Evolution of Raindrop Size Distribution by Coalescence, Breakup, and Evaporation: Theory and Observations

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  • 1 Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois
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Abstract

The evolution of raindrop size distribution by coalescence, collisional breakup, and evaporation is studied using the Low and List parameterization for collisions. The authors consider two models of the development of raindrop size distribution; model 1 is a spatially homogeneous, time-dependent model, and model 2 is a ID (vertical) time-dependent model. The authors present the governing equations for the drop size distribution, 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 under 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 is collision controlled and the distribution evolves rapidly to approximate the shape of the equilibrium distribution without evaporation. The second phase starts after the rainwater content has been sufficiently reduced by evaporation. In this phase the evolution is evaporation controlled, the peaks at small drop sizes are smoothed, but the tail of the distribution remains exponential and its slope changes only slowly with time. In model 2, with a steady input of raindrops at the top of the rain shaft, a steady distribution is attained at any height after the lapse of a sufficiently long time. After a sufficient distance of fall, the steady distribution becomes approximately invariant with distance of fall and very close to the equilibrium distribution of model 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 evolution. A comparison of the results of the calculations with observed raindrop 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 distributions is much smaller than the slope (65 cm−1) of the computed equilibrium distribution. This discrepancy suggests that either the Low and List parameterization is greatly overestimating drop breakup and/or the number of fragments formed by collisional breakup, or processes other than coalescence, breakup, and evaporation are strongly controlling the observed raindrop size distributions. Another possible factor contributing to the discrepancy may be the averaging of observed raindrop size distributions over considerable periods of time. It is recommended that in future observations attempts be made to obtain reliable drop size distributions in much shorter periods of time.

Abstract

The evolution of raindrop size distribution by coalescence, collisional breakup, and evaporation is studied using the Low and List parameterization for collisions. The authors consider two models of the development of raindrop size distribution; model 1 is a spatially homogeneous, time-dependent model, and model 2 is a ID (vertical) time-dependent model. The authors present the governing equations for the drop size distribution, 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 under 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 is collision controlled and the distribution evolves rapidly to approximate the shape of the equilibrium distribution without evaporation. The second phase starts after the rainwater content has been sufficiently reduced by evaporation. In this phase the evolution is evaporation controlled, the peaks at small drop sizes are smoothed, but the tail of the distribution remains exponential and its slope changes only slowly with time. In model 2, with a steady input of raindrops at the top of the rain shaft, a steady distribution is attained at any height after the lapse of a sufficiently long time. After a sufficient distance of fall, the steady distribution becomes approximately invariant with distance of fall and very close to the equilibrium distribution of model 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 evolution. A comparison of the results of the calculations with observed raindrop 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 distributions is much smaller than the slope (65 cm−1) of the computed equilibrium distribution. This discrepancy suggests that either the Low and List parameterization is greatly overestimating drop breakup and/or the number of fragments formed by collisional breakup, or processes other than coalescence, breakup, and evaporation are strongly controlling the observed raindrop size distributions. Another possible factor contributing to the discrepancy may be the averaging of observed raindrop size distributions over considerable periods of time. It is recommended that in future observations attempts be made to obtain reliable drop size distributions in much shorter periods of time.

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