Penetration of interferometric radar signals in Antarctic snow

Rott, Helmut; Scheiblauer, Stefan; Wuite, Jan; Krieger, Lukas; Floricioiu, Dana; Rizzoli, Paola; Libert, Ludivine; Nagler, Thomas

doi:https://doi.org/10.5194/tc-15-4399-2021

Articles | Volume 15, issue 9

https://doi.org/10.5194/tc-15-4399-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/tc-15-4399-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 15, issue 9

Research article

|

13 Sep 2021

Research article |

| 13 Sep 2021

Penetration of interferometric radar signals in Antarctic snow

Helmut Rott, Stefan Scheiblauer, Jan Wuite, Lukas Krieger, Dana Floricioiu, Paola Rizzoli, Ludivine Libert, and Thomas Nagler

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Final revised paper (published on 13 Sep 2021)
Supplement to the final revised paper
Preprint (discussion started on 19 Jan 2021)
Supplement to the preprint

Interactive discussion

Status: closed

RC1:
'Comment on tc-2020-380', Anonymous Referee #1, 26 Feb 2021

This paper concerns a new application of existing theory to estimate bias in InSAR-derived elevation measurements of ice sheets and glaciers caused by below-surface radar returns. The method is based on the relationship with volume scattering coherence, which can be determined from total coherence, knowledge of the signal to noise ratio and assumptions of coherence loss from smaller order terms. The estimated bias from volume scattering coherence measurement is compared with bias calculated from the difference between InSAR elevation measurements and REMA.

There is no question as to the importance of this study. Observation error of cryosphere changes from InSAR is essential, particularly given the high magnitudes observed (mean bias of around 5m) and potential for seasonal variation due to changes in the snow grain size and density. The consistency between the simulation results and observed bias is encouraging. This is a new, practical application of the theoretical work of Dall 2007.

My main concern about this study is that the Dall 2007 model is not applicable where there is significant surface scattering. While this may be valid considering the snow surface, there are a number of ice lenses and crusts within the snowpack (Figure 2) that act in a similar way. It was not clear from the snow backscatter modeling (section 4.1) how these were simulated but possible these were explicitly taken into account (e.g. ice layer with 2mm air bubbles). Discussion of the limitations of the Dall 2007 model should be included as well as the limitations of the methodology of the snow backscattering modeling. The impact of the use a subjective grain size and assumed stickiness on the retrieved bias should be discussed.

Overall the paper is detailed and would probably be better suited to a remote sensing journal in its current form. For broader applicability as a publication in The Cryosphere it needs to be more succinct. I would encourage the authors to look again at the balance of what must be provided for reproducibility, what is required for basic understanding and what information may be already available for those who really need to know the detail. For example, equations 11-15 may be better kept in the Dall 2007 reference as the jump from equation 10 to 16 will be easier to read for most. This may also allow some of the figures in the supplementary material to be brought into the main paper.

There is a lot of detail early in the paper on ICESat / ICESat-2 (section 2.2 – nearly a page) yet these are not actually used for the estimation of InSAR elevation bias, despite them being the observation with the lowest error. There is an indication in Table S1 for the ice-free slope and blue ice area, and for the area around pit P4 in Table S2 but not over the larger area. In table S2 the standard deviation is much higher than the actual measurement. This, and the positive height biases shown in Figure 1 should be discussed – what does it mean when the TDM DEM elevation is higher than the optical-derived DEM elevation?

Please could the authors check for consistency throughout the paper. For example, TDM is defined as the TanDEM-X mission, then TanDEM-X is used interchangeably with TDM in lines 60-70. DEM is defined twice. There are two separate definitions of Δh and dh, with opposite signs. SMRT is suggested as the backscatter model used, but then the rest of the text refers to DMRT. If DMRT then the version used needs to be stated. Line 553 refers to equation 4, but this is not the correct equation. These are all minor defects, but unfortunately make the paper difficult to follow.

Specific comments:

The abstract attributes angular gradients of backscatter intensity to anisotropy in the snow structure. This is misleading. Even if the summer observations at one angle can be compared to the winter observations at another angle (and I’m not convinced they can), this is a stratigraphic effect rather than anisotropy.

Section 2.1. Product reference should already contain the majority of this detail. Only additional processing steps done for this study need to be included.

Line 134 – please show the location of the 11 blocks (or was this part of a different study?)

Figure 2. Snow grain size legend is different in colour to the main plots. Please could you increase the snow grain type font size and/or resolution.

Section 3.2 Perhaps the processing steps would be better placed in the supplementary material. There is a lot of detail on the accuracy of REMA. It would be better to state the vertically registered DEM is treated as the truth, the errors briefly discussed as a limitation of the study and the reader referred to the supplement for more information.

Line 377. Stickiness of 0 breaks theoretical limits. The minimum stickiness is bounded by equation 35 in Löwe and Picard (2015).

Line 517. The two observations were taken 2.5 years apart. What microstructural changes could reasonably be expected during this time period, and what would the impact be on the backscatter / elevation bias estimate? The difference has been attributed to incidence angle, but other factors have not been discussed.

Line 590 hbinv is mentioned but not defined – presumably this is from rearrangement of equation 16? It is not clear why equation 17 been included in this paper – I think this is used to calculate the volume coherence from the exponential fit to the SMRT / DMRT backscatter curves for retrieval bias but it would help the reader to state clearly the steps taken.

