PT - JOURNAL ARTICLE
AU - Balister, Paul
AU - Balogh, József
AU - Bertuzzo, Enrico
AU - Bollobás, Béla
AU - Caldarelli, Guido
AU - Maritan, Amos
AU - Mastrandrea, Rossana
AU - Morris, Robert
AU - Rinaldo, Andrea
TI - River landscapes and optimal channel networks
AID - 10.1073/pnas.1804484115
DP - 2018 Jun 26
TA - Proceedings of the National Academy of Sciences
PG - 6548--6553
VI - 115
IP - 26
4099 - http://www.pnas.org/content/115/26/6548.short
4100 - http://www.pnas.org/content/115/26/6548.full
SO - Proc Natl Acad Sci USA2018 Jun 26; 115
AB - Optimal channel networks (OCNs) are a well-studied static model of river network structures. We present exact results showing that every OCN is a natural river tree where a landscape exist such that the flow directions are always directed along its steepest descent. We characterize the family of natural river trees in terms of certain forbidden structures, called “k-path obstacles.” We thus determine conditions for river landscapes to imply a rooted tree as its network of topographic gradients. Our results are significant in particular for applications where OCNs may be used to produce statistically identical replicas of realistic matrices for ecological interactions.We study tree structures termed optimal channel networks (OCNs) that minimize the total gravitational energy loss in the system, an exact property of steady-state landscape configurations that prove dynamically accessible and strikingly similar to natural forms. Here, we show that every OCN is a so-called natural river tree, in the sense that there exists a height function such that the flow directions are always directed along steepest descent. We also study the natural river trees in an arbitrary graph in terms of forbidden substructures, which we call k-path obstacles, and OCNs on a d-dimensional lattice, improving earlier results by determining the minimum energy up to a constant factor for every d≥2. Results extend our capabilities in environmental statistical mechanics.