A conceptual, distributed snow redistribution model

Frey, S.; Holzmann, H.

doi:https://doi.org/10.5194/hess-19-4517-2015

Articles | Volume 19, issue 11

https://doi.org/10.5194/hess-19-4517-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/hess-19-4517-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 19, issue 11

Research article

|

12 Nov 2015

Research article |

| 12 Nov 2015

A conceptual, distributed snow redistribution model

S. Frey and H. Holzmann

Download

Final revised paper (published on 12 Nov 2015)
Supplement to the final revised paper
Preprint (discussion started on 14 Jan 2015)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

- Printer-friendly version

- Supplement

RC C32: 'Reviewer comment on "A conceptual, distributed snow redistribution model", submitted to HESSD', Anonymous Referee #1, 28 Jan 2015
RC C156: 'Review of «A conceptual, distributed snow redistribution model»', Anonymous Referee #2, 13 Feb 2015
- AC C695: 'Joint answer to referee #1 and #2', Simon Frey, 27 Mar 2015
EC C160: 'Interesting manuscript but more work required on review, processes and parameterization', Jan Seibert, 13 Feb 2015

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (29 Mar 2015) by Jan Seibert

AR by Simon Frey on behalf of the Authors (07 May 2015) Author's response Manuscript

ED: Referee Nomination & Report Request started (07 May 2015) by Jan Seibert

RR by Anonymous Referee #1 (11 May 2015)

RR by Anonymous Referee #2 (18 May 2015)

Suggestions for revision or reasons for rejection

Re-review of «A conceptual, distributed snow redistribution model»
By S. Frey and H Holzman.

General comments: The authors have put in a lot of effort in improving the manuscript. I am especially pleased to the analysis on parameter uncertainty, although I found it difficult to understand the conclusions. I think you need to explain more clearly how you can state “narrower boundaries of the snowmelt factors” (p.14 l28). To me the analysis shows clearly a huge problem of equifinality in the model. 6 calibration parameters just in the snow module is a lot.

However, I do not think this is the main problem of the paper, namely that the authors model a process at a spatial scale for which it has not been observed. The paper addresses a very real problem, an abundance of snow in hydrological rainfall-runoff models that does not melt. In the previous review I suggested a few explanations to why such a problem is present. The authors only considered that of meteorological input, and not that of the spatial frequency distribution of SWE. In several rainfall- runoff models (including this one) snowfall is distributed lognormally, often with a fixed coefficient of variation (i.e which gives it a fixed skewness). The problem with this is that the new snowfall is distributed such that (a unrealistic) perfect spatial correlation is implicitly assumed, i.e. the fractional area receiving the most snow from the first event, also receives the most snow in future events. In this way, the spatial distribution of accumulated snow has the same skewness as the individual events (often skewed too much to the left), and the quantiles (i.e. spatial fractions, or here, snow classes) that continuously receive maximum snow will eventually build these “snowtowers”. The paper is not detailed enough so that I can claim this to be the problem the COSERO model, but I suggest the problem of snow distribution to be investigated as an alternative to the presented model which suggest snow redistribution processes at a spatial scale for which they have not really been observed.

The introduction unfortunately appears as a rather patchy review and not really leading to why the proposed model is a good idea. Some discussion of scale is present, but the proposed model with its 1X1 km scale comes as a surprising conclusion.

Can you please be more specific in your description of “snow classes”. I understand now (I think) it is quantiles of the lognormal distribution, but it really took me quite some time.

The notations need a make over, for example, S_SWEA (Eq. 12) does not do. You can also use S_SWE (t) for example in eq. 1. Or why not SWE(t) ?
The numbering of figures need to be checked.

Specific comments:
p.3. l 10 .. hemisphere, on south-facing slopes, …
p.3. l 26 what is final seasonal snow?
p.3. l 31. Is not SNOWPACK a point model? Is it relevant for this introduction?
p.4. l. 16. Strange sentence
p.5. l 7: ..time steps. It is, however, capable of ..
p.5. l 15: ..the present study.
p.5. l 221998), i.e. the influence…
p.5. l 28 check notations throughout the paper
p.6. l 15: M_red is lowered to a reduced..??
p.8. l 17: ..the snow pack, the higher the portion (of what?)
p.10. l 11:..a nd their areal fractions..
p.10. l 24: This limits… strange sentence
p11, l 24-27 : Rephrase, not clear
p.13, l 7-9: Rephrase, not clear
p.13, l 13: preferably??
p.14, l 27: However, redistribution…

