Snow Depth Retrieval Model for Xinjiang Integrating Physical Priors and Machine Learning

To address the limitations of traditional snow depth retrieval methods—such as insufficient physical mechanisms and limited generalization capability under complex underlying surface conditions—this study aims to develop a novel snow depth inversion model for Xinjiang, termed PhysDNN, which integrates physical priors with deep learning to improve retrieval accuracy, spatial resolution, and physical interpretability. Based on passive microwave brightness temperature data, the core physical relationship—"the brightness temperature difference (∆TB) is positively correlated with snow depth"—was incorporated into the model through a dual physical constraint mechanism: (1) embedding ∆TB as a key physical feature at the input level, and (2) adding a physics-consistency regularization term in the loss function to guide the neural network toward physically plausible mappings. Additionally, multi-source surface features—including topography, optical remote sensing indices (e.g., NDSI), and land use—were fused to construct a 1 km resolution PhysDNN inversion model. The model was trained and validated using ground-based observational data from meteorological stations across Xinjiang from 2020 to 2023.The results show that PhysDNN achieved the best overall performance, with a coefficient of determination (R²) of 0.871 and a root mean square error (RMSE) of 2.92 cm, significantly outperforming both the Chang algorithm and a baseline DNN model. SHAP interpretability analysis confirmed a strong positive correlation between model predictions and ∆TB (corr = +0.79), consistent with microwave scattering theory. Spatial error maps revealed that PhysDNN effectively mitigated the systematic underestimation of the Chang algorithm in complex mountainous regions such as the Tianshan and Altai Mountains, while demonstrating greater robustness in the arid southern Xinjiang region. The PhysDNN model, by synergistically integrating physical priors with deep learning, not only substantially enhances the accuracy and spatial detail of snow depth retrieval in Xinjiang but also improves physical consistency and generalization performance. It provides a reliable technical approach for snow monitoring in high-altitude arid regions and holds significant application value for hydrological modeling, snowmelt runoff forecasting, and climate change research.