# gsw_IPV_vs_fNsquared_ratio

    Ratio of the vertical gradient of potential
    density (with reference pressure, p_ref), to
    the vertical gradient of locally-referenced
    potential density (75-term equation)

## Contents

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

## USAGE:

    [IPV_vs_fNsquared_ratio, p_mid] =
                                 gsw_IPV_vs_fNsquared_ratio(SA,CT,p,p_ref)

## 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 (see Eqn. (3.20.17) of IOC et al. (2010)).
    The reference sea pressure of the potential density surface must have
    a constant value.

    IPV_vs_fNsquared_ratio is evaluated at the mid pressure between
    the individual data points in the vertical. This function uses the
    computationally-efficient 75-term expression for specific volume in
    terms of SA, CT and p (Roquet et al., 2015).

    Note that the 75-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. (2003).  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
    IPV vs fNsquared ratio.

## 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 sea pressure of the potential density surface
                                                                    [ dbar ]
    SA & CT need to have the same dimensions.
    p & p_ref may have dimensions 1x1 or 1xN or MxN, where SA & CT are MxN.

## OUTPUT:

    IPV_vs_fNsquared_ratio
                       =  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 is ouput on the same
                          vertical (M-1)xN grid as p_mid.
                          IPV_vs_fNsquared_ratio 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 ]

## 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;]
    p_ref = 0

    [IPV_vs_fNsquared_ratio, p_mid] = ...
                                  gsw_IPV_vs_fNsquared_ratio(SA,CT,p,p_ref)

    IPV_vs_fNsquared_ratio =

       0.999742244888022
       0.996939883468178
       0.986141997098021
       0.931595598713477
       0.861224354872028

    p_mid =

    1.0e+002 *

       0.300000000000000
       0.875000000000000
       1.875000000000000
       4.250000000000000
       8.000000000000000

## AUTHOR:

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

## VERSION NUMBER:

    3.05 (3rd June, 2016)

## 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, D.G. Wright and R. Feistel, 2003:
     Accurate and computationally efficient algorithms for potential
     temperature and density of seawater.  J. Atmosph. Ocean. Tech., 20,
     pp. 730-741.

    Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
     polynomial expressions for the density and specifc volume of seawater
     using the TEOS-10 standard. Ocean Modelling.

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