the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Dec 2023
Morphodynamics of the Mont Blanc glaciers and their recent evolution
Abstract. The surface velocity of glaciers is a key parameter that provides fundamental information on glacier dynamics and their adaptation to changes in climate; moreover, ice velocity measurements are a very important parameter for modelling glacier physics and their evolution. While a few decades ago ice velocity would rely on point measurements performed in the field, the processing of high temporal and spatial resolution information from satellites nowadays provides new insights and a vast quantity of data, on a global scale, for the measurement of ice velocity. As of today, few studies have been performed in Alpine regions, and rarely has the focus been on ice velocity evolution. In the present study, we analyse the average monthly velocities on Alpine glaciers in the Mont Blanc massif. Seven years of Sentinel-2 optical satellite imagery have been processed to obtain ice velocity data. The main objectives of the study are: (i) to characterise the variability of the velocity fields of such glaciers, referring both to their temporal (seasonal and interannual) and spatial variations; (ii) to find relationships between the morphology of glaciers and their kinematics. We measured the monthly velocities of thirty glaciers varying from 18.0 m yr-1 to 436.3 m yr-1, highlighting a breakpoint in the trends in 2020. This led to the identification of 13 glaciers showing accelerations of more than 20.0 m yr-2 between 2020 and 2022 compared to previous years. We identified five clusters of morphodynamic characteristics, thus describing five different glacier type classes.
-
Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
-
Preprint
(2868 KB)
-
Supplement
(523 KB)
-
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2868 KB) - Metadata XML
-
Supplement
(523 KB) - BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-2771', Anonymous Referee #1, 20 Dec 2023
The paper by Troilo et al., titled "Morphodynamics of the Mont Blanc glaciers and their recent evolution," presents a study on the evolution of glacial dynamics in the Mont Blanc massif. The authors used Sentinel-2 images to examine the monthly changes in flow velocity in this massif, as well as morphological characteristics of the glaciers, in order to classify the observed dynamic behaviors in this area.
General comment:
One point of concern that needs to be more highlighted is the results from a study published in 2023 (Rabatel et al., 2023). Indeed, this study shows trends that differ from the study by Troilo et al. For instance, in Rabatel et al., the Brenva glacier appears to be accelerating since 2016, whereas the Bossons and Argentière glaciers have significantly reduced their speed. One possible explanation for these differences may arise from the method used to observe these variations. The authors, by looking at an average speed over several points distributed across the glacier's surface, may tend to smooth out dynamic changes. Indeed, Rabatel et al. (2023), as well as the authors of this paper, have specifically noted that the strongest speed changes are not uniformly distributed along alpine glaciers, which can be polythermal in the Alps, and have generally much lower changes in accumulation regions. Thus, the method used to calculate speed changes in this paper will impact the amplitude of the seasonal cycle calculated in this study. Furthermore, important details of methodologies are still missing from the paper to determine whether the calculated trends here are robust (see below).
One critical point is a precise description of the repeat cycles (and their distribution through time) used to calculate speeds, which can significantly impact the errors associated with time series. Millan et al., 2019, demonstrated that for repeat cycles of 5 days for Sentinel-2, errors associated with speeds can exceed >40 m/yr (Figure 4 from their paper). Errors of this magnitude must be taken into consideration, especially considering the relatively small changes in speed observed on the glaciers. Using the error on each repeat cycle employed, Millan et al. notably compiled maps of the Mont Blanc massif, with the minimum cycles required to observe dynamic changes (Fig. 9 from their study). On these maps, we can see that the minimum cycle ranges from 10 to 30 days in the fastest parts of the glaciers (Bossons, Brenva, serac fall of Mer de Glace, Miages tributary glaciers). At all other sites, return cycles of over 300 days are necessary to observe dynamic changes with a satisfactory signal-to-noise ratio. Hence, I think the authors should filter out all their selected sampling points located in those slow-moving areas when deriving their monthly speed changes. At the moment, almost 70% of the glacier considered in Figure 7 does not have a sufficiently high speed to monitor monthly speed changes. Hence the monthly variations that are shown are likely due to noise in the ice velocity estimates. See later comment for more details.
Figure 7 of the paper absolutely needs to include error bars on these time series. An important piece of information that is currently missing would be to provide the raw time series with the monthly average overlaid on top. This provides essential information about the signal-to-noise ratio magnitude on these time series, as well as the robustness of the data used. Furthermore, methodological details need to be provided regarding the calculation of monthly velocity maps, specifically to understand whether the authors calculate a simple median or if they compute a weighted average. Data reduction methods have been described in Mouginot et al., 2023, and accounting for the precision of each pair of images is critical for maximizing the signal-to-noise ratio in monthly averages. Currently, description of error estimation comes way too late inside the manuscript and should one of the first points that opens the results section. Similarly,it would be necessary to show (at least in supplementary material) speed maps over stable regions throughout the entire area (similarly to Figure 5 but everywhere), and on a logarithmic scale, to provide a better understanding of the noise associated with the time series. It is particularly important when examining really small glaciers such as Charpoua, that are in the limits of what we are able to measure with Sentinel-2.
Finally, the paper's structure needs revision because numerous methodological elements are currently located in the "Results" section of the paper. This comment should really be considered for the clarity of the paper. For example. you have two sections both the Methods and Results that are entitled “Selection of Sampling Points” and “Sentinel-2 image selection.” This really gives the impression that the author did not put effort into the submission and structuring of the paper. Please provide a proper Data and Methods section. For example, all details related to Sentinel-2 imagery (e.g., 3.2 and 4.1 and 5.1) should be within the same section. All things related to the data and methods for morphometric analysis should be gathered in one single section (3.2 and 4.3). Finally, you should have one big part with ice velocity calculation and time-series analysis. Even the name of the section looks random: section 4.5 is “Glacier surface velocity mapping,” and section 5.2 is also “Glacier velocity mapping.”
Specific comments:
L27-29: The transition between sliding and surface velocities is a bit odd at that place since you are not discussing sliding velocities in the paper. Rephrase the sentence to say that measurements of sliding velocities are extremely difficult and rare, and that measuring surface flow velocities can be used as a strong alternative to invert for sliding speeds using ice sheet numerical models.
L42: Specify that it is a measurements of surface flow velocities made on the ground.
