gsw_rho_second_derivatives_wrt_enthalpy_CT_exact

second derivatives of density 
with respect to enthalpy

Contents

USAGE:

[rho_SA_SA_wrt_h, rho_SA_h, rho_h_h] = ...
                gsw_rho_second_derivatives_wrt_enthalpy_CT_exact(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.
Note that this function uses the full Gibbs function.  There is an 
alternative to calling this function, namely 
gsw_rho_second_derivatives_wrt_enthalpy(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 ]
       (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 (J/kg)^-1 ]
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_CT_exact(SA,CT,p)
rho_SA_SA_wrt_h =
   1.0e-03 *
   0.188124506388597
   0.187392915799686
   0.167214908475657
   0.116354239332502
   0.103802027436498
   0.092959759919644
rho_SA_h =
   1.0e-06 *
  -0.459894218037865
  -0.461081364269496
  -0.498969518512561
  -0.642785635927268
  -0.682351831685558
  -0.706800653783123
rho_h_h =
   1.0e-09 *
  -0.454241581845215
  -0.456033258712955
  -0.500601766903036
  -0.627882803785457
  -0.663096358715998
  -0.686453851147432

AUTHOR:

Paul Barker and Trevor McDougall          [ 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.
The software is available from http://www.TEOS-10.org