Physical-Statistical Retrieval of SWE and Snow Depth in Forested Areas from Airborne X And Ku-Band SAR Measurements

Singh, Siddharth; Vuyovich, Carrie; Barros, Ana P.

doi:10.5194/egusphere-2026-3588

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https://doi.org/10.5194/egusphere-2026-3588

Preprints

04 Aug 2026

| 04 Aug 2026

Status: this preprint is open for discussion and under review for The Cryosphere (TC).

Physical-Statistical Retrieval of SWE and Snow Depth in Forested Areas from Airborne X And Ku-Band SAR Measurements

Siddharth Singh, Carrie Vuyovich, and Ana P. Barros

Abstract. This study presents a physical-statistical Snow Water Equivalent (SWE) retrieval framework in forested areas using dual-frequency X- and Ku-band SAR airborne measurements. The methodology builds on previous work coupling snow hydrology and microwave propagation and backscatter models and introduces a parameterization of microwave propagation and scattering within the forest canopy based on the Water Cloud Model (WCM) modified to account for canopy closure effects. The retrieval framework was applied to SnowSAR measurements from four flights over Grand Mesa, Colorado and its performance was evaluated against snow pit observations and LiDAR snow depth measurements. Prior distributions of snowpack properties were generated using a multilayer snow hydrology model (MSHM) forced with Numerical Weather Prediction (NWP) analysis data. SAR measurements were spatially averaged to 90 m and 30 m resolution for retrieval. Prior distributions of vegetation and ground parameters were initialized using Ku-HH measurements, with effective soil and vegetation parameters estimated for frozen conditions. Soil parameters were estimated in open areas and spatially interpolated to nearby forested areas using ordinary kriging. SWE and snow depth retrievals for forested pixels at 90 m resolution were considered successful by accepting a relative residual backscatter (RRB) tolerance in the Bayesian optimization up to 30 % for individual pixels with incidence angles between 30°–50° along SnowSAR flight paths. Successful retrievals capture both the mean and spatial variance of snowpack properties across the Grand Mesa plateau consistent with the LiDAR survey with RRB generally below 5 %. Validation against collocated LiDAR snow depth and snow pit SWE measurements from the SnowEx ’17 campaign show a root mean square error (RMSE) of 0.033 m (< 8 % of maximum SWE for pits) and improved spatial patterns compared to snow hydrology predictions driven by NWP alone. The errors are larger in pixels with mixed land-cover (e.g., forest-grassland boundaries, land-margins of frozen ponds and lakes, and mixed forest) due to increased uncertainty in the estimation of vegetation parameters. Absolute relative differences (ARD) between LiDAR snow depth and SAR snow depth retrievals are below 10 % for 62 % of the forested pixels at 90 m resolution, and the fraction of successful retrievals increases to 82 % for ARD < 20 %. Retrievals at 30 m resolution achieve dramatic improvement with 78 % of the retrievals for ARD < 10 % due to reduced mixed land-cover uncertainty. These results demonstrate the feasibility of dual-frequency Bayesian SWE retrieval in forested landscapes by combining physical modeling with remote sensing at high spatial resolution enabled by SAR.

Received: 18 Jun 2026 – Discussion started: 04 Aug 2026

Competing interests: Carrie Vuyovich is a members of the editorial board of The Cryosphere

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 paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

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Siddharth Singh, Carrie Vuyovich, and Ana P. Barros

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RC1: 'Comment on egusphere-2026-3588', Anonymous Referee #1, 18 Sep 2026 reply

