## 3 Results and Discussion

Table 6: RMSE STATION ST 9. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \(\mathbf{NO_{2}}\) & \(\mathbf{NO_{X}}\) & \(\mathbf{PM_{10}}\) & \(\mathbf{SO_{2}}\) \\ \hline LI & 1.9863 & 4.4286 & 3.8917 & 1.5538 \\ PMM & 4.0866 & 9.6485 & 11.9426 & 5.1804 \\ RF & 4.1306 & 9.6750 & 11.5941 & 5.0176 \\ UMI & 6.5735 & 13.4647 & 15.2220 & 5.9825 \\ KNN & 3.0239 & 7.6957 & 9.1227 & 3.8284 \\ KALMAN & 1.9719 & 4.3355 & 3.7875 & 1.5584 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: RMSE STATION ST 11. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \(\mathbf{NO_{2}}\) & \(\mathbf{NO_{X}}\) & \(\mathbf{PM_{10}}\) & \(\mathbf{SO_{2}}\) \\ \hline LI & 2.5307 & 9.1267 & 3.6796 & 1.3225 \\ PMM & 6.0611 & 23.8287 & 12.1254 & 4.7245 \\ RF & 5.8515 & 22.6786 & 11.7949 & 4.5565 \\ UMI & 8.1936 & 27.8836 & 14.8984 & 4.6735 \\ KNN & 4.3469 & 19.0391 & 9.4373 & 3.4929 \\ KALMAN & 2.4808 & 9.6010 & 3.6274 & 1.3312 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: RMSE STATION ST 12. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \(\mathbf{NO_{2}}\) & \(\mathbf{NO_{X}}\) & \(\mathbf{PM_{10}}\) & \(\mathbf{SO_{2}}\) \\ \hline LI & 2.0815 & 5.2487 & 8.5045 & 2.0955 \\ PMM & 4.5285 & 11.2938 & 20.5134 & 5.6155 \\ RF & 3.9959 & 11.0202 & 20.2237 & 5.3490 \\ UMI & 6.2930 & 15.8865 & 31.1047 & 7.3355 \\ KNN & 2.9743 & 9.5360 & 18.5270 & 4.6613 \\ KALMAN & 2.0940 & 5.1613 & 8.3576 & 2.0418 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: RMSE STATION ST 18. In addition to the imputation methods indicated above, other imputation methods from the MICE package of the R software such as random Bayesian linear regression (norm function), bootstrap linear regression (norm.boot function) and linear regression predicted values (norm.predict function) were also tested but were discarded because they impute negative values in data sets which, by their nature as records of air pollutant concentration measurements, contain all non-negative values. Figure 6 shows the total RMSE value assigned to each station as the average RMSE error value of the 4 variables at each station indicated as a point for each of the imputation methods. The imputation methods are represented by different colours. The points between stations for each method were joined in the plot to emphasize how the RMSE error increases or decreases analogously at each station according to the imputation method used. Thus, a different colour curve is displayed for each imputation method. As shown in Figure 6, the average RMSE for each of the methods at each station behaves similarly at all stations. It can be seen that all the imputation methods have a lower RMSE at stations ST 1, ST 11 and ST 20. The linear and Kalman imputation methods have practically identical results and their curves in the graph in Figure 6 are the ones with the smallest variations between the maximum and minimum RMSE between stations in relation to the rest of the stations, i.e., they are the ones with the flattest curves. Figures 7-10 show the RMSE values for each pollutant: NO\({}_{2}\), NO\({}_{x}\), PM\({}_{10}\) and SO\({}_{2}\). In each of the figures, for each method, the RMSE values obtained are shown in bar graphs. These bars are grouped by each of the imputation methods and each one represents the value obtained at each station, differentiated by colours, as shown in the legend of the graph. The following sections discuss the results obtained for each of the variables. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **NO\({}_{2}\)** & **NO\({}_{X}\)** & **PM\({}_{10}\)** & **SO\({}_{2}\)** \\ \hline LI & 1.8332 & 3.9101 & 6.6309 & 1.9148 \\ PMM & 3.6602 & 7.7101 & 14.8029 & 4.9421 \\ RF & 3.4418 & 7.6308 & 14.7711 & 4.8554 \\ UMI & 6.0967 & 11.6046 & 22.8886 & 6.6373 \\ KNN & 2.5108 & 6.4942 & 12.7487 & 3.8834 \\ KALMAN & 1.8604 & 3.8728 & 6.5369 & 1.8960 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: RMSE STATION ST 20. Figure 6: RMSE error for all models and stations. Figure 8: RMSE error for NO\({}_{\rm X}\). Figure 7: RMSE error for NO\({}_{2}\).