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2 Journal of Volcanology and Geothermal Research (2012) Contents lists available at SciVerse ScienceDirect Journal of Volcanology and Geothermal Research journal homepage: Review The scientific management of volcanic crises Warner Marzocchi a,, Christopher Newhall b, Gordon Woo c a Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy b Earth Observatory of Singapore, Nanyang Technological University, Singapore c Risk Management Solutions, London, UK article info abstract Article history: Received 15 March 2012 Accepted 28 August 2012 Available online 31 August 2012 Keywords: Unrest Eruption forecasting Decision making Volcanic risk Sound scientific management of volcanic crises is the primary tool to reduce significantly volcanic risk in the short-term. At present, a wide variety of qualitative or semi-quantitative strategies is adopted, and there is not yet a commonly accepted quantitative and general strategy. Pre-eruptive processes are extremely complicated, with many degrees of freedom nonlinearly coupled, and poorly known, so scientists must quantify eruption forecasts through the use of probabilities. On the other hand, this also forces decision-makers to make decisions under uncertainty. We review the present state of the art in this field in order to identify the main gaps of the existing procedures. Then, we put forward a general quantitative procedure that may overcome the present barriers, providing guidelines on how probabilities may be used to take rational mitigation actions. These procedures constitute a crucial link between science and society; they can be used to establish objective and transparent decision-making protocols and also clarify the role and responsibility of each partner involved in managing a crisis Elsevier B.V. All rights reserved. Contents 1. Introduction Ahistoricalperspectiveofcopingwithvolcanicthreats:Limitationsandchallenges The scientific contribution to the decision-making process The role of uncertainty Operational forecasting Taking a decision under uncertainty Basic components of decision-making Quantitative methods: Cost-benefit analysis Science, decision-making and future developments Acknowledgments References Introduction Eruptions of high risk volcanoes are usually preceded by a phase of unrest. Sound management of this phase may help save many lives and reduce the economic impact of eruptions, for instance through the timely evacuation of threatened areas. In this paper we review the state of the art in this field and put forward a new perspective about how to improve the link between scientists and decision-makers in managing phases of unrest. Many of the points discussed here can be Corresponding author. Tel.: ; fax: address: warner.marzocchi@ingv.it (W. Marzocchi). generalized to many other hazards and risk mitigation actions. We will not review the vast literature on long-term hazard assessment or that based on elaborate computational models for ashfall, mudflow etc. However, the practical value of such models is greatly enhanced by having a probabilistic framework for decision making. The increasing human economic exposure to natural hazards drives scientists and decision-makers to look for operational risk reduction strategies at different time scales (e.g., Jordan et al., 2011). The establishment of effective risk mitigation actions requires a coordinated effort between scientists, decision-makers, and experts in communication. This task is complex and encompasses many aspects; one of the most critical is the link between scientists and decision-makers. Improving the connection between science and decision-making has /$ see front matter 2012 Elsevier B.V. All rights reserved.

3 182 W. Marzocchi et al. / Journal of Volcanology and Geothermal Research (2012) become imperative after the accusation of misconduct by scientists and decision makers after the L'Aquila, 2009, earthquake (Cartlidge, 2011). Uncertainties pose special challenges. Decision-makers invariably prefer small uncertainties and substantial agreement among experts because they fear that large uncertainties may undermine public confidence or open decisions to legal challenges (Aspinall, 2010; Nath, 2012). In some cases, decision makers may not be prepared or trained to deal with uncertain scientific information in a quantitative and objective way. In practice, the choice to take or not to take a mitigating action is typically based on qualitative information and personal judgment during a crisis, rather than on fully quantified information including all uncertainties and the quantified pros and cons of each planned mitigation action. While a qualitative approach can be workable for low to moderate risk volcanoes, the decision-making for high risk events requires a more objective and quantitative approach. More critically, the specific roles and responsibilities of scientists and decision-makers often become confused. Although civic leaders are empowered with the authority to make crucial societal decisions, scientists are often involved in the decision making process as scientific advisors. Sometimes, it is unclear if the advice should be related only to scientific assessments, or to possible actions to mitigate the impending risk. Worse, it is rarely clear what the liabilities for scientists are when they provide advice, be it strictly scientific or reaching beyond science (Aspinall, 2011; see also the trial after L'Aquila earthquake, Cartlidge, 2011). Scientists may be asked to recommend precautionary actions like, for instance, the evacuation of a threatened area. This approach is clearly problematic because any decision about acceptable risk must consider economics, the social fabric of a community, politics, and various other matters that are beyond the expertise, and often authority, of any scientist. This might be particularly awkward for volcanologists who work for governmental agencies that, in some cases, may be held accountable to the public in the same way as public officials are held accountable. Sometimes a volcanologist may be asked what he or she would do as the decision-maker. Such a hypothetical question cannot be answered without imposing the volcanologist's own aversion to risk. Motivated to advance their science through acquiring data in difficult circumstances, even from precarious positions of personal danger, volcanologists