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https://doi.org/10.5194/egusphere-2025-6334
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/egusphere-2025-6334
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
20 Jan 2026
| 20 Jan 2026
Contributions of supraglacial lakes to the Greenland Ice Sheet melting
Abstract. The Greenland Ice Sheet is considered a potential tipping element in the Earth system, as it may undergo rapid and irreversible ice loss. The complete loss of the ice sheet would lead to significant sea-level rise, posing an existential risk to humanity. Supraglacial lakes on the ice sheet enhance melting by reducing surface albedo and increasing melt rates during summer. We develop a simple conceptual model to investigate this process. The model consists of three coupled partial differential equations describing the temporal evolution of ice, water, and snow thickness within a simplified physical domain of Greenland, all driven by the annual temperature cycle. Model integrations show that, under realistic conditions, the presence of supraglacial lakes accelerates local ice melting and modifies the long-term ice-sheet topography. Regions with recurrent lake formation exhibit greater elevation differences. Under Shared Socioeconomic Pathway warming scenarios, only the lowest-emission scenarios prevent the onset of a self-sustaining melt–elevation feedback that could ultimately lead to complete ice-sheet loss. These results highlight the critical role of supraglacial lakes in amplifying ice-sheet melt and suggest that their influence should be more explicitly represented in comprehensive climate and ice-sheet models.
How to cite. Cotronei, A., Feudel, U., and Humbert, A.: Contributions of supraglacial lakes to the Greenland Ice Sheet melting, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2025-6334, 2026.
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RC1: 'Comment on egusphere-2025-6334', Anonymous Referee #1, 03 Mar 2026
The authors have developed a model that describes the effect of supraglacial lakes on the surface mass balance of ice sheets. They describe the model, sensitivities of simulations to certain model parameters, and the effect of global warming scenarios on ice sheet elevation as simulated by their model.I think that the effect of supraglacial lakes on the surface mass balance of ice sheet is relevant and deserves to be studied. Modeling it may be a way to better understand effects of these lakes, hence I welcome the model development effort. However, the model that has been developed for this study is neither evaluated, nor is its setup justified, nor are any hypotheses developed that would allow a later test. Hence I cannot recommend publication of this manuscript without major modifications. I will discuss these main concerns further in the following paragraphs.In the introduction, the authors state that "the motivation behind [their] work” is to "better understand and model their [supraglacial lakes] formation and evolution in a fashion that could be adapted from a climate model”. In the conclusions the authors seem to have forgotten this motivation. Potentials and limitations for including the author’s model in climate models are not discussed. Instead, in the conclusion the authors seem to concentrate on their “additional motivation”, "the necessity to characterize better the melt elevation feedback […] in Western Greenland”. They do this in particular by summarizing the results of projections using their model: "under reasonable conditions, the models suggest that the melt-induced feedback loop enhanced by lake formation may become a dominant contributor to Greenland mass loss as early as the end of the century.” A central issue I have with this manuscript is that for both purposes, inclusion in a climate model and use for offline projections, the model should be evaluated. An effort to do this is lacking in the study. I’m happy to admit that a direct evaluation is probably very difficult due to the lack of adequate data. An interesting result of the study may provide an angle for evaluation: In the simulations, supraglacial lakes increase in size (both depth and horizontal extension) over time. Can this effect of lakes on the ice-sheet landscape be observed?Instead of evaluating the model, the authors argue that their model "reproduces the relevant interactions between ice, snow, and water”. This, however, largely remains a claim. For example, the authors ignore a growing body of literature on effects of convection in melt ponds on the melting rates. Yang et al., e.g., argue for a bistability in radiatively heated melt ponds. In their direct numerical simulations depth of a pond and the insolation are key factors. However, the model presented here parameterizes the melting rate as a function of surface temperature that additionally accounts for lake depth. The authors would need to argue why despite ignoring insolation and in-lake circulation, the model does reproduce the relevant interactions. The authors write in L115 that "albedo plays the key role in the feedback loop”. It would need to be well justified why on can ignore solar insolation in the model and parameterize the melt rate depending on temperature. I assume that ponds exposed to more or less sunlight might behave very differently for the same temperature.Not to be misunderstood, it may be very valuable to develop a simple model. I could imagine even simpler models and the insensitivity to some parameter changes indicates that the proposed model is in some respect more complicated than necessary. However, without any evaluation and/or discussion of potentially missing processes that are discussed in the literature, the usefulness of the presented approach cannot be assessed by a reader.A formal, but nevertheless not small issue I have with the manuscript is the lack of rigour in the use of math.
- In particular the use of symbols is incoherent. Of course, there is no full consensus in the scientific community, but as a guideline I like to recommend the NIST guide: https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-10-more-printing-and-using-symbols-and-numbers. In this manuscript the use of roman and italic font seems mostly random. For some variables both font types are used. I also suggest to avoid the use of letter combinations as variables, here, e.g., MRI (used roman, italic, and with varying spacings between letters, spacings make it easy to misunderstand it as a multiplication of variables), TMA, SE, etc.