L57: ITS_LIVE (please correct accordingly). Furthermore, specify that the cross-correlation is derived at a resolution of 240 m and statistically downscaled to 120 m, which has major limitations for small mountain glaciers.
L57: You are never mentioning the Millan et al., 2022, which is the first dataset that covers all glaciers on earth (outside of the ice sheet), with a pixel size of 50 m, hence significantly gaining in resolution.
L107: This entire section and the following one needs to be better organized. See general comment.
L118: Millan et al 2019 on thousands of Sentinel-2 image pairs from the same orbits, in several mountain ranges, that errors on geolocation are closer to a value of 0.52 pixels, which corresponds to the absolute geolocation specification by ESA. This step is accounted for in the calibration procedure. Furthermore, you do not provide details about the co-registration scheme that you are using. Please add more description on that part.
L208: Please show in the supplementary material all the sampling points that are used on the glaciers.
L255: The number of images used per year seems really low compared to other work from Rabatel et al., 2023, and Mouginot et al., 2023. For example, Mouginot et al. assemble 5000 different pairs of images for years 2018-2019, which seems much higher than what the authors are showing here. Is it because you are limited to cycle of 20 to 40 days ? Why not considering longer cycle for slow moving region and inter-annual trends?
L261: This entire section 5.2 should go inside the Data/Method section, and I would suggest to call it “Study region.”
Figure 3: Please add the names of the main glaciers that you are studying on the map rather than just numbers. You have plenty of space to do that.
L284: Here I think that the discussion and figures are really limited to conclude about the “surge” behavior of Charpoua. Can you please provide a full raw data along-profile time series over Charpoua glacier since 2016? This would allow us to differentiate between seasonal signal vs abnormally high speeds. From Figure 7, it is difficult to conclude that the speed up of Charpoua is abnormal, but it looks rather like a seasonal cycle. Have you looked at thickness changes over this area (see Hugonnet et al., or papers from Berthier et al.) to conclude on typical mass changes patterns that would suggest a surge?
L286: In general, for land-terminating glaciers, we would expect the ice velocity to be maximum close to the ELA. What is the elevation of this glacier compared to others? Can you differentiate this pattern from the glacier surface slope? Here you also have a really small glacier, that is only a few pixels large, hence you are reaching the limits of what we can measure with Sentinel-2. Having more information on the level of noise in the data (see general comment) will provide more strength to the conclusions.
L293: What does this do inside the Results section? Please homogenize and merge this with the similar part in the Data/Methods.
Section 5.5: Please provide error bars on these estimates (see general comment)? Do you include what you call surge-type behavior in here? If yes, you have to differentiate that from “seasonal” velocity variations.
Figure 7: Adding error bars to these time series is critical. Furthermore, please adjust the range of y values so that it fits the max/min speeds calculated for each glacier.
Section 5.5: Add error estimates on all of the velocity values that are discussed.
L340: What do you mean by “robust” linear interpolation?
Section 6.1: This will need to be revised after considering the general comment made on the methodological aspect of the paper. Indeed, everything in the paper lies in the methods that are being conducted to derive the trends in ice velocities, which will affect the discussion.
L401-402: The authors should provide a more detailed description of the differences in trends with Rabatel et al., and more specifically over Brenva, Bosson, and Argentière.
L429: A critical piece of information that would be needed to classify a glaciers as a “surge type” is the pattern of changes in ice thickness. This would be drastically different if a surge occurs, showing a net mass transfer across the glacier. Hugonnet et al., 2022 provide changes in ice thicknesses since 2000 which is a key information to account for.
L442: Changes in ice thickness are available over this area. See the following papers:
Hugonnet, R., McNabb, R., Berthier, E., Menounos, B., Nuth, C., Girod, L., Farinotti, D., Huss, M., Dussaillant, I., Brun, F., and Kääb, A. Accelerated global glacier mass loss in the early twenty-first century. Nature, 592, 726-731, doi: 10.1038/s41586-021-03436-z, 2021
Berthier, E., Vincent, C., and Six, D. Exceptional thinning through the entire altitudinal range of Mont-Blanc glaciers during the 2021/22 mass balance year. Journal of Glaciology, in press, doi: 10.1017/jog.2023.100, 2023.
Berthier E., Cabot V., Vincent C. & Six D. Decadal region-wide and glacier-wide mass balances derived from multi-temporal ASTER satellite digital elevation models. Validation over the Mont-Blanc area Frontiers in Earth Sciences, 4, doi:10.3389/feart.2016.00063, 2016
Berthier E., Vincent C., Magnússon E., Gunnlaugsson Á. Þ., Pitte P., Le Meur E., Masiokas M., Ruiz L., Pálsson F., Belart J. M. C. and Wagnon P. Glacier topography and elevation changes derived from Pléiades sub-meter stereo images, The Cryosphere, 8(6), 2275-2291, doi: 10.5194/tc-8-2275-2014 (open access), 2014
Section 6.3: This section is coming way too late inside the manuscript. Part of this section should go inside the methods, and the description of the errors should be the first paragraph of the results! Furthermore, the error calculation here should be used throughout the entire results section to put error bars on the trends estimates and inside the figures. Why are the authors selecting 155 points on stable terrain? How are these points selected? Do you keep a uniform spatial distribution of these points? Millan et al calculated error on all available stable terrain and the same should be performed here. Another comment I have is the use of repeat cycles of 20-40 days. Millan et al., 2019 have shown that if you want to observe a speed change of 10% with good SNR, the 2-sigma precision of the velocity maps should be smaller than 1/10 of the magnitude of the ice slow locally (Figure 9 of their paper). Considering this, the sampling points that were chosen for the velocity trends, you should filter them out, otherwise they will bias the monthly velocity estimate. This is the case, for example, of Argentière, LexBlance, PetitMontBlanc, DesGlacier, Talefre, Taconnaz, Bionnassey glaciers (and lots of others ones from Fig 7), that have a speed typically <100 m/yr. With a 2-sigma precision of 22 meters/year, the monthly speed change observed in Figure 7 is mostly just noise in the data.
L482: A more important comparison would be the trends in surface flow velocity with Rabatel., 2023. You could both compare the amplitude of the seasonal signal and the multi-annual trends with their data, which are freely available.
L516-518: Can you better explain how you calculated these 40 m/yr regarding the uncertainty, the resolution of the images, and cross-correlation parameters (grid spacing)?
