Assessing vehicle fuel efﬁciency using a dense network of CO 2 observations

Abstract. Transportation represents the largest sector of anthropogenic CO2 emissions in urban areas. Timely reductions in urban transportation emissions are critical to reaching climate goals set by international treaties, national policies, and local governments. Transportation emissions also remain one of the largest contributors to both poor air quality (AQ) and to inequities in AQ exposure. As municipal and regional governments create policy targeted at reducing transportation emissions, the ability to evaluate the efficacy of such emission reduction strategies at the spatial and temporal scales of neighborhoods is increasingly important. However, the current state of the art in emissions monitoring does not provide the temporal, sectoral, or spatial resolution necessary to track changes in emissions and provide feedback on the efficacy of such policies at a neighborhood scale. The BErkeley Air Quality and CO2 Network (BEACO2N) has previously been shown to provide constraints on emissions from the vehicle sector in aggregate over a ~1300 km2 multi-city spatial domain. Here, we focus on a 5 km, high volume, stretch of highway in the SF Bay area. We show that inversion of the BEACO2N measurements can be used to understand two factors that affect fuel efficiency: vehicle speed and fleet composition. The CO2 emission rate of the average vehicle (g/vkm) are shown to vary by as much as 27 % at different times of a typical weekday because of changes in vehicle speed and fleet composition. The BEACO2N-derived emissions estimates are consistent to within ~3 % of estimates derived from publicly available measures of vehicle type, number, and speed, providing direct observational support for the accuracy of the Emissions FACtor model (EMFAC) of vehicle fuel efficiency.



Introduction
In S1, we describe the time series of the number of BEACO2N nodes reporting CO2 during the from January through June for the years 2018-2020. In S2, we show the locations in the PeMS measurement network in the region of the SF Bay Area shown on the map, as well as an estimate of LDV and HDV VMT for a typical week in this domain. In S3, we describe the hourly BEACO2N-STILT prior for the typical weekday for CO2 emissions in the 1km pixels that encompass the highway stretch that is the focus of our analysis. The figure also shows vkm traveled for each hour on this stretch of highway. In S4, error analysis for PeMS values for speed, LDV and HDV volume is described. In S5, we list EMFAC2017 vehicle classes and indicate whether we have classified them as LDV or HDV based on estimated vehicle length. In S6, we show both LDV and HDV emissions rates as a function of speed. We also compare a piece-wise linear to a spline fit of these two curves. In S7, we show the diel cycle for contribution to total emissions by congestion and vehicle type as estimated using PeMS-EMFAC. In S8, we describe the calculation of uncertainty in emissions rates derived using the BEACO2N-STILT system. In S9, we derive emission rates from the BEACO2N-STILT prior and discuss improvements of the posterior over the prior. In S10, we explore how non-constant speed may impact emissions rates for a given hourly average speed.
Throughout the period examined in this study, the number of BEACO2N sensors reporting data varied from due to power or instrument failure.

Section S3.
We focus our analysis on the hours 4am -10pm. During this period, emissions from traffic are much larger than all other sources in the pixels used in this analysis. From 11pm -3am, total vkm and therefore emissions from traffic are low.

Section S4.
We apply linear fits (for speed and LDV) and hourly ratios (for HDV) to nearest neighbors, second nearest neighbors, and third nearest neighbors to create modeled values for all times for which we have observations. Using these modeled values we estimate mean error and spread for all PeMS sites over the time period studied, finding that speed accurate to about 5km hr -1 , LDV/hr to ~300 vehicles and HDV to ~55 vehicles for the east and west directions of flow on I-80. Precision is much higher than these values as shown on the right.

Section S5.
While EMFAC2017 provided speed-dependent emission rate estimates for 41 vehicle classes, PeMS characterizes vehicles in two categories based on length. In order to use EMFAC2017 emission rates in combination with PeMS traffic counts to estimate total emissions, we classify EMFAC2017 categories as LDV or HDV based on length.

