Fractal relation of mainstream length to catchment area in river networks

Institute of Hydraulics, University of Genoa, ItalyMandelbrot's (1982) hypothesis that river length is fractal has been recently substantiated byHjelmfelt (1988) using eight rivers in Missouri. The fractal dimension of river length, d, is derived herefrom the Horton's laws of network composition. This results in a simple function of stream length andstream area ratios, that is, d = max (1, 2 log RL/\og RA). Three case studies are reported showing thisestimate to be coherent with measurements of d obtained from map analysis. The scaling properties ofthe network as a whole are also investigated, showing the fractal dimension of river network, D, todepend upon bifurcation and stream area ratios according to D = min (2, 2 log RB/log RA). Theseresults provide a linkage between quantitative analysis of drainage network composition and scalingproperties of river networks.

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