Physics-constrained generative machine learning-based high-resolution downscaling of Greenland's surface mass balance and surface temperature

Bochow, Nils; Hess, Philipp; Robinson, Alexander

doi:10.48550/arXiv.2507.22485

Preprints

https://doi.org/10.48550/arXiv.2507.22485

Preprints

28 Aug 2025

| 28 Aug 2025

Physics-constrained generative machine learning-based high-resolution downscaling of Greenland's surface mass balance and surface temperature

Nils Bochow, Philipp Hess, and Alexander Robinson

Abstract. Accurate, high-resolution projections of the Greenland ice sheet’s surface mass balance (SMB) and surface temperature are essential for understanding future sea-level rise, yet current approaches are either computationally demanding or limited to coarse spatial scales. Here, we introduce a novel physics-constrained generative modeling framework based on a consistency model (CM) to downscale low-resolution SMB and surface temperature fields by a factor of up to 32 (from 160 km to 5 km grid spacing) in a few sampling steps. The CM is trained on monthly outputs of the regional climate model MARv3.12 and conditioned on ice-sheet topography and insolation. By enforcing a hard conservation constraint during inference, we ensure approximate preservation of SMB and temperature sums on the coarse spatial scale as well as robust generalization to extreme climate states without retraining. On the test set, our constrained CM achieves a continued ranked probability score of 6.31 mmWE for the SMB and 0.1 K for the surface temperature, outperforming interpolation-based downscaling. Together with spatial power-spectral analysis, we demonstrate that the CM faithfully reproduces variability across spatial scales. We further apply bias-corrected outputs of the NorESM2 Earth System Model as inputs to our CM, to demonstrate the potential of our model to directly downscale ESM fields. Our approach delivers realistic, high-resolution climate forcing for ice-sheet simulations with fast inference and can be readily integrated into Earth-system and ice-sheet model workflows to improve projections of the future contribution to sea-level rise from Greenland and potentially other ice sheets and glaciers too.

Received: 12 Aug 2025 – Discussion started: 28 Aug 2025

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Journal article(s) based on this preprint

30 Mar 2026

Physics-constrained generative machine learning-based high-resolution downscaling of Greenland's surface mass balance and surface temperature

Nils Bochow, Philipp Hess, and Alexander Robinson

The Cryosphere, 20, 1841–1866, https://doi.org/10.5194/tc-20-1841-2026,https://doi.org/10.5194/tc-20-1841-2026, 2026

Short summary

Nils Bochow, Philipp Hess, and Alexander Robinson

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-3927', Anonymous Referee #1, 08 Oct 2025
The following is a review of “Physics-constrained generative machine learning-based high-resolution downscaling of Greenland’s surface mass balance and surface temperature,” by N. Bochow, et al.
This manuscript describes a new machine-learning based method using a consistency model (CM) for downscaling ice sheet surface mass balance. The authors focus on the Greenland Ice Sheet, evaluating their product against output from the regional climate model MAR. They demonstrate the ability of their method to reconstruct high-resolution surface mass balance over the historic period from downgraded input. They also illustrate how their method could be used to downscale low resolution bias-corrected output from an earth system model through the year 2100. They provide examples of different ways, with varying complexities, to inform the CM, and evaluate advancement in the method’s skill. The authors suggest that their approach could be integrated as interface between general circulation models and ice sheet models for improved certainty in sea-level projections.
This work is highly relevant to the ice sheet model community, because high spatial resolution is needed to force accurate ice sheet model estimates of future contribution to sea-level change. However, earth system models, such as those that participate in the CMIP experiments, run at much lower resolutions than needed. This is because they are typically global-scale models faced with significant computational constraints. Current state-of-the-art methods for downscaling to finer spatial scales also have strong computational constraints, because of the high spatial resolutions required to run. The method outlined in this manuscript tackles this issue. It is a novel approach that is capable of successfully downscaling to finer resolutions using a machine-learning based method. It is computationally efficient and has significant skill, on the condition that there are high-quality training sets (e.g., simulations from other methods) available. The emergence of this method is timely in that it could offer support for IPCC efforts, and the outlined approaches are clearly very promising for use by the ice sheet modeling community.
I find that the text is well-written, and the figures are high-quality. However, I do think the manuscript would benefit from restructuring, which I discuss below in general comments. Overall, my impression is that the authors were diligent and attentive to the needs of ice sheet modelers when designing and evaluating these new products. For this reason, I believe it is important that this work be published so that the authors can build upon their collaborations with ice sheet models, perhaps with implications for the next IPCC report.
Having said that, I am not convinced that this work is appropriate for publication in The Cryosphere. I find the manuscript to be highly focused on presenting and evaluating the approach, as it does not provide many results related to a science question. As presented, the main goals of the study are to introduce a method and evaluate its feasibility and robustness. Though the manuscript shows the method has strong potential to impact cryosphere science, there is no specific scientific hypothesis tested. In this way, the manuscript may perhaps be a better fit for GMD? For its publication in TC, on the other hand, I suggest that the authors think about building a more cryosphere-science driven story with their various downscaled products, particularly with development of the discussion section to expand upon for the reader, how the method advances ice sheet science. Focusing more on results pertaining to the projection runs could be a starting point.
General comments:
I suggest that the authors reorganize the sections of the manuscript for readability. The current organization seems to be set up in a letter format, with the Methods at the end. For The Cryosphere, I think it would be helpful to present the methods to the reader before the results, so that it is clear what is being presented in the results, discussion, and conclusion sections.

