Fractal analyses of tree-like channel networks from digital elevation model data

Digital elevation models (DEMs) are generally used to automatically map the channel network and to delineate subbasins. The most common approach to extract a channel network from DEMs consists of specifying a threshold area S which is the minimum area required to drain to a point for a channel to form. This threshold area is usually specified arbitrarily, although it is recognized that different threshold areas will result in substantially different channel networks for the same basin. In this paper, we study the effect of S (that is also the scale of observation) on the morphometric properties (external and internal links, length of drainage paths, mainstream length) and scaling properties (such as Horton's and Strahler's laws, and fractal dimension). Three basins, located in southern France, were extensively studied. The results indicate that morphometric properties vary considerably with S, and thus values reported without their associated S should be used in hydrologic analysis with caution. Then, the fractal geometry is used to take into account the dependence of measured values on observation scales, which is not possible with classical hydrological indexes. The use of fractals allows, first, to point out self-similarity in the structure of channel networks and then to quantify the tree-like organization. New catchment shape indexes, independent of the observation scale S, are defined. These indexes are useful for comparing catchments and for measuring the irregularity level of the channel network.