Data-Driven Gray Box Modeling for Predicting Basin-Scale Groundwater Variations in Central Taiwan

In this study, we present a data-driven approach, referred to as gray box modeling, that aims to achieve a balance between the transparency of white box models and the predictive power of black box models in groundwater level prediction. We conceptualized the groundwater system as a series of three interconnected tanks representing the surface, the unsaturated zone, and the saturated zone (aquifer). Each tank accounted for various hydrological processes, including rainfall, infiltration, interflow, recharge, groundwater discharge, and pumping. A signal processing approach called average magnitude of pumping (AMP) was used to evaluate the pumping rate. The methodology involved data collection and preparation, curve fitting using the least-squares method, and performance evaluation metrics such as root-mean-square error (RMSE), mean absolute error (MAE), and R2. The gray box model was validated by a training and testing process to ensure its accuracy. Then, the gray box model was applied on the entire data set to predict the groundwater level of three observation stations located in the Chou-Shui Chi alluvial fan. The groundwater budget results indicated higher rainfall recharge for the stations located in the top fan compared to the station in the middle fan, highlighting the impact of geological factors on groundwater recharge and response to rainfall. Furthermore, the results revealed a negative balance in the groundwater budget at one station; this can be attributed to a significant increase in pumping intensity, emphasizing the importance of understanding the relative contributions of various fluxes to groundwater level variations. Last, the gray box approach introduced in this study demonstrated applicability across diverse hydrogeological settings at large basin scales, especially in situations with data limitations for complex physically based models. The method is a valuable and efficient tool for sustainable management of extensive aquifer systems.