# 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.

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:

3.05 (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. See Eqns. (A.12.9) and (A.12.10) of this TEOS-10 Manual.

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