the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 May 2025
Influence of snowpack properties and local incidence angle on SAR signal depolarization: a mathematical model for high-resolution snow depth estimation
Abstract. Recently, Dual-Polarimetric Synthetic Aperture Radar (SAR) has been shown to be effective for large-scale snow cover monitoring, but it faces significant challenges when applied to finer resolutions, which are crucial for applications such as avalanche forecasting. In this study, we propose a novel mathematical model to retrieve snow properties from Sentinel-1 SAR data, leveraging variations in the Dual-Polarimetric Radar Vegetation Index (DpRVIc). We introduce the Snow Index SAR (SIsar), which quantifies variations in signal depolarization occurring within the snowpack. Our study, conducted in the Central Italian Alps, reveals a strong correlation between the SIsar index and the snowpack height, enabling accurate snow depth estimation. We also demonstrate the significant impact of the local incidence angle on signal depolarization during the accumulation season. Based on this, we derive a mathematical correction for the incidence angle, whose inclusion in the model reduces snow depth estimation errors by approximately 39 %. The model validation conducted in Tromso, Norway, confirms its applicability beyond the calibration area, with a root mean squared error (RMSE) of 30.7 cm and a mean absolute error (MAE) of 24.3 cm. These findings enhance our understanding of dual-polarimetric Sentinel-1 SAR data sensitivity for high-resolution snow monitoring, providing valuable insights for avalanche forecasting and hydrological applications.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-2160', Jonas-Frederik Jans, 20 Jun 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2160/egusphere-2025-2160-RC1-supplement.pdfCitation: https://doi.org/
10.5194/egusphere-2025-2160-RC1 - AC1: 'Reply on RC1', Alberto Mariani, 01 Jul 2025
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RC2: 'Comment on egusphere-2025-2160', Carlo Marin, 28 Jul 2025
This paper presents a novel approach to high-resolution snow depth monitoring by introducing the Snow Index SAR (SIsar), derived from dual-polarimetric Sentinel-1 data. The SIsar is defined as the difference between the Dual Polarimetric Radar Vegetation Index (DpRVIc) computed under snow-covered and average snow-free conditions. The study effectively demonstrates a correlation between SIsar and key snowpack variables, notably snowpack height and snow water equivalent. A critical finding and significant contribution of this work is the identification and subsequent correction for the influence of the LIA on the SIsar index, which improves snow depth estimations.
While the results are indeed promising and the methodology for LIA compensation shows great potential, the work, while novel in its application to Sentinel-1, resembles a substantial body of research conducted in the 1990s on C-band radar signatures of snow. Specifically, the seminal works by Kendra, Sarabandi, Ulaby, Strozzi, Wiesmann, and Mätzler (among the others) are directly relevant. These earlier studies explored C-band data collection under varying incidence angles and snow conditions, alongside the rigorous theoretical modeling of scattering mechanisms. The absence of these foundational references, and a more comprehensive literature review in general, is a significant oversight and detracts from the paper academic rigor. I strongly recommend the authors consult the (extensive) literature to provide proper context and build upon established and robust knowledge. It is highly recommended that the authors are revisiting and applying similar state of the art investigative principles for the most contemporary Sentinel-1 data. This would provide a much stronger theoretical foundation for the proposed SIsar index.
A fundamental question arises regarding the underlying electromagnetic justification of the proposed SIsar index. The paper suggests that SIsar is sensitive to snowpack properties, implying that the DpRVIc index effectively discriminates between volume and surface scattering through its relationship with VV and VH intensities and its capacity to describe depolarization (L68). However, this assertion requires further verification. Volume scattering is not the sole mechanism for depolarization; for instance, double-bounce effects, prevalent in very rough alpine terrain and due to strong individual scatterers, also may significantly depolarize the radar signal. The rationale for subtracting the summer mean DpRVIc from the snow-covered DpRVIc needs clearer justification. In alpine environments, surface scattering is a dominant factor, and its variability during summer, driven by soil moisture fluctuations, contrasts with its near-constant state in potentially frozen, high-altitude terrain during snow accumulation. Given this, it is difficult to see how this subtraction effectively isolates the scattering attributable solely to the snowpack. In this context, it is challenging to conceptualize how the specific proposed relationship between polarimetric intensities effectively discriminates between the different scattering mechanisms (surface and volume), particularly considering the observation (as highlighted in the response to Reviewer 1) that snow-free VV (across all LIAs) and VH (for LIAs from 0-25 and 70-90) backscattering are consistently higher than snow-covered backscattering, similar to findings by Strozzi et al. (1997). This indicates that the influence of snow volume scattering might be obscured by the prevailing ground contribution, consequently hindering the ability to derive meaningful insights into snow properties.
