The study by Abalos et al analyzes the Brewer-Dobson (BD) circulation in a subset of CMIP6 models for which relevant diagnostics are available. Both ability of the models to reproduce the observed features of the BD circulation as well as their future projections are analyzed. The main novelty of the study is that the results found in the previous generations of CMIP models, and other chemistry-climate model evaluations (e.g. CCMVal) such as acceleration of the BD circulation in response to global warming, are confirmed with the new generation of the models. On the other hand, the study also highlights considerable uncertainty in the quantitative estimates of the BD trend, both historical and predicted future trends. The uncertainty arises from the internal variability, but also from the intermodel differences. The latter is evident, in particular, from the fact that the models disagree about the driving forces of the trends.

I recommend the paper to publications and ask the authors to clarify some points listed below:

1. The use of CMIP6 data:

The authors use 1 member per model however I don't see a justification for this choice. There is considerable internal variability in BD diagnostics and, in order to get a better quantification of the signal, in particular the BD trends, I think all members should be considered.

2. Significance of w* historical trends:

This analysis is problematic. The authors conclude that w* historical trends shown in Fig. 4 are insignificant; however, looking at Fig.5c where all individual simulations show negative trends, I wonder whether the trends are indeed insignificant. I would expect that by averaging across many members all of which agree on the sign of the trend, the internal variability would be reduced, and the signal would emerge. Further, if w* trends are indeed insignificant then how one can see an influence of ozone hole (L137)? This need to be clarified.

Other comments:

L14: Perhaps you can refer to specific Chapter of the WMO report rather than to the whole report, here and in the other places? The reports are large, and the reader does not necessarily know which chapter to look at.   

L34: I think it is enough to write either "non-significant positive trends" or "slightly positive trends" depending on what you want to emphasize.

L45: "response to an IDEALIZED 1%/year CO2 increase"

L105: Fig.2 shows that MRI and JRA55 are nearly identical, and both represent the higher bound of the model spread in the lower stratosphere. Given that both, MRI and JRA55, are based on the JMA operational model (I believe so), would that indicate that the influence of assimilation on BDC is negligible, at least in JRA-55? Would this explain the spread across the reanalyses?

Figure 4: Do contours for AoA climatology in panels a-c start from 1 year?

L162: The models simulate an acceleration of the BD circulation over 1975-2014, not deceleration. Or?

L194: "strengthening of the polar vortex … leads to reduced equatorward refraction of planetary waves"

Fig. 3 from Hartmann et al (2000) shows that a strengthened polar vortex leads to an enhanced equatorward refraction of planetary waves, contrary to what the authors state. Also, given the spread in the widening across individual models, you could analyze the relationship between the changes in the turnaround latitudes and changes in the polar vortex across the models. At least for WACCM the mechanism does not seem to work, because this model simulates both poleward shift of the turnaround latitude (Fig. 7h) and vortex weakening (my own calculations). So, I am not convinced the proposed mechanism is valid.

Figure 9: Why AoA panels start from year 30? I understand that x-axis shows starting year, so why not start from year 0 as is done in w*?

Figure 9 caption: "… a comparable total number of simulations for both VARIABLES" (not magnitudes)

Figure 11: I cannot understand how you indicate negative contribution with semitransparent shading, I am sorry. Is there any other way to draw it?

Reference: Hartmann, D. L., J. M. Wallace, V. Limpasuvan, D. W. J. Thompson, and J. R. Holton (2000), Can ozone depletion and global warming interact to produce rapid climate change? Proc. Natl. Acad. Sci. U. S. A., 97, 1412– 1417, doi:10.1073/pnas.97.4.1412

The authors document the climatology of Brewer-Dobson Circulation in CMIP6 models, and its response to forcing in the historical and 1pctCO2 doubling integrations.  They contrast the behavior of models with available observations/reanalyses, and provide a process oriented exploration of the residual circulation, breaking down the role of resolved waves vs. parameterized gravity waves.  This is the first time CMIP class models have provided the necessary output for this analysis, and I expect this paper to become an important reference point for our understanding and discussion of the BDC.  I therefore strongly recommend publication of this thorough and well written manuscript pending consideration of the minor suggestions below.

I hope that authors see my suggestions below as a genuine attempt to help improve the paper.  This is a very strong manuscript, and I very much support its publication.

