the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Modeling Antarctic ice shelf basal melt patterns using the one-Layer Antarctic model for Dynamical Downscaling of Ice–ocean Exchanges (LADDIE)
André Jüling
Roderik S. W. van de Wal
Paul R. Holland
Abstract. A major source of uncertainty in future sea-level projections is the ocean-driven basal melt of Antarctic ice shelves. Whereas ice sheet models require a kilometer-scale resolution to realistically resolve ice shelf stability and grounding line migration, global or regional 3D ocean models are computationally too expensive to produce basal melt forcing fields at this resolution. To bridge this resolution gap, we introduce the 2D numerical model LADDIE (one-Layer Antarctic model for Dynamical Downscaling of Ice–ocean Exchanges) which allows for the computationally efficient modeling of basal melt rates. The model is flexible, and can be forced with output from coarse 3D ocean models or with vertical profiles of offshore temperature and salinity. In this study, we describe the model equations and numerics. To illustrate and validate the model performance, we apply the model to two test cases: the small Crosson-Dotson Ice Shelf in the warm Amundsen Sea region, and the large Filchner-Ronne Ice Shelf in the cold Weddell Sea. At ice-shelf wide scales, LADDIE reproduces observed patterns of basal melt and freezing that are also well reproduced by 3D ocean models. At scales of 0.5–5 km, which are unresolved by 3D ocean models and poorly constrained by observations, LADDIE produces plausible basal melt patterns. Most significantly, the simulated basal melt patterns are physically consistent with the applied ice shelf topography. These patterns are governed by the topographic steering and Coriolis deflection of meltwater flows, two processes that are poorly represented in basal melt parameterisations. The kilometer-scale melt patterns simulated by LADDIE include enhanced melt rates in basal channels, in some shear margins, and nearby grounding lines. As these regions are critical for ice shelf stability, we conclude that LADDIE can provide detailed basal melt patterns at the essential resolution that ice sheet models require. The physical consistency between the applied geometry and the simulated basal melt fields indicates that LADDIE can play a valuable role in the development of coupled ice–ocean modeling.
Erwin Lambert et al.
Status: final response (author comments only)
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RC1: 'Comment on tc-2022-225', Clara Burgard, 10 Jan 2023
The authors present the new simple model LADDIE that can be used (1) as a high-resolution parameterisation to link hydrographic properties in front of an ice shelf and melt at its base and (2) as a method to use information from coarse ocean models resolving the circulation in ice-shelf cavities to simulate high-resolution basal melt patterns. The authors present the model and its tuning (done on the Crosson-Dotson ice shelf) and then evaluate it on two ice shelves with different characteristics: Crosson-Dotson and Filchner-Ronne.
This model is an advancement compared to “classic” parameterisations in the sense that it includes 2D effects like the Coriolis force and provides the possibility to include fine-scale bathymetric characteristics in the resulting melt patterns. The topic is timely as the representation of basal melt in models remains a large source of uncertainty for future Antarctic ice-sheet projections. In particular, LADDIE enables the resolution of fine-scale channels and regions near the grounding line, where high melt occurs, and which are therefore crucial when forcing ice-sheet models. Its application therefore has the potential to improve the forcing of ice-sheet simulations.
The manuscript is pleasant to read and the procedure to set up and evaluate the model is thoroughly described. I am curious to see how the application of LADDIE will change the behaviour of ice-sheet simulations when it will be ready for a more widespread use!Before publication, however, I think that a few points need to be addressed to clarify this manuscript and make it more robust, especially concerning the evaluation procedure. I hope it is only a matter of restructuring and reformulating and does not involve redoing a major part of the analysis. I realise there are a lot of remarks but they come from sincere interest in the study. I hope that the authors can use them constructively and am looking forward to reading a clearer revised manuscript!
My comments are enclosed in the attached pdf.
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AC2: 'Reply on RC1', Erwin Lambert, 08 May 2023
The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2022-225/tc-2022-225-AC2-supplement.pdf
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AC2: 'Reply on RC1', Erwin Lambert, 08 May 2023
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CC1: 'Comment on tc-2022-225', Dorothée Vallot, 23 Feb 2023
Thanks for this very interesting paper! I have a comment/question on l. 171-172 where you affirm that "Cd,top is
commonly taken to be lower than Cd". Could you give a reference for that? I have not understood that from Asay-Davis et al., 2016.Citation: https://doi.org/10.5194/tc-2022-225-CC1 -
AC1: 'Reply on CC1', Erwin Lambert, 01 Mar 2023
Dear Dorothee,
Thank you for your question. You are right that this statement was a bit too strong.
Holland and Feltham (2006) mention using a lower value of Cd_top, compared to the bottom drag coefficient Cd, based on an out-dated argument that basal ice topography is generally smoother than the seabed. Another possible argument for a reduced value of Cd is the suppressed basal melt by stratification (see the recent observations by Davis et al, 2023), which is not accounted for in the three-equation formulation.
However, our statement that Cd_top is commonly lower in modeling studies is not accurate. This is the case for several NEMO simulations (Mathiot 2017, Jourdain 2017), but a higher value of Cd_top was found by tuning MITgcm (Naughten 2022). And as you point out correctly, the ISOMIP protocol prescribes equal values for Cd and Cd_top. Hence, we will remove this statement in the revision of our manuscript, stating instead that the top drag coefficient commonly differs from the bottom drag coefficient and is often used as a tuning parameter.I hope this clarifies things. If not, do not hesitate to reach out again.
Kind regards,
Erwin
Citation: https://doi.org/10.5194/tc-2022-225-AC1 -
CC2: 'Reply on AC1', Dorothée Vallot, 02 Mar 2023
Thanks for your answer!
