Modified Lagrangian-Mean Perspective of Annular Mode Variability

The leading mode of extratropical variability (i.e., annular mode) is characterized as a meridional seesaw of mass between middle and high latitudes or equivalently a barotropic dipole in the zonal wind anomaly field. With an understanding of the spatial structure of the annular mode variability, focus has shifted to the eddy-zonal flow interaction or Rossby wave breaking that leads to the persistence of the zonal wind anomalies. Much insight has been gained from the conventional relationship between the zonal mean flow and eddy fluxes, and the resulting mechanisms often involve eddies of different frequencies or barotropic versus baroclinic processes.

Here a new perspective of the annular mode variability is presented in the Modified Lagrangian-Mean formalism of the quasi-geostrophic (QG) model. Under adiabatic condition, the Lagrangian QG PV gradient can be described by a simple diffusive equation with the eddy fluxes absorbed in the Lagrangian mean, and the zonal mean wind variability and eddy PV flux can be obtained by a diffusive closure with the QG PV gradient. This formalism is applied to the baroclinic eddy life cycle and annular mode variability in an idealized model. It is shown that the change of the QG PV gradient during an eddy life cycle can be indeed described by a diffusive process, and that the type of life cycle can be attributed to the latitude of eddy diffusion relative to the mean jet. Furthermore, analysis of annular modes in the idealized model suggests that the wave activity associated with the annular mode variability is short-lived, and that the persistence of the annular may be attributed to the eddy diffusion of the QG PV gradient associated with Rossby wave breaking.