# 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:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## 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
     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