Apportionment of Vehicle Fleet Emissions by Linear Regression, Positive Matrix Factorization, and Emission Modeling

: Real-world emission factors for different vehicle types and their contributions to roadside air pollution are needed for air-quality management. Tunnel measurements have been used to estimate emission factors for several vehicle types using linear regression or receptor-based source apportionment. However, the accuracy and uncertainties of these methods have not been sufﬁciently discussed. This study applies four methods to derive emission factors for different vehicle types from tunnel measurements in Hong Kong, China: (1) simple linear regressions (SLR); (2) multiple linear regressions (MLR); (3) positive matrix factorization (PMF); and (4) EMission FACtors for Hong Kong (EMFAC-HK). Separable vehicle types include those fueled by liqueﬁed petroleum gas (LPG), gasoline, and diesel. PMF was the most useful, as it simultaneously seeks source proﬁles and source contributions. Diesel-, gasoline-, and LPG-fueled vehicle emissions accounted for 52%, 10%, and 5% of PM 2.5 mass, respectively, while ammonium sulfate (~20%), ammonium nitrate (6%), and road dust (7%) were also large contributors. MLR exhibited the highest relative uncertainties, typically over twice those determined by SLR. EMFAC-HK has the lowest relative uncertainties due to its assumption of a single average emission factor for each pollutant and each vehicle category under speciﬁc conditions. The relative uncertainties of SLR and PMF are comparable.


Introduction
On-road vehicle emissions are targeted for reductions due to their large contributions to greenhouse gases and air pollutants, including carbon dioxide (CO 2 ), carbon monoxide (CO), volatile organic compounds (VOC), nitrogen oxides (NO x ), particulate matter (PM), and other air toxics. Accurate emission factors (EFs), which describe the emitted pollutant mass (g) per distance driven (km) or amount of fuel consumed (kg) for different vehicle categories are needed for emission inventories, emission standards enforcement, and assessments of air quality and health effects.
EFs can be obtained from laboratory dynamometer testing, on-road or roadside plume identification, onboard measurements, remote sensing, and tunnel studies [1][2][3]. Among these methods, tunnel studies have the advantage of being able to sample many vehicles representative of local real-world fuel and fleet compositions under in-use conditions [4,5].
In-tunnel concentrations are dominated by traffic emissions, and the influence of background and other pollution sources can be determined by measurements at tunnel inlet and outlet locations.
Linear regression methods, as first introduced by Pierson et al. [6], have been used to apportion the measured fleet-average EFs to different vehicle fleets, typically gasoline and diesel vehicles (GV and DV, respectively) or light and heavy-duty vehicles (LD and HD, respectively). For example, when the measured EF is regressed against the DV fraction (f DV ), the intercept of the regression line with the vertical axis at f DV = 0 is the EF for GV, while the intercept at f DV = 100% is the EF for DV. Pierson et al. (1996) cautioned that single values of EFs for the two regressed vehicle categories are not exact, due to large vehicle-tovehicle emission variabilities within the same category. The linear regression method can be extended to include other factors affecting EFs. Colberg et al. [7] studied the effects of weekday and weekend differences as well as vehicle speed. The main challenge for tunnel data analysis with linear regression is that many tunnels have a limited range of DV or HD fractions (typically < 50%), which results in large uncertainties when extrapolating EFs from the narrow range of measured f HD fractions to the f HD of 0% and 100% end points [8]. For example, Song et al. [9] derived heavy-duty diesel vehicle (HDDV) EFs by extrapolating from measured data with f HDDV < 10% to EFs at f HDDV = 100%. To reduce these uncertainties, several studies used tunnels where LD and HD vehicles were separated into different bores. The Fort McHenry tunnel studied by Pierson et al. [6] had f HD of 0.2-4.0% in one bore and 4.4-72.5% in the other bore. For tunnels without vehicle separations, studies have sampled during different hours of the day to obtain larger f HD or f DV ranges. Decreasing sample durations (e.g., 1-h instead of 24-h averages) can also increase the fleet composition variability [8,9]. The large vehicle-to-vehicle emission variability and limited f HD or f DV ranges in tunnels are the main sources of uncertainty in emissions apportionment performed using the linear regression method.
More advanced receptor-based source apportionment methods seek solutions to the chemical-mass balance equations (CMB) [10]. Commonly used approaches include the effective variance solution (EV-CMB) [11] and multivariate factor analysis solutions, such as principal component analysis (PCA) [12] and positive matrix factorization (PMF) [13]. These solutions use the entire pattern of source and receptor measurements to obtain more source specificity and reduce uncertainty. As long as the number of source types is less than or equal to the number of measured properties, the EV-CMB can be solved for individual samples. However, the solution depends on measured source profiles that represent emissions from the different vehicle types [14,15]. One of the challenges for EV-CMB is that existing source profiles are often dated and do not contain modern markers or represent the specific sources in the study area. This is also true for vehicle emission profiles as advances in fuels, engine designs, and emission control technologies have caused continuous changes in source profiles [16]. Therefore, only a few studies applied EV-CMB to identify and quantify traffic-generated source contributions [17][18][19]. Other studies used factor analysis [20,21], such as the PCA or PMF solutions. The factor solutions also require measured source profiles to associate the factor with a source type, although the derived ratios among the marker species may differ. It is often the case, however, that the derived factors exhibit mixed profiles, as the different species concentrations tend to be highly correlated, thereby resulting in uncertainties associated with factor identification. The factor models are most accurate when datasets are large, exhibit large ranges of variability among the measured components, and have low correlations among the markers for different source types. PCA coupled with multiple linear regression analysis (MLRA) was applied in several studies to apportion traffic emissions [22,23]. PCA may lead to less adequate factor resolution and less plausible results than PMF [21,22]. Due to the uncertainties in source apportionment approaches, a "weight of evidence" approach is recommended to use additional available information (e.g., local emission inventories, source profiles, and modeling performance measures), apply several receptor-modeling techniques, and reconcile receptor-oriented and source-oriented models to evaluate the uncertainties and increase the degree of confidence [10,14,24].
