the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Jan 2024
Responses of Pine Island and Thwaites Glaciers to Melt and Sliding Parameterizations
Abstract. Pine Island and Thwaites glaciers are the two largest contributors to sea level rise from Antarctica. Here we examine the influence of basal friction and melt in determining projected losses. We examine both Weertman and Coulomb friction laws with explicit weakening as the ice thins to flotation, which many friction laws include implicitly via the effective pressure. We find relatively small differences with the choice of friction law (Weertman or Coulomb) but find losses are highly sensitive to the rate at which the basal traction is reduced as the area above the grounding line thins. Consistent with earlier work on Pine Island Glacier, we find sea level contributions from both glaciers vary linearly with the melt volume averaged over time and space, with little influence from the spatial or temporal distribution of melt. Based on recent estimates of melt from other studies, our work simulations suggest that melt-driven combined sea-level rise contribution from both glaciers is unlikely to exceed 10 cm by 2200. We do not include other factors, such as ice shelf breakup that might increase loss, nor factors such as increased accumulation and isostatic uplift that may mitigate loss.
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RC1: 'Comment on egusphere-2023-2929', Tyler Pelle, 10 Feb 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2023-2929/egusphere-2023-2929-RC1-supplement.pdf
- AC2: 'Reply on RC1', Ian Joughin, 06 Mar 2024
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RC2: 'Comment on egusphere-2023-2929', Anonymous Referee #2, 22 Feb 2024
Joughin et al. explored the sensitivity of projected 200-year mass loss from Pine Island and Thwaites Glaciers to the friction model, weakening of basal drag upstream the grounding line when ice approaches floatation, and the sub-shelf melt rates. They find relatively small differences between Weertman and Coulomb sliding laws but high sensitivity to the rate at which the basal drag is reduced when the ice approaches floatation. They also find the sea level contributions from both PIG and Thwaites glaciers are less sensitive to the spatial or temporal distribution of melt. The sea level contributions from these two glaciers is not likely to exceed 10 cm before end of 2200. Overall, the manuscript is well structured. However, the model setup section and some of the descriptions need improvements. There are quite a few typos in the texts and figures, especially the numbering of equations, which are misleading and need to be fixed. Information of some captions are insufficient and some statements in the discussion are a bit far-fetched.
Here are some general comments:
Some of the methods description is not quite clear. I suggest more details in the way how you generate the basal melt distributions at four different levels. Is it also not clear how you treat the basal drag and basal melt at the grounding line.
One of the key findings here is the small difference between Weertman and Coulomb friction model. However, this statement has a very important premise that the authors applied a linear weakening of the basal drag for both sliding laws. The statement will not hold without this premise, which should be mentioned in both abstract and the conclusion. Figure 7 and 8 even show a clear difference under low melt cases between Weertman and RCFi, which was not well discussed in the paper. In Fig 8, the mass loss at the front of the Thwaites Glacier is clearly higher in Weertman than using RCFi.
This study found the ice mass losses are highly sensitive to the choice of hT. However it’s not clear about how to choose the best value of hT if we change to a different glacier? The best fit of hT = 41 m for the Pine Island Glacier may not be the best choice for other glaciers in Antarctic or even for the Whole Antarctica. hT may need to be adjusted based on the significant geometry change with time. This should be more discussed in the paper. Moreover, the study suggests a spatial variable Ht is feasible in future study. Then how about the changes of hT with time? In Joughin 2019, a 20 years simulation suggests that 46 m is the best choice. However, in a century scale simulation, the geometry near the updated GL may change a lot, which is not discussed yet.
The last paragraph of Sect 4.2 is discussing the shortcomings of other sliding laws and conclude that ‘any law that relies solely on the local height above flotation to govern changes in effective pressure, and thus, basal friction over the entire domain is likely oversimplified and incorrect’. However, the authors did not discuss the shortcomings of RCFi in this study, like how to better decide hT used in RCFi considering different glacier may have different sensitivity to the choice of hT as you show in Fig 7b and 7c for the high melt level case.
Another statement in this paper is about the low sensitivity to the spatial or temporal distribution of melt rates. However, Fig 7and 9 did show sensitivity of GL retreat to the spatial distribution of melt as the author mentioned on Line 287-289. Recent studies indicate that the migration of the grounding line is extremely sensitive to how basal melt occurs adjacent to the grounding line (Arthern and Williams 2017; Reese et al., 2018; Goldberg et al., 2019). Modelling studies also suggest that ice sheet models are more sensitive to melt rates near the grounding line than to cavity-integrated melt rates beneath ice shelves, e.g. Gagliardini et al., 2010; Reese et al., 2018; Morlighem et al., 2021. Can you please justify it?
