# gsw_pot_enthalpy_ice_freezing_first_derivatives_poly

    first derivatives of the potential enthalpy of ice at
    the conditions where ice and seawater are in thermodynamic
    equilibrium (polynomial)

## Contents

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

## USAGE:

    [pot_enthalpy_ice_freezing_SA, pot_enthalpy_ice_freezing_P] = ...
            gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(SA,p)

## DESCRIPTION:

    Calculates the first derivatives of the potential enthalpy of ice Ih at
    which ice melts into seawater with Absolute Salinity SA and at pressure
    p.  This code uses the comptationally efficient polynomial fit of the
    freezing potential enthalpy of ice Ih (McDougall et al., 2015).

## INPUT:

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

    p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA is MxN.

## OUTPUT:

    _pot_enthalpy_ice_freezing_SA = the derivative of the potential enthalpy
                  of ice at freezing (ITS-90) with respect to Absolute
                  salinity at fixed pressure  [ (J/kg)/(g/kg) ] i.e. [ J/g ]

    pot_enthalpy_ice_freezing_P  = the derivative of the potential enthalpy
                  of ice at freezing (ITS-90) with respect to pressure
                  (in Pa) at fixed Absolute Salinity           [ (J/kg)/Pa ]

## 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_SA, pot_enthalpy_ice_freezing_P] = ...
            gsw_pot_enthalpy_ice_freezing_first_derivatives_poly(SA,p)

    pot_enthalpy_ice_freezing_SA =

       1.0e+02 *

      -1.183498006918154
      -1.184135169530602
      -1.184626138334419
      -1.184032656542549
      -1.183727371435808
      -1.183805326863513

    pot_enthalpy_ice_freezing_P =

        1.0e-03 *

      -0.202934280214689
      -0.203136950111241
      -0.203515960539503
      -0.204145112153220
      -0.205898365024147
      -0.207885289186464

## 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.

    The software is available from http://www.TEOS-10.org