Zhu et al. (2026) A global framework for subsurface soil moisture estimation: Coupling fractal Richards equation with Bayesian optimization

Identification

• Journal: Remote Sensing of Environment
• Year: 2026
• Date: 2026-02-18
• Authors: Ziyue Zhu, John Eylander, Venkataraman Lakshmi
• DOI: 10.1016/j.rse.2026.115318

Research Groups

• University of Virginia, Department of Civil and Environmental Engineering, Charlottesville, VA, USA
• U.S. Army Corps of Engineers, Cold Regions Research and Engineering Laboratory, Vicksburg, MS, USA

Short Summary

This study develops a global, satellite-based framework (ExpF-FRE) to extend near-surface soil moisture (SM) measurements (0–5 cm) to subsurface depths of 20 cm and 50 cm at 400 m daily resolution, demonstrating robust performance against in situ observations and reanalysis products without site-specific calibration.

Objective

• To develop a global, satellite-based framework for monitoring subsurface soil moisture (SM) at 20 cm and 50 cm depths, extending near-surface satellite SM measurements (0–5 cm) at 400 m daily temporal repeat, without requiring site-specific calibration.

Study Configuration

• Spatial Scale: Global (45°S–60°N, 180°W–180°E), 400 m spatial resolution.
• Temporal Scale: Daily, from 2017 to 2020.

Methodology and Data

• Models used:
  • Exponential Filter (ExpF)
  • Fractal Richards Equation (FRE)
  • Bayesian Optimization (Adaptive Bayesian Optimization - ABO)
  • ROSETTA model (for estimating saturated hydraulic conductivity, Ks)
• Data sources:
  • Satellite:
    • SMAP L2 radiometer observations (downscaled to 400 m surface SM)
    • MODIS (MOD11A1 Collection-6.1 daily L3 Land Surface Temperature - LST)
    • VIIRS (Leaf Area Index - LAI, LST)
    • GLC_FCS30 (Land Cover/Land Use Data)
  • Observation:
    • International Soil Moisture Network (ISMN) in-situ SM measurements (for calibration and validation)
  • Reanalysis/Database:
    • ERA5-Land Data (7–28 cm SM, 28–100 cm SM)
    • GLDAS-2.1 Noah Data (10–40 cm SM, 40–100 cm SM)
    • Harmonized World Soil Database version 2.0 (HWSD v2.0) (clay, silt, sand content, bulk density)
    • Koppen-Geiger world climate classification map
    • Climate Forecast System Reanalysis (CFSR) (for VIIRS LST atmospheric profiles)

Main Results

• The ExpF-FRE model demonstrated robust performance for subsurface SM estimation, with global-scale mean correlation coefficients (R) of approximately 0.804 at 20 cm and 0.623 at 50 cm.
• Unbiased root-mean-square errors (ubRMSE) were 0.033 m³/m³ at 20 cm and 0.041 m³/m³ at 50 cm, with minor biases of -0.005 m³/m³ and -0.011 m³/m³ respectively.
• The model reliably captures both seasonal dynamics and interannual variability in SM across diverse climate conditions, maintaining strong performance even under challenging environmental contexts such as winter/low-LST regimes and dense vegetation.
• Uncertainty was quantified via Monte-Carlo perturbations, highlighting depth-dependent confidence and targets for improvement.
• The physically derived characteristic transfer time (Topt) values predominantly range from 1 to 4 days (median: 27.3 hours, mean: 43.4 hours) at 20 cm depth, and shift significantly toward longer timescales at 50 cm depth (median: 144.9 hours, mean: 248.2 hours).
• Topt exhibits clear geographic heterogeneity linked to environmental and climatic variability, with shorter Topt in cold and tropical/temperate climates and longer in arid regions.

Contributions

• Developed a novel global, satellite-based framework (ExpF-FRE) that extends surface SM to 20 cm and 50 cm depths at 400 m daily resolution, bridging the critical gap in Earth observation for subsurface SM monitoring.
• Replaced the empirical characteristic transfer time (T) in the Exponential Filter with a physically derived, pixel- and depth-specific optimized timescale (Topt), informed by globally available soil hydraulics, satellite surface SM, and dynamic land-surface temperature and leaf area index.
• Enabled global root-zone moisture monitoring without site-specific calibration, providing observation-constrained, physically derived subsurface SM estimates that complement land-surface model products.
• Integrated empirical filtering with a fractal-diffusion representation of vertical transfer, calibrated via Bayesian optimization, offering a scalable and physically interpretable solution for global-scale subsurface SM estimation.
• Generated a globally consistent subsurface SM dataset spanning 2017–2020 at 400 m daily resolution.

Funding

• Project ERDC-CHL-2024-0004 from the U.S. Army Corps of Engineers – Engineer Research and Development Center - Coastal and Hydraulics Laboratory (ERDC CHL).

Citation

@article{Zhu2026global,
  author = {Zhu, Ziyue and Eylander, John and Lakshmi, Venkataraman},
  title = {A global framework for subsurface soil moisture estimation: Coupling fractal Richards equation with Bayesian optimization},
  journal = {Remote Sensing of Environment},
  year = {2026},
  doi = {10.1016/j.rse.2026.115318},
  url = {https://doi.org/10.1016/j.rse.2026.115318}
}