# gsw_specvol_second_derivatives

    second derivatives of specific volume (75-term equation)

## Contents

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

## USAGE:

    [v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives(SA,CT,p)

## DESCRIPTION:

    Calculates the following three second-order derivatives of specific
    volume (v),
     (1) v_SA_SA, second order derivative with respect to Absolute Salinity
         at constant CT & p.
     (2) v_SA_CT, second order derivative with respect to SA & CT at
         constant p.
     (3) v_CT_CT, second order derivative with respect to CT at constant
         SA & p.
     (4) v_SA_P, second-order derivative with respect to SA & P at
         constant CT.
     (5) v_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:

    v_SA_SA  =  The second derivative of specific volume with respect to
                Absolute Salinity at constant CT & p.  [ (m^3/kg)(g/kg)^-2 ]
    v_SA_CT  =  The second derivative of specific volume with respect to
                SA & CT at constant p.             [ (m^3/kg)(g/kg)^-1 K^-1]
    v_CT_CT  =  The second derivative of specific volume with respect to
                CT at constant SA and p.                  [ (m^3/kg) K^-2) ]
    v_SA_P  =  The second derivative of specific volume with respect to
                SA & P at constant CT.                    [ (m^3/kg) Pa^-1 ]
    v_CT_P  =  The second derivative of specific volume with respect to
                CT & P at constant SA.               [ (m^3/kg) 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;]

    [v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives(SA,CT,p)

    v_SA_SA =

       1.0e-08 *

       0.080906777599140
       0.080915086639384
       0.084568844270812
       0.096725108896007
       0.099111765836648
       0.100302277946072

    v_SA_CT =

       1.0e-08 *

       0.129965332117084
       0.130523053162130
       0.149555815430615
       0.217023290441810
       0.233892039070486
       0.243659989480325

    v_CT_CT =

       1.0e-07 *

      0.071409582006642
       0.071582962051991
       0.077436153664104
       0.095329736274850
       0.100105336953738
       0.103044572835472

    v_SA_P =

       1.0e-14 *

       0.141281359467752
       0.141507584673426
       0.147247234588907
       0.164580347761218
       0.168069801298412
       0.169948275518754

    v_CT_P =

       1.0e-14 *

       0.085542828707964
       0.086723632576213
       0.112156562396990
       0.188269893599500
       0.211615556759369
       0.228609575049911

## 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