the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Apr 2026
Transition to a much warmer climate for the global ocean and Antarctic Ice Sheet coupled system, and its reversibility
Abstract. In Antarctica, two plausible tipping points have been suggested: an ocean tipping point involving a cold-to-warm transition of ice shelf cavities, and an ice sheet tipping point associated with the marine ice sheet instability. This study explores the existence of such tipping points at the scale of Antarctica, using a coupled ocean–ice-sheet model. We first apply and then remove an abrupt perturbation to the ocean, instantaneously switching the atmospheric forcing to high-end 23rd century conditions, which shifts all ice shelf cavities of Antarctica to warm conditions. Our findings reveal that Antarctic continental shelf waters rapidly warm, leading to a regime shift with increased ice shelf melt rates, significant ice shelf thinning, and retreat of ice sheet grounding lines. The ocean conditions reverse over a few years when the atmospheric perturbation ceases, while the ice sheet’s response is much slower. Some regions of East Antarctica show signs of ice sheet reversibility over several centuries. In contrast, we identify 14 ice streams, primarily in the Ross, Amundsen, Filchner, Ronne, and Dronning Maud Land basins, that still undergo irreversible retreat several centuries after the removal of the perturbation.
Competing interests: At least one of the (co-)authors is a member of the editorial board of The Cryosphere.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.-
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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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Preprint
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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
-
RC1: 'Comment on egusphere-2026-927', Anonymous Referee #1, 15 May 2026
- AC1: 'Reply on RC1', Pierre Mathiot, 19 Jun 2026
-
RC2: 'Comment on egusphere-2026-927', Anonymous Referee #2, 15 May 2026
Review comments for “Transition to a much warmer climate for the global ocean and Antarctic Ice Sheet coupled system, and its reversibility” by Mathiot et al. (#egusphere-2026-927)
General Comment:
This study investigates the reversibility of oceanic and ice-sheet changes in Antarctica using a coupled ocean–ice-sheet model. The topic is important because the mass balance of the Antarctic Ice Sheet directly affects future sea-level rise, and ocean-driven melting beneath ice shelves can influence the dynamics of the grounded ice sheet through changes in buttressing and grounding-line retreat. Understanding how the Antarctic Ice Sheet responds to strong oceanic and atmospheric perturbations is therefore of broad relevance beyond the scientific community.The coupled modeling approach adopted in this study is valuable, and the contrast between a relatively rapid recovery of the ocean state and a much slower, partly irreversible ice-sheet response is potentially interesting. However, I have several concerns about the interpretation of the results, particularly regarding the robustness of the ocean reversibility claim and the influence of model assumptions such as the fixed ice-front position and the treatment of pseudo-collapsed ice shelves. I also think that additional diagnostics of the atmospheric forcing, sea-ice processes, regional ocean response, and ice-shelf geometry are needed to support the main conclusions.
I hope the authors will address these points in a revised manuscript.
Major Comments:
1. Interpretation of ocean reversibility under the fixed ice-front assumption
One of my main concerns is that the conclusion regarding the rapid reversibility of the ocean state may depend strongly on the model assumptions, especially the fixed position of the ice front / calving front. In the present model framework, the ice-shelf fronts do not retreat, even under very large increases in basal melting. As a result, the experiments do not represent potentially important changes in ocean geometry associated with ice-shelf front retreat, ice-shelf collapse, or the transition from an ice-shelf cavity to open ocean.This limitation is important for the interpretation of the reversibility experiment. The manuscript shows that ocean properties and basal melt rates largely recover after the atmospheric perturbation is removed. However, this recovery occurs within a framework in which the ice-front geometry is artificially maintained. Therefore, the result should be interpreted more cautiously as ocean reversibility within a fixed ice-front configuration, rather than as evidence that the Southern Ocean–ice-shelf system would generally recover rapidly after major ice-shelf retreat or collapse.
I therefore think that statements such as the Southern Ocean itself would not contribute to making large climate transitions irreversible are too strong in the current form. The authors should qualify this conclusion more explicitly and discuss how the fixed ice-front assumption may affect the simulated ocean recovery, especially through its influence on cavity geometry, sea-ice formation, dense-water production, and CDW access to the continental shelf.
