Chaotic climate system forecasting using an improved echo state network with sparse observations

L Ding and YL Bai and DH Zheng and XD Pan and MH Fan and X Li, SCIENCE CHINA-EARTH SCIENCES, 68, 2346-2360 (2025).

DOI: 10.1007/s11430-024-1593-9

Error accumulation in long-term predictions of chaotic climate systems is caused primarily by the model's high sensitivity to initial conditions and the absence of dynamic adjustment mechanisms, leading to gradual forecast divergence. This presents a critical challenge to achieving stable long-term predictions. While current data-driven approaches perform well in short-term forecasting, their accuracy deteriorates significantly over time. To overcome this limitation, we propose an autonomous echo state network with a snow ablation optimizer (AESN-SAO), which significantly improves the adaptability and robustness of data-driven methods under varying initial conditions. This approach not only eliminates the need for manual hyperparameter tuning in traditional AESNs but also effectively mitigates the common issue of initial conditions sensitivity in chaotic climate systems. Furthermore, we introduce a sparse observation insertion mechanism based on the Lyapunov time and valid prediction time (VPT), which enables AESN-SAO to correct errors prior to system divergence, effectively extending the prediction horizon. Numerical experiments conducted on the Lorenz-63 and Climate Lorenz-63 systems demonstrate that integrating sparse observations with AESN-SAO approach extends the VPT to approximately 99 Lyapunov times, markedly reducing error accumulation in long-term forecasts. This study provides a reliable and efficient framework for long-term predictions in climate systems with nonlinear and chaotic dynamics, with promising applications in weather forecasting, climate modeling, and disaster risk assessment.

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