Models Of Volcanic Plumes Research Articles

Results of the eruptive column model inter-comparison study

This study compares and evaluates one-dimensional (1D) and three-dimensional (3D) numerical models of volcanic eruption columns in a set of different inter-comparison exercises. The exercises were designed as a blind test in which a set of common input parameters was given for two reference eruptions, representing a strong and a weak eruption column under different meteorological conditions. Comparing the results of the different models allows us to evaluate their capabilities and target areas for future improvement. Despite their different formulations, the 1D and 3D models provide reasonably consistent predictions of some of the key global descriptors of the volcanic plumes. Variability in plume height, estimated from the standard deviation of model predictions, is within ~20% for the weak plume and ~10% for the strong plume. Predictions of neutral buoyancy level are also in reasonably good agreement among the different models, with a standard deviation ranging from 9 to 19% (the latter for the weak plume in a windy atmosphere). Overall, these discrepancies are in the range of observational uncertainty of column height. However, there are important differences amongst models in terms of local properties along the plume axis, particularly for the strong plume. Our analysis suggests that the simplified treatment of entrainment in 1D models is adequate to resolve the general behaviour of the weak plume. However, it is inadequate to capture complex features of the strong plume, such as large vortices, partial column collapse, or gravitational fountaining that strongly enhance entrainment in the lower atmosphere. We conclude that there is a need to more accurately quantify entrainment rates, improve the representation of plume radius, and incorporate the effects of column instability in future versions of 1D volcanic plume models.

FPLUME-1.0: An integral volcanic plume model accounting for ash aggregation

Abstract. Eruption source parameters (ESP) characterizing volcanic eruption plumes are crucial inputs for atmospheric tephra dispersal models, used for hazard assessment and risk mitigation. We present FPLUME-1.0, a steady-state 1-D (one-dimensional) cross-section-averaged eruption column model based on the buoyant plume theory (BPT). The model accounts for plume bending by wind, entrainment of ambient moisture, effects of water phase changes, particle fallout and re-entrainment, a new parameterization for the air entrainment coefficients and a model for wet aggregation of ash particles in the presence of liquid water or ice. In the occurrence of wet aggregation, the model predicts an effective grain size distribution depleted in fines with respect to that erupted at the vent. Given a wind profile, the model can be used to determine the column height from the eruption mass flow rate or vice versa. The ultimate goal is to improve ash cloud dispersal forecasts by better constraining the ESP (column height, eruption rate and vertical distribution of mass) and the effective particle grain size distribution resulting from eventual wet aggregation within the plume. As test cases we apply the model to the eruptive phase-B of the 4 April 1982 El Chichón volcano eruption (México) and the 6 May 2010 Eyjafjallajökull eruption phase (Iceland). The modular structure of the code facilitates the implementation in the future code versions of more quantitative ash aggregation parameterization as further observations and experiment data will be available for better constraining ash aggregation processes.

Uncertainty analysis of a model of wind-blown volcanic plumes.

Mathematical models of natural processes can be used as inversion tools to predict unobserved properties from measured quantities. Uncertainty in observations and model formulation impact on the efficacy of inverse modelling. We present a general methodology, history matching, that can be used to investigate the effect of observational and model uncertainty on inverse modelling studies. We demonstrate history matching on an integral model of volcanic plumes that is used to estimate source conditions from observations of the rise height of plumes during the eruptions of Eyjafjallajökull, Iceland, in 2010 and Grímsvötn, Iceland, in 2011. Sources of uncertainty are identified and quantified, and propagated through the integral plume model. A preliminary sensitivity analysis is performed to identify the uncertain model parameters that strongly influence model predictions. Model predictions are assessed against observations through an implausibility measure that rules out model inputs that are considered implausible given the quantified uncertainty. We demonstrate that the source mass flux at the volcano can be estimated from plume height observations, but the magmatic temperature, exit velocity and exsolved gas mass fraction cannot be accurately determined. Uncertainty in plume height observations and entrainment coefficients results in a large range of plausible values of the source mass flux. Our analysis shows that better constraints on entrainment coefficients for volcanic plumes and more precise observations of plume height are required to obtain tightly constrained estimates of the source mass flux.