tend to expose themselves more to volcanic danger than would be acceptable for the general public. Although volcanologists may not have a direct civic responsibility to the public, they have a legal duty of care as professionals, even if, as with physicians acting on emergencies, they may not be explicitly remunerated for their advice, and act purely pro bono (Aspinall, 2011). In general, any decision bears the psychological imprint of the decision-maker. The decision making process is inherently multidisciplinary and it requires experts in many fields. Beyond the kind of expertise already discussed a critical issue is the manner in which hazard information is communicated to society and even to decision makers. Here, social scientists and experts in communication may play a role (Mileti and Sorenson, 1990; Donovan et al., 2012a, 2012b). The inherent multidisciplinary issues notwithstanding, we argue that a clear distinction in roles and responsibilities between scientists and decision makers may be very helpful and desirable. This point will be explored in the next sections. 2. A historical perspective of coping with volcanic threats: Limitations and challenges For most individuals, volcanic threats are a relatively rare phenomenon that can be tolerated in return for the many benefits of living near volcanoes. When eruptions do impact communities, they cause either minor damage and inconvenience or major damage and death, with very little in between. The obvious strategy to live with volcanic hazards is to know where and when they will hit, and to evacuate temporarily when necessary. Where eruptions are frequent and well known, or where they have been large enough for geologists to recognize the footprints of where they would have been lethal, the areas that are subject to hazards can be known with a manageable degree of uncertainty. Oral traditions, historical accounts, and tell-tale deposits of pyroclastic flows, lahars, and other lethal activity identify areas that have been impacted before and are likely to be impacted in the future. Years of painstaking field and laboratory work are required to ferret out every detail of a volcano's eruptive history, e.g., work by Crandell and Mullineaux (1978) prior to the 1980 eruption of Mount St. Helens, in Washington State, USA. However, an experienced volcanic stratigrapher can piece together a useful provisional eruptive history within much less time, especially in the face of unexpected and urgent unrest, e.g., work by US and Philippine scientists in just 2 months before the 1991 eruption of Pinatubo (Newhall et al., 1996). Of course either rapid or more detailed analyses may still have a large uncertainty because the geological record is ephemeral. Erosion removes, weathering obscures, and burial hides a significant part of the geologic record of explosive volcanism. Geologists who study eruptions in progress are often astounded to find that just years after the eruption, many details of those eruptions are lost from the geologic record. Some of the most lethal volcanic hazards, e.g., pyroclastic surges and lateral blasts, are among the most ephemeral. Historically, information about the reach of volcanic hazards has been portrayed on printed hazard maps that outline, implicitly or explicitly, the so-called worst-case or worst-credible scenario (e.g., Rosi, 1996). Usually, areas subject to pyroclastic flows, tephra fall of various thicknesses, lava flows, and lahars are shown separately, in sometimes overlapping zones. The geologic record is too abstract for many non-geologists to understand. When a Mayor of Baños, at the base of Tungurahua volcano in Ecuador, was shown deposits of pyroclastic flows similar to those he had just seen illustrated in the IAVCEI video Understanding Volcanic Hazards, he could not relate the sand and gravel before him to what was shown in the film. He saw only a quarry of sand and gravel, not a story of horrific events in the recent geologic past. Many laymen also have trouble visualizing information that is on a flat map; Haynes et al. (2007) correctly called this to the attention of scientists who are accustomed to using flat maps to convey their results. Today, tools to overlay map information onto shaded relief or other 3D visualizations ease this problem. Moreover, conventional hazard maps have some scientific limitations. For instance they do not tell users how dangerous a particular hazard might be. This was a major problem in the City of Armero, Colombia, in 1985, when a hazard map correctly identified that Armero would be hit by a flujo de lodo (mudflow), but did not convey the severity of such an event, nor the magnitude of the disaster that could, and subsequently did, occur. Similarly, many hazard maps do not say how frequent a hazard might be, so users are left to judge for themselves whether they are faced with a 10-year event, a 100-year event, or a 1000-year event. In addition, terms like worst-case, credible, and worst-credible scenario are themselves risky. The definition of the worst scenario (if any) is a deterministic statement that requires an amount of knowledge that scientists rarely have. A recent example of failure of the worst scenario hypothesis in seismology is related to the occurrence of the Tohoku 2011 earthquake; this earthquake was much larger than the worst officially expected event in this area (Fujiwara et al., 2006). In principle, scientists can imagine a continuous spectrum of possible scenarios, each one of them with a probability of occurrence attached. In this view, the choice of the 'worst defines what can be neglected, and, consequently, it implicitly defines the acceptable risk that is, as said before, beyond the competences of scientists. Similarly, the term credible as used in nuclear safety evaluations (e.g., IAEA, in review)

