the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 May 2025
Sub-grid Parameterization of Iceberg Drag in a Coupled Iceberg-Ocean Model
Abstract. Ocean conditions in fjords play a key role in the accelerating ice mass loss of Greenland's marine terminating glaciers. Ice mélange and icebergs have been shown to impact fjord circulation, heat and freshwater fluxes, and the submarine melting of glacier termini. Previous attempts to model icebergs largely fall into two camps: small-scale models that resolve icebergs and represent the impact of form drag, and larger-scale models that parameterize sub-grid-scale icebergs but neglect iceberg drag. Here, we develop an extension of the large-scale style iceberg package for the MIT general circulation model (MITgcm) to implement a novel, scalable parameterization to incorporate the impact of iceberg drag while also improving overall computational performance of the iceberg package by ~ 90 %. To demonstrate our parameterization, we benchmark our method against existing iceberg-resolving models and compare to the previous configuration of iceberg. With the inclusion of sub-grid-scale drag, our model skillfully reproduces ocean conditions and iceberg melt rates of iceberg-resolving models, while reducing computational cost by orders of magnitude. When applied to a multi-month fjord-scale simulation, we find icebergs and iceberg drag have a significant impact on fjord and glacier-adjacent conditions, including cooling fjord waters and increasing circulation. We note that these effects are more moderate in the case of icebergs with drag, suggesting that studies without iceberg drag may overestimate the net impact of icebergs on the fjord system.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(7535 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-1555', Anonymous Referee #1, 02 Jul 2025
- AC1: 'Reply on RC1', Paul T. Summers, 15 Jul 2025
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RC2: 'Comment on egusphere-2025-1555', Anonymous Referee #2, 04 Jul 2025
Review of Sub-grid Parameterization of Iceberg Drag in a Coupled Iceberg-Ocean Model by Summers et al.
Summers et al. present a significantly improved means of representing icebergs and ice melange in the MITgcm ocean model. The improvement comes in the representation of iceberg drag and in making the code much more efficient. They show that when compared with high-resolution (~10m resolution) simulations that resolve individual icebergs, their parameterisation performs very well at resolutions (~100s-1000s m) that are more practical for longer fjord simulations. In addition, they explore the impact of icebergs and iceberg drag on glacier-adjacent conditions.
I found the manuscript - and the work - to be rigorous and meticulous. In places it was a bit difficult to follow the large number of simulations, but I think this is unavoidable and in general the writing is clear, and the figures are excellent. The improvement in representation of icebergs is much needed and will be of use to other researchers simulating icebergs in fjords. The topic is certainly of relevance to the Cryosphere. In general, I would be happy to see this published with minor revisions.
Major comments
My main overarching thought is whether aspects of the manuscript in its present form might have been better suited to a more technical modeling journal such as Geoscientific Model Development or the Journal of Advances in Modeling Earth Systems. The main contribution of this work is an improved package/parameterisation for representing icebergs in fjord models, the paper is quite technical (often referencing model variables and settings), and the take-homes in terms of improved physical understanding are not too prominent. As someone who has worked with icebergs in MITgcm, I was able to follow and find the paper to be a very good contribution, but for someone who does not have this background the paper might be quite technical and dense. As such, I feel the manuscript could do with dialling back the technicality a little and bringing out the physical implications further.
Minor comments
L24 – this sentence didn’t make sense to me – reword?
Figure 1 – I think it would be helpful to note in the caption that each picture here is a column(?) of MITgcm cells, and define variables like delta x, delta y etc in the caption.
L70 – for clarity, perhaps say “reduced to a volume fraction occupied by icebergs, …”
L88 – “hFacC, hFacS, hFacW” – I’ve come across these in using MITgcm but a more general reader won’t be able to follow here without a bit more description.
L95, 143, 147, 203. This may be preference, but in each of these places a figure is referred to that is much later in the paper. I find it awkward to flick forwards to find the one bit of that figure that is relevant without getting dragged into the rest of that figure, so maybe better to refer to the figures in order and remove these references?
Eqs. 4&5 – might it be helpful to have a plot showing alpha and beta versus phi to visualise how they differ?
L151 – “normal distribution of our iceberg drafts” – it isn’t clear to me that the distribution is normal, given the power laws in Eq. 6 and L138. Is the distribution indeed normal?
