# gsw_CT_from_rho_exact

    Conservative Temperature from density

## Contents

- USAGE:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## 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