Interpretable machine learning characterizes climate-dependent associations between riverine phosphorus and anthropogenic-environmental factors across a large monitoring network.

Phosphorus (P) pollution is a growing threat to freshwater ecosystems, yet climate-dependent statistical relationships between anthropogenic and environmental conditions and riverine P remain poorly characterized at large spatial scales. We compiled total P (TP) observations from 3460 monitoring stations in 520 basins (2012-2021) and fitted Generalized Additive Models (GAMs) separately for five Köppen-Geiger climate zones. For each zone, 11 progressively expanded models represented two-way interactions among 26 anthropogenic, environmental, climatic, spatial, and temporal predictors. Permutation feature importance and one- and two-dimensional partial dependence plots were used to assess the model's reliance on predictors and to visualize fitted marginal and joint associations. GAMs performed best in dry (R2 = 0.87) and tropical (R2 = 0.83) regions and least well in the temperate zone (R2 = 0.52). Anthropogenic and soil-P variables generally received the highest importance scores, with livestock variables especially prominent in temperate regions and topographic variables in dry regions. Fitted associations also differed among climate zones: TP was positively associated with population and runoff in continental regions; dry regions showed threshold-shaped relationships with temperature; polar regions exhibited seasonal variation in fitted TP relationships coinciding with snowmelt conditions; temperate regions showed strong model dependence on livestock and wastewater variables; and tropical regions showed temporal associations with soil-P variables and rainfall. Our results characterize statistical dependencies within the sampled monitoring network and provide hypotheses for subsequent process-based and causal investigation.