the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Evolution of the climate in the next million years: A reduced-complexity model for glacial cycles and impact of anthropogenic CO2 emissions
- Potsdam Institute for Climate Impact Research, Potsdam, 14473, Germany
- Potsdam Institute for Climate Impact Research, Potsdam, 14473, Germany
Abstract. We propose a reduced-complexity process-based model for the long-term evolution of the global ice volume, atmospheric CO2 concentration and global mean temperature. The model only external forcings are the orbital forcing and anthropogenic CO2 cumulative emissions. The model consists of a system of three coupled non-linear differential equations, representing physical mechanisms relevant for the evolution of the Climate – Ice Sheets – Carbon cycle System in timescales longer than thousands of years. The model is successful in reproducing the glacial-interglacial cycles of the last 800 kyr, in good agreement with the timing and amplitude of paleorecord fluctuations, with the best correlation between modelled and paleo global ice volume of 0.86. Using different model realisations, we produce a probabilistic forecast of the evolution of the Earth system over the next 1 million years under natural and several fossil-fuel CO2 release scenarios. In the natural scenario, the model assigns high probability of occurrence of long interglacials in the periods between present and 120 kyr after present, and between 400 kyr and 500 kyr after present. The next glacial inception is most likely to occur ~ 50 kyr after present with full glacial conditions developing ~ 90 kyr after present. The model shows that even already achieved cumulative CO2 anthropogenic emissions (500 PgC) are capable of affecting climate evolution for up to half million years, indicating that the beginning of the next glaciation is highly unlikely in the next 120 kyr. High cumulative anthropogenic CO2 emissions (3000 PgC or higher), which could potentially be achieved in the next two to three centuries if humanity does not curb the usage of fossil-fuels, will most likely provoke Northern Hemisphere landmass ice-free conditions throughout the next half million years, postponing the natural occurrence of the next glacial inception to 600 kyr after present or later.
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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
(1947 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.
Journal article(s) based on this preprint
Stefanie Talento and Andrey Ganopolski
Interactive discussion
Status: closed
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CC1: 'The model has been tuned to the late Pleistocene variability. Why not to the early Pleistocene?', Mikhail Verbitsky, 16 Mar 2021
It is well recognized that the ice-age history is the history of large ice sheets’ mass balance that in turn is an outcome of a delicate interplay between astronomical forcing and climate system positive and negative feedbacks. The changing balance between positive and negative feedbacks over the Pleistocene defines mid-Pleistocene transition (MPT) from about 40 kyr lower-amplitude variability of the early Pleistocene to longer-period (~100 kyr) and higher-amplitude variability of the late Pleistocene.
In the current study, the authors employ a reduced complexity model; therefore, naturally, the explicit calculations of all feedbacks involved are not expected. Instead, the authors have tuned their model to the late Pleistocene variability with a hope that the best choice of their tuning parameters now adequately represent the balance between positive and negative feedbacks and the model may be taken for the future predictions with a great deal of credibility.
This approach may be questionable. It is not unlikely that the landscape of future positive and negative feedbacks (especially for increased CO2 concentration) will be more analogous to the early Pleistocene climate and a renaissance of ice-ages (if any) may be rather of the early-Pleistocene type with a dominant period of 40 kyr and smaller amplitudes – not 100-kyr variability as this study suggests. Or it may be “MPT of the future” when glaciation variability (period and amplitude) may change in concert with the CO2 level.
Mikhail Verbitsky
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AC1: 'Reply on CC1', Stefanie Talento, 30 Mar 2021
We are thankful to Mikhail Verbitsky for his comment. We agree that it is important to discuss the validity of the assumption that the Earth system’s future evolution will be similar to that observed during the past million years and we will address it in the revised version of our manuscript.
Before answering the question of why the model parameters were calibrated using the late and not the early Quaternary, it is important to stress that the paleoclimate records have been used to optimise the modelling of the natural (both past and future) evolution of the Earth system. The response to the anthropogenic forcing is a separate issue (see below). The choice of the late Quaternary records for model calibration was motivated by the Clark and Pollard “regolith hypothesis” about the nature of the mid-Pleistocene transition (MPT). According to this hypothesis, the MPT was caused by the gradual removal of a thick sediment layer from the northern part of the Northern Hemisphere continents by glacial erosion. Our recent experiments with the CLIMBER-2 model (Willeit et al., 2019) provide a strong support to this mechanism of the MPT. These results also demonstrate that this type of regime changes in the Earth system dynamics does not require variations of climate feedbacks. The rebuilding of the thick regolith layer even in the absence of new glaciations is a very slow process that will take many millions of years. As a consequence, it is reasonable to assume that the Earth system's natural evolution during the next million years will be similar to the evolution during the later Quaternary. Of course, it is possible that future glaciations will continue to change sediments distribution and, after some time, a new regime of variability different both from the late and early Quaternary will arise. However, such “no-analogue” problem cannot be addressed by using paleoclimate data or any other available information.
Regarding the Earth system future evolution after an anthropogenic perturbation, it is expected that it will deviate significantly from the natural evolution until the anthropogenic CO2 atmospheric concentration anomaly will be finally removed by weathering processes (Fig. 7 and 8 of the manuscript). This is explicitly accounted for in the model by including the effect of CO2 on the surface mass balance of ice sheets (Eq. 3). This aspect of the model cannot be validated using late Quaternary paleodata because during the last 800 kyr CO2 was never much higher than the preindustrial value. This is why, to constrain additional model parameters we used results of simulations with the CLIMBER-2 model (Ganopolski et al., 2016). Can early Quaternary paleoclimate records be useful for simple model calibration in addition to the late Quaternary and CLIMBER-2 results? We doubt that for two reasons. First, very different thickness of terrestrial sediments during the early Quaternary implies also very different ice sheet dynamics. Second, CO2 concentrations during the early Quaternary are extremely uncertain (at least +-50%).
