A New Hybrid Spatio-Temporal Model For Estimating Daily Multi-Year PM_2.5 Concentrations Across Northeastern USA Using High Resolution Aerosol Optical Depth Data

Abstract

Background

The use of satellite-based aerosol optical depth (AOD) to estimate fine particulate matter (PM_2.5) for epidemiology studies has increased substantially over the past few years. These recent studies often report moderate predictive power, which can generate downward bias in effect estimates. In addition, AOD measurements have only moderate spatial resolution, and have substantial missing data.

Methods

We make use of recent advances in MODIS satellite data processing algorithms (Multi-Angle Implementation of Atmospheric Correction (MAIAC), which allow us to use 1 km (versus currently available 10 km) resolution AOD data. We developed and cross validated models to predict daily PM_2.5 at a 1×1km resolution across the northeastern USA (New England, New York and New Jersey) for the years 2003–2011, allowing us to better differentiate daily and long term exposure between urban, suburban, and rural areas. Additionally, we developed an approach that allows us to generate daily high-resolution 200 m localized predictions representing deviations from the area 1×1 km grid predictions. We used mixed models regressing PM_2.5 measurements against day-specific random intercepts, and fixed and random AOD and temperature slopes. We then use generalized additive mixed models with spatial smoothing to generate grid cell predictions when AOD was missing. Finally, to get 200 m localized predictions, we regressed the residuals from the final model for each monitor against the local spatial and temporal variables at each monitoring site.

Results

Our model performance was excellent (mean out-of-sample R²=0.88). The spatial and temporal components of the out-of-sample results also presented very good fits to the withheld data (R²=0.87, R²=0.87). In addition, our results revealed very little bias in the predicted concentrations (Slope of predictions versus withheld observations = 0.99).

Conclusion

Our daily model results show high predictive accuracy at high spatial resolutions and will be useful in reconstructing exposure histories for epidemiological studies across this region.

1. Introduction

The use of satellite-based aerosol optical depth (AOD) to estimate exposure to fine particulate matter (PM_2.5-particulate matter <2.53μm in aerodynamic diameter) concentrations for epidemiologic studies has increased substantially over the past few years (Chang et al., 2013; A. A. Chudnovsky et al., 2013; Chudnovsky et al., 2012; Kim et al., 2013; Kloog et al., 2012b, 2011; Lee et al., 2011; Lin et al., 2013; Nordio et al., 2013). Both short term (hours, days) and chronic (months, years) exposure to PM_2.5 has been extensively associated with detrimental human health effects (Halonen et al., 2008; Kloog et al., 2012a; Peacock et al., 2011; Zanobetti and Schwartz, 2009). Fine PM exposures were found to be associated with respiratory and cardiovascular morbidity, mortality from cardiovascular and respiratory diseases and an increase in hospital admissions (Dominici et al., 2006; Kloog et al., 2012a; Schwartz, 1996)

Traditionally, estimation of PM_2.5 exposures have been based on using measurements of a central ground monitor, and assigning these measurement to populations within a specified distance of the monitor (Laden et al., 2006; Samet et al., 2000). This approach introduces exposure error (also known as exposure misclassification), and likely biases the effect estimates downward due to spatial misalignment (Zeger et al., 2000). In recent years, to avoid this exposure misclassification, many studies have used regression models based on geographic covariates (termed “land use” regressions- LUR) to expand in situ measurements of PM_2.5 concentrations to large areas. LUR is essentially an interpolation technique that employs the PM_2.5 concentrations as the dependent variable, with proximate land use, traffic and physical environmental variables used as independent predictors (Beckerman et al., 2013; Gryparis et al., 2009; Hoek et al., 2008; Vienneau et al., 2010). Since the geographic covariates are generally not time varying, the temporal resolution of the LU model predictions is limited and thus can only be employed to assess long-term exposures for chronic health effects studies. Finally, current exposure assessments are limited to urban areas due to the paucity of monitoring sites in rural locations.

