# 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.

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 *

0.123012754427165 0.124662008871290 0.140829458783465 0.140646803448163 0.113684095615074 0.082286843477997

## AUTHOR:

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

## VERSION NUMBER:

3.06.12 (1st September, 2020)

## 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.

This software is available from http://www.TEOS-10.org