Much of zero emissions commitment occurs before reaching net zero emissions

We explore the response of the Earth’s coupled climate and carbon system to an idealized sequential addition and removal of CO2 to the atmosphere, following a symmetric and continuous emissions pathway, in contrast to the discontinuous emissions pathways that have largely informed our understanding of the climate response to net zero and net negative emissions to date. We find, using both an Earth system model and an ensemble of simple climate model realizations, that warming during the emissions reduction and negative emissions phases is defined by a combination of a proportionality of warming to cumulative emissions characterized by the transient climate response to emissions (TCRE), and a deviation from that proportionality that is governed by the zero emissions commitment (ZEC). About half of the ZEC is realized before reaching zero emissions, and the ZEC thus also controls the timing between peak cumulative CO2 emissions and peak temperature, such that peak temperature may occur before peak cumulative emissions if ZEC is negative, underscoring the importance of ZEC in climate policies aimed to limit peak warming. Thus we argue that ZEC is better defined as the committed warming relative to the expected TCRE proportionality, rather than as the additional committed warming that will occur after reaching net zero CO2 emissions. Once established, the combined TCRE and ZEC relationship holds almost to complete removal of prior cumulative CO2 emissions. As cumulative CO2 emissions approach zero through negative CO2 emissions, CO2 concentrations drop below preindustrial values, while residual long-term climate change continues, governed by multicentennial dynamical processes.


Introduction
Current climate policy is informed by the idea that the magnitude of global warming is proportional to cumulative CO 2 emissions (IPCC 2013(IPCC , 2021. This relationship emerges from complex interactions between the physics and biogeochemistry of the Earth system, and has been consistently found under scenarios of positive CO 2 emissions (Allen et al 2009, Matthews et al 2009. The simplicity and pathindependence of the relationship allow the creation of a remaining carbon budget consistent with limiting warming to a specific level. However, the pathindependence of the relationship between warming and cumulative CO 2 emissions, known as the transient climate response to cumulative CO 2 emissions (TCRE), is only approximate-for example it is possible that some CO 2 -driven temperature change will occur after emissions cease, which can be quantified as the zero emissions commitment (ZEC) (Matthews and Caldeira 2008, Solomon et al 2009, Jones et al 2019, that is used alongside the TCRE in constructing a remaining carbon budget for climate stabilization for policy applications .
The modeled proportionality of warming to cumulative emissions, despite emerging from complex and at least partially coincidental interactions (Raupach 2013, Goodwin et al 2015, MacDougall and Friedlingstein 2015, holds to a remarkably high amount of cumulative emissions (Tokarska et al 2016, Koven et al 2022. Likewise, under negative CO 2 emissions, the proportionality of warming to cumulative CO 2 emissions still holds as cumulative emissions decrease, subject to an asymmetry governed by the ZEC (Koven et al 2022) in both idealized (Tokarska et al 2019) and scenario-driven (Koven et al 2022) experiments for overshoots up to ∼300 PgC. Thus, a hypothetical framework for highly mitigated scenarios is that long-term warming equals the cumulative emissions times TCRE plus a committed ZEC value, which may hold from net zero to net negative emissions. While the expected time lag between CO 2 emissions and CO 2 -driven warming is only about a decade (Ricke and Caldeira 2014), the controls of that lag remain insufficiently quantified. The idealized experiments used to quantify TCRE and ZEC, where TCRE is the warming during the exponential CO 2 concentration growth phase (Arora et al 2020) and ZEC is the subsequent warming after emissions instantaneously go to zero (Jones et al 2019, MacDougall et al 2020 do not allow assessment of when ZEC may occur as emissions decrease on the path to net zero or net negative CO 2 emissions. It is also not clear