Abstract. The hydroxyl radical (OH), which is the dominant sink of methane (CH4), plays a key role in closing the global methane budget. Current top-down estimates of the global and regional CH4 budget using 3D models usually apply prescribed OH fields and attribute model–observation mismatches almost exclusively to CH4 emissions, leaving the uncertainties due to prescribed OH fields less quantified. Here, using a variational Bayesian inversion framework and the 3D chemical transport model LMDz, combined with 10 different OH fields derived from chemistry–climate models (Chemistry–Climate Model Initiative, or CCMI, experiment), we evaluate the influence of OH burden, spatial distribution, and temporal variations on the global and regional CH4 budget. The global tropospheric mean CH4-reaction-weighted [OH] ([OH]GM-CH4) ranges 10.3–16.3×105 molec cm−3 across 10 OH fields during the early 2000s, resulting in inversion-based global CH4 emissions between 518 and 757 Tg yr−1. The uncertainties in CH4 inversions induced by the different OH fields are similar to the CH4 emission range estimated by previous bottom-up syntheses and larger than the range reported by the top-down studies. The uncertainties in emissions induced by OH are largest over South America, corresponding to large inter-model differences of [OH] in this region. From the early to the late 2000s, the optimized CH4 emissions increased by 22±6 Tg yr−1 (17–30 Tg yr−1), of which ∼25 % (on average) offsets the 0.7 % (on average) increase in OH burden. If the CCMI models represent the OH trend properly over the 2000s, our results show that a higher increasing trend of CH4 emissions is needed to match the CH4 observations compared to the CH4 emission trend derived using constant OH. This study strengthens the importance of reaching a better representation of OH burden and of OH spatial and temporal distributions to reduce the uncertainties in the global and regional CH4 budgets.