Vol48/04/2005def 817 ANNALS OF GEOPHYSICS, VOL. 48, N. 4/5, August/October 2005 Key words numerical modeling – explosive vol- canic eruptions – conduit flow – multiphase flow simulation – stratospheric sulfate aerosol 1. Introduction and review of basic concepts Explosive eruptions are among the most fascinating and complex natural phenomena. At their initiation stage, gas-rich viscous mag- ma experiences a pressure drop (a little as in the uncorking of a champagne bottle but where the liquid would be 104 to 1012 times more vis- cous, and over-pressure is tens of bars). The exsolution of dissolved gases (mostly water and CO2), their thousand-fold expansion and acceleration toward the surface occur in suc- cession. Numerical simulation of explosive volcanic 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. Abstract Volcanic eruptions are unsteady multiphase phenomena, which encompass many inter-related processes across the whole range of scales from molecular and microscopic to macroscopic, synoptic and global. We provide an overview 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 like fragmentation, chemical reactions and mass transfer below the Earth surface. Other models simulate atmospheric dispersal of the erupted gas-particle mixture, focusing on rapid processes occurring in the jet, the lower convective regions, and pyroclastic density currents. The ascending eruption column and intrusive gravity current generated by it, as well as sedimentation and ash dispersal from those flows in the immediate environment of the volcano are examined 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 prediction of 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 complexity and 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 and of their effects on the ground, in the atmosphere, and on the global climate. Mailing address: Dr. Christiane Textor, Laboratoire des Sciences du Climat et de l’Environnement, CEA-CNRS L’Orme des Merisiers, F-91191 Gif-sur-Yvette Cedex, France; e-mail: christiane.textor@gmx.de (*) Now at: Centre for Atmospheric Science, Department Geography, University of Cambridge, Downing Place, Cam- bridge CB2 3EN, U.K. (**) Now at: Mercator and Ortelius Research Centre for Eruption Dynamics, Department of Geology and Soil Science, University of Ghent, Krijgslaan 281, S8, 9000 Gent, Belgium. 818 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 upward generating 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 than surrounding air. Decompression to atmospheric pressure, vigorous entrainment, rapid heat ex- change from pyroclasts (about 90% and 60% of them are typically less than 1 mm and 60 µm in size respectively) to the entrained air (on timescale of 1-100 s) and further expansion and lowering of bulk density happen next. This can generate a buoyant eruption column rising up to 10-50 km, from which ash falls out. Columns that remain negatively buoyant when the initial source momentum has been exhausted produce collapsing fountains and pyroclastic density cur- rents, which may also source giant volcanic clouds (e.g., Sparks et al., 1997; Gilbert and Sparks, 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 in potential energy at a certain height in the atmos- phere. Ultimately, the column reaches its height of neutral buoyancy, where its bulk density con- verges to that of air. At this level, either a radial or a parabolically-shaped current is generated (Carey and Sparks, 1986; Bursik et al., 1992a; Ernst et al., 1994; Rose et al., 2001). Most of the ash responsible for widespread dispersal and haz- ards is released from the eruption column and ad- vected within gravity currents flows (e.g., Bursik et 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 the eruption column. Ballistic particles are not dis- cussed here (and typically are not specifically considered by the models) because they con- tribute only a minor fraction to the total volcanic solid mass. Unlike small-sized ash, which is sus- pended by flow turbulence and moves with the fluid, ballistic particles are volumetrically very minor in the sort of intense explosive eruptions considered here (see Riedel et al., 2003, for more discussions about ballistic ejection and model- ling). The current of volcanic material injected into the stratosphere initially flows laterally under gravity while its leading edge is advected at the local wind speed. The current is then sheared by gradients in both wind direction and speed, dif- fused by atmospheric turbulence, may be trans- ported and stretched around or in between mesoscale eddies, and is finally dispersed zonal- ly and meridionally by the global circulation within some weeks and months, respectively (see Sparks et al., 1997; Gilbert and Sparks, 1998, for further reviews of physical concepts). Eruptions can produce hazardously high lo- cal atmospheric concentrations of volcanic ash, acidic gases and secondary particles (e.g., Baxter et al., 1999; Horwell et al., 2003a,b). Ash can be widely dispersed and have detrimental effects on people, their activities and the environment (e.g., Lipman and Mullineaux, 1981; Newhall and Punongbayan, 1996; Druitt and Kokelaar, 2002). The dispersal of the volcanic products, including silicate solid particles, gases (H2O, CO2, SO2, H2S, HCl, and others) and aerosols condensing from gases in the volcanic clouds can impact up- on the environment and human activities. Ash is hazardous as it falls on the ground (e.g., roof col- lapse hazard) where it accounts for 5% of direct casualties and for much of the widespread dam- age from explosive eruptions. Ash is also a haz- ard in the air where it disrupts international air traffic and airport operations, resulting in sub- stantial loss of revenues for air companies. Since 1980, 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 volcanic ash 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 been avoided indicates a need for more accurate, near- real-time, ash dispersal forecasts that can be communicated more rapidly and effectively (ICAO, 2000). In addition, volcanic activity leads to manifold effects on atmospheric chem- istry and climate. Ash settles within hours to weeks and thus does not directly affect global climate. Gases re- 819 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales main much longer aloft and can be dispersed widely and recurrently in the free troposphere (especially in between eruptions) and in the stratosphere (during less frequent but much larger explosive events). There, sulphur-con- taining gases (mainly SO2, and H2S), of special relevance to the atmosphere-climate effects, are oxidatively converted to sulphuric acid, which condenses to form sulphate aerosols on a char- acteristic timescale of about one to two months in the stratosphere (e.g., Bluth et al., 1993; Read et al., 1993). Stratospheric aerosol residence times are longer, accounting for effects lasting up to a several years before return to back- ground conditions (e.g., WMO, 2003). Sulphate aerosols alter the Earth’s radiation balance (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 backscatter part of the incoming solar radiation leading to surface cooling. The net result is a surface