Enhancing data-driven soil moisture modeling with physically-guided LSTM networks

In recent years, deep learning methods have shown significant potential in soil moisture modeling. However, a prominent limitation of deep learning approaches has been the absence of physical mechanisms. To address this challenge, this study introduces two novel loss functions designed around physical mechanisms to guide deep learning models in capturing physical information within the data. These two loss functions are crafted to leverage the monotonic relationships between surface water variables and shallow soil moisture as well as deep soil water. Based on these physically-guided loss functions, two physically-guided Long Short-Term Memory (LSTM) networks, denoted as PHY-LSTM and PHYs-LSTM, are proposed. These networks are trained on the global ERA5-Land dataset, and the results indicate a notable performance improvement over traditional LSTM models. When used for global soil moisture forecasting for the upcoming day, PHY-LSTM and PHYs-LSTM models exhibit closely comparable results. In comparison to conventional data-driven LSTM models, both models display a substantial enhancement in various evaluation metrics. Specifically, PHYs-LSTM exhibits improvements in several key performance indicators: an increase of 13.6% in Kling-Gupta Efficiency (KGE), a 20.7% increase in Coefficient of Determination (R2), an 8.2% reduction in Root Mean Square Error (RMSE), and a 4.4% increase in correlation coefficient (R). PHY-LSTM also demonstrates improvements, with a 14.8% increase in KGE, a 19.6% increase in R2, an 8.2% reduction in RMSE, and a 4.4% increase in R. Additionally, both models exhibit enhanced physical consistency over a wide geographical area. Experimental results strongly emphasize that the incorporation of physical mechanisms can significantly bolster the predictive capabilities of data-driven soil moisture models.