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We detail a new prediction-oriented procedure aimed at volcanic hazard assessment based on geophysical mass flow models constrained with heterogeneous and poorly defined data. Our method relies on an itemized application of the empirical falsification principle over an arbitrarily wide envelope of possible input conditions. We thus provide a first step towards a objective and partially automated experimental design construction. In particular, instead of fully calibrating model inputs on past observations, we create and explore more general requirements of consistency, and then we separately use each piece of empirical data to remove those input values that are not compatible with it. Hence, partial solutions are defined to the inverse problem. This has several advantages compared to a traditionally posed inverse problem: (i) the potentially nonempty inverse images of partial solutions of multiple possible forward models characterize the solutions to the inverse problem; (ii) the partial solutions can provide hazard estimates under weaker constraints, potentially including extreme cases that are important for hazard analysis; (iii) if multiple models are applicable, specific performance scores against each piece of empirical information can be calculated. We apply our procedure to the case study of the Atenquique volcaniclastic debris flow, which occurred on the flanks of Nevado de Colima volcano (Mexico), 1955. We adopt and compare three depth-averaged models currently implemented in the TITAN2D solver, available from https://vhub.org (Version 4.0.0 – last access: 23 June 2016). The associated inverse problem is not well-posed if approached in a traditional way. We show that our procedure can extract valuable information for hazard assessment, allowing the exploration of the impact of synthetic flows that are similar to those that occurred in the past but different in plausible ways. The implementation of multiple models is thus a crucial aspect of our approach, as they can allow the covering of other plausible flows. We also observe that model selection is inherently linked to the inversion problem.

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 ongoing work on using a dynamic data driven application system (DDDAS) based approach to the forecast of volcanic ash transport and dispersal. Our primary modeling tool will be a new code puffin formed by the 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 ensemble based uncertainty quantification and parameter estimation methodology – polynomial chaos quadrature in combination with data integration to complete the DDDAS loop.

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.

[1] 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.

The ability to dynamically change data input to a computation is a key feature enabling simulation to be used in many applications. In this study, computation of geophysical mass flow is updated on the fly by changing terrain data. Accommodating such changes in a parallel environment entails new developments in parallel data management and gridding. Adaptivity, and in particular unrefinement, is critical for maintaining parallel efficiency. The application under study in this work is the result of a multidisciplinary collaboration between engineers, mathematicians, geologists, and hazard assessment personnel. In addition, adaptive gridding enables efficient use of computational resources, allowing for run-time determination of optimal computing resources. Combining these attributes allows run time conditions to inform calculations, which in turn provide up-to-date information to hazard management personnel.