Examining PM_2.5 concentrations and exposure using multiple models

Abstract

Epidemiologic studies have found associations between fine particulate matter (PM_2.5) exposure and adverse health effects using exposure models that incorporate monitoring data and other relevant information. Here, we use nine PM_2.5 concentration models (i.e., exposure models) that span a wide range of methods to investigate i) PM_2.5 concentrations in 2011, ii) potential changes in PM_2.5 concentrations between 2011 and 2028 due to on-the-books regulations, and iii) PM_2.5 exposure for the U.S. population and four racial/ethnic groups. The exposure models included two geophysical chemical transport models (CTMs), two interpolation methods, a satellite-derived aerosol optical depth-based method, a Bayesian statistical regression model, and three data-rich machine learning methods. We focused on annual predictions that were regridded to 12-km resolution over the conterminous U.S., but also considered 1-km predictions in sensitivity analyses. The exposure models predicted broadly consistent PM_2.5 concentrations, with relatively high concentrations on average over the eastern U.S. and greater variability in the western U.S. However, differences in national concentration distributions (median standard deviation: 1.00 μg m⁻³) and spatial distributions over urban areas were evident. Further exploration of these differences and their implications for specific applications would be valuable. PM_2.5 concentrations were estimated to decrease by about 1 μg m⁻³ on average due to modeled emission changes between 2011 and 2028, with decreases of more than 3 μg m⁻³ in areas with relatively high 2011 concentrations that were projected to experience relatively large emission reductions. Agreement among models was closer for population-weighted than uniformly weighted averages across the domain. About 50% of the population was estimated to experience PM_2.5 concentrations less than 10 μg m⁻³ in 2011 and PM_2.5 improvements of about 2 μg m⁻³ due to modeled emission changes between 2011 and 2028. Two inequality metrics were used to characterize differences in exposure among the four racial/ethnic groups. The metrics generally yielded consistent information and suggest that the modeled emission reductions between 2011 and 2028 would reduce absolute exposure inequality on average.

1. Introduction

Epidemiologic studies have reported associations between concentrations of ambient fine particulate matter (PM_2.5) and health effects including mortality (e.g., Di et al., 2017; Pappin et al., 2019; Pope et al., 2020; USEPA, 2019). Globally, 4.2 million deaths have been attributed to PM_2.5 air pollution in 2015 (Cohen et al., 2017). Epidemiologic and health-impact studies rely on accurate characterizations of population exposure to provide understanding of the health effects of ambient PM_2.5. Due to the limited spatial and temporal coverage of routine monitoring networks, many PM_2.5 concentration models have been developed in recent years to provide complete coverage for exposure applications over large domains including the conterminous U.S.

PM_2.5 concentration models (hereafter exposure models) have been developed using various approaches including geophysical process modeling (Ostro et al., 2015; Wang et al., 2017), monitor-only methods (e.g., monitor averaging, nearest-monitor, interpolation) (Keller and Peng, 2019), hybrid land-use regression modeling (Beckerman et al., 2013; Jerrett et al., 2017), satellite-derived aerosol optical depth (AOD) methods (van Donkelaar et al., 2010), Bayesian statistical modeling (Berrocal et al., 2010), and data-rich machine learning models (Chen et al., 2019; Di et al., 2019; Di et al., 2016; Hu et al., 2017). These exposure models often demonstrate good predictive capability based on statistical performance metrics from cross-validation tests with withheld observations. For instance, several machine learning methods have reported R² values of 0.80 or greater based on ten-fold cross validation of daily PM_2.5 predictions over the conterminous U.S. in 2011 (Di et al., 2019; Di et al., 2016; Hu et al., 2017). However, model performance may vary with the spatial and temporal resolution of the application, and the suitability of a model could depend on the resolution and type of the epidemiologic analysis to be performed (e.g., cross-sectional analysis versus case-crossover design).

Epidemiologic studies have examined the influence of different exposure characterizations on PM_2.5-mortality associations and found some agreement in results. For instance, Jerrett et al. (2017) reported associations between PM_2.5 exposure and mortality risk using multiple exposure models, although methods that incorporated ground-based observations yield larger risks than those estimated based on a remote-sensing-only model. Di et al. (2017) reported associations between PM_2.5 exposure and mortality risks using the neural network exposure model of Di et al. (2016) and a nearest-monitor approach, with slightly larger risks based on the national exposure model. Health impact assessments have also examined the influence of differences in exposure characterization on outcomes. For instance, Jin et al. (2019) estimated a 28% uncertainty in the state-level mortality burden for New York associated with the choice of method used to estimate PM_2.5 exposure. Ford and Heald (2016) estimated similar variability in the mortality burden for the U.S. during 2004–2011 based on satellite-derived exposure estimates.

Comparisons of PM_2.5 concentrations based on different exposure models have also been performed. Jin et al. (2019) reported that seven publicly available PM_2.5 products captured the decrease in PM_2.5 concentrations over NY between 2002 and 2012, but that the models had limited ability to resolve the intra-urban spatial patterns of PM_2.5 evident in a high-resolution monitoring network. Studies have also reported increasing differences in concentration among methods and degradation in performance with increasing distance to the nearest monitor (Berrocal et al., 2020; Huang et al., 2018; Jin et al., 2019; Kelly et al., 2019a). These results indicate that performance for many methods degrades in very places where we need exposure estimates, locations far from monitors. Diao et al. (2019) recently reported inconsistencies in PM_2.5 estimates from several publicly available PM_2.5 products and encouraged future research efforts.

