A semi-empirical model to assess uncertainty of spatial patterns of erosion

Distributed erosion models are potentially good tools for locating soil sediment sources and guiding efficient Soil and Water Conservation (SWC) planning, but the uncertainty of model predictions may be high. In this study, the distribution of erosion within a catchment was predicted with a semi-empirical erosion model that combined a semi-distributed hydrological model with the Morgan, Morgan and Finney (MMF) empirical erosion model. The model was tested in a small catchment of the West Usambara Mountains (Kwalei catchment, Tanzania). Soil detachability rates measured in splash cups (0.48–1.16 g J− 1) were close to model simulations (0.30–0.35 g J− 1). Net erosion rates measured in Gerlach troughs (0.01–1.05 kg m− 2 per event) were used to calibrate the sediment transport capacity of overland flow. Uncertainties of model simulations due to parameterisation of overland flow sediment transport capacity were assessed with the Generalized Likelihood Uncertainty Estimation (GLUE) methodology. The quality of the spatial predictions was assessed by comparing the simulated erosion pattern with the field-observed erosion pattern, measuring the agreement with the weighted Kappa coefficient of the contingency table. Behavioural parameter sets (weighted Kappa > 0.50) were those with short reinfiltration length (< 1.5 m) and ratio of overland flow power α to local topography power γ close to 0.5. In the dynamic Hortonian hydrologic regime and the dissected terrain of Kwalei catchment, topography controlled the distribution of erosion more than overland flow. Simulated erosion rates varied from − 4 to + 2 kg m− 2 per season. The model simulated correctly around 75% of erosion pattern. The uncertainty of model predictions due to sediment transport capacity was high; around 10% of the fields were attributed to either slight or severe erosion. The difficult characterisation of catchment-scale effective sediment transport capacity parameters poses a major limit to distributed erosion modelling predicting capabilities.