Models Of Volcanic Plumes Research Articles

A One‐Dimensional Volcanic Plume Model for Predicting Ash Aggregation

AbstractDuring explosive volcanic eruptions, volcanic ash is ejected into the atmosphere, impacting aircraft safety and downwind communities. These volcanic clouds tend to be dominated by fine ash (<63 μm in diameter), permitting transport over hundreds to thousands of kilometers. However, field observations show that much of this fine ash aggregates into clusters or pellets with faster settling velocities than individual particles. Models of ash transport and deposition require an understanding of aggregation processes, which depend on factors like moisture content and local particle collision rates. In this study, we develop a Plume Model for Aggregate Prediction, a one‐dimensional (1D) volcanic plume model that predicts the plume rise height, concentration of water phases, and size distribution of resulting ash aggregates from a set of eruption source parameters. The plume model uses a control volume approach to solve mass, momentum, and energy equations along the direction of the plume axis. The aggregation equation is solved using a fixed pivot technique and incorporates a sticking efficiency model developed from analog laboratory experiments of particle aggregation within a novel turbulence tower. When applied to the 2009 eruption of Redoubt Volcano, Alaska, the 1D model predicts that the majority of the plume is over‐saturated with water, leading to a high rate of aggregation. Although the mean grain size of the computed Redoubt aggregates is larger than the measured deposits, with a peak at 1 mm rather than 500 μm, the present results provide a quantitative estimate for the magnitude of aggregation in an eruption.

Flow Development and Entrainment in Turbulent Particle‐Laden Jets

AbstractExplosive eruptions expel volcanic gases and particles at high pressures and velocities. Within this multiphase fluid, small ash particles affect the flow dynamics, impacting mixing, entrainment, turbulence, and aggregation. To examine the role of turbulent particle behavior, we conducted an analogue experiment using a particle‐laden jet. We used compressed air as the carrier fluid, considering turbulent conditions at Reynolds numbers from approximately 5,000 to 20,000. Two different particles were examined: 14‐μm diameter solid nickel spheres and 13‐μm diameter hollow glass spheres. These resulted in Stokes numbers between 1 and 35 based on the convective scale. The particle mass percentage in the mixture is varied from 0.3% to more than 20%. Based on a 1‐D volcanic plume model, these Stokes numbers and mass loadings corresponded to millimeter‐scale particle diameters at heights of 4–8 km above the vent during large, sustained eruptions. Through particle image velocimetry, we measured the mean flow behavior and the turbulence statistics in the near‐exit region, primarily focusing on the dispersed phase. We show that the flow behavior is dominated by the particle inertia, with high Stokes numbers reducing the entrainment by more than 40%. When applied to volcanic plumes, these results suggest that high‐density particles can greatly increase the probability of column collapse.

Dispersion and Aging of Volcanic Aerosols After the La Soufrière Eruption in April 2021

AbstractVolcanic aerosols change the atmospheric composition and thereby affect weather and climate. Aerosol dynamic processes such as nucleation, condensation, and coagulation modify the shape, size, and mass of aerosol particles, which influence their atmospheric lifetime and radiative properties. Nevertheless, most models omit these processes for ash particles. In this work, we explore the ash aerosol aging and sulfate production during the first 4 days following the 2021 La Soufrière (St. Vincent) eruption with the ICON‐ART model (ICOsahedral Nonhydrostatic model with Aerosol and Reactive Trace gases). Online coupling of ICON‐ART with a one‐dimensional volcanic plume model calculates volcanic emission, which makes it possible to resolve the different eruption phases of the noncontinuous La Soufrière eruption. We compared our simulated aerosol distribution and composition with observations from the Cloud‐Aerosol Lidar with Orthogonal Polarization (CALIOP) instrument, the Multiangle Imaging SpectroRadiometer (MISR) Research Aerosol (RA) Algorithm, and the Barbados Cloud Observatory (BCO). We show that online coupling is essential to adequately model the emissions and plume development close to the volcano. The modeled aerosol aging is in very good agreement with observations from MISR near the emission source and with CALIOP at larger distances. Furthermore, particle aging occurs faster in the troposphere than in the stratosphere due to the availability of water vapor and OH, but a layer of coated ash appears at the plume top due to faster oxidation of SO2 and lofting by aerosol‐radiation interaction. This paper gives the first direct comparison of aerosol aging in volcanic eruption plumes between simulations and observations.

