A probabilistic seabed-ice keel interaction model

Dupont, Frédéric; Dumont, Dany; Lemieux, Jean-François; Dumas-Lefebvre, Elie; Caya, Alain

doi:https://doi.org/10.5194/tc-2021-273

Preprints

https://doi.org/10.5194/tc-2021-273

Preprints

01 Nov 2021

Status: a revised version of this preprint was accepted for the journal TC and is expected to appear here in due course.

A probabilistic seabed-ice keel interaction model

Frédéric Dupont⁴, Dany Dumont¹, Jean-François Lemieux², Elie Dumas-Lefebvre¹, and Alain Caya³ Frédéric Dupont et al.

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¹Institut des sciences de la mer de Rimouski, Université du Québec à Rimouski, Rimouski QC, Canada
²Recherche en Prévision Numérique Environnementale/Environnement et Changement Climatique Canada, 2121 route Transcanadienne, Dorval QC, Canada
³Recherche en assimilation de données et météorologie satellitaire, Environnement et Changement Climatique Canada, 2121 route Transcanadienne, Dorval QC, Canada
⁴Service Météorologique Canadien, Environnement et Changement Climatique Canada, 2121 route Transcanadienne, Dorval QC, Canada

Received: 26 Aug 2021 – Discussion started: 01 Nov 2021

Abstract. In some coastal regions of the Arctic Ocean, as well as in shallow seasonally ice-covered seas, grounded ice ridges contribute to stabilizing and maintaining a landfast ice cover. Recently, a grounding scheme representing this effect on sea ice dynamics was introduced and tested in a coupled ice-ocean model. This grounding scheme, based on a parameterization of ridged keel thickness linearly correlated to the mean thickness, improves the simulation of landfast ice in many regions such as in the East Siberian Sea, the Laptev Sea and along the coast of Alaska. Nevertheless, this parameterization is based solely on the mean properties of sea ice. Here, we extend the parameterization by taking into account subgridscale ice thickness distribution and bathymetry distributions, which are generally non-normal, and by computing the maximum seabed stress as a joint probability interaction between the ice and the seabed. The probabilistic approach shows a reasonably good agreement with observations and with the previously proposed grounding scheme while potentially offering more physical insights in the formation of landfast ice.

Frédéric Dupont et al.

Status: closed

RC1:
'Comment on tc-2021-273', Andrew Mahoney, 06 Dec 2021

A probabilistic seabed-ice keel interaction model

by Frédéric Dupont, Dany Dumont, Jean-François Lemieux, Elie Dumas-Lefebvre, and Alain Caya

Submitted to The Cryosphere

Review by Andy Mahoney

December 5, 2021

Summary

This manuscript presents a probabilistic approach, dubbed ProbSI, for computing the basal shear stress arising due to interaction between sea ice pressure ridges and the seafloor for the purposes of improving the simulation of landfast sea ice in coupled ice-ocean models. The technique described is based upon that of Lemieux et al (2015), but with a more sophisticated approach that utilizes probability density functions of both the ice thickness and bathymetry in a grid cell rather than simply relying on the mean values. One result of this approach is that two grid cells with the same mean ice thickness might have different maximum keel depths, depending on the shape of the ice thickness distribution (ITD). Additionally, by relating the maximum keel depth to a fixed percentile of the ITD, the authors introduce a non-linear relationship between mean ice thickness and keel depth that better matches observations. Although the initial results from the ProbSI model do not appear to be a drastic improvement over the those derived using Lemieux et al’s (2015) linear keel depth parameterization, the authors demonstrate the sensitivity of the results to the variability of bathymetry within a grid cell and, hence, the importance of retaining the sub-grid bathymetric distribution.

Overall, the paper is well written and does a good of presenting complex concepts associated with the interaction of different probability distributions in a largely clear and concise way. However, I have one concern regarding the apparent conflation between mean ice thickness and level ice thickness (see comment 1) and I have some recommendations for improving the manuscript by revising some key figures (see comment 2) and including more discussion about early landfast ice formation mechanisms in the Laptev Sea (see comment 3). I provide a longer list of minor comments as well, but I do not think the authors will find it difficult to address any of my concerns. However, because my first major comment below relates to a fundamental part of the methodology, I believe this may qualify as requiring major revisions.

