Volcano

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ANNALS OF GEOPHYSICS, VOL. 48, N. 4/5, August/October 2005

Key words numerical modeling – explosive vol-canic eruptions – conduit flow – multiphase flowsimulation – stratospheric sulfate aerosol

1. Introduction and review of basic concepts

Explosive eruptions are among the mostfascinating and complex natural phenomena.At their initiation stage, gas-rich viscous mag-ma experiences a pressure drop (a little as inthe uncorking of a champagne bottle but wherethe liquid would be 104 to 1012 times more vis-cous, and over-pressure is tens of bars). Theexsolution of dissolved gases (mostly waterand CO2), their thousand-fold expansion andacceleration toward the surface occur in suc-cession.

Numerical simulation of explosivevolcanic eruptions from the conduit flow

to global atmospheric scales

Christiane Textor (1) (2), Hans-F. Graf (2) (*), Antonella Longo (3) (4), Augusto Neri (3), Tomaso Esposti Ongaro (3), Paolo Papale (3), Claudia Timmreck (2) and Gerald G.J. Ernst (5) (**)

(1) Laboratoire des Sciences du Climat et de l’Environnement, CEA-CNRS, Gif-sur-Yvette, France(2) Max-Planck-Institut für Meteorologie, Hamburg, Germany

(3) Istituto Nazionale di Geofisica e Vulcanologia, Sede di Pisa, Italy(4) Dipartimento di Scienze della Terra, Università degli Studi di Pisa, Italy

(5) Centre for Environmental and Geophysical Flows, Department of Earth Sciences, University of Bristol, U.K.

AbstractVolcanic eruptions are unsteady multiphase phenomena, which encompass many inter-related processes across thewhole range of scales from molecular and microscopic to macroscopic, synoptic and global. We provide anoverview of recent advances in numerical modelling of volcanic effects, from conduit and eruption column process-es to those on the Earth’s climate. Conduit flow models examine ascent dynamics and multiphase processes likefragmentation, chemical reactions and mass transfer below the Earth surface. Other models simulate atmosphericdispersal of the erupted gas-particle mixture, focusing on rapid processes occurring in the jet, the lower convectiveregions, and pyroclastic density currents. The ascending eruption column and intrusive gravity current generatedby it, as well as sedimentation and ash dispersal from those flows in the immediate environment of the volcano areexamined with modular and generic models. These apply simplifications to the equations describing the system de-pending on the specific focus of scrutiny. The atmospheric dispersion of volcanic clouds is simulated by ash track-ing models. These are inadequate for the first hours of spreading in many cases but focus on long-range predictionof ash location to prevent hazardous aircraft – ash encounters. The climate impact is investigated with global mod-els. All processes and effects of explosive eruptions cannot be simulated by a single model, due to the complexityand hugely contrasting spatial and temporal scales involved. There is now the opportunity to establish a closer in-tegration between different models and to develop the first comprehensive description of explosive eruptions andof their effects on the ground, in the atmosphere, and on the global climate.

Mailing address: Dr. Christiane Textor, Laboratoire desSciences du Climat et de l’Environnement, CEA-CNRSL’Orme des Merisiers, F-91191 Gif-sur-Yvette Cedex, France;e-mail: [email protected]

(*) Now at: Centre for Atmospheric Science, DepartmentGeography, University of Cambridge, Downing Place, Cam-bridge CB2 3EN, U.K.

(**) Now at: Mercator and Ortelius Research Centre forEruption Dynamics, Department of Geology and Soil Science,University of Ghent, Krijgslaan 281, S8, 9000 Gent, Belgium.

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Christiane Textor et al.

During an explosive eruption, an over-pres-sured magmatic foam is generated and frag-ments in the conduit (e.g., Carroll and Hol-loway, 1994; Gilbert and Sparks, 1998). The re-sulting fragmented medium accelerates upwardgenerating a multiphase, over-pressured and up-ward-directed, negatively buoyant, momentum-dominated jet. Multiphase flows exiting con-duits are modelled to be 5-300 times denser thansurrounding air. Decompression to atmosphericpressure, vigorous entrainment, rapid heat ex-change from pyroclasts (about 90% and 60% ofthem are typically less than 1 mm and 60 µm insize respectively) to the entrained air (ontimescale of 1-100 s) and further expansion andlowering of bulk density happen next. This cangenerate a buoyant eruption column rising up to10-50 km, from which ash falls out. Columnsthat remain negatively buoyant when the initialsource momentum has been exhausted producecollapsing fountains and pyroclastic density cur-rents, which may also source giant volcanicclouds (e.g., Sparks et al., 1997; Gilbert andSparks, 1998; Dartevelle et al., 2002).

An eruption column can ascend until the ki-netic and thermal energy, plus the latent heat en-ergy release from water vapour condensation,equal the work to be done against the increase inpotential energy at a certain height in the atmos-phere. Ultimately, the column reaches its heightof neutral buoyancy, where its bulk density con-verges to that of air. At this level, either a radialor a parabolically-shaped current is generated(Carey and Sparks, 1986; Bursik et al., 1992a;Ernst et al., 1994; Rose et al., 2001). Most of theash responsible for widespread dispersal and haz-ards is released from the eruption column and ad-vected within gravity currents flows (e.g., Bursiket al., 1992a,b; Sparks et al., 1992; Ernst et al.,1996; Bonadonna et al., 1998). Large particles(>>1 cm) are ejected along ballistic trajectories,which are decoupled from the fluid motion of theeruption column. Ballistic particles are not dis-cussed here (and typically are not specificallyconsidered by the models) because they con-tribute only a minor fraction to the total volcanicsolid mass. Unlike small-sized ash, which is sus-pended by flow turbulence and moves with thefluid, ballistic particles are volumetrically veryminor in the sort of intense explosive eruptions

considered here (see Riedel et al., 2003, for morediscussions about ballistic ejection and model-ling). The current of volcanic material injectedinto the stratosphere initially flows laterally undergravity while its leading edge is advected at thelocal wind speed. The current is then sheared bygradients in both wind direction and speed, dif-fused by atmospheric turbulence, may be trans-ported and stretched around or in betweenmesoscale eddies, and is finally dispersed zonal-ly and meridionally by the global circulationwithin some weeks and months, respectively (seeSparks et al., 1997; Gilbert and Sparks, 1998, forfurther reviews of physical concepts).

Eruptions can produce hazardously high lo-cal atmospheric concentrations of volcanic ash,acidic gases and secondary particles (e.g., Baxteret al., 1999; Horwell et al., 2003a,b). Ash can bewidely dispersed and have detrimental effects onpeople, their activities and the environment (e.g.,Lipman and Mullineaux, 1981; Newhall andPunongbayan, 1996; Druitt and Kokelaar, 2002).The dispersal of the volcanic products, includingsilicate solid particles, gases (H2O, CO2, SO2,H2S, HCl, and others) and aerosols condensingfrom gases in the volcanic clouds can impact up-on the environment and human activities. Ash ishazardous as it falls on the ground (e.g., roof col-lapse hazard) where it accounts for 5% of directcasualties and for much of the widespread dam-age from explosive eruptions. Ash is also a haz-ard in the air where it disrupts international airtraffic and airport operations, resulting in sub-stantial loss of revenues for air companies. Since1980, there have been well over 100 reported en-counters between volcanic clouds and jet air-planes (including very close calls in about 5-10% of cases). Even minute amounts of volcanicash far from its source and some days after emis-sions can substantially damage jet engines (e.g.,Casadevall, 1994; Grindle and Burcham, 2002,2003). That these encounters could not beenavoided indicates a need for more accurate, near-real-time, ash dispersal forecasts that can becommunicated more rapidly and effectively(ICAO, 2000). In addition, volcanic activityleads to manifold effects on atmospheric chem-istry and climate.

