Derivation and evaluation of landslide triggering thresholds by a Monte Carlo approach
Abstract. Rainfall thresholds are the basis of early warning systems able to promptly warn about the potential triggering of landslides in an area. Following a common empirical methodology, thresholds may be derived through the analysis of historical rainfall and landslide data, by drawing an envelope curve of triggering rainfall events, represented by their intensity and duration. Nonetheless, reliability of empirical thresholds is generally affected by the historical data quality and availability. Moreover, rainfall intensity and duration alone may not be able to capture most of the uncertainty related to landslide triggering. In this work Monte Carlo simulations are carried out to generate a synthetic rainfall series by a stochastic model and the corresponding landslide response by means of an hydrological and geotechnical model. The series are of virtually unlimited length and present no interruption in data availability, and the triggering instants can be precisely identified, overcoming some of the most important quality and availability drawbacks of using historical data. Receiver Operating Characteristic (ROC) analysis is carried out to derive and evaluate landslide triggering thresholds, considering both triggering and non-triggering rainfall. The effect of variability of both rainfall intensity within events and of initial conditions as determined by antecedent rainfall is analysed as well. The proposed methodology is applied to the landslide-prone area of Peloritani Mountains, Northeastern Sicily, Italy. Results show that power-law ID equations can adequately represent the triggering conditions due to transient infiltration response to temporally-variable rainfall and hence may be of good performance for a hillslope with small specific contributing area. On the other hand, as specific contributing areas become larger, past rainfall has an increasing importance, and an antecedent rainfall variable should be used in addition to ID power-laws to achieve adequate reliability. Results also indicate that for short rainfall durations uniform hyetographs may have a stronger destabilizing effect than the stochastically-variable ones, while the opposite may occur for greater durations. Thus a power-law ID threshold may perform better than a model deterministic one that is derived considering uniform hyetographs and a prefixed initial condition. Further analyses show that predictability of landslides decreases with soil depth and geomechanical strength.