Model Development for the Real-World Emission Factor Measurement of On-Road Vehicles Under Heterogeneous Traffic Conditions: An Empirical Analysis in Shanghai

Abstract

Global warming is attributed to anthropogenic emissions of CO₂ and the contribution from the transport sector is significant. Estimating on-road vehicle CO₂ emission factors is essential for guiding carbon-reduction efforts in transportation. In order to accurately calculate carbon emission factors from vehicles, this study built a multi-scenario model for open, semi-enclosed, and enclosed road environments based on Fick’s second law and the law of conservation of mass. During the model optimization phase, it was found that the model’s applicability domain effectively encompassed most urban roadway scenarios, making it suitable for estimating urban traffic CO₂ emissions. The spatiotemporal heterogeneity analysis of field measurements indicated that this method can effectively distinguish variations in CO₂ emission factors across different road types and time periods. The method proposed in this study offers an effective solution for the real-time monitoring of large-scale on-road vehicle carbon emissions.

1. Introduction

Anthropogenic emissions of carbon dioxide (CO₂) are very likely to cause global warming and many countries have taken action for carbon reduction [1,2]. In 2021, China mapped a path to carbon peak and neutrality [3]. Transport sector is an important contributor of anthropogenic emissions and accounted for about 10% of total emissions [4,5]. Moreover, transport takes a higher share of carbon emissions in developed regions (e.g., Shanghai) [6]. In order to achieve the goals of carbon peaking and carbon neutrality in the transportation sector, which fall under Sustainable Development Goals 11 (Sustainable Cities and Communities) and 13 (Climate Action) [7,8], one important step is to develop a robust model for estimating the carbon dioxide (CO₂) emission factor (EF) of on-road vehicles under heterogeneous traffic conditions.

Traditionally, the CO₂ emission factor is equivalent to fuel efficiency. Normally, a standardized driving cycle is carried out to quantify a vehicle’s emissions performance under predefined traffic conditions, such as in the Worldwide Harmonized Light Vehicles Test Procedure (WLTP) [9]. The UK Vehicle Certification Agency reported the Honda Civic’s fuel consumption of 4.40 L/100 km (ca. 101 g-CO₂/km/vehicle for CO₂ EF) under the WLTP standard cycle [10].

The US NHTSA issued that the minimum fuel economy standard for passenger vehicles manufactured for sale in 2025 was 48.1 mpg (approximately 115 g-CO₂/km/veh), with this value derived from a weighted average of FTP-75 city driving cycles and HWFET highway driving cycle [11]. However, external conditions (such as temperature and traffic conditions) significantly elevated vehicle fuel consumption. Compared to the standard test cycle, average on-road CO₂ emissions of diesel vehicles were approximately 33% higher, while those of gasoline vehicles were 41% higher [12]. In contrast to costly experimental measurements, researchers have developed efficient modeling methods (such as the IVE model) to calculate emission factors. In this method, the model’s internal baseline emission factor is adjusted via a set of correction factors—such as temperature and elevation adjustments—to yield the CO₂ emission factor [13,14,15]. However, modeling methods are based on laboratory test or regional data. In essence, they are mathematical extrapolations of laboratory test results or regional data, making it difficult for them to reflect the randomness of driving behavior and the complexity of road conditions. Seyed’s study found that the CO₂ emission factor obtained from onboard measurements was 1.28 times higher than that estimated by the IVE model [16].

The CO₂ emission factor of on-road vehicles not only depends on vehicle and traffic conditions but is also constrained by factors such as road conditions and traffic management, which has led to increasing interest in real-world measurements.

Portable Emission Measurement Systems (PEMSs) can continuously monitor vehicle emissions, providing a realistic representation of emission behavior throughout the driving process. Yang et. employed PEMSs to assess on-road emissions, revealing a CO₂ emission factor of 271.2 g/km/veh for a light-duty gasoline vehicle with a three-way catalyst on urban roads [17,18]. However, since PEMS data are limited to specific vehicle types and road segments, the monitoring efficiency remains low [19] and fails to meet the requirements for dynamic emission monitoring. In response to the pressing demand for improved monitoring efficiency, remote sensing has been developed as a practical approach. Gantina’s research employing remote sensing revealed a CO₂ emission factor of 46.50 g/km/veh for motorcycles [20]. Remote sensing can rapidly detect vehicular exhaust emissions near fixed monitoring sites, but it is applicable only in traffic with a single lane [21], which cannot satisfy the spatial coverage requirements for urban road CO₂ monitoring. To address this limitation, Zhang et al. employed a tunnel testing and reported a CO₂ emission factor of 390 g/km/veh based on measurements conducted in a tunnel in Guangzhou, China [22]. Despite its ability to measure average vehicle emissions on a particular road, the tunnel test is confined to tunnel environments and cannot be effectively applied to open roads, thereby failing to support real-time carbon emission monitoring for urban networks dominated by open roads [23,24]. In summary, although real-world measurements provide a more accurate representation of actual emissions than laboratory tests and model-based methods, current real-world measurements are limited by spatial coverage, data timeliness, and scenario adaptability. As a result, they are unable to simultaneously support continuous monitoring and dynamic updating across entire urban road, making them inadequate for real-time carbon emission monitoring in urban traffic systems.

As China’s largest economic center and an international metropolis located on the eastern coast, Shanghai serves as a major transportation hub with a vehicle fleet exceeding 5 million. The city’s road network is highly developed, encompassing elevated roads, expressways, and regular city roads, with a total mileage exceeding 13,000 km [25,26]. Against this backdrop, conducting in situ measurements of on-road vehicle carbon emission factors enables the precise evaluation of emissions across different road types, thereby providing the scientific basis for targeted reduction strategies and supporting Shanghai’s objectives of carbon peaking and carbon neutrality.

