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.