Fractal characterization of a hydrological basin using SAR satellite images

The self-similar organization of geological structures which results in the concept of fractality was pointed out in the 60's by Richardson [1] and has contributed to the establishment of a general theory by Mandelbrot [2]. Firstly applied to the coastlines, it proved to be of major interest when used for hydrological elements since it often reflects properties of the complete catchment basin, providing geomorphological information on large areas [3]. This paper addresses the automatic determination of some fractal dimensions attached to one precise area, the Maroni basin in the Amazonian forest. This determination is obtained from the radar satellite ERS-1 images. Radar satellites provide an efficient observation of the Earth, independent of cloud cover which often reduces the visibility in the equatorial belt. The excellent resolution of ERS-1 makes it possible to detect very thin structures (pixel size of 12.5 meters on the ground). The contribution of this paper is twofold: at first, a picture processing methodology is presented to determine the fractal dimension of lakes and rivers if such dimension exists. It is shown to be in good agreement with the mathematical concept of measure which lies at the very heart of the fractal theory. Then several results are obtained on one precise region of Surinam, which confirm the assumption that the geomorphological aspect of this region of interest obeys self-similarity laws in a very tight way. As a side result, two new relationships are suggested between geographical measures linking the length of a river stream and the catchment basin area to the river bed area.