Contents
USAGE:
[SA_final, CT_final, w_Ih_final] = ...
gsw_frazil_properties_potential_poly(SA_bulk,h_pot_bulk,p)
DESCRIPTION:
Calculates the mass fraction of ice (mass of ice divided by mass of ice
plus seawater), w_Ih_eq, which results from given values of the bulk
Absolute Salinity, SA_bulk, bulk potential enthalpy, h_pot_bulk,
occuring at pressure p. The final equilibrium values of Absolute
Salinity, SA_eq, and Conservative Temperature, CT_eq, of the
interstitial seawater phase are also returned. This code assumes that
there is no dissolved air in the seawater (that is, saturation_fraction
is assumed to be zero thoughout the code).
When the mass fraction w_Ih_final is calculated as being a positive
value, the seawater-ice mixture is at thermodynamic equlibrium.
This code returns w_Ih_final = 0 when the input bulk enthalpy, h_bulk,
is sufficiently large (i.e. sufficiently "warm") so that there is no ice
present in the final state. In this case the final state consists of
only seawater rather than being an equlibrium mixture of seawater and
ice which occurs when w_Ih_final is positive. Note that when
w_Ih_final = 0, the final seawater is not at the freezing temperature.
Note that this code uses the polynomial forms of CT_freezing and
pot_enthalpy_ice_freezing. This code is intended to be used in ocean
models where the model prognostic variables are SA_bulk and h_pot_bulk.
INPUT:
SA_bulk = bulk Absolute Salinity of the seawater and ice mixture
[ g/kg ]
h_pot_bulk = bulk potential enthalpy of the seawater and ice mixture
[ J/kg ]
p = sea pressure [ dbar ]
( i.e. absolute pressure - 10.1325 dbar )
SA_bulk and h_pot_bulk must have the same dimensions.
p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA_bulk and
h_pot_bulk are MxN.
OUTPUT:
SA_final = Absolute Salinity of the seawater in the final state,
whether or not any ice is present. [ g/kg ]
CT_final = Conservative Temperature of the seawater in the the final
state, whether or not any ice is present. [ deg C ]
w_Ih_final = mass fraction of ice in the final seawater-ice mixture.
If this ice mass fraction is positive, the system is at
thermodynamic equilibrium. If this ice mass fraction is
zero there is no ice in the final state which consists
only of seawater which is warmer than the freezing
temperature. [unitless]
EXAMPLE:
SA_bulk = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
h_pot_bulk = [-4.5544e4;-4.6033e4;-4.5830e4;-4.5589e4;-4.4948e4;-4.4027e4;]
p = [ 10; 50; 125; 250; 600; 1000;]
[SA_final, CT_final, w_Ih_final] = ...
gsw_frazil_properties_potential_poly(SA_bulk,h_pot_bulk,p)
SA_final =
39.098264696022831
39.343217436835218
39.434244243586633
39.159511498029801
38.820458704205542
38.542256756176229
CT_final =
-2.155537691991377
-2.200841508940901
-2.264094318382661
-2.344613208230164
-2.598663953454472
-2.900948531145453
w_Ih_final =
0.112190777010854
0.113150823111566
0.111797356032850
0.110121687760246
0.105198620534670
0.098848824039493
AUTHOR:
Trevor McDougall and 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
