We thank the reviewer for the detailed feedback on our manuscript. We will address all the comments in detail during the revision. However, there are number of comments, especially on the S-1 processing, on which we disagree and which we address here to stimulate the open discussion.

1. Reviewer comment: “With all the processing done to the SAR imagery, it is impossible to assess the physical interactions of the SAR signal with the snowpack since the data has been smoothed multiple times and transformed radiometrically and geometrically. You have multi-looking (averaging 10x10 pixels), border noise removal, thermal noise removal, terrain correction and reprojection to the WGS84 projection. The multi-looking is especially concerning given the topographic complexity of the Alps. It is smoothing all the topographic information (which is crucial for snow retrievals) and emphasizing only the areas of significant snow (snow drifts) which is not representative of a 100m grid cell in the Alps. Then you add incidence angle correction using a DEM (30m) that is of lower resolution than the pixel spacing (10m) of the original image. A DEM with similar resolution should be used but also, the topographic information has already been altered from the multi-looking which is not representative of the local topography. Then there's temporal averaging (Eq.2) which alters the signal even further. Finally, outliers are replaced by a 12-day average to smooth the data once more.”

Author response: We strongly argue for the opposite: Useful snow information can only be obtained if the processing of the S-1 data is adequate, and our processing is conforming the state-of-the-art. There are several steps involved in the S-1 data processing, but none of these steps involves ‘smoothing’:

• Border noise removal and thermal noise removal are very basic and standard procedures that are recommended by any literature source or handbook, and for any application that uses S-1 backscatter data.
• The data is corrected radiometrically for the local incidence angle impact, similar to the way gamma0 is calculated. This appropriately reduces the impact of the local incidence angle and therefore will better reveal the relationship between backscatter and snow depth. Note this is a rescaling rather than a smoothing operation.
• The data was geometrically corrected by range-Doppler terrain correction, which is also a standard processing step, especially in terrain with complex topography, that improves the geo-location of the radar measurements.
• We believe there is a misinterpretation of Eq. 2. This equation explains the bias-correction of the backscatter data by the rescaling of the mean and standard deviation. This is again not a smoothing but a rescaling step. We moreover strongly recommend such rescaling for any application that aims at combining measurements from different relative orbits of S-1.
• In summary, we are strongly convinced the above-mentioned processing steps are fully conform with the state-of-the-art.

The reviewer also mentions that the multi-looking to 100 m is especially concerning. We are surprised by this statement. The multi-looking effectively reduces the pixel spacing of the backscatter measurements from 10 m in the original S-1 data (which is below the ~20-m spatial resolution) to 100 m in the multi-looked data. The result is thus similar as if one would have an instrument that measures backscatter at a native pixel size of 100 m, but with reduced noise (e.g., speckle).

• If the 100-m scale is problematic to retrieve snow depth according to the reviewer, what is then the take on novel satellite mission concepts, such as dual-Ku band SAR, that propose resolutions up to 500 m?
• The multi-looking is not only applied to reduce speckle noise, but also to keep the computation time for the processing and the data storage feasible. Our intention is to perform a consistent processing also at the larger scale, including other mountain regions and the full S-1 archive. Such processing would no longer be feasible using the high-performance computer that we have access to at a further reduced pixel spacing.

1. Reviewer comment: “The errors obtained from the SAR retrievals (Figure 11) are most of the time larger than the precision of the reference data which is the model simulations. It is very difficult to determine that the correlations are statistically significant in this case and also looking at Figure 10, most of the comparison points are grouped around 0 which tends to falsely boost the correlation.”

Author response: Figure 11 does not show the accuracy of the model simulations, but the accuracy of the S-1 retrievals with respect to the in situ snow depth measurements. We did not show the validation of the model simulations in this study, in order to focus on the validation of the S-1 retrievals. Furthermore, the model simulations of OSHD are including the assimilation of in situ measurements, and can therefore not be independently validated using these same measurements. We are surprised that the reviewer questions the statistical significance of the time series correlations shown in Figure 11, which are mostly higher than 0.8 for sites reaching snow depths above 1 m. We agree that the inclusion of zero snow depths can slightly increase the correlations. Therefore, Figure 5 shows time series correlations (against model simulations) both with and without the exclusion of zero snow depths. Even though more data are clustered around low snow depths in Figure 10, the density plots clearly demonstrate the overall agreement between the S-1 retrievals and the in situ measurements also for the high snow depths, especially for the coarser 300 m and 1 km retrievals. 

Author responses below are in italic.

This paper builds on the work of Lievens et al., 2019 to extract snow depth from S-1 data in the Alps. As mentioned by the editor, this work is of high relevance to the snow community but also to many other research areas such as water management, tourism, climate change and biodiversity. I appreciate the work that is done here but in its current state, I cannot recommend this paper for publication since I feel there are too many unknowns and too much processing done on the S-1 imagery to be able to retrieve some sort of good quality snow information and give a proper assessment of the results shown here. This is reflected in my comments below.

