Forecasting volcanic eruptions

Forecasting is a central goal of volcanology. Intensive monitoring of recent eruptions has generated integrated time-series of data, which have resulted in several successful examples of warnings being issued on impending eruptions. Ability to forecast is being advanced by new technology, such as broad-band seismology, satellite observations of ground deformation and improved field spectrometers for volcanic gas studies, and spectacular advances in computer power and speed, leading to improvements in data transmission, data analysis and modelling techniques. Analytical studies of volcanic samples, experimental investigations and theoretical modelling are providing insights into the dynamics of magmatic systems, giving a physical framework with which to interpret volcanic phenomena. Magmas undergo profound changes in physical properties as pressure and temperature vary during magma chamber evolution, magma ascent and eruption. Degassing and cooling during magma ascent induce crystallisation and increases of viscosity, strength and compressibility, commonly by several orders of magnitude. Active magmatic systems also interact strongly with their surroundings, causing ground deformation, material failure and other effects such as disturbed groundwater systems and degassing. These processes and interactions lead to geophysical and phenomenological effects, which precede and accompany eruptions. Forecasting of hazardous volcanic phenomena is becoming more quantitative and based on understanding of the physics of the causative processes. Forecasting is evolving from empirical pattern recognition to forecasting based on models of the underlying dynamics. The coupling of highly non-linear and complex kinetic and dynamic processes leads to a rich range of behaviours. Due to intrinsic uncertainties and the complexity of non-linear systems, precise prediction is usually not achievable. Forecasts of eruptions and hazards need to be expressed in probabilistic terms that take account of uncertainties. - 2003 Elsevier Science B.V. All rights reserved.


Introduction
Forecasting is a fundamental objective of volcanology.Civil authorities and the public need to know when and where eruptions will occur, the kinds of volcanic phenomena that might occur, how long eruptions will last, and whether populations near the volcano will be a¡ected by hazards.These questions are much easier to ask than to answer.Recent advances are beginning to provide answers and to establish the scienti¢c agenda.Volcanoes are complex dynamical systems controlled by interactions of many processes, which are commonly non-linear and stochastic.There are many uncertainties in the controlling parameters [1].Further, volcanic systems have the potential for behaviours that are inherently unpredictable [2].However, complex, sometimes chaotic, systems are not unconstrained and eruptions can show systematic evolutionary trends and quite regular periodic behaviours.Volcanic eruptions also are constrained by physical laws that can be elucidated both empirically and by modelling.Forecasting can be achieved and, under speci¢c circumstances, with some con¢dence.Like the weather, volcano forecasting needs to be developed in terms of probabilities.
Several factors have advanced understanding of volcanic processes and bring the goal of robust forecasting closer.Several volcanic eruptions have been studied intensively by large multidisciplinary teams of scientists.Eruptions of Kilauea (Hawaii), Kra£a (Iceland), and Mount Etna (Italy) have provided important datasets for understanding basaltic volcanism.Mount St Helens (1980^86), Mount Unzen (1991^1995), Mount Pinatubo (1991) and the Soufrie 're Hills Volcano, Montserrat (1995^present) are examples of welldocumented andesite and dacite eruptions.Contemporaneously there have been major advances in monitoring techniques, data acquisition and data analysis, complemented by sophisticated analytical, experimental and theoretical studies and by orders of magnitude improvements in computer power and speed.
This review gives a £avour of the main developments and a sense of where volcanic forecasting is going.The article ¢rst considers monitoring techniques.A second section considers volcanoes as dynamical systems in which several non-linear processes are coupled and lead to complex behaviours.This leads into a third section where a probabilistic approach to forecasting is discussed.Newhall [3] provides a complementary article on Volcano Warnings.

Volcano monitoring
Volcanic activity is caused by the ascent of magma to the Earth's surface and its eruption.
During ascent magma interacts with surrounding rocks and £uids.Monitoring involves geophysical or geochemical techniques that detect magma movements and associated sub-surface interactions, and can record eruptive activity.

