This is a provisionnal version written in June 2005 : please send any comments to Sylvie Malardel of Jean-FranÃ§ois Geleyn (you can use the forum linked to this article).
Initialy, the hydrostatic equations used in the NWP model ARPEGE/ALADIN where designed for a synoptic scale forecasting system. In this context, the description of the liquid and solid species were based on a pseudo-adiabatic concept.
In practice, in a NWP model, instantaneous transformations are replaced by transformations during one time step.
The difficulty of the hypothesis about the precipitation done in ARPEGE/ALADIN is that the precipitations never are an ingredient of the air in a parcel because they are always instantaneously evacuated, but these precipitations interacts with the moist air.