Assessing PM_2.5 Exposures with High Spatiotemporal Resolution across the Continental United States

Abstract

A number of models have been developed to estimate PM_2.5 exposure, including satellite-based aerosol optical depth (AOD) models, land-use regression or chemical transport model simulation, all with both strengths and weaknesses. Variables like normalized difference vegetation index (NDVI), surface reflectance, absorbing aerosol index and meteoroidal fields, are also informative about PM_2.5 concentrations. Our objective is to establish a hybrid model which incorporates multiple approaches and input variables to improve model performance. To account for complex atmospheric mechanisms, we used a neural network for its capacity to model nonlinearity and interactions. We used convolutional layers, which aggregate neighboring information, into a neural network to account for spatial and temporal autocorrelation. We trained the neural network for the continental United States from 2000 to 2012 and tested it with left out monitors. Ten-fold cross-validation revealed a good model performance with total R² of 0.84 on the left out monitors. Regional R² could be even higher for the Eastern and Central United States. Model performance was still good at low PM_2.5 concentrations. Then, we used the trained neural network to make daily prediction of PM_2.5 at 1 km×1 km grid cells. This model allows epidemiologists to access PM_2.5 exposure in both the short-term and the long-term.

Graphical abstract

1. Introduction

Fine particulate matter (PM_2.5) is a major concern in public health.^1-6 An adverse health effect is associated with PM_2.5 exposure in the short term^{7, 8} and the long term.^{9, 10} PM_2.5 is found to be associated with morbidity,^{11, 12} mortality,⁶ cardiovascular disease,⁴ respiratory disease,¹³ myocardial infarction,¹⁴ an increase in hospital admission^{11, 15, 16} and others.¹⁷

Accurate exposure assessment of PM_2.5 is a prerequisite of to investigate its adverse health effect. Early studies estimated PM_2.5 at the nearest monitoring station.¹⁸ However, nearest monitors cannot capture all variability in PM_2.5 concentrations and nondifferential misclassification occurs.¹⁹

Various approaches have been developed to achieve better exposure assessment. Spatial interpolation, including nearest-neighbor interpolation and Kriging interpolation, was used to smooth PM_2.5 concentration and estimate local exposure. Nonetheless, interpolation adds no additional information to the model. Local emission like highways between two monitor sites is not captured by simple interpolation. Land-use regression (LUR) uses land-use terms, such as road density, percentage of urban and others, as proxies for PM_2.5 concentration.^{20, 21} Although LUR could achieve a high spatial resolution, it has limited temporal resolution since land-use terms are usually time-invariant.²² Recent improvements in land-use regression enable incorporation some level of time-variant factors,^{23, 24} but land-use terms are still inadequate in modeling short-term variations and often limited by short temporal coverage.²⁵

Satellite-based aerosol optical depth (AOD) measurements have been widely used to estimate PM_2.5 in various models for its large spatial coverage and repeated daily observations.²⁶ AOD measures the light extinction due to aerosol in the whole atmospheric column.²⁷ To obtain ground-level PM_2.5 concentration, vertical distribution of aerosol is needed. Recent studies proposed different calibration methods.^{26, 28-32} Most studies focused on quantifying relationship between AOD and PM_2.5 or predict a long-term average of PM_2.5, while epidemiological studies also need short-term PM_2.5 assessment. Some studies combined AOD and land-use regression and used mixed effect model to achieve improvements on model performance.^33-35 However, the drawback of AOD is missing data, which is caused by bright surfaces or cloud contamination, especially in winter.³⁶ Also, AOD measurements may also have abnormally large values caused by forest fires.³⁷ For grid cells with missing or abnormal values, the AOD-PM_2.5 relationship may be problematic, especially for daily PM_2.5 assessment. The relationship between column aerosol concentration and ground-level concentration can be influenced by multiple factors such as meteorological fields, chemical profile of aerosol, and others.^{38, 39} The absorbing aerosol index (AAI) provides information about aerosol type and is informative to PM_2.5 modeling.^{40, 41}

