EVOLUTION OF RAINDROP SIZE DISTRIBUTION BY COALESCENCE, BREAKUP, AND EVAPORATION - THEORY AND OBSERVATIONS

The evolution of raindrop size distribution by coalescence, collisiona l breakup, and evaporation is studied using the Low and List parameter ization for collisions. The authors consider two models of the develop ment of raindrop size distribution; model 1 is a spatially homogeneous , time-dependent model, and model 2 is a 1D (vertical) time-dependent model. The authors present the governing equations for the drop size d istribution, balance equations for the rainwater content and rainfall rate, and scaling relationships. The authors demonstrate that the two models are intimately related. For model 1, the authors find that unde r the action of coalescence and breakup the size distribution attains a steady equilibrium form with three peaks at small drop sizes and an exponential tail at large drop sizes with a slope of approximately 65 cm(-1). Under the action of coalescence, breakup, and evaporation, the evolution of a size distribution with a high enough rainwater content can be divided into two phases. In the initial phase, the evolution i s collision controlled and the distribution evolves rapidly to approxi mate the shape of the equilibrium distribution without evaporation. Th e second phase starts after the rainwater content has been sufficientl y reduced by evaporation. In this phase the evolution is evaporation c ontrolled, the peaks at small drop sizes are smoothed, but the tail of the distribution remains exponential and its slope changes only slowl y with time. In model 2, with a steady input of raindrops at the top o f the rain shaft, a steady distribution is attained at any height afte r the lapse of a sufficiently long time. After a sufficient distance o f fall, the steady distribution becomes approximately invariant with d istance of fall and very close to the equilibrium distribution of mode l 1. With evaporation also occurring, the evolution is similar to that for model 1, with distance of fall taking on the role of time of evol ution. A comparison of the results of the calculations with observed r aindrop size distributions, at high rainfall rates, supports the idea that the observed distributions are in or near collisional equilibrium . However, the slope (20-25 cm(-1)) of the tail of the observed distri butions is much smaller than the slope (65 cm(-1)) of the computed equ ilibrium distribution. This discrepancy suggests that either the Low a nd List parameterization is greatly overestimating drop breakup and/or the number of fragments formed by collisional breakup, or processes o ther than coalescence, breakup, and evaporation are strongly controlli ng the observed raindrop size distributions. Another possible factor c ontributing to the discrepancy may be the averaging of observed raindr op size distributions over considerable periods of time. It is recomme nded that in future observations attempts be made to obtain reliable d rop size distributions in much shorter periods of time.