Estimating countries’ additional carbon accountability for closing the mitigation gap based on past and future emissions

Domain: earth_science
Published: 2024-11-09
Editorial outcome: minor_revision

Abstract
Quantifying fair national shares of the remaining global carbon budget has proven challenging. Here, we propose an indicator—additional carbon accountability—that quantifies countries’ responsibility for mitigation and CO2 removal in addition to achieving their own targets. Considering carbon debts since 1990 and future claims based on countries’ emission pathways, the indicator uses an equal cumulative per capita emissions approach to allocate accountability for closing the mitigation gap among countries with a positive total excessive carbon claim. The carbon budget is exceeded by 576 Gigatonnes of fossil CO2 when limiting warming below 1.5°C (50% probability). Additional carbon accountability is highest for the United States and China, and highest per capita for the United Arab Emirates and Russia. Assumptions on carbon debts strongly impact the results for most countries. The ability to pay for this accountability is challenging for Iran, Kazakhstan and several BRICS+ members, in contrast to the G7 members.

Introduction
Currently, 195 parties have committed in the Paris Agreement to “holding the increase in the global average temperature to well below 2°C above pre-industrial levels and to pursue efforts to limit the temperature increase to 1.5°C” (Article 2.1)1. Any such target can be translated into a budget for the maximum amount of carbon dioxide emissions that can be emitted over time, given a specified probability2.

Due to historical emissions, the remaining global carbon budget compatible with not exceeding the 1.5°C level with at least 50% probability is small, and respecting the budget requires rapidly declining emissions2,3.

The climate action plans of the parties to the Paris Agreement—the Nationally Determined Contributions (NDCs)4—can be seen as national claims on the remaining global carbon budget. In addition to the NDCs, 148 countries, responsible for 88% of global emissions, have proposed some kind of long-term targets such as a net zero or climate-neutral commitment5. If countries meet their NDCs and their net-zero targets (NZTs), the temperature increase could be limited to 1.7–1.8°C6. However, many countries still lack implementation plans to achieve their pledges and considering only countries with credible pledges points towards a 2.4°C temperature increase7.

The Paris Agreement expresses the fairness principle of common but differentiated responsibilities and respective capabilities (CBDR-RC), which should be considered “in the light of different national circumstances” (Article 2.2)1. The principle has been part of international climate policy since the adoption of the United Nations Framework Convention on Climate Change (UNFCCC) in 19928. However, there is no agreement on how to operationalise this principle, other than that developed country parties should continue to take the lead (Articles 4.4 and 9.3)1.

Consequently, several approaches have been used for conceptualising and calculating fairness in relation to national carbon budgets9–12. These include Equal annual per capita emissions for countries, based on multiplying the annual global emissions, for a pathway in line with a certain global carbon budget, with the national share of the global population. Equal annual per capita allocations can also be extended to account for historical emissions by instead focusing on cumulative emissions, labelled as Equal cumulative per capita emissions9, where summed emissions starting from a historic year are equal per capita. This captures the CBDR principle but without the ‘respective capabilities’. A common approach to operationalize this RC part of the principle is to use a country’s Gross Domestic Product (GDP) per capita in relation to the global GDP per capita as a proxy for a fair allocation13. Grandfathering approaches are based on national emission reductions from present levels, so that the global remaining carbon budget is allocated based on current emission shares10. Per capita convergence, sometimes called Contraction and convergence14, starts with grandfathering and converges over time into an equal annual per capita approach by the end of a specified period, while staying within the global carbon budget11,13.

More than half (56%) of the NDCs consider fairness in relation to the country’s past, current and future shares of global emissions, drawing on a variety of equal per capita principles or relating to trends applying different metrics4. Since the NDCs are developed and adopted independently by each party, they can be seen as bottom-up approaches to fairness15. Governments’ perceptions of what is “fair enough” are manifested in negotiations and commitments like NDCs16. At the same time, the NDCs constitute roadmaps with a starting point in current emission levels. This grandfathering characteristic attributes legitimacy to the present unequal levels of emissions and risks perpetuating inequality11. Conversely, national equal annual and cumulative per capita allocations emphasise equity and could be seen as top-down approaches from a global budget15 but lack reference to national sovereignty and an agreed process for updating national commitments, which are the core of the NDCs17.

