# gsw_rho_second_derivatives_CT_exact

    second derivatives of rho

## Contents

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

## USAGE:

    [rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = ...
                                gsw_rho_second_derivatives_CT_exact(SA,CT,p)

## DESCRIPTION:

    Calculates the following three second-order derivatives of rho,
     (1) rho_SA_SA, second order derivative with respect to Absolute Salinity
         at constant CT & p.
     (2) rho_SA_CT, second order derivative with respect to SA & CT at
         constant p.
     (3) rho_CT_CT, second order derivative with respect to CT at constant
         SA & p.
     (4) rho_SA_P, second-order derivative with respect to SA & P at
         constant CT.
     (5) rho_CT_P, second-order derivative with respect to CT & P at
         constant SA

    Note that this function uses the full Gibbs function.  There is an
    alternative to calling this function, namely
    gsw_rho_second_derivatives(SA,CT,p), which uses the computationally
    efficient 75-term expression for specific volume in terms of SA, CT
    and p (Roquet et al., 2015).

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    CT  =  Conservative Temperature                                [ deg C ]
    p   =  sea pressure                                             [ dbar ]
           (i.e. absolute pressure - 10.1325 dbar)

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

## OUTPUT:

    rho_SA_SA = The second derivative of rho with respect to
                Absolute Salinity at constant CT & p.  [ (kg/m^3)(g/kg)^-2 ]
    rho_SA_CT = The second derivative of rho with respect to
                SA & CT at constant p.             [ (kg/m^3)(g/kg)^-1 K^-1]
    rho_CT_CT = The second derivative of rho with respect to
                CT at constant SA and p.                   [ (kg/m^3) K^-2 ]
    rho_SA_P  = The second derivative of rho with respect to
                SA & P at constant CT.           [ (kg/m^3)(g/kg)^-1 Pa^-1 ]
    rho_CT_P  = The second derivative of rho with respect to
                CT & P at constant SA.               [ (kg/m^3) K^-1 Pa^-1 ]

## EXAMPLE:

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

    [rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = ...
                                    gsw_rho_second_derivatives_CT_exact(SA,CT,p)

    rho_SA_SA =

       1.0e-03 *

        0.188147803529947
       0.187736836321965
       0.168284283716908
       0.118937108838259
       0.110314719705899
       0.104201573868626

    rho_SA_CT =

      -0.001836215029399
      -0.001840192571434
      -0.001989522503234
      -0.002559991033648
      -0.002710008063805
      -0.002798643987570

    rho_CT_CT =

      -0.007241739106885
      -0.007268592861024
      -0.007975897762363
      -0.010001038700960
      -0.010557570576970
      -0.010924662024630

    rho_SA_P =

       1.0e-09 *

      -0.618450119516638
      -0.619495810826076
      -0.659236700264537
      -0.765879906314218
      -0.791905157633432
      -0.809440672756091

    rho_CT_P =

       1.0e-08 *

      -0.116411869394607
      -0.117562611767344
      -0.142111284622683
      -0.214682405591971
      -0.237654164605583
      -0.255182895824723

## 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.

    Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
     polynomial expressions for the density and specifc volume of seawater
     using the TEOS-10 standard. Ocean Modelling.

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