Importance Sampling for Dispersion-managed Solitons

The dispersion-managed nonlinear Schrödinger (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 demonstrate this method by reconstructing the probability density function of amplitude and phase deviations of noise-perturbed dispersion-managed solitons and comparing the results to those of the original, unaveraged system

Importance Sampling for Dispersion-managed Solitons

The dispersion-managed nonlinear Schrödinger (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 demonstrate this method by reconstructing the probability density function of amplitude and phase deviations of noise-perturbed dispersion-managed solitons and comparing the results to those of the original, unaveraged system

Volcanic Hazard Assessment for an Eruption Hiatus, or Post-eruption Unrest Context: Modeling Continued Dome Collapse Hazards for Soufrière Hills Volcano

Effective volcanic hazard management in regions where populations live in close proximity to persistent volcanic activity involves understanding the dynamic nature of hazards, and associated risk. Emphasis until now has been placed on identification and forecasting of the escalation phase of activity, in order to provide adequate warning of what might be to come. However, understanding eruption hiatus and post-eruption unrest hazards, or how to quantify residual hazard after the end of an eruption, is also important and often key to timely post-eruption recovery. Unfortunately, in many cases when the level of activity lessens, the hazards, although reduced, do not necessarily cease altogether. This is due to both the imprecise nature of determination of the “end” of an eruptive phase as well as to the possibility that post-eruption hazardous processes may continue to occur. An example of the latter is continued dome collapse hazard from lava domes which have ceased to grow, or sector collapse of parts of volcanic edifices, including lava dome complexes. We present a new probabilistic model for forecasting pyroclastic density currents (PDCs) from lava dome collapse that takes into account the heavy-tailed distribution of the lengths of eruptive phases, the periods of quiescence, and the forecast window of interest. In the hazard analysis, we also consider probabilistic scenario models describing the flow’s volume and initial direction. Further, with the use of statistical emulators, we combine these models with physics-based simulations of PDCs at Soufrière Hills Volcano to produce a series of probabilistic hazard maps for flow inundation over 5, 10, and 20 year periods. The development and application of this assessment approach is the first of its kind for the quantification of periods of diminished volcanic activity. As such, it offers evidence-based guidance for dome collapse hazards that can be used to inform decision-making around provisions of access and reoccupation in areas around volcanoes that are becoming less active over time

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

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

Topographic Controls on Pyroclastic Density Current Hazard at Aluto Volcano (Ethiopia) Identified Using a Novel Zero‐Censored Gaussian Process Emulator

Aluto volcano (Central Ethiopia) displays a complex, hybrid topography, combining elements typical of caldera systems (e.g., a central, flat caldera floor) and stratovolcanoes (e.g., relatively high and steep, radial flanks, related to eruptions occurring clustered in space). The most recent known eruptions at Aluto have commonly generated column-collapse pyroclastic density currents (PDCs), a hazardous phenomenon that can pose a significant risk to inhabited areas on and around the volcano. In order to analyze and quantify the role that Aluto's complex topography has on PDC hazard, we apply a versatile probabilistic strategy, which merges the TITAN2D model for PDCs with a novel zero-censored Gaussian Process (zGP) emulator, enabling robust uncertainty quantification at tractable computational costs. Results from our analyses indicate a critical role of the eruptive vent location, but also highlight a complex interplay between the topography and PDC volume and mobility. The relative importance of each factor reciprocally depends on the other factors. Thus, large PDCs (≥0.1–0.5 km3) can diminish the influence of topography over proximal regions of flow propagation, but PDCs respond to large- and small-scale topographic features over medial to distal areas, and the zGP captures processes like PDC channelization and overbanking. The novel zGP can be applied to other PDC models and can enable specific investigations of PDC dynamics, topographic interactions, and PDC hazard at many volcanic systems worldwide. Potentially, it could also be used during volcanic crises, when time constraints usually only permit computation of scenario-based hazard assessments

International Coercion, Emulation and Policy Diffusion: Market-Oriented Infrastructure Reforms, 1977-1999

Why do some countries adopt market-oriented reforms such as deregulation, privatization and liberalization of competition in their infrastructure industries while others do not? Why did the pace of adoption accelerate in the 1990s? Building on neo-institutional theory in sociology, we argue that the domestic adoption of market-oriented reforms is strongly influenced by international pressures of coercion and emulation. We find robust support for these arguments with an event-history analysis of the determinants of reform in the telecommunications and electricity sectors of as many as 205 countries and territories between 1977 and 1999. Our results also suggest that the coercive effect of multilateral lending from the IMF, the World Bank or Regional Development Banks is increasing over time, a finding that is consistent with anecdotal evidence that multilateral organizations have broadened the scope of the “conditionality” terms specifying market-oriented reforms imposed on borrowing countries. We discuss the possibility that, by pressuring countries into policy reform, cross-national coercion and emulation may not produce ideal outcomes.http://deepblue.lib.umich.edu/bitstream/2027.42/40099/3/wp713.pd

A Surrogate-Based Approach to Nonlinear, non-Gaussian Joint State-Parameter Data Assimilation

Many recent advances in sequential assimilation of data into nonlinear high-dimensional models are modifications to particle filters which employ efficient searches of a high-dimensional state space. In this work, we present a complementary strategy that combines statistical emulators and particle filters. The emulators are used to learn and offer a computationally cheap approximation to the forward dynamic mapping. This emulator-particle filter (Emu-PF) approach requires a modest number of forward-model runs, but yields well-resolved posterior distributions even in non-Gaussian cases. We explore several modifications to the Emu-PF that utilize mechanisms for dimension reduction to efficiently fit the statistical emulator, and present a series of simulation experiments on an atypical Lorenz-96 system to demonstrate their performance. We conclude with a discussion on how the Emu-PF can be paired with modern particle filtering algorithms

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

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 currents from Soufrière 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 changes. 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 datasets 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 gap between eruption forecasting based on monitoring time series data and development of cutting edge probabilistic volcanic hazard maps

The zero problem: Gaussian process emulators for range-constrained computer models

We introduce a zero-censored Gaussian process as a systematic, model-based approach to building Gaussian process emulators for range-constrained simulator output. This approach avoids many pitfalls associated with modeling range-constrained data with Gaussian processes. Further, it is flexible enough to be used in conjunction with statistical emulator advancements such as emulators that model high-dimensional vector-valued simulator output. The zero-censored Gaussian process is then applied to two examples of geophysical flow inundation which have the constraint of nonnegativity