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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.

We present a benchmark study aimed at identifying the most effective modeling approach for tsunami generation, propagation, and hazard in an active volcanic context, such as the island of Stromboli (Italy). We take as a reference scenario the 2002 landslide-generated tsunami event at Stromboli simulated to assess the relative sensitivity of numerical predictions to the landslide and the wave models, with our analysis limited to the submarine landslide case. Two numerical codes, at different levels of approximation, have been compared in this study: the NHWAVE three-dimensional non-hydrostatic model in sigma-coordinates and the Multilayer-HySEA model. In particular, different instances of Multilayer-HySEA with one or more vertical discretization layers, in hydrostatic and non-hydrostatic formulation and with different landslide models have been tested. Model results have been compared for the maximum runup along the shores of Stromboli village, and the waveform sampled at four proximal sites (two of them corresponding to the locations of the monitoring gauges, offshore the Sciara del Fuoco). Both rigid and deformable (granular) submarine landslide models, with volumes ranging from 7 to 25 million of cubic meters, have been used to trigger the water waves, with different physical descriptions of the mass movement. Close to the source, the maximum surface elevation and the resulting runup at the Stromboli village shores obtained with hydrostatic and non-hydrostatic models are similar. However, hydrostatic models overestimate (with respect to non-hydrostatic ones) the amplitude of the initial positive wave crest, whose height increases with the distance. Moreover, as expected, results indicate significant differences between the waveforms produced by the different models at proximal locations. The accurate modeling of near-field waveforms is particularly critical at Stromboli in the perspective of using the installed proximal sea-level gauges, together with numerical simulations, to characterize tsunami source in an early-warning system. We show that the use of non-hydrostatic models, coupled with a multilayer approach, allows a better description of the waveforms. However, the source description remains the most sensitive (and uncertain) aspect of the modeling. We finally show that non-hydrostatic models, such as Multilayer-HySEA, solved on accelerated GPU architectures, exhibit the optimal trade-off between accuracy and computational requirements, at least for the envisaged problem size and for what concerns the proximal wave field of tsunamis generated by volcano landslides. Their application and future developments are opening new avenues to tsunami early warning at Stromboli.

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.

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.

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.

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.

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.

We have used a three-dimensional, non-equilibrium multiphase flow numerical model to simulate subplinian eruption scenarios at La Soufrière de Guadeloupe (Lesser Antilles, France). Initial and boundary conditions for computer simulations were set on the basis of independent estimates of eruption source parameters (i.e. mass eruption rate, volatile content, temperature, grain size distribution) from a field reconstruction of the 1530 CE subplinian eruption. This event is here taken as a reference scenario for hazard assessment at La Soufrière de Guadeloupe. A parametric study on eruption source parameters allowed us to quantify their influence on the simulated dynamics and, in particular, the increase of the percentage of column collapse and pyroclastic density current (PDC) intensity, at constant mass eruption rate, with variable vent diameter. Numerical results enabled us to quantify the effects of the proximal morphology on distributing the collapsing mass around the volcano and into deep and long valleys and to estimate the areas invaded by PDCs, their associated temperature and dynamic pressure. Significant impact (temperature > 300 °C and dynamic pressure > 1 kPa) in the inhabited region around the volcano is expected for fully collapsing conditions and mass eruption rates > 2 × 107 kg/s. We thus combine this spatial distribution of temperature and dynamic pressure with an objective consideration of model-related uncertainty to produce preliminary PDC hazard maps for the reference scenario. In such a representation, we identify three areas of varying degree of susceptibility to invasion by PDCs—very likely to be invaded (and highly impacted), susceptible to invasion (and moderately impacted), and unlikely to be invaded (or marginally impacted). The study also raises some key questions about the use of deterministic scenario simulations for hazard assessment, where probability distributions and uncertainties are difficult to estimate. Use of high-performance computing techniques will in part allow us to overcome such difficulties, but the problem remains open in a scientific context where validation of numerical models is still, necessarily, an incomplete and ongoing process. Nevertheless, our findings provide an important contribution to the quantitative assessment of volcanic hazard and risk at La Soufrière de Guadeloupe particularly in the context of the current unrest of the volcano and the need to prepare for a possible future reawakening of the volcano that could culminate in a magmatic explosive eruption. Supplementary Information The online version of this article (10.1007/s00445-020-01411-6) contains supplementary material, which is available to authorized users.