L157 – here (amongst other similar lines e.g., L286-287) is the sort of line that I feel is more suited to a journal like GMD/JAMES, because it is referring to specific modeling variable settings, which is not something I often see in Cryosphere papers. Might there be a way of avoiding these technicalities in the main text, for example by moving to an appendix or supplement?
Tables 1 & 2 – these are great and really helped me follow the results.
L164 (or near here) – it would be good to refer the reader to Fig. 2A at this point.
L169 – the non-physical temperature field – I follow what you’re trying to do, but is there a reason not to use salinity to get the required stratification, which would be more physical?
L176 – background diffusivity seems to be set twice here, or perhaps I am misreading, but reword for clarity.
L186 – this starts the description of melting before you’ve introduced the simulation that uses it (the melange melt second benchmark), right? If so, it would be better to move this description of melting into the paragraph below.
L189 – I’m confused about this definition, or perhaps just the notation – don’t lower case gammas usually denote an exchange velocity, so that there would be a velocity in this definition (see e.g., Holland & Jenkins, 1999, Journal of Physical Oceanography)?
L203 – “where horizontal resolution is 10 meters” – I guess this line is a mistake since the resolution is presumably coarser and it says so on L207?
L214 – In table 1 this value is C_bd = 0.025 – check for consistency through the manuscript.
L222 – normalized
L241 – should this be Figure 4, not 3?
Figure 4 – I found it hard to see the line denoting the driving velocity.
Figure 5 – it’s very cool how well the package performs even at coarser resolution.
L326 – I feel this repeats earlier material unnecessarily.
L330 – I didn’t see the terminology “High Melt” used in section 3.1.
Fig 8b-d – at what time through the simulation are these results extracted? Since there is time variability shown in panel a, this would be relevant information to include in the text and/or caption.
L356 – unnecessary comma and I presume “(D).” is a mistake.
L357 – highlights
L370 (or start of this section in general) – it would be great to refer to Fig. 9 at appropriate points here.
L421 and 489 – isn’t it more than 11,000x the computational expense? If there are 40 (=400/10) more grid cells in x and y, and the timestep presumably has to be ~40 times smaller, then the change in computational expense would be 40^3 = 64,000?
L461 – minimum melt speed of 0.04 m/s
L429 – Jain et al. preprint – it would be appropriate to cite this somewhere in the introduction.
Figure C1 – since the equivalent figures for the other 2 sets of simulations are in the main paper, perhaps this could be brought into the main paper?
Citation: https://doi.org/10.5194/egusphere-2025-1555-RC2 - AC2: 'Reply on RC2', Paul T. Summers, 15 Jul 2025
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-1555', Anonymous Referee #1, 02 Jul 2025
Dear editor and authors,
The submitted manuscript develops a new parameterization of iceberg melt, blocking, and drag effects into the pre-existing iceberg package of the MITgcm. The representation of blocking and drag reduces the magnitude of the iceberg-induced freshwater flux and the spatial variability in velocity and temperature across a simulated representative fjord. The new developments also increase the computational efficiency of the iceberg package. The manuscript is well-written, and I recommend minor revisions.
Major comments:
Lines 85-95: I am not sure I agree with the description of the way the MITgcm treats the partial cell factors hFacC, hFacS, hFacW. The authors state that they are “reset” by the non-linear free surface calculation at each time step. In fact, the background h0FacC, etc., remain the same, and they are only rescaled by the stretching of the vertical coordinate. This is an intended feature, and I do not agree that it is something that should be corrected in the case of iceberg blockage. Iceberg blocking effects and the vertical stretching of the coordinate system should both be allowed the same time. In this vein, I also do not necessarily agree that the previous studies that used the r* coordinate were deficient in that regard (I was not involved in any of those previous papers). Maybe the authors can revisit their case, and if they are still certain, they can present their argument more convincingly.
Section 2: You should describe the underlying assumptions behind the representation of iceberg dynamics and thermodynamics in this package. You may even consider a brief introduction to the pre-existing package and its capability. For instance, how is “udrift” in line 65 of the manuscript defined? How is the iceberg drift estimated? More generally, please state clearly which iceberg properties and fluxes are assumed to be constant in time.
