# gsw_t_freezing_first_derivatives_poly

    first derivatives of in-situ temperature at which seawater
    freezes (polynomial)

## Contents

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

## USAGE:

    [tfreezing_SA, tfreezing_P] = ...
              gsw_t_freezing_first_derivatives_poly(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_poly(SA,p,saturation_fraction)

    tfreezing_SA =

      -0.056810211094078
      -0.056855567524973
      -0.056901968693345
      -0.056903498206432
      -0.056975157476629
      -0.057083526206200

    tfreezing_P =

       1.0e-007 *

      -0.748987354878138
      -0.750288853857513
      -0.752676389629787
      -0.756549680608529
      -0.767482625710990
      -0.779985619685683

## 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