Overview:

The paper describes a new application of a flood-fill algorithm recently developed (Nicola et al., 2023, subm.) together with a box-model that parametrises basal melting in sub-ice shelf cavities (PICO, Reese et al., 2018) to study the impact of relative sea-level changes (RSL) on basal melting at glacial-deglacial timescales in Antarctica. RSL is calculated with a coupled ice-sheet – GIA – sea level simulation framework (Thorsten  et al., 2023, subm.), that covers the last deglaciation. The impact of RSL on basal melting is accounted in a simplified way, keeping  the present-day ice sheet grounding line configuration. The proposed method is an attempt to implement changes of water masses properties  due to vertical displacement caused by RSL changes on the continental shelf break, without the expense of running a high resolution ocean model.

Despite the understandable limits, which are mostly acknowledged, I find that some points in the methodology proposed here, also inherited  by the referenced method in Nicola et al. (2023, subm.) are not thoroughly justified. Some flaws are related to the oversimplified assumptions  in the oceanographic settings and dynamics and in the ice-ocean interactions, which are not well supported (see comments below).

The scientific value is difficult to assess, due to: the methodology limits; the application only to the actual grounding line configuration; and a  ack of development perspective in the application of the method to more realistic studies. An assessment on the evolution of the importance  of certain gateways for the deglacial AIS retreat would make the study of greater scientific value, in my opinion. The authors should mention and discuss potential ways to implement a more realistic application, such as an evolving grounding line configuration. Overall it is not very  clear what the study wants to achieve, since the “g” parameter remains free and the grounding line is kept at the present-day position. If the purpose is to produce a conceptual model I suggest strengthening the methodology to take into account a more accurate present-day oceanographic setting, which is also a key input for PICO.

Introduction:

The introduction describes the relevant processes that affect RSL changes at deglacial timescales. The GIA part is ok but there is a lack of  description of the oceanographic setting and gateways at present, which is a key point of the paper and would inform the reader on how far the method would be applicable to present and past scenarios.

Methods:

The method relies on the extrapolation of bathymetry at ocean gateways (i.e. deepest troughs in a identified coastal basin) along the shelf  break. The extrapolated bathymetry should indicate the depth at which the Circumpolar Deep Water (CDW) is able to reach the sub-ice shelf cavities grounding lines. The fraction of grounding line reached should represent the exposure of the sub-ice shelf cavity to CDW intruding from a certain gateway.

However the methodology for the calculation of critical access depth (as well as its definition) is not fully understandable as it is outlined in this paper, and need to be referenced continuously tothe companion paper Nicola et al., (2023, subm.). The definition of grounding line access “g”, which is a key free variable, is not clearly defined in either papers. There are inconsistencies with the definition of the input temperature and salinity terms employed in PICO, i.e. where they are extracted from: in this paper it is stated that they are from the continental shelf break,  whereas in Nicola et al., (2023, subm.) both properties from the continental shelf and the calving front are employed. PICO would need to be forced by realistic water masses at the calving front, and employing shelf break temperature and salinity, even only as anomalies with respect  to the present day, is not representative of the water masses entering the cavities. The only case may be for “warm” type continental shelves  (Thompson et al., 2018), where the CDW is actively pushed towards the ice shelf cavities by winds and by dynamical processes in the Along-Slope Front such as an Eastward flowing undercurrent (Silvano et al., 2022). The method could work in specific locations on “fresh” shelves  (Thompson et al., 2018), after applying some corrections to take into account mixing of CDW into “modified” CDW (mCDW), which also tilts the  isopycnals on the shelf break (may think of extrapolation along isopycnals). As for melting in multimodal cavities (e.g., Tinto et al., 2019), melt  by mCDW usually occurs at mid-depth, while the grounding line mostly melts with mode cold salty water (Mode 1, Silvano et al., 2016; Herraiz-Borreguero 2015). These features are not accounted for, and the methodology misrepresents the impact of mCDW in these cases, since there  is no direct connection between the mCDW and the grounding line. Also see e.g. Herraiz-Borreguero (2015), usually only the Eastern side in  multimodal cavities is affected by mCDW, while here the anomalies are applied to the whole basin. Therefore the method, although simplified,  would be fully applicable to “warm” continental shelves found mostly in West Antarctica.

