The final model is very flexible and includes autoregres-sive terms in time, different structures for the variance-covariance matrix of the errors, and can manage covariates available at different space-time resolutions. We deal with this type of data within a hierarchical Bayesian framework, in which observed measurements are modelled in the first stage of the hierarchy, while the unobserved spatio-temporal process is considered in the following stages. In this case, each spatio-temporal point has a number of measurements referring to the response variable observed several times over different locations in a close neighbourhood of the space-time point. Nonetheless, such a kind of data also arises when using a mobile monitoring station moving along a path for a certain period of time. Typically this situation arises when different measurements referring to several response variables are observed in each space-time point, for example, different pollutants or size resolved data on particular matter. This work deals with modelling spatio-temporal air quality data, when multiple measurements are available for each space-time point. Additional supporting information including source code to reproduce the results may be found in the online version of this article at the publisher's web-siteĮnvironmental data is typically indexed in space and time. Such features are consistent with the physics of atmospheric aerosol and the highlighted patterns provide a very useful ground for prospective model-based studies. Groups including coarser particles have more similar patterns, while those including finer particles show a more different behavior according to the period of the year. Results provide a good classification of the 21 size bins into a relatively small number of groups (between three and four) according to the season of the year. Functional cluster analysis is then performed to search for similarities among the 21 size channels in terms of their spatiotemporal pattern. FDA allows for a reduction of the dimensionality of each dataset and accounts for the high space-time resolution of the data. In fact, space is unidimensional since it is measured as the distance on the monorail from the base station of the Minimetrò. Here, we adopt a 2D functional data representation for each of the 21 spatiotemporal series. The OPC takes a sample of air every six seconds and counts the number of particles of urban aerosols with a diameter between 0.28 µm and 10 µm and classifies such particles into 21 size bins according to their diameter. An OPC (Optical Particle Counter) is integrated on a cabin of the Minimetrò, an urban transportation system, that moves along a monorail on a line transect of the town. Data come from a mobile measurement platform in the town of Perugia (Central Italy). In this work we propose the use of functional data analysis (FDA) to deal with a very large dataset of atmospheric aerosol size distribution resolved in both space and time.
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