ANALYTICAL AND NUMERICAL STUDY OF OPTIMAL CHANNEL NETWORKS

We analyze the optimal channel network model for river networks Using both analytical and numerical approaches. This is a lattice model in w hich a functional describing the dissipated energy is introduced and m inimized in order to find the optimal configurations. The fractal char acter of river networks is reflected ill the power-law behavior of var ious quantities characterizing the morphology of the basin, In the con text of a finite-size scaling ansatz, the exponents describing the pow er-law behavior are calculated exactly and show mean-field behavior, e xcept for two limiting values of a parameter characterizing the dissip ated energy, for which the system belongs to different universality cl asses. Two modified versions of the model, incorporating quenched diso rder, are considered: the first simulates heterogeneities in the local properties of the soil and the second considers the effects of a nonu niform rainfall. In the region of mean-field behavior, the model is sh own to be robust for both kinds of perturbations. In the two limiting cases the random rainfall is still irrelevant, whereas the heterogenei ty in the soil properties leads to different universality classes. Res ults of a numerical analysis of the model are reported that confirm an d complement the theoretical analysis of the global minimum. The stati stics of the local minima are found to resemble more strongly observat ional data on real rivers.