Investigations of PM_2.5 concentrations over the conterminous U.S. based on multiple methods of exposure are limited and have not included predictions of some of the most widely used methods. Also, previous studies have not examined the influence of exposure modeling methods on the future-year air quality projections commonly used in regulatory planning. Moreover, the implications of differences in modeling approaches for characterizing population exposure have received little consideration, despite the importance of exposure characterization for epidemiologic and health impact assessments. Finally, exposure models have recently been used to examine exposure inequality in Massachusetts (Rosofsky et al., 2018), but modeling of exposure inequality over larger domains is limited (Bravo et al., 2016) and has not considered possible future changes in PM_2.5 exposure inequality.

Here, we characterize annual average PM_2.5 concentrations in 2011 over the conterminous U.S. using nine exposure models that span a wide range of complexity and data sources. We then estimate the change in PM_2.5 concentrations between 2011 and 2028 due to modeled emission changes associated with a suite of on-the-books regulations. Finally, we characterize PM_2.5 exposure (i.e., population-weighted concentrations) and exposure inequality according to two metrics using modeled PM_2.5 concentrations for the 2011 and 2028 cases. The use of multiple models is intended to provide insights on current exposure modeling methods as well as a thorough characterization of PM_2.5 concentrations and exposure.

2. Methods

We characterized PM_2.5 concentrations for 2011 due to the greater availability of exposure model predictions for this period than more recent years. Also, chemical transport model (CTM) simulations are available from previous work to project 2011 PM_2.5 concentrations in response to emission changes estimated to occur between 2011 and 2028 (USEPA, 2017a). Nine exposure models were used that can loosely be classified into categories of geophysical process models, interpolation-based models, Bayesian statistical regression, a satellite-AOD-based model, and machine learning models. The models are based on a wide range of input data and algorithms and were developed independently by multiple research groups.

2.1. Exposure Models

PM_2.5 concentration estimates from two geophysical CTMs were used. CTMs simulate concentrations using scientific parameterizations of the key atmospheric processes that govern pollutant concentrations including emissions, transport, chemical reaction, and deposition. CTMs are therefore valuable for predicting PM_2.5 concentrations under hypothetical scenarios where observations are not possible. For exposure applications, CTM predictions are often calibrated to observations using statistical models. Here, we consider the uncalibrated CTM predictions as a reference for the statistical model predictions, and because CTM predictions are sometimes directly used in health studies (Ostro et al., 2015; Wang et al., 2017). First, PM_2.5 exposure fields were developed from a simulation of 2011 with the Community Multiscale Air Quality model, version 5.0.2. CMAQ was configured with the Carbon Bond 05 (CB05) chemical mechanism, and anthropogenic emissions were based version 1 of the 2011 national emission inventory (NEI11). The model configuration, performance evaluation, and emission inventory have been described in detail previously (Kelly et al., 2019b; USEPA, 2015a). Second, PM_2.5 exposure fields were developed using a simulation of 2011 based on the Community Atmosphere Model with Extensions (CAMx), version 6.3.2. CAMx was configured with the Carbon Bond chemical mechanism (CB6r4), and anthropogenic emissions were based on version 2 of NEI11. The CAMx model configuration and performance evaluation have been described in detail by USEPA (2017a), and model emissions have been described by USEPA (2016) and USEPA (2017b). The modeling domain for the CTM simulations covered the conterminous U.S. with 12-km grid spacing. The national emission totals for the CMAQ and CAMx simulations were within 2% for NOx, SO₂, and volatile organic compounds (VOCs), and primary PM_2.5 emissions were 4% higher in the CMAQ simulation.

A PM_2.5 exposure field was also developed by interpolating monitor concentrations to the 12-km CTM grid. We used the Voronoi neighbor averaging (VNA) interpolation approach, which calculates the PM_2.5 concentration at a prediction location as the inverse-distance-squared weighted average of monitored concentrations in neighboring Voronoi polygons (Abt, 2012; Fann et al., 2012). Additionally, PM_2.5 concentrations were estimated using the extended VNA approach that weights the VNA interpolation using the ratio of CTM predictions between the monitor location and the prediction point (Abt, 2012; Fann et al., 2012). This weighting effectively fuses the spatial gradients from the CTM field with the interpolated field of observations from VNA. The CAMx simulation described above was used in the eVNA calculations. VNA and eVNA predictions were made quarterly on the 12-km CTM grid using the Speciated Modeled Attainment Test-Community Addition (SMAT-CEv1.3) software. VNA and eVNA calculations are computationally efficient and can be made using publicly available software.

A PM_2.5 concentration field was also developed using a Bayesian statistical downscaling model (Berrocal et al., 2010) that incorporated PM_2.5 monitoring data and the CMAQ simulation described above. The downscaler model is a linear regression model that relates observed concentrations to CMAQ output using spatially and temporally varying coefficients. The downscaler is fit within a Bayesian framework and provides estimates of prediction uncertainty (Berrocal et al., 2020). The downscaler has been found to achieve relatively good model performance based on a limited amount of input data by explicitly accounting for the spatial dependence in PM_2.5 concentrations (Berrocal et al., 2020). Daily PM_2.5 predictions were made on the national 12-km CTM grid.

Also, PM_2.5 predictions were used from a model that first relates satellite-derived AOD retrievals to surface PM_2.5 concentrations using the geophysical relationship predicted by a global CTM (GEOS-Chem) with a nested simulation over North America. The initial PM_2.5 estimate (based on AOD and GEOS-Chem) is then calibrated to ground-based observations using geographically weighted regression as described by van Donkelaar et al. (2019; V4.NA.02). Here we characterize PM_2.5 concentrations over the conterminous U.S. using the V4.NA.02.MAPLE product, which modifies the original V4.NA.02 product with additional developments as part of the MAPLE (Mortality–Air Pollution Associations in Low-Exposure Environments) project. Annual predictions at 1-km resolution were available from this method (hereafter VD2019), although fine-scale features at 1-km resolution are not expected to be fully resolved due to the influence of some coarser resolution inputs on the final dataset. Previous studies have reported that earlier versions of the VD2019 approach perform relatively well in remote areas due to the use of remote sensing information (Jin et al., 2019; Lee et al., 2012).

