Modified model for solute loss from soil to surface runoff considering with dynamic water transfer rate

Abstract: Solute loss from soil into surface runoff water plays a significant role in agricultural non-point source pollution. Thus, studying the mathematical model of solute loss in runoff is important for forecasting and controlling fertilizer loss in farmland. Water transfer rate is taken as the function of soil erosion in this study, and water transfer rate is not a constant but an exponent function of time, which decreases with time and finally achieves an unchangeable value, residual water transfer rate. The soil erosion based model is modified and the numerical solution of solute concentration in surface runoff water is obtained through modifying the Hydrus-1D code. And, only the solute numerical model is modified for coupling the surface loss model which is discrete with the implicit difference method in Hydrus-1D code. Two groups of published experiment data are used to verify our modified model. The results show that the related coefficients (r), between forecasted results and observed data are no less than 0.81 in all cases. Moreover, both average value of absolute residual and root-mean-square error are remarkably smaller in all cases than the values published before, with the average decrease value of 35.42 and 60.77 mg/L, respectively, which suggests that the modified model in our study is much better than original model to predict solute transfer from soil into surface runoff water. Solute concentrations in both runoff and soil profile could be simulated well. This result suggests that the modified model characterizes the solute loss process in surface runoff or in underground drainage. The solute curve for the condition with or without ponding water can be simulated with the modified model by just setting the proper parameters. The sum of solute loss in runoff increases with the rainfall increasing and decreases with the time in the single experiment. Residual water transfer rate does not change with rainfall intensity. Under non-infiltration condition, solute loss account is much higher than free drainage and control drainage conditions. Residual water transfer rate slightly changes with the infiltration rate change. Such results may suggest that the residual water transfer rate is impacted by many experiment conditions and needs to be further researched. The modified model successfully rebuilds the experiment data under different experiment conditions. The original soil erosion based model fails to capture the observation data at early time. The modified model simulates the solute loss process much well, and the simulation results show that the sum of solute loss at early 1000 s is about 50% of the total loss in surface runoff. To predict and control the surface solute loss is very important work. Water transfer rate may not be a constant actually. The study results in this paper will provide the references for preventing and controlling agricultural non-point source pollution.