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One of the most hazardous phenomena which characterizes the summit activity at Mt. Etna (Italy) is represented by pyroclastic avalanches, gravity-driven flows of pyroclastic material at high particle concentration, characterized by modest volumes (usually lower than a few millions of cubic metres) and small thickness-to-length ratio. The frequency of pyroclastic avalanches at Mt. Etna has increased during the recent 2020-2022 volcanic activity, where a series of intense paroxysmal eruptions took place at the South East Crater (SEC). The accumulation of proximal deposits generated by the explosive activity led to the growth of SEC, which posed favorable conditions in triggering partial collapses of unstable flanks of the crater. Pyroclastic avalanches propagated mainly eastward and southward of the SEC, up to distances of about 2 km from the source.Numerical modeling of pyroclastic avalanche propagation and emplacement constitutes a powerful tool for hazard assessment, despite several difficulties in simulating the rheology of the polydisperse granular mixture. In this work, pyroclastic avalanches are simulated using the open-source code IMEX-SfloW2D. Depth-averaged equations are implemented in the code to model the granular flow as an incompressible, single-phase granular fluid, described by the Voellmy–Salm rheology. Comparison of numerical results with the well-documented pyroclastic avalanches occurred on 11 February 2014 and during the 10 February 2022 paroxysmal eruption (one of the most intense of the 2020-2022 series) allowed us to investigate the variability of the avalanche dynamics with its volume, the influence of the three-dimensional volcano morphology, and to statistically calibrate the unknown rheological parameters (i.e., the dry-friction coefficient µ and viscous-turbulent friction coefficient ξ). Finally, we provide a preliminary quantification of new potential collapse scenarios, to assess pyroclastic avalanche probabilistic hazard on the summit area, one of the most preferential tourists destination at Mt. Etna.

This review summarizes what the volcanology community has learned thus far from studying the deposits of pyroclastic currents (PCs) from the 1980 eruption sequence at Mount St. Helens. The review includes mass flow events during the May 18 eruption, including the lateral blast, the afternoon column collapse and boil-over PC activity, and some aspects of the debris avalanche. We also include a summary of PCs generated in the smaller eruptions following the climactic May 18 event. Our objective is to summarize the state of our understanding of PC transport and emplacement mechanisms from the combination of field and laboratory observations, granular flow experiments, and numerical modeling techniques. Specifically, we couple deposit characteristics, experiments, and numerical modeling techniques to critically address the problems of (1) constraining conditions in the flow boundary zone at the time of deposition; (2) the influence of substrate roughness and topography on PC behavior; (3) the prevalence, causes, and consequences of substrate erosion by PCs; and (4) the reconstruction of PC transportation and sedimentation processes from a combination of geophysical and sedimentological observations. We conclude by providing opportunities for future research as our field, experimental, and numerical research techniques advance.

Explosive volcanic eruptions are characterized by the ejection in the atmosphere of volcanic gases and fragments of magma and/or lithics at high temperature, pressure and velocity. They encompass a broad range of magnitudes, with volumes of ejecta spanning from less than 106 m3, to 109-1011 m3 of Plinian eruptions, up to the largest known volcanic events, able to erupt up to thousands of km3 of magma. Phreatic eruptions are among the smallest in this range; they do not involve the eruption of fresh magma, but are instead triggered by a sudden rise of pressure and temperature in a shallow magmatic-hydrothermal system. Despite their relatively small size, phreatic eruptions are frequent on Earth and difficult to anticipate, and represent therefore a significant hazard, testified by the recent eruptions in Tongariro’s Te-Maari crater (NZ, 2012), and during the tragic development of events in Ontake (JP, 2014) and Whakaari/White Island (NZ, 2019). The main challenges of the numerical simulation of explosive volcanic phenomena have traditionally been identified in the complex fluid dynamics of polydisperse multiphase mixtures (with particle grains ranging from a few microns to metres) and in the extremely broad range of relevant dynamical scales characterizing compressible turbulent flows of gas and particles in the atmosphere. Three-dimensional, high-performance computer models based on different approximations of the multiphase flow theory have been designed to simulate the fluid dynamics of explosive eruptions, and to define hazard and impact scenarios. However, until now, it was difficult to quantify the uncertainty associated with numerical predictions. We here discuss the present bottlenecks and challenges of the 3D modelling of phreatic volcanic eruptions in the quest for urgent definition of impact scenarios and probabilistic hazard assessment at Vulcano island (Aeolian archipelago, Italy). Exascale computing in these applications offers the opportunity to increase the complexity of the physical model (including new key processes as the flashing of liquid water), to describe the wide range of lithic fragments ejected during the eruption, to achieve unprecedently high spatial resolution at the source and close to the terrain, and to perform large ensembles of numerical simulations to quantify the epistemic uncertainty associated with the model initial and boundary conditions. Challenges associated with the development, maintenance and porting on new HPC architectures of numerical models are finally discussed.

Starting from February 2021, Mt. Etna (Italy) experienced a period of intense explosive activity with 17 lava fountain episodes between 16 February and 1 April 2021. During the eruptive cycle, the Istituto Nazionale di Geofisica e Vulcanologia-Osservatorio Etneo (INGV-OE) issued 62 alert notifications known as VONAs (Volcano Observatory Notice for Aviation) to inform the aeronautical authorities about the volcanic activity. We present an automated VONA-based workflow aimed at real-time assessment of the volcanic hazard due to tephra fallout at Mt. Etna. When a VONA reporting tephra emission is issued by INGV-OE, numerical simulations accounting for atmospheric and eruptive uncertainties are automatically initialized to produce probabilistic hazard maps of tephra fallout and atmospheric dispersal. We applied the workflow to three lava fountains that occurred during the 2021 eruptive cycle. To test the modelling results, we compared the simulated ground load with field data, and the extent and position of the simulated volcanic cloud with the observed or estimated volcanic cloud from the Toulouse Volcanic Ash Advisory Center. Overall, we found a good match between simulated and observed quantities (tephra loads and volcanic cloud position), especially when accurate information on eruptive conditions (column height and duration) are supplied by the VONAs. Finally, through a statistical analysis, we found that column height and wind field are fundamental in determining tephra ground accumulation. For this reason, these parameters should be constrained by observational data as accurately as possible when performing numerical simulations, especially in the line of developing operational workflows., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