The carbon debt, and with it the responsibility for historical emissions, varies among countries18. Future carbon claims compared to carbon budgets compatible with the Paris Agreement have also been analysed for the major world regions based on moral claims by developing countries combined with cost-effective, ambitious pathways for developed countries12,19. Moreover, studies use the equal cumulative per capita emissions approach to share the responsibility for Carbon Dioxide Removal (CDR) among countries, assuming that countries with large cumulative emissions have the highest responsibility20,21. However, the combined responsibility for historical emissions and future emission claims made by individual countries has not yet been estimated. Such an indicator could be used to assess the need for additional measures, including raised domestic and international emission reduction ambitions, as well as CDR, and to allocate responsibility for those additional measures.

The aim of this study is to estimate the additional carbon accountability for countries, defined as each country’s responsibility to mitigate or remove CO2, in addition to achieving its NDC and NZT pledges, to stay within its share of a specific global carbon budget allocated based on equal cumulative per capita emissions and accounting for carbon debts based on the same method. This additional carbon accountability indicator operationalises the common but differentiated responsibilities principle in the light of different national circumstances and complements previous research by combining bottom-up estimations of country emission pathways, based on pledges made by governments, with a top-down equal cumulative per capita approach. The ambition is to build on the Paris Agreement, being the internationally agreed climate treaty, and improve the fairness of its implementation by acknowledging common but differentiated responsibilities for past and future emissions.

On this basis, the article presents calculations of the additional carbon accountability for 37 countries, for the years 1990–2070, based on a remaining global carbon budget for holding the global average temperature increase below 1.5°C with 50% probability. We also analyse the countries’ ability to pay the estimated costs of fulfilling this accountability, and evaluate the sensitivity of our method to (i) different starting years for historical responsibility, (ii) the chosen principle for allocating the remaining global carbon budget and for redistributing emission allowances not used by countries with ambitious climate targets, and (iii) a global carbon budget for holding the global average temperature increase below 2°C with 83% probability. The results are thus relevant for the international climate negotiations and national climate policy design.

Results
Carbon debts and excessive carbon claims
First, we calculate both the carbon debt and the future excessive carbon claims for 37 countries (see definitions in Table 1 and results in Table 2). We classified the countries into four groups as defined by the income categories used by the World Bank (see Data sources). Note that the European Union (EU) is considered as one country. The ‘Rest of the World’ includes planned emissions by other countries (76%) and international transportation (24%) and is assumed to reach net zero emissions by 2070. Given a remaining global fossil carbon budget of 225 billion tonnes of carbon dioxide (GtCO2) (see “Methods”), the global excessive carbon claim, exceeding the 1.5°C carbon budget, is 576 GtCO2, if all countries deliver upon their NDCs and NZTs.

All 15 high-income countries in our sample except Chile have a carbon debt, whereas the United States (139 GtCO2) and the EU (50 GtCO2) have the largest debts. Of the 19 upper-middle-income countries, only four—China, South Africa, Iran and Kazakhstan—have a carbon debt. The total carbon debt of these 18 indebted countries is 341 GtCO2.

If we instead look to the future, the planned emission pathways 2023-2070 result in claims on the remaining carbon budget of 801 GtCO2 (Supplementary Table 1). Figure 1a shows the notable differences in claims between China (30.8% of global claims), India (11.5%), the United States (7.8%), Russia (5.4%) and the EU (4.4%). However, carbon claims per capita are generally highest for high-income countries with some important exceptions including Iran and China (Fig. 1b and Table 3).

Estimating countries’ additional carbon accountability
The additional carbon accountability is an indicator of holding a country accountable for its excessive historical and future carbon claims, on top of achieving its national targets. The sum of only positive total excessive carbon claims is 789 GtCO2 but the global net sum of excessive carbon claims is 576 GtCO2, since 14 countries plan to emit less than what follows from an equal cumulative per capita emission approach for 1990–2070. The difference, referred to as the emission allowances pool, corresponds to 213 GtCO2 or 27% of the large emitters’ total excessive carbon claims. The emission allowances pool is redistributed to countries with positive total excessive carbon claims based on equal cumulative per capita access to the pool for countries’ future populations.