Contrary to what has been stated by the authors in their response to the editor's comments, I am not skeptical of the relationship between the C-band signal and thick alpine snowpacks. I do question the physics of the approach used in this study and am concerned about the multiple layer of data smoothing in order to get good correlations with modelled data.

If the authors are willing to provide more information on the imagery processing and modify it to make it more physically accurate, I strongly believe this work has great value to the scientific community.

We would like to thank the reviewer for the detailed assessment of our work. We have responded earlier to a selection of the reviewer’s comments. In addition to that, a point-by-point reply is given below.

To address the reviewer’s main concern about the processing of the S-1, we have carried out a full re-processing of the S-1 data across the Alps with a revised methodology (see details below), without any significant change in the results or conclusions.

We however strongly disagree with the statement that the good correlations with modelled data are due to the multiple layer of data smoothing. The smoothing applied here is limited, as discussed below.

We are hopeful that the revised processing of the S-1 data and a more detailed discussion of the processing and algorithm steps (including some modifications, e.g. regarding the wet snow detection) adequately address the main concerns of the reviewer.

General Comments:

As mentioned above, I do agree with the authors that the cross-pol channel of S-1 can be sensitive to a thick snowpack but I disagree with the physical explanation of the authors. The physical interaction of the microwave signal with the snowpack is very complex and is not solely related to surface/volume scattering and single/double bounce. With snow layer thicknesses close or smaller than the wavelength, you have many interference and coherence effects in the signal. Recent work has shown that volume scattering and depolarization of the SAR signal comes mostly for the snow anisotropy (Leins et al., 2016) and the vertical/horizontal structuring of the snowpack at C-band. This can be achieved by a stratified snowpack horizontally or with snow grains that are structure vertically/horizontally through metamorphic processes. I would agree that with a thicker snowpack, chances are you will get more anisotropy but this is not shown with in situ measurements, temporal analysis or snowpack stratigraphic information.

We appreciate the reviewer’s comments on the physics of the signal. Although the mentioned work by Leinss et al. (2016) investigates only higher (X- and Ku-band) frequencies, we agree that the anisotropy of snow crystals and/or of clusters of crystals, as well as the snow stratigraphy, can play an important role. We will discuss this upon revision.

With all the processing done to the SAR imagery, it is impossible to assess the physical interactions of the SAR signal with the snowpack since the data has been smoothed multiple times and transformed radiometrically and geometrically. You have multi-looking (averaging 10x10 pixels), border noise removal, thermal noise removal, terrain correction and reprojection to the WGS84 projection. The multi-looking is especially concerning given the topographic complexity of the Alps. It is smoothing all the topographic information (which is crucial for snow retrievals) and emphasizing only the areas of significant snow (snow drifts) which is not representative of a 100m grid cell in the Alps. Then you add incidence angle correction using a DEM (30m) that is of lower resolution than the pixel spacing (10m) of the original image. A DEM with similar resolution should be used but also, the topographic information has already been altered from the multi-looking which is not representative of the local topography. Then there's temporal averaging (Eq.2) which alters the signal even further. Finally, outliers are replaced by a 12-day average to smooth the data once more.

We would argue for the contrary: a careful processing is a pre-requisite in order to assess the correspondence between the S-1 signal and snow depth. The processing steps included in our analysis (border noise removal, thermal noise removal, multi-looking, terrain correction and reprojection to a consistent grid) are all standard and necessary procedures, recommended by any manual or handbook on SAR processing. The multi-looking is arguably the only processing step that could be considered optional. However, this was included in order to (i) reduce the impact of radar speckle, (ii) reduce the processing time (note that more than 4000 S-1 images were processed), and (iii) reduce the data storage requirements. In this context, the multi-looking is an important step to keep the processing computationally feasible also for larger areas, not limited to the Alps. However, to address the reviewer’s comment about the correction with the DEM, we have re-processed the S-1 data over the Alps, by performing the range-Doppler terrain correction and terrain flattening at the 20 m S-1 resolution instead of at the multi-looked 100 m pixel spacing. We kept the original 30 m DEM (SRTM 1Sec HGT) because this is the standard suggested DEM for processing in the ESA SNAP toolbox and can also be applied in other regions (e.g., outside Europe, or where more detailed DEM information is lacking). However, the pixel sizes of the DEM and the S-1 data were now much more similar with the re-processing. Equation 2 is not performing temporal averaging as stated by the reviewer. It applies a bias correction (of the first two order moments, i.e., the mean and variance) to every individual backscatter observation, without averaging observations over time. The bias correction reduces the differences between observations from different orbits (e.g., caused by different incidence or azimuth angles) and we strongly recommend this step for any application that aims at combining information from different S-1 orbits. We have deactivated the outlier correction in the retrieval because we observed it was slightly interfering with the wet snow detection algorithm.

