The goal of the AERA is to quantify successive future trajectories of CO₂-forcing-equivalent (CO₂-fe) emissions that stabilize the global surface air temperature (GSAT) at a predetermined level . The concept of CO₂-fe emissions is used to unify the emissions of various radiative forcing agents and precursors into a single metric . CO₂-fe emissions for all non-CO₂ agents represent the CO₂ emissions that would produce the same radiative forcing trajectory as these non-CO₂ emissions. While cumulative CO₂ emissions largely determine anthropogenic warming, non-CO₂ radiative forcing agents such as methane, nitrous oxide and aerosols also play an important role. Quantifying the impact of these non-CO₂ agents on global temperatures is complicated by existing methodologies, which often use conventional global warming potentials or other metrics to convert the non-CO₂ radiative forcing agents into “CO₂-equivalent” emissions. The CO₂-fe emissions framework offers a well-suited alternative for comparing emissions from different agents in the context of temperature stabilization pathways . It also offers an opportunity to compare emission reductions in different radiative forcing agents for ecosystem impacts . The CO₂-fe emissions from non-CO₂ agents, Enon-CO2-fe, are estimated based on the radiative forcing time series of non-CO₂ agents : 1Enon-CO2-fe(t)=1αdFnon-CO2(t)dt+ρFnon-CO2(t), where Fnon-CO2 is the radiative forcing of non-CO₂ agents, ρ is the rate of decline in radiative forcing under zero emissions over decadal to centennial timescales (0.33 %), and α is a constant representing the forcing impact of ongoing CO₂ emissions (1.08 Wm⁻² per 1000 GtC). By varying the relative shares of CH₄ and N₂O emissions and radiative forcing from aerosols in the total CO₂-fe emissions, demonstrated the robustness of the CO₂-fe approach in translating contributions from different radiative forcing agents into CO₂-fe emissions.

AERA achieves the temperature stabilization at a predetermined warming level by estimating future CO₂-fe emissions based on the estimated TCRE-fe (the transient climate response to cumulative CO₂-fe emissions). The TCRE-fe in turn is derived from simulations of past annual GSAT, past fossil fuel and land use change CO₂ emissions, and CO₂-fe emissions from non-CO₂ forcing agents calculated from their radiative forcing estimates .

The AERA consists of three steps, which are repeated every 5 years, mirroring the stocktaking mechanism implemented in the Paris Agreement .

AERA estimates the anthropogenic warming ΔT from the simulated GSAT time series (relative to 1850–1900). The past anthropogenic warming is estimated here by applying a 31-year running mean with a linear extrapolation for the last 15 years, assuming a constant warming rate based on the last 31 years. This is in contrast to the original AERA method, which employs an impulse response function on radiative forcing and temperature estimates to determine anthropogenic warming . The simple running mean method was applied here as it yields more robust results in cases where the model's radiative forcing is unknown (as is the case for most ESMs) and after reaching the temperature level.

A total of 13 models have participated in the AERA-MIP: 10 fully coupled Earth system models (ACCESS-ESM1-5, CESM2, EC-Earth3-CC, NASA-GISS-E2-1-G-CC, GFDL-ESM2M, GFDL-ESM4, IPSL-CM6-LR-ESMCO2, MIROC-ES2L, MPI-ESM1-2-LR, and NorESM2-LM), 2 models of intermediate complexity (Bern3D-LPX and UVic-ESCM-2.10), and 1 atmosphere–ocean general circulation model coupled to a carbon cycle emulator (HadCM3-FaIR2; see Appendix , for a description of the configuration). Nine of the fully coupled ESMs participated in the sixth phase of the coupled model intercomparison project (CMIP6), and GFDL-ESM2M participated in CMIP5. Table  lists the models, their abbreviation used in this paper, the corresponding references, the simulated time period, and the number of ensemble members. A summary of their components has been already provided in several multi-ESM studies e.g..

Small initial condition ensembles were provided by two participating ESMs to estimate the uncertainty associated with internal variability (Table ). EC-Earth and GFDL-ESM2M provided a three-member and a five-member ensemble, respectively. Ideally, more ensemble members are necessary to properly quantify the internal variability . However, even the small number of ensemble members available here provide a first-order estimate of internal variability.

The ACCESS-ESM1-5 model is somewhat of an outlier. It also converges to both prescribed temperature levels but substantially later than all other models, and after a significant temperature overshoot. The model most likely overshoots and converges later due to a strong mismatch between the estimate of non-CO₂ radiative forcing used in the AERA to estimate CO₂-fe emissions (from the RCP/SSP database; see below) and the non-CO₂ radiative forcing simulated in the model based on the prescribed atmospheric non-CO₂ radiative agents. Hence, results from ACCESS were excluded from subsequent multi-model statistics but are still shown for transparency in Fig. . However, the inclusion of the ACCESS model in the ensemble modifies our results only slightly (Fig. ).

