Trevers et al. test several glacier sliding laws to see how well they reproduce the flow dynamics of Jakobshaven Isbrae gathered from 2009 to 2018. Specifically, they compare the more widely used Weertman and linear sliding laws to a regularized Coulomb sliding law. Theory suggests that the regularized Coulomb sliding law can account for basal cavitation and heterogeneous bed materials important for controlling glacier slip whereas the former two sliding laws cannot. Both the Weertman and linear sliding laws produce very poor model results. To improve model performance, Trevers implements an active reparameterization scheme that allows the model to update its parameters with changes in the glacier’s velocity field. While this reparameterization scheme improves model performance, its reliance on the velocity data prevent its use for any ice flow projections. In contrast, the regularized Coulomb sliding law can generally reproduce the variable sliding velocities at Jakobshaben Isbrae without reparameterization. The manuscript’s subject matter is of general interest to the earth science community as improving the sliding law parameterization is pivotal for accurately forecasting future sea-level rise. I found the manuscript to be well written and their conclusions to be well supported by their results. I had a few suggestions that I think would clarify some points, all of which are relatively minor. However, I am enthusiastic about this manuscript being published and think it is a significant contribution to the field.

General comments:

I think some clarification is needed for understanding what experiments you carried out and why. For instance, the suffix ‘TRANS’ was confusing for the model experiments that did not vary the C and phi parameters. I would emphasize why you are allowing the LV model to vary these parameters. My understanding is that it is to show that the RC model can produce essentially the same model fit without having to use detailed velocity data. This allows the RC model to be used more effectively for projections. I think this point is really important, but it wasn’t obvious during my first reading. I would suggest setting up the problem a bit better in the introduction and throughout the manuscript so that this impressive result isn’t saved until the discussion.

It is unclear to me how you are defining the ‘grounding zone’. More of the glacier is grounded beyond the box. I think my confusion here can be resolved with a change in word choice of grounding zone or clarification on what you mean by grounding zone. It follows that I was unsure how you determined the grounded area. Please elaborate on this in the text.

Specific comments:

Abstract – It is unclear from the abstract if you assimilate velocity data with the other sliding laws. I also think you can better setup the problem that you are trying to solve with these experiments to really drive home the importance of the work you’ve done here.

Section 1 - I think it’s worth pointing out here that the form of the hard bedded and soft bedded slip laws is similar. Otherwise, I don't think your point about a universal slip law makes sense.

Section1 – continued  - I think here is where you should also setup the problem and talk the reader through your hypothesis and how you are setting about to prove it. That is, lay the foundation for the importance of the experiments you are going to run in the paper.

Line 52 – Maybe too detailed, but I was interested in if we know why change in water circulation happened.

Line 127 – Why?

Line 142 – What is the resolution of BedMachine?

Line 143 – Please define GIMP.

Line 158 – How did you make the different datasets compatible spatially? Did you do any resampling?

Line 166 – I would suggest moving this to the beginning of the next paragraph.

Line 192 – What is the temporal and spatial resolution of RACMO?

Line 210 – I found the name scheme here a bit confusing. I thought the ‘STAT’ or ‘TRANS’ part of the names related to static to transient evolutions of C and phi. Is that incorrect? Also, I would put the name of the Weertman model here since you did it for all the others.

Line 210 – Why didn’t you use a transient C and phi with the Weertman and RC models? Again, I think this goes to better setup the problem you’re trying to solve.

Line 226 – Please explain somewhere why you didn’t establish an initial state with the different flow laws.

Line 229 – Please elaborate on this last point. At first, I didn’t quite follow why the inverse model would allow the LV_TRANS model to perform better after 2016.

259-267 – This is well explained here but I felt like the impact of this statement could have been setup better in the introduction and results. It took me reading it a few times to realize why the RC model was so much better even though it doesn’t look much different from the LV_TRANS model results.

274 – I’m having a difficult time understand how you calculated the grounded area. Are you somehow accounting for cavities or is it just the percent of the glacier that is not floating above the “grounding zone”.

305 –Somewhere in this section I would suggest explaining why it is better to be able to vary u_o over m.

310 – Fast-sliding speed is u_o correct? Please just use the symbol once you define it earlier on. You can define it again in the section heading or early in this section. I was a bit confused at first because you first introduce u_o with a lot of other variables and I quickly forgot the meaning of this specific one. I think putting parenthesis or commas around the symbols would also help the readers follow the definitions of these variables.

314 – Woodard et al., 2023 also talks about this.

Woodard JB, Zoet LK, Iverson NR, Helanow C. Inferring forms of glacier slip laws from estimates of ice-bed separation during glacier slip. Journal of Glaciology. 2023;69(274):324-332. doi:10.1017/jog.2022.63

Section 5 – I found this whole paragraph to be difficult to follow. Please consider rewriting. I’ll put a few specific issues I had below.

324 – LV can but it needs to be re-parameterized with velocity data. Maybe merge the first and second sentences to avoid confusion.

331 – Unclear to me what you mean by transition speed here. Is this u_o?

Figure 5 – I had a hard time seeing the colors in the legend. Consider making the points larger.