Related to this point, the treatment of pseudo-collapsed areas should also be examined more carefully. In the model, strongly thinned ice-shelf areas are retained as 1-m-thick ice shelves, whereas in reality such areas might become open ocean after ice-shelf breakup or calving-front retreat. A useful sensitivity experiment would be to remove the pseudo-collapsed areas and treat them as open ocean at the start of the REV experiment. This would help assess whether the rapid ocean recovery is robust to a more realistic representation of ice-shelf collapse and changes in cavity geometry.
2. Interpretation of basal melt in pseudo-collapsed areas
A substantial fraction of basal melt occurs in pseudo-collapsed areas, where the ice shelf is artificially maintained at a minimum thickness of 1 m. Melt in these regions may not represent typical CDW-driven melting in deep ice-shelf cavities. Because the ice base is located close to the ocean surface, melting there may be more strongly affected by near-surface warming and sea-ice loss, corresponding more closely to the “mode 3” melting described by Jacobs et al. (1992).More generally, the manuscript mainly discusses CDW-driven basal melting and MISI-driven grounding-line retreat. I think the introduction should provide a broader description of ice-shelf melt regimes, for example following Jacobs et al. (1992), and clarify which melt mechanisms are relevant in the present experiments. Similarly, the discussion of ice-sheet retreat could briefly acknowledge other possible instability mechanisms, such as marine ice-cliff instability, even if they are not represented in the model. This would help place the simulated CDW–MISI pathway in a broader physical context.
Jacobs, S.S., H.H. Hellmer, C.S.M. Doake, A. Jenkins, and R.M. Frolich. 1992. Melting of ice shelves and the mass balance of Antarctica. Journal of Glaciology 38(130):375–387.
3. Need for a more self-contained description of the ocean forcing and transition
The ocean transition mechanism appears to be largely the same as in MJ2023. This is not necessarily a problem, but the present manuscript relies too heavily on MJ2023 to explain the ocean response. As a result, it is difficult to understand the physical meaning of the perturbation and the resulting cold-to-warm transition from this manuscript alone.Because the imposed atmospheric perturbation controls the entire PERT experiment, the manuscript should show the key atmospheric anomalies, at least in the main text or supplementary material. Useful diagnostics would include near-surface air temperature, wind stress, freshwater flux, and radiative flux anomalies.
Overall, I think the manuscript should be more self-contained in its description of the ocean forcing and ocean transition, so that readers do not need to rely on MJ2023 to understand the main physical mechanism.
4. Need for sea-ice and dense-water diagnostics
The manuscript explains the ocean transition as a consequence of reduced sea-ice formation, weakened brine rejection, and the collapse of dense shelf-water formation. However, these key processes are not sufficiently documented in the results.I suggest that the authors show diagnostics such as sea-ice concentration or extent, sea-ice production, brine rejection, and dense shelf-water formation. These diagnostics should be shown for REF, PERT, and REV, because they are central to the proposed mechanism of both the cold-to-warm transition and the subsequent ocean recovery.
5. Need for a more regional analysis of the ocean response
The ice-sheet response is analyzed in detail at the basin and ice-stream scale, but the ocean response is mostly discussed using Antarctic-wide averages and a few representative sections. This makes the ocean analysis less balanced than the ice-sheet analysis. I suggest that the authors provide more regional ocean diagnostics, especially for sectors where irreversible ice-sheet retreat is identified.Other comments:
6. Fig. 4 and Section 3.1
The discussion of basal melt rates in Section 3.1 refers to differences from MJ2023 and to the observational estimates of Rignot et al. (2013). However, these values are not shown in Fig. 4, which makes the comparison difficult to follow. I suggest adding the MJ2023 and Rignot et al. (2013) values to Fig. 4, or providing an additional figure/table summarizing these comparisons for the major ice shelves.Citation: https://doi.org/10.5194/egusphere-2026-927-RC2 - AC2: 'Reply on RC2', Pierre Mathiot, 19 Jun 2026
Peer review completion
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2026-927', Anonymous Referee #1, 15 May 2026
GENERAL COMMENTS
The authors are investigating the effect of a sudden increased warming to the Southern ocean and the Antarctic ice sheet in a coupled ice-ocean simulation.
