Volume 10, Issue 10 e2022EF002715
Research Article
Open Access

Estimating the Likelihood of GHG Concentration Scenarios From Probabilistic Integrated Assessment Model Simulations

David Huard

Corresponding Author

David Huard

Ouranos, Montréal, QC, Canada

Correspondence to:

D. Huard,

[email protected]

Contribution: Conceptualization, Methodology, Software, Validation, Formal analysis, ​Investigation, Resources, Data curation, Writing - original draft, Visualization, Project administration, Funding acquisition, Writing - review & editing

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Jeremy Fyke

Jeremy Fyke

Canadian Centre for Climate Services, ECCC, Gatineau, QC, Canada

Contribution: Conceptualization, Data curation, Writing - original draft, Writing - review & editing

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Iñigo Capellán-Pérez

Iñigo Capellán-Pérez

Research Group on Energy, Economy and System Dynamics, Escuela de Ingenierías Industriales, University of Valladolid, Valladolid, Spain

Systems Engineering and Automatic Control, Escuela de Ingenierías Industriales, University of Valladolid, Valladolid, Spain

Contribution: Data curation, Writing - original draft, Writing - review & editing

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H. Damon Matthews

H. Damon Matthews

Concordia University, Montréal, QC, Canada

Contribution: Methodology, Writing - review & editing

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Antti-Ilari Partanen

Antti-Ilari Partanen

Climate System Research, Finnish Meteorological Institute, Helsinki, Finland

Contribution: Conceptualization, Data curation, Writing - review & editing

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First published: 19 September 2022
Citations: 4


The climate scenarios that form the basis for current climate risk assessments have no assigned probabilities, and this impedes the analysis of future climate risks. This paper proposes an approach to estimate the probability of carbon dioxide (CO2) concentration scenarios used in key climate change modeling experiments. It computes the CO2 emissions compatible with the concentrations prescribed by Coupled Model Intercomparison Project Phase 5 (CMIP5) and CMIP6 experiments. The distribution of these compatible cumulative emissions is interpreted as the likelihood of future emissions given a concentration pathway. Using Bayesian analysis, the probability of each pathway can be estimated from a probabilistic sample of future emissions. The approach is demonstrated with five probabilistic CO2 emission simulation ensembles from four Integrated Assessment Models (IAM), leading to independent estimates of the likelihood of the CO2 concentration of Representative Concentration Pathways (RCP) and Shared Socioeconomic Pathways (SSP). Results suggest that SSP5-8.5 is unlikely for the second half of the 21st century, but offer no clear consensus on which of the remaining scenarios is most likely. Estimates of likelihoods of CO2 concentrations associated with RCP and SSP scenarios are affected by sampling errors, differences in emission sources simulated by the IAMs, and a lack of a common experimental framework for IAM simulations. These shortcomings, along with a small IAM ensemble size, limit the applicability of the results presented here. Novel joint IAM and the Earth System Model experiments are needed to deliver actionable probabilistic climate risk assessments.

Key Points

  • Probabilistic Integrated Assessment Models (IAM) simulations of future carbon dioxide emissions are used to evaluate the relative probability of greenhouse gases concentration scenarios

  • Joint coordinated IAM and climate modeling experiments should be designed to enable probabilistic climate change risk assessments

Plain Language Summary

Climate model simulations are increasingly used to understand future trends in the severity and frequency of impactful climate hazards and associated physical and socioeconomic risks. Such simulations describe physical climate change in response to scenarios of greenhouse gases and land use change. However, the scenarios most widely used today as the basis for adaptation planning have no assigned probabilities; rather, they are explicitly intended to span a range of arbitrary climate futures. This reduces the applicability of resulting hazards projections for cost/benefit analysis of adaptation investments. To support risk-based adaptation decision-making, this study analyzes five sets of probabilistic carbon dioxide emissions simulated by four Integrated Assessment Models (IAM), along with Coupled Model Intercomparison Project Phase 5 (CMIP5) and CMIP6 climate model ensemble results, to estimate the probability of future greenhouse gases concentration scenarios. The results of the five IAMs simulations collated in this work vary, and although they might not be representative of the wider literature, most of them suggest that the high-emission scenario SSP5-8.5 becomes unlikely as we reach the second half of the century. Based on lessons learned in this exercise, we propose that new sets of IAM and climate model experiments be jointly designed to better support probabilistic climate change risk assessments.

1 Introduction

Future climate change impacts are captured in multimodel climate experiments designed and coordinated through the Coupled Model Intercomparison Project (CMIP). These climate modeling experiments explore, among other topics, the climate consequences of rising greenhouse gases (GHG) concentrations in the atmosphere (Taylor et al., 2012). Decision makers are now using these climate projections to assess hazards and make consequential planning and investment decisions. Often, however, risk assessments are carried out without the benefit of a fully probabilistic framework quantifying the leading sources of uncertainties that affect climate projections. These uncertainties include irreducible natural climate variability, modeling uncertainty due to the imperfect numerical representation of climatic processes, and scenario uncertainty owed to our limited capacity to forecast accurately future GHG and aerosol concentrations (Hawkins & Sutton, 2009).

While the climate community has been diligent in assessing and quantifying climate modeling uncertainties and natural variability (Lehner et al., 2020), and integrated assessment studies routinely evaluate socioeconomic uncertainties (Capellán-Pérez, 2016; Pastor et al., 2020), very little guidance is available regarding the relative probabilities of GHG scenarios underpinning the climate change simulations typically used to assess the impacts of climate change. In CMIP3, these transient climate change experiments were driven by a family of GHG emission scenarios called SRES (Special Report on Emission Scenarios), all considered “equally valid with no assigned probabilities of occurrence” (Murphy et al., 2009; Nakicenovic et al., 2000).

This reluctance to assign probabilities to GHG scenarios has continued in subsequent generations of GHG scenarios. In CMIP5, GHG concentration scenarios are defined by Representative Concentration Pathways (RCPs), and “no likelihood or preference is attached to any of the individual scenarios in the set” (van Vuuren et al., 2011). RCPs are meant to span a broad range of radiative forcing, but exclude any socioeconomic narrative. Conversely, CMIP6 Shared Socioeconomic Pathways (SSPs) explore how different socioeconomic factors (demography, education, economy, etc.) can lead to different radiative forcing levels, but still no probabilities are assigned to these narratives (Riahi et al., 2017).