The simulations of the AERA-MIP are performed until at least 2150 (except for HadCM3-FaIR2 until 2100) and up to 2300 to allow for enough time to reach the temperature level and stabilize global surface warming (Table ). Simulations have been conducted for both the 1.5 and 2.0 °C temperature levels. To remove biases in simulated warming over the historical period relative to observations, we use the concept of a relative temperature level . Under this concept, the remaining allowable warming in 2020 is first estimated from observations. In a second step, the AERA adds this observation-based remaining allowable warming to the models' anthropogenic warming in 2020 to calculate the absolute temperature level in each model see. Thus, each model estimates the emission trajectory for the same remaining allowable warming in 2020, which is here estimated to be 0.28 °C for the 1.5 °C warming level and 0.78 °C for the 2.0 °C level. These values were derived from the observation-based estimated warming of 1.22 °C in 2020 . Each initial condition ensemble member has its own anthropogenic temperature in year 2020, resulting in very small differences in absolute temperatures for that year (maximum differences across GFDL-ESM2M ensemble members of 0.067 °C).

Following a similar simulation strategy as in , all simulations branch off an emission-driven simulation (esm-hist) over the historical period following the CMIP6 protocol. After the end of the CMIP6 historical period in 2014, fossil fuel CO₂ emissions follow observed emissions until 2020 and projected emissions from the Nationally Determined Contributions (NDCs; Climate Action Tracker: https://climateactiontracker.org/global/temperatures/, last access: 1 December 2021) from 2021 to 2025. Starting at the end of the year 2025, fossil fuel CO₂ emissions prescribed to the model are obtained every 5 years from AERA (see below and the schematic in Fig. ) by subtracting CO₂-fe emissions from prescribed non-CO₂ radiative agents and land use land cover change from the AERA-derived total CO₂-fe emission curve. Non-CO₂ agents and land use and land cover change are prescribed as in the SSP1-2.6 scenario after 2015. This low-emission–high-mitigation scenario is often used in related climate stabilization approaches (e.g. ). An exception is the CMIP5-type GFDL-ESM2M, which follows the CMIP5 protocol for the historical period and the RCP2.6 scenario instead of the SSP1-2.6 scenario for the non-CO₂ forcing agents and land use and land cover change. After 2100, no further changes occur in non-CO₂ forcing agents, land use, and land cover. A schematic is provided in Fig. , summarizing the feedback loop between the AERA module and the ESM during the post-2025 period of the simulations.

As the AERA calculates the total CO₂-fe emissions, it requires information about emissions from non-CO₂ forcing agents (Enon-CO2-fe) and CO₂ emissions from land use and land cover change (ELUC; referred to as land use change emissions for simplicity from now on) to estimate the past TCRE-fe in addition to the past fossil fuel CO₂ emissions (EFOS). Moreover, the future EFOS values prescribed to the model after each stocktake are calculated as the difference between the CO₂-fe emission curve (Etotal-fe) from step 3 of AERA and the estimated future CO₂-fe emissions from land use change and non-CO₂ forcing agents: 3EFOS=Etotal-fe-ELUC-Enon-CO2-fe. As most models do not directly output the radiative forcing of non-CO₂ agents (required to derive Enon-CO2-fe), we estimate this time series from the radiative forcing given by the RCP/SSP database for both the historical period and SSP1-2.6 scenario. Some models, however, have provided an estimate of the simulated effective radiative forcing for all non-CO₂ radiative agents (see Table  and Fig. d). For these models, the internally calculated effective radiative forcing estimates were used to derive the CO₂-fe emissions from the non-CO₂ forcing agents . Similarly, some models (see Table  and Fig. c) have conducted additional simulations to estimate ELUC . In that case, the model-specific ELUC is prescribed to AERA instead of the default ELUC estimate stemming from the Bern3D-LPX model that was scaled to align with the Global Carbon Budget estimates from 1850 to 2020. The default Enon-CO2-fe and ELUC time series and the model-specific emissions for those that were able to estimate them are shown in Figs.  and .

Although the future ELUC and Enon-CO2-fe are prescribed in AERA to enable the extraction of future EFOS as input to the models (Fig. ), the future CO₂-fe emission curve Etotal-fe is largely insensitive to the chosen land use and non-CO₂ forcings (see tests in ).

Further details on the configuration of the AERA simulations are provided in Appendix .