4 W. Marzocchi et al. / Journal of Volcanology and Geothermal Research (2012) implicitly or explicitly assigns a minimum probability for credibility, below which events would be considered incredible until they occur. The IAEA is relatively conservative; others who use the term credible might have a higher threshold. These limitations notwithstanding, planners can use such hazard maps as the basis for contingency and land-use plans in a productive way. To a first order, conventional volcanic hazard maps such as described above have served communities very well, and many lives and homes have been saved by heeding them. Where communities already exist within areas subject to volcanic hazard, citizens and officials must decide whether to remain in the area or move the entire community. Almost always, the decision is to remain in the area and to rely on volcano monitoring and short-range warnings to alert them of imminent danger. Some reduction in the population at risk may be achieved by offering inducements to relocate. Fortunately for communities at risk, volcanoes usually signal when they are about to erupt. Magma ascent and decompression causes exsolution of different kinds of gas from the magma, and an increase of magma pressure and thus an increase of seismic activity and ground deformation. Magma ascent produces a wide variety of signals, many of which can be detected and tracked by instruments at the surface. Each volcano exhibits slight differences in the signs of magma ascent and pressurization, but there are enough commonalities that volcano observatories have become quite good at spotting unrest and knowing when magma is rising. Nearly all eruptions can in principle be anticipated from their precursory unrest. Lest anyone grow complacent, though, it must also be said that many volcanoes are not monitored at all. Even those which are monitored often show too many signs of unrest. Not all magma intrusions will reach the surface in fact, a majority do not yet the signs of intrusions that will stall at depth are very similar to those of intrusions that will erupt (e.g. Moran et al., 2011). Volcanologists face an ongoing challenge to discriminate between those magma intrusions that will and will not erupt. Because of the difficulty in knowing which intrusions will erupt, many observatories have adopted numerical or color codes to indicate increasing or decreasing probability of eruption, sometimes using very generic indicators to move from one level to the other (see Fig. 1). Usually, such color codes are directly translated into alert levels for taking mitigation actions without any further analysis. This transposition may be misleading, since what scientists define as low probability may not be low at all for decision making. For instance, a 1% of probability may be defined as a low probability by scientists, while, conversely, it is a very high chance if one's life is at stake. Volcanologists and decision makers often face the threat of an impending eruption by following mostly a set of informal and subjective procedures that are decided during the volcanic unrest. Uncertainties in the whole decision-making process are almost never clearly stated or represented (for example, the uncertainty in defining a reference scenario). This informal approach has brought some important successes in the past, in particular where evacuations were logistically easy and called close in time to the coming eruption. But this approach is hardly satisfactory where evacuation logistics are slow and complex, and the human stakes are very high. In the latter cases, any kind of decision is likely to have a large economic and social impact. This would raise much concern and criticism, or even worse, accusation of misconduct after the crisis, if proved to be ineffective. In the next sections we introduce the basic principles that underlie more quantitative and objective decision-making. In particular, we put forward a general procedure that may be used by decision-makers in order to manage scientific uncertainty in a rational way. Of particular note, this approach allows scientists and decision-makers to clarify ALERT LEVELS STATE OF THE VOLCANO ERUPTION PROBABILITY TIME OF THE ERUPTION Base No significantvariation of monitored parameters Very low Undefined, not less than several months Attentio n Significant variation of monitored parameters Low Undefined, not less than some months Warning Further variation inmonitored parameters Medium Undefined, not less than some weeks Alarm Appearance of phenomena and/or evolution of parameters suggesting a pre-eruption dynamic High From weeks to days ALERT LEVELS The alert system described in the emergency plan includes the following main levels: Attention: when monitored variables exceed their established thresholds; monitoring processes are further enforced and the local population and civil authorities are promptly alerted. Pre-alarm: when the probability of an eruption increases all bodies in volved in the emergency plan must enter a state of alertness and be dispatched on the area to be evacuated (red zone). Alarm: when the eruption is imminent and people are evacuated from the red zone. Fig. 1. Alert levels for Vesuvio. Different mitigation actions are associated with different state of the volcano and with categorized probabilities.

5 184 W. Marzocchi et al. / Journal of Volcanology and Geothermal Research (2012) the roles of each partner involved, and to establish transparent decision-making protocols before a crisis. These may serve as tools for communication with society and other scientists, and for justifying each step of the decision-making process. 3. The scientific contribution to the decision-making process 3.1. The role of uncertainty Volcanic systems, like all natural systems, are characterized by the ubiquitous presence of uncertainties. Pragmatically, uncertainties can be categorized as epistemic (due to the limited knowledge of the physical system that produce the eruption) and aleatoric (due to the intrinsic unpredictability of the processes). The distinction between these two kind of variables is not always sharp (e.g., Budnitz et al., 1997), but useful nonetheless because the epistemic uncertainty may be reduced through improving the state of knowledge of the volcano, while the presence of aleatoric uncertainty reminds scientists of the randomness of Nature. Aleatoric uncertainty is irreducible and it is an intrinsic feature of many natural systems that are governed by a high number of degrees of freedom that are often nonlinearly coupled (e.g. Gleick, 1987; Bak, 1997). Risk mitigation should try to lower epistemic uncertainties. This is certainly the prime motivation for scientists to keep studying volcanoes and to improve monitoring capabilities. Scientists can improve the knowledge about volcanic systems using theoretical and physical models, laboratory experiments, empirical analyses, and an increasing amount of high quality monitoring data