Gardar Johannesson

Bayesian Inference and Markov Chain Monte Carlo Sampling to Reconstruct a Contaminant Source on a Continental Scale

Abstract A methodology combining Bayesian inference with Markov chain Monte Carlo (MCMC) sampling is applied to a real accidental radioactive release that occurred on a continental scale at the end of May 1998 near Algeciras, Spain. The source parameters (i.e., source location and strength) are reconstructed from a limited set of measurements of the release. Annealing and adaptive procedures are implemented to ensure a robust and effective parameter-space exploration. The simulation setup is similar to an emergency response scenario, with the simplifying assumptions that the source geometry and release time are known. The Bayesian stochastic algorithm provides likely source locations within 100 km from the true source, after exploring a domain covering an area of approximately 1800 km × 3600 km. The source strength is reconstructed with a distribution of values of the same order of magnitude as the upper end of the range reported by the Spanish Nuclear Security Agency. By running the Bayesian MCMC algorit...

Dynamic multi-resolution spatial models

Data from remote-sensing platforms play an important role in monitoring environmental processes, such as the distribution of stratospheric ozone. Remote-sense data are typically spatial, temporal, and massive. Existing prediction methods such as kriging are computationally infeasible. The multi-resolution spatial model (MRSM) captures nonstationary spatial dependence and produces fast optimal estimates using a change-of-resolution Kalman filter. However, past data can provide valuable information about the current status of the process being investigated. In this article, we incorporate the temporal dependence into the process by developing a dynamic MRSM. An application of the dynamic MRSM to a month of daily total column ozone data is presented, and on a given day the results of posterior inference are compared to those for the spatial-only MRSM. It is apparent that there are advantages to using the dynamic MRSM in regions where data are missing, such as when a whole swath of satellite data is missing.

Evidence for long-lived subduction of an ancient tectonic plate beneath the southern Indian Ocean

In this study, ancient subducted tectonic plates have been observed in past seismic images of the mantle beneath North America and Eurasia, and it is likely that other ancient slab structures have remained largely hidden, particularly in the seismic-data-limited regions beneath the vast oceans in the Southern Hemisphere. Here we present a new global tomographic image, which shows a slab-like structure beneath the southern Indian Ocean with coherency from the upper mantle to the core-mantle boundary region—a feature that has never been identified. We postulate that the structure is an ancient tectonic plate that sank into the mantle along an extensive intraoceanic subduction zone that migrated southwestward across the ancient Tethys Ocean in the Mesozoic Era. Slab material still trapped in the transition zone is positioned near the edge of East Gondwana at 140 Ma suggesting that subduction terminated near the margin of the ancient continent prior to breakup and subsequent dispersal of its subcontinents.

Sequential Monte-Carlo Framework for Dynamic Data-Driven Event Reconstruction for Atmospheric Release

The release of hazardous materials into the atmosphere can have a tremendous impact on dense populations. We propose an atmospheric event reconstruction framework that couples observed data and predictive computer-intensive dispersion models via Bayesian methodology. Due to the complexity of the model framework, a sampling-based approach is taken for posterior inference that combines Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) strategies.

Variance-covariance modeling and estimation for multi-resolution spatial models

The tree-structured multi-resolution spatial models (MRSMs) yield optimal and computationally feasible spatial smoothers of massive spatial data with nonstationary behavior. The nonstationary spatial correlation structure of MRSMs is the result of inhomogeneous stochastic parent-child relationships at adjacent resolutions. Likelihood-based methods are presented for the estimation and modeling of variance-covariance parameters associated with the parent-child relationships, resulting in data-adaptive, nonstationary covariance structure. An application of the MRSMs is given to total column ozone (TCO) data obtained from a polar-orbiting satellite.

Spatial-Temporal Nonlinear Filtering Based on Hierarchical Statistical Models

A hierarchical statistical model is made up generically of a data model, a process model, and occasionally a prior model for all the unknown parameters. The process model, known as the state equations in the filtering literature, is where most of the scientist’s physical/chemical/biological knowledge about the problem is used. In the case of a dynamically changing configuration of objects moving through a spatial domain of interest, that knowledge is summarized through equations of motion with random perturbations. In this paper, our interest is in dynamically filtering noisy observations on these objects, where the state equations are nonlinear. Two recent methods of filtering, the Unscented Particle filter (UPF) and the Unscented Kalman filter, are presented and compared to the better known Extended Kalman filter. Other sources of nonlinearity arise when we wish to estimate nonlinear functions of the objects positions; it is here where the UPF shows its superiority, since optimal estimates and associated variances are straightforward to obtain. The longer computing time needed for the UPF is often not a big issue, with the ever faster processors that are available. This paper is a review of spatial-temporal nonlinear filtering, and we illustrate it in a Command and Control setting where the objects are highly mobile weapons, and the nonlinear function of object locations is a two-dimensional surface known as the danger-potential field.

Kriging for Cut-Offs and Other Difficult Problems

Selective environmental remediation and environmental-justice regulations require prediction of processes above a cut-off. This is an example of a nonlinear question that includes other difficult problems such as predicting transformations of the process or predicting the spatial cumulative distribution function. In this paper, we explore the notion of matching variances and covariances of a multivariate predictor with its multivariate predictand (Aldworth and Cressie, 2001). The resulting predictor has useful unbiasedness properties for prediction of nonlinear spatial functional. Surfaces are rougher than kriging surfaces and, in a sense, represent a compromise between kriging and conditional simulation.

A spatial-temporal statistical approach to command and control problems in battle-space digitization

There are considerable difficulties in the integration, visualization, and overall management of battle-space information for the purpose of Command and Control (C2). One problem that we see as being important is the timely combination of digital information from multiple (possibly disparate) sources in a dynamically evolving environment. That is, there is a need to assimilate incoming data rapidly, so as to provide the battle commander with up-to- date knowledge about the battle-space and thereby to facilitate the command-decision process. In this paper, we present a spatial-temporal approach to obtaining accurate estimates of the constantly changing battlefield, based on noisy data from multiple sources.

Adapting Existing Spatial Data Sets to New Uses: An Example from Energy Modeling

ABSTRACT Energy modeling and analysis often relies on data collected for other purposes such as census counts, atmospheric and air quality observations, and economic projections. These data are available at various spatial and temporal scales, which may be different from those needed by the energy modeling community. If the translation from the original format to the format required by the energy researcher is incorrect, then resulting models can produce misleading conclusions. This is of increasing importance because of the fine resolution data required by models for new alternative energy sources such as wind and distributed generation. This paper addresses the matter by applying spatial statistical techniques which improve the usefulness of spatial data sets (maps) that do not initially meet the spatial and/or temporal requirements of energy models. In particular, we focus on (1) aggregation and disaggregation of spatial data, (2) imputing missing data and (3) merging spatial data sets.