While the TCRE is commonly considered approximately constant, recent studies suggest a potential variability in TCRE when CO₂ emissions are reduced, owing partly to a non-zero ZEC . This indicates that the REB originally estimated at the end of 2025 may evolve over time, with the additional effect of potential non-linearities in the response of non-CO₂ forcing agents. To illustrate the temporal evolution of the REB from a fixed starting point, we reconstruct the CO₂-fe emission budget from the beginning of the year 2026 (EB₂₀₂₆) at each stocktake by summing the REB (i.e. all future emissions) calculated at the end of the stocktake year (tst) and the already emitted CO₂-fe emissions between 2026 and that year: 4EB2026(tst)=REB(tst)+∫2026tstEtotal-fe(t)dt. EB2026(2025) is by definition REB(2025).

Within individual ESMs, all sources and sinks of the carbon mass balance are known (disregarding ocean–sediment interactions and weathering, whose effects are negligible over the timescales considered in this study) and we can write the following equation: 5EFOS=GATM+SOCEAN+(SLAND-ELUC). EFOS indicates the prescribed global fossil fuel CO₂ emissions during the historical period and calculated by AERA post 2025. GATM indicates the simulated atmospheric CO₂ growth rate (in PgC yr⁻¹) using the conversion factor of 2.123 PgC ppm⁻¹ . SOCEAN is the net ocean carbon sink derived from the CO₂ flux into the ocean (CMIP6 variable fgco2). SLAND-ELUC denotes the net CO₂ flux into land and is derived from the net biosphere production (CMIP6 variable nbp). The net biosphere production includes the gross land carbon sink SLAND minus emissions from land use and land cover change ELUC.

For the eight models that estimate their ELUC term, we can quantify the gross land carbon sink SLAND (Fig.  and Appendix ) by adding the two diagnostics nbp +ELUC. Thus, by rearranging Eq. (), we can separate net sources and sinks of CO₂: 6EFOS+ELUC=GATM+SOCEAN+SLAND. As opposed to earlier studies , atmospheric CO₂ is freely evolving and not prescribed, whereas EFOS is prescribed and does not need to be diagnosed.

From Eq. (), we derive the cumulative airborne fraction (CAF), ocean-borne fraction (COF), and land-borne fraction (CLF): 7CAF(t)=∫GATM(t)dt∫(GATM(t)+SOCEAN(t)+SLAND(t))dt,8COF(t)=∫SOCEAN(t)dt∫(GATM(t)+SOCEAN(t)+SLAND(t))dt,9CLF(t)=∫SLAND(t)dt∫(GATM(t)+SOCEAN(t)+SLAND(t))dt, with the ∫ sign representing the time integral from 1850. Here we use GATM+SOCEAN+SLAND instead of EFOS+ELUC as the denominator of the cumulative fractions to avoid minor budget closure errors. These errors are negligible in most models and represent a maximum of a few percent (not shown), in which case they are very likely due to missing diagnostics.

For some models, the ELUC term prescribed to AERA was either the default estimate from the adjusted Bern3D-LPX time series or a model internal estimate but presented some errors. In the carbon stock analysis, we corrected these terms (see Appendix ).

The AERA effectively stabilizes the simulated GSAT in ESMs around the prescribed warming level within an uncertainty of ±0.2 °C (Fig. a, b). The uncertainty of ±0.2 °C corresponds to the uncertainty with which anthropogenic warming can be determined from observations . The IPSL model temporarily leaves the 1.5 °C uncertainty range, and MIROC briefly leaves the 2.0 °C uncertainty range. In the 1.5 °C simulation, the multi-model mean GSAT anomaly enters the warming level uncertainty range in 2026, i.e. the year when the first AERA period begins (thick black line in Fig. a). The temperature anomaly first peaks at 1.43 °C in 2043 (min–max model range: 1.20 to 1.57 °C), temporarily drops to 1.40 °C (1.23 to 1.50 °C) in 2069, and stabilizes around 1.44 °C (1.25 to 1.64 °C) between 2100 and 2150. In the 2.0 °C simulation (Fig. b), the multi-model mean GSAT anomaly enters the uncertainty envelope in 2061 and stabilizes at around 1.90 °C (1.77 to 2.09 °C) between 2100 and 2150.

The convergence to the temperature level here shows that the AERA approach works for both intermediate-complexity models, as shown previously , as well as for fully coupled ESMs. This is the case despite differences in ELUC and Enon-CO2-fe prescribed to the AERA framework and in the models themselves. An exception is the ACCESS model that only converges to the respective warming level by the late 22nd century after an overshoot of 0.3–0.5 °C (larger overshoot for the 1.5 °C warming level; see Sect. 2 for more details).

