A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere

Abstract

This paper discusses the generalization of ERTEL's PV to a cloudy, precipitating atmosphere. The recommended generalization is P = ρ -1 ζ . ⊇θ ρ , where p is the total density of moist air, ζ is the absolute vorticity, and θ ρ is the virtual potential temperature. Associated with this form are three important properties: (1) the solenoidal term is annihilated (i.e., ⊇θ ρ . (⊇ ρ x Vp) = 0, where p is the total pressure, the sum of the partial pressures of dry air and water vapor); (2) the limiting form for a dry atmosphere is the classical ERTEL PV; (3) P is invertible, i.e., it carries all the necessary dynamical information about the balanced wind and mass fields. Two other possible generalizations are discussed, ρ -1 ζ . ⊇θ e and ρ -1 ζ . ⊇θ* e , where θ e is the equivalent potential temperature and θ* e is the saturation equivalent potential temperature. The former is rejected because properties (1) and (3) are lost, while the latter is rejected because property (2) is lost.