General comments

The paper presents a new methodology (AMPLI) that uses the REMA DSM to simulate Sentinel-3 waveforms to improve altimeter retracking over the Antarctic Ice sheet. Results are compared against existing ESA Level-2 products, and bias calculations are performed against ICESat-2 to evaluate the performance of AMPLI over the Antarctic Ice Sheet.

The manuscript is well written, well-structured and clear, with the key references cited throughout. The methodology is well described, and the quality of the supplement is high and adds detail where needed. The results section supports the interpretations and conclusions in the manuscript. The figures are of high quality and support the manuscript text. I particularly liked the areas of improvement section, which tries to ascertain the impact of snow volume scattering.

Specific comments

I think when referencing Brown, 1977, you should add a few sentences talking a bit more about Brown’s 5 assumptions in the context of your simulations, as he mentions that some of the assumptions may be violated over a land surface. Specifically, the distinction that your surface heights are spatially correlated; whereas, brown assumes a non-correlated (random) surface (i.e The scattering surface may be considered to comprise a sufficiently large number of random independent scattering elements).

Technical corrections

The figures are of high quality and compliment the manuscript, the only (minor) comment that I would have is to increase the font size in the figures to improve legibility. Also in Figure 1, the cyan lines are difficult to see, perhaps try another color i.e magenta.

Review of A facet based numerical modelt o retrieve ice sheet topography from Sentinel-3 altimetry

The paper presents a new method to determine the point of closest approach (POCA) for SAR altimetry by using a facet-based numerical model. The approach is called AMPLI and makes use of the Antarctic reference elevation model (REMA) in the simulation of the 20 Hz SAR waveforms. In the simulation step a cross track backscatter distribution (CTBD) map is generated which is used in a second step to determine the POCA.

The results are evaluated over the Antarctic ice sheet against ESA Level-2 products, by performing a cross point error analysis with ICESat-2 elevation measurements, which are taken as reference.  

Secondly, the rates of change in surface elevation for the period (2019 to 2022) are calculated by comparing two gridded POCA-corrected elevation maps derived from three months of processed data for each year. SEC is evaluated against SEC derived from ICESat-2 and ESA Level2 corrected POCA, respectively.

The results of the new method are showing a great increase in the quality compared to the ESA Level_2 product for both, POCA correction and derived SEC.

The manuscript is well written, well-structured and clear, with most of the references cited. The quality of scientific content is high. The analysis applied are of high standard and well selected to show the improved performance of the new approach. Methods and supplements are described in detail in order to follow the developed method. The section on results supports the conclusions drawn and interpretation.

 The figures are of high quality and support the text.

In my opinion the manuscript is worth to publish and fits well in the scope of The Cryosphere.

I do have minor correction/suggestions, which I would like to see included in the final accepted paper:

My main point is the following:

Although your approach shows great progress, I think in your comparison or evaluation one data set is missing. This is a relocation based on adapted Roemer/LEPTA for SAR. You can easily implement this. You can search the POCA in the SAR footprint of the REMA DEM centered around the 20 Hz records and derive the across track lock angle as given in eq. 5. I would like to see the results of adapted Roemer/LEPTA in comparison to AMPLI and ESA L2 here as well. Because AMPLI needs lots of computing resources, which can be argued, if gained improvement is significant – as the comparison to ESA Level 2 shows. However, if the adapted Roemer / LEPTA for SAR shows similar results as AMPLI, it would be easier to implement or propose it as a new standard POCA correction for SAR, as the time consuming simulation step is no longer necessary. Therefore, I think that this comparison is needed to be included in the manuscript (including comparison to ICESat2 cross overs as well as SEC).  

Figures:

• labelling of all figures (axis and inserts) is too small. Please enlarge all.
• Figure 3,5: I hardly can’t read the red and green on top of the dark blue. It’s too small and of low contrast.
• Figure 4: contrast in not sufficient. Please adapt the selected range or consider to show the normalized backscatter in dB.

Introduction:

• A facet based model has been introduced before, but was so far only applied to LRM waveforms. Please add the reference: https://doi.org/10.5194/tc-18-3933-2024

Section 2 Modelling:

• Is there a need to consider beam steering in your approach, as this is the case for delay doppler processing. Usually when you form the DDMs at consecutive 20 Hz records, the individual doppler beams from different looks, which are collected in a stack before range migration, usually do not perfectly overlap. If no beam steering is applied the stacked waveform will be slightly blurred. Maybe it’s not needed as you use the simuated waveform in a correlation and later only use the CTBD for the POCA estimate, but at least you should mention it here or in the supplements.
• What is the consequence to only use 45 instead of 180 looks? Can you exemplarily compare waveforms generated using 45 and 180 looks?
• Please, give a number of the processing cost. How long does it take to simulate 10s of real data on a CPU. How long did it take you to process the full 3 months of data? This is important, if your new correction should become a new standard, then also processing costs need to be considered.
• Include processing costs, for the suggested adapted Roemer/LEPTA for SAR.