Ash settles within hours to weeks and thusdoes not directly affect global climate. Gases re-

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Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales

main much longer aloft and can be dispersedwidely and recurrently in the free troposphere(especially in between eruptions) and in thestratosphere (during less frequent but muchlarger explosive events). There, sulphur-con-taining gases (mainly SO2, and H2S), of specialrelevance to the atmosphere-climate effects, areoxidatively converted to sulphuric acid, whichcondenses to form sulphate aerosols on a char-acteristic timescale of about one to two monthsin the stratosphere (e.g., Bluth et al., 1993; Readet al., 1993). Stratospheric aerosol residencetimes are longer, accounting for effects lastingup to a several years before return to back-ground conditions (e.g., WMO, 2003).

Sulphate aerosols alter the Earth’s radiationbalance (e.g., Stenchikov et al., 1998): they ab-sorb and emit in the near-IR and longwave, caus-ing in situ local heating in the stratosphere and in-creasing the downward radiative flux, thus result-ing in surface warming. Aerosols also backscatterpart of the incoming solar radiation leading tosurface cooling. The net result is a surface cool-ing counteracting greenhouse warming for thefew years before aerosol loadings return to back-ground levels. The presence of volcanic aerosolin the stratosphere alters the chemistry and dy-namics of the stratosphere (e.g., Pitari, 1993;Pitari and Rizzi, 1993). For large equatorial ex-plosive eruptions, there is a dynamic feedback ontropospheric circulation from forcing upon differ-ential stratospheric heating, leading to abnormal-ly warm winters over the Northern Hemispherecontinents in the years following the eruption(Groisman, 1992; Robock and Mao, 1992).

Stratospheric volcanic aerosols can be trans-ported vertically across the tropopause (e.g.,Ansmann et al., 1996, 1997) and increase theamount and persistence of high-level clouds(Sassen, 1992; Sassen et al., 1995; Lohmann et al., 2003). There is strong evidence thatchanges in the radiative properties of cirrusclouds can last several years after large explo-sive eruptions (Minnis et al., 1993).

Stratospheric sulphate aerosols can alsoserve as sites for heterogeneous reactions, suchas those on polar stratospheric clouds, whichdeplete ozone in the presence of halogens likechlorine or bromine (e.g., Michelangeli et al.,1989; Hofmann and Solomon, 1989; Granier

and Brasseur, 1992; Solomon et al., 1996).Ozone depletion could be enhanced through di-rect stratospheric injection of volcanic halogens(Prather, 1992), although there is still much de-bate about how much of these gases actuallyreach the stratosphere (Tabazadeh and Turco,1993; Textor et al., 2003b,c).

The atmospheric effects of eruptions dependon magma composition (including volatile con-tent and nature), eruption style, and ambientconditions in both the lithosphere and atmos-phere. Specific volcanoes are capable of con-trasting styles of activity depending upon thestage of maturation reached in the magmachamber and conduit system and upon the phys-ical state of the volcanic edifice. Volcanic emis-sions undergo modification processes in theconduit and crater (especially in the case offlooded vents or of magmas coming into pro-longed contact with aquifers), in the eruptioncolumn and during long-range atmospherictransport. There is also a growing understandingthat volcanic clouds have a lot more in commonwith meteorological clouds than previously real-ized (e.g., Rose et al., 1995; Herzog et al., 1998;Durant and Ernst, 2003; Lacasse et al., 2003;Textor et al., 2005a,b). Prior to 1997-1998, me-teorological aspects (with the exception of a con-sideration of the latent heat effects on cloud rise;e.g., Woods, 1993; Glaze and Baloga, 1996) hadbeen left out of eruption cloud models. Smallscale processes within the eruption column havea large – albeit indirect – effect upon the atmos-phere and climate. Ash interacts with hydrome-teors and forms mixed phase aggregates duringascent and recirculation within the eruption col-umn (e.g., Veitch and Woods, 2001; Textor et al.,2005a,b). Gases condense and freeze on ash, hydrometeors and the aggregates (Tabazadeh and Turco, 1993; Textor et al., 2003b,c). Theseprocesses affect residence times, removal ratesand the stratospheric injection of gases (i.e., theinitial volcanic forcing upon climate). For a re-cent review on atmospheric effects of volcaniceruptions see Textor et al. (2003a).

Direct observations of conduit processeshave not been feasible so far, and key eruptiveparameters have not been measured in situ. Whatwe know about the explosive eruption processesoccurring below the Earth’s surface comes from

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analyses of eruptive products (Marti et al., 1999;Polacci et al., 2001; Klug et al., 2002), and ofgeophysical signals (Vergniolle and Brandeis,1994; Ripepe et al., 2001; Chouet, 2003), fromlaboratory experiments (for references seeGilbert and Sparks, 1998), and from numericalsimulations of magma ascent (e.g., Melnik andSparks, 2002). Liquid and multiphase magmarheology can be estimated in the laboratory for arelevant range of composition, temperature, dis-solved volatile contents and strain rates (Ding-well, 1998). This provides a basis for under-standing the rheological behaviour of viscoelas-tic magma, and the constitutive equations for usein numerical simulations of magma flow (Man-ga et al., 1998; Saar et al., 2001; Llewellin et al.,2002a,b). Fragmentation experiments are nowroutinely carried out in apparata, where a magmaparcel is pressurized at high temperature andthen suddenly depressurised and fragmented.The accelerated particles are collected and theirtextures compared with those of volcanic parti-cles (Martel et al., 2000, 2001; Spieler et al.,2003). Experiments on gas bubble nucleationand growth in liquids undergoing variable ratesof pressure decrease document that non-equilib-rium effects control the distribution of volatilecomponents in the liquid and gas phases (Navonand Lyakhovsky, 1998).

Similarly, direct measurements of volcanicemissions in the atmosphere are quite rare. How-ever, they can be studied remotely by ground-based, airborne and satellite instruments. Lidarsconstrain aerosol vertical distributions, but untilrecently they could only operate during the nightunder clear sky conditions. Observations ofemissions (mostly SO2) during small eruptiveevents and of quasi-permanent emissions arepossible with ground-based or airborne remoteinstruments like COSPEC, FTIR (e.g., Oppen-heimer et al., 2002) and DOAS (e.g., Bobrowskiet al., 2003) instruments. Direct sampling is ac-complished by balloon and research aircrafts,flown through the clouds. There are, however,only sporadic measurements, with no globalcoverage. Recent developments in satellite re-mote sensing have expanded the capability tomonitor volcanoes from space (e.g., Rose et al.,1995, 2000, 2001, 2003; and Lacasse et al.,2003), but satellite data for SO2 and ash are cur-

rently only useful for strong sources (e.g., Bluthet al., 1992). Eleven instruments have been de-ployed on satellites in the past 30 years. Most arelimited time research instruments without opera-tional capacity, SO2 is the only volcanic gas sofar monitored operationally by satellite.

Since the 1970s, there have been crucial ad-vances in understanding the basic physics ofexplosive eruptions, and their effects upon theatmosphere and climate. These are summarizedby Sparks et al. (1997) and Gilbert and Sparks(1998), and by McCormick et al. (1995) andRobock (2000), respectively. Since the 1990s,there have also been developments, not yet re-viewed, in numerical modelling. Numerical ad-vances can now be harvested to assess the time-dependent dynamics and microphysics of erup-tion clouds and of their impacts.

Here we provide an overview of these recentadvances. Section 2 describes conduit flow mod-elling. Section 3 focuses on numerical simula-tion of dispersal processes on the mesoscale-gamma (2-20 km – some tens of minutes), con-centrating on rapid processes in the jet, lowerconvective regions, and pyroclastic density cur-rents. The terms ‘mesoscale alpha, beta, gam-ma’, ‘regional’, and ‘global’ originate from theterminology of meteorology. The respective spa-tial and temporal scales are given in the text.Section 4 concentrates on the mesoscale-beta(20-200 km – some hundreds of minutes) con-cerning the eruption column. The far-field ashdispersion on the mesoscale-alpha (200-2000km – some tens of hours) and the regional scaleis illustrated in Section 5. Climate effects oferuptions on the global scale are discussed inSection 6. There is much yet to explore about thephysics of source eruption processes, the meteor-ology and climate effects of volcanic clouds.Multi-scale numerical modelling, and experi-mentation, together with remote sensing and insitu measurements will play a key role in ad-vancing understanding of these processes.

