# gsw_rho_second_derivatives_wrt_enthalpy_CT_exact

second derivatives of density with respect to enthalpy

## Contents

## USAGE:

[rho_SA_SA_wrt_h, rho_SA_h, rho_h_h] = ... gsw_rho_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)

## DESCRIPTION:

Calculates the following three second-order derivatives of density (rho), (1) rho_SA_SA_wrt_h, second-order derivative with respect to Absolute Salinity at constant h & p. (2) rho_SA_h, second-order derivative with respect to SA & h at constant p. (3) rho_h_h, second-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_second_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_SA_wrt_h = The second-order derivative of density with respect to Absolute Salinity at constant h & p. [ (kg/m^3)(g/kg)^-2 ] rho_SA_h = The second-order derivative of density with respect to SA and h at constant p. [ (kg/m^3)(g/kg)^-1 (J/kg)^-1 ] rho_h_h = The second-order derivative of density with respect to h at constant SA & p. [ (kg/m^3)(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;]

[rho_SA_SA_wrt_h, rho_SA_h, rho_h_h] = ... gsw_rho_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)

rho_SA_SA_wrt_h =

1.0e-03 *

0.188124506388597 0.187392915799686 0.167214908475657 0.116354239332502 0.103802027436498 0.092959759919644

rho_SA_h =

1.0e-06 *

-0.459894218037865 -0.461081364269496 -0.498969518512561 -0.642785635927268 -0.682351831685558 -0.706800653783123

rho_h_h =

1.0e-09 *

-0.454241581845215 -0.456033258712955 -0.500601766903036 -0.627882803785457 -0.663096358715998 -0.686453851147432

## 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