Simulating the Transport and Dispersal of Volcanic Ash Clouds With Initial Conditions Created by a 3D Plume Model

Volcanic ash transport and dispersion (VATD) models simulate atmospheric transport of ash from a volcanic source represented by parameterized concentration of ash with height. Most VATD models represent the volcanic plume source as a simple line with a parameterized ash emission rate as a function of height, constrained only by a total mass eruption rate (MER) for a given total rise height. However, the actual vertical ash distribution in volcanic plumes varies from case to case, having complex dependencies on eruption source parameters, such as grain size, speed at the vent, vent size, buoyancy flux, and atmospheric conditions. We present here for the first time the use of a three-dimensional (3D) plume model based on conservation laws to represent the ash cloud source without any prior assumption or simplification regarding plume geometry. By eliminating assumed behavior associated with a parameterized plume geometry, the predictive skill of VATD simulations is improved. We use our recently developed volcanic plume model based on a 3D smoothed-particle hydrodynamic Lagrangian method and couple the output to a standard Lagrangian VATD model. We apply the coupled model to the Pinatubo eruption in 1991 to illustrate the effectiveness of the approach. Our investigation reveals that initial particle distribution in the vertical direction, including within the umbrella cloud, has more impact on the long-range transport of ash clouds than does the horizontal distribution. Comparison with satellite data indicates that the 3D model-based distribution of ash particles through the depth of the volcanic umbrella cloud, which is much lower than the observed maximum plume height, produces improved long-range VATD simulations. We thus show that initial conditions have a significant impact on VATD, and it is possible to obtain a better estimate of initial conditions for VATD simulations with deterministic, 3D forward modeling of the volcanic plume. Such modeling may therefore provide a path to better forecasts lessening the need for user intervention, or attempts to observe details of an eruption that are beyond the resolution of any potential satellite or ground-based technique, or a posteriori creating a history of ash emission height via inversion.

PLUME-MoM-TSM 1.0.0: a volcanic column and umbrella cloud spreading model

Abstract. In this paper, we present a new version of PLUME-MoM, a 1-D integral volcanic plume model based on the method of moments for the description of the polydispersity in solid particles. The model describes the steady-state dynamics of a plume in a 3-D coordinate system, and a modification of the two-size moment (TSM) method is adopted to describe changes in grain size distribution along the plume, associated with particle loss from plume margins and with particle aggregation. For this reason, the new version is named PLUME-MoM-TSM. For the first time in a plume model, the full Smoluchowski coagulation equation is solved, allowing us to quantify the formation of aggregates during the rise of the plume. In addition, PLUME-MOM-TSM allows us to model the phase change of water, which can be either magmatic, added at the vent as liquid from external sources, or incorporated through ingestion of moist atmospheric air. Finally, the code includes the possibility to simulate the initial spreading of the umbrella cloud intruding from the volcanic column into the atmosphere. A transient shallow-water system of equations models the intrusive gravity current, allowing computation of the upwind spreading. The new model is applied first to the eruption of the Calbuco volcano in southern Chile in April 2015 and then to a sensitivity analysis of the upwind spreading of the umbrella cloud to mass flow rate and meteorological conditions (wind speed and humidity). This analysis provides an analytical relationship between the upwind spreading and some observable characteristic of the volcanic column (height of the neutral buoyancy level and plume bending), which can be used to better link plume models and volcanic-ash transport and dispersion models.