Hide

RR by Daphné Freudiger (12 Jun 2015)

Suggestions for revision or reasons for rejection

This paper addresses the problem of snow redistribution in conceptual hydrological models. The authors present a methodology for the redistribution of snow in the conceptual distributed rainfall-runoff (RR) model COSERO at the scale of 1 km2. The snow is redistributed from the summit of the mountains to the valley using the slope angle to determine the route of the snow redistribution, and the snow density and vegetation cover to determine the amount of snow available for transport. The implementation of the snow redistribution module in the RR-model improved the model efficiency regarding the estimation of the snow cover and the discharge in the Ötztaler Ache catchment in Austria. The main improvement of this method is the elimination of “snow towers” at high elevations, which is a well-known problem for hydrological modeling in mountainous regions.

The study presented in this paper represents an important contribution to hydrological modelling in mountainous regions, since the inter-annual accumulation of snow at high elevations is a well-known and unsolved problem. Furthermore, snow redistribution and therefore the variability of the snow cover may influence the discharge and the glacier mass balance. The method is clearly described in this paper and shows one interesting and simple approach to deal with the problem of snow redistribution in conceptual models. Although the method is certainly connected with uncertainties, the idea is worth to be published. However, the presented paper needs to be improved on four substantial aspects (described below). The issue of the manuscript is in the scope of HESS and I would support its publication after major revisions.

(1) Aims of the study: Throughout the paper, the authors focus on saying that the main goal of the study is to better model the discharge. In fact, the improvement of model efficiency achieved by the simulation with snow distribution compared to the usual model is very little for discharge (KGE 0.92 vs 0.9). In my opinion, the main improvement achieved by the model is the elimination of “snow towers” and the better representation of the snow cover according to the efficiency coefficient r2 (0.66 vs 0.74), which can indicate, as suggested in the conclusion, that the model works right for the right reasons. Therefore I suggest that the authors focus their discussion more on the improved modelling of the snow cover, snow melt, and glacier melt and less on the improvement of the simulated discharge. This would also allow being more optimistic regarding the potential of such a conceptual model, since it is stated in the discussion that snow redistribution is not important for discharge modelling at the large scale (p.13, l.20-21).

(2) Transferability of the method: The presented method showed very interesting results in the Ötztaler Ache catchment in Austria, but was it also tested in other catchments? Can you find similar results in other alpine catchments with different topographical properties, land cover, etc.? How transferable is this model? Since the model is conceptual and therefore should not need long calculation time, I suggest that the authors support their findings and test the model in 2-3 other catchments or at least discuss the transferability of their model in the discussion. This would add validity to the presented study.

(3) Reliability of the model: The authors should discuss how their results are situated compared to other studies. Are their results reliable? How did other studies model snow redistribution? Do they come to similar results (physically-based as well as conceptual model)? If not, why not? The model results for example show enhanced glacier melt (100 mm/yr) because of the glacier area being snow free earlier during the year (p. 12, lines 16-17; p.14, line 10-12, fig.8). Are 100 mm/year in agreement with mass balances studies made on glaciers in the catchment or in catchment with similar properties? A comparison of the results with other studies related on snow redistribution would improve the reliability of the results and therefore also of the model.

(4) Structure of the paper: The structure of the paper presents some weaknesses that need to be improved:

a. Overall, the introduction makes a good review of the snow transport processes and the existing models. However this section needs to be restructured more logically. For example in section 1.1 processes responsible for the variability of the snow cover are described, that are not all snow transport processes. I suggest that the authors rename this section accordingly. As other processes are also involved in the variability of the snow cover, they should better explain why their model focuses on the snow redistribution. The objectives of the study need to be reformulated (see above, point 1).
b. The authors should pay attention not to put results or part of the discussion or the methods in the figure captions. The figure captions should describe the figure but not analyze it. For example fig. 7: “Specific runoff at the outlet at Huben modelled with (model A) and without (model B) using the snow redistribution routine.” This is enough for the caption of the figure, the rest “In the early snow melt period, more runoff is generated by model A because snow accumulates rather in lower than in higher levels. In summer, enhanced glacier melt leads to more runoff by model A.” is part of the results and should be moved to the results section. The caption of fig. 2 to fig. 11 should be revised.
c. The conclusion should be reformulated. It should summarize the main findings of the study and relate to the importance of the work. Part of the conclusion should be moved to the discussion. The second paragraph for example (p. 14, lines 13-20) is rather a discussion of the results than a conclusion. This is also the case for the last paragraph (p.14, lines 26-29). In comparison, paragraph 3 belongs perfectly to the conclusion since it points out the contribution of the paper and the further work that needs to be done to have better hydrological models.
d. The language of the paper can be improved. Especially, long sentences should be avoided, since it makes them difficult to read and to understand.

