[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = gsw_rho_second_derivatives(SA,CT,p)
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
(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
(5) rho_CT_P, second-order derivative with respect to CT & P at
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".
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.
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 ]
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] = ...
Trevor McDougall and Paul Barker. [ email@example.com ]
3.05 (16th February, 2015)
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,
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