Wind Entrainment in Jets with Reversing Buoyancy: Implications for Volcanic Plumes

AbstractExplosive volcanic eruptions commonly undergo a transition from stable plume to collapsing fountain with associated destructive pyroclastic density currents. A major goal in physical volcanology is to predict quantitatively the limit between the flow regimes as a function of the source and environmental conditions. Atmospheric winds influence the dynamics and stability of the column causing bending and enhancing turbulent air entrainment. However, the predictions made with 1‐D models of volcanic plumes accounting for the presence of wind strongly depend on the wind entrainment coefficient β, a parameter whose value varies in the literature. Here we present a new theoretical model to identify an analytical criterion for column collapse in windy conditions. We then present new laboratory experiments on turbulent jets with reversing buoyancy rising in a crossflow in order to better constrain β. Our results show that a single value of can be used to describe the behavior of laboratory jets with arbitrary buoyancy. The results allow us to parameterize our 1‐D model of volcanic plumes PPM and to show the crucial importance of wind gradient and profile on volcanic column dynamics through the use of the 1991 Mt. Hudson eruption as a case study. Finally, we propose a new transition diagram between the stable plume and collapsing fountain regimes, as a function of wind speed and mass discharge rate only, which can be used for the rapid assessment of major hazards during an explosive eruption.

Transition from stable column to partial collapse during the 79 cal CE P3 Plinian eruption of Mt. Pelée volcano (Lesser Antilles)

Explosive volcanic eruptions commonly form sustained Plinian columns that collapse at some stage producing dangerous pyroclastic density currents (PDC) on the ground. Numerical and laboratory models of volcanic plumes show that the conditions leading to total column collapse are strongly controlled by the amount of exsolved gas at the source and the mass eruption rate. However, column collapse is rarely total and the volcanic jet often separates in a dense collapsing part feeding PDC and a buoyant rising plume spreading volcanic gases and pyroclasts in the atmosphere. This transitional regime has been directly observed and/or inferred from the structure of the deposits for several past eruptions, but the number of cases for which the partial collapse regime is described in detail, including the 79 CE Vesuvius, and the 186 CE Taupo eruptions, remains too small to fully constrain physical models. Here, we present a detailed reconstruction of the time evolution of the P3 eruption at Mt. Pelée volcano (Martinique, Lesser Antilles) that underwent partial column collapse in order to discuss the mechanisms controlling the eruption dynamics and improve the volcanological database on transitional eruptions. The P3 eruptive succession consists of seven major phases that produced a total of 1 km3 dense rock equivalent (DRE) of deposits (i.e., VEI 5 event), starting with a thick pumice fall deposit (0.1 km3 DRE) overlain by alternating pyroclastic density current (PDC) (0.7 km3 DRE) and pumice fall deposits (0.2 km3 DRE). We use physical models together with field data on deposit dispersal, thickness, and grain-size distribution to reconstruct the dynamical evolution of the volcanic column. Our results show that the mass eruption rate (MER) increased from 1.2 × 108 to 1.7 × 108 kg s−1 during the initial phase producing a 28 to 30 km-high Plinian plume. The MER later reached up to 2.5 × 108 kg s−1 and the column entered the partial collapse regime characterized by the formation of a small (i.e., 12 to 17 km-high) ash plume and contemporaneous PDCs mainly channelized in three paleo-valleys. These estimates are used together with published data on magmatic water contents in glass inclusions to decipher the mechanisms leading to partial collapse. The P3 eruption column collapsed due to an increase in mass eruption rate and a decrease in gas content. A similar evolution was also inferred for the 1300 CE P1 and 280 CE P2 eruption deposits, revealing a systematic behavior in the recent Plinian eruptions of Mt. Pelée volcano. The comparison of model predictions of column collapse and field data reveals a good agreement for the P1, P2, P3 and Taupo eruptions, but not for the 79 CE Vesuvius eruption where thermal disequilibrium between gas and pyroclasts most likely strongly affected the column dynamics.

Determining the three-dimensional structure of a volcanic plume using Unoccupied Aerial System (UAS) imagery

This study presents a photogrammetric method for 3D reconstruction of a volcanic plume outline to retrieve its spatial properties. A dataset of sequential multi-view images was collected, using a drone-mounted camera, for a small-scale volcanic plume emitted from Volcán Pacaya, Guatemala. A ‘Space Carving’ algorithm has been applied to estimate the plume shape, top height, volume and drift direction. The complete method workflow is presented herein, including data capture, camera projection, image segmentation, and model reconstruction. The process applied is considered the simplest approach to reconstruct a 3D plume model from sequential imagery, whilst accounting for scene evolution within a probabilistic framework. The algorithm is sensitive to the method of image segmentation, scene resolution and number of images used, with unquantifiable uncertainty in the estimated plume volume due to the lack of ground-truth data. This proof-of-concept investigation confirms that 3D quantification of volcanic plume geometry can be achieved using UAS-based photogrammetry and shows promising results for a new method of measuring volcanic source parameters to validate and adjust dispersion models of volcanic plumes.

