Parallel Algorithms for Multifractal Analysis of River Networks

Abstract

The dynamical properties of many natural phenomena can be related to their support fractal dimension. A relevant example is the connection between flood peaks produced in a river basin, as observed in flood hydrographs, and the multi-fractal spectrum of the river itself, according to the Multifractal Instantaneous Unit Hydrograph (MIUH) theory. Typically, the multifractal analysis of river networks is carried out by sampling large collections of points belonging to the river basin and analyzing the fractal dimensions and the Lipschitz-Hölder exponents of singularities through numerical procedures which involve different degrees of accuracy in the assessment of such quantities through different methods (box-counting techniques, the generalized correlation integral method by Pawelzik and Schuster (1987), the fixed-mass algorithms by Badii and Politi (1985), being some relevant examples). However, the higher accuracy in the determination of the fractal dimensions requires considerably higher computational times. For this reason, we recently developed a parallel version of some of the cited multifractal methods described above by using the MPI parallel library, by reaching almost optimal speed-ups in the computations. This will supply a tool for the assessment of the fractal dimensions of river networks (as well as of several other natural phenomena whose embedding dimension is 2 or 3) on massively parallel clusters or multi-core workstations.