# gsw_IPV_vs_fNsquared_ratio_CT25

    Ratio of the vertical gradient of potential
    density (with reference pressure, pr), to
    the vertical gradient of locally-referenced
    potential density (25-term equation)

## Contents

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

## USAGE:

    [IPV_vs_fNsquared_ratio_CT25, p_mid, in_funnel] =
                                 gsw_IPV_vs_fNsquared_ratio_CT25(SA,CT,p,pr)

## DESCRIPTION:

    Calculates the ratio of the vertical gradient of potential density to
    the vertical gradient of locally-referenced potential density.  This
    ratio is also the ratio of the planetary Isopycnal Potential
    Vorticity (IPV) to f times N^2, hence the name for this variable,
    IPV_vs_fNsquared_ratio_CT25 (see Eqn. (3.20.5) of IOC et al. (2010)).
    The reference sea pressure of the potential density surface must have
    a constant value.
    IPV_vs_fNsquared_ratio_CT25 is evaluated at the mid pressure between
    the individual data points in the vertical. This function uses the
    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
    IPV vs fNsquared_ratio.

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    CT  =  Conservative Temperature                                [ deg C ]
    p   =  sea pressure                                             [ dbar ]
           (ie. absolute pressure - 10.1325 dbar)
    pr  =  reference sea pressure of the potential density surface
                                                                    [ dbar ]
    SA & CT need to have the same dimensions.
    p & pr may have dimensions 1x1 or 1xN or MxN, where SA & CT are MxN.

## OUTPUT:

    IPV_vs_fNsquared_ratio_CT25
                       =  The ratio of the vertical gradient of potential
                          density referenced to pr, to the vertical gradient
                          of locally-referenced potential density.
                          IPV_vs_fNsquared_ratio_CT25 is ouput on the same
                          vertical (M-1)xN grid as p_mid.
                          IPV_vs_fNsquared_ratio_CT25 is dimensionless
                                                                [ unitless ]
    p_mid              =  mid pressure between the individual points of the
                          p grid. That is, p_mid is on a (M-1)xN grid.
                          p_mid has units of dbar.                  [ 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;]
    pr = 0;

    [IPV_vs_fNsquared_ratio_CT25, p_mid, in_funnel] = ...
                                  gsw_IPV_vs_fNsquared_ratio_CT25(SA,CT,p,pr)

    IPV_vs_fNsquared_ratio_CT25 =

     0.999732065602075
     0.996910961630710
     0.986201941290951
     0.931201954034279
     0.859810378247326

    p_mid =

    1.0e+002 *

     0.300000000000000
     0.875000000000000
     1.875000000000000
     4.250000000000000
     8.000000000000000

    in_funnel =

       1
       1
       1
       1
       1

## AUTHOR:

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

## VERSION NUMBER:

    2.0 (23rd 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 Eqn. (3.20.5) 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