A Physics-Hybrid Alpha Network (PHAN) approach for soil moisture retrieval using time series optical and SAR imagery

The coarse spatial resolution hinders the application of soil moisture (SM) in elucidating the interactions among water, energy and carbon cycles at regional and global scales. We propose a physics-hybrid differentiable network, termed the Physics-Hybrid Alpha-Net (PHAN), that integrates time-series C-band dual-polarization SAR and optical observations to retrieve 10-metre high-resolution SM maps. PHAN extends the Alpha approximation by enforcing a physics-based regularization on retrieved soil moisture (SM) and adding a cross-attention module that implicitly reduces vegetation-canopy scattering. By using optical and SAR imagery from 2019 to 2020 of Shandian River Basin, Naqu and Twente, PHAN outperformed machine learning (ML), deep learning (DL) and physics-guided baselines, achieving Pearson correlation coefficients (R) = 0.821, 0.861, 0.856 and unbiased root mean square error (ubRMSE) = 4.62, 5.54, 8.38 vol%. PHAN can improve applicability and accuracy while avoiding reliance on hard-to-obtain microwave driving parameters or opaque, purely data-driven methods. This physics-hybrid paradigm can also inspire future methodological extensions to the retrieval of other land surface parameters.