Analyzing Spatial Correlation Patterns of Water Quality Variables in Fluvial Networks

Abstract

Understanding how the correlation structure among water quality variables varies across space is critical for effective environmental monitoring and management. In this study, we propose a methodological framework to estimate and analyze spatially varying partial correlation matrices over a fluvial network, with a particular focus on the Piedmont region in northern Italy. We adopt the perspective of Object Oriented Data Analysis, treating correlation matrices as complex data objects defined over a graph-based domain. Given the limited number of repeated measurements available at each monitoring site, we develop a nonparametric, topology-aware kernel estimator to reconstruct and predict valid correlation matrices that respect the structure of the fluvial network. To summarize and compare these matrices, we further employ tools from Topological Data Analysis, such as Betti curves. Clustering these curves enables the identification of spatial patterns and seasonal dynamics in the interdependence of water quality variables. The integration of nonparametric smoothing, network-based prediction, and functional clustering offers an approach for detecting localized anomalies and guiding adaptive monitoring strategies in freshwater systems. As a result, the analysis reveals four clusters per season, potentially reflecting localized vulnerabilities driven by seasonal water availability and anthropogenic pressures such as water withdrawals.