We use PyBox, a new numerical implementation of the box-model approach, to reproduce pyroclastic density current (PDC) deposits from the Somma–Vesuvius volcano (Italy). Our simplified model assumes inertial flow front dynamics and mass deposition equations and axisymmetric conditions inside circular sectors. Tephra volume and density and total grain size distribution of EU3pf and EU4b/c, two well-studied PDC units from different phases of the 79 CE Pompeii eruption, are used as input parameters. Such units correspond to the deposits from variably dilute, turbulent PDCs. We perform a quantitative comparison and uncertainty quantification of numerical model outputs with respect to the observed data of unit thickness, inundation areas and grain size distribution as a function of the radial distance to the source. The simulations consider (i) polydisperse conditions, given by the total grain size distribution of the deposit, or monodisperse conditions, given by the mean Sauter diameter of the deposit; (ii) axisymmetric collapses either covering the whole 360∘ (round angle) or divided into two circular sectors. We obtain a range of plausible initial volume concentrations of solid particles from 2.5 % to 6 %, depending on the unit and the circular sector. Optimal modelling results of flow extent and deposit thickness are reached on the EU4b/c unit in a polydisperse and sectorialized situation, indicating that using total grain size distribution and particle densities as close as possible to the real conditions significantly improves the performance of the PyBox code. The study findings suggest that the simplified box-model approach has promise for applications in constraining the plausible range of the input parameters of more computationally expensive models. This could be done due to the relatively fast computational time of the PyBox code, which allows the exploration of the physical space of the input parameters.

Pyroclastic density currents (PDCs) are dangerous multiphase flows originating from volcanic eruptions. PDCs cause more than a third of volcanic fatalities globally and, therefore, development of robust PDC hazard models is a priority in volcanology and natural hazard science. However, the complexity of gas–particle interactions inside PDCs, as well as their hostile nature, makes quantitative measurements of internal flow properties, and the validation of hazard models, challenging. Within the last decade, major advances from large-scale experiments, field observations and computational and theoretical models have provided new insights into the enigmatic internal structure of PDCs and identified key processes behind their fluid-like motion. Recent developments have also revealed important links between newly recognized processes of mesoscale turbulence and PDC behaviour. In this Review, we consider how recent advances in PDC research close the gaps towards more robust hazard modelling, outline the need to measure the internal properties of natural flows using geophysical methods and identify critical future research challenges. Greater understanding of PDCs will also provide insights into the dynamics of other natural gravity currents and high-energy turbulent multiphase flows, such as debris avalanches and turbidity currents. Pyroclastic density currents are complex multiphase flows originating from volcanic eruptions and account for almost a third of volcanic fatalities globally. This Review discusses recent advances in understanding of the complex internal processes within pyroclastic density currents and how these influence the flow dynamics and hazard footprints.

The effects of volcanic hazards can be quantified by applying new methods to provide support for rational decision-making. Mt Etna is one the most active volcanoes in the world, producing both effusive and explosive eruptions together with a very intense seismic activity, which significantly affect the territory and human society. We present the preliminary results obtained in the framework of the PANACEA project (INGV’s project “Pianeta Dinamico”, funded by the Italian Ministero dell’Università e la Ricerca, MUR) regarding the multi-hazard assessment around Mt Etna. These include: (i) the production of an updated spatio-temporal probability map of vent opening at Etna, using a procedure exploiting different Kernel functions (e.g. the exponential, Cauchy, and Gaussian functions), and testing volcanic deformation patterns to explore possible dynamic, structural conditioning on the vent opening process; (ii) the identification of a set of cascading effects scenarios that account for volcanic phenomena (i.e., volcanic unrest, seismicity, volcanic explosions, volcanic effusive events, lava flows, tephra/ballistic fall, and PDC), as well as other external hazards potentially linked in such chains (e.g., flooding, forest fires, etc.); and (iii) the identification of scenarios involving systemic impacts (e.g., impacts on the functionality or connectivity of networks).

Pyroclastic currents (PCs) are composed of hot mixtures of gas and pyroclastic particles, which travel at moderate to very high speed (tens to hundreds of m/s), under the effect of their density contrast with the surrounding atmosphere. They can be flowing over obstacles with ease but their pathway is often controlled by the topography they flow over. These characteristics make them one of the most dangerous and inaccessible to direct study, natural phenomena. For this reason, the use of numerical modeling could be one of the most useful tools to provide key quantitative information about their internal dynamics. In this study, we used the available data about Pozzolane Rosse ignimbrite (Colli Albani, Italy) caldera-forming, - 460 ka, 63 km3 DRE - to model source and flow dynamics with a depth-averaged model for inertial PCs. Numerical simulations allowed us to test the effects of 1) atmospheric air entrainment, by varying the Richardson number (), 2) the initial flow thickness, 3) initial flow velocity, 4) grain-size distribution, and 5) mixture density on PCs runout and thickness decay pattern. Model validation was performed by comparing i) model runout and field data; ii) the thickness of the deposit compared to the thickness of the model output with the distance; iii) the mass fractions of the different grain size classes for the actual deposit compared to the model output. Several simulations were carried out considering i) the influence of parameters h and v; ii) the density; iii) the temperature and iv) the topography. The results allowed us to understand and quantify the first-order variables that characterize flow propagation (runout) and thickness decay pattern, indicating that the depth-averaged model may be suitable to represent the dynamics of large PCs, such as those of the Pozzolane Rosse.

