# gsw_geo_strf_isopycnal

    approximate isopycnal geostrophic streamfunction

## Contents

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

## USAGE:

    geo_strf_isopycnal = gsw_geo_strf_isopycnal(SA,CT,p,p_ref,Neutral_Density,p_Neutral_Density,A)

## DESCRIPTION:

    Calculates the approximate isopycnal geostrophic streamfunction as
    defined in McDougall-Klocker (2010)  (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 reference pressure, p_ref.  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 48-term expression for
    specific volume anomaly in terms of SA, CT and p (McDougall et al., 2011).

    The first three input arguments are a series of vertical profiles.  The
    fourth argument, p_ref, is the reference pressure to which the stream
    function is referenced.  When p_ref is zero, gsw_geo_strf_isopycnal
    returns the isopycnal geostrophic streamfunction with respect to the sea
    surface, otherwise, the function returns the geostrophic streamfunction
    with respect to the (deep) reference pressure p_ref.  The last three
    arguments pertain to the (usually relatively few) surfaces on which the
    isopycnal geostrophic streamfunction is to be calculated.  The two input
    arguments, Neutral_Density and p_Neutral_Density, are the Neutral
    Density label and the pressure of each of the (usually relatively 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 their
    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
    approximate isopycnal geostrophic streamfunction.

## INPUT:

    SA    =  Absolute Salinity                                      [ g/kg ]
    CT    =  Conservative Temperature                              [ deg C ]
    p     =  sea pressure                                           [ dbar ]
             ( i.e. absolute pressure - 10.1325 dbar )
    p_ref =  reference pressure                                     [ dbar ]
             ( i.e. reference 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.
    p_ref needs to be a unique value, it can have dimensions Mx1 or 1xN or
    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_isopycnal = isopycnal geostrophic streamfunction    [ m^2/s^2 ]
                         as defined by McDougall & Klocker (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;]
    p_ref = 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_isopycnal = ...
        gsw_geo_strf_isopycnal(SA,CT,p,p_ref,Neutral_Density,p_Neutral_Density)

    geo_strf_isopycnal =

      11.588574940289062
       4.278512371505300

## AUTHOR:

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

## VERSION NUMBER:

    3.01 (18th May, 2011)

## 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., P.M. Barker, R. Feistel and D.R. Jackett, 2011:  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 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