Model-Based Clustering of Trends and Cycles of Nitrate Concentrations in Rivers Across France

Elevated nitrate from human activity causes ecosystem and economic harm globally. The factors that control the spatiotemporal dynamics of riverine nitrate concentration remain difficult to describe and predict. We analyzed nitrate concentration from 4450 sites throughout France to group sites that exhibit similar trend and seasonal behaviors during 2010-2017 and relate these dynamics to catchment characteristics. We employed a latent-variable, Bayesian mixture of harmonic regressions model to infer site clustering based on multi-year trend and annual cycle amplitude and phase. We examined clustering patterns and relationships among nitrate level, trend, and seasonality parameters. Cluster membership probabilities were governed by continuous, latent variables that were informed with seven classes of covariates encompassing geology, hydrology, and land use. To relate interpretable parameters to the covariates, we modeled amplitude and phase separately in a novel framework employing a bivariate phase regression with the projected normal distribution. The analysis identified regional regimes of nitrate dynamics, including trend classifications. This approach can reveal general patterns that transcend small-scale heterogeneity, complementing site-level assessments to inform regional- to national-level progress in water quality. Supplementary materials accompanying this paper appear on-line.