The downscaling of future projections is buried in the Appendix, but these results are arguably the most interesting and relevant to the study’s motivation with respect to cryosphere science (i.e. possible future use for downscaling projections for CMIP/ISMIP). Including a timeseries plot with comparison against GT, for instance, would be helpful to evaluate the model results throughout the projection. Perhaps these projection results could be highlighted more and used to build/expand on a science-related story.

I find that all figure captions are written in a terse style, with many of the articles removed. Because this makes it difficult for a reader, I would suggest reviewing all the captions and revising as needed so that they flow better and can be more easily understood.

For clarity, please make sure all units are consistent. For instance, even if it is stated that the SMB or MAE are over a month period, the units should still reflect this (i.e. mmWE/month) in all references within the text and in the figures.

Specific comments and suggestions:
Page 3, line 2 – “using” openly available ?
Results, line 2-3 – Please describe how insolation is defined in your context. For instance, is it downward solar radiation at the ice sheet surface? Is it a climatological monthly average, calculated over a particular period, or is it a timeseries of monthly averages that is used?
Results, line 7-8 – Should these be “Fig, 2” and “Table 1”?
Section 2.1, line 13 – The phrase “compared to the ground truth” makes it sound like GT is not as accurate, which I don’t think is what the authors mean. Maybe “when compared with ground truth” or something similar that makes this statement clearer.
Section 2.1.1, line 5 – This is an example of where the units are not conveyed per unit time, but if appropriate, should be for clarity.
Section 2.2, line 10 – I may have missed this, but if not included, please add a reference for NorESM and version/output used in this study.
Discussion, line 9 and Section 5.1, line 19 – Please add a reference for U-Net and perhaps a short definition somewhere in the text, to help a more general audience follow your methods and discussion.
Section 5.4, line 2 – Please include a description of which variables are used for precipitation (total precipitation?) and near-surface temperature (2m air temperature?).
Figure 1, Caption – Here is an example where the caption is written informally with missing articles, i.e. “at the surface for a random month from the test set” is more appropriate. Also, for example, Figure 2, Caption – “for a warm month”.
Figure 1, Caption – “is visually indistinguishable” is used numerous times throughout the text, but it is not a scientifically precise or quantitative statement. Especially since, when looking at these plots, they have differences that can be detected visually. Figure B.1 for example is clearly visually different. Please rephrase your uses of “is visually indistinguishable” throughout the manuscript. I suggest including difference maps, maybe in the Appendix, to illustrate the method’s skill with respect to the spatial pattern.
Figure 3 (a,f,l), With reference to CM Constrained, it would be easier for a reader to make comparisons between the spatial plots and the line plot if the labeling for the same runs was consistent. Also, PSD is defined in Figure 4 (and in the text), but it should probably also be defined in Figure 3 since it would come before Figure 4.
Figure 5 and Figure B.2 – Instead of time index, could the simulation “date” be given on the x-axis?
Figures C.1, C.2, and C.3 – The letter labels are missing from all panels. In addition, it would be helpful per plot to be more specific about exactly which runs are “CM”, since CM is used in many earlier plots and it gets confusing for the reader to follow.
Figure C.1, Caption – “of precipitation, melt and runoff” -> “of precipitation, evaporation and runoff”?
Figure C.2 and C.3, Caption – Please specify that this is for NorESM in the caption. Also, there is only description included for 6 panels, not 8.
Figure C.4 – Should the units for (a) technically be mmWe/month?
Citation: https://doi.org/10.5194/egusphere-2025-3927-RC1
- AC1: 'Reply on RC1', Nils Bochow, 10 Nov 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3927/egusphere-2025-3927-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-3927-AC1
RC2:
'Comment on egusphere-2025-3927', Anonymous Referee #2, 17 Oct 2025

