Navigating the black box of fair national emissions targets

Global emissions pathways

Existing emissions pathways do not cover all parameter combinations in this analysis. To build a comprehensive database with such emissions pathways, we emulate pathways for different levels of peak temperature and climate sensitivity (or ‘probability’), based on existing information from different sources (Supplementary Table 4), through the following steps.

Step 1—non-CO2 pathways

The analysis starts with non-CO2 pathways, because these determine the CO2 budget, apart from other global settings. The IPCC AR6 WGIII database details temperature outcomes from each scenario. For each temperature level, a range of non-CO2 pathways exists. We utilize this information by varying a parameter in our framework (17–83%) that represents a quantile from the distribution in non-CO2 reduction levels by 2040 under a given temperature (and climate sensitivity), taken from the IPCC AR6 database. Note that non-CO2 projections from the AR6 scenario database have limitations of their own: not all models project all non-CO2 gases directly from all possible sources, for example. Therefore, we only focus on pathways of methane and nitrous oxide, being the two main anthropogenic non-CO2 greenhouse gases.

Step 2—remaining CO2 budget

For each level of peak temperature, climate sensitivity and non-CO2 reduction percentile, the remaining CO2 budget can be derived by combining the budgets derived by Forster et al2. with recent insights in the effect of varying non-CO2 assumptions on CO2 budgets28. We first use a linear regression between the parameters of temperature and climate sensitivity and the CO2 budget (on default non-CO2 pathways that were assumed by Forster). For some combinations this means that there is a (small) regression error of the budgets as reported by Forster et al. (2023)—Supplementary Information C. The regression is necessary to allow exploration of the full parameter space. Then, we deviate from these budgets based on varying non-CO2 peak warming quantiles: more warming implies a smaller budget. These quantiles are obtained from the (temperature-stratified) distribution in non-CO2 warmings at the century-peak temperature across scenario entries in the AR6 database, as computed by MAGICCv7.5.3 as part of the AR6 climate diagnostics, following related work3. Global warming potentials from IPCC AR6 are used.

Step 3—pathways of CO2 and all greenhouse gases

We derive CO2 pathway shapes by sampling from the AR6 database of IAM outputs, then adjust them to match the CO2 budget. We differentiate between pathways with immediate climate policy and those with delayed policy until 2030 (as per AR6 metadata). Whereas peak temperature and other factors constrain emissions before the peak, the pathway beyond that is more flexible and influenced by negative emissions. We incorporate this by sampling emissions pathways based on 2100 emissions quantiles in the AR6 scenarios as a proxy for the deployment of negative emissions technologies. The budget-corrected CO2 emissions pathways are added to the earlier derived non-CO2 pathways using GWP100 from AR6 (273 for N2O and 28.5 for CH4, which is the average of fossil and non-fossil sources) to obtain emissions pathways of all greenhouse gases.

Mathematical description of emissions pathways

For clarity, in equation (1), we provide a summary of the above in mathematical terms. We use \(E(t,{c}_\mathrm{w})\) here to indicate global emissions pathway, distinguishing from \(E(t,c)\), which is used for emissions allocations for country or region c later in the Methods.

Here the global GHG emissions over time t, are split in a global CO2 part (\({E}_{\mathrm{CO}_2}\)) and a global non-CO2 part (\({E}_{\mathrm{non}\text-\mathrm{CO}_2}\)). The former is dependent on the RCB being the remaining carbon budget, depending on peak temperature T, climate sensitivity S, the non-CO2 quantile \({Q}_{\mathrm{non}\text-\mathrm{CO}_2}\), the timing of mitigation action tmit and the negative emissions quantile Qneg. The peak temperature and climate sensitivity are also direct inputs to the CO2 pathways (not only via RCB) because they also determine the pathway shape—that is, not only the cumulative CO2 emissions. The non-CO2 part is only dependent on peak temperature, climate sensitivity and the non-CO2 quantile.

