# Calibration and Validation of a Measurements-Independent Model for Road Traffic Noise Assessment
## 1 Introduction
In such a complex scenario, the European Union issued the European Noise Directive related to the assessment and management of environmental noise, in which the main definitions and rules are provided to member states [21]. In particular, the noise indicators are defined as the equivalent continuous sound levels calculated for the day (\(L_{d}\)), evening (\(L_{e}\)), or night (\(L_{n}\)) timespans, as well as for the entire day (\(L_{dm}\)). The latter indicator includes a penalty for evening and night hours. The effort to harmonize noise assessment for many sources, including road traffic, has led to the development of the CNOSOS model, which is nowadays the reference model in Europe [22]. Regardless of the considered model, all of them assess the noise levels using various indicators, usually estimated at a fixed distance over a given time range. The most important is the equivalent continuous sound level, \(L_{eq}\), which is the constant sound level in dBA, with the same total sound energy as the fluctuating level measured in the considered timespan (such as 15 min, 1 h, a day, an evening, a night). In the present paper, developing an idea proposed by [PERSON] et al. in Ref. [23], the authors used a multilinear regressive model for the evaluation of noise from traffic in which the estimation of the noise level is implemented from computed data and not from real ones. The proposed model, in fact, aims to predict noise equivalent levels produced by road traffic, calibrating on a dataset of computed noise levels. The independent variables used for the calibration are the total traffic volume, the percentage of medium and heavy vehicles, the mean speed of each type of vehicle, and the distance between the center of the highway and the receiver. The computed level database is obtained with a random sampling of the independent variables listed above that feed the formula proposed by [PERSON] et al. [14]. Once the computed level database is obtained, a multiple linear regression technique--implemented with a self-written Python routine--is used to establish the correlation between the independent variables and the \(L_{eq,t}\) on a fixed time range, \(t\). This approach overcomes some shortcomings of the classic and statistical models. Firstly, the model can be calibrated without any field measurements by using a computed set of data. It is known, in fact, that model efficiency usually decreases when applying models to a site different from the ones where they were calibrated [16]. Secondly, the model can be recalibrated quickly when needed to include different traffic road conditions. Another advantage of this approach is that its independence from measured data makes it suitable to be applied to estimate the impact of traffic noise even for roads that do not yet exist, providing useful information when designing new roads in urban or non-urban areas. The outputs of the model are then validated with measured data coming from a Long-Term Monitoring Station (LTMS) system installed in the city of Saint-Berthevin (France) by the Universite Gustave Eiffel and Unite Mixte de Recherche en Acoustique Environmentale (UMRAE), Nantes. This study aims to deepen the understanding of physical phenomena in the field of environmental acoustics, correlating noise measurements at different acoustic masts with meteorological parameters collected over a period of ten years. The model was applied to part of the dataset and a prevision of the hourly equivalent level--_Leq,t_--was performed. The simulated data were compared with the measured ones to evaluate the goodness of the model. The same process was repeated in a 15 min timespan to check the robustness of the model in a different time range and on a larger set of data. The results show, in both cases, how the model is able to provide a good approximation of noise level distributions. The performance of the model has been quantitatively estimated via error distribution analysis and error metrics.