# gsw_pt_second_derivatives

    second derivatives of potential temperature

## Contents

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

## USAGE:

    [pt_SA_SA, pt_SA_CT, pt_CT_CT] = gsw_pt_second_derivatives(SA,CT)

## DESCRIPTION:

    Calculates the following three second-order derivatives of potential
    temperature (the regular potential temperature which has a reference
    sea pressure of 0 dbar),
     (1) pt_SA_SA, the second derivative with respect to Absolute Salinity
         at constant Conservative Temperature,
     (2) pt_SA_CT, the derivative with respect to Conservative Temperature
         and Absolute Salinity, and
     (3) pt_CT_CT, the second derivative with respect to Conservative
         Temperature at constant Absolute Salinity.

    Click for a more detailed description of the second
    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_SA  =  The second derivative of potential temperature (the
                 regular potential temperature which has reference sea
                 pressure of 0 dbar) with respect to Absolute Salinity
                 at constant Conservative Temperature.
                 pt_SA_SA has units of:                     [ K/((g/kg)^2) ]
    pt_SA_CT  =  The derivative of potential temperature with respect
                 to Absolute Salinity and Conservative Temperature.
                 pt_SA_CT has units of:                        [ (g/kg)^-1 ]
    pt_CT_CT  =  The second derivative of potential temperature (the
                 regular one with pr = 0 dbar) with respect to
                 Conservative Temperature at constant SA.
                 pt_CT_CT has units of:                             [ K^-1 ]

## 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_SA, pt_SA_CT, pt_CT_CT] = gsw_pt_second_derivatives(SA,CT)

    pt_SA_SA =

    1.0e-003 *

     0.160307058371208
     0.160785497957769
     0.168647220588324
     0.198377949876584
     0.210181899321236
     0.220018966513329

    pt_SA_CT =

     0.001185581323691
     0.001187068518686
     0.001217629686266
     0.001333254154015
     0.001379674342678
     0.001418371539325

    pt_CT_CT =

    1.0e-003 *

    -0.121979811279463
    -0.123711264754503
    -0.140136818504977
    -0.140645384127949
    -0.113781055410824
    -0.082417269009484

## 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.12.9) and (A.12.10) 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