Major Comments

1. Mismatch between mean ice thickness and level ice thickness

Near the beginning of Section 3.1.1, the authors note that both Melling and Riedel (1996) and Amundrud et al (2004) derived relationships between keel depths (h_dk) and the draft of surrounding level ice (h_dl). However, later in the same paragraph the text describes these relationships as being between keel depth and mean ice thickness (h_mean). I thought that this may have been a simple typo, but the x-axes in Figure 2 are labelled as h_mean and the text in the discussion on lines 347-348 again refers to mean ice thickness. I am therefore concerned that the authors may be incorrectly applying the findings of Melling & Riedel and Amundrud et al by applying their relationships to mean ice thickness instead of level ice thickness. Since mean thickness will almost always be greater than the level ice thickness in a grid cell, this will have the effect of moving the curves shown in Figure 2 downward, suggesting that x₉₉₇ may not be the best fit as claimed

2. Lack of clarity in key figures

Figures 1 and 3 are important figures, but both could use work to improve their usefulness to the reader. I found it necessary to read both the captions and the main body of text multiple times before I understood what either figure was supposed to be showing. Although I appreciate the avoidance of what Tufte (2001) describes as “chart junk”, I believe the information content of each figure as a whole would be greatly improved with better labelling. Specifically, I would recommend adding a legend to Figure 1 to explain the meaning of each curve and symbol without having to read a full-paragraph caption. This would also allow the caption to be shortened significantly.

I also recommend using textual axis labels so that the reader doesn’t have to refer back the main text to remember what each symbol or abbreviation means. For example, the y-axis in Figure 3c is labeled “Bathymetric PDF”, rather than b(y), and I recommend adopting this practice for all axes and legends. Also, for accuracy, the y-axes of Fig 1c-f should reference both ice thickness and bathymetry.

Lastly, I recommend using a different color to highlight the final ice thickness category in Figure 1a, since the choice of yellow suggests some relationship to the yellow curves in panels c-f.

3. Incomplete discussion of difference in landfast ice development in Laptev Sea

The authors draw attention to the earlier and more rapid development of simulated landfast ice in the Laptev Sea, as compared with observations of landfast ice in ice charts from the U.S. National Ice Center. They state that an “in-depth analysis is required to investigate what is behind this discrepancy” (lines 356-357), but suggest that it may be related to overestimated of keel depths resulting from deformation of thin ice. Although I do not want to suggest any new in-depth analyses, I would recommend additional discussion referring to the work Selyuzhenok et al (2015; 2017), which describes the formation of landfast ice in the Laptev Sea in some useful detail.

Specifically, Selyuzhenok et al (2015) identify a period of “initial formation" November and December, during which time landfast ice slowly approaches approximately 20% of its annual maximum extent. This is followed by brief period of rapid expansion when most of the remaining expansion takes place. These periods are robust features of the annual cycle of landfast ice in the Laptev Sea and are captured in the NIC-derived landfast ice extent shown in Figure 6. In their 2017 paper, Selyuzhenok et al go on to show that during the initial formation period, grounded features can form offshore while being entirely surrounded by ice that is still mobile. The drift speed of the mobile ice gradually decreases until the ice becomes stationary, at which point there is a rapid growth in landfast ice extent. Selyuzhenok et al (2015) attribute the onset of rapid growth to the achievement of a critical thickness or strength within the formerly mobile ice. Hence, the ProbSI model may not be overestimating keel depths, but instead overestimating the shear strength of the surrounding ice.

Minor comments

Line 27: Replace “Most” with “More”

Line 112: I assume that the symbol σ in equation 5 refers to the internal stress within, but since not all readers will be familiar with the sea ice momentum equation, it should be explicitly defined. Also, it appears that σ is used later in a different context (see comment for line 158), so further clarification maybe needed.