Citation: https://doi.org/10.5194/tc-2020-380-RC1
- AC1: 'Comment on tc-2020-380', Helmut Rott, 17 Mar 2021
  
  Manuscript tc-2020-380, Author comment AC1
  Response to Referee 1
  We wish to thank the Referee for the valuable comments and suggestions which are very helpful for improving the manuscript. We address the comments below and explain how these will be taken into account in the revised manuscript.
  Referee comments are in italics, our responses are in normal font.
  General Comment: This paper concerns a new application of existing theory to estimate bias in InSAR-derived elevation measurements of ice sheets and glaciers caused by below-surface radar returns. The method is based on the relationship with volume scattering coherence, which can be determined from total coherence, knowledge of the signal to noise ratio and assumptions of coherence loss from smaller order terms. The estimated bias from volume scattering coherence measurement is compared with bias calculated from the difference between InSAR elevation measurements and REMA.
  There is no question as to the importance of this study. Observation error of cryosphere changes from InSAR is essential, particularly given the high magnitudes observed (mean bias of around 5m) and potential for seasonal variation due to changes in the snow grain size and density. The consistency between the simulation results and observed bias is encouraging. This is a new, practical application of the theoretical work of Dall 2007.
  Response: We appreciate the positive feedback on the scope of our work. This comment very well reflects the main objectives of the paper.
  Main Comment 1: My main concern about this study is that the Dall 2007 model is not applicable where there is significant surface scattering. While this may be valid considering the snow surface, there are a number of ice lenses and crusts within the snowpack (Figure 2) that act in a similar way. It was not clear from the snow backscatter modeling (section 4.1) how these were simulated but possible these were explicitly taken into account (e.g. ice layer with 2mm air bubbles). Discussion of the limitations of the Dall 2007 model should be included as well as the limitations of the methodology of the snow backscattering modeling. The impact of the use a subjective grain size and assumed stickiness on the retrieved bias should be discussed.
  Response: The Dall model is based on an exponential loss function. The validity of this model can be assessed by comparing the inversion of this model in terms of the InSAR elevation bias with the elevation bias resulting from the difference between vertically co-registered InSAR and optical elevation data (dh, as defined in Eq. 3). The assessment of the performance of the InSAR elevation bias derived from volumetric coherence for polar firn is actually the main objective of this project. The comparison of the elevation bias from the inverted Dall model with the dh-values shows on the average good performance, confirming the general applicability of this model for dry polar firn with different structural properties (Table 3, Fig. 7). However, there is some over-, respectively under-estimation of the retrieved elevation bias for sites with specific structural properties. Performance and limitations of the Dall model are discussed Section 7.
  The inversion of the Dall model is not based on the multi-layer radiative transfer model that is applied in Section 4.1 for backscatter simulations. The inversion of such a model is not possible with the very limited set of input parameters. The main objective of the reported backscatter forward modelling activity is to assess the suitability of the exponential loss function for describing the vertical backscatter contributions of a layered polar snow/firn medium (line 403 to 407).
  By now there is no backscatter model available that specifically accounts for the complex layered structure of polar firn. We are well aware of the shortcomings of the current model. Constraints of the backscatter model and of the input parameters for characterizing the specific properties of the individual layers are addressed in the sections 4.1 and 7. Nevertheless, the selected model allows demonstrating the impact of differences in scattering of individual layers, parametrized by effective grain size and stickiness, in order to check the vertical backscatter distribution. The simulations show some deviations from the exponential loss function but not any fundamental difference. This is in accordance with the good performance of the Dall model.
  Main Comment 2: Overall the paper is detailed and would probably be better suited to a remote sensing journal in its current form. For broader applicability as a publication in The Cryosphere it needs to be more succinct. I would encourage the authors to look again at the balance of what must be provided for reproducibility, what is required for basic understanding and what information may be already available for those who really need to know the detail. For example, equations 11-15 may be better kept in the Dall 2007 reference as the jump from equation 10 to 16 will be easier to read for most. This may also allow some of the figures in the supplementary material to be brought into the main paper.
  Response: Our motivation for submitting the paper to The Cryosphere is the fact that many papers using TanDEM-X data for measuring glacier surface elevation change were published in this journal and that the correction of the penetration related elevation bias was addressed as a critical issue. We agree that some of the technical descriptions are too detailed and that a better focus on the main issues should be provided (including issues explained in our response to Main Comment 1). We will thoroughly check and revise the manuscript in this respect. We will also check options to shift some of the technical information to an appendix or to the supplement, for example the backscatter forward modelling (because this is not used directly for the inversion).
  Main Comment 3: There is a lot of detail early in the paper on ICESat / ICESat-2 (section 2.2 – nearly a page) yet these are not actually used for the estimation of InSAR elevation bias, despite them being the observation with the lowest error. There is an indication in Table S1 for the ice-free slope and blue ice area, and for the area around pit P4 in Table S2 but not over the larger area. In table S2 the standard deviation is much higher than the actual measurement. This, and the positive height biases shown in Figure 1 should be discussed – what does it mean when the TDM DEM elevation is higher than the optical-derived DEM elevation?
  Response: Regarding these issues, we want at first refer to Section 3, line 253 to 276, where the differences between the penetration-related InSAR elevation bias (Eq. 1), the height difference between non co-registered DEMs (Eq. 2) and the height difference between optical and InSAR elevation data, co-registered at surface scattering targets, (Eq. 3) is explained. Figure 1 shows the height difference between the global TanDEM-X DEM (TDMgl) and ICESat elevation. In lines 132 to 136 it is stated that for the TDMgl DEM over Antarctica bulk penetration corrections are applied. This explains the positive height bias which refers to areas where the actual penetration bias is smaller than the bulk penetration correction. Because the TDMgl DEM is widely used, we show in Figure 1 the height difference (elevation bias) for the original TDMgl DEM (rather than applying a specific adjustment for the Union Glacier area).