Results

The method produces an increase/decrease in melting by two mechanisms: 1) a vertical shift in the shelf-break water masses and 2) a  greater/lesser area of the grounding line being exposed to warm water masses at the calculated critical access depth. I find a limiting element  the fact that only where there is a vertical gradient of ocean properties, the extracted temperature and salinity at the critical access depth  produce an impact on basal melting. I imagine that a ticker layer of intruding CDW would have an impact even if the critical access depth was  below the thermocline. The impact on basal melting is calculated employing the present-day grounding line, with some adjustment to keep  the floating criterion. The main result of the paleo experiment LGM15ka is that at the basal melting by RSL change was lower in the EAIS and  higher in the WAIS during the LGM due to different subsidence patterns. In the year2300 simulation, slightly higher basal melting is obtained  in the East Antarctic Ice Sheet and lower values in the West Antarctic Ice Sheet. The icefree scenario is useful as a maximum estimate of future  sea-level induced basal melting, but it’s usefulness is doubtful, since it makes no sense to study basal melting in the case of no-more existing  ice sheets.

The resulting impact of RSL in different scenarios is of the same order of magnitude as other important climatic forcing. However the  comparison is always made with present-day grounding line configuration.

Discussion:

The points made in the discussion are clear, but something is missing. Is the method reliable in capturing the ocean impact on melting first?  Although it is not the purpose of the paper, a discussion of if and how the method works for different oceanographic settings is missing, e.g.  how reliable it would be in different types of continental shelves, i.e. “warm”, “dense” and “fresh” types (Thompson et al., 2018). Overall I think  that the method works better in “warm” continental shelves and could potentially work in “fresh” shelves type. "Fresh" shelves usually lie on the  Eastern side of the largest basins, which are also those that show multiples melting modes (Ross Sea, Weddell Sea, Prydz Bay), and with some adjustments to represent the local impact of CDW intrusions and mixing it could be sufficiently accurate. In the “dense” shelf type the method could not work, as there is no direct  connection between the CDW and the grounding line.

Kreutzer et al. assess the effect of modifications in ocean access depths on the Antarctic continental shelf due to changes in RSL. They assume different end-member scenarios (LGM, future) to compute RSL changes on the continental shelf and then compute access depths via a flood-fill algorithm following oceanic pathways along deep bathymetric throughs. They then apply the corresponding corrections to the present-day thermal forcing and compute PICO basal melt rates based on a modified current ice shelf geometry. They show that basal melt rates can change substantially simply by changes in RSL. The manuscript is obviously suited for The Cryosphere, it is well written and the figures are excellent (albeit sometimes difficult to read due to the many details).

My main question/comment is how transferable such an idealized assessment of critical access depth is to estimate the impact of oceanic continental shelf pathways on basal melt rates in an actual time evolving ice sheet simulation. Often in stand-alone ice sheet modelling averaged ocean conditions over typical access depths are assumed and computing critical access depths and identifying the relevant ocean waters for computation of basal melt rates as the authors suggest here is a much better approach. However, this would have to be done repeatedly during the simulation to account for the changes in bathymetry and ice sheet configuration. Also, ocean currents/thermal state would evolve (or at least changes would be prescribed with existing time evolving ESM-data or parameterized forcing). I am missing a more expansive discussion of the caveats and limitations of this approach.

Referring to the above, I think this manuscript could be even more valuable if the authors give some perspective on what their results mean for actual ice sheet model reconstructions/projections. One could for example run a transient simulation in which critical access depths are repeatedly calculated, and the thermal forcing is updated accordingly including the effects of ice sheet evolution on grounding line positions and ice shelf geometry. This could then be contrasted with a simulation without such a feedback. I understand that this would be very costly e.g. for a de-glaciation scenario (i.e running the model from LGM to PD). But it might be feasible to do this for a transient SSP-scenario (e.g. one of the extended ISMIP6 forcings). The authors don’t mention how costly their flood-fill algorithm is and what the minimal resolution of the bathymetry is to make this a valuable effort. Maybe it is computationally prohibitive to do this during runtime for a centennial-scale simulation.

If the authors decide that this is outside the scope of this manuscript than they should still expand their discussion of caveats accordingly.

Also, I recommend to clarify the experimental setup a little more, especially being more explicit with respect to the fact that ice sheet geometry is being kept constant at a present day configuration and that the changes in thermal forcing are based on ice sheet states which are completely different and thus not necessarily consistent. It is difficult to assess whether the change in access depth is a first or higher order effect in light of ocean circulation changes, ice shelf cavity changes and grounding zone evolution. The authors should provide a little more perspective on this.

In summary I’d recommend this interesting work for publication in The Cryosphere provided the authors address above comments. Below I add some general remarks and specific edits/comments.