For the 1.5 °C warming level, CO₂-fe emissions decrease strongly and immediately after 2025 for all models, albeit with a large inter-model spread (Fig. c; Table ). By 2030, CO₂-fe emissions drop to 8.1 (min–max range: 3.1 to 11.9) PgC yr⁻¹, a 40 % (7 % to 76 %) decline compared to 2025 levels of 13.7 (11.0 to 18.9) PgC yr⁻¹. During this strong decline phase, CO₂-fe emissions reach a maximum reduction of -2.0 (-0.4 to -3.6) PgC yr⁻². Afterwards, the emissions reach a temporary minimum at nearly zero in 2050 (0.2 PgC yr⁻¹; range: -3.6 to 5.0 PgC yr⁻¹), corresponding to a 98 % (57 % to 127 %) decline from 2025 levels, before peaking at 1.9 (-0.2 to 4.2) PgC yr⁻¹ in 2077. This bounce in the CO₂-fe emission curve could be explained by the very rapid mitigation of non-CO₂ forcing agents in the early decades of the SSP1-2.6 scenario, causing slightly negative forcing-equivalent emissions approximately from 2030 to 2100 (Enon-CO2-fe; see Fig. d). Because this decline in Enon-CO2-fe is not accounted for in the first estimate of the REB at the end of the year 2025, the emission budget is re-evaluated and increases in the stocktake years around 2050 relative to its 2025 estimate (Fig. a), leading to the on-average increase in emissions between 2050 and 2077. Subsequently, CO₂-fe emissions decrease again to 1.0 (-1.7 to 2.9) PgC yr⁻¹ between 2100 and 2150 when global mean temperatures have been stabilized. Until the end of the 22nd century, CO₂-fe emissions remain slightly positive on average. The positive emissions and large model spread during the temperature stabilization phase are consistent with the overall negative but highly uncertain multi-decade temperature response after zero CO₂ emissions across a range of EMICs and ESMs . In 4 out of 13 models (GFDL-ESM4, IPSL, MPI, UVic), negative CO₂-fe emissions are not necessary to stabilize at the 1.5 °C warming level.

Achieving the 2.0 °C warming level also requires strong CO₂-fe emission reductions, albeit less drastic than for the 1.5 °C level. By 2030, multi-model mean CO₂-fe emissions decrease to 13.0 (10.9 to 17.1) PgC yr⁻¹, a 5.2 % (-1% to 16 %) reduction from 2025 levels. By 2050, they drop further to 7.2 (1.3 to 11.4) PgC yr⁻¹, a 47 % (8 % to 92 %) decrease compared to 2025, and stabilize at 1.7 (range: -1.5 to 2.7) PgC yr⁻¹ between 2100 and 2150. The maximum reduction rate between 2026 and 2100 is -0.7 (range: -2.3 to -0.1) PgC yr⁻². Only two models, EC-Earth and CESM2, exhibit temporary negative CO₂-fe emissions before 2150.

Several models simulate decadal-scale oscillations in emissions trajectories after reaching the prescribed temperature level. These fluctuations partly stem from the challenge faced by AERA's anthropogenic warming estimation, utilizing an extended 31-year running mean, in distinguishing entirely between multi-decadal internal variability and anthropogenic trends in atmospheric temperature. In particular in NorESM2, large multi-decadal temperature variations due to Atlantic meridional overturning circulation (AMOC) decline and subsequent recovery have been shown to occur when emissions are phased out . However, these oscillations lead to temperature fluctuations that remain within the ±0.2 °C range around the temperature level, except for a small undershoot simulated in the IPSL model, which takes a few decades to recover towards the warming level. This slow evolution of GSAT could be partly related to the large low-frequency internal variability exhibited in this model .

Beyond 2200, a time period for which only three models provide results, CO₂-fe emissions necessary for maintaining temperature stabilization are still projected to evolve slightly. For example, GFDL-ESM2M shows a slower reduction in CO₂-fe emissions during the 21st century compared to other models due to its low TCRE and a negative temperature response to zero emissions on decadal timescales. However, by the mid-22nd to 23rd century, CO₂-fe emissions in this model become slightly negative and will remain so for several centuries in response to a time-varying ZEC and continued warming in this model on multi-centennial timescales under zero emissions . On the other hand, the Bern and MIROC models simulate continuous (albeit small) positive emissions on these timescales, reflecting continued cooling in these models under zero CO₂ emissions (negative ZEC) on multi-centennial timescales . This time dependency of the ZEC response following a period of CO₂ emissions erodes the value of the remaining budget concept as a fixed estimate beyond the first several decades around net zero.

