Let Us Change the Aerodynamic Roughness Length as a Function of Snow Depth

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript has an interesting topic that may attract attention on detailed snow modeling. There has been a lot of work put in both on the field and in office. In addition, several references are cited about the subject. On the other hand, there are various questions/comments/typos marked on the reviewed manuscript where some of the more important ones are reiterated below:

1. There are many initial Zo, primary roughness, slope, r2 values flying around the text (some are misprinted). It could be more organized and easier for the reader to follow if another table is created especially about station performances (slope, r2) (consider tabular values that are given in the PhD Thesis).
2. A lot of referencing is considered after each sentence. Sometimes site specific results are also cited which is found awkward. I hope AI help did not take over the text.
3. In Fig. 4, it is not clear why ds=0 values (no snow) are also plotted when almost in all of the stations this degrades the trend and hence lowers the coefficient of determination.
4. It is clear that since JC was more accessible it consists of several measurements, and that’s why a hysteresis analysis (accum and melt) was more applicable for that location (Fig. 6). Don’t TF and/or YJ station measurements show any similar results (they seem to have sufficient amount of measurements)?
5. YJ station measurements are considered to be somewhat disturbed due to snowmobile tracks. But Fig. 4 results (no of points, slope, r2) seem to be quite good. How could this be explained?
6. In the text, Fig. 4 is referred to several times on station snow accumulation and melt timing. However, Fig. 4 does not have a time axis on which to follow the time series of the samples. Would it be worthy having time series graphs either showing ds/Zo or indicating such values in a tabular form again as given in the PhD Thesis?
7. Overall, although the study is searching for a dynamic roughness length (Zo) which could well be considered in snow and/or atmospheric models: an average single snow year data, some disturbed station results, other scarce site measurements, leave the hysteresis analysis meaningful for a single site (JC) only. If these results could be strengthened, the manuscript has potential.
8. There are several misprinted values, unfinished sentences and insufficiently explained parts within the manuscript.

Comments for author File: Comments.pdf

Author Response

The manuscript has an interesting topic that may attract attention on detailed snow modeling. There has been a lot of work put in both on the field and in office. In addition, several references are cited about the subject. On the other hand, there are various questions/comments/typos marked on the reviewed manuscript where some of the more important ones are reiterated below:

 

1. There are many initial Zo, primary roughness, slope, r2 values flying around the text (some are misprinted). It could be more organized and easier for the reader to follow if another table is created especially about station performances (slope, r2) (consider tabular values that are given in the PhD Thesis).

 

• We have gone through all of the values to ensure that they are now consistent. We have put all the data and the “station performances (slope, r2)” in a table in an Appendix.

 

2. A lot of referencing is considered after each sentence. Sometimes site specific results are also cited which is found awkward. I hope AI help did not take over the text.

 

• We feel it is important to give credit to other researchers who have conducted similar research and adequately cite our paper. AI was not used in any way to write this.

 

3. In Fig. 4, it is not clear why ds=0 values (no snow) are also plotted when almost in all of the stations this degrades the trend and hence lowers the coefficient of determination.

 

• These values are critical to understand the greatest value z0 may reach. We explain that the ground surface has a z0 value, i.e., ds=0, and then z0 decreases as snow accumulates.

 

4. It is clear that since JC was more accessible it consists of several measurements, and that’s why a hysteresis analysis (accum and melt) was more applicable for that location (Fig. 6). Don’t TF and/or YJ station measurements show any similar results (they seem to have sufficient amount of measurements)?

 

• JC had 30 measurements while TF had 10 and YJ had 9. Further, the measurement dates at TF and YJ did not allow differentiation of accumulation versus melt for a range of snow depths, i.e., TF measurements during melt were only when the snow was deep and YJ measurements during accumulation were only when the snow was shallow. Thus, JC was used only for this analysis. A comment has been added to the Discussion.

 

5. YJ station measurements are considered to be somewhat disturbed due to snowmobile tracks. But Fig. 4 results (no of points, slope, r2) seem to be quite good. How could this be explained?