Pyroclastic surges are lethal hazards from volcanoes that exhibit enormous destructiveness through dynamic pressures of 100–102 kPa inside flows capable of obliterating reinforced buildings. However, to date, there are no measurements inside these currents to quantify the dynamics of this important hazard process. Here we show, through large-scale experiments and the first field measurement of pressure inside pyroclastic surges, that dynamic pressure energy is mostly carried by large-scale coherent turbulent structures and gravity waves. These perpetuate as low-frequency high-pressure pulses downcurrent, form maxima in the flow energy spectra and drive a turbulent energy cascade. The pressure maxima exceed mean values, which are traditionally estimated for hazard assessments, manifold. The frequency of the most energetic coherent turbulent structures is bounded by a critical Strouhal number of ~0.3, allowing quantitative predictions. This explains the destructiveness of real-world flows through the development of c. 1–20 successive high-pressure pulses per minute. This discovery, which is also applicable to powder snow avalanches, necessitates a re-evaluation of hazard models that aim to forecast and mitigate volcanic hazard impacts globally., The hazards of pyroclastic surges remain poorly mitigated globally. Here, the authors show that their destructiveness is amplified by turbulent excursions of dynamic pressure energy that focusses inside the largest eddies and internal gravity waves.

Understanding explosive eruption dynamics and assessment of their hazards continue to represent challenging issues to the present-day volcanology community. This is largely due to the complex and diverse nature of the phenomena, the variability and unpredictability of volcanic processes, and the difficulty of measuring them in the field and fully reproducing them at the laboratory scale. Nevertheless, important and continuing progress has been made in the last few decades in understanding the fundamental processes and forecasting the occurrences of these phenomena, thanks to significant advances in field, experimental, and theoretical modeling investigations. For more than four decades, for example, volcanologists have made major progress in the description of the nature of explosive eruptions, considerably aided by the development, improvement, and application of physical-mathematical models. First, integral steady-state homogeneous flow models were used to investigate the different controlling mechanisms and to infer the genesis and evolution of the phenomena. Through continuous improvements and quantum-leap developments, a variety of transient one/multi-dimensional multiphase flow models of volcanic phenomena now can implement state-of-the-art formulations of the underlying physics, new-generation analytical and experimental data, as well as high-performance computational techniques. These numerical models have proved to be able to provide key insights in the understanding of the dynamics of explosive eruptions (e.g., volcanic jets and blasts, convective plumes, collapsing columns, pyroclastic density currents, short-lived explosions, ballistic ejecta, etc., just to limit the phenomena to the atmospheric domain), as well as to represent a valuable tool in the quantification of potential eruptive scenarios and associated hazards.

Pyroclastic avalanches are a type of granular flow generated at active volcanoes by different mechanisms, including the collapse of steep pyroclastic deposits (e.g., scoria and ash cones), fountaining during moderately explosive eruptions, and crumbling and gravitational collapse of lava domes. They represent end-members of gravity-driven pyroclastic flows characterized by relatively small volumes (less than about 1 Mm3) and relatively thin (1–10 m) layers at high particle concentration (10–50 vol %), manifesting strong topographic control. The simulation of their dynamics and mapping of their hazards pose several different problems to researchers and practitioners, mostly due to the complex and still poorly understood rheology of the polydisperse granular mixture and to the interaction with the complex natural three-dimensional topography, which often causes rapid rheological changes. In this paper, we present IMEX_SfloW2D, a depth-averaged flow model describing the granular mixture as a single-phase granular fluid. The model is formulated in absolute Cartesian coordinates (whereby the fluid flow equations are integrated along the direction of gravity) and can be solved over a topography described by a digital elevation model. The numerical discretization and solution algorithms are formulated to allow for a robust description of wet–dry conditions (thus allowing us to accurately track the front propagation) and an implicit solution to the nonlinear friction terms. Owing to these features, the model is able to reproduce steady solutions, such as the triggering and stopping phases of the flow, without the need for empirical conditions. Benchmark cases are discussed to verify the numerical code implementation and to demonstrate the main features of the new model. A preliminary application to the simulation of the 11 February pyroclastic avalanche at the Etna volcano (Italy) is finally presented. In the present formulation, a simple semi-empirical friction model (Voellmy–Salm rheology) is implemented. However, the modular structure of the code facilitates the implementation of more specific and calibrated rheological models for pyroclastic avalanches.

Explosive volcanic eruptions release high amounts of ash into the atmosphere. Accurate tracking and forecasting of ash dispersal into the atmosphere and quantification of its uncertainty is of fundamental importance for volcanic hazard mitigation. Numerical models represent a powerful tool to monitor ash clouds in real-time, but limits and uncertainties affect numerical results. A way to improve numerical forecasts is by assimilating satellite observations of ash clouds through Data Assimilation algorithms, such as Ensemble-based Kalman Filters. In this study, we present the implementation of the so-called Local Ensemble Transform Kalman Filters inside a numerical procedure which simulates the release and transport of volcanic ash during explosive eruptions. The numerical procedure consists of the eruptive column model PLUME-MoM coupled with the tephra transport and dispersal model HYSPLIT. When satellite observations are available, ash maps supplied by PLUME-MoM/HYSPLIT are sequentially corrected/modified using ash column loading as retrieved from space. The new volcanic ash state represents the optimal solution with minimized uncertainties with respect to numerical estimates and observations. To test the Data Assimilation procedure, we used satellite observations of the volcanic cloud released during the explosive eruption that occurred at Mt. Etna (Italy) on 24 December 2018. Satellite observations have been carried out by the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) instrument, on board the Meteosat Second Generation (MSG) geostationary satellite. Results show that the assimilation procedure significantly improves the current ash state and the forecast. In addition, numerical tests show that the use of sequential Kalman Filters does not require a precise initialization of the numerical model, being able to improve the forecasts as the assimilation cycles are performed.

