Urban emissions currently account for ∼ 75 % of all anthropogenic CO2 emissions (Seto et al., 2014). By 2050, roughly two-thirds of the Earth's projected population of 9.3 billion is expected to reside within urban areas (Seto et al., 2014), meaning that effective greenhouse gas (GHG) emission reduction strategies must focus on urban emission reductions.

The transportation sector is responsible for ∼ 23 % of global GHG emissions worldwide (Seto et al., 2014) and represents the greatest sectoral percentage (∼ 25 %–66 %) of emissions from within the boundaries of urban areas in the United States (City of Oakland, 2020; Gurney et al., 2021). Although the fuel efficiency of new internal combustion engine vehicles has increased by ∼ 30 % over the last 20 years, and electric vehicles (EVs) are becoming more prevalent (e.g., https://arb.ca.gov/emfac/emissions-inventory, last access: 12 January 2022), emission reductions resulting from fuel efficiency gains in newer vehicles are negated by an increasing percentage of heavy-duty vehicles (HDVs) (Moua, 2020), speed-related reductions in fuel efficiency resulting from increases in congestion, and an increase in the total vehicle kilometers traveled. Over the past 20 years, even in locations with aggressive climate change policies, these factors have resulted in CO2 emissions from vehicles that have increased or stayed nearly constant. For example, the California Air Resources Board estimates that per capita vehicle emissions in the state of California in 2015 were only 2 % lower than in 2000, and per capita vehicle kilometers traveled increased ∼ 2.5 % over that time period (California Air Resources Board, 2018). In addition to GHG emissions, the transportation sector is responsible for a significant share of fine particulate matter (PM2.5) and NOx emissions, exacerbating PM2.5 and ozone exposure in BIPOC already experiencing disproportionate health burdens associated with poor air quality (Tessum et al., 2021).

Municipal and regional governments have increasingly shown interest in tracking and reducing CO2 emissions from all sectors, including transportation. For example, Boswell et al. (2019) found that 64 % of Californians live in a city with a climate action plan. For urban and regional governments to plan, monitor, and responsively adjust emission reduction policies, an up-to-date understanding of the spatial and temporal variations in total emissions and in emissions by sector and subsector processes is key.

For transportation, reductions in vehicle kilometers, congestion mitigation, and rules affecting fleet composition (e.g., limiting road access to HDVs, incentivizing use of electric vehicles, or buy-backs of older vehicles) are three levers that can be employed to reduce CO2 and AQ emissions from vehicles, thereby affecting the climate footprint, air quality (AQ), and environmental justice (EJ) in a region. However, the current state of the art in emission monitoring and modeling do not provide the temporal, sectoral, or spatial resolution necessary to track changes in urban emissions and provide feedback on the efficacy of each lever separately. Furthermore, current estimates of the magnitude and sectoral apportionment of urban CO2 emissions can vary widely. For example, Gurney et al. (2021) show how a consistent approach to total emissions from cities across the United States differs from locally constructed inventories in magnitude and sector by sector.

Spatial and temporal process-level maps of emissions are needed to improve the scientific basis for emission control strategies. The current state of the art involves finding aggregate emissions over large regions (e.g., counties or states) using economic data and then downscaling those totals using proxies such as road length, building type, or population density. These models meet the need for high spatial resolution (∼ 500 m) and capture emissions from many detailed subsectors (Gately et al., 2015; Gurney et al., 2012; McDonald et al., 2014). Because fuel sales are well characterized, these models are also likely to produce accurate region-wide CO2 emission totals from the transportation sector.

However, even the most detailed of these inventories do not presently describe the temporal variability in processes that affect emissions, such as the direct response of home heating or air conditioning to ambient temperature or, with one exception (Gately et al., 2017), the variations in emissions per kilometer when comparing free-flowing with stop-and-go traffic. These models often disagree with one another spatially (Gately and Hutyra, 2017), have been subject to only limited testing against observations of the atmosphere, and are not designed to be consistent with separately constructed AQ inventories that have been subject to much more extensive testing against observations.

