# gsw_rho_first_derivatives_wrt_enthalpy

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

## Contents

## USAGE:

[rho_SA_wrt_h, rho_h] = gsw_rho_first_derivatives_wrt_enthalpy(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.

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:

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(SA,CT,p)

rho_SA_wrt_h =

0.733147956395683 0.733595095849723 0.743886960725932 0.771275693420041 0.777414200285696 0.781030546340640

v_h =

1.0e-04 *

-0.831005413475887 -0.826243794873652 -0.721438289309903 -0.445892608094272 -0.377326924646647 -0.334475962698187

## AUTHOR:

Paul Barker and Trevor McDougall [ help@teos-10.org ]

## VERSION NUMBER:

3.06.16 (28th September, 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.

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

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