The manuscript presents research that is highly relevant to the cryospheric community and is of strong scientific quality. The authors propose a new machine-learning-based downscaling method for Earth System Models (ESMs). They have conducted a thorough analysis and present a substantial number of interesting and relevant results. According to the abstract, the study introduces a physics-constrained generative modeling framework based on a consistency model (CM) to downscale surface mass balance (SMB) and surface temperature fields over the Greenland Ice Sheet by up to a factor of 32 (from 160 km to 5 km resolution). The model is trained on MARv3.12 outputs and conditioned on topography and insolation, while enforcing conservation constraints to preserve large-scale totals and ensure robust generalization. The approach outperforms interpolation-based methods, accurately reproduces variability across spatial scales, and demonstrates strong potential for directly downscaling ESM outputs such as NorESM2. Overall, the method provides a computationally efficient and physically consistent way to generate high-resolution climate forcing for ice-sheet modeling and projections of sea-level rise.
However, I agree with the other reviewer that the current format is not well-suited for The Cryosphere. The manuscript is highly technical and method-focused, with limited analysis of the results and their implications for the cryospheric community.
I suggest that the authors consider submitting the work to a more technically oriented journal, such as Geoscientific Model Development (GMD) or JGR: Machine Learning and Computation. Alternatively, if the authors wish to keep it within The Cryosphere, substantial restructuring will be necessary. Specifically, the manuscript should follow the conventional structure: introduction, methods, results, discussion, and conclusion.
I also find that the results section would benefit from some re-writing to improve readability. As it stands, the text is quite dense, and readers may need to reread several passages to fully grasp the main points. I recommend that the authors break up long sections into shorter paragraphs and present metrics in parentheses to support the narrative, rather than in standalone paragraphs. Including a brief summary at the end of each results subsection would also help guide the reader. Finally, the authors should ensure that no new results are introduced in the figure captions, as this can make the presentation confusing.
The discussion section would also benefit from a clearer structure. I suggest that the authors divide it into subsections, each with an informative subtitle, to guide the reader through the different aspects of the discussion. For The Cryosphere, the discussion could be expanded somewhat, with particular emphasis on the broader impacts of the methodology and findings on cryospheric science.
In summary, the study presents very interesting and valuable results, and the authors have done excellent work overall. However, the manuscript would benefit from substantial rewriting and restructuring to make it suitable for publication in The Cryosphere.
PS: I've added a supplementary file with line-by-line comments.

Citation: https://doi.org/10.5194/egusphere-2025-3927-RC2
- AC2: 'Reply on RC2', Nils Bochow, 10 Nov 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3927/egusphere-2025-3927-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-3927-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-3927', Anonymous Referee #1, 08 Oct 2025
The following is a review of “Physics-constrained generative machine learning-based high-resolution downscaling of Greenland’s surface mass balance and surface temperature,” by N. Bochow, et al.
This manuscript describes a new machine-learning based method using a consistency model (CM) for downscaling ice sheet surface mass balance. The authors focus on the Greenland Ice Sheet, evaluating their product against output from the regional climate model MAR. They demonstrate the ability of their method to reconstruct high-resolution surface mass balance over the historic period from downgraded input. They also illustrate how their method could be used to downscale low resolution bias-corrected output from an earth system model through the year 2100. They provide examples of different ways, with varying complexities, to inform the CM, and evaluate advancement in the method’s skill. The authors suggest that their approach could be integrated as interface between general circulation models and ice sheet models for improved certainty in sea-level projections.
This work is highly relevant to the ice sheet model community, because high spatial resolution is needed to force accurate ice sheet model estimates of future contribution to sea-level change. However, earth system models, such as those that participate in the CMIP experiments, run at much lower resolutions than needed. This is because they are typically global-scale models faced with significant computational constraints. Current state-of-the-art methods for downscaling to finer spatial scales also have strong computational constraints, because of the high spatial resolutions required to run. The method outlined in this manuscript tackles this issue. It is a novel approach that is capable of successfully downscaling to finer resolutions using a machine-learning based method. It is computationally efficient and has significant skill, on the condition that there are high-quality training sets (e.g., simulations from other methods) available. The emergence of this method is timely in that it could offer support for IPCC efforts, and the outlined approaches are clearly very promising for use by the ice sheet modeling community.
I find that the text is well-written, and the figures are high-quality. However, I do think the manuscript would benefit from restructuring, which I discuss below in general comments. Overall, my impression is that the authors were diligent and attentive to the needs of ice sheet modelers when designing and evaluating these new products. For this reason, I believe it is important that this work be published so that the authors can build upon their collaborations with ice sheet models, perhaps with implications for the next IPCC report.
Having said that, I am not convinced that this work is appropriate for publication in The Cryosphere. I find the manuscript to be highly focused on presenting and evaluating the approach, as it does not provide many results related to a science question. As presented, the main goals of the study are to introduce a method and evaluate its feasibility and robustness. Though the manuscript shows the method has strong potential to impact cryosphere science, there is no specific scientific hypothesis tested. In this way, the manuscript may perhaps be a better fit for GMD? For its publication in TC, on the other hand, I suggest that the authors think about building a more cryosphere-science driven story with their various downscaled products, particularly with development of the discussion section to expand upon for the reader, how the method advances ice sheet science. Focusing more on results pertaining to the projection runs could be a starting point.
General comments:
I suggest that the authors reorganize the sections of the manuscript for readability. The current organization seems to be set up in a letter format, with the Methods at the end. For The Cryosphere, I think it would be helpful to present the methods to the reader before the results, so that it is clear what is being presented in the results, discussion, and conclusion sections.

