A non-Markovian model of rill erosion

Michael Damron, C. L. Winter

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We introduce a new model for rill erosion. We start with a network similar to that in the Discrete Web [7, 11] and instantiate a dynamics which makes the process highly non-Markovian. The behavior of nodes in the streams is similar to the behavior of Polya urns with time-dependent input. In this paper we use a combination of rigorous arguments and simulation results to show that the model exhibits many properties of rill erosion; in particular, nodes which are deeper in the network tend to switch less quickly.

Original languageEnglish (US)
Pages (from-to)731-753
Number of pages23
JournalNetworks and Heterogeneous Media
Issue number4
StatePublished - 2009
Externally publishedYes


  • Dynamical discrete web
  • Erosion
  • Exchangeability
  • Pólya urn
  • Rill erosion

ASJC Scopus subject areas

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics


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