the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Sep 2024
Anticipating CRISTAL: An exploration of multi-frequency satellite altimeter snow depth estimates over Arctic sea ice, 2018–2023
Abstract. The EU and ESA plan to launch a dual-frequency Ku- and Ka-band polar-orbiting synthetic aperture radar (SAR) altimeter, CRISTAL (Copernicus Polar Ice and Snow Topography Altimeter), by 2028 to monitor polar sea ice thickness and its overlying snow depth, among other applications. However, the interactions of Ku- and Ka-band radar waves with snow and sea ice are not fully understood, demanding further research effort before we can take full advantage of the CRISTAL observations. Here, we use three ongoing altimetry missions to mimic the sensing configuration of CRISTAL over Arctic sea ice and investigate the derived snow depth estimates obtained from dual-frequency altimetry. We apply a physical model for the backscattered radar altimeter echo over sea ice to CryoSat-2’s Ku-band altimeter in SAR mode and to the SARAL mission’s AltiKa Ka-band altimeter in low-resolution mode (LRM), then compare to reference laser altimetry observations from ICESat-2. ICESat-2 snow freeboards (snow + sea ice) are representative of the air-snow interface, whereas the radar freeboards of AltiKa are expected to represent a height at or close to the air-snow interface, and CryoSat-2 radar freeboards a height at or close to the snow-ice interface. The freeboards from AltiKa and ICESat-2 show similar patterns and distributions; however, the AltiKa freeboards do not thicken at the same rate over winter, implying that Ka-band height estimates can be biased low by 10 cm relative to the snow surface due to uncertain penetration over first-year ice in spring. Previously-observed mismatches between radar freeboards and independent airborne reference data have been frequently attributed to radar penetration biases, but can be significantly reduced by accounting for surface topography when retracking the radar waveforms. Waveform simulations of CRISTAL in its expected sea ice mode reveal that the heights of the detected snow and ice interfaces are more sensitive to multi-scale surface roughness than snow properties. For late-winter conditions, the simulations suggest that the CRISTAL Ku-band radar retrievals will track a median elevation 3 % above the snow-ice interface, because the radar return is dominated by surface scattering from the snow-ice interface which has a consistently smoother footprint-scale slope distribution than the air-snow interface. Significantly more backscatter is simulated to return from the air-snow interface and snow volume at Ka-band, with the radar retrievals tracking a median elevation 10 % below the air-snow interface. These model results generally agree with the derived satellite radar freeboards, which are consistently thicker for AltiKa than CryoSat-2, across all measured snow and sea ice conditions.
Competing interests: At least one of the (co-)authors is a member of the editorial board of The Cryosphere.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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CC1: 'Comment on egusphere-2024-2904', Zhaoqing Dong, 29 Sep 2024
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AC1: 'Reply on CC1', Jack Landy, 02 Oct 2024
Good question Zhaoqing,
For the AltiKa version of FBEM, we set
satellite velocity = 7470
synthetic beam gain = 1 (as a dummy, not used for LRM echoes)
along-track pattern term = (0.605*pi/180)/(2*sqrt(log(2)))
across-track pattern term = along-track pattern termMost AltiKa instrument parameters were obtained from https://directory.eoportal.org/web/eoportal/satellite-missions/s/saral
I've also now uploaded the SHELL.m script for AltiKa echoes to the FBEM github page.
All the best, Jack
Citation: https://doi.org/10.5194/egusphere-2024-2904-AC1
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AC1: 'Reply on CC1', Jack Landy, 02 Oct 2024
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CC2: 'Comment on egusphere-2024-2904', Arttu Jutila, 01 Nov 2024
Dear Jack and co-authors,
Kudos to you on your important and timely work on this topic! With this community comment, I would like to raise some points regarding the reference observations (L175ff).
