gsw_CT_second_derivatives

second derivatives of Conservative Temperature

Contents

USAGE:

[CT_SA_SA, CT_SA_pt, CT_pt_pt] = gsw_CT_second_derivatives(SA,pt)

DESCRIPTION:

Calculates the following three, second-order derivatives of Conservative
Temperature
 (1) CT_SA_SA, the second derivative with respect to Absolute Salinity
     at constant potential temperature (with pr = 0 dbar),
 (2) CT_SA_pt, the derivative with respect to potential temperature
    (the regular potential temperature which is referenced to 0 dbar)
     and Absolute Salinity, and
 (3) CT_pt_pt, the second derivative with respect to potential
     temperature (the regular potential temperature which is referenced
     to 0 dbar) at constant Absolute Salinity.
TEOS-10 
Click for a more detailed description of the second
derivatives of Conservative Temperature.

INPUT:

SA  =  Absolute Salinity                                        [ g/kg ]
pt  =  potential temperature (ITS-90)                          [ deg C ]
SA & pt need to have the same dimensions.

OUTPUT:

CT_SA_SA  =  The second derivative of Conservative Temperature with
             respect to Absolute Salinity at constant potential
             temperature (the regular potential temperature which
             has reference sea pressure of 0 dbar).
             The CT_SA_SA output has units of:          [ K/((g/kg)^2) ]
CT_SA_pt  =  The derivative of Conservative Temperature with
             respect to potential temperature (the regular one with
             pr = 0 dbar) and Absolute Salinity.
             CT_SA_pt has units of:                         [ 1/(g/kg) ]
CT_pt_pt  =  The second derivative of Conservative Temperature with
             respect to potential temperature (the regular one with
             pr = 0 dbar) at constant SA.
             CT_pt_pt has units of:                              [ 1/K ]

EXAMPLE:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
pt = [28.7832; 28.4209; 22.7850; 10.2305;  6.8292;  4.3245;]
[CT_SA_SA, CT_SA_pt, CT_pt_pt] = gsw_CT_second_derivatives(SA,pt)
CT_SA_SA =
1.0e-003 *
  -0.060718502077064
  -0.062065324400873
  -0.084017055354742
  -0.148436050120131
  -0.171270386500246
  -0.189920754900116
CT_SA_pt =
  -0.001197415000869
  -0.001198309530139
  -0.001226523296082
  -0.001335896286481
  -0.001380492698572
  -0.001417751669135
CT_pt_pt =
1.0e-003 *
   0.123012754427146
   0.124662008871271
   0.140829458783443
   0.140646803448166
   0.113684095615077
   0.082286843477998

AUTHOR:

Trevor McDougall and Paul Barker    [ help@teos-10.org ]

VERSION NUMBER:

3.01 (16th May, 2011)

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 appendix A.12 of this TEOS-10 Manual.
McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011:  A 
 computationally efficient 48-term expression for the density of 
 seawater in terms of Conservative Temperature, and related properties
 of seawater.  To be submitted to Ocean Science Discussions. 
This software is available from http://www.TEOS-10.org