Channelization cascade in landscape evolution

Sara Bonetti, Milad Hooshyar, Carlo Camporeale, Amilcare Porporato

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The hierarchy of channel networks in landscapes displays features that are characteristic of nonequilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial differential equations coupling landscape evolution dynamics with a specific catchment area equation. By means of a linear stability analysis we identify the critical conditions triggering channel formation and the emergence of characteristic valley spacing. The ensuing channelization cascade, described by a dimensionless number accounting for diffusive soil creep, runoff erosion, and tectonic uplift, is reminiscent of the subsequent instabilities in fluid turbulence, while the structure of the simulated patterns is indicative of a tendency to evolve toward optimal configurations, with anomalies similar to dislocation defects observed in pattern-forming systems. The choice of specific geomorphic transport laws and boundary conditions strongly influences the channelization cascade, underlying the nonlocal and nonlinear character of its dynamics.

Original languageEnglish (US)
Pages (from-to)1375-1382
Number of pages8
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number3
StatePublished - Jan 21 2020

All Science Journal Classification (ASJC) codes

  • General


  • Detachment limited
  • Drainage area
  • Landscape evolution model
  • Ridge and valley patterns
  • River networks


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