# gsw_melting_seaice_SA_CT_ratio

    ratio of SA to CT changes when sea ice melts
    into seawater

## Contents

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

## USAGE:

    melting_seaice_SA_CT_ratio = ...
              gsw_melting_seaice_SA_CT_ratio(SA,CT,p,SA_seaice,t_seaice)

## DESCRIPTION:

    Calculates the ratio of SA to CT changes when sea ice melts into seawater.
    It is assumed that a small mass of sea ice melts into an infinite mass of
    seawater.  Because of the infinite mass of seawater, the sea ice will
    always melt.

    Ice formed at the sea surface (sea ice) typically contains between 2 g/kg
    and 12 g/kg of salt (defined as the mass of salt divided by the mass of
    ice Ih plus brine) and this programme returns NaN's if the input
    SA_seaice is greater than 15 g/kg.  If the SA_seaice input is not zero,
    usually this would imply that the pressure p should be zero, as sea ice
    only occurs near the sea surface.  The code does not impose that p = 0 if
    SA_seaice is non-zero.  Rather, this is left to the user.

    The Absolute Salinity, SA_brine, of the brine trapped in little pockets
    in the sea ice, is in thermodynamic equilibrium with the ice Ih that
    surrounds these pockets.  As the seaice temperature, t_seaice, may be
    less than the freezing temperature, SA_brine is usually greater than the
    Absolute Salinity of the seawater at the time and place when and where
    the sea ice was formed.  So usually SA_brine will be larger than SA.

    The output, melting_seaice_SA_CT_ratio, is dSA/dCT rather than dCT/dSA.
    This is done so that when (SA - seaice_SA) = 0, the output, dSA/dCT is
    zero whereas dCT/dSA would be infinite.

## 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 seaice expressed in g of salt per kg of sea ice
                                                                    [ g/kg ]
    t_seaice = the in-situ temperature of the seaice (ITS-90)      [ deg C ]

    SA, CT, SA_seaice & t_seaice must all 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:

    melting_seaice_SA_CT_ratio = the ratio dSA/dCT of SA to CT changes when
                  sea ice melts into a large mass of seawater   [ g/(kg K) ]

## 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;     4.5;     2.5;     1;    0.4;]
    t_seaice = [-6.7856; -7.4329; -6.8103; -6.2600; -6.8863; -8.4036;]

    melting_seaice_SA_CT_ratio = ...
      gsw_melting_seaice_SA_CT_ratio(SA,CT,p,SA_seaice,t_seaice)

    melting_seaice_SA_CT_ratio =

       0.364261362558123
       0.364096494650099
       0.372793263312277
       0.387622982383739
       0.394351386317639
       0.390587252198724

## 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