Chemical transport models (CTMs), like GEOS-Chem,⁴² CMAQ,⁴³ and CHIMERE,⁴⁴ simulate the formation, dispersion and deposition of fine particles based on emission inventories and known atmospheric chemical reaction. CTM is another way to assess PM_2.5 concentration. Due to the complexity of reactions and atmospheric meteorological processes, simulated concentration often deviates from the real world. CTM outputs are often used after calibration.^{45, 46} CTM provides an aerosol vertical profile, which has been used as scaling factor in AOD calibration.^{29, 47} Due to the limit of computation, CTM usually has coarse spatial resolution. In a previous study, we have proposed a hybrid model which uses land-use regression to downscale CTM outputs. ⁴⁸

Existing approaches have both strengths and weaknesses, and often they complement to each other. In this paper, we incorporated multiple variables into a neural network-based hybrid model, including satellite-based AOD data, AAI, CTM outputs, land-use terms, and meteorological variables. We validated the model with 10-fold cross-validation and predicted daily PM_2.5 at 1 km×1 km resolution in the continental United States for the years 2000-2012. Prediction with such a high temporal and spatial resolution allows epidemiological studies to estimate health effect of PM_2.5 with greater reliability.

2. Materials

2.1. Study Domain

The study domain is the continental United States, including 48 contiguous states and Washington, D.C (Figure S1). The study period is from January 1st, 2000 to December 31st, 2012, a total of 4,749 days.

2.2. Monitoring Data

Monitoring data for PM_2.5 were collected by EPA Air Quality System (AQS). In total, there were 1,986 monitor stations available in this period and 1,928 of them were located in the study area. Not every monitoring site has data available throughout the study period. Monitoring sites were densely distributed along coastal areas and the Eastern part, while there were a few monitors in the Mountain Region (Figure S1). We calibrated our hybrid model to the daily average of monitored PM_2.5.

2.3. AOD Data

The Moderate Resolution Imaging Spectroradiometer (MODIS) is an instrument aboard the Earth Observing System (EOS) satellite.^{49, 50} Several algorithms have been developed to retrieve AOD data from MODIS measurement,⁵¹ including a recent algorithm called MAIAC, which retrieves AOD with a spatial resolution of 1 km×1 km.^52-54 We used MAIAC AOD data from Aqua satellite from 2003 to 2012 and Terra satellite from 2001 to 2012. The MAIAC algorithm arranges data at 600 km×600 km tile, which includes 360,000 1 km×1 km grid cells. In total 33 tiles and 11,880,000 grid cells were used in this study, which is also the grid cell we made predictions at. Grid cells over water bodies were excluded from the study.

AOD data has some portion of missing values, especially in the winter. Missing values are caused by bright surfaces (e.g. snow coverage) and cloud contamination.³⁶ In addition, AOD data may have abnormally large values due to extreme events like forest fires.³⁷ Usually AOD data with values above 1.5 are excluded from modeling, which also creates missing values.⁵⁵ Our previous study calibrated column aerosol mass from CTM outputs to satellite-based AOD and predicted AOD values when satellite-based AOD are missing.⁵⁶ For AOD data used in this study, we filled in the missing values using this method as preprocessing (Section 3, Supplementary Material).

2.4. Surface Reflectance

Surface characteristics and errors in AOD data products have been well documented by previous studies.⁵⁷ The MAIAC algorithm was designed to retrieve AOD over various surfaces, but surface brightness can still affect data quality.⁵⁴ We used MODIS surface reflectance data (MOD09A1) to control for that.⁵⁸ MOD13A1 has a spatial resolution of 500 m×500 m and a temporal resolution of 8 days. We used surface reflectance from Band 3 and linearly interpolated values for days without measurements.

2.5. Chemical Transport Model Outputs

We used GEOS-Chem, a chemical transport model, to simulate ground-level PM_2.5 concentration. GEOS-Chem is a global 3-dimensional chemical transport model, which uses meteorological inputs and emission inventories to simulate atmospheric components. The details of GEOS-Chem is articulated somewhere else.⁴² We performed a nested grid simulation (Version 9.0.2) for North America at 0.500°×0.667° from 2005 to 2012, with boundary conditions exported from a 2.0°×2.5° global simulation. Since meteorological inputs at 0.500°×0.667° are not available from 2000 to 2004, we used 2.0°×2.5° outputs instead. Based on previous studies and pilot testing, total PM_2.5 was defined as the sum of nitrate, sulfate, elemental carbon, organic carbon, ammonium, sea salt aerosol, dust aerosol and others (Table S2).⁵⁹