Methodological advances with respect to other work

This study improves on previous methods across a number of considerations. First, it includes non-CO2 emissions and land-use emissions. Adding non-CO2 emissions provides insight into the trade-off between non-CO2 warming and CO2 budgets but also adds complexity and uncertainty. Other studies focus on CO2 only or add non-CO2 emissions exogenously13,46. However, that may obscure how non-CO2 impacts the remaining CO2 budget. Emissions from LULUCF are often excluded14,16,27,46 because of uncertain historical estimates and the debate47 on which emissions are regarded as anthropogenic. We acknowledge these issues, but for completeness and argued by the importance of mitigation in land use, we decided to include them building on the newest insights48. We also account for emissions from international aviation and marine transport in all global results49 but subtract these when allocating them to countries.

The second improvement we make is a broad variation of interpretations of the Paris Agreement targets. There is a strong dependence on the assumed peak temperature and climate sensitivity (or achieving probability) for all of these calculations. Studies deal with this differently and we intentionally vary various of these interpretations in the database. We provide results for all combinations of these (and more) global parameters and set ‘default’ paths on peak temperatures of 1.6 °C at 50% chance (associated with 1.5 °C with a small overshoot; close to the average of IPCC AR6 WGIII category C1) and 2.0 °C at 67% chance. Other studies, such as Fekete et al.26 and van den Berg et al.13, use different carbon budgets (for example, 1.5 °C at 67% probability). In a recent report on this topic, the European Scientific Advisory Board on Climate Change determined global pathways based on a selection of IPCC WGIII scenarios24.

A third consideration in global emissions pathways is the starting point for allocation. Some studies use the 2015 Paris Agreement24, whereas others use earlier years, such as 201013,14,15. We chose 2021 for this study, the most recent possible given data availability, but acknowledge the effect of retaining emissions inequality for the historical period up to 2021. Starting later, near-term reduction targets become more lenient, but longer-term reduction targets become much more stringent due to a more depleted carbon budget over time. Depending on the context (for example, peak temperature), the ‘turning’ point on how the choice of starting year affects the reduction targets can be around 2030, 2035 or even later. The reverse is true for choosing a starting year earlier in the past.

A fourth improvement is the variety of results we provide—for various years of interest and scopes. We list different fair share calculations in Supplementary Fig. 2, categorized into four concepts as outcomes of a decision tree. Typically, concepts lower in the chart require more assumptions but are more aligned with political realities. Concept 1 allocates the RCB directly each country with a cumulative CO2 emissions budget without any indication for specific years. This is useful as a general indicator for mitigation burdens13,24. When requiring allocations over time, one of the simplest assumptions is a linear spending of the fair budget (concept 2). This concept serves as an intuitive calculation for individual countries26 and suggests a net-zero CO2 year as a consequence. However, it lacks detail on post-net-zero CO2 (and negative emissions), non-CO2 allocations and does not align the total emissions of all countries with a global pathway. Concepts 3 and 4 address these gaps. Concept 3 assumes an immediate jump (dashed lines) from current emissions to fair levels, tackling fairness in the first year13,27. Concept 4 does this gradually by starting from current emissions, allowing climate action and finance to increase (rapidly) within any defined time frame. We include results across all concepts in our database20 but focus on concept 4 in the main results of this paper.

Allocating emissions to countries

The allocation of emissions to countries can be done in many ways—and not all are regarded fair. Supplementary Information (notably Supplementary Fig. 3) discusses a schematic framework guiding how the global emissions can be allocated to countries. Below, we describe how these allocations are computed. All potential values of parameters following in the equations below are listed in Supplementary Table 4.

The Grandfathering (GF) allocation method, based on continuity, gives all countries the same reduction rate, thus retaining current emissions inequality and ignoring differences in terms of responsibility, ability to reduce and expected growth. Hence this is argued to be not equitable in the case of climate policy22,50, although this method is often used as a refs. 13,14,46. Equation (2) shows how it is computed, with E(t, c) the allocated emissions in year t for country c (cw representing the world) and t0 the analysis starting year (2021). \(E(t,{c}_\mathrm{w})\) is the global emissions pathway, subject to all global parameters—we drop all these parameters in the equations for simplicity; equation (1).

