https://orcid.org/0000-0001-8952-5644
Figures
Abstract
A range of recent studies have developed methods and data to attribute past and present global temperature change to individual emitters. We perform simulations that attribute the amount of global warming due to corporations, governments and other entities into the future. We utilize the Finite Amplitude Impulse Response (FaIR) model run until 2500, and the Carbon Majors dataset, a database with the emissions history associated with the top 178 oil, gas, coal, and cement producers. We perform counterfactual experiments to calculate the warming attributable to the emissions associated with these entities, using several different future emissions scenarios. The future atmospheric carbon dioxide (CO2) anomaly attributable to a company’s past emissions is smaller with less ensemble spread in a lower emissions future than it is in a high emissions future. This is due to smaller carbon cycle feedbacks with lower emissions. However, the temperature change from past emissions is larger in a lower emissions future, even with the smaller change in CO2. This is due primarily to the logarithmic sensitivity of CO2 radiative forcing to concentration. Methane concentration post-2080 experiences a negative anomaly, due to a decrease in methane lifetime from elevated temperature, which is a small negative feedback. For any future emissions scenario, the historical emissions from oil, gas, coal, and cement producers affect many aspects of the climate system, including CO2 in the atmosphere and other parts of the carbon cycle, methane, ozone, and stratospheric water vapor. The total radiative forcing induced by these elements stays positive throughout all simulations, which in turn causes positive temperature perturbations. Thus in addition to the damages that have already occurred, we expect the Carbon Majors to be responsible for calculable climate damages for many centuries into the future.
Citation: Frierson DMW, Henrie LA (2026) Centuries of global heating from Carbon Majors: Dependence on future emissions pathways. PLOS Clim 5(9): e0001036. https://doi.org/10.1371/journal.pclm.0001036
Editor: Valerio Lembo, CNR: Consiglio Nazionale delle Ricerche, ITALY
Received: October 28, 2025; Accepted: August 1, 2026; Published: September 23, 2026
Copyright: © 2026 Frierson, Henrie. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: Our Jupyter notebook, which branches from the calibrated_constrained_ensemble.ipynb example of fair v2.2.2, is available here: https://datadryad.org/dataset/doi:10.5061/dryad.zcrjdfnsk.
Funding: The author(s) received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
1. Introduction
When a climate disaster occurs, who is accountable? Methods to calculate the responsibility of individual fossil fuel and cement producers for specific events have been developed, based on well-substantiated climate science (e.g., [1,2]). The evidence chain starts with the effects of fossil fuel and cement emissions on atmospheric CO2 and methane concentrations, followed by increased radiative forcing and temperature, and finally extreme event dependence on background climate. Methods of analysis typically involve counterfactual simulations (e.g., [3]), in which pollution from fossil fuel and cement producers are subtracted out from historical emissions. Comparison with a control simulation then allows for a calculation of the climate impact of the fossil fuel and cement emissions.
Prior studies of climate accountability have focused almost exclusively on the past. However, due to the extreme persistence of carbon dioxide emissions [4–8], past emissions will continue to cause climate damages well into the future. In this study, we examine the climate effect of historical emissions from major oil, gas, coal, and cement producers across a wide range of future emissions pathways. We do this work in order to better understand the climate processes important for accountability quantification, and the aspects of emissions scenarios that affect temperature change caused by prior emissions.
1.1 Simple climate models
Attribution of global temperature change to individual entities requires a model that can simulate the effect of emissions on atmospheric CO2 and methane concentrations, and its subsequent effect on radiative forcing and temperature change. Although this can be performed with Earth System Models (ESMs), for significantly less computational cost one can use Simple Climate Models, or Reduced Complexity Models [9]. Some examples of Simple Climate Models include the Finite Amplitude Impulse Response (FaIR) [10–13], the Model for the Assessment of Greenhouse Gas Induced Climate Change (MAGICC) [14–16], and OSCAR [17].
In this study we examine simulations with FaIR, which is an open-source, well-documented, and frequently used model. FaIR has been used to determine whether emissions scenarios satisfy temperature thresholds (e.g., [18]), to calculate the temperature effect of COVID-19-induced emissions reductions [19], and to study the effect of airline emissions on climate [20]. The FaIR model has also been used in privately developed future scenarios including the Rhodium Climate Outlook [21], a probabilistic simulation of energy, emissions, and climate.
