EGUsphere EGUsphere EGUsphere EGUsphere Copernicus Publications Göttingen, Germany 10.5194/egusphere-2026-2687 Physically constrained multi-task learning for hourly joint estimation of evapotranspiration and transpiration from sparse sap-flow data Fu Hongyang 1 Yang Yuanyuan https://orcid.org/0000-0002-8391-2528 1 Liu Dengfeng https://orcid.org/0000-0003-3831-3865 1 Li Qiang 2 He Zhihua https://orcid.org/0000-0002-0183-693X 3 Lei Huimin https://orcid.org/0000-0002-1175-2334 4 Khan Mohd Yawar Ali 5 Hussain Fiaz 6 State Key Laboratory of Water Engineering Ecology and Environment in Arid Area, Xi’an University of Technology, Xi’an, 710048, China State Key Laboratory of Soil and Water Conservation and Desertification Control, College of Forestry, Northwest A&F University, Yangling 712100, China School of Civil Engineering, Sun-Yat-Sen University, Zhuhai 519000, China State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China Department of Hydrogeology, Faculty of Earth Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia Department of Land and Water Conservation Engineering, Faculty of Agricultural Engineering and Technology, PMAS-Arid Agriculture University Rawalpindi, Rawalpindi 46300, Pakistan 09 07 2026 2026 1 38 Copyright: © 2026 Hongyang Fu et al. 2026 This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/ This article is available from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2687/ The full text article is available as a PDF file from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2687/egusphere-2026-2687.pdf

Hourly evapotranspiration (<em>ET</em>) estimation helps resolve rapid land-surface water and energy responses to radiation, atmospheric dryness, and aerodynamic forcing. However, the same change in total <em>ET</em> 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 <em>ET</em> is modeled only as a single bulk flux. Sap-flow observations provide direct information on transpiration (<em>T</em>), 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 <em>ET</em> and <em>T</em>. MLF-ETT estimates total <em>ET</em> and the transpiration fraction <em>T</em>/<em>ET</em>, deriving <em>T</em> as a bounded component of total <em>ET</em> under 0 &le; <em>T</em> &le; <em>ET</em>, so that limited <em>T</em> data contribute to joint <em>ET</em>-<em>T</em> learning rather than serving only as isolated <em>T</em> targets. Compared with the baselines of single-task XGBoost and multilayer perceptron models, the multi-task framework primarily improved <em>T</em> 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 <em>T</em> supervision remained limited by cross-site process differences and uncertainty in sap-flow-derived <em>T</em> data. Input allocation between shared and task-specific branches strongly affected model performance, whereas increasing the <em>T</em>-supervision weight alone did not consistently improve performance. Overall, the framework incorporates limited sap-flow-derived <em>T</em> data into hourly joint <em>ET</em>-<em>T</em> learning and estimates <em>T</em> as a physically bounded component of total <em>ET</em>, providing a constrained reference for sub-daily <em>ET</em> partitioning.

 National Natural Science Foundation of China 52279025