# gsw_specvol_first_derivatives_wrt_enthalpy

    partial derivatives of specific volume
    with respect to enthalpy (75-term equation)

## Contents

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

## USAGE:

    [v_SA_wrt_h, v_h] = gsw_specvol_first_derivatives_wrt_enthalpy(SA,CT,p)

## DESCRIPTION:

    Calculates the following two first-order derivatives of specific
    volume (v),
     (1) v_SA_wrt_h, first-order derivative with respect to Absolute Salinity
         at constant h & p.
     (2) v_h, first-order derivative with respect to h at
         constant SA & p.

    This function uses the computationally-efficient 75-term
    expression for specific volume in terms of SA, CT and p (Roquet et al.,
    2015).

    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".

## 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_wrt_h  =  The first derivative of specific volume with respect to
                Absolute Salinity at constant CT & p.
                                             [ (m^3/kg)(g/kg)^-1 (J/kg)^-1 ]
    v_h  =  The first derivative of specific volume with respect to
                SA and CT at constant p.               [ (m^3/kg)(J/kg)^-1 ]

## 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_wrt_h, v_h] = gsw_specvol_first_derivatives_wrt_enthalpy(SA,CT,p)

    v_SA_wrt_h =

       1.0e-06 *

      -0.702143511679586
      -0.701991101310494
      -0.708834353735310
      -0.730130919555592
      -0.733018321892082
      -0.733342002723321

    v_h =

       1.0e-10 *

       0.795862623587769
       0.790648383268264
       0.687443468257647
       0.422105846942233
       0.355778874334799
       0.314053366403993

## 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.
      See appendix A.20 and appendix K of this TEOS-10 Manual.

    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