## 5 Experimental Results
### Qualitative Results  
To more intuitively analyze the effect of the initial states provided by different methods on the prediction performance of the Lorenz-96 model, we refer to Figure 7. At the same starting moment when \(\sigma_{y^{\prime}}=1.0\), different initial states are provided by applying different variance rescaling methods to the VarDA system. These initial states are then used to make predictions on eight Lyapunov time units without additional assimilation. The differences in their predictions with respect to \(\mathbf{x}^{\prime}\) are then calculated. DRL-AST can accurately predict two Lyapunov time units (as shown in Figure 7d, highlighted in the green box), which is twice as much as the standard of the Lorenz-96 model [64]. In contrast, almost all other methods reach the error saturation point within one Lyapunov time unit. This result underscores the effectiveness of DRL-AST in extending the predictability of chaotic systems. To further improve performance in the Lorenz-96 model and extend the effective forecast lead time, two key directions can be explored. One approach comprises refining the dynamic adaptation of **B**, where DRL-AST currently adjusts only the variance components. Dynamically tuning length scales could further enhance forecast stability across different atmospheric motion scales [65]. In regions where the error growth is rapid, particularly those associated with high Lyapunov exponents, an adaptive scale-rescaling strategy could be introduced to refine the off-diagonal components of **B**, mitigating nonphysical error amplification. Another approach involves enhancing the reinforcement learning framework to  
Figure 6: Comparison of averaged 10-day-forecast RMSE (**a**–**e**) and ACC (**f**–**j**) curves for different variance adjustment methods. DRL-AST is shown in red, NO in black, CON in green, and CUTE-ST in blue. Each column represents a different observational error standard deviation (\(\sigma_{y^{\prime}}\)), ranging from 0.5 to 2.5.  
optimize DRL-AST. Refining the reward function to explicitly reinforce long-term forecast objectives--such as incorporating Lyapunov time-weighted rewards--could enable the DRL agent to learn more robust assimilation policies. Additionally, employing adaptive exploration strategies, such as entropy-regularized learning, could prevent premature convergence to suboptimal solutions, thereby improving the generalization capacity of DRL-AST [66]. These potential improvements could further strengthen DRL-AST's adaptability in chaotic systems and provide a foundation for its application in more complex atmospheric dynamic models. The analysis of individual variables from assimilation to model prediction illustrates the degree of alignment between the analysis state obtained from assimilation as the initial state and the numerical model. Figure 8a-d depict the scenario at \(\sigma_{\psi^{\prime}}=0.5\), where the performance of the VarDA system, adjusted by various variance rescaling strategies, excels due to high-quality observations. However, at the inflection points (highlighted in red boxes), the VarDA system without variance adjustment (NO) exhibits a large forecast error. This divergence is further examined in Figure 9i-iv, which provide a magnified view of forecast trajectories around these critical points. Here, DRL-AST demonstrates the best prediction performance, with state variables that perform well maintaining accurate predictions close to the true model value for nearly 10 days (\(x10\), \(x20\), and \(x30\)) and even the low-performing \(x40\) producing valid predictions for one week. In contrast, other methods only sustain valid predictions for 6-7 days for well-performing state variables and merely 2 days for \(x40\). The large standard deviation of observations in Figure 8e-h indicates substantial observation errors, which result in varying degrees of degradation in assimilation performances. However, despite these errors, the assimilation process still preserves a time evolution similar to the model truth.