Contributed Session 9: Time & Clustering in Environmental Studies

The clustering of geo-referenced time series observed across different locations may be enhanced by incorporating spatial information to improve the interpretability of the resulting partitions. To achieve this, it is possible to define a suitable dissimilarity measure that accounts for spatial constraints. This paper explores three distinct approaches to integrating temporal and spatial dependencies within a Gaussian copula-based framework. The proposed methodologies are demonstrated through a case study involving climatological data.

We are interested in finding if there were structural breaks in the time series of greenhouse gases (GHGs) emissions in the UK and Italy since 1946. Specifically, we focus on the energy sector, which is the most relevant for GHG emissions. We compare breakpoints found by two different methods, that is, Hodrick Prescott filter with jumps and the Indicator Saturation regression model. We show that even if the time series exhibit very different pattern due to the country-specific economic and environmental History, several points of contacts between the methodologies exist. Indeed, most breaks are found by both methods on the same or very close dates.

Co-Fixed Rank Kriging (CFRK) is a hierarchical spatial mixed-effects model for complex data obtained by extending the Fixed Rank Kriging introduced by Cressie and J´ohannesson. In particular we focus on compositional data embedded in the Aitchison space. It integrates heterogeneous data sources by implementing the model on a hidden computational grid with a high resolution with respect to the observations layer. This hierarchical structure allows for upscaling and downscaling. We present a case study related to the air quality, with prediction of pollutant concentration at the municipal level. Finally, we discuss its advantages with respect to more traditional methods.