# Calibration and Validation of a Measurements-Independent Model for Road Traffic Noise Assessment
## 3 Results and Discussions
### Analysis on a 15 Min Timespan
In performing the outlier analysis, the authors discovered a behavior similar to the one found for the 1 h timespan application of the model. Specifically, outlier values corresponding to the largest errors occurred at low values of \(Q\), as shown in Figure 11b. The error of 37.9 dBA, for instance, corresponds to the measurement performed on 22 September 2004, from 10:30 to 10:45 a.m. In this time slot, the measured \(L_{eq,15 min}\) is 72.7 dBA with a total flow of two vehicles over 15 min, one light and one heavy, with a speed of 45 km/h for the light vehicle and 28 km/h for the heavy vehicle. Of course, something occurred in the measurement that is either the presence of an event that altered the noise level measurement or, most probably, a problem in the car counting system. Figure 8: (**a**) Linear regression for computed \(L_{eq,15 min}\) values and the X variable; (**b**) distribution of residuals. In general, given the structure of the model, which mimics only the contributions to the noise level from vehicles passing by, when the traffic flow is very small, the background sound level is not negligible. Following the same approach already described, the authors removed the outliers and performed a new validation process, obtaining the results presented in Figure 12.  
Figure 11: (a) Boxplot of the errors in the model when applied to the LTMS database with indications of whiskers and outliers (black diamonds); (b) and (c) are scatterplots of the errors as functions of \(Q\) and \(P\), respectively, where red dots are the occurrences corresponding to error outliers as indicated in (a). Figure 9: (a) Distribution of the simulated (blue) and measured (orange) \(L_{\text{eq},15 min}\) values; (b) scatterplot of the computed vs. measured \(L_{\text{eq},15 min}\) values. The absolute difference in the mean values of the \(L_{eq,15 min}\) distributions is now 0.88 dBA; the absolute difference in the skewness of the distributions is now 0.50; and the absolute difference in the kurtosis indexes is 1.88. Tables 3 and 4 summarize, respectively, the statistical values of the measured and simulated equivalent level distributions and error metrics, with and without outliers. It is possible to see how the statistics of the distributions for the simulation levels are very close to those from the measured distributions, even including outlier data. Similarly, the error metrics are comparable, showing a slight improvement just when the absolute error is considered for the MAE and the MAPE. The removal of outliers, in fact, was not \"symmetric\" since they were more gathered in the underestimation region; thus, the error metrics that consider the sign of the error tend to move away from zero (see the mean error and MPE in Table 4). On the contrary, the mean absolute error and mean absolute percentage error adopt the absolute value and, thus, decrease thanks to the removal of both high underestimations and overestimations. Furthermore, the data show that the model output does not have a significant improvement after the removal of outliers, neither for the \(L_{eq,h}\) nor \(L_{eq,15 min}\) simulations, suggesting that the model can work properly, on average, when nonstandard conditions occur. In addition, since all the regulations usually fix limits on day, evening, or night equivalent levels, as well as on entire day levels (\(L_{den}\)), as defined in the European Noise Directive [21], the on-average good performance of the model suggests that this tool can be successfully used to predict these indicators both in proximity to existing road traffic networks and when designing new infrastructures.