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 associatedwith 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.

The slope effect on flow erosivity and soil erosion still remains a controversial issue. This theoretical framework explained and quantified the direct slope effect by coupling the modified Green‐Ampt equation accounting for slope effect on infiltration, 1‐D kinematic wave overland flow routing model, and WEPP soil erosion model. The flow velocity, runoff rate, shear stress, interrill, and rill erosion were calculated on 0°–60° isotropic slopes with equal horizontal projective length. The results show that, for short‐duration rainfall events, the flow erosivity and erosion amounts exhibit a bell‐shaped trend which first increase with slope gradient, and then decrease after a critical slope angle. The critical slope angles increase significantly or even vanish with increasing rainfall duration but are nearly independent of the slope projective length. The soil critical shear stress, rainfall intensity, and temporal patterns have great influences on the slope effect trend, while the other soil erosion parameters, soil type, hydraulic conductivity, and antecedent soil moisture have minor impacts. Neglecting the slope effect on infiltration would generate smaller erosion and reduce critical slope angles. The relative slope effect on soil erosion in physically based model WEPP was compared to those in the empirical models USLE and RUSLE. The trends of relative slope effect were found quite different, but the difference may diminish with increasing rainfall duration. Finally, relatively smaller critical slope angles could be obtained with the equal slope length and the range of variation provides a possible explanation for the different critical slope angles reported in previous studies.

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