Satellite-based AOD provides physical daily measurements that can be used to estimate air quality and pollution due to its extensive spatial coverage and repeated observations of the earth surface and atmosphere. AOD is a measure of the extinction of electromagnetic radiation at a given wavelength due to the presence of aerosols in an atmospheric column. However, satellite-based AOD is a measure of light attenuation in the column which is affected by ambient conditions (such as vertical profile, chemical composition and humidity). In contrast, PM_2.5 is a measure of dry particle mass near the surface and thus we do not expect them to be strongly correlated (Chudnovsky et al., 2012).

In recent years many studies have used various statistical methods to establish quantitative relationships between AOD and PM_2.5 (Chang et al., 2013; A. Chudnovsky et al., 2013; Cordero et al., 2013; Gupta et al., 2013; Kim et al., 2013). Traditionally, the health exposure studies have used the standard MODIS (Moderate Resolution Imaging Spectroradiometer) AOD product of the “Dark Target” algorithm (Levy et al., 2007) which has a nadir resolution of 10×10 km². Lately, AOD at significantly higher spatial resolution (1×1 km2) has been offered by a new Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm. Chang and colleagues (Chang et al., 2013) used some novel ideas such as a statistical downscaling and data fusion techniques to predict PM_2.5 concentrations at spatial point locations in the southeastern United States during the period 2003–2005. Their model showed relatively high cross-validated predictions (R²=0.78 and a root mean-squared error (RMSE) of 3.61 μg/m³). Chudnovsky and colleagues (Chudnovsky et al., 2014) used one year of observations from MODIS based Aqua at a 1 km spatial resolution to obtain daily PM_2.5 estimates for AOD retrieval days. Their model results indicated that high resolution MAIAC (Multi-Angle Implementation of Atmospheric Correction) data better explains the variations in PM_2.5 However, the developed model was restricted to retrieval days, and the out-of-sample predictive performance spatially was similar to that estimated by Chang et al. (spatial R²=0.79)

These recent studies, while generally showing better fits than previous models, still leave room for improvement in terms of reducing exposure error. In addition, they all lack detailed high resolution predictions across large space-time domains (especially in rural areas) which is critical for acute exposure epidemiologic studies.

In this paper, we incorporate MAIAC-based AOD satellite data which allows us to present a much simplified model, while still improving significantly over currently available models. We developed and validated models to predict daily PM_2.5 at a 1×1 km resolution across the northeastern USA (New England, New York and New Jersey) for the years 2003–2011, allowing us to better differentiate daily and long term exposure between urban, suburban, and rural areas. Additionally, we developed an approach that allows us to generate daily high-resolution 200×200 m localized predictions that are separate from the area 1×1 km grid predictions.

2. Material and Methods

2.1 Study domain

The spatial domain of our region included the Northeastern part of the USA (Figure 1), and includes the states of Connecticut, Maine, Massachusetts, New Hampshire, New Jersey, New York, Rhode Island and Vermont. Many urban areas (notably New York and Boston) are included as well as rural hill towns, large forested regions, water bodies, mountains and the Atlantic sea shoreline. The study area included 285,284 discrete 1×1km satellite grid cells.

Figure 1.

Map of the study area showing the location of EPA and IMPROVE monitoring sites across the Northeastern USA.

2.2 AOD Data

One of the fundamental aerosol products from MODIS is spectral AOD (sometime referred to as Aerosol Optical Thickness or AOT). This is a global level 2 daily MODIS product. The details of the standard “Dark Target” (DT) MODIS algorithm over land providing 10×10 km2 resolution AOD have been broadly reported (Levy et al., 2007; Remer et al., 2005). Recently a new processing algorithm (MAIAC) has been developed that provides a high 1km resolution AOD from MODIS data (Chudnovsky et al., 2014; Lyapustin et al., 2011a, 2011b). MAIAC processing begins with the gridding of MODIS L1B data to a fixed 1km grid, and accumulation of up to 16 days of measurements in the memory. Then it uses time series analysis and processing of groups of pixels to derive surface bidirectional reflectance distribution function (BRDF) and aerosol parameters without assumptions typical of current MODIS operational processing algorithms. The spatio-temporal analysis also helps MAIAC’s cloud mask augmenting traditional pixel-level cloud detection techniques. In this analysis we used MAIAC AOD based on collection 6 MODIS Aqua L1B data for the years 2003–2011.

