This is the second time I am reviewing this article. The authors have adequately responded to both reviewer comments and extensively revised the article. The figures and the text in the article are much clearer, but there are still some notation inconsistencies and a few statements that need revision. As this is first of a kind study exploring the effect of damage on ice flow of a real (Thwaites) glacier, I recommend it for publication after the following comments are addressed. However, there are discrepancies between observations and simulation results, lack of understanding of how represent basal crevasse formation, and the damage model has a few deficiencies (due to the zero-stress approximation), which requires further research. This could be elaborated in the discussion and conclusion sections better.
Detailed Comments:
1) The following two sentences in the Introduction near Line #45 need to be revised.
- “They have one critical limitation, i.e., being diagnostic, which means that they investigate the instantaneous effect of damage on ice dynamics, but not the evolution of damage when ice thickness is allowed to evolve according to the applied changes.”
In the references cited in this paragraph, Huth et al. (2021, 2023) and Duddu et al (2020) do consider ice thickness changes. Huth et al solve the shallow shelf equations including the ice thickness evolution and Duddu et al. use an updated Lagrangian implementation to account for ice thickness evolution. However, because these works considered smaller time scales (months to years) there is no significant effect of damage on ice flow. Therefore, the above statement by the authors is not true in general.
- “They therefore fail to predict future ice sheet behavior or feedbacks induced by external changes, such as fracture enhancement due to atmospheric or oceanic forcing”
At least in the case of Huth et al. (2023) this is not true. Some studies just focused on the short time scales corresponding to rifting or crevasse propagation, over which ice thickness changes are not so significant.
2) There are several notation inconsistencies as per the continuum mechanics. I am listing a few below that could identify:
- In Eq. 1 and thereafter \tau and \epsilon are tensors so \boldsymbol should be used in LaTeX, whereas the equivalent stress is a scalar to which the n-1 is applied as exponent, so \boldsymbol should not be used here. In general vector and tensor fields are denoted using bold letters whereas scalars are denoted by normal letters.
- In Eq. (2) the notation D(\tau) implies that damage D is a function of the deviatoric stress, but this fundamentally wrong. First, the definition of this 3D damage function was never even defined as eventually the depth integrated damage d based on the zero-stress theory was used. Second, the 3D damage must be defined based on the principal stress or stress invariants and not based on a component of deviatoric stress. You can refer to Pralong and Funk (2005) or Duddu et al. (2013) for more details on this. Simple fix is to say damage D without \tau in parentheses.
- There are so many steps that are missing from Eq. (2) to Eq. (1) to Eq. (3), so I wonder why it is even necessary to have Eqs. (1) and (2). Perhaps, just directly start with how shallow ice flow model works and how damage is incorporated into the Kori-ULB model. Also, the parameter A is inversely related to the viscosity \mu, so I find it confusing that Eq. (3) has both A and \mu in it.
- In Eq. (4) and (5) to be consistent the density of meltwater in the surface crevasses must be denoted differently from that of seawater in the basal crevasses. Although I understand that this study did not include meltwater in surface crevasses.
- In Eq. (6) remove the star to denote multiplication, just writing C_1 h without the star implies multiplication in standard notation.
- In Eq. (7) the velocity term \bold{u} is not defined. Is it a 3D or 2D velocity field? This is important as this the divergence of 3D velocity is zero but not the 2D field. Also, the terms max and min should not be italicized as they are text descriptors, and subscripts such as tr, ab, b, s should not be italicized in the equations as they are descriptors and not indices. Whereas, on Line 122, below Eq. (7), \dot{m} must be italicized as it is a variable denoting basal melting rate.
3) On line 103, it is stated that “… ice damage is expressed as the total depth of crevasses …” I suggest you say – normalized depth of crevasses – as damage is non-dimensional variable so it cannot be equated to ice thickness.
