Estimates of the global magnitude of atmospheric methane sources are currently mainly based on direct flux measurements in source regions. Their extrapolation to the entire globe often involves large uncertainties. In this paper, we present an inverse modeling approach which can be used to deduce information on methane sources and sinks from the temporal and spatial variations of atmospheric methane mixing ratios. Our approach is based on a three-dimensional atmospheric transport model which, combined with a tropospheric background chemistry module, is also employed to calculate the global distribution of OH radicals which provide the main sink for atmospheric methane. The global mean concentration of OH radicals is validated with methyl chloroform (CH3CCl3) observations. The inverse modeling method optimizes the agreement between model-calculated and observed methane mixing ratios by adjusting the magnitudes of the various methane sources and sinks. The adjustment is constrained by specified a priori estimates and uncertainties of the source and sink magnitudes. We also include data on the 13C/12C isotope ratio of atmospheric methane and its sources in the model. Focusing on the 1980s, two scenarios of global methane sources are constructed which reproduce the main features seen in the National Oceanic and Atmospheric Administration's Climate Monitoring and Diagnostics Laboratory (NOAA/CMDL) methane observations. Differences between these two scenarios may probably be attributed to underestimated a priori uncertainties of wetland emissions. Applying the inverse model, the average uncertainty of methane source magnitudes could be reduced by at least one third. We also examined the decrease in the atmospheric methane growth rate during the early 1990s but could not uniquely associate it with changes in particular sources.