2.3 Monitoring data

Data for daily PM_2.5 mass concentrations across the Northeast region (see Figure 1) for the years 2003–2011 were obtained from the U.S. Environmental Protection Agency (EPA) Air Quality System (AQS) database as well as the IMPROVE (Interagency Monitoring of Protected Visual Environments) network. IMPROVE monitor sites are located in national parks and wilderness areas while EPA monitoring sites are located across the Mid-Atlantic including urban areas such as New York City, Boston, etc. There were 161 monitors with unique locations operating in the Northeast during the study period. The Mean PM_2.5 across the Northeast during the study period was 11.7 μg/m3 with a standard deviation of 7.8 μg/m3 and an interquartile range (IQR) of 9.1 μg/m3.

2.4 Spatial Predictors of PM_2.5

We used a hybrid model, containing both AOD, land use, and meteorological predictors. The following spatial predictors were used: population density, elevation, traffic density, percentages of land use according to 12 land use categories based on United States Geological Survey (USGS) National Land Cover Dataset (NLCD), point emissions and total area-source emissions (tons per year) for PM_2.5, PM₁₀, SO₂, and NO_x.

Elevation

Elevation data were added through a satellite-based digital elevation model from the USGS National Elevation Dataset (NED) covering the United States at a spatial resolution of 1 arc sec (Maune, 2007). There are sharp elevation contrasts across such a large study area and thus we used elevation as a spatial predictor (generally higher elevations are associated with lower air temperatures).

Traffic Density

Road data were obtained through the U.S. Census 2000 topologically integrated geographic encoding and referencing system (TIGER, 2006). We calculated the total A1 road length (class 1 roads that are hard surface highways including Interstate and U.S. numbered highways, primary State routes, and all controlled access highways) across the study area. The A1 roads were intersected with the 1×1 km grid and the resulting attribute tables contained the density of all A1 road segment lengths in each 1 km² grid cells.

Population Density

Population density data were obtained through the U.S. Census 2000 dataset (Census, 2000). We calculated the weight-averaged population for each 1×1 km grid cell based on the tracts intersecting these grid cells.

Point emissions

Additional point emissions data for PM_2.5, PM₁₀, SO₂, and NO_x were obtained through the 2005 U.S. EPA National Emissions Inventory (NEI) facility emissions report (EPA, 2010). Locations reporting zero emissions within the appropriate grid cell were assigned a value of one-half of the minimum value among all monitoring locations.

Area-source emissions

Area-source PM_2.5, PM₁₀, SO₂, and NO_x emissions data were obtained through the 2005 U.S. EPA-NEI tiered emissions reports (EPA, 2010), which provide estimates of total area-source emissions by county and year. Intersecting source emission areas for each 1×1 km grid were calculated by weight averaging the values from each intersecting areas intersecting n each 1×1km grid cell.

Percentages of land use

We used the NLCD from 2001 (Homer et al., 2004), available as raster files with a 30 m spatial resolution. We calculate the percentages of mixed forest, deciduous forest, evergreen, crop, pasture, grass, shrub, water, high development, medium development, low development and open development areas in each 1×1 km grid across the study area.

2.5 Temporal Predictors of PM_2.5

Meteorological data

All meteorological variables used in the analysis were obtained through the National Climatic Data Center (NCDC, 2010). Only continuous operating stations with daily data running from 2003–2011 were used (26 stations spread across the study area). Grid cells were matched to the closest weather station with available meteorological variables (24h means). We used the following meteorological variables: air temperature, wind speed, daily visibility, sea land pressure (SLP) and relative humidity. All the variables represent 24 hour averages except visibility, which is only computed during daylight hours.

NDVI

We used the publicly available monthly MODIS NDVI (Normalized Difference Vegetation Index) product (MOD13A3) at 1 km spatial resolution. The monthly resolution was chosen since NDVI values do not change considerably within a month except periods of spring green-up and fall senescence.