In the last years, the interest in three-dimensional physico-mathematical models for volcanic plumes has grown, motivated by the need of predicting accurately the dispersal patterns of volcanic ash in the atmosphere (to mitigate the risks for civil aviation and for the nearby inhabited regions) and pushed by improved remote sensing techniques and measurements. However, limitations due to the mesh resolution and numerical accuracy as well as the complexity entailed model formulations, have so far prevented a detailed study of turbulence in volcanic plumes at high resolution. Eruptive columns are indeed multiphase gas-particle turbulent flows, in which the largest (integral) scale is in the order of tens or hundreds of kilometers and the smallest scale is of the order of microns. Performing accurate numerical simulations of such phenomena remains therefore a challenging task.Modern HPC resources and recent model developments enable the study of multiphase turbulent structures of volcanic plumes with an unprecedented level of detail. However, a number of issues of the present model implementation need to be addressed in order to efficiently use the computational resources of modern supercomputing machines. Here we present an overview of an optimization strategy that allows us to perform large parallel simulations of volcanic plumes using ASHEE, a numerical solver based on OpenFOAM and one of the target flagship codes of the project ChEESE (Centre of Excellence for Exascale in Solid Earth). Such optimizations include: mixed precision floating point operations to increase computational speed and reduce memory usage, optimal domain decomposition for better communication load balancing and asynchronous I/O to hide I/O costs. Scaling analysis and volcanic plume simulations are presented to demonstrate the improvement in both computational performances and computing capability.

In this study we use PyBox, a new numerical implementation of the box-model approach, to reproduce pyroclastic density current (PDC) deposits from the Somma-Vesuvius volcano (Italy). Our simplified model assumes inertial flow front dynamics and mass deposition equations, and axisymmetric conditions inside circular sectors. Tephra volume and density, and Total Grain Size Distribution of EU3pf and EU4b/c, two well-studied PDC units from different phases of the AD 79 Pompeii eruption of Somma-Vesuvius (Italy) are used as input parameters. Such units correspond to the deposits from variably dilute, turbulent PDCs. We perform a quantitative comparison and uncertainty quantification of numerical model outputs with respect to the observed data of unit thickness, inundation areas, and grain size distribution as a function of the radial distance to the source. The simulations that we performed with PyBox were done considering: (i) polydisperse conditions, given by the total grain size distribution of the deposit, or monodisperse conditions, given by the mean Sauter diameter of the deposit; (ii) round-angle axisymmetrical collapses or divided in two circular sectors. We obtain a range of plausible initial volume concentrations of solid particles from 2.5 % to 6 %, depending on the unit and the circular sector. Optimal modelling results of flow extent and deposit thickness are reached on the EU4b/c unit in a polydisperse and sectorialized situation, indicating that using total grain size distribution and particle densities as close as possible to the real conditions significantly improve the performance of the PyBox code. The study findings suggest that the box model simplified approaches adopted have promising applications in constraining the plausible range of the input parameters of more computationally expensive models.

Accurate tracking and forecasting of ash dispersal in the atmosphere and quantification of its uncertainty are of fundamental importance for volcanic risk mitigation. Numerical models and satellite sensors offer two complementary ways to monitor ash clouds in real time, but limits and uncertainties affect both techniques. Numerical forecasts of volcanic clouds can be improved by assimilating satellite observations of atmospheric ash mass load. In this paper, we present a data assimilation procedure aimed at improving the monitoring and forecasting of volcanic ash clouds produced by explosive eruptions. In particular, we applied the Local Ensemble Transform Kalman Filter (LETKF) to the results of the Volcanic Ash Transport and Dispersion model HYSPLIT. To properly simulate the release and atmospheric transport of volcanic ash particles, HYSPLIT has been initialized with the results of the eruptive column model PLUME-MoM. The assimilation procedure has been tested against SEVIRI measurements of the volcanic cloud produced during the explosive eruption occurred at Mt. Etna on 24 December 2018. The results show how the assimilation procedure significantly improves the representation of the current ash dispersal and its forecast. In addition, the numerical tests show that the use of the sequential Ensemble Kalman Filter does not require a precise initialization of the numerical model, being able to improve the forecasts as the assimilation cycles are performed.

We developed a new fluid-dynamical numerical model, which we call convectiveFoam, designed to simulate fluids with very large Prandtl number. First we implemented the high-Pr case, in which advection still acts explicitly, and then the Pr → ∞ version, where the momentum equation becomes diagnostic (that is, without time derivatives) and it is formalized as an elliptic problem. The new solver, based on a finite volume integration method, is developed on the OpenFOAM platform and it exhibits a good performance in terms of computational costs and accuracy of the results. Scaling properties show a maximum performance around 16000 cells/core, in agreement with other works developed on the same platform. A systematic validation of the solver was performed for both 2D and 3D geometries, showing that convectiveFoam is able to reproduce the main results of several iso-viscous cases. This new solver can thus simulate idealized configurations of natural geophysical convection, such as in the Earth Mantle where Pr = 1023. This solver represents a starting point for general exploration of the behaviour and parameter dependence of several fluid systems of geological interest.

The technical report describes the physical principles, numerical method and implementation into a Python code of an integral (box) model to simulate the kinematics of pyroclastic density currents (PDCs) and the PDC invasion maps over a rugged topography.

In the framework of the IAVCEI (International Association of Volcanology and Chemistry of the Earth Interior) initiative on volcanic plume models intercomparison, we discuss three-dimensional numerical simulations performed with the multiphase flow model PDAC (Pyroclastic Dispersal Analysis Code). The model describes the dynamics of volcanic and atmospheric gases (in absence of wind) and two pyroclastic phases by adopting a non-equilibrium Eulerian–Eulerian formulation. Accordingly, gas and particulate phases are treated as interpenetrating fluids, interacting with each other through momentum (drag) and heat exchange. Numerical results describe the time-wise and spatial evolution of weak (mass eruption rate: 1.5 × 106 kg/s) and strong (mass eruption rate: 1.5 × 109 kg/s) plumes. The two tested cases display a remarkably different phenomenology, associated with the different roles of atmospheric stratification, compressibility and mechanism of buoyancy reversal, reflecting in a different structure of the plume, of the turbulent eddies and of the atmospheric circulation. This also brings about different rates of turbulent mixing and atmospheric air entrainment. The adopted multiphase flow model allows to quantify temperature and velocity differences between the gas and particles, including settling, preferential concentration by turbulence and thermal non-equilibrium, as a function of their Stokes number, i.e., the ratio between their kinetic equilibrium time and the characteristic large-eddy turnover time of the turbulent plume. As a result, the spatial and temporal distribution of coarse ash in the atmosphere significantly differs from that of the fine ash, leading to a modification of the plume shape. Finally, three-dimensional numerical results have been averaged in time and across horizontal slices in order to obtain a one-dimensional picture of the plume in a stationary regime. For the weak plume, the results are consistent with one-dimensional models, at least in the buoyant plume region, and allow to reckon a variable, effective entrainment coefficient with a mean value around 0.1 (consistently with laboratory experiments). For the strong plume, analysis of the results reveals that the two most critical assumptions of one-dimensional integral models are the self-similarity and the pressure equilibrium. In such a case, the plume appears to be controlled by the dynamics in the jet stage (below the buoyancy reversal) and by mesoscale vorticity associated with the development of the umbrella.

