Earth system responses to carbon dioxide removal as exemplified by ocean alkalinity enhancement: tradeoffs and lags

Carbon dioxide removal (CDR) is discussed for offsetting residual greenhouse gas emissions or even reversing climate change. All emissions scenarios of the Intergovernmental Panel on Climate Change that meet the ‘well below 2 °C’ warming target of the Paris Agreement include CDR. Ocean alkalinity enhancement (OAE) may be one possible CDR where the carbon uptake of the ocean is increased by artificial alkalinity addition. Here, we investigate the effect of OAE on modelled carbon reservoirs and fluxes in two observationally-constrained large perturbed parameter ensembles. OAE is assumed to be technically successful and deployed as an additional CDR in the SSP5-3.4 temperature overshoot scenario. Tradeoffs involving feedbacks with atmospheric CO2 result in a low efficiency of an alkalinity-driven atmospheric CO2 reduction of −0.35 [−0.37 to −0.33] mol C per mol alkalinity addition (skill-weighted mean and 68% c.i.). The realized atmospheric CO2 reduction, and correspondingly the efficiency, is more than two times smaller than the direct alkalinity-driven enhancement of ocean uptake. The alkalinity-driven ocean carbon uptake is partly offset by the release of carbon from the land biosphere and a reduced ocean carbon sink in response to lowered atmospheric CO2 under OAE. In a second step we use the Bern3D-LPX model in CO2 peak-decline simulations to address hysteresis and temporal lags of surface air temperature change (ΔSAT) in an idealized scenario where ΔSAT increases to ~2 °C and then declines to ~1.5 °C as result of CDR. ΔSAT lags the decline in CO2-forcing by 18 [14–22] years, depending close to linearly on the equilibrium climate sensitivity of the respective ensemble member. These tradeoffs and lags are an inherent feature of the Earth system response to changes in atmospheric CO2 and will therefore be equally important for other CDR methods.


Introduction
Human-caused emissions of carbon dioxide and other agents cause global warming and dangerous anthropogenic interference in the Earth system (Siegenthaler and Oeschger 1978).Climate targets are designed to inform policies that would limit the magnitude and impacts of climate change caused by anthropogenic emissions of greenhouse gases and other substances.The Paris Agreement sets a target for the global mean air temperature to 'Holding the increase in the global average temperature to well below 2 • C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5 • C above pre-industrial levels, recognizing that this would significantly reduce the risks and impacts of climate change.'(United Nations 2015).
Future emissions and concentration pathways toward meeting the Paris Agreement as well as other scenarios are typically developed with integrated assessment models (IAMs) (Riahi et al 2017, Rogelj et al 2018).The IAM scenarios that are roughly compatible with the goals of the Paris Agreement all require in the first place the rapid and global-scale deployment of non-fossil energy production from renewable sources such as solar or wind.Additionally, these 'low' emissions pathways, such as SSP5-3.4-OSor SSP1-2.6, with a forcing ceiling of 3.4 and 2.6 Wm −2 , respectively, require the application of carbon dioxide removal (CDR) technologies (Smith et al 2016, Fuss et al 2018).Under CDR, CO 2 emissions are directly or indirectly removed from the atmosphere for long-term storage.Different CDR approaches have been proposed (see e.g.Smith et al 2016, Minx et al 2017, 2018, for an overview).Very roughly, these approaches can be split among the reservoir where the activity occurs: land-based, ocean-based, and direct air capture.A further distinction can be made between methods that seek to accelerate the uptake of atmospheric CO 2 by enhancing natural sinks and methods that seek to engineer the removal and subsequent storage of CO 2 .An ocean-based approach that seeks to enhance a natural process called chemical weathering, which naturally removes up to 0.29 GtC yr −1 (Hartmann et al 2009), is ocean alkalinity enhancement (OAE, Ilyina et al 2013, González and Ilyina 2016, Caserini et al 2022), which is the addition of alkalinity to the surface ocean.This might be achieved by adding minerals (e.g.lime, limestone, olivine) or metal oxides to the ocean that dissolve in seawater.The increase in alkalinity then allows the ocean to absorb additional CO 2 from the atmosphere and permanently store it as bicarbonate or carbonate ions (Renforth andHenderson 2017, Campbell et al 2022), but there are significant barriers and uncertainties for effective OAE, e.g.related to scale (Köhler et al 2013), dissolution kinetics, and potential ecological impacts (Fakhraee et al 2023), as well as socio-economic concerns, e.g.public acceptance, governance, and costs (Cooley et al 2023).
