## 2 Methods
### Physical Modeling and Monitoring Devices  
A surface soil layer of Fengdu Mountain, close to the Yangtze River Bank, Chongqing, China was reproduced in a flume. The surface soil of Fengdu Mountain can be easily eroded under heavy rainfall (particle-size distribution curve in Figure 1). Fengdu Mountain is located at the Three Gorges Reservoir Area, where the average annual rainfall is 1074.6 mm and 70% of the annual rainfall occurs between May and September [13]. The average annual erosion rate is 2087 t/km\({}^{2}\) in Yangtze River Basin [14]. Soil properties were tested in the laboratory and consisted of quaternary eluvial material, clay, and silty clay. A model slope was constructed in a flume device made of Plexiglas (the blue dotted line in Figure 2 is the flume) with an area of 8250 cm\({}^{2}\) (length is 140 cm and width is 55 cm). A 10 cm deep layer simulates the real shallow layer of the hill and, furthermore, is convenient for installing the sensors for the hydrological investigation. The slope inclination is \(\sim\)26\({}^{\circ}\), close to that observed in the field [13]. A plate squeezed the soil layer with a force of 120 N to form the slope. In order to reduce the \"boundary effect,\" we used a covering of polytetrafluoroethylene (PTFE) (friction coefficient is 0.04) on both sides of the flume. In Figure 2,two moisture transducers (Model number DS200, Beijing Dingtek Technology Corp., Ltd, Beijing, China) (frequency domain sensors: measuring range 0%-100%, resolution 0.1%, deviation \(\pm\)2% with a soil contact area of less than 20 mm\({}^{2}\)) and one pore water pressure transducer (Model number CYY2, Xi'an Weizheng Technology Corp., Ltd, Xi'an, China) (diameter 3 cm, height 1.6 cm, measuring range \(\pm\)10 kPa, deviation \(\pm\)0.2%) are installed at three different positions along the hillslope; d1 is a drainage ditch (55 \(\times\) 3 cm) for calculation of the subsurface drainage. One high-definition digital camera is used to record images of the sediments in the front view (another camera helps to estimate the height of the sediment from side view). A water-pump supplies water resources through four nozzles (uniformity coefficient is 0.91) for rainfall simulation. A flow meter between pump and nozzles controls the rainfall intensity (10-250 mL/min). Rain fall is introduced in a series of six rainfall events, each with a constant rainfall duration (we took pictures every minute for six minutes) and with different intensity levels of approximately 15, 25, 35, 45, 55 and 65 mm/h, respectively (15 mm/h is close to the threshold of soil erosion and 65 mm/h is the maximum value achievable using the device). By approximately minute seven (under 65 mm/h rainfall intensity) and minute eight (under 55 mm/h rainfall intensity), progressive landslide failure occurs at the foot of the slope (this occurs in such a short time because of the high initial water content in the slope). This carries soil sediment away and could incur error in the volume calculations. Thus, a maximum time of six minutes ensures soil erosion without sediment loss. For every minute of six intense rainfall events, we took a measurement of eroded soil sediment volume (a total of 36 measurements and 29 eroded soil sediments were observed). For each test, we totally reconstructed the slope model and gave a pre-added rainfall (15 mm/h) for 1 h. After a 3 h interval, the experiment began. Each test was conducted under similar initial conditions of geometry, material, moisture content, and pore water pressure (PWP) (deviation \(\pm\)3%). Initial water content was relatively high in order to shorten the experiment time. Figure 1: Particle-size distribution curve (Natural cohesion is 3.4 kPa, Phi is 32\({}^{\circ}\) compared to saturated cohesion 0.1 kPa and Phi 28.4\({}^{\circ}\); the natural and saturated densities are 1.83 and 2.05 g/cm\({}^{3}\)).