From the point of view of users attempting to apply climate projections to climate change risk assessments, this lack of guidance on the probability of emission scenarios is a serious impediment to judgment formation, risk analysis, and ultimately, effective decision-making (Hieronymus, 2020; King et al., 2015; Schneider, 2001). According to Morgan and Keith (2008): “If judgments about likelihood are not supplied with the scenarios, they will be assumed by the users either explicitly or implicitly. The convention of not communicating information about the relative likelihood of scenarios therefore muddies communication between analysts and users.” The insistence on scenario-agnosticism leaves decision makers, with no special expertise in GHG scenarios, effectively responsible for assigning implicit or explicit likelihoods to future scenarios to craft high-cost, high-consequence adaptation plans (Ho et al., 2019).

To be fair, the probability of GHG emission scenarios is not a question climate modelers are well qualified to answer. The evolution of anthropogenic GHG emissions is influenced by policy, demography, economy, geopolitics and technology, topics well outside of the climate science needed to translate GHG emissions to changes in physical climate impacts. The description of these factors and their interactions are captured by another class of model called Integrated Assessment Models (IAM) (Agrawala et al., 2011; Koomey et al., 2019; Moss et al., 2010; Sokolov et al., 2005). The IAM community generates hundreds of different scenarios, predicated on assumptions regarding future climate policies, technological advances, demography, and energy markets. To simplify the task for climate modelers, the IAM community agrees on a set of socio-economic narratives, and a single marker IAM per narrative, whose output defines the GHG and land use scenarios underlying CMIP experiments. This selection is not meant to capture the most plausible scenarios, but rather to define representative pathways exploring the “full range of emission scenarios available in the current scientific literature, with and without climate policy” (van Vuuren et al., 2011).

The IAMs used in CMIP experiments simulate different storylines, but other avenues exist to assess emission scenario uncertainties. Indeed, van Vuuren et al. (2008) distinguish storyline-based scenarios and fully probabilistic scenarios. Storylines embody fundamentally different, yet internally consistent, representations of the future that can be represented by an IAM. Fully probabilistic scenarios are created by assigning probability distributions to key IAM input parameters and sampling from those distributions to create a set of probabilistic emission pathways. The “conditional probability approach” combines both storylines and probabilistic scenarios (see, e.g., Morris et al. (2022)), arguing that it is easier to define probability distributions for IAM parameters in the context of a storyline.

Defining probability distributions for IAM parameters is far from straightforward, and uncertainty analysis has been identified as one of the key current weaknesses of IAMs (Pastor et al., 2020; Rogelj et al., 2017). For example, one contentious topic relates to the parameterization of climate damages in cost-benefit IAMs. The family of cost-benefit IAMs traditionally relies on median damages, overlooking the low and high tails of the distribution for climate sensitivity. A lower or higher climate sensitivity implies smaller or larger climate hazards, and costs, for the same CO2 concentration pathway. If the climate sensitivity distribution has “fat tails,” using the median estimate could bias cost assessments (Ackerman et al., 2010; Keen, 2020; Stern, 2013; Weitzman, 2012). A related issue is the possibility of tipping points in the climate system and their impact on damage functions (Cai et al., 2016; Lontzek et al., 2015).

The need for quantitative probabilistic assessments of uncertainties was expressed in a guidance document to Intergovernmental Panel on Climate Change (IPCC) authors by Moss and Schneider (2000): “We believe it is more rational for scientists debating the specifics of a topic in which they are acknowledged experts to provide their best estimates of probability distributions and possible outliers based on their assessment of the literature than to have users less expert in such topics make their own determinations.” This comment was followed by the expectation that Bayesian approaches would be most appropriate to describe inherently subjective degrees of belief in our assessment of the state of knowledge. A Bayesian approach is one where probability is interpreted as a subjective degree of belief in a hypothesis, to be updated as new evidence becomes available, from an a priori probability to an a posteriori probability.

This view on the need for a Bayesian interpretation of uncertainties is often cited in later initiatives exploring or advocating for probabilistic emission scenarios. For example, M. Webster et al. (2002200320082012) sampled an a priori parameter distribution of the Emissions Predictions and Policy Analysis (EPPA) model to generate probabilistic GHG emission trajectories. These emissions were then fed into the MIT Integrated Global System Model (IGSM) to compute the posterior distribution for resulting temperature changes.

Schneider and Mastrandrea (2005), Sokolov et al. (2009), and Repetto and Easton (2015) similarly assigned probability distributions to parameters of the Dynamic Integrated Climate-Economy (DICE) model to assess the probability of dangerous anthropogenic interference with the climate system, and assess policy options. Schneider and Mastrandrea state: “We do not recommend that our quantitative results be taken literally, but we suggest that our probabilistic framework and methods be taken seriously: they produce relative trends and general conclusions that better represent a risk-management approach than estimates made without probabilistic representation of outcomes.”

Gillingham et al. (2018) ran multiple IAMs to assess the relative contribution of model structure and parametric uncertainty to future temperature, CO2 concentration, and economic output. Model parameters for population, productivity, and climate sensitivity were sampled from a priori probability distribution drawn from the literature.

This paper leverages similar future probabilistic emission simulations to estimate the probability for the CO2 scenarios of RCPs and SSPs. The paper targets experiments in which time-varying CO2 concentrations are prescribed to global climate models (GCM). In other words, probabilistic CO2 emission scenarios are used to assess the likelihood of CO2 concentrations associated with storyline scenarios.

2 Data and Methods

Contrary to a common misconception, coordinated climate change experiments typically used in climate impacts studies are not driven by GHG emissions, but instead use prescribed GHG concentrations. This reflects the fact that, historically, GCMs did not include biogeochemical processes involved in the translation of GHG emissions into atmospheric GHG concentrations. For recent CMIP iterations, emission scenarios drawn from select IAM simulations are harmonized (Gidden et al., 2019), converted into concentrations using the “model for the assessment of greenhouse gas-induced climate change” (MAGICC6 for CMIP5 (Meinshausen, Raper, & Wigley, 2011), and MAGICC7 for CMIP6 (Meinshausen et al., 2019)), and finally, downscaled and gridded (Feng et al., 2019). These gridded GHG concentrations are part of the boundary conditions prescribed to GCMs, along with land use scenarios, aerosol concentrations, and other important external climate boundary conditions. Thus, RCP and SSP CMIP experiments compare the climate consequences of reaching different GHG concentration levels, not the consequences of following different GHG emission pathways (Friedlingstein, 2015). Figure 1 illustrates how CMIP5 RCP experiments are tied to IAM scenarios.

