# gsw_CT_first_derivatives_wrt_t_exact

first derivatives of Conservative Temperature with respect to (or at constant) in-situ temperature

## Contents

## USAGE:

[CT_SA_wrt_t, CT_T_wrt_t, CT_P_wrt_t] = gsw_CT_first_derivatives_wrt_t_exact(SA,t,p)

## DESCRIPTION:

Calculates the following three derivatives of Conservative Temperature. These derivatives are done with respect to in-situ temperature t (in the case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of CT_SA_wrt_t and CT_P_wrt_t). (1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity at constant t and p, and (2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t at constant SA and p. (3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at constant SA and t. This function uses the full Gibbs function. Note that this function avoids the NaN that would exist in CT_SA_wrt_t at SA = 0 if it were evaluated in the straightforward way from the derivatives of the Gibbs function function.

## INPUT:

SA = Absolute Salinity [ g/kg ] t = in-situ temperature (ITS-90) [ deg C ] p = sea pressure [ dbar ] ( ie. absolute pressure - 10.1325 dbar )

SA & t need to have the same dimensions. p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & t are MxN.

## OUTPUT:

CT_SA_wrt_t = The first derivative of Conservative Temperature with respect to Absolute Salinity at constant t and p. [ K/(g/kg)] i.e. [ K kg/g ] CT_T_wrt_t = The first derivative of Conservative Temperature with respect to in-situ temperature, t, at constant SA and p. [ unitless ] CT_P_wrt_t = The first derivative of Conservative Temperature with respect to pressure P (in Pa) at constant SA and t. [ K/Pa ]

## EXAMPLE:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;] t = [28.7856; 28.4329; 22.8103; 10.2600; 6.8863; 4.4036;] p = [ 10; 50; 125; 250; 600; 1000;]

[CT_SA_wrt_t, CT_T_wrt_t, CT_P_wrt_t] = ... gsw_CT_first_derivatives_wrt_t_exact(SA,t,p)

CT_SA_wrt_t =

-0.041988694538987 -0.041596549088952 -0.034853545749326 -0.019067140454607 -0.015016439826591 -0.012233725491373

CT_T_wrt_t =

1.002752642867571 1.002243118597902 1.000835702767227 0.998194915250648 0.995219303532390 0.991780205482695

CT_P_wrt_t =

1.0e-007 *

-0.241011880838437 -0.239031676279078 -0.203649928441505 -0.119370679226136 -0.099140832825342 -0.086458168643579

## 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.

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