Further on the processing, I would avoid talking about sigma-nought when Eq. 1 converts the sigma-nought into a pseudo-gamma-nought multiplied by cos(40). I say pseudo here because the incidence angle used to convert sigma-nought is the 100m reprojected angle and not the gamma-nought values from the SAR imagery calibration.

At the time we processed the S-1 data, the calculation of gamma0 was not operational in the SNAP software version 7. In the revised processing, we appropriately calculated gamma0 using SNAP version 8, by first calibrating the backscatter observations to beta0 and subsequently applying terrain flattening. Hence, the analysis in the revised manuscript will be carried out using gamma0 and is thus more conform the state-of-the-art.

If we accept the processing chain of the SAR imagery, it is still unclear that what the correlations are showing is linked to the snow depth. The errors obtained from the SAR retrievals (Figure 11) are most of the time larger than the precision of the reference data which is the model simulations. It is very difficult to determine that the correlations are statistically significant in this case and also looking at Figure 10, most of the comparison points are grouped around 0 which tends to falsely boost the correlation.

We do not see any reason that supports not accepting the processing chain, especially considering the re-processing discussed above, which is fully compliant with the state-of-the-art. Figure 11 shows a comparison against in situ measurements as reference data (not model simulations). We are surprised that the reviewer questions the significance of the time series correlations in Figure 11, which are most of the time above 0.8 (for sites that feature snow depths thicker than a meter). We can provide an assessment of the significance along with the reported correlations in the revision. With respect to Figure 10, we agree that the abundance of low snow depths can impact the correlations. Therefore, Figure 5 shows time series correlations (against model simulations) both with and without the exclusion of zero snow depths. Even though more data are clustered around low snow depths in Figure 10, the density plots in our opinion still clearly demonstrate the overall agreement between the S-1 retrievals and the in situ measurements also for the high snow depths, especially for the coarser 300 m and 1 km retrievals.

Given that modelled data is often smoothed and often have difficulty capturing extreme snow conditions and that the SAR data has been smoothed many times and outliers replaced by temporal means, I can’t say I am surprised to see a good empirical relationship.

We disagree with this comment, as the S-1 processing does not include multiple smoothing steps as the reviewer states (see above). In our opinion, the strong relationship between the S-1 retrievals and the model simulations is encouraging, and is furthermore corroborated by the strong correspondence between the S-1 retrievals and in situ measurements.

Also, asking scientists to identify themselves in order to get access to the data used in this study does not comply with the open data policy.

We understand this comment. To share the snow data over the Alps, we have used the existing platform via which we also share the corresponding retrievals across the Northern Hemisphere mountains. Upon revision, we can provide the login details directly to access the ftp site anonymously.

Specific comments:

P.3L.5: I would disagree with the claim that an increase snow depth automatically causes an increase in volume scattering. If their is not sufficient anisotropy in the snowpack, there will not be any volume scattering in C-band. The theory will show that even if you increase the snow depth and keep all other snowpack parameters constant, you will not have a significant increase in volume scattering

We will better address the impact of snow microstructure in the revised manuscript. However, recent radiative transfer model simulations using Bic-DMRT have shown that cross-polarized backscatter at C-band can increase with an increase in SWE (or depth) while keeping other parameters (snow grain size, snow clustering) constant (personal communication with Prof. L. Tsang, University of Michigan).

P.3L.6: Again, this comment is highly dependent on the stratigraphy and anisotropy of the snowpack. This section needs to be supported by snowpit measurements of the studied area or referred to past work done in the area analyzing the snowpack properties.

The statements on P.3L.6 are general assumptions based on which the empirical change detection retrieval approach is built. We have not yet analyzed these assumptions using snowpit measurements as suggested by the reviewer, but this is foreseen in future research. However, Figures 3 and 4 (based on model simulations) support the statements that (i) an increase in snow depth generally increases (especially cross-pol) backscatter, that (ii) the snow scattering (in cross-pol) is not negligible compared to the ground scattering, and (iii) that ground surface properties remain relatively constant in time due to the insulating properties of snow, thus the main changes in backscatter over time relate to changes in the snowpack.

P.3L.7: This comment is most likely true for the studied area but again, no reference or field measurement is provided to support this claim.

Please refer to the response above.

P.3L.9: Again here, I strongly disagree with this claim. The microstructure, anisotropy changes and stratigraphy, especially in the bottom layers of the snowpack will most likely drive the changes in sigma0.

