1 Introduction

The in-tunnel air quality is one of big concerns for not only the owners but also the users of road tunnels during the tunnel’s service life. The main source of the air pollution inside an in-service road tunnel is the exhaust gas emitted from vehicles. While the category and quantity of the daily vehicle flows can be listed through the car counting campaigns, the actual exhaust emission is difficult to be figured out since it is affected by various issues: engine’s type, car’s quality, fuel’s type, fuel’s quality, driving regime, … The small and closed space inside a tunnel makes it more vulnerable to air pollution than other open-air transport structures (e.g., roads, bridges, viaducts) [1]. The natural and mechanical ventilation systems are equipped for road tunnels to provide the under-controlled air quality following the given design and operation technical regulations. When the tunnel’s traffic volume in real conditions surpasses the traffic growth scenarios in the planning and design documents, the tunnel’s ventilation effectiveness reduces [2]. As consequence, the in-tunnel air quality becomes vulnerable due to the inadequate ventilation regimes.

Studies on the correlation between the road tunnel’s air quality and meteorological parameters have been published. Knowing that the wind takes responsive in the dispersion and dilution of vehicle’s exhausted gas in tunnels [3], the actual influences of the wind on the air quality of different tunnels have been carried out [1, 4,5,6]. The temperature inside is normally higher than outside tunnels [2], so it creates the natural ventilation in the tunnel and the impacts to different air parameters inside tunnels [7,8,9]. Since the variation of humidity also plays a role in the pollution dispersion in road tunnels, the case studies on this meteorological parameter have been executed [7, 9,10,11].

Aiming at the understanding of the meteorology – air quality correlation in road tunnels, a case study on an open road tunnel on Vietnam National Highway 1A (NH1A) was carried out based on the recorded data of a previous air quality measurement. During two continuous days in November 2017, various parameters of the air quality, and meteorological data were recorded at one measurement station [12]. In this paper, the statistical data treatments were executed and the linear regression models between some typical ambient parameters were quested. Each model’s statistical reliability was analysed to find out the representative regression model for the correlation, and the commentaries were presented. The preliminary study showed the multiple impacts on the in-tunnel air quality through the proposed regression model of the total suspended particles, airborne lead, and three volatile organic compounds against the meteorological parameters and the vehicle flow density inside tunnel.

2 Tunnel and Meteorology Description

The tunnel was 6.28 km long, 11.5 m wide, stayed in the middle central area of Vietnam, on the busiest national transport rout (NH1A). The tunnel included of two longitudinal tubes: one main tube for two bi-directional circulation vehicle lanes, and one auxiliary tube for the evacuation. There were fifteen cross passages connecting the two tubes. The tunnel located in the climate boundary of the country. Some typical tunnel’s meteorological features at the measurement time were shown in Table 1.

Table 1. Typical tunnel’s meteorological features at the measurement time.

3 Linear Regression Study

Three meteorological parameters were analysed: temperature (T, 0C), relative humidity (H, %), wind velocity (W, m/s). Because the wind direction was always North-South, it was not considered in the study. At the same time, several typical air quality parameters were examined: total suspended particles (TSP, μm/m3), airborne lead (Pb, μm/m3), benzene (C6H6, μm/m3), toluene (C7H8, μm/m3), xylene (C8H10, μm/m3). The simple and multiple linear regression modelling technics using the least squares method with 95% of confidence was applied on the data to build the regression models between the parameters. The vehicle flow density (expressed by the number of vehicles per hour (V, car/h)) was also taken into consideration during the statistical treatments.

3.1 Total Suspended Particles

The total suspended particles concentration (TSP, μm/m3) in the air were studied and the correlations with the meteorological parameters (T, H, W) and vehicles per hour (V, car/h) were analysed. The simple and multiple linear regressions were done with the regression equations as follows:

$${\text{TSP }} = {\text{ a}}_{{1}} + {\text{ b}}_{{1}} .{\text{T }} + {\text{ c}}_{{1}} .{\text{H }} + {\text{ d}}_{{1}} .{\text{W }} + {\text{ e}}_{{1}} .{\text{V}}$$
(1)

The detail parameters of the linear regressions were presented in Table 2.

Table 2. Linear regression parameters of total suspended particles against meteorological parameters and vehicle per hour measured inside tunnel.

The measured data and the regression lines were sketched in Fig. 1.

Fig. 1.
figure 1

Measure data and regression lines of total suspended particles against meteorological parameters and vehicle per hour inside tunnel.

3.2 Airborne Lead

The airborne contaminants were released from the exhaust gas during the circulations of the motor vehicles in the tunnel. Emitted from gasoline vehicles, lead causes the direct and strong dangers to human being’s health. The data of particulate lead content of aerosols (Pb, μm/m3) in tunnel were examined. The influences of the meteorological parameters (T, H, W) and vehicle per hour (V) on the airborne lead concentration (Pb) were investigated with the proposed regression equations as follows:

$${\text{Pb }} = {\text{ a}}_{{2}} + {\text{ b}}_{{2}} .{\text{T }} + {\text{ c}}_{{2}} .{\text{H }} + {\text{ d}}_{{2}} .{\text{W }} + {\text{ e}}_{{2}} .{\text{V}}$$
(2)

The detail parameters of the linear regressions were shown in Table 3.

