A Unified Framework for Deep Learning-Based Ensemble-Free Data Assimilation and Forecast Error Correction

Abstract. Filter-based data assimilation, particularly the ensemble Kalman filter (EnKF), has been widely used for forecasting across a broad range of scales. However, maintaining and updating multiple ensemble members incurs substantial computational costs, and accumulated forecast errors progressively degrade forecast skill. To address these challenges, we use the Lorenz-63 system as a testbed and develop a unified deep learning framework that integrates ensemble-free data assimilation emulation – based on a data-assimilation multilayer perceptron (DAMLP) – with forecast-error correction. The experiments show that DAMLP substantially improves computational efficiency while producing analysis states with accuracy comparable to, or better than, that of EnKF. The periodic correction strategy effectively extends the useful forecast range, and its combination with a more accurate initial state yields a clear synergistic improvement, further slowing the growth of forecast errors. In addition, local Lyapunov exponents (LEs) are introduced to stratify the results according to local dynamical instability. These results demonstrate the potential of combining learned assimilation emulation with observation-free forecast-error correction for efficient forecasting of chaotic dynamical systems.