In additional to providing ground-level PM_2.5 estimation, GEOS-Chem also simulates vertical distribution of aerosol, which could be used for calibrating AOD. Previous studies used GEOS-Chem to compute the percentage of ground-level aerosol in the total column aerosol. This percentage was used in AOD calibration as a scaling factor.^{29, 60} Both studies utilized GEOS-Chem to provide both direct estimation for ground-level PM_2.5 and a scaling factor to calibrate AOD.

2.6. Meteorological Data

Meteorological fields were obtained from NCEP North American Regional Reanalysis data, which assimilates various data sources like land-surface, ship, radiosonde, pibal, aircraft, satellite and others.⁶¹ Meteorological data are daily estimate at 0.3° grid cells (about 32 km). In total 16 meteorological variables were used in this study. They include air temperature, accumulated total precipitation, downward shortwave radiation flux, accumulated total evaporation, planetary boundary layer height, low cloud area fraction, precipitable water for the entire atmosphere, pressure, specific humidity at 2m, visibility, wind speed, medium cloud area fraction, high cloud area fraction, and albedo. Wind speed was computed as the vector sum of u-wind (east-west component of the wind) at 10m and v-wind (north-south component) at 10m.

2.7. Aerosol Index Data

Absorbing aerosol index (AAI) indicates the presence of absorbing aerosols in the atmosphere. Major sources of absorbing aerosol include biomass burning and desert dust; other minor sources could be volcanic ash.⁶² AAI is informative for estimating absorbing aerosols, such as organic carbon and soil dust.^{63, 64} We used AAI Level 3 data products from the Ozone Monitoring Instrument (OMI), where two algorithms are used in retrieval. One is a near-UV algorithm, which retrieves UV aerosol index (OMI data product OMAERUVd);^{62, 64} and the other one uses multiwavelength aerosol algorithm, whose outputs include aerosol indexes at visible and UV range (OMI data product OMAEROe).⁶⁵ Both algorithms have pros and cons, which have been discussed previously.⁶⁶ Both data products are complementary, and thus we used both. OMI AAI data is available after October 2004. OMAERUVd data product has a spatial resolution of 1°; OMAEROe data product has a spatial resolution of 0.25°.

2.8. Land-use terms

Land-use terms serve as proxies for emissions and are used to capture variations at a small a spatial scale, which may not modeled by GEOS-Chem. The detailed process of obtaining land-terms like elevation, road density, NEI (National Emissions Inventory) emission inventory, population density, percentage of urban, and NDVI has been reported somewhere else.⁶⁷ For vegetation coverage, we used percentage of vegetation from NCEP North American Regional Reanalysis data and MODIS MOD13A2, a NDVI data product.⁶⁸ MOD13A2 has a spatial resolution of 1 km×1 km and a temporal resolution of 16 days. We linearly interpolated NDVI values for days without measurements.

2.9. Regional and Monthly Dummy

Previous studies found the relationship between AOD and PM_2.5 have regional and daily variation due to the difference in meteorology and aerosol composition.^{38, 69} Atmospheric mechanism is complex, and relationships between other variables could also differ temporally and spatially. To account for that, we used monthly and regional dummy variables. Regional dummy variable comes from major climate types in the United States (Figure S3).⁷⁰ Since the AOD-PM_2.5 relationship can change from day to day, daily dummy variables would be ideal. However, training a neural network with 365 indicator variables in addition to the other variables would be computationally intensive, and we used monthly dummy variables as a compromise.

