volcanic activity: frontiers and challenges in forecasting...

Volcanic Activity: Frontiers and Challenges in Forecasting,Prediction and Risk Assessment

R. S. J. Sparks

Department of Earth Sciences, University of Bristol, Bristol, UK.

W. P. Aspinall

Department of Earth Sciences, University of Bristol, Bristol, UK.Aspinall & Associates, Beaconsfield, Buckinghamshire, UK.

When a volcano shows signs of unrest scientists are asked to forecast whether aneruption will happen, when it will happen and what kind of eruption it will be.They are also expected to provide information on hazardous volcanic phenomenaand their effects, and how long the eruption will last. Eruptions are complex phe-nomena, however, involving magma ascent to the Earth’s surface and interactionswith surrounding crust and surface environments during eruption. Magma maychange its properties profoundly during ascent and eruption, and many of the gov-erning processes of heat and mass transfer can be highly non-linear. There are bothepistemic and aleatory uncertainties involved, which can be large, making preciseprediction of a certain event in time and space a formidable or impossible objec-tive; that is, volcanoes can be intrinsically unpredictable. As with other naturalphenomena, forecasting is a more achievable goal and needs to be expressed inprobabilistic terms that take account of the uncertainties. Ensemble modeling inwhich uncertainties are sampled with Monte Carlo techniques is likely to becomethe basis for such forecasting. Despite the limitations, there is significant progressin anticipating volcanic activity and, in favorable circumstances, in making pre-dictions. Data from enhanced monitoring techniques are being combined withadvanced numerical models of volcanic flows and their interactions with the envi-ronment. Statistical analysis of volcanological data and improvements in methodsto treat subjective information are also beginning to provide viable, complemen-tary approaches to basic numerical modeling.

INTRODUCTION

Earth scientists are required to look into the future to advisegovernments and inform the public about threats from natural

hazards. The challenges of prediction become immediate whena volcano is about to erupt. About 500 million people live closeenough to volcanoes to be affected by eruptions [Newhall,2000]. Volcanic phenomena can affect climate and are an impor-tant contributing factor in forecasting global environmentalchange. The challenges of forecasting volcanic activity areconsiderable and come at a time when the demands and expec-tations of society are increasingly onerous. Some societies are

The State of the Planet: Frontiers and Challenges in GeophysicsGeophysical Monograph 150, IUGG Volume 19Copyright 2004 by the International Union of Geodesy and Geophysicsand the American Geophysical Union.10.1029/150GM28

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becoming ever more litigious, and prospects of scientists hav-ing to justify their judgements in court are emerging.

Volcanic activity has many features in common with othernatural hazards, such as extreme weather, earthquakes andlandslides. Natural hazards are characteristically complexand involve numerous parameters and processes. Some ofthe controlling processes are highly non-linear, so that in cer-tain circumstances abrupt changes of behaviour can happen,such as the sudden transition from effusive to explosive erup-tion. Of particular significance is the need to understand andquantify uncertainty. There is both epistemic and aleatoryuncertainty in natural phenomena [Woo, 1999], the formerbeing defined as deficiencies in knowledge about naturalprocesses and the latter as natural variability within thoseprocesses. Many volcanic processes are stochastic, and needto be characterised by statistical models. Complex nonlin-ear systems can be very unstable close to critical thresholdsbetween stable states, becoming inherently unpredictable.Such attributes and the importance of quantifying uncer-tainty are now central in forecasting volcanic phenomena.As a consequence, volcanologists will inevitably shift fromdeterministic to probabilistic perspectives. This change infocus will require alterations in the conceptual frameworkwithin which observations on volcanoes are interpreted. Therewill be many challenges, because uncertainties in manyaspects of volcanic systems are large, and may prove hardto quantify.

Here we consider emerging new approaches to prediction,forecasting, the assessment of volcanic risk, and provisionof scientific advice. We also discuss the roles of statisticalanalysis and computer modelling. This paper complementsthose of Sparks [2003], who reviewed the methods of fore-casting volcanic eruptions based around interpretation ofmonitored data, and of Newhall and Hoblitt [2002], whodeveloped parallel themes.

VOLCANIC PROCESSES AND HAZARDS

Volcanism is caused by the buoyant ascent of magmas to theEarth’s surface. Magmas change their properties as they ascend,principally due to changes in pressure and temperature. Theproperties of a magma and its interactions with its surround-ings determine whether a given magma erupts or not, anddictate the nature of the activity, if it does erupt. These prop-erties and interactions give rise to a range of physical effectsthat can be monitored. Important interactions include: frac-turing of rocks due to propagation of dykes (Rubin, 1995),generating seismicity; escape of pressurised gases and heat-ing of ground waters, leading to ‘long-period’ volcano-seis-mic events [e.g. Chouet, 1996; Neuberg, 2000]; and variationsof magma pressure in chambers and conduits leading to grounddeformation [e.g. Voight et al., 1999; Dzurisin, 2000]. Ascend-ing or erupting magma can cause perturbations of electric,gravity and magnetic fields. Additionally, fluxes of magmaand gas, geochemical and petrological variations in eruptedproducts, and observations of surface activity provide impor-tant information. Observations from space of heat, strain,topography, gravity, electromagnetic transients and atmos-pheric emissions are also emerging as a major source of infor-mation [Wadge, 2003]. Systematic monitoring and observationsprovide the basis for forecasting, but require understanding ofthe processes to interpret.

Major types of volcanic hazards, their effects and extents arelisted in Table 1. The scale and occurrence of volcanic hazardsare inversely related, with small events occurring worldwideat a rate of 10–20 per month, whereas catastrophic eruptions(>10 km3), that might affect the economy of an entire coun-try, occur every hundred years or so [Pyle, 1998]. The verylargest volcanic eruptions (>1000 km3) could threaten civi-lization [Rampino, 2002] and occur about every 50,000 yearson average [Mason et al., 2004].

