Figure 2 . a) Shows the same ROC diagram as in Figure 1e for a future time window of \(T_{W}=\)1 year. ROC is the red curve, representing a plot of the true positive rate (hit rate) as a function of the false positive rate (false alarm rate). The diagonal line is the true positive rate for an ensemble of 50 random time series, each of which were obtained from the state variable time series \(\Theta(t)\) using a bootstrap procedure of random sampling with replacement. The ensemble of random time series is shown as the cyan curves grouped near the diagonal line. b) Shows the skill, as a function of the future time window \(T_{W}\) , for fixed EMAN -value and \(\lambda\)-value. c). Shows the skill indexSKI defined in equation (1), also as a function of \(T_{W}\). d). Shows the Shannon information entropy, equation (3), as a function of future time window \(T_{W}\). Here the information is computed from the probability mass function associated with the ROC curve. Horizontal dashed line is the information entropy for the random ROC curve (diagonal line), assuming N = 200 threshold values.