PM_2.5 exposure fields from three data-rich machine learning methods were also compared. Machine learning methods can model the complex nonlinear and interactive relationships among predictor variables across wide range of datasets relevant to PM_2.5 formation. PM_2.5 predictions were used from a neural network model that incorporated >50 predictor variables including predictions of a global CTM and satellite-derived AOD (Di et al., 2016). Daily PM_2.5 predictions over the conterminous U.S. were available from this method at 1-km resolution (hereafter DI2016). Predictions based on a random forest model with about 40 predictors variables were also used (Hu et al., 2017). Important predictor variables in the random forest included satellite-derived AOD and a convolutional layer for nearby PM_2.5 measurements. Daily PM_2.5 concentration predictions were developed at 12-km resolution with this method (hereafter: HU2017). Finally, PM_2.5 concentrations based on an ensemble of predictions from three machine learning methods (gradient boosting, random forest, and neural network) were used (Di et al., 2019). PM_2.5 estimates from the individual learners are optimally combined using a generalized additive model that accounts for geographic variations with thin-plate spline functions. This model (hereafter DI2019) incorporated a wide range of predictors including the CMAQ simulation described above.

The nine exposure models are summarized in Table 1. Due to differences in the spatial and temporal resolution of the methods and domain coverage, we averaged the fields to the coarsest spatial (12 km) and temporal (annual) resolution and included only grid cells where all models had coverage. Spatial averaging was done by calculating the mean of model prediction points located within a 12-km grid cell. The study therefore focuses on 12-km resolution, but we also consider 1-km fields in some cases to understand the effects of spatial averaging. The performance of the methods against withheld monitoring data has been reported previously and is consistent with the state-of-the-science for the individual approaches. Model performance is considered further in the Supporting Information (Text S1 and Figure S1), and the methods are summarized in Table 1. Note that the PM_2.5 from the CTMs is calculated as the sum of simulated PM_2.5 components and is not identical to the measured PM_2.5, which is operationally defined by the Federal Reference Method (Noble et al., 2001).

Table 1.

Summary of exposure modeling methods

Case	Method Description	Original Resolutiona	Performance Statisticsb	Reference
CMAQ	Geophysical process model based on unconstrained bottom-up methods	Hourly, 12-km	cTotal R2: 0.24 RMSE: 7.36 MB: 0.57 Slope: 0.62	USEPA (2015a); Kelly et al. (2019b)
CAMx	Geophysical process model based on unconstrained bottom-up methods	Hourly, 12-km	cTotal R2: 0.27 RMSE: 6.35 MB: −0.29 Slope: 0.53	USEPA (2017a)
VNA	Inverse-distance-squared weighted interpolation of PM2.5 observations in neighboring Voronoi polygons	Quarterly, 12-km	dTotal R2: 0.68 RMSE: 3.5 MB: 0.20 Slope: 0.74	Abt (2012); Kelly et al. (2019a)
eVNA	VNA Interpolation of monitor data but with interpolation weighted by the ratio of CTM predictions in the monitor cell to the prediction cell.	Quarterly, 12-km	dTotal R2: 0.48 RMSE: 5.60 MB: 0.40 Slope: 0.88	Abt (2012); Kelly et al. (2019a)
Downscaler	Bayesian statistical regression of CTM predictions and observations with spatially varying coefficients	Daily, 12-km	dTotal R2: 0.66 RMSE: 3.7 Bias: 0.8 Slope: 0.78	Berrocal et al. (2010); Kelly et al. (2019a)
VD2019	CTM scaling of satellite AOD to surface PM2.5 with geographic weighted regression of residuals.	Monthly, 1-km	eR2: 0.73 (0.55,0.86) RMSE: 1.8 (1.5,2.4) Bias: 0.05 (−0.09,0.20) Slope: 0.88 (0.72,0.95).	van Donkelaar et al. (2019), following Table 1, modified as per V4.NA.02.MAPLE update
DI2016	Neural network model based on wide range of predictors including satellite AOD and CTM modeling	Daily, 1-km	fTotal R2: 0.81 RMSE: 2.83 Bias: 0.38 Slope: 0.99	Di et al. (2016)
HU2017	Random forest model based on ~40 predictors including satellite AOD and CTM modeling	Daily, 12-km	fTotal R2: 0.80 RMSE: 2.83 Slope: 1.00	Hu et al. (2017)
DI2019	Ensemble model based on random forest, gradient boosting, and neural network learners with a wide range of predictors	Daily, 1-km	fTotal R2: 0.832 RMSE: 2.670 Bias: 0.742 Slope: 0.940	Di et al. (2019)

^aFields were averaged here to the annual period and a common 12-km grid

^bRMSE: root-mean-square error (μg m⁻³); MB: mean bias (μg m⁻³)

^cStatistics are based on daily PM_2.5 predictions for 2011 that were not constrained with observations

^dStatistics are based on 10-fold cross-validation of daily PM_2.5 predictions for 2015

^eStatistics are based on 10-fold cross-validation of annual PM_2.5 for 2000–2016 in the U.S. (mean and range for individual years)

^fStatistics are based on 10-fold cross-validation of daily PM_2.5 predictions for 2011

2.2. Projecting PM_2.5 based on 2011 and 2028 Emissions

We projected the 2011 PM_2.5 concentrations from the nine exposure models to 2028 using CAMx modeling based on emissions for 2011 and 2028. In addition to the 2011 simulation described above, a second CAMx simulation was available that accounted for emission changes expected to occur between 2011 and 2028 due to a suite of on-the-books regulations and other factors (e.g., planned plant shutdowns). Emission inputs for the 2028 CAMx simulation were developed by projecting emission sectors individually from the 2011 CAMx case described above using spatially and temporally resolved information. The emission totals for the 2011 and 2028 simulations are provided in Table 2, and a full description of the emission projections is available in USEPA (2017b). The largest contribution to the 63% decrease in SO₂ emissions over the conterminous U.S. between the 2011 and 2028 simulations was from electric generation units (76% decrease). The largest contribution to the 50% decrease in modeled NO_x (NO + NO₂) emissions was from the onroad mobile source sector (77% decrease) followed by electric generation units (61% decrease). Note that the meteorology and chemical boundary conditions in the 2028 CAMx simulation were fixed at their 2011 values, and so the 2028 CAMx modeling reflects changes compared to 2011 due to emission changes alone.

