# gsw_frazil_properties_potential_poly

Absolute Salinity, Conservative Temperature, and the ice mass fraction when at thermodynamic equilibrium between seawater and ice (polynomial)

## 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.

Click for a more detailed description of frazil properties potential poly. |

## 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 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