz)) [g/kg]
+! ct : Conservative Temperature (a profile (length nz)) [deg C]
+! p : sea pressure (a profile (length nz)) [dbar]
+! lat : latitude (a profile (length nz)) [deg N]
+! nz : number of levels in the profile
+! n2 : Brunt-Vaisala Frequency squared (length nz-1) [s^-2]
+! p_mid : Mid pressure between p grid (length nz-1) [dbar]
+*/
+void
+gsw_nsquared(double *sa, double *ct, double *p, double *lat, int nz,
+ double *n2, double *p_mid)
+{
+ GSW_TEOS10_CONSTANTS;
+ int k;
+ double p_grav, n_grav, grav_local, dsa, sa_mid, dct, ct_mid,
+ dp, rho_mid, alpha_mid, beta_mid;
+
+ if (nz < 2)
+ return;
+ p_grav = gsw_grav(lat[0],p[0]);
+ for (k = 0; k < nz-1; k++) {
+ n_grav = gsw_grav(lat[k+1],p[k+1]);
+ grav_local = 0.5*(p_grav + n_grav);
+ dsa = (sa[k+1] - sa[k]);
+ sa_mid = 0.5*(sa[k] + sa[k+1]);
+ dct = (ct[k+1] - ct[k]);
+ ct_mid = 0.5*(ct[k] + ct[k+1]);
+ dp = (p[k+1] - p[k]);
+ p_mid[k] = 0.5*(p[k] + p[k+1]);
+ rho_mid = gsw_rho(sa_mid,ct_mid,p_mid[k]);
+ alpha_mid = gsw_alpha(sa_mid,ct_mid,p_mid[k]);
+ beta_mid = gsw_beta(sa_mid,ct_mid,p_mid[k]);
+
+ n2[k] = (grav_local*grav_local)*(rho_mid/(db2pa*dp))*
+ (beta_mid*dsa - alpha_mid*dct);
+ p_grav = n_grav;
+ }
+}
+/*
+!==========================================================================
+function gsw_p_from_z(z,lat)
+!==========================================================================
+
+! Calculates the pressure p from height z
+!
+! z : height [m]
+! lat : latitude [deg]
+!
+! gsw_p_from_z : pressure [dbar]
+*/
+double
+gsw_p_from_z(double z, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double sinlat, sin2, gs, c1, p, df_dp, f, p_old, p_mid;
+
+ if (z > 5) return GSW_INVALID_VALUE;
+
+ sinlat = sin(lat*deg2rad);
+ sin2 = sinlat*sinlat;
+ gs = 9.780327*(1.0 + (5.2792e-3 + (2.32e-5*sin2))*sin2);
+
+ /* get the first estimate of p from Saunders (1981) */
+ c1 = 5.25e-3*sin2 + 5.92e-3;
+ p = -2.0*z/((1-c1) + sqrt((1-c1)*(1-c1) + 8.84e-6*z)) ;
+ /* end of the first estimate from Saunders (1981) */
+
+ df_dp = db2pa*gsw_specvol_sso_0(p); /* initial value of the derivative of f */
+
+ f = gsw_enthalpy_sso_0(p) + gs*(z - 0.5*gamma*(z*z));
+ /* - (geo_strf_dyn_height + sea_surface_geopotental); */
+ p_old = p;
+ p = p_old - f/df_dp;
+ p_mid = 0.5*(p + p_old);
+ df_dp = db2pa*gsw_specvol_sso_0(p_mid);
+ p = p_old - f/df_dp;
+
+ return p;
+}
+/*
+!==========================================================================
+elemental function gsw_pot_enthalpy_from_pt_ice (pt0_ice)
+!==========================================================================
+!
+! Calculates the potential enthalpy of ice from potential temperature of
+! ice (whose reference sea pressure is zero dbar).
+!
+! pt0_ice = potential temperature of ice (ITS-90) [ deg C ]
+!
+! gsw_pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pot_enthalpy_from_pt_ice(double pt0_ice)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double tau;
+ double complex h0_part, sqtau_t1, sqtau_t2;
+
+ tau = (pt0_ice + gsw_t0)*rec_tt;
+
+ sqtau_t1 = (tau/t1)*(tau/t1);
+ sqtau_t2 = (tau/t2)*(tau/t2);
+
+ h0_part = r1*t1*(clog(1.0 - sqtau_t1) + sqtau_t1)
+ + r20*t2*(clog(1.0 - sqtau_t2) + sqtau_t2);
+
+ return (g00 + tt*creal(h0_part));
+}
+/*
+!==========================================================================
+elemental function gsw_pot_enthalpy_from_pt_ice_poly (pt0_ice)
+!==========================================================================
+!
+! Calculates the potential enthalpy of ice from potential temperature of
+! ice (whose reference sea pressure is zero dbar). This is a
+! compuationally efficient polynomial fit to the potential enthalpy of
+! ice.
+!
+! pt0_ice = potential temperature of ice (ITS-90) [ deg C ]
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pot_enthalpy_from_pt_ice_poly(double pt0_ice)
+{
+ int iteration;
+ double df_dt, f, pot_enthalpy_ice,
+ pot_enthalpy_ice_mid, pot_enthalpy_ice_old,
+ p0 = -3.333601570157700e5,
+ p1 = 2.096693916810367e3,
+ p2 = 3.687110754043292,
+ p3 = 4.559401565980682e-4,
+ p4 = -2.516011957758120e-6,
+ p5 = -1.040364574632784e-8,
+ p6 = -1.701786588412454e-10,
+ p7 = -7.667191301635057e-13;
+
+ /*initial estimate of the potential enthalpy.*/
+ pot_enthalpy_ice = p0 + pt0_ice*(p1 + pt0_ice*(p2 + pt0_ice*(p3
+ + pt0_ice*(p4 + pt0_ice*(p5 + pt0_ice*(p6
+ + pt0_ice*p7))))));
+
+ df_dt = gsw_pt_from_pot_enthalpy_ice_poly_dh(pot_enthalpy_ice);
+
+ for (iteration = 1; iteration <= 5; iteration++) {
+ pot_enthalpy_ice_old = pot_enthalpy_ice;
+ f = gsw_pt_from_pot_enthalpy_ice_poly(pot_enthalpy_ice_old)
+ - pt0_ice;
+ pot_enthalpy_ice = pot_enthalpy_ice_old - f/df_dt;
+ pot_enthalpy_ice_mid = 0.5*(pot_enthalpy_ice+pot_enthalpy_ice_old);
+ df_dt = gsw_pt_from_pot_enthalpy_ice_poly_dh(pot_enthalpy_ice_mid);
+ pot_enthalpy_ice = pot_enthalpy_ice_old - f/df_dt;
+ }
+ /*
+ ! The error of this fit ranges between -6e-3 and 6e-3 J/kg over the
+ | potential temperature range of -100 to 2 deg C, or the potential
+ | enthalpy range of -5.7 x 10^5 to -3.3 x 10^5 J/kg.
+ */
+ return (pot_enthalpy_ice);
+}
+/*
+!==========================================================================
+elemental function gsw_pot_enthalpy_ice_freezing (sa, p)
+!==========================================================================
+!
+! Calculates the potential enthalpy of ice at which seawater freezes.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pot_enthalpy_ice_freezing = potential enthalpy of ice at freezing
+! of seawater [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pot_enthalpy_ice_freezing(double sa, double p)
+{
+ double pt0_ice, t_freezing;
+
+ t_freezing = gsw_t_freezing(sa,p,0.0) ;
+
+ pt0_ice = gsw_pt0_from_t_ice(t_freezing,p);
+
+ return (gsw_pot_enthalpy_from_pt_ice(pt0_ice));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_pot_enthalpy_ice_freezing_first_derivatives (sa, &
+ p, pot_enthalpy_ice_freezing_sa, pot_enthalpy_ice_freezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the potential enthalpy of ice at
+! which seawater freezes, with respect to Absolute Salinity SA and
+! pressure P (in Pa).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pot_enthalpy_ice_freezing_SA = the derivative of the potential enthalpy
+! of ice at freezing (ITS-90) with respect to Absolute
+! salinity at fixed pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! pot_enthalpy_ice_freezing_P = the derivative of the potential enthalpy
+! of ice at freezing (ITS-90) with respect to pressure
+! (in Pa) at fixed Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_pot_enthalpy_ice_freezing_first_derivatives(double sa, double p,
+ double *pot_enthalpy_ice_freezing_sa, double *pot_enthalpy_ice_freezing_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double cp_ihf, pt_icef, ratio_temp, tf, tf_p, tf_sa;
+ double saturation_fraction = 0.0;
+
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ pt_icef = gsw_pt0_from_t_ice(tf,p);
+ ratio_temp = (gsw_t0 + pt_icef)/(gsw_t0 + tf);
+
+ cp_ihf = gsw_cp_ice(tf,p);
+
+ if ((pot_enthalpy_ice_freezing_sa != NULL) &&
+ (pot_enthalpy_ice_freezing_p != NULL)) {
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tf_sa,&tf_p);
+ } else if (pot_enthalpy_ice_freezing_sa != NULL) {
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tf_sa, NULL);
+ } else if (pot_enthalpy_ice_freezing_p != NULL) {
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ NULL,&tf_p);
+ }
+
+ if (pot_enthalpy_ice_freezing_sa != NULL)
+ *pot_enthalpy_ice_freezing_sa = ratio_temp*cp_ihf*tf_sa;
+
+ if (pot_enthalpy_ice_freezing_p != NULL)
+ *pot_enthalpy_ice_freezing_p = ratio_temp*cp_ihf*tf_p
+ - (gsw_t0 + pt_icef)*gsw_gibbs_ice(1,1,tf,p);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(&
+ sa, p, pot_enthalpy_ice_freezing_sa, pot_enthalpy_ice_freezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the potential enthalpy of ice Ih at
+! which ice melts into seawater with Absolute Salinity SA and at pressure
+! p. This code uses the comptationally efficient polynomial fit of the
+! freezing potential enthalpy of ice Ih (McDougall et al., 2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pot_enthalpy_ice_freezing_SA = the derivative of the potential enthalpy
+! of ice at freezing (ITS-90) with respect to Absolute
+! salinity at fixed pressure [ (J/kg)/(g/kg) ] i.e. [ J/g ]
+!
+! pot_enthalpy_ice_freezing_P = the derivative of the potential enthalpy
+! of ice at freezing (ITS-90) with respect to pressure
+! (in Pa) at fixed Absolute Salinity [ (J/kg)/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(double sa, double p,
+ double *pot_enthalpy_ice_freezing_sa, double *pot_enthalpy_ice_freezing_p)
+{
+ double p_r, sa_r, x,
+ d1 = -1.249490228128056e4,
+ d2 = 1.336783910789822e4,
+ d3 = -4.811989517774642e4,
+ d4 = 8.044864276240987e4,
+ d5 = -7.124452125071862e4,
+ d6 = 2.280706828014839e4,
+ d7 = 0.315423710959628e3,
+ d8 = -3.592775732074710e2,
+ d9 = 1.644828513129230e3,
+ d10 = -4.809640968940840e3,
+ d11 = 2.901071777977272e3,
+ d12 = -9.218459682855746e2,
+ d13 = 0.379377450285737e3,
+ d14 = -2.672164989849465e3,
+ d15 = 5.044317489422632e3,
+ d16 = -2.631711865886377e3,
+ d17 = -0.160245473297112e3,
+ d18 = 4.029061696035465e2,
+ d19 = -3.682950019675760e2,
+
+ f1 = -2.034535061416256e4,
+ f2 = 0.315423710959628e3,
+ f3 = -0.239518382138314e3,
+ f4 = 0.822414256564615e3,
+ f5 = -1.923856387576336e3,
+ f6 = 0.967023925992424e3,
+ f7 = -0.263384562367307e3,
+ f8 = -5.051613740291480e3,
+ f9 = 7.587549005714740e2,
+ f10 = -3.562886653132620e3,
+ f11 = 5.044317489422632e3,
+ f12 = -2.105369492709102e3,
+ f13 = 6.387082316647800e2,
+ f14 = -4.807364198913360e2,
+ f15 = 8.058123392070929e2,
+ f16 = -5.524425029513641e2;
+
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ if (pot_enthalpy_ice_freezing_sa != NULL)
+ *pot_enthalpy_ice_freezing_sa =
+ (d1 + x*(d2 + x*(d3 + x*(d4 + x*(d5 + d6*x))))
+ + p_r*(d7 + x*(d8 + x*(d9 + x*(d10 + x*(d11 + d12*x))))
+ + p_r*(d13 + x*(d14 + x*(d15 + d16*x))
+ + p_r*(d17 + x*(d18 + d19*x)))))*1e-2;
+
+ if (pot_enthalpy_ice_freezing_p != NULL)
+ *pot_enthalpy_ice_freezing_p =
+ (f1 + sa_r*(f2 + x*(f3 + x*(f4 + x*(f5 + x*(f6 + f7*x)))))
+ + p_r*(f8 + sa_r*(f9 + x*(f10 + x*(f11 + f12*x)))
+ + p_r*(f13 + sa_r*(f14 + x*(f15 + f16*x)))))*1e-8;
+}
+/*
+!==========================================================================
+elemental function gsw_pot_enthalpy_ice_freezing_poly (sa, p)
+!==========================================================================
+!
+! Calculates the potential enthalpy of ice at which seawater freezes.
+! The error of this fit ranges between -2.5 and 1 J/kg with an rms of
+! 1.07, between SA of 0 and 120 g/kg and p between 0 and 10,000 dbar (the
+! error in the fit is between -0.7 and 0.7 with an rms of
+! 0.3, between SA of 0 and 120 g/kg and p between 0 and 5,000 dbar) when
+! compared with the potential enthalpy calculated from the exact in-situ
+! freezing temperature which is found by a Newton-Raphson iteration of the
+! equality of the chemical potentials of water in seawater and in ice.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pot_enthalpy_ice_freezing = potential enthalpy of ice at freezing
+! of seawater [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pot_enthalpy_ice_freezing_poly(double sa, double p)
+{
+ double p_r, sa_r, x,
+ c0 = -3.333548730778702e5,
+ c1 = -1.249490228128056e4,
+ c2 = 0.891189273859881e4,
+ c3 = -2.405994758887321e4,
+ c4 = 3.217945710496395e4,
+ c5 = -2.374817375023954e4,
+ c6 = 0.651630522289954e4,
+ c7 = -2.034535061416256e4,
+ c8 = -0.252580687014574e4,
+ c9 = 0.021290274388826e4,
+ c10 = 0.315423710959628e3,
+ c11 = -0.239518382138314e3,
+ c12 = 0.379377450285737e3,
+ c13 = 0.822414256564615e3,
+ c14 = -1.781443326566310e3,
+ c15 = -0.160245473297112e3,
+ c16 = -1.923856387576336e3,
+ c17 = 2.522158744711316e3,
+ c18 = 0.268604113069031e3,
+ c19 = 0.967023925992424e3,
+ c20 = -1.052684746354551e3,
+ c21 = -0.184147500983788e3,
+ c22 = -0.263384562367307e3;
+
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ return (c0 + sa_r*(c1 + x*(c2 + x*(c3 + x*(c4 + x*(c5 + c6*x)))))
+ + p_r*(c7 + p_r*(c8 + c9*p_r)) + sa_r*p_r*(c10 + p_r*(c12
+ + p_r*(c15 + c21*sa_r)) + sa_r*(c13 + c17*p_r + c19*sa_r)
+ + x*(c11 + p_r*(c14 + c18*p_r) + sa_r*(c16 + c20*p_r + c22*sa_r))));
+}
+/*
+!==========================================================================
+function gsw_pot_rho_t_exact(sa,t,p,p_ref)
+!==========================================================================
+
+! Calculates the potential density of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+! p_ref : reference sea pressure [dbar]
+!
+! gsw_pot_rho_t_exact : potential density [kg/m^3]
+*/
+double
+gsw_pot_rho_t_exact(double sa, double t, double p, double p_ref)
+{
+ double pt = gsw_pt_from_t(sa,t,p,p_ref);
+
+ return (gsw_rho_t_exact(sa,pt,p_ref));
+}
+/*
+!==========================================================================
+elemental function gsw_pressure_coefficient_ice (t, p)
+!==========================================================================
+!
+! Calculates pressure coefficient of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pressure_coefficient_ice = pressure coefficient of ice [Pa/K]
+! Note. The output units are Pa/K NOT dbar/K.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pressure_coefficient_ice(double t, double p)
+{
+ return (-gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(0,2,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_pressure_freezing_ct (sa, ct, saturation_fraction)
+!==========================================================================
+!
+! Calculates the pressure (in dbar) of seawater at the freezing
+! temperature. That is, the output is the pressure at which seawater,
+! with Absolute Salinity SA, Conservative Temperature CT, and with
+! saturation_fraction of dissolved air, freezes. If the input values are
+! such that there is no value of pressure in the range between 0 dbar and
+! 10,000 dbar for which seawater is at the freezing temperature, the
+! output, pressure_freezing, is put equal to NaN.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! pressure_freezing = sea pressure at which the seawater freezes [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pressure_freezing_ct(double sa, double ct, double saturation_fraction)
+{
+ GSW_TEOS10_CONSTANTS;
+ int i_iter, number_of_iterations = 3;
+ double ct_freezing_p0, ct_freezing_p10000, dctf_dp, f,
+ pf, pfm, pf_old, ctfreezing_p;
+
+ /*
+ ! rec_Pa2dbar is to have dCTf_dp in units of K/dbar rather than K/Pa
+
+ ! Find CT > CT_freezing_p0. If this is the case, the input CT value
+ ! represent seawater that will not be frozen at any positive p.
+ */
+ ct_freezing_p0 = gsw_ct_freezing(sa,0.0,saturation_fraction);
+ if (ct > ct_freezing_p0) {
+ return (GSW_INVALID_VALUE);
+ }
+ /*
+ ! Find CT < CT_freezing_p10000. If this is the case, the input CT value
+ ! represent seawater that is frozen even at p = 10,000 dbar.
+ */
+ ct_freezing_p10000 = gsw_ct_freezing(sa,1e4,saturation_fraction);
+ if (ct < ct_freezing_p10000) {
+ return (GSW_INVALID_VALUE);
+ }
+ /*
+ ! This is the initial (linear) guess of the freezing pressure, in dbar.
+ */
+ pf = rec_pa2db*(ct_freezing_p0 - ct)/
+ (ct_freezing_p0 - ct_freezing_p10000);
+
+ gsw_ct_freezing_first_derivatives(sa,pf,saturation_fraction,
+ NULL,&ctfreezing_p);
+ dctf_dp = rec_pa2db*ctfreezing_p;
+ /*
+ ! this dctf_dp is the initial value of the partial derivative of
+ ! ct_freezing with respect to pressure (in dbar) at fixed sa,
+ ! assuming that the saturation_fraction is zero.
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ pf_old = pf;
+ f = gsw_ct_freezing(sa,pf_old,saturation_fraction) - ct;
+ pf = pf_old - f/dctf_dp;
+ pfm = 0.5*(pf + pf_old);
+ gsw_ct_freezing_first_derivatives(sa,pfm,saturation_fraction,
+ NULL,&ctfreezing_p);
+ dctf_dp = rec_pa2db*ctfreezing_p;
+ pf = pf_old - f/dctf_dp;
+ }
+
+ if (gsw_sa_p_inrange(sa,pf))
+ return (pf);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+elemental function gsw_pt0_cold_ice_poly (pot_enthalpy_ice)
+!==========================================================================
+!
+! Calculates an initial estimate of pt0_ice when it is less than about
+! -100 deg C.
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!
+! pt0_cold_ice_poly = initial estimate of potential temperatur
+! of very cold ice in dgress C (not K) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt0_cold_ice_poly(double pot_enthalpy_ice)
+{
+ GSW_TEOS10_CONSTANTS;
+ double log_abs_theta0, log_h_diff,
+ /*h00 = gsw_enthalpy_ice(-gsw_t0,0)*/
+ h00 = -6.320202333358860e5,
+
+ s0 = 1.493103204647916,
+ s1 = 2.372788609320607e-1,
+ s2 = -2.014996002119374e-3,
+ s3 = 2.640600197732682e-6,
+ s4 = 3.134706016844293e-5,
+ s5 = 2.733592344937913e-6,
+ s6 = 4.726828010223258e-8,
+ s7 = -2.735193883189589e-9,
+ s8 = -8.547714991377670e-11;
+
+ log_h_diff = log(pot_enthalpy_ice - h00);
+
+ log_abs_theta0 = s0 + log_h_diff*(s1 + log_h_diff*(s2 + log_h_diff*(s3
+ + log_h_diff*(s4 + log_h_diff*(s5 + log_h_diff*(s6
+ + log_h_diff*(s7 + log_h_diff*s8)))))));
+
+ return (exp(log_abs_theta0) - gsw_t0);
+}
+/*
+!==========================================================================
+function gsw_pt0_from_t(sa,t,p)
+!==========================================================================
+
+! Calculates potential temperature with reference pressure, p_ref = 0 dbar.
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_pt0_from_t : potential temperature, p_ref = 0 [deg C]
+*/
+double
+gsw_pt0_from_t(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ int no_iter;
+ double pt0, pt0_old, dentropy, dentropy_dt;
+ double s1, true_entropy_part, pt0m;
+
+ s1 = sa/gsw_ups;
+
+ pt0 = t+p*( 8.65483913395442e-6 -
+ s1 * 1.41636299744881e-6 -
+ p * 7.38286467135737e-9 +
+ t *(-8.38241357039698e-6 +
+ s1 * 2.83933368585534e-8 +
+ t * 1.77803965218656e-8 +
+ p * 1.71155619208233e-10));
+
+ dentropy_dt = gsw_cp0/((gsw_t0+pt0)*(1.0-0.05*(1.0-sa/gsw_sso)));
+
+ true_entropy_part = gsw_entropy_part(sa,t,p);
+
+ for (no_iter=1; no_iter <= 2; no_iter++) {
+ pt0_old = pt0;
+ dentropy = gsw_entropy_part_zerop(sa,pt0_old) -
+ true_entropy_part;
+ pt0 = pt0_old - dentropy/dentropy_dt;
+ pt0m = 0.5*(pt0 + pt0_old);
+ dentropy_dt = -gsw_gibbs_pt0_pt0(sa,pt0m);
+ pt0 = pt0_old - dentropy/dentropy_dt;
+ }
+ return (pt0);
+}
+/*
+! =========================================================================
+elemental function gsw_pt0_from_t_ice (t, p)
+! =========================================================================
+!
+! Calculates potential temperature of ice Ih with a reference pressure of
+! 0 dbar, from in-situ temperature, t.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pt0_ice = potential temperature of ice Ih with reference pressure of
+! zero dbar (ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt0_from_t_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ int number_of_iterations;
+ double dentropy, dentropy_dt, pt0_ice,
+ pt0_ice_old, ptm_ice, true_entropy,
+ /*This is the starting polynomial for pt0 of ice Ih.*/
+ s1 = -2.256611570832386e-4,
+ s2 = -6.045305921314694e-7,
+ s3 = 5.546699019612661e-9,
+ s4 = 1.795030639186685e-11,
+ s5 = 1.292346094030742e-9,
+
+ p1 = -2.259745637898635e-4,
+ p2 = 1.486236778150360e-9,
+ p3 = 6.257869607978536e-12,
+ p4 = -5.253795281359302e-7,
+ p5 = 6.752596995671330e-9,
+ p6 = 2.082992190070936e-11,
+
+ q1 = -5.849191185294459e-15,
+ q2 = 9.330347971181604e-11,
+ q3 = 3.415888886921213e-13,
+ q4 = 1.064901553161811e-12,
+ q5 = -1.454060359158787e-10,
+ q6 = -5.323461372791532e-13;
+
+ true_entropy = -gsw_gibbs_ice_part_t(t,p);
+
+ if (t < -45.0 && t > -273.0) {
+
+ pt0_ice = t + p*(p1 + p*(p2 + p3*t) + t*(p4 + t*(p5 + p6*t)));
+
+ if (pt0_ice < -gsw_t0) pt0_ice = -gsw_t0;
+ /*
+ ! we add 0.05d0 to the initial estimate of pt0_ice at
+ ! temps less than -273 to ensure that it is never less than -273.15.
+ */
+ if (pt0_ice < -273.0) pt0_ice = pt0_ice + 0.05;
+
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(pt0_ice);
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ pt0_ice_old = pt0_ice;
+ dentropy = -gsw_gibbs_ice_pt0(pt0_ice_old) - true_entropy;
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt0_ice + pt0_ice_old);
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(ptm_ice);
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ }
+
+ } else {
+
+ pt0_ice = t + p*(s1 + t*(s2 + t*(s3 + t*s4)) + s5*p);
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(pt0_ice);
+
+ pt0_ice_old = pt0_ice;
+ dentropy = -gsw_gibbs_ice_pt0(pt0_ice_old) - true_entropy;
+
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt0_ice + pt0_ice_old);
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(ptm_ice);
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+
+ }
+
+ if (pt0_ice < -273.0) {
+
+ pt0_ice = t + p*(q1 + p*(q2 + q3*t) + t*(q4 + t*(q5 + q6*t)));
+ /*
+ ! add 0.01d0 to the initial estimate of pt_ice used in the
+ ! derivative to ensure that it is never less than -273.15d0
+ ! because the derivative approaches zero at absolute zero.
+ */
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(pt0_ice+0.01);
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ pt0_ice_old = pt0_ice;
+ dentropy = -gsw_gibbs_ice_pt0(pt0_ice_old) - true_entropy;
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt0_ice + pt0_ice_old);
+ /*
+ ! add 0.01d0 to the estimate of ptm_ice for temperatures less
+ | than -273 to ensure that they are never less than -273.15d0
+ ! because the derivative approaches zero at absolute zero and
+ ! the addition of 0.01d0 degrees c ensures that when we divide
+ ! by the derivatve in the modified newton routine the function
+ ! does not blow up.
+ */
+ ptm_ice = ptm_ice + 0.01;
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(ptm_ice);
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ }
+
+ }
+ /*
+ ! For temperatures less than -273.1 degsC the maximum error is less
+ ! than 2x10^-7 degsC. For temperatures between -273.1 and 273 the
+ ! maximum error is less than 8x10^-8 degsC, and for temperatures
+ ! greater than -273 degsC the ! maximum error is 1.5x10^-12 degsC.
+ ! These errors are over the whole ocean depths with p varying between
+ ! 0 and 10,000 dbar, while the in-situ temperature varied independently
+ ! between -273.15 and +2 degsC.
+ */
+
+ return (pt0_ice);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_pt_first_derivatives (sa, ct, pt_sa, pt_ct)
+! =========================================================================
+!
+! Calculates the following two partial derivatives of potential temperature
+! (the regular potential temperature whose reference sea pressure is 0 dbar)
+! (1) pt_SA, the derivative with respect to Absolute Salinity at
+! constant Conservative Temperature, and
+! (2) pt_CT, the derivative with respect to Conservative Temperature at
+! constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! pt_SA = The derivative of potential temperature with respect to
+! Absolute Salinity at constant Conservative Temperature.
+! [ K/(g/kg)]
+! pt_CT = The derivative of potential temperature with respect to
+! Conservative Temperature at constant Absolute Salinity.
+! pt_CT is dimensionless. [ unitless ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_pt_first_derivatives (double sa, double ct, double *pt_sa, double *pt_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double abs_pt, ct_pt, ct_sa, pt, pr0 = 0.0;
+ int n0=0, n1=1, n2=2;
+
+ pt = gsw_pt_from_ct(sa,ct);
+ abs_pt = (gsw_t0 + pt);
+
+ ct_pt = -(abs_pt*gsw_gibbs(n0,n2,n0,sa,pt,pr0))/gsw_cp0;
+
+ if (pt_sa != NULL) {
+
+ ct_sa = (gsw_gibbs(n1,n0,n0,sa,pt,pr0) -
+ abs_pt*gsw_gibbs(n1,n1,n0,sa,pt,pr0))/gsw_cp0;
+
+ *pt_sa = -ct_sa/ct_pt;
+
+ }
+
+ if (pt_ct != NULL)
+ *pt_ct = 1.0/ct_pt;
+}
+/*
+!==========================================================================
+function gsw_pt_from_ct(sa,ct)
+!==========================================================================
+
+! potential temperature of seawater from conservative temperature
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_pt_from_ct : potential temperature with [deg C]
+! reference pressure of 0 dbar
+*/
+double
+gsw_pt_from_ct(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double a5ct, b3ct, ct_factor, pt_num, pt_recden, ct_diff;
+ double pt, pt_old, ptm, dpt_dct, s1;
+ double a0 = -1.446013646344788e-2,
+ a1 = -3.305308995852924e-3,
+ a2 = 1.062415929128982e-4,
+ a3 = 9.477566673794488e-1,
+ a4 = 2.166591947736613e-3,
+ a5 = 3.828842955039902e-3,
+ b0 = 1.000000000000000e0,
+ b1 = 6.506097115635800e-4,
+ b2 = 3.830289486850898e-3,
+ b3 = 1.247811760368034e-6;
+
+ s1 = sa/gsw_ups;
+
+ a5ct = a5*ct;
+ b3ct = b3*ct;
+
+ ct_factor = (a3 + a4*s1 + a5ct);
+ pt_num = a0 + s1*(a1 + a2*s1) + ct*ct_factor;
+ pt_recden = 1.0/(b0 + b1*s1 + ct*(b2 + b3ct));
+ pt = pt_num*pt_recden;
+
+ dpt_dct = pt_recden*(ct_factor + a5ct - (b2 + b3ct + b3ct)*pt);
+
+ /*
+ ** Start the 1.5 iterations through the modified Newton-Raphson
+ ** iterative method.
+ */
+
+ ct_diff = gsw_ct_from_pt(sa,pt) - ct;
+ pt_old = pt;
+ pt = pt_old - ct_diff*dpt_dct;
+ ptm = 0.5*(pt + pt_old);
+
+ dpt_dct = -gsw_cp0/((ptm + gsw_t0)*gsw_gibbs_pt0_pt0(sa,ptm));
+
+ pt = pt_old - ct_diff*dpt_dct;
+ ct_diff = gsw_ct_from_pt(sa,pt) - ct;
+ pt_old = pt;
+ return (pt_old - ct_diff*dpt_dct);
+}
+/*
+! =========================================================================
+elemental function gsw_pt_from_entropy (sa, entropy)
+! =========================================================================
+!
+! Calculates potential temperature with reference pressure p_ref = 0 dbar
+! and with entropy as an input variable.
+!
+! SA = Absolute Salinity [ g/kg ]
+! entropy = specific entropy [ deg C ]
+!
+! pt = potential temperature [ deg C ]
+! with reference sea pressure (p_ref) = 0 dbar.
+! Note. The reference sea pressure of the output, pt, is zero dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_entropy(double sa, double entropy)
+{
+ GSW_TEOS10_CONSTANTS;
+ int number_of_iterations;
+ double c, dentropy, dentropy_dt, ent_sa, part1, part2, pt, ptm,
+ pt_old;
+
+ /*Find the initial value of pt*/
+ part1 = 1.0 - sa/gsw_sso;
+ part2 = 1.0 - 0.05*part1;
+ ent_sa = (gsw_cp0/gsw_t0)*part1*(1.0 - 1.01*part1);
+ c = (entropy - ent_sa)*(part2/gsw_cp0);
+ pt = gsw_t0*(exp(c) - 1.0);
+ dentropy_dt = gsw_cp0/((gsw_t0 + pt)*part2);
+
+ for (number_of_iterations = 1; number_of_iterations <= 2;
+ number_of_iterations++) {
+ pt_old = pt;
+ dentropy = gsw_entropy_from_pt(sa,pt_old) - entropy;
+ pt = pt_old - dentropy/dentropy_dt;
+ ptm = 0.5*(pt + pt_old);
+ dentropy_dt = -gsw_gibbs_pt0_pt0(sa,ptm);
+ pt = pt_old - dentropy/dentropy_dt;
+ }
+ /*
+ ! Maximum error of 2.2x10^-6 degrees C for one iteration.
+ ! Maximum error is 1.4x10^-14 degrees C for two iterations
+ ! (two iterations is the default, "for Number_of_iterations = 1:2").
+ */
+ return (pt);
+}
+/*
+!==========================================================================
+elemental function gsw_pt_from_pot_enthalpy_ice (pot_enthalpy_ice)
+!==========================================================================
+!
+! Calculates the potential temperature of ice from the potential enthalpy
+! of ice. The reference sea pressure of both the potential temperature
+! and the potential enthalpy is zero dbar.
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!
+! pt0_ice = potential temperature of ice (ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_pot_enthalpy_ice(double pot_enthalpy_ice)
+{
+ int iteration;
+ double df_dt, f, mod_pot_enthalpy_ice, pt0_cold_ice, recip_df_dt,
+ pt0_cold_ice_old, pt0_ice, pt0_ice_old, ptm_cold_ice, ptm_ice;
+ double h00 = -6.320202333358860e5, /*gsw_enthalpy_ice(-gsw_t0,0)*/
+ p0 = 0.0;
+
+ mod_pot_enthalpy_ice = max(pot_enthalpy_ice,h00);
+
+ if (mod_pot_enthalpy_ice >= -5.1e5) {
+ /*
+ ! For input potential enthalpies greater than -5.1e-5, the above part of
+ ! the code gives the output potential temperature of ice accurate to
+ | 1e-13 degrees C.
+ */
+ pt0_ice = gsw_pt_from_pot_enthalpy_ice_poly(mod_pot_enthalpy_ice);
+ /*
+ ! The variable "df_dt" below is the derivative of the above polynomial
+ ! with respect to pot_enthalpy_ice. This is the initial value of the
+ ! derivative of the function f.
+ */
+ recip_df_dt =
+ gsw_pt_from_pot_enthalpy_ice_poly_dh(mod_pot_enthalpy_ice);
+
+ pt0_ice_old = pt0_ice;
+ f = gsw_pot_enthalpy_from_pt_ice(pt0_ice_old)
+ - mod_pot_enthalpy_ice;
+ pt0_ice = pt0_ice_old - f*recip_df_dt;
+ ptm_ice = 0.5*(pt0_ice + pt0_ice_old);
+ recip_df_dt = 1.0/gsw_cp_ice(ptm_ice,p0);
+ pt0_ice = pt0_ice_old - f*recip_df_dt;
+
+ } else {
+ /*
+ ! For pot_enthalpy_ice < -5.1e5 (or pt0_ice less than about -100 deg c)
+ ! these temperatures are less than those found in nature on planet earth
+ */
+ pt0_cold_ice = gsw_pt0_cold_ice_poly(mod_pot_enthalpy_ice);
+
+ df_dt = gsw_cp_ice(pt0_cold_ice+0.02,p0);
+ /*
+ ! the heat capacity, cp, is
+ ! evaluated at 0.02 c greater than usual in order to avoid stability
+ ! issues and to ensure convergence near zero absolute temperature.
+ */
+ for (iteration = 1; iteration <= 6; iteration++) {
+ pt0_cold_ice_old = pt0_cold_ice;
+ f = gsw_pot_enthalpy_from_pt_ice(pt0_cold_ice_old)
+ - mod_pot_enthalpy_ice;
+ pt0_cold_ice = pt0_cold_ice_old - f/df_dt;
+ ptm_cold_ice = 0.5*(pt0_cold_ice + pt0_cold_ice_old);
+ df_dt = gsw_cp_ice(ptm_cold_ice+0.02,p0);
+ /*note the extra 0.02 c here as well*/
+ pt0_cold_ice = pt0_cold_ice_old - f/df_dt;
+ }
+ pt0_ice = pt0_cold_ice;
+ }
+/*
+!The potential temerature has a maximum error as listed in the table below.
+!
+! potential temerature error (deg C) | @ potential temerature (deg C)
+!--------------------------------------|--------------------------------
+! 0.012 | -273.15 to -273.12
+! 4 x 10^-4 | -232.12 to -273.0
+! 2.5 x 10^-6 | -273
+! 7 x 10^-9 | -272
+! 3.7 x 10^-10 | -270
+! 6 x 10^-11 | -268
+! 2.5 x 10^11 | -266
+! 3 x 10^-12 | -260
+! 7 x 10^-13 | -250
+! 2.2 x 10^-13 | -220
+! 1.7 x 10^-13 | >= -160
+!
+! Note. The above errors in each temperature range are machine precissions
+! for this calculation.
+*/
+
+ return (pt0_ice);
+}
+/*
+!==========================================================================
+elemental function gsw_pt_from_pot_enthalpy_ice_poly (pot_enthalpy_ice)
+!==========================================================================
+!
+! Calculates the potential temperature of ice (whose reference sea
+! pressure is zero dbar) from the potential enthalpy of ice. This is a
+! compuationally efficient polynomial fit to the potential enthalpy of
+! ice.
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!
+! pt0_ice = potential temperature of ice (ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_pot_enthalpy_ice_poly(double pot_enthalpy_ice)
+{
+ double q0 = 2.533588268773218e2,
+ q1 = 2.594351081876611e-3,
+ q2 = 1.765077810213815e-8,
+ q3 = 7.768070564290540e-14,
+ q4 = 2.034842254277530e-19,
+ q5 = 3.220014531712841e-25,
+ q6 = 2.845172809636068e-31,
+ q7 = 1.094005878892950e-37;
+/*
+! The error of this fit ranges between -5e-5 and 2e-4 deg C over the potential
+! temperature range of -100 to 2 deg C, or the potential enthalpy range of
+! -5.7 x 10^5 to -3.3 x 10^5 J/kg.
+*/
+ return (q0
+ + pot_enthalpy_ice*(q1 + pot_enthalpy_ice*(q2 + pot_enthalpy_ice*(q3
+ + pot_enthalpy_ice*(q4 + pot_enthalpy_ice*(q5 + pot_enthalpy_ice*(q6
+ + pot_enthalpy_ice*q7)))))));
+}
+/*
+!==========================================================================
+elemental function gsw_pt_from_pot_enthalpy_ice_poly_dh (pot_enthalpy_ice)
+!==========================================================================
+!
+! Calculates the derivative of potential temperature of ice with respect
+! to potential enthalpy. This is based on the compuationally-efficient
+! polynomial fit to the potential enthalpy of ice.
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!
+! dpt0_ice_dh = derivative of potential temperature of ice
+! with respect to potential enthalpy [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_pot_enthalpy_ice_poly_dh(double pot_enthalpy_ice)
+{
+ double q1 = 2.594351081876611e-3,
+ p2 = 3.530155620427630e-8,
+ p3 = 2.330421169287162e-13,
+ p4 = 8.139369017110120e-19,
+ p5 = 1.610007265856420e-24,
+ p6 = 1.707103685781641e-30,
+ p7 = 7.658041152250651e-37;
+
+ return (q1 + pot_enthalpy_ice*(p2 + pot_enthalpy_ice*(p3
+ + pot_enthalpy_ice*(p4 + pot_enthalpy_ice*(p5 + pot_enthalpy_ice*(p6
+ + pot_enthalpy_ice*p7))))));
+}
+/*
+!==========================================================================
+function gsw_pt_from_t(sa,t,p,p_ref)
+!==========================================================================
+
+! Calculates potential temperature of seawater from in-situ temperature
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+! p_ref : reference sea pressure [dbar]
+!
+! gsw_pt_from_t : potential temperature [deg C]
+*/
+double
+gsw_pt_from_t(double sa, double t, double p, double p_ref)
+{
+ GSW_TEOS10_CONSTANTS;
+ int n0=0, n2=2, no_iter;
+ double s1, pt, ptm, pt_old, dentropy, dentropy_dt,
+ true_entropy_part;
+
+ s1 = sa/gsw_ups;
+ pt = t+(p-p_ref)*( 8.65483913395442e-6 -
+ s1 * 1.41636299744881e-6 -
+ (p+p_ref) * 7.38286467135737e-9 +
+ t *(-8.38241357039698e-6 +
+ s1 * 2.83933368585534e-8 +
+ t * 1.77803965218656e-8 +
+ (p+p_ref) * 1.71155619208233e-10));
+
+ dentropy_dt = gsw_cp0/((gsw_t0 + pt)*(1.0-0.05*(1.0 - sa/gsw_sso)));
+ true_entropy_part = gsw_entropy_part(sa,t,p);
+ for (no_iter=1; no_iter <= 2; no_iter++) {
+ pt_old = pt;
+ dentropy = gsw_entropy_part(sa,pt_old,p_ref) - true_entropy_part;
+ pt = pt_old - dentropy/dentropy_dt;
+ ptm = 0.5*(pt + pt_old);
+ dentropy_dt = -gsw_gibbs(n0,n2,n0,sa,ptm,p_ref);
+ pt = pt_old - dentropy/dentropy_dt;
+ }
+ return (pt);
+}
+/*
+! =========================================================================
+elemental function gsw_pt_from_t_ice (t, p, p_ref)
+! =========================================================================
+!
+! Calculates potential temperature of ice Ih with the general reference
+! pressure, p_ref, from in-situ temperature, t.
+!
+! A faster gsw routine exists if p_ref is indeed zero dbar. This routine
+! is "gsw_pt0_from_t_ice(t,p)".
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! p_ref = reference pressure [ dbar ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_t_ice(double t, double p, double p_ref)
+{
+ GSW_TEOS10_CONSTANTS;
+ int number_of_iterations;
+ double dentropy, dentropy_dt, dp,
+ pt_ice, pt_ice_old, ptm_ice, true_entropy,
+
+ p1 = -2.259745637898635e-4,
+ p2 = 1.486236778150360e-9,
+ p3 = 6.257869607978536e-12,
+ p4 = -5.253795281359302e-7,
+ p5 = 6.752596995671330e-9,
+ p6 = 2.082992190070936e-11,
+
+ q1 = -5.849191185294459e-15,
+ q2 = 9.330347971181604e-11,
+ q3 = 3.415888886921213e-13,
+ q4 = 1.064901553161811e-12,
+ q5 = -1.454060359158787e-10,
+ q6 = -5.323461372791532e-13;
+ /*This is the starting polynomial for pt of ice Ih.*/
+
+ dp = p - p_ref;
+
+ pt_ice = t + dp*(p1 + (p + p_ref)*(p2 + p3*t) + t*(p4 + t*(p5 + p6*t)));
+
+ if (pt_ice < -gsw_t0) pt_ice = -gsw_t0;
+
+ if (pt_ice < -273.0) pt_ice = pt_ice + 0.05;
+ /*
+ ! we add 0.05 to the initial estimate of pt_ice at temps less than
+ ! -273 to ensure that it is never less than -273.15.
+ */
+ dentropy_dt = -gsw_gibbs_ice(2,0,pt_ice,p_ref);
+
+ true_entropy = -gsw_gibbs_ice_part_t(t,p);
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ pt_ice_old = pt_ice;
+ dentropy = -gsw_gibbs_ice_part_t(pt_ice_old,p_ref) - true_entropy;
+ pt_ice = pt_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt_ice + pt_ice_old);
+ dentropy_dt = -gsw_gibbs_ice(2,0,ptm_ice,p_ref);
+ pt_ice = pt_ice_old - dentropy/dentropy_dt;
+ }
+
+ if (pt_ice < -273.0) {
+
+ pt_ice = t + (p - p_ref)*(q1 + (p + p_ref)*(q2 + q3*t)
+ + t*(q4 + t*(q5 + q6*t)));
+
+ dentropy_dt = -gsw_gibbs_ice(2,0,pt_ice+0.01,p_ref);
+ /*
+ ! we add 0.01 to the initial estimate of pt_ice used in the derivative
+ ! to ensure that it is never less than -273.15 because the derivative
+ ! approaches zero at absolute zero.
+ */
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ pt_ice_old = pt_ice;
+ dentropy = -gsw_gibbs_ice_part_t(pt_ice_old,p_ref)
+ - true_entropy;
+ pt_ice = pt_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt_ice + pt_ice_old);
+ ptm_ice = ptm_ice + 0.01;
+ dentropy_dt = -gsw_gibbs_ice(2,0,ptm_ice,p_ref);
+ pt_ice = pt_ice_old - dentropy/dentropy_dt;
+ }
+
+ }
+/*
+! For temperatures less than -273.1 degsC the maximum error is less than
+! 2x10^-7 degsC. For temperatures between -273.1 and 273 the maximum error
+! is less than 8x10^-8 degsC, and for temperatures greater than -273 degsC the
+! maximum error is 1.5x10^-12 degsC. These errors are over the whole
+! ocean depths with both p and pref varying independently between 0 and
+! 10,000 dbar, while the in-situ temperature varied independently between
+! -273.15 and +2 degsC.
+*/
+ return (pt_ice);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_pt_second_derivatives (sa, ct, pt_sa_sa, &
+ pt_sa_ct, pt_ct_ct)
+! =========================================================================
+!
+! Calculates the following three second-order derivatives of potential
+! temperature (the regular potential temperature which has a reference
+! sea pressure of 0 dbar),
+! (1) pt_SA_SA, the second derivative with respect to Absolute Salinity
+! at constant Conservative Temperature,
+! (2) pt_SA_CT, the derivative with respect to Conservative Temperature
+! and Absolute Salinity, and
+! (3) pt_CT_CT, the second derivative with respect to Conservative
+! Temperature at constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! pt_SA_SA = The second derivative of potential temperature (the
+! regular potential temperature which has reference sea
+! pressure of 0 dbar) with respect to Absolute Salinity
+! at constant Conservative Temperature.
+! pt_SA_SA has units of: [ K/((g/kg)^2) ]
+! pt_SA_CT = The derivative of potential temperature with respect
+! to Absolute Salinity and Conservative Temperature.
+! pt_SA_CT has units of: [ 1/(g/kg) ]
+! pt_CT_CT = The second derivative of potential temperature (the
+! regular one with p_ref = 0 dbar) with respect to
+! Conservative Temperature at constant SA.
+! pt_CT_CT has units of: [ 1/K ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_pt_second_derivatives (double sa, double ct, double *pt_sa_sa,
+ double *pt_sa_ct, double *pt_ct_ct)
+{
+ double ct_l, ct_u, pt_ct_l, pt_ct_u, pt_sa_l, pt_sa_u, sa_l, sa_u,
+ dct = 1e-2, dsa = 1e-3;
+
+ if (pt_sa_sa != NULL) {
+
+ if ((sa_l = sa - dsa) < 0.0)
+ sa_l = 0.0;
+ sa_u = sa + dsa;
+
+ gsw_pt_first_derivatives(sa_l,ct,&pt_sa_l,NULL);
+ gsw_pt_first_derivatives(sa_u,ct,&pt_sa_u,NULL);
+
+ *pt_sa_sa = (pt_sa_u - pt_sa_l)/(sa_u - sa_l);
+
+ }
+
+ if (pt_sa_ct != NULL || pt_ct_ct != NULL) {
+
+ ct_l = ct - dct;
+ ct_u = ct + dct;
+
+ if ((pt_sa_ct != NULL) && (pt_ct_ct != NULL)) {
+
+ gsw_pt_first_derivatives(sa,ct_l,&pt_sa_l,&pt_ct_l);
+ gsw_pt_first_derivatives(sa,ct_u,&pt_sa_u,&pt_ct_u);
+
+ *pt_sa_ct = (pt_sa_u - pt_sa_l)/(ct_u - ct_l);
+ *pt_ct_ct = (pt_ct_u - pt_ct_l)/(ct_u - ct_l);
+
+ } else if ((pt_sa_ct != NULL) && (pt_ct_ct == NULL)) {
+
+ gsw_pt_first_derivatives(sa,ct_l,&pt_sa_l,NULL);
+ gsw_pt_first_derivatives(sa,ct_u,&pt_sa_u,NULL);
+
+ *pt_sa_ct = (pt_sa_u - pt_sa_l)/(ct_u - ct_l);
+
+ } else if ((pt_sa_ct == NULL) && (pt_ct_ct != NULL)) {
+
+ gsw_pt_first_derivatives(sa,ct_l,NULL,&pt_ct_l);
+ gsw_pt_first_derivatives(sa,ct_u,NULL,&pt_ct_u);
+
+ *pt_ct_ct = (pt_ct_u - pt_ct_l)/(ct_u - ct_l);
+ }
+ }
+}
+/*
+!--------------------------------------------------------------------------
+! density and enthalpy, based on the 48-term expression for density
+!--------------------------------------------------------------------------
+
+!==========================================================================
+function gsw_rho(sa,ct,p)
+!==========================================================================
+
+! Calculates in-situ density from Absolute Salinity and Conservative
+! Temperature, using the computationally-efficient expression for
+! specific volume in terms of SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho : in-situ density [kg/m]
+*/
+double
+gsw_rho(double sa, double ct, double p)
+{
+ return (1.0/gsw_specvol(sa,ct,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_rho_alpha_beta (sa, ct, p, rho, alpha, beta)
+!==========================================================================
+!
+! Calculates in-situ density, the appropiate thermal expansion coefficient
+! and the appropriate saline contraction coefficient of seawater from
+! Absolute Salinity and Conservative Temperature. This function uses the
+! computationally-efficient expression for specific volume in terms of
+! SA, CT and p (Roquet et al., 2014).
+!
+! Note that potential density (pot_rho) with respect to reference pressure
+! p_ref is obtained by calling this function with the pressure argument
+! being p_ref as in [pot_rho, ~, ~] = gsw_rho_alpha_beta(SA,CT,p_ref).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho = in-situ density [ kg/m ]
+! alpha = thermal expansion coefficient [ 1/K ]
+! with respect to Conservative Temperature
+! beta = saline (i.e. haline) contraction [ kg/g ]
+! coefficient at constant Conservative Temperature
+!--------------------------------------------------------------------------
+*/
+void
+gsw_rho_alpha_beta (double sa, double ct, double p, double *rho, double *alpha,
+ double *beta)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v, v_ct_part, v_sa_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ if (rho != NULL)
+ *rho = 1.0/v;
+
+ if (alpha != NULL) {
+
+ v_ct_part = a000 + xs*(a100 + xs*(a200 + xs*(a300
+ + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ *alpha = 0.025*v_ct_part/v;
+
+ }
+
+ if (beta != NULL) {
+
+ v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300
+ + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ *beta = -v_sa_part*0.5*gsw_sfac/(v*xs);
+
+ }
+}
+/*
+!==========================================================================
+subroutine gsw_rho_first_derivatives(sa, ct, p, drho_dsa, drho_dct, drho_dp)
+!==========================================================================
+
+! Calculates the three (3) partial derivatives of in situ density with
+! respect to Absolute Salinity, Conservative Temperature and pressure.
+! Note that the pressure derivative is done with respect to pressure in
+! Pa, not dbar. This function uses the computationally-efficient expression
+! for specific volume in terms of SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+! drho_dsa : partial derivatives of density [kg^2/(g m^3)]
+! with respect to Absolute Salinity
+! drho_dct : partial derivatives of density [kg/(K m^3)]
+! with respect to Conservative Temperature
+! drho_dp : partial derivatives of density [kg/(Pa m^3)]
+! with respect to pressure in Pa
+*/
+void
+gsw_rho_first_derivatives(double sa, double ct, double p,
+ double *drho_dsa, double *drho_dct, double *drho_dp)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double rho2, v_ct, v_p, v_sa, xs, ys, z, v;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ rho2 = pow(1.0/v, 2.0);
+
+ if (drho_dsa != NULL) {
+
+ v_sa = b000
+ + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ *drho_dsa = -rho2*0.5*gsw_sfac*v_sa/xs;
+ }
+
+ if (drho_dct != NULL) {
+
+ v_ct = a000
+ + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ *drho_dct = -rho2*0.025*v_ct;
+ }
+
+ if (drho_dp != NULL) {
+
+ v_p = c000
+ + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs))))
+ + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020
+ + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs)
+ + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201
+ + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs))
+ + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys)))
+ + z*(c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys)
+ + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z))));
+
+ *drho_dp = 1e-4*pa2db*-rho2*v_p;
+ }
+
+ return;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_rho_first_derivatives_wrt_enthalpy (sa, ct, p, &
+ rho_sa, rho_h)
+! =========================================================================
+!
+! Calculates two first-order derivatives of specific volume (v).
+! Note that this function uses the using the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho_SA = The first derivative of rho with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! rho_h = The first derivative of rho with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_rho_first_derivatives_wrt_enthalpy (double sa, double ct, double p,
+ double *rho_sa, double *rho_h)
+{
+ double rec_v2, v_h=0.0, v_sa;
+
+ if ((rho_sa != NULL) && (rho_h != NULL)) {
+
+ gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,&v_sa,&v_h);
+
+ } else if (rho_sa != NULL) {
+
+ gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,&v_sa,NULL);
+
+ } else if (rho_h != NULL) {
+
+ gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,NULL,&v_h);
+
+ }
+
+ rec_v2 = pow(1.0/gsw_specvol(sa,ct,p), 2);
+
+ if (rho_sa != NULL) *rho_sa = -v_sa*rec_v2;
+
+ if (rho_h != NULL) *rho_h = -v_h*rec_v2;
+}
+/*
+!==========================================================================
+elemental function gsw_rho_ice (t, p)
+!==========================================================================
+!
+! Calculates in-situ density of ice from in-situ temperature and pressure.
+! Note that the output, rho_ice, is density, not density anomaly; that
+! is, 1000 kg/m^3 is not subracted from it.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho_ice = in-situ density of ice (not density anomaly) [ kg/m^3 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_rho_ice(double t, double p)
+{
+ return (1.0/gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_rho_second_derivatives (sa, ct, p, rho_sa_sa, &
+ rho_sa_ct, rho_ct_ct, rho_sa_p, rho_ct_p)
+!==========================================================================
+!
+! Calculates five second-order derivatives of rho. Note that this function
+! uses the computationally-efficient expression for specific
+! volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho_SA_SA = The second-order derivative of rho with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! rho_SA_CT = The second-order derivative of rho with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+! rho_CT_CT = The second-order derivative of rho with respect to CT at
+! constant SA & p
+! rho_SA_P = The second-order derivative with respect to SA & P at
+! constant CT.
+! rho_CT_P = The second-order derivative with respect to CT & P at
+! constant SA.
+!--------------------------------------------------------------------------
+*/
+void
+gsw_rho_second_derivatives(double sa, double ct, double p, double *rho_sa_sa,
+ double *rho_sa_ct, double *rho_ct_ct, double *rho_sa_p,
+ double *rho_ct_p)
+{
+ double rec_v, rec_v2, rec_v3, v_ct, v_ct_ct, v_ct_p, v_p, v_sa,
+ v_sa_ct, v_sa_p, v_sa_sa;
+
+ gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct,&v_p);
+ gsw_specvol_second_derivatives(sa,ct,p,&v_sa_sa,&v_sa_ct,&v_ct_ct,
+ &v_sa_p,&v_ct_p);
+
+ rec_v = 1.0/gsw_specvol(sa,ct,p);
+ rec_v2 = pow(rec_v, 2);
+ rec_v3 = rec_v2*rec_v;
+
+ if (rho_sa_sa != NULL)
+ *rho_sa_sa = -v_sa_sa*rec_v2 + 2.0*v_sa*v_sa*rec_v3;
+
+ if (rho_sa_ct != NULL)
+ *rho_sa_ct = -v_sa_ct*rec_v2 + 2.0*v_sa*v_ct*rec_v3;
+
+ if (rho_ct_ct != NULL)
+ *rho_ct_ct = -v_ct_ct*rec_v2 + 2.0*v_ct*v_ct*rec_v3;
+
+ if (rho_sa_p != NULL)
+ *rho_sa_p = -v_sa_p*rec_v2 + 2.0*v_sa*v_p*rec_v3;
+
+ if (rho_ct_p != NULL)
+ *rho_ct_p = -v_ct_p*rec_v2 + 2.0*v_ct*v_p*rec_v3;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_rho_second_derivatives_wrt_enthalpy (sa, ct, p, &
+ rho_sa_sa, rho_sa_h, rho_h_h)
+! =========================================================================
+!
+! Calculates three second-order derivatives of rho with respect to enthalpy.
+! Note that this function uses the using the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho_SA_SA = The second-order derivative of rho with respect to
+! Absolute Salinity at constant h & p. [ J/(kg (g/kg)^2) ]
+! rho_SA_h = The second-order derivative of rho with respect to
+! SA and h at constant p. [ J/(kg K(g/kg)) ]
+! rho_h_h = The second-order derivative of rho with respect to h at
+! constant SA & p
+!--------------------------------------------------------------------------
+*/
+void
+gsw_rho_second_derivatives_wrt_enthalpy(double sa, double ct, double p,
+ double *rho_sa_sa, double *rho_sa_h, double *rho_h_h)
+{
+ double rec_v, rec_v2, rec_v3, v_h, v_h_h, v_sa, v_sa_h, v_sa_sa,
+ *pv_sa, *pv_h, *pv_sa_sa, *pv_sa_h, *pv_h_h;
+
+ pv_sa = ((rho_sa_sa != NULL) || (rho_sa_h != NULL)) ? &v_sa : NULL;
+ pv_h = ((rho_sa_h != NULL) || (rho_h_h != NULL)) ? &v_h : NULL;
+
+ gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,pv_sa,pv_h);
+
+ pv_sa_sa = ((rho_sa_sa != NULL)) ? &v_sa_sa : NULL;
+ pv_sa_h = ((rho_sa_h != NULL)) ? &v_sa_h : NULL;
+ pv_h_h = ((rho_h_h != NULL)) ? &v_h_h : NULL;
+
+ gsw_specvol_second_derivatives_wrt_enthalpy(sa,ct,p,
+ pv_sa_sa,pv_sa_h,pv_h_h);
+
+ rec_v = 1.0/gsw_specvol(sa,ct,p);
+ rec_v2 = rec_v*rec_v;
+ rec_v3 = rec_v2*rec_v;
+
+ if (rho_sa_sa != NULL)
+ *rho_sa_sa = -v_sa_sa*rec_v2 + 2.0*v_sa*v_sa*rec_v3;
+
+ if (rho_sa_h != NULL)
+ *rho_sa_h = -v_sa_h*rec_v2 + 2.0*v_sa*v_h*rec_v3;
+
+ if (rho_h_h != NULL)
+ *rho_h_h = -v_h_h*rec_v2 + 2.0*v_h*v_h*rec_v3;
+}
+/*
+!==========================================================================
+function gsw_rho_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates in-situ density of seawater from Absolute Salinity and
+! in-situ temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_rho_t_exact : in-situ density [kg/m^3]
+*/
+double
+gsw_rho_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (1.0/gsw_gibbs(n0,n0,n1,sa,t,p));
+}
+/*
+!==========================================================================
+pure subroutine gsw_rr68_interp_sa_ct (sa, ct, p, p_i, sa_i, ct_i)
+!==========================================================================
+!
+! Interpolate Absolute Salinity and Conservative Temperature values to
+! arbitrary pressures using the Reiniger and Ross (1968) interpolation
+! scheme.
+! Note that this interpolation scheme requires at least four observed
+! bottles on the cast.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! p_i = pressures to interpolate to.
+!
+! SA_i = interpolated SA values at pressures p_i.
+! CT_i = interpolated CT values at pressures p_i.
+!--------------------------------------------------------------------------
+*/
+static void rr68_interp_section(int sectnum, double *sa, double *ct, double *p,
+ int mp, int nsect, double *ip_sect,
+ int *ip_isect, double *p_i, double *sa_i, double *ct_i);
+/* forward reference */
+
+void
+gsw_rr68_interp_sa_ct(double *sa, double *ct, double *p, int mp, double *p_i,
+ int mp_i, double *sa_i, double *ct_i)
+{
+ int i, j, nshallow, ncentral, ndeep,
+ *ip, *ip_i, *ip_ishallow, *ip_icentral, *ip_ideep;
+ char *shallow, *central, *deep;
+ double *ip_shallow, *ip_central, *ip_deep, *dp, *p_ii;
+
+ if (mp < 4) {
+ /* need at least four bottles to perform this interpolation */
+ ct_i[0] = sa_i[0] = GSW_INVALID_VALUE;
+ return;
+ }
+
+ dp = malloc(mp*sizeof (double));
+ for (i=1; i<mp; i++) {
+ if ((dp[i-1] = (p[i] - p[i-1])) <= 0.0) {
+ free(dp);
+ ct_i[0] = sa_i[0] = GSW_INVALID_VALUE;
+ return;
+ }
+ }
+
+ shallow = malloc(3*mp_i*sizeof (char));
+ central = shallow+mp_i; deep = central+mp_i;
+ nshallow=ncentral=ndeep=0;
+ memset(shallow, 0, 3*mp_i*sizeof (char));
+ for (i=0; i<mp_i; i++) {
+ if (p_i[i] >= p[0] && p_i[i] <= p[1]) {
+ nshallow++;
+ shallow[i] = 1;
+ }
+ if (p_i[i] >= p[1] && p_i[i] <= p[mp-2]) {
+ ncentral++;
+ central[i] = 1;
+ }
+ if (p_i[i] >= p[mp-2] && p_i[i] <= p[mp-1]) {
+ ndeep++;
+ deep[i] = 1;
+ }
+ }
+
+ if ((nshallow == 0) || (ncentral == 0) || (ndeep == 0)) {
+ free(shallow); free(dp);
+ ct_i[0] = sa_i[0] = GSW_INVALID_VALUE;
+ return;
+ }
+
+ ip = malloc((mp+mp_i)*sizeof (int)); ip_i = ip+mp;
+ for (i=0; i<mp; i++)
+ ip[i] = i;
+ for (i=0; i<mp_i; i++)
+ ip_i[i] = i;
+
+ ip_ishallow = malloc((nshallow+ncentral+ndeep)*sizeof (int));
+ ip_icentral = ip_ishallow+nshallow; ip_ideep = ip_icentral+ncentral;
+ ip_shallow = malloc(2*(nshallow+ncentral+ndeep)*sizeof (double));
+ ip_central = ip_shallow+nshallow; ip_deep = ip_central+ncentral;
+ p_ii = ip_deep+ndeep;
+ /*
+ ! Calculate the 2 outer extrapolated values and the inner
+ ! interpolated values
+ */
+ for (i=j=0; i<mp_i; i++) {
+ if (central[i]) {
+ ip_icentral[j] = ip_i[i];
+ j++;
+ }
+ }
+ for (i=0; i<ncentral; i++)
+ p_ii[i] = p_i[ip_icentral[i]];
+ gsw_util_interp1q_int(mp,p,ip,ncentral,p_ii,ip_central);
+ rr68_interp_section(0,sa,ct,p,mp,ncentral,ip_central,ip_icentral,
+ p_i,sa_i,ct_i);
+
+ for (i=j=0; i<mp_i; i++) {
+ if (shallow[i]) {
+ ip_ishallow[j] = ip_i[i];
+ j++;
+ }
+ }
+ for (i=0; i<nshallow; i++)
+ p_ii[i] = p_i[ip_ishallow[i]];
+ gsw_util_interp1q_int(mp,p,ip,nshallow,p_ii,ip_shallow);
+ rr68_interp_section(-1,sa,ct,p,mp,nshallow,ip_shallow,ip_ishallow,
+ p_i,sa_i,ct_i);
+
+ for (i=j=0; i<mp_i; i++) {
+ if (deep[i]) {
+ ip_ideep[j] = ip_i[i];
+ j++;
+ }
+ }
+ for (i=0; i<ndeep; i++)
+ p_ii[i] = p_i[ip_ideep[i]];
+ gsw_util_interp1q_int(mp,p,ip,ndeep,p_ii,ip_deep);
+ rr68_interp_section(1,sa,ct,p,mp,ndeep,ip_deep,ip_ideep,p_i,sa_i,ct_i);
+
+ /*
+ ! Insert any observed bottles that are at the required interpolated
+ ! pressures
+ */
+ for (i=0; i<mp_i; i++) {
+ for (j=0; j<mp; j++) {
+ if (p_i[i] == p[j]) {
+ sa_i[i] = sa[j];
+ ct_i[i] = ct[j];
+ }
+ }
+ }
+ free(ip_shallow); free(ip_ishallow); free(ip); free(shallow); free(dp);
+}
+
+/*
+pure subroutine rr68_interp_section (sectnum, ip_sect, ip_isect, sa_i, ct_i)
+*/
+static void
+rr68_interp_section(int sectnum, double *sa, double *ct, double *p, int mp,
+ int nsect, double *ip_sect, int *ip_isect, double *p_i, double *sa_i,
+ double *ct_i)
+{
+ int i, *ip_1, *ip_2, *ip_3, *ip_4;
+ double m, *ct_12, *ct_13, *ct_23, *ct_34, ctp1,
+ ctp2, *ct_ref, ctref_denom,
+ ct_ref_minus_ctp1, ct_ref_minus_ctp2,
+ ctref_num,
+ gamma1_23, gamma1_24, gamma2_31,
+ gamma2_34, gamma2_41, gamma3_12,
+ gamma3_42, gamma4_12, gamma4_23,
+ *sa_12, *sa_13, *sa_23, *sa_34, sap1,
+ sap2, *sa_ref, saref_denom,
+ sa_ref_minus_sap1, sa_ref_minus_sap2,
+ saref_num, *p_ii;
+
+ ip_1 = malloc(4*nsect*sizeof (int)); ip_2 = ip_1+nsect;
+ ip_3 = ip_2+nsect; ip_4 = ip_3+nsect;
+
+ ct_12 = malloc(12*nsect*sizeof (double));
+ sa_12 = ct_12 + 1*nsect;
+ sa_13 = ct_12 + 2*nsect;
+ sa_23 = ct_12 + 3*nsect;
+ sa_34 = ct_12 + 4*nsect;
+ sa_ref = ct_12 + 5*nsect;
+ ct_13 = ct_12 + 6*nsect;
+ ct_23 = ct_12 + 7*nsect;
+ ct_34 = ct_12 + 8*nsect;
+ ct_ref = ct_12 + 9*nsect;
+ p_ii = ct_12 + 10*nsect;
+
+ if (sectnum < 0) { /* shallow */
+ for (i=0; i<nsect; i++) {
+ ip_1[i] = floor(ip_sect[i]);
+ ip_2[i] = ceil(ip_sect[i]);
+ ip_3[i] = ip_2[i] + 1;
+ ip_4[i] = ip_3[i] + 1;
+ }
+ } else if (sectnum == 0) { /* central */
+ for (i=0; i<nsect; i++) {
+ ip_2[i] = floor(ip_sect[i]);
+ ip_1[i] = ip_2[i] - 1;
+ ip_3[i] = ceil(ip_sect[i]);
+ ip_4[i] = ip_3[i] + 1;
+ }
+ } else if (sectnum > 0) { /* deep */
+ for (i=0; i<nsect; i++) {
+ ip_1[i] = ceil(ip_sect[i]);
+ ip_2[i] = floor(ip_sect[i]);
+ ip_3[i] = ip_2[i] - 1;
+ ip_4[i] = ip_3[i] - 1;
+ }
+ }
+
+ for (i=0; i<nsect; i++)
+ p_ii[i] = p_i[ip_isect[i]];
+
+ /* eqn (3d) */
+ for (i=0; i<nsect; i++) {
+ sa_34[i] = sa[ip_3[i]] + ((sa[ip_4[i]] - sa[ip_3[i]])
+ *(p_ii[i] - p[ip_3[i]])/ (p[ip_4[i]] - p[ip_3[i]]));
+ ct_34[i] = ct[ip_3[i]] + ((ct[ip_4[i]] - ct[ip_3[i]])
+ *(p_ii[i] - p[ip_3[i]])/ (p[ip_4[i]] - p[ip_3[i]]));
+ }
+ /*
+ ! Construct the Reiniger & Ross reference curve equation.
+ ! m = the power variable
+ */
+ m = 1.7;
+
+ if (sectnum == 0) {
+
+ gsw_linear_interp_sa_ct(sa,ct,p,mp,p_ii,nsect,sa_23,ct_23);
+
+ /* eqn (3a) */
+ for (i=0; i<nsect; i++) {
+ sa_12[i] = sa[ip_1[i]] + ((sa[ip_2[i]] - sa[ip_1[i]])
+ *(p_ii[i] - p[ip_1[i]])/ (p[ip_2[i]] - p[ip_1[i]]));
+ ct_12[i] = ct[ip_1[i]] + ((ct[ip_2[i]] - ct[ip_1[i]])
+ *(p_ii[i] - p[ip_1[i]])/ (p[ip_2[i]] - p[ip_1[i]]));
+
+ saref_num = (pow(fabs(sa_23[i]-sa_34[i]),m))*sa_12[i]
+ + (pow(fabs(sa_12[i]-sa_23[i]),m))*sa_34[i];
+ ctref_num = (pow(fabs(ct_23[i]-ct_34[i]),m))*ct_12[i]
+ + (pow(fabs(ct_12[i]-ct_23[i]),m))*ct_34[i];
+
+ saref_denom = pow(fabs(sa_23[i]-sa_34[i]),m)
+ + pow(fabs(sa_12[i]-sa_23[i]),m);
+ ctref_denom = pow(fabs(ct_23[i]-ct_34[i]),m)
+ + pow(fabs(ct_12[i]-ct_23[i]),m);
+
+ if (saref_denom == 0.0) {
+ sa_23[i] = sa_23[i] + 1.0e-6;
+ saref_num = (pow(fabs(sa_23[i]-sa_34[i]),m))*sa_12[i]
+ + (pow(fabs(sa_12[i]-sa_23[i]),m))*sa_34[i];
+ saref_denom = pow(fabs(sa_23[i]-sa_34[i]),m)
+ + pow(fabs(sa_12[i]-sa_23[i]),m);
+ }
+ if (ctref_denom == 0.0) {
+ ct_23[i] = ct_23[i] + 1.0e-6;
+ ctref_num = (pow(fabs(ct_23[i]-ct_34[i]),m))*ct_12[i]
+ + (pow(fabs(ct_12[i]-ct_23[i]),m))*ct_34[i];
+ ctref_denom = pow(fabs(ct_23[i]-ct_34[i]),m)
+ + pow(fabs(ct_12[i]-ct_23[i]),m);
+ }
+
+ sa_ref[i] = 0.5*(sa_23[i] + (saref_num/saref_denom));
+ ct_ref[i] = 0.5*(ct_23[i] + (ctref_num/ctref_denom));
+ }
+
+ } else {
+
+ gsw_linear_interp_sa_ct(sa,ct,p,mp,p_ii,nsect,sa_12,ct_12);
+
+ for (i=0; i<nsect; i++) {
+ sa_13[i] = sa[ip_1[i]] + ((sa[ip_3[i]] - sa[ip_1[i]])
+ *(p_ii[i] - p[ip_1[i]])/ (p[ip_3[i]] - p[ip_1[i]]));
+ ct_13[i] = ct[ip_1[i]] + ((ct[ip_3[i]] - ct[ip_1[i]])
+ *(p_ii[i] - p[ip_1[i]])/ (p[ip_3[i]] - p[ip_1[i]]));
+
+ sa_23[i] = sa[ip_2[i]] + ((sa[ip_3[i]] - sa[ip_2[i]])
+ *(p_ii[i] - p[ip_2[i]])/ (p[ip_3[i]] - p[ip_2[i]]));
+ ct_23[i] = ct[ip_2[i]] + ((ct[ip_3[i]] - ct[ip_2[i]])
+ *(p_ii[i] - p[ip_2[i]])/ (p[ip_3[i]] - p[ip_2[i]]));
+
+ /* eqn (3a') */
+ saref_num = (pow(fabs(sa_12[i]-sa_23[i]),m))*sa_34[i]
+ + (pow(fabs(sa_12[i]-sa_13[i]),m))*sa_23[i];
+ ctref_num = (pow(fabs(ct_12[i]-ct_23[i]),m))*ct_34[i]
+ + (pow(fabs(ct_12[i]-ct_13[i]),m))*ct_23[i];
+
+ saref_denom = pow(fabs(sa_12[i]-sa_23[i]),m)
+ + pow(fabs(sa_12[i]-sa_13[i]),m);
+ ctref_denom = pow(fabs(ct_12[i]-ct_23[i]),m)
+ + pow(fabs(ct_12[i]-ct_13[i]),m);
+
+ if (saref_denom == 0.0) {
+ sa_23[i] = sa_23[i] + 1.0e-6;
+ saref_num = (pow(fabs(sa_12[i]-sa_23[i]),m))*sa_34[i]
+ + (pow(fabs(sa_12[i]-sa_13[i]),m))*sa_23[i];
+ saref_denom = pow(fabs(sa_12[i]-sa_23[i]),m)
+ + pow(fabs(sa_12[i]-sa_13[i]),m);
+ }
+ if (ctref_denom == 0.0) {
+ ct_23[i] = ct_23[i] + 1.0e-6;
+ ctref_num = (pow(fabs(ct_12[i]-ct_23[i]),m))*ct_34[i]
+ + (pow(fabs(ct_12[i]-ct_13[i]),m))*ct_23[i];
+ ctref_denom = pow(fabs(ct_12[i]-ct_23[i]),m)
+ + pow(fabs(ct_12[i]-ct_13[i]),m);
+ }
+
+ sa_ref[i] = 0.5*(sa_12[i] + (saref_num/saref_denom));
+ ct_ref[i] = 0.5*(ct_12[i] + (ctref_num/ctref_denom));
+ }
+ }
+
+ for (i=0; i<nsect; i++) {
+ /* eqn (3c) */
+ gamma1_23 = ((p_ii[i] - p[ip_2[i]])*(p_ii[i] - p[ip_3[i]]))/
+ ((p[ip_1[i]] - p[ip_2[i]])*(p[ip_1[i]] - p[ip_3[i]]));
+ gamma2_31 = ((p_ii[i] - p[ip_3[i]])*(p_ii[i] - p[ip_1[i]]))/
+ ((p[ip_2[i]] - p[ip_3[i]])*(p[ip_2[i]] - p[ip_1[i]]));
+ gamma3_12 = ((p_ii[i] - p[ip_1[i]])*(p_ii[i] - p[ip_2[i]]))/
+ ((p[ip_3[i]] - p[ip_1[i]])*(p[ip_3[i]] - p[ip_2[i]]));
+
+ if (sectnum == 0) {
+ gamma2_34 = ((p_ii[i] - p[ip_3[i]])*(p_ii[i] - p[ip_4[i]]))/
+ ((p[ip_2[i]] - p[ip_3[i]])*(p[ip_2[i]] - p[ip_4[i]]));
+ gamma3_42 = ((p_ii[i] - p[ip_4[i]])*(p_ii[i] - p[ip_2[i]]))/
+ ((p[ip_3[i]] - p[ip_4[i]])*(p[ip_3[i]] - p[ip_2[i]]));
+ gamma4_23 = ((p_ii[i] - p[ip_2[i]])*(p_ii[i] - p[ip_3[i]]))/
+ ((p[ip_4[i]] - p[ip_2[i]])*(p[ip_4[i]] - p[ip_3[i]]));
+ } else {
+ gamma1_24 = ((p_ii[i] - p[ip_2[i]])*(p_ii[i] - p[ip_4[i]]))/
+ ((p[ip_1[i]] - p[ip_2[i]])*(p[ip_1[i]] - p[ip_4[i]]));
+ gamma2_41 = ((p_ii[i] - p[ip_4[i]])*(p_ii[i] - p[ip_1[i]]))/
+ ((p[ip_2[i]] - p[ip_4[i]])*(p[ip_2[i]] - p[ip_1[i]]));
+ gamma4_12 = ((p_ii[i] - p[ip_1[i]])*(p_ii[i] - p[ip_2[i]]))/
+ ((p[ip_4[i]] - p[ip_1[i]])*(p[ip_4[i]] - p[ip_2[i]]));
+ }
+
+ /* eqn (3b/3b') */
+ sap1 = gamma1_23*sa[ip_1[i]] + gamma2_31*sa[ip_2[i]]
+ + gamma3_12*sa[ip_3[i]];
+ ctp1 = gamma1_23*ct[ip_1[i]] + gamma2_31*ct[ip_2[i]]
+ + gamma3_12*ct[ip_3[i]];
+ if (sectnum == 0) {
+ sap2 = gamma2_34*sa[ip_2[i]] + gamma3_42*sa[ip_3[i]]
+ + gamma4_23*sa[ip_4[i]];
+ ctp2 = gamma2_34*ct[ip_2[i]] + gamma3_42*ct[ip_3[i]]
+ + gamma4_23*ct[ip_4[i]];
+ } else {
+ sap2 = gamma1_24*sa[ip_1[i]] + gamma2_41*sa[ip_2[i]]
+ + gamma4_12*sa[ip_4[i]];
+ ctp2 = gamma1_24*ct[ip_1[i]] + gamma2_41*ct[ip_2[i]]
+ + gamma4_12*ct[ip_4[i]];
+ }
+
+ /* eqn (3) */
+ sa_ref_minus_sap1 = fabs(sa_ref[i] - sap1);
+ sa_ref_minus_sap2 = fabs(sa_ref[i] - sap2);
+ if (sa_ref_minus_sap1 == 0.0 && sa_ref_minus_sap2 == 0.0) {
+ sa_ref[i] = sa_ref[i] + 1.0e-6;
+ sa_ref_minus_sap1 = fabs(sa_ref[i] - sap1);
+ sa_ref_minus_sap2 = fabs(sa_ref[i] - sap2);
+ }
+
+ ct_ref_minus_ctp1 = fabs(ct_ref[i] - ctp1);
+ ct_ref_minus_ctp2 = fabs(ct_ref[i] - ctp2);
+ if (ct_ref_minus_ctp1 == 0.0 && ct_ref_minus_ctp2 == 0.0) {
+ ct_ref[i] = ct_ref[i] + 1.0e-6;
+ ct_ref_minus_ctp1 = fabs(ct_ref[i] - ctp1);
+ ct_ref_minus_ctp2 = fabs(ct_ref[i] - ctp2);
+ }
+
+ sa_i[ip_isect[i]] = (sa_ref_minus_sap1*sap2+sa_ref_minus_sap2*sap1)/
+ (sa_ref_minus_sap1 + sa_ref_minus_sap2);
+ ct_i[ip_isect[i]] = (ct_ref_minus_ctp1*ctp2+ct_ref_minus_ctp2*ctp1)/
+ (ct_ref_minus_ctp1 + ct_ref_minus_ctp2);
+ }
+ free(ct_12); free(ip_1);
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_estimate (p, saturation_fraction, ct, t)
+!==========================================================================
+!
+! Form an estimate of SA from a polynomial in CT and p
+!
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_estimate(double p, double saturation_fraction, double *ct,
+ double *t)
+{
+ GSW_TEOS10_CONSTANTS;
+ double ctx, ctsat, sa,
+ /*note that aa = 0.502500117621d0/35.16504*/
+ aa = 0.014289763856964,
+ bb = 0.057000649899720,
+
+ p0 = 2.570124672768757e-1,
+ p1 = -1.917742353032266e1,
+ p2 = -1.413382858617969e-2,
+ p3 = -5.427484830917552e-1,
+ p4 = -4.126621135193472e-4,
+ p5 = -4.176407833276121e-7,
+ p6 = 4.688217641883641e-5,
+ p7 = -3.039808885885726e-8,
+ p8 = -4.990118091261456e-11,
+ p9 = -9.733920711119464e-9,
+ p10 = -7.723324202726337e-12,
+ p11 = 7.121854166249257e-16,
+ p12 = 1.256474634100811e-12,
+ p13 = 2.105103897918125e-15,
+ p14 = 8.663811778227171e-19;
+
+ /*A very rough estimate of sa to get the saturated ct*/
+ if (ct != NULL) {
+ sa = max(-(*ct + 9e-4*p)/0.06, 0.0);
+ ctx = *ct;
+ } else if (t != NULL) {
+ sa = max(-(*t + 9e-4*p)/0.06, 0.0);
+ ctx = gsw_ct_from_t(sa,*t,p);
+ } else {
+ return (0.0);
+ }
+ /*
+ ! CTsat is the estimated value of CT if the seawater were saturated with
+ ! dissolved air, recognizing that it actually has the air fraction
+ ! saturation_fraction; see McDougall, Barker and Feistel, 2014).
+ */
+ ctsat = ctx - (1.0-saturation_fraction)*
+ (1e-3)*(2.4-aa*sa)*(1.0+bb*(1.0-sa/gsw_sso));
+
+ return (p0 + p*(p2 + p4*ctsat + p*(p5 + ctsat*(p7 + p9*ctsat)
+ + p*(p8 + ctsat*(p10 + p12*ctsat) + p*(p11 + p13*ctsat + p14*p))))
+ + ctsat*(p1 + ctsat*(p3 + p6*p)));
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_from_ct (ct, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Absolute Salinity of seawater at the freezing temperature.
+! That is, the output is the Absolute Salinity of seawater, with
+! Conservative Temperature CT, pressure p and the fraction
+! saturation_fraction of dissolved air, that is in equilibrium
+! with ice at the same in situ temperature and pressure. If the input
+! values are such that there is no positive value of Absolute Salinity for
+! which seawater is frozen, the output is made a NaN.
+!
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! sa_freezing_from_ct = Absolute Salinity of seawater when it freezes,
+! for given input values of its Conservative Temperature,
+! pressure and air saturation fraction. [ g/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_from_ct(double ct, double p, double saturation_fraction)
+{
+ int i_iter, number_of_iterations = 3;
+ double ct_freezing_zero_sa, f, ctfreezing_sa, sa, sa_mean, sa_old;
+ /*
+ ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat
+ ! differently in calculating the initial values of both SA and dCT_dSA.
+ */
+ double sa_cut_off = 2.5;
+ /*
+ ! Find CT > CT_freezing_zero_SA. If this is the case, the input values
+ ! represent seawater that is not frozen (for any positive SA).
+ */
+ ct_freezing_zero_sa = gsw_ct_freezing(0.0,p,saturation_fraction);
+ if (ct > ct_freezing_zero_sa)
+ return (GSW_INVALID_VALUE);
+
+ /*Form the first estimate of SA from a polynomial in CT and p*/
+ sa = gsw_sa_freezing_estimate(p,saturation_fraction,&ct,NULL);
+ if (sa < -sa_cut_off)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! Form the first estimate of CTfreezing_SA,
+ ! the derivative of CT_freezing with respect to SA at fixed p.
+ */
+ sa = max(sa,0.0);
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,
+ &ctfreezing_sa, NULL);
+ /*
+ ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
+ ! with one based on (CT_freezing_zero_SA - CT).
+ */
+ if (fabs(sa) < sa_cut_off)
+ sa = (ct - ct_freezing_zero_sa)/ctfreezing_sa;
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin the modified Newton-Raphson method to solve
+ ! f = (CT_freezing - CT) = 0 for SA.
+ !-----------------------------------------------------------------------
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ sa_old = sa;
+ f = gsw_ct_freezing(sa,p,saturation_fraction) - ct;
+ sa = sa_old - f/ctfreezing_sa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_ct_freezing_first_derivatives(sa_mean,p,saturation_fraction,
+ &ctfreezing_sa, NULL);
+ sa = sa_old - f/ctfreezing_sa;
+ }
+
+ if (gsw_sa_p_inrange(sa,p))
+ return (sa);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_from_ct_poly (ct, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Absolute Salinity of seawater at the freezing temperature.
+! That is, the output is the Absolute Salinity of seawater, with the
+! fraction saturation_fraction of dissolved air, that is in equilibrium
+! with ice at Conservative Temperature CT and pressure p. If the input
+! values are such that there is no positive value of Absolute Salinity for
+! which seawater is frozen, the output is put equal to Nan.
+!
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! sa_freezing_from_ct = Absolute Salinity of seawater when it freezes,
+! for given input values of Conservative Temperature
+! pressure and air saturation fraction. [ g/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_from_ct_poly(double ct, double p, double saturation_fraction)
+{
+ int i_iter, number_of_iterations = 2;
+ double ct_freezing, ct_freezing_zero_sa, dct_dsa, sa, sa_old, sa_mean;
+ /*
+ ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat
+ ! differently in calculating the initial values of both SA and dCT_dSA.
+ */
+ double sa_cut_off = 2.5;
+ /*
+ ! Find CT > CT_freezing_zero_SA. If this is the case, the input values
+ ! represent seawater that is not frozen (at any positive SA).
+ */
+ ct_freezing_zero_sa = gsw_ct_freezing_poly(0.0,p,saturation_fraction);
+ if (ct > ct_freezing_zero_sa)
+ return (GSW_INVALID_VALUE);
+
+ /*Form the first estimate of SA from a polynomial in CT and p */
+ sa = gsw_sa_freezing_estimate(p,saturation_fraction,&ct,NULL);
+ if (sa < -sa_cut_off)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! Form the first estimate of dCT_dSA, the derivative of CT with respect
+ ! to SA at fixed p.
+ */
+ sa = max(sa,0.0);
+ gsw_ct_freezing_first_derivatives_poly(sa,p,saturation_fraction,
+ &dct_dsa, NULL);
+ /*
+ ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
+ ! with one based on (CT_freezing_zero_SA - CT).
+ */
+ if (fabs(sa) < sa_cut_off)
+ sa = (ct - ct_freezing_zero_sa)/dct_dsa;
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin the modified Newton-Raphson method to solve the root of
+ ! CT_freezing = CT for SA.
+ !-----------------------------------------------------------------------
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ sa_old = sa;
+ ct_freezing = gsw_ct_freezing_poly(sa_old,p,saturation_fraction);
+ sa = sa_old - (ct_freezing - ct)/dct_dsa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_ct_freezing_first_derivatives_poly(sa_mean,p,
+ saturation_fraction, &dct_dsa, NULL);
+ sa = sa_old - (ct_freezing - ct)/dct_dsa;
+ }
+
+ if (gsw_sa_p_inrange(sa,p))
+ return (sa);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_from_t (t, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Absolute Salinity of seawater at the freezing temperature.
+! That is, the output is the Absolute Salinity of seawater, with the
+! fraction saturation_fraction of dissolved air, that is in equilibrium
+! with ice at in-situ temperature t and pressure p. If the input values
+! are such that there is no positive value of Absolute Salinity for which
+! seawater is frozen, the output is set to NaN.
+!
+! t = in-situ Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+! (i.e., saturation_fraction must be between 0 and 1, and the default
+! is 1, completely saturated)
+!
+! sa_freezing_from_t = Absolute Salinity of seawater when it freezes, for
+! given input values of in situ temperature, pressure and
+! air saturation fraction. [ g/kg ]
+!---------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_from_t(double t, double p, double saturation_fraction)
+{
+ int i_iter, number_of_iterations = 2;
+ double f, sa, sa_mean, sa_old, t_freezing_zero_sa, tfreezing_sa;
+ /*
+ ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat
+ ! differently in calculating the initial values of both SA and dCT_dSA.
+ */
+ double sa_cut_off = 2.5;
+ /*
+ ! Find t > t_freezing_zero_SA. If this is the case, the input values
+ ! represent seawater that is not frozen (at any positive SA).
+ */
+ t_freezing_zero_sa = gsw_t_freezing(0.0,p,saturation_fraction);
+ if (t > t_freezing_zero_sa)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! This is the inital guess of SA using a purpose-built
+ ! polynomial in CT and p
+ */
+ sa = gsw_sa_freezing_estimate(p,saturation_fraction,NULL,&t);
+ if (sa < -sa_cut_off)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! Form the first estimate of tfreezing_SA, the derivative of
+ ! CT_freezing with respect to SA at fixed p.
+ */
+ sa = max(sa,0.0);
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tfreezing_sa,NULL);
+ /*
+ ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
+ ! with one based on (t_freezing_zero_SA - t).
+ */
+ if (fabs(sa) < sa_cut_off)
+ sa = (t - t_freezing_zero_sa)/tfreezing_sa;
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin the modified Newton-Raphson method to find the root of
+ ! f = (t_freezing - t) = 0 for SA.
+ !-----------------------------------------------------------------------
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ sa_old = sa;
+ f = gsw_t_freezing(sa_old,p,saturation_fraction) - t;
+ sa = sa_old - f/tfreezing_sa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_t_freezing_first_derivatives(sa_mean,p,saturation_fraction,
+ &tfreezing_sa, NULL);
+ sa = sa_old - f/tfreezing_sa;
+ }
+
+ if (gsw_sa_p_inrange(sa,p))
+ return (sa);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_from_t_poly (t, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Absolute Salinity of seawater at the freezing temperature.
+! That is, the output is the Absolute Salinity of seawater, with the
+! fraction saturation_fraction of dissolved air, that is in equilibrium
+! with ice at in-situ temperature t and pressure p. If the input values
+! are such that there is no positive value of Absolute Salinity for which
+! seawater is frozen, the output is put equal to Nan.
+!
+! t = in-situ Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! sa_freezing_from_t_poly = Absolute Salinity of seawater when it freezes,
+! for given input values of in situ temperature, pressure and
+! air saturation fraction. [ g/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_from_t_poly(double t, double p, double saturation_fraction)
+{
+ int i_iter, number_of_iterations = 5;
+ double dt_dsa, sa, sa_old, sa_mean, t_freezing, t_freezing_zero_sa;
+ /*
+ ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat
+ ! differently in calculating the initial values of both SA and dCT_dSA.
+ */
+ double sa_cut_off = 2.5;
+ /*
+ ! Find t > t_freezing_zero_SA. If this is the case, the input values
+ ! represent seawater that is not frozen (at any positive SA).
+ */
+ t_freezing_zero_sa = gsw_t_freezing_poly(0.0,p,saturation_fraction);
+ if (t > t_freezing_zero_sa)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! This is the inital guess of SA using a purpose-built
+ ! polynomial in CT and p
+ */
+ sa = gsw_sa_freezing_estimate(p,saturation_fraction,NULL,&t);
+ if (sa < -sa_cut_off)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! Form the first estimate of dt_dSA, the derivative of t with respect
+ ! to SA at fixed p.
+ */
+ sa = max(sa,0.0);
+ gsw_t_freezing_first_derivatives_poly(sa,p,saturation_fraction,
+ &dt_dsa, NULL);
+ /*
+ ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
+ ! with one based on (t_freezing_zero_SA - t).
+ */
+ if (fabs(sa) < sa_cut_off)
+ sa = (t - t_freezing_zero_sa)/dt_dsa;
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin the modified Newton-Raphson method to find the root of
+ ! t_freezing = t for SA.
+ !-----------------------------------------------------------------------
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ sa_old = sa;
+ t_freezing = gsw_t_freezing_poly(sa_old,p,saturation_fraction);
+ sa = sa_old - (t_freezing - t)/dt_dsa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_t_freezing_first_derivatives_poly(sa_mean,p,saturation_fraction,
+ &dt_dsa, NULL);
+ sa = sa_old - (t_freezing - t)/dt_dsa;
+ }
+
+ if (gsw_sa_p_inrange(sa,p))
+ return (sa);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+function gsw_sa_from_rho(rho,ct,p)
+!==========================================================================
+
+! Calculates the Absolute Salinity of a seawater sample, for given values
+! of its density, Conservative Temperature and sea pressure (in dbar).
+!
+! rho = density of a seawater sample (e.g. 1026 kg/m^3). [ kg/m^3 ]
+! Note. This input has not had 1000 kg/m^3 subtracted from it.
+! That is, it is 'density', not 'density anomaly'.
+! ct = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+!
+! sa = Absolute Salinity [g/kg]
+*/
+double
+gsw_sa_from_rho(double rho, double ct, double p)
+{
+ int no_iter;
+
+ double sa, v_lab, v_0, v_50, v_sa, sa_old, delta_v, sa_mean;
+
+ v_lab = 1.0/rho;
+ v_0 = gsw_specvol(0.0,ct,p);
+ v_50 = gsw_specvol(50.0,ct,p);
+
+ sa = 50.0*(v_lab - v_0)/(v_50 - v_0);
+ if (sa < 0.0 || sa > 50.0)
+ return (GSW_INVALID_VALUE);
+
+ v_sa = (v_50 - v_0)/50.0;
+
+ for (no_iter=1; no_iter <= 2; no_iter++) {
+ sa_old = sa;
+ delta_v = gsw_specvol(sa_old,ct,p) - v_lab;
+ sa = sa_old - delta_v/v_sa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_specvol_first_derivatives(sa_mean,ct,p,&v_sa,NULL,NULL);
+ sa = sa_old - delta_v/v_sa;
+ if (sa < 0.0 || sa > 50.0)
+ return (GSW_INVALID_VALUE);
+ }
+ return (sa);
+}
+/*
+!==========================================================================
+function gsw_sa_from_sp(sp,p,lon,lat)
+!==========================================================================
+
+! Calculates Absolute Salinity, SA, from Practical Salinity, SP
+!