 

• Yellow Jacket was a much rougher site initially due to shrubbery compared to LC (the other disturbed site). The initial roughness likely had an effect on this.

 

6. In the text, Fig. 4 is referred to several times on station snow accumulation and melt timing. However, Fig. 4 does not have a time axis on which to follow the time series of the samples. Would it be worthy having time series graphs either showing ds/Zo or indicating such values in a tabular form again as given in the PhD Thesis?

 

• We put all the data in a table.

 

7. Overall, although the study is searching for a dynamic roughness length (Zo) which could well be considered in snow and/or atmospheric models: an average single snow year data, some disturbed station results, other scarce site measurements, leave the hysteresis analysis meaningful for a single site (JC) only. If these results could be strengthened, the manuscript has potential.

 

• Yes, this was a start to highlight how variable z0 can be and why it should be considered dynamic. Larger scale studies would be required to fully strengthen and develop site-specific relations.

 

8. There are several misprinted values, unfinished sentences and insufficiently explained parts within the manuscript.

 

• Fixed

 

Also, we have attached the pdf provided by the reviewer with specific comments and responded to each comment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a valuable and well-executed study on the dynamic relationship between snow depth () and aerodynamic roughness length () using high-resolution terrestrial LiDAR data. The authors provide compelling evidence that  is not static but varies hysterically with snow depth during accumulation and melt phases. However, there are still some deficiencies that need to be revised and improved.

1. The abbreviation "SCA" is used in Figure 1 but is not defined in the caption. Please spell out the full term in the caption for clarity.
2. The relationship between and  mentioned in the abstract is presented as established background. The abstract should be strengthened to more prominently emphasize the new findings and conclusions of this study, such as the observed hysteresis and the influence of initial roughness and disturbances.
3. Please provide a clear definition or conceptual explanation of "hysteresis" in the context of the  relationship when it is first introduced in the manuscript (e.g., around Line 53), ensuring readers understand the specific meaning intended.
4. The hysteresis analysis is currently limited to one site (Julie Circle). While this is justified by data availability, the authors should more explicitly acknowledge this limitation in the discussion. Furthermore, please discuss the potential generalizability of the observed hysteresis pattern to other sites with different characteristics. Including a figure comparing accumulation and melt phases for multiple sites (even if only one has sufficient data for full hysteresis analysis) would be helpful to contextualize this finding.
5. The operational definition of "melt" (based on a decrease in since the previous scan) might be overly broad. The authors should consider and discuss the potential influence of other processes leading to snow depth decrease, such as settling and compaction, which are not necessarily synonymous with meltwater production. Clarifying how these factors were considered or might affect the interpretation of the "melt" phase data would strengthen the analysis.
6. In Figure 6, and similarly observable in some plots of Figure 4, there appears to be a steeper increase in (or ln()) at higher  values (lower snow depths during melt). The authors should investigate and discuss the potential reasons for this apparent change in behavior or non-linearity in the relationship. It might suggest that a single linear fit is not appropriate across the entire range of conditions, and different physical processes may dominate in deep vs. shallow/short snowpack stages.
7. The manuscript would benefit from a more conclusive summary that quantifies key findings. For instance:What is the typical magnitude of intra-annual and inter-site variability in  observed in this study? More specifically, what is the potential impact on model outcomes (e.g., simulated melt rates, snow water equivalent, energy fluxes) if the discovered   relationship, especially the hysteresis, were incorporated into numerical models? While scaling limitations are noted, offering more concrete recommendations or hypotheses on how dynamic  parameterizations  could be integrated into existing hydrological or snowpack models would significantly enhance the impact of the conclusion.

Comments for author File: Comments.pdf

Author Response

This manuscript presents a valuable and well-executed study on the dynamic relationship between snow depth () and aerodynamic roughness length () using high-resolution terrestrial LiDAR data. The authors provide compelling evidence that  is not static but varies hysterically with snow depth during accumulation and melt phases. However, there are still some deficiencies that need to be revised and improved.

1. The abbreviation "SCA" is used in Figure 1 but is not defined in the caption. Please spell out the full term in the caption for clarity.

