  Air pollution is one of the leading causes of death globally, and continues
to have a detrimental effect on our health. In light of these impacts, an
extensive range of statistical modelling approaches has been devised in order
to better understand air pollution statistics. However, the time-varying
statistics of different types of air pollutants are far from being fully
understood. The observed probability density functions (PDFs) of concentrations
depend very much on the spatial location and on the pollutant substance. In
this paper, we analyse a large variety of data from 3544 different European
monitoring sites and show that the PDFs of nitric oxide ($NO$), nitrogen
dioxide ($NO2$) and particulate matter ($PM10$ and $PM2.5$) concentrations
generically exhibit heavy tails and are asymptotically well approximated by
$q$-exponential distributions with a given width parameter $\lambda$. We
observe that the power-law parameter $q$ and the width parameter $\lambda$ vary
widely for the different spatial locations. For each substance, we find
different patterns of parameter clouds in the $(q, \lambda)$ plane. These
depend on the type of pollutants and on the environmental characteristics
(urban/suburban/rural/traffic/industrial/background). This means the effective
statistical physics description of air pollution exhibits a strong degree of
spatial heterogeneity.