In the framework of the IAVCEI (International Association of Volcanology and Chemistry of the Earth Interior) intercomparison study on volcanic plume models, we present three-dimensional (3D) numerical simulations carried out with the ASHEE (ASH Equilibrium Eulerian) model. The ASHEE model solves the compressible balance equations of mass, momentum, and enthalpy of a gas-particle mixture and is able to describe the kinematic decoupling for particles characterized by Stokes number (i.e., the ratio between the particle equilibrium time and the flow characteristic time) lower than 0.2 (or particles smaller than about 1 mm). The computational fluid dynamic model is designed to accurately simulate a turbulent flow field using a Large Eddy Simulation approach, and is thus suited to analyze the role of particle non-equilibrium in the dynamics of turbulent volcanic plumes. The two reference scenarios analyzed correspond to a weak (mass eruption rate = 1.5 * 10 6 kg/s) and a strong volcanic plume (mass eruption rate = 1.5 * 10 9 kg/s) in absence of wind. For each scenario, we compare the 3D results, averaged in space and time, with theoretical results obtained from integral plume models. Such an approach enables quantitative evaluation of the effects of grid resolution and the subgrid-scale turbulence model, and the influence of gas-particle non-equilibrium processes on the large-scale plume dynamics. We thus demonstrate that the uncertainty on the numerical solution associated with such effects can be significant (of the order of 20%), but still lower than that typically associated with input data and integral model approximations. In the Weak Plume case, 3D results are consistent with the predictions of integral models in the jet and plume regions, with an entrainment coefficient around 0.10 in the plume region. In the Strong Plume case, the self-similarity assumption is less appropriate and the entrainment coefficient in the plume region is more unstable, with an average value of 0.24. For both cases, integral model predictions diverge from the 3D plume behavior in the umbrella region. The presented analysis of 3D numerical simulations thus enables identification of the critical hypotheses that underlie integral models used in operational studies. In addition, high-resolution 3D runs allow reproduction of observable quantities (such as infrasound signals) which can be useful for constraining eruption dynamics during real events.

The gravitational collapse of eruption columns generates ground-hugging pyroclastic density currents (PDCs) with highly variable temperatures, high enough to be a threat for communities surrounding volcanoes. The reasons for such great temperature variability are debated in terms of eruptive versus transport and emplacement processes. Here, using a three-dimensional multiphase model, we show that the initial temperature of PDCs linearly correlates to the percentage of collapsing mass, with a maximum temperature decrease of 45% in the case of low percentages of collapse (10%), owing to an efficient entrainment of air into the jet structure. Analyses also demonstrate that column collapse limits the dispersal capabilities of volcanic plumes, reducing their maximum height by up to 45%. Our findings provide quantitative insights into the mechanism of turbulent mixing, and suggest that temperatures of PDC deposits may serve as a marker for determining column collapse conditions, which are of primarily importance in hazard studies., Pyroclastic density currents (PDCs) are a major threat during explosive volcanic eruptions, hence the possibility to forecast them would be a vital improvement for risk mitigation. Here the authors present a 3D flow model to quantify the thermal patterns leading to volcanic ash plume collapse conditions.

Understanding the dynamics and effects of hydrothermal eruptions is crucial to the hazard assessment in both volcanic and geothermal areas. Eruptions from hydrothermal centres may occur associated with magmatic phases, but also as isolated events without magmatic input, with the most recent examples being those of Te Maari (Tongariro, New Zealand) in 2012 and Ontake (Japan) in 2014. The most recent caldera of the Island of Vulcano (southern Italy) hosts in its centre the La Fossa cone, active since 5.5 ka and now characterised by continuous fumarolic degassing. In historical times, La Fossa cone has experienced several hydrothermal eruptions, with the most violent event being the Breccia di Commenda eruption that occurred during the thirteenth century ad. Based on analysis of 170 stratigraphic logs, we show that the Breccia di Commenda eruption occurred in three main phases. After an opening, low-intensity ash emission phase (phase 1), the eruption energy climaxed during phase 2, when a series of violent explosions produced an asymmetric shower of ballistic blocks and the contemporaneous emplacement of highly dispersed, lithic-rich, blast-like pyroclastic density currents (PDCs). The tephra units emplaced during phase 2, ranging in volume from 0.2 to 2.7 × 105 m3, were covered in turn by thin ash fall deposits (phase 3). The dynamics of the most violent and intense stage of the eruption (phase 2) was investigated by numerical simulations. A three-dimensional numerical model was applied, describing the eruptive mixture as a Eulerian–Eulerian, two-phase, non-equilibrium gas-particle fluid (plus a one-way coupled Lagrangian ballistic block fraction). At the initial simulation time, a mass of about 109 kg, with initial overpressure above 10 MPa, and a temperature of 250 °C, was suddenly ejected from a 200-m-long, eastward inclined, NNE–SSW trending fissure. The mass release formed blast-like PDCs on both sides of the fissure and launched ballistic blocks eastwards. Field investigations and numerical simulations confirm that hydrothermal explosions at La Fossa cone include intense ballistic fallout of blocks, emission of PDCs potentially travelling beyond the La Fossa caldera and significant ash fallout. The hazard associated with both ballistic impact and PDC ingress, as associated with hydrothermal eruption, is significantly larger with respect to that associated with Vulcanian-type events of La Fossa.

