Review of “Insights into Greenland Ice Sheet Surface roughness from Ku-/Ka-band Radar Altimetry Surface Echo Strengths” submitted to The Cryosphere in 2024 by Kirk M. Scanlan et al.

This study focuses on the quantification of surface topographic roughness of the Greenland ice sheet using CryoSat-2 and SARAL satellite radar measurements. The Radar Statistical Reconnaissance (RSR) method, developed in a recent publication by the same authors, is used for this purpose. The derived roughness properties are compared against airborne radar and laser scanner data from two campaigns, and with ICESat-2 ATL06 (20m intervals) data. The main question is whether the surface roughness can be accurately estimated using spaceborne radar, the main motivation being that the surface roughness is an important yet poorly constrained parameter for SMB models. This makes this study relevant for The Cryosphere. This study is also original, as novel insights are presented regarding the estimation of surface roughness using satellite radar datasets, such as the empirical correction for the RSR method (Eq. 4) that gives a better match with ICESat-2 data, and the unique spatio-temporal analysis of surface roughness (Fig. 10), which form a basis of future work using such data. The potential significance of this work is also high, since improved estimation of ice sheet roughness properties allow not only for potential improved SMB modelling but also improved radar postprocessing. The employed datasets and methods are sound, as far as I can assess as a non-radar expert.

Overall, the paper is well written. It makes use of adequate referencing from the remote sensing and SMB modelling perspectives, although it could benefit from more referencing in the field of the snow bedform quantification. Some examples are given below.  The introduction allows for the non-remote sensing expert to understand the overall topic. However, the methods and results sections are long and, in some places in the methods, technical terms are introduced which do not appear to be very relevant for the results. On the other hand, there is no mention on how the laser scanner and ICESat-2 data were processed and filtered, even though these data are used as reference. The results are very interesting, yet I have some concerns which are listed below. The discussion is a relevant and a welcome part as it presents the main limitation of the novel results for improved SMB modelling.  However, some more work is required to make this radar roughness estimation useful for SMB modeling, which I recommend should be done or at least discussed more quantitively before final publication. Is there absolutely no way to use spaceborne radar for improved roughness estimation relevant for SMB models ? At present a constant aerodynamic roughness value is still chosen over the entire ice sheet in climate models. 

To summarise, I would recommend publication after the main comments are clarified, and once the derived roughness can be (indirectly) used for SMB modelling.

Major comments

This study uses an airborne laser scanner (ALS) and ICESat-2 ATL06 data at 20m resolution as independent reference data. First of all, it is not clear what the accuracy of the ALS data is, and how the 1m effective ALS resolution (L114) relates to the resolution required to detect the relevant surface features in the areas of interest (sastrugi, snow dunes, etc…). Even with ~1m resolution and ~10cm vertical accuracy, the ALS is limited in capturing all the scales relevant for SMB modelling, which is the main aim of this work (according to the introduction). Therefore, I would invite the authors to also critically assess the ALS data in relation to the physical processes of interest. 

Similarly, at 20m resolution and >10cm vertical accuracy, the ICESat-2 ATL06 will evidently be even more limited limited in quantifying roughness features such as sastrugi and all the way down to the radar wavelength scale. Hence, I am skeptical about the interpretation of the empirical correction to the RSR method in Eq. 4. I would argue that this is an empirical or “data-based” correction that generates a better match of CryoSat-2 and SARAL data with ICESat-2 data, but it is not formally proved in this study that this correction allows for a more accurate roughness quantification. For this, roughness data at all the relevant scales (1cm – 100m) should be used, as obtained though terrestrial LiDAR, UAV photogrammetry , eddy covariance data or even manual probing.

Furthermore, in Section 4 (L252-253), a main result of this work is given based on the match that is found between the RSR derived roughness from the airborne radars, and the RMS roughness from ALS “at larger baselines (e.g. between 200 and 700 m)” (L249). Perhaps this is a lack of understanding of the RSR algorithm on my part, but I do not understand how the radar RSR roughness and the laser RMS roughness are related to each other.  These two methods seem fundamentally very different and sensitive to different scales of surface roughness: ~radar wavelength scale (cm) for radar RSR, and >100 m for ALS and ICESat-2 RMS, depending on the (arbitrary?) choice of the extrapolation interval. Hence the found match between RSR and RMS “between 200 and 700 m” in Fig 2 could as well be a coincidence, or the result of the postprocessing, such as how the data was detrended (L154). At least it does not seem to be physically based.  Perhaps the authors could explain this better and perform a sensitivity test by varying the extrapolation intervals (e.g. 50-500m, 200m-600m, 300-1000m, etc…) and detrending methods (linear, polynomial, high-pass filtering,...)

Finally, as a non-radar expert yet interested in improved SMB modelling, I am hoping that the estimated RSR roughness (with values between 0.01 mm and 1 mm on the ice sheet) could be translated to a more useful metric (such as standard deviation of heights, average obstacle height, etc... ), which is then directly compared and shown as a map together with the same metric as estimated from ICESat-2 in Figure 10. It becomes clear at the end in section 6.1 that this new map can’t unfortunately be used directly for aerodynamic roughness calculations, and I agree, yet I would invite the authors to make this clearer from the start and in the abstract/conclusion, and propose possible alternatives to overcome this limitation. Could this not be expected before the analysis, given the large footprint of the satellite radars?

