  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.