Hence, this study aimed to achieve the dynamic monitoring of vehicle carbon emission factors under complex urban road conditions, addressing the limitations of traditional measurement methods. This study aimed to (1) develop an estimation model for measuring on-road vehicle carbon emission factor and apply it to typical road conditions in Shanghai, (2) optimize and calibrate the model to precisely define its applicability, and (3) validate the model feasibility through field measurements on representative roads in Shanghai, finally obtaining localized emission factors. This research provides a scientific basis for dynamic monitoring and precise management of traffic-related carbon emissions.

2. Methods

2.1. Modeling Method

Based on the literature and established standards [27,28,29], this study defined the carbon emission factor as the mass of carbon dioxide emitted by a vehicle per kilometer traveled, with units of g/km/veh. This paper constructs a calculation model for EF based on the law of mass conservation and Fick’s second law and derives its mathematical expression.

Based on Fick’s second law, the rate of change of concentration over time is equal to the negative of the rate of change of the diffusion flux in that spatial direction in one-dimensional space, as given by Equation (1):

$${\displaystyle \frac{\partial c}{\partial t}}=-{\displaystyle \frac{\partial F_x}{\partial x}}$$

(1)

Here, $F_x$ denotes the diffusion-flux component in the x-direction. In three-dimensional space, the diffusion flux at any point is jointly determined by the x, y, and z directions. We denote the diffusion-flux components at that point by $F_x$, $F_y$, and $F_z$, corresponding to the x, y, and z directions. From this, the relationship between the concentration change rate and flux in three-dimensional space can be established, as represented by Equation (2):

$${\displaystyle \frac{\partial c}{\partial t}}=-{\displaystyle \frac{\partial F_x}{\partial x}}-{\displaystyle \frac{\partial F_y}{\partial y}}-{\displaystyle \frac{\partial F_z}{\partial z}}$$

(2)

Within a differential control-volume element, processes such as chemical reactions and pollutant emissions may occur. Therefore, a source–sink term R_n is introduced to represent the pollutant’s net generation rate within the element.

$${\displaystyle \frac{\partial c}{\partial t}}=-{\displaystyle \frac{\partial F_x}{\partial x}}-{\displaystyle \frac{\partial F_y}{\partial y}}-{\displaystyle \frac{\partial F_z}{\partial z}}+R_n$$

(3)

In the road environment, when considering sufficiently long time scales, instantaneous fluctuations in CO₂ concentration can be neglected. Thus, it is reasonable to assume that the temporal derivative of concentration is approximately zero, ${\displaystyle \frac{\partial c}{\partial t}}=0$. Accordingly, by simplifying and rearranging Equation (3), we obtain Equation (4).

$$R_n={\displaystyle \frac{\partial F_x}{\partial x}}+{\displaystyle \frac{\partial F_y}{\partial y}}+{\displaystyle \frac{\partial F_z}{\partial z}}$$

(4)

By multiplying both sides of Equation (4) by the volume $\mathsf{\Delta }V$, we establish a quantitative relationship between the emission rate of pollutants and the gradient of the flux, resulting in Equation (5).

$$\begin{array}{l}Emission Rate\left(\mathrm{g}·{\mathrm{day}}^{-1}\right)\\ =R_n·\Delta V\\ ={\displaystyle \frac{\partial F_x}{\partial x}}·\left(A_{yz}·\Delta x\right)+{\displaystyle \frac{\partial F_y}{\partial y}}·\left(A_{xz}·\Delta y\right)+{\displaystyle \frac{\partial F_z}{\partial z}}·\left(A_{xy}·\mathsf{\Delta }z\right)\\ \begin{array}{c}={\partial Flux}_x·A_{yz}+{\partial Flux}_y·A_{xz}+{\partial Flux}_z·A_{xy}\end{array}\end{array}$$

(5)

In Equation (5), A_yz, A_xz, and A_xy denotes the cross-sectional areas perpendicular to the X-, Y-, and Z-directions, respectively. ${\partial Flux}_x$, ${\partial Flux}_y$, and ${\partial Flux}_z$ denote the flux variations along the x, y, and z directions, respectively. Equation (5) indicates that the total emission rate of pollutants within a spatial volume is equal to the sum of the products of the diffusion flux gradients in each direction and the corresponding control surface areas. By normalizing the above total emission rate with respect to the traffic flow through the cross section and the unit travel distance, the emission factor (EF) is obtained, which represents the mass of pollutant emitted per vehicle per kilometer traveled (unit: g·km⁻¹·veh⁻¹).

$$Emission Factor={\displaystyle \frac{Emission Rate\left(\mathrm{g}·{\mathrm{day}}^{-1}\right)}{\partial x\left(\mathrm{km}\right)·volume\left(\mathrm{veh}·{\mathrm{day}}^{-1}\right)}}$$

(6)

Substituting Equation (5) into Equation (6) yields the general formula for calculating the emission factor.

$$Emission Factor\left(\mathrm{g}·{\mathrm{km}}^{-1}·{\mathrm{veh}}^{-1}\right)={\displaystyle \frac{{\partial Flux}_x}{\partial x}}·{\displaystyle \frac{A_{yz}}{vol}}+{\displaystyle \frac{{\partial Flux}_y}{vol}}·H+{\displaystyle \frac{{\partial Flux}_z}{vol}}·D$$

(7)

In this model, $H={\displaystyle \frac{A_{yz}}{\partial x}}$ refers to the on-road boundary layer height, $D={\displaystyle \frac{A_{xy}}{\partial x}}$ represents the width of the road, and vol represents the traffic volume passing through the cross-section per unit time.

In summary, this section has primarily introduced the general model for carbon emission factors. In the next section, we will further derive carbon emission factor models for different application scenarios.

2.2. Model Assumptions

The varied nature of road environments complicates accurate vehicle CO₂ emission factor modeling. Consequently, to streamline the model and guide instrument placement, this work, informed by field reality, formulates these assumptions concerning cross-section environmental conditions, the disturbed air layer, and CO₂ concentration variability for computational ease:

(1)

Meteorological conditions (e.g., wind speed, wind direction) and environmental conditions (e.g., temperature) are similar within the road cross-section. The purpose of this assumption is to substantially simplify the model’s complexity and data requirements. It reduces the need for intensive cross-road meteorological monitoring and greatly lowers the computational burden. Moreover, in experiments, deploying monitors only on the two sides of the road can approximate the cross-sectional mean state, avoiding placement in the hazardous roadway center and thereby easing the practical implementation of the monitoring scheme. However, vehicle bodies and their wakes can induce non-uniform wind-speed and temperature distributions across the roadway cross-section. Consequently, instruments sited at the road flanks may fail to represent conditions at the carriageway center, thereby introducing bias into the model.

