Integrating Physical Constraints Into Deep Learning for Enhanced Snow Depth Retrieval Over the Third Pole

Accurate snow depth (SD) data are essential for understanding and simulating hydrological processes, particularly in regions with uneven snow distribution and complex terrain, such as the Third Pole (TP). However, existing SD products often suffer from low spatial resolution, introducing uncertainties in regional snowpack and runoff modeling. In this study, we developed an integrated downscaling framework that combines deep learning (DL) with physical constraints to improve the resolution and accuracy of SD data for the TP region. First, a residual network incorporating multifactor spatial-terrain relationships is used to generate preliminary 500-m DL-downscaled SD data. Subsequently, by incorporating both snow cover fraction (SCF) data and snow depletion curve (SDC) as dual physical constraints, the new algorithm significantly improves the estimation accuracy in shallow snow areas. The proposed algorithm significantly enhances SD estimation accuracy, reducing the root-mean-square error (RMSE) from 1.99 to 0.75 cm, which represents a 62% improvement over the purely DL-based downscaling algorithm (RMSE = 1.02 cm). Notably, the improved algorithm demonstrates enhanced capability in terrain feature representation while simultaneously minimizing misclassification in snow-free areas and reducing overestimation in shallow snow regions. The results demonstrate progressive improvement in SD estimation accuracy across diverse geographical environments through stepwise validation of each downscaling step, confirming that integrating DL-based downscaling with physical constraints yields complementary advantages. Although the new algorithm significantly improves the accuracy of SD data, it is still underestimated in complex terrain areas and areas with SD exceeding 7 cm. Future research needs to deeply integrate physical constraint methods, comprehensively consider physical processes such as snow density, water content changes, and energy balance, and establish a more complete downscaling model.