Vehicle emission models are used to assess mobile source emissions and compile emission inventories [25]. These models typically use baseline EFs with several adjustment factors such as vehicle age, speed, and ambient temperature, which are typically derived from emission standards, laboratory testing, and real-world measurement. Comparing emission models with tunnel measurements enables the assessment of model performance by reconciling the differences between the source and receptor sides [1,26]. The detailed estimates of emissions by vehicle classes and fuels in emission models also offer guidance on emission control priorities [27].
While many tunnel studies attempt to apportion the measured fleet EFs to different vehicle types, few studies have compared the results from the apportionment methods. The main objectives of this study are to: (1) compare fuel-specific fleet EFs estimated by linear regressions, PMF, and emission modeling; (2) quantify emission contributions from different fleet components; and (3) evaluate PMF source profiles. Data from the Shing Mun Tunnel (SMT) in Hong Kong is used as a case study [28,29].

Vehicle Emission Measurements in the Shing Mun Tunnel
The SMT is a two-bore highway tunnel on the Hong Kong Route 9 expressway. Each bore has a cross-sectional area of 70 m 2 with two traffic lanes traveling in the same direction. Vehicle emissions were measured in the east section of the south bore, which has a total length of 1.6 km with an uphill grade of 1.054% from the entrance to the exit. The tunnel has a daily vehicle flow of~53,000 in both directions, with an average liquefied petroleum gas (LPG), gasoline, and diesel fleet mix of 13%, 45%, and 42% [28]. As the closest highway ramp is~2.5 km from the tunnel entrance, most vehicles are likely in hot-stabilized operating conditions, driving near the posted speed limit of 80 km h −1 .
Vehicle emission measurements were conducted in the SMT from January to March 2015, with experimental details described in previous publications [28][29][30]. The sampling configuration is illustrated in Figure S1 [28]. Briefly, measurements were carried out simultaneously at inlet and outlet sites separated by 600 m. Due to access and power constraints, the inlet sampling site was 686 m from the tunnel entrance, while the outlet sampling site was 350 m before the tunnel exit. Concentrations of CO, CO 2 , nitric oxide (NO), nitrogen dioxide (NO 2 ), and PM 2 . 5 (by light scattering) were measured with near real-time instruments at time resolutions of 1 s to 1 min. Wind speed, wind direction, barometric pressure (P), temperature (T), and relative humidity (RH) were monitored by weather stations every five minutes. Traffic flow was recorded by two video cameras. Non-methane hydrocarbons (NMHC) were collected in pre-cleaned and pre-evacuated 2 L stainless-steel canisters with a flow rate of 27.3 mL min −1 using a multi-port canister sampler. PM 2.5 samples were simultaneously collected on one Teflon-membrane filter and two quartz-fiber filters at a flowrate of 37.7 L min −1 each. While real-time gas and PM monitors, weather stations, and video cameras were operated continuously, integrated samples were collected over 2 h sampling periods, which covered morning and evening rush hours (i.e., 0800-1000 and 1700-1900 local standard time [LST]) as well as midday hours (i.e., 1100-1300 and 1400-1600 LST).
The distance-based emission factor (EF D ; in g veh −1 km −1 ) calculation uses the mass balance principle, i.e., the mass of pollutant i produced by vehicles in the tunnel section bounded by the inlet and outlet sites during a sampling period ∆t is the difference between the mass leaving the outlet site and that entering the inlet site [6]: where C i (g m −3 ) is the average concentration of the pollutant i, U (m s −1 ) is the wind speed, the subscripts in and out denote the values measured at the inlet and outlet sampling sites, respectively, A (m 2 ) is the tunnel cross-sectional area (70 m 2 for SMT); ∆t (s) is the sampling period, N is the number of vehicles passing through the tunnel section during ∆t, and L (m) is the length of the tunnel section between the inlet and outlet sampling sites (0.6 km in this study). The traffic videos taken from the tunnel entrance were used to manually classify the fleet into nine categories (i.e., motorcycle, private car, taxi, light goods vehicle, medium goods vehicle, heavy goods vehicle, light bus, single deck bus, and double-decker bus) with a time resolution of 15 min for each of the 2 h sampling period. The total vehicle numbers from manual counting differed by <4% from those recorded hourly by the SMT toll booths. The allocation of the fleet to LPG, GV, and DV was based on vehicle kilometers traveled (VKT) by different vehicle classes classified by Emission FACtors for Hong Kong (EMFAC-HK) [27].

Emission Apportionment by Linear Regressions
Linear regressions have been used in tunnel studies to apportion emissions to different fleet components using the following equation [6,40]: where EF i,m is the EF of pollutant i by the m th fleet component, f m is the percentage of the m th vehicle fleet component, and ε i is the error term. Most previous tunnel studies used simple linear regressions (SLR) to separate the fleet into two components (i.e., m = 2): LD and HD or non-diesel vehicles (NDV) and DV. An example of SLR is shown in Figure 1.
The fleet-average EF of NO x is plotted against the percentage of DV (f DV ). The intercepts of the regression line at 0% and 100% DV are the EFs for NDV and DV, respectively. Due to the fact that the fleet in the SMT consists of LPG, GV, and DV, multiple linear regressions (MLR) with m = 3 were also conducted to apportion EFs to these three fleet components.
