Numerical Modeling of Precipitation and Cloud Shadow Effects on Mountain-Induced Cumuli

Abstract

The effects of precipitation on a model of cumulus cloud initiation and development over mountains are studied by numerically integrating the equations of motion, equations of conservation of water substance, and the thermodynamic energy equation. The model is two-space dimensional with a vertical wind shear in a stable, incompressible atmosphere. Heating and evaporation at the valley and mountain interact with the initial ambient flow to initiate clouds which produce shadows on the surface and cut down both heating and evaporation. The model is restricted vertically to 3.5 km and horizontally to 7.0 km. Several precipitation parameters are studied in this model. One, the critical water content determines when cloud water converts to rainwater. A second, the autoconversion rate, determines how rapidly the cloud water converts to rainwater. The third parameter determines how quickly the precipitation evaporates beneath the cloud. The rainwater first forms by autoconversion and is then increased by the accretion process following techniques described by Kessler and Srivastava. Berry's formulation for autoconversion is also tested. The development of the cumulus clouds is similar for both precipitating and nonprecipitating clouds at their early stages. Virga phenomena are illustrated in these small cumulus clouds. At later stages the evaporation beneath and to the sides of the cloud makes the air cooler and creates a downdraft. Generally such effects shorten the clouds' life cycle. The shadow effects cause the clouds to move out of the model grid at a progressively faster rate and cause the clouds subsequent to the first one to be smaller. In a symmetric model integrated both with and without precipitation and with cloud shadow effects, the shadow causes multiple growths over the ridge, the third of three clouds being the only one to accelerate until impeded by the rigid upper boundary of the grid. The first two clouds dissipate shortly after formation. The downdrafts beneath the clouds are stronger in the precipitating case.