The Coupled Model Intercomparison Project (CMIP), for which CMIP phase 6 (CMIP6) is the most recent completed phase, provides the forum for state-of-the-art Earth System Models (ESMs) to submit results under carefully controlled climate model experimental protocols . One important component of CMIP is the Scenario Model Intercomparison Project (ScenarioMIP), which evaluates ESM projections into the future and provides insight into how human influences could affect climate due to greenhouse gases, aerosols and land use change . In ScenarioMIP, future socioeconomic projections (2015 onwards in CMIP6) are branched from the end of a historical hindcast (1850–2014) under a number of different pathways ranging from very high to very low climate forcing, resulting in a wide range of possible climate change trajectories over the 21st century . ScenarioMIP experiments provide our best estimates of future climates resulting from these trajectories and are invaluable for informing climate impact models . The climate impact models describe how climate change could affect human and natural systems such as crop productivity, biodiversity and human health .

In CMIP6, future climate projections are based upon the Shared Socioeconomic Pathway/Representative Concentration Pathway (SSP-RCP) matrix . Scenarios run in ESMs are of the form SSPn-x, where n=1,…,5 describes a specific socioeconomic storyline and x describes the approximate radiative forcing level (as a proxy for warming level and climate change mitigation effort) in the year 2100 in Wm-2 (Gidden et al., 2019). A total of eight SSP-RCP combinations were chosen for running in ESMs for CMIP6, spanning radiative forcing targets from 1.9 to 8.5 Wm-2 in 2100. For reference, present-day radiative forcing levels are around 3 Wm-2 .

For each SSP-RCP, an emissions pathway is produced by an integrated assessment model (IAM). The IAM uses inputs of population, GDP, education and urbanization, and produces greenhouse gas (GHG) and short-lived climate forcer (SLCF) emissions projections as an output. IAMs are internally consistent representations of the economy, energy and land use system, which typically find cost- or welfare-optimising solutions from the input boundary conditions subject to technological, socioeconomic, physical, and climatic constraints (here, the 2100 radiative forcing level). Typically, as the radiative forcing constraint tightens (decreasing Wm-2 target value), climate abatement costs increase and facilitate the requirement for negative emissions technologies. The ease of meeting particular radiative forcing levels depends on the SSP storyline which has different levels of challenges to mitigation and adaptation, with some RCP levels either above the no-mitigation baseline or not technologically feasible within given socioeconomic constraints in some SSPs .

IAMs produce time-varying emissions of CO2 and other forcers, but future climate experiments in ScenarioMIP and its earlier predecessors were driven by concentrations of CO2 and other GHGs. The concentrations in each SSP-RCP were calculated using a simple climate model, MAGICC, which uses a carbon cycle box model that is calibrated on full-complexity carbon cycle and Earth system models . However, in addition to supplying the concentration-driven ScenarioMIP experiments, around a dozen ESMs in CMIP6 were set up to run with prescribed emissions of CO2 . Performing emissions-driven runs allows us to sample an additional dimension of uncertainty, namely the strengths of climate-carbon-cycle feedbacks that define the atmospheric airborne fraction and land and oceanic uptake of CO2 emissions . Since humans emit greenhouse gases rather than having direct control over atmospheric concentrations, an emissions-driven experimental design is also more appropriate for determining the levels of residual or negative emissions required to stabilize and reverse anthropogenic climate change , as well as more clearly linking model responses to human efforts to reduce emissions.

Under CMIP6, a handful of CO2 emissions-driven simulations were performed under the SSP5-8.5 (fossil-fuel driven, very high emissions) and SSP5-3.4-over (following SSP5-8.5 until 2040, with rapid emissions reductions after 2040 and high levels of net negative CO2 emissions in the second half of the 21st century) under the Coupled Climate–Carbon Cycle Model Intercomparison Project (C4MIP) and Carbon Dioxide Removal Model Intercomparison Project (CDRMIP) components of CMIP6 respectively . While scientifically interesting and useful for impact studies , SSP5-8.5 has been criticised for being an unrealistically high emissions scenario , which would require a global reversal of policy and shift back to fossil fuels leading to warming projections at the end of the century in the region of 5 °C above pre-industrial . The ensuing climate damages from such a strong warming scenario would severely impact the economy and slow growth and ensuing emissions , making this scenario an unlikely reality. It has been argued that SSP5-3.4-over is also unrealistic given its abrupt turnaround and reliance on high levels of carbon dioxide removal .

The CMIP6 protocol allows for (concentration-driven) scenario projections to be extended beyond 2100 to 2300, but only a few models performed the extensions . Beyond 2100, climate responses in models can differ substantially, and slow feedbacks and irreversibilities only become apparent on these timescales . Furthermore, 2100 is now less than one human lifetime away . Further studies using emissions-driven experiments have been undertaken in recent years, but realistic experiments may usually only be run to 2100 , with longer term experiments tending to be more idealized scenarios such as immediate zeroing of CO2 emissions . For the reasons above, there is interest in running more plausible and policy-relevant climate scenarios in CO2 emissions-driven ESMs, and these are intended to play a more important role in the upcoming CMIP7 phase beyond 2100 .