Lines 118-119: I believe the cross reference to section 3 should be a reference to 3-point-something

Line 158: σ is apparently being used here to a different property than in equation 5 above (see comment for line 112). A different symbol should therefore be used either here or above. Also, I recommend providing a physical explanation of both σ and μ as expressed here.

Line 176-177: How are σ_b and μ_b related to σ and μ as defined in equations 7 and 8? Here, σ_b and μ_b are referred to as "mean value" and "spread". Is this how σ and μ should be interpretted?

Line 205: I recommend replacing “This figure” with “Figure 2”

Line 221: Where the text reads “the depth”, I assume the authors are referring to water depth. However, since the text regularly refers to both water depth and keel depth, I recommend taking care to specific each time the term depth is used

Lines 221-222: I'm confused here. Please explain why the probability of finding thicker ice is greater with the TU bathymetric distribution

Line 224: The use of "later" here is imprecise as it suggests a time-dependent process. I believe a phrase like "at a greater mean water depth" would be more appropriate.

Line 227: I find the phrase "visually very close" to be ambiguous. I recommend finding a more accurate and specific phrase.

Line 228: I believe "less impact that" should read "less impact than". Also, I assume the authors are referring the impact on basal shear stress, in which case I think it would help to add “on basal shear stress” after “impact”.

Figure 3: See major comment 2 above regarding the replacement of abbreviations in the legend with full text. Also, I believe the word "truncated" is missing on the 4th line of the caption before the second usage of “Gaussian”

Line 335: I am not convinced that the number of months of landfast ice per year is a meaningful metric when the timing of formation and breakup is not well reproduced. This approach would suggest the model is somehow more accurate if it simulates earlier dates of both formation and break up. Those are two separate errors that this metric will mask.

Line 336: I do not know what "stronger" means in the context of landfast ice onset. I recommend using plainer, clearer language. In this case, I think "earlier", or "more rapid" (or perhaps both) would be more appropriate.

Line 338: Please clarify what "lower number of landfast ice cover means". I think there maybe a typo here, but I can’t uniquely identify a solution

Line 338: I don't think "akin" is the right word here. Perhaps "prone" or "susceptible" would be more appropriate.

Line 339: While appreciate the graphically descriptive nature of the term "high frequency wiggles", I am sure the authors could find a phrase that more accurately describes the variability to which they are drawing attention.

References cited in this review that are not cited in the submitted manuscript

Selyuzhenok, V., T. Krumpen, A. Mahoney, M. Janout, and R. Gerdes (2015), Seasonal and interannual variability of fast ice extent in the southeastern Laptev Sea between 1999 and 2013, Journal of Geophysical Research: Oceans, 120(12), 7791-7806 10.1002/2015JC011135.

Selyuzhenok, V., A. Mahoney, T. Krumpen, G. Castellani, and R. Gerdes (2017), Mechanisms of fast-ice development in the south-eastern Laptev Sea: a case study for winter of 2007/08 and 2009/10, Polar Research, 36(1), 1411140 10.1080/17518369.2017.1411140.

Tufte, E. (2001), The visual display of quantitative information, edited, Cheshire: Graphic Press.–2001.–213 p.

Citation: https://doi.org/10.5194/tc-2021-273-RC1
- AC1: 'Reply on RC1', Frederic Dupont, 28 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-273/tc-2021-273-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-273-AC1
CC1:
'Comment on tc-2021-273', Katherine Hedstrom, 04 Jan 2022

I stumbled upon this scheme in the CICE manual. Given that I have a project with the goal to improve the landfast ice in a pan-Arctic model, I was quite interested. In attempting to bring the algorithm into the SIS2 model, the developer of that model insists on the code passing unit scaling tests.
This equation is problematic:

mu_i = log(m_i/sqrt(1.0 + v_i/m_i**2))

with m_i having units of meters per unit area and mu_i being dimensionless. It is used here:

x_kmax = exp(mu_i + sqrt(2.0*sigma_i)*1.9430)

where x_kmax is again in units of meters. I think there need to be some scaling constants mixed in, right?

