Reversibility of Greenland ice sheet mass loss under artificial carbon dioxide removal scenarios

With ongoing anthropogenic CO2 emissions, the Greenland ice sheet (GIS) approaches critical thresholds of inevitable, long-term mass loss. Future technologies might be able to efficiently remove CO2 from the atmosphere and thereby cool down our planet. We explore whether and to what extent a realization of this concept could lead to a regrowth of the GIS once it has partly melted. Using the fully coupled Earth system model of intermediate complexity CLIMBER-X, emission pulses between 0 and 4000 GtC are released into the atmosphere, and after 1 kyr, 2 kyr, and 5 kyr, the atmospheric CO2 concentration is reduced back to its pre-industrial value. We find that independent of a specific trajectory, once the southern part of the GIS has partly melted with a total mass loss of more than 0.4 m sea level equivalent, regrowth is inhibited. Uncertainties preclude determination of precise thresholds, but model results indicate that cumulative industrial-era emissions approaching 1000–1500 GtC and beyond increasingly risk irreversible mass loss of the GIS. Once this threshold is passed, artificial atmospheric carbon removal would need to be utilised within the next centuries at massive scale. Beyond that, artificial atmospheric carbon removal has limited abilities to avoid long-term mass loss of the GIS. In conclusion, keeping cumulative anthropogenic emissions below 1000–1500 GtC is the only safe way to avoid irreversible mass loss of the GIS.


Introduction
Negative anthropogenic atmospheric CO 2 emissions, also termed artificial carbon removal, is a possible component to remain below critical temperature thresholds (e.g.Tavoni and Socolow 2013, Lomax et al 2015, Carton et al 2020).Relying on this concept is however risky since it is not clear whether efficient carbon removal techniques will be deployed in the future, and it could lead to extreme global warming if humans fail to remove carbon from the atmosphere in large quantities (e.g.Fuss et al 2014, Anderson and Peters 2016, Williamson 2016).Furthermore, there is the risk that critical thresholds in the Earth system (also termed tipping points) will be crossed before realising net negative emissions (e.g.Shue 2017).Due to the non-linearity of the Earth system, changes could be irreversible, even if the atmospheric CO 2 would eventually successfully be reduced to preindustrial levels.
A major issue concerning the recovery of preindustrial conditions by removing atmospheric CO 2 is the associated recovery of the sea level.The reason for this is twofold: First, the sea level changes with a substantial time lag after changes in the atmospheric CO 2 .In fact, thermosteric sea level rise is not reversible on timescales of several centuries even with large net negative emissions (Solomon et al 2009, Zickfeld et al 2013, Tokarska and Zickfeld 2015).Secondly, sea level change due to melting and regrowth of ice sheets is strongly non-linear: due to positive feedback mechanisms such as the ice-elevation feedback, a substantial melting of an ice sheet may inhibit its regrowth on long timescales even if the atmospheric CO 2 concentration is substantially reduced (e.g.Solgaard andLangen 2012, Pattyn et al 2018).
One of the main contributors to global sea level rise is melting of the Greenland ice sheet (GIS, Aschwanden et al 2019, Goelzer et al 2020, Muntjewerf et al 2020, Van Breedam et al 2020, Box et al 2022).Previous studies have shown that the GIS features multiple equilibrium states within a global temperature anomaly of 2 K (e.g.Charbit et al 2008, Ridley et al 2010, Robinson et al 2012, Bochow et al 2023, Höning et al 2023), which may be approached depending on the initial ice volume.Specifically, for increasing atmospheric CO 2 starting from pre-industrial conditions, the equilibrium ice volume would first decrease only by a small extent, but if a bifurcation point is crossed, it would decrease substantially (e.g.Gregory et al 2004, Gregory and Huybrechts 2006, Irvalı et al 2020, Armstrong McKay et al 2022).Due to the hysteresis behaviour, if atmospheric CO 2 would then be reduced again, the GIS would not return to its initial state even in the longterm; instead, an atmospheric CO 2 concentration below its pre-industrial value may be required to grow the ice sheet back to its pre-industrial state.In Höning et al (2023), we found two critical thresholds of the GIS and explored the critical cumulative CO 2 emission that would lead to a crossing of these thresholds: a cumulative emission of more than 1000 GtC would cause long-term mass loss of the southern part of the GIS associated with a global long-term sea level rise of 1.8 m.For a cumulative emission of more than 2500 GtC, the entire ice sheet would melt in the long term, associated with a global sea level rise of ≈7 m.
In particular the first threshold is of immediate importance as half of the critical cumulative CO 2 emission to cross this threshold-about 500 GtChave already been released into the atmosphere.If the current annual anthropogenic emission rate of ≈10 GtC yr −1 remains constant in the future, this critical threshold would be crossed in ≈50 years.
The southern part of the GIS would not melt instantaneously as temperature rises.If future technologies allow for atmospheric carbon removal at the scale of many gigatons carbon per year, it might be possible to bring the atmospheric CO 2 concentration back to its pre-industrial level.However, whether or not long-term mass loss of the GIS would thereby be avoided not only depends on the cumulative carbon emission but also on the elapsed time until the preindustrial level of atmospheric CO 2 is restored.
In this paper, we investigate how mass change of the GIS would respond to different anthropogenic cumulative CO 2 emissions followed by artificial carbon removal.We explore different cumulative CO 2 emission scenarios as well as different time spans of elevated atmospheric CO 2 concentrations before artificial carbon removal.Specifically, we focus on the question of to what extent the GIS could be melted so that it would still regrow in case future technologies were able to reduce the atmospheric CO 2 concentration back to its pre-industrial level.

