gsw_specvol_second_derivatives

second derivatives of specific volume (75-term equation)

Contents

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