Citation: https://doi.org/10.5194/tc-2021-273-CC1
- AC2: 'Reply on CC1', Frederic Dupont, 28 Feb 2022
  
  Thanks for pointing out this dimensional inconsistency in the way the model is mathematically formulated. The equations are numerically correct if the random variable x' we use for thickness, that is represented by the log-normal distribution, is defined as x/1m, where x is the dimensional thickness in meters. The choice of the unit thickness is arbitrary though, in general. In the paper, I suggest we explicitly define this scaling as x' = x/𝜆, where 𝜆 is a unit thickness that is used in the ice model. This way, taking the log of x' is correct. When retrieving the dimensional thickness quantity, we need to multiply back by 𝜆 after taking the exponential. Then the expression for xkmax would need to be multiplied by 𝜆 for it to bear units.
  
  In the code, we can introduce a constant called
  
  onemeter = 1_dbl_kind
  
  which is used here
  
  m_i = sum(vcat)/onemeter
  
  here
  
  v_i = c0
  do n=1, ncat
  v_i = v_i + ncat(n)**2 / (max(acat(n), puny) * onemeter**2)
  enddo
  
  and here
  
  x_kmax = onemeter*exp(mu_i + sqrt(2.0*sigma_i)*1.9430).
  
  This new constant could be set to
  
  onemeter = 100_dbl_kind
  
  if the ice model has its thickness in cm, without the need to alter the numerical values used for tuning.
  
  Citation: https://doi.org/10.5194/tc-2021-273-AC2
CC2:
'Comment on tc-2021-273', Katherine Hedstrom, 06 Jan 2022

Another comment I have is that we are now using GEBCO 2020 which is very high resolution. The algorithm we use to generate bathymetric roughness is in the Adcroft paper cited here: https://github.com/nikizadehgfdl/ocean_model_topog_generator, plus the code is there too.

Citation: https://doi.org/10.5194/tc-2021-273-CC2
- AC3: 'Reply on CC2', Frederic Dupont, 28 Feb 2022
  
  This sounds quite interesting. if you could retain the standard deviation of the approximation (or better, of the original bathy data in each cell)], then you could use this value instead of the user-defined sigma_b. The Adcroft reference is quite useful too and was added in the paper as an example of subgrid bathymetry applications.
  
  Citation: https://doi.org/10.5194/tc-2021-273-AC3
RC2:
'Comment on tc-2021-273', Anonymous Referee #2, 15 Feb 2022

The manuscript describes extended version of grounding scheme by Lemieux et al., 2015. Authors provide theoretical description of the method, apply it for short term sea ice-ocean simulations and describe the results.

The paper is very well written, and enjoyable to read. Figures are also of a good quality. I have only several very small comments, and in my view, paper can be accepted after minor revision.

Minor comments:

Line 30. It would be nice to see a paragraph about other attempts to add fast ice in the Arctic Ocean simulations, like Lieser et al., 2004, Itkin et al., 2015 and Olason, 2016.

Lines 38-39: Please comment on computational efficiency as well.

Line 57. You probably mean then --> than.

Line 82. While it became obvious from the rest of the paper why you represent bathymetry as random variable, a simple additional sentence giving the motivation for it would be useful for ocean modelers like me, who often just take bathymetry as something that is well defined.

Line 118. …here (see Section 3) --> in this section

Line 119. “The following SUBsections”.

Line 163. You mean Subsection 3.3.1 here, I guess.

Line 242. Why so many EVP cycles? The standard value for CICE is around 120, if I am not mistaken?

Line 247. Please comment on what is the advantage of this forcing, which seem to be popular in regional ocean modelling, but is quite exotic for global modelling.

It would be good if you mention computational efficiency of the scheme in Section 3.4. Just if it decreases the model speed to a noticeable amount.

Line 325. “… a factor OF two”.

Discussion

The resolution in the model setup is around 12.5 km in the Arctic. Please comment on how well, you think, this grounding scheme will be working in higher resolution setups (e.g. ORCA12 and higher).

Please add to the discussion comparison to other studies, that try to simulate fast ice.

