The estimated feedback strength (denoted as $b_{FIL}$) is plotted in Figure 8c. When timescales longer than 200 days are used for the low-pass filtering, this method yields remarkably accurate results. [$b_{FIL}$ is calculated for each hemisphere of the 10 ensemble members of CTL, and 95$\%$ confidence intervals are then calculated assuming these samples follow Gaussian distribution. ]{} The pressure-latitude pattern of eddy flux anomaly associated with the annular mode is also constructed by regressing low-pass filtered eddy fluxes onto the low-pass filtered zonal index, and the results compares well with those from LRF, with a pattern correlation exceeding 0.9.

![image](F07.pdf){width="50.00000%"}

Application to the reanalysis data
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The above three statistical methods are applied to estimate the strength of eddy-jet feedback in the reanalysis data, and the results are summarized in Figure 13.

![image](g05.pdf){width="\textwidth"}

By minimizing the mean squared cross-correlations at lags longer than certain number of days as illustrated in Figure 4, $b_{LH}$ spans a range of values from around $0.06$ to $0.12$ day$^{-1}$ with the choices of decorrelation timescales of 5-20 days. The estimation for the reanalysis data is more sensitive to the choices of decorrelation and has larger margin of error compared to that of the idealized GCM 