Summary. This is an interesting, detailed, well prepared paper that has important implications for

deriving sea ice topography using a unique approach, with single-pass interferometry. I have some requests on clarifications that I will write down in Details. The methods are largely clearly described.

I think I have three main points about the paper as a whole that I suggest the authors consider. First, the paper is presented as being applicable to both polar sea ice covers. However, particularly in the Introduction and Basic Concepts, they really don’t distinguish sufficiently between the main differences in the sea ice between the Arctic and Antarctic. I have added some suggested references to include. So please add some more text about differences in ice type and snow layer. Next, it’s not clear to me that a two-layer model is sufficient, with both layers considered to be uniform, to correctly identify the phase center.  In Arctic first year ice, at the snow-ice surface particularly for young first year there is often a significant layer of high salinity slush ice that may also include frost flowers. There wil be some penetration below this thin layer where the salinity is much lower. Then of course in the Antarctic, flooding at the snow-ice layer occurs due to relatively deeper snow loading on the generally thinner ice layer, as compared to the Arctic. This flooded layer has a higher salinity than the ice below but is still not likely sufficient to minimize further penetration.  Plus of course there is increase in salinity near the ice-ocean boundary in all winter ice growth conditions. The slush layer is referred to in the paper, but I maintain that it is not sufficient to dismiss the possibility of a 3-layer without demonstrating otherwise which I suggest they do, as it may impact correct estimation of the phase center and therefore a modeled-derived height. Finally, last main point has two components – first while they compare with a DMS height as a narrow 2D transect, which is what is available and appropriate, they also show 3D output (Figure 13). However, there isn’t much discussion about the 3d output – do these appear to be representative of what might be expected or compared to other possible data or studies?  There are papers on ridge/sail characteristics plus a nice example in Tucker chapter 2 in Carsey sea ice microwave book. Second part of last point is that these 3D maps are really unique because they are not just narrow transects. How often for example could these 3D maps be generated with Tandem-X, spatially and temporally? I think Tandem-X is pretty limited by its duty cycle at least and perhaps storage/downlink too. It would be good to hear about longer term capabilities for deriving this product and what might be required to validate Arctic products, for example.

Detailed comments.

1. Lines16-18. Add references that discuss ridge characteristics, etc in addition to Rampal reference for both poles, for example for Antarctic, Lytle et al. Annals Glaciology 1998, two Tin and Jeffries papers in 2003/04, plus Timco and Burden 1997 for Arctic.

1. Line 24, Tucker et al reference is for first year ice only. please clarify.

1. Line 25. Petty reference discusses both FY and MY and differences. Please mention in text. Also following Toyota paper, there is a really good chapter on Snow by Sturm and Massom in Sea Ice book edited by Thomas and a recent chapter by Webster et al Nature Climate Change 2018.

1. Lines 30-31. Add journal papers that utilize DMS data in addition to Dotson and Aversen references.

1. Line 53. Substitute ‘deficient brine’ for ‘reduced brine’

1. Line 61. Substitute ‘obtain an’ for ‘obtain a more’ accurate.

1. Lines 77-83. This paragraph should be expanded to discuss thin salinity layers at snow-ice interface as mentioned in the summary with references

1. Figure 8. I guess I really don’t understand these figures. I looked and looked at how one might determine that these graphs suggest phase centers of 6-7cm and 15-33 cm as described in the text – Lines 312-315. I would appreciate an explanation of what information they are using from these figures and how they are deriving the phase centers.  I also hope the editors are getting a review from another person who has a lot more  INSAR and radar modeling expertise than me.

1. Figure 14. I think the grey lines for the removed sections are too distracting from both a) and b) and perhaps just not included in the graph. Are the grey removed sections the same segments as described in Figure 4 as being mis-registered and set at 0 height? If so, not sure why they need to be included in Figure 14 at all.

1. Lines 474. Snow depth is not well correlated with thickness or even FY or MY ice and in both polar regions.

1. Lines 509-511. This is a good sentence and touches back at some of my points in the summary and the need to clarify some references in the introduction and Basic Concept section, the idea of model that may need to improvement etc as well as how these type of products could be expanded in Tandem-X acquisitions and products.

1. Basic concepts or Model Development or Discussion. I really do think it’s important to consider a third thin high salinity layer at the snow-ice interface, whether on thin first year ice or flooded ice. I realize this might be a lot of extra work and at this stage of your study, it may not be of primary importance. This could also be added to the Model section or Discussion section too at minimum, as a topic for further research and what you think the impact might be on the model. Of course, the authors could tell me that they don’t think it’s a worthy topic at all and won’t make any difference. I do think firmly that their two-layer is not universally applicable to all the major ice types and conditions for both polar regions, based on my understanding of their model. New and young ice are often the trickiest anyway to deal with any radar algorithm. Throughout the paper as I was reviewing it, I kept thinking about those two thin salinity layers and differences between first year and multiyear etc in both poles and how this should all be considered in a model of radar penetrating sea ice.

Overview

The manuscript Antarctic snow-covered sea ice topography derivation from TanDEM-X using polarimetric SAR interferometry by Huang et al. presents the development and validation of a new two-layer plus volume sea ice model with the aim to correct for the height bias associated with InSAR penetration into the snow pack. This model is able to represent the sea ice/snow stratigraphy and associated scattering, and, when simplified and inverted, allows for the estimation of the sea ice plus snow surface topography from TanDEM-X. This retrieval technique shows strong agreement to an Operation IceBridge optical (DMS) DEM that was collected contemporaneously as part of the OIB/TanDEM-X Coordinated Science Campaign.

This manuscript is well-written and thoroughly presents novel methods and results that could be useful to the broader sea ice community. I have a few relatively minor comments and suggestions that should be considered, found in the general and specific comments below.