Effects of wind on entrainment efficiency in volcanic plumes

AbstractThe entrainment of air by turbulent mixing plays a central role in the dynamics of volcanic eruption clouds, as the amount of entrained air controls the height of the plume. In one‐dimensional models of volcanic plumes, the efficiency of entrainment under a wind field is parameterized using two empirical constants. The first is the coefficient associated with the entrainment caused by the shear between the volcanic plume and the ambient air (i.e., the radial entrainment coefficient), and the other is associated with the entrainment caused by wind (i.e., the wind entrainment coefficient). In this study, we used three‐dimensional numerical simulations of volcanic plumes to determine the effective values of these empirical constants from the relationship between eruption conditions and plume heights. These simulations suggest that the value of the radial entrainment coefficient is 0.05–0.06, which is slightly smaller than that of pure jets or plumes seen in laboratory experiments (0.07–0.15). The value of the wind entrainment coefficient was estimated to be 0.1–0.3, which is significantly smaller than those estimated from laboratory experiments (0.3–1.0). The entrainment coefficients derived from these simulations successfully explain the observations made during the 2011 Shinmoe‐dake eruptions in which the volcanic plumes were significantly distorted by the wind.

PLUME-MoM 1.0: A new integral model of volcanic plumes based on the method of moments

Abstract. In this paper a new integral mathematical model for volcanic plumes, named PLUME-MoM, is presented. The model describes the steady-state dynamics of a plume in a 3-D coordinate system, accounting for continuous variability in particle size distribution of the pyroclastic mixture ejected at the vent. Volcanic plumes are composed of pyroclastic particles of many different sizes ranging from a few microns up to several centimeters and more. A proper description of such a multi-particle nature is crucial when quantifying changes in grain-size distribution along the plume and, therefore, for better characterization of source conditions of ash dispersal models. The new model is based on the method of moments, which allows for a description of the pyroclastic mixture dynamics not only in the spatial domain but also in the space of parameters of the continuous size distribution of the particles. This is achieved by formulation of fundamental transport equations for the multi-particle mixture with respect to the different moments of the grain-size distribution. Different formulations, in terms of the distribution of the particle number, as well as of the mass distribution expressed in terms of the Krumbein log scale, are also derived. Comparison between the new moments-based formulation and the classical approach, based on the discretization of the mixture in N discrete phases, shows that the new model allows for the same results to be obtained with a significantly lower computational cost (particularly when a large number of discrete phases is adopted). Application of the new model, coupled with uncertainty quantification and global sensitivity analyses, enables the investigation of the response of four key output variables (mean and standard deviation of the grain-size distribution at the top of the plume, plume height and amount of mass lost by the plume during the ascent) to changes in the main input parameters (mean and standard deviation) characterizing the pyroclastic mixture at the base of the plume. Results show that, for the range of parameters investigated and without considering interparticle processes such as aggregation or comminution, the grain-size distribution at the top of the plume is remarkably similar to that at the base and that the plume height is only weakly affected by the parameters of the grain distribution. The adopted approach can be potentially extended to the consideration of key particle–particle effects occurring in the plume including particle aggregation and fragmentation.

Charge structure in volcanic plumes: a comparison of plume properties predicted by an integral plume model to observations of volcanic lightning during the 2010 eruption of Eyjafjallajökull, Iceland.

Observations of volcanic lightning made using a lightning mapping array during the 2010 eruption of Eyjafjallajökull allow the trajectory and growth of the volcanic plume to be determined. The lightning observations are compared with predictions of an integral model of volcanic plumes that includes descriptions of the interaction with wind and the effects of moisture. We show that the trajectory predicted by the integral model closely matches the observational data and the model well describes the growth of the plume downwind of the vent. Analysis of the lightning signals reveals information on the dominant charge structure within the volcanic plume. During the Eyjafjallajökull eruption both monopole and dipole charge structures were observed in the plume. By using the integral plume model, we propose the varying charge structure is connected to the availability of condensed water and low temperatures at high altitudes in the plume, suggesting ice formation may have contributed to the generation of a dipole charge structure via thunderstorm-style ice-based charging mechanisms, though overall this charging mechanism is believed to have had only a weak influence on the production of lightning.

