General comments

This paper investigates the possible consequences of two main instabilities mechanisms (MISI and MICI) for the Amundsen region of the Antarctic Ice Sheet (AIS) using the Parallel Ice Sheet Model (PISM). The authors use a simple cliff-calving parameterization and a mélange buttressing model that were proposed and tested on idealized cases in their previous papers and apply them to real glacier cases in this paper. MICI is an important mechanism that could lead to large uncertainties in modeling the physics of the ice sheets. Recent theoretical and modeling studies (Ma et al., 2017, Bassis et al., 2017, Mercenier et al., 2018) have investigated and analyzed mechanisms for MICI. Applying a more physically based cliff-calving law on real glaciers setting is the timely step to makes an important contribution to the MICI hypothesis. However, I have several concerns described below that need to be addressed before publication. The impact and usefulness of the paper could be improved further if it were expanded to clarify some fundamental issues associated with constraining the idealized mélange buttressing parameterizations. Without observationally constrained models, the results would be over/under- estimating sea level contribution as other papers the authors mention in the manuscript.

1. Constraining the idealized mélange buttressing parameterization

The authors of course acknowledge and raise this issue in the manuscript. However, the application of the mélange buttressing parameterization is still limited because the model parameters are not observationally constrained. For example, the authors choose u_ex=100 km/a that falls between mélange flow speed (10-18 km/a) and iceberg drift velocity (3000-5500 km/a) but it’s a quite large range (10~1000 km/a) and I think the authors arbitrarily choose this value (If I understand correctly). It seems that the results heavily depend on this u_ex value because it determines the upper bound of the calving rate (C_max) so constraining u_ex based on observations (e.g., observational calving rate) is key to applying the parameterization to real glacier cases. Please elaborate on how this u_ex is chosen and I suggest some sensitivity tests if needed. 

 Also, please elaborate on how other parameters for the cliff-calving law and mélange model are chosen or constrained with observations.

2. Model description

I think the methods section is a little scant on details on model description. See below for more details.

P2L10: “This is referred to as Marine Ice Cliff Instability (MICI)”: add references.

P4L6: “… at a horizontal resolution at 4 km”.  I think it would be beneficial if the authors could state the spatial and temporal resolution in a few sentences to make sure that results are numerically converged (i.e., independent of resolution) or the impact of resolution on the results.

P4L12: “The till friction angle is parameterized with bed elevation”

How is it parameterized? Please include details and references.

P6L4: “The ice sheet was spun up into thermal equilibrium with fixed bed and ice geometry”

Please include details on how the model is initialized, for example, how long was the model spun up? What data (SMB, temperature) were used for this procedure? Also, include references if there are any.

P6L9: “REF: a reference simulation with current day atmosphere and ocean conditions held constant”

What are the current day conditions for the atmosphere and ocean? Include details and references.

P7L1: “BMT: the ‘basal melt experiment…200 m/a”

Why 200 m/a? any reference? Consider moving sentences from P8L18-L20 to this section.

What about the ice front? I think there is no calving in this experiment. Although it is explained later in the Results, please add how the ice front is dealt with (fixed or move) for this experiment.

P7L3: “FLK: the ‘floatkill’ … removed”

Again, please add how the ice front is dealt with (fixed or move) for this experiment.

P8L2: “the three cliff calving experiments with small C_max”.

Specify “small C_max”.  2, 5, 10 km/a for C_max?

P8L1-3: “The ‘floatkill’ -parameterization… with C_max=20 km/a”

Where are the results of the extended simulations?

P8L31: “...reached the boundary of the inner WAIS region where cliff calving and the ‘floatkill’ parameterization are applied” -> floatkill parameterization are “not” applied.

P10L2: “see fig3c” -> Figure 6?

P10L14: “This results in a slightly lower overall calving discharge”

What is that compared to? C_max=2 m/a without floatkill parameterization?

Does this issue with partially filled cells only show up when C_max=2 m/a? or also with C_max =5 m/a? Does this issue depend on the resolution of the domain? Please elaborate.

P11L7: “…is shown in fig 3c.” -> Fig. 6

P13L7: “…with the FLK experiment being the slowest, arriving there after 150a”

I don’t see the results with extended time in the manuscript. Consider putting the results in the manuscript or appendix, or put “not shown here” in the text.

