Geostatistical modelling of complex environmental datasets

Large environmental datasets are increasingly available from multiple sources. These datasets are often characterised by heterogeneous data-generating mechanisms, varying uncertainty structures and differing spatial and temporal resolutions. This heterogeneity poses significant challenges to the production of coherent and reliable official environmental statistics, which are essential for monitoring environmental processes and informing evidence-based policy decisions. Model-based approaches provide a systematic way to integrate these complex data sources, enabling consistent estimation and uncertainty quantification. Air quality datasets sit at the intersection of many research fields. However, building a ready-to-use data product requires solving several statistical challenges, such as harmonising heterogeneous sources, detecting outliers, imputing missing data with propagated uncertainty and reconciling spatial supports across applications. In this work, we present the AQCLIM data product, which combines a variety of daily air quality and climate data for Italy from 2013 to 2023. Using the AQCLIM dataset, we study the change-of-support problem with a Fixed Rank Kriging (FRK) model and propose a multivariate Low-Rank State-Space Model (LR-SSM) implemented in the geossm Python package