Lu et al. (2026) Robustness of critical soil moisture to curve-fitting methods and its variability with soil depth, soil texture, and climatic conditions: insights from lysimeter data in Germany

Identification

• Journal: Journal of Hydrology
• Year: 2026
• Date: 2026-01-13
• Authors: Xiao Lu, Jannis Groh, Alexander Graf, Thomas Pütz, Horst Gerke, Ralf Gründling, Holger Rupp, Ralf Kiese, Hans Jörg Vogel, Mathieu Javaux, Harry Vereecken, Harrie-Jan Hendricks Franssen
• DOI: 10.1016/j.jhydrol.2026.134959

Research Groups

• Institute of Bio- and Geoscience IBG-3: Agrosphere, Forschungszentrum Jülich GmbH, Jülich, Germany
• Faculty of Georesources and Materials Engineering, RWTH Aachen University, Aachen, Germany
• Department of Soil Science and Soil Ecology, University of Bonn, Institute of Crop Science and Resource Conservation, Bonn, Germany
• Leibniz Centre for Agricultural Landscape Research (ZALF), Müncheberg, Germany
• Department of Soil System Science, Helmholtz-Centre for Environmental Research – UFZ, Halle, Saale, Germany
• Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research, Atmospheric Environmental Research (IMK-IFU), Garmisch-Partenkirchen, Germany
• Earth and Life Institute, Environmental Sciences, UCLouvain, Belgium
• Water, Energy and Environmental Engineering Research Unit, University of Oulu, Finland

Short Summary

This study quantifies critical soil moisture thresholds (θcrit) using lysimeter data, finding robust estimates across different evapotranspiration definitions and fitting curves, but significantly higher θcrit for the root zone than for the surface, with both decreasing as sand fraction and aridity increase.

Objective

• To quantify critical soil moisture thresholds (θcrit) using lysimeter measurements, specifically considering root zone soil moisture (SM) in addition to near-surface SM.
• To evaluate the robustness of θcrit estimates when using different definitions of relative evapotranspiration (Evaporative Fraction (EF), ratio of actual ET to grass reference ET (rET0), and ratio of actual ET to FAO-56 potential ET (rPETFAO)).
• To investigate if θcrit varies when using different fitting functions (linear-plus-plateau vs. spherical variogram).
• To determine how θcrit derived from surface SM (10 cm) differs from θcrit derived from root zone SM (0–60 cm).
• To examine how θcrit changes for the same ecosystem under varying climatic conditions (aridity index) using a modified "space-for-time" concept.

Study Configuration

• Spatial Scale: 61 weighable lysimeters from 7 sites across Germany (TERENO-SOILCan network), spanning distances from 0 to 680 km. Each lysimeter has a surface area of 1.0 m² and a depth of 1.5 m. Soil moisture was measured at 10 cm, 30 cm, and 50 cm depths, with surface SM defined at 10 cm and root zone SM integrated from 0–60 cm.
• Temporal Scale: Growing seasons (April to September for grass, mid-season for crops) over multiple years (exact range not specified, but includes 2019 example). Lysimeter mass changes were recorded at 1-minute intervals, SM at 30-minute intervals, and meteorological data at 10-minute intervals, aggregated to daytime (9 a.m. to 5 p.m.) or hourly values for analysis. Long-term climatological averages (1981–2010 or 1991–2010) were used for aridity index calculations.

Methodology and Data

• Models used:
  • Linear-plus-plateau model (for fET-SM relationship)
  • Spherical variogram model (alternative fitting curve for SM-fET)
  • FAO Penman-Monteith equation (for grass reference evapotranspiration, ET0)
  • Calorimetric method (for surface soil heat flux, G0)
  • Akaike’s Information Criteria (AIC) (for model selection)
  • Wilcoxon test (for statistical significance)
  • Coefficient of determination (R²)
  • Root Mean Square Deviation (RMSD)
• Data sources:
  • Lysimeter observations: Weighable lysimeters (TERENO-SOILCan network) providing in-situ measurements of actual evapotranspiration (ETa) from mass changes (1-minute resolution), soil moisture (SM) at 10 cm, 30 cm, and 50 cm depths (30-minute resolution), and soil heat flux (G10) at 10 cm depth.
  • Meteorological data: Lysimeter weather stations (Vaisala WXT510, Ott Pluvio2, Vaisala WXT520, ecoTech, LAMBRECHT meteo) measuring air temperature, air humidity, wind speed, air pressure, global radiation, and precipitation (10-minute resolution). Net radiation (Rn) from LP Net07 sensors.
  • Ancillary data: TERENO data portal for gap-filling, German Weather Service (DWD) grid maps for annual ET0, and FAO-56 guidelines for crop coefficients (Kc mid), field capacity (FC), and wilting point (WP).

Main Results

• θcrit estimates were robust across three relative evapotranspiration definitions (EF, rET0, rPETFAO) and two fitting curves (linear-plus-plateau, spherical variogram), with RMSD values for definition comparisons generally less than 0.02 m³/m³.
• Root zone θcrit (0–60 cm) was significantly higher than surface θcrit (10 cm) (p < 0.05), with a mean difference of 0.046 m³/m³ (RMSD).
• A high correlation (r = 0.83) was observed between surface and root zone θcrit.
• Both surface and root zone θcrit exhibited a declining trend with increasing sand fraction; this trend was statistically significant for surface θcrit (p < 0.05).
• Under changing climatic conditions (increasing aridity index), both surface and root zone θcrit generally decreased, although this trend was not statistically significant.
• Root zone θcrit values estimated from lysimeter observations generally fell within the range provided by FAO-56 guidelines (midpoint between field capacity and wilting point) for sandy loam, loam, and silt loam, but some sandy clay loam values were higher than the FAO-56 range.

Contributions

• First-time quantification of θcrit using high-precision weighable lysimeter measurements, allowing for a direct assessment of root zone soil moisture control on evapotranspiration.
• Comprehensive evaluation of the robustness of θcrit estimates against different definitions of relative evapotranspiration (EF, rET0, rPETFAO) and alternative curve-fitting functions (linear-plus-plateau, spherical variogram).
• Detailed comparison of θcrit derived from surface versus root zone soil moisture, highlighting their differences and correlation.
• Investigation of the influence of soil texture and changing climatic conditions (aridity index) on θcrit using a unique "space-for-time" experimental setup with translocated lysimeters.
• Validation of FAO-56 derived root zone θcrit ranges against observation-based estimates, providing insights into the practical applicability of FAO-56 guidelines.

Funding

• China Scholarship Council (CSC), Grant: 202006710010
• Helmholtz Association (HGF) (for TERENO and SOILCan)
• Federal Ministry of Education and Research (BMBF) (for TERENO and SOILCan)
• Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project no. 460817082 (for Jannis Groh)

Citation

@article{Lu2026Robustness,
  author = {Lu, Xiao and Groh, Jannis and Graf, Alexander and Pütz, Thomas and Gerke, Horst and Gründling, Ralf and Rupp, Holger and Kiese, Ralf and Vogel, Hans Jörg and Javaux, Mathieu and Vereecken, Harry and Franssen, Harrie-Jan Hendricks},
  title = {Robustness of critical soil moisture to curve-fitting methods and its variability with soil depth, soil texture, and climatic conditions: insights from lysimeter data in Germany},
  journal = {Journal of Hydrology},
  year = {2026},
  doi = {10.1016/j.jhydrol.2026.134959},
  url = {https://doi.org/10.1016/j.jhydrol.2026.134959}
}