Elaine T. Spiller

Using Statistical and Computer Models to Quantify Volcanic Hazards

Risk assessment of rare natural hazards, such as large volcanic block and ash or pyroclastic flows, is addressed. Assessment is approached through a combination of computer modeling, statistical modeling, and extreme-event probability computation. A computer model of the natural hazard is used to provide the needed extrapolation to unseen parts of the hazard space. Statistical modeling of the available data is needed to determine the initializing distribution for exercising the computer model. In dealing with rare events, direct simulations involving the computer model are prohibitively expensive. The solution instead requires a combination of adaptive design of computer model approximations (emulators) and rare event simulation. The techniques that are developed for risk assessment are illustrated on a test-bed example involving volcanic flow.

Automating Emulator Construction for Geophysical Hazard Maps

This paper describes an efficient and systematic process for using geophysical computer model simulations to guide efforts in probabilistic hazard mapping. The framework being proposed requires the simultaneous construction of many (

A Hybrid Particle–Ensemble Kalman Filter for Lagrangian Data Assimilation

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Pooling strength amongst limited datasets using hierarchical Bayesian analysis, with application to pyroclastic density current mobility metrics

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Importance Sampling for Dispersion-Managed Solitons ∗

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Dynamic Statistical Models for Pyroclastic Density Current Generation at Soufrière Hills Volcano

) statistical emulators, e.g., cheap model surrogates. This paper describes an automation process for choosing designs for and fitting these emulators. Throughout the description of this process, several useful modifications to standard emulators are explored. Additionally, this approach enables a fast and flexible uncertainty quantification for multiple sources of aleatory variability (natural randomness) and epistemic uncertainty (uncertainty in geophysical and statistical models) in the context of probabilistic hazard mapping. This process is illustrated through an application to granular volcanic flows.

A Hybrid Particle-Ensemble Kalman Filter for High Dimensional Lagrangian Data Assimilation

Lagrangian measurements from passive ocean instruments provide a useful source of data for estimating and forecasting the ocean’s state (velocity field, salinity field, etc.). However, trajectories from these instrumentsare often highly nonlinear, leading to difficulties with widely used data assimilationalgorithms such as the ensemble Kalmanfilter (EnKF). Additionally, the velocityfield is often modeled as a high-dimensional variable, which precludes the use of more accurate methods such as the particle filter (PF). Here, a hybrid particle‐ensemble Kalman filter is developed that applies the EnKF update to the potentially highdimensional velocity variables, and the PF update to the relatively low-dimensional, highly nonlinear drifter positionvariable. This algorithmis tested with twin experiments on the linearshallow water equations. In experiments with infrequent observations, the hybrid filter consistently outperformed the EnKF, both by better capturing the Bayesian posterior and by better tracking the truth.

Assimilating en-route Lagrangian observations

In volcanology, the sparsity of datasets for individual volcanoes is an important problem, which, in many cases, compromises our ability to make robust judgments about future volcanic hazards. In this contribution we develop a method for using hierarchical Bayesian analysis of global datasets to combine information across different volcanoes and to thereby improve our knowledge at individual volcanoes. The method is applied to the assessment of mobility metrics for pyroclastic density currents in order to better constrain input parameters and their related uncertainties for forward modeling. Mitigation of risk associated with such flows depends upon accurate forecasting of possible inundation areas, often using empirical models that rely on mobility metrics measured from the deposits of past flows, or on the application of computational models, several of which take mobility metrics, either directly or indirectly, as input parameters. We use hierarchical Bayesian modeling to leverage the global record of mobility metrics from the FlowDat database, leading to considerable improvement in the assessment of flow mobility where the data for a particular volcano is sparse. We estimate the uncertainties involved and demonstrate how they are improved through this approach. The method has broad applicability across other areas of volcanology where relationships established from broader datasets can be used to better constrain more specific, sparser, datasets. Employing such methods allows us to use, rather than shy away from, limited datasets, and allows for transparency with regard to uncertainties, enabling more accountable decision-making.

Probabilistic Quantification of Hazards: A Methodology Using Small Ensembles of Physics-based Simulations and Statistical Surrogates

The dispersion-managed nonlinear Schrodinger (DMNLS) equation governs the long-term dynamics of systems which are subject to large and rapid dispersion variations. We present a method to study large, noise-induced amplitude and phase perturbations of dispersion-managed solitons. The method is based on the use of importance sampling to bias Monte Carlo simulations toward regions of state space where rare events of interest—large phase or amplitude variations—are most likely to occur. Implementing the method thus involves solving two separate problems: finding the most likely noise realizations that produce a small change in the soliton parameters, and finding the most likely way that these small changes should be distributed in order to create a large, sought-after amplitude or phase change. Both steps are formulated and solved in terms of a variational problem. In addition, the first step makes use of the results of perturbation theory for dispersion-managed systems recently developed by the authors. We d...

Phase noise of dispersion-managed solitons

To mitigate volcanic hazards from pyroclastic density currents, volcanologists generate hazard maps that provide long-term forecasts of areas of potential impact. Several recent efforts in the field develop new statistical methods for application of flow models to generate fully probabilistic hazard maps that both account for, and quantify, uncertainty. However a limitation to the use of most statistical hazard models, and a key source of uncertainty within them, is the time-averaged nature of the datasets by which the volcanic activity is statistically characterized. Where the level, or directionality, of volcanic activity frequently changes, e.g. during protracted eruptive episodes, or at volcanoes that are classified as persistently active, it is not appropriate to make short term forecasts based on longer time-averaged metrics of the activity. Thus, here we build, fit and explore dynamic statistical models for the generation of pyroclastic density current from Soufriere Hills Volcano (SHV) on Montserrat including their respective collapse direction and flow volumes based on 1996-2008 flow datasets. The development of this approach allows for short-term behavioral changes to be taken into account in probabilistic volcanic hazard assessments. We show that collapses from the SHV lava dome follow a clear pattern, and that a series of smaller flows in a given direction often culminate in a larger collapse and thereafter directionality of the flows change. Such models enable short term forecasting (weeks to months) that can reflect evolving conditions such as dome and crater morphology changes and non-stationary eruptive behavior such as extrusion rate variations. For example, the probability of inundation of the Belham Valley in the first 180 days of a forecast period is about twice as high for lava domes facing Northwest toward that valley as it is for domes pointing East toward the Tar River Valley. As rich multi-parametric volcano monitoring dataset become increasingly available, eruption forecasting is becoming an increasingly viable and important research field. We demonstrate an approach to utilize such data in order to appropriately ‘tune’ probabilistic hazard assessments for pyroclastic flows. Our broader objective with development of this method is to help advance time-dependent volcanic hazard assessment, by bridging the