Physically constrained multi-task learning for hourly joint estimation of evapotranspiration and transpiration from sparse sap-flow data

Abstract. Hourly evapotranspiration (ET) estimation helps resolve rapid land-surface water and energy responses to radiation, atmospheric dryness, and aerodynamic forcing. However, the same change in total ET may arise from different combinations of vegetation transpiration, soil evaporation, and canopy interception evaporation, making it difficult to interpret transpiration and its sub-daily variability when ET is modeled only as a single bulk flux. Sap-flow observations provide direct information on transpiration (T), but their site coverage is sparse and tree-to-site upscaling remains uncertain. To address this issue, we integrate FLUXNET2015, SAPFLUXNET, and GIMMS LAI4g data to develop a physically constrained multi-task learning framework, termed MLF-ETT, for hourly joint estimation of ET and T. MLF-ETT estimates total ET and the transpiration fraction T/ET, deriving T as a bounded component of total ET under 0 ≤ T ≤ ET, so that limited T data contribute to joint ET-T learning rather than serving only as isolated T targets. Compared with the baselines of single-task XGBoost and multilayer perceptron models, the multi-task framework primarily improved T estimation, particularly under within-site temporal generalization and high evaporative-demand conditions characterized by high vapor pressure deficit, high air temperature, or both. Cross-site spatial generalization showed stronger site dependence, indicating that the transferability of sparse T supervision remained limited by cross-site process differences and uncertainty in sap-flow-derived T data. Input allocation between shared and task-specific branches strongly affected model performance, whereas increasing the T-supervision weight alone did not consistently improve performance. Overall, the framework incorporates limited sap-flow-derived T data into hourly joint ET-T learning and estimates T as a physically bounded component of total ET, providing a constrained reference for sub-daily ET partitioning.