PBL

We used publicly available daily data on the height of the planetary boundary layer (PBL) obtained from the NOAA Reanalysis Data (NOAA, 2010). The spatial scale of the data was 32×32 km. The height of the boundary layer may vary with wind speed (Oke, 1987), influencing the concentration and vertical profile of pollutants. The boundary layer not only controls transport and location of pollutants and aerosols but also their concentrations would be different in variable boundary layer structures (Angevine et al., 2013).

2.6 Statistical Methods

All modeling was done using the R statistical software version 3.02 and SAS (Statistical Analysis System) version 9.3.

As we have shown in previous studies (Chudnovsky et al., 2014; Kloog et al., 2012b, 2011) there is a varying spatial relationship between AOD and PM_2.5 on a single day due to differences in factors including particle composition, PBL, relative humidity, vertical profiles. Thus, we use a mixed effects model incorporating spatial and temporal predictors and day-specific random-effects to take into account these temporal variations in the PM2.5–AOD relationship. Since the exposure predictions generated by our model are primarily intended for use in epidemiologic health effect studies, we generate exposure predictions at two different spatial scales at which health data are typically collected: small area (zip code, census tract, etc) geocoded data (SAGD) and address-specific geocoded data (RGD). When only SAGD health data is available, we use predictions at the 1×1km grid cell level, whereas when RGD are available, we add an additional local daily estimation component at a very high resolution (200×200m) to the grid-level predictions. Using higher resolution MAIAC data compared to our previous 10×10 km MODIS AOD data allowed us to simplify our approach in this way.

All models were fit to data from each year (2003–2011) separately. To generate the daily 1×1km PM_2.5 predictions in each grid cell for the entire 2003–2011 period, we developed a prediction process using a series of models: The first model calibrates the AOD grid-level observations to the PM_2.5 monitoring data collected within 1km of an AOD value, while adjusting for the land use and meteorological variables. In the second model we predict daily PM_2.5 concentrations in grid cells without monitors but with available AOD measurements using the model 1 fit. Then in the third model, to estimate daily PM_2.5 in grid cells with no AOD on that day, we take advantage of the region-specific association between grid-cell AOD and PM_2.5 levels, and the association between PM_2.5 level in a given grid with that in neighboring grid cells.

To generate the daily 200×200m PM_2.5 local predictions for studies using RGD, we take the residuals of model 3 at each monitoring site (that is the ground level PM_2.5 data minus the model 3 predictions) and regress them against very fine (200×200) monitor-specific spatial and temporal predictors of PM_2.5 which included traffic density, population density, elevation, percent urban, distance to major roads (A1), distance to source emission points, PBL and visibility. This stage allows us to predict local PM throughout the study area on any given day.

To accommodate the fact that daily AOD data missingness is not random, the first stage model incorporated inverse probability weighting (IPW) to potentially avoid bias in the regression coefficient estimates and thus in the resulting predictions. This approach effectively up-weights dates and grid cells which are under-represented due to a large degree of missing data. To obtain the weights that account for the non-random missingness in AOD values, we fit the following logistic regression model for the probability (p) of observing an AOD value in cell i on day j:

$$\begin{array}{l}\mathit{ln}(\frac{\widehat{\mathit{p}}}{\mathbf{1}-\widehat{\mathit{p}}})={\mathrm{\beta }}_0+{\mathrm{\beta }}_1{\text{Elevation}}_{\mathrm{i}}+{\mathrm{\beta }}_2{\text{SLP}}_{\text{ij}}+{\mathrm{\beta }}_3{\text{Temperature}}_{\text{ij}}+\text{Month}\\ \mathit{IPW}=(\frac{1}{\widehat{p}})\end{array}$$ (Equation 1)

where (p) is the probability for availability of AOD in each day in each grid cell in each year. There were no observations which had a disproportionate influence in the yearly models.

