Dynamic Uncertainty in Cost-Benefit Analysis of Evacuation Prior to a Volcanic Eruption

Many cities around theworld lie in the shadowof dangerous volcanoes. This potential for disaster has led to constant extensive monitoring of possible precursors to an eruption and probabilistic techniques to transform this monitoring information into eruption probabilities. Less developed are the decision models that determine the probability level at which an evacuation should be called. A simple static criterion exists that balances the value of life lost in a missed evacuation against the cost of economic dislocation in the case of an unnecessary evacuation. However, dynamic facets such as the distribution of time to the eruption onset, the non-zero time required for an evacuation, spontaneous evacuation or return, the possible eruption size, and political pressures are not integrated into the criterion. A stochastic treatment of these variables is proposed, and the resulting effect on the evacuation dynamics derived. A detailed application to the case of a future eruption of Mount Vesuvius, expected to put at risk almost one million lives, is presented. A novel method is devised to invert the probability of eruption in a fixed time window into a statistical distribution for the time to eruption. Through an optimal cost-benefit based decision criterion, the probability threshold for immediate evacuation is calculated, and below this a time window during which the event probability can be refined before a decision must be made. The baseline model threshold is some 13 % lower than in the static model, and the sensitivity of the results to the estimated parameters is examined.