3. Methods

We trained a neural network with the above variables to PM_2.5 monitoring data from the AQS network. The relationships between input variables and PM_2.5 could be highly nonlinear with complex interactions. Neural networks have the potential to model any type of nonlinearity.^{71, 72} The details of the neural network, such as its structure and training method were articulated in the supplementary material. All input variables covered the entire study area, but some of them were not available in early years or had higher proportions of missing values. Missing values were especially common in Terra and Aqua AOD data. To deal with the missing values problem and different temporal coverages, we adopted the following steps. We used a calibration method to fill in the missing values in Aqua AOD data from 2003 to 2012 and Terra AOD data from 2001 to 2012 based on the association of GEOS-Chem outputs and land-use terms with non-missing AOD.⁵⁶ For the other variables with a low fraction of missing values, we interpolated at grid cells with missing values. Regarding temporal coverage, GEOS-Chem outputs, land-use terms, MODIS outputs, and meteorological variables were available throughout the study period. OMI data, Aqua AOD, and Terra AOD were unavailable in earlier years. For years with one or more unavailable variables, we fitted the model with the remaining available variables.

Most previous studies used only in situ variables for modeling. However, information from a neighboring cell can be informative as well. For example, nearby road density, forest coverage and other land-use variables as well as nearby PM_2.5 measurements either influence or correlate with local PM_2.5 measurements. They are informative for modeling and can improve model performance. We accounted for spatial correlation by using convolutional layers in the neural network.⁷³ A convolutional layer is computed by applying a convolution kernel on an input layer. Values from neighboring cells are combined through the use of the kernel function. The kernel takes the form a function (e.g. weighted average with Gaussian weights based on distance) that produces a scalar estimate from the multidimensional inputs. A convolution layer aggregates nearby information and can simulate some form of autocorrelation. We included convolutional layers for land-use terms and nearby PM_2.5 measurements as additional predictor variables to account for spatial autocorrelation. Multiple convolution layers were incorporated to allow the neural network to model even more complex autocorrelation or possible interaction with other variables (Supplementary material). In addition to nearby grid cells, observations from nearby days for the same grid cell can be also informative. To incorporate this, we first fitted a neural network and obtained an initial prediction for PM_2.5. We then computed temporal convolution layers and fitted the neural network again with them (Figure S5).

To validate model results and avoid overfitting, we used 10-fold cross-validation, in which all monitoring sites were randomly divided into 10%-90% splits. The model was trained with 90% of data and predicted PM_2.5 at the remaining 10%. The same process was repeated for other splits. Assembling predicted PM_2.5 at ten 10% testing sets yielded predicted PM_2.5 for all the monitors. We computed correlation between predicted PM_2.5 and monitored PM_2.5. Spatial and temporal R²s were also calculated. Details of calculating R² have been specified in the supplementary material.

The trained neural network was then used to make dailyPM_2.5 predictions for each gridcell (1 km×1 km) for each day.

All programming was implemented in Matlab (version 2014a, The MathWorks, Inc.).

4. Results

To determine input variables, we compared models with different combinations of input variables based on cross-validated total R². Model comparison indicated that (1) a hybrid model performed better than any subset models (Figure S6); (2) scaling factor was better to be incorporated as a separate input layer (Figure S7); (3) convolutional layers for land-use variables and predicted PM_2.5 both improved model performance (Figures S6, S8). Hence, input variables for the final model were GEOS-Chem outputs, Aqua and Terra AOD, scaling factor, OMI AAIs, meteorological variables, NDVI, surface reflectance, land-use terms, convolutional layers, and regional/monthly dummy variables. Table 1 presents model performance after conducting 10-fold cross-validation. Total R² between fitted and monitored PM_2.5 ranged from 0.74 to 0.88 and spatial R² was from 0.78 to 0.88. By season, the model usually performed better in summer, followed by autumn, spring, and winter (Table S3). By region, regions in the Eastern United States had the best model performance, followed by the Central United States. The Pacific and Mountain regions had a less satisfying model performance. We also found R² remained high before 2008 and dropped after 2010 for sub-regions and the whole study area (Table S4). We will discuss possible reasons later. Region name and division are from U.S. census division (Table S1, Figure S2). In terms of spatial pattern, we found an east-west gradient with model performing better in the Eastern and Central United States but less satisfying in the western coast and the Mountain Region (Figure 1). Besides, some areas in the Mountain Region (e.g. Great Basin and Colorado Plateau) with large variability in elevation and surface type have relative low R² all the year round. Even in the Eastern United States, where model performance is high in general, areas along Appalachian Mountains and around Ozark Plateau have less satisfying model performance.