Figure 7 – I had a hard time seeing the yellow in these plots. Especially the axis text. Please consider changing the color.

Figure S1 – I could not tell from this where the tongue was. Consider outlining the tongue to help orient the readers. A north arrow I think would also help here.

In this manuscript, Trevers et al. explore how well a range of commonly used sliding laws – linear-viscous, Weertman, and Coulomb-friction – perform in a model at mimicking observed speeds along the main trunk of Greenland’s Jakobshavn Glacier during the time period between 2009 and 2019. They find that, while no single sliding law with static (fixed in time) parameters does a good job of matching observed velocities for the entire time period, a regularized Coulomb-friction law does a much better job (relative to the others tested) at matching observations during the time period from 2012-2016, during which the glacier exhibited both the highest overall peak speeds and the largest range in annual speeds. The authors go on to discuss the reasons behind these different model behaviors, after which they hypothesize that a regularized, Coulomb-friction sliding law with a spatially variable regularization parameter may provide the optimal choice for best-matching observed speeds (without requiring time-dependent optimization, something that is obviously not a viable choice if the ultimate goal is to use the optimized model for projections of future change).

Overall, this is an informative paper that is well written and presents interesting and useful findings. It confirms and expands upon related findings from other recent work and will be appreciated by readers of The Cryosphere. Most of my comments below are minor and editorial in nature, aiming to improve the readability of the paper. I do think that the overall direction and findings of the paper could be more clearly hinted at and summarized up front. Because of the way the abstract and introduction are currently written, I was anticipating that the focus was going to be more on what was gained and learned from conducting a time-dependent initialization / assimilation of observations. As currently written, the conclusions may leave the reader a bit unsatisfied; having queued up the interest, we are left wanting to see the results of the proposed optimal sliding law, That is, a Coulomb-friction law with a spatially variable, optimized, regularization parameter. While I realize that may be beyond the scope of the current work, it could be nice to end with the proposal to conduct future work to this end, if that is indeed the author’s ultimate intention.

Abstract

3: “…range OF sliding laws…”

5: “…the OBSERVED large seasonal and …”

5: “… AND THAT the assimilation of regular …” (“while” does not seem appropriate here since the suggestions regarding the sliding-law-type and the assimilation of velocities are two distinct and very different topics).

7: “was” -> “is” ? Note that the tense in most of the rest of the abstract is present, not past (e.g., in next sentence you say “we find” rather than “we found”).

7: It might be more informative here to say “ … able to reproduce the range of speeds observed during the period of peak flow, from 20XX-20YY” (or something like this).  After readying the full paper it seems to me that this is the more important and interesting conclusion to highlight.

7: “Finally, we find …” (missing comma)

Last sentence – maybe make this a bit more clear, e.g. if you are putting forth a proposal for such a sliding law as part of this contribution.

Main Text

12-15: You might also add a reference here to Hillebrand et al., who conducted a somewhat similar set of exercises to try and model the behavior of Humboldt Glacier, Greenland, and found similar w.r.t. importance and sensitivity of power-law exponent in sliding law. There may also be some other findings from that paper w.r.t. sliding law types, param. values, calibration against observations, etc. that are relevant to / warrant some discussion here (The Cryosphere, 16, 4679–4700, 2022 https://doi.org/10.5194/tc-16-4679-2022).

21-20: As above, the findings from Hillebrand et al. may be relevant to discuss here.

37: “… ice tongue, which …” (comma after “which”)

47-48: “…flow speeds, in excess of 18km/yr, …” (missing commas?)

66: Maybe clarify “… block-structured mesh refinement …”?

91: “…soft ice, which …” and “… viscous ice, which …” (comma after “which”)

98: Again, comma after “which”? Note that I’ll stop mentioning this explicitly from here on and just suggest the authors check the remaining manuscript and ensure this is used correctly and consistently throughout (some places in do use a comma after which and some do not).

118: Move the colon forward? E.g., suggest “… with respect to C and phi: since we seek to unknown fields …”

Section 2.1.3: Did you try without the timeseries regularization? If so, what were the results? Or, put another way, would it make sense here to provide a bit of additional information on what motived this choice (as opposed to just taking the straight-up, best-fit optimization fields for every individual timeslice? I.e., it’s not entirely clear what you get from the time-lagged portion of the optimization (unless I’ve misunderstood it).

142-145: Was there any independent check done on the accuracy of the DEMs constructed in this way? It seems like simply accumulating dh/dt year on year for many years in a row could also result in the accumulation of error. Alternatively, were any estimates made of the potential errors in the constructed DEMs and/or the potential impact on those errors on the simulated velocities?

152: What does “as available” mean here? Were there 3 month periods for any given year where obs. vel. data were not available (and, if so, what was done to generate velocities for those time periods)?

152-154: Were the vels. for the faster moving trunk generated from feature tracking rather than interferometry? Perhaps in this section you could clarify if interferometry or feature tracking was used for the calculation of velocities (or if a combination of methods was used for velocities covering each scene at each time period).

160-164: Clarify if the temperature spin-up is done as part of the BISICLES model or using some other model. And what sort of temperature model is used? Does it count for both horizontal and vertical advection? A few additional details would be appreciated.

