A MINIMUM ENERGY DISSIPATION MODEL FOR RIVER NETWORKS AND THEIR ASSOCIATED TOPOGRAPHIES

Abstract

The model for the river networks presented here is based on minimum energy dissipation principles. The foundation for this model is the empirical relationship s~Qα between the link slope s in channel networks and the mean annual discharge Q in that link. The associated landscapes were constructed using a range of values for the exponent α. The surfaces appear to be more complex than simple self-affine fractals. The boundaries of drainage basins covering the entire drainage area were found to have an effective fractal dimension about 1.10 for all values of α in the range −1<α<0. A universal power-law size (area) distribution is also found for the drainage basins obtained from this minimum energy dissipation model.