1.2 Prior studies on attribution of warming to historical emitters
The Carbon Majors dataset, which consists of historical emissions information associated with top investor-owned, state-owned, and nation-state producers of oil, gas, coal, and cement, first appeared in 2014 [22], allowing major leaps forward in the attribution literature. The Carbon Majors dataset features Scope 1 and 3 emissions, which represent the direct burning of fossil fuels by the entities, and the emissions from burning the fossil fuels that were extracted by the entities. The dataset includes emissions of carbon dioxide, including product emissions, flaring emissions, venting emissions, and own fuel use emissions, and fugitive emissions of methane. We utilize all of these categories in this study, used as the specific species (not as CO2-equivalent).
The Carbon Majors dataset has been used in a variety of studies to calculate how individual producers are responsible for different aspects of climate change. Ekwurzel et al [3] attributed temperature, sea level, and CO2 changes through 2010 to entities in the Carbon Majors dataset using a simple climate model. Licker et al [23] ran a simple carbon cycle model and an ocean general circulation model (GCM) to attribute ocean acidification and its spatial patterns to Carbon Majors entities. Dahl et al [24] attributed the contribution of Carbon Majors entities to increases in vapor pressure deficit and burned forest area, employing a global energy balance carbon-cycle model and a burned area model. Callahan and Mankin [25] provided a framework for individual emitter attribution, and attributed economic losses of extreme heat to Carbon Major entities using FaIR. Quilcaille et al [2] attributed heatwaves to the emissions of the entities in the Carbon Majors dataset using observations, Earth system models and OSCAR.
An important prior study on attribution of future temperature change to historical emissions is Sadai et al [26], which used MAGICC to calculate the impact of Carbon Majors emissions on sea level rise. The study showed that historical emitters’ contribution to sea level rise into the future is largely insensitive to future emissions pathways, although some differences exist. The authors suggest that aspects of emissions scenarios such as the amount of overshoot, and physical processes such as interplays with forcing, the carbon cycle and other greenhouse gas cycles, and energy uptake may be important in determining the sensitivity of future sea level rise to past emissions [26]. In this study, we follow up on Sadai et al’s [26] work to study why there are differences in the amount of future climate change caused by historical emitters when different future emissions scenarios are prescribed.
2. Methods
2.1 FaIR model
In this study we use FaIR model version 2.1.4, calibration 1.4.1 [13]. The carbon cycle in FaIR [10] is a variation of the Joos et al [27] parameterization, with four pools with unperturbed timescales of infinity, 394.4, 36.5, and 4.3 years, and between 21–29% of emissions partitioned into each. In order to capture changes in airborne fraction with climate state, these timescales are modified by a factor ɑ that varies as a function of global mean temperature T, carbon uptake into sinks Cacc, and airborne cumulative carbon dioxide C:
where g0 = 0.0102, g1 = 11.41, and
is the integrated impulse response function (iIRF), with 4 calibration parameters r that vary across ensemble members. I is calculated over the following 100 years, and is expressed in units of years. The r parameters are chosen from a distribution that is calibrated from 11 CMIP6 ESMs, and constrained based on observed CO2 concentrations. The exponential fit for ɑ was developed by Leach et al [12] to approximate the solution of the nonlinear equation that relates iIRF to the fraction of CO2 remaining airborne after 100 years for a given ɑ. The exponential fit has errors less than 10% for I between 43 and 90, but substantial errors outside that range [28]. The model has a maximum allowed I value of 100, after which further increases in I have no effect on ɑ, i.e.,
for I ≥ 100. For I < 21.73 years, no solutions are allowed in the [6] formulation, so the expression above has infinite error in that range.
Atmospheric methane concentrations are modeled in FaIR using a variable timescale which depends on methane’s own concentration, nitrous oxide concentration, NOx emissions, VOC emissions, temperature and equivalent stratospheric chlorine.
The 1.4.1 tuning is the best fit using emissions updated through 2022. A calibrated set of FaIR parameter distributions is derived based on information from climate models and emissions datasets, and then after sampling from these distributions, a constrained set of simulations are chosen based on agreement with observations, e.g., of global averaged temperature change over the historical period. There are 841 ensemble members in the 1.4.1 calibration.
