A Simple Intermediate Coupled MJO-ENSO Model: Multiscale Interactions and ENSO Complexity

The Madden-Julian Oscillation (MJO) and the El Niño-Southern Oscillation (ENSO) are two dominant modes of tropical climate variability, each with profound global weather impacts. While their individual dynamics have been widely studied, their coupled interactions, particularly in the context of ENSO complexity, including spatial diversity (Central Pacific vs. Eastern Pacific events), temporal evolution (single-year and multi-year events), and intensity variations (moderate to extreme events), have received limited attention in modeling studies. In this paper, a simple intermediate coupled MJO-ENSO model is developed to address critical gaps in understanding their bidirectional feedback and its role in modulating ENSO complexity. The model integrates multiscale processes, bridging intraseasonal (MJO), interannual (ENSO), and decadal (Walker circulation) variability. Key mechanisms include: (1) interannual SST modulating MJO through latent heat and background states, (2) MJO-induced wind forcing triggering diverse ENSO events, and (3) decadal variability modulating the strength and occurrence frequency of Eastern Pacific and Central Pacific events. Effective stochastic parameterizations are incorporated to improve the characterization of multiscale MJO-ENSO interactions and the emergence of intermittency and extremes. The model captures several crucial observed MJO and ENSO features, including non-Gaussian statistics, seasonal cycles, energy spectra, and spatial event patterns. It also reproduces critical MJO-ENSO interactions: warm pool edge extension, convective activity adjustments that modulate SST, and ENSO's dependence on MJO-driven easterly and westerly wind anomalies. The model provides a useful tool to analyze long-term variations. It also advances the understanding of ENSO extreme events and their remote impacts, as well as seasonal forecasting and climate resilience.