# gsw_seaice_fraction_to_freeze_seawater

    sea ice mass fraction, which when melted into seawater,
    brings the seawater to the freezing temperature

## Contents

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

## USAGE:

    [SA_freeze, CT_freeze, w_seaice] = ...
         gsw_seaice_fraction_to_freeze_seawater(SA,CT,p,SA_seaice,t_seaice)

## DESCRIPTION:

    Calculates the mass fraction of sea ice (mass of sea ice divided by mass
    of sea ice plus seawater), which, when melted into seawater having the
    properties (SA,CT,p) causes the final seawater to be at the freezing
    temperature.  The other outputs are the Absolute Salinity and
    Conservative Temperature of the final seawater.

## INPUT:

    SA   =  Absolute Salinity of seawater                           [ g/kg ]
    CT   =  Conservative Temperature of seawater (ITS-90)          [ deg C ]
    p    =  sea pressure                                            [ dbar ]
              ( i.e. absolute pressure - 10.1325 dbar )
    SA_seaice =  Absolute Salinity of sea ice, that is, the mass fraction of
                 salt in sea ice, expressed in g of salt per kg of sea ice.
                                                                    [ g/kg ]
    t_seaice =  in-situ temperature of the sea ice at pressure p (ITS-90)
                                                                   [ deg C ]

    SA, CT, SA_seaice and t_seaice must have the same dimensions.
    p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA, CT, SA_seaice
    and t_seaice are MxN.

## OUTPUT:

    SA_freeze  =  Absolute Salinity of seawater after the mass fraction of
                  sea ice, w_seaice, at temperature t_seaice has melted into
                  the original seawater, and the final mixture is at the
                  freezing temperature of seawater.                 [ g/kg ]

    CT_freeze  =  Conservative Temperature of seawater after the mass
                  fraction, w_seaice, of sea ice at temperature t_seaice has
                  melted into the original seawater, and the final mixture
                  is at the freezing temperature of seawater.      [ deg C ]

    w_seaice   =  mass fraction of sea ice, at SA_seaice and t_seaice,
                  which, when melted into seawater at (SA,CT,p) leads to the
                  final mixed seawater being at the freezing temperature.
                  This output is between 0 and 1.                 [unitless]

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    CT = [-1.7856; -1.4329; -1.8103; -1.2600;  -0.6886;  0.4403;]
    p = [     10;      50;     125;     250;     600;    1000;]
    SA_seaice = [     5;      4.8;     3.5;     2.5;     1;    0.4;]
    t_seaice = [-5.7856; -4.4329; -3.8103; -4.2600;  -3.8863;  -3.4036;]

    [SA_freeze, CT_freeze, w_seaice] = ...
        gsw_seaice_fraction_to_freeze_seawater(SA,CT,p,SA_seaice,t_seaice)

    SA_freezee =

      34.671271207148074
      34.703449677481224
      34.950192062047861
      34.525277379661880
      34.077349518029997
      33.501836583274191

    CT_freezee =

      -1.895419711000293
      -1.927935638317893
      -1.999943183939312
      -2.071677444370745
      -2.318866154643864
      -2.603185031462614

    w_seaice =

       0.001364063868629
       0.006249283768465
       0.002391958850970
       0.009952101583387
       0.019541106156815
       0.035842627277027

## 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.

    McDougall, T.J., and S.J. Wotherspoon, 2014: 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