# gsw_IPV_vs_fNsquared_ratio

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

## 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".

## 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