Investigating the Accuracy of One‐Dimensional Volcanic Plume Models using Laboratory Experiments and Field Data

AbstractDuring volcanic eruptions, model predictions of plume height are limited by the accuracy of entrainment coefficients used in many plume models. Typically, two parameters are used, α and β, which relate the entrained air speed to the jet speed in the axial and cross‐flow directions, respectively. To improve estimates of these parameters, wind tunnel experiments have been conducted for a range of cross‐wind velocities and turbulence conditions. Measurements are compared directly to computations from the 1‐D plume model, Plumeria, in the near‐field, bending region of the jet. Entrainment coefficients are determined through regression analysis, demonstrating optimal combinations of effective α and β values. For turbulent conditions, all wind speeds overlapped at a single combination, α = 0.06 and β=0.46, each of which are slightly reduced from standard values. Refined coefficients were used to model plume heights for 20 historical eruptions. Model accuracy improves modestly in most cases, agreeing to within 3 km with observed plume heights. For weak eruptions, uncertainty in field measurements can outweigh the effects of these refinements, illustrating the challenge of applying plume models in practice.

Impacts of Climate Change on Volcanic Stratospheric Injections: Comparison of 1‐D and 3‐D Plume Model Projections

AbstractExplosive volcanic eruptions are one of the most important driver of climate variability. Yet, we still lack a fundamental understanding of how climate change may affect future eruptions. Here, we use an ensemble of simulations by 1‐D and 3‐D volcanic plume models spanning a large range of eruption source and atmospheric conditions to assess changes in the dynamics of future eruptive columns. Our results shed new light on differences between the predictions of 1‐D and 3‐D plume models. Furthermore, both models suggest that as a result of ongoing climate change, for tropical eruptions, (i) higher eruption intensities will be required for plumes to reach the upper troposphere/lower stratosphere and (ii) the height of plumes currently reaching the upper troposphere/lower stratosphere or above will increase. We discuss the implications of these results for the climatic impacts of future eruptions. Our simulations can directly inform climate model experiments on climate‐volcano feedback.

Marginally stable recent Plinian eruptions of Mt. Pelée volcano (Lesser Antilles): the P2 AD 280 eruption

Major volcanic hazards in the Lesser Antilles arc include powerful Plinian explosive eruptions that inject ash high into the atmosphere and produce dangerous pyroclastic density currents (PDC) on the ground. Understanding the key physical processes governing the dynamics and stability of past volcanic columns is a fundamental problem in volcanology as well as being central to assessing specific hazards in this region and elsewhere. However, the number of cases for which the transition of regime between a stable and collapsing eruptive plume is described in detail remains too small to constrain fully theoretical models of volcanic plumes. Here we present a detailed reconstruction of the time evolution of the P2 AD 280 eruption at Mt. Pelee volcano in Martinique, to expand the database available to test physical models. The P2 sequence, which forced the first inhabitants to flee to other islands for decades as suggested by archaeological evidence, starts with a basal ash layer interpreted as the result of an initial violent laterally directed explosion to the NE of the volcano. Most of the deposit sequence is made of a pumice fall deposit interbedded with a low-concentration PDC deposit interpreted as the result of a partial column collapse. The upper pumice fall unit shows an inverse gradation and is overlain by a final high-concentration PDC deposit or locally by the correlative low-concentration PDC deposit. Field data on deposit dispersal, thickness, and grain-size distribution are used together with physical models to reconstruct the dynamic evolution of this eruption. Empirical models of deposit thinning suggest that the minimum volume of pyroclastic deposits is 0.67–0.88 km3 dense rock equivalent (DRE), much larger than the 0.17 km3 DRE previously estimated. We find that the mass eruption rate increased from 6 × 107 to 1.1 × 108 kg s−1, producing an initially stable 23- to 26-km-high Plinian plume, which ultimately collapsed to form a fountain. We discuss the mechanisms leading to column collapse based on published data on magmatic water contents and our estimates of grain-size distributions and mass discharge rates. The eruption started close to the plume/fountain transition and the volcanic column ultimately collapsed mainly due to an increase in mass discharge rate. This marginally stable evolution was also inferred from analysis of the P1 AD 1300 eruption deposits, suggesting consistent behavior during the recent Plinian eruptions of Mt. Pelee volcano. In these two eruptions, the transition occurred at conditions well predicted by our theoretical model of volcanic plumes.

