title: A mathematical model for the transfer of soil solutes to runoff under water scouring.
abstract: The transfer of nutrients from soil to runoff often causes unexpected pollution in water bodies. In this study, a mathematical model that relates to the detachment of soil particles by water flow and the degree of mixing between overland flow and soil nutrients was proposed. The model assumes that the mixing depth is an integral of average water flow depth, and it was evaluated by experiments with three water inflow rates to bare soil surfaces and to surfaces with eight treatments of different stone coverages. The model predicted outflow rates were compared with the experimentally observed data to test the accuracy of the infiltration parameters obtained by curve fitting the models to the data. Further analysis showed that the comprehensive mixing coefficient (ke) was linearly correlated with Reynolds' number Re (R(2)>0.9), and this relationship was verified by comparing the simulated potassium concentration and cumulative mass with observed data, respectively. The best performance with the bias error analysis (Nash Sutcliffe coefficient of efficiency (NS), relative error (RE) and the coefficient of determination (R(2))) showed that the predicted data by the proposed model was in good agreement with the measured data. Thus the model can be used to guide soil-water and fertilization management to minimize nutrient runoff from cropland.
authors.affiliation: State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi'an University of Technology, Xi'an 710048, China; Department of Environmental Sciences, University of California, Riverside, CA 92521, USA.
authors.forename: Ting
authors.initials: T
authors.lastname: Yang
authors.affiliation: State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi'an University of Technology, Xi'an 710048, China; State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Northwest A&F University, 712100 Yangling, China. Electronic address: wquanjiu@163.com.
authors.forename: Quanjiu
authors.initials: Q
authors.lastname: Wang
authors.affiliation: Department of Environmental Sciences, University of California, Riverside, CA 92521, USA.
authors.forename: Laosheng
authors.initials: L
authors.lastname: Wu
authors.affiliation: State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi'an University of Technology, Xi'an 710048, China.
authors.forename: Pengyu
authors.initials: P
authors.lastname: Zhang
authors.affiliation: State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi'an University of Technology, Xi'an 710048, China.
authors.forename: Guangxu
authors.initials: G
authors.lastname: Zhao
authors.affiliation: State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi'an University of Technology, Xi'an 710048, China.
authors.forename: Yanli
authors.initials: Y
authors.lastname: Liu
keywords: Mixing depth; Simulation model; Soil detachment; Soil-solute transport; Surface runoff