Mathematical Modeling and Analysis of the Rainfall Process

拟议研究的总体目标是建立改进的降雨过程模型，并寻求适当的实地数据，以协调理论和观测。这项工作将需要改进雨滴凝聚和破裂的模型公式，以便详细研究降雨过程并应用于云系统的模型。研究将集中在雨滴大小分布的预测上，雨滴大小分布描述了单位空气体积内雨滴的数量和大小。雨滴大小分布的形式在理论和实践上都很重要，因为它影响着风暴的动力学和热力学，并决定了雨从大气中去除污染物的速度。研究的具体目标是：确定当前液滴分解模型公式中的不确定性范围，确定数据采集的具体需求和数据表示中的具体问题；改进现有的竖井降雨模式，在其上边界加入云水到雨水转换的模式，并将模式解与观测到的雨滴大小分布进行比较；发展用于云系统模型的竖井内雨滴大小分布的参数化；探讨降雨强度中常见但尚未解释的振荡现象；并开发了一个全新的模型，详细描述了两个雨滴的碰撞。将积极谋求利用各种雷达获得新的实地测量结果。

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.