Butterfly effect and a self-modulating El Niño response to global warming.

El Niño and La Niña, collectively referred to as the El Niño-Southern Oscillation (ENSO), are not only highly consequential1-6 but also strongly nonlinear7-14. For example, the maximum warm anomalies of El Niño, which occur in the equatorial eastern Pacific Ocean, are larger than the maximum cold anomalies of La Niña, which are centred in the equatorial central Pacific Ocean7-9. The associated atmospheric nonlinear thermal damping cools the equatorial Pacific during El Niño but warms it during La Niña15,16. Under greenhouse warming, climate models project an increase in the frequency of strong El Niño and La Niña events, but the change differs vastly across models17, which is partially attributed to internal variability18-23. Here we show that like a butterfly effect24, an infinitesimal random perturbation to identical initial conditions induces vastly different initial ENSO variability, which systematically affects its response to greenhouse warming a century later. In experiments with higher initial variability, a greater cumulative oceanic heat loss from ENSO thermal damping reduces stratification of the upper equatorial Pacific Ocean, leading to a smaller increase in ENSO variability under subsquent greenhouse warming. This self-modulating mechanism operates in two large ensembles generated using two different models, each commencing from identical initial conditions but with a butterfly perturbation24,25; it also operates in a large ensemble generated with another model commencing from different initial conditions25,26 and across climate models participating in the Coupled Model Intercomparison Project27,28. Thus, if the greenhouse-warming-induced increase in ENSO variability29 is initially suppressed by internal variability, future ENSO variability is likely to be enhanced, and vice versa. This self-modulation linking ENSO variability across time presents a different perspective for understanding the dynamics of ENSO variability on multiple timescales in a changing climate.