They base their simulation setup on an earlier stand-alone simulation and chose a high warming scenario to investigate the possibility of reversibility after a 50yrs increased warming period. Finding that while the ocean is relatively quickly reverting to its initial conditions that the ice sheet takes longer to revert and that a few ice streams undergo irreversible retreat.The study fits within the scope of TC, presents its findings in a clear way and is well written.
The findings are not especially novel, but contribute to the ongoing discussion of tipping points as part of several studies with the important aspect of ice-ocean coupling which is needed to better understand the complex Antarctic system of atmosphere, ocean and ice.
I include below a few points that require some further explanations, but otherwise I recommend accepting the paper after these points are addressed.
===
Overall comments:- Observations and present-day conditions:
How do your ocean and ice conditions at the start of the simulation relate to observations or other studies during the initial time period? Are your melt rates reasonable and the ice velocities and thickness reasonable? This information would be important for readers to better place the changes during the warming period, and the subsequent reversed state, into context.- Ocean boundary conditions:
While you address a few times the atmospheric forcing being the driver of changes and reversibility, I am missing the mentioning or explanations of the setting for the ocean-ocean boundary conditions. Do they play a role? Are they too far away to impact the continental shelf and ice cavities? (see also comment below in “specific comments”)
It would be helpful to mention somewhere (2.1.1?) how this boundary forcing is implemented and to clarify why they are not important for or discussed in the results and discussion sections.
- 1m ice shelf minimum thickness
L111-115: I understand the choice of minimum 1m ice shelf thickness. However, how does this additional 1m of ice impact the ocean compared to having no ice? And are those locations crucial for the ice shelves itself providing stability versus no ice might lead to quicker retreat?
You discuss this briefly in line 334ff, but I think it is worth explaining whether, and to what extent, this choice affects ocean circulation, particularly if a larger area in front of the ice shelf is directly exposed to atmospheric forcing rather than being covered by a thin ice layer. Related to this, how might this influence ice-shelf or grounding-line retreat, beyond the overestimated meltwater flux into the ocean?
Is the affected area large enough that atmospheric forcing over these ice-free regions would significantly influence the system, potentially making reversibility more difficult or slowing it down?
Furthermore, it would be useful to explicitly acknowledge the limitation of not including feedbacks from the ocean to the atmosphere, and to discuss whether such feedbacks could enable or strengthen tipping-point behavior. While I understand that the focus of the study is on ice–ocean interactions, a brief discussion of the neglected feedbacks, and a qualitative estimate of their potential impact on the main conclusions, would strengthen the manuscript, particularly given the emphasis on tipping points and reversibility.
SPECIFIC COMMENTS
- L183ff: The reversibility is described as being directly affected by the change in atmospheric forcing. How are ocean-ocean boundary conditions prescribed? Are they important or maybe just mention that they aren’t and why.
- L220-227:This paragraph seems important, but I struggle to understand the relationships, relative importance, and impacts of the factors mentioned on the overall outcome, as well as what the authors intend to convey here. Could you please reformulate this paragraph or add clarifying information to make the main points more clear?
- Fig 6: Please add a legend for the grounding line colors.
Rename second (b) to (c).
Maybe consider switching the color scheme: red for less ice and blue for more ice?
(c) and (d): it looks like there is thinning happening around the fast flowing areas on the grounded ice areas. Is this due ice velocity and grounding line change in reaction to the reverted ocean conditions?
- Fig 7: For better readability, I recommend to use REF, PERT and REV also in the Figure label - even though the explanations are nice.
- Fig 8c: The VAF seems to be increasing in REF & REF_ext for most of the basins. Is this an expected trend? wouldn’t we expect a more constant or even shrinking VAF in REF&REF_ext? Or is this due to the choice of SMB or due to underestimated melt rates?
- L291ff: How long does Garbe et al. or other studies you mention here enforce the warmer conditions before reverting back? This would be useful information to put your results into perspective. Especially in regards to the thought that your 50yrs choice might be too short. Furthermore, Garbe et al., state very strongly that there is no reversibility in certain areas under certain conditions, right?. Does the difference between Garbe et al. and this study imply that the reversibility depends on the choice of ocean and ice model (and setup)?