 

• This has been spelled out in the caption.

 

2. The relationship between and mentioned in the abstract is presented as established background. The abstract should be strengthened to more prominently emphasize the new findings and conclusions of this study, such as the observed hysteresis and the influence of initial roughness and disturbances.

 

• The models use z₀ as static, but previous work shows that it is dynamic. The abstract has been rewritten.

 

3. Please provide a clear definition or conceptual explanation of "hysteresis" in the context of the  relationship when it is first introduced in the manuscript (e.g., around Line 53), ensuring readers understand the specific meaning intended.

 

• We have altered the figure and added some text.

 

4. The hysteresis analysis is currently limited to one site (Julie Circle). While this is justified by data availability, the authors should more explicitly acknowledge this limitation in the discussion. Furthermore, please discuss the potential generalizability of the observed hysteresis pattern to other sites with different characteristics. Including a figure comparing accumulation and melt phases for multiple sites (even if only one has sufficient data for full hysteresis analysis) would be helpful to contextualize this finding.

 

• We have rewritten the Discussion and talk more about this and the limitation.

 

5. The operational definition of "melt" (based on a decrease in since the previous scan) might be overly broad. The authors should consider and discuss the potential influence of other processes leading to snow depth decrease, such as settling and compaction, which are not necessarily synonymous with meltwater production. Clarifying how these factors were considered or might affect the interpretation of the "melt" phase data would strengthen the analysis.

 

• We agree that our melt is a simplification. We have added text about this and related considerations in the Discussion.

 

6. In Figure 6, and similarly observable in some plots of Figure 4, there appears to be a steeper increase in (or ln()) at higher  values (lower snow depths during melt). The authors should investigate and discuss the potential reasons for this apparent change in behavior or non-linearity in the relationship. It might suggest that a single linear fit is not appropriate across the entire range of conditions, and different physical processes may dominate in deep vs. shallow/short snowpack stages.

 

• We have revised (former) Figures 4 and 6. For the hysteresis, we investigated the “non-linearity” further.

 

7. The manuscript would benefit from a more conclusive summary that quantifies key findings. For instance: What is the typical magnitude of intra-annual and inter-site variability in  observed in this study? More specifically, what is the potential impact on model outcomes (e.g., simulated melt rates, snow water equivalent, energy fluxes) if the discovered   relationship, especially the hysteresis, were incorporated into numerical models? While scaling limitations are noted, offering more concrete recommendations or hypotheses on how dynamic  parameterizations  could be integrated into existing hydrological or snowpack models would significantly enhance the impact of the conclusion.

 

• We have revised the Conclusions. Further we have added a paragraph to the Discussion on implications.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper investigates how the aerodynamic roughness length (z₀) evolves hysteretically as a function of snow depth (dₛ) in shallow, seasonal snowpacks. Using terrestrial LiDAR scans at nine sites in northwest Colorado during the 2019–2020 winter season, the authors quantify surface roughness dynamics across accumulation and melt phases. The manuscript makes a valuable contribution to understanding snow surface roughness dynamics and their modeling relevance. Addressing the following issues will make the paper suitable for publication:

1. The study is based on nine sites within one watershed and one season. Broader applicability (e.g., across climates, elevations, or snow types) is not fully demonstrated.
2. TLS scanning intervals were irregular (from two days to monthly), which may miss key short-term dynamics. The dataset, though robust, does not provide continuous temporal resolution.
3. Correlations are presented but lack advanced statistical testing (e.g., mixed-effects models, error quantification) that could generalize findings across sites.
4. While the motivation is to inform hydrologic and climate models, the paper does not include integration of dynamic z₀ into a modeling framework to quantify improvements.
5. Some site results are heavily influenced by external factors (e.g., snowmobiles), but the implications for natural undisturbed conditions are not deeply explored.
6. Line 61-62: “No other spatial or temporal variation in z₀ are represented” → should be “is represented.”
7. Line 212: missing space before “of.”
8. Occasional redundancy in citing the same references (e.g., Fassnacht et al. 2018 cited multiple times in similar contexts).
9. Figure captions (e.g., Fig. 5) are lengthy and include too much descriptive detail—better moved into main text.

