Under natural rainfall, the surface runoff erosion of sloping farmland tends to remove large quantities of soil particles and constitutes nonpoint source pollution. The existing sediment and nutrient loss models focus on estimating the total amount of pollutants in the long term. The Existing mathematical models that describe the nutrient loss process on slopes have some shortcomings, which have not accounted for the effect of infiltration on nutrient concentrations in the exchange layer before runoff starts. Here, an approximate semianalytical model of sediment yield and nutrient loss was based on surface runoff processes. Simulated rainfall experiments were performed to calibrate the model's parameters and verify its reliability. The established model incorporated raindrop splashing, diffusion, and water infiltration effects on nutrient transfer in the exchange layer. Raindrop splashing played a leading role in nutrient translocation from the exchange layer to runoff. The simulated runoff, sediment, and nutrient matched their measured values reasonably well (R² > 0.8; Nash–Sutcliffe efficiency > 0.347). The model's sediment yield items were more sensitive to runoff erosion than splash erosion. The raindrop‐induced water transfer rate in the nutrient loss simulation dramatically affected the peak nutrient loss rates, whereas the depth of the exchange layer clearly affected the overall range of change in nutrient loss rate and boosted the total nutrient loss. Therefore, measures such as vegetation coverage or deep fertilization should be adopted to weaken raindrops’ kinetic energy and reduce nutrient concentrations in the exchange layer to prevent agricultural nonpoint source pollution in the Loess Plateau.

中文翻译：

---

降雨条件下边坡沉积物和养分运移的近似半解析模型

在自然降雨条件下，坡耕地的地表径流侵蚀趋向于清除大量土壤颗粒，构成面源污染。现有的沉积物和养分流失模型着重于长期估算污染物总量。描述斜坡上养分流失过程的现有数学模型存在一些缺陷，这些缺陷没有考虑到径流开始之前渗透对交换层养分浓度的影响。这里，基于地表径流过程的泥沙产量和养分流失的近似半分析模型。进行了模拟降雨实验，以校准模型的参数并验证其可靠性。建立的模型包括雨滴飞溅，扩散，和水分渗透对交换层中养分转移的影响。雨滴飞溅在养分从交换层到径流的迁移中起着主导作用。模拟的径流，沉积物和养分与测量值相当吻合（R ²  > 0.8；纳什-苏特克利夫效率> 0.347）。该模型的沉积物产量项目对径流侵蚀比对飞溅侵蚀更敏感。在营养损失模拟中，雨滴引起的水分转移速率极大地影响了峰值营养损失率，而交换层的深度显然影响了营养损失率变化的总体范围，并增加了总营养损失。因此，应采取植被覆盖或深施肥等措施来减弱雨滴的动能并降低交换层中的养分含量，以防止黄土高原农业面源污染。