# gsw_CT_from_rho

    Conservative Temperature from density
    (48-term equation)

## Contents

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

## 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 48-term expression for density in terms
    of SA, CT and p (McDougall et al., 2013).

    Note that the 48-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. (2013).  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 =

      28.785919240184850
      28.434000931649784
      22.810740149969192
      10.262124247240154
       6.887196810485858
       4.401886081747603

    CT_multiple =

       NaN
       NaN
       NaN
       NaN
       NaN
       NaN

## AUTHOR:

    Trevor McDougall & Paul Barker                      [ help@teos-10.org ]

## VERSION NUMBER:

    3.02 (17th November, 2012)

## 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., P.M. Barker, R. Feistel and D.R. Jackett, 2013:  A
      computationally efficient 48-term expression for the density of
      seawater in terms of Conservative Temperature, and related properties
      of seawater.  To be submitted to J. Atm. Ocean. Technol., xx, yyy-zzz.

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