360 VOLCANIC ACTIVITY: FORECASTING, PREDICTION AND RISK ASSESSMENT

Volcanic hazards can be entirely caused by the volcanicactivity itself, but external factors can be important. Lavas andpyroclastic flows, for example, are strongly influenced bytopography. Tephra fall hazards depend on wind strength anddirection [e.g. Bonadonna et al., 2002]. Collapse of a lavadome to form pyroclastic flows can be triggered by intenserainfall [Matthews et al., 2002]. Flank collapses can be trig-gered by earthquakes, as happened on 18th May 1980 atMount St Helens [Endo et al., 1981]. Separate earth-quake–volcano interactions can apparently take place oversurprisingly long distances and time-scales [Linde and Sacks,1998; Hill et al., 2002]. Other, subtle complex-systemsdynamics [e.g. stochastic resonance; Weisenfeld and Moss,1995] may link volcanic responses to low-level external forc-ings, such as tides or atmospheric pressure or hydrologicalcycles [Jupp et al., 2004]. Thus forecasting of hazards inboth space and time requires not only understanding of theeruptive processes themselves, but also understanding of thesurface and subsurface environment and external processesthat interact with volcanic phenomena.

PREDICTION AND FORECASTING

Prediction and forecasting are sometimes used inter-changeably, but can be usefully distinguished. A predictioninvolves a statement about a specific event that is regarded asinevitable within certain defined time limits and, in its mostdeveloped form, is found in established laws of physics (e.g.Newton’s Laws of motion of bodies). Scientists may judge, forexample, that a volcano that is showing unrest will definitelyerupt and that lava will reach a village. The prediction willhave limited value unless some constraints on time, place andscale are specified, even if these assessments are themselvesuncertain to some degree. Forecasting, on the other hand, is aprobabilistic statement that a specific event might occur witha certain likelihood in a given time-frame, commonly withassociated scales and effects being defined as well.

The requirements for prediction, as defined above, are strin-gent, because the event must be inevitable. It might be thoughtthat a volcano like Vesuvius, with an historical record of fre-quent eruptions, would meet the requirements of inevitabilityof another eruption. However, all volcanoes become extinct andthe criteria for recognising that a volcano has had its last evereruption are very problematic, if not unknowable (and con-ditional on definitions of ‘eruption’ and ‘extinct’). One can-not be certain that the 1944 eruption of Vesuvius was not itslast ever eruption, even though the probability that this is sowould be widely judged as diminishingly small. In most erup-tions the case for inevitability cannot be easily made.

Many volcanoes erupt in such a way that patterns of behav-iour can be established and an eruption can be forecast, and

even predicted if these patterns are repeated sufficiently often.In 2000, the eruption of Mount Hekla in Iceland was accu-rately predicted. Several years earlier borehole strain metershad been deployed in central Iceland and, in the 1991 erup-tion, large and systematic strain variations (Figure 1), togetherwith seismic data, traced the propagation to the surface of adyke from a magma chamber about 6 km below Hekla [Lindeet al., 1993]. The agreement between the observations andconceptual model gave a high degree of confidence that aneruption was inevitable when the same pattern was repeatedin March 2000. Scientists from the Icelandic MeteorologicalOffice informed Icelandic radio that an eruption was immi-nent in 20 minutes. The prediction was announced at thebeginning of a news broadcast and the eruption occurredwithin 2 minutes of the expected time. In the 1981–1983activity of Mount St. Helens, patterns of periodic dome growthwith precursory ground deformation allowed accurate fore-casts to be made of the timing of dome extrusion events[Swanson et al., 1983]. These forecasts became increasinglyfocussed on narrow time windows to the extent that they,too, might be viewed as predictions.

The above examples show that forecasting and predictionare easier at persistently active volcanoes or in long-livederuptions with established and repeatable patterns of activity;forecasting and prediction become more difficult for dor-mant volcanoes with a limited or no historical record. The

SPARKS AND ASPINALL 361

Figure 1. Strain measured in five borehole strainmeters in Icelandin 1991 associated with the eruption of Hekla Volcano [after Lindeet al., 1993]. The eruption took place within 20 minutes of the startof the changes in strain at the time when the strain at BUR reacheda minimum. Four of the stations show an expansion (positive changes)and the closest station to the volcano (BUR) shows an initial con-traction. The data are interpreted as the ascent of a dyke from themagma chamber to the surface.

issue of whether a restless volcano is going to erupt has beena source of angst, controversy and, in some cases, the under-mining of scientific credibility. The cause célèbre is the 1976volcanic crisis at La Soufrière, Guadeloupe, which led tomajor public disagreements between scientists [Fiske, 1984].One group, led by Haroun Tazieff, judged that the seismicswarm and phreatic activity was not the prelude to a majoreruption. Others regarded these disturbances as potentialsigns of a major eruption, which would endanger over 70,000people, and so advised an evacuation. The authorities, con-cerned to incur no public risk in the light of events in Mar-tinique in 1902, accepted the precautionary advice and theconsequent three-month evacuation caused hardship and con-siderable economic cost, running into several hundreds ofmillions of dollars. A magmatic eruption did not happen and,in some sense, Tazieff ’s assessment might be construed as“right”. A considered appraisal of the Guadeloupe case sug-gests, however, that the more cautious scientists had betterappreciation of scientific uncertainties and the inadequacyof knowledge about how volcanoes work, a view supportedby subsequent analysis [Feuillard et al., 1983]. In contrast, theclimatic eruption of Mount Pinatubo in June 1991 is a goodexample of a successful forecast based on a spread of evi-dence, including precursory seismicity, and variations in SO2emissions [Punongbayan et al., 1996]. The prospect of a verysubstantial explosive eruption was deduced from geologicalevidence of past eruptions and dating of pyroclastic deposits.The decision to evacuate 250,000 people based on the vari-ous strands of evidence was a judgement call and the adviceof the Philippine Institute of Volcanology and US GeologicalSurvey to the authorities avoided huge loss of life.

In view of the inherent difficulties in prediction of vol-canic phenomena it is often better to address future volcanicactivity in terms of probabilistic forecasting. For many erup-tions, forecasts are qualitative and expressed in terms such as‘very likely’ or more cautious statements that a volcano isshowing the signs of unrest and might erupt. Every volca-nologist is, however, acutely aware of the problems provokedby calling an evacuation and then nothing happens. The sci-entists are perceived to have been “wrong”, and to have raiseda false alarm. For this reason it is better to present forecastsrather than predictions, and to find ways of expressing thesein probabilistic terms based on quantitative scientific evi-dence and analysis.

