The interaction between El Niño and the Madden-Julian Oscillation is recognized as important for forecasting extreme weather, but complex climate models often reproduce it poorly. Many models overestimate eastern Pacific events and underestimate central Pacific ones, and also misrepresent non-Gaussian characteristics. Conceptual models help isolate key mechanisms, but previously they were built separately for ENSO and MJO. This work stands apart: nearby in the archive are studies on neutrinos, brain signals, and other topics, and the closest topical neighbor is a paper on neutrino oscillations, which underscores the novelty of directly coupling ENSO and MJO in a single conceptual model.
The ocean component is a three-box recharge oscillator covering the western, central, and eastern equatorial Pacific. The atmospheric component uses a stochastic skeleton model for the MJO, truncated to the first three zonal Fourier modes, preserving large-scale eastward propagation. Coupling between ocean and atmosphere proceeds via two pathways: MJO wind stress forces the ocean, while latent heat from the ocean surface affects convection and moisture in the atmosphere. Additionally, state-dependent noise is introduced, which enhances statistical feedback and helps reproduce extreme events. A slow decadal process modulates the background state, determining the predominance of eastern or central Pacific events. The model contains about two dozen equations and was tuned manually against observations.
The model reproduces the observed diversity of El Niño: moderate and extreme eastern Pacific events, central Pacific events, multi-year events, and La Niña. Event frequencies over 70 years match data within confidence intervals. Sea surface temperature spectra have a peak at 3–5 years, and non-Gaussian probability distributions capture positive skewness for the eastern region and negative skewness for the central region. The model also reproduces the seasonal locking of ENSO to winter and MJO spectra in the intraseasonal band of 30–90 days. Lagged correlation between MJO amplitude and ocean temperature shows MJO enhancement before and during El Niño, consistent with observations. Sensitivity experiments show that removing any of the coupling channels—wind stress, latent heat, or state-dependent noise—degrades the statistics and reduces the frequency of extreme events.
This work is the first to couple ENSO and MJO in a single stochastic conceptual model where the MJO is explicitly resolved rather than prescribed as noise. This differs from neighboring studies that treat these phenomena separately or use heavily parameterized atmospheres. The model shows that state-dependent noise is as important as deterministic wind forcing for reproducing observed statistics. This approach provides a controlled environment for testing theories and studying the role of nonlinearity and noise in the coupled system.
The model can be used to study ENSO predictability in the presence of the MJO, and to test how necessary explicit MJO resolution is in forecasting systems. The decadal variable allows investigation of the coupled system's response to changes in Walker circulation strength under global warming. Its low computational cost makes the model suitable for generating long time series needed for analyzing rare events and training machine learning methods.
The results may improve understanding and prediction of extreme events associated with El Niño, in the tropics and beyond.
A next step could be incorporating the model into multi-model ensembles to improve reanalysis and initialization of more complex climate models.
This work directly addresses an unresolved problem in climate science: why CMIP models poorly reproduce ENSO diversity and non-Gaussian statistics. The proposed approach shows that explicit MJO resolution and state-dependent noise may be key missing ingredients.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors built a stochastic conceptual model that couples ENSO and the Madden–Julian oscillation (MJO): the ocean is represented as a three-box recharge oscillator, the atmosphere as the first three modes of the MJO skeleton model, the coupling goes through wind stress and latent heat, and a slow decadal process modulates the background state. The model reproduces the diversity of El Niño events, the non-Gaussian statistics of sea surface temperatures, MJO spectra, and seasonal locking, and it also shows the importance of state-dependent noise.
Where its strength is
The strength of the work lies in combining ENSO and the MJO in a single conceptual model with explicit MJO resolution, which allows investigating their interaction mechanisms and the statistics of extreme events at low computational cost.
Where it could go next
Worth trying
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.49, against a usual 0.64. It looks like few have drilled nearby.
The model reproduces the extreme El Niño of 1997–1998, when sea surface temperatures in the eastern Pacific rose by more than 2.5 degrees Celsius.