gsw_t_freezing_first_derivatives

first derivatives of in-situ temperature 
at which seawater freezes

Contents

USAGE:

[tfreezing_SA, tfreezing_P] = gsw_t_freezing_first_derivatives(SA,p,saturation_fraction)

DESCRIPTION:

Calculates the frist derivatives of the in-situ temperature at which 
seawater freezes with respect to Absolute Salinity SA and pressure P (in
Pa).  These expressions come from differentiating the expression that
defines the freezing temperature, namely the equality between the 
chemical potentials of water in seawater and in ice.

INPUT:

SA  =  Absolute Salinity                                        [ g/kg ]
p  =  sea pressure                                              [ dbar ]
        ( i.e. absolute pressure - 10.1325 dbar )
        
OPTIONAL:
saturation_fraction = the saturation fraction of dissolved air in 
                        seawater
  (i.e., saturation_fraction must be between 0 and 1, and the default 
    is is 0, air free) 
p & saturation_fraction (if provided) may have dimensions 1x1 or Mx1 or 
1xN or MxN, where SA is MxN.

OUTPUT:

tfreezing_SA = the derivative of the in-situ freezing temperature 
               (ITS-90) with respect to Absolute Salinity at fixed    
               pressure                     [ K/(g/kg) ] i.e. [ K kg/g ]               

tfreezing_P = the derivative of the in-situ freezing temperature (ITS-90) with respect to pressure (in Pa) at fixed Absolute Salinity [ K/Pa ]

EXAMPLE:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
p =  [     10;      50;     125;     250;     600;    1000;]
saturation_fraction = [1; 0.8; 0.6; 0.5; 0.4; 0;]
[tfreezing_SA, tfreezing_P] = gsw_t_freezing_first_derivatives(SA,p,saturation_fraction)
tfreezing_SA =
  -0.056811800705787
  -0.056856999671114
  -0.056903079789292
  -0.056904020028541
  -0.056974588411844
  -0.057082363270642
tfreezing_P =
   1.0e-007 *
  -0.748468312442338
  -0.749793159537290
  -0.752225023995510
  -0.756170965034610
  -0.767279572670040
  -0.779936552091913

AUTHOR:

Trevor McDougall & Paul Barker       [ help@teos-10.org ]

VERSION NUMBER:

3.05 (20th March, 2017)

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