Assessment of susceptibility to earth-flow landslide using logistic regression and multivariate adaptive regression splines: A case of the Belice River basin (western Sicily, Italy)

In this paper, terrain susceptibility to earth-flow occurrence was evaluated by using geographic information systems (GIS) and two statistical methods: Logistic regression (LR) and multivariate adaptive regression splines (MARS). LR has been already demonstrated to provide reliable predictions of earth-flow occurrence, whereas MARS, as far as we know, has never been used to generate earth-flow susceptibility models.The experiment was carried out in a basin of western Sicily (Italy), which extends for 51km2 and is severely affected by earth-flows. In total, we mapped 1376 earth-flows, covering an area of 4.59km2. To explore the effect of pre-failure topography on earth-flow spatial distribution, we performed a reconstruction of topography before the landslide occurrence. This was achieved by preparing a digital terrain model (DTM) where altitude of areas hosting landslides was interpolated from the adjacent undisturbed land surface by using the algorithm topo-to-raster. This DTM was exploited to extract 15 morphological and hydrological variables that, in addition to outcropping lithology, were employed as explanatory variables of earth-flow spatial distribution.The predictive skill of the earth-flow susceptibility models and the robustness of the procedure were tested by preparing five datasets, each including a different subset of landslides and stable areas. The accuracy of the predictive models was evaluated by drawing receiver operating characteristic (ROC) curves and by calculating the area under the ROC curve (AUC). The results demonstrate that the overall accuracy of LR and MARS earth-flow susceptibility models is from excellent to outstanding. However, AUC values of the validation datasets attest to a higher predictive power of MARS-models (AUC between 0.881 and 0.912) with respect to LR-models (AUC between 0.823 and 0.870). The adopted procedure proved to be resistant to overfitting and stable when changes of the learning and validation samples are performed.In conclusion, the highly acceptable predictive skill of the statistical models confirms the reliability of the procedure adopted to reconstruct the pre-failure topographic conditions. Such a method solves the conceptual problem arising when post-failure elevation data are the only source of topographic information available to model landslide susceptibility. Furthermore, with respect to other solutions proposed in the past, which identify as unstable the conditions of landslide surroundings, our approach allows for more accurate measurement of those variables (e.g. curvature, convergence index, topographic position index) that depend on the relative position of a cell with respect to its nearby pixels.