# AERQ--A Web-Based Decision Support Tool for Air Quality Assessment
## 2 Materials and Methods
### Calibration and Validation of the Model  
The average hourly concentration of nitrogen oxides observed by the monitoring stations in 2019 reveals two peaks, occurring at 8:00 a.m. and 8:00 p.m., and two lows, at 4:00 a.m. and 3:00 p.m. The daily average concentration is 25.84 micrograms per cubic meter. The standard deviation of hourly observations indicates significant variability, with an average of 14.78. The largest fluctuations occurred in the early morning hours, between 1:00 a.m. and 5:00 a.m. These high standard deviations suggest that pollutant levels are widely dispersed, likely influenced by traffic volume and meteorological conditions [36]. The development of the air dispersion model is influenced by three key sources of uncertainty: conceptual model uncertainty, input uncertainty, and parameter uncertainty. Conceptual model uncertainty arises from the fundamental assumptions and structure of the model itself, reflecting how accurately it represents real-world conditions. Input uncertainty involves variations in the data used, such as meteorological and climatic conditions as well as pollution sources, which may not always be precisely known. Finally, parameter uncertainty relates to the specific constants and variables within the model calculations, which can impact the accuracy and reliability of the model's predictions. Together, these uncertainties play a significant role in shaping the model's performance, making it essential to address them for greater accuracy and robustness. The Cagliari model addresses air dispersion, excluding photochemical reactions and pollutant transformations. The calibration period is March and April 2019 (Figure 2). To assess the model's performance, the objective functions Mean Squared Error (MSE), Mean Squared Error of Prediction (MSEP), and R-squared (R\({}^{2}\)) are used. \[\text{MSE}=\frac{\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})2}{n} \tag{1}\]Here, y represents the measured value, \(\hat{\mathbf{y}}\) denotes the simulated value, and \(\overline{\mathbf{y}}\) is the arithmetic mean of the measured observations. The Mean Squared Error (MSE) represents the average of the squared differences between actual and predicted values, providing a direct measure of error in predictions. A related metric, the Mean Squared Error of Prediction (MSEP), particularly evaluates the model's accuracy in predicting unseen data. Lower values of the MSEP indicate that the model's predictions closely match actual outcomes, signaling strong predictive accuracy. R-squared (R\({}^{2}\)), also known as the coefficient of determination, measures the extent to which the model explains variability in the data. This value ranges from 0 to 1, where 0 means the predictor variables do not explain any of the response variable's variability, and 1 means they explain it completely. A higher R\({}^{2}\) value suggests a stronger relationship between predictor variables and the outcome, indicating that the model effectively captures the data's variability. MSE/MSEP and R\({}^{2}\) provide a comprehensive view of the model's fit and predictive accuracy (Table 1). Vehicle emission loads fluctuate hourly based on workdays, holidays, seasons (winter, spring, summer, and fall), and the specific roads. To account for these variations, average hourly emission loads were calculated for each season and each road segment. Thus, emission coefficients were adjusted to improve consistency in model performance. In the model, the Urban Heat Island effect (UHI) was also incorporated, which refers to urban areas being hotter than their rural surroundings due to human activities, building materials, and dense infrastructure. The UHI influences local meteorology by altering wind \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **MSEP** & **MSE** & **R\({}^{2}\)** \\ \hline First Run & 15.1 & 257.9 & 0.21 \\ Best Run & 2.5 & 43.9 & 0.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The calibration period cover March and April 2019. The MSE, MSEP, and R\({}^{2}\) have deeply improved in the calibration process.