# gsw_Turner_Rsubrho

    Turner angle & Rsubrho (48-term equation)

## Contents

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

## USAGE:

    [Tu, Rsubrho, p_mid] = gsw_Turner_Rsubrho(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 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 the Turner
    angle & Rsubrho.

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    CT  =  Conservative Temperature                                [ deg C ]
    p   =  sea pressure                                             [ dbar ]
           ( i.e. 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 ]

## 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] = gsw_Turner_Rsubrho(SA,CT,p)

    Tu =

      -2.064830032393999
      41.758285540907067
      47.607293931126598
      53.714708172363480
      45.527415163693554

    Rsubrho =

     1.0e+002 *

      -0.009304018848608
      -0.176556664605209
       0.219600192807469
       0.065238283043563
       1.086319945640579

    p_mid =

     1.0e+002 *

       0.300000000000000
       0.875000000000000
       1.875000000000000
       4.250000000000000
       8.000000000000000

## 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 Eqns. (3.15.1) and (3.16.1) 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