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

The strength of the eddy-jet feedback in the midlatitude atmosphere is important for both internal variability and response to external forcing. 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 quantify the strength of the eddy-jet feedback associated with the annular mode in an idealized GCM. Following a classic simple feedback model, the results confirm the presence of a positive eddy-jet feedback in the annular mode dynamics, with a feedback strength of 0.083 day−1. Statistical methods proposed by earlier studies to quantify the feedback strength are evaluated against the result from the LRF, and it is shown that results of the previous methods are interfered by the quasi-oscillatory nature of the eddy forcing. 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 0.053 day−1, which is argued to be an improvement over previous estimates. The present study provides a framework to quantify the eddy-jet feedback strength in models and reanalysis data.