Decadal variability of ENSO is present in historical and paleo records, and has been simulated by a hierarchy of dynamical and statistical models. The ENSO variability in the IPCC AR4 Coupled GCMs ranges from constant periodicity or amplitude to significant inter-decadal variability in both period and amplitude. In the 2000-yr long simulation of the GFDL CM2.1 model, ENSO exhibits striking modulation in the absence of external forcing that could induce persistent regimes. This (multi)decadal variability in the CM2.1 ENSO, along with the length of the simulation, provides new ground for investigation of the causes of long-term modulation of ENSO behavior and the implications for predictability at multiple time-scales from the short-range to the decadal.

In this work, we investigate ENSO predictability in the unforced simulation of the GFDL's CM2.1 GCM in a dynamical systems theory context. We compute the Local Lyapunov Exponents (LLEs) of the NINO3 time series, and use them as a means of classifying epochs of distinct ENSO behavior.

Decadal variations in ENSO amplitude and frequency are accompanied by decadal variations in predictability, as measured by the LLEs. Epochs of moderate, nearly sinusoidal ENSO events are classified by the LLEs as the most predictable. The results also show that active and inactive ENSO periods correspond to periods of increased and decreased predictability. The magnitude and sign of ENSO events also seems to affect predictability ahead of each event, depending on the epoch. In addition, we examine the 'loss' or 'gain' of predictability across these epochs and their relation to the physical evolution of the ENSO events. In particular, we investigate the role of the thermocline depth anomalies in the initiation of warm ENSO events and its effect on predictability, as characterized by the LLEs. Finally, the correspondence of the LLE statistics with prediction error in 'perfect-model' reforecasts is discussed.