It is important to improve estimates of large-scale carbon fluxes over the boreal forest because the responses of this biome to global change may influence the dynamics of atmospheric carbon dioxide in ways that may influence the magnitude of climate change. Two methods currently being used to estimate these fluxes are process-based modeling by terrestrial biosphere models (TBMs), and atmospheric inversions in which fluxes are derived from a set of observations on atmospheric CO2 concentrations via an atmospheric transport model. Inversions do not reveal information about processes and therefore do not allow for predictions of future fluxes, while the process-based flux estimates are not necessarily consistent with atmospheric observations of CO2. In this study we combine the two methods by using the fluxes from four TBMs as a priori fluxes for an atmospheric Bayesian Synthesis Inversion. By doing so we learn about both approaches. The results from the inversion indicate where the results of the TBMs disagree with the atmospheric observations of CO2, and where the results of the inversion are poorly constrained by atmospheric data, the process-based estimates determine the flux results. The analysis indicates that the TBMs are modeling the spring uptake of CO2 too early, and that the inversion shows large uncertainty and more dependence on the initial conditions over Europe and Boreal Asia than Boreal North America. This uncertainty is related to the scarcity of data over the continents, and as this problem is not likely to be solved in the near future, TBMs will need to be developed and improved, as they are likely the best option for understanding the impact of climate variability in these regions.