A physics-constrained deep learning framework for actual evapotranspiration estimation using ground station observations and remote sensing data

Evapotranspiration (ET) is a key process in the water cycle. While machine learning-based methods have been increasingly applied to ET estimation, they typically neglect physical mechanisms and ecological impacts. This study proposes a physics-constrained hybrid model (TST-PHY) that incorporates Penman-Monteith-derived physical knowledge into the time series transformer (TST). The framework integrates Bayesian optimization to automatically determine optimal weights for physical mechanisms within the data-driven modeling workflow. The arid and semi-arid regions of Northern China (ASNC) were chosen as the study area, and our results show that the proposed framework optimally balances estimation error and the physical law, with value and trend constraint weights of 0.26 and 0.41, respectively. Moreover, proper physical constraints can improve the prediction accuracy, generalization, and physical consistency of TST-PHY at various spatiotemporal scales. In conclusion, this study establishes a novel paradigm for evapotranspiration estimation in data-sparse regions through the synergistic integration of data-driven and knowledge-based models.