gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact

second derivatives of specific volume 
with respect to enthalpy

Contents

USAGE:

[v_SA_SA_wrt_h, v_SA_h, v_h_h] = ...
             gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)

DESCRIPTION:

Calculates the following three second-order derivatives of specific
volume (v),
 (1) v_SA_SA_wrt_h, second-order derivative with respect to Absolute 
     Salinity at constant h & p.
 (2) v_SA_h, second-order derivative with respect to SA & h at 
     constant p. 
 (3) v_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_specvol_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:

v_SA_SA_wrt_h = The second-order derivative of specific volume with
                respect to Absolute Salinity at constant h & p.
                                         [ (m^3/kg)(g/kg)^-2 (J/kg)^-1 ]
v_SA_h  = The second-order derivative of specific volume with respect to 
          SA and h at constant p.        [ (m^3/kg)(g/kg)^-1 (J/kg)^-1 ]
v_h_h   = The second-order derivative with respect to h at 
          constant SA & p.                         [ (m^3/kg)(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;]
[v_SA_SA_wrt_h, v_SA_h, v_h_h] = ...
                 gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)
v_SA_SA_wrt_h =
   1.0e-08 *
   0.082738436622270
   0.082820472626935
   0.087012384310439
   0.098568931415547
   0.100885432010628
   0.102276246439309
v_SA_h =
   1.0e-12 *
  0.326217843241685
   0.327716371538871
   0.375607041087142
   0.545165574576489
   0.589676769358126
   0.616103304530989
v_h_h =
   1.0e-15 *
   0.447981834829075
   0.449172935265639
   0.486697221526866
   0.598047368579426
   0.627835291967017
   0.646576186556108

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.
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, 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