+! sp : Practical Salinity [unitless]
+! p : sea pressure [dbar]
+! lon : longitude [DEG E]
+! lat : latitude [DEG N]
+!
+! gsw_sa_from_sp : Absolute Salinity [g/kg]
+*/
+double
+gsw_sa_from_sp(double sp, double p, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double saar, gsw_sa_baltic;
+
+ gsw_sa_baltic = gsw_sa_from_sp_baltic(sp,lon,lat);
+ if (gsw_sa_baltic < GSW_ERROR_LIMIT)
+ return (gsw_sa_baltic);
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return (gsw_ups*sp*(1.e0 + saar));
+}
+/*
+!==========================================================================
+function gsw_sa_from_sp_baltic(sp,lon,lat)
+!==========================================================================
+
+! For the Baltic Sea, calculates Absolute Salinity with a value
+! computed analytically from Practical Salinity
+!
+! sp : Practical Salinity [unitless]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! sa_from_sp_baltic : Absolute Salinity [g/kg]
+*/
+double
+gsw_sa_from_sp_baltic(double sp, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_BALTIC_DATA;
+ double xx_left, xx_right, return_value;
+
+ if (xb_left[1] < lon && lon < xb_right[0] && yb_left[0] < lat &&
+ lat < yb_left[2]) {
+
+ xx_left = gsw_util_xinterp1(yb_left, xb_left, 3, lat);
+
+ xx_right = gsw_util_xinterp1(yb_right, xb_right, 2, lat);
+
+ if (xx_left <= lon && lon <= xx_right)
+ return_value =((gsw_sso - 0.087)/35.0)*sp + 0.087;
+ else
+ return_value = GSW_INVALID_VALUE;
+ } else
+ return_value = GSW_INVALID_VALUE;
+
+ return (return_value);
+}
+/*
+!==========================================================================
+function gsw_sa_from_sstar(sstar,p,lon,lat)
+!==========================================================================
+
+! Calculates Absolute Salinity, SA, from Preformed Salinity, Sstar.
+!
+! Sstar : Preformed Salinity [g/kg]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sa_from_sstar : Absolute Salinity [g/kg]
+*/
+double
+gsw_sa_from_sstar(double sstar, double p, double lon, double lat)
+{
+ double saar;
+
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ /*
+ **! In the Baltic Sea, Sstar = SA, and note that gsw_saar returns zero
+ **! for SAAR in the Baltic.
+ */
+ return (sstar*(1e0 + saar)/(1e0 - 0.35e0*saar));
+}
+/*
+!==========================================================================
+elemental function gsw_sa_p_inrange (sa, p)
+!==========================================================================
+!
+! Check for any values that are out of the TEOS-10 range ...
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!---------------------------------------------------------------------------
+*/
+int
+gsw_sa_p_inrange(double sa, double p)
+{
+ if (p > 10000.0 || sa > 120.0 ||
+ (p + sa*71.428571428571402) > 13571.42857142857)
+ return (0);
+ return (1);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_seaice_fraction_to_freeze_seawater (sa, ct, p, &
+ sa_seaice, t_seaice, sa_freeze, ct_freeze, w_seaice)
+!==========================================================================
+!
+! Calculates the mass fraction of sea ice (mass of sea ice divided by mass
+! of sea ice plus seawater), which, when melted into seawater having the
+! properties (SA,CT,p) causes the final seawater to be at the freezing
+! temperature. The other outputs are the Absolute Salinity and
+! Conservative Temperature of the final seawater.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction of
+! salt in sea ice, expressed in g of salt per kg of sea ice.
+! [ g/kg ]
+! t_seaice = in-situ temperature of the sea ice at pressure p (ITS-90)
+! [ deg C ]
+!
+! SA_freeze = Absolute Salinity of seawater after the mass fraction of
+! sea ice, w_seaice, at temperature t_seaice has melted into
+! the original seawater, and the final mixture is at the
+! freezing temperature of seawater. [ g/kg ]
+!
+! CT_freeze = Conservative Temperature of seawater after the mass
+! fraction, w_seaice, of sea ice at temperature t_seaice has
+! melted into the original seawater, and the final mixture
+! is at the freezing temperature of seawater. [ deg C ]
+!
+! w_seaice = mass fraction of sea ice, at SA_seaice and t_seaice,
+! which, when melted into seawater at (SA,CT,p) leads to the
+! final mixed seawater being at the freezing temperature.
+! This output is between 0 and 1. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_seaice_fraction_to_freeze_seawater(double sa, double ct, double p,
+ double sa_seaice, double t_seaice, double *sa_freeze, double *ct_freeze,
+ double *w_seaice)
+{
+ int number_of_iterations;
+ double ctf, ctf_mean, ctf_old, ctf_plus1, ctf_zero,
+ dfunc_dsaf, func, func_plus1, func_zero, h, h_brine,
+ h_ih, sa_freezing, saf, saf_mean, saf_old,
+ salt_ratio, tf_sa_seaice, h_hat_sa, h_hat_ct, ctf_sa,
+ sa0 = 0.0, saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*The seawater ct input is below the freezing temp*/
+ *sa_freeze = *ct_freeze = *w_seaice = GSW_INVALID_VALUE;
+ return;
+ }
+
+ tf_sa_seaice = gsw_t_freezing(sa_seaice,p,saturation_fraction)
+ - 1e-6;
+ if (t_seaice > tf_sa_seaice) {
+ /*
+ ! The 1e-6 C buffer in the allowable t_seaice is to ensure that there is
+ ! some ice Ih in the sea ice. Without this buffer, that is if t_seaice
+ ! is allowed to be exactly equal to tf_sa_seaice, the sea ice is
+ ! actually 100% brine at Absolute Salinity of SA_seaice.
+ */
+ *sa_freeze = *ct_freeze = *w_seaice = GSW_INVALID_VALUE;
+ return;
+ }
+
+ sa_freezing = gsw_sa_freezing_from_t(t_seaice,p,saturation_fraction);
+ if (sa_freezing > GSW_ERROR_LIMIT) {
+ *sa_freeze = *ct_freeze = *w_seaice = GSW_INVALID_VALUE;
+ return;
+ }
+ h_brine = gsw_enthalpy_t_exact(sa_freezing,t_seaice,p);
+ salt_ratio = sa_seaice/sa_freezing;
+
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+
+ ctf_plus1 = gsw_ct_freezing(sa+1.0,p,saturation_fraction);
+ func_plus1 = (sa - sa_seaice)
+ *(gsw_enthalpy_ct_exact(sa+1.0,ctf_plus1,p)
+ - h) - (h - h_ih) + salt_ratio*(h_brine - h_ih);
+
+ ctf_zero = gsw_ct_freezing(sa0,p,saturation_fraction);
+ func_zero = (sa - sa_seaice)
+ *(gsw_enthalpy_ct_exact(sa0,ctf_zero,p) - h)
+ + sa*((h - h_ih) - salt_ratio*(h_brine - h_ih));
+
+ saf = -(sa+1.0)*func_zero/(func_plus1 - func_zero);
+ /*initial guess of saf*/
+ ctf = gsw_ct_freezing(saf,p,saturation_fraction);
+ gsw_enthalpy_first_derivatives_ct_exact(saf,ctf,p,&h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(saf,p,saturation_fraction,
+ &ctf_sa, NULL);
+
+ dfunc_dsaf = (sa - sa_seaice)*(h_hat_sa + h_hat_ct*ctf_sa)
+ - (h - h_ih) + salt_ratio*(h_brine - h_ih);
+
+ for (number_of_iterations = 1; number_of_iterations <= 4;
+ number_of_iterations++) {
+ saf_old = saf;
+ ctf_old = ctf;
+ func = (sa - sa_seaice)
+ *(gsw_enthalpy_ct_exact(saf_old,ctf_old,p) - h)
+ - (saf_old - sa)*((h - h_ih) - salt_ratio*(h_brine - h_ih));
+ saf = saf_old - func/dfunc_dsaf;
+ saf_mean = 0.5*(saf + saf_old);
+ ctf_mean = gsw_ct_freezing(saf_mean,p,saturation_fraction);
+ gsw_enthalpy_first_derivatives_ct_exact(saf_mean,ctf_mean,p,
+ &h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(saf_mean,p,saturation_fraction,
+ &ctf_sa, NULL);
+ dfunc_dsaf = (sa - sa_seaice)*(h_hat_sa + h_hat_ct*ctf_sa)
+ - (h - h_ih) + salt_ratio*(h_brine - h_ih);
+ saf = saf_old - func/dfunc_dsaf;
+ ctf = gsw_ct_freezing(saf,p,saturation_fraction);
+ }
+/*
+! After these 4 iterations of this modified Newton-Raphson method, the
+! errors in SA_freeze is less than 1.5x10^-12 g/kg, in CT_freeze is less than
+! 2x10^-13 deg C and in w_seaice is less than 2.8x10^-13 which represent machine
+! precision for these calculations.
+*/
+ *sa_freeze = saf;
+ *ct_freeze = ctf;
+ *w_seaice = (h - gsw_enthalpy_ct_exact(*sa_freeze,*ct_freeze,p)) /
+ (h - h_ih - salt_ratio*(h_brine - h_ih));
+ return;
+}
+/*
+!==========================================================================
+function gsw_sigma0(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 0 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+! This function uses the computationally-efficient 48-term expression for
+! density in terms of SA, CT and p (IOC et al., 2010).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! gsw_sigma0 : potential density anomaly with reference pressure of 0
+! (48 term equation)
+*/
+double
+gsw_sigma0(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double vp0, xs, ys;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+
+ vp0 = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys)))));
+
+ return (1.0/vp0 - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sigma1(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 1000 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! sigma1 : potential density anomaly with reference pressure of 1000
+*/
+double
+gsw_sigma1(double sa, double ct)
+{
+ return (gsw_rho(sa,ct,1000.0) - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sigma2(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 2000 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! sigma2 : potential density anomaly with reference pressure of 2000
+*/
+double
+gsw_sigma2(double sa, double ct)
+{
+ return (gsw_rho(sa,ct,2000.0) - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sigma3(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 3000 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! sigma3 : potential density anomaly with reference pressure of 3000
+*/
+double
+gsw_sigma3(double sa, double ct)
+{
+ return (gsw_rho(sa,ct,3000.0) - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sigma4(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 4000 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! sigma4 : potential density anomaly with reference pressure of 4000
+*/
+double
+gsw_sigma4(double sa, double ct)
+{
+ return (gsw_rho(sa,ct,4000.0) - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sound_speed(sa,ct,p)
+!==========================================================================
+
+! Calculates the speed of sound in seawater. This function has inputs of
+! Absolute Salinity and Conservative Temperature. This function uses the
+! computationally-efficient expression for specific volume in terms of SA,
+! CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! sound_speed : speed of sound in seawater [m/s]
+*/
+double
+gsw_sound_speed(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v, v_p, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ v_p = c000
+ + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs))))
+ + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020
+ + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs)
+ + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201
+ + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs))
+ + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys)))
+ + z*( c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys)
+ + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z))));
+
+ return (10000.0*sqrt(-v*v/v_p));
+}
+/*
+!==========================================================================
+elemental function gsw_sound_speed_ice (t, p)
+!==========================================================================
+!
+! Calculates the compression speed of sound in ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! sound_speed_ice = compression speed of sound in ice [ m/s ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sound_speed_ice(double t, double p)
+{
+ double gi_tp, gi_tt;
+
+ gi_tt = gsw_gibbs_ice(2,0,t,p);
+ gi_tp = gsw_gibbs_ice(1,1,t,p);
+
+ return (gsw_gibbs_ice(0,1,t,p) *
+ sqrt(gi_tt/(gi_tp*gi_tp - gi_tt*gsw_gibbs_ice(0,2,t,p))));
+}
+/*
+!==========================================================================
+function gsw_sound_speed_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates the speed of sound in seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_sound_speed_t_exact : sound speed [m/s]
+*/
+double
+gsw_sound_speed_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1, n2=2;
+ double g_tt, g_tp;
+
+ g_tt = gsw_gibbs(n0,n2,n0,sa,t,p);
+ g_tp = gsw_gibbs(n0,n1,n1,sa,t,p);
+
+ return (gsw_gibbs(n0,n0,n1,sa,t,p) *
+ sqrt(g_tt/(g_tp*g_tp - g_tt*gsw_gibbs(n0,n0,n2,sa,t,p))));
+}
+/*
+!--------------------------------------------------------------------------
+! Practical Salinity (SP), PSS-78
+!--------------------------------------------------------------------------
+
+!==========================================================================
+function gsw_sp_from_c(c,t,p)
+!==========================================================================
+
+! Calculates Practical Salinity, SP, from conductivity, C, primarily using
+! the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical
+! Salinity is only valid in the range 2 < SP < 42. If the PSS-78
+! algorithm produces a Practical Salinity that is less than 2 then the
+! Practical Salinity is recalculated with a modified form of the Hill et
+! al. (1986) formula. The modification of the Hill et al. (1986)
+! expression is to ensure that it is exactly consistent with PSS-78
+! at SP = 2. Note that the input values of conductivity need to be in
+! units of mS/cm (not S/m).
+!
+! c : conductivity [ mS/cm ]
+! t : in-situ temperature [ITS-90] [deg C]
+! p : sea pressure [dbar]
+!
+! sp : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_c(double c, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SP_COEFFICIENTS;
+ double sp, t68, ft68, r, rt_lc, rp, rt, rtx,
+ hill_ratio, x, sqrty, part1, part2,
+ sp_hill_raw;
+
+ t68 = t*1.00024e0;
+ ft68 = (t68 - 15e0)/(1e0 + k*(t68 - 15e0));
+ /*
+ ! The dimensionless conductivity ratio, R, is the conductivity input, C,
+ ! divided by the present estimate of C(SP=35, t_68=15, p=0) which is
+ ! 42.9140 mS/cm (=4.29140 S/m), (Culkin and Smith, 1980).
+ */
+
+ r = c/gsw_c3515; /* 0.023302418791070513 = 1./42.9140 */
+
+ /*rt_lc corresponds to rt as defined in the UNESCO 44 (1983) routines.*/
+ rt_lc = c0 + (c1 + (c2 + (c3 + c4*t68)*t68)*t68)*t68;
+ rp = 1e0 + (p*(e1 + e2*p + e3*p*p))/(1e0 + d1*t68 + d2*t68*t68 +
+ (d3 + d4*t68)*r);
+ rt = r/(rp*rt_lc);
+
+ if (rt < 0.0) {
+ return (GSW_INVALID_VALUE);
+ }
+
+ rtx = sqrt(rt);
+
+ sp = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx +
+ ft68*(b0 + (b1 + (b2 + (b3 +
+ (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx);
+ /*
+ ! The following section of the code is designed for SP < 2 based on the
+ ! Hill et al. (1986) algorithm. This algorithm is adjusted so that it is
+ ! exactly equal to the PSS-78 algorithm at SP = 2.
+ */
+
+ if (sp < 2) {
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ x = 400e0*rt;
+ sqrty = 10e0*rtx;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ sp_hill_raw = sp - a0/part1 - b0*ft68/part2;
+ sp = hill_ratio*sp_hill_raw;
+ }
+
+ /* This line ensures that SP is non-negative. */
+ if (sp < 0.0) {
+ sp = GSW_INVALID_VALUE;
+ }
+
+ return (sp);
+}
+/*
+!==========================================================================
+function gsw_sp_from_sa(sa,p,lon,lat)
+!==========================================================================
+
+! Calculates Practical salinity, sp, from Absolute salinity, sa
+!
+! sa : Absolute Salinity [g/kg]
+! p : sea pressure [dbar]
+! lon : longitude [DEG E]
+! lat : latitude [DEG N]
+!
+! gsw_sp_from_sa : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_sa(double sa, double p, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double saar, gsw_sp_baltic;
+
+ gsw_sp_baltic = gsw_sp_from_sa_baltic(sa,lon,lat);
+ if (gsw_sp_baltic < GSW_ERROR_LIMIT)
+ return (gsw_sp_baltic);
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return ((sa/gsw_ups)/(1e0 + saar));
+}
+/*
+!==========================================================================
+function gsw_sp_from_sa_baltic(sa,lon,lat)
+!==========================================================================
+
+! For the Baltic Sea, calculates Practical Salinity with a value
+! computed analytically from Absolute Salinity
+!
+! sa : Absolute Salinity [g/kg]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sp_from_sa_baltic : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_sa_baltic(double sa, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_BALTIC_DATA;
+ double xx_left, xx_right, return_value;
+
+ if (xb_left[1] < lon && lon < xb_right[0] && yb_left[0] < lat &&
+ lat < yb_left[2]) {
+
+ xx_left = gsw_util_xinterp1(yb_left, xb_left, 3, lat);
+
+ xx_right = gsw_util_xinterp1(yb_right, xb_right, 2, lat);
+
+ if (xx_left <= lon && lon <= xx_right)
+ return_value = (35.0/(gsw_sso - 0.087))*(sa - 0.087);
+ else
+ return_value = GSW_INVALID_VALUE;
+ } else
+ return_value = GSW_INVALID_VALUE;
+
+ return (return_value);
+}
+/*
+!==========================================================================
+function gsw_sp_from_sk(sk)
+!==========================================================================
+
+! Calculates Practical Salinity, SP, from SK
+!
+! SK : Knudsen Salinity [parts per thousand, ppt]
+!
+! gsw_sp_from_sk : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_sk(double sk)
+{
+ GSW_TEOS10_CONSTANTS;
+ double gsw_sp_from_sk_value;
+
+
+ gsw_sp_from_sk_value = (sk - 0.03e0)*(gsw_soncl/1.805e0);
+
+ if (gsw_sp_from_sk_value < 0e0)
+ gsw_sp_from_sk_value = GSW_INVALID_VALUE;
+
+ return (gsw_sp_from_sk_value);
+}
+/*
+!==========================================================================
+function gsw_sp_from_sr(sr)
+!==========================================================================
+
+! Calculates Practical Salinity, sp, from Reference Salinity, sr.
+!
+! sr : Reference Salinity [g/kg]
+!
+! gsw_sp_from_sr : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_sr(double sr)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return(sr/gsw_ups);
+}
+/*
+!==========================================================================
+function gsw_sp_from_sstar(sstar,p,lon,lat)
+!==========================================================================
+
+! Calculates Practical Salinity, SP, from Preformed Salinity, Sstar.
+!
+! sstar : Preformed Salinity [g/kg]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sp_from_Sstar : Preformed Salinity [g/kg]
+*/
+double
+gsw_sp_from_sstar(double sstar, double p, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double saar, sp_baltic;
+
+ /*
+ **! In the Baltic Sea, SA = Sstar.
+ */
+ sp_baltic = gsw_sp_from_sa_baltic(sstar,lon,lat);
+ if (sp_baltic < GSW_ERROR_LIMIT)
+ return (sp_baltic);
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return ((sstar/gsw_ups)/(1.0 - 0.35e0*saar));
+}
+/*
+!==========================================================================
+function gsw_specvol(sa,ct,p)
+!==========================================================================
+!
+! Calculates specific volume from Absolute Salinity, Conservative
+! Temperature and pressure, using the computationally-efficient
+! polynomial expression for specific volume (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! specvol: specific volume [m^3/kg]
+*/
+double
+gsw_specvol(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double xs, ys, z, value;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ value = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ return (value);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_alpha_beta (sa, ct, p, specvol, alpha, &
+ beta)
+!==========================================================================
+!
+! Calculates specific volume, the appropiate thermal expansion coefficient
+! and the appropriate saline contraction coefficient of seawater from
+! Absolute Salinity and Conservative Temperature. This function uses the
+! computationally-efficient expression for specific volume in terms of
+! SA, CT and p (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! specvol = specific volume [ m/kg ]
+! alpha = thermal expansion coefficient [ 1/K ]
+! with respect to Conservative Temperature
+! beta = saline (i.e. haline) contraction [ kg/g ]
+! coefficient at constant Conservative Temperature
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_alpha_beta(double sa, double ct, double p, double *specvol,
+ double *alpha, double *beta)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v, v_ct, v_sa_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ if (specvol != NULL)
+ *specvol = v;
+
+ if (alpha != NULL) {
+
+ v_ct = a000 + xs*(a100 + xs*(a200 + xs*(a300
+ + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ *alpha = 0.025*v_ct/v;
+
+ }
+
+ if (beta != NULL) {
+
+ v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300
+ + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ *beta = -v_sa_part*0.5*gsw_sfac/(v*xs);
+
+ }
+}
+/*
+!==========================================================================
+function gsw_specvol_anom_standard(sa,ct,p)
+!==========================================================================
+!
+! Calculates specific volume anomaly of seawater.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! specvol_anom : specific volume anomaly of seawater
+*/
+double
+gsw_specvol_anom_standard(double sa, double ct, double p)
+{
+ return (gsw_specvol(sa,ct,p) - gsw_specvol_sso_0(p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_first_derivatives (sa, ct, p, v_sa, v_ct, &
+ v_p, iflag)
+! =========================================================================
+!
+! Calculates three first-order derivatives of specific volume (v).
+! Note that this function uses the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! v_SA = The first derivative of specific volume with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! v_CT = The first derivative of specific volume with respect to
+! CT at constant SA and p. [ J/(kg K(g/kg)) ]
+! v_P = The first derivative of specific volume with respect to
+! P at constant SA and CT. [ J/(kg K^2) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_first_derivatives (double sa, double ct, double p,
+ double *v_sa, double *v_ct, double *v_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v_ct_part, v_p_part, v_sa_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ if (v_sa != NULL) {
+
+ v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300
+ + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ *v_sa = 0.5*gsw_sfac*v_sa_part/xs;
+
+ }
+
+ if (v_ct != NULL) {
+
+ v_ct_part = a000 + xs*(a100 + xs*(a200 + xs*(a300
+ + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z))) ;
+
+ *v_ct = 0.025*v_ct_part;
+
+ }
+
+ if (v_p != NULL) {
+
+ v_p_part = c000 + xs*(c100 + xs*(c200 + xs*(c300
+ + xs*(c400 + c500*xs))))
+ + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020
+ + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs)
+ + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201
+ + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs))
+ + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys)))
+ + z*( c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys)
+ + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z))));
+
+ *v_p = 1e-8*v_p_part;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_first_derivatives_wrt_enthalpy (sa, ct, &
+ p, v_sa, v_h, iflag)
+! =========================================================================
+!
+! Calculates two first-order derivatives of specific volume (v).
+! Note that this function uses the using the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! v_SA = The first derivative of specific volume with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! v_h = The first derivative of specific volume with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_first_derivatives_wrt_enthalpy(double sa, double ct, double p,
+ double *v_sa, double *v_h)
+{
+ double h_ct=1.0, h_sa, rec_h_ct, vct_ct, vct_sa;
+
+ if (v_sa != NULL) {
+
+ gsw_specvol_first_derivatives(sa,ct,p,&vct_sa,&vct_ct,NULL);
+ gsw_enthalpy_first_derivatives(sa,ct,p,&h_sa,&h_ct);
+
+ } else if (v_h != NULL) {
+
+ gsw_specvol_first_derivatives(sa,ct,p,NULL,&vct_ct,NULL);
+ gsw_enthalpy_first_derivatives(sa,ct,p,NULL,&h_ct);
+
+ }
+
+ rec_h_ct = 1.0/h_ct;
+
+ if (v_sa != NULL)
+ *v_sa = vct_sa - (vct_ct*h_sa)*rec_h_ct;
+
+ if (v_h != NULL)
+ *v_h = vct_ct*rec_h_ct;
+
+ return;
+}
+/*
+!==========================================================================
+elemental function gsw_specvol_ice (t, p)
+!==========================================================================
+!
+! Calculates the specific volume of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! specvol_ice = specific volume [ m^3/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_specvol_ice(double t, double p)
+{
+ return (gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_second_derivatives (sa, ct, p, v_sa_sa, &
+ v_sa_ct, v_ct_ct, v_sa_p, v_ct_p, iflag)
+! =========================================================================
+!
+! Calculates five second-order derivatives of specific volume (v).
+! Note that this function uses the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! v_SA_SA = The second derivative of specific volume with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! v_SA_CT = The second derivative of specific volume with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+! v_CT_CT = The second derivative of specific volume with respect to
+! CT at constant SA and p. [ J/(kg K^2) ]
+! v_SA_P = The second derivative of specific volume with respect to
+! SA and P at constant CT. [ J/(kg K(g/kg)) ]
+! v_CT_P = The second derivative of specific volume with respect to
+! CT and P at constant SA. [ J/(kg K(g/kg)) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_second_derivatives (double sa, double ct, double p,
+ double *v_sa_sa, double *v_sa_ct, double *v_ct_ct, double *v_sa_p,
+ double *v_ct_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v_ct_ct_part, v_ct_p_part, v_sa_ct_part, v_sa_p_part,
+ v_sa_sa_part, xs, xs2, ys, z;
+
+ xs2 = gsw_sfac*sa + offset;
+ xs = sqrt(xs2);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ if (v_sa_sa != NULL) {
+
+ v_sa_sa_part = (-b000 + xs2*(b200 + xs*(2.0*b300 + xs*(3.0*b400
+ + 4.0*b500*xs))) + ys*(-b010 + xs2*(b210 + xs*(2.0*b310
+ + 3.0*b410*xs)) + ys*(-b020 + xs2*(b220 + 2.0*b320*xs)
+ + ys*(-b030 + b230*xs2 + ys*(-b040 - b050*ys)))) + z*(-b001
+ + xs2*(b201 + xs*(2.0*b301 + 3.0*b401*xs)) + ys*(-b011
+ + xs2*(b211 + 2.0*b311*xs) + ys*(-b021 + b221*xs2
+ + ys*(-b031 - b041*ys))) + z*(-b002 + xs2*(b202 + 2.0*b302*xs)
+ + ys*(-b012 + b212*xs2 + ys*(-b022 - b032*ys)) + z*(-b003
+ - b013*ys - b004*z))))/xs2;
+
+ *v_sa_sa = 0.25*gsw_sfac*gsw_sfac*v_sa_sa_part/xs;
+
+ }
+
+ if (v_sa_ct != NULL) {
+
+ v_sa_ct_part = (b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(2.0*(b020 + xs*(b120 + xs*(b220 + b320*xs)))
+ + ys*(3.0*(b030 + xs*(b130 + b230*xs)) + ys*(4.0*(b040
+ + b140*xs) + 5.0*b050*ys))) + z*(b011 + xs*(b111 + xs*(b211
+ + b311*xs)) + ys*(2.0*(b021 + xs*(b121 + b221*xs))
+ + ys*(3.0*(b031 + b131*xs) + 4.0*b041*ys)) + z*(b012
+ + xs*(b112 + b212*xs) + ys*(2.0*(b022 + b122*xs)
+ + 3.0*b032*ys) + b013*z)))/xs;
+
+ *v_sa_ct = 0.025*0.5*gsw_sfac*v_sa_ct_part;
+
+ }
+
+ if (v_ct_ct != NULL) {
+
+ v_ct_ct_part = a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(2.0*(a020 + xs*(a120 + xs*(a220 + a320*xs)))
+ + ys*(3.0*(a030 + xs*(a130 + a230*xs)) + ys*(4.0*(a040
+ + a140*xs) + 5.0*a050*ys))) + z*( a011 + xs*(a111 + xs*(a211
+ + a311*xs)) + ys*(2.0*(a021 + xs*(a121 + a221*xs))
+ + ys*(3.0*(a031 + a131*xs) + 4.0*a041*ys)) + z*(a012
+ + xs*(a112 + a212*xs) + ys*(2.0*(a022 + a122*xs)
+ + 3.0*a032*ys) + a013*z));
+
+ *v_ct_ct = 0.025*0.025*v_ct_ct_part;
+
+ }
+
+ if (v_sa_p != NULL) {
+
+ v_sa_p_part = b001 + xs*(b101 + xs*(b201 + xs*(b301
+ + b401*xs))) + ys*(b011 + xs*(b111 + xs*(b211
+ + b311*xs)) + ys*(b021 + xs*(b121 + b221*xs)
+ + ys*(b031 + b131*xs + b041*ys))) + z*(2.0*(b002 + xs*(b102
+ + xs*(b202 + b302*xs)) + ys*(b012 + xs*(b112
+ + b212*xs) + ys*(b022
+ + b122*xs + b032*ys))) + z*(3.0*(b003 + b103*xs + b013*ys)
+ + 4.0*b004*z));
+
+ *v_sa_p = 1e-8*0.5*gsw_sfac*v_sa_p_part;
+
+ }
+
+ if (v_ct_p != NULL) {
+
+ v_ct_p_part = a001 + xs*(a101 + xs*(a201 + xs*(a301
+ + a401*xs))) + ys*(a011
+ + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs)
+ + ys*(a031 + a131*xs + a041*ys))) + z*(2.0*(a002 + xs*(a102
+ + xs*(a202 + a302*xs)) + ys*(a012 + xs*(a112 + a212*xs)
+ + ys*(a022 + a122*xs + a032*ys))) + z*(3.0*(a003
+ + a103*xs + a013*ys) + 4.0*a004*z));
+
+ *v_ct_p = 1e-8*0.025*v_ct_p_part;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_second_derivatives_wrt_enthalpy (sa, ct, &
+ p, v_sa_sa, v_sa_h, v_h_h, iflag)
+! =========================================================================
+!
+! Calculates three first-order derivatives of specific volume (v) with
+! respect to enthalpy. Note that this function uses the using the
+! computationally-efficient expression for specific volume
+! (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! v_SA_SA = The second-order derivative of specific volume with respect to
+! Absolute Salinity at constant h & p. [ J/(kg (g/kg)^2) ]
+! v_SA_h = The second-order derivative of specific volume with respect to
+! SA and h at constant p. [ J/(kg K(g/kg)) ]
+! v_h_h = The second-order derivative with respect to h at
+! constant SA & p.
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_second_derivatives_wrt_enthalpy (double sa, double ct, double p,
+ double *v_sa_sa, double *v_sa_h, double *v_h_h)
+{
+ double h_ct, h_ct_ct, h_sa, h_sa_ct, h_sa_sa, rec_h_ct, v_h_h_part,
+ rec_h_ct2, v_ct, vct_ct_ct, vct_sa_ct, vct_sa_sa, v_sa_h_part;
+
+ gsw_specvol_first_derivatives(sa,ct,p,NULL, &v_ct, NULL);
+
+ if ((v_sa_sa != NULL) || (v_sa_h != NULL))
+ gsw_enthalpy_first_derivatives(sa,ct,p,&h_sa,&h_ct);
+ else
+ gsw_enthalpy_first_derivatives(sa,ct,p,NULL,&h_ct);
+
+ if (v_sa_sa != NULL)
+ gsw_specvol_second_derivatives(sa,ct,p,&vct_sa_sa,&vct_sa_ct,
+ &vct_ct_ct, NULL, NULL);
+ else if (v_sa_h != NULL)
+ gsw_specvol_second_derivatives(sa,ct,p,NULL,&vct_sa_ct,&vct_ct_ct,
+ NULL, NULL);
+ else
+ gsw_specvol_second_derivatives(sa,ct,p,NULL,NULL,&vct_ct_ct,
+ NULL, NULL);
+
+ if (v_sa_sa != NULL)
+ gsw_enthalpy_second_derivatives(sa,ct,p,&h_sa_sa,&h_sa_ct,&h_ct_ct);
+ else if (v_sa_h != NULL)
+ gsw_enthalpy_second_derivatives(sa,ct,p,NULL,&h_sa_ct,&h_ct_ct);
+ else
+ gsw_enthalpy_second_derivatives(sa,ct,p,NULL,NULL,&h_ct_ct);
+
+ rec_h_ct = 1.0/h_ct;
+ rec_h_ct2 = rec_h_ct*rec_h_ct;
+
+ v_h_h_part = (vct_ct_ct*h_ct - h_ct_ct*v_ct)*(rec_h_ct2*rec_h_ct);
+
+ if (v_h_h != NULL) *v_h_h = v_h_h_part;
+
+ if ((v_sa_sa != NULL) || (v_sa_h != NULL)) {
+
+ v_sa_h_part = (vct_sa_ct*h_ct - v_ct*h_sa_ct)*rec_h_ct2
+ - h_sa*v_h_h_part;
+
+ if (v_sa_h != NULL) *v_sa_h = v_sa_h_part;
+
+ if (v_sa_sa != NULL)
+ *v_sa_sa = vct_sa_sa - (h_ct*(vct_sa_ct*h_sa
+ - v_ct*h_sa_sa) + v_ct*h_sa*h_sa_ct)*rec_h_ct2
+ - h_sa*v_sa_h_part;
+ }
+}
+/*
+!==========================================================================
+function gsw_specvol_sso_0(p)
+!==========================================================================
+
+! This function calculates specific volume at the Standard Ocean Salinty,
+! SSO, and at a Conservative Temperature of zero degrees C, as a function
+! of pressure, p, in dbar, using a streamlined version of the CT version
+! of specific volume, that is, a streamlined version of the code
+! "gsw_specvol(SA,CT,p)".
+!
+! p : sea pressure [dbar]
+! 3 -1
+! specvol_sso_0 : specvol(sso,0,p) [m kg ]
+*/
+double
+gsw_specvol_sso_0(double p)
+{
+ GSW_SPECVOL_COEFFICIENTS;
+ double z, return_value;
+
+ z = p*1.0e-4;
+
+ return_value = 9.726613854843870e-04 + z*(-4.505913211160929e-05
+ + z*(7.130728965927127e-06 + z*(-6.657179479768312e-07
+ + z*(-2.994054447232880e-08 + z*(v005 + v006*z)))));
+ return (return_value);
+}
+/*
+!==========================================================================
+function gsw_specvol_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates the specific volume of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! specvol_t_exact : specific volume [kg/m^3]
+*/
+double
+gsw_specvol_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (gsw_gibbs(n0,n0,n1,sa,t,p));
+}
+/*
+!==========================================================================
+function gsw_spiciness0(sa,ct)
+!==========================================================================
+!
+! Calculates spiciness from Absolute Salinity and Conservative
+! Temperature at a pressure of 0 dbar, as described by McDougall and
+! Krzysik (2015). This routine is based on the computationally-efficient
+! expression for specific volume in terms of SA, CT and p (Roquet et al.,
+! 2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! spiciness0 = spiciness referenced to a pressure of 0 dbar,
+! i.e. the surface [ kg/m^3 ]
+!
+*/
+
+double
+gsw_spiciness0(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double s01 = -9.22982898371678e1, s02 = -1.35727873628866e1,
+ s03 = 1.87353650994010e1, s04 = -1.61360047373455e1,
+ s05 = 3.76112762286425e1, s06 = -4.27086671461257e1,
+ s07 = 2.00820111041594e1, s08 = 2.87969717584045e2,
+ s09 = 1.13747111959674e1, s10 = 6.07377192990680e1,
+ s11 = -7.37514033570187e1, s12 = -7.51171878953574e1,
+ s13 = 1.63310989721504e2, s14 = -8.83222751638095e1,
+ s15 = -6.41725302237048e2, s16 = 2.79732530789261e1,
+ s17 = -2.49466901993728e2, s18 = 3.26691295035416e2,
+ s19 = 2.66389243708181e1, s20 = -2.93170905757579e2,
+ s21 = 1.76053907144524e2, s22 = 8.27634318120224e2,
+ s23 = -7.02156220126926e1, s24 = 3.82973336590803e2,
+ s25 = -5.06206828083959e2, s26 = 6.69626565169529e1,
+ s27 = 3.02851235050766e2, s28 = -1.96345285604621e2,
+ s29 = -5.74040806713526e2, s30 = 7.03285905478333e1,
+ s31 = -2.97870298879716e2, s32 = 3.88340373735118e2,
+ s33 = -8.29188936089122e1, s34 = -1.87602137195354e2,
+ s35 = 1.27096944425793e2, s36 = 2.11671167892147e2,
+ s37 = -3.15140919876285e1, s38 = 1.16458864953602e2,
+ s39 = -1.50029730802344e2, s40 = 3.76293848660589e1,
+ s41 = 6.47247424373200e1, s42 = -4.47159994408867e1,
+ s43 = -3.23533339449055e1, s44 = 5.30648562097667,
+ s45 = -1.82051249177948e1, s46 = 2.33184351090495e1,
+ s47 = -6.22909903460368, s48 = -9.55975464301446,
+ s49 = 6.61877073960113;
+ double xs, ys, spiciness0;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+
+ spiciness0= s01+ys*(s02+ys*(s03+ys*(s04+ys*(s05+ys*(s06+s07*ys)))))
+ +xs*(s08+ys*(s09+ys*(s10+ys*(s11+ys*(s12+ys*(s13+s14*ys)))))
+ +xs*(s15+ys*(s16+ys*(s17+ys*(s18+ys*(s19+ys*(s20+s21*ys)))))
+ +xs*(s22+ys*(s23+ys*(s24+ys*(s25+ys*(s26+ys*(s27+s28*ys)))))
+ +xs*(s29+ys*(s30+ys*(s31+ys*(s32+ys*(s33+ys*(s34+s35*ys)))))
+ +xs*(s36+ys*(s37+ys*(s38+ys*(s39+ys*(s40+ys*(s41+s42*ys)))))
+ +xs*(s43+ys*(s44+ys*(s45+ys*(s46+ys*(s47+ys*(s48+s49*ys)))))
+ ))))));
+ return (spiciness0);
+}
+/*
+!==========================================================================
+function gsw_spiciness1(sa,ct)
+!==========================================================================
+!
+! Calculates spiciness from Absolute Salinity and Conservative
+! Temperature at a pressure of 1000 dbar, as described by McDougall and
+! Krzysik (2015). This routine is based on the computationally-efficient
+! expression for specific volume in terms of SA, CT and p (Roquet et al.,
+! 2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! spiciness1 = spiciness referenced to a pressure of 1000 dbar [ kg/m^3 ]
+!
+*/
+double
+gsw_spiciness1(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double s01 = -9.19874584868912e1, s02 = -1.33517268529408e1,
+ s03 = 2.18352211648107e1, s04 = -2.01491744114173e1,
+ s05 = 3.70004204355132e1, s06 = -3.78831543226261e1,
+ s07 = 1.76337834294554e1, s08 = 2.87838842773396e2,
+ s09 = 2.14531420554522e1, s10 = 3.14679705198796e1,
+ s11 = -4.04398864750692e1, s12 = -7.70796428950487e1,
+ s13 = 1.36783833820955e2, s14 = -7.36834317044850e1,
+ s15 = -6.41753415180701e2, s16 = 1.33701981685590,
+ s17 = -1.75289327948412e2, s18 = 2.42666160657536e2,
+ s19 = 3.17062400799114e1, s20 = -2.28131490440865e2,
+ s21 = 1.39564245068468e2, s22 = 8.27747934506435e2,
+ s23 = -3.50901590694775e1, s24 = 2.87473907262029e2,
+ s25 = -4.00227341144928e2, s26 = 6.48307189919433e1,
+ s27 = 2.16433334701578e2, s28 = -1.48273032774305e2,
+ s29 = -5.74545648799754e2, s30 = 4.50446431127421e1,
+ s31 = -2.30714981343772e2, s32 = 3.15958389253065e2,
+ s33 = -8.60635313930106e1, s34 = -1.22978455069097e2,
+ s35 = 9.18287282626261e1, s36 = 2.12120473062203e2,
+ s37 = -2.21528216973820e1, s38 = 9.19013417923270e1,
+ s39 = -1.24400776026014e2, s40 = 4.08512871163839e1,
+ s41 = 3.91127352213516e1, s42 = -3.10508021853093e1,
+ s43 = -3.24790035899152e1, s44 = 3.91029016556786,
+ s45 = -1.45362719385412e1, s46 = 1.96136194246355e1,
+ s47 = -7.06035474689088, s48 = -5.36884688614009,
+ s49 = 4.43247303092448;
+ double xs, ys, spiciness1;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ spiciness1= s01+ys*(s02+ys*(s03+ys*(s04+ys*(s05+ys*(s06+s07*ys)))))
+ +xs*(s08+ys*(s09+ys*(s10+ys*(s11+ys*(s12+ys*(s13+s14*ys)))))
+ +xs*(s15+ys*(s16+ys*(s17+ys*(s18+ys*(s19+ys*(s20+s21*ys)))))
+ +xs*(s22+ys*(s23+ys*(s24+ys*(s25+ys*(s26+ys*(s27+s28*ys)))))
+ +xs*(s29+ys*(s30+ys*(s31+ys*(s32+ys*(s33+ys*(s34+s35*ys)))))
+ +xs*(s36+ys*(s37+ys*(s38+ys*(s39+ys*(s40+ys*(s41+s42*ys)))))
+ +xs*(s43+ys*(s44+ys*(s45+ys*(s46+ys*(s47+ys*(s48+s49*ys)))))
+ ))))));
+ return (spiciness1);
+}
+/*
+!==========================================================================
+function gsw_spiciness2(sa,ct)
+!==========================================================================
+!
+! Calculates spiciness from Absolute Salinity and Conservative
+! Temperature at a pressure of 2000 dbar, as described by McDougall and
+! Krzysik (2015). This routine is based on the computationally-efficient
+! expression for specific volume in terms of SA, CT and p (Roquet et al.,
+! 2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! spiciness2 = spiciness referenced to a pressure of 2000 dbar [ kg/m^3 ]
+!
+*/
+double
+gsw_spiciness2(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double s01 = -9.17327320732265e1, s02 = -1.31200235147912e1,
+ s03 = 2.49574345782503e1, s04 = -2.41678075247398e1,
+ s05 = 3.61654631402053e1, s06 = -3.22582164667710e1,
+ s07 = 1.45092623982509e1, s08 = 2.87776645983195e2,
+ s09 = 3.13902307672447e1, s10 = 1.69777467534459,
+ s11 = -5.69630115740438, s12 = -7.97586359017987e1,
+ s13 = 1.07507460387751e2, s14 = -5.58234404964787e1,
+ s15 = -6.41708068766557e2, s16 = -2.53494801286161e1,
+ s17 = -9.86755437385364e1, s18 = 1.52406930795842e2,
+ s19 = 4.23888258264105e1, s20 = -1.60118811141438e2,
+ s21 = 9.67497898053989e1, s22 = 8.27674355478637e2,
+ s23 = 5.27561234412133e-1, s24 = 1.87440206992396e2,
+ s25 = -2.83295392345171e2, s26 = 5.14485994597635e1,
+ s27 = 1.29975755062696e2, s28 = -9.36526588377456e1,
+ s29 = -5.74911728972948e2, s30 = 1.91175851862772e1,
+ s31 = -1.59347231968841e2, s32 = 2.33884725744938e2,
+ s33 = -7.87744010546157e1, s34 = -6.04757235443685e1,
+ s35 = 5.27869695599657e1, s36 = 2.12517758478878e2,
+ s37 = -1.24351794740528e1, s38 = 6.53904308937490e1,
+ s39 = -9.44804080763788e1, s40 = 3.93874257887364e1,
+ s41 = 1.49425448888996e1, s42 = -1.62350721656367e1,
+ s43 = -3.25936844276669e1, s44 = 2.44035700301595,
+ s45 = -1.05079633683795e1, s46 = 1.51515796259082e1,
+ s47 = -7.06609886460683, s48 = -1.48043337052968,
+ s49 = 2.10066653978515;
+ double xs, ys, spiciness2;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+
+ spiciness2= s01+ys*(s02+ys*(s03+ys*(s04+ys*(s05+ys*(s06+s07*ys)))))
+ +xs*(s08+ys*(s09+ys*(s10+ys*(s11+ys*(s12+ys*(s13+s14*ys)))))
+ +xs*(s15+ys*(s16+ys*(s17+ys*(s18+ys*(s19+ys*(s20+s21*ys)))))
+ +xs*(s22+ys*(s23+ys*(s24+ys*(s25+ys*(s26+ys*(s27+s28*ys)))))
+ +xs*(s29+ys*(s30+ys*(s31+ys*(s32+ys*(s33+ys*(s34+s35*ys)))))
+ +xs*(s36+ys*(s37+ys*(s38+ys*(s39+ys*(s40+ys*(s41+s42*ys)))))
+ +xs*(s43+ys*(s44+ys*(s45+ys*(s46+ys*(s47+ys*(s48+s49*ys)))))
+ ))))));
+ return (spiciness2);
+}
+/*
+!==========================================================================
+function gsw_sr_from_sp(sp)
+!==========================================================================
+
+! Calculates Reference Salinity, SR, from Practical Salinity, SP.
+!
+! sp : Practical Salinity [unitless]
+!
+! gsw_sr_from_sp : Reference Salinity [g/kg]
+*/
+double
+gsw_sr_from_sp(double sp)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (sp*gsw_ups);
+}
+/*
+!==========================================================================
+function gsw_sstar_from_sa(sa,p,lon,lat)
+!==========================================================================
+
+! Calculates Preformed Salinity, Sstar, from Absolute Salinity, SA.
+!
+! sa : Absolute Salinity [g/kg]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sstar_from_sa : Preformed Salinity [g/kg]
+*/
+double
+gsw_sstar_from_sa(double sa, double p, double lon, double lat)
+{
+ double saar;
+
+ saar = gsw_saar(p,lon,lat);
+ /*
+ ! In the Baltic Sea, Sstar = sa, and note that gsw_saar returns zero
+ ! for saar in the Baltic.
+ */
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return (sa*(1e0 - 0.35e0*saar)/(1e0 + saar));
+}
+/*
+!==========================================================================
+function gsw_sstar_from_sp(sp,p,lon,lat)
+!==========================================================================
+
+! Calculates Preformed Salinity, Sstar, from Practical Salinity, SP.
+!
+! sp : Practical Salinity [unitless]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sstar_from_sp : Preformed Salinity [g/kg]
+*/
+double
+gsw_sstar_from_sp(double sp, double p, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double saar, sstar_baltic;
+
+ /*
+ !In the Baltic Sea, Sstar = SA.
+ */
+ sstar_baltic = gsw_sa_from_sp_baltic(sp,lon,lat);
+ if (sstar_baltic < GSW_ERROR_LIMIT)
+ return (sstar_baltic);
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return (gsw_ups*sp*(1 - 0.35e0*saar));
+}
+/*
+!==========================================================================
+elemental function gsw_t_deriv_chem_potential_water_t_exact (sa, t, p)
+!==========================================================================
+!
+! Calculates the temperature derivative of the chemical potential of water
+! in seawater so that it is valid at exactly SA = 0.
+!
+! SA = Absolute Salinity [ g/kg ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! chem_potential_water_dt = temperature derivative of the chemical
+! potential of water in seawater [ J g^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_t_deriv_chem_potential_water_t_exact(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g03_t, g08_sa_t, x, x2, y, z, g08_t, kg2g = 1e-3;
+/*
+! Note. The kg2g, a factor of 1e-3, is needed to convert the output of this
+! function into units of J/g. See section (2.9) of the TEOS-10 Manual.
+*/
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*rec_db2pa;
+ /* the input pressure (p) is sea pressure in units of dbar. */
+
+ g03_t = 5.90578347909402 + z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 + (28.9796526294175 -
+ 2.13290083518327*z)*z))) +
+ y*(-24715.571866078 + z*(2910.0729080936 +
+ z*(-1513.116771538718 + z*(546.959324647056 +
+ z*(-111.1208127634436 + 8.68841343834394*z)))) +
+ y*(2210.2236124548363 + z*(-2017.52334943521 +
+ z*(1498.081172457456 + z*(-718.6359919632359 +
+ (146.4037555781616 - 4.9892131862671505*z)*z))) +
+ y*(-592.743745734632 + z*(1591.873781627888 +
+ z*(-1207.261522487504 + (608.785486935364 -
+ 105.4993508931208*z)*z)) +
+ y*(290.12956292128547 + z*(-973.091553087975 +
+ z*(602.603274510125 + z*(-276.361526170076 +
+ 32.40953340386105*z))) +
+ y*(-113.90630790850321 + y*(21.35571525415769 -
+ 67.41756835751434*z) +
+ z*(381.06836198507096 + z*(-133.7383902842754 +
+ 49.023632509086724*z)))))));
+
+ g08_t = x2*(168.072408311545 +
+ x*(-493.407510141682 + x*(543.835333000098 +
+ x*(-196.028306689776 + 36.7571622995805*x) +
+ y*(-137.1145018408982 + y*(148.10030845687618 +
+ y*(-68.5590309679152 + 12.4848504784754*y))) -
+ 22.6683558512829*z) + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-86.1329351956084 + z*(766.116132004952 +
+ z*(-108.3834525034224 + 51.2796974779828*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(3.50240264723578 + 938.26075044542*z)))));
+
+ g08_sa_t = 1187.3715515697959 +
+ x*(-1480.222530425046 + x*(2175.341332000392 +
+ x*(-980.14153344888 + 220.542973797483*x) +
+ y*(-548.4580073635929 + y*(592.4012338275047 +
+ y*(-274.2361238716608 + 49.9394019139016*y))) -
+ 90.6734234051316*z) + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-258.3988055868252 + z*(2298.348396014856 +
+ z*(-325.1503575102672 + 153.8390924339484*z)) +
+ y*(-90.2046337756875 - 4142.8793862113125*z +
+ y*(10.50720794170734 + 2814.78225133626*z))));
+
+ return (kg2g*((g03_t + g08_t)*0.025 - 0.5*gsw_sfac*0.025*sa*g08_sa_t));
+}
+/*
+!==========================================================================
+function gsw_t_freezing(sa,p,saturation_fraction)
+!==========================================================================
+
+! Calculates the in-situ temperature at which seawater freezes
+!
+! sa : Absolute Salinity [g/kg]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction : the saturation fraction of dissolved air
+! in seawater
+!
+! t_freezing : in-situ temperature at which seawater freezes.[deg C]
+*/
+double
+gsw_t_freezing(double sa, double p, double saturation_fraction)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_FREEZING_POLY_COEFFICIENTS;
+ double sa_r, x, p_r;
+ double df_dt, tf, tfm, tf_old, f, return_value;
+
+ /* The initial value of t_freezing_exact (for air-free seawater) */
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ tf = t0
+ + sa_r*(t1 + x*(t2 + x*(t3 + x*(t4 + x*(t5 + t6*x)))))
+ + p_r*(t7 + p_r*(t8 + t9*p_r))
+ + sa_r*p_r*(t10 + p_r*(t12 + p_r*(t15 + t21*sa_r))
+ + sa_r*(t13 + t17*p_r + t19*sa_r)
+ + x*(t11 + p_r*(t14 + t18*p_r) + sa_r*(t16 + t20*p_r
+ + t22*sa_r)));
+
+ /* Adjust for the effects of dissolved air */
+ tf -= saturation_fraction*(1e-3)*(2.4 - sa/(2.0*gsw_sso));
+
+ df_dt = 1e3*gsw_t_deriv_chem_potential_water_t_exact(sa,tf,p) -
+ gsw_gibbs_ice(1,0,tf,p);
+/*
+! df_dt here is the initial value of the derivative of the function f whose
+! zero (f = 0) we are finding (see Eqn. (3.33.2) of IOC et al (2010)).
+*/
+
+ tf_old = tf;
+ f = 1e3*gsw_chem_potential_water_t_exact(sa,tf_old,p) -
+ gsw_gibbs_ice(0,0,tf_old,p);
+ tf = tf_old - f/df_dt;
+ tfm = 0.5*(tf + tf_old);
+ df_dt = 1e3*gsw_t_deriv_chem_potential_water_t_exact(sa,tfm,p) -
+ gsw_gibbs_ice(1,0,tfm,p);
+ tf = tf_old - f/df_dt;
+
+ tf_old = tf;
+ f = 1e3*gsw_chem_potential_water_t_exact(sa,tf_old,p) -
+ gsw_gibbs_ice(0,0,tf_old,p);
+ tf = tf_old - f/df_dt;
+
+ /* Adjust for the effects of dissolved air */
+ return_value = tf -
+ saturation_fraction*(1e-3)*(2.4 - sa/(2.0*gsw_sso));
+ return (return_value);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_t_freezing_first_derivatives (sa, p, &
+ saturation_fraction, tfreezing_sa, tfreezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the in-situ temperature at which
+! seawater freezes with respect to Absolute Salinity SA and pressure P (in
+! Pa). These expressions come from differentiating the expression that
+! defines the freezing temperature, namely the equality between the
+! chemical potentials of water in seawater and in ice.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! tfreezing_SA = the derivative of the in-situ freezing temperature
+! (ITS-90) with respect to Absolute Salinity at fixed
+! pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! tfreezing_P = the derivative of the in-situ freezing temperature
+! (ITS-90) with respect to pressure (in Pa) at fixed
+! Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_t_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa, double *tfreezing_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double rec_denom, tf, g_per_kg = 1000.0;
+
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ rec_denom = 1.0/
+ (g_per_kg*gsw_t_deriv_chem_potential_water_t_exact(sa,tf,p)
+ + gsw_entropy_ice(tf,p));
+
+ if (tfreezing_sa != NULL)
+ *tfreezing_sa =
+ gsw_dilution_coefficient_t_exact(sa,tf,p)*rec_denom
+ + saturation_fraction*(1e-3)/(2.0*gsw_sso);
+
+ if (tfreezing_p != NULL)
+ *tfreezing_p =
+ -(gsw_specvol_t_exact(sa,tf,p) - sa*gsw_gibbs(1,0,1,sa,tf,p)
+ - gsw_specvol_ice(tf,p))*rec_denom;
+
+ return;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_t_freezing_first_derivatives_poly (sa, p, &
+ saturation_fraction, tfreezing_sa, tfreezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the in-situ temperature at which
+! seawater freezes with respect to Absolute Salinity SA and pressure P (in
+! Pa). These expressions come from differentiating the expression that
+! defines the freezing temperature, namely the equality between the
+! chemical potentials of water in seawater and in ice.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! tfreezing_SA = the derivative of the in-situ freezing temperature
+! (ITS-90) with respect to Absolute Salinity at fixed
+! pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! tfreezing_P = the derivative of the in-situ freezing temperature
+! (ITS-90) with respect to pressure (in Pa) at fixed
+! Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_t_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa, double *tfreezing_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_FREEZING_POLY_COEFFICIENTS;
+ double p_r, sa_r, x, c = 1e-3/(2.0*gsw_sso);
+
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ if (tfreezing_sa != NULL)
+ *tfreezing_sa =
+ (t1 + x*(1.5*t2 + x*(2.0*t3 + x*(2.5*t4 + x*(3.0*t5
+ + 3.5*t6*x)))) + p_r*(t10 + x*(1.5*t11 + x*(2.0*t13
+ + x*(2.5*t16 + x*(3.0*t19 + 3.5*t22*x))))
+ + p_r*(t12 + x*(1.5*t14 + x*(2.0*t17 + 2.5*t20*x))
+ + p_r*(t15 + x*(1.5*t18 + 2.0*t21*x)))))*1e-2
+ + saturation_fraction*c;
+
+ if (tfreezing_p != NULL)
+ *tfreezing_p =
+ (t7 + sa_r*(t10 + x*(t11 + x*(t13 + x*(t16 + x*(t19 + t22*x)))))
+ + p_r*(2.0*t8 + sa_r*(2.0*t12 + x*(2.0*t14 + x*(2.0*t17
+ + 2.0*t20*x))) + p_r*(3.0*t9 + sa_r*(3.0*t15 + x*(3.0*t18
+ + 3.0*t21*x)))))*1e-8;
+
+ return;
+}
+/*
+!==========================================================================
+elemental function gsw_t_freezing_poly (sa, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the in-situ temperature at which seawater freezes from a
+! computationally efficient polynomial.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! t_freezing = in-situ temperature at which seawater freezes. [ deg C ]
+! (ITS-90)
+!--------------------------------------------------------------------------
+*/
+double
+gsw_t_freezing_poly(double sa, double p, double saturation_fraction)
+{
+ GSW_TEOS10_CONSTANTS;
+ double ctf, return_value;
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ return_value = gsw_t_from_ct(sa,ctf,p);
+ return (return_value);
+}
+/*
+!==========================================================================
+function gsw_t_from_ct(sa,ct,p)
+!==========================================================================
+
+! Calculates in-situ temperature from Conservative Temperature of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! gsw_t_from_ct : in-situ temperature [deg C]
+*/
+double
+gsw_t_from_ct(double sa, double ct, double p)
+{
+ double pt0, p0=0.0;
+
+ pt0 = gsw_pt_from_ct(sa,ct);
+ return (gsw_pt_from_t(sa,pt0,p0,p));
+}
+/*
+! =========================================================================
+elemental function gsw_t_from_pt0_ice (pt0_ice, p)
+! =========================================================================
+!
+! Calculates in-situ temperature from the potential temperature of ice Ih
+! with reference pressure, p_ref, of 0 dbar (the surface), and the
+! in-situ pressure.
+!
+! pt0_ice = potential temperature of ice Ih with reference pressure of
+! zero dbar (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!--------------------------------------------------------------------------
+*/
+double
+gsw_t_from_pt0_ice(double pt0_ice, double p)
+{
+ double p0 = 0.0;
+
+ return (gsw_pt_from_t_ice(pt0_ice,p0,p));
+}
+/*
+!==========================================================================
+function gsw_thermobaric(sa,ct,p)
+!==========================================================================
+
+! Calculates the thermobaric coefficient of seawater with respect to
+! Conservative Temperature. This routine is based on the
+! computationally-efficient expression for specific volume in terms of
+! SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! thermobaric : thermobaric coefficient with [1/(K Pa)]
+! respect to Conservative Temperature (48 term equation)
+*/
+double
+gsw_thermobaric(double sa, double ct, double p)
+{
+ double v_ct, v_ct_p, v_sa, v_sa_p;
+
+ gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct,NULL);
+
+ gsw_specvol_second_derivatives(sa,ct,p,NULL,NULL,NULL,&v_sa_p,&v_ct_p);
+
+ return (gsw_rho(sa,ct,p)*(v_ct_p - (v_ct/v_sa)*v_sa_p));
+}
+/*
+!==========================================================================
+subroutine gsw_turner_rsubrho(sa,ct,p,nz,tu,rsubrho,p_mid)
+!==========================================================================
+
+! Calculates the Turner angle and the Rsubrho as a function of pressure
+! down a vertical water column. These quantities express the relative
+! contributions of the vertical gradients of Conservative Temperature
+! and Absolute Salinity to the vertical stability (the square of the
+! Brunt-Vaisala Frequency squared, N^2). Tu and Rsubrho are evaluated at
+! the mid pressure between the individual data points in the vertical.
+!
+! Note that in the double-diffusive literature, papers concerned with
+! the "diffusive" form of double-diffusive convection often define the
+! stability ratio as the reciprocal of what is defined here as the
+! stability ratio.
+
+! sa : Absolute Salinity (a profile (length nz)) [g/kg]
+! ct : Conservative Temperature (a profile (length nz)) [deg C]
+! p : sea pressure (a profile (length nz)) [dbar]
+! nz : number of bottles
+! tu : Turner angle, on the same (nz-1) grid as p_mid.
+! Turner angle has units of: [ degrees of rotation ]
+! rsubrho : Stability Ratio, on the same (nz-1) grid as p_mid.
+! Rsubrho is dimensionless. [ unitless ]
+! p_mid : Mid pressure between p grid (length nz-1) [dbar]
+*/
+void
+gsw_turner_rsubrho(double *sa, double *ct, double *p, int nz,
+ double *tu, double *rsubrho, double *p_mid)
+{
+ GSW_TEOS10_CONSTANTS;
+ int k;
+ double dsa, sa_mid, dct, ct_mid, alpha_mid, beta_mid;
+
+ if (nz < 2)
+ return;
+
+ for (k = 0; k < nz-1; k++) {
+ dsa = (sa[k] - sa[k+1]);
+ sa_mid = 0.5e0*(sa[k] + sa[k+1]);
+ dct = (ct[k] - ct[k+1]);
+ ct_mid = 0.5e0*(ct[k] + ct[k+1]);
+ p_mid[k] = 0.5e0*(p[k] + p[k+1]);
+ gsw_specvol_alpha_beta(sa_mid,ct_mid,p_mid[k],NULL,&alpha_mid,
+ &beta_mid);
+ tu[k] = rad2deg*atan2((alpha_mid*dct + beta_mid*dsa),
+ (alpha_mid*dct - beta_mid*dsa));
+ if (dsa == 0.0)
+ rsubrho[k] = GSW_INVALID_VALUE;
+ else
+ rsubrho[k] = (alpha_mid*dct)/(beta_mid*dsa);
+ }
+}
+/*
+!==========================================================================
+subroutine gsw_util_indx(x,n,z,k)
+!==========================================================================
+
+! Finds the index of the value in a monotonically increasing array
+!
+! x : array of monotonically increasing values
+! n : length of the array
+! z : value to be indexed
+!
+! K : index K - if X(K) <= Z < X(K+1), or
+! N-1 - if Z = X(N)
+!
+*/
+int
+gsw_util_indx(double *x, int n, double z)
+{
+ int k, ku, kl, km;
+
+ if (z > x[0] && z < x[n-1]) {
+ kl = 0;
+ ku = n-1;
+ while (ku-kl > 1) {
+ km = (ku+kl)>>1;
+ if (z > x[km])
+ kl = km;
+ else
+ ku = km;
+ }
+ k = kl;
+ if (z == x[k+1])
+ k++;
+ } else if (z <= x[0])
+ k = 0;
+ else
+ k = n-2;
+
+ return (k);
+}
+/*
+!==========================================================================
+pure function gsw_util_interp1q_int (x, iy, x_i) result(y_i)
+!==========================================================================
+! Returns the value of the 1-D function iy (integer) at the points of column
+! vector x_i using linear interpolation. The vector x specifies the
+! coordinates of the underlying interval.
+!==========================================================================
+*/
+double *
+gsw_util_interp1q_int(int nx, double *x, int *iy, int nxi, double *x_i,
+ double *y_i)
+{
+ char *in_rng;
+ int *j, *k, *r, *jrev, *ki, imax_x, imin_x, i, n, m, ii;
+ double *xi, *xxi, u, max_x, min_x;
+
+ if (nx <= 0 || nxi <= 0)
+ return (NULL);
+
+ min_x = max_x = x[0];
+ imin_x = imax_x = 0;
+ for (i=0; i<nx; i++) {
+ if (x[i] < min_x) {
+ min_x = x[i];
+ imin_x = i;
+ } else if (x[i] > max_x) {
+ max_x = x[i];
+ imax_x = i;
+ }
+ }
+ in_rng = malloc(nxi*sizeof (char));
+ memset(in_rng, 0, nxi*sizeof (char));
+
+ for (i=n=0; i<nxi; i++) {
+ if (x_i[i] <= min_x) {
+ y_i[i] = iy[imin_x];
+ } else if (x_i[i] >= max_x) {
+ y_i[i] = iy[imax_x];
+ } else {
+ in_rng[i] = 1;
+ n++;
+ }
+ }
+ if (n==0)
+ return (y_i);
+
+ xi = malloc(n*sizeof (double));
+ k = malloc(3*n*sizeof (int)); ki = k+n; r = ki+n;
+ m = nx + n;
+ xxi = malloc(m*sizeof (double));
+ j = malloc(2*m*sizeof (int)); jrev = j+m;
+
+ ii = 0;
+ for (i = 0; i<nxi; i++) {
+ if (in_rng[i]) {
+ xi[ii] = x_i[i];
+ ki[ii] = i;
+ ii++;
+ }
+ }
+ free(in_rng);
+ /*
+ ** Note that the following operations on the index
+ ** vectors jrev and r depend on the sort utility
+ ** gsw_util_sort_real() consistently ordering the
+ ** sorting indexes either in ascending or descending
+ ** sequence for replicate values in the real vector.
+ */
+ gsw_util_sort_real(xi, n, k);
+ for (i = 0; i<nx; i++)
+ xxi[i] = x[i];
+ for (i = 0; i<n; i++)
+ xxi[nx+i] = xi[k[i]];
+ gsw_util_sort_real(xxi, nx+n, j);
+
+ for (i = 0; i<nx+n; i++)
+ jrev[j[i]] = i;
+ for (i = 0; i<n; i++)
+ r[k[i]] = jrev[nx+i] - i-1;
+
+ for (i = 0; i<n; i++) {
+ u = (xi[i]-x[r[i]])/(x[r[i]+1]-x[r[i]]);
+ y_i[ki[i]] = iy[r[i]] + (iy[r[i]+1]-iy[r[i]])*u;
+ }
+ free(j); free(xxi); free(k); free(xi);
+ return (y_i);
+}
+/*
+!==========================================================================
+pure function gsw_util_linear_interp (x, y, x_i) result(y_i)
+!==========================================================================
+! Returns the values of the functions y{ny} at the points of column
+! vector x_i using linear interpolation. The vector x specifies the
+! coordinates of the underlying interval, and the matrix y specifies
+| the function values at each x coordinate. Note that y has dimensions
+| nx x ny and y_i has dimensions nxi x ny.
+! This function was adapted from Matlab's interp1q.
+!==========================================================================
+*/
+double *
+gsw_util_linear_interp(int nx, double *x, int ny, double *y, int nxi,
+ double *x_i, double *y_i)
+{
+ char *in_rng;
+ int *j, *k, *r, *jrev, *ki, imax_x, imin_x, i, n, m, ii, jy,
+ jy0, jyi0, r0;
+ double *xi, *xxi, u, max_x, min_x;
+
+ if (nx <= 0 || nxi <= 0 || ny <= 0)
+ return (NULL);
+
+ min_x = max_x = x[0];
+ imin_x = imax_x = 0;
+ for (i=0; i<nx; i++) {
+ if (x[i] < min_x) {
+ min_x = x[i];
+ imin_x = i;
+ } else if (x[i] > max_x) {
+ max_x = x[i];
+ imax_x = i;
+ }
+ }
+ in_rng = malloc(nxi*sizeof (char));
+ memset(in_rng, 0, nxi*sizeof (char));
+
+ for (i=n=0; i<nxi; i++) {
+ if (x_i[i] <= min_x) {
+ for (jy=jy0=jyi0=0; jy<ny; jy++, jy0+=nx, jyi0+=nxi)
+ y_i[jyi0+i] = y[jy0+imin_x];
+ } else if (x_i[i] >= max_x) {
+ for (jy=jy0=jyi0=0; jy<ny; jy++, jy0+=nx, jyi0+=nxi)
+ y_i[jyi0+i] = y[jy0+imax_x];
+ } else {
+ in_rng[i] = 1;
+ n++;
+ }
+ }
+ if (n==0)
+ return (y_i);
+ xi = malloc(n*sizeof (double));
+ k = malloc(3*n*sizeof (int)); ki = k+n; r = ki+n;
+ m = nx + n;
+ xxi = malloc(m*sizeof (double));
+ j = malloc(2*m*sizeof (int)); jrev = j+m;
+
+ ii = 0;
+ for (i = 0; i<nxi; i++) {
+ if (in_rng[i]) {
+ xi[ii] = x_i[i];
+ ki[ii] = i;
+ ii++;
+ }
+ }
+ free(in_rng);
+ /*
+ ** This algorithm mimics the Matlab interp1q function.
+ **
+ ** An explaination of this algorithm:
+ ** We have points we are interpolating from (x) and
+ ** points that we are interpolating to (xi). We
+ ** sort the interpolating from points, concatenate
+ ** them with the interpolating to points and sort the result.
+ ** We then construct index r, the interpolation index in x for
+ ** each point in xi.
+ **
+ ** Note that the following operations on the index
+ ** vectors jrev and r depend on the sort utility
+ ** gsw_util_sort_real() consistently ordering the
+ ** sorting indexes either in ascending or descending
+ ** sequence for replicate values in the real vector.
+ */
+ gsw_util_sort_real(xi, n, k);
+ memmove(xxi, x, nx*sizeof (double));
+ memmove(xxi+nx, xi, n*sizeof (double));
+ gsw_util_sort_real(xxi, m, j);
+
+ for (i = 0; i<m; i++)
+ jrev[j[i]] = i;
+ for (i = 0; i<n; i++)
+ r[k[i]] = jrev[nx+i] - i - 1;
+ /* this is now the interpolation index in x for a point in xi */
+
+ for (jy=jy0=jyi0=0; jy < ny; jy++, jy0+=nx, jyi0+=nxi) {
+ for (i = 0; i<n; i++) {
+ u = (xi[i]-x[r[i]])/(x[r[i]+1]-x[r[i]]);
+ r0 = jy0+r[i];
+ y_i[jyi0+ki[i]] = y[r0] + (y[r0+1]-y[r0])*u;
+ }
+ }
+ free(j); free(xxi); free(k); free(xi);
+ return (y_i);
+}
+/*
+pure function gsw_util_sort_real (rarray) result(iarray)
+*/
+
+#if (defined __APPLE__ || defined __MACH__ || defined __DARWIN__ || \
+ defined __FREEBSD__ || defined __BSD__ || \
+ defined _WIN32 || defined _WIN64 || defined __WINDOWS__)
+static int
+compare(void *rarray, const void *p1, const void *p2)
+#else
+
+extern void qsort_r(void *, size_t, size_t, int (*)(const void *, const void *,
+ void *), void *);
+static int
+compare(const void *p1, const void *p2, void *rarray)
+#endif
+{
+ double *rdata = rarray;
+ if (rdata[*(int *)p1] < rdata[*(int *)p2])
+ return (-1);
+ if (rdata[*(int *)p1] > rdata[*(int *)p2])
+ return (1);
+ /*
+ ** Note that the library functions using this utility
+ ** depend on the fact that for replicate values in rdata
+ ** the indexes are returned in descending sequence.
+ */
+ if (*(int *)p1 < *(int *)p2)
+ return (1);
+ return (0);
+}
+
+/*
+** Sort the double array rarray into ascending value sequence
+** returning an index array of the sorted result. This function
+** is thread-safe.
+*/
+void
+gsw_util_sort_real(double *rarray, int nx, int *iarray)
+{
+ int i;
+
+ for (i=0; i<nx; i++)
+ iarray[i] = i;
+#if (defined __APPLE__ || defined __MACH__ || defined __DARWIN__ || \
+ defined __FREEBSD__ || defined __BSD__ )
+ qsort_r(iarray, nx, sizeof (int), (void *)rarray, compare);
+#elif (defined _WIN32 || defined _WIN64 || defined __WINDOWS__)
+ qsort_s(iarray, nx, sizeof (int), compare, (void *)rarray);
+#else
+ qsort_r(iarray, nx, sizeof (int), compare, (void *)rarray);
+#endif
+}
+/*
+!==========================================================================
+function gsw_util_xinterp1(x,y,n,x0)
+!==========================================================================
+
+! Linearly interpolate a real array
+!
+! x : y array (Must be monotonic)
+! y : y array
+! n : length of X and Y arrays
+! x0 : value to be interpolated
+!
+! gsw_xinterp1 : Linearly interpolated value
+*/
+double
+gsw_util_xinterp1(double *x, double *y, int n, double x0)
+{
+ int k;
+ double r;
+
+ k = gsw_util_indx(x,n,x0);
+ r = (x0-x[k])/(x[k+1]-x[k]);
+ return (y[k] + r*(y[k+1]-y[k]));
+}
+/*
+!==========================================================================
+function gsw_z_from_p(p,lat)
+!==========================================================================
+
+! Calculates the height z from pressure p
+!
+! p : sea pressure [dbar]
+! lat : latitude [deg]
+!
+! gsw_z_from_p : height [m]
+*/
+double
+gsw_z_from_p(double p, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x, sin2, b, c, a;
+
+ x = sin(lat*deg2rad);
+ sin2 = x*x;
+ b = 9.780327*(1.0 + (5.2792e-3 + (2.32e-5*sin2))*sin2);
+ a = -0.5*gamma*b;
+ c = gsw_enthalpy_sso_0(p);
+
+ return (-2.0*c/(b + sqrt(b*b - 4.0*a*c)));
+}
+
+/*
+** The End
+**!==========================================================================
+*/
diff --git a/src/c_gsw/gsw_saar.c b/src/c_gsw/gsw_saar.c
new file mode 100644
index 0000000..c5a060a
--- /dev/null
+++ b/src/c_gsw/gsw_saar.c
@@ -0,0 +1,272 @@
+/*
+** $Id: gsw_saar.c,v b04abca68ac0 2015/09/13 17:47:28 fdelahoyde $
+** $Version: 3.05.0-2 $
+**
+** GSW TEOS-10 V3.05
+*/
+#include "gswteos-10.h"
+#include "gsw_internal_const.h"
+#include "gsw_saar_data.c"
+
+#ifdef _MSC_VER
+# include <float.h>
+# if _MSC_VER < 1900
+# define isnan(x) _isnan(x)
+# endif
+#endif
+
+static double
+gsw_sum(double *x, int n)
+{
+ int i;
+ double val;
+
+ for (val=0.0, i=0; i<n; val += x[i], i++);
+ return (val);
+}
+
+#define max(a,b) (((a)>(b))?(a):(b))
+#define sum(x) gsw_sum(x, sizeof (x)/sizeof (double))
+
+/*
+!==========================================================================
+function gsw_saar(p,long,lat)
+!==========================================================================
+
+! Calculates the Absolute Salinity Anomaly Ratio, SAAR at a geographic point.
+!
+! p : sea pressure [dbar]
+! long : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_saar : Absolute Salinity Anomaly Ratio [unitless]
+*/
+double
+gsw_saar(double p, double lon, double lat)
+{
+ GSW_SAAR_DATA;
+ int nx=gsw_nx, ny=gsw_ny, nz=gsw_nz;
+ int indx0, indy0, indz0, k, ndepth_index;
+ double saar[4], saar_old[4];
+ double sa_upper, sa_lower, dlong, dlat;
+ double r1, s1, t1, ndepth_max, return_value;
+
+
+ return_value = GSW_INVALID_VALUE;
+
+ if (isnan(lat) || isnan(lon) || isnan(p))
+ return (return_value);
+
+ if (lat < -86.0 || lat > 90.0)
+ return (return_value);
+
+ if (lon < 0.0)
+ lon += 360.0;
+
+ dlong = longs_ref[1]-longs_ref[0];
+ dlat = lats_ref[1]-lats_ref[0];
+
+ indx0 = floor(0 + (nx-1)*(lon-longs_ref[0])/(longs_ref[nx-1]-
+ longs_ref[0]));
+ if (indx0 == nx-1)
+ indx0 = nx-2;
+
+ indy0 = floor(0 + (ny-1)*(lat-lats_ref[0])/(lats_ref[ny-1]-
+ lats_ref[0]));
+ if(indy0 == ny-1)
+ indy0 = ny-2;
+/*
+! Look for the maximum valid "ndepth_ref" value around our point.
+! Note: invalid "ndepth_ref" values are NaNs (a hangover from the codes
+! Matlab origins), but we have replaced the NaNs with a value of "9e90",
+! hence we need an additional upper-limit check in the code below so they
+! will not be recognised as valid values.
+*/
+ ndepth_max = -1.0;
+ for (k=0; k < 4; k++) {
+ ndepth_index = indy0+delj[k]+(indx0+deli[k])*ny;
+ if (ndepth_ref[ndepth_index] > 0.0 &&
+ ndepth_ref[ndepth_index] < 1e90)
+ ndepth_max = max(ndepth_max, ndepth_ref[ndepth_index]);
+ }
+/*
+! If we are a long way from the ocean then there will be no valid "ndepth_ref"
+! values near the point (ie. surrounded by NaNs) - so just return SAAR = 0.0
+*/
+ if (ndepth_max == -1.0)
+ return (0.0);
+
+ if (p > p_ref[(int)(ndepth_max)-1])
+ p = p_ref[(int)(ndepth_max)-1];
+ indz0 = gsw_util_indx(p_ref,nz,p);
+
+ r1 = (lon-longs_ref[indx0])/(longs_ref[indx0+1]-longs_ref[indx0]);
+ s1 = (lat-lats_ref[indy0])/(lats_ref[indy0+1]-lats_ref[indy0]);
+ t1 = (p-p_ref[indz0])/(p_ref[indz0+1]-p_ref[indz0]);
+
+ for (k=0; k<4; k++)
+ saar[k] = saar_ref[indz0+nz*(indy0+delj[k]+(indx0+deli[k])*ny)];
+
+ if (longs_pan[0] <= lon && lon <= longs_pan[npan-1]-0.001 &&
+ lats_pan[npan-1] <= lat && lat <= lats_pan[0]) {
+ memmove(saar_old,saar,4*sizeof (double));
+ gsw_add_barrier(saar_old,lon,lat,longs_ref[indx0],
+ lats_ref[indy0],dlong,dlat,saar);
+ } else if (fabs(sum(saar)) >= GSW_ERROR_LIMIT) {
+ memmove(saar_old,saar,4*sizeof (double));
+ gsw_add_mean(saar_old,saar);
+ }
+
+ sa_upper = (1.0-s1)*(saar[0] + r1*(saar[1]-saar[0])) +
+ s1*(saar[3] + r1*(saar[2]-saar[3]));
+
+ for (k=0; k<4; k++)
+ saar[k] = saar_ref[indz0+1+nz*(indy0+delj[k]+
+ (indx0+deli[k])*ny)];
+
+ if (longs_pan[0] <= lon && lon <= longs_pan[npan-1]-0.001 &&
+ lats_pan[npan-1] <= lat && lat <= lats_pan[0]) {
+ memmove(saar_old,saar,4*sizeof (double));
+ gsw_add_barrier(saar_old,lon,lat,longs_ref[indx0],
+ lats_ref[indy0],dlong,dlat,saar);
+ } else if (fabs(sum(saar)) >= GSW_ERROR_LIMIT) {
+ memmove(saar_old,saar,4*sizeof (double));
+ gsw_add_mean(saar_old,saar);
+ }
+
+ sa_lower = (1.0-s1)*(saar[0] + r1*(saar[1]-saar[0])) +
+ s1*(saar[3] + r1*(saar[2]-saar[3]));
+ if (fabs(sa_lower) >= GSW_ERROR_LIMIT)
+ sa_lower = sa_upper;
+ return_value = sa_upper + t1*(sa_lower-sa_upper);
+
+ if (fabs(return_value) >= GSW_ERROR_LIMIT)
+ return_value = GSW_INVALID_VALUE;
+
+ return (return_value);
+}
+
+/*
+!==========================================================================
+function gsw_deltasa_atlas(p,lon,lat)
+!==========================================================================
+
+! Calculates the Absolute Salinity Anomaly atlas value, delta_SA_atlas.
+!
+! p : sea pressure [dbar]
+! lon : longiture [deg E]
+! lat : latitude [deg N]
+!
+! deltasa_atlas : Absolute Salinity Anomaly atlas value [g/kg]
+*/
+double
+gsw_deltasa_atlas(double p, double lon, double lat)
+{
+ GSW_SAAR_DATA;
+ int nx=gsw_nx, ny=gsw_ny, nz=gsw_nz;
+ int indx0, indy0, indz0, k, ndepth_index;
+ double dsar[4], dsar_old[4];
+ double dlong, dlat;
+ double return_value, sa_upper, sa_lower;
+ double r1, s1, t1, ndepth_max;
+
+ return_value = GSW_INVALID_VALUE;
+
+ if (isnan(lat) || isnan(lon) || isnan(p))
+ return (return_value);
+
+ if (lat < -86.0 || lat > 90.0)
+ return (return_value);
+
+ if (lon < 0.0)
+ lon += 360.0;
+
+ dlong = longs_ref[1]-longs_ref[0];
+ dlat = lats_ref[1]-lats_ref[0];
+
+ indx0 = floor(0 + (nx-1)*(lon-longs_ref[0])/
+ (longs_ref[nx-1]-longs_ref[0]));
+ if (indx0 == nx-1)
+ indx0 = nx-2;
+
+ indy0 = floor(0 + (ny-1)*(lat-lats_ref[0])/
+ (lats_ref[ny-1]-lats_ref[0]));
+ if (indy0 == ny-1)
+ indy0 = ny-2;
+/*
+! Look for the maximum valid "ndepth_ref" value around our point.
+! Note: invalid "ndepth_ref" values are NaNs (a hangover from the codes
+! Matlab origins), but we have replaced the NaNs with a value of "9e90",
+! hence we need an additional upper-limit check in the code below so they
+! will not be recognised as valid values.
+*/
+ ndepth_max = -1;
+ for (k=0; k<4; k++) {
+ ndepth_index = indy0+delj[k]+(indx0+deli[k])*ny;
+ if (ndepth_ref[ndepth_index] > 0.0 &&
+ ndepth_ref[ndepth_index] < 1e90)
+ ndepth_max = max(ndepth_max, ndepth_ref[ndepth_index]);
+ }
+/*
+! If we are a long way from the ocean then there will be no valid "ndepth_ref"
+! values near the point (ie. surrounded by NaNs) - so deltasa_atlas = 0.0
+*/
+ if (ndepth_max == -1.0)
+ return (0.0);
+
+ if (p > p_ref[(int)(ndepth_max)-1])
+ p = p_ref[(int)(ndepth_max)-1];
+ indz0 = gsw_util_indx(p_ref,nz,p);
+
+ r1 = (lon-longs_ref[indx0])/
+ (longs_ref[indx0+1]-longs_ref[indx0]);
+ s1 = (lat-lats_ref[indy0])/
+ (lats_ref[indy0+1]-lats_ref[indy0]);
+ t1 = (p-p_ref[indz0])/
+ (p_ref[indz0+1]-p_ref[indz0]);
+
+ for (k=0; k < 4; k++)
+ dsar[k] = delta_sa_ref[indz0+nz*(indy0+delj[k]+
+ (indx0+deli[k])*ny)];
+
+ if (longs_pan[0] <= lon && lon <= longs_pan[npan-1]-0.001 &&
+ lats_pan[npan-1] <= lat && lat <= lats_pan[0]) {
+ memmove(dsar_old,dsar,4*sizeof (double));
+ gsw_add_barrier(dsar_old,lon,lat,longs_ref[indx0],
+ lats_ref[indy0],dlong,dlat,dsar);
+ } else if (fabs(sum(dsar)) >= GSW_ERROR_LIMIT) {
+ memmove(dsar_old,dsar,4*sizeof (double));
+ gsw_add_mean(dsar_old,dsar);
+ }
+
+ sa_upper = (1.0-s1)*(dsar[0] + r1*(dsar[1]-dsar[0])) +
+ s1*(dsar[3] + r1*(dsar[2]-dsar[3]));
+
+ for (k=0; k<4; k++)
+ dsar[k] = delta_sa_ref[indz0+1+nz*(indy0+delj[k]+
+ (indx0+deli[k])*ny)];
+
+ if (longs_pan[0] <= lon && lon <= longs_pan[npan-1] &&
+ lats_pan[npan-1] <= lat && lat <= lats_pan[0]) {
+ memmove(dsar_old,dsar,4*sizeof (double));
+ gsw_add_barrier(dsar_old,lon,lat,longs_ref[indx0],
+ lats_ref[indy0],dlong,dlat,dsar);
+ } else if (fabs(sum(dsar)) >= GSW_ERROR_LIMIT) {
+ memmove(dsar_old,dsar,4*sizeof (double));
+ gsw_add_mean(dsar_old,dsar);
+ }
+
+ sa_lower = (1.0-s1)*(dsar[0] + r1*(dsar[1]-dsar[0])) +
+ s1*(dsar[3] + r1*(dsar[2]-dsar[3]));
+ if (fabs(sa_lower) >= GSW_ERROR_LIMIT)
+ sa_lower = sa_upper;
+ return_value = sa_upper + t1*(sa_lower-sa_upper);
+
+ if (fabs(return_value) >= GSW_ERROR_LIMIT)
+ return (GSW_INVALID_VALUE);
+
+ return (return_value);
+}
+/*
+** The End
+*/
diff --git a/src/c_gsw/gsw_saar_data.c b/src/c_gsw/gsw_saar_data.c
new file mode 100644
index 0000000..e073659
--- /dev/null
+++ b/src/c_gsw/gsw_saar_data.c
@@ -0,0 +1,122859 @@
+/*
+** $Id$
+** Extracted from gsw_data_v3_0.nc
+*/
+static int gsw_nx = 91, gsw_ny = 45, gsw_nz = 45;
+static char *gsw_version_date = "15th_May_2011";
+static char *gsw_version_number = "3.05.6";
+
+void gsw_get_version(char **version_date, char **version_number)
+{
+ *version_date = gsw_version_date;
+ *version_number = gsw_version_number;
+}
+static double p_ref[45] = {
+0, 10, 20, 30, 40, 50, 76, 101, 126, 151, 176, 202, 252, 303, 353, 404, 505,
+606, 707, 808, 909, 1010, 1111, 1213, 1314, 1416, 1517, 1771, 2025, 2279, 2534,
+2789, 3045, 3300, 3556, 3812, 4069, 4325, 4583, 4840, 5098, 5355, 5614, 5872,
+6131
+};
+
+static double lats_ref[45] = {
+-86, -82, -78, -74, -70, -66, -62, -58, -54, -50, -46, -42, -38, -34, -30, -26,
+-22, -18, -14, -10, -6, -2, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50,
+54, 58, 62, 66, 70, 74, 78, 82, 86, 90
+};
+
+static double longs_ref[91] = {
+0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76,
+80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144,
+148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208,
+212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 260, 264, 268, 272,
+276, 280, 284, 288, 292, 296, 300, 304, 308, 312, 316, 320, 324, 328, 332, 336,
+340, 344, 348, 352, 356, 360
+};
+
+static double saar_ref[184275] = {
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
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+43, 42, 41, 40, 39, 39, 39, 39, 39, 39, 39, 39, 41, 41, 43, 43, 43, 42, 43, 43,
+44, 39, 39, 38, 36, 35, 2, 8.9999999999999998e+90, 33, 35, 36, 36, 34, 38,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 38, 39,
+40, 41, 39, 40, 41, 43, 42, 41, 40, 39, 38, 37, 39, 39, 39, 39, 39, 39, 40, 41,
+41, 43, 42, 41, 41, 42, 42, 39, 38, 37, 35, 33, 8.9999999999999998e+90,
+8.9999999999999998e+90, 31, 35, 36, 36, 34, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 35, 38, 40, 40, 39, 39, 41, 41,
+41, 41, 39, 38, 37, 37, 37, 38, 39, 39, 39, 39, 40, 41, 41, 42, 41, 40, 40, 41,
+41, 39, 36, 36, 32, 11, 8.9999999999999998e+90, 8.9999999999999998e+90, 28, 35,
+35, 36, 34, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 33, 38, 41, 41, 39, 39, 38, 40, 40, 40, 39, 37, 37, 37,
+37, 37, 39, 39, 39, 39, 40, 40, 40, 41, 40, 40, 39, 41, 40, 39, 33, 32, 13,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 16, 28,
+35, 36, 34, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 31, 38, 41, 42, 39, 38, 37, 39, 39, 39, 39, 36, 36, 36,
+36, 37, 39, 39, 39, 39, 39, 40, 40, 40, 40, 39, 38, 39, 39, 36, 33, 27,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 17, 17, 33, 35, 34, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 31, 38, 41, 41, 41, 36, 37, 37,
+40, 39, 38, 36, 35, 35, 35, 36, 38, 38, 38, 39, 38, 38, 39, 38, 38, 38, 38, 37,
+27, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 17, 17, 31, 35, 34, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 24, 39, 41, 41, 41, 35, 34, 36,
+37, 38, 37, 35, 35, 34, 35, 35, 38, 38, 38, 37, 38, 38, 38, 37, 37, 38, 38, 27,
+6, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 6, 15,
+17, 28, 35, 33, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 21, 38, 41, 41, 41, 37, 35, 33, 34, 34, 34, 33, 35, 37,
+35, 35, 36, 37, 37, 37, 38, 37, 38, 36, 36, 36, 20, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 10, 10, 16, 19, 32, 32, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 28, 38, 41, 41, 42, 38, 36, 35,
+35, 36, 35, 34, 36, 36, 37, 36, 36, 36, 36, 36, 37, 37, 38, 38, 37, 32,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 7, 7,
+15, 17, 31, 32, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 26, 39, 41, 42, 42, 39, 38, 38, 37, 37, 36, 35, 36, 37,
+37, 38, 39, 38, 35, 35, 36, 35, 35, 38, 30, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 6, 13,
+16, 16, 31, 32, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 12, 39, 40, 42, 41, 39, 39, 38, 39, 39, 36, 35, 36, 37,
+37, 37, 38, 38, 35, 35, 35, 37, 40, 40, 2, 2, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 6, 11, 13, 18, 29, 32, 38,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 17, 39,
+40, 42, 42, 42, 40, 38, 38, 37, 36, 36, 36, 37, 38, 37, 37, 37, 35, 35, 36, 39,
+44, 32, 34, 34, 7, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 7, 7, 2, 15, 15, 16, 28, 31, 38, 17, 17, 17, 18, 39,
+40, 41, 42, 42, 40, 38, 38, 36, 37, 36, 37, 38, 38, 38, 37, 37, 36, 34, 36, 37,
+42, 27, 36, 36, 17, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 9, 10, 8.9999999999999998e+90, 13, 16, 16, 27, 30, 38,
+17, 17, 17, 17, 37, 39, 41, 43, 42, 40, 39, 37, 37, 37, 36, 37, 38, 39, 39, 39,
+37, 35, 34, 35, 40, 40, 39, 38, 36, 32, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 6, 12, 12, 7, 10, 17, 16, 27, 31, 38, 17, 17, 17, 17,
+37, 39, 41, 42, 41, 39, 38, 38, 38, 37, 37, 37, 39, 39, 40, 39, 39, 38, 35, 36,
+36, 27, 41, 39, 34, 22, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8, 12,
+12, 14, 8, 19, 16, 27, 31, 38, 17, 17, 17, 17, 36, 39, 41, 42, 40, 38, 36, 38,
+38, 38, 37, 39, 39, 39, 41, 41, 39, 38, 36, 36, 35, 36, 45, 38, 28, 22, 17,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 8,
+10, 13, 16, 6, 20, 15, 27, 31, 38, 17, 17, 17, 15, 36, 37, 40, 41, 38, 37, 36,
+38, 39, 40, 39, 39, 41, 41, 41, 26, 8.9999999999999998e+90,
+8.9999999999999998e+90, 28, 36, 35, 37, 43, 40, 42, 42, 40, 32, 6,
+8.9999999999999998e+90, 8.9999999999999998e+90, 7, 8, 15, 11, 8, 21, 17, 25,
+31, 38, 17, 17, 17, 2, 21, 36, 39, 39, 38, 7, 2, 15, 38, 41, 44, 45, 45, 45,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 30, 38,
+38, 42, 42, 42, 42, 38, 16, 2, 8.9999999999999998e+90, 8.9999999999999998e+90,
+2, 15, 8, 28, 28, 19, 19, 31, 38, 17, 17, 17, 2, 21, 34, 38, 38, 28, 9, 8,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 28, 41, 45, 45, 43, 42, 42, 41, 36, 12, 14,
+8.9999999999999998e+90, 13, 19, 21, 29, 30, 17, 17, 30, 38, 17, 17, 17, 17, 9,
+19, 38, 38, 39, 13, 9, 9, 2, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 36, 40,
+45, 45, 44, 42, 41, 41, 40, 12, 14, 8.9999999999999998e+90, 13, 19, 27, 30, 30,
+16, 19, 29, 38, 17, 17, 17, 18, 18, 18, 40, 39, 39, 31, 35, 31, 7, 2,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8, 33,
+43, 45, 45, 45, 44, 42, 41, 41, 28, 16, 16, 32, 32, 27, 29, 29, 16, 19, 27, 38,
+17, 17, 17, 22, 23, 28, 40, 40, 40, 44, 45, 43, 38, 6, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 29, 40, 43, 44, 45, 45, 45, 42,
+42, 41, 34, 14, 33, 34, 34, 23, 18, 19, 8.9999999999999998e+90, 17, 29, 38, 16,
+16, 16, 28, 34, 35, 37, 41, 40, 45, 45, 44, 42, 38, 12, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 2, 4, 38, 41, 42, 43, 45, 45,
+44, 43, 42, 42, 32, 31, 35, 35, 34, 21, 17, 2, 8.9999999999999998e+90, 17, 31,
+38, 16, 16, 16, 28, 36, 39, 39, 40, 41, 45, 45, 44, 42, 40, 36, 30, 2,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 6, 35, 38, 41, 41, 40, 40, 40, 42, 43, 42, 42, 37, 37,
+37, 36, 33, 2, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 16, 33, 38, 19, 19, 19, 33, 37, 39, 41, 41, 39, 45, 45,
+41, 41, 41, 37, 34, 23, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 36, 38, 40, 41, 40, 41, 40, 40,
+39, 41, 41, 41, 40, 38, 37, 35, 24, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 16, 33,
+38, 24, 24, 24, 37, 38, 40, 40, 37, 36, 45, 45, 42, 41, 40, 39, 38, 35, 32, 34,
+8.9999999999999998e+90, 8.9999999999999998e+90, 38, 39, 40, 41, 43, 44, 44, 43,
+40, 37, 41, 41, 40, 39, 37, 35, 33, 18, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 16, 34, 38, 22, 22, 22, 36, 38,
+40, 40, 35, 38, 44, 44, 42, 41, 40, 38, 39, 40, 39, 39, 40, 37, 39, 39, 39, 44,
+45, 45, 44, 45, 41, 36, 39, 39, 39, 39, 35, 33, 33, 29, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 16, 35, 38, 21, 21, 21, 36, 39,
+40, 40, 39, 45, 42, 42, 42, 41, 39, 39, 42, 42, 40, 42, 42, 42, 40, 39, 40, 45,
+45, 43, 45, 45, 41, 37, 35, 37, 38, 38, 37, 32, 33, 31, 11,
+8.9999999999999998e+90, 8.9999999999999998e+90, 15, 35, 38, 16, 16, 16, 37, 39,
+40, 44, 45, 45, 41, 41, 40, 39, 39, 41, 43, 43, 43, 43, 43, 43, 43, 38, 40, 44,
+44, 41, 43, 44, 42, 41, 36, 33, 35, 36, 36, 34, 29, 29, 16, 2,
+8.9999999999999998e+90, 17, 36, 38, 7, 7, 7, 37, 40, 41, 45, 45, 45, 40, 41,
+40, 38, 40, 41, 43, 44, 43, 43, 45, 43, 44, 40, 40, 43, 42, 39, 42, 43, 42, 42,
+39, 38, 38, 38, 37, 34, 31, 26, 26, 16, 2, 28, 37, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 37, 40, 41, 41, 41, 41, 40, 39,
+38, 37, 37, 39, 42, 43, 43, 43, 45, 43, 44, 41, 40, 41, 40, 36, 39, 40, 41, 42,
+44, 43, 40, 40, 39, 33, 32, 22, 27, 23, 12, 35, 37, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 32, 40, 41, 41, 41, 41, 38, 37,
+35, 35, 36, 37, 39, 39, 39, 39, 39, 39, 40, 42, 40, 39, 34, 32, 31, 36, 39, 41,
+42, 42, 42, 40, 39, 31, 31, 26, 27, 30, 13, 37, 37, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 15, 40, 41, 42, 41, 39, 37, 37,
+39, 37, 37, 37, 37, 39, 37, 37, 36, 36, 40, 41, 40, 3, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 28, 37, 40, 42, 42, 41, 39, 32,
+31, 28, 28, 30, 33, 17, 37, 38, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 40, 41,
+42, 41, 37, 37, 37, 39, 38, 38, 39, 41, 41, 41, 39, 40, 40, 41, 41, 36,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 21, 38, 38, 41, 41, 32, 29, 29,
+34, 34, 33, 35, 32, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 39, 41, 42, 41, 36, 37, 39, 40,
+41, 40, 40, 43, 43, 42, 43, 43, 43, 41, 41, 35, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 28, 28, 36, 40, 9, 8, 21, 34,
+35, 35, 35, 35, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 39, 41, 42, 43, 38, 37, 40, 41,
+41, 41, 40, 43, 43, 43, 44, 43, 44, 41, 41, 39, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 30, 32, 28, 12, 6, 7, 10, 32,
+35, 35, 35, 35, 36, 38, 38
+};
+
diff --git a/src/c_gsw/gswteos-10.h b/src/c_gsw/gswteos-10.h
new file mode 100644
index 0000000..b6e8957
--- /dev/null
+++ b/src/c_gsw/gswteos-10.h
@@ -0,0 +1,294 @@
+/*
+** $Id: gswteos-10.h,v 045882f2da27 2015/09/13 23:47:38 fdelahoyde $
+** $Version: 3.05.0-2 $
+**
+** GSW TEOS-10 V3.05 definitions and prototypes.