First off, the minor technicalities:
- Could you please update the reference Jutila et al. (2021) from the preprint in The Cryosphere Discussions to the published article that has been available now for nearly three years? I mention this here because I have encountered recent papers where this has not always been caught even after professional copy-editing.
- Jutila, A., Hendricks, S., Ricker, R., von Albedyll, L., Krumpen, T., and Haas, C.: Retrieval and parameterisation of sea-ice bulk density from airborne multi-sensor measurements, The Cryosphere, 16, 259–275, https://doi.org/10.5194/tc-16-259-2022, 2022.
- While the geophysical measurement data have not changed, I would appreciate if you would refer to the most recent version (v2) of the AWI IceBird dataset as:
- Jutila, A., Hendricks, S., Ricker, R., von Albedyll, L., and Haas, C.: Airborne sea ice parameters during the IceBird Winter 2019 campaign in the Arctic Ocean, Version 2 [dataset publication series], PANGAEA, https://doi.org/10.1594/PANGAEA.966057, 2024.
Then to the more interesting bit, which is applying pySnowRadar and the peakiness method to the April 2019 OIB data.
- Which flights have you processed exactly? The snow radar parameter spreadsheet (snow_param_2019_Greenland_P3.xls available at https://gitlab.com/openpolarradar/opr_params) lists a total of six, not five, flights over sea ice (sheet “cmd”, column “mission_names”, “Sea Ice:*”). Also NSIDC has six files with those dates in 2019 data (https://doi.org/10.5067/GRIXZ91DE0L9).
- On L185, you mention using “the same pySnowRadar parameters as the IceBird data”, but I guess you mean the peakiness method parameters? pySnowRadar contains also other retrieval algorithm modules like the wavelet method (Newman et al., 2014) with very different parameters for very different purposes.
- From the snow radar parameter spreadsheet notes, it is also obvious that some OIB flights were carried out with a reduced bandwidth (2-8 GHz instead of the full 2-18 GHz) and/or at an unusually high altitude of 3500 ft (nominally ~1500 ft). The peakiness method was not developed and has not been tested for such missions, and I am curious how the snow depth retrieval results looked like. Did you compare them against the official OIB product at NSIDC (https://doi.org/10.5067/GRIXZ91DE0L9)?
- While its impact is rather minor, which snow density value did you use in the processing? Later, on L193, you mention assuming snow density of 350 kg m-3. Or was it perhaps varying according to Mallett (2024)? In AWI IceBird, it was fixed at 300 kg m-3.
Citation: https://doi.org/10.5194/egusphere-2024-2904-CC2 - AC2: 'Reply on CC2', Jack Landy, 18 Jul 2025
- Could you please update the reference Jutila et al. (2021) from the preprint in The Cryosphere Discussions to the published article that has been available now for nearly three years? I mention this here because I have encountered recent papers where this has not always been caught even after professional copy-editing.
-
RC1: 'Comment on egusphere-2024-2904', Anonymous Referee #1, 01 Nov 2024
This paper explores existing satellite and airborne radar and laser altimetry observations over the Arctic from 2018-2023 to assess potential future observations from dual frequency Ka and Ku radar from CRISTAL. The study is very well organized, and thoroughly explores similarities and differences in current observations with strong ties to understanding the physical basis for differences. The results are highly impactful and will be an extremely useful reference in preparation for CRISTAL and understanding differences in Ku and Ka radar as well as laser altimetry missions.
I did not see any major technical errors and the explanations and figures were very clear. I just noted some questions that arose while reading the manuscript as outlined below. These are all minor and I would otherwise suggest publication subject to some minor revisions.
L118: What is meant by calibrated and uncalibrated observations in this sentence?
L203-204: Can you describe in more detail how the interpolation is done between tie points? Is it linear and over what length scale?
L225-230: Are these four parameter terms independent or are they linked together in some way e.g. the surface topography root-mean square height and mm-cm ‘radar-scale’ roughness?
L259: There looks to be a typo here in 95 8%
L270-275: How are the initial starting point values for the lsqnonlin solver determined?
