ONE-DAY WORKSHOP: MARCH 25 2003 A one-day workshop on "Physical-Statistical Modeling and Data Assimilation" will be held at SAMSI on Tuesday, March 25, 2003. This is part of the current SAMSI program on Large Scale Computer Models for Environmental Systems.
The focus of the workshop is statistical and applied mathematical methods for integrating physics and data analysis in the context of ocean and atmosphere systems. The featured speakers are:
Chris Wikle, Department of Statistics, University of Missouri
Mark Berliner, Department of Statistics, Ohio State University
Chris Jones, Department of Mathematics, UNC-Chapel Hill
A detailed timetable and abstract of the talks are given below.
The workshop will be held in the NISS Lecture Room. Directions to SAMSI/NISS are at http://www.samsi.info/directions.html. Information about SAMSI and the environmental program are at http://www.samsi.info.
Lunch will be provided for a charge of $10. PREREGISTRATION FOR THE WORKSHOP IS NOT REQUIRED BUT PLEASE EMAIL NICOLE SCOTT AT nicole@samsi.info IF YOU WOULD LIKE LUNCH, SO THAT WE CAN HAVE AN IDEA HOW MANY LUNCHES TO ORDER.
Time Table:
9:30-10:15 Mark Berliner, Essentials of Physical-Statistical Modeling
10:15-11:00 Chris Wikle, (a) Hierarchical Modeling of Advection Diffusion Processes, (b) Hierarchical Bayesian Boundary Value Problems
11:00-11:30 Coffee break
11:30-12:30 Mark Berliner, Bayesian Hierarchical Modeling of Air-Sea Interaction
12:30-1:15 lunch
1:15-2:15 Chris Wikle, Bayesian Hierarchical Modeling of Air-Sea Interaction (continuation)
2:15-2:30 break
2:30-4:00 Chris Jones, Ocean Modeling and Lagrangian Analysis
Abstracts:
Essentials of Physical-Statistical Modeling (Mark Berliner)
I will review selected aspects of physical modeling and the transition to stochastic modeling in the presence of uncertainty. The notions presented are linked to the hierarchical statistical modeling with emphasis on Bayesian approaches. An brief example of Bayesian analysis for stochastic differential equation process models relying on the Fokker-Planck equation is presented. Further motivation of physical statistical modeling is derived from use of combinations of simplified physical models and numerical techniques in the presence of observational data.
Hierarchical Modeling of Advection Diffusion Processes (Chris Wikle)
The hierarchical Bayesian approach to physical-statistical modeling will be illustrated with a simple advection-diffusion equation. The methodology will be illustrated from both a physical-space and spectral-space perspective. An ecological example showing the spread of an invasive species will be presented.
Hierarchical Bayesian Boundary Value Problems (Chris Wikle)
Boundary value problems are ubiquitous in the atmospheric and ocean sciences. Typical settings include bounded, partially bounded, global and limited area domains, discretized for applications of numerical models of the relevant fluid equations. Often, limited area models are constructed to interpret intensive datasets collected over a specific region, from a variety of observational platforms. These data are noisy and they typically do not span the domain of interest uniformly in space and time. Traditional numerical procedures cannot easily account for these uncertainties. A hierarchical Bayesian modeling framework is developed for solving boundary value problems in such settings. By allowing the boundary process to be stochastic, and conditioning the interior process on this boundary, one can account for the uncertainties in the boundary process in a reasonable fashion. In the presence of data and all its uncertainties, this idea can be related through Bayes' Theorem to produce distributions of the interior process given the observational data. The method is illustrated with an example of obtaining atmospheric streamfunction fields in the Labrador Sea region, given scatterometer-derived observations of the surface wind field.
Bayesian Hierarchical Modeling of Air-Sea Interaction (Mark Berliner and Chris Wikle)
We develop a Bayesian hierarchical model for aspects of vigorous air-sea interactions on a basin scale. The approach relies on both physical reasoning and statistical techniques for data processing and uncertainty management. The crucial component of the modeling involves development of a stochastic model for the ocean conditional and atmospheric behavior based on quasi-geostrophic modeling and a stochastic model for the atmospheric elements. To demonstrate the strategy, we apply it in the context of an Observing System Simulation Experiment. An ocean "truth" simulation is driven by idealized surface winds in a testbed domain abstracted from the Labrador Sea. This truth simulation is not based on quasi-geostrophic modeling, but rather uses a primitive equation-shallow water equation model. Artificial observations analogous to scatterometer and altimeter data are incorporated and comparisons made with the evolution of the "truth" simulation over a ten day experiment. The presentation reviews Berliner, Milliff, and Wikle (2003, In Press), Journal of Geophysical Research-Oceans.
Ocean Modeling and Lagrangian Analysis (Chris Jones)
Much data in the ocean is Lagrangian in that it is derived from subsurface floats or surface drifters following the flow. At the same time, many questions about the ocean involve transport and mixing, and therefore raise Lagrangian issues. Advances in the use of dynamical systems ideas have afforded a deeper understanding of Lagrangian transport. An application that elucidates cholorophyll dispersion in the Gulf of Mexico will be presented. A strategy for model analysis, based on this theory, at both model input and output, will be described. This will include Lagrangian data assimilation, optimal float placement design and a new approach to model evaluation.