These considerations motivate two research questions:

how do overshoot and negative emissions manifest in responses in the global carbon cycle?

Fully answering both research questions requires a longer time horizon than 2100 to analyse long-term impacts and reversibility, and an ensemble of simulations to account for internal variability in climate and the carbon cycle. explored the responses in regional and extreme climate in overshoot scenarios in a multi-model ensemble context to 2100, and found that there was asymmetry in the responses before and after peak warming. used extended simulations to 2300 available for four models in ssp534-over, for which the longer term AMOC response exhibits a wide variety of behaviours. evaluated the global temperature, carbon stock and AMOC behaviour in five ESMs and one ESM of intermediate complexity in SSP5-3.4-over and SSP5-8.5 simulations run to 2300, noting substantial differences in AMOC and carbon uptake. However, these studies used simulations with prescribed concentrations, limiting the insight that changing emissions has on the carbon cycle and global climate.

In this paper, we run two ESMs under SSP1-1.9 (very low emissions, consistent with the 1.5 °C Paris Agreement goal), SSP2-4.5 (moderate emissions, most closely aligned to current policies with a projected warming in 2100 of around 2.5–3 °C), as well as adding additional simulations of SSP5-3.4-over (included under the Carbon Dioxide Removal Model Intercomparison Project (CDRMIP; )) to 2300. Therefore, we fill in the emissions-driven scenario space at the low and moderate levels compared to the availability of CMIP6 simulations. These runs are primed to study this question because emission-driven ESM simulations give a more detailed representation of the carbon cycle compared to concentration-driven simulations, which take their prescribed concentration pathways from simpler climate models or emulators . While emissions-driven experiments for net-zero and net negative pathways do exist, they have tended to be run with idealized, CO2-only trajectories . Running emissions-driven scenarios for a longer timeframe allows us to determine the carbon cycle, reversibility, and climate response to climate overshoot under negative emissions. These topics will become increasingly important as the 1.5 and 2 °C warming thresholds are approached in the absence of robust mitigation .

We use two emissions-driven ESMs: the Norwegian Earth System Model (NorESM2-LM; ) and the Max-Planck-Institute Earth System Model (MPI-ESM1.2-LR; ). These two ESMs are two of the best performing models with respect to reproducing observed atmospheric CO2 concentrations in the historical period (Fig. ). Given their good correspondence to historical concentrations, the MPI-ESM1.2-LR and NorESM2-LM models are appropriate for the analysis of future CO2 emissions-driven simulations.

The future scenarios are run from 2015 to 2300 and are labelled esm-ssp119, esm-ssp245, and esm-ssp534-over for SSP1-1.9, SSP2-4.5 and SSP5-3.4-over respectively. They are branched from CO2 emissions-driven historical simulations (1850–2014) known as esm-hist. In this paper, we follow the CMIP convention of labelling scenarios, which disallows the period “.” symbol (so the radiative forcing target is multiplied by 10) and removes the dash “-” between the SSP and RCP part of the scenario name. For additional distinction we italicize the CMIP6 name, hence ssp119 = SSP1-1.9. Furthermore, we again follow the CMIP6 convention of labelling CO2 emissions-driven scenarios as run in “Earth system model” mode, so our emissions-driven scenarios are prepended with “esm-”, e.g. esm-ssp119. Table  shows the ESM simulations performed within the project along with the number of ensemble members available for each model.

The ESMs are forced with the CO2 emission pathways used in the SSP scenarios, extended after the year 2100 as described in . Figure  shows the prescribed evolution of fossil fuel and industrial CO2 emissions in both models. The original CMIP6 extension protocol mandates that positive levels of CO2 emissions in 2100 are extended linearly to zero between 2100–2250, while negative emissions in 2100 are held constant for 40 years. After that, CO2 emissions linearly approach zero, which takes 30 years in esm-ssp534-over and 45 years in esm-ssp119. MPI-ESM1.2-LR implemented this protocol exactly, while NorESM2-LM implemented it differently such that negative emissions in esm-ssp119 start to linearly approach zero from 2100 with no phase of constant negative emissions. CO2 emissions from land use change are part of the terrestrial carbon cycle and are determined interactively by each ESMs. Land use transitions follow that of the underlying CMIP6 scenario, and no further land use transitions occur after 2100. Harvest rates are also held constant at 2100 levels for the post-2100 extensions. Non-CO2 GHGs are prescribed using pre-calculated concentration time series from .

