# gsw_specvol_second_derivatives_CT_exact

second derivatives of specific volume

## Contents

## USAGE:

[v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives_CT_exact(SA,CT,p)

## DESCRIPTION:

Calculates the following three second-order derivatives of specific volume (v), (1) v_SA_SA, second order derivative with respect to Absolute Salinity at constant CT & p. (2) v_SA_CT, second order derivative with respect to SA & CT at constant p. (3) v_CT_CT, second order derivative with respect to CT at constant SA & p. (4) v_SA_P, second-order derivative with respect to SA & P at constant CT. (5) v_CT_P, second-order derivative with respect to CT & P at constant SA

Note that this function uses the full Gibbs function. There is an alternative to calling this function, namely gsw_specvol_second_derivatives(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 ] (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:

v_SA_SA = The second derivative of specific volume with respect to Absolute Salinity at constant CT & p. [ (m^3/kg)(g/kg)^-2 ] v_SA_CT = The second derivative of specific volume with respect to SA & CT at constant p. [ (m^3/kg)(g/kg)^-1 K^-1] v_CT_CT = The second derivative of specific volume with respect to CT at constant SA and p. [ (m^3/kg) K^-2) ] v_SA_P = The second derivative of specific volume with respect to SA & P at constant CT. [ (m^3/kg)(g/kg)^-1 Pa^-1 ] v_CT_P = The second derivative of specific volume with respect to CT & P at constant SA. [ (m^3/kg) K^-1 Pa^-1 ]

## 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;]

[v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives_CT_exact(SA,CT,p)

v_SA_SA =

1.0e-08 *

0.082747972220243 0.082798176655947 0.086916803740167 0.098324796761055 0.100275947818790 0.101230704457043

v_SA_CT =

1.0e-08 *

0.130277044003024 0.130784915228726 0.149689281804061 0.217013951069468 0.233995663194746 0.243673021659962

v_CT_CT =

1.0e-07 *

0.071415166013777 0.071591303894948 0.077547238247366 0.095261850570592 0.099967277032840 0.102907243947244

v_SA_P =

1.0e-14 *

0.116986078360622 0.116992068444784 0.121867881822378 0.136113230189008 0.139000449643749 0.140519129568244

v_CT_P =

1.0e-14 *

0.085363651161808 0.086548662105251 0.112536803643252 0.188528204436210 0.211570045408395 0.228501837692148

## AUTHOR:

Trevor McDougall and Paul Barker. [ 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

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