2022 Volume 84 Issue 4 Pages 309-321
In a numerical model, the dynamics of an avalanche, such as the runout distance, flow velocity, and flow thickness, are calculated under the initial conditions of the model. These initial conditions are selected according to assumed distributions, which are derived from field observations or theoretically. These distributions are called uncertainties of the model input, and the model output depends on the input. An output calculated with an input based on the distribution reflects these uncertainties. The uncertainties in inputs are propagated in outputs through the numerical model, which is called uncertainty propagation. This propagation is utilized for hazard mapping while considering the uncertainties in output. A hazard map enables us to estimate the quantitative risk of an avalanche. In this study, three methods are employed to evaluate an uncertainty: Monte Carlo (MC), Latin hypercube sampling (LHS), and polynomial chaos quadrature (PCQ). We use the models to quantify the uncertainty of initial volume of an avalanche, and then draw resultant hazard maps using each method. A comparison of maps based on MC, LHS, and PCQ revealed that (i) PCQ had the best result in terms of computational cost and map quality, and (ii) a proper condition is required for PCQ to obtain the highest map quality. Here, the condition is NP=NQ, where NP represents the order of polynomial chaos expansion and NQ denotes Gaussian quadrature points.
