A hybrid model for spatially and temporally resolved ozone exposures in the continental United States

Figures & data

Figure 1. Ozone monitoring sites in the United States.

Table 1. Cross-validated total R², spatial R², temporal R², and corresponding MSE between monitored and predicted ozone in each year for the study area.

Year	Total R^2	RMSE	Spatial R^2	RMSE	Temporal R^2	RMSE	Bias	Slope
2000	0.79	8.09	0.82	3.30	0.78	7.42	1.38	0.99
2001	0.78	8.12	0.80	3.51	0.77	7.34	1.21	0.99
2002	0.80	8.09	0.82	3.30	0.80	7.39	1.12	0.99
2003	0.77	7.98	0.78	3.21	0.77	7.33	1.33	0.99
2004	0.76	7.44	0.76	2.98	0.76	6.83	1.34	0.99
2005	0.78	7.84	0.78	3.11	0.77	7.22	1.37	0.99
2006	0.77	7.52	0.78	2.95	0.76	6.94	1.10	0.99
2007	0.77	7.32	0.85	2.88	0.76	6.76	1.13	0.99
2008	0.76	7.12	0.82	2.75	0.75	6.58	1.09	0.99
2009	0.76	6.61	0.79	2.57	0.75	6.13	1.18	0.98
2010	0.74	6.90	0.82	2.58	0.73	6.42	1.31	0.98
2011	0.75	7.01	0.80	2.72	0.74	6.50	1.08	0.99
2012	0.78	6.76	0.83	2.59	0.77	6.29	0.96	0.99
Mean	0.76	7.36	0.80	2.91	0.75	6.79	1.20	0.99

Note. Unit for RMSE (root mean square error) is ppb; the unit for bias is ppb.

Table 2. Cross-validated total R², spatial R², temporal R², and corresponding MSE between monitored and predicted ozone in each year divided by season.

Year	Spring R^2	RMSE	Summer R^2	RMSE	Autumn R^2	RMSE	Winter R^2	RMSE	Annual R^2	RMSE
2000	0.70	7.78	0.73	9.23	0.77	7.72	0.69	6.30	0.79	8.09
2001	0.71	7.54	0.71	9.59	0.74	7.61	0.69	6.27	0.78	8.12
2002	0.67	6.97	0.75	9.70	0.80	7.87	0.66	6.34	0.80	8.09
2003	0.71	7.55	0.71	9.19	0.75	7.70	0.67	6.10	0.77	7.98
2004	0.68	7.03	0.70	8.42	0.77	7.22	0.65	6.36	0.76	7.44
2005	0.67	7.16	0.70	9.18	0.77	7.52	0.70	6.05	0.78	7.84
2006	0.65	7.08	0.70	8.93	0.73	6.89	0.68	5.66	0.77	7.52
2007	0.71	6.76	0.71	8.59	0.75	7.06	0.66	5.91	0.77	7.32
2008	0.68	6.48	0.70	8.34	0.74	6.80	0.69	5.47	0.76	7.12
2009	0.68	6.34	0.70	7.43	0.75	6.41	0.66	5.83	0.76	6.61
2010	0.64	6.53	0.69	7.77	0.75	6.73	0.65	6.16	0.74	6.90
2011	0.63	6.51	0.69	8.08	0.75	6.68	0.65	5.36	0.75	7.01
2012	0.69	6.28	0.72	8.09	0.73	6.39	0.65	5.95	0.78	6.76
Mean	0.68	6.92	0.71	8.66	0.75	7.12	0.67	5.98	0.76	7.36

Note. The definition of seasons was specified in Figure 2. Unit for RMSE (root mean square error) is ppb; the unit for bias is ppb.

Table 3. Cross-validated total R², spatial R², temporal R², and corresponding MSE between monitored and predicted ozone in each year divided by U.S. Census Divisions.

Year	New England	Middle Atlantic	East North Central	West North Central	South Atlantic	East South Central	West South Central	Mountain	Pacific	National
2000	0.70	0.81	0.79	0.74	0.78	0.74	0.79	0.77	0.80	0.79
2001	0.70	0.83	0.81	0.73	0.79	0.74	0.76	0.73	0.78	0.78
2002	0.74	0.85	0.85	0.76	0.82	0.79	0.76	0.74	0.78	0.80
2003	0.68	0.81	0.81	0.70	0.77	0.74	0.76	0.76	0.78	0.77
2004	0.63	0.81	0.77	0.71	0.76	0.72	0.76	0.74	0.78	0.76
2005	0.69	0.82	0.81	0.76	0.79	0.74	0.76	0.73	0.76	0.78
2006	0.71	0.82	0.79	0.74	0.76	0.72	0.77	0.73	0.76	0.77
2007	0.69	0.82	0.82	0.73	0.78	0.75	0.77	0.73	0.75	0.77
2008	0.71	0.82	0.77	0.69	0.80	0.73	0.74	0.72	0.76	0.76
2009	0.72	0.78	0.77	0.72	0.75	0.75	0.76	0.69	0.77	0.76
2010	0.71	0.80	0.72	0.69	0.76	0.68	0.74	0.68	0.75	0.74
2011	0.66	0.78	0.75	0.67	0.75	0.72	0.77	0.68	0.75	0.75
2012	0.69	0.82	0.81	0.78	0.75	0.76	0.75	0.74	0.77	0.78
Mean	0.60	0.73	0.69	0.62	0.68	0.62	0.69	0.67	0.73	0.70

Note. Unit for RMSE (root mean square error) is ppb; the unit for bias is ppb.

Figure 2. Model performance in the continental United States. This figure visualizes the total R² between monitored and predicted ozone. We interpolated R² to areas without monitors using Kriging interpolation. Spring was defined as March to May; summer was defined as June to August; autumn was defined as September to November; winter was from December to February of the next year.

Figure 3. Spatial distribution of predicted ozone. The trained neural network predicted ozone at 1 km × 1 km grid cells. Those figures visualize annual averages and seasonal averages of predicted ozone for 2000~2004, 2005~2008, and 2009~2012. (Seasons were defined as in Figure 2.)

Figure 4. Regional trend in ozone levels at national and regional levels. Concentration is defined by annual fourth maximums of daily 8hr-max.

Figure 5. Seasonal averages by urban and rural area. Seasonal averages were computed by averaging predicted ozone at all 1 km × 1 km grid cells in urban or rural areas. Urban areas are defined by developed areas above 50% based on National Land Cover Database (NLCD) 2001, 2006, and 2011 (Fry et al., 2011; Xian et al., 2011).

Figure 6. Relationship between measured and predicted ozone. We fitted a regression of predicted ozone on monitored ozone with penalized spline. To assess the linearity between predicted and monitored ozone, we did not specify the degrees of freedom. This figure is for year 2009.

Fry, J.A., G. Xian, S. Jin, J.A. Dewitz, C.G. Homer, Y. LIMIN, C.A. Barnes, N.D. Herold, and J. D Wickham. 2011. Completion of the 2006 National Land Cover Database for the conterminous United States. Photogramm. Eng. Rem. S. 77:858–64.

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Xian, G., C. Homer, J. Dewitz, J. Fry, N. Hossain, and J. Wickham. 2011. Change of impervious surface area between 2001 and 2006 in the conterminous United States. Photogramm. Eng. Rem. S. 77:758–62

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