In MPI-ESM1.2-LR, aerosols are prescribed using concentrations, in the form of the aerosol optical depth (AOD) from the MACv2-SP simulator . AOD is reduced linearly to zero between 2100 and 2250 if aerosol emissions are mostly associated with industrial processes in a specific region. In contrast to that, they are held constant after 2100 if they are mostly associated with biomass burning. This matches the information given to the land modules of the ESMs. In NorESM2-LM, aerosols are emissions-driven, and emissions of black carbon, organic carbon and sulfur follow the extension pathways of .

We present two CO2 emissions-driven ESMs run to 2300 under three different emissions scenarios: esm-ssp119 (a scenario designed to limit long-term warming to 1.5 °C with a small and temporary overshoot), esm-ssp245 (a roughly “current policies” scenario leading to around 2.5–3 °C warming in 2100) and esm-ssp534-over (a “high overshoot” scenario with very high greenhouse gas emissions in the short term and large amounts of carbon removal in the longer term). Each ESM has run multiple ensemble members for each scenario, which enables us to separate the forced signal from internal variability. The number of ensemble members required depends on the phenomenon being investigated: for global and regional mean state variables reported in this paper (temperature, precipitation, NPP, carbon fluxes and stocks, AMOC strength, thermosteric sea-level rise and ocean oxygen content) three members is likely sufficient to determine significant differences, though extremes (not evaluated in this paper) would benefit from a larger ensemble. We note several similarities and differences between the models. The two models have very different temperature responses, due to differences in the response of ocean circulation to climate forcing, especially for scenarios esm-ssp119 and esm-ssp534-over. Both NorESM2-LM and MPI-ESM1.2-LR peak in temperature in the 21st century, but while MPI-ESM1.2-LR declines and stabilizes thereafter, NorESM2-LM goes into a new warming phase that stabilizes in the 23rd century. Despite these differences, there are many responses that are similar in the two models. Considering esm-ssp534-over specifically we find that both models show:

a similar global distribution of anthropogenic carbon emissions among the atmosphere, ocean, and land. At the beginning of the simulations, most of the carbon remains in the atmosphere, but in the long term, the ocean becomes the dominant carbon reservoir;

In contrast, there are differences in the global and regional responses to CO2 emissions between the models resulting from varying sink strengths in the global carbon cycle and patterns of ocean warming. NorESM2-LM shows substantial hysteresis in its AMOC strength and regional patterns of warming when comparing periods before and after peak warming. MPI-ESM1.2-LR is more reversible in its AMOC and regional pattern of warming. While the main focus of our analysis of irreversibility was the esm-ssp534-over simulations, we note qualitatively similar behaviour for the smaller overshoot esm-ssp119 scenario for global temperature as a function of emissions. We find a similar pattern of regional temperature and precipitation response to periods before and after peak warming in the MPI-ESM1.2-LR model to concentration-driven scenarios in , indicating that physical climate responses are likely not sensitive to whether scenarios are run with prescribed emissions or concentrations.

While esm-ssp534-over was designed as a relatively extreme narrative to test the responses of ESMs to negative emissions, a large class of emissions scenarios that peak warming in the 1.5–2.0 °C range before declining towards the end of the 21st century were submitted by IAM teams to the IPCC Sixth Assessment Report . It is very likely that overshoot is required to limit global mean warming to 1.5 °C in the long term due to a lack of action on greenhouse gas emissions reductions in the last decade . Therefore, given the diversity of the responses of these two models to these scenarios, further investigation should target a larger set of models and additional overshoot pathways.

From a peak global mean temperature perspective, the results presented in this paper probably represent a “best case” scenario. Both models have a (150-year Gregory regression-derived) climate sensitivity on the low side of the CMIP6 range, and have a strongly negative ZEC meaning that temperatures are expected to cool after net zero CO2 is reached , notwithstanding the influence of non-CO2 forcers. The esm-ssp119 simulations peak below 1.5 °C in both models and are likely biased cool relative to historical GSAT change. The combination of low (Gregory) climate sensitivity, strong negative ZEC, and potential low-biased ensemble mean warming levels mean that the outcomes presented in the paper may underestimate the risks and challenges associated with overshoot scenarios. In addition, while on the cool side in terms of GSAT, the projections from NorESM2-LM suggest that large abrupt changes in AMOC, rapid phase of warming during the late 22nd century, and substantial regional changes such as cooling in Europe during the slowdown phase may pose more severe adaptation challenges than a model with higher peak warming but a more reversible regional climate profile. In reality, the Earth system's response could be more severe, with greater irreversibility and fewer opportunities for recovery. In order to sample the full range of plausible futures in response to CO2 emissions, more participating models running several different CO2 emissions-driven scenarios, with and without overshoot, are required . Even within our two-model ensemble we see very different long-term behaviours, and NorESM2-LM suggests that the risks of AMOC slowdown and regional cooling over Europe, as well as an unexpected warming rebound once negative emissions cease, cannot be ruled out.