# gsw_pt_first_derivatives

    first derivatives of potential temperature

## Contents

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

## USAGE:

    [pt_SA, pt_CT] = gsw_pt_first_derivatives(SA,CT)

## DESCRIPTION:

    Calculates the following two partial derivatives of potential
    temperature (the regular potential temperature whose reference sea
    pressure is 0 dbar)
     (1) pt_SA, the derivative with respect to Absolute Salinity at
         constant Conservative Temperature, and
     (2) pt_CT, the derivative with respect to Conservative Temperature at
         constant Absolute Salinity.

    Click for a more detailed description of the first
    derivatives of potential temperature.

## INPUT:

    SA  =   Absolute Salinity                                       [ g/kg ]
    CT  =   Conservative Temperature                               [ deg C ]

    SA & CT need to have the same dimensions.

## OUTPUT:

    pt_SA =  The derivative of potential temperature with respect to
             Absolute Salinity at constant Conservative Temperature.
                                                                 [ K/(g/kg)]
    pt_CT =  The derivative of potential temperature with respect to
             Conservative Temperature at constant Absolute Salinity.
             pt_CT is dimensionless.                            [ unitless ]

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    CT = [28.8099; 28.4392; 22.7862; 10.2262;  6.8272;  4.3236;]

    [pt_SA, pt_CT] = gsw_pt_first_derivatives(SA,CT)

    pt_SA =

     0.041863223165431
     0.041452303483011
     0.034682095247246
     0.018711079068408
     0.014079958329844
     0.010577326129948

    pt_CT =

     0.997192967140242
     0.997451686508335
     0.998357568277750
     0.999996224076267
     1.000283719083268
     1.000525947028218

## AUTHOR:

    Trevor McDougall and Paul Barker [ help_gsw@csiro.au ]

## VERSION NUMBER:

    2.0 (26th August, 2010)

## 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 Eqns. (A.12.6), (A.12.3), (P.6) and (P.8) of this TEOS-10 Manual.

    McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson, R.
     Feistel and R. W. Hallberg, 2010:  A computationally efficient 25-term
     expression for the density of seawater in terms of Conservative
     Temperature, and related properties of seawater.  To be submitted
     to Ocean Science Discussions.

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