Analysis of sea ice deformation and influencing factors in the western Arctic from 2022 to 2023

Chang, Xiaomin; Ji, Lei; Zhu, Bowen; Zuo, Guangyu; Dou, Yinke; Yan, Tongliang

doi:https://doi.org/10.5194/egusphere-2024-1593

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https://doi.org/10.5194/egusphere-2024-1593

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09 Jul 2024

| 09 Jul 2024

Analysis of sea ice deformation and influencing factors in the western Arctic from 2022 to 2023

Xiaomin Chang, Lei Ji, Bowen Zhu, Guangyu Zuo, Yinke Dou, and Tongliang Yan

Abstract. Sea ice governs the global climate, safeguards ecological equilibrium in polar regions, and influences ocean circulation; however, the factors impacting the spatial characteristics of sea ice deformation have not been comprehensively analyzed. This study examined the effects of wind speed, air temperature (T2m), and sea ice thickness on the variation in sea ice deformation within the western Arctic based on the Lagrangian diffusion theory using buoy data from March 2022 to March 2023. The total sea ice deformation gradually declined in all seasons except for the melting season, especially in the fall and winter. Owing to the ongoing sea ice consolidation, the average total deformation was lower in the fall and winter than in the spring. The total deformation of sea ice diminished as the spatial scale increased. As sea ice is thinner on average in spring, geostrophic winds are the primary factor influencing the spatial characteristics of sea ice deformation. In contrast, the larger average ice thickness in fall and winter reduces the significance of the external force, and T2m/sea ice thickness is the primary factor influencing the spatial characteristics of sea ice deformation. Our multivariate nonlinear regression model effectively predicted the total sea ice deformation. This study provides a scientific basis for climate change research, sea ice change prediction, climate model validation, resource management, and environmental protection.

Received: 29 May 2024 – Discussion started: 09 Jul 2024

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Xiaomin Chang, Lei Ji, Bowen Zhu, Guangyu Zuo, Yinke Dou, and Tongliang Yan

Status: closed

RC1:
'Comment on egusphere-2024-1593', Jennifer Hutchings, 16 Aug 2024

This paper is attempting to analyze sea ice kinematics, in particular horizontal deformation in the Beaufort Sea over one full year. A linear regression model is employed to relate the estimated deformation to winds, air temperature and ice thickness. It is not clear how useful this approach is for understanding the relative roles of ice thickness and wind forcing in the dynamics, and I have some issues with the methodology that must be addressed before the validity of the regression model results can be assessed.

My major concern with this paper lies in the choice of buoy arrays used to estimate divergence and shear with the Green's theorem method. When I transferred this methodology from the RGPS procedures to be used for arrays of drifting buoys I was aware that if an array of buoys becomes highly skewed the shear estimate will be biased, and this error will swamp the estimate. Hence my 2012 paper describing the methodology includes information about needing to not use skewed arrays. I estimate how skewed arrays are by considering the ration of the longest and shortest dimension across the array. For the small arrays I was using in that paper I chose to not include data from arrays for which this value was greater than 2. Practically, for the much larger arrays in this paper you can probably use a less stringent criteria, but you still need to avoid including very skewed arrays. Looking at figure 1b it is clear to me that you have a large number of highly skewed arrays in your analysis. In fact most of the arrays are highly skewed. I suspect this is why you see the relative contribution of shear to the total divergence is about 3 times the contribution of divergence (figure 5). This is in fact very unphysical. Divergence and shear rates, on average, should be similar magnitude.

As I do not believe your estimate of total deformation is not biased, I can not trust any of the other results in this paper. For example, in Figure 7 you have higher values for Beta than other studies have shown, and this is likely due to this unphysical bias in the total divergence. Incidentally, did you choose threshold for the different panels in this figure by eye or with an objective method?

While this is my major concern about the studies methodology, I do have some other points that would be important to address if the point is addressed (if it can be addressed, you may not be able to make reasonable non-skewed triangles with this data set).

Is one year of data sufficient to develop your regression model? What about interannual variability in winds and temperature? We also know that from year to year the ice thickness in this part of the Beaufort Sea can display variability, do you need more than one year to represent seasonally detrended thickness variability?

I was disappointed to see some poor literature review practices in the introduction. Some references were misrepresented, and sometimes the first source of information was not quoted but rather a derivative source of that.

