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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.

In this paper, we present new ideas to greatly enhance the quality of uncertainty quantification in the DDDAS framework. We build on ongoing work in large scale transport of geophysical mass of volcanic origin – a danger to both land based installations and airborne vehicles. The principal new idea introduced is the concept of a localized Bayes linear model as a surrogate for the expensive simulator. Probability of ash presence is compared to earlier work.

In this paper we will present early work on using a DDDAS based approach to the construction of probabilistic estimates of volcanic ash transport and dispersal. Our primary modeling tools will be a combination of a plume eruption model BENT and the ash transport model PUFF. Data from satellite imagery, observation of vent parameters and windfields will drive our simulations. We will use uncertainty quantification methodology – polynomial chaos quadrature in combination with data integration to complete the DDDAS loop.

Debris flows, avalanches, landslides, and other geophysical mass flows can contain O(106–1010) m3 or more of material. These flows commonly consist of mixture of soil and rocks with a significant quantity of interstitial fluid. They can be tens of meters deep, and their runouts can extend many kilometers. The complicated rheology of such a mixture challenges every constitutive model that can reasonably be applied; the range of length and timescales involved in such mass flows challenges the computational capabilities of existing systems.This paper extends recent efforts to develop a depth averaged "thin layer" model for geophysical mass flows that contain a mixture of solid material and fluid. Concepts from the engineering community are integrated with phenomenological findings in geo-science, resulting in a theory that accounts for the principal solid and fluid forces as well as interactions between the phases, across a wide range of solid volume fraction. A principal contribution here is to present drag and phase interaction terms that comport with the literature in geo-sciences. The program predicts the evolution of the concentration and dynamic pressure. The theory is validated with with data from one dimensional dam break solutions and it is verified with data from artificial channel experiments.

This paper describes the development of highly accurate adaptive discontinuous Galerkin schemes for the solution of the equations arising from a thin layer type model of debris flows. Such flows have wide applicability in the analysis of avalanches induced by many natural calamities, e.g. volcanoes, earthquakes, etc. These schemes are coupled with special parallel solution methodologies to produce a simulation tool capable of very high-order numerical accuracy. The methodology successfully replicates cold rock avalanches at Mount Rainier, Washington and hot volcanic particulate flows at Colima Volcano, Mexico.

The collapse and decrepitation of a lava dome at the summit of a volcano generally results in the generation of dense granular flows, often referred to as block and ash flows. As the dome particles propagate from the source, they break apart by internal pressure as well as collision. The propagation of block and ash flows can be simulated to some accuracy with a depth averaged numerical model of the equations of continuity and momentum for a material with a frictional resistance. However, important features of such flows, such as the influence of remote stress through force chains, erosion of the volcano substrate, and shock formation and pressurization upon particle break up are poorly understood. In the near future, the influence of these factors will be incorporated into depth averaged models. Various numerical techniques based on particles will some day yield results that can be compared not only with bulk flow properties, but to the internal layering of block and ash flow deposits.

The Titan2D geophysical mass-flow model is evaluated by comparing its simulation results and those obtained from another flow model, FLOW3D, with published data on the 1963 Little Tahoma Peak avalanches on Mount Rainier, Washington. The avalanches, totaling approximately 10� 10 6 m 3 of broken lava blocks and other debris, traveled 6.8 km horizontally and fell 1.8 km vertically (H/L=0.246). Velocities calculated from runup range from 24 to 42 m/s and may have been as high as 130 m/s while the avalanches passed over Emmons Glacier. Titan2D is a code for an incompressible Coulomb continuum; it is a depth-averaged, dshallow-waterT, granular-flow model. The conservation equations for mass and momentum are solved with a Coulomb-type friction term at the basal interface. The governing equations are solved on multiple processors using a parallel, adaptive mesh, Godunov scheme. Adaptive gridding dynamically concentrates computing power in regions of special interest; mesh refinement and coarsening key on the perimeter of the moving avalanche. The model flow initiates as a pile defined as an ellipsoid by a height (z) and an elliptical base defined by radii in the x and y planes. Flow parameters are the internal friction angle and bed friction angle. Results from the model are similar in terms of velocity history, lateral spreading, location of runup areas, and final distribution of the Little Tahoma Peak deposit. The avalanches passed over the Emmons Glacier along their upper flow paths, but lower in the valley they traversed stream gravels and glacial outwash deposits. This presents difficulty in assigning an appropriate bed friction angle for the entire deposit. Incorporation of variable bed friction angles into the model using GIS will help to resolve this issue. D 2004 Elsevier B.V. All rights reserved.

We present a framework for modeling a dry geophysical mass of granular material -- a debris or volcanic avalanche or landslide -- flowing over an erodible surface. We also describe a computing environment that incorporates topographical data into a parallel, adaptive mesh computational algorithm that solves the model equations.