We will further investigate the impact of microstructure and stratigraphy in future research, based on tower-mounted radar measurements currently being collected in the Rocky Mountains, US. We will generalize the statement to “the main changes in σ0 over time can be related to changes of the snowpack”.

P.3L.30: Even though this is common processing of SAR imagery, this is considerably altering the SAR signal, considerably smoothing it and making it very difficult to link to any ground snow properties.

The alternative (i.e., not performing thermal noise removal, border noise removal, radiometric calibration, and terrain correction) would lead to inferior processing results, which we believe would be far less suitable to investigate the relationship between backscatter and snow depth. The multi-looking has been adjusted and is not impacting the terrain correction and terrain flattening in the re-processing. Please also refer to our responses above.

P.3L.32: Multi-looking (or block averaging here) is a good way to reduce speckle noise in flat terrain. Here though, the topography is very complex (as mentioned by the authors) and it is emphasizing on the geometric distortions and the areas of significant snow (snow drifts) which is often not representative of a 100m grid cell in alpine areas.

Please refer to our responses above.

P.4L.10: Using "local" incidence angle correction on a multi-looked image is not an accurate method. A DEM with similar resolution as the raw image should be used to correct for local incidence angle before multi-looking.

This has been addressed by the reprocessing to gamma0 with terrain correction and flattening being applied at the 20 m S-1 resolution.

P.4L.15: This relationship was developed for areas of flat terrain and is not representative of the studied area. Proper analysis of the backscattered signal as a function of local incidence angle needs to be conducted in alpine areas in order to find the proper normalization relationship. A before and after image should show that this is not normalizing the image properly. Also, this is exactly taking sigma-nought and converting it to gamma-nought and then multiplying it by cos(40).

This comment has been accounted for by processing to gamma0.

P.4Eq.2: Here again, temporal smoothing of the data. There's no way of linking the spatio-temporal snow properties of the original SAR imagery.

We disagree. Equation 2 is not performing temporal smoothing, but bias correction, which results in an improved S-1 processing quality and therefore benefits the analysis with respect to snow depth.

P.4L.27: Excluding March to July is very subjective here. First, it is removing a lot of snow properties variability which can occur in March. Anisotropy and stratigraphy is stronger in the later winter season. Second, with climate change, we know that wet snow is detected outside of this period.

In the revised version, we will limit our entire analysis (processing and retrieval evaluation) to the winter season until end of March, to avoid the strongest impacts of wet snow (from April onwards). We fully agree that wet snow can also impact the observations earlier than March. We will revise the wet snow detection in the retrieval algorithm, to not limit the detection only to the period from February onwards (as is currently the case).

P.4 L.30: This is not rigorous. Removing outliers is another method to smooth out the data and get better correlation with modelled data. But here they are not only removed, they are replaced by a smoothed average.

We have deactivated the outlier removal, because we observed it was slightly interfering with the wet snow detection. More specifically, the outlier removal caused some wet snow events to be undetected, because the backscatter had been modified by the outlier correction.  

P.5 Eq.5: Is A applied to the ratio or only the cross-pol channel?

A is applied only to the cross-pol channel, enhancing the sensitivity to snow depth which is primarily driven by the cross-pol observations.

P.6L.17: I appreciate this approach where the index varies in time but I feel like the threshold is still limiting. I would see a temporal analysis of the SAR signal through multiple years to try and identify the proper threshold.

We have tested a range of threshold values. The lower the threshold, the better wet snow impacts are reduced, however, at the expense of reducing the coverage. We identified a threshold of 1.25 (which may be revised to 1.5) to strike a balance between wet snow filtering and data coverage.

P.6L.25: Again, the February start is very subjective as wet snow conditions can be detected earlier and the September-November period is most likely to be the period where you have the highest backscatter and all the values that are 3dB below might be because of small surface moisture or percolating water which is not uncommon in Alpine snow.

In the revised version, we will activate the wet snow detection earlier (in January), and include a second wet snow detection mechanism. The latter will consist of (i) excluding backscatter observations (for any time step during the full snow season) that are a threshold (e.g., 2 dB) below the 10-percentile of backscatter observations during snow-free conditions (this approach is more similar than that proposed by Nagler et al., 2016), and (ii) excluding negative snow index values from January onwards. More specifically, approach (i) improves the detection of early wet snow, often in autumn, whereas (ii) mainly improves the wet snow detection in the valleys, where a sharp decrease in backscatter during snowmelt is often lacking. Furthermore, the wet snow will be provided along with the unmasked snow depth retrievals, allowing the user to choose whether or not to mask out wet snow, or to use another mask (e.g., derived from modeling or an alternative wet snow detection approach). In the 300-m and 1-km datasets, the wet snow will be provided as a fraction (0-1) of wet snow pixels, which allows a user to define the level of wet snow allowed. A first evaluation of this approach at the 1 km resolution shows for instance that a spatio-temporal correlation of 0.84 is obtained when no masking is applied. This correlation improves to 0.90 when eliminating pixels with a wet snow fraction larger than 0. Intermediate performances are found when applying fractions in-between.