how far the relationship between warming, cumulative emissions and ZEC described above would hold under negative emissions. Here we ask whether temperature remains proportional to cumulative emissions, plus a ZEC value, as far as to the removal of all anthropogenic CO 2 emissions in pursuit of restoring the climate system to a preindustrial-like state, which we term a restoration scenario. Previous work on the reversibility of climate change under declining CO 2 has used timereversed CO 2 concentration scenarios, with either idealized (Boucher et al 2012, Zickfeld et al 2016, Keller et al 2018, MacDougall 2019, Ziehn et al 2020 or scenario-driven (MacDougall 2013, John et al 2015 experiments. These experiments find asymmetries in the climate and carbon cycle with respect to changing CO 2 concentrations, e.g. that there is a substantial lag between global temperature change and CO 2 concentrations after concentrations reversal (Lee et al 2021). While, in general, concentration-driven experiments can be used to infer emissions and thus frame climate outcomes in terms of compatible emissions, the abrupt reversal from increasing to declining CO 2 concentrations in some of these scenarios requires a highly discontinuous emissions timeseries. For example in the Coupled Model Intercomparison Project phase 6 (CMIP6) Carbon Dioxide Removal Model Intercomparison Project (CDRMIP) 1% yr −1 concentration reversal, this requires instantly changing emissions by ∼50 PgC yr −1 from large positive to large negative values (figure S1(a)). Because the inertia of the Earth system acts like a low-pass filter, it is possible that this abrupt and very large change in emissions, which also holds for pulse CO 2 emission or removal experiments (Ricke andCaldeira 2014, Zickfeld et al 2021), pushes the path-independence of the TCRE to the point where it may no longer hold on shorter timescales. For example, in idealized 1% yr −1 reversal experiments, the proportionality of warming to cumulative emissions does not generally hold, as global temperatures are warmer for a given level of emission during the negative emissions period than during the positive emissions period (Zickfeld et al 2016), which we also find for the CMIP6 CDRMIP ensemble mean (figure S1(b)). In scenario-based overshoot projections, the transition from positive to negative emissions takes decades (figure S2), thus such large abrupt emissions changes are unlikely to occur. MacDougall (2019) also argue against the abrupt emissions changes required for exponential concentrations reversals and propose as a solution a logistic CO 2 concentration pathway. We argue that forcing with CO 2 emissions rather than concentrations has a further benefit of more cleanly separating the peak emissions amount and the timing of net zero as independent rather than dependent variables of the scenario design.
We thus design an idealized emissions-driven carbon dioxide removal (CDR) experiment with the following three goals: we seek first to avoid sharp discontinuities in emissions, so as not to break the path-independence of the TCRE relationship or the timing of ZEC emergence due to any such discontinuities; second to have roughly exponential rampup of emissions early in the scenario to match the shape of historical emissions, and third to keep emissions symmetric in time before and after net zero to explore asymmetries in carbon fluxes and climate responses with respect to emissions. A simple experimental design that satisfies these criteria is for cumulative CO 2 emissions to follow a Gaussian curve over a given interval, and thus annual emissions follow the first derivative of a Gaussian. We force climate models under this scenario, with cumulative emissions reaching a maximum of 1000 PgC after 150 years of simulation and returning to zero after 300 years (figures 1(a) and (b)). This climate restoration experiment allows us to ask three related questions: (a) how would the Earth system respond to the removal of all previously-emitted CO 2 and thus cumulative net zero CO 2 emissions, (b) what are the lags and asymmetries of the transient response of climate and carbon cycle dynamics to a symmetric shift from positive to negative CO 2 emissions, and (c) how does the ZEC impact the relative timing between peak cumulative emissions and peak warming?