  We will shorten Section 2.2, omitting general information on features of ICESat provided in the cited references. Regarding the ICEsat data used in the study, these are essential for checking the temporal variability of surface height which is of relevance for estimating the InSAR elevation bias using non-coincident optical data. For the spatially detailed analysis we use REMA because it provides full spatial coverage. The standard deviation of the height difference between ICESat and REMA on the blue ice area, used for vertical co-registration, refers to very high resolution data (8 x 8 m pixels) (line 314). Table S2 shows the mean height difference between the original TDMgl DEM and ICESat for 25 footprints of each track and the standard deviation for the 25 points. This is stated in the caption of Table S2.
  Main Comment 4: Please could the authors check for consistency throughout the paper. For example, TDM is defined as the TanDEM-X mission, then TanDEM-X is used interchangeably with TDM in lines 60-70. DEM is defined twice. There are two separate definitions of Δh and dh, with opposite signs. SMRT is suggested as the backscatter model used, but then the rest of the text refers to DMRT. If DMRT then the version used needs to be stated. Line 553 refers to equation 4, but this is not the correct equation. These are all minor defects, but unfortunately make the paper difficult to follow.
  Response: Many thanks for pointing this out. We will thoroughly check and correct these points. Regarding Dh and dh, these are actually two different quantities referring to sequential steps in the procedure for deriving the elevation bias, as explained in Section 3, line 253 to 276 (see also the response to Main Comment 3). We prefer to keep these two parameters separated in order to stress the importance of vertical co-registration on surface scattering targets and to provide full traceability.
  SMRT is a model framework, comprising different models for describing electromagnetic wave propagation and the snow microstructure (stated in line 348 to line 350). Out of this framework, two suitable models were selected for this study (line 350 to 352). Details on the SMRT and the different models are provided by Picard et al. (2018). DMRT is the general term for dense medium radiative transfer models. The backscatter simulations in this paper are based on the Improved Born Approximation for a dense medium.
  Equation 4 in line 553 is the correct reference. This equation describes the vertical backscatter distribution of a volume with uniform scattering and extinction properties.
  Specific comments (SC):
  SC1: The abstract attributes angular gradients of backscatter intensity to anisotropy in the snow structure. This is misleading. Even if the summer observations at one angle can be compared to the winter observations at another angle (and I’m not convinced they can), this is a stratigraphic effect rather than anisotropy.
  Response: Layered media show structural anisotropy causing directional differences in signal propagation and scattering. The statement on anisotropy in the abstract (line 30) refers to the snow/firn volume (as stated there) and not to individual snow grains. Regarding differences in scattering properties between images acquired in winter and summer, we analyzed several scenes from different seasons showing that these are negligible. Between late 2016 and 2018 many scenes with similar observation geometry were acquired all year round confirming the stability. Stable backscatter properties for different seasons conform with the fact that the observed signal is made up by volume backscatter contributions down to several metres depth and seasonal differences would affect only a thin surface layer.
  SC2: The Section 2.1. Product reference should already contain the majority of this detail. Only additional processing steps done for this study need to be included.
  Response: TanDEM-X has about 100 different operation and acquisition modes. Therefore it is important to provide specifications for the products used in this study.
  SC3: Line 134 – please show the location of the 11 blocks (or was this part of a different study?)
  Response: The blocks are distributed all over Antarctica (at large distances), shown in Rizzoli et al., 2017 (cited in line 133).
  SC4: Figure 2. Snow grain size legend is different in colour to the main plots. Please could you increase the snow grain type font size and/or resolution.
  Response: We will increase the snow grain type font size.
  SC5: Section 3.2 Perhaps the processing steps would be better placed in the supplementary material. There is a lot of detail on the accuracy of REMA. It would be better to state the vertically registered DEM is treated as the truth, the errors briefly discussed as a limitation of the study and the reader referred to the supplement for more information.
  Response: The vertical coregistration and potential errors is very important for deriving height differences between different topographic data sets. Therefore we prefer retaining this section within the main paper. Besides, Section 3.2 is short (15 lines).
  SC6: Line 377. Stickiness of 0 breaks theoretical limits. The minimum stickiness is bounded by equation 35 in Löwe and Picard (2015).
  Response: According to the theory of electromagnetic wave propagation in dense random media stickiness zero corresponds to infinite stickiness (Tsang et al., 2013). The maximum stickiness value for snow (reported in the literature) is 0.1. This is mentioned in the paper. We will skip the reference to the (theoretical) zero value.
  SC7: Line 517. The two observations were taken 2.5 years apart. What microstructural changes could reasonably be expected during this time period, and what would the impact be on the backscatter / elevation bias estimate? The difference has been attributed to incidence angle, but other factors have not been discussed.
  Response: The backscatter signatures, as well as the surface elevation, are remarkably stable over years (quite common in the dry snow zone of Antarctica). This was one of the reasons for selecting this area for the penetration study. See also the comment to SC1. The mean differences in sigma-0 between the 2016 and 2018 data on the snow pit sites (Table S3) and the main glacier area (Table 3) are within the absolute radiometric uncertainty for the difference (0.85 dB). The elevation bias estimate is based on coherence. The backscatter intensity is only used for computing the signal-to-noise ratio which is a minor factor for deriving the volumetric coherence from the total coherence.
  Besides, significant deviations of the angular gradient in sigma-0 from isotropic scattering are prevalent for density-stratified polar firn. Ground-based scatterometer measurements in the dry snow zone of Dronning Maud Land, East Antarctica, show for X-band co-polarized sigma-0 differences of 5 dB to 6 dB between 20 and 40 degree incidence angles (Rott et al., 1993), similar to the Pit 3 and Pit 5 sites on Union Glacier.
  SC8: Line 590 hbinv is mentioned but not defined – presumably this is from rearrangement of equation 16? It is not clear why equation 17 been included in this paper – I think this is used to calculate the volume coherence from the exponential fit to the SMRT / DMRT backscatter curves for retrieval bias but it would help the reader to state clearly the steps taken.
  Response: hbinv is defined in the caption of Table 3 (line 448). We will repeat the definition in the text and mention that it is computed by means of Eq. 16. The volumetric coherence is computed with Eq. 17 which is based on the uniform volume approach. We will revise Section 4.2 and rearrange the sequence of the equations in order facilitate the understanding and improve the traceability.
  
