Multi-scale dynamic spatiotemporal graph attention network for forecasting karst spring discharge

Abstract

Karst aquifers are important groundwater resources that supply drinking water for approximately 25 % of the world’s population. Their complex hydrogeological structures, dual-flow regimes, and highly heterogeneous flow pose significant challenges for accurate hydrodynamic modeling and sustainable management. Traditional modeling approaches often struggle to capture the intricate spatial dependencies and multi-scale temporal patterns inherent in karst systems, particularly the interactions between rapid conduit flow and slower matrix flow. This study proposes a novel multi-scale dynamic graph attention network integrated with long short-term memory model (GAT-LSTM) to innovatively learn and integrate spatial and temporal dependencies in karst systems for forecasting spring discharge. The model introduces several innovative components: (1) graph-based neural networks with dynamic edge-weighting mechanism are proposed to learn and update spatial dependencies based on both geographic distances and learned hydrological relationships, (2) a multi-head attention mechanism is adopted to capture different aspects of spatial relationships simultaneously, and (3) a hierarchical temporal architecture is incorporated to process hydrological temporal patterns at both monthly and seasonal scales with an adaptive fusion mechanism for final results. These features enable the proposed model to effectively account for the dual-flow dynamics in karst systems, where rapid conduit flow and slower matrix flow coexist. The newly proposed model is applied to the Barton Springs of the Edwards Aquifer in Texas. The results demonstrate that it can obtain more accurate and robust prediction performance across various time steps compared to traditional temporal and spatial deep learning approaches. Based on the multi-scale GAT-LSTM model, a comprehensive ablation analysis and permutation feature important are conducted to analyze the relative contribution of various input variables on the final prediction. These findings highlight the intricate nature of karst systems and demonstrate that effective spring discharge prediction requires comprehensive monitoring networks encompassing both primary recharge contributors and supplementary hydrological features that may serve as valuable indicators of system-wide conditions.