captures less than half of the total eddy forcing calculated from 6-hourly wind anomalies in the idealized GCM (Figure 10a). The results suggest that the eddy-jet feedback will be strongly underestimated without accounting for medium-scale waves. In fact, with daily model outputs, $b_{LRF}$ is around 0.083 day$^{-1}$, 40$\%$ weaker than that calculated using 6-hourly model outputs.

![image](g06.pdf){width="\textwidth"}

[Although the focus of the present work is on the annular mode (i.e., the leading EOF of the zonal mean zonal wind), we also apply the LRF framework to the second EOF, which is characterized by a tripolar pattern of zonal wind anomalies and corresponds to the fluctuations of the amplitude of the jet (Figure 11a). With a stronger midlatitude jet, temperature gradient is enhanced between 30$^\circ$S-40$^\circ$S below around 300 hPa (Figure 11b). Poleward eddy heat flux is strengthened due to sharper temperature gradient (Figure 11d), and the anomalous eddy momentum flux associated with second EOF tends to export momentum out of the jet (Figure 11c). Using another ensemble of 10 simulations with an external forcing calculated for the second EOF, it is found that the eddy feedback associated with the second EOF is negative, and the strength of the feedback is -0.264 