A minimum energy dissipation model for drainage basins that explicitly differentiates between channel networks and hillslopes

A channel initiation process has been incorporated into the minimum energy dissipation models for channel networks. When a scale parameter λ becomes very large, the model introduced here becomes identical to the standard minimum energy dissipation model of Rigon et al. The structure of the channel networks obtained from this model are more similar to natural river networks on small length scales than those from previous models. The drainage densities Dd of the minimum energy dissipation drainage basins are found to be independent of the size A of the basin but proportional to the average hillslopes inclination σ in the basin. The Strahler version of Horton's relationships among the number of streams NS, the average channel length LS and the average drainage areaAS are found to be hold well for the minimum energy dissipation channel networks and the Strahler bifurcation ratio is very close to that found in nature. The scaling relationships characterizing the main streams and the boundaries of the drainage networks generated from the minimum energy dissipation model with hillslope processes are similar to those of the drainage networks generated from the standard minimum energy dissipation models without hillslope processes. A universal power law area distribution is also found for the drainage basins obtained from this minimum energy dissipation model.