gsw_rho_second_derivatives

second derivatives of rho (75-term equation)

Contents

USAGE:

[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = gsw_rho_second_derivatives(SA,CT,p)

DESCRIPTION:

Calculates the following three second-order derivatives of rho,
 (1) rho_SA_SA, second order derivative with respect to Absolute Salinity
     at constant CT & p.
 (2) rho_SA_CT, second order derivative with respect to SA & CT at
     constant p.
 (3) rho_CT_CT, second order derivative with respect to CT at constant
     SA & p.
 (4) rho_SA_P, second-order derivative with respect to SA & P at 
     constant CT. 
 (5) rho_CT_P, second-order derivative with respect to CT & P at 
     constant SA
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 ]
       (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:

rho_SA_SA = The second derivative of rho with respect to
            Absolute Salinity at constant CT & p.  [ (kg/m^3)(g/kg)^-2 ]
rho_SA_CT = The second derivative of rho with respect to
            SA & CT at constant p.             [ (kg/m^3)(g/kg)^-1 K^-1]
rho_CT_CT = The second derivative of rho with respect to
            CT at constant SA and p.                   [ (kg/m^3) K^-2 ]
rho_SA_P  = The second derivative of rho with respect to
            SA & P at constant CT.           [ (kg/m^3)(g/kg)^-1 Pa^-1 ]
rho_CT_P  = The second derivative of rho with respect to
            CT & P at constant SA.               [ (kg/m^3) K^-1 Pa^-1 ]

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;]
[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = ...
                              gsw_rho_second_derivatives(SA,CT,p)
rho_SA_SA =
   1.0e-03 *
   0.207364734477357
   0.207415414547223
   0.192903197286004
   0.135809142211237
   0.122627562106076
   0.114042431905783
rho_SA_CT =
  -0.001832856561477
  -0.001837354806146
  -0.001988065808078
  -0.002560181494807
  -0.002708939446458
  -0.002798484050141
rho_CT_CT =
  -0.007241243828334
  -0.007267807914635
  -0.007964270843331
  -0.010008164822017
  -0.010572200761984
  -0.010939294762200
rho_SA_P =
   1.0e-08 *
  -0.087202931942412
  -0.087558612009845
  -0.092549696987409
  -0.106661486272630
  -0.110022261844240
  -0.112287954816717
rho_CT_P =
   1.0e-08 *
  -0.116597992537549
  -0.117744271236102
  -0.141712549466964
  -0.214414626736539
  -0.237704139801551
  -0.255296606034074

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.
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