A theoretical model of a volcanic plume, based on applying the equations of motion in a plume‐centered coordinate system, suggests that the interaction between a volcanic plume and wind causes ...enhanced entrainment of air and horizontal momentum, plume bending, and a decrease in plume rise height at constant eruption rate. Because of rapid dilution in the high windspeeds of the polar jet, plumes that vary over more than one order of magnitude in mass eruption rate (106 to 107–108 kg/s), if injected into the polar jet, may all attain rise heights only slightly different from that of the core of the jet, ∼ 10 km, as opposed to 17–33 km in a still atmosphere.
The behaviour of low-viscosity, pressure-driven compressible pore fluid flows in viscously deformable porous media is studied here with specific application to gas flow in lava domes. The combined ...flow of gas and lava is shown to be governed by a two-equation set of nonlinear mixed hyperbolic–parabolic type partial differential equations describing the evolution of gas pore pressure and lava porosity. Steady state solution of this system is achieved when the gas pore pressure is magmastatic and the porosity profile accommodates the magmastatic pressure condition by increased compaction of the medium with depth. A one-dimensional (vertical) numerical linear stability analysis (LSA) is presented here. As a consequence of the pore-fluid compressibility and the presence of gravitation compaction, the gradients present in the steady-state solution cause variable coefficients in the linearized equations which generate instability in the LSA despite the diffusion-like and dissipative terms in the original system. The onset of this instability is shown to be strongly controlled by the thickness of the flow and the maximum porosity, itself a function of the mass flow rate of gas. Numerical solutions of the fully nonlinear system are also presented and exhibit nonlinear wave propagation features such as shock formation. As applied to gas flow within lava domes, the details of this dynamics help explain observations of cyclic lava dome extrusion and explosion episodes. Because the instability is stronger in thicker flows, the continued extrusion and thickening of a lava dome constitutes an increasing likelihood of instability onset, pressure wave growth and ultimately explosion.
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.
•We present the main results of an eruptive column model inter-comparison exercise.•Simulations with standard inputs for strong and weak eruptive plumes were performed.•We compare results of empirical, one-dimensional, and three-dimensional models.•Results allowed for evaluating model capabilities and areas for model improvement.
Volcanic ash advisory centers are charged with forecasting the movement of volcanic ash plumes, for aviation, health and safety preparation. Deterministic mathematical equations model the advection ...and dispersion of these plumes. However initial plume conditions – height, profile of particle location, volcanic vent parameters – are known only approximately at best, and other features of the governing system such as the windfield are stochastic. These uncertainties make forecasting plume motion difficult. As a result of these uncertainties, ash advisories based on a deterministic approach tend to be conservative, and many times over/under estimate the extent of a plume. This paper presents an end-to-end framework for generating a probabilistic approach to ash plume forecasting. This framework uses an ensemble of solutions, guided by Conjugate Unscented Transform (CUT) method for evaluating expectation integrals. This ensemble is used to construct a polynomial chaos expansion that can be sampled cheaply, to provide a probabilistic model forecast. The CUT method is then combined with a minimum variance condition, to provide a full posterior pdf of the uncertain source parameters, based on observed satellite imagery.
The April 2010 eruption of the Eyjafjallajökull volcano in Iceland is employed as a test example. The puff advection/dispersion model is used to hindcast the motion of the ash plume through time, concentrating on the period 14–16 April 2010. Variability in the height and particle loading of that eruption is introduced through a volcano column model called bent. Output uncertainty due to the assumed uncertain input parameter probability distributions, and a probabilistic spatial-temporal estimate of ash presence are computed.
High-fidelity computational simulation can be an invaluable tool in planning strategies for hazard risk mitigation. The accuracy and reliability of the predictions are crucial elements of these tools ...being successful. We present here a new simulation tool for dry granular avalanches using several new techniques for enhancing numerical solution accuracy.
Highlights of our new methodology are the use of a depth-averaged model of the conservation laws and an adaptive grid Godunov solver to solve the resulting equations. The software is designed to run on distributed memory supercomputers and makes use of digital elevation data dynamically, i.e., refine the grid and input data to finer resolutions to better capture flow features as the flow evolves. Our simulations are validated using quantitative and qualitative comparisons to tabletop experiments and data from field observations. Our software is freely available and uses only publicly available libraries and hence can be used on a wide range of hardware and software platforms.