Table 2.

Modeled emission totals¹ for conterminous U.S. in 2011 and 2028 CAMx simulations.

Pollutant	2011 (t yr−1)	2028 (t yr−1)	Change 2011 to 2028
SO2	6,403,986	2,351,163	−63%
NOx	14,163,826	7,135,556	−50%
VOC	17,160,045	13,660,423	−20%
PM2.5	4,599,665	4,413,668	−4%

¹Emission totals were developed by projecting sectors individually with spatially and temporally resolved information. Projections for electric generation unit emissions include the Final Mercury and Air Toxics rule (December 21, 2011); the Cross-State Air Pollution Rule (CSAPR) (July 6, 2011); and the CSAPR Update Rule (October 26, 2016). Projections for onroad mobile sources include the Tier-3 Vehicle Emissions and Fuel Standards Program (March 2014); the California Low-Emission Vehicle (LEVIII) program; and Light-Duty Vehicle Greenhouse Gas Emissions and Corporate Average Fuel Economy Standards (October, 2012); and Greenhouse Gas Emissions Standards and Fuel Efficiency Standards for Medium- and Heavy-Duty Engines and Vehicles (September, 2011). See USEPA (2017b) for more details.

To help reduce the influence of model bias, PM_2.5 concentrations were projected using relative response factors (RRFs) developed from the ratios of modeled 2011 and 2028 PM_2.5 concentrations (Cohan and Chen, 2014; NRC, 2004; USEPA, 2018). RRFs are generally applied on a species-specific basis to help mitigate the potential influence of a large model bias for one species dominating the overall response of PM_2.5. RRFs for total PM_2.5 in each grid cell were developed from RRFs for individual particle components by taking the species-weighted average of the component RRFs:

$${RRF}_{species}=\frac{C_{2028,species}}{C_{2011,species}}$$ (1)

$${RRF}_{Tot,PM2.5}=\frac{\sum C_{Obs,species}{RRF}_{species}}{\sum C_{Obs,species}}$$ (2)

where C_2028,species and C_2011,species are the modeled PM_2.5 component concentrations in the 2028 and 2011 CAMx simulations, respectively; RRF_species is the RRF for a given PM_2.5 particle component; C_Obs,species is the PM_2.5 component concentration in 2011 based on VNA interpolation of observations that have been adjusted for consistency with total PM_2.5 measurements (Frank, 2006); and RRF_Tot,PM2.5 is the RRF for total PM_2.5. Calculation of C_obs,species and RRF_species was done using SMAT-CEv1.3. Finally, PM_2.5 concentrations were projected from 2011 to 2028 using the RRFs for total PM_2.5 as follows:

$${PM2.5}_{Mod,2028}={RRF}_{Tot,PM2.5}{PM2.5}_{Mod,2011}$$ (3)

where PM2.5_Mod,2011 is the modeled PM_2.5 concentration in 2011 and PM25_Mod,2028 is the modeled PM_2.5 concentration in the 2028 emission case. Therefore the 2028 projected PM_2.5 concentrations are influenced both by the RRFs (from CAMx) and the 2011 modeled concentrations (from each of the nine exposure models).

2.3. Population Data and Exposure Metrics

To examine population exposure using the modeled concentration fields, we calculated population-weighted concentrations for the total population in the domain and for racial/ethnic subgroups as follows:

$$C_{PM2.5,Pop.weighted}=\frac{\sum {Pop}_i{C}_{PM2.5,i}}{\sum {Pop}_i}$$ (4)

where C_{PM25,Pop.weighted} is the population-weighted concentration of PM_2.5 for a given population group, Pop_i is the population size in grid cell i for the given population group, and C_PM2.5,i is the PM_2.5 concentration in grid cell i.

We used 2010 Census data based on the 1-km gridded product available from the Socioeconomic Data and Applications Center (CIESIN, 2017) to characterize population distributions. In addition to total U.S. population, we considered the following racial/ethnic groups: non-Hispanic Black (NH-Black), non-Hispanic white (NH-white), non-Hispanic other (NH-other), and Hispanic. For exposure calculations based on 12-km concentration fields, the 1-km population data were regridded to the 12-km domain used for the exposure models. For calculations with 1-km fields, modeled concentrations were matched with the nearest-neighbor grid point from the 1-km population data product. Population data were fixed at 2010 levels in all calculations, and so changes in exposure between 2011 and 2028 are due to concentration changes only.

