A new analytical model for predicting overland flow and nutrient loss on hillslopes

Abstract

Water and nutrient loss from farmland in the Chinese Loess Plateau reduces land productivity and generates non-point source pollution. More effort is needed to develope mathematical models that can predict runoff and nutrients in this region and explore the migration mechanisms of runoff and nutrients. In this study, the runoff submodel was based on the water balance equation and the assumption that the slope flow pattern is transitional flow. To obtain the analytical solution of the runoff submodel, the excess rainfall was considered to be fixed over a short time interval. The nutrient loss submodel assumed that raindrop splash was the only way for nutrients to transfer to runoff from soil, and the equivalent mixing depth increased with the passage of runoff time. A total of 16 sets of runoff data and 64 sets of nutrient data under 16 simulated rainfall events were used to validate the model. The runoff submodel and nutrient loss submodel accurately simulated the runoff and nutrient loss processes, and the R2 values were between 0.813 to 0.981 and 0.609 to 0.982, respectively. The global sensitivity of the newly developed model was analyzed using Sobol’s method. The sensitivity of the runoff submodel to the shape factor of the ponding profile k was higher than that to the slope topographic synthesis coefficient SC. The sensitivity of the nutrient loss submodel to the initial equivalent mixing depth EMD0 and parameter m was higher than that to the raindrop-detached water transfer rate er. Therefore, the prevention and control of agricultural non-point source pollution require improvements in soil surface conditions to reduce the equivalent mixed layer depth, which can effectively reduce the loss of soil nutrients. The results of this study provide theoretical insights that will aid the control of soil and nutrient loss in the Chinese Loess Plateau.