P16L7: “we use an estimate of u_ex=100 km/a. However, smaller or larger values would also be consistent with observations”

Why do you choose this value? Is the model calibrated against observation with this value? Please clarify what’s consistent with observations. Have you done the sensitivity tests with u_ex values? 

P16L15: “4.1.2 Melange build-up can stop MICI under winter conditions”

The title of this section could be misleading since the results show that mélange can stop MICI only if the winter condition (u_ex=0) lasts for several years, which is unlikely in real climate conditions.

P18L6: “This seasonality can be modelled with a time-dependent …”

Does this experiment include melting/freezing of mélange? How are the results affected with melting/freezing of mélange?

P18L26: “The mélange parameterization assumes a constant calving rate…”

Do you mean “the upper bound on calving rates (C_max)?

P20L2: “The processes by which ice shelves fracture… in an ice sheet model”

Add references.

P22L14: “…but it could provide enough buttressing to enable ice shelf regrowth, which would then stop further MICI progress.”

Is the ice shelf regrowth shown in model results or just from observations of Jakobshavn glacier?

Figure 4a: How is “calving discharge” calculated? Is this “(calving rate) x (area)” or ice discharge, that is “(velocity) X (area)”? If “calving discharge” is (calving rate) x (area), how is that calculated from the floatkill experiment which does not have calving?  If calving discharge is ice discharge, the term “calving discharge” could be confusing.

Figure 4b: The calving amplification value for C_max 20 km/a experiment seems larger than 6 but it’s cut off. Please consider including the full extent if possible. Also, I am wondering why it suddenly increases toward the end of the simulation. From Figure 4a, the overall calving discharge for C_max 20 km/a looks highest near t=60a and decreases towards the end of the simulation.

Figure 5: Why do authors prohibit calving for the shaded area? Is it because of the bed topography>0 for that area? Include 0 m contour of bed topography since it’s hard to see in the grey scale.

The manuscript describes a set of experiments with enforced removal of the grounded ice performed using the PISM ice-sheet model for the Amundsen Sea Embayment region in West Antarctica. The first author appears to be a graduate student and I have sympathy to them. However, I have no sympathy for the senior coauthors who did not spend time and effort required to conduct a meaningful study and produce a good manuscript. The manuscript has a number of misconceptions, unsupported claims, self-inconsistencies, and conclusions that do not appear to be supported by the study results. The study itself appears to be based on ad-hoc parameterizations, which are not physically justified. 

The Marine Ice Sheet Instability is valid for to steady-state conditions only, i.e. all internal and external parameters do not change in time. In the described experiments, the ice shelves were artificially removed, additionally the grounded ice is artificially removed according to an ad-hoc "calving" parameterization. The evolving glacier configurations are due to this enforced removal of ice and have little to do with concepts of Marine Ice Sheet and Ice Cliff Instabilities that are instabilities of steady state configurations. The experiments use parameterizations, which main property is simplicity, however, the manuscript does not provide physical justification for their use. The interpretation of the results ignores a large body of studies of marine outlet glacier dynamics (a non-exhaustive list is below). 

It is difficult to assess the model results because the results of individual experiments are highly sensitive to the parameters used in parameterizations, and differences in "sea-level contributions" between different scenarios are primarily determined by the parameter choice. The manuscript describes only "sea-level contributions", which is an integral metric and the grounding line positions, which are difficult to interpret on their own. In the absence of ice-dynamics related parameters such as ice velocities, thickness, stresses or strain rates, it is impossible to asses the reasonableness of the obtained solutions. With the used model resolution of 4 km, the simulated grounding line dynamics is questionable, as the required spatial resolution should be 2 km or higher (Seroussi et al., 2014).

In terms of the manuscript presentation, the manuscript should be self-sufficient and have enough information to follow it without in-depth reading of referenced publications. A brief description, and a physical justification of chosen parameterizations would be sufficient. The manuscript has contradicting statements. The title of the section 3.4 is "Bed topography controls rate of grounding line retreat", the line 31 of page 14 states "In summary, we find no clear statistical correlation between the bed topography and the grounding line retreat rate." 

As apparent from above, the manuscript cannot be published in its present form.