This paper presents several standard and new methods for characterizing the effect of input data uncertainty on model output for hazardous geophysical mass flows. Note that we do not attempt here to ...characterize the inherent randomness of such flow events. We focus here on the problem of characterizing uncertainty in model output due to lack of knowledge of such input for a particular event. Methods applied include classical Monte Carlo and Latin hypercube sampling and more recent stochastic collocation, polynomial chaos, spectral projection and a newly developed extension thereof named polynomial chaos quadrature. The simple and robust samplings based Monte Carlo type methods are usually computationally intractable for reasonable physical models, while the more sophisticated and computationally efficient polynomial chaos method often breaks down for complex models. The spectral projection and polynomial chaos quadrature methods discussed here produce results of quality comparable to the polynomial chaos type methods while preserving the simplicity and robustness of the Monte Carlo‐type sampling based approaches at much lower cost. The computational efficiency, however, degrades with increasing numbers of random variables. A procedure for converting the output uncertainty characterization into a map showing the probability of a hazard threshold being exceeded is also presented. The uncertainty quantification procedures are applied first in simple settings to illustrate the procedure and then subsequently applied to the 1991 block‐and‐ash flows at Colima Volcano, Mexico.
Characteristics of the Panum block-and-ash flow (BAF) deposit, Mono Craters, CA, were analyzed to determine the mechanisms of collapse of the parent dome and dynamics of emplacement of the BAF. ...Granulometry, componentry, and obsidian water content data were used to define distinct facies of the Panum BAF deposit. These suggest a sequential, three-stage collapse model for the ancestral dome of the Panum vent, with destabilization first of its cold, brittle outer margins and then of its hot, ductile interior to an estimated depth of ~260m below the free-air surface.
Impact marks on clast faces that resulted from clast-to-clast interactions recorded details of the impacting mechanism. We analyzed ~15,000 marks and report for the first time their size, shape, and sorting to infer the flow regime of the BAF during emplacement, to a distance of ~2.6km from the vent. Clast-to-clast interactions occurred over a broad spectrum from purely collisional (normal to clast faces) to purely frictional (clasts shearing in a unidirectional flow), and recorded a transition to a more frictional flow regime in distal reaches as the sliding head of the BAF decelerated and halted. Finally, we briefly differentiate a similar, but previously undescribed older deposit that predates the 1325–1350A.D. North Mono eruptive episode.
•Impact marks record clast-to-clast interactions during block-and-ash flow emplacement•Impact style can be used to infer flow regime during flow emplacement•Flow regime shifts to more frictional component as flow slows and stops•Separate facies of the deposit indicate sequence, mechanism of parent dome collapse
This paper describes a new methodology to quantify the variation in the output of a computational fluid dynamics model for block and ash flows, when the digital elevation model (DEM) of the terrain ...and other inputs are given as a range of possible values with a prescribed uncertainty. Integrating these variations in the possible flows as a function of input uncertainties provides well-defined hazard probabilities at specific locations, i.e. a hazard map. Earlier work provided a methodology for assessing hazards based on variations in flow initiation and friction parameters. This paper extends this approach to include the effect of terrain error and uncertainty. The results are based on potential flows at Mammoth Mountain, CA, and Galeras Volcano, Colombia. The analysis establishes the soundness of the approach and the effect of including the uncertainty in DEMs in the construction of probabilistic hazard maps.
Uncertainty in predictions from a model of volcanic ash transport in the atmosphere arises from uncertainty in both eruption source parameters and the model wind field. In a previous contribution, we ...analyzed the probability of ash cloud presence using weighted samples of volcanic ash transport and dispersal model runs and a reanalysis wind field to propagate uncertainty in eruption source parameters alone. In this contribution, the probabilistic modeling is extended by using ensemble forecast wind fields as well as uncertain source parameters. The impact on ash transport of variability in wind fields due to unresolved scales of motion as well as model physics uncertainty is also explored. We have therefore generated a weighted, probabilistic forecast of volcanic ash transport with only a priori information, exploring uncertainty in both the wind field and the volcanic source.
Key Points:
First time‐varying probabilistic ash cloud forecast maps
High‐fidelity probability mapping with moment optimization and high‐resolution winds
Testing of outputs with standard metrics and against multimodel and SKEB
Digital elevation models (DEMs) used in geospatial analysis like the simulation of geophysical flows, such as floods, landslides, and block and ash flows, differ in resolution, acquisition time and ...generation methodology, which results in varied representation of topographic features. This study investigates the effects of DEMs on the output of a granular flow model, TITAN2D by comparing the output using different DEMs to that obtained with a “true” representation of the terrain, which is considered to be that obtained by using TOPSAR 5 m data. Seven DEMs at four resolutions from four sources were used for Mammoth Mountain, California, a cumulodome volcano. TITAN2D was run for seven different locations of an eruption of a potential dome and two different collapse volumes. The resulting outputs were subsequently compared with TOPSAR 5 m output, and qualitative and statistical inferences were drawn. DEMs with different resolutions and sources generated different outputs that led to different flow maps. For moderate and smaller scale flows (
m
3
–
), different representations can affect the computation of accurate footprint of the flow and fine DEM resolution is critical for correct characterization of these flows.
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