Interpretable Soil Moisture Prediction with a Physics-guided Deep Learning Approach

Abstract. Soil moisture is a critical component of the hydrological cycle, but accurately predicting it remains challenging due to the nonlinearity of soil water transport, variability in boundary conditions, and the intricate nature of soil properties. Recently, deep learning has shown promise in this domain, typically by modeling temporal dependencies for soil moisture predictions. In this study, we propose non-local neural networks (NLNN) to convert this problem into a single-time-step, simultaneous multi-depth soil moisture forecasting. By facilitating mutual compensation among different depths, this method enables a representation of vertical heterogeneity and inter-layer connectivity without physical assumptions, leading to precise and efficient predictions in diverse scenarios. Our non-local operation design includes the embedded Gaussian operations and disentangled physics-guided operations, resulting in two variants: the self-attention non-local neural network (SA-NLNN) and the physics-guided non-local neural network (PG-NLNN). The models offer visual interpretability, providing insights into intricate mechanisms of soil moisture dynamics. Notably, the model guided by physics yields more stable and reasonable qualitative interpretations. With in-situ observations, we demonstrate that our proposed models perform satisfactorily. The physics-guided non-local operations significantly enhance accuracy and reliability. Additionally, our models adapt to diverse time-scale situations while maintaining high computational efficiency. Both models exhibit robust noise resistance, with physics guidance enhancing PG-NLNN’s noise resistance. In summary, our work addresses the soil moisture prediction challenge in a novel way, highlighting the potential of NLNN and the importance of incorporating physic guidance in data-driven models.