Ganopolski, A., Winkelmann, R. and Schellnhuber, H. J.: Critical insolation–CO2 relation for diagnosing past and future glacial inception, Nature, 529(7585), 200–203, https://doi.org/10.1038/nature16494, 2016.
Willeit, M., Ganopolski, A., Calov, R. and Brovkin, V.: Mid-Pleistocene transition in glacial cycles explained by declining CO2 and regolith removal, Sci. Adv., 5(4), eaav7337, https://doi.org/10.1126/sciadv.aav7337, 2019.
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AC1: 'Reply on CC1', Stefanie Talento, 30 Mar 2021
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RC1: 'Comment on esd-2021-2', Anonymous Referee #1, 09 Apr 2021
This manuscript presents possible scenarios for the Earth’s climate during the next million years. It brings interesting and new material to this rather overlooked and under-researched area. Overall, I am favourable to publication, but I have nevertheless several important comments that the authors should consider in a revised version of the manuscript. Most importantly, the whole exercise is based on shaky hypotheses: I am aware that there aren’t many alternatives, but it is all the more important to present and discuss them thoroughly.
1 – Using Quaternary climate (and more precisely the last 800 kyr period) to calibrate a conceptual model to be applied to the future is certainly not the ideal choice since there are no very hot periods, but mostly glacial ones. The (partial or complete) melting of Greenland or Antarctica is therefore not considered, and the effect of high CO2 levels cannot be calibrated. In other words, the whole exercise is more an extrapolation than an interpolation. This is something known to be quite dangerous. I perfectly understand this choice, based on the availability of data, but it remains nonetheless not satisfactory. This should be stated much more clearly in the paper.
2 – Our knowledge of the long-term carbon cycle and of the ultimate fate of fossil-fuel carbon is also very thin, shaky or uncertain. The manuscript uses model results (Lord et al. 2016; based on Lenton et al. 2006) that have unfortunately no “real world” tests. The imposed exponential decay of carbon is therefore based on the (mostly theoretical) idea that the carbon cycle is regulated uniquely through silicate weathering. This approach neglects many other important processes that are known to have played a critical role on these timescales in the past and even today, like organic matter burial or kerogen weathering. Again, I do not contest the value of using a simple hypothesis, but this should be explained and discussed.
To summarize, sentences like “we produce a probabilistic forecast” (line 14 in the abstract) are not acceptable. This is obviously not a “forecast” but only a possible scenario, based on our very limited knowledge of the dynamics of geological transitions in the past.
We are clearly not able today to “forecast” what the Anthropocene era will be, and this should be stated much more clearly.
Other comments:
3 – It appears that one of the most critical parameter, K, is not well constrained using the conceptual model or the chosen paleoclimatic dataset, as explained in §3.2.
« Our results indicate that with the model derived in this study the possible values of the coefficient K range between -1279 and -31 W m-2, with a median of -393 W m-2 »
Using results from an Emic model (CLIMBER-2, Ganopolski et al, 2016) the authors decided to select only a very small subset of solutions (“Accepted”) that are all in the tail of the distribution of “Valid” solutions as shown on Fig.2. This appears as a strong shift in the overall strategy and raises a few questions:
- How does the correlation to data vary across the histogram on Fig.2? Are the “Valid” solutions close to the 0.7 correlation limit and the center of the distribution farther away from this limit?
- The Ganopolski et al (2016) insolation-CO2 threshold is also based on a parameter selection using a comparison to (basically) the same ice volume data. The problem is therefore not that the paleodata does not constrain well the K parameter but that the chosen conceptual model and the CLIMBER-2 model do not represent the role of CO2 onto the dynamics of ice sheets in the same way. Why do the authors choose to trust one model against the other? And to adjust on model on the other?
- More technically, how are inceptions defined in the conceptual model?
4 – Another strong limitation concerns the simple addition of “natural” and “anthropogenic” carbon, as presented line 182:
« In addition, we assume that natural and anthropogenic CO2 anomalies can be simply summed up and that at the preindustrial time the global Carbon cycle was in equilibrium. This is, obviously, a very strong assumption since even a rather small imbalance in the global Carbon cycle which is impossible to detect at the millennial timescales can result in a very large “drift” of the Earth system from its preindustrial state at the million years timescale. »
Indeed. This is actually why the anthropogenic CO2 decreases through a small imbalance between silicate weathering and carbonate preservation. The conceptual model assumes that there is NO natural dynamics in the carbon cycle besides glacial cycles. On Fig.8b the CO2 is just following the imposed decrease in the absence of (northern hemisphere) ice-sheets. But what about a possible role of Antarctica? What about some internal dynamics? And even on the calibration period (Fig.4b) the CO2 results are quite different from the data. In other words, the added value of a dynamic CO2 component in this conceptual model is not obvious.
5 – It seems to me that the 3 variables (v, CO2 and T) are almost identical (up to scaling) in the natural and in the no-anthropogenic cases. Are these 3 variables necessary at all to express the dynamics of the system? I believe only one variable could have produced almost the same results.
Other comments:
Line 86 :
« the last 800 kyr (see below). This period was selected because it is dominated by the long glacial cycles which are expected to continue in the future »
This is not the case with anthropogenic forcing… I would prefer the authors to acknowledge that this is the only period where we know both the ice-sheet and CO2 evolutions. Using another time period (much warmer) would be preferable for the next million-years.
Line 99 :
« This approach, obviously, is not applicable for a possible future Antarctic and Greenland melting under high CO2 concentrations. This is why we do not consider future sea level rise above the preindustrial level and it is required that v≥0 at any time»
This appears a strong limitation of the study and it should be acknowledged as such in the abstract and in the conclusion. A discussion on how to lift this problem would also be appreciated.
