# gsw_CT_second_derivatives

    second derivatives of Conservative Temperature

## Contents

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

## USAGE:

    [CT_SA_SA, CT_SA_pt, CT_pt_pt] = gsw_CT_second_derivatives(SA,pt)

## DESCRIPTION:

    Calculates the following three, second-order derivatives of Conservative
    Temperature
     (1) CT_SA_SA, the second derivative with respect to Absolute Salinity
         at constant potential temperature (with pr = 0 dbar),
     (2) CT_SA_pt, the derivative with respect to potential temperature
        (the regular potential temperature which is referenced to 0 dbar)
         and Absolute Salinity, and
     (3) CT_pt_pt, the second derivative with respect to potential
         temperature (the regular potential temperature which is referenced
         to 0 dbar) at constant Absolute Salinity.

    Click for a more detailed description of the second
    derivatives of Conservative Temperature.

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    pt  =  potential temperature (ITS-90)                          [ deg C ]

    SA & pt need to have the same dimensions.

## OUTPUT:

    CT_SA_SA  =  The second derivative of Conservative Temperature with
                 respect to Absolute Salinity at constant potential
                 temperature (the regular potential temperature which
                 has reference sea pressure of 0 dbar).
                 The CT_SA_SA output has units of:          [ K/((g/kg)^2) ]
    CT_SA_pt  =  The derivative of Conservative Temperature with
                 respect to potential temperature (the regular one with
                 pr = 0 dbar) and Absolute Salinity.
                 CT_SA_pt has units of:                        [ (g/kg)^-1 ]
    CT_pt_pt  =  The second derivative of Conservative Temperature with
                 respect to potential temperature (the regular one with
                 pr = 0 dbar) at constant SA.
                 CT_pt_pt has units of:                             [ K^-1 ]

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    pt = [28.7832; 28.4209; 22.7850; 10.2305;  6.8292;  4.3245;]

    [CT_SA_SA, CT_SA_pt, CT_pt_pt] = gsw_CT_2nd_derivatives(SA,pt)

    CT_SA_SA =

    1.0e-003 *

    -0.060718502073595
    -0.062065324397404
    -0.084017055351272
    -0.148436050118396
    -0.171270386500246
    -0.189920754897514

    CT_SA_pt =

    -0.001197415000868
    -0.001198309530139
    -0.001226523296082
    -0.001335896286480
    -0.001380492698572
    -0.001417751669135

    CT_pt_pt =

    1.0e-003 *

     0.123012754427146
     0.124662008871271
     0.140829458783443
     0.140646803448166
     0.113684095615077
     0.082286843477998

## 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 appendix A.12 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