Ensemble-Mean Dynamics of ENSO Forced by Multiplicative Stochastic Noise in a Spatiotemporal Oscillator Model

Abstract This study examines how rapid atmospheric variability influences ensemble-mean dynamics of El Niño–Southern Oscillation (ENSO) by implementing a spatially structured, state-dependent Ornstein–Uhlenbeck stochastic process within a spatiotemporal oscillator (STO) model. Through applying Gaussian closure, we obtain analytic solutions for both the ensemble-mean and second-order moment equations. The second-order moment solution emerges as a superposition of damped oscillations, whose frequencies align precisely with the natural eigenfrequencies of the deterministic STO model. Notably, this second-order variability—combined with the spatial pattern of stochastic process—forces the ensemble mean through two mechanisms: a persistent harmonic oscillation that has the same frequency with the natural frequency of the original deterministic STO model and a transient damping oscillation that only exhibits its influence in a short time scale of around several months and is negligible for subsequent variation. Correspondingly, while retaining the original oscillation frequency, the ensemble-mean oscillation exhibits modified amplitude and phase compared to the deterministic one. The first mechanism explicitly demonstrates the noise-induced drift in ensemble-mean evolution of ENSO. It reveals how ENSO acts both as a predictable oscillator and a chaos-driven system. Significance Statement The fast atmospheric variability such as westerly wind bursts (WWBs) and Madden–Julian oscillation (MJO) are thought to be important for the development of El Niño–Southern Oscillation (ENSO). This study advances the understanding of noise–ENSO interactions by rigorously quantifying how spatially structured atmospheric noise modulates ENSO’s ensemble-mean dynamics. We demonstrate that state-dependent stochastic forcing induces noise-induced drift through two distinct pathways: phase-amplitude modulation via frequency-synchronized oscillations matching the system’s intrinsic eigenmodes and transient damping in a subseasonal time scale. These findings establish a mathematical foundation for ENSO’s dual nature as both cyclic phenomenon and stochastically modulated system, resolving previous discrepancies between deterministic models and observed irregularity. The analytical framework bridges scale interactions from synoptic stochastic forcing to interannual variability, offering new capacity to simulate ENSO’s characteristic amplitude-phase modulations within unified dynamics.