Understanding Phosphorus Flux and Its Challenges: Innovations in Predictive Modeling

Human activities have drastically altered the natural phosphorus (P) cycle, ramping up annual phosphorus flux in the biosphere to an alarming 29 teragrams per year (Tg yr⁻¹) as highlighted by Yuan et al. in 2018. This surge can be largely attributed to agricultural runoff, wastewater discharge, and industrial activities, which have led to a significant accumulation of phosphorus in the environment. Unfortunately, the global recycling efficiency of phosphorus remains low, causing much of this nutrient to remain trapped in ecosystems. The consequence? Heightened risks of eutrophication in freshwater systems, posing severe threats to aquatic ecosystems and the services they provide.

The Need for Predictive Techniques and Source Tracing

The challenge of managing phosphorus pollution necessitates effective predictive techniques and source tracing methods. To tackle this, numerical models have become essential tools, aiding researchers and policymakers in predicting various water quality indicators and pinpointing pollution sources. These models offer high spatiotemporal resolution, making them effective for regional assessments. However, tidal river networks complicate this endeavor significantly. The interplay between tidal dynamics from the ocean and freshwater discharge from land introduces challenges in accurately simulating pollutant transport.

Internal factors, such as salinity gradients, channel morphology, and biogeochemical processes, further complicate the situation. This intricate relationship presents substantial challenges for traditional process-based models (PBMs), limiting their capacity to fully capture the dynamics of pollution transport in these complex environments. As a result, there is an urgent need for more effective models to predict phosphorus concentrations specifically in tidal river systems.

Advances in Deep Learning for Water Quality Prediction

Recent advancements in monitoring methods have resulted in the generation of extensive datasets, enabling the use of data-driven models powered by deep learning (DL) techniques for water quality simulation and prediction. For instance, researchers like Zheng et al. (2023) employed a multilayer perceptron (MLP) to predict key water quality parameters in the Zhujiang tidal river network. By integrating socio-economic features such as land use and population data, this model achieved impressive results with R² values exceeding 0.8 across multiple parameters.

Similarly, Hanson et al. (2020) compared a recurrent neural network (RNN) with a PBM for predicting phosphorus dynamics in Lake Mendota. While the RNN exhibited a superior overall fit and lower residuals, it sometimes produced extreme daily predictions outside realistic biogeochemical flux ranges. This points to a persistent issue: the data-driven nature of DL models can lead to violations of physical principles, particularly in systems with tightly coupled processes.

Theory-Guided Models: Merging Data with Physics

To address the limitations of purely data-driven models, researchers have turned to theory-guided approaches that integrate physical equations into the DL training process. For instance, Karpatne et al. (2017) advocated for models that incorporate physical laws directly in the loss function calculation. An exemplary study by Read et al. (2019) showcased this approach by guiding the training of a long short-term memory (LSTM) model with an energy conservation equation for lake temperature predictions. This hybrid model outperformed both standalone LSTMs and traditional PBMs, demonstrating the value of combining data-driven methodologies with physical constraints.

Identifying Pollution Sources: A Critical Step

Accurate predictions of environmental variables are essential, but identifying the sources of pollutants is equally critical in preventing further contamination. Various methods have been developed to address high-dimensional inverse problems, including Markov Chain Monte Carlo approaches and ensemble Kalman filters. Yet, these traditional techniques often require significant computational resources, especially when iterating with complex models.

Recent research has sought to meld DL techniques with interpretable methods to tackle these challenges. For example, Wang et al. (2022) used eXtreme Gradient Boosting (XGBoost) alongside Shapely additive explanation (SHAP) to identify pollution sources effectively. Similar efforts by Zhou et al. (2022) integrated graph neural networks with GNNExplainer to predict and track contamination patterns. While these methods have shown promise, they still rely heavily on individual predictions, which can lead to errors, particularly when dealing with smaller datasets.

Introducing the A-PSTGCN Model

To overcome the limitations faced by traditional DL models in predicting total phosphorus (TP), we developed the attention physically guided spatiotemporal graph convolutional neural network (A-PSTGCN). This innovative model integrates convective diffusion equations as physical constraints to enhance the model’s training and improve the accuracy of spatiotemporal predictions.

The A-PSTGCN employs an attention-based method for tracing pollution sources, distinguishing itself from existing physically-guided graph neural networks (PG-GNNs). While PG-GNNs primarily focus on static spatial relationships, our A-PSTGCN captures both temporal dynamics and spatial dependencies, essential for accurately modeling environmental processes. Furthermore, by incorporating physical mechanisms, the model constrains training in both time and space, ensuring physical knowledge influences how information is transmitted across the network.

Application in the Taihu Lake Basin

We implemented the A-PSTGCN in the Taihu Lake Basin in China, a complex tidal river system that poses unique challenges for predictive modeling. Using multi-scenario datasets derived from calibrated MIKE11 simulations, our proposed model demonstrated robust predictive performance, yielding accurate and physically consistent spatiotemporal predictions of regional TP concentrations.

Upon comparison with other predictive models, such as spatiotemporal graph convolutional networks and CNN-LSTM architectures, the A-PSTGCN showcased its superiority in predictive capability. Not only did it deliver enhanced accuracy, but it also effectively identified the primary sources of TP pollution within the region, revealing the principal controls on the variation.

By analyzing flow velocity and pollutant contributions before and after the extension of the Xinmeng River, we illustrated the complex interactions between dilution and resuspension in determining TP concentrations. These results emphasized the significant role of hydrodynamic processes—driven by both hydraulic engineering interventions and natural hydrological variability—in governing the transport and transformation of phosphorus within tidal river networks.

The developments surrounding the A-PSTGCN represent a promising frontier in environmental modeling, promising timely insights and robust predictions crucial for addressing phosphorus pollution in complex aquatic systems.