gsw_ice_fraction_to_freeze_seawater

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

Contents

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 
 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