The simulated uncertainty range in CO₂-fe emission pathways across the models is caused by model differences and by internal variability (as diagnosed by the range across individual ensemble members of one model; Table , Figs. b and b). The internal variability uncertainty range diagnosed here represents a lower bound of the true internal variability uncertainty from ESMs as only a few ensemble members are available. Across the five ensemble members of GFDL-ESM2M, the min–max range in CO₂-fe emissions in 2050 is 3.9 PgC yr⁻¹ for the 1.5 °C level and 0.7 PgC yr⁻¹ for the 2.0 °C level, corresponding to 45 % and 7 % of the multi-model range, respectively. These numbers rise to 66 % and 53 % between 2100 and 2150, respectively. The EC-Earth three-member ensemble represents 33 % and 53 % of the multi-model range CO₂-fe emissions in 2050 and 34 % and 29 % between 2100 and 2150 for the 1.5 °C and 2.0 °C levels, respectively. The inter-member spread decreases during the temperature stabilization period. For example, in the 2.0 °C warming level ensemble by GFDL-ESM2M, the inter-member range decreases from 2.7 PgC yr⁻¹ in 2100–2150 to 1.1 PgC yr⁻¹ in 2250–2300 (Fig. b). As for the maximum reduction rate in CO₂-fe emissions between 2026 and 2100, the GFDL-ESM2M ensemble members range from -1.3 to -0.1 PgC yr⁻² for the 2.0 °C warming level, corresponding to 56 % of the spread across all models.

Fossil fuel emissions (EFOS; see Eq. ) closely track the evolution of the CO₂-fe curve (Fig. a, b). In the 1.5 °C scenario, the multi-model mean emissions remain slightly positive throughout the simulation, reaching a minimum in 2046 of 0.9 (-2.7 to 6.6) PgC yr⁻¹, peaking in 2069 at 1.7 (-1.0 to 5.4) PgC yr⁻¹, and gradually declining towards zero by the end of the 22nd century. Although the multi-model mean suggests that EFOS can remain positive if emission reductions are fast and strong, negative emissions may still be necessary as five models simulate negative EFOS, reaching -4.5 to -1.6 PgC yr⁻¹ before 2050.

In the 2.0 °C simulation, the multi-model mean reaches 8.2 (1.4 to 11.9) PgC yr⁻¹ in 2050, stabilizes at 1.3 (-1.7 to 3.2) PgC yr⁻¹ between 2100 and 2150, and slightly declines thereafter. In this scenario, only two models (CESM2 and EC-Earth) simulate non-negligible negative fossil fuel emissions before 2150, reaching -1.5 to -2.0 PgC yr⁻¹. A temporary increase in EFOS occurs post 2025 in the 2.0 °C simulation due to rapid reductions in non-CO₂ emissions (Enon-CO2-fe) as prescribed in the SSP1-2.6 scenario (Fig. d).

The prescribed CO₂-fe emissions from non-CO₂ agents based on SSP1-2.6 (Fig. d; coloured lines for models that were able to estimate their internal radiative forcing, while the black line is for the others; see Sect. 2) exhibit a rapid decrease after year 2026, reaching maximum negative emissions around year 2054 of -1.4 PgC yr⁻¹ and stabilizing at slightly positive levels of 0.2 PgC yr⁻¹ after 2100 for the default prescribed emissions (black line). The simulated CO₂ emissions based on prescribed land use change from SSP1-2.6 (Fig. c) generally remain slightly positive throughout the 21st century, except in the NASA-GISS, EC-Earth, and ACCESS models, where they are temporarily negative. Post-2100, the land use change CO₂ emissions prescribed to AERA stabilize around zero, consistent with the constant land use area forcing. For the UVic and MPI simulations, the values prescribed to AERA post-2100 in ELUC were kept positive and constant, although this does not correspond to the land use forcing. These time series were corrected in the remaining emissions budgets reported in Sect.  and in the carbon stock analysis of Sect.  (see Appendix ). Both the non-CO₂ and the land use change CO₂-fe emissions follow identical trajectories for the 1.5 and 2.0 °C global warming level simulations, as they follow the SSP1-2.6 scenario for both warming levels.

The simulated model-specific CO₂ emissions from land use change and CO₂-fe emissions from non-CO₂ agents are not available as output from all models. Nevertheless, negative CO₂-fe emissions from non-CO₂ radiative forcing agents are only possible if the radiative forcing from these agents is decreasing. However, the radiative forcing agents follow the SSP1-2.6 or RCP2.6 scenario, and after 2100 they are set to constant values for all models, suggesting that substantial negative non-CO₂ emissions are unlikely post-2100. In addition, land use area is also set to be constant after 2100. Considering that CO₂ emissions from both land use change and non-CO₂ agents are likely to be zero or slightly above zero after temperature stabilization, it is reasonable to conclude that the positive CO₂-fe and fossil fuel CO₂ emissions after stabilizing warming are more likely a consequence of the overall negative zero emissions commitment rather than net negative forcing from non-CO₂ forcing or from land use change.

