The topography of optimal drainage basins

Abstract

A model for drainage networks and their associated landscapes has been developed. This model is based on the minimum energy dissipation principle and an empirical relationship s ∼ Qα between the slope s of each link in a channel network and the mean annual discharge Q that flows through it. The model was studied using six different values for the exponent α. The surfaces of these minimum energy dissipation drainage networks appear to be more complex than simple self‐affine fractals. The drainage basins in these optimal drainage networks have power law size (area) distributions with a universal exponent, which is independent of the value of α. For the minimum energy dissipation drainage networks obtained using a particular value for α, the basin shapes are similar to each other. An empirical relationship has also been found to relate the basins' “length‐width” ratio to the value of α.