2.2 Counterfactuals and emissions
We construct counterfactual simulations by removing 1854–2024 emissions of CO2 and methane from the 2026 update of the Carbon Majors database [29] from the SSP scenarios [14] (Figs 1 and 2). The counterfactual experiments present alternative histories in which the Scope 1 and Scope 3 emissions from the Carbon Majors never existed. The Carbon Majors dataset has little emissions until the early 20th century, and rises to make up approximately 30 GtCO2 in 2024. The cumulative emissions in the Carbon Majors dataset is 1.25 TtCO2, equivalent to 160.6 ppm CO2 if all were to stay in the atmosphere. In FaIR, the fraction of emissions into the pool with infinite timescale is 0.2173. Thus the counterfactual experiments have 35 ppm (0.2173 times 160.6 ppm) less CO2 concentration in that pool after 2023, an anomaly that persists forever.
We use the SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5 scenarios from [14]. Total CO2 emissions from the SSP scenarios, Carbon Majors, and the counterfactual for SSP2-4.5 are plotted in Fig 1. Counterfactuals differ slightly between 2015 and 2024 since the SSP scenarios begin in 2015, while the difference between scenario and counterfactual is the same for all experiments.
Methane emissions for the SSPs, Carbon Majors, and the counterfactual scenarios and the Carbon Majors dataset are plotted in Fig 2. Methane emissions double by 2100 in the SSP3-7.0, increase less in SSP5-8.5, and decrease in the other simulations, with an especially sharp drop in SSP1-2.6. Carbon Majors calculates fugitive methane emissions from oil, gas, and coal entities, and although these make up a smaller fraction of total emissions as for CO2, the emissions are still around 30% of total global methane emissions.
The Carbon Majors emissions from 1854-2024 are subtracted from each of the 4 scenarios to calculate past and future warming from historical emissions to create our counterfactual scenarios. We make no attempt to subtract out future emissions from the Carbon Majors, which means there is a discontinuity in emissions of CO2 and CH4 in 2025, when emissions jump back to the scenario values. Since fossil fuel extraction by the Carbon Majors was non-zero in 2025 and will persist for some years even in the most climate-friendly futures, our calculation is a lower limit for the effect of the Carbon Majors. The code to recreate all our experiments is publicly available on Dryad at https://doi.org/10.5061/dryad.zcrjdfnsk [30].
3. Results
We plot the global temperature anomalies from the 1850–1900 average in the SSP scenario simulations and counterfactual simulations in Fig 3. Our simulations begin in 1750, but since the Carbon Majors emissions are comparatively small prior to the mid-20th century, we begin all plots in 1940. The SSP simulations span a very large range of warming, with median warming reaching over 7 K (4.2--12.3 K 5–95% ensemble spread) in 2500 in SSP5-8.5, down to less than 2 K (0.7-2.1 K) in 2500 in SSP1-2.6. The counterfactual simulations are lower in all cases in every year. This occurs both over the historical period, and into the future. The historical Carbon Majors emissions have a heating effect that persists for centuries.
5-95% ensemble spread is shaded.
We calculate the temperature increase ΔT caused by the Carbon Majors by subtracting the counterfactual simulations from the scenarios, plotted in Fig 4. The temperature perturbation is maximum around 2024, the last year of the Carbon Majors dataset, when the median of the ensemble is over 0.6 K in all cases. The simulations diverge into the future, but all have persistent warming of several tenths of a degree. The most warming is experienced by the simulations with the least background temperature change, i.e., the SSP1-2.6 simulations. The temperature increase in 2500 due to the Carbon Majors in SSP1-2.6 is 0.45 K (0.30-0.77 K for the 5–95% range of the ensemble), but only 0.31 K (0.16-0.56 K) in SSP5-8.5 in 2500. Compared with the induced warming in 2025 of ~0.66 K (0.49-0.85 K), the 2500 temperature change in the SSP1-2.6 case is 68% (52–100%) of the 2025 warming, and 49% (28–79%) in the SSP5-8.5 scenario (fractional changes are calculated on an ensemble member by ensemble member basis).
16-84% and 5-95% ensemble spreads are shaded.
