On the unified theory of atmospheric particle systems part ii: self–affine particles

As the second attempt at unifying treatment of atmospheric particle systems, this paper further examines shape characterization of atmospheric particles. First, to support the theoretical framework developed in Part I, methods for studying non-spherical particles are reviewed. It is argued that these different methods can be unified under fractal geometry through the generalized power laws given in Part I. Empirical power-laws for hydrometeors scattered in literature since 1935 are summarized and reevaluated in terms of fractals. Second, generalization from self-similar to self-afflne particles is discussed. Self-affinity of atmospheric particles is exemplified by examining the exponents in the power laws between the length along a- and c-axis of ice crystals. It is argued that unlike Euclidean and self-similar particles, self-affine particles do not have a simple dimensional relation between original particles and their projections; the relation for projection of self-similar particles and Mandelbrot’ thumb rules for intersection respectively set the lower and upper bound. Using published data, self-affine particles are shown to exist in the atmosphere. The existence of self-affine particles in turn calls for instruments that can simultaneously measure mass, area and maximum diameter (or their equivalents).