(2)

The height of the air layer disturbed by vehicle motion is 1.5 times the vehicle height, and CO₂ concentration is uniformly distributed within that layer. Following eddy-covariance height-selection principles from ecological studies, the disturbed-layer height was set to 1.5 times the vehicle height, and instruments were sited accordingly to avoid direct wake effects and to confine the flux-monitoring footprint. Assuming a uniform CO₂ concentration within this disturbed layer substantially simplifies the monitoring scheme. However, the actual disturbed-layer height varies dynamically with vehicle type and travel speed, so fixing it at 1.5 times the vehicle height may substantially deviate from the true physical boundary. Moreover, CO₂ concentrations within the disturbed layer are often non-uniform. Both factors can introduce measurement errors in the instrumentation.

(3)

The CO₂ concentration maintains a spatial steady state with no significant temporal variation, i.e., ${\displaystyle \frac{\partial c}{\partial t}}=0$. During monitoring periods when both meteorological conditions and traffic flow remain relatively steady, CO₂ emissions and dispersion processes can be considered to approximate a dynamic equilibrium. In addition, we processed the CO₂ concentration time series using a moving-average method to suppress short-term fluctuations and yield a more stable concentration profile. When atmospheric conditions are unstable or traffic congestion is severe, CO₂ concentrations vary significantly over time, ${\displaystyle \frac{\partial c}{\partial t}}\ne 0$. Temporal accumulation term must be incorporated into the model to accurately calculate the emission factor.

$$R_n={\displaystyle \frac{\partial F_x}{\partial x}}+{\displaystyle \frac{\partial F_y}{\partial y}}+{\displaystyle \frac{\partial F_z}{\partial z}}+{\displaystyle \frac{\partial c}{\partial t}}$$

3. Study Case

3.1. Study Area

The experimental sites, as shown in Figure 1, are located in Shanghai and include various types of roads, such as urban branch roads, urban main roads, suburban main roads, suburban branch roads, tunnels, and highways.

3.2. On-Road Measurement

3.2.1. Experimental Equipment and Sites

A three-dimensional ultrasonic anemometer (WERY-W3D) and a data logger (CR1000) were utilized to collect three-dimensional wind speed information. Two open-path carbon dioxide infrared analyzers were utilized to collect CO₂ concentration information on both sides of the road. Furthermore, cameras installed by the roadside were used to collect traffic volume and vehicle speed information. The experimental sites, as shown in Figure 1, are located in Shanghai, including various types of roads such as urban branch roads, urban main roads, suburban main roads, suburban branch roads, and highways.

3.2.2. Data Processing

(1)

Spike screening: Influenced by factors like instruments, the collected carbon dioxide concentration and wind speed data had outliers. Consequently, spike screening was carried out on all datasets. In detail, a time interval of 10 min (each interval including 600 data points) was used, and data points whose absolute difference from the mean was beyond ±3 standard deviations were defined as outliers. The outliers were replaced through linear interpolation using the data before and after them, and this process was repeated until no outliers were present in the dataset [31]. Approximately 1% of the data was replaced as outliers. In addition, it was necessary to perform corrections such as temperature correction [32] and coordinate rotation on the raw data [33].

(2)

Statistics of traffic volume: This paper applies Python-based video (version 3.8.15) analysis techniques to achieve vehicle recognition and quantification. The process begins with background modeling to extract dynamic targets, and morphological operations are then applied for denoising and enhancement, thereby improving the accuracy of vehicle detection. Following this, vehicle contours are refined through width and height constraints to exclude non-motor vehicles. Vehicle counting is then achieved by tracking the motion of vehicle centroids and identifying whether they intersect with a predefined detection line, producing traffic statistics that include time information. In order to verify the reliability of the counting results, manual traffic counts were carried out at selected locations during critical time periods, and the data were compared against the program’s output.

(3)

Standardization of traffic volume: Based on relevant national standards, this study assumed that the carbon emission factor of high-emission vehicle types (e.g., trucks and lorries) was 1.5 times that of low-emission vehicle types (e.g., passenger cars) [34,35], and that the driving carbon emission factor of electric vehicles was considered zero. Next, the proportions of electric vehicles, low-emission vehicles, and high-emission vehicles were manually calculated over a period of time. Based on the vehicle type proportions and the CO₂ emission factors of each category, a conversion coefficient was calculated using the weighted average method, thereby achieving the standardization of traffic volume. This process converts the observed traffic into equivalent standard vehicles, effectively eliminating the influence of vehicle composition differences on emission factors and ensuring the accuracy and comparability of the results.

(4)

Time lag adjustment: Since CO₂ transported by the prevailing wind takes time to diffuse from the upwind to downwind sensor locations, we conducted a time lag study to align the data temporally. Cross-correlation analysis revealed that the time lag between the CO₂ signals from sensors on both sides of the road was significantly shorter than the sliding average time window. This indicates that the wind-driven concentration signal arrived at the downwind sensor within the same sliding average window, making the impact of this time lag on the final smoothed concentration data negligible.

(5)

CO₂ instrument calibration: Two calibrated CO₂ sensors were placed synchronously in a sealed, interference-free chamber to record data. Results showed a high correlation in the concentration time series (R² > 0.99), and the mean concentration difference was less than the instrument detection error. This confirms that the inter-instrument variation was within acceptable limits and suitable for field sampling.

