A statistical analysis of mesoscale rainfall as a random cascade

Abstract

The paper considers the random cascade theory for spatial rainfall. Particular attention was given to the following four areas: (1) the relationship of the random cascade theory of rainfall to the simple scaling and the hierarchical cluster-point-process theories, (2) the mathematical foundations for some of the formalisms commonly applied in the develpment of statistical cascade theory, (3) the empirical evidence for a random cascade theory of rainfall, and (4) the way of using data for making estimates of parameters and for making statistical inference within this theoretical framework. An analysis of space-time rainfall data is presented. Cascade simulations are carried out to provide a comparison with methods of analysis that are applied to the rainfall data.