+*/
+#ifndef GSWTEOS_10_H
+#define GSWTEOS_10_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#include <complex.h>
+#include <errno.h>
+
+#define GSW_INVALID_VALUE 9e15 /* error return from gsw_saar et al. */
+#define GSW_ERROR_LIMIT 1e10
+
+/*
+** Prototypes:
+*/
+extern void gsw_add_barrier(double *input_data, double lon, double lat,
+ double long_grid, double lat_grid, double dlong_grid,
+ double dlat_grid, double *output_data);
+extern void gsw_add_mean(double *data_in, double *data_out);
+extern double gsw_adiabatic_lapse_rate_from_ct(double sa, double ct, double p);
+extern double gsw_adiabatic_lapse_rate_ice(double t, double p);
+extern double gsw_alpha(double sa, double ct, double p);
+extern double gsw_alpha_on_beta(double sa, double ct, double p);
+extern double gsw_alpha_wrt_t_exact(double sa, double t, double p);
+extern double gsw_alpha_wrt_t_ice(double t, double p);
+extern double gsw_beta_const_t_exact(double sa, double t, double p);
+extern double gsw_beta(double sa, double ct, double p);
+extern double gsw_cabbeling(double sa, double ct, double p);
+extern double gsw_c_from_sp(double sp, double t, double p);
+extern double gsw_chem_potential_water_ice(double t, double p);
+extern double gsw_chem_potential_water_t_exact(double sa, double t, double p);
+extern double gsw_cp_ice(double t, double p);
+extern double gsw_cp_t_exact(double sa, double t, double p);
+extern void gsw_ct_first_derivatives (double sa, double pt, double *ct_sa,
+ double *ct_pt);
+extern void gsw_ct_first_derivatives_wrt_t_exact(double sa, double t,
+ double p, double *ct_sa_wrt_t, double *ct_t_wrt_t,
+ double *ct_p_wrt_t);
+extern double gsw_ct_freezing(double sa, double p, double saturation_fraction);
+extern void gsw_ct_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa,
+ double *ctfreezing_p);
+extern void gsw_ct_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa,
+ double *ctfreezing_p);
+extern double gsw_ct_freezing_poly(double sa, double p,
+ double saturation_fraction);
+extern double gsw_ct_from_enthalpy(double sa, double h, double p);
+extern double gsw_ct_from_enthalpy_exact(double sa, double h, double p);
+extern double gsw_ct_from_entropy(double sa, double entropy);
+extern double gsw_ct_from_pt(double sa, double pt);
+extern void gsw_ct_from_rho(double rho, double sa, double p, double *ct,
+ double *ct_multiple);
+extern double gsw_ct_from_t(double sa, double t, double p);
+extern double gsw_ct_maxdensity(double sa, double p);
+extern void gsw_ct_second_derivatives(double sa, double pt, double *ct_sa_sa,
+ double *ct_sa_pt, double *ct_pt_pt);
+extern double gsw_deltasa_atlas(double p, double lon, double lat);
+extern double gsw_deltasa_from_sp(double sp, double p, double lon, double lat);
+extern double gsw_dilution_coefficient_t_exact(double sa, double t, double p);
+extern double gsw_dynamic_enthalpy(double sa, double ct, double p);
+extern double gsw_enthalpy_ct_exact(double sa, double ct, double p);
+extern double gsw_enthalpy_diff(double sa, double ct, double p_shallow,
+ double p_deep);
+extern double gsw_enthalpy(double sa, double ct, double p);
+extern void gsw_enthalpy_first_derivatives_ct_exact(double sa, double ct,
+ double p, double *h_sa, double *h_ct);
+extern void gsw_enthalpy_first_derivatives(double sa, double ct, double p,
+ double *h_sa, double *h_ct);
+extern double gsw_enthalpy_ice(double t, double p);
+extern void gsw_enthalpy_second_derivatives_ct_exact(double sa, double ct,
+ double p, double *h_sa_sa, double *h_sa_ct, double *h_ct_ct);
+extern void gsw_enthalpy_second_derivatives(double sa, double ct, double p,
+ double *h_sa_sa, double *h_sa_ct, double *h_ct_ct);
+extern double gsw_enthalpy_sso_0(double p);
+extern double gsw_enthalpy_t_exact(double sa, double t, double p);
+extern void gsw_entropy_first_derivatives(double sa, double ct,
+ double *eta_sa, double *eta_ct);
+extern double gsw_entropy_from_ct(double sa, double ct);
+extern double gsw_entropy_from_pt(double sa, double pt);
+extern double gsw_entropy_from_t(double sa, double t, double p);
+extern double gsw_entropy_ice(double t, double p);
+extern double gsw_entropy_part(double sa, double t, double p);
+extern double gsw_entropy_part_zerop(double sa, double pt0);
+extern void gsw_entropy_second_derivatives(double sa, double ct,
+ double *eta_sa_sa, double *eta_sa_ct, double *eta_ct_ct);
+extern double gsw_fdelta(double p, double lon, double lat);
+extern void gsw_frazil_properties(double sa_bulk, double h_bulk, double p,
+ double *sa_final, double *ct_final, double *w_ih_final);
+extern void gsw_frazil_properties_potential(double sa_bulk, double h_pot_bulk,
+ double p, double *sa_final, double *ct_final,
+ double *w_ih_final);
+extern void gsw_frazil_properties_potential_poly(double sa_bulk,
+ double h_pot_bulk, double p, double *sa_final, double *ct_final,
+ double *w_ih_final);
+extern void gsw_frazil_ratios_adiabatic(double sa, double p, double w_ih,
+ double *dsa_dct_frazil, double *dsa_dp_frazil,
+ double *dct_dp_frazil);
+extern void gsw_frazil_ratios_adiabatic_poly(double sa, double p,
+ double w_ih, double *dsa_dct_frazil, double *dsa_dp_frazil,
+ double *dct_dp_frazil);
+extern double *gsw_geo_strf_dyn_height(double *sa, double *ct, double *p,
+ double p_ref, int n_levels, double *dyn_height);
+extern double *gsw_geo_strf_dyn_height_pc(double *sa, double *ct,
+ double *delta_p, int n_levels, double *geo_strf_dyn_height_pc,
+ double *p_mid);
+extern double gsw_gibbs_ice (int nt, int np, double t, double p);
+extern double gsw_gibbs_ice_part_t(double t, double p);
+extern double gsw_gibbs_ice_pt0(double pt0);
+extern double gsw_gibbs_ice_pt0_pt0(double pt0);
+extern double gsw_gibbs(int ns, int nt, int np, double sa, double t, double p);
+extern double gsw_gibbs_pt0_pt0(double sa, double pt0);
+extern double gsw_grav(double lat, double p);
+extern double gsw_helmholtz_energy_ice(double t, double p);
+extern double gsw_hill_ratio_at_sp2(double t);
+extern void gsw_ice_fraction_to_freeze_seawater(double sa, double ct,
+ double p, double t_ih, double *sa_freeze, double *ct_freeze,
+ double *w_ih);
+extern double gsw_internal_energy(double sa, double ct, double p);
+extern double gsw_internal_energy_ice(double t, double p);
+extern void gsw_ipv_vs_fnsquared_ratio(double *sa, double *ct, double *p,
+ double p_ref, int nz, double *ipv_vs_fnsquared_ratio,
+ double *p_mid);
+extern double gsw_kappa_const_t_ice(double t, double p);
+extern double gsw_kappa(double sa, double ct, double p);
+extern double gsw_kappa_ice(double t, double p);
+extern double gsw_kappa_t_exact(double sa, double t, double p);
+extern double gsw_latentheat_evap_ct(double sa, double ct);
+extern double gsw_latentheat_evap_t(double sa, double t);
+extern double gsw_latentheat_melting(double sa, double p);
+extern void gsw_linear_interp_sa_ct(double *sa, double *ct, double *p, int np,
+ double *p_i, int npi, double *sa_i, double *ct_i);
+extern double gsw_melting_ice_equilibrium_sa_ct_ratio(double sa, double p);
+extern double gsw_melting_ice_equilibrium_sa_ct_ratio_poly(double sa, double p);
+extern void gsw_melting_ice_into_seawater(double sa, double ct, double p,
+ double w_ih, double t_ih, double *sa_final, double *ct_final,
+ double *w_ih_final);
+extern double gsw_melting_ice_sa_ct_ratio(double sa, double ct, double p,
+ double t_ih);
+extern double gsw_melting_ice_sa_ct_ratio_poly(double sa, double ct, double p,
+ double t_ih);
+extern double gsw_melting_seaice_equilibrium_sa_ct_ratio(double sa, double p);
+extern double gsw_melting_seaice_equilibrium_sa_ct_ratio_poly(double sa,
+ double p);
+extern void gsw_melting_seaice_into_seawater(double sa, double ct, double p,
+ double w_seaice, double sa_seaice, double t_seaice,
+ double *sa_final, double *ct_final);
+extern double gsw_melting_seaice_sa_ct_ratio(double sa, double ct, double p,
+ double sa_seaice, double t_seaice);
+extern double gsw_melting_seaice_sa_ct_ratio_poly(double sa, double ct,
+ double p, double sa_seaice, double t_seaice);
+extern void gsw_nsquared(double *sa, double *ct, double *p, double *lat,
+ int nz, double *n2, double *p_mid);
+extern double gsw_pot_enthalpy_from_pt_ice(double pt0_ice);
+extern double gsw_pot_enthalpy_from_pt_ice_poly(double pt0_ice);
+extern double gsw_pot_enthalpy_ice_freezing(double sa, double p);
+extern void gsw_pot_enthalpy_ice_freezing_first_derivatives(double sa,
+ double p, double *pot_enthalpy_ice_freezing_sa,
+ double *pot_enthalpy_ice_freezing_p);
+extern void gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(double sa,
+ double p, double *pot_enthalpy_ice_freezing_sa,
+ double *pot_enthalpy_ice_freezing_p);
+extern double gsw_pot_enthalpy_ice_freezing_poly(double sa, double p);
+extern double gsw_pot_rho_t_exact(double sa, double t, double p, double p_ref);
+extern double gsw_pressure_coefficient_ice(double t, double p);
+extern double gsw_pressure_freezing_ct(double sa, double ct,
+ double saturation_fraction);
+extern double gsw_pt0_cold_ice_poly(double pot_enthalpy_ice);
+extern double gsw_pt0_from_t(double sa, double t, double p);
+extern double gsw_pt0_from_t_ice(double t, double p);
+extern void gsw_pt_first_derivatives (double sa, double ct, double *pt_sa,
+ double *pt_ct);
+extern double gsw_pt_from_ct(double sa, double ct);
+extern double gsw_pt_from_entropy(double sa, double entropy);
+extern double gsw_pt_from_pot_enthalpy_ice(double pot_enthalpy_ice);
+extern double gsw_pt_from_pot_enthalpy_ice_poly_dh(double pot_enthalpy_ice);
+extern double gsw_pt_from_pot_enthalpy_ice_poly(double pot_enthalpy_ice);
+extern double gsw_pt_from_t(double sa, double t, double p, double p_ref);
+extern double gsw_pt_from_t_ice(double t, double p, double p_ref);
+extern void gsw_pt_second_derivatives (double sa, double ct, double *pt_sa_sa,
+ double *pt_sa_ct, double *pt_ct_ct);
+extern void gsw_rho_alpha_beta (double sa, double ct, double p, double *rho,
+ double *alpha, double *beta);
+extern double gsw_rho(double sa, double ct, double p);
+extern void gsw_rho_first_derivatives(double sa, double ct, double p,
+ double *drho_dsa, double *drho_dct, double *drho_dp);
+extern void gsw_rho_first_derivatives_wrt_enthalpy (double sa, double ct,
+ double p, double *rho_sa, double *rho_h);
+extern double gsw_rho_ice(double t, double p);
+extern void gsw_rho_second_derivatives(double sa, double ct, double p,
+ double *rho_sa_sa, double *rho_sa_ct, double *rho_ct_ct,
+ double *rho_sa_p, double *rho_ct_p);
+extern void gsw_rho_second_derivatives_wrt_enthalpy(double sa, double ct,
+ double p, double *rho_sa_sa, double *rho_sa_h, double *rho_h_h);
+extern double gsw_rho_t_exact(double sa, double t, double p);
+extern void gsw_rr68_interp_sa_ct(double *sa, double *ct, double *p, int mp,
+ double *p_i, int mp_i, double *sa_i, double *ct_i);
+extern double gsw_saar(double p, double lon, double lat);
+extern double gsw_sa_freezing_estimate(double p, double saturation_fraction,
+ double *ct, double *t);
+extern double gsw_sa_freezing_from_ct(double ct, double p,
+ double saturation_fraction);
+extern double gsw_sa_freezing_from_ct_poly(double ct, double p,
+ double saturation_fraction);
+extern double gsw_sa_freezing_from_t(double t, double p,
+ double saturation_fraction);
+extern double gsw_sa_freezing_from_t_poly(double t, double p,
+ double saturation_fraction);
+extern double gsw_sa_from_rho(double rho, double ct, double p);
+extern double gsw_sa_from_sp_baltic(double sp, double lon, double lat);
+extern double gsw_sa_from_sp(double sp, double p, double lon, double lat);
+extern double gsw_sa_from_sstar(double sstar, double p,double lon,double lat);
+extern int gsw_sa_p_inrange(double sa, double p);
+extern void gsw_seaice_fraction_to_freeze_seawater(double sa, double ct,
+ double p, double sa_seaice, double t_seaice, double *sa_freeze,
+ double *ct_freeze, double *w_seaice);
+extern double gsw_sigma0(double sa, double ct);
+extern double gsw_sigma1(double sa, double ct);
+extern double gsw_sigma2(double sa, double ct);
+extern double gsw_sigma3(double sa, double ct);
+extern double gsw_sigma4(double sa, double ct);
+extern double gsw_sound_speed(double sa, double ct, double p);
+extern double gsw_sound_speed_ice(double t, double p);
+extern double gsw_sound_speed_t_exact(double sa, double t, double p);
+extern void gsw_specvol_alpha_beta(double sa, double ct, double p,
+ double *specvol, double *alpha, double *beta);
+extern double gsw_specvol_anom_standard(double sa, double ct, double p);
+extern double gsw_specvol(double sa, double ct, double p);
+extern void gsw_specvol_first_derivatives(double sa, double ct, double p,
+ double *v_sa, double *v_ct, double *v_p);
+extern void gsw_specvol_first_derivatives_wrt_enthalpy(double sa, double ct,
+ double p, double *v_sa, double *v_h);
+extern double gsw_specvol_ice(double t, double p);
+extern void gsw_specvol_second_derivatives (double sa, double ct, double p,
+ double *v_sa_sa, double *v_sa_ct, double *v_ct_ct,
+ double *v_sa_p, double *v_ct_p);
+extern void gsw_specvol_second_derivatives_wrt_enthalpy(double sa, double ct,
+ double p, double *v_sa_sa, double *v_sa_h, double *v_h_h);
+extern double gsw_specvol_sso_0(double p);
+extern double gsw_specvol_t_exact(double sa, double t, double p);
+extern double gsw_sp_from_c(double c, double t, double p);
+extern double gsw_sp_from_sa_baltic(double sa, double lon, double lat);
+extern double gsw_sp_from_sa(double sa, double p, double lon, double lat);
+extern double gsw_sp_from_sk(double sk);
+extern double gsw_sp_from_sr(double sr);
+extern double gsw_sp_from_sstar(double sstar, double p,double lon,double lat);
+extern double gsw_spiciness0(double sa, double ct);
+extern double gsw_spiciness1(double sa, double ct);
+extern double gsw_spiciness2(double sa, double ct);
+extern double gsw_sr_from_sp(double sp);
+extern double gsw_sstar_from_sa(double sa, double p, double lon, double lat);
+extern double gsw_sstar_from_sp(double sp, double p, double lon, double lat);
+extern double gsw_t_deriv_chem_potential_water_t_exact(double sa, double t,
+ double p);
+extern double gsw_t_freezing(double sa, double p, double saturation_fraction);
+extern void gsw_t_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa,
+ double *tfreezing_p);
+extern void gsw_t_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa,
+ double *tfreezing_p);
+extern double gsw_t_freezing_poly(double sa, double p,
+ double saturation_fraction);
+extern double gsw_t_from_ct(double sa, double ct, double p);
+extern double gsw_t_from_pt0_ice(double pt0_ice, double p);
+extern double gsw_thermobaric(double sa, double ct, double p);
+extern void gsw_turner_rsubrho(double *sa, double *ct, double *p, int nz,
+ double *tu, double *rsubrho, double *p_mid);
+extern int gsw_util_indx(double *x, int n, double z);
+extern double *gsw_util_interp1q_int(int nx, double *x, int *iy, int nxi,
+ double *x_i, double *y_i);
+extern double *gsw_util_linear_interp(int nx, double *x, int ny, double *y,
+ int nxi, double *x_i, double *y_i);
+extern void gsw_util_sort_real(double *rarray, int nx, int *iarray);
+extern double gsw_util_xinterp1(double *x, double *y, int n, double x0);
+extern double gsw_z_from_p(double p, double lat);
+extern double gsw_p_from_z(double z, double lat);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* GSWTEOS_10_H */
diff --git a/src/method_bodies.c b/src/method_bodies.c
new file mode 100644
index 0000000..1dac9fb
--- /dev/null
+++ b/src/method_bodies.c
@@ -0,0 +1,69 @@
+/* Custom wrappers for GSW functions that are not suitable for ufuncs.
+*/
+
+
+/*
+double * Returns NULL on error, dyn_height if okay
+gsw_geo_strf_dyn_height(double *sa, double *ct, double *p, double p_ref,
+ int n_levels, double *dyn_height)
+*/
+
+static PyObject *
+geo_strf_dyn_height(PyObject *NPY_UNUSED(self), PyObject *args)
+{
+ PyObject *sa_o, *ct_o, *p_o, *dh_o;
+ double p_ref;
+ PyArrayObject *sa_a, *ct_a, *p_a, *dh_a;
+ int n_levels;
+ double *ret = NULL; /* NULL on error, dyn_height if OK */
+
+ if (!PyArg_ParseTuple(args, "OOOd", &sa_o, &ct_o, &p_o, &p_ref))
+ return NULL;
+
+ sa_a = (PyArrayObject *)PyArray_ContiguousFromAny(sa_o, NPY_DOUBLE, 1, 1);
+ if (sa_a == NULL)
+ goto error;
+ ct_a = (PyArrayObject *)PyArray_ContiguousFromAny(ct_o, NPY_DOUBLE, 1, 1);
+ if (ct_a == NULL)
+ goto error;
+ p_a = (PyArrayObject *)PyArray_ContiguousFromAny(p_o, NPY_DOUBLE, 1, 1);
+ if (p_a == NULL)
+ goto error;
+
+ n_levels = PyArray_DIM(sa_a, 0);
+ if (PyArray_DIM(ct_a, 0) != n_levels || PyArray_DIM(p_a, 0) != n_levels)
+ {
+ PyErr_SetString(PyExc_ValueError,
+ "Arguments SA, CT, and p must have the same dimensions.");
+ goto error;
+ }
+
+ dh_a = PyArray_NewLikeArray(sa_a, NPY_CORDER, NULL, 0);
+ if (dh_a == NULL)
+ goto error;
+
+ ret = gsw_geo_strf_dyn_height((double *)PyArray_DATA(sa_a),
+ (double *)PyArray_DATA(ct_a),
+ (double *)PyArray_DATA(p_a),
+ p_ref,
+ n_levels,
+ (double *)PyArray_DATA(dh_a));
+
+ if (ret == NULL)
+ {
+ PyErr_SetString(PyExc_RuntimeError,
+ "gws_geo_strf_dyn_height failed; check input arguments");
+ Py_XDECREF(dh_a);
+ goto error;
+ }
+
+ error:
+ Py_XDECREF(sa_a);
+ Py_XDECREF(ct_a);
+ Py_XDECREF(p_a);
+
+ if (ret == NULL)
+ return NULL;
+
+ return (PyObject *)dh_a;
+}
diff --git a/src/method_def_entries.c b/src/method_def_entries.c
new file mode 100644
index 0000000..5bfa770
--- /dev/null
+++ b/src/method_def_entries.c
@@ -0,0 +1,3 @@
+/* Entries in the GswMethods table. */
+{"geo_strf_dyn_height", geo_strf_dyn_height, METH_VARARGS,
+ "geostrophic streamfunction dynamic height"},
diff --git a/src2/_ufuncs.c b/src2/_ufuncs.c
new file mode 100644
index 0000000..c0a32ac
--- /dev/null
+++ b/src2/_ufuncs.c
@@ -0,0 +1,2751 @@
+
+/*
+This file is auto-generated--do not edit it.
+
+This is python 3-only (for simplicity) to begin with.
+*/
+
+#include "Python.h"
+#include "math.h"
+#include "numpy/ndarraytypes.h"
+#include "numpy/ufuncobject.h"
+#include "numpy/npy_3kcompat.h"
+#include "gswteos-10.h"
+
+/* possible hack for MSVC: */
+#ifndef NAN
+ static double NAN = 0.0/0.0;
+#endif
+
+#ifndef isnan
+# define isnan(x) ((x) != (x))
+#endif
+
+#define CONVERT_INVALID(x) ((x == GSW_INVALID_VALUE)? NAN: x)
+
+
+/* 1 in, 1 out */
+static void loop1d_d_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *out0 = args[1];
+ npy_intp out_step0 = steps[1];
+ double (*func)(double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_d_d[] = {&loop1d_d_d};
+
+static char types_d_d[] = {
+ NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 2 in, 1 out */
+static void loop1d_dd_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *out0 = args[2];
+ npy_intp out_step0 = steps[2];
+ double (*func)(double, double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0, *(double *)in1);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dd_d[] = {&loop1d_dd_d};
+
+static char types_dd_d[] = {
+ NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 3 in, 1 out */
+static void loop1d_ddd_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *out0 = args[3];
+ npy_intp out_step0 = steps[3];
+ double (*func)(double, double, double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddd_d[] = {&loop1d_ddd_d};
+
+static char types_ddd_d[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 4 in, 1 out */
+static void loop1d_dddd_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *out0 = args[4];
+ npy_intp out_step0 = steps[4];
+ double (*func)(double, double, double, double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dddd_d[] = {&loop1d_dddd_d};
+
+static char types_dddd_d[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 5 in, 1 out */
+static void loop1d_ddddd_d(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *in4 = args[4];
+ npy_intp in_step4 = steps[4];
+ char *out0 = args[5];
+ npy_intp out_step0 = steps[5];
+ double (*func)(double, double, double, double, double);
+ double outd0;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)||isnan(*(double *)in4)) {
+ *((double *)out0) = NAN;
+ } else {
+ outd0 = func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, *(double *)in4);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ in4 += in_step4;
+ out0 += out_step0;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddddd_d[] = {&loop1d_ddddd_d};
+
+static char types_ddddd_d[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE,
+};
+
+/* 2 in, 2 out */
+static void loop1d_dd_dd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *out0 = args[2];
+ npy_intp out_step0 = steps[2];
+ char *out1 = args[3];
+ npy_intp out_step1 = steps[3];
+ void (*func)(double, double, double *, double *);
+ double outd0, outd1;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, &outd0, &outd1);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ out0 += out_step0;
+ out1 += out_step1;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dd_dd[] = {&loop1d_dd_dd};
+
+static char types_dd_dd[] = {
+ NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 3 in, 2 out */
+static void loop1d_ddd_dd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *out0 = args[3];
+ npy_intp out_step0 = steps[3];
+ char *out1 = args[4];
+ npy_intp out_step1 = steps[4];
+ void (*func)(double, double, double, double *, double *);
+ double outd0, outd1;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, &outd0, &outd1);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ out0 += out_step0;
+ out1 += out_step1;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddd_dd[] = {&loop1d_ddd_dd};
+
+static char types_ddd_dd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 3 in, 3 out */
+static void loop1d_ddd_ddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *out0 = args[3];
+ npy_intp out_step0 = steps[3];
+ char *out1 = args[4];
+ npy_intp out_step1 = steps[4];
+ char *out2 = args[5];
+ npy_intp out_step2 = steps[5];
+ void (*func)(double, double, double, double *, double *, double *);
+ double outd0, outd1, outd2;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, &outd0, &outd1, &outd2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddd_ddd[] = {&loop1d_ddd_ddd};
+
+static char types_ddd_ddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 6 in, 2 out */
+static void loop1d_dddddd_dd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *in4 = args[4];
+ npy_intp in_step4 = steps[4];
+ char *in5 = args[5];
+ npy_intp in_step5 = steps[5];
+ char *out0 = args[6];
+ npy_intp out_step0 = steps[6];
+ char *out1 = args[7];
+ npy_intp out_step1 = steps[7];
+ void (*func)(double, double, double, double, double, double, double *, double *);
+ double outd0, outd1;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)||isnan(*(double *)in4)||isnan(*(double *)in5)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, *(double *)in4, *(double *)in5, &outd0, &outd1);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ in4 += in_step4;
+ in5 += in_step5;
+ out0 += out_step0;
+ out1 += out_step1;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dddddd_dd[] = {&loop1d_dddddd_dd};
+
+static char types_dddddd_dd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 2 in, 3 out */
+static void loop1d_dd_ddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *out0 = args[2];
+ npy_intp out_step0 = steps[2];
+ char *out1 = args[3];
+ npy_intp out_step1 = steps[3];
+ char *out2 = args[4];
+ npy_intp out_step2 = steps[4];
+ void (*func)(double, double, double *, double *, double *);
+ double outd0, outd1, outd2;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, &outd0, &outd1, &outd2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dd_ddd[] = {&loop1d_dd_ddd};
+
+static char types_dd_ddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 4 in, 3 out */
+static void loop1d_dddd_ddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *out0 = args[4];
+ npy_intp out_step0 = steps[4];
+ char *out1 = args[5];
+ npy_intp out_step1 = steps[5];
+ char *out2 = args[6];
+ npy_intp out_step2 = steps[6];
+ void (*func)(double, double, double, double, double *, double *, double *);
+ double outd0, outd1, outd2;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, &outd0, &outd1, &outd2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ }
+}
+
+static PyUFuncGenericFunction funcs_dddd_ddd[] = {&loop1d_dddd_ddd};
+
+static char types_dddd_ddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 5 in, 3 out */
+static void loop1d_ddddd_ddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *in3 = args[3];
+ npy_intp in_step3 = steps[3];
+ char *in4 = args[4];
+ npy_intp in_step4 = steps[4];
+ char *out0 = args[5];
+ npy_intp out_step0 = steps[5];
+ char *out1 = args[6];
+ npy_intp out_step1 = steps[6];
+ char *out2 = args[7];
+ npy_intp out_step2 = steps[7];
+ void (*func)(double, double, double, double, double, double *, double *, double *);
+ double outd0, outd1, outd2;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)||isnan(*(double *)in3)||isnan(*(double *)in4)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, *(double *)in3, *(double *)in4, &outd0, &outd1, &outd2);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ in3 += in_step3;
+ in4 += in_step4;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddddd_ddd[] = {&loop1d_ddddd_ddd};
+
+static char types_ddddd_ddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+
+/* 3 in, 5 out */
+static void loop1d_ddd_ddddd(char **args, npy_intp *dimensions,
+ npy_intp* steps, void* data)
+{
+ npy_intp i;
+ npy_intp n = dimensions[0];
+ char *in0 = args[0];
+ npy_intp in_step0 = steps[0];
+ char *in1 = args[1];
+ npy_intp in_step1 = steps[1];
+ char *in2 = args[2];
+ npy_intp in_step2 = steps[2];
+ char *out0 = args[3];
+ npy_intp out_step0 = steps[3];
+ char *out1 = args[4];
+ npy_intp out_step1 = steps[4];
+ char *out2 = args[5];
+ npy_intp out_step2 = steps[5];
+ char *out3 = args[6];
+ npy_intp out_step3 = steps[6];
+ char *out4 = args[7];
+ npy_intp out_step4 = steps[7];
+ void (*func)(double, double, double, double *, double *, double *, double *, double *);
+ double outd0, outd1, outd2, outd3, outd4;
+ func = data;
+
+ for (i = 0; i < n; i++) {
+ if (isnan(*(double *)in0)||isnan(*(double *)in1)||isnan(*(double *)in2)) {
+ *((double *)out0) = NAN;*((double *)out1) = NAN;*((double *)out2) = NAN;*((double *)out3) = NAN;*((double *)out4) = NAN;
+ } else {
+ func(*(double *)in0, *(double *)in1, *(double *)in2, &outd0, &outd1, &outd2, &outd3, &outd4);
+ *((double *)out0) = CONVERT_INVALID(outd0);
+ *((double *)out1) = CONVERT_INVALID(outd1);
+ *((double *)out2) = CONVERT_INVALID(outd2);
+ *((double *)out3) = CONVERT_INVALID(outd3);
+ *((double *)out4) = CONVERT_INVALID(outd4);
+ }
+ in0 += in_step0;
+ in1 += in_step1;
+ in2 += in_step2;
+ out0 += out_step0;
+ out1 += out_step1;
+ out2 += out_step2;
+ out3 += out_step3;
+ out4 += out_step4;
+ }
+}
+
+static PyUFuncGenericFunction funcs_ddd_ddddd[] = {&loop1d_ddd_ddddd};
+
+static char types_ddd_ddddd[] = {
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+ NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
+};
+static void *data_enthalpy_sso_0[] = {&gsw_enthalpy_sso_0};
+static void *data_gibbs_ice_pt0[] = {&gsw_gibbs_ice_pt0};
+static void *data_gibbs_ice_pt0_pt0[] = {&gsw_gibbs_ice_pt0_pt0};
+static void *data_hill_ratio_at_sp2[] = {&gsw_hill_ratio_at_sp2};
+static void *data_pot_enthalpy_from_pt_ice[] = {&gsw_pot_enthalpy_from_pt_ice};
+static void *data_pot_enthalpy_from_pt_ice_poly[] = {&gsw_pot_enthalpy_from_pt_ice_poly};
+static void *data_pt0_cold_ice_poly[] = {&gsw_pt0_cold_ice_poly};
+static void *data_pt_from_pot_enthalpy_ice[] = {&gsw_pt_from_pot_enthalpy_ice};
+static void *data_pt_from_pot_enthalpy_ice_poly[] = {&gsw_pt_from_pot_enthalpy_ice_poly};
+static void *data_pt_from_pot_enthalpy_ice_poly_dh[] = {&gsw_pt_from_pot_enthalpy_ice_poly_dh};
+static void *data_sp_from_sk[] = {&gsw_sp_from_sk};
+static void *data_sp_from_sr[] = {&gsw_sp_from_sr};
+static void *data_specvol_sso_0[] = {&gsw_specvol_sso_0};
+static void *data_sr_from_sp[] = {&gsw_sr_from_sp};
+static void *data_adiabatic_lapse_rate_ice[] = {&gsw_adiabatic_lapse_rate_ice};
+static void *data_alpha_wrt_t_ice[] = {&gsw_alpha_wrt_t_ice};
+static void *data_chem_potential_water_ice[] = {&gsw_chem_potential_water_ice};
+static void *data_cp_ice[] = {&gsw_cp_ice};
+static void *data_ct_from_entropy[] = {&gsw_ct_from_entropy};
+static void *data_ct_from_pt[] = {&gsw_ct_from_pt};
+static void *data_ct_maxdensity[] = {&gsw_ct_maxdensity};
+static void *data_enthalpy_ice[] = {&gsw_enthalpy_ice};
+static void *data_entropy_from_ct[] = {&gsw_entropy_from_ct};
+static void *data_entropy_from_pt[] = {&gsw_entropy_from_pt};
+static void *data_entropy_ice[] = {&gsw_entropy_ice};
+static void *data_entropy_part_zerop[] = {&gsw_entropy_part_zerop};
+static void *data_gibbs_ice_part_t[] = {&gsw_gibbs_ice_part_t};
+static void *data_gibbs_pt0_pt0[] = {&gsw_gibbs_pt0_pt0};
+static void *data_grav[] = {&gsw_grav};
+static void *data_helmholtz_energy_ice[] = {&gsw_helmholtz_energy_ice};
+static void *data_internal_energy_ice[] = {&gsw_internal_energy_ice};
+static void *data_kappa_const_t_ice[] = {&gsw_kappa_const_t_ice};
+static void *data_kappa_ice[] = {&gsw_kappa_ice};
+static void *data_latentheat_evap_ct[] = {&gsw_latentheat_evap_ct};
+static void *data_latentheat_evap_t[] = {&gsw_latentheat_evap_t};
+static void *data_latentheat_melting[] = {&gsw_latentheat_melting};
+static void *data_melting_ice_equilibrium_sa_ct_ratio[] = {&gsw_melting_ice_equilibrium_sa_ct_ratio};
+static void *data_melting_ice_equilibrium_sa_ct_ratio_poly[] = {&gsw_melting_ice_equilibrium_sa_ct_ratio_poly};
+static void *data_melting_seaice_equilibrium_sa_ct_ratio[] = {&gsw_melting_seaice_equilibrium_sa_ct_ratio};
+static void *data_melting_seaice_equilibrium_sa_ct_ratio_poly[] = {&gsw_melting_seaice_equilibrium_sa_ct_ratio_poly};
+static void *data_p_from_z[] = {&gsw_p_from_z};
+static void *data_pot_enthalpy_ice_freezing[] = {&gsw_pot_enthalpy_ice_freezing};
+static void *data_pot_enthalpy_ice_freezing_poly[] = {&gsw_pot_enthalpy_ice_freezing_poly};
+static void *data_pressure_coefficient_ice[] = {&gsw_pressure_coefficient_ice};
+static void *data_pt0_from_t_ice[] = {&gsw_pt0_from_t_ice};
+static void *data_pt_from_ct[] = {&gsw_pt_from_ct};
+static void *data_pt_from_entropy[] = {&gsw_pt_from_entropy};
+static void *data_rho_ice[] = {&gsw_rho_ice};
+static void *data_sigma0[] = {&gsw_sigma0};
+static void *data_sigma1[] = {&gsw_sigma1};
+static void *data_sigma2[] = {&gsw_sigma2};
+static void *data_sigma3[] = {&gsw_sigma3};
+static void *data_sigma4[] = {&gsw_sigma4};
+static void *data_sound_speed_ice[] = {&gsw_sound_speed_ice};
+static void *data_specvol_ice[] = {&gsw_specvol_ice};
+static void *data_spiciness0[] = {&gsw_spiciness0};
+static void *data_spiciness1[] = {&gsw_spiciness1};
+static void *data_spiciness2[] = {&gsw_spiciness2};
+static void *data_t_from_pt0_ice[] = {&gsw_t_from_pt0_ice};
+static void *data_z_from_p[] = {&gsw_z_from_p};
+static void *data_adiabatic_lapse_rate_from_ct[] = {&gsw_adiabatic_lapse_rate_from_ct};
+static void *data_alpha[] = {&gsw_alpha};
+static void *data_alpha_on_beta[] = {&gsw_alpha_on_beta};
+static void *data_alpha_wrt_t_exact[] = {&gsw_alpha_wrt_t_exact};
+static void *data_beta[] = {&gsw_beta};
+static void *data_beta_const_t_exact[] = {&gsw_beta_const_t_exact};
+static void *data_c_from_sp[] = {&gsw_c_from_sp};
+static void *data_cabbeling[] = {&gsw_cabbeling};
+static void *data_chem_potential_water_t_exact[] = {&gsw_chem_potential_water_t_exact};
+static void *data_cp_t_exact[] = {&gsw_cp_t_exact};
+static void *data_ct_freezing[] = {&gsw_ct_freezing};
+static void *data_ct_freezing_poly[] = {&gsw_ct_freezing_poly};
+static void *data_ct_from_enthalpy[] = {&gsw_ct_from_enthalpy};
+static void *data_ct_from_enthalpy_exact[] = {&gsw_ct_from_enthalpy_exact};
+static void *data_ct_from_t[] = {&gsw_ct_from_t};
+static void *data_deltasa_atlas[] = {&gsw_deltasa_atlas};
+static void *data_dilution_coefficient_t_exact[] = {&gsw_dilution_coefficient_t_exact};
+static void *data_dynamic_enthalpy[] = {&gsw_dynamic_enthalpy};
+static void *data_enthalpy[] = {&gsw_enthalpy};
+static void *data_enthalpy_ct_exact[] = {&gsw_enthalpy_ct_exact};
+static void *data_enthalpy_t_exact[] = {&gsw_enthalpy_t_exact};
+static void *data_entropy_from_t[] = {&gsw_entropy_from_t};
+static void *data_entropy_part[] = {&gsw_entropy_part};
+static void *data_fdelta[] = {&gsw_fdelta};
+static void *data_internal_energy[] = {&gsw_internal_energy};
+static void *data_kappa[] = {&gsw_kappa};
+static void *data_kappa_t_exact[] = {&gsw_kappa_t_exact};
+static void *data_pressure_freezing_ct[] = {&gsw_pressure_freezing_ct};
+static void *data_pt0_from_t[] = {&gsw_pt0_from_t};
+static void *data_pt_from_t_ice[] = {&gsw_pt_from_t_ice};
+static void *data_rho[] = {&gsw_rho};
+static void *data_rho_t_exact[] = {&gsw_rho_t_exact};
+static void *data_sa_freezing_from_ct[] = {&gsw_sa_freezing_from_ct};
+static void *data_sa_freezing_from_ct_poly[] = {&gsw_sa_freezing_from_ct_poly};
+static void *data_sa_freezing_from_t[] = {&gsw_sa_freezing_from_t};
+static void *data_sa_freezing_from_t_poly[] = {&gsw_sa_freezing_from_t_poly};
+static void *data_sa_from_rho[] = {&gsw_sa_from_rho};
+static void *data_sa_from_sp_baltic[] = {&gsw_sa_from_sp_baltic};
+static void *data_saar[] = {&gsw_saar};
+static void *data_sound_speed[] = {&gsw_sound_speed};
+static void *data_sound_speed_t_exact[] = {&gsw_sound_speed_t_exact};
+static void *data_sp_from_c[] = {&gsw_sp_from_c};
+static void *data_sp_from_sa_baltic[] = {&gsw_sp_from_sa_baltic};
+static void *data_specvol[] = {&gsw_specvol};
+static void *data_specvol_anom_standard[] = {&gsw_specvol_anom_standard};
+static void *data_specvol_t_exact[] = {&gsw_specvol_t_exact};
+static void *data_t_deriv_chem_potential_water_t_exact[] = {&gsw_t_deriv_chem_potential_water_t_exact};
+static void *data_t_freezing[] = {&gsw_t_freezing};
+static void *data_t_freezing_poly[] = {&gsw_t_freezing_poly};
+static void *data_t_from_ct[] = {&gsw_t_from_ct};
+static void *data_thermobaric[] = {&gsw_thermobaric};
+static void *data_deltasa_from_sp[] = {&gsw_deltasa_from_sp};
+static void *data_enthalpy_diff[] = {&gsw_enthalpy_diff};
+static void *data_melting_ice_sa_ct_ratio[] = {&gsw_melting_ice_sa_ct_ratio};
+static void *data_melting_ice_sa_ct_ratio_poly[] = {&gsw_melting_ice_sa_ct_ratio_poly};
+static void *data_pot_rho_t_exact[] = {&gsw_pot_rho_t_exact};
+static void *data_pt_from_t[] = {&gsw_pt_from_t};
+static void *data_sa_from_sp[] = {&gsw_sa_from_sp};
+static void *data_sa_from_sstar[] = {&gsw_sa_from_sstar};
+static void *data_sp_from_sa[] = {&gsw_sp_from_sa};
+static void *data_sp_from_sstar[] = {&gsw_sp_from_sstar};
+static void *data_sstar_from_sa[] = {&gsw_sstar_from_sa};
+static void *data_sstar_from_sp[] = {&gsw_sstar_from_sp};
+static void *data_melting_seaice_sa_ct_ratio[] = {&gsw_melting_seaice_sa_ct_ratio};
+static void *data_melting_seaice_sa_ct_ratio_poly[] = {&gsw_melting_seaice_sa_ct_ratio_poly};
+static void *data_ct_first_derivatives[] = {&gsw_ct_first_derivatives};
+static void *data_entropy_first_derivatives[] = {&gsw_entropy_first_derivatives};
+static void *data_pot_enthalpy_ice_freezing_first_derivatives[] = {&gsw_pot_enthalpy_ice_freezing_first_derivatives};
+static void *data_pot_enthalpy_ice_freezing_first_derivatives_poly[] = {&gsw_pot_enthalpy_ice_freezing_first_derivatives_poly};
+static void *data_pt_first_derivatives[] = {&gsw_pt_first_derivatives};
+static void *data_ct_freezing_first_derivatives[] = {&gsw_ct_freezing_first_derivatives};
+static void *data_ct_freezing_first_derivatives_poly[] = {&gsw_ct_freezing_first_derivatives_poly};
+static void *data_ct_from_rho[] = {&gsw_ct_from_rho};
+static void *data_enthalpy_first_derivatives[] = {&gsw_enthalpy_first_derivatives};
+static void *data_enthalpy_first_derivatives_ct_exact[] = {&gsw_enthalpy_first_derivatives_ct_exact};
+static void *data_rho_first_derivatives_wrt_enthalpy[] = {&gsw_rho_first_derivatives_wrt_enthalpy};
+static void *data_specvol_first_derivatives_wrt_enthalpy[] = {&gsw_specvol_first_derivatives_wrt_enthalpy};
+static void *data_t_freezing_first_derivatives[] = {&gsw_t_freezing_first_derivatives};
+static void *data_t_freezing_first_derivatives_poly[] = {&gsw_t_freezing_first_derivatives_poly};
+static void *data_ct_first_derivatives_wrt_t_exact[] = {&gsw_ct_first_derivatives_wrt_t_exact};
+static void *data_enthalpy_second_derivatives[] = {&gsw_enthalpy_second_derivatives};
+static void *data_enthalpy_second_derivatives_ct_exact[] = {&gsw_enthalpy_second_derivatives_ct_exact};
+static void *data_frazil_properties[] = {&gsw_frazil_properties};
+static void *data_frazil_properties_potential[] = {&gsw_frazil_properties_potential};
+static void *data_frazil_properties_potential_poly[] = {&gsw_frazil_properties_potential_poly};
+static void *data_frazil_ratios_adiabatic[] = {&gsw_frazil_ratios_adiabatic};
+static void *data_frazil_ratios_adiabatic_poly[] = {&gsw_frazil_ratios_adiabatic_poly};
+static void *data_rho_alpha_beta[] = {&gsw_rho_alpha_beta};
+static void *data_rho_first_derivatives[] = {&gsw_rho_first_derivatives};
+static void *data_rho_second_derivatives_wrt_enthalpy[] = {&gsw_rho_second_derivatives_wrt_enthalpy};
+static void *data_specvol_alpha_beta[] = {&gsw_specvol_alpha_beta};
+static void *data_specvol_first_derivatives[] = {&gsw_specvol_first_derivatives};
+static void *data_specvol_second_derivatives_wrt_enthalpy[] = {&gsw_specvol_second_derivatives_wrt_enthalpy};
+static void *data_melting_seaice_into_seawater[] = {&gsw_melting_seaice_into_seawater};
+static void *data_ct_second_derivatives[] = {&gsw_ct_second_derivatives};
+static void *data_entropy_second_derivatives[] = {&gsw_entropy_second_derivatives};
+static void *data_pt_second_derivatives[] = {&gsw_pt_second_derivatives};
+static void *data_ice_fraction_to_freeze_seawater[] = {&gsw_ice_fraction_to_freeze_seawater};
+static void *data_melting_ice_into_seawater[] = {&gsw_melting_ice_into_seawater};
+static void *data_seaice_fraction_to_freeze_seawater[] = {&gsw_seaice_fraction_to_freeze_seawater};
+static void *data_rho_second_derivatives[] = {&gsw_rho_second_derivatives};
+static void *data_specvol_second_derivatives[] = {&gsw_specvol_second_derivatives};
+
+
+#include "method_bodies.c"
+
+static PyMethodDef GswMethods[] = {
+# include "method_def_entries.c"
+ {NULL, NULL, 0, NULL}
+};
+
+static struct PyModuleDef moduledef = {
+ PyModuleDef_HEAD_INIT,
+ "npufunc",
+ NULL,
+ -1,
+ GswMethods,
+ NULL,
+ NULL,
+ NULL,
+ NULL
+};
+
+
+PyMODINIT_FUNC PyInit__gsw_ufuncs(void)
+{
+ PyObject *m, *d;
+
+ PyObject *ufunc_ptr;
+
+ m = PyModule_Create(&moduledef);
+ if (!m) {
+ return NULL;
+ }
+
+ d = PyModule_GetDict(m);
+
+ import_array();
+ import_umath();
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_enthalpy_sso_0,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_sso_0",
+ "enthalpy_sso_0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_sso_0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_gibbs_ice_pt0,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "gibbs_ice_pt0",
+ "gibbs_ice_pt0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "gibbs_ice_pt0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_gibbs_ice_pt0_pt0,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "gibbs_ice_pt0_pt0",
+ "gibbs_ice_pt0_pt0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "gibbs_ice_pt0_pt0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_hill_ratio_at_sp2,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "hill_ratio_at_sp2",
+ "hill_ratio_at_sp2_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "hill_ratio_at_sp2", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pot_enthalpy_from_pt_ice,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_from_pt_ice",
+ "pot_enthalpy_from_pt_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_from_pt_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pot_enthalpy_from_pt_ice_poly,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_from_pt_ice_poly",
+ "pot_enthalpy_from_pt_ice_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_from_pt_ice_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pt0_cold_ice_poly,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt0_cold_ice_poly",
+ "pt0_cold_ice_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt0_cold_ice_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pt_from_pot_enthalpy_ice,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_pot_enthalpy_ice",
+ "pt_from_pot_enthalpy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_pot_enthalpy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pt_from_pot_enthalpy_ice_poly,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_pot_enthalpy_ice_poly",
+ "pt_from_pot_enthalpy_ice_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_pot_enthalpy_ice_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_pt_from_pot_enthalpy_ice_poly_dh,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_pot_enthalpy_ice_poly_dh",
+ "pt_from_pot_enthalpy_ice_poly_dh_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_pot_enthalpy_ice_poly_dh", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_sp_from_sk,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sk",
+ "sp_from_sk_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sk", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_sp_from_sr,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sr",
+ "sp_from_sr_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sr", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_specvol_sso_0,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_sso_0",
+ "specvol_sso_0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_sso_0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_d_d,
+ data_sr_from_sp,
+ types_d_d,
+ 1, 1, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sr_from_sp",
+ "sr_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sr_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_adiabatic_lapse_rate_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "adiabatic_lapse_rate_ice",
+ "adiabatic_lapse_rate_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "adiabatic_lapse_rate_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_alpha_wrt_t_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "alpha_wrt_t_ice",
+ "alpha_wrt_t_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "alpha_wrt_t_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_chem_potential_water_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "chem_potential_water_ice",
+ "chem_potential_water_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "chem_potential_water_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_cp_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "cp_ice",
+ "cp_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "cp_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_ct_from_entropy,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_entropy",
+ "ct_from_entropy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_entropy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_ct_from_pt,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_pt",
+ "ct_from_pt_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_pt", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_ct_maxdensity,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_maxdensity",
+ "ct_maxdensity_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_maxdensity", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_enthalpy_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_ice",
+ "enthalpy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_entropy_from_ct,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_from_ct",
+ "entropy_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_entropy_from_pt,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_from_pt",
+ "entropy_from_pt_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_from_pt", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_entropy_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_ice",
+ "entropy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_entropy_part_zerop,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_part_zerop",
+ "entropy_part_zerop_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_part_zerop", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_gibbs_ice_part_t,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "gibbs_ice_part_t",
+ "gibbs_ice_part_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "gibbs_ice_part_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_gibbs_pt0_pt0,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "gibbs_pt0_pt0",
+ "gibbs_pt0_pt0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "gibbs_pt0_pt0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_grav,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "grav",
+ "grav_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "grav", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_helmholtz_energy_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "helmholtz_energy_ice",
+ "helmholtz_energy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "helmholtz_energy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_internal_energy_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "internal_energy_ice",
+ "internal_energy_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "internal_energy_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_kappa_const_t_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "kappa_const_t_ice",
+ "kappa_const_t_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "kappa_const_t_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_kappa_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "kappa_ice",
+ "kappa_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "kappa_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_latentheat_evap_ct,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "latentheat_evap_ct",
+ "latentheat_evap_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "latentheat_evap_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_latentheat_evap_t,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "latentheat_evap_t",
+ "latentheat_evap_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "latentheat_evap_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_latentheat_melting,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "latentheat_melting",
+ "latentheat_melting_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "latentheat_melting", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_melting_ice_equilibrium_sa_ct_ratio,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_equilibrium_sa_ct_ratio",
+ "melting_ice_equilibrium_sa_ct_ratio_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_equilibrium_sa_ct_ratio", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_melting_ice_equilibrium_sa_ct_ratio_poly,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_equilibrium_sa_ct_ratio_poly",
+ "melting_ice_equilibrium_sa_ct_ratio_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_equilibrium_sa_ct_ratio_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_melting_seaice_equilibrium_sa_ct_ratio,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_equilibrium_sa_ct_ratio",
+ "melting_seaice_equilibrium_sa_ct_ratio_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_equilibrium_sa_ct_ratio", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_melting_seaice_equilibrium_sa_ct_ratio_poly,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_equilibrium_sa_ct_ratio_poly",
+ "melting_seaice_equilibrium_sa_ct_ratio_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_equilibrium_sa_ct_ratio_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_p_from_z,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "p_from_z",
+ "p_from_z_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "p_from_z", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pot_enthalpy_ice_freezing,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_ice_freezing",
+ "pot_enthalpy_ice_freezing_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_ice_freezing", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pot_enthalpy_ice_freezing_poly,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_ice_freezing_poly",
+ "pot_enthalpy_ice_freezing_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_ice_freezing_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pressure_coefficient_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pressure_coefficient_ice",
+ "pressure_coefficient_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pressure_coefficient_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pt0_from_t_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt0_from_t_ice",
+ "pt0_from_t_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt0_from_t_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pt_from_ct,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_ct",
+ "pt_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_pt_from_entropy,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_entropy",
+ "pt_from_entropy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_entropy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_rho_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_ice",
+ "rho_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma0,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma0",
+ "sigma0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma1,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma1",
+ "sigma1_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma1", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma2,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma2",
+ "sigma2_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma2", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma3,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma3",
+ "sigma3_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma3", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sigma4,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sigma4",
+ "sigma4_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sigma4", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_sound_speed_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sound_speed_ice",
+ "sound_speed_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sound_speed_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_specvol_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_ice",
+ "specvol_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_spiciness0,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "spiciness0",
+ "spiciness0_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "spiciness0", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_spiciness1,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "spiciness1",
+ "spiciness1_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "spiciness1", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_spiciness2,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "spiciness2",
+ "spiciness2_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "spiciness2", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_t_from_pt0_ice,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_from_pt0_ice",
+ "t_from_pt0_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_from_pt0_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_d,
+ data_z_from_p,
+ types_dd_d,
+ 1, 2, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "z_from_p",
+ "z_from_p_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "z_from_p", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_adiabatic_lapse_rate_from_ct,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "adiabatic_lapse_rate_from_ct",
+ "adiabatic_lapse_rate_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "adiabatic_lapse_rate_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_alpha,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "alpha",
+ "alpha_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "alpha", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_alpha_on_beta,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "alpha_on_beta",
+ "alpha_on_beta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "alpha_on_beta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_alpha_wrt_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "alpha_wrt_t_exact",
+ "alpha_wrt_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "alpha_wrt_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_beta,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "beta",
+ "beta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "beta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_beta_const_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "beta_const_t_exact",
+ "beta_const_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "beta_const_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_c_from_sp,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "c_from_sp",
+ "c_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "c_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_cabbeling,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "cabbeling",
+ "cabbeling_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "cabbeling", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_chem_potential_water_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "chem_potential_water_t_exact",
+ "chem_potential_water_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "chem_potential_water_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_cp_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "cp_t_exact",
+ "cp_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "cp_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_freezing,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_freezing",
+ "ct_freezing_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_freezing", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_freezing_poly,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_freezing_poly",
+ "ct_freezing_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_freezing_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_from_enthalpy,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_enthalpy",
+ "ct_from_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_from_enthalpy_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_enthalpy_exact",
+ "ct_from_enthalpy_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_enthalpy_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_ct_from_t,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_t",
+ "ct_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_deltasa_atlas,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "deltasa_atlas",
+ "deltasa_atlas_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "deltasa_atlas", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_dilution_coefficient_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "dilution_coefficient_t_exact",
+ "dilution_coefficient_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "dilution_coefficient_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_dynamic_enthalpy,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "dynamic_enthalpy",
+ "dynamic_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "dynamic_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_enthalpy,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy",
+ "enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_enthalpy_ct_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_ct_exact",
+ "enthalpy_ct_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_ct_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_enthalpy_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_t_exact",
+ "enthalpy_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_entropy_from_t,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_from_t",
+ "entropy_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_entropy_part,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_part",
+ "entropy_part_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_part", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_fdelta,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "fdelta",
+ "fdelta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "fdelta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_internal_energy,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "internal_energy",
+ "internal_energy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "internal_energy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_kappa,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "kappa",
+ "kappa_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "kappa", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_kappa_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "kappa_t_exact",
+ "kappa_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "kappa_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_pressure_freezing_ct,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pressure_freezing_ct",
+ "pressure_freezing_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pressure_freezing_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_pt0_from_t,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt0_from_t",
+ "pt0_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt0_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_pt_from_t_ice,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_t_ice",
+ "pt_from_t_ice_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_t_ice", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_rho,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho",
+ "rho_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_rho_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_t_exact",
+ "rho_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_freezing_from_ct,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_freezing_from_ct",
+ "sa_freezing_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_freezing_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_freezing_from_ct_poly,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_freezing_from_ct_poly",
+ "sa_freezing_from_ct_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_freezing_from_ct_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_freezing_from_t,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_freezing_from_t",
+ "sa_freezing_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_freezing_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_freezing_from_t_poly,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_freezing_from_t_poly",
+ "sa_freezing_from_t_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_freezing_from_t_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_from_rho,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_from_rho",
+ "sa_from_rho_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_from_rho", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sa_from_sp_baltic,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_from_sp_baltic",
+ "sa_from_sp_baltic_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_from_sp_baltic", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_saar,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "saar",
+ "saar_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "saar", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sound_speed,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sound_speed",
+ "sound_speed_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sound_speed", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sound_speed_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sound_speed_t_exact",
+ "sound_speed_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sound_speed_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sp_from_c,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_c",
+ "sp_from_c_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_c", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_sp_from_sa_baltic,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sa_baltic",
+ "sp_from_sa_baltic_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sa_baltic", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_specvol,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol",
+ "specvol_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_specvol_anom_standard,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_anom_standard",
+ "specvol_anom_standard_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_anom_standard", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_specvol_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_t_exact",
+ "specvol_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_t_deriv_chem_potential_water_t_exact,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_deriv_chem_potential_water_t_exact",
+ "t_deriv_chem_potential_water_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_deriv_chem_potential_water_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_t_freezing,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_freezing",
+ "t_freezing_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_freezing", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_t_freezing_poly,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_freezing_poly",
+ "t_freezing_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_freezing_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_t_from_ct,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_from_ct",
+ "t_from_ct_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_from_ct", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_d,
+ data_thermobaric,
+ types_ddd_d,
+ 1, 3, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "thermobaric",
+ "thermobaric_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "thermobaric", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_deltasa_from_sp,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "deltasa_from_sp",
+ "deltasa_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "deltasa_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_enthalpy_diff,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_diff",
+ "enthalpy_diff_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_diff", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_melting_ice_sa_ct_ratio,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_sa_ct_ratio",
+ "melting_ice_sa_ct_ratio_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_sa_ct_ratio", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_melting_ice_sa_ct_ratio_poly,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_sa_ct_ratio_poly",
+ "melting_ice_sa_ct_ratio_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_sa_ct_ratio_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_pot_rho_t_exact,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_rho_t_exact",
+ "pot_rho_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_rho_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_pt_from_t,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_from_t",
+ "pt_from_t_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_from_t", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sa_from_sp,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_from_sp",
+ "sa_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sa_from_sstar,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sa_from_sstar",
+ "sa_from_sstar_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sa_from_sstar", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sp_from_sa,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sa",
+ "sp_from_sa_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sa", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sp_from_sstar,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sp_from_sstar",
+ "sp_from_sstar_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sp_from_sstar", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sstar_from_sa,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sstar_from_sa",
+ "sstar_from_sa_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sstar_from_sa", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_d,
+ data_sstar_from_sp,
+ types_dddd_d,
+ 1, 4, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "sstar_from_sp",
+ "sstar_from_sp_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "sstar_from_sp", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_d,
+ data_melting_seaice_sa_ct_ratio,
+ types_ddddd_d,
+ 1, 5, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_sa_ct_ratio",
+ "melting_seaice_sa_ct_ratio_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_sa_ct_ratio", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_d,
+ data_melting_seaice_sa_ct_ratio_poly,
+ types_ddddd_d,
+ 1, 5, 1, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_sa_ct_ratio_poly",
+ "melting_seaice_sa_ct_ratio_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_sa_ct_ratio_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_ct_first_derivatives,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_first_derivatives",
+ "ct_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_entropy_first_derivatives,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_first_derivatives",
+ "entropy_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_pot_enthalpy_ice_freezing_first_derivatives,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_ice_freezing_first_derivatives",
+ "pot_enthalpy_ice_freezing_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_ice_freezing_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_pot_enthalpy_ice_freezing_first_derivatives_poly,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pot_enthalpy_ice_freezing_first_derivatives_poly",
+ "pot_enthalpy_ice_freezing_first_derivatives_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pot_enthalpy_ice_freezing_first_derivatives_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_dd,
+ data_pt_first_derivatives,
+ types_dd_dd,
+ 1, 2, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_first_derivatives",
+ "pt_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_ct_freezing_first_derivatives,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_freezing_first_derivatives",
+ "ct_freezing_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_freezing_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_ct_freezing_first_derivatives_poly,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_freezing_first_derivatives_poly",
+ "ct_freezing_first_derivatives_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_freezing_first_derivatives_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_ct_from_rho,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_from_rho",
+ "ct_from_rho_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_from_rho", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_enthalpy_first_derivatives,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_first_derivatives",
+ "enthalpy_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_enthalpy_first_derivatives_ct_exact,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_first_derivatives_ct_exact",
+ "enthalpy_first_derivatives_ct_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_first_derivatives_ct_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_rho_first_derivatives_wrt_enthalpy,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_first_derivatives_wrt_enthalpy",
+ "rho_first_derivatives_wrt_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_first_derivatives_wrt_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_specvol_first_derivatives_wrt_enthalpy,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_first_derivatives_wrt_enthalpy",
+ "specvol_first_derivatives_wrt_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_first_derivatives_wrt_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_t_freezing_first_derivatives,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_freezing_first_derivatives",
+ "t_freezing_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_freezing_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_dd,
+ data_t_freezing_first_derivatives_poly,
+ types_ddd_dd,
+ 1, 3, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "t_freezing_first_derivatives_poly",
+ "t_freezing_first_derivatives_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "t_freezing_first_derivatives_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_ct_first_derivatives_wrt_t_exact,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_first_derivatives_wrt_t_exact",
+ "ct_first_derivatives_wrt_t_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_first_derivatives_wrt_t_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_enthalpy_second_derivatives,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_second_derivatives",
+ "enthalpy_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_enthalpy_second_derivatives_ct_exact,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "enthalpy_second_derivatives_ct_exact",
+ "enthalpy_second_derivatives_ct_exact_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "enthalpy_second_derivatives_ct_exact", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_properties,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_properties",
+ "frazil_properties_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_properties", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_properties_potential,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_properties_potential",
+ "frazil_properties_potential_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_properties_potential", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_properties_potential_poly,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_properties_potential_poly",
+ "frazil_properties_potential_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_properties_potential_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_ratios_adiabatic,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_ratios_adiabatic",
+ "frazil_ratios_adiabatic_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_ratios_adiabatic", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_frazil_ratios_adiabatic_poly,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "frazil_ratios_adiabatic_poly",
+ "frazil_ratios_adiabatic_poly_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "frazil_ratios_adiabatic_poly", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_rho_alpha_beta,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_alpha_beta",
+ "rho_alpha_beta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_alpha_beta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_rho_first_derivatives,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_first_derivatives",
+ "rho_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_rho_second_derivatives_wrt_enthalpy,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_second_derivatives_wrt_enthalpy",
+ "rho_second_derivatives_wrt_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_second_derivatives_wrt_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_specvol_alpha_beta,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_alpha_beta",
+ "specvol_alpha_beta_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_alpha_beta", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_specvol_first_derivatives,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_first_derivatives",
+ "specvol_first_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_first_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddd,
+ data_specvol_second_derivatives_wrt_enthalpy,
+ types_ddd_ddd,
+ 1, 3, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_second_derivatives_wrt_enthalpy",
+ "specvol_second_derivatives_wrt_enthalpy_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_second_derivatives_wrt_enthalpy", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddddd_dd,
+ data_melting_seaice_into_seawater,
+ types_dddddd_dd,
+ 1, 6, 2, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_seaice_into_seawater",
+ "melting_seaice_into_seawater_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_seaice_into_seawater", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_ddd,
+ data_ct_second_derivatives,
+ types_dd_ddd,
+ 1, 2, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ct_second_derivatives",
+ "ct_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ct_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_ddd,
+ data_entropy_second_derivatives,
+ types_dd_ddd,
+ 1, 2, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "entropy_second_derivatives",
+ "entropy_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "entropy_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dd_ddd,
+ data_pt_second_derivatives,
+ types_dd_ddd,
+ 1, 2, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "pt_second_derivatives",
+ "pt_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "pt_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_dddd_ddd,
+ data_ice_fraction_to_freeze_seawater,
+ types_dddd_ddd,
+ 1, 4, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "ice_fraction_to_freeze_seawater",
+ "ice_fraction_to_freeze_seawater_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "ice_fraction_to_freeze_seawater", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_ddd,
+ data_melting_ice_into_seawater,
+ types_ddddd_ddd,
+ 1, 5, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "melting_ice_into_seawater",
+ "melting_ice_into_seawater_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "melting_ice_into_seawater", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddddd_ddd,
+ data_seaice_fraction_to_freeze_seawater,
+ types_ddddd_ddd,
+ 1, 5, 3, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "seaice_fraction_to_freeze_seawater",
+ "seaice_fraction_to_freeze_seawater_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "seaice_fraction_to_freeze_seawater", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddddd,
+ data_rho_second_derivatives,
+ types_ddd_ddddd,
+ 1, 3, 5, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "rho_second_derivatives",
+ "rho_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "rho_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+ ufunc_ptr = PyUFunc_FromFuncAndData(funcs_ddd_ddddd,
+ data_specvol_second_derivatives,
+ types_ddd_ddddd,
+ 1, 3, 5, // ndatatypes, nin, nout
+ PyUFunc_None,
+ "specvol_second_derivatives",
+ "specvol_second_derivatives_docstring",
+ 0);
+
+ PyDict_SetItemString(d, "specvol_second_derivatives", ufunc_ptr);
+ Py_DECREF(ufunc_ptr);
+
+
+ return m;
+}
diff --git a/src2/c_gsw/LICENSE b/src2/c_gsw/LICENSE
new file mode 100644
index 0000000..6119a6f
--- /dev/null
+++ b/src2/c_gsw/LICENSE
@@ -0,0 +1,34 @@
+Licence for the use of the Gibbs SeaWater (GSW) Oceanographic Toolbox
+
+Copyright (c) 2011, SCOR/IAPSO WG127 (Scientific Committee on Oceanic Research/
+International Association for the Physical Sciences of the Oceans, Working Group 127).
+
+All rights reserved.
+
+Redistribution and use, in source and binary forms, without modification, is permitted
+provided that the following conditions are met:
+
+• Redistributions of source code must retain the above copyright notice, this list
+ of conditions and the following disclaimer.
+
+• Redistributions in binary form must reproduce the above copyright notice, this
+ list of conditions and the following disclaimer in the documentation and/or other
+ materials provided with the distribution.
+
+• Neither the name of SCOR/IAPSO WG127 nor the names of its contributors may be used
+ to endorse or promote products derived from this software without specific prior
+ written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
+EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
+SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
+BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
+DAMAGE.
+
+The software is available from http://www.TEOS-10.org
+
diff --git a/src2/c_gsw/gsw_internal_const.h b/src2/c_gsw/gsw_internal_const.h
new file mode 100644
index 0000000..4abd7a8
--- /dev/null
+++ b/src2/c_gsw/gsw_internal_const.h
@@ -0,0 +1,500 @@
+/*
+** $Id: gsw_internal_const.h,v a1406e71e2a9 2016/01/08 08:01:43 fdelahoyde $
+**
+** Internal constants for GSW-TEOS-10 V3.05.
+*/
+#ifndef GSW_INTERNAL_CONST_H
+#define GSW_INTERNAL_CONST_H
+
+/*
+** The following hack is used to ensure that gcc (and gcc emulating compilers
+** such as Macosx clang) do not emit unused variable warning messages.
+*/
+#ifdef __GNUC__
+#define UNUSED __attribute__ ((unused))
+#else
+#define UNUSED
+#endif
+
+#define GSW_TEOS10_CONSTANTS \
+UNUSED double db2pa = 1.0e4, \
+ rec_db2pa = 1.0e-4, \
+ pa2db = 1.0e-4, \
+ rec_pa2db = 1.0e4, \
+ pi = 3.141592653589793, \
+ deg2rad = pi/180.0, \
+ rad2deg = 180.0/pi, \
+ gamma = 2.26e-7, \
+/*\
+! cp0 = The "specific heat" for use [ J/(kg K) ]\
+! with Conservative Temperature \
+*/\
+ gsw_cp0 = 3991.86795711963, \
+/*\
+! T0 = the Celsius zero point. [ K ]\
+*/\
+ gsw_t0 = 273.15, \
+/*\
+! P0 = Absolute Pressure of one standard atmosphere. [ Pa ]\
+*/\
+ gsw_p0 = 101325.0, \
+/*\
+! SSO = Standard Ocean Reference Salinity. [ g/kg ]\
+*/\
+ gsw_sso = 35.16504, \
+ gsw_sqrtsso = 5.930011804372737, \
+/*\
+! uPS = unit conversion factor for salinities [ g/kg ]\
+*/\
+ gsw_ups = gsw_sso/35.0, \
+/*\
+! sfac = 1/(40*gsw_ups)\
+*/\
+ gsw_sfac = 0.0248826675584615, \
+/*\
+! deltaS = 24, offset = deltaS*gsw_sfac\
+*/\
+ offset = 5.971840214030754e-1, \
+/*\
+! C3515 = Conductivity at (SP=35, t_68=15, p=0) [ mS/cm ]\
+*/\
+ gsw_c3515 = 42.9140, \
+/*\
+! SonCl = SP to Chlorinity ratio [ (g/kg)^-1 ]\
+*/\
+ gsw_soncl = 1.80655, \
+/*\
+! valence_factor = valence factor of sea salt of Reference Composition\
+! [ unitless ]\
+*/\
+ gsw_valence_factor = 1.2452898, \
+/*\
+! atomic_weight = mole-weighted atomic weight of sea salt of Reference \
+! Composition [ g/mol ]\
+*/\
+ gsw_atomic_weight = 31.4038218
+
+
+#define GSW_SPECVOL_COEFFICIENTS \
+UNUSED double a000 = -1.56497346750e-5, \
+ a001 = 1.85057654290e-5, \
+ a002 = -1.17363867310e-6, \
+ a003 = -3.65270065530e-7, \
+ a004 = 3.14540999020e-7, \
+ a010 = 5.55242129680e-5, \
+ a011 = -2.34332137060e-5, \
+ a012 = 4.26100574800e-6, \
+ a013 = 5.73918103180e-7, \
+ a020 = -4.95634777770e-5, \
+ a021 = 2.37838968519e-5, \
+ a022 = -1.38397620111e-6, \
+ a030 = 2.76445290808e-5, \
+ a031 = -1.36408749928e-5, \
+ a032 = -2.53411666056e-7, \
+ a040 = -4.02698077700e-6, \
+ a041 = 2.53683834070e-6, \
+ a050 = 1.23258565608e-6, \
+ a100 = 3.50095997640e-5, \
+ a101 = -9.56770881560e-6, \
+ a102 = -5.56991545570e-6, \
+ a103 = -2.72956962370e-7, \
+ a110 = -7.48716846880e-5, \
+ a111 = -4.73566167220e-7, \
+ a112 = 7.82747741600e-7, \
+ a120 = 7.24244384490e-5, \
+ a121 = -1.03676320965e-5, \
+ a122 = 2.32856664276e-8, \
+ a130 = -3.50383492616e-5, \
+ a131 = 5.18268711320e-6, \
+ a140 = -1.65263794500e-6, \
+ a200 = -4.35926785610e-5, \
+ a201 = 1.11008347650e-5, \
+ a202 = 5.46207488340e-6, \
+ a210 = 7.18156455200e-5, \
+ a211 = 5.85666925900e-6, \
+ a212 = -1.31462208134e-6, \
+ a220 = -4.30608991440e-5, \
+ a221 = 9.49659182340e-7, \
+ a230 = 1.74814722392e-5, \
+ a300 = 3.45324618280e-5, \
+ a301 = -9.84471178440e-6, \
+ a302 = -1.35441856270e-6, \
+ a310 = -3.73971683740e-5, \
+ a311 = -9.76522784000e-7, \
+ a320 = 6.85899736680e-6, \
+ a400 = -1.19594097880e-5, \
+ a401 = 2.59092252600e-6, \
+ a410 = 7.71906784880e-6, \
+ a500 = 1.38645945810e-6, \
+ b000 = -3.10389819760e-4, \
+ b003 = 3.63101885150e-7, \
+ b004 = -1.11471254230e-7, \
+ b010 = 3.50095997640e-5, \
+ b013 = -2.72956962370e-7, \
+ b020 = -3.74358423440e-5, \
+ b030 = 2.41414794830e-5, \
+ b040 = -8.75958731540e-6, \
+ b050 = -3.30527589000e-7, \
+ b100 = 1.33856134076e-3, \
+ b103 = 3.34926075600e-8, \
+ b110 = -8.71853571220e-5, \
+ b120 = 7.18156455200e-5, \
+ b130 = -2.87072660960e-5, \
+ b140 = 8.74073611960e-6, \
+ b200 = -2.55143801811e-3, \
+ b210 = 1.03597385484e-4, \
+ b220 = -5.60957525610e-5, \
+ b230 = 6.85899736680e-6, \
+ b300 = 2.32344279772e-3, \
+ b310 = -4.78376391520e-5, \
+ b320 = 1.54381356976e-5, \
+ b400 = -1.05461852535e-3, \
+ b410 = 6.93229729050e-6, \
+ b500 = 1.91594743830e-4, \
+ b001 = 2.42624687470e-5, \
+ b011 = -9.56770881560e-6, \
+ b021 = -2.36783083610e-7, \
+ b031 = -3.45587736550e-6, \
+ b041 = 1.29567177830e-6, \
+ b101 = -6.95849219480e-5, \
+ b111 = 2.22016695300e-5, \
+ b121 = 5.85666925900e-6, \
+ b131 = 6.33106121560e-7, \
+ b201 = 1.12412331915e-4, \
+ b211 = -2.95341353532e-5, \
+ b221 = -1.46478417600e-6, \
+ b301 = -6.92888744480e-5, \
+ b311 = 1.03636901040e-5, \
+ b401 = 1.54637136265e-5, \
+ b002 = -5.84844329840e-7, \
+ b012 = -5.56991545570e-6, \
+ b022 = 3.91373870800e-7, \
+ b032 = 7.76188880920e-9, \
+ b102 = -9.62445031940e-6, \
+ b112 = 1.09241497668e-5, \
+ b122 = -1.31462208134e-6, \
+ b202 = 1.47789320994e-5, \
+ b212 = -4.06325568810e-6, \
+ b302 = -7.12478989080e-6, \
+ c000 = -6.07991438090e-5, \
+ c001 = 1.99712338438e-5, \
+ c002 = -3.39280843110e-6, \
+ c003 = 4.21246123200e-7, \
+ c004 = -6.32363064300e-8, \
+ c005 = 1.17681023580e-8, \
+ c010 = 1.85057654290e-5, \
+ c011 = -2.34727734620e-6, \
+ c012 = -1.09581019659e-6, \
+ c013 = 1.25816399608e-6, \
+ c020 = -1.17166068530e-5, \
+ c021 = 4.26100574800e-6, \
+ c022 = 8.60877154770e-7, \
+ c030 = 7.92796561730e-6, \
+ c031 = -9.22650800740e-7, \
+ c040 = -3.41021874820e-6, \
+ c041 = -1.26705833028e-7, \
+ c050 = 5.07367668140e-7, \
+ c100 = 2.42624687470e-5, \
+ c101 = -1.16968865968e-6, \
+ c102 = 1.08930565545e-6, \
+ c103 = -4.45885016920e-7, \
+ c110 = -9.56770881560e-6, \
+ c111 = -1.11398309114e-5, \
+ c112 = -8.18870887110e-7, \
+ c120 = -2.36783083610e-7, \
+ c121 = 7.82747741600e-7, \
+ c130 = -3.45587736550e-6, \
+ c131 = 1.55237776184e-8, \
+ c140 = 1.29567177830e-6, \
+ c200 = -3.47924609740e-5, \
+ c201 = -9.62445031940e-6, \
+ c202 = 5.02389113400e-8, \
+ c210 = 1.11008347650e-5, \
+ c211 = 1.09241497668e-5, \
+ c220 = 2.92833462950e-6, \
+ c221 = -1.31462208134e-6, \
+ c230 = 3.16553060780e-7, \
+ c300 = 3.74707773050e-5, \
+ c301 = 9.85262139960e-6, \
+ c310 = -9.84471178440e-6, \
+ c311 = -2.70883712540e-6, \
+ c320 = -4.88261392000e-7, \
+ c400 = -1.73222186120e-5, \
+ c401 = -3.56239494540e-6, \
+ c410 = 2.59092252600e-6, \
+ c500 = 3.09274272530e-6, \
+ h001 = 1.07699958620e-3, \
+ h002 = -3.03995719050e-5, \
+ h003 = 3.32853897400e-6, \
+ h004 = -2.82734035930e-7, \
+ h005 = 2.10623061600e-8, \
+ h006 = -2.10787688100e-9, \
+ h007 = 2.80192913290e-10, \
+ h011 = -1.56497346750e-5, \
+ h012 = 9.25288271450e-6, \
+ h013 = -3.91212891030e-7, \
+ h014 = -9.13175163830e-8, \
+ h015 = 6.29081998040e-8, \
+ h021 = 2.77621064840e-5, \
+ h022 = -5.85830342650e-6, \
+ h023 = 7.10167624670e-7, \
+ h024 = 7.17397628980e-8, \
+ h031 = -1.65211592590e-5, \
+ h032 = 3.96398280870e-6, \
+ h033 = -1.53775133460e-7, \
+ h042 = -1.70510937410e-6, \
+ h043 = -2.11176388380e-8, \
+ h041 = 6.91113227020e-6, \
+ h051 = -8.05396155400e-7, \
+ h052 = 2.53683834070e-7, \
+ h061 = 2.05430942680e-7, \
+ h101 = -3.10389819760e-4, \
+ h102 = 1.21312343735e-5, \
+ h103 = -1.94948109950e-7, \
+ h104 = 9.07754712880e-8, \
+ h105 = -2.22942508460e-8, \
+ h111 = 3.50095997640e-5, \
+ h112 = -4.78385440780e-6, \
+ h113 = -1.85663848520e-6, \
+ h114 = -6.82392405930e-8, \
+ h121 = -3.74358423440e-5, \
+ h122 = -1.18391541805e-7, \
+ h123 = 1.30457956930e-7, \
+ h131 = 2.41414794830e-5, \
+ h132 = -1.72793868275e-6, \
+ h133 = 2.58729626970e-9, \
+ h141 = -8.75958731540e-6, \
+ h142 = 6.47835889150e-7, \
+ h151 = -3.30527589000e-7, \
+ h201 = 6.69280670380e-4, \
+ h202 = -1.73962304870e-5, \
+ h203 = -1.60407505320e-6, \
+ h204 = 4.18657594500e-9, \
+ h211 = -4.35926785610e-5, \
+ h212 = 5.55041738250e-6, \
+ h213 = 1.82069162780e-6, \
+ h221 = 3.59078227600e-5, \
+ h222 = 1.46416731475e-6, \
+ h223 = -2.19103680220e-7, \
+ h231 = -1.43536330480e-5, \
+ h232 = 1.58276530390e-7, \
+ h241 = 4.37036805980e-6, \
+ h301 = -8.50479339370e-4, \
+ h302 = 1.87353886525e-5, \
+ h303 = 1.64210356660e-6, \
+ h311 = 3.45324618280e-5, \
+ h312 = -4.92235589220e-6, \
+ h313 = -4.51472854230e-7, \
+ h321 = -1.86985841870e-5, \
+ h322 = -2.44130696000e-7, \
+ h331 = 2.28633245560e-6, \
+ h401 = 5.80860699430e-4, \
+ h402 = -8.66110930600e-6, \
+ h403 = -5.93732490900e-7, \
+ h411 = -1.19594097880e-5, \
+ h421 = 3.85953392440e-6, \
+ h412 = 1.29546126300e-6, \
+ h501 = -2.10923705070e-4, \
+ h502 = 1.54637136265e-6, \
+ h511 = 1.38645945810e-6, \
+ h601 = 3.19324573050e-5, \
+ v000 = 1.0769995862e-3, \
+ v001 = -6.0799143809e-5, \
+ v002 = 9.9856169219e-6, \
+ v003 = -1.1309361437e-6, \
+ v004 = 1.0531153080e-7, \
+ v005 = -1.2647261286e-8, \
+ v006 = 1.9613503930e-9, \
+ v010 = -3.1038981976e-4, \
+ v011 = 2.4262468747e-5, \
+ v012 = -5.8484432984e-7, \
+ v013 = 3.6310188515e-7, \
+ v014 = -1.1147125423e-7, \
+ v020 = 6.6928067038e-4, \
+ v021 = -3.4792460974e-5, \
+ v022 = -4.8122251597e-6, \
+ v023 = 1.6746303780e-8, \
+ v030 = -8.5047933937e-4, \
+ v031 = 3.7470777305e-5, \
+ v032 = 4.9263106998e-6, \
+ v040 = 5.8086069943e-4, \
+ v041 = -1.7322218612e-5, \
+ v042 = -1.7811974727e-6, \
+ v050 = -2.1092370507e-4, \
+ v051 = 3.0927427253e-6, \
+ v060 = 3.1932457305e-5, \
+ v100 = -1.5649734675e-5, \
+ v101 = 1.8505765429e-5, \
+ v102 = -1.1736386731e-6, \
+ v103 = -3.6527006553e-7, \
+ v104 = 3.1454099902e-7, \
+ v110 = 3.5009599764e-5, \
+ v111 = -9.5677088156e-6, \
+ v112 = -5.5699154557e-6, \
+ v113 = -2.7295696237e-7, \
+ v120 = -4.3592678561e-5, \
+ v121 = 1.1100834765e-5, \
+ v122 = 5.4620748834e-6, \
+ v130 = 3.4532461828e-5, \
+ v131 = -9.8447117844e-6, \
+ v132 = -1.3544185627e-6, \
+ v140 = -1.1959409788e-5, \
+ v141 = 2.5909225260e-6, \
+ v150 = 1.3864594581e-6, \
+ v200 = 2.7762106484e-5, \
+ v201 = -1.1716606853e-5, \
+ v202 = 2.1305028740e-6, \
+ v203 = 2.8695905159e-7, \
+ v210 = -3.7435842344e-5, \
+ v211 = -2.3678308361e-7, \
+ v212 = 3.9137387080e-7, \
+ v220 = 3.5907822760e-5, \
+ v221 = 2.9283346295e-6, \
+ v222 = -6.5731104067e-7, \
+ v230 = -1.8698584187e-5, \
+ v231 = -4.8826139200e-7, \
+ v240 = 3.8595339244e-6, \
+ v300 = -1.6521159259e-5, \
+ v301 = 7.9279656173e-6, \
+ v302 = -4.6132540037e-7, \
+ v310 = 2.4141479483e-5, \
+ v311 = -3.4558773655e-6, \
+ v312 = 7.7618888092e-9, \
+ v320 = -1.4353633048e-5, \
+ v321 = 3.1655306078e-7, \
+ v330 = 2.2863324556e-6, \
+ v400 = 6.9111322702e-6, \
+ v401 = -3.4102187482e-6, \
+ v402 = -6.3352916514e-8, \
+ v410 = -8.7595873154e-6, \
+ v411 = 1.2956717783e-6, \
+ v420 = 4.3703680598e-6, \
+ v500 = -8.0539615540e-7, \
+ v501 = 5.0736766814e-7, \
+ v510 = -3.3052758900e-7, \
+ v600 = 2.0543094268e-7
+
+#define GSW_SP_COEFFICIENTS \
+UNUSED double a0 = 0.0080, \
+ a1 = -0.1692, \
+ a2 = 25.3851, \
+ a3 = 14.0941, \
+ a4 = -7.0261, \
+ a5 = 2.7081, \
+ b0 = 0.0005, \
+ b1 = -0.0056, \
+ b2 = -0.0066, \
+ b3 = -0.0375, \
+ b4 = 0.0636, \
+ b5 = -0.0144, \
+ c0 = 0.6766097, \
+ c1 = 2.00564e-2, \
+ c2 = 1.104259e-4, \
+ c3 = -6.9698e-7, \
+ c4 = 1.0031e-9, \
+ d1 = 3.426e-2, \
+ d2 = 4.464e-4, \
+ d3 = 4.215e-1, \
+ d4 = -3.107e-3, \
+ e1 = 2.070e-5, \
+ e2 = -6.370e-10, \
+ e3 = 3.989e-15, \
+ k = 0.0162
+
+#define GSW_SAAR_DATA \
+UNUSED int deli[4] = {0,1,1,0}, delj[4] = {0,0,1,1}, npan = 6; \
+UNUSED double longs_pan[6] = {260.00, 272.59, 276.50, 278.65, 280.73, 292.0},\
+ lats_pan[6] = { 19.55, 13.97, 9.60, 8.10, 9.33, 3.4}
+
+
+#define GSW_GIBBS_ICE_COEFFICIENTS \
+UNUSED std::complex<double> t1 ( 3.68017112855051e-2, 5.10878114959572e-2), \
+ t2 ( 3.37315741065416e-1, 3.35449415919309e-1), \
+ r1 ( 4.47050716285388e1, 6.56876847463481e1), \
+ r20 (-7.25974574329220e1, -7.81008427112870e1), \
+ r21 (-5.57107698030123e-5, 4.64578634580806e-5), \
+ r22 (2.34801409215913e-11, -2.85651142904972e-11);\
+/*\
+! 1./Pt, where Pt = 611.657; Experimental triple-point pressure in Pa.\
+*/\
+double rec_pt = 1.634903221903779e-3, \
+ tt = 273.16, /*Triple-point temperature, kelvin (K).*/ \
+ rec_tt = 3.660858105139845e-3, /*= 1/tt */ \
+ g00 = -6.32020233335886e5, \
+ g01 = 6.55022213658955e-1, \
+ g02 = -1.89369929326131e-8, \
+ g03 = 3.3974612327105304e-15, \
+ g04 = -5.564648690589909e-22
+
+
+#define GSW_FREEZING_POLY_COEFFICIENTS \
+UNUSED double c0 = 0.017947064327968736, \
+ c1 = -6.076099099929818, \
+ c2 = 4.883198653547851, \
+ c3 = -11.88081601230542, \
+ c4 = 13.34658511480257, \
+ c5 = -8.722761043208607, \
+ c6 = 2.082038908808201, \
+ c7 = -7.389420998107497, \
+ c8 = -2.110913185058476, \
+ c9 = 0.2295491578006229, \
+ c10 = -0.9891538123307282, \
+ c11 = -0.08987150128406496, \
+ c12 = 0.3831132432071728, \
+ c13 = 1.054318231187074, \
+ c14 = 1.065556599652796, \
+ c15 = -0.7997496801694032, \
+ c16 = 0.3850133554097069, \
+ c17 = -2.078616693017569, \
+ c18 = 0.8756340772729538, \
+ c19 = -2.079022768390933, \
+ c20 = 1.596435439942262, \
+ c21 = 0.1338002171109174, \
+ c22 = 1.242891021876471, \
+/* \
+! Note that a = 0.502500117621,/gsw_sso \
+*/ \
+ a = 0.014289763856964, \
+ b = 0.057000649899720, \
+ t0 = 0.002519, \
+ t1 = -5.946302841607319, \
+ t2 = 4.136051661346983, \
+ t3 = -1.115150523403847e1, \
+ t4 = 1.476878746184548e1, \
+ t5 = -1.088873263630961e1, \
+ t6 = 2.961018839640730, \
+ t7 = -7.433320943962606, \
+ t8 = -1.561578562479883, \
+ t9 = 4.073774363480365e-2, \
+ t10 = 1.158414435887717e-2, \
+ t11 = -4.122639292422863e-1, \
+ t12 = -1.123186915628260e-1, \
+ t13 = 5.715012685553502e-1, \
+ t14 = 2.021682115652684e-1, \
+ t15 = 4.140574258089767e-2, \
+ t16 = -6.034228641903586e-1, \
+ t17 = -1.205825928146808e-2, \
+ t18 = -2.812172968619369e-1, \
+ t19 = 1.877244474023750e-2, \
+ t20 = -1.204395563789007e-1, \
+ t21 = 2.349147739749606e-1, \
+ t22 = 2.748444541144219e-3
+
+
+#define GSW_BALTIC_DATA \
+/*\
+! Coordinate data for the Baltic Sea\
+*/\
+UNUSED double xb_left[3]={12.6, 7.0, 26.0},\
+ yb_left[3]={50.0, 59.0, 69.0},\
+ xb_right[2]={45.0, 26.0},\
+ yb_right[2]={50.0, 69.0}
+
+#ifndef max
+#define max(a,b) (((a)>(b))?(a):(b))
+#endif
+#ifndef min
+#define min(a,b) (((a)<(b))?(a):(b))
+#endif
+
+#endif /* GSW_INTERNAL_CONST_H */
diff --git a/src2/c_gsw/gsw_oceanographic_toolbox.cpp b/src2/c_gsw/gsw_oceanographic_toolbox.cpp
new file mode 100644
index 0000000..468d376
--- /dev/null
+++ b/src2/c_gsw/gsw_oceanographic_toolbox.cpp
@@ -0,0 +1,10704 @@
+/*
+** $Id: gsw_oceanographic_toolbox-head,v c61271a7810d 2016/08/19 20:04:03 fdelahoyde $
+** Version: 3.05.0-3
+**
+** This is a translation of the original f90 source code into C
+** by the Shipboard Technical Support Computing Resources group
+** at Scripps Institution of Oceanography -- sts-cr at sio.ucsd.edu.
+** The original notices follow.
+**
+==========================================================================
+ Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS-10 (Fortran)
+==========================================================================
+
+ This is a subset of functions contained in the Gibbs SeaWater (GSW)
+ Oceanographic Toolbox of TEOS-10.
+
+ Version 1.0 written by David Jackett
+ Modified by Paul Barker (version 3.02)
+ Modified by Glenn Hyland (version 3.04+)
+
+ For help with this Oceanographic Toolbox email: help at teos-10.org
+
+ This software is available from http://www.teos-10.org
+
+==========================================================================
+
+ gsw_data_v3_0.nc
+ NetCDF file that contains the global data set of Absolute Salinity Anomaly
+ Ratio, the global data set of Absolute Salinity Anomaly atlas, and check
+ values and computation accuracy values for use in gsw_check_function.
+ The data set gsw_data_v3_0.nc must not be tampered with.
+
+ gsw_check_function.f90
+ Contains the check functions. We suggest that after downloading, unzipping
+ and installing the toolbox the user runs this program to ensure that the
+ toolbox is installed correctly and there are no conflicts. This toolbox has
+ been tested to compile and run with gfortran.