In the USA public and political decision-makers are usedto weather forecasts. In general, weather forecasters have gainedpublic credibility both by a record of improving the accuracyof forecasts and by getting the public accustomed to basic con-cepts of probability. The statement that there is an 80% chanceof rain in a particular town is familiar, and most people willaccept that if it doesn’t rain then it was not necessarily a wrong

forecast. Even in this arena, however, forecasters still have dif-ficulties with extreme conditions and can lose credibility whenthe weather is much more severe than anticipated. Likewise vol-canologists have considerable problems with forecasting theonset and effects of extreme volcanic events.

We now illustrate some of these matters and present prac-tices with the example of the Soufrière Hills volcano, Montser-rat, since that ongoing eruption (which started in July 1995)is very familiar to us.

MONTSERRAT: CASE STUDY IN FORECASTING,PREDICTION AND RISK ASSESSMENT

The focus on the Soufrière Hills volcano, Montserrat isselective, but the eruption has displayed a wide range of vol-canic phenomena and has proved to be a very good testingground for development of new approaches to prediction,forecasting and risk assessment. Here we illustrate the prin-ciples of probabilistic forecasting with the example of tephrafall hazards. We also consider pyroclastic flow hazards onMontserrat to illustrate methods of risk assessment.

Tephra Fall Hazards

Tephra fall is one of the better understood of volcanicprocesses (Plate 1). Understanding the dynamics of volcanicplumes is reasonably advanced, as summarised in Sparks etal. [1997], with quantitative models for plume ascent, forthe interaction of plumes with the wind, and for tephra trans-port. These models have been calibrated against observedevents and consequently there is confidence that the modelsare simulating natural processes appropriately. There is alsoinformation on hazardous effects; for example, mass accu-


Plate 1. An ash-laden volcanic plume at the Soufrière Hills Volcanois blown across Montserrat. Note that the source of the plume is froma pyroclastic flow about 1 km to the east of the crater of the volcano.

mulations of tephra that can lead to roof collapse are welldocumented [Blong, 1984].

The study of Bonadonna et al. [2002] on assessment oftephra fall hazards on Montserrat illustrates the main fea-tures of probabilistic modelling. The model treated the tephradispersal as an advection–diffusion problem with a sourcefunction that reflected the observed origin of the ash plumesfrom above the pyroclastic flows along the valleys, and theobserved approximately exponential decrease of plume heightwith distance along the valley. The model also consideredVulcanian explosions sourced at the crater. Model simula-tions were first run for individual volcanic events and for theeffects of activity in the sequence from June 1996 to June1997, under the atmospheric conditions prevailing at the time(wind speeds and directions). Parameters in the model werethen adjusted to give best-fits to the observed thickness vari-ations. The volcanic activity of 1996–1998 was then used tobuild a characteristic scenario for the volcano of combina-tions of dome collapses, pyroclastic flows and explosions.This scenario was then run several hundred times using re-sampling of the statistical data on daily wind speeds anddirections at 1 km intervals up to a height of 20 km for1992–1996, to generate a statistical distribution of resultingtephra accumulations across the island.

Figure 2 plots the model output in contours of probability(as a percentage) that tephra accumulation will exceed 12kg/m2 (Figure 2a) and 120 kg/m2 (Figure 2b). The first valuerepresents the threshold above which crops commonly fail,and the latter value is the threshold at which roof collapsebecomes a problem. This particular model assumes that eithererosion or human intervention (e.g. sweeping roofs) removesthe ash between each tephra fall event. Such probabilisticmodels were used on Montserrat to assess vulnerability toroof collapse and to make a risk assessment of the health haz-ards due to respirable volcanic dust. The forecasts have alsobeen used to guide the UK government in planning the sus-tainable development of the island.

Tephra fall also poses health hazards. In the case ofMontserrat the volcanic dust (<10 µm) contains 10–25 wt%cristobalite, which is a carcinogen and causes silicosis, achronic lung disease [Baxter et al., 1999]. The model ofBonadonna et al. [2002] was an input into a risk assessmentcommissioned by the UK Department of Health. In thisassessment, simulations of tephra dispersal were combined ina synthesis with other information and processes, includingmodels of ash suspension, epidemiological data and biolog-ical data such as in vivo and in vitro experimental results.Multiple model runs were made to assess the exposure ofthe population to suspended ash. The results of this studyhave identified outdoor workers (eg gardeners) and childrenas having relatively high exposure. This study illustrates the

way in which relatively ‘soft’ qualitative data can be incor-porated into a multi-factor simulation. To produce a proba-bilistic assessment of human exposure to suspended dusts itis, for example, necessary to parameterise the erosion process,since once ash is eroded it is no longer available for suspen-sion. At the moment, it is beyond present understanding toreplicate in a model all the complex processes of tephra ero-sion and redistribution on a tropical island, but a simple time-dependent removal scheme could be parameterised fromempirical information. This was combined with statisticalinformation on rainfall to provide a significant advance on theend member probabilistic maps in Figure 2.

Such modelling can always be improved. An ambitious tar-get might be to produce a probabilistic model of dome growth,collapse and explosion rather than simply adopt a specific,albeit plausible, single scenario as a class example. MonteCarlo sampling of all uncertainties in key parameters thatcontrol the underlying volcanic processes could then be incor-porated to represent a wide range of potential scenarios. How-ever, the processes of dome growth are not yet well enoughunderstood to do more than develop ‘soft’ parameterisations,


Figure 2. Maps showing contours of probability (as a percentage)across the island of Montserrat of accumulation of 12 and 120 kg/m2

or more of volcanic ash over a 3-year period [after Bonadonna et al.,2002]. The maps are based on a scenario of activity similar to thatexperienced on the island. Pyroclastic flows extend in the scenariodown the valleys and plumes (co-PF) are source at the points indicatedby the solid diamonds. The mass accumulations are equivalent to ashthicknesses of about 1 cm (for 12 kg/m2) and 10 cm (for 120 kg/m2).

as in the case of erosion. Such models are in the future and willrequire significant computing power and code development,although adroit use of newly-emerging model inference tech-niques [O’Hagan et al., 1999] offer the prospect of reducedcomputing costs. Eventually one can imagine volcano fore-casting centres that assist observatory teams with synopticoutputs, just as weather centres have sprung up to underpinlocal and regional forecasts.