Seismicity
Seismic monitoring can give real-time data and correlations have been established between magma movements, eruptive phenomena and seismicity.Before eruption, ascending magma has to push rocks apart and this perturbs stress distributions and pore £uid pressures, commonly resulting in fracturing and numerous small-magnitude earthquakes.Earthquakes above background levels are commonly the ¢rst warning signs of impending eruption, although an eruption may not happen.Indeed the majority of volcano-tectonic crises do not lead to eruption [3,4].Once an eruption starts seismicity provides information on the Fig. 1.Real-time seismic amplitude measurements (RSAM) for two stations (RDN and RED) before the explosive eruption of 14 December 1989 at Redoubt Volcano, Alaska (after [7]).The data show the changes in the intensity of shallow long-period earthquakes over a 24 h period prior to the onset of the explosive eruption shown by arrows marking the beginning and end of the eruption.The continuous and dotted lines show the raw and corrected data respectively (see [7] for details).Note that the RSAM data at RED reach a maximum about 6 h before the eruption.Such a response can be interpreted as weakening of the system approaching failure.RSAM is a measure of seismic energy.
style of activity and detects changes in the physical system.Key developments in volcano seismology have been the recognition of di¡erent types of earthquake that can be linked to particular volcanic phenomena, and the recognition of long-period signals related to £ow of volcanic gases and geothermal £uids [5^7].These developments have been augmented by the installation of networks of three-component and broad-band seismometers.The eruption of Mount Redoubt, Alaska (1989^1990) illustrates a success story in seismic forecasting [7].Here 11 swarms of long-period earthquakes were precursory to explosive eruptions.Warnings were issued for the explosive eruptions of 14 December 1989 and 2 January 1990 based on the characteristics of the swarms (Fig. 1).The forecast was based on two concepts.First the long-period events were interpreted as movement of pressurised £uids along fractures.Second the waxing and waning of the swarm intensity (Fig. 1) was attributed to mechanical weakening of the system before a catastrophic failure and explosive eruption.
Seismic data have been used to evaluate the materials failure forecast method (FFM) [8,9].The FFM is based on laws of material failure in which failure time is forecast from the inverse relationship between time and a proxy for strain rate, such as ground deformation or seismic energy release.Retrospective analyses of seismic energy release patterns at Mount St Helens, Mount Redoubt and Mount Pinatubo indicate that the eruptions could have been predicted within a few hours or days using this approach (Fig. 2).Seismologists can distinguish and interpret different types of earthquake signal.Several types of earthquake have been recognised at the Soufrie 're Hills Volcano, Montserrat [6,10].Volcano-tectonic earthquakes are distinguished from shallow earthquakes that contain long-period components (Fig. 3).The former was prominent in the precursory as magma forcibly created a pathway to the surface.The latter were associated with growth of the lava dome; the occurrence of such earthquakes in November 1999 was used to recognise that dome growth had resumed after 20 months of inactivity [11].Seismicity in dome-forming eruptions is also associated with rock-falls and pyroclastic £ows generated by dome instability.Seismic signals have been used to locate £ow pathways and to estimate their speed [12,13].The seismic signal of a pyroclastic £ow slowly emerges and then decays as the £ow moves towards and then past the seismic station.This Doppler e¡ect can be exploited because di¡erent stations record peak amplitude and signal duration that are controlled by £ow position relative to the station.The signals can be calibrated to £ow size and then related to models of £ow run-out.
Fig. 4 shows the spectra over a 20 min interval of long-period seismicity leading up to a Vulcanian explosion on Montserrat [6].The seismicity has several dominant spectral modes and there are systematic shifts of these peaks with an approximately exponential change of each peak frequency with time.The data provide an empirical basis for forecasting.Neuberg [6] interpreted these relationships as a consequence of the great sensitivity of seismic wave velocity to bubble content of the magma.He proposed that the spectral gliding is due to magma vesiculation and associated pressurisation in the upper conduit, developing conditions for an explosion.