An important question to address under CDR is how the Earth system in general, and its carbon inventories in particular, respond to CDR (Keller et al 2018a).The artificial direct removal of CO 2 from the atmosphere influences carbon fluxes between the atmosphere and land and ocean and leads to less carbon uptake than without CDR (Jeltsch-Thömmes et al 2020).Similarly, tradeoffs in carbon fluxes and inventories can also be expected under ocean-and land-based CDR approaches.Another question is related to inertia and (ir-)reversibility in the climate system (Frölicher and Joos 2010).For example, ocean deoxygenation and sea level rise continue for centuries to millennia after emissions stoppage (Clark et al 2016, Battaglia and Joos 2018, Oschlies 2021 Here, we apply ensembles of two Earth System Models of Intermediate Complexity, the Bern3D-LPX and the University of Victoria Earth System Climate Model (UVic-ESCM), in a probabilistic observationconstrained framework to investigate the effect of OAE on carbon fluxes and inventories and climate in the SSP5-3.4overshoot scenario.SSP5-3.4covers the main driver of global warming-fossil CO 2and a wide range of other forcing agents and precursors with complex temporal evolution.This complexity may partly obscure forcing-response relationships.Therefore, we specifically investigate the timescales connected with the reversibility of surface air temperature (SAT) in an idealized CO 2only overshoot scenario.We address the following questions: (i) What is the trade-off in carbon storage between the atmosphere, ocean, and land under OAE and what does this mean for the efficiencies (ε) of OAE to increase ocean carbon storage and to lower atmospheric CO 2 ?(ii) What is the role of Earth system inertia in CO 2forcing overshoot (peak-decline) scenarios?How long does it take for global-mean SAT to return to the value passed under increasing forcing?From the historical run, future scenarios are branched off (see figure 1) and run until 2100 CE (UVic-ESCM) or 2300 CE (Bern3D-LPX).Emissions follow data from the SSP database (Riahi et al 2017), land-use forcing data from Hurtt et al (2020), and other forcing according to Dentener et al (2021).From the different scenarios, the SSP5-3.4overshoot scenario (from hereon SSP5-3.4) is run once in its regular design and once with additional OAE.Under OAE, alkalinity is added uniformly to the ice-free surface ocean grid cells between 60 • S and 70 • N. OAE begins in the year 2025 CE and is linearly ramped up to its maximum value of 0.1375 Pmol yr −1 (0.135 in the case of UVic-ESCM) at the start of the year 2035 CE and constant thereafter.At the end of year 2220 CE, OAE is abruptly stopped and kept at zero thereafter.

Methods
In addition to the OAE experiment on top of SSP5-3.4,we conduct an idealized CO 3 peak-decline experiment with the Bern3D-LPX ensemble.In this experiment, atmospheric CO 2 is assumed to increase exponentially from the pre-industrial level of 276.58 ppm to 648 ppm within 116 years.Afterward, CO 2 declines at the same rate until stabilization at 431 ppm (figures 1(c) and 4(a)).This decline can be thought of as the result of any kind of CDR.The CO 2 -forcing corresponds to a linear increase in radiative forcing to 4.5 Wm −2 and a decrease to 2.4 Wm −2 and was selected to result in a peak warming of 2 • C followed by a cooling to 1.5 • C when applying the Bern3D-LPX standard parameters.
