The authors use data from the ICESat-2 satellite to measure sea ice topography and, based on previously developed parameterizations, they use those measurements to generate estimates of time-and-space varying atmosphere-ice neutral drag coefficients throughout the Arctic.

Drag coefficients over sea ice are not well constrained — especially in the winter — and as such are often used at "tuning" parameters in models. The results of this study provide evidence for seasonal and spatial variability in atmosphere-ice neutral drag coefficients, with notable differences for first-year-ice (FYI) and multi-year-ice (MYI) covered areas. These results highlight that neutral drag coefficients are not the constant values often used in models and other studies, and show that pan-Arctic maps of drag coefficients can be produced using remote sensing measurements.

My primary concern with this study is that the derived drag coefficients are only as accurate as the Garbrecht et al. (2002) parameterization scheme used to convert from topographic measurements to drag. While Garbrecht et al. (2002) show a good comparison between parameterized and measured values of drag, the observations they use are still limited to just a few distinct, short measurement campaigns. Furthermore, the parameterization still relies on some unconstrained factors; namely the coefficients of resistance, the surface roughness length, and the effects of sheltering (different values and formulations for each of these have been suggested throughout the literature). Additional testing of the parameterization scheme is obviously beyond the scope of the current study and the data available. The lack of additional experimental verification of the scheme does not invalidate the results of the present study. However, the uncertainties associated with the scheme should be acknowledged by the authors, and quantified where possible. For example, how sensitive are patterns of spatial or temporal variability to the chosen formulation for the coefficient of resistance, or to the floe edge drag coefficient? Would the results be similar if other schemes (e.g., one of those from Lupkes et al., 2012) were to be adopted instead? It's likely that such changes would slightly modify the drag coefficients without majorly impacting the spatial or temporal patterns of interest—but this should be tested. I recognize that previous studies that similarly convert ice topography to drag coefficients (Castellani et al., 2014; Petty et al., 2017) don't include such discussion but I nonetheless feel that it is important to acknowledge some of these unknowns.

Despite this critique, I find the subject matter and results of this study to be important, the methods and analysis to be robust, and the quality and readability of the manuscript to be good. I recommend this study for publication after revisions to address my concerns with the parameterization scheme and some further minor comments, below. I don't believe that these revisions should take a substantive effort, but am marking my recommendation as a major revision on the basis of what I feel is the importance of discussing the uncertainties associated with application of a parameterization scheme.

General comments:

 - I appreciate that the study accounted for the spatial resolution of the ICESat-2 sampling by making comparisons with OIB ATM data. The authors chose to do so by developing a scaling (eq 6) based on linear regression between the computed form drag coefficients from each data source. I am interested in the choice of regressing the computed coefficients (which depend non-linearly on each of the two topographic variables) versus regressing the topographic variables He and xe directly. Based on some of the details gleaned from Fig 1 and related text, one might expect that the mean obstacle spacing xe is most impacted by the smoothing rather than obstacle height He, so separate regressions might yield better results. Did the authors explore these different options? It is not necessary to provide a detailed analysis in the study exploring all of the different options for regressions, but the authors should acknowledge (either in §3.1 or in an appendix) if they performed these tests and either (a) overall scaling was the same; or (b) they chose to use the option with the best regression. 

- The results of this study highlight the spatiotemporal variability of drag coefficients and suggest an importance of being better able to characterize obstacle statistics in numerical models. I think that there are some opportunities in the study to share some other information about the obstacle statistics that might be useful for other researchers thinking about empirically-based or simplified parameterizations. In particular, in some figures in the study the mean He and xe appear to fairly strongly negatively correlated with one another (consistent with under-ice measurements from Brenner et al, 2021; https://doi.org/10.1029/2020JC016977). I would be curious how robust such a correlation may be, or if it differs in space/time or for FYI/MYI? Furthermore, Martin (2007 Thesis; and others) suggest relationships between sail height and level ice thickness (which can be found from the modal surface level in these measurements) that might be worth sharing for these data.

