Thank you for your comments and suggestions, and especially for your patience with this response. We have included our replies within the provided text.



Anonymous Referee #1

General comments:  

• This study evaluates the performance of the Sentinel-3 SAR altimeter over the Antarctic Ice Sheet using the REMA DEM. It finds that 90% of acquisitions capture the POCA within the Level-1b range window, but performance declines in complex terrain, missing 24% of topographic variance. The findings highlight limitations in capturing backscattered energy over steep or rough surfaces and provide insights to guide improvements for future missions like CRISTAL. 

• The study is using REMA as a baseline for applying a SVD analysis to generate self-consistent surface slope and roughness datasets for the Antarctic Ice Sheet. The S3 altimeter performance is assessed by evaluating different topographic regimes by analysing the relationship between surface complexity and altimeter data quality. Furthermore, a waveform decorrelation analysis is made to assess the along-track impact of topography on waveform decorrelation to understand how varying terrain affects signal quality and backscattered energy capture. 

• The methods and results concerning slope and roughness are well-executed and insightful. 

• The research is valuable, addressing a gap in the literature. However, it’s disappointing that the authors did not utilize the latest Sentinel-3 processing (B005), which has been available for over a year and addresses some of the highlighted issues. While the conclusions might remain valid with the reprocessed dataset, the omission weakens the study, as this remains uncertain. To make the impact the manuscript deserves, I suggest redoing the study using B005; at the very least, the new processed data should be mentioned, and what impacts the new processing has on this study.

The reason that the Thematic product was not used in our original analysis was that it was not publicly available at the time that the majority of our analysis was performed. That being said, we appreciate the relevance of this new dataset, and so as part of our revisions we will re-perform this analysis with respect to this dataset, in order to address this point.

• The technical depth of the manuscript is inconsistent. For instance, the detailed reviews of retracking, REMA, and OCOG may not be necessary. In favor of the authors, they do present the topics in a clear and accessible manner, making them useful for newcomers. 

We acknowledge that not all sections had a consistent level of technical depth. We will therefore undertake a thorough review of the manuscript to ensure greater consistency. Further details are provided in the related comments below.

Specific comments: 

Principal of radar altimetry: 

• Page 2-3, Lines 55-73: While textbook examples exist, the authors provide an exceptionally clear and convincing explanation. It could be highly beneficial for newcomers, though its relevance to this study should be carefully considered.  

Thank you for your appreciation of the care we have put into writing these sections. Although we agree that the level of detail goes beyond what is commonly found in papers these days, we would prefer to keep this text because, as highlighted by all reviewers, it provides a valuable explanation for newcomers, which we found otherwise lacking in the literature.

• P3: Surface Tracking: For your information, Several places over Antarctica have been changed to open-loop acquisitions in 2021 and 2024. It would be nice to see if that has had a positive impact. 

Thanks – we are aware of these sporadic acquisitions, but believe that an analysis of Sentinel-3's non-operational open loop mode is beyond the scope of the current work, which was intentionally focused on assessing the performance in nominal closed loop tracking, which could be done at the ice sheet scale and thus provide a comprehensive assessment. That being said, we agree that – as part of future work – such an assessment would be worthwhile, e.g. within the context of CRISTAL, and we hope that our study will provide a framework for how this could be done. As part of our revisions, we will make these points clear in the text.

• P4, L48 Retrackers: You mention OCOG as part of S3 ground segment. True, but S3 products also include the UCL ice retracker, a beta-retracker or model-fit retracker (Wingham and Wallies, 2010). 

We agree that this is important to mention, and we will adjust the text accordingly.

Data: 

• A fundamental weakness is choosing not to use the B005 Thematic Land Ice product, released over a year ago and specifically designed for land ice. This product uses extended window processing optimized for rough or steeply sloping surfaces. Further information is available in the B005 Validation Report: https://sentiwiki.copernicus.eu/__attachments/1681931/S3MPC-STM_RP_0114%20-%20Reprocessing%20Campaign%20BC005%20Validation%20Report%202023%20-%201.1.pdf?inst-v=bd8109db-ca17-4318-bc73-caad47319d7e and the data is currently in review in Nature Scientific Data by J. Aublanc. 