I think i understand what you meant now but this was not what I understood from what I read first. If I read your comment properly you use a Cd different at the bottom and at the top. This is probably a good guess. But in my understanding, from your manuscript, Cd was the coefficient of drag used for the momentum equation (and by the way, you write eq. 1 but it appears in eq 2) and Cd,top, the one used in the 3 equations model. So I understood that you also use Cd at the top boundary in the momentum equation. That would mean that you would use two different Cd at the top for both sets of equations.
In Nemo, I suppose this is the case as the momentum equation is solved in the first wet cell and the 3 equations in the Losch layer so even if the same Cd is given, one could think of an "effective Cd" which is different in the Losch layer and in the 1st wet cell.
Citation: https://doi.org/10.5194/tc-2022-225-CC2
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CC2: 'Reply on AC1', Dorothée Vallot, 02 Mar 2023
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AC1: 'Reply on CC1', Erwin Lambert, 01 Mar 2023
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RC2: 'Comment on tc-2022-225', Anonymous Referee #2, 02 Mar 2023
This paper introduces LADDIE, a 2D model that implements the depth-averaged navier stokes equations for ocean physics over a mixed layer thickness. The equations have been implemented before (e.g. Holland and Feltham 2006), but there are new modifications (for instance avoidig a hard constraint on minimum thickness), and moreover it is written in the form of an open source python code intended for wide use (though I have not tried it, and am not clear on how easy it is to port to another domain!) The model results are carefully compared against available observations for select ice shelves with high quality modelling and satellite observations of ice ocean interactions.
I have very few issues with this paper. The model itself is a step forward, and the reasons for it being a step forward are explained thoroughly, legibly, and carefully within the introduction, results and methods sections. The paper does make a very good point that there is a limit to how useful 3D ocean models can be due to cost and resolution required -- but is very clear on what LADDIE is *not* able to do ie model deep cavity dynamics -- and i found the discussion of its limitations (and possible extensions) to be very thougtful. As a scientific paper i feel adequate attention is given to the extensive literature on modelling and observing ice ocean interactions. I would recommend publication following the address of a few minor comments, which i feel will be quite easy.
two general but still minor comments are on the Dotson/Crosson results section:
a) there have been other studies with 3D ocean models run at higher resolution e.g. 1km, I wonder why you did not want to compare to these?
b) Given the emphasis on the channelised melt, I think it is worth mentioning that a recent coupled modelling study (Goldberg and Holland 2022) saw this channel melt completely through within 50 years (in line with the extrapolation of Gourmelen 2017), and the ice-dynamic impact was minimal, somewhat downgrading its importance. The same is not true for the internal shear margin and grounding line of course!
line 34: "presumed stagnant" -- this is an assumption of LADDIE, not the physics of entrainment into the actual ML, which is how this reads.
line 44: at-->over
eqs 1-5: it would be nice to state whether these differ from the PDEs solved in Gladish et al 2012, and how if so. Also, this is for the author to decide, but an appendix showing how to do the integration that arises in the pressure terms (1st 2 terms on the LHS of (2) and (3)) would actually be quite helpful -- because im not sure i've ever seen clearly how these come about, or how to do the layer integration and with which boundary conditions. For your consideration.
eqs 1, 8-10, and 14. Can you state that m_dot>0 indicates melt (if this is true). I don't think you do. (1) indicates it is, and i can reason this is consistent with (8) without referring to other papers. But i have not seen (14) before -- my simple understanding of it is that entrainment is enabled by positive TKE production, and (where there is freezing) by negative buoyancy flux. All seems consistent but it would be nice to be sure.
L192: i don't understand what a weighted average between free and no slip is. are you solving the model twice at each time step with different boundary conditions? would showing an equation help?
L213: "one can interpret"... i think this is only true if the 3D model is isopycnal.
L215: i like this rather than a hard constraint.
L224-5: "to ensure continuity" -- by you, or the satellite analysts?
L339: just to point out that these values for Ah are not huge but bigger, for instance, than that suggested by the MISOMIP protocol. What happens when you have Ah=5, do things change then? or is LADDIE unstable?
L400: "near-zero due to the lack of simulated barotropic flow" -- you don't show any evidence of this, or of it being the cause of low melt rates. My recollection is that the column here is quite a bit bigger than at the Smith and Pope grounding line. On the other hand the Naughten model has pretty coarse vertical resolution at this depth and so the resolution of near-ice variation is particularly poor.. could this be a another potential reason?
Figure 6: could you show profiles from the 3D model as well?
line 444: what do you mean by the remote sensing not showing conclusive evidence? of channelised melt? or of specific features mentioned above? Im also not sure what you highlight in 3a -- there is very little detail here.
L 458: it is possible that channelisation can lead to enhanced stresses and damage, but a reference would be nice here.
L495 -- where does this warm water come from? surface-warmed or other?
L534: propose-->suggest
L608: a good point about subgl outflow. Is it not in fact trivial to add this?
L620-623 -- a really good point about thin columns. Should note though this assumes detailed knowledge of bathymetry, which i think can only be this good if there is drilling, no?
references:
Goldberg, D. N., and P. R. Holland. "The Relative Impacts of Initialization and Climate Forcing in Coupled Ice Sheet‐Ocean Modeling: Application to Pope, Smith, and Kohler Glaciers." Journal of Geophysical Research: Earth Surface 127.5 (2022): e2021JF006570.
Citation: https://doi.org/10.5194/tc-2022-225-RC2 -
AC3: 'Reply on RC2', Erwin Lambert, 08 May 2023
The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2022-225/tc-2022-225-AC3-supplement.pdf
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AC3: 'Reply on RC2', Erwin Lambert, 08 May 2023
Erwin Lambert et al.
Erwin Lambert et al.
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