Methods
As in Höning et al (2023), we use the fully coupled Earth system model of intermediate complexity CLIMBER-X (Willeit et al 2022, 2023a, 2023b).The model includes the 3D polythermal ice sheet model SICOPOLIS v5.1 (Greve 1997), which is applied to the GIS at a horizontal resolution of 16 km.Due to the relatively coarse resolution of the ice sheet, we include a parameterization for ice discharge into the ocean (Calov et al 2015).The interface between the ice sheet and the atmosphere is modelled using the surface energy and mass balance scheme SEMI (Calov et al 2005).A representation of the global carbon cycle is also included (Willeit et al 2023a).
A characteristic feature of CLIMBER-X is the fully coupled climate-ice sheet-carbon cycle model setup and the use of a physically based surface energy and mass balance interface.In Höning et al (2023), we compared the SMB from historical runs with CLIMBER-X using prescribed ice sheets with regional climate models and found differences in the spatial patterns but good agreement of the integrated SMB.For more details, the reader is referred to Höning et al (2023).
For the sake of simplicity, the orbital configuration is kept constant at its present-day state.We initialize the GIS using present-day observations and an ice temperature of −10 • C and let the model run for 10 kyr, allowing the ice sheet to reach a quasiequilibrium.We then force the fully-coupled climateice sheet-carbon cycle model with different CO 2 emission pulses with cumulative emissions between 0 and 4000 GtC, evenly spread throughout a time interval of 100 yr.CO 2 is an interactive part of the system and we let the system respond to the elevated atmospheric CO 2 concentration for a fixed period of 1, 2, and 5 kyr.After that, we mimic net carbon removal by prescribing the atmospheric CO 2 concentration to exponentially decrease towards zero and keep it constant as soon as it reaches its pre-industrial value after 1 kyr.In addition, we test a rapid CO 2 removal scenario starting 100 yr after the emission pulse and with a duration of 500 yr.Compared to applying a negative emission pulse, our approach has two significant advantages: First, it bypasses the problem that the carbon removal rate would be required to be continuously adjusted to keep the CO 2 level at pre-industrial values as CO 2 keeps being released from the oceans and other Earth system components over long timescales.Secondly, it avoids the problem that if carbon removal is applied at a too high rate, the atmospheric CO 2 concentration could temporally be smaller than its pre-industrial value.The exponentially-shaped decline towards the preindustrial level is motivated by the fact that carbon removal is more efficient at higher atmospheric CO 2 concentrations (e.g.Tokarska and Zickfeld 2015).We neglect changes in short-lived greenhouse gases like methane in our study, since these are less relevant on the timescale associated with melting of the GIS.Consideration of non-CO 2 greenhouse gases would influence our quantitative results, but not to such an extent that our qualitative conclusions would change.

