An Eddy-Zonal Flow Feedback Model for Propagating Annular Modes and their Dynamics

There is strong evidence that a positive feedback between the zonal-mean wind anomalies and the eddies (i.e. a positive feedback of EOF1 onto itself) is important for maintaining the wind anomalies associated with the annular modes. However, a recent study by Lubis and Hassanzadeh, (2021, JAS) shows that under some circumstances, EOF1 and EOF2 can interact and exert feedbacks on each other at some lag times, affecting the time scale of the annular modes. Building upon the seminal work of Lorenz and Hartmann (2001, JAS), we introduced a reduced-order model for coupled EOF1 and EOF2 that accounts for potential cross-EOF eddy-zonal flow feedbacks. Using the analytical solution of this model, we derive conditions for the existence of the propagating regime based on the feedback strengths. Using this model, and idealized GCMs and stochastic prototypes, we show that cross-EOF feedbacks play an important role in controlling the persistence of the annular modes by setting the frequency of the oscillation. We find that stronger cross-EOF feedbacks lead to less persistent annular modes. The underlying dynamics of the cross-EOF feedbacks for propagating annular modes in both reanalysis and an idealized GCM are also investigated. Using a finite-amplitude wave activity (FAWA) framework, we show that the cross-EOF feedbacks result from the out-of-phase oscillations of EOF1 (north-south jet displacement) and EOF2 (jet pulsation) leading to an orchestrated combination of equatorward propagation of wave activity (a baroclinic process) and nonlinear wave breaking (a barotropic process), which altogether act to reduce the total eddy forcings. The results highlight the importance of considering the coupling of EOFs and cross-EOF feedbacks to fully understand the natural and forced variability of the zonal-mean large-scale circulation.

Reference: Lubis, S. W., & Hassanzadeh, P. (2021). An Eddy–Zonal Flow Feedback Model for Propagating Annular Modes, Journal of the Atmospheric Sciences, 78(1), 249-267.