Propagating Annular Modes: Empirical Orthogonal Functions, Principal Oscillation Patterns, and Timescales

The two leading Empirical Orthogonal Functions (EOFs) of zonal mean zonal wind describe north-south fluctuations, and intensification and narrowing, respectively, of the midlatitude jet. Under certain circumstances, these two leading EOFs cannot be regarded as independent, but are in fact, manifestations of a single, coupled, underlying mode of the dynamical system describing the evolution in time of zonal wind anomalies. The true modes are revealed by the Principal Oscillation Patterns (POPs). The leading mode and its associated eigenvalue are complex, its structure involves at least two EOFs, and it describes poleward (or equatorward) propagation of zonal mean zonal wind anomalies. In this propagating regime, the Principal Component (PC) time series associated with the two leading EOFs decay non-exponentially, and the response of the system to external forcing in a given EOF does not depend solely on the PC decorrelation time nor on the projection of the forcing onto that EOF. These considerations are illustrated using results from an idealized dynamical core model. Results from southern hemisphere ERA-I data are partly consistent with the behavior of the model’s propagating regime. Amongst other things, these results imply that the timescale that determines the sensitivity of a model to external forcing might be different from the decorrelation time of the leading PC, and involves both the rate of decay of the dynamical mode, and the period associated with propagation.