# gsw_enthalpy_first_derivatives

    first derivatives of enthalpy (75-term equation)

## Contents

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

## USAGE:

    [h_SA, h_CT] = gsw_enthalpy_first_derivatives(SA,CT,p)

## DESCRIPTION:

    Calculates the following two derivatives of specific enthalpy (h),
    of seawater using the computationally-efficient 75-term expression
    for specific volume in terms of SA, CT and p (Roquet et al., 2015).
     (1) h_SA, the derivative with respect to Absolute Salinity at
         constant CT and p, and
     (2) h_CT, derivative with respect to CT at constant SA and 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 first
    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   =  The first derivative of specific enthalpy with respect to
              Absolute Salinity at constant CT and p.
                                              [ J/(kg (g/kg))]  i.e. [ J/g ]
    h_CT   =  The first derivative of specific enthalpy with respect to
              CT at constant SA and p.                          [ J/(kg K) ]

## 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, h_CT] = gsw_enthalpy_first_derivatives(SA,CT,p)

    h_SA =

      -0.070223912348929
      -0.351159768365102
      -0.887025065692568
      -1.829602387915694
      -4.423463748270238
      -7.405100077558673

    h_CT =

    1.0e+003 *

       3.991899705530481
       3.992025640520101
       3.992210365030743
       3.992284150250490
       3.992685389122658
       3.993014168534175

## AUTHOR:

    Trevor McDougall.                      [ help@teos-10.org ]

## VERSION NUMBER:

    3.05.6 (20th March, 2017)

## 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 Eqns. (A.11.18), (A.11.15) and (A.11.12) 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 and P.M. Barker, 2015: Accurate
     polynomial expressions for the density and specific volume of seawater
     using the TEOS-10 standard.  Ocean Modelling, 90, pp. 29-43.
     http://dx.doi.org/10.1016/j.ocemod.2015.04.002

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