This work sits at the intersection of machine learning and climate science, where neighboring studies have already shown that deep neural networks can predict the ENSO index 17–20 months ahead, but they require large ensembles of climate model simulations for training. Other adjacent work examines seasonal predictability barriers and how AI might overcome them. This paper stands out because it uses only a short record of satellite observations (about 350–520 monthly snapshots) and still reaches a 24-month horizon without resorting to climate model simulations. It is the first test of entropy-based learning in a 'small data' regime for such a long ENSO phase forecast.
The authors assembled monthly data on global sea surface temperature, vertical gradient of subsurface temperature, and wind stresses over the tropical Pacific from September 1981 to December 2024. Each field underwent principal component analysis with a 12-month lag (singular spectral analysis), retaining 160 components for surface temperature, 140 for the gradient, and 100 for winds, plus the Niño-3.4 index and warm water volume, yielding 402 features in total. For each forecast lead time (from 1 to 24 months), they trained an ensemble of 50 eSPA models on 80% of the data, selecting the best one by ranked probability score on the validation 20% subset. To account for seasonality, models were trained only on months with the same target season. Then they trained an eSPA meta-model that predicts the probability of each base model being correct based on 30 interpretable characteristics, and used those probabilities to weight the ensemble.
In retrospective forecasts from January 2012 to December 2022, eSPA showed positive ranked probability skill scores (RPSS) up to 22 months, whereas the IRI plume retains skill only up to 10 months. Accuracy remains above climatology up to 24 months, and the area under the ROC curve (AUC) remains above chance up to 24 months for El Niño and up to 21 months on average across classes. Differences with IRI are not statistically significant at the 95% level, but eSPA outperforms in AUC at lead times of 2–6 months. The model successfully predicted the 2015/16 and 2018/19 El Niño events 24 months ahead, as well as the 2016/17, 2017/18, and 2020/21 La Niña events 24 months ahead. The 2021/22 and 2022/23 La Niña events proved harder, being predicted only 12 and 8 months ahead. Computational cost for a full 24-month forecast was about 0.113 kWh, which is 1000–10000 times less than a single ensemble member of the dynamical model GloSea5-GC2.
This work shows that entropy-based learning can extract predictable information from short observational records without overfitting, placing it on par with the best deep networks but with far less data and computational resources. Unlike neighboring studies that use transfer learning on large climate model ensembles, here training is done only on real observations, avoiding inherited model biases. Meta-learning that weights the ensemble by interpretable features opens the way to more reliable probabilistic forecasts under climate non-stationarity.
The method can be extended to regression forecasting of the Niño-3.4 index itself, as well as to other modes of variability such as the Madden–Julian Oscillation or the Indian Ocean Dipole. Adaptive learning across different climate regimes could help cope with non-stationarity induced by anthropogenic warming. In the long run, it may be possible to build a unified data-driven model of tropical intraseasonal and interannual variability.
The results could improve operational seasonal forecasts for agriculture, water resource management, and energy, especially in ENSO-sensitive regions. The low computational cost makes the method accessible to meteorological services in developing countries.
Test the method in real-time mode on new data after 2022. Investigate the reasons for reduced skill for the June–August target season and improve handling of consecutive La Niña events.
The paper directly addresses the 'spring predictability barrier' problem of ENSO and the limited observational record, which is a key challenge for statistical and dynamical models. It also contributes to the small-data problem in climate machine learning, showing that sparse probabilistic models can compete with deep networks without large training sets.
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 applied entropy-optimal sparse probabilistic approximation (eSPA) to satellite data since 1981 to predict the ENSO phase with lead times up to 24 months. They trained an ensemble of 50 models on 80% of the data, selecting the best ones by a ranked probabilistic score on a validation set, and aggregated their predictions with a meta-model that estimates the probability of each forecast being correct. In retrospective tests for 2012-2022, eSPA retains skill up to 22 months in RPSS and up to 24 months in accuracy and AUC, with computational costs 3-4 orders of magnitude lower than dynamical models.
Where its strength is
This work demonstrates that entropy-based training effectively extracts predictable information from short observational records, achieving a forecast horizon comparable to deep neural networks, but without the need for large ensembles of climate models.
Where it could go next
Worth trying
Why this may matter
If the eSPA approach proves effective on independent data and is reproduced by other groups, it could become a cost-effective alternative to dynamical models for operational ENSO forecasting, especially under limited computational resources.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.59, against a usual 0.64. It looks like few have drilled nearby.
A full 24-month eSPA forecast consumes about as much energy as a typical laptop running for roughly 2 hours, whereas a single run of a dynamical seasonal forecast model is comparable to the monthly electricity use of an average apartment.
In Kim Stanley Robinson's novel 'The Ministry for the Future', accurate long-term forecasts of climate anomalies become the basis for global economic decisions. This method, predicting El Niño two years ahead, brings such a possibility closer.