A non-Markovian model of rill erosion

TL;DR

This paper introduces a novel non-Markovian network model for rill erosion, combining rigorous analysis and simulations to replicate key erosion behaviors such as slower switching in deeper nodes.

Contribution

The paper presents a new non-Markovian model for rill erosion based on a network similar to the Discrete Web, incorporating time-dependent dynamics and Polya urn-like behavior.

Findings

Nodes deeper in the network switch less frequently.

The model exhibits properties consistent with real rill erosion.

Simulation results support the theoretical analysis.

Abstract

We introduce a new model for rill erosion. We start with a network similar to that in the Discrete Web 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.