day$^{-1}$. This is consistent with the findings of LH01, who inferred from a lag-regression analysis that the feedback is negative. LH01 also argued that the anomalous eddy momentum flux associated with the second EOF tend to weaken the jet as a result of increased barotropic shear, i.e. the barotropic governor effect]{} [@James1987].

![image](F04b.pdf){width="\textwidth"}

Fitting cross-correlation functions (LH01)
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In a pioneering study, LH01 inferred the existence of a positive eddy-jet feedback in the annular mode dynamics from the reanalysis data and based on the the assumption that the mean-state-independent eddy forcing has short memory (i.e., the time series of $\tilde{m}$ has a short decorrelation timescale), and proposed the following method to quantify the strength of the feedback by fitting the covariance functions. If $b$ = 0, Equation 4 becomes,

$$\renewcommand{\theequation}{5}
i\omega \tilde{Z} = \tilde{M} - \tilde{Z}/{\tau},$$

where $\tilde{Z}$ denotes the zonal index in a system without eddy-jet feedback. The covariance between $\tilde{z}$ and $\tilde{m}$ must be close to zero when $\tilde{z}$ leads $\tilde{m}$ by a period longer than the decorrelation timescale of the mean-state-independent eddies. It has been shown that the covariance between $\tilde{z}$ and $\tilde{m}$ is a function of $b$ and the covariance between ${z}$ and ${m}$ (see LH01 