Testing the accuracy of a 1‐D volcanic plume model in estimating mass eruption rate

AbstractDuring volcanic eruptions, empirical relationships are used to estimate mass eruption rate from plume height. Although simple, such relationships can be inaccurate and can underestimate rates in windy conditions. One‐dimensional plume models can incorporate atmospheric conditions and give potentially more accurate estimates. Here I present a 1‐D model for plumes in crosswind and simulate 25 historical eruptions where plume height Hobs was well observed and mass eruption rate Mobs could be calculated from mapped deposit mass and observed duration. The simulations considered wind, temperature, and phase changes of water. Atmospheric conditions were obtained from the National Center for Atmospheric Research Reanalysis 2.5° model. Simulations calculate the minimum, maximum, and average values (Mmin, Mmax, and Mavg) that fit the plume height. Eruption rates were also estimated from the empirical formula Mempir = 140Hobs4.14 (Mempir is in kilogram per second, Hobs is in kilometer). For these eruptions, the standard error of the residual in log space is about 0.53 for Mavg and 0.50 for Mempir. Thus, for this data set, the model is slightly less accurate at predicting Mobs than the empirical curve. The inability of this model to improve eruption rate estimates may lie in the limited accuracy of even well‐observed plume heights, inaccurate model formulation, or the fact that most eruptions examined were not highly influenced by wind. For the low, wind‐blown plume of 14–18 April 2010 at Eyjafjallajökull, where an accurate plume height time series is available, modeled rates do agree better with Mobs than Mempir.

Using simple plume models to refine the source mass flux of volcanic eruptions according to atmospheric conditions

A simple three-dimensional volcanic plume model that incorporates the effects of moisture and ambient wind is presented and used iteratively to refine the source mass flux, obtained from an empirical relationship between the plume rise height and source mass flux, according to the prevailing atmospheric conditions. It is applied to the eruption of Eyjafjallajökull in May 2010 using realistic atmospheric profiles appropriate to the time of the eruption. It is shown that the ambient wind has the largest effect on the refined source mass flux with moisture playing a secondary though still important role. It is also shown that significant differences in the values of the revised source mass fluxes can arise when the realistic atmospheric profiles are approximated by idealised profiles. The revised source mass flux is used to initialise a long-range dispersion model of ash in the atmosphere.

Interaction between volcanic plumes and wind during the 2010 Eyjafjallajökull eruption, Iceland

Estimates of volcanic source mass flux, currently deduced from observations of plume height, are crucial for ash dispersion models for aviation and population hazard. This study addresses the role of the atmospheric wind in determining the height at which volcanic plumes spread in the atmosphere and the relationship between source mass flux and plume height in a wind field. We present a predictive model of volcanic plumes that describes the bending over of the plume trajectory in a crosswind and show that model predictions are in accord with a dataset of historic eruptions if the profile of atmospheric wind shear is described. The wind restricts the rise height of volcanic plumes such that obtaining equivalent rise heights for a plume in a windy environment would require an order of magnitude increase in the source mass flux over a plume in a quiescent environment. Our model calculations are used to calibrate a semi‐empirical relationship between the plume height and the source mass flux that explicitly includes the atmospheric wind speed. We demonstrate that the model can account for the variations in plume height observed during the first explosive phase of the 2010 Eyjafjallajökull eruption using independently measured wind speeds and show that changes in the observed plume height are better explained by changing meteorology than abrupt changes in the source mass flux. This study shows that unless the wind is properly accounted for, estimates of the source mass flux during an explosive eruption are likely to be very significant underpredictions of the volcanic source conditions.

