A MULTICOMPONENT DECOMPOSITION OF SPATIAL RAINFALL FIELDS .1. SEGREGATION OF LARGE-SCALE AND SMALL-SCALE FEATURES USING WAVELET TRANSFORMS

Issues of scaling characteristics in spatial rainfall have attracted increasing attention over the last decade. Several methods based on simple and multiscaling and multifractal ideas have been proposed and parameter estimation techniques developed for the hypothesized models. Simulations based on these models have realistic resemblance to ''generic rainfall fields.'' In this research we analyze rainfall data for scaling characteristics without an a priori assumed model. We look at the behavior of rainfall fluctuations obtained at several scales, via orthogonal wavelet transform of the data, to infer the precise nature of scaling exhibited by spatial rainfall. The essential idea behind the analysis is to segregate large-scale (long wavelength) features from small-scale features and study each of them independently. The hypothesis is set forward that rainfall might exhibit scaling in small-scale fluctuations, if at all, and at large scale this behavior will break down to accommodate the effects of external factors affecting the particular rain-producing mechanism. The validity of this hypothesis is examined. In the first of these papers we develop the methodology for the segregation of large- and small-scale features and apply it to a severe spring time midlatitude squall line storm. The second paper (Kumar and Foufoula-Georgiou, this issue) develops a framework for testing the presence and studying the nature of self-similarity in the fluctuations.