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

参数化碰撞引起的雨滴破碎的随机方法：对雨滴尺寸分布的影响

• 批准号: 0209765
• 负责人: Greg McFarquhar
• 金额: $ 20.15万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-01 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0209765&HistoricalAwards=false
• 关键词: Stochastic; Approach; Parameterizing; Collision; Induced

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.

雨滴的下落速度取决于它们的大小，当较大的雨滴覆盖较小的雨滴时，它们可能会相互碰撞。碰撞通过合并产生更大的液滴，但也可以产生更小的液滴，这是碰撞诱导的破裂的结果。要了解一组液滴在坠落和相互作用时大小的演变，需要知道每次液滴碰撞产生的液滴碎片的数量和大小，作为碰撞对大小的函数。目前还没有预测碎片大小的理论，所有这些信息都是基于实验室实验。其中最全面的是Thomas Low和Roland List的实验，他们研究了直径从0.395 mm到4.6mm的十个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，实验都重复了多次(平均140次)，并对片段进行了分析。LOW和LIST将重复试验的结果组合在一起，给出了每个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，试图利用这些结果来模拟雨滴通过碰撞和合并而产生的演化。一个具有挑战性的问题是对结果进行内插，以丢弃任意大小的配对。这个项目重新分析了原始的LOW和LIST数据--所有1369个实验的单个碎片分布，而不仅仅是10个平均分布--试图提供一个用于数值云微物理模式的液滴破碎的参数。方法是通过对每个滴对的数据进行采样和重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，还可以估计平均碎片的统计置信度--这是早期研究中缺乏的一个量。每一对的平均分布将被建模为高斯分布、对数正态分布和增量函数分布的组合。这些分布的参数及其不确定性将使用综合方法进行量化。利用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产生对滴谱演变的有意义的估计，如果是，则确定最终通过在合并和破裂之间取得平衡而实现的平衡分布的形式。这项工作对于理解降雨的发展和解释降雨的遥感观测是很重要的。