Comments for author File: Comments.pdf

Author Response

This paper investigates how the aerodynamic roughness length (z₀) evolves hysteretically as a function of snow depth (dₛ) in shallow, seasonal snowpacks. Using terrestrial LiDAR scans at nine sites in northwest Colorado during the 2019–2020 winter season, the authors quantify surface roughness dynamics across accumulation and melt phases. The manuscript makes a valuable contribution to understanding snow surface roughness dynamics and their modeling relevance. Addressing the following issues will make the paper suitable for publication:

 

1. The study is based on nine sites within one watershed and one season. Broader applicability (e.g., across climates, elevations, or snow types) is not fully demonstrated.

 

• Correct, but this study was completed within the greatest scope available for a single person conducting all fieldwork.

 

2. TLS scanning intervals were irregular (from two days to monthly), which may miss key short-term dynamics. The dataset, though robust, does not provide continuous temporal resolution.

 

• This is true, however, sites were spread out and some more difficult to access than others. It was the best we could do during the season as a field team of 1.

 

3. Correlations are presented but lack advanced statistical testing (e.g., mixed-effects models, error quantification) that could generalize findings across sites.

 

• We have added a fit statistic for all the correlations.

 

4. While the motivation is to inform hydrologic and climate models, the paper does not include integration of dynamic z₀ into a modeling framework to quantify improvements.

 

• This is not the focus of the paper. This is mentioned in the future studies section. Additionally, further detail is described here: https://doi.org/10.1016/j.polar.2024.101110

 

5. Some site results are heavily influenced by external factors (e.g., snowmobiles), but the implications for natural undisturbed conditions are not deeply explored.

 

• There are other studies which do explore this further. The purpose in this paper was to highlight the small-scale effects of these external factors and note that they should be considered when discussing snowpack over a larger area.

 

6. Line 61-62: “No other spatial or temporal variation in z₀ are represented” → should be “is represented.”

 

•  

 

7. Line 212: missing space before “of.”

 

•  

 

8. Occasional redundancy in citing the same references (e.g., Fassnacht et al. 2018 cited multiple times in similar contexts).

 

• We want to ensure sufficient recognition of past and similar work in all contexts.

 

9. Figure captions (e.g., Fig. 5) are lengthy and include too much descriptive detail—better moved into main text.

 

• This figure in particular requires a lot of text. With all the values, we feel it is better to reference all relevant information in the caption.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

BRIEF SUMMARY

This paper documents experimental results for the aerodynamic roughness length of snow-covered areas in Colorado. It is found that generally, the roughness length decreases with increasing snow depth, as snow conforms to the underlying terrain. There is, however, no perfect correlation between the roughness length and snow depth, the relationship varies between the sites studies, and it may differ between the snow accumulation and snow melt
periods.

GENERAL COMMENTS

This an interesting study, but there are quite a lot of small issues with the numerical values and with the language, suggesting that the paper has been written in a hurry. My comments on the scientific content are relatively minor.

SPECIFIC COMMENTS

1. At many places in the paper, inconsistent numerical values are given for the same z₀ value; either with a difference in the last decimal or values off by orders of magnitude:

-  Caption of Fig. 3: The snow-free z₀ is stated to be 0.40 x 10^-3 m here but 40 x 10^-3 m in Table 1. The last value 35 x 10^-3 m also seems to be  wrong (by a factor of 100?).
- line 157: 3.5 x 10^-3 m is not consistent with Fig. 4a and 6.
- line 164: 4.8 x 10^-3 m here, 5.0 x 10^-3 m in Table 1.
- line 185: 5.6 x 10^-1 m here, 570 x 10^-3 m = 5.7 x 10^-1 m in Table 1.
- line 210: 40 x 10^-1 m vs. 40 x 10^-3 m in Table 1.
- line 212: 16 x 10^-1 m should be 16 x 10^-3 m?
- line 259: 9.4 x 10^-3 m here, 9.0 x 10^-3 m in Table 1.
- line 281: 4.8 x 10^-3 m here, 5.0 x 10^-3 m in Table 1.
- line 329: 39 x 10^-3 and 56 x 10^-3 vs. 390 x 10^-3 and 570 x 10^-3 m in Table 1.