Ground deformation
Magma stored in chambers and £owing along conduits varies in pressure leading to deformation of the surrounding crustal rocks.Most ground deformation techniques measure the resulting changes on or near the Earth's surface.Standard techniques include electronic distance measurements (EDM) using re£ected laser or infrared light, measurement of ground tilt, use of the global positioning system (GPS), precise levelling and borehole sensors including strainmeters and tiltmeters.EDM, GPS, and precise levelling require networks of stations and are labour-intensive.The developments of continuous GPS and synthetic aperture radar (SAR) have provided a revolution in the quality and quantity of data [14,15].Data are acquired rapidly and for SAR a continuous deformation ¢eld is documented (Fig. 5).
Ground in£ation is commonly observed before the onset of eruption [16,17].However, substantial ground deformation can occur due to magma intrusion without eruption [18,19] and can also be related to tectonics, isostatic adjustment and changes in geothermal systems.Some volcanoes erupt without any deformation being detected.Interpretations of deformation have generally been based on the Mogi model of a pressure source in an elastic half-space [20].More elaborate models consider topography and variations in source geometry [15,21].However, the models do not yet capture the full complexity of crustal responses to magma pressurisation.Since the crust becomes ductile at shallow depths (V5^10 km) below volcanoes it is unlikely that purely elastic models are adequate.Deformation can be measured earlier than other types of eruption pre- cursors ; for example seismicity does not start until a strain threshold (typically about 10 34 ) is exceeded.
Some hazardous volcanic eruptions involve £ank instability.For Mount St Helens in 1980 magma intruded into the volcanic edi¢ce and outward movement of the north £ank of the volcano was recorded at 1^2 m/day [22].The size of the eventual collapse was anticipated [23], but its timing was not predicted.The volcanic blast at Soufrie 're Hills Volcano, Montserrat was anticipated based on observations of ground deformation, which started in October 1996 [24] and led to a precautionary evacuation.The collapse did not take place until 26 December 1997.These examples highlight the di⁄culties in predicting the structural stability of volcanoes and timing of failure [24].
Observations are becoming important using instruments in boreholes because this environment greatly reduces noise and instrument sensitivity.Borehole strainmeters can detect changes of 10 312 [25], and can be deployed at greater distances than other instruments.Their utility was demonstrated in the 1991 eruption of Hekla, Iceland [25].Five borehole strainmeters located 15^45 km from the volcano recorded marked dilatational strain over a 30 min period during the propagation of a dyke to the surface (Fig. 6).The strain pattern, together with increased seismicity, enabled the 2000 Hekla eruption to be forecast [26]; based on warnings issued by the Icelandic scientists the national radio announced that an eruption would start in 15 min; it started after 17 min.
Tiltmeters have been used to forecast explosions at Sakurajima volcano, Japan [27].Here in-£ationary radial tilt is observed for periods of 10 min to 7 h prior to explosions at the summit crater, allowing automated warnings to be issued.

Volcanic gases
Gas monitoring has been di⁄cult because reliable data had to be obtained from high-temperature fumaroles often in hazardous circumstances.However, remote spectroscopic methods from satellites and from ground-based instruments are greatly improving the quantity of data [28,29].Signi¢cant correlations have emerged between gas £uxes and other geophysical signals [30,31].Time-series of gas £ux can now be produced comparable in detail and quality to seismic and geodetic studies [28].
Understanding of gas compositions is now good enough that the presence of magma at shallow depth can be distinguished from tectonic or hydrothermal degassing when volcanic unrest starts.At Pinatubo high SO 2 £uxes indicated that unrest was magmatic rather than hydrothermal in origin, and a decrease of SO 2 £ux (in early June 1991) suggested that the system was sealing, pressurising and approaching conditions for explosive activity [32].SO 2 measurements, combined with seismic and deformation data, helped the scientists to evaluate correctly the nature of the unrest, the state of the volcano, and to anticipate the eruption.At Montserrat dome growth ceased in March 1998.However, high SO 2 £uxes (10003 000 tonnes/day) continued throughout the next 20 months before dome growth resumed in November 1999 [11].This observation was critical in the assessment that the eruption had not ceased.
Increases of CO 2 have also been used to indicate replenishment of magmatic systems [33,34].