Please see our prior response relating to the use of B005 – we acknowledge the value of this and will incorporate this into our revised analysis.

• Resampling REMA to 200 m, why? Have you considered using ICESat-2's gridded products? 

This resampling was originally done in order to reduce computational overhead (P7, L191). However, as we are intending to re-do the analysis with the B005 Thematic Land Ice product, and have since introduced significant optimisations to our code, we will consider using the REMA V2 mosaic at its native resolution of 100 m. Regarding the ICESat-2 gridded product, we selected REMA in preference, because it is formed from stereoscopic techniques, and therefore provides an inherently 2D product for computing slope and roughness. In contrast ICESat-2 requires interpolation between tracks, especially as across-track spacing diverges away from the poles, and as such is therefore less well-suited to resolving slope and roughness. For visual reference, we have included some example figures comparing REMA to the ICESat-2 ATl14 product (https://nsidc.org/data/atl14/versions/1).

In Figure 2 (attached), it is evident that the ATL14 DEM contains more data gaps.

We also refer to the ICESat-2 ATL14 ATBD (https://nsidc.org/sites/default/files/icesat2_atl14_atl15_atbd_r001_0.pdf), which states that “ATL14 and ATL15 are both limited as to the features they can resolve by (1) the spatial resolution of ICESat-2 tracks”, and that “the products should be treated with some caution at short (few-km or less) spatial scales”.

We appreciate that our reasons for picking REMA were not clearly articulated, so we will add some clarifying text to help improve this.

Methodology: 

• P6, L238: Results interpreted as 68% of the roughness variance.  Where does this number come from? 

This value represents the proportion of points in each window that fall within ±1 standard deviation of the mean of the orthogonal residuals to the fitted slope, assuming a normal distribution. However, after discussion, we have decided to instead measure roughness using the difference between the maximum and minimum orthogonal residuals within each window. This is essentially an estimate of the peak-to-trough elevation difference, which we believe is more aligned with a reader’s likely intuition.

• I am unfamiliar with the word seed waveform, but I assume it is a kind of a "first" waveform. How do you determine this seed waveform? Is it unclear if you calculate all waveforms as seed and then calculate the correlation to the 50 subsequent waveforms, or if the seed waveform is specially chosen? 

We agree that this explanation is poor and will adjust accordingly. Here, a seed waveform refers to the first waveform by which the correlation of 50 consecutive waveforms is compared against. This is computed for every single waveform, which is referred to as the “seed” waveform when it is the focus of these correlation computations.

Results: 

• P13, L3556-358: 23.7% of echoes are not captured within 60m range window. Could you elaborate on the discussion? Could this be solved with the current S3 setup?  Is it only a SWOT processing that would solve the problem? I am missing some consideration of the ability to change the on-board tracking modes for S3.  

Within the beam-limited footprint of all records analysed in the given cycle, we compute the highest REMA elevation and the lowest. We then calculate the proportion of cases where this range is larger than the 60 m spanned by the range window. This indicates that for 23.7% of records the topographic variability is too large to be successfully captured in its entirety. This is regardless of range window placement, and so is symptomatic of the range window size relative to the topography being sampled, rather than the onboard tracking. In the revised version we will check and modify the text if needed, to make sure that this point is clear.

• P14, L363: It would be nice to see how data processing baseline B005 performs. or at least discuss why it would still be an issue with the new dataset.  

Please see our prior response relating to the use of B005 – we acknowledge the value of this and will incorporate this into our revised analysis.

• P15, L370: Please elaborate on what you mean about this statement 

In order to successfully identify the leading edge of a waveform, it is important that there are a small number of bins proceeding it. Range window placement should consider this fact, allowing for a small buffer above the point-of-closest approach to the surface. We will revise the text to make this point clearer.

• P16, L401-403: The results of LPCs are fine, but again this is not what was improved by S3 processing baseline B005? 