Singh et al. extend the physical-statistical Bayesian SWE retrieval framework from 2024 work by the same lead author from open areas to forested landscapes, using dual-frequency (X- and Ku-band) SnowSAR backscatter observations from the SnowEx'17 campaign across Grand Mesa, Colorado. The authors couple a multilayer snow hydrology model (MSHM) with the Microwave Emission Model of Layered Snowpacks (MEMLS) and introduce a modified Water Cloud Model (WCM) to represent canopy backscatter and transmissivity, adding an intermediate Bayesian step to estimate vegetation parameters (A, B, Mv) alongside snow and ground properties. Retrievals at 90 m and 30 m resolution are evaluated against snow pit SWE and ASO LiDAR snow depth observations, with reported RMSE of 0.033 m (~8% of maximum pit SWE) and improved agreement with LiDAR relative to MSHM priors alone. Performance is strongest for pixels with forest fraction greater than 70% and at finer (30 m) resolution, where mixed land-cover contamination is reduced; error is concentrated at forest edges, ecotones, and in topographically complex terrain.
This is a meaningful, timely, and reproducible contribution to forested SWE retrieval, outlined to meet the NASEM Decadal Survey requirements. The figures are clear throughout, and the conceptual ones contribute significantly to outlining the retrieval workflow.
Primary feedback (attached) centers on quantifying uncertainty that the manuscript currently treats qualitatively or not at all.

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Citation: https://doi.org/10.5194/egusphere-2026-3588-RC1
RC2:
'Comment on egusphere-2026-3588', Anonymous Referee #2, 23 Sep 2026 reply
Review of “Physical-Statistical Retrieval of SWE and Snow Depth in Forested Areas from Airborne X And Ku-Band SAR Measurements”, by Singh, Vuyovich and Barros
The authors present an algorithm to retrieve SWE from airborne radar measurements, adapting the algorithm for forests. This is a significant advance that should be of great interest to the broader community, as previous literature focuses on areas without forests. Prior to publication, I have identified a few issues, some of them that appear to be major, that should be addressed.
Major Comments
On the whole, the results the authors present here will undoubtedly continue to bolster the conclusion that SWE retrieval from airborne platforms is a demonstrated technology, even in forested areas. This conclusion will help support calls for a future satellite mission to measure snow. However, I think the manuscript currently does not fully discuss some of the key results, especially the fact that some of the retrieval error stats are better for the prior MSHM model than they are for the posterior retrieval. In particular, the retrieval mean snow depth and the root mean square difference is higher for the retrieval than for the MSHM for all four flights (Table 8). The authors highlight that the retrieval improves both the standard deviation and the shape of the statistical distribution (as measured by the Bhattacharya coefficient). However, reading section 4, page 14, one would not know that the retrievals improve two of the metrics and degrade two others. The authors do an admirable job digging into the results through the rest of the paper, but they must additionally come right out and both describe that the retrievals degrade over the prior on two of the four metrics, and why they would still argue that the retrievals are “better” than the prior. The mention that outliers bias the metrics (line 336) is not an adequate argument: see my minor comment on line 336, below. There are multiple ways they could go about making the case that the posterior is superior to the prior despite it degrading two of the performance metrics (for some additional material see my specific comment on line 337), and to be clear, I still see immense value in the paper, and am confident the authors will be able to fully address this comment. But I do think this mixed performance must be featured in a central spot in the paper; i.e. it should be mentioned here in the beginning of section 4, and highlighted in both the conclusions and the abstract.

Line 294: It would be helpful here in the methods to provide further clarification of what a “successful retrieval” means. I actually was not clear on this until the Conclusion (!) line 409, where it is finally made explicit that all retrieval results presented in the paper are only those that they classify as successful retrievals. I think this may confuse many readers. The authors must describe in more detail what they mean by a successful retrieval, why they define it as they do, and why this is reasonable. I think in general, if the MCMC posterior backscatter is not close to the observation it means the models cannot find a reasonable snowpack parameter posterior solution, and thus the retrieval failed. This is entirely reasonable, and I wish more retrieval studies included this. It’s basically a quality flag. The authors must also report what fraction of their retrievals are successful, and which ones fail.

