In January 2006, we searched the Science Citation Index database for publications between 1997 and 2005 with keywords related to the spatial extent of mobile source related air pollution. We considered as relevant studies about on-road vehicles, construction engines/equipment, ports, and locomotives. We focused our search on four significant air pollutants related to mobile sources: particulate matter (PM), carbon monoxide (CO), benzene, and nitrogen oxides (NOx). CO and benzene represent non-reactive gaseous pollutants, while NO and NO2 represent gaseous pollutants that undergo rapid chemical reactions after being emitted. We include PM and particularly fine particles (PM2.5) because they pose a health risk [16, 17] and because spatial patterns may differ in important ways for particles of different size fractions (i.e., ultrafine particles vs. particle mass).
Keywords used include
• Air pollution related terms such as "air pollution", "automobile exhaust", "particulate matter", "elemental carbon", "carbon monoxide", "benzene", "nitrogen oxides", and "hydrocarbons" as well as any variations of these terms (e.g., PM instead of particulate matter, NOx or oxides of nitrogen instead of nitrogen oxides);
• Spatial extent-related terms: e.g., "distance", "spatial extent", "spatial variability" or "spatial variation";
• Mobile source-related terms such as "highway", "traffic", "mobile source", "ferry", "marine vessel", "locomotive" as well as any variations of these terms
Among articles that met the search criteria, we excluded those studies that did not focus on air pollution dispersion from mobile sources (e.g., studies on mobile source emission factors, point sources). We also excluded studies with distance or spatial variation used in a general sense or as a continuous regression variable without conclusions about the spatial extent. We included a few earlier publications (before 1997), if they themselves satisfy the above criteria (except for the year of publication) and were cited by the publications which satisfied the above criteria.
In addition to the peer-reviewed literature, we collected government reports that focused on the spatial extent of mobile source (e.g., automobile, ferry, locomotive) air pollution. These studies provide either data on the spatial extent or an indication of how the literature has been interpreted in a policy context. Since there is no search database for reports that span a variety of government agencies (including federal and state agencies), we collected information through a targeted internet search on specific agency websites and from a previous report by Environmental Defense . The reports reviewed here were not meant to be inclusive of all governmental reports on this topic, but rather provide a representative sample.
From the identified studies, we extracted information about significant factors that would be hypothesized to influence the spatial extent within the study. This included the pollutant, background concentration, emission rate, and meteorological factors, as well as the site and season of the study, the methodology of the study, and its implicit or explicit definition of spatial extent. It is worth noting that most of the studies reviewed do not directly focus on spatial extent. Instead, information on spatial extent is provided as an ancillary part of the study findings. Therefore, not all information is available or meaningful for all studies. We either contacted the authors of these studies for clarification/additional information or used our judgments to determine proxies of these factors in cases where direct information was not available. Below, we briefly describe the rationale for each factor and our data extraction methodology.
Five types of studies potentially satisfy the search criteria: monitoring, air dispersion modeling, land use regression, epidemiology, and biomonitoring studies. In addition, some studies combine more than one of these study types (hybrid studies). Monitoring and air dispersion modeling studies directly provide information on the pollutant concentration gradient and the resulting spatial extent. Biomonitoring studies, which use organisms to assess or monitor environmental conditions (often analysis of trace elements in plants or plant species composition near the source of interest), are also directly informative, albeit with an indirect measurement methodology.
Land use regression model studies predict pollutant concentrations at a given site based on surrounding traffic and land use characteristics within various radii (or buffers) around the site . This type of study is receptor-based rather than source-based, so is not directly informative about the spatial extent of mobile source impact, but the variables chosen for the final regression model can provide some insight on this issue. Similarly, epidemiological studies provide information on the distance from a roadway most strongly associated with health outcomes, an indirect measure of spatial extent. However, epidemiological studies which find no association between increased health risk and mobile source proximity provide little insight about the spatial extent of air pollution, as a null association could be related to many other factors (i.e., a lack of a causal association between the pollutant and health outcome in question).
For the quantitative meta-analysis, we created a categorical variable that indicated whether a study used monitoring/biomonitoring, dispersion modeling, epidemiology, or land-use regression.