Detailed comments:

p.1, l.18: observed discharge and MODIS derived snow covered area instead of “runoff and MODIS data”.
p.1, abstract: The improvement of the model efficiency for snow cover (r2) is good and should be added to the abstract.
p.2, l.4 and throughout the text: “degree-day” instead of “day-degree”
p.2, l.7-9: Introduce here the term “snow-tower”.
p.2, l.13 & l.18-20: what is the difference between micro/macro scales and plot/catchment scales? If it is the same, there is no need to define it a second time and only one term should be used.
p.3, l.25-28: The meaning of the sentence “Scipión et al. (2013) however…” is not clear to me, please reformulate.
p.5, l18-30: It is not clear to me how the 5 classes are included in the modeling. Is the SWE of the grid cell the mean value of all classes? Please describe how the classes are taken into account and explain in the discussion how the use of the classes influences the results.
p.5, l30: Define the abbreviation “SWE”.
p.6, l.6 & throughout the text: use the same writing for all the units “[°C]”, “[mm° C-1]”.
p.6, l.25: “… a grid cell is partly snow free (due to melting) …” How can a grid cell be partly snow free? Does that mean that at least 1 of the 5 classes is snow free?
p.7, l.5: the unit for water holding capacity is missing.
p.7, l.9: the unit for refreezing factor is missing.
p.8, l.9-10: “Several authors…” this sentence belongs to the introduction or to the discussion
p.8, l.17-18: with “the portion which is available for the redistribution routine” is fp meant here? Clarify.
p.9, l.5-7: “Since other geomorphological properties […] as driving force for the model”. Move to the discussion and rephrase.
p.9, l.18-19: “A similar approach …” How similar? How does the other approach work? What is new in the presented approach? Discuss it and move to the discussion.
p.11, l.8: fig. 7 instead of fig.6. Please check the reference of the figure numbers throughout the text.
p.11, l.10-11: “…the model efficiency (KGE) could be improved for the discharge by 0.05…”
p.11, l.15: replace “than” by “compared with”.
p.11, l.15: Describe the results of fig. 8 (glacier melt and snowmelt) here more in detail.
p.11, section 4.2: equifinality should come after section 4.3 and 4.4
p.11, l.24-28: “So are cold periods in the summer,…” This sentence is very hard to understand. Please rephrase and split in 2-3 sentences.
p.11, l.28: Talk here about the improvement of the model efficiency found for snow cover (see table 2).
p.12, section 4.4: snow accumulation is unclear; rename the section with “inter-annual snow accumulation”.
p.12, l.2-3: “The main reason…” this should be in the introduction or in the discussion.
p.12, l.15-23: Discuss the peaks in runoff difference in September and October. From the snow redistribution, one would expect that snow is redistributed from the steepest slope to the glacier area leading to more snow on the glacier area (e.g. Kuhn 2003). How can you explain that the glacier get snow free earlier in the year? Is the entire glacier area getting snow free or only the lower part? Please discuss this more in detail.
p.12, l.29: snow depth or snow cover area?
p.13, l.3-5: I disagree, some small differences can be observed between the 2 models and what about the better efficiency r2?
p.13, l.20-29: The discussion should not end on a negative thought. It might not have signification for the large scale modelling, but it still allows to better model the snow covered area.
p.13, discussion: A discussion on the meaning and the influence of the chosen scale is missing and discuss the patterns of the net snow deposition (fig.11).
p.13, discussion: Discuss the problem of equifinality more in detail (citing only the supplement is not enough). The main findings of the Monte Carlo simulation (from the supplement) should be summarized in the discussion for better understanding. Why is it expected to have this problem and why is the model anyhow reliable? Cite references to support your point of view.
p.14, l.18-20: “consequently the objective function…” I don’t understand this sentence. Please rephrase. Where is the Rosenbrook’s routine used (refer to the supplement)? It “differ much” from what? Please explain and move it to the discussion.
p.22, table 1: Please give the unit of snow holding capacity (-). And please give the reference for the CORINE land cover data.
p.23, Table2: “Note, that…” does not belong to the table caption, please move to method.
p.29, Figure 6: For clarity, number the different graphs (with a), b))

Throughout the text:
-Be consequent with the expressions used. For example snow redistribution/snow transport, avoid using both for clarity reasons.
-use the terms runoff and discharge adequately, they are no synonyms.