Two metrics were used to characterize differences in exposure for population sub-groups. First, we calculated the difference in population-weighted PM_2.5 concentrations between the most and least exposed groups by state (i.e., the exposure gap), which is similar to the risk gap of Thind et al. (2019). The exposure gap is an absolute metric that uses the best-off group as the reference and does not include an explicit inequality aversion parameter (Harper et al., 2013; Levy et al., 2006). Second, we calculated the Between Group Atkinson index (AI_BG), which was recently applied by Rosofsky et al. (2018) to examine trends in PM_2.5 exposure inequality in Massachusetts. The AI_BG is a relative metric that uses average exposure as the reference and includes an explicit inequality parameter, ε, which reflects the level of societal concern for inequality (Harper et al., 2013). The AI_BG ranges from zero to one, with higher values indicating a less-equal distribution. Following Rosofsky et al. (2018), we calculate the AI_BG as follows:

$${AI}_{BG}=1-{\left(\sum _{j=1}^n{f}_j{\left[\frac{\stackrel{-}{y_j}}{\stackrel{-}{y}}\right]}^{1-\epsilon }\right)}^{\frac{1}{1-\epsilon }}$$ (5)

where n represents the number of subgroups in the population, f_j represents the fraction of the total population in each subgroup, ӯ_j represents mean exposure of each subgroup, and ӯ represents the mean exposure over the full population within a given geographic boundary (i.e., state).

Here we set ε to 0.75 consistent with previous studies (Fann et al., 2018; Fann et al., 2011; Levy et al., 2006; Rosofsky et al., 2018). We perform all AI_BG calculations using the inverse of the PM_2.5 concentrations, since the AI was originally developed for income distributions, where high income is considered desirable, whereas we are assessing PM_2.5 exposure, where high exposure is undesirable (Harper et al., 2013; Rosofsky et al., 2018).

3. Results and Discussion

3.1. 2011 PM_2.5 Concentrations

Annual average PM_2.5 concentrations predicted by the nine models are shown in Figure 1. In general, PM_2.5 concentrations are higher in the eastern than western U.S., with some exceptions such as the high concentrations in the San Joaquin Valley and South Coast Air Basin of California. By U.S. climate region (Figure S2), the highest concentrations on average were predicted in the Ohio Valley region, where mean PM_2.5 ranged from 9.2 to 10.7 μg m⁻³ across all models (see Table S1 for the mean and range of model concentrations by region). The lowest concentrations were predicted in the Southwest region, where mean concentrations ranged from 2.6 to 5.3 μg m⁻³. The spatial variation in concentrations in the western U.S., where some of the cleanest and most polluted areas are located, tended to be greater than in the eastern U.S. (Figure 1).

Figure 1.

Annual average PM_2.5 concentrations (μg m⁻³) in 2011 based on nine exposure models averaged to a common 12-km grid.

The model predictions are in general agreement and are consistent with previous observation-based characterizations of PM_2.5 spatial distributions in the U.S. (Hand et al., 2012; USEPA, 2019). However, differences in the methodologies and input datasets lead to a range of model predictions. For instance, the CTMs predicted lower domain-wide average concentrations than the non-CTM models (i.e. 5.7 μg m⁻³ vs. 6.3 to 7.6 μg m⁻³) but relatively high concentrations in urban areas in the eastern U.S. (Figure 1). The standard deviation (sd) across the models (excluding the CTMs) is shown in Figure 2a to illustrate the spatial distribution of the spread in model predictions (see Figure S3 for the maximum difference across models). The median (25th, 75th percentile) sd over all U.S. grid cells is 1.00 (0.78,1.26) μg m⁻³, with the highest values in the western U.S. The sd divided by the mean (i.e., the coefficient of variation, cv) is shown in percentage units in Figure 2b. The median (25^th, 75^th percentile) cv over all U.S. grid cells is 15.49 (9.34,25.19) %. The cv is lower in the east than the west—e.g., the median value is 9.60% for grid cells east of 100W and 25.05% for cells west of 100W. This difference is due in part to the generally higher PM_2.5 concentrations in the eastern than western U.S. Modeling PM_2.5 concentrations in the west is more challenging than in the east due to factors such as complex terrain, prevalent wildfire, relatively sparse monitoring, and areas with low PM_2.5 concentration and sharp PM_2.5 gradients (Di et al., 2016; Geng et al., 2018; Kelly et al., 2019b).

Figure 2.

Standard deviation and coefficient of variation for PM_2.5 concentrations from the exposure models in Figure 1, excluding the CTMs (CMAQ and CAMx).

The sd has limited variation as a function of PM_2.5 concentration, with slightly higher values in the 5–7 μg m⁻³ range (Figure S4a). In contrast, the cv increases with decreasing PM_2.5 concentration (Figure S4b). Previous studies have reported some degradation in the R² performance statistic with decreasing concentration, whereas bias and RMSE were relatively insensitive to concentration (e.g., Just et al., 2020; van Donkelaar et al., 2019). This behavior could be due to increases in the proportion of the PM_2.5 distribution that is explained by less predictable stochastic variation as concentrations decrease (Just et al., 2020). The implications for specific applications of differences in performance according to different metrics is an area of current research and relates to what types of performance are most relevant for the research question of interest (e.g., daily variation or absolute pollutant levels).

In Figure 3a, PM_2.5 concentrations over Los Angeles in 2011 are shown for the exposure fields averaged to a common 12-km grid. The spatial distributions in PM_2.5 concentrations vary across methods, but realistic features are generally evident in the fields. These features include relatively high PM_2.5 concentrations near downtown LA, the Long Beach ports, and to the east of downtown LA (i.e., downwind of LA on the sea-breeze). Also, the methods generally capture the relatively low PM_2.5 over the mountains to the north of LA, although this feature is muted in the relatively smooth VNA and Downscaler fields. Since VNA predictions are based solely on monitor data, the limited basin-to-mountain gradient in PM_2.5 concentrations may be attributed to limited monitoring in the elevated terrain. The higher PM_2.5 concentrations for CMAQ than CAMx could be related to differences in the emission inventories and potentially less atmospheric mixing in CMAQ (updates were made to enhance mixing in CMAQ version 5.1 (USEPA, 2015b) compared with version 5.0.2 used here).

Figure 3.

