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<p>The accurate estimation of reference evapotranspiration (ET₀) is critical to the effective and sustainable management of water resources, especially in regions where water scarcity and climate change are prevalent. In this article, the authors propose two novel hybrid models, SFS-ELM and SFS-LSTM, that integrate Stochastic Fractal Search (SFS) and state-of-the-art artificial intelligence algorithms to improve the accuracy and dependability of ET₀ predictions. The models incorporate MODIS satellite-based ET data and critical meteorological factors such as temperature, humidity, wind speed, and solar radiation to improve the accuracy and dependability of ET₀ predictions. The authors conducted the research in two geographically and climatically diverse regions in the north of Iran, namely Babolsar and Bandar Anzali, characterized by considerable climatic variability and scarcity of ground-based meteorological data, making the task extremely challenging. The performance of the models was evaluated through various statistical indicators, including RMSE, NSE, R², and WI, to assess the accuracy and dependability of the models’ predictions. The results showed that the proposed models, specifically the SFS-LSTM, outperformed the standalone LSTM model in the first region, where the RMSE and NSE values were 0.28&#xa0;mm/day and 0.99, respectively, as opposed to the standalone LSTM model’s 0.34&#xa0;mm/day and 0.98, respectively. In the second region, the proposed models also outperformed the standalone LSTM, where the RMSE and NSE were 0.37&#xa0;mm/day and 0.99, respectively, as opposed to the standalone LSTM’s 0.94&#xa0;mm/day and 0.86, respectively. The SHAP analysis revealed that the most critical factors affecting the accuracy of the models’ predictions are temperature and solar radiation, while humidity plays a moderating role in the models’ predictions, although to a lesser extent. The authors also tested the models’ performance with reduced variables, and the results showed considerable accuracy, indicating the potential of the models as alternatives to the conventional models, especially in regions where data is scarce and variability is considerable. The proposed models, specifically the hybrids, are highly accurate and dependable, and the results show that the models can be used to predict ET₀ with considerable accuracy and dependability, regardless of the climate and variability of the region, making the models extremely useful to the water resource management sector, especially in regions where water scarcity is considerable.</p>

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Optimized deep learning frameworks for evapotranspiration modeling: integrating MODIS satellite data and stochastic fractal search

  • 期刊论文

  • 发表日期：

    2026年7月21日

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  • Zahra Rousta,
  • Saeed Samadianfard,
  • Reza Delirhasannia,
  • Sadra Karimzadeh

摘要

The accurate estimation of reference evapotranspiration (ET₀) is critical to the effective and sustainable management of water resources, especially in regions where water scarcity and climate change are prevalent. In this article, the authors propose two novel hybrid models, SFS-ELM and SFS-LSTM, that integrate Stochastic Fractal Search (SFS) and state-of-the-art artificial intelligence algorithms to improve the accuracy and dependability of ET₀ predictions. The models incorporate MODIS satellite-based ET data and critical meteorological factors such as temperature, humidity, wind speed, and solar radiation to improve the accuracy and dependability of ET₀ predictions. The authors conducted the research in two geographically and climatically diverse regions in the north of Iran, namely Babolsar and Bandar Anzali, characterized by considerable climatic variability and scarcity of ground-based meteorological data, making the task extremely challenging. The performance of the models was evaluated through various statistical indicators, including RMSE, NSE, R², and WI, to assess the accuracy and dependability of the models’ predictions. The results showed that the proposed models, specifically the SFS-LSTM, outperformed the standalone LSTM model in the first region, where the RMSE and NSE values were 0.28 mm/day and 0.99, respectively, as opposed to the standalone LSTM model’s 0.34 mm/day and 0.98, respectively. In the second region, the proposed models also outperformed the standalone LSTM, where the RMSE and NSE were 0.37 mm/day and 0.99, respectively, as opposed to the standalone LSTM’s 0.94 mm/day and 0.86, respectively. The SHAP analysis revealed that the most critical factors affecting the accuracy of the models’ predictions are temperature and solar radiation, while humidity plays a moderating role in the models’ predictions, although to a lesser extent. The authors also tested the models’ performance with reduced variables, and the results showed considerable accuracy, indicating the potential of the models as alternatives to the conventional models, especially in regions where data is scarce and variability is considerable. The proposed models, specifically the hybrids, are highly accurate and dependable, and the results show that the models can be used to predict ET₀ with considerable accuracy and dependability, regardless of the climate and variability of the region, making the models extremely useful to the water resource management sector, especially in regions where water scarcity is considerable.