Conversely as the reviewer hypothesizes, the September-November period is typically the period in time with the lowest S-1 backscatter values, especially in cross-pol (if not including wet snow conditions in spring). Earlier (in summer), vegetation often contributes to higher backscatter, whereas in mid-winter, a higher backscatter is caused by snow accumulation. Part of the lower backscatter values in September-November can also be explained by the potential freezing of the soil surface, and/or by early wet snow.

P.11L.7: There is no mention of layering and anisotropy which is most likely the main reason of signal backscattering of dry snowpacks.

We will include this in the revised version.

P.11L.11-13: These comparisons do not really apply to the current studies. As was mentioned by the authors in the response to the editor these studies were conducted in shallow snow conditions in tundra/taiga landscapes.

The Alps include areas with shallow snow for which the references to literature are relevant. The literature comparison also helps to indicate that (to our best knowledge) studies with cross-pol observations in deep snow are lacking.

P.11L.20: This is a strong assumption since in alpine regions you can have strong surface roughness that will depolarize your signal.

The ratio of cross- over co-polarized backscatter is considerably lower in areas with limited vegetation. Hence, this statement is supported by S-1 observations.

P.11L.33: This is normal since most of the volume scattering and depolarization will come from the forest cover. For this study, I would have masked out the forested areas because this adds unnecessary complexity to a study that is already complex. Masking the forested areas would allow to focus on the snow retrieval without getting confused in multiple empirical relationships and heavy data processing.

One could either mask out the forested regions, or stratify the performance based on forest cover. We here opted for the stratified performance assessment (see Figure 6), which is more complete. We do not consent with the assessment of ‘heavy’ data processing.

Author responses below are in italic.

The authors present an application of a change-detection algorithm to estimate SWE in the Alps using Sentinel-1 C-band SAR. They explore the effect of spatial resolution on their retrievals. This is an important and timely contribution, and should be of great interest to the community. The paper is well-written so I have very few minor comments. Instead, I’ll focus on a really key point which is that I think there is a great chance for readers to misunderstand the maturity level of the algorithm, based on how the paper is presented. This review is five related major comments that unpack this idea.

We are grateful for the assessment of our work by the reviewer. Please find below our response to the five posted comments.

Major Comments

First, I do not think that the paper adequately reflects the fact that we still do not understand why this method works, even at a basic level. The manuscript instead makes it sound clear that the mechanisms are understood: e.g. in the introduction, page 2, lines 32-page 3, line 2. Taking their points one by one: to their first point (page 2 line 33), no reference was given, and no reason why having lower ground backscatter would change sensitivity to depth; to their second point (page 2, line 33), Chang et al. 2014 do not make this point, that I could see. Readers will assume after reading the introduction that it is obvious why the C-band cross-pol is correlated with snow depth, which is not true. In fact, the authors of this study only introduce the idea that the “physical mechanisms that cause this increase are still uncertain” in the Results & Discussion section (page 10, line 13). Please, bring this critical point into the abstract, introduction and conclusion!

We fully agree that we need to better inform the reader about the current limitations in physical understanding of C-band sensitivity to snow, upfront in the paper. We will modify this in the abstract, introduction and conclusion of the revised version.

Regarding the statements on page 2, lines 32 to page 3, line 2: The first statement on page 2 line 33 (“surface scattering from the ground is significantly weaker in cross-polarization”) refers to the common understanding that cross-polarized backscatter is typically several dB lower than co-polarized backscatter. This is especially the case in regions with limited vegetation and for smoother surfaces (vegetation and surface roughness increase depolarization and thus the cross-polarized backscatter, which, however, will generally still remain lower than the co-polarized backscatter). It is also common understanding that in a logarithmic (dB) scale as used in the retrieval algorithm, an increase in scatter intensity (in linear scale) will have a relatively larger impact when the prior intensity is low; hence the statement that a lower ground backscatter can be beneficial for the sensitivity to snow.

Regarding the reference to Chang et al. (2014): They mention the following statements in their introduction that support our quote (i.e., “dry snow represents a dense medium of irregularly-shaped and clustered ice crystals that primarily causes volume scattering in cross-polarization”): “In snow, the ice particles are packed closely together”, “ice grains in snow do not scatter independently”, “shapes are irregular and there are clustering effects”, “In conventional scattering models, there is no cross-polarization in scattering when particles are spheres. In the dense media model, the electric dipole interactions of closely packed ice grains result in strong cross-polarization in the phase matrices”.

