Correlated Stochastic Processes in Physical Meteorology

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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.