4. Results and Discussion

4.1. Construction of Model in Three Typical Road Scenarios

This study established a classification system based on the degree of separation between roads and their surrounding environments. Fully enclosed roads (e.g., tunnels, Figure 2a) were completely isolated from the environment by physical barriers, forming independent traffic spaces. Semi-enclosed roads (e.g., highway with sound barriers, Figure 2b) incorporated partial separation designs, maintaining limited environmental interfaces. Open-environment roads (e.g., normal roadway, Figure 2c) had no physical isolation and were fully integrated with the surrounding environment. This section presents the derivation of carbon emission factor models for these three representative road types.

4.1.1. Enclosed-Environment Road

For completely enclosed road environments, due to the complete enclosure of the surrounding environment, carbon dioxide can only diffuse along the driving direction (x-direction).

In fully enclosed road environments, the surrounding enclosure suppresses diffusion in the y- and z-directions, so CO₂ can diffuse only along the driving (x) direction. As a result, ${\partial \mathrm{F}\mathrm{l}\mathrm{u}\mathrm{x}}_{\mathrm{y}}={\partial \mathrm{F}\mathrm{l}\mathrm{u}\mathrm{x}}_{\mathrm{z}}=0$. In this case, the carbon emission factor formula becomes the following:

$$Emission Factor\left(\mathrm{mg}·{\mathrm{m}}^{-1}·{\mathrm{veh}}^{-1}\right)={\displaystyle \frac{{\mathsf{\Delta }Flux}_x}{\partial x}}·{\displaystyle \frac{A_{yz}}{vol}}$$

(8)

According to the Reynolds averaging method [36,37], every variable is split into an average part and a perturbation part, Therefore, the calculation of the average flux in the x-direction is as follows:

$$\overline{{\mathsf{\Delta }Flux}_x}=\overline{u}·\left(\overline{c_{out}}-\overline{c_{in}}\right)+\left(\overline{u^{\prime }·c_{out}^{\prime }}-\overline{u^{\prime }·c_{in}^{\prime }}\right)$$

(9)

In Equations (8) and (9), L denotes the distance between the inlet and outlet (m); $\overline{c_{out}}$ and $\overline{c_{in}}$ are the mean pollutant concentrations at the outlet and inlet, respectively (mg·m⁻³).$vol$ is the traffic flow rate (veh·s⁻¹), $\overline{u}$ denotes the mean wind speed along the road(x–direction)(m·s⁻¹), and $\overline{u^{\prime }}$ denotes the mean x-direction wind-speed perturbation (m·s⁻¹). $\overline{c_{out}^{\prime }}$ and $\overline{c_{in}^{\prime }}$ are the mean concentration perturbations at the outlet and inlet, respectively (mg·m⁻³).

In Equation (9), the first term, which is the product of the average velocity and the difference between the average concentrations at the outlet and inlet, reflects the small-scale and large-scale average convective processes. The second term signifies the interactive effects of the perturbation terms, illustrating the influence of turbulence or small-scale disturbances on the system.

4.1.2. Semi-Enclosed-Environment Road

For semi-enclosed roads (such as elevated roads equipped with soundproof walls), it is first assumed that the variation of carbon emission flux in the vehicle driving direction (x-direction) can be neglected, that is, ${\displaystyle \frac{{\partial Flux}_x}{\partial x}}=0$. This assumption is based on the continuous and stable emission characteristics of vehicles. During vehicle driving, the continuous and stable emission of CO₂ makes the CO₂ concentration relatively stable along the vehicle driving path, thereby causing the variation of CO₂ flux in the x-direction also close to zero. In the subsequent model optimization part, the rationality of this assumption will be further verified through field measurement data. Additionally, due to the sound barriers on both sides of the road, the horizontal wind speed is small and can be neglected, leading to the assumption that the flux in the y-direction is zero, i.e., ${\mathsf{\Delta }Flux}_y=0$. Therefore, the carbon emission factor formula becomes as follows:

$$Emission Factor\left(\mathrm{mg}·{\mathrm{m}}^{-1}·{\mathrm{veh}}^{-1}\right)={\displaystyle \frac{{\mathsf{\Delta }Flux}_z}{vol}}·D$$

(10)

$$\overline{{\mathsf{\Delta }Flux}_z}=\overline{w}·\overline{c}+\overline{w^{\prime }·c^{\prime }}$$

(11)

Here, D is the width of the road; $\overline{w}$ is the mean wind speed in the vertical direction (z-direction) and $\overline{w^{\prime }}$ is the mean of the vertical wind-speed fluctuations.

4.1.3. Open-Environment Road

In the case of open road environments, the emissions from vehicles are continuous and stable, meaning that in the vehicle movement direction (x-direction), the carbon emission concentration remains relatively constant. As the change in concentration is small, the concentration gradient can be neglected, leading to ${\displaystyle \frac{{\partial Flux}_x}{\partial x}}=0$.

In open road environments, the CO₂ emission factor model can thus be simplified to the following:

$$Emission Factor\left(\mathrm{mg}·{\mathrm{m}}^{-1}·{\mathrm{veh}}^{-1}\right)={\displaystyle \frac{{\Delta Flux}_y}{vol}}·H+{\displaystyle \frac{{\Delta Flux}_z}{vol}}·D$$

(12)

According to the Reynolds averaging method, the calculation of the average flux in the y-direction and z-direction is as follows:

$$\overline{{\Delta Flux}_y}=\overline{v}·\left(\overline{c_{out}}-\overline{c_{in}}\right)+\left(\overline{v^{\prime }·c_{out}^{\prime }}-\overline{v^{\prime }·c_{in}^{\prime }}\right)$$

(13)

$$\overline{{\Delta Flux}_z}=\overline{w}·\left(\overline{c_{out}}-\overline{c_{in}}\right)+\overline{w^{\prime }·c^{\prime }}$$

(14)

Here, H denotes the air layer height; $\overline{w}$ represents the mean cross-road horizontal wind speed (y-direction), and $\overline{v^{\prime }}$ is the mean of the y-direction wind-speed fluctuations.

In summary, based on the conventional emission factor model, this section has developed emission-factor models for enclosed, semi-enclosed, and open-road environments, thereby providing a foundational methodology for traffic CO₂ emission calculations across various scenarios.

