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

雨滴落下的速度取决于它们的大小，并且当较大的雨滴超过较小的雨滴时，它们会相互碰撞。 碰撞通过聚结产生更大的液滴，但也可以由于碰撞诱导的分裂而产生更小的液滴。 为了理解液滴群体在它们下落和相互作用时的大小的演变，需要知道由每次液滴碰撞产生的液滴碎片的数量和大小，作为碰撞对的大小的函数。 没有理论可以预测碎片的大小，所有这些信息都是基于实验室实验。 其中最全面的是托马斯洛和罗兰李斯特的实验，他们研究了直径范围从0.395到4.6毫米的十种液滴对组合产生的碎片尺寸分布。对于十种组合中的每一种，实验重复多次（平均140次）并分析碎片。 Low和List结合了重复试验的结果，给出了每个液滴对组合的平均片段大小分布。 其他研究人员已经研究了这些平均分布，寻找方法来利用这些结果来模拟雨滴通过碰撞和合并的演变。 一个具有挑战性的问题是插值的结果丢弃任意大小的对。 该项目重新分析了原始的Low和List数据-来自所有1369个实验的单个碎片分布，而不仅仅是10个平均分布-试图提供用于数值云微物理模型的液滴破碎参数化。 该方法是通过对每个液滴对的数据进行采样和重新采样来综合创建更大的数据集。 这使得不仅可以估计平均碎片分布，而且可以估计平均值的统计置信度-这是早期研究中缺乏的量。 每对的平均分布将建模为高斯、对数正态和δ函数分布的组合。 这些分布的参数及其不确定性将使用合成方法进行量化。 利用关于碎片分布的新信息进行的数值研究将确定Low和List数据及其伴随的不确定性是否能够对液滴谱演变作出有意义的估计，如果能够，则确定最终通过合并和分裂之间的平衡而实现的平衡分布的形式。 这项工作对于了解降雨的发展和解释降雨的遥感观测具有重要意义。

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.