Differentiable modeling for soil moisture retrieval by unifying deep neural networks and water cloud model

Machine learning has been widely used in surface soil moisture (SSM) retrieval studies, but in recent years, this purely data-driven retrieval method has been controversial due to its lack of physical interpretability and generalization ability. Physical retrieval models based on the theory of radiative transfer equations respect physical laws, but their retrieval accuracy is generally lower than that of machine learning retrieval methods. In order to explore the retrieval method of unifying these two types of models to maximize the advantages of integrating machine learning models and physical models in the retrieval process, this study took high-resolution soil moisture retrieval as an example, and constructed a differentiable model (DM), which was based on the differentiability of neural networks, and united the water cloud model (WCM) and neural networks by implementing differentiable programming of the WCM in a machine learning platform. The differentiable soil moisture retrieval model took the WCM as the skeleton, and realized SSM retrieval with 10 m resolution based on synthetic aperture radar data, optical data and other auxiliary data. Relying on the DM, we have successfully transformed the problem of physical model parameter calibration into a neural network training problem, which made the retrieval model physically interpretable while allowing the model to be trained using gradient descent for more accurate retrieval results. In addition, the model was comparatively evaluated from multiple perspectives to demonstrate its advantages over machine learning retrieval models and physical retrieval models. This study provides new ideas for the combination of machine learning and physical knowledge in other retrieval studies, and provide new cases for physical knowledge-guided machine learning research in earth sciences.