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<p>Potential evapotranspiration (ET₀) is a key component of hydrological and ecological processes, yet its reliable estimation remains challenging in data-scarce regions. This study develops a stacking ensemble framework that integrates Transformer, Informer, and FEDformer models to improve daily ET₀ estimation in the Songliao Basin, Northeast China, using limited meteorological inputs. The proposed model employs Hargreaves–Samani–based potential evapotranspiration (HS ET₀), together with daily minimum and maximum air temperatures (<i>T</i><sub><i>min</i></sub> and <i>T</i><sub><i>max</i></sub>) as model inputs. Ground-based ET₀ calculated using the FAO-56 Penman–Monteith method is used for model training, validation, and testing. Results show that the stacking ensemble consistently outperforms individual base models and achieves a reduction in RMSE of <b>10.22%~10.32%</b> comparing with the previous best-performing machine learning models, including Multilayer Perceptron (MLP), Convolutional Neural Network (CNN), Random Forest (RF), Support Vector Machine (SVM) and Long Short-Term Memory (LSTM) networks. SHAP-based sensitivity analysis indicates that HS ET₀ accounts for <b>56.96%~70.76%</b> of the total mean absolute SHAP value, highlighting its dominant contribution to ET₀ prediction under limited data conditions. Overall, the proposed framework provides a robust and practical solution for daily ET₀ estimation when complete meteorological observations are unavailable.</p>

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Stacking Ensemble Learning for Daily Potential Evapotranspiration using Limited Climate Data

  • 期刊论文

  • 发表日期：

    2026年2月18日

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  • Dong Zhang,
  • Yangyu Deng,
  • Yakun Liu,
  • Di Zhang

摘要

Potential evapotranspiration (ET₀) is a key component of hydrological and ecological processes, yet its reliable estimation remains challenging in data-scarce regions. This study develops a stacking ensemble framework that integrates Transformer, Informer, and FEDformer models to improve daily ET₀ estimation in the Songliao Basin, Northeast China, using limited meteorological inputs. The proposed model employs Hargreaves–Samani–based potential evapotranspiration (HS ET₀), together with daily minimum and maximum air temperatures (Tmin and Tmax) as model inputs. Ground-based ET₀ calculated using the FAO-56 Penman–Monteith method is used for model training, validation, and testing. Results show that the stacking ensemble consistently outperforms individual base models and achieves a reduction in RMSE of 10.22%~10.32% comparing with the previous best-performing machine learning models, including Multilayer Perceptron (MLP), Convolutional Neural Network (CNN), Random Forest (RF), Support Vector Machine (SVM) and Long Short-Term Memory (LSTM) networks. SHAP-based sensitivity analysis indicates that HS ET₀ accounts for 56.96%~70.76% of the total mean absolute SHAP value, highlighting its dominant contribution to ET₀ prediction under limited data conditions. Overall, the proposed framework provides a robust and practical solution for daily ET₀ estimation when complete meteorological observations are unavailable.