Citation: https://doi.org/10.5194/egusphere-2023-2771-RC1 - AC1: 'Reply on RC1', Niccolò Dematteis, 13 Mar 2024
-
RC2: 'Comment on egusphere-2023-2771', Maximillian Van Wyk de Vries, 07 Jan 2024
Review of - Morphodynamics of the Mont Blanc glaciers and their recent evolution
By Fabrizio Troilo, Niccolò Dematteis, Francesco Zucca, Martin Funk, Daniele Giordan.
The authors have created a new multitemporal velocity map for all glaciers in the Mont Blanc Massif using Sentinel-2 imagery. They make a number of derivative analysis, both classifying the glaciers based on velocity and morphology into new ‘categories/types’ and investigating temporal trends. Overall, the paper is well written, the analysis is robust, and the topic appears relevant to this journal. I do, however, have a number of questions and comments about the paper structure and certain of the follow-up analyses, and so propose that this paper undergoes major revisions at this stage.
A few specific comments or concerns are:
- One of the motivations which you present is that the glaciers of Alpine regions, and even the Mt Blanc massif specifically, have been understudied. However, they have been studied quite intensely for many years and are actually one of the most data rich glaciated regions on the planet. This does not diminish the usefulness of your study (this is not a direct repeat of a previous study) but this needs to be better recognized so that the previous contributions are built on.
- For the timeseries analysis, I am not sure whether you have really located a breakpoint in 2020 since this is a date you chose yourself. Showing that the trend pre- and post-2020 is different is not the same thing as determining that this is the specific year that something changed (e.g. if you chose 2019 or 2021 as the year, would it not likely still show different trends either side?). If you want to show this I would perhaps expect to see some automated breakpoint analysis technique applied so that you can remove the a-priori assumption of 2020 being a change point. I don’t necessarily see a justification for a 2-piece rather than a single fit for many of the timeseries. Many of the resulting trends seem to be related to truncating the seasonal cycle more so than a major shift in glacier dynamics.
- The glacier classification was not very convincing as presented in the current manuscript. I think the method itself you are using (PCA + K-means clustering) is fine, but I am not sure you have sufficiently explained why it might be useful. I definitely don’t think you should give these names as you currently have (‘surging’, ‘energetic’, etc) which imply more understanding of processes or already have specific meanings which are not necessarily met here (e.g. ‘surge’). I’d just call them ‘Group/Class 1’, ‘Group/Class 2’ etc to avoid this and clearly decouple data and interpretation. You need to clearly explain why you chose 5 categories, and make sure the wording clearly reflects that this is a parameter choice rather than a fundamental property of the data. The categories are presented, but you do not show that they represent a particular difference in the glacier processes in different types or that they are likely to respond in different ways. With some thought and engagement with the local literature you could probably do the latter – i.e. frame it as the categories providing a convenient frameworks to identify similar glaciers and compare their evolution.
- The structure is a bit mixed with pieces of methods in the results and discussions, etc. Better getting this in one place will improve the readability. You should add some more information about the specific parameter choices used for the feature tracking so that we have the full info (even knowing GIV well I cannot figure it all out).
As I mentioned, none of these issues are fundamental and should be addressed with a round of major revisions. I’ll provide some more specific comments for given lines:
L1 / title: I think the title could be more closely linked to the study, it is a bit vague. Mention ice velocity in there. E.g. ‘Velocity and dynamic change of the Mt Blanc Glaciers, 2016-22’. I’ve not seen the term ‘morphodynamics’ used for glaciers before and am not sure it quite applies here.
L9 Velocity is not a parameter, it is a physical property.
L10 Glaciers don’t really ‘adapt’ to climate change. Perhaps ‘their sensitivity’ or ‘their response’ would be better.
L13-14 ‘Few studies have been performed in alpine regions’ – this is just not true. There are certainly tens, and likely hundreds of papers on ice velocity in Alpine regions. They are also relatively better studied than many other area (the Mt Blanc massif in particular has many datasets, some unique in the globe). I’d just remove this sentence.
L19 See my comment about the ‘2020 breakpoint’ – since you chose this date yourself, I am not sure you have shown this
L21 Needs some info about what these classes show, or why the classification is valuable. Otherwise the readers will think ‘so what?’. Also, since you chose the number of classes (why 5?) this phrasing is slightly confusing.
L29 – Do you mean in the field?
L30-36 This paragraph could use a revision for clarity. The information is mostly OK, but is presented in a messy and somewhat confusing manner.
L37 I don’t understand what you are saying. Surface displacements are not a proxy for ice flow, they are the result of ice flow.
L41 Again not a proxy
L65-66 What about Millan et al 2019 (https://doi.org/10.3390/rs11212498), Rabatel et al. 2023 (https://doi.org/10.3390/data8040066), etc? to just name a couple of recent studies. It is fair to say more work is needed, but what you have written here is not true.
L86-91 Not sure this paragraph has much useful information
L107 I do not think this section is needed at all. I would just merge one or two sentences about what S2 images you used into the methods and leave it at that.
L111 A lot more background info about very basics of the mission than needed. We need to know what band you used, how many images, date limits, but not all the rest.
L123 Just add this to the methods and remove the section
L128 I tend to call this optical feature tracking, though DIC is also widely used (and PIV, pixel offset tracking, etc etc). Could be worth an ‘also known as’ parenthesis?
L133 I wonder if an ‘inset’ here giving a little more detail about the ‘Digital image correlation’ procedure would help? I know the details of the model, but this won’t necessarily be the case for most readers. The timeseries processing and so on in GIV in particular is not necessarily ‘standard’ procedure.
L154 What do you mean an ‘active’ glacier? Try and use precise language.
L160 The orientation filter pre-processing in GIV is generally quite good at handling shadowed areas so long as features remain visible to some extent.
L168 Could you show a map, here or in sup mat, of the included/excluded glaciers?
L173-175 I am not sure if it is a problem with your workflow or with your description of it but this sounds very subjective here. On what basis did you split / merge glaciers? I would say you need an objective criteria (e.g. separated by at least x pixel of exposed rock) or stick to the RGI for consistency. For instance, why was the main branch of Miage glacier not analyzed?
L186 Did you consider using other thickness estimates, e.g. from Farinotti 2019?
L200 Technically GIV does not coregister images, it instead calculates stable-ground shifts to correct for georeferencing errors without the image degradation which coregistration can introduce.
