Entropic learning enables skilful forecasts of ENSO phase at up to two years lead time

This paper extends previous work (Groom et al., \emph{Artif. Intell. Earth Syst.}, 2024) in applying the entropy-optimal Sparse Probabilistic Approximation (eSPA) algorithm to predict ENSO phase, defined by thresholding the Ni\~no3.4 index. Only satellite-era observational datasets are used for training and validation, while retrospective forecasts from 2012 to 2022 are used to assess out-of-sample skill at lead times up to 24 months. Rather than train a single eSPA model per lead, we introduce an ensemble approach in which multiple eSPA models are aggregated via a novel meta-learning strategy. The features used include the leading principal components from a delay-embedded EOF analysis of global sea surface temperature, vertical temperature gradient (a thermocline proxy), and tropical Pacific wind stresses. Crucially, the data is processed to prevent any form of information leakage from the future, ensuring realistic real-time forecasting conditions. Despite the limited number of training instances, eSPA avoids overfitting and produces probabilistic forecasts with skill comparable to the International Research Institute for Climate and Society (IRI) ENSO prediction plume. Beyond the IRI's lead times, eSPA maintains skill out to 22 months for the ranked probability skill score and 24 months for accuracy and area under the ROC curve, all at a fraction of the computational cost of a fully-coupled dynamical model. Furthermore, eSPA successfully forecasts the 2015/16 and 2018/19 El Ni\~no events at 24 months lead, the 2016/17, 2017/18 and 2020/21 La Ni\~na events at 24 months lead and the 2021/22 and 2022/23 La Ni\~na events at 12 and 8 months lead.