Minor comments:
Lines 169-172: Could you explain more clearly why you need to set up the nonphysical temperature field? Is it not possible to achieve the same match to Hughes (2022) using the combination of 0°C temperature and 36.24 PSU salinity that you yourself mention?
Figure 2 legends: “Anomonly” should read “Anomaly”
Line 246: You may consider rephrasing “the sinusoidal nature of velocity” as “the sinusoidal profile of velocity.”
Line 285: Point the reader back to Table 2.
Citation: https://doi.org/10.5194/egusphere-2025-1555-RC1 - AC1: 'Reply on RC1', Paul T. Summers, 15 Jul 2025
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RC2: 'Comment on egusphere-2025-1555', Anonymous Referee #2, 04 Jul 2025
Review of Sub-grid Parameterization of Iceberg Drag in a Coupled Iceberg-Ocean Model by Summers et al.
Summers et al. present a significantly improved means of representing icebergs and ice melange in the MITgcm ocean model. The improvement comes in the representation of iceberg drag and in making the code much more efficient. They show that when compared with high-resolution (~10m resolution) simulations that resolve individual icebergs, their parameterisation performs very well at resolutions (~100s-1000s m) that are more practical for longer fjord simulations. In addition, they explore the impact of icebergs and iceberg drag on glacier-adjacent conditions.
I found the manuscript - and the work - to be rigorous and meticulous. In places it was a bit difficult to follow the large number of simulations, but I think this is unavoidable and in general the writing is clear, and the figures are excellent. The improvement in representation of icebergs is much needed and will be of use to other researchers simulating icebergs in fjords. The topic is certainly of relevance to the Cryosphere. In general, I would be happy to see this published with minor revisions.
Major comments
My main overarching thought is whether aspects of the manuscript in its present form might have been better suited to a more technical modeling journal such as Geoscientific Model Development or the Journal of Advances in Modeling Earth Systems. The main contribution of this work is an improved package/parameterisation for representing icebergs in fjord models, the paper is quite technical (often referencing model variables and settings), and the take-homes in terms of improved physical understanding are not too prominent. As someone who has worked with icebergs in MITgcm, I was able to follow and find the paper to be a very good contribution, but for someone who does not have this background the paper might be quite technical and dense. As such, I feel the manuscript could do with dialling back the technicality a little and bringing out the physical implications further.
Minor comments
L24 – this sentence didn’t make sense to me – reword?
Figure 1 – I think it would be helpful to note in the caption that each picture here is a column(?) of MITgcm cells, and define variables like delta x, delta y etc in the caption.
L70 – for clarity, perhaps say “reduced to a volume fraction occupied by icebergs, …”
L88 – “hFacC, hFacS, hFacW” – I’ve come across these in using MITgcm but a more general reader won’t be able to follow here without a bit more description.
L95, 143, 147, 203. This may be preference, but in each of these places a figure is referred to that is much later in the paper. I find it awkward to flick forwards to find the one bit of that figure that is relevant without getting dragged into the rest of that figure, so maybe better to refer to the figures in order and remove these references?
Eqs. 4&5 – might it be helpful to have a plot showing alpha and beta versus phi to visualise how they differ?
L151 – “normal distribution of our iceberg drafts” – it isn’t clear to me that the distribution is normal, given the power laws in Eq. 6 and L138. Is the distribution indeed normal?
L157 – here (amongst other similar lines e.g., L286-287) is the sort of line that I feel is more suited to a journal like GMD/JAMES, because it is referring to specific modeling variable settings, which is not something I often see in Cryosphere papers. Might there be a way of avoiding these technicalities in the main text, for example by moving to an appendix or supplement?
Tables 1 & 2 – these are great and really helped me follow the results.
L164 (or near here) – it would be good to refer the reader to Fig. 2A at this point.
L169 – the non-physical temperature field – I follow what you’re trying to do, but is there a reason not to use salinity to get the required stratification, which would be more physical?
L176 – background diffusivity seems to be set twice here, or perhaps I am misreading, but reword for clarity.
L186 – this starts the description of melting before you’ve introduced the simulation that uses it (the melange melt second benchmark), right? If so, it would be better to move this description of melting into the paragraph below.
