In Somerville, CALINE4, R-LINE, AERMOD, QUIC, and the regression model predicted near-highway PNC gradients that approached background concentrations at ~200 m from the edge of I–93 (Figure 2). In addition, arterial roads began to influence measurements at distances from I–93 greater than ~200 m. Therefore, all model evaluations and comparisons in both Somerville and Chinatown were made from 0–200 m from the edges of I–93 and I–90. The models reasonably predicted Somerville scenario measurements (Figure S1) for warm hours (Scenarios SV-3 and SV-4) and the cold hour when the wind was perpendicular to I–93 (Scenario SV-1; Table S2). QUIC most closely approximated the shape of the measured PNC distance-decay curves; however, CALINE4, AERMOD, and R-LINE also performed reasonably well (and outperformed QUIC when the wind was parallel to the highway). Agreement of model predictions with measurements ranged from moderate to acceptable for individual scenarios (R² =0.43–0.96, NMSE ≤ 0.22, |FB| =0.12–0.90; Table S2). The Somerville regression model generally performed better for the four scenarios (R²=0.69, 0.28, 0.96, and 0.72) than it did for the full CAFEH dataset (R²=0.42).²² An exception to the overall good performance was for the cold hour with wind parallel to I–93 (Scenario SV-2), when a wide zone of elevated PNC near I–93 was not predicted by the models (e.g., R² ≤0.52 for all models). During the overcast midday of SV-2, PNC was unusually high both near I–93 (~75,000 particles/cm³) and in the urban background area (~50,000 particles/cm³), suggesting that decreased vertical mixing in the morning contributed to the buildup of PNC.

In Somerville, there was high agreement among models; Pearson’s r among model predictions was >0.82 overall and >0.58 for individual scenarios (Table S3). QUIC generally predicted the highest PNC and the near-road gradient with the shape closest to that of the smoothed data, except for Scenario SV-2 (cold air temperature, winds parallel to I–93) when QUIC was unable to predict a near-road gradient. The highest correlations were found for predictions from the three Gaussian dispersion models (CALINE4, AERMOD, and R-LINE), which had similar curves with r>0.98 for all four scenarios. CALINE4 predicted slightly higher PNC than AERMOD and R-LINE near I–93 during cold hours (Scenarios SV-1 and SV-2) and slightly lower concentrations during hot hours (Scenarios SV-3 and SV-4). The regression model predicted lower PNC than the dispersion models except for when the wind was blowing perpendicular to I–93 from the west on a cold day (Scenario SV-1). Low correlations were found for QUIC relative to all other models in Scenario SV-3 (r = 0.78–0.80), and for the regression model relative to other models for Scenario SV-2 (r = 0.63 for CALINE4, 0.75 for R-LINE, and 0.58 for AERMOD). However, all the models had generally acceptable performance and could be applied to neighborhoods like Somerville.

On average, the models predicted weak near-highway concentration gradients extending 100–200 m downwind (west) of the edges of I–93 (Figure 3) and (north and south of) I–90 (Figure S2) in Chinatown. Gradients from the individual highways were more difficult to discern than those in Somerville. Complexities in spatial trends in Chinatown were not accurately captured due to the generally high background PNC and contributions from multiple highways. All the models underestimated measured PNC in most Chinatown scenarios and underestimated the range in PNC upwind and downwind of I–93 and I–90 for warm and cold hours (Scenarios CT-1 to CT-6; Figure S3). R² was ≤0.45 and NMSE was ≤0.26 for all five models under all individual Chinatown test scenarios, and FAC2 (≤70% for all dispersion models) and FB (−1.21 to 0.68) were outside of generally accepted standards (Table S4). The performance of the Chinatown regression model for the six test scenarios (R²=0.37, 0.00, 0.00, 0.26, 0.43, and 0.36) varied substantially compared to the model performance in the CAFEH dataset as a whole (R²=0.24).²³7 The poor performance of the models in Chinatown reflected the inability to capture the more complex spatial patterns in PNC. In sensitivity analyses, changes to increase the loess smooth span (Figure S4, Figure S5) and the assumed background PNC (Figure S6) improved the fraction of predictions within a factor of 2 and 1.5 and the fractional bias. Neither the R² nor the NMSE was affected by these adjustments (Table S5) because the changes did not substantially affect the spatial trends in PNC. Similar results were obtained when only those receptors downwind of I–90 were considered. While removing receptors upwind of I–90 improved FAC2 and FAC1.5 by ~12% on average (Table S6), correlations between measurements and PNC predictions at downwind receptors were not generally better than those using the full set of receptors (Figure S7).

