El Niño–Southern Oscillation (ENSO) is the dominant mode of interannual variability in the tropical Pacific. Strong El Niño events, such as those in 1982–83, 1997–98, and 2015–16, cause global weather anomalies and severe economic impacts. Forecasting the strength of such events remains a challenge: the widely publicized forecasts of 2014 predicted an event a year earlier than it actually occurred. The scientific community has long debated whether ENSO is a self-sustaining oscillation or is excited by random noise, and what role the seasonal cycle plays in generating unpredictability. This work contributes to this context by identifying a new mechanism that limits predictability, related to bistability and chaotic dynamics.
The authors used the low-dimensional conceptual Jin-Timmermann (JT) model, which describes three variables: the sea surface temperature difference between the eastern and western equatorial Pacific, the western Pacific surface temperature relative to a nominal value, and the western thermocline depth. The model includes nonlinear terms representing feedbacks from wind, ocean currents, and thermocline dynamics. Numerical integration was performed in MATLAB using the DOP853 algorithm with tight error tolerances (on the order of 10⁻¹²). Parameters were tuned using the MATCONT software to locate Hopf bifurcation points and continue periodic orbits to the chaotic attractor. Then, a weak periodic (seasonal) or stochastic perturbation of parameter a was introduced to investigate switching between attractors.
For the chosen parameters, the model exhibits coexistence of two attractors: a periodic orbit of mixed-mode oscillations (MMO) with a period of about 12.1 years, containing one intense El Niño per cycle, and a chaotic attractor with smaller oscillation amplitude. The basins of attraction of these attractors are interwoven and have fractal boundaries. Even a very weak periodic forcing with amplitude 0.001 causes irregular switching between regimes: in a 6000-year simulation, the maximum number of consecutive MMO cycles was 24, the minimum was 1, and epochs of chaotic oscillations could last more than 200 years. Similar results were obtained with weak multiplicative noise. Sensitivity to initial conditions near basin boundaries is extremely high: the return map stretches the y-coordinate by a factor of 10³.
This work reveals a new mechanism limiting the predictability of strong El Niño events: irregular switching between an oscillatory state with strong events and a chaotic state without them. This differs from traditional explanations based on the spring predictability barrier or interaction with the seasonal cycle. The discovery of bistability in a simple conceptual model suggests that similar dynamics may exist in more complex ENSO models, imposing fundamental limits on long-term prediction of event strength. Compared to neighboring works that examine El Niño from the perspective of prediction or historical data, this paper focuses on intrinsic dynamical unpredictability arising from the attractor structure.
The topic could develop toward searching for precursors of regime switching in real data and more complex models. It may be possible to investigate the influence of climate change on model parameters and hence on switching frequency. Also interesting is how the spatial structure of initial errors interacts with bistability to refine predictability limits. Developing methods for analyzing fractal basin boundaries in climate models could help assess risks of extreme events.
The results may influence the development of ENSO forecasting systems, emphasizing the need for probabilistic approaches and consideration of intrinsic unpredictability. They are also important for interpreting paleoclimate reconstructions that show decadal ENSO variability.
The next step could be to test for bistability in more realistic ENSO models, such as intermediate-complexity models or global climate models. It is also important to attempt to identify precursors of switching in observational data, for example in sea surface temperature indices.
This work directly relates to the fundamental problem of climate system predictability: to what extent long-term forecasts of extreme events are possible in principle. It shows that even in a deterministic system, internal dynamics can generate unpredictability comparable to random noise.
In a 6000-year simulation of the model, an epoch without strong El Niño could last more than two centuries, then suddenly give way to a series of intense events, all without any external forcing other than a weak seasonal cycle.