4) On lines 180 and 181, the RMSE and rRMSE are denoted. I think it is better to say difference or deviation instead of error, so RMSD and rRMSD. In numerical modeling, the term error means something specific – the difference between the exact analytical solution and the approximate numerical solution. Unless I misunderstood, you are reporting here are the differences between different model results.
5) On line 206 – it is stated “For the period 1990–2020, the simulated mean net mass balance for Group 1 (with damage) is -26.5 Gt a-1, which is comparable to satellite-derived observations (-46.1 ± 7.2 Gt a-1 over 1992–2017; mean ± 1 s.d.).” It seems the satellite observations are two times larger than the simulated mean net mass balance for Group 1. Please clarify in the text here what are the reasons for this mismatch. Also, why wasn’t the group 2 mass loss reported here.
6) If Fig8. even in the extreme experiments the SLC is less than 18 cm by 2200. Thwaites is referred to as the doomsday glacier in some news articles, perhaps a comment can be added on this result in the context of how catastrophic the projected SLC of 18 – 24 cm is.
7) On line 360, it is stated that “As damage is advected with the ice flow, this fraction 360 increases toward the ice front, reaching 0.3 in lower-damage cases to 0.7 in higher-damage cases, with particularly high damage concentrated in the shear zone.” My intuition was that the increasing strain rate toward the ice front is the major contributor to this damage increase and not the advection. Please clarify the relative contribution of advection and damage nucleation to the increase in damage downstream.
8) On line 409, it is stated “Instead of solely relying on ice sheet mass loss data, future efforts should incorporate observational datasets of crevasse distributions.” I do not disagree with this suggestion but there is a more nuanced discussion missing here. From our modeling studies, we find that most of the damage in ice shelves must be in the form of basal crevasses, especially if there is no hydrofracture in surface crevasses. Due to the ocean water pressure at the terminus, there is simply not enough driving force in floating ice shelves to propagate surface cracks deeper into the ice below the waterline. Our studies on Larsen C ice shelf in Huth et al. (2023) indicate that rift propagation is almost entire driven by basal crevasses formation. Also, Clayton et al. (2024) shows that crevasses can propagate deeper in ice shelves due to the less dense firn layers near the top surface. There are no observations of basal crevasses, and the extent of firn layer is not so well quantified that can rightly inform future modeling efforts. My comment is that this requires basin/ice-shelf scale process modeling (e.g. full Stokes and phase field fracture) to better understand and represent basal crevasses evolution.
Clayton, T., Duddu, R., Hageman, T., & Martínez-Pañeda, E. (2024). The influence of firn layer material properties on surface crevasse propagation in glaciers and ice shelves. The Cryosphere, 18(12), 5573-5593.
9) On lines 412, it is stated “hindcasts for 1990–2020 (Schimdtko et al., 2014; Kittel et al., 2021) do not necessarily reflect the actual imbalance of the ice sheet during that period.” I did not understand this sentence. Please explain this in more detail. What does it mean to do hindcast simulations and which figures in the paper show these results.
10) On line 424, it is stated that “Our results suggest that ice damage could be a key driver of Thwaites Glacier’s rapid ice loss, offering an alternative explanation to previous hypotheses.” Please clarify what is meant by rapid ice loss. The sea level contribution is 18 - 24 cm by 2300 in the extreme scenarios, which is significant, but does it warrant the use of the term “rapid.”
11) Line 440, instead of saying “increasing damage intensity …” it is clearer to say “an increase in damage intensity …”
12) Overall, the figures are quite well made, and the caption are comprehensive and informative. However, I have a few minor questions or suggestions below.
- I do not understand what the length white-gray, black-gray bars in subfigures 1(a), 1(b) and 1(d). Also, what the black regions in (a) and (b), are these the ocean regions or grounded regions that are removed from the images.
- In Fig. 2a, I do not see the black line corresponding to observational estimates.
- In Fig. 10 there are positive ice thickness changes (red regions in second and third figure columns) ahead of the ice shelves. Is that due to ice mélange changes or is that something that is unphysical. Please clarify in the caption. |
Please see the attached pdf.