We will readdress these conclusions after reprocessing with baseline B005.

• Fig 5/6(b): It would be nice if the blue and purple colors were more distinct, but it is impossible to differentiate between the colors on the map. 

The intention of these colour choices was to visually group classes that are above and below the range window as being equally unsuccessful cases of POCA capture. We agree that this colour choice makes the spatial figures difficult to read and so will consider changing them.

• A along-track correlation study demonstrates that slope and roughness impact the result. We also see this in how the elevations are having trouble wrt. REMA or IceSat-2 results in the marginal zone. What do we gain from this method? Is this method better? It sounds like it takes a large amount of computational power. 

We realise that the relevance of this section is not clearly conveyed. Within the revision we will therefore thoroughly review this section.

• How does S3 perform in this sense compared to other altimeter satellites?

We believe that the work involved in performing such an assessment for other satellite would be considerable, and falls outside the scope of this current work, which was purely focused on developing novel analysis for understanding the performance of S3. We do agree that similar analysis for other satellites in the future would be worthwhile, and we hope that the approach developed and presented here for S3 can serve as a framework for similar assessments of other satellite altimetry missions in the future.

Technical comments:

• P6, L182: the dataset name appears to be incorrect ("S2_2_LAND__"); it should be "S3_2_LAN__". 

Thank you for spotting this; we will correct this.

Thank you for your comments and suggestions, and especially for your patience with this response. We have included our replies within the provided text.





Community Referee #1 (Benjamin Smith)

This is a quick and non-exhaustive review of “Assessment of Sentinel-3 Altimeter Performance over Antarctica using High Resolution Digital Elevation Models” by Phillips and McMillan, which uses the REMA mosaic to investigate how well range windows selected by the SENTINEL radar altimeters capture the surface in Antarctica.  I found the manuscript to be nicely written, and thought that it gave a very good background discussion of how radar altimeters work, and that it presented its findings quite clearly.

I would like to raise one question about the scope of the study, and one about the presentation of the SVD analysis, and my only significant remaining concern relates to font sizes in the figures (hint: they’re not too large).

Question 1: Scope of the study. 

The study analyses the performance of the SENTINEL-3 altimeters over a range of Antarctic surfaces, and finds that in a lot of interesting places, the telemetered range window does not capture the POCA return from the surface and/or does not capture the full range of elevations illuminated by the radar beam pattern.   This finding suggests that the SENTINEL missions and future missions should use a larger range window, and should consider implementing open-loop surface tracking to better position the range window relative to the surface.  It would have been nice to see an explicit analysis of how these two options could be implemented- for example, the study could analyze how large the range window would need to be to consistently capture the surface, and could analyze the resolution of the on-board surface elevation model needed to consistently capture the surface. 

We agree that an analysis focussed on determining the optimal range window size is an interesting question, although it would add considerable computational cost, as it would necessitate iterating through multiple realisations of the window size. We will therefore consider whether there is a way to efficiently perform such an analysis within a reasonable compute time and, if this is found to be the case, we will include it in the revision.

Regarding the resolution of the DEM used to form the OLTC – whilst we agree that this is an interesting question with regard to future satellites that will operate nominally with open loop tracking, we emphasise that the scope of this current work is to focus on an assessment of the closed loop tracking acquisitions routinely made by Sentinel-3, which do not utilise such a DEM. Thus we believe that this analysis, whilst interesting, is beyond the scope of the current study. That being said, we do hope that this work will serve as a framework for future assessment of altimeters that will operate in open loop tracking, such as CRISTAL, and also for defining the technical requirements of future radar altimeter missions. In our revisions, we will make sure that these points are clearly made.

I was left behind a bit by the discussion of topographic capture.  My naïve assumption is that as long as the waveform captures the POCA point, the rest of the waveform structure is not generally interpreted.  If this is the case, then perhaps section 6.2 is not needed in as much detail.