2. Conduit flow modelling

Volcanic conduits connect the deep regionsof magma accumulation inside the crust withthe Earth’s surface. Transit times for magmas

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ascending in conduits and leading to sustainedexplosive eruptions are typically of the order ofminutes, up to 10-20 min. Here the physicaland chemical processes are so effective thatthey produce order of magnitude changes inflow variables, and deeply modify the continu-um properties of magma through magma frag-mentation and production of gas-particle mix-tures.

The modelling of magma ascent dynamicsis currently well developed. Typical assump-tions include steady, one-dimensional, isother-mal, multiphase non-equilibrium flow. This ac-counts for a relatively large number of factorscharacterizing real magmas, like their chemicalcomposition (10 major oxides plus 2 majorvolatile components H2O and CO2) and solidcontent (crystals and eroded rock fragments)

(Papale et al., 1998; Papale and Polacci, 1999),to predict the occurrence of fragmentation un-der dynamic constraints (Papale, 1999a; Mel-nik, 2000), and to take into account variableamounts of different pyroclast componentsoriginated by the fragmentation process (Pa-pale, 2001). Non-isothermal flow of one-phase(homogeneous) magma has been considered byBuresti and Casarosa (1989) and Mastin andGhiorso (2000). Transient magma flow is con-sidered by Turcotte et al. (1990), Ramos(1995), and Melnik (2000). Proussevitch andSahagian (1998) modelled transient conduitflow to investigate the role and dynamics ofnon-equilibrium nucleation and growth of gasbubbles in silicic magma. A review of pre-1998work on conduit flow modeling can be found inPapale (1998).

Fig. 1. Mass flow-rate as a function of amount and composition of volatiles (H2O and CO2) in magma, com-puted through the model in Papale (2001). The bold lines correspond to cases with equal total volatile contentof 5, 7, and 9 wt%, and variable CO2/H2O ratios. Eruptive conditions correspond to rhyolitic magma (composi-tion in Papale and Polacci, 1999) at 1100 K, no crystals in magma, conduit length 7 km, pressure at the cham-ber top 175 MPa, vertical conduit with circular cross-section 100 m in diameter, unvesicular ash 200 µm in di-ameter formed at fragmentation.

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The use of sets of constitutive equations de-scribing phase properties and interphase as wellas phase-wall mechanical interactions has al-lowed investigation of the relationships be-tween ascent dynamics and the multiphase,multicomponent nature of real magmas. Theseinteractions are strongly non-linear, implyingthat generalization of numerical results shouldbe avoided. The relatively large number of nu-merical simulations made to date allows somepreliminary conclusions to be drawn. One ofthem concerns the roles of volatiles in the dy-namics of magma ascent. Magmatic volatilesrepresent the engine of explosive eruptions,since volatile exsolution leads to over-pressurein magma chambers and cracking of chamberwalls, thus initiating magma ascent (Tait et al.,1989). It is the combined effect of further exso-lution and gas expansion upon depressurisationthat leads to magma acceleration, and ultimate-ly to fragmentation and explosive eruption.

Numerical simulations show that differentvolatiles can have opposing effects on ascentand eruption dynamics. Water is the mainvolatile component of magmatic gases. Dis-solved water reduces magma viscosity, and af-fects ascent dynamics by increasing the erup-tion mass flow-rate (Wilson et al., 1980; Papaleet al., 1998; Dingwell, 1998). CO2, the secondmain volatile component in magmas, reducesmass flow-rate, at least up to CO2 mass frac-tions of 50 wt% of the total volatile content (Pa-pale and Polacci, 1999), see fig. 1. These differ-ent roles are related to the different solubilitiesof H2O and CO2 in the magma under conduitconditions. CO2 is poorly soluble; thus, its pres-ence causes gas exsolution at much higher pres-sure than if H2O was the only volatile species(Holloway and Blank, 1994; Papale, 1999b).Once a separate gas phase has developed, it car-ries a fraction of all the volatile components,and thus reduces the amount of H2O dissolvedin magma. Increasing carbon dioxide can thusboth result in more gas available for expansionand acceleration, thus favouring magma flow,as well as in more viscous magma, thus hinder-ing magma flow. Numerical simulations sug-gest that the latter effect is the dominant one.Hence, knowledge of the true magmaticvolatile abundances is needed to simulate erup-

tions. Recent modelling of the compositional-dependent saturation surface of multicompo-nent volatiles in magmas allowed sulphurspecies to be treated together with water andcarbon dioxide (Moretti et al., 2003). New in-sights will be gained from the simulation ofmagma ascent by including multicomponentvolatile saturation.

Melnik (2000) considered the homogeneous(one-phase) flow of bubbly magma below frag-mentation, and the two-phase (separated) flowof gas and particles above fragmentation. Themain difference from previous conduit flowmodels is in the calculated pressure differencebetween gas and liquid phases. This pressuredifference originates from the finite time re-quired for gas bubbles to equilibrate to ambientpressure, and from the high magma viscosity,which acts to increase the equilibration time.Gas-liquid pressure difference over an assignedthreshold is also used as the magma fragmenta-tion criterion. The coupling between viscosity,acceleration, and fragmentation leads to a dy-namic fragmentation criterion, mathematicallysimilar to that in Papale (1999a), where frag-mentation relates to the transition from a vis-cous to an elastic rheological response of thestressed magma. Thus, fragmentation occurswhen the product of viscosity and strain rate ex-ceeds a critical threshold. The threshold thatmust be exceeded is different in the two mod-els, being dictated by the elastic properties ofmagma in the viscous to elastic transition mod-el (Dingwell and Webb, 1989; Papale, 1999a),and by the kinetics of gas bubble expansion inthe bubble over-pressure model (Melnik, 2000).In the latter case, the threshold is a function ofbubble over-pressure and thus also of magmaexpansion and acceleration. In turn, the gasdensity and volume fraction are not directly re-lated to pressure as in Papale (1999a), but alsodepend on the depressurisation rate along theconduit. The result is that multiple regimes ofcontrasting eruption intensity (or mass flow-rate) are possible for one starting set of eruptiveconditions (or input data in the simulations).The appearance of such multiple steady-statesolutions requires a pressure drop at the base ofthe conduit (or at the top of the underlying mag-ma chamber) significantly below the volatile

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saturation pressure, and may explain abrupttransitions in eruptive intensity, sometimes in-ferred from eruption products.

The above studies consider the entire con-duit length from the top of a hypothetical mag-ma chamber up to the base of a volcanic crater,above which one-dimensional flow can nolonger be assumed. Other investigations for re-searcher focused on specific aspects of magmaflow, without solving the entire flow from thedeep homogeneous flow regions below gas ex-solution to the shallow gas-pyroclast regionsabove fragmentation up to the conduit exit.Massol and Jaupart (1999) analysed the cross-sectional pre-fragmentation pressure variationsin conduits. They documented a decrease in gaspressure from the conduit axis to the walls, im-plying contrasting depressurisation and de-gassing histories of distinct magma parcelserupted simultaneously. Costa and Macedonio(2003) analysed the shear-induced viscous dis-sipation close to the conduit walls, and foundthat a large temperature increase is expecteddue to the high viscosities and velocities ofmagma discharged during explosive eruptions.Their predicted velocity profiles develop a cen-tral plug (despite the assumed Newtonian mag-ma rheology) and a region of concentratedshear near the conduit walls. These findings ac-count for the contrasting textures of pumicefrom some explosive eruptions (Polacci et al.,2001).