Methods
The annual emissions timeseries E(t) [PgC yr −1 ] for year t follows the form of the first derivative of a Gaussian curve: We use values of a (maximum cumulative emissions) of 1004 PgC, b (year of peak cumulative emissions) of year 150, and c (timescale for emissions reversal) of 45. We use a of 1004 PgC, rather than 1000 PgC, because the cumulative emissions at year 1 is 4 PgC, thus the total integrated emissions over the period years 1-150 is 1000 PgC, and years 151-300 is −1000 PgC. After year 300, we set annual emissions to zero. Emission fluxes are distributed equally over the planet. Since the magnitude of ZEC is a function of maximum cumulative emissions (MacDougall et al 2020), we use the same maximum cumulative emissions (1000 PgC) as the standard ZEC Model Intercomparison Project experiment. This peak cumulative emissions is also close to the value used to calculate TCRE (at 2x CO 2 , i.e. year 70 of the 1% yr −1 idealized concentration run), which minimizes any inconsistencies that might be introduced by calculating these metrics at different amounts of cumulative CO 2 emissions.
We use the CESM2 (Danabasoglu et al 2020), version 2.1.3, in an emissions-driven mode, (compset 'B1850_BPRP') with the default initial conditions for the emissions-driven configuration (year 151 of (CESM developers 2019)). For the transient simulation, all non-CO 2 aspects of the model were kept at constant preindustrial values, and CO 2 concentrations were prognostic in response to the specified emissions timeseries. Output fluxes and climate variables were smoothed using an 11 year Savitzky-Golay filter to remove interannual variability.
We conduct a large perturbed parameter ensemble (PPE) using the finite amplitude impulse response (FaIR) 1.3 simple climate model (Millar et al 2017, Smith et al 2018. We use 1000 ensemble members, with model radiative forcing parameters sampled following (Smith et al 2018), with an extended sampling of model thermal and carbon timescale parameters sampled as detailed in tables S1-S3, where parameter ranges are informed by a number of studies exploring the emulation of Earth system models with an impulse response formulation (Caldeira and Myhrvold 2013, Proistosescu and Huybers 2017, Rugenstein and Armour 2021. Ensemble configurations are filtered according to their ability to reproduce historical global temperature pathways as in (Thompson et al 2015), leaving 207 filtered ensemble members. For each ensemble member, we calculate the response to the idealized CDR pathways, as well as standard emissions-driven metrics of TCRE (MacDougall 2016) and ZEC (MacDougall et al 2020). TCRE is here calculated as the warming in year 70 of a concentration driven simulation (where concentrations increase from pre-industrial levels at 1% yr −1 until concentrations are doubled in approximately year 70) divided by compatible emissions (E 1pct ) derived using an inverse FaIR simulation (Smith et al 2018). ZEC is calculated by running the forward model with (E 1pct ) until year 70, with zero emissions thereafter (Jones et al 2019). ZEC 50 and ZEC 100 are measured as the temperature change between year 70 and years 120 and 170 respectively.

Results
Carbon fluxes between the atmosphere and both the land and ocean in the CESM2 simulations follow emissions, with both land and ocean sinks changing sign to become sources after the reversal from positive to negative CO 2 emissions (figure 1(a)). Lags, as quantified by the interval of maximum lagged correlation, between emissions and sinks are longer for the land (20 years) than the ocean (11 years), with the combined land and ocean sink in between (16 years). At the time of maximum cumulative emissions, the lag in land and ocean sinks with respect to emissions means that the sinks are still positive, and thus the atmospheric CO 2 concentration is already declining before emissions reach zero. Thus peak concentrations occur before zero emissions, and more generally, this means that the rate of change of atmospheric CO 2 leads emissions, here by 13 years. This result-that atmospheric CO 2 change leads emissions by approximately the same timescale that sinks lag emissions-follows from the general trigonometric identity for the phase of summed functions if both emissions and sinks follow sinusoidal curves (SI text). The lead of atmospheric growth rate