- L306-315: You do not mention the choice of ice model resolution: 1km finest resolution is fair for Antarctica due to computation time, but could impact grounding line dynamics and the choice of resolution would define existing pinning points (or omit them). On top of this are the uncertainties in the bedrock data.
- References: please go through the list. A few are missing doi, a few seem to have a different format or different information supplied
- L399: Remove the three times number-code in the reference: e2022JC018621
- L423ff Garbe double reference? 2020a and 2020b or wrong reference in 2020b?Citation: https://doi.org/10.5194/egusphere-2026-927-RC1 - AC1: 'Reply on RC1', Pierre Mathiot, 19 Jun 2026
-
RC2: 'Comment on egusphere-2026-927', Anonymous Referee #2, 15 May 2026
Review comments for “Transition to a much warmer climate for the global ocean and Antarctic Ice Sheet coupled system, and its reversibility” by Mathiot et al. (#egusphere-2026-927)
General Comment:
This study investigates the reversibility of oceanic and ice-sheet changes in Antarctica using a coupled ocean–ice-sheet model. The topic is important because the mass balance of the Antarctic Ice Sheet directly affects future sea-level rise, and ocean-driven melting beneath ice shelves can influence the dynamics of the grounded ice sheet through changes in buttressing and grounding-line retreat. Understanding how the Antarctic Ice Sheet responds to strong oceanic and atmospheric perturbations is therefore of broad relevance beyond the scientific community.The coupled modeling approach adopted in this study is valuable, and the contrast between a relatively rapid recovery of the ocean state and a much slower, partly irreversible ice-sheet response is potentially interesting. However, I have several concerns about the interpretation of the results, particularly regarding the robustness of the ocean reversibility claim and the influence of model assumptions such as the fixed ice-front position and the treatment of pseudo-collapsed ice shelves. I also think that additional diagnostics of the atmospheric forcing, sea-ice processes, regional ocean response, and ice-shelf geometry are needed to support the main conclusions.
I hope the authors will address these points in a revised manuscript.
Major Comments:
1. Interpretation of ocean reversibility under the fixed ice-front assumption
One of my main concerns is that the conclusion regarding the rapid reversibility of the ocean state may depend strongly on the model assumptions, especially the fixed position of the ice front / calving front. In the present model framework, the ice-shelf fronts do not retreat, even under very large increases in basal melting. As a result, the experiments do not represent potentially important changes in ocean geometry associated with ice-shelf front retreat, ice-shelf collapse, or the transition from an ice-shelf cavity to open ocean.This limitation is important for the interpretation of the reversibility experiment. The manuscript shows that ocean properties and basal melt rates largely recover after the atmospheric perturbation is removed. However, this recovery occurs within a framework in which the ice-front geometry is artificially maintained. Therefore, the result should be interpreted more cautiously as ocean reversibility within a fixed ice-front configuration, rather than as evidence that the Southern Ocean–ice-shelf system would generally recover rapidly after major ice-shelf retreat or collapse.
I therefore think that statements such as the Southern Ocean itself would not contribute to making large climate transitions irreversible are too strong in the current form. The authors should qualify this conclusion more explicitly and discuss how the fixed ice-front assumption may affect the simulated ocean recovery, especially through its influence on cavity geometry, sea-ice formation, dense-water production, and CDW access to the continental shelf.
Related to this point, the treatment of pseudo-collapsed areas should also be examined more carefully. In the model, strongly thinned ice-shelf areas are retained as 1-m-thick ice shelves, whereas in reality such areas might become open ocean after ice-shelf breakup or calving-front retreat. A useful sensitivity experiment would be to remove the pseudo-collapsed areas and treat them as open ocean at the start of the REV experiment. This would help assess whether the rapid ocean recovery is robust to a more realistic representation of ice-shelf collapse and changes in cavity geometry.