Figure 2: Can you describe the methodology for discarding secondary peaks? Does this differ between CryoSat-2 and AltiKA?
L331: Is a consistent snow density as outlined here used also in the processing of the snow radar data?
L396-400: Can you calculate a skewness for the results? They do indeed appear Gaussian visually, but perhaps this metric could show this quantitatively.
L428: I was confused by the reference to the Beaufort Sea and MOSAiC transects here though see these are discussed a bit later in the paper. The MOSAiC measurements could be discussed in more detail in Section 2 as well.
L588: I’m not sure the statement about filtering out dark leads applies here. Dark leads are only not considered for sea surface height determination, but their freeboard heights still remain in the product.
Citation: https://doi.org/10.5194/egusphere-2024-2904-RC1 - AC3: 'Reply on RC1', Jack Landy, 18 Jul 2025
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RC2: 'Comment on egusphere-2024-2904', Anonymous Referee #2, 10 Jun 2025
General comment
The study presented in this paper is one of the most advanced analyses of multi-frequency altimetric measurements of sea ice and its snow cover. In a first phase, it provides measurements of the sea ice freeboard using the Ka AltiKa radar altimeter on the Saral satellite, obtained using the LARM physical retracker. This result is already an innovation, as it is the first Ka-band radar freeboard product that provides a realistic topography of sea ice; previous studies focused exclusively on the Ka/Ku differential for snow depth retrieval. This freeboard is then used in combination with the Ku radar freeboard obtained with LARM retracker applied on CryoSat-2 to estimate snow depth. An initial analysis then evaluates this solution against that obtained by combining Ku radar and lidar (KuLa), as well as with airborne snow thickness measurements and the Lagrangian model SnowModelLG. This analysis shows that the snow depth estimate obtained with KuKa seems realistic at the beginning of winter but greatly underestimates this thickness throughout the winter accumulation, even if a slight thickening is observed.
To better understand the origins of this underestimation, an in-depth comparative analysis of each of the freeboards involved in these thickness measurements is provided below, with the aim of better understanding the reasons for these discrepancies: Are they due to retracking problems? to the effects of surface roughness on retracking? to overestimation or underestimation of penetration (or more precisely, variations in the backscatter ratios from air/snow and snow/ice surfaces, and snow volume)?
The results show that it is a combination of these different aspects and allows some of them to be quantified, such as the effect of surface roughness on Ka radar freeboard, which seems to have a negligible effect except in rare situations (high freeboard and low roughness). Nevertheless the Ka freeboard obtained with LARM is underestimated on average relative to IceSat-2, and this is more pronounced for low freeboards aiming to lower snow depth retrieval with KaKu than with LaKu that can reach to only a third of this last one.
The last section presents a simulation of the next CRISTAL dual-frequency altimetry mission which suggests that Ka-band may be underestimated by 10% the total freeboard and the Ku-band overestimated by 3% the ice freeboard. The last section presents a simulation of the upcoming CRISTAL dual-frequency altimetry mission, which suggests that the Ka band could underestimate the total freeboard by 10% and that the Ku band could overestimate the ice freeboard by 3%. These results are very promising but show that there is still room for improvement. The authors propose various avenues for further study and also emphasize the importance of additional baseline measures.
Given the originality, scientific quality, significance of the implications, and quality of the presentation, I recommend publication of this article with a few minor revisions.
Detailed remarks
Lines 19 and 22: In the following sentences, could you clarify what the percentages refer to? “a median elevation 3% above the snow-ice interface”, “median elevation 10% below the air-snow interface”.
Line 41: CRISTAL will be ready for launch at the end of 2027. This remains the official date for the time being.
Lines 65 and 71: I don't believe that Ku could penetrate 60-90% of the snow depth and Ka 0-40% whatever is the snow depth…
Line 93-95: could be interesting to specify (if possible) from which order of magnitude of altitude the coherent radar reflection becomes dominant for the following analyses; i.e., when going from ground to airborne measurements? or from airborne to space measurements?