relative to emissions is consistent with that between diagnosed fossil fuel emissions in SSP scenarios that reach net zero as reported by (Liddicoat et al 2020) where, e.g. in the SSP5-3.4-overshoot scenario, CO 2 concentrations peak in 2062, while net fossil CO 2 emissions reach zero between 2068 and 2078, depending on the model. Integrated CO 2 fluxes (figure 1(b)) show asymmetries in carbon pools between the positive and negative emissions periods. In particular, at the point of reaching zero cumulative emissions near the end of the experiment, the cumulative atmospheric sink is negative, i.e. CO 2 concentrations are below the preindustrial value, reaching a minimum value of 258 ppm, versus an initial value of 289 ppm and maximum value of 506 ppm (figure 2(a)). Land carbon at the end is also slightly below the preindustrial value, with the excess carbon in the ocean. Looking further at the partitioning of carbon within the land and ocean systems (figures 1(c) and (d)) shows the excess carbon is at depth, with shallow ocean dissolved inorganic carbon anomalies following closely the atmospheric timeseries and lag increasing with depth. Thus, even though the ocean shows a shorter lag than the land with respect to flux correlations against emissions, the difference at the end of the simulations is greater. The positive emissions pulse is able to propagate more fully into the deep ocean than the negative emissions pulse, leading to the positive ocean carbon difference at the end of the simulation. On land, there is a difference in lags between vegetation and soil carbon ( figure 1(d)), as well as an asymmetric response in that both lose carbon after peak emissions more rapidly than they gained carbon prior to the peak, following the asymmetry of atmospheric CO 2 concentrations. At the end of the simulation, most carbon lost from land relative to the start of the scenario comes from vegetation rather than soil carbon pools ( figure 1(d)). Zonal-mean land carbon changes (figure S3) show a stronger latitudinal dependence to the timing of soil carbon than vegetation carbon responses, and some net loss of soil carbon from high latitudes.
The phasing between the physical climate and CO 2 emissions (figure 2(a)) shows that global mean surface temperature leads the CO 2 emissions, with a maximum correlation at lead of 5 years. This happens because atmospheric CO 2 concentrations lead emissions by more than the physical climate lags CO 2 concentrations. This result is consistent with, though stronger than, the current policy framework that reaching zero emissions will lead to effectively immediate stabilization of CO 2 -driven global warming. Here, the suggestion from CESM2 is that CO 2driven temperature stabilization may actually occur before reaching net zero CO 2 emissions. Global precipitation anomalies lag both temperature and CO 2 emissions ( figure 2(a)). CESM2 has a particularly strongly negative ZEC 50 value of −0.31 • C, which may be manifesting fairly soon after the emissions peak and decline, as was also found in the comparison between ZEC diagnosed from instantaneous transition to net zero versus Gaussian emissions (MacDougall et al 2020).
As described above, the hypothesis here is that long-term warming after achieving net negative emissions equals the sum of cumulative emissions (CE) times TCRE, plus a committed ZEC value (Koven et al 2022). Thus we expect that CESM2, which has a strongly negative ZEC 50 value of −0.31 • C (MacDougall et al 2020), will have an equally negative overshoot asymmetry, i.e. with colder temperatures for a given amount of cumulative emissions after reaching net negative emission than before. This is roughly what we find ( figure 2(b)). For most of the positive emissions period, temperature follows the expected proportionality given the previouslyreported value of TCRE for the model of 2.13 • C/EgC (Arora et al 2020), however, the model falls off the ∆T = TCRE * CE line after emission rates begin to decline from their maximum values, and relaxes towards a line representing ∆T = TCRE * CE + ZEC, and then follows that line from the point of reaching net negative emissions through almost all the way until net cumulative CO 2 emissions are back to zero. After that point, global mean surface temperatures begin to rise again, even though cumulative emissions continue to fall to zero.