Results
To explore the response of the GIS volume to changes in the atmospheric CO 2 concentration, we first focus on equilibrium states of the GIS (figure 1), adapted from Höning et al (2023).These states have been derived by running the model at constant atmospheric CO 2 concentration until the GIS volume changes at rate smaller than 1 mm kyr −1 .Starting from the pre-industrial GIS (state A) and increasing atmospheric CO 2 , the GIS follows the solid black curve and passes through a bifurcation point between B and C, thereby melting its southern part.If, starting at point C, the atmospheric CO 2 is reduced again, the GIS follows the dashed black curve and reaches state D at 280 ppm where still a large part of the south remains melted.We note that these states are equilibrium states and that even a short overshoot of a bifurcation point would not necessarily cause the system to irreversibly transition to another stable state.
In our model runs with interactive CO 2 , cumulative emissions between 0 and 4000 GtC result in an elevated atmospheric CO 2 concentration that naturally starts declining shortly after the end of the pulse (figure 2(a)).After 1 kyr (solid), 2 kyr (dashed), and 5 kyr (dashed-dotted curves), the atmospheric CO 2 concentration is set to exponentially decrease until it reaches its pre-industrial value throughout an additional time interval of 1 kyr, thereby mimicking net negative emissions.The atmospheric CO 2 concentration controls the global mean temperature (figure 2(b)).The global mean temperature anomaly temporally rises up to 6 • C for cumulative emissions of 4000 GtC and then continues to follow the fate of declining atmospheric CO 2 .Elevated temperatures GIS volume as a function of time after cumulative emission pulses of 0 (black), 1000 GtC (blue), 2000 GtC (red), 3000 GtC (green), 4000 GtC (yellow).After a time span ∆t of 1 kyr (solid), 2 kyr (dashed), and 5 kyr (dashed-dotted), the atmospheric CO2 concentration is exponentially reduced until it reaches its pre-industrial value after a time interval of 1 kyr and then kept constant.cause a melting of the GIS (figure 2(c)): while small cumulative emissions (1000 GtC, blue curve) lead to only limited mass loss, if at all, higher emission pulses cause significant mass loss, in particular if a long time passes until the atmospheric CO 2 concentration is reduced to its pre-industrial value.It also becomes apparent that once the GIS loses mass to a certain extent (by ≈1 m sea level equivalent sle, such as for 2000 GtC and ∆t = 2 kyr, dashed red curve), the ice sheet does not regrow to its pre-industrial state even after the atmospheric CO 2 is reduced accordingly.
The combination of cumulative CO 2 emission and time interval ∆t before negative CO 2 emissions are applied controls the total mass loss and regrowth of the GIS (figure 3).The fact that the points corresponding to different combinations (colors and shapes of the points in figure 3) lie on the same single line indicates that regrowth of GIS depends on the total mass loss prior to CO 2 removal, rather than on a specific trajectory.Therefore, the two parameters-cumulative CO 2 emission and time span ∆t-can be reduced to single one: the total mass loss before negative CO 2 emission.If the total mass loss before CO 2 reduction is small due to small cumulative emission and/or small ∆t (i.e. points plotted on the left, light red area in figure 3), the GIS can efficiently regrow (small y-values in figure 3(d)).However, once the ice volume crosses a kyr after the pre-industrial atmospheric CO2 level has been restored.Model simulations include cumulative emission pulses between 0 (blue) and 4000 GtC (yellow) and the time span ∆t between the positive emission pulse and the reduction of CO2 to pre-industrial is 1 kyr (circle), 2 kyr (square), and 5 kyr (diamond).In the left, light-red column of each sub-figure, the southern part of the GIS is frozen, in the centre column it is partly melted, and in the right, dark-red column, it is completely melted.The transitions between these columns of 0.26 m sle and 1.8 m sle refer to points B and C in figure 1.The dashed, black lines of 0.93 m sle refers to state D, which is the equilibrium GIS volume anomaly (relative to pre-industrial) for an atmospheric CO2 concentration of 280 ppm if started from point C and subsequently reducing atmospheric CO2 (dashed curve in figure 1).critical threshold (near the transition to the mid-red column), complete GIS regrowth is inhibited.This transition is termed point B and separates an icecovered and a partly melted southern part of the GIS.The transition towards the right, dark-red column is termed point C and indicates the transition towards a completely melted southern part of the GIS.The vertical dashed black line (point D) depicts the equilibrium GIS volume anomaly at 280 ppm if started from point C reducing CO 2 .We also plot this value as a horizontal black dashed line, depicting the ice regrow after CO 2 reduction.We observe that GIS only regrows to this state: once the southern part of the GIS is (partly) melted, this part will not regrow, even if atmospheric CO 2 is reduced to pre-industrial levels.

