Graph Learning for River Water Quality Forecasting: Advances in Hydrological Connectivity Representation, Dynamic Topology, and Physics-Informed Modeling

Abstract

Graph neural networks are increasingly used for river water-quality forecasting because they can represent interactions among monitoring locations that conventional site-wise time-series models cannot capture. However, the usefulness of graph learning depends strongly on whether graph structure reflects the hydrological processes governing pollutant transport. This review examines recent advances in river-network graph learning from the perspectives of graph construction, dynamic connectivity, propagation delay, physical constraints, and model validation. Existing approaches are organized into geometric, correlation-based, hydrological topology, transport-weighted, dynamic, and physics-informed graphs. To clarify their increasing physical content, we propose a graph physical-fidelity ladder from H0 to H6 and evaluate validation strength independently on a V0–V3 axis, thereby separating what a graph represents from how rigorously that representation is tested. Current studies commonly rely on fixed adjacency structures, while variations in discharge, flow direction, travel time, tributary contributions, reservoir regulation, and pollutant-specific transformation remain incompletely represented. Particular attention is given to dynamic edge updating, event- and pollutant-adaptive graphs, travel-time-aware message passing, mass-conserving architectures, and cross-basin representation learning. We further argue that predictive accuracy alone is insufficient for establishing hydrological credibility. Learned connectivity and edge importance should be tested against flow direction, transport time, mass balance, and structural counterfactuals, including edge reversal, deletion, weight perturbation, and dynamic-graph freezing. Future progress will depend on matching the complexity of graph representations to the physical claims they support and on evaluating predictive skill together with structural validity, physical consistency, uncertainty, and transferability. Such hydrologically faithful graph learning could provide more reliable and operationally defensible river water quality forecasts.