  Citation: https://doi.org/10.5194/tc-2020-380-AC1
RC2:
'Comment on tc-2020-380', Anonymous Referee #2, 11 Mar 2021

General Comments:

In the manuscript "Penetration of interferometric radar signals in Antarctic snow" the authors study the relation between radar penetration depth into Antarctic snow and the interferometric coherence obtained from the single-pass InSAR mission TanDEM-X. They apply great effort for vertical alignment of different elevation models. For inversion they apply a model developed by (Dall, 2007) which assumes an uniform scattering efficiency of the snow volume. Based on snow pit measurements and depth-resolved radar backscatter models they conclude that despite a strong vertical variability of the scattering efficiency the depth-integrated backscatter signal represents well the model suggested by (Dall, 2007). They also found that modeling of the backscatter signal with the SMRT model based on grain size and layer thickness cannot explain the strong incidence angle dependence of the observed backscatter signal.

These findings make the manuscript in general suitable for publication in The Cryosphere. However, I have major concerns about the objectiveness of presented results and think that the manuscript requires a major restructuring to present and to focus on the most relevant results listed above. Below I first detail my main concerns on section 4-6, followed by minor comments and technical corrections. I would also suggest the authors to use the common structure of Data - Method - Results - Discussion - Conclusion and to write the manuscript more concise, instead of the currently used sequential form of sub-method-sub-results mixed with interpretation and discussion.

Major comments:

Section 4.1: This section about modeling the backscatter contributions from different layers lacks a thoroughly analysis and results seem to be presented in a selective manner. I understand that modeling the backscatter signal from the complex snow structure is challenging. Therefore, I think results should be presented in a more objective way to allow the reader to draw his own conclusions. Specifically, I have the following comments:

- line 268: Why did the author choose 25 layers and not the 30+ layers shown for the snow pits?

- line 370: When adopting the density profiles from firn cores, how was the layer thickness chosen? Fig. 3 indicates that, despite using the same firn core, different layer thicknesses were used below 2 meters. Please also mention that half of the simulated backscatter contribution originates from the adopted firn core. Only the upper half of simulated backscatter is based on snow pit data.

- Fig. 3: What are the "spikes" in Fig. 3(a) and (c)?

line 388: "Fig. 3 shows ... simulations for 40° ... of Pit 2 and 4." Why were these two pits chosen for the figure? Why not showing simulations for all snow pits (at least for one incidence angle)?

- line 393: "Both values differ less than 0.3 dB from the mean values of the 2013 and 2014 TDM scenes (40 deg)": This information is meaningless, considering that the standard deviation of the 2013 and 2014 measurements is around 1 dB; further, as stated by the authors, for 22 degree incidence angle, the model deviates 3 to 8 dB from the measurements and requires more tuning for a reasonable agreement.

line 395-397: The modeled two-way penetration depths for Pit 2 is 4.72m and 7.25m for Pit 4. The distance between the snow pits is about 7 km, but modeled results differ by 2.5 meters apparently due to different snow properties. Therefore I think it is meaningless to compare the penetration depth of Pit 2 with similar results from East Antarctica (Rott 1993) except for increasing the self-citation index. Please remove the reference or provide a more tracable comparision.

To present more objective results, I suggest to show a scatter plot presenting modeled vs. simulated backscatter intensity for all(!) 30 or 40 backscatter values listed in Table S3. Then the authors can discuss in a more objective manner what they think what causes the strong discrepancies. Different symbols or color could allow to separate different incidence angles and test sites(e.g., you could use numbers as plot symbols referring to the snow pits).

