An analytical model of fine-sediment transport under shallow overland flow

Fine sediment mobilized by raindrop impact and shallow overland flow controls event-scale sediment export from hillslopes. This study develops a closed-form analytical extension of the Hairsine-Rose framework to describe suspended fine-sediment concentration under splash-dominated interrill conditions. The formulation explicitly incorporates slope gradient and longitudinal hydraulic diffusivity and yields a series solution for spatiotemporal sediment concentration under shallow overland flow. The model was evaluated against published pan and flume sediment-concentration datasets, and reproduced early concentration peaks and recession behavior using a single calibrated diffusivity parameter, including a 6 m flume case with R² = 0.92. Sensitivity analyses showed that greater hydraulic diffusivity attenuated and redistributed outlet concentration peaks, steeper slopes accelerated downslope sediment delivery, greater water depth suppressed splash-driven detachment, and surface coverage controlled peak timing and event duration. Simulations by particle-size class indicated that particles finer than 20 μm dominate the early suspended phase, whereas 20-50 μm particles can remain important later in the event. The formulation is not a contaminant-transport or contaminant-chemistry model. However, when independently measured sediment-associated contaminant loading is available, the predicted sediment concentration time series may be used as a source term for subsequent particulate-contaminant analysis. The model provides a low-parameter analytical tool for interpreting fine-sediment pulses under shallow overland flow.