A Hybrid Model Coupling Physical Constraints and Machine Learning to Estimate Daily Evapotranspiration in the Heihe River Basin

Accurate estimation of surface evapotranspiration (ET) in the Heihe River Basin using remote sensing data is crucial for understanding water dynamics in arid regions. In this paper, by coupling physical constraints and machine learning for hybrid modeling, we develop a hybrid model based on surface conductance optimization. A hybrid modeling algorithm, two physical process-based ET algorithms (Penman–Monteith-based and Priestley–Taylor-based ET algorithms), and three pure machine learning algorithms (Random Forest, Extreme Gradient Boosting, and K Nearest Neighbors) are comparatively analyzed for estimating the ET. The results showed that, in general, the machine learning model optimized by parameters was able to better predict the surface conductance of the hybrid model. Driver analyses showed that radiation, normalized difference vegetation index (NDVI), and air temperature had high correlations with ET. The hybrid model had a better prediction performance for ET than the other five models, and it improved the R2 of the two physical process-based algorithms to 0.9, reduced the root mean square error (RMSE) to 0.5 mm/day, reduced the BIAS to 0.2 mm/day, and improved the Kling–Gupta efficiency (KGE) to 0.9. The hybrid model outperformed the others across different time scales, displaying lower BIAS, RMSE, and higher KGE. Spatially, its ET patterns aligned with regional vegetation changes, with superior accuracy in annual ET estimation compared to the other models. Comparison with other ET products shows that the estimation results based on the hybrid model have better performance. This approach not only improves the accuracy of ET estimation but also improves the understanding of the physical mechanism of ET estimation by pure machine learning models. This study can provide important support for understanding ET and hydrological processes under different climatic and biotic vegetation in other arid and semi-arid regions.