As outlined in a reply to anonymous reviewer #2, our motivation here was to optimise data volume retrieval, with a view to future methodological innovations that may allow retrieval of topographic information from beyond the leading edge; for example based on numerical waveform simulation or machine learning approaches. We agree, however, that this motivation was not clear and could have been better described, and we will address this within the text.

I was also unsure of the significance of the waveform decorrelation discussion. While this is interesting in the abstract, its importance for understanding the ice sheet is not as clear.  Beyond this, I thought that section 6.4 would have benefitted from a little more discission of the mechanisms that determine waveform shape.  I would assume that surface slope across the beam would be the most important driver of waveform shape, and that the correlation would then be more or less determined by the along-track consistency of surface slope and roughness.  This seems testable using REMA.

We realise that the relevance of this section was not clearly conveyed. Within the revision we will therefore thoroughly review this section, and revise it where needed. We also agree that an additional discussion on the impact of surface characteristics on waveform shape would be informative and we will include this in our revised text.

Question 2: Presentation of the SVD. 

Upon first reading, it was not at all clear to me why the SVD of the surface would give an estimate of the surface slope.  I think section 5.1 would be much improved by a couple more equations describing the SVD approach.  I’m not sure why the SVD is preferred over a simple least-squares calculation of the surface slope based on a the elevations within a small window on the ice sheet surface, which would in general be much easier to compute than the SVD because the matrix relating the surface elevations and the slope could be computed once and applied to every window on the ice sheet in the same way.  It would also be good to define clearly the shape of the region to which the slope analysis was applied: it is not clear whether “The centre points in each region”  (line 328) means the 5x5-pixel window, or some subset thereof.

As outlined in our response to anonymous reviewer #2, our initial motivation for using SVD was that it directly provides the normal vector to the fitted plane via the left singular matrix. This allowed us to compute orthogonal residuals efficiently by taking the dot product of the centred elevation points with this normal vector. We agree, however, that – on reflection and having run some tests  – least-squares is a more efficient better approach, and so we will update our analysis to use it instead of SVD. Regarding the region used for the slope analysis – “The centre points in each region” refers to the pixels within the 5x5 window after subtracting the means along the x, y, and z axis. We agree this was worded poorly, and we will adjust it accordingly in our revisions.

Specific editorial comments:

Line 43: It is the failure of the assumptions that leads to difficulties

We agree and will adjust the text to make this clear.

Line 77: low-> short

Agreed, we will make this change.

Line 145: specify “track-to-track spacing” rather than “across-track spacing”

We will make this change.

Line 155: no hyphen between range and window

We will make this change.

Line 221: “As such, values determined for slope and roughness calculated in this way encode each other via complex, non-linear interactions.”  I don’t understand this sentence, and if I did, I think I would disagree with it.

The reasoning here is that when roughness is measured using the residuals along the z-axis to a fitted plane, the resulting values are highly dependent on the slope of that plane. In other words, slope and roughness calculated this way become interdependent in a way that does not necessarily reflect their true geophysical relationship, making it more difficult to isolate their individual effects on a given independent variable. The motivation for using orthogonal residuals is that they are far less sensitive to this issue. We agree that the original sentence was unclear, and that the use of “non-linear” in particular had no clear mathematical grounding, and so we will use alternative language and revise it for clarity.

Section 5.4: please check the tense of the first and second paragraphs.  The first paragraph should be in present tense.

We will change the first paragraph to be in the present tense.

Lines 320-325:

Please define R

Here, R referrers to the Pearson correlation coefficient. We will make this clear.

Please give an equation for the line approximating the correlation function.  What are the units of the slope?  It appears that they are (15 km)^(-1).

We will include a supporting equation and believe that the units of the slope are km^-1.

Figures:

These are nice figures, but I had to blow them up to the size of a large pizza to make out the text.  The fonts need to be much larger! 

We completely agree that the text is too small and we will adjust accordingly.

Thank you for your comments and suggestions, and especially for your patience with this response. We have included our replies within the provided text.

Anonymous Referee #2

The manuscript provides a very detailed description and history of radar altimetry, which is particularly beneficial for newcomers seeking to better understand the needs and various steps involved in processing the data. It also provides a good template for future analysis and mission instrument design. 