Seismic Data, Photographic Images and Physical Modeling of Volcanic Plumes as a Tool for Monitoring the Activity of Nevado del Ruiz Volcano, Colombia

Quantification of volcanic plume parameters is a fundamental task to know the behavior of an active volcano. Volcanic plume mass, flow rate and ash injection were determined from integration of scaling laws of several volcanic plume models, seismic data, and photographic images for the period 1985–2017 for Nevado del Ruiz Volcano (NRV), Colombia, with the aim to quantify the ash emitted volume during this period and to establish a relationship between seismicity and those volcanic plume parameters. The results show a decrease of ~ two orders of magnitude in the volume of ash plumes from the November 13, 1985 eruption (0.12 km3) to the September 1, 1989 eruption (1.43x10-3 km3). This pattern is preserved for the June 30, 2012 eruption and 2015-2017 eruptive cycle, with volumes five times smaller than in 1989. The results also show a correlation between radiated seismic energy (RSE) of the volcanic tremor and ash load for higher (>1 km) and longer-duration (>240 s) plumes. It was possible to calculate a minimum value of ash load based on radiated seismic energy (RSE) release and reduced displacement (RD) of volcanic tremor signal associated with the eruption, which could be used as a monitoring tool. Moreover, for the period 2015-2017 changes in volume of ash plume were correlated with changes in reduced displacement (RD, a way of normalizing volcanic tremor to a common scale) and RSE, associated with different stages of volcanic activity. The continuous decreasing of ash plume volumes from 1985 to 2017 suggests a same volcanic cycle almost ending. On the other hand, the evidence of new magmatic input in 2007 might suggest that a new volcanic cycle started on that date and still in process of magma ascending. Probably in the next future surface evidence of the new cycle can be observed at NRV or other volcanoes around it.

Plume-SPH 1.0: a three-dimensional, dusty-gas volcanic plume model based on smoothed particle hydrodynamics

Abstract. Plume-SPH provides the first particle-based simulation of volcanic plumes. Smoothed particle hydrodynamics (SPH) has several advantages over currently used mesh-based methods in modeling of multiphase free boundary flows like volcanic plumes. This tool will provide more accurate eruption source terms to users of volcanic ash transport and dispersion models (VATDs), greatly improving volcanic ash forecasts. The accuracy of these terms is crucial for forecasts from VATDs, and the 3-D SPH model presented here will provide better numerical accuracy. As an initial effort to exploit the feasibility and advantages of SPH in volcanic plume modeling, we adopt a relatively simple physics model (3-D dusty-gas dynamic model assuming well-mixed eruption material, dynamic equilibrium and thermodynamic equilibrium between erupted material and air that entrained into the plume, and minimal effect of winds) targeted at capturing the salient features of a volcanic plume. The documented open-source code is easily obtained and extended to incorporate other models of physics of interest to the large community of researchers investigating multiphase free boundary flows of volcanic or other origins. The Plume-SPH code (https://doi.org/10.5281/zenodo. 572819) also incorporates several newly developed techniques in SPH needed to address numerical challenges in simulating multiphase compressible turbulent flow. The code should thus be also of general interest to the much larger community of researchers using and developing SPH-based tools. In particular, the SPH−ε turbulence model is used to capture mixing at unresolved scales. Heat exchange due to turbulence is calculated by a Reynolds analogy, and a corrected SPH is used to handle tensile instability and deficiency of particle distribution near the boundaries. We also developed methodology to impose velocity inlet and pressure outlet boundary conditions, both of which are scarce in traditional implementations of SPH. The core solver of our model is parallelized with the message passing interface (MPI) obtaining good weak and strong scalability using novel techniques for data management using space-filling curves (SFCs), object creation time-based indexing and hash-table-based storage schemes. These techniques are of interest to researchers engaged in developing particles in cell-type methods. The code is first verified by 1-D shock tube tests, then by comparing velocity and concentration distribution along the central axis and on the transverse cross with experimental results of JPUE (jet or plume that is ejected from a nozzle into a uniform environment). Profiles of several integrated variables are compared with those calculated by existing 3-D plume models for an eruption with the same mass eruption rate (MER) estimated for the Mt. Pinatubo eruption of 15 June 1991. Our results are consistent with existing 3-D plume models. Analysis of the plume evolution process demonstrates that this model is able to reproduce the physics of plume development.

