## 5 Conclusions  
Complete and accurate GMOD are crucial for social and economic development and people's daily lives, but data can be lost due to various issues during collection, transmission, and storage. As a result, numerous techniques have been developed for recovering lost data. Machine-learning methods are among the most widely used methods for interpolating meteorological missing values, as they offer high accuracy, simple operation, and other benefits. However, when utilizing machine-learning methods to interpolate meteorological data, the intrinsic relationship among the observation variables has been overlooked by many studies, and only a small number of studies have thoroughly assessed the performance of different machine-learning methods across a wide range of sites. In this paper, we propose a machine-learning-based multidimensional meteorological data imputation framework (MMDIF), which can use machine-learning predictions to reconstruct GMOD with random missing values across multiple attributes. We used this \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Duration(s)**} \\ \cline{2-7}
**Method** & **Missing Rate** & **Missing Rate** & **Missing Rate** & **Missing Rate** & **Missing Rate** & **Average** \\  & **10\%** & **20\%** & **40\%** & **60\%** & **80\%** & **Duration** \\ \hline MLR & 0.395 & 0.396 & 0.421 & 0.405 & 0.331 & 0.389 \\ Ridge & 167.428 & 153.703 & 141.661 & 117.065 & 90.136 & 133.999 \\ Lasso & 153.925 & 146.388 & 143.651 & 127.361 & 106.294 & 135.524 \\ Enet & 153.351 & 147.633 & 144.169 & 127.264 & 107.077 & 135.899 \\ BR & 273.696 & 265.083 & 261.950 & 230.349 & 193.824 & 244.980 \\ ARD & 382.077 & 380.746 & 404.102 & 377.901 & 322.452 & 373.456 \\ KNN & 1.844 & 2.508 & 3.846 & 4.373 & 4.377 & 3.390 \\ DTR & 0.969 & 0.923 & 0.884 & 0.771 & 0.636 & 0.837 \\ RF & 70.141 & 67.158 & 64.987 & 55.351 & 45.508 & 60.629 \\ AdaBoost & 2.090 & 2.730 & 3.867 & 4.155 & 3.460 & 3.260 \\ GBDT & 21.040 & 19.391 & 18.618 & 16.150 & 12.622 & 17.564 \\ ERT & 0.576 & 0.574 & 0.614 & 0.556 & 0.471 & 0.558 \\ Bagging & 8.836 & 8.597 & 8.632 & 7.599 & 6.277 & 7.988 \\ SVR & 43.255 & 44.390 & 46.883 & 38.067 & 27.519 & 40.023 \\ Perceptron & 127.659 & 116.002 & 107.112 & 93.163 & 78.459 & 104.479 \\ MLP & 145.523 & 131.159 & 119.722 & 104.000 & 89.925 & 118.066 \\ RNN & 432.557 & 382.919 & 349.538 & 281.223 & 231.763 & 335.600 \\ LSTM & 1235.162 & 1195.449 & 1025.659 & 781.857 & 609.432 & 969.512 \\ BiLSTM & 1856.816 & 1683.721 & 1472.877 & 1139.001 & 909.946 & 1412.472 \\ TCN & 446.149 & 423.100 & 394.256 & 345.127 & 299.772 & 381.681 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The training time of each algorithm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Joseph’s Research**} & \multicolumn{2}{c}{**MMDIF-RF**} \\ \cline{2-5}
**Observation Elements** & **RMSE** & **MAE** & **RMSE** & **MAE** \\ \hline TBOS & 0.63 & 0.43 & 0.61 & 0.35 \\ TMAX & 0.72 & 0.53 & 0.68 & 0.34 \\ TMIN & 0.92 & 0.70 & 0.77 & 0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the results of the two studies (°C). framework to compare the missing value imputation performance of 20 machine-learning methods. The data we used were sourced from 10 years of observation data of 124 stations in six climate zones of the continental U.S., including 11 variables. Based on four evaluation indicators for assessing the predictive performance of models, R\({}^{2}\), SMAPE, RMSE, and MAE, we find that RF, BiLSTM, and TCN had the best imputation effects for missing data. They were more accurate than the other regression methods for most stations, especially the RF. The RF performed better than the other methods in interpolating 11 meteorological variables under the six climate types in this paper, especially for TBOS, TMIN, TMAX, DPTP, PVPV, RHUM, RHUMN, and RHUMX. For these eight variables, RF achieves a R\({}^{2}\) above 0.9 and a SMAPE below 9% (R\({}^{2}\) and SMAPE are the average values of the imputation results at five missing rates).