The finite-time instability and associated predictability of atmospheric of atmospheric circulations are defined in terms of the largest singular values, and associated singular vectors, of the linear evolution operator determined form given equations of motion. These quantities are calculated in both a barotropic and a three-level quasi-geostrophic model, using as basic states realistic large-scale northern wintertime flows that represent the climatological state, regime composites, and specific realizations of these regimes. for time-invariant basic states, the singular vectors are compared with the corresponding normal-mode solutions; it is shown that the perturbations defined (at the initial time) by the singular vectors have much larger growth rates than the normal modes, and possess a more localized spatial structure.
The regimes studied have opposite values of the Pacific/North American (PNA) index, and growth rates for the barotropic basis states appear to confirm earlier studies that the barotropic instability of the negative PNA states may be larger than the corresponding positive PNA states. The evolution of the singular-vector perturbations, with emphasis on the vertical structure, is compared for time-evolving and time-invariant baroclinic basis states; the effects of nonlinearity are also discusses. It is shown that, in the baroclinic model, interactions between synoptic-scale eddies in the time-evolving basic state and in the perturbation field are fundamental for studying the predictability of transitions in the large-scale circulation. Consequently results obtained from linear calculations using very smooth basic states cannot properly account for such predictability.
These results form the basis of a technique used to initialize ensembles of forecasts made with a primitive-equation model, and are described in the companion paper (Mureau et al. 1993).