L203-205 You are missing some key information to understand your feature tracking results here. What were your min and max temporal bounds? What was your ‘target resolution’ (used by GIV to set the pixel matching scale)? What was your overlap between matching windows (was it the default of 0.5?)? Did you adjust any other parameters from the defaults? State that all else was at default, and include your parameter file in the sup mat.
L211 Missing some key info. What did you use to evaluate coherence – was it using the snr output from GIV? Some other measure?
On the whole I don’t really understand the idea of manually selecting points. This seems like it would inevitably introduce some bias, and the location of each point is not justified. It would be better if you instead used (i) a glacier centreline or (ii) a zone of the glacier x km from the front / x% between the front and ELA or something of this type. It is very risky to manually select points you perceive as having lower noise levels as this will almost certainly bias outputs. I would therefore like to see this analysis redone with one of these other criteria, or much stronger justification of the point distribution.
L218 ‘averaging’ through what operation. Taking the arithmetic mean?
L219 ‘Outliers removal was manual’ …based on what? Again, I would much prefer an automated filtering of some kind, or at least much better explanation of what was done.
L225 Why is the median named ‘GlobalAvg’? This is misleading.
L228-230 This is confusing – are the reference period always the same or different then? Please tell us exactly what they are, is it 01 Dec-end April and 01July – end Sept?
L231 The max in a given year or over the entire period?
L241 Why did you select 5 classes? This seems like a very fundamental question given the following analyses with this. How do the results differ with 2, 3, 4, 6, 7 classes? Given that you manually selected this, do we expect the classes to have any physical meaning? Would a clustering mechanism which does not require pre-selection of the number of classes be more appropriate?
There are a lot of questions you have to answer here, and they affect the interpretability of a large portion of the following manuscript so require some serious attention.
L243-248 Not sure this text is needed.
L249-260 This is methods not results.
L270 Not clear, given the lack of description, whether 40m is the native resolution of the GIV output here or whether it was resampled to a new resolution.
L273 Coming back to this again, but why is Miage mostly excluded? Were you excluding debris-covered regions?
L278 You describe elongation ratio as length divided by area, so I guess it has units of metres?
How precise is your length? Worth rounding to the nearest 10m?
Same for the mean ice thickness, do you really have cm precision? Even to the nearest m seems to be pushing it.
For all of these, could you include uncertainties. You mention the thickness is from Millan’s paper, they have an error estimate. Same for area, length slope, etc.
L283 What data led you to identify this glacier in particular? Could you show a plot of summer/winter vel ratio for all glaciers?
L284-286 This does not match the typical definition of a surge, this looks more like ‘typical’ uneven seasonal variability for a glacier with high sensitivity. Consider if the language is appropriate.
L296-299 This seems like methods not results.
L310-317 Can you report these values with error bars?
L328 / Fig 7 I am concerned looking at some of these linear fits that you have not fully considered the implications of a seasonal cycle on your results. Many of the ‘significant’ results (e.g. PraSec, Dome, Freney, Planpincieux, Brouillard, Mt Blanc) seem to be at least partly related to the fact that your timeseries is starting during the low part (winter) of the seasonal cycle. In this case the assumptions you are using to test for statistical significance are probably not valid.
I would recommend doing one of the following:
- Subtract the seasonal cycle from each timeseries and calculate the linear trends of your residuals
- Instead of fitting only a linear term, fit a linear term summed with a 1-yr period sinusoidal term.
There are decent toolboxed in python/matlab for doing the latter if you want to do that, and the former is easy to set up.
L340-342 Considering trends for only summer/winter does help, but it does not solve the problem above as the plots clearly show that there are regular seasonal trends within these subdivisions still.
L355 What do you mean ‘less statistically significative’? Presumably, it is or is not statistically significant for a given threshold.
L368 What is a ‘gentle’ glacier?
L371 This seems a bit misleading to say, it was not the model that identified 5 classes but rather you that set 5 classes as a parameter (and it is not clear why).
L373 / Fig9 The PCA plot here is interesting, but as I have mentioned there is not enough info to judge why the clustering is being done as you have done it (or even why it is being done at all).
L377-398 A lot of this seems like it might fit in the intro or be greatly shortened rather than be here.
L398-399 As mentioned, the issue of timeseries splitting in a seasonal cycle needs to be considered in more depth before we can be confident about these results.
L418 I would like you to elaborate in more detail if the trends remain robust after addressing the issue of seasonal cycle. What mechanisms do you envisage for a climatic regime change to affect regional glacier velocities? A more intense early summer melt pulse driving high basal pressures and more sliding before efficient drainage is established?
L423 ‘Detachment’ is usually the term used for this glacier collapse process as at Aru
L428 Again, quite misleading to say this since you parameterized to model to identify 5 groups.
L429-444 These are not meeting the typical glaciological definition of a surge. It would be better to not label them this way.
L445 Since they are moving still, ‘stagnant’ is also not really accurate
L429-471 This whole section goes into a lot of detail about the different glacier classes/groups defined by the K-means clustering, but is really missing information to understand why these might be useful. As far as I can tell from this manuscript it seems to be a fairly artificial separation which doesn’t necessarily reflect different underlying processes or other commonalities within the clusters.
Are you suggesting that there might be some generalizable rule about these different types of glaciers? That these classes might be found in other Alpine, or even non-alpine areas?
Where does the number 5 come from? How do we know there shouldn’t be 4, or 6 classes?
L472 It would be good to move the error analysis and evaluation to the results, it is necessary to understand the quality of the subsequent work.
L497 / Figure 10 It would be good to plot this figure with error bars from your data and from Millan et al.
L501 / Table 2 Please label ‘Mean difference’ instead of just ‘Mean’, and include the error bars here too.
L509-510 It is unclear what you mean by ‘anomalous’ here, how can this be determined for a given velocity increase? I agree about you point that a better understanding of baseline velocity variability is necessary to identify precursory changes to a detachment.
L519-520 If we include both short and long baselines it is possible to improve resolving power over slow-moving areas but still capture short events. The post-processing can be more complex however.
L532 See comments above- reasons for 5 groups not clear.
L550 This data availability statement is not really aligned with the FAIR (Findable, Accessible, Interoperable, and Reusable) principles which is expected for this journal. Unless there is a particularly compelling reason, I would expect you to upload the glacier outline shapefiles to an online repository and link to them here.
