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A novel integration of cross variable transformer and signal decomposition for real-time prediction of river water level: an implication for sustainable water resources management
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  • Published: 16 February 2026

A novel integration of cross variable transformer and signal decomposition for real-time prediction of river water level: an implication for sustainable water resources management

  • Md. Jobayer Parvez Ratul1 na1,
  • Usmi Akter1 na1,
  • Tajrian Mollick2,
  • Md. Mahmudul Hasan  ORCID: orcid.org/0009-0004-5235-41313,4,5,
  • Md. Tasim Ferdous3,4,6,
  • N M Refat Nasher3,4 &
  • …
  • Md. Jahir Uddin1 

Scientific Reports , Article number:  (2026) Cite this article

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We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Environmental sciences
  • Hydrology
  • Water resources

Abstract

Conventional data-driven models require a substantial volume of meteorological and hydrological variables as input for the accurate prediction of river water level, which may not be feasible for many river basins having data scarcity. More particularly, the accurate prediction of river water level using a univariate approach often becomes difficult employing the conventional models. Placing this challenge as the key motivator, this study aims to propose a novel data-driven approach by combining five sophisticated preprocessing techniques, EMD, EEMD, CEEMDAN, VMD, and SVMD with a recently proposed model, namely cross-variable linear integrated enhanced Transformer (CLIENT), for improving the univariate predictions of river water level. The Rupsa-Pasur River, located at the southwestern coastal region of Bangladesh, was chosen as the study region due to its highly stochastic hydrological dynamics. Four statistical metrics, i.e., NRMSE, MAE, KGE, and NSE, were computed for all the developed models at both the training and testing phases following a uniform train-test ratio of 8:2. The Borda count strategy was implemented with a view to identifying the optimal data-driven model. Compared to the traditional lag features-based input combinations, the proposed framework achieved superior performance at both stations. Results exhibited that the SVMD-enhanced CLIENT model (referred to as the C6 model) outperformed all other models for both stations. The C6 model demonstrated better capability of recognizing the major portion of the hidden and advantageous signals within the time series. This led to in an NSE value of 0.999 during both the training and testing phases, indicating a notable enhancement compared to existing literature, while also achieving considerably lower computational costs for both stations. The framework’s capability to provide precise predictions based solely on historical water level data underscores its applicability in regions with limited data availability. Thereafter, an interactive graphical user interface (GUI) was developed with the C6 model following a five-fold cross validation and external validation.

Data availability

The datasets generated and/or analysed during the current study are available from the corresponding author, Md. Mahmudul Hasan, on reasonable request.

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Acknowledgements

The authors would like to express their sincere gratitude to the Editor-in-Chief and the anonymous reviewers for their insightful, constructive, and detailed feedback. We are grateful to the Bangladesh Water Development Board (BWDB) and the Texas Water Development Board (TWDB) for providing the historical water level datasets that were essential for the development and external validation of our models. The corresponding author, Md. Mahmudul Hasan, gratefully acknowledges Professor Dr. Mallik Akram Hossain, Dean of the Faculty of Life and Earth Sciences and former Chairman of the Department of Geography & Environment, Jagannath University, Dhaka, for his recognition and support in publishing this article.

Author information

Author notes

  1. Md. Jobayer Parvez Ratul and Usmi Akter contributed equally to this work.

Authors and Affiliations

  1. Department of Civil Engineering, Khulna University of Engineering & Technology, Khulna, 9203, Bangladesh

    Md. Jobayer Parvez Ratul, Usmi Akter & Md. Jahir Uddin

  2. Institute of Energy, University of Dhaka, Dhaka, 1000, Bangladesh

    Tajrian Mollick

  3. Department of Geography & Environment, Jagannath University, Dhaka, 1100, Bangladesh

    Md. Mahmudul Hasan, Md. Tasim Ferdous & N M Refat Nasher

  4. Data-Driven Research on Environment and AI Modelling (DREAM Lab), Jagannath University, Dhaka-1100, Bangladesh

    Md. Mahmudul Hasan, Md. Tasim Ferdous & N M Refat Nasher

  5. Dream Research and Development Foundation, DRDF, Dhaka-1207, Bangladesh

    Md. Mahmudul Hasan

  6. Department of Construction Engineering, École de Technologie Supérieure, Université du Québec, Montréal, QC H3C 1K3, Canada

    Md. Tasim Ferdous

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Contributions

Md. Jobayer Parvez Ratul: Conceptualization; Methodology; Software; Validation; Formal analysis; Investigation; Resources; Data curation; Visualization; Roles/Writing – original draft; and Writing – review & editing. Usmi Akter: Conceptualization; Methodology; Software; Validation; Formal analysis; Investigation; Resources; Data curation; Visualization; Roles/Writing – original draft; and Writing – review & editing. Md. Mahmudul Hasan: Supervision; Conceptualization; Project management; Resources; Data curation; Investigation; Visualization; Resources; Roles/Writing – original draft; and Writing – review & editing. Md. Tasim Ferdous:  Roles/Writing – original draft; and Writing – review & editing; Tajrian Mollick, N M Refat Nasher & Md. Jahir Uddin: Writing – review & editing.

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Correspondence to Md. Mahmudul Hasan.

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Ratul, M., Akter, U., Mollick, T. et al. A novel integration of cross variable transformer and signal decomposition for real-time prediction of river water level: an implication for sustainable water resources management. Sci Rep (2026). https://doi.org/10.1038/s41598-026-39591-4

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  • Received: 30 September 2025

  • Accepted: 05 February 2026

  • Published: 16 February 2026

  • DOI: https://doi.org/10.1038/s41598-026-39591-4

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Keywords

  • Time series forecasting
  • Coastal hydrology
  • Data-driven modeling
  • Transformer model
  • Decomposition
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ISSN 2045-2322 (online)

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