Minimum energy dissipation river networks with fractal boundaries

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Abstract
The effects of the entire drainage area boundary on the drainage basins and their size distributions have been studied using the minimum energy dissipation model for river networks. A simple scaling relationship τ=1+D/2 between the values of the exponents τ in the power law basin size distibutions and the fractal dimension D of the boundary of the entire drainage area has been established. The scaling relationship has been tested using simulations, with external perimeters (D=4/3) or hulls (D=7/4) of invasion percolation clusters, as the boundaries for the entire drainage areas.

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