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Bursik, Marcus
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- PublicationOpen AccessA probabilistic hazard mapping tool for the Long Valley volcanic region (CA, USA)(2017)
; ; ; ; ; ; ;Probabilistic hazard maps are used to graphically represent forecasts of potentially hazardous volcanic processes associated with an eruption. The construction of a probabilistic hazard map requires the characterization of all possible scenarios (aleatoric variability) that might lead to an event of interest. These scenarios then must be “fed in” to a physical model of the geophyiscal process which are typically computationally expensive to exercise. We present a hazard-mapping tool for the Long Valley region of California. This tool utilizes statistical surrogates of the physical model (in this demonstration, TITAN2D simulations of pyroclastic density currents) to perform rapid hazard assessment. It effectively replaces simulations that take O(min)-O(hours) with function evaluation which take a fraction of a second to exercise. This speed up enables tremendous flexibility in scenario modeling as we can quickly construct and compare probabilistic hazard maps under a variety of scenario models. Furthermore, we can quickly update a probabilistic hazard map as new data or emergent situations arise.39 23 - PublicationOpen AccessNovel statistical emulator construction for volcanic ash transport model Ash3d with physically motivated measures(2020-09)
; ; ; ; ; ; ; ; ; Statistical emulators are a key tool for rapidly producing probabilistic hazard analysis of geophysical processes. Given output data computed for a relatively small number of parameter inputs, an emulator interpolates the data, providing the expected value of the output at untried inputs and an estimate of error at that point. In this work, we propose to fit Gaussian Process emulators to the output from a volcanic ash transport model, Ash3d. Our goal is to predict the simulated volcanic ash thickness from Ash3d at a location of interest using the emulator. Our approach is motivated by two challenges to fitting emulators—characterizing the input wind field and interactions between that wind field and variable grain sizes. We resolve these challenges by using physical knowledge on tephra dispersal. We propose new physically motivated variables as inputs and use normalized output as the response for fitting the emulator. Subsetting based on the initial conditions is also critical in our emulator construction. Simulation studies characterize the accuracy and efficiency of our emulator construction and also reveal its current limitations. Our work represents the first emulator construction for volcanic ash transport models with considerations of the simulated physical process.455 19 - PublicationOpen AccessDynamic Probabilistic Hazard Mapping in the Long Valley Volcanic Region CA: Integrating Vent Opening Maps and Statistical Surrogates of Physical Models of Pyroclastic Density CurrentsIdeally, probabilistic hazard assessments combine available knowledge about physical mechanisms of the hazard, data on past hazards, and any precursor information. Systematically assessing the probability of rare, yet catastrophic hazards adds a layer of difficulty due to limited observation data. Via computer models, one can exercise potentially dangerous scenarios that may not have happened in the past but are probabilistically consistent with the aleatoric nature of previous volcanic behavior in the record. Traditional Monte Carlo-based methods to calculate such hazard probabilities suffer from two issues: they are computationally expensive, and they are static. In light of new information, newly available data, signs of unrest, and new probabilistic analysis describing uncertainty about scenarios the Monte Carlo calculation would need to be redone under the same computational constraints. Here we present an alternative approach utilizing statistical emulators that provide an efficient way to overcome the computational bottleneck of typical Monte Carlo approaches. Moreover, this approach is independent of an aleatoric scenario model and yet can be applied rapidly to any scenario model making it dynamic.We present and apply this emulator-based approach to create multiple probabilistic hazard maps for inundation of pyroclastic density currents in the Long Valley Volcanic Region. Further, we illustrate how this approach enables an exploration of the impact of epistemic uncertainties on these probabilistic hazard forecasts. Particularly, we focus on the uncertainty of vent opening models and how that uncertainty both aleatoric and epistemic impacts the resulting probabilistic hazard maps of pyroclastic density current inundation.
