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Abstract
Spatiotemporal processes are ubiquitous in the environmental and physical sciences. This is certainly true of atmospheric and oceanic processes, which typically exhibit many different scales of spatial and temporal variability. The complexity of these processes and the large number of observation/prediction locations preclude the use of traditional covariance-based spatiotemporal statistical methods. Alternatively, we focus on conditionally specified (i.e., hierarchical) spatiotemporal models. These methods offer several advantages over traditional approaches. Primarily, physical and dynamical constraints can be easily incorporated into the conditional formulation, so that the series of relatively simple yet physically realistic conditional models leads to a much more complicated spatiotemporal covariance structure 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 resolution but limited global coverage. In contrast, wind fields provided by the major weather centers provide complete coverage but have low spatial resolution. The goal is to combine these data in a manner that incorporates the space-time dynamics inherent in the surface wind field. This is an essential task to enable meteorological research, because no complete high-resolution surface wind datasets exist over the world oceans. High-resolution datasets of this type are crucial for improving our understanding of global air–sea interactions affecting climate and tropical disturbances, and for driving large-scale ocean circulation models.