Th predicted values are reported using 95% confidence intervals to represent uncertainties. The estimates are statistically different from zero if the corresponding confidence intervals do not cover zero. Outliers can distort the representativeness of regression analysis results [8,22]. The median absolute deviation (MAD) method is applied to remove outliers [41]. Specifically, the absolute value of the difference between each observed value and the median of the data is calculated to generate a new median of the differences, which is multiplied by an empirical constant to yield the MAD. An observed value is classified as an outlier if it exceeds three times the MAD value. ries are linearly dependent on the vehicle number fraction for each category. Since vehicles under the same category may have different EFs (e.g., gasoline-fueled motorcycles and passenger cars), the vehicle number fraction may not be an accurate indicator for emissions. Furthermore, other emission sources, such as non-tailpipe emissions, will also affect measured pollutant concentrations. A more appropriate method to apportion emissions to different fleet components could be receptor-based source apportionment.

Vehicle Source Apportionment by PMF
The CMB equations link source profiles and source contributions to ambient chemical concentrations: where Ci,t is the measured concentration of species i at time t, Fi,j is the fraction of species i in source profile j, and Sj,t is the source contribution estimate (SCE) of source j at time t. εi,t is the deviation between the modeled and measured concentrations due to random variability, which is the term that is minimized in the PMF calculation. PMF solves Fi,j and Sj,t simultaneously by minimizing the Q value as below: where ΔCi,t is the weighting factor for Ci,t, which mainly corresponds to the random and/or systematic measurement uncertainties. The number of source factors in the model is pre-specified, usually based on a sensitivity test [42]. The tunnel study acquired 132 ambient PM2.5 samples (from both inlet and outlet sites) characterized for over 200 inorganic and organic species. Among these, 61 samples also had concurrent NMHC measurements. To ensure that all measured species are used in the model while the missing values are heavily down-weighted in the fitting process, all missing data were replaced with the average concentrations throughout the study period, with uncertainties of 100 times the respective concentrations [43]. Sensitivity tests showed that varying the uncertainties from 10 to 100 times the average values did not The linear regression method assumes that emissions from different vehicle categories are linearly dependent on the vehicle number fraction for each category. Since vehicles under the same category may have different EFs (e.g., gasoline-fueled motorcycles and passenger cars), the vehicle number fraction may not be an accurate indicator for emissions. Furthermore, other emission sources, such as non-tailpipe emissions, will also affect measured pollutant concentrations. A more appropriate method to apportion emissions to different fleet components could be receptor-based source apportionment.

Vehicle Source Apportionment by PMF
The CMB equations link source profiles and source contributions to ambient chemical concentrations: where C i,t is the measured concentration of species i at time t, F i,j is the fraction of species i in source profile j, and S j,t is the source contribution estimate (SCE) of source j at time t. ε i,t is the deviation between the modeled and measured concentrations due to random variability, which is the term that is minimized in the PMF calculation. PMF solves F i,j and S j,t simultaneously by minimizing the Q value as below: where ∆C i,t is the weighting factor for C i,t , which mainly corresponds to the random and/or systematic measurement uncertainties. The number of source factors in the model is pre-specified, usually based on a sensitivity test [42]. The tunnel study acquired 132 ambient PM 2.5 samples (from both inlet and outlet sites) characterized for over 200 inorganic and organic species. Among these, 61 samples also had concurrent NMHC measurements. To ensure that all measured species are used in the model while the missing values are heavily down-weighted in the fitting process, all missing data were replaced with the average concentrations throughout the study period, with uncertainties of 100 times the respective concentrations [43]. Sensitivity tests showed that varying the uncertainties from 10 to 100 times the average values did not change the SCEs and profiles appreciably. Additionally, PM 2 . 5 and NMHC species, CO 2 , CO, NO,  NO 2 , NO x , and SO 2 were averaged into two-hour intervals and included in the receptor model.
Major sources contributing to SMT samples include: (1) vehicle (LPG, GV, and DV) exhaust, (2) resuspended road dust and non-tailpipe emissions, and (3) background air. The background air in Hong Kong, especially around the SMT, was dominated by motor vehicle exhausts and secondary sulfate and/or nitrate [44]. Conceptually, at least six sources of PM 2.5 and NMHC are required for the SMT source apportionment, namely diesel (exhaust), gasoline (exhaust), LPG (exhaust), (road) dust, secondary ammonium sulfate ((NH 4 ) 2 SO 4 ), and secondary ammonium nitrate (NH 4 NO 3 ). Profiles for secondary (NH 4 ) 2 SO 4 and NH 4 NO 3 should only contain secondary species, as the primary species should be incorporated into primary source profiles [45,46]. Road dust samples in the tunnel were collected and analyzed for the same species as the ambient PM 2.5 samples to construct a "dust" source profile, which further constrained the PM factors. Source profiles for LPG, GV, and DV exhaust specific to Hong Kong with all the markers acquired in this study were not available, though previous studies have identified important marker compounds in these emissions.
The PMF calculation was carried out using the Hybrid Environmental Receptor Model (HERM), which allows specifying known source profiles as constraints on the PMF solutions [47][48][49]. In the HERM formulation, the weighting factor ∆C i,t 2 is replaced with EV i,t that takes into account uncertainties of both measured pollutant concentrations (∆C i,t ) and profile abundances (∆F i,j ): where δ i,j = 0 if the source profile element F i,j is specified, and δ i,j = 1 when F i,j is to be solved. Three-to nine-factor solutions were explored, with the first three factors constrained by the secondary (NH 4 ) 2 SO 4 , secondary NH 4 NO 3 , and dust source profiles. The fractional change of Q value (∆Q m ) from the m to m + 1 factor solutions was calculated, and this showed little change after m = 6 ( Figure S2). This is consistent with a six-factor solution being appropriate for the dataset; any additional source types would be minor contributors.