511 21 - PublicationOpen AccessVent opening maps dataset for Long Valley volcanic regionFILE - VOmaps.zip Random instances of vent opening map probability distributions for the Long Valley volcanic region, according to the combined statistical model in: Bevilacqua, A., M. Bursik, A. Patra, E. B. Pitman, and R. Till (2017) Bayesian construction of a long-term vent opening map in the Long Valley volcanic region (CA, USA), Statistics in Volcanology 3.1 : 1 − 36. DOI: http://dx.doi.org/10.5038/2163-338X.3.1. 250 maps are available in ASCII text-file format, and included in a zip archive. Each ASCII file is identified with a sample number N from 1 to 250. For each N, the file "SampleN.asc" contains a list of M = 100,489 = 3172 UTM coordinates (Northing, Easting), zone 11 North, WGS84 horizontal datum. These coordinates define M spatial locations at which a new hypothetical vent/fissure is supposed to open, randomly sampled according to the pdf of the Nth vent opening map. These samples are obtained with a Latin Hypercube sampler based on Orthogonal Arrays.
44 1 - PublicationOpen AccessStatistical theory of probabilistic hazard maps: a probability distribution for the hazard boundary locationThe study of volcanic flow hazards in a probabilistic framework centers around systematic experimental numerical modeling of the hazardous phenomenon and the subsequent generation and interpretation of a probabilistic hazard map (PHM). For a given volcanic flow (e.g., lava flow, lahar, pyroclastic flow, ash cloud), the PHM is typically interpreted as the point-wise probability of inundation by flow material. In the current work, we present new methods for calculating spatial representations of the mean, standard deviation, median, and modal locations of the hazard’s boundary as ensembles of many deterministic runs of a physical model. By formalizing its generation and properties, we show that a PHM may be used to construct these statistical measures of the hazard boundary which have been unrecognized in previous probabilistic hazard analyses. Our formalism shows that a typical PHM for a volcanic flow not only gives the pointwise inundation probability, but also represents a set of cumulative distribution functions for the location of the inundation boundary with a corresponding set of probability density functions. These distributions run over curves of steepest probability gradient ascent on the PHM. Consequently, 2-D space curves can be constructed on the map which represents the mean, median, and modal locations of the likely inundation boundary. These curves give well-defined answers to the question of the likely boundary location of the area impacted by the hazard. Additionally, methods of calculation for higher moments including the standard deviation are presented, which take the form of map regions surrounding the mean boundary location. These measures of central tendency and variance add significant value to spatial probabilistic hazard analyses, giving a new statistical description of the probability distributions underlying PHMs. The theory presented here may be used to aid construction of improved hazard maps, which could prove useful for planning and emergency management purposes. This formalism also allows for application to simplified processes describable by analytic solutions. In that context, the connection between the PHM, its moments, and the underlying parameter variation is explicit, allowing for better source parameter estimation from natural data, yielding insights about natural controls on those parameters.