cool- ing counteracting greenhouse warming for the few years before aerosol loadings return to back- ground levels. The presence of volcanic aerosol in 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 on tropospheric circulation from forcing upon differ- ential stratospheric heating, leading to abnormal- ly warm winters over the Northern Hemisphere continents 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 the amount and persistence of high-level clouds (Sassen, 1992; Sassen et al., 1995; Lohmann et al., 2003). There is strong evidence that changes in the radiative properties of cirrus clouds can last several years after large explo- sive eruptions (Minnis et al., 1993). Stratospheric sulphate aerosols can also serve as sites for heterogeneous reactions, such as those on polar stratospheric clouds, which deplete ozone in the presence of halogens like chlorine 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 actually reach the stratosphere (Tabazadeh and Turco, 1993; Textor et al., 2003b,c). The atmospheric effects of eruptions depend on magma composition (including volatile con- tent and nature), eruption style, and ambient conditions in both the lithosphere and atmos- phere. Specific volcanoes are capable of con- trasting styles of activity depending upon the stage of maturation reached in the magma chamber and conduit system and upon the phys- ical state of the volcanic edifice. Volcanic emis- sions undergo modification processes in the conduit and crater (especially in the case of flooded vents or of magmas coming into pro- longed contact with aquifers), in the eruption column and during long-range atmospheric transport. There is also a growing understanding that volcanic clouds have a lot more in common with 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) had been left out of eruption cloud models. Small scale processes within the eruption column have a large – albeit indirect – effect upon the atmos- phere and climate. Ash interacts with hydrome- teors and forms mixed phase aggregates during ascent 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). These processes affect residence times, removal rates and the stratospheric injection of gases (i.e., the initial volcanic forcing upon climate). For a re- cent review on atmospheric effects of volcanic eruptions see Textor et al. (2003a). Direct observations of conduit processes have not been feasible so far, and key eruptive parameters have not been measured in situ. What we know about the explosive eruption processes occurring below the Earth’s surface comes from 820 Christiane Textor et al. analyses of eruptive products (Marti et al., 1999; Polacci et al., 2001; Klug et al., 2002), and of geophysical signals (Vergniolle and Brandeis, 1994; Ripepe et al., 2001; Chouet, 2003), from laboratory experiments (for references see Gilbert and Sparks, 1998), and from numerical simulations of magma ascent (e.g., Melnik and Sparks, 2002). Liquid and multiphase magma rheology can be estimated in the laboratory for a relevant 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 use in numerical simulations of magma flow (Man- ga et al., 1998; Saar et al., 2001; Llewellin et al., 2002a,b). Fragmentation experiments are now routinely carried out in apparata, where a magma parcel is pressurized at high temperature and then suddenly depressurised and fragmented. The accelerated particles are collected and their textures compared with those of volcanic parti- cles (Martel et al., 2000, 2001; Spieler et al., 2003). Experiments on gas bubble nucleation and growth in liquids undergoing variable rates of pressure decrease document that non-equilib- rium effects control the distribution of volatile components in the liquid and gas phases (Navon and Lyakhovsky, 1998). Similarly, direct measurements of volcanic emissions in the atmosphere are quite rare. How- ever, they can be studied remotely by ground- based, airborne and satellite instruments. Lidars constrain aerosol vertical distributions, but until recently they could only operate during the night under clear sky conditions. Observations of emissions (mostly SO2) during small eruptive events and of quasi-permanent emissions are possible with ground-based or airborne remote instruments like COSPEC, FTIR (e.g., Oppen- heimer et al., 2002) and DOAS (e.g., Bobrowski et 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 global coverage. Recent developments in satellite re- mote sensing have expanded the capability to monitor 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., Bluth et al., 1992). Eleven instruments have been de- ployed on satellites in the past 30 years. Most are limited time research instruments without opera- tional capacity, SO2 is the only volcanic gas so far monitored operationally by satellite. Since the 1970s, there have been crucial ad- vances in understanding the basic physics of explosive eruptions, and their effects upon the atmosphere and climate. These are summarized by Sparks et al. (1997) and Gilbert and Sparks (1998), and by McCormick et al. (1995) and Robock (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 recent advances. 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, lower convective regions, and pyroclastic density cur- rents. The terms ‘mesoscale alpha, beta, gam- ma’, ‘regional’, and ‘global’ originate from the terminology 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 ash dispersion on the mesoscale-alpha (200-2000 km – some tens of hours) and the regional scale is illustrated in Section 5. Climate effects of eruptions on the global scale are discussed in Section 6. There is much yet to explore about the physics 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 in situ measurements will play a key role in ad- vancing understanding of these processes. 2. Conduit flow modelling Volcanic conduits connect the deep regions of magma accumulation inside the crust with the Earth’s surface. Transit times for magmas 821 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales ascending in conduits and leading to sustained explosive eruptions are typically of the order of minutes, up to 10-20 min. Here the physical and chemical processes are so effective that they produce order of magnitude changes in flow 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 dynamics is 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 factors characterizing real magmas, like their chemical composition (10 major oxides plus 2 major volatile components H2O and CO2) and solid content (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 variable amounts of different pyroclast components originated by the fragmentation process (Pa- pale, 2001). Non-isothermal flow of one-phase (homogeneous) magma has been considered by Buresti and Casarosa (1989) and Mastin and Ghiorso (2000). Transient magma flow is con- sidered by Turcotte et al. (1990), Ramos (1995), and Melnik (2000). Proussevitch and Sahagian (1998) modelled transient conduit flow to investigate the role and dynamics of non-equilibrium nucleation and growth of gas bubbles in silicic magma. A review of pre-1998 work on conduit flow modeling can be found in Papale (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 content of 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. 