Physical Insights into Sentinel-1 SAR-Based Snow Depth Estimation Using Machine Learning and Explainable AI Across Different Mountainous Regions

Mountain snow is a critical component of the hydrological cycle and climate system, making reliable information on snow depth (SD) essential for water resource management and climate studies. Estimating SD in mountainous terrain remains challenging due to complex topography, heterogeneous land cover, and highly variable snow and weather conditions. Synthetic Aperture Radar (SAR) is suitable in such environments, as it provides frequent observations, high spatial resolution, and sensitivity to snow properties independent of cloud cover and illumination. In particular, Sentinel-1 C-band SAR backscatter-based method enables large-scale and continuous SD monitoring, but faces limitations in vegetated, shallow, or wet snow conditions. To overcome these limitations, this study proposes an improved machine learning (ML) framework that incorporates new input variables derived from Sentinel-1 and other optical data, improving upon existing Sentinel-1–based ML approaches for SD estimation. Additionally, the framework is designed for efficient implementation using preprocessed Sentinel-1 data available in Google Earth Engine, thereby minimising the computational burden of handling SAR data and facilitating scalable application across regions and time periods. The methodology is implemented across three climatically and physiographically distinct mountainous regions: the Colorado Rocky Mountains, the European Alps, and the Indian Western Himalayas. Across all three regions, the proposed model substantially performs better than the existing methods, achieving MAE(r) values of 7.9 cm (0.96), 22.3 cm (0.91), and 68.4 cm (0.72), respectively. Since the physical scattering processes governing C-band SAR responses to snow are not yet fully characterized, explainable AI techniques are applied to interpret model predictions and quantify the influence of input variables under varying environmental conditions. The results show region-specific and seasonal dependencies linked to snow type, vegetation cover, and surface conditions, providing new physical insights into the sensitivity of Sentinel-1 C-band backscatter to snow depth.