ABSTRACT
This chapter reviews inversion techniques, places them in the context of statistical estimation, and considers the limits to resolution imposed by the ill-conditioning of the inverse problem. For a quantitative uncertainty analysis, an inversion should be treated as a process of statistical estimation. The statistical formulation of inverse problems is espoused by A. Tarantola as a general principle, and forms the basis of the analysis of meteorological data assimilation by E. Kalnay. The principle of trace gas inversions is that the observed spatial distribution of concentrations reflects the combined effect of the spatial distribution of sources and sinks and of atmospheric transport. While much of the research effort in global-scale trace gas inversions has concentrated on CO2, inversion studies have been undertaken for other gases such as methane and various halogenated compounds. There have been a number of reviews of trace gas inversions.