References:

Lieser, J. (2004), A numerical model for short-term sea ice forecasting in the Arctic (Ein numerisches Modell zur Meereisvorhersage in der Arktis), Rep. Polar Mar. Res. (Berichte zur Polar Meeresforschung), vol. 485, 93 pp.

Einar Olason, A dynamical model of Kara Sea landâfast ice, Journal of Geophysical Research: Oceans, 10.1002/2016JC011638, 121, 5, (3141-3158), (2016).

Itkin, P., Losch, M., and Gerdes, R. (2015), Landfast ice affects the stability of the Arctic halocline: Evidence from a numerical model, J. Geophys. Res. Oceans, 120, 2622– 2635, doi:10.1002/2014JC010353.

Citation: https://doi.org/10.5194/tc-2021-273-RC2
- AC4: 'Reply on RC2', Frederic Dupont, 28 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-273/tc-2021-273-AC4-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-273-AC4

Status: closed

RC1:
'Comment on tc-2021-273', Andrew Mahoney, 06 Dec 2021

A probabilistic seabed-ice keel interaction model

by Frédéric Dupont, Dany Dumont, Jean-François Lemieux, Elie Dumas-Lefebvre, and Alain Caya

Submitted to The Cryosphere

Review by Andy Mahoney

December 5, 2021

Summary

This manuscript presents a probabilistic approach, dubbed ProbSI, for computing the basal shear stress arising due to interaction between sea ice pressure ridges and the seafloor for the purposes of improving the simulation of landfast sea ice in coupled ice-ocean models. The technique described is based upon that of Lemieux et al (2015), but with a more sophisticated approach that utilizes probability density functions of both the ice thickness and bathymetry in a grid cell rather than simply relying on the mean values. One result of this approach is that two grid cells with the same mean ice thickness might have different maximum keel depths, depending on the shape of the ice thickness distribution (ITD). Additionally, by relating the maximum keel depth to a fixed percentile of the ITD, the authors introduce a non-linear relationship between mean ice thickness and keel depth that better matches observations. Although the initial results from the ProbSI model do not appear to be a drastic improvement over the those derived using Lemieux et al’s (2015) linear keel depth parameterization, the authors demonstrate the sensitivity of the results to the variability of bathymetry within a grid cell and, hence, the importance of retaining the sub-grid bathymetric distribution.

Overall, the paper is well written and does a good of presenting complex concepts associated with the interaction of different probability distributions in a largely clear and concise way. However, I have one concern regarding the apparent conflation between mean ice thickness and level ice thickness (see comment 1) and I have some recommendations for improving the manuscript by revising some key figures (see comment 2) and including more discussion about early landfast ice formation mechanisms in the Laptev Sea (see comment 3). I provide a longer list of minor comments as well, but I do not think the authors will find it difficult to address any of my concerns. However, because my first major comment below relates to a fundamental part of the methodology, I believe this may qualify as requiring major revisions.

Major Comments

1. Mismatch between mean ice thickness and level ice thickness

Near the beginning of Section 3.1.1, the authors note that both Melling and Riedel (1996) and Amundrud et al (2004) derived relationships between keel depths (h_dk) and the draft of surrounding level ice (h_dl). However, later in the same paragraph the text describes these relationships as being between keel depth and mean ice thickness (h_mean). I thought that this may have been a simple typo, but the x-axes in Figure 2 are labelled as h_mean and the text in the discussion on lines 347-348 again refers to mean ice thickness. I am therefore concerned that the authors may be incorrectly applying the findings of Melling & Riedel and Amundrud et al by applying their relationships to mean ice thickness instead of level ice thickness. Since mean thickness will almost always be greater than the level ice thickness in a grid cell, this will have the effect of moving the curves shown in Figure 2 downward, suggesting that x₉₉₇ may not be the best fit as claimed

2. Lack of clarity in key figures

Figures 1 and 3 are important figures, but both could use work to improve their usefulness to the reader. I found it necessary to read both the captions and the main body of text multiple times before I understood what either figure was supposed to be showing. Although I appreciate the avoidance of what Tufte (2001) describes as “chart junk”, I believe the information content of each figure as a whole would be greatly improved with better labelling. Specifically, I would recommend adding a legend to Figure 1 to explain the meaning of each curve and symbol without having to read a full-paragraph caption. This would also allow the caption to be shortened significantly.

