# gsw_specvol_second_derivatives_wrt_enthalpy

second derivatives of specific volume with respect to enthalpy (75-term equation)

## Contents

## USAGE:

[v_SA_SA_wrt_h, v_SA_h, v_h_h] = ... gsw_specvol_second_derivatives_wrt_enthalpy(SA,CT,p)

## DESCRIPTION:

Calculates the following three second-order derivatives of specific volume (v), (1) v_SA_SA_wrt_h, second-order derivative with respect to Absolute Salinity at constant h & p. (2) v_SA_h, second-order derivative with respect to SA & h at constant p. (3) v_h_h, second-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:

v_SA_SA_wrt_h = The second-order derivative of specific volume with respect to Absolute Salinity at constant h & p. [ (m^3/kg)(g/kg)^-2 (J/kg)^-1 ] v_SA_h = The second-order derivative of specific volume with respect to SA and h at constant p. [ (m^3/kg)(g/kg)^-1 (J/kg)^-1 ] v_h_h = The second-order derivative with respect to h at constant SA & p. [ (m^3/kg)(J/kg)^-2 ]

## 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;]

[v_SA_SA_wrt_h, v_SA_h, v_h_h] = ... gsw_specvol_second_derivatives_wrt_enthalpy(SA,CT,p)

v_SA_SA_wrt_h =

1.0e-08 *

0.080900028996264 0.080937999675000 0.084663065647101 0.096973364985384 0.099727453432293 0.101353037979356

v_SA_h =

1.0e-12 *

0.325437133570796 0.327060462851431 0.375273569184178 0.545188833073084 0.589424881889351 0.616101548209175

v_h_h =

1.0e-15 *

0.447949998681476 0.449121446914278 0.485998151346315 0.598480711660961 0.628708349875318 0.647433212216398

## AUTHOR:

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

## VERSION NUMBER:

3.05 (27th 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.

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