![image](g04.pdf){width="\textwidth"}

While we do not have the LRF to separate out the mean-state-independent eddy forcing in the reanalysis, the low-pass filtering method only assumes that the mean-state-independent eddy forcing is sufficiently weak at the low-frequency limit so that the first term on the right hand side of Equation 9 is substantially smaller than the feedback factor $b$. Given that eddies are mostly generated at synoptic timescales, this seems a rather reasonable assumption. [A caveat of this assumption is that in the presence of an external low-frequency forcing (for example, due to stratospheric variability), the mean-state-independent eddy forcing might not be small at low frequencies (see an illustrative example in]{} @Byrne2016 [and more discussions in the next section).]{}

Discussions and summary
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The temporal persistence of the atmospheric annular mode has long been attributed to a positive eddy-jet feedback (e.g., Feldstein and Lee 1998; Robinson 2000; LH01), and statistical methods have been used to quantify the strength of the eddy feedback (LH01; S13). However, a recent study argues that one cannot discern the difference between the presence of an internal eddy feedback and external interrannual forcing using only the statistical methods [@Byrne2016]. Due to the stochastic nature of eddies, it is 