2. lines 14-16. "the rate of change in the z₀ versus d_s correlation was  almost constant". It is not clear what this refers to. Constant with respect to what? Clearly not with respect to the location (the slopes varied a lot between the sites).

3. lines 30, 38 and 43: Is reference [9] relevant here? It doesn't seem to mention roughness at all.

4. line 52: in reference [21] the hysteresis refers to the different behavior of snow cover fraction vs. snow depth between accumulation and melt seasons, not explicitly to z_0. 

5. line 61: "No other spatial or temporal variation in z₀ are represented". This is not very clear. What does "other" refer to here? Do you mean to say that z₀ is assumed constant for each watershed but can differ between different watersheds due to differences in topography and vegetation?

6. line 88 and elsewhere: The term "correlation" is used loosely to characterize the relationship between z₀ and d_s. But of course correlation has a specific meaning: it is related to how large a fraction of the changes in z₀ is explained by the changes in d_s, not how fast z₀ changes with d_s.
However, what you mostly discuss in this paper is the latter, i.e. the regression slope (in fact, specifically the regression of d_s vs. log(z₀)). Try to be careful with the terminology.

7. Eq. (1): it should be H* (with superscript).

8. line 135: Delete "1." after "scans".

9. line 137: it would be appropriate to note that classifying a time step as a "melt time step" does not necessarily mean that the snow was actually melting. Snow depth can decrease also due to snow densification, which occurs because snow metamorphism takes place even at subzero temperatures. (This is acknowledged on lines 309-310, but it would be better to note it already here).

10. Figure 4. The question underlying this work is how to estimate the roughness length z₀ given the snow depth d_s. Therefore, it would be more logical to calculate regressions of log(z₀) vs. d_s, rather than vice versa. That is, to switch x and y axis in Fig. 4 and define the slopes as Δlog(z₀) / Δd_s rather than Δd_s / Δlog(z₀). Obviously, this would affect all slope values given in the text.

11. line 161: add units "m" after 0.07 x 10^-3.

12. lines 182-194: Adding a scatter plot of initial z₀ vs. roughness feature height would make this discussion easier to follow. Moreover, this discussion might be better located before the slope values are discussed.

13. line 200: "attributed to the data being forces through the origin of plot". I guess "data" should be "regression line", but I can't figure out what origin means in Fig. 4c.

14. line 205 and Fig. 6: The differences between the slope values and regression lines for the accumulation and melt periods seem quite small to me. So if there is a hysteresis effect, it is not very strong in this case?

15. Figure 7: Would it be possible to mark the area of interest in the figure? It is much smaller than the area shown here. Also, how come that the  vegetation/trees seem to be taller in Fig. 7b than in Fig. 7a?

16. line 245: According to Table 1, the initial z₀ at Yellow Jacket was 330 x 10^-3 m, which is only the 3rd highest.

17. line 245: "Figure 4c" should be "Figure 4d". And vice versa on line 253.

18. line 247: "Figure 4e,f" should be "Figure 5e,f".

19. line 257: "... initial ground roughness played a critical role in the slope of the data". Consider demonstrating this with a scatter plot of initial z₀ vs. slope.

20. line 340: It is not clear what "scaling roughness-based energy balance assessments" means. Taking into account temporal variations of roughness in energy balance assessments?

21. line 353: This is true for all sites except for a site (Lost Creek) disturbed by a snowmobile track.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

1. line 205: replace "varying" with "different".

2. line 217: "lack of correlation ...". This can be stated simpler and more correctly: "the highest d_s did not correspond to the lowest z₀".

3. line 219: "within the point clouds the pockmarks in the snowpack surface". Something wrong or missing here?

4. line 240: "were often warmer than". Something missing?

5. line 251: add "for" after "than".

6. line 272: this should be "aligns better with"?