Pyroclastic Flow Hazards

The principal hazard on Montserrat during the eruption isthe formation of pyroclastic flows from collapse of the lavadome [Cole et al., 2002]. The assessment of hazards and atten-dant risks from pyroclastic flows and their accompanying hotturbulent clouds of ash (surges) is described here to illustrategeneric issues in relation to prediction and methods of prob-abilistic forecasting.

The andesite dome has grown in pulses [Watts et al., 2002].In each pulse a lobe of lava extrudes in a particular direction(Plate 2a). Rockfalls and collapse-induced pyroclastic flowsare generated preferentially at the leading edge of a lobe (Plate2b) and tend to flow away in the same direction as the extru-sion direction [Calder et al., 2002]. This behaviour is veryuseful for forecasting, since the probability of flows goingdown a particular valley is greatly increased when the domeis extruded in that direction. Pulses in extrusion rate can bemarked by the onset of shallow seismicity or by changes incyclic patterns of ground deformation, as recorded by tilt-meters [Voight et al., 1999], and both symptoms are com-monly associated with formation of a new lobe in a newgrowth direction.

Most major dome collapses on Montserrat (defined hereas 3 million cubic metres or greater since only flows of thissize or above are large enough to threaten populated areas)occurred within a few hours or days of a pulse in extrusionrate. There have been many such pulses and switches in theextrusion direction, which tend to occur at intervals of a fewweeks to a few months. From May to December 1997 thesurges and accompanying major dome collapses occurredquite regularly at 6–7 week intervals [Voight et al., 1999;Sparks and Young, 2002]. For a while, the regularity of thepattern was sufficiently clear to provide a basis for fore-casting. On the other hand, some of the largest dome col-lapses appear to have been triggered by intense rainfall[Voight and Elsworth, 2000; Matthews et al., 2002]. One ofthese occurred on 3 July 1998 in a period when there was nodome growth. Two large dome collapses occurred on 20March 2000 and 29 July 2001 (volumes of 20 and 45 millionm3, respectively) and were associated with intense rainfall ofover 80 mm/hour.

The critical issues in hazard forecasting of pyroclastic flowsare the areas that a flow (or series of flows) will inundate andthe occurrence of the associated overlying clouds of hot tur-bulent suspended ash (known as surges) that can spill out ofthe valleys that confine the main flows. Data on run-out dis-tances and areas affected on Montserrat have led to empiricalrelationships between flow volume and run-out distance[Calder et al., 1999]. The observed distributions of particularflow deposits can be used to construct a semi-empirical modelof run-out [Wadge et al., 1998]. The model incorporates grav-itational flow across the observed topography, which isdescribed by a digital elevation model (DEM). The modelcontains three friction parameters, which can be adjusted bytrial and error, or by Monte Carlo techniques, to give a best-


Plate 2. Activity of the Soufrière Hills volcano, Montserrat illus-trating factors determining the directions of pyroclastic flows. In (a)a lobe of lava is extruded towards the north between August 5 and 9,2002 (view from the east), and in (b) small collapses from the lead-ing edge of a lava lobe generates rock-falls and pyroclastic flowstowards the north of the island (view from the north). Images repro-duced by permission of the Montserrat Volcano Observatory.

fit to the observations. The model can then be run for eventsthat have not yet happened to assess volcanic hazards. Suchmodels have many uncertainties and hidden assumptions. Forexample, at Soufrière Hills dome collapses typically last fortens of minutes to several hours and may involve numerousindividual avalanches. On 25 June 1997, there were threemain collapses in 20 minutes [Loughlin et al., 2002]. Using thefinal total volume of the deposits in a particular collapseepisode as a basis for defining mobility by run-out distance,or inundation area, or to estimate friction coefficients mightlead to misleading or inappropriate results. There is rarelysufficient information to discriminate the volumes of indi-vidual pulses. The fact that dome collapse episodes are almostalways pulsed multi-collapse events [Calder et al., 2002]means that there are intrinsic uncertainties and pitfalls inanalysing the resulting field data. Another element of semi-empirical models is that the frictional parameters not onlyreflect the true frictional properties of the flow but implicitlyincorporate topographic effects on flow which, as yet, are notexplicitly modelled.

The behaviour of the surge clouds is even more problematicbecause quantitative models of surge generation and dynam-ics are not yet available. On Montserrat, the development ofsurge clouds seems to be linked not only with flow volume, butalso with the internal pressurisation of the dome, which itselfis thought to be related to the extrusion rate [Cole et al., 2002;Calder et al., 2002]. Surge cloud generation and behaviour canalso be sensitive to topographic features and can be influ-enced by wind. Finally, surge clouds can generate dense “sec-ondary” pyroclastic flows, which can move obliquely downvalleys away from the main originating flow [Druitt et al.,2002b]. Thus the dispersal of surge clouds is not yet amenableto rigorous modelling and so the assessment of hazards mustdepend more on qualitative judgements based on observa-tions in circumstances of considerable uncertainty.

Risk Assessment of Dome-Collapse Pyroclastic Flows

We illustrate the development of a quantitative risk assess-ment of pyroclastic flow hazards, the main hazards issue inthe management of the Montserrat crisis, using the recentexample of one particular residential area, the Belham Val-ley. The problem emerged in 2002 when relentless domegrowth raised concerns that a large collapse could inundatethe lower parts of the Belham Valley, northwest of the vol-cano (Plate 3). This section describes the modelling proce-dures that were used to estimate risks and thus informdecisions by the civil authorities. The accompanying map(Figure 3) shows the area evacuated after 8 October 2002on the basis of scientific advice. This area was re-occupiedin August 2003 after a huge dome collapse to the east, on 12

July 2003, removed the threat. For Montserrat, a Risk Assess-ment Panel has conducted such assessments and involvesthe scientific staff of MVO and external experts. The authorsacted as Chair of the Panel (RSJS) and expert in risk assess-ment methods (WPA).

