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[1] Despite volcanic risk having been defined quantitatively more than 30 years ago, this risk has been managed without being effectively measured. The recent substantial progress in quantifying eruption probability paves the way for a new era of rational science-based volcano risk management, based on what may be termed ''volcanic risk metrics'' (VRM). In this paper, we propose the basic principles of VRM, based on coupling probabilistic volcanic hazard assessment and eruption forecasting with cost-benefit analysis. The VRM strategy has the potential to rationalize decision making across a broad spectrum of volcanological questions. When should the call for evacuation be made? What early preparations should be made for a volcano crisis? Is it worthwhile waiting longer? What areas should be covered by an emergency plan? During unrest, what areas of a large volcanic field or caldera should be evacuated, and when? The VRM strategy has the paramount advantage of providing a set of quantitative and transparent rules that can be established well in advance of a crisis, optimizing and clarifying decision-making procedures. It enables volcanologists to apply all their scientific knowledge and observational information to assist authorities in quantifying the positive and negative risk implications of any decision.

One of the most challenging decisions in the domain of natural hazards is whether to evacuate a densely populated region around a volcano that appears to threaten a major eruption. The economic expense of mass evacuation is high, yet the cost in possible human casualties is potentially much greater if an evacuation is not called, or is called late. To assist officials in weighing these considerations, probabilistic criteria for evacuation decision-making are developed within a cost-benefit analysis framework. It is shown that such criteria may be quantitatively expressed in terms of the proportion of the evacuees owing their lives to the evacuation call. The underlying principles are illustrated with some case studies where eruption probabilities have been estimated.

One of the most critical practical actions to reduce volcanic risk is the evacuation of people from threatened areas during volcanic unrest. Despite its importance, this decision is usually arrived at subjectively by a few individuals, with little quantitative decision support. Here, we propose a possible strategy to integrate a probabilistic scheme for eruption forecasting and cost‐benefit analysis, with an application to the call for an evacuation of one of the highest risk volcanoes: Vesuvius. This approach has the following merits. First, it incorporates a decision‐analysis framework, expressed in terms of event probability, accounting for all modes of available hazard knowledge. Secondly, it is a scientific tool, based on quantitative and transparent rules that can be tested. Finally, since the quantitative rules are defined during a period of quiescence, it allows prior scrutiny of any scientific input into the model, so minimizing the external stress on scientists during an actual emergency phase. Whilst we specifically report the case of Vesuvius during the MESIMEX exercise, the approach can be generalized to other types of natural catastrophe.

An event catalog is a foundation of the risk analysis for any natural hazard. Especially if the catalog is comparatively brief relative to the return periods of possible events, it may well be deficient in extreme events that are of special importance to risk stakeholders. It is common practice for quantitative risk analysts to construct ensembles of future scenarios that include extreme events that are not in the event catalog. But past poor experience for many hazards shows that these ensembles are still liable to be missing crucial unknown events. An explicit systematic procedure is proposed here for searching for these key missing events. This procedure starts with the historical catalog events, and explores alternative realizations of them where things turned for the worse. These are termed downward counterfactuals. By repeatedly exploring ways in which the event loss might have been incrementally worse, missing events can be discovered that may take risk analysts, and risk stakeholders, by surprise. The downward counterfactual search for extreme events is illustrated with examples drawn from a variety of natural hazards. Attention is drawn to the problem of overfitting to the historical record, and the value of stochastic modeling of the past.

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We analyse the economic risks from two influenza pandemics that represent extremes along the virulence‐infectiousness continuum of possible pandemics: a high virulence–low infectiousness event and a low virulence–high infectiousness event. Our analysis involves linking an epidemiological model and a quarterly computable general equilibrium model. We find that global economic activity is more strongly affected by a pandemic with high infection rates rather than high virulence rates, all else being equal. Regions with a higher degree of economic integration with the world economy face greater risks of negative effects than less integrated regions.