Toward improved lumped groundwater level predictions at catchment scale: Mutual integration of water balance mechanism and deep learning method

• A novel hybrid model for simulating groundwater level was developed. • The hybrid model integrated water balance equations with deep learning algorithm. • The proposed model presented the superiority and powerful simulation ability. • The automatic parameterizing ability enhanced the model for cross-region simulation. Model development in groundwater simulation and physics informed deep learning (DL) has been advancing separately with limited integration. This study develops a general hybrid model for groundwater level (GWL) simulations, wherein water balance-based groundwater processes are embedded as physics constrained recurrent neural layers into prevalent DL architectures. Because of the automatic parameterizing process, physics-informed deep learning algorithm (DLA) equips the hybrid model with enhanced abilities of inferring geological structures of catchment and unobserved groundwater-related processes implicitly. The main purposes of this study are: 1) to explore an optimized data-driven method as alternative to complicated groundwater models; 2) to improve the awareness of hydrological knowledge of DL model for lumped GWL simulation; and 3) to explore the lumped data-driven groundwater models for cross-region applications. The 91 illustrative cases of GWL modeling across the middle eastern continental United States (CONUS) demonstrate that the hybrid model outperforms the pure DL models in terms of prediction accuracy, generality, and robustness. More specifically, the hybrid model outperforms the pure DL models in 78 % of catchments with the improved Δ NSE = 0.129. Meanwhile, the hybrid model simulates more stably with different input strategies. This study reveals the superiority and powerful simulation ability of the DL model with physical constraints, which increases trust in data-driven approaches on groundwater modellings.