Preprint #97-24

A Dimension-Reduction Approach to Space-Time Kalman Filtering

by

Christopher K. Wikle and Noel Cressie

Most climatological processes involve variability over both space and time. The extension of traditional geostatistical methods, such as kriging, to the spatio-temporal domain is one possible approach to characterize this variability. Due to difficulties caused by large data sets and the modeling of space, time, and spatio-temporal interactions, this approach is limited. In this article, we present an approach to space-time prediction that achieves dimension reduction and uses a statistical model that is temporally dynamic and spatially descriptive. That is, it exploits the unidirectional flow of time (in an autoregressive framework) and is spatially "descriptive" in that the autoregressive process is spatially colored. With the inclusion of a measurement equation, this formulation naturally leads to the development of a spatio- temporal Kalman filter that achieves dimension reduction in the analysis of large spatio-temporal data sets. We use this Kalman filter to predict at times and locations for which we do not have data. The method is applied to a data set of near-surface winds, obtained from a blending of observations and a deterministic atmospheric model, and is shown to perform better than independently applying simple kriging to each time slice of the spatial field. That is, we can improve prediction by exploiting the dynamic structure of the spatial fields evolving in time. The improvement becomes more pronounced as the signal-to-noise ratio decreases.


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