You say that the glacier velocities are available as a supplement, but I cannot access them. There only seems to be the pdf supplement. Since they are fairly large files, perhaps they would be better hosted in an external repository (e.g. Zenodo). You could, perhaps, add a section to the pdf supplement with your GIV parameter choices to enable easy reproducibility.
Overall, this is an interesting paper and the basic data looks robust, but changes and clarifications to some of the follow-up analyses and restructuring of the text is needed before it is ready to publish here.
-Max
- AC2: 'Reply on RC2', Niccolò Dematteis, 13 Mar 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-2771', Anonymous Referee #1, 20 Dec 2023
The paper by Troilo et al., titled "Morphodynamics of the Mont Blanc glaciers and their recent evolution," presents a study on the evolution of glacial dynamics in the Mont Blanc massif. The authors used Sentinel-2 images to examine the monthly changes in flow velocity in this massif, as well as morphological characteristics of the glaciers, in order to classify the observed dynamic behaviors in this area.
General comment:
One point of concern that needs to be more highlighted is the results from a study published in 2023 (Rabatel et al., 2023). Indeed, this study shows trends that differ from the study by Troilo et al. For instance, in Rabatel et al., the Brenva glacier appears to be accelerating since 2016, whereas the Bossons and Argentière glaciers have significantly reduced their speed. One possible explanation for these differences may arise from the method used to observe these variations. The authors, by looking at an average speed over several points distributed across the glacier's surface, may tend to smooth out dynamic changes. Indeed, Rabatel et al. (2023), as well as the authors of this paper, have specifically noted that the strongest speed changes are not uniformly distributed along alpine glaciers, which can be polythermal in the Alps, and have generally much lower changes in accumulation regions. Thus, the method used to calculate speed changes in this paper will impact the amplitude of the seasonal cycle calculated in this study. Furthermore, important details of methodologies are still missing from the paper to determine whether the calculated trends here are robust (see below).
One critical point is a precise description of the repeat cycles (and their distribution through time) used to calculate speeds, which can significantly impact the errors associated with time series. Millan et al., 2019, demonstrated that for repeat cycles of 5 days for Sentinel-2, errors associated with speeds can exceed >40 m/yr (Figure 4 from their paper). Errors of this magnitude must be taken into consideration, especially considering the relatively small changes in speed observed on the glaciers. Using the error on each repeat cycle employed, Millan et al. notably compiled maps of the Mont Blanc massif, with the minimum cycles required to observe dynamic changes (Fig. 9 from their study). On these maps, we can see that the minimum cycle ranges from 10 to 30 days in the fastest parts of the glaciers (Bossons, Brenva, serac fall of Mer de Glace, Miages tributary glaciers). At all other sites, return cycles of over 300 days are necessary to observe dynamic changes with a satisfactory signal-to-noise ratio. Hence, I think the authors should filter out all their selected sampling points located in those slow-moving areas when deriving their monthly speed changes. At the moment, almost 70% of the glacier considered in Figure 7 does not have a sufficiently high speed to monitor monthly speed changes. Hence the monthly variations that are shown are likely due to noise in the ice velocity estimates. See later comment for more details.
Figure 7 of the paper absolutely needs to include error bars on these time series. An important piece of information that is currently missing would be to provide the raw time series with the monthly average overlaid on top. This provides essential information about the signal-to-noise ratio magnitude on these time series, as well as the robustness of the data used. Furthermore, methodological details need to be provided regarding the calculation of monthly velocity maps, specifically to understand whether the authors calculate a simple median or if they compute a weighted average. Data reduction methods have been described in Mouginot et al., 2023, and accounting for the precision of each pair of images is critical for maximizing the signal-to-noise ratio in monthly averages. Currently, description of error estimation comes way too late inside the manuscript and should one of the first points that opens the results section. Similarly,it would be necessary to show (at least in supplementary material) speed maps over stable regions throughout the entire area (similarly to Figure 5 but everywhere), and on a logarithmic scale, to provide a better understanding of the noise associated with the time series. It is particularly important when examining really small glaciers such as Charpoua, that are in the limits of what we are able to measure with Sentinel-2.
Finally, the paper's structure needs revision because numerous methodological elements are currently located in the "Results" section of the paper. This comment should really be considered for the clarity of the paper. For example. you have two sections both the Methods and Results that are entitled “Selection of Sampling Points” and “Sentinel-2 image selection.” This really gives the impression that the author did not put effort into the submission and structuring of the paper. Please provide a proper Data and Methods section. For example, all details related to Sentinel-2 imagery (e.g., 3.2 and 4.1 and 5.1) should be within the same section. All things related to the data and methods for morphometric analysis should be gathered in one single section (3.2 and 4.3). Finally, you should have one big part with ice velocity calculation and time-series analysis. Even the name of the section looks random: section 4.5 is “Glacier surface velocity mapping,” and section 5.2 is also “Glacier velocity mapping.”
Specific comments:
L27-29: The transition between sliding and surface velocities is a bit odd at that place since you are not discussing sliding velocities in the paper. Rephrase the sentence to say that measurements of sliding velocities are extremely difficult and rare, and that measuring surface flow velocities can be used as a strong alternative to invert for sliding speeds using ice sheet numerical models.
L42: Specify that it is a measurements of surface flow velocities made on the ground.
L57: ITS_LIVE (please correct accordingly). Furthermore, specify that the cross-correlation is derived at a resolution of 240 m and statistically downscaled to 120 m, which has major limitations for small mountain glaciers.
L57: You are never mentioning the Millan et al., 2022, which is the first dataset that covers all glaciers on earth (outside of the ice sheet), with a pixel size of 50 m, hence significantly gaining in resolution.
L107: This entire section and the following one needs to be better organized. See general comment.
L118: Millan et al 2019 on thousands of Sentinel-2 image pairs from the same orbits, in several mountain ranges, that errors on geolocation are closer to a value of 0.52 pixels, which corresponds to the absolute geolocation specification by ESA. This step is accounted for in the calibration procedure. Furthermore, you do not provide details about the co-registration scheme that you are using. Please add more description on that part.
L208: Please show in the supplementary material all the sampling points that are used on the glaciers.
L255: The number of images used per year seems really low compared to other work from Rabatel et al., 2023, and Mouginot et al., 2023. For example, Mouginot et al. assemble 5000 different pairs of images for years 2018-2019, which seems much higher than what the authors are showing here. Is it because you are limited to cycle of 20 to 40 days ? Why not considering longer cycle for slow moving region and inter-annual trends?