The risk to the lower Belham Valley area is a function of theprobability that a pyroclastic flow will inundate part or all ofthe area and the vulnerability of people there. Historical dataindicate that 90% of people in areas directly affected by pyro-clastic flows and surges are killed [Baxter, 1990]. Only thoseon the fringes of the devastated area might survive and sovulnerability is very high. To estimate risk quantitatively theMontserrat Panel was required to estimate the probability thata flow would happen over a fixed period of time. The timewindow used was 6 months as this was a useful timescale fordecision-makers and was commensurate with the temporalvariations in dome-building eruptions.

The procedure for estimating the hazards involved a sys-tematic series of steps in a structured discussion and use of pro-cedures to combine relatively hard and soft information. Therisk assessments used, wherever possible, quantitative modelsof volcanic processes. Thus to assess the run-out distancesempirical correlations [Calder et al., 1999] and models (e.g.Wadge et al., 1998) were used. For Belham Valley, the Panelconcluded that collapses of 3 million cubic metres or morewould have a high likelihood of reaching the lower valley andthat collapses of 10 million cubic metres or more would reachthe sea and affect most, if not all of the area.


Plate 3. The andesite lava dome of the Soufrière Hills volcano,Montserrat in May 2003, showing the main features pertinent tohazard assessment. If the dome were to collapse down Tyres Ghautthen pyroclastic flows would enter into the lower Belham Valley (seeFigure 6), an area that was evacuated after 8th October 2002 becauseof this threat. (note: ‘ghaut’ is used locally to denote a valley with astream or river).

The assessment also used a structured method of expertelicitation in which the judgements of the Risk AssessmentPanel were pooled. The method, described in Cooke [1991],has become a common approach in many scientific and engi-neering situations that involve significant uncertainty, and ithas been applied for the first time in a volcanic crisis onMontserrat. Each expert assesses their judgement of someparameter and his or her confidence limits on that assess-ment, based on shared, available scientific information. Expertsare calibrated by a facilitator, so that the pooled results of thegroup are weighted according to the individual experts’ abil-ity to be informative and knowledgeable. This procedure isdesigned to give greater weight to those individuals with goodjudgement in urgent circumstances; that is, a ranking rele-vant to decision-making capabilities in crisis conditions, andnot merely a metric of considered scholarship. The procedurehas the advantage of reducing the influence of overconfident,

vocal or highly opinionated individuals, while providing aneutral medium for the inclusive incorporation of a spectrumof views, and the outcome can be viewed as a mathematicallyrational consensus of the opinions of all participants.

A formalised expert elicitation provides a mechanism forstructured scientific discussions in an evidence-based approachin which all sources of information (e.g. observations, empir-ical relationships and theoretical models) are utilised. In thecase of the Belham Valley assessment the directionality ofdome growth and surge cloud behaviour are examples of com-ponents in the estimation of overall probabilities of pyro-clastic flow hazards where expert judgement elicitations haveproved helpful. For endogenous collapses, directionality ofthe lava lobe was judged on empirical evidence to be the maindeterminant of the collapse direction. However, the group dis-cussion concluded that the evidence did not support a ran-dom process, since certain directions had not been commonduring the eruption (possibly related to buttressing effects ofolder, pre-existing domes) and that switches which might trig-ger collapses tended to occur away from the direction of pre-vious stagnated lobes, which acted as a barrier [Watts et al.,2002]. The Panel also considered the chances of a collapsetriggered by rainfall unrelated to dome growth direction. In thiscase the previous episodes had all been down the easternflanks of the volcano. Additionally, the chances of such anevent would be greater in the rainy season than in the dry sea-son. An important factor also was the frequency of collapsesof 3 million cubic metres or above; not all switches caused asignificant collapse. Other factors included the chances ofthe eruption stopping, and large collapses in directions otherthan to the northwest over the 6-month period, which wouldeither reduce or entirely remove the threat to the Belham Val-ley. Thus relatively soft information was integrated into the pro-cedure to produce probabilities of a range of collapse eventsthat might affect the Belham Valley.

The final stage of the risk assessment involved Monte Carlore-sampling of the probability density functions (pdf) of allcontrolling factors that contribute to the hazards in differentareas, in repeated simulations. The final output evaluates theintegrated probability of occurrence of life-threatening events,expressed as the risk of a person being killed in a particulararea, or as the associated probability of exceeding a numberof casualties in the population at large (Figure 4). The indi-vidual risk exposure can be compared with a suitable riskscale: for Montserrat, the comparison was with the UK ChiefMedical Officer’s Risk Scale. Societal risk diagrams like Fig-ure 4 help illustrate to public officials the consequences ofdecisions. Volcanic risks can also be compared with otherkinds of risk: for instance, casualty exceedance curves in Fig-ure 4 compare the case of the lower Belham Valley beingoccupied by residents with the case the area is evacuated.


Figure 3. A map showing the location of the Belham Valley, TyresGhaut (marked T) and the area (shaded) which was evacuated after8th October 2002 due to the assessed high level of potential risk fromcollapse of the lava dome to the northwest. Contour intervals are200 feet.

Evacuation reduces societal risk by a factor of 10, to levelsbelow those associated with hurricanes in the Caribbean andclose to the long-term exposure to earthquakes.

STATISTICS IN VOLCANOLOGY

We now consider the statistical analysis of data, particu-larly time series data, to extract information on volcanicprocesses in the context of forecasting and assessment of haz-ards and risks. With burgeoning amounts of instrumental andother data being acquired statistical analysis is emerging as amajor area of research that goes well beyond simply provid-ing measures of uncertainty. Here we give two examples.

