Discrete-Time Markov Chain Modelling of the Ontario Air Quality Health Index

The Air Quality Health Index (AQHI) is an aggregate indicator of air pollution used to communicate to Canadians the health impact of short-term exposure to current air pollutant levels. Understanding the stochastic behaviour of the AQHI can aid public health officials in predicting air pollution levels, determining the likelihood and duration of air quality advisories, and planning for increased strain on the health care system during periods of higher air pollution. Previous research has applied discrete-time Markov chains to investigate stochastic behaviour of air pollution indices but only in a handful of regions and none with the same climatic characteristics as Canadian regions. In this study, we investigated the stochastic behaviour of AQHI risk categories in Ontario (34 air monitoring stations) for 5 years from 2015 to 2019. We employed discrete-time Markov chains using three of the AQHI risk categories (Low Risk, Moderate Risk, High Risk) as states to determine (1) the transition probabilities between these states, (2) the long-run proportion of time spent in each state, and (3) the mean persistence time of each state. These results were then used to assess spatial trends in the stochastic behaviour of AQHI risk categories and the likelihood and duration of air quality advisories. Overall, the air quality (as characterised by the AQHI) in Ontario tends to decrease as population density increases. Urban areas spent a greater proportion of time in higher risk categories, and tended to remain in the higher risk categories for longer before transitioning.