Two referees have provided comments on the latest version of your paper. Referee 1 was one of the original referees (who recommended rejection of the first version of the paper). Referee 2 is new. Referee 1 now recommends publication after minor revision. They set out quite a substantial list of recommended revisions and make some additional comments. Referee 2 recommends publication after major revision, though they qualify that to say that the revision they are recommending is somewhere between major and minor.

(You may have noted that a third referee was potentially available to provide a report. This was another new referee. My feeling on the basis of the two reports that I had received was that I could make a sensible decision on on the paper and I therefore agreed with the third referee that, in the interests of time, they would not provide a report.)

My interpretation is that both Referees see positive points in the paper and are therefore take the view that it should ultimately be published, notwithstanding what they regard as significant uncertainties.

Please can you consider the current set of referees' comments carefully, provide responses and, make changes according to their recommendations, unless you think there is very good reason not to do so (which you should justify in your comments). I hope then to be able to accept the paper without further input from the referees, though I will want to be able to assure the referees, on the basis of your responses and revisions, that their recommendations and comments have been taken properly into account.

This paper has gone through several rounds of reviews and I think that it is appropriate that no further substantial revision is demanded before it appears in ACP. I strongly recommend the following minor changes in order to make the content of the paper as clear as possible to the reader. Please provide a revised version of the paper in which these changes or something equivalent have been made and I will then be pleased to accept the paper for publication.

l4-8: You should be explicit about what information you are presenting in the paper -- to make sure that a reader does not look at your figures and imagine that they are showing something that they are not. Please modify to 'The method used for this purpose was the direct inversion of the two-dimensional continuity equation for the trace gas concentrations. This inversion predicts an 'effective velocity'' that gives the best fit for the evolution of the concentrations on the assumption that Fickian diffusion can be neglected and it is this 'effective velocity' field that is used to characterise the mean meridional circulation. Multiannual monthly mean effective velocity fields are presented along with their variabilities. According to this measure the stratospheric circulation is ...'

[Note that the above is exploiting the term 'effective velocity' which I think is useful and which you have already chosen to introduce in the main body of the text.]

l55: 'Our results contain considerably more information ... ( ... spent in the stratosphere).' -- this doesn't make any sense at this point because you have said nothing at all about what 'your results' are. I recommend moving to the end of the following paragraph.

l96: 'and (optionally) mixing coefficients' -- it is vital that the reader understands that mixing coefficients are NOT being determined by the method that you actually use -- please remove 'and (optionally) mixing coefficients' -- if you wish you could follow with a parenthetical separate sentence -- '(In principle it is possible also to determine mixing coefficients from this inversion, but that is not done in the calculations used for this paper.)'.

[The following comments are less important -- it is up to you whether you take account of them or not.]

l9: 'The deep branch ... are not separate but intertwined phenomena' -- personally I think that it would be better to keep on emphasising that this an similar conclusions are 'according to the effective velocity characterisation of the circulation' -- further work is needed to establish which (if either) of the traditional 'TEM advection + eddy mixing' description or your 'effective velocity' characterisation is the most physically meaningful.

l55 (again) 'contains considerably more information .. and they provide a better time-resolved understanding ... than the age-of-air method' -- that is still open to argument -- if one wants a simple measure of the effect of the circulation over several years then the age-of-air measure may be more useful than information on the month-to-month time variation of the circulation.

A final question that occurs to me is how well the effective velocity would function in a forward model where trace gases were assumed to be transported by advection by the effective velocity with minimal added diffusion. Do you have any information on that?

I am pleased to accept the current version of your paper for publication in ACP. Thank you for your determination over a long period through several sets of referees comments and several stages of revision. (At the same time I also thank the referees for their careful scrutiny of the paper at the different stages.)