The increase in temperatures at the end of the CESM2 simulation, as cumulative emissions approach zero, shows a distinct regional pattern, with maximum cooling in mid-high northern latitudes at years 200-250, followed by a reversal to warming afterwards ( figure S4(a)). The spatial pattern and timing relative to the reversal of CO 2 emissions is consistent with that of CESM2 for the SPP5-3.4-overshoot scenario, due to a re-strengthening of Atlantic meridional overturning circulation (AMOC) after its transient weakening with warming, where it is the only CMIP6 model to show such behavior (Koven et al 2022). A similar dynamic occurs here, but even more so, with AMOC strengthening above its preindustrial value in response to the negative emissions ( figure S4(b)). Thus the long-timescale warming reflects interactions between the direct forced temperature changes from CO 2 with the indirect response of AMOC and associated heat transport. Any single Earth system model represents only one estimate of the complex dynamics of the Earth system. To understand more generally how the carbon-climate sensitivity metrics TCRE and ZEC govern the transient dynamics of the Earth system to emissions reversal, we perform a PPE of the FaIR simple climate model (Smith et al 2018) using the same emissions. We find that the 10-90th percentile range of global mean surface temperature variation in response to the forcing broadly follows the pattern of the CESM2 simulation ( figure 3(a)). Differences between CESM2 and the FaIR ensemble are strongest at the end of the experiment, when CESM2 shows a pronounced warming due to AMOC restrengthening (a process not included in FaIR), while the FaIR simulations show a range of responses, from cooling to warming. Figures 3(b)-(g) shows scatterplots of TCRE and ZEC for each ensemble against key climate response variables. Peak warming is highly correlated with TCRE (figures 3(b) and (c)), the lag between peak emissions and peak warming is governed primarily by ZEC (figures 3(d) and (e)), and a weak control by ZEC on the temperature change at the end of the simulation (figures 3(f) and (g)). We find that using both TCRE and ZEC in a multivariate linear prediction of end of simulation warming provides no additional predictive skill over using ZEC alone (not shown).
We show when different combinations of sensitivity metrics (i.e. TCRE and ZEC at different timescales) have the strongest predictive power by plotting temperature versus cumulative emissions for each of the FaIR PPE simulations and noting when the minimum spread across the ensemble occurs (figure 4), which is equivalent to asking when each normalization explains the most variance in temperature across the ensemble Normalizing the warming of each FaIR ensemble member by that ensemble's TCRE (figure 4(a)) shows a minimum ensemble spread (vertical dashed lines) midway through the positive emissions phase, with spread increasing as cumulative emissions approach their maximum. Normalizing warming by TCRE plus half of the ZEC 50 for each ensemble member ( figure 4(b)) moves the minimum ensemble spread to the point of maximum cumulative emissions, i.e. half of the ZEC has already manifested in these simulations at the point of reaching zero emissions (figure S5). Normalizing by TCRE plus either ZEC 50 (figure 4(c)) or ZEC 100 (figure 4(d)) shifts the point of minimum ensemble spread to either early (figure 4(c)) or midway (figure 4(d)) in the negative emissions period, showing that the timescale by which ZEC is quantified governs when in the negative emissions phase that sensitivity is realized.
The experiment here is only one realization from a wide set of possible idealized CO 2 emissions reversibility experiments. Key variables that may affect the carbon and climate response are the -(g) Relationship between peak warming, lag of peak temperature to peak warming, and warming at the end of the experiment to the climate sensitivity metrics TCRE and 100-year ZEC (ZEC100), using FaIR simple climate model. Vertical dashed lines in (a) note times of peak cumulative CO2 emissions and return to zero cumulative emissions. total peak emissions and the timescale for emissions growth and reversal. We use FaIR to explore how the dynamics may vary in response to these alternate emissions trajectories (figure 5). We find: (a) that the transient drop in CO 2 concentrations below preindustrial values near the end of the simulation is robust with respect to variation in the timescale and amplitude within the range explored here (figures 5(b) and (e)); (b) that the peak warming amount is roughly insensitive to the timescale of emissions (figure 5(c)); (c) that there tends to be a minimum in warming late in the period of net negative CO 2 emissions, which is followed by a re-emergence of warming after the negativeemissions phase (figures 5(c) and (f)); (d) that the lag between peak emissions and peak warming increases with higher peak cumulative emissions (Zickfeld and Herrington 2015) (figure 5(f)); and (e) that the long-term warming after emissions reversal is higher with higher peak cumulative emissions ( figure 5(f)).

