Studies of discrete fluctuations in atmospheric phenomena

Many theories of atmospheric microphysics implicitly assume that atmospheric constituents are spatially distributed in a perfectly random manner. However, empirical observation strongly suggests that aerosol particles, cloud droplets, and raindrops often exhibit spatial structure that is not consistent with a perfectly random description.; The existence of these "correlations" among particles has been investigated in some detail. Other than very brief periods of so-called "steady" rain, it seems spatial correlations may be ubiquitous among aerosol particles, cloud droplets, and raindrops. This conclusion can be verified using any number of different statistical tools. When making an effort to meaningfully quantify the deviations from pure randomness the pair-correlation function, the correlation-fluctuation theorem, and fractal analysis of the underlying data-set aid in understanding the nature and magnitude of the correlations.; The statistical properties of real aerosols, clouds, and rainfall data can be recreated by using mathematical results from point process theory. Depending on whether a statistically homogeneous or inhomogeneous description is appropriate, one can invoke an appropriate point-process model to generate realistic distributions of particles that recreate specific statistical properties of observed data.; The ultimate goal of this work is to better understand how the deviations from pure spatial randomness alter the theoretical predications made for atmospheric microphysical processes including droplet size distribution evolution and stability, radiative properties of clouds, aerosol activation, coagulation, and more practical matters like sampling considerations for Z-R relations.; In the following chapters we discuss the mathematical formulations and methodologies associated with quantifying atmospheric particulate clustering, including techniques that can be used to model spatial positions. We follow this with empirical observations of aerosol, cloud, and rain particle clustering that we attempt to quantify and model with the mathematical techniques developed earlier. We then analyze and discuss the influences of the observed clustering on problems in radar meteorology and radiation attenuation. Finally, we close by including some discussion associated with more speculative applications of particle clustering in the atmospheric sciences and elsewhere.