Table 3. Linear regression parameters of airborne lead against meteorological parameters and vehicle per hour measured inside tunnel.

The measured data and the regression lines were sketched in Fig. 2.

Fig. 2.
figure 2

Measure data and regression lines of airborne lead against meteorological parameters and vehicle per hour inside tunnel.

3.3 Volatile Organic Compounds

Dangerous to human, the volatile organic compounds (VOCs) are top priority chemical pollutants in the air [14]. The concentration of benzene (C6H6, μm/m3), toluene (C7H8, μm/m3), and xylene (C8H10, μm/m3) inside tunnel were studied to find out the correlation with three mention meteorological parameters (T, H, W) and the traffic volume (V). Among the built regression models, the ones whose Significance F greater than 5% were listed in Table 4.

Table 4. Linear regression parameters of volatile organic compounds against the meteorological parameters measured inside tunnel.

3.4 Discussions

The significance F smaller than 5% was the criterion for the model’s acceptance. The correlation coefficient R was utilised to give commentaries on the correlation status (R = 0: non correlated, R = 1: strong correlated) and to select the representative regression model. The preliminary discussions were obtained.

3.4.1 Case 1

In the linear regressions of TSP against T, H, W, and V, five models were all concluded to be statistical reliable. While the temperature and the wind velocity showed the positive relationships, the relative humidity expressed the negative correlations with the total suspended particles concentration. The positive slope of the (TSP-V) fitted line showed the direct proportion of the TSP to the traffic volume inside tunnel. The multiple models exhibited the stronger correlation coefficients than the simple ones. Two multiple regression models were recommended to be the representatives.

The 1st representative model represented the combined action of the meteorological parameters on the total suspended particles concentration in tunnel:

$${\text{TSP }} = \, - {1682}.{89 } + { 1}0{3}.{\text{61T }} - { 22}.{\text{58H }} + { 159}.0{\text{5W}}$$
(3)

The 2nd representative model represented the combined action of the meteorological parameters and the traffic volume on the total suspended particles concentration in tunnel:

$${\text{TSP }} = \, - {1369}.0{8 } + { 93}.{\text{93T }} - { 22}.{\text{6H }} + { 136}.{\text{46W }} + \, 0.{\text{14V}}$$
(4)

3.4.2 Case 2

In the linear regressions of Pb against T, H, W, and V, five models were all considered to be statistical reliable. While the temperature and the wind velocity showed the positive relationships, the relative humidity expressed the negative correlations with the airborne lead concentration. The positive slope of the (Pb-V) fitted line expressed the direct proportion of the airborne lead concentration to the traffic volume inside tunnel. The vehicle-related models owned the stronger correlation coefficients than the non-vehicle-related ones. The negative trend of Pb against W in the 2nd multiple regression model was not clearly understood. Further studies should be supplied. In the scoop of this paper, the 4th simple and the 1st multiple regression model were recommended as the representatives.

The 1st representative model represented the correlation of the airborne lead concentration and the traffic volume in tunnel:

$${\text{Pb }} = \, - 0.{11 } + \, 0.00{\text{1V}}$$
(5)

The 2nd representative model represented the combined action of the meteorological parameters on the airborne lead concentration in tunnel:

$${\text{Pb }} = \, - {2}.{28 } + \, 0.0{\text{8T }} - \, 0.0{\text{1H }} + \, 0.0{\text{7W}}$$
(6)

3.4.3 Case 3

Among the built linear regression models of VOCs against T, H, W, and V, those who were presented in Table 4 were found to be non statistical reliable and were eliminated. It did not mean the non correlation between them. A richer source of measured data to increase the regression observations was suggested. Other statistical reliable regression models were found but they did not show the strong correlations (R < 0.5). In the scoop of this paper, no representative regression model for the VOCs – meteorology – traffic volume correlation was proposed.

4 Conclusions

The in-tunnel air quality strongly impacts the operation of a road tunnel. The vehicle’s clear visibility is essential for the smooth and safe circulation inside tunnels. Besides, the non harmful effects to the drivers’ health during their passage through tunnel are also demanded. A bad air quality potentially provides the unsafeness to the circulations inside road tunnels. Using the statistical treatments, the paper explored the recorded data of a previous air quality measurement in an opened road tunnel on Vietnam National highway 1A. The linear regression models using the least squares method with 95% of confidence were found. Three study cases were attacked and the representative models for two cases were proposed. From the representative models, it was understood that the combination of high temperature, strong wind and low humidity potentially decreased the tunnel’s air quality. The negative slope of the regression lines of TSP and Pb against H proved that a wet road surface could probably reduce the pollution in road tunnels as mentioned in [10, 11]. The important role of the in-tunnel traffic volume in the deterioration of the tunnel’s air quality was also confirmed. The study in the scoop of this paper was hoped to underline of role of the meteorological parameters in the in-tunnel air quality studies.