822 Christiane Textor et al. The use of sets of constitutive equations de- scribing phase properties and interphase as well as phase-wall mechanical interactions has al- lowed investigation of the relationships be- tween ascent dynamics and the multiphase, multicomponent nature of real magmas. These interactions are strongly non-linear, implying that generalization of numerical results should be avoided. The relatively large number of nu- merical simulations made to date allows some preliminary conclusions to be drawn. One of them concerns the roles of volatiles in the dy- namics of magma ascent. Magmatic volatiles represent the engine of explosive eruptions, since volatile exsolution leads to over-pressure in magma chambers and cracking of chamber walls, thus initiating magma ascent (Tait et al., 1989). It is the combined effect of further exso- lution and gas expansion upon depressurisation that leads to magma acceleration, and ultimate- ly to fragmentation and explosive eruption. Numerical simulations show that different volatiles can have opposing effects on ascent and eruption dynamics. Water is the main volatile 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; Papale et al., 1998; Dingwell, 1998). CO2, the second main volatile component in magmas, reduces mass 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 solubilities of H2O and CO2 in the magma under conduit conditions. 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 dissolved in magma. Increasing carbon dioxide can thus both result in more gas available for expansion and 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 magmatic volatile abundances is needed to simulate erup- tions. Recent modelling of the compositional- dependent saturation surface of multicompo- nent volatiles in magmas allowed sulphur species to be treated together with water and carbon dioxide (Moretti et al., 2003). New in- sights will be gained from the simulation of magma ascent by including multicomponent volatile saturation. Melnik (2000) considered the homogeneous (one-phase) flow of bubbly magma below frag- mentation, and the two-phase (separated) flow of gas and particles above fragmentation. The main difference from previous conduit flow models is in the calculated pressure difference between gas and liquid phases. This pressure difference originates from the finite time re- quired for gas bubbles to equilibrate to ambient pressure, and from the high magma viscosity, which acts to increase the equilibration time. Gas-liquid pressure difference over an assigned threshold is also used as the magma fragmenta- tion criterion. The coupling between viscosity, acceleration, and fragmentation leads to a dy- namic fragmentation criterion, mathematically similar to that in Papale (1999a), where frag- mentation relates to the transition from a vis- cous to an elastic rheological response of the stressed magma. Thus, fragmentation occurs when the product of viscosity and strain rate ex- ceeds a critical threshold. The threshold that must be exceeded is different in the two mod- els, being dictated by the elastic properties of magma in the viscous to elastic transition mod- el (Dingwell and Webb, 1989; Papale, 1999a), and by the kinetics of gas bubble expansion in the bubble over-pressure model (Melnik, 2000). In the latter case, the threshold is a function of bubble over-pressure and thus also of magma expansion and acceleration. In turn, the gas density and volume fraction are not directly re- lated to pressure as in Papale (1999a), but also depend on the depressurisation rate along the conduit. The result is that multiple regimes of contrasting eruption intensity (or mass flow- rate) are possible for one starting set of eruptive conditions (or input data in the simulations). The appearance of such multiple steady-state solutions requires a pressure drop at the base of the conduit (or at the top of the underlying mag- ma chamber) significantly below the volatile 823 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales saturation pressure, and may explain abrupt transitions 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 no longer be assumed. Other investigations for re- searcher focused on specific aspects of magma flow, without solving the entire flow from the deep homogeneous flow regions below gas ex- solution to the shallow gas-pyroclast regions above fragmentation up to the conduit exit. Massol and Jaupart (1999) analysed the cross- sectional pre-fragmentation pressure variations in conduits. They documented a decrease in gas pressure from the conduit axis to the walls, im- plying contrasting depressurisation and de- gassing histories of distinct magma parcels erupted simultaneously. Costa and Macedonio (2003) analysed the shear-induced viscous dis- sipation close to the conduit walls, and found that a large temperature increase is expected due to the high viscosities and velocities of magma discharged during explosive eruptions. Their predicted velocity profiles develop a cen- tral plug (despite the assumed Newtonian mag- ma rheology) and a region of concentrated shear near the conduit walls. These findings ac- count for the contrasting textures of pumice from some explosive eruptions (Polacci et al., 2001). Future magma ascent modelling advances may benefit from formulation and solution of a transient, multidimensional, multiphase flow model including the full set of mass, momen- tum, and energy transport equations, as well as constitutive equations approaching the behav- iour of real multiphase multicomponent mag- mas. Such a model would allow all of the above complex 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 entire system from magma chamber to the surface. Coupling with the mechanics of surrounding rocks would allow to take into account both the opening and closing phases of volcanic erup- tions, as well as both time-dependent shape variations 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 subsurface volcanic processes in the next decades. 3. Numerical simulation of atmospheric dispersal processes by using multiphase flow models on the mesoscale-gamma (2-20 km – some tens of minutes) In the last 20 years significant progress in understanding of pyroclastic dispersal process- es was obtained through development of multi- dimensional, transient and multiphase flow models. These are able to treat the eruptive mixture as a non-homogeneous fluid (Wohletz et al., 1984; Valentine and Wohletz, 1989; Do- bran et al., 1993; Neri and Macedonio, 1996; Neri et al., 2003). Such an approach is based on the extension of fundamental transport continu- um mechanics equations to a multiphase and multicomponent mixture. According to the multiphase flow theory, the volume occupied by a generic gaseous, solid, or liquid phase can- not be occupied at the same position in time and space by the remaining phases. It is from such a distinction that it is possible to introduce the phase 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 mass fraction under typical eruptive conditions justi- fies the continuum assumption for pyroclasts smaller than about one centimeter (larger