Finally, since the daily PM-AOD calibration factors can vary spatially, the study area is divided into 7 regions. The day-specific intercept, AOD, and temperature random effects in the model are nested within regions of the study. Specifically, the first model can be written as

$$\begin{array}{l}{\text{PM}}_{\text{ij}}=(\mathrm{\alpha }+{\mathrm{u}}_{\mathrm{j}}+{\mathrm{g}}_{\mathrm{j}(\text{reg})})+({\mathrm{\beta }}_1+{\mathrm{v}}_{\mathrm{j}}+{\mathrm{h}}_{\mathrm{j}(\text{reg})}){\text{AOD}}_{\text{ij}}+({\mathrm{\beta }}_2+{\mathrm{k}}_{\mathrm{j}}){\text{Temperature}}_{\text{ij}}+{\mathrm{\sum }}_{m=1}^5{\gamma }_{1m}{X}_{1mi}+{\mathrm{\sum }}_{m=1}^{28}{\gamma }_{2m}{X}_{2mj}+{\mathrm{\sum }}_{m=1}^2{\gamma }_{3m}{X}_{3\mathit{mij}}+{\mathrm{\epsilon }}_{\text{ij}}\\ ({\mathrm{u}}_{\mathrm{j}}{\mathrm{v}}_{\mathrm{j}}{\mathrm{k}}_{\mathrm{j}})~N[(000),\mathrm{\sum }]\\ ({\mathrm{g}}_{\mathrm{j}(\text{reg})},{\mathrm{h}}_{\mathrm{j}(\text{reg})}~\mathrm{N}[(00),{\mathrm{\sum }}_{\text{REG}}]\end{array}$$ (Equation 2)

where PM_ij is the measured PM2.5 concentration at a spatial site i on day j; α and u_j are the fixed and random (day-specific) intercepts, respectively, AOD_ij is the AOD value in the grid cell corresponding to site i on day j; β₁ and v_j are the fixed and day-specific random slopes, respectively. Temperature_ij is the temperature value in the grid cell corresponding to site i on day j; and, β₂ and k_j are the fixed and random slopes for temperature. X_1mi is the value of the mth spatial predictor at site i, X_2mj is the value of the mth temporal predictor on day j, and X_3mij is the value of the mth spatial-temporal predictor at site i on day j. g_j(reg) and h_j(reg) are the daily random intercepts and AOD slopes specific to each study area region, nested within the overall random effects u_j and v_j. Here, we assume Σ is a 3 × 3 diagonal matrix with diagonal elements σ²_u, σ²_v, σ²_k,, and Σ_REG is a 2 × 2 diagonal matrix with diagonal elements σ²_g, σ²_h.

We used ten-folds out of sample cross validation (CV) to validate our model 1 predictions. We randomly divide our data into 90 and 10 percent splits ten times. We predict for the 10% data sets using the model fitted from the remaining 90% of the data. We then report these computed R² values. To test our results for bias we regress the measured PM value for a given site and day against the corresponding predicted value. We estimated the model prediction precision by taking the square root of the mean squared prediction errors (RMSPE). In addition we calculated prediction errors from a model that contained the spatial components only, to make it more comparable to the commonly used monthly/yearly prediction models available such as Yanosky (Yanosky et al., 2008). Temporal R² was calculated by regressing Delta PM against Delta predicted where: Delta PM is the difference between the actual PM in place i at time j and the annual mean PM at that location, and Delta predicted is defined similarly for the predicted values generated from the model. Spatial R² was calculated by regressing the site-specific annual means in observed PM versus the same annual means for predicted PM.

The next model (model 2), uses the fit of model 1 to predict a PM_2.5 concentration for each day and grid cell at which we have an observed AOD value. This resulted in yearly datasets with PM_2.5 prediction for all day-grid cell combinations with available AOD.

In model 3 of the sequence, we estimate daily PM_2.5 for all grid cells in the study area even in days when no AOD data are present. We fit a generalized additive model with a smooth function of latitude and longitude (using the grid cell centroids) and a random intercept for each cell. This is similar to other interpolation techniques (universal kriging, etc.) to use nearby grid cells to help fill in the missing, however we also construct a 100 km buffer around each grid cell and fit a regression analysis relating the predicted PM at each grid cell to the the daily mean PM_2.5 from the stations in each buffer around that grid cell, which also aids in predicting the value on missing days. The 100 km buffer size was chosen since we wanted a small enough buffer to ensure relevance and hence improve the R² of the monitored value on the grid cell values, but large enough a buffer to include multiple PM monitors to produce more stable estimates (again improving the prediction R²). To allow for temporal variations in the spatial correlation, we fit a separate spatial surface for each two-month period of each year. Using this method provides additional information about the concentration in the missing grid cells that classic interpolation would not provide. Specifically, we fit the following semiparametric regression model:

$$\begin{array}{l}{\text{PredPM}}_{\text{ij}}=(\mathrm{\alpha }+{\mathrm{u}}_{\mathrm{i}})+({\mathrm{\beta }}_1+{\mathrm{v}}_{\mathrm{i}}){\text{MPM}}_{\text{ij}}+\mathrm{s}{({\mathrm{X}}_{\mathrm{i}},{\mathrm{Y}}_{\mathrm{i}})}_{\mathrm{k}(\mathrm{j})}+{\mathrm{\epsilon }}_{\text{ij}},\\ ({\mathrm{u}}_{\mathrm{i}}{\mathrm{v}}_{\mathrm{i}})~[(\mathbf{0}\mathbf{0}),{\mathit{\Omega }}_{\beta }]\end{array}$$ (Equation 3)

where Pred PM_ij is the predicted PM_2.5 concentration at a grid cell i on a day j from the model 2; MPM_ij is the mean PM in the relevant 100km buffer for site i on a day j; α and u_i are the fixed and grid-cell specific random intercepts, respectively; β₁ and v_i are the fixed and random slopes, respectively. The smooth X_i, Y_i are the latitude and longitude, respectively, of the centroid of grid cell i, and s(X_i, Y_i) _k(j) is the a smooth function of location (modeled by thin plate splines) specific to the two-month period k(j) in which day j falls (that is, a separate spatial smooth was fit for each two-month period).

To estimate the goodness of fit and due to computational limits, we used a “leave 10 out” approach where we randomly selected 10 monitors to leave out of the model 3 predictions. We the test the fit and bias (regressing the measured PM values against the predicted values and predicting PM levels at the left out monitoring locations).

Finally, we run a forth model where we take the residuals constructed by taking the difference between a given daily monitored PM_2.5 concentration and the 1km × 1km corresponding daily model 3 prediction, and regress that against spatial and temporal predictors of PM_2.5 at each monitor. Specifically, we fit the following model:

$$\begin{array}{l}{\mathit{ResidPM}}_{ij}=f_1(\mathit{Traffic}{\mathit{Density}}_i,\mathit{Population}{\mathit{Density}}_i)+f_2({\mathit{Elevation}}_i)+f_3(\mathit{Percent}{\mathit{Urban}}_i)+\\ f_4(\mathit{Distance}toA1{\mathit{roads}}_i)+f_5(\mathit{Distance}to\mathit{Point}{\mathit{emissions}}_i)+f_6(PB{L}_{ij})+f_7(\mathit{Traffic}{\mathit{Density}}_i,{\mathit{PBL}}_{ij})+\\ +f_{8ij}(\mathit{Traffic}{\mathit{Density}}_i,{\mathit{Visibility}}_{ij})+{\epsilon }_{ij}\end{array}$$ (Equation 4)

Where ResidPM_ij is the residual at a spatial monitor site i on day j; f₁ denotes a penalized spline for an interaction between traffic density and population density at a spatial monitor site i;, f₂−f₆ denote (potentially nonlinear) effects of elevation, percent urban land use, distance to A1 road, distance to point emissions and PBL respectively at a spatial monitor site i (and day j for PBL). f₇ denotes a penalized spline for an interaction between traffic density and PBL at a spatial monitor site i on day j and f₈ denotes a penalized spline for an interaction between traffic density and visibility at a spatial monitor site i on day j. Finally ε_ij is the error.

4. Results

Overall mean for MAIAC AOD was 0.25. Figure 2 presents the mean ground PM_2.5 measurements across all years (2003–2011) and the difference between monitor and predicted PM_2.5 concentrations at each monitoring site. The figure shows how measured PM_2.5 concentrations at monitors corresponds well with our predicted concentrations, and the differences at 95% of the monitoring sites are within ±1.3 μg/m3, clearly showing excellent agreement between observed and predicted values. Figure 3a presents a density plot exhibiting the daily variation of AOD slopes between 2003 and 2011 during model 1 calibrations, while Figure 3b presents a density plot exhibiting the daily variation of temperature slopes for the same period. The figure shows there is considerable day-to-day variability in these slopes.