New insights on entrainment and condensation in volcanic plumes: Constraints from independent observations of explosive eruptions and implications for assessing their impacts

The turbulent entrainment of atmosphere and the condensation of water vapor govern the heights of explosive volcanic plumes. These processes thus determine the delivery and the lifetime of volcanic ash and aerosols into the atmosphere. Predictions of plume heights using one-dimensional “integral” models of volcanic plumes, however, suffer from very large uncertainties, related to parameterizations for entrainment and condensation. In particular, the wind entrainment coefficient β, which governs the contribution of crosswinds to turbulent entrainment, is subject to uncertainties of one order of magnitude, leading to relative uncertainties of the order of 50% on plume height. In this study, we use a database of 94 eruptive phases with independent estimates of mass eruption rate and plume height to constrain and evaluate four popular 1D models. We employ re-sampling methods to account for observational uncertainties. We show that plume height predictions are significantly improved when: i) the contribution of water vapor condensation to the plume buoyancy flux is excluded; and ii) the wind entrainment coefficient β is held constant between 0.1 and 0.4. We explore implications of these results for predicting the climate impacts of explosive eruptions and the likelihood that eruptions will form stable umbrella clouds or devastating pyroclastic flows. Last, we discuss the sensitivity of our results to the definition of plume height in the model in light of a recent set of laboratory experiments and draw conclusions for improving future databases of eruption parameters.

Large Eddy Simulation of gas–particle kinematic decoupling and turbulent entrainment in volcanic plumes

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 1mm). 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*106 kg/s) and a strong volcanic plume (mass eruption rate=1.5*109 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.

Inter-comparison of three-dimensional models of volcanic plumes

We performed an inter-comparison study of three-dimensional models of volcanic plumes. A set of common volcanological input parameters and meteorological conditions were provided for two kinds of eruptions, representing a weak and a strong eruption column. From the different models, we compared the maximum plume height, neutral buoyancy level (where plume density equals that of the atmosphere), and level of maximum radial spreading of the umbrella cloud. We also compared the vertical profiles of eruption column properties, integrated across cross-sections of the plume (integral variables). Although the models use different numerical procedures and treatments of subgrid turbulence and particle dynamics, the inter-comparison shows qualitatively consistent results. In the weak plume case (mass eruption rate 1.5×106kgs−1), the vertical profiles of plume properties (e.g., vertical velocity, temperature) are similar among models, especially in the buoyant plume region. Variability among the simulated maximum heights is ~20%, whereas neutral buoyancy level and level of maximum radial spreading vary by ~10%. Time-averaging of the three-dimensional (3D) flow fields indicates an effective entrainment coefficient around 0.1 in the buoyant plume region, with much lower values in the jet region, which is consistent with findings of small-scale laboratory experiments. On the other hand, the strong plume case (mass eruption rate 1.5×109kgs−1) shows greater variability in the vertical plume profiles predicted by the different models. Our analysis suggests that the unstable flow dynamics in the strong plume enhances differences in the formulation and numerical solution of the models. This is especially evident in the overshooting top of the plume, which extends a significant portion (~1/8) of the maximum plume height. Nonetheless, overall variability in the spreading level and neutral buoyancy level is ~20%, whereas that of maximum height is ~10%. This inter-comparison study has highlighted the different capabilities of 3D volcanic plume models, and identified key features of weak and strong plumes, including the roles of jet stability, entrainment efficiency, and particle non-equilibrium, which deserve future investigation in field, laboratory, and numerical studies.

