gsw_specvol_second_derivatives_wrt_enthalpy

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

Contents

USAGE:

[v_SA_SA_wrt_h, v_SA_h, v_h_h] = ...
                    gsw_specvol_second_derivatives_wrt_enthalpy(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.
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:

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(SA,CT,p)
v_SA_SA_wrt_h =
   1.0e-08 *
   0.080900028996264
   0.080937999675000
   0.084663065647101
   0.096973364985384
   0.099727453432293
   0.101353037979356
v_SA_h =
   1.0e-12 *
  0.325437133570796
   0.327060462851431
   0.375273569184178
   0.545188833073084
   0.589424881889351
   0.616101548209175
v_h_h =
   1.0e-15 *
   0.447949998681476
   0.449121446914278
   0.485998151346315
   0.598480711660961
   0.628708349875318
   0.647433212216398

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