Contending with space–time interaction in the spatial prediction of pollution: Vancouver's hourly ambient PM₁₀ field

Abstract

SUMMARYIn this article we describe an approach for predicting average hourly concentrations of ambient PM 10 in Vancouver. We know our solution also applies to hourly ozone fields and believe it may be quite generally applicable. We use a hierarchical Bayesian approach. At the primary level we model the logarithmic field as a trend model plus Gaussian stochastic residual. That trend model depends on hourly meteorological predictors and is common to all sites. The stochastic component consists of a 24-hour vector response that we model as a multivariate AR(3) temporal process with common spatial parameters. Removing the trend and AR structure leaves 'whitened' time series of vector series. With this approach (as opposed to using 24 separate univariate time series models), there is little loss of spatial correlation in these residuals compared with that in just the detrended residuals (prior to removing the AR component). Moreover our multivariate approach enables predictions for any given hour to 'borrow strength' through its correlation with adjoining hours. On this basis we develop a spatial predictive distribution for these residuals at unmonitored sites. By transforming the predicted residuals back to the original data scales we can impute Vancouver's hourly PM 10 field.

Influence of meteorology on PM<sub>10</sub> trends and variability in Switzerland from 1991 to 2008

“…Assuming that the primary aerosol emissions are similar during all the weekdays, the increase during weekdays might be attributed, on the one hand to the production of secondary aerosols and on the other to a possible buildup of aerosols in consecutive days with high emissions. A similar weekly PM 10 pattern was found by Zidek et al (2002) for the city of Vancouver. The explanatory variables that were chosen for more than half (at least 7) of the models are summarized in Table 3.…”

Spatial‐temporal model for ambient air pollutants in the state of Kuwait

“…At each time t medians of temperature, wind speed and relative humidity are calculated from the six stations in addition to the prevailing wind directions are included in the deterministic term, so we can write X s ðtÞ ¼ XðtÞ. More variables can be added here such as monthly effect and seasonality effect if exist (see, for example Zidek et al, 2002;Carroll et al, 1997). Figure 2 shows time series plots of logged SO 2 and NCH 4 for Mansouriya and Rabiya stations, respectively.…”

“…Hierarchical Bayesian approaches for spatial prediction of air pollution have been developed in recent years. See for example Harrison and Stevens (1976), Mardia and Goodall (1993), Brown et al (1994) and Zidek et al (2002). Based on a set of vector valued responses together with the associated level of covariates, levels of pollutant responses for the same sites are predicted and hence the values of the loss function for these different models are compared.…”

A multivariate prediction of spatial process with non-stationary covariance for Kuwait non-methane hydrocarbons levels

“…Statistical modeling and prediction of one or more pollutants generated at each of a regular series of timepoints over a non-overlapping regions of the same geographical domain has been a concern of statisticians. For example, Carroll et al (1997) studied ozone exposure in Harris country Texas, Zidek et al (2002) dealt with particulate matter PM 10 for Vancouver city, Kibria et al (2002) predicted PM 2.5 exposure for Philadelphia, and Huerta et al (2004) considered hourly readings of concentration of ozone O 3 over Mexico City. Tonellato (2001) analyzed concentration of carbon monoxide CO 2 in city of Venice.…”