REEXAMINING THE DETERMINATION OF THE FRACTAL DIMENSION OF RIVER NETWORKS

In analyzing the literature on the fractal nature of river networks on e can recognize several points that require clarification or additiona l investigations. For instance, many interpretations, with different c onclusions, have been given to the important empirical results found i n the previous literature or, river geomorphology. Similarly, the argu ment concerning a possible ''more likely'' value of the fractal dimens ions of river networks has not yet found a convincing answer. In an at tempt to shed more light on the topic, particularly on the latter poin t, we have reexamined the basic aspects related to selfsimilarity in r iver networks using uniquely the fundamental concepts of fractal geome try. This approach leads to relations for the determination of the fra ctal dimensions which hold exactly for deterministic self-similar tree s and are compatible with related findings reported in literature. Res ults obtained from application of these relations to several river net works in southern Italy indicate very low variability around the avera ge values of about 1.7, 1.5, and 1.1 for the fractal dimensions of the whole river network, of its topological equivalent, and of its indivi dual streams, respectively. This outcome, in addition to comparable re sults taken from the literature, provides new arguments to the hypothe sis that natural networks tend to have the same fractal dimensions.