4.2. Model Optimization

Based on the analysis of model construction and subsequent research on emission factors in the preceding text, this paper has identified that the concentration along the travel direction, horizontal wind speed, and traffic volume are three key variables significantly impacting the application of the model. To enhance the reliability and predictive accuracy of the model, this section will carry out specific research on the above factors.

4.2.1. Concentration Uniformity Along Travel Direction in Open/Semi-Open Roads

This study conducted continuous half-hour observations on one side of a straight road using two CO₂ concentration sensors spaced 5 m apart. The data (Figure 3) were analyzed through time lag analysis, statistical tests, and directional-concentration-difference quantification to validate the hypothesis that the CO₂ flux in the vehicle travel direction (x-direction) was negligible. The analysis of time lag showed that the correlation coefficient peaked at t = 0, indicating the temporal consistency of CO₂ concentrations on both sides of the road. Statistical tests confirmed the distributional similarity between the two datasets, as evidenced by the two-sample Kolmogorov–Smirnov test (p = 0.177 > 0.05), the paired t-test (p = 0.325 > 0.05), and the coefficient of variation analysis (C₁ = 27.6%, C₂ = 27.0%), which examined their distribution patterns, mean values, and variability, respectively. Furthermore, Figure 3d shows that the mean concentration difference in the direction perpendicular to traffic flow (y-direction, $\mathsf{\Delta }$C_y = 43.1 ppm) was 10.2 times higher than that in the vehicle travel direction (x-direction, $\mathsf{\Delta }$C_x = 4.24 ppm), emphasizing the negligible impact of the x-direction concentration gradient.

In conclusion, the analyses confirmed that the differences in CO₂ concentration along the vehicle travel direction in open/semi-open roads can be negligible, thereby justifying the CO₂ flux in the travel direction(x-direction) and simplifying the carbon emission factor estimation model for open-road environments.

4.2.2. Model Optimization Based on Critical Horizontal Wind Speed Threshold

The CO₂ diffusion flux is calculated based on the theoretical framework of concentration gradients in the transverse (y-direction) and vertical (z-direction) directions in the developed carbon emission factor model. However, when the horizontal wind speed (y-direction) exceeds a critical threshold, the vehicle-emitted CO₂ plume rapidly migrates to the far field under high-speed wind forcing, reducing the y-direction concentration gradient below instrument resolution. This causes an error in the model’s carbon dioxide diffusion rate and emission intensity estimation. Therefore, it is essential to define a critical wind speed threshold for the model using theoretical derivation and empirical data. When the actual wind speed exceeds this threshold, the model is no longer valid for determining CO₂ emission factors.

This paper uses the Gaussian dispersion model [38,39] to simulate and determine the downwind concentration of carbon dioxide in the atmosphere. The use of the model is the most extensively applied approach for calculating the downwind concentration of pollutants released into the atmosphere, with its fundamental assumption being that the pollutant concentration exhibits a Gaussian distribution in both horizontal and vertical directions.

$$C_{\left(x,y,z,H\right)}={\displaystyle \frac{Q}{2\pi \overline{u}{\sigma }_y{\sigma }_z}}exp\left(-{\displaystyle \frac{y^2}{2{\sigma }_y^2}}\right)\left\{exp\left[-{\displaystyle \frac{{\left(z-H\right)}^2}{2{\sigma }_z^2}}\right]+exp\left[-{\displaystyle \frac{{\left(z+H\right)}^2}{2{\sigma }_z^2}}\right]\right\}$$

(15)

Based on previous literature and practical considerations [40,41], the relevant parameters in the Gaussian dispersion model (Figure 4a) are determined. By simplifying Equation (14), the instantaneous contribution of the pollutant source to the roadside carbon dioxide concentration when a vehicle passes under ideal meteorological conditions is derived.

In high-wind scenarios, the carbon dioxide plume is quickly carried away to the far field by the strong wind, leading to the pollutant source contribution C_{(x, 0, z, H)}, being lower than the instrument’s measurement error (ME).

$$C_{(x,y,z,H)}<ME$$

This demonstrates that the pollutant source’s effect on the local carbon dioxide concentration can be disregarded under these meteorological conditions.

By substituting the parameters into the equation, the critical horizontal wind speed threshold ${\overline{v}}_{max}=3.92 \mathrm{m}/\mathrm{s}$ was derived. When horizontal wind speeds exceed this threshold, the predictive accuracy diminishes significantly, rendering it inapplicable beyond this critical value.

In this study, we established a curve linking the critical horizontal wind speed threshold to the instrument measurement error (Figure 4b), revealing a quantitative relationship: as the measurement error (ME) increases, the critical wind speed threshold markedly decreases, and the two follow an inverse proportional function. Accordingly, the criterion for selecting instrument parameters is that in areas with higher wind speeds, high-precision CO₂ analyzers should be used to enhance the accuracy of dispersion model calculations.

In conclusion, this study, using Shanghai as a case study, identified a critical horizontal wind speed threshold of 3.92 m/s. More importantly, it revealed a general inverse relationship between instrument measurement error and the critical horizontal wind speed threshold, providing essential theoretical guidance and a quantitative basis for optimizing monitoring equipment under varying regional and wind speed conditions.

4.2.3. Model Optimization Based on Traffic Volume

In this study, we partitioned traffic volume and CO₂ emissions by multiple time scales and summed each segment’s data. The combined dataset was then plotted together and fitted with a least-squares curve (see Figure 5).

As shown in Figure 5, the traffic volume level is a governing factor in the variability of emission factors. In regions where traffic volume (V) approaches zero (corresponding to shorter time scales), the data points are more dispersed and the emission factors fluctuate widely. This is because the cumulative traffic volume is small; the emission differences between individual vehicles can significantly affect the total emissions. But in areas with high traffic volumes (corresponding to longer time scales), the data points are more clustered and the emission factors fluctuate less. This may obscure the instantaneous relationship between traffic flow and emissions, reducing the model’s sensitivity to real-world traffic conditions. In order to obtain more precise emission factors and prevent their distortion under excessively low or high traffic volumes caused by an improper time-scale selection, it is crucial to choose the right time scale.

