# gsw_specvol_second_derivatives_CT_exact

    second derivatives of specific volume

## Contents

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

## USAGE:

    [v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives_CT_exact(SA,CT,p)

## DESCRIPTION:

    Calculates the following three second-order derivatives of specific
    volume (v),
     (1) v_SA_SA, second order derivative with respect to Absolute Salinity
         at constant CT & p.
     (2) v_SA_CT, second order derivative with respect to SA & CT at
         constant p.
     (3) v_CT_CT, second order derivative with respect to CT at constant
         SA & p.
     (4) v_SA_P, second-order derivative with respect to SA & P at
         constant CT.
     (5) v_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_specvol_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:

    v_SA_SA  =  The second derivative of specific volume with respect to
                Absolute Salinity at constant CT & p.  [ (m^3/kg)(g/kg)^-2 ]
    v_SA_CT  =  The second derivative of specific volume with respect to
                SA & CT at constant p.             [ (m^3/kg)(g/kg)^-1 K^-1]
    v_CT_CT  =  The second derivative of specific volume with respect to
                CT at constant SA and p.                  [ (m^3/kg) K^-2) ]
    v_SA_P  =  The second derivative of specific volume with respect to
                SA & P at constant CT.                    [ (m^3/kg) Pa^-1 ]
    v_CT_P  =  The second derivative of specific volume with respect to
                CT & P at constant SA.               [ (m^3/kg) 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;]

    [v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives_CT_exact(SA,CT,p)

    v_SA_SA =

       1.0e-08 *

       0.082747972220243
       0.082798176655947
       0.086916803740167
       0.098324796761055
       0.100275947818790
       0.101230704457043

    v_SA_CT =

       1.0e-08 *

       0.130277044003024
       0.130784915228726
       0.149689281804061
       0.217013951069468
       0.233995663194746
       0.243673021659962

    v_CT_CT =

       1.0e-07 *

       0.071415166013777
       0.071591303894948
       0.077547238247366
       0.095261850570592
       0.099967277032840
       0.102907243947244

    v_SA_P =

       1.0e-14 *

       0.116986078360622
       0.116992068444784
       0.121867881822378
       0.136113230189008
       0.139000449643749
       0.140519129568244

    v_CT_P =

       1.0e-14 *

       0.085363651161808
       0.086548662105251
       0.112536803643252
       0.188528204436210
       0.211570045408395
       0.228501837692148

## 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