Review of “Arctic supraglacial lake derived bathymetry combining ICESat-2 and spectral stratification of satellite imagery“ by Jinhoa Lv et al.

Does the paper address relevant scientific questions within the scope of TC? Yes.

Does the paper present novel concepts, ideas, tools, or data? Yes. The method appears novel, though further clarification is needed about how it differs from the approach described in a previous publication by the same author (Lv et al, 2024).

Are substantial conclusions reached? The method yields slightly improved depth estimates for the four lakes investigated when compared to closely related, but less advanced variant. However, since both methods are conceptually similar, incorporating comparisons with more distinct methods would strengthen the scientific merit and contextual relevance of the study.

Are the scientific methods and assumptions valid and clearly outlined? The method appears valid and shows potential, but major revisions are needed to ensure the methodology is clearly and fully described.

Are the results sufficient to support the interpretations and conclusions? Yes

Is the description of experiments and calculations sufficiently complete and precise to allow their reproduction by fellow scientists (traceability of results)? No. As currently presented, the methodology lacks clarity and completeness, which limits reproducibility.

Do the authors give proper credit to related work and clearly indicate their own new/original contribution? Yes.

Does the title clearly reflect the contents of the paper? Not entirely. The title should be revised to reflect that the study focuses on four supraglacial lakes in Southwest Greenland, rather than implying Arctic-wide applicability.

Does the abstract provide a concise and complete summary? Mostly yes, but it should be adjusted to clarify the role of ICESat-2 data in the methodology.

Is the overall presentation well structured and clear? No. The manuscript requires restructuring to improve clarity and logical flow.

Is the language fluent and precise? The language could be improved for clarity and precision.

Are mathematical formulae, symbols, abbreviations, and units correctly defined and used? Not consistently. For example, the ‘Lyzenga’ model and the ‘Otsu’ algorithm are introduced without sufficient explanation.

Should any parts of the paper (text, formulae, figures, tables) be clarified, reduced, combined, or eliminated? Yes, several figures need clarification, and additional figures may be needed to support the analysis.

Are the number and quality of references appropriate? Generally appropriate, but the manuscript would benefit from a review of reference relevance and completeness, particularly for datasets.

Is the amount and quality of supplementary material appropriate? Not applicable.

General comments

The paper presents a novel approach for estimating the bathymetry of supraglacial lakes by integrating ICESat-2 laser altimetry with Sentinel-2 multispectral imagery. The method combines spectral stratification (“Otsu algorithm”) and a classical regression model (“Lyzenga model”) and is tested on four lakes in Southwest Greenland. The topic is timely and relevant, and the authors’ effort to improve bathymetric inversion accuracy is commendable. The results show modest improvements in accuracy compared to the Lyzenga model without spectral stratification, which are encouraging.  

However, the manuscript requires substantial revision before it can be considered for publication. In particular, the methodology needs to be presented more clearly and systematically, with sufficient detail to allow reproducibility and critical evaluation. Below are the main concerns that should be addressed.

Title and scope:

The current title implies broad applicability across Arctic supraglacial lakes, which is not supported by the limited dataset used in the study. Since the method is only applied to four lakes in Southwest Greenland, the title should be revised to reflect this scope more accurately. Additionally, the discussion should include a thorough assessment of the method’s generalizability to supraglacial lakes on other regions of the Greenland Ice Sheet (and other Arctic ice masses), including potential limitations.

Methodological clarity:

Several key components of the methodology are insufficiently described:

• Lyzenga Model: This model is central to the study but is only briefly introduced. A more comprehensive explanation is needed, including its assumptions (e.g., uniform water clarity, bed type, and spectral behavior). Clarifying these assumptions is essential for understanding the model’s applicability and limitations.
• Use of ICESat-2 data: The role of ICESat-2 data in the workflow is unclear. The abstract does not mention it, and the main text provides only a brief reference to its use as training data. It is important to specify how the data is used for calibration of the Lyzenga model: Which parameters are calibrated? And is data from both weak and strong ICESat-2 beams considered. Furthermore, it should be clarified whether the photons identified as originating from the bed are used directly as discrete point data, or if this point cloud is processed into a continuous bathymetric surface beforehand (such as through fitting a smooth model).
• Otsu Algorithm: The algorithm is mentioned without adequate explanation. While some details are provided in Section 3.2, a clearer and more complete description of how the algorithm is applied to spectral stratification would benefit readers unfamiliar with this technique.
• Training strategy: The manuscript does not specify whether the model is trained individually for each lake or whether data from all lakes are pooled to form a single training dataset. Clarifying this point is essential for evaluating the robustness and scalability of the approach. The authors note (L291) that the method is constrained by the limited availability of ICESat-2 data for training. However, if ICESat-2 data from, say, hundreds of lakes are pooled, the volume of training data could be significantly increased. Conversely, if the model is trained separately for each lake, its applicability would be restricted to lakes directly intersected by an ICESat-2 track, limiting its broader utility.

Comparison with other methods:

The manuscript would benefit from a broader comparison with recent approaches, such as those proposed by Datta et al (2021) and Melling et al. (2024). Including validation metrics from these methods – applied to the same four lakes – would help contextualize the contribution of the present study and highlight its strengths and limitations relatively to existing techniques. At present, the two models compared in the manuscript – the classical Lyzenga model and the spectral stratified variant – are closely related and yield relatively similar performance. A comparison with more distinct methodologies would provide a more meaningful benchmark and significantly enhance the scientific value of the study.

Evaluation and visualization:

The evaluation of the method relies solely on scatter plots comparing estimated water depths with ArcticDEM-derived values. While informative, this approach would benefit from being complemented by spatial difference maps to visualize where discrepancies occur. Such maps could reveal whether both models struggle in the same regions and under what conditions, offering insights into potential sources of error and guiding future improvements.

Summary

In summary, the manuscript addresses an important topic and presents a promising approach. However, substantial revisions are needed to improve clarity, methodological transparency, and contextualization. I encourage the authors to restructure the presentation of the method, provide more detailed descriptions of key components, and expand the discussion to include broader applicability and comparative analysis.

Specific comments

L16 + L84: The manuscript states that the four lakes are “representative,” but it is unclear what they are representative of. Are they meant to reflect characteristics of all supraglacial lakes across the Greenland Ice Sheet? Please clarify the criteria used for selecting these lakes and substantiate the claim of representativeness.

L13: In the abstract, the Otsu algorithm is referred to as the “maximum between-class variance method,” but the paper does not explain what this entails or how the algorithm functions. A clear description should be added to the methods section.

L22: The introduction would benefit from a more detailed explanation of the role of supraglacial lakes in glacier dynamics, particularly their potential to rapidly route meltwater to the glacier bed during drainage events.

L62: Please clarify how this work differs from the authors’ previous study (Lv et al., 2024), which also uses Sentinel-2 and ICESat-2 data to derive bathymetry, seemingly for the same lakes.

Figure 1: Lakes C and D appear to be intersected by both yellow and red ICESat-2 tracks. Why is data from only one track used? Please clarify.

L140–143: If the L1C dataset is not used in the analysis, it should be omitted from the text and from the workflow diagram in Figure 2. Only the radiometrically corrected L2A data should be mentioned.

Figure 2: The workflow diagram could be a valuable aid for understanding the method, but several steps are unclear. For example, what is meant by “water column extraction” (is this the lake area delineation?), and what does “SGLs water-leaving radiance” refer to? The figure and its caption should be revised to ensure the diagram is self-explanatory.

L148: Please explain how the ice mask is generated.

L172: The vertical adjustment of ICESat-2 photons is mentioned but not clearly described. Please elaborate on the rationale and procedure for this adjustment.

Figure 4: What do the blue colors in the lower panel images represent? A legend and/or explanation is needed.

Figure 5: Consider adding difference plots comparing water depths from both models to ArcticDEM-derived depths (using ICESat-2 surface elevations). These would help identify where and under what conditions the models diverge.