Ensemble generation, sampled parameters, and calculation of ensemble member skill scores differ slightly between the two models.In the case of Bern3D-LPX, a 1000-member perturbed parameter ensemble was generated where 27 key model parameters were sampled using Latin Hypercube sampling (McKay et al 1979).The perturbed model parameters affect the diffusivities in atmosphere and ocean, atmosphere-ocean gas transfer, the radiative forcing from greenhouse gases and aerosols, terrestrial photosynthesis, hydrology, vegetation dynamics, soil organic matter decomposition, and turnover, as well as the nominal climate sensitivity of the model (see table 1 in the SI).The selection of parameters builds upon earlier work (Steinacher et al 2013, Steinacher and Joos 2016, Lienert and Joos 2018), by choosing the prior distributions of the parameters for this study according to constrained posterior distributions from the studies above.
In the case of UVic-ESCM, 18 model parameters were perturbed, representing important processes in all the main components of the model, i.e. atmospheric energy and moisture balance, climate sensitivity, ocean physics, ocean biogeochemistry, terrestrial biogeochemistry, and the cryosphere.To reduce uncertainties, we exploit a broad set of observation-based data (SI figure 1 and SI tables 2 and 4) and constrain both model ensembles to realizations that are compatible with observations, thereby probing both, the mean state and the transient response in space and time of the ensemble members.The data set combines information from satellite, ship-based, ice-core, and in-situ measurements and includes estimates of SAT change, ocean heat uptake, seasonal and decadal atmospheric CO 2 change, and ocean and land carbon uptake rates, eight physical and biogeochemical three-dimensional ocean tracer fields, including carbon isotopes, as well as land carbon stocks, fluxes, and fraction of absorbed radiation.

Results
Mean projections for CO 2 and SAT change since pre-industrial (∆SAT) agree between the two model systems within uncertainties (figure 1).Uncertainty estimates are similar for CO 2 but larger in ∆SAT for the constrained Bern3D-LPX ensemble than the constrained UVic-ESCM-emulator ensemble (right panels in figures 1(c) and (d)).The cumulative mean ocean uptake until 2100 CE across the different scenarios is larger by ~50-100 GtC in the Bern3D-LPX than in the UVic-ESCM ensemble.On the other hand, land biosphere uptake is ~50-100 GtC larger in UVic-ESCM than in Bern3D-LPX, leaving the total land-ocean sink more similar across the two model ensembles.Bern3D-LPX is known to feature a relatively weak terrestrial carbon sink in comparison to observational estimates (Lienert and Joos 2018).

Changes and trade-offs in the global carbon sinks, atmospheric CO 2 , and the efficiency of CDR
Under CDR, the ocean stores more carbon as a result of OAE.However, Earth system feedbacks linked to atmospheric CO 2 partly offset the direct alkalinitydriven ocean uptake.We use the symbol δ to denote the difference in carbon inventories between simulations with and without OAE.
In simulations with prescribed CO 2 and, thus, with suppressed feedback from δCO 2 , δocean is quantified to 251 GtC (20.9 Pmol) in response to the addition of 26.26 Pmol of alkalinity until the end of the year 2220 CE for the standard parameter Bern3D-LPX ensemble member.The massive application of OAE would thus allow for an additional 251 GtC of emissions until 2220 CE while keeping CO 2 at the same level as without OAE.
We define the efficiency of alkalinization, ε δinventory , as the ratio of δinventory per unit alkalinity added in mol (i.e.mol carbon per mol alkalinity, table 1).Then, for the ocean, ε δocean is 0.8 mol mol −1 (20.9 Pmol/26.26Pmol).The atmospheric CO 2 reduction (δatm) in the corresponding emission-driven (superscript e), δCO 2 -feedbackenabled simulations with the full ensemble amounts to In conclusion, ~56% of the alkalinity-driven ocean uptake is offset by a reduction in the land and ocean sink due to lower CO 2 in the δCO 2 -feedbackenabled simulations with freely evolving atmospheric CO 2 at the end of OAE in year 2220.Similar tradeoffs hold for other CDR methods and vice-versa for Table 1.Efficiency (ε δinventory ) of OAE for the ocean and atmosphere carbon reservoirs in concentration-driven (no CO2-feedbacks) and emissions-driven (superscript e) simulations for the Bern3D-LPX and UVic-ESCM (where available).In the emission-driven case, skill-weighted mean and 68% c.i. are shown, while for the concentration-driven case, values from the standard parameter Bern3D-LPX ensemble member are reported.positive emissions, where only a fraction accumulates in the atmosphere (airborne fraction).Although absolute numbers differ (table 1), the same behavior is apparent for the UVic-ESCM ensemble: an increased ocean carbon sink as a result of OAE is partly offset by reduced uptake/release of land carbon, leading to lower atm.CO 2 as compared to no OAE (figure 2).The relationship between δland, δocean and δatm is visualized for individual Bern3D ensemble members at the end of OAE application (figure 2(d)).In general, there is a negative relationship between δocean and δland: the larger δocean, the larger δland carbon due to OAE.Largest reductions in atmospheric CO 2 (δatm) are achieved for large δocean in interplay with small δland sources.

