Dear authors,

The manuscript presents a novel method for simplifying a multi-layer snowpack to a simplified 2- or 3-layer snowpack, while preserving snow mass and backscatter, in order to

• improve the computational cost of the forward model, and
• reduce the mathematical complexity of the cost function used in the associated inverse problem of retrieving snow properties (primarily SWE) from remote sensing observations.

The method is applied to several sites with different environmental conditions reflected in the meteorological input data used. Otherwise, the study is based on simulations. The proposed method is compared with the complex multi-layered snowpack and other simpler methods used in previous studies. The manuscript is well written and concise and addresses a well-defined problem in snow remote sensing. However, the manuscript does not discuss how the proposed method would be used in retrieval problems. As this is the motivating problem for the study, such a discussion is necessary. In addition, I would like to see a more detailed description and/or discussion of some aspects of the paper (see specific comments below).

Specific Comments

1. Lines 35-38, end of paragraph “…, but can prove challenging for remote sensing applications.” Could you elaborate on some of these challenges?
2. Your proposed method is based on K-means clustering. Being a central part of the proposed method, could you add more detailed description of the method? (sections 2.4. and 3.1. of the manuscript).
3. The K-means clustering algorithm is known to converge to a local minimum, which is not necessarily a global one. Therefore, the results can depend on the chosen initial points of the cluster means. The initial points should be mentioned in the manuscript.
4. It would be interesting to see an example of the plane with the data points, initial mean points, and the converged clusters. If you don’t consider this figure informative, it does not have to appear in the manuscript, but perhaps you could produce it in the comments?
5. You are using a two-dimensional parameter space in the K-means clustering. Could you comment on the choice of the parameter space? Is there a reason to consider the extinction coefficient instead of both scattering and absorption coefficients in a three-dimensional parameter space?
6. In section 2.4. of the manuscript, you describe the K-means clustering and the equal thickness grouping in rather equal terms, although the proposed method uses the K-means clustering. If you find it appropriate, please consider reorganising the section so that the K-means is described first as the primary method, and the equal thickness grouping is described then as a secondary method that is used for comparison. In my opinion, this would make the section easier to read.
7. In section 2.4. of the manuscript, you describe the weighting of the more complex snowpack into the simplified layers. You use the thickness based weighting (h-weighting) for the equal thickness grouping and optical thickness based weighting (τ-weighting) for the 3- and 2-means clusters. Does this not make the comparison between the two clustering methods unfair?
8. The last paragraph of section 2.4. (lines 162-170) describes the problem of removing interfaces when merging layers. This is a very important and an interesting point. However, I found the paragraph somewhat difficult to read. If you agree, please consider reorganising the paragraph so that the problem is introduced first, and then the solution.
9. Paragraph on lines 221-226 discusses the case when K-means finds clusters of layers that are not connected. In the averaging of such layers, scattering and absorption properties of the layers are not the only things affecting, but also the (optical) depth of the layers in the snowpack. For example, if two layers with equal thickness and extinction coefficient are placed at the top and bottom of the snowpack respectively, their effect to the total backscatter is not the same. In such a case moving one of the layers either from top to bottom or from bottom to up might not make sense. Could you comment on this?
10. The proposed method is based on an idea of running a snow process model with a high number of layers. However, this can also be computationally challenging. Can you comment on how computationally demanding it is to run the snow process model compared to the radiative transfer model? How does the computational cost increase with increasing number of layers (e.g. is running a 4-layer simulation much less expensive than running a 40-layer simulation?)
11. Your proposed method merges the snow layers based on their microwave properties, whereas the snow process model merges them (when the maximum number of layers is reached) based on their physical properties. The latter preserves the physical properties of the snowpack, while in the former does not. In terms of the computational cost of the radiative transfer simulation and the complexity of the cost function, the same benefits are obtained by running a snow process model with the maximum number of layers set to three. How does the simulated backscatter from such a snow process model run compare with that simulated using your proposed method? Does your method have a clear advantage in terms of the backscatter when both options are compared with the 50-layer run?
12. How could your proposed method be applied to different snow retrieval problems?
    
    
    • Is it only suitable for retrieving SWE or can it also be used to retrieve other snow variables? When simplifying the snowpack, the averaging of the physical snow variables is done using extinction coefficient. Therefore, the effective values don’t have the same physical meaning. Does this limit the potential application of the proposed method?
    • In the Bayesian retrieval, the cost function is defined as the sum of the mismatch term (between the observed and the modelled microwave signature) and the prior term. Your proposed method affects both terms; the mismatch term through the forward model configuration (how many layers are assumed) and the prior term. Can you comment on the use of the proposed method in this case?
    • On the other hand, in the data assimilation approach (e.g. particle filter), your method seems to have a more straightforward application to simplify the snowpack before the radiative transfer simulation to save computation time in the radiative transfer simulation. However, this approach would require an ensemble of snow process model runs, which can be computationally expensive. Can you comment on the use of the proposed method in this case?

