## 7 Conclusions  
This study proposes a deep reinforcement learning-based strategy, DRL-AST, leveraging a GRU-enhanced actor-critic framework for spatio-temporally adaptive variancesrescaling in the VarDA system. The method formalizes the variance adjustment of the **B**-matrix--estimated via the NMC method--as an MDP, in which the analysis state \(\mathbf{x}_{t}^{x}\) serves as the environment state. A policy network is trained using the PPO algorithm to generate a chunk-wise rescaling vector \(\mathbf{W}=[w_{1},\ldots,w_{ck}]\) to produce an adaptively rescaled matrix \(\mathbf{B}_{\mathbf{W}}\). This rescaled matrix is then used in the VarDA system to compute the updated analysis state. The resulting \(\mathbf{x}_{t}^{a}\) serves as the initial condition for the next forecast cycle, thereby completing the sequential forecast-assimilation cycle. This framework enables dynamic, cycle-wise variance rescaling driven by the evolving forecast state, thereby enhancing the integration of observations and contributing to improved forecast accuracy across assimilation cycles. Compared to the constant rescaling factor in the CON method and the semi-adaptive strategy of CUTE-ST, which requires the manual tuning of the parameter \(\alpha\) within the range of 0 to 1, DRL-AST achieves a fully adaptive spatio-temporal variance rescaling. Numerical experiments demonstrate that DRL-AST provides competitive forecast skill across different observational error levels by generating initial conditions that are more dynamically consistent. After training, DRL-AST can be seamlessly integrated into the assimilation system as a forward computation step without incurring additional computational costs. This feature allows DRL-AST to maintain computational efficiency while enhancing forecast performance, making it well suited for long-term numerical forecasting tasks. Further analyses reveal that the GRU module in the DRL-AST policy network effectively captures the historical evolution of assimilation states, thereby implicitly learning the dynamical structure of the forecast model. The experimental results indicate that the initial state optimized by DRL-AST extends the effective prediction skill of the forecast model to approximately two Lyapunov times, whereas other methods typically exhibit rapid error growth and saturation after a single Lyapunov time. This advantage is particularly evident in predictions following univariate assimilation analysis. Overall, the DRL-AST-enhanced VarDA system provides initial conditions that better align with the dynamical constraints of numerical models, ensuring improved stability and accuracy in long-term forecasts. Future research will focus on extending DRL-AST to high-dimensional NWP models, particularly within complex frameworks such as WRF. To enhance operational feasibility, DL-based dimensionality reduction techniques will be explored to mitigate computational costs. Additionally, DRL-AST's policy network can be transferred to 4D-Var to broaden its applicability. However, given the high computational cost of 4D-Var, ensuring efficient RL training remains a critical challenge. In summary, DRL-AST is an efficient and scalable spatio-temporally adaptive data assimilation strategy that not only demonstrates competitive performance in the Lorenz-96 model but also holds great potential for extension to high-dimensional numerical weather prediction systems. Future research will further optimize its computational efficiency, enhance its adaptability to complex atmospheric systems, and explore its applicability across various DA systems. Conceptualization, L.H., H.L. and J.S. ; methodology, L.H., H.L. and D.W.; software, L.H. and D.W.; validation, L.H., H.L., D.W. and W.W.; formal analysis, L.H., H.L., D.W. and W.W.; investigation, L.H., H.L., J.S., R.H. and H.C.; resources, L.H., H.L., W.W., R.H. and H.C.; data curation, L.H. and H.L. ; writing--original draft preparation, L.H. ; writing--review and editing, L.H., H.L. and W.W.; visualization, L.H. ; supervision, H.L. and J.S.