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

This is a review paper published on PNAS, that I co-authored. Actually a review with some new results that were the outcome of my recent efforts with Java.  OCN stands for Optimal Channel Networks, a theory I co-authored with Ignacio Rodriguez-Iturbe (also here), Andrea Rinaldo, Raphael Bras, Ede Ijjasz-Vasquez (also here), and that produced a thread of papers of mine that are mentioned in a previous post, here.
This is the reunion of a old group of guys that made some good thing together, and hopefully not the last paper together.  The list of co-author of this specific paper also includes Amos Maritan (also here) and Jayanth Banavar (also here).  OCNs revealed a very interesting metaphor for many other networks, including blood vessels, and could be a key to explain the ratio between form and structure of living being. Browsing Rinaldo's production you can find several applications of the concept.

Here below, the abstract of the paper that you can preview here (or clicking under the figure):


"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 re- markable that dynamically accessible configurations, the local optima, stabilize into diverse metastable forms that are nevertheless characterized by universal statistical features. Such universal features ex- plain 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."

Some geomorphologist do not understand OCNs and tend to overlook them. However, I bet OCNs will resist for many and many years as a sound theory, and sooner or later, someone will close the open issues we left behind.