The uncertainty across models found here in residual fossil fuel emissions (Fig. a, b) compatible with temperature stabilization appears to be in agreement with the results from , who diagnosed compatible emissions with halting warming after 1pctCO2 and 1.5 °C-compatible CO₂ emission-driven experiments. They calculate these emissions based on a theoretical framework (defining the RAZE parameter, i.e. the rate of adjustment to zero emissions), results from the ZECMIP simulations, and a climate emulator. In their scenario in which non-CO₂ forcing agents follow SSP1-1.9 and CO₂ emissions linearly decrease to zero between 2021 and 2050, the best estimate of CO₂ emissions compatible with halting warming after 2050 is given at 0.66 PgC yr⁻¹ (2.2 GtCO₂ yr⁻¹), with a 5th–95th percentile range of -2.2 to 1.9 PgC yr⁻¹. In their formulation of the multi-decade ZEC response, this equates to a small negative RAZE parameter, the uncertainty of which spans zero. On the other hand, find that net negative fossil fuel CO₂ emissions are necessary to stabilize global surface temperature at 1.5 °C in an observation-constrained carbon cycle perturbed-parameter ensemble of the UVic model. In their study, they used RCP2.6 non-CO₂ forcing extended to the year 2200, which in total causes positive radiative forcing between the first time the temperature is reached in 2055 and the period of stabilization until 2200. They discuss that this is a likely cause for the net-negative CO₂ emissions.

Since the simulations are CO₂ emission-driven, atmospheric CO₂ evolves dynamically (Fig. e, f). The multi-model mean atmospheric CO₂ reaches 420 ppm in 2020, slightly higher than the observed 412 ppm . In both temperature stabilization simulations, the multi-model mean exhibits a peak and subsequent decline behaviour. Atmospheric CO₂ peaks at 438 ppm in 2031 for the 1.5 °C scenario and at 499 ppm in 2070 for the 2.0 °C scenario, subsequently decreasing to 410 ppm in the 1.5 °C scenario and to 480 ppm in the 2.0 °C scenario by 2150. Thus, atmospheric CO₂ should start to decrease around 2030 to reach the 1.5 °C level, according to the multi-model mean. Some models do not simulate such a smooth peak-and-decline behaviour and in addition simulate a (temporary) rise in atmospheric CO₂ due to a temporary rise in CO₂ emissions during or after the decline (Fig. a).

The different CO₂ emissions and the strength of the land and ocean carbon sinks lead to large differences in atmospheric CO₂. The model min–max range in atmospheric CO₂ of 53 ppm in year 2025 originates from different ocean and land carbon sinks and ELUC emissions during the historical period as all models have identical prescribed fossil fuel CO₂ emissions until 2025 (Fig. a, b; note HadCM3-FaIR2 differs due to the emissions being diagnosed and not prescribed; see Appendix ). After year 2025, the spread in atmospheric CO₂ is also driven by the divergent EFOS pathways and thus strongly increases, as EFOS also evolves with the model-dependent AERA calculation every 5 years. The model min–max range expands to 105 ppm (1.5 °C simulation) and 55 ppm (2.0 °C) by the year 2050, 125 ppm (1.5 °C) and 139 ppm (2.0 °C) by the year 2100, and 123 ppm (1.5 °C) and 141 ppm (2.0 °C) by the year 2150.

Part of these large uncertainties may stem from internal variability (Figs. c and c). GFDL-ESM2M's five ensemble members show a min–max range of 54 ppm (1.5 °C) and 49 ppm (2.0 °C) by 2100, approximately 43 % and 40 %, respectively, of the multi-model range. EC-Earth's three ensemble members represent 29 % and 27 % of the model range in 2100. GFDL-ESM2M's range tends to decrease over the 23rd century, reaching 24 ppm (1.5 °C) and 41 ppm (2.0 °C) by 2300. Sensitivity simulations with the Bern model, covering likely range of TCRE as determined by the IPCC AR6, exhibit an inter-member spread in atmospheric CO₂ levels that is as large as the inter-model spread, persisting during stabilization (not shown). Thus, while internal variability certainly plays an important role by 2100, differences in TCRE among the models remain the primary driver for the substantial model uncertainties in simulated atmospheric CO₂. Additional processes may be at play in explaining the model spread that are not explained by differences in TCRE, such as the sensitivity to evolving non-CO₂ agents and the representation of land use land cover changes in the models. For example, the MIROC model has a low TCRE and negative ZEC , and yet it exhibits the lowest levels of atmospheric CO₂ at the end of the historical period (Fig. e, f).