The downscaling of future projections is buried in the Appendix, but these results are arguably the most interesting and relevant to the study’s motivation with respect to cryosphere science (i.e. possible future use for downscaling projections for CMIP/ISMIP). Including a timeseries plot with comparison against GT, for instance, would be helpful to evaluate the model results throughout the projection. Perhaps these projection results could be highlighted more and used to build/expand on a science-related story.

I find that all figure captions are written in a terse style, with many of the articles removed. Because this makes it difficult for a reader, I would suggest reviewing all the captions and revising as needed so that they flow better and can be more easily understood.

For clarity, please make sure all units are consistent. For instance, even if it is stated that the SMB or MAE are over a month period, the units should still reflect this (i.e. mmWE/month) in all references within the text and in the figures.

Specific comments and suggestions:
Page 3, line 2 – “using” openly available ?
Results, line 2-3 – Please describe how insolation is defined in your context. For instance, is it downward solar radiation at the ice sheet surface? Is it a climatological monthly average, calculated over a particular period, or is it a timeseries of monthly averages that is used?
Results, line 7-8 – Should these be “Fig, 2” and “Table 1”?
Section 2.1, line 13 – The phrase “compared to the ground truth” makes it sound like GT is not as accurate, which I don’t think is what the authors mean. Maybe “when compared with ground truth” or something similar that makes this statement clearer.
Section 2.1.1, line 5 – This is an example of where the units are not conveyed per unit time, but if appropriate, should be for clarity.
Section 2.2, line 10 – I may have missed this, but if not included, please add a reference for NorESM and version/output used in this study.
Discussion, line 9 and Section 5.1, line 19 – Please add a reference for U-Net and perhaps a short definition somewhere in the text, to help a more general audience follow your methods and discussion.
Section 5.4, line 2 – Please include a description of which variables are used for precipitation (total precipitation?) and near-surface temperature (2m air temperature?).
Figure 1, Caption – Here is an example where the caption is written informally with missing articles, i.e. “at the surface for a random month from the test set” is more appropriate. Also, for example, Figure 2, Caption – “for a warm month”.
Figure 1, Caption – “is visually indistinguishable” is used numerous times throughout the text, but it is not a scientifically precise or quantitative statement. Especially since, when looking at these plots, they have differences that can be detected visually. Figure B.1 for example is clearly visually different. Please rephrase your uses of “is visually indistinguishable” throughout the manuscript. I suggest including difference maps, maybe in the Appendix, to illustrate the method’s skill with respect to the spatial pattern.
Figure 3 (a,f,l), With reference to CM Constrained, it would be easier for a reader to make comparisons between the spatial plots and the line plot if the labeling for the same runs was consistent. Also, PSD is defined in Figure 4 (and in the text), but it should probably also be defined in Figure 3 since it would come before Figure 4.
Figure 5 and Figure B.2 – Instead of time index, could the simulation “date” be given on the x-axis?
Figures C.1, C.2, and C.3 – The letter labels are missing from all panels. In addition, it would be helpful per plot to be more specific about exactly which runs are “CM”, since CM is used in many earlier plots and it gets confusing for the reader to follow.
Figure C.1, Caption – “of precipitation, melt and runoff” -> “of precipitation, evaporation and runoff”?
Figure C.2 and C.3, Caption – Please specify that this is for NorESM in the caption. Also, there is only description included for 6 panels, not 8.
Figure C.4 – Should the units for (a) technically be mmWe/month?
Citation: https://doi.org/10.5194/egusphere-2025-3927-RC1
- AC1: 'Reply on RC1', Nils Bochow, 10 Nov 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3927/egusphere-2025-3927-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-3927-AC1
RC2:
'Comment on egusphere-2025-3927', Anonymous Referee #2, 17 Oct 2025