Specific comments:

§1

- L201-22: I wholly agree with the statement that "the surface roughness of sea ice... needs to be better understood". However, the authors don't properly justify that statement here. Why is roughness important? Some of this motivation is found later, e.g., in L33-37, but I would introduce the qualitative importance of roughness before explaining it's origin. 

- L41-45: Consider restructuring these sentences to improve the flow of the text: by starting with the definition of 'z' and its additional explanation, you disrupt the list of variables which makes it awkward to come back to the rest of them on L43. Instead shift the other items on the list (rho, U, k, theta) earlier and end with z. As a personal preference, I don't like sentences starting with a variable if it can be avoided. Rearranging the list would avoid starting a sentence with rho. Similarly, the sentence introducing the stability function, fm, can be combined with the previous one: "The drag coefficient Cd is usually written as a product of Cdn and a surface roughness dependent stability function fm"

- L60: The statement that the parameterization has been used "successfully" can probably interpreted in multiple ways. To me, it implies that the application of the parameterization has matched observational estimates of drag; however, the cited papers don't test that. Are there any observational studies that test the parameterization aside from Garbrecht et al. (2002)?

§2

- L105-113: What is the effective horizontal resolution of the ATM data after processing? Does the 1m footprint result in a 1m horizontal spacing?

- L130-134: Some type of schematic/visualization somewhere around here might be useful for understanding the data spacing referenced here and visualizing how satellite tracks fit in the 25 km gridboxes, the associated time-space variability of the data within a gridbox (i.e, colouring tracks in the schematic by time offsets or similar), and maybe the overlapping 10km segmentation.

- L148: "...Rayleigh Criterion (explained below)" Where is the explanation for the Rayleigh criterion? I was expecting this to be defined somewhere following the numbered list, but don't see an explanation or relevant citation in the manuscript.

- L204-205: Mention where the cw formulation comes from (this is the one recommended by Garbrecht et al. 2002, but they also test a few other formulations). You may also be interested in seeing Zu et al., 2021 (doi.org/10.1029/2020JC016976) who use laboratory and numerical modelling in an attempt to constrain the formulation for this coefficient as applied to under-ice ridges.

- L226-228: It might be worthwhile to provide some context for the version of the edge-drag scheme introduced here, especially given the later suggestion (L442-443) to further estimate this.

- L233: In my opinion there is no need to repeat the value of Cd,s from equation 4; it's already listed on L213.

§3

- L273 and Fig 2: In my opinion, it doesn't seem necessary to include the 15m and 45m filters when it is already established that the ICESat-2 data have an effective 30m spacing and the 30m filtering produces the best result. If they are kept as a part of the figure it might be helpful to include some justification about why they may be of interest to readers.

- Fig 2: For the no-smoothing-fit, it is hard to see the different colour contours in the heatmap (on initial look I thought it was all a single colour). For the 15m and 30m-fits it is hard to see the different colour contours in the heatmap because the 45m-fit heatmap is overlapping. In fact, I only realized that there were different colour contours because of the visibility of the core of the 45m-fit heatmap.

- L278-280: To be clear, the drag coefficients here just the form drag coefficients, not the total drag coefficients? (Consider using the Cd,o notation from eq. 5)

- Fig 3 caption: mention the equations for calculating drag coefficients in panels C, D (e.g., eq. 3 & 5 for C, and eq. 3, 5 & 6 for D).

- L300-305 and Fig. 4: Despite the fact that the two data sets are not perfectly co-temporal, I would initially have expected a better regressor slope than 0.5 given that the basis for much of the analysis (binning in time/space) is implicitly based on slowly-varying statistics. My initial reaction to seeing this is some suspicion that eq. 6 is not valid across all different obstacle statistics, and wondering if separate scalings of He and xe (as suggested in my general comments, above) would produce a better fit. That initial thought may prove not to be correct, but in any case I think that the authors are fairly quick to dismiss the value of the slope. In fact, I became more hung up on the slope value than necessary since the histograms in Fig 4B and discussion in L305-310 show that the difference between the datasets is not that drastic and generally a good fit. Perhaps some reorganization here could help prevent similar hang ups?