United States (167 GtCO2) and China (150 GtCO2) have by far the largest additional carbon accountability (Table 2). In total, 18 of the 37 countries in our sample are accountable for increasing their ambitions to stay within their equal share of the global carbon budget for 1.5°C. The 19 countries with no additional accountability include all low-income and lower-middle-income countries, two high-income countries (Switzerland and Chile), and eight upper-middle-income countries: Argentina, Costa Rica, Mexico, Brazil, Peru, Thailand, Colombia, and Indonesia (Table 2).

The large total excessive carbon claims (Table 1) by high-income countries together originate mainly from carbon debts, while middle-income countries often have larger excessive carbon claims 2023–2070 (Fig. 2). Only five countries—Nigeria, Ethiopia, Kenya, Gambia, and Costa Rica—have no excessive carbon claims 2023–2070. These countries also do not have a carbon debt.

The additional carbon accountability per capita may be a more adequate measurement, which puts the United Arab Emirates at the top, followed by Russia, Saudi Arabia, the United States, Australia, Canada, and Kazakhstan—all of them major fossil fuel producers.

For high-income countries, the additional carbon accountability for the 1.5°C budget (Table 2) is typically larger than their planned future emissions (Supplementary Table 1). It means that these countries cannot meet their accountabilities with more ambitious domestic emission reductions alone but would need to also increase ambitions for CDR or for emission reductions in other countries.

Five of 18 countries with additional carbon accountability have larger planned future emissions than additional accountabilities: Türkiye, China, New Zealand, Iran and South Africa. They could theoretically fulfil their entire additional carbon accountability with stricter domestic emission reductions than stipulated in their NDCs and NZTs. For China, New Zealand, Iran and South Africa, this would however require a large portion of their planned future emissions, hence CDR is probably needed too.

Our results also show that even if all countries in our dataset with additional carbon accountability would reduce their emissions to zero today, the global carbon budget for 1.5°C would still be exceeded. Future emissions from countries without additional carbon accountability and in the Rest of the World category are large enough for the 1.5°C budget to be exceeded.

Analysis of results for G7 and BRICS+ countries
In geopolitical terms, the G7 countries (United States, European Union, United Kingdom, Canada and Japan) together have a carbon debt (231 GtCO2) more than double their excessive carbon claims 2023–2070 (99 GtCO2). Conversely, the nine BRICS+ countries (Brazil, Russia, India, China and South Africa, as well as the four confirmed new members United Arab Emirates, Iran, Egypt and Ethiopia) have a notable negative carbon debt (−83 GtCO2), mainly due to India, but large excessive carbon claims (351 GtCO2), mainly due to China (Table 3).

Our analysis suggests that the statement above, that the grandfathering characteristic of NDCs and NZTs attributes legitimacy to the present unequal levels of emissions and risks perpetuating inequality11, is only partially true. The timing of countries’ NZTs plays a larger role in future cumulative emissions. For example, if we assume that a country chooses 2070 as NZT over 2050 and that their emissions pathway is linear from 2023 onwards towards the target, then choosing net zero by 2070 implies 71% higher cumulative emissions compared to choosing 2050. Many large, developed countries take the lead in mitigation, hence respecting Article 4.4 of the Paris Agreement. Indeed, we found that two middle-income countries in the BRICS+ group—Iran and China—have larger carbon claims (planned emissions) per capita than any of the G7 countries (Table 3).

Robustness of the additional carbon accountability
We tested how sensitive our indicator is to different assumptions by varying: (i) the extent of historical responsibility (i.e. starting year for estimating the carbon debt), (ii) the allocation principles (i.e. the principle used to estimate a country’s fair share in the remaining carbon budget and for redistributing the remaining emission allowances pool), and (iii) the global carbon budgets (i.e. implying a different long-term temperature target with a different probability). The methods used for the alternative allocation principles are based on previous studies10,22 and described in Supplementary Note 1.

First, similar to the Climate Equity Reference Framework23, using historical emissions for countries´ responsibilities, we show that an earlier starting year for the carbon debt calculations generally implies larger additional carbon accountability for high-income countries and lower additional carbon accountability for middle-income countries, and vice versa for later starting years (Supplementary Fig. 4). Supplementary Fig. 4 shows the additional carbon accountability, additional carbon accountability per capita, and the changes compared to the main case for starting years 1960, 1980, 1990, and 2000, and a case with no carbon debt. The exceptions to this pattern are New Zealand, South Korea, and Kazakhstan which show an opposite trend. For some countries, the choice of starting year for historical responsibility only makes a small difference (Norway, Singapore, United Arab Emirates, Saudi Arabia, and South Africa).

