Inverse problems in atmospheric constituent studies. I. Determination of surface sources under a diffusive transport approximation

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Abstract
The authors study inverse problems arising in atmospheric chemistry. They study the structure of the particular problem of deducing the distribution of sources and sinks of carbon dioxide over the surface of the Earth from available concentration measurements coupled with a model of transport within the atmosphere. With a simplistic but reasonable model in which transport is by diffusion only, the problem of deducing the source distribution from surface concentration data is shown to be mildly ill-posed with linear growth in error amplification (conversely with linear damping of information). However, in practice the limited nature of available data does not allow full recovery of all information that is theoretically available. In contrast the deduction of the source distribution from high-altitude concentration data is shown to be severely ill-posed with exponential growth in error amplification.