General points:

What relevance has a scenario where all ice is gone for basal melt rate computation? The concept of basal melt rates is a rather pointless notion in this case I’d say (having now read the entire manuscript the authors touch on this point in the discussion at the end). Except for glaciation scenarios after such a complete de-glaciation. However, it would be anyone’s guess how ocean conditions would look like in such a scenario. I am a little unsure how informative this high-end member is. The same holds true for LGM conditions as you compute critical access depth in regions which would be completely covered by grounded ice (i.e. no ice shelf cavity). In case of de-glacial retreat of course this would open access to these over deepened throughs but due to MISI (or forced retreat) the bedrock would also rebound again modifying critical access depth. In summary, while I find the methodological approach by the authors quite interesting, however, I am not entirely sure what significance it has for actual transient simulations of the Antarctic Ice Sheet. I fail to understand the significance of modified critical access depths based on LGM or high-end future climate scenarios for a present day ice sheet geometry. Instead, one would have to recompute the critical access depth continuously as the ice sheet responds to the respective change in climate forcing to get a more realistic forcing for e.g. PICO derived from the 3D ESM-data. I could imagine that this would slow down the model somewhat due to the flood fill algorithm.

Ocean access does not solely work via the deepest gateways but arguably most of the warm water e.g. in the Amundsen Sea is channeled via these gateways, does your approach also reflect the change in basal shelf melt rates at the grounding line for the bulk advection of CDW/mCDW etc. across the continental shelf and into the cavity?

At times the description of your computation of deepest gateways and corrections to bathymetry is a bit convoluted and difficult to follow.

Disentangling the different aspects of SL fall/rise, RSL, GIA on continental shelf bathymetry is a complex task. I like Figure 1 which illustrates how these effects can play out. However, I think it would be nice to also include a conceptual figure (reduced complexity) illustrating the bathymetric elevation changes and their effect on access depths.

L46 during the LGM

L58 «Antarctica loses up to 3.13 m of sea-level equivalent ice» 3.12 m is a very precise upper estimate and I think it is alright to write ca. 3.1 m here given the substantial uncertainties associated with these projections.

L68 I suggest to rephrase to something like “has to be designed/parameterized/prescribed in a robust manner”. “… appropriate way” is quite subjective given the scarce proxy-constraints for paleo climate states and evolution.

L77 “As (positive) values of RSL indicate … ”

I assume changes in RSL can go both ways (positive and negative), therefore same for bedrock topg. Or do you refer to only positive anomalies?

L86 do you refer with “flow pattern” to ice flow or ocean circulation changes? I assume ice shelf flow?

L86-88 if I follow your argument correctly this is assuming that ocean circulation does not change right? A real scenario with 100 m RSL changes would, I presume, be associated with ocean circulation changes as well. Not so straightforward to disentangle the actual effect in a coupled system, but I’m aware that this is not what you are discussing here. However I’d suggest to include this caveat somewhere in the discussion.

L109 “a configuration with all continental ice masses transformed into liquid water (GMSL ≈ +70 m).” repeating myself here, but what relevance has such a scenario? If all ice is gone, the concept of basal melt rates is rather meaningless? Except for glaciation scenarios after such a complete de-glaciation. However, it would be anyone’s guess how ocean conditions would look like in such a scenario. I am a little unsure how informative this high-end member is.

Section 2.2. is this the algorithm developed by X. Davis for ISMIP6? If so, please reference. Nevermind, just saw in Nicola that this is similar to ISMIP6.

Figure 1. This is a nice figure. I’d suggest to restrict the top left inset to the FRIS region/continental shelf otherwise it’s a bit small to read.

P5 L129 VILMA solves the global sea-level equation self-consistently,

L136 same question as above, for sea level drop (LGM scen.) I understand the negative offset to bathymetry. For regional/local SLR this should be a positive offset right?

L145 again, difficulties to understand this, you start the flood fill algorithm in the open ocean, i.e. beyond the continental shelf break and then work your way forward towards the same or lower bathymetry? In this case you would never reach the continental shelf. I seem to misunderstand something here, but maybe consider to rephrase this. For me “lower bathymetry” means deeper ocean bed.

Section 2.4 If I understand correctly, you derive a 2D forcing field for PICO from averaging over the thermal forcing acquired over the continental shelf taking into account critical access depth of pathways instead of simply averaging over a continuous depth range? Maybe state this more explicitly somewhere.

L190 suggest to rephrase this. E.g. : this agrees well with e.g. Clark et al, 2009 suggesting an Antarctic delay of 4.5 – 12 kyr with respect to the global LGM sea level lowstand.

L197 does that mean you integrate PISM for 86 kyrs at 4 km resolution (in L181 you mention 4km resolution in your initialisation)?? That would be very impressive indeed. 

