Paper Summary

• Motivation (i.e., the title): Why does September Arctic-average drift speed decline in model projections?
• Conclusion (focused on CESM-LE)
  • Freshening of Arctic Ocean (and warming, but mostly the freshening) >> Changes in sea surface height that reduce sea surface height gradients >> Reduced speed in Beaufort Gyre and Transpolar Drift in September
  • SSH changes are an annual change, but in March, changes in internal stress & wind stress more than compensate for weakening SSH gradient >> faster speed
• Issues for Future Work
  • Are internal stresses in summer too weak in the models (relative to tilt forces)?
  • The full ensemble of CMIP6 models shows wide range of regional SSH patterns, so role of SSH is less certain in full suite.

Paper Evaluation

This paper is clearly written. The methods are precisely defined, the equations and figures are integrated well, and I barely found a typo. Well done on that part – especially with the equations. I too often find it’s either no equations to demonstrate the physical theory or inadequate text provided to explain what the equations show. This paper has a good balance.

By the science, again, this is a strong study. The narrative line from research question to research design to results to conclusions is logical and organized. The authors do a good job emphasizing the September slow-down as the key point of interest while also providing context. They also deliver on the promise of that mystery by providing robust physical explanations supported by a combination of evidence from their results and theory. There’s nuance and plenty of limitations, but the authors describe those without making me feel too bogged down in the detail. Job well done. Great science. I think this should be published after some minor revisions.

Line-by-line Comments

1. Line 25-26: This sentence sounds contradictory, starting with “Record-low SIE has been frequently observed since the mid-2010s” and ending with “no record recorded during this time period”. If talking about September SIE, the latter statement is correct (2012 is still the lowest). However, the thrust of this paragraph seems to be emphasizing a negative trend, so I wonder if the authors actually meant to convey that SIE has frequently been below the 5^th percentile of 1981-2010 average daily SIE, or something like that.

2. Line 100: Sorry, this is a long comment for a small problem. It might even be minor enough to not be noticeable in the end, but because it might change a minor result noticeably, I must mention it.

The NESM3 model fields downloaded from the ESGF are still on the rotated ocean grid, so the smallest grid cells by area do not neatly align with the highest latitude. Therefore, a simple latitude-weighting will introduce some bias, providing too little weight approaching 90°N (e.g., rows 366 and 367, columns 159 and 160 in the NESM3 ocean grid, which all have a latitude of 89.7°N) and too much weight for certain other locations (e.g., latitude = 80.3°N, longitude = 320.4°N, which is row 383, column 159 in the NESM3 ocean grid). (Note: Those indices assume counting starts at 0.)

If you use the lat_bnds and the lon_bnds variables, you can find the latitude and longitude of the four corners of each cell and then calculate the area of the quadrilateral using line integrals (with Green’s Theorem) or using Girard’s Theorem. Line integrals is what MatLab’s areaint function uses, and it seems to be preferred in GIS software (from what I can tell). But either works better than the simple cosine method for this application. There are example Python implementations of each here: https://stackoverflow.com/questions/4681737/how-to-calculate-the-area-of-a-polygon-on-the-earths-surface-using-python.

If you’re doubtful, let me attempt to convince you with an example. Let’s compare two points I will arbitrarily call “point 1” (row = 337, col = 134) and “point 2” (row = 383, col = 159) in the NESM3 ocean grid.  The center of point 1 is (70.334°N, 105.192°E) and the center of point 2 is (80.313°N, 320.143°E). Based on the cosine of the latitude, the weight of point 1 should be 2.00 times larger than the weight of point 2. But point 2 is near the convergence point for the NESM3 ocean grid. So that’s underestimating. Using Girard’s Theorem and using the lat_bnds and lon_bnds variables, point 1 should really have 10.52 times more weight than point 2. Using Green’s Theorem, point 1 should have 10.55 times more weight than point 2. That magnitude of difference was enough to convince me I should bring this up in the review. But again, if it only affects NESM3, there’s no chance this has a major impact on any conclusions – only a minor impact for that one model in Figure 1 and A1.

p.s. I already had daily NESM3 sea ice fields on my computer and recently went through this entire process for a project of my own, so I was primed to be pedantic about this.

3. Line 117: I presume by “BCC-CSM2-1”, the authors mean “BCC-CSM2-MR”, as labeled in Table 1.

4. Line 162: Replace “and much our analysis” with “and much of our analysis”.

5. Figure 1: The labels “March” and “September” need to be exchanged in this figure to match the caption and the text.

6. Line 227-228: At first glance, it seems contradictory to declare that one can assume steady state for a variable undergoing a long-term trend. The resolution of that contradiction, of course, is the time scale, but it might be nice for the authors to note that explicitly. In other words, the daily ∂v/∂t can be ignored.