Annual average PM_2.5 concentrations over Los Angeles in 2011 based on (a) 12-km and (b) 1-km gridded exposure fields, and (c) difference between 12-km and 1-km fields (12 km – 1 km).

In Figure 3b, PM_2.5 concentrations over Los Angeles are shown for the three 1-km fields. Terrain features and fine-scale spatial variability in PM_2.5 over the area are better represented in the 1-km than 12-km fields. However, differences in fine-scale spatial features exist among the three 1-km exposure fields, and some of the features are counterintuitive. For instance, PM_2.5 concentrations are slightly lower over the major roadways than over neighboring areas in the DI2019 method (the opposite pattern exists in some other urban areas such as Denver, Figure S5), and roadway features are indistinct in the DI2016 and VD2019 fields. Variability in the roadway features across cities in the DI2019 method may be due to differences in the relative values of the predictor variables (e.g., elevation) or influence of base learners across cities. Differences in roadway features between DI2016 and DI2019 could be related to the use of random forest and gradient boosting (in addition to neural network) in DI2019 but neural network alone in DI2016, since both models were trained using road density variables. Traffic influence was considered indirectly in the VD2019 method (via AOD, GEOS-Chem, and monitoring), which may not fully resolve the fine-scale features associated with roadways. Considering that the models were optimized over large domains (i.e., conterminous U.S. for DI2016 and DI2019, and North America for VD2019) using different data and algorithms, differences in fine-scale features among the models are not surprising. For city-specific applications, recent studies have demonstrated the promise of urban-scale models that incorporate non-regulatory data (Huang et al., 2019) and low-cost monitors (Bi et al., 2020; Eilenberg et al., 2020; Li et al., 2020).

In Figure 3c, the difference in PM_2.5 concentrations between the 12-km and 1-km grids is shown. The largest differences occur for grid cells that span a wide range of terrain. For instance, a band of cells to the north of Pasadena had lower concentrations at 12-km than 1-km resolution just south of the mountains, and higher concentrations over the mountains. Similarly, relatively large differences between 12-km and 1-km fields are evident for cells to the east of LA that include a relatively wide range of terrain elevation (e.g., see VD2019 field). Spatial maps for additional urban areas are provided in Figures S5-S10 to further illustrate features of the exposure fields.

3.2. ΔPM_2.5 Concentrations: 2028–2011

The modeled change in PM_2.5 concentrations between the simulations for 2028 and 2011 is shown in Figure 4. Nationally, the average ΔPM_2.5 ranged from −0.85 to −1.02 μg m⁻³ across the models. Regional air quality improvements were greater than the national average for the Ohio Valley region (−2.1 to −2.4 μg m⁻³) and lower for the Southwest region (−0.1 to −0.2 μg m⁻³). These patterns are consistent with the locations of the modeled emission reductions (e.g., large SO₂ emission reductions from electric generation units were projected for the Ohio Valley region).

Figure 4.

Change in annual average PM_2.5 concentrations (2028–2011; μg m⁻³) based on nine exposure models averaged to a common 12-km grid.

Since the same RRFs (i.e., from CAMx) were used to project all exposure fields, the differences in ΔPM_2.5 among models are associated with differences in the 2011 PM_2.5 concentrations alone (i.e., PM2.5_Mod,2011 in Eqn. 3). The spatial patterns of ΔPM_2.5 in Figure 4 therefore resemble the concentration fields in Figure 1 (e.g., Downscaler predicts relatively large, smooth values in the Ohio Valley and CMAQ predicts relatively narrow peaks in urban areas). The spatial distribution of the maximum difference in ΔPM_2.5 across the non-CTM models is illustrated in Figure S11. Developing RRFs from multiple CTM simulations would introduce additional variability into results, although such modeling is not available.

In Figure 5, distributions of ΔPM_2.5 are shown as a function of different strata of the 2011 PM_2.5 concentrations for the different models. The air quality improvements from 2011 to 2028 generally increase with increasing 2011 concentration. This behavior reflects the influence of emission reductions from sources that contributed to the relatively high PM_2.5 concentrations in 2011. There was general agreement in ΔPM_2.5 estimates among models as a function of 2011 PM_2.5 concentration, especially for the non-CTM models. For instance, the median ΔPM_2.5 ranged from −1.77 to −2.01 μg m⁻³ across models for 2011 PM_2.5 concentrations between 9 and 11 μg m⁻³. The range in the median ΔPM_2.5 across methods is slightly greater for 2011 concentrations between 7 and 9 μg m⁻³ (−0.95 to −1.54 μg m⁻³) and 11 and 20 μg m⁻³ (−1.92 to −2.67 μg m⁻³). Overall, the impacts of the emission changes on PM_2.5 concentrations are broadly consistent among methods, although the CTMs tended to have slightly greater impacts, which may be due to the larger uncertainty in the CTM simulations than the observationally constrained methods. Note also that the agreement in ΔPM_2.5 among models is due in part to the use of the same RRFs for projecting the 2011 PM_2.5 fields. Uncertainty in the RRFs, which was not examined here, likely contributes more to the uncertainty in ΔPM_2.5 than does uncertainty in 2011 PM_2.5 field.

Figure 5.

Box and whisker plot depicting distributions of modeled ΔPM_2.5 (2028–2011) as a function of 2011 PM_2.5 concentration. The boxes bracket the interquartile range (IQR; 25th to 75th percentiles), the horizontal line within the box represents the median, whiskers represent 1.5 times the IQR from either end of the box, and circles represent individual values less than and greater than the range of the whiskers, respectively.