The equality principle reflects the principle that every human being has equal rights to emissions allowances. This excludes any weights of other factors such as income, technology, differences in climate and economic structure. There are several allocation methods that quantify this principle. We include an immediate per capita rule (yellow), which takes into effect immediately (that is, 2022) and leads to a discontinuity between the historical emissions trend and the allocation (with the possibility of countries paying for this difference). It is computed as follows, with P representing population (which is independent of socio-economic scenario s for t = t0):

Another rule associated with equality is the per capita convergence rule51,52 (PCC), which moves from grandfathering to a fully per capita allocation, providing a transition period, but also ensuring a longer-term equality among nations based on population53. Since, for the initial period, this approach is similar to equal relative reduction, the same critical observations apply22. An important consideration for these rules (Supplementary Table 4) is the year (tconv) in which per capita convergence is fully converged to a per capita allocation.

where operator M(x) equals 0 if x ≤ 0, x if 0 ≤ x ≤ 1 and 1 if x ≥ 1, hence, the convergence is linear over time and after convergence to PC, it remains equal to that rule. On the basis of a combination of the equality and responsibility principles, the method equal cumulative per capita (ECPC) weights historic and future emissions based on population fractions per year. The results are substantially impacted by the year (thist) from which and on historical emissions are incorporated and the rate (rd) of discounting them. In this work, we use values of thist the years 1850, 1950 and 1990 and discount rates of 0%, 1.6%, 2.0% and 2.8% (ref. 54). The reasoning for discounting is, in part, physical: the natural removal of CO2 from the atmosphere. The socio-economic scenario (s), which implicates future population growth, also impacts the results of this rule. The allocation is done in three steps. First, the cumulative (past and future) allocated GHG emissions B′ECPC(c, s, thist, rd) of country c is computed based on the cumulative population share of country c and is taken as fraction of the total (past and future) global emissions—in which \(B\left({c}_\mathrm{w}\right)\) represents the global (future) budget:

Second, we compute what the country already historically emitted and subsequently subtract this from BECPC to arrive at the (net) future ECPC emissions budget:

This budget is negative for many developed countries, implying a historical debt (if negative; leftover if positive). Allocating this over time according to concept 4 in Supplementary Fig. 2 dictates starting at current emissions levels (which can still be positive for developed countries), and the definition of a convergence year (tconv) by which the historical debts or leftovers are accounted for. After the convergence year, the ECPC allocation principle allocates purely on a per capita basis—which does not add any new debt or leftover. Call the part of debt (or leftover) that is left at any moment in time D(t, \(c,s,{t}_{\mathrm{hist}},{r}_\mathrm{d}\)): being the total debt minus what is already repaid in terms of previous ECPC allocations, plus what at that year, the country is indebted to according to a per capita allocation:

As this requires input of all previously allocated EECPC, the ECPC allocations themselves are an iterative function, involving a sine-deviation from PCC based on the responsibility–inequality at time t:

The dependency of D on previous ECPC allocations makes sure that as t approaches tconv, D approaches 0 and that early action is promoted over purely following the sine shape (which would in contrast maximize the responsibility effect exactly halfway to the convergence year). D approaches zero with a small error of order 1% of original responsibility debt or leftover when reaching the convergence year. To capture the principle of capability—that is, wealthy nations mitigate more of their emissions—the ability to pay (AP)55 rule starts at a country’s baseline emissions \({E}_{\mathrm{base}}\left(t,{c}_\mathrm{w},s\right)\,\) (which are SSP dependent marked by variable s) and computes a deviation from that based on GDP per capita. First, a fraction of country c’s baseline emissions is determined, based on its GDP per capita. These are the first-order emissions to be subtracted from the baseline emissions: Esub(t, c):

The implicit assumption is that marginal abatement costs are quadratically increasing (following previous work13), which yields total abatement costs that are cubically increasing with emissions reduction. Hence the 1/3 exponent makes sure that this steep increase is counterbalanced and mitigation costs as fraction of GDP are equalized among countries. Because the reliance on GDP per capita does not fully scale linearly (that is, the sum of countries does not equal the total), we need a correction factor. Adding this yields the final equation of the ability to pay rule:

Potentially, this rule could be combined by implementing an income level below which a country does not need to reduce its emissions56. The Greenhouse Development Rights (GDR) rule combines capability and historical responsibility in the responsibility–capability index (RCI, controlled by a weighting factor wRCI between the two principles), which emphasizes enabling countries to reach a decent level (l) of sustainable development57. Full GDR allocations are computed as follows:

