Mathematical Modeling and Analysis of the Rainfall Process

布朗/摘要拟议研究的广泛目标是开发改进的降雨过程模型，并寻找适当的现场数据，以便使理论和观测结果相一致。这项工作将需要改进雨滴合并和分解的模型公式，以便详细研究降雨过程并应用于云系模型。这项研究将集中在雨滴大小分布的预测上，该分布描述了单位体积空气中的雨滴数量和大小。水滴大小分布的形式在理论上和实践上都很重要，因为它影响风暴的动力学和热力学，并决定了雨水从大气中清除污染物的速度。研究的具体目标是：确定目前水滴破碎模式公式中的不确定性范围，并确定对数据获取和数据表示方面的具体需要；通过在上边界采用云-水-雨-水转换模式来改进现有的竖井降雨模式，并将模型解与观测到的雨滴大小分布进行比较；开发竖井内雨滴尺寸分布的参数，用于云系模式；调查常见但无法解释的降雨强度振荡现象；以及开发一个详细说明两个雨滴碰撞情况的全新模式。将积极探索利用各种雷达获取新的现场测量数据的前景。

Brown/Abstract The broad objective of the proposed research is to develop improved models of the rainfall process and to seek appropriate field data in order to reconcile theory and observation. The work will entail improved model formulation of raindrop coalescence and breakup for detailed study of the rain process and for application in models of cloud systems. The research will focus on prediction of the raindrop size distribution that describes the number and sizes of drops within a unit volume of air. The form of the drop size distribution is of both theoretical and practical importance, as it affects the dynamics and thermodynamics of the storm and determines the rate at which the rain removes pollutants from the atmosphere. Specific objectives of the research are: to determine the range of uncertainty in the current model formulation of drop breakup and to identify specific needs for data acquisition and qpecific problems in data representation; to improve an existing model of rainfall in a vertical shaft by incorporating a model of cloud-water to rain-water conversion at the upper boundary and to compare the model solutions with observed drop size distributions; to develop a parameterization of the raindrop size distribution within the shaft for use in models of cloud systems; to investigate the common but unexplained phenomenon of oscillation in rainfall intensity; and to develop an entirely new model that details the collision of two raindrops. The active prospect of obtaining new field measurements, using various radars, will be pursued.