Paciorek and Liu analyses, missing AOD retrievals cause one to rely on a subset of days (determined by weather conditions that also affect PM2.5 lev- els, so AOD patterns represent only cloud- free conditions) with AOD retrievals to estimate monthly or yearly pollution. Over land, MODIS, MISR, and GOES retrievals are available, on average over the entire mid- Atlantic region, 16%, 4%, and 38%, respec- tively, of the days in 2004. Also, for MODIS and MISR, the occurrence of AOD snap- shots at the same time every day may not well match daily average pollution. To assess the long-term spatial relationship of AOD and PM2.5, we considered associations of yearly PM2.5 and AOD, relating average AOD from available retrievals to average PM2.5 based on all available PM2.5 monitoring, not just PM2.5 data matched by day to AOD retrievals. These associations eliminate temporal correlations within a site that can obscure the spatial asso- ciation. However, simple yearly averaging does not account for the differential frequency of successful AOD retrievals over the seasons in the year (which overweights summer AOD values) or allow us to consider monthly asso- ciations, so we report results at the monthly level in the Supplementary Material (http:// www.ehponline.org/members/2009/0800360/ suppl.pdf). Statistical modeling. The exploratory analyses do not account for complications such as differing numbers of PM2.5 obser- vations and AOD retrievals by location and very fine-scale heterogeneity in PM2.5. Most important, correlations of AOD and PM2.5 may reflect variability in PM2.5 that could be predicted by other sources of information, such as land use or meteorology or estima- tion of large-scale regional variation through spatial smoothing of monitored values, so they may overstate the usefulness of AOD as a predictor in light of other readily available information. To address these issues we turn to formal statistical modeling, analyzing the mid-Atlantic region. Both models are speci- fied in a Bayesian context and are fitted by standard Markov chain Monte Carlo meth- ods. We did not use MISR because of the limited number of retrievals. Using AOD as proxy data. Recent statisti- cal efforts have focused on combining mul- tiple sources of information by treating the sources as reflecting a true, unknown spatial process (Fuentes and Raftery 2005; Gelfand and Sahu, in press; McMillan et al. 2009). Accordingly, we fit statistical models for indi- vidual months in which PM2.5 and AOD observations are considered to be separate data sources that reflect the unknown PM2.5 surface for a given month. The first stage of the model contains two likelihood terms rep- resenting the probabilistic relationships of the PM2.5 and AOD data to the underlying 906 processes and covariates. For PM2.5, for an individual month, we specify the likelihood, PMi = yi ∼ N[Ps(i) + Σk fk (zk,i), σy2,i], [1] where the core of the model is the unknown true pollution surface that we want to esti- mate, represented on a 4-km grid as Ps, where s indexes grid cells. We represent the monthly averages of available 24-hr concentration mea- surements in terms of the gridded pollution surface, locating individual observations, yi, indexed by location i, within the appropri- ate grid cell, s(i). fk(zk,i) are smooth regression functions that reflect the effects of local covari- ates, zk, that affect PM2.5 at scales below 4 km, a decomposition similar to that of Beelen et al. (2007). In particular, we use distance to the nearest A1 and A2 roads, forcing the effect to be zero beyond 500 m (Zhou and Levy 2007). By modeling the effect of nearby roads (and point emissions), we attempt to account for differences between AOD and PM2.5 caused by fine-scale heterogeneity captured by PM2.5 monitors but smoothed over in the AOD pixel-level values. Thus, we assess the ability of AOD to capture spatial heterogene- ity in PM2.5 at small scales (tens of kilometers) but not extremely fine scales (meters to kilo- meters). σ2y,i reflects various components of uncorrelated error and accounts for the varying number of daily observations by location. We present below the likelihood term for AOD. The unknown pollution process on the grid is represented as Ps = µ + Σk hk (wk,s) + gs, [2] where µ is an overall mean and hk(wk,s) are smooth regression functions of grid-scale cova- riates: the density of A1, A2, and A3 roads, population density, elevation, and nonpoint- source area emissions. gs is a smooth spatial term representing residual spatial structure unaccounted for by covariates, in particular regional variation. Because we fitted the model individually for each month, we omitted mete- orologic covariates, which tend to be spatially smooth and whose influence would be difficult to separate from gs, causing their influence to be reflected in the estimate of gs. Also included in the model is a smooth term that accounts for the effect of point emissions within 100 km, where the effect declines with distance and is estimated from the data within the model fitting. This term is used both as a covariate affecting the individual PM2.5 observations based on the point location of each monitor (in Equation 1) and as a covariate affecting the gridded process, Ps (based on averaging over a subgrid of 16 points within each cell). We specify the AOD retrievals in an individual month as reflecting the unknown PM2.5 process, AODs = as ∼ N [β0 + β1Ps + fcloud (zcloud,s), σa2,s], [3] up to additive (β0) and multiplicative (β1) bias, with a smooth regression function of cloud cover, fcloud(zcloud,s), where zcloud,s is the monthly average proportion of cloud- free retrievals in the cell, based on the GOES cloud retrieval algorithm. We included this to help account for bias from retrievals systemat- ically missing because of clouds (Koelemeijer et al. 2006; Paciorek et al. 2008). σa2,s reflects various components of uncorrelated error and accounts for the varying number of daily retrievals by location. A complicating factor is that for different satellite orbits on different days, the MODIS pixels shift spa- tially. Therefore, we consider the overlap of all the pixels in an orbit with the 4-km grid, assigning to each grid cell, s, the value of the MODIS pixel in which the cell centroid falls. Taking the retrievals assigned to each cell, we then average to the monthly level for each cell, giving as. For GOES the pixel locations are constant over time, so we average to the monthly level and then assign each grid cell the weighted average AOD of the GOES pix- els that the cell overlaps, weighted by the area of overlap. Although they are simplistic, we believe these approaches cause minimal dis- tortion in the AOD values used in the model- ing, because of the reasonably smooth local variation in daily AOD values from pixel to pixel. In this model, we assume any difference between AOD and PM2.5 is spatially uncor- related noise, which causes estimation of Ps to reflect the spatial structure in both PM2.5 and AOD observations. However, maps of monthly average AOD show strong spatial structure (e.g., Figure 1A) with limited spatially uncorrelated noise (i.e., white noise) apparent. This spatial structure may be caused in part by systematic, spatially correlated differences between AOD and PM2.5, rather than reflecting spatial struc- ture in ground-level PM2.5. Factors likely to contribute to such differences, which would operate even if AOD were measured per- fectly, include spatial structure in pollution aloft above the boundary layer and daily spa- tial patterns of missing retrievals from clouds with aggregate effect at the monthly level. Of course, AOD is not measured perfectly (Knapp et al. 2002; Remer et al. 2005), as reflected in moderate correlations between monthly average MODIS and GOES AOD and induced in part by spatial variability in surface reflectivity and PM2.5 composition. The summed effect of all these differences, which we refer to as systematic discrepancy, could be substantial, and this, rather than pixel-scale white noise, may be the dominant factor explaining low correlations with PM2.5 seen in our exploratory analyses. Models that ovlume 117 | number 6 | June 2009 • Environmental Health Perspectives