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<p>Accurate runoff prediction is crucial for flood mitigation, reservoir operation, and water resource management, while existing machine learning models for runoff prediction are plagued by peak flow underestimation, high uncertainty and poor robustness, unable to well address the time-variability and non-stationarity of runoff series. To solve these problems, this study proposes ER-CA-Transformer-BiLSTM, a hybrid physical-machine learning model combining Transformer and BiLSTM, which integrates the CEEMDAN-ARIMA decomposition module and a correction module based on multi-source physical data. Taking the Jingle Basin in the middle reaches of the Yellow River as the study area, the model was validated with daily runoff data from 2006 to 2014, and its performance was compared with the Xin’anjiang model, LSTM, Transformer, Transformer-BiLSTM and CA-Transformer-BiLSTM. At a 2-day lead time, the model achieved NSE = 0.994, KGE = 0.986, RMSE = 2.011&#xa0;m³/s and MAE = 1.401&#xa0;m³/s in the validation period with minimal peak flow error, proving that decomposition preprocessing and physical data correction can effectively boost predictive performance. Combined with the Bootstrap method for interval forecasting, the model obtained PICP = 98.501%, ACE = 1.325% and PINAW = 0.075 in validation, showing lower uncertainty than benchmark models. Even with the lead time extended to 4–6 days, the model maintained stable accuracy and robustness, with its NSE values outperforming the other four machine learning models by 5.83%–15.56%. These results provide an important reference for integrating physical mechanisms with deep learning in interval runoff forecasting, and lay a scientific foundation for basin flood prevention and mitigation.</p>

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Application of Transformer Hybrid Model in Runoff Process Prediction Based on Frequency Decomposition and Physical Correction of Multi-Source Data

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Gan Miao,
  • Wenzhong Li,
  • Chengshuai Liu,
  • Caihong Hu,
  • Xin Dong,
  • Haojie Li,
  • Yi Zhou,
  • Zhili Zhu

摘要

Accurate runoff prediction is crucial for flood mitigation, reservoir operation, and water resource management, while existing machine learning models for runoff prediction are plagued by peak flow underestimation, high uncertainty and poor robustness, unable to well address the time-variability and non-stationarity of runoff series. To solve these problems, this study proposes ER-CA-Transformer-BiLSTM, a hybrid physical-machine learning model combining Transformer and BiLSTM, which integrates the CEEMDAN-ARIMA decomposition module and a correction module based on multi-source physical data. Taking the Jingle Basin in the middle reaches of the Yellow River as the study area, the model was validated with daily runoff data from 2006 to 2014, and its performance was compared with the Xin’anjiang model, LSTM, Transformer, Transformer-BiLSTM and CA-Transformer-BiLSTM. At a 2-day lead time, the model achieved NSE = 0.994, KGE = 0.986, RMSE = 2.011 m³/s and MAE = 1.401 m³/s in the validation period with minimal peak flow error, proving that decomposition preprocessing and physical data correction can effectively boost predictive performance. Combined with the Bootstrap method for interval forecasting, the model obtained PICP = 98.501%, ACE = 1.325% and PINAW = 0.075 in validation, showing lower uncertainty than benchmark models. Even with the lead time extended to 4–6 days, the model maintained stable accuracy and robustness, with its NSE values outperforming the other four machine learning models by 5.83%–15.56%. These results provide an important reference for integrating physical mechanisms with deep learning in interval runoff forecasting, and lay a scientific foundation for basin flood prevention and mitigation.