To give a few examples of the results for individual countries, the starting year of 1980 resulted in a 24% increase in the additional carbon accountability for the European Union and a 17% increase for the United States, but a 38% decrease for China. Going as far back as 1960, results in an increase of 65%, an increase of 49%, and a decrease of 97%, for the European Union, the United States and China, respectively. Including no carbon debt at all has the opposite effect, where high-income countries are assigned notably lower additional carbon accountability. In this case, the additional carbon accountability for the European Union and the United States are 47% and 68% lower than in the main case, respectively, but 42% higher for China. Shifting from using 1960 for historical responsibility, to ignoring it, implies 195 GtCO2 lower additional carbon accountability for the United States and 209 GtCO2 higher for China, hence assumptions about carbon debts have significant effects.

Second, we analyse the impact of different aspects of the chosen allocation principle—the principle used for allocating the carbon budget (Supplementary Fig. 5), and the principle used for redistributing the emissions allowances pool (Supplementary Fig. 6). Note that these figures assume all other parameters to be equal to the main case. The results show that the impact on the results of choosing a different allocation principle for the remaining carbon budget (i.e. capability, contraction and convergence, grandfathering, and equal cumulative per capita) is relatively small, with opposite patterns for the EU and the USA. Generally, the impact of the choice of allocation principle for the carbon budget is low (up to 12% change) for countries with additional carbon accountability over 100 tCO2 per capita in the main case (Supplementary Fig. 5). The impact is larger for the choice of principle for redistributing the emission allowances pool (up to 41% change) for countries with additional carbon accountability over 100 tCO2 per capita in the main case (Supplementary Fig. 6). For countries with low additional carbon accountability in the main case, the relative impact of allocation principle can be notably higher (especially for Türkiye that has a very low additional carbon accountability in the main case, but also New Zealand, United Kingdom, Norway, and South Africa stand out). Both for the allocation of the remaining carbon budget and for the redistribution of the emission allowances pool, there are fewer clear patterns depending on income group as compared to the sensitivity analysis of the carbon debt. Hence, the results suggest that our indicator is generally less sensitive to the choice of allocation principle than the choice of considering countries’ carbon debt.

Third, we show that the additional carbon accountability is notably reduced for all countries if a different temperature target—2.0°C with 83% probability—is chosen, which implies a global carbon budget of 775 GtCO2 (see “Methods”). This budget is more than three times as large as the 1.5°C budget and only 26 GtCO2 smaller than future planned emissions. Hence, national targets largely determine the results within the 2.0°C budget and the equal cumulative per capita approach, which is decisive for allocating accountability within the 1.5°C budget, allocates only small additional carbon accountability. For example, the total excessive carbon claim by the United States for the 2.0°C budget is 171 GtCO2 but its additional accountability is only 12 GtCO2 (Supplementary Table 1). Note though that carbon budgets are associated with large uncertainties24.

Accountability and countries’ ability to pay
If we return to the main results, we can analyse different countries’ ability to pay to meet their additional carbon accountability. Mitigation or removal of the total excessive carbon claims of 576 Gt (1.5°C budget) would cost 86,400 bn US Dollars (USD) if we assume an average cost of 150 USD/ton (see “Methods”). This would be 1728 bn USD per year on average over a 50-year period, which is 1.71% of the global GDP in 2022. This annual cost of returning below the 1.5°C budget by 2100 may be lower than the annual global military expenditures which were 2240 bn USD in 202225.

The countries in our sample have different abilities to pay for their accountability. With high historical and future emissions and a low per capita income, Iran, followed by Kazakhstan and Russia, turned out to have the greatest economic challenges to meeting its additional carbon accountability (Table 4).

Five of the top seven countries in this table belong to the BRICS+ group. All high-income countries except Russia, Saudi Arabia and the United Arab Emirates have committed to net zero by 2050. Eleven countries have an additional carbon accountability larger than 100% of their GDP. Between the year of net zero and 2100, the annual cost as a share of GDP for meeting the additional carbon accountability would be higher than the current military spending for ten countries. For these countries, the ability to finance their additional accountability by the year 2100 may be an economic challenge, although co-benefits from mitigation should also be considered26.

