On the fractal dimension of stream networks

The geometric pattern of the stream network of a drainage basin can be viewed as a “fractal” with a fractional dimension (Mandelbrot, 1982). For an ordered drainage system, the authors first proposed to derive the fractal dimension from Horton's laws of stream number and stream lengths (La Barbera and Rosso, 1987). This results in a simple function of bifurcation and stream length ratios of the drainage system, the analytical derivation of which is presented. Accordingly, the fractal dimension could generally vary from 1 to 2, the latter value descending from the modal values of Horton's order ratios for topological randomness. However, the analysis of a large sample of field data shows the typical fractal dimension of river networks to lie between 1.5 and 2, with an average of 1.6÷1.7. Fractality can be used to investigate the scaling properties of the attributes and parameters describing drainage basin form and process.