Interaction effects of rainfall and soil factors on runoff, erosion, and their predictions in different geographic regions

• A new concept runoff-ability ra is proposed to predict surface runoff. • Significant interactions of rainfall and soil factors exist in water erosion model. • The tendency to underestimate small and overestimate large events is not absolute. • Prediction bias of runoff and erosion in small or large events is predictable. Water erosion is a complex process driven by many factors, such as rainfall, soil, topography, vegetation, and land use management practices. Much research has been done to assess the separate effect of every single factor, while studies devoted to the interaction effects among these factors are rarely reported. The complex interactions among factors are generally poured into the pool of soil erodibility ( K factor) in the USLE-based models, which induces uncertainty of the K factor and thus causes prediction errors. The interaction between rainfall ( R ) and soil ( K ) factors is the first and foremost step to dissect the entire interaction complex, but also the objective this study intended to investigate. Quality-controlled data from long-term field observations on four bare steep slopes in different geographic regions of China were selected and standardized to exclude the effect of unconcerned factors. The interaction effects of rainfall and soil factors were visualized by the nonlinearities of accumulative rainfall-runoff-erosion relationships and then further quantified by the evaluation of prediction errors for the cases that ignore the nonlinearities and by the approach of partial least squares-structural equation modelling (PLS-SEM). The results indicated that the interaction between rainfall and soil factors exists in water erosion processes and obscures the hydrological and erosion prediction. (1) The potentialities of both runoff and erosion varied with the level of rainfall erosivity in different patterns among soils, indicating diverse nonlinearities of rainfall-runoff-erosion relationships and the complex interaction effects behind it. (2) The addition of the interaction effects in the SEM model constructions increased 9.2% and 6.0% of variance explanations for the predictions of annual runoff and erosion, respectively. Whereas, the exclusion of interaction effects tended to cause overestimations on steep slopes that were hard to be calibrated by existing formulas. (3) The well-known tendency to underestimate small and overestimate large events does not suit every soil, especially for the soil with coarse texture and shallow soil with fractured bedrock. And prediction bias was found predictable and rooted in the interaction between rainfall and soil. This study yields a deeper understanding of interaction effects, and is helpful for the improvement of runoff and erosion predictions.