Average Predictability Time. Part II: Seamless Diagnoses of Predictability on Multiple Time Scales

Abstract

This paper proposes a new method for diagnosing predictability on multiple time scales without time averaging. The method finds components that maximize the average predictability time (APT) of a system, where APT is defined as the integral of the average predictability over all lead times. Basing the predictability measure on the Mahalanobis metric leads to a complete, uncorrelated set of components that can be ordered by their contribution to APT, analogous to the way principal components decompose variance. The components and associated APTs are invariant to nonsingular linear transformations, allowing variables with different units and natural variability to be considered in a single state vector without normalization. For prediction models derived from linear regression, maximizing APT is equivalent to maximizing the sum of squared multiple correlations between the component and the time-lagged state vector. The new method is used to diagnose predictability of 1000-hPa zonal velocity on time scales from 6 h to decades. The leading predictable component is dominated by a linear trend and presumably identifies a climate change signal. The next component is strongly correlated with ENSO indices and hence is identified with seasonal-to-interannual predictability. The third component is related to annular modes and presents decadal variability as well as a trend. The next few components have APTs exceeding 10 days. A reconstruction of the tropical zonal wind field based on the leading seven components reveals eastward propagation of anomalies with time scales consistent with the Madden?Julian oscillation. The remaining components have time scales less than a week and hence are identified with weather predictability. The detection of predictability on these time scales without time averaging is possible by virtue of the fact that predictability on different time scales is characterized by different spatial structures, which can be optimally extracted by suitable projections.