  Outdoor air pollution is estimated to cause a huge number of premature deaths
worldwide, it catalyses many diseases on a variety of time scales, and it has a
detrimental effect on the environment. In light of these impacts it is
necessary to obtain a better understanding of the dynamics and statistics of
measured air pollution concentrations, including temporal fluctuations of
observed concentrations and spatial heterogeneities. Here we present an
extensive analysis for measured data from Europe. The observed probability
density functions (PDFs) of air pollution concentrations depend very much on
the spatial location and on the pollutant substance. We analyse a large number
of time series data from 3544 different European monitoring sites and show that
the PDFs of nitric oxide ($NO$), nitrogen dioxide ($NO_{2}$) and particulate
matter ($PM_{10}$ and $PM_{2.5}$) concentrations generically exhibit heavy
tails. These are asymptotically well approximated by $q$-exponential
distributions with a given entropic index $q$ and width parameter $\lambda$. We
observe that the power-law parameter $q$ and the width parameter $\lambda$ vary
widely for the different spatial locations. We present the results of our data
analysis in the form of a map that shows which parameters $q$ and $\lambda$ are
most relevant in a given region. A variety of interesting spatial patterns is
observed that correlate to properties of the geographical region. We also
present results on typical time scales associated with the dynamical behaviour.
