Isentropic potential vorticity is available directly from the NCEP/NCAR 40-Year
Reanalysis CD-ROM on theta surfaces of 315 K, 330 K, and 450 K. Observations
are made at 00Z. Overlaid plots including isentropic potential vorticity show
the isentropic potential vorticity at 00Z on the date shown in the plot title.
Monthly mean vertical cross sections are also available.
The units shown here for isentropic potential vorticity are a bit different from
the units seen in textbooks and journal articles. First, note that the values
have been multiplied by 1*109 to make them easy
to read on the plots. The units are not
1*106 m2 K
s-1 kg-1 (1 PVU).
Here is an explanation from the
Units: 1*109 m2s-1 kg-1
How does NCEP/NCAR reanalysis compute the potential vorticity
on isentropic surfaces? [12/06/96]
First the static stability N**2=g/T*(dT/dz+g/cp) is computed on model levels.
Then the winds, temperature and static stability are interpolated to isentropic
surfaces linearly in log(theta). (Outside the model domain, the fields are held
constant for now and will later be compressed out of the final product.) Then
the absolute vorticity zeta is spectrally computed on the isentropic surfaces,
where the shortest wavelength in the spectral domain is about 4 grid lengths.
(The vorticity is computed in the T36 spectral domain for the 2.5x2.5 degree grid.)
The density rho=(T/theta)**(cp/R)*p0/(R*T) is also computed at this time directly
on the isentropic surfaces. Finally, the NCEP potential vorticity is computed as
zeta*N**2/(g*rho). Thus the units of NCEP PV are m**2/s/kg, which is different
from the usual units of K*m**2/s/kg; one must multiply the NCEP PV by theta to
compare them. The NCEP PV is still a form of the Ertel potential vorticity, since
log(theta) is as well conserved as theta. Packing the PV in these units is
simpler. The NCEP PV is currently rounded to the nearest 1e-10 m**2/s/kg for
packing. The physical constants used are g=9.8, R=287.05, cp=1004.6 and
omega=7.2921e-5. (by Dr. Mark Iredell)