Spatial patterns in carbon sinks
Next, we discuss where the carbon is stored which is taken out of the atmosphere under SSP5-3.4(∆C) and additionally in response to OAE (δC; SSP5-3.4+OAEminus SSP5-3.4).The simulated spatial pattern for the column inventory of ∆DIC (figures 3(a) and (b)) is similar to reconstructions of historical anthropogenic carbon uptake (Sabine et al 2004), with large inventories in the North Atlantic and Antarctic Intermediate Waters.The pattern of the OAE-driven DIC increase, δDIC, is similar to that of ∆DIC (figure 3) despite alkalinity being added uniformly to the ice-free surface ocean between 60 • S and 70 • N. Simulations with dye tracers and further analyses imply that the high δDIC column inventories in the Atlantic result primarily from circulation, causing a net transport of δDIC from the Indo-Pacific into the Atlantic, with modifications by carbon-climate feedbacks (see also Supplementary Information).On land, the pattern of changes in carbon storage under SSP5-3.4 is diverse and certain regions change from a carbon sink in 2069-2100 CE to a source in 2269-2300 CE (cf figures 3(a) and (b)).With OAE, the land biosphere loses carbon almost everywhere compared to SSP5-3.4 due to lower CO 2 (figures 3(c) and (d)).

Temporal lags in an idealized overshoot scenario
The question addressed in this section is to which extent climate change lags behind a decline in CO 2 achieved by a successful implementation of CDR.In other words, how long does it take for Earth system responses to manifest after the implementation of CDR.For illustration, we analyse the ∆SAT results from the idealized CO 2 peak-decline experiment conducted with the Bern3D-LPX model.
Earth system inertia causes ∆SAT to lag the decline in CO 2 (figures 4(a) and (b)).In response to the CO 2 forcing, ∆SAT peaks at 2.0 The temporal lag of the decline in ∆SAT behind the declining forcing is quantified following the schematic of figure 4(a).When CO 2 reaches 541 ppm (corresponding to 1.5 • C warming with the Bern3D-LPX standard parameter set), ∆SAT is 1.5 [1.3-1.7]• C during the warming phase at time t 1 but 1.8 [1.6-2.1]• C during the cooling phase at t 3 .The additional time, τ lag , required for ∆SAT to return to the value simulated at t 1 is 18 [14-22] years (figure 4(b)).τ lag increases close to linearly with ECS (and consequently with TCR) and is around 20 years for an equilibrium climate sensitivity (ECS) of 3 • C (figure 4(c)).This relationship can be understood, simply put, as the more heat has accumulated (in the ocean), the longer it takes to get rid of this heat again.We conclude that inertia in the climate system causes the reduction in global warming to lag behind the implementation of CDR and the reduction in radiative forcing by several decades.

