Encoding hydrologic information via a fractal geometric approach and its extensions

We present the application of a deterministic fractal geometric approach—the so-called fractal-multifractal procedure, FMFP—to the modeling of hydrologic data at different resolutions. The FMFP can generate a wide range of complex patterns that are virtually indistinguishable from observed hydrologic data sets (e.g., rainfall series, radar images, clouds, contamination plumes, width functions). We illustrate the use of the FMFP for hydrologic data encoding and model simplification by comparing a few representative rainfall time series to FMFP-generated patterns. We also present the time evolution of two-dimensional FMFP-patterns reminiscent of rainfall-radar images. As the deterministic FMFP-generated patterns are completely characterized by a small number of geometric parameters, we discuss the prospect of compact descriptions of hydrologic data sets. We also discuss how this parsimonious deterministic parameterization may eventually lead to the classification of patterns and simplification in the records’ parameter space. Finally, we highlight some connections between the FMFP and nonlinear and chaotic dynamics