## 6 Discussion
### Feasibility and Applicability of DRL-AST in High-Dimensional NWP Systems
The Parallel Data Assimilation Framework (PDAF) supports 3D-Var, EnKF, and hybrid methods, and its modular design facilitates efficient coupling with SPEEDY for DA experiments [72]. The WRF Data Assimilation (WRFDA) system offers a comprehensive suite of DA techniques and is tightly integrated with WRF, supporting the assimilation of diverse real-world observations to improve initial conditions [73]. For this study, we consider 3D-Var as the baseline assimilation framework due to its computational efficiency and suitability for frequent RL-environment interactions. Unlike four-dimensional variational assimilation (4D-Var) and EnKF, which involve high computational costs, 3D-Var employs a static **B**, allowing for rapid gradient-based optimization. However, static **B** cannot dynamically adapt to evolving weather regimes, potentially resulting in assimilation errors, particularly in rapidly changing systems such as deep convection and tropical cyclones. By leveraging DRL-AST to adaptively optimize the variance component of **B**, we anticipate improving 3D-Var's performance across different meteorological conditions. 3. **Design and optimization of the action space:** the DRL-AST action space must align with the formulation of **B** in the intermediate-to-complex DA system, such as those employed for SPEEDY and WRF models. Instead of storing **B** explicitly as a full-rank matrix, DA frameworks like PDAF and WRFDA utilize a control variable transform (CVT) approach to model **B**[18]. This approach decomposes **B** into key statistical components, including variances (\(\sigma^{2}\)), eigenvectors, eigenvalues, and horizontal/vertical length scales. These elements provide a compact yet accurate approximation of **B**, preserving its essential statistical characteristics while substantially reducing storage demands and computational costs. Therefore, in experiments involving these DA systems, the action space of DRL-AST is formulated as a vector comprising spatially adaptive variance scaling factors at time step \(t-1\). These factors govern the variance of different control variables across distinct regions and are dynamically adjusted by the RL agent to optimize assimilation performance. At each subsequent time step, this vector evolves, enabling a temporally adaptive adjustment mechanism. The spatial distribution of variance in **B** is influenced by multiple factors, including topography, large-scale circulation patterns, observational network density, and model errors. For instance, complex terrain (e.g., mountainous regions) often amplifies local dynamical processes, resulting in increased variance estimates, while observation-sparse regions such as oceans may suffer from underestimated or overestimated background errors. To identify an appropriate spatial partitioning scheme--whether based on latitude, topography, or meteorological considerations--we will draw upon literature reviews, sensitivity experiments, and data-driven statistical analyses. Furthermore, since these DA systems represent **B** through CVT, future extensions could refine horizontal and vertical length scales and other key components by expanding the action space. This would enable the more precise spatio-temporal tuning of **B**, improving variational assimilation accuracy. 4. **Bridging idealized and operational reward functions:** a key challenge in extending DRL-AST from idealized environments to intermediate-to-complex NWP systems lies in constructing reward functions that remain valid when the true state of the atmosphere is not observable, as is typical in operational settings. A widely adopted solution in AI for Earth system science is to use reanalysis datasets, such as the fifth-generation ECMWF reanalysis dataset (ERA5), as proxies for the true state during training and evaluation [37]. Although ERA5 has limitations--including coarse spatial resolution and assimilation-induced biases--it provides a physically consistent and globally accessible benchmark.