+
+ cd test
+ make
+ ./gsw_check
+
+ Note that gfortran is the name of the GNU Fortran project, developing a
+ free Fortran 95/2003/2008 compiler for GCC, the GNU Compiler Collection.
+ It is available from http://gcc.gnu.org/fortran/
+
+==========================================================================
+*/
+#include "gswteos-10_cpp.h"
+#include "gsw_internal_const.h"
+
+/*
+!==========================================================================
+subroutine gsw_add_barrier(input_data,lon,lat,long_grid,lat_grid,dlong_grid,dlat_grid,output_data)
+!==========================================================================
+
+! Adds a barrier through Central America (Panama) and then averages
+! over the appropriate side of the barrier
+!
+! data_in : data [unitless]
+! lon : Longitudes of data degrees east [0 ... +360]
+! lat : Latitudes of data degrees north [-90 ... +90]
+! longs_grid : Longitudes of regular grid degrees east [0 ... +360]
+! lats_grid : Latitudes of regular grid degrees north [-90 ... +90]
+! dlongs_grid : Longitude difference of regular grid degrees [deg longitude]
+! dlats_grid : Latitude difference of regular grid degrees [deg latitude]
+!
+! output_data : average of data depending on which side of the
+! Panama canal it is on [unitless]
+*/
+void
+gsw_add_barrier(double *input_data, double lon, double lat,
+ double long_grid, double lat_grid, double dlong_grid,
+ double dlat_grid, double *output_data)
+{
+ GSW_SAAR_DATA;
+ int above_line[4];
+ int k, nmean, above_line0, kk;
+ double r, lats_line, data_mean;
+
+ k = gsw_util_indx(longs_pan,npan,lon);
+ /* the lon/lat point */
+ r = (lon-longs_pan[k])/(longs_pan[k+1]-longs_pan[k]);
+ lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]);
+
+ above_line0 = (lats_line <= lat);
+
+ k = gsw_util_indx(longs_pan,npan,long_grid);
+ /*the 1 & 4 lon/lat points*/
+ r = (long_grid-longs_pan[k])/
+ (longs_pan[k+1]-longs_pan[k]);
+ lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]);
+
+ above_line[0] = (lats_line <= lat_grid);
+ above_line[3] = (lats_line <= lat_grid+dlat_grid);
+
+ k = gsw_util_indx(longs_pan,6,long_grid+dlong_grid);
+ /*the 2 & 3 lon/lat points */
+ r = (long_grid+dlong_grid-longs_pan[k])/
+ (longs_pan[k+1]-longs_pan[k]);
+ lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]);
+
+ above_line[1] = (lats_line <= lat_grid);
+ above_line[2] = (lats_line <= lat_grid+dlat_grid);
+
+ nmean = 0;
+ data_mean = 0.0;
+
+ for (kk=0; kk<4; kk++) {
+ if ((fabs(input_data[kk]) <= 100.0) &&
+ above_line0 == above_line[kk]) {
+ nmean = nmean+1;
+ data_mean = data_mean+input_data[kk];
+ }
+ }
+ if (nmean == 0)
+ data_mean = 0.0; /*errorreturn*/
+ else
+ data_mean = data_mean/nmean;
+
+ for (kk=0; kk<4; kk++) {
+ if ((fabs(input_data[kk]) >= 1.0e10) ||
+ above_line0 != above_line[kk])
+ output_data[kk] = data_mean;
+ else
+ output_data[kk] = input_data[kk];
+ }
+
+ return;
+}
+/*
+!==========================================================================
+subroutine gsw_add_mean(data_in,data_out)
+!==========================================================================
+
+! Replaces NaN's with non-nan mean of the 4 adjacent neighbours
+!
+! data_in : data set of the 4 adjacent neighbours
+!
+! data_out : non-nan mean of the 4 adjacent neighbours [unitless]
+*/
+void
+gsw_add_mean(double *data_in, double *data_out)
+{
+ int k, nmean;
+ double data_mean;
+
+ nmean = 0;
+ data_mean = 0.0;
+
+ for (k=0; k<4; k++) {
+ if (fabs(data_in[k]) <= 100.0) {
+ nmean++;
+ data_mean = data_mean+data_in[k];
+ }
+ }
+
+ if (nmean == 0.0)
+ data_mean = 0.0; /*errorreturn*/
+ else
+ data_mean = data_mean/nmean;
+
+ for (k=0; k<4; k++) {
+ if (fabs(data_in[k]) >= 100.0)
+ data_out[k] = data_mean;
+ else
+ data_out[k] = data_in[k];
+ }
+ return;
+}
+/*
+!==========================================================================
+function gsw_adiabatic_lapse_rate_from_ct(sa,ct,p)
+!==========================================================================
+
+! Calculates the adiabatic lapse rate from Conservative Temperature
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_adiabatic_lapse_rate_from_ct : adiabatic lapse rate [K/Pa]
+*/
+double
+gsw_adiabatic_lapse_rate_from_ct(double sa, double ct, double p)
+{
+ int n0=0, n1=1, n2=2;
+ double pt0, pr0=0.0, t;
+
+ pt0 = gsw_pt_from_ct(sa,ct);
+ t = gsw_pt_from_t(sa,pt0,pr0,p);
+
+ return (-gsw_gibbs(n0,n1,n1,sa,t,p)/gsw_gibbs(n0,n2,n0,sa,t,p));
+
+}
+/*
+!==========================================================================
+elemental function gsw_adiabatic_lapse_rate_ice (t, p)
+!==========================================================================
+!
+! Calculates the adiabatic lapse rate of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! Note. The output is in unit of degress Celsius per Pa,
+! (or equivilently K/Pa) not in units of K/dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_adiabatic_lapse_rate_ice(double t, double p)
+{
+ return (-gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(2,0,t,p));
+}
+/*
+!==========================================================================
+function gsw_alpha(sa,ct,p)
+!==========================================================================
+
+! Calculates the thermal expansion coefficient of seawater with respect to
+! Conservative Temperature using the computationally-efficient 48-term
+! expression for density in terms of SA, CT and p (IOC et al., 2010)
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_alpha : thermal expansion coefficient of seawater (48 term equation)
+*/
+double
+gsw_alpha(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double xs, ys, z, v_ct_part;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v_ct_part = a000
+ + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ return (0.025*v_ct_part/gsw_specvol(sa,ct,p));
+}
+/*
+!==========================================================================
+function gsw_alpha_on_beta(sa,ct,p)
+!==========================================================================
+
+! Calculates alpha divided by beta, where alpha is the thermal expansion
+! coefficient and beta is the saline contraction coefficient of seawater
+! from Absolute Salinity and Conservative Temperature. This function uses
+! the computationally-efficient expression for specific volume in terms of
+! SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+!
+! alpha_on_beta
+! : thermal expansion coefficient with respect to [kg g^-1 K^-1]
+! Conservative Temperature divided by the saline
+! contraction coefficient at constant Conservative
+! Temperature
+*/
+double
+gsw_alpha_on_beta(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double xs, ys, z, v_ct_part, v_sa_part;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v_ct_part = a000
+ + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ v_sa_part = b000
+ + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ return (-(v_ct_part*xs)/(20.0*gsw_sfac*v_sa_part));
+}
+/*
+!==========================================================================
+function gsw_alpha_wrt_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates thermal expansion coefficient of seawater with respect to
+! in-situ temperature
+!
+! sa : Absolute Salinity [g/kg]
+! t : insitu temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_alpha_wrt_t_exact : thermal expansion coefficient [1/K]
+! wrt (in-situ) temperature
+*/
+double
+gsw_alpha_wrt_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (gsw_gibbs(n0,n1,n1,sa,t,p)/gsw_gibbs(n0,n0,n1,sa,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_alpha_wrt_t_ice (t, p)
+!==========================================================================
+!
+! Calculates the thermal expansion coefficient of ice with respect to
+! in-situ temperature.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! alpha_wrt_t_ice = thermal expansion coefficient of ice with respect
+! to in-situ temperature [ 1/K ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_alpha_wrt_t_ice(double t, double p)
+{
+ return (gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+function gsw_beta(sa,ct,p)
+!==========================================================================
+
+! Calculates the saline (i.e. haline) contraction coefficient of seawater
+! at constant Conservative Temperature using the computationally-efficient
+! expression for specific volume in terms of SA, CT and p
+! (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! beta : saline contraction coefficient of seawater [kg/g]
+! at constant Conservative Temperature
+*/
+double
+gsw_beta(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double xs, ys, z, v_sa_part;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v_sa_part = b000
+ + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ return (-v_sa_part*0.5*gsw_sfac/(gsw_specvol(sa,ct,p)*xs));
+}
+/*
+!==========================================================================
+function gsw_beta_const_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates saline (haline) contraction coefficient of seawater at
+! constant in-situ temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! beta_const_t_exact : haline contraction coefficient [kg/g]
+*/
+double
+gsw_beta_const_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (-gsw_gibbs(n1,n0,n1,sa,t,p)/gsw_gibbs(n0,n0,n1,sa,t,p));
+}
+/*
+!==========================================================================
+function gsw_c_from_sp(sp,t,p)
+!==========================================================================
+
+! Calculates conductivity, C, from (SP,t,p) using PSS-78 in the range
+! 2 < SP < 42. If the input Practical Salinity is less than 2 then a
+! modified form of the Hill et al. (1986) fomula is used for Practical
+! Salinity. The modification of the Hill et al. (1986) expression is to
+! ensure that it is exactly consistent with PSS-78 at SP = 2.
+!
+! The conductivity ratio returned by this function is consistent with the
+! input value of Practical Salinity, SP, to 2x10^-14 psu over the full
+! range of input parameters (from pure fresh water up to SP = 42 psu).
+! This error of 2x10^-14 psu is machine precision at typical seawater
+! salinities. This accuracy is achieved by having four different
+! polynomials for the starting value of Rtx (the square root of Rt) in
+! four different ranges of SP, and by using one and a half iterations of
+! a computationally efficient modified Newton-Raphson technique (McDougall
+! and Wotherspoon, 2012) to find the root of the equation.
+!
+! Note that strictly speaking PSS-78 (Unesco, 1983) defines Practical
+! Salinity in terms of the conductivity ratio, R, without actually
+! specifying the value of C(35,15,0) (which we currently take to be
+! 42.9140 mS/cm).
+!
+! sp : Practical Salinity [unitless]
+! t : in-situ temperature [ITS-90] [deg C]
+! p : sea pressure [dbar]
+!
+! c : conductivity [ mS/cm ]
+*/
+double
+gsw_c_from_sp(double sp, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SP_COEFFICIENTS;
+ double p0 = 4.577801212923119e-3, p1 = 1.924049429136640e-1,
+ p2 = 2.183871685127932e-5, p3 = -7.292156330457999e-3,
+ p4 = 1.568129536470258e-4, p5 = -1.478995271680869e-6,
+ p6 = 9.086442524716395e-4, p7 = -1.949560839540487e-5,
+ p8 = -3.223058111118377e-6, p9 = 1.175871639741131e-7,
+ p10 = -7.522895856600089e-5, p11 = -2.254458513439107e-6,
+ p12 = 6.179992190192848e-7, p13 = 1.005054226996868e-8,
+ p14 = -1.923745566122602e-9, p15 = 2.259550611212616e-6,
+ p16 = 1.631749165091437e-7, p17 = -5.931857989915256e-9,
+ p18 = -4.693392029005252e-9, p19 = 2.571854839274148e-10,
+ p20 = 4.198786822861038e-12,
+ q0 = 5.540896868127855e-5, q1 = 2.015419291097848e-1,
+ q2 = -1.445310045430192e-5, q3 = -1.567047628411722e-2,
+ q4 = 2.464756294660119e-4, q5 = -2.575458304732166e-7,
+ q6 = 5.071449842454419e-3, q7 = 9.081985795339206e-5,
+ q8 = -3.635420818812898e-6, q9 = 2.249490528450555e-8,
+ q10 = -1.143810377431888e-3, q11 = 2.066112484281530e-5,
+ q12 = 7.482907137737503e-7, q13 = 4.019321577844724e-8,
+ q14 = -5.755568141370501e-10, q15 = 1.120748754429459e-4,
+ q16 = -2.420274029674485e-6, q17 = -4.774829347564670e-8,
+ q18 = -4.279037686797859e-9, q19 = -2.045829202713288e-10,
+ q20 = 5.025109163112005e-12,
+ s0 = 3.432285006604888e-3, s1 = 1.672940491817403e-1,
+ s2 = 2.640304401023995e-5, s3 = 1.082267090441036e-1,
+ s4 = -6.296778883666940e-5, s5 = -4.542775152303671e-7,
+ s6 = -1.859711038699727e-1, s7 = 7.659006320303959e-4,
+ s8 = -4.794661268817618e-7, s9 = 8.093368602891911e-9,
+ s10 = 1.001140606840692e-1, s11 = -1.038712945546608e-3,
+ s12 = -6.227915160991074e-6, s13 = 2.798564479737090e-8,
+ s14 = -1.343623657549961e-10, s15 = 1.024345179842964e-2,
+ s16 = 4.981135430579384e-4, s17 = 4.466087528793912e-6,
+ s18 = 1.960872795577774e-8, s19 = -2.723159418888634e-10,
+ s20 = 1.122200786423241e-12,
+ u0 = 5.180529787390576e-3, u1 = 1.052097167201052e-3,
+ u2 = 3.666193708310848e-5, u3 = 7.112223828976632e0,
+ u4 = -3.631366777096209e-4, u5 = -7.336295318742821e-7,
+ u6 = -1.576886793288888e+2, u7 = -1.840239113483083e-3,
+ u8 = 8.624279120240952e-6, u9 = 1.233529799729501e-8,
+ u10 = 1.826482800939545e+3, u11 = 1.633903983457674e-1,
+ u12 = -9.201096427222349e-5, u13 = -9.187900959754842e-8,
+ u14 = -1.442010369809705e-10, u15 = -8.542357182595853e+3,
+ u16 = -1.408635241899082e0, u17 = 1.660164829963661e-4,
+ u18 = 6.797409608973845e-7, u19 = 3.345074990451475e-10,
+ u20 = 8.285687652694768e-13;
+
+ double t68, ft68, x, rtx=0.0, dsp_drtx, sqrty,
+ part1, part2, hill_ratio, sp_est,
+ rtx_old, rt, aa, bb, cc, dd, ee, ra,r, rt_lc, rtxm,
+ sp_hill_raw;
+
+ t68 = t*1.00024e0;
+ ft68 = (t68 - 15e0)/(1e0 + k*(t68 - 15e0));
+
+ x = sqrt(sp);
+
+ /*
+ |--------------------------------------------------------------------------
+ ! Finding the starting value of Rtx, the square root of Rt, using four
+ ! different polynomials of SP and t68.
+ !--------------------------------------------------------------------------
+ */
+
+ if (sp >= 9.0) {
+ rtx = p0 + x*(p1 + p4*t68 + x*(p3 + p7*t68 + x*(p6
+ + p11*t68 + x*(p10 + p16*t68 + x*p15))))
+ + t68*(p2+ t68*(p5 + x*x*(p12 + x*p17) + p8*x
+ + t68*(p9 + x*(p13 + x*p18)+ t68*(p14 + p19*x + p20*t68))));
+ } else if (sp >= 0.25 && sp < 9.0) {
+ rtx = q0 + x*(q1 + q4*t68 + x*(q3 + q7*t68 + x*(q6
+ + q11*t68 + x*(q10 + q16*t68 + x*q15))))
+ + t68*(q2+ t68*(q5 + x*x*(q12 + x*q17) + q8*x
+ + t68*(q9 + x*(q13 + x*q18)+ t68*(q14 + q19*x + q20*t68))));
+ } else if (sp >= 0.003 && sp < 0.25) {
+ rtx = s0 + x*(s1 + s4*t68 + x*(s3 + s7*t68 + x*(s6
+ + s11*t68 + x*(s10 + s16*t68 + x*s15))))
+ + t68*(s2+ t68*(s5 + x*x*(s12 + x*s17) + s8*x
+ + t68*(s9 + x*(s13 + x*s18)+ t68*(s14 + s19*x + s20*t68))));
+ } else if (sp < 0.003) {
+ rtx = u0 + x*(u1 + u4*t68 + x*(u3 + u7*t68 + x*(u6
+ + u11*t68 + x*(u10 + u16*t68 + x*u15))))
+ + t68*(u2+ t68*(u5 + x*x*(u12 + x*u17) + u8*x
+ + t68*(u9 + x*(u13 + x*u18)+ t68*(u14 + u19*x + u20*t68))));
+ }
+
+ /*
+ !--------------------------------------------------------------------------
+ ! Finding the starting value of dSP_dRtx, the derivative of SP with respect
+ ! to Rtx.
+ !--------------------------------------------------------------------------
+ */
+ dsp_drtx = a1 + (2e0*a2 + (3e0*a3 +
+ (4e0*a4 + 5e0*a5*rtx)*rtx)*rtx)*rtx
+ + ft68*(b1 + (2e0*b2 + (3e0*b3 + (4e0*b4 +
+ 5e0*b5*rtx)*rtx)*rtx)*rtx);
+
+ if (sp < 2.0) {
+ x = 400e0*(rtx*rtx);
+ sqrty = 10.0*rtx;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ dsp_drtx = dsp_drtx
+ + a0*800e0*rtx*(1.5e0 + 2e0*x)/(part1*part1)
+ + b0*ft68*(10e0 + sqrty*(20e0 + 30e0*sqrty))/
+ (part2*part2);
+ dsp_drtx = hill_ratio*dsp_drtx;
+ }
+
+ /*
+ !--------------------------------------------------------------------------
+ ! One iteration through the modified Newton-Raphson method (McDougall and
+ ! Wotherspoon, 2012) achieves an error in Practical Salinity of about
+ ! 10^-12 for all combinations of the inputs. One and a half iterations of
+ ! the modified Newton-Raphson method achevies a maximum error in terms of
+ ! Practical Salinity of better than 2x10^-14 everywhere.
+ !
+ ! We recommend one and a half iterations of the modified Newton-Raphson
+ ! method.
+ !
+ ! Begin the modified Newton-Raphson method.
+ !--------------------------------------------------------------------------
+ */
+ sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx
+ + ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx);
+ if (sp_est < 2.0) {
+ x = 400e0*(rtx*rtx);
+ sqrty = 10e0*rtx;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ sp_hill_raw = sp_est - a0/part1 - b0*ft68/part2;
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ sp_est = hill_ratio*sp_hill_raw;
+ }
+
+ rtx_old = rtx;
+ rtx = rtx_old - (sp_est - sp)/dsp_drtx;
+
+ rtxm = 0.5e0*(rtx + rtx_old); /*This mean value of Rtx, Rtxm, is the
+ value of Rtx at which the derivative dSP_dRtx is evaluated.*/
+
+ dsp_drtx= a1 + (2e0*a2 + (3e0*a3 + (4e0*a4 +
+ 5e0*a5*rtxm)*rtxm)*rtxm)*rtxm
+ + ft68*(b1 + (2e0*b2 + (3e0*b3 + (4e0*b4 +
+ 5e0*b5*rtxm)*rtxm)*rtxm)*rtxm);
+ if (sp_est < 2.0) {
+ x = 400e0*(rtxm*rtxm);
+ sqrty = 10e0*rtxm;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ dsp_drtx = dsp_drtx
+ + a0*800e0*rtxm*(1.5e0 + 2e0*x)/(part1*part1)
+ + b0*ft68*(10e0 + sqrty*(20e0 + 30e0*sqrty))/
+ (part2*part2);
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ dsp_drtx = hill_ratio*dsp_drtx;
+ }
+
+ /*
+ !--------------------------------------------------------------------------
+ ! The line below is where Rtx is updated at the end of the one full
+ ! iteration of the modified Newton-Raphson technique.
+ !--------------------------------------------------------------------------
+ */
+ rtx = rtx_old - (sp_est - sp)/dsp_drtx;
+ /*
+ !--------------------------------------------------------------------------
+ ! Now we do another half iteration of the modified Newton-Raphson
+ ! technique, making a total of one and a half modified N-R iterations.
+ !--------------------------------------------------------------------------
+ */
+ sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx
+ + ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx);
+ if (sp_est < 2.0) {
+ x = 400e0*(rtx*rtx);
+ sqrty = 10e0*rtx;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ sp_hill_raw = sp_est - a0/part1 - b0*ft68/part2;
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ sp_est = hill_ratio*sp_hill_raw;
+ }
+ rtx = rtx - (sp_est - sp)/dsp_drtx;
+
+ /*
+ !--------------------------------------------------------------------------
+ ! Now go from Rtx to Rt and then to the conductivity ratio R at pressure p.
+ !--------------------------------------------------------------------------
+ */
+ rt = rtx*rtx;
+
+ aa = d3 + d4*t68;
+ bb = 1e0 + t68*(d1 + d2*t68);
+ cc = p*(e1 + p*(e2 + e3*p));
+ /* rt_lc (i.e. rt_lower_case) corresponds to rt as defined in
+ the UNESCO 44 (1983) routines. */
+ rt_lc = c0 + (c1 + (c2 + (c3 + c4*t68)*t68)*t68)*t68;
+
+ dd = bb - aa*rt_lc*rt;
+ ee = rt_lc*rt*aa*(bb + cc);
+ ra = sqrt(dd*dd + 4e0*ee) - dd;
+ r = 0.5e0*ra/aa;
+
+ /*
+ ! The dimensionless conductivity ratio, R, is the conductivity input, C,
+ ! divided by the present estimate of C(SP=35, t_68=15, p=0) which is
+ ! 42.9140 mS/cm (=4.29140 S/m^).
+ */
+ return (gsw_c3515*r);
+}
+/*
+!==========================================================================
+function gsw_cabbeling(sa,ct,p)
+!==========================================================================
+
+! Calculates the cabbeling coefficient of seawater with respect to
+! Conservative Temperature. This function uses the computationally-
+! efficient expression for specific volume in terms of SA, CT and p
+! (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! cabbeling : cabbeling coefficient with respect to [1/K^2]
+! Conservative Temperature.
+*/
+double
+gsw_cabbeling(double sa, double ct, double p)
+{
+ double alpha_ct, alpha_on_beta, alpha_sa, beta_sa, rho,
+ v_sa, v_ct, v_sa_sa, v_sa_ct, v_ct_ct;
+
+ gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct, NULL);
+
+ gsw_specvol_second_derivatives(sa,ct,p,&v_sa_sa,&v_sa_ct,&v_ct_ct,
+ NULL, NULL);
+
+ rho = gsw_rho(sa,ct,p);
+
+ alpha_ct = rho*(v_ct_ct - rho*v_ct*v_ct);
+
+ alpha_sa = rho*(v_sa_ct - rho*v_sa*v_ct);
+
+ beta_sa = -rho*(v_sa_sa - rho*v_sa*v_sa);
+
+ alpha_on_beta = gsw_alpha_on_beta(sa,ct,p);
+
+ return (alpha_ct +
+ alpha_on_beta*(2.0*alpha_sa - alpha_on_beta*beta_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_chem_potential_water_ice (t, p)
+!==========================================================================
+!
+! Calculates the chemical potential of water in ice from in-situ
+! temperature and pressure.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! chem_potential_water_ice = chemical potential of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_chem_potential_water_ice(double t, double p)
+{
+ return (gsw_gibbs_ice(0,0,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_chem_potential_water_t_exact (sa, t, p)
+!==========================================================================
+!
+! Calculates the chemical potential of water in seawater.
+!
+! SA = Absolute Salinity [ g/kg ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! chem_potential_water_t_exact = chemical potential of water in seawater
+! [ J/g ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_chem_potential_water_t_exact(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g03_g, g08_g, g_sa_part, x, x2, y, z, kg2g = 1e-3;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*1e-4;
+
+ g03_g = 101.342743139674 + z*(100015.695367145 +
+ z*(-2544.5765420363 + z*(284.517778446287 +
+ z*(-33.3146754253611 + (4.20263108803084 - 0.546428511471039*z)*z)))) +
+ y*(5.90578347909402 + z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 +
+ (28.9796526294175 - 2.13290083518327*z)*z))) +
+ y*(-12357.785933039 + z*(1455.0364540468 +
+ z*(-756.558385769359 + z*(273.479662323528 +
+ z*(-55.5604063817218 + 4.34420671917197*z)))) +
+ y*(736.741204151612 + z*(-672.50778314507 +
+ z*(499.360390819152 + z*(-239.545330654412 +
+ (48.8012518593872 - 1.66307106208905*z)*z))) +
+ y*(-148.185936433658 + z*(397.968445406972 +
+ z*(-301.815380621876 + (152.196371733841 - 26.3748377232802*z)*z)) +
+ y*(58.0259125842571 + z*(-194.618310617595 +
+ z*(120.520654902025 + z*(-55.2723052340152 + 6.48190668077221*z))) +
+ y*(-18.9843846514172 + y*(3.05081646487967 - 9.63108119393062*z) +
+ z*(63.5113936641785 + z*(-22.2897317140459 + 8.17060541818112*z))))))));
+
+ g08_g = x2*(1416.27648484197 +
+ x*(-2432.14662381794 + x*(2025.80115603697 +
+ y*(543.835333000098 + y*(-68.5572509204491 +
+ y*(49.3667694856254 + y*(-17.1397577419788 +
+ 2.49697009569508*y))) - 22.6683558512829*z) +
+ x*(-1091.66841042967 - 196.028306689776*y +
+ x*(374.60123787784 - 48.5891069025409*x +
+ 36.7571622995805*y) + 36.0284195611086*z) +
+ z*(-54.7919133532887 + (-4.08193978912261 -
+ 30.1755111971161*z)*z)) +
+ z*(199.459603073901 + z*(-52.2940909281335 +
+ (68.0444942726459 - 3.41251932441282*z)*z)) +
+ y*(-493.407510141682 + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-43.0664675978042 + z*(383.058066002476 +
+ z*(-54.1917262517112 + 25.6398487389914*z)) +
+ y*(-10.0227370861875 - 460.319931801257*z +
+ y*(0.875600661808945 + 234.565187611355*z))))) +
+ y*(168.072408311545));
+
+ g_sa_part = 8645.36753595126 +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y*(2175.341332000392 + y*(-274.2290036817964 +
+ y*(197.4670779425016 + y*(-68.5590309679152 +
+ 9.98788038278032*y))) - 90.6734234051316*z) +
+ x*(-5458.34205214835 - 980.14153344888*y +
+ x*(2247.60742726704 - 340.1237483177863*x +
+ 220.542973797483*y) + 180.142097805543*z) +
+ z*(-219.1676534131548 + (-16.32775915649044 -
+ 120.7020447884644*z)*z)) +
+ z*(598.378809221703 + z*(-156.8822727844005 +
+ (204.1334828179377 - 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 + z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(2.626801985426835 + 703.695562834065*z))))) +
+ y*(1187.3715515697959);
+
+ return (kg2g*(g03_g + g08_g - 0.5*x2*g_sa_part));
+}
+/*
+!==========================================================================
+elemental function gsw_cp_ice (t, p)
+!==========================================================================
+!
+! Calculates the isobaric heat capacity of seawater.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! gsw_cp_ice = heat capacity of ice [J kg^-1 K^-1]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_cp_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (-(t + gsw_t0)*gsw_gibbs_ice(2,0,t,p));
+}
+/*
+!==========================================================================
+function gsw_cp_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates isobaric heat capacity of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_cp_t_exact : heat capacity [J/(kg K)]
+*/
+double
+gsw_cp_t_exact(double sa, double t, double p)
+{
+ int n0, n2;
+
+ n0 = 0;
+ n2 = 2;
+
+ return (-(t+273.15e0)*gsw_gibbs(n0,n2,n0,sa,t,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_first_derivatives (sa, pt, ct_sa, ct_pt)
+!==========================================================================
+!
+! Calculates the following two derivatives of Conservative Temperature
+! (1) CT_SA, the derivative with respect to Absolute Salinity at
+! constant potential temperature (with pr = 0 dbar), and
+! 2) CT_pt, the derivative with respect to potential temperature
+! (the regular potential temperature which is referenced to 0 dbar)
+! at constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! pt = potential temperature (ITS-90) [ deg C ]
+! (whose reference pressure is 0 dbar)
+!
+! CT_SA = The derivative of Conservative Temperature with respect to
+! Absolute Salinity at constant potential temperature
+! (the regular potential temperature which has reference
+! sea pressure of 0 dbar).
+! The CT_SA output has units of: [ K/(g/kg)]
+! CT_pt = The derivative of Conservative Temperature with respect to
+! potential temperature (the regular one with pr = 0 dbar)
+! at constant SA. CT_pt is dimensionless. [ unitless ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_first_derivatives(double sa, double pt, double *ct_sa, double *ct_pt)
+{
+ GSW_TEOS10_CONSTANTS;
+ double abs_pt, g_sa_mod, g_sa_t_mod, x, y_pt;
+
+ abs_pt = gsw_t0 + pt ;
+
+ if (ct_pt != NULL)
+ *ct_pt = -(abs_pt*gsw_gibbs_pt0_pt0(sa,pt))/gsw_cp0;
+
+ if (ct_sa == NULL)
+ return;
+
+ x = sqrt(gsw_sfac*sa);
+ y_pt = 0.025*pt;
+
+ g_sa_t_mod = 1187.3715515697959 + x*(-1480.222530425046
+ + x*(2175.341332000392 + x*(-980.14153344888
+ + 220.542973797483*x) + y_pt*(-548.4580073635929
+ + y_pt*(592.4012338275047 + y_pt*(-274.2361238716608
+ + 49.9394019139016*y_pt)))) + y_pt*(-258.3988055868252
+ + y_pt*(-90.2046337756875 + y_pt*10.50720794170734)))
+ + y_pt*(3520.125411988816 + y_pt*(-1351.605895580406
+ + y_pt*(731.4083582010072 + y_pt*(-216.60324087531103
+ + 25.56203650166196*y_pt))));
+ g_sa_t_mod = 0.5*gsw_sfac*0.025*g_sa_t_mod;
+
+ g_sa_mod = 8645.36753595126 + x*(-7296.43987145382
+ + x*(8103.20462414788 + y_pt*(2175.341332000392
+ + y_pt*(-274.2290036817964 + y_pt*(197.4670779425016
+ + y_pt*(-68.5590309679152 + 9.98788038278032*y_pt))))
+ + x*(-5458.34205214835 - 980.14153344888*y_pt
+ + x*(2247.60742726704 - 340.1237483177863*x
+ + 220.542973797483*y_pt))) + y_pt*(-1480.222530425046
+ + y_pt*(-129.1994027934126 + y_pt*(-30.0682112585625
+ + y_pt*(2.626801985426835 ))))) + y_pt*(1187.3715515697959
+ + y_pt*(1760.062705994408 + y_pt*(-450.535298526802
+ + y_pt*(182.8520895502518 + y_pt*(-43.3206481750622
+ + 4.26033941694366*y_pt)))));
+ g_sa_mod = 0.5*gsw_sfac*g_sa_mod;
+
+ *ct_sa = (g_sa_mod - abs_pt*g_sa_t_mod)/gsw_cp0;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_first_derivatives_wrt_t_exact (sa, t, p, &
+ ct_sa_wrt_t, ct_t_wrt_t, ct_p_wrt_t)
+!==========================================================================
+!
+! Calculates the following three derivatives of Conservative Temperature.
+! These derivatives are done with respect to in-situ temperature t (in the
+! case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of
+! CT_SA_wrt_t and CT_P_wrt_t).
+! (1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity
+! at constant t and p, and
+! (2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t
+! at constant SA and p.
+! (3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at
+! constant SA and t.
+!
+! This function uses the full Gibbs function. Note that this function
+! avoids the NaN that would exist in CT_SA_wrt_t at SA = 0 if it were
+! evaluated in the straightforward way from the derivatives of the Gibbs
+! function function.
+!
+! SA = Absolute Salinity [ g/kg ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar)
+!
+! CT_SA_wrt_t = The first derivative of Conservative Temperature with
+! respect to Absolute Salinity at constant t and p.
+! [ K/(g/kg)] i.e. [ K kg/g ]
+! CT_T_wrt_t = The first derivative of Conservative Temperature with
+! respect to in-situ temperature, t, at constant SA and p.
+! [ unitless ]
+! CT_P_wrt_t = The first derivative of Conservative Temperature with
+! respect to pressure P (in Pa) at constant SA and t.
+! [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_first_derivatives_wrt_t_exact(double sa, double t, double p,
+ double *ct_sa_wrt_t, double *ct_t_wrt_t, double *ct_p_wrt_t)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g_sa_mod, g_sa_t_mod, pt0, x, y, y_pt, z;
+
+ pt0 = gsw_pt0_from_t(sa,t,p);
+
+ if (ct_sa_wrt_t != NULL) {
+
+ x = sqrt(gsw_sfac*sa);
+ y = 0.025*t;
+ y_pt = 0.025*pt0;
+ z = rec_db2pa*p;
+ /* the input pressure (p) is sea pressure in units of dbar */
+
+ g_sa_t_mod = 1187.3715515697959 + z*(1458.233059470092 +
+ z*(-687.913805923122 + z*(249.375342232496 +
+ z*(-63.313928772146 + 14.09317606630898*z)))) +
+ x*(-1480.222530425046 + x*(2175.341332000392 +
+ x*(-980.14153344888 + 220.542973797483*x) +
+ y*(-548.4580073635929 + y*(592.4012338275047 +
+ y*(-274.2361238716608 + 49.9394019139016*y))) -
+ 90.6734234051316*z) + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-258.3988055868252 + z*(2298.348396014856 +
+ z*(-325.1503575102672 + 153.8390924339484*z)) +
+ y*(-90.2046337756875 - 4142.8793862113125*z +
+ y*(10.50720794170734 + 2814.78225133626*z)))) +
+ y*(3520.125411988816 + y*(-1351.605895580406 +
+ y*(731.4083582010072 + y*(-216.60324087531103 +
+ 25.56203650166196*y) + z*(-2381.829935897496 +
+ (597.809129110048 - 291.8983352012704*z)*z)) +
+ z*(4165.4688847996085 + z*(-1229.337851789418 +
+ (681.370187043564 - 66.7696405958478*z)*z))) +
+ z*(-3443.057215135908 + z*(1349.638121077468 +
+ z*(-713.258224830552 +
+ (176.8161433232 - 31.68006188846728*z)*z))));
+ g_sa_t_mod = 0.5*gsw_sfac*0.025*g_sa_t_mod;
+
+ g_sa_mod = 8645.36753595126 +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y_pt*(2175.341332000392 + y_pt*(-274.2290036817964 +
+ y_pt*(197.4670779425016 + y_pt*(-68.5590309679152 +
+ 9.98788038278032*y_pt)))) +
+ x*(-5458.34205214835 - 980.14153344888*y_pt +
+ x*(2247.60742726704 - 340.1237483177863*x +
+ 220.542973797483*y_pt))) +
+ y_pt*(-1480.222530425046 +
+ y_pt*(-129.1994027934126 +
+ y_pt*(-30.0682112585625 + y_pt*(2.626801985426835 ))))) +
+ y_pt*(1187.3715515697959 +
+ y_pt*(1760.062705994408 + y_pt*(-450.535298526802 +
+ y_pt*(182.8520895502518 + y_pt*(-43.3206481750622 +
+ 4.26033941694366*y_pt)))));
+ g_sa_mod = 0.5*gsw_sfac*g_sa_mod;
+
+ *ct_sa_wrt_t = (g_sa_mod - (gsw_t0+pt0)*g_sa_t_mod)/gsw_cp0;
+
+ }
+
+ if (ct_t_wrt_t != NULL)
+ *ct_t_wrt_t = -(gsw_t0+pt0)*gsw_gibbs(0,2,0,sa,t,p)/gsw_cp0;
+
+ if (ct_p_wrt_t != NULL)
+ *ct_p_wrt_t = -(gsw_t0+pt0)*gsw_gibbs(0,1,1,sa,t,p)/gsw_cp0;
+}
+/*
+!==========================================================================
+elemental function gsw_ct_freezing (sa, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Conservative Temperature at which seawater freezes. The
+! Conservative Temperature freezing point is calculated from the exact
+! in-situ freezing temperature which is found by a modified Newton-Raphson
+! iteration (McDougall and Wotherspoon, 2013) of the equality of the
+! chemical potentials of water in seawater and in ice.
+!
+! An alternative GSW function, gsw_CT_freezing_poly, it is based on a
+! computationally-efficient polynomial, and is accurate to within -5e-4 K
+! and 6e-4 K, when compared with this function.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! CT_freezing = Conservative Temperature at freezing of seawater [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_freezing(double sa, double p, double saturation_fraction)
+{
+ double t_freezing;
+
+ t_freezing = gsw_t_freezing(sa,p,saturation_fraction);
+ return (gsw_ct_from_t(sa,t_freezing,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_freezing_first_derivatives (sa, p, &
+ saturation_fraction, ctfreezing_sa, ctfreezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the Conservative Temperature at
+! which seawater freezes, with respect to Absolute Salinity SA and
+! pressure P (in Pa).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! CTfreezing_SA = the derivative of the Conservative Temperature at
+! freezing (ITS-90) with respect to Absolute Salinity at
+! fixed pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! CTfreezing_P = the derivative of the Conservative Temperature at
+! freezing (ITS-90) with respect to pressure (in Pa) at
+! fixed Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa, double *ctfreezing_p)
+{
+ double tf_sa, tf_p, ct_sa_wrt_t, ct_t_wrt_t, ct_p_wrt_t, tf;
+
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+
+ if (ctfreezing_sa != NULL && ctfreezing_p != NULL) {
+
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tf_sa,&tf_p);
+ gsw_ct_first_derivatives_wrt_t_exact(sa,tf,p,
+ &ct_sa_wrt_t,&ct_t_wrt_t,&ct_p_wrt_t);
+
+ *ctfreezing_sa = ct_sa_wrt_t + ct_t_wrt_t*tf_sa;
+ *ctfreezing_p = ct_p_wrt_t + ct_t_wrt_t*tf_p;
+
+ } else if (ctfreezing_sa != NULL && ctfreezing_p == NULL) {
+
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tf_sa, NULL);
+ gsw_ct_first_derivatives_wrt_t_exact(sa,tf,p,
+ &ct_sa_wrt_t,&ct_t_wrt_t,NULL);
+
+ *ctfreezing_sa = ct_sa_wrt_t + ct_t_wrt_t*tf_sa;
+
+ } else if (ctfreezing_sa == NULL && ctfreezing_p != NULL) {
+
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ NULL, &tf_p);
+ gsw_ct_first_derivatives_wrt_t_exact(sa,tf,p,
+ NULL,&ct_t_wrt_t,&ct_p_wrt_t);
+
+ *ctfreezing_p = ct_p_wrt_t + ct_t_wrt_t*tf_p;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_freezing_first_derivatives_poly (sa, p, &
+ saturation_fraction, ctfreezing_sa, ctfreezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the Conservative Temperature at
+! which seawater freezes, with respect to Absolute Salinity SA and
+! pressure P (in Pa) of the comptationally efficient polynomial fit of the
+! freezing temperature (McDougall et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! CTfreezing_SA = the derivative of the Conservative Temperature at
+! freezing (ITS-90) with respect to Absolute Salinity at
+! fixed pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! CTfreezing_P = the derivative of the Conservative Temperature at
+! freezing (ITS-90) with respect to pressure (in Pa) at
+! fixed Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa,
+ double *ctfreezing_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_FREEZING_POLY_COEFFICIENTS;
+ double p_r, sa_r, x, d = -a - a*b - 2.4*b/gsw_sso,
+ e = 2.0*a*b/gsw_sso;
+
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ if (ctfreezing_sa != NULL) *ctfreezing_sa =
+ (c1 + x*(1.5*c2 + x*(2.0*c3 + x*(2.5*c4 + x*(3.0*c5
+ + 3.5*c6*x)))) + p_r*(c10 + x*(1.5*c11 + x*(2.0*c13
+ + x*(2.5*c16 + x*(3.0*c19 + 3.5*c22*x))))
+ + p_r*(c12 + x*(1.5*c14 + x*(2.0*c17 + 2.5*c20*x))
+ + p_r*(c15 + x*(1.5*c18 + 2.0*c21*x)))))*1e-2
+ - saturation_fraction*1e-3*(d - sa*e);
+
+ if (ctfreezing_p != NULL) *ctfreezing_p =
+ (c7 + sa_r*(c10 + x*(c11 + x*(c13 + x*(c16 + x*(c19 + c22*x)))))
+ + p_r*(2.0*c8 + sa_r*(2.0*c12 + x*(2.0*c14 + x*(2.0*c17
+ + 2.0*c20*x))) + p_r*(3.0*c9 + sa_r*(3.0*c15 + x*(3.0*c18
+ + 3.0*c21*x)))))*1e-8;
+}
+/*
+!==========================================================================
+elemental function gsw_ct_freezing_poly (sa, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Conservative Temperature at which seawater freezes.
+! The error of this fit ranges between -5e-4 K and 6e-4 K when compared
+! with the Conservative Temperature calculated from the exact in-situ
+! freezing temperature which is found by a Newton-Raphson iteration of the
+! equality of the chemical potentials of water in seawater and in ice.
+! Note that the Conservative temperature freezing temperature can be found
+! by this exact method using the function gsw_CT_freezing.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! CT_freezing = Conservative Temperature at freezing of seawater [ deg C ]
+! That is, the freezing temperature expressed in
+! terms of Conservative Temperature (ITS-90).
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_freezing_poly(double sa, double p, double saturation_fraction)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_FREEZING_POLY_COEFFICIENTS;
+ double p_r, sa_r, x, return_value;
+
+ sa_r = sa*1.0e-2;
+ x = sqrt(sa_r);
+ p_r = p*1.0e-4;
+
+ return_value = c0
+ + sa_r*(c1 + x*(c2 + x*(c3 + x*(c4 + x*(c5 + c6*x)))))
+ + p_r*(c7 + p_r*(c8 + c9*p_r)) + sa_r*p_r*(c10 + p_r*(c12
+ + p_r*(c15 + c21*sa_r)) + sa_r*(c13 + c17*p_r + c19*sa_r)
+ + x*(c11 + p_r*(c14 + c18*p_r) + sa_r*(c16 + c20*p_r + c22*sa_r)));
+
+ /* Adjust for the effects of dissolved air */
+ return_value = return_value - saturation_fraction*
+ (1e-3)*(2.4 - a*sa)*(1.0 + b*(1.0 - sa/gsw_sso));
+
+ return (return_value);
+}
+/*
+!==========================================================================
+elemental function gsw_ct_from_enthalpy (sa, h, p)
+!==========================================================================
+!
+! Calculates the Conservative Temperature of seawater, given the Absolute
+! Salinity, specific enthalpy, h, and pressure p.
+!
+! SA = Absolute Salinity [ g/kg ]
+! h = specific enthalpy [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+!
+! CT = Conservative Temperature ( ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_from_enthalpy(double sa, double h, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double ct, ct_freezing, ct_mean, ct_old, f, h_freezing, h_ct, h_40,
+ ct_40 = 40.0;
+
+ ct_freezing = gsw_ct_freezing(sa,p,0.0);
+
+ h_freezing = gsw_enthalpy(sa,ct_freezing,p);
+ if (h < (h_freezing - gsw_cp0)) {
+ /*
+ ! The input, seawater enthalpy h, is less than the enthalpy at the
+ ! freezing temperature, i.e. the water is frozen.
+ */
+ return (GSW_INVALID_VALUE);
+ }
+
+ h_40 = gsw_enthalpy(sa,ct_40,p);
+ if (h > h_40) {
+ /*
+ ! The input seawater enthalpy is greater than the enthalpy
+ ! when CT is 40C
+ */
+ return (GSW_INVALID_VALUE);
+ }
+
+ /* first guess of ct */
+ ct = ct_freezing + (ct_40 - ct_freezing)*(h - h_freezing)/
+ (h_40 - h_freezing);
+ gsw_enthalpy_first_derivatives(sa,ct,p,NULL,&h_ct);
+
+ /*
+ !------------------------------------------------------
+ ! Begin the modified Newton-Raphson iterative procedure
+ !------------------------------------------------------
+ */
+
+ ct_old = ct;
+ f = gsw_enthalpy(sa,ct_old,p) - h;
+ ct = ct_old - f/h_ct;
+ ct_mean = 0.5*(ct + ct_old);
+ gsw_enthalpy_first_derivatives(sa,ct_mean,p,NULL,&h_ct);
+ ct = ct_old - f/h_ct;
+
+ ct_old = ct;
+ f = gsw_enthalpy(sa,ct_old,p) - h;
+ ct = ct_old - f/h_ct;
+ /*
+ ! After 1.5d0 iterations of this modified Newton-Raphson iteration,
+ ! the error in CT is no larger than 4x10^-13 degrees C, which
+ ! is machine precision for this calculation.
+ */
+ return (ct);
+}
+/*
+!==========================================================================
+elemental function gsw_ct_from_enthalpy_exact (sa, h, p)
+!==========================================================================
+!
+! Calculates the Conservative Temperature of seawater, given the Absolute
+! Salinity, specific enthalpy, h, and pressure p.
+!
+! SA = Absolute Salinity [ g/kg ]
+! h = specific enthalpy [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+!
+! CT = Conservative Temperature ( ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_from_enthalpy_exact(double sa, double h, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double ct, ct_freezing, ct_mean, ct_old, f, h_freezing, h_ct, h_40,
+ ct_40 = 40.0;
+
+ ct_freezing = gsw_ct_freezing(sa,p,0.0);
+
+ h_freezing = gsw_enthalpy_ct_exact(sa,ct_freezing,p);
+ if (h < (h_freezing - gsw_cp0)) {
+ /*
+ ! The input, seawater enthalpy h, is less than the enthalpy at the
+ ! freezing temperature, i.e. the water is frozen.
+ */
+ return (GSW_INVALID_VALUE);
+ }
+
+ h_40 = gsw_enthalpy_ct_exact(sa,ct_40,p);
+ if (h > h_40) {
+ /*
+ ! The input seawater enthalpy is greater than the enthalpy
+ ! when CT is 40C
+ */
+ return (GSW_INVALID_VALUE);
+ }
+
+ /* First guess of ct */
+ ct = ct_freezing + (ct_40 - ct_freezing)*(h - h_freezing)/
+ (h_40 - h_freezing);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ct,p,NULL,&h_ct);
+ /*
+ !------------------------------------------------------
+ ! Begin the modified Newton-Raphson iterative procedure
+ !------------------------------------------------------
+ */
+ ct_old = ct;
+ f = gsw_enthalpy_ct_exact(sa,ct_old,p) - h;
+ ct = ct_old - f/h_ct;
+ ct_mean = 0.5*(ct + ct_old);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ct_mean,p,NULL,&h_ct);
+ ct = ct_old - f/h_ct;
+ /*
+ ! After 1 iteration of this modified Newton-Raphson iteration,
+ ! the error in CT is no larger than 5x10^-14 degrees C, which
+ ! is machine precision for this calculation.
+ */
+ return (ct);
+}
+/*
+!=========================================================================
+elemental function gsw_ct_from_entropy (sa, entropy)
+!=========================================================================
+!
+! Calculates Conservative Temperature with entropy as an input variable.
+!
+! SA = Absolute Salinity [ g/kg ]
+! entropy = specific entropy [ deg C ]
+!
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_from_entropy(double sa, double entropy)
+{
+ double pt;
+
+ pt = gsw_pt_from_entropy(sa,entropy);
+ return (gsw_ct_from_pt(sa,pt));
+}
+/*
+!==========================================================================
+function gsw_ct_from_pt(sa,pt)
+!==========================================================================
+
+! Calculates Conservative Temperature from potential temperature of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! pt : potential temperature with [deg C]
+! reference pressure of 0 dbar
+!
+! gsw_ct_from_pt : Conservative Temperature [deg C]
+*/
+double
+gsw_ct_from_pt(double sa, double pt)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, pot_enthalpy;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = pt*0.025e0; /*! normalize for F03 and F08 */
+ pot_enthalpy = 61.01362420681071e0 + y*(168776.46138048015e0 +
+ y*(-2735.2785605119625e0 + y*(2574.2164453821433e0 +
+ y*(-1536.6644434977543e0 + y*(545.7340497931629e0 +
+ (-50.91091728474331e0 - 18.30489878927802e0*y)*y))))) +
+ x2*(268.5520265845071e0 + y*(-12019.028203559312e0 +
+ y*(3734.858026725145e0 + y*(-2046.7671145057618e0 +
+ y*(465.28655623826234e0 + (-0.6370820302376359e0 -
+ 10.650848542359153e0*y)*y)))) +
+ x*(937.2099110620707e0 + y*(588.1802812170108e0+
+ y*(248.39476522971285e0 + (-3.871557904936333e0-
+ 2.6268019854268356e0*y)*y)) +
+ x*(-1687.914374187449e0 + x*(246.9598888781377e0 +
+ x*(123.59576582457964e0 - 48.5891069025409e0*x)) +
+ y*(936.3206544460336e0 +
+ y*(-942.7827304544439e0 + y*(369.4389437509002e0 +
+ (-33.83664947895248e0 - 9.987880382780322e0*y)*y))))));
+
+ return (pot_enthalpy/gsw_cp0);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_from_rho (rho, sa, p, ct, ct_multiple)
+! =========================================================================
+!
+! Calculates the Conservative Temperature of a seawater sample, for given
+! values of its density, Absolute Salinity and sea pressure (in dbar).
+!
+! rho = density of a seawater sample (e.g. 1026 kg/m^3) [ kg/m^3 ]
+! Note. This input has not had 1000 kg/m^3 subtracted from it.
+! That is, it is 'density', not 'density anomaly'.
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! CT_multiple = Conservative Temperature (ITS-90) [ deg C ]
+! Note that at low salinities, in brackish water, there are two possible
+! Conservative Temperatures for a single density. This programme will
+! output both valid solutions. To see this second solution the user
+! must call the programme with two outputs (i.e. [CT,CT_multiple]), if
+! there is only one possible solution and the programme has been
+! called with two outputs the second variable will be set to NaN.
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_from_rho(double rho, double sa, double p, double *ct,
+ double *ct_multiple)
+{
+ int number_of_iterations;
+ double a, alpha_freezing, alpha_mean, b, c, ct_a, ct_b, ct_diff,
+ ct_freezing, ct_max_rho, ct_mean, ct_old,
+ delta_ct, delta_v, factor, factorqa, factorqb,
+ rho_40, rho_extreme, rho_freezing, rho_max, rho_mean,
+ rho_old, sqrt_disc, top, v_ct, v_lab;
+
+ /*alpha_limit is the positive value of the thermal expansion coefficient
+ ! which is used at the freezing temperature to distinguish between
+ ! salty and fresh water.*/
+ double alpha_limit = 1e-5;
+
+ /*rec_half_rho_TT is a constant representing the reciprocal of half the
+ ! second derivative of density with respect to temperature near the
+ ! temperature of maximum density.*/
+ double rec_half_rho_tt = -110.0;
+
+ rho_40 = gsw_rho(sa,40.0,p);
+ if (rho < rho_40) {
+ *ct = GSW_INVALID_VALUE;
+ if (ct_multiple != NULL) *ct_multiple = *ct;
+ return;
+ }
+
+ ct_max_rho = gsw_ct_maxdensity(sa,p);
+ rho_max = gsw_rho(sa,ct_max_rho,p);
+ rho_extreme = rho_max;
+
+ /*Assumes that the seawater is always unsaturated with air*/
+ ct_freezing = gsw_ct_freezing_poly(sa,p,0.0);
+
+ gsw_rho_alpha_beta(sa,ct_freezing,p,&rho_freezing,&alpha_freezing,NULL);
+
+ /*reset the extreme values*/
+ if (ct_freezing > ct_max_rho) rho_extreme = rho_freezing;
+
+ if (rho > rho_extreme) {
+ *ct = GSW_INVALID_VALUE;
+ if (ct_multiple != NULL) *ct_multiple = *ct;
+ return;
+ }
+
+ if (alpha_freezing > alpha_limit) {
+
+ ct_diff = 40.0 - ct_freezing;
+ top = rho_40 - rho_freezing + rho_freezing*alpha_freezing*ct_diff;
+ a = top/(ct_diff*ct_diff);
+ b = -rho_freezing*alpha_freezing;
+ c = rho_freezing - rho;
+ sqrt_disc = sqrt(b*b - 4*a*c);
+ *ct = ct_freezing + 0.5*(-b - sqrt_disc)/a;
+
+ } else {
+
+ ct_diff = 40.0 - ct_max_rho;
+ factor = (rho_max - rho)/(rho_max - rho_40);
+ delta_ct = ct_diff*sqrt(factor);
+
+ if (delta_ct > 5.0)
+ *ct = ct_max_rho + delta_ct;
+ else {
+ /*Set the initial value of the quadratic solution roots.*/
+ ct_a = ct_max_rho + sqrt(rec_half_rho_tt*(rho - rho_max));
+ for (number_of_iterations = 1; number_of_iterations <= 7;
+ number_of_iterations++) {
+ ct_old = ct_a;
+ rho_old = gsw_rho(sa,ct_old,p);
+ factorqa = (rho_max - rho)/(rho_max - rho_old);
+ ct_a = ct_max_rho + (ct_old - ct_max_rho)*sqrt(factorqa);
+ }
+
+ if ((ct_freezing - ct_a) < 0.0) {
+ *ct = GSW_INVALID_VALUE;
+ if (ct_multiple != NULL) *ct_multiple = *ct;
+ return;
+ }
+
+ *ct = ct_a;
+ if (ct_multiple == NULL) return;
+
+ /*Set the initial value of the quadratic solution roots.*/
+ ct_b = ct_max_rho - sqrt(rec_half_rho_tt*(rho - rho_max));
+ for (number_of_iterations = 1; number_of_iterations <= 7;
+ number_of_iterations++) {
+ ct_old = ct_b;
+ rho_old = gsw_rho(sa,ct_old,p);
+ factorqb = (rho_max - rho)/(rho_max - rho_old);
+ ct_b = ct_max_rho + (ct_old - ct_max_rho)*sqrt(factorqb);
+ }
+ /*
+ ! After seven iterations of this quadratic iterative procedure,
+ ! the error in rho is no larger than 4.6x10^-13 kg/m^3.
+ */
+ if ((ct_freezing - ct_b) < 0.0) {
+ *ct = GSW_INVALID_VALUE;
+ *ct_multiple = *ct;
+ return;
+ }
+ *ct_multiple = ct_b;
+ return;
+ }
+ }
+
+ /*Begin the modified Newton-Raphson iterative method*/
+
+ v_lab = 1.0/rho;
+ gsw_rho_alpha_beta(sa,*ct,p,&rho_mean,&alpha_mean,NULL);
+ v_ct = alpha_mean/rho_mean;
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ ct_old = *ct;
+ delta_v = gsw_specvol(sa,ct_old,p) - v_lab;
+ *ct = ct_old - delta_v/v_ct;
+ ct_mean = 0.5*(*ct + ct_old);
+ gsw_rho_alpha_beta(sa,ct_mean,p,&rho_mean,&alpha_mean,NULL);
+ v_ct = alpha_mean/rho_mean;
+ *ct = ct_old - delta_v/v_ct ;
+ }
+ /*
+ ! After three iterations of this modified Newton-Raphson iteration,
+ ! the error in rho is no larger than 1.6x10^-12 kg/m^3.
+ */
+ if (ct_multiple != NULL) *ct_multiple = GSW_INVALID_VALUE;
+ return;
+}
+/*
+!==========================================================================
+function gsw_ct_from_t(sa,t,p)
+!==========================================================================
+
+! Calculates Conservative Temperature from in-situ temperature
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_ct_from_t : Conservative Temperature [deg C]
+*/
+double
+gsw_ct_from_t(double sa, double t, double p)
+{
+ double pt0;
+
+ pt0 = gsw_pt0_from_t(sa,t,p);
+ return (gsw_ct_from_pt(sa,pt0));
+}
+/*
+!==========================================================================
+elemental function gsw_ct_maxdensity (sa, p)
+!==========================================================================
+!
+! Calculates the Conservative Temperature of maximum density of seawater.
+! This function returns the Conservative temperature at which the density
+! of seawater is a maximum, at given Absolute Salinity, SA, and sea
+! pressure, p (in dbar).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! CT_maxdensity = Conservative Temperature at which [ deg C ]
+! the density of seawater is a maximum for
+! given Absolute Salinity and pressure.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_ct_maxdensity(double sa, double p)
+{
+ int number_of_iterations;
+ double alpha, ct, ct_mean, ct_old, dalpha_dct,
+ dct = 0.001;
+
+ ct = 3.978 - 0.22072*sa; /*the initial guess of ct.*/
+
+ dalpha_dct = 1.1e-5; /*the initial guess for dalpha_dct.*/
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ ct_old = ct;
+ alpha = gsw_alpha(sa,ct_old,p);
+ ct = ct_old - alpha/dalpha_dct;
+ ct_mean = 0.5*(ct + ct_old);
+ dalpha_dct = (gsw_alpha(sa,ct_mean+dct,p)
+ - gsw_alpha(sa,ct_mean-dct,p))/(dct + dct);
+ ct = ct_old - alpha/dalpha_dct;
+ }
+ /*
+ ! After three iterations of this modified Newton-Raphson (McDougall and
+ ! Wotherspoon, 2012) iteration, the error in CT_maxdensity is typically
+ ! no larger than 1x10^-15 degress C.
+ */
+ return (ct);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ct_second_derivatives (sa, pt, ct_sa_sa, ct_sa_pt, &
+ ct_pt_pt)
+!==========================================================================
+!
+! Calculates the following three, second-order derivatives of Conservative
+! Temperature
+! (1) CT_SA_SA, the second derivative with respect to Absolute Salinity
+! at constant potential temperature (with p_ref = 0 dbar),
+! (2) CT_SA_pt, the derivative with respect to potential temperature
+! (the regular potential temperature which is referenced to 0 dbar)
+! and Absolute Salinity, and
+! (3) CT_pt_pt, the second derivative with respect to potential
+! temperature (the regular potential temperature which is referenced
+! to 0 dbar) at constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! pt = potential temperature (ITS-90) [ deg C ]
+! (whose reference pressure is 0 dbar)
+!
+! CT_SA_SA = The second derivative of Conservative Temperature with
+! respect to Absolute Salinity at constant potential
+! temperature (the regular potential temperature which
+! has reference sea pressure of 0 dbar).
+! CT_SA_SA has units of: [ K/((g/kg)^2) ]
+! CT_SA_pt = The derivative of Conservative Temperature with
+! respect to potential temperature (the regular one with
+! p_ref = 0 dbar) and Absolute Salinity.
+! CT_SA_pt has units of: [ 1/(g/kg) ]
+! CT_pt_pt = The second derivative of Conservative Temperature with
+! respect to potential temperature (the regular one with
+! p_ref = 0 dbar) at constant SA.
+! CT_pt_pt has units of: [ 1/K ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ct_second_derivatives(double sa, double pt, double *ct_sa_sa,
+ double *ct_sa_pt, double *ct_pt_pt)
+{
+ double ct_pt_l, ct_pt_u, ct_sa_l, ct_sa_u, pt_l, pt_u, sa_l, sa_u,
+ dsa = 1e-3, dpt = 1e-2;
+
+ if ((ct_sa_sa != NULL)) {
+
+ if ((sa_l = sa - dsa) < 0.0)
+ sa_l = 0.0;
+ sa_u = sa + dsa;
+
+ gsw_ct_first_derivatives(sa_l,pt,&ct_sa_l,NULL);
+ gsw_ct_first_derivatives(sa_u,pt,&ct_sa_u,NULL);
+
+ *ct_sa_sa = (ct_sa_u - ct_sa_l)/(sa_u - sa_l);
+
+ }
+
+ if ((ct_sa_pt != NULL) || (ct_pt_pt != NULL)) {
+
+ pt_l = pt - dpt;
+ pt_u = pt + dpt;
+
+ if ((ct_sa_pt != NULL) && (ct_pt_pt != NULL)) {
+
+ gsw_ct_first_derivatives(sa,pt_l,&ct_sa_l,&ct_pt_l);
+ gsw_ct_first_derivatives(sa,pt_u,&ct_sa_u,&ct_pt_u);
+
+ *ct_sa_pt = (ct_sa_u - ct_sa_l)/(pt_u - pt_l);
+ *ct_pt_pt = (ct_pt_u - ct_pt_l)/(pt_u - pt_l);
+
+ } else if ((ct_sa_pt != NULL) && (ct_pt_pt == NULL)) {
+
+ gsw_ct_first_derivatives(sa,pt_l,&ct_sa_l,NULL);
+ gsw_ct_first_derivatives(sa,pt_u,&ct_sa_u,NULL);
+
+ *ct_sa_pt = (ct_sa_u - ct_sa_l)/(pt_u - pt_l);
+
+ } else if ((ct_sa_pt == NULL) && (ct_pt_pt != NULL)) {
+
+ gsw_ct_first_derivatives(sa,pt_l,NULL,&ct_pt_l);
+ gsw_ct_first_derivatives(sa,pt_u,NULL,&ct_pt_u);
+
+ *ct_pt_pt = (ct_pt_u - ct_pt_l)/(pt_u - pt_l);
+
+ }
+ }
+}
+/*
+!==========================================================================
+function gsw_deltasa_from_sp(sp,p,lon,lat)
+!==========================================================================
+
+! Calculates Absolute Salinity Anomaly, deltaSA, from Practical Salinity, SP.
+!
+! sp : Practical Salinity [unitless]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_deltasa_from_sp : Absolute Salinty Anomaly [g/kg]
+*/
+double
+gsw_deltasa_from_sp(double sp, double p, double lon, double lat)
+{
+ double res;
+
+ res = gsw_sa_from_sp(sp,p,lon,lat) - gsw_sr_from_sp(sp);
+ if (res > GSW_ERROR_LIMIT)
+ res = GSW_INVALID_VALUE;
+ return (res);
+}
+/*
+!==========================================================================
+elemental function gsw_dilution_coefficient_t_exact (sa, t, p)
+!==========================================================================
+!
+! Calculates the dilution coefficient of seawater. The dilution
+! coefficient of seawater is defined as the Absolute Salinity times the
+! second derivative of the Gibbs function with respect to Absolute
+! Salinity, that is, SA.*g_SA_SA.
+!
+! SA = Absolute Salinity [ g/kg ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! dilution_coefficient_t_exact = dilution coefficient [ (J/kg)(kg/g) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_dilution_coefficient_t_exact(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g08, x, x2, y, z;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*1e-4;
+ /*note.the input pressure (p) is sea pressure in units of dbar.*/
+
+ g08 = 2.0*(8103.20462414788 +
+ y*(2175.341332000392 +
+ y*(-274.2290036817964 +
+ y*(197.4670779425016 +
+ y*(-68.5590309679152 + 9.98788038278032*y))) -
+ 90.6734234051316*z) +
+ 1.5*x*(-5458.34205214835 - 980.14153344888*y +
+ (4.0/3.0)*x*(2247.60742726704 -
+ 340.1237483177863*1.25*x + 220.542973797483*y) +
+ 180.142097805543*z) +
+ z*(-219.1676534131548 +
+ (-16.32775915649044 - 120.7020447884644*z)*z));
+
+ g08 = x2*g08 +
+ x*(-7296.43987145382 +
+ z*(598.378809221703 +
+ z*(-156.8822727844005 +
+ (204.1334828179377 - 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 +
+ z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 +
+ z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(2.626801985426835 + 703.695562834065*z))))) +
+ 11625.62913253464 + 1702.453469893412*y;
+
+ return (0.25*gsw_sfac*g08);
+/*
+! Note that this function avoids the singularity that occurs at SA = 0 if
+! the straightforward expression for the dilution coefficient of seawater,
+! SA*g_SA_SA is simply evaluated as SA.*gsw_gibbs(2,0,0,SA,t,p).
+*/
+}
+/*
+!==========================================================================
+function gsw_dynamic_enthalpy(sa,ct,p)
+!==========================================================================
+
+! Calculates dynamic enthalpy of seawater using the computationally-
+! efficient expression for specific volume in terms of SA, CT and p
+! (Roquet et al., 2014). Dynamic enthalpy is defined as enthalpy minus
+| potential enthalpy (Young, 2010).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! dynamic_enthalpy : dynamic enthalpy [J/kg]
+*/
+double
+gsw_dynamic_enthalpy(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_enthalpy_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ dynamic_enthalpy_part =
+ z*(h001 + xs*(h101 + xs*(h201 + xs*(h301 + xs*(h401
+ + xs*(h501 + h601*xs))))) + ys*(h011 + xs*(h111 + xs*(h211 + xs*(h311
+ + xs*(h411 + h511*xs)))) + ys*(h021 + xs*(h121 + xs*(h221 + xs*(h321
+ + h421*xs))) + ys*(h031 + xs*(h131 + xs*(h231 + h331*xs)) + ys*(h041
+ + xs*(h141 + h241*xs) + ys*(h051 + h151*xs + h061*ys))))) + z*(h002
+ + xs*(h102 + xs*(h202 + xs*(h302 + xs*(h402 + h502*xs)))) + ys*(h012
+ + xs*(h112 + xs*(h212 + xs*(h312 + h412*xs))) + ys*(h022 + xs*(h122
+ + xs*(h222 + h322*xs)) + ys*(h032 + xs*(h132 + h232*xs) + ys*(h042
+ + h142*xs + h052*ys)))) + z*(h003 + xs*(h103 + xs*(h203 + xs*(h303
+ + h403*xs))) + ys*(h013 + xs*(h113 + xs*(h213 + h313*xs)) + ys*(h023
+ + xs*(h123 + h223*xs) + ys*(h033 + h133*xs + h043*ys))) + z*(h004
+ + xs*(h104 + h204*xs) + ys*(h014 + h114*xs + h024*ys) + z*(h005
+ + h105*xs + h015*ys + z*(h006 + h007*z))))));
+
+ return (dynamic_enthalpy_part*db2pa*1e4);
+}
+/*
+!==========================================================================
+function gsw_enthalpy(sa,ct,p)
+!==========================================================================
+
+! Calculates specific enthalpy of seawater using the computationally-
+! efficient expression for specific volume in terms of SA, CT and p
+! (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! enthalpy : specific enthalpy of seawater [J/kg]
+*/
+double
+gsw_enthalpy(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ return (gsw_cp0*ct + gsw_dynamic_enthalpy(sa,ct,p));
+}
+/*
+!==========================================================================
+elemental function gsw_enthalpy_ct_exact (sa, ct, p)
+!==========================================================================
+!
+! Calculates specific enthalpy of seawater from Absolute Salinity and
+! Conservative Temperature and pressure.
+!
+! Note that this function uses the full Gibbs function.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! enthalpy_CT_exact = specific enthalpy [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_enthalpy_ct_exact(double sa, double ct, double p)
+{
+ double t;
+
+ t = gsw_t_from_ct(sa,ct,p);
+ return (gsw_enthalpy_t_exact(sa,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_enthalpy_diff (sa, ct, p_shallow, p_deep)
+!==========================================================================
+!
+! Calculates the difference of the specific enthalpy of seawater between
+! two different pressures, p_deep (the deeper pressure) and p_shallow
+! (the shallower pressure), at the same values of SA and CT. This
+! function uses the computationally-efficient expression for specific
+! volume in terms of SA, CT and p (Roquet et al., 2014). The output
+! (enthalpy_diff_CT) is the specific enthalpy evaluated at (SA,CT,p_deep)
+! minus the specific enthalpy at (SA,CT,p_shallow).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p_shallow = upper sea pressure [ dbar ]
+! ( i.e. shallower absolute pressure - 10.1325 dbar )
+! p_deep = lower sea pressure [ dbar ]
+! ( i.e. deeper absolute pressure - 10.1325 dbar )
+!
+! enthalpy_diff_CT = difference of specific enthalpy [ J/kg ]
+! (deep minus shallow)
+!--------------------------------------------------------------------------
+*/
+double
+gsw_enthalpy_diff(double sa, double ct, double p_shallow, double p_deep)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_enthalpy_shallow, dynamic_enthalpy_deep,
+ part_1, part_2, part_3, part_4, part_5, xs, ys,
+ z_deep, z_shallow;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z_shallow = p_shallow*1e-4;
+ z_deep = p_deep*1e-4;
+
+ part_1 = h001 + xs*(h101 + xs*(h201 + xs*(h301 + xs*(h401
+ + xs*(h501 + h601*xs))))) + ys*(h011 + xs*(h111 + xs*(h211+ xs*(h311
+ + xs*(h411 + h511*xs)))) + ys*(h021 + xs*(h121 + xs*(h221 + xs*(h321
+ + h421*xs))) + ys*(h031 + xs*(h131 + xs*(h231 + h331*xs)) + ys*(h041
+ + xs*(h141 + h241*xs) + ys*(h051 + h151*xs + h061*ys)))));
+
+ part_2 = h002 + xs*(h102 + xs*(h202 + xs*(h302 + xs*(h402 + h502*xs))))
+ + ys*(h012 + xs*(h112 + xs*(h212 + xs*(h312 + h412*xs))) + ys*(h022
+ + xs*(h122 + xs*(h222 + h322*xs)) + ys*(h032 + xs*(h132 + h232*xs)
+ + ys*(h042 + h142*xs + h052*ys))));
+
+ part_3 = h003 + xs*(h103 + xs*(h203 + xs*(h303 + h403*xs))) + ys*(h013
+ + xs*(h113 + xs*(h213 + h313*xs)) + ys*(h023 + xs*(h123 + h223*xs)
+ + ys*(h033 + h133*xs + h043*ys)));
+
+ part_4 = h004 + xs*(h104 + h204*xs) + ys*(h014 + h114*xs + h024*ys);
+
+ part_5 = h005 + h105*xs + h015*ys;
+
+ dynamic_enthalpy_shallow = z_shallow*(part_1 + z_shallow*(part_2
+ + z_shallow*(part_3 + z_shallow*(part_4 + z_shallow*(part_5
+ + z_shallow*(h006 + h007*z_shallow))))));
+
+ dynamic_enthalpy_deep = z_deep*(part_1 + z_deep*(part_2 + z_deep*(part_3
+ + z_deep*(part_4+z_deep*(part_5 + z_deep*(h006 + h007*z_deep))))));
+
+ return ((dynamic_enthalpy_deep - dynamic_enthalpy_shallow)*db2pa*1e4);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_enthalpy_first_derivatives (sa, ct, p, h_sa, h_ct)
+!==========================================================================
+!
+! Calculates the following two derivatives of specific enthalpy (h) of
+! seawater using the computationally-efficient expression for
+! specific volume in terms of SA, CT and p (Roquet et al., 2014).
+! (1) h_SA, the derivative with respect to Absolute Salinity at
+! constant CT and p, and
+! (2) h_CT, derivative with respect to CT at constant SA and p.
+! Note that h_P is specific volume (1/rho) it can be caclulated by calling
+! gsw_specvol(SA,CT,p).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! h_SA = The first derivative of specific enthalpy with respect to
+! Absolute Salinity at constant CT and p.
+! [ J/(kg (g/kg))] i.e. [ J/g ]
+! h_CT = The first derivative of specific enthalpy with respect to
+! CT at constant SA and p. [ J/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_enthalpy_first_derivatives(double sa, double ct, double p, double *h_sa,
+ double *h_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_h_ct_part, dynamic_h_sa_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ if (h_sa != NULL) {
+
+ dynamic_h_sa_part = z*(h101 + xs*(2.0*h201 + xs*(3.0*h301
+ + xs*(4.0*h401 + xs*(5.0*h501 + 6.0*h601*xs)))) + ys*(h111
+ + xs*(2.0*h211 + xs*(3.0*h311 + xs*(4.0*h411
+ + 5.0*h511*xs))) + ys*(h121 + xs*(2.0*h221 + xs*(3.0*h321
+ + 4.0*h421*xs)) + ys*(h131 + xs*(2.0*h231 + 3.0*h331*xs)
+ + ys*(h141 + 2.0*h241*xs + h151*ys)))) + z*(h102
+ + xs*(2.0*h202 + xs*(3.0*h302 + xs*(4.0*h402
+ + 5.0*h502*xs))) + ys*(h112 + xs*(2.0*h212 + xs*(3.0*h312
+ + 4.0*h412*xs)) + ys*(h122 + xs*(2.0*h222 + 3.0*h322*xs)
+ + ys*(h132 + 2.0*h232*xs + h142*ys ))) + z*(h103 + xs*(2.0*h203
+ + xs*(3.0*h303 + 4.0*h403*xs)) + ys*(h113 + xs*(2.0*h213
+ + 3.0*h313*xs) + ys*(h123 + 2.0*h223*xs + h133*ys))
+ + z*(h104 + 2.0*h204*xs + h114*ys + h105*z))));
+
+ *h_sa = 1e8*0.5*gsw_sfac*dynamic_h_sa_part/xs;
+
+ }
+
+ if (h_ct != NULL) {
+
+ dynamic_h_ct_part = z*(h011 + xs*(h111
+ + xs*(h211 + xs*(h311 + xs*(h411
+ + h511*xs)))) + ys*(2.0*(h021 + xs*(h121 + xs*(h221 + xs*(h321
+ + h421*xs)))) + ys*(3.0*(h031 + xs*(h131 + xs*(h231 + h331*xs)))
+ + ys*(4.0*(h041 + xs*(h141 + h241*xs)) + ys*(5.0*(h051
+ + h151*xs) + 6.0*h061*ys)))) + z*(h012 + xs*(h112 + xs*(h212
+ + xs*(h312 + h412*xs))) + ys*(2.0*(h022 + xs*(h122 + xs*(h222
+ + h322*xs))) + ys*(3.0*(h032 + xs*(h132 + h232*xs))
+ + ys*(4.0*(h042 + h142*xs) + 5.0*h052*ys))) + z*(h013
+ + xs*(h113 + xs*(h213 + h313*xs)) + ys*(2.0*(h023 + xs*(h123
+ + h223*xs)) + ys*(3.0*(h033 + h133*xs) + 4.0*h043*ys))
+ + z*(h014 + h114*xs + 2.0*h024*ys + h015*z ))));
+
+ *h_ct = gsw_cp0 + 1e8*0.025*dynamic_h_ct_part;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_enthalpy_first_derivatives_ct_exact (sa, ct, p, &
+ h_sa, h_ct)
+!==========================================================================
+!
+! Calculates the following two derivatives of specific enthalpy (h)
+! (1) h_SA, the derivative with respect to Absolute Salinity at
+! constant CT and p, and
+! (2) h_CT, derivative with respect to CT at constant SA and p.
+! Note that h_P is specific volume (1/rho) it can be calulated by calling
+! gsw_specvol_CT_exact(SA,CT,p). This function uses the full Gibbs function.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! h_SA = The first derivative of specific enthalpy with respect to
+! Absolute Salinity at constant CT and p.
+! [ J/(kg (g/kg))] i.e. [ J/g ]
+! h_CT = The first derivative of specific enthalpy with respect to
+! CT at constant SA and p. [ J/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_enthalpy_first_derivatives_ct_exact(double sa, double ct, double p,
+ double *h_sa, double *h_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g_sa_mod_pt, g_sa_mod_t, pt0, t, temp_ratio, x, y, y_pt, z;
+
+ t = gsw_t_from_ct(sa,ct,p);
+ pt0 = gsw_pt_from_ct(sa,ct);
+
+ temp_ratio = (gsw_t0 + t)/(gsw_t0 + pt0);
+
+ if (h_ct != NULL) *h_ct = gsw_cp0*temp_ratio;
+
+ if (h_sa == NULL) return;
+
+ x = sqrt(gsw_sfac*sa);
+ y = 0.025*t;
+ z = rec_db2pa*p;
+ /*note.the input pressure (p) is sea pressure in units of dbar.*/
+
+ g_sa_mod_t = 8645.36753595126 + z*(-6620.98308089678 +
+ z*(769.588305957198 + z*(-193.0648640214916 +
+ (31.6816345533648 - 5.24960313181984*z)*z))) +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y*(2175.341332000392 + y*(-274.2290036817964 +
+ y*(197.4670779425016 + y*(-68.5590309679152 + 9.98788038278032*y)))
+ - 90.6734234051316*z) +
+ x*(-5458.34205214835 - 980.14153344888*y +
+ x*(2247.60742726704 - 340.1237483177863*x + 220.542973797483*y)
+ + 180.142097805543*z) +
+ z*(-219.1676534131548 + (-16.32775915649044
+ - 120.7020447884644*z)*z)) +
+ z*(598.378809221703 + z*(-156.8822727844005 + (204.1334828179377
+ - 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 + z*(-525.876123559641 + (249.57717834054571
+ - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 + z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z + y*(2.626801985426835
+ + 703.695562834065*z))))) +
+ y*(1187.3715515697959 + z*(1458.233059470092 +
+ z*(-687.913805923122 + z*(249.375342232496 + z*(-63.313928772146
+ + 14.09317606630898*z)))) +
+ y*(1760.062705994408 + y*(-450.535298526802 +
+ y*(182.8520895502518 + y*(-43.3206481750622 + 4.26033941694366*y) +
+ z*(-595.457483974374 + (149.452282277512 - 72.9745838003176*z)*z)) +
+ z*(1388.489628266536 + z*(-409.779283929806 + (227.123395681188
+ - 22.2565468652826*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 - 15.84003094423364*z)*z)))));
+
+ g_sa_mod_t = 0.5*gsw_sfac*g_sa_mod_t;
+
+ y_pt = 0.025*pt0;
+
+ g_sa_mod_pt = 8645.36753595126 +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y_pt*(2175.341332000392 + y_pt*(-274.2290036817964 +
+ y_pt*(197.4670779425016 + y_pt*(-68.5590309679152
+ + 9.98788038278032*y_pt)))) +
+ x*(-5458.34205214835 - 980.14153344888*y_pt +
+ x*(2247.60742726704 - 340.1237483177863*x
+ + 220.542973797483*y_pt))) +
+ y_pt*(-1480.222530425046 + y_pt*(-129.1994027934126 +
+ y_pt*(-30.0682112585625 + y_pt*2.626801985426835)))) +
+ y_pt*(1187.3715515697959 + y_pt*(1760.062705994408
+ + y_pt*(-450.535298526802 +
+ y_pt*(182.8520895502518 + y_pt*(-43.3206481750622
+ + 4.26033941694366*y_pt)))));
+
+ g_sa_mod_pt = 0.5*gsw_sfac*g_sa_mod_pt;
+
+ *h_sa = g_sa_mod_t - temp_ratio*g_sa_mod_pt;
+}
+/*
+!==========================================================================
+elemental function gsw_enthalpy_ice (t, p)
+!==========================================================================
+!
+! Calculates the specific enthalpy of ice (h_Ih).
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! gsw_enthalpy_ice : specific enthalpy of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_enthalpy_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double tau, dzi, g0;
+ std::complex<double> r2, sqtau_t1, sqtau_t2, g;
+
+ tau = (t + gsw_t0)*rec_tt;
+
+ dzi = db2pa*p*rec_pt;
+
+ g0 = g00 + dzi*(g01 + dzi*(g02 + dzi*(g03 + g04*dzi)));
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ sqtau_t1 = (tau*tau)/(t1*t1);
+ sqtau_t2 = (tau*tau)/(t2*t2);
+
+ g = r1*t1*(log(1.0 - sqtau_t1) + sqtau_t1)
+ + r2*t2*(log(1.0 - sqtau_t2) + sqtau_t2);
+
+ return (g0 + tt*real(g));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_enthalpy_second_derivatives (sa, ct, p, h_sa_sa, &
+ h_sa_ct, h_ct_ct)
+! =========================================================================
+!
+! Calculates the following three second-order derivatives of specific
+! enthalpy (h),using the computationally-efficient expression for
+! specific volume in terms of SA, CT and p (Roquet et al., 2014).
+! (1) h_SA_SA, second-order derivative with respect to Absolute Salinity
+! at constant CT & p.
+! (2) h_SA_CT, second-order derivative with respect to SA & CT at
+! constant p.
+! (3) h_CT_CT, second-order derivative with respect to CT at constant SA
+! and p.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! h_SA_SA = The second derivative of specific enthalpy with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! h_SA_CT = The second derivative of specific enthalpy with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+! h_CT_CT = The second derivative of specific enthalpy with respect to
+! CT at constant SA and p. [ J/(kg K^2) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_enthalpy_second_derivatives(double sa, double ct, double p,
+ double *h_sa_sa, double *h_sa_ct, double *h_ct_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_h_ct_ct_part, dynamic_h_sa_ct_part,
+ dynamic_h_sa_sa_part, xs, xs2, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ if (h_sa_sa != NULL) {
+
+ xs2 = pow(xs,2);
+ dynamic_h_sa_sa_part = z*(-h101 + xs2*(3.0*h301 + xs*(8.0*h401
+ + xs*(15.0*h501 + 24.0*h601*xs))) + ys*(- h111
+ + xs2*(3.0*h311 + xs*(8.0*h411 + 15.0*h511*xs)) + ys*(-h121
+ + xs2*(3.0*h321 + 8.0*h421*xs) + ys*(-h131 + 3.0*h331*xs2
+ + ys*(-h141 - h151*ys)))) + z*(-h102 + xs2*(3.0*h302
+ + xs*(8.0*h402 + 15.0*h502*xs)) + ys*(-h112 + xs2*(3.0*h312
+ + 8.0*h412*xs) + ys*(-h122 + 3.0*h322*xs2 + ys*(-h132
+ - h142*ys ))) + z*(xs2*(8.0*h403*xs + 3.0*h313*ys)
+ + z*(-h103 + 3.0*h303*xs2 + ys*(-h113 + ys*(-h123 - h133*ys))
+ + z*(-h104 - h114*ys - h105*z)))));
+
+ *h_sa_sa = 1e8*0.25*gsw_sfac*gsw_sfac*dynamic_h_sa_sa_part/
+ pow(xs,3);
+
+ }
+
+ if (h_sa_ct != NULL) {
+
+ dynamic_h_sa_ct_part = z*(h111 + xs*(2.0*h211 + xs*(3.0*h311
+ + xs*(4.0*h411 + 5.0*h511*xs))) + ys*(2.0*h121
+ + xs*(4.0*h221 + xs*(6.0*h321 + 8.0*h421*xs))
+ + ys*(3.0*h131 + xs*(6.0*h231 + 9.0*h331*xs)
+ + ys*(4.0*h141 + 8.0*h241*xs + 5.0*h151*ys ))) + z*(h112
+ + xs*(2.0*h212 + xs*(3.0*h312 + 4.0*h412*xs))
+ + ys*(2.0*h122 + xs*(4.0*h222 + 6.0*h322*xs)
+ + ys*(3.0*h132 + 6.0*h232*xs + 4.0*h142*ys)) + z*(h113
+ + xs*(2.0*h213 + 3.0*h313*xs) + ys*(2.0*h123
+ + 4.0*h223*xs + 3.0*h133*ys) + h114*z)));
+
+ *h_sa_ct = 1e8*0.025*0.5*gsw_sfac*dynamic_h_sa_ct_part/xs;
+
+ }
+
+ if (h_ct_ct != NULL) {
+
+ dynamic_h_ct_ct_part = z*(2.0*h021 + xs*(2.0*h121 + xs*(2.0*h221
+ + xs*(2.0*h321 + 2.0*h421*xs))) + ys*(6.0*h031
+ + xs*(6.0*h131 + xs*(6.0*h231 + 6.0*h331*xs))
+ + ys*(12.0*h041 + xs*(12.0*h141 + 12.0*h241*xs)
+ + ys*(20.0*h051 + 20.0*h151*xs + 30.0*h061*ys)))
+ + z*(2.0*h022 + xs*(2.0*h122 + xs*(2.0*h222
+ + 2.0*h322*xs)) + ys*(6.0*h032 + xs*(6.0*h132
+ + 6.0*h232*xs) + ys*(12.0*h042 + 12.0*h142*xs
+ + 20.0*h052*ys)) + z*(2.0*h023 + xs*(2.0*h123
+ + 2.0*h223*xs) + ys*(6.0*h133*xs + 6.0*h033
+ + 12.0*h043*ys) + 2.0*h024*z)));
+
+ *h_ct_ct = 1e8*6.25e-4*dynamic_h_ct_ct_part;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_enthalpy_second_derivatives_ct_exact (sa, ct, p, &
+ h_sa_sa, h_sa_ct, h_ct_ct)
+!==========================================================================
+!
+! Calculates three second-order derivatives of specific enthalpy (h).
+! Note that this function uses the full Gibbs function.
+!
+! sa = Absolute Salinity [ g/kg ]
+! ct = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! h_sa_sa = The second derivative of specific enthalpy with respect to
+! Absolute Salinity at constant ct & p. [ J/(kg (g/kg)^2) ]
+! h_sa_ct = The second derivative of specific enthalpy with respect to
+! sa and ct at constant p. [ J/(kg K(g/kg)) ]
+! h_ct_ct = The second derivative of specific enthalpy with respect to
+! ct at constant sa and p. [ J/(kg K^2) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_enthalpy_second_derivatives_ct_exact(double sa, double ct, double p,
+ double *h_sa_sa, double *h_sa_ct, double *h_ct_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double factor, gsa_pt0, gsat_pt0, gsat, part_b, pt0, h_ct_ct_val,
+ rec_abs_pt0, rec_gtt_pt0, rec_gtt, t, temp_ratio,
+ gsasa, gsasa_pt0, pr0 = 0.0, sa_small = 1e-100;
+ int n0=0, n1=1, n2=2;
+
+ pt0 = gsw_pt_from_ct(sa,ct);
+ rec_abs_pt0 = 1.0/(gsw_t0 + pt0);
+ t = gsw_pt_from_t(sa,pt0,pr0,p);
+ temp_ratio = (gsw_t0 + t)*rec_abs_pt0;
+
+ rec_gtt_pt0 = 1.0/gsw_gibbs(n0,n2,n0,sa,pt0,pr0);
+ rec_gtt = 1.0/gsw_gibbs(n0,n2,n0,sa,t,p);
+
+ /*h_ct_ct is naturally well-behaved as sa approaches zero.*/
+ h_ct_ct_val = gsw_cp0*gsw_cp0*
+ (temp_ratio*rec_gtt_pt0 - rec_gtt)*(rec_abs_pt0*rec_abs_pt0);
+
+ if (h_ct_ct != NULL) *h_ct_ct = h_ct_ct_val;
+
+ if ((h_sa_sa == NULL) && (h_sa_ct == NULL)) return;
+
+ gsat_pt0 = gsw_gibbs(n1,n1,n0,sa,pt0,pr0);
+ gsat = gsw_gibbs(n1,n1,n0,sa,t,p);
+ gsa_pt0 = gsw_gibbs(n1,n0,n0,sa,pt0,pr0);
+
+ part_b = (temp_ratio*gsat_pt0*rec_gtt_pt0 - gsat*rec_gtt)*rec_abs_pt0;
+ factor = gsa_pt0/gsw_cp0;
+
+ if (h_sa_sa != NULL) {
+
+ gsasa = gsw_gibbs(n2,n0,n0,sa,t,p);
+ gsasa_pt0 = gsw_gibbs(n2,n0,n0,sa,pt0,pr0);
+ /*
+ ! h_sa_sa has a singularity at sa = 0, and blows up as sa
+ ! approaches zero.
+ */
+ *h_sa_sa = gsasa - temp_ratio*gsasa_pt0
+ + temp_ratio*gsat_pt0*gsat_pt0*rec_gtt_pt0
+ - gsat*gsat*rec_gtt
+ - 2.0*gsa_pt0*part_b + (factor*factor)*h_ct_ct_val;
+
+ }
+ if (h_sa_ct == NULL) return;
+
+ /*
+ ! h_sa_ct should not blow up as sa approaches zero.
+ ! The following lines of code ensure that the h_sa_ct output
+ ! of this function does not blow up in this limit.
+ ! That is, when sa < 1e-100 g/kg, we force the h_sa_ct
+ ! output to be the same as if sa = 1e-100 g/kg.
+ */
+ if (sa < sa_small) {
+ rec_gtt_pt0 = 1.0/gsw_gibbs(n0,n2,n0,sa_small,pt0,pr0);
+ rec_gtt = 1.0/gsw_gibbs(n0,n2,n0,sa_small,t,p);
+ gsat_pt0 = gsw_gibbs(n1,n1,n0,sa_small,pt0,pr0);
+ gsat = gsw_gibbs(n1,n1,n0,sa_small,t,p);
+ gsa_pt0 = gsw_gibbs(n1,n0,n0,sa_small,pt0,pr0);
+ part_b = (temp_ratio*gsat_pt0*rec_gtt_pt0
+ - gsat*rec_gtt)*rec_abs_pt0;
+ factor = gsa_pt0/gsw_cp0;
+ }
+
+ *h_sa_ct = gsw_cp0*part_b - factor*h_ct_ct_val;
+}
+/*
+!==========================================================================
+function gsw_enthalpy_sso_0(p)
+!==========================================================================
+
+! This function calculates enthalpy at the Standard Ocean Salinity, SSO,
+! and at a Conservative Temperature of zero degrees C, as a function of
+! pressure, p, in dbar, using a streamlined version of the
+! computationally-efficient expression for specific volume, that is, a
+! streamlined version of the code "gsw_enthalpy(SA,CT,p)".
+!
+! p : sea pressure [dbar]
+!
+! enthalpy_sso_0 : enthalpy(sso,0,p)
+*/
+double
+gsw_enthalpy_sso_0(double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double dynamic_enthalpy_sso_0_p, z;
+
+ z = p*1.0e-4;
+
+ dynamic_enthalpy_sso_0_p =
+ z*( 9.726613854843870e-4 + z*(-2.252956605630465e-5
+ + z*( 2.376909655387404e-6 + z*(-1.664294869986011e-7
+ + z*(-5.988108894465758e-9 + z*(h006 + h007*z))))));
+ return (dynamic_enthalpy_sso_0_p*db2pa*1.0e4);
+}
+/*
+!==========================================================================
+function gsw_enthalpy_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates the specific enthalpy of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_enthalpy_t_exact : specific enthalpy [J/kg]
+*/
+double
+gsw_enthalpy_t_exact(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ int n0=0, n1=1;
+
+ return (gsw_gibbs(n0,n0,n0,sa,t,p) -
+ (t+gsw_t0)*gsw_gibbs(n0,n1,n0,sa,t,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_entropy_first_derivatives (sa, ct, eta_sa, eta_ct)
+! =========================================================================
+!
+! Calculates the following two partial derivatives of specific entropy
+! (eta)
+! (1) eta_SA, the derivative with respect to Absolute Salinity at
+! constant Conservative Temperature, and
+! (2) eta_CT, the derivative with respect to Conservative Temperature at
+! constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! eta_SA = The derivative of specific entropy with respect to
+! Absolute Salinity (in units of g kg^-1) at constant
+! Conservative Temperature.
+! eta_SA has units of: [ J/(kg K(g/kg))] or [ J/(g K) ]
+! eta_CT = The derivative of specific entropy with respect to
+! Conservative Temperature at constant Absolute Salinity.
+! eta_CT has units of: [ J/(kg K^2) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_entropy_first_derivatives(double sa, double ct, double *eta_sa,
+ double *eta_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double pt, pr0 = 0.0;
+ int n0=0, n1=1;
+
+ pt = gsw_pt_from_ct(sa,ct);
+
+ if (eta_sa != NULL)
+ *eta_sa = -(gsw_gibbs(n1,n0,n0,sa,pt,pr0))/(gsw_t0 + pt);
+
+ if (eta_ct != NULL)
+ *eta_ct = gsw_cp0/(gsw_t0 + pt);
+}
+/*
+!=========================================================================
+elemental function gsw_entropy_from_ct (sa, ct)
+!=========================================================================
+!
+! Calculates specific entropy of seawater from Conservative Temperature.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! entropy = specific entropy [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_entropy_from_ct(double sa, double ct)
+{
+ double pt0;
+
+ pt0 = gsw_pt_from_ct(sa, ct);
+ return (-gsw_gibbs(0,1,0,sa,pt0,0));
+}
+/*
+!==========================================================================
+elemental function gsw_entropy_from_pt (sa, pt)
+!==========================================================================
+!
+! Calculates specific entropy of seawater.
+!
+! SA = Absolute Salinity [ g/kg ]
+! pt = potential temperature (ITS-90) [ deg C ]
+!
