Predictive Oscillation Patterns: A Synthesis of Methods for Spatial-Temporal Decomposition of Random Fields

Spatial-temporal decompositions of climatologic fields have been obtained using a range of techniques, including principal component analysis (PCA) and principal oscillation patterns (POPS). PCA decompositions are forced to be correlated to the original field, but they may not capture interesting aspects of temporal variation. On the other hand, POPS decompositions focus on temporal variation but are not forced to correlate to the field. Here we introduce a hybrid of these methods that attempts to retain desirable aspects of both PCA and POPS. The approach attempts to project the field onto a lower dimensional subspace with the property that the average error associated with forecasting a future state of the field on the basis of the history contained in the projection is minimized. A recursive algorithm for estimating a spatial-temporal decomposition based on this idea is developed. The methodology is applied to a 47-year climatological record of the 5-day average 500-millibar-height anomaly field, sampled on a 445 grid over the Northern Hemisphere extra-tropics. Some asymptotic properties of the estimation method for the new technique are examined in a simple situation. Although the estimation method requires a consistent estimator of a certain spectral density matrix, the target parameters are estimated at a parametric rate. Interestingly, the details of the nonparametric estimation of the spectral density, such as the choice of the smoothing kernel, do not appear to affect the asymptotic variance of the target parameters.