# Calibration and Validation of a Measurements-Independent Model for Road Traffic Noise Assessment
## 3 Results and Discussions
### Analysis on a 15 Min Timespan  
Additional validation of the model's functioning was performed on the field measurements extracted from the raw LTMS database to evaluate the performance of the model when applied to a set of data provided over 15 min. The choice of applying the model to the same data but with a different timespan thus allowed us to verify the model's reliability and its usage in situations where an hourly time range is not suitable (for instance, strong variations in the sources) and check the performance of the model using a larger and more detailed set of data. As mentioned in the previous sections, the computed \(L_{eq,h}\) values used for the calibration of the model were obtained with a logarithmic sum where a time-dependent factor was present (1/3600; see Equation (3)). In order to change the timespan to 900 s, a different step of calibration for the model was performed, setting the time factor of Equation (3) to 1/900. The results of the multilinear regression confirm that the \(L_{eq}\) slope lies on the coefficient of the regression, while the intercept accounts for the vertical shift in the simulations (Figure 7). The difference between the intercepts of the two regression lines is 6.02 dBA, which is exactly a result of 10 log(3600/900), i.e., the conversion from 1 h to 15 min. Figure 6: (**a**) Distribution of the simulated (green) and the measured (orange) \(L_{eq,h}\) values; (**b**) scatterplot of the computed vs. measured \(L_{eq,h}\) values for the dataset without outliers. Figure 7: Regression lines of computed \(L_{eq,t}\) when the computation is performed with a 3600 s database (\(L_{eq,h}\), red dots) or a 900 s database (\(L_{eq,15 min}\), blue dots). Such an interesting result strongly confirms the possibility of rescaling the computation to any desired time interval, thus adapting to whatever situation needs to be simulated. As for the comparison between the measured and simulated \(L_{eq,15 min}\) values, the authors performed the very same approach described above by analyzing the calibration residuals and the validation errors and performing a study on the model performance with and without outlier values. In Figure 8a, the linear regression of the \(L_{eq,15 min}\) values vs. the X variable is presented, while in Figure 8b, the distribution of the residuals of the calibration is shown. Just like the previous application, the residual distribution has a mean value that is basically null (4.3 \(\times\) 10\({}^{-14}\) dBA) and a standard deviation of 0.92 dBA. The kurtosis index is 1.07, making the distribution slightly \"leptokurtic\", and the skewness is 0.69, with the right tail more pronounced than the left one. Statistical indexes of residuals, then, are basically equal to the ones obtained when the model was run for \(L_{eq,h}\), suggesting the goodness of the calibration is independent of the selected timespan. The next step is the validation of the model by using the real traffic data provided by the LTMS database for a 15 min time range and a comparison between the measured and the simulated equivalent levels. In Figure 9, the results are summarized: in the same way as hourly data, the superimposition of the \(L_{eq,15 min}\) value distributions shows their similarity, confirmed using statistical indexes. The absolute difference between the mean values is 0.72 dBA. The skewness of the measured \(L_{eq,15 min}\) value distribution is \(-2.04\), while the one for the simulated \(L_{eq,15 min}\) is \(-1.52\) (absolute difference, 0.51). The kurtosis indexes are 6.11 and 4.24, respectively, for the measured and simulated \(L_{eq,15 min}\) value distributions (absolute difference, 1.87). Figure 10a shows the scatterplot of the validation errors versus the measured \(L_{eq,15 min}\). The error distribution reported in Figure 10b has a mean value of \(-0.72\) dBA and exhibits a quite symmetric shape. The statistical indexes to confirm this visualization are 0.84 for the skewness and 5.11 for the kurtosis.