Kuhn, M., 2003. Redistribution of snow and glacier mass balance from a hydrometeorological model. Journal of Hydrology, 282(1-4), pp.95–103.

Hide

ED: Reconsider after major revisions (20 Jun 2015) by Jan Seibert

AR by Simon Frey on behalf of the Authors (31 Aug 2015) Author's response Manuscript

ED: Referee Nomination & Report Request started (09 Sep 2015) by Jan Seibert

RR by Anonymous Referee #2 (21 Sep 2015)

Suggestions for revision or reasons for rejection

Re-re-review of «A conceptual, distributed snow redistribution model”
By S. Frey and H. Holzman
General comments.
This paper keeps improving, but I still think the problem of mismatch between the spatial scale of the model and those of the physical processes of redistribution (wind and avalanches) remains.
The authors address the maladies of snow distribution and -melt models and I agree that that “snow towers” in conceptual hydrological models is a commonly observed problem. I also agree on that temperature- index models for melting represents a problem for mountainous catchments which contains areas in elevations which never experience temperature above zero. I agree on that, most likely, the reason for the “snow tower” problems are due to how the spatial distribution of snow is modelled. What I find difficult to agree on is that we experience such problems because we have not included redistribution due to wind and avalanches in our 1x1km2 scale model. The authors try to justify this approach in the introduction by listing redistribution mechanisms and scale. In section 1.1 we find that “wind redistribution influences snow depth distribution on scales of 100- 1000 square meters” (1000 m2 is 0.001 km2 ). “Avalanches are capable of transporting large snow masses over distance of tens to hundreds of meters.” These scales are far from the scale of the proposed model (1x1km2). It comes hence as a surprise that wind and avalanches are responsible for the erroneous spatial distribution of snow in our conceptual 1x1km2 model. I might be wrong in this, but I think that the author have to justify this aspect better so that the reader think that redistribution of snow is the logical solution to snow distribution problems at the 1x1km2 scale.

Specific comments:
P1,l 13:..resolution for meso- and large scale ?
P1,l 16: ..of the Austrian Inn basin in Tyrol, more specifically the ötztaler Ache catchment, but….
P1,l 19-22: reformulate sentence
P1,l 26:.. predict discharge with more accuracy leading…
P2,l 23: determine whether you will have numbers or letters
P4,l 13-7: I think you will have to include that the precipitation pattern from the radar was measured a few hundred meters above ground and for a tiny area, 1.5 km. Scale is important here as well.
P4,l 26: In addition, …
P11,l 16-17: drift or transport?, decide on terminology
P12,l 1-2:reformulate sentence
P14-15,l 30: reformulate sentences starting with “For instance..” and the next one starting with “Given that..”.
P15,l 29:..five years due to longer..

Hide

RR by Daphné Freudiger (07 Oct 2015)

Suggestions for revision or reasons for rejection

General comment: The authors significantly improved their manuscript in its structure and in its content. Especially the goals of the study were defined more clearly and the discussion was improved. However, some concerns remain unchanged (See below). I would therefore support the publication of the manuscript after minor revisions that however include substantial restructuring of some sections.

Introduction: As explained in my precedent review, the introduction gives a good review of the snow transport processes and the existing models, but I agree with Referee #1 on the fact, that the introduction, as it is structured now, “appears as a patchy review” and that it is difficult to follow how this literature review leads to the development of the proposed snow transport model. The introduction describes all processes for the variability of snow cover but the model focuses only on snow transport. Since all processes are explained in detail, it is not clear enough why the authors “only” account for the snow transport and not for other processes. Are the processes really taken into account in the model or is only the problem of snow towers solved? I would suggest the authors to completely restructure the introduction in order to lead more logically to the aim of the study.

