# gsw_enthalpy_second_derivatives

    second derivatives of enthalpy (75-term equation)

## Contents

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

## USAGE:

    [h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)

## DESCRIPTION:

    Calculates the following three second-order derivatives of specific
    enthalpy (h),
     (1) h_SA_SA, second order derivative with respect to Absolute Salinity
         at constant CT & p.
     (2) h_SA_CT, second order derivative with respect to SA & CT at
         constant p.
     (3) h_CT_CT, second order derivative with respect to CT at constant
         SA & p.

    Note that the 75-term equation has been fitted in a restricted range of
    parameter space, and is most accurate inside the "oceanographic funnel"
    described in  McDougall et al. (2003).  The GSW library function
    "gsw_infunnel(SA,CT,p)" is avaialble to be used if one wants to test if
    some of one's data lies outside this "funnel".

    Click for a more detailed description of the second
    derivatives of specific enthalpy.

## 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:

    h_SA_SA  =  The second derivative of specific enthalpy with respect to
                Absolute Salinity at constant CT & p.
                                    [ (J/kg)(g/kg)^-2) ] i.e. [ (J kg/g^2) ]
    h_SA_CT  =  The second derivative of specific enthalpy with respect to
                SA and CT at constant p.                  [ J/(kg K(g/kg)) ]
    h_CT_CT  =  The second derivative of specific enthalpy with respect to
                CT at constant SA and p.                      [ J/(kg K^2) ]

## 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;]

    [h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)

    h_SA_SA =

       0.000080922482023
       0.000404963500641
       0.001059800046742
       0.002431088963823
       0.006019611828423
       0.010225411250217

     h_SA_CT =

       0.000130004715129
       0.000653614489248
       0.001877220817849
       0.005470392103793
       0.014314756132297
       0.025195603327700

     h_CT_CT =

       0.000714303909834
       0.003584401249266
       0.009718730753139
       0.024064471995224
       0.061547884081343
       0.107493969308119

## 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.
      See Notes on the first and second order isobaric derivatives of
      specific enthalpy.

    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.

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