Discussion & summary
There are several implications from our study.First, the impact of CDR on atmospheric CO 2 will always be partly offset by subsequent weakened land and ocean carbon sinks, or even carbon losses, resulting in a muted atmospheric CO 2 reduction (e.g.Keller et al 2014, 2018a, González and Ilyina 2016, Jones et al 2016, Lenton et al 2018, Schwinger et al 2022).Here, we find in emission-driven simulations the effect of OAE on atmospheric CO 2 being partly offset by a loss of carbon from the land biosphere and a reduced marine carbon uptake in response to lower CO 2 with than without OAE.These responses in land and ocean uptake to OAE are in line with earlier studies (e.g.Keller et al 2014, González and Ilyina 2016, Lenton et al 2018), and further provide a longer perspective with simulations extending until 2300 CE, which seems important for the consideration of land biosphere effects (figure 1).A novel finding of our study is that the efficiency of OAE, defined as mol ocean carbon uptake per mol alkalinity added to the ocean, is about 40% lower in emission-driven than concentration-driven simulations (table 1) and the atmospheric carbon inventory is reduced by only −0.35 [−0.37 to −0.33] mol C per mol alkalinity in the emission-driven Bern3D-LPX simulations.The atmospheric reduction by OAE is less than half of the direct alkalinity-driven enhancement of ocean uptake.Results from the UVic-ESCMemulator ensemble, run until 2100 CE, support these findings.The same effects will hold for other oceanbased and vice versa for land-based CDRs (Oschlies 2009).The effectiveness of CDR in lowering atmospheric CO 2 (and thereby temperature) is therefore dependent on the response of the ocean and land biosphere to altered CO 2 and climate.The low efficiency of CDR in reducing atmospheric CO 2 , as identified in this study, should arguably be considered when discussing the implementation of OAE and other CDR methods.Future research could investigate the efficiencies of a portfolio of simultaneous land-and ocean-based CDR applications.
Second, in overshoot scenarios, the timing of the peak, the decline, and the stabilization deviates between the forcing and the SAT response, leading to hysteresis (Boucher et al 2012, Zickfeld et al 2016).Hysteresis of SAT in the cumulative emission space has been shown to increase with higher ECS (Jeltsch-Thömmes et al 2020), while the lag, or lead, of maximum warming with respect to maximum forcing seems to depend on the zero emissions commitment, i.e. the warming, or cooling, after emission stoppage (Koven et al 2022(Koven et al , 2023)).Joos et al (2013), based on 100 GtC pulse-release experiments, determined peak warming to lag the CO 2 emissions pulse by about 10 years.The lag results from an interplay of carbon cycle dynamics, climate sensitivity, and ocean thermal inertia and is influenced by the size of the emissions pulse (Zickfeld and Herrington 2015).
Here, using an idealized scenario, we find the response in ∆SAT to lag behind the declining forcing by about two decades (τ lag : 18 [14-22] years) for a threshold temperature of around 1.5 • C (figure 4).The exact value of the lag depends on the scenario choice and the selected threshold.τ lag increases ~linearly with ECS.The higher the ECS and thus the more heat has accumulated in the system, the larger τ lag as it takes longer to get the excess heat out of the system (see figure 4(c)).This finding underlines the importance of considering uncertainties in our quantitative understanding of the Earth system reflected in the uncertainty of climate metrics such as, for example, the ECS.
There are limitations to our study.We apply Earth system models of intermediate complexity, in which many processes are highly parameterized.Examples include the remineralization of organic matter in the ocean or atmospheric heat and water fluxes following an energy-moisture balance.
For UVic, Gaussian Process emulation was applied to sample the 18-dimensional parameter space.An unavoidable trade-off exists between accuracy and efficiency as a result of using a fast statistical estimation to model the climate model's behaviour.The advantage of Gaussian Process emulation is that it provides an estimation of the uncertainty stemming from the emulator itself, and we take this uncertainty into account when computing the skill scores to weigh the ensemble (Supplementary Information).Another issue arising from the use of statistical estimation is that the quantities being emulated are not physically consistent, and therefore, mass conservation is not guaranteed.For instance, uncertainties in the emulated atmospheric, land, and ocean carbon budgets mean that the three terms do not necessarily sum to zero.Nevertheless, these simplifications and the low computational cost allow for large perturbed parameter ensembles, constraining these large ensembles with observational estimates, assigning skill scores to individual ensemble members, and enabling the calculation of probabilistic estimates of changes.For Bern3D-LPX, emulation was not needed and the 27dimensional parameter space was explored with the coupled Bern3D-LPX.
