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ABSTRACT. The present work addresses the urgent demand for methods of quantifying the uncertainties inherent in the current procedures for avalanche hazard assessment. A Monte Carlo approach to hazard mapping is proposed for this purpose. This statistical samplinganalysis method allows us to evaluate the probability distributions of the relevant variables for avalanche hazard assessment ö essentially runout distance and impact pressure ö once the release variables and the model parameters are expressed in terms of suitable probability distributions. In this way it is possible to explicitly account for uncertainties both in the inputdata definition of the dynamic models and in the mapping results. The overall methodology is presented in detail and applied to a real-world avalanche mapping problem. The one-dimensional version of the VARA models is used for avalanche dynamics simulations.

An innovative methodology to perform avalanche hazard mapping over large undocumented areas is herewith presented and discussed. The method combines GIS tools, computational routines, and statistical analysis in order to provide a ''semi-automatic'' definition of areas potentially affected by avalanche release and motion. The method includes two main modules. The first module is used to define zones of potential avalanche release, based on the consolidated relations on slope, morphology, and vegetation. For each of the identified zones of potential release, a second module, named Avalanche Flow and Run-out Algorithm (AFRA), provides an automatic definition of the areas potentially affected by avalanche motion and run-out. The definition is generated by a specifically implemented ''flow-routing algorithm'' which allows for the determination of flow behaviour in the track and in the run-out zone. In order to estimate the avalanche outline in the run-out zone, AFRA uses a ''run-out cone'', which is a 3D projection of the angle of reach a. The a-value is evaluated by statistical analysis of historical data regarding extreme avalanches. Pre-and post-processing of the AFRA input/output data is done in an open source GIS environment (GRASS GIS). The method requires only a digital terrain model and an indication of the areas covered by forest as input parameters. The procedure, which allows rapid mapping of large areas, does not in principle require any site-specific historical information. Furthermore, it has proven to be effective in all cases where a preliminary cost-efficient analysis of the territories potentially affected by snow avalanche was needed.

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Use of formal risk analysis to assess avalanche danger is currently limited by a lack of knowledge of how avalanche impact pressures damage structures and cause fatalities. That is, the vulnerability component of risk is poorly specified. In this paper we outline a method for deriving vulnerability values as a function of position downslope for a range of avalanche sizes. The method is based on the weighted average of vulnerability and uses an avalanchedynamics model embedded within a statistical framework. The models seem to behave in a consistent manner. By allowing avalanche size and stopping position to vary and calculating vulnerability as a function of distance from the stopping position, vulnerability values are less approximate than the assumption of a constant vulnerability value for each individual size. When the assumptions underlying the impact pressure -vulnerability relation are perturbed, the results seem to be robust. The method outlined here should provide a way for avalanche experts to reformulate danger zones based on return period and impact pressure so that they are set within a risk framework.Résumé : L'utilisation d'analyse formelle de risques pour évaluer le danger d'avalanche est couramment limitée par le manque de connaissances sur la façon dont les pressions d'impact des avalanches endommagent les structures et sur les causes des morts. En somme, la composante vulnérabilité du risque est mal spécifiée. Dans cet article, on décrit une méthode pour dériver les valeurs de vulnérabilité en fonction de la position dans la pente à partir du sommet pour une plage de dimensions d'avalanches. La méthode est basée sur la moyenne pondérée de la vulnérabilité et utilise un modèle de dynamique d'avalanche enchâsser dans un cadre statistique. Les modèles semblent se comporter de manière conséquente. En permettant la variation de la dimension de l'avalanche et de la position d'arrêt, et en calculant la vulnérabilité en fonction de la distance de la position d'arrêt, les valeurs de vulnérabilité sont moins approximatives que l'hypothèse d'une valeur de vulnérabilité constante pour chaque dimension particulière. Lorsque les hypothèses soustendant la relation pression d'impact/vulnérabilité sont perturbées, les résultats semblent solides. La méthode décrite ici devrait fournir une façon pour les experts en avalanches de reformuler les zones dangereuses sur la base de la période de retour et de la pression d'impact de telle sorte qu'elles soient placées à l'intérieur d'un cadre de risques. Keylock and Barbolini 229Fig. 2. The town of Súðavík, the avalanche path (Suhl02aa) used in this study, and the outline of the 1995 avalanche (bold line). Contours in metres.