parti- cles need to be treated with a Lagrangian ap- proach). The fundamental mass, momentum and energy conservation equations are now solved for each specific phase. This system needs to be closed by constitutive equations ex- pressing the viscous and interphase transport terms 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 element methods, on computational domains extending some tens of kilometres in radial and vertical directions and so far for times of several min- 824 Christiane Textor et al. utes. The simulation outcome typically consists in the temporal and spatial evolution of several variables – 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 demand for computing power, they have been mostly applied to the analysis of relatively rapid, local- ized, and non-equilibrium processes, such as those occurring in the jet, lower convective re- gions and pyroclastic density currents, herein also named pyroclastic flows sensu lato, gener- ated by gravitational collapse. Processes inves- tigated include the blast dynamics from caldera-forming eruptions (Wohletz et al., 1984), transient motion of ascending eruption columns (Valentine and Wohletz, 1989), inter- action between pyroclastic flows and caldera rims (Valentine et al., 1992), the formation of co-ignimbrite clouds (Dobran et al., 1993), propagation of pyroclastic flows as transient waves (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 multiparticle dynamics of collapsing volcanic column and pyroclastic flows (Neri et al., 2003). The models were also used to reconstruct the eruptive dynamics of historic and on-going eruptions. Simulations have been compared to direct or indirect observations whenever avail- able. In more detail, the conduit ascent model described in the previous section (Papale et al., 1998) was used to determine vent boundary conditions for the multiphase flow model (Neri et al., 1998). The linking of two models permit- ted the reconstruction of the dynamics for the 79 A.D. eruption of Vesuvius. The influence of magmatic properties on the eruptive style of two main phases of the eruption (white and grey pumices) was elucidated (Neri et al. 2002b). Similarly, the multiparticle flow model of Neri et al. (2003) was used to simulate the dynamics 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 conditions based on observations provided the initial con- ditions for transient, axi-symmetric, multi- phase flow simulations of pyroclastic disper- sion. The relationships between the dynamics and the conduit parameters, including volatile content, overpressure, and particle size distri- bution were examined. Model results illustrated that i) observations of explosions were best re- produced using initial conditions that best matched 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 similar effects in that they generally increase plume buoyancy, pyroclastic current runout, Dense Rock Equivalent (DRE) ejected and develop- ment of ash plumes above pyroclastic currents. Some of the multiphase flow models were applied to assess pyroclastic flow hazards in high-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 time wise distribution of the total particle volumetric fraction and gas flow field along the southern flank 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 the Tyrrhenian Sea 7 km away from the crater in about 6 min. Hot, dilute, fine ash-laden plumes rise above the vent and flows. Important flow variables are quantified, e.g., pyroclastic flow density, 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. 825 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales 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 exponents to the base 10 of particle concentration and correspond to value of −8, −7, −6, −5, −4, −3, −2, and −1 (modified from Todesco et al., 2002). 826 Christiane Textor et al. Firstly, the peculiar nature of volcanic process- es requires the formulation of more physically- sound models. For example, the influence of dispersed particles on the turbulence of the car- rier phase (turbulence modulation), and parti- cle-particle interactions in the poly-dispersed mixtures need to be more accurately described. Secondly, experimental research – both in the laboratory and in the field – is necessary to im- prove the equations of physical, thermal, and rheological properties, and to better validate the theoretical models. Thirdly, the development of more effective numerical techniques, including the use of parallel computing, are necessary to allow the simulation of more realistic events in three dimensions and for longer simulation times. Finally, the simulation of the dynamics of 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 – some hundreds of minutes) Numerical simulations of atmospheric processes on the mesoscale-beta require de- scription of the conditions both within the erup- tion column and in its local environment. The high 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 dynamics and thermodynamics. Conditions in the dispers- ing plume and background atmosphere are less vigorous, and do not necessitate such a com- plex algorithm. The comprehensive models de- scribed in the previous section are currently much too demanding in terms of computer time and memory to simulate eruption column and advected cloud dispersal on longer time scales or to consider a higher number of column processes, e.g., microphysics or chemistry. Var- ious numerical models exist for simulation of larger 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, and also for far-field ash dispersal modelling, as discussed in the next section. Yet many of the simplifying assumptions applied in atmospher- ic models are not valid for the high-energy processes close to the vent and in the rising col- umn. Thus models were developed specifically for the simulation of the eruption column and subsequent dispersal, based on novel concepts reviewed hereafter. The first studies of the fluid dynamics of buoyant plumes built upon the seminal work of Morton et al. (1956). They derived a simple for- mula for the first-order estimation of plume height based on the relation between the erupted buoyancy 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 a fairly good agreement with observations for the limit case of powerful plumes in comparatively negligible wind (see Sparks et al., 1997). The analytical studies of Wilson (1976), Sparks and Wilson (1982), and others provided insights into the structure of eruption columns. Time-aver- aged, Gaussian profiles are assumed at each height for quantities like temperature, velocity, and particle concentration. Interactions between components 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 (Wilson and Walker, 1987; Woods, 1988, 1993), which solve the equations of conservation for mass, momentum, and heat, accounting for separate components (e.g., dry air, water vapour, liquid condensates, and solid particles) within the ho- mogenous fluid approximation. Turbulent mix- ing (i.e. entrainment) into the eruption column is determined by an entrainment parameter, which relates entrainment to the upward velocity in the column. Such models are suitable for steady state eruptions, e.g., so-called