Searching for structure in air pollutants concentration measurements

When studying air pollution measurements at different sites in a spatial area, we may search for a typical pattern,common to all curves, describing the underlying air pollution process in a pre-specified period. Another area ofinterest to support local authorities in air quality management may be the classification of the different sites inhomogeneous clusters and the group ranking that follows. Yet, there is variation in both amplitude and dynamicsamong the air pollutant concentrations measured at the different monitoring stations. Analyzing such measurements,where the basic unit of information is the entire observed process rather than a string of numbers, involvesfinding the time shifts or the warping functions among curves. The analysis is much more complicated if weconsider a multivariate process, that is, vector-valued air pollutant measurements. Following our previous workwhere an improved dynamic time-warping algorithm has been developed, especially in the multivariate case, andused both for classifying functional data and estimating the structural mean of a sample of curves, we analyzed themeasurements of some air pollutants in Emilia Romagna (northern Italy). In addition, for the univariate analyses,we applied the self-modeling warping function approach, which is also convenient for these data. Indeed, thismethod was found to be model-free and enough flexible to capture very complex and highly non-linear patterns.