L261: This entire section 5.2 should go inside the Data/Method section, and I would suggest to call it “Study region.”
Figure 3: Please add the names of the main glaciers that you are studying on the map rather than just numbers. You have plenty of space to do that.
L284: Here I think that the discussion and figures are really limited to conclude about the “surge” behavior of Charpoua. Can you please provide a full raw data along-profile time series over Charpoua glacier since 2016? This would allow us to differentiate between seasonal signal vs abnormally high speeds. From Figure 7, it is difficult to conclude that the speed up of Charpoua is abnormal, but it looks rather like a seasonal cycle. Have you looked at thickness changes over this area (see Hugonnet et al., or papers from Berthier et al.) to conclude on typical mass changes patterns that would suggest a surge?
L286: In general, for land-terminating glaciers, we would expect the ice velocity to be maximum close to the ELA. What is the elevation of this glacier compared to others? Can you differentiate this pattern from the glacier surface slope? Here you also have a really small glacier, that is only a few pixels large, hence you are reaching the limits of what we can measure with Sentinel-2. Having more information on the level of noise in the data (see general comment) will provide more strength to the conclusions.
L293: What does this do inside the Results section? Please homogenize and merge this with the similar part in the Data/Methods.
Section 5.5: Please provide error bars on these estimates (see general comment)? Do you include what you call surge-type behavior in here? If yes, you have to differentiate that from “seasonal” velocity variations.
Figure 7: Adding error bars to these time series is critical. Furthermore, please adjust the range of y values so that it fits the max/min speeds calculated for each glacier.
Section 5.5: Add error estimates on all of the velocity values that are discussed.
L340: What do you mean by “robust” linear interpolation?
Section 6.1: This will need to be revised after considering the general comment made on the methodological aspect of the paper. Indeed, everything in the paper lies in the methods that are being conducted to derive the trends in ice velocities, which will affect the discussion.
L401-402: The authors should provide a more detailed description of the differences in trends with Rabatel et al., and more specifically over Brenva, Bosson, and Argentière.
L429: A critical piece of information that would be needed to classify a glaciers as a “surge type” is the pattern of changes in ice thickness. This would be drastically different if a surge occurs, showing a net mass transfer across the glacier. Hugonnet et al., 2022 provide changes in ice thicknesses since 2000 which is a key information to account for.
L442: Changes in ice thickness are available over this area. See the following papers:
Hugonnet, R., McNabb, R., Berthier, E., Menounos, B., Nuth, C., Girod, L., Farinotti, D., Huss, M., Dussaillant, I., Brun, F., and Kääb, A. Accelerated global glacier mass loss in the early twenty-first century. Nature, 592, 726-731, doi: 10.1038/s41586-021-03436-z, 2021
Berthier, E., Vincent, C., and Six, D. Exceptional thinning through the entire altitudinal range of Mont-Blanc glaciers during the 2021/22 mass balance year. Journal of Glaciology, in press, doi: 10.1017/jog.2023.100, 2023.
Berthier E., Cabot V., Vincent C. & Six D. Decadal region-wide and glacier-wide mass balances derived from multi-temporal ASTER satellite digital elevation models. Validation over the Mont-Blanc area Frontiers in Earth Sciences, 4, doi:10.3389/feart.2016.00063, 2016
Berthier E., Vincent C., Magnússon E., Gunnlaugsson Á. Þ., Pitte P., Le Meur E., Masiokas M., Ruiz L., Pálsson F., Belart J. M. C. and Wagnon P. Glacier topography and elevation changes derived from Pléiades sub-meter stereo images, The Cryosphere, 8(6), 2275-2291, doi: 10.5194/tc-8-2275-2014 (open access), 2014
Section 6.3: This section is coming way too late inside the manuscript. Part of this section should go inside the methods, and the description of the errors should be the first paragraph of the results! Furthermore, the error calculation here should be used throughout the entire results section to put error bars on the trends estimates and inside the figures. Why are the authors selecting 155 points on stable terrain? How are these points selected? Do you keep a uniform spatial distribution of these points? Millan et al calculated error on all available stable terrain and the same should be performed here. Another comment I have is the use of repeat cycles of 20-40 days. Millan et al., 2019 have shown that if you want to observe a speed change of 10% with good SNR, the 2-sigma precision of the velocity maps should be smaller than 1/10 of the magnitude of the ice slow locally (Figure 9 of their paper). Considering this, the sampling points that were chosen for the velocity trends, you should filter them out, otherwise they will bias the monthly velocity estimate. This is the case, for example, of Argentière, LexBlance, PetitMontBlanc, DesGlacier, Talefre, Taconnaz, Bionnassey glaciers (and lots of others ones from Fig 7), that have a speed typically <100 m/yr. With a 2-sigma precision of 22 meters/year, the monthly speed change observed in Figure 7 is mostly just noise in the data.
L482: A more important comparison would be the trends in surface flow velocity with Rabatel., 2023. You could both compare the amplitude of the seasonal signal and the multi-annual trends with their data, which are freely available.
L516-518: Can you better explain how you calculated these 40 m/yr regarding the uncertainty, the resolution of the images, and cross-correlation parameters (grid spacing)?
Citation: https://doi.org/10.5194/egusphere-2023-2771-RC1 - AC1: 'Reply on RC1', Niccolò Dematteis, 13 Mar 2024
-
RC2: 'Comment on egusphere-2023-2771', Maximillian Van Wyk de Vries, 07 Jan 2024
Review of - Morphodynamics of the Mont Blanc glaciers and their recent evolution
By Fabrizio Troilo, Niccolò Dematteis, Francesco Zucca, Martin Funk, Daniele Giordan.
The authors have created a new multitemporal velocity map for all glaciers in the Mont Blanc Massif using Sentinel-2 imagery. They make a number of derivative analysis, both classifying the glaciers based on velocity and morphology into new ‘categories/types’ and investigating temporal trends. Overall, the paper is well written, the analysis is robust, and the topic appears relevant to this journal. I do, however, have a number of questions and comments about the paper structure and certain of the follow-up analyses, and so propose that this paper undergoes major revisions at this stage.