Mobile monitoring campaigns and high-density measurement networks highlight the importance of characterizing and identifying the processes contributing to sharp neighborhood-scale AQ and GHG hot spots and point to the importance of traffic emissions at neighborhood scales. For example, Apte et al. (2017) showed that concentrations of NOx and black carbon (BC) can vary by as much as a factor of ∼ 8 on the scale of tens to hundreds of meters. Caubel et al. (2019) showed BC concentrations to be ∼ 2.5 times higher on trucking routes than on neighboring streets. Such gradients are not represented in inventories based on downscaled economic data.

Observations of CO2 and other GHGs can play an important role in improving and maintaining the accuracy of emission models – especially during a time of rapid proposed changes. CO2 measurements paired with Bayesian inverse models have been shown to provide a quantitative assessment of emissions (Lauvaux et al., 2016, 2020; Turner et al., 2020a). To date, most attempts at quantifying urban CO2 emissions have focused on extracting a temporally averaged (often a full year) total of the anthropogenic CO2 across the full extent of city. A few studies have attempted to disaggregate emissions by sector or fuel type or to describe large shifts in aggregate emissions (Newman et al., 2016; Nathan et al., 2018; Lauvaux et al., 2020; Turner et al., 2020a), but none characterize the subsector processes of vehicle emissions.

High-spatial-density observations offer promise as a means to explore process-level emission details. The BErkeley Air Quality and CO2 Network (BEACO2N) is an observing network deployed in the San Francisco Bay Area and other cities with a measurement spacing of ∼ 2 km (Fig. 1, left). In a prior analysis, Turner et al. (2020a) showed that BEACO2N measurements can detect variation in CO2 emissions with time of the day and day of the week in addition to the dramatic changes in CO2 emissions due to the COVID-related decrease in driving.

Here, we analyze hourly, spatially allocated CO2 emissions derived from the inversion of BEACO2N observations (Turner et al., 2020a) to explore how well they constrain the CO2 emissions from a 5 km stretch of highway. This stretch was chosen because of its location upwind of consistently active BEACO2N sites, for completeness of traffic data, and because emission rates are highly affected by speed (vehicles use more fuel per kilometer at very low and high speeds) and fleet composition (HDVs emit more CO2 per kilometer than light-duty vehicles, LDVs). The variation in the ratio of total fleet CO2 emissions per vehicle kilometer traveled (grams of CO2 per vehicle kilometer) is used to explore variations in on-road fuel efficiency and the factors responsible for that variation. We show that the average fuel efficiency of the vehicle fleet on the road varies by as much as 27 % over the course of a typical weekday.

To gain insight into the relative impacts of congestion and fleet composition, we first calculate fleet-wide vehicle emission rates (in grams of CO2 per vehicle kilometer) using two different methods. For both methods, the Caltrans Performance Measurement System (PeMS; http://pems.dot.ca.gov, last access: 12 January 2022) provides vehicle counts, speed, and vehicle category (HDVs or LDVs). Using these data and estimates of fuel consumption per kilometer from the EMission FACtor 2017 (EMFAC) model, we calculate the CO2 emissions per kilometer for the average vehicle with an hourly time resolution, as described above. Second, we use the PeMS data in combination with the grams of CO2 per unit area derived from the BEACO2N-STILT inversion system. We focus on the ∼ 5 km stretch of Interstate 80 just north of the San Francisco–Oakland Bay Bridge (Fig. 2). Interstate 80 is an east–west Highway whose orientation along this stretch is mainly north–south, with eastbound lanes traveling north and westbound lanes traveling south. The road has five lanes in each direction and is often subject to high congestion (vehicles traveling slower than the posted speed).

