Soil erosion by water is a major component of global land degradation; in areas such as western Europe, rill erosion is dominant. Although the latest generation of soil erosion models are able to simulate the processes of rill erosion on hillslopes reasonably well (Favis-Mortlock, in press), none attempts to model the initiation of rills: also subsequent rill evolution is commonly highly idealised. This means that model parameters which describe along-contour rill spacing, the along-profile location of rill heads, and rill cross-section must be assumed or input a priori. The USDA Water Erosion Prediction Project (WEPP) model (Flanagan & Nearing, 1995), for example, presupposes that rills have a uniform spacing of one metre and a uniform rectangular cross-section, with a width which is a function only of flow rate, and that all rills are equally hydrologically efficient. Field evidence suggests these assumptions to be overly simplistic. On smooth planar hillslopes, along-contour rill spacing (where this is not controlled by tillage) is indeed commonly observed to be broadly uniform (e.g. Boardman & Robinson, 1985; Boardman, 1988). However, Parsons (1987) found hillslope rill density to be correlated with slope angle, and rill dimensions to be related to soil properties but not to slope.
This paper adopts an evolutionary approach (e.g. Langton, 1989; Langton et al., 1992; Coveney & Highfield, 1995: Chapter 5) to modelling the initiation and development of hillslope rills. From field observation, Evans (1995) describes a downslope sequence which has small and very short 'trace' rills toward the top of the slope; below this are 'discontinuous' rills, well defined but usually less than a metre in length; and below this are continuous rills. Similar sequences have been noted in laboratory studies where slope length is sufficiently great (e.g. Bryan & Poesen, 1989). A long flume study by Slattery & Bryan (1992) noted that "Rill incision always arose through the formation of a knickpoint, although not all knickpoints became rills". The model described in this paper, RILLGROW, puts these observations together. It assumes that trace rills, formed as a result of the overflow of ponded surface water through knickpoints, 'compete'. The most 'successful' become discontinuous rills, which in their turn also compete (cf. Bryan, 1987), with a subset dominating to form continuous rills.
RILLGROW models this interaction spatially on an idealised hillslope. It is written in C++, runs on a PC under Windows; the Geographical Information System IDRISI is used for the visualisation of output.
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