Functional stochastic modeling and prediction of spatiotemporal processes

Many geophysical processes exhibit complex spatiotemporal interaction. In this paper a class of nonstationary statistical models with finite‐order autoregressive spatiotemporal dynamics is introduced. The associated prediction problem is solved by implementing the Kalman filter in terms of multivariate versions of the spatial Karhunen‐Loève and wavelet transforms. To illustrate the methodology, the AR(2) spatiotemporal interaction model is considered to represent a spatiotemporal data set from near‐surface wind speed. The implementation of the Kalman filter is achieved in terms of the method of moments and the principal component analysis.