# gsw_CT_from_rho

Conservative Temperature from density (75-term equation)

## Contents

## USAGE:

[CT, CT_multiple] = gsw_CT_from_rho(rho,SA,p)

## DESCRIPTION:

Calculates the Conservative Temperature of a seawater sample, for given values of its density, Absolute Salinity and sea pressure (in dbar) using the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is avaialble to be used if one wants to test if some of one's data lies outside this "funnel".

Click for a more detailed description of calculating Conservative Temperature from density. |

## INPUT:

rho = density of a seawater sample (e.g. 1026 kg/m^3) [ kg/m^3 ] Note. This input has not had 1000 kg/m^3 subtracted from it. That is, it is 'density', not 'density anomaly'. SA = Absolute Salinity [ g/kg ] p = sea pressure [ dbar ] ( i.e. absolute pressure - 10.1325 dbar )

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

## OUTPUT:

CT = Conservative Temperature (ITS-90) [ deg C ] CT_multiple = Conservative Temperature (ITS-90) [ deg C ] Note that at low salinities, in brackish water, there are two possible temperatures for a single density. This programme will output both valid solutions. To see this second solution the user must call the programme with two outputs (i.e. [CT, CT_multiple]), if there is only one possible solution and the programme has been called with twooutputs the second variable will be set to NaN.

## EXAMPLE:

rho = [1021.8484; 1022.2647; 1024.4207; 1027.7841; 1029.8287; 1031.9916;] SA = [ 34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;] p = [ 10; 50; 125; 250; 600; 1000;]

[CT, CT_multiple] = gsw_CT_from_rho(rho,SA,p)

CT =

28.784377302226968

28.432402127485858

22.808745445250068

10.260169334807866

6.887336649146716

4.404594162282834

CT_multiple =

NaN NaN NaN NaN NaN NaN

## AUTHOR:

Trevor McDougall & 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 sections 3.1 and 3.3 of this TEOS-10 Manual.

McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741.

Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate polynomial expressions for the density and specifc volume of seawater using the TEOS-10 standard. Ocean Modelling.

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