A mass balance inverse modelling procedure is applied with a time-dependent methane concentration boundary condition and a chemical transport model to relate observed changes in the surface distribution of methane mixing ratios during the 1990s to changes in its surface sources. The model reproduces essential features of the global methane cycle, such as the latitudinal distribution and seasonal cycle of fluxes, without using a priori knowledge of methane fluxes. A detailed description of the temporal and spatial variability of the fluxes diagnosed by the inverse procedure is presented, and compared with previously hypothesised changes in the methane budget, and previous inverse modelling studies. The sensitivity of the inverse results to the forcing data supplied by surface measurements of methane from the NOAA CMDL cooperative air sampling network is also examined. This work serves as an important starting point for future inverse modelling work examining changes in both the source and sink terms in the methane budget together.