Improvement of streamflow simulation by combining physically hydrological model with deep learning methods in data-scarce glacial river basin

Robust streamflow simulation at glacial basins is essential for the improvement of water sustainability assessment, water security evaluation, and water resource management under the rapidly changing climate. Therefore, we proposed a hybrid modelling framework to link the SWAT+ model considering glacial hydrological processes (GSWAT+) with Gated Recurrent Unit (GRU) neural networks to improve the model simulations and to establish a framework for the robust simulation and forecast of high and low flows in glacial river basins, which could be further used for the explorations of extreme hydrological events under a warming climate. The performance of different models (GSWAT+, GRU, and GRU-GSWAT+, respectively) were thoroughly investigated based on numerical experiments for two data-scarce glacial watersheds in Northwest China. The results suggested that the hybrid model (GRU-GSWAT+) outperformed both the individual deep learning (DL) model (GRU) and the conventional hydrological model (GSWAT+) in terms of simulation and prediction accuracy. Notably, the proposed hybrid model considerably enhanced the simulations of low and high flows that the conventional GSWAT+ failed to capture. Furthermore, utilizing suitable data integration (DI) schemes on feature and target sequences can substantially help to strengthen model stability and representativeness for monthly and annual streamflow sequences. Specifically, introducing one order differential method and decomposition approach, such as ensemble empirical signal decomposition (EEMD) and complete EEMD with adaptive noise (CEEMDAN), into feature and target sequences enriched the learnable ancillary information, which consequently strengthened the predictive performance of the proposed model. Overall, the proposed hybrid model with the suitable DI scheme has the potential to significantly enhance the accuracy of streamflow simulation in data-scarce glacial river basins. This hybrid model not only upheld the fundamental physical principles from the GSWAT+ model, but also considerably mitigated the accumulated bias errors, which caused by the shortage of climate data and inadequate hydrological principles, by using DL based model and DI schemes.