Table 1. Cross-validated R² for the whole study area.

Year	Total R2	RMSE	Spatial R2	RMSE	Temporal R2	RMSE	Bias	Slope
2000	0.86	3.35	0.85	1.52	0.85	3.07	0.22	1.01
2001	0.84	3.58	0.86	1.40	0.83	3.35	0.22	1.01
2002	0.88	2.99	0.88	1.24	0.88	2.75	0.25	1.00
2003	0.88	2.80	0.87	1.21	0.88	2.57	0.23	1.00
2004	0.88	2.69	0.79	1.50	0.88	2.45	0.22	1.00
2005	0.88	2.94	0.84	1.45	0.89	2.66	0.27	1.00
2006	0.86	2.77	0.80	1.34	0.86	2.50	0.25	1.00
2007	0.87	2.95	0.83	1.31	0.87	2.72	0.21	1.00
2008	0.85	2.64	0.79	1.26	0.86	2.40	0.19	1.00
2009	0.82	2.73	0.81	1.09	0.82	2.54	0.21	1.00
2010	0.81	2.85	0.84	1.21	0.81	2.60	0.51	0.98
2011	0.81	2.83	0.81	1.11	0.81	2.60	0.38	0.99
2012	0.74	3.15	0.78	1.16	0.74	2.92	0.32	1.00
Mean	0.84	2.94	0.83	1.29	0.84	2.70	0.27	1.00

Figure 1. Model performance in the continental United States.

We calculated total R² between monitored and predicted PM_2.5 for each monitoring site and interpolated R² to places without monitors using Kriging interpolation. Spring was defined as March to May; summer was defined as June to August; autumn was defined as September to November; winter was from December to February of the next year (same below). The red color stands for high R², and the blue color stands for low R².

Figure 2 shows the spatial distribution of total PM_2.5 in the study area. The Eastern United States generally had higher PM_2.5 levels than the Western part. The area around Illinois and Ohio, areas around New York City and Philadelphia, and parts of the Southeastern United States witnessed the heaviest PM_2.5 pollutions in the study area, especially in summer. The San Joaquin Valley, Salt Lake City, and Denver stood out in the Western United States for their high PM_2.5 levels. Regarding the temporal trend, the national average dropped from 9.2 μg/m³ in 2003 to 7.5 μg/m³ 2012 (Figure 3). By regions, the declining trend was predominantly in the Eastern United States, with largest reduction occurring in East South Central Region (5.8 μg/m³).

Figure 2. Spatial distribution of predicted PM_2.5.

Trained neural network predicted daily total PM_2.5 concentration at 1 km×1 km grid cell in the study area. The red color stands for high concentrations, and the blue color stands for low concentrations.

Figure 3. Annual means by month of year and by region.

Annual averages were computed by averaging all predicted PM_2.5 values at 1 km×1 km grid cells in that region or in that month.

One additional way to validate our exposure estimates is to see if they can reproduce the spatial autocorrelation in PM_2.5 concentrations. To do this, we calculated the correlation among all pairs of PM_2.5 monitors in the EPA network, and plotted them as a function of distance. We compared that to the same plot, but using our predicted PM_2.5 concentrations instead (Figure 4). The results show essential identical trends and substantial overlap between the correlations of actual vs modeled PM_2.5 with distance.

Figure 4. Relationship between correlation and distance between any two monitor sites.

For 1,928 monitoring sites in the study area, we computed the correlation of PM_2.5 measurements and distance (in degree) between any two monitoring site pairs and plotted the between-site correlation versus between-site distance (red dots). We repeated the same process for predicted PM_2.5 and plotted the correlation of predicted PM_2.5 and monitored PM_2.5 between two site pairs versus distance (blue dots). This figure is for year 2012.

5. Discussion

Our hybrid model incorporated existing PM_2.5 models as well as multiple variables and achieved high out-of-sample R²,averaging 0.84 (0.74∼0.88 by year) over the study period. The model performed better in some eastern regions, with an average out of sample R² of 0.86∼0.89 by region. To our best knowledge, our model performance surpasses existing similar studies. Meanwhile, we predicted PM_2.5 daily concentrations at nationwide 1 km×1 km grid cells from 2000 to 2012. As discussed below, this level of resolution and coverage is an improvement over current PM_2.5 models and could be beneficial to epidemiological studies. Epidemiologists could identify long-term and short-term exposure of PM_2.5 in the whole continental United States at individual level, which helps study adverse health effect of PM_2.5 with higher accuracy.

