Quantitative Evaluation of Probabilistic Hazard Mapping With Polynomial Chaos Quadrature and Its Practical Application

Abstract

Snow avalanches pose a significant threat to settlements and their inhabitants. Consequently, hazard maps that delineate avalanche runout areas serve as valuable tools for mitigating their destructive impact. Dynamic models have been used to visualize areas affected by avalanches; however, these models require uncertain inputs. This study develops probabilistic hazard maps by quantifying uncertain input variables through probability density functions. These maps represent the probability of model outputs, such as maximum flow thickness, exceeding specific thresholds, allowing for more quantitative hazard assessments. Three uncertainty quantification methods—Monte Carlo, Latin hypercube sampling, and polynomial chaos quadrature (PCQ)—are employed to generate probabilistic hazard maps for snow avalanches. These maps are compared with a reference hazard map created using parameter sets that cover the entire parameter space. Among the three methods, PCQ yields the most accurate results for a given number of simulations, assuming a uniform distribution for each input. The optimal PCQ settings, which deliver superior results with fewer simulations, are then determined. Additionally, a PCQ application is proposed to generate hazard maps based on non-uniform input distributions without requiring extra simulations. This approach reduces the computational cost associated with creating hazard maps for non-uniform distributions if PCQ has already been applied to a uniform case. The application generates two types of probabilistic hazard maps: one considering all potential parameter ranges during the snow season using uniform distributions, and another reflecting non-uniform distributions that account for uncertainty in near-term current snow cover conditions.