Equivalent potential vorticity
equivalent potential vorticity (EPV)
EPV = −(∇ × u)∙∇θes,
where ∇ is the three-dimensional gradient operator, u is the three-dimensional velocity vector relative to the rotating earth, and θes is saturated equivalent potential temperature.
When the atmosphere is statically and inertially stable, EPV can be used in diagnosing the existence of moist symmetric instability, which when released would produce slantwise convection. When used as a diagnostic tool for moist symmetric instability, u is sometimes set to the geostrophic wind and θes is sometimes set to θe, the equivalent potential temperature.
Historically, it was believed that diagnosing EPV would be useful when forecasting the potential for narrow bands of heavier precipitation, especially for winter storms. Now it is recognized that the release of conditional instability and inertial instability can also lead to narrow precipitation bands.
McCann, D. W., 1995: Three-dimensional computations of equivalent potential vorticity. Wea. Forecasting, 10, 798–802, doi:10.1175/1520-0434(1995)010<0798:TDCOEP>2.0.CO;2.
Schultz, D. M., and P. N. Schumacher, 1999: The use and misuse of conditional symmetric instability. Mon. Wea. Rev., 127, 2709–2732, doi:10.1175/1520-0493(1999)127<2709:TUAMOC>2.0.CO;2; Corrigendum, 128, 1573, doi:10.1175/1520-0493(1999)127<1573:CORRIG>2.0.CO;2.
(Term added 5/23/2014, edited 8/8/2014)