zonal wind and temperature, so that the difference of the equilibrium mean states between EXP and CTL matches the pattern of the annular mode in CTL. This external forcing is calculated using the LRF found by @Pedram2016a, and EXP is essentially the same as Test 3 in their article. The LRF ($\mathbf{L}$ in Equation 1) relates anomalous state vector $\mathbf{x}$ to its temporal tendency and an external forcing $\mathbf{f}$ as,

$$\renewcommand{\theequation}{1}
\frac{d\mathbf{x}}{dt} = \mathbf{L} \mathbf{x} + \mathbf{f},$$

in which $\mathbf{x}$ consists of $[\mathbf{u}]$ and $[\mathbf{T}]$, zonally averaged (denoted by square brackets) zonal wind and temperature anomalies from the mean state of CTL. Assuming that eddies are in statistical equilibrium with the mean flow in the long-term integrations, Equation 1 is valid for weak external forcings (see Hassanzadeh and Kuang 2016a for more details). With $\mathbf{x}_{o}$ denoting the anomalous state vector associated with the annular mode, the particular external forcing for EXP is $\mathbf{f}_{o} = -\mathbf{L} \mathbf{x}_{o}$.

[It is worth mentioning that Hassanzadeh and Kuang (2016a) have shown that the leading EOF of \[u\] and \[T\] strongly resembles the singular vector of the LRF that has the smallest singular number]{} [the so-called neutral vector, see @Goodman2002], [which confirms that the annular 