# Calibration and Validation of a Measurements-Independent Model for Road Traffic Noise Assessment
## 3 Results and Discussions
### Validation of Field Measurements
The mean value of the errors is \(-0.82\) dBA, and the standard deviation is \(2.25\) dBA, while the skewness and kurtosis of the distributions are, respectively, \(0.68\) and \(1.64\). The overall error analysis, then, indicates a good-performing model for the case study of the LTMS database. Nevertheless, the authors wanted to deepen the investigation of the performing metrics of the model itself. To do so, the relationship between the error outliers and some specific independent variables was investigated. The investigation was at first carried out using a boxplot analysis (Figure 5a), where the data falling into the interquartile range were represented in the box, and the black diamonds refer to the data falling outside the boundaries of the box \(\pm\) 1.5 times the interquartile range. The total number of outliers so calculated was \(3.93\%\) of the total. These data are also represented by red dots in Figure 5b,c, where error values are represented as a function of \(Q\) and \(P\). The outlier data are listed in Appendix A. As for the graph in Figure 5b, it is clear that the outlier positive values of errors mostly correspond to a low \(Q\) value, meaning that the most significant underestimations of the model have to be investigated in periods in which uncommonly high \(L_{eq,h}\) values are associated with a limited amount of traffic. These \(L_{eq,h}\) values are generally related to low \(P\) values and high speeds. Such conditions suggest an expectation of values of noise levels lower than those measured (see Table A1 in Appendix A). This discrepancy can be related to several reasons; one of them could be the presence of other noise sources occurring during the measurement. Similarly, outliers corresponding to large overestimations are associated with low measured \(L_{eq,h}\) values for the observed flows and speeds. This suggests that some specific situations, not considered in the presented model, could happen during measurements. The scatterplot of errors vs. \(P\) (Figure 5c) represents a similar pattern, and yet, it is more spread over the whole \(P\) range. Once they identified the outliers, the authors removed such data and performed a new step of simulation with the \"cleaned\" dataset to validate the model excluding nonstandard conditions. For the new dataset, the same approach described before was applied by investigating the distributions and the scatterplot of the measured vs. simulated \(L_{eq,h}\) levels reported in Figure 6. A visual comparison between the two histograms is good, and the statistical analyses are comparable: the mean values of the measured and simulated \(L_{eq,h}\) differ in an absolute value of \(1.02\) dBA; the skewness index of the measured and simulated \(L_{eq,h}\) differs by \(0.55\), where the kurtosis indexes are now \(5.09\) and \(2.24\) for the measured and simulated \(L_{eq,h}\). The mean and the standard deviations of the error distribution after the removal of the outliers are, respectively, \(-1.02\) dBA and \(1.91\) dBA, showing a slight worsening of the mean error and a small improvement in the  
Figure 5: (**a**) Boxplot of the errors of 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**). standard deviation with respect to the analysis including the outliers (mean error and standard deviation, respectively: \(-0.82\) dBA and \(2.25\) dBA). This result confirms that the model can also provide a good average performance when nonstandard conditions of traffic and/or background levels occur.