A visualizable deep learning model for multiscale precipitation-driven karst spring discharge

Groundwater from karst aquifers provides drinking water for 25% of the world's population. However, the complexity of karst terrain and karst aquifer heterogeneity hinders comprehensively understanding and predicting karst hydrological processes. This study proposes a deep learning model coupling a multiscale transformer (TSF) with a direction-constrained graph neural network (GNN) for forecasting karst spring discharge. The TSF deciphers the time-dependent patterns between precipitation and spring discharge, while the directed GNN tracks surface water convergence and the groundwater diffusion. Applying the model to Shentou Spring in northern China, we discover that visualization of attention weights in the TSF can reveal the multiscale temporal dependence of spring discharge on precipitation through successive transmission over a 12-month lead time, while the memory effect of transmitted information decays over time. Moreover, we find that the intra-patch attention weights at annual and seasonal scales follow normal distributions. The variability of spring discharge is most profound on an annual scale in the year's first half. At the seasonal scale, the variability of spring discharge driven by precipitation is the most significant in the summer and the slightest in the winter. On the other hand, visualization of edge weights in the directed GNN highlights the spatial dependence of spring discharge, depicting surface water convergence and groundwater diffusion. In addition, the groundwater flow field-based graph enables the GNN to yield the best predictive performance compared to the complete and information flow graph.