The manuscript "Estimating differential penetration of green (532 nm) laser light over sea ice with NASA’s Airborne Topographic Mapper: observations and models" examines possible reasons for the apparent negative elevation bias of thin ice (and possibly other materials that exhibit sub-surface scattering) in LIDAR measurements at 532 nm and proposes a correction-mechanism based on scattering simulations. The most important consequence of biased elevation measurements for the case of ice floes is that centimeter-scale uncertainties in freeboard result in decimeter-scale uncertainties in sea ice thickness with respective implications for calculations of total ice volumes. The results from air-borne measurements presented in this manuscript might be suitable to correct to space-borne LIDAR altimetry data, which is relevant for current research earth science, particularly in relation to global warming.

In general, the work is concise and well-written. However, a reader not familiar with the field (e.g., I am a laser physicist, not particularly familiar with the intricacies of LIDAR altimetry) might benefit from additional details and justifications that are potentially obvious to someone in the field. Hopefully, some of these points become clearer with the questions below.

Review criteria (according to instructions):

Does the paper address relevant scientific questions within the scope of TC?

1. Does the paper present novel concepts, ideas, tools, or data?

   -Yes, it proposes a scatter correction to elevation measurements relevant to earth science.

2. Are substantial conclusions reached?

   - Yes, the proposed corrections (scattering length >> elevation bias) seem to accurately capture the observed effects.

3. Are the scientific methods and assumptions valid and clearly outlined?

   - Partly.Appropriate references are made throughout the text, however, I believe that the manuscript would benefit from a direct discussion of the instrumentation, post-processing and analysis, as the observed effects of sub-surface scattering are at the limit of the experimental precision (see below for additional comments/suggestions).

4. Are the results sufficient to support the interpretations and conclusions?

   - As for point 3, the manuscript would benefit from additional details.

5. Is the description of experiments and calculations sufficiently complete and precise to allow their reproduction by fellow scientists (traceability of results)?

   - Including references (also to an upcoming work that will provide details of the sub-surface scattering calculations relevant to the results in this manuscript) the work seems complete and precise. See, however, points 3 and 4.

6. Do the authors give proper credit to related work and clearly indicate their own new/original contribution?

   - Yes.

7. Does the title clearly reflect the contents of the paper?

   - Yes.

8. Does the abstract provide a concise and complete summary?

   - Yes, but it is a bit long and missing a broader “outlook” or a quick overview of the implications of the work.

9. Is the overall presentation well structured and clear?

   - Yes.

10. Is the language fluent and precise?

    - Yes.

11. Are mathematical formulae, symbols, abbreviations, and units correctly defined and used?

    - Yes.

12. Should any parts of the paper (text, formulae, figures, tables) be clarified, reduced, combined, or eliminated?

    - Yes, clarified (see below).

13. Are the number and quality of references appropriate?

    - Yes.

14. Is the amount and quality of supplementary material appropriate?

    - Yes.

General questions:

Have laser wavelengths between 532 nm and 1064 nm been considered, such that return signals are stronger than at 1064 nm, while sub-surface scattering is reduced compared to 532 nm? Or are there currently no viable alternatives to what I assume are Q-switched Nd:YAG lasers?

Since the manuscript deals with signal differences that are close to the precision limit, it might be worth discussing the technical implementation, as well as the post-processing (particularly the algorithms used to determine the slant range and elevation) explicitly, instead of referring to previously published work. This would make the paper more comprehensible and give the reader a chance to better understand the problem at hand, without having to search through additional literature.

Naively, I would expect the rising edge of the waveform to be most sensitive to timing changes (largest change in signal amplitude upon temporal shift). In addition, would an algorithm using the earliest return photons, i.e. those scattering directly from the surface, not be less dependent of waveform broadening effects? As mentioned above, an explicit discussion of signal post-processing, specifically why the slant ranges are determined via the centroid tracking algorithm will be beneficial to the manuscript, as it is immediately relevant to the problem you are trying to address.

Regarding the previous: If I understand correctly (DOI: 10.1109/IGARSS.2011.6050002) using the rising edge for slant range determination is not invariant with signal integration / photon accumulation. However, for single passes over a water lead (the scenarios described in this manuscript) would it be feasible to use a constant integration length/time for all surface types involved? Would this allow using a threshold tracking algorithm and potentially provide bias free elevation measurements in the present case?

