Regional analyses of atmospheric trace gases can improve knowledge of fluxes at high resolution but rely on specified boundary conditions (BCs) at the domain edges. Biases in the often-uncertain BCs propagate to the inferred fluxes. We develop a framework to explain how errors in the BCs influence the optimized fluxes, derive two metrics to estimate this influence, and compare two methods to correct for the biases. We demonstrate correcting BCs directly is more effective at reducing bias.