Paciorek and Liu raw AOD give similar conclusions. In sum- mary, systematic discrepancies are considerable and critical to include, and predictions are very sensitive to assumptions about the discrepancy term. If the spatial discrepancy were estimated to be a relatively smooth process, able to be resolved from having PM2.5 and AOD data in the same region, the modeling approach pro- vides a means to improve PM2.5 prediction by combining the data sources while accounting for the discrepancy. However, these results sug- gest the discrepancy process is not smooth and Predicted PM, model 1 Predicted PM, model 2 Spatial bias, model 2 Predicted PM, model 3 Spatial bias, model 3 24 22 20 18 16 14 12 24 22 20 18 16 14 12 24 22 20 18 16 14 12 24 22 20 18 16 14 12 E F G H Model 1 assumes no spatial bias Model 4 does not use AOD to predict PM, so spatial bias is not applicable A B C D Predicted PM, model 4 Figure 2. Sensitivity of predicted PM to the characterization of spatial bias. The left column shows PM pre- dictions for models in which AOD and PM observations are treated as data reflecting a common unknown PM process, using calibrated MODIS AOD for July 2004. (A) Model 1: excluding the spatial bias term, φs, thereby treating AOD as a simple proxy for PM with simple additive and multiplicative bias. (B) Model 2: φs constrained to be a somewhat smooth process with a maximum of 55 degrees of freedom (df) (a penalized spline with 55 knots). (C) Model 3: φs relatively unconstrained with a maximum of 755 df. (D) Model 4: AOD not used. The right column shows the corresponding estimated φs surfaces, except that for model 1, φs is not included in the model (E); for model 4 AOD is not used, so φs is not involved in the model (H). (F and G) Spatial discrepancy for models 2 and 3, respectively. Table 2. Cross-validation R2 (mean squared prediction error) for predictions of yearly and monthly average PM from regression style models with and without calibrated AOD and other predictors. Yearly averagesa,b Monthly averagesa Model No AOD With calibrated MODIS AOD With calibrated GOES AOD No AOD With calibrated MODIS AOD With calibrated GOES AOD Models including land use, emissions, and meteorologic predictors Models without land use, emissions, and meteorologic predictorsd All monitors (n = 151) 0.580 (1.04) 0.573 (1.06) 0.572 (1.06) 0.463 (1.33) 0.467 (1.32) 0.467 (1.33) Population exposurec monitors (n = 130) 0.570 (0.93) 0.564 (0.94) 0.563 (0.95) 0.456 (1.18) 0.459 (1.17) 0.458 (1.17) All monitors (n = 1,793) 0.827 (2.71) 0.825 (2.73) 0.825 (2.73) 0.794 (3.22) 0.794 (3.22) 0.794 (3.22) Population exposurec monitors (n = 1,542) 0.839 (2.48) 0.839 (2.50) 0.838 (2.50) 0.810 (2.94) 0.810 (2.94) 0.810 (2.94) aFor a given location, only months for which the location has at least four PM daily values are included. Results exclude one site with high PM values outside Pittsburgh that is just downwind of a major industrial facility. bYearly average results include only locations with at least 6 available months of PM data. cThe “population exposure” designation assigned to monitors by U.S. EPA indicates that such monitors are not likely to be affected by large, local sources. dThese models include the GOES cloud term for consistency of comparisons between the AOD and no-AOD models. 908 ovlume 117 | number 6 | June 2009 • Environmental Health Perspectives 0.4 0.3 0.2 0.1 0.0 –0.1 –0.2 0.6 0.4 0.2 0.0 –0.2 –0.4 cannot be adequately estimated without denser PM2.5 data, which are not available and would largely obviate the need for AOD as a proxy. Using AOD as a predictor: effects on pre- dictive ability. With AOD as a predictor, pre- dictive ability at both the monthly and yearly resolutions does not improve when either calibrated MODIS or GOES AOD is added to the model (Equations 4 and 5) already containing the other predictors (Table 2). If we exclude the other predictors (except the GOES cloud term for consistency in com- paring the AOD and no-AOD models) and account for spatial variability solely based on spatial smoothing of the observations within the model framework, addition of AOD still shows essentially no improvement in predic- tions (Table 2). Results are similar when avoid- ing locations that are most likely affected by very local sources (Table 2). Sensitivity analyses indicate that there was similarly limited effect of AOD on predictive power when using raw AOD instead, when restricting to monitors in areas with sparse monitoring, or when restrict- ing to everyday monitors (which avoids the extra noise caused by missing monitor values) (data not shown). The higher predictability of monthly compared with yearly PM2.5 in Table 2 occurs because of the importance of temporal variation, which is easy to estimate based on the monitoring. The results of including AOD are consistent with the estimates of β1,t, which are small in magnitude, with wide uncertainty intervals that cover zero. Correlations of predic- tions with and without AOD are > 0.999, indi- cating that there would be negligible impact in an epidemiologic analysis. Discussion We urge caution in assuming that currently available remotely sensed AOD can help improve exposure estimation for PM2.5 and particular caution in using AOD to estimate spatial heterogeneity where there is little ground-level PM2.5 data for ground truthing, based on the lack of strong spatial correlation between available AOD retrievals and long- term average PM2.5. In a setting in which rea- sonably dense PM2.5 data are available, our statistical modeling results indicate little or no improvement in prediction of long-term aver- age PM2.5 when adding AOD. To the extent that raw correlations of AOD and PM2.5 reflect the ability of AOD to capture some of the pat- tern in PM2.5, our results suggest that these can be better estimated by simple spatial smoothing of the available PM2.5 data and regression on other predictors, rendering the AOD informa- tion extraneous. Koelemeijer et al. (2006) found much stronger correlations of yearly average MODIS AOD and PM10 in Europe; this may be related to their focus on rural background sites, their larger spatial domain, and the greater variability in their PM2.5 concentrations.