Evaporation and Precipitation Surface Effects in Local Mass Continuity Laws of Moist Air

The local mass balance equations of cloudy air are formulated for a model system composed of dry air, water vapor, and four categories of water condensate particles, as typically adopted for numerical weather prediction and climate models. The choice of the barycentric velocity as reference motion provides the most convenient form of the total mass continuity equation. Mass transfer across the earth’s surface due to precipitation and evaporation causes a nonvanishing barycentric vertical velocity ws and is proportional to the local difference between evaporation rate and rain plus snow rate. Hence ws vanishes only in the special situation that evaporation and precipitation balance exactly. Alternative concepts related to different reference motions are reviewed. However, the choice of the barycentric velocity turns out to be advantageous for several reasons. The implication of the nonvanishing total mass transport across the earth’s surface is estimated from model simulations for two extreme weather situations: a polar cold air outbreak and a tropical cyclone. While the effect is small in the first case, it is important in the latter. The large precipitation rates in the tropical cyclone case cause a loss of atmospheric mass, which corresponds to a vertical velocity at the surface larger than −20 mm s−1, and an instantaneous drop in pressure, which if sustained for 6 h, would correspond to about 49 hPa; this demonstrates the necessity of using the correct formulation of the mass balance in simulation models for moist air.