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<p>Accurate streamflow forecasting plays a vital role in effective water resource management, flood control, and hydrological planning. Traditional process-based approaches often face challenges in identifying and modeling the complex temporal dependencies inherent in streamflow data. Therefore, this study evaluates the performance of two deep learning models including Patch Time Series Transformer (PatchTST) and Long Short-Term Memory (LSTM) network for daily streamflow forecasting of the Sefidrud River. The LSTM model captures sequential and long-term dependencies in time series, whereas PatchTST leverages the Transformer architecture to extract both local and global features simultaneously. To enhance forecasting accuracy, two ensemble learning approaches, Stacking and Weighted Averaging, were developed to exploit the complementary strengths of the two base models. The number of input lags was determined using the Vector Autoregression (VAR) method, which identified two optimal lag terms as model inputs. Model performance was assessed using both numerical indices and graphical analyses. The results showed that the PatchTST model outperformed the LSTM model in forecasting daily streamflow values. Furthermore, the ensemble methods, particularly the Stacking Ensemble, significantly improved forecasting accuracy by integrating the complementary strengths of the two models. The Stacking approach achieved the best overall performance, with RMSE = 1.593&#xa0;m³/s, MAE = 1.333&#xa0;m³/s, NS = 0.991, and CC = 0.998. These findings highlight the potential of the Stacking Ensemble as a robust and promising framework for hydrological forecasting, particularly for daily streamflow prediction in mountainous and semi-humid regions.</p>

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Streamflow Forecasting Based on PatchTST, LSTM, and Ensemble Learning Approaches

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Hajar Feizi,
  • Mohammad Taghi Sattari

摘要

Accurate streamflow forecasting plays a vital role in effective water resource management, flood control, and hydrological planning. Traditional process-based approaches often face challenges in identifying and modeling the complex temporal dependencies inherent in streamflow data. Therefore, this study evaluates the performance of two deep learning models including Patch Time Series Transformer (PatchTST) and Long Short-Term Memory (LSTM) network for daily streamflow forecasting of the Sefidrud River. The LSTM model captures sequential and long-term dependencies in time series, whereas PatchTST leverages the Transformer architecture to extract both local and global features simultaneously. To enhance forecasting accuracy, two ensemble learning approaches, Stacking and Weighted Averaging, were developed to exploit the complementary strengths of the two base models. The number of input lags was determined using the Vector Autoregression (VAR) method, which identified two optimal lag terms as model inputs. Model performance was assessed using both numerical indices and graphical analyses. The results showed that the PatchTST model outperformed the LSTM model in forecasting daily streamflow values. Furthermore, the ensemble methods, particularly the Stacking Ensemble, significantly improved forecasting accuracy by integrating the complementary strengths of the two models. The Stacking approach achieved the best overall performance, with RMSE = 1.593 m³/s, MAE = 1.333 m³/s, NS = 0.991, and CC = 0.998. These findings highlight the potential of the Stacking Ensemble as a robust and promising framework for hydrological forecasting, particularly for daily streamflow prediction in mountainous and semi-humid regions.