Contents
USAGE:
[rho_SA_SA_wrt_h, rho_SA_h, rho_h_h] = ...
gsw_rho_second_derivatives_wrt_enthalpy(SA,CT,p)
DESCRIPTION:
Calculates the following three second-order derivatives of density
(rho),
(1) rho_SA_SA_wrt_h, second-order derivative with respect to Absolute
Salinity at constant h & p.
(2) rho_SA_h, second-order derivative with respect to SA & h at
constant p.
(3) rho_h_h, second-order derivative with respect to h at
constant SA & p.
This function uses the computationally-efficient 75-term
expression for specific volume in terms of SA, CT and p (Roquet et al.,
2015).
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 ]
(ie. 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_wrt_h = The second-order derivative of density with
respect to Absolute Salinity at constant h & p.
[ (kg/m^3)(g/kg)^-2 ]
rho_SA_h = The second-order derivative of density with respect to
SA and h at constant p. [ (kg/m^3)(g/kg)^-1 (J/kg)^-1 ]
rho_h_h = The second-order derivative of density with respect to
h at constant SA & p. [ (kg/m^3)(J/kg)^-2 ]
EXAMPLE:
SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
CT = [28.8099; 28.4392; 22.7862; 10.2262; 6.8272; 4.3236;]
p = [ 10; 50; 125; 250; 600; 1000;]
[rho_SA_SA_wrt_h, rho_SA_h, rho_h_h] = ...
gsw_rho_second_derivatives_wrt_enthalpy(SA,CT,p)
rho_SA_SA_wrt_h =
1.0e-03 *
0.207325714908677
0.207131960039965
0.192001360206293
0.133399974356615
0.116504845152129
0.103433221305694
rho_SA_h =
1.0e-06 *
-0.459053080088382
-0.460370569872258
-0.498605615416296
-0.642833108550133
-0.682091962941161
-0.706793055445909
rho_h_h =
1.0e-09 *
-0.454213854637790
-0.455984900239309
-0.499870030989387
-0.628337767293403
-0.664021595759308
-0.687367088752173
AUTHOR:
Paul Barker and Trevor McDougall [ help@teos-10.org ]
VERSION NUMBER:
3.06.16 (12th October, 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
The software is available from http://www.TEOS-10.org