This manuscript can now be published; the authors have made a fair job revising the text in response to the reviewers. Even though the present approach is clearly still limited given the paucity of available arctic atmospheric observations, it presents a first regional top-down constraint on CH4 emissions from the ESAS. As the discussion phase showed, this manuscript is somewhat controversial, as the main finding is at odds to alternative emission estimates from the ESAS which are based on upscaling in situ measurements. It is up to future studies to elucidate the causes of this discrepancy hopefully with more observations and refined atmospheric modelling approaches.

The manuscript needs still a few technical corrections: (1) a thorough reread for errors in spelling or English language, (2) some text is duplicated in section 3.3, (3) Figure 5 mentions "red" color, but on my copy this is only brown? (4) it is not clear to me why the emission unit is labelled "TgCH4.yr-1" - the period between the "4" and the "y" is confusing.