Correlated Stochastic Processes in Physical Meteorology

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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.