Dear authors,



I have read your manuscript entitled "Water depth estimate and flood extent enhancement for satellite-based inundation maps" with great interest.

The manuscript’s focus on the development of the FLEXTH algorithm to address the limitations of existing flood mapping methodologies is commendable. The algorithm's utilization of topographic information for enhancing flood delineation and providing estimates of water level and depth across entire flood extents represents an advancement in the field. However, the discussion on the algorithm's key features, such as accuracy, limited supervision requirements, and computational efficiency, lacks credibility due to the weakness or absence of supporting evidence. As a result, its potential applicability in large-scale flood assessments is called into question.

The introduction section offers a comprehensive review of methodologies for estimating flooded area and water depth, highlighting both the limitations and advancements in current approaches. This provides valuable insights into the current state of the field. However, apparent lack of awareness regarding some of the latest developments in the field casts doubt on the claims of novelty surrounding the method presented in the manuscript.

Overall, the paper is well-written, logically structured, and most of the figures are appropriate. The introduction of the FLEXTH algorithm represents a notable contribution to the field, with the potential to enhance flood assessment and disaster response strategies. The open access Python script is also a welcome addition to facilitate further research and collaboration within the scientific community.

Detailed below are some specific comments. I strongly suggest a significant revision of this manuscript to address these issues thoroughly.

Detailed comments:

1. Line 4's mention of “billions of euros” seems Europe-centric, overlooking the global nature of flooding, which disproportionately impacts lower socio-economic regions over developed countries. It would be beneficial to provide a more inclusive perspective on the economic impacts of flooding, considering the varying economic contexts and vulnerabilities worldwide. Additionally, emphasizing the socioeconomic disparities exacerbated by flooding in vulnerable regions can underscore the urgency of addressing this global challenge.
2. The term "Exclusion Mask" introduced in Line 51 and used throughout the manuscript pertains specifically to the Global Flood Monitoring (GFM) product. However, a more suitable term might be "No Data Areas," as this is commonly encountered in satellite-derived flood extents regardless of the satellite or product used. While it's assumed that no data areas can be treated similarly to the exclusion mask mentioned here, this assumption should be explicitly addressed.
3. The assertion in line 75 regarding the unproven applicability of water depth estimation approaches for large-scale assessments is inaccurate. For instance, Teng et al. (2022) (https://doi.org/10.1029/2022WR032031) have conducted a comprehensive comparison of various methods and conclusively demonstrated their effectiveness for large-scale assessments. Peter et al. (2022) (https://doi.org/1 0.1109/LGRS.2020.3031190) have also implemented FwDET into Google Earth Engine for rapid and large-scale flood analysis. It is imperative to acknowledge and incorporate these findings to ensure the accuracy and completeness of discussion on this matter.
4. In lines 87-89, the claim regarding computational efficiency uses the term "for areas of up to tens of thousands of square kilometres”, which lacks rigor and specificity, particularly in terms of resolution. It is recommended to provide the number of grid cells or include the specific resolution considered to accurately assess its significance in the context of flood mapping. In addition, you are making a claim about the computational advantages of the proposed method without providing solid evidence or comparisons with other existing approaches in terms of run speed. It's essential to provide empirical data or benchmarks to support this claim and accurately assess the computational efficiency of the proposed method relative to other methods in the field.
5. I find it difficult to follow Figure 1 in its current horizontal layout. Consider changing it to a vertical layout and using standard flow chart shapes to improve clarity and ease of understanding.
6. Section 2.1 is titled "Input and Output Products" but does not mention output at all. Consider revising the title to accurately reflect the content or include information about output products in the section.
7. In the paragraph starting from Line 156, Method A is effectively using Inverse Distance Weighting (IDW), while Method B seems to be a crude percentile-based averaging algorithm. It would be beneficial to consider other interpolation methods such as Spline, Kriging, or more advanced machine learning methods. These alternative approaches may offer advantages in terms of accuracy, robustness, and flexibility, especially in handling complex spatial relationships and varying data distributions. Therefore, exploring and comparing these different interpolation techniques could provide a more comprehensive understanding of the flood water level along the dry-wet borders and potentially improve the accuracy of the results.
8. Figure 2（especially C） requires additional clarification to enhance its interpretability in its current form. Providing detailed annotations, labels, and a clear legend could help elucidate the information presented and make the figure more intuitive for readers to understand. Additionally, including a brief description of the data represented in Figure 2C within the main text could provide context and aid in interpretation.
9. The approach introduced in Section 2.3 is novel. It delineates new dry-wet borders informed by DTM in excluded or no data areas. This method, while simple, represents a step forward and deserves emphasis as the main novelty of this manuscript. However, the manuscript does not sufficiently demonstrate the effectiveness of the flood propagation routine. To address this, it is recommended to block out areas of flood extent and propagate flood into those areas as if they were excluded, then compare the results with the actual border. This step is critical to substantiate the effectiveness of this novel method.
10. One significant critique of this study is its reliance on a single case study: the Pakistan 2022 case study. This limited scope is insufficient, particularly considering the lack of easily accessible validation data for this specific case study. Moreover, it hinders the ability to compare the method's accuracy and computational efficiency with other existing approaches. To address this limitation, it is recommended to include additional case studies using published datasets. This would allow for a more convincing demonstration of the advantages of the proposed method.
11. Lines 234-235, how does this run speed compare to other existing approaches? You are claiming computational advantages without solid evidence.
12. Line 243: Please clarify the meaning of CEMS. Please spell out acronyms before their first reference. Similarly, for EMSR629, FABDAM, and other acronyms, provide their full expansion before their initial mention.
13. You are using one satellite product to validate another satellite product of flood extent, which warrants clarification. Please explicitly state the advantage of CEMS over GFM flood extents for validation purpose.
14. In addition to the metrics listed in Table 2, it would be recommended to include F-stat as an additional accuracy metric.
15. Using ICESat-2 altimetry data as truth to validate water depth estimates could be problematic due to mismatching of footprint and timing, as you have discussed in Section 4. To mitigate this concern, it would be advisable to incorporate additional case studies with more suitable validation data, as mentioned in the comments above.
16. Line 322 acknowledges the critical importance of DTM accuracy and resolution. However, it raises the question of why the study does not utilize high-resolution and high-accuracy DEM data, which are available in many regions globally. If data accessibility is an issue, it would be more beneficial to include additional case studies that utilize such data to enhance the robustness and applicability of the findings.
17. Thank you for providing the source code. After reviewing the code, I was unable to identify memory control or chunking algorithms that would support your claims of computational efficiency for large-scale studies. Could you please clarify this aspect?
18. Validation data have not been provided along with the source code.