Other methods
There are many other methods: gravity, remote sensing of temperature, electric ¢elds, and acoustic emissions.As yet little studied phenomena concern unusual water emissions and changes in water tables prior to eruptions.Water poured out of ¢ssures at Mont Pele ¤e in 1902 [35] to form mud £ows in the days before eruption.Water levels in boreholes around Mayon volcano, Philippines increased by several metres before eruption [36].Several months before the Mount Usu (Japan) eruption in 2000 water levels in two boreholes dropped and then increased [37].Water spouted out of the wells and out of eruptive vents at the beginning of the eruption [37,38].These e¡ects are likely caused by rising magma opening up fracture systems and disturbing groundwater systems.

Integrated datasets
Integration of datasets using several co-ordinated monitoring techniques is the key to successful forecasting.For Mount Pinatubo (1991) integration of data on precursory seismicity, ground deformation, and SO 2 emissions, together with geological studies [39] led to a successful forecast and timely evacuation of tens of thousands of people.
The Soufrie 're Hills eruption, Montserrat demonstrates the advantages of integrated data.In 1997 the MVO installed two tiltmeters on the rim of English's crater adjacent to the growing lava dome.The tilt data revealed correlations between ground deformation, swarms of hybrid (long-period) earthquakes and volcanic activity [40].Periodic cycles of tilt were observed (Fig. 7) with periods lasting a few hours to a few days.In each cycle there was a seismic swarm associated with ground in£ation.During the de-£ation there was low or no conduit seismicity, but rock-falls from the dome increased substantially.The cycle peaks were commonly characterised by vigorous ash venting and in early August 1997 by Radial tilt (microradians) Fig. 7.The tilt pattern at Chances Peak and seismicity at the Soufrie 're Hills Volcano, Montserrat in June 1997 (after [40]).The tiltmeter was approximately 400 m from the centre of the dome with the tilt axis for data shown being approximately radial to the dome centre.The earthquake event frequency in events per hour (left hand vertical axis) at the Gage's seismometer is shown as histograms.The tilt variation in Wradians (right hand vertical axis) is shown as the continuous curves.All the instrument output displays the cyclic pattern of deformation and seismicity, with hybrid earthquakes occurring in the in£ation periods and rock-fall signals occurring during the de£ation periods.Marked episodes of degassing were observed at the peaks in the tilt cycle and during de£ation (see [40]).Vulcanian explosions.These observations led to an interpretation of cyclic pressurisation of magma in the upper conduit, with a surge of dome growth and release of pressurised gas at the peak of a cycle and during de£ation.The cycles were commonly highly regular in period for several days to a couple of weeks and the MVO used these patterns for forecasting [40].

Volcanoes as dynamical systems
Improvements in forecasting are closely linked to advances in understanding of the underlying dynamical processes.Volcanic £ows are complex and applied mathematicians, engineers and physicists are becoming involved in modelling studies in collaboration with earth scientists.The strongly non-linear and time-dependent character of volcanic systems introduces fundamental issues for forecasting of uncertainty and complexity.

Physical properties of magmas and their surroundings
Magmas are complex materials with strong dependence of rheology on temperature, melt composition and water content [41].Viscosity can vary between 10 0 and 10 14 Pa s.Although pure melts are normally Newtonian, they can become non-Newtonian at high strain rates [41].Magma rheology is greatly complicated by the presence of suspended crystals and gas bubbles [42,43], particularly at high concentrations where rheology becomes strongly non-Newtonian.Many other important properties that can in£uence £ow dynamics, including magma density, thermal conductivity, compressibility, acoustic speed and diffusivity of dissolved gases, also vary widely.The Earth's crust with which magma interacts is made of complex and variable materials.Mechanical properties and responses to magma ascent and eruptions can be expected to vary as a consequence of geological and structural heterogeneities, stress variations, temperature, and disturbance of hydrothermal or groundwater systems.In some places the crust might deform as an elastic material and in others in ductile style, depend-ing on factors such as strain rate, lithology, temperature and pore pressure.Magma £ow can alter the surroundings by the action of magma pressure, heat transfer and chemical reactions.Flank instability highlights the need for geotechnical data as input to dynamical models [23].

