Environmental Science & Technology GSHOPit = α + β1z1i + β2xspring + β3xsummer + β4xwinter + β5z2i + β6z2ixspring + β7z2ixsummer + β8z2ixwinter + h(t) + eit (4) where the residual term eit (compound symmetric, chosen based on the CV R2) and h(t) are speciﬁed as above in eq 1 and where z1i is NOXHGV100, z2i is PM10BT50, and the xSeason terms are dummy variables for each season. A Mg year−1 increase in NOXHGV100 was associated with a 0.12 decrease in GSH OP μg−1. Increased PM10BT50 was positively associated with GSH OP in each season, with this eﬀect largest in summer and smallest in autumn, with estimated values of 7.3, 11.0, 11.3, and 5.6 for winter, spring, summer, and autumn, respectively (all in GSH OP μg−1 for a Mg year−1 increase in PM10). Table S2 in the Supporting Information contains further details on the model parameters. The reduced slope in autumn and the peaks in the time trend term corresponding to the autumn season suggest that GSH OP levels are higher but less spatially variable (i.e., less local) during this time of year. Despite the moderate correlation (Pearson’s r = 0.70) between PM10BT50 and NOXHGV100, only PM10BT50 was signiﬁcant in univariate models (slope (SE) of 4.86 (1.22) with no seasonal interaction). Upon inclusion in the same multivariable model, the sign of the slope for NOXHGV100 became negative (Supporting Information Table S2). This may reﬂect changes in the mixture of PM10 components due to diﬀerences in vehicle composition, suggesting that locations with higher NOX tailpipe emissions from heavy-goods vehicles have lower levels of GSH OP-active PM10 components per unit PM10 mass. The model explained about half of the variability in weekly GSH OP levels (model R2 = 0.52), and thus, in comparison with the CV R , overﬁtting of the model was moderately well 2 controlled for at 8.1%. The smooth function for time trend used 40.5 degrees of freedom (df) and showed a marked seasonal pattern, with an increase in late autumn of each year (Supporting Information Figure S2), typically around October or November. Predictive accuracy was moderate for weekly levels (CV R2 = 0.44), but increased considerably when evaluating only spatial variability (Table 1; spatial CV R2 = 0.73), and also increased when predicting only temporal variability (Table 1; temporal CV R2 = 0.71). Also, predictive accuracy for weekly levels was increased among sites with at least 88 measurements (CV R2 = 0.54), and when comparing annual-averages (Table 2; CV R2 = 0.67). We found little bias in weekly model predictions (linear regression slope = 0.97 and MFB = 7.8%), but only moderate to poor precision (Table 1; RMSPE = 0.29 OP μg−1 or 39% of the mean; MFE = 37.4%). However, precision improved consid- erably for spatial predictions (Table 1; RMSPE = 0.13 OP μg−1 or 17% of the mean). Additionally, predictive accuracy and precision by season, year, tertiles of urban volumetric density, and site type are shown in Table 1. Additional details regarding model performance by these categories can be found in the Supporting Information. To further explore the impact of emission type (tailpipe vs brake and tire wear) and vehicle group (heavy-goods, light- goods, and “other”) of PM10 emissions within 50 m on spatial variation in GSH OP, we substituted covariates from each of these categories in the ﬁnal GSH OP prediction model. The results in Table 2 show that the strongest of these predictors was brake and tire wear PM10 emissions from all vehicles (“total” category) from the ﬁnal GSH OP prediction model. Table 2. GSH OP Model Performance Statistics by Emission Type and Vehicle Group Categories cross-validation R2 RMSPEa weeklyb spatialc weeklyb spatialc 0.40 0.35 0.19 0.41 0.44 0.28 0.36 0.43 0.63 0.51 0.00 0.65 0.73 0.15 0.51 0.71 0.31 0.32 0.36 0.30 0.29 0.34 0.32 0.30 Article 0.15 0.17 0.26 0.14 0.13 0.22 0.17 0.13 PM10 emissions within 50 m tailpipe brake and tire wear vehicle group total heavy- goods light-goods otherd total heavy- goods light-goods otherd aRMSPE is root mean squared prediction error. Units are OP μg−1. bAcross 2118 weekly averages at 34 locations. cTo calculate “spatial” values, measurements and predictions were averaged over time at sites with at least 40 weeks of data. d“Other” category includes buses, cars, motorcycles, and taxis. However, among individual vehicle groups, the “other” category (buses, cars, motorcycles, and taxis) had the highest predictive accuracy, again suggesting diﬀerences in the composition of PM10 emissions from roadways with high “other” vehicle traﬃc (with likely a higher proportion of petrol (gasoline)-fueled vehicles) vs those with higher heavy-goods traﬃc (with likely a higher proportion of diesel-fueled vehicles). These alternate models were identical except that diﬀerent spatial predictors were included; therefore, diﬀerences in predictive accuracy were more pronounced when comparing spatial rather than weekly CV R2 values. The maps in Supporting Information Figure S3 display the spatial and temporal variability in predicted GSH OP levels in central London. Using a conventional sums of squares decomposition, the variability in weekly predictions at the grid points shown in Figure S3 was 12% spatial and 87% temporal, with the remainder attributable to rounding error. Maps showing the impact of the seasonally varying eﬀects of the PM10 brake and tire wear emissions covariate on the spatial variability in modeled GSH OP are presented in Supporting Information Figure S4. PM10. The form of the space-time PM10 prediction model was PM10it = α + β1z1i + h(t) + eit (5) where the terms are as above in eq 1, z1i is M0306HED in μg m−3, and eit ∼ N(0, σ2e). Again the untransformed outcome performed as well as alternatives, and therefore PM10 was modeled on the original scale. The referent model for PM10 included only an intercept, α, and a smooth function for time trend, h(t), as ﬁxed-eﬀects (Supporting Information Table S1), and did not include a smooth spatial term g(si). Inclusion of M0306HED improved predictive accuracy compared to the referent model (CV R2 = 0.74 without and 0.83 with). Because the hybrid emissions- dispersion/regression model included the inﬂuence of roadway emissions and other small scale eﬀects, it, not surprisingly, described micro- to middle-scale (0−500 m) spatial variation in PM10 levels better than spatial smoothing splines alone. As was the case for GSH OP, a linear covariate eﬀect performed better than a nonlinear spline. The slope for this covariate, M0306HED, was near unity (1.01; Supporting Information Table S2), 7616 dx.doi.org/10.1021/es3010305 | Environ. Sci. Technol. 2012, 46, 7612−7620