# gsw_CT_freezing_first_derivatives

`first derivatives of Conservative Temperature at which seawater freezes`

## USAGE:

`[CTfreezing_SA, CTfreezing_P] = gsw_CT_freezing_first_derivatives(SA,p,saturation_fraction)`

## DESCRIPTION:

```Calculates the frist derivatives of the Conservative Temperature at
which seawater freezes, with respect to Absolute Salinity SA and
pressure P (in Pa). ```

## 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 0, air free) ```
```p & saturation_fraction (if provided) may have dimensions 1x1 or Mx1 or
1xN or MxN, where SA is MxN.```

## OUTPUT:

```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 ]```

## 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;]```
`[CTfreezing_SA, CTfreezing_P] = gsw_CT_freezing_first_derivatives(SA,p,saturation_fraction)`
`CTfreezing_SA =`
```  -0.058193253897272
-0.058265158334170
-0.058345661671901
-0.058373842446463
-0.058534544740846
-0.058730846361252```
`CTfreezing_P =`
`    1.0e-007 *`
```  -0.765300390432684
-0.766942996466485
-0.769892679988284
-0.774561011527902
-0.787769143040504
-0.802771548245855```

## AUTHOR:

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

## VERSION NUMBER:

`3.05 (16th February, 2015)`

## 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`