Details are in the caption following the image

In Coupled Model Intercomparison Project Phase 5 (CMIP5) Representative Concentration Pathways (RCP) experiments, global climate models are prescribed greenhouse gases (GHG) concentrations estimated by the model for the assessment of greenhouse gas-induced climate change (MAGICC6) from emission scenarios simulated by four Integrated Assessment Models: IMAGE, Global Change Analysis Model (GCAM), AIM, and MESSAGE. In contrast, ESMs participating to the esmrcp85 experiment are driven by GHG emissions and compute concentrations through internal biogeochemical processes. Although details differ, the experimental setup for CMIP6 is conceptually similar.

The experimental setup shown in Figure 1 does not fully account for the carbon cycle modeling uncertainties and the significant coupling between the carbon cycle and the remainder of the climate system. Recognizing that the global carbon cycle and global physical climate system are in reality closely coupled, global climate modeling groups are increasingly integrating comprehensive representations of the carbon cycle (and other biogeochemical cycles) directly into model code. One practical outcome of this work is that these models (termed “Earth system models” instead of “global climate models” in recognizance of their increased process representation) can be forced directly by emission fluxes. This approach is reflected in standardized CMIP experimental protocols, esmrcp85 and esm-ssp585, in which ESMs are driven directly by GHG emissions. Analysis of such emission-driven climate simulations (e.g., as defined by the Coupled Climate–Carbon Cycle Model Intercomparison Project (C. D. Jones et al., 2016)) typically indicates that uncertainties in carbon cycle feedbacks and their representation in ESMs can lead to a broad range of future atmospheric concentrations for a given emissions forcing pathway (Booth et al., 2013). Assessing the probability of concentration-driven experiments based directly on their IAM emissions would thus neglect carbon cycle uncertainties and make results sensitive to biases in MAGICC.

An RCP or SSP scenario is a shorthand to describe an elaborate experimental design (Eyring et al., 2015), of which the CO2 concentration trajectory is just one component (note that we use “SSP scenario” to refer to CMIP experiments, not the socio-economic storyline). Climate modeling teams set up their model following this experimental design, run one or many simulations (realizations), then archive model outputs according to precise data and metadata specifications meant to facilitate model intercomparisons. Model outputs include hundreds of different variables, from which many climate hazards can be derived: heatwaves, sea level rise, extreme rainfall, droughts, etc. To quantify uncertainties, climate impact studies typically include results from multiple realizations from multiple models driven by multiple GHG concentration scenarios. With these results in hand, a legitimate question by decision makers could be: “considering known uncertainties and available CMIP6 results, what is the probability of precipitation exceeding a threshold over the period 2050–2070?”

2.1 A Probabilistic Framework to Assess Climate Hazards

Let us denote a climate hazard as H. Risk analysts and decision makers are interested in P(H(t)), the probability of occurrence of hazard H at some time t in the future (to lighten the presentation, time dependence t is implicitly assumed in the following). Here, we use the term probability to denote a subjective degree of belief in a hypothesis, not a frequency of occurrence. First, we first suggest that GCM simulation results M, of a CMIP experiment based on a CO2 concentration scenario S, can provide a probability estimate of climate hazards conditional to that concentration scenario occurring: P(HM, S). Second, we make the claim that probabilistic emission simulations from IAMs eP = eP,1, …, eP,n can be used to inform the probability of those same scenarios S.

Although in principle CMIP offers multiple experiments to draw from, the climate impact community has mostly relied on a limited set of concentration-driven experiments. For CMIP5, these include rcp26, rcp45, rcp60, and rcp85, here denoted as SCMIP5, the set of concentration-driven CMIP5 RCP experiments. CMIP6 counts nine such ScenarioMIP experiments (O’Neill et al., 2016), but participating models are minimally expected to contribute simulations to four Tier 1 experiments, ssp126, ssp245, ssp370, and ssp585, denoted here as SCMIP6. If we assume that the future climate is captured by either set of scenarios (SSP(S) = 1), then we propose that the hazard probability can be estimated given GCM simulations M and probabilistic emission simulations eP, by a weighted sum of conditional hazard probabilities based on CMIP experiments:

The term P(HM, S) of Equation 1 is what climate impact studies routinely compute (note that eP was dropped from the expression, since it adds no further information relevant to assess H). Its computation can be as simple as a fit of a normal distribution to the hazards simulated by a multimodel ensemble, or can include considerations regarding model performance or model independence (Knutti et al., 2017). Our focus in this paper is on the second term, the probability of an RCP or SSP scenario, given data on future emissions and GCM results. A simple way to compute this term would be to use kernel density estimation (KDE) to construct a nonparametric probability density function (PDF) for the probabilistic emissions eP, then compute the likelihood of each scenario's emissions. The weakness of this approach is that we would use the emission scenario probability to weigh concentration-driven hazards and implicitly assume no bias nor uncertainties affect MAGICC's carbon cycle representation.

We suggest that in Equation 1, hazards estimated from concentration-driven experiments should be weighted by the probability of their concentration pathway, not their emission pathway. Comparing the concentration pathways to probabilistic IAM emissions, however, requires a mechanism to convert one into another. Here, we suggest to use an approach described in Jones et al. (2013) to diagnose emissions compatible with prescribed emissions (described in the next section). For each CMIP experiment, this will yield an ensemble of compatible emissions eC,S, which can be compared with probabilistic emissions. Again, a simple way to compute the likelihood of those compatible emissions would be to evaluate their PDF against the probabilistic emissions' KDE. Trials with this approach, however, yield very noisy likelihoods at the start of the IAM simulations when the PDF is extremely narrow.

The approach proposed here is to use Bayes' theorem, to evaluate the probability of probabilistic emissions conditional on compatible emission, so that the second term of Equation 1 becomes:

The term P(ePeC,S) of Equation 2 stands for the probabilistic emissions likelihood given compatible emissions diagnosed from concentration-driven GCM simulations, and its computation is discussed in the next section. The term P(S) is the prior for the scenario. It can be set by the risk analyst to reflect subjective opinions, calculated based on other independent evidence, or assigned uniform values to denote a lack of a priori preferences. The choice of prior is not addressed in this paper.

Note that ideally, scenario likelihood should be evaluated on all the significant components of scenarios: CO2, methane, other GHGs and aerosols concentrations, as well as land use changes. To reduce the problem's scope, here we demonstrate an evaluation of scenario likelihood based only on the global CO2 trajectory and ignore the influence of other scenario components. This is a strong caveat of the results presented in this paper because land use change, non-CO2 GHGs, and aerosol emissions also make significant contributions to radiative forcing and consequent physical climate impact changes (IPCC, 2021).