3.1 Carbon dioxide
The CO2 concentration in the scenarios and counterfactual simulations is plotted in Fig 5. In SSP1-2.6, the concentration reaches ~450 ppm around 2060, while the counterfactual peaks at 375 ppm at approximately the same year, both with little ensemble spread. In the higher emissions scenarios, the CO2 concentrations still exceed the counterfactual simulations, but the ensemble spread is greatly increased, indicating a large spread in carbon cycle feedbacks.
5-95% ensemble spread is shaded. Note the different y-axes on the top and bottom rows.
The carbon dioxide anomalies ΔCCO2 are plotted in Fig 6. The Carbon Majors cause 80 ppm (76–82 ppm in the 5–95% ensemble spread) of additional atmospheric CO2 in 2025, equivalent to 623 GtCO2 in the atmosphere. This is 48% of the total emissions of 1.29 TtCO2 in the Carbon Majors dataset, meaning the other 52% has been taken up by sinks. The CO2 trajectories diverge significantly into the future, with SSP1-2.6 and SSP2-4.5 decreasing with relatively little variance across the ensemble, while SSP3-7.0 and SSP5-8.5 experience an increase in CO2 concentration, with the median increasing by 20–40 ppm. It is notable that the largest median CO2 increase occurs in the simulations with the least warming (i.e., SSP5-8.5). Also, the extremely large ensemble spread in SSP5-8.5 means that the 5th percentile carbon dioxide increase is the least for much of the last 400 years, despite the median being largest.
16-84% and 5-95% ensemble spreads are shaded.
How can the CO2 change induced by Carbon Majors, ΔCCO2, vary across different future emissions scenarios? Since the Carbon Majors cause changes in temperature, airborne CO2 and CO2 in sinks, there are three influences on carbon cycle timescales, or equivalently, via the iIRF I. Each of these three have an expected lengthening effect. Changes in timescales via ɑ can then affect both the CO2 perturbation from the Carbon Majors that exists at the end of the historical period (equal to 80 ppm), or the persistence of future emissions. There are corresponding physical processes that cause changes in the carbon cycle, e.g., increased respiration rates with warming, decreased ocean uptake with acidification and higher temperature, greening with higher CO2 levels, and permafrost losses [6] which are simulated in some ESMs and underpin the tuning of FaIR’s carbon cycle parameters.
In 2025, there is little variance in ΔCCO2 across ensemble members. The four pools (listed with descending timescales) contain 36.1 ppm, 30.3 (29.1-31.2) ppm, 11.6 (9.7-13.2) ppm, and 1.6 (1.2-2.0) ppm in 2025. The first pool, which has infinite timescale, has no variance across ensemble members and does not decay away, so is an eventual limit that ΔCCO2 approaches as time goes to infinity. The second pool, with unperturbed timescale 394.4 years, can contain perturbations from the Carbon Majors even in 2500, especially if ɑ exceeds 1. The induced carbon cycle timescale changes from the Carbon Majors also cause future emissions (positive or negative) to last longer, if the change in I is positive. Since ΔCCO2 increases after 2023 in most of the SSP5-8.5 ensemble members, the latter mechanism must be important in that case.
The values of I for the scenarios and counterfactual simulations are plotted in Fig 7. At the end of the historical period in the scenarios, I = 40 (with 37–42 5–95% ensemble spread), corresponding to ɑ = 0.34 (0.26-0.40). The timescales around the present day are thus much smaller than the parameterization of [27], which were derived from pulse experiments about 2010 conditions. This is discussed as a weakness of the FaIR carbon cycle model in Frierson et al [28], as small ɑ values mean that FaIR has less persistence of CO2 than the ESMs and Earth System Models of Intermediate Complexity (EMICs) on which the parameterization was based.
5-95% ensemble spread is shaded.
In the future projections of the scenarios, the SSP1-2.6 and SSP2-4.5 cases have median I values between 39–43 (30–49 for the 5–95% ensemble spread), and 39–50 (24–66), respectively. The timescale coefficient ɑ = 1 when I = 52.4, so each of these lower emissions scenarios have timescales that are smaller than the set in Joos et al [27] for all times. The SSP3-7.0 simulations have I values between ~10–100 (0.02 < ɑ < 65) in the last 300 years. The extreme range in I in the SSP5-8.5 case from 2150 onward indicates that the upper limit of I = 100 (corresponding to ɑ = 68) is exceeded in some ensemble members in this case. On the low end of the SSP5-8.5 simulation, some ensemble members experience I values below zero (ɑ < 0.01). These show that the approximation in Leach et al 12] is well outside of its tuned range, as solutions to the formulation of the FaIR carbon cycle in Millar et al [10] do not exist in this regime.