Line 151 :
« Namely, we assume that on the relevant timescales (103-105 yrs), the natural component of CO2 concentration is in equilibrium with external conditions and can be expressed through a linear combination of global temperature and global ice volume »
This is probably why the “natural CO2” results are not so good (Fig.1b & 4b)…? They are mostly simple ”mirrors” to the ice-volume and temperature ones.
Equa (7) :
Change dT into âT ?
Line 227
« We select a climate sensitivity equal to 3.9 C, which coincides with the multimodel mean in the Coupled Model Intercomparison Project 6 (CMIP6; Zelinka et al., 2020) »
How sensitive are the results to this choice? This could be critical and should be discussed a bit more.
Line 240 :
« First, we assume that for the recent interstadials and any future time, v cannot be negative. »
See above comments: what about melting currently existing ice-sheets?
Line 245
« This is why we prescribe that before the MBT the minimum ice volume must be 0.05 in normalized units: »
This seems a very ad-hoc assumption: I do not understand the reason for this adjustment, beyond providing artificially a better correlation.
Line 258 :
« the new glacial inception will not be met in the near future even in the absence of anthropogenic influence on climate. »
Again, this seems a very ad-hoc constraint: the physical explanation is to be found in the insolation forcing, and the tuned models should provide this mostly as a result, not as an a priori constraint.
Line 266 :
« corr(x,y) denotes the linear Person correlation »
The correlation is not always the best metric, though it is simple to compute… Why only using the correlation with ice-volume data and not the two other paleoclimatic data?
Change “Person” into “Pearson”
Line 286 :
« For the selection of solutions, no conditions are imposed on the goodness of fit »
Well, it seems to me that Equation (16) is a condition on the goodness of fit! This also contradicts line 265:
« We wish to find P to maximize the optimization target function Cv »
Probably the authors should clarify their language: they are only choosing parameters that satisfy all the constraints (including (16)): this is a feasibility problem, not an optimisation problem (though it is usually provided in optimisation packages).
Why choosing correlation > 0.7 (or why selecting 353 parameter sets)? Is there a need to have a large enough parameter set with a large enough dispersion? Or does this relates to the parameter K problem (see above comment) ?
Line 293 :
« For global mean surface temperature anomalies (with respect to preindustrial conditions) we use two reconstructions »
Some discussion on the nature and on the accuracy of these proxies could be useful. In particular why using “ice-volume” as a preferred target? Overall, the temperature does not have any dynamic role in the model (it can be replaced by v and CO2). So why using it?
Line 315 :
« some solutions display an amplitude range significantly larger than the observed one, reaching the imposed lower limit of 150 ppm »
Actually, not “some” solutions, but “most” or even “all” solutions.
Line 314-317 :
Correlations of 0.5 or 0.56 appear not very good to me. Why optimizing only the correlation with ice volume?
Line 327 :
« In general, we conclude that the model has a satisfactory ability also when used in predictive mode and, thus, we confidently venture to utilize it as a tool for the forecast of the next 1 Myr climatic evolution. »
This is overly optimistic : the climate system is very different in the anthropogenic case. The word “forecasting” is fully inappropriate: the system is obviously non-stationary and a “statistical forecast” has here no meaning at all. At best, you can call this a possible scenario.
Line 356 :
« the relationship between fcritial and log(CO2) is not well constrained by paleoclimate data »
See my comment above: Ganopolski et al (2016) was based on the same data, so the paleoclimate data CAN constrain the K parameter. But possibly the conceptual model does not capture well this threshold behaviour…
Line 383 :
« The high positive temperature anomalies during some previous interglacials, however, are questionable. »
There was no discussion on « data » in the manuscript, except this sentence... Why is it questionable ? This should certainly be explained a bit more.
Line 449 : lesss -> less
Line 450 :
« Most of the solutions agree that the planet will remain in a long interglacial state for the next 50 kyr »
Not « most » but « all » since it was built into the assumptions (something questionable, see above). I do not understand this statement: the contrary would be problematic.
Line 532 :
« the past does not perfectly constraint the future evolution of the climate – ice sheets – Carbon cycle system. »
In particular using only the last 800 ka Quaternary period. The main question is the choice of the time window used in the past.
Line 534 :
« The selected model versions exhibit a large sensitivity to fossil-fuel CO2 releases »
How does this relate to the K parameter choice (based on Climber results)? It seems to me that the “Valid” set is even more sensitive. This should certainly be discussed in much more details since it represents a large part of the manuscript.
Conclusions:
« this relationship is poorly constrained by the paleoclimatic data because during previous interglacials CO2 was close to or lower than the preindustrial level. »
« Reducing this uncertainty by performing experiments similar to those described in Ganopolski et al. (2016) but with more advanced Earth system models can help to reduce uncertainties in future projections. »
As explained above, I do not like this conclusion. The Ganopolski et al. (2016) threshold was based on the same data, so the difficulty is not so much within the data, but much more with the model. Besides, enlarging the scope outside the Quaternary would certainly help a lot. The authors should better highlight the key difficulties (my main comments 1 & 2).
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AC2: 'Reply on RC1', Stefanie Talento, 08 Jul 2021
We thank the reviewer for the insightful and constructive comments. Please find attached a point-by-point response, marked in blue. In order to address some of the reviewer’s questions and assess the robustness of the results to several criteria involved in the design of the model or parameter selection strategy, we performed a series of sensitivity experiments. The results from these experiments are briefly discussed here in response to specific comments and will be included in a revised manuscript.
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RC2: 'Comment on esd-2021-2', Anonymous Referee #2, 30 Apr 2021
Review of “Evolution of the climate in the next million years: A reduced-comlexity model for glacial cycles and impact of anthropogenic CO2 emissons” by Stefanie Talento and Andrey Ganopolski.
