# pot_enthalpy_icepoly

    potential enthalpy of ice at which seawater freezes (polynomial)

## Contents

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

## USAGE:

    pot_enthalpy_ice_freezing = gsw_pot_enthalpy_ice_freezing_poly(SA,p)

## DESCRIPTION:

    Calculates the potential enthalpy of ice at which seawater freezes.

    The error of this fit ranges between -2.5 and 1 J/kg with an rms of
    1.07, between SA of 0 and 120 g/kg and p between 0 and 10,000 dbar (the
    error in the fit is between -0.7 and 0.7 with an rms of
    0.3, between SA of 0 and 120 g/kg and p between 0 and 5,000 dbar) when
    compared with the potential enthalpy calculated from the exact in-situ
    freezing temperature which is found by a Newton-Raphson iteration of the
    equality of the chemical potentials of water in seawater and in ice.
    Note that the potential enthalpy at freezing can be found
    by this exact method using the function gsw_pot_enthalpy_ice_freezing.

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    p   =  sea pressure                                             [ dbar ]
           ( i.e. absolute pressure - 10.1325 dbar )

    p may have dimensions 1x1 or Mx1or 1xN or MxN, where SA is MxN.

## OUTPUT:

    pot_enthalpy_ice_freezing = potential enthalpy of ice at freezing
                                  of seawater                      [ J/kg ]

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    p =  [     10;      50;     125;     250;     600;    1000;]

    pot_enthalpy_ice_freezing = gsw_pot_enthalpy_ice_freezing_poly(SA,p)

    pot_enthalpy_ice_freezing =

      1.0e+05 *

      -3.373370858777002
      -3.374395733068549
      -3.376079507278181
      -3.378416106344322
      -3.385460970578123
      -3.393731732645173

## AUTHOR:

    Paul Barker, Trevor McDougall and Rainer Feistal   [ 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.
      See section 3.3 of this TEOS-10 Manual.

    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