gsw_pt_second_derivatives

second derivatives of potential temperature

Contents

USAGE:

[pt_SA_SA, pt_SA_CT, pt_CT_CT] = gsw_pt_second_derivatives(SA,CT)

DESCRIPTION:

Calculates the following three second-order derivatives of potential
temperature (the regular potential temperature which has a reference
sea pressure of 0 dbar),
 (1) pt_SA_SA, the second derivative with respect to Absolute Salinity
     at constant Conservative Temperature,
 (2) pt_SA_CT, the derivative with respect to Conservative Temperature
     and Absolute Salinity, and
 (3) pt_CT_CT, the second derivative with respect to Conservative
     Temperature at constant Absolute Salinity.
TEOS-10 
Click for a more detailed description of the second
derivatives of potential temperature.

INPUT:

SA  =  Absolute Salinity                                        [ g/kg ]
CT  =  Conservative Temperature                                [ deg C ]
SA & CT need to have the same dimensions.

OUTPUT:

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

EXAMPLE:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
CT = [28.8099; 28.4392; 22.7862; 10.2262;  6.8272;  4.3236;]
[pt_SA_SA, pt_SA_CT, pt_CT_CT] = gsw_pt_second_derivatives(SA,CT)
pt_SA_SA =
1.0e-003 *
   0.160307058371208
   0.160785497957769
   0.168647220588324
   0.198377949876584
   0.210181899321236
   0.220018966513329
pt_SA_CT =
   0.001185581323691
   0.001187068518686
   0.001217629686266
   0.001333254154015
   0.001379674342678
   0.001418371539325
pt_CT_CT =
1.0e-003 *
  -0.121979811279463
  -0.123711264754503
  -0.140136818504977
  -0.140645384127949
  -0.113781055410824
  -0.082417269009484

AUTHOR:

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

VERSION NUMBER:

3.01 (26th August, 2010)

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 Eqns. (A.12.9) and (A.12.10) 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