The authors developed the simple model (which consists of three differential equations) which reproduces the last 800-kyr evolution of the global ice volume, atmospheric CO2 concentration and global mean temperature. Based on this model, the authors accessed the anthropogenic influence on the deep future glacial cycles. This is a challenging attempt and I enjoyed reading the manuscript. Although there are many issues which need to be investigated further, this is a nice study which gives us valuable inspirations about the climate evolution in the deep future. Therefore, I can recommend the publication of this manuscript. Followings are my comments which I hope will be useful for the authors to prepare the final manuscript.
Specific comments
Line100-101: The statement “This is why we do not consider future sea level rise …” is not clear.
Line126 (Eq3): Please explicitly describe the physical explanation about the first (b01*v) and the last (-b06) terms, which I think was missing or not very clearly stated in the manuscript.
Line136 (Eq6): Why did the authors re-wrote the equation?
Line 144 (and Lines 150, 181,182, etc): Carbon -> carbon
Line 231: (10) and (11) -> (9) and (10)
Line 248-249 (Eqs11,12): Different treatment about minimum values (i.e., 0 or 0.05) seems somewhat artificial and its effect on the results appeared very small. Is this different treatment really required?
Line 257-258: The meaning of the statement “the conditions for the new glacial inception will not be met in the near future” was not clear for me.
Line 286: Why? (Is optimization of “CO2” and “temperature” in addition to “ice volume” technically difficult?)
Line 312: “respectively). .“ -> “respectively).”
L311-312: It might be useful if you can discuss the reason for the overestimation in MIS 18 and 14.
L351-353: It was difficult for me to understand the details about how the authors calculate (estimate) the value “K” in their model. Additional explanation might be helpful.
L378-379: I feel that prediction of CO2 changes appears not very successful because the simulated amplitude of CO2 changes tends to be always overestimated. I’m curious about effects of CO2 errors on the ice volume. For example, if you “prescribe” the paleo-recorded CO2 changes instead of predicting it, how much does this improve the reproducibility of ice volume?
L503-504: What does the authors mean by “data not used for training”? (temperature and CO2?)
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AC3: 'Reply on RC2', Stefanie Talento, 08 Jul 2021
We thank the reviewer for the insightful evaluation and constructive comments. Please find attached a point-by-point response, marked in blue. In order to address some of the reviewer’s questions and assess the robustness of the results to several criteria involved in the design of the model or parameter selection strategy, we performed a series of sensitivity experiments. The results from these experiments are briefly discussed here in response to specific comments and will be included in a revised version of the manuscript.
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AC3: 'Reply on RC2', Stefanie Talento, 08 Jul 2021
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CC2: 'Comment on esd-2021-2', Alan Kennedy-Asser, 13 May 2021
This is an interesting paper and I feel the many steps in the modelling process are relatively well described. While I think it is reasonable to use conceptual models for this kind of study, there are a few assumptions which I find a little questionable and should be justified better (or the implications of which should be discussed in more detail). After having read the paper, I have read the comments made by other reviewers and I am inclined to agree with many of the points raised by Reviewer 1.
In particular, I think the following assumptions require further discussion:
- The constraining the minimum ice volume to the pre-industrial levels is not well justified in my opinion and its impacts are unclear. As others have commented here in the reviews, perhaps at least considering other past warmer periods is necessary if this study is to be seriously considered as realistic, particularly for the warmer high emissions scenarios.
- Likewise, constraining the ice volume to not glaciate for the first part of the record – what effect does this have if this constraint not included? Does the model often glaciate without it? Although it seems unlikely, I don’t think there is so much evidence against this being a possibility that it can simply be prescribed.
- What might be the impact of the assumption that natural and anthropogenic CO2 signal are separate and can be linearly combined? This was also raised by the reviewers.
- One point which I had not thought of, but was mentioned by Reviewer 1 (their comment 3) and I think is worth echoing relates to the choice of the Pearson’s correlation threshold of >0.7 and the ‘accepted’ simulations out of the full ‘valid’ set. Are the ‘accepted’ simulations in general those with higher correlations?
I have a few other queries which the authors may want to consider clarifying:
- I am curious to know do you have an explanation of why the 10kyr time lag between the natural and 500PgC scenario in Figure 8?
- Line 422: Does the low 500 PgC scenario suggest a scenario where some of the CO2 already emitted is drawn back down? This value is less than what has already emitted as quoted from the Le Quere et al. 2018 paper. I think this should be clarified.
- Finally, it might be useful to reference a technical report on a similar topic that was produced for SKB (similar to Nagra who funded this work), where probabilistic future projections (or maybe ‘scenarios’ is a more appropriate word, following on from Reviewer 1’s comments) are shown. The report is available here https://www.researchgate.net/profile/Jens-Ove_Naeslund/project/Climate-and-radioactive-waste/attachment/5dd2830fcfe4a777d4f1f887/AS:826544842870784@1574075055393/download/TR-19-09.pdf?context=ProjectUpdatesLog
- AC4: 'Reply on CC2', Stefanie Talento, 08 Jul 2021
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RC3: 'Comment on esd-2021-2', Anonymous Referee #3, 28 May 2021
This paper cannot be published as it is and must be rejected. This work is not mature enough for publication. It needs a profound revision and reworks. Concepts are being mixed and the goal itself is unclear to the authors. The framework and the selected statistical modeling/validation approaches are weakly justified and poorly and/or incorrectly applied and most importantly the methodology is inadequate as it does not account for any source of uncertainty.I am attaching a full review in a pdf file.This paper really made me sad.