+! entropy = specific entropy [ J/(kg*K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_entropy_from_pt(double sa, double pt)
+{
+ int n0 = 0, n1 = 1;
+ double pr0 = 0.0;
+
+ return (-gsw_gibbs(n0,n1,n0,sa,pt,pr0));
+}
+/*
+!==========================================================================
+function gsw_entropy_from_t(sa,t,p)
+!==========================================================================
+
+! Calculates the specific entropy of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_entropy_from_t : specific entropy [J/(kg K)]
+*/
+double
+gsw_entropy_from_t(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (-gsw_gibbs(n0,n1,n0,sa,t,p));
+
+}
+/*
+!==========================================================================
+elemental function gsw_entropy_ice (t, p)
+!==========================================================================
+!
+! Calculates specific entropy of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! ice_entropy = specific entropy of ice [ J kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_entropy_ice(double t, double p)
+{
+ return (-gsw_gibbs_ice(1,0,t,p));
+}
+/*
+!==========================================================================
+function gsw_entropy_part(sa,t,p)
+!==========================================================================
+
+! entropy minus the terms that are a function of only SA
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! entropy_part : entropy part
+*/
+double
+gsw_entropy_part(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, z, g03, g08;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*1e-4;
+
+ g03 = z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 +
+ (28.9796526294175 - 2.13290083518327*z)*z))) +
+ y*(-24715.571866078 + z*(2910.0729080936 +
+ z*(-1513.116771538718 + z*(546.959324647056 +
+ z*(-111.1208127634436 + 8.68841343834394*z)))) +
+ y*(2210.2236124548363 + z*(-2017.52334943521 +
+ z*(1498.081172457456 + z*(-718.6359919632359 +
+ (146.4037555781616 - 4.9892131862671505*z)*z))) +
+ y*(-592.743745734632 + z*(1591.873781627888 +
+ z*(-1207.261522487504 + (608.785486935364 -
+ 105.4993508931208*z)*z)) +
+ y*(290.12956292128547 + z*(-973.091553087975 +
+ z*(602.603274510125 + z*(-276.361526170076 +
+ 32.40953340386105*z))) +
+ y*(-113.90630790850321 + y*(21.35571525415769 -
+ 67.41756835751434*z) +
+ z*(381.06836198507096 + z*(-133.7383902842754 +
+ 49.023632509086724*z)))))));
+
+ g08 = x2*(z*(729.116529735046 +
+ z*(-343.956902961561 + z*(124.687671116248 +
+ z*(-31.656964386073 + 7.04658803315449*z)))) +
+ x*( x*(y*(-137.1145018408982 + y*(148.10030845687618 +
+ y*(-68.5590309679152 + 12.4848504784754*y))) -
+ 22.6683558512829*z) + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-86.1329351956084 + z*(766.116132004952 +
+ z*(-108.3834525034224 + 51.2796974779828*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(3.50240264723578 + 938.26075044542*z)))) +
+ y*(1760.062705994408 + y*(-675.802947790203 +
+ y*(365.7041791005036 + y*(-108.30162043765552 +
+ 12.78101825083098*y) +
+ z*(-1190.914967948748 + (298.904564555024 -
+ 145.9491676006352*z)*z)) +
+ z*(2082.7344423998043 + z*(-614.668925894709 +
+ (340.685093521782 - 33.3848202979239*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 -
+ 15.84003094423364*z)*z)))));
+
+ return (-(g03 + g08)*0.025);
+}
+
+/*
+!==========================================================================
+function gsw_entropy_part_zerop(sa,pt0)
+!==========================================================================
+
+! entropy part evaluated at the sea surface
+!
+! sa : Absolute Salinity [g/kg]
+! pt0 : insitu temperature [deg C]
+!
+! entropy_part_zerop : entropy part at the sea surface
+*/
+double
+gsw_entropy_part_zerop(double sa, double pt0)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, g03, g08;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = pt0*0.025;
+
+ g03 = y*(-24715.571866078 + y*(2210.2236124548363 +
+ y*(-592.743745734632 + y*(290.12956292128547 +
+ y*(-113.90630790850321 + y*21.35571525415769)))));
+
+ g08 = x2*(x*(x*(y*(-137.1145018408982 + y*(148.10030845687618 +
+ y*(-68.5590309679152 + 12.4848504784754*y)))) +
+ y*(-86.1329351956084 + y*(-30.0682112585625 +
+ y*3.50240264723578))) +
+ y*(1760.062705994408 + y*(-675.802947790203 +
+ y*(365.7041791005036 + y*(-108.30162043765552 +
+ 12.78101825083098*y)))));
+
+ return (-(g03 + g08)*0.025);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_entropy_second_derivatives (sa, ct, eta_sa_sa, &
+ eta_sa_ct, eta_ct_ct)
+! =========================================================================
+!
+! Calculates the following three second-order partial derivatives of
+! specific entropy (eta)
+! (1) eta_SA_SA, the second derivative with respect to Absolute
+! Salinity at constant Conservative Temperature, and
+! (2) eta_SA_CT, the derivative with respect to Absolute Salinity and
+! Conservative Temperature.
+! (3) eta_CT_CT, the second derivative with respect to Conservative
+! Temperature at constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! eta_SA_SA = The second derivative of specific entropy with respect
+! to Absolute Salinity (in units of g kg^-1) at constant
+! Conservative Temperature.
+! eta_SA_SA has units of: [ J/(kg K(g/kg)^2)]
+! eta_SA_CT = The second derivative of specific entropy with respect
+! to Conservative Temperature at constant Absolute
+! Salinity. eta_SA_CT has units of: [ J/(kg (g/kg) K^2) ]
+! eta_CT_CT = The second derivative of specific entropy with respect
+! to Conservative Temperature at constant Absolute
+! Salinity. eta_CT_CT has units of: [ J/(kg K^3) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_entropy_second_derivatives(double sa, double ct,
+ double *eta_sa_sa, double *eta_sa_ct, double *eta_ct_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double abs_pt, ct_pt, ct_sa, pt, ct_ct, pr0 = 0.0;
+ int n0=0, n1=1, n2=2;
+
+ pt = gsw_pt_from_ct(sa,ct);
+ abs_pt = gsw_t0 + pt;
+
+ ct_pt = -(abs_pt*gsw_gibbs(n0,n2,n0,sa,pt,pr0))/gsw_cp0;
+
+ ct_ct = -gsw_cp0/(ct_pt*abs_pt*abs_pt);
+
+ if ((eta_sa_ct != NULL) || (eta_sa_sa != NULL)) {
+
+ ct_sa = (gsw_gibbs(n1,n0,n0,sa,pt,pr0) -
+ (abs_pt*gsw_gibbs(n1,n1,n0,sa,pt,pr0)))/gsw_cp0;
+
+ if (eta_sa_ct != NULL) *eta_sa_ct = -ct_sa*ct_ct;
+
+ if (eta_sa_sa != NULL)
+ *eta_sa_sa = -gsw_gibbs(n2,n0,n0,sa,pt,pr0)/abs_pt +
+ ct_sa*ct_sa*ct_ct;
+ }
+
+ if (eta_ct_ct != NULL) *eta_ct_ct = ct_ct;
+}
+/*
+!==========================================================================
+function gsw_fdelta(p,lon,lat)
+!==========================================================================
+
+! Calculates fdelta.
+!
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_fdelta : Absolute Salinty Anomaly [unitless]
+*/
+double
+gsw_fdelta(double p, double lon, double lat)
+{
+ double sa, saar;
+
+ saar = gsw_saar(p,lon,lat);
+ if (saar >= GSW_ERROR_LIMIT)
+ sa = GSW_INVALID_VALUE;
+ else
+ sa = ((1.0 + 0.35)*saar)/(1.0 - 0.35*saar);
+ return (sa);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_properties (sa_bulk, h_bulk, p, &
+ sa_final, ct_final, w_ih_final)
+!==========================================================================
+!
+! Calculates the mass fraction of ice (mass of ice divided by mass of ice
+! plus seawater), w_Ih_final, which results from given values of the bulk
+! Absolute Salinity, SA_bulk, bulk enthalpy, h_bulk, occuring at pressure
+! p. The final values of Absolute Salinity, SA_final, and Conservative
+! Temperature, CT_final, of the interstitial seawater phase are also
+! returned. This code assumes that there is no dissolved air in the
+! seawater (that is, saturation_fraction is assumed to be zero
+! throughout the code).
+!
+! When the mass fraction w_Ih_final is calculated as being a positive
+! value, the seawater-ice mixture is at thermodynamic equlibrium.
+!
+! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk,
+! is sufficiently large (i.e. sufficiently "warm") so that there is no ice
+! present in the final state. In this case the final state consists of
+! only seawater rather than being an equlibrium mixture of seawater and
+! ice which occurs when w_Ih_final is positive. Note that when
+! w_Ih_final = 0, the final seawater is not at the freezing temperature.
+!
+! SA_bulk = bulk Absolute Salinity of the seawater and ice mixture
+! [ g/kg ]
+! h_bulk = bulk enthalpy of the seawater and ice mixture [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! SA_final = Absolute Salinity of the seawater in the final state,
+! whether or not any ice is present. [ g/kg ]
+! CT_final = Conservative Temperature of the seawater in the the final
+! state, whether or not any ice is present. [ deg C ]
+! w_Ih_final = mass fraction of ice in the final seawater-ice mixture.
+! If this ice mass fraction is positive, the system is at
+! thermodynamic equilibrium. If this ice mass fraction is
+! zero there is no ice in the final state which consists
+! only of seawater which is warmer than the freezing
+! temperature. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_properties(double sa_bulk, double h_bulk, double p,
+ double *sa_final, double *ct_final, double *w_ih_final)
+{
+ int number_of_iterations;
+ double cp_ih, ctf_sa, ctf, dfunc_dw_ih, dfunc_dw_ih_mean_poly,
+ func, func0, hf, h_hat_ct, h_hat_sa,
+ h_ihf, sa, tf_sa, tf, w_ih_mean, w_ih_old, w_ih,
+ /*
+ ! Throughout this code seawater is taken to contain
+ ! no dissolved air.
+ */
+ saturation_fraction = 0.0,
+ num_f = 5.0e-2, num_f2 = 6.9e-7, num_p = 2.21;
+ /*
+ !---------------
+ ! Finding func0
+ !--------------
+ */
+ ctf = gsw_ct_freezing(sa_bulk,p,saturation_fraction);
+ func0 = h_bulk - gsw_enthalpy_ct_exact(sa_bulk,ctf,p);
+ /*
+ !-----------------------------------------------------------------------
+ ! When func0 is zero or positive we can immediately calculate the three
+ ! outputs, as the bulk enthalpy, h_bulk, is too large to allow any ice
+ ! at thermodynamic equilibrium. The result will be (warm) seawater with
+ ! no frazil ice being present. The three outputs can be set and the rest
+ ! of this code does not need to be performed.
+ !-----------------------------------------------------------------------
+ */
+ if (func0 >= 0.0) {
+ *sa_final = sa_bulk;
+ *ct_final = gsw_ct_from_enthalpy_exact(sa_bulk,h_bulk,p);
+ *w_ih_final = 0.0;
+ return;
+ }
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin to find the solution for those data points that have func0 < 0,
+ ! implying that the output will be a positive ice mass fraction
+ ! w_Ih_final.
+ !
+ ! Do a quasi-Newton step with a separate polynomial estimate of the
+ ! derivative of func with respect to the ice mass fraction. This
+ ! section of the code delivers initial values of both w_Ih and SA to
+ ! the rest of the more formal modified Newtons Method approach of
+ ! McDougall and Wotherspoon (2014).
+ !-----------------------------------------------------------------------
+ */
+ dfunc_dw_ih_mean_poly = 3.347814e+05
+ - num_f*func0*(1.0 + num_f2*func0) - num_p*p;
+ w_ih = min(-func0/dfunc_dw_ih_mean_poly, 0.95);
+ sa = sa_bulk/(1.0 - w_ih);
+ if (sa < 0.0 || sa > 120.0) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+ /*
+ !-----------------------------------------------------------------------
+ ! Calculating the estimate of the derivative of func, dfunc_dw_Ih, to be
+ ! fed into the iterative Newton's Method.
+ !-----------------------------------------------------------------------
+ */
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ hf = gsw_enthalpy_ct_exact(sa,ctf,p);
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ h_ihf = gsw_enthalpy_ice(tf,p);
+ cp_ih = gsw_cp_ice(tf,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,
+ &h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,&ctf_sa,
+ NULL);
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,&tf_sa,NULL);
+
+ dfunc_dw_ih = hf - h_ihf
+ - sa*(h_hat_sa + h_hat_ct*ctf_sa + w_ih*cp_ih*tf_sa/
+ (1.0 - w_ih));
+ /*
+ !-----------------------------------------------------------------------
+ ! Enter the main McDougall-Wotherspoon (2014) modified Newton-Raphson
+ | loop
+ !-----------------------------------------------------------------------
+ */
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+
+ if (number_of_iterations > 1) {
+ /* on the first iteration these values are already known */
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ hf = gsw_enthalpy_ct_exact(sa,ctf,p);
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ h_ihf = gsw_enthalpy_ice(tf,p);
+ }
+
+ func = h_bulk - (1.0 - w_ih)*hf - w_ih*h_ihf;
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih;
+ w_ih_mean = 0.5*(w_ih + w_ih_old);
+
+ if (w_ih_mean > 0.9) {
+ /*This ensures that the mass fraction of ice never exceeds 0.9*/
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa = sa_bulk/(1.0 - w_ih_mean);
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ hf = gsw_enthalpy_ct_exact(sa,ctf,p);
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ h_ihf = gsw_enthalpy_ice(tf,p);
+ cp_ih = gsw_cp_ice(tf,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,
+ &h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,&ctf_sa,
+ NULL);
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,&tf_sa,
+ NULL);
+
+ dfunc_dw_ih = hf - h_ihf - sa*(h_hat_sa + h_hat_ct*ctf_sa
+ + w_ih_mean*cp_ih*tf_sa/
+ (1.0 - w_ih_mean));
+
+ w_ih = w_ih_old - func/dfunc_dw_ih;
+
+ if (w_ih > 0.9) {
+ /*This ensures that the mass fraction of ice never exceeds 0.9*/
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa = sa_bulk/(1.0 - w_ih);
+ }
+
+ *sa_final = sa;
+ *ct_final = gsw_ct_freezing(sa,p,saturation_fraction);
+ *w_ih_final = w_ih;
+
+ if (*w_ih_final < 0.0) {
+ /*
+ ! This will only trap cases that are smaller than zero by just
+ ! machine precision
+ */
+ *sa_final = sa_bulk;
+ *ct_final = gsw_ct_from_enthalpy_exact(*sa_final,h_bulk,p);
+ *w_ih_final = 0.0;
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_properties_potential (sa_bulk, h_pot_bulk,&
+ p, sa_final, ct_final, w_ih_final)
+!==========================================================================
+!
+! Calculates the mass fraction of ice (mass of ice divided by mass of ice
+! plus seawater), w_Ih_final, which results from given values of the bulk
+! Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk,
+! occuring at pressure p. The final equilibrium values of Absolute
+! Salinity, SA_final, and Conservative Temperature, CT_final, of the
+! interstitial seawater phase are also returned. This code assumes that
+! there is no dissolved air in the seawater (that is, saturation_fraction
+! is assumed to be zero thoughout the code).
+!
+! When the mass fraction w_Ih_final is calculated as being a positive
+! value, the seawater-ice mixture is at thermodynamic equlibrium.
+!
+! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk,
+! is sufficiently large (i.e. sufficiently "warm") so that there is no ice
+! present in the final state. In this case the final state consists of
+! only seawater rather than being an equlibrium mixture of seawater and
+! ice which occurs when w_Ih_final is positive. Note that when
+! w_Ih_final = 0, the final seawater is not at the freezing temperature.
+!
+! Note that this code uses the exact forms of CT_freezing and
+! pot_enthalpy_ice_freezing.
+!
+! SA_bulk = bulk Absolute Salinity of the seawater and ice mixture
+! [ g/kg ]
+! h_pot_bulk = bulk potential enthalpy of the seawater and ice mixture
+! [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! SA_final = Absolute Salinity of the seawater in the final state,
+! whether or not any ice is present. [ g/kg ]
+! CT_final = Conservative Temperature of the seawater in the the final
+! state, whether or not any ice is present. [ deg C ]
+! w_Ih_final = mass fraction of ice in the final seawater-ice mixture.
+! If this ice mass fraction is positive, the system is at
+! thermodynamic equilibrium. If this ice mass fraction is
+! zero there is no ice in the final state which consists
+! only of seawater which is warmer than the freezing
+! temperature. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_properties_potential(double sa_bulk, double h_pot_bulk, double p,
+ double *sa_final, double *ct_final, double *w_ih_final)
+{
+ GSW_TEOS10_CONSTANTS;
+ int iterations, max_iterations;
+ double ctf_sa, ctf, dfunc_dw_ih, dfunc_dw_ih_mean_poly,
+ dpot_h_ihf_dsa, func, func0, h_pot_ihf, sa, w_ih_old, w_ih,
+ x, xa, y, z;
+
+ double f01 = -9.041191886754806e-1,
+ f02 = 4.169608567309818e-2,
+ f03 = -9.325971761333677e-3,
+ f04 = 4.699055851002199e-2,
+ f05 = -3.086923404061666e-2,
+ f06 = 1.057761186019000e-2,
+ f07 = -7.349302346007727e-2,
+ f08 = 1.444842576424337e-1,
+ f09 = -1.408425967872030e-1,
+ f10 = 1.070981398567760e-1,
+ f11 = -1.768451760854797e-2,
+ f12 = -4.013688314067293e-1,
+ f13 = 7.209753205388577e-1,
+ f14 = -1.807444462285120e-1,
+ f15 = 1.362305015808993e-1,
+ f16 = -9.500974920072897e-1,
+ f17 = 1.192134856624248,
+ f18 = -9.191161283559850e-2,
+ f19 = -1.008594411490973,
+ f20 = 8.020279271484482e-1,
+ f21 = -3.930534388853466e-1,
+ f22 = -2.026853316399942e-2,
+ f23 = -2.722731069001690e-2,
+ f24 = 5.032098120548072e-2,
+ f25 = -2.354888890484222e-2,
+ f26 = -2.454090179215001e-2,
+ f27 = 4.125987229048937e-2,
+ f28 = -3.533404753585094e-2,
+ f29 = 3.766063025852511e-2,
+ f30 = -3.358409746243470e-2,
+ f31 = -2.242158862056258e-2,
+ f32 = 2.102254738058931e-2,
+ f33 = -3.048635435546108e-2,
+ f34 = -1.996293091714222e-2,
+ f35 = 2.577703068234217e-2,
+ f36 = -1.292053030649309e-2,
+
+ g01 = 3.332286683867741e5,
+ g02 = 1.416532517833479e4,
+ g03 = -1.021129089258645e4,
+ g04 = 2.356370992641009e4,
+ g05 = -8.483432350173174e3,
+ g06 = 2.279927781684362e4,
+ g07 = 1.506238790315354e4,
+ g08 = 4.194030718568807e3,
+ g09 = -3.146939594885272e5,
+ g10 = -7.549939721380912e4,
+ g11 = 2.790535212869292e6,
+ g12 = 1.078851928118102e5,
+ g13 = -1.062493860205067e7,
+ g14 = 2.082909703458225e7,
+ g15 = -2.046810820868635e7,
+ g16 = 8.039606992745191e6,
+ g17 = -2.023984705844567e4,
+ g18 = 2.871769638352535e4,
+ g19 = -1.444841553038544e4,
+ g20 = 2.261532522236573e4,
+ g21 = -2.090579366221046e4,
+ g22 = -1.128417003723530e4,
+ g23 = 3.222965226084112e3,
+ g24 = -1.226388046175992e4,
+ g25 = 1.506847628109789e4,
+ g26 = -4.584670946447444e4,
+ g27 = 1.596119496322347e4,
+ g28 = -6.338852410446789e4,
+ g29 = 8.951570926106525e4,
+
+ saturation_fraction = 0.0;
+ /*
+ !-----------------------------------------------------------------------
+ ! Finding func0. This is the value of the function, func, that would
+ ! result in the output w_Ih_final being exactly zero.
+ !-----------------------------------------------------------------------
+ */
+ func0 = h_pot_bulk - gsw_cp0
+ *gsw_ct_freezing(sa_bulk,p,saturation_fraction);
+ /*
+ !-----------------------------------------------------------------------
+ ! Setting the three outputs for data points that have func0 non-negative
+ !-----------------------------------------------------------------------
+ */
+ if (func0 >= 0.0) {
+ /*
+ ! When func0 is zero or positive then the final answer will contain
+ ! no frazil ice; that is, it will be pure seawater that is warmer
+ ! than the freezing temperature. If func0 >= 0 we do not need to go
+ ! through the modified Newton-Raphson procedure and we can simply
+ ! write down the answer, as in the following 4 lines of code.
+ */
+ *sa_final = sa_bulk;
+ *ct_final = h_pot_bulk/gsw_cp0;
+ *w_ih_final = 0.0;
+ return;
+ }
+ /*
+ !-----------------------------------------------------------------------
+ !Begin finding the solution for data points that have func0 < 0, so that
+ !the output will have a positive ice mass fraction w_Ih_final.
+ !-----------------------------------------------------------------------
+ */
+
+ /*Evalaute a polynomial for w_Ih in terms of SA_bulk, func0 and p*/
+ x = sa_bulk*1e-2;
+ y = func0/3e5;
+ z = p*1e-4;
+
+ w_ih = y*(f01 + x*(f02 + x*(f03 + x*(f04 + x*(f05 + f06*x))))
+ + y*(f07 + x*(f08 + x*(f09 + x*(f10 + f11*x))) + y*(f12 + x*(f13
+ + x*(f14 + f15*x)) + y*(f16 + x*(f17 + f18*x) + y*(f19 + f20*x
+ + f21*y)))) + z*(f22 + x*(f23 + x*(f24 + f25*x)) + y*(x*(f26
+ + f27*x)
+ + y*(f28 + f29*x + f30*y)) + z*(f31 + x*(f32 + f33*x) + y*(f34
+ + f35*x + f36*y))));
+
+ if (w_ih > 0.9) {
+ /*
+ ! The ice mass fraction out of this code is restricted to be
+ !less than 0.9.
+ */
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ /*
+ !The initial guess at the absolute salinity of the interstitial seawater
+ */
+ sa = sa_bulk/(1.0 - w_ih);
+ /*
+ !-----------------------------------------------------------------------
+ ! Doing a Newton step with a separate polynomial estimate of the mean
+ ! derivative dfunc_dw_Ih_mean_poly.
+ !-----------------------------------------------------------------------' */
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing(sa,p);
+ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf;
+
+ xa = sa*1e-2;
+
+ dfunc_dw_ih_mean_poly = g01 + xa*(g02 + xa*(g03 + xa*(g04 + g05*xa)))
+ + w_ih*(xa*(g06 + xa*(g07 + g08*xa)) + w_ih*(xa*(g09 + g10*xa)
+ + w_ih*xa*(g11 + g12*xa + w_ih*(g13 + w_ih*(g14 + w_ih*(g15
+ + g16*w_ih)))))) + z*(g17 + xa*(g18 + g19*xa) + w_ih*(g20
+ + w_ih*(g21 + g22*w_ih) + xa*(g23 + g24*xa*w_ih))
+ + z*(g25 + xa*(g26 + g27*xa) + w_ih*(g28 + g29*w_ih)));
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih_mean_poly;
+
+ sa = sa_bulk/(1.0 - w_ih);
+ /*
+ !-----------------------------------------------------------------------
+ ! Calculating the estimate of the derivative of func, dfunc_dw_Ih, to be
+ ! fed into Newton's Method.
+ !-----------------------------------------------------------------------
+ */
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing(sa,p);
+
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,&ctf_sa,
+ NULL);
+ gsw_pot_enthalpy_ice_freezing_first_derivatives(sa,p,&dpot_h_ihf_dsa,
+ NULL);
+
+ dfunc_dw_ih = gsw_cp0*ctf - h_pot_ihf -
+ sa*(gsw_cp0*ctf_sa + w_ih*dpot_h_ihf_dsa/(1.0 - w_ih));
+
+ if (w_ih >= 0.0 && w_ih <= 0.20 && sa > 15.0
+ && sa < 60.0 && p <= 3000.0) {
+ max_iterations = 1;
+ } else if (w_ih >= 0.0 && w_ih <= 0.85 && sa > 0.0
+ && sa < 120.0 && p <= 3500.0) {
+ max_iterations = 2;
+ } else {
+ max_iterations = 3;
+ }
+
+ for (iterations = 1; iterations <= max_iterations; iterations++) {
+
+ if (iterations > 1) {
+ /*On the first iteration ctf and h_pot_ihf are both known*/
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing(sa,p);
+ }
+
+ /*This is the function, func, whose zero we seek ...*/
+ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf;
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih;
+
+ if (w_ih > 0.9) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa = sa_bulk/(1.0 - w_ih);
+
+ }
+
+ if (w_ih < 0.0) {
+ *sa_final = sa_bulk;
+ *ct_final = h_pot_bulk/gsw_cp0;
+ *w_ih_final = 0.0;
+ } else {
+ *sa_final = sa;
+ *ct_final = gsw_ct_freezing(sa,p,saturation_fraction);
+ *w_ih_final = w_ih;
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_properties_potential_poly (sa_bulk, &
+ h_pot_bulk, p, sa_final, ct_final, w_ih_final)
+!==========================================================================
+!
+! Calculates the mass fraction of ice (mass of ice divided by mass of ice
+! plus seawater), w_Ih_final, which results from given values of the bulk
+! Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk,
+! occuring at pressure p. The final equilibrium values of Absolute
+! Salinity, SA_final, and Conservative Temperature, CT_final, of the
+! interstitial seawater phase are also returned. This code assumes that
+! there is no dissolved air in the seawater (that is, saturation_fraction
+! is assumed to be zero thoughout the code).
+!
+! When the mass fraction w_Ih_final is calculated as being a positive
+! value, the seawater-ice mixture is at thermodynamic equlibrium.
+!
+! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk,
+! is sufficiently large (i.e. sufficiently "warm") so that there is no ice
+! present in the final state. In this case the final state consists of
+! only seawater rather than being an equlibrium mixture of seawater and
+! ice which occurs when w_Ih_final is positive. Note that when
+! w_Ih_final = 0, the final seawater is not at the freezing temperature.
+!
+! Note that this code uses the polynomial forms of CT_freezing and
+! pot_enthalpy_ice_freezing. This code is intended to be used in ocean
+! models where the model prognostic variables are SA_bulk and h_pot_bulk.
+!
+! SA_bulk = bulk Absolute Salinity of the seawater and ice mixture
+! [ g/kg ]
+! h_pot_bulk = bulk potential enthalpy of the seawater and ice mixture
+! [ J/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! SA_final = Absolute Salinity of the seawater in the final state,
+! whether or not any ice is present. [ g/kg ]
+! CT_final = Conservative Temperature of the seawater in the the final
+! state, whether or not any ice is present. [ deg C ]
+! w_Ih_final = mass fraction of ice in the final seawater-ice mixture.
+! If this ice mass fraction is positive, the system is at
+! thermodynamic equilibrium. If this ice mass fraction is
+! zero there is no ice in the final state which consists
+! only of seawater which is warmer than the freezing
+! temperature. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_properties_potential_poly(double sa_bulk, double h_pot_bulk,
+ double p, double *sa_final, double *ct_final, double *w_ih_final)
+{
+ GSW_TEOS10_CONSTANTS;
+ int iterations, max_iterations;
+ double ctf_sa, ctf, dfunc_dw_ih, dfunc_dw_ih_mean_poly, dpot_h_ihf_dsa,
+ func, func0, h_pot_ihf, sa, w_ih_old, w_ih, x, xa, y, z;
+
+ double f01 = -9.041191886754806e-1,
+ f02 = 4.169608567309818e-2,
+ f03 = -9.325971761333677e-3,
+ f04 = 4.699055851002199e-2,
+ f05 = -3.086923404061666e-2,
+ f06 = 1.057761186019000e-2,
+ f07 = -7.349302346007727e-2,
+ f08 = 1.444842576424337e-1,
+ f09 = -1.408425967872030e-1,
+ f10 = 1.070981398567760e-1,
+ f11 = -1.768451760854797e-2,
+ f12 = -4.013688314067293e-1,
+ f13 = 7.209753205388577e-1,
+ f14 = -1.807444462285120e-1,
+ f15 = 1.362305015808993e-1,
+ f16 = -9.500974920072897e-1,
+ f17 = 1.192134856624248,
+ f18 = -9.191161283559850e-2,
+ f19 = -1.008594411490973,
+ f20 = 8.020279271484482e-1,
+ f21 = -3.930534388853466e-1,
+ f22 = -2.026853316399942e-2,
+ f23 = -2.722731069001690e-2,
+ f24 = 5.032098120548072e-2,
+ f25 = -2.354888890484222e-2,
+ f26 = -2.454090179215001e-2,
+ f27 = 4.125987229048937e-2,
+ f28 = -3.533404753585094e-2,
+ f29 = 3.766063025852511e-2,
+ f30 = -3.358409746243470e-2,
+ f31 = -2.242158862056258e-2,
+ f32 = 2.102254738058931e-2,
+ f33 = -3.048635435546108e-2,
+ f34 = -1.996293091714222e-2,
+ f35 = 2.577703068234217e-2,
+ f36 = -1.292053030649309e-2,
+
+ g01 = 3.332286683867741e5,
+ g02 = 1.416532517833479e4,
+ g03 = -1.021129089258645e4,
+ g04 = 2.356370992641009e4,
+ g05 = -8.483432350173174e3,
+ g06 = 2.279927781684362e4,
+ g07 = 1.506238790315354e4,
+ g08 = 4.194030718568807e3,
+ g09 = -3.146939594885272e5,
+ g10 = -7.549939721380912e4,
+ g11 = 2.790535212869292e6,
+ g12 = 1.078851928118102e5,
+ g13 = -1.062493860205067e7,
+ g14 = 2.082909703458225e7,
+ g15 = -2.046810820868635e7,
+ g16 = 8.039606992745191e6,
+ g17 = -2.023984705844567e4,
+ g18 = 2.871769638352535e4,
+ g19 = -1.444841553038544e4,
+ g20 = 2.261532522236573e4,
+ g21 = -2.090579366221046e4,
+ g22 = -1.128417003723530e4,
+ g23 = 3.222965226084112e3,
+ g24 = -1.226388046175992e4,
+ g25 = 1.506847628109789e4,
+ g26 = -4.584670946447444e4,
+ g27 = 1.596119496322347e4,
+ g28 = -6.338852410446789e4,
+ g29 = 8.951570926106525e4,
+
+ saturation_fraction = 0.0;
+ /*
+ !-----------------------------------------------------------------------
+ ! Finding func0. This is the value of the function, func, that would
+ ! result in the output w_Ih_final being exactly zero.
+ !-----------------------------------------------------------------------
+ */
+ func0 = h_pot_bulk - gsw_cp0
+ *gsw_ct_freezing_poly(sa_bulk,p,saturation_fraction);
+ /*
+ !-----------------------------------------------------------------------
+ ! Setting the three outputs for data points that have func0 non-negative
+ !-----------------------------------------------------------------------
+ */
+ if (func0 >= 0.0) {
+ /*
+ ! When func0 is zero or positive then the final answer will contain
+ ! no frazil ice; that is, it will be pure seawater that is warmer
+ ! han the freezing temperature. If func0 >= 0 we do not need to go
+ ! through the modified Newton-Raphson procedure and we can simply
+ ! write down the answer, as in the following 4 lines of code.
+ */
+ *sa_final = sa_bulk;
+ *ct_final = h_pot_bulk/gsw_cp0;
+ *w_ih_final = 0.0;
+ return;
+ }
+ /*
+ !-----------------------------------------------------------------------
+ !Begin finding the solution for data points that have func0 < 0, so that
+ !the output will have a positive ice mass fraction w_Ih_final.
+ !-----------------------------------------------------------------------
+ */
+
+ /*Evalaute a polynomial for w_Ih in terms of SA_bulk, func0 and p*/
+ x = sa_bulk*1e-2;
+ y = func0/3e5;
+ z = p*1e-4;
+
+ w_ih = y*(f01 + x*(f02 + x*(f03 + x*(f04 + x*(f05 + f06*x))))
+ + y*(f07 + x*(f08 + x*(f09 + x*(f10 + f11*x))) + y*(f12 + x*(f13
+ + x*(f14 + f15*x)) + y*(f16 + x*(f17 + f18*x) + y*(f19 + f20*x
+ + f21*y)))) + z*(f22 + x*(f23 + x*(f24 + f25*x)) + y*(x*(f26
+ + f27*x)
+ + y*(f28 + f29*x + f30*y)) + z*(f31 + x*(f32 + f33*x) + y*(f34
+ + f35*x + f36*y))));
+
+ if (w_ih > 0.9) {
+ /*
+ ! The ice mass fraction out of this code is restricted to be
+ ! less than 0.9.
+ */
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+ /*
+ ! The initial guess at the absolute salinity of the interstitial
+ ! seawater
+ */
+ sa = sa_bulk/(1.0 - w_ih);
+ /*
+ !-----------------------------------------------------------------------
+ ! Doing a Newton step with a separate polynomial estimate of the mean
+ ! derivative dfunc_dw_Ih_mean_poly.
+ !-----------------------------------------------------------------------
+ */
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing_poly(sa,p);
+ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf;
+
+ xa = sa*1e-2;
+
+ dfunc_dw_ih_mean_poly = g01 + xa*(g02 + xa*(g03 + xa*(g04 + g05*xa)))
+ + w_ih*(xa*(g06 + xa*(g07 + g08*xa)) + w_ih*(xa*(g09 + g10*xa)
+ + w_ih*xa*(g11 + g12*xa + w_ih*(g13 + w_ih*(g14 + w_ih*(g15
+ + g16*w_ih)))))) + z*(g17 + xa*(g18 + g19*xa) + w_ih*(g20
+ + w_ih*(g21 + g22*w_ih) + xa*(g23 + g24*xa*w_ih))
+ + z*(g25 + xa*(g26 + g27*xa) + w_ih*(g28 + g29*w_ih)));
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih_mean_poly;
+
+ sa = sa_bulk/(1.0 - w_ih);
+ /*
+ !-----------------------------------------------------------------------
+ ! Calculating the estimate of the derivative of func, dfunc_dw_Ih, to be
+ ! fed into Newton's Method.
+ !-----------------------------------------------------------------------
+ */
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing_poly(sa,p);
+
+ gsw_ct_freezing_first_derivatives_poly(sa,p,saturation_fraction,&ctf_sa,
+ NULL);
+ gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(sa,p,
+ &dpot_h_ihf_dsa, NULL);
+
+ dfunc_dw_ih = gsw_cp0*ctf - h_pot_ihf -
+ sa*(gsw_cp0*ctf_sa + w_ih*dpot_h_ihf_dsa/(1.0 - w_ih));
+
+ if (w_ih >= 0.0 && w_ih <= 0.20 && sa > 15.0
+ && sa < 60.0 && p <= 3000.0) {
+ max_iterations = 1;
+ } else if (w_ih >= 0.0 && w_ih <= 0.85 && sa > 0.0
+ && sa < 120.0 && p <= 3500.0) {
+ max_iterations = 2;
+ } else {
+ max_iterations = 3;
+ }
+
+ for (iterations = 1; iterations <= max_iterations; iterations++) {
+
+ if (iterations > 1) {
+ /*On the first iteration ctf and h_pot_ihf are both known*/
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ h_pot_ihf = gsw_pot_enthalpy_ice_freezing_poly(sa,p);
+ }
+
+ /*This is the function, func, whose zero we seek ...*/
+ func = h_pot_bulk - (1.0 - w_ih)*gsw_cp0*ctf - w_ih*h_pot_ihf;
+
+ w_ih_old = w_ih;
+ w_ih = w_ih_old - func/dfunc_dw_ih;
+
+ if (w_ih > 0.9) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa = sa_bulk/(1.0 - w_ih);
+
+ }
+
+ if (w_ih < 0.0) {
+ *sa_final = sa_bulk;
+ *ct_final = h_pot_bulk/gsw_cp0;
+ *w_ih_final = 0.0;
+ } else {
+ *sa_final = sa;
+ *ct_final = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ *w_ih_final = w_ih;
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_ratios_adiabatic (sa, p, w_ih, &
+ dsa_dct_frazil, dsa_dp_frazil, dct_dp_frazil)
+!==========================================================================
+!
+! Calculates the ratios of SA, CT and P changes when frazil ice forms or
+! melts in response to an adiabatic change in pressure of a mixture of
+! seawater and frazil ice crystals.
+!
+! Note that the first output, dSA_dCT_frazil, is dSA/dCT rather than
+! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT, is zero
+! whereas dCT/dSA would then be infinite.
+!
+! Also note that both dSA_dP_frazil and dCT_dP_frazil are the pressure
+! derivatives with the pressure measured in Pa not dbar.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure of seawater at which melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! w_Ih = mass fraction of ice, that is the mass of ice divided by the
+! sum of the masses of ice and seawater. That is, the mass of
+! ice divided by the mass of the final mixed fluid.
+! w_Ih must be between 0 and 1. [ unitless ]
+!
+! dSA_dCT_frazil = the ratio of the changes in Absolute Salinity
+! to that of Conservative Temperature [ g/(kg K) ]
+! dSA_dP_frazil = the ratio of the changes in Absolute Salinity
+! to that of pressure (in Pa) [ g/(kg Pa) ]
+! dCT_dP_frazil = the ratio of the changes in Conservative Temperature
+! to that of pressure (in Pa) [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_ratios_adiabatic (double sa, double p, double w_ih,
+ double *dsa_dct_frazil, double *dsa_dp_frazil, double *dct_dp_frazil)
+{
+ double bracket1, bracket2, cp_ih, gamma_ih, h, h_ih, part,
+ rec_bracket3, tf, wcp, h_hat_sa, h_hat_ct, tf_sa, tf_p,
+ ctf, ctf_sa, ctf_p;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ h = gsw_enthalpy_ct_exact(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(tf,p);
+ cp_ih = gsw_cp_ice(tf,p);
+ gamma_ih = gsw_adiabatic_lapse_rate_ice(tf,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,&tf_sa,&tf_p);
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,
+ &ctf_sa,&ctf_p);
+
+ wcp = cp_ih*w_ih/(1.0 - w_ih);
+ part = (tf_p - gamma_ih)/ctf_p;
+
+ bracket1 = h_hat_ct + wcp*part;
+ bracket2 = h - h_ih - sa*(h_hat_sa + wcp*(tf_sa - part*ctf_sa));
+ rec_bracket3 = 1.0/(h - h_ih - sa*(h_hat_sa + h_hat_ct*ctf_sa
+ + wcp*tf_sa));
+
+ *dsa_dct_frazil = sa*(bracket1/bracket2);
+ *dsa_dp_frazil = sa*ctf_p*bracket1*rec_bracket3;
+ *dct_dp_frazil = ctf_p*bracket2*rec_bracket3;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_frazil_ratios_adiabatic_poly (sa, p, w_ih, &
+ dsa_dct_frazil, dsa_dp_frazil, dct_dp_frazil)
+!==========================================================================
+!
+! Calculates the ratios of SA, CT and P changes when frazil ice forms or
+! melts in response to an adiabatic change in pressure of a mixture of
+! seawater and frazil ice crystals.
+!
+! Note that the first output, dSA_dCT_frazil, is dSA/dCT rather than
+! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT, is zero
+! whereas dCT/dSA would then be infinite.
+!
+! Also note that both dSA_dP_frazil and dCT_dP_frazil are the pressure
+! derivatives with the pressure measured in Pa not dbar.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure of seawater at which melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! w_Ih = mass fraction of ice, that is the mass of ice divided by the
+! sum of the masses of ice and seawater. That is, the mass of
+! ice divided by the mass of the final mixed fluid.
+! w_Ih must be between 0 and 1. [ unitless ]
+!
+! dSA_dCT_frazil = the ratio of the changes in Absolute Salinity
+! to that of Conservative Temperature [ g/(kg K) ]
+! dSA_dP_frazil = the ratio of the changes in Absolute Salinity
+! to that of pressure (in Pa) [ g/(kg Pa) ]
+! dCT_dP_frazil = the ratio of the changes in Conservative Temperature
+! to that of pressure (in Pa) [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_frazil_ratios_adiabatic_poly(double sa, double p, double w_ih,
+ double *dsa_dct_frazil, double *dsa_dp_frazil, double *dct_dp_frazil)
+{
+ double bracket1, bracket2, cp_ih, gamma_ih, h, h_ih, part,
+ rec_bracket3, tf, wcp, h_hat_sa, h_hat_ct, tf_sa, tf_p,
+ ctf, ctf_sa, ctf_p;
+ double saturation_fraction = 0.0;
+
+ tf = gsw_t_freezing_poly(sa,p,saturation_fraction);
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ h = gsw_enthalpy(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(tf,p);
+ cp_ih = gsw_cp_ice(tf,p);
+ gamma_ih = gsw_adiabatic_lapse_rate_ice(tf,p);
+ gsw_enthalpy_first_derivatives(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+ gsw_t_freezing_first_derivatives_poly(sa,p,saturation_fraction,
+ &tf_sa,&tf_p);
+ gsw_ct_freezing_first_derivatives_poly(sa,p,saturation_fraction,
+ &ctf_sa,&ctf_p);
+
+ wcp = cp_ih*w_ih/(1.0 - w_ih);
+ part = (tf_p - gamma_ih)/ctf_p;
+
+ bracket1 = h_hat_ct + wcp*part;
+ bracket2 = h - h_ih - sa*(h_hat_sa + wcp*(tf_sa - part*ctf_sa));
+ rec_bracket3 = 1.0/(h - h_ih - sa*(h_hat_sa + h_hat_ct*ctf_sa
+ + wcp*tf_sa));
+
+ *dsa_dct_frazil = sa*(bracket1/bracket2);
+ *dsa_dp_frazil = sa*ctf_p*bracket1*rec_bracket3;
+ *dct_dp_frazil = ctf_p*bracket2*rec_bracket3;
+}
+/*
+!==========================================================================
+pure function gsw_geo_strf_dyn_height (sa, ct, p, p_ref)
+!==========================================================================
+!
+! Calculates dynamic height anomaly as the integral of specific volume
+! anomaly from the pressure p of the bottle to the reference pressure
+! p_ref.
+!
+! Hence, geo_strf_dyn_height is the dynamic height anomaly with respect
+! to a given reference pressure. This is the geostrophic streamfunction
+! for the difference between the horizontal velocity at the pressure
+! concerned, p, and the horizontal velocity at p_ref. Dynamic height
+! anomaly is the geostrophic streamfunction in an isobaric surface. The
+! reference values used for the specific volume anomaly are
+! SSO = 35.16504 g/kg and CT = 0 deg C. This function calculates
+! specific volume anomaly using the computationally efficient
+! expression for specific volume of Roquet et al. (2015).
+!
+! This function evaluates the pressure integral of specific volume using
+! SA and CT interpolated with respect to pressure using the method of
+! Reiniger and Ross (1968). It uses a weighted mean of (i) values
+! obtained from linear interpolation of the two nearest data points, and
+! (ii) a linear extrapolation of the pairs of data above and below. This
+! "curve fitting" method resembles the use of cubic splines.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! p_ref = reference pressure [ dbar ]
+! ( i.e. reference absolute pressure - 10.1325 dbar )
+!
+! geo_strf_dyn_height = dynamic height anomaly [ m^2/s^2 ]
+! Note. If p_ref exceeds the pressure of the deepest bottle on a
+! vertical profile, the dynamic height anomaly for each bottle
+! on the whole vertical profile is returned as NaN.
+!--------------------------------------------------------------------------
+*/
+static void p_sequence(double p1,double p2,double max_dp_i,double *pseq,
+ int *nps); /* forward reference */
+
+double * /* Returns NULL on error, dyn_height if okay */
+gsw_geo_strf_dyn_height(double *sa, double *ct, double *p, double p_ref,
+ int n_levels, double *dyn_height)
+{
+ GSW_TEOS10_CONSTANTS;
+ int m_levels = (n_levels <= 0) ? 1 : n_levels,
+ p_cnt, top_pad, i, nz, ibottle, ipref, np_max, np, ibpr=0,
+ *iidata;
+ double dp_min, dp_max, p_min, p_max, max_dp_i,
+ *b, *b_av, *dp, *dp_i, *sa_i=NULL, *ct_i, *p_i=NULL,
+ *geo_strf_dyn_height0;
+
+/*
+!--------------------------------------------------------------------------
+! This max_dp_i is the limit we choose for the evaluation of specific
+! volume in the pressure integration. That is, the vertical integration
+! of specific volume with respect to pressure is perfomed with the pressure
+! increment being no more than max_dp_i (the default value being 1 dbar).
+!--------------------------------------------------------------------------
+*/
+ max_dp_i = 1.0;
+
+ if ((nz = m_levels) <= 1)
+ return (NULL);
+
+ dp = (double *) malloc(nz*sizeof (double));
+ dp_min = 11000.0;
+ dp_max = -11000.0;
+ for (i=0; i<nz-1; i++) {
+ if ((dp[i] = p[i+1] - p[i]) < dp_min)
+ dp_min = dp[i];
+ if (dp[i] > dp_max)
+ dp_max = dp[i];
+ }
+
+ if (dp_min <= 0.0) {
+ /* pressure must be monotonic */
+ free(dp);
+ return (NULL);
+ }
+ p_min = p[0];
+ p_max = p[nz-1];
+
+ if (p_ref > p_max) {
+ /*the reference pressure p_ref is deeper than all bottles*/
+ free(dp);
+ return (NULL);
+ }
+
+ /* Determine if there is a "bottle" at exactly p_ref */
+ ipref = -1;
+ for (ibottle = 0; ibottle < nz; ibottle++) {
+ if (p[ibottle] == p_ref) {
+ ipref = ibottle;
+ break;
+ }
+ }
+ if ((dp_max <= max_dp_i) && (p[0] == 0.0) && (ipref >= 0)) {
+ /*
+ !vertical resolution is good (bottle gap is no larger than max_dp_i)
+ ! & the vertical profile begins at the surface (i.e. at p = 0 dbar)
+ ! & the profile contains a "bottle" at exactly p_ref.
+ */
+ b = (double *) malloc(3*nz*sizeof (double));
+ b_av = b+nz; geo_strf_dyn_height0 = b_av+nz;
+ for (i=0; i<nz; i++) {
+ b[i] = gsw_specvol_anom_standard(sa[i],ct[i],p[i]);
+ if (i > 0)
+ b_av[i-1] = 0.5*(b[i] + b[i-1]);
+ }
+ /*
+ ! "geo_strf_dyn_height0" is the dynamic height anomaly with respect
+ ! to p_ref = 0 (the surface).
+ */
+ geo_strf_dyn_height0[0] = 0.0;
+ for (i=1; i<nz; i++)
+ geo_strf_dyn_height0[i] = b_av[i]*dp[i]*db2pa;
+ for (i=1; i<nz; i++) /* cumulative sum */
+ geo_strf_dyn_height0[i] = geo_strf_dyn_height0[i-1]
+ - geo_strf_dyn_height0[i];
+ for (i=0; i<nz; i++)
+ dyn_height[i] = geo_strf_dyn_height0[i]
+ - geo_strf_dyn_height0[ipref];
+ free(b);
+ } else {
+ /*
+ ! Test if there are vertical gaps between adjacent "bottles" which are
+ ! greater than max_dp_i, and that there is a "bottle" exactly at the
+ ! reference pressure.
+ */
+ iidata = (int *) malloc((nz+1)*sizeof (int));
+
+ if ((dp_max <= max_dp_i) && (ipref >= 0)) {
+ /*
+ ! Vertical resolution is already good (no larger than max_dp_i), and
+ ! there is a "bottle" at exactly p_ref.
+ */
+ sa_i = (double *) malloc(2*(nz+1)*sizeof (double));
+ ct_i = sa_i+nz+1;
+ p_i = (double *) malloc((nz+1)*sizeof (double));;
+
+ if (p_min > 0.0) {
+ /*
+ ! resolution is fine and there is a bottle at p_ref, but
+ ! there is not a bottle at p = 0. So add an extra bottle.
+ */
+ for (i=0; i<nz; i++) {
+ sa_i[i+1] = sa[i];
+ ct_i[i+1] = ct[i];
+ p_i[i+1] = p[i];
+ }
+ sa_i[0] = sa[0];
+ ct_i[0] = ct[0];
+ p_i[0] = 0.0;
+ ibpr = ipref+1;
+ p_cnt = nz+1;
+ for (i=0; i<p_cnt; i++)
+ iidata[i] = i;
+ } else {
+ /*
+ ! resolution is fine, there is a bottle at p_ref, and
+ ! there is a bottle at p = 0
+ */
+ memmove(sa_i, sa, nz*sizeof (double));
+ memmove(ct_i, ct, nz*sizeof (double));
+ memmove(p_i, p, nz*sizeof (double));
+ ibpr = ipref;
+ for (i=0; i<nz; i++)
+ iidata[i] = i;
+ p_cnt = nz;
+ }
+
+ } else {
+ /*
+ ! interpolation is needed.
+ */
+ np_max = 2*rint(p[nz-1]/max_dp_i+0.5);
+ p_i = (double *) malloc(np_max*sizeof (double));
+ /* sa_i is allocated below, when its size is known */
+
+ if (p_min > 0.0) {
+ /*
+ ! there is not a bottle at p = 0.
+ */
+ if (p_ref < p_min) {
+ /*
+ ! p_ref is shallower than the minimum bottle pressure.
+ */
+ p_i[0] = 0.0;
+ p_sequence(p_i[0],p_ref,max_dp_i, p_i+1,&np);
+ ibpr = p_cnt = np;
+ p_cnt++;
+ p_sequence(p_ref,p_min,max_dp_i, p_i+p_cnt,&np);
+ p_cnt += np;
+ top_pad = p_cnt;
+ } else {
+ /*
+ ! p_ref is deeper than the minimum bottle pressure.
+ */
+ p_i[0] = 0.0;
+ p_i[1] = p_min;
+ top_pad = 2;
+ p_cnt = 2;
+ }
+ } else {
+ /*
+ ! there is a bottle at p = 0.
+ */
+ p_i[0] = p_min;
+ top_pad = 1;
+ p_cnt = 1;
+ }
+
+ for (ibottle=0; ibottle < nz-1; ibottle++) {
+
+ iidata[ibottle] = p_cnt-1;
+ if (p[ibottle] == p_ref) ibpr = p_cnt-1;
+
+ if (p[ibottle] < p_ref && p[ibottle+1] > p_ref) {
+ /*
+ ! ... reference pressure is spanned by bottle pairs -
+ ! need to include p_ref as an interpolated pressure.
+ */
+ p_sequence(p[ibottle],p_ref,max_dp_i, p_i+p_cnt,&np);
+ p_cnt += np;
+ ibpr = p_cnt-1;
+ p_sequence(p_ref,p[ibottle+1],max_dp_i,p_i+p_cnt,&np);
+ p_cnt += np;
+ } else {
+ /*
+ ! ... reference pressure is not spanned by bottle pairs.
+ */
+ p_sequence(p[ibottle],p[ibottle+1],max_dp_i,
+ p_i+p_cnt,&np);
+ p_cnt += np;
+ }
+
+ }
+
+ iidata[nz-1] = p_cnt-1;
+ if (p[nz-1] == p_ref) ibpr = p_cnt-1;
+
+ sa_i = (double *) malloc(2*p_cnt*sizeof (double));
+ ct_i = sa_i+p_cnt;
+
+ if (top_pad > 1) {
+ gsw_linear_interp_sa_ct(sa,ct,p,nz,
+ p_i,top_pad-1,sa_i,ct_i);
+ }
+ gsw_rr68_interp_sa_ct(sa,ct,p,nz,p_i+top_pad-1,p_cnt-top_pad+1,
+ sa_i+top_pad-1,ct_i+top_pad-1);
+ }
+
+ b = (double *) malloc(4*p_cnt*sizeof (double));
+ b_av = b+p_cnt; dp_i = b_av+p_cnt;
+ geo_strf_dyn_height0 = dp_i+p_cnt;
+ for (i=0; i<p_cnt; i++) {
+ b[i] = gsw_specvol_anom_standard(sa_i[i],ct_i[i],p_i[i]);
+ if (i > 0) {
+ dp_i[i-1] = p_i[i]-p_i[i-1];
+ b_av[i-1] = 0.5*(b[i] + b[i-1]);
+ }
+ }
+ /*
+ ! "geo_strf_dyn_height0" is the dynamic height anomaly with respect
+ ! to p_ref = 0 (the surface).
+ */
+ geo_strf_dyn_height0[0] = 0.0;
+ for (i=1; i<p_cnt; i++)
+ geo_strf_dyn_height0[i] = b_av[i-1]*dp_i[i-1];
+ for (i=1; i<p_cnt; i++) /* cumulative sum */
+ geo_strf_dyn_height0[i] = geo_strf_dyn_height0[i-1]
+ - geo_strf_dyn_height0[i];
+ for (i=0; i<nz; i++)
+ dyn_height[i] = (geo_strf_dyn_height0[iidata[i]]
+ - geo_strf_dyn_height0[ibpr])*db2pa;
+
+ free(b);
+ free(iidata);
+ if (sa_i != NULL)
+ free(sa_i);
+ if (p_i != NULL)
+ free(p_i);
+
+ }
+ free(dp);
+ return (dyn_height);
+}
+
+static void
+p_sequence(double p1, double p2, double max_dp_i, double *pseq, int *nps)
+{
+ double dp, pstep;
+ int n, i;
+
+ dp = p2 - p1;
+ n = ceil(dp/max_dp_i);
+ pstep = dp/n;
+
+ if (nps != NULL) *nps = n;
+
+ for (i=1; i<=n; i++)
+ pseq[i-1] = p1+pstep*i;
+}
+/*
+!==========================================================================
+pure subroutine gsw_geo_strf_dyn_height_pc (sa, ct, delta_p, &
+ geo_strf_dyn_height_pc, p_mid)
+!==========================================================================
+!
+! Calculates dynamic height anomaly as the integral of specific volume
+! anomaly from the the sea surface pressure (0 Pa) to the pressure p.
+! This function, gsw_geo_strf_dyn_height_pc, is to used when the
+! Absolute Salinity and Conservative Temperature are piecewise constant in
+! the vertical over sucessive pressure intervals of delta_p (such as in
+! a forward "z-coordinate" ocean model). "geo_strf_dyn_height_pc" is
+! the dynamic height anomaly with respect to the sea surface. That is,
+! "geo_strf_dyn_height_pc" is the geostrophic streamfunction for the
+! difference between the horizontal velocity at the pressure concerned, p,
+! and the horizontal velocity at the sea surface. Dynamic height anomaly
+! is the geostrophic streamfunction in an isobaric surface. The reference
+! values used for the specific volume anomaly are SA = SSO = 35.16504 g/kg
+! and CT = 0 deg C. The output values of geo_strf_dyn_height_pc are
+! given at the mid-point pressures, p_mid, of each layer in which SA and
+! CT are vertically piecewice constant (pc). This function calculates
+! enthalpy using the computationally-efficient 75-term expression for
+! specific volume of Roquet et al., (2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! delta_p = difference in sea pressure between the deep and [ dbar ]
+! shallow extents of each layer in which SA and CT
+! are vertically constant. delta_p must be positive.
+!
+! Note. sea pressure is absolute pressure minus 10.1325 dbar.
+!
+! geo_strf_dyn_height_pc = dynamic height anomaly [ m^2/s^2 ]
+! p_mid = mid-point pressure in each layer [ dbar ]
+!--------------------------------------------------------------------------
+*/
+double *
+gsw_geo_strf_dyn_height_pc(double *sa, double *ct, double *delta_p, int n_levels,
+ double *geo_strf_dyn_height_pc, double *p_mid)
+{
+ int i, np;
+ double *delta_h, delta_h_half, dyn_height_deep=0.0,
+ *p_deep, *p_shallow;
+
+ for (i=0; i<n_levels; i++)
+ if (delta_p[i] < 0.0)
+ return (NULL);
+
+ np = n_levels;
+ delta_h = (double *) malloc(3*np*sizeof (double));
+ p_deep = delta_h+np; p_shallow = p_deep+np;
+
+ for (i=0; i<np; i++) {
+ p_deep[i] = (i==0)? delta_p[0] : p_deep[i-1] + delta_p[i];
+ p_shallow[i] = p_deep[i] - delta_p[i];
+ delta_h[i] = gsw_enthalpy_diff(sa[i],ct[i],p_shallow[i],p_deep[i]);
+ }
+
+ for (i=0; i<np; i++) {
+ dyn_height_deep = dyn_height_deep - delta_h[i];
+ /* This is Phi minus Phi_0 of Eqn. (3.32.2) of IOC et al. (2010).*/
+ p_mid[i] = 0.5*(p_shallow[i] + p_deep[i]);
+ delta_h_half = gsw_enthalpy_diff(sa[i],ct[i],p_mid[i],p_deep[i]);
+
+ geo_strf_dyn_height_pc[i] = gsw_enthalpy_sso_0(p_mid[i]) +
+ dyn_height_deep + delta_h_half;
+ }
+ free(delta_h);
+ return (geo_strf_dyn_height_pc);
+}
+/*
+!==========================================================================
+function gsw_gibbs(ns,nt,np,sa,t,p)
+!==========================================================================
+!
+! seawater specific Gibbs free energy and derivatives up to order 2
+!
+! ns : order of s derivative
+! nt : order of t derivative
+! np : order of p derivative
+! sa : Absolute Salinity [g/kg]
+! t : temperature [deg C]
+! p : sea pressure [dbar]
+! -1
+! gsw_gibbs : specific Gibbs energy or its derivative [J kg ]
+*/
+double
+gsw_gibbs(int ns, int nt, int np, double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, z, g03, g08, return_value = 0.0;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*1e-4;
+
+ if (ns == 0 && nt == 0 && np == 0) {
+ g03 = 101.342743139674 + z*(100015.695367145 +
+ z*(-2544.5765420363 + z*(284.517778446287 +
+ z*(-33.3146754253611 + (4.20263108803084 -
+ 0.546428511471039*z)*z)))) +
+ y*(5.90578347909402 + z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 +
+ (28.9796526294175 - 2.13290083518327*z)*z))) +
+ y*(-12357.785933039 + z*(1455.0364540468 +
+ z*(-756.558385769359 + z*(273.479662323528 +
+ z*(-55.5604063817218 + 4.34420671917197*z)))) +
+ y*(736.741204151612 + z*(-672.50778314507 +
+ z*(499.360390819152 + z*(-239.545330654412 +
+ (48.8012518593872 - 1.66307106208905*z)*z))) +
+ y*(-148.185936433658 + z*(397.968445406972 +
+ z*(-301.815380621876 + (152.196371733841 -
+ 26.3748377232802*z)*z)) +
+ y*(58.0259125842571 + z*(-194.618310617595 +
+ z*(120.520654902025 + z*(-55.2723052340152 +
+ 6.48190668077221*z))) +
+ y*(-18.9843846514172 + y*(3.05081646487967 -
+ 9.63108119393062*z) +
+ z*(63.5113936641785 + z*(-22.2897317140459 +
+ 8.17060541818112*z))))))));
+
+ g08 = x2*(1416.27648484197 + z*(-3310.49154044839 +
+ z*(384.794152978599 + z*(-96.5324320107458 +
+ (15.8408172766824 - 2.62480156590992*z)*z))) +
+ x*(-2432.14662381794 + x*(2025.80115603697 +
+ y*(543.835333000098 + y*(-68.5572509204491 +
+ y*(49.3667694856254 + y*(-17.1397577419788 +
+ 2.49697009569508*y))) - 22.6683558512829*z) +
+ x*(-1091.66841042967 - 196.028306689776*y +
+ x*(374.60123787784 - 48.5891069025409*x +
+ 36.7571622995805*y) + 36.0284195611086*z) +
+ z*(-54.7919133532887 + (-4.08193978912261 -
+ 30.1755111971161*z)*z)) +
+ z*(199.459603073901 + z*(-52.2940909281335 +
+ (68.0444942726459 - 3.41251932441282*z)*z)) +
+ y*(-493.407510141682 + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-43.0664675978042 + z*(383.058066002476 +
+ z*(-54.1917262517112 + 25.6398487389914*z)) +
+ y*(-10.0227370861875 - 460.319931801257*z +
+ y*(0.875600661808945 + 234.565187611355*z))))) +
+ y*(168.072408311545 + z*(729.116529735046 +
+ z*(-343.956902961561 + z*(124.687671116248 +
+ z*(-31.656964386073 + 7.04658803315449*z)))) +
+ y*(880.031352997204 + y*(-225.267649263401 +
+ y*(91.4260447751259 + y*(-21.6603240875311 +
+ 2.13016970847183*y) +
+ z*(-297.728741987187 + (74.726141138756 -
+ 36.4872919001588*z)*z)) +
+ z*(694.244814133268 + z*(-204.889641964903 +
+ (113.561697840594 - 11.1282734326413*z)*z))) +
+ z*(-860.764303783977 + z*(337.409530269367 +
+ z*(-178.314556207638 + (44.2040358308 -
+ 7.92001547211682*z)*z))))));
+
+ if (sa > 0.0)
+ g08 = g08 + x2*(5812.81456626732 +
+ 851.226734946706*y)*log(x);
+
+ return_value = g03 + g08;
+
+ } else if (ns == 1 && nt == 0 && np == 0) {
+
+ g08 = 8645.36753595126 + z*(-6620.98308089678 +
+ z*(769.588305957198 + z*(-193.0648640214916 +
+ (31.6816345533648 - 5.24960313181984*z)*z))) +
+ x*(-7296.43987145382 + x*(8103.20462414788 +
+ y*(2175.341332000392 + y*(-274.2290036817964 +
+ y*(197.4670779425016 + y*(-68.5590309679152 +
+ 9.98788038278032*y))) - 90.6734234051316*z) +
+ x*(-5458.34205214835 - 980.14153344888*y +
+ x*(2247.60742726704 - 340.1237483177863*x +
+ 220.542973797483*y) + 180.142097805543*z) +
+ z*(-219.1676534131548 + (-16.32775915649044 -
+ 120.7020447884644*z)*z)) +
+ z*(598.378809221703 + z*(-156.8822727844005 +
+ (204.1334828179377 - 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 + z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(2.626801985426835 + 703.695562834065*z))))) +
+ y*(1187.3715515697959 + z*(1458.233059470092 +
+ z*(-687.913805923122 + z*(249.375342232496 +
+ z*(-63.313928772146 + 14.09317606630898*z)))) +
+ y*(1760.062705994408 + y*(-450.535298526802 +
+ y*(182.8520895502518 + y*(-43.3206481750622 +
+ 4.26033941694366*y) +
+ z*(-595.457483974374 + (149.452282277512 -
+ 72.9745838003176*z)*z)) +
+ z*(1388.489628266536 + z*(-409.779283929806 +
+ (227.123395681188 - 22.2565468652826*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 -
+ 15.84003094423364*z)*z)))));
+
+ if (sa > 0.0)
+ g08 = g08 + (11625.62913253464 + 1702.453469893412*y)*
+ log(x);
+ else
+ g08 = 0.0;
+
+ return_value = 0.5*gsw_sfac*g08;
+
+ } else if (ns == 0 && nt == 1 && np == 0) {
+
+ g03 = 5.90578347909402 + z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 +
+ (28.9796526294175 - 2.13290083518327*z)*z))) +
+ y*(-24715.571866078 + z*(2910.0729080936 +
+ z*(-1513.116771538718 + z*(546.959324647056 +
+ z*(-111.1208127634436 + 8.68841343834394*z)))) +
+ y*(2210.2236124548363 + z*(-2017.52334943521 +
+ z*(1498.081172457456 + z*(-718.6359919632359 +
+ (146.4037555781616 - 4.9892131862671505*z)*z))) +
+ y*(-592.743745734632 + z*(1591.873781627888 +
+ z*(-1207.261522487504 + (608.785486935364 -
+ 105.4993508931208*z)*z)) +
+ y*(290.12956292128547 + z*(-973.091553087975 +
+ z*(602.603274510125 + z*(-276.361526170076 +
+ 32.40953340386105*z))) +
+ y*(-113.90630790850321 + y*(21.35571525415769 -
+ 67.41756835751434*z) +
+ z*(381.06836198507096 + z*(-133.7383902842754 +
+ 49.023632509086724*z)))))));
+
+ g08 = x2*(168.072408311545 + z*(729.116529735046 +
+ z*(-343.956902961561 + z*(124.687671116248 +
+ z*(-31.656964386073 + 7.04658803315449*z)))) +
+ x*(-493.407510141682 + x*(543.835333000098 +
+ x*(-196.028306689776 + 36.7571622995805*x) +
+ y*(-137.1145018408982 + y*(148.10030845687618 +
+ y*(-68.5590309679152 + 12.4848504784754*y))) -
+ 22.6683558512829*z) + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-86.1329351956084 + z*(766.116132004952 +
+ z*(-108.3834525034224 + 51.2796974779828*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(3.50240264723578 + 938.26075044542*z)))) +
+ y*(1760.062705994408 + y*(-675.802947790203 +
+ y*(365.7041791005036 + y*(-108.30162043765552 +
+ 12.78101825083098*y) +
+ z*(-1190.914967948748 + (298.904564555024 -
+ 145.9491676006352*z)*z)) +
+ z*(2082.7344423998043 + z*(-614.668925894709 +
+ (340.685093521782 - 33.3848202979239*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 -
+ 15.84003094423364*z)*z)))));
+
+ if (sa > 0.0)
+ g08 = g08 + 851.226734946706*x2*log(x);
+
+ return_value = (g03 + g08)*0.025;
+
+ } else if (ns == 0 && nt == 0 && np == 1) {
+
+ g03 = 100015.695367145 + z*(-5089.1530840726 +
+ z*(853.5533353388611 + z*(-133.2587017014444 +
+ (21.0131554401542 - 3.278571068826234*z)*z))) +
+ y*(-270.983805184062 + z*(1552.307223226202 +
+ z*(-589.53765264366 + (115.91861051767 -
+ 10.664504175916349*z)*z)) +
+ y*(1455.0364540468 + z*(-1513.116771538718 +
+ z*(820.438986970584 + z*(-222.2416255268872 +
+ 21.72103359585985*z))) +
+ y*(-672.50778314507 + z*(998.720781638304 +
+ z*(-718.6359919632359 + (195.2050074375488 -
+ 8.31535531044525*z)*z)) +
+ y*(397.968445406972 + z*(-603.630761243752 +
+ (456.589115201523 - 105.4993508931208*z)*z) +
+ y*(-194.618310617595 + y*(63.5113936641785 -
+ 9.63108119393062*y +
+ z*(-44.5794634280918 + 24.511816254543362*z)) +
+ z*(241.04130980405 + z*(-165.8169157020456 +
+ 25.92762672308884*z)))))));
+
+ g08 = x2*(-3310.49154044839 + z*(769.588305957198 +
+ z*(-289.5972960322374 + (63.3632691067296 -
+ 13.1240078295496*z)*z)) +
+ x*(199.459603073901 + x*(-54.7919133532887 +
+ 36.0284195611086*x - 22.6683558512829*y +
+ (-8.16387957824522 - 90.52653359134831*z)*z) +
+ z*(-104.588181856267 + (204.1334828179377 -
+ 13.65007729765128*z)*z) +
+ y*(-175.292041186547 + (166.3847855603638 -
+ 88.449193048287*z)*z +
+ y*(383.058066002476 + y*(-460.319931801257 +
+ 234.565187611355*y) +
+ z*(-108.3834525034224 + 76.9195462169742*z)))) +
+ y*(729.116529735046 + z*(-687.913805923122 +
+ z*(374.063013348744 + z*(-126.627857544292 +
+ 35.23294016577245*z))) +
+ y*(-860.764303783977 + y*(694.244814133268 +
+ y*(-297.728741987187 + (149.452282277512 -
+ 109.46187570047641*z)*z) +
+ z*(-409.779283929806 + (340.685093521782 -
+ 44.5130937305652*z)*z)) +
+ z*(674.819060538734 + z*(-534.943668622914 +
+ (176.8161433232 - 39.600077360584095*z)*z)))));
+
+ return_value = (g03 + g08)*1.0e-8;
+
+ } else if (ns == 0 && nt == 2 && np == 0) {
+
+ g03 = -24715.571866078 + z*(2910.0729080936 + z*
+ (-1513.116771538718 + z*(546.959324647056 +
+ z*(-111.1208127634436 + 8.68841343834394*z)))) +
+ y*(4420.4472249096725 + z*(-4035.04669887042 +
+ z*(2996.162344914912 + z*(-1437.2719839264719 +
+ (292.8075111563232 - 9.978426372534301*z)*z))) +
+ y*(-1778.231237203896 + z*(4775.621344883664 +
+ z*(-3621.784567462512 + (1826.356460806092 -
+ 316.49805267936244*z)*z)) +
+ y*(1160.5182516851419 + z*(-3892.3662123519 +
+ z*(2410.4130980405 + z*(-1105.446104680304 +
+ 129.6381336154442*z))) +
+ y*(-569.531539542516 + y*(128.13429152494615 -
+ 404.50541014508605*z) +
+ z*(1905.341809925355 + z*(-668.691951421377 +
+ 245.11816254543362*z))))));
+
+ g08 = x2*(1760.062705994408 + x*(-86.1329351956084 +
+ x*(-137.1145018408982 + y*(296.20061691375236 +
+ y*(-205.67709290374563 + 49.9394019139016*y))) +
+ z*(766.116132004952 + z*(-108.3834525034224 +
+ 51.2796974779828*z)) +
+ y*(-60.136422517125 - 2761.9195908075417*z +
+ y*(10.50720794170734 + 2814.78225133626*z))) +
+ y*(-1351.605895580406 + y*(1097.1125373015109 +
+ y*(-433.20648175062206 + 63.905091254154904*y) +
+ z*(-3572.7449038462437 + (896.713693665072 -
+ 437.84750280190565*z)*z)) +
+ z*(4165.4688847996085 + z*(-1229.337851789418 +
+ (681.370187043564 - 66.7696405958478*z)*z))) +
+ z*(-1721.528607567954 + z*(674.819060538734 +
+ z*(-356.629112415276 + (88.4080716616 -
+ 15.84003094423364*z)*z))));
+
+ return_value = (g03 + g08)*0.000625;
+
+ } else if (ns == 1 && nt == 0 && np == 1) {
+
+ g08 = -6620.98308089678 + z*(1539.176611914396 +
+ z*(-579.1945920644748 + (126.7265382134592 -
+ 26.2480156590992*z)*z)) +
+ x*(598.378809221703 + x*(-219.1676534131548 +
+ 180.142097805543*x - 90.6734234051316*y +
+ (-32.65551831298088 - 362.10613436539325*z)*z) +
+ z*(-313.764545568801 + (612.4004484538132 -
+ 40.95023189295384*z)*z) +
+ y*(-525.876123559641 + (499.15435668109143 -
+ 265.347579144861*z)*z +
+ y*(1149.174198007428 + y*(-1380.9597954037708 +
+ 703.695562834065*y) +
+ z*(-325.1503575102672 + 230.7586386509226*z)))) +
+ y*(1458.233059470092 + z*(-1375.827611846244 +
+ z*(748.126026697488 + z*(-253.255715088584 +
+ 70.4658803315449*z))) +
+ y*(-1721.528607567954 + y*(1388.489628266536 +
+ y*(-595.457483974374 + (298.904564555024 -
+ 218.92375140095282*z)*z) +
+ z*(-819.558567859612 + (681.370187043564 -
+ 89.0261874611304*z)*z)) +
+ z*(1349.638121077468 + z*(-1069.887337245828 +
+ (353.6322866464 - 79.20015472116819*z)*z))));
+
+ return_value = g08*gsw_sfac*0.5e-8;
+
+ } else if (ns == 0 && nt == 1 && np == 1) {
+
+ g03 = -270.983805184062 + z*(1552.307223226202 +
+ z*(-589.53765264366 + (115.91861051767 -
+ 10.664504175916349*z)*z)) +
+ y*(2910.0729080936 + z*(-3026.233543077436 +
+ z*(1640.877973941168 + z*(-444.4832510537744 +
+ 43.4420671917197*z))) +
+ y*(-2017.52334943521 + z*(2996.162344914912 +
+ z*(-2155.907975889708 + (585.6150223126464 -
+ 24.946065931335752*z)*z)) +
+ y*(1591.873781627888 + z*(-2414.523044975008 +
+ (1826.356460806092 - 421.9974035724832*z)*z) +
+ y*(-973.091553087975 + z*(1205.20654902025 +
+ z*(-829.084578510228 + 129.6381336154442*z)) +
+ y*(381.06836198507096 - 67.41756835751434*y +
+ z*(-267.4767805685508 + 147.07089752726017*z))))));
+
+ g08 = x2*(729.116529735046 + z*(-687.913805923122 +
+ z*(374.063013348744 + z*(-126.627857544292 +
+ 35.23294016577245*z))) +
+ x*(-175.292041186547 - 22.6683558512829*x +
+ (166.3847855603638 - 88.449193048287*z)*z +
+ y*(766.116132004952 + y*(-1380.9597954037708 +
+ 938.26075044542*y) +
+ z*(-216.7669050068448 + 153.8390924339484*z))) +
+ y*(-1721.528607567954 + y*(2082.7344423998043 +
+ y*(-1190.914967948748 + (597.809129110048 -
+ 437.84750280190565*z)*z) +
+ z*(-1229.337851789418 + (1022.055280565346 -
+ 133.5392811916956*z)*z)) +
+ z*(1349.638121077468 + z*(-1069.887337245828 +
+ (353.6322866464 - 79.20015472116819*z)*z))));
+
+ return_value = (g03 + g08)*2.5e-10;
+
+ } else if (ns == 1 && nt == 1 && np == 0) {
+
+ g08 = 1187.3715515697959 + z*(1458.233059470092 +
+ z*(-687.913805923122 + z*(249.375342232496 +
+ z*(-63.313928772146 + 14.09317606630898*z)))) +
+ x*(-1480.222530425046 + x*(2175.341332000392 +
+ x*(-980.14153344888 + 220.542973797483*x) +
+ y*(-548.4580073635929 + y*(592.4012338275047 +
+ y*(-274.2361238716608 + 49.9394019139016*y))) -
+ 90.6734234051316*z) +
+ z*(-525.876123559641 + (249.57717834054571 -
+ 88.449193048287*z)*z) +
+ y*(-258.3988055868252 + z*(2298.348396014856 +
+ z*(-325.1503575102672 + 153.8390924339484*z)) +
+ y*(-90.2046337756875 - 4142.8793862113125*z +
+ y*(10.50720794170734 + 2814.78225133626*z)))) +
+ y*(3520.125411988816 + y*(-1351.605895580406 +
+ y*(731.4083582010072 + y*(-216.60324087531103 +
+ 25.56203650166196*y) +
+ z*(-2381.829935897496 + (597.809129110048 -
+ 291.8983352012704*z)*z)) +
+ z*(4165.4688847996085 + z*(-1229.337851789418 +
+ (681.370187043564 - 66.7696405958478*z)*z))) +
+ z*(-3443.057215135908 + z*(1349.638121077468 +
+ z*(-713.258224830552 + (176.8161433232 -
+ 31.68006188846728*z)*z))));
+
+ if (sa > 0.0)
+ g08 = g08 + 1702.453469893412*log(x);
+
+ return_value = 0.5*gsw_sfac*0.025*g08;
+
+ } else if (ns == 2 && nt == 0 && np == 0) {
+
+ g08 = 2.0*(8103.20462414788 +
+ y*(2175.341332000392 + y*(-274.2290036817964 +
+ y*(197.4670779425016 + y*(-68.5590309679152 +
+ 9.98788038278032*y))) - 90.6734234051316*z) +
+ 1.5*x*(-5458.34205214835 - 980.14153344888*y +
+ (4.0/3.0)*x*(2247.60742726704 - 340.1237483177863*1.25*x +
+ 220.542973797483*y) + 180.142097805543*z) +
+ z*(-219.1676534131548 + (-16.32775915649044 -
+ 120.7020447884644*z)*z));
+
+ if (x > 0.0) {
+ g08 += (-7296.43987145382 + z*(598.378809221703 +
+ z*(-156.8822727844005 + (204.1334828179377 -
+ 10.23755797323846*z)*z)) +
+ y*(-1480.222530425046 + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-129.1994027934126 + z*(1149.174198007428 +
+ z*(-162.5751787551336 + 76.9195462169742*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(2.626801985426835 + 703.695562834065*z)))))/x +
+ (11625.62913253464 + 1702.453469893412*y)/x2;
+ } else
+ g08 = 0.0;
+
+ return_value = 0.25*gsw_sfac*gsw_sfac*g08;
+
+ } else if (ns == 0 && nt == 0 && np == 2) {
+
+ g03 = -5089.1530840726 + z*(1707.1066706777221 +
+ z*(-399.7761051043332 + (84.0526217606168 -
+ 16.39285534413117*z)*z)) +
+ y*(1552.307223226202 + z*(-1179.07530528732 +
+ (347.75583155301 - 42.658016703665396*z)*z) +
+ y*(-1513.116771538718 + z*(1640.877973941168 +
+ z*(-666.7248765806615 + 86.8841343834394*z)) +
+ y*(998.720781638304 + z*(-1437.2719839264719 +
+ (585.6150223126464 - 33.261421241781*z)*z) +
+ y*(-603.630761243752 + (913.178230403046 -
+ 316.49805267936244*z)*z +
+ y*(241.04130980405 + y*(-44.5794634280918 +
+ 49.023632509086724*z) +
+ z*(-331.6338314040912 + 77.78288016926652*z))))));
+
+ g08 = x2*(769.588305957198 + z*(-579.1945920644748 +
+ (190.08980732018878 - 52.4960313181984*z)*z) +
+ x*(-104.588181856267 + x*(-8.16387957824522 -
+ 181.05306718269662*z) +
+ (408.2669656358754 - 40.95023189295384*z)*z +
+ y*(166.3847855603638 - 176.898386096574*z +
+ y*(-108.3834525034224 + 153.8390924339484*z))) +
+ y*(-687.913805923122 + z*(748.126026697488 +
+ z*(-379.883572632876 + 140.9317606630898*z)) +
+ y*(674.819060538734 + z*(-1069.887337245828 +
+ (530.4484299696 - 158.40030944233638*z)*z) +
+ y*(-409.779283929806 + y*(149.452282277512 -
+ 218.92375140095282*z) +
+ (681.370187043564 - 133.5392811916956*z)*z))));
+
+ return_value = (g03 + g08)*1e-16 ;
+
+ } else
+ return_value = GSW_INVALID_VALUE;
+
+ return (return_value);
+}
+/*
+! =========================================================================
+elemental function gsw_gibbs_ice (nt, np, t, p)
+! =========================================================================
+!
+! Ice specific Gibbs energy and derivatives up to order 2.
+!
+! nt = order of t derivative [ integers 0, 1 or 2 ]
+! np = order of p derivative [ integers 0, 1 or 2 ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+!
+! gibbs_ice = Specific Gibbs energy of ice or its derivatives.
+! The Gibbs energy (when nt = np = 0) has units of: [ J/kg ]
+! The temperature derivatives are output in units of:
+! [ (J/kg) (K)^(-nt) ]
+! The pressure derivatives are output in units of:
+! [ (J/kg) (Pa)^(-np) ]
+! The mixed derivatives are output in units of:
+! [ (J/kg) (K)^(-nt) (Pa)^(-np) ]
+! Note. The derivatives are taken with respect to pressure in Pa, not
+! withstanding that the pressure input into this routine is in dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_gibbs_ice (int nt, int np, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double dzi, g0, g0p, g0pp, sqrec_pt;
+ std::complex<double> r2, r2p, r2pp, g, sqtau_t1, sqtau_t2, tau,
+ tau_t1, tau_t2;
+ double s0 = -3.32733756492168e3;
+
+ tau = (t + gsw_t0)*rec_tt;
+
+ dzi = db2pa*p*rec_pt;
+
+ if (nt == 0 && np == 0) {
+
+ tau_t1 = tau/t1;
+ sqtau_t1 = tau_t1*tau_t1;
+ tau_t2 = tau/t2;
+ sqtau_t2 = tau_t2*tau_t2;
+
+ g0 = g00 + dzi*(g01 + dzi*(g02 + dzi*(g03 + g04*dzi)));
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ g = r1*(tau*log((1.0 + tau_t1)/(1.0 - tau_t1))
+ + t1*(log(1.0 - sqtau_t1) - sqtau_t1))
+ + r2*(tau*log((1.0 + tau_t2)/(1.0 - tau_t2))
+ + t2*(log(1.0 - sqtau_t2) - sqtau_t2));
+
+ return real(g0 - tt*(s0*tau - real(g))); // EF: bug in original.
+
+ } else if (nt == 1 && np == 0) {
+
+ tau_t1 = tau/t1;
+ tau_t2 = tau/t2;
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ g = r1*(log((1.0 + tau_t1)/(1.0 - tau_t1)) - 2.0*tau_t1)
+ + r2*(log((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2);
+
+ return (-s0 + real(g));
+
+ } else if (nt == 0 && np == 1) {
+
+ tau_t2 = tau/t2;
+ sqtau_t2 = tau_t2*tau_t2;
+
+ g0p = rec_pt*(g01 + dzi*(2.0*g02 + dzi*(3.0*g03 + 4.0*g04*dzi)));
+
+ r2p = rec_pt*(r21 + 2.0*r22*dzi);
+
+ g = r2p*(tau*log((1.0 + tau_t2)/(1.0 - tau_t2))
+ + t2*(log(1.0 - sqtau_t2) - sqtau_t2));
+
+ return (g0p + tt*real(g));
+
+ } else if (nt == 1 && np == 1) {
+
+ tau_t2 = tau/t2;
+
+ r2p = rec_pt*(r21 + 2.0*r22*dzi) ;
+
+ g = r2p*(log((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2);
+
+ return (real(g));
+
+ } else if (nt == 2 && np == 0) {
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ g = r1*(1.0/(t1 - tau) + 1.0/(t1 + tau) - 2.0/t1)
+ + r2*(1.0/(t2 - tau) + 1.0/(t2 + tau) - 2.0/t2);
+
+ return (rec_tt*real(g));
+
+ } else if (nt == 0 && np == 2) {
+
+ sqrec_pt = rec_pt*rec_pt;
+
+ tau_t2 = tau/t2;
+ sqtau_t2 = tau_t2*tau_t2;
+
+ g0pp = sqrec_pt*(2.0*g02 + dzi*(6.0*g03 + 12.0*g04*dzi));
+
+ r2pp = 2.0*r22*sqrec_pt;
+
+ g = r2pp*(tau*log((1.0 + tau_t2)/(1.0 - tau_t2))
+ + t2*(log(1.0 - sqtau_t2) - sqtau_t2));
+
+ return (g0pp + tt*real(g));
+
+ } else
+ return (GSW_INVALID_VALUE);
+}
+/*
+! =========================================================================
+elemental function gsw_gibbs_ice_part_t (t, p)
+! =========================================================================
+!
+! part of the the first temperature derivative of Gibbs energy of ice
+! that is the outout is gibbs_ice(1,0,t,p) + S0
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+!
+! gibbs_ice_part_t = part of temperature derivative [ J kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_gibbs_ice_part_t(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double dzi, tau;
+ std::complex<double> g, tau_t1, tau_t2, r2;
+
+ tau = (t + gsw_t0)*rec_tt;
+
+ dzi = db2pa*p*rec_pt;
+
+ tau_t1 = tau/t1;
+ tau_t2 = tau/t2;
+
+ r2 = r20 + dzi*(r21 + r22*dzi);
+
+ g = r1*(log((1.0 + tau_t1)/(1.0 - tau_t1)) - 2.0*tau_t1)
+ + r2*(log((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2);
+
+ return (real(g));
+}
+/*
+! =========================================================================
+elemental function gsw_gibbs_ice_pt0 (pt0)
+! =========================================================================
+!
+! Part of the the first temperature derivative of Gibbs energy of ice
+! that is the outout is "gibbs_ice(1,0,pt0,0) + s0"
+!
+! pt0 = potential temperature with reference sea pressure of zero dbar
+! [ deg C ]
+!
+! gsw_gibbs_ice_pt0 = part of temperature derivative [ J kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_gibbs_ice_pt0(double pt0)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double tau;
+ std::complex<double> g, tau_t1, tau_t2;
+
+ tau = (pt0 + gsw_t0)*rec_tt;
+
+ tau_t1 = tau/t1;
+ tau_t2 = tau/t2;
+
+ g = r1*(log((1.0 + tau_t1)/(1.0 - tau_t1)) - 2.0*tau_t1)
+ + r20*(log((1.0 + tau_t2)/(1.0 - tau_t2)) - 2.0*tau_t2);
+
+ return (real(g));
+}
+/*
+! =========================================================================
+elemental function gsw_gibbs_ice_pt0_pt0 (pt0)
+! =========================================================================
+!
+! The second temperature derivative of Gibbs energy of ice at the
+! potential temperature with reference sea pressure of zero dbar. That is
+! the output is gibbs_ice(2,0,pt0,0).
+!
+! pt0 = potential temperature with reference sea pressure of zero dbar
+! [ deg C ]
+!
+! gsw_gibbs_ice_pt0_pt0 = temperature second derivative at pt0
+!--------------------------------------------------------------------------
+*/
+double
+gsw_gibbs_ice_pt0_pt0(double pt0)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double tau;
+ std::complex<double> g;
+
+ tau = (pt0 + gsw_t0)*rec_tt;
+
+ g = r1*(1.0/(t1 - tau) + 1.0/(t1 + tau) - 2.0/t1)
+ + r20*(1.0/(t2 - tau) + 1.0/(t2 + tau) - 2.0/t2);
+
+ return (rec_tt*real(g));
+}
+/*
+!==========================================================================
+function gsw_gibbs_pt0_pt0(sa,pt0)
+!==========================================================================
+
+! gibbs_tt at (sa,pt,0)
+!
+! sa : Absolute Salinity [g/kg]
+! pt0 : potential temperature [deg C]
+!
+! gibbs_pt0_pt0 : gibbs_tt at (sa,pt,0)
+*/
+double
+gsw_gibbs_pt0_pt0(double sa, double pt0)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x2, x, y, g03, g08;
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = pt0*0.025;
+
+ g03 = -24715.571866078 +
+ y*(4420.4472249096725 +
+ y*(-1778.231237203896 +
+ y*(1160.5182516851419 +
+ y*(-569.531539542516 + y*128.13429152494615))));
+
+ g08 = x2*(1760.062705994408 + x*(-86.1329351956084 +
+ x*(-137.1145018408982 + y*(296.20061691375236 +
+ y*(-205.67709290374563 + 49.9394019139016*y))) +
+ y*(-60.136422517125 + y*10.50720794170734)) +
+ y*(-1351.605895580406 + y*(1097.1125373015109 +
+ y*(-433.20648175062206 + 63.905091254154904*y))));
+
+ return ((g03 + g08)*0.000625);
+}
+/*
+!==========================================================================
+function gsw_grav(lat,p)
+!==========================================================================
+
+! Calculates acceleration due to gravity as a function of latitude and as
+! a function of pressure in the ocean.
+!
+! lat = latitude in decimal degress north [ -90 ... +90 ]
+! p = sea pressure [ dbar ]
+!
+! grav : grav = gravitational acceleration [ m s^-2 ]
+*/
+double
+gsw_grav(double lat, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x, sin2, gs, z;
+
+ x = sin(lat*deg2rad); /* convert to radians */
+ sin2 = x*x;
+ gs = 9.780327*(1.0 + (5.2792e-3 + (2.32e-5*sin2))*sin2);
+
+ z = gsw_z_from_p(p,lat);
+
+ return (gs*(1.0 - gamma*z)); /* z is the height corresponding to p.
+ Note. In the ocean z is negative. */
+}
+/*
+!==========================================================================
+elemental function gsw_helmholtz_energy_ice (t, p)
+!==========================================================================
+!
+! Calculates the Helmholtz energy of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! Helmholtz_energy_ice = Helmholtz energy of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_helmholtz_energy_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (gsw_gibbs_ice(0,0,t,p)
+ - (db2pa*p + gsw_p0)*gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+function gsw_hill_ratio_at_sp2(t)
+!==========================================================================
+
+! Calculates the Hill ratio, which is the adjustment needed to apply for
+! Practical Salinities smaller than 2. This ratio is defined at a
+! Practical Salinity = 2 and in-situ temperature, t using PSS-78. The Hill
+! ratio is the ratio of 2 to the output of the Hill et al. (1986) formula
+! for Practical Salinity at the conductivity ratio, Rt, at which Practical
+! Salinity on the PSS-78 scale is exactly 2.
+!
+! t : in-situ temperature (ITS-90) [deg C]
+! hill_ratio_at_sp2 : Hill ratio [dimensionless]
+*/
+double
+gsw_hill_ratio_at_sp2(double t)
+{
+ GSW_SP_COEFFICIENTS;
+ double g0 = 2.641463563366498e-1, g1 = 2.007883247811176e-4,
+ g2 = -4.107694432853053e-6, g3 = 8.401670882091225e-8,
+ g4 = -1.711392021989210e-9, g5 = 3.374193893377380e-11,
+ g6 = -5.923731174730784e-13, g7 = 8.057771569962299e-15,
+ g8 = -7.054313817447962e-17, g9 = 2.859992717347235e-19,
+ sp2 = 2.0;
+ double t68, ft68, rtx0, dsp_drtx, sp_est, rtx, rtxm, x, part1, part2;
+ double sqrty, sp_hill_raw_at_sp2;
+
+ t68 = t*1.00024;
+ ft68 = (t68 - 15.0)/(1.0 + k*(t68 - 15.0));
+
+ /*!------------------------------------------------------------------------
+ **! Find the initial estimates of Rtx (Rtx0) and of the derivative dSP_dRtx
+ **! at SP = 2.
+ **!------------------------------------------------------------------------
+ */
+ rtx0 = g0 + t68*(g1 + t68*(g2 + t68*(g3 + t68*(g4 + t68*(g5
+ + t68*(g6 + t68*(g7 + t68*(g8 + t68*g9))))))));
+
+ dsp_drtx= a1 + (2*a2 + (3*a3 + (4*a4 + 5*a5*rtx0)*rtx0)*rtx0)*rtx0 +
+ ft68*(b1 + (2*b2 + (3*b3 + (4*b4 + 5*b5*rtx0)*rtx0)*rtx0)*rtx0);
+
+ /*!-------------------------------------------------------------------------
+ **! Begin a single modified Newton-Raphson iteration to find Rt at SP = 2.
+ **!-------------------------------------------------------------------------
+ */
+ sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx0)*rtx0)*rtx0)*rtx0)*rtx0
+ + ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx0)*rtx0)*rtx0)*
+ rtx0)*rtx0);
+ rtx = rtx0 - (sp_est - sp2)/dsp_drtx;
+ rtxm = 0.5*(rtx + rtx0);
+ dsp_drtx= a1 + (2*a2 + (3*a3 + (4*a4 + 5*a5*rtxm)*rtxm)*rtxm)*rtxm
+ + ft68*(b1 + (2*b2 + (3*b3 + (4*b4 + 5*b5*rtxm)*
+ rtxm)*rtxm)*rtxm);
+ rtx = rtx0 - (sp_est - sp2)/dsp_drtx;
+ /*
+ **! This is the end of one full iteration of the modified Newton-Raphson
+ **! iterative equation solver. The error in Rtx at this point is equivalent
+ **! to an error in SP of 9e-16 psu.
+ */
+
+ x = 400.0*rtx*rtx;
+ sqrty = 10.0*rtx;
+ part1 = 1.0 + x*(1.5 + x);
+ part2 = 1.0 + sqrty*(1.0 + sqrty*(1.0 + sqrty));
+ sp_hill_raw_at_sp2 = sp2 - a0/part1 - b0*ft68/part2;
+
+ return (2.0/sp_hill_raw_at_sp2);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_ice_fraction_to_freeze_seawater (sa, ct, p, &
+ t_ih, sa_freeze, ct_freeze, w_ih)
+!==========================================================================
+!
