Correlated Stochastic Processes in Physical Meteorology

这项研究的主要目标是继续探索相关性在云和降水物理、雷达气象学以及通过云的辐射传输中的作用。其数学基础是统计平稳但相关的随机过程理论。这一框架还为这一研究方案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程度的变化，其特征是计算和测量相关的相关函数。详细探讨了负关联的含义及其在涨落能级中的抑制作用。具体目标是：1.云、雨和雪的小尺度纹理：对气溶胶计数器、云探测器和视频仪的数据进行进一步的理论研究和分析，重点是与尺度相关的液滴和雨滴的聚集和反聚集。扩散对液滴增长的影响，以及通过修正的碰撞统计在暖雨启动中的作用。雷达气象学：通过雷达反射率-降雨量关系，雨滴在空间和时间上的相关性对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。阈值回波统计与目标异质性。云滴聚集和反聚集在辐射传输中的含义，如可能偏离Beer-Lambert定律，有效截面与关联长度的显式表达式以及路径长度统计。这项研究可能会对云滴的增长和降水的开始产生广泛的影响，改进降雨空间结构的特征，以便更好地利用天气雷达估计降雨量，以及云的辐射特性。该程序还具有内在的智力优势，因为对相关涨落的基础研究可能会对随机介质的结构、流体混合、信号分析和非均质材料中的光衰减产生深刻的见解。

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.