- CC3: 'Reply on RC3', Michel Crucifix, 31 May 2021
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AC5: 'Reply on RC3', Stefanie Talento, 08 Jul 2021
Reviewer#3 claimed and devoted most of the spate to two statements: 1) we used the wrong modelling approach to simulate the possible future evolution of the Earth under and after a significant anthropogenic perturbation of climate; 2) we have no clue about Milankovitch theory and the current status of modelling and understanding of the Quaternary glacial cycles. In the attached response, we show that both these statements are fatally wrong. And although we provide in the attached document scientific responses to the reviewer’s critique, first we would like to make it very clear to both the editor and reviewer#3, that writing reviews in such an offensive manner is unacceptable.
- AC6: 'Reply on AC5', Stefanie Talento, 12 Jul 2021
Peer review completion
Interactive discussion
Status: closed
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CC1: 'The model has been tuned to the late Pleistocene variability. Why not to the early Pleistocene?', Mikhail Verbitsky, 16 Mar 2021
It is well recognized that the ice-age history is the history of large ice sheets’ mass balance that in turn is an outcome of a delicate interplay between astronomical forcing and climate system positive and negative feedbacks. The changing balance between positive and negative feedbacks over the Pleistocene defines mid-Pleistocene transition (MPT) from about 40 kyr lower-amplitude variability of the early Pleistocene to longer-period (~100 kyr) and higher-amplitude variability of the late Pleistocene.
In the current study, the authors employ a reduced complexity model; therefore, naturally, the explicit calculations of all feedbacks involved are not expected. Instead, the authors have tuned their model to the late Pleistocene variability with a hope that the best choice of their tuning parameters now adequately represent the balance between positive and negative feedbacks and the model may be taken for the future predictions with a great deal of credibility.
This approach may be questionable. It is not unlikely that the landscape of future positive and negative feedbacks (especially for increased CO2 concentration) will be more analogous to the early Pleistocene climate and a renaissance of ice-ages (if any) may be rather of the early-Pleistocene type with a dominant period of 40 kyr and smaller amplitudes – not 100-kyr variability as this study suggests. Or it may be “MPT of the future” when glaciation variability (period and amplitude) may change in concert with the CO2 level.
Mikhail Verbitsky
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AC1: 'Reply on CC1', Stefanie Talento, 30 Mar 2021
We are thankful to Mikhail Verbitsky for his comment. We agree that it is important to discuss the validity of the assumption that the Earth system’s future evolution will be similar to that observed during the past million years and we will address it in the revised version of our manuscript.
Before answering the question of why the model parameters were calibrated using the late and not the early Quaternary, it is important to stress that the paleoclimate records have been used to optimise the modelling of the natural (both past and future) evolution of the Earth system. The response to the anthropogenic forcing is a separate issue (see below). The choice of the late Quaternary records for model calibration was motivated by the Clark and Pollard “regolith hypothesis” about the nature of the mid-Pleistocene transition (MPT). According to this hypothesis, the MPT was caused by the gradual removal of a thick sediment layer from the northern part of the Northern Hemisphere continents by glacial erosion. Our recent experiments with the CLIMBER-2 model (Willeit et al., 2019) provide a strong support to this mechanism of the MPT. These results also demonstrate that this type of regime changes in the Earth system dynamics does not require variations of climate feedbacks. The rebuilding of the thick regolith layer even in the absence of new glaciations is a very slow process that will take many millions of years. As a consequence, it is reasonable to assume that the Earth system's natural evolution during the next million years will be similar to the evolution during the later Quaternary. Of course, it is possible that future glaciations will continue to change sediments distribution and, after some time, a new regime of variability different both from the late and early Quaternary will arise. However, such “no-analogue” problem cannot be addressed by using paleoclimate data or any other available information.
Regarding the Earth system future evolution after an anthropogenic perturbation, it is expected that it will deviate significantly from the natural evolution until the anthropogenic CO2 atmospheric concentration anomaly will be finally removed by weathering processes (Fig. 7 and 8 of the manuscript). This is explicitly accounted for in the model by including the effect of CO2 on the surface mass balance of ice sheets (Eq. 3). This aspect of the model cannot be validated using late Quaternary paleodata because during the last 800 kyr CO2 was never much higher than the preindustrial value. This is why, to constrain additional model parameters we used results of simulations with the CLIMBER-2 model (Ganopolski et al., 2016). Can early Quaternary paleoclimate records be useful for simple model calibration in addition to the late Quaternary and CLIMBER-2 results? We doubt that for two reasons. First, very different thickness of terrestrial sediments during the early Quaternary implies also very different ice sheet dynamics. Second, CO2 concentrations during the early Quaternary are extremely uncertain (at least +-50%).
Ganopolski, A., Winkelmann, R. and Schellnhuber, H. J.: Critical insolation–CO2 relation for diagnosing past and future glacial inception, Nature, 529(7585), 200–203, https://doi.org/10.1038/nature16494, 2016.
Willeit, M., Ganopolski, A., Calov, R. and Brovkin, V.: Mid-Pleistocene transition in glacial cycles explained by declining CO2 and regolith removal, Sci. Adv., 5(4), eaav7337, https://doi.org/10.1126/sciadv.aav7337, 2019.
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AC1: 'Reply on CC1', Stefanie Talento, 30 Mar 2021
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RC1: 'Comment on esd-2021-2', Anonymous Referee #1, 09 Apr 2021
This manuscript presents possible scenarios for the Earth’s climate during the next million years. It brings interesting and new material to this rather overlooked and under-researched area. Overall, I am favourable to publication, but I have nevertheless several important comments that the authors should consider in a revised version of the manuscript. Most importantly, the whole exercise is based on shaky hypotheses: I am aware that there aren’t many alternatives, but it is all the more important to present and discuss them thoroughly.
