# gsw_rho_second_derivatives_CT_exact

second derivatives of rho

## Contents

## USAGE:

[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = ... gsw_rho_second_derivatives_CT_exact(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 this function uses the full Gibbs function. There is an alternative to calling this function, namely gsw_rho_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:

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_CT_exact(SA,CT,p)

rho_SA_SA =

1.0e-03 *

0.188147803529947 0.187736836321965 0.168284283716908 0.118937108838259 0.110314719705899 0.104201573868626

rho_SA_CT =

-0.001836215029399 -0.001840192571434 -0.001989522503234 -0.002559991033648 -0.002710008063805 -0.002798643987570

rho_CT_CT =

-0.007241739106885 -0.007268592861024 -0.007975897762363 -0.010001038700960 -0.010557570576970 -0.010924662024630

rho_SA_P =

1.0e-09 *

-0.618450119516638 -0.619495810826076 -0.659236700264537 -0.765879906314218 -0.791905157633432 -0.809440672756091

rho_CT_P =

1.0e-08 *

-0.116411869394607 -0.117562611767344 -0.142111284622683 -0.214682405591971 -0.237654164605583 -0.255182895824723

## AUTHOR:

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

## VERSION NUMBER:

3.05 (16th February, 2015)

## 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, P.M. Barker, 2015: Accurate polynomial expressions for the density and specifc volume of seawater using the TEOS-10 standard. Ocean Modelling.

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