dry plinian erup- tions with a low occurrence of liquid water (Sparks et al., 1997). They have been useful for first estimations of plume dynamics, like vertical density and velocity profiles, and for under- standing transition between collapsing and non- 827 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales collapsing flows. For comprehensive overviews see Sparks et al. (1997), or Woods (1998). Mod- els of this type have been employed for a variety of applications, like the assessment of the influ- ence of the ambient conditions on the plume height (Glaze and Baloga, 1996), or for the in- vestigation of extraterrestrial volcanic eruptions (Glaze and Baloga, 2002). In spite of its quite coarse assumptions, this model type has been employed for important first estimations about the injections of water vapour (Glaze et al., 1997) and volcanic gases (Tabazadeh and Turco, 1993) into the stratosphere. It has recently been used for the investigation of particle recycling and aggregation in volcanic plumes (Veitch and Woods, 2000, 2001, 2002). The limitations of utilizing a one-dimensional, steady state model for these kinds of questions were discussed in detail by Textor and Ernst (2004) and by Veitch and Woods (2004). The dispersion and sedimentation of tephra in the proximal region of the volcano were ex- amined with sedimentation models, which focus on the fallout of ash from the margins of turbu- lent particle-fluid suspensions. They use simple relationships derived from the work of Morton et al. (1956) to calculate the variation of the plume width and speed with height. The growth of the umbrella cloud is also modelled as a func- tion of time (Sparks et al., 1997). The dynamics in the eruption column is not explicitly predicted although it relates to first principles and sound experimental insights (e.g., Martin and Nokes, 1988). Microphysical processes are not consid- ered. Far-field dispersal was then simulated by others under the assumption that it is dominated by atmospheric motions, and can be described by the turbulent advection-diffusion equation in different degrees of completeness. The effects of different plume geometries, atmospheric stratifi- cation, crosswind and re-entrainment, and parti- cle aggregation were investigated in detail. For comprehensive overviews see Sparks et al. (1997), or Bursik (1998). More recently a further model class became available, in which both the rise of the eruption column from the lithosphere to the stratosphere, and the dispersal of the plume of volcanic parti- cles and gases are simulated. Calculations on time scales of hours covering spatial scales of hundreds of kilometres, and the inclusion of a higher number of transported quantities and processes necessitate some simplifications in contrast to the multiphase flow models de- scribed in the previous section. This is realized within the concept of the model ATHAM (Ac- tive Tracer High resolution Atmospheric Model) (Herzog et al., 1998; Oberhuber et al., 1998; for a different approach see Suzuki et al., 2005). The ATHAM model is a non-hydrostatic model solves the full set of Navier-Stokes equations for the multiphase system. The temporal evolu- tion of the volcanic eruption cloud in the atmos- phere is now simulated, including unsteady eruptions. Tracers (liquid and solid particles and gases) are not passively transported with the mean flow as in usual atmospheric models, be- cause they can be locally highly-concentrated in the erupted gas-particle mixture. These ‘active tracers’ influence the dynamics by altering the mixture’s density and heat capacity. The system description requires a large set of dynamic and thermodynamic equations for each component and the interactions between them. However, on the condition that all particles are smaller than about a millimetre, it can be as- sumed that the gas-particle mixture is in thermal and in dynamical equilibrium. Under these as- sumptions, the equations have to be solved for volume mean quantities only (but different trac- ers can still have different fall velocities). To avoid conflicts with the model assumptions processes in the high pressure, hot temperature regime within and close to the crater cannot be modelled, and vent topography is neglected. However, the inclusion of a higher number of tracers and processes, and longer simulation times are possible. A turbulence closure scheme describes sub-scale processes in the eruption col- umn (Herzog et al., 2003). Examinations of spe- cific processes and of the parameters controlling them within the rising column and associated ash cloud were carried out. These included investi- gations focusing on the influence of the ambient conditions 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 828 Fig. 3. Eruption column of volcanic ash after 30 min of simulation with ATHAM. The dimensions of the grid are 50 km in the horizontal and 25 km in the vertical direction. Three ash size classes are shown (10 µm, 200 µm, 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. The dimensions of the grid are 50 km in the horizontal and 25 km in the vertical direction. The dark shading beside the column indicates liquid water. Ice and 10 µm ash are indicated by the light grey shading. Christiane Textor et al. 829 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales to be approximated 1) by discretisation in time and space, and 2) by applying advanced numeri- cal techniques to integrate the system. Hence, the representation of sub-grid and simultaneous processes 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 eruptions compare favourably to expectations based on first principles. We are currently rigorously eval- uating ATHAM eruption simulations against fundamental observations from satellites and ground-based volcanological data. Results so far support ATHAM as a robust model. Figure 3 shows a simulated eruption column with ash of three different size classes, and fig. 4 illustrates the eruption column of fine ash and hydromete- ors from an ATHAM model simulation at 30 min of eruption (Herzog et al., 2003). Other numerical models focus on the source-dispersal relationship for volcanic gas emissions to the atmosphere. The link between geochemical analyses and remote sensing data helps 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 processes within the eruption column and near-volcano environment at the same time can now be run in three dimensions (Herzog et al., 2003). The model results can be compared to observations in order to better understand the interactions of dynamics, turbulence, cloud and particle micro- physics, and chemistry for different environ- mental and volcanic conditions. The parameter- isations of individual processes employed in all these different models reflect the current state of knowledge about volcanic eruptions in the atmosphere. Sensitivity studies, where a single process or factor is modified, help to under- stand and better determine the complex interac- tions. The results from such simulations can then be utilized to design investigations of the most relevant quantities by laboratory and field experiments. In addition, the source strength of volcanic emissions can be estimated for differ- ent volcanic and environmental conditions. This information is essential for the assessment of the climate impact of volcanic emissions. A more comprehensive representation of some processes like the microphysics of clouds and ash, or gas adsorption at particle surfaces should be envisaged in the future. The descrip- tions of volcanic particle properties (e.g., shape, porosity) during atmospheric transport have to be improved in accordance with new observations. The effects of electric fields within the volcanic eruption column have not been tackled by nu- merical simulation so far, but might be important for ash aggregation (e.g., Sparks et al., 1997; James et al., 2000). 