Enhancing the predictability limits of ENSO with physics-guided deep echo state 
networks

Zhang, Zejing; Meng, Jun; Qiu, Zhongpu; Duan, Wansuo; Gao, Jian; Yan, Zixiang; Xiao, Jinghua; Chen, Xiaosong; Cai, Wenju; Kurths, Jürgen; Havlin, Shlomo; Fan, Jingfang

doi:10.1038/s41612-026-01360-5

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Enhancing the predictability limits of ENSO with physics-guided deep echo state networks

Authors

Zhang, Zejing
External Organizations;

Meng, Jun
External Organizations;

Qiu, Zhongpu
External Organizations;

Duan, Wansuo
External Organizations;

Gao, Jian
External Organizations;

Yan, Zixiang
External Organizations;

Xiao, Jinghua
External Organizations;

Chen, Xiaosong
External Organizations;

Cai, Wenju
External Organizations;

/persons/resource/Juergen.Kurths

Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

Havlin, Shlomo
External Organizations;

/persons/resource/Jingfang.Fan

Fan, Jingfang
Potsdam Institute for Climate Impact Research;

External Resource

https://github.com/zhangzejing/RC-ENSO
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Zhang_2026_s41612-026-01360-5.pdf
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Citation

Zhang, Z., Meng, J., Qiu, Z., Duan, W., Gao, J., Yan, Z., Xiao, J., Chen, X., Cai, W., Kurths, J., Havlin, S., Fan, J. (2026): Enhancing the predictability limits of ENSO with physics-guided deep echo state networks. - npj Climate and Atmospheric Science, 9, 92.
https://doi.org/10.1038/s41612-026-01360-5

Cite as: https://publications.pik-potsdam.de/pubman/item/item_34765

Abstract

The El Niño-Southern Oscillation (ENSO) is a dominant mode of interannual climate variability, yet the mechanisms limiting its long-lead predictability remain unclear. Here, we develop a physics-guided Deep Echo State Network (DESN) that operates on physically interpretable climate modes selected from the extended recharge oscillator (XRO) framework. DESN achieves skillful Niño 3.4 predictions up to 16–20 months ahead with minimal computational cost. Mechanistic experiments show that extended predictability arises from nonlinear coupling between warm water volume and inter-basin climate modes. Error-growth analysis further indicates a finite ENSO predictability horizon of approximately 30 months. These results demonstrate that physics-guided reservoir computing provides an efficient and interpretable framework for diagnosing and predicting ENSO at long lead times.