## 3 Methodology
### Results of Predictive Modeling  
This paper selected NO\({}_{2}\) as an important air pollutant that threatens human health and the environment. It is produced by the burning of fossil fuels emitted from traffic and factories, and short and long-term exposure to these emissions can cause health problems [56]. Four atmospheric parameters were selected as input indicators, namely wind speed, temperature, humidity, and precipitation, in addition to the NO\({}_{2}\) concentration itself. To measure the relationship between the observed and predicted concentrations of NO\({}_{2}\), the performance of the three models was evaluated after training and testing the models on the datasets using three criteria, namely the RMSE, MAE, and MAPE, and the results are recorded in Table 8. As shown in this table, the addition of batch normalization into the improved model slightly improves the forecasting quality, as lower metric values indicate a smaller distance between the predicted and actual NO\({}_{2}\) levels. Furthermore, incorporating a Time2 Vec layer to capture temporal patterns significantly enhances prediction quality, as demonstrated in Table 8 and Figure 5. Figure 5 shows a graphical representation of the predicted and observed concentrations of nitrogen dioxide in the three cities using the proposed model. These concentrations show a strong correlation with each other for nitrogen dioxide. These results indicate that the proposed model outperformed the prediction performance of the models without using Time2 Vec. This demonstrates that including the time vector can improve the prediction performance and is an effective approach to improving the accuracy of atmospheric pollutant concentration prediction. Figure 5: Original and predicted values of NO\({}_{2}\) levels in the improved LSTM model with Time2 Vec for the three cities. The x-axis represents the test data, while the y-axis represents the concentration of NO\({}_{2}\). (**a**) Al Juhail; (**b**) Al Riyadh; and (**c**) Najran. Training and validation loss curves for the three cities are shown in Figures 6 and 7. Figure 5 depicts the case using the optimized LSTM model without Time2 Vec, while Figure 6 illustrates the curves after incorporating Time2 Vec into the improved model. These curves indicate that neither overfitting nor underfitting occurred during training. Figure 8 summarizes the box plot of the NO\({}_{2}\) values when calculating the absolute difference between the original observed and predicted values in the test phase for all three cities. Each box represents the average error in predicting the air pollution level for each month. The bottom and top of the box show the 25 th and 75 th percentiles, respectively. Based on the graph, we can make the following observations:  
* In Najran, prediction accuracy varies with the mean absolute error, with the model having the greatest difficulty accurately predicting nitrogen concentrations during May and August, with the highest mean absolute errors. March and December have  
Figure 6: Training and validation of the improved LSTM model for the three cities. (**a**) Al Juhail; (**b**) Al Riyadh; and (**c**) Najran. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Model**} & \multicolumn{3}{c}{**Al Riyadh**} & \multicolumn{3}{c}{**Al Juhail**} & \multicolumn{3}{c}{**Najran**} \\ \cline{2-10}  & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** \\  & **[ug/m3]** & **[ug/m3]** & **[\%]** & **[ug/m3]** & **[ug/m3]** & **[\%]** & **[\%]** & **[ug/m3]** & **[ug/m3]** & **[\%]** \\ \hline LSTM & 42.77 & 55.91 & 33.75 & 42.97 & 55.83 & 33.98 & 15.10 & 22.28 & 19.62 \\ \hline Improve LSTM & 42.07 & 54.74 & 33.43 & 42.23 & 55.15 & 32.76 & 14.92 & 21.79 & 19.24 \\ \hline Proposed Model & 41.57 & 54.44 & 33.07 & 41.29 & 54.13 & 31.57 & 14.34 & 20.90 & 18.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Evaluation metrics for the three cities using the three prediction models.