Interpretable soil moisture prediction with a knowledge-guided deep learning approach

Abstract. Soil moisture (SM) 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 (NLNNs) to convert this problem into a single-time-step, simultaneous multi-depth soil moisture forecasting. The non-local operation design includes embedded Gaussian operations and disentangled knowledge-guided operations, resulting in two variants: the self-attention non-local neural network (SA-NLNN) and the knowledge-guided non-local neural network (KG-NLNN). The knowledge-guided non-local operation is designed to capture vertical soil moisture relationships by decomposing the influences on soil moisture at a given depth into four components, each governed by distinct physical processes. The models offer visual interpretability through learned non-local weights, which reveal interactions among soil moisture across different depths, thereby enabling a qualitative representation of inter-layer connectivity. Notably, the model guided by soil moisture transport knowledge yields more stable and reasonable interpretations. With in-situ observations, we demonstrate that our proposed models perform satisfactorily. The knowledge-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 knowledge guidance enhancing KG-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.