Gudmundsson, G. H., Krug, J., Durand, G., Favier, L., and Gagliardini, O. (2012). The stability of grounding lines on retrograde slopes, The Cryosphere, 6, 1497–1505, https://doi.org/10.5194/tc-6-1497-2012.

 Gudmundsson, G. H. (2013). Ice-shelf buttressing and the stability of marine ice sheets, The Cryosphere, 7, 647–655, https://doi.org/10.5194/tc-7-647-2013. 

 

 Haseloff, M. and Sergienko, O. V. (2018) The effect of buttressing on grounding line dynamics. Journal of Glaciology. 64(245), 417–431. doi: 10.1017/jog.2018.30

 

 Kowal, K, Pegler, SS and Worster, M (2016) Dynamics of laterally confined marine ice sheets. Journal of Fluid Mechanics 980, 648–680. doi: 10.1017/jfm.2016.37.

 

 Pegler, SS (2018) Suppression of marine ice sheet instability. Journal of Fluid Mechanics 857, 648–680. doi: 10.1017/jfm.2018.742.

 

 Pegler, S. (2018). Marine ice sheet dynamics: The impacts of ice-shelf buttressing. Journal of Fluid Mechanics, 857, 605-647. doi:10.1017/jfm.2018.741

 

 Robel, AA, Schoof, C and Tziperman, E (2014) Rapid grounding line migration induced by internal ice stream variability. Journal of Geophysical Research: Earth Surface 119(11), 2430–2447. doi: 10.1002/2014JF003251

 

 Robel, AA, Schoof, C and Tziperman, E (2016) Persistence and variability of ice-stream grounding lines on retrograde bed slopes. The Cryosphere 10(4), 1883–1896. doi: 10.5194/tc-10-1883-2016

 

 Schoof, C, Devis, A. D. and Popa, T. V. (2017) Boundary layer models for calving marine outlet glaciers. The Cryosphere 11(5), 2283–2303. doi: 10.5194/tc-11-2283-2017

 

 Sergienko, O. V. and Wingham, D. J. (2019) Grounding line stability in a regime of low driving and basal stresses. Journal of Glaciology 65(253), 833–849. doi: 10.1017/jog.2019.53

 

 Sergienko, O., and Wingham, D. (2021). Bed topography and marine ice-sheet stability. Journal of Glaciology, 1-15. doi:10.1017/jog.2021.79

 

 Seroussi, H., Morlighem, M., Larour, E., Rignot, E., and Khazendar A. (2014). Hydrostatic grounding line parameterization in ice sheet models, The Cryosphere, 8, 2075–2087, https://doi.org/10.5194/tc-8-2075-2014

General comments

Schlemm et al investigate the progression and sea-level contribution potential of two proposed ice sheet instabilities in Antarctica.  They use the Parallel Ice Sheet Model to simulate the retreat of the Amundsen Sea sector of the West Antarctic Ice Sheet at centennial scale, first in a “reference" case and then in seven experimental cases.  The authors then compare sea-level contributions from the Marine Ice Cliff Instability (MICI) with those from the Marine Ice Sheet Instability (MISI) alone.

Overall, the manuscript raises interesting questions and presents a great deal of work toward addressing them.  However, I found the organization confusing.  Many results appear together with uneven levels of detail in the discussion.  One of the major conclusions seems to be about interpreting an upper bound on cliff calving rate; the framing of that analysis in particular confused me.  I would encourage the authors to carefully consider what key points they wish to highlight, and to thoroughly rework the manuscript to focus on those points.

I have self-cited in my specific comments below; I would prefer to avoid that but feel the work is relevant.  I am therefore signing my review in the interest of transparency.

All the best,

Lizz Ultee

Specific comments

1. The authors find that their results depend strongly on what value is imposed as an “upper bound” on calving rate.  This result makes intuitive sense. The authors also describe the calving rate parametrization as “loosely constrained”. Here I am confused.  There are two possible interpretations:

• Do the authors mean that the SLR contribution depends on the value of C_{max} they impose in their simulations?  That is certainly true, but does not make sense as a main result, because the authors have the ability to compute an adaptive C_{max} that depends on local geometry.  Results from an adaptive C_{max} experiment are presented in Figure 3 and 4.
• Do the authors mean that the parameters in Equation 1 are loosely constrained?  I think this is the more interesting point, and it could be more prominent in the text.  The authors briefly discuss the value of the exit velocity u_{ex} but do not further explore uncertainties in the adaptive calving rate.  If related sensitivity studies have already been done, for example in Schlemm & Levermann 2021, it would be helpful to describe their key findings.

