# Comparisons of Dynamic Landslide Models on GIS Platforms
## 4 Results and Discussion
### Reason for Differences
#### 4.1.3 Differences Caused by Description  
In this section, we show the 3-D sliding block used to analyze the influence of different descriptions. In this case, we assumed the acceleration in the \(x\)- and \(y\)-direction is 5 m/s\({}^{2}\), and that the \(x\)-direction and \(y\)-direction interval is 10 m. The location of the center of the block is (200, 200) (Figure 6A). In this motion process, the deformation of the block is zero, and the block can be considered as a rigid body. After 20 s, the block moves to (1200, 1200) based on [PERSON]'s second law. We selected the lumped mass model in the Lagrangian description and the depth-averaged model in the Eulerian description to simulate the same motion. Figure 4: Rockfall simulations using RA: (**A**) in ArcGIS 9.x and (**B**) in ArcGIS 10.x. Figure 5: Numerical diffusion and numerical oscillation: (**A**) numerical diffusion obtained by the Lax–Friedrichs scheme, and (**B**) numerical oscillation obtained by the Lax–Wendroff scheme. In the Lagrangian description, the lumped mass model is simple (Figure 6B) because the block assumes a mass point in the model. Based on the lumped mass model, we can calculate the location and the result close to the observed one. In the Eulerian description, we used depth-averaged theory and the McCormack-TVD scheme. After 20 s, the block also moves to (1200, 1200) (Figure 6C). However, numerical diffusion (the green area) is notable at the boundary of the block, even though the TVD method is applied to reduce diffusion (Figure 6C). Additionally, the calculation efficiency is far lower than the method based on the Lagrangian description, when reaching the same precision. This case shows that proper model assumptions are a prerequisite for good results. Suitable assumptions can reduce some errors in the calculation process. The lumped mass model is simple and obtains results quickly and accurately. Therefore, the lumped mass model is more suitable for this motion. In the 3-D landslide simulation, we selected the Yigong landslides to evaluate the influence of different numerical schemes. The Yigong landslide happened at the head of the Zhamolong guilty (30.178\({}^{\circ}\) N; 94.940\({}^{\circ}\) E) on 9 April 2000 [68] and blocked the Yi Gong River at the foot of the slope with 3 \(\times\) 10\({}^{8}\) m\({}^{3}\) of sediment that formed a 60 m high dam [69]. Aiming at the characteristics of long-distance and high-speed movement of the Yigong landslide, researchers use many numerical models to investigate it. We selected different descriptions to simulate this process. Based on previous studies [70,71], the Voellmy model can obtain a suitable result [72]. In this case, the basal friction angle is 12\({}^{\circ}\), the internal friction angle is 13\({}^{\circ}\), and the turbulence assumes 1000 s\({}^{2}\)/m (Table 3). In numerical schemes, we selected the NOC-TVD scheme in the Eulerian description, which is applied in r.avaflow, and the depth-averaged SPH method in the Lagrangian description to analyze the differences. The states of 50 s, 100 s, and 200 s using two methods are given in Figure 7. From the simulation, both methods obtain similar results. The Yigong landslide reached the foot of the mountain at 200 s. In detail, the process calculated in the Eulerian description is smoother than that in the Lagrangian description. The material in the Lagrangian description is concentrated in the channel. The maximum height is higher than the model in the Eulerian description. As for the maximum speed, the NOC-TVD scheme is 90.23 m/s, and the depth-averaged SPH is 97.20 m/s. The precision of the SPH model is related to the number of particles or the number of columns. The more particles or columns, the finer the description and the closer to the analytical solution of the fluid equation. Fewer particles or columns will result in lower interaction forces between columns or particles. Additionally, the computational cost of SPH simulations per number