7. Lines 312-318 or Lines 337-345: I can’t find a paper that shows maps of Arctic summer precipitation or P-E change in CESM2 or CESM2-LE, but I do know that CMIP6 models in general produce positive trends in JJA precipitation over the Arctic under warming scenarios (McCrystall et al., 2021; IPCC AR6 WGI Figure 8.14), and the CESM2 produces positive trends in precipitation annually over the Arctic (Meehl et al., 2020). These ideas might be worth citing in discussion of the trend in sea surface salinity. The authors do a great job describing why the surface salinity pattern is different from the integrated salinity impact on sea-surface height, but I feel like there’s a good opportunity to also discuss whether precipitation (directly or via river input) has any role to play in freshening at the surface (in like a sentence).

8. Figure 9: This is the only figure where I have trouble seeing everything the authors are describing. The SSH filled contours are clear, but the sea ice motion vectors are sub-optimal because there aren’t enough of them for me to adequately see the spatial patterns. Of course, I can’t just recommend adding more arrows because that risks over-crowding. Therefore, I also recommend the authors do any/everything they can to increase the map size, giving more space for arrows. For example, make the figure taller, make the quiver keys smaller (e.g., by declaring the units just once in the figure), and maybe even shift that color bar into the blank space in the lower-right.

If the authors don’t think they can adequately plot more vectors, then I advise they make another figure (main or appendix) that shows maps of the September 1979-2014 SSH and motion climatology for each model. That at least would give a reference for readers when trying to visualize the description in the results. Actually, this might be a good idea even if the authors can improve Figure 9, but I only think it’s a must-have if they the authors prefer to leave Figure 9 as-is.

Works cited in this review

IPCC, 2021: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2391 pp. doi:10.1017/9781009157896.

McCrystall, M. R., J. Stroeve, M. Serreze, B. C. Forbes, and J. A. Screen, 2021: New climate models reveal faster and larger increases in Arctic precipitation than previously projected. Nat Commun, 12, 6765, https://doi.org/10.1038/s41467-021-27031-y.

Meehl, G. A., and Coauthors, 2020: Characteristics of Future Warmer Base States in CESM2. Earth Space Sci., 7, https://doi.org/10.1029/2020ea001296.

The authors present diagnostics of the sea ice momentum balances in a series

of GCMs with the goal of understanding the projected decrease in sea ice

drift velocities in the Arctic under a future increasing CO2 scenario.

It is found that changes in SSH in the models are primarily responsible for

the change in drift velocity. While this is correct, I think it would be

clearer to state that the change in drift velocity results from a change in

the ocean currents. Since the wind stress and internal stresses do not change

significantly that means the ice drift relative to the ocean also does not

change (assuming the drag coefficient is similar), so it is really the ocean

currents that drive the change. This is of course directly related to SSH

through geostrophy but I think the interpretation is clearer. In fact, if 

one assumes that the surface velocity in the ocean is in geostrophic balance

with SSH gradients, the tilt terms drop out and the Coriolis term is 

acting on the difference between the ice and ocean velocities, making the

underlying mechanism clear.

line 13: But the models do not reproduce the observed ADDS increase in summer

for the historical period, so I think it is optimistic to assume that the

models will be correct in the future. More explicit discussion of the model

shortcomings in summer are needed (around line 64).

line 26: no record recorded? Please clarify

line 67: What is the Representative Concentration Pathway? What is 8.5 W/m^2? 

Anomalous radiation averaged over the globe? Uniformly distributed? Same for 

line 83. I see this is explained layer, but maybe note that here.

line 85: What does r1i1p1f1 (and similar) mean?

line 101: Clarify - does this weighted averaging reflects the area of each

model grid cell?

Line 105: What do you do in regions where the summer ice disappears over

the duration of the experiment?  If you neglect those points, how does this

bias your estimate?

Figure 1: It would be helpful if you could add the drift speeds derived from

satellite data when it is available.  This would help the reader to understand

the shortcomings in the models representing the recent observational record.

Also, it looks like the y-axis labels are incorrect.

line 171: Why is it supposed that the ice drift velocity results from a

change in ice thickness and not a change in winds or ice-ocean drag coefficient

(because ice is younger)?

Fig. 2c, d: It would be clearer to plot the change in drift as vectors.

I am having a hard time visualizing the change from the individual velocity 

components. The same for Fig. 3. This would also reduce the number of panels.

I do not see the benefit added for Figs. 4 c-f. All this information is 

contained in Figs. 4a and b.

line 237: Are the only assumptions that the ice balance is steady and linear?

line 254: Again, I think trend vectors would be clearer.

line 267: The lack of seasonality indicates that the geostrophic trends are

not due to seasonal ice melt but instead probably due to changes in the 

permanent halocline.

Fig. 6: Can you interpret why the internal stress term changes in the

way that it does? Is it due to convergence or shear?

Fig. 9: vectors are too small

Discussion and Conclusion: The decline appears to be driven by a (spatially 

variable) freshening of the Arctic.  However, in recent decades the Arctic below

the halocline has been getting saltier as more Atlantic-origin waters are

penetrating into the basin. Do the climate models reproduce this effect?

If not, why should we  believe what the climate models predict for the future?

It should be discussed how well the models represent this important shift in

the hydrography of the Arctic.