Section 5.2 is extremely hard to read. The main message of this section is not clear and backscatter results and discussions are mixed with inversion results of the penetration depth. Results from the snow pit locations are mixed with area-wide maps and scatter plots representing the same variables. Please restructure this section thoroughly and present only the most relevant results (estimation of interferometric bias) in a well-structured way. Currently, it's not clear to me why you also discuss and interpret backscatter values in this section. Specific suggestions:

- line 522-540 should go to the methods.

- Figures and tables: Why not showing a full page or full column figure with six rows and two or three colums of subplots (6 TDM scenes x 3 types or scatter plot) where each subplot shows a scatter plot of 1:(gamma_vol over dh), 2:(h_binv over dh) and possibly 3:(sigma_0 over dh). For each subplot, you could indicate the datapoint corresponding to a snow pit with a black symbol. This would then provide a solid basis for discussion of the inversion results with different incidence angles and baselines. At the same time you avoid discussion of mean values calculated over the strongly inhomogeneous areas of the LGA.

- I think you could merge Section 5.2 with 5.3.

- following a result-section about penetration estimation, you could - if it's worth - add a section presenting result on backscatter.

Minor comments:

abstract, l.23. "The average depth-dependent... can be approximated.." It's not clear if that's a general statement or a finding of the study. Please indicate.

abstract l.29: "The angular gradients of the backscatter intensity": Unclear what "angular gradients" are. Looking at line 420-427 I think you mean that simulated backscatter data do not match the backscatter measurements at different incidence-angles?

line 42-44: "Backscatter contributions ... within a volume scattering medium, observed under slightly different incidence angles, are causing a spectral wavenumber shift and decorrelation (Gatelli 1994)": I think that two different things have been mixed in this sentence. The observation under slightly different incidence angles (or InSAR nbaselines) causes a phase ramp (flat earth phase) modulated by topography (topographic phase). The sum of these two phases causes the spectral wavenumber shift which can be corrected for by spectral filtering (Section III-A in Gatelli 1994) and which is not caused by volume scattering. In my opinion, another effect is volume decorrelation (Section III-B in Gatelli 1994) which occurs when different scatterers exist within the same resolution cell but at different viewing angles, hence they scatter with different inSAR phases which sum up coherently but random, therefore causing decorrelation.

line 75: "data from optical satellite sensors": which?

line 96: "... bare ice appears on the surface (Fig. 1). The blue ice area (BIA)..." : Could you indicate consistently the location of the BIA on the map? The captions indicate the BIA with "B". Maybe, replace it with "BIA". or/and change "(Fig. 1)" do "(BIA in Fig. 1)". Could you add an arrow to the map indicating the wind direction and the location of its measurement? Possibly, also add the location of the stakes to the map as e.g., little black dots. As you are refering later to the ALE camp, could you also add it's location to the map?

line 119-124: Could you add the transect, and possibly the thickness of the firn layers, to Fig. 1?

line 124 and 137: "raw SAR data". What do you mean with raw SAR data? Level 0 raw data or level 1b CoSSC data?

line 140: "the SAR amplitude, the backscattering coefficient": Are they not identical? Or do the authors mean different normalizations? Did the authors consider a backscatter dependence or normalization with respect to the local topography? If no radiometric terrain correction was applied, please justify and mention the expected error. See [D. Small, "Flattening Gamma: Radiometric Terrain Correction for SAR Imagery," in IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 8, pp. 3081-3093, Aug. 2011, doi: https://doi.org/10.1109/TGRS.2011.2120616.]

line 190: Even though stated in the introduction, I would repeat the information that snow pit measurements were done in Dec. 2016. This information is relevant for comparison of the snow pit data with the TanDEM-X data from different years.

line 198 (also 371): "grain size": The next sentence indicates you measured "D_max"? Please specify. Maybe, add a reference, e.g. Mätzler et al (2002) "Relation between grain-size and correlation length of snow": https://doi.org/10.3189/172756502781831287 or the references to Colbeck 1990 or Armstrong 1993 therein.

line 209: "snow age following from different accumulation rates": Did you estimate accumulation rates or snow age from the snow pit measurements or from the accumulation stakes?

line 221: "accumulation rate near the ALE camp" Do you refer to snow pit P3 or to the accumulation stakes?

line 388: To clarify that refraction has been considered, I suggest to write "backscatter simulations for $\theta_i = 40°$". Could you mention in line 338 how you obtained the refraction angle $\theta_r$ from snow density and $\theta_i$?

line 422: "The need for different parameter settings ... is an indication for structural anisotropy": Please rephrase. Neglecting a possibly(!) existing structural anisotropy (please define! see next comment) could be a possible reason, amongst others(!), why the backscatter model does not fit the observations.

line 423-427: What do you mean with "structural anisotropy"? Do you mean the structural anisotropy of the microstructure (e.g. Leinss et al. "Modeling the evolution of the structural anisotropy of snow" The Cryosphere, 14, 51–75, 2020 https://doi.org/10.5194/tc-14-51-2020) or do you mean that horizontal layers with different density create a structural anisotropy of the snow pack (in the extreme case ice layers)? For such a layered snow pack I would expect a strongly angle-dependent backscatter dependency due to directional reflection at the layer-interfaces.

