A graph neural network-based model for spring discharge forecasting

Groundwater from karst aquifers supplies freshwater for 25% of the world population. Worldwidely, groundwater level has been descending, spring discharge has declined, and some springs have dried up due to climate changes and anthropogenic activities. Spring discharge as a proxy, can reflects the state of karst hydrological processes. Thus, simulation of spring discharge is vital in water resources development, utilization and management.

The forming processes of spring discharge in a basin include surface water convergence, dictated by terrains, and groundwater diffusion, controlled by heterogeneous aquifers. Consideration of the physical processes can better understand karst hydrological processes. Many machine learning models have recently been used to simulate karst spring processes, however, without considering the physical mechanisms. This paper develops a graph neural network (GNN) embedded with a heat kernel (HK) model to depict rainfall-runoff converging and groundwater diffusing processes in data insufficient area and finally realize spring discharge modeling. Application of the model to Niangziguan Springs, China, demonstrates that the GNN with the second-order HK has better metric performance than the first-order model in forecasting multi-time step spring discharge processes. The optimal graph structure of the model varies with the forecasting time step. The structure of one- and two-step forecasting is an information flow graph, which mainly describes the convergence of surface flow, while the structure of three- and four-step forecasting is a groundwater flow graph that stresses groundwater diffusion. The facts reveal that surface water convergence is completed within two months, and groundwater diffusion mainly happens between three and four months. GNN with HK is robust in depicting the karst hydrological processes with interpretability.