Discussion
The Paris agreement calls for stabilization of the global climate at levels well below two degrees Celsius, and IPCC AR6 assesses that such climate stabilization requires reaching net zero CO 2 emissions (IPCC 2021). Overshoot scenarios are predicated on the idea that we may exceed target warming levels and require net negative CO 2 emissions to cool and then stabilize the climate system at the agreed warming levels. Significant climate impacts are already evident at the current warming of 1.1 • C. Thus future generations, if they are able to develop the means to generate the large net negative CO 2 emissions required for and blue for the negative emissions phase (years 151-300) of the scenario. Panels differ in the normalization of warming for each ensemble member on the y axis, in order to show where along the trajectory each normalization minimizes the spread across the ensemble: (a) warming divided by TCRE * peak cumulative emissions (CE peak , which equals 1000 PgC for all ensembles); (b) warming divided by TCRE * CE peak + half of the ZEC50; (c) warming divided by TCRE * CE peak + ZEC50; (c) warming divided by TCRE * CE peak + ZEC100. Positive emissions phase curves are foregrounded in panels a-b, negative emissions phase curves are foregrounded in panels c-d. Vertical dashed lines show the cumulative emissions that correspond to minimum ensemble spread in normalized temperature across the ensemble for each panel, also colored by the emissions phase during which that minimum spread occurs (red = positive, blue = negative).
overshoot, may wish to try to restore the climate system to a preindustrial-like state, rather than stabilize it at some level of warming well above the preindustrial. While it is not clear whether long-term CDR technologies could ever be deployed at the scale necessary to reach net-negative CO 2 emissions (Anderson and Peters 2016), particularly at the scale considered here (Smith et al 2015, Fuss et al 2018, or, even if they could, whether the deleterious effects of these technologies would outweigh their potential benefits (Fuss et al 2018, Hanssen et al 2022, it is nonetheless important to understand how the coupled carbonclimate system would respond to a transient reversal from net positive, through net zero, and to net negative CO 2 emissions.
We find that under this restoration scenario the land and ocean carbon sinks follow the trajectories of CO 2 emissions, becoming sources soon after emissions become negative, consistent with overshoot scenarios (Jones et al 2016, Koven et al 2022. The relative timing of this transition differs between land and ocean: the ocean responds in CESM2 more rapidly than land in its sink-to-source transition, though the ocean also shows a greater stock of carbon at the end of the simulation, and thus a longer memory to carbon perturbations, than the land. This is consistent with pulse experiments, which show that both land and ocean exchange carbon with the atmosphere at multiple timescales , Eby et al 2009, Joos et al 2013, for land due to the sequence of live and dead pools that carbon passes through, and for the ocean due to the strong gradient with depth in timescales of carbon response to atmospheric perturbations, which give the ocean greater continued uptake at long timescales than land. In this scenario, for both CESM2 and FaIR, the relationship between global mean temperature and emissions can roughly be broken into three phases. In the first phase, temperature change is proportional to cumulative emissions, with a proportionality described by the TCRE (∆T = TCRE * CE). In the second phase, the influence of the ZEC begins, as the relationship shifts towards one characterized by ∆T = TCRE * CE + ZEC. The second phase begins roughly at the time of peak emissions rates, i.e. well before reaching net zero, and lasts through most of the period of net negative CO 2 emissions and almost towards the point where cumulative emissions reach zero. Because much of the ZEC influence occurs before reaching net zero, its magnitude governs both the timing between peak cumulative emissions and peak temperature as well as the peak warming that is reached. The third phase is characterized by longterm climate and carbon responses that govern the committed temperature change even after all anthropogenic carbon is removed from the system. ZEC governs several aspects of the global temperature dynamics in this scenario. First, we find a strong relationship between the ZEC and the lag between peak cumulative emissions and peak temperature, such that if ZEC is negative then peak temperature may actually lead peak cumulative emissions. IPCC AR6 assessed that the best estimate of ZEC is 0 ± 0.3 • C, with low confidence in sign (Lee et al 2021). If Earth's ZEC is negative, then CO 2driven climate change may begin to reverse slightly before reaching net zero CO 2 emissions, sooner than the decade-lag that is currently estimated (Ricke andCaldeira 2014, Lee et al 2021), with important implications for policy. Second, ZEC, alongside TCRE, affects the magnitude of peak warming. Third, ZEC governs the asymmetry in the temperature to cumulative emissions relationship between the positive and negative emissions phases, and fourth the long-term warming.
