Abstract: The organization of an ensemble of initial perturbations by a nonlinear dynamical system can produce highly non-Gaussian patterns, evidence of which is clearly observed in position-amplitude-scale features of coherent fluids. The true distribution of the ensemble is unknown, in part because models are in error and imperfect. A variety of distributions have been proposed in the context of Bayesian inference, including for example, mixture and kernel models. We contend that seeking posterior modes in non-Gaussian inference is fraught with heightened sensitivity to model error and demonstrate this fact by showing that a large component of the total variance remains unaccounted for as more modes emerge. Further, we show that in the presence of bias, this unaccounted variance slows convergence and produces distributions with lower information that require extensive auxiliary clean up procedures such as resampling. These procedures are difficult in large-scale problems where ensemble members may be generated through myriad schemes. We show that by treating the estimation problem entailed as a regression machine, multiple objectives can be incorporated in inference. The relative importance of these objectives can morph over time and can be dynamically adjusted by the data. In particular, we show that both variance reduction and nonlinear modes can be targeted using a stacked cascade generalization. We demonstrate this approach by constructing a new sequential filter called the Boosted Mixture Ensemble Filter and illustrating this on a lorenz system.

Abstract: This paper presents one approach to determining the hazard threat to a locale due to a large volcanic avalanche. The methodology employed includes large-scale numerical simulations, field data reporting the volume and runout of flow events, and a detailed statistical analysis of uncertainties in the modeling and data. The probability of a catastrophic event impacting a locale is calculated, together with a estimate of the uncertainty in that calculation. By a careful use of simulations, a hazard map for an entire region can be determined. The calculation can be turned around quickly, and the methodology can be applied to other hazard scenarios.

Abstract: This paper introduces a numerically-stable multiscale scheme to efficiently generate probabilistic hazard maps for volcanic ash transport using models of transport, dispersion and wind. The scheme relies on graph-based algorithms and low-rank approximations of the adjacency matrix of the graph. This procedure involves representing both the parameter space and physical space by a weighted graph. A combination of clustering and low rank approximation is then used to create a good approximation of the original graph. By performing a multiscale data sampling, a well-conditioned basis of a low rank Gaussian kernel matrix, is identified and used for out-of-sample extensions used in generating the hazard maps.

Abstract: The effects of forest fires cause a widespread devastation throughout the world every year. A good prediction of fire behavior can help on coordination and management of human and material resources in the extinction of these emergencies. Given the high uncertainty of fire behavior and the difficulty of extracting information required to generate accurate predictions, one system able to adapt to fire dynamics considering the uncertainty of the data is necessary. In this work two different systems based on Dynamic Data Driven Application are applied and a new probabilistic method based on the combination of both approaches is presented. This new method uses the computational power provided by high performance computing systems to adapt the chances in these kind of dynamic environments.

Abstract: Wildfires are critical for ecosystems in many geographical regions. However, our current urbanized existence in these environments is inducing this ecological balance to evolve into a different dynamic leading to the biggest fires in history. Wildfire wind speeds and directions change in an instant, and first responders can only be effective if they take action as quickly as the conditions change. What is lacking in disaster management today is a system integration of real-time sensor networks, satellite imagery, near-real time data management tools, wildfire simulation tools, and connectivity to emergency command centers before, during and after a wildfire. As a first time example of such an integrated system, the WIFIRE project is building an end-to-end cyberinfrastructure for real-time and data-driven simulation, prediction and visualization of wildfire behavior. This paper summarizes the approach and early results of the WIFIRE project to integrate networked observations, e.g., heterogeneous satellite data and real-time remote sensor data with computational techniques in signal processing, visualization, modeling and data assimilation to provide a scalable, technological, and educational solution to monitor weather patterns to predict a wildfire’s Rate of Spread.