Spatiotemporal Modeling of Ambient Sulfur Dioxide Concentrations in Rural Western Canada

Abstract

The provinces of Saskatchewan, Alberta, and British Columbia are major oil- and gas-producing regions in western Canada. With increasing oil and gas production activities, there has been a growing concern of the effect of oil and gas industry emissions on health. Nevertheless, lack of proper tools to estimate the exposure to these emissions has been a hindrance to epidemiological studies and risk assessment. This paper presents a spatiotemporal modeling approach to estimating ambient sulfur dioxide (SO₂) levels based on environmental monitoring data (N = 10,295), which were collected at rural sites (591 per month on average) of this region from June 1, 2001 to May 31, 2002. Based on the model, illustrative maps consistently revealed high and low SO₂ concentration sub-regions. The sub-regions with elevated SO₂ concentrations had increased levels during the winter months from December 2001 to March 2002 and then decreased during the spring of 2002. This statistical modeling approach may help researchers estimate the SO₂ levels within the study area for their epidemiological studies or risk assessment.

Appendix

Assume that our interest is to predict SO₂ for August 2001 at the point S = (s ₁, s ₂). From the Eq. 4a, the predicted value of log-transformed SO₂ concentration ($\hat Y_{\left( {s,t} \right)}$) at S at time t = 3 becomes

$$\ifmmode\expandafter\hat\else\expandafter\^\fi{Y}_{{{\left( {s,3} \right)}}} = {\left( {\ifmmode\expandafter\hat\else\expandafter\^\fi{x}_{{_{1} }} \times \ifmmode\expandafter\hat\else\expandafter\^\fi{k}_{{_{1} }} + \ifmmode\expandafter\hat\else\expandafter\^\fi{x}_{{_{2} }} \times \ifmmode\expandafter\hat\else\expandafter\^\fi{k}_{{_{2} }} + \ldots + \ifmmode\expandafter\hat\else\expandafter\^\fi{x}_{{_{{64}} }} \times \ifmmode\expandafter\hat\else\expandafter\^\fi{k}_{{_{{64}} }} } \right)} + \ifmmode\expandafter\hat\else\expandafter\^\fi{\mu }_{3}$$

where ${\mathop x\limits^ \wedge }_{{_{1} }} ,{\mathop x\limits^ \wedge }_{{_{2} }} ,...{\text{ }}{\mathop x\limits^ \wedge }_{{_{{64}} }}$ correspond to the latent variables at the supporting sites as exemplified in the fourth column of Table 4 for August 2001 (t = 3) with all 64 elements, $\hat \mu _3 {\text{ = 0}}{\text{.03}}$ (mean for August 2001 (t = 3) taken from Table 2), and $\hat k_{_1 } ,\hat k_{_2 } , \ldots ,{\text{and}}\,\hat k_{_{64} }$ correspond to the kernel elements, which are a function of the distance from each supporting site ω ₁, ω ₂,…,ω ₆₄ (defined in the manuscript) to the point S = (s ₁, s ₂)

For example, $\hat k_{_1 }$is a bivariate Gaussian kernel function with mean 0 and standard deviation 200 km (determined from semivariograms in the manuscript) and is given by the equation

$$\ifmmode\expandafter\hat\else\expandafter\^\fi{k}_{{_{1} }} = \frac{1}{{2\pi \sigma ^{2} }}\exp {\left[ { - \frac{{d_{{_{1} }} ^{2} }}{{2\sigma ^{2} }}} \right]} = \frac{1}{{2\pi \times 200^{2} }}\exp {\left[ { - \frac{{{\left( {s_{1} - \omega _{{_{{11}} }} } \right)}^{2} + {\left( {s_{2} - \omega _{{_{{12}} }} } \right)}^{2} }}{{2 \times 200^{2} }}} \right]}$$

where d ₁ is the Euclidian distance from the point S = (s ₁, s ₂) to the supporting site ω ₁ = (ω ₁₁, ω ₁₂)

The concentration of SO₂ at the point S for August 2001 will be equal to $e^{\hat Y_{\left( {s,3} \right)} }$.