Rill erosion: Exploring the relationship between experiments, modelling and field observations

Abstract

Predicting rill erosion rates for a given discharge and slope minimally requires a model for rill hydraulics that allows the prediction of hydraulic parameters and a model for sediment detachment. Several relationships that describe rill hydraulics and/or sediment detachment within an eroding rill have been proposed and are incorporated into state of the art soil erosion models. In this paper a critical review of the theoretical concepts that are underpinning current rill flow and sediment detachment models is made in the light of recent experimental results. Approaches to define detachment–hydraulics relationship are generally based on developments in alluvial river hydraulics. However, experimental evidence to support the use of these concepts in models of rill erosion is scarce and recent experimental findings suggest that the basic assumptions used to model rill erosion are to some extent flawed. An analysis of empirically collected data on rill hydraulics conclusively shows that the empirical Manning equation does not hold for rill flow and should therefore not be used in rill erosion models. An empirical power law relationship relating velocity to discharges is much better in agreement with available experimental data, both for soils with and without rock fragments. In the absence of vegetation residue and/or other macroscopic, immobile elements such as rock fragments, total shear stress and unit length shear force can be used to predict soil detachment. The use of unit length shear force has the advantage that no information about rill geometry is necessary. The evidence for sediment load and rill flow detachment interaction is somewhat conflicting: the presence of a heavy sediment load appears to restrict rill flow detachment, but the exact form of the relationship between detachment rate and sediment load remains unclear. The effect of the presence of a sediment load on flow detachments under natural conditions is also limited by the nature of the detachment and transporting capacity relationships: on a rectilinear hillslope, transporting capacity increases much more rapidly with discharge than detachment capacity. We propose modifications to the theoretical formulations used in rill erosion models so that they are in better agreement with experimental evidence. Finally, we illustrate the potential of simplified models and conclude that the combination of empirical equations for flow detachment and rill hydraulics leads to results that are consistent with empirical data relating rill erosion rates to topography.