A dimension-reduced approach to space-time Kalman filtering

Many physical/biological processes involve variability over both space and time. As a result of difficulties caused by large datasets and the modellin g of space, time and spatiotemporal interactions, traditional space-time me thods are limited. In this paper, we present an approach to space-time pred iction that achieves dimension reduction and uses a statistical model that is temporally dynamic and spatially descriptive. That is, it exploits the u nidirectional flow of time, in an autoregressive framework, and is spatiall y 'descriptive' in that the autoregressive process is spatially coloured. W ith the inclusion of a measurement equation, this formulation naturally lea ds to the development of a spatio-temporal Kalman filter that achieves dime nsion reduction in the analysis of large spatio-temporal datasets. Unlike o ther recent space-time Kalman filters, our model also allows a nondynamic s patial component. The method is applied to a dataset of near-surface winds over the topical Pacific ocean. Spatial predictions with this dataset are i mproved by considering the additional non-dynamic spatial process. The impr ovement becomes more pronounced as the signal-to-noise ratio decreases.