# gsw_CT_first_derivatives_wrt_t_exact

    first derivatives of Conservative Temperature with
    respect to (or at constant) in-situ temperature

## Contents

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

## USAGE:

    [CT_SA_wrt_t, CT_T_wrt_t, CT_P_wrt_t] = gsw_CT_first_derivatives_wrt_t_exact(SA,t,p)

## DESCRIPTION:

    Calculates the following three derivatives of Conservative Temperature.
    These derivatives are done with respect to in-situ temperature t (in the
    case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of
    CT_SA_wrt_t and CT_P_wrt_t).
     (1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity
         at constant t and p, and
     (2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t
         at constant SA and p.
     (3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at
         constant SA and t.
    This function uses the full Gibbs function. Note that this function
    avoids the NaN that would exist in CT_SA_wrt_t at SA = 0 if it were
    evaluated in the straightforward way from the derivatives of the Gibbs
    function function.

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    t    =   in-situ temperature (ITS-90)                          [ deg C ]
    p    =   sea pressure                                           [ dbar ]
            ( ie. absolute pressure - 10.1325 dbar )

    SA & t need to have the same dimensions.
    p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & t are MxN.

## OUTPUT:

    CT_SA_wrt_t  =  The first derivative of Conservative Temperature with
                    respect to Absolute Salinity at constant t and p.
                                                [ K/(g/kg)]  i.e. [ K kg/g ]
    CT_T_wrt_t  =   The first derivative of Conservative Temperature with
                    respect to in-situ temperature, t, at constant SA and p.
                                                                [ unitless ]
    CT_P_wrt_t  =   The first derivative of Conservative Temperature with
                    respect to pressure P (in Pa) at constant SA and t.
                                                                    [ K/Pa ]

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    t =  [28.7856; 28.4329; 22.8103; 10.2600;  6.8863;  4.4036;]
    p =  [     10;      50;     125;     250;     600;    1000;]

    [CT_SA_wrt_t, CT_T_wrt_t, CT_P_wrt_t] = ...
                              gsw_CT_first_derivatives_wrt_t_exact(SA,t,p)

    CT_SA_wrt_t =

      -0.041988694538987
      -0.041596549088952
      -0.034853545749326
      -0.019067140454607
      -0.015016439826591
      -0.012233725491373

    CT_T_wrt_t =

       1.002752642867571
       1.002243118597902
       1.000835702767227
       0.998194915250648
       0.995219303532390
       0.991780205482695

    CT_P_wrt_t =

      1.0e-007 *

      -0.241011880838437
      -0.239031676279078
      -0.203649928441505
      -0.119370679226136
      -0.099140832825342
      -0.086458168643579

## AUTHOR:

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

## VERSION NUMBER:

    3.05 (16th February, 2015)

## 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.

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