Again, I think it would be clearer to state that the change in drift 

velocity is due to a change in ocean velocity rather than a change in SSH tilt.

All figures are too small. Show only down to 70N would increase the area of

interest.

This paper aims to answer the question posed in its title: why do climate projections show a decrease in Arctic sea-ice drift speed? The authors analyse the outputs from 17 CMIP6 models and ten members of the CESM2 large ensemble. By decomposing the different contributions to the sea-ice drift in these models, they conclude that in winter, the drift increases because the internal ice stress decreases due to the ice thinning. In summer, they conclude that the drift decreases because of a reduced sea-surface height gradient caused by the freshening of the Arctic Ocean. The paper is clearly written, understandable, and logically structured. The paper's conclusions also appear well-founded and reasonable, but the attribution to SSH gradient in September needs clarification and further work - as discussed below.

I'm asking for major revisions because I want to review the revised manuscript. I'm not sure that there is a very substantial amount of work required, though.

I have two substantial comments and a few minor comments, as follows.

Firstly, in line 92, you say that "calculating drift speed from monthly output of drift components produces highly inaccurate results". This statement is not correct. Sea-ice drift speed is highly dependent on the time scale at which it is observed; i.e. calculating the drift speed from a daily displacement of a buoy and then taking a monthly average will give a very different result from calculating the speed directly from the monthly displacement. The same goes for using a model's monthly or daily velocity components to calculate the speed (as pointed out by Tandon et al., 2018). It is, however, important to note that both approaches are equally "correct" and "accurate". They are separate ways of observing the system from which we can learn different things. In this context, the only incorrect thing to do is to compare the speed obtained at a given time scale with that obtained at another - as Rampal et al. (2009) did.

Secondly, I struggled with the two paragraphs starting at line 237. In the first paragraph, you describe how you calculate the "reconstructed trends" and then say that these only capture 50% of the total velocity trend. We need a justification for the rest of the analysis when half the signal is missing, and this should come in the following paragraph, but I don't find it convincing.

You say that you tried using equation (3) to calculate the change in velocity between two days but that you got quantitative discrepancies. This conclusion doesn't make sense because equation (3) is a steady-state equation - so I assume you mean that you tried recreating the velocity field directly, not calculating the change. Still, you ascribe the discrepancies between your results and the model fields to sub-daily variability, and I also have a problem with this. If we can assume a steady state (as is appropriate for climate models), then equation (3) holds, and as it is linear, then the mean equals the mean of the components. Sub-daily variability, while present, doesn't enter into it. It is even questionable how much sub-daily variability is present in a climate model - but this is a different story. So, I'm not convinced that you miss 50% of the trend to sub-daily variability, but even if you do, that begs the question of why the sub-daily variability decreases, which you need to address.

Ultimately, I don't think computing the ensemble mean, as you have done, is the right way to go. I assume you calculate each term of equation (3) for each member and then work with the mean of these across the ensemble at a daily time scale. If you do this, you are essentially filtering out the synoptic signal; each member will have different weather systems, so the mean will only give you the long-term motion. Comparing this against the speed calculated at the daily time scale is not appropriate, and I suspect this is why the reconstructed trends are 50% smaller than the actual trends. Doing the reconstruction with monthly values for the component terms would be more appropriate, as this also filters out the synoptic motion. There is probably a more sophisticated way to do this, but I can't think of one now.

If I am right above, your conclusion holds, with the caveat that it only pertains to the long-term motion. This is perfectly reasonable, but you can't state this about the synoptic scale motion because your method loses you 50% of the trend. This is probably not a problem because the ice is essentially in free drift in September in future scenarios, and we don't expect a trend in any of the terms - except SSH. The slow-down must, therefore, indeed be due to the reduction in the SSH slope. But the details are fuzzy as the paper stands.

To cut a long story short: I think you've reached the right conclusion, but you need to explain better what happens with 50% of the trend in your reconstruction and why that doesn't matter for the results.

Minor comments:

L42: You say that improved models produce results that better agree with observations, but this is not the point in Kay et al. (which is now published in JAMES, btw). They just tune some parameters to get better results.

L99: Skip the text in the parentheses and just say grid cell area instead of areacello variable in the line below.

L119: It's not really a "pole hole", but rather a coordinate singularity.

L125: Why are you using different scenarios? Isn't that a problem?

Figure 1: It would be nice to have the observed drift speed on these graphs as well. In the CESM2-LE graphs, the lines for the individual members are almost invisible. The legend is too small to read. The Y-axis labels are switched (September should be March, and vice versa).

• I'm suspicious of the velocities going to zero in September. This probably coincides with the Arctic becoming ice-free in these models, but the velocity is undefined in that case - not zero. It looks like you made a mistake with the area averaging.

Figures 2 - 9: Those figures have a lot of white in them. You include all of the Greenland, Norwegian, and Barents Seas, which are not of interest here. And there's a lot of space between subfigures. Reducing this would allow you to show more detail.

Figures 4-6: The contours are unclear and I'm not sure how useful this way of presenting the results is. But it could be good with larger figures.