Longevity of the Soufrière Hills Volcanic Eruption

The Soufrière Hills eruption has continued for over eightyears. The civil authorities have asked the scientists at MVOhow long the eruption will last, as an accurate assessmenthas implications for the sustainable development of the island.To address this issue, duration data on 137 dome-formingeruptions taken from the Smithsonian Institution database[Simkin and Siebert, 1994] were gathered, re-interpreted, andfitted to a Generalised Pareto Distribution model (Figure 5).The Generalised Pareto family of distributions have specialproperties that make them particularly appropriate foranalysing extreme-value information in a peaks-over-thresh-old approach, the mathematical utility of which for ‘heavy-tailed’ distributions has been recently elucidated (Woo, 1999).An unanticipated outcome was the identification of two dis-tinct groupings in the size distribution of the selected dataset:most dome eruptions (85%) last less than 5 years and fall ona frequency-duration trend (Figure 5) different to those thatlast more than 5 years. In the latter cases, the eruptions canbe very long-lived. Based on this analysis (and no other infor-mation) there was, for instance, only a 3% chance of theeruption lasting less than a further 6 months, having alreadylasted 94 months. There is a 50% chance that the eruptionduration will last 20 years or longer, and a 5% chance of last-ing more than 180 years.

Such analyses are limited by the quality and nature of thedata. There are problems in defining durations because thebeginning of an eruption is usually accurately recorded but theending is often poorly or vaguely recorded. Further, there are


Figure 4. Example of probability curves for societal risk in Montser-rat. Each curve shows the probability plotted against number of casu-alties over a 6-month period, and is the mean of thousands ofsimulations using Monte Carlo re-sampling from uncertainty dis-tributions on the parameters that influence risk. The upper curve(solid line) is the exposure with the Belham Valley area (Figure 3)populated before the evacuation, and the lower curve (dashed line)shows the reduction in risk with evacuation. Regional risk curvesfor hurricanes and tectonic earthquakes are shown for comparison.Note that for each curve uncertainties at the 5% and 95% levels werecalculated but are not shown for clarity.

Figure 5. The exceedence probability distribution for the durationsof 137 dome-building eruptions, drawn from the Smithsonian data-base. The data for eruptions lasting longer than 86 months are fittedto a Generalised Pareto Distribution law, which can be used to esti-mate the likelihood of the duration of an eruption exceeding a givennumber of months. In the text we have used the distribution for long-lived eruptions (>86 months) to assess the probability of the eruptionstopping, given that the eruption had lasted 94 months.

only 15 cases of eruptions lasting more than 5 years so the data-base is very limited and, in some of these cases, conservativedecisions had to be made about what constituted a coherentlong-term episode of dome-building when punctuated activ-ity is reported. Nevertheless, the two different distributions arequite distinctive and alternative assumptions on the reliabil-ity and uncertainties in the Smithsonian database fail to removethe feature.

This example shows that process information can beextracted by a data-analytic approach, which invites the ques-tion of why dome eruptions that last much more than 5 yearstend to become very long-lived. A possible answer is that thisis sufficiently long for conduits to become mature and sta-bilise so that heat loss to the walls is balanced or even exceededby heat advection by magma flow with the longevity of theeruption being controlled by the dynamics of the chamberrather than by gradual freezing of the magma at shallowerlevel. This is certainly not the only possibility; the point isthat the data and its analysis provoke scientific enquiry.

Explosion Sequence Time Series

Seventy-five Vulcanian explosions occurred at the SoufrièreHills volcano between 22 September and 22 October 1997. Thetimings of this sequence were investigated by Connor et al.[2003]: on average, there was an explosion every 9.5 hours, butindividual intervals varied from as short as 4 hours to as longas 33 hours. Voight and Cornelius [1991] had found that, in therun-up to an eruption, time series of volcanic data, such asReal Time Seismic Amplitude Measurement (RSAM) ordeformation rate, could fit a Weibull distribution which, inthe context of engineering reliability, is widely used to representtimes-to-failure in materials. However, the Soufrière Hillsexplosion data did not fit this form of relationship (Figure6a), suggesting that the physical controls on intervals betweenthe events were not just an analogue of material mechanics inwhich strain rate increased with time until failure (explosion)was inevitable. A memory-less (Poisson) process also failedto reflect the data, indicating that the timing to the next explo-sion had some independence on previous explosions. Instead,Connor et al. [2003] found that the explosion interval datafitted a log-logistic statistical distribution extremely well.

They proposed the following dynamic equation as repre-senting the causative processes:

(1)

where t is the time since the last explosion, Ω is some statevariable, k is a power-law exponent and Ωeq is a character-istic value of Ω when the two right hand terms are equal. A

log logistic survivor function that describes the statisticaldistribution of repose periods can then be defined [Connoret al., 2003] which fits the observations within 99% confi-dence limits (Figure 6b). This kind of analysis illustratesthat constraints or process information with relevance tohazards can be extracted from such an analysis; in other

2

eq

d kt kdtΩ = Ω − Ω

Ω


Figure 6. Statistics of intervals between Vulcanian explosions at theSoufrière Hills volcano, Montserrat in September and October 1997.(a) Comparison of the observed interval distribution (open circles)and calculated distributions using the Weibull model with a timeconstant of µ = 9.6 hours and various values of the power exponentk [after Connor et al., 2003]. Using k = 4, estimated from experi-mental data, gives a good fit to the observed distribution at t < µ, buta poor fit at t > µ. The exponential (Poisson) model corresponds tok = 1, and does not fit the observed distribution. (b) The observed dis-tribution of repose intervals are fit with > 99% confidence using alog-logistic survivor function with a time constant of µ = 9.0 hours(observed distribution median) and an exponent of k = 4 [after Con-nor et al., 2003].

words, it throws light on the context of what is, otherwise,an abstract statistical model.

