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



melting_seaice_SA_CT_ratio = ...


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. 


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.


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) ]               


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 = ...
melting_seaice_SA_CT_ratio =


Trevor McDougall & Paul Barker       [ ]


3.05 (16th February, 2015)


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