In each case, the Carbon Majors have the effect of slightly increasing the median I at all times. This amounts to around a 3–4 year increase in the median for each simulation, although there are some individual ensemble members that have negative change of I in each scenario. Increases in I lead to an increase in ɑ, and more persistent CO2 anomalies. Since ɑ is an exponential function of I, the increase in timescale is much larger when I is already large. The change in I can be written as
where ΔE is the emissions difference due to Carbon Majors, equal to 1,290 GtCO2 in any year past 2024. This term alone causes a median change in ΔI of 1.5 years (-5.4-7.5 years for 5–95% spread). For a 0.5 K temperature increase, the ΔT term adds 1 year (-0.6-2.9 years). The ΔC term adds 0.7 years (-2.3-3.9 years).
The I values in the scenarios are well-correlated with ΔCCO2, with three regimes of behavior, as shown in Fig 8. We choose the year 2500 for the scenario I value on the x-axis as a representative time only; since the distributions of I have largely stabilized by 2200, using earlier times for I gives similar results. A first regime occurs for I < 25 (corresponding to ɑ < 0.09 in the approximation of [12]), the timescales are sufficiently short so that even the second carbon pool (with unperturbed timescale of 394.4 years) has had enough time to decay away. Thus what remains from the Carbon Majors perturbation is only the first pool amount, 36 ppm, as described in Section 2. Further, CO2 emissions in all simulations are zero after 2250. Thus any differential effect on future emissions has decayed away as well by 2500.
Each point represents one ensemble member, and is colored based on the simulation. Note the three regimes with near-constant ΔCCO2 ≅ 35 ppm (-30 < I < 25), ΔCCO2 generally increasing with I (25 < I < 100) and a decreasing regime (I > 100).
For values of I from 25 < I < 100 (0.09 < ɑ < 65), higher I values have higher ΔCCO2, with a larger change in higher emissions scenarios. As timescales lengthen due to the Carbon Majors, there is more CO2 that persists from the emissions which occur up to the 2250, and from the historical perturbations. Finally, for I > 100, the upper limit on ɑ has been hit, so increases in I have no further effect on timescale. Thus there is less change compared with I < 100.
Although the median increase in carbon dioxide concentration in 2500 is over three times larger in SSP5-8.5 than in SSP1-2.6case, the CO2 radiative forcing is least in SSP5-8.5 and more similar across the other cases (Fig 9). This is because the radiative forcing is near logarithmic in concentration, taking the following form, based on the formula in [14]:
16-84% and 5-95% ensemble spreads are shaded.
with tadj, CO2 = 0.05 is the tropospheric adjustment factor for CO2, d1 = 5.2488 W/m2, a1 = -2.4785e-7 W/m2/ppm2, b1 = 7.5906e-4 W/m2/ppm, c1 = -0.0021492 W/m2/ppb-1/2, C0 = 277.15 ppm, N is the nitrous oxide concentration, and fscale, CO2 is a calibration parameter. The derivative of this expression with respect to CO2 concentration is plotted in Fig 10, with a mid-range value of N = 400 ppb. In a Taylor expansion, this represents the change in CO2 radiative forcing from a small addition of CO2. The linear expression is useful even in our finite amplitude case to understand how an increase in ~120 ppm in the median of the SSP5-8.5 case (with a background CO2 concentration of around 1600 ppm) causes less than 0.5 W/m2 of radiative forcing, while a ~ 40 ppm increase in the SSP1-2.6 case (with a background CO2 of around 360 ppm) causes more than 0.6 W/m2. The carbon cycle and CO2 radiative forcing effects oppose each other so that the future temperature change from Carbon Majors is similar across scenarios.
The median, 16-84 percentiles, and 5-95 percentiles are indicated.