Campi Flegrei is an active volcanic area situated in the Campanian Plain (Italy) and dominated by a resurgent caldera. The great majority of past eruptions have been explosive, variable in magnitude, intensity, and in their vent locations. In this hazard assessment study we present a probabilistic analysis using a variety of volcanological data sets to map the background spatial probability of vent opening conditional on the occurrence of an event in the foreseeable future. The analysis focuses on the reconstruction of the location of past eruptive vents in the last 15 ka, including the distribution of faults and surface fractures as being representative of areas of crustal weakness. One of our key objectives was to incorporate some of the main sources of epistemic uncertainty about the volcanic system through a structured expert elicitation, thereby quantifying uncertainties for certain important model parameters and allowing outcomes from different expert weighting models to be evaluated. Results indicate that past vent locations are the most informative factors governing the probabilities of vent opening, followed by the locations of faults and then fractures. Our vent opening probability maps highlight the presence of a sizeable region in the central eastern part of the caldera where the likelihood of new vent opening per kilometer squared is about 6 times higher than the baseline value for the whole caldera. While these probability values have substantial uncertainties associated with them, our findings provide a rational basis for hazard mapping of the next eruption at Campi Flegrei caldera.

Campi Flegrei (CF) is an example of an active caldera containing densely populated settlements at very high risk of pyroclastic density currents (PDCs). We present here an innovative method for assessing background spatial PDC hazard in a caldera setting with probabilistic invasion maps conditional on the occurrence of an explosive event. The method encompasses the probabilistic assessment of potential vent opening positions, derived in the companion paper, combined with inferences about the spatial density distribution of PDC invasion areas from a simplified flow model, informed by reconstruction of deposits from eruptions in the last 15 ka. The flow model describes the PDC kinematics and accounts for main effects of topography on flow propagation. Structured expert elicitation is used to incorporate certain sources of epistemic uncertainty, and a Monte Carlo approach is adopted to produce a set of probabilistic hazard maps for the whole CF area. Our findings show that, in case of eruption, almost the entire caldera is exposed to invasion with a mean probability of at least 5%, with peaks greater than 50% in some central areas. Some areas outside the caldera are also exposed to this danger, with mean probabilities of invasion of the order of 5–10%. Our analysis suggests that these probability estimates have location-specific uncertainties which can be substantial. The results prove to be robust with respect to alternative elicitation models and allow the influence on hazard mapping of different sources of uncertainty, and of theoretical and numerical assumptions, to be quantified.

This study presents a new method for producing long-term hazard maps for pyroclastic density currents (PDC) originating at Campi Flegrei caldera. Such method is based on a doubly stochastic approach and is able to combine the uncertainty assessments on the spatial location of the volcanic vent, the size of the flow and the expected time of such an event. The results are obtained by using a Monte Carlo approach and adopting a simplified invasion model based on the box model integral approximation. Temporal assessments are modelled through a Cox-type process including self-excitement effects, based on the eruptive record of the last 15 kyr. Mean and percentile maps of PDC invasion probability are produced, exploring their sensitivity to some sources of uncertainty and to the effects of the dependence between PDC scales and the caldera sector where they originated. Conditional maps representative of PDC originating inside limited zones of the caldera, or of PDC with a limited range of scales are also produced. Finally, the effect of assuming different time windows for the hazard estimates is explored, also including the potential occurrence of a sequence of multiple events. Assuming that the last eruption of Monte Nuovo (A.D. 1538) marked the beginning of a new epoch of activity similar to the previous ones, results of the statistical analysis indicate a mean probability of PDC invasion above 5% in the next 50 years on almost the entire caldera (with a probability peak of ~25% in the central part of the caldera). In contrast, probability values reduce by a factor of about 3 if the entire eruptive record is considered over the last 15 kyr, i.e. including both eruptive epochs and quiescent periods.

The dynamics of underexpanded volcanic jets is studied by means of a Eulerian multiphase flow model, accounting for kinetic and thermal non-equilibrium between gas and particles. Two-dimensional numerical simulations are analysed in terms of the scaling properties of the gas–solid flow based on the particle Stokes number St , defined as the ratio of the particle relaxation time τ s and a typical flow time scale, here taken as the formation time of the jet Mach disk τ M . For monodisperse mixtures, fine particles with St ≪ 1 are tightly coupled to the gas during decompression and the typical flow patterns of supersonic free jets are reproduced. The multiphase flow model, in this case, gives results comparable to a dusty-gas model. However, for St ≫ 1 we demonstrate that the effects of particle inertia and gas–particle drag are so relevant that the shock wave structure associated with gas decompression is obliterated, although the mixture velocity remains supersonic. We are therefore able to identify two different regimes of jet decompression (with/without Mach disk) that appear to be associated exclusively with the size of the ejected particles. For bidisperse mixtures, multiphase flow numerical simulations show that the features of underexpanded jet depend on the relative mass load of fine and coarse particles. A scaling analysis has been performed by means of a hybrid multiphase flow model, in which fine particles are mixed with the gas (in a dusty-gas approximation), while coarse particles are modelled as a disperse phase, with a modified Stokes number accounting for the mixture properties of the carrier pseudofluid. Both scaling analysis and numerical simulations with the hybrid model corroborate the analysis based on the Stokes number for bidisperse underexpanded jets, although particle–particle momentum exchange between particles of different size can affect the multiphase flow dynamics, especially in regimes with St ~ 1. We finally extend our analysis to polydisperse mixtures, by defining a threshold between fine and coarse particles on the basis of their Stokes number. Numerical simulations and scaling analysis based on the hybrid model (in which all fine particles are mixed with the gas in the dusty-gas approximation and the coarsest particles are described by a single hydraulically equivalent disperse phase) demonstrate that the total particle size distribution can have a significant effect on the jet decompression dynamics, potentially affecting the stability and large-scale behaviour of the volcanic column.

