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The effect of rill network planforms on hillslope rainfall-runoff and soil erosion processes is usually neglected in modeling practices, although they can markedly alter the hydrologic and geomorphic processes. Based on the CeRIRM model and WEPP erosion theory, a simple approach is developed to account for these effects. In the framework, several characteristic parameters including the average rill width, rill orientation angle, the number of rills, and number of discontinuous rills and their variations along the hillslope are introduced to represent the planar characteristics of the rill network. The model is tested against experimental erosion data from a hillslope subjected to three successive rainfall events, resulting in continuous rill network evolution. The results show that rill network planforms alter the partitioning of interrill and rill flows, thereby modifying the hydraulics, erosion, and sedimentation in the rills. Rill characteristics are found to significantly affect the amount of rill erosion. The new approach is compared to WEPP, which ignores rill network features. The WEPP approach of simulating rill erosion on hillslopes using one set of model parameters leads to errors that are up to 30% larger than the new approach that is able to account for spatially and temporally varying rill characteristics. The differences in cumulative rill erosion amounts between the two models vary significantly with slope length, slope angle, rill orientation angle, number of rills, and discontinuous rills. The results are valuable for the development of general rainfall-runoff and soil erosion models on hillslopes with complex geomorphic features.

Plain Language Summary Rill erosion is one of the main forms of soil erosion and is associated with fast flowing water in networks of small channels, that is, rills. Modeling rill erosion is an important yet challenging task informing soil conservation. Although actual rill networks are usually composed of irregular, tortuous, and even discontinuous rills, using parallel and straight rills to simplify the actual rill network is still the prevailing method in current models. This study demonstrates the impact of the irregular planform of rill network on soil erosion and proposes a simple and effective conceptualization to represent complex rill networks using only a few parameters, including rill orientation angle, number of rills, and number of discontinuous rills. The approach can better represent the spatially intricate partitioning of interrill and rill flow and improve the modeling of rill hydraulics, erosion, and sedimentation prediction. Owing to its improved physical basis, the proposed approach simulates both the total amount and the spatial distribution of erosion with improved accuracy. The results of this study are expected to help improve general rainfall-runoff and soil erosion models for hillslopes with complex geomorphic features, and benefit other scientific fields involving transport through complex rill networks.