3.2 Methane
Aspects of the background climate affect the methane cycle as well [31]; for instance, higher methane concentrations decrease OH concentrations, which lengthens methane lifetime. Increased temperature also affects the methane cycle, via increased emission rates, changes in wetland distribution and indeed, methane concentrations are also affected by removal of the Carbon Majors emissions, as shown in Fig 11. In terms of background concentrations across scenarios, the SSP3-7.0 case exceeds 3 ppm before decreasing and stabilizing between 2-2.5 ppm. The SSP2-4.5 and SSP5-8.5 simulations peak over 2 ppm in the 21st century before decreasing to around 1940s levels by 2250. The SSP1-2.6 simulation exhibits an immediate decrease in methane concentrations to sub-1940 levels by the early 2100s. Methane concentrations in the simulations generally follow emissions with a slight lag, due to the fact that methane’s lifetime is around a decade.
5-95% ensemble spread is shaded.
The Carbon Majors emissions cause a large increase in methane concentrations from the mid-20th century until the mid-21st century (Fig 12). The maximum difference is approximately 450 ppb at the end of the historical period. After the emissions jump back up to the scenario values in 2025, concentrations converge within a few decades. Unlike carbon dioxide, methane concentration anomalies induced by the Carbon Majors eventually become negative in all the simulations. The negative methane perturbation is largest in SSP3-7.0, the scenario with the largest methane emissions.
16-84% and 5-95% ensemble spreads are shaded.
The eventual decrease in methane concentration can be understood by examining methane lifetime. Methane lifetimes in FaIR are proportional to a scaling parameter ɑCH4 calculated as
where Ai are the concentration or emissions of the 5 species that affect methane lifetime: methane concentration, nitrous oxide concentration, equivalent effective stratospheric chlorine concentration, NOx emissions, and VOC emissions. The Si coefficients for each species and the temperature coefficient ST take single values for each calibration, i.e., there is no ensemble spread in these. In calibration 1.4.1, the preindustrial lifetime is τCH4, base = 16.8 yrs.
Only two of the factors change in response to the Carbon Majors emissions: temperature and methane itself. Increases in temperature decrease timescales (ST = -0.0463 K-1), while increases in methane concentration lengthen the timescale (SCH4 = 1.67283e-4 ppb-1). The latter provides a positive feedback, amplifying any change in methane. Emissions of NOx and VOCs and concentration of N2O vary across scenarios, providing differences in background methane lifetime.
We plot the methane lifetimes in Fig 13, which shows longer lifetimes with less ensemble spread in the simulations with less warming. In each simulation, inclusion of the Carbon Majors causes a shorter lifetime for methane, due to the increased temperature in those simulations, and from a positive feedback from the methane concentration decrease itself.
5-95% ensemble spread is shaded.
Near the end of the simulation, the methane concentrations have approximately stabilized in all simulations, so to a close approximation,
Thus an decrease in timescale causes an decrease in concentration. Timescale decreases due to the Carbon Majors are relatively similar in each case. The methane decrease is largest in the SSP3-7.0 case primarily because the end-of-scenario emissions are largest in that case.
Methane concentrations affect other radiative forcing agents, specifically stratospheric water vapor, ozone, and aerosol-radiation interactions. Each of these take simple additive forms, so we can write the total radiative forcing of methane (which we call CH4 + forcing) as
where tadj, CH4 = -0.14 is the tropospheric adjustment parameter for methane, fH2O = 4.4e-5 W/m2/ppb is the proportionality coefficient of stratospheric water vapor to methane, and fscale, CH4, fscale, strat, and fozone, CH4 are scaling parameters which take different values for different ensemble members. The forcing from these aspects of methane are plotted in Fig 14. Forcing peaks around 0.3 W/m2 at the end of the historical period, and drops to below zero by the late 21st century. The forcing is most negative for the SSP3-7.0 case, due to the larger negative anomalies in that case.
16-84% and 5-95% ensemble spreads are shaded.
