## 5 Experimental Results
### Quantitative Results
#### 5.3.3 Performance of DA System and Model Forecasting
Across all tested standard deviations of observational errors, the proposed DRL-AST method consistently achieves competitive average \(RMSE_{\mathbf{s}}\) values and relatively small standard deviations over a 5-year continuous assimilation period. However, when \(\sigma_{\varphi^{\prime}}=1.5\), CUTE-ST exhibited slightly better improvements than DRL-AST (as shown in Table 3, row 5; although both methods achieve an \(RMSE_{\mathbf{s}}\) value of 0.63 when rounded to two decimal places, the unrounded value for CUTE-ST is marginally smaller). This may be attributed to the fact that CUTE-ST not only iteratively updates the variances of the **B**-matrix but also modifies its correlation structure, resulting in an additional impact on the assimilation results. For fair comparison, the settings of CUTE-ST were strictly reproduced in this study. Nevertheless, when \(\sigma_{\varphi^{\prime}}=0.5,1,\) and \(2.5\), the improvement ratio of DRL-AST remains comparable to or slightly better than that of CUTE-ST and CON. In contrast to NO, the proposed DRL-AST method demonstrates stable assimilation performances across varying observational error levels by adaptively selecting rescaling factors through spatio-temporal optimization. Furthermore, we have included a comparison of the computational time required for the 5-year assimilation cycle under different variance adjustment methods. Specifically, when the scaling factor is 1.0, NO and CON require approximately 108 s, while the adaptive variance-adjustment methods CUTE-ST and DRL-AST achieve lower average computational times of 97 s and 89 s, respectively. To further quantify the inference efficiency, each inference step of the trained DRL-AST policy requires approximately 0.14 million floating-point operations (MFLOPs), a computational cost that is negligible relative to the processing capacity of modern GPUs (e.g., 35.58 TFLOPs for an RTX 3090), and thus unlikely to incur appreciable overhead in operational DA cycles. **Comparison of the forecast states (\(RMSE_{\mathbf{f}}\)):** since the core objective of DA is to generate initial states that support accurate forecasting, the analysis states produced by different variance rescaling methods are used to initialize the prediction model. Forecasts are then conducted over short-term (72 h), medium-term (7 d), and long-term (15 d) periods to directly evaluate the effectiveness of each method. Table 3 (rows 8-22) presents the forecast performance of various methods within the Lorenz-96 model framework. The proposed DRL-AST method shows potential improvements, evidenced by its effective adaptation to observations with varying standard deviations and its optimized prediction performance across different forecast timescales compared to other methods. Despite DRL-AST's slightly lower forecasting performance than CUTE-ST in the medium and long terms when \(\sigma_{\varphi^{\prime}}=1.5\), its optimization level remains comparable to CUTE-ST. These results are attributed to the incorporation of the GRU module in the DRL-AST policy network, which effectively memorizes historical information by encoding the temporal evolution of the Lorenz-96 model, enabling the DRL-AST policy to make spatio-temporally informed decisions during each assimilation cycle. As a result, the analysis states generated are better aligned with the forecast model dynamics, leading to enhanced forecast accuracy across varying assimilation conditions. However, the overlapping standard deviations in Table 3 suggest that the differences in performance between methods may not be statistically significant, given the limited sample size (50 experiments) and the random nature of observational errors. This is a common challenge in Lorenz-96 experiments, where'mean RMSE \(\pm\) standard deviation' is a widely accepted metric for evaluating DA methods [62]. Additionally, the anomaly correlation coefficient (ACC) serves as a crucial metric for evaluating the spatial consistency between forecast states and reference datasets, such as reanalysis data, in NWP [63].