Figure 2.

EPA and IMPROVE PM_2.5 annual means and the difference between measured and estimated PM_2.5 concentrations at each PM_2.5 monitor.

Figure 3.

Density plots exhibiting the daily variation of AOD slopes (a) and temperature slopes (b) between 2003 and 2011 during the stage 1 calibrations.

Table 1 presents results from our model 1 calibration analysis. The yearly predictive power of our model is extremely high, with an overall ”out of sample” R² for daily values of 0.88 (year-to-year variation 0.82–0.90), with a highly significant association between PM _2.5 and the main explanatory variable-AOD. The models yield almost no bias in our cross validation results as the slope of observed versus predicted =0.99 (year-to-year variation 0.98–1.01). The spatial and temporal out-of-sample results also presented excellent fits (Table 1): For the temporal model, the mean ”out of sample” R² was 0.87 (year-to-year variation 0.81–0.90) and for the spatial model the mean ”out of sample” R² was 0.87 (year-to-year variation 0.80–0.93). When looking at Root Mean Square Prediction Error (RMSPE), our models exhibit very low RMSPE values of 2.33 μg/m3 (year-to-year variation 1.95–2.89 μg/m3). Our “spatial” component only RMSPE is much lower at 0.82 μg/m3. The final prediction model (model 3) presents very similar results and is presented in table 2.

Table 1.

Prediction accuracy: Ten-fold cross-validated R² for PM_2.5 stage 1predictions (Calibration stage for 2003–2011).

year	R2	Slope	Spatial R2	Temporal R2	RMSPE (μg/m3)	Spatial RMSPE (μg/m3)
2003	0.89	0.98	0.87	0.88	2.89	1.05
2004	0.89	0.99	0.90	0.88	2.34	0.85
2005	0.88	0.98	0.87	0.87	2.85	1.00
2006	0.89	1.00	0.85	0.88	2.30	0.81
2007	0.90	1.01	0.93	0.90	2.34	0.73
2008	0.88	0.99	0.92	0.86	2.22	0.72
2009	0.86	0.98	0.86	0.84	1.97	0.71
2010	0.90	0.99	0.84	0.89	1.85	0.69
2011	0.82	0.99	0.80	0.81	2.22	0.82
Overall Mean 2003–2011	0.88	0.99	0.87	0.87	2.33	0.82

Table 2.

Prediction accuracy: R² for Stage 3 PM_2.5 predictions (final prediction model including locations without AOD for 2003–2011).

year	R2	Slope	Spatial R2	Temporal R2	RMSPE (μg/m3)	Spatial RMSPE (μg/m3)	Slope for leave 10-out
2003	0.91	1.02	0.88	0.91	2.69	0.65	1.09
2004	0.89	1.01	0.93	0.88	2.47	0.60	1.09
2005	0.88	1.01	0.93	0.88	2.79	0.63	1.10
2006	0.89	1.02	0.93	0.89	2.37	0.53	1.08
2007	0.91	1.01	0.96	0.91	2.26	0.47	1.04
2008	0.87	0.99	0.96	0.86	2.30	0.42	1.03
2009	0.87	1.01	0.94	0.86	1.95	0.37	1.06
2010	0.89	1.00	0.96	0.88	1.91	0.29	1.04
2011	0.84	1.01	0.92	0.83	2.09	0.39	1.05
Overall Mean	0.88	1.01	0.93	0.88	2.32	0.48	1.07

Figure 4 shows the spatial pattern of predicted PM_2.5 concentrations in Boston from the AOD models, averaged over the entire study period. The spatial variation in these long term PM2.5 predictions ranges from 2.36 μg/m3 to 40.12 μg/m3 showing a good range of variability for our model.

Figure 4.

