PREDICTIVE OSCILLATION PATTERNS - A SYNTHESIS OF METHODS FOR SPATIAL-TEMPORAL DECOMPOSITION OF RANDOM-FIELDS

Spatial-temporal decompositions of climatologic fields have been obtai ned using a range of techniques, including principal component analysi s (PCA) and principal oscillation patterns (POPS). PCA decompositions are forced to be correlated to the original held, but they may not cap ture interesting aspects of temporal variation. On the other hand, POP S decompositions focus on temporal variation but are not forced to cor relate to the field. Here we introduce a hybrid of these methods that attempts to retain desirable aspects of both PCA and POPS. The approac h attempts to project the field onto a lower dimensional subspace with the property that the average error associated with forecasting a fut ure state of the held on the basis of the history contained in the pro jection is minimized. A recursive algorithm for estimating a spatial-t emporal decomposition based on this idea is developed. The methodology is applied to a 47-year climatological record of the 5-day average 50 0-millibar-height anomaly field, sampled on a 445 grid over the Northe rn Hemisphere extra-tropics. Some asymptotic properties of the estimat ion method for the new technique are examined in a simple situation. A lthough the estimation method requires a consistent estimator of a cer tain spectral density matrix, the target parameters are estimated at a parametric rate. Interestingly, the details of the nonparametric esti mation of the spectral density, such as the choice of the smoothing ke rnel, do not appear to affect the asymptotic variance of the target pa rameters.