Spatial statistical modeling of shallow landslides—Validating predictions for different landslide inventories and rainfall events

Abstract

Statistical models that exploit the correlation between landslide occurrence and geomorphic properties are often used to map the spatial occurrence of shallow landslides triggered by heavy rainfalls. In many landslide susceptibility studies, the true predictive power of the statistical model remains unknown because the predictions are not validated with independent data from other events or areas. This study validates statistical susceptibility predictions with independent test data. The spatial incidence of landslides, triggered by an extreme rainfall in a study area, was modeled by logistic regression. The fitted model was then used to generate susceptibility maps for another three study areas, for which event-based landslide inventories were also available. All the study areas lie in the northern foothills of the Swiss Alps. The landslides had been triggered by heavy rainfall either in 2002 or 2005. The validation was designed such that the first validation study area shared the geomorphology and the second the triggering rainfall event with the calibration study area. For the third validation study area, both geomorphology and rainfall were different. All explanatory variables were extracted for the logistic regression analysis from high-resolution digital elevation and surface models (2.5 m grid). The model fitted to the calibration data comprised four explanatory variables: (i) slope angle (effect of gravitational driving forces), (ii) vegetation type (grassland and forest; root reinforcement), (iii) planform curvature (convergent water flow paths), and (iv) contributing area (potential supply of water). The area under the Receiver Operating Characteristic (ROC) curve ( AUC) was used to quantify the predictive performance of the logistic regression model. The AUC values were computed for the susceptibility maps of the three validation study areas (validation AUC), the fitted susceptibility map of the calibration study area (apparent AUC: 0.80) and another susceptibility map obtained for the calibration study area by 20-fold cross-validation (cross-validation AUC: 0.74). The AUC values of the first and second validation study areas (0.72 and 0.69, respectively) and the cross-validation AUC matched fairly well, and all AUC values were distinctly smaller than the apparent AUC. Based on the apparent AUC one would have clearly overrated the predictive performance for the first two validation areas. Rather surprisingly, the AUC value of the third validation study area (0.82) was larger than the apparent AUC. A large part of the third validation study area consists of gentle slopes, and the regression model correctly predicted that no landslides occur in the flat parts. This increased the predictive performance of the model considerably. The predicted susceptibility maps were further validated by summing the predicted susceptibilities for the entire validation areas and by comparing the sums with the observed number of landslides. The sums exceeded the observed counts for all the validation areas. Hence, the logistic regression model generally over-estimated the risk of landslide occurrence. Obviously, a predictive model that is based on static geomorphic properties alone cannot take a full account of the complex and time dependent processes in the subsurface. However, such a model is still capable of distinguishing zones highly or less prone to shallow landslides.