Line 148: to be coherent with titles 2.1 and 2.3, the title 2.2 should be: “SARAL AltiKa Observations” as SARAL is the satellite and AltiKa the altimeter.
Line 193: 350kg/m3 for the snow density seems a high value. Could it be justify? Even if the impact is low it could worth to adapt this value.
Line 296: Strange sentence: With revised classes the waveforms previously classed as ambiguous are now generally classed as sea ice.
Line 330: Now the snow density varies from 266 to 329 kg/m3 which is not coherent with the previous 350kg/m3 line 193. Could you specify the used speed propagation equation?
Line 496: See last comment (for line 674).
Figure 10a: It’s strange to mix-up Ku-band, Ka-band and laser freeboards (both for satellite and airborne)! They should not measure the same surface (air-snow versus snow-ice). Have you applied corrections for the snow impacts (load + speed propagation)? Please justify.
Figure 10b: Which data are used here? LARM? TFMRA? Both? Also it’s strange to see a CS2 freeboard greater than IS2 and SRL. The offset is not clearly shown (add arrows?) and it makes the comparisons difficult.
Figure 11: Very interesting plots but Figures 11a and 11c show exactly the opposite results. I suppose there is an error on the name of the y-axis for 11c (should be SRL-IS2 instead of IS2-SRL).
Line 561: It would be useful to recall here in a short sentence the concept of Mie scattering, as it is very important for understanding the interactions between snow and radar waves.
Line 605: This very important section is not as clear as the previous ones. It could be much clearer if you shortly introduce the objective of the following demonstration instead of just the introductive word ‘here’.
Lines 496 and 674: All the analyses regarding the threshold to be used to retrieve coherent results are very interesting but it is important to have in mind that the threshold approach is stable only if its value corresponds to the steepest slope of the waveform leading edge and far from its maximum, i.e. between 30% to 50% as shown Figure 10a in Laforge et al. 2021 https://doi.org/10.1016/j.asr.2020.02.001. For example, in the extreme case of a 100% threshold, this corresponds to take the maximum of the waveform sampled by the altimeter, i.e., a measurement of the epoch on a sampling gate and therefore with a resolution equal to that of the altimeter (about 20 cm for CryoSat-2 SAR). While this does not affect averages over large areas, it does significantly increase the noise in each measurement. Laforge et al. 2021 propose an alternative that involves correcting the range rather than the threshold, as is done for Sea State Bias in the open sea (see Figure 10). I think it is important to keep this alternative in mind. However, retrackers based on a physical model are clearly the best option.
- AC4: 'Reply on RC2', Jack Landy, 18 Jul 2025
Status: closed
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CC1: 'Comment on egusphere-2024-2904', Zhaoqing Dong, 29 Sep 2024
Hey, Jack!
I just curious about these specific values of satellite velocity, synthetic beam gain, along-track antenna parameter and across-track antenna parameter of pulse-limited altimeter AltiKa SARAL of pulse-limited altimeter. How do you set these parameters in FBEM model? Thank you for your explanation!
Cheers,
Zhaoqing
Citation: https://doi.org/10.5194/egusphere-2024-2904-CC1 -
AC1: 'Reply on CC1', Jack Landy, 02 Oct 2024
Good question Zhaoqing,
For the AltiKa version of FBEM, we set
satellite velocity = 7470
synthetic beam gain = 1 (as a dummy, not used for LRM echoes)
along-track pattern term = (0.605*pi/180)/(2*sqrt(log(2)))
across-track pattern term = along-track pattern termMost AltiKa instrument parameters were obtained from https://directory.eoportal.org/web/eoportal/satellite-missions/s/saral
I've also now uploaded the SHELL.m script for AltiKa echoes to the FBEM github page.