+! Calculates the mass fraction of ice (mass of ice divided by mass of ice
+! plus seawater), which, when melted into seawater having (SA,CT,p) causes
+! the final dilute seawater to be at the freezing temperature. The other
+! outputs are the Absolute Salinity and Conservative Temperature of the
+! final diluted seawater.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! t_Ih = in-situ temperature of the ice at pressure p (ITS-90) [ deg C ]
+!
+! SA_freeze = Absolute Salinity of seawater after the mass fraction of
+! ice, ice_fraction, at temperature t_Ih has melted into the
+! original seawater, and the final mixture is at the freezing
+! temperature of seawater. [ g/kg ]
+!
+! CT_freeze = Conservative Temperature of seawater after the mass
+! fraction, w_Ih, of ice at temperature t_Ih has melted into
+! the original seawater, and the final mixture is at the
+! freezing temperature of seawater. [ deg C ]
+!
+! w_Ih = mass fraction of ice, having in-situ temperature t_Ih,
+! which, when melted into seawater at (SA,CT,p) leads to the
+! final diluted seawater being at the freezing temperature.
+! This output must be between 0 and 1. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_ice_fraction_to_freeze_seawater(double sa, double ct, double p, double t_ih,
+ double *sa_freeze, double *ct_freeze, double *w_ih)
+{
+ int no_iter;
+ double ctf, ctf_mean, ctf_old, ctf_plus1, ctf_zero,
+ dfunc_dsaf, func, func_plus1, func_zero, h, h_ih,
+ saf, saf_mean, saf_old, tf, h_hat_sa, h_hat_ct, ctf_sa;
+ double sa0 = 0.0, saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*The seawater ct input is below the freezing temp*/
+ *sa_freeze = GSW_INVALID_VALUE;
+ *ct_freeze = *sa_freeze;
+ *w_ih = *sa_freeze;
+ return;
+ }
+
+ tf = gsw_t_freezing(sa0,p,saturation_fraction);
+ if (t_ih > tf) {
+ /*The input, t_Ih, exceeds the freezing temperature at sa = 0*/
+ *sa_freeze = GSW_INVALID_VALUE;
+ *ct_freeze = *sa_freeze;
+ *w_ih = *sa_freeze;
+ return;
+ }
+
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_ih,p);
+
+ ctf_zero = gsw_ct_freezing(sa0,p,saturation_fraction);
+ func_zero = sa*(gsw_enthalpy_ct_exact(sa0,ctf_zero,p) - h_ih);
+
+ ctf_plus1 = gsw_ct_freezing(sa+1.0,p,saturation_fraction);
+ func_plus1 = sa*(gsw_enthalpy_ct_exact(sa+1.0,ctf_plus1,p) - h)
+ - (h - h_ih);
+
+ saf = -(sa+1.0)*func_zero/(func_plus1 - func_zero); /*initial guess*/
+ ctf = gsw_ct_freezing(saf,p,saturation_fraction);
+ gsw_enthalpy_first_derivatives_ct_exact(saf,ctf,p,&h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(saf,p,1.0,&ctf_sa,NULL);
+
+ dfunc_dsaf = sa*(h_hat_sa + h_hat_ct*ctf_sa) - (h - h_ih);
+
+ for (no_iter = 1; no_iter <= 2; no_iter++) {
+ saf_old = saf;
+ ctf_old = ctf;
+ func = sa*(gsw_enthalpy_ct_exact(saf_old,ctf_old,p) - h)
+ - (saf_old - sa)*(h - h_ih);
+ saf = saf_old - func/dfunc_dsaf;
+ saf_mean = 0.5*(saf + saf_old);
+ ctf_mean = gsw_ct_freezing(saf_mean,p,saturation_fraction);
+ gsw_enthalpy_first_derivatives_ct_exact(saf_mean,ctf_mean,p,
+ &h_hat_sa, &h_hat_ct);
+ gsw_ct_freezing_first_derivatives(saf_mean,p,saturation_fraction,
+ &ctf_sa, NULL);
+ dfunc_dsaf = sa*(h_hat_sa + h_hat_ct*ctf_sa) - (h - h_ih);
+ saf = saf_old - func/dfunc_dsaf;
+ ctf = gsw_ct_freezing(saf,p,saturation_fraction);
+ }
+ /*
+ ! After these 2 iterations of this modified Newton-Raphson method, the
+ ! error in SA_freeze is less than 1.3d0x10^-13 g/kg, in CT_freeze is
+ ! less than ! 4x10^-13 deg C and in w_Ih is less than 3.8d0x10^-15
+ ! which represent machine precision for these calculations.
+ */
+
+ *sa_freeze = saf;
+ *ct_freeze = ctf;
+ *w_ih = (h - gsw_enthalpy_ct_exact(*sa_freeze,*ct_freeze,p))/(h - h_ih);
+}
+/*
+!==========================================================================
+function gsw_internal_energy(sa,ct,p)
+!==========================================================================
+
+! Calculates internal energy of seawater.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! internal_energy : internal_energy of seawater [J/kg]
+*/
+double
+gsw_internal_energy(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (gsw_enthalpy(sa,ct,p) - (gsw_p0 + db2pa*p)
+ *gsw_specvol(sa,ct,p));
+}
+/*
+!==========================================================================
+elemental function gsw_internal_energy_ice (t, p)
+!==========================================================================
+!
+! Calculates the specific internal energy of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! internal_energy_ice = specific internal energy (u) [J/kg]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_internal_energy_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (gsw_gibbs_ice(0,0,t,p)
+ - (gsw_t0 + t)*gsw_gibbs_ice(1,0,t,p)
+ - (db2pa*p + gsw_p0)*gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+subroutine gsw_ipv_vs_fnsquared_ratio(sa,ct,p,pref,nz,ipv_vs_fnsquared_ratio,p_mid)
+!==========================================================================
+
+! Calculates the ratio of the vertical gradient of potential density to
+! the vertical gradient of locally-referenced potential density. This
+! ratio is also the ratio of the planetary Isopycnal Potential Vorticity
+! (IPV) to f times N^2, hence the name for this variable,
+! IPV_vs_fNsquared_ratio (see Eqn. (3.20.5) of IOC et al. (2010)).
+! The reference sea pressure, p_ref, of the potential density surface must
+! have a constant value.
+!
+! IPV_vs_fNsquared_ratio is evaluated at the mid pressure between the
+! individual data points in the vertical.
+
+! sa : Absolute Salinity (a profile (length nz)) [g/kg]
+! ct : Conservative Temperature (a profile (length nz)) [deg C]
+! p : sea pressure (a profile (length nz)) [dbar]
+! p_ref : reference sea pressure of the potential density surface
+! ( i.e. absolute reference pressure - 10.1325 dbar ) [dbar]
+! nz : number of bottles
+! IPV_vs_fNsquared_ratio
+! : The ratio of the vertical gradient of potential density
+! referenced to p_ref, to the vertical gradient of locally-
+! referenced potential density. It is ouput on the same
+! vertical (M-1)xN grid as p_mid.
+! IPV_vs_fNsquared_ratio is dimensionless. [ unitless ]
+! p_mid : Mid pressure between p grid (length nz-1) [dbar]
+*/
+void
+gsw_ipv_vs_fnsquared_ratio(double *sa, double *ct, double *p, double p_ref,
+ int nz, double *ipv_vs_fnsquared_ratio, double *p_mid)
+{
+ int k;
+ double dsa, sa_mid, dct, ct_mid;
+ double alpha_mid, beta_mid;
+ double alpha_pref, beta_pref, numerator, denominator;
+
+ if (nz < 2) {
+ *p_mid = *ipv_vs_fnsquared_ratio = GSW_INVALID_VALUE;
+ return;
+ }
+ for (k = 0; k < nz-1; k++) {
+ dsa = (sa[k] - sa[k+1]);
+ dct = (ct[k] - ct[k+1]);
+ sa_mid = 0.5*(sa[k] + sa[k+1]);
+ ct_mid = 0.5*(ct[k] + ct[k+1]);
+ p_mid[k] = 0.5*(p[k] + p[k+1]);
+
+ alpha_mid = gsw_alpha(sa_mid,ct_mid,p_mid[k]);
+ beta_mid = gsw_beta(sa_mid,ct_mid,p_mid[k]);
+ alpha_pref = gsw_alpha(sa_mid,ct_mid,p_ref);
+ beta_pref = gsw_beta(sa_mid,ct_mid,p_ref);
+
+ numerator = dct*alpha_pref - dsa*beta_pref;
+ denominator = dct*alpha_mid - dsa*beta_mid;
+
+ if (denominator == 0.0)
+ ipv_vs_fnsquared_ratio[k] = GSW_INVALID_VALUE;
+ else
+ ipv_vs_fnsquared_ratio[k] = numerator/denominator;
+ }
+}
+/*
+!==========================================================================
+function gsw_kappa(sa,ct,p)
+!==========================================================================
+
+! Calculates isentropic compressibility of seawater. This function
+! has inputs of Absolute Salinity and Conservative Temperature. This
+! function uses the computationally-efficient expression for
+! specific volume in terms of SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! kappa : isentropic compressibility [1.0/Pa]
+*/
+double
+gsw_kappa(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v, v_p, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ v_p = c000
+ + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs))))
+ + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020
+ + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs)
+ + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201
+ + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs))
+ + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys)))
+ + z*( c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys)
+ + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z))));
+
+ return (-1e-8*v_p/v);
+}
+/*
+!==========================================================================
+elemental function gsw_kappa_const_t_ice (t, p)
+!==========================================================================
+!
+! Calculates isothermal compressibility of ice.
+! Note. This is the compressibility of ice AT CONSTANT IN-SITU
+! TEMPERATURE
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! kappa_const_t_ice = isothermal compressibility [ 1/Pa ]
+! Note. The output units are 1/Pa not 1/dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_kappa_const_t_ice(double t, double p)
+{
+ return (-gsw_gibbs_ice(0,2,t,p)/gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_kappa_ice (t, p)
+!==========================================================================
+!
+! Calculates the isentropic compressibility of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! kappa_ice = isentropic compressibility [ 1/Pa ]
+! Note. The output units are 1/Pa not 1/dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_kappa_ice(double t, double p)
+{
+ double gi_tp, gi_tt;
+
+ gi_tt = gsw_gibbs_ice(2,0,t,p);
+ gi_tp = gsw_gibbs_ice(1,1,t,p);
+
+ return ((gi_tp*gi_tp - gi_tt*gsw_gibbs_ice(0,2,t,p))/
+ (gsw_gibbs_ice(0,1,t,p)*gi_tt));
+}
+/*
+!==========================================================================
+function gsw_kappa_t_exact(sa,t,p)
+!==========================================================================
+
+! isentropic compressibility of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_kappa_t_exact : isentropic compressibility [1/Pa]
+*/
+double
+gsw_kappa_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1, n2=2;
+ double g_tt, g_tp;
+
+ g_tt = gsw_gibbs(n0,n2,n0,sa,t,p);
+ g_tp = gsw_gibbs(n0,n1,n1,sa,t,p);
+
+ return ((g_tp*g_tp - g_tt*gsw_gibbs(n0,n0,n2,sa,t,p)) /
+ (gsw_gibbs(n0,n0,n1,sa,t,p)*g_tt));
+}
+/*
+!==========================================================================
+function gsw_latentheat_evap_ct(sa,ct)
+!==========================================================================
+
+! Calculates latent heat, or enthalpy, of evaporation.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! latentheat_evaporation : latent heat of evaporation [J/kg]
+*/
+double
+gsw_latentheat_evap_ct(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double c0 = 2.499065844825125e6, c1 = -1.544590633515099e-1,
+ c2 = -9.096800915831875e4, c3 = 1.665513670736000e2,
+ c4 = 4.589984751248335e1, c5 = 1.894281502222415e1,
+ c6 = 1.192559661490269e3, c7 = -6.631757848479068e3,
+ c8 = -1.104989199195898e2, c9 = -1.207006482532330e3,
+ c10 = -3.148710097513822e3, c11 = 7.437431482069087e2,
+ c12 = 2.519335841663499e3, c13 = 1.186568375570869e1,
+ c14 = 5.731307337366114e2, c15 = 1.213387273240204e3,
+ c16 = 1.062383995581363e3, c17 = -6.399956483223386e2,
+ c18 = -1.541083032068263e3, c19 = 8.460780175632090e1,
+ c20 = -3.233571307223379e2, c21 = -2.031538422351553e2,
+ c22 = 4.351585544019463e1, c23 = -8.062279018001309e2,
+ c24 = 7.510134932437941e2, c25 = 1.797443329095446e2,
+ c26 = -2.389853928747630e1, c27 = 1.021046205356775e2;
+
+ double x, y;
+
+ x = sqrt(gsw_sfac*sa);
+ y = ct/40.0;
+
+ return (c0 + x*(c1 + c4*y + x*(c3
+ + y*(c7 + c12*y) + x*(c6 + y*(c11 + y*(c17 + c24*y))
+ + x*(c10 + y*(c16 + c23*y) + x*(c15 + c22*y + c21*x)))))
+ + y*(c2 + y*(c5 + c8*x + y*(c9 + x*(c13 + c18*x)
+ + y*(c14 + x*(c19 + c25*x) + y*(c20 + c26*x + c27*y))))));
+}
+/*
+!==========================================================================
+function gsw_latentheat_evap_t(sa,t)
+!==========================================================================
+!
+! Calculates latent heat, or enthalpy, of evaporation.
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+!
+! gsw_latentheat_evap_t : latent heat of evaporation [J/kg]
+*/
+double
+gsw_latentheat_evap_t(double sa, double t)
+{
+
+ double ct = gsw_ct_from_pt(sa,t);
+
+ return (gsw_latentheat_evap_ct(sa,ct));
+}
+/*
+!--------------------------------------------------------------------------
+! isobaric melting enthalpy and isobaric evaporation enthalpy
+!--------------------------------------------------------------------------
+
+!==========================================================================
+function gsw_latentheat_melting(sa,p)
+!==========================================================================
+
+! Calculates latent heat, or enthalpy, of melting.
+!
+! sa : Absolute Salinity [g/kg]
+! p : sea pressure [dbar]
+!
+! latentheat_melting : latent heat of melting [kg/m^3]
+*/
+double
+gsw_latentheat_melting(double sa, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double tf = gsw_t_freezing(sa,p,0.0);
+
+ return (1000.0*(gsw_chem_potential_water_t_exact(sa,tf,p)
+ - (gsw_t0 + tf)*gsw_t_deriv_chem_potential_water_t_exact(sa,tf,p))
+ - gsw_enthalpy_ice(tf,p));
+}
+/*
+!==========================================================================
+pure subroutine gsw_linear_interp_sa_ct (sa, ct, p, p_i, sa_i, ct_i)
+!==========================================================================
+! This function interpolates the cast with respect to the interpolating
+! variable p. This function finds the values of SA, CT at p_i on this cast.
+!
+! VERSION NUMBER: 3.05 (27th January 2015)
+!
+! This function was adapted from Matlab's interp1q.
+!==========================================================================
+*/
+void
+gsw_linear_interp_sa_ct(double *sa, double *ct, double *p, int np,
+ double *p_i, int npi, double *sa_i, double *ct_i)
+{
+ char *in_rng;
+ int *j, *k, *r, *jrev, *ki, imax_p, imin_p, i, n, m, ii;
+ double *xi, *xxi, u, max_p, min_p;
+
+ min_p = max_p = p[0];
+ imin_p = imax_p = 0;
+ for (i=1; i<np; i++) {
+ if (p[i] < min_p) {
+ min_p = p[i];
+ imin_p = i;
+ } else if (p[i] > max_p) {
+ max_p = p[i];
+ imax_p = i;
+ }
+ }
+ in_rng = (char *) malloc(npi*sizeof (char));
+ memset(in_rng, 0, npi*sizeof (char));
+ for (i=n=0; i<npi; i++) {
+ if (p_i[i] <= min_p) {
+ sa_i[i] = sa[imin_p];
+ ct_i[i] = ct[imin_p];
+ } else if (p_i[i] >= max_p) {
+ sa_i[i] = sa[imax_p];
+ ct_i[i] = ct[imax_p];
+ } else {
+ in_rng[i] = 1;
+ n++;
+ }
+ }
+ if (n==0)
+ return;
+
+ xi =(double *) malloc(n*sizeof (double));
+ k = (int *) malloc(3*n*sizeof (int)); ki = k+n; r = ki+n;
+ m = np + n;
+ xxi = (double *) malloc(m*sizeof (double));
+ j = (int *) malloc(2*m*sizeof (int)); jrev = j+m;
+
+ ii = 0;
+ for (i = 0; i<npi; i++) {
+ if (in_rng[i]) {
+ xi[ii] = p_i[i];
+ ki[ii] = i;
+ ii++;
+ }
+ }
+ free(in_rng);
+ /*
+ ** Note that the following operations on the index
+ ** vectors jrev and r depend on the sort utility
+ ** gsw_util_sort_real() consistently ordering the
+ ** sorting indexes either in ascending or descending
+ ** sequence for replicate values in the real vector.
+ */
+ gsw_util_sort_real(xi, n, k);
+ for (i = 0; i<np; i++)
+ xxi[i] = p[i];
+ for (i = 0; i<n; i++)
+ xxi[np+i] = xi[k[i]];
+ gsw_util_sort_real(xxi, m, j);
+
+ for (i = 0; i<m; i++)
+ jrev[j[i]] = i;
+ for (i = 0; i<n; i++)
+ r[k[i]] = jrev[np+i]-i-1;
+
+ for (i = 0; i<n; i++) {
+ u = (xi[i]-p[r[i]])/(p[r[i]+1]-p[r[i]]);
+ sa_i[ki[i]] = sa[r[i]] + (sa[r[i]+1]-sa[r[i]])*u;
+ ct_i[ki[i]] = ct[r[i]] + (ct[r[i]+1]-ct[r[i]])*u;
+ }
+ free(j); free(xxi); free(k); free(xi);
+}
+/*
+!==========================================================================
+elemental function gsw_melting_ice_equilibrium_sa_ct_ratio (sa, p)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when ice melts into seawater
+! with both the seawater and the seaice temperatures being almost equal to
+! the equilibrium freezing temperature. It is assumed that a small mass
+! of ice melts into an infinite mass of seawater. If indeed the
+! temperature of the seawater and the ice were both equal to the freezing
+! temperature, then no melting or freezing would occur an imbalance
+! between these three temperatures is needed for freezing or melting to
+! occur (the three temperatures being (1) the seawater temperature,
+! (2) the ice temperature, and (3) the freezing temperature.
+!
+! The output, melting_ice_equilibrium_SA_CT_ratio, is dSA/dCT rather than
+! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero
+! whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+!
+! melting_ice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT
+! changes when ice melts into seawater, with
+! the seawater and seaice being close to the
+! freezing temperature. [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_ice_equilibrium_sa_ct_ratio(double sa, double p)
+{
+ double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ t_seaice = gsw_t_freezing(sa,p,saturation_fraction);
+
+ h = gsw_enthalpy_ct_exact(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+ /*note that h_hat_ct is equal to cp0*(273.15 + t)/(273.15 + pt0)*/
+
+ return (sa*h_hat_ct/(h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_ice_equilibrium_sa_ct_ratio_poly (sa, p)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when ice melts into seawater
+! with both the seawater and the seaice temperatures being almost equal to
+! the equilibrium freezing temperature. It is assumed that a small mass
+! of ice melts into an infinite mass of seawater. If indeed the
+! temperature of the seawater and the ice were both equal to the freezing
+! temperature, then no melting or freezing would occur an imbalance
+! between these three temperatures is needed for freezing or melting to
+! occur (the three temperatures being (1) the seawater temperature,
+! (2) the ice temperature, and (3) the freezing temperature.
+!
+! The output, melting_ice_equilibrium_SA_CT_ratio, is dSA/dCT rather than
+! dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is zero
+! whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+!
+! melting_ice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT
+! changes when ice melts into seawater, with
+! the seawater and seaice being close to the
+! freezing temperature. [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_ice_equilibrium_sa_ct_ratio_poly(double sa, double p)
+{
+ double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ t_seaice = gsw_t_freezing_poly(sa,p,saturation_fraction);
+
+ h = gsw_enthalpy(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+ /*note that h_hat_ct is equal to cp0*(273.15 + t)/(273.15 + pt0)*/
+
+ return (sa*h_hat_ct / (h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_melting_ice_into_seawater (sa, ct, p, w_ih, t_ih,&
+ sa_final, ct_final, w_ih_final)
+!==========================================================================
+!
+! Calculates the final Absolute Salinity, final Conservative Temperature
+! and final ice mass fraction that results when a given mass fraction of
+! ice melts and is mixed into seawater whose properties are (SA,CT,p).
+! This code takes the seawater to contain no dissolved air.
+!
+! When the mass fraction w_Ih_final is calculated as being a positive
+! value, the seawater-ice mixture is at thermodynamic equlibrium.
+!
+! This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk,
+! is sufficiently large (i.e. sufficiently "warm") so that there is no ice
+! present in the final state. In this case the final state consists of
+! only seawater rather than being an equlibrium mixture of seawater and
+! ice which occurs when w_Ih_final is positive. Note that when
+! w_Ih_final = 0, the final seawater is not at the freezing temperature.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! w_Ih = mass fraction of ice, that is the mass of ice divided by the
+! sum of the masses of ice and seawater. That is, the mass of
+! ice divided by the mass of the final mixed fluid.
+! w_Ih must be between 0 and 1. [ unitless ]
+! t_Ih = the in-situ temperature of the ice (ITS-90) [ deg C ]
+!
+! SA_final = Absolute Salinity of the seawater in the final state,
+! whether or not any ice is present. [ g/kg ]
+! CT_final = Conservative Temperature of the seawater in the the final
+! state, whether or not any ice is present. [ deg C ]
+! w_Ih_final = mass fraction of ice in the final seawater-ice mixture.
+! If this ice mass fraction is positive, the system is at
+! thermodynamic equilibrium. If this ice mass fraction is
+! zero there is no ice in the final state which consists
+! only of seawater which is warmer than the freezing
+! temperature. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_melting_ice_into_seawater(double sa, double ct, double p, double w_ih,
+ double t_ih, double *sa_final, double *ct_final, double *w_ih_final)
+{
+ double ctf, h_bulk, sa_bulk, tf_ih;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*The seawater ct input is below the freezing temp*/
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ tf_ih = gsw_t_freezing(0.0,p,saturation_fraction) - 1e-6;
+ if (t_ih > tf_ih) {
+ /*
+ ! t_ih input exceeds the freezing temp.
+ ! The 1e-6 C buffer in the allowable
+ ! t_Ih is to ensure that there is some ice Ih in the sea ice.
+ */
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+
+ sa_bulk = (1.0 - w_ih)*sa;
+ h_bulk = (1.0 - w_ih)*gsw_enthalpy_ct_exact(sa,ct,p)
+ + w_ih*gsw_enthalpy_ice(t_ih,p);
+ gsw_frazil_properties(sa_bulk,h_bulk,p,sa_final,ct_final,w_ih_final);
+ if (*sa_final > GSW_ERROR_LIMIT) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ *w_ih_final = *sa_final;
+ return;
+ }
+}
+/*
+!==========================================================================
+elemental function gsw_melting_ice_sa_ct_ratio (sa, ct, p, t_ih)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when ice melts into seawater.
+! It is assumed that a small mass of ice melts into an infinite mass of
+! seawater. Because of the infinite mass of seawater, the ice will always
+! melt.
+!
+! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA.
+! This is done so that when SA = 0, the output, dSA/dCT is zero whereas
+! dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! t_Ih = the in-situ temperature of the ice (ITS-90) [ deg C ]
+!
+! melting_ice_SA_CT_ratio = the ratio of SA to CT changes when ice melts
+! into a large mass of seawater
+! [ g kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_ice_sa_ct_ratio(double sa, double ct, double p, double t_ih)
+{
+ double ctf, h, h_ih, tf, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*the seawater ct input is below the freezing temperature*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ tf = gsw_t_freezing(0.0,p,saturation_fraction);
+ if (t_ih > tf) {
+ /*t_ih exceeds the freezing temperature at sa = 0*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_ih,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ct,p,&h_hat_sa,&h_hat_ct);
+ /*Note that h_hat_CT is equal to cp0*(273.15 + t)/(273.15 + pt0)*/
+
+ return (sa*h_hat_ct/(h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_ice_sa_ct_ratio_poly (sa, ct, p, t_ih)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when ice melts into seawater.
+! It is assumed that a small mass of ice melts into an infinite mass of
+! seawater. Because of the infinite mass of seawater, the ice will always
+! melt.
+!
+! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA.
+! This is done so that when SA = 0, the output, dSA/dCT is zero whereas
+! dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325d0 dbar )
+! t_Ih = the in-situ temperature of the ice (ITS-90) [ deg C ]
+!
+! melting_ice_SA_CT_ratio = the ratio of SA to CT changes when ice melts
+! into a large mass of seawater
+! [ g kg^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_ice_sa_ct_ratio_poly(double sa, double ct, double p, double t_ih)
+{
+ double ctf, h, h_ih, tf, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*the seawater ct input is below the freezing temperature*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ tf = gsw_t_freezing_poly(0.0,p,saturation_fraction);
+ if (t_ih > tf) {
+ /*t_ih exceeds the freezing temperature at sa = 0*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ h = gsw_enthalpy(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_ih,p);
+ gsw_enthalpy_first_derivatives(sa,ct,p,&h_hat_sa,&h_hat_ct);
+ /*Note that h_hat_CT is equal to cp0*(273.15 + t)/(273.15 + pt0)*/
+
+ return (sa*h_hat_ct/(h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_seaice_equilibrium_sa_ct_ratio (sa, p)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when sea ice melts into
+! seawater with both the seawater and the sea ice temperatures being
+! almost equal to the equilibrium freezing temperature. It is assumed
+! that a small mass of seaice melts into an infinite mass of seawater. If
+! indeed the temperature of the seawater and the sea ice were both equal
+! to the freezing temperature, then no melting or freezing would occur; an
+! imbalance between these three temperatures is needed for freezing or
+! melting to occur (the three temperatures being (1) the seawater
+! temperature, (2) the sea ice temperature, and (3) the freezing
+! temperature.
+!
+! Note that the output of this function, dSA/dCT is independent of the
+! sea ice salinity, SA_seaice. That is, the output applies equally to
+! pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result
+! is proven in the manuscript, McDougall et al. (2013).
+!
+! The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather
+! than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is
+! zero whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! melting_seaice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT
+! changes when sea ice melts into seawater, with
+! the seawater and sea ice being close to the
+! freezing temperature. [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_seaice_equilibrium_sa_ct_ratio(double sa, double p)
+{
+ double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ t_seaice = gsw_t_freezing(sa,p,saturation_fraction);
+
+ h = gsw_enthalpy_ct_exact(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+
+ return (sa*h_hat_ct / (h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_seaice_equilibrium_sa_ct_ratio_poly (sa, p)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when sea ice melts into
+! seawater with both the seawater and the sea ice temperatures being
+! almost equal to the equilibrium freezing temperature. It is assumed
+! that a small mass of seaice melts into an infinite mass of seawater. If
+! indeed the temperature of the seawater and the sea ice were both equal
+! to the freezing temperature, then no melting or freezing would occur; an
+! imbalance between these three temperatures is needed for freezing or
+! melting to occur (the three temperatures being (1) the seawater
+! temperature, (2) the sea ice temperature, and (3) the freezing
+! temperature.
+!
+! Note that the output of this function, dSA/dCT is independent of the
+! sea ice salinity, SA_seaice. That is, the output applies equally to
+! pure ice Ih and to sea ice with seaice salinity, SA_seaice. This result
+! is proven in the manuscript, McDougall et al. (2013).
+!
+! The output, melting_seaice_equilibrium_SA_CT_ratio, is dSA/dCT rather
+! than dCT/dSA. This is done so that when SA = 0, the output, dSA/dCT is
+! zero whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! melting_seaice_equilibrium_SA_CT_ratio = the ratio dSA/dCT of SA to CT
+! changes when sea ice melts into seawater, with
+! the seawater and sea ice being close to the
+! freezing temperature. [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_seaice_equilibrium_sa_ct_ratio_poly(double sa, double p)
+{
+ double ctf, h, h_ih, t_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ t_seaice = gsw_t_freezing_poly(sa,p,saturation_fraction);
+
+ h = gsw_enthalpy(sa,ctf,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives(sa,ctf,p,&h_hat_sa,&h_hat_ct);
+
+ return (sa*h_hat_ct / (h - h_ih - sa*h_hat_sa));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_melting_seaice_into_seawater (sa, ct, p, &
+ w_seaice, sa_seaice, t_seaice, sa_final, ct_final)
+!==========================================================================
+!
+! Calculates the Absolute Salinity and Conservative Temperature that
+! results when a given mass of sea ice (or ice) melts and is mixed into a
+! known mass of seawater (whose properties are (SA,CT,p)).
+!
+! If the ice contains no salt (e.g. if it is of glacial origin), then the
+! input 'SA_seaice' should be set to zero.
+!
+! Ice formed at the sea surface (sea ice) typically contains between 2 g/kg
+! and 12 g/kg of salt (defined as the mass of salt divided by the mass of
+! ice Ih plus brine) and this programme returns NaN's if the input
+! SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero,
+! usually this would imply that the pressure p should be zero, as sea ice
+! only occurs near the sea surface. The code does not impose that p = 0
+! if SA_seaice is non-zero. Rather, this is left to the user.
+!
+! The Absolute Salinity, SA_brine, of the brine trapped in little pockets
+! in the sea ice, is in thermodynamic equilibrium with the ice Ih that
+! surrounds these pockets. As the sea ice temperature, t_seaice, may be
+! less than the freezing temperature, SA_brine is usually greater than the
+! Absolute Salinity of the seawater at the time and place when and where
+! the sea ice was formed. So usually SA_brine will be larger than SA.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! w_seaice = mass fraction of sea ice, that is the mass of sea ice
+! divided by the sum of the masses of sea ice and seawater.
+! That is, the mass of sea ice divided by the mass of the
+! final mixed fluid. w_seaice must be between 0 and 1.
+! [ unitless ]
+! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction of
+! salt in sea ice, expressed in g of salt per kg of sea ice.
+! [ g/kg ]
+! t_seaice = the in-situ temperature of the sea ice (or ice) (ITS-90)
+! [ deg C ]
+!
+! SA_final = Absolute Salinity of the mixture of the melted sea ice
+! (or ice) and the orignal seawater [ g/kg ]
+! CT_final = Conservative Temperature of the mixture of the melted
+! sea ice (or ice) and the orignal seawater [ deg C ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_melting_seaice_into_seawater(double sa, double ct, double p,
+ double w_seaice, double sa_seaice, double t_seaice,
+ double *sa_final, double *ct_final)
+{
+ double ctf, h, h_brine, h_final, h_ih, sa_brine, tf_sa_seaice;
+ double saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*The seawater ct input is below the freezing temp*/
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ return;
+ }
+
+ tf_sa_seaice = gsw_t_freezing(sa_seaice,p,saturation_fraction)
+ - 1e-6;
+ if (t_seaice > tf_sa_seaice) {
+ /*
+ ! The 1e-6 C buffer in the allowable t_seaice is to ensure that there is
+ ! some ice Ih in the sea ice. Without this buffer, that is if t_seaice
+ ! is allowed to be exactly equal to tf_sa_seaice, the seaice is
+ ! actually 100% brine at Absolute Salinity of SA_seaice.
+ */
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ return;
+ }
+
+ sa_brine = gsw_sa_freezing_from_t(t_seaice,p,saturation_fraction);
+ if (sa_brine >= GSW_ERROR_LIMIT) {
+ *sa_final = GSW_INVALID_VALUE;
+ *ct_final = *sa_final;
+ return;
+ }
+ h_brine = gsw_enthalpy_t_exact(sa_brine,t_seaice,p);
+
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+
+ h_final = h - w_seaice*(h - h_ih - (h_brine - h_ih)*sa_seaice/sa_brine);
+
+ *sa_final = sa - w_seaice*(sa - sa_seaice);
+ /*
+ !ctf = gsw_ct_freezing(sa_final,p,saturation_fraction)
+ !
+ !if (h_final .lt. gsw_enthalpy_ct_exact(sa_final,ctf,p)) then
+ ! ! Melting this much seaice is not possible as it would result in
+ ! ! frozen seawater
+ ! sa_final = gsw_error_code(4,func_name)
+ ! ct_final = sa_final
+ ! return
+ !end if
+ */
+ *ct_final = gsw_ct_from_enthalpy_exact(*sa_final,h_final,p);
+ if (*ct_final > GSW_ERROR_LIMIT) {
+ *sa_final = *ct_final;
+ return;
+ }
+}
+/*
+!==========================================================================
+elemental function gsw_melting_seaice_sa_ct_ratio (sa, ct, p, sa_seaice, &
+ t_seaice)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when sea ice melts into seawater.
+! It is assumed that a small mass of sea ice melts into an infinite mass of
+! seawater. Because of the infinite mass of seawater, the sea ice will
+! always melt.
+!
+! Ice formed at the sea surface (sea ice) typically contains between 2 g/kg
+! and 12 g/kg of salt (defined as the mass of salt divided by the mass of
+! ice Ih plus brine) and this programme returns NaN's if the input
+! SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero,
+! usually this would imply that the pressure p should be zero, as sea ice
+! only occurs near the sea surface. The code does not impose that p = 0 if
+! SA_seaice is non-zero. Rather, this is left to the user.
+!
+! The Absolute Salinity, SA_brine, of the brine trapped in little pockets
+! in the sea ice, is in thermodynamic equilibrium with the ice Ih that
+! surrounds these pockets. As the seaice temperature, t_seaice, may be
+! less than the freezing temperature, SA_brine is usually greater than the
+! Absolute Salinity of the seawater at the time and place when and where
+! the sea ice was formed. So usually SA_brine will be larger than SA.
+!
+! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA.
+! This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is
+! zero whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction
+! of salt in sea ice expressed in g of salt per kg of
+! sea ice [ g/kg ]
+! t_seaice = the in-situ temperature of the sea ice (ITS-90) [ deg C ]
+!
+! melting_seaice_SA_CT_ratio = the ratio dSA/dCT of SA to CT changes when
+! sea ice melts into a large mass of seawater [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_seaice_sa_ct_ratio(double sa, double ct, double p,
+ double sa_seaice, double t_seaice)
+{
+ double ctf, delsa, h, h_brine, h_ih, sa_brine,
+ tf_sa_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ if (sa_seaice < 0.0 || sa_seaice > 15.0) {
+ return (GSW_INVALID_VALUE);
+ }
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) { /*the seawater ct input is below the freezing temp*/
+ return (GSW_INVALID_VALUE);
+ }
+ tf_sa_seaice = gsw_t_freezing(sa_seaice,p,saturation_fraction) - 1e-6;
+ if (t_seaice > tf_sa_seaice) { /*t_seaice exceeds the freezing sa*/
+ return (GSW_INVALID_VALUE);
+ }
+ /*
+ !-----------------------------------------------------------------------
+ !The 1e-6 C buffer in the allowable t_seaice is to ensure that there is
+ !some ice Ih in the sea ice. Without this buffer, that is if t_seaice
+ !is allowed to be exactly equal to tf_sa_seaice, the sea ice is actually
+ !100% brine at Absolute Salinity of SA_seaice.
+ !-----------------------------------------------------------------------
+ */
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives_ct_exact(sa,ct,p,&h_hat_sa,&h_hat_ct);
+
+ sa_brine = gsw_sa_freezing_from_t(t_seaice,p,saturation_fraction);
+ if (sa_brine > GSW_ERROR_LIMIT) {
+ return (GSW_INVALID_VALUE);
+ }
+ h_brine = gsw_enthalpy_t_exact(sa_brine,t_seaice,p);
+ delsa = sa - sa_seaice;
+
+ return (h_hat_ct*delsa /
+ (h - h_ih - delsa*h_hat_sa - sa_seaice*(h_brine - h_ih)/sa_brine));
+}
+/*
+!==========================================================================
+elemental function gsw_melting_seaice_sa_ct_ratio_poly (sa, ct, p, &
+ sa_seaice, t_seaice)
+!==========================================================================
+!
+! Calculates the ratio of SA to CT changes when sea ice melts into seawater.
+! It is assumed that a small mass of sea ice melts into an infinite mass of
+! seawater. Because of the infinite mass of seawater, the sea ice will
+! always melt.
+!
+! Ice formed at the sea surface (sea ice) typically contains between 2 g/kg
+! and 12 g/kg of salt (defined as the mass of salt divided by the mass of
+! ice Ih plus brine) and this programme returns NaN's if the input
+! SA_seaice is greater than 15 g/kg. If the SA_seaice input is not zero,
+! usually this would imply that the pressure p should be zero, as sea ice
+! only occurs near the sea surface. The code does not impose that p = 0 if
+! SA_seaice is non-zero. Rather, this is left to the user.
+!
+! The Absolute Salinity, SA_brine, of the brine trapped in little pockets
+! in the sea ice, is in thermodynamic equilibrium with the ice Ih that
+! surrounds these pockets. As the seaice temperature, t_seaice, may be
+! less than the freezing temperature, SA_brine is usually greater than the
+! Absolute Salinity of the seawater at the time and place when and where
+! the sea ice was formed. So usually SA_brine will be larger than SA.
+!
+! The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA.
+! This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is
+! zero whereas dCT/dSA would be infinite.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure at which the melting occurs [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction
+! of salt in sea ice expressed in g of salt per kg of
+! sea ice [ g/kg ]
+! t_seaice = the in-situ temperature of the sea ice (ITS-90) [ deg C ]
+!
+! melting_seaice_SA_CT_ratio = the ratio dSA/dCT of SA to CT changes when
+! sea ice melts into a large mass of seawater [ g/(kg K) ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_melting_seaice_sa_ct_ratio_poly(double sa, double ct, double p,
+ double sa_seaice, double t_seaice)
+{
+ double ctf, delsa, h, h_brine, h_ih, sa_brine, ct_brine,
+ tf_sa_seaice, h_hat_sa, h_hat_ct;
+ double saturation_fraction = 0.0;
+
+ if (sa_seaice < 0.0 || sa_seaice > 15.0) {
+ return (GSW_INVALID_VALUE);
+ }
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ if (ct < ctf) { /*the seawater ct input is below the freezing temp*/
+ return (GSW_INVALID_VALUE);
+ }
+
+ tf_sa_seaice = gsw_t_freezing_poly(sa_seaice,p,saturation_fraction)
+ - 1e-6;
+ if (t_seaice > tf_sa_seaice) { /*t_seaice exceeds the freezing sa*/
+ return (GSW_INVALID_VALUE);
+ }
+ /*
+ !-----------------------------------------------------------------------
+ !The 1e-6 C buffer in the allowable t_seaice is to ensure that there is
+ !some ice Ih in the sea ice. Without this buffer, that is if t_seaice
+ !is allowed to be exactly equal to tf_sa_seaice, the sea ice is actually
+ !100% brine at Absolute Salinity of SA_seaice.
+ !-----------------------------------------------------------------------
+ */
+ h = gsw_enthalpy(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+ gsw_enthalpy_first_derivatives(sa,ct,p,&h_hat_sa,&h_hat_ct);
+
+ sa_brine = gsw_sa_freezing_from_t_poly(t_seaice,p,saturation_fraction);
+ if (sa_brine > GSW_ERROR_LIMIT) {
+ return (GSW_INVALID_VALUE);
+ }
+ ct_brine = gsw_ct_from_t(sa_brine,t_seaice,p);
+ h_brine = gsw_enthalpy(sa_brine,ct_brine,p);
+ delsa = sa - sa_seaice;
+
+ return (h_hat_ct*delsa /
+ (h - h_ih - delsa*h_hat_sa - sa_seaice*(h_brine - h_ih)/sa_brine));
+}
+/*
+!--------------------------------------------------------------------------
+! water column properties, based on the 48-term expression for density
+!--------------------------------------------------------------------------
+
+!==========================================================================
+subroutine gsw_nsquared(sa,ct,p,lat,nz,n2,p_mid)
+!==========================================================================
+
+! Calculates the buoyancy frequency squared (N^2)(i.e. the Brunt-Vaisala
+! frequency squared) at the mid pressure from the equation,
+!
+!
+! 2 2 beta.d(SA) - alpha.d(CT)
+! N = g .rho_local. -------------------------
+! dP
+!
+! The pressure increment, dP, in the above formula is in Pa, so that it is
+! 10^4 times the pressure increment dp in dbar.
+!
+! sa : Absolute Salinity (a profile (length nz)) [g/kg]
+! ct : Conservative Temperature (a profile (length nz)) [deg C]
+! p : sea pressure (a profile (length nz)) [dbar]
+! lat : latitude (a profile (length nz)) [deg N]
+! nz : number of levels in the profile
+! n2 : Brunt-Vaisala Frequency squared (length nz-1) [s^-2]
+! p_mid : Mid pressure between p grid (length nz-1) [dbar]
+*/
+void
+gsw_nsquared(double *sa, double *ct, double *p, double *lat, int nz,
+ double *n2, double *p_mid)
+{
+ GSW_TEOS10_CONSTANTS;
+ int k;
+ double p_grav, n_grav, grav_local, dsa, sa_mid, dct, ct_mid,
+ dp, rho_mid, alpha_mid, beta_mid;
+
+ if (nz < 2)
+ return;
+ p_grav = gsw_grav(lat[0],p[0]);
+ for (k = 0; k < nz-1; k++) {
+ n_grav = gsw_grav(lat[k+1],p[k+1]);
+ grav_local = 0.5*(p_grav + n_grav);
+ dsa = (sa[k+1] - sa[k]);
+ sa_mid = 0.5*(sa[k] + sa[k+1]);
+ dct = (ct[k+1] - ct[k]);
+ ct_mid = 0.5*(ct[k] + ct[k+1]);
+ dp = (p[k+1] - p[k]);
+ p_mid[k] = 0.5*(p[k] + p[k+1]);
+ rho_mid = gsw_rho(sa_mid,ct_mid,p_mid[k]);
+ alpha_mid = gsw_alpha(sa_mid,ct_mid,p_mid[k]);
+ beta_mid = gsw_beta(sa_mid,ct_mid,p_mid[k]);
+
+ n2[k] = (grav_local*grav_local)*(rho_mid/(db2pa*dp))*
+ (beta_mid*dsa - alpha_mid*dct);
+ p_grav = n_grav;
+ }
+}
+/*
+!==========================================================================
+function gsw_p_from_z(z,lat)
+!==========================================================================
+
+! Calculates the pressure p from height z
+!
+! z : height [m]
+! lat : latitude [deg]
+!
+! gsw_p_from_z : pressure [dbar]
+*/
+double
+gsw_p_from_z(double z, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double sinlat, sin2, gs, c1, p, df_dp, f, p_old, p_mid;
+
+ if (z > 5) return GSW_INVALID_VALUE;
+
+ sinlat = sin(lat*deg2rad);
+ sin2 = sinlat*sinlat;
+ gs = 9.780327*(1.0 + (5.2792e-3 + (2.32e-5*sin2))*sin2);
+
+ /* get the first estimate of p from Saunders (1981) */
+ c1 = 5.25e-3*sin2 + 5.92e-3;
+ p = -2.0*z/((1-c1) + sqrt((1-c1)*(1-c1) + 8.84e-6*z)) ;
+ /* end of the first estimate from Saunders (1981) */
+
+ df_dp = db2pa*gsw_specvol_sso_0(p); /* initial value of the derivative of f */
+
+ f = gsw_enthalpy_sso_0(p) + gs*(z - 0.5*gamma*(z*z));
+ /* - (geo_strf_dyn_height + sea_surface_geopotental); */
+ p_old = p;
+ p = p_old - f/df_dp;
+ p_mid = 0.5*(p + p_old);
+ df_dp = db2pa*gsw_specvol_sso_0(p_mid);
+ p = p_old - f/df_dp;
+
+ return p;
+}
+/*
+!==========================================================================
+elemental function gsw_pot_enthalpy_from_pt_ice (pt0_ice)
+!==========================================================================
+!
+! Calculates the potential enthalpy of ice from potential temperature of
+! ice (whose reference sea pressure is zero dbar).
+!
+! pt0_ice = potential temperature of ice (ITS-90) [ deg C ]
+!
+! gsw_pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pot_enthalpy_from_pt_ice(double pt0_ice)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_GIBBS_ICE_COEFFICIENTS;
+ double tau;
+ std::complex<double> h0_part, sqtau_t1, sqtau_t2;
+
+ tau = (pt0_ice + gsw_t0)*rec_tt;
+
+ sqtau_t1 = (tau/t1)*(tau/t1);
+ sqtau_t2 = (tau/t2)*(tau/t2);
+
+ h0_part = r1*t1*(log(1.0 - sqtau_t1) + sqtau_t1)
+ + r20*t2*(log(1.0 - sqtau_t2) + sqtau_t2);
+
+ return (g00 + tt*real(h0_part));
+}
+/*
+!==========================================================================
+elemental function gsw_pot_enthalpy_from_pt_ice_poly (pt0_ice)
+!==========================================================================
+!
+! Calculates the potential enthalpy of ice from potential temperature of
+! ice (whose reference sea pressure is zero dbar). This is a
+! compuationally efficient polynomial fit to the potential enthalpy of
+! ice.
+!
+! pt0_ice = potential temperature of ice (ITS-90) [ deg C ]
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pot_enthalpy_from_pt_ice_poly(double pt0_ice)
+{
+ int iteration;
+ double df_dt, f, pot_enthalpy_ice,
+ pot_enthalpy_ice_mid, pot_enthalpy_ice_old,
+ p0 = -3.333601570157700e5,
+ p1 = 2.096693916810367e3,
+ p2 = 3.687110754043292,
+ p3 = 4.559401565980682e-4,
+ p4 = -2.516011957758120e-6,
+ p5 = -1.040364574632784e-8,
+ p6 = -1.701786588412454e-10,
+ p7 = -7.667191301635057e-13;
+
+ /*initial estimate of the potential enthalpy.*/
+ pot_enthalpy_ice = p0 + pt0_ice*(p1 + pt0_ice*(p2 + pt0_ice*(p3
+ + pt0_ice*(p4 + pt0_ice*(p5 + pt0_ice*(p6
+ + pt0_ice*p7))))));
+
+ df_dt = gsw_pt_from_pot_enthalpy_ice_poly_dh(pot_enthalpy_ice);
+
+ for (iteration = 1; iteration <= 5; iteration++) {
+ pot_enthalpy_ice_old = pot_enthalpy_ice;
+ f = gsw_pt_from_pot_enthalpy_ice_poly(pot_enthalpy_ice_old)
+ - pt0_ice;
+ pot_enthalpy_ice = pot_enthalpy_ice_old - f/df_dt;
+ pot_enthalpy_ice_mid = 0.5*(pot_enthalpy_ice+pot_enthalpy_ice_old);
+ df_dt = gsw_pt_from_pot_enthalpy_ice_poly_dh(pot_enthalpy_ice_mid);
+ pot_enthalpy_ice = pot_enthalpy_ice_old - f/df_dt;
+ }
+ /*
+ ! The error of this fit ranges between -6e-3 and 6e-3 J/kg over the
+ | potential temperature range of -100 to 2 deg C, or the potential
+ | enthalpy range of -5.7 x 10^5 to -3.3 x 10^5 J/kg.
+ */
+ return (pot_enthalpy_ice);
+}
+/*
+!==========================================================================
+elemental function gsw_pot_enthalpy_ice_freezing (sa, p)
+!==========================================================================
+!
+! Calculates the potential enthalpy of ice at which seawater freezes.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pot_enthalpy_ice_freezing = potential enthalpy of ice at freezing
+! of seawater [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pot_enthalpy_ice_freezing(double sa, double p)
+{
+ double pt0_ice, t_freezing;
+
+ t_freezing = gsw_t_freezing(sa,p,0.0) ;
+
+ pt0_ice = gsw_pt0_from_t_ice(t_freezing,p);
+
+ return (gsw_pot_enthalpy_from_pt_ice(pt0_ice));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_pot_enthalpy_ice_freezing_first_derivatives (sa, &
+ p, pot_enthalpy_ice_freezing_sa, pot_enthalpy_ice_freezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the potential enthalpy of ice at
+! which seawater freezes, with respect to Absolute Salinity SA and
+! pressure P (in Pa).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pot_enthalpy_ice_freezing_SA = the derivative of the potential enthalpy
+! of ice at freezing (ITS-90) with respect to Absolute
+! salinity at fixed pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! pot_enthalpy_ice_freezing_P = the derivative of the potential enthalpy
+! of ice at freezing (ITS-90) with respect to pressure
+! (in Pa) at fixed Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_pot_enthalpy_ice_freezing_first_derivatives(double sa, double p,
+ double *pot_enthalpy_ice_freezing_sa, double *pot_enthalpy_ice_freezing_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double cp_ihf, pt_icef, ratio_temp, tf, tf_p, tf_sa;
+ double saturation_fraction = 0.0;
+
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ pt_icef = gsw_pt0_from_t_ice(tf,p);
+ ratio_temp = (gsw_t0 + pt_icef)/(gsw_t0 + tf);
+
+ cp_ihf = gsw_cp_ice(tf,p);
+
+ if ((pot_enthalpy_ice_freezing_sa != NULL) &&
+ (pot_enthalpy_ice_freezing_p != NULL)) {
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tf_sa,&tf_p);
+ } else if (pot_enthalpy_ice_freezing_sa != NULL) {
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tf_sa, NULL);
+ } else if (pot_enthalpy_ice_freezing_p != NULL) {
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ NULL,&tf_p);
+ }
+
+ if (pot_enthalpy_ice_freezing_sa != NULL)
+ *pot_enthalpy_ice_freezing_sa = ratio_temp*cp_ihf*tf_sa;
+
+ if (pot_enthalpy_ice_freezing_p != NULL)
+ *pot_enthalpy_ice_freezing_p = ratio_temp*cp_ihf*tf_p
+ - (gsw_t0 + pt_icef)*gsw_gibbs_ice(1,1,tf,p);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(&
+ sa, p, pot_enthalpy_ice_freezing_sa, pot_enthalpy_ice_freezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the potential enthalpy of ice Ih at
+! which ice melts into seawater with Absolute Salinity SA and at pressure
+! p. This code uses the comptationally efficient polynomial fit of the
+! freezing potential enthalpy of ice Ih (McDougall et al., 2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pot_enthalpy_ice_freezing_SA = the derivative of the potential enthalpy
+! of ice at freezing (ITS-90) with respect to Absolute
+! salinity at fixed pressure [ (J/kg)/(g/kg) ] i.e. [ J/g ]
+!
+! pot_enthalpy_ice_freezing_P = the derivative of the potential enthalpy
+! of ice at freezing (ITS-90) with respect to pressure
+! (in Pa) at fixed Absolute Salinity [ (J/kg)/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(double sa, double p,
+ double *pot_enthalpy_ice_freezing_sa, double *pot_enthalpy_ice_freezing_p)
+{
+ double p_r, sa_r, x,
+ d1 = -1.249490228128056e4,
+ d2 = 1.336783910789822e4,
+ d3 = -4.811989517774642e4,
+ d4 = 8.044864276240987e4,
+ d5 = -7.124452125071862e4,
+ d6 = 2.280706828014839e4,
+ d7 = 0.315423710959628e3,
+ d8 = -3.592775732074710e2,
+ d9 = 1.644828513129230e3,
+ d10 = -4.809640968940840e3,
+ d11 = 2.901071777977272e3,
+ d12 = -9.218459682855746e2,
+ d13 = 0.379377450285737e3,
+ d14 = -2.672164989849465e3,
+ d15 = 5.044317489422632e3,
+ d16 = -2.631711865886377e3,
+ d17 = -0.160245473297112e3,
+ d18 = 4.029061696035465e2,
+ d19 = -3.682950019675760e2,
+
+ f1 = -2.034535061416256e4,
+ f2 = 0.315423710959628e3,
+ f3 = -0.239518382138314e3,
+ f4 = 0.822414256564615e3,
+ f5 = -1.923856387576336e3,
+ f6 = 0.967023925992424e3,
+ f7 = -0.263384562367307e3,
+ f8 = -5.051613740291480e3,
+ f9 = 7.587549005714740e2,
+ f10 = -3.562886653132620e3,
+ f11 = 5.044317489422632e3,
+ f12 = -2.105369492709102e3,
+ f13 = 6.387082316647800e2,
+ f14 = -4.807364198913360e2,
+ f15 = 8.058123392070929e2,
+ f16 = -5.524425029513641e2;
+
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ if (pot_enthalpy_ice_freezing_sa != NULL)
+ *pot_enthalpy_ice_freezing_sa =
+ (d1 + x*(d2 + x*(d3 + x*(d4 + x*(d5 + d6*x))))
+ + p_r*(d7 + x*(d8 + x*(d9 + x*(d10 + x*(d11 + d12*x))))
+ + p_r*(d13 + x*(d14 + x*(d15 + d16*x))
+ + p_r*(d17 + x*(d18 + d19*x)))))*1e-2;
+
+ if (pot_enthalpy_ice_freezing_p != NULL)
+ *pot_enthalpy_ice_freezing_p =
+ (f1 + sa_r*(f2 + x*(f3 + x*(f4 + x*(f5 + x*(f6 + f7*x)))))
+ + p_r*(f8 + sa_r*(f9 + x*(f10 + x*(f11 + f12*x)))
+ + p_r*(f13 + sa_r*(f14 + x*(f15 + f16*x)))))*1e-8;
+}
+/*
+!==========================================================================
+elemental function gsw_pot_enthalpy_ice_freezing_poly (sa, p)
+!==========================================================================
+!
+! Calculates the potential enthalpy of ice at which seawater freezes.
+! The error of this fit ranges between -2.5 and 1 J/kg with an rms of
+! 1.07, between SA of 0 and 120 g/kg and p between 0 and 10,000 dbar (the
+! error in the fit is between -0.7 and 0.7 with an rms of
+! 0.3, between SA of 0 and 120 g/kg and p between 0 and 5,000 dbar) when
+! compared with the potential enthalpy calculated from the exact in-situ
+! freezing temperature which is found by a Newton-Raphson iteration of the
+! equality of the chemical potentials of water in seawater and in ice.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pot_enthalpy_ice_freezing = potential enthalpy of ice at freezing
+! of seawater [ J/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pot_enthalpy_ice_freezing_poly(double sa, double p)
+{
+ double p_r, sa_r, x,
+ c0 = -3.333548730778702e5,
+ c1 = -1.249490228128056e4,
+ c2 = 0.891189273859881e4,
+ c3 = -2.405994758887321e4,
+ c4 = 3.217945710496395e4,
+ c5 = -2.374817375023954e4,
+ c6 = 0.651630522289954e4,
+ c7 = -2.034535061416256e4,
+ c8 = -0.252580687014574e4,
+ c9 = 0.021290274388826e4,
+ c10 = 0.315423710959628e3,
+ c11 = -0.239518382138314e3,
+ c12 = 0.379377450285737e3,
+ c13 = 0.822414256564615e3,
+ c14 = -1.781443326566310e3,
+ c15 = -0.160245473297112e3,
+ c16 = -1.923856387576336e3,
+ c17 = 2.522158744711316e3,
+ c18 = 0.268604113069031e3,
+ c19 = 0.967023925992424e3,
+ c20 = -1.052684746354551e3,
+ c21 = -0.184147500983788e3,
+ c22 = -0.263384562367307e3;
+
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ return (c0 + sa_r*(c1 + x*(c2 + x*(c3 + x*(c4 + x*(c5 + c6*x)))))
+ + p_r*(c7 + p_r*(c8 + c9*p_r)) + sa_r*p_r*(c10 + p_r*(c12
+ + p_r*(c15 + c21*sa_r)) + sa_r*(c13 + c17*p_r + c19*sa_r)
+ + x*(c11 + p_r*(c14 + c18*p_r) + sa_r*(c16 + c20*p_r + c22*sa_r))));
+}
+/*
+!==========================================================================
+function gsw_pot_rho_t_exact(sa,t,p,p_ref)
+!==========================================================================
+
+! Calculates the potential density of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+! p_ref : reference sea pressure [dbar]
+!
+! gsw_pot_rho_t_exact : potential density [kg/m^3]
+*/
+double
+gsw_pot_rho_t_exact(double sa, double t, double p, double p_ref)
+{
+ double pt = gsw_pt_from_t(sa,t,p,p_ref);
+
+ return (gsw_rho_t_exact(sa,pt,p_ref));
+}
+/*
+!==========================================================================
+elemental function gsw_pressure_coefficient_ice (t, p)
+!==========================================================================
+!
+! Calculates pressure coefficient of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pressure_coefficient_ice = pressure coefficient of ice [Pa/K]
+! Note. The output units are Pa/K NOT dbar/K.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pressure_coefficient_ice(double t, double p)
+{
+ return (-gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(0,2,t,p));
+}
+/*
+!==========================================================================
+elemental function gsw_pressure_freezing_ct (sa, ct, saturation_fraction)
+!==========================================================================
+!
+! Calculates the pressure (in dbar) of seawater at the freezing
+! temperature. That is, the output is the pressure at which seawater,
+! with Absolute Salinity SA, Conservative Temperature CT, and with
+! saturation_fraction of dissolved air, freezes. If the input values are
+! such that there is no value of pressure in the range between 0 dbar and
+! 10,000 dbar for which seawater is at the freezing temperature, the
+! output, pressure_freezing, is put equal to NaN.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! pressure_freezing = sea pressure at which the seawater freezes [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pressure_freezing_ct(double sa, double ct, double saturation_fraction)
+{
+ GSW_TEOS10_CONSTANTS;
+ int i_iter, number_of_iterations = 3;
+ double ct_freezing_p0, ct_freezing_p10000, dctf_dp, f,
+ pf, pfm, pf_old, ctfreezing_p;
+
+ /*
+ ! rec_Pa2dbar is to have dCTf_dp in units of K/dbar rather than K/Pa
+
+ ! Find CT > CT_freezing_p0. If this is the case, the input CT value
+ ! represent seawater that will not be frozen at any positive p.
+ */
+ ct_freezing_p0 = gsw_ct_freezing(sa,0.0,saturation_fraction);
+ if (ct > ct_freezing_p0) {
+ return (GSW_INVALID_VALUE);
+ }
+ /*
+ ! Find CT < CT_freezing_p10000. If this is the case, the input CT value
+ ! represent seawater that is frozen even at p = 10,000 dbar.
+ */
+ ct_freezing_p10000 = gsw_ct_freezing(sa,1e4,saturation_fraction);
+ if (ct < ct_freezing_p10000) {
+ return (GSW_INVALID_VALUE);
+ }
+ /*
+ ! This is the initial (linear) guess of the freezing pressure, in dbar.
+ */
+ pf = rec_pa2db*(ct_freezing_p0 - ct)/
+ (ct_freezing_p0 - ct_freezing_p10000);
+
+ gsw_ct_freezing_first_derivatives(sa,pf,saturation_fraction,
+ NULL,&ctfreezing_p);
+ dctf_dp = rec_pa2db*ctfreezing_p;
+ /*
+ ! this dctf_dp is the initial value of the partial derivative of
+ ! ct_freezing with respect to pressure (in dbar) at fixed sa,
+ ! assuming that the saturation_fraction is zero.
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ pf_old = pf;
+ f = gsw_ct_freezing(sa,pf_old,saturation_fraction) - ct;
+ pf = pf_old - f/dctf_dp;
+ pfm = 0.5*(pf + pf_old);
+ gsw_ct_freezing_first_derivatives(sa,pfm,saturation_fraction,
+ NULL,&ctfreezing_p);
+ dctf_dp = rec_pa2db*ctfreezing_p;
+ pf = pf_old - f/dctf_dp;
+ }
+
+ if (gsw_sa_p_inrange(sa,pf))
+ return (pf);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+elemental function gsw_pt0_cold_ice_poly (pot_enthalpy_ice)
+!==========================================================================
+!
+! Calculates an initial estimate of pt0_ice when it is less than about
+! -100 deg C.
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!
+! pt0_cold_ice_poly = initial estimate of potential temperatur
+! of very cold ice in dgress C (not K) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt0_cold_ice_poly(double pot_enthalpy_ice)
+{
+ GSW_TEOS10_CONSTANTS;
+ double log_abs_theta0, log_h_diff,
+ /*h00 = gsw_enthalpy_ice(-gsw_t0,0)*/
+ h00 = -6.320202333358860e5,
+
+ s0 = 1.493103204647916,
+ s1 = 2.372788609320607e-1,
+ s2 = -2.014996002119374e-3,
+ s3 = 2.640600197732682e-6,
+ s4 = 3.134706016844293e-5,
+ s5 = 2.733592344937913e-6,
+ s6 = 4.726828010223258e-8,
+ s7 = -2.735193883189589e-9,
+ s8 = -8.547714991377670e-11;
+
+ log_h_diff = log(pot_enthalpy_ice - h00);
+
+ log_abs_theta0 = s0 + log_h_diff*(s1 + log_h_diff*(s2 + log_h_diff*(s3
+ + log_h_diff*(s4 + log_h_diff*(s5 + log_h_diff*(s6
+ + log_h_diff*(s7 + log_h_diff*s8)))))));
+
+ return (exp(log_abs_theta0) - gsw_t0);
+}
+/*
+!==========================================================================
+function gsw_pt0_from_t(sa,t,p)
+!==========================================================================
+
+! Calculates potential temperature with reference pressure, p_ref = 0 dbar.
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_pt0_from_t : potential temperature, p_ref = 0 [deg C]
+*/
+double
+gsw_pt0_from_t(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ int no_iter;
+ double pt0, pt0_old, dentropy, dentropy_dt;
+ double s1, true_entropy_part, pt0m;
+
+ s1 = sa/gsw_ups;
+
+ pt0 = t+p*( 8.65483913395442e-6 -
+ s1 * 1.41636299744881e-6 -
+ p * 7.38286467135737e-9 +
+ t *(-8.38241357039698e-6 +
+ s1 * 2.83933368585534e-8 +
+ t * 1.77803965218656e-8 +
+ p * 1.71155619208233e-10));
+
+ dentropy_dt = gsw_cp0/((gsw_t0+pt0)*(1.0-0.05*(1.0-sa/gsw_sso)));
+
+ true_entropy_part = gsw_entropy_part(sa,t,p);
+
+ for (no_iter=1; no_iter <= 2; no_iter++) {
+ pt0_old = pt0;
+ dentropy = gsw_entropy_part_zerop(sa,pt0_old) -
+ true_entropy_part;
+ pt0 = pt0_old - dentropy/dentropy_dt;
+ pt0m = 0.5*(pt0 + pt0_old);
+ dentropy_dt = -gsw_gibbs_pt0_pt0(sa,pt0m);
+ pt0 = pt0_old - dentropy/dentropy_dt;
+ }
+ return (pt0);
+}
+/*
+! =========================================================================
+elemental function gsw_pt0_from_t_ice (t, p)
+! =========================================================================
+!
+! Calculates potential temperature of ice Ih with a reference pressure of
+! 0 dbar, from in-situ temperature, t.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! pt0_ice = potential temperature of ice Ih with reference pressure of
+! zero dbar (ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt0_from_t_ice(double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ int number_of_iterations;
+ double dentropy, dentropy_dt, pt0_ice,
+ pt0_ice_old, ptm_ice, true_entropy,
+ /*This is the starting polynomial for pt0 of ice Ih.*/
+ s1 = -2.256611570832386e-4,
+ s2 = -6.045305921314694e-7,
+ s3 = 5.546699019612661e-9,
+ s4 = 1.795030639186685e-11,
+ s5 = 1.292346094030742e-9,
+
+ p1 = -2.259745637898635e-4,
+ p2 = 1.486236778150360e-9,
+ p3 = 6.257869607978536e-12,
+ p4 = -5.253795281359302e-7,
+ p5 = 6.752596995671330e-9,
+ p6 = 2.082992190070936e-11,
+
+ q1 = -5.849191185294459e-15,
+ q2 = 9.330347971181604e-11,
+ q3 = 3.415888886921213e-13,
+ q4 = 1.064901553161811e-12,
+ q5 = -1.454060359158787e-10,
+ q6 = -5.323461372791532e-13;
+
+ true_entropy = -gsw_gibbs_ice_part_t(t,p);
+
+ if (t < -45.0 && t > -273.0) {
+
+ pt0_ice = t + p*(p1 + p*(p2 + p3*t) + t*(p4 + t*(p5 + p6*t)));
+
+ if (pt0_ice < -gsw_t0) pt0_ice = -gsw_t0;
+ /*
+ ! we add 0.05d0 to the initial estimate of pt0_ice at
+ ! temps less than -273 to ensure that it is never less than -273.15.
+ */
+ if (pt0_ice < -273.0) pt0_ice = pt0_ice + 0.05;
+
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(pt0_ice);
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ pt0_ice_old = pt0_ice;
+ dentropy = -gsw_gibbs_ice_pt0(pt0_ice_old) - true_entropy;
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt0_ice + pt0_ice_old);
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(ptm_ice);
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ }
+
+ } else {
+
+ pt0_ice = t + p*(s1 + t*(s2 + t*(s3 + t*s4)) + s5*p);
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(pt0_ice);
+
+ pt0_ice_old = pt0_ice;
+ dentropy = -gsw_gibbs_ice_pt0(pt0_ice_old) - true_entropy;
+
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt0_ice + pt0_ice_old);
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(ptm_ice);
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+
+ }
+
+ if (pt0_ice < -273.0) {
+
+ pt0_ice = t + p*(q1 + p*(q2 + q3*t) + t*(q4 + t*(q5 + q6*t)));
+ /*
+ ! add 0.01d0 to the initial estimate of pt_ice used in the
+ ! derivative to ensure that it is never less than -273.15d0
+ ! because the derivative approaches zero at absolute zero.
+ */
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(pt0_ice+0.01);
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ pt0_ice_old = pt0_ice;
+ dentropy = -gsw_gibbs_ice_pt0(pt0_ice_old) - true_entropy;
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt0_ice + pt0_ice_old);
+ /*
+ ! add 0.01d0 to the estimate of ptm_ice for temperatures less
+ | than -273 to ensure that they are never less than -273.15d0
+ ! because the derivative approaches zero at absolute zero and
+ ! the addition of 0.01d0 degrees c ensures that when we divide
+ ! by the derivatve in the modified newton routine the function
+ ! does not blow up.
+ */
+ ptm_ice = ptm_ice + 0.01;
+ dentropy_dt = -gsw_gibbs_ice_pt0_pt0(ptm_ice);
+ pt0_ice = pt0_ice_old - dentropy/dentropy_dt;
+ }
+
+ }
+ /*
+ ! For temperatures less than -273.1 degsC the maximum error is less
+ ! than 2x10^-7 degsC. For temperatures between -273.1 and 273 the
+ ! maximum error is less than 8x10^-8 degsC, and for temperatures
+ ! greater than -273 degsC the ! maximum error is 1.5x10^-12 degsC.
+ ! These errors are over the whole ocean depths with p varying between
+ ! 0 and 10,000 dbar, while the in-situ temperature varied independently
+ ! between -273.15 and +2 degsC.
+ */
+
+ return (pt0_ice);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_pt_first_derivatives (sa, ct, pt_sa, pt_ct)
+! =========================================================================
+!
+! Calculates the following two partial derivatives of potential temperature
+! (the regular potential temperature whose reference sea pressure is 0 dbar)
+! (1) pt_SA, the derivative with respect to Absolute Salinity at
+! constant Conservative Temperature, and
+! (2) pt_CT, the derivative with respect to Conservative Temperature at
+! constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! pt_SA = The derivative of potential temperature with respect to
+! Absolute Salinity at constant Conservative Temperature.
+! [ K/(g/kg)]
+! pt_CT = The derivative of potential temperature with respect to
+! Conservative Temperature at constant Absolute Salinity.
+! pt_CT is dimensionless. [ unitless ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_pt_first_derivatives (double sa, double ct, double *pt_sa, double *pt_ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double abs_pt, ct_pt, ct_sa, pt, pr0 = 0.0;
+ int n0=0, n1=1, n2=2;
+
+ pt = gsw_pt_from_ct(sa,ct);
+ abs_pt = (gsw_t0 + pt);
+
+ ct_pt = -(abs_pt*gsw_gibbs(n0,n2,n0,sa,pt,pr0))/gsw_cp0;
+
+ if (pt_sa != NULL) {
+
+ ct_sa = (gsw_gibbs(n1,n0,n0,sa,pt,pr0) -
+ abs_pt*gsw_gibbs(n1,n1,n0,sa,pt,pr0))/gsw_cp0;
+
+ *pt_sa = -ct_sa/ct_pt;
+
+ }
+
+ if (pt_ct != NULL)
+ *pt_ct = 1.0/ct_pt;
+}
+/*
+!==========================================================================
+function gsw_pt_from_ct(sa,ct)
+!==========================================================================
+
+! potential temperature of seawater from conservative temperature
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_pt_from_ct : potential temperature with [deg C]
+! reference pressure of 0 dbar
+*/
+double
+gsw_pt_from_ct(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double a5ct, b3ct, ct_factor, pt_num, pt_recden, ct_diff;
+ double pt, pt_old, ptm, dpt_dct, s1;
+ double a0 = -1.446013646344788e-2,
+ a1 = -3.305308995852924e-3,
+ a2 = 1.062415929128982e-4,
+ a3 = 9.477566673794488e-1,
+ a4 = 2.166591947736613e-3,
+ a5 = 3.828842955039902e-3,
+ b0 = 1.000000000000000e0,
+ b1 = 6.506097115635800e-4,
+ b2 = 3.830289486850898e-3,
+ b3 = 1.247811760368034e-6;
+
+ s1 = sa/gsw_ups;
+
+ a5ct = a5*ct;
+ b3ct = b3*ct;
+
+ ct_factor = (a3 + a4*s1 + a5ct);
+ pt_num = a0 + s1*(a1 + a2*s1) + ct*ct_factor;
+ pt_recden = 1.0/(b0 + b1*s1 + ct*(b2 + b3ct));
+ pt = pt_num*pt_recden;
+
+ dpt_dct = pt_recden*(ct_factor + a5ct - (b2 + b3ct + b3ct)*pt);
+
+ /*
+ ** Start the 1.5 iterations through the modified Newton-Raphson
+ ** iterative method.
+ */
+
+ ct_diff = gsw_ct_from_pt(sa,pt) - ct;
+ pt_old = pt;
+ pt = pt_old - ct_diff*dpt_dct;
+ ptm = 0.5*(pt + pt_old);
+
+ dpt_dct = -gsw_cp0/((ptm + gsw_t0)*gsw_gibbs_pt0_pt0(sa,ptm));
+
+ pt = pt_old - ct_diff*dpt_dct;
+ ct_diff = gsw_ct_from_pt(sa,pt) - ct;
+ pt_old = pt;
+ return (pt_old - ct_diff*dpt_dct);
+}
+/*
+! =========================================================================
+elemental function gsw_pt_from_entropy (sa, entropy)
+! =========================================================================
+!
+! Calculates potential temperature with reference pressure p_ref = 0 dbar
+! and with entropy as an input variable.
+!
+! SA = Absolute Salinity [ g/kg ]
+! entropy = specific entropy [ deg C ]
+!
+! pt = potential temperature [ deg C ]
+! with reference sea pressure (p_ref) = 0 dbar.
+! Note. The reference sea pressure of the output, pt, is zero dbar.
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_entropy(double sa, double entropy)
+{
+ GSW_TEOS10_CONSTANTS;
+ int number_of_iterations;
+ double c, dentropy, dentropy_dt, ent_sa, part1, part2, pt, ptm,
+ pt_old;
+
+ /*Find the initial value of pt*/
+ part1 = 1.0 - sa/gsw_sso;
+ part2 = 1.0 - 0.05*part1;
+ ent_sa = (gsw_cp0/gsw_t0)*part1*(1.0 - 1.01*part1);
+ c = (entropy - ent_sa)*(part2/gsw_cp0);
+ pt = gsw_t0*(exp(c) - 1.0);
+ dentropy_dt = gsw_cp0/((gsw_t0 + pt)*part2);
+
+ for (number_of_iterations = 1; number_of_iterations <= 2;
+ number_of_iterations++) {
+ pt_old = pt;
+ dentropy = gsw_entropy_from_pt(sa,pt_old) - entropy;
+ pt = pt_old - dentropy/dentropy_dt;
+ ptm = 0.5*(pt + pt_old);
+ dentropy_dt = -gsw_gibbs_pt0_pt0(sa,ptm);
+ pt = pt_old - dentropy/dentropy_dt;
+ }
+ /*
+ ! Maximum error of 2.2x10^-6 degrees C for one iteration.
+ ! Maximum error is 1.4x10^-14 degrees C for two iterations
+ ! (two iterations is the default, "for Number_of_iterations = 1:2").
+ */
+ return (pt);
+}
+/*
+!==========================================================================
+elemental function gsw_pt_from_pot_enthalpy_ice (pot_enthalpy_ice)
+!==========================================================================
+!
+! Calculates the potential temperature of ice from the potential enthalpy
+! of ice. The reference sea pressure of both the potential temperature
+! and the potential enthalpy is zero dbar.
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!
+! pt0_ice = potential temperature of ice (ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_pot_enthalpy_ice(double pot_enthalpy_ice)
+{
+ int iteration;
+ double df_dt, f, mod_pot_enthalpy_ice, pt0_cold_ice, recip_df_dt,
+ pt0_cold_ice_old, pt0_ice, pt0_ice_old, ptm_cold_ice, ptm_ice;
+ double h00 = -6.320202333358860e5, /*gsw_enthalpy_ice(-gsw_t0,0)*/
+ p0 = 0.0;
+
+ mod_pot_enthalpy_ice = max(pot_enthalpy_ice,h00);
+
+ if (mod_pot_enthalpy_ice >= -5.1e5) {
+ /*
+ ! For input potential enthalpies greater than -5.1e-5, the above part of
+ ! the code gives the output potential temperature of ice accurate to
+ | 1e-13 degrees C.
+ */
+ pt0_ice = gsw_pt_from_pot_enthalpy_ice_poly(mod_pot_enthalpy_ice);
+ /*
+ ! The variable "df_dt" below is the derivative of the above polynomial
+ ! with respect to pot_enthalpy_ice. This is the initial value of the
+ ! derivative of the function f.
+ */
+ recip_df_dt =
+ gsw_pt_from_pot_enthalpy_ice_poly_dh(mod_pot_enthalpy_ice);
+
+ pt0_ice_old = pt0_ice;
+ f = gsw_pot_enthalpy_from_pt_ice(pt0_ice_old)
+ - mod_pot_enthalpy_ice;
+ pt0_ice = pt0_ice_old - f*recip_df_dt;
+ ptm_ice = 0.5*(pt0_ice + pt0_ice_old);
+ recip_df_dt = 1.0/gsw_cp_ice(ptm_ice,p0);
+ pt0_ice = pt0_ice_old - f*recip_df_dt;
+
+ } else {
+ /*
+ ! For pot_enthalpy_ice < -5.1e5 (or pt0_ice less than about -100 deg c)
+ ! these temperatures are less than those found in nature on planet earth
+ */
+ pt0_cold_ice = gsw_pt0_cold_ice_poly(mod_pot_enthalpy_ice);
+
+ df_dt = gsw_cp_ice(pt0_cold_ice+0.02,p0);
+ /*
+ ! the heat capacity, cp, is
+ ! evaluated at 0.02 c greater than usual in order to avoid stability
+ ! issues and to ensure convergence near zero absolute temperature.
+ */
+ for (iteration = 1; iteration <= 6; iteration++) {
+ pt0_cold_ice_old = pt0_cold_ice;
+ f = gsw_pot_enthalpy_from_pt_ice(pt0_cold_ice_old)
+ - mod_pot_enthalpy_ice;
+ pt0_cold_ice = pt0_cold_ice_old - f/df_dt;
+ ptm_cold_ice = 0.5*(pt0_cold_ice + pt0_cold_ice_old);
+ df_dt = gsw_cp_ice(ptm_cold_ice+0.02,p0);
+ /*note the extra 0.02 c here as well*/
+ pt0_cold_ice = pt0_cold_ice_old - f/df_dt;
+ }
+ pt0_ice = pt0_cold_ice;
+ }
+/*
+!The potential temerature has a maximum error as listed in the table below.
+!
+! potential temerature error (deg C) | @ potential temerature (deg C)
+!--------------------------------------|--------------------------------
+! 0.012 | -273.15 to -273.12
+! 4 x 10^-4 | -232.12 to -273.0
+! 2.5 x 10^-6 | -273
+! 7 x 10^-9 | -272
+! 3.7 x 10^-10 | -270
+! 6 x 10^-11 | -268
+! 2.5 x 10^11 | -266
+! 3 x 10^-12 | -260
+! 7 x 10^-13 | -250
+! 2.2 x 10^-13 | -220
+! 1.7 x 10^-13 | >= -160
+!
+! Note. The above errors in each temperature range are machine precissions
+! for this calculation.
+*/
+
+ return (pt0_ice);
+}
+/*
+!==========================================================================
+elemental function gsw_pt_from_pot_enthalpy_ice_poly (pot_enthalpy_ice)
+!==========================================================================
+!
+! Calculates the potential temperature of ice (whose reference sea
+! pressure is zero dbar) from the potential enthalpy of ice. This is a
+! compuationally efficient polynomial fit to the potential enthalpy of
+! ice.
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!
+! pt0_ice = potential temperature of ice (ITS-90) [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_pot_enthalpy_ice_poly(double pot_enthalpy_ice)
+{
+ double q0 = 2.533588268773218e2,
+ q1 = 2.594351081876611e-3,
+ q2 = 1.765077810213815e-8,
+ q3 = 7.768070564290540e-14,
+ q4 = 2.034842254277530e-19,
+ q5 = 3.220014531712841e-25,
+ q6 = 2.845172809636068e-31,
+ q7 = 1.094005878892950e-37;
+/*
+! The error of this fit ranges between -5e-5 and 2e-4 deg C over the potential
+! temperature range of -100 to 2 deg C, or the potential enthalpy range of
+! -5.7 x 10^5 to -3.3 x 10^5 J/kg.
+*/
+ return (q0
+ + pot_enthalpy_ice*(q1 + pot_enthalpy_ice*(q2 + pot_enthalpy_ice*(q3
+ + pot_enthalpy_ice*(q4 + pot_enthalpy_ice*(q5 + pot_enthalpy_ice*(q6
+ + pot_enthalpy_ice*q7)))))));
+}
+/*
+!==========================================================================
+elemental function gsw_pt_from_pot_enthalpy_ice_poly_dh (pot_enthalpy_ice)
+!==========================================================================
+!
+! Calculates the derivative of potential temperature of ice with respect
+! to potential enthalpy. This is based on the compuationally-efficient
+! polynomial fit to the potential enthalpy of ice.
+!
+! pot_enthalpy_ice = potential enthalpy of ice [ J/kg ]
+!
+! dpt0_ice_dh = derivative of potential temperature of ice
+! with respect to potential enthalpy [ deg C ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_pot_enthalpy_ice_poly_dh(double pot_enthalpy_ice)
+{
+ double q1 = 2.594351081876611e-3,
+ p2 = 3.530155620427630e-8,
+ p3 = 2.330421169287162e-13,
+ p4 = 8.139369017110120e-19,
+ p5 = 1.610007265856420e-24,
+ p6 = 1.707103685781641e-30,
+ p7 = 7.658041152250651e-37;
+
+ return (q1 + pot_enthalpy_ice*(p2 + pot_enthalpy_ice*(p3
+ + pot_enthalpy_ice*(p4 + pot_enthalpy_ice*(p5 + pot_enthalpy_ice*(p6
+ + pot_enthalpy_ice*p7))))));
+}
+/*
+!==========================================================================
+function gsw_pt_from_t(sa,t,p,p_ref)
+!==========================================================================
+
+! Calculates potential temperature of seawater from in-situ temperature
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+! p_ref : reference sea pressure [dbar]
+!
+! gsw_pt_from_t : potential temperature [deg C]
+*/
+double
+gsw_pt_from_t(double sa, double t, double p, double p_ref)
+{
+ GSW_TEOS10_CONSTANTS;
+ int n0=0, n2=2, no_iter;
+ double s1, pt, ptm, pt_old, dentropy, dentropy_dt,
+ true_entropy_part;
+
+ s1 = sa/gsw_ups;
+ pt = t+(p-p_ref)*( 8.65483913395442e-6 -
+ s1 * 1.41636299744881e-6 -
+ (p+p_ref) * 7.38286467135737e-9 +
+ t *(-8.38241357039698e-6 +
+ s1 * 2.83933368585534e-8 +
+ t * 1.77803965218656e-8 +
+ (p+p_ref) * 1.71155619208233e-10));
+
+ dentropy_dt = gsw_cp0/((gsw_t0 + pt)*(1.0-0.05*(1.0 - sa/gsw_sso)));
+ true_entropy_part = gsw_entropy_part(sa,t,p);
+ for (no_iter=1; no_iter <= 2; no_iter++) {
+ pt_old = pt;
+ dentropy = gsw_entropy_part(sa,pt_old,p_ref) - true_entropy_part;
+ pt = pt_old - dentropy/dentropy_dt;
+ ptm = 0.5*(pt + pt_old);
+ dentropy_dt = -gsw_gibbs(n0,n2,n0,sa,ptm,p_ref);
+ pt = pt_old - dentropy/dentropy_dt;
+ }
+ return (pt);
+}
+/*
+! =========================================================================
+elemental function gsw_pt_from_t_ice (t, p, p_ref)
+! =========================================================================
+!
+! Calculates potential temperature of ice Ih with the general reference
+! pressure, p_ref, from in-situ temperature, t.
+!
+! A faster gsw routine exists if p_ref is indeed zero dbar. This routine
+! is "gsw_pt0_from_t_ice(t,p)".
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! p_ref = reference pressure [ dbar ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_pt_from_t_ice(double t, double p, double p_ref)
+{
+ GSW_TEOS10_CONSTANTS;
+ int number_of_iterations;
+ double dentropy, dentropy_dt, dp,
+ pt_ice, pt_ice_old, ptm_ice, true_entropy,
+
+ p1 = -2.259745637898635e-4,
+ p2 = 1.486236778150360e-9,
+ p3 = 6.257869607978536e-12,
+ p4 = -5.253795281359302e-7,
+ p5 = 6.752596995671330e-9,
+ p6 = 2.082992190070936e-11,
+
+ q1 = -5.849191185294459e-15,
+ q2 = 9.330347971181604e-11,
+ q3 = 3.415888886921213e-13,
+ q4 = 1.064901553161811e-12,
+ q5 = -1.454060359158787e-10,
+ q6 = -5.323461372791532e-13;
+ /*This is the starting polynomial for pt of ice Ih.*/
+
+ dp = p - p_ref;
+
+ pt_ice = t + dp*(p1 + (p + p_ref)*(p2 + p3*t) + t*(p4 + t*(p5 + p6*t)));
+
+ if (pt_ice < -gsw_t0) pt_ice = -gsw_t0;
+
+ if (pt_ice < -273.0) pt_ice = pt_ice + 0.05;
+ /*
+ ! we add 0.05 to the initial estimate of pt_ice at temps less than
+ ! -273 to ensure that it is never less than -273.15.
+ */
+ dentropy_dt = -gsw_gibbs_ice(2,0,pt_ice,p_ref);
+
+ true_entropy = -gsw_gibbs_ice_part_t(t,p);
+
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ pt_ice_old = pt_ice;
+ dentropy = -gsw_gibbs_ice_part_t(pt_ice_old,p_ref) - true_entropy;
+ pt_ice = pt_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt_ice + pt_ice_old);
+ dentropy_dt = -gsw_gibbs_ice(2,0,ptm_ice,p_ref);
+ pt_ice = pt_ice_old - dentropy/dentropy_dt;
+ }
+
+ if (pt_ice < -273.0) {
+
+ pt_ice = t + (p - p_ref)*(q1 + (p + p_ref)*(q2 + q3*t)
+ + t*(q4 + t*(q5 + q6*t)));
+
+ dentropy_dt = -gsw_gibbs_ice(2,0,pt_ice+0.01,p_ref);
+ /*
+ ! we add 0.01 to the initial estimate of pt_ice used in the derivative
+ ! to ensure that it is never less than -273.15 because the derivative
+ ! approaches zero at absolute zero.
+ */
+ for (number_of_iterations = 1; number_of_iterations <= 3;
+ number_of_iterations++) {
+ pt_ice_old = pt_ice;
+ dentropy = -gsw_gibbs_ice_part_t(pt_ice_old,p_ref)
+ - true_entropy;
+ pt_ice = pt_ice_old - dentropy/dentropy_dt;
+ ptm_ice = 0.5*(pt_ice + pt_ice_old);
+ ptm_ice = ptm_ice + 0.01;
+ dentropy_dt = -gsw_gibbs_ice(2,0,ptm_ice,p_ref);
+ pt_ice = pt_ice_old - dentropy/dentropy_dt;
+ }
+
+ }
+/*
+! For temperatures less than -273.1 degsC the maximum error is less than
+! 2x10^-7 degsC. For temperatures between -273.1 and 273 the maximum error
+! is less than 8x10^-8 degsC, and for temperatures greater than -273 degsC the
+! maximum error is 1.5x10^-12 degsC. These errors are over the whole
+! ocean depths with both p and pref varying independently between 0 and
+! 10,000 dbar, while the in-situ temperature varied independently between
+! -273.15 and +2 degsC.
+*/
+ return (pt_ice);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_pt_second_derivatives (sa, ct, pt_sa_sa, &
+ pt_sa_ct, pt_ct_ct)
+! =========================================================================
+!
+! Calculates the following three second-order derivatives of potential
+! temperature (the regular potential temperature which has a reference
+! sea pressure of 0 dbar),
+! (1) pt_SA_SA, the second derivative with respect to Absolute Salinity
+! at constant Conservative Temperature,
+! (2) pt_SA_CT, the derivative with respect to Conservative Temperature
+! and Absolute Salinity, and
+! (3) pt_CT_CT, the second derivative with respect to Conservative
+! Temperature at constant Absolute Salinity.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! pt_SA_SA = The second derivative of potential temperature (the
+! regular potential temperature which has reference sea
+! pressure of 0 dbar) with respect to Absolute Salinity
+! at constant Conservative Temperature.
+! pt_SA_SA has units of: [ K/((g/kg)^2) ]
+! pt_SA_CT = The derivative of potential temperature with respect
+! to Absolute Salinity and Conservative Temperature.
+! pt_SA_CT has units of: [ 1/(g/kg) ]
+! pt_CT_CT = The second derivative of potential temperature (the
+! regular one with p_ref = 0 dbar) with respect to
+! Conservative Temperature at constant SA.
+! pt_CT_CT has units of: [ 1/K ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_pt_second_derivatives (double sa, double ct, double *pt_sa_sa,
+ double *pt_sa_ct, double *pt_ct_ct)
+{
+ double ct_l, ct_u, pt_ct_l, pt_ct_u, pt_sa_l, pt_sa_u, sa_l, sa_u,
+ dct = 1e-2, dsa = 1e-3;
+
+ if (pt_sa_sa != NULL) {
+
+ if ((sa_l = sa - dsa) < 0.0)
+ sa_l = 0.0;
+ sa_u = sa + dsa;
+
+ gsw_pt_first_derivatives(sa_l,ct,&pt_sa_l,NULL);
+ gsw_pt_first_derivatives(sa_u,ct,&pt_sa_u,NULL);
+
+ *pt_sa_sa = (pt_sa_u - pt_sa_l)/(sa_u - sa_l);
+
+ }
+
+ if (pt_sa_ct != NULL || pt_ct_ct != NULL) {
+
+ ct_l = ct - dct;
+ ct_u = ct + dct;
+
+ if ((pt_sa_ct != NULL) && (pt_ct_ct != NULL)) {
+
+ gsw_pt_first_derivatives(sa,ct_l,&pt_sa_l,&pt_ct_l);
+ gsw_pt_first_derivatives(sa,ct_u,&pt_sa_u,&pt_ct_u);
+
+ *pt_sa_ct = (pt_sa_u - pt_sa_l)/(ct_u - ct_l);
+ *pt_ct_ct = (pt_ct_u - pt_ct_l)/(ct_u - ct_l);
+
+ } else if ((pt_sa_ct != NULL) && (pt_ct_ct == NULL)) {
+
+ gsw_pt_first_derivatives(sa,ct_l,&pt_sa_l,NULL);
+ gsw_pt_first_derivatives(sa,ct_u,&pt_sa_u,NULL);
+
+ *pt_sa_ct = (pt_sa_u - pt_sa_l)/(ct_u - ct_l);
+
+ } else if ((pt_sa_ct == NULL) && (pt_ct_ct != NULL)) {
+
+ gsw_pt_first_derivatives(sa,ct_l,NULL,&pt_ct_l);
+ gsw_pt_first_derivatives(sa,ct_u,NULL,&pt_ct_u);
+
+ *pt_ct_ct = (pt_ct_u - pt_ct_l)/(ct_u - ct_l);
+ }
+ }
+}
+/*
+!--------------------------------------------------------------------------
+! density and enthalpy, based on the 48-term expression for density
+!--------------------------------------------------------------------------
+
+!==========================================================================
+function gsw_rho(sa,ct,p)
+!==========================================================================
+
+! Calculates in-situ density from Absolute Salinity and Conservative
+! Temperature, using the computationally-efficient expression for
+! specific volume in terms of SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho : in-situ density [kg/m]
+*/
+double
+gsw_rho(double sa, double ct, double p)
+{
+ return (1.0/gsw_specvol(sa,ct,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_rho_alpha_beta (sa, ct, p, rho, alpha, beta)
+!==========================================================================
+!
+! Calculates in-situ density, the appropiate thermal expansion coefficient
+! and the appropriate saline contraction coefficient of seawater from
+! Absolute Salinity and Conservative Temperature. This function uses the
+! computationally-efficient expression for specific volume in terms of
+! SA, CT and p (Roquet et al., 2014).
+!
+! Note that potential density (pot_rho) with respect to reference pressure
+! p_ref is obtained by calling this function with the pressure argument
+! being p_ref as in [pot_rho, ~, ~] = gsw_rho_alpha_beta(SA,CT,p_ref).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho = in-situ density [ kg/m ]
+! alpha = thermal expansion coefficient [ 1/K ]
+! with respect to Conservative Temperature
+! beta = saline (i.e. haline) contraction [ kg/g ]
+! coefficient at constant Conservative Temperature
+!--------------------------------------------------------------------------
+*/
+void
+gsw_rho_alpha_beta (double sa, double ct, double p, double *rho, double *alpha,
+ double *beta)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v, v_ct_part, v_sa_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ if (rho != NULL)
+ *rho = 1.0/v;
+
+ if (alpha != NULL) {
+
+ v_ct_part = a000 + xs*(a100 + xs*(a200 + xs*(a300
+ + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ *alpha = 0.025*v_ct_part/v;
+
+ }
+
+ if (beta != NULL) {
+
+ v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300
+ + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ *beta = -v_sa_part*0.5*gsw_sfac/(v*xs);
+
+ }
+}
+/*
+!==========================================================================
+subroutine gsw_rho_first_derivatives(sa, ct, p, drho_dsa, drho_dct, drho_dp)
+!==========================================================================
+
+! Calculates the three (3) partial derivatives of in situ density with
+! respect to Absolute Salinity, Conservative Temperature and pressure.
+! Note that the pressure derivative is done with respect to pressure in
+! Pa, not dbar. This function uses the computationally-efficient expression
+! for specific volume in terms of SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+! p : sea pressure [dbar]
+! drho_dsa : partial derivatives of density [kg^2/(g m^3)]
+! with respect to Absolute Salinity
+! drho_dct : partial derivatives of density [kg/(K m^3)]
+! with respect to Conservative Temperature
+! drho_dp : partial derivatives of density [kg/(Pa m^3)]
+! with respect to pressure in Pa
+*/
+void
+gsw_rho_first_derivatives(double sa, double ct, double p,
+ double *drho_dsa, double *drho_dct, double *drho_dp)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double rho2, v_ct, v_p, v_sa, xs, ys, z, v;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ rho2 = pow(1.0/v, 2.0);
+
+ if (drho_dsa != NULL) {
+
+ v_sa = b000
+ + xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ *drho_dsa = -rho2*0.5*gsw_sfac*v_sa/xs;
+ }
+
+ if (drho_dct != NULL) {
+
+ v_ct = a000
+ + xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ *drho_dct = -rho2*0.025*v_ct;
+ }
+
+ if (drho_dp != NULL) {
+
+ v_p = c000
+ + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs))))
+ + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020
+ + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs)
+ + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201
+ + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs))
+ + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys)))
+ + z*(c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys)
+ + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z))));
+
+ *drho_dp = 1e-4*pa2db*-rho2*v_p;
+ }
+
+ return;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_rho_first_derivatives_wrt_enthalpy (sa, ct, p, &
+ rho_sa, rho_h)
+! =========================================================================
+!