1 – Using Quaternary climate (and more precisely the last 800 kyr period) to calibrate a conceptual model to be applied to the future is certainly not the ideal choice since there are no very hot periods, but mostly glacial ones. The (partial or complete) melting of Greenland or Antarctica is therefore not considered, and the effect of high CO2 levels cannot be calibrated. In other words, the whole exercise is more an extrapolation than an interpolation. This is something known to be quite dangerous. I perfectly understand this choice, based on the availability of data, but it remains nonetheless not satisfactory. This should be stated much more clearly in the paper.
2 – Our knowledge of the long-term carbon cycle and of the ultimate fate of fossil-fuel carbon is also very thin, shaky or uncertain. The manuscript uses model results (Lord et al. 2016; based on Lenton et al. 2006) that have unfortunately no “real world” tests. The imposed exponential decay of carbon is therefore based on the (mostly theoretical) idea that the carbon cycle is regulated uniquely through silicate weathering. This approach neglects many other important processes that are known to have played a critical role on these timescales in the past and even today, like organic matter burial or kerogen weathering. Again, I do not contest the value of using a simple hypothesis, but this should be explained and discussed.
To summarize, sentences like “we produce a probabilistic forecast” (line 14 in the abstract) are not acceptable. This is obviously not a “forecast” but only a possible scenario, based on our very limited knowledge of the dynamics of geological transitions in the past.
We are clearly not able today to “forecast” what the Anthropocene era will be, and this should be stated much more clearly.
Other comments:
3 – It appears that one of the most critical parameter, K, is not well constrained using the conceptual model or the chosen paleoclimatic dataset, as explained in §3.2.
« Our results indicate that with the model derived in this study the possible values of the coefficient K range between -1279 and -31 W m-2, with a median of -393 W m-2 »
Using results from an Emic model (CLIMBER-2, Ganopolski et al, 2016) the authors decided to select only a very small subset of solutions (“Accepted”) that are all in the tail of the distribution of “Valid” solutions as shown on Fig.2. This appears as a strong shift in the overall strategy and raises a few questions:
- How does the correlation to data vary across the histogram on Fig.2? Are the “Valid” solutions close to the 0.7 correlation limit and the center of the distribution farther away from this limit?
- The Ganopolski et al (2016) insolation-CO2 threshold is also based on a parameter selection using a comparison to (basically) the same ice volume data. The problem is therefore not that the paleodata does not constrain well the K parameter but that the chosen conceptual model and the CLIMBER-2 model do not represent the role of CO2 onto the dynamics of ice sheets in the same way. Why do the authors choose to trust one model against the other? And to adjust on model on the other?
- More technically, how are inceptions defined in the conceptual model?
4 – Another strong limitation concerns the simple addition of “natural” and “anthropogenic” carbon, as presented line 182:
« In addition, we assume that natural and anthropogenic CO2 anomalies can be simply summed up and that at the preindustrial time the global Carbon cycle was in equilibrium. This is, obviously, a very strong assumption since even a rather small imbalance in the global Carbon cycle which is impossible to detect at the millennial timescales can result in a very large “drift” of the Earth system from its preindustrial state at the million years timescale. »
Indeed. This is actually why the anthropogenic CO2 decreases through a small imbalance between silicate weathering and carbonate preservation. The conceptual model assumes that there is NO natural dynamics in the carbon cycle besides glacial cycles. On Fig.8b the CO2 is just following the imposed decrease in the absence of (northern hemisphere) ice-sheets. But what about a possible role of Antarctica? What about some internal dynamics? And even on the calibration period (Fig.4b) the CO2 results are quite different from the data. In other words, the added value of a dynamic CO2 component in this conceptual model is not obvious.
5 – It seems to me that the 3 variables (v, CO2 and T) are almost identical (up to scaling) in the natural and in the no-anthropogenic cases. Are these 3 variables necessary at all to express the dynamics of the system? I believe only one variable could have produced almost the same results.
Other comments:
Line 86 :
« the last 800 kyr (see below). This period was selected because it is dominated by the long glacial cycles which are expected to continue in the future »
This is not the case with anthropogenic forcing… I would prefer the authors to acknowledge that this is the only period where we know both the ice-sheet and CO2 evolutions. Using another time period (much warmer) would be preferable for the next million-years.
Line 99 :
« This approach, obviously, is not applicable for a possible future Antarctic and Greenland melting under high CO2 concentrations. This is why we do not consider future sea level rise above the preindustrial level and it is required that v≥0 at any time»
This appears a strong limitation of the study and it should be acknowledged as such in the abstract and in the conclusion. A discussion on how to lift this problem would also be appreciated.
Line 151 :
« Namely, we assume that on the relevant timescales (103-105 yrs), the natural component of CO2 concentration is in equilibrium with external conditions and can be expressed through a linear combination of global temperature and global ice volume »
This is probably why the “natural CO2” results are not so good (Fig.1b & 4b)…? They are mostly simple ”mirrors” to the ice-volume and temperature ones.
Equa (7) :
Change dT into âT ?
Line 227
« We select a climate sensitivity equal to 3.9 C, which coincides with the multimodel mean in the Coupled Model Intercomparison Project 6 (CMIP6; Zelinka et al., 2020) »
How sensitive are the results to this choice? This could be critical and should be discussed a bit more.
Line 240 :
« First, we assume that for the recent interstadials and any future time, v cannot be negative. »
See above comments: what about melting currently existing ice-sheets?
Line 245
« This is why we prescribe that before the MBT the minimum ice volume must be 0.05 in normalized units: »
This seems a very ad-hoc assumption: I do not understand the reason for this adjustment, beyond providing artificially a better correlation.
Line 258 :
« the new glacial inception will not be met in the near future even in the absence of anthropogenic influence on climate. »
Again, this seems a very ad-hoc constraint: the physical explanation is to be found in the insolation forcing, and the tuned models should provide this mostly as a result, not as an a priori constraint.