Processes occurring in volcanic conduits, the pathways through which magma travels from its storage region to the surface, have a fundamental control on the nature of eruptions and associated phenomena. It has been well established that magma flows, crystallizes, degasses, and fragments in conduits, that fluids migrate in and out of conduits, and that seismic and acoustic waves are generated and travel within conduits. A better un- derstanding of volcanic conduits and related processes is of paramount importance for improving eruption forecasting, volcanic hazard assess- ment and risk mitigation. However, despite escalating advances in the characterization of individual conduit processes, our understanding of their mutual interactions and the consequent control on volcanic activity is still limited. With the purpose of addressing this topic, a multidisci- plinary workshop led by a group of international scientists was hosted from 25 to 27 October 2014 by the Pisa branch of the Istituto Nazionale di Geofisica e Vulcanologia under the sponsorship of the MeMoVolc Re- search Networking Programme of the European Science Foundation. The workshop brought together the experimental, theoretical, and observa- tional communities devoted to volcanological research. After 3 days of oral and poster presentations, breakout sessions, and plenary discussions, the participants identified three main outstanding issues common to ex- perimental, analytical, numerical, and observational volcanology: unsteadiness (or transience), disequilibrium, and uncertainty. A key out- come of the workshop was to identify the specific knowledge areas in which exchange of information among the sub-disciplines would lead to efficient progress in addressing these three main outstanding issues. It was clear that multidisciplinary collaboration of this sort is essential for progressing the state of the art in understanding of conduit magma dynamics and eruption behavior. This holistic approach has the ultimate aim to deliver fundamental improvements in understanding the underly- ing processes generating and controlling volcanic activity.

Multiphase flow models represent valuable tools for the study of the complex, non-equilibrium dynamics of pyroclastic density currents. Particle sedimentation, flow stratification and rheological changes, depending on the flow regime, interaction with topographic obstacles, turbulent air entrainment, buoyancy reversal, and other complex features of pyroclastic currents can be simulated in two and three dimensions, by exploiting efficient numerical solvers and the improved computational capability of modern supercomputers. However, numerical simulations of polydisperse gas-particle mixtures are quite computationally expensive, so that their use in hazard assessment studies (where there is the need of evaluating the probability of hazardous actions over hundreds of possible scenarios) is still challenging. To this aim, a simplified integral (box) model can be used, under the appropriate hypotheses, to describe the kinematics of pyroclastic density currents over a flat topography, their scaling properties and their depositional features. In this work, multiphase flow simulations are used to evaluate integral model approximations, to calibrate its free parameters and to assess the influence of the input data on the results. Two-dimensional numerical simulations describe the generation and decoupling of a dense, basal layer (formed by progressive particle sedimentation) from the dilute transport system. In the Boussinesq regime (i.e., for solid mass fractions below about 0.1), the current Froude number (i.e., the ratio between the current inertia and buoyancy) does not strongly depend on initial conditions and it is consistent to that measured in laboratory experiments (i.e., between 1.05 and 1.2). For higher density ratios (solid mass fraction in the range 0.1–0.9) but still in a relatively dilute regime (particle volume fraction lower than 0.01), numerical simulations demonstrate that the box model is still applicable, but the Froude number depends on the reduced gravity. When the box model is opportunely calibrated with the numerical simulation results, the prediction of the flow runout is fairly accurate and the model predicts a rapid, non-linear decay of the flow kinetic energy (or dynamic pressure) with the distance from the source. The capability of PDC to overcome topographic obstacles can thus be analysed in the framework of the energy-conoid approach, in which the predicted kinetic energy of the flow front is compared with the potential energy jump associated with the elevated topography to derive a condition for blocking. Model results show that, although preferable to the energy-cone, the energy-conoid approach still has some serious limitations, mostly associated with the behaviour of the flow head. Implications of these outcomes are discussed in the context of probabilistic hazard assessment studies, in which a calibrated box model can be used as a fast pyroclastic density current emulator for Monte Carlo simulations.

An immersed boundary technique suitable for the solution of multiphase compressible equations of gas–particle flows of volcanic origin over complex 2D and 3D topographies has been developed and applied. This procedure combines and extends different existing methods designed for incompressible flows. Furthermore, the extension to compressible multiphase flows is achieved through a flux correction term in the mass continuity equations of the immersed cells that accounts for density variations in the partial volumes. The technique is computationally accurate and inexpensive, if compared to the use and implementation of the finite-volume technique on unstructured meshes. The first applications that we consider are the simulations of pyroclastic density currents generated by the collapse of a volcanic column in 2D axisymmetric geometry and by a dome explosion in 3D. Results show that the immersed boundary technique can significantly improve the description of the no-slip flow condition on an irregular topography even with relatively coarse meshes. Although the net effect of the present technique on the results is difficult to quantify in general terms, its adoption is recommended any time that cartesian grids are used to describe the large-scale dynamics of pyroclastic density currents over volcano topographies.

Pyroclastic density currents (PDCs) represent a formidable challenge for volcanology. This is true in terms of scientific understanding of their dynamics, and also in terms of assessment of their hazard and risk. These phenomena occurred in the famous, lethal 79 AD Pompeii eruption of Mt. Vesuvius, although recognition in “modern” times dates from observations made in 1902 at Montagne Pelee. Major progress in understanding has developed in the last few decades, due both to direct observations and improved modeling capability. Currently, PDC generation and propagation mechanisms are deeply investigated by field reconstructions, and also via detailed experimental and modeling studies. In this chapter we review the current status of knowledge on the dynamics of PDCs, and highlight the key processes and impacts as revealed by recent eruptive events. Some current approaches and modeling studies aimed at PDC hazard assessment are then illustrated, with specific reference to short-to-medium term hazard assessments carried out at the Soufriere Hills volcano at Montserrat (West Indies, UK), and to long-term assessments at the high-risk Vesuvius volcano and Campi Flegrei caldera (Italy). We conclude this review with remarks on the current and evolving state of knowledge of this dangerous volcanic phenomenon, and implications on the challenges for hazards mitigation. Significant limitations exist in our current ability to accurately forecast zones at risk from some PDCs, and in practice, hazard evaluations require cautious good judgment and not over-reliance on computations based on oversimplified algorithms and inputs.

