Mathematical Geosciences

, Volume 48, Issue 5, pp 581–593 | Cite as

Air Quality Index Revisited from a Compositional Point of View

  • Eusebi Jarauta-BragulatEmail author
  • Carme Hervada-Sala
  • Juan José Egozcue
Special Issue


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.


Air pollution Air Quality Index Compositional data analysis Log-contrast Balance 



This work has been supported by the Ministerio de Economía y Competitividad of Spain under projects ENE2012-36871-C02-01, partially funded by the European Union, and METRICS Ref. MTM2012-33236; and within the framework of Consolidated Research Group of the Generalitat de Catalunya (Spain) AGAUR 2014-SGR-551. Authors also are thankful to Ayuntamiento de Madrid (Spain) for granting air pollution data.


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Copyright information

© International Association for Mathematical Geosciences 2015

Authors and Affiliations

  • Eusebi Jarauta-Bragulat
    • 1
    Email author
  • Carme Hervada-Sala
    • 2
  • Juan José Egozcue
    • 1
  1. 1.Departament de Matemàtica Aplicada III, ETS Enginyers de Camins, Canals i Ports de BarcelonaUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Departament de Física i Enginyeria Nuclear, Escola d’Enginyeria de TerrassaUniversitat Politècnica de CatalunyaTerrassaSpain

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