Line 266 :
« corr(x,y) denotes the linear Person correlation »
The correlation is not always the best metric, though it is simple to compute… Why only using the correlation with ice-volume data and not the two other paleoclimatic data?
Change “Person” into “Pearson”
Line 286 :
« For the selection of solutions, no conditions are imposed on the goodness of fit »
Well, it seems to me that Equation (16) is a condition on the goodness of fit! This also contradicts line 265:
« We wish to find P to maximize the optimization target function Cv »
Probably the authors should clarify their language: they are only choosing parameters that satisfy all the constraints (including (16)): this is a feasibility problem, not an optimisation problem (though it is usually provided in optimisation packages).
Why choosing correlation > 0.7 (or why selecting 353 parameter sets)? Is there a need to have a large enough parameter set with a large enough dispersion? Or does this relates to the parameter K problem (see above comment) ?
Line 293 :
« For global mean surface temperature anomalies (with respect to preindustrial conditions) we use two reconstructions »
Some discussion on the nature and on the accuracy of these proxies could be useful. In particular why using “ice-volume” as a preferred target? Overall, the temperature does not have any dynamic role in the model (it can be replaced by v and CO2). So why using it?
Line 315 :
« some solutions display an amplitude range significantly larger than the observed one, reaching the imposed lower limit of 150 ppm »
Actually, not “some” solutions, but “most” or even “all” solutions.
Line 314-317 :
Correlations of 0.5 or 0.56 appear not very good to me. Why optimizing only the correlation with ice volume?
Line 327 :
« In general, we conclude that the model has a satisfactory ability also when used in predictive mode and, thus, we confidently venture to utilize it as a tool for the forecast of the next 1 Myr climatic evolution. »
This is overly optimistic : the climate system is very different in the anthropogenic case. The word “forecasting” is fully inappropriate: the system is obviously non-stationary and a “statistical forecast” has here no meaning at all. At best, you can call this a possible scenario.
Line 356 :
« the relationship between fcritial and log(CO2) is not well constrained by paleoclimate data »
See my comment above: Ganopolski et al (2016) was based on the same data, so the paleoclimate data CAN constrain the K parameter. But possibly the conceptual model does not capture well this threshold behaviour…
Line 383 :
« The high positive temperature anomalies during some previous interglacials, however, are questionable. »
There was no discussion on « data » in the manuscript, except this sentence... Why is it questionable ? This should certainly be explained a bit more.
Line 449 : lesss -> less
Line 450 :
« Most of the solutions agree that the planet will remain in a long interglacial state for the next 50 kyr »
Not « most » but « all » since it was built into the assumptions (something questionable, see above). I do not understand this statement: the contrary would be problematic.
Line 532 :
« the past does not perfectly constraint the future evolution of the climate – ice sheets – Carbon cycle system. »
In particular using only the last 800 ka Quaternary period. The main question is the choice of the time window used in the past.
Line 534 :
« The selected model versions exhibit a large sensitivity to fossil-fuel CO2 releases »
How does this relate to the K parameter choice (based on Climber results)? It seems to me that the “Valid” set is even more sensitive. This should certainly be discussed in much more details since it represents a large part of the manuscript.
Conclusions:
« this relationship is poorly constrained by the paleoclimatic data because during previous interglacials CO2 was close to or lower than the preindustrial level. »
« Reducing this uncertainty by performing experiments similar to those described in Ganopolski et al. (2016) but with more advanced Earth system models can help to reduce uncertainties in future projections. »
As explained above, I do not like this conclusion. The Ganopolski et al. (2016) threshold was based on the same data, so the difficulty is not so much within the data, but much more with the model. Besides, enlarging the scope outside the Quaternary would certainly help a lot. The authors should better highlight the key difficulties (my main comments 1 & 2).
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AC2: 'Reply on RC1', Stefanie Talento, 08 Jul 2021
We thank the reviewer for the insightful and constructive comments. Please find attached a point-by-point response, marked in blue. In order to address some of the reviewer’s questions and assess the robustness of the results to several criteria involved in the design of the model or parameter selection strategy, we performed a series of sensitivity experiments. The results from these experiments are briefly discussed here in response to specific comments and will be included in a revised manuscript.
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RC2: 'Comment on esd-2021-2', Anonymous Referee #2, 30 Apr 2021
Review of “Evolution of the climate in the next million years: A reduced-comlexity model for glacial cycles and impact of anthropogenic CO2 emissons” by Stefanie Talento and Andrey Ganopolski.
The authors developed the simple model (which consists of three differential equations) which reproduces the last 800-kyr evolution of the global ice volume, atmospheric CO2 concentration and global mean temperature. Based on this model, the authors accessed the anthropogenic influence on the deep future glacial cycles. This is a challenging attempt and I enjoyed reading the manuscript. Although there are many issues which need to be investigated further, this is a nice study which gives us valuable inspirations about the climate evolution in the deep future. Therefore, I can recommend the publication of this manuscript. Followings are my comments which I hope will be useful for the authors to prepare the final manuscript.
Specific comments
Line100-101: The statement “This is why we do not consider future sea level rise …” is not clear.
Line126 (Eq3): Please explicitly describe the physical explanation about the first (b01*v) and the last (-b06) terms, which I think was missing or not very clearly stated in the manuscript.
Line136 (Eq6): Why did the authors re-wrote the equation?
Line 144 (and Lines 150, 181,182, etc): Carbon -> carbon
Line 231: (10) and (11) -> (9) and (10)
Line 248-249 (Eqs11,12): Different treatment about minimum values (i.e., 0 or 0.05) seems somewhat artificial and its effect on the results appeared very small. Is this different treatment really required?
