This study explores improvements in the estimation of snow water equivalent (SWE) over snow‐covered terrain using an ensemble‐based data assimilation (DA) framework. The NASA Catchment land surface model is used as the prognostic model in the assimilation of Advanced Microwave Scanning Radiometer for EOS passive microwave (PMW) brightness temperature spectral differences (ΔTb) where support vector machine regression is employed as the observation operator. A series of synthetic twin experiments are conducted using different precipitation boundary conditions. The results show, at times, DA degrades modeled SWE estimates (compared to the land surface model without assimilation) over complex terrain. To mitigate this degradation, a physically informed approach using different ΔTb for shallow‐to‐medium or medium‐to‐deep snow conditions along with a “data‐thinning” strategy is explored. Overall, both strategies improve the model ability to encapsulate more of the evaluation data and mitigate model ensemble collapse. The physically informed DA and 3‐days thinning DA strategies show marginal improvements of basin‐averaged SWE in terms of reduction of bias from 10 mm (baseline DA) to−5.2 mm and −2.5 mm, respectively. When the estimated forcings are greater than the truth, the baseline DA, physically informed DA, and 3‐days thinning DA improve SWE the most with ∼30%, 31%, and 24% reduction of RMSE (relative to OL), respectively. Overall, these results highlight the limited utility of PMW ΔTb observations in the estimation of snow in complex terrain, but do demonstrate that a physically based constraint approach and data thinning strategy can add more utility to the ΔTb observations in the estimation of SWE. Key Points Synthetic assimilation of passive microwave (PMW) brightness temperature is explored in the Volga River basin Assimilation of PMW brightness temperature spectral differences improves modeled snow water equivalent (SWE) estimates Physically informed data assimilation yields larger improvements in modeled SWE than a traditional approach