Volcanoes as non-linear dynamical systems
Variations of physical properties of magmas and their surroundings are governed by non-linear, time-dependent processes, such as crystallisation and degassing in magma and fracture network evolution, pore pressure variations and strain weakening in a volcanic edi¢ce.These processes are typically coupled, so that, for example, gas exsolution and heat loss in ascending magma can induce crystallisation and vesiculation [2,44,45].Flowing magma is driven away from thermodynamic equilibrium by the changing pressure and temperature and towards equilibrium by processes such as crystallisation and gas exsolution.These changes are time-dependent, because crystallisation and vesiculation are controlled by complex kinetics and cause very large changes in rheology and £ow behaviour.Similarly there are complex interactions between gas bubble nucleation, growth, coalescence, and segregation in ascending magmas which are themselves coupled to £ow dynamics through the e¡ects of bubbles on magma density, rheology and compressibility [43,46^48].
The rocks around a conduit, the edi¢ce and the groundwater are expected to respond in non-linear ways to magma ascent and eruption [23,37].Examples of external e¡ects are stress corrosion, in which hydrothermal £uids attack and weaken country rock [49], mineral precipitation from hydrothermal £uids that reduce wall-rock permeability and inhibit degassing of ascending magma [50] and stress changes related to edi¢ce growth or destruction [51].
Models are emerging to explain pulsatory and periodic behaviours in lava dome eruptions.In such eruptions £uctuations in magma discharge rate can vary on time scales from hours to decades [40,52].Sometimes the pulsations are quite regular, as exempli¢ed by the tilt cycles on Mont-serrat [40] and the 1980^1986 activity of Mount St Helens [53].Dome growth can also be steady for many months or years [53].Whitehead and Hellfrich [54] showed that a £uid with strongly temperature-dependent viscosity £owing through a conduit with lateral cooling displays periodic £uctuations in £ow rate.For the short-time-scale (hours to days) cycles observed at Soufrie 're Hills and Pinatubo, models have linked the behaviour to the coupled processes of degassing, crystallisation and rheological sti¡ening of ascending magma together with stick-slip behaviour of non-Newtonian magma [40,55,56].Melnik and Sparks [2] considered coupled conduit £ow and lava dome extrusion, taking into account the coupling between gas exsolution, gas escape by permeable £ow, and crystallisation kinetics with magma rheology and density.Barmin et al. [52] extended this model by considering unsteady £ow evolution and simulating eruptive behaviours that resemble those observed at lava dome eruptions.
Fig. 8 illustrates a mechanism to cause periodic and complex behaviours in lava dome eruptions [52].A chamber with elastic walls is supplied with magma at a constant rate.The ratio of output (eruption rate) to input is plotted against magma chamber pressure.The steady solutions to the mathematical description of this system yield a sigmoidal curve with an upper linear branch and a lower parabolic branch.The upper linear branch represents £ows that are too fast for degassing-induced crystallisation to occur, whereas the lower limb of the parabolic branch represents the case of very slow £ows where crystallisation occurs and the viscosity is higher.Multiple steady states exist such that at a ¢xed magma chamber pressure three possible eruption states exist.Such systems can be extremely sensitive to slight changes in conditions especially near cusp points.Periodic behaviour can be understood by starting at an arbitrary point on the lower branch (A).Since input to the chamber is greater than output the chamber pressure builds up and the output increases.Beyond cusp point B there is no steady solution so the eruption enters an unsteady regime and £ow rate increases until the upper linear branch is reached at C where output is greater than input.At this stage chamber pressure re-duces and the system evolves to cusp point D and then unsteadily back to A. Thus a cyclic pattern is established.
Eruptive patterns similar to Mount St Helens and Santiaguito can be reproduced by such a dynamical model (Fig. 9), including both periodic behaviour and steady outputs.These models, however, are not yet fully realistic.For example, the models are one-dimensional and make simpli-¢cations such as constant input to the chamber and constant lava dome height.Massol and Jaupart [48] have shown that large lateral pressure gradients can develop across volcanic conduits and that there will be lateral coupling between degassing rates, crystallisation and rheology.Realistic models will need to take such two-dimensional e¡ects into account.Additionally the models make simple assumptions about the response of the surroundings.Flow models will need to be coupled into models of edi¢ce deformation and groundwater responses.This is a ¢eld in its infancy, but future studies promise to reveal rich behaviours.A system only requires three non-linearly coupled time-dependent variables to have the potential for chaotic behaviours.
Such models link £ow dynamics with geophysical and eruptive phenomena.Melnik and Sparks [2] found that large magmatic overpressures develop in the uppermost parts of volcanic conduits due to rheological sti¡ening.This concept pro- vides an explanation for shallow pressure sources inferred from ground deformation, shallow seismicity and occurrences of sudden Vulcanian explosions in dome eruptions.