to constrain theoretical and empirical models. Nonetheless, monitoring of seismicity, ground deformation, gas emissions, and other changes are inherently indirect, because scientists simply cannot access and measure magma itself. The most important parameters needed for forecasting purposes, e.g., viscosity, gas content, temperature, pressure, volume, and subsurface distribution of magma must all be inferred from indirect proxies. This poses a natural lower limit on uncertainty reduction. In practice, we are still very far above this limit. Funding and scientific manpower constraints limit how many volcanoes can be monitored, or how well they can be monitored. There are simply too many volcanoes for the available instruments and manpower. Out of roughly 1,500 volcanoes thought to have erupted during the Holocene (Siebert et al., 2010), only about have any monitoring at all. Volcano observatories routinely must prioritize their monitoring on the basis of risk and apparent gaps, using some measure of both, e.g., the method of Ewert (2007). Another common strategy is to deploy minimal instrumentation at many volcanoes, e.g., a single seismometer, and establish baselines for other parameters so that latter can be re-measured frequently in case of unrest. Both of these strategies are workable, but Nature sometimes serves up a wild card, such as an eruption from a volcano that was thought to have a low probability of eruption and was not monitored, e.g., Pinatubo, 1991 or Sinabung, Uncertainties pose a limit to our forecasting capability. Society and decision-makers must accept that the incapability to eliminate all uncertainties should not be seen as a failure of scientists, but rather as a reality of the forecasting process Operational forecasting Decision-making could be (almost) trivial if volcanologists could predict the time and magnitude of the next volcanic eruption with small uncertainty. This has been done in a few exceptional cases, with a lead-time to the eruption of few minutes/hours (e.g., Swanson et al., 1983; Iguchi et al., 2008). But aside from these few cases, the size of the impending eruption remains highly uncertain (e.g., Marzocchi et al., 2004). Large uncertainties when it is still early enough to take mitigation actions necessitate probabilistic forecasts instead. Indeed, we argue that sound scientific management of a volcanic crisis requires that volcanologists develop an operational forecasting capability. Borrowing the definition from seismology (Jordan et al., 2011), operational forecasting comprises procedures for gathering and disseminating authoritative, scientific, consistent, and timely information about the time dependence of probabilistic volcanic hazards to help communities prepare for potentially destructive eruptions. The use of the term forecast instead of prediction highlights the fact that uncertainties always exist and cannot be completely eliminated. Quantitative forecasts should be always stated in terms of probabilities (see also UNDRO, 1985; Decker, 1986). We emphasize the importance of the qualifying term authoritative. If, during a crisis, different interpretations among scientists become publicly contentious, the result is to confuse officials and the public and to distract scientists from their more important tasks. Scientific debate is both healthy and necessary, but most scientists agree that debate should be held behind closed doors and authoritative, consensus statements should be given to officials, to the media, and to the public. In cases where scientific disagreements have been raised in the newspapers or TV, credibility may be judged more from personality than from scientific expertise. The scientific effort can be divided, and the most damaging consequence is loss of trust in scientists by officials and the public. The importance of scientists speaking with one authoritative voice, or, at least, having disagreements presented by a neutral spokesperson, is discussed further in IAVCEI Guidelines for Professional Conduct during Volcanic Crises (IAVCEI, 2000). In specific technical terms, operational forecasting involves assessing probabilities for future possible scenarios. As more and more information is obtained, probabilities can be updated from a chosen baseline using Bayes' theorem, which is a powerful general tool for drawing evidence-based inferences. In contrast with the so-called frequentist statistical approach to assigning probabilities, which applies in data-rich contexts, the sparsity of volcanological data may necessitate some relaxation in objectivity through encoding the degree of belief of experts. The concept of degree of belief is of paramount importance in practical cases (e.g., Woo, 2011). For example, consider this hypothetical scenario (that is very similar to many real situations). From volcanological studies we are able to calculate the past frequency of eruption (objective probability) for a volcano that has not experienced any monitored eruption; let us call P the weekly probability of eruption estimated from the historical catalog. During a phase of unrest we may observe strong seismic activity migrating towards the surface accompanied by localized ground deformation. Even though we do not have any data from a past monitored eruption, any volcanologist would concur that the new weekly probability of eruption has become much higher than P. Due to the lack of past monitored eruptions, we cannot express such a new probability in terms of frequency, but we may estimate it in terms of degree of belief that can be obtained through expert elicitation procedures (e.g., Aspinall et al., 2002; Neri et al., 2008; Selva et al., 2010). To date there is a general agreement that the degree of belief obtained by a group of experts is likely to be more consistent with the axioms of probability, i.e. coherent (De Finetti, 1931), than the degree of belief of each individual (see Gillies, 2000). This procedure is also adopted by many important scientific initiatives like seismic hazard assessment (see, e.g., Budnitz et al., 1997) and climate change assessment (Solomon et al., 2007). In actual situations, volcanologists usually have sparse data along with some rough conceptual models to base their expert opinion. A sound probabilistic assessment has to be capable of using all input information in a rational and transparent way. There are many conceivable probabilistic models to accomplish this goal, but, to date, applications in volcanology are mostly based on the (Bayesian) Event Tree (Newhall and Hoblitt, 2002; Marzocchi et al., 2004, 2008) and the Bayesian Belief Network (Aspinall et al., 2003; Aspinall, 2006). These two procedures have a similar general structure, but the