Our application of OAE is idealized and neglects any barriers by assuming a linear increase in OAE capacity starting in 2025 CE up to a maximum deployment of 0.1375 Pmol yr −1 in 2035 CE.It is debatable, whether the amount of the maximum deployment is realistic at all (Köhler et al 2013), as it would mean mining, transporting, and distribution in the vast ocean ~5 Pg of an alkalizing agent such as Ca(OH) 2 (see Keller et al 2018b) every year.Fakhraee et al (2023) discuss in detail the attenuation of alkalinity release in the surface ocean through the removal (sinking) of particles prior to full dissolution.In their modeling study, they find that crystalline basalt and olivine release only <10% and ~50% of the alkalinity in the surface ocean (<80 m), respectively, while the effectiveness of alkalinity release is higher for artificial alkalizing agents such as MgO and CaO. Further, Fakhraee et al (2023) show a negative impact of olivine and basalt deployment on the marine biological pump based on their modeling study, while Ferderer et al (2022) find only moderate effects on various phytoplankton groups but a reduction in diatom biogenic silica buildup and silicic acid drawdown under OAE in microcosm studies.Another possible limitation of massive OAE relates to the secondary precipitation of CaCO 3 as a result of high alkalinity concentrations (Moras et al 2022, Hartmann et al 2023).The precipitation of CaCO 3 would reduce alkalinity and DIC in a 2:1 ratio, thereby shifting the acid-base balance towards higher CO 2 and, in turn, causing outgassing of CO 2 from the surface ocean to the atmosphere (e.g.Sarmiento and Gruber 2006).Further, the applied OAE comes on top of CDR already included in the SSP5-3.4scenario itself.However, the primary aim of this study is to investigate trade-offs in the carbon cycle and temporal lags under ocean-based CDR, putting the technical or societal feasibility of such an approach aside.
In summary, OAE leads to additional uptake of carbon by the ocean, thereby lowering atmospheric CO 2 .This additional uptake from the atmosphere is partly offset by the release of carbon from the land biosphere and reduced ocean uptake under lower CO 2 .Generally, the effectiveness of any CDR method in reducing atmospheric CO 2 and warming is muted by the response of the land and ocean carbon pools.
The parameter selection builds upon previous works exploring model parametric uncertainty and sensitivity analysis(Goes et al 2010, Olson et al 2012,  MacDougall and Knutti 2016, Mengis 2016, Ehlert et al 2017, Tran et al 2020).As the UVic-ESCM is more computationally expensive, running thousands of simulations to thoroughly explore the 18dimension parameter space is not practical.Instead, we used Gaussian process emulation(Sacks et al  1989, Kennedy and O'Hagan 2001, Rasmussen and  Williams 2006)  in combination with history matching(Andrianakis et al 2015, Williamson et al 2017)  to efficiently sample the inputs of interest and to serve as a statistical proxy for the full model.More details on sampled ranges of the parameters can be found in the Supplementary Information.

Figure 1 .
Figure 1.Time series of prescribed (a) fossil-fuel (FF) CO2 emissions, (b) total non-CO2 radiative forcing and simulated (c) atmospheric CO2, (d) surface air temperature (SAT, relative to 1850-1900 CE), (e) cumulative atmosphere-ocean carbon flux, and (f) cumulative atmosphere-biosphere carbon flux.For the Bern3D-LPX model the skill-weighted mean (solid lines) and 68% confidence interval (c.i., shading) and for the UVic-ESCM model the skill-weighted mean (dashed lines) are shown.Black arrows indicate the difference (δ) between SSP5-3.4 with and without OAE.Panels on the right of subplots (c)-(f) show the 68% c.i. of the skill-weighted ensemble in the year 2100 CE.Cumulative carbon fluxes prior to 1850 (simulation start of the UVic-ESCM ensemble) of Bern3D-LPX have been added to UVic-ESCM data in panels (c) and (d).Forcing of SSP5-3.4 + OAE is the same as SSP5-3.4without OAE in panels (a) and (b).

Figure 2 .