5. Atmospheric simulation of Ash dispersal on the mesoscale-alpha (200-2000 km – some tens of hours), and on the regional scale Far-field dispersal is no longer determined by the 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 turbulent diffusion. The particle dispersion is simulated by a 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 sets from observations or from other model simula- tions. These models include among others: La- grangian Trajectory Volcanic Ash Tracking Model (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 Forecast Transport And Dispersion (VAFTAD) model (http://www.arl.noaa.gov/ss/models/vaftad.html); Hybrid Particle And Concentration Transport Model (HYPACT) (http://www.atmet.com/html/hy- pact_soft.shtml); CANadian Emergency Response 830 Christiane Textor et al. Model (CANERM) (http://www.cmc.ec.gc.ca/cmc/ CMOE/vaac/pph/A-pph.html); TRAjectory of Volcanic materials (TRAV) and MEDIA (http:// www.meteo.fr/aeroweb/info/vaac/). The focus of these models is the forecast of the location of the volcanic ash in space and time. Some of these models are operationally used by the nine Volcanic Ash Advisory Cen- tres (VAACs) (ICAO, 2000), which serve as an interface 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 resolve the eruption column. They have to prescribe the initial spatial distribution of the ash cloud. In particular the cloud height and its variation with different 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 by the observational systems currently in use. Hence, a quantitative estimation of the source strength based on volcanological parameters would be highly desirable (Chen, 2003). In ad- dition, the ash dispersal models often have too coarse 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 forecasts of ash dispersal lead to substantial over or un- der warning, and thus to enhanced risks and costs 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, especially in least developed countries are unchecked and/or not quantified. Despite official multilateral agree- ments, regional VAACs are often informed about eruptions only after the event, when it is no longer hazardous for air traffic (e.g., A. Tupper, Darwin VAAC, pers. comm.). Ash emissions rep- resent an increasing threat for international air traffic. 6. Global simulations The main objective of simulations on the global 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 sulphate aerosol 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 it is 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 are required, which can be obtained in two ways. First, observed global fields of the volcanic aerosol size distribution (extinction, surface area density) can be used. Second, the aerosol microphysics 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 volcanic aerosols have been collected for only 20 years. They include two major volcanic eruptions (El Chichón in April 1982 and Mt. Pinatubo in June 1991) and a few minor ones (e.g., Ruiz - 1985; Kelut - 1990; Hudson - 1991; Spurr - 1992; Nya- muragira - 2001). In particular, the dispersal of the Pinatubo cloud and the subsequent changes in the atmospheric system (temperature, trace gas concentration) were detected by in situ air- borne and remote sensing measurements (lidar and satellite). Global simulations with General Circulation Models (GCMs), which used such observed 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 radiative transport models (Kinnison et al., 1994; Ro- senfield et al., 1998) focused on the Pinatubo aerosol impact upon stratospheric trace gas con- centrations. Model studies investigating the climate im- pact of volcanoes on centennial and decadal time scales use monthly and latitudinal varying 831 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales 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 of atmospheric extinction, and since 1979 satellite data) and ice core data. Recently, Amman et al. (2003) published a monthly volcanic forcing data set for climate modelling from 1890 to 1999. Aerosol from each event is individually evolved spatially at monthly resolution derived from off-line calculations. These are based on an observed peak aerosol loading and a simple parameterisation for the stratospheric aerosol time evolution and transport. The advantage of using prescribed aerosol is the possibility to thoroughly study the atmos- pheric effects of eruptions in a computationally efficient way. This approach is, however, high- ly dependent on the quality and amount of available observations, which are only suffi- cient for the last two decades. It is difficult to assess 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 prescribed volcanic aerosol approach. 6.2. Prognostic volcanic aerosol approach The formation and temporal development of the aerosol is simulated from the stratospheric input of volcanic gases. This requires detailed in- formation on the timing, the eruption height, the amount of emissions, and the initial spatial di- mensions of the volcanic cloud. The usage of a bulk aerosol model is the simplest way to simu- late global dispersal. Simulations of the Pinatubo aerosol using such an approach (Young et al., 1994; Timmreck et al., 1999) showed that local in situ heating has an important effect on vol- canic cloud transport. A number of bulk volcanic aerosol simulations have been performed for his- torical eruptions. Stevenson et al. (2003) studied the chemical impact of the 1783-1884 Laki fis- sure eruption, and Graf and Timmreck (2001) in- vestigated radiative forcing by the Laacher See eruption (10 990 BP). The capability of aerosol simulations using a bulk 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 development of the aerosol size distribution and chemical composition are needed for more realistic radia- tion as well as chemistry calculations. This re- quires the treatment of aerosol microphysical processes in the global model. The microphysi- cal processes to be considered are the formation of 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 deposition and 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 chemistry transport models including sulphate aerosol mi- crophysics were published. These studies focus on the impact of present day eruptions (Bekki and Pyle, 1994; Tie et al., 1994a,b; Weisenstein et al., 1997) but there exist also studies for past events (Bekki, 1995; Bekki et al., 1996). Chem- istry models, which include aerosol micro- physics together with the various interactions necessary to completely analyse the climatic impact of volcanic eruptions, are presently still missing. There are, however, first steps in that direction. Pitari and Mancini (2002) assessed the climate impact of the Pinatubo eruption with a global model, in which ozone and aerosols are transported, and aerosol microphysical process- es are calculated explicitly. But they used a cou- pled model system consisting of a chemistry transport 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 microphysical processes explicitly, but treated aerosol mass as prognostic variable and derive parameters for the aerosol size distribution from the aerosol mass using a parameterisation based on ob- served correlations between aerosol mass and surface. Figure 5 shows the global dispersal of the Pinatubo cloud simulated with the chemistry- climate model MAECHAM4 (Timmreck et al., 2003). 