All the best, Jack
Citation: https://doi.org/10.5194/egusphere-2024-2904-AC1
-
AC1: 'Reply on CC1', Jack Landy, 02 Oct 2024
-
CC2: 'Comment on egusphere-2024-2904', Arttu Jutila, 01 Nov 2024
Dear Jack and co-authors,
Kudos to you on your important and timely work on this topic! With this community comment, I would like to raise some points regarding the reference observations (L175ff).
First off, the minor technicalities:
- Could you please update the reference Jutila et al. (2021) from the preprint in The Cryosphere Discussions to the published article that has been available now for nearly three years? I mention this here because I have encountered recent papers where this has not always been caught even after professional copy-editing.
- Jutila, A., Hendricks, S., Ricker, R., von Albedyll, L., Krumpen, T., and Haas, C.: Retrieval and parameterisation of sea-ice bulk density from airborne multi-sensor measurements, The Cryosphere, 16, 259–275, https://doi.org/10.5194/tc-16-259-2022, 2022.
- While the geophysical measurement data have not changed, I would appreciate if you would refer to the most recent version (v2) of the AWI IceBird dataset as:
- Jutila, A., Hendricks, S., Ricker, R., von Albedyll, L., and Haas, C.: Airborne sea ice parameters during the IceBird Winter 2019 campaign in the Arctic Ocean, Version 2 [dataset publication series], PANGAEA, https://doi.org/10.1594/PANGAEA.966057, 2024.
Then to the more interesting bit, which is applying pySnowRadar and the peakiness method to the April 2019 OIB data.
- Which flights have you processed exactly? The snow radar parameter spreadsheet (snow_param_2019_Greenland_P3.xls available at https://gitlab.com/openpolarradar/opr_params) lists a total of six, not five, flights over sea ice (sheet “cmd”, column “mission_names”, “Sea Ice:*”). Also NSIDC has six files with those dates in 2019 data (https://doi.org/10.5067/GRIXZ91DE0L9).
- On L185, you mention using “the same pySnowRadar parameters as the IceBird data”, but I guess you mean the peakiness method parameters? pySnowRadar contains also other retrieval algorithm modules like the wavelet method (Newman et al., 2014) with very different parameters for very different purposes.
- From the snow radar parameter spreadsheet notes, it is also obvious that some OIB flights were carried out with a reduced bandwidth (2-8 GHz instead of the full 2-18 GHz) and/or at an unusually high altitude of 3500 ft (nominally ~1500 ft). The peakiness method was not developed and has not been tested for such missions, and I am curious how the snow depth retrieval results looked like. Did you compare them against the official OIB product at NSIDC (https://doi.org/10.5067/GRIXZ91DE0L9)?
- While its impact is rather minor, which snow density value did you use in the processing? Later, on L193, you mention assuming snow density of 350 kg m-3. Or was it perhaps varying according to Mallett (2024)? In AWI IceBird, it was fixed at 300 kg m-3.
Citation: https://doi.org/10.5194/egusphere-2024-2904-CC2 - AC2: 'Reply on CC2', Jack Landy, 18 Jul 2025
- Could you please update the reference Jutila et al. (2021) from the preprint in The Cryosphere Discussions to the published article that has been available now for nearly three years? I mention this here because I have encountered recent papers where this has not always been caught even after professional copy-editing.
-
RC1: 'Comment on egusphere-2024-2904', Anonymous Referee #1, 01 Nov 2024
This paper explores existing satellite and airborne radar and laser altimetry observations over the Arctic from 2018-2023 to assess potential future observations from dual frequency Ka and Ku radar from CRISTAL. The study is very well organized, and thoroughly explores similarities and differences in current observations with strong ties to understanding the physical basis for differences. The results are highly impactful and will be an extremely useful reference in preparation for CRISTAL and understanding differences in Ku and Ka radar as well as laser altimetry missions.