Lastly, I think it is very important to point out that the conclusion ‘our work simulations suggest that melt-driven combined sea-level rise contribution from both glaciers is unlikely to exceed 10 cm by 2200’ is under some assumptions, like the hT=41m is the best fit for both glaciers in the coming two centuries.
Specific Comments:
L66: what is the citation for typical value of to be 0.5?
L82: Why the is much higher near GL (175 kPa) compared with Trunk (10 kPa) and inland tributary (100 kPa)? Same for title of Figure 3.
L83: You mean haf =45 m here rather than hf right? If yes, I think you need to explain what haf is. I don’t quite follow the legend on Figure 1 and this sentence. What’s the meaning of different values of haf for Eq(3) and (4)? Why do you say the Weerman condition is not fond where hf = 45?
L85: “transition to Coulomb sliding” how do you get the number of 67 m here?
L87: please refer to the section you did the inversion for rather than just saying ‘as described below’.
L86: I still don’t understand how you pick the four values 1, 41, 86, 176 m here. 1 m is easy but how about the rest three values?
L119: The legend did not show Eq(7) at all. I guess the light blue line for RCF equation (6) should be RCF equation (7)?
L121: I think it is worth mentioning that Gillet-Chaulet et al., 2016 used a power law rather that Coulomb law.
L147: In the text, you refer to Eq 7 for pink line of Fig3, but the legend says the pink line is from Eq 9.
L154: hT = 41 or 46 m
L155: it should be 2021b rather than 2021a. hT = 123 m, m = 3
L178: Equation (7)
L186-189: It’s not clear about the sequence of inversion here. Do you invert basal friction law parameters first and then A with a second inversion or invert both at the same time? Which sliding law do you use in the inversion?
L193: It is not clear about how you generate the melt distribution until I further read through the whole text. I suggest you specify how you treat the melt distribution here. I suspect you run each experiment with 30 melt distributions and normalise it to four different melt levels (57, 75, 100, 125 Gt/yr), and then update this melt distribution with an updated grounding line position. What is the time step size?
L269: I don’t quite follow this. Do you mean poorer quality of the velocity used to invert the basal drag coefficient and A?
L272-274: I think you need to specify the slight thickening and grounding line advance occur in PIG rather than both glaciers. I saw a few ensembles show more GL retreat in Weertman case (Fig 9f) compared with RCFi case (Fig 9b). Similar things also occur by comparing Fig 9h and Fig 9d. Why is it?
L271-274: All of these are talking about PIG so it’s better to specify it. I think the velocity contours in Fig8 is distracting to tell the VAF loss near the GL, which is important. When you say ‘consistent with Fig7’, it’s hard to tell the thickening from Fig 7.
L284-285: Then what is causing the lowest VAF loss from Weertman with hT = 172 at low melt level cases (57 Gt/yr) for PIG compared with other hT?
L286: In Fig 8, we can clearly tell the difference between RCFi and Weertman for low melt cases (57 Gt/yr and 75 Gt/yr) at the front of Thwaites region (Fig 8a,b and Fig 8e,f). Similarly in Fig 7c, the dashed line from hT = 41 m and 86 m gave more mass loss than solid line for low melt case (57 Gt/yr).
L287: It will be good if you can show a map of the basal melt distribution for the Thwaites region. Just pick one of the melt realisations to prove what you said here. Does this sentence mean that the distribution of melt did affect the grounding line retreat in Thwaites, which conflicts with your statement that it is not sensitive to the spatial distribution of basal melt.
L290-291: how do you get the 20% and 50%?
L297-301: This comparison between this study and others in the same regions are important. I suggest a figure to compare the basal drag between their regularized Coulomb friction and RCFi in this study for the fast-flowing regions. Again, I don’t understand how you decide they produce Coulomb friction for regions where h-hf < 86 m?
L304: Equation (6)?
L310: basal drag of the area near the grounding line is weaker rather than ‘area is weaker’.
L317-318: From Fig 7, the diverge in ice loss for Thwaites is less compared with PIG at low melt values. It’s not ‘nearly the same’ to me with a difference of 10 mm sle.
L334-335: Could you further explain how you translate the values of Ht based on of Barnes and Gudmundsson (2022)?
L364: Equation (5) ? à Equation (6)
L373: you refer to Equation (7) here? so confusing.