L200 “plausible RSL change rates as observed by GNSS measurements” I suggest to show this in supplementary materials.

“Then, from present-day onwards” assume this means 2005?

L205 “which can potentially increase Antarctic ice loss dramatically but is poorly constrained …”

L206 “To also include …”

L206.. “To include also non-Antarctic cryospheric changes and reflect redistributions in the global water budget, we add a uniform GMSL contribution of 3.68 m on ” is this contribution added in a timeseries or all at once? While being a secondary effect later on it would affect your results at least somewhat if you already add this during the 21^st and 22^ndcenturies.

L215-220 I find your methodological approach very intriguing, however I am missing a caveat paragraph mentioning that ocean circulation amongst other things would change in light of these large scenario differences which might actually make the critical access depth a secondary effect (or vice versa enhance it even).

Also, maybe I missed this in the introduction or methods, but how do you force your LGM15k scenario? ESM-time slice, parameterized, …? What ocean conditions do you provide as baseline before correcting for bathymetry changes?

Figure 2 b) I do not understand this figure, if you’d remove all ice you’d get a ca. 1/3*H (ice thickness) bedrock rebound due to the missing ice load. That would put most of East Antarctica far above sea level. How is sea level defined in this case? East Antarctica would mostly be above sea level? This comes back to my general comment about rather meaningless impact on basal melt rates where you neither have ice nor contact with the ocean. Or do you always consider a present-day ice sheet configuration and compute the offset in thermal forcing due to difference access depths which are caused by LGM or future changes in ice load/RSL? What does “adjusted grounding line” mean in this case? Comment: this all becomes clear later on in the manuscript but I’d recommend clarifying this much earlier.

Wouldn’t it make more sense to compute the change in thermal forcing for the actual ice sheet configuration used to compute the RSL changes?

Generally, the figure is quite hard to read due to the small subplots.

L239 amount

L271 potential access of ocean currents to the grounding line?

L286 “For comparability we use a grounding line position corresponding to the present-day ice thickness for all scenarios, which has been horizontally adjusted to obtain the floatation criterion for applied bedrock changes ” I suggest to mention this definition already in the method section.

L289-291 again, while it is interesting to see what such a shift would mean for basal melting it is still a bit hypothetical as the grounding line would be far advanced for the LGM-state and thus most of the area you are discussing here would be covered by grounded ice.  If I understand correctly (and maybe I don’t) you compute basal melt rates for a present-day ice sheet configuration (albeit with a horizontally adjusted grl, see comment above) given an offset in the critical access depth due to a completely different scenario of ice cover.

Figure 4+5 what’s the second black line (not the continental shelf), ice shelf front?

L326-332 this is a nice summary and could be well positioned in the introduction already.

L333 what do you mean by “the implied potential change of present-day temperatures”? temperature change due to change in critical access depth or applied lgm anomaly?

Figure 6. This is a nice figure but also contains a ton of information, I had to look at it for quiet some time to understand what’s going on. Maybe the caption could be a little more explicit and expanded to guide the reader through.

L345 “The icefree scenario shows a maximum difference of ±0.5◦C in continental-shelf break temperatures” again I presume this relates to delta T due to changes of access depths?

L398 Colleoni et al. (2018) discuss how oceanic heat supply to AIS margins (shelf edge?) can operate …

L401 do you mean exchange between different shelves or do you mean “along-shelf transport”

L392-404 this discussion/clarification/caveats should occur already in the intro/motivation. E.g. while reading the manuscript it wasn’t clear to me that you employ a present day ocean to compute the basal melt rate changes due to scenario dependent changes in bathymetry.

L409 Why do you not assume this? Please elaborate. On might wonder if considerable higher grl depths don’t change the outcome why would changes in critical access depth at coarser resolution matter? A short explanation would be nice here.

L438 topographic structure

L439-441 very true (see my general comments). I am missing the reason why to include such a scenario as it wouldn’t mean anything for an actual ice sheet (or better to say absent ice sheet).

L443 we adjust the grounding line position (I don’t follow the choice of bold face font in the discussion).

L446 here I don’t know why you correct for the RSL effect on floatation while ignoring the fact that the critical access depths are due to completely different extreme ice sheet geometries.

L481 Maybe also cite Hellmer et al 2012 here who where I think amongst the first to point out this possibility.

L493 “We compare our estimates to similar effects induced by shifts in climatic boundary conditions, associated with altered wind patterns, sea ice and ocean dynamics.” Where is this comparison except for noting it in the discussion?

L495 the relevance