Minimum energy dissipation model for river basin geometry.

Abstract

A simple minimum energy dissipation model has been used to simulate the distribution of rivers and river basins in a region with a square boundary. The cumulative distribution of basin areas N(A>${\mathit{A}}^{\mathrm{*}}$) was found to have a power law form N(A>${\mathit{A}}^{\mathrm{*}}$)\ensuremath{\sim}${\mathit{A}}^{\mathrm{*}\mathrm{\ensuremath{-}}(\mathrm{\ensuremath{\tau}}\mathrm{\ensuremath{-}}1)}$ with an exponent (\ensuremath{\tau}-1) that is close to the value of 1/2 obtained from a simple scaling theory. The boundaries of the river basins were found to be self-similar with a fractal dimension of about 1.10. In many respects (distribution of stream internal link lengths, distribution of energy dissipation, basin boundary geometry, etc.) the results obtained from this model are similar to data obtained from natural channel networks. In other respects significant differences remain. In particular, the main channels of the individual rivers are much straighter than those of real rivers.