Modeling the Characteristics of Unhealthy Air Pollution Events: A Copula Approach

This study proposes the concept of duration (D) and severity (S) measures, which were derived from unhealthy air pollution events. In parallel with that, the application of a copula model is proposed to evaluate unhealthy air pollution events with respect to their duration and severity characteristics. The bivariate criteria represented by duration and severity indicate their structural dependency, long-tail, and non-identically marginal distributions. A copula approach can provide a good statistical tool to deal with these issues and enable the extraction of valuable information from air pollution data. Based on the copula model, several statistical measurements are proposed for describing the characteristics of unhealthy air pollution events, including the Kendall's τ correlation of the copula, the conditional probability of air pollution severity based on a given duration, the joint OR/AND return period, and the conditional D|S and conditional S|D return periods. A case study based on air pollution data indices was conducted in Klang, Malaysia. The results indicate that a copula approach is beneficial for deriving valuable information for planning and mitigating the risks of unhealthy air pollution events.