# gsw_CT_freezing_first_derivatives

    first derivatives of Conservative Temperature at which seawater freezes

## Contents

- USAGE:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## 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