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A linear response function (LRF) that relates the temporal tendency of zonalmean temperature and zonal wind to their anomalies and external forcing is usedto accurately quantify the strength of the eddy-jet feedback associated withthe annular mode in an idealized GCM. Following a simple feedback model, theresults confirm the presence of a positive eddy-jet feedback in the annularmode dynamics, with a feedback strength of 0.137 day$^{-1}$ in the idealizedGCM. Statistical methods proposed by earlier studies to quantify the feedbackstrength are evaluated against results from the LRF. It is argued that themean-state-independent eddy forcing reduces the accuracy of these statisticalmethods because of the quasi-oscillatory nature of the eddy forcing. A newmethod is proposed to approximate the feedback strength as the regressioncoefficient of low-pass filtered eddy forcing onto low-pass filtered annularmode index, which converges to the value produced by the LRF when timescaleslonger than 200 days are used for the low-pass filtering. Applying the newlow-pass filtering method to the reanalysis data, the feedback strength in theSouthern annular mode is found to be 0.121 day$^{-1}$, which is presented as animprovement over previous estimates. This work also highlights the importanceof using sub-daily data in the analysis by showing the significant contributionof 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 studyprovides a framework to quantify the eddy-jet feedback strength in models andreanalysis data.

Quantifying the eddy-jet feedback strength of the annular mode in an idealized GCM and reanalysis data