Despite the limitations, perhaps an assumption could be made that the RMS between a certain scale range  (e.g. 1 cm – 100m) is relevant for surface drag calculations, which can be indirectly estimated from the RSR or RMS algorithms. A typical roughness height from CryoSat-2, SARAL and ICESat-2 for these scales could be plotted as the final result, thereby paving the way for improved SMB modelling.

Other comments

• Title: Consider removing “Insights into” .
• L16: (mentioned in Major comments) As far as I understand, it is an assumption by the authors and not a proved result that the revised empirical correction gives a better match to ICESat-2 because the “surface roughness across the GrIS is primarily scale-dependent”. The better match is obtained by construction.
• L20: Please rephrase “wavelength-baseline linear projection of the scale-dependent surface roughness”.
• L40: Rephrase into “Numerical estimates of GrIS SMB are based on coupled climate/subsurface models”.
• L85: What are conventional surface roughness metrics ?
• Section 2.1: please include some information about the ALS data processing and accuracy (also mentioned in major comments)
• Figure 1: Is this actual data from the ALS ? If so, please include the location and time of this measurements. If not, consider using real data with a quantitative x-axis which would help the reader to better understand the “raw” data.
• L154: Wouldn’t it be more consistent to filter out the same larger wavelengths using the same high-pass filter for all ALS and ICESat-2 data ? The background plane depends on the length of the dataset, which makes it hard to compare short ALS data (1 km) with longer ICESat-2 data (10km), as done later in Figure 4.
• L182: How was this 1.5 degree threshold chosen? What are the potential effects of off-nadir instrument point on the results?
• L189: I would strongly recommend that the authors better explain how the coherent and incoherent powers are estimated, as these are the backbone of the methods. Perhaps some formulas or a schematic (possibly in the appendix) would be beneficial.
• L194-208. These sentences could be shortened while still conveying the same information and being clearer at the same time.
• L200: what data selection / what metrics have been applied to ensure quality of the ICESat-2 data ?
• L209-211: Is it possible that some words are missing from this sentence ?
• L214: What is effectively the highest sigma_h that can be estimated using CryoSat-2 using this method ? How does this compare to the RMS of the actual expected topography on the Greenland ice sheet ? If this method only works for sigma_h < ~6 mm (for CryoSat-2), that leaves out most of the ice sheet surface with ice hummocks, sastrugi, dunes, etc…
• L215: please define the “surface correlation length”.
• L230: How are the densities recovered using RSR ? Consider adding a bit more background information in Section 3.2.
• Figure 2: In panels c and d, the triangles can’t be discerned. In panel d, the resolution of the T21 ALS seems much higher than for the other locations.
• L239 On what is the assumption based that the RSR radar roughness corresponds to the RMS at the wavelength scale? please also specify “radar wavelength” to avoid confusion about which wavelength was used.  How were the shaded areas 200-700 m chosen if not arbitrarily?
• L244: It took me quite some time to understand Figure 2c/d, so perhaps “immediately clear” is not the most accurate phrasing
• L252-253: mentioned in major comments
• Figure 3: Please adjust the color scale of Fig3d.
• Figure 4: The ALS and ICESat-2 ATL06 data are very different and show different behavior in the 100m-1km range, which is unexpected. Is this due to the different detrending of the data ?
• L380: This is very interesting, but perhaps adding the elevation lines in Figure 9 would help to better place this specific area with anomalous RSR retrievals in a broader context. What are the ICESat-2 RMS values in this region ? Can this also be related to noise in the ICESat-2 data ?
• Figure 10: why is the average roughness only shown for 2 transects ? If the data is available, consider plotting the data for the entire ice sheet. Also, why is only SARAL roughness shown and not also CryoSat-2 and ICESat-2 ?
• L420: Consider renaming section 6.1
• L429: This seems to be the first moment where the actual topography of the ice sheet is discussed. Perhaps the typical surface features could be introduced in an earlier stage for better overall understanding of what the satellite radars are supposed to detect (e.g. Between sections 2 and 3, or in the introduction). Some inspiration for this purpose :
  • Filhol, S., & Sturm, M. (2015). Snow bedforms: A review, new data, and a formation mode. Journal of Geophysical Research: Earth Surface, 1645–1669. https://doi.org/10.1002/2015JF003529
  • Picard, G., Arnaud, L., Caneill, R., Lefebvre, E., & Lamare, M. (2019). Observation of the process of snow accumulation on the Antarctic Plateau by time lapse laser scanning. Cryosphere, 13(7), 1983–1999. https://doi.org/10.5194/tc-13-1983-2019
  • Zuhr, A. M., Münch, T., Steen-Larsen, H. C., Hörhold, M., & Laepple, T. (2021). Local-scale deposition of surface snow on the Greenland ice sheet. The Cryosphere, 15(10), 4873–4900. https://doi.org/10.5194/tc-15-4873-2021
• L465: Please include in 3.2 how the density is computed, which helps the reader to understand this adjustment term.

