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Development and validation of physically constrained machine learning for improving remote sensing-based evapotranspiration estimation
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DOI：10.1016/j.rse.2026.115460.png)
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Abstract
En 中文
Accurate estimation of terrestrial evapotranspiration (ET) is vital for understanding water and carbon cycles. Advances in satellite remote sensing (RS) techniques have greatly prompted the development of ET models, yet their performance varies inconsistently across biomes due to structural and parameterization errors. Machine learning (ML) offers data-driven alternatives, but often lacks physical mechanism-based generalization. Here, we employed automatic ML (AutoML) to develop three model categories: unconstrained ML and deep learning (DL) models, input data-constrained models integrating physical ET estimates into training data, and loss function-constrained models incorporating physical equations into DL loss functions. Validation with site-based observations in the Heihe River Basin (HRB) (75% training, 25% validation) showed all models achieved root mean square errors (RMSEs) below 0.6 mm/d, with physical constraints enhancing generalization under extreme conditions. Out-of-sample tests indicated physical constraints improved spatial extrapolation ability, with DL models benefiting most with RMSEs reduction from 0.32 mm/d to 0.47 mm/d. Utilizing the best unconstrained (MLU), input data-constrained (MLI_SGC), and loss function-constrained (DLL_PM) models, we generated daily ET for the HRB spanning 2000–2021. Water balance-based validation revealed DLL_PM reduced mean absolute percent errors (MAPEs) by 53.9%, 5.2%, and 4.1% in the upper, middle, and lower reaches versus MLU, while outperforming MLI_SGC and two mainstream RS ET products (ETMonitor, PML-V2). Furthermore, we demonstrate that input data constraints enhance physical consistency by increasing the importance of physically based ET features, whereas loss function constraints reshape the DL learning process by modifying network weights and biases. The Akaike Information Criterion (AIC) further indicates that physically constrained models achieve accuracy gains with negligible increases in model complexity during training. These findings represent a meaningful step toward understanding how to effectively integrate physical constraints into ML models for ET estimation, and hold promise for advancing large scale water and energy cycle assessments under changing environmental conditions.
Keywords:
Machine learning
Evapotranspiration estimation
Physical constraints
Remote sensing
Deep learning
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11.4
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1.1W
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9.4W
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