Future magma ascent modelling advancesmay benefit from formulation and solution of atransient, multidimensional, multiphase flowmodel including the full set of mass, momen-tum, and energy transport equations, as well asconstitutive equations approaching the behav-iour of real multiphase multicomponent mag-mas. Such a model would allow all of the abovecomplex processes to be accounted for in com-prehensive numerical simulations of magma as-cent dynamics, and in principle it could be em-ployed to describe the dynamics of the entiresystem from magma chamber to the surface.Coupling with the mechanics of surroundingrocks would allow to take into account both theopening and closing phases of volcanic erup-tions, as well as both time-dependent shapevariations of magma chamber and conduit

walls, and the occurrence of caldera collapse.Such a comprehensive model will be the chal-lenge for the researchers focused on subsurfacevolcanic processes in the next decades.

3. Numerical simulation of atmosphericdispersal processes by using multiphaseflow models on the mesoscale-gamma (2-20 km – some tens of minutes)

In the last 20 years significant progress inunderstanding of pyroclastic dispersal process-es was obtained through development of multi-dimensional, transient and multiphase flowmodels. These are able to treat the eruptivemixture as a non-homogeneous fluid (Wohletzet al., 1984; Valentine and Wohletz, 1989; Do-bran et al., 1993; Neri and Macedonio, 1996;Neri et al., 2003). Such an approach is based onthe extension of fundamental transport continu-um mechanics equations to a multiphase andmulticomponent mixture. According to themultiphase flow theory, the volume occupiedby a generic gaseous, solid, or liquid phase can-not be occupied at the same position in time andspace by the remaining phases. It is from sucha distinction that it is possible to introduce thephase volume fraction as a new dependent vari-able. A multifield approach is defined, accord-ing to which different phases are treated as in-terpenetrating continua. The high particle massfraction under typical eruptive conditions justi-fies the continuum assumption for pyroclastssmaller than about one centimeter (larger parti-cles need to be treated with a Lagrangian ap-proach). The fundamental mass, momentumand energy conservation equations are nowsolved for each specific phase. This systemneeds to be closed by constitutive equations ex-pressing the viscous and interphase transportterms as well as the equation of state of the in-volved phases. The reader is referred to Soo(1967) and Gidaspow (1994) for a complete de-scription of these equations. The system of par-tial differential equations can be solved numer-ically, using finite difference or finite elementmethods, on computational domains extendingsome tens of kilometres in radial and verticaldirections and so far for times of several min-

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utes. The simulation outcome typically consistsin the temporal and spatial evolution of severalvariables – such as concentration, flow field,temperature – for each phase considered.

The application of this type of models al-lowed description of new and somehow non-in-tuitive, physical processes occurring during ex-plosive eruptions. Due to the specific character-istics of these models, and their large demandfor computing power, they have been mostlyapplied to the analysis of relatively rapid, local-ized, and non-equilibrium processes, such asthose occurring in the jet, lower convective re-gions and pyroclastic density currents, hereinalso named pyroclastic flows sensu lato, gener-ated by gravitational collapse. Processes inves-tigated include the blast dynamics fromcaldera-forming eruptions (Wohletz et al.,1984), transient motion of ascending eruptioncolumns (Valentine and Wohletz, 1989), inter-action between pyroclastic flows and calderarims (Valentine et al., 1992), the formation ofco-ignimbrite clouds (Dobran et al., 1993),propagation of pyroclastic flows as transientwaves (Neri and Dobran, 1994), unstable be-haviour at the transition between fully convec-tive and fully collapsing regimes (Neri et al.,2002a; Di Muro et al., 2004), and multiparticledynamics of collapsing volcanic column andpyroclastic flows (Neri et al., 2003).

The models were also used to reconstructthe eruptive dynamics of historic and on-goingeruptions. Simulations have been compared todirect or indirect observations whenever avail-able. In more detail, the conduit ascent modeldescribed in the previous section (Papale et al.,1998) was used to determine vent boundaryconditions for the multiphase flow model (Neriet al., 1998). The linking of two models permit-ted the reconstruction of the dynamics for the79 A.D. eruption of Vesuvius. The influence ofmagmatic properties on the eruptive style oftwo main phases of the eruption (white andgrey pumices) was elucidated (Neri et al.2002b). Similarly, the multiparticle flow modelof Neri et al. (2003) was used to simulate thedynamics of transient short-lived Vulcanian ex-plosions observed at the Soufrière Hills Vol-cano, Montserrat, West Indies, during August-October 1997 (Clarke et al., 2002). A simplified

description of pre-explosive conduit conditionsbased on observations provided the initial con-ditions for transient, axi-symmetric, multi-phase flow simulations of pyroclastic disper-sion. The relationships between the dynamicsand the conduit parameters, including volatilecontent, overpressure, and particle size distri-bution were examined. Model results illustratedthat i) observations of explosions were best re-produced using initial conditions that bestmatched observationally-constrained input da-ta; ii) vent conditions were highly transient,therefore, models assuming steady vent condi-tions can not be applied to Vulcanian explo-sions; iii) decreasing conduit pressure and in-creasing magmatic water content have similareffects in that they generally increase plumebuoyancy, pyroclastic current runout, DenseRock Equivalent (DRE) ejected and develop-ment of ash plumes above pyroclastic currents.

Some of the multiphase flow models wereapplied to assess pyroclastic flow hazards inhigh-risk regions, e.g. in the Vesuvian Area,Italy (Dobran et al., 1994; Esposti Ongaro et al.,2002; Todesco et al., 2002). Input data were de-fined based on knowledge of the magmatic sys-tem, its eruptive record, as well as using mag-ma ascent modelling. Figure 2 shows the timewise distribution of the total particle volumetricfraction and gas flow field along the southernflank for a typical sub-Plinian eruption of Vesu-vius at three different times after onset of col-lapse. The three plots illustrate the transient na-ture of the over-pressured jet and rapid propa-gation of the flow fed by the pulsating fountain.In this specific case, the flow reaches theTyrrhenian Sea 7 km away from the crater inabout 6 min. Hot, dilute, fine ash-laden plumesrise above the vent and flows. Important flowvariables are quantified, e.g., pyroclastic flowdensity, temperature, dynamic pressure, etc.,that are all crucial in the assessment of the en-vironmental impact.

In all these applications model results ap-peared to be qualitatively, and in some circum-stances quantitatively consistent with observa-tions and, in most cases, able to provide quanti-tative insights into eruption dynamics that can-not readily be obtained by other means. How-ever, there is still much progress to be made.

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Fig. 2. Distribution of total particle volumetric fraction and gas flow velocity at 90, 300 and 600 s from the be-ginning of the collapse for a pyroclastic-flow-generating volcanic column at Vesuvius. The simulation scale is rep-resentative of a sub-Plinian type eruption at Vesuvius similar to the 1631 eruption. The topographic profile as-sumed in the simulation is representative of the southern sector of Vesuvius. Contour levels refer to the exponentsto the base 10 of particle concentration and correspond to value of −8, −7, −6, −5, −4, −3, −2, and −1 (modifiedfrom Todesco et al., 2002).

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Firstly, the peculiar nature of volcanic process-es requires the formulation of more physically-sound models. For example, the influence ofdispersed particles on the turbulence of the car-rier phase (turbulence modulation), and parti-cle-particle interactions in the poly-dispersedmixtures need to be more accurately described.Secondly, experimental research – both in thelaboratory and in the field – is necessary to im-prove the equations of physical, thermal, andrheological properties, and to better validate thetheoretical models. Thirdly, the development ofmore effective numerical techniques, includingthe use of parallel computing, are necessary toallow the simulation of more realistic events inthree dimensions and for longer simulationtimes. Finally, the simulation of the dynamicsof larger particles such as lapilli or clasts re-mains a challenge, because the continuum as-sumption is no longer applicable (see for in-stance Wilson, 1972; Fagent and Wilson, 1993;Lo Savio, 2004).