2. Interpretation of basal melt in pseudo-collapsed areas
A substantial fraction of basal melt occurs in pseudo-collapsed areas, where the ice shelf is artificially maintained at a minimum thickness of 1 m. Melt in these regions may not represent typical CDW-driven melting in deep ice-shelf cavities. Because the ice base is located close to the ocean surface, melting there may be more strongly affected by near-surface warming and sea-ice loss, corresponding more closely to the “mode 3” melting described by Jacobs et al. (1992).More generally, the manuscript mainly discusses CDW-driven basal melting and MISI-driven grounding-line retreat. I think the introduction should provide a broader description of ice-shelf melt regimes, for example following Jacobs et al. (1992), and clarify which melt mechanisms are relevant in the present experiments. Similarly, the discussion of ice-sheet retreat could briefly acknowledge other possible instability mechanisms, such as marine ice-cliff instability, even if they are not represented in the model. This would help place the simulated CDW–MISI pathway in a broader physical context.
Jacobs, S.S., H.H. Hellmer, C.S.M. Doake, A. Jenkins, and R.M. Frolich. 1992. Melting of ice shelves and the mass balance of Antarctica. Journal of Glaciology 38(130):375–387.
3. Need for a more self-contained description of the ocean forcing and transition
The ocean transition mechanism appears to be largely the same as in MJ2023. This is not necessarily a problem, but the present manuscript relies too heavily on MJ2023 to explain the ocean response. As a result, it is difficult to understand the physical meaning of the perturbation and the resulting cold-to-warm transition from this manuscript alone.Because the imposed atmospheric perturbation controls the entire PERT experiment, the manuscript should show the key atmospheric anomalies, at least in the main text or supplementary material. Useful diagnostics would include near-surface air temperature, wind stress, freshwater flux, and radiative flux anomalies.
Overall, I think the manuscript should be more self-contained in its description of the ocean forcing and ocean transition, so that readers do not need to rely on MJ2023 to understand the main physical mechanism.
4. Need for sea-ice and dense-water diagnostics
The manuscript explains the ocean transition as a consequence of reduced sea-ice formation, weakened brine rejection, and the collapse of dense shelf-water formation. However, these key processes are not sufficiently documented in the results.I suggest that the authors show diagnostics such as sea-ice concentration or extent, sea-ice production, brine rejection, and dense shelf-water formation. These diagnostics should be shown for REF, PERT, and REV, because they are central to the proposed mechanism of both the cold-to-warm transition and the subsequent ocean recovery.
5. Need for a more regional analysis of the ocean response
The ice-sheet response is analyzed in detail at the basin and ice-stream scale, but the ocean response is mostly discussed using Antarctic-wide averages and a few representative sections. This makes the ocean analysis less balanced than the ice-sheet analysis. I suggest that the authors provide more regional ocean diagnostics, especially for sectors where irreversible ice-sheet retreat is identified.Other comments:
6. Fig. 4 and Section 3.1
The discussion of basal melt rates in Section 3.1 refers to differences from MJ2023 and to the observational estimates of Rignot et al. (2013). However, these values are not shown in Fig. 4, which makes the comparison difficult to follow. I suggest adding the MJ2023 and Rignot et al. (2013) values to Fig. 4, or providing an additional figure/table summarizing these comparisons for the major ice shelves.Citation: https://doi.org/10.5194/egusphere-2026-927-RC2 - AC2: 'Reply on RC2', Pierre Mathiot, 19 Jun 2026
Peer review completion
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Pierre Mathiot
Nicolas C. Jourdain
Benoit Urruty
Fabien Gillet-Chaulet
Olivier Gagliardini
Gaël Durand
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(5023 KB) - Metadata XML
GENERAL COMMENTS
The authors are investigating the effect of a sudden increased warming to the Southern ocean and the Antarctic ice sheet in a coupled ice-ocean simulation.
They base their simulation setup on an earlier stand-alone simulation and chose a high warming scenario to investigate the possibility of reversibility after a 50yrs increased warming period. Finding that while the ocean is relatively quickly reverting to its initial conditions that the ice sheet takes longer to revert and that a few ice streams undergo irreversible retreat.
The study fits within the scope of TC, presents its findings in a clear way and is well written.
The findings are not especially novel, but contribute to the ongoing discussion of tipping points as part of several studies with the important aspect of ice-ocean coupling which is needed to better understand the complex Antarctic system of atmosphere, ocean and ice.
