Feizi et al. (2026) Streamflow Forecasting Based on PatchTST, LSTM, and Ensemble Learning Approaches

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-01-01
• Authors: Hajar Feizi, Mohammad Taghi Sattari
• DOI: 10.1007/s11269-025-04397-y

Research Groups

• Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran
• Water Sciences and Hydroinformatics Research Center, Khazar University, Baku, Azerbaijan

Short Summary

This study evaluates the performance of PatchTST and LSTM deep learning models for daily streamflow forecasting of the Sefidrud River, demonstrating that a Stacking Ensemble approach significantly enhances prediction accuracy compared to individual models.

Objective

• To investigate the effectiveness of the Patch Time Series Transformer (PatchTST) model for daily streamflow forecasting.
• To benchmark PatchTST's performance against the Long Short-Term Memory (LSTM) network.
• To assess whether ensemble learning approaches (Stacking and Weighted Averaging) can further enhance predictive skill for the Sefidrud River.

Study Configuration

• Spatial Scale: Sefidrud River, Iran, located approximately 100 km from the Caspian Sea, at the confluence of the Qezel Ozan and Shahrood rivers. The region is characterized as mountainous and semi-humid.
• Temporal Scale: Daily streamflow data collected from 2001 to 2024.

Methodology and Data

• Models used: Patch Time Series Transformer (PatchTST), Long Short-Term Memory (LSTM), Stacking Ensemble (using Random Forest as a meta-learner), Weighted Averaging Ensemble. Optimal input lag selection was performed using the Vector Autoregression (VAR) method with Akaike Information Criterion (AIC) and Schwarz Information Criterion (SIC).
• Data sources: Daily streamflow observations from the Sefidrud River, Iran. The dataset was split into 70% for training, 10% for validation, and 20% for testing.

Main Results

• The optimal number of time lags for model inputs was determined to be two, based on the VAR method's AIC and SIC criteria.
• The PatchTST model outperformed the LSTM model in forecasting daily streamflow values. For the test set, PatchTST achieved RMSE = 10.78 m³/s and MAE = 3.77 m³/s, while LSTM recorded RMSE = 21.31 m³/s and MAE = 7.75 m³/s.
• The ensemble methods, particularly the Stacking Ensemble, significantly improved forecasting accuracy. The Stacking Ensemble, utilizing Random Forest as the meta-learner, achieved the best overall performance with RMSE = 1.593 m³/s, MAE = 1.333 m³/s, NS = 0.991, and CC = 0.998 on the test set.
• The Stacking Ensemble model demonstrated superior capability in capturing streamflow fluctuations, especially during peak flow periods, with over 90% of its predictions having absolute errors below 5 m³/s.
• The Weighted Ensemble model (90% PatchTST, 10% LSTM) showed performance similar to the individual PatchTST model.

Contributions

• First application of the PatchTST model to hydrological forecasting, specifically for streamflow prediction.
• First evaluation of PatchTST's capability for streamflow prediction in the Sefidrud River.
• Exploration of ensemble frameworks to leverage the complementary strengths of distinct deep learning models (PatchTST and LSTM) in the context of streamflow forecasting.
• Demonstration of the superior performance and robustness of the Stacking Ensemble approach as a promising framework for daily streamflow prediction in mountainous and semi-humid regions.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Citation

@article{Feizi2026Streamflow,
  author = {Feizi, Hajar and Sattari, Mohammad Taghi},
  title = {Streamflow Forecasting Based on PatchTST, LSTM, and Ensemble Learning Approaches},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-025-04397-y},
  url = {https://doi.org/10.1007/s11269-025-04397-y}
}