For the Montserrat case, the best-fit statistical model sug-gests that the stochastic dynamics of the system must havecertain properties: equation (1) represents two competingprocesses acting on different time scales which, respectively,increase and decrease internal gas pressure. Connor et al.[2003] postulated that after an explosion, gas pressure increasesby exsolution from magma, but gas escape by permeable flowthrough the magma reduces the gas pressure. At early stages,gas exsolution is dominant and gas pressure increases. Later,gas escape plays an increasingly important role and counter-acts the exsolution-driven increase in gas pressure. This com-peting-processes model is consistent with currentunderstanding of the mechanisms of repetitive explosive erup-tions at Montserrat [Voight et al., 1999; Druitt et al., 2002a;Melnik and Sparks, 2002]. However, a full fluid dynamicmodel of magma ascent that incorporates all the complexinteracting processes involved has not yet been developed.Indeed, a test for the viability of numerical models should bethat their outputs mimic closely both the statistical and tem-poral properties of the natural data.

Such an approach has forecasting relevance, as proposedby Voight and Cornelius [1991]. Almost all statistical mod-els can lead to some form of distributional ‘hazard function’which, in this case, can be interpreted as the relative proba-bility of an explosion at some definite time after a previousexplosion. This probability is constant for a Poisson arrivalprocess, asymptotic after some definite time for a Weibulldistribution, but reaches a maximum before declining for alog-logistic model.

This type of analysis of a complex stochastic dynamic sys-tem, the analysis of large sample data, and the assessmentof uncertainty in wider areas of public concern are some-what outside the traditional realms of statistical inference[see, e.g., Chatfield, 2002], but constitute important propo-sitions for advancing volcanology. As such, they need to beintegrated into an overall strategy for modelling volcanicactivity, hazards and risks.

MODELLING STRATEGIES IN VOLCANOLOGY

Forecasting of complex volcanic phenomena involves acombination of empiricism, understanding (often at an intu-itive level) of the underlying physical processes, and model-ling. Monitoring data and observations provide the ingredientsfor the empirical approach in that patterns may be recognisedand interpreted within a framework of physical theory or con-ceptual models. Monitoring data can also validate quantitativemodels to increase confidence in their output (althoughschemes that generate self-fulfilling prophecies must be

avoided). However, models should be used with awarenessof their limitations as well as their strengths.

The issue of quantifying uncertainty is becoming moreprominent. Simplified (scenario-based) deterministic modelsare exceedingly useful for gaining a good first-order under-standing of volcanic processes, but are likely to prove inad-equate when it comes to providing models with utility forforecasting and prediction. Given the stochastic and nonlin-ear nature of many volcanic processes and the uncertainties(which can be large) in the controlling parameters, practicalmodels are likely to follow the approaches now routinelyadopted in other natural hazards forecasting, such as floodsand extreme weather events. In meteorology, for instance,the integration of results from an array of prediction models,with explicit perturbations to model formulations, initial con-ditions and parameter probability distributions, generate anensemble of outcomes that can be treated in a statistical man-ner and presented as a full probabilistic forecast [see, e.g.,Palmer, 2000]. This is only just beginning to happen in vol-canology. A major challenge is to ensure that such ensembleforecasting encompasses all the key factors involved in thenatural processes. In particular, the existence of epistemicuncertainty has to be recognised and assimilated into the pro-cedure, which will entail a suitable suite of alternative mod-els being interrogated jointly. While, in practical terms, thiswould be a non-trivial undertaking, it would provide a properrational basis for evaluating the value of such forecasts[Palmer, 2000].

In volcanology numerical modelling is becoming an impor-tant aspect of forecasting and risk assessment, and evolvingapproaches have largely focused on numerical simulations.Aided by increasing computer power as well as improvingunderstanding of the physics involved, such models are becom-ing increasingly sophisticated [e.g. Neri and Macedonio, 1996;Papale, 1999; Melnik and Sparks, 1999]. A presumption isthat such models will eventually simulate nature so well thatthey can be used for forecasting. These expectations mayprove to be optimistic, not least because experience has demon-strated with climate modelling that, when uncertainties insuch models are disaggregated and appraised individually,the spread of overall uncertainty increases [Morgan and Keith,1995]. Here we discuss the limitations of modelling and con-sider complementary strategies, while recognizing that numer-ical models give important insights into volcanic processes.

Most computer modelling of natural phenomena has adopteda strategy of simplification to make matters tractable: thosedetails that are thought to matter most are represented as accu-rately as possible, and other details, not considered impor-tant, are abridged or omitted. Knowing, however, which detailsmatter most can be tricky: models are prone to be incomplete,sometimes leaving out details that could matter under certain


conditions. Parametric or even structural uncertainties remainimplicit, so that no matter how detailed the model that is cre-ated, complete confidence cannot be invested in its predic-tions about the behaviour of the real system.

Typically, numerical models for volcano dynamics involveseveral partial differential equations and equations of state thatdescribe the system behaviour. The number of degrees of free-dom in the system, and hence number of parameters needed tocharacterize it adequately, is typically large (commonly a fewtens). To make the models computationally manageable andhelp interpret outputs, simplifications have to be made. Forexample, published models of pyroclastic flows only involvetwo particle sizes [Neri and Macedonio, 1996]. Certain featuresof volcanic flow systems are exceedingly computationallydemanding: vesiculation processes in explosive eruptions mayinvolve formation of 1015 bubbles per cubic metre. Keepingtrack of what every bubble and melt region does cannot beachieved without making major simplifications that may intro-duce artificial or unphysical features into the model. As com-puter codes become more complicated the chances of errors andnumerical artifacts increase, and complex codes need sub-stantiating. There may be a limit, however: Oreskes et al. [1994]assert that absolute validation is impossible for numerical mod-els in the Earth Sciences.

When numerical models are compared to natural data theissue of uniqueness emerges. It is relatively easy for a skilledmodeller to make a model with large numbers of parametersfit the data: the process is one of hindcasting, rather thanforecasting. For example, Barmin et al. [2002] investigateda model of periodic behaviour of lava dome eruptions andwere able to generate simulations similar to the activity ofMount St Helens and Santiaguito lava domes. Such modelsare very good for gaining insight into how Nature has behaved,but are not unique. There is also inevitably much empiricismin all such models; for example, in high-speed multiphaseflows assumptions are made about turbulence based on empir-ical closure models that have yet to be confirmed in particle-gas mixtures.

