Spatiotemporal hierarchical Bayesian modeling: Tropical ocean surface winds

Spatiotemporal processes are ubiquitous in the environmental and physical s ciences. This is certainly true of atmospheric and oceanic processes, which typically exhibit many different scales of spatial and temporal variabilit y. The complexity of these processes and the large number of observation/pr ediction locations preclude the use of traditional covariance-based spatiot emporal statistical methods. Alternatively, we focus on conditionally speci fied (i.e., hierarchical) spatiotemporal models. These methods offer severa l advantages over traditional approaches. Primarily, physical and dynamical constraints can be easily incorporated into the conditional formulation, s o that the series of relatively simple yet physically realistic conditional models leads to a much more complicated spatiotemporal covariance structur e than can be specified directly. Furthermore, by making use of the sparse structure inherent in the hierarchical approach, as well as multiresolution (wavelet) bases, the models can be computed with very large datasets. This modeling approach was necessitated by a scientifically meaningful problem in the geosciences. Satellite-derived wind estimates have high spatial reso lution but limited global coverage. In contrast, wind fields provided by th e major weather centers provide complete coverage but have low spatial reso lution. The god is to combine these data in a manner that incorporates the space-time dynamics inherent in the surface wind field. This is an essentia l task to enable meteorological research, because no complete high-resoluti on surface wind datasets exist over the world oceans. High-resolution datas ets of this type are crucial for improving our understanding of global air- sea interactions affecting climate and tropical disturbances, and for drivi ng large-scale ocean circulation models.