For example

Line 25 and 29: Rampal et al. (2009) do not show that weakening of the ice, which would result in reduction of internal ice stresses, results in increased drift speeds. They simply state this as a fact which is unverified and not supported. It is a commonly held thought that because we model compressive ice strength to be a function of thickness, such that it decreases with decreasing thickness, that this will reduce internal ice stresses. This is the case in the model, but it has not been observed to my knowledge.

line 30, page 1: The paper that should be referenced here is Marsan et al. (2004), not Stern et al. (2009).

line 38-40: Hutter et al. used satellite data in their study, so it is not sensical to say their findings are consistent with satellite data as if this study was verifying the previous finding.

line 41-42: You reference a paper for no apparent reason. While Hibler et al. 2006 is interesting (I might be biased, I was the second author and wrote the text of this paper), multi-equilibrium flow states has nothing to do with the narrative of your paper.

Finally, the English in this paper is technically correct and readable. However there are many places where word choice, order of words or grammar change the meaning from what I believe the authors intend. To the point that the desired meaning is not conveyed to the reader. I try to point out some of the places this happens in my specific comments, but please note, I decided not to provide my full editing help, which would require several hours of effort, because this paper has deeper scientific problems that need to be addressed before publication.

Specific Comments

Abstract line 9: Word choice: Sea ice does not govern climate. Perhaps a better word here is "regulates", but you might want to think through the role sea ice has in the climate system in choosing an appropriate word here.

First line of the abstract. I disagree that the factors impacting the spatial characteristics of sea ice deformation have not been comprehensively analyzed. In particular field experiments they have been. Perhaps this overly general statement needs to be clarified, what do you mean by spatial characteristics and comprehensive?

Line 15: Sea ice is not thinner than average in Spring. In spring, just before the onset of melt, the ice is at it's maximum thickness.

line 29: positively is an ambiguous word choice. How is this a positive relationship?
line 59: An example of overly general language that conveys little meaning as to what you did. There are several places this is an issue in the paper. "stdies on the factors affecting sea ice deformation characteristics at large ranges of spatial and temporal scales are limited". Which factors? which characteristics? You do not introduce even what limited work has been done and what factors need to be considered.
line 67: Is Lagrangian diffusion theory a made up word? I can not find any definition of this or explanation of what it is.
In this paragraph you appear to be mixing up descriptions of different kinds of analysis that would result in different scaling exponents that are not equivelent to each other. Beta is not the same as the value of scaling exponent found if considering dispersion (which is my best guess of what you are calculating with Lagrangian diffusion theory). This is one example of where concepts need to be more tightly explained in the paper.
section 2.2, first paragraph: There is another method that has been recently developed.

Aksamit, N. O., Scharien, R. K., Hutchings, J. K., & Lukovich, J. V. (2023). A quasi-objective single-buoy approach for understanding Lagrangian coherent structures and sea ice dynamics. The Cryosphere, 17(4), 1545-1566.
In places variables in equations are not defined. Also, you have not chosen variable labels that follow convention in the field. The use of epsilon for total deformation might be misleading, because epsilon is typically used for strain. The two are not equivalent. you use x and y as indices and variables in multiple equations, which is confusing. The choice of variable names in your regression equation 10 makes this equation hard to read. Why not use symbols that can more easily be seen to be wind speed, temperature and ice thickness by the reader. For example V_w, T_2m, h_i.
You are calling the maximum shear simply as shear. It would be more correct to refer to the value calculated in equation 7 as the maximum shear.
line 183-185: Grammar here is mangling the sentences.
Figure 4: You could include a line for your definition of ice free.
section 3.3. introductory paragraph. This is out of place and should be at the front of the paper in the introduction.
lines 265-270: Contradictory sentences and meaning mangled.
line 296: What is "each factor" exactly?
line 300: Very confusing sentence
line 319: What is the "critical value", as in how do you define this?
line 330 and your interpretation of Stern et al. (2009)'s result that Beta increases from winter into summer. I agree with you that there can be a discrepancy due to changing sizes in the buoy arrays. My recent paper (Hutchings et al. 2024) shows that the relationship between total deformation and length scale is not log-log linear, and hence if you make a linear fit to data that has different ranges of length scale you will get a different estimate of Beta.

Hutchings, J. K., Bliss, A. C., Mondal, D., & Elosegui, P. (2024). Sea ice deformation is not scale invariant over length scales greater than a kilometer. Geophysical Research Letters, 51(12), e2024GL108582.
Lines around 335: I am really not sure how your results "emphasize" the impact of seasonal changes on sea ice deformation in the Arctic. This section is hard to follow and I am wondering if it would be simpler to say that your results follow those of Stern et al. (2009).