Despite these critical conceptual questions surrounding the method construction, the presented results are fairly impressive, much like those of the original Lievens et al. (2019) and following algorithms. To foster transparency and facilitate community understanding, I strongly recommend that the authors present the individual behaviors of the VV and VH signals in their paper (mean and std if more than one pixel is used and example also with only one pixel to see the impact of the speckle noise), allowing for direct comparison with the findings of Kendra et al 1998 and Strozzi et al, 1997, alongside the behavior of the DpRVIc index. Following the rationale and addressing the primary doubts raised in both Strozzi et al. (1997) and Kendra et al. (1998), I suggest that the calibration test sites should be as homogeneous as possible and thoroughly characterized. This means ensuring: uniform land cover, minimal presence of large scatterers (e.g., large rocks or boulders), absence of vegetation, consistent aspect angles, and comprehensive insights into snow conditions. If diverse "object classes" are necessary for the study, they should be clearly defined and analyzed separately, with distinct plots presented for each, similar to the approach adopted by Strozzi et al. (1997). This will provide clear evidence that varying snow depths produce significantly different backscattering responses in SIsar (even if the surface scattering change). Moreover, adopting such rigorous site selection and characterization will significantly enhance the scientific value of your work, providing critical elements for future research even in the absence of a definitive electromagnetic explanation.
Detail comments:
The current title seems a bit too generic. I suggest incorporating your finding of a quadratic relationship between the SIsar index and LIA directly into the title (specifying what a mathematical model is). This would immediately highlight a significant contribution of your work.
L35: From a scientific standpoint, the initial question revolved around whether microwave can effectively be employed to extract pertinent information from snow. The selection of SAR in this context is primarily driven by its inherent capability to provide the requisite spatial resolution for detailed analysis especially in mountain areas.
L38: for SAR signals interactions with snow please read the fundamentals literature and books from Ulaby, Mätzler, Picard, Löwe, Tsang and many others. The dielectric constant, which is the real part of the permittivity is only one small ingredient. I suggest to read the review from Mätzler “Applications of the interaction of microwaves with the natural snow cover” (written in 1989!) to better shape the introduction.
L47: this seems not be true. See Strozzi et al, 1997.
L68: While I am not a polarimetry expert, I question whether volume scattering is the exclusive source of depolarization, as individual scatterers or very rough surfaces can also induce polarization rotation.
Study area: The land cover and soil type require characterization. Which DEM was utilized?
Snowpack modeling: To ensure clarity and adhere to established standards, I suggest adopting the symbols from Appendix D of The International Classification for Seasonal Snow on the Ground. For instance, E is typically used for grain size, and ρ for the density. Presently, ρHS might be confused with SWE.
L166: Regarding the measurement, could you specify whether the units are in percent by volume or millimeters? It is also worth considering that averaging across the entire snowpack might introduce inaccuracies, given that microwave signal attenuation, particularly in the presence of significant wet superficial layer that can limit the penetration depth.
L170: did you use the “projected LIA” from SNAP?
L174: Could you please explain the rationale for using the refined Lee filter?
L175: Given the S1 SAR sensor native resolution of 5m x 20m and the subsequent application of spatial filtering, a final resolution of 10m appears optimistic. A resolution closer to 20m seems more analytically consistent with these parameters.
Eq 1 and Eq 2: can you better justify why you choose this index and why you made the difference between the indexes? What does it change if you change the reference? Would it be more appropriate to select as reference the initial backscattering after a significant accumulation, accounting for soil insulation that will persist for all the season long (if no permafrost is present)?
It would be beneficial to understand why the aspect angle i.e., the angle between the sensor flight direction and the surfaces orientation, was not considered into the analysis. This raises the question of whether the surface and snow are being implicitly assumed as isotropic mediums
L204: It is important to carefully review the symbols used here to ensure they are consistent across the entire paper.
L206: I am seeking further clarification regarding the methodology. Specifically, the justification for integrating the Random Forest algorithm to find the most predominant features, with a Least Squares method later, needs more comprehensive explanation (at least to me in the present form). Can you do the same using only one method?