+! Calculates two first-order derivatives of specific volume (v).
+! Note that this function uses the using the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho_SA = The first derivative of rho with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! rho_h = The first derivative of rho with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_rho_first_derivatives_wrt_enthalpy (double sa, double ct, double p,
+ double *rho_sa, double *rho_h)
+{
+ double rec_v2, v_h=0.0, v_sa;
+
+ if ((rho_sa != NULL) && (rho_h != NULL)) {
+
+ gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,&v_sa,&v_h);
+
+ } else if (rho_sa != NULL) {
+
+ gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,&v_sa,NULL);
+
+ } else if (rho_h != NULL) {
+
+ gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,NULL,&v_h);
+
+ }
+
+ rec_v2 = pow(1.0/gsw_specvol(sa,ct,p), 2);
+
+ if (rho_sa != NULL) *rho_sa = -v_sa*rec_v2;
+
+ if (rho_h != NULL) *rho_h = -v_h*rec_v2;
+}
+/*
+!==========================================================================
+elemental function gsw_rho_ice (t, p)
+!==========================================================================
+!
+! Calculates in-situ density of ice from in-situ temperature and pressure.
+! Note that the output, rho_ice, is density, not density anomaly; that
+! is, 1000 kg/m^3 is not subracted from it.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho_ice = in-situ density of ice (not density anomaly) [ kg/m^3 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_rho_ice(double t, double p)
+{
+ return (1.0/gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_rho_second_derivatives (sa, ct, p, rho_sa_sa, &
+ rho_sa_ct, rho_ct_ct, rho_sa_p, rho_ct_p)
+!==========================================================================
+!
+! Calculates five second-order derivatives of rho. Note that this function
+! uses the computationally-efficient expression for specific
+! volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho_SA_SA = The second-order derivative of rho with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! rho_SA_CT = The second-order derivative of rho with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+! rho_CT_CT = The second-order derivative of rho with respect to CT at
+! constant SA & p
+! rho_SA_P = The second-order derivative with respect to SA & P at
+! constant CT.
+! rho_CT_P = The second-order derivative with respect to CT & P at
+! constant SA.
+!--------------------------------------------------------------------------
+*/
+void
+gsw_rho_second_derivatives(double sa, double ct, double p, double *rho_sa_sa,
+ double *rho_sa_ct, double *rho_ct_ct, double *rho_sa_p,
+ double *rho_ct_p)
+{
+ double rec_v, rec_v2, rec_v3, v_ct, v_ct_ct, v_ct_p, v_p, v_sa,
+ v_sa_ct, v_sa_p, v_sa_sa;
+
+ gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct,&v_p);
+ gsw_specvol_second_derivatives(sa,ct,p,&v_sa_sa,&v_sa_ct,&v_ct_ct,
+ &v_sa_p,&v_ct_p);
+
+ rec_v = 1.0/gsw_specvol(sa,ct,p);
+ rec_v2 = pow(rec_v, 2);
+ rec_v3 = rec_v2*rec_v;
+
+ if (rho_sa_sa != NULL)
+ *rho_sa_sa = -v_sa_sa*rec_v2 + 2.0*v_sa*v_sa*rec_v3;
+
+ if (rho_sa_ct != NULL)
+ *rho_sa_ct = -v_sa_ct*rec_v2 + 2.0*v_sa*v_ct*rec_v3;
+
+ if (rho_ct_ct != NULL)
+ *rho_ct_ct = -v_ct_ct*rec_v2 + 2.0*v_ct*v_ct*rec_v3;
+
+ if (rho_sa_p != NULL)
+ *rho_sa_p = -v_sa_p*rec_v2 + 2.0*v_sa*v_p*rec_v3;
+
+ if (rho_ct_p != NULL)
+ *rho_ct_p = -v_ct_p*rec_v2 + 2.0*v_ct*v_p*rec_v3;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_rho_second_derivatives_wrt_enthalpy (sa, ct, p, &
+ rho_sa_sa, rho_sa_h, rho_h_h)
+! =========================================================================
+!
+! Calculates three second-order derivatives of rho with respect to enthalpy.
+! Note that this function uses the using the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! rho_SA_SA = The second-order derivative of rho with respect to
+! Absolute Salinity at constant h & p. [ J/(kg (g/kg)^2) ]
+! rho_SA_h = The second-order derivative of rho with respect to
+! SA and h at constant p. [ J/(kg K(g/kg)) ]
+! rho_h_h = The second-order derivative of rho with respect to h at
+! constant SA & p
+!--------------------------------------------------------------------------
+*/
+void
+gsw_rho_second_derivatives_wrt_enthalpy(double sa, double ct, double p,
+ double *rho_sa_sa, double *rho_sa_h, double *rho_h_h)
+{
+ double rec_v, rec_v2, rec_v3, v_h, v_h_h, v_sa, v_sa_h, v_sa_sa,
+ *pv_sa, *pv_h, *pv_sa_sa, *pv_sa_h, *pv_h_h;
+
+ pv_sa = ((rho_sa_sa != NULL) || (rho_sa_h != NULL)) ? &v_sa : NULL;
+ pv_h = ((rho_sa_h != NULL) || (rho_h_h != NULL)) ? &v_h : NULL;
+
+ gsw_specvol_first_derivatives_wrt_enthalpy(sa,ct,p,pv_sa,pv_h);
+
+ pv_sa_sa = ((rho_sa_sa != NULL)) ? &v_sa_sa : NULL;
+ pv_sa_h = ((rho_sa_h != NULL)) ? &v_sa_h : NULL;
+ pv_h_h = ((rho_h_h != NULL)) ? &v_h_h : NULL;
+
+ gsw_specvol_second_derivatives_wrt_enthalpy(sa,ct,p,
+ pv_sa_sa,pv_sa_h,pv_h_h);
+
+ rec_v = 1.0/gsw_specvol(sa,ct,p);
+ rec_v2 = rec_v*rec_v;
+ rec_v3 = rec_v2*rec_v;
+
+ if (rho_sa_sa != NULL)
+ *rho_sa_sa = -v_sa_sa*rec_v2 + 2.0*v_sa*v_sa*rec_v3;
+
+ if (rho_sa_h != NULL)
+ *rho_sa_h = -v_sa_h*rec_v2 + 2.0*v_sa*v_h*rec_v3;
+
+ if (rho_h_h != NULL)
+ *rho_h_h = -v_h_h*rec_v2 + 2.0*v_h*v_h*rec_v3;
+}
+/*
+!==========================================================================
+function gsw_rho_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates in-situ density of seawater from Absolute Salinity and
+! in-situ temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_rho_t_exact : in-situ density [kg/m^3]
+*/
+double
+gsw_rho_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (1.0/gsw_gibbs(n0,n0,n1,sa,t,p));
+}
+/*
+!==========================================================================
+pure subroutine gsw_rr68_interp_sa_ct (sa, ct, p, p_i, sa_i, ct_i)
+!==========================================================================
+!
+! Interpolate Absolute Salinity and Conservative Temperature values to
+! arbitrary pressures using the Reiniger and Ross (1968) interpolation
+! scheme.
+! Note that this interpolation scheme requires at least four observed
+! bottles on the cast.
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! p_i = pressures to interpolate to.
+!
+! SA_i = interpolated SA values at pressures p_i.
+! CT_i = interpolated CT values at pressures p_i.
+!--------------------------------------------------------------------------
+*/
+static void rr68_interp_section(int sectnum, double *sa, double *ct, double *p,
+ int mp, int nsect, double *ip_sect,
+ int *ip_isect, double *p_i, double *sa_i, double *ct_i);
+/* forward reference */
+
+void
+gsw_rr68_interp_sa_ct(double *sa, double *ct, double *p, int mp, double *p_i,
+ int mp_i, double *sa_i, double *ct_i)
+{
+ int i, j, nshallow, ncentral, ndeep,
+ *ip, *ip_i, *ip_ishallow, *ip_icentral, *ip_ideep;
+ char *shallow, *central, *deep;
+ double *ip_shallow, *ip_central, *ip_deep, *dp, *p_ii;
+
+ if (mp < 4) {
+ /* need at least four bottles to perform this interpolation */
+ ct_i[0] = sa_i[0] = GSW_INVALID_VALUE;
+ return;
+ }
+
+ dp = (double *) malloc(mp*sizeof (double));
+ for (i=1; i<mp; i++) {
+ if ((dp[i-1] = (p[i] - p[i-1])) <= 0.0) {
+ free(dp);
+ ct_i[0] = sa_i[0] = GSW_INVALID_VALUE;
+ return;
+ }
+ }
+
+ shallow = (char *) malloc(3*mp_i*sizeof (char));
+ central = shallow+mp_i; deep = central+mp_i;
+ nshallow=ncentral=ndeep=0;
+ memset(shallow, 0, 3*mp_i*sizeof (char));
+ for (i=0; i<mp_i; i++) {
+ if (p_i[i] >= p[0] && p_i[i] <= p[1]) {
+ nshallow++;
+ shallow[i] = 1;
+ }
+ if (p_i[i] >= p[1] && p_i[i] <= p[mp-2]) {
+ ncentral++;
+ central[i] = 1;
+ }
+ if (p_i[i] >= p[mp-2] && p_i[i] <= p[mp-1]) {
+ ndeep++;
+ deep[i] = 1;
+ }
+ }
+
+ if ((nshallow == 0) || (ncentral == 0) || (ndeep == 0)) {
+ free(shallow); free(dp);
+ ct_i[0] = sa_i[0] = GSW_INVALID_VALUE;
+ return;
+ }
+
+ ip = (int *) malloc((mp+mp_i)*sizeof (int)); ip_i = ip+mp;
+ for (i=0; i<mp; i++)
+ ip[i] = i;
+ for (i=0; i<mp_i; i++)
+ ip_i[i] = i;
+
+ ip_ishallow = (int *) malloc((nshallow+ncentral+ndeep)*sizeof (int));
+ ip_icentral = ip_ishallow+nshallow; ip_ideep = ip_icentral+ncentral;
+ ip_shallow = (double *) malloc(2*(nshallow+ncentral+ndeep)*sizeof (double));
+ ip_central = ip_shallow+nshallow; ip_deep = ip_central+ncentral;
+ p_ii = ip_deep+ndeep;
+ /*
+ ! Calculate the 2 outer extrapolated values and the inner
+ ! interpolated values
+ */
+ for (i=j=0; i<mp_i; i++) {
+ if (central[i]) {
+ ip_icentral[j] = ip_i[i];
+ j++;
+ }
+ }
+ for (i=0; i<ncentral; i++)
+ p_ii[i] = p_i[ip_icentral[i]];
+ gsw_util_interp1q_int(mp,p,ip,ncentral,p_ii,ip_central);
+ rr68_interp_section(0,sa,ct,p,mp,ncentral,ip_central,ip_icentral,
+ p_i,sa_i,ct_i);
+
+ for (i=j=0; i<mp_i; i++) {
+ if (shallow[i]) {
+ ip_ishallow[j] = ip_i[i];
+ j++;
+ }
+ }
+ for (i=0; i<nshallow; i++)
+ p_ii[i] = p_i[ip_ishallow[i]];
+ gsw_util_interp1q_int(mp,p,ip,nshallow,p_ii,ip_shallow);
+ rr68_interp_section(-1,sa,ct,p,mp,nshallow,ip_shallow,ip_ishallow,
+ p_i,sa_i,ct_i);
+
+ for (i=j=0; i<mp_i; i++) {
+ if (deep[i]) {
+ ip_ideep[j] = ip_i[i];
+ j++;
+ }
+ }
+ for (i=0; i<ndeep; i++)
+ p_ii[i] = p_i[ip_ideep[i]];
+ gsw_util_interp1q_int(mp,p,ip,ndeep,p_ii,ip_deep);
+ rr68_interp_section(1,sa,ct,p,mp,ndeep,ip_deep,ip_ideep,p_i,sa_i,ct_i);
+
+ /*
+ ! Insert any observed bottles that are at the required interpolated
+ ! pressures
+ */
+ for (i=0; i<mp_i; i++) {
+ for (j=0; j<mp; j++) {
+ if (p_i[i] == p[j]) {
+ sa_i[i] = sa[j];
+ ct_i[i] = ct[j];
+ }
+ }
+ }
+ free(ip_shallow); free(ip_ishallow); free(ip); free(shallow); free(dp);
+}
+
+/*
+pure subroutine rr68_interp_section (sectnum, ip_sect, ip_isect, sa_i, ct_i)
+*/
+static void
+rr68_interp_section(int sectnum, double *sa, double *ct, double *p, int mp,
+ int nsect, double *ip_sect, int *ip_isect, double *p_i, double *sa_i,
+ double *ct_i)
+{
+ int i, *ip_1, *ip_2, *ip_3, *ip_4;
+ double m, *ct_12, *ct_13, *ct_23, *ct_34, ctp1,
+ ctp2, *ct_ref, ctref_denom,
+ ct_ref_minus_ctp1, ct_ref_minus_ctp2,
+ ctref_num,
+ gamma1_23, gamma1_24, gamma2_31,
+ gamma2_34, gamma2_41, gamma3_12,
+ gamma3_42, gamma4_12, gamma4_23,
+ *sa_12, *sa_13, *sa_23, *sa_34, sap1,
+ sap2, *sa_ref, saref_denom,
+ sa_ref_minus_sap1, sa_ref_minus_sap2,
+ saref_num, *p_ii;
+
+ ip_1 = (int *) malloc(4*nsect*sizeof (int)); ip_2 = ip_1+nsect;
+ ip_3 = ip_2+nsect; ip_4 = ip_3+nsect;
+
+ ct_12 = (double *) malloc(12*nsect*sizeof (double));
+ sa_12 = ct_12 + 1*nsect;
+ sa_13 = ct_12 + 2*nsect;
+ sa_23 = ct_12 + 3*nsect;
+ sa_34 = ct_12 + 4*nsect;
+ sa_ref = ct_12 + 5*nsect;
+ ct_13 = ct_12 + 6*nsect;
+ ct_23 = ct_12 + 7*nsect;
+ ct_34 = ct_12 + 8*nsect;
+ ct_ref = ct_12 + 9*nsect;
+ p_ii = ct_12 + 10*nsect;
+
+ if (sectnum < 0) { /* shallow */
+ for (i=0; i<nsect; i++) {
+ ip_1[i] = floor(ip_sect[i]);
+ ip_2[i] = ceil(ip_sect[i]);
+ ip_3[i] = ip_2[i] + 1;
+ ip_4[i] = ip_3[i] + 1;
+ }
+ } else if (sectnum == 0) { /* central */
+ for (i=0; i<nsect; i++) {
+ ip_2[i] = floor(ip_sect[i]);
+ ip_1[i] = ip_2[i] - 1;
+ ip_3[i] = ceil(ip_sect[i]);
+ ip_4[i] = ip_3[i] + 1;
+ }
+ } else if (sectnum > 0) { /* deep */
+ for (i=0; i<nsect; i++) {
+ ip_1[i] = ceil(ip_sect[i]);
+ ip_2[i] = floor(ip_sect[i]);
+ ip_3[i] = ip_2[i] - 1;
+ ip_4[i] = ip_3[i] - 1;
+ }
+ }
+
+ for (i=0; i<nsect; i++)
+ p_ii[i] = p_i[ip_isect[i]];
+
+ /* eqn (3d) */
+ for (i=0; i<nsect; i++) {
+ sa_34[i] = sa[ip_3[i]] + ((sa[ip_4[i]] - sa[ip_3[i]])
+ *(p_ii[i] - p[ip_3[i]])/ (p[ip_4[i]] - p[ip_3[i]]));
+ ct_34[i] = ct[ip_3[i]] + ((ct[ip_4[i]] - ct[ip_3[i]])
+ *(p_ii[i] - p[ip_3[i]])/ (p[ip_4[i]] - p[ip_3[i]]));
+ }
+ /*
+ ! Construct the Reiniger & Ross reference curve equation.
+ ! m = the power variable
+ */
+ m = 1.7;
+
+ if (sectnum == 0) {
+
+ gsw_linear_interp_sa_ct(sa,ct,p,mp,p_ii,nsect,sa_23,ct_23);
+
+ /* eqn (3a) */
+ for (i=0; i<nsect; i++) {
+ sa_12[i] = sa[ip_1[i]] + ((sa[ip_2[i]] - sa[ip_1[i]])
+ *(p_ii[i] - p[ip_1[i]])/ (p[ip_2[i]] - p[ip_1[i]]));
+ ct_12[i] = ct[ip_1[i]] + ((ct[ip_2[i]] - ct[ip_1[i]])
+ *(p_ii[i] - p[ip_1[i]])/ (p[ip_2[i]] - p[ip_1[i]]));
+
+ saref_num = (pow(fabs(sa_23[i]-sa_34[i]),m))*sa_12[i]
+ + (pow(fabs(sa_12[i]-sa_23[i]),m))*sa_34[i];
+ ctref_num = (pow(fabs(ct_23[i]-ct_34[i]),m))*ct_12[i]
+ + (pow(fabs(ct_12[i]-ct_23[i]),m))*ct_34[i];
+
+ saref_denom = pow(fabs(sa_23[i]-sa_34[i]),m)
+ + pow(fabs(sa_12[i]-sa_23[i]),m);
+ ctref_denom = pow(fabs(ct_23[i]-ct_34[i]),m)
+ + pow(fabs(ct_12[i]-ct_23[i]),m);
+
+ if (saref_denom == 0.0) {
+ sa_23[i] = sa_23[i] + 1.0e-6;
+ saref_num = (pow(fabs(sa_23[i]-sa_34[i]),m))*sa_12[i]
+ + (pow(fabs(sa_12[i]-sa_23[i]),m))*sa_34[i];
+ saref_denom = pow(fabs(sa_23[i]-sa_34[i]),m)
+ + pow(fabs(sa_12[i]-sa_23[i]),m);
+ }
+ if (ctref_denom == 0.0) {
+ ct_23[i] = ct_23[i] + 1.0e-6;
+ ctref_num = (pow(fabs(ct_23[i]-ct_34[i]),m))*ct_12[i]
+ + (pow(fabs(ct_12[i]-ct_23[i]),m))*ct_34[i];
+ ctref_denom = pow(fabs(ct_23[i]-ct_34[i]),m)
+ + pow(fabs(ct_12[i]-ct_23[i]),m);
+ }
+
+ sa_ref[i] = 0.5*(sa_23[i] + (saref_num/saref_denom));
+ ct_ref[i] = 0.5*(ct_23[i] + (ctref_num/ctref_denom));
+ }
+
+ } else {
+
+ gsw_linear_interp_sa_ct(sa,ct,p,mp,p_ii,nsect,sa_12,ct_12);
+
+ for (i=0; i<nsect; i++) {
+ sa_13[i] = sa[ip_1[i]] + ((sa[ip_3[i]] - sa[ip_1[i]])
+ *(p_ii[i] - p[ip_1[i]])/ (p[ip_3[i]] - p[ip_1[i]]));
+ ct_13[i] = ct[ip_1[i]] + ((ct[ip_3[i]] - ct[ip_1[i]])
+ *(p_ii[i] - p[ip_1[i]])/ (p[ip_3[i]] - p[ip_1[i]]));
+
+ sa_23[i] = sa[ip_2[i]] + ((sa[ip_3[i]] - sa[ip_2[i]])
+ *(p_ii[i] - p[ip_2[i]])/ (p[ip_3[i]] - p[ip_2[i]]));
+ ct_23[i] = ct[ip_2[i]] + ((ct[ip_3[i]] - ct[ip_2[i]])
+ *(p_ii[i] - p[ip_2[i]])/ (p[ip_3[i]] - p[ip_2[i]]));
+
+ /* eqn (3a') */
+ saref_num = (pow(fabs(sa_12[i]-sa_23[i]),m))*sa_34[i]
+ + (pow(fabs(sa_12[i]-sa_13[i]),m))*sa_23[i];
+ ctref_num = (pow(fabs(ct_12[i]-ct_23[i]),m))*ct_34[i]
+ + (pow(fabs(ct_12[i]-ct_13[i]),m))*ct_23[i];
+
+ saref_denom = pow(fabs(sa_12[i]-sa_23[i]),m)
+ + pow(fabs(sa_12[i]-sa_13[i]),m);
+ ctref_denom = pow(fabs(ct_12[i]-ct_23[i]),m)
+ + pow(fabs(ct_12[i]-ct_13[i]),m);
+
+ if (saref_denom == 0.0) {
+ sa_23[i] = sa_23[i] + 1.0e-6;
+ saref_num = (pow(fabs(sa_12[i]-sa_23[i]),m))*sa_34[i]
+ + (pow(fabs(sa_12[i]-sa_13[i]),m))*sa_23[i];
+ saref_denom = pow(fabs(sa_12[i]-sa_23[i]),m)
+ + pow(fabs(sa_12[i]-sa_13[i]),m);
+ }
+ if (ctref_denom == 0.0) {
+ ct_23[i] = ct_23[i] + 1.0e-6;
+ ctref_num = (pow(fabs(ct_12[i]-ct_23[i]),m))*ct_34[i]
+ + (pow(fabs(ct_12[i]-ct_13[i]),m))*ct_23[i];
+ ctref_denom = pow(fabs(ct_12[i]-ct_23[i]),m)
+ + pow(fabs(ct_12[i]-ct_13[i]),m);
+ }
+
+ sa_ref[i] = 0.5*(sa_12[i] + (saref_num/saref_denom));
+ ct_ref[i] = 0.5*(ct_12[i] + (ctref_num/ctref_denom));
+ }
+ }
+
+ for (i=0; i<nsect; i++) {
+ /* eqn (3c) */
+ gamma1_23 = ((p_ii[i] - p[ip_2[i]])*(p_ii[i] - p[ip_3[i]]))/
+ ((p[ip_1[i]] - p[ip_2[i]])*(p[ip_1[i]] - p[ip_3[i]]));
+ gamma2_31 = ((p_ii[i] - p[ip_3[i]])*(p_ii[i] - p[ip_1[i]]))/
+ ((p[ip_2[i]] - p[ip_3[i]])*(p[ip_2[i]] - p[ip_1[i]]));
+ gamma3_12 = ((p_ii[i] - p[ip_1[i]])*(p_ii[i] - p[ip_2[i]]))/
+ ((p[ip_3[i]] - p[ip_1[i]])*(p[ip_3[i]] - p[ip_2[i]]));
+
+ if (sectnum == 0) {
+ gamma2_34 = ((p_ii[i] - p[ip_3[i]])*(p_ii[i] - p[ip_4[i]]))/
+ ((p[ip_2[i]] - p[ip_3[i]])*(p[ip_2[i]] - p[ip_4[i]]));
+ gamma3_42 = ((p_ii[i] - p[ip_4[i]])*(p_ii[i] - p[ip_2[i]]))/
+ ((p[ip_3[i]] - p[ip_4[i]])*(p[ip_3[i]] - p[ip_2[i]]));
+ gamma4_23 = ((p_ii[i] - p[ip_2[i]])*(p_ii[i] - p[ip_3[i]]))/
+ ((p[ip_4[i]] - p[ip_2[i]])*(p[ip_4[i]] - p[ip_3[i]]));
+ } else {
+ gamma1_24 = ((p_ii[i] - p[ip_2[i]])*(p_ii[i] - p[ip_4[i]]))/
+ ((p[ip_1[i]] - p[ip_2[i]])*(p[ip_1[i]] - p[ip_4[i]]));
+ gamma2_41 = ((p_ii[i] - p[ip_4[i]])*(p_ii[i] - p[ip_1[i]]))/
+ ((p[ip_2[i]] - p[ip_4[i]])*(p[ip_2[i]] - p[ip_1[i]]));
+ gamma4_12 = ((p_ii[i] - p[ip_1[i]])*(p_ii[i] - p[ip_2[i]]))/
+ ((p[ip_4[i]] - p[ip_1[i]])*(p[ip_4[i]] - p[ip_2[i]]));
+ }
+
+ /* eqn (3b/3b') */
+ sap1 = gamma1_23*sa[ip_1[i]] + gamma2_31*sa[ip_2[i]]
+ + gamma3_12*sa[ip_3[i]];
+ ctp1 = gamma1_23*ct[ip_1[i]] + gamma2_31*ct[ip_2[i]]
+ + gamma3_12*ct[ip_3[i]];
+ if (sectnum == 0) {
+ sap2 = gamma2_34*sa[ip_2[i]] + gamma3_42*sa[ip_3[i]]
+ + gamma4_23*sa[ip_4[i]];
+ ctp2 = gamma2_34*ct[ip_2[i]] + gamma3_42*ct[ip_3[i]]
+ + gamma4_23*ct[ip_4[i]];
+ } else {
+ sap2 = gamma1_24*sa[ip_1[i]] + gamma2_41*sa[ip_2[i]]
+ + gamma4_12*sa[ip_4[i]];
+ ctp2 = gamma1_24*ct[ip_1[i]] + gamma2_41*ct[ip_2[i]]
+ + gamma4_12*ct[ip_4[i]];
+ }
+
+ /* eqn (3) */
+ sa_ref_minus_sap1 = fabs(sa_ref[i] - sap1);
+ sa_ref_minus_sap2 = fabs(sa_ref[i] - sap2);
+ if (sa_ref_minus_sap1 == 0.0 && sa_ref_minus_sap2 == 0.0) {
+ sa_ref[i] = sa_ref[i] + 1.0e-6;
+ sa_ref_minus_sap1 = fabs(sa_ref[i] - sap1);
+ sa_ref_minus_sap2 = fabs(sa_ref[i] - sap2);
+ }
+
+ ct_ref_minus_ctp1 = fabs(ct_ref[i] - ctp1);
+ ct_ref_minus_ctp2 = fabs(ct_ref[i] - ctp2);
+ if (ct_ref_minus_ctp1 == 0.0 && ct_ref_minus_ctp2 == 0.0) {
+ ct_ref[i] = ct_ref[i] + 1.0e-6;
+ ct_ref_minus_ctp1 = fabs(ct_ref[i] - ctp1);
+ ct_ref_minus_ctp2 = fabs(ct_ref[i] - ctp2);
+ }
+
+ sa_i[ip_isect[i]] = (sa_ref_minus_sap1*sap2+sa_ref_minus_sap2*sap1)/
+ (sa_ref_minus_sap1 + sa_ref_minus_sap2);
+ ct_i[ip_isect[i]] = (ct_ref_minus_ctp1*ctp2+ct_ref_minus_ctp2*ctp1)/
+ (ct_ref_minus_ctp1 + ct_ref_minus_ctp2);
+ }
+ free(ct_12); free(ip_1);
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_estimate (p, saturation_fraction, ct, t)
+!==========================================================================
+!
+! Form an estimate of SA from a polynomial in CT and p
+!
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_estimate(double p, double saturation_fraction, double *ct,
+ double *t)
+{
+ GSW_TEOS10_CONSTANTS;
+ double ctx, ctsat, sa,
+ /*note that aa = 0.502500117621d0/35.16504*/
+ aa = 0.014289763856964,
+ bb = 0.057000649899720,
+
+ p0 = 2.570124672768757e-1,
+ p1 = -1.917742353032266e1,
+ p2 = -1.413382858617969e-2,
+ p3 = -5.427484830917552e-1,
+ p4 = -4.126621135193472e-4,
+ p5 = -4.176407833276121e-7,
+ p6 = 4.688217641883641e-5,
+ p7 = -3.039808885885726e-8,
+ p8 = -4.990118091261456e-11,
+ p9 = -9.733920711119464e-9,
+ p10 = -7.723324202726337e-12,
+ p11 = 7.121854166249257e-16,
+ p12 = 1.256474634100811e-12,
+ p13 = 2.105103897918125e-15,
+ p14 = 8.663811778227171e-19;
+
+ /*A very rough estimate of sa to get the saturated ct*/
+ if (ct != NULL) {
+ sa = max(-(*ct + 9e-4*p)/0.06, 0.0);
+ ctx = *ct;
+ } else if (t != NULL) {
+ sa = max(-(*t + 9e-4*p)/0.06, 0.0);
+ ctx = gsw_ct_from_t(sa,*t,p);
+ } else {
+ return (0.0);
+ }
+ /*
+ ! CTsat is the estimated value of CT if the seawater were saturated with
+ ! dissolved air, recognizing that it actually has the air fraction
+ ! saturation_fraction; see McDougall, Barker and Feistel, 2014).
+ */
+ ctsat = ctx - (1.0-saturation_fraction)*
+ (1e-3)*(2.4-aa*sa)*(1.0+bb*(1.0-sa/gsw_sso));
+
+ return (p0 + p*(p2 + p4*ctsat + p*(p5 + ctsat*(p7 + p9*ctsat)
+ + p*(p8 + ctsat*(p10 + p12*ctsat) + p*(p11 + p13*ctsat + p14*p))))
+ + ctsat*(p1 + ctsat*(p3 + p6*p)));
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_from_ct (ct, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Absolute Salinity of seawater at the freezing temperature.
+! That is, the output is the Absolute Salinity of seawater, with
+! Conservative Temperature CT, pressure p and the fraction
+! saturation_fraction of dissolved air, that is in equilibrium
+! with ice at the same in situ temperature and pressure. If the input
+! values are such that there is no positive value of Absolute Salinity for
+! which seawater is frozen, the output is made a NaN.
+!
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! sa_freezing_from_ct = Absolute Salinity of seawater when it freezes,
+! for given input values of its Conservative Temperature,
+! pressure and air saturation fraction. [ g/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_from_ct(double ct, double p, double saturation_fraction)
+{
+ int i_iter, number_of_iterations = 3;
+ double ct_freezing_zero_sa, f, ctfreezing_sa, sa, sa_mean, sa_old;
+ /*
+ ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat
+ ! differently in calculating the initial values of both SA and dCT_dSA.
+ */
+ double sa_cut_off = 2.5;
+ /*
+ ! Find CT > CT_freezing_zero_SA. If this is the case, the input values
+ ! represent seawater that is not frozen (for any positive SA).
+ */
+ ct_freezing_zero_sa = gsw_ct_freezing(0.0,p,saturation_fraction);
+ if (ct > ct_freezing_zero_sa)
+ return (GSW_INVALID_VALUE);
+
+ /*Form the first estimate of SA from a polynomial in CT and p*/
+ sa = gsw_sa_freezing_estimate(p,saturation_fraction,&ct,NULL);
+ if (sa < -sa_cut_off)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! Form the first estimate of CTfreezing_SA,
+ ! the derivative of CT_freezing with respect to SA at fixed p.
+ */
+ sa = max(sa,0.0);
+ gsw_ct_freezing_first_derivatives(sa,p,saturation_fraction,
+ &ctfreezing_sa, NULL);
+ /*
+ ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
+ ! with one based on (CT_freezing_zero_SA - CT).
+ */
+ if (fabs(sa) < sa_cut_off)
+ sa = (ct - ct_freezing_zero_sa)/ctfreezing_sa;
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin the modified Newton-Raphson method to solve
+ ! f = (CT_freezing - CT) = 0 for SA.
+ !-----------------------------------------------------------------------
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ sa_old = sa;
+ f = gsw_ct_freezing(sa,p,saturation_fraction) - ct;
+ sa = sa_old - f/ctfreezing_sa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_ct_freezing_first_derivatives(sa_mean,p,saturation_fraction,
+ &ctfreezing_sa, NULL);
+ sa = sa_old - f/ctfreezing_sa;
+ }
+
+ if (gsw_sa_p_inrange(sa,p))
+ return (sa);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_from_ct_poly (ct, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Absolute Salinity of seawater at the freezing temperature.
+! That is, the output is the Absolute Salinity of seawater, with the
+! fraction saturation_fraction of dissolved air, that is in equilibrium
+! with ice at Conservative Temperature CT and pressure p. If the input
+! values are such that there is no positive value of Absolute Salinity for
+! which seawater is frozen, the output is put equal to Nan.
+!
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! sa_freezing_from_ct = Absolute Salinity of seawater when it freezes,
+! for given input values of Conservative Temperature
+! pressure and air saturation fraction. [ g/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_from_ct_poly(double ct, double p, double saturation_fraction)
+{
+ int i_iter, number_of_iterations = 2;
+ double ct_freezing, ct_freezing_zero_sa, dct_dsa, sa, sa_old, sa_mean;
+ /*
+ ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat
+ ! differently in calculating the initial values of both SA and dCT_dSA.
+ */
+ double sa_cut_off = 2.5;
+ /*
+ ! Find CT > CT_freezing_zero_SA. If this is the case, the input values
+ ! represent seawater that is not frozen (at any positive SA).
+ */
+ ct_freezing_zero_sa = gsw_ct_freezing_poly(0.0,p,saturation_fraction);
+ if (ct > ct_freezing_zero_sa)
+ return (GSW_INVALID_VALUE);
+
+ /*Form the first estimate of SA from a polynomial in CT and p */
+ sa = gsw_sa_freezing_estimate(p,saturation_fraction,&ct,NULL);
+ if (sa < -sa_cut_off)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! Form the first estimate of dCT_dSA, the derivative of CT with respect
+ ! to SA at fixed p.
+ */
+ sa = max(sa,0.0);
+ gsw_ct_freezing_first_derivatives_poly(sa,p,saturation_fraction,
+ &dct_dsa, NULL);
+ /*
+ ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
+ ! with one based on (CT_freezing_zero_SA - CT).
+ */
+ if (fabs(sa) < sa_cut_off)
+ sa = (ct - ct_freezing_zero_sa)/dct_dsa;
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin the modified Newton-Raphson method to solve the root of
+ ! CT_freezing = CT for SA.
+ !-----------------------------------------------------------------------
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ sa_old = sa;
+ ct_freezing = gsw_ct_freezing_poly(sa_old,p,saturation_fraction);
+ sa = sa_old - (ct_freezing - ct)/dct_dsa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_ct_freezing_first_derivatives_poly(sa_mean,p,
+ saturation_fraction, &dct_dsa, NULL);
+ sa = sa_old - (ct_freezing - ct)/dct_dsa;
+ }
+
+ if (gsw_sa_p_inrange(sa,p))
+ return (sa);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_from_t (t, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Absolute Salinity of seawater at the freezing temperature.
+! That is, the output is the Absolute Salinity of seawater, with the
+! fraction saturation_fraction of dissolved air, that is in equilibrium
+! with ice at in-situ temperature t and pressure p. If the input values
+! are such that there is no positive value of Absolute Salinity for which
+! seawater is frozen, the output is set to NaN.
+!
+! t = in-situ Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+! (i.e., saturation_fraction must be between 0 and 1, and the default
+! is 1, completely saturated)
+!
+! sa_freezing_from_t = Absolute Salinity of seawater when it freezes, for
+! given input values of in situ temperature, pressure and
+! air saturation fraction. [ g/kg ]
+!---------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_from_t(double t, double p, double saturation_fraction)
+{
+ int i_iter, number_of_iterations = 2;
+ double f, sa, sa_mean, sa_old, t_freezing_zero_sa, tfreezing_sa;
+ /*
+ ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat
+ ! differently in calculating the initial values of both SA and dCT_dSA.
+ */
+ double sa_cut_off = 2.5;
+ /*
+ ! Find t > t_freezing_zero_SA. If this is the case, the input values
+ ! represent seawater that is not frozen (at any positive SA).
+ */
+ t_freezing_zero_sa = gsw_t_freezing(0.0,p,saturation_fraction);
+ if (t > t_freezing_zero_sa)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! This is the inital guess of SA using a purpose-built
+ ! polynomial in CT and p
+ */
+ sa = gsw_sa_freezing_estimate(p,saturation_fraction,NULL,&t);
+ if (sa < -sa_cut_off)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! Form the first estimate of tfreezing_SA, the derivative of
+ ! CT_freezing with respect to SA at fixed p.
+ */
+ sa = max(sa,0.0);
+ gsw_t_freezing_first_derivatives(sa,p,saturation_fraction,
+ &tfreezing_sa,NULL);
+ /*
+ ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
+ ! with one based on (t_freezing_zero_SA - t).
+ */
+ if (fabs(sa) < sa_cut_off)
+ sa = (t - t_freezing_zero_sa)/tfreezing_sa;
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin the modified Newton-Raphson method to find the root of
+ ! f = (t_freezing - t) = 0 for SA.
+ !-----------------------------------------------------------------------
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ sa_old = sa;
+ f = gsw_t_freezing(sa_old,p,saturation_fraction) - t;
+ sa = sa_old - f/tfreezing_sa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_t_freezing_first_derivatives(sa_mean,p,saturation_fraction,
+ &tfreezing_sa, NULL);
+ sa = sa_old - f/tfreezing_sa;
+ }
+
+ if (gsw_sa_p_inrange(sa,p))
+ return (sa);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+elemental function gsw_sa_freezing_from_t_poly (t, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the Absolute Salinity of seawater at the freezing temperature.
+! That is, the output is the Absolute Salinity of seawater, with the
+! fraction saturation_fraction of dissolved air, that is in equilibrium
+! with ice at in-situ temperature t and pressure p. If the input values
+! are such that there is no positive value of Absolute Salinity for which
+! seawater is frozen, the output is put equal to Nan.
+!
+! t = in-situ Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! sa_freezing_from_t_poly = Absolute Salinity of seawater when it freezes,
+! for given input values of in situ temperature, pressure and
+! air saturation fraction. [ g/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sa_freezing_from_t_poly(double t, double p, double saturation_fraction)
+{
+ int i_iter, number_of_iterations = 5;
+ double dt_dsa, sa, sa_old, sa_mean, t_freezing, t_freezing_zero_sa;
+ /*
+ ! This is the band of sa within +- 2.5 g/kg of sa = 0, which we treat
+ ! differently in calculating the initial values of both SA and dCT_dSA.
+ */
+ double sa_cut_off = 2.5;
+ /*
+ ! Find t > t_freezing_zero_SA. If this is the case, the input values
+ ! represent seawater that is not frozen (at any positive SA).
+ */
+ t_freezing_zero_sa = gsw_t_freezing_poly(0.0,p,saturation_fraction);
+ if (t > t_freezing_zero_sa)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! This is the inital guess of SA using a purpose-built
+ ! polynomial in CT and p
+ */
+ sa = gsw_sa_freezing_estimate(p,saturation_fraction,NULL,&t);
+ if (sa < -sa_cut_off)
+ return (GSW_INVALID_VALUE);
+ /*
+ ! Form the first estimate of dt_dSA, the derivative of t with respect
+ ! to SA at fixed p.
+ */
+ sa = max(sa,0.0);
+ gsw_t_freezing_first_derivatives_poly(sa,p,saturation_fraction,
+ &dt_dsa, NULL);
+ /*
+ ! For -SA_cut_off < SA < SA_cut_off, replace the above estimate of SA
+ ! with one based on (t_freezing_zero_SA - t).
+ */
+ if (fabs(sa) < sa_cut_off)
+ sa = (t - t_freezing_zero_sa)/dt_dsa;
+ /*
+ !-----------------------------------------------------------------------
+ ! Begin the modified Newton-Raphson method to find the root of
+ ! t_freezing = t for SA.
+ !-----------------------------------------------------------------------
+ */
+ for (i_iter = 1; i_iter <= number_of_iterations; i_iter++) {
+ sa_old = sa;
+ t_freezing = gsw_t_freezing_poly(sa_old,p,saturation_fraction);
+ sa = sa_old - (t_freezing - t)/dt_dsa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_t_freezing_first_derivatives_poly(sa_mean,p,saturation_fraction,
+ &dt_dsa, NULL);
+ sa = sa_old - (t_freezing - t)/dt_dsa;
+ }
+
+ if (gsw_sa_p_inrange(sa,p))
+ return (sa);
+ return (GSW_INVALID_VALUE);
+}
+/*
+!==========================================================================
+function gsw_sa_from_rho(rho,ct,p)
+!==========================================================================
+
+! Calculates the Absolute Salinity of a seawater sample, for given values
+! of its density, Conservative Temperature and sea pressure (in dbar).
+!
+! rho = density of a seawater sample (e.g. 1026 kg/m^3). [ kg/m^3 ]
+! Note. This input has not had 1000 kg/m^3 subtracted from it.
+! That is, it is 'density', not 'density anomaly'.
+! ct = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+!
+! sa = Absolute Salinity [g/kg]
+*/
+double
+gsw_sa_from_rho(double rho, double ct, double p)
+{
+ int no_iter;
+
+ double sa, v_lab, v_0, v_50, v_sa, sa_old, delta_v, sa_mean;
+
+ v_lab = 1.0/rho;
+ v_0 = gsw_specvol(0.0,ct,p);
+ v_50 = gsw_specvol(50.0,ct,p);
+
+ sa = 50.0*(v_lab - v_0)/(v_50 - v_0);
+ if (sa < 0.0 || sa > 50.0)
+ return (GSW_INVALID_VALUE);
+
+ v_sa = (v_50 - v_0)/50.0;
+
+ for (no_iter=1; no_iter <= 2; no_iter++) {
+ sa_old = sa;
+ delta_v = gsw_specvol(sa_old,ct,p) - v_lab;
+ sa = sa_old - delta_v/v_sa;
+ sa_mean = 0.5*(sa + sa_old);
+ gsw_specvol_first_derivatives(sa_mean,ct,p,&v_sa,NULL,NULL);
+ sa = sa_old - delta_v/v_sa;
+ if (sa < 0.0 || sa > 50.0)
+ return (GSW_INVALID_VALUE);
+ }
+ return (sa);
+}
+/*
+!==========================================================================
+function gsw_sa_from_sp(sp,p,lon,lat)
+!==========================================================================
+
+! Calculates Absolute Salinity, SA, from Practical Salinity, SP
+!
+! sp : Practical Salinity [unitless]
+! p : sea pressure [dbar]
+! lon : longitude [DEG E]
+! lat : latitude [DEG N]
+!
+! gsw_sa_from_sp : Absolute Salinity [g/kg]
+*/
+double
+gsw_sa_from_sp(double sp, double p, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double saar, gsw_sa_baltic;
+
+ gsw_sa_baltic = gsw_sa_from_sp_baltic(sp,lon,lat);
+ if (gsw_sa_baltic < GSW_ERROR_LIMIT)
+ return (gsw_sa_baltic);
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return (gsw_ups*sp*(1.e0 + saar));
+}
+/*
+!==========================================================================
+function gsw_sa_from_sp_baltic(sp,lon,lat)
+!==========================================================================
+
+! For the Baltic Sea, calculates Absolute Salinity with a value
+! computed analytically from Practical Salinity
+!
+! sp : Practical Salinity [unitless]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! sa_from_sp_baltic : Absolute Salinity [g/kg]
+*/
+double
+gsw_sa_from_sp_baltic(double sp, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_BALTIC_DATA;
+ double xx_left, xx_right, return_value;
+
+ if (xb_left[1] < lon && lon < xb_right[0] && yb_left[0] < lat &&
+ lat < yb_left[2]) {
+
+ xx_left = gsw_util_xinterp1(yb_left, xb_left, 3, lat);
+
+ xx_right = gsw_util_xinterp1(yb_right, xb_right, 2, lat);
+
+ if (xx_left <= lon && lon <= xx_right)
+ return_value =((gsw_sso - 0.087)/35.0)*sp + 0.087;
+ else
+ return_value = GSW_INVALID_VALUE;
+ } else
+ return_value = GSW_INVALID_VALUE;
+
+ return (return_value);
+}
+/*
+!==========================================================================
+function gsw_sa_from_sstar(sstar,p,lon,lat)
+!==========================================================================
+
+! Calculates Absolute Salinity, SA, from Preformed Salinity, Sstar.
+!
+! Sstar : Preformed Salinity [g/kg]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sa_from_sstar : Absolute Salinity [g/kg]
+*/
+double
+gsw_sa_from_sstar(double sstar, double p, double lon, double lat)
+{
+ double saar;
+
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ /*
+ **! In the Baltic Sea, Sstar = SA, and note that gsw_saar returns zero
+ **! for SAAR in the Baltic.
+ */
+ return (sstar*(1e0 + saar)/(1e0 - 0.35e0*saar));
+}
+/*
+!==========================================================================
+elemental function gsw_sa_p_inrange (sa, p)
+!==========================================================================
+!
+! Check for any values that are out of the TEOS-10 range ...
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!---------------------------------------------------------------------------
+*/
+int
+gsw_sa_p_inrange(double sa, double p)
+{
+ if (p > 10000.0 || sa > 120.0 ||
+ (p + sa*71.428571428571402) > 13571.42857142857)
+ return (0);
+ return (1);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_seaice_fraction_to_freeze_seawater (sa, ct, p, &
+ sa_seaice, t_seaice, sa_freeze, ct_freeze, w_seaice)
+!==========================================================================
+!
+! Calculates the mass fraction of sea ice (mass of sea ice divided by mass
+! of sea ice plus seawater), which, when melted into seawater having the
+! properties (SA,CT,p) causes the final seawater to be at the freezing
+! temperature. The other outputs are the Absolute Salinity and
+! Conservative Temperature of the final seawater.
+!
+! SA = Absolute Salinity of seawater [ g/kg ]
+! CT = Conservative Temperature of seawater (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! SA_seaice = Absolute Salinity of sea ice, that is, the mass fraction of
+! salt in sea ice, expressed in g of salt per kg of sea ice.
+! [ g/kg ]
+! t_seaice = in-situ temperature of the sea ice at pressure p (ITS-90)
+! [ deg C ]
+!
+! SA_freeze = Absolute Salinity of seawater after the mass fraction of
+! sea ice, w_seaice, at temperature t_seaice has melted into
+! the original seawater, and the final mixture is at the
+! freezing temperature of seawater. [ g/kg ]
+!
+! CT_freeze = Conservative Temperature of seawater after the mass
+! fraction, w_seaice, of sea ice at temperature t_seaice has
+! melted into the original seawater, and the final mixture
+! is at the freezing temperature of seawater. [ deg C ]
+!
+! w_seaice = mass fraction of sea ice, at SA_seaice and t_seaice,
+! which, when melted into seawater at (SA,CT,p) leads to the
+! final mixed seawater being at the freezing temperature.
+! This output is between 0 and 1. [unitless]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_seaice_fraction_to_freeze_seawater(double sa, double ct, double p,
+ double sa_seaice, double t_seaice, double *sa_freeze, double *ct_freeze,
+ double *w_seaice)
+{
+ int number_of_iterations;
+ double ctf, ctf_mean, ctf_old, ctf_plus1, ctf_zero,
+ dfunc_dsaf, func, func_plus1, func_zero, h, h_brine,
+ h_ih, sa_freezing, saf, saf_mean, saf_old,
+ salt_ratio, tf_sa_seaice, h_hat_sa, h_hat_ct, ctf_sa,
+ sa0 = 0.0, saturation_fraction = 0.0;
+
+ ctf = gsw_ct_freezing(sa,p,saturation_fraction);
+ if (ct < ctf) {
+ /*The seawater ct input is below the freezing temp*/
+ *sa_freeze = *ct_freeze = *w_seaice = GSW_INVALID_VALUE;
+ return;
+ }
+
+ tf_sa_seaice = gsw_t_freezing(sa_seaice,p,saturation_fraction)
+ - 1e-6;
+ if (t_seaice > tf_sa_seaice) {
+ /*
+ ! The 1e-6 C buffer in the allowable t_seaice is to ensure that there is
+ ! some ice Ih in the sea ice. Without this buffer, that is if t_seaice
+ ! is allowed to be exactly equal to tf_sa_seaice, the sea ice is
+ ! actually 100% brine at Absolute Salinity of SA_seaice.
+ */
+ *sa_freeze = *ct_freeze = *w_seaice = GSW_INVALID_VALUE;
+ return;
+ }
+
+ sa_freezing = gsw_sa_freezing_from_t(t_seaice,p,saturation_fraction);
+ if (sa_freezing > GSW_ERROR_LIMIT) {
+ *sa_freeze = *ct_freeze = *w_seaice = GSW_INVALID_VALUE;
+ return;
+ }
+ h_brine = gsw_enthalpy_t_exact(sa_freezing,t_seaice,p);
+ salt_ratio = sa_seaice/sa_freezing;
+
+ h = gsw_enthalpy_ct_exact(sa,ct,p);
+ h_ih = gsw_enthalpy_ice(t_seaice,p);
+
+ ctf_plus1 = gsw_ct_freezing(sa+1.0,p,saturation_fraction);
+ func_plus1 = (sa - sa_seaice)
+ *(gsw_enthalpy_ct_exact(sa+1.0,ctf_plus1,p)
+ - h) - (h - h_ih) + salt_ratio*(h_brine - h_ih);
+
+ ctf_zero = gsw_ct_freezing(sa0,p,saturation_fraction);
+ func_zero = (sa - sa_seaice)
+ *(gsw_enthalpy_ct_exact(sa0,ctf_zero,p) - h)
+ + sa*((h - h_ih) - salt_ratio*(h_brine - h_ih));
+
+ saf = -(sa+1.0)*func_zero/(func_plus1 - func_zero);
+ /*initial guess of saf*/
+ ctf = gsw_ct_freezing(saf,p,saturation_fraction);
+ gsw_enthalpy_first_derivatives_ct_exact(saf,ctf,p,&h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(saf,p,saturation_fraction,
+ &ctf_sa, NULL);
+
+ dfunc_dsaf = (sa - sa_seaice)*(h_hat_sa + h_hat_ct*ctf_sa)
+ - (h - h_ih) + salt_ratio*(h_brine - h_ih);
+
+ for (number_of_iterations = 1; number_of_iterations <= 4;
+ number_of_iterations++) {
+ saf_old = saf;
+ ctf_old = ctf;
+ func = (sa - sa_seaice)
+ *(gsw_enthalpy_ct_exact(saf_old,ctf_old,p) - h)
+ - (saf_old - sa)*((h - h_ih) - salt_ratio*(h_brine - h_ih));
+ saf = saf_old - func/dfunc_dsaf;
+ saf_mean = 0.5*(saf + saf_old);
+ ctf_mean = gsw_ct_freezing(saf_mean,p,saturation_fraction);
+ gsw_enthalpy_first_derivatives_ct_exact(saf_mean,ctf_mean,p,
+ &h_hat_sa,&h_hat_ct);
+ gsw_ct_freezing_first_derivatives(saf_mean,p,saturation_fraction,
+ &ctf_sa, NULL);
+ dfunc_dsaf = (sa - sa_seaice)*(h_hat_sa + h_hat_ct*ctf_sa)
+ - (h - h_ih) + salt_ratio*(h_brine - h_ih);
+ saf = saf_old - func/dfunc_dsaf;
+ ctf = gsw_ct_freezing(saf,p,saturation_fraction);
+ }
+/*
+! After these 4 iterations of this modified Newton-Raphson method, the
+! errors in SA_freeze is less than 1.5x10^-12 g/kg, in CT_freeze is less than
+! 2x10^-13 deg C and in w_seaice is less than 2.8x10^-13 which represent machine
+! precision for these calculations.
+*/
+ *sa_freeze = saf;
+ *ct_freeze = ctf;
+ *w_seaice = (h - gsw_enthalpy_ct_exact(*sa_freeze,*ct_freeze,p)) /
+ (h - h_ih - salt_ratio*(h_brine - h_ih));
+ return;
+}
+/*
+!==========================================================================
+function gsw_sigma0(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 0 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+! This function uses the computationally-efficient 48-term expression for
+! density in terms of SA, CT and p (IOC et al., 2010).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! gsw_sigma0 : potential density anomaly with reference pressure of 0
+! (48 term equation)
+*/
+double
+gsw_sigma0(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double vp0, xs, ys;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+
+ vp0 = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys)))));
+
+ return (1.0/vp0 - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sigma1(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 1000 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! sigma1 : potential density anomaly with reference pressure of 1000
+*/
+double
+gsw_sigma1(double sa, double ct)
+{
+ return (gsw_rho(sa,ct,1000.0) - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sigma2(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 2000 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! sigma2 : potential density anomaly with reference pressure of 2000
+*/
+double
+gsw_sigma2(double sa, double ct)
+{
+ return (gsw_rho(sa,ct,2000.0) - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sigma3(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 3000 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! sigma3 : potential density anomaly with reference pressure of 3000
+*/
+double
+gsw_sigma3(double sa, double ct)
+{
+ return (gsw_rho(sa,ct,3000.0) - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sigma4(sa,ct)
+!==========================================================================
+
+! Calculates potential density anomaly with reference pressure of 4000 dbar,
+! this being this particular potential density minus 1000 kg/m^3. This
+! function has inputs of Absolute Salinity and Conservative Temperature.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! sigma4 : potential density anomaly with reference pressure of 4000
+*/
+double
+gsw_sigma4(double sa, double ct)
+{
+ return (gsw_rho(sa,ct,4000.0) - 1000.0);
+}
+/*
+!==========================================================================
+function gsw_sound_speed(sa,ct,p)
+!==========================================================================
+
+! Calculates the speed of sound in seawater. This function has inputs of
+! Absolute Salinity and Conservative Temperature. This function uses the
+! computationally-efficient expression for specific volume in terms of SA,
+! CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! sound_speed : speed of sound in seawater [m/s]
+*/
+double
+gsw_sound_speed(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v, v_p, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ v_p = c000
+ + xs*(c100 + xs*(c200 + xs*(c300 + xs*(c400 + c500*xs))))
+ + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020
+ + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs)
+ + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201
+ + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs))
+ + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys)))
+ + z*( c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys)
+ + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z))));
+
+ return (10000.0*sqrt(-v*v/v_p));
+}
+/*
+!==========================================================================
+elemental function gsw_sound_speed_ice (t, p)
+!==========================================================================
+!
+! Calculates the compression speed of sound in ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! sound_speed_ice = compression speed of sound in ice [ m/s ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_sound_speed_ice(double t, double p)
+{
+ double gi_tp, gi_tt;
+
+ gi_tt = gsw_gibbs_ice(2,0,t,p);
+ gi_tp = gsw_gibbs_ice(1,1,t,p);
+
+ return (gsw_gibbs_ice(0,1,t,p) *
+ sqrt(gi_tt/(gi_tp*gi_tp - gi_tt*gsw_gibbs_ice(0,2,t,p))));
+}
+/*
+!==========================================================================
+function gsw_sound_speed_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates the speed of sound in seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! gsw_sound_speed_t_exact : sound speed [m/s]
+*/
+double
+gsw_sound_speed_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1, n2=2;
+ double g_tt, g_tp;
+
+ g_tt = gsw_gibbs(n0,n2,n0,sa,t,p);
+ g_tp = gsw_gibbs(n0,n1,n1,sa,t,p);
+
+ return (gsw_gibbs(n0,n0,n1,sa,t,p) *
+ sqrt(g_tt/(g_tp*g_tp - g_tt*gsw_gibbs(n0,n0,n2,sa,t,p))));
+}
+/*
+!--------------------------------------------------------------------------
+! Practical Salinity (SP), PSS-78
+!--------------------------------------------------------------------------
+
+!==========================================================================
+function gsw_sp_from_c(c,t,p)
+!==========================================================================
+
+! Calculates Practical Salinity, SP, from conductivity, C, primarily using
+! the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical
+! Salinity is only valid in the range 2 < SP < 42. If the PSS-78
+! algorithm produces a Practical Salinity that is less than 2 then the
+! Practical Salinity is recalculated with a modified form of the Hill et
+! al. (1986) formula. The modification of the Hill et al. (1986)
+! expression is to ensure that it is exactly consistent with PSS-78
+! at SP = 2. Note that the input values of conductivity need to be in
+! units of mS/cm (not S/m).
+!
+! c : conductivity [ mS/cm ]
+! t : in-situ temperature [ITS-90] [deg C]
+! p : sea pressure [dbar]
+!
+! sp : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_c(double c, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SP_COEFFICIENTS;
+ double sp, t68, ft68, r, rt_lc, rp, rt, rtx,
+ hill_ratio, x, sqrty, part1, part2,
+ sp_hill_raw;
+
+ t68 = t*1.00024e0;
+ ft68 = (t68 - 15e0)/(1e0 + k*(t68 - 15e0));
+ /*
+ ! The dimensionless conductivity ratio, R, is the conductivity input, C,
+ ! divided by the present estimate of C(SP=35, t_68=15, p=0) which is
+ ! 42.9140 mS/cm (=4.29140 S/m), (Culkin and Smith, 1980).
+ */
+
+ r = c/gsw_c3515; /* 0.023302418791070513 = 1./42.9140 */
+
+ /*rt_lc corresponds to rt as defined in the UNESCO 44 (1983) routines.*/
+ rt_lc = c0 + (c1 + (c2 + (c3 + c4*t68)*t68)*t68)*t68;
+ rp = 1e0 + (p*(e1 + e2*p + e3*p*p))/(1e0 + d1*t68 + d2*t68*t68 +
+ (d3 + d4*t68)*r);
+ rt = r/(rp*rt_lc);
+
+ if (rt < 0.0) {
+ return (GSW_INVALID_VALUE);
+ }
+
+ rtx = sqrt(rt);
+
+ sp = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx +
+ ft68*(b0 + (b1 + (b2 + (b3 +
+ (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx);
+ /*
+ ! The following section of the code is designed for SP < 2 based on the
+ ! Hill et al. (1986) algorithm. This algorithm is adjusted so that it is
+ ! exactly equal to the PSS-78 algorithm at SP = 2.
+ */
+
+ if (sp < 2) {
+ hill_ratio = gsw_hill_ratio_at_sp2(t);
+ x = 400e0*rt;
+ sqrty = 10e0*rtx;
+ part1 = 1e0 + x*(1.5e0 + x);
+ part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
+ sp_hill_raw = sp - a0/part1 - b0*ft68/part2;
+ sp = hill_ratio*sp_hill_raw;
+ }
+
+ /* This line ensures that SP is non-negative. */
+ if (sp < 0.0) {
+ sp = GSW_INVALID_VALUE;
+ }
+
+ return (sp);
+}
+/*
+!==========================================================================
+function gsw_sp_from_sa(sa,p,lon,lat)
+!==========================================================================
+
+! Calculates Practical salinity, sp, from Absolute salinity, sa
+!
+! sa : Absolute Salinity [g/kg]
+! p : sea pressure [dbar]
+! lon : longitude [DEG E]
+! lat : latitude [DEG N]
+!
+! gsw_sp_from_sa : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_sa(double sa, double p, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double saar, gsw_sp_baltic;
+
+ gsw_sp_baltic = gsw_sp_from_sa_baltic(sa,lon,lat);
+ if (gsw_sp_baltic < GSW_ERROR_LIMIT)
+ return (gsw_sp_baltic);
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return ((sa/gsw_ups)/(1e0 + saar));
+}
+/*
+!==========================================================================
+function gsw_sp_from_sa_baltic(sa,lon,lat)
+!==========================================================================
+
+! For the Baltic Sea, calculates Practical Salinity with a value
+! computed analytically from Absolute Salinity
+!
+! sa : Absolute Salinity [g/kg]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sp_from_sa_baltic : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_sa_baltic(double sa, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_BALTIC_DATA;
+ double xx_left, xx_right, return_value;
+
+ if (xb_left[1] < lon && lon < xb_right[0] && yb_left[0] < lat &&
+ lat < yb_left[2]) {
+
+ xx_left = gsw_util_xinterp1(yb_left, xb_left, 3, lat);
+
+ xx_right = gsw_util_xinterp1(yb_right, xb_right, 2, lat);
+
+ if (xx_left <= lon && lon <= xx_right)
+ return_value = (35.0/(gsw_sso - 0.087))*(sa - 0.087);
+ else
+ return_value = GSW_INVALID_VALUE;
+ } else
+ return_value = GSW_INVALID_VALUE;
+
+ return (return_value);
+}
+/*
+!==========================================================================
+function gsw_sp_from_sk(sk)
+!==========================================================================
+
+! Calculates Practical Salinity, SP, from SK
+!
+! SK : Knudsen Salinity [parts per thousand, ppt]
+!
+! gsw_sp_from_sk : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_sk(double sk)
+{
+ GSW_TEOS10_CONSTANTS;
+ double gsw_sp_from_sk_value;
+
+
+ gsw_sp_from_sk_value = (sk - 0.03e0)*(gsw_soncl/1.805e0);
+
+ if (gsw_sp_from_sk_value < 0e0)
+ gsw_sp_from_sk_value = GSW_INVALID_VALUE;
+
+ return (gsw_sp_from_sk_value);
+}
+/*
+!==========================================================================
+function gsw_sp_from_sr(sr)
+!==========================================================================
+
+! Calculates Practical Salinity, sp, from Reference Salinity, sr.
+!
+! sr : Reference Salinity [g/kg]
+!
+! gsw_sp_from_sr : Practical Salinity [unitless]
+*/
+double
+gsw_sp_from_sr(double sr)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return(sr/gsw_ups);
+}
+/*
+!==========================================================================
+function gsw_sp_from_sstar(sstar,p,lon,lat)
+!==========================================================================
+
+! Calculates Practical Salinity, SP, from Preformed Salinity, Sstar.
+!
+! sstar : Preformed Salinity [g/kg]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sp_from_Sstar : Preformed Salinity [g/kg]
+*/
+double
+gsw_sp_from_sstar(double sstar, double p, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double saar, sp_baltic;
+
+ /*
+ **! In the Baltic Sea, SA = Sstar.
+ */
+ sp_baltic = gsw_sp_from_sa_baltic(sstar,lon,lat);
+ if (sp_baltic < GSW_ERROR_LIMIT)
+ return (sp_baltic);
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return ((sstar/gsw_ups)/(1.0 - 0.35e0*saar));
+}
+/*
+!==========================================================================
+function gsw_specvol(sa,ct,p)
+!==========================================================================
+!
+! Calculates specific volume from Absolute Salinity, Conservative
+! Temperature and pressure, using the computationally-efficient
+! polynomial expression for specific volume (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! specvol: specific volume [m^3/kg]
+*/
+double
+gsw_specvol(double sa, double ct, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double xs, ys, z, value;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ value = v000
+ + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ return (value);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_alpha_beta (sa, ct, p, specvol, alpha, &
+ beta)
+!==========================================================================
+!
+! Calculates specific volume, the appropiate thermal expansion coefficient
+! and the appropriate saline contraction coefficient of seawater from
+! Absolute Salinity and Conservative Temperature. This function uses the
+! computationally-efficient expression for specific volume in terms of
+! SA, CT and p (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! specvol = specific volume [ m/kg ]
+! alpha = thermal expansion coefficient [ 1/K ]
+! with respect to Conservative Temperature
+! beta = saline (i.e. haline) contraction [ kg/g ]
+! coefficient at constant Conservative Temperature
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_alpha_beta(double sa, double ct, double p, double *specvol,
+ double *alpha, double *beta)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v, v_ct, v_sa_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ v = v000 + xs*(v010 + xs*(v020 + xs*(v030 + xs*(v040 + xs*(v050
+ + v060*xs))))) + ys*(v100 + xs*(v110 + xs*(v120 + xs*(v130 + xs*(v140
+ + v150*xs)))) + ys*(v200 + xs*(v210 + xs*(v220 + xs*(v230 + v240*xs)))
+ + ys*(v300 + xs*(v310 + xs*(v320 + v330*xs)) + ys*(v400 + xs*(v410
+ + v420*xs) + ys*(v500 + v510*xs + v600*ys))))) + z*(v001 + xs*(v011
+ + xs*(v021 + xs*(v031 + xs*(v041 + v051*xs)))) + ys*(v101 + xs*(v111
+ + xs*(v121 + xs*(v131 + v141*xs))) + ys*(v201 + xs*(v211 + xs*(v221
+ + v231*xs)) + ys*(v301 + xs*(v311 + v321*xs) + ys*(v401 + v411*xs
+ + v501*ys)))) + z*(v002 + xs*(v012 + xs*(v022 + xs*(v032 + v042*xs)))
+ + ys*(v102 + xs*(v112 + xs*(v122 + v132*xs)) + ys*(v202 + xs*(v212
+ + v222*xs) + ys*(v302 + v312*xs + v402*ys))) + z*(v003 + xs*(v013
+ + v023*xs) + ys*(v103 + v113*xs + v203*ys) + z*(v004 + v014*xs + v104*ys
+ + z*(v005 + v006*z)))));
+
+ if (specvol != NULL)
+ *specvol = v;
+
+ if (alpha != NULL) {
+
+ v_ct = a000 + xs*(a100 + xs*(a200 + xs*(a300
+ + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z)));
+
+ *alpha = 0.025*v_ct/v;
+
+ }
+
+ if (beta != NULL) {
+
+ v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300
+ + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ *beta = -v_sa_part*0.5*gsw_sfac/(v*xs);
+
+ }
+}
+/*
+!==========================================================================
+function gsw_specvol_anom_standard(sa,ct,p)
+!==========================================================================
+!
+! Calculates specific volume anomaly of seawater.
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! specvol_anom : specific volume anomaly of seawater
+*/
+double
+gsw_specvol_anom_standard(double sa, double ct, double p)
+{
+ return (gsw_specvol(sa,ct,p) - gsw_specvol_sso_0(p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_first_derivatives (sa, ct, p, v_sa, v_ct, &
+ v_p, iflag)
+! =========================================================================
+!
+! Calculates three first-order derivatives of specific volume (v).
+! Note that this function uses the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! v_SA = The first derivative of specific volume with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! v_CT = The first derivative of specific volume with respect to
+! CT at constant SA and p. [ J/(kg K(g/kg)) ]
+! v_P = The first derivative of specific volume with respect to
+! P at constant SA and CT. [ J/(kg K^2) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_first_derivatives (double sa, double ct, double p,
+ double *v_sa, double *v_ct, double *v_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v_ct_part, v_p_part, v_sa_part, xs, ys, z;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ if (v_sa != NULL) {
+
+ v_sa_part = b000 + xs*(b100 + xs*(b200 + xs*(b300
+ + xs*(b400 + b500*xs))))
+ + ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ + xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ + z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ + ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ + xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ + z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ + xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ + z*(b003 + b103*xs + b013*ys + b004*z)));
+
+ *v_sa = 0.5*gsw_sfac*v_sa_part/xs;
+
+ }
+
+ if (v_ct != NULL) {
+
+ v_ct_part = a000 + xs*(a100 + xs*(a200 + xs*(a300
+ + xs*(a400 + a500*xs))))
+ + ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ + xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ + z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ + ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ + z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ + xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ + z*(a003 + a103*xs + a013*ys + a004*z))) ;
+
+ *v_ct = 0.025*v_ct_part;
+
+ }
+
+ if (v_p != NULL) {
+
+ v_p_part = c000 + xs*(c100 + xs*(c200 + xs*(c300
+ + xs*(c400 + c500*xs))))
+ + ys*(c010 + xs*(c110 + xs*(c210 + xs*(c310 + c410*xs))) + ys*(c020
+ + xs*(c120 + xs*(c220 + c320*xs)) + ys*(c030 + xs*(c130 + c230*xs)
+ + ys*(c040 + c140*xs + c050*ys)))) + z*(c001 + xs*(c101 + xs*(c201
+ + xs*(c301 + c401*xs))) + ys*(c011 + xs*(c111 + xs*(c211 + c311*xs))
+ + ys*(c021 + xs*(c121 + c221*xs) + ys*(c031 + c131*xs + c041*ys)))
+ + z*( c002 + xs*(c102 + c202*xs) + ys*(c012 + c112*xs + c022*ys)
+ + z*(c003 + c103*xs + c013*ys + z*(c004 + c005*z))));
+
+ *v_p = 1e-8*v_p_part;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_first_derivatives_wrt_enthalpy (sa, ct, &
+ p, v_sa, v_h, iflag)
+! =========================================================================
+!
+! Calculates two first-order derivatives of specific volume (v).
+! Note that this function uses the using the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! v_SA = The first derivative of specific volume with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! v_h = The first derivative of specific volume with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_first_derivatives_wrt_enthalpy(double sa, double ct, double p,
+ double *v_sa, double *v_h)
+{
+ double h_ct=1.0, h_sa, rec_h_ct, vct_ct, vct_sa;
+
+ if (v_sa != NULL) {
+
+ gsw_specvol_first_derivatives(sa,ct,p,&vct_sa,&vct_ct,NULL);
+ gsw_enthalpy_first_derivatives(sa,ct,p,&h_sa,&h_ct);
+
+ } else if (v_h != NULL) {
+
+ gsw_specvol_first_derivatives(sa,ct,p,NULL,&vct_ct,NULL);
+ gsw_enthalpy_first_derivatives(sa,ct,p,NULL,&h_ct);
+
+ }
+
+ rec_h_ct = 1.0/h_ct;
+
+ if (v_sa != NULL)
+ *v_sa = vct_sa - (vct_ct*h_sa)*rec_h_ct;
+
+ if (v_h != NULL)
+ *v_h = vct_ct*rec_h_ct;
+
+ return;
+}
+/*
+!==========================================================================
+elemental function gsw_specvol_ice (t, p)
+!==========================================================================
+!
+! Calculates the specific volume of ice.
+!
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! specvol_ice = specific volume [ m^3/kg ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_specvol_ice(double t, double p)
+{
+ return (gsw_gibbs_ice(0,1,t,p));
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_second_derivatives (sa, ct, p, v_sa_sa, &
+ v_sa_ct, v_ct_ct, v_sa_p, v_ct_p, iflag)
+! =========================================================================
+!
+! Calculates five second-order derivatives of specific volume (v).
+! Note that this function uses the computationally-efficient
+! expression for specific volume (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! v_SA_SA = The second derivative of specific volume with respect to
+! Absolute Salinity at constant CT & p. [ J/(kg (g/kg)^2) ]
+! v_SA_CT = The second derivative of specific volume with respect to
+! SA and CT at constant p. [ J/(kg K(g/kg)) ]
+! v_CT_CT = The second derivative of specific volume with respect to
+! CT at constant SA and p. [ J/(kg K^2) ]
+! v_SA_P = The second derivative of specific volume with respect to
+! SA and P at constant CT. [ J/(kg K(g/kg)) ]
+! v_CT_P = The second derivative of specific volume with respect to
+! CT and P at constant SA. [ J/(kg K(g/kg)) ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_second_derivatives (double sa, double ct, double p,
+ double *v_sa_sa, double *v_sa_ct, double *v_ct_ct, double *v_sa_p,
+ double *v_ct_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_SPECVOL_COEFFICIENTS;
+ double v_ct_ct_part, v_ct_p_part, v_sa_ct_part, v_sa_p_part,
+ v_sa_sa_part, xs, xs2, ys, z;
+
+ xs2 = gsw_sfac*sa + offset;
+ xs = sqrt(xs2);
+ ys = ct*0.025;
+ z = p*1e-4;
+
+ if (v_sa_sa != NULL) {
+
+ v_sa_sa_part = (-b000 + xs2*(b200 + xs*(2.0*b300 + xs*(3.0*b400
+ + 4.0*b500*xs))) + ys*(-b010 + xs2*(b210 + xs*(2.0*b310
+ + 3.0*b410*xs)) + ys*(-b020 + xs2*(b220 + 2.0*b320*xs)
+ + ys*(-b030 + b230*xs2 + ys*(-b040 - b050*ys)))) + z*(-b001
+ + xs2*(b201 + xs*(2.0*b301 + 3.0*b401*xs)) + ys*(-b011
+ + xs2*(b211 + 2.0*b311*xs) + ys*(-b021 + b221*xs2
+ + ys*(-b031 - b041*ys))) + z*(-b002 + xs2*(b202 + 2.0*b302*xs)
+ + ys*(-b012 + b212*xs2 + ys*(-b022 - b032*ys)) + z*(-b003
+ - b013*ys - b004*z))))/xs2;
+
+ *v_sa_sa = 0.25*gsw_sfac*gsw_sfac*v_sa_sa_part/xs;
+
+ }
+
+ if (v_sa_ct != NULL) {
+
+ v_sa_ct_part = (b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ + ys*(2.0*(b020 + xs*(b120 + xs*(b220 + b320*xs)))
+ + ys*(3.0*(b030 + xs*(b130 + b230*xs)) + ys*(4.0*(b040
+ + b140*xs) + 5.0*b050*ys))) + z*(b011 + xs*(b111 + xs*(b211
+ + b311*xs)) + ys*(2.0*(b021 + xs*(b121 + b221*xs))
+ + ys*(3.0*(b031 + b131*xs) + 4.0*b041*ys)) + z*(b012
+ + xs*(b112 + b212*xs) + ys*(2.0*(b022 + b122*xs)
+ + 3.0*b032*ys) + b013*z)))/xs;
+
+ *v_sa_ct = 0.025*0.5*gsw_sfac*v_sa_ct_part;
+
+ }
+
+ if (v_ct_ct != NULL) {
+
+ v_ct_ct_part = a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ + ys*(2.0*(a020 + xs*(a120 + xs*(a220 + a320*xs)))
+ + ys*(3.0*(a030 + xs*(a130 + a230*xs)) + ys*(4.0*(a040
+ + a140*xs) + 5.0*a050*ys))) + z*( a011 + xs*(a111 + xs*(a211
+ + a311*xs)) + ys*(2.0*(a021 + xs*(a121 + a221*xs))
+ + ys*(3.0*(a031 + a131*xs) + 4.0*a041*ys)) + z*(a012
+ + xs*(a112 + a212*xs) + ys*(2.0*(a022 + a122*xs)
+ + 3.0*a032*ys) + a013*z));
+
+ *v_ct_ct = 0.025*0.025*v_ct_ct_part;
+
+ }
+
+ if (v_sa_p != NULL) {
+
+ v_sa_p_part = b001 + xs*(b101 + xs*(b201 + xs*(b301
+ + b401*xs))) + ys*(b011 + xs*(b111 + xs*(b211
+ + b311*xs)) + ys*(b021 + xs*(b121 + b221*xs)
+ + ys*(b031 + b131*xs + b041*ys))) + z*(2.0*(b002 + xs*(b102
+ + xs*(b202 + b302*xs)) + ys*(b012 + xs*(b112
+ + b212*xs) + ys*(b022
+ + b122*xs + b032*ys))) + z*(3.0*(b003 + b103*xs + b013*ys)
+ + 4.0*b004*z));
+
+ *v_sa_p = 1e-8*0.5*gsw_sfac*v_sa_p_part;
+
+ }
+
+ if (v_ct_p != NULL) {
+
+ v_ct_p_part = a001 + xs*(a101 + xs*(a201 + xs*(a301
+ + a401*xs))) + ys*(a011
+ + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ + xs*(a121 + a221*xs)
+ + ys*(a031 + a131*xs + a041*ys))) + z*(2.0*(a002 + xs*(a102
+ + xs*(a202 + a302*xs)) + ys*(a012 + xs*(a112 + a212*xs)
+ + ys*(a022 + a122*xs + a032*ys))) + z*(3.0*(a003
+ + a103*xs + a013*ys) + 4.0*a004*z));
+
+ *v_ct_p = 1e-8*0.025*v_ct_p_part;
+
+ }
+}
+/*
+!==========================================================================
+elemental subroutine gsw_specvol_second_derivatives_wrt_enthalpy (sa, ct, &
+ p, v_sa_sa, v_sa_h, v_h_h, iflag)
+! =========================================================================
+!
+! Calculates three first-order derivatives of specific volume (v) with
+! respect to enthalpy. Note that this function uses the using the
+! computationally-efficient expression for specific volume
+! (Roquet et al., 2014).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! v_SA_SA = The second-order derivative of specific volume with respect to
+! Absolute Salinity at constant h & p. [ J/(kg (g/kg)^2) ]
+! v_SA_h = The second-order derivative of specific volume with respect to
+! SA and h at constant p. [ J/(kg K(g/kg)) ]
+! v_h_h = The second-order derivative with respect to h at
+! constant SA & p.
+!--------------------------------------------------------------------------
+*/
+void
+gsw_specvol_second_derivatives_wrt_enthalpy (double sa, double ct, double p,
+ double *v_sa_sa, double *v_sa_h, double *v_h_h)
+{
+ double h_ct, h_ct_ct, h_sa, h_sa_ct, h_sa_sa, rec_h_ct, v_h_h_part,
+ rec_h_ct2, v_ct, vct_ct_ct, vct_sa_ct, vct_sa_sa, v_sa_h_part;
+
+ gsw_specvol_first_derivatives(sa,ct,p,NULL, &v_ct, NULL);
+
+ if ((v_sa_sa != NULL) || (v_sa_h != NULL))
+ gsw_enthalpy_first_derivatives(sa,ct,p,&h_sa,&h_ct);
+ else
+ gsw_enthalpy_first_derivatives(sa,ct,p,NULL,&h_ct);
+
+ if (v_sa_sa != NULL)
+ gsw_specvol_second_derivatives(sa,ct,p,&vct_sa_sa,&vct_sa_ct,
+ &vct_ct_ct, NULL, NULL);
+ else if (v_sa_h != NULL)
+ gsw_specvol_second_derivatives(sa,ct,p,NULL,&vct_sa_ct,&vct_ct_ct,
+ NULL, NULL);
+ else
+ gsw_specvol_second_derivatives(sa,ct,p,NULL,NULL,&vct_ct_ct,
+ NULL, NULL);
+
+ if (v_sa_sa != NULL)
+ gsw_enthalpy_second_derivatives(sa,ct,p,&h_sa_sa,&h_sa_ct,&h_ct_ct);
+ else if (v_sa_h != NULL)
+ gsw_enthalpy_second_derivatives(sa,ct,p,NULL,&h_sa_ct,&h_ct_ct);
+ else
+ gsw_enthalpy_second_derivatives(sa,ct,p,NULL,NULL,&h_ct_ct);
+
+ rec_h_ct = 1.0/h_ct;
+ rec_h_ct2 = rec_h_ct*rec_h_ct;
+
+ v_h_h_part = (vct_ct_ct*h_ct - h_ct_ct*v_ct)*(rec_h_ct2*rec_h_ct);
+
+ if (v_h_h != NULL) *v_h_h = v_h_h_part;
+
+ if ((v_sa_sa != NULL) || (v_sa_h != NULL)) {
+
+ v_sa_h_part = (vct_sa_ct*h_ct - v_ct*h_sa_ct)*rec_h_ct2
+ - h_sa*v_h_h_part;
+
+ if (v_sa_h != NULL) *v_sa_h = v_sa_h_part;
+
+ if (v_sa_sa != NULL)
+ *v_sa_sa = vct_sa_sa - (h_ct*(vct_sa_ct*h_sa
+ - v_ct*h_sa_sa) + v_ct*h_sa*h_sa_ct)*rec_h_ct2
+ - h_sa*v_sa_h_part;
+ }
+}
+/*
+!==========================================================================
+function gsw_specvol_sso_0(p)
+!==========================================================================
+
+! This function calculates specific volume at the Standard Ocean Salinty,
+! SSO, and at a Conservative Temperature of zero degrees C, as a function
+! of pressure, p, in dbar, using a streamlined version of the CT version
+! of specific volume, that is, a streamlined version of the code
+! "gsw_specvol(SA,CT,p)".
+!
+! p : sea pressure [dbar]
+! 3 -1
+! specvol_sso_0 : specvol(sso,0,p) [m kg ]
+*/
+double
+gsw_specvol_sso_0(double p)
+{
+ GSW_SPECVOL_COEFFICIENTS;
+ double z, return_value;
+
+ z = p*1.0e-4;
+
+ return_value = 9.726613854843870e-04 + z*(-4.505913211160929e-05
+ + z*(7.130728965927127e-06 + z*(-6.657179479768312e-07
+ + z*(-2.994054447232880e-08 + z*(v005 + v006*z)))));
+ return (return_value);
+}
+/*
+!==========================================================================
+function gsw_specvol_t_exact(sa,t,p)
+!==========================================================================
+
+! Calculates the specific volume of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! t : in-situ temperature [deg C]
+! p : sea pressure [dbar]
+!
+! specvol_t_exact : specific volume [kg/m^3]
+*/
+double
+gsw_specvol_t_exact(double sa, double t, double p)
+{
+ int n0=0, n1=1;
+
+ return (gsw_gibbs(n0,n0,n1,sa,t,p));
+}
+/*
+!==========================================================================
+function gsw_spiciness0(sa,ct)
+!==========================================================================
+!
+! Calculates spiciness from Absolute Salinity and Conservative
+! Temperature at a pressure of 0 dbar, as described by McDougall and
+! Krzysik (2015). This routine is based on the computationally-efficient
+! expression for specific volume in terms of SA, CT and p (Roquet et al.,
+! 2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! spiciness0 = spiciness referenced to a pressure of 0 dbar,
+! i.e. the surface [ kg/m^3 ]
+!
+*/
+
+double
+gsw_spiciness0(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double s01 = -9.22982898371678e1, s02 = -1.35727873628866e1,
+ s03 = 1.87353650994010e1, s04 = -1.61360047373455e1,
+ s05 = 3.76112762286425e1, s06 = -4.27086671461257e1,
+ s07 = 2.00820111041594e1, s08 = 2.87969717584045e2,
+ s09 = 1.13747111959674e1, s10 = 6.07377192990680e1,
+ s11 = -7.37514033570187e1, s12 = -7.51171878953574e1,
+ s13 = 1.63310989721504e2, s14 = -8.83222751638095e1,
+ s15 = -6.41725302237048e2, s16 = 2.79732530789261e1,
+ s17 = -2.49466901993728e2, s18 = 3.26691295035416e2,
+ s19 = 2.66389243708181e1, s20 = -2.93170905757579e2,
+ s21 = 1.76053907144524e2, s22 = 8.27634318120224e2,
+ s23 = -7.02156220126926e1, s24 = 3.82973336590803e2,
+ s25 = -5.06206828083959e2, s26 = 6.69626565169529e1,
+ s27 = 3.02851235050766e2, s28 = -1.96345285604621e2,
+ s29 = -5.74040806713526e2, s30 = 7.03285905478333e1,
+ s31 = -2.97870298879716e2, s32 = 3.88340373735118e2,
+ s33 = -8.29188936089122e1, s34 = -1.87602137195354e2,
+ s35 = 1.27096944425793e2, s36 = 2.11671167892147e2,
+ s37 = -3.15140919876285e1, s38 = 1.16458864953602e2,
+ s39 = -1.50029730802344e2, s40 = 3.76293848660589e1,
+ s41 = 6.47247424373200e1, s42 = -4.47159994408867e1,
+ s43 = -3.23533339449055e1, s44 = 5.30648562097667,
+ s45 = -1.82051249177948e1, s46 = 2.33184351090495e1,
+ s47 = -6.22909903460368, s48 = -9.55975464301446,
+ s49 = 6.61877073960113;
+ double xs, ys, spiciness0;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+
+ spiciness0= s01+ys*(s02+ys*(s03+ys*(s04+ys*(s05+ys*(s06+s07*ys)))))
+ +xs*(s08+ys*(s09+ys*(s10+ys*(s11+ys*(s12+ys*(s13+s14*ys)))))
+ +xs*(s15+ys*(s16+ys*(s17+ys*(s18+ys*(s19+ys*(s20+s21*ys)))))
+ +xs*(s22+ys*(s23+ys*(s24+ys*(s25+ys*(s26+ys*(s27+s28*ys)))))
+ +xs*(s29+ys*(s30+ys*(s31+ys*(s32+ys*(s33+ys*(s34+s35*ys)))))
+ +xs*(s36+ys*(s37+ys*(s38+ys*(s39+ys*(s40+ys*(s41+s42*ys)))))
+ +xs*(s43+ys*(s44+ys*(s45+ys*(s46+ys*(s47+ys*(s48+s49*ys)))))
+ ))))));
+ return (spiciness0);
+}
+/*
+!==========================================================================
+function gsw_spiciness1(sa,ct)
+!==========================================================================
+!
+! Calculates spiciness from Absolute Salinity and Conservative
+! Temperature at a pressure of 1000 dbar, as described by McDougall and
+! Krzysik (2015). This routine is based on the computationally-efficient
+! expression for specific volume in terms of SA, CT and p (Roquet et al.,
+! 2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! spiciness1 = spiciness referenced to a pressure of 1000 dbar [ kg/m^3 ]
+!
+*/
+double
+gsw_spiciness1(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double s01 = -9.19874584868912e1, s02 = -1.33517268529408e1,
+ s03 = 2.18352211648107e1, s04 = -2.01491744114173e1,
+ s05 = 3.70004204355132e1, s06 = -3.78831543226261e1,
+ s07 = 1.76337834294554e1, s08 = 2.87838842773396e2,
+ s09 = 2.14531420554522e1, s10 = 3.14679705198796e1,
+ s11 = -4.04398864750692e1, s12 = -7.70796428950487e1,
+ s13 = 1.36783833820955e2, s14 = -7.36834317044850e1,
+ s15 = -6.41753415180701e2, s16 = 1.33701981685590,
+ s17 = -1.75289327948412e2, s18 = 2.42666160657536e2,
+ s19 = 3.17062400799114e1, s20 = -2.28131490440865e2,
+ s21 = 1.39564245068468e2, s22 = 8.27747934506435e2,
+ s23 = -3.50901590694775e1, s24 = 2.87473907262029e2,
+ s25 = -4.00227341144928e2, s26 = 6.48307189919433e1,
+ s27 = 2.16433334701578e2, s28 = -1.48273032774305e2,
+ s29 = -5.74545648799754e2, s30 = 4.50446431127421e1,
+ s31 = -2.30714981343772e2, s32 = 3.15958389253065e2,
+ s33 = -8.60635313930106e1, s34 = -1.22978455069097e2,
+ s35 = 9.18287282626261e1, s36 = 2.12120473062203e2,
+ s37 = -2.21528216973820e1, s38 = 9.19013417923270e1,
+ s39 = -1.24400776026014e2, s40 = 4.08512871163839e1,
+ s41 = 3.91127352213516e1, s42 = -3.10508021853093e1,
+ s43 = -3.24790035899152e1, s44 = 3.91029016556786,
+ s45 = -1.45362719385412e1, s46 = 1.96136194246355e1,
+ s47 = -7.06035474689088, s48 = -5.36884688614009,
+ s49 = 4.43247303092448;
+ double xs, ys, spiciness1;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+ spiciness1= s01+ys*(s02+ys*(s03+ys*(s04+ys*(s05+ys*(s06+s07*ys)))))
+ +xs*(s08+ys*(s09+ys*(s10+ys*(s11+ys*(s12+ys*(s13+s14*ys)))))
+ +xs*(s15+ys*(s16+ys*(s17+ys*(s18+ys*(s19+ys*(s20+s21*ys)))))
+ +xs*(s22+ys*(s23+ys*(s24+ys*(s25+ys*(s26+ys*(s27+s28*ys)))))
+ +xs*(s29+ys*(s30+ys*(s31+ys*(s32+ys*(s33+ys*(s34+s35*ys)))))
+ +xs*(s36+ys*(s37+ys*(s38+ys*(s39+ys*(s40+ys*(s41+s42*ys)))))
+ +xs*(s43+ys*(s44+ys*(s45+ys*(s46+ys*(s47+ys*(s48+s49*ys)))))
+ ))))));
+ return (spiciness1);
+}
+/*
+!==========================================================================
+function gsw_spiciness2(sa,ct)
+!==========================================================================
+!
+! Calculates spiciness from Absolute Salinity and Conservative
+! Temperature at a pressure of 2000 dbar, as described by McDougall and
+! Krzysik (2015). This routine is based on the computationally-efficient
+! expression for specific volume in terms of SA, CT and p (Roquet et al.,
+! 2015).
+!
+! SA = Absolute Salinity [ g/kg ]
+! CT = Conservative Temperature (ITS-90) [ deg C ]
+!
+! spiciness2 = spiciness referenced to a pressure of 2000 dbar [ kg/m^3 ]
+!
+*/
+double
+gsw_spiciness2(double sa, double ct)
+{
+ GSW_TEOS10_CONSTANTS;
+ double s01 = -9.17327320732265e1, s02 = -1.31200235147912e1,
+ s03 = 2.49574345782503e1, s04 = -2.41678075247398e1,
+ s05 = 3.61654631402053e1, s06 = -3.22582164667710e1,
+ s07 = 1.45092623982509e1, s08 = 2.87776645983195e2,
+ s09 = 3.13902307672447e1, s10 = 1.69777467534459,
+ s11 = -5.69630115740438, s12 = -7.97586359017987e1,
+ s13 = 1.07507460387751e2, s14 = -5.58234404964787e1,
+ s15 = -6.41708068766557e2, s16 = -2.53494801286161e1,
+ s17 = -9.86755437385364e1, s18 = 1.52406930795842e2,
+ s19 = 4.23888258264105e1, s20 = -1.60118811141438e2,
+ s21 = 9.67497898053989e1, s22 = 8.27674355478637e2,
+ s23 = 5.27561234412133e-1, s24 = 1.87440206992396e2,
+ s25 = -2.83295392345171e2, s26 = 5.14485994597635e1,
+ s27 = 1.29975755062696e2, s28 = -9.36526588377456e1,
+ s29 = -5.74911728972948e2, s30 = 1.91175851862772e1,
+ s31 = -1.59347231968841e2, s32 = 2.33884725744938e2,
+ s33 = -7.87744010546157e1, s34 = -6.04757235443685e1,
+ s35 = 5.27869695599657e1, s36 = 2.12517758478878e2,
+ s37 = -1.24351794740528e1, s38 = 6.53904308937490e1,
+ s39 = -9.44804080763788e1, s40 = 3.93874257887364e1,
+ s41 = 1.49425448888996e1, s42 = -1.62350721656367e1,
+ s43 = -3.25936844276669e1, s44 = 2.44035700301595,
+ s45 = -1.05079633683795e1, s46 = 1.51515796259082e1,
+ s47 = -7.06609886460683, s48 = -1.48043337052968,
+ s49 = 2.10066653978515;
+ double xs, ys, spiciness2;
+
+ xs = sqrt(gsw_sfac*sa + offset);
+ ys = ct*0.025;
+
+ spiciness2= s01+ys*(s02+ys*(s03+ys*(s04+ys*(s05+ys*(s06+s07*ys)))))
+ +xs*(s08+ys*(s09+ys*(s10+ys*(s11+ys*(s12+ys*(s13+s14*ys)))))
+ +xs*(s15+ys*(s16+ys*(s17+ys*(s18+ys*(s19+ys*(s20+s21*ys)))))
+ +xs*(s22+ys*(s23+ys*(s24+ys*(s25+ys*(s26+ys*(s27+s28*ys)))))
+ +xs*(s29+ys*(s30+ys*(s31+ys*(s32+ys*(s33+ys*(s34+s35*ys)))))
+ +xs*(s36+ys*(s37+ys*(s38+ys*(s39+ys*(s40+ys*(s41+s42*ys)))))
+ +xs*(s43+ys*(s44+ys*(s45+ys*(s46+ys*(s47+ys*(s48+s49*ys)))))
+ ))))));
+ return (spiciness2);
+}
+/*
+!==========================================================================
+function gsw_sr_from_sp(sp)
+!==========================================================================
+
+! Calculates Reference Salinity, SR, from Practical Salinity, SP.
+!
+! sp : Practical Salinity [unitless]
+!
+! gsw_sr_from_sp : Reference Salinity [g/kg]
+*/
+double
+gsw_sr_from_sp(double sp)
+{
+ GSW_TEOS10_CONSTANTS;
+
+ return (sp*gsw_ups);
+}
+/*
+!==========================================================================
+function gsw_sstar_from_sa(sa,p,lon,lat)
+!==========================================================================
+
+! Calculates Preformed Salinity, Sstar, from Absolute Salinity, SA.
+!
+! sa : Absolute Salinity [g/kg]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sstar_from_sa : Preformed Salinity [g/kg]
+*/
+double
+gsw_sstar_from_sa(double sa, double p, double lon, double lat)
+{
+ double saar;
+
+ saar = gsw_saar(p,lon,lat);
+ /*
+ ! In the Baltic Sea, Sstar = sa, and note that gsw_saar returns zero
+ ! for saar in the Baltic.
+ */
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return (sa*(1e0 - 0.35e0*saar)/(1e0 + saar));
+}
+/*
+!==========================================================================
+function gsw_sstar_from_sp(sp,p,lon,lat)
+!==========================================================================
+
+! Calculates Preformed Salinity, Sstar, from Practical Salinity, SP.