2.2 Likelihood of Emission Trajectories

This section explains how the likelihood term P(ePeC,S) of Equation 2 is computed. The first step is to diagnose, for each CMIP experiment, emissions compatible with prescribed CO2 concentrations. Compatible CO2 emissions are the anthropogenic fossil fuel CO2 emissions that balance CO2 fluxes between the air, land, and ocean when GCMs are prescribed a CO2 concentration pathway. If ca, co and cl stand respectively for the carbon stored in the atmosphere, the ocean, and the land surface, then compatible fossil fuel emissions ec are given by the imbalance in the CO2 budget:

The first term on the right of Equation 3 is computed by taking the time derivative of the CO2 concentration pathway prescribed by RCPs (Meinshausen, Smith, et al., 2011) and SSPs (Gidden et al., 2019; Riahi et al., 2017). The other two terms are estimated by the CO2 fluxes from the atmosphere into the ocean and land simulated by CMIP GCMs (Liddicoat et al., 2021).

All CMIP5 RCP and CMIP6 SSP Tier 1 model simulations for which both the gas exchange CO2 flux into the ocean (fgco2) and the CO2 flux from the atmosphere into the land (nbp) were available on the Earth System Grid Federation and free from defects are used (the number of simulations available per model is listed for CMIP5 and CMIP6 in Tables A1 and A2 respectively). Global fluxes are computed by multiplying ocean and land fluxes by the respective fractional ocean area (sftof) and land area (sftlf) as well as the respective grid cell area (areacello, areacella), and summing over the entire globe. Annual compatible emissions ec estimated by Equation 3 are shown in Figure 2. For models whose preindustrial simulations (piControl) are available, the mean compatible emissions over the last 30 years of the preindustrial period (see Tables B1 and B2) are subtracted from historical and future emissions.

Details are in the caption following the image

Compatible fossil carbon dioxide (CO2) emissions diagnosed from Coupled Model Intercomparison Project Phase 5 (CMIP5) (left) and CMIP6 (right) simulations from historical (gray) and future (color) scenarios. Thin lines denote individual climate model simulations, thick solid lines the multimodel mean for each experiment, and thick dashed lines the Integrated Assessment Models (IAM) scenario emissions described by Representative Concentration Pathways (RCPs) and Shared Socioeconomic Pathways (SSPs). Differences in the carbon cycle representation of ESMs such as vegetation dynamics, fire-carbon interactions, or ocean biochemistry explain the inter-model spread. Note that the mean is not always centered on individual simulations because it is first calculated over ensemble members, then over models. This is especially visible in the right panel for SSP5-8.5, where a cluster of 50 CanESM5 simulations stands apart.

For each RCP and SSP experiment, we thus have an ensemble of emissions that are compatible with the CO2 concentration scenario. These emissions are different from the original RCP and SSP emission pathways, in part due to differences in the carbon cycle representation of individual GCMs compared to MAGICC. If we assume that the probability density of those compatible emissions can be described by a normal distribution, taking the mean μS(t) and variance urn:x-wiley:23284277:media:eft21151:eft21151-math-0004 of diagnosed emissions for each scenario S lets us define a time-dependent functional form for the emission likelihood:
where urn:x-wiley:23284277:media:eft21151:eft21151-math-0006 stands for the PDF of the normal distribution, and Ei[⋅] for the mean over dimension i, here the set of all probabilistic emission simulations (i = 1…, n).
To account for the varying number of realizations per GCM, ensemble statistics are first evaluated across realizations for each model, then across models within each experiment. More explicitly, if eS,m,r stands for compatible emission from experiment S, model m and realization r, and if Ed[⋅] and Vd[⋅] stand for the mean and variance over dimension d respectively, then.

Table 1 shows the number of simulations and models available to compute those statistics for CMIP5 and CMIP6. Note that for RCP6.0, only seven models were available.

Table 1. Number of Simulations and Global Climate Models With at Least One Simulation Available for Each Coupled Model Intercomparison Project Phase 5 (CMIP5) and CMIP6 Experiment
CMIP5 Historical RCP2.6 RCP4.5 RCP6.0 RCP8.5
Simulations 35 23 27 10 27
Models 13 11 13 7 13
CMIP6 Historical SSP1-2.6 SSP2-4.5 SSP3-7.0 SSP5-8.5
Simulations 233 121 155 131 112
Models 22 17 16 18 16
  • Note. For a breakdown per model, see Tables A1 and A2.

2.3 Probabilistic IAM Emission Simulation Ensembles

The emission likelihood, defined in Equation 4 and parameterized with the statistics of compatible emissions for each RCP and SSP, can now be estimated for different ensembles of probabilistic emission simulations. Probabilistic emission simulations (Figure 3) are taken from five papers, two of those using the same IAM. These papers were selected opportunistically based on two main criteria: ensembles of probabilistic CO2 emission time series up to 2100 were available publicly or from the authors, and the simulations did not explicitly constrain emissions to meet policy ambitions. Note that these IAMs were not intended to yield predictive emissions for real-world decision making; hence, results derived from those simulations should not be interpreted too literally. They are used here mainly to illustrate the potential of probabilistic IAM simulations to inform climate risks. To lighten the text, each paper is identified by an abbreviation.

Details are in the caption following the image

Stochastic CO2 emissions (left) and cumulative emissions (right) from Fyke and Matthews (2015) [FM15], Capellán-Pérez et al. (2016) [CP16], Raftery et al. (2017) [R17], Liu and Raftery (2021) [LR21], and Capellán-Pérez et al. (2020) [CP20] (gray), overlaid with Integrated Assessment Model emissions from Coupled Model Intercomparison Project Phase 5 (CMIP5) Representative Concentration Pathways (RCPs) (solid lines) and CMIP6 Shared Socioeconomic Pathways (SSPs) (dashed lines). Note that for CP20, abrupt jumps in the emission time series are likely due to the lack of geological constraints to fossil fuel extraction rates. Nonrenewable resource availability is modeled using supply cost curves, and when a resource is depleted, its extraction drops to zero the following year.

Fyke and Matthews (2015) [FM15] have developed a reduced-form numerical carbon emission IAM based on differential equations describing the exchange of carbon between geological and exogenous (atmosphere, ocean, and biosphere) reservoirs. The fluxes between those reservoirs depend on extraction and consumption rates, which in turn depend on availability and prices for fossil fuel and its alternatives. The model counts 28 parameters, 17 of which have significant uncertainty. For each of these uncertain parameters, a probability distribution describing its uncertainty was defined based on published estimates and expert judgment. The parameters were sampled (n = 100,000) from their prior distributions using a Latin hypercube sampler, and time series (2012–2100) of carbon emissions were generated from the model equations. The parameters whose uncertainty had the greatest impact on emissions are the minimum future nonfossil energy cost, the maximum size of potential fossil energy resources, and the maximum potential carbon pricing.

