Singh et al. (2025) Physics‐Aware Probabilistic Modeling of Subsurface Soil Moisture Using Diffusion Processes Across Different Climate Settings

Identification

• Journal: Geophysical Research Letters
• Year: 2025
• Date: 2025-10-16
• Authors: Abhilash Singh, Vidhi Singh, Kumar Gaurav
• DOI: 10.1029/2025gl118607

Research Groups

• School of Mathematics, Faculty of Engineering and Physical Sciences, University of Leeds, Leeds, UK
• Fluvial Geomorphology and Remote Sensing Laboratory, Department of Earth and Environmental Sciences, Indian Institute of Science Education and Research Bhopal, Bhopal, India

Short Summary

This study developed a physics-aware probabilistic denoising diffusion model to estimate subsurface soil moisture (10–40 cm) solely from surface observations, demonstrating robust and accurate performance across 24 globally distributed sites with diverse climate settings and varying temporal resolutions. The model eliminates the need for site-specific physical parameters by integrating Fickian diffusion principles as weak physical constraints within a data-driven framework.

Objective

• Can a purely data-driven model, augmented with physics-inspired regularization, generalize across diverse hydro-climatic conditions?
• How does the ensemble size affect the stability and reliability of predictions?
• What is the sensitivity of the model to input uncertainty?
• Can the model maintain predictive performance when applied to high-frequency input data?

Study Configuration

• Spatial Scale: 20 globally distributed sites across seven networks (AMMA-CATCH, CTP-SMTMN, MAQU, NAQU, NGARI, SKKU, TWENTE) covering six Köppen–Geiger climate classes in Benin, China, South Korea, and Netherlands. Additionally, four validation stations in Zambia. Soil moisture measurements at depths of 5 cm (surface input), 10 cm, 20 cm, and 40 cm (subsurface predictions).
• Temporal Scale: Hourly soil moisture data for 20 stations (temporal coverage ranging from 7 months to 12 years). 10-minute resolution soil moisture data for four stations in Zambia (monitoring duration over 2–5 years).

Methodology and Data

• Models used: Physics-aware denoising diffusion probabilistic model (DDPM) incorporating smoothness and curvature regularization terms inspired by Fickian diffusion theory. Compared against 17 benchmark regression algorithms: AdaBoost, BayesianRidge, DecisionTree, ExtraTrees, GradientBoosting, HuberRegressor, KNeighbors, LinearRegression, LinearSVR, MLP, PLSRegression, PassiveAggressive, PolySVR, RBF_SVR, RandomForest, Ridge, and SVR.
• Data sources: In situ soil moisture data from the International Soil Moisture Network repository. High-resolution 10-minute soil moisture observations from four stations in Zambia, managed by the Zambia Meteorological Department (ZMD).

Main Results

• The model achieved high accuracy (coefficient of determination, R², ranging from 0.91 to 0.99) and low bias across 20 global sites and diverse climatic zones for subsurface depths (10–40 cm).
• It demonstrated strong generalization across all climatic zones, with lower error metrics in regions with well-defined seasonal patterns and increased error dispersion in complex environments (e.g., freeze-thaw, monsoonal).
• The proposed model consistently outperformed 17 benchmark regression algorithms, showing superior consistency and robustness across all tested depths and evaluation metrics.
• Statistical significance tests (Tukey's Honest Significant Difference) confirmed the proposed model's superior predictive performance, showing significant differences from benchmark models at a majority of sites (e.g., 12 sites registered 17 significant comparisons).
• Stochastic robustness analysis across 30 independent runs showed high stability and consistency, with an average standard deviation of R² at 10 cm of approximately 0.0066. Variability increased with depth, with the standard deviation of R² at 40 cm increasing by an average of 158% compared to 10 cm.
• Ensemble size analysis indicated saturating improvements beyond an ensemble size of 50, suggesting diminishing returns for larger ensembles (e.g., mean R² increased by approximately 0.65% from N=5 to N=100).
• Input uncertainty analysis revealed that the 20 cm depth was most susceptible to input noise (average deviation of 10.65%), followed by 10 cm (7.26%) and 40 cm (8.11%). Autocorrelated Noise had the strongest impact among the tested noise types.
• The model maintained strong predictive performance on high-temporal resolution (10-minute) data from four Zambian sites, with R² values ranging from 0.95 to 0.96 for three sites and 0.82 for one site.

Contributions

• Development of a novel physics-aware probabilistic denoising diffusion model for subsurface soil moisture estimation that relies solely on surface measurements, eliminating the need for explicit physical inputs or site-specific soil parameters.
• Integration of weak physical constraints (smoothness and curvature regularization derived from Fickian diffusion theory) into a data-driven framework, ensuring physically consistent predictions without parametric assumptions.
• Provision of uncertainty quantification for subsurface soil moisture predictions.
• Extensive validation demonstrating robust performance and generalization across diverse global climate settings and varying temporal resolutions (hourly to 10-minute), outperforming numerous established benchmark models.
• Offers a scalable, lightweight, and transferable solution for operational soil moisture monitoring, particularly beneficial in data-sparse or heterogeneous regions.

Funding

• Indo-French Center for the Promotion of Advanced Research: IFCPAR/CEFIPRA (Research Grant 6707-1)
• Institutional grant from IISERB

Citation

@article{Singh2025PhysicsAware,
  author = {Singh, Abhilash and Singh, Vidhi and Gaurav, Kumar},
  title = {Physics‐Aware Probabilistic Modeling of Subsurface Soil Moisture Using Diffusion Processes Across Different Climate Settings},
  journal = {Geophysical Research Letters},
  year = {2025},
  doi = {10.1029/2025gl118607},
  url = {https://doi.org/10.1029/2025gl118607}
}