Vehicle emissions calculation for urban roads based on the Macroscopic Fundamental Diagram method and real-time traffic information

Vehicle emissions calculation methods mostly use ownership information or annual road monitoring data as the activity level to calculate air pollutant emissions, but it is hard to reflect either the emissions intensity under different conditions or the spatiotemporal characteristics in various sections based on such approaches. This paper presents a method based on the Macroscopic Fundamental Diagram and real-time traffic data to calculate vehicle emissions, which could reflect the operation conditions and emission characteristics of vehicles. Following the ‘Technical Guide for the Compiling of Road Vehicle Air Pollutant Emissions Inventories’, the emissions of three roads with different lane numbers and road grades in Beijing were estimated and verified using this method. Compared with monitoring data, the average deviations of the traffic flow on the Fifth Expressway, Jingfu National Highway, and Jingzhou Provincial Highway were −25.5%, −26.5%, and −13.4%, respectively, and the average deviations of nitrogen oxides emissions were −27.7%, −12.9%, and −12%, respectively. This method showed good application potentials to construct the emissions inventory applied to the block-scale model and analyze the spatiotemporal distribution characteristics of motor vehicle emissions in urban areas. 基于MFD及实时路况的城市道路机动车排放计算方法


Introduction
Road motor vehicle emissions are one of the most important sources of air pollution. The results of source apportionment of atmospheric particulates in 15 cities including Beijing and Shanghai suggested that the contribution of mobile sources to PM 2.5 (particulate matter with a diameter of less than 2.5 µm) concentrations in local emission sources was ranging from 13.5% to 52.1% (MEEPRC 2018). In order to specify current situations and characteristics of road vehicle emissions, researchers around the world have applied lots of effort in vehicle emissions studies. Zheng, Che, and Wang (2009) proposed the 'spatial allocation method' of regional vehicle pollutant emissions based on traffic flow and 'standard road length' of the road network. Wu et al. (2016) estimated China's motor vehicle emissions from 1980 to 2013. Wang et al. (2017) estimated the road vehicle exhaust emissions characteristics of the national highways and provincial highways in 2015 using the average annual monitoring data from traffic monitoring stations. Wang et al. (2010) analyzed the emissions inventory for motor vehicles in Beijing, Shanghai, and Guangzhou from 1995 to 2009 using the Computer Programme to Calculate Emissions from Road Transport (COPERT) model. Fan et al. (2015) estimated the road emissions characteristics in Beijing by investigating the composition of vehicle types and their driving conditions using the COPERT model.
Most studies take the motor vehicles as the subjects, and the ownership or average annual road monitoring data as the activity level in their calculations of CONTACT Yuan LIU liuyuan5002@163.com atmospheric pollutant emissions, but this is unable to reflect the spatial and temporal characteristics of the motor vehicle emissions in each section, nor can it present the characteristics of the emissions intensity under different traffic conditions. The operation state of road motor vehicles varies greatly due to traffic flow directions and peak hours, which leads to large variations in their emissions. Different emission correction factors were prescribed with different vehicle models in the 'Technical Guide for the Compiling of Road Vehicle Air Pollutant Emissions Inventories' (MEEPRC 2015). Various tools such as the COPERT model, MOVES (Motor Vehicle Emission Simulator) model and IVE (International Vehicle Emissions) model have been developed and modified to adjust these emission factors under different traffic conditions. As a main aspect, the speed of the vehicle was proven to have significant influence on the emission factors (USEPA 2002;Sun 2013). When driving at low speeds (< 30 km h −1 ), vehicle emission factors are relatively high due to low engine load and unstable combustion. When driving at moderate or high speeds, the combustion conditions of the engine improves, thus lowering the emission factors (Ma, Zhao, and Liang 2010).
With the increase in environmental management requirements and technology developments, calculation methods are expected to be able to estimate vehicle emissions based on a single road, and to further determine their contributions to the generation of PM 2.5 and ozone (Kim et al. 2017). Therefore, real-time road emission characteristics are significant for the presentation of emissions estimates. In the present work, taking Beijing as an example, we generated estimated reference data using real-time readouts from traffic-flow observation stations on 1 March 2018. We chose the Fifth Expressway, Jingfu National Highway, and Jingzhou Provincial Highway as research subjects, each with different lane numbers and road grades, to construct a calculation method for vehicle emissions based on the Macroscopic Fundamental Diagram (MFD) method and real-time road conditions. By comparing with the emissions values obtained from monitoring data, the method was verified with average deviations lower than 30%.