It is thus difficult to envisage how deterministic modelscan be used successfully in forecasting. Interestingly, mostof the models that have been developed so far as forecastingtools in volcanology are less physics-based and more overtlyempirical, as exemplified by the tephra fall and pyroclasticflow run-out models used on Montserrat. One new directionfor numerical models will be to incorporate the quantificationof uncertainty. An obvious approach will be to assign uncer-tainties to every parameter and run ensemble models in whichsample the uncertainties using Monte Carlo techniques andrepeat calculations a large number of times.

On the topic of uncertainty, an emerging issue for numer-ical models is the difficult but critical difference between

aleatory and epistemic uncertainty, and how to recognize it.Any system has aleatory uncertainty that is real and reflectstruly random features like noise and time evolution of magmasystem properties. Unfortunately model parameters alwaysinvolve a mixture of both kinds of uncertainty. A good exam-ple is conduit dimensions, which are critically important toconduit flow models because of the high powers of flow ratedependence on conduit shape (e.g the fourth power of diam-eter for a cylindrical conduit). Conduits are non-uniform inNature and cannot be measured directly, so their shape anddimensions are inevitably poorly constrained with large epis-temic uncertainty. Notwithstanding this, conduits are com-monly assumed to have a fixed simple geometry (e.g. cylindersof constant diameter). In reality, conduit dimensions mighthave small aleatory uncertainty (sensu stricto), if they couldbe accessed, but they can evolve with time and be hard todefine spatially if there are property gradients between themagma and the wall-rock. So it is unlikely that conduit mod-els can ever be very accurate.

On top of that, many volcanic processes are also highlynon-linear. Modelling research in simplified volcanic sys-tems has identified multiple solutions, such that a system canjump suddenly from one state to another [Jaupart and Allegré,1991; Melnik and Sparks, 1999; Slezin, 2002]. Where sys-tems are close to thresholds for instability, technically knownas cusps in catastrophe theory, they can become inherentlyunpredictable. Worryingly, complex numerical models areunlikely to capture this kind of behaviour easily because of thelarge epistemic uncertainties in some critical parameters.

Greater use of statistical models and methods should providean alternative and complementary approach to multivariate,multiparameter forward numerical models. Here we have illus-trated how statistical analyses can lead to insights into processes.Statistical models should be given considerable weight in haz-ards assessments as they are data-based, reflecting how thesystem actually behaves rather than how it might behave. Suchmodels are effectively free of epistemic uncertainty, exceptwith respect to the measurements themselves. This point hasbeen made strongly by Young et al. [2002] in the context ofmodelling stochastic systems, in particular the climate.

We suggest that the future direction of modelling researchfor volcanology will involve combining statistical and numer-ical modeling techniques in a common strategy, with inter-play between both. For example, a good test of the validity ofa numerical model is that is can reproduce the statistical fea-tures of natural data.

THE STATE OF A VOLCANIC PLANET

Over the coming century there are likely to be several majorvolcanic eruptions (defined as those exceeding 1 km3), which


will affect large numbers of people. With the increasing globalpopulation, the dramatic growth of megacities close to activevolcanoes, and stresses related to rapid environmental changeand globalisation, there is the potential for much larger andmore serious volcanic crises and disasters than in the twenti-eth century. It is certainly plausible that the casualties in alarge eruption near an area of dense population could greatlyexceed the largest death toll of the last century (30,000 peo-ple at Mont Pelée), and might create sufficient destruction toimperil the economies of individual countries and perhapseven continental regions. Human beings are, without doubt,much more vulnerable to volcanic hazards as a consequenceof rapid environmental change and globalisation. On the otherhand, the advances in understanding of volcanic processescombined with the huge advances in science and technologymean that the scientific community is in a much better posi-tion to anticipate volcanic eruptions and, in some circum-stances, predict their occurrence, estimate their impact andtake steps to protect populations and mitigate the effects.

Many of the scientific tools for dealing with volcanic crisesare already available and will continue to improve. The nextfew decades are bound to produce an increasing number of vol-canoes that are adequately monitored. As computer powerincreases and cheap data storage moves from gigabytes toterabytes there will be huge improvements in the analysis ofdata from monitoring networks and in the modeling of volcanicprocesses. There are also likely to be major advances in tech-nology (e.g. satellites, nanotechnology instruments and detec-tors), which will have significant impact on the ability toanalyse signals and monitor volcanoes: remote measurementsfrom space, in particular, offer great promise for enhancingoperational forecast models [Wadge, 2003].

The approaches to hazards analysis and prediction arelikely to move towards probabilistic assessments and,inevitably, to increased use of statistical models. In the lattercase, numerical simulations of volcanic processes will bedeveloped in ensemble style, incorporating elements of epis-temic and aleatory uncertainty, with comparison of statisti-cal properties of model outputs with real data. Atransformation is taking place in the scientific expertise thatwill be needed to develop these vital quantitative forecastingand prediction tools, and much needs to be done to providevolcanologists with the appropriate knowledge and skills tomeet the challenges.

Despite reasons for optimism only a small number of activevolcanoes are adequately monitored, and many of these are vol-canoes within the Developed World. Most of the world’s activevolcanoes and a large proportion of the 500 million people liv-ing close to volcanic threats are in less developed regionswhere such volcanoes are either not monitored at all or, atbest, have only rudimentary observational or instrumental

networks. The challenge is therefore to provide these regionswith working access to the technological and scientif icadvances that can mitigate disaster and assist sustainabledevelopment.

Acknowledgements. RSJS acknowledges a Royal Society-Wolf-son Award and support from research grants including the EC (MUL-TIMO EVG1-2000-00574) and NERC. WPA acknowledges aBenjamin Meaker Visiting Fellowship at IAS, Bristol, and supportfrom EC projects MULTIMO EVG1-2000-00574 and EXPLORISEVR1-CT-2002-40026. The authors acknowledge the tremendoushelp of staff of the Montserrat Volcano Observatory and many col-leagues involved in the hazards and risk assessments on Montserrat.The authors thank Gordon Woo for stimulating discussions, andColin Wilson, Chris Newhall and Chris Hawkesworth for carefuland helpful reviews. Table 1 follows a suggestion from Colin Wilson.

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