Mean PM_2.5 concentrations in each 1×1 km grid cell in Boston during 2003 predicted by the AOD models

Figure 5 shows the deviation of the estimated local PM_2.5 concentrations (model 4) from the average 1×1km PM_2.5 concentrations at a very fine resolution (200×200m) aggregated over a year (2003) in Boston.

Figure 5.

The deviations of the estimated local pollution concentrations at a very fine resolution (200×200 m) from the average 1×1km grid PM_2.5 aggregated over a year (2003) in Boston

4. Discussion

In this paper we used novel 1 km AOD MODIS data based on the MAIAC algorithm to predict PM_2.5 concentrations across the Northeastern USA. Using the newly available MAIAC data allows us to simplify our previously described models while still gaining much better predictive power and reducing the exposure error. In addition, in our updated model we introduce significant methodological improvements with the predictions for daily fine resolution (200×200m) PM exposure, which can better capture pollution attributed to local sources such as traffic. Our models yield extremely good model fits and observed versus predicted slopes that were practically ‘1’, which clearly show that there is no bias in the resulting exposure predictions.

It is important to compare the predictions of our models to the other ‘state of the art’ prediction models that are available today. While the various existing models have all advanced in the past few years (including some models that use MAIAC data as well), they all still lack the ability to generate daily predictions for studies of the acute effects (short term) of air pollution as well as chronic (long term) effects, which are useful in epidemiologic studies aiming to estimate both acute and chronic effects of exposure. Sampson and colleagues (Sampson et al., 2013) recently published a universal kriging model using Partial Least Squares regression for estimating annual PM_2.5 concentrations. They present a high accuracy of prediction with an overall R² of 0.88 and well-calibrated predictive intervals. While the prediction accuracy of this model for long-term exposures is high, this model (1) does not predict daily and (2) is complex and requires an enormous number of spatial variables that are not always freely-available to researchers. In contrast our model presents similar spatial accuracy (R²=0.87), but with the additional advantage of yielding daily predictions also with very good prediction accuracy (temporal R²=0.87). Hu and colleagues (Hu et al., 2014) published a study estimating ground-level PM_2.5 concentrations in the Southeastern United States. Similar to our model they used MODIS based MAIAC data with a two-stage spatial statistical model with meteorological fields and land use parameters as ancillary variables to estimate daily mean PM_2.5 concentrations. The model was run in southeastern USA, for the year 2003. They used cross validation and predicted for only days with available MAIAC data resulting in an R² of 0.67 and RMSPE of 3.88 μg/m3. Their models do not yield daily predictions (in every grid cell on every day) and are less accurate compared to our presented model (such as cross validated RMSPE of 3.88 μg/m3 compared to 2.33 μg/m3 in our model). Other models published recently have all similar issues with lack of highly accurate daily predictions across the study area (Kim et al., 2013; Lin et al., 2013; Liu et al., 2009; Yanosky et al., 2008; Yap and Hashim, 2013). It is important to note that Beckerman (Beckerman et al., 2013) recently published results showing that in a Hybrid model estimating national scale spatiotemporal variability of pm_2.5 the inclusion of satellite based AOD into the LUR model did not improve the model. The study though used the older 10×10 MODIS data and generally the cross validated results were lower than our presented models (R²=0.79).

Although the new 1×1 km MAIAC data is a considerable improvement over the previous MODIS 10×10 km data (for example, R²=0.83 for our previously published 10 km model versus R²=0.88 in the current MAIAC model, spatial R²=0.78 versus R²=0.87), finer scale or less noisy future satellite-based data could further reduce exposure error bias resulting in larger and more accurate health effects estimates. Jerrett and colleagues have previously demonstrated how fine-scale variations in PM_2.5 are associated with larger health effects than those that vary regionally (Jerrett et al., 2005). We partly address this limitation in our model by adding our new local stage model 4 predictions at very fine 200×200 m scale that complements our 1×1 km predictions.

Research highlights.

• Our Models resulted in very high out-of-sample R² (R²=0.88)

• Our model performed well both spatially and temporally (R²=0.87, R²=0.87)

• Our results revealed very little bias (Slope of predictions versus withheld observations = 0.99)

• Importantly, these R² are for daily, rather than monthly or yearly, values.