This paper employs error propagation formulas to evaluate the impact of varying time scales on emission factors. The emission factor is calculated using the emission (EM) and vehicle flow rate (V),

$$EF={\displaystyle \frac{{EM}_{seg}}{V_{seg}}}$$

(16)

${EM}_{seg}$ denotes the total emissions over a specific time period and $V_{seg}$ denotes the total traffic volume during the same period. Based on the error propagation formula, the following can be derived:

$${\left({\displaystyle \frac{{\mathsf{\sigma }}_{\mathrm{E}\mathrm{F}}}{\mathrm{E}\mathrm{F}}}\right)}^2={\left({\displaystyle \frac{{\sigma }_{{EM}_{seg}}}{{EM}_{seg}}}\right)}^2+{\left({\displaystyle \frac{{\sigma }_{V_{seg}}}{V_{seg}}}\right)}^2$$

(17)

The standard deviation of the traffic volume per unit time, V, is denoted as ${\sigma }_v$. Since the fluctuations in each time interval are independent, the standard deviation of ${\mathrm{V}}_{\mathrm{s}\mathrm{e}\mathrm{g}}=\mathrm{V}\times \mathsf{\Delta }t$ is as follows:

$${\sigma }_{{\mathrm{V}}_{\mathrm{s}\mathrm{e}\mathrm{g}}}={\sigma }_V\times \sqrt{\mathsf{\Delta }t}$$

(18)

Since carbon emission data is obtained using high-precision instruments, its relative deviation is much smaller than that of traffic volume. Therefore, the uncertainty in emissions can be disregarded in error propagation analysis. Therefore,

$${\displaystyle \frac{{\sigma }_{EF}}{EF}}={\displaystyle \frac{{\sigma }_{{\mathrm{V}}_{\mathrm{s}\mathrm{e}\mathrm{g}}}}{{\mathrm{V}}_{\mathrm{s}\mathrm{e}\mathrm{g}}}}$$

(19)

Hence, substituting Equation (18) into Equation (19) yields the formula for the standard deviation of the emission factor:

$${\displaystyle \frac{{\sigma }_{EF}}{EF}}={\displaystyle \frac{{\sigma }_{{\mathrm{V}}_{\mathrm{s}\mathrm{e}\mathrm{g}}}}{{\mathrm{V}}_{\mathrm{s}\mathrm{e}\mathrm{g}}}}={\displaystyle \frac{{\sigma }_V\times \sqrt{\mathsf{\Delta }t}}{V\times \mathsf{\Delta }t}}={\displaystyle \frac{{\sigma }_V}{V\times \sqrt{\mathsf{\Delta }t}}}$$

(20)

The formula shows that a smaller time scale allows for high-resolution emission factors in both space and time, but the emission factors fluctuate more significantly. As the time scale increases, the emission factor resolution lowers, while fluctuations in the emission factors become less pronounced, resulting in more stable outcomes.

At sampling location 2, the traffic flow is 10.0 vehicles per minute. To keep ${\displaystyle \frac{{\sigma }_{EF}}{EF}}$ below 0.05, the time scale needs to exceed 35.6 min, making 35.6 min the minimum time scale for this sampling site. Similarly, at sampling location 4, with a traffic flow of 7.91 vehicles per minute, the minimum time scale required is 47.2 min. This means that in areas with low traffic flow, a larger time scale is required to reduce fluctuations in emission factors. This study plotted the relationship between traffic volume and time scale (see Figure 6). From Figure 6 and the above examples, it is clear that in areas with low traffic flow, a larger time scale accumulation is needed to reduce the uncertainty in emission-factor estimates.

Moreover, the fitted lines indicate that CO₂ emissions do not drop to zero when traffic volume is zero, suggesting contributions from non-traffic sources such as industrial processes, residential emissions, or other stationary background sources [42,43]. To apply the model more effectively and minimize interference from non-traffic emission sources, we calculated the critical traffic volume at each monitoring point, with a mean value of 2.07 vehicles per minute (shown by the blue line in Figure 6). In practical applications of the model, when actual traffic flow exceeds the critical threshold, the model can more accurately determine the CO₂ emission factor of traffic sources, since interference from non-traffic emissions is minimal under these conditions. Most traffic volumes exceed this threshold on urban roads, so the model can be effectively applied to estimate CO₂ emissions from traffic sources, robustly meeting the practical needs of urban traffic emission monitoring and management.

In summary, this study demonstrated that traffic volume (V) is a key variable in regulating the emission factor (EF). Based on error propagation theory, it establishes that under low-traffic scenarios, a longer observation time window is required to improve the accuracy of EF estimation. In addition, this study identified a critical traffic volume threshold that effectively isolated background emission interference and enhanced the model’s reliability.

4.3. Application of Model to Enclosed-Environment Roads

Since the model’s approach to estimation in enclosed-road environments closely follows tunnel testing methods frequently cited in the literature, this research conducted validation using tunnel data to ensure its reliability.

The tunnel testing method, based on the law of mass conservation, simplifies the tunnel into an ideal cylindrical volume. By calculating the mass difference of pollutants between two cross-sections, this approach determines the total emissions from motor vehicles within that segment. Combining the vehicle flow rate with tunnel parameters then yields the average emission factor per vehicle. The calculation formula is as follows:

$$\mathrm{E}\mathrm{F}={\displaystyle \frac{{(\mathrm{c}}_{\mathrm{o}\mathrm{u}\mathrm{t}}\times {\mathrm{u}}_{\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{c}}_{\mathrm{i}\mathrm{n}}\times {\mathrm{u}}_{\mathrm{i}\mathrm{n}})\times \mathrm{A}}{\mathrm{L}\times \mathrm{v}\mathrm{o}\mathrm{l}}}$$

(21)

In Equation (21), EF denotes the average emission factor of the mixed fleet over the sampling period. vol represents the total number of vehicles passing through the tunnel during that period. L is the distance between the two sampling points inside the tunnel. c_out and c_in refer to pollutant concentrations at the exit and entry sampling stations. u_out and u_in are the corresponding wind speeds. A denotes the tunnel’s cross-sectional area.

