Information Theory and Predictability for Low-Frequency Variability

A predictability framework, based on relative entropy, is applied here to low-frequency variability in a standard T21 barotropic model on the sphere with realistic orography. Two types of realistic climatology, corresponding to different heights in the troposphere, are used. The two dynamical regimes with different mixing properties, induced by the two types of climate, allow the testing of the predictability framework in a wide range of situations. The leading patterns of empirical orthogonal functions, projected onto physical space, mimic the large-scale teleconnections of observed flow, in particular the Arctic Oscillation, Pacific– North American pattern, and North Atlantic Oscillation. In the ensemble forecast experiments, relative entropy is utilized to measure the lack of information in three different situations: the lack of information in the climate relative to the forecast ensemble, the lack of information by using only the mean state and variance of the forecast ensemble, and information flow—the time propagation of the lack of information in the direct product of marginal probability densities relative to joint probability density in a forecast ensemble. A recently developed signal–dispersion–cross-term decomposition is utilized for climate-relative entropy to determine different physical sources of forecast information. It is established that though dispersion controls both the mean state and variability of relative entropy, the sum of signal and cross-term governs physical correlations between a forecast ensemble and EOF patterns. Information flow is found to be responsible for correlated switches in the EOF patterns within a forecast ensemble.