An Adaptive Variance Adjustment Strategy for a Static Background Error Covariance Matrix—Part I: Verification in the Lorenz-96 Model

Accurate initial conditions are crucial for improving numerical weather prediction (NWP). Variational data assimilation relies on a static background error covariance matrix (B), yet its variance estimation is often inaccurate, affecting assimilation and forecast performance. This study introduces DRL-AST, a deep reinforcement learning-based adaptive variance rescaling strategy that dynamically adjusts the variances of B to optimize forecast skill through improved assimilation performance. By formulating variance rescaling as a Markov Decision Process and employing an actor–critic framework with Proximal Policy Optimization, DRL-AST autonomously selects spatio-temporal rescaling factors, enhancing assimilation and forecast accuracy without additional computational cost. As a new paradigm for adaptive variance tuning, DRL-AST demonstrates competitive improvements in forecast skill in experiments with the Lorenz-96 model by generating initial states that better conform to model dynamical consistency. Given its adaptability and efficiency, DRL-AST holds great potential for application in high-dimensional NWP models, where deep learning-based dimensionality reduction and reinforcement learning techniques could further enhance its feasibility and effectiveness in complex assimilation frameworks.