Line 257-258: The meaning of the statement “the conditions for the new glacial inception will not be met in the near future” was not clear for me.
Line 286: Why? (Is optimization of “CO2” and “temperature” in addition to “ice volume” technically difficult?)
Line 312: “respectively). .“ -> “respectively).”
L311-312: It might be useful if you can discuss the reason for the overestimation in MIS 18 and 14.
L351-353: It was difficult for me to understand the details about how the authors calculate (estimate) the value “K” in their model. Additional explanation might be helpful.
L378-379: I feel that prediction of CO2 changes appears not very successful because the simulated amplitude of CO2 changes tends to be always overestimated. I’m curious about effects of CO2 errors on the ice volume. For example, if you “prescribe” the paleo-recorded CO2 changes instead of predicting it, how much does this improve the reproducibility of ice volume?
L503-504: What does the authors mean by “data not used for training”? (temperature and CO2?)
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AC3: 'Reply on RC2', Stefanie Talento, 08 Jul 2021
We thank the reviewer for the insightful evaluation and constructive comments. Please find attached a point-by-point response, marked in blue. In order to address some of the reviewer’s questions and assess the robustness of the results to several criteria involved in the design of the model or parameter selection strategy, we performed a series of sensitivity experiments. The results from these experiments are briefly discussed here in response to specific comments and will be included in a revised version of the manuscript.
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AC3: 'Reply on RC2', Stefanie Talento, 08 Jul 2021
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CC2: 'Comment on esd-2021-2', Alan Kennedy-Asser, 13 May 2021
This is an interesting paper and I feel the many steps in the modelling process are relatively well described. While I think it is reasonable to use conceptual models for this kind of study, there are a few assumptions which I find a little questionable and should be justified better (or the implications of which should be discussed in more detail). After having read the paper, I have read the comments made by other reviewers and I am inclined to agree with many of the points raised by Reviewer 1.
In particular, I think the following assumptions require further discussion:
- The constraining the minimum ice volume to the pre-industrial levels is not well justified in my opinion and its impacts are unclear. As others have commented here in the reviews, perhaps at least considering other past warmer periods is necessary if this study is to be seriously considered as realistic, particularly for the warmer high emissions scenarios.
- Likewise, constraining the ice volume to not glaciate for the first part of the record – what effect does this have if this constraint not included? Does the model often glaciate without it? Although it seems unlikely, I don’t think there is so much evidence against this being a possibility that it can simply be prescribed.
- What might be the impact of the assumption that natural and anthropogenic CO2 signal are separate and can be linearly combined? This was also raised by the reviewers.
- One point which I had not thought of, but was mentioned by Reviewer 1 (their comment 3) and I think is worth echoing relates to the choice of the Pearson’s correlation threshold of >0.7 and the ‘accepted’ simulations out of the full ‘valid’ set. Are the ‘accepted’ simulations in general those with higher correlations?
I have a few other queries which the authors may want to consider clarifying:
- I am curious to know do you have an explanation of why the 10kyr time lag between the natural and 500PgC scenario in Figure 8?
- Line 422: Does the low 500 PgC scenario suggest a scenario where some of the CO2 already emitted is drawn back down? This value is less than what has already emitted as quoted from the Le Quere et al. 2018 paper. I think this should be clarified.
- Finally, it might be useful to reference a technical report on a similar topic that was produced for SKB (similar to Nagra who funded this work), where probabilistic future projections (or maybe ‘scenarios’ is a more appropriate word, following on from Reviewer 1’s comments) are shown. The report is available here https://www.researchgate.net/profile/Jens-Ove_Naeslund/project/Climate-and-radioactive-waste/attachment/5dd2830fcfe4a777d4f1f887/AS:826544842870784@1574075055393/download/TR-19-09.pdf?context=ProjectUpdatesLog
- AC4: 'Reply on CC2', Stefanie Talento, 08 Jul 2021
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RC3: 'Comment on esd-2021-2', Anonymous Referee #3, 28 May 2021
This paper cannot be published as it is and must be rejected. This work is not mature enough for publication. It needs a profound revision and reworks. Concepts are being mixed and the goal itself is unclear to the authors. The framework and the selected statistical modeling/validation approaches are weakly justified and poorly and/or incorrectly applied and most importantly the methodology is inadequate as it does not account for any source of uncertainty.I am attaching a full review in a pdf file.This paper really made me sad.
- CC3: 'Reply on RC3', Michel Crucifix, 31 May 2021
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AC5: 'Reply on RC3', Stefanie Talento, 08 Jul 2021
Reviewer#3 claimed and devoted most of the spate to two statements: 1) we used the wrong modelling approach to simulate the possible future evolution of the Earth under and after a significant anthropogenic perturbation of climate; 2) we have no clue about Milankovitch theory and the current status of modelling and understanding of the Quaternary glacial cycles. In the attached response, we show that both these statements are fatally wrong. And although we provide in the attached document scientific responses to the reviewer’s critique, first we would like to make it very clear to both the editor and reviewer#3, that writing reviews in such an offensive manner is unacceptable.
- AC6: 'Reply on AC5', Stefanie Talento, 12 Jul 2021
Peer review completion
Journal article(s) based on this preprint
Stefanie Talento and Andrey Ganopolski
Data sets
Data: Evolution of the climate in the next Million years: A Reduced-Complexity Model for Glacial Cycles and Impact of anthropogenic CO2 emissions Stefanie Talento https://doi.org/10.17605/OSF.IO/KB76G
Model code and software
Data: Evolution of the climate in the next Million years: A Reduced-Complexity Model for Glacial Cycles and Impact of anthropogenic CO2 emissions Stefanie Talento https://doi.org/10.17605/OSF.IO/KB76G
Stefanie Talento and Andrey Ganopolski
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