Discussion
Future artificial carbon removal from the atmosphere is a potential concept to reduce the atmospheric CO 2 concentration in order to limit global warming or even to restore pre-industrial climate conditions.In this paper, we tested this concept with a focus on the crossing of critical thresholds of the GIS that could inhibit regrow.We found that once the GIS has lost mass by more than ≈0.4 m sle, it would not regrow if atmospheric CO 2 is reduced to pre-industrial, independent of the particular combination of cumulative CO 2 emission and time interval before deploying artificial carbon removal.Once the GIS has lost mass by more than ≈0.9 m sle, artificial carbon removal could only lead to a regrow of the GIS up to this value (0.9 m sle mass loss relative to pre-industrial), but not further.The reason for this is the multistability of the GIS due to positive feedback mechanisms.For example, an increase in surface melt enlarges the area at lower elevations exposed to higher air temperatures, which in turn leads to enhanced melt.If a critical threshold is crossed, the equilibrium ice volume would decrease substantially and would not recover even if global temperature declines again (Charbit et al 2008, Ridley et al 2010, Robinson et al 2012, Solgaard and Langen 2012).In our simulations, the multistability is related to a melting of the southern part of the GIS (compare figure 1).
Theoretically, atmospheric CO 2 could be reduced below pre-industrial values, which could allow a regrowth of the GIS despite crossing critical thresholds (compare Höning et al 2023).However, we consider this an extremely unlikely scenario, as already bringing down CO 2 to pre-industrial levels can be considered a big challenge.Reducing CO 2 below pre-industrial levels would also be undesirable as it could trigger a glacial inception over other NH continents, considering that we are at present close to a minimum in NH summer insolation and it has been suggested that at pre-industrial CO 2 concentrations we were close to the bifurcation point to trigger glacial inception (Ganopolski et al 2016, Talento et al 2023).
Ridley et al (2010) used the atmosphere-ocean general circulation model HadCM3 (Pope et al 2000) to study the reversibility of mass loss of the GIS and derived its initial state from a single, high-CO 2 scenario.They found that after restoring pre-industrial atmospheric CO 2 levels, the GIS converges towards three distinct steady states, a pre-industrial GIS, a melted GIS, and an intermediate state.The threshold that prevents the GIS from complete regrowth was found to lie between 80 and 90% of the pre-industrial GIS volume (Ridley et al 2010).This range corresponds to a total mass loss of the GIS between 0.75 and 1.5 sle.In contrast, in the present paper, we used a fully coupled climate-ice sheet-carbon cycle model, which allowed us to combine different CO 2 emission pulse scenarios with different time intervals during which the climate-ice sheet model responds to the elevated temperatures.This approach yields a variety of mass loss scenarios of the GIS that can directly be traced back to the respective emission scenario.Instead of distinct steady states that the GIS approaches, we found that between 0.4 and 0.9 m sle total mass loss, that GIS mass volume hardly changes after the pre-industrial level of atmospheric CO 2 has been restored.This result implies irreversible mass loss of the GIS starting much earlier (for mass loss >0.4 m sle) than found by Ridley et al (2010), although a crossing of this threshold would not apply further, inevitable mass loss towards another steady state after restoring pre-industrial atmospheric CO 2 but rather inhibited regrowth.
Simulating the emission pulses, we assumed an even distribution throughout a time interval of 100 yr, which allows for a straightforward comparison between different cumulative emission scenarios.While the specific shape of the emission pulse may affect mass loss of the GIS within the first few hundred years, it becomes negligible on a millennia timescale (Charbit et al 2008, Höning et al 2023), which is the timescale relevant in this paper.
Instead of applying negative CO 2 emissions pulses, with the onset of artificial carbon removal, we mimicked the latter by prescribing the atmospheric CO 2 concentration to decrease exponentially until it reaches its pre-industrial level over a fixed time interval of 1 kyr and then kept the CO 2 concentration constant.Again, the specific shape of carbon removal is not important for the long-term evolution of the GIS, and our choice has the advantage that the carbon sink does not need to be continuously adjusted when oceans and land reservoirs continue to release CO 2 into the atmosphere over hundreds of years.
Given the large timescale of several tens of thousands of years needed to simulate mass loss and regrowth of the GIS, we chose a relatively coarse ice sheet resolution of 16 km.Using a finer ice sheet resolution would probably be needed to simulate the fate of the ice sheet on a centennial timescale, but on a timescale >1 kyr as relevant for this study, the choice of the resolution is less important (Aschwanden et al 2019).
The choice of the ice sheet model SICOPOLIS could also have an effect on our results.Essential for our findings is the existence of an intermediate stable state where the southern part of the GIS is melted.Using the ice sheet models PISM (Winkelmann et al 2011) and Yelmo (Robinson et al 2020), Bochow et al (2023) explored the response of the GIS to temperature forcing overshooting critical thresholds.While they found several intermediate states between 50% and 90% of the current GIS at 1 • C global mean temperature anomaly with PISM, the ice sheet model Yelmo did not show an intermediate stable state.Both ice sheet models showed a modest sensitivity to warming in the southwest part (Bochow et al 2023).Similar to our results, Bochow et al (2023) concludes that both peak warming at AD 2100 and a reduction of temperature after centuries are essential to mitigate a critical loss of the GIS.
Another key factor of uncertainty is related to the equilibrium climate sensitivity (ECS).The ECS in the standard model is 3 K, which is the best current estimate (IPCC 2021).However, values of 2 K on the lower end and 4.5 K on the upper end cannot be ruled out.To explore the effect of this uncertainty, we have rerun all simulations mimicking ECS values of 2 K and 4.5 K and show the results in figures 4(a)-(f).
As expected, for an ECS of 2 K (figure 4, top row), the temperature anomaly rises up to 4 • C for an emission pulse of 4000 GtC (compared to up to 6 • C for the reference model with a climate sensitivity of 3 K (figure 4(b)), and melting of the GIS is correspondingly smaller (figure 4(c)).Figure 5 indicates that the total mass loss at the end of the simulation as a function of total mass loss directly before the negative emission pulse follows the same single curve as before, with some outliers at high cumulative The time span before negative emissions are applied is 1 kyr (solid), 2 kyr (dashed) and 5 kyr (dashed-dotted), and as in figure 3, the duration of negative emissions is 1 kyr.The bottom row corresponds a scenario of rapid negative emissions (time span before negative emissions are applied of 100 yr and duration of negative emissions of 500 yr), while the climate sensitivity is 3 K.
emissions, which we attribute to the circulation of the southern ocean (not shown here).For cumulative emissions between 1500 and 2250 GtC (depending on the time span before atmospheric CO 2 is reduced), melting of the GIS is so extensive that a complete regrowth is inhibited even if the pre-industrial level of atmospheric CO 2 is restored.For a climate sensitivity of 4.5 K (figure 4, centre row), melting of the GIS is irreversible already for cumulative emissions about 1000 GtC for a time span before atmospheric CO 2 is reduced of 1 kyr.
Finally, melting of the GIS takes time, and in our reference model, we tested time spans before restoring the pre-industrial level of atmospheric CO 2 of 1, 2, and 5 kyr and then reduced atmospheric CO 2 throughout an interval of 1 kyr.Certainly, if artificial carbon removal techniques that are able to remove significant amounts of carbon from the atmosphere were deployed in large quantities within the next decades or centuries, pre-industrial levels of atmospheric CO 2 might be restored before the GIS has lost significant mass (≈0.4 m sle).Figure 4 (bottom row) shows model results using a time span before atmospheric CO 2 is decreased of 100 yr and a time interval throughout which atmospheric CO 2 is decreased of 500 yr (figure 4(a)).We find that in this case even high emissions of 4000 GtC are not sufficient to significantly melt the GIS and restoring its pre-industrial state is therefore feasible.However, this endeavour would require to remove hundreds to thousands of Gt carbon from the atmosphere within the next few centuries.Given the long timescales associated with ice sheet mass loss and regrowth, this carbon would then be needed to be stored over millennia, which only leaves a limited number of relevant carbon removal techniques such as enhanced rock weathering and direct air carbon capture and storage (IPCC 2022).With ongoing anthropogenic CO 2 emissions, pursuing this option would become more and more challenging.Therefore, limiting anthropogenic carbon emissions remains a key factor to avoid irreversible melting of the GIS.4).For comparison, the results from our reference model (figure 3) are plotted in grey colour.

