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 AMSR-E passive microwave (PMW) brightness temperature spectral differences ($\Delta$$T_b$) where support vector machine (SVM) regression is employed as the observation operator. A series of synthetic twin experiments are conducted using different precipitation boundary conditions. The results show, at times, DA degrades modeled SWE estimates (compared to the land surface model without assimilation) over complex terrain. To mitigate this degradation, a physically-constrained approach using different $\Delta$$T_b$ for shallow-to-medium or medium-to-deep snow conditions along with a â\euroœdata-thinningâ\euro strategy are explored. Overall, both strategies improve the model ability to encapsulate more of the evaluation data and mitigate model ensemble collapse. The physically-constrained DA and 3-day 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-constrained DA, and 3-day thinning DA improve SWE the most with approximately 30\%, 31\%, and 24\% reduction of RMSE (relative to OL), respectively. Overall, these results highlight the limited utility of PMW $\Delta$$T_b$ observations in the estimation of snow in complex terrain, but do demonstrate that a physically-based constraint approach and data thinning strategy can add more utility to the $\Delta$$T_b$ observations in the estimation of SWE.