# gsw_specvol_second_derivatives

second derivatives of specific volume (75-term equation)

## Contents

## USAGE:

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

v_SA_SA =

1.0e-08 *

0.080906777599140 0.080915086639384 0.084568844270812 0.096725108896007 0.099111765836648 0.100302277946072

v_SA_CT =

1.0e-08 *

0.129965332117084 0.130523053162130 0.149555815430615 0.217023290441810 0.233892039070486 0.243659989480325

v_CT_CT =

1.0e-07 *

0.071409582006642 0.071582962051991 0.077436153664104 0.095329736274850 0.100105336953738 0.103044572835472

v_SA_P =

1.0e-14 *

0.116889015000936 0.116897424150385 0.121500614193893 0.136008673596132 0.139023051292893 0.140581903529772

v_CT_P =

1.0e-14 *

0.085542828707964 0.086723632576213 0.112156562396990 0.188269893599500 0.211615556759369 0.228609575049911

## AUTHOR:

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

## VERSION NUMBER:

3.06.16 (28th September, 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.

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