L231: With the addition of difference plots, this section could describe more precisely where the models differ and potentially suggest explanations for why they differ.

L236: The statement that the lake bed consists of “bedrock” is confusing. Supraglacial lakes typically have ice beds, not bedrock. Moreover, since the ice surface evolves over time, some discrepancies between ArcticDEM and Sentinel-2 data collected 2–4 months apart are likely.

Figures 6 & 8: What does the “density” color scale represent? Please clarify in the figure captions.

Figure 7: Consider adding ICESat-2 track lines and difference maps comparing both models to ArcticDEM, as well as a direct comparison between the two models.

L255–258: The claim regarding discrepancies between models should be supported with visual evidence—such as a plot—to allow readers to assess this directly.

Technical comments

Figure captions: The figure texts (e.g., Figs 3, 5, 6, 9) are repetitive and should be written more concisely.  Where appropriate, captions should be revised to ensure that they are self-contained and provide sufficient context for stand-alone interpretation.

L10 & L31: An important reason for the limited use of airborne LiDAR and shipborne sonar in supraglacial lake (SGL) bathymetry is the rapid temporal variability in lake depth. This should be explicitly mentioned alongside the logistical and environmental challenges.

L11: Clarify here the nature of the data, i.e. specify that ICESat-2 provides photon-counting laser altimetry and Sentinel-2 offers multispectral optical imagery.

L26: Revise to "SGLs are formed *in* surface depressions" for grammatical accuracy.

L37: References should be placed immediately after the respective models are introduced to improve readability and attribution.

L41: “Precise measurement data” is vague. Specify the type of measurements (e.g., lake surface elevation, lake bed depth).

L43–L56: This section is overly broad, focusing on global shallow water bathymetry. It should be shortened and refocused on SGL-specific applications. Conversely, the discussion of prior SGL bathymetry methods could be expanded to better distinguish the proposed approach.

L58: Add “to” in “validated them to ICESat-2”

L65: Given the multiple examples cited, it is inaccurate to state that the method has “rarely” been applied to SGLs. Please revise accordingly.

L74: The claim that the method supports predictions of Arctic glacier melt is overstated. The results pertain to four lakes in Southwest Greenland and should be framed accordingly.

L80: Remove “in the Arctic”—the location of the Greenland Ice Sheet is well known and does not need reiteration.

Figure 1: Lake D is not visible in the main Sentinel-2 background image. Consider adjusting the inset map to focus on Greenland rather than the entire Arctic to improve clarity of the study area.

L102 & L114: Provide proper citations for the data sources (e.g., Copernicus Open Access Hub for Sentinel-2, NASA Earthdata for ICESat-2), rather than stating they were “downloaded from the internet.”

L109–112: The description of ICESat-2 track geometry is unclear, and several terms are either unclear or possibly misapplied (e.g., orbital spacing). Rewrite this section more concisely and accurately, using standard terminology.  Also, specify the ICESat-2 product used (e.g., ATL03), including version number and citation.

L119: Clarify that ArcticDEM strip data were used, not the mosaic. Include a brief explanation of the dataset’s origin (e.g., derived from satellite stereophotogrammetry).

L121: Melling et al. (2024) is not the correct reference for ArcticDEM. Please cite the Polar Geospatial Center instead.

L125: Rather than listing acquisition dates in the text, refer to Table 1 for a clearer overview.

Table 1: Remove “Southwest Greenland Ice Sheet” from the table header—it is redundant given the context.

L148: Revise to "unmelted ice cover *on the lake*" to avoid confusion with general ice sheet coverage.

L169–171: This important note about temporal alignment between ICESat-2 and Sentinel-2 data should be moved earlier in the manuscript, ideally in the data or methodology section.

L222: Avoid referring to lake surface ice as “ice sheets,” which has a distinct glaciological meaning.

L263–269: Consider moving this information into a table and referencing it from the main text to improve readability.

L284: The phrase “low temporal resolution” is misleading. Instead, refer to the “sparse temporal coverage” of ArcticDEM data.

Please see attached document