6 W. Marzocchi et al. / Journal of Volcanology and Geothermal Research (2012) technical procedures to account for data and expert opinion vary significantly. A review of these procedures can be found in Marzocchi and Bebbington (2012). There is an important practical difference of when expert opinion is sought. On one side, during an emergency in Montserrat, opinions of experts have been elicited to gauge the probability of different scenarios according to the monitoring observations (Aspinall et al., 2002; Aspinall, 2006). This elicitation procedure can be further elaborated by drawing data inferences using a Bayesian Belief Network. In other applications to Etna (Brancato et al., 2012), and to two Civil Defense exercises at Vesuvius (MESIMEX; Marzocchi and Woo, 2007) and Auckland Volcanic Field (Ruaumoko; Lindsay et al., 2010), the expected eruption precursors were established before the crisis. The second approach has two main advantages. First, when a crisis does arise, forecasts can be made quickly and without debate, strictly as a function of the monitoring measures (Lindsay et al., 2010). Second, scientists have much more time to establish rules and to find a consensus over them; this also reduces the stress of scientists during an emergency when cognition can be biased by intense pressure. The essence of the eruption forecasting using the Bayesian Event Tree code (BET; Marzocchi et al., 2008) is to identify parameters and relative thresholds that may identify a phase of unrest (node 1 in Fig. 2), the presence of magma driving the unrest (node 2), and the uprising magma towards the surface (node 3). Other nodes for the location and size can be included in the event tree if necessary (Fig. 2). Once thresholds have been defined, possible anomalies in the monitoring observations can be identified; these anomalies are then translated into a probabilistic assessment with the relative uncertainty for each node (see Marzocchi et al., 2008 for more details). Finally, the probability of eruption is given by the multiplication of the conditional probabilities at the first three nodes (Fig. 2). Specifically, for the Ruaumoko exercise (Lindsay et al., 2010), the relevant parameters and thresholds were established before the exercise during discussions with the GeoNet scientists responsible for monitoring activity in the AVF. Of course, any set of rules that may be adopted are not fixed in stone; rather, we believe that they have to represent the actual and accurate picture of the present knowledge of the pre-eruptive phase at the volcano considered, and they must be revised periodically, whenever new information emerges from future studies. It is stressed that the output of the BET code is a probability distribution, not just one single value (Fig. 2); the best estimate for the probability of eruption is given by the central value, while the dispersion around it represents the confidence in the estimate. Note that in this view, the role of scientists is to conduct volcano monitoring and interpret the data for probabilistic operational forecasting, irrespective of the consequences of the threatening events. This is fundamental, in order to not introduce any bias in the scientific assessment. The extent of possible losses guides the kind of mitigation actions that can be made, as discussed in the next sections. 4. Taking a decision under uncertainty 4.1. Basic components of decision-making Taking decisions comes naturally to everyone, rather like speaking a language. Just as one can speak a mother tongue without being taught basic grammar, so one can make decisions without being taught the basic grammar of decision analysis, which was developed in the second half of the 20th century in academic schools of business and applied economics (Bell et al., 1988). There is no formal regulation of grammar; individuals are free to speak as they wish. Similarly, individuals are free to decide as they wish. Indeed, in everyday life, personal decisions are made often unfettered by any kind of logic. But just as a civic official would be expected to communicate grammatically, he or she should know the rudiments of decision analysis, even if the general public is oblivious of them. Moreover, while in our private decision-making we are only responsible to ourselves and personal contacts for possible (a posteriori) failures, at a societal level, a civic official has to be ready to justify each step of the decision-making process. Principles of decision theory need not necessarily be upheld in practice by civic officials, but if they are not, they should be aware of this, especially where public safety is involved. All decisions involve some degree of uncertainty, even if it is just doubt over whether the decision will be liked after it is made. Decisions tend to become progressively harder when the uncertainties facing the decision-maker increase. Where matters of life and death are involved, and uncertainty is high, which is often the case in volcanic crises, decisions become extremely fraught, requiring some measure of decision support. The management of volcanic crises exemplifies this traditional approach. Volcanologists advise the civic decision-makers who then decide on the basis of their own best judgment. The following question arises: what level of quantitative decision support should accompany such advice? Three factors combine to suggest that a significant level is warranted: the considerable uncertainty over the imminence of an eruption; the potential for serious loss of life; and the economic dislocation contingent on an evacuation. Where there are few economic consequences of an evacuation, as with isolated volcanoes, this decision can be made without recourse to economic analysis. However, with increasing populations living around active volcanoes, the economic consequences of any evacuation are often significant enough to warrant the introduction of decision analysis tools borrowed from the domain of applied economics. The problem is sketched in Fig. 3, which shows a simplified scheme illustrating where rational