3.3. Population Exposure

In this section, we combine the modeled PM_2.5 concentrations with population data to examine PM_2.5 exposure levels in an approach often called population-weighting. In Figure 6a, the percentage of U.S. grid cells and population exposed to 2011 PM_2.5 levels are shown for the exposure models. For instance, a negligible percentage of grid cells have concentrations less than about 2 μg m⁻³ across all models, and almost all grid cells have concentrations less than about 12.5 μg m⁻³ (Figure 6a, left panel). A roughly 2.8 μg m⁻³ spread exists among models (1.7 μg m⁻³ excluding the CTMs) in the concentration predicted at the 50% exposure level across U.S. grid cells. Agreement is closer for population-weighted averages (Figure 6a, right panel) than uniformly weighted averages across the domain. A roughly 1 μg m⁻³ spread exists among models (0.8 μg m⁻³ excluding the CTMs) in the concentration predicted at the 50% exposure level for the U.S. population. The closer agreement in terms of population weighting than for equal weighting of all grid cells is because relatively large differences among models occur in sparsely populated parts of the western U.S. (e.g., Figure 2a).

Figure 6.

The percentage of (a) U.S. grid cells and population exposed to PM_2.5 concentrations less than the values depicted by the curves and (b) U.S. population exposed to ΔPM_2.5 concentrations less than the values depicted. Population data is based on the 2010 Census.

Cumulative exposure curves for the U.S. population to ΔPM_2.5 concentrations (2028 – 2011) are shown in Figure 6b. Good agreement exists among model estimates for population-weighted ΔPM_2.5 concentrations. For instance, a 0.2 μg m⁻³ spread exists among models in the ΔPM_2.5 concentration predicted at the 50% exposure level. The agreement among models is due in part to the use of the same RRFs in projecting all exposure fields from 2011 to 2028. Overall, the results in Figure 6 indicate that agreement among models is closer for population exposure than for average domain levels, and the change in population exposure is relatively insensitive to differences in the baseline exposure field. However, CTM results deviate by a relatively large amount from the other models and demonstrate the value of calibrating CTMs with monitoring data in exposure applications.

Modeled 2011 PM_2.5 exposure concentrations are shown for the total population and the four racial/ethnic groups in Figure 7a. The spread among the non-CTM models in the average population-weighted concentration ranges from to 0.5 to 0.9 μg m⁻³ for the five population categories. The relative rank in exposure concentration for the racial/ethnic groups is similar among models, with all models estimating the lowest exposure concentrations for the NH-white population and highest for the NH-Black population. This result is consistent with previous studies (Bell and Ebisu, 2012; Miranda et al., 2011). Population-weighted average concentrations for the 1-km fields (i.e., DI2016, DI2019, and VD2019) are generally similar to those for the respective 12-km fields, but with slightly higher values for the 1-km field in the DI2019 (up to 0.3 μg m⁻³) and VD2019 (up to 0.5 μg m⁻³) cases (Figure S12).

Figure 7.

Population-weighted average (a) 2011 PM_2.5 and (b) ΔPM_2.5 (2028–2011) concentrations for the total population and four racial/ethnic groups based on 2010 Census data. DS: Downscaler.

Population-weighted average ΔPM_2.5 concentrations (2028–2011) are shown for the total population and four racial/ethnic groups in Figure 7b. The values are similar among models for the five population groups. The NH-Black population, which experienced the highest exposure in 2011, is projected to experience the greatest reduction in exposure among racial/ethnic groups by 2028. The smallest air quality improvement is projected for the Hispanic group, possibly due to the relatively large percentage of the Hispanic population in the western U.S. and parts of the domain that experienced fewer PM_2.5 reductions (c.f., Figure S13 and Figure 4). On a percentage basis, the reductions in population-weighted PM_2.5 between 2011 and 2028 were similar for the NH-white (−19%) and NH-Black (−20%) populations and slightly lower for the Hispanic population (−15%).

In Figure 8a, the difference in population-weighted PM_2.5 concentrations between the highest and lowest exposed racial/ethnic group (i.e., the exposure gap) is shown by state, with labels for the highest exposed group when differences exceed 0.5 μg m⁻³ (this value was selected considering the sd among model predictions, discussed below). Results in Figure 8a are based on the mean concentration across the non-CTM models. The exposure gap in 2011 is less than 1 μg m⁻³ in most states but approaches 2 μg m⁻³ in Arizona and South Dakota. The relatively large gaps in these states appear to be driven by the distribution of the NH-Black population toward the the cities (e.g., Soux Falls, SD and Pheonix, AZ), where PM_2.5 concentrations are relatively high, compared with the relatively broad distribution of the NH-other population throughout the state, where PM_2.5 concentrations are lower on average (c.f., Figure 1 and Figure S13). The distributions of the NH-other population in these states appear to be strongly influenced by those of the American Indian and Alaskan Native population (Figure S14). The exposure gap is projected to decrease from 2011 to 2028, with most states having values less than 0.5 μg m⁻³ and all states having values less than 1.5 μg m⁻³ in the 2028 case. This projected decrease continues a trend of decreasing absolute exposure disparity associated with roughly proportional reductions in PM_2.5 concentrations in recent decades (Colmer et al., 2020).

Figure 8.

(a) Difference in population-weighted PM_2.5 concentration based on the mean of the non-CTM models between the highest and lowest exposed racial/ethnic group (i.e., exposure gap) with labels for the highest exposed group when differences exceeded 0.5 μg m⁻³ and (b) the sd of the exposure gap calculated from the seven non-CTM models, with the number of models that identified the same most-exposed group as the median field.

Although the general patterns in Figure 8a are consistent with results for the individual models (Figure S15), some variability in the magnitude of the exposure gap and identity of the most-exposed group is evident. In Figure 8b, the sd of the exposure gap across the non-CTM models is shown along with the number of models that identified the same most-exposed group as for the mean concentration field used in Figure 8a. The sd for the fields is less than 0.5 μg m⁻³ in all states except Wisconsin, where a relatively large difference in concentration between the urban and northwestern areas led to a greater gap in the VD2019 field (c.f. Figure 1 and S15). Also, there is general agreement in the most exposed group among models (Figure 8b). This agreement builds confidence in the use of the models for large-scale exposure applications, although distinguishing small differences in exposure among groups in a given area may require development of an area-specific model that incoporates local information.