Eruption transitions
Forecasting explosive eruptions is a critical issue.At Mount St Helens in 1980 the major explosive eruption occurred near the beginning of the eruption and was followed by episodic lava extrusions and more moderate explosive activity in the 1980^86 period.At Mount Pinatubo in 1991 the catastrophic eruption of 15 June was preluded by a magnitude 7.8 earthquake on the Philippine fault in August 1990 [57].Felt earthquakes occurred in March 1991 and the ¢rst phreatic eruptions began on 2 April.A brief 4 day period of escalating dome growth and explosive activity preceded the paroxysmal eruption on 15 June.Lascar volcano, Chile started a slow e¡usion of an andesite lava dome in 1984, but unexpectedly had a very high-intensity explosive eruption in April 1993 [58].The Lascar case highlights the problem that relatively benign lava e¡usions can suddenly change to very hazardous explosive activity after many years of eruption.
The dynamics of gas escape during magma ascent controls the transitions between explosive and e¡usive activity.Taylor et al. [59] introduced the idea of a permeable magma foam.As pressure decreases gas bubble concentration increases and bubbles interact and coalesce.Once gas bubbles become interconnected the exsolving gas can escape through permeable magma and the conduit walls.Models of the coupling between gas exsolution, gas loss and eruptive styles [60,61] show multiple steady solutions to the mathematical descriptions so that sudden transitions between eruptive £ow regimes (e.g.explosive versus e¡usive) can occur.These transitions may happen with little warning and forecasting may be problematic when a volcanic system is in an unstable or sensitive state.

Predictability, unpredictability and probabilities
Precise prediction is not achievable in many situations.Erupting volcanoes can become critical systems so that they can move from one state to another with only a very minor external or internal trigger.An example of an external trigger is the sector collapse of Mount St Helens in 1980.
Here magma had been intruding into the edi¢ce for several weeks, causing bulging of the northern £anks.The collapse and paroxysmal eruption on 18 May was triggered by a magnitude 5 earthquake [22].Although the eruption was moving towards catastrophic eruption anyway [23], the eruption timing could have been signi¢cantly different without this trigger.Material failure is typically highly non-linear [8].Thus the build-up to possible eruption might take years or months without ever being certain that the eruption will take place.Close to the threshold conditions for failure the system can accelerate and observations con¢rming that an eruption is inevitable may only be manifest a matter of days or hours before.
Multiple steady-state solutions are a signi¢cant feature of conduit £ow models [2,60,61].Thus, even if every controlling parameter were known exactly, behaviour would not be predictable without a very complete knowledge of the system's history.There are large uncertainties in the values of controlling parameters, and likewise the precise history will not be known.Thus in certain respects volcanoes are inherently unpredictable.As in other dynamical systems, very slight changes in initial conditions or slight changes in controlling parameters might have completely di¡erent longterm outcomes.
In forecasting volcanic hazards and assessing risks one needs to estimate the probability that a hazardous event will happen, the probability that the event will a¡ect a particular place and the probability that the e¡ects will include fatalities and property damage.Forecasting of volcanic hazards requires knowledge both of the dynamical phenomena and of uncertainties.For example, the assessment of tephra fall hazards is now quite advanced.Models have been developed to estimate the dispersal of tephra and to evaluate critical hazard parameters, such as threshold values of mass loading to cause roof collapse [62,63].Results are expressed in probabilistic terms.Quantitative approaches are being developed for lava [64], lahars [65] and pyroclastic £ows [66,67].

