Date:

Monday, October 29, 2007,
11:00 am - 12:00 pm.

Place:

Mathematics Conference Room 626, UCD Building, 1250 14th St., Denver.

Speaker:

Sai Ravela.

Affiliation:

Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology.

Title:

Data Assimilation by Field Alignment

Abstract:

Algorithms that constrain numerical models with real-world observations play an important role in understanding earth's processes. Estimation problems characteristic of earth's systems have to contend with nonlinear (even chaotic) processes, sparse & noisy observations, and imperfect models with uncertain parameters, initial & boundary conditions, and parameterizations. In earth sciences, these problems are studied under the area of "data assimilation." In this (potentially) two-part talk, I will use the filtering problem in meso-scale phenomena (such as hurricanes, squall-lines, and thunderstorms) to motivate my work. Whilst mesoscale forecasts typically contain position and amplitude errors, current assimilation methods can be viewed as just amplitude-adjustment methods. Adjusting positions with amplitude changes can produce states with distorted coherence, adversely effecting current estimates and subsequent forecasts. The culprits generating position errors are many and they couple in nonlinear ways. Therefore, calculating their relative contributions is difficult, and as this work shows, unnecessary for state-estimation problems. The joint estimation problem in positions and amplitudes is straightforward when positions can be easily associated with features of fields. Difficulties arise when features are hard to detect, for example when sensors are sparse, the shapes of fields are complicated, or measurements are noisy. We formulate an approach that brings two fields into agreement by "bending" and "blending" them relative to one another. In our approach, position error is represented as a displacement field, and treated as an auxiliary state-variable. In this talk, after describing the conditions under which position errors impact amplitude estimates adversely, I will present a Bayesian formulation of our approach, synthesize a variational problem, and discuss constraints appropriate for finding a solution. Although solutions can be found using a variety of methods, I will describe a solution using the Euler-Lagrange equations, which produces an easy-to-use preprocessor ("bend" then "blend") for existing data-assimilation methods. I will also (briefly) argue that "bending and blending" -- the joint position-amplitude minimization problem -- could be useful in several fields. Time permitting, I will go on to the second part of this talk, where I will present the first (to the best of our present knowledge) realtime observatory for a laboratory analog of the large-scale planetary circulation. I will argue informally that this platform can be useful to advance prediction and predictability research in particular, and computational earth science in general, in a more effective way than is currently possible.

Short Bio:

Sai Ravela studied Computer Vision and Robotics at the University of Massachusetts at Amherst. Having been affected by sustainability issues, his interests moved to inverse probems in ecology, energy and environment. So, as a post-doc, he studied state and parameter estimation in ocean/atmosphere modeling at the earth, atmospheric and planetary sciences (EAPS) at MIT. He is presently a Research Scientist at MIT, where he develops inference algorithms with specific contributions in the areas of data-assimilation, natural-hazard predictability and risk modeling, photographic recapture methods in conservation biology, image estimation and control-coordination. He is a founder of Windrisktech, a company that assesses the risk from hurricanes. More information can be found at web.mit.edu/ravela/.