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