Contents
USAGE:
[SA_freeze, CT_freeze, w_seaice] = ...
gsw_seaice_fraction_to_freeze_seawater(SA,CT,p,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 )
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 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;]
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,SA_seaice,t_seaice)
SA_freezee =
34.671271207148074
34.703449677481224
34.950192062047861
34.525277379661880
34.077349518029997
33.501836583274191
CT_freezee =
-1.895419711000293
-1.927935638317893
-1.999943183939312
-2.071677444370745
-2.318866154643864
-2.603185031462614
w_seaice =
0.001364063868629
0.006249283768465
0.002391958850970
0.009952101583387
0.019541106156815
0.035842627277027
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, 2014: 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