Propagating Annular Modes

The leading “annular mode” in each hemisphere — usually defined as the dominant EOF of surface pressure or of zonal mean zonal wind variability — appears as a dipolar structure straddling the mean midlatitude jet and thus seems to describe north-south wobbling of the jet latitude. However, extratropical zonal wind anomalies frequently tend to migrate poleward. This behavior can be described by the first two EOFs, the first (AM1) being the dipolar structure, and the second (AM2) having a tripolar structure centered on the mean jet. (AM2 explains a significant amount of variance, though less than AM1.) Taken in isolation, AM1 thus describes a north-south wobbling of the jet position, while AM2 describes a strengthening and narrowing (or weakening and broadening) of the jet. However, despite the fact that they are spatially orthogonal, and their corresponding time series temporally orthogonal, AM1 and AM2 are not independent, but show significant lag-correlations which reveal the poleward propagation.

The EOFs are not modes of the underlying dynamical system governing the zonal flow evolution. The true modes can be estimated using principal oscillation pattern (POP) analysis. The leading POPs manifest themselves as a pair of complex conjugate structures with conjugate eigenvalues thus, in reality, constituting a single, complex, mode that describes poleward propagating anomalies. This mode then shows up as AM1 and AM2 in EOF analyses. Even though the principal components associated with the two leading EOFs decay at different rates, each decays faster than the true mode. In the propagating regime, these facts have implications for the use of autocorrelations and cross-correlations to quantify eddy feedback and the susceptibility of the mode to external perturbations. It is now well known that certain climate perturbations, especially those arising from increasing greenhouse gases and springtime polar ozone depletion, seem to show up in the form of AM1 structures.  There are some examples to the contrary: previous work has shown that the surface signal accompanying the “final warming” of the springtime stratosphere does not correspond too well to the AM1 structure.  If one interprets the annular modes as the modes of the system, then simple theory predicts that the response to steady forcing will usually be dominated by AM1, typically the mode with the longest time scale.  However, such arguments should really be applied to the true modes and, in situations where the leading POPs form a conjugate pair, there is only one relevant time scale.  In that case, whether the response looks like AM1 or AM2 depends on the spatial structure of the forcing.  Experiments with a simplified GCM show that the midlatitude climate response to perturbations can take the form of either AM1 or AM2, and more generally a combination of both.