Calculation method
Monitoring data on the expressway, national highway, and provincial highway were chosen to build and verify our method. The multi-scale emissions of road vehicles were estimated by using the method proposed in the 'Technical Guide for the Compiling of Road Vehicle Air Pollutant Emissions Inventories' (MEEPRC 2015). An average flow-average velocity model was established based on the MFD descriptions of flow, speed, and density. The activity levels of road motor vehicles were obtained from the average traffic flow in each section by analyzing average speeds in real-time road conditions. The traffic situations in Beijing on 1 March 2018 and in March 2015 were obtained through the Gaode Maps application programming interface (API) to calculate the emissions from the Fifth Expressway, Jingfu National Highway, and Jingzhou Provincial Highway separately.

MFD and real-time road conditions data
The MFD method was proposed by Geroliminis and Daganzo (2008) to reflect the correlations among traffic parameters of flow, speed, and density (Geroliminis and Daganzo 2008;Yue 2015): (1) where q u , k u , and v u are the average traffic flow, average density, and average speed of the road network, respectively; N is the total number of sections; and i is the section ID. The method has been widely used in the dynamic division of small areas and traffic density prediction (Ma and Liao 2014;Gayah and Dixit 2013). Gayah and Dixit (2013) used MFDs to predict the real-time network traffic density with floating car data. With less data and simple calculation, the MFD approach gave them promising results with high accuracy. Real-time road traffic data are multi-dimensional spatial data obtained by vehicle locations and road monitoring equipment. They can reflect the operation states of the traffic network in real time, including road traffic speed and the degree of congestion. Typical data, such as probe vehicle data and traffic situation data, can be obtained through the API of electronic maps, such as Gaode Maps Dong et al. 2014). The real-time road condition data contain real-time speed information in different sections, which can be used in the calculation of road vehicle emissions.

Calculation method of exhaust emission from road vehicles
The exhaust emissions from road vehicles were calculated as follows: where E is the monthly emissions of CO (carbon monoxide), NO x (nitrogen oxides), PM 2.5 , and PM 10 (particulate matter with a diameter of less than 10 µm) from different motor vehicle emission sources (units: tons); Q refers to the average flow rate of one-lane motor vehicles (units: vehicles per hour); EF is the comprehensive emissions factor of the pollutants in exhaust emissions per unit distance of a vehicle (units: g km −1 ); L is the driving distance of a vehicle on the road (units: km/ vehicle); and R is the reduction coefficient of the road. The integrated emissions factor, EF, is a comprehensive factor that includes the proportion of different vehicles and the emissions factor under certain conditions: where i is the section number, j is the pollutant type, t is the time, and z is the motor vehicle type. Therefore, EF i;j;t is the comprehensive emissions factor of a pollutant at a certain time in a certain section; P i;z is the proportion of a motor vehicle type in section i; J i;j;z;t is the reference emissions factor correction coefficient of a certain vehicle type in a certain section at time t, which can be obtained through the vehicle emissions model or other correction functions; and n z is the number of the vehicle type z.
In the case of multi-lane driving, motor vehicle traffic behaviors in the same direction will influence each other, thus affecting the traffic capacity of adjacent lanes. Therefore, the calculation of emissions was conducted by replacing the number of lanes with the reduction coefficient of the road R . When the number of lanes was 1, 2, 3, 4, and 5, the corresponding lane conversion factors were 1.00, 1.87, 2.65, 3.20, and 3.65, respectively.