The HERM-PMF results can be evaluated through performance measures, particularly the correlation between the measured and calculated concentrations (r i 2 ) and the scaled residuals (χ i 2 ). HERM calculates r i 2 and χ i 2 by the following equations: where I, J, and K are the total number of species, factors, and samples, respectively [47]. High correlation coefficients and/or low residuals indicate a good fit. As shown in Figure  S3, the six-factor solution explained the majority of PM 2.5 inorganic components with r i 2 > 0.9, including OC, EC, S, NO 3 − , NH 4 + , and key mineral elements (e.g., Si, Fe, and K). Some of these species showed χ i 2 values greater than 1, and thus dominated the Q value (and PMF solution) due to higher measurement precisions. Organic markers did not fit well with r i 2 < 0.9, though their χ i 2 values were generally low (<1). This is consistent with a lower signal-to-noise ratio for these organic markers. Species such as vanadium (V), nickel (Ni), chloride (Cl − ), and acenaphthylene (ACNAPY) showed poor fits (low correlations and larger scaled residuals) implying potential impacts from additional sources (e.g., crude oil/coal combustion and sea salt) [50]. As noted, contributions from these sources to tunnel PM 2.5 were too small to be quantified by PMF even if the number of factors was increased to Atmosphere 2022, 13, 1066 7 of 19 7 or 8 and/or after factor rotations. They are not expected to bias the SCEs for major sources (i.e., mobile exhausts and road dust) as they are minor components in these emissions.
The PMF performance for NMHCs and gases is shown in Figure S4. Most species showed χ i 2 values between 0.1 and 10, indicating that the Q values were more evenly distributed among all species, possibly due to a more uniform estimate of measurement uncertainty. Species that were reproduced well by the HERM-PMF solution include markers for LPG exhaust: isobutane, propane, and n-butane (r i 2 > 0.95), as well as propene (r i 2 = 0.98), a marker for diesel exhaust [51]. The model also fitted NO, NO 2 , and NO x (r i 2 = 0.93-0.95) better than CO (r i 2 = 0.79). Isoprene and α-pinene, markers for biogenic emissions, were not well-explained by the PMF solution; they were small portions of the total NMHCs in the tunnel. Ethylbenzene, mp-xylene, and o-xylene had high scaled residuals, mainly because a few outliers were found at the outlet sampling site on two sampled days. The extreme concentrations (>10 times the average) of these outliers may result from unknown contamination, as they only appeared at the outlet sampling site. These outliers were weighted much less in the PMF due to the robust fitting algorithm [52].
The differences between outlet and inlet concentrations for each pollutant were used to calculate the fleet-average EF Fleet using Equation (1). Due to the fact that the chemical speciation of PM 2.5 and NMHCs were conducted for 2 h integrated samples, EF Fleet were calculated for each of the valid 2 h integrated samples. Diesel-vehicle specific EFs were then calculated using the equation below: where FSC DV is the fractional DV contribution to the pollutant (e.g., PM 2.5 ), determined from the PMF source apportionment, and f DV is the fraction of DV in the fleet. Secondary (NH 4 ) 2 SO 4 , secondary NH 4 NO 3 , and road dust did not contribute to EFs appreciably, as evidenced by similar concentrations between the outlet and inlet measurements [28]. Therefore, FSC DV is defined as: Equations (8) and (9) were also applied to LPG and GV as well as NDV (sum of LPG and GV) to determine EF LPG , EF GV , and EF NDV . Since the EFs were determined for each 2 h sample, the average EFs and 95% confidence intervals of the means are reported as the final EFs and uncertainties for the LPG, GV, and DV.

Vehicle Emission Estimates by EMFAC-HK
EMFAC-HK is the vehicle emission model used to develop the official Hong Kongwide vehicle emission inventories, and the "Emfac" mode of the EMFAC-HK V4.2 was used to model tunnel vehicle emissions in this study [27]. The model generates a matrix of EFs at a range of temperatures (0-40 • C), RH (0-100%), and vehicle speeds (0-130 km h −1 ) for each vehicle class-fuel combination. Running exhaust EFs (in g veh −1 km −1 ), i.e., emissions from the vehicle tailpipe while it is traveling on the road, were calculated for methane (CH 4 ), total hydrocarbon (THC), CO, CO 2 , NO 2 , NO x , PM 2.5 , and PM 10 . The EF for NO (as NO 2 ) was calculated by subtracting NO 2 EF from that of NO x (as NO 2 ). Additionally, evaporative running-loss EFs during vehicle operation (in g veh −1 min −1 ) were calculated for CH 4 and THC. Since the EMFAC-HK does not directly output NMHC emissions, running exhaust emissions of NMHC were calculated by subtracting CH 4 from THC emissions. These EFs were organized as lookup tables associated with the combinations of T, RH, and vehicle speed values.
Vehicle emissions between the SMT outlet and inlet for each 15 min vehicle counting period were calculated as follows: EFs were determined from the lookup table assuming a constant vehicle speed of 80 km h −1 (speed limit) and average ambient T and RH over each period. For running exhaust emissions, the source activity is the VKT (i.e., the number of vehicles in each class multiplied by the 0.6 km distance between the inlet and outlet sites). For CH 4 and THC evaporative running losses, the source activity is the average transit time (0.45 min) through the tunnel section times the number of vehicles in each class. LPG, GV, and DV emissions were calculated by summing emissions from all vehicles powered by the respective fuels; and the EFs for the entire fleet, as well as for each fuel, were calculated by dividing the total emissions by tunnel VKT of the fleet or vehicles with each fuel, either for every 15 min vehicle counting period or every 2 h integrated sample collection period.