The carbon-emission-factor model for enclosed-road environments proposed in this study and the tunnel test are both fundamentally based on the law of mass conservation. They determine the emission factor from the change in pollutant mass between two sampling points within the tunnel. Although our model extends the tunnel test by accounting for turbulent diffusion effects, the results show that, compared with convective diffusion, turbulence has a relatively minor impact on the outcomes and can therefore be neglected in calculations.

This study validated the carbon emission factor model through experiments conducted in a tunnel. As shown in Figure 7, both the difference in CO₂ concentration between the tunnel entrance and exit and the traffic volume exhibited clear diurnal variations. From 5:00 to 8:00 a.m., traffic volume began to rise and reached a peak during the morning rush hour between 7:00 and 9:00, during which the CO₂ concentration difference also reached its first peak. After the morning peak, both traffic volume and the CO₂ concentration difference declined slightly. Between 16:00 and 18:00 in the evening, traffic volume rose again to a second peak, and the CO₂ concentration difference likewise increased to its second maximum. This phenomenon is attributable to people commuting to work during the morning and evening peak hours or engaging in other daily activities. In this study, the average emission factor in the tunnel was 228 g/km/veh, higher than the 180 g/km/veh recorded by Jin in the Zhengzhou tunnel [44]. This discrepancy may have been due to various factors, including regional traffic conditions, vehicle fleet composition, and driving habits.

In summary, through comparison with the tunnel testing method and validation against measured tunnel data, this section has shown that the model can capture temporal emission variations and estimate CO₂ emission factors for vehicles in enclosed road environments, providing a reference for calculating CO₂ emission factors of vehicles in enclosed-road environments.

4.4. Application of Model to Open-Environment Roads

The previous section validated the emission-factor model for enclosed-environment roads. Given that the narrow space in semi-enclosed roads severely limits instrument deployment, and that open-road environments are more complex and better represent urban roads, this study conducted on-site measurements directly in open-road settings. This section presents the results of the open-road experiments.

4.4.1. Comparison of CO₂ Emission Factors in Different Roads

This study measured vehicle emission factors in an open-road environment, with a mean value of 368 g·km⁻¹·veh⁻¹ and a 95% confidence interval (CI) of 329–407 g·km⁻¹·veh⁻¹ (

Table 1. Statistical analysis of road traffic CO₂ emission factors in Shanghai (mean and 95% confidence interval).

Road Type	Mean EF (g/km/veh)	95%CI (g/km/veh)
Suburban branch road	328	249–407
Urban main road	341	289–394
Overall a	368	329–407

^a: Overall results calculated from suburban arterial, urban arterial, suburban local, urban local, and expressway measurements.

).

Table 2. Measured carbon emission factors for different roads in Shanghai.

Scheme	Road Name	Road Type	EF (g/km/veh)
L1	Point 1 at Jiasong North Rd	suburban main road	288 (274–306) a
L2	Point 2 at Jiasong North Rd	suburban main road	277 (251–298)
L3	Point 1 at Beiqing Rd	suburban main road	347 (312–393)
L4	Point 2 at Beiqing Rd	suburban main road	400 (342–539)
L5	Yumai Rd	suburban branch road	451 (392–535)
L6	Point 1 at Zhongshan North Second Rd	urban main road	354 (321–378)
L7	Point 2 at Zhongshan North Second Rd	urban main road	359 (344–399)
L8	Fushun Rd	urban branch road	460 (421–509)
L9	Outer Ring Expressway	Highway	401 (366–449)

^a: Emission factors in the table are presented in the form of “mean (minimum–maximum)”, with a consistent format used for similar data.

lists the CO₂ emission factors measured in this study for different road types in open-road environments in Shanghai. The study showed that the average vehicle carbon emission factor on suburban main roads (328 g/km/veh) was lower than that on urban main roads (344 g/km/veh) (p < 0.01). This was likely due to the higher traffic flow on urban main roads, which caused frequent accelerations, decelerations, and extended idling, increasing carbon emissions. In comparison, suburban main roads, with lower traffic volume, allowed vehicles to maintain a more consistent speed, thus reducing carbon emissions.

The study results showed that vehicle carbon emission factors on urban branch roads (433 g/km/veh) and suburban branch roads (460 g/km/veh) were 30.1% and 37.5% higher, respectively, compared to those on main roads in the same region. This can be attributed to branch roads being located near residential areas, where vehicles operate at slow speeds (below 20 km·h⁻¹), resulting in decreased engine thermal efficiency and an increased proportion of incomplete fuel combustion. Furthermore, roadside parking combined with the coexistence of pedestrians and non-motorized traffic diminishes the effective roadway width, with frequent stop-and-go movements further amplifying carbon emission levels. The CO₂ EF was higher at sampling location 6 than at sampling location 7. The main reason for this was that location 6 is located at a traffic light, where vehicles experience prolonged idling and frequent stops and starts, causing an increase in carbon emissions [45].

In summary, the model effectively captures the impact of different road spatial characteristics on on-road vehicle CO₂ emission factors, providing technical support for refined urban traffic carbon management and region-specific emission reduction strategies.

4.4.2. Comparison of Emission Factors Between Workday and Weekend

From Figure 8, it can be seen that the emission factor of urban roads on weekdays was 13.3%–15.7% higher than on weekends. The primary causation can be attributed to characteristic commuting patterns during workdays. The directional clustering of commuter vehicles towards business districts and office hubs leads to a surge in traffic demand on urban roads. Consequently, traffic flow overload during peak hours triggers systemic road congestion, forcing vehicles into prolonged low-speed cruising (average speed <30 km·h⁻¹) accompanied by frequent start-stop maneuvers. Conversely, during the weekend, traffic flow is lower due to a decrease in commuting demand, leading to higher vehicle speeds and thus a lower emission factor. In contrast, the monitoring results in suburban areas exhibited no significant variations in emission factors between weekdays and weekends. This phenomenon may have been related to the relatively small fluctuations in suburban traffic volume. Therefore, the basic operation mode of the vehicle remained unchanged, ultimately resulting in negligible differences in emission factor amplitudes on different days of the week.

