Isentropic Potential Vorticity

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 NCEP/NCAR Reanalysis FAQ page:

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)

Units: 1*109 m2s-1 kg-1