L235: It is important to note that snow distribution is highly preferential, influenced by both topography and meteorological conditions. This inherent variability is precisely why utilizing such high-resolution data is crucial for accurate analysis.
L297: just shadow.
Fig 2. Following the criteria outlined by Nagler and Rott 2000, the presence of layover is identified for LIA less than 17° and shadow regions for LIA greater than 78°. Ensuring consistency with these thresholds throughout the analysis is appreciated for better reading the plots. Additionally, please standardize the LIA classification scheme across all plots for coherence. Could you also provide comments on the source of the standard deviation and outliers, as raised in the general comments? Finally, it would be beneficial to discuss the influence of aspect angle and the different land cover types on the results.
Fig3. Could you please explain why, beyond an incidence angle of 60 degrees, the backscattering for a snow depth of 60 cm becomes higher in terms of SIsar?
Regarding Figures 5 and 6, were these HS measurements obtained manually?
L321: Could you elaborate on the statement that the snowpack contains a larger ice component (if I understood what a "snow mass inside a snowpack" is)? Specifically, how was it determined that this implies a higher concentration of grains and discontinuities? Furthermore, I am not entirely convinced that snow layers with varying relative permittivity alone can depolarize the signal; this would be an interesting hypothesis to demonstrate.
L322 and on. For a more pertinent comparison, I suggest referencing Kendra et al. (1998) and Strozzi et al. (1997), given their direct relevance, as opposed to broader X-band research.
L355: Given the likely significant disparity in scatterer size between vegetation and snow, I am not convinced that a direct or simple analogy between their scattering properties is entirely straightforward
Table 2: Could you please specify the total number of validation points
Fig 7: I am not certain I have fully understood the representation in this figure. It does not appear to align with the solutions of any radiative transfer equations commonly used for the snow problem that I am familiar with. Specifically, could you explain why the VV polarization appears unaffected by the presence of snow? Furthermore, the contribution of surface scattering, which could be dominant, seems to be unrepresented. Please refer to Figure 6 of the paper of Kendra et al, 1998 for a complete first order volume scattering mechanism representation for a snow layer.
L401: If the geographical aspect varies E-W (or W-E) while the slope remains constant, the LIA should remain the same.
J. R. Kendra, K. Sarabandi and F. T. Ulaby, "Radar measurements of snow: experiment and analysis," in IEEE Transactions on Geoscience and Remote Sensing, vol. 36, no. 3, pp. 864-879, May 1998, doi: 10.1109/36.673679.
T. Strozzi, A. Wiesmann and C. Mätzler, "Active microwave signatures of snow covers at 5.3 and 35 GHz," in Radio Science, vol. 32, no. 2, pp. 479-495, March-April 1997, doi: 10.1029/96RS03777
Citation: https://doi.org/10.5194/egusphere-2025-2160-RC2 - AC2: 'Reply on RC2', Alberto Mariani, 25 Aug 2025
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-2160', Jonas-Frederik Jans, 20 Jun 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2160/egusphere-2025-2160-RC1-supplement.pdf
- AC1: 'Reply on RC1', Alberto Mariani, 01 Jul 2025
-
RC2: 'Comment on egusphere-2025-2160', Carlo Marin, 28 Jul 2025
This paper presents a novel approach to high-resolution snow depth monitoring by introducing the Snow Index SAR (SIsar), derived from dual-polarimetric Sentinel-1 data. The SIsar is defined as the difference between the Dual Polarimetric Radar Vegetation Index (DpRVIc) computed under snow-covered and average snow-free conditions. The study effectively demonstrates a correlation between SIsar and key snowpack variables, notably snowpack height and snow water equivalent. A critical finding and significant contribution of this work is the identification and subsequent correction for the influence of the LIA on the SIsar index, which improves snow depth estimations.
While the results are indeed promising and the methodology for LIA compensation shows great potential, the work, while novel in its application to Sentinel-1, resembles a substantial body of research conducted in the 1990s on C-band radar signatures of snow. Specifically, the seminal works by Kendra, Sarabandi, Ulaby, Strozzi, Wiesmann, and Mätzler (among the others) are directly relevant. These earlier studies explored C-band data collection under varying incidence angles and snow conditions, alongside the rigorous theoretical modeling of scattering mechanisms. The absence of these foundational references, and a more comprehensive literature review in general, is a significant oversight and detracts from the paper academic rigor. I strongly recommend the authors consult the (extensive) literature to provide proper context and build upon established and robust knowledge. It is highly recommended that the authors are revisiting and applying similar state of the art investigative principles for the most contemporary Sentinel-1 data. This would provide a much stronger theoretical foundation for the proposed SIsar index.
