Mathematical Modeling and Analysis of the Rainfall Process

棕色/抽象 拟议研究的广泛目标是开发改进的降雨过程模型，并寻求适当的实地数据，以调和理论和观测。 这项工作将需要改进雨滴合并和分裂的模式公式，以便详细研究降雨过程和应用于云系模式。 这项研究将集中在雨滴尺寸分布的预测，描述了单位体积空气中雨滴的数量和尺寸。 水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：确定目前液滴破碎模型公式中的不确定性范围，并确定数据采集的具体需要和数据表示中的具体问题;通过将云水模型与降雨模型相结合来改进现有的竖井降雨模型，水在上边界的转化率，并将模型解与观察到的液滴尺寸分布进行比较; 发展一个用于云系模型的雨滴大小分布参数化方法;研究常见但无法解释的降雨强度振荡现象;以及发展一个全新的模型，详细描述两个雨滴的碰撞。 将积极探索利用各种雷达获得新的实地测量数据的前景。

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.