Physics-Informed Enhanced Machine Learning for Global Vegetation Optical Depth Retrieval Using Spaceborne GNSS-R

Vegetation Optical Depth (VOD), as a key parameter of vegetation, plays an important role in the process of vegetation growth and change. The Spaceborne Global Navigation Satellite System Reflectometry (GNSS-R) technology in the L-band provides a new monitoring method for retrieving vegetation optical thickness. In GNSS-R VOD retrieval, empirical or semi-empirical retrieval models follow physical mechanisms, while Machine Learning (ML) models can autonomously learn nonlinear relationships. Combining physical mechanisms with ML methods is currently a research hotspot. However, due to the complex reflections and scattering within vegetation and interference from other surface factors, existing methods cannot balance the relationship between data-driven and physical constraints. To alleviate these issues and achieve high-precision retrieval on a global scale. This article is based on the sensitivity analysis of Cyclone Global Navigation Satellite System (CYGNSS) reflectivity to vegetation, surface roughness, soil moisture, and their respective incident angle dependencies. It introduces a physical information neural network and adds physical processes related to GNSS-R surface scattering to the network feature space to constrain and enhance network training. A Physical Enhanced Machine Learning (PEML) Network is proposed to increase the interpretability and generalization ability of the model. Model testing shows that the Correlation Coefficient (CC) between globally retrieved VOD and Soil Moisture Active Passive (SMAP) VOD is 0.85, and the Root Mean Square Error (RMSE) is 0.147. Compared with the Advanced Microwave Scanning Radiometer 2 (AMSR2) VOD, the CC is 0.73. It exhibits strong generalization ability on surface types containing vegetation. In addition, the time series of Vegetation Water Content (VWC) and Normalized Difference Vegetation Index (NDVI) indicate that the model can capture seasonal changes, and the retrieval results also show a strong linear correlation with Canopy Height (CH). Our retrieval results can provide valuable references for the fusion modeling of GNSS-R land surface.