Simulating field soil temperature variations with physics-informed neural networks

Information on soil temperature is crucial for modeling hydrological and climatic processes. Nevertheless, direct measurements of soil temperature are usually rather limited in space, leading to an urgent need for improved spatial resolution. To address this issue, a Physics-Informed Neural Networks (PINN) method for estimating soil temperature ( T ) profile variations was proposed in this study. This method combines the advantages of Deep Neural Networks (DNN) in modeling complex non-linear relationships and physical laws for more robust predictions. The performance was evaluated using in-situ annual soil T at depths of 5 cm, 10 cm and 20 cm on a maize field in Northeast China. Cross-validation was used, a PINN was used to derive the new T data at unobserved depth from T observations at the other two depths. The results demonstrated that the performance of the PINN was superior to the commonly used process-based method and a DNN for all situations. Compared to the traditional method, the PINN achieved a 0.69 degrees C and 0.39 degrees C reduction in root-mean-square error (RMSE) for T estimates at 10 cm and 20 cm depths, respectively, under plowed tillage condition, while it could also accurately estimate T at 5 cm depth with RMSE of 0.56 degrees C. In addition, the PINN does not require inputs of soil thermal properties e.g., apparent thermal diffusivity ( kappa), as the space and time-dependent kappa values could also be learned during the training process. The results presented here demonstrated that a PINN could successfully utilize limited observation data to estimate unknown soil T profiles, and solve some challenging problems beyond the reach of existing methods in simulating soil thermal dynamics.