and quantitative decision-making is needed. In particular, evacuations can be called simply following a precautionary approach and without specific evaluation when the number of people is limited, or when the likelihood of false alarm is low. When the number of evacuees is high and the likelihood of false alarm is high, the decision making has to rely on quantitative and clear decision making rules. A few civic leaders are entrusted with special responsibility to make decisions on behalf of communities. Traditionally, during times of community crisis, the designated civic decision-makers arrive at their decisions themselves, after deliberating carefully over the pros and cons. The process of deliberation may involve consultation with expert advisers, but not any formal decision support that a decision analyst would recognize as systematic and reasonably free of cognitive bias. In the case of large evacuations or costly mitigation measures this attitude may be severely criticized if the actions taken turn to be a posteriori ineffective. In circumstances where the threatened event is both rare and extreme, decision-making is an exceptional challenge. When Hurricane Katrina headed towards New Orleans in August 2005, Mayor Nagin hesitated and delayed calling for the first mandatory evacuation in the city's history this decision was ultimately made by President Bush himself. By contrast, when Hurricane Irene headed towards New York six years later, Mayor Bloomberg boldly called for the mass evacuation of 370,000 from coastal areas of the city. As it turned out, by the time Hurricane Irene arrived at Manhattan, its intensity had decreased to a level at which the storm surge abated. But in weighing the costs of an unnecessary evacuation against the benefits of saving lives from drowning, Mayor Bloomberg had struck the right balance (we discuss this point more in detail in the next section), notwithstanding some post-event recriminations over city business interruption. In order to have successful evacuation, one important (and often overlooked) aspect is how the people react to an increase of threat. Whereas decision analysts propose rational procedures for better decision-making, behavioral psychologists are more interested in understanding the various ways that people actually make decisions. Iyengar (2010) has examined a wide range of aspects of how people choose what to do. Our choices reflect not just who we are and what

7 186 W. Marzocchi et al. / Journal of Volcanology and Geothermal Research (2012) P1 P2 P3 UNREST ORIGIN OUTCOME LOCATION MAGNITUDE Unrest No Unrest Magma Eruption No Magma No Eruption Zone 1 Zone 2 Zone k Zone J4 SIZE 1 SIZE 2 SIZE K SIZE J 5 ERUPTION FORECASTING (EF) VOLCANIC HAZARD (VH) PHENOMENA 6 AREA 7 OVERCOMING THRESHOLD 8 RISK ASSESSMENT EXPOSURE VULNERABILITY 9 10 Tephra fall Pyroclastic flow Lahars Lava flow Area 1 Area 2 Area k Area J 7 Yes No People Buildings P(eruption)= P(unrest) P(magmatic unrest unrest) P(eruption magmatic unrest) P1 P2 P3 5 central value 4 PDF 3 2 dispersion P(eruption) Fig. 2. In the upper panel we show the Bayesian Event Tree scheme (a full description of all nodes can be found in Marzocchi et al., 2008, 2010). The product of the probabilities associated with the first three nodes gives the eruption forecast. The probabilities are not single numbers but distributions; therefore, the final eruption probability is a distribution itself (see lower panel; PDF stands for probability density function). The central value represents the best guess, while the dispersion of the distribution gives an idea about the confidence on the best guess. For example, if a rich database of past monitored eruptions is available the dispersion would be small, while the case in which we have few data and a wide range of different experts' opinion tends to have a large dispersion. we want, but also how those choices will be interpreted by others. We survey our social environment to figure out what others think of particular choices available. Thus the actions that a person chooses to take do not depend solely on what is perceived to be in the individual's best interest, but depends also on the attitude of others to his or her choice. Before deciding how to react to a hazard warning, an individual will seek to discuss the alternatives with family, friends, neighbors, colleagues etc. The extent of peer pressure in reacting to hazard warnings will vary from one group to another. This process of social interaction in individual decision-making engenders a degree of selforganization supporting the capability of individuals to take their own decisions in situations of perceived danger. The public dissemination of hazard advisories should recognize this societal mechanism for dealing with a communal threat (Mileti and Sorenson, 1990; see also

8 W. Marzocchi et al. / Journal of Volcanology and Geothermal Research (2012) HIGH Number of evacuees LOW Hurricane Remote large tsunami Tornado Lava flow LOW the special volume on Volcanic Risk Perception published by Journal of Volcanology and Geothermal Research; Gaillard and Dibben, 2008). Environmental cues, such as the visual observation of emissions from a volcano, or the physical sensing of volcanic tremors, encourage the public perception that the hazard is real, and that risk mitigating action is warranted (Perry, 1982). The presence of environmental cues makes it easier for individual citizens to act upon operational forecasts Quantitative methods: Cost-benefit analysis Bomb alert Likelihood of false alarm Explosive eruption in high risk volcanoes (Small) flank collapse at Stromboli HIGH Fig. 3. Decision chart for hazard evacuation. In each box we report examples from natural hazards and volcanology. The upper right panel represents the case where a quantitative decision-making protocol is preferable. The purpose of a decision support tool is to assist the decisionmaker in arriving at his or her decisions most definitely not to make the decisions themselves. In its decision support function, such a tool should be transparent, auditable, and simple enough to be comprehended by those without formal training in risk management, and perhaps lacking specific computational skills. Fitting these requirements is the foundation of decision analysis: cost-benefit analysis (CBA), which has its historical roots in 19th century welfare economics, balancing