## 5 Experimental Results
### Quantitative Results
#### 5.3.3 Performance of DA System and Model Forecasting
To ensure the reliability of the experimental results and to eliminate random effects, each control experiment was independently repeated 50 times, with the mean value was reported as the final result, as summarized in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Metrics**} & \multirow{2}{*}{**Time**} & \multirow{2}{*}{\(\mathbf{\sigma^{y^{\bullet}}}\)} & \multicolumn{4}{c}{**Methods**} \\ \cline{5-6}  & & & **NO** & **CON** & **CUTE-ST** & **DRL-AST (Ours)** \\ \hline \multirow{6}{*}{RMSE\({}_{a}\)} & \multirow{6}{*}{5 years} & \multirow{6}{*}{1.0} & 0.5 & 0.36 \(\pm\) 0.0006 & \(\underline{0.27}\)\(\pm\) 0.0011, & 0.29 \(\pm\) 0.0006, & \(\underline{0.25}\)\(\pm\) 0.0006, \\  & & & 24.46\% \(\pm\) 0.33\% & 18.12\% \(\pm\) 0.21\% & 29.47\% \(\pm\) 0.20\% \\ \cline{3-6}  & & & 0.53 \(\pm\) 0.0017 & \(\underline{0.51}\)\(\pm\) 0.0018, & 0.52 \(\pm\) 0.0011, & \(\underline{0.44}\)\(\pm\) 0.0016, \\  & & & 3.36\% \(\pm\) 0.37\% & 2.07\% \(\pm\) 0.37\% & 17.57\% \(\pm\) 0.42\% \\ \cline{3-6}  & & & 0.75 \(\pm\) 0.0057 & \(\underline{0.74}\)\(\pm\) 0.0049, & \(\underline{0.63}\)\(\pm\) 0.0021, & \(\underline{0.63}\)\(\pm\) 0.0021, \\  & & & 1.12\% \(\pm\) 1.04\% & 15.82\% \(\pm\) 0.75\% & 15.71\% \(\pm\) 0.70\% \\ \cline{3-6}  & & & 0.77 \(\pm\) 0.0062, & \(\underline{0.86}\)\(\pm\) 0.0090, & \(\underline{0.83}\)\(\pm\) 0.0037, \\  & & & 16.97\% \(\pm\) 1.33\% & 26.18\% \(\pm\) 1.46\% & 29.00\% \(\pm\) 1.18\% \\ \cline{3-6}  & & & 2.5 & 1.80 \(\pm\) 0.0252 & \(\underline{1.20}\)\(\pm\) 0.0078, & \(\underline{1.37}\)\(\pm\) 0.0187, & \(\underline{1.08}\)\(\pm\) 0.0035, \\  & & & 33.42\% \(\pm\) 1.06\% & 23.69\% \(\pm\) 1.54\% & 39.93\% \(\pm\) 0.86\% \\ \hline \multirow{6}{*}{72 h} & \multirow{6}{*}{1.0} & 0.5 & 0.72 \(\pm\) 0.20 & \(\underline{0.67}\)\(\pm\) 0.17, & 0.68 \(\pm\) 0.19, & \(\underline{0.58}\)\(\pm\) 0.18, \\  & & & 6.61\% \(\pm\) 5.77\% & 6.40\% \(\pm\) 6.51\% & 20.10\% \(\pm\) 8.86\% \\ \cline{3-6}  & & & 1.21 \(\pm\) 0.30 & \(\underline{1.19}\)\(\pm\) 0.35, & \(\underline{1.11}\)\(\pm\) 0.29, & \(\underline{0.94}\)\(\pm\) 0.24, \\  & & & 2.18\% \(\pm\) 6.45\% & 8.00\% \(\pm\) 4.39\% & 21.80\% \(\pm\) 3.40\% \\ \cline{3-6}  & & & 1.60 \(\pm\) 0.45 & \(\underline{1.54}\)\(\pm\) 0.33, & \(\underline{1.33}\)\(\pm\) 0.32, & \(\underline{1.32}\)\(\pm\) 0.29, \\  & & & 1.74\% \(\pm\) 7.09\% & 15.71\% \(\pm\) 6.08\% & 15.62\% \(\pm\) 6.06\% \\ \cline{3-6}  & & & 2.0 & 2.18 \(\pm\) 0.61 & 2.03 \(\pm\) 0.49, & \(\underline{1.74}\)\(\pm\) 0.46, & \(\underline{1.74}\)\(\pm\) 0.45, \\  & & & 5.89\% \(\pm\) 5.03\% & 19.84\% \(\pm\) 3.41\% & 19.55\% \(\pm\) 4.11\% \\ \cline{3-6}  & & & 2.61 \(\pm\) 0.57 & \(\underline{2.26}\)\(\pm\) 0.47, & \(\underline{2.32}\)\(\pm\) 0.54, & \(\underline{1.96}\)\(\pm\) 0.44, \\  & & & 13.07\% \(\pm\) 3.89\% & 11.29\% \(\pm\) 5.31\% & 24.62\% \(\pm\) 3.54\% \\ \hline \multirow{6}{*}{72 h} & \multirow{6}{*}{1.0} & 0.5 & 1.91 \(\pm\) 0.43 & \(\underline{1.76}\)\(\pm\) 0.44, & \(\underline{1.87}\)\(\pm\) 0.46, & \(\underline{1.56}\)\(\pm\) 0.47, \\  & & & 8.20\% \(\pm\) 3.50\% & 2.62\% \(\pm\) 4.58\% & 19.06\% \(\pm\) 7.63\% \\ \cline{3-6}  & & & 2.39 \(\pm\) 0.43 & \(\underline{2.46}\)\(\pm\) 0.52, & \(\underline{2.34}\)\(\pm\) 0.41, & \(\underline{2.07}\)\(\pm\) 0.42, \\  & & & \(-\)2.42\% \(\pm\) 6.74\% & 2.02\% \(\pm\) 3.38\% & 13.99\% \(\pm\) 5.43\% \\ \cline{3-6}  & & & 2.70 \(\pm\) 0.47 & \(\underline{2.72}\)\(\pm\) 0.47, & \(\underline{2.51}\)\(\pm\) 0.44, & \(\underline{2.52}\)\(\pm\) 0.39, \\  & & & \(-\)0.66\% \(\pm\) 4.33\% & 7.02\% \(\pm\) 4.34\% & 6.08\% \(\pm\) 6.80\% \\ \cline{3-6}  & & & 2.0 & 3.15 \(\pm\) 0.56 & \(\underline{3.03}\)\(\pm\) 0.49, & \(\underline{2.84}\)\(\pm\) 0.45, & \(\underline{2.83}\)\(\pm\) 0.45, \\  & & & 3.27\% \(\pm\) 5.23\% & 9.38\% \(\pm\) 3.01\% & 9.53\% \(\pm\) 7.61\% \\ \cline{3-6}  & & & 2.5 & 3.33 \(\pm\) 0.41 & \(\underline{3.29}\)\(\pm\) 0.35, & \(\underline{3.05}\)\(\pm\) 0.46, & \(\underline{3.02}\)\(\pm\) 0.46, \\  & & & 1.04\% \(\pm\) 3.09\% & 8.78\% \(\pm\) 6.16\% & 9.65\% \(\pm\) 3.88\% \\ \hline \multirow{6}{*}{15 days} & \multirow{6}{*}{1.0} & 0.5 & 3.34 \(\pm\) 0.34 & \(\underline{3.29}\)\(\pm\) 0.31, & \(\underline{3.31}\)\(\pm\) 0.37, & \(\underline{3.06}\)\(\pm\) 0.35, \\  & & & 1.57\% \(\pm\) 2.56\% & 1.01\% \(\pm\) 2.73\% & 8.51\% \(\pm\) 3.21\% \\ \cline{3-6}  & & & 3.76 \(\pm\) 0.36, & \(\underline{3.63}\)\(\pm\) 0.31, & \(\underline{3.52}\)\(\pm\) 0.32, \\  & & & 0.52\% \(\pm\) 2.01\% & 3.88\% \(\pm\) 1.44\% & 6.98  
**Comparison of the analysis states (\(RMSE_{\mathbf{s}}\)):** as shown in Table 3 (specifically, rows 3 to 7), the \(RMSE_{\mathbf{s}}\) results, which reflect the assimilation performance, indicate that any method for rescaling the variances of the **B**-matrix or reconstructing the **B**-matrix positively impacts the average performance of the long-term assimilation cycle, regardless of the quality of the observations.