A few specific comments or concerns are:
- One of the motivations which you present is that the glaciers of Alpine regions, and even the Mt Blanc massif specifically, have been understudied. However, they have been studied quite intensely for many years and are actually one of the most data rich glaciated regions on the planet. This does not diminish the usefulness of your study (this is not a direct repeat of a previous study) but this needs to be better recognized so that the previous contributions are built on.
- For the timeseries analysis, I am not sure whether you have really located a breakpoint in 2020 since this is a date you chose yourself. Showing that the trend pre- and post-2020 is different is not the same thing as determining that this is the specific year that something changed (e.g. if you chose 2019 or 2021 as the year, would it not likely still show different trends either side?). If you want to show this I would perhaps expect to see some automated breakpoint analysis technique applied so that you can remove the a-priori assumption of 2020 being a change point. I don’t necessarily see a justification for a 2-piece rather than a single fit for many of the timeseries. Many of the resulting trends seem to be related to truncating the seasonal cycle more so than a major shift in glacier dynamics.
- The glacier classification was not very convincing as presented in the current manuscript. I think the method itself you are using (PCA + K-means clustering) is fine, but I am not sure you have sufficiently explained why it might be useful. I definitely don’t think you should give these names as you currently have (‘surging’, ‘energetic’, etc) which imply more understanding of processes or already have specific meanings which are not necessarily met here (e.g. ‘surge’). I’d just call them ‘Group/Class 1’, ‘Group/Class 2’ etc to avoid this and clearly decouple data and interpretation. You need to clearly explain why you chose 5 categories, and make sure the wording clearly reflects that this is a parameter choice rather than a fundamental property of the data. The categories are presented, but you do not show that they represent a particular difference in the glacier processes in different types or that they are likely to respond in different ways. With some thought and engagement with the local literature you could probably do the latter – i.e. frame it as the categories providing a convenient frameworks to identify similar glaciers and compare their evolution.
- The structure is a bit mixed with pieces of methods in the results and discussions, etc. Better getting this in one place will improve the readability. You should add some more information about the specific parameter choices used for the feature tracking so that we have the full info (even knowing GIV well I cannot figure it all out).
As I mentioned, none of these issues are fundamental and should be addressed with a round of major revisions. I’ll provide some more specific comments for given lines:
L1 / title: I think the title could be more closely linked to the study, it is a bit vague. Mention ice velocity in there. E.g. ‘Velocity and dynamic change of the Mt Blanc Glaciers, 2016-22’. I’ve not seen the term ‘morphodynamics’ used for glaciers before and am not sure it quite applies here.
L9 Velocity is not a parameter, it is a physical property.
L10 Glaciers don’t really ‘adapt’ to climate change. Perhaps ‘their sensitivity’ or ‘their response’ would be better.
L13-14 ‘Few studies have been performed in alpine regions’ – this is just not true. There are certainly tens, and likely hundreds of papers on ice velocity in Alpine regions. They are also relatively better studied than many other area (the Mt Blanc massif in particular has many datasets, some unique in the globe). I’d just remove this sentence.
L19 See my comment about the ‘2020 breakpoint’ – since you chose this date yourself, I am not sure you have shown this
L21 Needs some info about what these classes show, or why the classification is valuable. Otherwise the readers will think ‘so what?’. Also, since you chose the number of classes (why 5?) this phrasing is slightly confusing.
L29 – Do you mean in the field?
L30-36 This paragraph could use a revision for clarity. The information is mostly OK, but is presented in a messy and somewhat confusing manner.
L37 I don’t understand what you are saying. Surface displacements are not a proxy for ice flow, they are the result of ice flow.
L41 Again not a proxy
L65-66 What about Millan et al 2019 (https://doi.org/10.3390/rs11212498), Rabatel et al. 2023 (https://doi.org/10.3390/data8040066), etc? to just name a couple of recent studies. It is fair to say more work is needed, but what you have written here is not true.
L86-91 Not sure this paragraph has much useful information
L107 I do not think this section is needed at all. I would just merge one or two sentences about what S2 images you used into the methods and leave it at that.
L111 A lot more background info about very basics of the mission than needed. We need to know what band you used, how many images, date limits, but not all the rest.
L123 Just add this to the methods and remove the section
L128 I tend to call this optical feature tracking, though DIC is also widely used (and PIV, pixel offset tracking, etc etc). Could be worth an ‘also known as’ parenthesis?
L133 I wonder if an ‘inset’ here giving a little more detail about the ‘Digital image correlation’ procedure would help? I know the details of the model, but this won’t necessarily be the case for most readers. The timeseries processing and so on in GIV in particular is not necessarily ‘standard’ procedure.
L154 What do you mean an ‘active’ glacier? Try and use precise language.
L160 The orientation filter pre-processing in GIV is generally quite good at handling shadowed areas so long as features remain visible to some extent.
L168 Could you show a map, here or in sup mat, of the included/excluded glaciers?
L173-175 I am not sure if it is a problem with your workflow or with your description of it but this sounds very subjective here. On what basis did you split / merge glaciers? I would say you need an objective criteria (e.g. separated by at least x pixel of exposed rock) or stick to the RGI for consistency. For instance, why was the main branch of Miage glacier not analyzed?
L186 Did you consider using other thickness estimates, e.g. from Farinotti 2019?
L200 Technically GIV does not coregister images, it instead calculates stable-ground shifts to correct for georeferencing errors without the image degradation which coregistration can introduce.
L203-205 You are missing some key information to understand your feature tracking results here. What were your min and max temporal bounds? What was your ‘target resolution’ (used by GIV to set the pixel matching scale)? What was your overlap between matching windows (was it the default of 0.5?)? Did you adjust any other parameters from the defaults? State that all else was at default, and include your parameter file in the sup mat.
L211 Missing some key info. What did you use to evaluate coherence – was it using the snr output from GIV? Some other measure?
On the whole I don’t really understand the idea of manually selecting points. This seems like it would inevitably introduce some bias, and the location of each point is not justified. It would be better if you instead used (i) a glacier centreline or (ii) a zone of the glacier x km from the front / x% between the front and ELA or something of this type. It is very risky to manually select points you perceive as having lower noise levels as this will almost certainly bias outputs. I would therefore like to see this analysis redone with one of these other criteria, or much stronger justification of the point distribution.
L218 ‘averaging’ through what operation. Taking the arithmetic mean?
L219 ‘Outliers removal was manual’ …based on what? Again, I would much prefer an automated filtering of some kind, or at least much better explanation of what was done.