Discussion
This review of eruption forecasting indicates reasons for optimism.Magma ascent causes crustal deformations and disturbances that can be detected easily.The build-up to eruptions typically occurs over periods of days to years so that sci-entists can usually issue long-term warnings.However, there are still major problems in assessing whether detected subterranean magma movements will actually lead to eruption.The ¢nal system failure that just precedes the onset of an eruption typically can only be recognised over rather short time scales of days to only minutes.Theories, such as those based on materials failure or the changing seismic properties of pressurising bubbly magma, are promising from retrospective analysis, and have the potential to interpret geophysical data in real-time leading to quite accurate forecasts.However, con¢dent forecasts may only be possible shortly before an event, giving little time for civil responses and evacuation.The value of forecasts will be negated if there are not very e¡ective communication systems for rapid response by the authorities and if the community is not well-prepared [3].Erroneous forecasts can also lose scientists credibility.
Once an eruption starts, then the principles behind the causative magmatic £ows and their relationship to geophysical phenomena are beginning to be discerned.The new generation of models, together with investigations of the physical properties of magmas, indicate that volcanic systems are highly non-linear and in certain respects may be inherently unpredictable.Such models can simulate complex patterns of eruptive £uctuations and transitions and thus provide a conceptual framework for forecasting.
What is likely to happen over the next decade or so is development of ensemble models, which make volcanic forecasts that take account of both uncertainties and non-linear dynamics [1].Considerable e¡ort will be placed on reducing uncertainties, such as in material properties of magmas, and improving monitoring techniques, but overall uncertainties will remain.Integrated models of volcanic processes will be aimed at simulating the geophysical signals, eruptive behaviours and hazardous phenomena.These models can be evaluated with comprehensive integrated datasets.Data assimilation methods and Bayesian updates will be used to improve forecasting models.As in weather forecasting, ever increasing computer power will allow ensemble runs to build up probabilistic forecasts as well as testing model sensitiv-ities.Inevitably there will be more eruptions to document and learn from.Such studies are likely to become inputs to inform systematic procedures for evaluating possible outcomes for volcanic activity, such as expert elicitation, construction of event trees and running risk assessment models for the ultimate purpose of issuing warnings and giving clear scienti¢c advice [1,68,69].

Fig. 4 .
Fig. 4. Gliding spectral lines prior to a Vulcanian explosion on Montserrat at station MBRY on 7 January 1999 (details in [6]).The upper diagram shows the seismic signal of the explosion.

Fig. 5 .
Fig.5.Ground surface deformation before and during the 1997 eruption of Okmok Volcano, Alaska, detected by satellite radar interferometry (after[17]).Interferograms constructed from ERS-1/ERS-2 InSAR images indicated surface in£ation of more than 18 cm between 1992 and 1995 (a,b) prior to an eruption in February^April 1997, and surface subsidence of more than 140 cm during the eruption (c).

Fig. 6 .
Fig.6.Five days of strain data from borehole instruments located in Iceland, recording the January 1991 eruption of Mount Hekla, Iceland, after Linde et al.[25].The curves are the continuous data with four of the stations showing expansion and the closest station to the volcano (BUR) showing contraction.The solid circles show a model in which magma ascends in a dyke from a magma chamber at 6.5 km depth and the chamber de£ates over 2 days.The minimum in strain at BUR coincides with the approximate time of surface break-out.

Fig. 8 .
Fig.8.A general schematic diagram of steady-state £ow rate up a conduit against magma chamber pressure to illustrate the abrupt changes in £ow regime that can occur.The two stable branches (A^B and C^D) relate, in the models of Melnik and Sparks[2] and Barmin et al.[52], to the kinetics of crystallisation (see text).The arrows indicate the variations of £ow rate with chamber pressure.The dashed lines represent the unsteady transitions in the system.

Fig. 9 .
Fig. 9. Discharge rate versus time for (a) growth of Mount St Helens, USA (1980^1986) and (b) Santiaguito Volcano, Guatemala (1922^2000).Dashed curves are the observed £uctuations in discharge rate and solid lines are the best-¢t model simulations (details in [52]).