PNC predictions from the five models had less agreement in Chinatown than in Somerville (Table S7). During cold hours correlations among predictions were as low as 0.57 between CALINE4 and AERMOD (Scenario CT-1: east wind perpendicular to I–93) and 0.77 between CALINE4 and R-LINE (Scenario CT-5: north wind perpendicular to I–90). Surprisingly, QUIC and the regression model sometimes predicted trends in the opposite direction from the other models. For example, during cold (Scenario CT-2) and hot (Scenario CT-3) hours with wind from the southwest, predictions from QUIC and the regression model were negatively correlated with predictions from CALINE4, AERMOD, and R-LINE (r= −0.75 to −0.11). These inconsistent results when the wind was from the southwest may be related to air recirculation in the street canyon formed by buildings north and south of I–90.²⁰ QUIC predicted upward air flow on the north edge of the street canyon and downward flow on the south side, leading to upward dispersion of particles north of I–90 (Figure S8). Because I–90 is actually below grade but was modeled at ground level in all five models, the wind flow deviations due to street canyon effects may have been larger than the deviations predicted by QUIC and therefore the models may have overestimated PNC relative to models of a below-grade highway.

Our main findings that the five models tested were in generally good agreement with each other, but not necessarily with measurements, are consistent with the few available near-road PNC model evaluations. Our results are in line with studies that had qualitatively good agreement with measurements for both QUIC²⁸ and CALINE4,⁶³ and had R² of 0.2–0.5 between hourly or sub-hourly near-road PNC regression models and measurements.^17,23,25 In addition, our correlations between predictions from QUIC and regression models of PNC in Somerville (R²=0.82) and Chinatown (R²=0.79) were similar to those reported for New York City (R²=0.80).²⁴

Our results are also similar to other studies comparing models of traffic emissions. In previous studies of model performance, predictions of NO₂ and tracers (i.e., sulfur hexafluoride) have been within a factor of two of observations with reasonable agreement among models (e.g., CALINE4, AERMOD, R-LINE, QUIC, CAR, Urban, and regression).^31–39 We found that our tested models generally underestimated PNC relative to measurements, consistent with previous studies that reported underestimation of traffic-related air pollution by dispersion models for conditions of atmospheric instability, wind direction perpendicular to the highway, or low concentrations.^11,36,37,45 However, our results were different from studies that reported overestimation of traffic-related air pollution during stable or parallel wind conditions, and when concentrations were relatively high.^{11,27,36,44,45,64} Differences between our study and those reporting overestimations of concentrations could be related to model characteristics (e.g., the importance of aerosol chemistry or other primary and secondary PNC sources) and uncertainty in the emission factor inputs. In addition, although dispersion models (e.g., AERMOD, CALINE4, and R-LINE) of near-road traffic-related air pollution have generally been reported to perform better for wind speeds >1 m/s,^{11,21,37,38,45} we did not observe any consistent differences between high and low wind speeds in our study, possibly because we did not model any hours with low enough wind speeds to observe a difference.