General Comments:

In Section 2.3, a general description of different slope correction algorithms is presented, which is excellent for the reader. However, I find the section lacks a more definitive conclusion regarding how much better or worse the different algorithms perform. I recommend including more details here, such as why certain algorithms are better and by how much (e.g., statistical comparisons). Additionally, it would be helpful to describe how these algorithms improve elevation change estimates, particularly in areas such as outlet glaciers or regions with significant topographical variation.

We agree and will add additional text to expand upon these points.

In Section 2.4, you discuss the geophysical corrections and provide ranges for the magnitudes of these corrections. It would be beneficial to add similar range information to the sections detailing retracking and slope corrections to maintain consistency and provide a more comprehensive overview.

We agree and will therefore provide additional magnitude information relating to the retracking and slope correction sections.

In Section 4, there is significant discussion about using REMA, but it lacks detailed reasoning as to why REMA is particularly important. I’ve outlined specific comments on this below. Could you expand on why REMA is advantageous? Furthermore, if you intend to resample the DEM, I recommend avoiding NN (nearest neighbor) resampling when transitioning from higher to lower resolution. A more accurate approach would be to use the average of the pixels to avoid introducing bias.

We agree and will add supporting text to emphasise the reasons for selecting REMA in this context, particularly with respect to our response to anonymous reviewer #1 regarding comparisons between REMA and ICESat-2. As outlined in this prior response, we will also consider using the REMA V2 100 m product at its native resolution, subject to computational considerations, and otherwise we agree that averaging is a better choice than NN for interpolation.

In Section 5.1, I understand the approach taken and the rationale behind it, but I would appreciate more details and statistics to support the arguments. For instance, if a more traditional approach (e.g., based on Horn or similar methods) were used, what would be the statistical differences compared to the method you propose? Additionally, what are the benefits of using SVD compared to a simple least-squares approach for generating slope and roughness parameters?

Our initial motivation for using SVD was that it directly provides the normal vector to the fitted plane via the left singular matrix. This allows us to compute orthogonal residuals efficiently by taking the dot product of the centred elevation points with this normal vector. However, after conducting some tests in response to the point raised by the reviewer, we have found that the least-squares approach is indeed faster, despite requiring an additional step to compute the normal vector via trigonometry. Given this, we will reprocess our data using the least-squares method and update the text accordingly. We also acknowledge that statistical comparisons of our new slope measurements relative to alternative slope methodologies such as Horn’s method would be beneficial and will therefore also include these comparisons within our revision.

Section 5.2 is somewhat unclear, particularly the last paragraph. Could you elaborate further on this section and include more details? As it stands, the explanation is too general to follow clearly.

We agree that this section would benefit from additional clarification and supporting text. The intention of this component of the analysis was to determine the proportion of the surface (as defined by REMA) illuminated by the beam footprint that falls above, within, and below the defined range window for each record. We then aimed to identify the vertical positioning of the range window that maximizes the proportion of the surface captured. By comparing the actual proportion of the surface captured to the proportion captured with an optimally placed range window (where the goal is maximal capture), we obtain a performance metric that quantifies how well the current placement performs relative to the optimal case, whilst recognising the inherent limitations imposed by the range window size. We will revise the text to make these points clearer and provide additional details where necessary.

The font size in your figures needs to be increased, especially for the smaller inset figures, as they are difficult to read.

We agree and will adjust accordingly.

For Section 6.1, it would greatly enhance the manuscript to include a comparison to established slope and roughness algorithms or datasets, as you are presenting this as a novel approach. Consider creating a figure for traditional slope/roughness algorithms similar to Figure 3 to highlight the differences.

We agree and will provide statistical comparisons of our new slope measurements relative to Horn’s method and evaluate our roughness metric against a widely used alternative, such as the peak-to-trough (max-min) of the residuals along the z-axis.

Specific Comments:

• L48: Clarify why the use of REMA is advantageous for evaluating design choices. Is it due to its resolution, quality, or another factor? Be more specific.