Definition of spatial extent
The various spatial extent definitions used by different studies are generally based on absolute or relative comparisons. For relative comparisons, downwind concentrations as a percentage of a defined reference point concentration are compared with a cutoff value to determine spatial extent. The most commonly used reference point is the maximum concentration measured at the location nearest to the mobile source under study. The cutoff values used in the studies reviewed range from 50 percent of maximum concentration  to 10 percent [20, 21]. For absolute comparisons, downwind pollutant concentrations or health risks are compared directly with threshold values or measurements upwind or at other distances to determine whether there are significant differences. The threshold values include health risk values such as 1 in a million [13, 22] or incremental concentrations such as 0.01 ppm for NO2 . Other approaches include selection of significant covariates in land-use regression models or epidemiological studies.
For the meta-analysis, we created a categorical variable indicating whether the study estimated the percentage decrease from a maximum concentration, a significant absolute difference from background levels, or all other approaches. These are broad categories with significant variability within each category, but we lacked the statistical power to address the nuances in these spatial extent definitions within our meta-analysis. This issue is addressed within our dispersion modeling case study.
Pollutant type will clearly influence the spatial extent, based both on chemical properties and background concentrations. For relatively inert pollutants such as CO, downwind concentrations mainly decrease through dilution with ambient air. For more reactive pollutants, their concentration profiles can also be influenced by the rate of chemical reactions. For example, NO reacts with ambient ozone to form NO2 near the emission source. For NO, the combination of the reaction and the dilution in the surrounding air mass results in a rapid decrease in concentration with downwind distance. For NO2, on the other hand, the dominant formation process slows down its dilution and the concentrations decrease at a gradual rate. Both the intrinsic reaction rate and the abundance of substances involved in the reactions such as O3 can play an important part in the concentration distribution. These factors would imply that there could be important seasonal influences on the spatial extent of reactive pollutants, so we gathered information about season of study where available.
Particulate matter is involved in different processes depending on particle size. For particles larger than about 1 μm, turbulent diffusion and gravitational settling are the dominant processes, whereas, for particles smaller than 0.1 μm, Brownian diffusion becomes increasingly important . Due to coagulation processes wherein aerosol particles collide with one another and adhere to form larger particles , there will be a continuous decrease in number concentration coupled with an increase in particle size. For smaller particles (e.g., particles smaller than 0.1 μm), the combination of coagulation and dilution results in a rapid decrease in concentration with downwind distance. For larger particles, the formation through coagulation slows down the dilution and the concentrations decrease at a gradual rate. Thus, particle size and consideration of number vs. mass are key factors to consider.
Related to pollutant type is the magnitude of background concentrations relative to concentrations attributable to the source in question. For monitoring studies, the concentrations measured at different distances from the roadway include both background concentrations and the incremental contribution from the mobile source of interest. Therefore, the resulting concentration profile would be very different for two pollutants with and without significant background concentrations, even if the same amount of them are emitted from the source under study and they have similar dispersion characteristics. For example, suppose that the emissions from the source of interest result in a concentration increase of 1 μg/m3 at 10 m and 0.1 μg/m3 at 100 m for both pollutant A and B. If A has no background concentration while B has a uniform background concentration of 10 μg/m3, then it appears that the measured concentration of A at 100 m is only 10% of that at 10 m (90% decrease) while for B, the concentration at 100 m is still 92% of that at 10 m (less than 10% decrease), even though the source contribution is the same. This will have an influence on statistical significance tests and any "spatial extent" definitions based on concentration ratios.
Among the pollutants we focus on, CO, benzene and NOx have relatively low background concentrations. Mobile sources (both on-road and nonroad) are responsible for about 80 percent of benzene and CO, and more than half of all NOx emissions in the United States . PM2.5 is primarily related to regional transport with the majority contributed by non-mobile sources , but ultrafine particles (smaller than 0.1 μm) and elemental carbon/black smoke are more closely related to local sources. For the meta-analysis, we develop a categorical variable combining pollutant type and background concentrations. We categorize each study as either "inert pollutant, high background" (PM mass without background removed in the analysis), "inert pollutant, low background or background removed" (CO, benzene, EC/black smoke, PM mass with background removed in the analysis), "reactive pollutant, near-source removal" (NO, ultrafine particles), "reactive pollutant, near-source formation" (NO2). Of note, background concentrations are generally not addressed in air dispersion modeling studies, but are explicitly reported in monitoring studies in which the comparison between the downwind concentrations and that of the background is used to define spatial extent.
