Abstract. Runoff estimations play an important role in water resource planning and management. Existing hydrological models can be divided into physical models and data-driven models. Although the physical model contains certain physical knowledge and can be well generalized to new scenarios, the application of physical models is limited by the high professional knowledge requirements, difficulty in obtaining data and high computational costs. The data-driven model can fit the observed data well, but the estimation may not be physically consistent. In this letter, we propose a hybrid physical data (HPD) model combining physical model and deep learning model for runoff estimation. The model uses the output of a physical hydrological model together with the driving factors as another input of the neural network to estimate the monthly runoff of the upper Heihe River Basin in China. We show that the use of the HPD model improves the quality of runoff estimation, and results in high R2, NSE values of 0.969, and a low RMSE value of 9.645. It is indicated that the new model had an excellent learning capability to simulate runoff and flexible ability to extract complex relevant information; At the same time, the estimation capacity of peak runoff is optimized.
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