EMFAC Vehicle Class
Grouping for this work All Other Buses 0  Table S1. Breakdown of EMFAC vehicle classes we characterize as LDV or HDV based on length. "1" denotes LDV and "0" denotes HDV.

Section S6.
As described in the main text, emission rates for LDV and HDV on each road segment between individual PeMS monitoring stations are computed hourly as a function hourly average speed.
Here we show emission rates as a function of speed.
We also compare piece-wise linear fits to the spline fits used in this study. With the exception of emissions rates for LDV at speeds lower than 20 km h -1 , there is little difference between these fits. High uncertainty in emission rates at low hourly average speeds because of travel at nonconstant speeds is likely to outweigh any difference between these fits (see Fig S7). Section S7. Figure S5 shows the hourly variation in the relative contributions of LDV speed, HDV percentage, and HDV speed to the deviation in CO2 / vkm from the reference value of 265 g CO2 / vkm. The solid line is the mean, and the shaded envelope represents the day-to-day variance. In the morning and mid-day, HDV percentage and LDV speed have opposite impacts on CO2 / vkm, leading to smaller variations in CO2 /vkm than the variations in the separate effects of speed and HDV %. 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-today variance in emission rates, shown as the envelope surrounding the solid line. At times near midnight, large, positive deviations are observed, mostly as a consequence of high HDV percentage, but also because traffic flows at rates higher than 104.6 kph, leading to higher emission rates. Night-to-night variance in HDV percentage is low, thus variance in nighttime predicted CO2 / vkm is small. HDV speed has little impact on CO2 / vkm. Section S7.

Determination of Uncertainty in Emissions Rate Estimates
For the set of BEACO2N emissions corresponding in time to the data in each 7.8 g CO2 / vkm bin of PeMS-derived emissions rates, we find a BEACO2N-derived emissions rate estimate. To do this, we take all BEACO2N traffic emissions occurring simultaneously with the PeMS-derived emissions rates and further bin these points based on vkm, as shown in Figure 3. For each vkm bin, we then find the median emissions value and the variance of emissions values,  2 . We assume the error in our estimate of the median emissions for each vkm bin to be =  √ .
We then fit median emissions values to the line = 2 , to find , using as weights in the MATLAB fitlm function, and take the reported SE in slope to be the error in our calculated .

Section S9.
The prior inventory was constructed to reflect vehicle type (LDV v. HDV) dependence on emissions, but not speed-dependence in emissions. In order to illustrate improvement of the posterior (Figure 3) over the prior, we repeat the analysis described in the main text to show emission rates calculated for the prior. Calculated emissions rates for the prior are nearly constant over a wide range (237.5 -262.5 g CO2 / vkm) of PeMS-EMFAC emission rates. Where they do vary, they are substantially different than those estimated in the posterior.

Figure S7:
Emission rate estimates calculated for the BEACO2N-STILT prior in the same manner in which they were calculated for the posterior vs. PeMS-EMFAC emissions estimates with uncertainty estimate. Black line shows fit of to posterior (Fig 3) weighted by variance: y = 0.97(.01)x . Grey envelope is 5% deviation from fit. Red line represents 1:1 line.
While PeMS reports hourly averaged speeds for each sensing station, non-constant speeds due to congestion can result in range of possible emissions rates that can occur for a particular hourly averaged speed.

Figure: S8
The dark line indicates the emissions rate corresponding to driving the speed indicated on the x axis at a constant velocity. The shaded region represents er distribution resulting from vehicle travel at non-constant speeds. For each speed, we calculate all possible emissions rates (g CO2 / vkm) that could be generated assuming that the vehicle fleet (here, 8% HDV as is common during AM rush hour) drives at 2 different speeds between 8 kph and 130 kph for the times required to result in the average speed represented on the x axis. The spread for each speed represents the 16 th -84 th percentiles of possible emissions rates.