gsw_enthalpy_second_derivatives

second derivatives of enthalpy (75-term equation)

Contents

USAGE:

[h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)

DESCRIPTION:

Calculates the following three second-order derivatives of specific
enthalpy (h),
 (1) h_SA_SA, second order derivative with respect to Absolute Salinity
     at constant CT & p.
 (2) h_SA_CT, second order derivative with respect to SA & CT at
     constant p.
 (3) h_CT_CT, second order derivative with respect to CT at constant
     SA & p.
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".
TEOS-10 
Click for a more detailed description of the second
derivatives of specific enthalpy.

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:

h_SA_SA  =  The second derivative of specific enthalpy with respect to
            Absolute Salinity at constant CT & p.
                                [ (J/kg)(g/kg)^-2) ] i.e. [ (J kg/g^2) ]
h_SA_CT  =  The second derivative of specific enthalpy with respect to
            SA and CT at constant p.                  [ J/(kg K(g/kg)) ]
h_CT_CT  =  The second derivative of specific enthalpy with respect to
            CT at constant SA and p.                      [ J/(kg K^2) ]

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;]
[h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)
h_SA_SA =
   0.000080922482023
   0.000404963500641
   0.001059800046742
   0.002431088963823
   0.006019611828423
   0.010225411250217
  
 h_SA_CT =
 
   0.000130004715129
   0.000653614489248
   0.001877220817849
   0.005470392103793
   0.014314756132297
   0.025195603327700
  
 h_CT_CT =

   0.000714303909834
   0.003584401249266
   0.009718730753139
   0.024064471995224
   0.061547884081343
   0.107493969308119

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.
  See Notes on the first and second order isobaric derivatives of
  specific enthalpy.
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.
This software is available from http://www.TEOS-10.org