I did not see any major technical errors and the explanations and figures were very clear. I just noted some questions that arose while reading the manuscript as outlined below. These are all minor and I would otherwise suggest publication subject to some minor revisions.
L118: What is meant by calibrated and uncalibrated observations in this sentence?
L203-204: Can you describe in more detail how the interpolation is done between tie points? Is it linear and over what length scale?
L225-230: Are these four parameter terms independent or are they linked together in some way e.g. the surface topography root-mean square height and mm-cm ‘radar-scale’ roughness?
L259: There looks to be a typo here in 95 8%
L270-275: How are the initial starting point values for the lsqnonlin solver determined?
Figure 2: Can you describe the methodology for discarding secondary peaks? Does this differ between CryoSat-2 and AltiKA?
L331: Is a consistent snow density as outlined here used also in the processing of the snow radar data?
L396-400: Can you calculate a skewness for the results? They do indeed appear Gaussian visually, but perhaps this metric could show this quantitatively.
L428: I was confused by the reference to the Beaufort Sea and MOSAiC transects here though see these are discussed a bit later in the paper. The MOSAiC measurements could be discussed in more detail in Section 2 as well.
L588: I’m not sure the statement about filtering out dark leads applies here. Dark leads are only not considered for sea surface height determination, but their freeboard heights still remain in the product.
Citation: https://doi.org/10.5194/egusphere-2024-2904-RC1 - AC3: 'Reply on RC1', Jack Landy, 18 Jul 2025
-
RC2: 'Comment on egusphere-2024-2904', Anonymous Referee #2, 10 Jun 2025
General comment
The study presented in this paper is one of the most advanced analyses of multi-frequency altimetric measurements of sea ice and its snow cover. In a first phase, it provides measurements of the sea ice freeboard using the Ka AltiKa radar altimeter on the Saral satellite, obtained using the LARM physical retracker. This result is already an innovation, as it is the first Ka-band radar freeboard product that provides a realistic topography of sea ice; previous studies focused exclusively on the Ka/Ku differential for snow depth retrieval. This freeboard is then used in combination with the Ku radar freeboard obtained with LARM retracker applied on CryoSat-2 to estimate snow depth. An initial analysis then evaluates this solution against that obtained by combining Ku radar and lidar (KuLa), as well as with airborne snow thickness measurements and the Lagrangian model SnowModelLG. This analysis shows that the snow depth estimate obtained with KuKa seems realistic at the beginning of winter but greatly underestimates this thickness throughout the winter accumulation, even if a slight thickening is observed.
To better understand the origins of this underestimation, an in-depth comparative analysis of each of the freeboards involved in these thickness measurements is provided below, with the aim of better understanding the reasons for these discrepancies: Are they due to retracking problems? to the effects of surface roughness on retracking? to overestimation or underestimation of penetration (or more precisely, variations in the backscatter ratios from air/snow and snow/ice surfaces, and snow volume)?
The results show that it is a combination of these different aspects and allows some of them to be quantified, such as the effect of surface roughness on Ka radar freeboard, which seems to have a negligible effect except in rare situations (high freeboard and low roughness). Nevertheless the Ka freeboard obtained with LARM is underestimated on average relative to IceSat-2, and this is more pronounced for low freeboards aiming to lower snow depth retrieval with KaKu than with LaKu that can reach to only a third of this last one.
The last section presents a simulation of the next CRISTAL dual-frequency altimetry mission which suggests that Ka-band may be underestimated by 10% the total freeboard and the Ku-band overestimated by 3% the ice freeboard. The last section presents a simulation of the upcoming CRISTAL dual-frequency altimetry mission, which suggests that the Ka band could underestimate the total freeboard by 10% and that the Ku band could overestimate the ice freeboard by 3%. These results are very promising but show that there is still room for improvement. The authors propose various avenues for further study and also emphasize the importance of additional baseline measures.
Given the originality, scientific quality, significance of the implications, and quality of the presentation, I recommend publication of this article with a few minor revisions.