- Fig 4B: are the histogram bar heights probabilities? Probability densities? Counts? Label the y-axis.

- L333-334: Roughly what is the percent coverage of ICESat-2 data relative to total sea ice area?

- Fig. 6A: It would be interesting to see this broken up by the contribution of all the different terms in eq. 5 (perhaps in an appendix figure), or at least similarly to columns III and IV in fig. 5 (panel A in fig. 6 corresponds to column IV in fig. 5; an additional panel could be included in fig. 6 corresponding to column III).

- Fig. 6D: Can this panel also include the total sea ice area for reference? If not reasonable to do so, I'd recommend changing the title to "Total sampled area" or something similar.

- Fig. 6: Date label format is hard to read. Also, if including axis ticks for only 2 months of each year, consider using March and September to correspond to the annual sea ice maximum/minimum.

- L359-368: A number of areas are mentioned here (and elsewhere in the paper) by name when describing spatial characteristics of the ice, but not everyone is familiar with these different geographic features. Including the names on a map or figure somewhere would be helpful.

- L376-377: The use of ATL03 data for similar statistical measurements should be mentioned much earlier (back in §2.1). The use of ATL07 seems well justified by the discussion in this section and it's appropriate to keep most of that discussion here, but the ability to use ATLO3 to derive roughness should be acknowledged before this section.

- §3.6: I appreciate the inclusion of this section and explicit statements of the study's significance. 

- L392-393: Accounting for stability effects is (rightfully) outside the scope of the present study; however, seasonality in the surface stress in eq. 1 will depend on both seasonality in neutral drag and seasonality in the stability. It would be beneficial if the authors were to very roughly describe the impacts of stability here: specifically, would it be expected to it enhance the neutral drag coefficient seasonality or counter it?

- L401-402: "FYI ice peaks sometime in July-August (blue line in Fig. 6A)" This is hard to discern from figure 6A, especially as (I think) the blue line doesn't seem to even include July-August data (unless I'm misreading the date labels). The secondary peaks in ~August for each year are only in the "all ice" black lines, and are below the primary peaks. Elevated values of drag seem to exist for FYI each September.

- L410: "All other Arctic Seas (mostly FYI)" Consider including a figure showing FYI/MYI extents when available, perhaps as another column in fig. 5? (This isn't totally necessary, but would be helpful for the discussion here and in §3.3).

- L418-419: This whole study is based on the use of a form drag parameterization and frequently cites Tsamados et al., (2014) who describe the implementation of a similar parameterization in a modelling framework; however, this statement argues that further drag parameterization is necessary. This seems contradictory and should probably be rephrased. Nonetheless, I agree that more work needs to be done in this regard; specifically, the results indicate the need for further ability to model obstacle heights/spacings and for the implementation and use of form drag parameterizations. Also see my general comment regarding additional data presentation for simplified parameterizations.

§4

- L425: This is nit-picky, but I dislike the phrasing here. Saying that the study *relates* the topography to drag coefficients could be construed to mean that the two are measured independently. The study *uses* measured sea-ice topography to calculate temporal and spatial variations of atmospheric drag coefficients.

- L443-444: Not a subject of this study, but I am curious how you plan to account for the floe sizes when considering the edge drag component. Do you intend to also determine those using ICESat-2 data (e.g, Horvat et al., 2019; https://doi.org/10.5194/tc-13-2869-2019)?

 

§A

- L457-460: I am finding this sentence hard to parse (the one beginning "As a result...").

Other grammar and typos: 

- L5: Grammar error in: "though it cannot resolve as well airborne surveys"

- L200: Use an in-text citation instead of a parenthetical citation for Castellani et al., 2014

- L271: Suspected missing decimal in "OIB ATM occupy a wider range (~03−1.3·10^−3 )"; should probably be 0.3 instead of 03

- L300-303: Awkward sentence structure for sentence that begins: "Correlation (0.51) and slope...". Consider revising or maybe breaking up the sentence.