Ed Gerber

General minor suggestions

1) I feel there was tension, starting from the abstract, about the narrative on the comparison of observations and models, particularly in the upper stratosphere.  For instance, at line 4 of the abstract suggest that the models are inconsistent, but then immediately following, at line 6, it is suggested that there is great uncertainty in the model trends.  I am not an expert in the observed trends, and my main suggestion is chiefly to be more consistent with the message.  Do the authors mean something like "while there is great uncertainty in trends in the upper branch of the BDC in models, model trends appear to be statistically distinguishable from observed trends"?  If this is the case, I would first highlight the uncertainty, and then state that despite this great uncertainty, models cannot be reconciled with observations.  

And this said, I continue to worry that the uncertainty in observed trends may be underestimated.  Am I correct that the key mismatch is with Engel et al. 2017 (Air Core measurements at two sites) and MIPAS retrievals from Stiller et al. (2012, 2020), though the MIPAS estimate has become closer with the revision of our treatment of SF6 (Fritsch et al. 2020). 

As highlighted, for example, by Garcia and Randall (2011), there are significant uncertainties associated with the fact that observation estimates (as with air core samples) are based on sparse measurements relative to the model based estimates using global averages.

https://journals.ametsoc.org/view/journals/atsc/68/1/2010jas3527.1.xml

To be constructive, I am curious if an apples-to-apples comparison with Engel et al would be possible.  As highlighted by Garcia and Randall (2011), the uncertainty on age of air may increase if you only sample it at a few locations and times, as opposed to globally.  I suspect that model based estimate of uncertainty will increase markedly with limit sampling. 

And finally, given the uncertainty associated with SF6 decay rates, I still worry that maybe our problem is being able to model SF6, as opposed, to being able to model age.

All this said, this was meant to be a minor suggestion.  If the message is that models are still inconsistent, I would just highlight that there is a lot of uncertainty first, and then say that despite this, we cannot yet reconcile model trends with available observations.

2)  As noted by the authors, there term Brewer-Dobson Circulation has been used in many ways in the literature.  As I feel this paper will become a very important reference point for the BDC, I would urge the authors to set a tone of best practices, and always refer to w* as the residual circulation (or the diabatic circulation / mean overturning circulation).

An example where this would be helpful would be lines 323-4, where I think the authors mean to refer to changes in the residual circulation.  Even though w* weakens in the southern hemisphere polar vortex (e.g. Figure 7), the age of air consistently decreases here.  In the sense of tracer transport, then, the models are still suggesting an increase, even though w* has the opposite trend.  

Note that I regret that I myself have used the terms loosely in the past!  This meant as a minor suggestion.

Minor suggestions by line number

2  consider "...in order to simulate surface climate variability and change."

12  I would have thought the BDC describes the transport of *mass*, heat, and trace gases.  The difference between the net transport of mass vs. trace gases is a nice way to highlight the role of isentropic mixing. 

20  Consider deleting "which accounts for zonal asymmetries and" so that this reads " and two-way mixing, the irreversible  tracer transport..."

My concern is that residual mean circulation depends fundamentally on eddies (in many regions, the "zonal mean" transport is in the opposite direction), and I wouldn't want a reader to think that eddies only matter for the mixing.

27 Consider "transport diagnostic that quantifies the elapsed time"

30 Linz et al. 2017 use AoA measurements to quantify the residual circulation.  It might be fair to include a discussion of this paper here, or perhaps later on, in the discussion of observations.  Linz et al. found that MIPAS SF6 age would imply huge problems with the reanalyses and models, or could reflect uncertainty in the lifetime of SF6.

77 Given the small number of models, 66% might give an unfairly precise estimate of the uncertainty.  There are only 8 models, so naively, you are saying 6/8 models must agree.  But for the residual circulation, there are only 7, and AoA, only 5 at best.  Perhaps you could say, we ask that at least 2/3rds of the model agree, which in practice meant 5 of 7 for diagnostics of the residual circulation, and 4 of 5 for the age of air.

141 consider "which quantifies the influence of"

165 It might be appropriate to also reference Linz et al. 2016, which makes this very explicit.

Figure 5, the model AOA trends at 30 hPa in panel (b) are global mean trends, right?  Is this a fair comparison with Engel et al. 2017, which I believe is based on measurements at 2 midlatitude NH locations?   If nothing, else, the Engel trend should also be given with significance: 0.15 +/- 0.18, or 0 to 6 %.  And I would discuss the issue of sampling brought up by Garcia and Randal (2011), which I think is still relevant.