I also recommend using textual axis labels so that the reader doesn’t have to refer back the main text to remember what each symbol or abbreviation means. For example, the y-axis in Figure 3c is labeled “Bathymetric PDF”, rather than b(y), and I recommend adopting this practice for all axes and legends. Also, for accuracy, the y-axes of Fig 1c-f should reference both ice thickness and bathymetry.

Lastly, I recommend using a different color to highlight the final ice thickness category in Figure 1a, since the choice of yellow suggests some relationship to the yellow curves in panels c-f.

3. Incomplete discussion of difference in landfast ice development in Laptev Sea

The authors draw attention to the earlier and more rapid development of simulated landfast ice in the Laptev Sea, as compared with observations of landfast ice in ice charts from the U.S. National Ice Center. They state that an “in-depth analysis is required to investigate what is behind this discrepancy” (lines 356-357), but suggest that it may be related to overestimated of keel depths resulting from deformation of thin ice. Although I do not want to suggest any new in-depth analyses, I would recommend additional discussion referring to the work Selyuzhenok et al (2015; 2017), which describes the formation of landfast ice in the Laptev Sea in some useful detail.

Specifically, Selyuzhenok et al (2015) identify a period of “initial formation" November and December, during which time landfast ice slowly approaches approximately 20% of its annual maximum extent. This is followed by brief period of rapid expansion when most of the remaining expansion takes place. These periods are robust features of the annual cycle of landfast ice in the Laptev Sea and are captured in the NIC-derived landfast ice extent shown in Figure 6. In their 2017 paper, Selyuzhenok et al go on to show that during the initial formation period, grounded features can form offshore while being entirely surrounded by ice that is still mobile. The drift speed of the mobile ice gradually decreases until the ice becomes stationary, at which point there is a rapid growth in landfast ice extent. Selyuzhenok et al (2015) attribute the onset of rapid growth to the achievement of a critical thickness or strength within the formerly mobile ice. Hence, the ProbSI model may not be overestimating keel depths, but instead overestimating the shear strength of the surrounding ice.

Minor comments

Line 27: Replace “Most” with “More”

Line 112: I assume that the symbol σ in equation 5 refers to the internal stress within, but since not all readers will be familiar with the sea ice momentum equation, it should be explicitly defined. Also, it appears that σ is used later in a different context (see comment for line 158), so further clarification maybe needed.

Lines 118-119: I believe the cross reference to section 3 should be a reference to 3-point-something

Line 158: σ is apparently being used here to a different property than in equation 5 above (see comment for line 112). A different symbol should therefore be used either here or above. Also, I recommend providing a physical explanation of both σ and μ as expressed here.

Line 176-177: How are σ_b and μ_b related to σ and μ as defined in equations 7 and 8? Here, σ_b and μ_b are referred to as "mean value" and "spread". Is this how σ and μ should be interpretted?

Line 205: I recommend replacing “This figure” with “Figure 2”

Line 221: Where the text reads “the depth”, I assume the authors are referring to water depth. However, since the text regularly refers to both water depth and keel depth, I recommend taking care to specific each time the term depth is used

Lines 221-222: I'm confused here. Please explain why the probability of finding thicker ice is greater with the TU bathymetric distribution

Line 224: The use of "later" here is imprecise as it suggests a time-dependent process. I believe a phrase like "at a greater mean water depth" would be more appropriate.

Line 227: I find the phrase "visually very close" to be ambiguous. I recommend finding a more accurate and specific phrase.

Line 228: I believe "less impact that" should read "less impact than". Also, I assume the authors are referring the impact on basal shear stress, in which case I think it would help to add “on basal shear stress” after “impact”.

