the eddy-jet feedback, which will be briefly explained in this section. With the same notations as in LH01, $z(t)$ indicates the zonal index, and $m(t)$ denotes the time series of eddy forcing on the annular mode, which is defined as the projection of the anomalous eddy momentum convergence onto the leading EOF of $\langle [\mathbf{u}]\rangle$. As discussed in LH01, the tendency of $z$ is formulated as, $$\renewcommand{\theequation}{2a}
 dz/dt = m - z/\tau,$$

in which $\tau$ is the damping timescale. Equation 2a can be interpreted as the zonally and vertically averaged zonal momentum equation (LH01), $$%\renewcommand{\theequation}{}
 \frac{\partial \langle[u]\rangle}{\partial t} = \frac{1}{\cos^2 \phi} \frac{\partial(\langle[u'v']\rangle \cos^2 \phi)}{a \partial \phi} - F,$$ [where $u'$ and $v'$ are deviations of zonal wind and meridional wind from their respective zonal means, $\phi$ is the latitude, $a$ is the Earth’s radius, and $F$ includes the effects of surface drag and secondary circulation.]{}

With capital letters denoting the Fourier transform of the corresponding lower case variables and $\omega$ denoting [angular]{} frequency, Equation 2a can be written as,

$$\renewcommand{\theequation}{2b}
i\omega Z = M - {Z}/{\tau}$$

Figure 3a shows the power spectrum of the zonal index in the reanalysis data, with a lowest resolved frequency of 1/1024 cycles per day 