Capellán-Pérez et al. (2016) [CP16] leverage the Global Change Analysis Model (GCAM), combined with a probabilistic assessment of recoverable energy resources, supply cost curves, and climate sensitivity, to analyze the relative importance of these factors in the temperature response at the end of the century. The study focuses on energy availability considerations, adopting the “remaining ultimately recoverable resources” (RURR) approach to estimate non-renewable energy sources. Uncertain parameters are sampled (n = 1,000) from their respective prior distribution by Monte Carlo, fed into GCAM to obtain CO2 emissions, which are ingested by MAGICC to compute total radiative forcing and the global temperature response over the period 2005–2100. GCAM is run in baseline mode, meaning that no climate policy is imposed. The results reveal that the coal RURR uncertainty is the determinant factor among the fossil fuel resources considered. It also shows that not accounting for the values in the upper ranges of fossil fuel availability can lead to an underestimate of total radiative forcing by the end of the century.

Raftery et al. (2017) [R17] propose a model based on the country-level Kaya identity, where the future carbon emissions of a country are given by the product of population, gross domestic product (GDP) per capita, and carbon intensity (carbon emitted by GDP). Probabilistic population projections up to 2100 are taken from the United Nations (2015), reflecting data up to 2015. A joint Bayesian hierarchical model for GDP and carbon intensity is calibrated on data from 1960 to 2010. The model assumes an evolving world technology frontier, to which countries' GDP converge at country-specific rates, and that all countries have reached a carbon intensity peak and are now on a declining trend. Model parameters are sampled by Monte Carlo (n = 100,000) and the distribution of emissions analyzed to assess the relative importance of population (2%), GDP (50%), and carbon intensity (48%). The model omits explicit future climate policy, but the fact that model parameters are calibrated on historical data ensures that the influence of past and current policies are included in projections.

Liu and Raftery (2021) [LR21] use the same model as Raftery et al. (2017), but with five additional years of population (United Nations, 2019), economic, and emission data. Slower growth in emissions during the 2010–2015 period, compared to the 1960–2010 period, explains the lower global annual emissions.

Capellán-Pérez et al. (2020) [CP20] describe the MEDEAS-W IAM developed within the homonymous EU project (Modeling Energy System Development under Environmental and Socioeconomic constraints). The model describes interactions between the economy, energy demand, energy availability, energy infrastructures, and return on energy invested, minerals, land use, water, climate, emissions, and social and environmental impact indicators. The model is meant to inform decision-making regarding the transition to sustainable energy systems, and pays considerable attention to biophysical constraints to growth and energy availability, mineral and energy investments for energy shifts, sectoral economic structure, and climate change damages. The model accounts for the characteristics of 25 energy sources, and technologies, including reserves, extraction rate, intermittency of some renewable energy sources and requirements for storage and overcapacity. The model assumes technological improvements and substitution mechanisms, but also constraints to the potential for renewables due, for example, to lower quality siting and thermodynamical limits to generation efficiency. A nonlinear climate damage function affects production and growth rate, consistent with the interpretation of “dangerous climate change” beyond CO2 concentration thresholds. Monte Carlo simulations (n = 1,000) are run to perform an uncertainty analysis for 72 inputs. Figure 3 shows CO2 emissions (1995–2100) simulated for the reference (Ref) scenario, a conditional probability approach based on the business as usual storyline.

Comparing the studies above highlights several themes. It is particularly notable that each of the studies apply very different modeling frameworks, including fundamental differences in model design, choices of endogenous/exogenous variables, and sampling methods for exogenous variables, to arrive at a very similar output measure—that is, probabilistic estimates of future emissions. For example, R17 and LR21 construct a data-driven statistical model framework that applies the simple Kaya identity at multiple points of time to develop emission time series. In contrast, FM15, CP16, and CP20 use more sophisticated time stepping numerical models with inherent system dynamics, albeit with very different numerical methods. FM15 treats the global fossil fuel resource volume as an endogenous model component, whereas CP16 treats fossil fuel resources as an exogenous input variable and focus numerical efforts on estimating prices consistent with cleared markets, a concept which is entirely absent in the FM15 approach. In CP20, the total amount of reserves is fixed, and the extraction rate is subject to physical constraints (maximum extraction curves).

Second, the studies described here apply notably different methods to sample exogenous inputs to the respective model frameworks. R17 and LR21 dedicate the most effort toward this aspect in applying a hierarchical Bayesian model framework approach for estimating modeled input parameters. Indeed, the term “model” in their study primarily applies to the statistical models which derive the inputs for the Kaya Identity relationship, rather than the functional equation itself. In contrast, FM15 use relatively simpler sampling of a larger number of uncertain, scalar, model parameters based on a normal distribution-weighted Latin hypercube sampling approach that does not discriminate potential interdependencies between parameters. Providing further contrast, CP16 sample input parameters from empirical distribution functions for key input parameters, with distribution functions for important input parameters developed from available published literature values. In CP20, 72 uncertain parameters are sampled from uniform distributions, with ranges that go from ±20% around the reference scenario for most parameters, to ±50% or even [−50%, +100%] for the most uncertain parameters.

A critical additional difference across studies is the definition of CO2 emissions and the processes that contribute to them. FM15 simulates emissions from fossil fuel combustion only, while R17 and LR21 also include cement production. CP16 emissions account for industrial processes, fossil fuel combustion, and land use change, and in CP20 losses from energy transformation and distribution are included as well.

Despite model methodological differences, several fundamental similarities emerge across the studies. Per selection criteria, all papers adopted methodologies for model design and simulation production that avoided any predefinition of final results that model simulations are forced to meet (so-called perfect foresight or “policy optimization” modeling). This contrasts fundamentally with the CMIP scenario families, which are constrained by design to reach predetermined radiative forcing levels in 2100. It also contrasts with scenarios exploring pathways consistent with avoidance of exceedance of temperature thresholds (e.g., 2°C above preindustrial temperature). Avoiding the “perfect foresight” approach is a necessary precondition for any fully scoped probabilistic assessment of future emissions, because it allows probabilistic assessments to develop in a free-running manner without a priori constraints on final emission levels, radiative forcing anomalies, or temperature targets.

