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Rock avalanches can be a significant hazard to communities located in mountainous areas. Probabilistic predictions of the 3D impact area of these events are crucial for assessing rock avalanche risk. Semi-empirical, calibration-based numerical runout models are one tool that can be used to make these predictions. When doing so, uncertainties resulting from both noisy calibration data and uncertain governing movement mechanism(s) must be accounted for. In this paper, a back-analysis of a database of 31 rock avalanche case histories is used to assess both of these sources of uncertainty. It is found that forecasting results are dominated by uncertainties associated with the bulk basal resistance of the path material. A method to account for both calibration and mechanistic uncertainty is provided, and this method is evaluated using pseudo-forecasts of two case histories. These pseudo-forecasts show that inclusion of expert judgement when assessing the bulk basal resistance along the path can reduce mechanistic uncertainty and result in more precise predictions of rock avalanche runout. [ABSTRACT FROM AUTHOR]

Extremely rapid, flow-like landslides pose a significant hazard worldwide; however, the analysis of the impact area and velocity of these flows is not routine. Semi-empirical numerical models are one tool that is available for performing this sort of analysis. These models are physically based; however, certain input parameters are determined through model calibration, using back-analysis of real landslide cases. Objective, repeatable calibration methods are needed for this approach to be useful for landslide runout prediction. The present analysis describes the application of optimization theory and Bayesian statistics to calibrate these types of models. Two complementary methods are presented. The first uses the Gauss-Marquardt-Levenberg optimization algorithm to efficiently determine a set of best-fit calibrated model parameters. The second uses a posterior analysis to quantify errors associated with parameter calibration, which can then be used for probabilistic forward analysis. Three case histories are presented to demonstrate how the new methods are able to rapidly calibrate a runout model, reduce subjectivity inherent in the calibration process, and provide information on parameter uncertainty. [ABSTRACT FROM AUTHOR]

Portfolio risk diversification is a well established concept in finance. While aggregation of several risky assets generally reduces the overall investment risk due to diversification, the effectiveness of diversification depends on the stochastic behaviour of the returns of the assets comprising the portfolio. The paper proposes a new approach to quantifying the effect of portfolio tail diversification by looking at the asymptotic behaviour of the ratio of the largest loss on the portfolio to the sum of the largest losses on the individual investments held on the stand-alone basis. It is assumed that independent and identically distributed random vectors from the underlying distribution, describing the behaviour of returns on the assets in the portfolio, can be scaled to converge onto a deterministic limit set. This property is satisfied by a number of distributions commonly used in finance. Several analytical examples are given to illustrate the proposed asymptotic diversification index as a measure of the effect of risk aggregation on extremes as well as to quantify the impact of dimension on the diversification and as a tool in optimal portfolio selection. [ABSTRACT FROM AUTHOR]