General Comments

The main comments I have on the manuscript deal with (1) the height threshold used (2) X-band scattering/slush layers and (3) the snow depth parameter.

GC1: To me, it appears there is some mix-up with the height threshold used to keep model-error accuracy to within 25%. In section 4.4, it was stated that the ice volume (z₁-z₂) needs to be thicker than ~1.5m to achieve this accuracy. However, in later sections only ice+snow heights above the local sea surface (effectively the total freeboard) above 1.5m are used. Doing so filters out ice volumes much thicker than 1.5m, since most of the ice volume is below the waterline.

I would suggest the authors confirm that the 1.5m threshold is indeed for the ice volume, and recommend that they filter the InSAR retrieved heights accordingly (which should result in a much lower height-above-sea-surface threshold).

GC2: (This is similar to that from reviewer 1) While the scattering impacts of a slush layer are briefly mentioned, I feel that their impact should either be discussed further or/and incorporated into the model in some way. A slush layer at the snow-ice interface would surely effect the radar return differently than if the snow-ice interface was smooth and dry. Also, some mention of the effects of surface roughness would be beneficial, as snow surface/interface roughness has been found to influence X-band backscatter (Nandan et al. 2016, Remote Sens. Of Envir., https://doi.org/10.1016/j.rse.2016.10.004). Finally, while surface melt may not be present in this particular region or season, a wet snow surface could also influence the X-band backscatter (Dufour-Beauséjour et al. 2020, The Cryosphere, https://doi.org/10.5194/tc-14-1595-2020). This would need to be taken into account if applying this technique to other regions and/or seasons.

GC3: The paper states that the influence of snow depth on γ_{mod_T}  is not negligible, and that a priori data from external sources must be used in the simplified model. If I understand correctly, the passive-microwave-derived snow depth data used as the sole model parameter results in a single snow depth value (18 cm) for each pixel across the scene. While I understand that high-resolution snow depth data is generally not available, this single value is likely not representative of the actual spatial snow depth distribution (and perhaps not realistic for heights >1.5m, as a quick hydrostatic calculation of ice thickness with this snow depth yields abnormally thick ice). Therefore, I’m curious as to the impact of the snow depth parameter on the experimental results (beyond what is shown in the simulated results of figure 8), and if/how the retrieved heights would agree with the DMS DEM under e.g. spatially-varying snow depths.

Specific Comments

-Lines 23-25: I find this sentence slightly confusing as it’s written, especially since Petty et al. 2016 also mention the “close correspondence” between the predicted (surface height+square root relation) and OIB-measured thickness. Just noting the +/-2m difference makes it sound like a poor retrieval.

Lines 29-31: Since you mention that characterization of sea ice topography is an active area of research (line 28), I would suggest citing more recent studies using laser altimetry and photogrammetry (e.g. Farrell et al. 2020, https://doi.org/10.1029/2020GL090708; Li et al. 2019 https://doi.org/10.3390/rs11070784; and/or others).

Line 87: By previous work, do you mean Huang and Hajnsek (2021)? Or previous studies in general?

Line 91: Same as above comment. If previous work is referring to Huang and Hajnsek (2021), I would suggest writing that explicitly.

Line 179-180: How are water-surface points selected? And how many pixels/points are used in this scene? More information would be useful to ensure that these reference surface elevations are not biased due to e.g. newly frozen leads.

Line 199: How many segments are removed vs used due to mis-coregistration? A percentage of rejected or accepted segments would be useful here.

Figure 8: This figure should have subplots labeled (a-f) on the figure, since they are referenced as such in the text. I agree with reviewer #1 that it is not apparent how phase centers are derived from these figures.

Line 393: Similar to above points, what percentage of pixels are processed (i.e. heights above 1.5m) vs not? With a scene-average height of 1.27m along the DMS DEM (line 494), I suspect that a large portion has been removed.

Line 398: I assume 18cm is the average snow depth of the whole region, including ice <1.5m? If only samples >1.5m are selected for processing (line 394) I am curious how your results would look if you were able to use snow depth on just the ice with elevation >1.5m. While I know this information may not be available, using some type of spatially-varying snow depth assumption may help to constrain possible retrieved topographies.

Figure 13: It’s fairly tough to see the DMS DEM in between grey lines in (b)-(d) and draw any conclusion about its agreement with the SAR data. I would recommend making the lines thinner or reducing the width of the zoomed sections, if possible, so that more of the DMS heights are shown. If inclined, a difference map (InSAR height – DMS height) would be useful to provide a more quantitative 2-D verification.

Figure 13 also: How are heights less than 1.5m calculated in this SAR image if not selected for processing with this model? Subplot (d) in particular appears to have regions of 0m height that I suspect are not entirely physical.

Line 456: I would suggest clarifying that h_Model in this case is the simplified model. While I understand it is in the “simplified model” section, to me the third row in Table 1 is the Theoretical model row (as it is the third method). The fact that the RMSE ranges between 0.22 and 0.27 for both models further adds to the confusion.

Line 487: This line (particularly “larger baselines respectively larger k_z values”) doesn’t quite sound correct as written. Do you perhaps mean the possessive “ baselines’ “?

Line 499: Should be “25%-error accuracy” to be consistent with previous sections

Technical Corrections

Line 59: Icebridge -> IceBridge

Line 143: iceberg -> icebergs

Figure 1 caption: rectangular -> rectangle

Line 215: ‘flat-earth removed’ should be written as ‘flat-earth-removed’

Line 254: Provide full names of TDF and TSX at first mention

Line 470: (grammar) well correct -> e.g. adequately/sufficiently/suitably correct

Line 501: comma after “For instance”