Section 3 Results:

• Can you please put the outlier detection from supplements S3 to results. I think it is important to see that AMPLI has also the potential to flag bad waveforms.
• For a fair comparison against ICESat-2, I think you need to use exactly the same amount of data for both methods. Therefore, please consider only values were both ESA level2 and AMPLI are identified as valid.
• Once again, please include a comparison to adapted Roemer/LEPTA for SAR.

Section 5.1

• Please include in your discussion as well reference https://doi.org/10.5194/tc-18-3933-2024 as this paper addresses the penetration affect for Ku-Band and its worth to note that you observe with KU-SAR a penetration effect, which is smaller than for LRM but still present.

Section 5.2

• Line 517: I disagree with the statement, that the relocation method (Roemer, LEPTA) is affected by temporal elevation changes more than AMPLI. In both cases this will only be the case if the topography is changing within the footprint, as one takes the spatial closest position (x,y) coordinates of the DEM but use z from the radar range measurement itself.
• I think it is also worth to discuss if and how the simulation process could be speed up – how important is a 10m facet resolution? Will 25m or 50m will result in similar simulated waveforms and CTBD’s. If yes this could significantly speed up the processing. Maybe put some numbers in. How long does it take to  simulate 10s of real data  for 10m, 20m, 50m resolution?

Review of Aublanc et al: A facet based numerical model to retrieve ice sheet topography from Sentinel-3 altimetry

This paper concerns a new method of retrieving ice sheet elevation by estimating the point of radar first return with a combination of modelling altimeter waveform and a priori information from the Reference Elevation Model of Antarctica (REMA). This is then applied to the entire Antarctic ice sheet and an improved performance was obtained in comparison to existing Sentinel-3 products, particularly in topographically challenging areas. The improvements demonstrated in Figure 8a are particularly impressive, and this new method offers a promising development that can enhance understanding of the Antarctic Ice Sheet behaviour in coastal areas, where changes are most prominent. The paper is generally well written and methodology explained.

General comments:

1. What is the impact of the REMA accuracy on the AMPLI accuracy? If a <+/- 1m random noise is added to REMA, how would Figure 7 differ (if at all) (1m error from https://tc.copernicus.org/articles/15/4421/2021/)
2. How are data gaps in REMA handled? It’s probably worth highlighting the issues with REMA (e.g. it’s static) to emphasize the benefits of AMPLI.
3. It appears from Table S1 that the surface backscattering coefficient in equation 1 is constant. This was also covered in the discussion as a possible source of error. How was this determined and what is the impact on surface elevation retrieval for a realistic range of values?
4. Equation 5 – I found this confusing – should delta H and delta R be written as vectors rather than scalars for dot/cross products? Although simple, a geometry image may help. Are x_r, y_r and z_r derived from REMA?
5. Section 4.1. Please could you clarify why it is more computationally efficient to calculate the elevation DEM residuals against REMA rather than differencing the elevations derived in the two time periods? Does this magnify or reduce the effect of REMA uncertainties? Although presumably possible to use a small test area to process the full time-series of S3, including this would likely complicate this paper unnecessarily – perhaps you could comment in response whether you plan to do this in future work.
6. Figure 7. Please could you comment on why the Antarctic Peninsula thinning shown in IceSat is not captured by S3. Excluding central Antarctica centre is justified for statistical calculations, but should be included in this figure.

Specific comments:

• Figure 1a. It’s difficult to see the ‘nadir’ because it’s green on cyan on green. Please could you change this font colour. Also state yellow line is F_i=0).
• Figure 2. Include Point of First Radar Return on this (presumably instead of POCA)
• Figure 3 Please increase font size
• Line 215. Define u_begin and u_end. State here what % measurements were ambiguous and therefore discarded (or refer to section S3).
• Line 310-311. Separate S3 and IceSat 3 numbers – it is unclear whether there are 1,787 or 1,787 million S3 observations. Line 272 suggests 27 million.
• Line 321. ‘As the population…’ is an incomplete sentence.
• Line 460. Please could you comment about the effects of surface roughness e.g. sastrugi for both radar and laser observations.
• Figure title for Figure S6c should be (b)-(a) not (b)-(c)