A Deterministic Geometric Representation of Temporal Rainfall: Results for a Storm in Boston

Abstract

The use of a deterministic fractal‐multifractal (FM) representation to model high‐resolution rainfall time series via projections of fractal interpolating functions weighed by multifractal measures is reported. It is shown that the intrinsic shape and variability of an 8‐hour Boston storm recorded every 15 s on October 25, 1980, may be encoded wholistically, employing the fractal geometric methodology. It is illustrated that the FM methodology provides very faithful descriptions of both major trends and small (noisy) fluctuations for this storm, resulting in preservation of not only classical statistical characteristics of the records but also multifractal and chaotic properties present in them. These results, and those for other storms, suggest that a stochastic framework for rainfall may be bypassed in favor of a deterministic representation based on projections.