Analysis and Parameterization of the Combined Coalescence, Breakup, and Evaporation Processes

Philip S. Brown Jr. Mathematics Department, Trinity College, Hartford, Connecticut

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Abstract

A parameterization of raindrop coalescence and breakup has been extended to include evaporation. The parameterization is developed through analysis of accurate numerical solutions of the coalescence/breakup/evaporation equation. Modeled drop size distributions are found to evolve first toward a trimodal form characteristic of the equilibrium distribution that occurs when only collisional processes are at work. With sustained evaporation, the trimodality disappears and a unimodal-type drop size distribution emerges. The results imply that the trimodal form occurs when collisional processes are dominant but that a unimodal distribution prevails as the water mass is reduced. The mass reduction causes collisions to become infrequent and allows evaporation to deplete the small-sized raindrop population. When subjected to continued evaporation, the coalescence/breakup equilibrium itself undergoes a transition from trimodal to unimodal form, and it is this evolving form toward which all other drop size distributions converge. In the transition, the liquid water content decreases exponentially with a time constant of 300 S−1 s, where S is the saturation deficit; furthermore, the shape of the evaporating distribution is determined by the ratio of the liquid water content to the saturation deficit. The parameterization procedure makes use of the analysis results in order to describe system behavior.

Abstract

A parameterization of raindrop coalescence and breakup has been extended to include evaporation. The parameterization is developed through analysis of accurate numerical solutions of the coalescence/breakup/evaporation equation. Modeled drop size distributions are found to evolve first toward a trimodal form characteristic of the equilibrium distribution that occurs when only collisional processes are at work. With sustained evaporation, the trimodality disappears and a unimodal-type drop size distribution emerges. The results imply that the trimodal form occurs when collisional processes are dominant but that a unimodal distribution prevails as the water mass is reduced. The mass reduction causes collisions to become infrequent and allows evaporation to deplete the small-sized raindrop population. When subjected to continued evaporation, the coalescence/breakup equilibrium itself undergoes a transition from trimodal to unimodal form, and it is this evolving form toward which all other drop size distributions converge. In the transition, the liquid water content decreases exponentially with a time constant of 300 S−1 s, where S is the saturation deficit; furthermore, the shape of the evaporating distribution is determined by the ratio of the liquid water content to the saturation deficit. The parameterization procedure makes use of the analysis results in order to describe system behavior.

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