# gsw_enthalpy_first_derivatives

first derivatives of enthalpy (75-term equation)

## Contents

## 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