Average flow-average velocity model
Common models describing the relationships between average flow and average velocity include linear models, exponential models, and logarithmic models, among which the Underwood Index Model fits well with both low, medium, and high-density data and the measured data (Yue 2015). By using this model, an average flow-average velocity model was established as follows: where q u is the average traffic flow (units: pcu (passenger car unit) h −1 /lane); v is the average vehicle speed (units: km h −1 ); v f refers to the driving speed without mutual interference between vehicles or influence of traffic conditions (units: km h −1 ); and ρ max is the density corresponding to the maximum traffic flow, also known as the optimal density (units: pcu km −1 /lane), which is deduced as follows (Sun 2013): where q c is the traffic flow, which refers to the maximum number of vehicles that can pass through a certain section per unit time (units: pcu h −1 ). The road design capacity of different grades is listed in Table 1. The conversion of traffic flow q used small passenger cars as the standard model. Different types of vehicles on different roads are different. For example, the proportion of medium and small passenger cars on expressways is about 62%-67%, and that of national and provincial medium and small passenger cars is about 47%-49% (Wang et al. 2017). Different vehicle models have different emission factors. Therefore, the traffic flow of different roads should be converted according to vehicle types in the calculation. The conversion coefficients corresponding to passenger cars, large buses, large freight cars, and articulated vehicles are 1.0, 2.0, 2.5, and 3.0, respectively (MOHURD 2012).

Data sources
Real-time traffic data in Beijing on 1 March 2018 were obtained through the Gaode Open Platform (http://lbs.amap.com/), as shown in Figure 1. The daily average data in Beijing obtained by traffic flow monitoring stations in March 2015 were used as the activity-level data for verification. Relative information of the Fifth Expressway, Jingfu National Highway, and Jingzhou Provincial Highway were extracted from the traffic network data.
As the emission factors of different vehicle types are different, it is important to determine the proportion of vehicle types on different roads. In this study, we analyzed the monitoring data of the Fifth Expressway, Jingfu National Highway, and Jingzhou Provincial Highway in March to obtain the proportion of different road types. With this proportion as the weight, the emission factors under different speed ranges on each road were  Table 2. Free flow velocity, optimal density, and capacity are the basic parameters to calculate the average flow-average velocity model in the MFD (Equation (4)). Yue (2015) constructed the characteristic parameter values of road traffic flow at all road levels (expressways, trunk roads, sub-branch roads) in Beijing through statistical analysis. In our study, the basic parameters of the Fifth Expressway, Jingfu National Highway, and Jingzhou Provincial Highway were modified according to the design capacity of different grades of road (Table 1), the speed limit regulation of specific roads, the number of lanes, etc. (Table 3).

Estimation of road traffic flow
Based on the speed data in the real-time road conditions data, the average traffic flow on each road at different times was estimated with the road grade, number of lanes, and by using the average speed-average flow model. The results reflected well the changes in traffic flow during the morning and evening peaks, as shown in Figure 2.
The deviation between the estimated average daily traffic flow value and measured value on Jingzhou Provincial Highway was less than 15%, as presented in Table 4. The deviations between the estimated values and the measured values on the Fifth Expressway and Jingfu National Highway were all above 25%, which might be related to the calculation defects, the uncertainty of the selected parameters, and the difference between data collection years. As the speed limits in different sections are different and vary regularly, errors could be generated as well. Besides, setting the free-flow velocity as a uniform value might introduce some errors.   However, the estimation of traffic flow based on the MFD method reflects well the real-time status of traffic operations by discriminating different lane numbers and road grades.

