On aggregation errors in atmospheric transport inversions

This paper explores the consequences of resolution of surface fluxes on synthesis inversions of carbon dioxide. Synthesis inversion divides the Earth's surface into a set of regions and solves for the magnitudes of fluxes from these regions. The regions are generally quite large. By considering an inversion performed at the resolution of the underlying transport model we show that the aggregation to large regions can cause significant differences in the final results, with errors of the same order of magnitude as the fluxes themselves. Using a simple model, we derive an algorithm to reduce this error. This algorithm accounts for the extra data uncertainty that is caused by uncertainty in the small-scale flux components. In the spatial synthesis inversion this extra data uncertainty reaches a maximum value of 3.5 ppmv. Accounting for it can halve the aggregation error. We provide suggestions for dealing with this problem when high-resolution inversions are not feasible.