# gsw_rho_second_derivatives

    second derivatives of rho (75-term equation)

## Contents

- USAGE:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## 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