societal benefits against market forces (Mulreany, 2002). In times of volcanic crisis, decisions on societal risk mitigation have to weigh the safety benefits of evacuation against the socio-economic costs of an evacuation process that may last for weeks or months. An alternative perspective, quite widely adopted for public exposure to industrial risks, is based on the concept of acceptable risk. If the risk of a large number of casualties exceeds some specified safety threshold, then the societal risk is deemed not to be acceptable. Here, we focus on the cost-benefit formalism. It is worth noting that CBA allows any specific choice of acceptable risk threshold to be quantitatively justified; moreover, CBA allows societal issues to be brought down to an individual level. It has been argued that whilst many costs and benefits of mitigation actions can be easily evaluated, there are also intangible factors that are hardly quantifiable. An extension of CBA is the use of multi-criteria analysis, which considers a broader range of evaluation criteria, including variables that are less tangible and have no market price, e.g. ethical issues, and psychological aspects of individual well-being, such as emotional stress and unhappiness. For this extension to be practically viable, it is necessary for decision-makers and stakeholders to have the opportunity to express their valuation of the relative importance of the various criteria. While laudable as an exercise in participatory decision making, the reluctance and discomfort of decision makers and stakeholders in articulating complex issues of preference renders this approach especially prone to excessive subjectivity. The essential argument underlying the recommended use of basic CBA is that this captures the core elements in the evacuation decision. Living in the shadow of an active volcano is inextricably linked with some measure of expected loss due to future volcanic activity. Nobody in harm's way wants to become a casualty, but then nobody wants life to be disrupted unnecessarily. The loss to a community from its exposure to a natural hazard should be minimized. To take action now to mitigate the potential loss from a natural hazard falls within a common important category of economic decisions: pay a sum now to avert paying a larger sum later, contingent on the occurrence of an uncertain hazard event. The economic character of this class of decisions is exemplified by the simple cost-loss model. Consider a hazardous situation where a decision-maker has to choose between two actions: either (a) protect; or (b) do not protect. The cost of protection is C. In the absence of protection, the decision-maker incurs a loss L which exceeds C if an adverse hazard state arises. The time interval between the act of protection and the occurrence of the adverse hazard state is assumed to be sufficiently short that financial discounting is negligible. Let the probability of the adverse hazard state arising, within a specified time window, be denoted by p. If the expected expense is to be minimized, then the optimal policy is to protect if p exceeds C/L, but not to protect if p is less than C/L. The minimal expense is then min{c, pl}. In other terms, the ratio C/L for each planned mitigation action defines a set of probability thresholds. Once the probability p of the adverse hazard state overcomes one specific threshold, the associated mitigation action is worth being taken. For an evacuation decision (Marzocchi and Woo, 2007; Woo, 2008; Marzocchi and Woo, 2009), the principal protection cost C is the economic dislocation which may last for weeks or even months. This may be estimated from GDP per capita for the country concerned. An explicit financial realization of this protection emerged in 2009 from a volcanic crisis in Saudi Arabia, which is a country of rather modest volcanic hazard (Pallister et al., 2010). On May 19th, 2009, up to 30 tremors measuring between 3 and 5.4 on the Richter scale shook the Arabian Peninsula region. Al-Ais, a town 550 km northeast of Jeddah and on the fringe of a volcano field, had been suffering tremors for a month. When they attained the magnitude threshold of 5 for the first time, the Saudi government moved 40,000 residents of Al-Ais and surrounding villages to the neighboring cities of Yanbu and Medina, where they stayed in apartments paid for by the state (Pallister et al., 2010). Families also received between 2,000 to 3,000 riyals ($500 to $800) in financial assistance. ( world/middle-east/saudi-town-evacuated-after-dozens-of-earthquakes). Three months later, after enduring further seismic alarms, the evacuees were allowed to return. Volcanic hazard in the whole of Saudi Arabia, including Al-Ais, has been historically quite low apart from a moderate eruption in The likelihood of an imminent explosive eruption that could impact directly people was considered negligible. Nonetheless, there was an indirect risk from collapse of the un-reinforced mud and block buildings from ground shaking. The chance of this event was estimated considering the probability of additional earthquakes of various magnitudes (John Pallister, personal communication, 2012). Using an Event Tree (Pallister et al., 2010), the probability of earthquakes with magnitude 5 or larger was estimated at about 5% over a three month period starting on 19 May 2009 (or about 13% if there were additional intrusions during the same period). In this case, the proportion of the people at risk who would have owed their lives to the evacuation call would also have been quite modest, perhaps at most 5%. Assuming a basic 3-month cost disruption of about $2500 per evacuee, the Willingness to Pay for Life Saved (WPLS; see below) works out to be about $1 million. Another example is the evacuation called in New York for Hurricane Irene in August On August 24, it reached category 3 status. At this intensity, it threatened immense harm to people on the East coast. From general hurricane disaster experience, about 1% of those at risk might have lost their lives if Hurricane Irene had reached Manhattan generating a severe storm surge and flooding low lying areas. At the time of the evacuation call, there seemed at least a 10% chance of this happening. In the absence of an evacuation order,