2.4 Annual Versus Cumulative Emissions

Key climate change features, such as changes to global air temperature, surface ocean temperature, and sea level, are nearly linearly related to cumulative emissions (Matthews et al., 2009; Williams et al., 2012). Given our objective is to assess the probability of such climate impacts, it makes sense to compute Equation 4 on cumulative emissions rather than annual emissions. This slightly complicates the analysis, because results now hinge on the year from which we start accumulating emissions.

Historical CMIP5 and CMIP6 experiments start in 1850, while future scenarios start in 2006 for CMIP5 and 2015 for CMIP6. On the other hand, the five probabilistic IAM emissions simulations presented above start in 1990, 1995, 2010, 2012, and 2015. To align all results to a common starting point, all emissions are accumulated from 1750 onward, using observations taken from the Global Carbon Budget project (Friedlingstein et al., 2020) to fill gaps. For example, the probabilistic cumulative emissions from FM15, starting in 2012, are incremented by the 2011 observed cumulative emission. Diagnosed compatible cumulative emissions for historical simulations are similarly incremented by observations from the year before the start of the experiment (1849 for CMIP6 and 1861 for CMIP5 to account for missing data in some simulations). Future simulations are matched with historical simulations from the same model, and whenever possible, the same realization.

2.5 Data Access and Analysis Software

CMIP5 and CMIP6 CO2 land and ocean fluxes, grid cell areas, and land-sea fractions were downloaded from ESGF using Synda (Nasser et al., 2020). Probabilistic emission simulations were obtained from authors (FM15, CP16, and CP20), or reproduced by running publicly available code (R17, LR21, see Data Availability Statement). Computations were carried out in the Python programming language using xarray (Hoyer & Hamman, 2017), pandas (McKinney, 2010), NumPy (Harris et al., 2020) and SciPy (Virtanen et al., 2020), and graphics created with Matplotlib (Hunter, 2007). Analysis-ready data and code to reproduce results from this paper are available at the Federated Research Data Repository (Huard, 2022).

3 Results

The following sections discuss different types of emissions, and to avoid confusion, we use the following terminology. Scenario emissions refer to CO2 emissions pathways defined in RCP and SSP scenarios. Compatible emissions are inferred from carbon fluxes simulated by CMIP models using Equation 3. Finally, probabilistic emissions denote ensembles of probabilistic CO2 emission trajectories simulated by the IAMs described in Section 2.3.

The mean and standard deviation of compatible cumulative emissions for RCPs and SSPs are shown in Figure 4. For CMIP5 experiments, RCP6.0 and 8.5, compatible cumulative emissions are considerably smaller than scenario emissions. In other words, lower emissions are needed in CMIP models than in MAGICC6 to reach the same CO2 concentration. This could suggest that positive carbon feedbacks might be more powerful in GCMs than in MAGICC6, or that MAGICC6 has more effective ocean or land carbon sinks. See Jones et al. (2013) and Friedlingstein et al. (2014) for further discussions. The inverse is true for CMIP6, where the ensemble mean of compatible emissions is systematically larger than SSP scenario emissions. Note that although RCP8.5 and SSP5-8.5 have approximately the same radiative forcing in 2100, their CO2 concentrations are different, and the differences in emissions are expected. These differences have important repercussions for the interpretation of scenario probability.

Details are in the caption following the image

Mean (thick solid line) and standard deviation (envelope) of cumulative compatible emissions diagnosed from carbon fluxes in Coupled Model Intercomparison Project Phase 5 (CMIP5) Representative Concentration Pathway (RCP) (left) and CMIP6 Shared Socioeconomic Pathway (SSP) (right) Tier 1 experiments. The thick dashed lines display cumulative emissions from RCP and SSP scenarios.

Equation 4 evaluates the overlap between the distribution of compatible cumulative emissions for each scenario and the distribution of probabilistic IAM cumulative emissions. This is illustrated for CMIP6 SSPs in Figure 5 for one ensemble of probabilistic emissions, R17, and one year, 2100. Although the time-dependence of scenario likelihood may feel counter-intuitive, it is useful in cases where we are interested in climate impacts over a given period. Indeed, it would not make sense for a probabilistic assessment focussing on 2050 to be affected by later scenario behavior in 2100. Of course, what happens prior is obviously relevant, and this is partially ensured by relying on cumulative emissions rather than annual emissions.

Details are in the caption following the image

Illustrative histogram of cumulative emissions from Raftery et al. (2017) compared to a normal fit of cumulative compatible emissions (full line) for the four Shared Socioeconomic Pathway (SSP) scenarios in 2100. SSP scenario cumulative emissions (dashed line) are shown for reference.

For each of the five probabilistic emission simulation ensembles, the likelihoods of the RCP and SSP scenarios are computed using Equation 4, then normalized such that on each year their sum equals one. Figure 6 shows the results. A notable feature is that high-end emission scenario RCP8.5 remains reasonably likely in all five IAMs until around 2060, although it lies in the upper tail of probabilistic emissions from R17, LR21, and CP20. This is due to Equation 4 evaluating scenario likelihood against compatible emissions, which for RCP8.5 are smaller than scenario emissions (see Figure 2). Another feature worth highlighting is the consistently low likelihood of RCP2.6. Interestingly, for R17, LR21, and CP20, SSP1-2.6 is more likely than SSP3-7.0 by the end of the century.

Details are in the caption following the image

Bayesian likelihood for Coupled Model Intercomparison Project Phase 5 (CMIP5) Representative Concentration Pathways (RCPs; top) and CMIP6 Shared Socioeconomic Pathways (SSPs) (bottom) CO2 concentration pathways conditional on Integrated Assessment Models' probabilistic CO2 cumulative emission simulation ensembles from FM15, CP16, R17, LR21, and CP20. Theoretically, all scenarios should start with a likelihood close to 25% because the CO2 concentration is identical at the start of each experiment. Discrepancies seen in CMIP5 RCP6.0 and SSP3-70 are due to differences in the CMIP ensemble makeup.

As mentioned earlier, results from this probability assessment should not be interpreted too literally. For one, probabilistic CO2 emissions are not directly comparable among the different IAMs. The CO2 emission processes simulated by each IAM are different: some include cement production and industrial uses, while others do not. Also, emissions from CP16 and CP20 account for land use changes, while compatible emissions do not. Those differences directly affect the estimated likelihoods.

Second, each IAM deals with policies very differently. Capellán-Pérez et al. (2020) include numerous policies regarding low-carbon technologies, energy efficiency, recycling, transportation, and afforestation. Fyke and Matthews (2015) include policy-related parameters such as a maximum carbon price, a carbon tax, or nonfossil energy unit cost. In contrast, Capellán-Pérez et al. (2016), Raftery et al. (2017), and Liu and Raftery (2021) include no explicit parameterization for climate policies.

