A mathematical model using an equivalent exchange layer for predicting raindrop-induced nutrient ejection from soil to runoff on bare and vegetated slopes

Abstract

Nutrient loss from the topsoil reduces agricultural productivity and contributes to the eutrophication of water bodies like rivers and lakes. To reduce agricultural non-point source pollution, ongoing efforts must be made to develop mathematical models that can accurately forecast the process of nutrient loss and provide a theoretical foundation for developing prevention and control strategies. In this study, the concept of an ‘equivalent exchange layer, EEL’, which consists of an ‘equivalent runoff layer’ and an ‘equivalent infiltration layer’, was proposed. The equivalent exchange model (EEM), which describes nutrient migration from upper soil to runoff, was developed on this basis. The EEM was validated, and its parameters were calibrated using 12 sets of K+ loss data on bare slopes and 30 sets of NH4+-N loss data on six vegetation growths. Overall, EEM exhibited good accuracy in forecasting the process by which the of K+ and NH4+-N concentrations changed and as the total amount of K+ and NH4+-N in the runoff (R2 ≥ 0.713,RMSE ≤ 2.373 mg/L, NSE ≥ 0.701). Compared to the model developed by Shao et al. (2021), EEM outperformed in terms of simulation performance when predicting the total amount of nutrient loss (R2 ≥ 0.963, NSE ≥ 0.911), effectively resolving the problem that the total amount of nutrient loss is overestimated. A single parameter perturbation simulation and a global sensitivity analysis revealed that the raindrop-induced nutrient transfer rate er and the depth of the equivalent exchange layer EED were the primary variables controlling nutrient loss, while the initial ratio of the depth of the equivalent infiltration layer to the equivalent exchange layer α0 and index m were the secondary variables accurately predicting nutrient content in the stable runoff stage. This research contributes to understanding the mechanisms underlying nutrient transfer on slopes.