Conclusions
Using the Earth system model of intermediate complexity CLIMBER-X, we explored whether future artificial CO 2 removal could lead to a regrowth of the GIS once it has partly melted.We found that once anthropogenic CO 2 emissions and associated global temperature rise cause the southern part of the GIS to partly melt with a decrease of the total GIS volume by more than ≈0.4 m sle, complete regrowth is inhibited even if the pre-industrial level of atmospheric CO 2 is restored.This finding is attributed to the hysteresis behaviour of the GIS (see also Robinson et al 2012, Höning et al 2023).
The critical cumulative carbon emission that causes a crossing of this threshold depends on the time before negative emissions are realised but also on model-specific parameters, above all the climate sensitivity.For example, for the currently best estimate of a climate sensitivity of 3 K, the threshold is crossed for cumulative emissions between 1250 and 1500 GtC if atmospheric CO 2 is artificially reduced 1 kyr after the emission pulse, but also for cumulative emissions between 1000 and 1250 GtC if CO 2 is artificially reduced 5 kyr after the emission pulse.Allowing for the whole possible range of values for the climate sensitivity between 2 and 4.5 K widens the critical cumulative carbon emission: for example, if CO 2 is artificially reduced 1 kyr after the emission pulse leaves a range between 1000 to 2250 GtC for the critical cumulative carbon emission.In our simulations, only immediate removal (that is, a few centuries after the emission) can avoid long-term mass loss of the GIS.
Despite these quantitative uncertainties, our results highlight the risk that relying on future artificial CO 2 removal techniques while CO 2 continues to accumulate in the atmosphere could cause the Earth system to cross critical thresholds if artificial CO 2 removal is utilized too late.CO 2 removal to restore the pre-industrial level could then avoid further mass loss but would not cause a re-build of the pre-industrial GIS.Keeping cumulative anthropogenic CO 2 emissions below the critical range of ≈1000-1500 GtC is therefore the only save way to avoid significant, irreversible mass loss of the GIS.

