|The authors have responded well to the requests and criticisms of the reviewers. I have only a few very minor comments still, as outlined below. Then I would consider it appropriate for publication in ACP.|
P 2, L29-33: I would rephrase the characterization of the Stephens et al. (2007) findings. Saying that the NH sink and tropical source were found to be overestimated "when constraining models with aircraft CO2 profiles" really makes it sound as if the aircraft profiles were assimilated, which isn't the case.
P3, L13: These forward model dependencies of CH4 concentrations *on* vertical transport
P3, L23: emissions -> emission OR emissions fluxes -> emissions OR emissions fluxes -> fluxes
P6, L7-11: Both reviewers commented on the oddness of this approach for deriving pseudo-aseasonal fluxes, which you explained as being due to a technical limitation of the model setup. Please include this justification here as well, and not only in the Conclusions. Perhaps you could refer to Figure 13 in the appendix as well.
P6, L12-15: Reads a bit awkwardly and as a result is a bit unclear. Perhaps break it into two sentences, or rewrite in some way.
P8, L5: in the both the base and -> in both the base and
P12, Figure 7 caption: Reunion is not in the Northern Hemisphere, which is implied here.
P14, L11-12: "The model’s stratospheric response to emissions perturbations differ from that of the troposphere and are subject to different transport and loss errors." -> "The model’s stratospheric response to emission perturbations differs from that of the troposphere and is subject to different transport and loss errors."
P15: in text on Figure 9, change "Emissions Seasonality" to either "Emissions' Seasonality" or "Emission Seasonality"
P15, L2: emissions errors -> emission errors OR emissions' errors
P15, L5-6: "These posterior emissions are scaled for each sector according to their a priori fraction of total emissions in each grid box." Well, it depends a bit on the inversion set-up. Not every system does it quite like this, it depends also on the a prior uncertainties assigned to each sector/process. I don't disagree with the general conclusions, but if you're going to describe a specific inversion approach, please reference it as such. It is possible to not specify the seasonal cycle in the prior, but have it driven by the data alone.
P 15: "derived by calculating the total emissions resulting from an increase of 1 ppb of CH4 in each tropospheric column and scaling". I better understood what you did after reading the response to my comment. Please integrate this information into the manuscript so that other readers may also benefit from this clarification (explaining, for instance, that transport is not considered, which is a critical limitation of the approach). And please, reword this sentence to say "the total emissions required to produce an increase of 1 ppb..."
P17, L35: scaled -> scales
P21, L6: wrong style of reference to Wunch et al. (2015)
P23, L3: as reference -> for reference