Title
Newton and Bayes: Physical-Statistical Modeling of Geophysical Processes
Speaker
Mark Berliner, Department of Statistics, The Ohio State University
Abstract
Modeling and prediction of geophysical processes typically relies on the combination of both scientific understanding, reflected through mathematical models, and observations. However, the mathematical models are often very complex and subject to a variety of uncertainties; that is, approximate physics are applied approximately. Further, though very large observational datasets are often available, they are typically composed of disparate data types, and, despite their size, cover only small portions of the processes of interest. The hierarchical Bayesian viewpoint is suggested to provide a framework for combining scientific reasoning and observational data, in a fashion that quantitatively accounts for our uncertainty. To indicate the potential, I describe work-in-progress, joint with Ralph Milliff (National Center for Atmospheric Research) and Chris Wikle (U. of Missouri), on air-sea modeling to be applied to The Labrador Sea. This is a region of very complex air-sea interaction involving momentum convergences in the upper ocean, driven by energetic atmospheric cyclones or "polar lows". The ocean and atmosphere circulations are modeled physically using quasi-geostrophic (QG) approximations. (Alert to Statisticians: translation of that statement into something more accessible will not be attempted nor needed in this talk.) However, important ageostrophic effects in the planetary boundary layer (region where the interaction of air and sea is very complicated) are not represented in QG. We seek to exploit satellite remote sensing observations to augment (prior) QG approximations. This leads to challenging modeling and computational issues. The ideas and computations are illustrated an air-sea testbed model involving simulated observations derived from a non-QG "truth field" (i.e., the truth is based on a shallow fluid model. Again, Statisticians do not need to know what that means).
