Physically Based Susceptibility Assessment of Rainfall-Induced Shallow Landslides Using a Fuzzy Point Estimate Method

The physically based model has been widely used in rainfall-induced shallow landslide susceptibility analysis because of its capacity to reproduce the physical processes governing landslide occurrence and a higher predictive capability. However, one of the difficulties in applying the physically based model is that uncertainties arising from spatial variability, measurement errors, and incomplete information apply to the input parameters and analysis procedure. Uncertainties have been recognized as an important cause of mismatch between predicted and observed distributions of landslide occurrence. Therefore, probabilistic analysis has been used to quantify the uncertainties. However, some uncertainties, because of incomplete information, cannot be managed satisfactorily using a probabilistic approach. Fuzzy set theory is applicable in this case. In this study, in order to handle uncertainty propagation through a physical model, fuzzy set theory, coupled with the vertex method and the point estimate method, was adopted for regional landslide susceptibility assessment. The proposed approach was used to evaluate susceptibility to rainfall-induced shallow landslides for a regional study area, and the analysis results were compared with landslide inventory to evaluate the performance of the proposed approach. The AUC values arising from the landslide susceptibility analyses using the proposed approach and probabilistic analysis were 0.734 and 0.736, respectively. However, when the COV values of the input parameters were reduced, the AUC values of the proposed approach and the probabilistic analysis were reduced to 0.722 and 0.688, respectively. It means that the performance of the fuzzy approach is similar to that of probabilistic analysis but is more robust against variation of input parameters. Thus, at catchment scale, the fuzzy approach can respond appropriately to the uncertainties inherent in physically based landslide susceptibility analysis, and is especially advantageous when the amount of quality data is very limited.