ARS | Publication request: Controls on the spacing and geometry of rill networks on hillslopes: Rainsplash detachment, initial hillslope roughness, and the competition between fluvial and colluvial transport 2171

Submitted to: Journal of Geophysical Research
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: December 3, 2012
Publication Date: N/A

Interpretive Summary: Rills are small channels that form on hillslopes during the erosion of topsoil. Rill networks are the spatial patterns that form from the development of several individual rills. Rill networks have been studied for a long time but we still lack a complete understanding of what controls the spacing of rills and the geometry of rill networks on hillslopes. Learning this and understanding the formation of rill networks would be a major advance to the science of soil erosion. This study was undertaken in order to develop a set of mathematical equations and their solutions that will allow scientists to better understand and compute the formation of rill networks. The data used were taken from an earlier study conducted by ARS scientists at the ARS National Soil Erosion Research Laboratory. The results were remarkably good. The model was able to mimic the fundamental processes of soil erosion by both raindrop splash and surface water flow. It was able to mimic how the flow of water across the soil surface became concentrated in the experiment and formed rills, and the patterns formed by the model were quite close to those measured in the laboratory. The impact of this work is that it contributes to the greater understanding of soil erosion processes, which leads to better mathematical formulations of soil erosion that are routinely used to design conservation practices and assess soil erosion on America’s agricultural soils.

Technical Abstract: Rill networks have been a focus of study for many decades but we still lack a complete understanding of what variables control the spacing of rills and the geometry of rill networks (e.g. parallel or dendritic) on hillslopes. In this paper we investigate the controls on the spacing and geometry of rill networks using numerical modeling and comparison of the model results to terrestrial-laser-scanner-derived topographic data from real rill networks formed in physical experiments. During each time step of the model, rainfall in excess of infiltration is routed over the hillslope topography using the shallow water equations. The subsequent change in bed elevation is controlled by a landscape evolution equation that accounts for the transport of sediment due to rain splash, fluvial entrainment and transport, and deposition. In order to develop realistic rill networks in the model, we find that it is necessary to incorporate the effects of raindrop impact on the breakdown of soil aggregates. When raindrop-aided fluvial sediment transport is accounted for, the model is capable of creating rill networks with mean spacings and depths similar to those formed in physical experiments. A model without raindrop-aided fluvial sediment transport is unable to form rill networks consistent with experimental data. The initial micro-topographic roughness and the relative importance of diffusive and advective sediment transport mechanisms are found to exert significant control on the geometry of the resulting rill network. Dendritic networks form most often in cases of high initial topographic roughness and high rates of advective (fluvial) sediment transport relative to diffusive (colluvial) transport. Parallel networks form in low-roughness cases under a wide range of relative advective and diffusive transport rates as well as in high roughness cases in which diffusive sediment transport is high relative to advective transport. The transition from dendritic to parallel rill networks is shown to occur gradually rather than being associated with a particular threshold. Finally, we present a scaling relationship based on a balance between diffusive and advective sediment transport processes that predicts the mean rill spacing in cases of parallel rilling.