## 4 Results
### Model Performance at Different Observations
Regardless of whether it is based on the R\({}^{2}\) or SMAPE, all methods will achieve the best performance of the method at a low missing rate (10%). The reason for this is that when the missing value rate is small, the missing items have a limited influence on the overall distribution of the data samples. As the missing rate increases gradually, the original distribution characteristics of the data are altered by the growing number of missing values, which leads to a decline in the imputation method's performance with the higher missing rate. Among all methods, the RF is the most reliable imputation method. Based on the SMAPE, the RF performs better than other algorithms in all imputation experiments with all missing value rates presented in this paper. Meanwhile, based on the R\({}^{2}\), the RF performs better than other methods when the missing rate is 10%, 20%, and 40%, and the RF's R\({}^{2}\) is slightly lower than the TCN only when the missing rate is 60% and 80%. Figure 3 shows the imputation results of the MMDIF combined with RF on all sites. Each scatter point in the figure represents the imputation result of MMDIF-RF on a dataset. The distribution of scatter points in the figure reflects the robustness of the algorithm on different datasets, and the more densely the data points are distributed in the vertical direction, the more stable the algorithm is. RF performed very well at a low data missing rate of 10%, with the R\({}^{2}\) above 0.9 for 116 stations (93.5% of the total) and the SMAPE below 5% for 91 stations (73.4% of the total). As the data missing rate increases to 20%, the R\({}^{2}\) remains above 0.9 for 85 stations (68.5% of the total), and the SMAPE stays below 5% for 65 stations (52.4% of the total). However, at a high data missing rate of 60%, RF's R\({}^{2}\) drops significantly to around 0.8 for most stations (97 out of 124), and the SMAPE rises to an average of 7.59%, with a large variation among stations. At an extremely high data missing rate of 80%, both the R\({}^{2}\) and SMAPE become sparse and unstable, indicating poor data imputation results. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{5}{c}{**Missing Rate (R\({}^{2}\) \(|\) SMAPE)**} \\ \cline{2-6}  & **10\%** & **20\%** & **40\%** & **60\%** & **80\%** \\ \hline AdaBoost & 0.841 9.17 & 0.81 19.90 & 0.73 11.51 & 0.65 13.07 & 0.57 14.54 \\ Perceptron & 0.90 1 6.14 & 0.87 16.95 & 0.82 8.46 & 0.75 19.97 & 0.68 11.57 \\ ARD & 0.87 17.49 & 0.84 8.33 & 0.78 19.75 & 0.71 11.21 & 0.63 12.89 \\ Bagging & 0.91 5.05 & 0.89 15.57 & 0.84 16.60 & 0.79 17.90 & 0.72 19.48 \\ BR & 0.87 17.48 & 0.84 18.33 & 0.78 19.75 & 0.71 11.22 & 0.63 12.89 \\ BiLSTM & 0.91 5.42 & 0.89 16.17 & 0.84 17.52 & 0.77 19.10 & 0.70 10.80 \\ MLP & 0.90 1 6.16 & 0.87 16.97 & 0.81 18.46 & 0.75 19.98 & 0.68 11.59 \\ DTR & 0.85 17.80 & 0.81 8.62 & 0.74 19.99 & 0.65 11.48 & 0.53 13.02 \\ ENet & 0.87 17.62 & 0.84 18.46 & 0.78 19.82 & 0.71 11.12 & 0.63 12.83 \\ ERT & 0.84 15.98 & 0.80 16.70 & 0.73 18.11 & 0.64 19.75 & 0.51 11.56 \\ GBDT & 0.90 15.97 & 0.87 16.70 & 0.82 18.07 & 0.77 19.43 & 0.70 10.85 \\ KNN & 0.89 16.71 & 0.86 17.53 & 0.80 18.82 & 0.75 110.08 & 0.67 11.42 \\ Lasso & 0.87 17.62 & 0.84 18.46 & 0.78 19.82 & 0.71 11.26 & 0.63 12.83 \\ MLR & 0.88 1 7.46 & 0.84 18.32 & 0.78 19.74 & 0.71 11.21 & 0.63 12.89 \\ LSTM & 0.90 1 5.80 & 0.88 16.47 & 0.82 17.92 & 0.76 19.55 & 0.68 11.21 \\ RF & 0.92 1 4.90 & 0.90 15.39 & 0.86 16.36 & 0.81 17.59 & 0.74 19.13 \\ Ridge & 0.87 17.47 & 0.84 18.33 & 0.78 19.75 & 0.71 11.123 & 0.63 12.90 \\ RNN & 0.90 1 6.31 & 0.87 17.14 & 0.81 8.62 & 0.75 110.16 & 0.67 111.76 \\ SVR & 0.90 1 6.67 & 0.88 17.17 & 0.81 8.36 & 0.77 19.76 & 0.69 11.32 \\ TCN & 0.86 17.51 & 0.86 17.56 & 0.84 18.13 & 0.82 19.10 & 0.76 10.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The imputation accuracy of various algorithms under different missing rates. Neural network-based techniques fall into the second category. Of these methods, BiLSTM performs well.