Deterministic Nonlinearity Over Stochastic Noise: Resolving MJO's Complexity and Predictability Drivers

The complex behavior of the Madden–Julian Oscillation (MJO), a key source for global subseasonal-to-seasonal predictability, has often been attributed to stochastic forcing by unresolved processes. Here, we demonstrate that its erratic evolution is fundamentally deterministic. Our data-driven model reveals a spectral dichotomy in low-dimensional MJO dynamics: predictable, quasi-periodic oscillations coexist with and are perturbed by deterministic chaotic forcing. The latter governs the emergent complexity of the system. Contrasting true deterministic forcing against stochastic surrogates shows that the system with deterministic forcing preserves bounded amplitude, while the stochastic processes induce unboundedness. Furthermore, we quantify how deterministic forcing yields greater complexity and unpredictability in the MJO’s evolution than stochastic surrogates. Specifically, deterministic mechanisms induce chaos through the mixing of periodic orbits within the spectral dichotomy, whereas stochastic forcing can only generate quasi-periodic behavior via resonant interaction with these orbits. These results reveal the deterministic origins of MJO complexity and offer new pathways for improving its prediction and understanding its predictability.