A bivariate space-time downscaler under space and time misalignment

Abstract

Ozone and particulate matter PM(2.5) are co-pollutants that have long been associated with increased public health risks. Information on concentration levels for both pollutants come from two sources: monitoring sites and output from complex numerical models that produce concentration surfaces over large spatial regions. In this paper, we offer a fully-model based approach for fusing these two sources of information for the pair of co-pollutants which is computationally feasible over large spatial regions and long periods of time. Due to the association between concentration levels of the two environmental contaminants, it is expected that information regarding one will help to improve prediction of the other. Misalignment is an obvious issue since the monitoring networks for the two contaminants only partly intersect and because the collection rate for PM(2.5) is typically less frequent than that for ozone.Extending previous work in Berrocal et al. (2009), we introduce a bivariate downscaler that provides a flexible class of bivariate space-time assimilation models. We discuss computational issues for model fitting and analyze a dataset for ozone and PM(2.5) for the ozone season during year 2002. We show a modest improvement in predictive performance, not surprising in a setting where we can anticipate only a small gain.

Figure 1

Sites reporting concentration of ozone and PM_2.5 used in our case study. Sites measuring only ozone are represented with dots, sites reporting only PM_2.5 concentrations are represented with triangles, while sites measuring concentration for both pollutants are represented with squares. Black symbols are used to display sites used to fit the model, while grey symbols indicate validation sites.

Figure 2

Normal Q-Q plots of: (a) square root of observed ozone; (b) log of observed PM_2.5.

Figure 3

Time series of: (a) daily mean (open circles) and daily standard deviation (black dots) of square root of observed ozone; (b) daily mean (open circles) and daily standard deviation (black dots) of log of observed PM_2.5.

Figure 4

Spatial maps of the estimates of the coefficients of the linear regressions of the square root of observed concentration of ozone (panels (a), (c) and (e)) and of the logarithm of the observed concentration of PM_2.5 (panels (b), (d) and (f)) on the square root of the CMAQ predicted concentration of ozone and on the log of the CMAQ predicted concentration of PM_2.5: (a)-(b) intercept term; (c)-(d) coefficient of the CMAQ model output for ozone; (e)-(f) coefficient of the CMAQ model output for PM_2.5. In all panels, the linear regression has been carried out between the normalized response and the normalized covariates.

Figure 5

(a) Observed ozone on June 25, 2002; (b) Predicted ozone as obtained from CMAQ on June 25, 2002; (c) Predicted ozone as obtained via kriging for June 25, 2002; (d) Predicted ozone as obtained from the bivariate downscaler model for June 25, 2002.

Figure 6

(a) Observed PM_2.5 on June 25, 2002; (b) Predicted PM_2.5 as obtained from CMAQ on June 25, 2002; (c) Predicted PM_2.5 as obtained via kriging for June 25, 2002; (d) Predicted PM_2.5 as obtained from the bivariate downscaler model for June 25, 2002.

Figure 7

Posterior predictive mean of: (a) β₁₀(s, t) for June 25, 2002; (b) β₂₀(s, t) for June 25, 2002 as obtained from the bivariate downscaler model.

Figure 8

Posterior predictive distribution for the difference in average ozone and PM_2.5 concentration between Mid-Atlantic and Midwest, Mid-Atlantic and South and Midwest and South on June 25, 2002, as obtained using the bivariate downscaler.