# gsw_Turner_Rsubrho_CT25

    Turner angle & Rsubrho (25-term equation)

## Contents

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

## USAGE:

    [Tu, Rsubrho, p_mid, in_funnel] = gsw_Turner_Rsubrho_CT25(SA,CT,p)

## DESCRIPTION:

    Calculates the Turner angle and the Rsubrho as a function of pressure
    down a vertical water column.  These quantities express the relative
    contributions of the vertical gradients of Conservative Temperature and
    Absolute Salinity to the vertical stability (the square of the
    Brunt-Vaisala Frequency squared, N^2).  Tu and Rsubrho are evaluated at
    the mid pressure between the individual data points in the vertical.
    This function uses computationally-efficient 25-term expression for
    density in terms of SA, CT and p (McDougall et al., 2010).

    Click for a more detailed description of the Turner
    angle & Rsubrho.

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    CT  =  Conservative Temperature                                [ deg C ]
    p   =  sea pressure                                             [ dbar ]
           (ie. absolute pressure - 10.1325 dbar)

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

## OUTPUT:

    Tu        =    Turner angle, on the same (M-1)xN grid as p_mid.
                   Turner angle has units of:        [ degrees of rotation ]
    Rsubrho   =    Stability Ratio, on the same (M-1)xN grid as p_mid.
                   Rsubrho is dimensionless.                    [ unitless ]
    p_mid     =    mid pressure between the indivual points of the p grid.
                   That is, p_mid is on a (M-1)xN grid in the vertical.
                   p_mid has units of:                              [ dbar ]
    in_funnel  =   0, if (SA, CT and p) are outside the "funnel"
               =   1, if (SA, CT and p) are inside the "funnel"
    Note. The term "funnel" describes the range of SA, CT and p over which
      the error in the fit of the computationally-efficient 25-term
      expression for density was calculated (McDougall et al., 2010).

## EXAMPLE:

    SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
    CT = [28.8099; 28.4392; 22.7862; 10.2262;  6.8272;  4.3236;]
    p =  [     10;      50;     125;     250;     600;    1000;]

    [Tu, Rsubrho, p_mid, in_funnel] = gsw_Turner_Rsubrho_CT25(SA,CT,p)

    Tu =

      -2.081599636326501
      41.758226366707646
      47.604100420927587
      53.716687678781497
      45.527957856195947

    Rsubrho =

     1.0e+002 *

      -0.009298559867815
      -0.176553434913642
       0.219869869025208
       0.065223236816021
       1.085203244744855

    p_mid =

     1.0e+002 *

      0.300000000000000
      0.875000000000000
      1.875000000000000
      4.250000000000000
      8.000000000000000

    in_funnel =

       1
       1
       1
       1
       1
       1

## AUTHOR:

    Trevor McDougall & Paul Barker [ help_gsw@csiro.au ]

## VERSION NUMBER:

    2.0 (26th August, 2010)

## 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 Eqns. (3.15.1) and (3.16.1) of this TEOS-10 Manual.

    McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson, R.
     Feistel and R. W. Hallberg, 2010:  A computationally efficient 25-term
     expression for the density of seawater in terms of Conservative
     Temperature, and related properties of seawater.  To be submitted
     to Ocean Science Discussions.

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