PeMS-EMFAC-derived emission rates give us insight into (1) the expected variation in emission rates across a typical day (Fig. 2) and (2) the relative impacts of congestion vs. the HDV percentage as factors leading to this variation (Fig. S6). For example, while the westbound segment experiences speeds significantly below free-flow during both morning and evening rush hours, the eastbound segment experiences significant congestion only during the evening. Because of a steep gradient in LDV emission rates between 20 and 50 km h-1 (Fig. S5), the westbound congestion in this segment occurs at speeds that are more fuel efficient than free flow. The overall variance in emission rates over the whole stretch is significantly smaller than in either of the directions shown individually.

From PeMS-EMFAC-derived emission factors, we predict a median diel cycle with the emissions per kilometer traveled ranging from ∼ 247 to ∼ 314 g CO2 per vehicle kilometer. For reference, if all vehicles were driving at the speed limit of 104.6 km h-1 (65 mph) and the fleet mix was 6 % HDVs and 94 % LDVs, we calculate an emission rate of 265 g CO2 per vehicle kilometer. The range of predicted emissions is narrower on the weekend (238–276 g CO2 per vehicle kilometer), as fewer HDVs use the road and there is a smaller range with respect to speed.

Figure S6 shows the hourly variation in the relative contributions of LDV speed, HDV percentage, and HDV speed to the deviation in grams of CO2 per vehicle kilometer from the reference value of 265 g CO2 per vehicle kilometer. The solid line is the mean, and the shaded envelope represents the day-to-day variance. In the morning and at midday, the HDV percentage and LDV speed have opposite impacts on the grams of CO2 per vehicle kilometer, leading to small variations in the grams of CO2 per vehicle kilometer over the day, despite substantial variations in the separate effects of speed and HDV percentage. During evening rush hour, low vehicle speeds result in higher emission rates, leading to large positive deviations. High day-to-day variance in vehicle speed contributes to high day-to-day variance in emission rates. At times near midnight, large, positive deviations are observed, mostly as a consequence of a high HDV percentage but also because traffic flows at rates higher than 104.6 km h-1, leading to higher emission rates. Night-to-night variance in the HDV percentage is low; thus, variance in the nighttime predicted grams of CO2 per vehicle kilometer is small. The HDV speed has little impact on the grams of CO2 per vehicle kilometer.

We use CO2 measurements from 50 BEACO2N sites across the San Francisco Bay Area combined with the BEACO2N-STILT inversion system to assess highway emissions from our stretch of interest. In Fig. 1, we show the location of BEACO2N sites, the stretch of interest, and emission estimates for this stretch. Note that the posterior emissions move substantially from prior emissions towards what is estimated from PeMS-EMFAC, particularly during the evening rush hour, when the prior overestimates emissions by ∼ 20 %.

We compare BEACO2N-derived and PeMS-EMFAC-derived emission rates (grams CO2 per vehicle kilometer) and find remarkable agreement. The PeMS-EMFAC-derived emission rates range from 225 to 300 g CO2 per vehicle kilometer and include the effects of both fleet composition and variation in speed. For BEACO2N, we use the total CO2 emissions from the inversion at times corresponding to narrow bins of PeMS-EMFAC (grams of CO2 per vehicle kilometer). Figure 3a shows an example of data selected at times with PeMS-EMFAC-derived fuel efficiency in the range of 271.4 to 279 g CO2 per vehicle kilometer. There is a range of emissions at each vehicle kilometer because of noise in the inversion, variation in speed, and variation in the fleet composition. The slope of a fit to the data in Fig. 3a is an estimate of the emission rate (Eq. 4), where CO2 emissions are defined as hourly emissions summed over BEACO2N pixels corresponding to our highway stretch of interest (Fig. 2): 4ergCO2vkm-1=CO2emissonsvkm. Using 18 months of data for weekdays between 04:00 and 22:00 local time, we compare PeMS-EMFAC-derived and BEACO2N-derived CO2 per vehicle kilometer (Fig. 3b). These hours were chosen, because they represent the hours for which we expect traffic emissions to be substantially larger than emissions from other sources in our area of interest (see Fig. S3). When fitting to a line forced through the origin, emission rates found via the BEACO2N inversion are within 3 % (0.97±0.01) of those predicted using PeMS-EMFAC traffic counts. A more complete description of this fitting and error calculation process can be found in Sect. S8, and a comparison to the results from applying this method to the prior can be found in Sect. S9. Using the definition of the limit of detection as 3 times our uncertainty, we calculate that we would be able to detect an 11 % change in individual points (representing bins of fuel efficiency from a combination of HDV percentage and speed) and a 3 % change in the slope. Because 18 months of data was required to reach this level of certainty, if we assume the 2.3 %–3.8 % yr-1 decrease in the emission rate found by Kim et al. (2021), we should be able to detect a change in the overall fuel efficiency with 3 full years of BEACO2N-STILT output.

