The key components of the analysis include predicting emissions corresponding with traffic congestion for 83 individual urban areas based on travel demand models, developing estimates of changes in ambient concentrations associated with these emissions, applying concentration-response functions for the contaminants of concern, and finally, integrating the components of the model to estimate potential health risks associated with exposure to pollutants attributable to congestion. We focus on primary and secondary PM2.5 as the constituents of concern, and evaluate only premature mortality attributable to PM2.5 exposures, noting that there are numerous morbidity effects including respiratory and cardiovascular outcomes that are not considered in this analysis.
We note that there are two primary exposures potentially resulting from emissions during congestion events: the first is in-cabin exposures for drivers in their vehicles, and the second is a general increase in ambient concentrations of contaminants that impact the surrounding population. In the present study we focus solely on quantifying impacts associated with increases in ambient concentrations.
We develop estimates of vehicle miles traveled (VMT) based on data and methods from the Center for Urban Transportation Research (CUTR) at the University of Central Florida . We use MOBILE6 to estimate city-specific emissions per VMT based on year, temperature profile, and average vehicle speed. We focus on emissions from the baseline year (2000) until 2030. The analysis is conducted for 83 individual urban areas that were previously evaluated by the Texas Transportation Institute (TTI)  and are in the lower 48 states. The following sections provide more detail concerning each of these analytical steps.
Vehicle Miles Traveled (VMT) Estimation
We obtained census data and projections for different age classes from Woods & Poole , for each county of the United States, for the years 2000 - 2015, 2020, 2025, and 2030. To properly apply the CUTR model, we first determined the population in each of the 83 urban areas modeled (Additional file 1, Table S1). To approximate urban area population, we began by establishing baseline population data using 2000 US Census data at census block resolution, overlaying these data on shapefiles for the urban areas of interest. This provided estimates not only of the population within each urban area as a whole, but also estimates split by county when the urban area spanned multiple counties.
To determine urban area population for past and future years, we calculated the percentage change in population for each county relative to 2000 using Woods & Poole data, and we assumed that these percentages were applicable to the portions of the urban areas located within each county.
Next, predictions of traffic volume were based on a model derived from an analysis of the National Household Travel Survey, part of the 2000 US Census, developed by Polzin and Chu at CUTR  in a spreadsheet model they made available. The CUTR model inputs include age distribution, population density, gender distribution, and residency tenure distribution as covariates. We estimated population age distribution using Woods & Poole data, we calculated population density directly from the population estimates, and residency tenure distributions were provided in the CUTR model on a state-by-state basis for 2001 and 2035, and were linearly interpolated to provide values for the intervening years. These age, population density, and residency tenure covariates, represented as proportion of the population, were multiplied by factors determined by the CUTR analysis to estimate the different factors of travel behavior - person-trips/person, person-miles/person-trip, and vehicle-miles/person-mile.
Person-miles/person-trip and vehicle-miles/person-mile were calculated similarly, and the product of these three terms and population provided VMT, as indicated below.
We estimated VMT on a per-county basis using the fraction of the population of that county actually residing in the urban area, then summed across the entire urban area to generate estimates applicable for that urban area. The VMT estimates then fed into the travel demand and congestion model developed by TTI. We note that the TTI model links VMT with congestion but does not include forecasted VMT, necessitating the use of two different models, but that this leads to some incompatibilities (e.g., the CUTR model is driven by population within the urban area, whereas the historical TTI analyses are driven by traffic volume data that includes people not residing in the urban area). To evaluate our approach before proceeding with the core analyses, we compared our VMT estimates to those from TTI for past years (1985, 1990, 1995, and 2000 - 2005), while recognizing that the models would not be expected to yield identical outputs given these differing assumptions between the TTI and CUTR model inputs.
Travel Demand and Congestion Modeling
We combined the VMT estimates derived above with population data at the census tract level for the 83 urban areas addressed by TTI. The household travel survey provides the data which CUTR used to construct the traffic demand function. This is difficult to estimate, as the data do not address induced travel resulting from increased roadway capacity [16–18]. The baseline scenario presented here assumes the demand elasticity for trip rate, trip length, and occupancy derived from analyses of the CUTR surveys. Demand elasticities are primarily related to fuel price, travel time, and income .
Estimates of the infrastructure in each urban area were provided by TTI. Data were only provided for years between 1985 and 2005, and we used values for 2005 for all subsequent years (e.g., a fixed infrastructure over time). The values for VMT in each urban area were divided by the available infrastructure to generate daily traffic per lane. This fed into equations used to estimate average vehicle speed on freeway and arterial streets, and are based on uncongested to extremely congested conditions .
The percent of daily travel under congested conditions was based on the roadway congestion index, estimated as the ratio of daily traffic volume to the number of lane-miles of arterial streets and freeways. TTI  provides a non-linear function relating roadway congestion index to the amount of travel occurring in congested conditions (Additional file 1, Table S2) that imposes a maximum of 50% of daily traffic occurring in congestion. Using traffic volume and infrastructure estimates, the average speed on both arterial streets and freeways in both peak and off-peak directions can be estimated using the equations provided by TTI (Additional file 1, Table S3). The split of traffic between peak and off-peak directions was assumed at 65% and 35%, respectively, in accordance with median values reported previously .
