Correlated Stochastic Processes in Physical Meteorology

这项研究的主要目标是继续探索云和降水物理学，雷达气象学，并通过云的辐射传输的相关性的作用。数学基础是统计平稳但相关的随机过程理论。该框架还为该研究计划提供了一个统一的主题：空间和时间的相关性以及由此产生的波动水平的变化，其特征在于相关相关函数的计算和测量。负相关的影响和由此产生的抑制波动水平进行了详细的探讨。具体目标是：1.云、雨和雪的小尺度结构：对来自气溶胶计数器、云探测器和视频散射计的数据的进一步理论研究和分析，重点是尺度依赖的液滴和雨滴聚束和反聚束。通过修正的碰撞动力学，扩散和波动在暖雨启动中的作用对液滴增长的影响。雷达气象学：雨滴在空间和时间上的相关性对通过雷达反射率-降雨关系进行定量降雨测量的影响;雷达回波的非瑞利信号统计，以及同相/正交雷达随机特征。阈值回波统计和目标非均匀性.在辐射传输中液滴聚束和反聚束的影响，例如可能偏离Beer-Lambert定律，有效截面与相关长度和路径长度统计的显式表达式。这项研究可能对云滴增长和降水开始产生广泛影响，改进降雨空间结构的表征，以便更好地用天气雷达估计降雨，云的辐射特性。该计划也具有内在的智力价值，因为相关波动的基础研究可能会产生对随机介质结构，流体混合，信号分析和非均匀材料中的光衰减的见解。

The primary objective of this research is to continue exploring the role of correlations in cloud and precipitation physics, radar meteorology, and in radiative transfer through clouds. The mathematical basis is the theory of statistically stationary but correlated stochastic processes. This framework also provides a unifying theme for this research program: correlations in space and time and the resulting change in the level of fluctuations as characterized by calculations and measurements of relevant correlation functions. The implications of negative correlations and the resulting suppression in fluctuation level are explored in detail. The specific objectives are:1. Small scale texture of clouds, rain and snow: further theoretical investigation and analysis of data from aerosol counters, cloud probes and video disdrometers with emphasis on scale-dependent droplet and raindrop bunching and anti-bunching. Implications in droplet growth by diffusion and the role of fluctuations in warm rain initiation via modified collision statistics.2. Radar meteorology: implications of raindrop correlations in space and time on quantitative rainfall measurements via radar reflectivity-rainfall relations; non-Rayleigh signal statistics of radar echoes, and in-phase/quadrature radar stochastic signatures. Threshold echo statistics and target heterogeneity.3. Implications of droplet bunching and anti-bunching in radiative transfer such as possible deviations from the Beer-Lambert law, explicit expressions for the effective cross-section vs. correlation length and for the path-length statistics.This research is likely to have broad impacts with respect to the cloud droplet growth and onset of precipitation, improved characterization of rainfall spatial structure for better rainfall estimation with weather radar, and radiative properties of clouds. This program is also of intrinsic intellectual merit because the basic study of correlated fluctuations is likely to yield insights into structure of random media, fluid mixing, signal analysis, and light attenuation in heterogeneous materials.