# gsw_rho_first_derivatives_wrt_enthalpy_CT_exact

    partial derivatives of density
    with respect to enthalpy

## Contents

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

## USAGE:

    [rho_SA_wrt_h, rho_h] = ...
                   gsw_rho_first_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)

## DESCRIPTION:

    Calculates the following two first-order derivatives of density
    (rho),
     (1) rho_SA_wrt_h, first-order derivative with respect to Absolute Salinity
         at constant h & p.
     (2) rho_h, first-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_rho_first_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:

    rho_SA_wrt_h  =  The first derivative of density with respect to
                     Absolute Salinity at constant CT & p.
                                             [ (kg/m^3)(g/kg)^-1 (J/kg)^-1 ]
    rho_h  =  The first derivative of density with respect to
              SA and CT at constant p.                 [ (kg/m^3)(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;]

    [rho_SA_wrt_h, rho_h] = ...
                    gsw_rho_first_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)

    rho_SA_wrt_h =

       0.733151009574085
       0.733595363339989
       0.743894868710786
       0.771284465943169
       0.777425432958621
       0.781045978855291

    v_h =

       1.0e-04 *

      -0.831181890518531
      -0.826419232735932
      -0.721524248257955
      -0.445734602809698
      -0.377273768705780
      -0.334507617639847

## 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.

    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