## 6 Discussion
### Feasibility and Applicability of DRL-AST in High-Dimensional NWP Systems  
This study demonstrated the effectiveness of the DRL-AST method in optimizing the variance component of the **B**-matrix within the Lorenz-96 model. While the Lorenz-96 model serves as a well-established chaotic system that is widely used for testing DA techniques, its simplified structure--lacking vertical stratification and comprehensive physical processes--limits its ability to represent the multiscale interactions present in real atmospheric systems. Therefore, to assess the operational potential of DRL-AST, it is essential to validate the method within a more complex NWP model. The Simplified Parameterizations, Primitive-Equation Dynamics (SPEEDY) model, characterized by its intermediate-scale with O(\(10^{4}\)) variables, efficient computational performance, and simplified yet representative physical parameterization schemes (e.g., convection and radiation), serves as a practical testbed for the validation of DRL-AST under computationally tractable and dynamically richer environment conditions [70]. Further transitioning to the Weather Research and Forecasting (WRF) model, with its high-resolution simulation capability, flexible physical parameterizations, and the ability to assimilate real-world observations, provides a suitable platform for evaluating the adaptability and robustness of DRL-AST in realistic forecasting environments [71]. We provide a detailed discussion of the key considerations involved in extending DRL-AST from simplified models to more complex, high-dimensional systems below:  
1. **State space expands from low to high dimensions:** a key challenge in transitioning DRL-AST from the Lorenz-96 model to more complex NWP models like SPEEDY and WRF is the dramatic increase in the dimensionality of the state space. Unlike the low-dimensional structure of Lorenz-96, both the SPEEDY and WRF models simulate multivariate atmospheric states, such as temperature, wind velocity, and humidity. This substantial expansion in state dimensionality introduces computational complexity, impeding efficient RL training by exacerbating convergence difficulties, increasing computational cost, and limiting policy generalization. To mitigate these challenges, future research should explore using DL for feature extraction, enablingdimensionality reduction while retaining the key physical characteristics of the atmospheric state. Possible approaches include convolutional neural networks (CNNs) for local feature extraction, variational autoencoders (VAEs) for compact latent representations, and Transformer-based attention mechanisms to enhance long-range dependencies between atmospheric variables. These methods collectively facilitate efficient state encoding, reducing computational costs and improving the RL model's trainability. Furthermore, to enhance training stability and computational efficiency in high-dimensional NWP models, manifold-learning-based dimensionality reduction strategies, such as principal component analysis (PCA) and locally linear embedding (LLE), may be investigated. These approaches help ensure that reduced state representations retain essential physical information while minimizing redundant computations. Additionally, incorporating multi-scale feature fusion networks could further improve DRL-AST's adaptability to diverse dynamical regimes, ensuring robust policy generalization across varying meteorological conditions. After policy inference, an inverse mapping technique may be employed to reconstruct the full atmospheric state from the reduced feature space, allowing RL-driven optimization to be effectively applied to SPEEDY and WRF models. This approach avoids direct RL applications in high-dimensional spaces, alleviating computational bottlenecks and enhancing training stability. 2. **Selecting a collaborative data assimilation system:** to validate DRL-AST beyond idealized testing, we plan to first implement it within the SPEEDY model and subsequently extend it to the WRF model.