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 are a valuable tool for
mitigating their 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 near-term real-world snow
cover conditions.