Evolution and selection of river networks: Statics, dynamics, and complexity

Moving from the exact result that drainage network configurations minimizing total energy dissipation are stationary solutions of the general equation describing landscape evolution, we review the static properties and the dynamic origins of the scale-invariant structure of optimal river patterns. Optimal Channel Networks (OCNs) are fea- sible optimal configurations of a spanning network mimicking land- scape evolution and network selection through imperfect searches for dynamically accessible states. OCNs are spanning loopless con- figurations, however, only under precise physical requirements that arise under the constraints imposed by river dynamics – every span- ning tree is exactly a local minimum of total energy dissipation. It is remarkable that dynamically accessible configurations, the local optima, stabilize into diverse metastable forms which are neverthe- less characterized by universal statistical features. Such universal features explain very well the statistics of, and the linkages among, the scaling features measured for fluvial landforms across a broad range of scales regardless of geology, exposed lithology, vegetation or climate, and differ significantly from those of the ground state, known exactly. New results are provided on the emergence of criti- cality through adaptative evolution and on the yet unexplored range of applications of the OCN concept.