An Eddy–Zonal Flow Feedback Model for Propagating Annular Modes

Abstract

The variability of the zonal-mean large-scale extratropical circulation is often studied using individual modes obtained from empirical orthogonal function (EOF) analyses. The prevailing reduced-order model of the leading EOF (EOF1) of zonal-mean zonal wind, called the annular mode, consists of an eddy-mean flow interaction mechanism that results in a positive feedback of EOF1 onto itself. However, a few studies have pointed out that under some circumstances in observations and GCMs, strong couplings exist between EOF1 and EOF2 at some lag times, resulting in decaying-oscillatory, or propagating, annular modes. Here, we introduce 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. Applying the coupled-EOF model to the Southern Hemisphere reanalysis data shows the existence of strong cross-EOF feedbacks. 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.

The Intrinsic 150‐Day Periodicity of the Southern Hemisphere Extratropical Large‐Scale Atmospheric Circulation

“…In one setup, the parameter settings, forcing, and dissipation are identical to those in the "Held-Suarez benchmark" (Held & Suarez, 1994) in which an analytical profile approximating a troposphere in unstable radiative-convective equilibrium and an isothermal stratosphere are used in the Newtonian relaxation scheme (with an equinoxial condition). The annular mode in this setup is in the non-propagating regime, similar to Lubis and Hassanzadeh (2021). It is known that this setup's annular mode is overly persistent (compared to the reanalysis), which had been often attributed to a too-strong EOF1-onto-EOF1 positive feedback in past studies (Chen & Plumb, 2009;Hassanzadeh & Kuang, 2019).…”

“…It is known that this setup's annular mode is overly persistent (compared to the reanalysis), which had been often attributed to a too-strong EOF1-onto-EOF1 positive feedback in past studies (Chen & Plumb, 2009;Hassanzadeh & Kuang, 2019). Recently, Lubis and Hassanzadeh (2021) showed that the too-persistent annular mode in this setup is at least partly (if not entirely) due to the lack of cross-EOF feedbacks.…”

“…After calculating the EOFs, the zonal indices (z 1 and z 2 ) and time-series of eddy forcing (m 1 and m 2 ) are calculated as the projection of the vertically averaged 𝐴𝐴 (⟨⋅⟩) zonal-mean 𝐴𝐴 (⋅) zonal wind 𝐴𝐴 ⟨ ū𝑢⟩ anomalies and vertically averaged zonal-mean eddy momentum flux convergence 𝐴𝐴 ⟨ F𝐹 ⟩ anomalies onto the leading EOFs of 𝐴𝐴 ⟨ ū𝑢⟩ anomalies (Lorenz & Hartmann, 2001;Lubis & Hassanzadeh, 2021;Ma et al, 2017;Simpson et al, 2013):…”

“…Based on this new model, not only the two leading EOFs of the zonal-mean zonal wind (EOF1 and EOF2) have feedbacks on themselves, as already suggested by Lorenz and Hartmann (2001), but they also exert feedbacks on each other through varying eddy momentum fluxes (i.e., cross-EOF feedbacks) at lag times of around 10-20 days. The ∼150-day periodicity is closely tied to the existence of cross-EOF feedbacks (Lubis & Hassanzadeh, 2021).…”

“…Nonetheless, it has remained the general understanding that unlike the BAM, the SAM has no intrinsic periodicity. That said, a little noticed 1994 paper by P. M. James et al (1994) based on a very idealized GCM, recent work by Sheshadri and Plumb (2017), based on a principal oscillation pattern (POP), also known as dynamic mode decomposition (DMD), and theoretical predictions from a newly developed reduced-order model of SAM by Lubis and Hassanzadeh (2021) implied-but did not further examine-that the SAM might have a ∼150-day periodicity.…”