Diffusion-Based Physics-Aware Modeling of Subsurface Soil Moisture

Accurate characterization of soil moisture at subsurface depths is essential for hydrological modeling, agricultural management, and climate risk assessment. However, in-situ subsurface measurements remain sparse and often discontinuous due to logistical and operational constraints, especially in data-limited regions. This creates a pressing need for approaches that can reliably infer deeper soil moisture states from surface observations, which are more readily available from both remote sensing platforms and ground-based sensors. This study proposes a probabilistic, physics-aware denoising diffusion model designed to estimate soil moisture at subsurface depths using only surface moisture measurements. The model integrates smoothness and curvature regularization terms inspired by Fickian diffusion theory as weak physics to guide the learning process, without requiring explicit or site-specific physical parameters, thereby enhancing its practicality and ensuring broader applicability across diverse hydroclimatic conditions. The model is trained and evaluated across 20 global ISMN (International Soil Moisture Network) sites at 10, 20 and 40 cm depths with hourly observations spanning six distinct Köppen–Geiger climate classes and four high-resolution African stations with 10-min data.

Across global stations, the model demonstrated consistently high predictive skill (R² ranging from 0.91 to 0.99) with lower errors in climates characterized by stable seasonal patterns, and comparatively higher uncertainty in regions affected by freeze-thaw dynamics or monsoonal variability. Benchmarking against 17 state-of-the-art algorithms using Dolan–Moré profiles showed strong and reliable performance across depths and metrics. A stochastic robustness analysis with 30 random seeds and varying ensemble sizes indicated that moderate-sized ensembles provide an effective balance between accuracy and stability. Sensitivity experiments with white, autocorrelated, and structured noise revealed that the 20 cm layer is most susceptible to surface-level perturbations, while deeper layer remain comparatively resilient. The model also highlighted a strong performance on higher-resolution datasets, with prediction errors tightly centered around zero and exhibiting very low standard deviation. The generalisation of the proposed diffusion-based model across spatial, temporal, and climatic variability highlights its potential as a lightweight and transferable alternative for hydrological forecasting in data-scarce or operationally constrained environments.