## 3 Results and Analysis
### Spatial and Temporal Differences in Flow Velocity  
As shown in Figure 4, Under the examined slope gradients, the escalation in rainfall intensity leads to substantial growth in flow rate. Using the 40\({}^{\circ}\) slope gradient as an example, with rainfall intensities of 50, 80, and 110 mm/h, the mean flow velocities are 0.15, 0.18, and 0.26 m/s, while the peak flow velocities are 0.17, 0.23, and 0.32 m/s, respectively. As the rainfall intensity rises from 50 to 80 mm/h, the average flow velocity experiences a 23% enhancement, and the peak velocity shows a 35% expansion. When the rainfall intensity climbs from 80 to 110 mm/h, the average flow velocity exhibits a 35% increment, and the peak velocity demonstrates a 40% amplification. Hence, the upsurge in rainfall intensity has a notable impact on the flow velocity.  
The maximum flow velocity reaches 0.32 m/s, while the minimum flow velocity is a mere 0.09 m/s. The timing of the peak flow velocity does not coincide with the timing of runoff and sediment production. This is due to the formation of rills on the slope during erosion by overland flow, which alters the slope's shape, rendering it uneven and causing the overland flow to deviate from uniform laminar flow. The impact of rills on  
Figure 3: Changes in sediment yield rate with time under different rainfall intensities for the same slope. (**a**) Slope is 10\({}^{\circ}\). (**b**) Slope is 20\({}^{\circ}\). (**c**) Slope is 30\({}^{\circ}\). (**d**) Slope is 40\({}^{\circ}\).  
overland flow is multifaceted. Runoff within rills can continuously affect their inner walls, making them smoother, thereby diminishing resistance and augmenting flow velocity. Simultaneously, rills may also evolve along the cross-section, raising the height difference between the fill and the original slope, consequently generating a height drop in the slope flow and diminishing the flow velocity.  
During simulated rainfall, the flow velocity on the slope exhibits fluctuations with a general upward tendency. The flow velocity demonstrates a significant positive correlation with both slope gradient and rainfall intensity. As the flow velocity escalates, the slope flow intensifies the erosion of the slope, and the continuous erosion of the slope surface by runoff leads to the emergence of rills on the slope surface. Rills predominantly appear in the middle section of the slope, while their presence in the upper and lower sections is scarce. This can be ascribed to the flow velocity and slope strength. The flow velocity in the upper part of the slope is comparatively low, and the volume of runoff is relatively small; as a result, the erosive force is insufficient to erode the slope. The flow velocity in the middle section is relatively high, and the volume of runoff is larger. In this scenario, the erosive force on the slope is relatively significant, culminating in the formation of rills of varying sizes in the middle section of the slope under the action of erosion from runoff. Although the flow velocity in the lower slope section is relatively substantial, the slope strength exceeds that of other sections. Consequently, the volume of runoff in the lower section of the slope is larger than in the upper section but smaller than in the middle section.  
Figure 4: Comparison of slope flow velocity under different slope gradients. (**a**) Slope is \(10^{\circ}\). (**b**) Slope is \(20^{\circ}\). (**c**) Slope is \(30^{\circ}\). (**d**) Slope is \(40^{\circ}\).