[IPV_vs_fNsquared_ratio, p_mid] =
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".
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.
= 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 ]
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] = ...
Trevor McDougall and Paul Barker [ email@example.com ]
3.05 (3rd June, 2016)
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,
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