equivalent potential vorticity (EPV)

A form of potential vorticity that is a function of the three-dimensional vorticity and the gradient of equivalent potential temperature, given by the following equation:

EPV = −(∇ × u)∙∇θ_es,

where ∇ is the three-dimensional gradient operator, u is the three-dimensional velocity vector relative to the rotating earth, and θ_es 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 θ_es is sometimes set to θ_e, 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.

References:

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)