Physics-augmented deep learning models for improving evapotranspiration estimation in global land regions

Existing evapotranspiration (ET) estimation models face inherent limitations when relying solely on physics-based or data-driven paradigms. To address this issue, we propose three data-physics hybrid modeling methods for improving instantaneous ET estimation in this study. A Physics-Data Learning (PDL) model is first formed by adding a complementary physical variable generated by Penman–Monteith (PM) equation to a deep learning (DL) model along with driving variables to regress latent heat flux. Building on the PDL, a Physics-Augmented Learning (PAL) model is then formulated by introducing a physics-augmented term into the loss function. Finally, a Physics-Augmented Residual Learning (PARL) model is developed by using the residual learning technique to deeply integrate the PM and pure DL baseline models. Using the FLUXNET dataset, three proposed models are compared with the baselines on ten vegetation types (VTs) across the globe. The results show that all proposed models improve the accuracy of two baselines and reduce the uncertainty of pure DL to different extents. Among them, the PARL achieves the highest accuracy and robustness, with NSE (RMSE) ranging from 0.71–0.82 (22.40–43.14 W/m2) across ten VTs. The PAL ranks second and effectively mitigates the PDL’s sensitivity to imperfect physical knowledge. Although three proposed models show better extrapolation ability than the pure DL under conditions of limited data, the PARL stands out for its superior generalization under four created extreme climate scenarios. These results confirm the potential of data-physics hybrid modeling in ET estimation, which is conducive to supporting efficient irrigation water management.