An improved Alpha approximation algorithm for time-series surface soil moisture inversion from Sentinel-1 SAR data

• The optimization of constraint strategy is achieved using a “dynamic constraint” • The underdetermination problem is revised by adding effective information. • The retrieval precision of the improved Alpha approximation algorithm is validated. • An improved algorithm for soil moisture inversion from microwave data is presented. Accurate measurement of soil moisture content has significant scientific value and social benefits for studying global or regional water cycle mechanisms, developing climate and hydrological models, and advancing sustainable agricultural development. The Alpha approximation algorithm is regarded as one of the primary representatives among change detection methods and has been widely applied in soil moisture inversion. However, as the inversion time extends, the accumulation and propagation of inversion errors lead to a decrease in the inversion accuracy of the alpha approximation algorithm. In this study, three soil moisture observation networks, Tianjun, Nagqu, and Daman, in northwestern China are used as the research region. The optimization of the constraint strategy of the Alpha approximation algorithm is conducted by combining the Dubois model and Juxtaposition approach. The underdetermination issue of the Alpha approximation algorithm is also resolved by incorporating multi-angle synchronous observations to enrich the number of effective equations. Finally, we obtain an improved Alpha approximation algorithm based on the above approaches, and its inversion accuracy is also validated in the three study areas. Compared to the original alpha approximation algorithm, the improved algorithm demonstrates a significant enhancement in inversion accuracy. The RMSE, Bias, and R 2 of the retrieval results in Tianjun region are 0.074 cm 3 /cm 3 , 0.452, and 0.682, respectively. Furthermore, the improved Alpha approximation algorithm also shows satisfactory performance across different regions and land surfaces. The RMSE, Bias, and R 2 of the retrieval results in Nagqu observation networks are 0.076 cm 3 /cm 3 , 0.437, and 0.732 respectively. The RMSE, Bias, and R 2 of the retrieval results in Daman observation networks are 0.05 cm 3 /cm 3 , 0.269, and 0.533, respectively. Meanwhile, the freezing and thawing processes, vegetation changes, and agriculture practices are the major considerations influencing the inversion accuracy of the Alpha approximation algorithm.