Pollutant Apportionment by Linear Regression
Linear regressions were first conducted with continuous measurement data averaged to a 2 h time resolution to match the collection periods of the integrated samples. A plot of NO x EF vs. f DV is shown in Figure 1a as an example. The data has only a moderate linear trend, with a correlation coefficient (r) of 0.50. A simple linear regression using Equation (2) results in NO x EFs average ± expanded uncertainty at 95% confidence intervals values of 0.66 ± 0.52 g veh −1 km −1 for NDV and 2.68 ± 0.87 g veh −1 km −1 for DV obtained at f DV = 0 and 100%, respectively. The relative uncertainties (expanded uncertainty divided by average) are 79% and 32% for NDV and DV, respectively. These uncertainties were significantly reduced to 33% and 14% when the concentrations were averaged over the 15 min traffic counting periods. As shown in Figure 1b, the ranges of NO x EFs improved to 0.74 ± 0.24 g veh −1 km −1 and 2.51 ± 0.34 g veh −1 km −1 for NDV and DV, respectively. Regression analyses for all measured pollutants are presented in Figure S5. Two factors contributed to this uncertainty reduction: first, as the number of data points increased eight times, the standard errors of the estimators decreased; second, the shorter averaging time increased the differentiation of emissions among different vehicle types, causing less overlap of contributions from different vehicle types to each data point [21]. Therefore, all linear regressions used 15 min average data except NMHC, for which only 2 h integrated data were available. Figure 1 also shows the effects of including or excluding outliers for the SLR solution. Based on the outlier criterion of 3 times the value of MAD away from the median of the data, four outliers were identified in Figure 1a. Including the outliers resulted in NO x EFs of 0.79 ± 0.77 g veh −1 km −1 for NDV and 2.63 ± 1.17 g veh −1 km −1 for DV, 20% higher and 2% lower than EFs without including the outliers, respectively. Similarly, seven outliers were identified in Figure 1b. Including outliers resulted in NO x EFs of 0.75 ± 0.27 g veh −1 km −1 for NDV and 2.60 ± 0.38 g veh −1 km −1 for DV, which are, respectively, 1% and 3.5% higher than the EFs without including the outliers. The differences in mean EFs by including or excluding the outliers were < ±20% for most species.
EFs by SLR and MLR are compared in Table 1 and Table S1. For average DV EFs, the estimates using both methods agreed within 3% for NO, NO x , and SO 2 . The mean EFs for PM 2.5 and NO 2 were statistically similar, although PM 2.5 was 11% lower (p = 0.61) while NO 2 was 23% higher (p = 0.16) by MLR. The EF for CO 2 was 24% lower by MLR than that by SLR, and the difference was statistically significant (p < 0.05). The largest difference was found for CO, with SLR and MLR giving 1.83 ± 0.23 and 0.20 ± 0.43 g veh −1 km −1 , respectively. As shown in Figure S5b, the CO linear regression line has a shallow slope, resulting in a poor separation of NDV from DV contributions. Due to the additional separation of the NDV emissions to LPG and GV in MLR, the EF uncertainties by MLR are approximately twice those from SLR, causing LPG and NDV EFs for all pollutants except CO 2 and CO to not be statistically different from zero. Further, the differences between SLR and MLR can be partially explained by how the apportionment was obtained: MLR is based on multiple linear regression, while the results of SLR are predicted values at 0% and 100% based on simple linear regression.

Comparison of Emission Factors Using Linear Regression, PMF, and EMFAC-HK
The EFs obtained from SLR, MLR, PMF, and EMFAC for LPG, GV, NDV, and DV are summarized in Table 1 and compared in Figure S6. The relative uncertainties are listed in Table S2, and the Student's t-test p-values for paired comparison are listed in Table S3, with p < 0.05 indicating EFs being statistically different.
Among the different apportionment methods, EMFAC-HK has the lowest (<2%) relative uncertainties (Table S2). This low variation is because EMFAC-HK aggregates the vehicle fleet into 16 categories and assigns a single average EF value to each category under specific environmental and operating conditions. This process artificially reduces the EF variabilities among vehicles, e.g., between low and high emitters [27]. On the other hand, MLR has the highest relative uncertainties, with many values exceeding ±100%, causing LPG and NDV EFs for many pollutants to not be statistically different from zero (Table S1). The relative uncertainties of SLR and PMF are comparable for many EFs by DV and NDV.
The main challenge in the evaluation of different apportionment methods is that the true EFs are unknown; therefore, the accuracy of each method cannot be assessed. For CO 2 , the fleet EF from tunnel measurement and EMFAC-HK estimate agreed within 3% [27]. The CO 2 EFs, by most apportionment methods and EMFAC-HK, were statistically similar. The exception was for DV; the CO 2 EFs by SLR and MLR were significantly lower than those by PMF and EMFAC-HK. In principle, EMFAC-HK estimates CO 2 EFs most accurately among all pollutants, as fuel efficiency is the only factor to be modeled. The agreement of EMFAC-HK and PMF CO 2 EFs adds credibility to the PMF apportionment, especially considering that the PMF method does not explicitly use vehicle fraction information. MLR reported lower CO 2 EFs than SLR for both DV and NDV, implying that biases caused by assuming the same EFs for GV and LPG in SLR could not be ignored.
For CO, MLR and PMF were statistically similar for all vehicle categories, while most other methods were different. SLR showed the highest EFs for DV and NDV, likely because of the shallow slope in the regression causing inaccurate apportionment to NDV and DV ( Figure S5b). EMFAC-HK may not estimate CO emissions accurately as it reported a fleetaverage EF for CO that is lower than the value measured in the tunnel by~30% [27]. For NMHC, the fleet EF estimated by EMFAC-HK was~50% higher than the measured value. Correspondingly, the EFs by EMFAC-HK were higher than those by PMF for all vehicle categories except LPG, for which they were comparable. SLR was applied to 2 h average data, resulting in larger uncertainties. For NO, NO 2 , and NO x , the EFs calculated by most methods were statistically similar for NDV and DV, likely due to their larger EF differences, as reflected by the higher slopes in Figure S5d-f. More variabilities are observed in the EFs for LPG and GV due to their lower EF values and higher uncertainties. For SO 2 , PMF and MLR had an excellent agreement for LPG, GV, and NDV; similarly, SLR and MLR agree on NDV and DV. The only exception is that the SO 2 EF by PMF was about half of that by SLR and MLR for DV. For PM 2.5 , emissions are dominated by DV, and the EFs for DV by different methods agree reasonably well (0.043-0.057 g veh −1 km −1 ). For LPG, GV, and NDV, due to their lower emissions, the PM 2.5 EFs by SLR and MLR were not statistically different from zero; similarly, the EFs by EMFAC-HK were also low, because it assumes no PM emission from LPG vehicles. On the other hand, PMF reported PM 2 . 5 EF values of 0.011 ± 0.003, 0.007 ± 0.002, and 0.008 ± 0.002 g veh −1 km −1 for LPG, GV, and NDV, respectively, that differed significantly from zero.