Temperature gradient seems to be relatively low, but (Montagnat et a. (2020) "On the Birth of Structural and Crystallographic Fabric Signals in Polar Snow: A Case Study From the EastGRIP Snowpack". Front. Earth Sci. 8:365. doi: https://doi.org/10.3389/feart.2020.00365) found for similar snow conditions a strong structural anisotropy of both, the c-axis and the microstructure. given the availability of VV and HH polarized acquisitions you could quickly check the copolar phase difference (Leinss, S., Löwe, et al.: Anisotropy of seasonal snow measured by polarimetric phase differences in radar time series, The Cryosphere, 10, 1771–1797, https://doi.org/10.5194/tc-10-1771-2016, 2016.) to estimate whether a strong structural anisotropy of the microstructure exists or whether you interpret the model-data discrepancy of the backscatter signal with incidence angle dependence through horizontal density variations as suggested by (Tan et al. 2017). In the latter case, I guess, without knowing the surface-roughness of each layer it seems impossible to model the precise incidence-angle dependent backscatter response of each layer. For discussing this effect, the work by Oh, Ulaby et al. could help: [Oh, Yisok, Kamal Sarabandi, and Fawwaz T. Ulaby. "An empirical model and an inversion technique for radar scattering from bare soil surfaces." IEEE transactions on Geoscience and Remote Sensing 30.2 (1992): 370-381.]

line 425: "angular gradients of the backscatter": Here and other places (especially also in the abstract) angular could refer to any direction or angle. Please be specific: I would rephrase that to "incidence angle dependence of the backscatter coefficient". Same for "angular difference".

line 484: What is LGA? Please introduce abbreviation (level glacier area).

line 484: Why did the authors exclude the BIA?

line 468: "coherence phase...is uniquely defined by the coherence magnitude" - That is only true for small penetration depth compared to the height of ambiguity which is given in your case, please clarify. See also Fischer et al. "Modeling Multifrequency Pol-InSAR Data From the Percolation Zone of the Greenland Ice Sheet" in IEEE Transactions on Geoscience and Remote Sensing, vol. 57, no. 4, pp. 1963-1976, April 2019, doi: https://doi.org/10.1109/TGRS.2018.2870301.

Line 470-480: You describe two models (Dall 2007, Zebker 2000) to estimate the penetration depth from the coherence but both models provide different results. Could you provide reasons why you have chosen the model of Dall 2007 and why you think that this model describes better the relation between coherence and penetration depth?

Line 543-544: Please specify the wavenumber instead of using large / small.

Line 544: "The scene T2018 ... shows the smallest gradient" I see more a point cloud than a clear linear relation in Fig. 6b. Anyway, you write "as expected according to theory." Could you specify which theory you are referring to? Eq. 16?

Line 633-644: These lines reads like a general introduction rather than a discussion of your results. I would remove these lines.

Line 656-663: Strongly shorten this section about the structural anisotropy to max. 1 sentence. You cannot start with "This can be explained.." to finish with "However, such layers are absent... excluding anisotropy as a main explanation"

Section 7: Please split this section into two sections, 7) Discussion and 8) conclusion. Line 689: I think here starts the conclusion.

I think it is worth mentioning in the conclusion that despite its simplicity the approach from Dall 2007 provided reasonable results.

Line 682-688: Please check references with cited content. They might have been flipped.

Line 702-708: I don't see a point of citing the work of Parrella here because the authors have excluded the structural anisotropy as a reason for the observed incidence-angle dependent scattering.

technical corrections:

line 64: "DEM" is already defined in line 33.

line 77/78: "a well equipped field station" I guess, this is the "ALE camp" to which you are refering later. I think this is a better place to introduce the abbreviation "ALE" or "ALE camp". Currently, mentioning Antarctic Logistics & Expeditions sounds a bit like company adverticement, but I guess the name is important to define the location of the ALE camp.

Fig. 2: Please check whether the symbol size of grain shapes (and also fonts) is appropriate for the final layout.

line 286: Here you introduce the abbreviation "IC2" which is sporadically used later. I think it's more consistent to define the appreviation at the very first location where IceSat-2 is introduced and use it then consistently. Or avoid the abbreviation if you prefer.

Equation 4 (and other equations, variables and mathematical expressions): Only variables should be italic; functions "exp" and descriptive indices like "tot" should be upright. Latex: P_\text{tot}\text{exp}...

line 334: 37% reads a bit random. I guess you mean "attenuated to e^{-1}".

line 485: level areas -> horizontal areas.

line 494: "high values indicate large scattering elements": ... or steep slopes / layover / strong topographic variations.

Line 502 - referring to Fig. S2: Could the authors extend the color scale to cover the full range of backscatter differences? Possibly, clip the range at the 1 and 99% percentil to define the colorscale.