832 F ig . 5. G lo ba l di sp er sa l of t he P in at ub o vo lc an ic c lo ud ( pp b su lf ur ) at 2 4 km e le va ti on f or f ou r sp ec if ic d ay s du ri ng t he f ir st f ou r m on th a ft er t he er up ti on ( T im m re ck et a l. , 20 03 ). Christiane Textor et al. 833 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales The advantage of the prognostic volcanic aerosol approach is the possibility to study at- mospheric effects of explosive volcanic erup- tions on the global scale, independently from existing observations. This gives the chance to perform sensitivity studies and to integrate fu- ture scenarios. However, as discussed above, a global model that treats all processes in a so- phisticated manner is still missing. Information about the emissions of gases and ash, and about the column height is required for the simulation of 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 is worth mentioning that due to the coarse vertical (about 1-2 km) and horizontal resolution (sever- al 100 km2) of global models, the dispersal of the volcanic cloud can only be coarsely repre- sented, and some processes like stratosphere- troposphere exchange or streamer transport might be critical points. Global prognostic aerosol simulations should not be mixed up with reality, but rather be considered as tools to study and understand the atmospheric effects of ex- plosive volcanic eruptions. Since the 1980s and up to recently, atmos- pheric scientists were exclusively interested in the impact of extreme volcanic eruptions that inject large amounts (1-10 000 Mt) of volcanic emissions into the stratosphere and lead to cli- matic anomalies. Now, there is an increasing recognition that, not just large episodic events, but also the many small emissions and pro- longed degassing at many volcanoes worldwide can also have an atmospheric (global sulphur budget) and climatic impact (Graf et al., 1997, 1998). Active volcanoes generally reach con- siderable elevations and most of their emissions are injected into the free troposphere, above the well-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 are slower, and volcanic sulphur has thus longer residence 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. This was illustrated by numerical experiments with atmospheric general circulation models includ- ing a simplified sulphur cycle (Graf et al., 1997). Furthermore, tropospheric sulphate aerosols act as Cloud Condensation Nuclei (CCN) and modify the radiative properties and lifetime of clouds (Twomey, 1974). The increase in cloud droplet number concentration due to the CCN enhancement in turn increases cloud albedo, enhancing surface cooling. Knowledge of these effects can affect our ability to accurately pre- dict the global climate and its evolution. In the absence of continuous monitoring of volcanic degassing on the global scale, the total amount of volcanic sulphur emissions in the troposphere is highly uncertain and still under discussion (see for details e.g., Textor et al., 2003a). A comprehensive dataset of volcanic degassing into the troposphere is needed to im- prove global models. The ideal dataset would not only include explosive events, which can partly be observed by satellite, but also long- term low-level degassing from craters, lava lakes, 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 in global atmospheric models still differ between the models (Barrie et al., 2001; Lohmann et al., 2001) mainly due to the contrasting complexity of the tropospheric chemistry accounted for. 7. Discussion A profound knowledge of the fluxes and species distribution of volcanic emissions is es- sential for the assessment of the effects of vol- canic eruptions in the atmosphere. It is a major challenge to establish a volcanic observation network, which would deliver all information needed 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. Extreme differences exist between the eruption styles of volcanoes of different types, but also between 834 Christiane Textor et al. the phases of activity for volcanoes of the same type. These differences aggravate the principal understanding of the volcanic system, and thus the extrapolation of observational data to non- monitored volcanoes. Volcanic emissions are the 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 long time series of high quality data. Important fieldwork has been done at indi- vidual volcanoes in recent decades, although the majority of active volcanoes (perhaps 80% of them), which are in least developed coun- tries, remain unstudied. Laboratory experiments provided essential information on the eruption dynamics and the chemistry of the magmatic system. Numerical models are based on and constrained by the findings of these studies, and simulation results should be carefully validated against observa- tional data. Systematic field and observational studies are rather scarce or virtually inexistent. Much more systematic petrological and field volcanological data need to be collected so that new predictions of complex conduit and source processes can be independently tested. Equally, eruption and deposit parameters, ash cloud dis- persal, and time dependent characteristics should be investigated and quantified. A data- base of the emissions from thousands of fluctu- ating low level volcanic gas sources as well as from the largest of eruptions is needed in order to improve our understanding of the volcanic impact 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 partly substitute time consuming, expensive, danger- ous or even impossible experiments and obser- vations. There are generally two main ap- proaches to numerical modelling, which also pertain to the simulation of volcanic eruptions. In the first approach one attempts to simu- late an event under a certain aspect, like aircraft safety, 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 an equation system, which entirely describes all relevant processes. As a last resort, simplifying parameterisations, that is, empirical descrip- tions of the natural processes are employed. Obviously, even sophisticated semi-empirical predictions can only be as good as the database used to derive them. Furthermore, this method is based on the assumption that the net result of a partly parameterised system can substitute a complex analytical simulation