L225 Why is the median named ‘GlobalAvg’? This is misleading.
L228-230 This is confusing – are the reference period always the same or different then? Please tell us exactly what they are, is it 01 Dec-end April and 01July – end Sept?
L231 The max in a given year or over the entire period?
L241 Why did you select 5 classes? This seems like a very fundamental question given the following analyses with this. How do the results differ with 2, 3, 4, 6, 7 classes? Given that you manually selected this, do we expect the classes to have any physical meaning? Would a clustering mechanism which does not require pre-selection of the number of classes be more appropriate?
There are a lot of questions you have to answer here, and they affect the interpretability of a large portion of the following manuscript so require some serious attention.
L243-248 Not sure this text is needed.
L249-260 This is methods not results.
L270 Not clear, given the lack of description, whether 40m is the native resolution of the GIV output here or whether it was resampled to a new resolution.
L273 Coming back to this again, but why is Miage mostly excluded? Were you excluding debris-covered regions?
L278 You describe elongation ratio as length divided by area, so I guess it has units of metres?
How precise is your length? Worth rounding to the nearest 10m?
Same for the mean ice thickness, do you really have cm precision? Even to the nearest m seems to be pushing it.
For all of these, could you include uncertainties. You mention the thickness is from Millan’s paper, they have an error estimate. Same for area, length slope, etc.
L283 What data led you to identify this glacier in particular? Could you show a plot of summer/winter vel ratio for all glaciers?
L284-286 This does not match the typical definition of a surge, this looks more like ‘typical’ uneven seasonal variability for a glacier with high sensitivity. Consider if the language is appropriate.
L296-299 This seems like methods not results.
L310-317 Can you report these values with error bars?
L328 / Fig 7 I am concerned looking at some of these linear fits that you have not fully considered the implications of a seasonal cycle on your results. Many of the ‘significant’ results (e.g. PraSec, Dome, Freney, Planpincieux, Brouillard, Mt Blanc) seem to be at least partly related to the fact that your timeseries is starting during the low part (winter) of the seasonal cycle. In this case the assumptions you are using to test for statistical significance are probably not valid.
I would recommend doing one of the following:
- Subtract the seasonal cycle from each timeseries and calculate the linear trends of your residuals
- Instead of fitting only a linear term, fit a linear term summed with a 1-yr period sinusoidal term.
There are decent toolboxed in python/matlab for doing the latter if you want to do that, and the former is easy to set up.
L340-342 Considering trends for only summer/winter does help, but it does not solve the problem above as the plots clearly show that there are regular seasonal trends within these subdivisions still.
L355 What do you mean ‘less statistically significative’? Presumably, it is or is not statistically significant for a given threshold.
L368 What is a ‘gentle’ glacier?
L371 This seems a bit misleading to say, it was not the model that identified 5 classes but rather you that set 5 classes as a parameter (and it is not clear why).
L373 / Fig9 The PCA plot here is interesting, but as I have mentioned there is not enough info to judge why the clustering is being done as you have done it (or even why it is being done at all).
L377-398 A lot of this seems like it might fit in the intro or be greatly shortened rather than be here.
L398-399 As mentioned, the issue of timeseries splitting in a seasonal cycle needs to be considered in more depth before we can be confident about these results.
L418 I would like you to elaborate in more detail if the trends remain robust after addressing the issue of seasonal cycle. What mechanisms do you envisage for a climatic regime change to affect regional glacier velocities? A more intense early summer melt pulse driving high basal pressures and more sliding before efficient drainage is established?
L423 ‘Detachment’ is usually the term used for this glacier collapse process as at Aru
L428 Again, quite misleading to say this since you parameterized to model to identify 5 groups.
L429-444 These are not meeting the typical glaciological definition of a surge. It would be better to not label them this way.
L445 Since they are moving still, ‘stagnant’ is also not really accurate
L429-471 This whole section goes into a lot of detail about the different glacier classes/groups defined by the K-means clustering, but is really missing information to understand why these might be useful. As far as I can tell from this manuscript it seems to be a fairly artificial separation which doesn’t necessarily reflect different underlying processes or other commonalities within the clusters.
Are you suggesting that there might be some generalizable rule about these different types of glaciers? That these classes might be found in other Alpine, or even non-alpine areas?
Where does the number 5 come from? How do we know there shouldn’t be 4, or 6 classes?
L472 It would be good to move the error analysis and evaluation to the results, it is necessary to understand the quality of the subsequent work.
L497 / Figure 10 It would be good to plot this figure with error bars from your data and from Millan et al.
L501 / Table 2 Please label ‘Mean difference’ instead of just ‘Mean’, and include the error bars here too.
L509-510 It is unclear what you mean by ‘anomalous’ here, how can this be determined for a given velocity increase? I agree about you point that a better understanding of baseline velocity variability is necessary to identify precursory changes to a detachment.
L519-520 If we include both short and long baselines it is possible to improve resolving power over slow-moving areas but still capture short events. The post-processing can be more complex however.
L532 See comments above- reasons for 5 groups not clear.
L550 This data availability statement is not really aligned with the FAIR (Findable, Accessible, Interoperable, and Reusable) principles which is expected for this journal. Unless there is a particularly compelling reason, I would expect you to upload the glacier outline shapefiles to an online repository and link to them here.
You say that the glacier velocities are available as a supplement, but I cannot access them. There only seems to be the pdf supplement. Since they are fairly large files, perhaps they would be better hosted in an external repository (e.g. Zenodo). You could, perhaps, add a section to the pdf supplement with your GIV parameter choices to enable easy reproducibility.
Overall, this is an interesting paper and the basic data looks robust, but changes and clarifications to some of the follow-up analyses and restructuring of the text is needed before it is ready to publish here.
-Max
- AC2: 'Reply on RC2', Niccolò Dematteis, 13 Mar 2024
Peer review completion
Journal article(s) based on this preprint
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 468 | 191 | 33 | 692 | 64 | 23 | 27 |
- HTML: 468
- PDF: 191
- XML: 33
- Total: 692
- Supplement: 64
- BibTeX: 23
- EndNote: 27
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Fabrizio Troilo
Niccolò Dematteis
Francesco Zucca
Martin Funk
Daniele Giordan
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2868 KB) - Metadata XML
-
Supplement
(523 KB) - BibTeX
- EndNote
- Final revised paper