ZEC has typically been described as the committed temperature change expected to occur a given period after reaching net zero CO 2 emissions (Jones et al 2019, MacDougall et al 2020. If the relationship between temperature and cumulative CO 2 emissions were strictly path-independent, it would follow that ZEC would have to be exactly zero. Thus a nonzero ZEC implies path dependence of the temperature to cumulative emissions relationship, and more generally, ZEC can be thought of as a measure of that path dependence under strong mitigation. The widely-used approximation for the temperature to cumulative emissions relationship is a linear TCRE that is quantified using a 1% yr −1 increasing concentration experiment (Arora et al 2020). Because this is the same experiment that the standard ZEC quantification is made relative to (Jones et al 2019, MacDougall et al 2020, that ZEC quantification is also consistent with a second definition of ZEC as the committed temperature change relative to expectations from TCRE proportionality at the point of reaching zero CO 2 emissions. This experiment, as well as the Gaussian emissions experiment described in (MacDougall et al 2020), show that the second interpretation is more correct, because the ZEC can become evident before reaching net zero when the transition occurs gradually. Put another way, ZEC cannot describe the amount of temperature change that is still to occur after reaching net zero when half, or even all in the case of CESM2, of that temperature change actually occurs before reaching net zero emissions. While such a definition of ZEC also subsumes deviations from linearity in the temperature to cumulative emissions relationship as well as path dependencies, within the range of emissions relevant to climate mitigation, the nonlinear contribution, as measured in increasing CO 2 experiments, is expected to be small (Tokarska et al 2016) and thus we expect that ZEC should be dominated by path dependencies, which are themselves controlled by interactions between timescales of forcing and response in both physical and carbon cycle feedbacks. In less idealized scenarios, the relative timing between peak warming and peak cumulative CO 2 emissions will also be governed by non-CO 2 greenhouse gasses, in particular the relative emission declines of cooling versus warming short-lived climate pollutants.
There is a consistent relationship between committed global warming and cumulative emissions, which is that committed warming is equal to TCRE times cumulative emissions, plus ZEC. This relationship holds across a wide range of high-mitigation scenarios whether, after reaching peak cumulative CO 2 emissions, subsequent emission rates remain at net zero or become net negative. If net negative CO 2 emissions are both possible and pursued, we should expect temperatures to follow the same TCRE slope in response to those emissions down almost to the point of cumulative net zero CO 2 emissions, underscoring the potential efficacy of net negative CO 2 emissions for restoration of the climate system. Lastly, the result that much of the ZEC may occur by the time of reaching net zero emissions underscores the importance of ZEC, even on the short timescales required to reach net zero in order to reach Paris Agreement targets, and that better quantifying ZEC is crucial to understand both peak CO 2 -driven warming and the relative timing between peak warming and peak cumulative CO 2 emissions.

Data availability statement
All scripts to generate and analyze climate model output here are available at https://github.com/ckoven/ idealized_emissionsdriven_cdr_scenario.
The data that support the findings of this study are openly available at the following URL: https://portal. nersc.gov/archive/home/c/cdkoven/www/idealized_ emissdriven_cdr_cesm2.