Given that the authors have already derived the adaptive bound and implemented it in a PISM experiment, I do not understand their focus on the four constant-C_{max} experiments.  Perhaps the constant-C_{max} experiments are intended to provide context for the range of possibilities of a poorly constrained adaptive C_{max}?  If so, I need more framing from the authors to aid that interpretation.

The authors are right to point out the limitations in DeConto & Pollard’s (2016) approach, which imposes a very fast cliff calving retreat rate. However, in my view, applying various constant cliff calving rates as upper bounds is not much improvement on DeConto & Pollard (2016).  For one thing, the theoretical upper bound on cliff calving rate depends on outlet glacier geometry, local climate, and the yield strength of ice (Bassis & Ultee 2019; implemented for all grounded GrIS outlets in Ultee & Bassis 2020).  Secondly, the authors themselves have derived a parametrization for melange-buttressed cliff calving, which brings in more interesting physics than the constant rates.

One way to reorganize might be to focus more directly on the adaptive calving rate experiment in the main text, and separate the constant-rate experiments into a supplement or even into their own “brief communication” style manuscript.  I don’t insist on this—simply a suggestion for how a more focused manuscript might read.

2. I could use more explanation of the assumptions of the C_{max} bound.  The authors write on p5, L22: “In order to estimate Cmax for a given grounding line configuration, we assume that the entire embayment is filled with mélange.” I do not understand how this is an upper bound on calving rate.  An embayment entirely filled with mélange would be the configuration that results in the most suppression of calving, but couldn’t there be *more* calving if the embayment were not filled with mélange?

3. The experiments presented in Section 3.4 allow the ice divides and grounding lines of Thwaites and PIG to retreat all the way across WAIS to the Ross and Ronne-Filchner Ice Shelves.  How realistic is this?  In such cases, I’d expect some lateral motion of the ice divides and resulting adjustment in the grounding lines.  It would be helpful to have more guidance from the authors in interpreting the real-world context of these results.

4. The authors describe seasonal variations in the strength of mélange buttressing in Section 4.1.2.  I have two concerns with this.  First, the results are buried much later in the manuscript than other primary results of experiments.  I was confused to see them there.  Second, the title of the section reads “Mélange build-up can stop MICI under winter conditions”, and p16, L16 indicates that result, but p18,L14 reads “…winter freezing of mélange is not sufficient to stop calving.”  I am left unsure whether frozen mélange inhibits MICI or not.

Technical corrections

P5, L8: “can lead to very large calving rates” - please clarify whether this refers to large calving rates in the model or in observations

P10, L13-16: “Cliff calving with a small value of C_{max}…in this case.” I do not understand this explanation.  Consider rephrasing or elaborating.

P11, L3-4: “Because the embayment becomes wider…the upper bound on calving rate decreases with grounding line retreat into the Amundsen basin.”  This does not agree with the decline in buttressing that I interpret from Figure 2 and previous description.  Please check this and/or clarify the explanation.

Figures 3 & 4: Please consider using thicker lines for the legend entries, or labelling C_{max} directly on the plot.  I find the colors hard to distinguish with the thin lines currently in the legend.

Section 4.3: The official name of Greenland’s fastest outlet, formerly called Jakobshavn Isbræ, is Sermeq Kujalleq (Bjørk, Kruse & Michaelsen 2015).  Please update the nomenclature you use to discuss it.

References in this review

1. Bassis & Ultee (2019).  A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers. JGR Earth Surface, 124(8): 2036-2055. https://doi.org/10.1029/2019JF005160.  See Equation 54.
2. Ultee & Bassis (2020). SERMeQ model produces a realistic upper bound on calving retreat for 155 Greenland outlet glaciers. Geophysical Research Letters, 47(21): e2020GL090213. https://doi.org/10.1029/2020GL090213
3. Bjørk, Kruse & Michaelsen (2015). Brief communication: Getting Greenland’s glaciers right – a new data set of all official Greenlandic glacier names. The Cryosphere, 9: 2215–2218. https://tc.copernicus.org/articles/9/2215/2015/