Second, I think it is critical to communicate more clearly throughout that this is an empirical algorithm with calibration parameters that require known SWE data over the domain. The word “empirical” needs to appear in the abstract, in my opinion. Please somehow get this idea into the introduction, abstract, and conclusion.

We agree and will modify the text accordingly.

Third, the authors need to point out that the algorithm only works well if you have accurate SWE data to calibrate against. Indeed, they need to just note explicitly that the accuracy of the approach they are using here is limited to the accuracy of their training data. I think this needs to be presented explicitly in the abstract and conclusions, to avoid reader misunderstanding.

The approach indeed requires reference data (snow depth) in order to estimate the scaling coefficient that translates the changes in backscatter into changes in snow depth. However, we would like to highlight that the approach works already reasonably well when using a single, constant (both in time and space) scaling coefficient. For instance, Lievens et al. (2019) apply a constant scaling factor across all mountain ranges in the Northern Hemisphere, which still leads to relatively accurate retrievals. Therefore, the need for accurate reference data is not considered to be critical. 

Figure 8 shows a positive (but overall limited) impact of refining the scaling coefficient, by allowing it to vary in space (but still not in time). Such refinement of the scaling coefficient may indeed require more accurate reference snow depth data, but again, this impact is limited.

Fourth, the authors should point out that in this study, they are calibrating here against very accurate model results. Here, they are applying the algorithm in this study over a domain where (in my opinion) the most accurate model results are available anywhere in the world. There is no other mountain range, to my knowledge, with the density of observations available in the Alps. Further, globally available model results in mountain ranges are inadequate for most applications, in terms of their spatial resolution and accuracy. See e.g. Mortimer et al. 2020. I think this needs to be mentioned in the conclusions.

We will mention the potential challenges to replicate our approach (with respect to refining the scaling coefficient based on model simulations) in other mountain ranges, due to the limitations in model simulations. But as mentioned above (and shown in Figure 8), the added value of the spatially varying scaling coefficient is not critical.

Fifth, the authors need to acknowledge explicitly that the first four points mean that you could not use this approach globally, calibrated to models, and achieve the kind of results shown here; this point almost certainly will be lost on readers of the abstract alone. This is a major issue with the manuscript that needs to be addressed in the abstract and conclusions.

The approach with constant scaling factor is applicable globally (in regions with sufficient snow accumulation) and has previously been applied over the Northern Hemisphere (Lievens et al., 2019). We here show that only a slight reduction in performance is to be expected in the case that insufficient or inaccurate reference data would preclude a (spatial) refinement of the scaling coefficient. We will mention this implication in the revised version.

I hope the authors do not misinterpret any of these comments: they have done an amazing job uncovering this important new dataset. It has very important possible applications. Reworking the way the paper is presented should help the community get on board with this new dataset as quickly as possible.

Thank you for this supportive comment.

Mortimer, C., Mudryk, L., Derksen, C., Luojus, K., Brown, R., Kelly, R., & Tedesco, M. (2020). Evaluation of long-term Northern Hemisphere snow water equivalent products. The Cryosphere, 14(5), 1579–1594. https://doi.org/10.5194/tc-14-1579-2020

Lievens, H., Demuzere, M., Marshall, H.-P., Reichle, R. H., Brucker, L., Branger, I., de Rosnay, P., Dumont, M., Girotto, M., Immerzeel, W. W., Jonas, T., Kim, E. J., Koch, I., Marty, C., Saloranta, T., Schöber J., and De Lannoy, G. J. M., Snow depth variability in the Northern Hemisphere mountains observed from space, Nature Communications, 10, 4629, 2019.

We thank Helmut Rott for providing important feedback and comments to our manuscript. Please find below an initial response to the comments, which we’ll further address during the revision.

Comment: “The objective of the work, promoting the wider use of operational SAR data for snow monitoring, is a very relevant undertaking, in particular as the spatially detailed monitoring of snow depth and mass in areas of complex topography is an open issue. However, as mentioned by the reviewers, the physical basis of the presented method is not clear. On page 5, line 17, the authors explain that the method is based “on the physical principle of an increase in snow volume scattering with increase in snow depth”. I am not aware of any physical principle relating the radar backscatter intensity of a snow-ground medium to snow depth. As thoroughly proven by theory and experimental studies, the magnitude of the volume scattering signal of snow is largely determined by the size, shape and distribution of the scattering elements and their relations to the radar wavelength (e.g. Tsang et al., 2013). For backscatter modelling the description of the complex microstructure of snow as a sintered medium is critical (Löwe and Picard, 2015). The diversity of snow microstructure is probably a reason for the large spread of the scaling factor for converting the snow index to snow depth, changing according to Figure 7 by about one order of magnitude from low to high elevations.”