Figure 2. Potential impacts of ocean alkalinization on major carbon inventories.Timeseries illustrating the temporal evolution and ensemble spread (±1σ and ±2σ) in the (a) annual-mean atmospheric carbon inventory, the cumulative (b) air-sea, and (c) air-land carbon flux differences (δ) between [SSP5-3.4+OAEincluding artificial ocean alkalinization] minus [SSP5-3.4]for the Bern3D (orange) and UVic-ESCM (green) ensembles.(d) scatterplot summarizing mean changes (prior to OAE stoppage, 2190-2220) in the three carbon reservoirs for individual Bern3D ensemble members (crosses).Note in (c) also the skill-weighted mean response in the soil and vegetation carbon pool for Bern3D-LPX is shown (black dashed and dotted line).

Figure
Figure Skill-weighted mean changes (∆) in ocean and land carbon inventory under SSP5-3.4from the Bern3D-LPX for the period (a) 2069-2100 CE and (b) 2269-2300 CE relative to the 1850-1900 CE period as well as (c) and (d) the differences between SSP5-3.4 including ocean alkalinity enhancement (OAE) and SSP5-3.4(δ) for the same periods.
3], declines afterward to a minimum of 1.3 • C [1.1-1.5] and slowly increases by about 0.1 • C [0.1-0.2] over the next 300 years under constant CO 2 and thus radiative forcing (figure 4(b)).Peak ∆SAT lags peak forcing by 5 [4-6] years and minimum ∆SAT is reached 47 [35-66] years after forcing has stabilized.Uncertainty in ∆SAT increases over time (purple shading in figure 4(b), as individual ensemble members reach their respective ∆SAT maximum/minimum at different times.

Figure 4 .
Figure 4. Idealized simulations to address temporal lags in overshoot scenarios.(a) Schematic how τ lag is determined.Threshold ∆SAT is determined for each ensemble member at t1, where CO2 = 541 ppm (corresponding to 1.5 • C warming with the Bern3D-LPX standard parameter set).t2 indicates the time at peak CO2 and t3 when CO2 is the same as at t1. t4 is the time when ∆SAT reaches the threshold value and τ lag = t4-t3.(b) Temporal evolution of simulated ∆SAT (skill-weighted ensemble mean and 68% c.i.; purple line and shading, right y-axis) and prescribed CO2 (black line, left y-axis).(c) Scatter plot of τ lag vs. equilibrium climate sensitivity (ECS, see also the discussion) for individual ensemble members (crosses); colors show cumulative ocean heat uptake until peak CO2 (∆OHC peak ).Only ensemble members are included with ∆SAT reaching again the threshold value within an uncertainty of 0.1 • C.
). Temperature and other, Boucher et al 2012levated for decades even after emissions have peaked and declined(Frölicher and Joos 2010, Boucher et al 2012, MacDougall 2013, Tokarska and Zickfeld 2015,  Zickfeld et al 2016, Tokarska etal 2019, Jeltsch-Thömmes et al 2020, Schwinger et al 2022).It is therefore important to study and quantify inertia and hysteresis in the Earth system.Previous model studies have investigated various aspects of OAE in both CO 2 -driven (e.g.Köhler et al 2013, Burt et al 2021, Wang et al 2023) and emission-driven simulations (e.g.Keller et al 2014, González and Ilyina 2016, Lenton et al 2018, Köhler 2020) and ranging from box-models (e.g.Köhler et al 2013) to highly-resolved regional ocean models (e.g.Wang et al 2023).Investigated aspects include questions related to regional vs. global OAE application and responses (e.g.González and Ilyina 2016, Lenton et al 2018, Burt et al 2021), dissolution of alkaline minerals and potential effects on marine biota (e.g.Köhler et al 2013, Fakhraee et al 2023), and OAE stoppage (e.g.Keller et al 2014).While some of the studies touch upon the partitioning of carbon between atmosphere, land, and ocean, to our knowledge no study has yet systematically investigated the tradeoffs in carbon storage between these carbon reservoirs and what it means for the efficiency (ε) of OAE to increase ocean carbon storage and to lower atmospheric CO 2 .Further, to our knowledge large perturbed parameter ensemble studies investigating OAE have not yet been conducted and thus a knowledge gap about uncertainties remains.
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