(Figure 13a), which may partly be attributed to the shorter temporal length of the reanalysis data. Using lag regression, the estimated feedback strength is a function of lag days, and the margin of error grows with increasing lag (Figure 13b). Also, $b_{S}$ is more sensitive to the choices of lag days and has larger uncertainties than its counterpart with model outputs.

Although there is no “ground truth" for the reanalysis data, the result obtained from regression with low-pass filtered data seems encouraging (Figure 13c). $b_{FIL}$ converges to around 0.121 day$^{-1}$ at low-frequency limit, which matches well with $b_{LH}$ with the decorrelation time of around 2 weeks. [There is also a significant contribution of medium-scales waves to total eddy forcing at intreaseasonal to interannual timescales in the reanalysis data (Figure 10b), and with daily data, $b_{FIL}$ is only around 0.053 day$^{-1}$.]{} The pattern of anomalous eddy fluxes associated with the annular mode is also calculated by regressing low-pass filtered time series (Figure 14). As expected, anomalous eddy flux converges zonal momentum into 60$^\circ$S-70$^\circ$S in the upper troposphere, and reinforces the anomalous zonal wind. Eddy anomalies originate from 60$^\circ$S-75$^\circ$S near the surface, where eddy heat flux is strengthened due to increased baroclinicity.

