Predicting Intra-Urban Variation in Air Pollution Concentrations with Complex Spatio-Temporal Dependencies

Abstract

We describe a methodology for assigning individual estimates of long-term average air pollution concentrations that accounts for a complex spatio-temporal correlation structure and can accommodate spatio-temporally misaligned observations. This methodology has been developed as part of the Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air), a prospective cohort study funded by the U.S. EPA to investigate the relationship between chronic exposure to air pollution and cardiovascular disease. Our hierarchical model decomposes the space-time field into a "mean" that includes dependence on covariates and spatially varying seasonal and long-term trends and a "residual" that accounts for spatially correlated deviations from the mean model. The model accommodates complex spatio-temporal patterns by characterizing the temporal trend at each location as a linear combination of empirically derived temporal basis functions, and embedding the spatial fields of coefficients for the basis functions in separate linear regression models with spatially correlated residuals (universal kriging). This approach allows us to implement a scalable single-stage estimation procedure that easily accommodates a significant number of missing observations at some monitoring locations. We apply the model to predict long-term average concentrations of oxides of nitrogen (NO_x) from 2005-2007 in the Los Angeles area, based on data from 18 EPA Air Quality System regulatory monitors. The cross-validated R² is 0.67. The MESA Air study is also collecting additional concentration data as part of a supplementary monitoring campaign. We describe the sampling plan and demonstrate in a simulation study that the additional data will contribute to improved predictions of long-term average concentrations.

Keywords: Air Pollution; Exposure Assessment; Hierarchical Modeling; Maximum Likelihood; Spatio-Temporal Modeling; Universal Kriging.

Figure 1

AQS and MESA Air monitoring locations in Los Angeles, and the 200 cohort residence locations used for validation in simulation scenario. (All home locations jittered on map to protect confidentiality)

Figure 2

Example time series of log-transformed two-week average NO_x concentrations at three AQS monitors in the Los Angeles area for the period July 2005 through December 2007

Figure 3

Smoothed (line) and unsmoothed (points) empirical orthogonal basis functions based on AQS NO_x two-week averages in Los Angeles area (centered and normalized to SD=0.707 for smooth version).

Figure 4

Empirical autocorrelation functions for two-week average residuals after fitting to empirical orthogonal basis functions. (18 AQS monitors in Los Angeles area.)

Figure 5

Density plot and Normal Q-Q plot for log two-week average residuals after fitting to empirical orthogonal basis functions. (18 AQS monitors in Los Angeles area.)

Figure 6

Empirical variograms for the estimated spatial fields of long-term averages (β̂_0s) and coefficients of seasonal basis functions (β̂_1s, β̂_2s). The black curve represents a classical variogram estimate, and the red curve is derived using the robust modulus method. (18 AQS monitors in Los Angeles area.)

Figure 7

Cross-validated predictions of long-term average NO_x concentrations for 18 AQS monitors in Los Angeles area. The RMSE is 4.21 and the R² is 0.67. The formula used to compute R² is given in Section 4.5.

Figure 8

Simulation study results for the first twelve Monte-Carlo realizations. Scatter plots of predicted vs. true long-term average NO_x concentrations at 200 subject homes in validation set. Results based on using all AQS and MESA Air monitoring locations for parameter estimation and prediction.

Figure 9

Simulation study results for the first twelve Monte-Carlo realizations. Scatter plots of predicted vs. true long-term average NO_x concentrations at 200 subject homes in validation set. Results based on using only AQS and MESA Air “fixed sites” for parameter estimation and prediction.

Figure 10

Simulation study results for 48 Monte-Carlo realizations. Average root mean squared error for predicted vs. true long-term average NO_x concentrations at 200 subject homes in validation set. Results based on using different subsets of the AQS and MESA Air monitoring locations for parameter estimation and prediction in the spatio-temporal hierarchical model.

Figure 11

Simulation study results for 48 Monte-Carlo realizations. Average R² for predicted vs. true long-term average NO_x concentrations at 200 subject homes in validation set. Results based on using different subsets of the AQS and MESA Air monitoring locations for parameter estimation and prediction in the spatio-temporal hierarchical model. The formula used to compute R² is given in Section 4.5.