Improving Hydrological Modeling with Hybrid Models: A Comparative Study of Different Mechanisms for Coupling Deep Learning Models with Process-based Models

Accurate hydrological modeling is crucial for water resources management. Process-based models (PBMs) are physically interpretable yet cannot fully utilize large datasets. Deep learning models, especially Long Short-Term Memory (LSTM) networks, have exhibited remarkable simulation accuracy but lack physical interpretability. To integrate the strengths of PBMs and LSTM, this paper develops three hybrid models (HLUDC, HLBDC, and HLBDCT) by coupling LSTM with the HBV model. HLUDC incorporates the output of HBV into LSTM to enhance modeling capability. HLBDC connects the HBV model to an LSTM that estimates the parameters of HBV. HLBDCT further introduces time-varying parameters. Notably, the possible limitation of these models in data-scarce basins is unclear, as all models are trained with available observations. Therefore, we further evaluate the impact of the training data length on model stability. The hybrid models are applied to the daily streamflow simulation in the Jialing River Basin. The results indicate that the hybrid models effectively enhance streamflow simulation compared to benchmark models. HLBDCT performs the best with a 2.44%-13.43% improvement in Nash-Sutcliffe efficiency coefficient over HBV and LSTM, followed by HLBDC, while HLUDC performs the least. HLBDCT also performed well in simulating extreme flow. Both HLBDCT and HLBDC accurately estimate actual evapotranspiration without being trained on it, demonstrating their robust physical coherence. Furthermore, HBV, HLBDC, and HLBDCT exhibit higher stability when trained with different lengths of data compared to HLUDC and LSTM. Overall, this study provides a better understanding of the potential for using hybrid models to enhance hydrological simulation accuracy.