A Transformer-weakly coupled ensemble data assimilation framework for error correction

Machine learning is increasingly being integrated into data assimilation. Transformer models are capable of capturing long-range temporal dependencies, enabling them to correct errors in the analysis outputs of traditional filters and thereby enhancing assimilation performance. This paper proposes a weakly coupled integration framework for error correction within a sequential assimilation structure by leveraging Transformer-based residual prediction. The framework preserves the original forecast-analysis workflow and statistical assumptions of the conventional filter, while at observation times, it employs a pre-trained Transformer model to predict residuals for correcting the analysis field, thereby establishing a weakly coupled, readily integrable learning-enhanced assimilation scheme. Numerical experiments based on the Lorenz-96 system are conducted to evaluate assimilation performance under varying sensitivity settings. The results demonstrate that the proposed weakly coupled Transformer method offers enhanced resistance to assimilation noise and greater robustness in analysis field generation under sparse observation conditions. Under standard covariance localization and multiplicative inflation, the framework retains approximately 56–61% root mean squared error (RMSE) reduction, confirming its complementary value with practical filter configurations. A 20-seed window-length ablation shows that shortening the input window from L = 101 to L = 5 reduces the RMSE improvement from 42% to 1.5%, identifying temporal context as the central design element. All results are obtained within a perfect-model Observing System Simulation Experiment (OSSE) framework in which the true state is known; extension to real observational scenarios where the truth is unavailable remains a direction for future work.