treat AOD as a proxy for PM2.5 without accounting for potential systematic discrepan- cies may predict spatial patterns of PM2.5 that do not match reality. We assessed sensitivity to assumptions about systematic discrepan- cies by including an additive spatial bias term, φs, represented at the grid scale, replacing the constant bias, β0, in Equation 3. Models that include such a term allow for the possibility that AOD retrievals are telling us about spatial processes specific to the retrievals that do not reflect spatial patterns in ground-level PM2.5. We estimated φs using a penalized thin-plate spline approach that penalizes complex spatial surfaces, thereby favoring simple surfaces if the data can be sufficiently well explained by a smooth surface (Ruppert et al. 2003). We also used such an approach for the other smooth terms in the model, fitted naturally within the Bayesian context with the level of smoothing determined by the data. For computational reasons and because the key results are best visualized in model fits of individual months, we fitted the model separately for each of the 12 months. The advantage of this modeling approach is that it naturally treats AOD retrievals as data and allows for missing retrievals. By con- sidering different assumptions about spatial bias, we can assess the concordance of spatial patterns between AOD and PM2.5 and inves- tigate the assumption that the spatial pattern in AOD represents signal that is informative about PM2.5. Using AOD as a predictor of PM2.5. We also consider a model in which AOD is used as a predictor on the right-hand side of a regression-style model, treating the PM2.5 data as the gold standard. This has the benefit of directly calibrating PM2.5 to AOD and, if there is little empirical association, discount- ing AOD as a predictor of PM2.5. In this model, we modeled PM2.5 observa- tions as in Equation 1, PMit = yit ∼ N[Ps(i),t + Σk fk (zk,i), σi2t], whereas the unknown smooth pollution pro- cess, Ps,t, is similar to Equation 2 but includes AOD, As,t, as a predictor: Pst = µt + β1,tAs,t + Σk hk (wk,s,t) + gs,t. This model is fit simultaneously to all 12 months, indexed by the t subscript. For simplicity, we assume that gs,t, the residual spatial structure, is not correlated over time, which eases computations. Previous work sug- gests month-to-month correlation is limited and that including correlation would do little to improve predictions (Paciorek et al. 2009), so the assumption should not affect our ability to assess whether AOD can improve PM2.5 predictions. We allow β1,t to vary in an [4] [5] Environmental Health Perspectives • volume 117 | number 6 | June 2009 Remotely sensed aerosol and particulate matter unstructured way with time in case the rela- tionship of AOD and PM2.5 varies by season (Paciorek et al. 2008). Based on some limited variable selection, the covariates wk,s,t (some of which do not vary with time) are population density, elevation, area emissions, point emis- sions, density of A3 roads, wind speed, and temperature. We also include monthly aver- age cloudiness to help account for bias from missing AOD retrievals. For this approach, a downside is that we require AOD values at all locations. We used the Markov random field approximation to a thin-plate spline described in the Supple- mentary Material (http://www.ehponline. org/members/2009/0800360/suppl.pdf) to smooth the observed AOD retrievals and make predictions, As,t, at unobserved locations. Preprocessing of pixel-level AOD values to align with the 4-km grid is as described previously. Results Exploratory analyses. Correlations between daily PM2.5 and AOD (matched by day and location) that reflect both temporal and spatial associations are higher than correlations for individual days, taken across spatial locations (Table 1), which reflect only spatial associa- tions. The spatiotemporal associations roughly match those seen in the literature that have been used as evidence of the potential of AOD as a proxy for PM2.5 (e.g., Engel-Cox et al. 2004; Liu et al. 2005; Paciorek et al. 2008). Using AOD directly does not account for meteorologic factors and systematic temporal and spatial variability that modify the relation- ship between AOD and PM2.5, so we also considered the calibrated version of AOD, which somewhat improved the correlations (Table 1). Table 1 shows near-zero correlations of yearly average PM2.5 from all available 24-hr values (everyday or every-third-day sampling) with AOD from available retrievals. Note that for monitors reporting only every 3 days, miss- ing PM2.5 values contribute to noise in the associations seen here. After calibration, AOD is moderately correlated with PM2.5. The calibration includes an overall spatial term, adjusting for any large-scale regional mismatch between AOD and PM2.5 that is consistent over the year. This term is responsible for much of the increase in correlation after calibration because it necessarily causes the large-scale pat- terns of long-term average AOD and PM2.5 to more closely match. Our hope is that correct- ing for such large-scale mismatch allows us to explore whether there is independent infor- mation in AOD for predicting smaller-scale patterns of PM2.5, a question answered in the statistical modeling. For results at the monthly level, see the Supplementary Material (http:// www.ehponline.org/members/2009/0800360/ suppl.pdf). Using AOD as proxy data: sensitivity to systematic discrepancies. For July 2004 for MODIS AOD, Figure 2 shows model-based predictions of PM2.5 and estimates of φs based on Equations 1–3, allowing different amounts of complexity in φ . When the model omits s the spatial bias term (Figure 2A,E), represent- ing AOD as reflecting PM2.5 up to simple additive and multiplicative bias, predictions of PM2.5 strongly track AOD spatial patterns (i.e., Figure 1A). As we introduce spatial bias (Figure 2B,F) and allow more flexibility in the spatial bias term (Figure 2C,G), predictions increas- ingly track the PM2.5 observations (i.e., Figure 1B) and results from a model fitted without AOD (Figure 2D,H). The fit of the penalized spline model does not stabilize on a smooth bias surface. When we force the bias term to be smooth, the model cannot adequately repre- sent the AOD data based on the PM2.5 surface, the smooth bias, and white noise error. This suggests there is little common spatial pattern to PM2.5 and AOD observations and that true PM2.5 is best modeled solely based on ground- level PM2.5 data with AOD variability modeled separately. This is demonstrated in Figure 2C and G, where the model essentially disregards AOD in predicting PM2.5 and attributes most of the variability in AOD to φs. Results for the other 11 months and using GOES AOD or Table 1. Correlations of daily AOD with matched 24-hr PM for the eastern United States and yearly aver- age AOD with PM, matched in space, for our mid-Atlantic focal region. Type of variation Daily values, eastern United States Temporal plus spatial variation: overall correlation of daily values across all sites and days Spatial variation only: average of daily spatial correlationsb Yearly averages, mid-Atlantic focal regionc Spatial variation only: correlation of yearly averages MODIS 0.60 0.35 0.09 Raw AOD MISR 0.50 0.30 0.25 GOES 0.38 0.23 –0.07 MODIS Calibrated AODa MISR 0.64 0.45 0.49 0.57 0.32 0.22 aCalibrated AOD has been adjusted to account for the effects of PBL, RH, season, and regional variation in modifying the relationship between daily AOD and PM. bOnly days with at least 20 matched sites. cYearly averages reflect all available AOD retrievals and all available 24-hr average PM concentrations. Yearly results include only sites with at least 100 daily PM observations and exclude one site with high PM levels outside Pittsburgh that is just downwind of a major industrial facility. GOES 0.40 0.29 0.53 907