Combining Information Across Spatial Scales

Spatial and spatial-temporal processes in the physical, environmental, and biological sciences often exhibit complicated and diverse patterns across different spacetime scales. Both scientific understanding, often reflected in computer models, and observational data vary in form and content across scales. We develop and examine a Bayesian hierarchical framework by which the combination of such information sources can be accomplished. Our approach is targeted to settings in which various special spatial scales arise. These scales may be dictated by the data-collection methods, availability of prior information, and/or goals of the analysis. The approach restricts to to a few essential scales. Hence, we avoid the challenging problem of constructing a model that can be used at all scales. This means that we can only provide inferences at the preselected special scales. However, problems involving special scales are sufficiently common to justify the trade-off between our comparatively simple modeling and analysis strategy with the formidable task of forming models valid at all scales. The methodology is demonstrated for the spatial prediction of an important quantity known as streamfunction based on wind information from satellite observations and weather center, computer model output. ∗Corresponding Author: Christopher K. Wikle, Department of Statistics, University of Missouri, 222 Math Science Building, Columbia, MO 65203. e-mail: [email protected]