The main sources of uncertainty in model predictions of near-highway PNC include factors related to model inputs (e.g., emission factors and local street traffic) and structure (e.g., treatment of plume meander and particle dynamics). The uncertainty in particle number emission factors is about a factor of 10 because limited data are available on how particle number emission rates change as a function of fleet composition, vehicle speed, traffic congestion, and meteorological conditions.^54,65 To maximize the applicability of the EF_PN to this study, we used temperature-adjusted EF_PN from a study in the Boston Central Artery Tunnel.⁵⁴ Using these emission factors, we achieved reasonably good fits to measurements in Somerville but underestimated PNC in Chinatown by about a factor of 3 (Table 2). These results suggest that an emission factor closer to that reported for the Williamsburg Bridge in Brooklyn, NY (5.7 × 10¹⁴ # veh⁻¹ km⁻¹, ~2.5 times higher than our emission factors) might be more appropriate for neighborhoods like Chinatown than the tunnel-derived values.²⁴

Similarly, changes in local-scale meteorology and emissions from highway and non-highway sources could impact PNC gradients near highways.^9,66,67 The monitoring data were not adjusted using fixed sites because the models were built to reflect the traffic and meteorological conditions when the measurements for the test scenarios were performed, and sub-hourly measurements were not available from any fixed site. In Chinatown, emissions from local traffic, diesel trains at South Station, and airplanes at Logan Airport east of I–93 may have contributed to the differences between the PNC models and measurements. In some applications, models of PNC from highway traffic might be appropriate even if the models do not agree with measurements of total PNC. However, researchers modeling total PNC would be well served to invest in modeling all nearby sources of ultrafine particles, especially in more complex areas like Chinatown.

Different treatments of plume meander and exclusion of aerosol particle dynamics contribute to structural uncertainties in near-road models of PNC. Treatment of plume meander is one of the major structural differences among the models considered here; AERMOD and R-LINE assume radial dispersion at low wind speeds, CALINE4 has a parameter for the standard deviation of wind direction, and QUIC does not account for deviations from the mean wind direction unless a physical obstacle is present.^{21,45,4749,64} However, all of the tested dispersion models had similar PNC predictions at the low (<2 m/s) wind speeds (e.g., Scenarios SV-1, CT-2 and CT-5) in which plume meander is applied in CALINE and R-LINE. Similarly, while particle formation and removal can be important during episodes of very high PNC and over large distances,^12,15,30 these processes are not likely to be important for the near-road environments considered in this paper. Review articles suggest time-scales of ~200 s for advection, ~1000 s for deposition, and ~10,000 s for coagulation for near-road environments with typical PNC (10⁴–10⁵ particles/cm³).^12,68 Therefore, particles are likely to be advected out of the near-road environment (0–200 m) before evolving enough to substantially change the number concentrations.

This is one of the first studies, and the most comprehensive to date, comparing multiple near-road models of PNC on an hourly time-scale. We showed that near-road air pollution models agree in some, but not all, likely meteorological and building scenarios. This result is important because exposure assessment^4,69,70 and epidemiology^5,71 of traffic-related air pollution are increasingly incorporating participant time-activity patterns. Therefore, understanding the errors in different air pollution models over short periods is valuable for predicting potential biases in exposure assessment for those models.

Based on our results, we recommend that researchers carefully consider the impacts of choice of dispersion or regression model on their near-road PNC predictions. Differences among models may be most important in areas with complex roadway geometries and wind patterns like our urban center neighborhood (i.e., Chinatown) or <50 m from the highway edge, where all five models tested under-predicted the measurements by up to a factor of three. Overall, the most important parameters affecting the model predictions were the locations of particle sources and buildings relative to wind direction. Depending on area geometry, modelers may choose to use a hybrid approach with one model (e.g., QUIC) for wind directions where street canyon effects dominate and another model for other wind directions where the benefits of including wind flow around individual buildings might not be realized.

The models and study areas used in this investigation were selected to maximize generalizability for other near-road PNC modeling efforts. The four dispersion models we tested are freely available to the air pollution modeling community and have been used in research and regulatory applications;^{21,24,28,41,44–4542–44,46,48,58,64} the regression models are similar to those being developed and used in epidemiological studies.^{13,17,29,33,36} While the Somerville study area presented some modeling challenges (i.e., I–93 was elevated, had a noise barrier, and was parallel to a state highway), it is typical of the complexity of many urban neighborhoods near highways. In contrast, Chinatown was typical of an urban core area where model performance can be degraded by complex roadway and building geometries. While we expect our methods and results to be broadly generalizable to hourly models of PNC in similar urban areas near highways in the United States, future work is needed to assess the generalizability of the model comparisons to other locations and over longer time periods.