Proceeding with their development...

Next, define:

$$ Max(\ell,r,y) = Max \{ |X(r,\ell,y,\tau)| : \: \tau_{min} \leq \tau \leq \tau_{max} \} $$

$$ Std(\ell,r,y) = Std \{ |X(r,\ell,y,\tau)| : \: \tau_{min} \leq \tau \leq \tau_{max} \} $$

$$ W(\ell,r,y) = Max(\ell,r,y) \, / \, Std(\ell,r,y) $$

$ W(\ell,r,y) $ is called the _correlation strength_ of the link between $\ell$ and $r$ during year $y$.

The value of $\tau$ at which $ Max(\ell,r,y) $ is achieved is the _time delay_ between points $\ell$ and $r$ during year $y$.