L408: it should be 0.96 or greater.
L796: basis boundaries à basin boundaries?
L409: why the regression value for the ensemble data in Fig 10 (dashed lines) is not consistent with Figure 7 (solid lines)?
L427: I think you refer to Figure 10 rather than Figure 9 here.
L455: citation please.
L457: But it is also possible that PIG will have higher basal melt than 67+21 = 88 Gt/yr for the second century, which would exceed your 125 Gt/yr.
L464: You mean with hT =41 m? If this whole section 4.4 is talking about experiments with hT = 41, it’s better to make it clear at the start of this section.
L470: when did the melt reach 220 Gt/yr in Bett et al. (2023)’s model? The end of 2100 or 2200?
L476: the most aggressive parameterized melt rate function for Thwaites is B&G but is 160_700 when you talk about PIG. It’s hard to tell it from Fig S2.
L795: Figure 8, for those who is not family with PIG and Thwaites, it’s har d to tell the corresponding values of the velocity contours.
L797: I guess you refer to Figure 9 here.
L800: Figure 9, is the red line showing the location of the grounding line? What are the scattered points in Fig 9c and 9d?
Figure S2: mr_4 in the legend but mr_2 in the caption?
Rererfences
Arthern, R. J., and C. R. Williams (2017), The sensitivity of West Antarctica to the submarine melting feedback, Geophys. Res. Lett., 44, 2352–2359, doi:10.1002/2017GL072514.
Gagliardini, O., G. Durand, T. Zwinger, R. C. A. Hindmarsh, and E. Le Meur (2010), Coupling of ice-shelf melting and buttressing is a key process in ice-sheets dynamics, Geophys. Res. Lett., 37, L14501, doi:10.1029/2010GL043334.
Goldberg, D. N., Gourmelen, N., Kimura, S., Millan, R., & Snow, K. (2019). How accurately should we model ice shelf melt rates? Geophysical Research Letters, 46, 189–199. https://doi.org/10.1029/2018GL080383
Morlighem, M., Goldberg, D., Dias dos Santos, T., Lee, J., & Sagebaum, M. (2021). Mapping the sensitivity of the Amundsen Sea Embayment to changes in external forcings using automatic differentiation. Geophysical Research Letters, 48, e2021GL095440. https://doi.org/10.1029/2021GL095440
Reese, R., Albrecht, T., Mengel, M., Asay-Davis, X., and Winkelmann, R.: Antarctic sub-shelf melt rates via PICO, The Cryosphere, 12, 1969–1985, https://doi.org/10.5194/tc-12-1969-2018, 2018.
Citation: https://doi.org/10.5194/egusphere-2023-2929-RC2 - AC1: 'Reply on RC2', Ian Joughin, 06 Mar 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-2929', Tyler Pelle, 10 Feb 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2023-2929/egusphere-2023-2929-RC1-supplement.pdf
- AC2: 'Reply on RC1', Ian Joughin, 06 Mar 2024
-
RC2: 'Comment on egusphere-2023-2929', Anonymous Referee #2, 22 Feb 2024
Joughin et al. explored the sensitivity of projected 200-year mass loss from Pine Island and Thwaites Glaciers to the friction model, weakening of basal drag upstream the grounding line when ice approaches floatation, and the sub-shelf melt rates. They find relatively small differences between Weertman and Coulomb sliding laws but high sensitivity to the rate at which the basal drag is reduced when the ice approaches floatation. They also find the sea level contributions from both PIG and Thwaites glaciers are less sensitive to the spatial or temporal distribution of melt. The sea level contributions from these two glaciers is not likely to exceed 10 cm before end of 2200. Overall, the manuscript is well structured. However, the model setup section and some of the descriptions need improvements. There are quite a few typos in the texts and figures, especially the numbering of equations, which are misleading and need to be fixed. Information of some captions are insufficient and some statements in the discussion are a bit far-fetched.
Here are some general comments:
Some of the methods description is not quite clear. I suggest more details in the way how you generate the basal melt distributions at four different levels. Is it also not clear how you treat the basal drag and basal melt at the grounding line.
One of the key findings here is the small difference between Weertman and Coulomb friction model. However, this statement has a very important premise that the authors applied a linear weakening of the basal drag for both sliding laws. The statement will not hold without this premise, which should be mentioned in both abstract and the conclusion. Figure 7 and 8 even show a clear difference under low melt cases between Weertman and RCFi, which was not well discussed in the paper. In Fig 8, the mass loss at the front of the Thwaites Glacier is clearly higher in Weertman than using RCFi.
