Here is their justification for choosing the threshold $Q = 2$:
> When observing the probability density function of $W$ it is clear that for non-El Niño time regimes, W = 2 is actually the minimal value that exists. It therefore appears that choosing this threshold makes the network very sensitive to El Niño events while remaining insensitive to other changes in climate. The reason is that the distribution of $W(\ell,r,y)$ tends to typical lower values of $W(\ell,r,y)$ during El Niño, as can clearly be seen in Fig. 3 (A-E). A remarkable property of this softening is that the lower limit of the distribution drops from being close to 2 to some significantly lower value. Changes in climate around the world due to El Niño events thus share a unified property of the correlation pattern, which can be tracked in a reliable way by the number of surviving links $n_k(y)$ in the climate network.