A simple dynamical model is presented for the basic spatial and temporal structure of the large-scale modes of intraseasonal variability and associated variations in the zonal index. Such variability in the extratropical atmosphere is known to be represented by fairly well-defined patterns, and among the most prominent are the North Atlantic Oscillation (NAO) and a more zonally symmetric pattern known as an annular mode, which is most pronounced in the Southern Hemisphere. These patterns may be produced by the momentum fluxes associated with large-scale midlatitude stirring, such as that provided by baroclinic eddies. It is shown how such stirring, as represented by a simple stochastic forcing in a barotropic model, leads to a variability in the zonal flow via a variability in the eddy momentum flux convergence and to patterns similar to those observed. Typically, the leading modes of variability may be characterized as a mixture of “wobbles” in the zonal jet position and “pulses” in the zonal jet strength. If the stochastic forcing is statistically zonally uniform, then the resulting patterns of variability as represented by empirical orthogonal functions are almost zonally uniform and the pressure pattern is dipolar in the meridional direction, resembling an annular mode. If the forcing is enhanced in a zonally localized region, thus mimicking the effects of a storm track over the ocean, then the resulting variability pattern is zonally localized, resembling the North Atlantic Oscillation. This suggests that the North Atlantic Oscillation and annular modes are produced by the same mechanism and are manifestations of the same phenomenon.
The time scale of variability of the patterns is longer than the decorrelation time scale of the stochastic forcing, because of the temporal integration of the forcing by the equations of motion limited by the effects of nonlinear dynamics and friction. For reasonable parameters these produce a decorrelation time of the order of 5–10 days. The model also produces some long-term (100 days or longer) variability, without imposing such variability via the external parameters except insofar as it is contained in the nearly white stochastic forcing.