A comparison of mathematical models for chemical transfer from soil to surface runoff with the impact of rain

•We compared three chemical transport models, and proposed application conditions for each model.•We give an equation of estimating the effective-mixing depth with knowing the impact factors.•Parameters α and β in the incomplete-mixing model is 0.2 and 0.1 in this research.•Solute loss can be accurately predicted by three mathematical models with knowing the corresponding parameters.

Chemical transfer is considered as one of the main contributors to water pollution. Three physical based models (complete-, incomplete-mixing models and the equivalent model of convection) were refined and applied to describe the process of solute transport into runoff on loessial slope land. The effects of rain intensity, slope gradient and initial water content on solute transport was studied with simulated rain. Most parameters in the models can be measured directly, some parameters, for example, α (the solute concentration ratio between the infiltration and the effective mixing depth), β (the solute concentration ratio between the runoff and the effective mixing depth) and S (the soil adsorptivity) in the incomplete-mixing model were determined by curve fitting method based on the experimental data. And, hm (the effective mixing depth in the complete-mixing model), hm′ (the effective mixing depth in the incomplete mixing model) and H0 (the equivalent depth of transfer) can be expressed with a regression equation related to rain intensity, slope gradient and initial water content, respectively. Simulated results indicated that the three models are suitable to predict the amount of solute loss, and the refined equivalent model of convection fits solute transport process in runoff rather than the effective-mixing models on loessial plateau area. The complete-mixing model and the refined equivalent model of convection are convenient to use for simplified parameters, and the incomplete-mixing model was more appropriate for practical situations.