The impact of the atmosphere on the Eyjafjallajökull 2010 eruption plume

The eruption of Eyjafjallajökull volcano in 2010 lasted 39 days, 14 April–23 May. The eruption had two explosive phases separated by a phase with lava formation and reduced explosive activity. During the explosive phases there were episodes of strong winds that advected ash to the south and southeast leading to widespread disruptions in air traffic. The height of the eruption plume was monitored with a weather radar and with web cameras mounted with a view of the volcano. Three different types of the impact of the ambient atmosphere on the eruption plume are described. First, the weather situation throughout the eruption has been analyzed. The frequency of northerly wind component is found to be unusually high, or 71% in comparison to 49% on average in spring. Secondly, during the effusive phase of the eruption diurnal variation was observed in the plume altitude and there is evidence that suggest that nocturnal inversions may have played a role, limiting the rise of the weak plume. Thirdly, images from a web camera were analyzed and the rise of individual cloud heads associated with explosions at the volcano vent mapped. The velocity profiles obtained largely agree with conceptual models of volcanic plumes.

Complex proximal sedimentation from Plinian plumes: the example of Tarawera 1886

The 1886 eruption of Tarawera, New Zealand, was unusual for a Plinian eruption because it involved entirely basaltic magma, originated in a 17-km-long fissure, and produced extremely overthickened proximal deposits with a complex geometry. This study focuses on an 8-km-long segment cutting across Mount Tarawera where over 50 point-source vents were active during the 5.5-h eruption. A detailed characterization of the proximal deposits is developed and used to interpret the range of styles and intensities of the vents, including changes with time. We identify the four vents that contributed most heavily to the Plinian fall and evaluate the extent to which current volcanic plume models are compatible with the depositional patterns at Tarawera. Three proximal units are mapped that have phreatomagmatic, magmatic, and phreatomagmatic characteristics, respectively. Within the magmatic proximal unit, beds of like character are grouped into packages and delineated on scaled cross sections. Package dispersal is quantified by measuring the linear thickness half-distance (t1/2) in the planes of the fissure walls. Most packages have localized dispersals (low t1/2), indicating that Strombolian-style activity dominated most vents. The more widely dispersed packages (high t1/2) reflect contributions from additional transport regimes that were more vigorous but still contributed considerable material to the proximal region. We conclude that the geometry of the observed proximal deposits requires three modes of fall transport: (1) fallout from the upper portions of the Plinian plumes produced principally by vents in four craters; (2) sedimentation from the margins of the lower portions of the Plinian plumes including the jets and possibly the lower convective regions; and (3) ejection by weak Strombolian-style explosions from vents that did not contribute significant volumes of particles to the high plume. We suggest that the curvature of the velocity profile across the jet region of each plume (1–4 km height) was important, and that the lower velocity at the margins allowed proximal deposition of a large volume of material with a wide grain-size range.

Density, construction, and drag coefficient of electrostatic volcanic ash aggregates

Recent laboratory experiments have demonstrated that electrostatic charges generated during the fragmentation of volcanic pumice cause rapid aggregation of the silicate particles produced. Here, we present measurements of the mass and component particle size distribution of individual, electrostatically bound aggregates produced during these experiments. Particles produced by fracturing pumice aggregated as they fell ∼1.5 m within an enclosed fall chamber. Aggregate mass measurements indicate aggregate densities of ∼200 kg m−3 or less. The component particle size analysis demonstrates exponential‐type cumulative distributions which are dominated (on a volume basis) by particles ∼10–40 μm in diameter and contain few particles >70 μm. By representing these particles as disks of 5 μm thickness the calculated aggregate densities are in agreement with those derived from the aggregate mass measurements and indicate a relatively constant aggregate density with size (in contrast with previous results from fall velocities). Combining the density measurements with fall velocity data allows the drag coefficient of aggregates to be determined. Empirical equations developed to describe the particle size distribution within aggregates are used to derive relative aggregation coefficients for the electrostatic aggregation process. Our results can be used within numerical models of volcanic plumes in order to improve their representation of electrostatic aggregation processes.