Authors response: We agree that the exact physical principles of snow scattering at C-band are not yet fully understood and require further investigation. Therefore, this work focuses on the use of observations in an empirical change detection retrieval approach. The snow microstructure, i.e., the size, shape and distribution of the snow crystals, can indeed have an important impact on the scattering. But, also the amount of snow crystals, which is related to snow depth, will have an important effect. The physical principle noted in the manuscript refers to the fact that more snow crystals (a thicker snowpack) will generally increase the scattering (especially in cross-pol and subject to a dry state of the snow, as demonstrated in Figs. 3-5). We will better articulate this in the text upon revision. Furthermore, other structural snowpack properties could have an effect especially at lower frequencies (e.g., C-band compared to Ku-band), such as the anisotropy of individual crystals, or more likely of clusters of crystals, and the stratigraphy (as rightly pointed out by reviewer 1). Identifying the impact of these snow properties is recommended for future investigation. In this context, Prof. L. Tsang (University of Michigan) is currently investigating the radiative transfer modeling of snow at C-band, accounting for the effects of snow layering and clustering. Preliminary results are supporting the Sentinel-1 observations, by showing an increase in backscatter of a few (2-3) dB with an increase in SWE to 300 mm, primarily in cross-polarization (personal communication with Prof. L. Tsang).  

Overall, the spatially dynamic scaling factor has a limited impact on the snow depth retrievals (i.e. only a small improvement; see Fig. 8). Between elevations of ~1000 m and 3000 m, the scaling factor varies only moderately, from ~0.9 to ~1.2. The strong variation at low elevations (<1000 m) is driven by the slight overestimation of shallow snow depths in the valleys. Note that a large difference in scaling factor will still only cause a small absolute difference in the case of a low value that is being rescaled. The strong decrease for high elevations (>3000 m) was found to be caused mostly by glaciated areas, where the radar signal shows a strong increase during winter that is likely not only caused by changes in the snowpack. We will exclude glaciated areas for the calculation of the scaling factor during the revision to improve this aspect. Differences in snow microstructure with elevation can play a role, but addressing these impacts will be the subject of future investigation (including tower measurements, radiative transfer modeling and snow microstructure measurements).    

Comment: “In order to learn about the impact of physical snow properties and microstructure on the backscatter signals and to test the retrieval algorithm, we tried to retrace the processing steps described in the manuscript, based on Sentinel-1 data and snow measurements in an Alpine test site. However, we could not proceed due to missing information, in particular regarding the procedures related to equations 2 and 5. Equation 2 describes the bias correction for sigma-0 of a particular orbit and date in which the average sigma-0 from different orbits and the temporal mean backscatter of the individual orbit are decisive factors. It is not specified to which time span the temporal mean refers. Regarding the calculation of the statistical numbers, I assume backscatter intensity values in linear scale are used, as required for statistical analysis.”

Authors response: For Equation 2, the mean and standard deviation of the backscatter are derived from the full time series (Aug 2017 through July 2019; excluding the months of March to June). The bias correction is performed in dB scale, as this scale is also used in the change detection algorithm. Note that the distribution function of backscatter in linear scale has long tails, which could otherwise have a confounding impact on the bias correction. We strongly appreciate your effort to investigate the observed increase in backscatter with snow accumulation. We are open to provide support or exchange ideas, and would encourage to investigate this backscatter increase also in a spatial context (not only for one or few in situ sites).

Comment: “Equation 5 describes the relation (CR ratio) between cross-and co-polarized sigma-0. The cross-polarized ratio in dB (logarithmic scale) is multiplied by a constant factor (A = 2.0) in linear scale. This would yield a very low value for the first term on the right hand side of Eq. 5 and thus result in a large difference between the cross- and co-polarized terms. Possibly there is a syntax error, and A should be specified in logarithmic scale, yielding a shift by 3 dB for the first term. However, it is unclear why a constant value of 3 dB should be added to the sigma-0-VH values, in particular as subsequently the temporal changes in the snow index are clipped or reduced in order to avoid impacts of large changes in CR.”

Authors response: We are aware that the cross-ratio (VH/VV) originally used in Lievens et al. (2019) was somewhat more intuitive than the rescaled version presented in this manuscript. However, we observed that the rescaled version improved the performance. Equation 5 is applied in dB scale. Therefore, multiplying the VH component by 2 indeed causes low values. However, this is not a problem within the empirical change detection algorithm. To the contrary, the factor 2 enhances the temporal variability in the VH component, which results in a better retrieval performance. 

Comment: “”Essential components of the retrieval algorithm are the bias corrections and the spatial and temporal averaging procedures. The assumptions and rules related to these processing steps are hard to capture. In order to improve the traceability it would be helpful getting a concise account on these procedures in tabular and graphic form. This should cover the technical or physical constraints for subdividing the observations into true and biased values, as well as the various temporal and spatial merging and averaging procedures applied in the subsequent processing steps.”

