Differences between measured concentrations of atmospheric trace gases at different locations across the globe contain information about the locations of the sources of these gases. We use an orthogonal function approach and experiments with a three-dimensional transport model to determine what source distributions can, in principle, be identified from such information. The ability to detect and to locate localized sources is severely limited by the number of observational sites and by the error growth implicit in the inverse problem. The former limitation appears to be the most severe restriction in practice, in contrast to results obtained using two-dimensional (zonally averaged) models. Differences between results from two and three-dimensional models are especially severe for tropical sources.