Quantifying the Eddy-Jet Feedback Strength of the Annular Mode in an Idealized GCM and Reanalysis Data

The annular modes, which correspond to the leading empirical orthogonal function of zonal mean zonal wind in both hemispheres, are a dominant mode of variability of the extratropical circulation on intraseasonal to interannual timescales. A positive feedback between anomalous zonal flow and eddy fluxes has been argued to be responsible for the persistence of the annular mode. Quantifying the strength of the eddy-jet feedback is important for understanding both internal variability and response to external forcing. Statistical methods have been proposed to quantify the feedback strength (e.g., Lorenz and Hartmann, 2001, JAS; Simpson et al., 2013, JC). However, how well the statistical methods quantify the feedback has not been established. Furthermore, a recent study (Byrne et al., 2016, GRL) has demonstrated the shortcomings of these statistical methods in distinguishing between an eddy feedback and an interannual variability that is external to any processes in the mid-latitude troposphere (e.g., stratospheric variability). It is argued that previous evidence for the existence of a positive eddy feedback is more likely attributable to the external interannual variability.

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.