If we assume a linear relationship between concentration and emission rate, an increased emission rate will increase the spatial extent of the impacts, if the spatial extent is defined as the distance at which a risk threshold is reached, the distance before which the concentration change is greater than a predefined value, or statistical significance tests are being used. Few studies directly report emission rates, but there are multiple useful proxies. Most monitoring studies use higher traffic counts to indicate higher emission rates, so we created a categorical variable for traffic count above/below the median across studies reporting traffic counts.
The importance of meteorological factors is apparent when considering a simple Gaussian equation  for estimating the concentrations downwind of a continuously emitting infinite line source for relatively inert pollutants: , in which C is the downwind concentration (μg/m3), Q is the source strength per unit distance (μg/(m•s)), U is the average wind speed (m/s), and σz is the vertical dispersion coefficient (m).
Wind speed determines the extent to which pollutants are initially diluted, with the inverse relationship between the wind speed and concentration given in the Gaussian equation. Wind speed also plays an important role in the dispersion parameter computations. At lower wind speeds, both initial vertical dispersion and vehicle-induced thermal effects lead to higher estimates of the vertical dispersion parameter and, hence, lower concentration estimates. In addition, wind speed will affect travel time to the measurement location, which can have an influence on (for example) the amount of coagulation for ultrafine particles. Wind speed can therefore have somewhat complex relationships with the spatial extent, due to sometimes competing effects on initial dilution, vertical dispersion, and for ultrafine particles, coagulation. Wind direction will also be influential, as whether the wind is parallel or perpendicular to the road (in upwind or downwind directions) will influence concentration patterns substantially.
In addition, according to the Gaussian equation above, a higher vertical dispersion coefficient (σz) corresponds to lower downwind concentrations. Dispersion coefficients are functions of downwind distance and atmospheric stability. At the same downwind distance, unstable conditions correspond to higher dispersion coefficients than neutral conditions, followed by stable conditions. Stability classification in turn depends on measures of mechanical turbulence (such as surface roughness), measures of convective turbulence during daytime (such as mixing depth) and wind speed and wind direction fluctuations . Therefore, if all other factors are the same, the spatial extent of influence for the same pollutant is smaller under unstable conditions.
To incorporate meteorological factors, we gathered information where possible on wind speed and direction. We coded each measurement as either being downwind from the road or upwind/parallel (with multiple estimates often available from an individual study as a function of wind direction). Wind speed was coded as above or below 2 m/s (the median value across studies). Few studies directly presented information on atmospheric stability or other meteorological factors, so we considered these factors only within our dispersion model application.
To pool the evidence across selected studies, we considered two different dependent variables. The first is the reported spatial extent extracted from each of the studies. We evaluated predictors of the spatial extent in one-way and factorial ANOVAs. However, a number of studies reported no significant concentration gradient. Rather than omitting those studies from the analysis, we assigned each of these studies to have the maximum spatial extent reported across all studies of the same type (i.e., monitoring studies). Because of the potential that this approach could influence our findings, we also considered predictors of a dummy variable for above/below 500 meters.
To corroborate the findings from the meta-analysis and to provide insight about the influence of multiple factors in a controlled setting, we conducted an illustrative case study. Assuming a flat terrain, we calculate the downwind incremental concentration (Ci) of a relatively inert pollutant A from a continuously emitting infinite line source, when the wind direction is perpendicular to the line, by (as described above). The total concentration of this pollutant is the sum of the background (Cb) and incremental concentration (Ci):
For the base case, we assume a source strength per unit distance of 5 μg/(m·s), wind speed of 4 m/s, neutral stability (Pasquill stability class D), and background concentration of zero. The vertical dispersion coefficient (σz) can be calculated as , combining the CALINE4 mixing zone calculation  (σz, M) with a formula reflecting dispersion outside of the mixing zone  (σz, B). The mixing zone is defined as the region over the traffic lanes plus three meters on either side. When wind is perpendicular to the line source, CALINE4 models the mixing zone vertical dispersion coefficient as σz, M= 1.5+ 0.05 × W/U, in which W is the width of the mixing zone and U is the wind speed. Assuming a mixing zone width of 24 m and our base case wind speed, σz, M= 1.8 m. Under stability class D, σ
= 0.06x(1+0.0015x)-0.5, in which × is the downwind distance from the edge of the mixing zone in meters.
With the above information, we calculate the downwind concentration at different distances from the source for different values of parameters deemed important in our meta-analysis (for inert pollutants only).