Fig. 4: Could the authors add the LGA mask to Fig. 4 for orientation?

line 507: "left of the camp" - do you mean ALE camp? As you are referring to the map, could you also indicate the location of the camp in Fig. 4 and 5?

line 509: "The angular difference... of ...-13.3.. is characteristic for" -> "The strong incidence angle dependence of the backscatter signal ... is characteristic for ... " (The current formulation implies that the specific values of the BIA are characteristic for ... )

line 517: "has an also impact" -> "also has an impact"

Citation: https://doi.org/10.5194/tc-2020-380-RC2
- AC2: 'Reply on RC2', Helmut Rott, 13 Apr 2021
  
  We would like to thank the reviewer for his efforts in reviewing the manuscript and the valuable comments.The comment was uploaded in the form of a supplement.
  
  Citation: https://doi.org/10.5194/tc-2020-380-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (further review by editor and referees) (15 Apr 2021) by Etienne Berthier

AR by Helmut Rott on behalf of the Authors (10 Jun 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (11 Jun 2021) by Etienne Berthier

RR by Anonymous Referee #2 (24 Jun 2021)

Suggestions for revision or reasons for rejection

Review of revision of the manuscript tc-2020-380 "Penetration of interferometric radar signals in Antarctic snow" by H. Rott et al.

The authors thoroughly revised the manuscript. The revision is better balanced and provides a more objective interpretation of the numerous observations and results. The results are valuable for interpretation of radar penetration, coherence and backscatter response over ice sheets and glaciers. While the authors present promising results using the relatively simple Dall model to correct for radar penetration, they also address problems in simulating the backscatter response from stratified snow. Overall, I can recommend publication of the manuscript in TC. Below are some technical corrections which I encourage the authors to consider before submitting the final manuscript.

technical corrections:

line 146: What do you mean by "absolute radiometric calibration and terrain-corrected geocoding" ? Do you mean, the backscatter signal was radiametrically terrain corrected? gamma_0 or sigma_0? Or was it only geometrically terrain corrected (orthorectified) as written above ("geocoded rasters of ... SAR amplitude")

Figure 2: Comparing the colorbar for grain size with the color-coded column "GS" appears as different color scales were used. Please correct.

line 306: "Normalizing the coherence by the interferometric phase of the volume surface": Could you provide an equation make this sentence more comprehensible? Do you divide two complex numbers here?

line 310: "As according to this relation [Eq. 10] the coherence phase, <gamma, is uniquely defined by the coherence magnitude": Eq. 10 does not illustrate that the coherence phase is uniquely defined by the coherence magnitude.

line 397: "total normalized coherence": could you provide a reference to an equation which defines the "total normalized coherence"?

line 399: "excluding (...) and slopes smaller than 5° inclination": I guess you mean larger than 5°?

line 422: "Large angular gradients" - See original comment by Referee #2: "angular gradients of the backscatter" Here and other places (...) angular could refer to any direction or angle. Please be specific: I would rephrase that to "incidence angle dependence".
Same for "Angular difference" in Fig. S2. I suggest to delete "angular" in the caption as the different incidence angles are already given in parenthesis.

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RR by Anonymous Referee #1 (06 Jul 2021)

