Physics-Aware Probabilistic Modeling of Subsurface Soil Moisture Using Diffusion Processes Across Different Climate Settings

Abstract

We developed a physics-aware denoising diffusion based probabilistic model for estimating subsurface soil moisture from surface observations. Unlike traditional physical-based methods that rely on site-specific soil parameters, our approach leverages a data-driven framework constrained by smoothness and Fickian diffusion principles to ensure physically consistent predictions. The model is trained and evaluated on hourly soil moisture data from 20 globally distributed sites, and further validated on high-resolution 10-min observations from four African stations. The results demonstrate robust performance across depths (10–40 cm), with the model maintaining high accuracy and low bias, even under varying temporal resolutions. We also analyzed the effect of input noise through a structured uncertainty experiment, highlighting the model's stability and reliability. By eliminating the need for explicit physical inputs and enabling uncertainty quantification, this framework offers a scalable solution for operational soil moisture monitoring, particularly in data-sparse or heterogeneous regions.