Correlated Stochastic Processes in Physical Meteorology

对云滴和雨滴的观测表明，水滴浓度作为一个随机变量，可能具有偏离泊松分布的概率分布，如果水滴在任何地方具有相等的概率并且彼此独立，则可以预期这种分布。因此，据说水滴有聚集的倾向。在任何给定的时间，空间的某些区域可能比泊松分布的预期浓度高，而其他区域可能低。这些偏差可以用对相关函数来定量表征，而对相关函数又与液滴浓度的空间自相关函数有关。在相关随机过程理论的基础上，本项目有三个目标：1。通过对云探测器和云差仪数据的分析，提高对云和雨的精细尺度结构的认识；评估碰撞和凝聚对液滴生长的影响。确定聚类是否会在云和降水的雷达信号中产生相干散射分量；设计识别这个组件的方法。研究聚类对辐射传递的影响；特别是，确定聚类是否可以解释与比尔-朗伯消光定律的偏差。这项工作通过提供对跌落种群的随机变异性的更完整的描述，为云物理的基础做出了贡献。它可以使人们更好地了解云滴聚结形成雨的过程，并改进云遥感的方法。

Observations of cloud droplets and raindrops indicate that the drop concentration, regarded as a random variable, may have a probability distribution that deviates from the Poisson distribution, which would be expected if the drops had equal probability of being located anywhere and were independent of each other. Drops therefore are said to have a tendency to cluster. At any given time, some regions of space may have greater concentrations than expected for a Poisson distribution and other regions less. The deviations may be characterized quantitatively by the pair-correlation function, which in turn is related to the spatial autocorrelation function of drop concentration. Building on the theory of correlated stochastic processes, this project has three objectives:1. Advance the understanding of the fine-scale structure of clouds and rain by analyzing data from cloud probes and disdrometers; assess the implications for droplet growth by collisions and coalescence.2. Determine whether clustering can give rise to a coherent scattering component in radar signals from clouds and precipitation; devise methods to recognize this component.3. Study the effects of clustering on radiative transfer; in particular, determine whether clustering can explain deviations from the Beer-Lambert law of extinction.The work contributes to the foundations of cloud physics by providing a more complete description of the random variability of drop populations. It may lead to improved understanding of rain formation by coalescence of cloud droplets and to a refinement of methods of cloud remote sensing.