Emissions are estimated using the MOBILE6 vehicle emission modeling software from the US EPA , the most robust software available at the time of our analysis. Given interests in PM2.5-related health risks, we derived emissions estimates for nitrogen oxides (NOx), sulfur dioxide (SO2), and primary PM2.5 for all model years, based on monthly averages of daily maximum and minimum ambient temperature, average vehicle speed for the two road types from the speed model, and MOBILE6 default fleet composition and performance for that year. A key limitation of MOBILE6 is that emissions are estimated using an average speed; thus, significant aspects of stop and go traffic and fast acceleration and deceleration, hallmarks of travel in congestion, are not adequately captured. Because of this limitation, within our study, we modeled the emissions that occur during congested conditions (with 100% of the emissions during periods of congestion attributed to "congestion"), rather than evaluating the proportion of emissions due solely to reduced vehicle speeds. In other words, the emissions outputs from MOBILE6 for each urban area were multiplied by the amount of VMT that occurs in congestion. This provided an estimate of the health risks associated with periods of congestion, but not information on (for example) the marginal difference between current conditions and an enhanced infrastructure that would allow for the same traffic volume at higher speeds, which was beyond the capabilities of MOBILE6 and therefore outside of the scope of our study.
To estimate the marginal concentration changes associated with congestion-related emissions from each urban area, we applied a source-receptor (S-R) matrix [22, 23]. S-R matrix is a reduced-form model containing county-to-county transfer factors across the United States, considering both primary PM2.5 and secondary formation of sulfate and nitrate particles. It is based on an underlying sector-averaged Gaussian dispersion model with wet and dry deposition and first-order chemical conversion. The S-R matrix is simplified relative to gold standard chemistry-transport models such as the Community Multiscale Air Quality model (CMAQ), but it is computationally tractable for an application such as this, and it has been shown to yield similar population health impact estimates to CMAQ [24, 25] and CALPUFF  at a fraction of the computational time and cost. It also includes a calibration step to ensure correspondence with ambient monitoring data. The calibration factors were developed comparing the modeled PM2.5 concentrations at county centroids with spatially interpolated monitored data at county centroids. For the monitored data, 2001 National Emissions Inventory (NEI) and data from the Federal Reference Method (FRM) and EPA's Speciation Network (ESPN) monitor sites were used.
Concentration-Response Function for PM2.5 Mortality
PM2.5 has been associated with a number of morbidity outcomes as well as premature mortality. For the purpose of this assessment, we focus on mortality due to long-term exposure to PM2.5, which has previously dominated monetized externality estimates in comparison with morbidity endpoints [9, 27]. As in recent health impact assessments , we derive our concentration-response function from a combination of published cohort studies and an expert elicitation study addressing the concentration-response function for PM2.5-related mortality. Two major cohort studies are generally thought to provide estimates that are most robust and applicable to the general population, with the Harvard Six Cities Study publications reporting central estimates of an approximate 1.2-1.6% increase in all-cause mortality per μg/m3 increase in annual average PM2.5[7, 8], and the American Cancer Society studies reporting estimates of approximately 0.4-0.6% [6, 29], with higher estimates when exposure characterization was more spatially refined . Within the expert elicitation study , the median concentration-response function across experts was approximately 1%, midway between these cohort estimates, with a median 5th percentile of 0.3% and a median 95th percentile of 2.0%. For this first-order health impact calculation, we consider a value of a 1% increase in all-cause mortality per μg/m3 increase in annual average PM2.5 to be well-justified and applicable, but consider the implications of alternative values in sensitivity analyses. We applied this function to the baseline mortality rate and the number of people in each census tract 25 years of age or older (the population in the Six Cities Study). We assumed that the age-specific mortality rate would not change over time, but given shifts in the age distribution of the population, that the overall mortality rate could change over time.
Monetized Estimates of Premature Mortality
To monetize the resulting estimates of mortality attributable to congestion, we applied a value of a statistical life (VSL) of approximately $7.7 M in 2007 dollars (for 2000 GDP), the central estimate used in recent EPA regulatory impact analyses . We increased VSL as a function of predicted increase in real GDP (as reported by the Bureau of Labor Statistics) and an income elasticity of 0.5, noting that recent epidemiological evidence indicates that the time lag between exposure to PM2.5 and mortality is relatively short , indicating that our value would not be sensitive to choice or application of discount rate.
Comparisons between Public Health and Economic Impacts
One of our primary objectives is to compare the monetized public health damages with the economic damages associated with congestion, over time and across urban areas. Although economic damages from fuel and time wasted have been derived previously, we re-estimated these values to correspond with our VMT estimates and to provide consistency with our public health estimates. We applied algorithms from TTI [1, 14] to calculate time and fuel spent in traffic at the modeled speeds and at free-flow. We calculated the difference between the time and fuel consumed at modeled speeds and at free-flow, which gave us the time and fuel wasted as a result of time spent in congestion, allowing us to compare economic and public health costs from each of these sources.
While the structure of our analyses did not allow for formal uncertainty propagation, given the numerous parameters with no plausible uncertainty quantification, we recognize that the uncertainties in our monetized public health damage estimates are significant. In our core results, we present public health damages based on central estimates for each parameter to provide a first approximation of impacts, and within limited sensitivity analyses, focus on the influence of selected parameter values on qualitative conclusions regarding the relative magnitudes of public health and economic damages.