Atmosphere 2022, 13, x FOR PEER REVIEW 11 of 18 its use as a gasoline additive to increase the octane index in Hong Kong [53]. High abundances of aromatic species were also found in gasoline vehicle exhaust in several previous studies [54,58]. The diesel profile shows more abundant ethene (14.4 wt%), ethyne (6.6 wt%), and ethane (7.1 wt%). Similar to the profile derived by Ling and Guo [59], the diesel profile also has high abundances of propane, isobutane, and n-butane, overlapping with the LPG profile. In addition, the diesel profile has the highest CO2 and NOx abundances among the three fuels.   For the PM 2.5 samples, EC (33.8 ± 8.6%) and organic matter (OM; 27.5 ± 7.9%) are the most abundant constituents, followed by SO 4 2− (16.9 ± 5.4%), NH 4 + (6.9 ± 2.3%), and geological materials (5.1 ± 3.3%). Figure 2b shows the PM 2.5 profile for ions, carbon, and elements. Additionally, the high abundances of total carbon (TC; sum of OC and EC), EC, OC, SO 4 2− , NH 4 + , NO 3 − , and some trace elements indicative of lubrication oil additives (e.g., Mg, S, Ca, and Zn) and wear of vehicle, brake, or road surface (e.g., Al, Fe, and Cu) [55] were present at higher than 0.05% of PM 2.5 abundance. The PM 2.5 source profile for road dust is plotted in Figure 2c. The dust particles were enriched with OC, EC, and geological elements (e.g., Si, Ca, Fe, and Al). Some abundant elements could also originate from tire wear (e.g., Zn) and brake wear (e.g., Cu, Zn, Zr, Mo, and Sn) [20,56,57]. Figure 3 shows LPG, GV, and DV emission profiles resolved by PMF for CO 2 , CO, NO x , SO 2 , and NMHC (normalized to the total measured NMHC mass concentrations). The most abundant NMHC species in the LPG profile were isobutane (23.2%), n-butane (23.0%), and propane (12.0%), indicating unburned LPG fuel. Guo et al. [54] found that these three species were the most abundant NMHCs from chassis dynamometer testing of LPG-fueled taxis at 70 km/h, with mass percentages of 16.0%, 19.4%, and 37.2% for isobutane, n-butane, and propane, respectively. The characteristic molar ratio of propane/(n-butane + isobutane) of LPG fuel vapor is 0.38 [53], while the measured propane/(n-butane + isobutane) ratio was 0.36 ± 0.07 in this tunnel study. The similar ratios between the LPG vapor and the tunnel samples indicate the contributions of evaporative losses from LPG vehicles to tunnel NMHCs. This observation contradicts the assumption that LPG vehicles do not have evaporative emissions in EMFAC-HK [27]. The gasoline profile contained the highest levels of aromatics, including toluene (22.8 wt%), m/p-xylene (6.6 wt%), and ethylbenzene (4.7 wt%). The high toluene level is likely related to its use as a gasoline additive to increase the octane index in Hong Kong [53]. High abundances of aromatic species were also found in gasoline vehicle exhaust in several previous studies [54,58]. The diesel profile shows more abundant ethene (14.4 wt%), ethyne (6.6 wt%), and ethane (7.1 wt%). Similar to the profile derived by Ling and Guo [59], the diesel profile also has high abundances of propane, isobutane, and n-butane, overlapping with the LPG profile. In addition, the diesel profile has the highest CO 2 and NO x abundances among the three fuels.  Only species with abundances >1% of total measured NMHC mass are shown for clarity. Error bars indicate the standard deviation from 10 replicate model runs.
The PMF-derived PM2.5 source profiles for gasoline, LPG, and diesel emission are compared in Figure S7. The LPG profile has an EC/OC ratio of zero, in comparison with 0.36 and 2.9 for the gasoline and diesel profiles. The LPG profile has overall higher abundances of particulate n-alkane/alkene, PAHs, hopane, and sterane. Due to the fact that LPG is a relatively simple mixture of hydrocarbon components with superior vaporizing characteristics, less PM is emitted from the fuel combustion process as compared to DV and GV [60]. Therefore, a larger fraction of LPG PM originates from lubrication oil,  Only species with abundances >1% of total measured NMHC mass are shown for clarity. Error bars indicate the standard deviation from 10 replicate model runs.
