A new class of nonseparable and nonstationary covariance models for wind fields

Classical geostatistical methods are powerful tools to study the spatial-temporal structure of stationary processes. Separability is also a common assumption to avoid many of the problems of space and time modeling. This subclass of separable spatial-temporal processes has several advantages, including rapid fitting and simple extensions of many techniques developed and successfully used in time series analyses and geostatistics. However, in real applications spatial-temporal processes are rarely stationary and separable; then an important extension of these traditional geostatistical methods is to processes that have a nonstationary and nonseparable covariance. In this work, some new approaches to estimate and model nonstationarity and nonseparability are presented. The most important scientific contributions of the research proposed here are; the estimation of the complex spatial-temporal dependence of environmental processes in general situations (nonstationarity, anisotropy, nonseparability), and the introduction of flexible models for spatial prediction of environmental processes. We apply the statistical methods proposed here to model the spatialtemporal patterns of wind fields, and for wind field mapping, which combines numerical meteorological model output with observational data. The data used in this phase of the research came from the subregion surrounding and including the Chesapeake Bay for July 2002. The ability to accurately forecast wind speed and direction in coastal locations is critical for support of shipping, marine recreational activities, and national security issues related to contaminant transport.