Discussion:
- What I am still missing in the discussion is a specific discussion on the spatial scale of the model (1x1 km2) (see my precedent comment: p.13, discussion: A discussion on the meaning and the influence of the chosen scale is missing). Since this is an unusual scale for the modeling of snow transport, it would be interesting to read in the discussion what can be reached with a model of this scale and what are the limitations.
- Regarding the transferability of the model, I disagree with the author’s response: “ We think that modeling and presentation of any additional catchment does not improve the manuscript”. I personally think that modeling different catchments would in fact give more reliability to the model results, and especially if the results in other catchments lead to similar conclusions. If for example the comparison of the modeled snow cover with the LiDAR snow cover data is also better in other catchments, it would support the fact that the snow paths chosen by the model for snow transport are more realistic. However, including a paragraph on model transferability can be enough but the argumentation must be developed a little bit more. Especially the comparison with other models is in my opinion in this form not detailed enough. On page 13, line 30, the authors talk about several other models that agree with their results and only the study of Frey (2015) is cited there. What are the other models? And how does this study differ from the present paper? What model was used?
- Reliability of the model: I disagree with the authors response: “ We think that reliability of the model is given by the fact, that the model is able to reproduce both, the discharge and the snow cover extent (MODIS) more accurate.” Of course, the fact that the new model gives better efficiency is a good sign that the model is better. But the model could still work “right for the wrong reasons”. Therefore, I think that it is important to compare the obtained results with the literature. Of course, glacier mass balance is not the purpose of the paper, but if more glacier melt is produced by Model A compared to Model B, it has to be discussed. As I explained in my earlier comment, I would expect more snow on glacier area with a snow transport model, why is that not the case? The model transports the snow from the summit to the valley, this can be compared to other studies with snow transport models that were successfully conducted in other basins and that could support the results found in this paper. Overall, I find the discussion very interesting but I think it would improve the quality if the results and the model would be compared to existing studies (e.g. the points mentioned about the “Blaueiferner” in the response to the comments ). Please include this in your revisions.

Figure captions: Most figure captions still contain too much information. Most of the text in the figure captions belongs to the methods, results, or discussion. Please shorten.

It would be good to remind sometimes throughout the paper what model A and B is. It makes it easier to read.

Detailed comments:

p. 4, l.27: “Schöber et al. [...] with a resolution of 50x50m.“ I don’t understand the relation between this sentence and the previous ones. Please reformulate.
p.7, l.20: the unit of Slp is missing
p.9, l.17 – 21: move this paragraph to the discussion. This would be a good point to discuss the effects of the spatial scale of the model (see above)
p.11, l.21: insert a space before “ Besides”.
p.12, l.1: replace “minus 9” by “-9”.
p.12, l.14: Snow tower was already defined in the introduction, delete “-accumulation of snow cover over several years in high mountain regions”.
p.12, l.16-18: “This elevation was chosen…” I don’t understand the meaning of this sentence. How did you come to the elevation 2800?
p.13, l. 29: insert a space after behavior
p.14, l.1-4: “This is a result… “ this sentence is very difficult to understand, please rephrase.
p.14, l.17: Please give the percentage of area instead of the amount of grid cells “four grid cells”.
p.14, l.20-21: Was this observed somewhere else? References?
p.14, l.25: Are there other studies that found 2800m asl? (The whole discussion is lacking references!)
p.14, l.27: What do you mean with “remain”? I thought that the snow melted more thanks to the snow transport, therefore it should not remain in the basin. Unclear.
p.14, l.26: Where do the results for the Inn basin come from? Own modeling? Other studies?
p.15, l.28: -500 mm is the mass balance and 100 mm is the glacier runoff. It is not clear what is meant here.

Hide

ED: Publish subject to minor revisions (Editor review) (16 Oct 2015) by Jan Seibert

AR by Simon Frey on behalf of the Authors (26 Oct 2015) Author's response Manuscript

ED: Publish as is (04 Nov 2015) by Jan Seibert

AR by Simon Frey on behalf of the Authors (05 Nov 2015) Manuscript

Short summary

Temperature index melt models often lead to snow accumulation in high mountainous elevations. We developed a simple conceptual snow redistribution model working on a commonly used grid cell size of 1x1km. That model is integrated in the hydrological rainfall runoff model COSERO. Applying the model to the catchment of Oetztaler Ache, Austria, could prevent the accumulation of snow in the upper altitudes and lead to an improved model efficiency regarding discharge and snow coverage (MODIS).