indeed impossible to separate the mean-state-dependent eddy flux from the mean-state-independent eddy flux and infer causality in the reanalysis data. In the present study, an LRF is used to identify the eddy response to anomalous mean flow associated with the annular mode in an idealized GCM, in which a positive eddy-jet feedback is confirmed unequivocally. With little spread across ten 44500-day integrations, EXP yields an eddy feedback strength of around 0.137 day$^{-1}$. [When the LRF is applied to the second EOF of zonal mean zonal wind, it yields a negative eddy feedback of -0.264 day$^{-1}$, consistent with the findings of LH01 who inferred the existence of a negative feedback in the second EOF of the observed Southern annular mode and attributed it to the barotropic governor effect (James 1987)]{}.

Using the LRF, the present study is able to provide a reasonably accurate estimation of the mean-state-independent eddy forcing. It is found that the spectral peak at synoptic timescales in the power spectrum of total eddy forcing ($m$) is dominated by the mean-state-independent eddy forcing ($\tilde{m}$). At intraseasonal and longer timescales, the amplitude of the mean-state-independent eddy forcing decreases with decreasing frequency[, and the total eddy forcing is dominated by mean-state-dependent 