- Some variables are not defined (e.g. x as a horizontal coordinate, which is additionally used in another function). In the algorithm, M is not defined, and T is used for tolerance thresholds while it was earlier used for temperature.
- W in Eq. 3 probably needs a unit.
- For the state variables W, S, and I it is never said that they are functions of x, which creates an issue, e.g., in Eq. 4.
- Units are used inconsistently. In line 19 “y" is used for years, in the caption of Fig. 3 “yrs". “a" would be most common.
- “mean” (eq. 8) needs to be specified and not indicated by text.
- L208: “long-term mean July air temperature TMJ”. Why is TMJ suddenly a long-term mean air temperature and what exactly are long-term means? In the equation above TMJ was defined as future temperatures (without any definition for future).
- In Eq. 14 the subscript y is used to indicate a yearly mean why earlier subscript a was used.
- Eq. 15 uses TMA for two different things, both different to the earlier use of TMA.
- The above list of issues is likely incomplete.
I list further issues according to their occurrence in the text:L17 “Assuming …”: Please provide a reference for this rate. And which temperature is meant? At the surface, at 2m, something else?L47 “effect is comparable”: Effect on what?L58: This sounds as if ice sheets are generally modelled in stat-of-the-art climate models, which is still the exception.L65: I don’t understand this comparison of complexity. Please be more precise.Fig. 2: This is difficult to understand. Can snow accumulate on liquid water? Try to describe this precisely.L107 (and section 4): “we consider m_l = 2m_i” Why isn’t the melt rate considered an uncertainty factor to be studied in Section 4, given that the factor of 2 is apparently based on a single study with two observed ponds. More generally in Section 4 the comparison of the different factors needs to be discussed. Directly comparing effects for the same relative uncertainty range of [1/2,2] makes only sense if the relative uncertainties ar similar. Wouldn’t one expect very different uncertainties e.g. for seepage rate and atmospheric lapse rate?Eq. 4: Is this indeed a local equation? Can’t non-local melt fill a lake through run-off?L149 “called frequently after integration steps, in particular …”: Sounds odd. So when else is the water flow calculated? What is the time step?L153 “Most of the computations …”: Please be precise.Algorithm “Move 50% …”: Why only 50%?L189: Define acronyms.L190: A concentration on Greenland's western coastal zones is fine, but doesn’t it clash with the stated intention to develop a model that can be adopted from a climate model? Also the conclusions would need to be restricted to Greenland's western coastal zones. Another question: Does rain play a role in filling ponds?L243: How is runoff calculated?Table 1: Where does the value of 5m for instant drainage come from?Fig. 4: The color scale used in panel c is very hard to identify, probably because the cross markers are very fine.Seepage rate and Laplacian coefficient: I think that If indeed these two parameters have basically no effect on the simulation result, the inclusion of these processes in a model for which the goal of simplicity is stated should be revisited.L289 "Although it does not affect the scenario if supraglacial lakes are not present …”: Isn’t this a banality? No lakes, no drainage.L294 "complete melting of the ice profile in less than 200 years”: This value seems arbitrary because likely it strongly depends on modeling choices like thickness of the initial ice sheet and temperature.L329 “sea ice”?L339 I’m still confused by the treatment of snow on lakes: Is the assumption that lakes can lose liquid water all year long, even when they are snow covered?L346 “However ....”: Simplicity is fine, but I find it hard to understand this sentence.L350: What is meant with the term “structural differences”?L351: What are "reasonable conditions”?L352: If I read Fig. 8 correctly, the inclusion of lakes enhances melt in all cases, but is not the “dominant contributor”, but rather increases the ice loss by often only 10% or so. It would be good to provide such a number, or a range of this number for different scenarios and conditions.Citation: https://doi.org/10.5194/egusphere-2025-6334-RC1 - RC2: 'Comment on egusphere-2025-6334', Anonymous Referee #2, 20 Mar 2026
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Code for the manuscript "Contributions of supraglacial lakes to the Greenland Ice Sheet melting", A. Cotronei, A. Humbert, U. Feudel A. Cotronei https://zenodo.org/records/17413871
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Department of Mathematics and Statistics, UiT - The Arctic University of Norway, Forskningsparken 1, Tromsø, Norway
Ulrike Feudel
Institute for Chemistry and Biology for the Marine Environment, Carl von Ossietzky University Oldenburg, Carl-von-Ossietzky-Straße 9 - 11, Oldenburg, Germany
Angelika Humbert
Alfred-Wegener-Institut Helmholtz Zentrum für Polar- und Meeresforschung, Am Alten Hafen 26, Bremerhaven, Germany
Short summary
We construct a mathematical model to describe the formation of lakes on the Greenland Ice Sheet across multiple years. The model represents the dynamics of ice, snow, and surface water, accounting for the influence of air temperature. Our results indicate that lakes can enhance ice melt by absorbing sunlight, thereby accelerating the loss of Greenland ice under realistic scenarios of temperature increase.
We construct a mathematical model to describe the formation of lakes on the Greenland Ice Sheet...