Again regarding the previous: According to Yi et al. 2015, DOI: 10.1109/TGRS.2014.2339737 there is a 3 cm precision improvement when using Gaussian or centroid methods compared to thresholding. However, wouldn't the reduced precision be acceptable in light of 10s of centimeter bias over various ice types?

It might be worth plotting return times on x-axis to allow for visual identification of centroid shift to longer return times (and resulting slant ranges). In addition, I would be interested in a visual comparison of the centroid shift with the shift in a threshold value, e.g. at 50% rise of the leading edge of the waveform.

Specific questions:

l. 250ff – Is the ice-type classification simply based on visual analysis of the natural-color images and if so, which parameters and features (brightness, visual layer overlap, … ) are used? Have these features in the past been identified and characterized by ground-truth measurements?

l. 265 – By “[…] classify laser footprints based on their visual appearance […]” do you mean based on their location with respect to the natural-color image? It is not clear, if the classification at this points is solely based on comparison with the optical image, or if it already involves analysis of the LIDAR waveforms.

Fig. 2 – Adding a panel showing the corrected LIDAR elevation measurements (result of this work) would be good.

Fig. 2 – Can you explain why over the water lead many data points are missing in the center of the scanned track?

Fig. 2 d): Please indicate the meaning of the two white arrows in the image or in the caption.

Figs. 2 and 3 – The shape of the symbols are hardly discernible.

l. 265 – Laser footprint(s) sounds like a term for the spatial dimension and distribution of the laser beam on the surface. Maybe in this context LIDAR data points would be a preferred terminology?

Fig. 4 – Please consider adding standard deviations for the averaged waveforms.

Fig. 9 – You show slant range differences of 0.28 m, however, the elevation bias for single layer thin ice is only 0.1 m. Is there a minimum distance that can be resolved in terms of surface and bottom return pulses, before the return pulses coalesce?

Related to the previous: Could you distinguish broadening due to volume scattering from the scenario in which one pulse is reflected from the water surface and a second from the ice, if the ice were submerged by only a few centimeters?

l. 334f – Would broadening of the return waveform over water, possibly due to sub-surface scattering induced by turbidity or the presence of submerged particles, thwart the efforts to find a universal range bias correction, as the reference signal for zero elevation would change?

l. 330 – I believe the reference should be to Fig. 4 a) and not to Fig. 4 b).

l. 331 – “The shift in centroid […] is negligible.” If the shift in panel a) for water is negligible, then the shift in panel b) for single-layer ice (0.58 and 0.8 versus 0.66 and 0.83) also seems negligible.

l. 333f – “… most of the laser light is reflected away from the receiver …” I don't think this statement is correct, because at the mentioned incidence angles less than 10% of the light will be reflected (specular) by the surface. Most will be refracted and enter the water (and be absorbed in the absence of scattering). Either way, the return signal strength will be very low.

l. 339 – The main text does not discuss the data presented in Fig. 4 b).

l. 368f – I believe the figure reference should again be to Fig. 4 a), since the sentence discussion the open water case.

4.2.3 – You state that roughness and slope broaden the waveform symmetrically, while sub-surface scattering leads to asymmetric waveform broadening. Yet, the broadening for single-layer ice in Fig. 4 b) seems rather symmetric than asymmetric, when compared to the range calibration waveform. Can you comment on this?

l. 440ff – Could you confirm you hypothesis that part of the ice is flooded by calculating the NDWI_ice for the image in Fig. 7? Since even the shallow edges of melt ponds in Fig. 8 b) show a clear NDWI_ice signal, wouldn't this be applicable to the flooding case as well? I am assuming the flooding is only by a few centimeters.

Fig. 10 – Consider adding a plot with corrected LIDAR elevations. Are you able to verify the corrected elevations via ground-truth measurements or other means?

Fig. 11 – Maybe you could include the waveform centroid in addition to the calculated bias. Am I assuming correctly that for the thin ice case, the centroid lies between 0 and the height bias value? In that case – since the centroid is a measure for elevation – showing the centroid values would highlight the main message of the manuscript.

Reference MacGregor et al. 2021a has duplicate 2021b.

Reference Kurtz et al. 2013a and 2013b are duplicates.