2.2.2: I’m confused about how the time-series optimization works. Is the same reference state always used (i.e., the first quarter of 2009) or is a new reference state – linked to the optimization from the prior quarter – used each time?

179-180: “… AN ice sheet surface … and TO reduce …”

188: “…were calculated by equating Tau_b WITH ITS OPTIMZED VALUE (?) in the relevant expressions.”

179-184: It’s unclear to me how the generated DEMs factor in here. If you relaxed the initial sfc elevation via forward modeling, then presumably that sfc is much different from that of the initial DEM. Did you accumulate anomalies from the DEM differences to your modeled sfc elevation? Were the DEMs just used for the optimization of the sliding coefficients, etc. …but then not necessarily consistent with the model ice sheet surface for those same time periods?

190-197: Is the calving front position is specified by observations or calculated? Initially here, it sounds like you calculate the calving rate required to match the observed ice front. But then below that you say that it’s only the centerline that gets this treatment and the rest of the ice front (?) is scaled according to this rate and the local velocity. In that case, does any other ice front position than the centerline match the observed ice front position over time? A little additional clarification would help here.

198-200: Perhaps this addresses my question above. It sounds like the observed thinning rates (inland of 15 km) are applied to the model sfc state. Is this in addition to or instead of any thinning that the model calculates for these locations? Is the mix of observed vs. modeled thinning rates between 15km and the terminus just a linear combination based on the distance along the flowline between the two regions?

207-208: Clarify – linear interpolation was done between the quarterly inputs determined from inversions?

257: “and required the inference of changes in” … could this just be “and required changes in”? If the inference part is important, then it seems like you may want to make the additional clarification in this sentence that you are talking about the modeling of these velocity changes (as opposed to the actual changes themselves).

261-263, 265-267: I think it could worth explaining more clearly and early on in the paper, when you first discuss the methods and different sliding laws used, that you are not advocating here for time-dependent optimization of basal slide parameters (since in some sense, as you point out here, this is “cheating” a bit). Rather, this is your baseline for clearly identifying if / that changes in basal sliding / basal traction are required to fit the observations. After that, your goal is to find the best sliding law and set of fixed parameters for that law that also allow you to best match the time-varying observations. This is something that you might also consider trying to clarify / prepare the reader for a bit better in the introduction and abstract.

270-282: Another way to think about this (or possibly explain it) is that ungrounding and loss of basal traction at one point has to be made up for at some other location (in order to obey force balance); the loss of support at the bed requires the transfer of stress, laterally or longitudinally, to another part of the bed. For a more linear sliding law, this transfer can be quite local (neighboring grid cells) but for a coulomb-friction law and a semi-uniform failure strength in a region (here, the grounding zone), this is not possible. That stress transfer will simply increase traction at neighboring regions, leading to failure of the bed there as well. In this sense, the Coulomb-friction law leads to / requires a non-local transfer of stress.

282-283: “Through this mechanism … is able to account for in effective pressure without explicitly …”. Can you elaborate further on what you mean here? I’m not sure I follow exactly (and maybe other readers will have a similar problem).

290: “The results from further …”. Something missing from / wrong with the beginning of this sentence that makes the rest of it confusing.

292-293: Can you be explicit here if / that the transition between “slow” speeds and the faster speeds allowed by a Coulomb law is in fact given by the value of u_0 (i.e., if u_0 is 1000 m/yr, do we expect linear-viscous behavior below that speed and Coulomb behavior above it?).

308-309: Practically speaking though, is there much difference? In each case, you would need to figure out / specify the spatially varying parameter field values. Do you think that a spatially varying u_0 is more physically reasonable / intuitive than a spatially varying m?

310-320: Be explicit here that by “the fast sliding speed” you mean the value of u_0 (?). Again, in 317 you say that (presumably) this value subsumes the role of effective pressure. Can you be clear about what you mean by that and why? Is this simply a mathematical / functional argument because it appears in the denominator as effective pressure often does (and so both u_0 and eff. pressure have an inverse relationship with basal traction)? Note that this may be the same question I’m asking about above for lines 282-283.

328: “We explore the use of different sliding laws” … add some more here to clarify to what end? E.g. “… in addressing this limitation.”

332: “… may vary”. Spatially? Temporally? Both?

Figures

Figure 1 (caption): The meaning of “Annual year start ice fronts” is a little bit unclear here, and an awkward way to start this sentence. Consider revising? “… from SAR intensity images OF Lemos et al …”

Figure 4: Clarify in caption what the grey region represents?

Figure 5a: Suggest making the symbols in the legend larger (i.e., use filled circles rather than dots). The colored dots on their own there are difficult to see and their colors are difficult to discern from one another (the clouds of dots in the actual figure body are ok as is).

Figure 8: The actual line colors in the figure here do not seem to agree with the colors as described in the caption. “Vertical-dashed lines indicate the value of u_0”. This is confusing since you just said that the colors of the lines (at least for two of them) are for different values of u_0. Do you mean that the dashed-line represents the values assumed over a certain region for the modeling done here?