Figure 3: See major comment 2 above regarding the replacement of abbreviations in the legend with full text. Also, I believe the word "truncated" is missing on the 4th line of the caption before the second usage of “Gaussian”

Line 335: I am not convinced that the number of months of landfast ice per year is a meaningful metric when the timing of formation and breakup is not well reproduced. This approach would suggest the model is somehow more accurate if it simulates earlier dates of both formation and break up. Those are two separate errors that this metric will mask.

Line 336: I do not know what "stronger" means in the context of landfast ice onset. I recommend using plainer, clearer language. In this case, I think "earlier", or "more rapid" (or perhaps both) would be more appropriate.

Line 338: Please clarify what "lower number of landfast ice cover means". I think there maybe a typo here, but I can’t uniquely identify a solution

Line 338: I don't think "akin" is the right word here. Perhaps "prone" or "susceptible" would be more appropriate.

Line 339: While appreciate the graphically descriptive nature of the term "high frequency wiggles", I am sure the authors could find a phrase that more accurately describes the variability to which they are drawing attention.

References cited in this review that are not cited in the submitted manuscript

Selyuzhenok, V., T. Krumpen, A. Mahoney, M. Janout, and R. Gerdes (2015), Seasonal and interannual variability of fast ice extent in the southeastern Laptev Sea between 1999 and 2013, Journal of Geophysical Research: Oceans, 120(12), 7791-7806 10.1002/2015JC011135.

Selyuzhenok, V., A. Mahoney, T. Krumpen, G. Castellani, and R. Gerdes (2017), Mechanisms of fast-ice development in the south-eastern Laptev Sea: a case study for winter of 2007/08 and 2009/10, Polar Research, 36(1), 1411140 10.1080/17518369.2017.1411140.

Tufte, E. (2001), The visual display of quantitative information, edited, Cheshire: Graphic Press.–2001.–213 p.

Citation: https://doi.org/10.5194/tc-2021-273-RC1
- AC1: 'Reply on RC1', Frederic Dupont, 28 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-273/tc-2021-273-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-273-AC1
CC1:
'Comment on tc-2021-273', Katherine Hedstrom, 04 Jan 2022

I stumbled upon this scheme in the CICE manual. Given that I have a project with the goal to improve the landfast ice in a pan-Arctic model, I was quite interested. In attempting to bring the algorithm into the SIS2 model, the developer of that model insists on the code passing unit scaling tests.
This equation is problematic:

mu_i = log(m_i/sqrt(1.0 + v_i/m_i**2))

with m_i having units of meters per unit area and mu_i being dimensionless. It is used here:

x_kmax = exp(mu_i + sqrt(2.0*sigma_i)*1.9430)

where x_kmax is again in units of meters. I think there need to be some scaling constants mixed in, right?

Citation: https://doi.org/10.5194/tc-2021-273-CC1
- AC2: 'Reply on CC1', Frederic Dupont, 28 Feb 2022
  
  Thanks for pointing out this dimensional inconsistency in the way the model is mathematically formulated. The equations are numerically correct if the random variable x' we use for thickness, that is represented by the log-normal distribution, is defined as x/1m, where x is the dimensional thickness in meters. The choice of the unit thickness is arbitrary though, in general. In the paper, I suggest we explicitly define this scaling as x' = x/𝜆, where 𝜆 is a unit thickness that is used in the ice model. This way, taking the log of x' is correct. When retrieving the dimensional thickness quantity, we need to multiply back by 𝜆 after taking the exponential. Then the expression for xkmax would need to be multiplied by 𝜆 for it to bear units.
  
  In the code, we can introduce a constant called
  
  onemeter = 1_dbl_kind
  
  which is used here
  
  m_i = sum(vcat)/onemeter
  
  here
  
  v_i = c0
  do n=1, ncat
  v_i = v_i + ncat(n)**2 / (max(acat(n), puny) * onemeter**2)
  enddo
  
  and here
  
  x_kmax = onemeter*exp(mu_i + sqrt(2.0*sigma_i)*1.9430).
  
  This new constant could be set to
  
  onemeter = 100_dbl_kind
  
  if the ice model has its thickness in cm, without the need to alter the numerical values used for tuning.
  