Non-equilibrium processes in ash-laden volcanic plumes: new insights from 3D multiphase flow simulations

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.

On the relationship between eruption intensity and volcanic plume height: Insights from three-dimensional numerical simulations

Height of plumes generated during explosive volcanic eruptions is commonly used to estimate the associated eruption intensity (i.e., mass eruption rate; MER). In order to quantify the relationship between plume height and MER, we performed a parametric study using a three-dimensional (3D) numerical model of volcanic plumes for different vent sizes. The results of five simulations indicate that the flow pattern in the lower region of the plume systematically changes with vent size, and hence, with MER. For MERs <4×107kgs−1, the flow in the lower region has a jet-like structure (the jet-like regime). For MERs >108kgs−1, the flow shows a fountain-like structure (the fountain-like regime). The flow pattern of plumes with 4×107kgs−1<MERs <108kgs−1 shows transitional features between the two flow regimes. Within each of the two flow regimes, the plume height increases as the MER increases, whereas plume heights remain almost constant or even decrease as MER increases in the transitional regime; as a result, the jet-like and fountain-like regimes show distinct relationships of plume height and MER. The different relationships between the two regimes reflect the fact that the efficiency of entrainment of ambient air in the jet-like regime is substantially lower than that in the fountain-like regime. It is suggested that, in order to estimate eruption intensity from the observed plume heights, it is necessary to take the different flow regimes depending on MER into account.

A global sensitivity analysis of the PlumeRise model of volcanic plumes

Integral models of volcanic plumes allow predictions of plume dynamics to be made and the rapid estimation of volcanic source conditions from observations of the plume height by model inversion. Here we introduce PlumeRise, an integral model of volcanic plumes that incorporates a description of the state of the atmosphere, includes the effects of wind and the phase change of water, and has been developed as a freely available web-based tool. The model can be used to estimate the height of a volcanic plume when the source conditions are specified, or to infer the strength of the source from an observed plume height through a model inversion. The predictions of the volcanic plume dynamics produced by the model are analysed in four case studies in which the atmospheric conditions and the strength of the source are varied. A global sensitivity analysis of the model to a selection of model inputs is performed and the results are analysed using parallel coordinate plots for visualisation and variance-based sensitivity indices to quantify the sensitivity of model outputs. We find that if the atmospheric conditions do not vary widely then there is a small set of model inputs that strongly influence the model predictions. When estimating the height of the plume, the source mass flux has a controlling influence on the model prediction, while variations in the plume height strongly effect the inferred value of the source mass flux when performing inversion studies. The values taken for the entrainment coefficients have a particularly important effect on the quantitative predictions. The dependencies of the model outputs to variations in the inputs are discussed and compared to simple algebraic expressions that relate source conditions to the height of the plume.

Sensitivity analysis of a one-dimensional model of a volcanic plume with particle fallout and collapse behavior

We run a volcanic plume model with uncertain boundary conditions and entrainment related model parameters. Output variables tested for their sensitivity to the inputs are total rise height, and mass flux of particles into the umbrella cloud or downwind plume. Boundary or source conditions are vent radius, initial velocity, grain size mean and grain size standard deviation. Model parameters are entrainment rate, α, wind entrainment rate, β, and wind speed.Five sensitivity metrics were considered. Three of these are calculated for each given point in the input parameter space, by perturbing the input variable around fixed points. Two global sensitivity measures quantify the impact on the output of the input over its entire uncertain domain.We find that vent radius and initial speed have a much more profound effect on both outputs than does total grain size distribution. Plume rise height and particle mass flux are sensitive to the entrainment parameters, α and β, but these parameters are not of greater importance than the wind speed. This suggests that while efforts to better characterize entrainment parameters through laboratory experiments is important, similar efforts should be made to collect appropriate meteorological data for the region near the site of the eruption.