Abstract: Accurate estimation of the background error covariance matrix denoted as B remains a critical challenge in numerical weather prediction (NWP), directly influencing data assimilation (DA) performance and forecast accuracy. Although hybrid ensemble–variational (EnVar) methods combine static and flow-dependent matrices to improve assimilation, their effectiveness is constrained by empirically fixed weights. To address this limitation, we propose DRL-EnVar, an adaptive hybrid EnVar DA method enhanced with deep reinforcement learning. DRL-EnVar integrates deep learning (DL) components, including a novel cyclic convolution module to extract abstract features from data, and employs reinforcement learning (RL) to dynamically optimize hybrid weighting strategies. The system adaptively combines multiple ensemble-based flow-dependent matrices with one or more static matrices to construct a time-varying hybrid matrix B that better reflects real-time background errors. Experimental results demonstrate that DRL-EnVar performs better than the traditional ensemble Kalman filter (EnKF) and hybrid covariance DA (HCDA) methods, especially under sparse observations or transitional changes in state variables. It achieves competitive or superior assimilation accuracy with lower computational cost, and can be flexibly integrated into both three-dimensional variational assimilation (3DVar) and four-dimensional variational assimilation (4DVar) frameworks. Overall, DRL-EnVar offers a novel and efficient approach to adaptive DA, particularly valuable for improving forecast skill during transitional weather regimes.

Key words: Adaptive data assimilation; Hybrid ensemble–variational method; Background error covariance; Deep reinforcement learning

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