gsw_rho_second_derivatives_CT_exact

Contents

USAGE:

[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = ...
                            gsw_rho_second_derivatives_CT_exact(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 this function uses the full Gibbs function.  There is an 
alternative to calling this function, namely 
gsw_rho_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:

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_CT_exact(SA,CT,p)

rho_SA_SA =

   1.0e-03 *

    0.188147803529947
   0.187736836321965
   0.168284283716908
   0.118937108838259
   0.110314719705899
   0.104201573868626

rho_SA_CT =

  -0.001836215029399
  -0.001840192571434
  -0.001989522503234
  -0.002559991033648
  -0.002710008063805
  -0.002798643987570

rho_CT_CT =

  -0.007241739106885
  -0.007268592861024
  -0.007975897762363
  -0.010001038700960
  -0.010557570576970
  -0.010924662024630

rho_SA_P =

   1.0e-09 *

  -0.618450119516638
  -0.619495810826076
  -0.659236700264537
  -0.765879906314218
  -0.791905157633432
  -0.809440672756091

rho_CT_P =

   1.0e-08 *

  -0.116411869394607
  -0.117562611767344
  -0.142111284622683
  -0.214682405591971
  -0.237654164605583
  -0.255182895824723

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