# gsw_ice_fraction_to_freeze_seawater

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

## USAGE:

```[SA_freeze, CT_freeze, w_Ih] = ...
gsw_ice_fraction_to_freeze_seawater(SA,CT,p,t_Ih)```

## DESCRIPTION:

```Calculates the mass fraction of ice (mass of ice divided by mass of ice
plus seawater), which, when melted into seawater having (SA,CT,p) causes
the final diluted seawater to be at the freezing temperature.  The other
outputs are the Absolute Salinity and Conservative Temperature of the
final diluted 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 )
t_Ih =  in-situ temperature of the ice at pressure p (ITS-90)  [ deg C ]```
```SA, CT and t_Ih must have the same dimensions.
p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA, CT and t_Ih
are MxN.```

## OUTPUT:

```SA_freeze  = Absolute Salinity of seawater after the mass fraction of
ice, w_Ih, at temperature t_Ih 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_Ih, of ice at temperature t_Ih has melted into
the original seawater, and the final mixture is at the
freezing temperature of seawater.                 [ deg C ]

w_Ih       = mass fraction of ice, having in-situ temperature t_Ih,
which, when melted into seawater at (SA,CT,p) leads to the
final diluted seawater being at the freezing temperature.
This output must be between 0 and 1.             [unitless]```

## EXAMPLE:

```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
CT = [28.7856; 28.4329; 22.8103; 10.2600;  6.8863;  4.4036;]
p = [     10;      50;     125;     250;     600;    1000;]
t_Ih = [-10.7856; -13.4329; -12.8103; -12.2600; -10.8863; -8.4036;]```
```[SA_freeze, CT_freeze, w_Ih] = ...
gsw_ice_fraction_to_freeze_seawater(SA,CT,p,t_Ih)```
`SA_freezee =`
```  25.823952352620722
26.120495895535438
27.460572941868072
30.629978769577168
31.458222332943784
32.121170316796444```
`CT_freezee =`
```  -1.389936216242376
-1.437013334134283
-1.569815847128818
-1.846419165657020
-2.166786673735941
-2.522730879078756```
`w_Ih =`
```   0.256046867272203
0.251379393389925
0.215985652155336
0.121020375537284
0.094378196687535
0.075181377710828```

## 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, 2013: A simple modification of
Newtonâ€™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`