- Figure 6: mismatched capitalization in plot titles for panels B and C.

- L408: Missing figure reference

General comments

The authors present a method to estimate pan-Arctic drag coefficients using observations of sea ice surface feature parameters from ICESat-2. The results show that the drag coefficient is both spatially and temporally variable, and that pan-Arctic drag coefficients can be estimated with the use of satellite observations. It is the first analysis of monthly pan-Arctic drag coefficient estimates of its kind. I assume this will be welcomed in the model community.

Below I will address some specific scientific questions and technical corrections. Based on these, I would like to suggest minor corrections to be made before publication. 

My biggest concern is the use of the OIB/ICESat-2 correction and the lack of discussion on the uncertainties and errors this will introduce. The regression is only trained on 4 days of observations in April for a specific location of the Arctic, and is then assumed to still hold over different types of sea ice and other months of the year. I understand there is no more data to use and thus I won’t suggest changes to the methods, but I do think a discussion on the downsides of this method is necessary.

See below for additional comments.

Specific comments

• One of the big uncertainties introduced by the methods used in this paper is the OIB model correction to the observed form drag coefficient. This model is trained on the comparison between OIB airborne lidar measurements and ICESat-2 satellite observations for the near-coinciding 4 days in April 2019 in the Lincoln Sea and the Arctic Ocean north of Greenland. This region is for the majority covered in MYI, also in the month these observations were made (see https://nsidc.org/data/nsidc-0611/versions/4).
  
  This model is then applied to the observations for the full pan-Arctic area discussed in this study, and to each season and for the years 2019, 2020 and 2021. I doubt this relation between the ICESat-2 form drag coefficient and the OIB ATM form drag coefficient will be the same in areas that are predominantly covered in FYI or in other seasons of the year. I understand there are not more near-coincident observations in other regions and months available, so this is the best that can be done now, but I think it is important to include a discussion on the effects these assumptions have on the presented modelled drag coefficient, especially because the model regression coefficient is large and impacts the results a lot. 
• One the same argument, it would be useful to present some statistics on the presented regression model (Eq. 6). How good is the fit? It would also be interesting to see this fit for the observations of the 4 days seperately. Are they similar or does it change for the different days and different flight paths?
• Explain why the value of 0.2 m is used as threshold (line 153). You’ve mentioned you have also tested using 0.8 m, but no other values where tried? 
• Figure 4A: if you already know this is not a good direct comparison because of the ice drift in between days, maybe it’s better to leave this figure out? I think it will only raise doubts and confusion because the fit does not look good, even though you don’t really expect it to be good? I think Figure 4B is better because here the drift doesn’t influence the comparison. 
• One of the most exciting things of this preprint is the pan-Arctic sea ice roughness dataset it accompanies. I would suggest making this dataset easily accessible: add a link to the data availability statement and include the dataset as an asset on the The Cryosphere page

Technical corrections

L4. Add ‘Ice’ to the full name of ICESat-2

L5. Replace ‘as well airborne surveys’ with ‘as well as airborne surveys’.

L12. I would clarify that it is the drag coefficient of MYI that is above 2.0·10^-3

L13. I don’t understand this last sentence. Do you mean the drag coefficient of this region of MYI is at least 1.5·10^-3 everywhere every year?

L22. ‘which needs to be better understood’: why? There is more discussion of the importance and relevance later in the text, but it would be good to have at least one sentence here to convince the reader this topic is important before going into the more technical details.

L32. ‘Smoother in comparison’ with what?

L110. Change ‘campaign’ to plural: ‘campaigns’

L147. The Rayleigh Criterion introduced here is never explained.

L185. Replace ; with ‘and’.

L204. The function to compute the coefficient of resistance might need a reference?

L271. Change 03 to 0.3

L347. Change ‘a annual’ to ‘an annual’

L408. Add figure number

L436. Change ‘first-ice’ to ‘first-year ice’ or ‘FYI’