Global Sensitivity Analysis of Rainfall Triggered Shallow Landslide Model

In this study, to analyze the global sensitivity features of a transient, one-dimensional rainfall triggered shallow landslide model, seven model inputs, including the slope angle, soil thickness, initial groundwater depth, saturated hydraulic conductivity, friction angle, cohesion, and unit weights of saturated soil were involved and the Monte Carlo Simulation method was employed to obtain the semi-partial correlation coefficients (SPC) between the model output (i.e., safety factor, FS) and individual model input. The square of SPC measures the fraction of the model output variance explained by the model input variance. The variability of slope angle results from the random error of digital elevation model (DEM). Thus, two 5 m grid space DEMs with 2.0 m and 0.3 m root mean square errors (RMSE), respectively, were considered. In mountain area, the 2.0 m and 0.3 m RMSEs are typically found in the 5 m grid space DEMs produced from aerial photogrammetry and LiDAR, respectively. For the case with 2.0 m RMSE of DEM, the friction angle and cohesion are the most sensitivity inputs for the estimation of FS over the whole duration of a rainstorm event, while the unit weight of saturated soil is insensitive due to its inherent invariability. The variation of slope angle also has significant effect on the variance of FS. The maximum absolute values of SPC for friction angle, cohesion, and slope angle are 0.7, 0.6, and 0.3 respectively which means the variance of FS could be reduced 94% if the values of those variables are well determined. The sensitivities of initial groundwater depth and saturated hydraulic conductivity significantly varied during a rainfall event due to the increase of accumulative rainfall depth and the associated change of pore water pressure. The maximum absolute values of SPC for initial groundwater depth and saturated hydraulic conductivity are 0.2 and 0.15, respectively. For the case with 0.3 m RMSE of DEM, the maximum absolute values of SPC for friction angle and cohesion are 0.8 and 0.6, respectively. The maximum absolute values of SPC for soil thickness, initial groundwater depth, saturated hydraulic conductivity, and unit weights of saturated soil do not have significant changes. However, the maximum absolute value of SPC for slope angle is only 0.08 due to the great reduction of the RMSE of DEM. This study showed that for the use of physical based shallow landslide model, the variability of friction angle and cohesion have great influence on the estimation of FS and their values should be carefully determined. Moreover, the variability of slope angle which is often ignored by the model user might also significantly affect the variance of FS. Thus, the quality of a DEM should be evaluated before using it to calculate the slope angle.