A fundamental question arises regarding the underlying electromagnetic justification of the proposed SIsar index. The paper suggests that SIsar is sensitive to snowpack properties, implying that the DpRVIc index effectively discriminates between volume and surface scattering through its relationship with VV and VH intensities and its capacity to describe depolarization (L68). However, this assertion requires further verification. Volume scattering is not the sole mechanism for depolarization; for instance, double-bounce effects, prevalent in very rough alpine terrain and due to strong individual scatterers, also may significantly depolarize the radar signal. The rationale for subtracting the summer mean DpRVIc from the snow-covered DpRVIc needs clearer justification. In alpine environments, surface scattering is a dominant factor, and its variability during summer, driven by soil moisture fluctuations, contrasts with its near-constant state in potentially frozen, high-altitude terrain during snow accumulation. Given this, it is difficult to see how this subtraction effectively isolates the scattering attributable solely to the snowpack. In this context, it is challenging to conceptualize how the specific proposed relationship between polarimetric intensities effectively discriminates between the different scattering mechanisms (surface and volume), particularly considering the observation (as highlighted in the response to Reviewer 1) that snow-free VV (across all LIAs) and VH (for LIAs from 0-25 and 70-90) backscattering are consistently higher than snow-covered backscattering, similar to findings by Strozzi et al. (1997). This indicates that the influence of snow volume scattering might be obscured by the prevailing ground contribution, consequently hindering the ability to derive meaningful insights into snow properties.
Despite these critical conceptual questions surrounding the method construction, the presented results are fairly impressive, much like those of the original Lievens et al. (2019) and following algorithms. To foster transparency and facilitate community understanding, I strongly recommend that the authors present the individual behaviors of the VV and VH signals in their paper (mean and std if more than one pixel is used and example also with only one pixel to see the impact of the speckle noise), allowing for direct comparison with the findings of Kendra et al 1998 and Strozzi et al, 1997, alongside the behavior of the DpRVIc index. Following the rationale and addressing the primary doubts raised in both Strozzi et al. (1997) and Kendra et al. (1998), I suggest that the calibration test sites should be as homogeneous as possible and thoroughly characterized. This means ensuring: uniform land cover, minimal presence of large scatterers (e.g., large rocks or boulders), absence of vegetation, consistent aspect angles, and comprehensive insights into snow conditions. If diverse "object classes" are necessary for the study, they should be clearly defined and analyzed separately, with distinct plots presented for each, similar to the approach adopted by Strozzi et al. (1997). This will provide clear evidence that varying snow depths produce significantly different backscattering responses in SIsar (even if the surface scattering change). Moreover, adopting such rigorous site selection and characterization will significantly enhance the scientific value of your work, providing critical elements for future research even in the absence of a definitive electromagnetic explanation.
Detail comments:
The current title seems a bit too generic. I suggest incorporating your finding of a quadratic relationship between the SIsar index and LIA directly into the title (specifying what a mathematical model is). This would immediately highlight a significant contribution of your work.
L35: From a scientific standpoint, the initial question revolved around whether microwave can effectively be employed to extract pertinent information from snow. The selection of SAR in this context is primarily driven by its inherent capability to provide the requisite spatial resolution for detailed analysis especially in mountain areas.
L38: for SAR signals interactions with snow please read the fundamentals literature and books from Ulaby, Mätzler, Picard, Löwe, Tsang and many others. The dielectric constant, which is the real part of the permittivity is only one small ingredient. I suggest to read the review from Mätzler “Applications of the interaction of microwaves with the natural snow cover” (written in 1989!) to better shape the introduction.
L47: this seems not be true. See Strozzi et al, 1997.
L68: While I am not a polarimetry expert, I question whether volume scattering is the exclusive source of depolarization, as individual scatterers or very rough surfaces can also induce polarization rotation.
Study area: The land cover and soil type require characterization. Which DEM was utilized?
Snowpack modeling: To ensure clarity and adhere to established standards, I suggest adopting the symbols from Appendix D of The International Classification for Seasonal Snow on the Ground. For instance, E is typically used for grain size, and ρ for the density. Presently, ρHS might be confused with SWE.
