Daily Runoff Forecasting Using a Hybrid Model Based on Variational Mode Decomposition and Deep Neural Networks

  • Xinxin He
  • Jungang Luo
  • Ganggang Zuo
  • Jiancang Xie


Accurate and reliable runoff forecasting plays an increasingly important role in the optimal management of water resources. To improve the prediction accuracy, a hybrid model based on variational mode decomposition (VMD) and deep neural networks (DNN), referred to as VMD-DNN, is proposed to perform daily runoff forecasting. First, VMD is applied to decompose the original runoff series into multiple intrinsic mode functions (IMFs), each with a relatively local frequency range. Second, predicted models of decomposed IMFs are established by learning the deep feature values of the DNN. Finally, the ensemble forecasting result is formulated by summing the prediction sub-results of the modelled IMFs. The proposed model is demonstrated using daily runoff series data from the Zhangjiashan Hydrological Station in Jing River, China. To fully illustrate the feasibility and superiority of this approach, the VMD-DNN hybrid model was compared with EMD-DNN, EEMD-DNN, and multi-scale feature extraction -based VMD-DNN, EMD-DNN and EEMD-DNN. The results reveal that the proposed hybrid VMD-DNN model produces the best performance based on the Nash-Sutcliffe efficiency (NSE = 0.95), root mean square error (RMSE = 9.92) and mean absolute error (MAE = 3.82) values. Thus the proposed hybrid VMD-DNN model is a promising new method for daily runoff forecasting.


Daily runoff forecasting Hybrid model Variational mode decomposition Deep neural networks 



This work was supported by the National Key R&D Program of China under Grant No. 2016YFC0401409 and the National Natural Science Foundation of China under Grant Nos. 51679186 and 51679188.

Compliance with Ethical Standards

Conflict of Interest

The authors declare no conflicts of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Xinxin He
    • 1
  • Jungang Luo
    • 1
  • Ganggang Zuo
    • 1
  • Jiancang Xie
    • 1
  1. 1.State Key Laboratory of Eco-hydraulics in Northwest Arid RegionXi’an University of TechnologyXi’anChina

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