## Contents

## 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 ]
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:

3.06.15 (1st June, 2022)

## 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 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

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