where  \(F\left(y\right)\)represents the m -step-ahead forecast from PDSI \(\left\{X_t\right\}\) on \(N\) years for ensemble (Rth)–runs;  \(S_t\) is the smoothed PDSI at decadal scale centred on time-year \(t\) . \(\) is the actual PDSI; \(\alpha\) is the smoothing parameter for the data; \(I_{t-p}\) is the smoothed cycle index at the end of period t with its number defined by the the number of periods \(\left(p\right)\) in the seasonal cycle: