Diffusion Models Bridge Deep Learning and Physics in ENSO Forecasting
Weifeng Xu, Xiang Zhu, Xiaoyong Li, Qiang Yao, Xiaoli Ren, Kefeng Deng, Song Wu, Chengcheng Shao, Xiaolong Xu, Juan Zhao, Chengwu Zhao, Jianping Cao, Jingnan Wang, Wuxin Wang, Qixiu Li, Xiaori Gao, Xinrong Wu, Huizan Wang, Xiaoqun Cao, Weiming Zhang, Junqiang Song, Kaijun Ren
TL;DR
The paper introduces a conditional diffusion model for ENSO forecasting that treats future SST as a probabilistic distribution conditioned on six months of history, enabling explicit uncertainty quantification and long-range forecasts. Through a physics-guided reverse-time SDE, the model uncovers a mechanistic link to the recharge-discharge ENSO oscillator, consistent with the Van der Pol framework, thereby marrying data-driven prediction with deterministic dynamics. Key findings include extended lead times up to ~26–30 months with competitive skill, improved 21st-century forecasts via observation-based training, and the ability to reproduce extreme events and early SPB signals through ensemble uncertainty. This work offers a transferable, interpretable probabilistic forecasting paradigm for complex geophysical systems and demonstrates how diffusion models can encode fundamental physical processes while delivering practical predictive performance.
Abstract
Accurate long-range forecasting of the El \Nino-Southern Oscillation (ENSO) is vital for global climate prediction and disaster risk management. Yet, limited understanding of ENSO's physical mechanisms constrains both numerical and deep learning approaches, which often struggle to balance predictive accuracy with physical interpretability. Here, we introduce a data driven model for ENSO prediction based on conditional diffusion model. By constructing a probabilistic mapping from historical to future states using higher-order Markov chain, our model explicitly quantifies intrinsic uncertainty. The approach achieves extending lead times of state-of-the-art methods, resolving early development signals of the spring predictability barrier, and faithfully reproducing the spatiotemporal evolution of historical extreme events. The most striking implication is that our analysis reveals that the reverse diffusion process inherently encodes the classical recharge-discharge mechanism, with its operational dynamics exhibiting remarkable consistency with the governing principles of the van der Pol oscillator equation. These findings establish diffusion models as a new paradigm for ENSO forecasting, offering not only superior probabilistic skill but also a physically grounded theoretical framework that bridges data-driven prediction with deterministic dynamical systems, thereby advancing the study of complex geophysical processes.