PhySoilNet: A deep learning downscaling model for microwave satellite soil moisture with physical rule constraint

• A new physics-informed soil moisture downscaling deep neural network. • An effective coupling of physical rules and data-driven based on loss function. • Physical constraints improve the generalization ability of neural network. • More reasonable soil moisture output range based on boundary constraint. Surface soil moisture (SM) plays an important role in water and energy cycles. Passive microwave remote sensing observation has become the main means of obtaining large-scale surface SM. Due to its low spatial resolution, the spatial downscaling is required. With the development of artificial intelligence, data-driven SM downscaling models have emerged in recent years and have shown better accuracy than traditional physical models. However, data-driven SM downscaling models still have problems such as poor interpretability and easy overfitting. Therefore, this paper proposes a new SM downscaling model based on physical rule-constrained deep learning, named Physics-informed Soil Moisture Downscaling Deep Neural Network (PhySoilNet). This model adds the physical relationship between SM and the downscaling factor Land surface Evaporative Efficiency, as well as the saturated and residual boundary of SM into the Loss function of deep learning, thereby constraining the neural network. Results showed that PhySoilNet successfully downscaled the 9 km Soil Moisture Active Passive (SMAP) SM to 500 m, and performed well in the evaluations with in-situ, aerial, and SMAP SM. Compared to the downscaling model of only data-driven, the PhySoilNet had better performance in all evaluations, and the metrics in the in-situ SM network evaluation were improved by 20 % for R, 9.9 % for ubRMSE, 7.2 % for MAE, and 7.2 % for RMSE. At the same time, the number of SM predicted by PhySoilNet that outside the reasonable SM boundary range was significantly reduced. This fully demonstrates that data-driven based on physical rule constraints can achieve SM downscaling more effectively. Coupling physical rules and deep learning can fully utilize the powerful fitting ability of data-driven methods while improving the generalization ability and interpretability of downscaling models through prior physical knowledge.