Minor Comments
Line 197: Shouldn’t equation (1) have tau^2, instead of tau? The radar wave must penetrate through the tree (thus being modulated by tau), then scatter off the snowpack, then return through the tree (thus being modulated by tau again). I may be wrong, however. In any case, please consult a radiative transfer textbook, and cite section and equation number in the revision to allow readers to verify the formulation from a known starting point

Line 280-281: does the table show standard deviations (as stated in text) or variances (as stated in table caption)? The values seem intuitively right if they are variances, but possibly express too much confidence in the prior if they are standard deviations.

Line 292: Is the retrieval evaluated using pits within 100 m (as stated in the text) or within 90 m (as stated in the caption for Figure 6, and printed on Figure 6 itself)?

Line 297: Figure 6, it is quite hard to see the markers. Can you make them stand out more against the background image?

Line 297: Figure 6. Can you please provide more information about the contour lines? What is the interval between the lines?

Line 315-316: This sentence reads more like methods: please move to methods

Line 318-319: It is not clear that this point in Figure 6b with higher error is near the edge of the mesa, nor near steep terrain, at least not from the contour lines shown in Figure 6. Around the point in question (which I believe is just northwest of 39.00, -108.1) the contour lines seem spaced far apart. The “edge of the mesa” is not clear from the figure.

Line 336: If this mention that outliers bias the RMSD statistic is being used as a reason to dismiss concerns that posterior RMSD is greater than prior RMSD, then some additional attention may be warranted here. For example, outliers could first be detected using a standard outlier test, and then RMSD could be computed on the non-outlier pixels. Another way to do this is to compare MSHM and retrieval posterior empirical cumulative distribution functions of the error. It is possible that the value of the retrieval (clear in the BC and standard deviation) will emerge in the CDFs. A non-parametric measure of dispersion could be used to summarize the error, such as the 67^th percentile of the absolute value of the error.

Line 337: There is a paradox here that the retrieval improves two error metrics and degrades two others. However, this can be resolved somewhat by noting that mean square error (i.e. RMSD^2) is equal to the square of the mean error plus the square of the error standard deviation. Since the authors show that mean error gets worse, standard deviation improves, but RMSD gets worse, it is mathematically almost certain that the degradation in the mean error outweighs the improvement in the spatial pattern, in the RMSD statistic. Some comments on this could be helpful in trying to make sense of the paradox!

Line 397: Figure 13. Please add lat/long coordinates on the axes of all plots, to enable relating the quantities plotted to other maps. This is especially important for the land cover, since the authors claim (lines 361-366) that places with high forest fraction and high canopy closure indicate deciduous trees. Readers may want to compare Figure 13 to Figure 6, where Forest-1 and Forest-2 map to needleleaf and broadleaf forests respectively which (in this area) will further map to evergreen and deciduous, respectively.

Lines 387-389: Interesting about the land cover complexity being invoked to explain the more noisy results. Can you quantify this? Does the 30 m land cover map shown in Figure 6b show a higher degree of spatial variability within the 90 m pixels than elsewhere? This would really help to buttress the authors’ explanation for the poor performing area.

Lines 409-416: This is a result, or possibly discussion: it is really out of place as a conclusion, since it is presenting new material not yet introduced, as opposed to summarizing already-presented material.

Lines 423-431: Here or somewhere in the conclusion, it would be very helpful to put this study in context with the snow-free study presented by the authors a couple of years ago (Singh et al. 2024). The common-sense expectation is that the retrieval should improve over the prior, but perhaps not quite as much as it did in the snow-free study, since the trees obscure at least some part of the response to snow quantity. Is this expectation borne out by the results?

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Citation: https://doi.org/10.5194/egusphere-2026-3588-RC2

Siddharth Singh, Carrie Vuyovich, and Ana P. Barros

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Short summary

Forests make it difficult to measure how much water is stored in snow because trees block and scatter signals from aircraft and satellites. This study combines weather-driven snow modeling with airborne radar observations to estimate snow depth and water stored in forested snowpacks. Results compared well with field and airborne measurements, showing that this approach can improve snow monitoring in forested regions important for water supply and flood forecasting.


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