An effective inversion strategy for fractal–multifractal encoding of a storm in Boston

Hydrologic data sets such as precipitation records typically feature complex geometries that are difficult to represent as a whole using classical stochastic methods. In recent years, we have developed variants of a deterministic procedure, the fractal–multifractal (FM) method, whose patterns share not only key statistical properties of natural records but also the fine details and textures present on individual data sets. This work presents our latest efforts at encoding a celebrated rainfall data set from Boston and shows how a modified particle swarm optimization (PSO) procedure yields compelling solutions to the inverse problem for such a set. As our FM fits differ from the actual data set by less than 2% in maximum cumulative deviations and yield compression ratios ranging from 76:1 to 228:1, our models can be considered, for all practical purposes, faithful and parsimonious deterministic representations of the storm.