In Figure 9, the AI_BG for 2011 and 2028 is shown by state based on the mean PM_2.5 concentrations across the seven non-CTM exposure models. The spatial pattern of AI_BG resembles that of the exposure gap metric in Figure 8a, with relatively high values in SD, AZ, NM, NY, and CA. The AI_BG also decreases from 2011 to 2028 due to reductions in the relatively high PM_2.5 concentrations (Figure 5) that narrow the distribution of exposure across groups in 2028. However, the sd for the AI_BG appears to be relatively large in relation to the mean compared with the exposure gap metric. For example, the cv is 99% for the AI_BG in South Dakota in 2011, compared with 23% for the exposure gap. The relatively large cv for the AI_BG might be related to the use of the mean concentration as the reference (Eqn. 5) compared with the best-off group for the exposure gap metric (i.e., deviations from the mean may be harder to distinguish compared with the full exposure gap). This information, as well as the general consistency in results for AI_BG and the exposure gap and other properties of the metrics (Harper et al., 2013; Levy et al., 2006), may be useful in guiding future study design.

Figure 9.

(a) AI_BG for 2011 and 2028 based on the mean PM_2.5 concentrations from the non-CTM models and (b) the sd of the AI_BG calculated from the seven non-CTM models.

4. Conclusions

At regional and national scales, the nine exposure models provided broadly consistent estimates of annual average 2011 PM_2.5 concentrations, with relatively high concentrations in the eastern U.S. and more variability in the west. The general agreement among the non-CTM models suggests that exposure studies based on the individual models may yield broadly similar conclusions in some cases. Yet differences in model performance for the methods are evident from previous reports, and some differences in PM_2.5 concentration predictions were found here due to the differences in model algorithms and input data. The median sd for the non-CTM models that had been averaged to a common 12-km grid was 1.00 μg m⁻³ nationally. The CTMs, which are not constrained by observations, predicted lower domain-average concentrations than the other models (i.e. 5.7 μg m⁻³ vs. 6.3 to 7.6 μg m⁻³) but relatively high concentrations in urban areas in the eastern U.S.

All models estimated relatively high PM_2.5 concentrations over urban areas compared with surrounding areas, but differences in the spatial patterns within urban areas were evident. Fine-scale features associated with terrain and major roadways that were present in the 1-km fields were largely removed when concentrations were based on the 12-km grid. However, fine-scale features were inconsistent among the 1-km fields. Considering these differences and the similarity in results for the 12-km and 1-km fields in terms of national population-weighted concentrations and model-observation comparisons, the 12-km resolution may be justified for estimating exposure statistics over large domains. High-resolution exposure applications for individual cities may benefit in the future from the development of city-specific models that incorporate local information (e.g., low-cost sensors).

PM_2.5 concentrations were estimated to decrease by about 1 μg m⁻³ on average due to modeled emission changes between 2011 and 2028 associated with on-the-books regulations. Decreases of more than 3 μg m⁻³ were predicted in areas with relatively high 2011 PM_2.5 concentrations (e.g., the Ohio Valley region) due in part to SO₂ emission reductions from electric generation units. The projected pattern of greater PM_2.5 improvements for areas with relatively high 2011 PM_2.5 concentrations was generally consistent among the models.

Cumulative distributions of PM_2.5 concentrations over the U.S. illustrated the spread in predicted concentrations among models. For the non-CTM models, a roughly 1.7 μg m⁻³ spread exists in the 2011 PM_2.5 concentration estimated at the 50% exposure level for model grid cells, and a smaller spread (roughly 0.8 μg m⁻³) exists in terms of population exposure. The closer agreement in terms of population-weighted averages than uniformly weighted averages is due to the relatively large differences among models in sparsely populated and monitored parts of the western U.S. About 50% of the population was estimated to experience PM_2.5 concentrations less than 10 μg m⁻³ in 2011 and PM_2.5 improvements of about 2 μg m⁻³ due to modeled emission changes between 2011 and 2028.

Differences in population-weighted concentrations among the non-CTM models ranged from 0.5 to 0.9 μg m⁻³ nationally for the total U.S. population and four racial/ethnic groups. The relative rank in the average exposure concentration for the racial/ethnic groups was similar among models. The NH-Black population was estimated by all models to have the highest PM_2.5 exposure in 2011 and experience the greatest reduction in PM_2.5 exposure between 2011 and 2028.

Eight states were predicted to have exposure gaps among racial/ethnic groups greater than 1 μg m⁻³ in 2011, but this decreased to three states in 2028 due to the modeled emission reductions. The AI_BG metric also suggested improvements in exposure inequality between 2011 and 2028. The projected decrease in absolute exposure inequality continues a trend over recent decades (Colmer et al., 2020). The sd in the AI_BG metric among the non-CTMs was relatively large compared with the sd in the exposure gap metric in relation to the respective values calculated using the mean concentration field. These differences could be due to the use of mean exposure as a reference in the AI_BG metric and best-off group in the exposure gap.

By examining predictions of multiple models, our study provided insights on current exposure modeling methods as well as a thorough characterization of PM_2.5 concentrations and exposure. However, the performance of the individual models and their suitability for operational use varies, and so a multi-model approach may be less effective than a single-model approach in a specific application, and the choice of method may influence results depending on the exposure features that are of interest and model performance. Improved understanding of how model skill in terms of various performance metrics relates to outcomes in specific applications would help inform future study design. Relating the PM_2.5 exposure concentrations described above to health risks would also be valuable.