# gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact

    second derivatives of specific volume
    with respect to enthalpy

## Contents

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

## USAGE:

    [v_SA_SA_wrt_h, v_SA_h, v_h_h] = ...
                 gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)

## DESCRIPTION:

    Calculates the following three second-order derivatives of specific
    volume (v),
     (1) v_SA_SA_wrt_h, second-order derivative with respect to Absolute
         Salinity at constant h & p.
     (2) v_SA_h, second-order derivative with respect to SA & h at
         constant p.
     (3) v_h_h, second-order derivative with respect to h at
         constant SA & p.

    Note that this function uses the full Gibbs function.  There is an
    alternative to calling this function, namely
    gsw_specvol_second_derivatives_wrt_enthalpy(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 ]
           (ie. 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_wrt_h = The second-order derivative of specific volume with
                    respect to Absolute Salinity at constant h & p.
                                             [ (m^3/kg)(g/kg)^-2 (J/kg)^-1 ]
    v_SA_h  = The second-order derivative of specific volume with respect to
              SA and h at constant p.        [ (m^3/kg)(g/kg)^-1 (J/kg)^-1 ]
    v_h_h   = The second-order derivative with respect to h at
              constant SA & p.                         [ (m^3/kg)(J/kg)^-2 ]

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    CT = [28.8099; 28.4392; 22.7862; 10.2262;  6.8272;  4.3236;]
    p =  [     10;      50;     125;     250;     600;    1000;]

    [v_SA_SA_wrt_h, v_SA_h, v_h_h] = ...
                     gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)

    v_SA_SA_wrt_h =

       1.0e-08 *

       0.082738436622270
       0.082820472626935
       0.087012384310439
       0.098568931415547
       0.100885432010628
       0.102276246439309

    v_SA_h =

       1.0e-12 *

      0.326217843241685
       0.327716371538871
       0.375607041087142
       0.545165574576489
       0.589676769358126
       0.616103304530989

    v_h_h =

       1.0e-15 *

       0.447981834829075
       0.449172935265639
       0.486697221526866
       0.598047368579426
       0.627835291967017
       0.646576186556108

## AUTHOR:

    Paul Barker and Trevor McDougall          [ 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.

    McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003:
     Accurate and computationally efficient algorithms for potential
     temperature and density of seawater.  J. Atmosph. Ocean. Tech., 20,
     pp. 730-741.

    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.

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