Finally, the relatively small number of IAMs and the fact that GCM ensembles are not homogeneous across experiments artificially distort the likelihood estimation. For instance, we would expect likelihoods to start at 25%, because scenarios share the same initial CO2 concentration. With identical CO2 concentration, the diagnosed emissions and their statistics should be very similar, except for small variations due to natural variability. Small ensemble sizes and differences in model makeup can shift the mean (Equation 5) and standard deviation (Equation 6) of compatible emissions compared to the other scenarios, artificially perturbing the likelihood. This example gives a sense of the magnitude of the sampling error's influence on the results and cast doubts on the applicability of these specific likelihood assessments for decision-making.

4 Discussion

The motivation for this paper is grounded in the day-to-day experience of climate service providers. Climate services strive to translate the best available climate science into actionable information. Because key climate projection experiments utilize prescribed GHG concentration scenarios, derivative products such as climate impact assessments or risk analyses are also conditional on GHG concentration scenarios. In applications such as engineering or flood zone mapping, where a single value reflecting a level of risk is required, the lack of guidance on scenario probability acts as a barrier to climate adaptation.

One argument against assigning probabilities to emission scenarios is that it would be affected by reflexive uncertainty originating from human feedback to new information (Dessai & Hulme, 2004; van Vuuren et al., 2008). That is, the act of assigning probabilities to scenarios would change the probability of these scenarios, making future climate change “unquantifiable.” Although this argument might hold in the abstract, the idea that an academic paper would have a significant influence on global carbon emissions nowadays can only be met with irony. Also, the climate risk assessments targeted by this study take place at a project or organization level and are almost entirely uncoupled from questions of global carbon emissions policy.

The reluctance of the climate community to assign probabilities to future GHG emission scenarios has led to the study of alternative decision-making approaches, often called “Decision-Making under Deep Uncertainty” (DMDU) (Stanton & Roelich, 2021). One suggestion stemming from these efforts is to switch the focus of discussions from agreement-on-assumptions, for example, climate modeling assumptions, to agreement-on-decisions in order to find solutions that perform well under a wide array of future conditions and minimize regret (Kalra et al., 2014). Although valuable and illuminating, these concepts are not easily applied to decisions bound by strict regulatory frameworks, such as engineering or flood safety. Asking practitioners to overhaul laws, professional norms, and regulations to account for climate change's deep uncertainties is sure to delay adaptation actions.

Lacking a fully probabilistic decision-making framework, real-world adaptation decisions are made by nonexperts, relying on an ad hoc selection of climate scenarios based on data availability, the precautionary principle, personal opinions, or hearsay. Even among experts, debates around the relative likelihood of climate change scenarios often struggle with the emission versus concentration aspects of climate change experiments (Hausfather & Peters, 2020a2020b; Schwalm et al., 2020a2020b). The argument that “RCP8.5 is unlikely because it requires an implausible increase in coal use” may be true for the scenario's emissions (Ritchie & Dowlatabadi, 2017), but on its own does not imply that impacts derived from the concentration-driven rcp85 CMIP experiment are also unlikely. As long as climate hazards are determined by concentration-driven modeling experiments, arguments referring to emissions' likelihood will have to account for uncertainties in carbon cycle simulations and carbon feedbacks.

To assess the probability of climate hazards, we suggest a possible design for a joint, coordinated multimodel experiment for emissions-forced ESMs and IAMs. First, an ensemble of 20–30 representative future emission pathways would be defined from IAM simulations. Pathways would be selected to cover a wide range of plausible future GHG emissions, but with no specified a priori probability. These would then be prescribed to a multimodel ensemble of ESMs minimally running one simulation per pathway. In parallel, IAM modelers would run probabilistic forecasts accounting for the main sources of GHG emission uncertainties. We use the word forecast intentionally to clarify that these simulations represent a partly subjective, best effort description of future emissions. Both the ESM and IAM experiment would include a historical period to allow for evaluations of model performance against observations. The ensemble of IAM simulations could then be used to assign probabilities to each representative emission pathway. These pathway weights, combined with ESM's performance weights, could then be used to post-stratify ESM simulations and yield probabilistic distributions of future climate hazards.

Such an emission-driven experiment would have the benefit of accounting explicitly for uncertainties in carbon feedbacks, which are partially neglected by concentration-driven experiments (van Vuuren et al., 2011). The results would likely change the partitioning of uncertainty (Hawkins & Sutton, 2009), and allow for fine-grained cost-benefit analyses of emission mitigation options. Together, this joint IAM-ESM experiment would yield the basic materials to conduct probabilistic climate change impact assessments and answer a long-standing request from the climate service community and its stakeholders.

5 Conclusion

This paper adopts the argument that “it is very unhelpful to presume that all futures are equally likely” (Mckibbin et al., 2004) and suggests an approach to estimate CO2 concentration scenario probability using probabilistic emissions simulated by IAMs. Because climate models are prescribed concentration pathways, these probabilistic emissions are not compared directly to scenario emissions but rather to CO2 emissions compatible with prescribed concentrations. Compatible emissions are estimated for CMIP5 RCPs and CMIP6 SSPs using simulated CO2 fluxes. The distribution of those compatible emissions is compared against the distribution of five IAMs' emission ensembles to estimate each scenario's likelihood.

Although IAMs vary considerably in their structure and assumptions, the likelihoods obtained share similar traits. All rank RCP2.6 as the least likely until 2075. Although RCP8.5 depicts extremely high emissions, it remains relatively likely up until 2060. This is because compatible emissions for high-end scenarios are considerably lower than their corresponding scenario emissions. For three IAMs out of five, SSP1-2.6 ends up more likely than SSP3-7.0 and SSP5-8.5 by the end of the century, with SSP5-8.5's likelihood dropping to zero in three IAMs.

The approach and results presented here are subject to several important caveats, and we stress that our objective is not for the likelihoods presented here to be used in practice, but rather to illustrate the potential of IAMs to inform scenario probability. Overcoming these caveats should be the focus of continued research and novel coordinated climate and IAM experiments, with the objective of delivering fully probabilistic information in support of real-world climate change risk assessments.


We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups (whose models are listed in Tables A1 and A2 of this paper) for producing and making available their model output. For CMIP, the U.S. Department of Energy's Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. D.H. work is funded in part by Transport Canada. Many thanks go to Ramón de Elía for the impetus to write this paper, Diane Chaumont for the opportunity to finish it, and Martin Leduc and Patrick Grenier for their suggestions. The authors also thank David Álvarez Antelo for rerunning the n = 1,000 Monte Carlo simulations for CP20 and extract CO2 samples, Gaëlle Rigoudy and Roland Séférian for help regarding CNRM-ESM2.1 fluxes, Michio Kawamiya for help regarding MIROC-ESM, and Spencer Liddicoat for clarifications regarding compatible flux computations.

