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The nutrient loss caused by soil erosion is the main reason for soil degradation and environmental pollution, and polyacrylamide (PAM) as a common soil amendment has a great influence on runoff and erosion processes at the slope. In order to investigate the mechanism of nutrient transport with runoff, a field experiment was conducted and a simple mathematical model was developed in this study. Four PAM application rates (0, 1, 2, and 4 g·m−2) and two rainfall intensities (50 and 80 mm·h−1) were applied in the field experiment. The results revealed that runoff rate of 2 g·m−2 PAM application treatments decreased by 5.3%-10.6% compared with the control groups, but it increased by10.9%-18.7% at 4 g·m−2 PAM application treatments. Polyacrylamide application reduced ammonium nitrogen concentrations of runoff by 10.0% to 44.3% relative to the control groups. The best performance with correlation coefficient (R2) and Nash–Sutcliffe efficiency (NSE) showed that the ammonium transport with runoff could be well described by the proposed model. Furthermore, the model parameter of the depth of the mixing layer (hm) linearly increased with an increase in flow velocity, but exponentially decreased with an increase in PAM application rate.

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