Bayesian Hierarchical Spatial-Temporal Models for Wind Prediction

Abstract

Wind fields along coastlines are composed of many features that are spatially and temporally complex in nature, and they are well recognized as nonstationary spatial-temporal processes. The difficulties of spatial-temporal modeling can be overcome by using separable spatial-temporal processes. This subclass of spatial-temporal processes has several advantages, including rapid fitting and simple extensions of many techniques developed and used in time series analysis and classical geostatistics. However, these separable models are not always realistic. An empirical test for separability is proposed to aid in understanding spatial-temporal structure.

Also a new class of nonseparable stationary covariance models is introduced. A special case in this new nonseparable covariance class is the Matérn covariance model with a scale parameter. The scale parameter is used to take into account the change of units between the spatial and temporal domain. For nonstationarity, we represent a nonstationary process as a mixture of local orthogonal stationary spatial-temporal processes. Compared to the moving-cylinder spatial-temporal kriging method by Haas, this new nonstationary model is simultaneously defined everywhere. The empirical test for separability can be used to determine the covariance structure of local stationary spatial-temporal processes. We apply the methodology to the wind fields over Chesapeake Bay. The goal of this application is to evaluate the ability of MM5, a mesoscale meteorological model, to forecast the wind fields over the Bay. Simple models are specified for observed wind data and MM5 output in terms of the underlying true wind process which is nonstationary and nonseparable, and estimate them in a Bayesian way. Then the numerical model evaluation consists of comparing the observed wind values with their predictive distributions given the MM5 output. Moreover, the improved wind fields can be simulated via the Bayesian posterior distribution of the underlying true winds.