# gsw_melting_seaice_SA_CT_ratio

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

## 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`