There are several advantages and innovations in our approach. First of all, our model covered the whole United States with a spatial resolution of 1 km×1 km and a temporal resolution of 1 day and achieved high R². As far as we know, if taking coverage, resolution and model performance into consideration, our model performs better than existing models. As mentioned in the Introduction, most PM_2.5 modeling work that used AOD data focused on the AOD-PM_2.5 relationship, instead of making predictions. For studies with a similar research goal as ours, some of them have done AOD calibration at global scale, but their estimation was long-term average²⁹ or annual average, with some degree of bias (slope=0.68) and modest R² (R²=0.65).⁴⁷ A previous study calibrated AOD to daily monitored PM_2.5 in the Northeastern United States using a mixed model and achieved R² around 0.725∼0.904.³¹ A similar study used the similar method for the Southeastern United States and achieved R² around 0.63 to 0.85.³² Compared with both regional models, our hybrid nationwide model performs slightly better in the Northeastern United States and much better in the Southeastern United States (Table S6). One reason is that aerosol formation in the Southeastern United States is affected by biogenic isoprene emission from trees;⁷⁴ while isoprene emission from trees in the Northeastern United States is less of a concern. Secondary organic aerosol that results from isoprene has different absorption than other PM_2.5 components,⁷⁵ which is not well captured by AOD. AAI provides some information about absorption profile, which helps our hybrid model perform much better in the Southeast and almost the same or a little better in the Northeast.

Second, our hybrid model integrated most variables that are known to be informative to PM_2.5 modeling and improved model performance. This study reminds the importance of hybrid framework and also proposes a possible neural network-based approach to implement that. Atmospheric mechanism is complex, and a single variable can only capture an incomplete picture. For example, AOD measures the light extinction due to aerosol in the whole atmosphere column. Different aerosols vary in terms of aerosol absorption, which can affect AOD. More complexly, even the same aerosol type could have various absorptions under different meteorological conditions and emission features.³⁹ This discovery suggests that when modeling PM_2.5 with AOD data, AAI (proxy for aerosol type), meteorological fields, and emission profiles are also necessary. There could be many unknown mechanisms intertwining with other variables. Multiple variables are not redundant but complementary, which can recover the original picture of atmospheric process and improve model performance to the best.

Third, we used a convolutional layer in the neural network for PM_2.5 modeling, which is an innovation of our study. Primarily used in computer science, a convolutional kernel is placed over nearby pixels to produce a convolutional layer. Similarly, we used convolutional layers in exposure assessment to aggregate variable values from nearby grid cells or monitoring sites. Previous studies incorporated nearby information by using nearby monitoring measurements, nearby road density, or others, which were all prespecified. Our hybrid model takes multiple convolutional layers, which stand for various ways of aggregating nearby information, and lets learning algorithm decide their relative importance in the model. This approach is versatile and is able to model different neighboring influences, as well as potential interactions with other variables.

Last but not least, we used AOD data with missing values been filled by some calibration model. No further processing is required to deal with missing AOD data, which could have been lengthy and cumbersome in previous studies.

For the east-west gradient in model performance (Figure 1), previous studies also reported that correlation between MODIS AOD and ground-measured PM_2.5 is better in the eastern part but poor in the western part, and they attributed poor model performance to relative low PM_2.5 level and variability of terrain.^{31, 41} This study lends support to both statements. We quantified the relationship between model performance and elevation at each monitoring site and found a negative correlation despite of much noise (Figure S10). Similarly, a positive association exists between PM_2.5 level and model performance (Figure S10), which implies that the drop of model performance after 2010 is probably caused by substantive reduction in PM_2.5 level after 2010. This is also the reason why the Mountain region, with low PM_2.5 level, has poor model performance. A lower level of PM_2.5 means a lower signal-to-noise ratio, and model performance drops as model uncertainty keeps constant. Besides, the reduction of sulfate is mainly responsible for decreasing the PM_2.5 level. Sulfate is better modeled in GEOS-Chem than other major components like nitrate and ammonium,⁷⁶ so dropping sulfate causes unsatisfying model performance. For the same reason, we saw a less satisfying model performance in California despite its high PM_2.5 level, for the reason that California has a high amount of nitrate originated from vehicle exhaust compared with the Eastern United States. This argument suggests that it would be informative to include sulfate in PM_2.5 modeling work in the future.

