A Stochastic Approach for Parameterizing Collision-Induced Breakup of Raindrops: Implications for Raindrop Size Distributions

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Raindrops fall with speeds that depend on their size, and can collide with each other as the larger drops overtake smaller ones. The collisions create still larger drops by coalescence but can also generate smaller droplets as a result of collision-induced breakup. To understand the evolution of the sizes of a population of drops as they fall and interact requires knowing the numbers and sizes of the droplet fragments produced by every drop collision, as a function of the sizes of the colliding pair. There is no theory that predicts the fragment sizes, and all such information is based on laboratory experiments. The most comprehensive of these are the experiments of Thomas Low and Roland List, who investigated the fragment size distributions produced by ten drop-pair combinations over the diameter range from 0.395 to 4.6 mm. For each of the ten combinations, the experiment was repeated many times (on the average, 140) and the fragments analyzed. Low and List combined the results of the repeated trials to give the average fragment size distribution for each of the drop-pair combinations. Other researchers have worked with these average distributions, seeking ways to use the results for modeling raindrop evolution by collisions and coalescence. A challenging problem is to interpolate the results to drop pairs of arbitrary size. This project reanalyzes the original Low and List data - the individual fragment distributions from all 1369 experiments, not just the ten average distributions - in an attempt to provide a parameterization of drop breakup for use in numerical cloud microphysical models. The approach is to create a much larger data set synthetically by sampling and resampling the data for each of the drop pairs. This enables an estimate of not only the average fragment distribution but also the statistical confidence of the average - a quantity lacking in earlier studies. The average distributions for each pair will be modeled as combinations of Gaussian, lognormal, and delta-function distributions. The parameters of these distributions, and their uncertainty, will be quantified using the synthetic approach. Numerical studies using the new information on fragment distributions will determine whether the Low and List data, with their attendant uncertainty, are capable of producing meaningful estimates of drop-spectrum evolution and, if so, the form of the equilibrium distribution that is eventually achieved by a balance between coalescence and breakup. This work is important for understanding the development of rain and for interpreting remotely-sensed observations of rain.