4. Simulation of the eruption column and the distal environment on the mesoscale-beta (20-200 km – somehundreds of minutes)

Numerical simulations of atmosphericprocesses on the mesoscale-beta require de-scription of the conditions both within the erup-tion column and in its local environment. Thehigh velocities, temperatures, particle concen-trations, and large gradients in an eruption col-umn complicate the solution of the equation al-gorithm that describes the eruption dynamicsand thermodynamics. Conditions in the dispers-ing plume and background atmosphere are lessvigorous, and do not necessitate such a com-plex algorithm. The comprehensive models de-scribed in the previous section are currentlymuch too demanding in terms of computer timeand memory to simulate eruption column andadvected cloud dispersal on longer time scalesor to consider a higher number of columnprocesses, e.g., microphysics or chemistry. Var-ious numerical models exist for simulation oflarger scale atmospheric flows on the meso-scale-alpha. These are used for simulation of

phenomena like air pollution dispersion, atmos-pheric boundary layer or cloud processes, andalso for far-field ash dispersal modelling, asdiscussed in the next section. Yet many of thesimplifying assumptions applied in atmospher-ic models are not valid for the high-energyprocesses close to the vent and in the rising col-umn. Thus models were developed specificallyfor the simulation of the eruption column andsubsequent dispersal, based on novel conceptsreviewed hereafter.

The first studies of the fluid dynamics ofbuoyant plumes built upon the seminal work ofMorton et al. (1956). They derived a simple for-mula for the first-order estimation of plumeheight based on the relation between the eruptedbuoyancy flux, which is associated with the tem-perature and the mass, and the atmospheric strat-ification. The Morton formula, neglecting the in-creased stability of the stratosphere, shows afairly good agreement with observations for thelimit case of powerful plumes in comparativelynegligible wind (see Sparks et al., 1997). Theanalytical studies of Wilson (1976), Sparks andWilson (1982), and others provided insights intothe structure of eruption columns. Time-aver-aged, Gaussian profiles are assumed at eachheight for quantities like temperature, velocity,and particle concentration. Interactions betweencomponents of the fluid are neglected; the gas-particle mixture is treated as a homogenous mix-ture, similar to fine-grained, diluted columns.Based on these assumptions, one-dimensional,steady-state models were developed (Wilsonand Walker, 1987; Woods, 1988, 1993), whichsolve the equations of conservation for mass,momentum, and heat, accounting for separatecomponents (e.g., dry air, water vapour, liquidcondensates, and solid particles) within the ho-mogenous fluid approximation. Turbulent mix-ing (i.e. entrainment) into the eruption column isdetermined by an entrainment parameter, whichrelates entrainment to the upward velocity in thecolumn. Such models are suitable for steadystate eruptions, e.g., so-called dry plinian erup-tions with a low occurrence of liquid water(Sparks et al., 1997). They have been useful forfirst estimations of plume dynamics, like verticaldensity and velocity profiles, and for under-standing transition between collapsing and non-

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collapsing flows. For comprehensive overviewssee Sparks et al. (1997), or Woods (1998). Mod-els of this type have been employed for a varietyof applications, like the assessment of the influ-ence of the ambient conditions on the plumeheight (Glaze and Baloga, 1996), or for the in-vestigation of extraterrestrial volcanic eruptions(Glaze and Baloga, 2002). In spite of its quitecoarse assumptions, this model type has beenemployed for important first estimations aboutthe injections of water vapour (Glaze et al.,1997) and volcanic gases (Tabazadeh and Turco,1993) into the stratosphere. It has recently beenused for the investigation of particle recyclingand aggregation in volcanic plumes (Veitch andWoods, 2000, 2001, 2002). The limitations ofutilizing a one-dimensional, steady state modelfor these kinds of questions were discussed indetail by Textor and Ernst (2004) and by Veitchand Woods (2004).

The dispersion and sedimentation of tephrain the proximal region of the volcano were ex-amined with sedimentation models, which focuson the fallout of ash from the margins of turbu-lent particle-fluid suspensions. They use simplerelationships derived from the work of Morton et al. (1956) to calculate the variation of theplume width and speed with height. The growthof the umbrella cloud is also modelled as a func-tion of time (Sparks et al., 1997). The dynamicsin the eruption column is not explicitly predictedalthough it relates to first principles and soundexperimental insights (e.g., Martin and Nokes,1988). Microphysical processes are not consid-ered. Far-field dispersal was then simulated byothers under the assumption that it is dominatedby atmospheric motions, and can be describedby the turbulent advection-diffusion equation indifferent degrees of completeness. The effects ofdifferent plume geometries, atmospheric stratifi-cation, crosswind and re-entrainment, and parti-cle aggregation were investigated in detail. Forcomprehensive overviews see Sparks et al.(1997), or Bursik (1998).

More recently a further model class becameavailable, in which both the rise of the eruptioncolumn from the lithosphere to the stratosphere,and the dispersal of the plume of volcanic parti-cles and gases are simulated. Calculations ontime scales of hours covering spatial scales of

hundreds of kilometres, and the inclusion of ahigher number of transported quantities andprocesses necessitate some simplifications incontrast to the multiphase flow models de-scribed in the previous section. This is realizedwithin the concept of the model ATHAM (Ac-tive Tracer High resolution Atmospheric Model)(Herzog et al., 1998; Oberhuber et al., 1998; fora different approach see Suzuki et al., 2005).The ATHAM model is a non-hydrostatic modelsolves the full set of Navier-Stokes equationsfor the multiphase system. The temporal evolu-tion of the volcanic eruption cloud in the atmos-phere is now simulated, including unsteadyeruptions. Tracers (liquid and solid particles andgases) are not passively transported with themean flow as in usual atmospheric models, be-cause they can be locally highly-concentrated inthe erupted gas-particle mixture. These ‘activetracers’ influence the dynamics by altering themixture’s density and heat capacity.

The system description requires a large set ofdynamic and thermodynamic equations for eachcomponent and the interactions between them.However, on the condition that all particles aresmaller than about a millimetre, it can be as-sumed that the gas-particle mixture is in thermaland in dynamical equilibrium. Under these as-sumptions, the equations have to be solved forvolume mean quantities only (but different trac-ers can still have different fall velocities). Toavoid conflicts with the model assumptionsprocesses in the high pressure, hot temperatureregime within and close to the crater cannot bemodelled, and vent topography is neglected.However, the inclusion of a higher number oftracers and processes, and longer simulationtimes are possible. A turbulence closure schemedescribes sub-scale processes in the eruption col-umn (Herzog et al., 2003). Examinations of spe-cific processes and of the parameters controllingthem within the rising column and associated ashcloud were carried out. These included investi-gations focusing on the influence of the ambientconditions upon plume development (Graf et al.,1999), on cloud microphysics (Herzog et al.,1998), gas scavenging (Textor et al., 2003b,c)and ash aggregation (Textor et al., 2005a,b).

In order to perform numerical simulations,the equation system describing the eruption has

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Fig. 3. Eruption column of volcanic ash after 30 min of simulation with ATHAM. The dimensions of the gridare 50 km in the horizontal and 25 km in the vertical direction. Three ash size classes are shown (10 µm, 200µm, and 4 mm in radius), increasingly dark grey shading indicates the increase in size.

Fig. 4. Eruption column of fine volcanic ash and hydrometeors after 30 min of simulation with ATHAM. Thedimensions of the grid are 50 km in the horizontal and 25 km in the vertical direction. The dark shading besidethe column indicates liquid water. Ice and 10 µm ash are indicated by the light grey shading.


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to be approximated 1) by discretisation in timeand space, and 2) by applying advanced numeri-cal techniques to integrate the system. Hence, therepresentation of sub-grid and simultaneousprocesses is a difficult issue. The ATHAM mod-el has been validated for the simulation of a bio-mass burning plume (Trentmann et al., 2002).Key aspects of simulated explosive eruptionscompare favourably to expectations based onfirst principles. We are currently rigorously eval-uating ATHAM eruption simulations againstfundamental observations from satellites andground-based volcanological data. Results so farsupport ATHAM as a robust model. Figure 3shows a simulated eruption column with ash ofthree different size classes, and fig. 4 illustratesthe eruption column of fine ash and hydromete-ors from an ATHAM model simulation at 30 minof eruption (Herzog et al., 2003).

