A self-organizing dynamic systems approach to the simulation of rill initiation and development on hillslopes

Abstract Whereas current erosion models are able to make quantitative estimates of rates of soil erosion by water on hillslopes with reasonable success, they are less competent when there is a need to apply a spatial dimension to their estimates. In particular, the initiation and development of rill networks is poorly modelled. Observations from field and laboratory suggest that it is possible to apply an evolutionary analogy to rill growth and development. Microrills, formed both by the runoff resulting from individual raindrops and from the overflow of ponded surface water through knickpoints, can be thought of as “competing”. The most “successful” of these become discontinuous rills, which in their turn also compete, with a subset dominating to form continuous rills. Rill “success” will depend on both the position on the slope and microtopography. However, microtopography will itself be modified by erosional processes such as rill growth. This creates a feedback loop. Is it possible to use this perspective to model the evolution of hillslope rill networks? This study investigates the feasibility of such an approach. A novel model is described which applies simple rules to govern the iterative interaction between microtopography, runoff routing and soil loss. Runoff is conceptualized as consisting of discrete “packets” so that a Lagrangian frame of reference is adopted, in contrast to the more usual Eulerian perspective. Results from several experiments are described, using both measured and synthetic microtopographic surfaces. The model appears able to reproduce many of the larger-scale “emergent” features of erosional systems. Planform rill networks appear realistic, as does rill depth, which increases both downslope and below confluences. Simulated rill spacing conforms with observed relationships to slope angle; the spatial balance between rill and interrill erosion similarly echoes observational evidence, as does total erosion and change in microtopographic roughness.

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