Encoding daily rainfall records via adaptations of the fractal multifractal method

Abstract

A deterministic geometric approach, the fractal–multifractal (FM) method, already found useful in modeling storm events, is adapted here in order to encode, for the first time, highly intermittent daily rainfall records gathered over a water year and containing many days of zero rain. Through application to data sets gathered at Laikakota in Bolivia and Tinkham in Washington, USA, it is demonstrated that the modified FM approach can represent erratic rainfall records faithfully, while using only a few FM parameters. It is shown that the modified FM approach, by capturing the rain accumulated over the season, ends up preserving other statistical attributes as well as the overall “texture” of the records, leading to FM sets that are indistinguishable from observed sets and certainly within the limits of accuracy of measured rainfall. This fact is further corroborated comparing 20 consecutive years at Laikakota and a modified FM representation, via common statistical qualifiers, such as histogram, entropy function, and inter-arrival times.