Liu et al. (2025) The impact of nonlinear surface energy partitioning on potential evapotranspiration: A machine learning study based on FLUXNET data

Identification

• Journal: Agricultural and Forest Meteorology
• Year: 2025
• Date: 2025-12-31
• Authors: Weiqi Liu, Shaoxiu Ma, Haiyang Xi, Linhao Liang, Kun Feng, Atsushi Tsunekawa
• DOI: 10.1016/j.agrformet.2025.111005

Research Groups

• Key Laboratory of Ecological Safety and Sustainable Development in Arid Lands, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, China
• University of Chinese Academy of Sciences, Beijing, China
• International Platform for Dryland Research and Education, Tottori University, Tottori, Japan

Short Summary

This study investigates the nonlinear relationship of the no-water-limited Bowen ratio (βNWL) with environmental factors using global FLUXNET data and machine learning, developing a new PET model (PETβNWL−RF) that significantly improves daily potential evapotranspiration estimation and drought monitoring accuracy.

Objective

• To investigate the dominant factors influencing the no-water-limited Bowen ratio (βNWL) and simulate its nonlinear relationship with environmental factors using global flux observations and machine learning.
• To develop and evaluate an energy balance-based potential evapotranspiration (PET) model (PETβNWL−RF) incorporating the nonlinear βNWL, comparing its performance against commonly used PET models under various conditions, including drought.

Study Configuration

• Spatial Scale: Global, utilizing data from 157 FLUXNET observation sites across diverse plant functional types and climatic regions. ERA5 reanalysis precipitation data at 0.25° spatial resolution and Global Aridity Index data at approximately 1 km spatial resolution were also used.
• Temporal Scale: Daily observations from FLUXNET, with no-water-limited days predominantly identified between 2006 and 2023 (mostly April to September). Monthly ERA5 precipitation data and WorldClim 2.1 climate data (1970–2000) were used for aridity index calculations. The study evaluated daily PET and analyzed performance during the 2012 summer drought (May–August).

Methodology and Data

• Models used:
  • Machine Learning: Random Forest (RF) model for simulating the nonlinear relationship of βNWL with environmental factors.
  • Developed PET model: PETβNWL−RF (an energy balance-based model incorporating RF-simulated βNWL).
  • Compared PET models:
    • Energy balance-based: Priestley–Taylor model (PETβNWL−PT), Milly and Dunne model (PETβNWL−MD), Tu et al. model (PETβNWL−Tu).
    • Combination models: Reference crop evapotranspiration model (PETrc), PETco2 model.
• Data sources:
  • Global FLUXNET2015 dataset.
  • Regional flux datasets: AmeriFlux, OZFlux, and ICOS.
  • ERA5 reanalysis dataset for precipitation.
  • Global Aridity Index and Potential Evapotranspiration Database v3 from the CGIAR Consortium for Spatial Information (CSI).
  • WorldClim 2.1 climate data (1970–2000).

Main Results

• The no-water-limited Bowen ratio (βNWL) exhibits significant spatiotemporal variability across vegetation types, climatic conditions, and seasons, challenging the assumption of a constant value.
• Gross Primary Productivity (GPP) is the most influential factor affecting βNWL dynamics, accounting for 31% of relative importance, followed by CO₂ concentration, incoming shortwave radiation (SWin), vapor pressure deficit (VPD), and air temperature (Ta).
• The developed PETβNWL−RF model demonstrated superior accuracy in daily PET estimation compared to observations, achieving R² ≥ 0.93, Taylor Skill Score (TSS) ≥ 0.96, Root Mean Square Error (RMSE) ≤ 0.48 mm/day, and Mean Bias (MB) between -0.04 mm/day and 0.06 mm/day.
• The PETβNWL−RF model achieved the highest Global Performance Index (GPI) across all vegetation types, significantly outperforming commonly used PET models, especially in grasslands and open shrublands.
• Commonly used PET models exhibited significant biases (overestimation or underestimation) in PET estimation, particularly under drought conditions and during extreme drought events, with combination models showing larger deviations than energy balance-based models.

Contributions

• Reveals the significant spatiotemporal variability and nonlinear nature of the no-water-limited Bowen ratio (βNWL), challenging the fixed-parameter assumptions in many existing PET models.
• Identifies Gross Primary Productivity (GPP) as the dominant environmental driver of βNWL dynamics, providing crucial insights into surface energy partitioning.
• Develops a novel hybrid PET model (PETβNWL−RF) by integrating a Random Forest machine learning algorithm with a physical energy balance framework, leading to significantly improved accuracy and robustness in daily PET estimation.
• Demonstrates that the PETβNWL−RF model effectively reduces uncertainty and systematic biases in PET estimation, particularly under drought conditions, thereby enhancing the reliability of drought monitoring and hydrological applications.

Funding

• National Natural Science Foundation of China [grant numbers: 52379031]
• “Light of the West” Cross-team Project of the Chinese Academy of Sciences [grant numbers: xbzg-zdsys-202103]
• Gansu Provincial Science and Technology Planning Project [grant numbers: 23ZDFA018]
• 2025 Gansu Provincial Science and Technology Planning Project [grant numbers: E531890116]
• 2022 Gansu Postdoctoral Funding Program-Provincial Department of Human Resources and Social Affairs [grant numbers: E339880217]

Citation

@article{Liu2025impact,
  author = {Liu, Weiqi and Ma, Shaoxiu and Xi, Haiyang and Liang, Linhao and Feng, Kun and Tsunekawa, Atsushi},
  title = {The impact of nonlinear surface energy partitioning on potential evapotranspiration: A machine learning study based on FLUXNET data},
  journal = {Agricultural and Forest Meteorology},
  year = {2025},
  doi = {10.1016/j.agrformet.2025.111005},
  url = {https://doi.org/10.1016/j.agrformet.2025.111005}
}