Here, a linear response function (LRF), which relates the temporal tendencies of zonal mean temperature and zonal wind to their anomalies and external forcing (Hassanzadeh and Kuang, 2016, JAS), is used to quantify the strength of the eddy-jet feedback associated with the annular mode in an idealized GCM. With the LRF, we are able to separate the mean-state-dependent eddy forcing from the mean-state-independent eddy forcing and thus isolate the part of the eddy variations that contributes to the feedback from the part that does not. Following a simple feedback model of Lorenz and Hartman (2001, JAS), the results confirm the presence of a positive eddy-jet feedback in the annular mode dynamics, with a feedback strength of 0.13 day-1 for this idealized GCM. Statistical methods proposed by earlier studies to quantify the feedback strength are evaluated against the results from the LRF, and it is shown that, because of the quasi-oscillatory nature of the eddy forcing, results of the previous methods are interfered by eddy forcing not caused by changes in the jet. A new method based on low-pass filtering is employed to reduce the interference from the spectral peak of eddy forcing at synoptic timescales, and the feedback strength is approximated by the regression coefficient of low-pass filtered eddy forcing on low-pass filtered zonal index, which converges to the value produced by the LRF when timescales longer than 200 days are used for the low-pass filtering.
Different statistical methods are then applied to Southern Hemisphere reanalysis data. The feedback strength estimated using the new low-pass filtering method is 0.12 day-1, which is presented as an improvement over previous estimates. Seasonality of the eddy-jet feedback is also explored. In addition, the results highlight a strong control of the annular mode on high frequency baroclinic waves (with periods less than 2 days) at intraseasonal to interannual timescales, which was underappreciated in previous research. The present study provides a framework to quantify the eddy-jet feedback strength in models and reanalysis data. Implications for the dynamics of the annular mode in the real atmosphere and potential caveats will also be discussed.