Multifractal Formalism for Remote Sensing: A Contribution to the Description and the Understanding of Meteorological Phenomena in Satellite Images

The ability of fractals to mimic Nature has led to the widespread acceptance of fractal, and, beyond, multifractal models. Such models are in the roots of new approaches in environmental sciences for processing images displaying turbulent-like systems. This paper addresses the problem of detecting critical areas associated with convection in satellite meteorological images. The technique we propose takes information about the spatial domain and relies on general statistical concepts. Due to the turbulent character of the observed atmospheric systems, the multifractal approach is naturaly adopted herein to describe not only the geometrical properties of images but also the underlying physical phenomena involved. The multifractal formalism leads first to the classification of different chaotic parts of systems according to their dynamical significance. It is further exploited to extract information about the places at which convection takes place in the flow. It is shown that it finally allows the determination of information that would be otherwise hidden. Without any temporal information, this remote sensing technique has potential application to infer the convective-scale processes occurring in individual convective systems. More generally, it leads to new insights into the analysis of natural phenomena from still images.