We assess the contribution made to the interannual variability of the global methane accumulation rate from its atmospheric sink using the STOCHEM tropospheric chemistry model coupled to the HadCM3 climate model. For both control and climate change scenarios, the standard deviation of the detrended accumulation rate was 1.4 ppbv/yr for the period 1990--2009, compared with the measured standard deviation of 3.1 ppbv/yr for the period 1984--1999. As the model emissions have no variability, the methane sink processes in the model are responsible for all the simulated variability of the methane accumulation rate. This appears to explain a significant fraction of the observed variability and was well correlated with simulated water vapour. The largest component of the model interannual variability is derived from the El-Ni¿o Southern Oscillation cycle in the coupled Ocean-Atmosphere model, and this mode of variation is shown to be present in the methane accumulation rate.