The potential vorticity principle for a nonhydrostatic, moist, precipitating atmosphere is derived. An appropriate generalization of the well-known (dry) Ertel potential vorticity is found to be P 1 (2 u) , where is the total density, consisting of the sum of the densities of dry air, airborne moisture (vapor and cloud condensate), and precipitation; u is the velocity of the dry air and airborne moisture; and T is the virtual potential
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Schubert et al. (2001) studied this question.
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