gsw_t_freezing_first_derivatives

```first derivatives of in-situ temperature
at which seawater freezes```

USAGE:

`[tfreezing_SA, tfreezing_P] = gsw_t_freezing_first_derivatives(SA,p,saturation_fraction)`

DESCRIPTION:

```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.```

INPUT:

```SA  =  Absolute Salinity                                        [ g/kg ]
p  =  sea pressure                                              [ dbar ]
( i.e. absolute pressure - 10.1325 dbar )

OPTIONAL:
saturation_fraction = the saturation fraction of dissolved air in
seawater
(i.e., saturation_fraction must be between 0 and 1, and the default
is is 0, air free) ```
```p & saturation_fraction (if provided) may have dimensions 1x1 or Mx1 or
1xN or MxN, where SA is MxN.```

OUTPUT:

```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 ]```

EXAMPLE:

```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
p =  [     10;      50;     125;     250;     600;    1000;]
saturation_fraction = [1; 0.8; 0.6; 0.5; 0.4; 0;]```
`[tfreezing_SA, tfreezing_P] = gsw_t_freezing_first_derivatives(SA,p,saturation_fraction)`
`tfreezing_SA =`
```  -0.056811800705787
-0.056856999671114
-0.056903079789292
-0.056904020028541
-0.056974588411844
-0.057082363270642```
`tfreezing_P =`
`   1.0e-007 *`
```  -0.748468312442338
-0.749793159537290
-0.752225023995510
-0.756170965034610
-0.767279572670040
-0.779936552091913```

AUTHOR:

`Trevor McDougall & Paul Barker       [ help@teos-10.org ]`

VERSION NUMBER:

`3.05 (20th March, 2017)`

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 the TEOS-10 web site.```
```McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014:
Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation.
Journal of Physical Oceanography, 44, 1751-1775.```
`The software is available from http://www.TEOS-10.org`