A Probabilistic STA-Bayesian Algorithm for GNSS-R Retrieval of Arctic Soil Freeze–Thaw States

Soil freeze-thaw (F/T) states are a key indicator of the Arctic climate, highlighting the need for their accurate retrieval. Global Navigation Satellite System-Reflectometry (GNSSR) offers a promising approach for retrieving soil F/T states, as F/T states significantly affect soil dielectric properties and reflectivity. Traditional reflectivity-based retrieval algorithms, such as the seasonal threshold algorithm (STA), are highly susceptible to surface interference, including vegetation attenuation and terrain effects, which limits their retrieval accuracy when using a fixed classification threshold. This study proposes an STA-Bayesian algorithm that formulates soil F/T retrieval as a probabilistic inference task. By combining seasonal prior information with GNSS-R observation likelihoods under frozen and thawed states, the algorithm derives posterior probabilities for Bayesian-optimal F/T state decisions, replacing fixed-threshold retrieval with a probabilistic approach that is more robust to surface heterogeneity. The algorithm is applied to GNSS-R data from the Fengyun-3E (FY-3E) satellite and Tianmu-1 (TM-1) constellation. In validation against ERA5-Land soil temperature-derived F/T states, the STA-Bayesian F/T product attains an average accuracy of 92.97%, outperforming both the STA (75.35%) and the SMAP (85.22%). The STA-Bayesian algorithm shows substantial improvements over both the STA and SMAP F/T products in densely vegetated regions (e.g., forests and shrublands) and demonstrates greater robustness to terrain roughness effects. The results demonstrate the STA-Bayesian algorithm's promise for soil F/T monitoring over heterogeneous surfaces and its adaptability to retrieval in the complex environmental conditions of the Arctic.