The PMF-derived PM 2.5 source profiles for gasoline, LPG, and diesel emission are compared in Figure S7. The LPG profile has an EC/OC ratio of zero, in comparison with 0.36 and 2.9 for the gasoline and diesel profiles. The LPG profile has overall higher abundances of particulate n-alkane/alkene, PAHs, hopane, and sterane. Due to the fact that LPG is a relatively simple mixture of hydrocarbon components with superior vaporizing characteristics, less PM is emitted from the fuel combustion process as compared to DV and GV [60]. Therefore, a larger fraction of LPG PM originates from lubrication oil, which is known to produce hopanes, steranes, and high-molecular-weight organics [61]. However, these differences could also be caused by uncertainties in the PMF apportionment. To our knowledge, no studies have reported detailed chemical compositions of PM 2.5 from directly measured LPG vehicle tailpipe emissions; such studies are warranted in the future to validate the PM 2.5 source profile for LPG vehicle emissions. Indeno[1,2,3-cd]pyrene and benzo[ghi]perylene were identified as markers for gasoline exhausts by Chow et al. [62]. However, they have relatively higher abundances in the LPG profile, indicating that these species may not be as useful gasoline markers when the traffic has a substantial LPG vehicle fraction. On the other hand, some heavier PAHs such as retene, benzo(ghi)fluoranthene, and methylfluoranthene were found to be most enriched in the gasoline profile. The diesel profile features much higher EC abundances (64%) compared to gasoline (21%) and LPG (0%). Figure 4 compares the relative contributions of LPG, gasoline, and diesel vehicles to gaseous and PM 2.5 emissions from the vehicle fleet as estimated by PMF and EMFAC-HK, showing reasonable agreement. DV has the largest contribution to CO 2 (~65%), NO (77-80%), NO 2 (83-98%), NO x (78-83%), SO 2 (66%; only available from PMF), and PM 2.5 (78-96%). It is expected that conventional DV has higher NO x and PM 2.5 emissions than LPG and GV, and technological breakthroughs are needed to reduce NO x and PM at the same time [63]. The higher CO 2 and SO 2 contributions are related to the higher EFs and lower fuel economy of DV [27]. DV contributions via PMF and EMFAC-HK estimates agree within 15% for most pollutants, with CO 2 , NMHC, NO, and NO x differing less than 3%. EMFAC-HK showed 18% higher DV contribution to PM 2.5 , partially because EMFAC-HK assumes that LPG does not emit PM 2 . 5   Both GV and LPG have high contributions to CO and source attributions by PMF and EMFAC-HK differed less than 15%. These two methods also apportion similar CO2 contributions by GV and LPG. However, larger differences are found for other pollutants. Most of these species have the largest contributions from DV and the differences in DV contributions by PMF and EMFAC-HK led to discrepancies in LPG and GV apportionments. The EMFAC-HK attributed a much larger contribution of NMHCs by GV (56%) than LPG (18%), which is likely due to its unrealistic assumption that LPG and DV Both GV and LPG have high contributions to CO and source attributions by PMF and EMFAC-HK differed less than 15%. These two methods also apportion similar CO 2 contributions by GV and LPG. However, larger differences are found for other pollutants.
Most of these species have the largest contributions from DV and the differences in DV contributions by PMF and EMFAC-HK led to discrepancies in LPG and GV apportionments. The EMFAC-HK attributed a much larger contribution of NMHCs by GV (56%) than LPG (18%), which is likely due to its unrealistic assumption that LPG and DV do not have any evaporative losses of NMHC. Figure 5 shows PMF-derived source contribution estimates for PM 2.5 concentrations in the tunnel. In addition to vehicle emissions, secondary inorganic aerosols and road dust are included. DV emissions account for over 50% of tunnel PM 2.5 mass concentrations, followed by secondary sulfate (~20%). Road dust (including resuspended dust as well as brake, tire, and road surface wear) contributes to~7% of PM 2.5 mass. Although not measured, the road dust contribution to the PM 10 mass is expected to be higher due to larger-sized particles. Chemical composition analysis of PM 2.5 collected in the SMT shows that geological mineral abundances increased from 2% in 2003 to 5% in 2015, indicating that non-tailpipe emissions are becoming more important as tailpipe emissions decrease [28,64].

Conclusions
Estimations of EFs for different vehicle fleet compositions and their contributions to roadside air pollutant concentrations are valuable for emission control and air quality management policies. Due to the fact that all conventional vehicle tailpipe emissions originate from the internal combustion of hydrocarbon fuels, most combustion products are similar, making the separation of emissions by different vehicle types challenging. Tunnel studies have been used to determine real-world on-road vehicle emissions, and EFs by different vehicle types are estimated by linear regression, receptor-based source apportionment, or emission models. However, the accuracy and uncertainties of these methods have not been sufficiently discussed. This study applied SLR, MLR, PMF, and EMFAC-HK to estimate the EFs of LPG, GV, and DV measured in the SMT in Hong Kong to compare the performance of these methods. The key findings of this study are: 1. Increasing the time resolution of the pollutant concentration and fleet composition data significantly reduces EF uncertainties by linear regressions. By increasing the time resolution from 2 h to 15 min, the relative uncertainties of the NOx EFs reduced from 79% to 33% for NDV and from 32% to 14% for DV. The increased time resolution not only increases the number of data points in the regression, but also enhances the differentiation of emissions among different vehicle types. The time resolution is determined by the data intervals of gas and particle sampling as well as that of traffic categorization. It is also influenced by traffic volume as too high time resolution will likely increase traffic-counting statistical errors. The optimum time resolution needs to be determined from sensitivity tests at several time resolutions for each study. 2. While SLR is the simplest among the four apportionment methods, caution should be taken when using SLR with very narrow traffic composition ranges, as the uncertainties of EFs by extrapolating the regression to fDV of 0% and 100% can be excessively large. Efforts should be made to increase the fleet composition's variability, such as measuring in tunnels with separated LD and HD traffic or by measuring different periods with a variety of fleet mixes.