In summary, the model can effectively capture the temporal characteristics of on-road vehicle CO₂ emission factors, providing a scientific basis for formulating time-specific emission reduction strategies.

4.4.3. Specific-Field EFs in Shanghai and Global Comparisons

Table 3. Comparison of CO₂ factor estimations between this study and existing research.

Region	Carbon Emission Factor (g/km/veh)	Experimental Method	Reference
England	101 a	Laboratory test	VCA [10]
China	231	Laboratory test	CATARC [34]
China	GDI:201 PFI:250	Laboratory test	Zhu, R., 2016 [46]
Thailand	Light gasoline vehicle: 171 ± 14.9 Light diesel vehicle: 186 ± 12.9	Laboratory test	Sirithian, D., 2022 [29]
Iran	400–550	PEMS	Ataei, S.M., 2022 [16]
Malaysia	236 ± 15.0	PEMS	Sofwan, N.M., 2021 [47]
China	277–460	On-road measurement	This paper

^a: Based on the 4.4 L/100 km value measured by the VCA [10] under the WLTP protocol, and assuming gasoline contains 85% carbon, which is fully converted to CO₂ upon complete combustion, the CO₂ emission factor is calculated to be 101 g/km/veh.

lists the vehicle emission factors measured by various methods in the literature over the years. The emission factors in this study exceeded those in the studies [10,29,46], mainly because these references used controlled-environment measurements, which are usually carried out under controlled environments and with standardized vehicle operation, which may have contributed to the observed lower emission factors [10,29,46].But in [9], PEMS testing was carried out in a spatially restricted parking garage, where intensive start–stop operations of vehicles increased CO₂ emissions and thus produced a greater emission factor compared to the current work [16]. In addition, on-road measurements were conducted using a PEMS under open-road conditions in Reference [47]. The resulting emission factor was slightly lower than that of the current study, which may have been attributable to differences in vehicle types, traffic flow characteristics, and national emission standards [47]. In this study, the experimentally measured average CO₂ emission factor for vehicles was 368 g/km/veh. According to national standards [34], the maximum gasoline consumption limit for light commercial vehicles is 11.7 L/100 km (roughly 231 g-CO₂/km/vehicle for CO₂ EF). A comparison reveals that the emission factor observed in this study was significantly higher than the standard, highlighting the urgent need to formulate and implement emission reduction strategies to effectively lower on-road vehicle carbon emissions.

In summary, by comparing our findings with multiple published studies, we have demonstrated the model’s practical applicability to open-environment roads. Furthermore, the CO₂ EFs measured in Shanghai significantly exceed the national standard limits. This indicates the need to develop effective strategies to reduce on-road vehicle carbon emissions.

5. Conclusions

The accurate quantification of vehicle carbon emission factors is a key prerequisite for dynamically assessing traffic pollution contributions and optimizing regional emission reduction strategies. This study developed a model for calculating carbon emission factors of on-road vehicles, based on Fick’s second law and the law of conservation of mass, and applied it to three types of road environments: enclosed-environment roads, semi-enclosed-environment roads, and open-environment roads.

During the model-optimization phase, this study analyzed three key variables that significantly influence the model’s application: concentration along the travel direction, horizontal wind speed, and traffic volume. The results indicate that concentration gradients along the direction of travel are negligible in open and semi-enclosed roads, and that the model produces more reliable estimates under conditions of horizontal wind speed below 3.92 m/s and traffic volume above 120 vehicles/hour. This applicability range effectively covers most urban road scenarios, making the model highly suitable for estimating on-road vehicle CO₂ emission factors. During the model-validation phase, field measurements conducted in a tunnel and on open roads yielded empirical vehicle CO₂ emission factors. Field measurements demonstrated that the carbon emission factors for urban main roads and suburban main roads were 344 g/km/veh and 328 g/km/veh, respectively, which were consistent with the ranges documented in prior studies. Spatiotemporal heterogeneity analysis indicated that, in the spatial dimension, the mean carbon emission factor of urban arterial roads was significantly approximately 4.91% higher than that of suburban arterial roads. Furthermore, statistically significant increases of 30.1% and 37.5% were observed in the emission factors of urban and suburban branch roads, respectively, compared to regional main roads. In the temporal analysis, urban road emission factors, covering both main and branch roads, exhibited a significant 6.58 ± 1.17% increase on weekdays relative to weekends. This indicates that the method can effectively differentiate emission factors across varying road types and temporal conditions. The model proposed in this study provides an effective solution for the real-time monitoring of large-scale road vehicle carbon emissions. It has the advantages of not interfering with normal vehicle operations and being applicable to various road environments. Overall, this study provided a robust model for quantifying transportation-related carbon emissions that is capable of resolving the temporal and spatial heterogeneity of CO₂ emission factors. This work might provide critical data support for low-carbon urban transport planning (SDG 11: Sustainable Cities and Communities) [7] and assist in the formulation of refined emission-reduction strategies. Meanwhile, it establishes a solid foundation for scientifically evaluating the effectiveness of climate actions in the transport sector, providing a strong support for advancing and achieving carbon neutrality goals (SDG 13: Climate Action) [8].

In future research, it is necessary to reduce biases arising from simplifying assumptions through methods such as adding lateral monitoring points to verify spatial representativeness and characterizing airflow dispersion to optimize sensor-height design. At the same time, there is an urgent need to develop intelligent methods for extracting multiple vehicle parameters from roadside surveillance videos (e.g., vehicle class, age, and fuel type) to enable refined, vehicle-specific emission-factor analysis. Furthermore, the approach can be extended to other pollutants such as NO_X and PM_2.5 to construct multi-pollutant emission inventories for real road networks, thereby providing a scientific basis for targeted traffic-pollution control.