L189 – I’m confused about this definition, or perhaps just the notation – don’t lower case gammas usually denote an exchange velocity, so that there would be a velocity in this definition (see e.g., Holland & Jenkins, 1999, Journal of Physical Oceanography)?
L203 – “where horizontal resolution is 10 meters” – I guess this line is a mistake since the resolution is presumably coarser and it says so on L207?
L214 – In table 1 this value is C_bd = 0.025 – check for consistency through the manuscript.
L222 – normalized
L241 – should this be Figure 4, not 3?
Figure 4 – I found it hard to see the line denoting the driving velocity.
Figure 5 – it’s very cool how well the package performs even at coarser resolution.
L326 – I feel this repeats earlier material unnecessarily.
L330 – I didn’t see the terminology “High Melt” used in section 3.1.
Fig 8b-d – at what time through the simulation are these results extracted? Since there is time variability shown in panel a, this would be relevant information to include in the text and/or caption.
L356 – unnecessary comma and I presume “(D).” is a mistake.
L357 – highlights
L370 (or start of this section in general) – it would be great to refer to Fig. 9 at appropriate points here.
L421 and 489 – isn’t it more than 11,000x the computational expense? If there are 40 (=400/10) more grid cells in x and y, and the timestep presumably has to be ~40 times smaller, then the change in computational expense would be 40^3 = 64,000?
L461 – minimum melt speed of 0.04 m/s
L429 – Jain et al. preprint – it would be appropriate to cite this somewhere in the introduction.
Figure C1 – since the equivalent figures for the other 2 sets of simulations are in the main paper, perhaps this could be brought into the main paper?
Citation: https://doi.org/10.5194/egusphere-2025-1555-RC2 - AC2: 'Reply on RC2', Paul T. Summers, 15 Jul 2025
Peer review completion
Journal article(s) based on this preprint
Data sets
Sub-grid Parameterization of Iceberg Drag in a Coupled Ice-Ocean Model: Dataset and Plotting Paul T. Summers et al. https://zenodo.org/records/15116445
Model code and software
somonesummers/ICEBERG2: ICEBERG2 Paul T. Summers https://zenodo.org/records/14721713
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Paul T. Summers
Rebecca H. Jackson
Alexander A. Robel
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(7535 KB) - Metadata XML
Dear editor and authors,
The submitted manuscript develops a new parameterization of iceberg melt, blocking, and drag effects into the pre-existing iceberg package of the MITgcm. The representation of blocking and drag reduces the magnitude of the iceberg-induced freshwater flux and the spatial variability in velocity and temperature across a simulated representative fjord. The new developments also increase the computational efficiency of the iceberg package. The manuscript is well-written, and I recommend minor revisions.
Major comments:
Lines 85-95: I am not sure I agree with the description of the way the MITgcm treats the partial cell factors hFacC, hFacS, hFacW. The authors state that they are “reset” by the non-linear free surface calculation at each time step. In fact, the background h0FacC, etc., remain the same, and they are only rescaled by the stretching of the vertical coordinate. This is an intended feature, and I do not agree that it is something that should be corrected in the case of iceberg blockage. Iceberg blocking effects and the vertical stretching of the coordinate system should both be allowed the same time. In this vein, I also do not necessarily agree that the previous studies that used the r* coordinate were deficient in that regard (I was not involved in any of those previous papers). Maybe the authors can revisit their case, and if they are still certain, they can present their argument more convincingly.
Section 2: You should describe the underlying assumptions behind the representation of iceberg dynamics and thermodynamics in this package. You may even consider a brief introduction to the pre-existing package and its capability. For instance, how is “udrift” in line 65 of the manuscript defined? How is the iceberg drift estimated? More generally, please state clearly which iceberg properties and fluxes are assumed to be constant in time.
Minor comments:
Lines 169-172: Could you explain more clearly why you need to set up the nonphysical temperature field? Is it not possible to achieve the same match to Hughes (2022) using the combination of 0°C temperature and 36.24 PSU salinity that you yourself mention?
Figure 2 legends: “Anomonly” should read “Anomaly”
Line 246: You may consider rephrasing “the sinusoidal nature of velocity” as “the sinusoidal profile of velocity.”
Line 285: Point the reader back to Table 2.