A parallel code for fixed mass multifractal analysis.

Abstract:

Many objects of geophysical interest are multifractals, in the sense that they have complicated structures made of self-similar branches or corrugations. The geometric properties of such objects influence their physical behaviour. A typical example, important in hydrology, are the river basins, which have a branching structure. When such branches are filled up with water during precipitations, the resulting flood hydrographs at the outlet of the river network will depend on this branching structure. Some hydrographic models, in particular the Multifractal Instantaneous Unit Hydrograph (MIUH) correlate the flood peaks with the multifractal spectrum of the river network. Therefore, a precise determination of such multifractal spectrum is of utmost importance for the flood forecasting.

Historically, this has been accomplished by picking up a representative sample of points of the river basins (net-points) and carrying out a multifractal analysis of such sample through several methods. Fixed-mass methods, like the famous “box-counting” technique, are easier to implement and faster to run on practical cases, but they generally give much less precise predictions in the zones of the river basin in which the density of the net-points is low. Fixed-mass methods, on the contrary, supply more precise values for the multifractal spectrum, but they are much more complicated to implement and the numerical computation generally takes very long times to be carried out. In this work, we present an efficient parallel code that allows the implementation of the fixed-mass method for considerably high number of net-points. The code uses an hybrid MPI-OpenMP approach to achieve a parallelization which scales almost ideally with the number of processors, thus allowing to perform the fixed-mass multifractal analysis at a reasonable computational cost both on small clusters and even on multi-core workstations.