Estimation of monthly average road emissions
The traffic flow and integrated emission factors under different operating conditions were estimated by the MFD method, as shown in Table 2. According to the exhaust emissions of road vehicles (Equation (2)), the emissions of road vehicles at different times on each road were estimated and compared with the monthly average emissions calculated by actual monitoring flow (Table 5). It was observed that deviations between the estimated monthly average emissions calculated by the MFD method and the measured emissions on Jingzhou Provincial Highway and Jingfu National Highway were around 10%, while for the Fifth Expressway the deviation was around 25%. The estimation of the traffic flow could lead to these deviations of the calculated average traffic flow, and further influence the accuracy of the estimated monthly emissions as mentioned above. In addition, despite assuming all the motor vehicle speeds in different sections to be the same, when calculating estimated emissions, different emission factors were applied based on different sections, which also led to certain deviations. Although in the estimation of traffic flow the deviations between the Fifth Expressway and Jingfu National Highway were at similar levels, the emission calculation result of Jingfu National Highway was significantly smaller than that of the Fifth Expressway. The main reason was that the speed of the traffic flow on Jingfu National Highway fluctuated significantly along the variation of the traffic demand, which led to relatively large differences in emission factors in different sections at different time (Table 2). However, the changes in traffic flow speed for the Fifth Expressway were small, which led to relatively small variations of emission factors in different   sections at different times. Overall, the deviations among emissions estimations were mainly related to the difference in estimated traffic flow.

Spatial and temporal emission characteristics of road vehicles
NO x is a typical gaseous pollutant generated by road motor vehicles. In this study, we took NO x emissions along the Fifth Expressway as an example to study the spatial and temporal emission characteristics reflected by the MFD estimation method. The emissions of NO x at 0000 LST and 1200 LST (as the traffic troughs), as well as at 0900 LST and 1800 LST (as the traffic peaks), were compared, as shown in Figure 3. Combined with Figure 2, it can be seen that the overall emissions during the morning peak (0900 LST) and evening peak (1800 LST) were much higher than those at 0000 LST and 1200 LST. The highest nitrogen oxide emissions were found in the northeastern part of the city and the intersections. The overall NO x emissions at 0000 LST and 1200 LST were relatively low, which were mainly generated in traffic hubs. In addition, the emissions from the intersections on the Fifth Expressway and the Jingkai Highway were consistently high at each time period.
By comparing the hourly results of the average PM 2.5 concentration data in March 2018 from traffic environmental monitoring stations and non-traffic environmental monitoring stations in Beijing, it was found that PM 2.5 concentrations had a significant peak at traffic monitoring stations at night. The highest estimated hourly emissions of PM 2.5 were found on the Fifth Expressway as it is the main expressway in Beijing with heavy traffic flow, and the lowest was found on Jingfu National Highway, as shown in Figure 4(a). The emissions of PM 2.5 on Jingzhou Provincial Highway were about 40% higher than on Jingfu National Highway. The Fifth Expressway and Jingzhou Provincial Highway showed similarly small peaks of PM 2.5 emissions from 0000 LST to 1800 LST, which could be related to higher PM 2.5 concentrations monitored at traffic stations, as shown in Figure 4(b). Such results imply that trucks running at night in Beijing could be one of the main sources of PM 2.5 emissions.

Conclusions
The estimated vehicle traffic flow and emission results based on the MFD method and real-time road conditions data were close to the measured results. Compared with monitoring data in March 2015, the average deviations of the traffic flow on the Fifth Expressway, Jingfu National Highway, and Jingzhou Provincial Highway were −25.5%, −26.5%, and −13.4% respectively, and the average deviations of NO x emissions were −27.7%, −12.9%, and −12%, respectively.
In this study, the inaccuracy of the traffic flow estimation based on the MFD and real-time road conditions data was mainly due to the following reasons: (1) the uncertainty of free-flow speed and optimal density parameters in basic parameters of the MFD; (2) the uncertainty of real-time road conditions data and road network information. Also, the inaccuracy of the traffic emissions calculation was mainly because of the uncertainty in the vehicle type distribution, emission factors, traffic flow, and operation conditions. This method based on the MFD and real-time traffic data can reflect the operation conditions and emission characteristics of vehicles. The method shows promising application potential in the construction of emissions inventories as applied to block-scale models and analysis of the spatiotemporal distribution characteristics of motor vehicle emissions in urban areas.

Disclosure statement
No potential conflict of interest was reported by the authors.