Figure 1 .
Figure 1.Equilibrium states of the GIS volume for fixed atmospheric CO2 concentrations starting from pre-industrial GIS following the path of increasing CO2 (solid black curve) and from point B following the path of decreasing CO2 (dashed curve).States A and D both refer to equilibrium states of the GIS at pre-industrial atmospheric CO2, of which state D is reached when starting from the ice sheet at point C reducing atmospheric CO2.The hysteresis diagram covers the upper part of the hysteresis diagram in figure 1 of Höning et al (2023).

Figure 2 .
Figure 2. Simulated (a) atmospheric CO2 concentration, (b) global mean temperature anomaly relative to pre-industrial, and (c)GIS volume as a function of time after cumulative emission pulses of 0 (black), 1000 GtC (blue), 2000 GtC (red), 3000 GtC (green), 4000 GtC (yellow).After a time span ∆t of 1 kyr (solid), 2 kyr (dashed), and 5 kyr (dashed-dotted), the atmospheric CO2 concentration is exponentially reduced until it reaches its pre-industrial value after a time interval of 1 kyr and then kept constant.

Figure 3 .
Figure3.Total GIS volume anomaly (relative to pre-industrial) at the end of the simulation (y-axes) as a function of total GIS volume anomaly right before negative emissions are applied (x-axes).End of simulation is (a) 3 kyr, (b) 6 kyr, (c) 9 kyr, and (d) 12 kyr after the pre-industrial atmospheric CO2 level has been restored.Model simulations include cumulative emission pulses between 0 (blue) and 4000 GtC (yellow) and the time span ∆t between the positive emission pulse and the reduction of CO2 to pre-industrial is 1 kyr (circle), 2 kyr (square), and 5 kyr (diamond).In the left, light-red column of each sub-figure, the southern part of the GIS is frozen, in the centre column it is partly melted, and in the right, dark-red column, it is completely melted.The transitions between these columns of 0.26 m sle and 1.8 m sle refer to points B and C in figure1.The dashed, black lines of 0.93 m sle refers to state D, which is the equilibrium GIS volume anomaly (relative to pre-industrial) for an atmospheric CO2 concentration of 280 ppm if started from point C and subsequently reducing atmospheric CO2 (dashed curve in figure1).

Figure 4 .
Figure 4. Model results using a climate sensitivity of 2 K (top row) and 4.5 K (centre row).The time span before negative emissions are applied is 1 kyr (solid), 2 kyr (dashed) and 5 kyr (dashed-dotted), and as in figure3, the duration of negative emissions is 1 kyr.The bottom row corresponds a scenario of rapid negative emissions (time span before negative emissions are applied of 100 yr and duration of negative emissions of 500 yr), while the climate sensitivity is 3 K.

Figure 5 .
Figure 5.Total mass loss 12 kyr after the negative emission as a function of the total mass loss before the negative emission.(a) Climate sensitivity of 2 K, (b) climate sensitivity of 4.5 K, and (c) a scenario of rapid negative emissions with a time span before negative emissions are applied of 100 yr and a duration of negative emissions of 500 yr (compare figure4).For comparison, the results from our reference model (figure3) are plotted in grey colour.