# gsw_geo_strf_McD_Klocker_pc

    McDougall-Klocker geostrophic streamfunction
    for piecewise constant profiles

## Contents

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

## USAGE:

    [geo_strf_McD_Klocker_pc, p_mid, in_funnel] = gsw_geo_strf_McD_Klocker_pc(SA,CT,delta_p,gamma_n,layer_indx,A)

## DESCRIPTION:

    Calculates the McDougall-Klocker geostrophic streamfunction
    (see Eqn. (3.30.1) of IOC et al. (2010)).  This function is to used
    when the Absolute Salinity and Conservative Temperature are piecewise
    constant in the vertical over sucessive pressure intervals of delta_p
    (such as in a forward "z-coordinate" ocean model, and in isopycnal
    layered ocean models).  The McDougall-Klocker geostrpohic streamfunction
    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) or
    sigma_2.

    Click for a more detailed description of the
    McDougall-Klocker geostrophic streamfunction
    for piecewise constant profiles

## INPUT:

    SA         =  Absolute Salinity                                 [ g/kg ]
    CT         =  Conservative Temperature                         [ deg C ]
    delta_p    =  difference in sea pressure between the deep and shallow
                  extents of each layer in which SA and CT are vertically
                  constant.  delta_p must be positive.              [ dbar ]
    Note. Sea pressure is absolute pressure minus 10.1325 dbar.

    gamma_n    =  Neutral Density anomaly                         [ kg/m^3 ]
                  (i.e. Neutral Density minus 1000 kg/m^3)
    layer_indx =  Index of the layers of the gamma_n surfaces

    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 & delta_p need to have the same dimensions.
    gamma_n & layer_indx need to have the same dimensions, there should be
    only one "gamma_n" or "sigma_2" value per level of interest.
    A needs to be 1x1.

## OUTPUT:

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

    p_mid                   =  mid-point pressure in each layer     [ 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;]
    delta_p = [     10;      40;      75;     125;     350;     400;]

    gamma_n    =  [26.7; 27.8;]
    layer_indx =  [   3;    5;]

    [geo_strf_McD_Klocker_pc, p_mid, in_funnel] = ...
                gsw_geo_strf_McD_Klocker_pc(SA,CT,delta_p,gamma_n,layer_indx)

    geo_strf_McD_Klocker_pc =

      -5.2753
     -10.3684

    p_mid =

      87.5000
     425.0000

    in_funnel =

        1
        1

## AUTHOR:

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

## VERSION NUMBER:

    2.0 (17th 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.
      See section 8 of this paper for a discussion of this piecewise-
     constant version of the McDougall-Klocker geostrophic streamfunction.

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