Citation: https://doi.org/10.5194/egusphere-2024-1593-RC1
- AC1: 'Reply on RC1', Lei Ji, 24 Sep 2024
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1593/egusphere-2024-1593-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-1593-AC1
RC2: 'Comment on egusphere-2024-1593', Anonymous Referee #2, 11 Oct 2024

Dear authors,
thanks for your contribution. Please find my assessment in the attached pdf file.

Citation: https://doi.org/10.5194/egusphere-2024-1593-RC2

Status: closed

RC1:
'Comment on egusphere-2024-1593', Jennifer Hutchings, 16 Aug 2024

This paper is attempting to analyze sea ice kinematics, in particular horizontal deformation in the Beaufort Sea over one full year. A linear regression model is employed to relate the estimated deformation to winds, air temperature and ice thickness. It is not clear how useful this approach is for understanding the relative roles of ice thickness and wind forcing in the dynamics, and I have some issues with the methodology that must be addressed before the validity of the regression model results can be assessed.

My major concern with this paper lies in the choice of buoy arrays used to estimate divergence and shear with the Green's theorem method. When I transferred this methodology from the RGPS procedures to be used for arrays of drifting buoys I was aware that if an array of buoys becomes highly skewed the shear estimate will be biased, and this error will swamp the estimate. Hence my 2012 paper describing the methodology includes information about needing to not use skewed arrays. I estimate how skewed arrays are by considering the ration of the longest and shortest dimension across the array. For the small arrays I was using in that paper I chose to not include data from arrays for which this value was greater than 2. Practically, for the much larger arrays in this paper you can probably use a less stringent criteria, but you still need to avoid including very skewed arrays. Looking at figure 1b it is clear to me that you have a large number of highly skewed arrays in your analysis. In fact most of the arrays are highly skewed. I suspect this is why you see the relative contribution of shear to the total divergence is about 3 times the contribution of divergence (figure 5). This is in fact very unphysical. Divergence and shear rates, on average, should be similar magnitude.

As I do not believe your estimate of total deformation is not biased, I can not trust any of the other results in this paper. For example, in Figure 7 you have higher values for Beta than other studies have shown, and this is likely due to this unphysical bias in the total divergence. Incidentally, did you choose threshold for the different panels in this figure by eye or with an objective method?

While this is my major concern about the studies methodology, I do have some other points that would be important to address if the point is addressed (if it can be addressed, you may not be able to make reasonable non-skewed triangles with this data set).

Is one year of data sufficient to develop your regression model? What about interannual variability in winds and temperature? We also know that from year to year the ice thickness in this part of the Beaufort Sea can display variability, do you need more than one year to represent seasonally detrended thickness variability?

I was disappointed to see some poor literature review practices in the introduction. Some references were misrepresented, and sometimes the first source of information was not quoted but rather a derivative source of that.

For example

Line 25 and 29: Rampal et al. (2009) do not show that weakening of the ice, which would result in reduction of internal ice stresses, results in increased drift speeds. They simply state this as a fact which is unverified and not supported. It is a commonly held thought that because we model compressive ice strength to be a function of thickness, such that it decreases with decreasing thickness, that this will reduce internal ice stresses. This is the case in the model, but it has not been observed to my knowledge.

line 30, page 1: The paper that should be referenced here is Marsan et al. (2004), not Stern et al. (2009).

line 38-40: Hutter et al. used satellite data in their study, so it is not sensical to say their findings are consistent with satellite data as if this study was verifying the previous finding.

line 41-42: You reference a paper for no apparent reason. While Hibler et al. 2006 is interesting (I might be biased, I was the second author and wrote the text of this paper), multi-equilibrium flow states has nothing to do with the narrative of your paper.

Finally, the English in this paper is technically correct and readable. However there are many places where word choice, order of words or grammar change the meaning from what I believe the authors intend. To the point that the desired meaning is not conveyed to the reader. I try to point out some of the places this happens in my specific comments, but please note, I decided not to provide my full editing help, which would require several hours of effort, because this paper has deeper scientific problems that need to be addressed before publication.

Specific Comments

Abstract line 9: Word choice: Sea ice does not govern climate. Perhaps a better word here is "regulates", but you might want to think through the role sea ice has in the climate system in choosing an appropriate word here.

