The Estimating the Circulation and Climate of the Ocean (ECCO) consortium’s ocean and sea ice state estimate is a dynamically consistent model-data synthesis, providing an invaluable tool for climate research. The official ECCO release has undergone formal optimization to reduce the model-data misfit, but uncertainties remain in the solution due to sparse and uncertain assimilated data constraints, model representation error, and other factors. As a result, small amplitude perturbations to the optimized controls may yield notable differences in the estimated state without notably increasing the model-data misfit, i.e., they provide distinct but equally acceptable solutions to the inverse problem. We pursue this possibility and focus on the impact of uncertainty in the atmospheric control variables via an ensemble perturbation approach. Our focus allows the covariance of control variables to be accounted for in the ensemble construction and avoids the complexity of assessing interactions between surface and interior sources of uncertainty. Time-mean adjustments are found to be critical in reducing model-data misfits and generating an acceptable solution to the inverse problem. Time-varying adjustments principally correct errors in the seasonal cycle and show fingerprints of changes to the ocean observing system and optimization framework. Truncating a low order representation of these adjustments across our ensemble yields distinct but acceptable solutions with moderate changes in climate-relevant metrics. Our results highlight the value of rigorous uncertainty quantification to support future applications of ECCO and ocean reanalysis in forecasting and climate research.