184  I think AoA converges faster not just because it has memory (integrating in time), but also because it integrates in space.  The age at any point in the atmosphere depends not just on the local circulation, but on the integrated solution below.  You could simply state "being an integrated quantity in both time and space."

212 Weaker trends in the tropics relative to the high latitudes is consistent with the acceleration of the residual circulation.  As suggested by Linz et al, 2016, increasing the residual circulation should reduce the gradient in age; hence a stronger reduction of midlatitude age.  This result was first established by Neu et al. 1999 with the leaky pipe!

219  I worry that variability at 30 years here is Gibbs ringing.  The 30 year box car average used to compute the trends will amplify any variability at this frequency relative to others.

Figure 10.  I am curious if the kink in resolved wave forcing c. 7 hPa is due to issues with one model, or an artifact of the vertical resolution of the data set (such that it shows up in all the models).

254-6.  I had to reread this a few times. I gather that the contribution of NOGW is uniformly small at this level, but the role of OGW is more uncertain; it plays a significant role in 4 models, and hardly any at all in 3.

265-8  This is an interesting result, which is consistent with the suggestion of Oberlander-Hayn et al. (2016) that much of the trend at this level can be understood as a lifting of the climatological overturning circulation.  I appreciate that this paper is making a similar argument to al the studies listed at line 244-5, but I think the difference is the emphasis on why there is a trend.  Downward control always makes one look above, while a lifting of the circulation points to the rise in the tropopause and the expansion of the troposphere in response to surface warming.

304  I'm not sure if I follow the argument here.  The fact that the global vs. tropical sensitivity is different on interannual times scales (13a) suggests that it's naive to just consider the tropical SSTs.

312-3  consider "Consistent with previous multi-model studies, there remains a clear disagreement ..."  (just to avoid agreement /disagreement in the same sentence!)

More importantly, please consider discussing this mismatch in more detail, as I do not think it is yet an apples-to-apples comparison.  It might also be good to provide references to the previous modeling studies, and the observational studies as well.  (I know they are provided elsewhere, but it's helpful for people who focus on the conclusions to read the paper quickly.)

324 As noted in my general comment, might be good to say the residual circulation here, as opposed to BDC. 

General comment:

This paper investigates the stratospheric Brewer-Dobson circulation in CMIP6 models in terms of residual circulation and mean age of air. Both the climatology and trends, for both past and future, are inter-compared. The results show quite some differences between the models regarding the climatology, but the paper states that all models are within the uncertainty range from observations. The model trends show a clear acceleration of the shallow branch but a less robust pattern of the deep branch, which is likely related to differences in wave forcing among models.

Overall, I regard this paper a very valuable model inter-comparison which is likely of high interest in the community. The paper is well written and the results are clearly presented. However, I think at some places the paper could still be improved to enhance its relevance, clarity and also some discussion could be placed into better context. Please note that the list of detailed comments below is clearly related to my strong interest in the subject and not to criticism of the paper. I rate my comments in this regard as minor and specific but would encourage the authors to elaborate a bit further on these, and hopw this would further improve the paper. After addressing the comments, I would strongly recommend publication.

Minor comments:

1. Comparison to CMIP5:

I can imagine that a key interest of readers when considering this paper concerns changes from CMIP5 to CMIP6 models. Several of these are briefly reported in the manuscript (e.g., L87, L266, L193). However, the paper could benefit significantly from a clearer presentation and discussion of these changes. In this spirit, I would suggest to include results from the previous CMIP5 project in several figures (regarding both climatology and trends), similar to what is done in Fig. 5 for CCMI models, for ease of comparison. Also, the various differences between CMIP5 and CMIP6 could be discussed together in a short subsection.

2. Comparison to observed trends:

This comment is related to the discussion of the comparison of mean age trends from models with those from balloon observations, mainly on p8/L150ff. I think this is a point of high interest to many readers. However, after reading the paper, at least to me, the question still remains: Do we really have a discrepancy between simulated and observed trends? The paper states at several places that there is "an inconsistency in BDC trends" (e.g., L4, L343), but also says that the recent results of Fritsch et al. (2020) and also potential sampling issues in the observational data (as argued by Garcia and Randel, 2011) could explain these differences. So my question is (related to a comment of another Reviewer): How large is the remaining trend difference if one accounts for method and sampling uncertainties? If the proper sampling of model data is not possible, at least the discussion of these aspects could be clarified. And if the conclusions are not clear, I would avoid too strong related statements in the abstract and conclusions section.