Consider the difference in radiative forcing due to Carbon Majors from CH4+ and CO2 in the SSP3-7.0 and SSP1-2.6 cases, and call these ΔFCH4+, 370 and ΔFCH4+, 370, etc. This forcing difference is larger in SSP1-2.6 for both CH4+ and CO2, i.e., ΔFCH4+, 126 > ΔFCH4+, 370 and ΔFCO2, 126 > ΔFCO2, 370. For the medians, ΔFCH4+, 126 - ΔFCH4+, 370 = 0.025-0.035 W/m2 from 2050 onward, while ΔFCO2, 126vlow - ΔFCO2, 370high = 0-0.2 W/m2. This indicates that methane plays a contributing but secondary role to CO2 in causing the SSP1-2.6 case to have the largest temperature change due to Carbon Majors. CO2 forcing also causes the vast majority of the ensemble spread in radiative forcing, with 0.08-0.15 W/m2 standard deviation of ΔFCO2, 126 - ΔFCO2, 370 across ensemble members past 2100, while the methane forcing causes less than 0.015 W/m2.
4. Discussion
Using counterfactual simulations with FaIR, we showed that the effect of the Carbon Majors persists for many centuries, with warming of several tenths of a degree in 2500. The dependence on background warming scenario is relatively weak, although the simulations with less future warming show a larger warming due to Carbon Majors (0.5 K in the median of SSP1-2.6, compared with 0.3 K in the median of SSP5-8.5). The temperature changes are thus substantially larger in a fractional sense for the SSP1-2.6 case (~30% of the median total warming in 2500), as compared with the SSP5-8.5 future (~5%).
The primary reason that there are larger temperature changes in SSP1-2.6 is the approximately logarithmic radiative forcing dependence on CO2 concentration. There are several other factors that contribute, however, including some that make the sensitivity to future emissions less than what the logarithmic forcing effect alone would give. Because both temperature change and CO2 in the atmosphere and in sinks affect the persistence of CO2, future carbon cycle timescales are lengthened by the Carbon Majors. This increases CO2 more in the higher emissions scenarios, meaning that the radiative forcing from CO2 changes is less different across scenarios. Methane, on the other hand, contributes in the same direction as the logarithmic CO2 forcing. Since methane lifetime decreases with temperature, methane experiences a slight decrease in concentration due to the Carbon Majors once the historical methane emissions have decayed away.
The strong carbon cycle sensitivity in the highest emission case cause significantly higher CO2 concentration changes in the median of that case, and a very large ensemble spread. It is clear, however, that FaIR is far outside its tuned range in the SSP3-7.0 and SSP5-8.5 scenarios, and some of the behavior casts doubt on the fidelity of its carbon cycle in the current tuning, as also emphasized in Frierson et al [28]. Experiments should be performed in other emissions-to-temperature models, including ESMs, to provide further quantification of these results and understanding of important processes. Further work to compare reduced complexity models with ESMs is also needed to assure processes are accurately simulated. We expect the qualitative result to be robust: that temperature change due to historical emitters will be relatively insensitive to future climate state because the logarithmic CO2 radiative forcing effect opposes the carbon cycle sensitivity effects.
Our simulations suggest potential follow-up studies on future climate accountability. We assumed all future fossil fuel emissions are unchanged from the future scenarios. Therefore, there is a large jump in the time series we subtract when creating the counterfactuals, from 31.0 Gt CO2 and 132 Mt CH4 removed in 2024, to no removal in 2025. Emissions that have occurred since 2024 have already invalidated this as a future projection, and thus underestimate the effect of the Carbon Majors on current and future climate. Any entity’s eventual climate impact continues to increase until its activity reaches zero. One could estimate the eventual effect on future climate with simulations that include projections of future fossil fuel emissions, derived, e.g., from a companies’ own business plans or scenarios, including reduction scenarios to hit particular thresholds, as in [32]. One could also use statistical forecasting methods, e.g., as Raftery et al [33] performed for global emissions.
For future attribution, the primary caveat, of course, is that the temperature changes have not yet occurred, so there is no assurance that any model simulation will continue to have fidelity given the actual emissions pathway. Further tuning of model parameters should be performed as new updates to the climate state come in (e.g., [34]), and the FaIR-calibration procedure [13] is well-suited to perform updates as frequently as needed.
The existing framework for attributing global temperature change to individual fossil fuel and cement companies is now well-grounded in established methods. The tools to attribute individual events and their economic damages to entities are quickly being constructed, allowing for financial damages and liability to be calculated for more and more types of events. As the burning of fossil fuels continues and climate disasters become more severe, we can only expect more attention on attribution and accountability research.
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