The manuscript presents research that is highly relevant to the cryospheric community and is of strong scientific quality. The authors propose a new machine-learning-based downscaling method for Earth System Models (ESMs). They have conducted a thorough analysis and present a substantial number of interesting and relevant results. According to the abstract, the study introduces a physics-constrained generative modeling framework based on a consistency model (CM) to downscale surface mass balance (SMB) and surface temperature fields over the Greenland Ice Sheet by up to a factor of 32 (from 160 km to 5 km resolution). The model is trained on MARv3.12 outputs and conditioned on topography and insolation, while enforcing conservation constraints to preserve large-scale totals and ensure robust generalization. The approach outperforms interpolation-based methods, accurately reproduces variability across spatial scales, and demonstrates strong potential for directly downscaling ESM outputs such as NorESM2. Overall, the method provides a computationally efficient and physically consistent way to generate high-resolution climate forcing for ice-sheet modeling and projections of sea-level rise.
However, I agree with the other reviewer that the current format is not well-suited for The Cryosphere. The manuscript is highly technical and method-focused, with limited analysis of the results and their implications for the cryospheric community.
I suggest that the authors consider submitting the work to a more technically oriented journal, such as Geoscientific Model Development (GMD) or JGR: Machine Learning and Computation. Alternatively, if the authors wish to keep it within The Cryosphere, substantial restructuring will be necessary. Specifically, the manuscript should follow the conventional structure: introduction, methods, results, discussion, and conclusion.
I also find that the results section would benefit from some re-writing to improve readability. As it stands, the text is quite dense, and readers may need to reread several passages to fully grasp the main points. I recommend that the authors break up long sections into shorter paragraphs and present metrics in parentheses to support the narrative, rather than in standalone paragraphs. Including a brief summary at the end of each results subsection would also help guide the reader. Finally, the authors should ensure that no new results are introduced in the figure captions, as this can make the presentation confusing.
The discussion section would also benefit from a clearer structure. I suggest that the authors divide it into subsections, each with an informative subtitle, to guide the reader through the different aspects of the discussion. For The Cryosphere, the discussion could be expanded somewhat, with particular emphasis on the broader impacts of the methodology and findings on cryospheric science.
In summary, the study presents very interesting and valuable results, and the authors have done excellent work overall. However, the manuscript would benefit from substantial rewriting and restructuring to make it suitable for publication in The Cryosphere.
PS: I've added a supplementary file with line-by-line comments.

Citation: https://doi.org/10.5194/egusphere-2025-3927-RC2
- AC2: 'Reply on RC2', Nils Bochow, 10 Nov 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3927/egusphere-2025-3927-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-3927-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Publish subject to revisions (further review by editor and referees) (01 Dec 2025) by Ruth Mottram

AR by Nils Bochow on behalf of the Authors (14 Jan 2026) Author's response Author's tracked changes Manuscript

ED: Publish subject to revisions (further review by editor and referees) (10 Feb 2026) by Ruth Mottram

AR by Nils Bochow on behalf of the Authors (11 Feb 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (03 Mar 2026) by Ruth Mottram

AR by Nils Bochow on behalf of the Authors (12 Mar 2026) Manuscript

Journal article(s) based on this preprint

30 Mar 2026

Physics-constrained generative machine learning-based high-resolution downscaling of Greenland's surface mass balance and surface temperature

Nils Bochow, Philipp Hess, and Alexander Robinson

The Cryosphere, 20, 1841–1866, https://doi.org/10.5194/tc-20-1841-2026,https://doi.org/10.5194/tc-20-1841-2026, 2026

Short summary

Nils Bochow, Philipp Hess, and Alexander Robinson

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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.

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Final revised paper

Short summary

This study presents a fast, physics-guided machine-learning method that downscales coarse climate fields to fine resolution while enforcing conservation of large-scale totals. Trained on regional climate simulations and driven by Earth system model output, it handles extremes and outperforms linear interpolation, providing realistic, high-resolution forcing for ice-sheet models and improving projections of Greenland’s sea-level contribution.


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