# gsw_rho_second_derivatives

second derivatives of rho (75-term equation)

## Contents

## USAGE:

[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = gsw_rho_second_derivatives(SA,CT,p)

## DESCRIPTION:

Calculates the following three second-order derivatives of rho, (1) rho_SA_SA, second order derivative with respect to Absolute Salinity at constant CT & p. (2) rho_SA_CT, second order derivative with respect to SA & CT at constant p. (3) rho_CT_CT, second order derivative with respect to CT at constant SA & p. (4) rho_SA_P, second-order derivative with respect to SA & P at constant CT. (5) rho_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:

rho_SA_SA = The second derivative of rho with respect to Absolute Salinity at constant CT & p. [ (kg/m^3)(g/kg)^-2 ] rho_SA_CT = The second derivative of rho with respect to SA & CT at constant p. [ (kg/m^3)(g/kg)^-1 K^-1] rho_CT_CT = The second derivative of rho with respect to CT at constant SA and p. [ (kg/m^3) K^-2 ] rho_SA_P = The second derivative of rho with respect to SA & P at constant CT. [ (kg/m^3)(g/kg)^-1 Pa^-1 ] rho_CT_P = The second derivative of rho with respect to CT & P at constant SA. [ (kg/m^3) 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;]

[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = ... gsw_rho_second_derivatives(SA,CT,p)

rho_SA_SA =

1.0e-03 *

0.207364734477357 0.207415414547223 0.192903197286004 0.135809142211237 0.122627562106076 0.114042431905783

rho_SA_CT =

-0.001832856561477 -0.001837354806146 -0.001988065808078 -0.002560181494807 -0.002708939446458 -0.002798484050141

rho_CT_CT =

-0.007241243828334 -0.007267807914635 -0.007964270843331 -0.010008164822017 -0.010572200761984 -0.010939294762200

rho_SA_P =

1.0e-09 *

-0.617330965378778 -0.618403843947729 -0.655302447133274 -0.764800777480716 -0.792168044875350 -0.810125648949170

rho_CT_P =

1.0e-08 *

-0.116597992537549 -0.117744271236102 -0.141712549466964 -0.214414626736539 -0.237704139801551 -0.255296606034074

## 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