9 188 W. Marzocchi et al. / Journal of Volcanology and Geothermal Research (2012) lawyers for victims might have sued the city for compensation well in excess of a million dollars each. Even with just a very slim chance of about 0.1% of a coastal resident being a victim, it would have been well worthwhile for the city to bear an economic cost per evacuee of about a thousand dollars for accommodation and loss of livelihood for a few days. For a non-evacuation decision, the principal loss incurred is that of human life. No decision-maker wants to lose a single life from a hazard crisis. Accordingly, it is a minimum value of a human life that is relevant for crisis applications of CBA. No decision should be made that significantly undervalues human life. This might happen if an evacuation is called too late for people to travel through congested and gridlocked streets and find safe refuge. In particular, for citizens with mobility problems, evacuation may have to be prioritized, as perhaps it might have been for the Japanese tsunami of March 11, 2011, which preferentially drowned the less mobile. Indeed, CBA provides a systematic framework for segmenting evacuation by geography and community, assisting also in delineating hazard exclusion zones (Marzocchi and Woo, 2009; Sandri et al., 2012). In CBA applications, human loss is usually measured using the economic concept of Willingness to Pay for Life Saved (WPLS). WPLS represents the amount of money available to reduce a specific lethal risk per person. It is necessarily a bounded value because resources are finite, and risks cannot all be eliminated. In some volcanic highrisk zones, such as the red hazard zone around Vesuvius, residents may be encouraged to relocate through the offer of a resettlement allowance, which may be converted to an equivalent WPLS estimate (Marzocchi and Woo, 2009). Quantitative decision support might consist of bulletins being presented to the decision-maker, making explicit the trade-offs of costs and benefit involved in an evacuation call. As with other technical issues concerning public safety, the decision-maker can undertake or commission an independent CBA. Starting from a basic CBA calculation, the decision-maker has the discretion to add other factors into the mix of considerations leading to the ultimate decision. One of these is comparative aversion to societal economic disruption compared to the avoidance of danger. A delay in an evacuation call may be understood as indicating an enhanced aversion to societal disruption, which might eventually prove unwarranted. On the other hand, an early evacuation call would signify a heightened aversion to human casualties. 5. Science, decision-making and future developments Ideally, a quantitative and rational decision-making protocol should be defined before a crisis. It should be part of the role of scientists to make up-to-date estimates of probabilities for different scenarios (Operational Eruption Forecasting). Decision-makers must define the probability threshold for each mitigation action envisioned (see Marzocchi and Woo, 2007, 2009; Jordan et al., 2011; Sandri et al., 2012). As the probability of a specific event exceeds a threshold, some commensurate mitigation action may become worth taking (Fig. 4). Through such a systematic operational forecasting procedure, the whole decision-making process can become clear, transparent and auditable. These protocols must be set by scientists and decision-makers working together. This makes it easier to shape questions and answers in a comprehensive way, to facilitate the communication among partners with different backgrounds, and to improve understanding of what scientists can offer, and what they cannot. Furthermore, these protocols have to be flexible enough to manage desirable future improvements of scientific knowledge and new prospects for mitigating risk. Transparent decision-making protocols have several important advantages: i) they allow scientists and decision-makers to justify the actions taken, or not taken, at any time; ii) they have educational value for society, decision-makers and scientists in improving understanding of the scientific and practical choices made; iii) they make it easier to manage the sometimes frequent changes in personnel involved in the decision-making process; iv) they clarify the role and responsibility of any partner involved in the decision-making process. A full application of these procedures requires time and energy. On one side, scientists have to become more familiar with probabilistic forecasting and develop improved probabilistic tools to achieve this goal. On the other side, decision-makers have to be aware that their role requires a basic level of training in decision-making under uncertainty, and risk assessment; this may require a broad range of expertise like economy, politics, social science and communication. The last step for successful risk mitigation actions consists of establishing a proper way to convey the message from decision makers to society. In this paper, we have only addressed the scientific aspects of the management of a volcanic crisis and we did not explore the fundamental issue of communicating warnings. But we note that there seems not to be a universal strategy to communicate warnings Probability average per month (a) Probability threshold for calling an evacuation (b) * Fault Lava domes Crater rims Remnants of volcanic edifices Fossil marine cliff Neapolitan Yellow Tuff (15ka) caldera Campanian Ignimbrite (39ka) caldera # Monitoring Bulletin YES NO Fig. 4. Example of decision making under uncertainty. (a) Example of the evacuation around Vesuvius during the MESIMEX exercise (modified by Marzocchi and Woo, 2007). The plot reports the evolution of the probability of pyroclastic flow occurrence as a function of the monitoring data contained in bulletins released during the simulated emergency. The upper part of the plot represents probabilities that are higher than the threshold calculated through cost-benefit analysis. At bulletin 4, the monitoring data raised the probability of pyroclastic flow occurrence above the threshold. This means that the evacuation is worth being called according to CBA. (b) Hypothetical example of an evacuation in Campi Flegrei caldera (modified by Marzocchi and Woo, 2009); using a plot like the one reported in panel (a) for each cell of a grid that covers the caldera, which cells of the grid that are worth being evacuated can be determined (gray boxes in the plot).