    Appendix A: CMIP Simulations Availability

    Search requests on ESGF for CMIP5 and CMIP6 simulations were last updated in August 2021. A simulation is considered available if both variables fgco2 and nbp are present for the historical period and at least one future experiment. In CMIP5, models MRI-ESM1 and CMCC-CESM were not considered due to the presence of abnormalities in the data. Also, INMCM4 was kept out of the analysis because it does not represent land use changes. The number of simulations per model used in this study is shown for CMIP5 and CMIP6 in Tables A1 and A2 respectively.

    Table A1. Number of Simulations Storing Land and Ocean Carbon Fluxes for Each Coupled Model Intercomparison Project Phase 5 Transient Scenario Experiment
    Model name Historical RCP2.6 RCP4.5 RCP6.0 RCP8.5
    CanESM2 5 5 5 0 5
    GFDL-ESM2G 1 1 1 1 1
    GFDL-ESM2M 1 1 1 1 1
    HadGEM2-CC 3 0 1 0 3
    HadGEM2-ES 4 4 4 4 4
    IPSL-CM5A-LR 6 4 4 1 4
    IPSL-CM5A-MR 3 1 1 0 1
    IPSL-CM5B-LR 1 0 1 0 1
    MIROC-ESM 3 1 1 1 1
    MIROC-ESM-CHEM 1 1 1 1 1
    MPI-ESM-LR 3 3 3 0 3
    MPI-ESM-MR 3 1 3 0 1
    NorESM1-ME 1 1 1 1 1
    Table A2. Number of Simulations Storing Land and Ocean Carbon Fluxes for Each Coupled Model Intercomparison Project Phase 6 Tier 1 ScenarioMIP Experiment
    Model name Historical SSP1-2.6 SSP2-4.5 SSP3-7.0 SSP5-8.5
    ACCESS-ESM1-5 29 10 12 10 10
    CESM2 11 3 3 3 3
    CESM2-FV2 3 0 0 0 0
    CESM2-WACCM 3 1 5 3 5
    CESM2-WACCM-FV2 3 0 0 0 0
    CMCC-ESM2 1 1 1 1 1
    CNRM-ESM2-1 9 5 10 5 5
    CanESM5 65 50 50 50 50
    CanESM5-CanOE 3 3 3 3 3
    EC-Earth3-CC 1 0 1 0 0
    GFDL-ESM4 1 1 0 1 0
    INM-CM4-8 1 1 1 1 1
    INM-CM5-0 3 1 1 5 1
    IPSL-CM5A2-INCA 1 1 0 1 0
    IPSL-CM6A-LR 32 6 11 11 6
    MIROC-ES2L 31 10 30 10 10
    MPI-ESM-1-2-HAM 3 0 0 3 0
    MPI-ESM1-2-LR 9 10 10 10 10
    MRI-ESM2-0 1 0 0 0 1
    NorESM2-LM 3 1 3 3 1
    NorESM2-MM 3 1 1 1 1
    UKESM1-0-LL 17 16 13 10 4

    Appendix B: Preindustrial Mean Emissions

    Even without anthropogenic carbon emissions, some models exhibit non-zero carbon fluxes. This may be due to models not having reached equilibrium, or in other cases, to how they account for river outgassing. To try to avoid attributing these fluxes to fossil fuel emissions, the mean preindustrial compatible emissions are subtracted from compatible emission time series of the historical and future periods. Tables B1 and B2 present the mean compatible emissions computed over the last 30–50 years of the piControl simulation.

    Table B1. Mean Preindustrial Compatible Emissions From the Coupled Model Intercomparison Project Phase 5 piControl Experiment
    Model name Member Emissions (PgC)
    CanESM2 r1i1p1 −0.07
    GFDL-ESM2G r1i1p1 0.22
    HadGEM2-CC r1i1p1 0.34
    HadGEM2-ES r1i1p1 −0.29
    IPSL-CM5A-MR r1i1p1 0.00
    IPSL-CM5B-LR r1i1p1 −0.10
    MIROC-ESM r1i1p1 0.09
    MPI-ESM-LR r1i1p1 −0.06
    NorESM1-ME r1i1p1 0.17
    Table B2. Mean Preindustrial Compatible Emissions From the Coupled Model Intercomparison Project Phase 6 piControl Experiment
    Model name Member Emissions (PgC)
    ACCESS-ESM1-5 r1i1p1f1 −0.21
    CESM2 r1i1p1f1 −0.06
    CESM2-FV2 r1i1p1f1 −0.07
    CESM2-WACCM r1i1p1f1 −0.09
    CNRM-ESM2-1 r1i1p1f2 −0.71
    CanESM5 r1i1p1f1 −0.09
    CanESM5-CanOE r1i1p2f1 −0.07
    INM-CM4-8 r1i1p1f1 1.12
    INM-CM5-0 r1i1p1f1 1.15
    IPSL-CM6A-LR r1i1p1f1 −0.01
    MIROC-ES2L r1i1p1f2 0.11
    MPI-ESM1-2-LR r1i1p1f1 −0.03
    MPI-ESM1-2-LR r2i1p1f1 0.15
    MRI-ESM2-0 r1i2p1f1 0.41
    UKESM1-0-LL r1i1p1f2 −0.09

    Data Availability Statement

    Compatible emissions, probabilistic emissions, scenario emissions, and observations used in this paper are available at the Federated Research Data Repository at https://doi.org/10.20383/102.0549, along with code to compute the likelihood and to create graphics and tables. CMIP data was downloaded from the Earth System Grid Federation using Synda. SSP scenario emissions are based on data from the SSP database hosted by the IIASA Energy Program at https://tntcat.iiasa.ac.at/SspDb. Time series of CO2 concentrations for RCP and SSP scenarios were obtained from the International Institute for Applied Systems Analysis (IIASA) RCP and SSP databases. Observed CO2 time series from the Global Carbon Budget were obtained from the Integrated Carbon Observing System (https://www.icos-cp.eu/). Code for the FM15 model is available at https://github.com/JeremyFyke/CEPM. Code to generate probabilistic emissions from R17 can be found at https://github.com/PPgp/CO2projections. Code to generate probabilistic emissions from LR21 can be found at https://github.com/PPgp/BayesianClimateProjections.