However, RCI is only defined up to 2030. Therefore, a convergence rule is implemented towards AP (similar to PCC):

Baseline emissions and downscaling

Baseline emissions, required for the ability to pay (AP) and greenhouse development rights (GDR) allocation rules, are obtained from the IMAGE IAM58 for SSP1–3. Baseline emissions for SSP4 and SSP5 were not (up-to-date) available, but their future population and GDP projections were. IMAGE provides emissions projections for 26 regions, which we downscale to the country level using a procedure that closely follows the approach outlined in Van Vuuren et al. (2007)59. Using historical energy data from the International Energy Agency (IEA)60, it lets country-based primary energy per GDP converge at a constant growth rate from 2015 levels, such that it would reach regional average levels by 2150. Primary energy by carrier is distributed based on historical fractions for some involving convergence to regional fractions. We implement a harmonization step to ensure that the sum of each variable across all countries aligns with the regional total. CO2 emissions are computed from these projections along with emissions factors specific to each energy carrier, which is scaled to GHG emissions based on 2015 country-based ratios of CO2 to GHG emissions. The proportion of primary energy by carrier mitigated with CCS is assumed to be uniform across all countries.

We recognize that downscaling introduces additional uncertainties. Deployment of CCS may create heterogeneities among countries that are difficult to predict at this point, especially in the long run. Another key uncertainty is the translation of the downscaled CO2 emissions to GHG emissions. However, we estimate these uncertainties to play only a minor role in the main conclusions of this paper, as downscaling is only relevant for the AP rule (and GDR, which is not used in the main results) and not for major regions such as the USA, the European Union, China and India, which are native in IMAGE.

Sobol analysis

The Sobol analysis was conducted using the Python SALib package61,62. Random samples (size 1,024) were drawn for this analysis, varying all factors for every year increment between 2030 and 2100. For the results in Fig. 2, the total Sobol index (that is, including higher-order terms) was used. For the Sobol analysis, we used temperature levels between 1.5 and 2.0 degrees, with climate sensitivity percentiles, non-CO2 reduction and negative emissions quantiles of 33%, 50% and 67%, and SSP1–SSP3. For more information on Sobol analysis, we refer to previous literature21,40,63. Convergence years of 2040, 2050 and 2080 are included for the ECPC and PCC allocation rules.

Note that the selection and range of factors to include in the Sobol analysis is subject to some freedom. For example, if one would add very (unfoundedly) high discount factors of historical emissions, this would add a source of variability that the Sobol analysis would attribute to the equity dimension. Therefore, this range and selection of factors is carefully chosen based on values found in literature and scenario projections in the IPCC WGIII AR6 database37 (Supplementary Table 4). Analogously, we chose to proxy the equality, responsibility and capability principles with PCC, ECPC and AP. Naturally, alternations to this choice may be a source of uncertainty for the Sobol analysis.

In the Sobol analysis results in Fig. 2, we also see individual parameters such as the convergence year of historical discounting. Those parameters sometimes only affect part but not all of the three rules (PCC, ECPC or AP). That naturally decreases the impact of these parameters on the total variance explained. For example, convergence year (tconv) only affects PCC and ECPC results—it is not a parameter in the equation for AP.

Harmonization steps

Historical emissions data from Jones et al. (2024)48, mainly based on the PRIMAP database, serves as the reference for emissions. CO2 and non-CO2 pathways from the IPCC WGIII AR6 database are harmonized by aligning historical and projected emissions in 2021 and fully converging to their raw pathways by 2030, using a ramp function that linearly reduces the emissions gap. Population data are interpolated linearly between 2000 (end of UN data) and 2020 (start of SSP data).

Cost-optimal scenarios

For comparing fair emissions allocations with cost-optimal results (Figs. 3 and 4), we use cost-optimal scenarios from the IPCC WGIII37 C1 category: 1.5 °C peak temperatures and limited overshoot. These scenarios, produced by IAMs, project emissions under global cost optimality, using various socio-economic assumptions. Large countries such as the USA, China and India are model native, whereas for others, especially in the global south, we implemented a downscaling of cost-optimal results at R10-regional level to country-level based on current emissions fractions. Average cost-optimal projections are used (in Fig. 4, the uncertainty range is added).