Conclusions
Estimations of EFs for different vehicle fleet compositions and their contributions to roadside air pollutant concentrations are valuable for emission control and air quality management policies. Due to the fact that all conventional vehicle tailpipe emissions originate from the internal combustion of hydrocarbon fuels, most combustion products are similar, making the separation of emissions by different vehicle types challenging. Tunnel studies have been used to determine real-world on-road vehicle emissions, and EFs by different vehicle types are estimated by linear regression, receptor-based source apportionment, or emission models. However, the accuracy and uncertainties of these methods have not been sufficiently discussed. This study applied SLR, MLR, PMF, and EMFAC-HK to estimate the EFs of LPG, GV, and DV measured in the SMT in Hong Kong to compare the performance of these methods. The key findings of this study are: 1. Increasing the time resolution of the pollutant concentration and fleet composition data significantly reduces EF uncertainties by linear regressions. By increasing the time resolution from 2 h to 15 min, the relative uncertainties of the NO x EFs reduced from 79% to 33% for NDV and from 32% to 14% for DV. The increased time resolution not only increases the number of data points in the regression, but also enhances the differentiation of emissions among different vehicle types. The time resolution is determined by the data intervals of gas and particle sampling as well as that of traffic categorization. It is also influenced by traffic volume as too high time resolution will likely increase traffic-counting statistical errors. The optimum time resolution needs to be determined from sensitivity tests at several time resolutions for each study. 2. While SLR is the simplest among the four apportionment methods, caution should be taken when using SLR with very narrow traffic composition ranges, as the uncertainties of EFs by extrapolating the regression to f DV of 0% and 100% can be excessively large. Efforts should be made to increase the fleet composition's variability, such as measuring in tunnels with separated LD and HD traffic or by measuring different periods with a variety of fleet mixes. 3. With respect to the four EF calculation methods, MLR has the highest relative uncertainties, with many values exceeding ±100%, causing LPG and NDV EFs for many pollutants not statistically different from zero. Compared to SLR, MLR may resolve EFs for more than two vehicle categories, but EFs uncertainties by MLR were typically over twice those by SLR. EMFAC-HK has the lowest (<2%) relative uncertainties, due to its assignment of a single average EF value for each category under specific environmental and operating conditions. The relative uncertainties of SLR and PMF are comparable for many EFs by DV and NDV. 4. Among the apportionment methods compared in this study, PMF is likely the most reliable and useful, as it simultaneously seeks the source signatures and source contributions by minimizing the deviation between modeled and measured concentrations. In addition to contributions from different vehicle categories, it also identifies contributions from other sources. In SMT, diesel, gasoline, and LPG vehicle emissions account for 52%, 10%, and 5% of PM 2 . 5 concentrations, while ammonium sulfate (~20%), ammonium nitrate (6%), and road dust (7%) are also large contributors. Additionally, PMF produces source profiles indicating key signature chemical composition for each source. 5. PMF and EMFAC-HK agree reasonably well for the relative contributions of LPG, gasoline, and diesel vehicles to gases and PM 2 . 5 emissions by the vehicle fleet in the SMT. DV makes the largest contribution to CO 2 , NO x , and PM 2.5 , while GV makes the largest contribution to CO. Comparing source-and receptor-oriented models is recommended in source apportionment studies to reveal and resolve potential errors in the models and to reduce modeling uncertainties. 6. The LPG gas source profile shows abundant isobutane, n-butane, and propane, indicating unburned LPG fuel; the LPG PM 2.5 source profile has a higher abundance of organic molecules but nearly zero EC. The GV gas profile contains the highest levels of aromatics, including toluene, m/p-xylene, and ethylbenzene; the GV PM 2.5 source profile shows higher abundances of heavier PAHs such as retene, benzo(ghi)fluoranthene, and methylfluoranthene. The DV gas profile has the highest CO 2 and NO x abundances, and the DV PM 2.5 source profile shows the highest EC abundance. Due to continuous changes in fuels, combustion technologies, and emission controls, the vehicle source profiles vary with location and time and need to be continuously evaluated and updated. 7. Several knowledge gaps remain. The EMFAC-HK assumes zero tailpipe PM emissions from LPG vehicles, which may not be true as lubrication oil generates particles. To our best knowledge, there have not been direct tailpipe emission measurements from LPG vehicles; these measurements are needed to accurately determine EFs and source profiles of PM from LPG vehicles. The EMFAC-HK also assumes that LPG and DV do not have evaporative NMHC emissions, which does not agree with the abundant LPG fuel molecules observed in this study. In the interest of further reducing ozone and secondary organic aerosol pollutions, future studies should quantify the evaporative emission contributions for both LPG and DV and include these in emission models. 8. As the true emissions by different fleet compositions are not known, the apportionment accuracy cannot be assessed by comparing with true values. A "weight of evidence" approach using additional available information (e.g., local emission inventories, source profiles, and modeling performance measures), running multiple receptormodeling techniques, or reconciling receptor-oriented and source-oriented models can increase the degree of confidence.  Figure S1. Schematic diagram of: (a) sampling configuration in the east section of the Shing Mun Tunnel (SMT) and (b) sampling setup at the outlet site of the SMT in 2015; Figure S2. The fraction of the Q value change as the number of factors increases from m to m + 1 in the PMF modeling. Q value change stabilizes after m = 6, indicating that a 6-factor solution is appropriate for this dataset; Figure S3. PMF fitting performance by PM 2.5 components, as indicated by the scaled residual vs. correlation between measured and modeled concentrations. Key PM 2.5 species are labeled; Figure S4. PMF fitting performance by gas species, as indicated by the scaled residual vs. correlation between measured and modeled NMHC concentrations. Key species are labeled; Figure S5. Linear regression of pollutant emission factors vs. diesel vehicle fractions. The red solid line shows robust regression excluding the outlier (unfilled symbols) data points. The blue dashed lines indicate the 95% coincidence intervals for the robust regression; Figure S6. Comparison of emission factors for fleet components by different methods. Error bars represent the 95% confidence intervals of the mean. Figure S7. PMF-derived PM 2.5 factors associated with diesel, LPG, and gasoline vehicles (left panel: ions, carbon, elements, and PAHs; right panel: alkanes, alkenes, hopanes, and steranes). Only species with abundances >0.01% of measured PM 2.5 mass are shown for clarity. Error bars indicate variability (standard deviation) from 10 replicate model runs. Table S1. Emission factors (EF D ; average ± 95% confidence interval) by simple linear regression (SLR) and multiple linear regression (MLR). Data with a red font indicate that the estimates are not statistically significant. Table S2. Relative uncertainties (expanded uncertainty/average) of emission factors by different methods. Data with an italic purple font indicate that the absolute relative uncertainty exceeds 100%. Table S3. Statistical significance (p-values) of differences between emission factors obtained by different methods. Green font indicates p ≥ 0.05.