Bayesian Approach to cinsider Uncertainties in Avalanche Simulation

Artikel aus einem Buch

17574BU

200204858

ABSTRACT: Over the last decades, an increasing number of software tools for modelling rapid mass flows (e.g. avalanches, debris flows) has been developed, tested and applied in scientific and practical studies. But the accurate description of the involved processes still remains a challenge and assumptions are necessary for a simplified description of the natural process. Due to these assumptions, model parameters (e.g. friction) may not present physical properties and thus are commonly back-calculated to fit observed data, which also involve a degree of uncertainty. We present a Bayesian approach to perform a parameter optimization for the mass flow model r.avaflow, based on documented avalanche events, where uncertainties arising from model simplifications and imprecise observations are explicitly considered. To compare simulation results and documentation data, multiple avalanche characteristics (e.g. run-out lengths, deposition patterns or maximum velocities) are investigated. To derive a posterior distribution for the parameters of the basal friction relation, the Metropolis-Hastings algorithm is applied. The posterior distribution is used to perform (i) a probabilistic forward simulation of the same avalanche event and (ii) a probabilistic prediction for a ’theoretical unknown’ avalanche track. The dynamic peak pressure results of multiple model runs are evaluated in terms of probability maps. These display the probabilities, that an avalanche hits a certain region of the respective avalanche track, conditional on the used optimization data and considered uncertainties. Observations allow an assessment of the correspondence between theoretically predicted and real events. The outcome illustrates that including uncertainties in both the optimization and prediction process helps to asses the reliability of simulation results for future avalanche events. Keywords: Bayes’ theorem, Metropolis-Hastings algorithm, parameter estimation, probabilistic simulation, posterior distribution, back calculation, prediction