gsw_rho_second_derivatives_wrt_enthalpy

second derivatives of density 
with respect to enthalpy (75-term equation)

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 (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(SA,CT,p)
rho_SA_SA_wrt_h =
   1.0e-03 *
   0.207312267114544
   0.207065033523473
   0.191848346945039
   0.133182862881598
   0.116049034622904
   0.102745309429078
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:

3.05 (27th March, 2017)

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