# gsw_geo_strf_McD_Klocker

    McDougall-Klocker geostrophic streamfunction

## Contents

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

## USAGE:

    [geo_strf_McD_Klocker, in_funnel] = gsw_geo_strf_McD_Klocker(SA,CT,p,Neutral_Density,p_Neutral_Density,A)

## DESCRIPTION:

    Calculates the McDougall-Klocker geostrophic streamfunction (see Eqn.
    (3.30.1) of IOC et al. (2010)).  This is the geostrophic streamfunction
    for the difference between the horizontal velocity at the pressure
    concerned, p, and the horizontal velocity at the sea surface.  It is
    designed to be used as the geostrophic streamfunction in an
    approximately neutral surface (such as a Neutral Density surface, a
    potential density surface or an omega surface (Klocker et al. (2009)).
    Reference values of Absolute Salinity, Conservative Temperature and
    pressure are found by interpolation of a one-dimensional look-up table,
    with the interpolating variable being Neutral Density (gamma_n).  This
    function calculates specific volume anomaly using the computationally
    efficient 25-term expression for specific volume in terms of SA, CT and
    p (McDougall et al., 2010).

    The first three input arguments are a series of vertical profiles, while
    the last two argumnents pertain to the (usually relatively few) surfaces
    on which the McDougall-Klocker geostrophic streamfunction is to be
    calculated.  These last two input arguments, Neutral_Density and
    p_Neutral_Density, are the Neutral density label and the pressure of
    each of the (usually relately few) surfaces.  p_Neutral_Density is the
    series of pressures where the surfaces intersect the vertical profiles.
    These surfaces do not have to be the very best approximately neutral
    surfaces; rather the onus is on the user to use a surface that is
    sufficiently neutral for his/her purpose.   The input variable
    "Neutral_Density" is used to find reference values of SA, CT and p
    by vertcal interpolation down a single reference cast.  As an
    alternative to the user supplying Neutral Density for this purpose,
    the code allows for sigma_2 to be used as the vertical interpolating
    variable instead of Neutral Density.

    Click for a more detailed description of the
    McDougall-Klocker geostrophic streamfunction.

## INPUT:

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

    Neutral_Density   =  Neutral Density anomaly                  [ kg/m^3 ]
                         (i.e. Neutral Density minus 1000 kg/m^3)
    p_Neutral_Density =  pressure of the Neutral_Density surface.

    OPTIONAL:

    A            =  if nothing is entered the programme defaults to "Neutral
                    Density" as the vertical interpolating variable.
                 = 's2' or 'sigma2', for sigma_2 as the vertical interpolating
                    variable.

    SA & CT need to have the same dimensions.
    p may have dimensions Mx1 or 1xN or MxN, where SA & CT are MxN.
    Neutral_Density & p_Neutral_Density need to have the same dimensions,
    and they need to have dimensions BxN, where B is the number of surfaces.

## OUTPUT:

    geo_strf_McD_Klocker = McDougall & Klocker (2010)            [ m^2/s^2 ]
                           geostrophic streamfunction

    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:

    For each oceanographic profile consisting of (SA, CT, p)

    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;]

    Both the "Neutral_Density" and the pressure of each of the neutral
    density surfaces needs to be pre-computed and supplied. In this
    example we are interested in only two neutral surfaces
    (26.7 & 27.8 kg/m^3)

    Neutral_Density   = [26.7; 27.8;]
    p_Neutral_Density = [ 650;  810;]

    [geo_strf_McD_Klocker, in_funnel] = ...
        gsw_geo_strf_McD_Klocker(SA,CT,p,Neutral_Density,p_Neutral_Density)

    geo_strf_McD_Klocker =           in_funnel =

       -6.2998                         1
      -13.5984                         1

## AUTHOR:

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

## VERSION NUMBER:

    2.0 (1st September, 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 section 3.30 of this TEOS-10 Manual.

    Jackett, D. R. and T. J. McDougall, 1997: A neutral density variable
     for the world’s oceans. Journal of Physical Oceanography, 27, 237-263.

    Klocker, A., T. J. McDougall and D. R. Jackett, 2009: A new method
     for forming approximately neutral surfaces.  Ocean Sci., 5, 155-172.

    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.

    McDougall, T. J. and A. Klocker, 2010: An approximate geostrophic
     streamfunction for use in density surfaces.  Ocean Modelling, 32,
     105-117.
      The McDougall-Klocker geostrophic streamfunction is defined in
     Eqn. (62) of this paper.

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