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Daily Runoff Forecasting Using a Cascade Long Short-Term Memory Model that Considers Different Variables

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Accurate forecasts of daily runoff are essential for facilitating efficient resource planning and management of a hydrological system. In practice, daily runoff is needed for various practical applications and can be predicted using precipitation and evapotranspiration data. To this end, a long short-term memory (LSTM) under a cascade framework (C-LSTM) approach is proposed for forecasting daily runoff. This C-LSTM model is composed of a 2-level forecasting process. (1) In the first level, an LSTM is established to learn the relationship between the precipitation and evapotranspiration at present and to learn several meteorological variables one day in advance. (2) In the second level, an LSTM is constructed to forecast the daily runoff using the historical and simulated precipitation and evapotranspiration data produced by the first LSTM. Through cascade modeling, the complex features of the numerous targets in the different stages can be sufficiently extracted and learned by multiple models in a single framework. In order to evaluate the performance of the C-LSTM approach, four mesoscale sub-catchments of the Ljubljanica River in Slovenia were investigated. The results indicate that based on the root-mean-square error, the Pearson correlation coefficient, and the Nash-Sutcliffe model efficiency coefficient, the proposed model yields better results than two other tested models, including the normal LSTM and other neural network approaches. Based on the results of this study, we conclude that the LSTM under the cascade architecture is a valuable approach and can be regarded as a promising model for forecasting daily runoff.

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This work is supported in part by the National Natural Science Foundation of China (71801044, 71771033), the international cooperation of the Ministry of Science and Technology of China (12-24: bilateral project between China and Slovenia), the China Scholarship Council (201908500020), and the Natural Science Foundation of Chongqing (cstc2018jcyjAX0436). N. Bezak gratefully acknowledges funding by the Slovenian Research Agency (grants J2-7322 and P2-0180). We also would like to thank the Slovenian Environment Agency for data provision ( and LetPub ( for its linguistic assistance of this manuscript.


National Natural Science Foundation of China (71801044, 71771033), International Cooperation of the Ministry of Science and Technology of China (12–24: bilateral project between China and Slovenia), China Scholarship Council (201908500020), Natural Science Foundation of Chongqing (cstc2018jcyjAX0436), and Slovenian Research Agency (grants J2-7322 and P2-0180).

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Conceptualization: Y.B.; Methodology: Y.B. and C.L.; Formal analysis and investigation, Y.B. and N.B.; Writing - original draft preparation: Y.B. and N.B.; Writing - review and editing: K.S. and J.Z.; Funding acquisition: Y.B., N.B., and B.Z.; Resources: N.B.

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Correspondence to Yun Bai.

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Bai, Y., Bezak, N., Zeng, B. et al. Daily Runoff Forecasting Using a Cascade Long Short-Term Memory Model that Considers Different Variables. Water Resour Manage 35, 1167–1181 (2021).

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