Contents
USAGE:
[v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives_CT_exact(SA,CT,p)
DESCRIPTION:
Calculates the following three second-order derivatives of specific
volume (v),
(1) v_SA_SA, second order derivative with respect to Absolute Salinity
at constant CT & p.
(2) v_SA_CT, second order derivative with respect to SA & CT at
constant p.
(3) v_CT_CT, second order derivative with respect to CT at constant
SA & p.
(4) v_SA_P, second-order derivative with respect to SA & P at
constant CT.
(5) v_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_specvol_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:
v_SA_SA = The second derivative of specific volume with respect to
Absolute Salinity at constant CT & p. [ (m^3/kg)(g/kg)^-2 ]
v_SA_CT = The second derivative of specific volume with respect to
SA & CT at constant p. [ (m^3/kg)(g/kg)^-1 K^-1]
v_CT_CT = The second derivative of specific volume with respect to
CT at constant SA and p. [ (m^3/kg) K^-2) ]
v_SA_P = The second derivative of specific volume with respect to
SA & P at constant CT. [ (m^3/kg)(g/kg)^-1 Pa^-1 ]
v_CT_P = The second derivative of specific volume with respect to
CT & P at constant SA. [ (m^3/kg) 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;]
[v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives_CT_exact(SA,CT,p)
v_SA_SA =
1.0e-08 *
0.082747972220243
0.082798176655947
0.086916803740167
0.098324796761055
0.100275947818790
0.101230704457043
v_SA_CT =
1.0e-08 *
0.130277044003024
0.130784915228726
0.149689281804061
0.217013951069468
0.233995663194746
0.243673021659962
v_CT_CT =
1.0e-07 *
0.071415166013777
0.071591303894948
0.077547238247366
0.095261850570592
0.099967277032840
0.102907243947244
v_SA_P =
1.0e-14 *
0.116986078360622
0.116992068444784
0.121867881822378
0.136113230189008
0.139000449643749
0.140519129568244
v_CT_P =
1.0e-14 *
0.085363651161808
0.086548662105251
0.112536803643252
0.188528204436210
0.211570045408395
0.228501837692148
AUTHOR:
Trevor McDougall and Paul Barker. [ help@teos-10.org ]
VERSION NUMBER:
3.06.15 (1st June, 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.
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