STATISTICAL METHODS TO ASSESS ROCKFALL SUSCEPTIBILITY IN AN ALPINE ENVIRONMENT: A FOCUS ON CLIMATIC FORCING AND GEOMECHANICAL VARIABLES

The overarching goal of the doctoral thesis was thus the development of a systematic procedure capable to examine and enhance the role of geomechanical and climatic processes in rockfall susceptibility, performed with statistically based and Machine Learning techniques. To achieve this purpose, two case studies were analysed in the Italian Alps (Valchiavenna, Lombardy Region; Mountain Communities of Mont Cervin and Mont Emilius, Aosta Valley Region). For both case studies, Generalized Additive Models (GAM) were used for rockfall susceptibility assessment; for the Valchiavenna case study, a Random Forest (RF) model was tested too. All models were validated through k-fold cross validation routines and their performance evaluated in terms of area under the receiver operating characteristic curve (AUROC). Predictors’ behaviour physical plausibility was verified through the analysis of the mathematical functions describing the predictors-susceptibility modelled relationships. Specific objectives of the two case studies differed. The Valchiavenna case study was dedicated to testing the role of the outcrop-scale geomechanical properties in a rockfall susceptibility model. Specific objectives were: (i) the optimal selection of sampling points for the execution of geomechanical surveys to be integrated within an already available dataset; (ii) the regionalization over the study area of three geomechanical properties, namely Joint Volumetric Count (Jv), rock-mass weathering index (Wi) and rock-mass equivalent permeability (Keq); (iii) the implementation of the regionalized properties as predictors in a rockfall susceptibility model, along with the traditional morphometric variables; (iv) the investigation of prediction limitations related to inventory incompleteness; (v) the implementation of a methodology for the interpretation of predictors’ behaviour in the RF model, usually considered a black box algorithm; (vi) the integration of the RF and GAM outputs to furnish a spatially distributed measure of uncertainty; (vii) the exploitation of satellite-derived ground deformation data to verify susceptibility outputs and interpret them in an environmental management perspective. The additional geomechanical sampling points were selected by means of the Spatial Simulated Annealing technique. Once collected the necessary geomechanical data, regionalization of the geomechanical target properties was carried out by comparing different deterministic, regressive and geostatistical techniques. The most suitable technique for each property was selected and geomechanical predictors were implemented in the susceptibility models. To verify rockfall inventory completeness related effects, the GAM model was performed both on rockfall data from the official landslide Italian inventory (IFFI) and on its updating with a field-mapped rockfall dataset. Regarding the RF model, the Shapely Additive exPlanations (SHAP) were employed for the interpretation of the predictors’ behaviour. A comparison between GAM and RF related outputs was carried out to verify their coherency, as well as a quantitative integration of the resulting susceptibility maps to reduce uncertainties. Finally, the rockfall susceptibility maps were coupled with Synthetic Aperture Radar (SAR) data from 2014 to 2021: a qualitative geomorphological verification of the outputs was performed, and composite maps were produced. The key results were: (i) geomechanical predictor maps were obtained applying an ordinary kriging for Jv and Wi (NRMSE equal to 13.7% and 14.5%, respectively) and by means of Thin Plate Splines for Keq (NRMSE= 18.5%). (ii) Jv was the most important geomechanical predictor both in the GAM (witha deviance explained of 7.5%) and in the RF model, with a rockfall susceptibility increase in correspondence of the most fractured rock masses. (iii) Wi and Keq were penalized (i.e., they had low influence on rockfall susceptibility) in the GAM model, whereas Keq showed an importance comparable to Jv in the RF model. (iv) In a complex Machine Learning model (RF), the SHAPs allowed the interpretation of predictors’ behaviour, which demonstrated to be coherent with that shown in the GAM model. (v) The models including the geomechanical predictors resulted in acceptable rockfall discrimination capabilities (AUROC>0.7). (vi) The introduction of the geomechanical predictors led to a redistribution of the high-susceptibility areas in plausible geomorphological contexts, such as in correspondence of active slope deformations and structural lineaments, otherwise not revealed by the topographic predictors alone. (vii) Models built with solely the IFFI inventory, resulted in physically implausible susceptibility maps and predictor behaviour, highlighting a bias in the official inventory. (viii) The discordance in predicting rockfall susceptibility between the GAM and the RF models varied from 13% to 8% of the total study area. (ix) From the integration of InSAR data and susceptibility maps, a “SAR Integrated Susceptibility Map”, and an “Intervention Priority Map” were developed as operational products potentially exploitable in environmental planning activities. The Aosta Valley case study was dedicated to challenge the concept of “susceptibility stationarity” by including the climate component in the rockfall susceptibility model. The availability of a large historical rockfall inventory and an extensive, multi-variable meteorological dataset for the period 1990-2020 were crucial input for the analysis. Specific objectives were: (i) the identification of climate conditions related to rockfall occurrence (ii) the summary of the identified relationships in variables to be used in a susceptibility model; (iii) the optimization of a rockfall susceptibility model, including both topographic, climatic and additional snow-related predictors (from a SWE weekly gridded dataset). Starting from an hourly meteorological dataset, climate conditions were summarized in indices related to short-term rainfall (STR), effective water inputs (EWI, including rainfall and snow melting), wet-dry cycles (WD) and freeze-thaw cycles (FT). Climate indices and rockfall occurrence time series were paired. Critical thresholds relating rockfall occurrence to climate indices not-ordinary values (>75th percentile) were derived through a statistical analysis. As summary variables for the susceptibility analysis, the mean annual threshold exceedance frequency for each index was calculated. Model optimization consisted in stepwise modifications of the model settings in order to handle issues related to inventory bias, physical significance of climatic predictors and concurvity (i.e., predictors collinearity in GAMs). The starting point was a “blind model”, i.e., a susceptibility model created without awareness of the rockfall inventory characteristics and of the physical processes potentially influencing susceptibility. To reduce the inventory bias, “visibility” masks were produced so to limit the modelling domain according to the rockfall collection procedures adopted by administrations. Thirdly, models were optimized according to the physical plausibility of climatic predictors, analysed through the smooth functions relating them to susceptibility. Finally, to reduce concurvity, a Principal Component Analysis (PCA) including climatic and snow-related predictors was carried out. Subsequently, the obtained principal components were used to replace the climatic predictors in the susceptibility model. The key results were: (i) the 95% of the rockfalls occurred in severe (or not ordinary) conditions for at least one among the EWI, WD and FT indices; (ii) ignoring inventory bias led to excellent model performance (0.80≤AUROC ≤0.90) but physically implausible outputs; (iii) the selection of non-rockfall points inside the “visibility mask” was a valuable approach to manage the inventory bias influence on outputs; (iv) the inclusion of climate predictors resulted in an improvement of the susceptibility model performance (AUROC up to 3%) in comparison to a topographic-based model; (v) the most important physically plausible climate predictors were EWI, WD, with a deviance explained varying from 5% to 10% each, followed by the maximum cumulated snow melting with a deviance explained varying from 3% to 5%. The effect of FT was masked by elevation. (vi) When the climate and snow related predictors were inserted in the susceptibility model as principal components, concurvity was efficiently reduced. The inclusion of climate processes as non-stationary predictors (i.e., considering climate change) could be a valuable approach both to derive long-term rockfall susceptibility future scenarios and in combination with short-term weather forecasts to adapt susceptibility models to an early warning system for Civil Protection purpose.