Document Type : Research Paper

Authors

• Negin Rashidi ¹
• Vahid Moosavi ²

¹ M.Sc. Graduate in Watershed Science and Engineering, Department of Watershed Engineering, Faculty of Natural Resources, Tarbiat Modares University, Noor, Iran

² Associate Professor, Department of Watershed Science and Engineering, Faculty of Natural Resources, Tarbiat Modares University, Noor, Iran

Abstract

Introduction
Groundwater level modeling has always been a major challenge in groundwater resource management due to its complex, nonlinear, and spatiotemporally dependent nature. The main objective of this study was to develop and evaluate a distributed deep learning-based modeling approach for the simultaneous prediction of groundwater levels in a network of piezometric wells within the Kouchesfahan aquifer located in the Sefidroud watershed. In this framework, each well was considered as a node in a graph network, and the model predicted groundwater levels for each well at the next monthly time step (t+1). By integrating graph neural networks with convolutional structures and long short-term memory architectures, the study aimed to identify the spatial and temporal dependencies governing aquifer behavior and improve prediction accuracy compared to conventional methods.
 
Materials and methods
In this study, four graph-based deep learning architectures, including Graph Neural Network (GNN), Graph Attention Network (GAT), Graph Convolutional Network (GCN), and the hybrid GCN–LSTM model, were employed. Here, GNN refers to the baseline GCN-based graph neural architecture using the standard graph convolution operator. Each piezometric well was represented as a graph node, and the adjacency matrix was constructed using inverse-distance weighting. Input data included hydroclimatic variables, geological information, pumping characteristics, and spatial distances related to hydrogeological factors. Model performance was evaluated using R², RMSE, MAE, NSE, and KGE indices. In the proposed model, GCN layers were first applied to the spatial graph of wells to extract spatial features and hydraulic dependencies. The resulting hidden representations were then transferred to the LSTM network to model temporal dependencies and groundwater level dynamics.
 
Results and discussion
The results indicated that while the GNN model could partially reconstruct the general trends of groundwater level changes, it lacked accuracy in representing extreme behaviors and temporal dependencies. The GAT model showed a slight improvement over GNN but remained limited in extracting deep temporal patterns. In contrast, the GCN model demonstrated better performance in identifying spatial dependencies, leading to a significant improvement in evaluation metrics. The best performance was achieved by the GCN-LSTM model, which effectively represented both spatial and temporal features simultaneously, showing the highest overlap with observed data. This model reached an R² of 0.896, RMSE of 0.336, and MAE of 0.269, indicating its high accuracy in predicting groundwater levels.
 
Conclusion
Hybrid graph-sequential architectures, especially GCN-LSTM, are highly effective for modeling complex aquifer hydrodynamics. This model predicted groundwater levels with high accuracy and outperformed purely graph-based models. Therefore, it is recommended for operational groundwater prediction and sustainable water management, serving as a novel framework to support better decision-making in water resources.

Keywords

• Adjacency Matrix
• Aquifer
• Artificial Intelligence
• Prediction
• Spatio-temporal Deep Learning