# gsw_t_freezing

    in-situ temperature freezing point

## Contents

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

## USAGE:

    t_freezing = gsw_t_freezing(SA,p,saturation_fraction)

## DESCRIPTION:

    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.

    An alternative GSW function, gsw_t_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.

## 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:

    t_freezing = in-situ temperature at which seawater freezes.    [ deg C ]
                 (ITS-90)

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    p =  [     10;      50;     125;     250;     600;    1000;]
    saturation_fraction = 1;

    t_freezing = gsw_t_freezing(SA,p,saturation_fraction)

    t_freezing =

      -1.902730710149803
      -1.942908619287183
      -2.006861069199743
      -2.090985086875259
      -2.351293130342102
      -2.660498762776720

## AUTHOR:

    Paul Barker, Trevor McDougall and Rainer Feistal    [ 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.
      See section 3.3 of this TEOS-10 Manual.

    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.

    McDougall, T.J. and S.J. Wotherspoon, 2013: A simple modification of
     Newton’s method to achieve convergence of order "1 + sqrt(2)". Applied
     Mathematics Letters, 29, 20-25.
     http://dx.doi.org/10.1016/j.aml.2013.10.008

    The software is available from http://www.TEOS-10.org