Preprints
https://doi.org/10.5194/egusphere-2023-2710
https://doi.org/10.5194/egusphere-2023-2710
10 Jan 2024
 | 10 Jan 2024

Combining Recurrent Neural Networks with Variational Mode Decomposition and Multifractals to Predict Rainfall Time Series

Hai Zhou, Daniel Schertzer, and Ioulia Tchiguirinskaia

Abstract. Rainfall time series prediction is essential for monitoring urban hydrological systems, but it is challenging and complex due to the extreme variability of rainfall. A hybrid deep learning model (VMD-RNN) is used in order to improve prediction performance. In this study, variational mode decomposition (VMD) is first applied to decompose the original rainfall time series into several sub-sequences according to the frequency domain, where the number of decomposed sub-sequences is determined by power spectral density (PSD) analysis. To prevent the disclosure of forthcoming data, non-training time series are sequentially appended for generating the decomposed testing samples. Following that, different recurrent neural network (RNN) variant models are used to predict individual sub-sequences and the final prediction is reconstructed by summing the prediction results of sub-sequences. These RNN-variants are long short-term memory (LSTM), gated recurrent unit (GRU), bidirectional LSTM (BiLSTM) and bidirectional GRU (BiGRU), which are optimal for sequence prediction. In addition to three common evaluation criteria, mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE), the framework of universal multifractals (UM) is also introduced to assess the performance of predictions, which enables the extreme variability of predicted rainfall time series to be characterized. The study employs two rainfall time series with daily and hourly resolutions, respectively. The results indicate that the hybrid VMD-RNN model provides a reliable one-step-ahead prediction, with better performance in predicting high and low values than the pure LSTM model without decomposition.

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Journal article(s) based on this preprint

17 Sep 2025
Combining recurrent neural networks with variational mode decomposition and multifractals to predict rainfall time series
Hai Zhou, Daniel Schertzer, and Ioulia Tchiguirinskaia
Hydrol. Earth Syst. Sci., 29, 4437–4455, https://doi.org/10.5194/hess-29-4437-2025,https://doi.org/10.5194/hess-29-4437-2025, 2025
Short summary
Hai Zhou, Daniel Schertzer, and Ioulia Tchiguirinskaia

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-2710', Anonymous Referee #1, 26 Feb 2024
    • AC1: 'Reply on RC1', Hai Zhou, 11 Mar 2024
  • AC1: 'Reply on RC1', Hai Zhou, 11 Mar 2024
  • RC2: 'Comment on egusphere-2023-2710', Anonymous Referee #2, 06 Apr 2024
    • AC2: 'Reply on RC2', Hai Zhou, 01 May 2024

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-2710', Anonymous Referee #1, 26 Feb 2024
    • AC1: 'Reply on RC1', Hai Zhou, 11 Mar 2024
  • AC1: 'Reply on RC1', Hai Zhou, 11 Mar 2024
  • RC2: 'Comment on egusphere-2023-2710', Anonymous Referee #2, 06 Apr 2024
    • AC2: 'Reply on RC2', Hai Zhou, 01 May 2024

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload
ED: Publish subject to revisions (further review by editor and referees) (11 Jul 2024) by Pierre Gentine
AR by Hai Zhou on behalf of the Authors (06 Sep 2024)  Author's response   Author's tracked changes   Manuscript 
ED: Referee Nomination & Report Request started (17 Feb 2025) by Thom Bogaard
RR by Anonymous Referee #1 (21 Mar 2025)
RR by Anonymous Referee #3 (30 Apr 2025)
ED: Publish subject to minor revisions (review by editor) (13 Jun 2025) by Thom Bogaard
AR by Hai Zhou on behalf of the Authors (23 Jun 2025)  Author's response   Author's tracked changes   Manuscript 
ED: Publish as is (07 Jul 2025) by Thom Bogaard
AR by Hai Zhou on behalf of the Authors (11 Jul 2025)

Journal article(s) based on this preprint

17 Sep 2025
Combining recurrent neural networks with variational mode decomposition and multifractals to predict rainfall time series
Hai Zhou, Daniel Schertzer, and Ioulia Tchiguirinskaia
Hydrol. Earth Syst. Sci., 29, 4437–4455, https://doi.org/10.5194/hess-29-4437-2025,https://doi.org/10.5194/hess-29-4437-2025, 2025
Short summary
Hai Zhou, Daniel Schertzer, and Ioulia Tchiguirinskaia
Hai Zhou, Daniel Schertzer, and Ioulia Tchiguirinskaia

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Latest update: 17 Sep 2025
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Short summary
The hybrid VMD-RNN model provides a reliable one-step-ahead prediction, with better performance in predicting high and low values than the pure LSTM model. The universal multifractals technique is also introduced to evaluate prediction performance, thus validating the usefulness and applicability of the hybrid model.
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