A stochastically forced nonlinear dynamics model for El Niņo-Southern Oscillation (ENSO) is advanced to explore the nature of the highly irregular ENSO cycle. The model physics includes nonlinear dynamics of the coupled ocean-atmosphere system, high-frequency stochastic forcing, and the annual foreign of a prescribed climatological basic state.

The model irregular ENSO-like oscillation arises from three different origins: stochastic resonance, coupled nonlinear instability and stochastic transition. When the basic state is stable, the stochastic forcing excites irregular oscillations by stochastic resonance. When the system is unstable and the coupled dynamics sustain a nonlinear oscillation (stable limit cycle), the stochastic forcing perturbs the deterministic trajectory of the limit cycle in the phase-space, generating irregularities and modifying the oscillation period. When the system possesses multi-equilibrium states, the stochastic forcing may render the system oscillatory by randomly switching the system between a warm and a cold stable steady state.

The stochastic response depends not only on the nonlinear dynamic regimes of the ENSO system but also on the temporal structure (spectrum) and strength of the stochastic forcing. White and red noises are shown to be much more effective than band-limited white noises in stochastic resonance and in altering the characteristics of the nonlinear oscillation. The intraseasonal noise can alter the dominant period of intrinsic nonlinear oscillation, favoring biennial oscillation, especially when the intraseasonal forcing is modulated by monsoon (annual cycle). Stronger forcing yields an enhanced resonant oscillation with a prolonged period. A sufficiently strong white noise forcing, however, can destroy the nonlinear or resonant oscillation, leading to a Markovian process. The basic state annual variation tends to enhance the resonant oscillation but reduces the oscillation period considerably in the marginally stable regime.

The model results suggest that ENSO may arise from multi-mechanisms. The different mechanisms may be at work in various phases of the ENSO evolution, depending on the basic state and the nonlinear dynamics of the system. The monsoon may affect ENSO through modulation of intraseasonal stochastic forcing, enhancing the biennial component of ENSO.