# gsw_enthalpy_second_derivatives

second derivatives of enthalpy (75-term equation)

## Contents

## USAGE:

[h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)

## DESCRIPTION:

Calculates the following three second-order derivatives of specific enthalpy (h), (1) h_SA_SA, second order derivative with respect to Absolute Salinity at constant CT & p. (2) h_SA_CT, second order derivative with respect to SA & CT at constant p. (3) h_CT_CT, second order derivative with respect to CT at constant SA & 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 second 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_SA = The second derivative of specific enthalpy with respect to Absolute Salinity at constant CT & p. [ (J/kg)(g/kg)^-2) ] i.e. [ (J kg/g^2) ] h_SA_CT = The second derivative of specific enthalpy with respect to SA and CT at constant p. [ J/(kg K(g/kg)) ] h_CT_CT = The second derivative of specific enthalpy with respect to CT at constant SA and p. [ J/(kg K^2) ]

## 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_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)

h_SA_SA =

0.000080922482023 0.000404963500641 0.001059800046742 0.002431088963823 0.006019611828423 0.010225411250217 h_SA_CT = 0.000130004715129 0.000653614489248 0.001877220817849 0.005470392103793 0.014314756132297 0.025195603327700 h_CT_CT = 0.000714303909834 0.003584401249266 0.009718730753139 0.024064471995224 0.061547884081343 0.107493969308119

## AUTHOR:

Trevor McDougall and Paul Barker. [ 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. See Notes on the first and second order isobaric derivatives of specific enthalpy.

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, P.M. Barker, 2015: Accurate polynomial expressions for the density and specifc volume of seawater using the TEOS-10 standard. Ocean Modelling.

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