result from the oscillatory behavior of eddy forcing, and positive values at large lags suggest a positive eddy-jet feedback according to LH01.

![image](g03.pdf){width="50.00000%"}

Despite some biases, the CTL is able to capture the general features of the system as in the reanalysis data described above (Figure 5). The broad peak of eddy forcing at synoptic timescales in the power spectrum is more pronounced in the model, which indicates that the eddy forcing is more oscillatory in the idealized GCM. @Chen2009 argued that the shoulders in the autocorrelation function of the zonal index at around $\pm$4-day lag can be attributed to the strong oscillatory nature of eddy forcing in the idealized GCM. Also, the annular mode is more persistent in this GCM, as the cross-correlation between $m$ and $z$ decays more slowly compared to that in the reanalysis data (Figures 4 and 6), or equivalently, the simulated zonal index has higher power at intraseasonal and longer timescales compared to that in the reanalysis data. Note that this is not just a bias of this idealized GCM. Too persistent annular modes are seen in GCMs of varying degrees of complexity, the cause of which is unknown and remains an important topic of 