Ensemble Mean Dynamics of the ENSO Spatiotemporal Oscillator with Fractional Stochastic Forcing

This study investigates the impact of long-term memory stochastic forcing on the ensemble mean dynamics of the El Niño–Southern Oscillation (ENSO) by incorporating a fractional Ornstein-Uhlenbeck (FOU) process as external forcing into an ENSO spatiotemporal oscillator (STO) conceptual model. Unlike the classic Ornstein-Uhlenbeck (OU) process, the FOU process exhibits a slow power-law decay in auto-correlation and can trigger an anomalous growth rate that persistently influences the divergence/dissipation of the ensemble mean system. Furthermore, theoretical and quantitative analyses verify that the anomalous growth rate is determined by the ensemble mean of the FOU process, reflecting the cumulative nature of long-memory forcing. Crucially, the anomalous growth rate is positive and thus induces system divergence when the FOU process exhibits a positive ensemble mean, whereas it is negative and induces dissipation when the ensemble mean is negative. Also, the anomalous growth rate intensifies with decreasing fractional order. On the other hand, FOU forcing can also modulate the phase of the ensemble mean oscillation for ENSO. When the phases of the natural and forced oscillations are in phase alignment, the phase of the ensemble mean oscillation leads relative to the natural oscillation. Conversely, when the phases of the natural and forced oscillations are in anti-phase alignment, the phase of the ensemble mean oscillation lags behind relative to the natural oscillation. Future work would address the case when the external forcing has a spatial structure and seek observational validation of the identified growth rate signatures and phase shifts.