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https://doi.org/10.5194/egusphere-2024-3169
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/egusphere-2024-3169
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
25 Oct 2024
| 25 Oct 2024
Status: this preprint is open for discussion and under review for The Cryosphere (TC).
Radar Equivalent Snowpack: reducing the number of snow layers while retaining its microwave properties and bulk snow mass
Abstract. Snow water equivalent (SWE) retrieval from Ku-band radar measurements is possible with complex retrieval algorithms involving prior information on the snowpack microstructure and a microwave radiative transfer model to link backscatter measurements to snow properties. A key variable in a retrieval is the number of snow layers, with more complex layering yielding richer information but at increased computational cost. Here, we show the capabilities of a new method to simplify a complex multilayered snowpack to less than or equal to 3 layers, while preserving the microwave scattering behavior of the snowpack and conserving the bulk snow water equivalent. The method is based on a K-means clustering algorithm to group the snow layers based on the extinction coefficient and the height of the layer. Then, a weighted average using the extinction coefficient and the thickness was applied to the snow properties. We evaluated our method using snow properties from simulations of the SVS-2/Crocus physical snow model at 11 sites spanning a large variety of climates across the world and the Snow Microwave Radiative Transfer model to calculate backscatter at 17.25 GHz. Grouping and averaging snow stratigraphy into 3 layers effectively reproduced the total snowpack backscatter of multi-layered snowpacks with overall root mean squared error = 0.5 dB and R2 = 0.98. Using this methodology, SWE retrievals can be applied to simplified snowpacks, while maintaining similar scattering behavior, without compromising the modeled snowpack properties. Reduction in the mathematical complexity of SWE retrieval cost functions and reduction in computation of up to 80 % can be gained by using fewer layers in the SWE retrieval.
How to cite. Meloche, J., Leroux, N. R., Montpetit, B., Vionnet, V., and Derksen, C.: Radar Equivalent Snowpack: reducing the number of snow layers while retaining its microwave properties and bulk snow mass, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2024-3169, 2024.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
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RC1: 'Comment on egusphere-2024-3169', Anonymous Referee #1, 03 Jan 2025
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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
- Lines 35-38, end of paragraph “…, but can prove challenging for remote sensing applications.” Could you elaborate on some of these challenges?
- 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).
- 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.
- 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?
- 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?
- 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.
- 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?
- 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.
- 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?
- 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?)
- 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?
- 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
- Line 151: ”We investigated three different ways of averageing: …”. Only two are mentioned in the text.
- Line 26-27: “More typically, observations are unavailable, so snowpack information must come from …”. “must” is perhaps too strong word?
- 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?
- Line 119: “where p_11= … and p_22 = … are defined from the phase function.” repeats line 116.
- Line 121: Reference should be (Sihvola,1999)?
- Lines 145,149,150,etc.: I don’t think symbols after text require parenthesis. E.g. “extinction coefficient (κe)” --> “extinction coefficient κe” and “layer thickness (hi)” --> “layer thickness hi”.
- Should section 3 of the manuscript be “Results and Discussions”?
- Lines 176,177: The word “scattering” is used but is supposed to be “extinction”?
- Suggestion: Consider using “h-weighting” and “τ-weighting” (instead of keD) for the two layer-averaging methods.
- 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.
- Similarly, “3-equal-hi” 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.
- 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.
- Figure 3: Y label of the bottom figures should be “difference” as “bias” represents systematic or average difference. Same in figure caption.
- Line 230: “Frequency analysis” has other meanings. Consider different expression.
Citation: https://doi.org/10.5194/egusphere-2024-3169-RC1
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Climate Research Division, Environment and Climate Change Canada, Ontario, Canada
Nicolas R. Leroux
Meteorological Research Division, Environment and Climate Change Canada, Quebec, Canada
Benoit Montpetit
Climate Research Division, Environment and Climate Change Canada, Ontario, Canada
Vincent Vionnet
Meteorological Research Division, Environment and Climate Change Canada, Quebec, Canada
Chris Derksen
Climate Research Division, Environment and Climate Change Canada, Ontario, Canada
Short summary
Measuring the snow mass from radar measurements is possible with information on the snow and a radar model to link the measurements to snow. A key variable in a retrieval is the number of snow layers, with more layer yielding richer information but at increased computational cost. Here, we show the capabilities of a new method to simplify a complex snowpack, while preserving the scattering behavior of the snowpack and conserving the mass.
Measuring the snow mass from radar measurements is possible with information on the snow and a...