Authors response: Bias correction methods are standard procedure in many remote sensing, modeling and data assimilation applications. We here perform a simple bias correction of the first two order moments (mean and variance) of the backscatter data between different Sentinel-1 relative orbits. The only temporal averaging that is performed is the calculation of weekly average backscatter. The spatial aggregation is performed by linearly averaging the snow depth retrievals from 100 m to 300 m and to 1 km. The prior spatial aggregation of the backscatter data (from ~20 m to 100 m) during the preprocessing is appropriately performed in linear scale.

Further comments:

Comment: “Page 5, line 18: Hard to understand why the Sentinel-1 data are used for retrieving the snow depth but not for detecting the snow extent. If a reliable signal on snow depth is available, this implicitly should account for the presence of snow. Besides, the selected optical snow extent product has 1 km resolution, not suitable for capturing the complex pattern induced by topography.”

Authors response: Early snow cover can be relatively shallow or wet (decreasing the backscatter in this case) and the difference with the snow-off backscatter can therefore be ambiguous. Gradually, during the snow accumulation, we observe a corresponding backscatter increase primarily in cross-pol, offering a mechanism for snow depth retrieval. The Sentinel-1 snow depth retrieval algorithm relies on a time series change detection and is not an algorithm for spatial snow-on or snow-off detection. Snow cover observations at the corresponding 100 m resolution would indeed be better suited for input use in the retrieval algorithm. However, the currently existing data at 100 m (or finer) have temporal gaps due to cloud cover, or include a gap-filling over relatively long time periods with no observations, increasing the uncertainty. The 1 km IMS snow cover data merges different input data sources with quality control procedures to ensure daily coverage. In the future, the use of higher-resolution snow cover data is expected to improve the retrieval performance.   

Comment: “Figure 2 (page 8): According to this figure most of the stations in the Eastern Alps of Austria are either in valleys or in lowlands, including many sites within inhabited areas. This impairs the comparison in Alpine terrain.”

Authors response: We agree. Likely, an improved performance would be obtained when relatively more measurement sites would be located at higher elevations with deeper snow. A comparison with other grid-scale reference data (in addition to the model simulations used here), such as lidar snow depth retrievals, is foreseen in the near future.

Comment: “Figure 4 (page 12): In the plots (a, b, c, d) different scales are used for the y-axis in respect to sigma-0. For example, the scaling factor (delta y/ delta sigma-0 VH) in plot (b) is 0.6 times the factor used in plot (a), adjusted in order to achieve good visual agreement between sigma-0 and snow depth in both cases. Actually there is a major difference in the VH backscatter response to snow depth between both sites, though being located at similar altitude.”

Authors response: The scale bars have been adjusted to enhance the visual interpretation. We will clearly mention this in the revised version. Note that the input used in the change detection method is a combination of the different polarizations. Therefore, it is not advised to directly relate the dynamic range in backscatter for one polarization with the dynamic range in snow depth. Fig. 8 shows that, in general, the spatial distribution in snow depth agrees well between Sentinel-1 retrievals and model simulations. 

Comment: “Sections 3.2 and 3.3, correlations: There are two issues calling for further explanations. (i) It is mentioned repeatedly that spatio-temporal correlations were computed. This implies multiple correlation in which one dependent variable is related to two predictive variables representing temporal, respectively spatial, components. Details on the individual relations and their weights regarding the combined prediction of the dependent variable should be provided. (ii) In particular for snow depth larger than 2 m the correlation with in situ snow depth (shown in Fig. 11) is very high whereas the density plots in Fig. 10 show large scatter and a substantial bias. Possibly the correlations shown in Fig. 10 are based on a different sample?”

Authors response: Our intention is to show to the fullest possible extent the correspondence between the retrievals and in situ measurements. Therefore, we made density plots that include all available measurements and retrievals. Note that the temporal correlations between retrievals and measurements are separated from the spatial analysis in Fig. 11. To further clarify, this figure panel (a) shows the average and standard deviation of the time series correlation coefficients obtained for all individual sites. We agree that for some sites, underestimation occurs especially for large snow depths (shown in Fig. 11b). This could be caused by limitations of the algorithm, or by (undetected) wet snow, or spatial representativeness differences.  

References:

Löwe, H., and Picard, G.: Microwave scattering coefficient of snow in MEMLS and DMRT-ML revisited: the relevance of sticky hard spheres and tomography-based estimates of stickiness, The Cryosphere, 9, 2101–2117, 2015.

Tsang, L., K. H. Ding, S. Huang, and Xu, X: Electromagnetic computation in scattering of electromagnetic waves by random rough surface and dense media in microwave remote sensing of land surfaces, Proc. IEEE, 101 (2), 255–279, 2013.