This study found the ice mass losses are highly sensitive to the choice of hT. However it’s not clear about how to choose the best value of hT if we change to a different glacier? The best fit of hT = 41 m for the Pine Island Glacier may not be the best choice for other glaciers in Antarctic or even for the Whole Antarctica. hT may need to be adjusted based on the significant geometry change with time. This should be more discussed in the paper. Moreover, the study suggests a spatial variable Ht is feasible in future study. Then how about the changes of hT with time? In Joughin 2019, a 20 years simulation suggests that 46 m is the best choice. However, in a century scale simulation, the geometry near the updated GL may change a lot, which is not discussed yet.
The last paragraph of Sect 4.2 is discussing the shortcomings of other sliding laws and conclude that ‘any law that relies solely on the local height above flotation to govern changes in effective pressure, and thus, basal friction over the entire domain is likely oversimplified and incorrect’. However, the authors did not discuss the shortcomings of RCFi in this study, like how to better decide hT used in RCFi considering different glacier may have different sensitivity to the choice of hT as you show in Fig 7b and 7c for the high melt level case.
Another statement in this paper is about the low sensitivity to the spatial or temporal distribution of melt rates. However, Fig 7and 9 did show sensitivity of GL retreat to the spatial distribution of melt as the author mentioned on Line 287-289. Recent studies indicate that the migration of the grounding line is extremely sensitive to how basal melt occurs adjacent to the grounding line (Arthern and Williams 2017; Reese et al., 2018; Goldberg et al., 2019). Modelling studies also suggest that ice sheet models are more sensitive to melt rates near the grounding line than to cavity-integrated melt rates beneath ice shelves, e.g. Gagliardini et al., 2010; Reese et al., 2018; Morlighem et al., 2021. Can you please justify it?
Lastly, I think it is very important to point out that the conclusion ‘our work simulations suggest that melt-driven combined sea-level rise contribution from both glaciers is unlikely to exceed 10 cm by 2200’ is under some assumptions, like the hT=41m is the best fit for both glaciers in the coming two centuries.
Specific Comments:
L66: what is the citation for typical value of to be 0.5?
L82: Why the is much higher near GL (175 kPa) compared with Trunk (10 kPa) and inland tributary (100 kPa)? Same for title of Figure 3.
L83: You mean haf =45 m here rather than hf right? If yes, I think you need to explain what haf is. I don’t quite follow the legend on Figure 1 and this sentence. What’s the meaning of different values of haf for Eq(3) and (4)? Why do you say the Weerman condition is not fond where hf = 45?
L85: “transition to Coulomb sliding” how do you get the number of 67 m here?
L87: please refer to the section you did the inversion for rather than just saying ‘as described below’.
L86: I still don’t understand how you pick the four values 1, 41, 86, 176 m here. 1 m is easy but how about the rest three values?
L119: The legend did not show Eq(7) at all. I guess the light blue line for RCF equation (6) should be RCF equation (7)?
L121: I think it is worth mentioning that Gillet-Chaulet et al., 2016 used a power law rather that Coulomb law.
L147: In the text, you refer to Eq 7 for pink line of Fig3, but the legend says the pink line is from Eq 9.
L154: hT = 41 or 46 m
L155: it should be 2021b rather than 2021a. hT = 123 m, m = 3
L178: Equation (7)
L186-189: It’s not clear about the sequence of inversion here. Do you invert basal friction law parameters first and then A with a second inversion or invert both at the same time? Which sliding law do you use in the inversion?
L193: It is not clear about how you generate the melt distribution until I further read through the whole text. I suggest you specify how you treat the melt distribution here. I suspect you run each experiment with 30 melt distributions and normalise it to four different melt levels (57, 75, 100, 125 Gt/yr), and then update this melt distribution with an updated grounding line position. What is the time step size?
L269: I don’t quite follow this. Do you mean poorer quality of the velocity used to invert the basal drag coefficient and A?
L272-274: I think you need to specify the slight thickening and grounding line advance occur in PIG rather than both glaciers. I saw a few ensembles show more GL retreat in Weertman case (Fig 9f) compared with RCFi case (Fig 9b). Similar things also occur by comparing Fig 9h and Fig 9d. Why is it?
L271-274: All of these are talking about PIG so it’s better to specify it. I think the velocity contours in Fig8 is distracting to tell the VAF loss near the GL, which is important. When you say ‘consistent with Fig7’, it’s hard to tell the thickening from Fig 7.
