Deciphering chaos in the Madden-Julian oscillation

The Madden-Julian Oscillation (MJO), having far-reaching impact on Earth’s climate and human society, is an important tropical phenomenon characterized by a typical 30–90-day period in phase evolution. The MJO was hardly being connected to chaos, which is featured with aperiodicity. However, unlike the quasi-periodic phase evolution, the event-to-event changes of MJO, to some extent represented by its amplitude evolution, is irregular. By presenting multiple evidence, we demonstrate that the MJO’s amplitude evolution is deterministically chaotic. Combining eigen-time-delay embedding and Koopman operator into a regression model, we further reveal the cause of chaos through a data-drive approach. We show that the dynamics of MJO amplitude can be decomposed into multiple periodic obits and nonlinear interaction between them. The aperiodic motion resulted from these nonlinear interactions disturbs the periodic obits asynchronously, leading to chaotic evolution of MJO amplitude. The findings here unveil the strong nonlinear nature of the MJO, explaining the difficulties in the long-term MJO prediction and providing new insight into MJO’s complexity.