A modified model for predicting nutrient loss in runoff using a time-varying mixing layer

Abstract Nutrient loss caused by runoff reduces the fertility of cultivated land and pollutes the environment. Accurate prediction of such nutrient loss can inform prevention and control measures to reduce agricultural nonpoint source pollution and promote sustainable agriculture, particularly in vulnerable habitats such as the Loess Plateau, China, and for high-quality development projects such as those in the Yellow River Basin, China. In this study, a time-varying mixing layer was established to improve the nutrient transfer models already in use. 36 sets of empirical data on nutrient loss (K+, PO43−-P, NO3−-N) were compiled for the parameters α, β, and km. Another 45 sets of empirical data were used to evaluate the accuracy of the modified model. The modified and previous models were compared, and the modified model (coefficient of determination > 0.81, root mean square error   0.77) was the most accurate. The Markov chain Monte Carlo method was used to estimate the parameters (α, β, km) under conditions of varying rainfall intensity (p), soil initial moisture content (θ0), and slope degree (s), and as a result the mean value of parameter β (0.105) is recommended for the model. The modified model successfully simulated the processes of nutrient loss, with the greatest sensitivity for α, followed by km and β. This model can be used to improve the theoretical basis for developing runoff and erosion control methods.