3. Abstract:

I find the abstract somewhat unspecific and coming short in stating the main results of the paper. E.g., it is said that "CMIP6 results confirm the well-known inconsistency in BDC trends", or "paper reflects the current knowledge and main uncertainties" but it remains unclear what the "well-known inconsistency" or "current knowledge" are. I would recommend to avoid such unspecific terms but clearly state the results of the CMIP6 investigation regarding BDC climatology, trends, and forcing (even giving some numbers, e.g., MMM trend values).

4. Definition of deep branch:

In this paper, 1.5hPa is chosen as a characteristic level for the deep branch. The authors briefly say on p5/L99 that this level is substantially higher than used in most other studies (actually all studies I'm aware of). I don't really understand the reasoning  given on the same page. Why should the fact that "upwelling minimizes at 1.5hPa" be a good reason for choosing this level as characteristic for the deep branch? As the 1.5hPa choice here is very different from other studies, it would be good to further clarify this argumentation. Also, I would recommend to add a discussion of previous studies on separating the deep from shallow branch and their criteria. Related questions I have are: Why do Lin and Fu (2013, Fig. 3) use 30hPa for the deep branch and find a seasonal cycle compared to the semi-annual cycle found here? In my view, also the Birner and Boenisch (2011) results would be more consistent with this choise and finding. Could it be that the 1.5hPa surface used here is indeed located above the actual BDC deep branch and the semi-annual cycle found here is actually related to the secondary circulation associated with the semi-annual oscillation and not the BDC?

5. Relation to surface warming:

It is stated that there is a "close connection between the BDC shallow branch and surface temp." (e.g., P16, L275), but I'm unsure how Fig. 12 proves that connection. If I understand the figure correctly, it just illustrates mass flux and surface temperature trends from the different models as ratios. If this is true, I don't see why this suggests causality. Wouldn't it be better to plot BDC trends vs. temperature trends for all models/simulations (e.g., scatter plots), to see whether those models with strongest surface warming also simulate strongest BDC trends? 

Specific comments:

P2, L41: I would explicitly state that the Fritsch et al. results also concern the age trends, e.g. add "...observational AoA and trend estimates... "

P6, L116: Regarding the comparison to observed age (Fig. 3) I would also state that a clear difference is the generally too weak extratropics-tropics age gradient in the models. Only CNRM and MRI models simulate subtropical gradients somewhat similar to observations, but these models show a high-bias in tropical age. In addition, I'm wondering how the age gradients here are related to upwelling differences (using the relation derived by Linz et al., 2016). At first glance, it seems to me that e.g. the GFDL model simulates a rather weak gradient but has a rather slow upwelling at 70hPa (Fig. 2) - this would actually be opposite as expected from the simple Linz et al. relation. Any ideas/comments?

P6, L120: I find this sentence about the Linz et al. paper at the end of this paragraph quiet confusing. Has the extratropics-tropics age gradient been used here?

P7, L148: Maybe the sentence "reanalyses do not provide robust trend estimates" is too general. I understand that the result of Abalos et al. (2015) which is referred to here, is the fact that different w* estimates provide different trends for ERA-Interim. Aren't most estimates considered in that paper (8 out of 9) rather robust in their trends, at least in parts of the stratosphere? I would suggest to reformulate like "... for upwelling due to difficulties when calculating w* trends from reanalyses".

Figure 4: What is the reason for the strange trend pattern in MMM 1998-2014 trends (Fig. 4f) in the tropics above about 10hPa? (A similar pattern occurs also in Fig. 7e).

P10, L183: Why is there larger inter-annual variability in the deep branch than in the shallo branch? It would also be helpful to say what variability is represented in the considered simulations (here for the UKESM model), and how reliable this is. Can the results based on UKESM simulations be generalized to other models, as the text here suggests?

P11, L195: "A similar but more modest behavior is found in the CMIP6 MMM...". Actually, I can see this widening only for HadGem and WACCM.

Figure 7: Why is the upwelling region for the GISS model so broad? Is this realistic? Maybe add some comment on this.

P15, L255: Any idea why the GFDL model has that low contribution from resolved waves? (Similar for WACCM at 1.5hPa, L263).

Figure 13: It would be good to add a measure of significance in Fig. 13 (and Fig. 12), e.g. the standard deviation from the regression as error bars.

Technical comments:

P2, L20: "Lagrangian"

P2, L26: "net strength in stratospheric tracer transport"

P3, L73: "significance in"

P11, L204: "substances"

P17, L293: delete "a" after "about"