gsw_seaice_fraction_to_freeze_seawater

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

Contents

USAGE:

[SA_freeze, CT_freeze, w_seaice] = ...
     gsw_seaice_fraction_to_freeze_seawater(SA,CT,p,saturation_fraction,SA_seaice,t_seaice)

DESCRIPTION:

Calculates the mass fraction of sea ice (mass of sea ice divided by mass 
of sea ice plus seawater), which, when melted into seawater having the
properties (SA,CT,p) causes the final seawater to be at the freezing 
temperature.  The other outputs are the Absolute Salinity and 
Conservative Temperature of the final 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 )
saturation_fraction = the saturation fraction of dissolved air in 
             seawater. saturation_fraction must be between 0 and 1.
SA_seaice =  Absolute Salinity of sea ice, that is, the mass fraction of             
             salt in sea ice, expressed in g of salt per kg of sea ice.
                                                                [ g/kg ]
t_seaice =  in-situ temperature of the sea ice at pressure p (ITS-90) 
                                                               [ deg C ]
SA, CT, SA_seaice and t_seaice must have the same dimensions.
p and saturation_fraction may have dimensions 1x1 or Mx1 or 1xN or MxN,
where SA, CT, SA_seaice and t_seaice are MxN.

OUTPUT:

SA_freeze  =  Absolute Salinity of seawater after the mass fraction of
              sea ice, w_seaice, at temperature t_seaice 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_seaice, of sea ice at temperature t_seaice has melted into the original seawater, and the final mixture is at the freezing temperature of seawater. [ deg C ]
w_seaice = mass fraction of sea ice, at SA_seaice and t_seaice, which, when melted into seawater at (SA,CT,p) leads to the final mixed seawater being at the freezing temperature. This output is between 0 and 1. [unitless]

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;]
saturation_fraction = [1; 0.8; 0.6; 0.5; 0.4; 0;]
SA_seaice = [     5;      4.8;     3.5;     2.5;     1;    0.4;]
t_seaice = [-5.7856; -4.4329; -3.8103; -4.2600;  -3.8863;  -3.4036;] 
[SA_freeze, CT_freeze, w_seaice] = ...
    gsw_seaice_fraction_to_freeze_seawater(SA,CT,p,saturation_fraction,SA_seaice,t_seaice)
SA_freezee =
  34.670582346850559
  34.702880864146486
  34.949748394724637
  34.524906626924761
  34.077046690910336
  33.501836583274191
CT_freezee =
  -1.897285403040842
  -1.929426136463819
  -2.001056696238295
  -2.072607862458515
  -2.319610736856991
  -2.603185031462614
w_seaice =
   0.001387248606595
   0.006268186559444
   0.002406032090598
   0.009963563247367
   0.019550082376104
   0.035842627277027

AUTHOR:

Trevor McDougall & Paul Barker       [ help@teos-10.org ]

VERSION NUMBER:

3.04 (10th December, 2013)

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. 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