title: Evolution and selection of river networks: statics, dynamics, and complexity.
abstract: 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 feasible optimal configurations of a spanning network mimicking landscape evolution and network selection through imperfect searches for dynamically accessible states. OCNs are spanning loopless configurations, however, only under precise physical requirements that arise under the constraints imposed by river dynamics--every spanning 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 that are nevertheless 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. Results are provided on the emergence of criticality through adaptative evolution and on the yet-unexplored range of applications of the OCN concept.
authors.affiliation: Laboratory of Ecohydrology, Environmental Engineering Institute, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
authors.forename: Andrea
authors.initials: A
authors.lastname: Rinaldo
authors.forename: Riccardo
authors.initials: R
authors.lastname: Rigon
authors.forename: Jayanth R
authors.initials: JR
authors.lastname: Banavar
authors.forename: Amos
authors.initials: A
authors.lastname: Maritan
authors.forename: Ignacio
authors.initials: I
authors.lastname: Rodriguez-Iturbe
mesh_terms: D004777:Environment; D055593:Geological Phenomena; D057446:Hydrodynamics; D008962:Models, Theoretical; D045483:Rivers
keywords: adaptive evolution; erosional mechanics; feasible optimality; river network patterns; trees and networks