The manuscript presents a new algorithm for improving and enhancing remote sensing-derived flood inundation maps. The algorithm was developed to address limitations in the Copernicus Global Flood Monitoring (GFM) system but can be used for other applications. The algorithm fills gaps in the flood maps by expanding the flooded domain into the GFM 'Exclusion mask' area and calculates water depth.  The approach builds nicely on recent efforts in this field and presents a considerable advancement. The manuscript is very well written and the algorithm evaluation analysis is well-reasoned and presented. I have two main concerns: (1) the evaluation benchmark is a flood map (and water depth) derived from different satellite sensors which likely suffers from somewhat similar (or other form of) biases as the SAR map; (2) the algorithm description is not as clear as it should be. The authors acknowledge the issues with the benchmark dataset used for evaluation and frame the results in this context. They also rightly assert that robust data for large-scale flooding is scarce. One remedy is to enhance the AOI-based analysis and add locations in which there is higher confidence in the benchmark data. 

Specific issues:

Line 118: clarify 'last flooded pixel'

Line 127: what do you mean by '"morphological" closing'?

Section 2.2 is not clear enough.

The small paragraph starting in line 132 is not very clear.

Figure 2 can be better explained and referenced in the text.

Line 154: not sure what you mean by '4-connectivity'

Figure 3: clarify if these are purely synthetic (1D) results (i.e. not using the full algorithm)

I don't recall you explicitly explaining when the recursion ends (I assume when water cannot be further propagated). It is also not entirely clear the 'seeding' of the reduction - is every pixel at the edge of the flood a seed? 

Table 2 and text: consider reporting the overall improvement in terms of %.

Line 235: how many pixels and what is the resolution used?

Line 272: I don't understand what 'i=1,2' stands for.

Line 289: consider removing 'To conclude'

Figure 6: what is RMSE represent - error compared to what?

The use of ICESat-2 altimetry data to evaluate the water depth prediction is quite novel (to my knowledge) and could be of great interest. The limitations in the data acquisition and processing is well described but additional emphasis needs to be made on the limitations and unknowns associated with your approach - highlighting the need for additional research focused on this approach.

Line 394: 'hydraulic connectivity' is a good term to use in this context - consider adding it to the algorithm description.

Line 403: 'FLEXTH can [also] be effectively applied to...'

The algorithm applies the expansion procedure to masked areas which you found to be a potential limitation. Did you look into running it without this limit?