L166: Regarding the measurement, could you specify whether the units are in percent by volume or millimeters? It is also worth considering that averaging across the entire snowpack might introduce inaccuracies, given that microwave signal attenuation, particularly in the presence of significant wet superficial layer that can limit the penetration depth.
L170: did you use the “projected LIA” from SNAP?
L174: Could you please explain the rationale for using the refined Lee filter?
L175: Given the S1 SAR sensor native resolution of 5m x 20m and the subsequent application of spatial filtering, a final resolution of 10m appears optimistic. A resolution closer to 20m seems more analytically consistent with these parameters.
Eq 1 and Eq 2: can you better justify why you choose this index and why you made the difference between the indexes? What does it change if you change the reference? Would it be more appropriate to select as reference the initial backscattering after a significant accumulation, accounting for soil insulation that will persist for all the season long (if no permafrost is present)?
It would be beneficial to understand why the aspect angle i.e., the angle between the sensor flight direction and the surfaces orientation, was not considered into the analysis. This raises the question of whether the surface and snow are being implicitly assumed as isotropic mediums
L204: It is important to carefully review the symbols used here to ensure they are consistent across the entire paper.
L206: I am seeking further clarification regarding the methodology. Specifically, the justification for integrating the Random Forest algorithm to find the most predominant features, with a Least Squares method later, needs more comprehensive explanation (at least to me in the present form). Can you do the same using only one method?
L235: It is important to note that snow distribution is highly preferential, influenced by both topography and meteorological conditions. This inherent variability is precisely why utilizing such high-resolution data is crucial for accurate analysis.
L297: just shadow.
Fig 2. Following the criteria outlined by Nagler and Rott 2000, the presence of layover is identified for LIA less than 17° and shadow regions for LIA greater than 78°. Ensuring consistency with these thresholds throughout the analysis is appreciated for better reading the plots. Additionally, please standardize the LIA classification scheme across all plots for coherence. Could you also provide comments on the source of the standard deviation and outliers, as raised in the general comments? Finally, it would be beneficial to discuss the influence of aspect angle and the different land cover types on the results.
Fig3. Could you please explain why, beyond an incidence angle of 60 degrees, the backscattering for a snow depth of 60 cm becomes higher in terms of SIsar?
Regarding Figures 5 and 6, were these HS measurements obtained manually?
L321: Could you elaborate on the statement that the snowpack contains a larger ice component (if I understood what a "snow mass inside a snowpack" is)? Specifically, how was it determined that this implies a higher concentration of grains and discontinuities? Furthermore, I am not entirely convinced that snow layers with varying relative permittivity alone can depolarize the signal; this would be an interesting hypothesis to demonstrate.
L322 and on. For a more pertinent comparison, I suggest referencing Kendra et al. (1998) and Strozzi et al. (1997), given their direct relevance, as opposed to broader X-band research.
L355: Given the likely significant disparity in scatterer size between vegetation and snow, I am not convinced that a direct or simple analogy between their scattering properties is entirely straightforward
Table 2: Could you please specify the total number of validation points
Fig 7: I am not certain I have fully understood the representation in this figure. It does not appear to align with the solutions of any radiative transfer equations commonly used for the snow problem that I am familiar with. Specifically, could you explain why the VV polarization appears unaffected by the presence of snow? Furthermore, the contribution of surface scattering, which could be dominant, seems to be unrepresented. Please refer to Figure 6 of the paper of Kendra et al, 1998 for a complete first order volume scattering mechanism representation for a snow layer.
L401: If the geographical aspect varies E-W (or W-E) while the slope remains constant, the LIA should remain the same.
J. R. Kendra, K. Sarabandi and F. T. Ulaby, "Radar measurements of snow: experiment and analysis," in IEEE Transactions on Geoscience and Remote Sensing, vol. 36, no. 3, pp. 864-879, May 1998, doi: 10.1109/36.673679.
T. Strozzi, A. Wiesmann and C. Mätzler, "Active microwave signatures of snow covers at 5.3 and 35 GHz," in Radio Science, vol. 32, no. 2, pp. 479-495, March-April 1997, doi: 10.1029/96RS03777
Citation: https://doi.org/10.5194/egusphere-2025-2160-RC2 - AC2: 'Reply on RC2', Alberto Mariani, 25 Aug 2025
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Alberto Mariani
Jacopo Borsotti
Franz Livio
Giacomo Villa
Martin Metzger
Fabiano Monti
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.