I include below a few points that require some further explanations, but otherwise I recommend accepting the paper after these points are addressed.
===
Overall comments:
- Observations and present-day conditions:
How do your ocean and ice conditions at the start of the simulation relate to observations or other studies during the initial time period? Are your melt rates reasonable and the ice velocities and thickness reasonable? This information would be important for readers to better place the changes during the warming period, and the subsequent reversed state, into context.
- Ocean boundary conditions:
While you address a few times the atmospheric forcing being the driver of changes and reversibility, I am missing the mentioning or explanations of the setting for the ocean-ocean boundary conditions. Do they play a role? Are they too far away to impact the continental shelf and ice cavities? (see also comment below in “specific comments”)
It would be helpful to mention somewhere (2.1.1?) how this boundary forcing is implemented and to clarify why they are not important for or discussed in the results and discussion sections.
- 1m ice shelf minimum thickness
L111-115: I understand the choice of minimum 1m ice shelf thickness. However, how does this additional 1m of ice impact the ocean compared to having no ice? And are those locations crucial for the ice shelves itself providing stability versus no ice might lead to quicker retreat?
You discuss this briefly in line 334ff, but I think it is worth explaining whether, and to what extent, this choice affects ocean circulation, particularly if a larger area in front of the ice shelf is directly exposed to atmospheric forcing rather than being covered by a thin ice layer. Related to this, how might this influence ice-shelf or grounding-line retreat, beyond the overestimated meltwater flux into the ocean?
Is the affected area large enough that atmospheric forcing over these ice-free regions would significantly influence the system, potentially making reversibility more difficult or slowing it down?
Furthermore, it would be useful to explicitly acknowledge the limitation of not including feedbacks from the ocean to the atmosphere, and to discuss whether such feedbacks could enable or strengthen tipping-point behavior. While I understand that the focus of the study is on ice–ocean interactions, a brief discussion of the neglected feedbacks, and a qualitative estimate of their potential impact on the main conclusions, would strengthen the manuscript, particularly given the emphasis on tipping points and reversibility.
SPECIFIC COMMENTS
- L183ff: The reversibility is described as being directly affected by the change in atmospheric forcing. How are ocean-ocean boundary conditions prescribed? Are they important or maybe just mention that they aren’t and why.
- L220-227:This paragraph seems important, but I struggle to understand the relationships, relative importance, and impacts of the factors mentioned on the overall outcome, as well as what the authors intend to convey here. Could you please reformulate this paragraph or add clarifying information to make the main points more clear?
- Fig 6: Please add a legend for the grounding line colors.
Rename second (b) to (c).
Maybe consider switching the color scheme: red for less ice and blue for more ice?
(c) and (d): it looks like there is thinning happening around the fast flowing areas on the grounded ice areas. Is this due ice velocity and grounding line change in reaction to the reverted ocean conditions?
- Fig 7: For better readability, I recommend to use REF, PERT and REV also in the Figure label - even though the explanations are nice.
- Fig 8c: The VAF seems to be increasing in REF & REF_ext for most of the basins. Is this an expected trend? wouldn’t we expect a more constant or even shrinking VAF in REF&REF_ext? Or is this due to the choice of SMB or due to underestimated melt rates?
- L291ff: How long does Garbe et al. or other studies you mention here enforce the warmer conditions before reverting back? This would be useful information to put your results into perspective. Especially in regards to the thought that your 50yrs choice might be too short. Furthermore, Garbe et al., state very strongly that there is no reversibility in certain areas under certain conditions, right?. Does the difference between Garbe et al. and this study imply that the reversibility depends on the choice of ocean and ice model (and setup)?
- L306-315: You do not mention the choice of ice model resolution: 1km finest resolution is fair for Antarctica due to computation time, but could impact grounding line dynamics and the choice of resolution would define existing pinning points (or omit them). On top of this are the uncertainties in the bedrock data.
- References: please go through the list. A few are missing doi, a few seem to have a different format or different information supplied
- L399: Remove the three times number-code in the reference: e2022JC018621
- L423ff Garbe double reference? 2020a and 2020b or wrong reference in 2020b?