520 27 - PublicationOpen AccessThe Failure Forecast Method applied to the GPS and seismic data collected in the Campi Flegrei caldera (Italy) in 2011-2020.(2020-12)
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;; ; ;; ; ; ; Episodes of slow uplift and subsidence of the ground, called bradyseism, characterize the recent dynamics of the Campi Flegrei caldera (Italy). In the last decades two major bradyseismic crises occurred, in 1969/1972 and in 1982/1984, with a ground uplift of 1.70 m and 1.85 m, respectively. Thousands of earthquakes, with a maximum magnitude of 4.2, caused the partial evacuation of the town of Pozzuoli in October 1983. This was followed by about 20 years of overall subsidence, about 1 m in total, until 2005. After 2005 the Campi Flegrei caldera has been rising again, with a slower rate, and a total maximum vertical displacement in the central area of ca. 70 cm. The two signals of ground deformation and background seismicity have been found to share similar accelerating trends. The failure forecast method can provide a first assessment of failure time on present‐day unrest signals at Campi Flegrei caldera (Italy) based on the monitoring data collected in [2011, 2020] and under the assumption to extrapolate such a trend into the future. In this study, we apply a probabilistic approach that enhances the well‐established method by incorporating stochastic perturbations in the linearized equations. The stochastic formulation enables the processing of decade‐long time windows of data, including the effects of variable dynamics that characterize the unrest. We provide temporal forecasts with uncertainty quantification, potentially indicative of eruption dates. The basis of the failure forecast method is a fundamental law for failing materials: ẇ^-α ẅ = A, where ẇ is the rate of the precursor signal, and α, A are model parameters that we fit on the data. The solution when α >1 is a power law of exponent 1/(1 − α) diverging at time Tf , called failure time. In our case study, Tf is the time when the accelerating signals collected at Campi Flegrei would diverge if we extrapolate their trend. The interpretation of Tf as the onset of a volcanic eruption is speculative. It is important to note that future variations of monitoring data could either slow down the increase so far observed, or suddenly further increase it leading to shorter failure times than those here reported. Data from observations at all locations in the region were also aggregated to reinforce the computations of Tf reducing the impact of observation errors.152 49 - PublicationOpen AccessProbabilistic forecasting of plausible debris flows from Nevado de Colima (Mexico) using data from the Atenquique debris flow, 1955We 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 depthaveraged 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.
567 48 - PublicationOpen AccessVolcanic eruption time eruption forecasting using a stochastic enhancement of the Failure Forecasting Method(2018-12)
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; In this study, we use a doubly stochastic model to develop a short-term eruption forecasting method based on precursory signals. The method enhances the Failure Forecast Method (FFM) equation, which represents the potential cascading of signals leading to failure. The reliability of such forecasts is affected by uncertainty in data and volcanic system behavior and, sometimes, a classical approach poorly predicts the time of failure. To address this, we introduce stochastic noise into the original ordinary differential equation, converting it into a stochastic differential equation, and systematically characterize the uncertainty. Embedding noise in the model can enable us to have greater forecasting skill by focusing on averages and moments. In our model, the prediction is thus perturbed inside a range that can be tuned, producing probabilistic forecasts. Furthermore, our doubly stochastic formulation is particularly powerful in that it provides a complete posterior probability distribution, allowing users to determine a worst-case scenario with a specified level of confidence. We verify the new method on simple historical datasets of precursory signals already studied with the classical FFM. The results show the increased forecasting skill of our doubly stochastic formulation. We then present a preliminary application of the method to more recent and complex monitoring signals.70 18 - PublicationOpen AccessValidation data for manuscript "Novel statistical emulator construction for volcanic ash transport model Ash3d with physically-motivated measures"This database presents the testing and validation data used and presented in the manuscript titled "Novel statistical emulator construction for volcanic ash transport model Ash3d with physically-motivated measures". The manuscript is submitted to the Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. Please refer to the readme file for more details of the data.
54 6 - PublicationRestrictedLate Quaternary Eruption Record and Probability of Future Volcanic Eruptions in the Long Valley Volcanic Region (CA, USA)(2018)
; ; ; ; ; ; ; ; ; ; ; ; ;The Long Valley volcanic region, eastern California, has been characterized by recurrent and generally explosive eruptions in the past 180,000 years, originating from a N/S elongated area ~50 km in extent, including the Mammoth Mountain lava dome complex, the Mono-Inyo volcanic chain, and their peripheries. Several temporal clusters of activity have been observed in a relatively well-preserved time-stratigraphic record, which is nevertheless affected by uncertainties. This study has two main objectives: (1) to fully describe the past eruption record by using a stochastic model capable of combining radiometric ages and stratigraphic constraints and, (2) based on the uncertainty assessment, to develop a doubly stochastic, long-term temporal model based on the current situation. Multiple approaches are described and compared, and multimodel forecasts are also presented. Our findings provide fundamental information for hazard assessment and forecasting of the next eruption in the Long Valley volcanic region, of which the mean probability of occurrence is estimated to be ~2.5% in the next 10 years and ~22.5% in the next 100 years.320 3
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