Our model performance is still good even at low PM_2.5 levels. To prove that, we fitted a spline regression of prediction PM_2.5 to measured PM_2.5. Linearity between measured and predicted PM_2.5 holds when PM_2.5 level is below 70 μg/m³ and become less obvious above 80 μg/m³ due to insufficient measurements (Figure 5). Bias at high concentration is less of our concern, since there are few days with the PM_2.5 level above 80 μg/m³ in the study area. If constraining to monitored PM_2.5 below 35 μg/m³, the EPA daily standard for PM_2.5, our hybrid model performed even better. Mean R² increased to 0.85; slope is close 1; and intercept is close to 0 (Table S5). Good model performance at low PM_2.5 concentrations enables epidemiologists to estimate the adverse effect of PM_2.5 even below EPA daily standard.

Figure 5. Relationship between measured PM_2.5 and predicted PM_2.5.

We fit a penalized spline between measured PM_2.5 and predicted PM_2.5 without specifying degree of freedom. This figure is for year 2009.

Figure 2 visualizes the spatial distribution of annual and seasonal average of PM_2.5. There is also an east-west gradient of the PM_2.5 level. The Eastern and Central United States suffered relatively heavy PM_2.5 pollutions, except for the Appalachian Mountains, the Florida Peninsula, and some remote areas in the Northeast. The Southeastern United States, especially Alabama and Georgia, witnessed a high PM_2.5 level in summer and less noticeably in spring and autumn, which results from isoprene emission from trees. Isoprene emission from trees increases with temperature^{74, 77} and peaks in hot summer.⁷⁸ The Western United States had relatively low PM_2.5 levels, but the San Joaquin Valley, Salt Lake City, and Denver stood out for their abnormally high PM_2.5 level, which was also featured by clear seasonality and a high PM_2.5 level in winter. This is caused by temperature inversion in winter which prevents atmospheric convection and trapped air pollution near the surface. For temporal trend, the Eastern and Central United States witnessed a decreasing trend in the PM_2.5 level (Figure 3), which is caused by the reduction of sulfur dioxide from power plant emission. For seasonal cycle, PM_2.5 level peaks in summer in the Eastern and Central United States due to long-term transported sulfate from power plants and isoprene-related organic carbon. The winter peaks are probably caused by increased fuel burning for heat and local temperature inversion that prevents pollution dispersion.

Exposure assessments are essential for epidemiological studies. The traditional method of exposure assessment relies on nearest monitors, which constraints the number of available participants and introduces measurement errors. Besides, monitoring data from some monitors are intermittent. Our PM_2.5 predictions have temporal resolution of 1 day and spatial resolution of 1 km×1 km, which lifts the above limitations. Besides, our hybrid model performs still well at low concentrations. Linearity between predicted and monitored PM_2.5 still holds at low concentrations, without any signal of bias (Figure 5). Cross-validated R² indicates a good fit when daily PM_2.5 level is below 35 μg/m³ (Table S5), which enable epidemiologists to assess the adverse effect of PM_2.5 even below the EPA standard. In the long term, there is little discrepancy between long-term averages of predicted and monitored PM_2.5, with difference below 1 μg/m³ (Figure S9).

Some limitations remain. Our model requires quite a lot of variables, which limits the application in other countries. This data-intensive approach could be difficulty in other regions where public data is sparse. For regions with less data available, we might have to make a tradeoff between model performance and resolution. For example, instead of daily prediction PM_2.5 at 1 km×1 km, we may model annual average of PM_2.5 or at coarse spatial resolution. Besides, the chemical profile of PM_2.5 is not available in this framework. Previous epidemiological studies suggest various toxicities of PM_2.5 chemical components,^{79, 80} which is worthy of further investigation.