7. line 275: replace "reasoning for this was" with "reasons for this were".

8. line 287: replace "is typically occurs" with "typically occur".

9. line 316: replace "being" with "beginning".

10. line 342: "errors of uncertainty". Should it be "errors or uncertainty"?

11. line 357: "the variability of z0 can change by orders of magnitude". Remove "the variability of"?

12. line 358: "the use in an area changes the correlation". Something missing?

Author Response

somehow the responses to the comments did not transfer over, so we are attaching a word version.

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

Review to

Let Us Change the Aerodynamic Roughness Length Hysteretically as a Function of Snow Depth

This study aims to address an important issue: accounting for changes in snow surface roughness during the winter season as snow cover depth increases, as well as identifying characteristic features and differences between areas with different characteristics (grass fields, fields with sedge, etc.). The importance of this study stems from the fact that, in the current stage of global warming, the uncertainty and variability of winter weather increases, with repeated thaws, changing precipitation patterns, fluctuating wind loads, and so on. All of these changes create heterogeneity in snow surface roughness, both during the winter season and across different landscape types. These factors complicate the parameterization of roughness for subsequent use in hydrological models.

The authors conducted a fairly large-scale field campaign over the course of one winter season, including periods of snow accumulation and melt, and demonstrated that, in most of the sample plots studied, roughness decreased during the snow accumulation and increased during the melting. For one key site, a difference was found in the rate of roughness change during the snow accumulation and melting phases.

This study will undoubtedly be of interest to a wide range of researchers, especially those developing models of snow cover evolution over winter.

In my opinion, further research is needed to establish clearer relationships, as the authors themselves point out in the "Next Steps" section.

The manuscript may be published after minor corrections (typos, etc.) are made. Some comments are included in the file.

 

Comments for author File: Comments.pdf

Author Response

This review appears to be the same as Reviewer 2.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Authors have made considerable effort to improve the manuscript by taking into consideration the reviewer comments/suggestions. The text is now easier to follow with the corrections and explanations. At present, there are a few more minor comments marked on the text to be considered. These points are on:

• Ordering of the sites in Table 1.
• Some more explanation on the TF site outlier (both text and Figure 4)
• Incomplete data in Table A1.
• A few more text corrections.

Comments for author File: Comments.pdf

Author Response

Ordering of the sites in Table 1.

• We had reformatted this table to fit Figure 5. We have now reorganized it to match Figure 1, so by land cover from Aspen to Grass, to PJ to Sagebrush and then from west to east and north to south

 

Some more explanation on the TF site outlier (both text and Figure 4)

• Interestingly TF is not actually an outlier in the snow-free z0 versus feature height figure (Figure 4). When it is removed, the R^2 is reduced to 0.64 since CC and YJ are also outliers. Removing TF and CC increases R^2 to 0.93. Removing TF, CC and YJ increases the 0.99. Just removing CC, increase R^2 to 0.96. This has been added to the Results.
• For ds versus ln z0 (Figure 5), it is possible that the TF data could be split into accumulation versus ablation (see Figure 7). Using the accumulation-melt differentiation from JC, most of the points on the left correspond to accumulation and the points on the right to melt. Separating those points yields an accumulation slope of -0.049 and a melt slope of -0.11, which seem to align better with CR11 and JC. A FIGURE WITH THIS SEPARATION HAS BEEN ATTACHED.
• Text has been added for these two points.

 

Incomplete data in Table A1.

• This is a formatting issue - the table needs to extend over multiple pages and that is not in the LaTeX code somehow. We ask the editorial/copyedit staff to help with that.

 

A few more text corrections. 

• The points in the text have been addressed below.

 

Line 122: “since it was determined experimentally to determine a site specific drag coefficient”

• rewritten as “since it was determined experimentally as a site specific …”

 

Figure 7 caption

• the extra parenthesis has been removed

 

line 357: “ This would consider …”

• changed to “This could consider …”

 

Conclusions first sentence: “At all study locations, it was …”

• changed to “At all study locations that were undisturbed, it was …”

 

Author Response File: Author Response.pdf