Detailed remarks
Lines 19 and 22: In the following sentences, could you clarify what the percentages refer to? “a median elevation 3% above the snow-ice interface”, “median elevation 10% below the air-snow interface”.
Line 41: CRISTAL will be ready for launch at the end of 2027. This remains the official date for the time being.
Lines 65 and 71: I don't believe that Ku could penetrate 60-90% of the snow depth and Ka 0-40% whatever is the snow depth…
Line 93-95: could be interesting to specify (if possible) from which order of magnitude of altitude the coherent radar reflection becomes dominant for the following analyses; i.e., when going from ground to airborne measurements? or from airborne to space measurements?
Line 148: to be coherent with titles 2.1 and 2.3, the title 2.2 should be: “SARAL AltiKa Observations” as SARAL is the satellite and AltiKa the altimeter.
Line 193: 350kg/m3 for the snow density seems a high value. Could it be justify? Even if the impact is low it could worth to adapt this value.
Line 296: Strange sentence: With revised classes the waveforms previously classed as ambiguous are now generally classed as sea ice.
Line 330: Now the snow density varies from 266 to 329 kg/m3 which is not coherent with the previous 350kg/m3 line 193. Could you specify the used speed propagation equation?
Line 496: See last comment (for line 674).
Figure 10a: It’s strange to mix-up Ku-band, Ka-band and laser freeboards (both for satellite and airborne)! They should not measure the same surface (air-snow versus snow-ice). Have you applied corrections for the snow impacts (load + speed propagation)? Please justify.
Figure 10b: Which data are used here? LARM? TFMRA? Both? Also it’s strange to see a CS2 freeboard greater than IS2 and SRL. The offset is not clearly shown (add arrows?) and it makes the comparisons difficult.
Figure 11: Very interesting plots but Figures 11a and 11c show exactly the opposite results. I suppose there is an error on the name of the y-axis for 11c (should be SRL-IS2 instead of IS2-SRL).
Line 561: It would be useful to recall here in a short sentence the concept of Mie scattering, as it is very important for understanding the interactions between snow and radar waves.
Line 605: This very important section is not as clear as the previous ones. It could be much clearer if you shortly introduce the objective of the following demonstration instead of just the introductive word ‘here’.
Lines 496 and 674: All the analyses regarding the threshold to be used to retrieve coherent results are very interesting but it is important to have in mind that the threshold approach is stable only if its value corresponds to the steepest slope of the waveform leading edge and far from its maximum, i.e. between 30% to 50% as shown Figure 10a in Laforge et al. 2021 https://doi.org/10.1016/j.asr.2020.02.001. For example, in the extreme case of a 100% threshold, this corresponds to take the maximum of the waveform sampled by the altimeter, i.e., a measurement of the epoch on a sampling gate and therefore with a resolution equal to that of the altimeter (about 20 cm for CryoSat-2 SAR). While this does not affect averages over large areas, it does significantly increase the noise in each measurement. Laforge et al. 2021 propose an alternative that involves correcting the range rather than the threshold, as is done for Sea State Bias in the open sea (see Figure 10). I think it is important to keep this alternative in mind. However, retrackers based on a physical model are clearly the best option.
- AC4: 'Reply on RC2', Jack Landy, 18 Jul 2025
Data sets
University of Tromso Arctic Ocean freeboard and snow depth product from CryoSat-2, AltiKa and ICESat-2 Jack Landy https://doi.org/10.5281/zenodo.13774843
Model code and software
Facet-Based SAR Altimeter Echo Model Jack Landy https://github.com/jclandy/FBEM
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- 1
Hey, Jack!
I just curious about these specific values of satellite velocity, synthetic beam gain, along-track antenna parameter and across-track antenna parameter of pulse-limited altimeter AltiKa SARAL of pulse-limited altimeter. How do you set these parameters in FBEM model? Thank you for your explanation!
Cheers,
Zhaoqing