First line of the abstract. I disagree that the factors impacting the spatial characteristics of sea ice deformation have not been comprehensively analyzed. In particular field experiments they have been. Perhaps this overly general statement needs to be clarified, what do you mean by spatial characteristics and comprehensive?

Line 15: Sea ice is not thinner than average in Spring. In spring, just before the onset of melt, the ice is at it's maximum thickness.

line 29: positively is an ambiguous word choice. How is this a positive relationship?
line 59: An example of overly general language that conveys little meaning as to what you did. There are several places this is an issue in the paper. "stdies on the factors affecting sea ice deformation characteristics at large ranges of spatial and temporal scales are limited". Which factors? which characteristics? You do not introduce even what limited work has been done and what factors need to be considered.
line 67: Is Lagrangian diffusion theory a made up word? I can not find any definition of this or explanation of what it is.
In this paragraph you appear to be mixing up descriptions of different kinds of analysis that would result in different scaling exponents that are not equivelent to each other. Beta is not the same as the value of scaling exponent found if considering dispersion (which is my best guess of what you are calculating with Lagrangian diffusion theory). This is one example of where concepts need to be more tightly explained in the paper.
section 2.2, first paragraph: There is another method that has been recently developed.

Aksamit, N. O., Scharien, R. K., Hutchings, J. K., & Lukovich, J. V. (2023). A quasi-objective single-buoy approach for understanding Lagrangian coherent structures and sea ice dynamics. The Cryosphere, 17(4), 1545-1566.
In places variables in equations are not defined. Also, you have not chosen variable labels that follow convention in the field. The use of epsilon for total deformation might be misleading, because epsilon is typically used for strain. The two are not equivalent. you use x and y as indices and variables in multiple equations, which is confusing. The choice of variable names in your regression equation 10 makes this equation hard to read. Why not use symbols that can more easily be seen to be wind speed, temperature and ice thickness by the reader. For example V_w, T_2m, h_i.
You are calling the maximum shear simply as shear. It would be more correct to refer to the value calculated in equation 7 as the maximum shear.
line 183-185: Grammar here is mangling the sentences.
Figure 4: You could include a line for your definition of ice free.
section 3.3. introductory paragraph. This is out of place and should be at the front of the paper in the introduction.
lines 265-270: Contradictory sentences and meaning mangled.
line 296: What is "each factor" exactly?
line 300: Very confusing sentence
line 319: What is the "critical value", as in how do you define this?
line 330 and your interpretation of Stern et al. (2009)'s result that Beta increases from winter into summer. I agree with you that there can be a discrepancy due to changing sizes in the buoy arrays. My recent paper (Hutchings et al. 2024) shows that the relationship between total deformation and length scale is not log-log linear, and hence if you make a linear fit to data that has different ranges of length scale you will get a different estimate of Beta.

Hutchings, J. K., Bliss, A. C., Mondal, D., & Elosegui, P. (2024). Sea ice deformation is not scale invariant over length scales greater than a kilometer. Geophysical Research Letters, 51(12), e2024GL108582.
Lines around 335: I am really not sure how your results "emphasize" the impact of seasonal changes on sea ice deformation in the Arctic. This section is hard to follow and I am wondering if it would be simpler to say that your results follow those of Stern et al. (2009).

Citation: https://doi.org/10.5194/egusphere-2024-1593-RC1
- AC1: 'Reply on RC1', Lei Ji, 24 Sep 2024
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1593/egusphere-2024-1593-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-1593-AC1
RC2: 'Comment on egusphere-2024-1593', Anonymous Referee #2, 11 Oct 2024

Dear authors,
thanks for your contribution. Please find my assessment in the attached pdf file.

Citation: https://doi.org/10.5194/egusphere-2024-1593-RC2

Xiaomin Chang, Lei Ji, Bowen Zhu, Guangyu Zuo, Yinke Dou, and Tongliang Yan

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https://doi.org/10.5194/egusphere-2024-1593-supplement

Xiaomin Chang, Lei Ji, Bowen Zhu, Guangyu Zuo, Yinke Dou, and Tongliang Yan

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Short summary

The purpose of this study was to use Lagrangian diffusion theory to investigate the effects of wind speed, air temperature (T2m), and sea ice thickness on variations in sea ice deformation in the Western Arctic. This study examines the sequence of changes in sea ice deformation in the western Arctic between March 2022 and March 2023.


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