Search for the optimality signature of river network development

Whether the evolution of natural river networks pursues a certain optimal state has been a most intriguing and fundamental question. There have been many optimality hypotheses proposed but it has yet to be proved which of these best serves as a quantitative signature of river network development. Here, this fundamental question is investigated for the five hypotheses of "minimum total energy expenditure," "minimum total energy dissipation rate," "minimum total stream power," "minimum global energy expenditure rate," and "minimum topological energy." Using simple example landscapes, I examined whether any of these hypotheses pursues both the treelike river network formation and the concave stream longitudinal profile, the two characteristic patterns of natural landscapes. It is found that none of these hypotheses captures both patterns under the steady-state condition where the balance between tectonic uplift and sediment loss is satisfied. These findings are further verified through simulations of landscapes that satisfy given optimality criteria using an optimization method.