Other numerical models focus on thesource-dispersal relationship for volcanic gasemissions to the atmosphere. The link betweengeochemical analyses and remote sensing datahelps to better understand the factors, which de-termine the source strength (e.g., Edmonds et al., 2001). A study on the atmospheric life-time of SO2 by Oppenheimer et al. (1998) indi-cated that meteorological and geographic fac-tors, as well as degassing rates, should be con-sidered when interpreting measured SO2 fluxes.

Simulations of time-dependent processeswithin the eruption column and near-volcanoenvironment at the same time can now be run inthree dimensions (Herzog et al., 2003). Themodel results can be compared to observationsin order to better understand the interactions ofdynamics, turbulence, cloud and particle micro-physics, and chemistry for different environ-mental and volcanic conditions. The parameter-isations of individual processes employed in allthese different models reflect the current stateof knowledge about volcanic eruptions in theatmosphere. Sensitivity studies, where a singleprocess or factor is modified, help to under-stand and better determine the complex interac-tions. The results from such simulations canthen be utilized to design investigations of themost relevant quantities by laboratory and fieldexperiments. In addition, the source strength ofvolcanic emissions can be estimated for differ-

ent volcanic and environmental conditions.This information is essential for the assessmentof the climate impact of volcanic emissions.

A more comprehensive representation ofsome processes like the microphysics of cloudsand ash, or gas adsorption at particle surfacesshould be envisaged in the future. The descrip-tions of volcanic particle properties (e.g., shape,porosity) during atmospheric transport have to beimproved in accordance with new observations.The effects of electric fields within the volcaniceruption column have not been tackled by nu-merical simulation so far, but might be importantfor ash aggregation (e.g., Sparks et al., 1997;James et al., 2000).

5. Atmospheric simulation of Ash dispersalon the mesoscale-alpha (200-2000 km –some tens of hours), and on the regionalscale

Far-field dispersal is no longer determined bythe eruption itself, but by atmospheric motions.This motion can be described by the advection-diffusion equation, as mentioned above for simu-lation of the proximal ash transport, often ex-tended with special approximations for turbulentdiffusion. The particle dispersion is simulated bya Lagrangian or a Eulerian formulation of advec-tion, fallout and turbulent dispersion.

Ash tracking models have been used by var-ious agencies to mitigate volcanic ash hazard.All these models simulate the movement of air-borne ash using meteorological field data setsfrom observations or from other model simula-tions. These models include among others: La-grangian Trajectory Volcanic Ash TrackingModel (PUFF) (http://puff.images.alaska.edu/index.html); Nuclear Accident Model (NAME) (http://www.metoffice.gov.uk/research/nwp/publications/nwp_gazette/dec00/name.html);Single-Particle Lagrangian Integrated Trajecto-ry (HYSPLIT) model (http://www.arl.noaa.gov/ready/hysp_info.html); Volcanic Ash ForecastTransport And Dispersion (VAFTAD) model(http://www.arl.noaa.gov/ss/models/vaftad.html);Hybrid Particle And Concentration TransportModel (HYPACT) (http://www.atmet.com/html/hy-pact_soft.shtml); CANadian Emergency Response

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Model (CANERM) (http://www.cmc.ec.gc.ca/cmc/CMOE/vaac/pph/A-pph.html); TRAjectory ofVolcanic materials (TRAV) and MEDIA (http://www.meteo.fr/aeroweb/info/vaac/).

The focus of these models is the forecast ofthe location of the volcanic ash in space andtime. Some of these models are operationallyused by the nine Volcanic Ash Advisory Cen-tres (VAACs) (ICAO, 2000), which serve as aninterface between volcano observatories, mete-orological agencies and air traffic control cen-tres in order to prevent hazards to aircrafts.

Ash tracking models are not able to resolvethe eruption column. They have to prescribe theinitial spatial distribution of the ash cloud. Inparticular the cloud height and its variation withdifferent atmospheric conditions is a crucial pa-rameter for accurately forecasting ash disper-sion (e.g., Tupper et al., 2003). However, it can-not be determined with sufficient accuracy bythe observational systems currently in use.Hence, a quantitative estimation of the sourcestrength based on volcanological parameterswould be highly desirable (Chen, 2003). In ad-dition, the ash dispersal models often have toocoarse a resolution to accurately resolve small-scale weather phenomena, e.g., thunderstorms,and they do not include particle removal by pre-cipitation, or ash aggregation. Wrong forecastsof ash dispersal lead to substantial over or un-der warning, and thus to enhanced risks andcosts to the aviation industry (e.g., Casadevall,1994; Grindle and Burcham, 2002, 2003; Simp-son et al., 2002; Rose et al., 2003; Lacasse et al., 2003).

Ash emissions at many volcanoes, especiallyin least developed countries are unchecked and/ornot quantified. Despite official multilateral agree-ments, regional VAACs are often informed abouteruptions only after the event, when it is nolonger hazardous for air traffic (e.g., A. Tupper,Darwin VAAC, pers. comm.). Ash emissions rep-resent an increasing threat for international airtraffic.

6. Global simulations

The main objective of simulations on theglobal scale is to understand the impact of large

volcanic eruptions, which reached the strato-sphere on atmospheric dynamics and chemistry.To assess the climate impact of volcanic erup-tions, the interactions of volcanic sulphateaerosol particles with atmospheric dynamics,chemistry and radiation have to be treated accu-rately. For the calculation of the mutual feed-back mechanisms between these components itis not sufficient to simply calculate the disper-sal of the volcanic cloud. Instead, detailed rep-resentations of the formation and temporal de-velopment of the aerosol size distribution arerequired, which can be obtained in two ways.First, observed global fields of the volcanicaerosol size distribution (extinction, surfacearea density) can be used. Second, the aerosolmicrophysics processes can be explicitly calcu-lated within the global model. These two ap-proaches are illustrated in more detail below.

6.1. Prescribed volcanic aerosol approach

Atmospheric observations of volcanicaerosols have been collected for only 20 years.They include two major volcanic eruptions (ElChichón in April 1982 and Mt. Pinatubo in June1991) and a few minor ones (e.g., Ruiz - 1985;Kelut - 1990; Hudson - 1991; Spurr - 1992; Nya-muragira - 2001). In particular, the dispersal ofthe Pinatubo cloud and the subsequent changesin the atmospheric system (temperature, tracegas concentration) were detected by in situ air-borne and remote sensing measurements (lidarand satellite). Global simulations with GeneralCirculation Models (GCMs), which used suchobserved volcanic aerosol fields, mainly ad-dressed the Pinatubo and the El Chichón erup-tions (e.g., Graf et al., 1993; Kirchner et al.,1999; Ramachandran et al., 2000; Stenchikov et al., 2002; Collins, 2003; Shindell et al., 2003).Chemistry climate models (Al-Saadi et al., 2001;Rozanov et al., 2002) and 2D chemical radiativetransport models (Kinnison et al., 1994; Ro-senfield et al., 1998) focused on the Pinatuboaerosol impact upon stratospheric trace gas con-centrations.

Model studies investigating the climate im-pact of volcanoes on centennial and decadaltime scales use monthly and latitudinal varying

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data sets of volcanic forcing (e.g., Sato et al.,1993; Andronova et al., 1999; Crowley, 2000;Robertson et al., 2001) which are based on ob-servations (phyrheliometric measurements ofatmospheric extinction, and since 1979 satellitedata) and ice core data. Recently, Amman et al.(2003) published a monthly volcanic forcingdata set for climate modelling from 1890 to1999. Aerosol from each event is individuallyevolved spatially at monthly resolution derivedfrom off-line calculations. These are based onan observed peak aerosol loading and a simpleparameterisation for the stratospheric aerosoltime evolution and transport.

The advantage of using prescribed aerosolis the possibility to thoroughly study the atmos-pheric effects of eruptions in a computationallyefficient way. This approach is, however, high-ly dependent on the quality and amount ofavailable observations, which are only suffi-cient for the last two decades. It is difficult toassess the impact of past and future eruptions.The feedback of aerosol-induced radiative forc-ing and ozone changes on volcanic cloud trans-port cannot be addressed with the prescribedvolcanic aerosol approach.

