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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. 

Karst groundwater is a critical freshwater resource for numerous regions worldwide. Monitoring and predicting karst spring discharge is essential for effective groundwater management and the preservation of karst ecosystems. However, the high heterogeneity and karstification pose significant challenges to physics-based models in providing robust predictions of karst spring discharge. In this study, an interpretable multi-step hybrid deep learning model called selective EEMD-TFT is proposed, which adaptively integrates temporal fusion transformers (TFT) with ensemble empirical mode decomposition (EEMD) for predicting karst spring discharge. The selective EEMD-TFT hybrid model leverages the strengths of both EEMD and TFT techniques to learn inherent patterns and temporal dynamics from nonlinear and nonstationary signals, eliminate redundant components, and emphasize useful characteristics of input variables, leading to the improvement of prediction performance and efficiency. It consists of two stages: in the first stage, the daily precipitation data is decomposed into multiple intrinsic mode functions using EEMD to extract valuable information from nonlinear and nonstationary signals. All decomposed components, temperature and categorical date features are then fed into the TFT model, which is an attention- based deep learning model that combines high-performance multi-horizon prediction and interpretable insights into temporal dynamics. The importance of input variables will be quantified and ranked. In the second stage, the decomposed precipitation components with high importance are selected to serve as the TFT model’s input features along with temperature and categorical date variables for the final prediction. Results indicate that the selective EEMD-TFT model outperforms other sequence-to-sequence deep learning models, such as LSTM and single TFT models, delivering reliable and robust prediction performance. Notably, it maintains more consistent prediction performance at longer forecast horizons compared to other sequence-to-sequence models, highlighting its capacity to learn complex patterns from the input data and efficiently extract valuable information for karst spring prediction. An interpretable analysis of the selective EEMD-TFT model is conducted to gain insights into relationships among various hydrological processes and analyze temporal patterns.