The determination of the methane emissions distribution from observations of the surface concentration and isotopic composition of atmospheric methane is studied using geophysical inverse methods and a chemical transport model of the atmosphere. First, the latitudinal and temporal distribution of methane emissions is estimated using the observations of the atmospheric concentration of methane at the Earth's surface and the truncated singular value decomposition (TSVD) as a solution technique. The singular value decomposition (SVD) analysis of this inverse methane source problem identifies the spatial and temporal components of the methane emissions distribution resolvable by the observations, quantifies the sensitivity of each component to errors in the observations, and predicts how many components must be retained to produce a modeled surface concentration consistent; with the observations. A latitudinal and temporal distribution of the methane emissions distribution is estimated using the truncated singular value decomposition as a solution technique. The sensitivity of this emissions estimate to perturbations in the model parameters is investigated. The SVD analysis is then applied to the deduction of the (CH4)-C-13/(CH4)-C-12 isotopic ratio of the methane emissions from observations of this ratio at the Earth's surface. This analysis identifies the spatial and temporal components of the isotopic ratio of the methane emissions distribution resolvable by the observations, quantifies the sensitivity of each component to errors in the observations, and predicts how many components must be retained to produce a modeled isotopic composition of atmospheric methane consistent with observations. The results show that the solution is sensitive to errors in the observations, with this sensitivity being dominated by errors in the observed atmospheric concentration rather than errors in the observed isotopic ratio. The minimum uncertainty obtainable in the estimate of the (CH4)-C-13/(CH4)-C-12 isotopic ratio of methane emissions within a region is found to be too large to effectively constrain the relative fluxes of the individual methane sources. The feasibility of improving this uncertainty by increasing the spatial density of the (CH4)-C-13/(CH4)-C-12 observational network is investigated.