The manuscript "Estimating differential penetration of green (532 nm) laser light over sea ice with NASA’s Airborne Topographic Mapper: observations and models" by Studinger et.al.

identifies and quantifies differential penetration of green laser light (532 nm wave length) into snow and ice.

The authors make use of high-resolution imagery with coincident, co-located airborne lidar data over sea ice.  They quantify penetration by using relative differences of elevation estimates from penetration free open leads and the adjacent sea ice returns.  

Findings indicate that elevation of newly formed thin and finger rafted thin ice

can be up to several tens of cm below the water surface of surrounding leads. This coincides with broadening of the laser pulse caused by subsurface volume scattering.

Their interpretation is supported by a scattering model of light in snow and ice. The model was used to match observed widened pulse shapes using the scattering length as a fit parameter. Largest scattering lengths are found for thin ice, introducing an elevation offset towards negative elevations as found by the observations.

Finally, the authors find a similar correlation of pulse width and negative freeboard in lower level ICESat2 data suggesting that biased elevations caused by differential penetration are also present in those data products.

Depending on the frequency of thin ice, the results could have implications for ICESat2's estimates of sea ice thickness on a larger scale.

In general, the manuscript tackles an important question of possible penetration of green laser into snow and ice and fits well into the scope of The Cryopshere. Applied methods are well described and adequate and results are clearly shown and discussed. The manuscript is sound well written and concise. Figures are of high quality with room for improvement.

As the topic is of high relevance, I miss the attempt of the authors to offer a correction which in my view can be easily provided and discussed within the scope of the paper.

Review criteria (according to instructions):

Does the paper address relevant scientific questions within the scope of TC?

• Does the paper present novel concepts, ideas, tools, or data?

-Yes, it clearly shows that penetration of green laser light into thin sea ice is taking place, leading to tens of centimeters range error, which is important for sea ice thickness estimates in general.

• Are substantial conclusions reached?

- Yes, the elevation bias can be explained by a pulse widening which is strongly correlated to  the scattering length of laser light in snow/ice. Furthermore, negative freeboard estimates of ICESat2 are also correlated to widened laser pulse width.

• Are the scientific methods and assumptions valid and clearly outlined?

- Partly. The applied methods are valid and support the findings. But I miss a bit more details of the scattering model or explanations of the process why the scattering length is very long especially in thin sea ice and not in dry snow. Is this related to grain size or density? What are the main drivers of long scattering length? As already mentioned above I certainly miss an approach to correct the observed bias by using another technique to estimate the range from the returned pulses. Also the ICESat2 data analysis can be improved (see below).

• Are the results sufficient to support the interpretations and conclusions?

-Yes, but see point 3

• Is the description of experiments and calculations sufficiently complete and precise to allow their reproduction by fellow scientists (traceability of results)?

Partly. I miss more details of the scattering model.

• Do the authors give proper credit to related work and clearly indicate their own new/original contribution?

- Yes.

• Does the title clearly reflect the contents of the paper?

- Yes. Maybe a bit too long. (Maybe remove with NASA’s Airborne Topographic Mapper)

• Does the abstract provide a concise and complete summary?

- Yes, I find it a bit too long and it would be good to mentioned that large range bias (or penetration) of tens of cm is found over thin sea ice and not over dry snow,

• Is the overall presentation well structured and clear?

- Need to be improved. I find the paper sometimes very technical and full of details, which might be shortened and restructured.

E.g. chapter 2.2 Natural-color optical imagery is very detailed (is this needed for understanding?)

3.2 Lidar data characteristics is placed under methods but would fit better to 2.1 or

4.2 here a discussion is already started in the results chapter

• Is the language fluent and precise?

- Yes.

• Are mathematical formulae, symbols, abbreviations, and units correctly defined and used?

- Yes.

• Should any parts of the paper (text, formulae, figures, tables) be clarified, reduced, combined, or eliminated?

- Yes, clarified (see below).

• Are the number and quality of references appropriate?

- Yes.

• Is the amount and quality of supplementary material appropriate?

- Yes.

General:

Despite the paper is clear and of high quality I miss an assessment to improve the laser range detection to minimize the penetration effect of green laser light using different tracking approaches. This would be very beneficial and could guide an improvement of the ICESat2 range retrieval.