Atmosphere, ocean, and land carbon fluxes exhibit peak and decline patterns, albeit with distinct differences between all three sinks (Fig. ). In this section, our emphasis is on the 2.0 °C scenario. In addition, the analysis for the 1.5 °C scenario is shown in Appendix B (Fig. ), and the numbers for the cumulative emissions and sinks are reported for both scenarios in Tables  and .

The atmospheric CO₂ growth rate, GATM, initially mirrors fossil fuel emissions, reaching 4.7 (3.5 to 5.7) PgC yr⁻¹ in 2020 (Fig. a), consistent with the observation-based estimate of 5.0±0.2 PgC yr⁻¹ . As emissions decrease, GATM deviates from fossil fuel emission trends, turning negative and reaching -0.5 (range: -2.7 to 1.7) PgC yr⁻¹ between 2100–2150 due to continued carbon uptake by the ocean and land. The ocean remains a consistent carbon sink, with multi-model mean uptake decreasing from 2.9 (2.2 to 3.3) PgC yr⁻¹ in 2020 to 1.2 (0.2 to 1.9) PgC yr⁻¹ by 2100–2150 (Fig. c). Conversely, the net land carbon sink (SLAND-ELUC) undergoes a transition from a net source to a sink between 1850–1950. The net land carbon sink peaks at 2.1 (0.5 to 4.1) PgC yr⁻¹ in 2020 and remains a net sink or neutral until 2200 (Fig. g). Notably, the land sink reaches a neutral state faster than the ocean sink, even temporarily shifting to a small carbon source by the end of the 22nd century. The simulated ocean and land carbon uptake in 2020 align well with the observation-based estimates: 3.0±0.4 PgC for ocean carbon uptake and 2.0 PgC yr⁻¹ (SLAND=2.9±1.0 PgC yr⁻¹ minus ELUC=0.9±0.7 PgC yr⁻¹) for land carbon uptake . Among the models providing land use change emissions estimates, the gross land carbon uptake SLAND emerges as a larger sink than the net land carbon flux SLAND-ELUC (Fig. e), trending towards neutrality or even displaying a source tendency on longer timescales in GFDL-ESM2M. SLAND in NASA-GISS, which lies at the lower end of the model range, is small because its sensitivity to CO₂ fertilization is damped: while the model simulates enhanced photosynthetic uptake of CO₂, its vegetation structure remains fixed, and the extra carbon is instead allocated to the soil where it can still be respired back to the atmosphere. In addition, the NASA-GISS model does not capture regrowth from secondary forest. These together lead to a relatively small cumulative land-borne fraction (Fig. f) and larger cumulative ocean-borne fraction by compensation (Fig. d).

The net ocean carbon flux initially has a narrow spread across models during the historical period, with a min–max range of 0.8 PgC yr⁻¹ over 2000–2020. However, this spread notably widens after 2025, reaching 1.5 PgC yr⁻¹ over 2040–2060 and 1.7 PgC yr⁻¹ over 2100–2150. Pre-2025 differences among models are mainly due to various representations of ocean circulation and biogeochemistry in ESMs . After 2025, the widening spread also results from differing emission pathways. In contrast, the land carbon flux exhibits a much wider spread during the historical period, reaching 4.0 PgC yr⁻¹ over 2000–2020. This range only increases slightly after 2025 to 5.0 PgC yr⁻¹ over 2040–2060, reverting to 4.0 PgC yr⁻¹ over 2100–2150. The substantial spread in land carbon flux, not entirely depicted in Fig.  due to a 31-year average for visual clarity, arises from the diverse representations of land carbon processes across models .

From 1850 to 2020, 294 PgC (ranging from 236 to 354 PgC) of the total cumulative CO₂ emissions from fossil fuels (462 PgC) and land use change (170 PgC) remained in the atmosphere. During the same period, the ocean has taken up 173 PgC (ranging from 128 to 208 PgC), while the land absorbed 168 PgC (ranging from 79 to 254 PgC) (Table ). This partitioning translates to a cumulative airborne fraction of 0.48 (0.41 to 0.53), an ocean-borne fraction of 0.27 (0.24 to 0.31), and a land-borne fraction of 0.26 (0.16 to 0.33). These values are similar to observation-based estimates for 1850–2020 of 0.26 for the ocean sink and 0.30 for the land sink . Over the simulation period, the cumulative airborne fraction steadily decreases alongside declining emissions after 2025, signifying the gradual uptake of anthropogenic carbon by the ocean and the land (Fig. b, d, f). By the year 2150, the cumulative airborne fraction decreases to 0.34 (0.26 to 0.42), with an average of 416 (284 to 354) PgC of anthropogenic carbon still remaining in the atmosphere. Concurrently, the ocean-borne fraction consistently rises, emerging as the dominant fraction by the end of the simulations. In 2150, the ocean-borne fraction increases to 0.36 (0.30 to 0.45), surpassing both the land-borne fraction of 0.30 (0.13 to 0.44) and the airborne fraction. The cumulative ocean sink by 2150 amounts to 426 (330 to 556) PgC, while the land has taken up 370 (113 to 540) PgC. Nonetheless, substantial variability persists among model estimates for each fraction.