  Citation: https://doi.org/10.5194/tc-2021-273-AC2
CC2:
'Comment on tc-2021-273', Katherine Hedstrom, 06 Jan 2022

Another comment I have is that we are now using GEBCO 2020 which is very high resolution. The algorithm we use to generate bathymetric roughness is in the Adcroft paper cited here: https://github.com/nikizadehgfdl/ocean_model_topog_generator, plus the code is there too.

Citation: https://doi.org/10.5194/tc-2021-273-CC2
- AC3: 'Reply on CC2', Frederic Dupont, 28 Feb 2022
  
  This sounds quite interesting. if you could retain the standard deviation of the approximation (or better, of the original bathy data in each cell)], then you could use this value instead of the user-defined sigma_b. The Adcroft reference is quite useful too and was added in the paper as an example of subgrid bathymetry applications.
  
  Citation: https://doi.org/10.5194/tc-2021-273-AC3
RC2:
'Comment on tc-2021-273', Anonymous Referee #2, 15 Feb 2022

The manuscript describes extended version of grounding scheme by Lemieux et al., 2015. Authors provide theoretical description of the method, apply it for short term sea ice-ocean simulations and describe the results.

The paper is very well written, and enjoyable to read. Figures are also of a good quality. I have only several very small comments, and in my view, paper can be accepted after minor revision.

Minor comments:

Line 30. It would be nice to see a paragraph about other attempts to add fast ice in the Arctic Ocean simulations, like Lieser et al., 2004, Itkin et al., 2015 and Olason, 2016.

Lines 38-39: Please comment on computational efficiency as well.

Line 57. You probably mean then --> than.

Line 82. While it became obvious from the rest of the paper why you represent bathymetry as random variable, a simple additional sentence giving the motivation for it would be useful for ocean modelers like me, who often just take bathymetry as something that is well defined.

Line 118. …here (see Section 3) --> in this section

Line 119. “The following SUBsections”.

Line 163. You mean Subsection 3.3.1 here, I guess.

Line 242. Why so many EVP cycles? The standard value for CICE is around 120, if I am not mistaken?

Line 247. Please comment on what is the advantage of this forcing, which seem to be popular in regional ocean modelling, but is quite exotic for global modelling.

It would be good if you mention computational efficiency of the scheme in Section 3.4. Just if it decreases the model speed to a noticeable amount.

Line 325. “… a factor OF two”.

Discussion

The resolution in the model setup is around 12.5 km in the Arctic. Please comment on how well, you think, this grounding scheme will be working in higher resolution setups (e.g. ORCA12 and higher).

Please add to the discussion comparison to other studies, that try to simulate fast ice.

References:

Lieser, J. (2004), A numerical model for short-term sea ice forecasting in the Arctic (Ein numerisches Modell zur Meereisvorhersage in der Arktis), Rep. Polar Mar. Res. (Berichte zur Polar Meeresforschung), vol. 485, 93 pp.

Einar Olason, A dynamical model of Kara Sea landâfast ice, Journal of Geophysical Research: Oceans, 10.1002/2016JC011638, 121, 5, (3141-3158), (2016).

Itkin, P., Losch, M., and Gerdes, R. (2015), Landfast ice affects the stability of the Arctic halocline: Evidence from a numerical model, J. Geophys. Res. Oceans, 120, 2622– 2635, doi:10.1002/2014JC010353.

Citation: https://doi.org/10.5194/tc-2021-273-RC2
- AC4: 'Reply on RC2', Frederic Dupont, 28 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-273/tc-2021-273-AC4-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-273-AC4

Frédéric Dupont et al.

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Short summary

In some shallow seas, grounded ice ridges contribute to stabilizing and maintaining a landfast ice cover. A scheme has already proposed where the keel thickness varies linearly with the mean thickness. Here, we extend the approach by taking into account the ice thickness and bathymetry distributions. The probabilistic approach shows a reasonably good agreement with observations and previous grounding scheme while potentially offering more physical insights in the formation of landfast ice.


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