Campi Flegrei (CF) is an example of an active caldera containing densely populated settlements at very high risk of pyroclastic density currents (PDCs). We present here an innovative method for assessing background spatial PDC hazard in a caldera setting with probabilistic invasion maps conditional on the occurrence of an explosive event. The method encompasses the probabilistic assessment of potential vent opening positions, derived in the companion paper, combined with inferences about the spatial density distribution of PDC invasion areas from a simplified flow model, informed by reconstruction of deposits from eruptions in the last 15 ka. The flow model describes the PDC kinematics and accounts for main effects of topography on flow propagation. Structured expert elicitation is used to incorporate certain sources of epistemic uncertainty, and a Monte Carlo approach is adopted to produce a set of probabilistic hazard maps for the whole CF area. Our findings show that, in case of eruption, almost the entire caldera is exposed to invasion with a mean probability of at least 5%, with peaks greater than 50% in some central areas. Some areas outside the caldera are also exposed to this danger, with mean probabilities of invasion of the order of 5-10%. Our analysis suggests that these probability estimates have location-specific uncertainties which can be substantial. The results prove to be robust with respect to alternative elicitation models and allow the influence on hazard mapping of different sources of uncertainty, and of theoretical and numerical assumptions, to be quantified.

Pyroclastic density currents (PDCs) are gravity currents produced by the collapse and lateral spreading of particle-laden mixtures produced during volcanic eruptions. PDCs encompass a vast array of physical processes operating at many scales of motion from the grain scale to the scale of the whole current, and these currents are widely regarded as some of the most hazardous volcanic phenomena for populations near volcanic edifices due to their rapid propagation along the ground and high temperatures. In this chapter we review the physical processes operating inside PDCs and how these processes govern the current dynamics and eventual deposits.

Vulcanian eruptions, however, are more complex to classify. Vulcanian eruptions were first distinguished by Mercalli and Silvestri (1891) who noticed that the 1888–1890 eruption of Vulcano in the Aeolian Islands was somewhat different from eruptions of nearby Stromboli volcano. Both volcanoes produced small to moderate scale, short-lived intermittent explosions, but explosions of Vulcano were louder, perhaps due to shock waves, eruption clouds were darker in color (almost black due to the presence of abundant ash), and ejected material had lower temperatures (few or no glowing ejecta were visible during daytime). The morphology of the juvenile products indicated higher viscosity and lower vesicularitymagma at Vulcano; ballistics ranged from “bread-crust bombs” to dense, angular, glassy blocks. Mercalli thus suggested that Vulcanian activity is typical for magmas of intermediate composition.

Campi Flegrei is an active volcanic area situated in the Campanian Plain (Italy) and dominated by a resurgent caldera. The great majority of past eruptions have been explosive, variable in magnitude, intensity, and in their vent locations. In this hazard assessment study we present a probabilistic analysis using a variety of volcanological data sets to map the background spatial probability of vent opening conditional on the occurrence of an event in the foreseeable future. The analysis focuses on the reconstruction of the location of past eruptive vents in the last 15 ka, including the distribution of faults and surface fractures as being representative of areas of crustal weakness. One of our key objectives was to incorporate some of the main sources of epistemic uncertainty about the volcanic system through a structured expert elicitation, thereby quantifying uncertainties for certain important model parameters and allowing outcomes from different expert weighting models to be evaluated. Results indicate that past vent locations are the most informative factors governing the probabilities of vent opening, followed by the locations of faults and then fractures. Our vent opening probability maps highlight the presence of a sizeable region in the central eastern part of the caldera where the likelihood of new vent opening per kilometer squared is about 6 times higher than the baseline value for the whole caldera. While these probability values have substantial uncertainties associated with them, our findings provide a rational basis for hazard mapping of the next eruption at Campi Flegrei caldera.

Explosive volcanic eruptions are certainly one of the most complex phenomena occurring in nature. In addition, the occurrence of pyroclastic flows, i.e. of high-velocity and high-temperature ground-hugging flows produced by the collapse of volcanic column, represent a very hazardous phenomenon for the nearby urbanized areas. To study and better understand this phenomena a parallel computer code able to simulate 3D pyroclastic flows (PDAC) has been developed. It turns out that supercomputers are required to run sufficiently accurate simulations with realistic flow conditions of explosive volcanic eruptions.

We investigate the dynamics of turbulent pyroclastic density currents (PDCs) by adopting a 3D, Eulerian-Eulerian multiphase flow model, in which solid particles are treated as a continuum and the grain-size distribution is simplified by assuming two particulate phases. The turbulent sub-grid stress of the gas phase is modelled within the framework of Large-Eddy Simulation (LES) by means of a eddy-viscosity model together with a wall closure. Despite the significant numerical diffusion associated to the upwind method adopted for the Finite-Volume discretization, numerical simulations demonstrate the need of adopting a Sub-Grid Scale (SGS) model, while revealing the complex interplay between the grid and the SGS filter sizes. We also analyse the relationship between the averaged flow dynamic pressure and the action exerted by the PDC on a cubic obstacle, to evaluate the impact of a PDC on a building. Numerical results suggest that the average flow dynamic pressure can be used as a proxy for the force per unit surface acting on the building envelope (Fig. 5), even for such steeply stratified flows. However, it is not possible to express such proportionality as a constant coefficient such as the drag coefficient in a steady-state current. The present results indeed indicate that the large epistemic and aleatory uncertainty on initial and boundary conditions has an impact on the numerical predictions which is comparable to that of grid resolution.

[1] We applied a new simulation model, based on multiphase transport laws, to describe the 4D (3D spatial coordinates plus time) dynamics of explosive eruptions. Numerical experiments, carried out on a parallel supercomputer, describe the collapse of the volcanic eruption column and the propagation of pyroclastic density currents (PDCs), for selected medium scale (sub-Plinian) eruptive scenarios at Vesuvius, Italy. Simulations provide crucial insights into the effects of the generation mechanism of the flows - partial collapse vs boiling-over - on their evolution and hazard potential, the unstable dynamics of the fountain, and the influence of Mount Somma on the propagation of PDCs into the circum-Vesuvian area, one of the world's most hazardous volcanic settings. Results also show that it is possible to characterize the volcanic column behavior in terms of percentage of the mass of pyroclasts collapsed to the ground and how this parameter strongly influences the dynamics and hazard of the associated PDCs.