# gsw_CT_from_rho_exact

`Conservative Temperature from density`

## USAGE:

`[CT, CT_multiple] = gsw_CT_from_rho_exact(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).```
```Note that this function uses the full Gibbs function.  There is an
alternative to calling this function, namely gsw_CT_from_rho(rho,SA,p),
which uses the computationally efficient 75-term expression for specific
volume in terms of SA, CT and p (Roquet et al., 2015).``` ```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 two
outputs 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_exact(rho,SA,p)`
`CT =`
`  28.785118589681630  28.433134593869998  22.810525577671346  10.260445791010170   6.886933933676899   4.404197563039265`
`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.```
```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`