We will include additional supporting text to justify and clarify our use of REMA

• L63: “Followed by gradual decay in the received power” – clarify the cause of this decay. What does it signify?

As requested, we will include text to clarify the cause of this gradual decay in received power.

• L69: Backscatter is not the only parameter used to determine surface characteristics. Mention other commonly used parameters, such as leading edge width etc.

Agreed, we will mention the use of other parameters such as leading edge width for determining surface characteristics.

• L85: Specify which DEM is used for Jason-2 or Sentinel-3A, including the resolution of the onboard DEM.

We will specify the onboard DEMs used for Jason-2 and Sentinel-3 and their corresponding resolutions where available.

• L95: Provide additional references here; citing only (Quartly et al., 2020b) does not sufficiently encompass the breadth of prior work on retracking and scattering corrections.

Agreed, we will include additional references as requested.

• L100: Add references to Curt Davis’s work, particularly his “threshold retracker,” which significantly advanced the field and built upon the ICE-1 tracker (OCOG).

Agreed, we will reference Curt Davis’s work as requested.

• L105: Emphasize that “slope correction” is likely the largest source of uncertainty in the current processing pipeline, as corrections can vary by 1–100 m vertically and span kilometers across track.

Agreed, we will emphasise this in the text.

• L159: Elaborate on the decision to favor closed-loop tracking. What motivated this choice?

We will elaborate on this, as requested.

• L271: Are you evaluating the slope correction provided in the L2 product and comparing it with your own? If so, what are the differences, and why are they significant? Is the L2-provided correction insufficient for determining alignment within the 3dB beamwidth?

To clarify – the purpose of this work was not to develop a new slope correction method but rather to assess the current approach. Specifically, we aimed to determine the extent to which the provided POCA location falls within the beam-limited footprint and range window, and thus whether the assumptions inherent to the L2 processing chain are self-consistent. In other words, we sought to evaluate whether the elevation measurement extracted from the waveform can reasonably be attributed to the provided POCA location.

The alternative Roemer-derived approach was intended as a simple, point-based baseline for comparison, where we take the point in the REMA DEM closest to the satellite. We will clarify this distinction within the revised text.

• L292: Consider using interpolation for the comparison, as it accounts for gradients in the data. Although 200 m is smaller than the footprint, significant variations may still occur within a 1600x300 m altimeter footprint. Refer to Roemer et al. (2007), who suggest using a resolution of 10 m for improved location accuracy.

Whilst we agree that there are potential benefits to fine-scale interpolation when using this approach to estimate surface height with high precision (e.g. for resolving cm-scale elevation trends etc), we emphasise that this is not the purpose of our analysis here. Rather, here we are using Roemer as the basis for a coarse-scale, discrete classification of the POCA location relative to the position of the range window in 3d space. As such, we do not believe that interpolation to higher resolution would significantly alter this classification, whilst it would introduce a substantial computational overhead. However, as mentioned in a prior response, we are considering using the 100 m resolution of REMA, which will provide improved spatial accuracy.

• L308: Clarify what “removing any bins that lie beyond the bounds of the original waveform sample” means.

We agree that this wording is unclear and will revise accordingly. This refers to the process of removing the parts of the two waveforms that do not intersect when they are aligned according to their COG.

• L327: Do you mean the range from -1 to 0?

Thanks for spotting this; yes we do and will change this.

• L364: Which part of the waveform do you expect to record? If it is only a portion (e.g., the trailing edge), explain the value of recording just that part.

This varies, but our motivation here is that more data is better. Although we are currently largely constrained to leading edge-based approaches in non-interferometric cases, there may be a point in the future where more information can be obtained from other parts of the waveform. As we are interested in the evolution of the ice sheet, it is important that as much information is obtained as feasible at any one time. We agree that this could do with some supporting text and will include it.

• L398: Why was the modal value used? Provide reasoning for this choice.

The modal value was used here as the data is discrete. We will include text to make this clearer.

• L499: Specify the algorithm used in the S3 product for slope correction.

We will include this in the revision.