# gsw_CT_first_derivatives

    first derivatives of Conservative Temperature

## Contents

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

## USAGE:

    [CT_SA, CT_pt] = gsw_CT_first_derivatives(SA,pt)

## DESCRIPTION:

    Calculates the following two derivatives of Conservative Temperature
    (1) CT_SA, the derivative with respect to Absolute Salinity at
        constant potential temperature (with pr = 0 dbar), and
    (2) CT_pt, the 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 first the
    derivatives of Conservative Temperature.

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    pt  =  potential temperature (ITS-90)                          [ deg C ]
           (whose reference pressure is 0 dbar)

    SA & pt need to have the same dimensions.

## OUTPUT:

    CT_SA  =  The 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 output has units of:                    [ K/(g/kg) ]
    CT_pt  =  The derivative of Conservative Temperature with respect to
              potential temperature (the regular one with pr = 0 dbar)
              at constant SA. CT_pt is dimensionless.           [ unitless ]

## 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, CT_pt] = gsw_CT_first_derivatives(SA,pt)

    CT_SA =

      -0.041981092877806
      -0.041558140199508
      -0.034739209004865
      -0.018711103772892
      -0.014075941811725
      -0.010571716552295

    CT_pt =

       1.002814937296636
       1.002554817053239
       1.001645140295163
       1.000003771100520
       0.999716359504731
       0.999474326580093

## AUTHOR:

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

## VERSION NUMBER:

    3.01 (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.12.3) and (A.12.9a,b) 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