Hybrid Lake Model (HyLake) v1.0: unifying deep learning and physical principles for simulating lake-atmosphere interactions

Abstract. Lake-atmosphere interactions play a critical role in Earth systems dynamics. However, accurately modelling key indicators of these interactions remains challenging due to their oversimplified physics in traditional process-based models or the limited interpretability of purely data-driven approaches. Hybrid models, which integrate physical principles with sparse observations, offer a promising path forward. This study introduces the Hybrid Lake Model v1.0 (HyLake v1.0), a novel framework that combines physics-based surface energy balance equations with a Bayesian Optimized Bidirectional Long Short-Term Memory-based (BO-BLSTM-based) surrogate to approximate lake surface temperature (LST) dynamics. The model was trained using data from the Meiliangwan (MLW) site in Lake Taihu. We evaluate HyLake v1.0 against the Freshwater Lake (FLake) model and other hybrid benchmarks (Baseline and TaihuScene) across multiple sites in Lake Taihu using both eddy flux covariance observations and ECMWF Reanalysis v5 (ERA5) data. Results show that HyLake v1.0 outperformed all comparative models at the MLW site and demonstrated strong capability in simulating lake-atmosphere interactions. In experiments assessing generalization and transferability in ungauged lake sites, HyLake v1.0 consistently exhibited superior performance over FLake and TaihuScene across all Lake Taihu sites using both observation- and ERA5-based forcing. It also maintained excellent skill when applied to the ungauged Chaohu, confirming its robustness even with unlearned forcing datasets. This study underscores the potential of hybrid modeling to advance the representation land-atmosphere interaction in Earth system models.