L284-285: Then what is causing the lowest VAF loss from Weertman with hT = 172 at low melt level cases (57 Gt/yr) for PIG compared with other hT?
L286: In Fig 8, we can clearly tell the difference between RCFi and Weertman for low melt cases (57 Gt/yr and 75 Gt/yr) at the front of Thwaites region (Fig 8a,b and Fig 8e,f). Similarly in Fig 7c, the dashed line from hT = 41 m and 86 m gave more mass loss than solid line for low melt case (57 Gt/yr).
L287: It will be good if you can show a map of the basal melt distribution for the Thwaites region. Just pick one of the melt realisations to prove what you said here. Does this sentence mean that the distribution of melt did affect the grounding line retreat in Thwaites, which conflicts with your statement that it is not sensitive to the spatial distribution of basal melt.
L290-291: how do you get the 20% and 50%?
L297-301: This comparison between this study and others in the same regions are important. I suggest a figure to compare the basal drag between their regularized Coulomb friction and RCFi in this study for the fast-flowing regions. Again, I don’t understand how you decide they produce Coulomb friction for regions where h-hf < 86 m?
L304: Equation (6)?
L310: basal drag of the area near the grounding line is weaker rather than ‘area is weaker’.
L317-318: From Fig 7, the diverge in ice loss for Thwaites is less compared with PIG at low melt values. It’s not ‘nearly the same’ to me with a difference of 10 mm sle.
L334-335: Could you further explain how you translate the values of Ht based on of Barnes and Gudmundsson (2022)?
L364: Equation (5) ? à Equation (6)
L373: you refer to Equation (7) here? so confusing.
L408: it should be 0.96 or greater.
L796: basis boundaries à basin boundaries?
L409: why the regression value for the ensemble data in Fig 10 (dashed lines) is not consistent with Figure 7 (solid lines)?
L427: I think you refer to Figure 10 rather than Figure 9 here.
L455: citation please.
L457: But it is also possible that PIG will have higher basal melt than 67+21 = 88 Gt/yr for the second century, which would exceed your 125 Gt/yr.
L464: You mean with hT =41 m? If this whole section 4.4 is talking about experiments with hT = 41, it’s better to make it clear at the start of this section.
L470: when did the melt reach 220 Gt/yr in Bett et al. (2023)’s model? The end of 2100 or 2200?
L476: the most aggressive parameterized melt rate function for Thwaites is B&G but is 160_700 when you talk about PIG. It’s hard to tell it from Fig S2.
L795: Figure 8, for those who is not family with PIG and Thwaites, it’s har d to tell the corresponding values of the velocity contours.
L797: I guess you refer to Figure 9 here.
L800: Figure 9, is the red line showing the location of the grounding line? What are the scattered points in Fig 9c and 9d?
Figure S2: mr_4 in the legend but mr_2 in the caption?
Rererfences
Arthern, R. J., and C. R. Williams (2017), The sensitivity of West Antarctica to the submarine melting feedback, Geophys. Res. Lett., 44, 2352–2359, doi:10.1002/2017GL072514.
Gagliardini, O., G. Durand, T. Zwinger, R. C. A. Hindmarsh, and E. Le Meur (2010), Coupling of ice-shelf melting and buttressing is a key process in ice-sheets dynamics, Geophys. Res. Lett., 37, L14501, doi:10.1029/2010GL043334.
Goldberg, D. N., Gourmelen, N., Kimura, S., Millan, R., & Snow, K. (2019). How accurately should we model ice shelf melt rates? Geophysical Research Letters, 46, 189–199. https://doi.org/10.1029/2018GL080383
Morlighem, M., Goldberg, D., Dias dos Santos, T., Lee, J., & Sagebaum, M. (2021). Mapping the sensitivity of the Amundsen Sea Embayment to changes in external forcings using automatic differentiation. Geophysical Research Letters, 48, e2021GL095440. https://doi.org/10.1029/2021GL095440
Reese, R., Albrecht, T., Mengel, M., Asay-Davis, X., and Winkelmann, R.: Antarctic sub-shelf melt rates via PICO, The Cryosphere, 12, 1969–1985, https://doi.org/10.5194/tc-12-1969-2018, 2018.
Citation: https://doi.org/10.5194/egusphere-2023-2929-RC2 - AC1: 'Reply on RC2', Ian Joughin, 06 Mar 2024
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Ian Joughin
Daniel Shapero
Pierre Dutrieux
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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