  A linear response function (LRF) that relates the temporal tendency of zonal
mean temperature and zonal wind to their anomalies and external forcing is used
to accurately quantify the strength of the eddy-jet feedback associated with
the annular mode in an idealized GCM. Following a simple feedback model, the
results confirm the presence of a positive eddy-jet feedback in the annular
mode dynamics, with a feedback strength of 0.137 day$^{-1}$ in the idealized
GCM. Statistical methods proposed by earlier studies to quantify the feedback
strength are evaluated against results from the LRF. It is argued that the
mean-state-independent eddy forcing reduces the accuracy of these statistical
methods because of the quasi-oscillatory nature of the eddy forcing. A new
method is proposed to approximate the feedback strength as the regression
coefficient of low-pass filtered eddy forcing onto low-pass filtered annular
mode index, which converges to the value produced by the LRF when timescales
longer than 200 days are used for the low-pass filtering. Applying the new
low-pass filtering method to the reanalysis data, the feedback strength in the
Southern annular mode is found to be 0.121 day$^{-1}$, which is presented as an
improvement over previous estimates. This work also highlights the importance
of using sub-daily data in the analysis by showing the significant contribution
of medium-scale waves of periods less than 2 days to the annular mode dynamics,
which was under-appreciated in most of previous research. The present study
provides a framework to quantify the eddy-jet feedback strength in models and
reanalysis data.