6.2. Prognostic volcanic aerosol approach

The formation and temporal development ofthe aerosol is simulated from the stratosphericinput of volcanic gases. This requires detailed in-formation on the timing, the eruption height, theamount of emissions, and the initial spatial di-mensions of the volcanic cloud. The usage of abulk aerosol model is the simplest way to simu-late global dispersal. Simulations of the Pinatuboaerosol using such an approach (Young et al.,1994; Timmreck et al., 1999) showed that localin situ heating has an important effect on vol-canic cloud transport. A number of bulk volcanicaerosol simulations have been performed for his-torical eruptions. Stevenson et al. (2003) studiedthe chemical impact of the 1783-1884 Laki fis-sure eruption, and Graf and Timmreck (2001) in-vestigated radiative forcing by the Laacher Seeeruption (10990 BP).

The capability of aerosol simulations using abulk approach as described above for the assess-

ment of atmospheric effects of volcanic erup-tions is however limited by the lack of knowl-edge about the aerosol size distribution. Infor-mation on formation and temporal developmentof the aerosol size distribution and chemicalcomposition are needed for more realistic radia-tion as well as chemistry calculations. This re-quires the treatment of aerosol microphysicalprocesses in the global model. The microphysi-cal processes to be considered are the formationof new particles due to binary homogeneous nu-cleation of H2SO4/H2O, condensation and evap-oration of H2SO4 and H2O, Brownian coagula-tion, gravitational sedimentation, dry depositionand the wet removal of the particles due to in-cloud and below cloud scavenging.

In the last years several simulations of vol-canic eruptions with two dimensional chemistrytransport models including sulphate aerosol mi-crophysics were published. These studies focuson the impact of present day eruptions (Bekkiand Pyle, 1994; Tie et al., 1994a,b; Weisensteinet al., 1997) but there exist also studies for pastevents (Bekki, 1995; Bekki et al., 1996). Chem-istry models, which include aerosol micro-physics together with the various interactionsnecessary to completely analyse the climaticimpact of volcanic eruptions, are presently stillmissing. There are, however, first steps in thatdirection. Pitari and Mancini (2002) assessedthe climate impact of the Pinatubo eruption witha global model, in which ozone and aerosols aretransported, and aerosol microphysical process-es are calculated explicitly. But they used a cou-pled model system consisting of a chemistrytransport model and a global circulation model,so that not all interactions were fully included.Timmreck et al. (2003) used a chemistry cli-mate model with interactive and prognostic vol-canic aerosol and ozone to study the same erup-tion. They did not calculate microphysicalprocesses explicitly, but treated aerosol mass asprognostic variable and derive parameters forthe aerosol size distribution from the aerosolmass using a parameterisation based on ob-served correlations between aerosol mass andsurface. Figure 5 shows the global dispersal ofthe Pinatubo cloud simulated with the chemistry-climate model MAECHAM4 (Timmreck et al.,2003).

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The advantage of the prognostic volcanicaerosol approach is the possibility to study at-mospheric effects of explosive volcanic erup-tions on the global scale, independently fromexisting observations. This gives the chance toperform sensitivity studies and to integrate fu-ture scenarios. However, as discussed above, aglobal model that treats all processes in a so-phisticated manner is still missing. Informationabout the emissions of gases and ash, and aboutthe column height is required for the simulationof volcanic eruptions. This information is com-monly scarce, especially for past eruptions.Simulations with smaller scale numerical mod-els can help to provide initial conditions, as dis-cussed in detail in Section 7. In addition, it isworth mentioning that due to the coarse vertical(about 1-2 km) and horizontal resolution (sever-al 100 km2) of global models, the dispersal ofthe volcanic cloud can only be coarsely repre-sented, and some processes like stratosphere-troposphere exchange or streamer transportmight be critical points. Global prognosticaerosol simulations should not be mixed up withreality, but rather be considered as tools to studyand understand the atmospheric effects of ex-plosive volcanic eruptions.

Since the 1980s and up to recently, atmos-pheric scientists were exclusively interested inthe impact of extreme volcanic eruptions thatinject large amounts (1-10000 Mt) of volcanicemissions into the stratosphere and lead to cli-matic anomalies. Now, there is an increasingrecognition that, not just large episodic events,but also the many small emissions and pro-longed degassing at many volcanoes worldwidecan also have an atmospheric (global sulphurbudget) and climatic impact (Graf et al., 1997,1998). Active volcanoes generally reach con-siderable elevations and most of their emissionsare injected into the free troposphere, above thewell-mixed Planetary Boundary Layer (PBL),which typically extends upward from the sur-face to several hundreds of meters. At high ele-vations above the PBL, removal processes areslower, and volcanic sulphur has thus longerresidence times than anthropogenic sulphur,which is mostly emitted from low elevations.Consequently, the radiative effect on the atmos-phere of volcanic sulphur is disproportionately

larger than that of anthropogenic sulphur. Thiswas illustrated by numerical experiments withatmospheric general circulation models includ-ing a simplified sulphur cycle (Graf et al.,1997).

Furthermore, tropospheric sulphate aerosolsact as Cloud Condensation Nuclei (CCN) andmodify the radiative properties and lifetime ofclouds (Twomey, 1974). The increase in clouddroplet number concentration due to the CCNenhancement in turn increases cloud albedo,enhancing surface cooling. Knowledge of theseeffects can affect our ability to accurately pre-dict the global climate and its evolution.

In the absence of continuous monitoring ofvolcanic degassing on the global scale, the totalamount of volcanic sulphur emissions in thetroposphere is highly uncertain and still underdiscussion (see for details e.g., Textor et al.,2003a). A comprehensive dataset of volcanicdegassing into the troposphere is needed to im-prove global models. The ideal dataset wouldnot only include explosive events, which canpartly be observed by satellite, but also long-term low-level degassing from craters, lavalakes, lava domes, fumarolic activity and dissi-pative emissions at the volcano flanks. Al-though some promising studies are available,such a data set is currently missing. The repre-sentations of the tropospheric sulphur cycle inglobal atmospheric models still differ betweenthe models (Barrie et al., 2001; Lohmann et al.,2001) mainly due to the contrasting complexityof the tropospheric chemistry accounted for.

7. Discussion

A profound knowledge of the fluxes andspecies distribution of volcanic emissions is es-sential for the assessment of the effects of vol-canic eruptions in the atmosphere. It is a majorchallenge to establish a volcanic observationnetwork, which would deliver all informationneeded to create a data set with complete spa-tial and temporal coverage on the global scale,because of the high temporal, spatial and inten-sity variability of volcanic emissions. Extremedifferences exist between the eruption styles ofvolcanoes of different types, but also between

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the phases of activity for volcanoes of the sametype. These differences aggravate the principalunderstanding of the volcanic system, and thusthe extrapolation of observational data to non-monitored volcanoes. Volcanic emissions arethe consequence of a long-term evolution. Pre-cise understanding of the current state of a giv-en volcano regarding its eruptive cycle and fur-ther evolution requires the collection of longtime series of high quality data.

Important fieldwork has been done at indi-vidual volcanoes in recent decades, althoughthe majority of active volcanoes (perhaps 80%of them), which are in least developed coun-tries, remain unstudied.

Laboratory experiments provided essentialinformation on the eruption dynamics and thechemistry of the magmatic system. Numericalmodels are based on and constrained by thefindings of these studies, and simulation resultsshould be carefully validated against observa-tional data. Systematic field and observationalstudies are rather scarce or virtually inexistent.Much more systematic petrological and fieldvolcanological data need to be collected so thatnew predictions of complex conduit and sourceprocesses can be independently tested. Equally,eruption and deposit parameters, ash cloud dis-persal, and time dependent characteristicsshould be investigated and quantified. A data-base of the emissions from thousands of fluctu-ating low level volcanic gas sources as well asfrom the largest of eruptions is needed in orderto improve our understanding of the volcanicimpact on the global environment.

