Penland, C., and M. Ghil, 1993: Forecasting Northern Hemisphere 700mb geopotential height anomalies using empirical normal modes. Mon. Wea. Rev., 121, 2355-2371.
Multivariate linear prediction based on single-lag inverse modeling is developed further and critically examined. The method is applied to the National Meteorological Center analyses of Northern Hemisphere 700-mb geopotential height anomalies, which have been filtered to eliminate periods shorter than 10 days. Empirically derived normal modes of the randomly forced linear system are usually correlated, even at zero lag, suggesting that combinations of modes should be used in predictions. Due to nonlinearities in the dynamics and the neglect of interactions with other pressure levels, the lag at which the analysis is performed is crucial; best predictions obtain when the autocovariances involved in the analysis are calculated at a lag comparable to the exponential decay times of the modes. Errors in prediction have a significant seasonal dependence, indicating that the annual cycle affects the higher-order statistics of the field. Optimized linear predictions using this method are useful for about half a day longer than predictions made by persistence.
Conditional probabilities are much more efficiently calculated using normal-mode parameters than from histograms, and yield similar results. Maps of the model's Fourier spectra-integrated over specified frequency intervals and consistent with the assumptions made in a linear analysis-agree with maps obtained from fast Fourier transforms of the data.