We also consider how emission rates compare throughout the day (Fig. 4a). During the evening, PeMS-EMFAC-derived and BEACO2N-derived emission rates are in good agreement. The BEACO2N grams of CO2 per vehicle kilometer increases from 256 g CO2 per vehicle kilometer before rush hour (14:00) to 324 g CO2 per vehicle kilometer during peak rush hour (17:00). Likewise, the PeMS-EMFAC-derived CO2 per vehicle kilometer increases from 256 to 320 CO2 per vehicle kilometer over the same time period. The BEACO2N prior has a slightly larger increase in the emission rate over this period (256 g CO2 per vehicle kilometer at 14:00 to 361 g CO2 per vehicle kilometer at 17:00). In contrast, during the morning rush hours, we see less agreement between PeMS-EMFAC-derived and BEACO2N-derived emission rate estimates. The BEACO2N inversion is similar to the PeMS-EMFAC estimate at 05:00 local time (280 g CO2 per vehicle kilometer), and the BEACO2N estimate then increases over the morning rush hour to 330 g CO2 per vehicle kilometer at 8:00. This behavior is different from both the BEACO2N prior (175 g CO2 per vehicle kilometer at 05:00 and 275 g CO2 per vehicle kilometer at 08:00) and the PeMS-EMFAC calculation which decreases over this period (275 g CO2 per vehicle kilometer at 05:00 and 250 g CO2 per vehicle kilometer at 08:00).

The discrepancy in the morning between emissions derived from PeMS-EMFAC and BEACO2N can potentially be reconciled by congestion. There is a nonlinear relationship between vehicle speed and the rate of emissions. As such, congestion involving nonconstant speeds can result in higher emissions than would be estimated using the average vehicle speed. This can be seen from a simple example. Consider two cases: (1) an LDV traveling at a constant 50 km h-1 for 1 h and (2) an LDV traveling at 100 km h-1 for 20 min and at 25 km h-1 for 40 min. Both vehicles travel 50 km in 1 h and, therefore, have the same average speed; however, the emission rate is 461.5 g CO2 per vehicle kilometer at 25 km h-1, 195 g CO2 per vehicle kilometer at 50 km h-1, and 221 g CO2 per vehicle kilometer at 100 km h-1. Using these emission rates, the vehicle in the first case would emit 9.75 kg of CO2, whereas the vehicle with the variable speed in the second case would emit 15 kg of CO2.

Contrasting the speeds (Fig. 4c) during these two periods, we see that while both show a bimodal speed distribution, a greater fraction of morning speeds fall into the 40–100 km h-1 range, whereas a greater fraction of evening speeds are < 40 or > 100 km h-1. In Fig. S8, we show that emission rate estimates based on hourly averaged speeds between 0 and 40 km h-1 and between 100 and 140 km h-1 (more common in evening rush hour) are likely an upper bound on possible emission rates corresponding to those hourly averaged speeds, whereas emission rate estimates based on hourly averaged speeds between 40 and 100 km h-1 (more common in morning rush hour) likely represent a lower bound of emissions. The predicted range in the emission rate, resulting from nonconstant speeds combined with a larger HDV percentage, in the morning (Fig. 4c) is large enough to explain the mismatch observed during the morning rush hour.

