gsw_specvol_second_derivatives_CT_exact

second derivatives of specific volume

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) 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:

3.05 (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