Air Quality Index Revisited from a Compositional Point of View

Abstract

The so-called Air Quality Index (AQI), expresses the quality of atmospheric air. The overall AQI is determined from the AQIs of some reference air pollutants, which are calculated by a transform of the respective concentrations. Concentrations of air pollutants are compositional data; they are expressed as part of mass of each pollutant in a total air volume or mass. Therefore, air pollution concentration data, as compositional data, just provide ratio information between concentrations of pollutants. Operations involved in the computation of overall AQI are not admissible operations in the framework of compositional data analysis, as they destroy the original ratio information. Consequently, the standard methodology should be reviewed for such calculations, taking into account the principles and operations of compositional data analysis. The objective of this article is to present a first approach to incorporate compositional perspective to air quality expression. For this, it is proposed to use a balance log-contrast of concentrations expressed in $\upmu$g/m$^3$ to define a new kind of air quality indicator. Furthermore, the geometric mean of the concentrations is applied to obtain a new and simple scale air quality index, avoiding definition of piecewise linear interpolations used in the standard AQI computation. As an illustrative example, statistical analysis of atmospheric pollution data series (2004–2013) of the city of Madrid (Spain) has been carried out.