A Bayesian MCMC approach for snow density estimation from SMOS over the Northern Hemisphere

Snow density is a key parameter for calculating snow water equivalent, snow albedo, snow emissivity, and snow mechanical properties. It is therefore essential in water resource management, snow-air energy exchange computation, cold regions engineering design, and avalanche prevention. In a warming climate, snow density is undergoing rapid changes, which pose challenges for static snow density evolution equations in predicting spatiotemporal variability. Therefore, in this paper, we developed a physically-based snow density retrieval algorithm in the Northern Hemisphere based on SMOS (Soil Moisture and Ocean Salinity) L-band multi-angle radiometer. We first mitigated signal contamination from water bodies through sub-pixel decomposition and explicitly accounted for forest canopy and soil contribution using a coupled forest-snow-soil radiative transfer model. A Bayesian framework incorporating priors from snow classification and ERA5-Land reanalysis was further introduced to improve retrieval stability. The algorithm was tested over the 2019–2020 snow season and evaluated against 1,460 in-situ sites from the SNOTEL, CanSWE, and SnMar observation networks across North America and Eurasia. Results show that our algorithm corrects the systematic underestimation of ERA5-Land snow density during early- and mid-snow seasons. During the stable snow cover period (January-March 2020), the retrieval achieves an RMSE of 42.6 kg/m 3 and a mean bias of −4.0 kg/m 3 , corresponding to reductions of approximately 25 % and 89 % compared to respective values of 56.7 kg/m 3 and −36.4 kg/m 3 for ERA5-Land. These results highlight the value of microwave remote sensing in providing independent information to improve the snow density estimation in land surface modeling.