This manuscript is a methodical work that builds upon Scanlan et al. [2023] to pursue the layout of the foundations for using RSR-derived surface parameters at the GrIS. Eventually, it will become an entirely new type of measurement to assess the surface properties of the GrIS and the AIS. It is also the first study (all planetary bodies combined) that carefully confront RSR to altimetry roughness to better understand the baseline at which RSR roughness is derived. The manuscript is well written with a clear language and layout that both help its understanding by non-specialists in this intricated topic. The manuscript should definitely be considered for publication after the points below are addressed. The main improvements could come from extended discussions to better understand the possible causes and implications of some of the observations made. Of importance, roughness derived from laser altimetry measurements should be presented from a more critical standpoint to better understand the comparison with the RSR measurements.

Critic of Laser Altimetry Measurements

The authors adopt a critical stance toward the RSR-derived roughness, which is appropriate given the relative novelty of this type of measurement, and it is in line with the goal of the manuscript to strengthen the understanding of the RSR-derived parameters for a confident use in polar science. To that aim, airborne and space-born laser altimetry are presented as reference measurements that have to be matched by the RSR for it to be validated. Laser altimetry is not necessarily deprived of possible bias, however, and this should be further discussed.

Laser- and RSR-derived roughness proceed from measurements implying different physical interactions with the surface. Laser altimetry is a discrete measurement of evenly-spaced signal delay translated into surface heights; while RSR-derived roughness fundamentally proceeds from the coherent summation of all the electric fields scattered back be each finite elements forming the surface within the radar footprint. Here are some thoughts that the authors could partly use if desired for further discussion in comparing the two measurements and explain their possible mismatch:

• What is the footprint size of the laser altimeters compared to the baseline measured? If the laser footprint is greater than the baseline, would that create a bias in the roughness derivation such as the observed on Fig.2?
• I suppose the laser altimetry heights are arranged along-track (i.e., a 1-D spatial direction) making any derived roughness highly sensitive to surface anisotropy. Conversely, I expect the RSR to be less sensitive to anisotropy as it "senses" the surface over a 2-D spatial footprint.

Other Comments

l.129. I understand the pulses are sumed along-track. Could you comment on how this could affect the Pc/Pn ratio and the related roughness derivation? Could that affect the mismatch between the empirical and analytical RSR roughness?

l.185. Could you recall to the reader why the echo is corrected from the nadir surface slope? For planetary radar sounders, this is usualy not done because the radiation pattern is not directive wrt. to the surface slope. If the transmitted signal is directive, the slope correction might work up to a certain angle depending of the beam shape (unless you also correct for the beam gain).

l.207. Maybe recall that this condition on the correlation coefficient is arbitrary, bit it enables to discard some of those terrains with more than one roughness regime in order to comply with the assumption behind the HK statistics.

Fig.2.c-d and the related discussion. I'm intrigued about this scale-invariant roughness for the laser. Would it be possible for it to be a bias due to the technique? This mode happend for very low baselines (< 10m). How does this compare with the laser footprint?

l.251-53. Could you discuss this observation? I wonder if there is a physical sense that could explain that this 200-700m baseline is better for radar roughness downscaling. Is this baseline range related to the radar footprint somehow? This is the tricky part for the radar. Any individual scattering is usually associated to a wavelength-scale baseline (although this is a just common theoretical assumption), but the coherent wave front recorded at the antenna is the summation of all those scattereres from within a much wider footprint. In the end, the scale of the footprint migth also have a role in the derived roughness.

l.310. Throughout the paper, the RMS deviation (aka. Allan deviation) and RMS heigth appears to be used interchangeably. I understand the authors do know they are different, but it is not clearly highligthed in the text and the reader could be misled, especially when those two parameters are compared on the same 1:1 plot (Fig.6b). A brief discussion on the difference between RMS deviation and RMS heigth should be added to understand if one should expect any bias in that figure or not.

Eq.4. Although the methodology to obtain such relationship could be used elsewhere, its coefficients migth not. It is then necessary to discuss the perceived validity domain of this equation to avoid the community to use it with any radar system and in any environment.

Fig.8. It sounds too me there is also another outlier group of points between 0.01. and 0.1m, just below the bottom dotted line. Does this group of points have a spatial cohesivness?

l.380-84. The authors suggestion is completly valid. I would like to propose additional explanations that could change the Pc/Pn ratio used to derive the radar roughness. The authors are free to consider them or not:

• A differential volume scattering between two terrains will also affect the Pc/Pn ratio. Volume scattering will add incoherent energy.
• If there is a strong roughness anysotropy, the along-track measurements of laser altimetry migth differ from the radar sensitive to more spatially distributed scatterers.
• Thin layering (firn crust?) could change the coherent energy.
• When the surface is too rough, the surface mean slopes will start to scatter most of the energy off-nadir. The Pn measured at the antenna is then an underestimate of the integrated incoherent energy arising from that surface

l.391. The RSR is not especially lower quality, it is indicative of some sort of additional surface properties that is not caught by the laser (they are hard to disentangle, though) as mentioned in l.457-58.

l.481. larger "than".