The sources and sinks of important climatic trace gases such as carbon dioxide (CO2) are often deduced from spatial and temporal variations in atmospheric concentrations. Reducing uncertainties in our understanding of the contemporary carbon budget and its underlying dynamics, however, requires significantly denser observations globally than is practical with in situ measurements. Space-based measurements appear technically feasible but require innovations in data analysis approaches. We develop a variational data assimilation scheme to estimate surface CO2 fluxes at fine time/space scales from such dense atmospheric data. Global flux estimates at a daily time step and model-grid spatial resolution (4° × 5° here) are rapidly achieved after only a few dozen minimization steps. We quantify the flux errors from existing, planned and hypothetical surface and space-borne observing systems. Simulations show that the planned NASA Orbital Carbon Observatory (OCO) satellite should provide significant additional information beyond that from existing and proposed in situ observations. Improvements in data assimilation techniques and in mechanistic process models are both needed to fully exploit the emerging global carbon observing system.