Suggestions for revision or reasons for rejection

The authors should be commended for making this paper more readable for a broader audience. The structure of this revised manuscript is much improved, with clearer separation of the theory and assumptions that underpin the method and the application of it. The paper appears technically correct but would benefit from further clarifications to aid the reader and to ensure reproducibility. It would also be better to try to reduce the number of acronyms (perhaps in addition make a table in the appendix): it is jarring to try to recall what these are (particularly if they are used infrequently) and this interrupts the flow. Specific comments are:
Line 60: define SP-InSAR as single pass InSAR.
Line 127. It would really help to add a sentence here indicating why both the TDMgl and tiles are used in this study.
Line 140: ‘geocoded rasters of the height error’ – is this the Height Error Map from line 150 and comes directly from ITP?
Line 168: It would really help to add a sentence here to indicate IceSat / IceSat2 data are used to assess the temporal stability of the surface elevation and REMA is used to assess elevation bias because of its spatial coverage.
Line 214: ‘At lower depth equi-temperature metamorphism takes over as dominant process for grain growth’. There are few measurements deeper than 2m and of these the grain type isn’t showing strong evidence for equitemperature metamorphism: these crystal types are also prolific higher in the pack which is dominated by temperature gradient metamorphism.
Line 215: ‘Estimates on accumulation rates are based on stake measurements (Rivera et al., 2014), the ice core between pit 2 and pit 3 (Hoffmann et al., 2020), and the summer melt crust in pit 5’. These accumulation rates and a brief description of how they were derived need to be presented, particularly as the discussion and even the abstract links the elevation bias to accumulation rates.
Figure 2: Colors in grain size legend still don’t match the colors in the figure. E.g. on my computer smallest grain size in legend is #dde7f3, next smallest is #96b4f8. Lightest grain size in pit 5 is #b5bbde. I have not compared the hardness grayscale but would be hard-pushed to identify which category each would belong to. Would recommend switching hardness to different filling techniques (hatching). Please align the symbols used for crystal types with the International Classification for Seasonal Snow on the Ground – the symbol for ‘faceted and rounded particles, closely packed’ is not part of the classification and also is mismatched with the figure itself, which shows a closed form. You can download and use the fonts from https://cryosphericsciences.org/publications/snow-classification/.
Line 247: ‘The total snow mass down to 2.04 m amounts to 0.80 m w.e’. From Table 2, mean density for P4 is 403.75 kg / m3. For a depth of 2.04 m, this equates to a water equivalent of 2.04*403.75/1000 m = 0.82 m. Does 0.80 m w.e. refer to just P4 or a mean of more than one pit?
Line 311. Add in Dall 2007 reference again to show equation 11 is derived there not here.
Line 338. ‘For the elevation bias estimate derived from the volumetric coherence we use the notation hbInv’. Is this the same as hb in equation 11? If so, hbInv should be in equation 11. My understanding is that hbinv is expected to be the same as hb provided that hs is itself error-free. Unfortunately it is not because of potential temporal changes and the correction of REMA to CryoSat2 with its penetration correction and the following sections look at this. It would be helpful to provide some similar indication (or a correction of my understanding) to the reader to set the scene for sections 4.1.2 and 4.1.3.
Line 340 ‘On these surfaces the raw TDM DEMs show vertical offsets up to a few metres because for these data an absolute height calibration is not performed routinely’. Add reference into section 2.1 as this is presumably the 0.7 to 3m height error on line 158. If it is not, please add in an appropriate reference and explanation.
Line 377: ‘theTDMgl’ -> ‘the TDMgl’
Line 380: ‘Subtracting the TDMgl offset of -6.76 m yields a dh value of -6.67 m due to signal penetration’ would benefit from a rephrase: subtraction of a negative gives a positive.
Line 407. Supplementary figures are out of order. S4 is referenced before S1.
Figure 3 and all relevant figures (especially Figure 5, difference a vs b and c vs d). Please put incidence angles in captions for ease of reading (rather than having to look them up in Table 1. The importance of incidence angle isn’t evident before line 411, which is a long way past Table 1.
Line 417. This entire paragraph discusses supplementary figure S2. This is not supplementary and belongs in the same paper. Switching between files interrupts the flow of the paper.
Line 429. ‘The coherence image of 6 May 2013 (Fig. 4) shows the lowest coherence on glacier sections with large signal penetration’. Where is the signal penetration shown? The following two sentences then contradict this. Coherence for BIA (surface reflection, no penetration) is 0.79 whereas the low accumulation areas (penetration) has coherence of 0.85 to 0.9. Please highlight the features of interest much more clearly.
Lines 433-437 discuss the role of incidence angle in interpreting the relationship between coherence and backscatter, supported by Figure S3. Figure S3 belongs in the main body of the paper.
Line 438. ‘shows the expected variations in dependence of the height of ambiguity and incidence angle’. Please state here what the expected variations are as these are not obvious.
Line 485. ‘In order to check effects of the incidence angle the data derived from the T2013/14 and from the T2016/18 scenes are displayed separately’ should come earlier, before Figure 5.
Discussion. This isn’t a criticism but merely noticeable that the first three paragraphs of the discussion cover material presented in the Appendix and supplementary material. It’s a very interesting discussion but this gives the impression that the interesting material isn’t in the main body of the paper. I’m not sure what to suggest here – perhaps no change needed.
Line 555 – this paragraph appears without context. The structural anisotropy of Leinss et al is not the same as macroscale anisotropy (e.g. sastrugi) mentioned in the previous paragraph. This paragraph (if included) should be restructured to clarify the intended point.
Line 574 – ‘On the average’ -> ‘On average’
Line 580 – ‘Both the dh and hbInv values indicate deeper penetration for T2018 compared to 2016, amounting on the LGA to 0.42 m, respectively 0.68 m’ needs rephrasing. Does this mean e.g. ‘Both the dh and hbInv values indicate deeper penetration for T2018 compared to 2016, amounting to 0.42 m for dh and 0.68 m for hbInv over the LGA’?
Line 689. ‘mean penetration depth which is deduced from the mean elevation difference’ – how is this deduced? Does this mean that the mean penetration depth is assumed equal to the mean elevation difference?
Line 697. ‘smaller gain size’ -> ‘smaller grain size’
Figure A1. Please explain how these simulations were carried out. It is not clear how the backscatter from below a layer is derived from total surface backscatter. How deep was the simulated profile? What was the lower boundary condition? Sufficient information must be given for these simulations to be recreatable.
Figure A1. Not for this paper, but it would be really interesting to try to understand how the relative differences between the uniform volume approach and the layered scattering model approach translates to penetration bias. 3dB (line 704) is a large error. The error for pits 2-5 should be reported here rather than simply stating ‘The RT simulations are able to reproduce the observed total backscatter intensity at snow pit sites 2 to 5’.
Line 707. ‘Such an angular difference is typical for density-layered firn’ – does this refer to the 1.3 or 5.9 dB?

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ED: Publish subject to minor revisions (review by editor) (06 Jul 2021) by Etienne Berthier

AR by Helmut Rott on behalf of the Authors (09 Aug 2021) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (10 Aug 2021) by Etienne Berthier

AR by Helmut Rott on behalf of the Authors (16 Aug 2021) Author's response Manuscript

Short summary

We studied relations between interferometric synthetic aperture radar (InSAR) signals and snow–firn properties and tested procedures for correcting the penetration bias of InSAR digital elevation models at Union Glacier, Antarctica. The work is based on SAR data of the TanDEM-X mission, topographic data from optical sensors and field measurements. We provide new insights on radar signal interactions with polar snow and show the performance of penetration bias retrievals using InSAR coherence.