+!
+! sp : Practical Salinity [unitless]
+! p : sea pressure [dbar]
+! lon : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_sstar_from_sp : Preformed Salinity [g/kg]
+*/
+double
+gsw_sstar_from_sp(double sp, double p, double lon, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double saar, sstar_baltic;
+
+ /*
+ !In the Baltic Sea, Sstar = SA.
+ */
+ sstar_baltic = gsw_sa_from_sp_baltic(sp,lon,lat);
+ if (sstar_baltic < GSW_ERROR_LIMIT)
+ return (sstar_baltic);
+ saar = gsw_saar(p,lon,lat);
+ if (saar == GSW_INVALID_VALUE)
+ return (saar);
+ return (gsw_ups*sp*(1 - 0.35e0*saar));
+}
+/*
+!==========================================================================
+elemental function gsw_t_deriv_chem_potential_water_t_exact (sa, t, p)
+!==========================================================================
+!
+! Calculates the temperature derivative of the chemical potential of water
+! in seawater so that it is valid at exactly SA = 0.
+!
+! SA = Absolute Salinity [ g/kg ]
+! t = in-situ temperature (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!
+! chem_potential_water_dt = temperature derivative of the chemical
+! potential of water in seawater [ J g^-1 K^-1 ]
+!--------------------------------------------------------------------------
+*/
+double
+gsw_t_deriv_chem_potential_water_t_exact(double sa, double t, double p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double g03_t, g08_sa_t, x, x2, y, z, g08_t, kg2g = 1e-3;
+/*
+! Note. The kg2g, a factor of 1e-3, is needed to convert the output of this
+! function into units of J/g. See section (2.9) of the TEOS-10 Manual.
+*/
+
+ x2 = gsw_sfac*sa;
+ x = sqrt(x2);
+ y = t*0.025;
+ z = p*rec_db2pa;
+ /* the input pressure (p) is sea pressure in units of dbar. */
+
+ g03_t = 5.90578347909402 + z*(-270.983805184062 +
+ z*(776.153611613101 + z*(-196.51255088122 + (28.9796526294175 -
+ 2.13290083518327*z)*z))) +
+ y*(-24715.571866078 + z*(2910.0729080936 +
+ z*(-1513.116771538718 + z*(546.959324647056 +
+ z*(-111.1208127634436 + 8.68841343834394*z)))) +
+ y*(2210.2236124548363 + z*(-2017.52334943521 +
+ z*(1498.081172457456 + z*(-718.6359919632359 +
+ (146.4037555781616 - 4.9892131862671505*z)*z))) +
+ y*(-592.743745734632 + z*(1591.873781627888 +
+ z*(-1207.261522487504 + (608.785486935364 -
+ 105.4993508931208*z)*z)) +
+ y*(290.12956292128547 + z*(-973.091553087975 +
+ z*(602.603274510125 + z*(-276.361526170076 +
+ 32.40953340386105*z))) +
+ y*(-113.90630790850321 + y*(21.35571525415769 -
+ 67.41756835751434*z) +
+ z*(381.06836198507096 + z*(-133.7383902842754 +
+ 49.023632509086724*z)))))));
+
+ g08_t = x2*(168.072408311545 +
+ x*(-493.407510141682 + x*(543.835333000098 +
+ x*(-196.028306689776 + 36.7571622995805*x) +
+ y*(-137.1145018408982 + y*(148.10030845687618 +
+ y*(-68.5590309679152 + 12.4848504784754*y))) -
+ 22.6683558512829*z) + z*(-175.292041186547 +
+ (83.1923927801819 - 29.483064349429*z)*z) +
+ y*(-86.1329351956084 + z*(766.116132004952 +
+ z*(-108.3834525034224 + 51.2796974779828*z)) +
+ y*(-30.0682112585625 - 1380.9597954037708*z +
+ y*(3.50240264723578 + 938.26075044542*z)))));
+
+ g08_sa_t = 1187.3715515697959 +
+ x*(-1480.222530425046 + x*(2175.341332000392 +
+ x*(-980.14153344888 + 220.542973797483*x) +
+ y*(-548.4580073635929 + y*(592.4012338275047 +
+ y*(-274.2361238716608 + 49.9394019139016*y))) -
+ 90.6734234051316*z) + z*(-525.876123559641 +
+ (249.57717834054571 - 88.449193048287*z)*z) +
+ y*(-258.3988055868252 + z*(2298.348396014856 +
+ z*(-325.1503575102672 + 153.8390924339484*z)) +
+ y*(-90.2046337756875 - 4142.8793862113125*z +
+ y*(10.50720794170734 + 2814.78225133626*z))));
+
+ return (kg2g*((g03_t + g08_t)*0.025 - 0.5*gsw_sfac*0.025*sa*g08_sa_t));
+}
+/*
+!==========================================================================
+function gsw_t_freezing(sa,p,saturation_fraction)
+!==========================================================================
+
+! Calculates the in-situ temperature at which seawater freezes
+!
+! sa : Absolute Salinity [g/kg]
+! p : sea pressure [dbar]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction : the saturation fraction of dissolved air
+! in seawater
+!
+! t_freezing : in-situ temperature at which seawater freezes.[deg C]
+*/
+double
+gsw_t_freezing(double sa, double p, double saturation_fraction)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_FREEZING_POLY_COEFFICIENTS;
+ double sa_r, x, p_r;
+ double df_dt, tf, tfm, tf_old, f, return_value;
+
+ /* The initial value of t_freezing_exact (for air-free seawater) */
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ tf = t0
+ + sa_r*(t1 + x*(t2 + x*(t3 + x*(t4 + x*(t5 + t6*x)))))
+ + p_r*(t7 + p_r*(t8 + t9*p_r))
+ + sa_r*p_r*(t10 + p_r*(t12 + p_r*(t15 + t21*sa_r))
+ + sa_r*(t13 + t17*p_r + t19*sa_r)
+ + x*(t11 + p_r*(t14 + t18*p_r) + sa_r*(t16 + t20*p_r
+ + t22*sa_r)));
+
+ /* Adjust for the effects of dissolved air */
+ tf -= saturation_fraction*(1e-3)*(2.4 - sa/(2.0*gsw_sso));
+
+ df_dt = 1e3*gsw_t_deriv_chem_potential_water_t_exact(sa,tf,p) -
+ gsw_gibbs_ice(1,0,tf,p);
+/*
+! df_dt here is the initial value of the derivative of the function f whose
+! zero (f = 0) we are finding (see Eqn. (3.33.2) of IOC et al (2010)).
+*/
+
+ tf_old = tf;
+ f = 1e3*gsw_chem_potential_water_t_exact(sa,tf_old,p) -
+ gsw_gibbs_ice(0,0,tf_old,p);
+ tf = tf_old - f/df_dt;
+ tfm = 0.5*(tf + tf_old);
+ df_dt = 1e3*gsw_t_deriv_chem_potential_water_t_exact(sa,tfm,p) -
+ gsw_gibbs_ice(1,0,tfm,p);
+ tf = tf_old - f/df_dt;
+
+ tf_old = tf;
+ f = 1e3*gsw_chem_potential_water_t_exact(sa,tf_old,p) -
+ gsw_gibbs_ice(0,0,tf_old,p);
+ tf = tf_old - f/df_dt;
+
+ /* Adjust for the effects of dissolved air */
+ return_value = tf -
+ saturation_fraction*(1e-3)*(2.4 - sa/(2.0*gsw_sso));
+ return (return_value);
+}
+/*
+!==========================================================================
+elemental subroutine gsw_t_freezing_first_derivatives (sa, p, &
+ saturation_fraction, tfreezing_sa, tfreezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the in-situ temperature at which
+! seawater freezes with respect to Absolute Salinity SA and pressure P (in
+! Pa). These expressions come from differentiating the expression that
+! defines the freezing temperature, namely the equality between the
+! chemical potentials of water in seawater and in ice.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! tfreezing_SA = the derivative of the in-situ freezing temperature
+! (ITS-90) with respect to Absolute Salinity at fixed
+! pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! tfreezing_P = the derivative of the in-situ freezing temperature
+! (ITS-90) with respect to pressure (in Pa) at fixed
+! Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_t_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa, double *tfreezing_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ double rec_denom, tf, g_per_kg = 1000.0;
+
+ tf = gsw_t_freezing(sa,p,saturation_fraction);
+ rec_denom = 1.0/
+ (g_per_kg*gsw_t_deriv_chem_potential_water_t_exact(sa,tf,p)
+ + gsw_entropy_ice(tf,p));
+
+ if (tfreezing_sa != NULL)
+ *tfreezing_sa =
+ gsw_dilution_coefficient_t_exact(sa,tf,p)*rec_denom
+ + saturation_fraction*(1e-3)/(2.0*gsw_sso);
+
+ if (tfreezing_p != NULL)
+ *tfreezing_p =
+ -(gsw_specvol_t_exact(sa,tf,p) - sa*gsw_gibbs(1,0,1,sa,tf,p)
+ - gsw_specvol_ice(tf,p))*rec_denom;
+
+ return;
+}
+/*
+!==========================================================================
+elemental subroutine gsw_t_freezing_first_derivatives_poly (sa, p, &
+ saturation_fraction, tfreezing_sa, tfreezing_p)
+!==========================================================================
+!
+! Calculates the first derivatives of the in-situ temperature at which
+! seawater freezes with respect to Absolute Salinity SA and pressure P (in
+! Pa). These expressions come from differentiating the expression that
+! defines the freezing temperature, namely the equality between the
+! chemical potentials of water in seawater and in ice.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! tfreezing_SA = the derivative of the in-situ freezing temperature
+! (ITS-90) with respect to Absolute Salinity at fixed
+! pressure [ K/(g/kg) ] i.e. [ K kg/g ]
+!
+! tfreezing_P = the derivative of the in-situ freezing temperature
+! (ITS-90) with respect to pressure (in Pa) at fixed
+! Absolute Salinity [ K/Pa ]
+!--------------------------------------------------------------------------
+*/
+void
+gsw_t_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa, double *tfreezing_p)
+{
+ GSW_TEOS10_CONSTANTS;
+ GSW_FREEZING_POLY_COEFFICIENTS;
+ double p_r, sa_r, x, c = 1e-3/(2.0*gsw_sso);
+
+ sa_r = sa*1e-2;
+ x = sqrt(sa_r);
+ p_r = p*1e-4;
+
+ if (tfreezing_sa != NULL)
+ *tfreezing_sa =
+ (t1 + x*(1.5*t2 + x*(2.0*t3 + x*(2.5*t4 + x*(3.0*t5
+ + 3.5*t6*x)))) + p_r*(t10 + x*(1.5*t11 + x*(2.0*t13
+ + x*(2.5*t16 + x*(3.0*t19 + 3.5*t22*x))))
+ + p_r*(t12 + x*(1.5*t14 + x*(2.0*t17 + 2.5*t20*x))
+ + p_r*(t15 + x*(1.5*t18 + 2.0*t21*x)))))*1e-2
+ + saturation_fraction*c;
+
+ if (tfreezing_p != NULL)
+ *tfreezing_p =
+ (t7 + sa_r*(t10 + x*(t11 + x*(t13 + x*(t16 + x*(t19 + t22*x)))))
+ + p_r*(2.0*t8 + sa_r*(2.0*t12 + x*(2.0*t14 + x*(2.0*t17
+ + 2.0*t20*x))) + p_r*(3.0*t9 + sa_r*(3.0*t15 + x*(3.0*t18
+ + 3.0*t21*x)))))*1e-8;
+
+ return;
+}
+/*
+!==========================================================================
+elemental function gsw_t_freezing_poly (sa, p, saturation_fraction)
+!==========================================================================
+!
+! Calculates the in-situ temperature at which seawater freezes from a
+! computationally efficient polynomial.
+!
+! SA = Absolute Salinity [ g/kg ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+! saturation_fraction = the saturation fraction of dissolved air in
+! seawater
+!
+! t_freezing = in-situ temperature at which seawater freezes. [ deg C ]
+! (ITS-90)
+!--------------------------------------------------------------------------
+*/
+double
+gsw_t_freezing_poly(double sa, double p, double saturation_fraction)
+{
+ GSW_TEOS10_CONSTANTS;
+ double ctf, return_value;
+
+ ctf = gsw_ct_freezing_poly(sa,p,saturation_fraction);
+ return_value = gsw_t_from_ct(sa,ctf,p);
+ return (return_value);
+}
+/*
+!==========================================================================
+function gsw_t_from_ct(sa,ct,p)
+!==========================================================================
+
+! Calculates in-situ temperature from Conservative Temperature of seawater
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature [deg C]
+!
+! gsw_t_from_ct : in-situ temperature [deg C]
+*/
+double
+gsw_t_from_ct(double sa, double ct, double p)
+{
+ double pt0, p0=0.0;
+
+ pt0 = gsw_pt_from_ct(sa,ct);
+ return (gsw_pt_from_t(sa,pt0,p0,p));
+}
+/*
+! =========================================================================
+elemental function gsw_t_from_pt0_ice (pt0_ice, p)
+! =========================================================================
+!
+! Calculates in-situ temperature from the potential temperature of ice Ih
+! with reference pressure, p_ref, of 0 dbar (the surface), and the
+! in-situ pressure.
+!
+! pt0_ice = potential temperature of ice Ih with reference pressure of
+! zero dbar (ITS-90) [ deg C ]
+! p = sea pressure [ dbar ]
+! ( i.e. absolute pressure - 10.1325 dbar )
+!--------------------------------------------------------------------------
+*/
+double
+gsw_t_from_pt0_ice(double pt0_ice, double p)
+{
+ double p0 = 0.0;
+
+ return (gsw_pt_from_t_ice(pt0_ice,p0,p));
+}
+/*
+!==========================================================================
+function gsw_thermobaric(sa,ct,p)
+!==========================================================================
+
+! Calculates the thermobaric coefficient of seawater with respect to
+! Conservative Temperature. This routine is based on the
+! computationally-efficient expression for specific volume in terms of
+! SA, CT and p (Roquet et al., 2014).
+!
+! sa : Absolute Salinity [g/kg]
+! ct : Conservative Temperature (ITS-90) [deg C]
+! p : sea pressure [dbar]
+!
+! thermobaric : thermobaric coefficient with [1/(K Pa)]
+! respect to Conservative Temperature (48 term equation)
+*/
+double
+gsw_thermobaric(double sa, double ct, double p)
+{
+ double v_ct, v_ct_p, v_sa, v_sa_p;
+
+ gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct,NULL);
+
+ gsw_specvol_second_derivatives(sa,ct,p,NULL,NULL,NULL,&v_sa_p,&v_ct_p);
+
+ return (gsw_rho(sa,ct,p)*(v_ct_p - (v_ct/v_sa)*v_sa_p));
+}
+/*
+!==========================================================================
+subroutine gsw_turner_rsubrho(sa,ct,p,nz,tu,rsubrho,p_mid)
+!==========================================================================
+
+! Calculates the Turner angle and the Rsubrho as a function of pressure
+! down a vertical water column. These quantities express the relative
+! contributions of the vertical gradients of Conservative Temperature
+! and Absolute Salinity to the vertical stability (the square of the
+! Brunt-Vaisala Frequency squared, N^2). Tu and Rsubrho are evaluated at
+! the mid pressure between the individual data points in the vertical.
+!
+! Note that in the double-diffusive literature, papers concerned with
+! the "diffusive" form of double-diffusive convection often define the
+! stability ratio as the reciprocal of what is defined here as the
+! stability ratio.
+
+! sa : Absolute Salinity (a profile (length nz)) [g/kg]
+! ct : Conservative Temperature (a profile (length nz)) [deg C]
+! p : sea pressure (a profile (length nz)) [dbar]
+! nz : number of bottles
+! tu : Turner angle, on the same (nz-1) grid as p_mid.
+! Turner angle has units of: [ degrees of rotation ]
+! rsubrho : Stability Ratio, on the same (nz-1) grid as p_mid.
+! Rsubrho is dimensionless. [ unitless ]
+! p_mid : Mid pressure between p grid (length nz-1) [dbar]
+*/
+void
+gsw_turner_rsubrho(double *sa, double *ct, double *p, int nz,
+ double *tu, double *rsubrho, double *p_mid)
+{
+ GSW_TEOS10_CONSTANTS;
+ int k;
+ double dsa, sa_mid, dct, ct_mid, alpha_mid, beta_mid;
+
+ if (nz < 2)
+ return;
+
+ for (k = 0; k < nz-1; k++) {
+ dsa = (sa[k] - sa[k+1]);
+ sa_mid = 0.5e0*(sa[k] + sa[k+1]);
+ dct = (ct[k] - ct[k+1]);
+ ct_mid = 0.5e0*(ct[k] + ct[k+1]);
+ p_mid[k] = 0.5e0*(p[k] + p[k+1]);
+ gsw_specvol_alpha_beta(sa_mid,ct_mid,p_mid[k],NULL,&alpha_mid,
+ &beta_mid);
+ tu[k] = rad2deg*atan2((alpha_mid*dct + beta_mid*dsa),
+ (alpha_mid*dct - beta_mid*dsa));
+ if (dsa == 0.0)
+ rsubrho[k] = GSW_INVALID_VALUE;
+ else
+ rsubrho[k] = (alpha_mid*dct)/(beta_mid*dsa);
+ }
+}
+/*
+!==========================================================================
+subroutine gsw_util_indx(x,n,z,k)
+!==========================================================================
+
+! Finds the index of the value in a monotonically increasing array
+!
+! x : array of monotonically increasing values
+! n : length of the array
+! z : value to be indexed
+!
+! K : index K - if X(K) <= Z < X(K+1), or
+! N-1 - if Z = X(N)
+!
+*/
+int
+gsw_util_indx(double *x, int n, double z)
+{
+ int k, ku, kl, km;
+
+ if (z > x[0] && z < x[n-1]) {
+ kl = 0;
+ ku = n-1;
+ while (ku-kl > 1) {
+ km = (ku+kl)>>1;
+ if (z > x[km])
+ kl = km;
+ else
+ ku = km;
+ }
+ k = kl;
+ if (z == x[k+1])
+ k++;
+ } else if (z <= x[0])
+ k = 0;
+ else
+ k = n-2;
+
+ return (k);
+}
+/*
+!==========================================================================
+pure function gsw_util_interp1q_int (x, iy, x_i) result(y_i)
+!==========================================================================
+! Returns the value of the 1-D function iy (integer) at the points of column
+! vector x_i using linear interpolation. The vector x specifies the
+! coordinates of the underlying interval.
+!==========================================================================
+*/
+double *
+gsw_util_interp1q_int(int nx, double *x, int *iy, int nxi, double *x_i,
+ double *y_i)
+{
+ char *in_rng;
+ int *j, *k, *r, *jrev, *ki, imax_x, imin_x, i, n, m, ii;
+ double *xi, *xxi, u, max_x, min_x;
+
+ if (nx <= 0 || nxi <= 0)
+ return (NULL);
+
+ min_x = max_x = x[0];
+ imin_x = imax_x = 0;
+ for (i=0; i<nx; i++) {
+ if (x[i] < min_x) {
+ min_x = x[i];
+ imin_x = i;
+ } else if (x[i] > max_x) {
+ max_x = x[i];
+ imax_x = i;
+ }
+ }
+ in_rng = (char *) malloc(nxi*sizeof (char));
+ memset(in_rng, 0, nxi*sizeof (char));
+
+ for (i=n=0; i<nxi; i++) {
+ if (x_i[i] <= min_x) {
+ y_i[i] = iy[imin_x];
+ } else if (x_i[i] >= max_x) {
+ y_i[i] = iy[imax_x];
+ } else {
+ in_rng[i] = 1;
+ n++;
+ }
+ }
+ if (n==0)
+ return (y_i);
+
+ xi = (double *) malloc(n*sizeof (double));
+ k = (int *) malloc(3*n*sizeof (int)); ki = k+n; r = ki+n;
+ m = nx + n;
+ xxi = (double *) malloc(m*sizeof (double));
+ j = (int *) malloc(2*m*sizeof (int)); jrev = j+m;
+
+ ii = 0;
+ for (i = 0; i<nxi; i++) {
+ if (in_rng[i]) {
+ xi[ii] = x_i[i];
+ ki[ii] = i;
+ ii++;
+ }
+ }
+ free(in_rng);
+ /*
+ ** Note that the following operations on the index
+ ** vectors jrev and r depend on the sort utility
+ ** gsw_util_sort_real() consistently ordering the
+ ** sorting indexes either in ascending or descending
+ ** sequence for replicate values in the real vector.
+ */
+ gsw_util_sort_real(xi, n, k);
+ for (i = 0; i<nx; i++)
+ xxi[i] = x[i];
+ for (i = 0; i<n; i++)
+ xxi[nx+i] = xi[k[i]];
+ gsw_util_sort_real(xxi, nx+n, j);
+
+ for (i = 0; i<nx+n; i++)
+ jrev[j[i]] = i;
+ for (i = 0; i<n; i++)
+ r[k[i]] = jrev[nx+i] - i-1;
+
+ for (i = 0; i<n; i++) {
+ u = (xi[i]-x[r[i]])/(x[r[i]+1]-x[r[i]]);
+ y_i[ki[i]] = iy[r[i]] + (iy[r[i]+1]-iy[r[i]])*u;
+ }
+ free(j); free(xxi); free(k); free(xi);
+ return (y_i);
+}
+/*
+!==========================================================================
+pure function gsw_util_linear_interp (x, y, x_i) result(y_i)
+!==========================================================================
+! Returns the values of the functions y{ny} at the points of column
+! vector x_i using linear interpolation. The vector x specifies the
+! coordinates of the underlying interval, and the matrix y specifies
+| the function values at each x coordinate. Note that y has dimensions
+| nx x ny and y_i has dimensions nxi x ny.
+! This function was adapted from Matlab's interp1q.
+!==========================================================================
+*/
+double *
+gsw_util_linear_interp(int nx, double *x, int ny, double *y, int nxi,
+ double *x_i, double *y_i)
+{
+ char *in_rng;
+ int *j, *k, *r, *jrev, *ki, imax_x, imin_x, i, n, m, ii, jy,
+ jy0, jyi0, r0;
+ double *xi, *xxi, u, max_x, min_x;
+
+ if (nx <= 0 || nxi <= 0 || ny <= 0)
+ return (NULL);
+
+ min_x = max_x = x[0];
+ imin_x = imax_x = 0;
+ for (i=0; i<nx; i++) {
+ if (x[i] < min_x) {
+ min_x = x[i];
+ imin_x = i;
+ } else if (x[i] > max_x) {
+ max_x = x[i];
+ imax_x = i;
+ }
+ }
+ in_rng = (char *) malloc(nxi*sizeof (char));
+ memset(in_rng, 0, nxi*sizeof (char));
+
+ for (i=n=0; i<nxi; i++) {
+ if (x_i[i] <= min_x) {
+ for (jy=jy0=jyi0=0; jy<ny; jy++, jy0+=nx, jyi0+=nxi)
+ y_i[jyi0+i] = y[jy0+imin_x];
+ } else if (x_i[i] >= max_x) {
+ for (jy=jy0=jyi0=0; jy<ny; jy++, jy0+=nx, jyi0+=nxi)
+ y_i[jyi0+i] = y[jy0+imax_x];
+ } else {
+ in_rng[i] = 1;
+ n++;
+ }
+ }
+ if (n==0)
+ return (y_i);
+ xi = (double *) malloc(n*sizeof (double));
+ k = (int *) malloc(3*n*sizeof (int)); ki = k+n; r = ki+n;
+ m = nx + n;
+ xxi = (double *) malloc(m*sizeof (double));
+ j = (int *) malloc(2*m*sizeof (int)); jrev = j+m;
+
+ ii = 0;
+ for (i = 0; i<nxi; i++) {
+ if (in_rng[i]) {
+ xi[ii] = x_i[i];
+ ki[ii] = i;
+ ii++;
+ }
+ }
+ free(in_rng);
+ /*
+ ** This algorithm mimics the Matlab interp1q function.
+ **
+ ** An explaination of this algorithm:
+ ** We have points we are interpolating from (x) and
+ ** points that we are interpolating to (xi). We
+ ** sort the interpolating from points, concatenate
+ ** them with the interpolating to points and sort the result.
+ ** We then construct index r, the interpolation index in x for
+ ** each point in xi.
+ **
+ ** Note that the following operations on the index
+ ** vectors jrev and r depend on the sort utility
+ ** gsw_util_sort_real() consistently ordering the
+ ** sorting indexes either in ascending or descending
+ ** sequence for replicate values in the real vector.
+ */
+ gsw_util_sort_real(xi, n, k);
+ memmove(xxi, x, nx*sizeof (double));
+ memmove(xxi+nx, xi, n*sizeof (double));
+ gsw_util_sort_real(xxi, m, j);
+
+ for (i = 0; i<m; i++)
+ jrev[j[i]] = i;
+ for (i = 0; i<n; i++)
+ r[k[i]] = jrev[nx+i] - i - 1;
+ /* this is now the interpolation index in x for a point in xi */
+
+ for (jy=jy0=jyi0=0; jy < ny; jy++, jy0+=nx, jyi0+=nxi) {
+ for (i = 0; i<n; i++) {
+ u = (xi[i]-x[r[i]])/(x[r[i]+1]-x[r[i]]);
+ r0 = jy0+r[i];
+ y_i[jyi0+ki[i]] = y[r0] + (y[r0+1]-y[r0])*u;
+ }
+ }
+ free(j); free(xxi); free(k); free(xi);
+ return (y_i);
+}
+/*
+pure function gsw_util_sort_real (rarray) result(iarray)
+*/
+
+#if (defined __APPLE__ || defined __MACH__ || defined __DARWIN__ || \
+ defined __FREEBSD__ || defined __BSD__ || \
+ defined _WIN32 || defined _WIN64 || defined __WINDOWS__)
+static int
+compare(void *rarray, const void *p1, const void *p2)
+#else
+
+extern void qsort_r(void *, size_t, size_t, int (*)(const void *, const void *,
+ void *), void *);
+static int
+compare(const void *p1, const void *p2, void *rarray)
+#endif
+{
+ double *rdata = (double *) rarray;
+ if (rdata[*(int *)p1] < rdata[*(int *)p2])
+ return (-1);
+ if (rdata[*(int *)p1] > rdata[*(int *)p2])
+ return (1);
+ /*
+ ** Note that the library functions using this utility
+ ** depend on the fact that for replicate values in rdata
+ ** the indexes are returned in descending sequence.
+ */
+ if (*(int *)p1 < *(int *)p2)
+ return (1);
+ return (0);
+}
+
+/*
+** Sort the double array rarray into ascending value sequence
+** returning an index array of the sorted result. This function
+** is thread-safe.
+*/
+void
+gsw_util_sort_real(double *rarray, int nx, int *iarray)
+{
+ int i;
+
+ for (i=0; i<nx; i++)
+ iarray[i] = i;
+#if (defined __APPLE__ || defined __MACH__ || defined __DARWIN__ || \
+ defined __FREEBSD__ || defined __BSD__ )
+ qsort_r(iarray, nx, sizeof (int), (void *)rarray, compare);
+#elif (defined _WIN32 || defined _WIN64 || defined __WINDOWS__)
+ qsort_s(iarray, nx, sizeof (int), compare, (void *)rarray);
+#else
+ qsort_r(iarray, nx, sizeof (int), compare, (void *)rarray);
+#endif
+}
+/*
+!==========================================================================
+function gsw_util_xinterp1(x,y,n,x0)
+!==========================================================================
+
+! Linearly interpolate a real array
+!
+! x : y array (Must be monotonic)
+! y : y array
+! n : length of X and Y arrays
+! x0 : value to be interpolated
+!
+! gsw_xinterp1 : Linearly interpolated value
+*/
+double
+gsw_util_xinterp1(double *x, double *y, int n, double x0)
+{
+ int k;
+ double r;
+
+ k = gsw_util_indx(x,n,x0);
+ r = (x0-x[k])/(x[k+1]-x[k]);
+ return (y[k] + r*(y[k+1]-y[k]));
+}
+/*
+!==========================================================================
+function gsw_z_from_p(p,lat)
+!==========================================================================
+
+! Calculates the height z from pressure p
+!
+! p : sea pressure [dbar]
+! lat : latitude [deg]
+!
+! gsw_z_from_p : height [m]
+*/
+double
+gsw_z_from_p(double p, double lat)
+{
+ GSW_TEOS10_CONSTANTS;
+ double x, sin2, b, c, a;
+
+ x = sin(lat*deg2rad);
+ sin2 = x*x;
+ b = 9.780327*(1.0 + (5.2792e-3 + (2.32e-5*sin2))*sin2);
+ a = -0.5*gamma*b;
+ c = gsw_enthalpy_sso_0(p);
+
+ return (-2.0*c/(b + sqrt(b*b - 4.0*a*c)));
+}
+
+/*
+** The End
+**!==========================================================================
+*/
diff --git a/src2/c_gsw/gsw_saar.cpp b/src2/c_gsw/gsw_saar.cpp
new file mode 100644
index 0000000..4fd09a0
--- /dev/null
+++ b/src2/c_gsw/gsw_saar.cpp
@@ -0,0 +1,267 @@
+/*
+** $Id: gsw_saar.c,v b04abca68ac0 2015/09/13 17:47:28 fdelahoyde $
+** $Version: 3.05.0-2 $
+**
+** GSW TEOS-10 V3.05
+*/
+#include "gswteos-10_cpp.h"
+#include "gsw_internal_const.h"
+#include "gsw_saar_data.c"
+
+static double gsw_sum(double *x, int n);
+
+static double
+gsw_sum(double *x, int n)
+{
+ int i;
+ double val;
+
+ for (val=0.0, i=0; i<n; val += x[i], i++);
+ return (val);
+}
+
+#define max(a,b) (((a)>(b))?(a):(b))
+#define sum(x) gsw_sum(x, sizeof (x)/sizeof (double))
+
+/*
+!==========================================================================
+function gsw_saar(p,long,lat)
+!==========================================================================
+
+! Calculates the Absolute Salinity Anomaly Ratio, SAAR at a geographic point.
+!
+! p : sea pressure [dbar]
+! long : longitude [deg E]
+! lat : latitude [deg N]
+!
+! gsw_saar : Absolute Salinity Anomaly Ratio [unitless]
+*/
+double
+gsw_saar(double p, double lon, double lat)
+{
+ GSW_SAAR_DATA;
+ int nx=gsw_nx, ny=gsw_ny, nz=gsw_nz;
+ int indx0, indy0, indz0, k, ndepth_index;
+ double saar[4], saar_old[4];
+ double sa_upper, sa_lower, dlong, dlat;
+ double r1, s1, t1, ndepth_max, return_value;
+
+
+ return_value = GSW_INVALID_VALUE;
+
+ if (std::isnan(lat) || std::isnan(lon) || std::isnan(p))
+ return (return_value);
+
+ if (lat < -86.0 || lat > 90.0)
+ return (return_value);
+
+ if (lon < 0.0)
+ lon += 360.0;
+
+ dlong = longs_ref[1]-longs_ref[0];
+ dlat = lats_ref[1]-lats_ref[0];
+
+ indx0 = floor(0 + (nx-1)*(lon-longs_ref[0])/(longs_ref[nx-1]-
+ longs_ref[0]));
+ if (indx0 == nx-1)
+ indx0 = nx-2;
+
+ indy0 = floor(0 + (ny-1)*(lat-lats_ref[0])/(lats_ref[ny-1]-
+ lats_ref[0]));
+ if(indy0 == ny-1)
+ indy0 = ny-2;
+/*
+! Look for the maximum valid "ndepth_ref" value around our point.
+! Note: invalid "ndepth_ref" values are NaNs (a hangover from the codes
+! Matlab origins), but we have replaced the NaNs with a value of "9e90",
+! hence we need an additional upper-limit check in the code below so they
+! will not be recognised as valid values.
+*/
+ ndepth_max = -1.0;
+ for (k=0; k < 4; k++) {
+ ndepth_index = indy0+delj[k]+(indx0+deli[k])*ny;
+ if (ndepth_ref[ndepth_index] > 0.0 &&
+ ndepth_ref[ndepth_index] < 1e90)
+ ndepth_max = max(ndepth_max, ndepth_ref[ndepth_index]);
+ }
+/*
+! If we are a long way from the ocean then there will be no valid "ndepth_ref"
+! values near the point (ie. surrounded by NaNs) - so just return SAAR = 0.0
+*/
+ if (ndepth_max == -1.0)
+ return (0.0);
+
+ if (p > p_ref[(int)(ndepth_max)-1])
+ p = p_ref[(int)(ndepth_max)-1];
+ indz0 = gsw_util_indx(p_ref,nz,p);
+
+ r1 = (lon-longs_ref[indx0])/(longs_ref[indx0+1]-longs_ref[indx0]);
+ s1 = (lat-lats_ref[indy0])/(lats_ref[indy0+1]-lats_ref[indy0]);
+ t1 = (p-p_ref[indz0])/(p_ref[indz0+1]-p_ref[indz0]);
+
+ for (k=0; k<4; k++)
+ saar[k] = saar_ref[indz0+nz*(indy0+delj[k]+(indx0+deli[k])*ny)];
+
+ if (longs_pan[0] <= lon && lon <= longs_pan[npan-1]-0.001 &&
+ lats_pan[npan-1] <= lat && lat <= lats_pan[0]) {
+ memmove(saar_old,saar,4*sizeof (double));
+ gsw_add_barrier(saar_old,lon,lat,longs_ref[indx0],
+ lats_ref[indy0],dlong,dlat,saar);
+ } else if (fabs(sum(saar)) >= GSW_ERROR_LIMIT) {
+ memmove(saar_old,saar,4*sizeof (double));
+ gsw_add_mean(saar_old,saar);
+ }
+
+ sa_upper = (1.0-s1)*(saar[0] + r1*(saar[1]-saar[0])) +
+ s1*(saar[3] + r1*(saar[2]-saar[3]));
+
+ for (k=0; k<4; k++)
+ saar[k] = saar_ref[indz0+1+nz*(indy0+delj[k]+
+ (indx0+deli[k])*ny)];
+
+ if (longs_pan[0] <= lon && lon <= longs_pan[npan-1]-0.001 &&
+ lats_pan[npan-1] <= lat && lat <= lats_pan[0]) {
+ memmove(saar_old,saar,4*sizeof (double));
+ gsw_add_barrier(saar_old,lon,lat,longs_ref[indx0],
+ lats_ref[indy0],dlong,dlat,saar);
+ } else if (fabs(sum(saar)) >= GSW_ERROR_LIMIT) {
+ memmove(saar_old,saar,4*sizeof (double));
+ gsw_add_mean(saar_old,saar);
+ }
+
+ sa_lower = (1.0-s1)*(saar[0] + r1*(saar[1]-saar[0])) +
+ s1*(saar[3] + r1*(saar[2]-saar[3]));
+ if (fabs(sa_lower) >= GSW_ERROR_LIMIT)
+ sa_lower = sa_upper;
+ return_value = sa_upper + t1*(sa_lower-sa_upper);
+
+ if (fabs(return_value) >= GSW_ERROR_LIMIT)
+ return_value = GSW_INVALID_VALUE;
+
+ return (return_value);
+}
+
+/*
+!==========================================================================
+function gsw_deltasa_atlas(p,lon,lat)
+!==========================================================================
+
+! Calculates the Absolute Salinity Anomaly atlas value, delta_SA_atlas.
+!
+! p : sea pressure [dbar]
+! lon : longiture [deg E]
+! lat : latitude [deg N]
+!
+! deltasa_atlas : Absolute Salinity Anomaly atlas value [g/kg]
+*/
+double
+gsw_deltasa_atlas(double p, double lon, double lat)
+{
+ GSW_SAAR_DATA;
+ int nx=gsw_nx, ny=gsw_ny, nz=gsw_nz;
+ int indx0, indy0, indz0, k, ndepth_index;
+ double dsar[4], dsar_old[4];
+ double dlong, dlat;
+ double return_value, sa_upper, sa_lower;
+ double r1, s1, t1, ndepth_max;
+
+ return_value = GSW_INVALID_VALUE;
+
+ if (std::isnan(lat) || std::isnan(lon) || std::isnan(p))
+ return (return_value);
+
+ if (lat < -86.0 || lat > 90.0)
+ return (return_value);
+
+ if (lon < 0.0)
+ lon += 360.0;
+
+ dlong = longs_ref[1]-longs_ref[0];
+ dlat = lats_ref[1]-lats_ref[0];
+
+ indx0 = floor(0 + (nx-1)*(lon-longs_ref[0])/
+ (longs_ref[nx-1]-longs_ref[0]));
+ if (indx0 == nx-1)
+ indx0 = nx-2;
+
+ indy0 = floor(0 + (ny-1)*(lat-lats_ref[0])/
+ (lats_ref[ny-1]-lats_ref[0]));
+ if (indy0 == ny-1)
+ indy0 = ny-2;
+/*
+! Look for the maximum valid "ndepth_ref" value around our point.
+! Note: invalid "ndepth_ref" values are NaNs (a hangover from the codes
+! Matlab origins), but we have replaced the NaNs with a value of "9e90",
+! hence we need an additional upper-limit check in the code below so they
+! will not be recognised as valid values.
+*/
+ ndepth_max = -1;
+ for (k=0; k<4; k++) {
+ ndepth_index = indy0+delj[k]+(indx0+deli[k])*ny;
+ if (ndepth_ref[ndepth_index] > 0.0 &&
+ ndepth_ref[ndepth_index] < 1e90)
+ ndepth_max = max(ndepth_max, ndepth_ref[ndepth_index]);
+ }
+/*
+! If we are a long way from the ocean then there will be no valid "ndepth_ref"
+! values near the point (ie. surrounded by NaNs) - so deltasa_atlas = 0.0
+*/
+ if (ndepth_max == -1.0)
+ return (0.0);
+
+ if (p > p_ref[(int)(ndepth_max)-1])
+ p = p_ref[(int)(ndepth_max)-1];
+ indz0 = gsw_util_indx(p_ref,nz,p);
+
+ r1 = (lon-longs_ref[indx0])/
+ (longs_ref[indx0+1]-longs_ref[indx0]);
+ s1 = (lat-lats_ref[indy0])/
+ (lats_ref[indy0+1]-lats_ref[indy0]);
+ t1 = (p-p_ref[indz0])/
+ (p_ref[indz0+1]-p_ref[indz0]);
+
+ for (k=0; k < 4; k++)
+ dsar[k] = delta_sa_ref[indz0+nz*(indy0+delj[k]+
+ (indx0+deli[k])*ny)];
+
+ if (longs_pan[0] <= lon && lon <= longs_pan[npan-1]-0.001 &&
+ lats_pan[npan-1] <= lat && lat <= lats_pan[0]) {
+ memmove(dsar_old,dsar,4*sizeof (double));
+ gsw_add_barrier(dsar_old,lon,lat,longs_ref[indx0],
+ lats_ref[indy0],dlong,dlat,dsar);
+ } else if (fabs(sum(dsar)) >= GSW_ERROR_LIMIT) {
+ memmove(dsar_old,dsar,4*sizeof (double));
+ gsw_add_mean(dsar_old,dsar);
+ }
+
+ sa_upper = (1.0-s1)*(dsar[0] + r1*(dsar[1]-dsar[0])) +
+ s1*(dsar[3] + r1*(dsar[2]-dsar[3]));
+
+ for (k=0; k<4; k++)
+ dsar[k] = delta_sa_ref[indz0+1+nz*(indy0+delj[k]+
+ (indx0+deli[k])*ny)];
+
+ if (longs_pan[0] <= lon && lon <= longs_pan[npan-1] &&
+ lats_pan[npan-1] <= lat && lat <= lats_pan[0]) {
+ memmove(dsar_old,dsar,4*sizeof (double));
+ gsw_add_barrier(dsar_old,lon,lat,longs_ref[indx0],
+ lats_ref[indy0],dlong,dlat,dsar);
+ } else if (fabs(sum(dsar)) >= GSW_ERROR_LIMIT) {
+ memmove(dsar_old,dsar,4*sizeof (double));
+ gsw_add_mean(dsar_old,dsar);
+ }
+
+ sa_lower = (1.0-s1)*(dsar[0] + r1*(dsar[1]-dsar[0])) +
+ s1*(dsar[3] + r1*(dsar[2]-dsar[3]));
+ if (fabs(sa_lower) >= GSW_ERROR_LIMIT)
+ sa_lower = sa_upper;
+ return_value = sa_upper + t1*(sa_lower-sa_upper);
+
+ if (fabs(return_value) >= GSW_ERROR_LIMIT)
+ return (GSW_INVALID_VALUE);
+
+ return (return_value);
+}
+/*
+** The End
+*/
diff --git a/src2/c_gsw/gsw_saar_data.c b/src2/c_gsw/gsw_saar_data.c
new file mode 100644
index 0000000..e073659
--- /dev/null
+++ b/src2/c_gsw/gsw_saar_data.c
@@ -0,0 +1,122859 @@
+/*
+** $Id$
+** Extracted from gsw_data_v3_0.nc
+*/
+static int gsw_nx = 91, gsw_ny = 45, gsw_nz = 45;
+static char *gsw_version_date = "15th_May_2011";
+static char *gsw_version_number = "3.05.6";
+
+void gsw_get_version(char **version_date, char **version_number)
+{
+ *version_date = gsw_version_date;
+ *version_number = gsw_version_number;
+}
+static double p_ref[45] = {
+0, 10, 20, 30, 40, 50, 76, 101, 126, 151, 176, 202, 252, 303, 353, 404, 505,
+606, 707, 808, 909, 1010, 1111, 1213, 1314, 1416, 1517, 1771, 2025, 2279, 2534,
+2789, 3045, 3300, 3556, 3812, 4069, 4325, 4583, 4840, 5098, 5355, 5614, 5872,
+6131
+};
+
+static double lats_ref[45] = {
+-86, -82, -78, -74, -70, -66, -62, -58, -54, -50, -46, -42, -38, -34, -30, -26,
+-22, -18, -14, -10, -6, -2, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50,
+54, 58, 62, 66, 70, 74, 78, 82, 86, 90
+};
+
+static double longs_ref[91] = {
+0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76,
+80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144,
+148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208,
+212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 260, 264, 268, 272,
+276, 280, 284, 288, 292, 296, 300, 304, 308, 312, 316, 320, 324, 328, 332, 336,
+340, 344, 348, 352, 356, 360
+};
+
+static double saar_ref[184275] = {
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
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+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
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+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
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+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
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+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
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+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
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+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
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+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+0.00014707758753855013, 0.00014484153206733623, 0.00013380245562909864,
+0.00013291662443260478, 0.00013332240587826324, 0.00013886558155402462,
+0.00014644997457083559, 0.00015627617122821526, 0.00016518743573043658,
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+0.00022029628455431306, 0.00022617579627871452, 0.00023229659533942956,
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+0.00025726647081191417, 0.00025925557935473867, 0.00026000492224336055,
+0.00026145519407443844, 0.00026271582634058673, 0.00026357545464873695,
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+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+0.00012868546702237676, 0.00011321740652559621, 0.00011878394475709721,
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+43, 42, 41, 40, 39, 39, 39, 39, 39, 39, 39, 39, 41, 41, 43, 43, 43, 42, 43, 43,
+44, 39, 39, 38, 36, 35, 2, 8.9999999999999998e+90, 33, 35, 36, 36, 34, 38,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 38, 39,
+40, 41, 39, 40, 41, 43, 42, 41, 40, 39, 38, 37, 39, 39, 39, 39, 39, 39, 40, 41,
+41, 43, 42, 41, 41, 42, 42, 39, 38, 37, 35, 33, 8.9999999999999998e+90,
+8.9999999999999998e+90, 31, 35, 36, 36, 34, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 35, 38, 40, 40, 39, 39, 41, 41,
+41, 41, 39, 38, 37, 37, 37, 38, 39, 39, 39, 39, 40, 41, 41, 42, 41, 40, 40, 41,
+41, 39, 36, 36, 32, 11, 8.9999999999999998e+90, 8.9999999999999998e+90, 28, 35,
+35, 36, 34, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 33, 38, 41, 41, 39, 39, 38, 40, 40, 40, 39, 37, 37, 37,
+37, 37, 39, 39, 39, 39, 40, 40, 40, 41, 40, 40, 39, 41, 40, 39, 33, 32, 13,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 16, 28,
+35, 36, 34, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 31, 38, 41, 42, 39, 38, 37, 39, 39, 39, 39, 36, 36, 36,
+36, 37, 39, 39, 39, 39, 39, 40, 40, 40, 40, 39, 38, 39, 39, 36, 33, 27,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 17, 17, 33, 35, 34, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 31, 38, 41, 41, 41, 36, 37, 37,
+40, 39, 38, 36, 35, 35, 35, 36, 38, 38, 38, 39, 38, 38, 39, 38, 38, 38, 38, 37,
+27, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 17, 17, 31, 35, 34, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 24, 39, 41, 41, 41, 35, 34, 36,
+37, 38, 37, 35, 35, 34, 35, 35, 38, 38, 38, 37, 38, 38, 38, 37, 37, 38, 38, 27,
+6, 8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 6, 15,
+17, 28, 35, 33, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 21, 38, 41, 41, 41, 37, 35, 33, 34, 34, 34, 33, 35, 37,
+35, 35, 36, 37, 37, 37, 38, 37, 38, 36, 36, 36, 20, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 10, 10, 16, 19, 32, 32, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 28, 38, 41, 41, 42, 38, 36, 35,
+35, 36, 35, 34, 36, 36, 37, 36, 36, 36, 36, 36, 37, 37, 38, 38, 37, 32,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 7, 7,
+15, 17, 31, 32, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 26, 39, 41, 42, 42, 39, 38, 38, 37, 37, 36, 35, 36, 37,
+37, 38, 39, 38, 35, 35, 36, 35, 35, 38, 30, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 6, 13,
+16, 16, 31, 32, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 12, 39, 40, 42, 41, 39, 39, 38, 39, 39, 36, 35, 36, 37,
+37, 37, 38, 38, 35, 35, 35, 37, 40, 40, 2, 2, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 6, 11, 13, 18, 29, 32, 38,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 17, 39,
+40, 42, 42, 42, 40, 38, 38, 37, 36, 36, 36, 37, 38, 37, 37, 37, 35, 35, 36, 39,
+44, 32, 34, 34, 7, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 7, 7, 2, 15, 15, 16, 28, 31, 38, 17, 17, 17, 18, 39,
+40, 41, 42, 42, 40, 38, 38, 36, 37, 36, 37, 38, 38, 38, 37, 37, 36, 34, 36, 37,
+42, 27, 36, 36, 17, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 9, 10, 8.9999999999999998e+90, 13, 16, 16, 27, 30, 38,
+17, 17, 17, 17, 37, 39, 41, 43, 42, 40, 39, 37, 37, 37, 36, 37, 38, 39, 39, 39,
+37, 35, 34, 35, 40, 40, 39, 38, 36, 32, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 6, 12, 12, 7, 10, 17, 16, 27, 31, 38, 17, 17, 17, 17,
+37, 39, 41, 42, 41, 39, 38, 38, 38, 37, 37, 37, 39, 39, 40, 39, 39, 38, 35, 36,
+36, 27, 41, 39, 34, 22, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8, 12,
+12, 14, 8, 19, 16, 27, 31, 38, 17, 17, 17, 17, 36, 39, 41, 42, 40, 38, 36, 38,
+38, 38, 37, 39, 39, 39, 41, 41, 39, 38, 36, 36, 35, 36, 45, 38, 28, 22, 17,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 2, 8,
+10, 13, 16, 6, 20, 15, 27, 31, 38, 17, 17, 17, 15, 36, 37, 40, 41, 38, 37, 36,
+38, 39, 40, 39, 39, 41, 41, 41, 26, 8.9999999999999998e+90,
+8.9999999999999998e+90, 28, 36, 35, 37, 43, 40, 42, 42, 40, 32, 6,
+8.9999999999999998e+90, 8.9999999999999998e+90, 7, 8, 15, 11, 8, 21, 17, 25,
+31, 38, 17, 17, 17, 2, 21, 36, 39, 39, 38, 7, 2, 15, 38, 41, 44, 45, 45, 45,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 30, 38,
+38, 42, 42, 42, 42, 38, 16, 2, 8.9999999999999998e+90, 8.9999999999999998e+90,
+2, 15, 8, 28, 28, 19, 19, 31, 38, 17, 17, 17, 2, 21, 34, 38, 38, 28, 9, 8,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 28, 41, 45, 45, 43, 42, 42, 41, 36, 12, 14,
+8.9999999999999998e+90, 13, 19, 21, 29, 30, 17, 17, 30, 38, 17, 17, 17, 17, 9,
+19, 38, 38, 39, 13, 9, 9, 2, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 36, 40,
+45, 45, 44, 42, 41, 41, 40, 12, 14, 8.9999999999999998e+90, 13, 19, 27, 30, 30,
+16, 19, 29, 38, 17, 17, 17, 18, 18, 18, 40, 39, 39, 31, 35, 31, 7, 2,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 8, 33,
+43, 45, 45, 45, 44, 42, 41, 41, 28, 16, 16, 32, 32, 27, 29, 29, 16, 19, 27, 38,
+17, 17, 17, 22, 23, 28, 40, 40, 40, 44, 45, 43, 38, 6, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 29, 40, 43, 44, 45, 45, 45, 42,
+42, 41, 34, 14, 33, 34, 34, 23, 18, 19, 8.9999999999999998e+90, 17, 29, 38, 16,
+16, 16, 28, 34, 35, 37, 41, 40, 45, 45, 44, 42, 38, 12, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 2, 4, 38, 41, 42, 43, 45, 45,
+44, 43, 42, 42, 32, 31, 35, 35, 34, 21, 17, 2, 8.9999999999999998e+90, 17, 31,
+38, 16, 16, 16, 28, 36, 39, 39, 40, 41, 45, 45, 44, 42, 40, 36, 30, 2,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 6, 35, 38, 41, 41, 40, 40, 40, 42, 43, 42, 42, 37, 37,
+37, 36, 33, 2, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 16, 33, 38, 19, 19, 19, 33, 37, 39, 41, 41, 39, 45, 45,
+41, 41, 41, 37, 34, 23, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 36, 38, 40, 41, 40, 41, 40, 40,
+39, 41, 41, 41, 40, 38, 37, 35, 24, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 16, 33,
+38, 24, 24, 24, 37, 38, 40, 40, 37, 36, 45, 45, 42, 41, 40, 39, 38, 35, 32, 34,
+8.9999999999999998e+90, 8.9999999999999998e+90, 38, 39, 40, 41, 43, 44, 44, 43,
+40, 37, 41, 41, 40, 39, 37, 35, 33, 18, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 16, 34, 38, 22, 22, 22, 36, 38,
+40, 40, 35, 38, 44, 44, 42, 41, 40, 38, 39, 40, 39, 39, 40, 37, 39, 39, 39, 44,
+45, 45, 44, 45, 41, 36, 39, 39, 39, 39, 35, 33, 33, 29, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 16, 35, 38, 21, 21, 21, 36, 39,
+40, 40, 39, 45, 42, 42, 42, 41, 39, 39, 42, 42, 40, 42, 42, 42, 40, 39, 40, 45,
+45, 43, 45, 45, 41, 37, 35, 37, 38, 38, 37, 32, 33, 31, 11,
+8.9999999999999998e+90, 8.9999999999999998e+90, 15, 35, 38, 16, 16, 16, 37, 39,
+40, 44, 45, 45, 41, 41, 40, 39, 39, 41, 43, 43, 43, 43, 43, 43, 43, 38, 40, 44,
+44, 41, 43, 44, 42, 41, 36, 33, 35, 36, 36, 34, 29, 29, 16, 2,
+8.9999999999999998e+90, 17, 36, 38, 7, 7, 7, 37, 40, 41, 45, 45, 45, 40, 41,
+40, 38, 40, 41, 43, 44, 43, 43, 45, 43, 44, 40, 40, 43, 42, 39, 42, 43, 42, 42,
+39, 38, 38, 38, 37, 34, 31, 26, 26, 16, 2, 28, 37, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 37, 40, 41, 41, 41, 41, 40, 39,
+38, 37, 37, 39, 42, 43, 43, 43, 45, 43, 44, 41, 40, 41, 40, 36, 39, 40, 41, 42,
+44, 43, 40, 40, 39, 33, 32, 22, 27, 23, 12, 35, 37, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 32, 40, 41, 41, 41, 41, 38, 37,
+35, 35, 36, 37, 39, 39, 39, 39, 39, 39, 40, 42, 40, 39, 34, 32, 31, 36, 39, 41,
+42, 42, 42, 40, 39, 31, 31, 26, 27, 30, 13, 37, 37, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 15, 40, 41, 42, 41, 39, 37, 37,
+39, 37, 37, 37, 37, 39, 37, 37, 36, 36, 40, 41, 40, 3, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 28, 37, 40, 42, 42, 41, 39, 32,
+31, 28, 28, 30, 33, 17, 37, 38, 38, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90, 40, 41,
+42, 41, 37, 37, 37, 39, 38, 38, 39, 41, 41, 41, 39, 40, 40, 41, 41, 36,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 21, 38, 38, 41, 41, 32, 29, 29,
+34, 34, 33, 35, 32, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 39, 41, 42, 41, 36, 37, 39, 40,
+41, 40, 40, 43, 43, 42, 43, 43, 43, 41, 41, 35, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 28, 28, 36, 40, 9, 8, 21, 34,
+35, 35, 35, 35, 36, 38, 38, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 39, 41, 42, 43, 38, 37, 40, 41,
+41, 41, 40, 43, 43, 43, 44, 43, 44, 41, 41, 39, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 8.9999999999999998e+90,
+8.9999999999999998e+90, 8.9999999999999998e+90, 30, 32, 28, 12, 6, 7, 10, 32,
+35, 35, 35, 35, 36, 38, 38
+};
+
diff --git a/src2/c_gsw/gswteos-10.h b/src2/c_gsw/gswteos-10.h
new file mode 100644
index 0000000..b6e8957
--- /dev/null
+++ b/src2/c_gsw/gswteos-10.h
@@ -0,0 +1,294 @@
+/*
+** $Id: gswteos-10.h,v 045882f2da27 2015/09/13 23:47:38 fdelahoyde $
+** $Version: 3.05.0-2 $
+**
+** GSW TEOS-10 V3.05 definitions and prototypes.
+*/
+#ifndef GSWTEOS_10_H
+#define GSWTEOS_10_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#include <complex.h>
+#include <errno.h>
+
+#define GSW_INVALID_VALUE 9e15 /* error return from gsw_saar et al. */
+#define GSW_ERROR_LIMIT 1e10
+
+/*
+** Prototypes:
+*/
+extern void gsw_add_barrier(double *input_data, double lon, double lat,
+ double long_grid, double lat_grid, double dlong_grid,
+ double dlat_grid, double *output_data);
+extern void gsw_add_mean(double *data_in, double *data_out);
+extern double gsw_adiabatic_lapse_rate_from_ct(double sa, double ct, double p);
+extern double gsw_adiabatic_lapse_rate_ice(double t, double p);
+extern double gsw_alpha(double sa, double ct, double p);
+extern double gsw_alpha_on_beta(double sa, double ct, double p);
+extern double gsw_alpha_wrt_t_exact(double sa, double t, double p);
+extern double gsw_alpha_wrt_t_ice(double t, double p);
+extern double gsw_beta_const_t_exact(double sa, double t, double p);
+extern double gsw_beta(double sa, double ct, double p);
+extern double gsw_cabbeling(double sa, double ct, double p);
+extern double gsw_c_from_sp(double sp, double t, double p);
+extern double gsw_chem_potential_water_ice(double t, double p);
+extern double gsw_chem_potential_water_t_exact(double sa, double t, double p);
+extern double gsw_cp_ice(double t, double p);
+extern double gsw_cp_t_exact(double sa, double t, double p);
+extern void gsw_ct_first_derivatives (double sa, double pt, double *ct_sa,
+ double *ct_pt);
+extern void gsw_ct_first_derivatives_wrt_t_exact(double sa, double t,
+ double p, double *ct_sa_wrt_t, double *ct_t_wrt_t,
+ double *ct_p_wrt_t);
+extern double gsw_ct_freezing(double sa, double p, double saturation_fraction);
+extern void gsw_ct_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa,
+ double *ctfreezing_p);
+extern void gsw_ct_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa,
+ double *ctfreezing_p);
+extern double gsw_ct_freezing_poly(double sa, double p,
+ double saturation_fraction);
+extern double gsw_ct_from_enthalpy(double sa, double h, double p);
+extern double gsw_ct_from_enthalpy_exact(double sa, double h, double p);
+extern double gsw_ct_from_entropy(double sa, double entropy);
+extern double gsw_ct_from_pt(double sa, double pt);
+extern void gsw_ct_from_rho(double rho, double sa, double p, double *ct,
+ double *ct_multiple);
+extern double gsw_ct_from_t(double sa, double t, double p);
+extern double gsw_ct_maxdensity(double sa, double p);
+extern void gsw_ct_second_derivatives(double sa, double pt, double *ct_sa_sa,
+ double *ct_sa_pt, double *ct_pt_pt);
+extern double gsw_deltasa_atlas(double p, double lon, double lat);
+extern double gsw_deltasa_from_sp(double sp, double p, double lon, double lat);
+extern double gsw_dilution_coefficient_t_exact(double sa, double t, double p);
+extern double gsw_dynamic_enthalpy(double sa, double ct, double p);
+extern double gsw_enthalpy_ct_exact(double sa, double ct, double p);
+extern double gsw_enthalpy_diff(double sa, double ct, double p_shallow,
+ double p_deep);
+extern double gsw_enthalpy(double sa, double ct, double p);
+extern void gsw_enthalpy_first_derivatives_ct_exact(double sa, double ct,
+ double p, double *h_sa, double *h_ct);
+extern void gsw_enthalpy_first_derivatives(double sa, double ct, double p,
+ double *h_sa, double *h_ct);
+extern double gsw_enthalpy_ice(double t, double p);
+extern void gsw_enthalpy_second_derivatives_ct_exact(double sa, double ct,
+ double p, double *h_sa_sa, double *h_sa_ct, double *h_ct_ct);
+extern void gsw_enthalpy_second_derivatives(double sa, double ct, double p,
+ double *h_sa_sa, double *h_sa_ct, double *h_ct_ct);
+extern double gsw_enthalpy_sso_0(double p);
+extern double gsw_enthalpy_t_exact(double sa, double t, double p);
+extern void gsw_entropy_first_derivatives(double sa, double ct,
+ double *eta_sa, double *eta_ct);
+extern double gsw_entropy_from_ct(double sa, double ct);
+extern double gsw_entropy_from_pt(double sa, double pt);
+extern double gsw_entropy_from_t(double sa, double t, double p);
+extern double gsw_entropy_ice(double t, double p);
+extern double gsw_entropy_part(double sa, double t, double p);
+extern double gsw_entropy_part_zerop(double sa, double pt0);
+extern void gsw_entropy_second_derivatives(double sa, double ct,
+ double *eta_sa_sa, double *eta_sa_ct, double *eta_ct_ct);
+extern double gsw_fdelta(double p, double lon, double lat);
+extern void gsw_frazil_properties(double sa_bulk, double h_bulk, double p,
+ double *sa_final, double *ct_final, double *w_ih_final);
+extern void gsw_frazil_properties_potential(double sa_bulk, double h_pot_bulk,
+ double p, double *sa_final, double *ct_final,
+ double *w_ih_final);
+extern void gsw_frazil_properties_potential_poly(double sa_bulk,
+ double h_pot_bulk, double p, double *sa_final, double *ct_final,
+ double *w_ih_final);
+extern void gsw_frazil_ratios_adiabatic(double sa, double p, double w_ih,
+ double *dsa_dct_frazil, double *dsa_dp_frazil,
+ double *dct_dp_frazil);
+extern void gsw_frazil_ratios_adiabatic_poly(double sa, double p,
+ double w_ih, double *dsa_dct_frazil, double *dsa_dp_frazil,
+ double *dct_dp_frazil);
+extern double *gsw_geo_strf_dyn_height(double *sa, double *ct, double *p,
+ double p_ref, int n_levels, double *dyn_height);
+extern double *gsw_geo_strf_dyn_height_pc(double *sa, double *ct,
+ double *delta_p, int n_levels, double *geo_strf_dyn_height_pc,
+ double *p_mid);
+extern double gsw_gibbs_ice (int nt, int np, double t, double p);
+extern double gsw_gibbs_ice_part_t(double t, double p);
+extern double gsw_gibbs_ice_pt0(double pt0);
+extern double gsw_gibbs_ice_pt0_pt0(double pt0);
+extern double gsw_gibbs(int ns, int nt, int np, double sa, double t, double p);
+extern double gsw_gibbs_pt0_pt0(double sa, double pt0);
+extern double gsw_grav(double lat, double p);
+extern double gsw_helmholtz_energy_ice(double t, double p);
+extern double gsw_hill_ratio_at_sp2(double t);
+extern void gsw_ice_fraction_to_freeze_seawater(double sa, double ct,
+ double p, double t_ih, double *sa_freeze, double *ct_freeze,
+ double *w_ih);
+extern double gsw_internal_energy(double sa, double ct, double p);
+extern double gsw_internal_energy_ice(double t, double p);
+extern void gsw_ipv_vs_fnsquared_ratio(double *sa, double *ct, double *p,
+ double p_ref, int nz, double *ipv_vs_fnsquared_ratio,
+ double *p_mid);
+extern double gsw_kappa_const_t_ice(double t, double p);
+extern double gsw_kappa(double sa, double ct, double p);
+extern double gsw_kappa_ice(double t, double p);
+extern double gsw_kappa_t_exact(double sa, double t, double p);
+extern double gsw_latentheat_evap_ct(double sa, double ct);
+extern double gsw_latentheat_evap_t(double sa, double t);
+extern double gsw_latentheat_melting(double sa, double p);
+extern void gsw_linear_interp_sa_ct(double *sa, double *ct, double *p, int np,
+ double *p_i, int npi, double *sa_i, double *ct_i);
+extern double gsw_melting_ice_equilibrium_sa_ct_ratio(double sa, double p);
+extern double gsw_melting_ice_equilibrium_sa_ct_ratio_poly(double sa, double p);
+extern void gsw_melting_ice_into_seawater(double sa, double ct, double p,
+ double w_ih, double t_ih, double *sa_final, double *ct_final,
+ double *w_ih_final);
+extern double gsw_melting_ice_sa_ct_ratio(double sa, double ct, double p,
+ double t_ih);
+extern double gsw_melting_ice_sa_ct_ratio_poly(double sa, double ct, double p,
+ double t_ih);
+extern double gsw_melting_seaice_equilibrium_sa_ct_ratio(double sa, double p);
+extern double gsw_melting_seaice_equilibrium_sa_ct_ratio_poly(double sa,
+ double p);
+extern void gsw_melting_seaice_into_seawater(double sa, double ct, double p,
+ double w_seaice, double sa_seaice, double t_seaice,
+ double *sa_final, double *ct_final);
+extern double gsw_melting_seaice_sa_ct_ratio(double sa, double ct, double p,
+ double sa_seaice, double t_seaice);
+extern double gsw_melting_seaice_sa_ct_ratio_poly(double sa, double ct,
+ double p, double sa_seaice, double t_seaice);
+extern void gsw_nsquared(double *sa, double *ct, double *p, double *lat,
+ int nz, double *n2, double *p_mid);
+extern double gsw_pot_enthalpy_from_pt_ice(double pt0_ice);
+extern double gsw_pot_enthalpy_from_pt_ice_poly(double pt0_ice);
+extern double gsw_pot_enthalpy_ice_freezing(double sa, double p);
+extern void gsw_pot_enthalpy_ice_freezing_first_derivatives(double sa,
+ double p, double *pot_enthalpy_ice_freezing_sa,
+ double *pot_enthalpy_ice_freezing_p);
+extern void gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(double sa,
+ double p, double *pot_enthalpy_ice_freezing_sa,
+ double *pot_enthalpy_ice_freezing_p);
+extern double gsw_pot_enthalpy_ice_freezing_poly(double sa, double p);
+extern double gsw_pot_rho_t_exact(double sa, double t, double p, double p_ref);
+extern double gsw_pressure_coefficient_ice(double t, double p);
+extern double gsw_pressure_freezing_ct(double sa, double ct,
+ double saturation_fraction);
+extern double gsw_pt0_cold_ice_poly(double pot_enthalpy_ice);
+extern double gsw_pt0_from_t(double sa, double t, double p);
+extern double gsw_pt0_from_t_ice(double t, double p);
+extern void gsw_pt_first_derivatives (double sa, double ct, double *pt_sa,
+ double *pt_ct);
+extern double gsw_pt_from_ct(double sa, double ct);
+extern double gsw_pt_from_entropy(double sa, double entropy);
+extern double gsw_pt_from_pot_enthalpy_ice(double pot_enthalpy_ice);
+extern double gsw_pt_from_pot_enthalpy_ice_poly_dh(double pot_enthalpy_ice);
+extern double gsw_pt_from_pot_enthalpy_ice_poly(double pot_enthalpy_ice);
+extern double gsw_pt_from_t(double sa, double t, double p, double p_ref);
+extern double gsw_pt_from_t_ice(double t, double p, double p_ref);
+extern void gsw_pt_second_derivatives (double sa, double ct, double *pt_sa_sa,
+ double *pt_sa_ct, double *pt_ct_ct);
+extern void gsw_rho_alpha_beta (double sa, double ct, double p, double *rho,
+ double *alpha, double *beta);
+extern double gsw_rho(double sa, double ct, double p);
+extern void gsw_rho_first_derivatives(double sa, double ct, double p,
+ double *drho_dsa, double *drho_dct, double *drho_dp);
+extern void gsw_rho_first_derivatives_wrt_enthalpy (double sa, double ct,
+ double p, double *rho_sa, double *rho_h);
+extern double gsw_rho_ice(double t, double p);
+extern void gsw_rho_second_derivatives(double sa, double ct, double p,
+ double *rho_sa_sa, double *rho_sa_ct, double *rho_ct_ct,
+ double *rho_sa_p, double *rho_ct_p);
+extern void gsw_rho_second_derivatives_wrt_enthalpy(double sa, double ct,
+ double p, double *rho_sa_sa, double *rho_sa_h, double *rho_h_h);
+extern double gsw_rho_t_exact(double sa, double t, double p);
+extern void gsw_rr68_interp_sa_ct(double *sa, double *ct, double *p, int mp,
+ double *p_i, int mp_i, double *sa_i, double *ct_i);
+extern double gsw_saar(double p, double lon, double lat);
+extern double gsw_sa_freezing_estimate(double p, double saturation_fraction,
+ double *ct, double *t);
+extern double gsw_sa_freezing_from_ct(double ct, double p,
+ double saturation_fraction);
+extern double gsw_sa_freezing_from_ct_poly(double ct, double p,
+ double saturation_fraction);
+extern double gsw_sa_freezing_from_t(double t, double p,
+ double saturation_fraction);
+extern double gsw_sa_freezing_from_t_poly(double t, double p,
+ double saturation_fraction);
+extern double gsw_sa_from_rho(double rho, double ct, double p);
+extern double gsw_sa_from_sp_baltic(double sp, double lon, double lat);
+extern double gsw_sa_from_sp(double sp, double p, double lon, double lat);
+extern double gsw_sa_from_sstar(double sstar, double p,double lon,double lat);
+extern int gsw_sa_p_inrange(double sa, double p);
+extern void gsw_seaice_fraction_to_freeze_seawater(double sa, double ct,
+ double p, double sa_seaice, double t_seaice, double *sa_freeze,
+ double *ct_freeze, double *w_seaice);
+extern double gsw_sigma0(double sa, double ct);
+extern double gsw_sigma1(double sa, double ct);
+extern double gsw_sigma2(double sa, double ct);
+extern double gsw_sigma3(double sa, double ct);
+extern double gsw_sigma4(double sa, double ct);
+extern double gsw_sound_speed(double sa, double ct, double p);
+extern double gsw_sound_speed_ice(double t, double p);
+extern double gsw_sound_speed_t_exact(double sa, double t, double p);
+extern void gsw_specvol_alpha_beta(double sa, double ct, double p,
+ double *specvol, double *alpha, double *beta);
+extern double gsw_specvol_anom_standard(double sa, double ct, double p);
+extern double gsw_specvol(double sa, double ct, double p);
+extern void gsw_specvol_first_derivatives(double sa, double ct, double p,
+ double *v_sa, double *v_ct, double *v_p);
+extern void gsw_specvol_first_derivatives_wrt_enthalpy(double sa, double ct,
+ double p, double *v_sa, double *v_h);
+extern double gsw_specvol_ice(double t, double p);
+extern void gsw_specvol_second_derivatives (double sa, double ct, double p,
+ double *v_sa_sa, double *v_sa_ct, double *v_ct_ct,
+ double *v_sa_p, double *v_ct_p);
+extern void gsw_specvol_second_derivatives_wrt_enthalpy(double sa, double ct,
+ double p, double *v_sa_sa, double *v_sa_h, double *v_h_h);
+extern double gsw_specvol_sso_0(double p);
+extern double gsw_specvol_t_exact(double sa, double t, double p);
+extern double gsw_sp_from_c(double c, double t, double p);
+extern double gsw_sp_from_sa_baltic(double sa, double lon, double lat);
+extern double gsw_sp_from_sa(double sa, double p, double lon, double lat);
+extern double gsw_sp_from_sk(double sk);
+extern double gsw_sp_from_sr(double sr);
+extern double gsw_sp_from_sstar(double sstar, double p,double lon,double lat);
+extern double gsw_spiciness0(double sa, double ct);
+extern double gsw_spiciness1(double sa, double ct);
+extern double gsw_spiciness2(double sa, double ct);
+extern double gsw_sr_from_sp(double sp);
+extern double gsw_sstar_from_sa(double sa, double p, double lon, double lat);
+extern double gsw_sstar_from_sp(double sp, double p, double lon, double lat);
+extern double gsw_t_deriv_chem_potential_water_t_exact(double sa, double t,
+ double p);
+extern double gsw_t_freezing(double sa, double p, double saturation_fraction);
+extern void gsw_t_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa,
+ double *tfreezing_p);
+extern void gsw_t_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa,
+ double *tfreezing_p);
+extern double gsw_t_freezing_poly(double sa, double p,
+ double saturation_fraction);
+extern double gsw_t_from_ct(double sa, double ct, double p);
+extern double gsw_t_from_pt0_ice(double pt0_ice, double p);
+extern double gsw_thermobaric(double sa, double ct, double p);
+extern void gsw_turner_rsubrho(double *sa, double *ct, double *p, int nz,
+ double *tu, double *rsubrho, double *p_mid);
+extern int gsw_util_indx(double *x, int n, double z);
+extern double *gsw_util_interp1q_int(int nx, double *x, int *iy, int nxi,
+ double *x_i, double *y_i);
+extern double *gsw_util_linear_interp(int nx, double *x, int ny, double *y,
+ int nxi, double *x_i, double *y_i);
+extern void gsw_util_sort_real(double *rarray, int nx, int *iarray);
+extern double gsw_util_xinterp1(double *x, double *y, int n, double x0);
+extern double gsw_z_from_p(double p, double lat);
+extern double gsw_p_from_z(double z, double lat);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* GSWTEOS_10_H */
diff --git a/src2/c_gsw/gswteos-10_cpp.h b/src2/c_gsw/gswteos-10_cpp.h
new file mode 100644
index 0000000..c39c8d4
--- /dev/null
+++ b/src2/c_gsw/gswteos-10_cpp.h
@@ -0,0 +1,294 @@
+/*
+** $Id: gswteos-10.h,v 045882f2da27 2015/09/13 23:47:38 fdelahoyde $
+** $Version: 3.05.0-2 $
+**
+** GSW TEOS-10 V3.05 definitions and prototypes.
+*/
+#ifndef GSWTEOS_10_H
+#define GSWTEOS_10_H
+
+#ifdef __cplusplus
+#include <complex>
+extern "C" {
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#include <errno.h>
+
+#define GSW_INVALID_VALUE 9e15 /* error return from gsw_saar et al. */
+#define GSW_ERROR_LIMIT 1e10
+
+/*
+** Prototypes:
+*/
+extern void gsw_add_barrier(double *input_data, double lon, double lat,
+ double long_grid, double lat_grid, double dlong_grid,
+ double dlat_grid, double *output_data);
+extern void gsw_add_mean(double *data_in, double *data_out);
+extern double gsw_adiabatic_lapse_rate_from_ct(double sa, double ct, double p);
+extern double gsw_adiabatic_lapse_rate_ice(double t, double p);
+extern double gsw_alpha(double sa, double ct, double p);
+extern double gsw_alpha_on_beta(double sa, double ct, double p);
+extern double gsw_alpha_wrt_t_exact(double sa, double t, double p);
+extern double gsw_alpha_wrt_t_ice(double t, double p);
+extern double gsw_beta_const_t_exact(double sa, double t, double p);
+extern double gsw_beta(double sa, double ct, double p);
+extern double gsw_cabbeling(double sa, double ct, double p);
+extern double gsw_c_from_sp(double sp, double t, double p);
+extern double gsw_chem_potential_water_ice(double t, double p);
+extern double gsw_chem_potential_water_t_exact(double sa, double t, double p);
+extern double gsw_cp_ice(double t, double p);
+extern double gsw_cp_t_exact(double sa, double t, double p);
+extern void gsw_ct_first_derivatives (double sa, double pt, double *ct_sa,
+ double *ct_pt);
+extern void gsw_ct_first_derivatives_wrt_t_exact(double sa, double t,
+ double p, double *ct_sa_wrt_t, double *ct_t_wrt_t,
+ double *ct_p_wrt_t);
+extern double gsw_ct_freezing(double sa, double p, double saturation_fraction);
+extern void gsw_ct_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa,
+ double *ctfreezing_p);
+extern void gsw_ct_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *ctfreezing_sa,
+ double *ctfreezing_p);
+extern double gsw_ct_freezing_poly(double sa, double p,
+ double saturation_fraction);
+extern double gsw_ct_from_enthalpy(double sa, double h, double p);
+extern double gsw_ct_from_enthalpy_exact(double sa, double h, double p);
+extern double gsw_ct_from_entropy(double sa, double entropy);
+extern double gsw_ct_from_pt(double sa, double pt);
+extern void gsw_ct_from_rho(double rho, double sa, double p, double *ct,
+ double *ct_multiple);
+extern double gsw_ct_from_t(double sa, double t, double p);
+extern double gsw_ct_maxdensity(double sa, double p);
+extern void gsw_ct_second_derivatives(double sa, double pt, double *ct_sa_sa,
+ double *ct_sa_pt, double *ct_pt_pt);
+extern double gsw_deltasa_atlas(double p, double lon, double lat);
+extern double gsw_deltasa_from_sp(double sp, double p, double lon, double lat);
+extern double gsw_dilution_coefficient_t_exact(double sa, double t, double p);
+extern double gsw_dynamic_enthalpy(double sa, double ct, double p);
+extern double gsw_enthalpy_ct_exact(double sa, double ct, double p);
+extern double gsw_enthalpy_diff(double sa, double ct, double p_shallow,
+ double p_deep);
+extern double gsw_enthalpy(double sa, double ct, double p);
+extern void gsw_enthalpy_first_derivatives_ct_exact(double sa, double ct,
+ double p, double *h_sa, double *h_ct);
+extern void gsw_enthalpy_first_derivatives(double sa, double ct, double p,
+ double *h_sa, double *h_ct);
+extern double gsw_enthalpy_ice(double t, double p);
+extern void gsw_enthalpy_second_derivatives_ct_exact(double sa, double ct,
+ double p, double *h_sa_sa, double *h_sa_ct, double *h_ct_ct);
+extern void gsw_enthalpy_second_derivatives(double sa, double ct, double p,
+ double *h_sa_sa, double *h_sa_ct, double *h_ct_ct);
+extern double gsw_enthalpy_sso_0(double p);
+extern double gsw_enthalpy_t_exact(double sa, double t, double p);
+extern void gsw_entropy_first_derivatives(double sa, double ct,
+ double *eta_sa, double *eta_ct);
+extern double gsw_entropy_from_ct(double sa, double ct);
+extern double gsw_entropy_from_pt(double sa, double pt);
+extern double gsw_entropy_from_t(double sa, double t, double p);
+extern double gsw_entropy_ice(double t, double p);
+extern double gsw_entropy_part(double sa, double t, double p);
+extern double gsw_entropy_part_zerop(double sa, double pt0);
+extern void gsw_entropy_second_derivatives(double sa, double ct,
+ double *eta_sa_sa, double *eta_sa_ct, double *eta_ct_ct);
+extern double gsw_fdelta(double p, double lon, double lat);
+extern void gsw_frazil_properties(double sa_bulk, double h_bulk, double p,
+ double *sa_final, double *ct_final, double *w_ih_final);
+extern void gsw_frazil_properties_potential(double sa_bulk, double h_pot_bulk,
+ double p, double *sa_final, double *ct_final,
+ double *w_ih_final);
+extern void gsw_frazil_properties_potential_poly(double sa_bulk,
+ double h_pot_bulk, double p, double *sa_final, double *ct_final,
+ double *w_ih_final);
+extern void gsw_frazil_ratios_adiabatic(double sa, double p, double w_ih,
+ double *dsa_dct_frazil, double *dsa_dp_frazil,
+ double *dct_dp_frazil);
+extern void gsw_frazil_ratios_adiabatic_poly(double sa, double p,
+ double w_ih, double *dsa_dct_frazil, double *dsa_dp_frazil,
+ double *dct_dp_frazil);
+extern double *gsw_geo_strf_dyn_height(double *sa, double *ct, double *p,
+ double p_ref, int n_levels, double *dyn_height);
+extern double *gsw_geo_strf_dyn_height_pc(double *sa, double *ct,
+ double *delta_p, int n_levels, double *geo_strf_dyn_height_pc,
+ double *p_mid);
+extern double gsw_gibbs_ice (int nt, int np, double t, double p);
+extern double gsw_gibbs_ice_part_t(double t, double p);
+extern double gsw_gibbs_ice_pt0(double pt0);
+extern double gsw_gibbs_ice_pt0_pt0(double pt0);
+extern double gsw_gibbs(int ns, int nt, int np, double sa, double t, double p);
+extern double gsw_gibbs_pt0_pt0(double sa, double pt0);
+extern double gsw_grav(double lat, double p);
+extern double gsw_helmholtz_energy_ice(double t, double p);
+extern double gsw_hill_ratio_at_sp2(double t);
+extern void gsw_ice_fraction_to_freeze_seawater(double sa, double ct,
+ double p, double t_ih, double *sa_freeze, double *ct_freeze,
+ double *w_ih);
+extern double gsw_internal_energy(double sa, double ct, double p);
+extern double gsw_internal_energy_ice(double t, double p);
+extern void gsw_ipv_vs_fnsquared_ratio(double *sa, double *ct, double *p,
+ double p_ref, int nz, double *ipv_vs_fnsquared_ratio,
+ double *p_mid);
+extern double gsw_kappa_const_t_ice(double t, double p);
+extern double gsw_kappa(double sa, double ct, double p);
+extern double gsw_kappa_ice(double t, double p);
+extern double gsw_kappa_t_exact(double sa, double t, double p);
+extern double gsw_latentheat_evap_ct(double sa, double ct);
+extern double gsw_latentheat_evap_t(double sa, double t);
+extern double gsw_latentheat_melting(double sa, double p);
+extern void gsw_linear_interp_sa_ct(double *sa, double *ct, double *p, int np,
+ double *p_i, int npi, double *sa_i, double *ct_i);
+extern double gsw_melting_ice_equilibrium_sa_ct_ratio(double sa, double p);
+extern double gsw_melting_ice_equilibrium_sa_ct_ratio_poly(double sa, double p);
+extern void gsw_melting_ice_into_seawater(double sa, double ct, double p,
+ double w_ih, double t_ih, double *sa_final, double *ct_final,
+ double *w_ih_final);
+extern double gsw_melting_ice_sa_ct_ratio(double sa, double ct, double p,
+ double t_ih);
+extern double gsw_melting_ice_sa_ct_ratio_poly(double sa, double ct, double p,
+ double t_ih);
+extern double gsw_melting_seaice_equilibrium_sa_ct_ratio(double sa, double p);
+extern double gsw_melting_seaice_equilibrium_sa_ct_ratio_poly(double sa,
+ double p);
+extern void gsw_melting_seaice_into_seawater(double sa, double ct, double p,
+ double w_seaice, double sa_seaice, double t_seaice,
+ double *sa_final, double *ct_final);
+extern double gsw_melting_seaice_sa_ct_ratio(double sa, double ct, double p,
+ double sa_seaice, double t_seaice);
+extern double gsw_melting_seaice_sa_ct_ratio_poly(double sa, double ct,
+ double p, double sa_seaice, double t_seaice);
+extern void gsw_nsquared(double *sa, double *ct, double *p, double *lat,
+ int nz, double *n2, double *p_mid);
+extern double gsw_pot_enthalpy_from_pt_ice(double pt0_ice);
+extern double gsw_pot_enthalpy_from_pt_ice_poly(double pt0_ice);
+extern double gsw_pot_enthalpy_ice_freezing(double sa, double p);
+extern void gsw_pot_enthalpy_ice_freezing_first_derivatives(double sa,
+ double p, double *pot_enthalpy_ice_freezing_sa,
+ double *pot_enthalpy_ice_freezing_p);
+extern void gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(double sa,
+ double p, double *pot_enthalpy_ice_freezing_sa,
+ double *pot_enthalpy_ice_freezing_p);
+extern double gsw_pot_enthalpy_ice_freezing_poly(double sa, double p);
+extern double gsw_pot_rho_t_exact(double sa, double t, double p, double p_ref);
+extern double gsw_pressure_coefficient_ice(double t, double p);
+extern double gsw_pressure_freezing_ct(double sa, double ct,
+ double saturation_fraction);
+extern double gsw_pt0_cold_ice_poly(double pot_enthalpy_ice);
+extern double gsw_pt0_from_t(double sa, double t, double p);
+extern double gsw_pt0_from_t_ice(double t, double p);
+extern void gsw_pt_first_derivatives (double sa, double ct, double *pt_sa,
+ double *pt_ct);
+extern double gsw_pt_from_ct(double sa, double ct);
+extern double gsw_pt_from_entropy(double sa, double entropy);
+extern double gsw_pt_from_pot_enthalpy_ice(double pot_enthalpy_ice);
+extern double gsw_pt_from_pot_enthalpy_ice_poly_dh(double pot_enthalpy_ice);
+extern double gsw_pt_from_pot_enthalpy_ice_poly(double pot_enthalpy_ice);
+extern double gsw_pt_from_t(double sa, double t, double p, double p_ref);
+extern double gsw_pt_from_t_ice(double t, double p, double p_ref);
+extern void gsw_pt_second_derivatives (double sa, double ct, double *pt_sa_sa,
+ double *pt_sa_ct, double *pt_ct_ct);
+extern void gsw_rho_alpha_beta (double sa, double ct, double p, double *rho,
+ double *alpha, double *beta);
+extern double gsw_rho(double sa, double ct, double p);
+extern void gsw_rho_first_derivatives(double sa, double ct, double p,
+ double *drho_dsa, double *drho_dct, double *drho_dp);
+extern void gsw_rho_first_derivatives_wrt_enthalpy (double sa, double ct,
+ double p, double *rho_sa, double *rho_h);
+extern double gsw_rho_ice(double t, double p);
+extern void gsw_rho_second_derivatives(double sa, double ct, double p,
+ double *rho_sa_sa, double *rho_sa_ct, double *rho_ct_ct,
+ double *rho_sa_p, double *rho_ct_p);
+extern void gsw_rho_second_derivatives_wrt_enthalpy(double sa, double ct,
+ double p, double *rho_sa_sa, double *rho_sa_h, double *rho_h_h);
+extern double gsw_rho_t_exact(double sa, double t, double p);
+extern void gsw_rr68_interp_sa_ct(double *sa, double *ct, double *p, int mp,
+ double *p_i, int mp_i, double *sa_i, double *ct_i);
+extern double gsw_saar(double p, double lon, double lat);
+extern double gsw_sa_freezing_estimate(double p, double saturation_fraction,
+ double *ct, double *t);
+extern double gsw_sa_freezing_from_ct(double ct, double p,
+ double saturation_fraction);
+extern double gsw_sa_freezing_from_ct_poly(double ct, double p,
+ double saturation_fraction);
+extern double gsw_sa_freezing_from_t(double t, double p,
+ double saturation_fraction);
+extern double gsw_sa_freezing_from_t_poly(double t, double p,
+ double saturation_fraction);
+extern double gsw_sa_from_rho(double rho, double ct, double p);
+extern double gsw_sa_from_sp_baltic(double sp, double lon, double lat);
+extern double gsw_sa_from_sp(double sp, double p, double lon, double lat);
+extern double gsw_sa_from_sstar(double sstar, double p,double lon,double lat);
+extern int gsw_sa_p_inrange(double sa, double p);
+extern void gsw_seaice_fraction_to_freeze_seawater(double sa, double ct,
+ double p, double sa_seaice, double t_seaice, double *sa_freeze,
+ double *ct_freeze, double *w_seaice);
+extern double gsw_sigma0(double sa, double ct);
+extern double gsw_sigma1(double sa, double ct);
+extern double gsw_sigma2(double sa, double ct);
+extern double gsw_sigma3(double sa, double ct);
+extern double gsw_sigma4(double sa, double ct);
+extern double gsw_sound_speed(double sa, double ct, double p);
+extern double gsw_sound_speed_ice(double t, double p);
+extern double gsw_sound_speed_t_exact(double sa, double t, double p);
+extern void gsw_specvol_alpha_beta(double sa, double ct, double p,
+ double *specvol, double *alpha, double *beta);
+extern double gsw_specvol_anom_standard(double sa, double ct, double p);
+extern double gsw_specvol(double sa, double ct, double p);
+extern void gsw_specvol_first_derivatives(double sa, double ct, double p,
+ double *v_sa, double *v_ct, double *v_p);
+extern void gsw_specvol_first_derivatives_wrt_enthalpy(double sa, double ct,
+ double p, double *v_sa, double *v_h);
+extern double gsw_specvol_ice(double t, double p);
+extern void gsw_specvol_second_derivatives (double sa, double ct, double p,
+ double *v_sa_sa, double *v_sa_ct, double *v_ct_ct,
+ double *v_sa_p, double *v_ct_p);
+extern void gsw_specvol_second_derivatives_wrt_enthalpy(double sa, double ct,
+ double p, double *v_sa_sa, double *v_sa_h, double *v_h_h);
+extern double gsw_specvol_sso_0(double p);
+extern double gsw_specvol_t_exact(double sa, double t, double p);
+extern double gsw_sp_from_c(double c, double t, double p);
+extern double gsw_sp_from_sa_baltic(double sa, double lon, double lat);
+extern double gsw_sp_from_sa(double sa, double p, double lon, double lat);
+extern double gsw_sp_from_sk(double sk);
+extern double gsw_sp_from_sr(double sr);
+extern double gsw_sp_from_sstar(double sstar, double p,double lon,double lat);
+extern double gsw_spiciness0(double sa, double ct);
+extern double gsw_spiciness1(double sa, double ct);
+extern double gsw_spiciness2(double sa, double ct);
+extern double gsw_sr_from_sp(double sp);
+extern double gsw_sstar_from_sa(double sa, double p, double lon, double lat);
+extern double gsw_sstar_from_sp(double sp, double p, double lon, double lat);
+extern double gsw_t_deriv_chem_potential_water_t_exact(double sa, double t,
+ double p);
+extern double gsw_t_freezing(double sa, double p, double saturation_fraction);
+extern void gsw_t_freezing_first_derivatives_poly(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa,
+ double *tfreezing_p);
+extern void gsw_t_freezing_first_derivatives(double sa, double p,
+ double saturation_fraction, double *tfreezing_sa,
+ double *tfreezing_p);
+extern double gsw_t_freezing_poly(double sa, double p,
+ double saturation_fraction);
+extern double gsw_t_from_ct(double sa, double ct, double p);
+extern double gsw_t_from_pt0_ice(double pt0_ice, double p);
+extern double gsw_thermobaric(double sa, double ct, double p);
+extern void gsw_turner_rsubrho(double *sa, double *ct, double *p, int nz,
+ double *tu, double *rsubrho, double *p_mid);
+extern int gsw_util_indx(double *x, int n, double z);
+extern double *gsw_util_interp1q_int(int nx, double *x, int *iy, int nxi,
+ double *x_i, double *y_i);
+extern double *gsw_util_linear_interp(int nx, double *x, int ny, double *y,
+ int nxi, double *x_i, double *y_i);
+extern void gsw_util_sort_real(double *rarray, int nx, int *iarray);
+extern double gsw_util_xinterp1(double *x, double *y, int n, double x0);
+extern double gsw_z_from_p(double p, double lat);
+extern double gsw_p_from_z(double z, double lat);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* GSWTEOS_10_H */
diff --git a/src2/method_bodies.c b/src2/method_bodies.c
new file mode 100644
index 0000000..1dac9fb
--- /dev/null
+++ b/src2/method_bodies.c
@@ -0,0 +1,69 @@
+/* Custom wrappers for GSW functions that are not suitable for ufuncs.
+*/
+
+
+/*
+double * Returns NULL on error, dyn_height if okay
+gsw_geo_strf_dyn_height(double *sa, double *ct, double *p, double p_ref,
+ int n_levels, double *dyn_height)
+*/
+
+static PyObject *
+geo_strf_dyn_height(PyObject *NPY_UNUSED(self), PyObject *args)
+{
+ PyObject *sa_o, *ct_o, *p_o, *dh_o;
+ double p_ref;
+ PyArrayObject *sa_a, *ct_a, *p_a, *dh_a;
+ int n_levels;
+ double *ret = NULL; /* NULL on error, dyn_height if OK */
+
+ if (!PyArg_ParseTuple(args, "OOOd", &sa_o, &ct_o, &p_o, &p_ref))
+ return NULL;
+
+ sa_a = (PyArrayObject *)PyArray_ContiguousFromAny(sa_o, NPY_DOUBLE, 1, 1);
+ if (sa_a == NULL)
+ goto error;
+ ct_a = (PyArrayObject *)PyArray_ContiguousFromAny(ct_o, NPY_DOUBLE, 1, 1);
+ if (ct_a == NULL)
+ goto error;
+ p_a = (PyArrayObject *)PyArray_ContiguousFromAny(p_o, NPY_DOUBLE, 1, 1);
+ if (p_a == NULL)
+ goto error;
+
+ n_levels = PyArray_DIM(sa_a, 0);
+ if (PyArray_DIM(ct_a, 0) != n_levels || PyArray_DIM(p_a, 0) != n_levels)
+ {
+ PyErr_SetString(PyExc_ValueError,
+ "Arguments SA, CT, and p must have the same dimensions.");
+ goto error;
+ }
+
+ dh_a = PyArray_NewLikeArray(sa_a, NPY_CORDER, NULL, 0);
+ if (dh_a == NULL)
+ goto error;
+
+ ret = gsw_geo_strf_dyn_height((double *)PyArray_DATA(sa_a),
+ (double *)PyArray_DATA(ct_a),
+ (double *)PyArray_DATA(p_a),
+ p_ref,
+ n_levels,
+ (double *)PyArray_DATA(dh_a));
+
+ if (ret == NULL)
+ {
+ PyErr_SetString(PyExc_RuntimeError,
+ "gws_geo_strf_dyn_height failed; check input arguments");
+ Py_XDECREF(dh_a);
+ goto error;
+ }
+
+ error:
+ Py_XDECREF(sa_a);
+ Py_XDECREF(ct_a);
+ Py_XDECREF(p_a);
+
+ if (ret == NULL)
+ return NULL;
+
+ return (PyObject *)dh_a;
+}
diff --git a/src2/method_def_entries.c b/src2/method_def_entries.c
new file mode 100644
index 0000000..5bfa770
--- /dev/null
+++ b/src2/method_def_entries.c
@@ -0,0 +1,3 @@
+/* Entries in the GswMethods table. */
+{"geo_strf_dyn_height", geo_strf_dyn_height, METH_VARARGS,
+ "geostrophic streamfunction dynamic height"},
--
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