of the real sys- tem. The main target of such modelling is to provide the quantitative information needed for policy makers concerned with risk mitigation to tackle questions of practical and sometimes ur- gent public concerns. An example is the estima- tion of the extent of high-risk areas around highly-populated volcanoes like Montserrat based on numerical simulations (see e.g., Bona- donna et al., 2002). The second approach, in contrast, typically isolates a few parameters, which are thought to mainly control the system. These parameters are then examined within an idealistic model of the real system, typically through analytical modelling or laboratory analogue experiments. The obvious limitation of this second approach to numerical modelling is that it ignores many other parameters, of which the importance can- not be known a priori. Such idealistic models are not directly usable to solve practical prob- lems as in the parameterised models mentioned above. The relative simplicity of these models allows, however, insights on the fundamental mechanisms controlling volcanic eruptions and their impacts. The method helps to understand individual controls, which can then be evaluat- ed rigorously against observations as well as the other forms of simple modelling on the same aspect. This way, one hopes to explore the system in a step-by-step approach. An example of this second approach can be found in the publications of Ernst et al. (1996), or Melnik and Sparks (2002a,b). The two approaches to numerical simulations introduced here serve complementary purposes and are both helpful and needed. The models de- scribed in this contribution are rather based on the first approach, since they are not purely analyti- cal models. However, important advances in un- derstanding volcanic eruptions and in computing facilities allow nowadays for the formulation of 835 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales increasingly comprehensive models. A large progress was achieved since the development of the first, simple one-dimensional homogeneous and steady-state models. Today, complex multidi- mensional multiphase, transient models provide more accurate hazard assessment, and they can also be utilized to identify single relevant param- eters, e.g., in sensitivity studies, when single pa- rameters are modified (see for example Neri et al., 2003; Textor et al., 2003c). This latter type of numerical simulations can be regarded as a hy- brid of the two approaches. We have presented models for numerical simulations of volcanic eruptions on different scales, tracking volcanic emissions during transport from the lithosphere to the strato- sphere, finally influencing the global climate. Explosive volcanic eruptions and their effects on the ground and in the atmosphere cannot be simulated by one single model, because of the complexity of the topic and contrasting spatial and temporal scales involved. However, the in- dividual models presented in this paper cover many relevant processes and scales. The com- Fig. 6. Schematic representation of the chain of numerical models of volcanic eruptions on different spatial scales. 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. 836 Christiane Textor et al. 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 during a volcanic eruption, numerical simulations are especially insightful in the investigation of the system’s complexity. Model results have to be carefully validated with observations, and no model can be better than comprehensive obser- vations. Quantities or processes, which are not amenable to measurements, and which cannot be calculated within one model, are simulated in detail by another one. Figure 6 summarizes the chain of models, which is now available for the investigation of explosive volcanic erup- tions on a broad range of spatial and temporal scales. The sizes of the model domains increase from the bottom to the top, along with a de- crease of the spatial and temporal resolution. Each model has been developed for a specific area of research, and each of them is based on a different set of equations and parameterisa- tions, valid for the specific model applications, shown in the boxes to the right. The potential for the mutual exchange of simulation results is indicated beside the vertical arrows. The small- er-scale models can provide information about the volcanic forcing for the larger ones, which in turn can supply information on the atmos- pheric conditions for the smaller-scale models. Results from a conduit ascent model can be used to determine the volcanic forcing at the vent for the simulation of ash dispersal and mi- crophysical processes within the eruption col- umn, to explore the influence of magmatic properties 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 column models, because these models are not able to sufficiently resolve the region closest to the vent. The eruption heights gained from the sim- ulations with the ATHAM model, for example, are found to be highly sensitive to the initial conditions at the base of the eruption column after equilibration to atmospheric pressure. Up to 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 conduit models connected with those focusing on the jet region 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-scale simulations, or for global simulations in climate change research can be obtained from eruption column models. The injection height is a crucial parameter for the further dispersal and atmos- pheric residence time of volcanic material, which is, in turn, crucial for aircraft safety and climate impacts. The injection height cannot be measured 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 of gases and particles erupted, which reach the stratosphere and influence the global climate. These uncertainties are caused by the difficul- ties of directly observing the processes within explosive volcanic eruption clouds, and by the lack of fundamental studies in an extreme pa- rameter regime. Simulations with eruption col- umn models perfectly fill in this gap, since they focus on the investigation of processes, which could otherwise not be accessed. We plan, for example, a consecutive study where we investi- gate the impact of the water vapour and ice in- jection calculated by an eruption column model on 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 various scales involved, not all processes could be ad- dressed so far. Different models have been de- veloped, which each work best over a limited and contrasting range of spatial and temporal scales. These models focus on different erup- tion processes and phases. The existence of 837 Numerical simulation of explosive volcanic eruptions from the conduit flow to global atmospheric scales such a chain of increasingly advanced models offers a new opportunity to explore the various aspects of the volcanic system in a joint effort in combination with various experimentations and observations both in the laboratory and in the 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 de la Vocation’ for a supporting award (Golden Clover 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. 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