# gsw_frazil_ratios_adiabatic

    ratios of SA, CT and P changes when frazil ice forms due
    to the adiabatic change in pressure of a mixture of
    seawater and ice

## Contents

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

## USAGE:

    [dSA_dCT_frazil, dSA_dP_frazil, dCT_dP_frazil] = ...
                                        gsw_frazil_ratios_adiabatic(SA,p,w_Ih)

## DESCRIPTION:

    Calculates the ratios of SA, CT and P changes when frazil ice forms or
    melts in response to an adiabatic change in pressure of a mixture of
    seawater and frazil ice crystals.

    Note that the first output, dSA_dCT_frazil, is dSA/dCT rather than
    dCT/dSA.  This is done so that when SA = 0, the output, dSA/dCT, is
    zero whereas dCT/dSA would then be infinite.

    Also note that both dSA_dP_frazil and dCT_dP_frazil are the pressure
    derivatives with the pressure measured in Pa not dbar.

## INPUT:

    SA   =  Absolute Salinity of seawater                         [ g/kg ]
    p    =  sea pressure of seawater at which melting occurs      [ dbar ]
           ( i.e. absolute pressure - 10.1325 dbar )
    w_Ih =  mass fraction of ice, that is the mass of ice divided by the
            sum of the masses of ice and seawater.  That is, the mass of
            ice divided by the mass of the final mixed fluid.
            w_Ih must be between 0 and 1.                     [ unitless ]

    SA & w_Ih must have the same dimensions.
    p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA and w_Ih
    are MxN.

## OUTPUT:

    dSA_dCT_frazil = the ratio of the changes in Absolute Salinity
                      to that of Conservative Temperature     [ g/(kg K) ]

    dSA_dP_frazil  = the ratio of the changes in Absolute Salinity
                      to that of pressure (in Pa)            [ g/(kg Pa) ]

    dCT_dP_frazil  = the ratio of the changes in Conservative Temperature
                      to that of pressure (in Pa)                 [ K/Pa ]

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    p =  [     10;      50;     125;     250;     600;    1000;]
    w_Ih = [  0.9;    0.84;     0.4;    0.25;    0.05;    0.01;]

    [dSA_dCT_frazil, dSA_dP_frazil, dCT_dP_frazil] = ...
                                    gsw_frazil_ratios_adiabatic(SA,p,w_Ih)

    dSA_dCT_frazil =

        3.035152370800401
       1.932548405396193
       0.613212115809003
       0.516103092738565
       0.436656742034200
       0.425827266533876

    dSA_dP_frazil =

      1.0e-006 *

       -0.197406834470366
      -0.133213926580032
      -0.045580136143659
      -0.038806356507548
      -0.033541272953744
      -0.033350141194082

    dCT_dP_frazil =

      1.0e-007 *

      -0.650401727338347
      -0.689317412221414
      -0.743301297684333
      -0.751910946738026
      -0.768138213038669
      -0.783184728059898

## 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.

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