10.1109/IGARSS.2011.6050002 already showed that green laser tends to widen the pulse leading to an offset of elevation estimates especially for the centroid method. In this paper the findings of 10.1109/IGARSS.2011.6050002 are confirmed by more and better use cases, but the opportunity to improve the elevation product with the help of the scattering model is not taken.

Therefore, I would recommend, that the authors apply next to the centroid a threshold (e.g. TCOG or TFMRA of the leading edge) or a combination of a gaussian fit and threshold tracking for comparison. The best threshold (giving highest precision) could be first evaluated using simulated returns or by using a subset of open water lead returns. This could be compared to the precision of the centroid tracker. Then this threshold tracker can be applied to all data and compared to the centroid estimates over different sea ice regimes.

In addition, I would recommend that the authors try to understand the ICESat2 negative freeboard in more detail by using lower level ATL03 photon data set. Here, they also could apply the threshold tracker on the photon distribution or a gaussian fit of the photon distribution and evaluate if the freeboard can be corrected by maintaining the same accuracy. For the sea ice community this would be a very important finding.

Figures:

Please use CVD conform color palettes

(https://www.nature.com/articles/s41467-020-19160-7?s=09).

I can hardly see differences between green, orange or red colors in most of your figures!

Fig1, Fig2, Fig 7. Can you please enlarge the symbol size of the laser points. Hard to see.

I would recommend that you provide next to Fig2, Fig5, Fig7 where you show the elevation also a figure with the elevation distribution w.r.t to open water as histogram for the each of the different ice types for each of your selected sites.

Please also use in all figures, which show the elevation the same CVD friendly color scale and please always plot the elevation wrt. open water.

Fig 4 Please enlarge the font size of axis labeling and text

Fig3 and Fig4

I don’t understand the connection of both figures or at least they are not showing what is explained in the text.

In line 306 you write “The mean pulse broadening w.r.t. the mean pulse width over open water is 0.6 ns for the single-layer ice and 2.1 ns for the finger-rafted ice”

Fig4 shows 8.72ns pulse width for open water and 10.19ns for single layer ice at 35% amplitude threshold. The difference is 1.47ns! The difference for finger rafted ice is 1.98ns.

At the same time the centroid position for open water/calibrated range is 0.66ns.

When this is taken as zero elevation then the difference for single layer would be: 0.58 – 0.66 = -0.08ns and for finger rafted 0.76 – 0.66 = 0.1ns.

With the velocity of light these transfer in a negative range bias of 2.3 cm for single layer and a positive range bias of 3 cm. However, this is not reflected in Fig3. What I’m doing wrong?

Fig 7 Why you show the elevation wrt. WGS84? With different tidal states this is changing and leads to confusion! Please refer elevation to open water as you do in the other figures and please enlarge symbol size.

In line 443 you mention that the surface brightness of the ice north of the lead changed.

However, to me it seems that also the ice above water (upper left area) is darker in panel (a). Can you please verify if you use the same gray scaling for each of the images?

Fig 8 Color scale! All looks the same for me. Maybe you narrow the min/max elevation as well. Maybe you zoom in even more so that you really focus on the lake.

Fig9. Please enlarge font size. In the figure caption you talk about slant range. Why not add the slant range as additional x-axis label?

Fig.11 I don’t understand the positioning of the hbias in 11(d). Is this the estimated centroid which gives the range? When looking at the waveform it seems that the hbias when this is representing the centroid should be closer to zero. In the text Line 340 you write that only small changes in the pulse shape are visible in the leading edge but figure 11d shows a clear widening when compared to 11(a). Can you comment on this?

L510 ff

Based on your modeling approach. Could you please briefly summarize what parameter drives the most significant change in scattering length. Is this density, grain size or temperature? At which grain sizes you see a change? Is this a linear or abrupt change? As shown for dry snow you expect little penetration or at least little effect of subsurface scattering on range estimates. Is this a valid assumption for green laser penetration over dry snow in general (e.g. is this valid over the whole Greenland and Antarctic ice sheet)? Maybe you can add a line in chapter 7 when you discuss the broader context of green laser light penetration in snow and ice as this is also important for the land ice community when they compare ICESat2 with radar altimetry.

L695 Here it might be worth to accumulate all ATM returns to match the footprint size of ICESat2 and check if the differential penetration is still existing in the ATM data.