What makes an annular mode “annular”?

The exploration of zonal, "annular" motions in the atmosphere dates back to seminal work by Rossby and coauthors in the 1930s. After reaching a relative high point with the formulation of the zonal index cycle c. 1950, it fell out of favor as observations revealed that variations in weather are not significantly zonally uniform. Interest in variability in the zonal circulation has remerged in recent years, but it still remains unclear to what extent such variability reflects physically meaningful zonal coherence in the extratropical circulation.

Here we explore the annularity of "annular" motions in a hierarchy of toy stochastic systems, an idealized atmospheric model, and reanalysis. We demonstrate that an "annular mode” can arise from EOF analysis due to both 1) annular motions (i.e. zonally uniform anomalies of the circulation) and 2) annular statistics (i.e. zonally uniform statistical properties of the circulation). The results suggest that the separation between the variance explained by successive EOFs provides a key measure of the physical significance of annular motions, i.e., whether they reflect zonally coherent motions or simply zonally coherent statistics of the flow. The results provide insight into the ubiquity of annular structures in both observations and models.