The continuous ocean carbon uptake until the end of the simulations is limited to specific regions (Fig. a, c, d). While the ocean carbon sink increases almost everywhere from the early 20th century to the mid-21st century, it only continues to take up carbon after temperature stabilization at the end of the 21st century in the Southern Ocean and the low-latitude regions close to the Equator. The Southern Ocean around 60° S remains an especially prominent and enduring carbon sink post temperature stabilization, a consistent feature across models (no stippling in Fig. a, d). Cumulatively, the Southern Ocean south of 30° S, representing 35 % of the ocean area, takes up 42 % (35 % to 46 %) of the global ocean carbon uptake by 2020, rising to 46 % (35 % to 57 %) by 2150 in the 2.0 °C simulation shown here. This region remains a sink until 2300 for the models that have run long simulations (GFDL-ESM2M, MIROC, Bern, not shown). Another strong present-day carbon sink (Fig. c), the subpolar North Atlantic, ceases to absorb carbon when the surface temperature stabilizes (Fig. d). The subpolar North Atlantic north of 40° N (and using the northern boundary of ) represents 3 % of the ocean area but takes up 7 % (3 % to 11 %) of global ocean carbon uptake by 2020, a fraction that decreases to 5 % (1 % to 11 %) by 2150. The prevalence of the Southern Ocean carbon sink is consistent with results from CMIP5 and CMIP6 simulations for the historical period and for idealized 1pctCO2 experiments . The pronounced long-term steady carbon sink in the Southern Ocean can be attributed to the high carbon concentration feedback and efficient surface-to-depth export of anthropogenic carbon shown in earlier studies . In the mid-latitude subtropics, some models even simulate less carbon uptake or outgassing due to the accumulation of anthropogenic carbon near the surface layers .

The land carbon uptake also persists only in particular regions during temperature stabilization (Fig. b, e, f). Some strong and robust carbon sink regions in the present era (2011–2030), particularly in tropical areas like South America, central Africa, and parts of Indonesia, experience a complete cessation of carbon uptake after 2100. However, strong terrestrial carbon uptake persists in the Northern Hemisphere during temperature stabilization, including regions like Central America and temperate and boreal forests in eastern North America and Eurasia.

Compared to the ocean carbon uptake, locally the land carbon uptake has a larger uncertainty across models, although much of this uncertainty is located in regions where no carbon exchange is found during the pre-industrial period (e.g. desertic regions) and is thus an artefact of the method and therefore not indicated by stipples on the maps (see caption of Fig. ).

The land and ocean carbon sink patterns look qualitatively similar to previous results based on low-emission scenarios . The novelty of these simulations is a quantification of these sinks for a given temperature level and the representation of carbon cycle dynamics beyond the 21st century under strong mitigation scenarios. For example, here we show that the North Atlantic ocean sink vanishes during and after stabilization, whereas the Southern Ocean remains an active sink. The divergence in carbon uptake between these regions can be attributed to distinct ocean circulation patterns. The Southern Ocean is the region where old, anthropogenic CO₂-poor circumpolar deep waters are being upwelled e.g., even during global surface climate stabilization. This upwelling results in continuous carbon uptake due to the positive air–sea gradient in anomalous pCO₂ . On the other hand, when global temperature stabilizes, the Atlantic Meridional Overturning Circulation (AMOC) is expected, at least in some models, to recover after an initial decrease e.g., a phenomenon associated with a recovery of deep convection in the subpolar North Atlantic, enhanced mixing of anthropogenic CO₂-rich waters previously sequestered at depth, and a consequently lower ocean carbon uptake in this region. A stronger AMOC would also transport more warm surface waters with high anthropogenic carbon concentrations to the high latitudes where the anthropogenic carbon would be outgassed during cooling , a phenomenon already simulated for the present time in the Arctic Ocean while atmospheric CO₂ is still increasing . The exact drivers of the vanishing Atlantic Ocean carbon sink under temperature stabilization will be the subject of future dedicated studies using the AERA-MIP simulations.