Once they have been carefully validated,numerical models can be employed for a vari-ety of tests and sensitivity studies, which partlysubstitute time consuming, expensive, danger-ous or even impossible experiments and obser-vations. There are generally two main ap-proaches to numerical modelling, which alsopertain to the simulation of volcanic eruptions.

In the first approach one attempts to simu-late an event under a certain aspect, like aircraftsafety, or climate effects. The comprehensive-ness and the lack of understanding (or of com-puter power) of volcanic eruptions make it im-possible to set up and analytically solve anequation system, which entirely describes all

relevant processes. As a last resort, simplifyingparameterisations, that is, empirical descrip-tions of the natural processes are employed.Obviously, even sophisticated semi-empiricalpredictions can only be as good as the databaseused to derive them. Furthermore, this methodis based on the assumption that the net result ofa partly parameterised system can substitute acomplex analytical simulation of the real sys-tem. The main target of such modelling is toprovide the quantitative information needed forpolicy makers concerned with risk mitigation totackle questions of practical and sometimes ur-gent public concerns. An example is the estima-tion of the extent of high-risk areas aroundhighly-populated volcanoes like Montserratbased on numerical simulations (see e.g., Bona-donna et al., 2002).

The second approach, in contrast, typicallyisolates a few parameters, which are thought tomainly control the system. These parametersare then examined within an idealistic model ofthe real system, typically through analyticalmodelling or laboratory analogue experiments.The obvious limitation of this second approachto numerical modelling is that it ignores manyother parameters, of which the importance can-not be known a priori. Such idealistic modelsare not directly usable to solve practical prob-lems as in the parameterised models mentionedabove. The relative simplicity of these modelsallows, however, insights on the fundamentalmechanisms controlling volcanic eruptions andtheir impacts. The method helps to understandindividual controls, which can then be evaluat-ed rigorously against observations as well asthe other forms of simple modelling on thesame aspect. This way, one hopes to explore thesystem in a step-by-step approach. An exampleof this second approach can be found in thepublications of Ernst et al. (1996), or Melnikand Sparks (2002a,b).

The two approaches to numerical simulationsintroduced here serve complementary purposesand are both helpful and needed. The models de-scribed in this contribution are rather based on thefirst approach, since they are not purely analyti-cal models. However, important advances in un-derstanding volcanic eruptions and in computingfacilities allow nowadays for the formulation of

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increasingly comprehensive models. A largeprogress was achieved since the development ofthe first, simple one-dimensional homogeneousand steady-state models. Today, complex multidi-mensional multiphase, transient models providemore accurate hazard assessment, and they canalso be utilized to identify single relevant param-eters, e.g., in sensitivity studies, when single pa-rameters are modified (see for example Neri etal., 2003; Textor et al., 2003c). This latter type ofnumerical simulations can be regarded as a hy-brid of the two approaches.

We have presented models for numericalsimulations of volcanic eruptions on differentscales, tracking volcanic emissions duringtransport from the lithosphere to the strato-sphere, finally influencing the global climate.Explosive volcanic eruptions and their effectson the ground and in the atmosphere cannot besimulated by one single model, because of thecomplexity of the topic and contrasting spatialand temporal scales involved. However, the in-dividual models presented in this paper covermany relevant processes and scales. The com-

Fig. 6. Schematic representation of the chain of numerical models of volcanic eruptions on different spatialscales. The regions of interest are indicated in bold letters in the central oval boxes. The focus of each model is de-scribed in the right boxes in italics. Possible interactions between them can be found beside the vertical arrows.

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bination of these tools provides the unique pos-sibility to derive a more comprehensive de-scription of the volcanic system.

Due to the difficulty or impossibility of ob-serving many processes and parameters duringa volcanic eruption, numerical simulations areespecially insightful in the investigation of thesystem’s complexity. Model results have to becarefully validated with observations, and nomodel can be better than comprehensive obser-vations. Quantities or processes, which are notamenable to measurements, and which cannotbe calculated within one model, are simulatedin detail by another one. Figure 6 summarizesthe chain of models, which is now available forthe investigation of explosive volcanic erup-tions on a broad range of spatial and temporalscales. The sizes of the model domains increasefrom the bottom to the top, along with a de-crease of the spatial and temporal resolution.Each model has been developed for a specificarea of research, and each of them is based on adifferent set of equations and parameterisa-tions, valid for the specific model applications,shown in the boxes to the right. The potentialfor the mutual exchange of simulation results isindicated beside the vertical arrows. The small-er-scale models can provide information aboutthe volcanic forcing for the larger ones, whichin turn can supply information on the atmos-pheric conditions for the smaller-scale models.

Results from a conduit ascent model can beused to determine the volcanic forcing at thevent for the simulation of ash dispersal and mi-crophysical processes within the eruption col-umn, to explore the influence of magmaticproperties on the eruptive style. Models focus-ing on the jet region, in turn, provide the bound-ary conditions for dynamical variables describ-ing the volcanic forcing (e.g., temperature, ver-tical velocity) in larger scale eruption columnmodels, because these models are not able tosufficiently resolve the region closest to thevent. The eruption heights gained from the sim-ulations with the ATHAM model, for example,are found to be highly sensitive to the initialconditions at the base of the eruption columnafter equilibration to atmospheric pressure. Upto now, the initial vertical velocity, the gas frac-tion, and the horizontal extension, which cannot

be directly observed during a violent eruption,had to be estimated based on theoretical consid-erations. The use of data gained from conduitmodels connected with those focusing on the jetregion will reduce this uncertainty, and we in-tend to perform such joint experiments.

The initial spatial distribution and concen-tration of the volcanic cloud for larger-scalesimulations, or for global simulations in climatechange research can be obtained from eruptioncolumn models. The injection height is a crucialparameter for the further dispersal and atmos-pheric residence time of volcanic material,which is, in turn, crucial for aircraft safety andclimate impacts. The injection height cannot bemeasured with the desired accuracy by the cur-rent observation techniques (e.g., Holasek et al.,1996; Oppenheimer, 1998), and can only be in-verted with 20-30% error from tephra fall de-posit characteristics of past eruptions (e.g.,Bonadonna et al., 1998, and references therein).High uncertainties exist about the proportion ofgases and particles erupted, which reach thestratosphere and influence the global climate.These uncertainties are caused by the difficul-ties of directly observing the processes withinexplosive volcanic eruption clouds, and by thelack of fundamental studies in an extreme pa-rameter regime. Simulations with eruption col-umn models perfectly fill in this gap, since theyfocus on the investigation of processes, whichcould otherwise not be accessed. We plan, forexample, a consecutive study where we investi-gate the impact of the water vapour and ice in-jection calculated by an eruption column modelon the microphysics and chemistry in the strat-osphere calculated by a global model.

8. Conclusions

In recent years, numerical simulation of vol-canic eruptions has greatly advanced. However,because of the complexity and the variousscales involved, not all processes could be ad-dressed so far. Different models have been de-veloped, which each work best over a limitedand contrasting range of spatial and temporalscales. These models focus on different erup-tion processes and phases. The existence of

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such a chain of increasingly advanced modelsoffers a new opportunity to explore the variousaspects of the volcanic system in a joint effortin combination with various experimentationsand observations both in the laboratory and inthe field. We plan such an effort in the future,exploring the linking of the results from simu-lations with the various models. This may re-duce uncertainties in assessing the environmen-tal and climate impact of eruptions.

Acknowledgements

G.G.J. Ernst thanks the ‘Fondation Belge dela Vocation’ for a supporting award (GoldenClover Prize) and acknowledges support as a re-searcher at Gent by the Belgian NSF (FWO –Vlaanderen). A. Neri and P. Papale have benefit-ed from the funds of GNV-INGV Projects 2001-03/9 and 2001-03/17. C. Textor acknowledgessupport by the Volkswagen Foundation underthe project EVA, the Max-Planck-Institute forMeteorology, Germany, and the Laboratoire desSciences du Climat et de l’Environnement,France. The work of C. Timmreck was support-ed by the BMBF project KODYACS (Grant07ATF43) and by the European Commissiongrant EVK2-CT-2001-000112 (project PARTS).

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