A hierarchical transformer and graph neural network model for high-accuracy watershed nitrate prediction

Non-point source pollution from agricultural activities poses a significant threat to water quality by introducing excess nutrients like nitrogen into aquatic ecosystems, leading to issues such as eutrophication and groundwater contamination. In agricultural watersheds, nitrate transport involves intricate physical, chemical, and biological processes influenced by meteorological conditions, hydrological features, and spatial topologies, making accurate short-term predictions challenging. Traditional data-driven deep learning models often fail to incorporate physical constraints and complex spatiotemporal dynamics, limiting their interpretability and predictive accuracy. Here we show a hierarchical transformer and graph neural network model that accurately predicts watershed nitrate concentrations by integrating multi-source data and simulating pollutant migration. The model captures nonlinear multivariate temporal patterns through hierarchical transformers, fuses global meteorological and local hydrological features via neural networks, and models runoff topologies with physically constrained graph neural networks. For predicting the concentration changes of pollutants discharged from watersheds, it outperforms baselines like multi-layer perceptrons, recurrent neural networks, and long short-term memory networks, with state-of-the-art performance in root mean square error, mean absolute error, and <i>R</i> ². Ablation studies confirm the essential roles of multi-source data integration and watershed topological modeling in enhancing performance. This method of directly modeling physical processes by leveraging the characteristics of different neural network architectures opens up a new path for addressing the interpretability problem in neural earth system modeling, apart from the process-guided deep learning and differentiable modelling methods.