Technical Comments

1. Line 151: ”We investigated three different ways of averageing: …”. Only two are mentioned in the text.
2. Line 26-27: “More typically, observations are unavailable, so snowpack information must come from …”. “must” is perhaps too strong word?
3. Line 104: “The choice of the electromagnetic model does not influence the final result of this method, …”. This could be wrongly understood to mean that the used electromagnetic model does affect the simulated backscatter (the result) and through that, the conclusions of the manuscript. Could you use another expression?
4. Line 119: “where p_11= … and p_22 = … are defined from the phase function.” repeats line 116.
5. Line 121: Reference should be (Sihvola,1999)?
6. Lines 145,149,150,etc.: I don’t think symbols after text require parenthesis. E.g. “extinction coefficient (κ_e)” --> “extinction coefficient κ_e” and “layer thickness (h_i)”  --> “layer thickness h_i”.
7. Should section 3 of the manuscript be “Results and Discussions”?
8. Lines 176,177: The word “scattering” is used but is supposed to be “extinction”?
9. Suggestion: Consider using “h-weighting” and “τ-weighting” (instead of keD) for the two layer-averaging methods.
10. Line 190-191: “3-Kmeans-hi” can be slightly confusing. “K” stands for the number of clusters; would it make more sense to write “3-means”? Also, in my opinion separating the clustering and averaging methods could make the expression clearer. Suggestion: “3-means clustering with h-weighting.” Apply as you see fit.
11. Similarly, “3-equal-h_i” could be “3-equal-thickness” or “3-equal-h” omitting the subindex i as it is used to refer to the 50-layer snowpack. Using “3-equal-thickness” for clustering and “h-weighting” for the weighting could help to avoid confusion between the two. Apply as you see fit.
12. Lines 202,205: Same suggestion; consider changing “3-Kmeans-keD” to something along the lines “3-means clustering with τ-weighting” or “3-means clustering with τ-averaging”. Apply as you see fit.
13. Figure 3: Y label of the bottom figures should be “difference” as “bias” represents systematic or average difference. Same in figure caption.
14. Line 230: “Frequency analysis” has other meanings. Consider different expression.

In this study, the author analyzed the number of layers of snowpacks needed to retain the same radar signals as the measurements.

One question for this topic is whether the layer simplification was utilized directly in the snow process simulation (e.g., using Crocus) or it was solely utilized in the microwave simulation. A clarification may be needed in the abs.

Another point is that the authors did experiments for 11 sites globally, whereas only results from three sites were explicitly presented in Fig. 3-5. However, I may be more interested in knowing how snow differs in different sites and what is the key characteristic (wind slab, melting?) that results in the requirement for 2-3 snow layers.

The authors didn't clearly state whether they focus mainly on dry snow.

More detailed comments are as follows:

1. Lines 35-38: Actually, multiple layers provide a continuous, high-resolution temperature profile inside the snowpack, which benefits most to the accuracy of snow microstructure simulation. To retain snow mass, people don't need a fine-resolution snow process model. In addition, this kind of model has great potential to accurately simulate the snowmelt process, because the fine-resolution snow layers can have different snow temperatures, for the model to evaluate whether the melting point has met.

2. Line 40: In Pan et al. (2017), only two snow layers were retrieved. Therefore, it does not have the "large numbers of layers" problem mentioned in the lines 42–43 followed. This part needs a revision.

3. Lines 44-49: It is suggested to separate the retrieval studies that considered only one layer and two layers. The use of two layers had been a tradeoff between simulation accuracy and retrieval feasibility. It is ok that the authors think they should at least consider one more layer, i.e., to consider 3 layers in total. However, the following sentence sounds really strange in the current manuscript:

"This is why current retrievals typically employ a one or two-layer model (Saberi et al., 2021; Durand et al., 2024; Pan et al., 2017). However, neglecting stratigraphy by using a small number of layers model reduces the performance of the retrieval (Durand et al., 2011) because layering strongly influences the backscattering properties of snow (Rutter et al., 2016)."

Actually, the studies in Saberi et al., 2021 and Pan et al., 2017 have considered the snow stratigraphy in some sense.

Line 56: It is suggested to consider this reference:

Yu, Y., Pan, J., Shi, J., 2021. Evaluation of the effective microstructure parameter of the microwave emission model of layered snowpack for multiple-layer snow. Remote Sens. 13. https://doi.org/10.3390/rs13102012.

By retaining air-snow and snow-soil boundary reflectivities using the topmost and bottom-most snow density instead of the profile-average density, the idea of Yu et al. (2021) becomes an indirect supporter of your 3-layer configuration suggestion.

Line 56: The snow type in Pan et al. (2017) was taiga snow. It does not have a wind-slab layer.

Line 5: According to line 65, it is better to say, "2-3 layers" directly in the abs.

Line 88: Could you add more details for the wind-slab and basal vegetation consideration and state why they are important in your study?

Line 127: The use of "presented" is confusing here. Better say, could be different for different snow grain types, according to Picard et al., 2022.

Line 130: However, the key point and importance for evaluating using different frequencies is that one can use a single profile to simulate multiple frequencies correctly, despite different penetration depths.

Section 2.4: A K-means classification will not work well directly, because you usually will not be allowed to combine layers that are not adjacent. More details are needed here.

Line 153: To preserve mass and snow depth, one can also actually only tune the snow microstructure parameter, because any change you make will not go into the subsequent CROCUS simulation. The snow layer simplification for RT calculation was operated stand-alone.

Figure 2 shows two examples where the existence of surface wind slabs and intermediate melt-freeze crusts inside the snowpacks can be two reasons to suggest using 3 layers, respectively. Are the first and second rows for the same site?

Line 189: Which does the "keD method" refer to in the context of Section 2.4?

From Figure 2, did you compare the differences in efficiency between applying K-means grouping on extinction coefficients and on original snow physical parameters (SSA, density, etc.)?

Lines 195-196: The error increases with increasing snow depth and increasing SSA, too, as the snowpack evolves with time. From my experience, your results shown in Fig. 3 have not included the snowmelt period yet. Therefore, it should not be caused by warmer snow temperatures, at least solely. By the way, it could be better to add subplots showing snow depth and air temperature time series together in Fig. 3. 

Lines 214: What does "transparent layer simulation" mean again? Did you mean mandatorily setting the interface transmissivities to 1 and interface reflectivities to 0, although there are 3 layers with different refraction indexes?