The strategic reduction of emissions from transportation is important for both reducing total GHG emissions and improving AQ. To make informed decisions that reduce GHGs and exposure to poor AQ, policy makers need to know (1) how much is being emitted, (2) the location and timing of emissions, and (3) the relative impact of various subsector processes (e.g., vehicle kilometers and fleet composition).

To effectively capture emissions from subsector processes, models are also reliant on emission factor models, such as the EMFAC2017 model used in this paper. While our BEACO2N-STILT-based estimates largely agree with EMFAC2017 with respect to CO2, tracking on-road changes in emission factors will be especially important as the impacts of congestion and fleet composition evolve rapidly, making timely updates essential to creating spatially accurate inventories. For example, the EMFAC model predicts an 18 % decrease in overall CO2 emission rates by 2030, resulting from the improved fuel efficiency of combustion engine vehicles and a transition to hybrid vehicles and EVs (∼ 6.8 % of LDV vehicle kilometers and ∼ 6 % of HDV vehicle kilometers are expected to be traveled by EVs by 2030). While the increased share of hybrid vehicles and EVs should work to decrease the impact of congestion, a projected increase in total congestion and the congested vehicle kilometer share by HDVs (Texas A&M Transportation Institute, 2019) is likely to work against that trend, making the overall result difficult to predict.

To our knowledge, this paper represents the first demonstration that a high-density atmospheric observing network can both diagnose and quantify the relative contributions of subsector processes at the neighborhood scale. We demonstrate that the BEACO2N network (∼ 2 km spacing) of low-cost CO2 sensors can be used to quantify emission rates at a specific location (a ∼ 5 km stretch) and by time of day. We show that, on the highway stretch examined, activity-based emission estimates that account for speed and HDV percentage match the inference from atmospheric measurements to within 3 %. Finally, we demonstrate that the BEACO2N-STILT system detects daily changes in fuel efficiency that range from 200 to 300 g CO2 per vehicle kilometer and that this system would be capable of detecting fleet-wide changes in fuel efficiency in ∼ 3 years.

In this work, we have demonstrated that the BEACO2N-STILT system was able to infer emission rates from vehicles along a specific stretch of highway. To understand the extent to which this method can be applied to other contexts, future work should investigate the extent to which various elements of the BEACO2N-STILT system, including measurement density, error in meteorology used to calculate STILT trajectories, and the quality of the prior, impact the ability of similar systems to estimate emissions.

For example, it is possible that the mismatch that we observe during the morning rush hour may be due to a larger relative meteorological model error in the morning compared with the afternoon and early evening, during which time the boundary layer is relatively well mixed. Because a highly mixed boundary layer is important for minimizing discrepancies between particle trajectories in the STILT model and real transport (Lin et al., 2003), inversions typically use only measurements taken during the afternoon, (Lauvaux et al., 2016, 2020; Nathan et al., 2019) when the boundary layer is relatively well mixed. However, as discussed by Martin et al. (2019), the impacts of meteorological mismatch during the morning may be offset by a stronger signal, and future work should explore the extent to which averaging results over long time periods or strategic filtering of meteorological mismatches can combat emission error.

Beyond further exploration of the elements influencing the sensitivity and precision of the BEACO2N-STILT system, because each BEACO2N node measures CO, NOx, and PM2.5in addition to CO2 (Kim et al., 2018), the method presented in this paper has the potential to shed light on subsector processes impacting the emission factors of these co-emitted species. This is salient because plume-based emission factor measurements of co-emitted pollutants show that various emission factor models systematically underestimate emissions (Bishop, 2021), fail to capture spatial heterogeneity in these factors due to fleet composition (age and compliance with control technologies) for PM (Haugen et al., 2018; Park, et al., 2016) and black carbon (Preble et al., 2018), or fail to capture the impact of temperature on emission factors.

Applying these methods across a broader spatial area and to other species (e.g., PM2.5, NOx, and CO) should yield information of interest to both scientists and policy makers by

revealing spatial and temporal trends in emission rates and emission factors across an urban area and quantifying the contributions of congestion, fleet composition, or other factors to spatial variations;