Methods
To achieve the aim of this study—estimating countries’ additional carbon accountability—we proceed in three steps: calculating the country’s carbon debt based on its historical emissions, estimating the country’s excessive carbon claims on the remaining global carbon budget, and estimating the country’s accountability to mitigate or remove CO2, in addition to its NDC and NZT pledges. Each step is described below.

Some studies30,31 advocate for using consumption-based emission accounting as a basis for fair allocations of the remaining carbon budget. Our analysis uses territorial emission accounting since the Paris Agreement is designed around national policies focused on emissions and removals within each country and consumption-based emission accounting is not easily incorporated into the Paris Agreement’s transparency framework32.

National carbon debt
We estimate the national carbon debt by subtracting a country’s equal cumulative per capita share of historical global emissions from its cumulative emissions over the period 1990–2022, as Eq. (1). This method uses a country’s cumulative population ratio to the global cumulative population as a factor for estimating each country’s historical emission allocation given a certain level of cumulative global emissions. The approach encompasses the population dynamics of each country over the period analysed, rather than relying on isolated yearly data points.

Carbon debt = \sum_{t=1990}^{2022} E_{country}(t) - \sum_{t=1990}^{2022} E_{global}(t) \cdot \frac{\sum_{t=1990}^{2022} P_{country}(t)}{\sum_{t=1990}^{2022} P_{global}(t)} (1)

where E_{global} is the global emissions, E_{country} is the national emissions, P_{global} is the global population, and P_{country} is the national population—all in the year, t.

In line with Matthews18, we argue that countries accumulate a carbon debt over time that is equal to the difference between the country’s historic emissions and a per-capita allocation of global historic emissions. However, in contrast to Matthews18, who uses an annual per capita allocation for historic emissions, we use equal cumulative per capita emissions also for the historic period. This choice is made to reduce the impact of individual years on the results given the close-to-linear relationship between cumulative emissions of CO2 and global warming—the transient climate response to cumulative CO2 emissions (TCRE)2.

An alternative formulation would be to not distinguish between carbon debt and excessive carbon claims and estimate a country’s share in the carbon budget from a historic starting year, such as 1990, combining historic emissions with the remaining global carbon budget. Robiou du Pont et al.22 suggest such a formulation for the equal cumulative per capita emissions allocation principle. However, all countries have agreed to limit global warming and reduce emissions as of the adoption of the United Nations Framework Convention on Climate Change in 19928. Hence, the comparatively higher emissions allocated to the historic period in our method is a joint failure of the parties to the UNFCCC. While one could argue that this is not entirely fair, the alternative—to calculate the equal share for a carbon budget that covers all years over the period 1990–2070—would result in future populations being given the right to (and responsibility for) historic emissions. Indeed, we included this method in our sensitivity analyses, see Supplementary Note 1 for details on the methodological choices tested and Supplementary Figs. 4, 5, and 6 for the results.

Similar to Fyson et al.20 and Ganti et al.19, we choose to estimate the carbon debt from 1990, when the first IPCC assessment report signified an emerging global scientific consensus and the negotiations on the UNFCCC started. However, this assumption is normative10,19,20 and we have therefore also included other starting years—1960, 1980, and 2000—in the sensitivity analysis (Supplementary Fig. 4). We also provide estimates of countries’ carbon debts using consumption-based emission accounting in comparison to territorial emission accounting (Supplementary Fig. 7) based on available data (i.e. for 1990–2021 and excluding Norway and Gambia).

Excessive carbon claims
Excessive carbon claims estimate the difference between a country’s expected future cumulative emissions, CE_{country}, based on pathways where it achieves its NDC and NZT, and an equal cumulative per capita allocation of the remaining global carbon budget (CB) for each respective country, also based on Robiou du Pont et al.’s22 approach for allocating a carbon budget based on equal cumulative per capita emissions, see Eq. (2). The robustness of the choice of allocation principle is tested by estimating the additional carbon accountability also using alternative allocation principles based on previous studies24,25. The mathematic formulations for these alternatives are provided in Supplementary Note 1 and results are provided in Supplementary Figs. 4, 5, and 6.

Excessive carbon claims = CE_{country} - CB \cdot \frac{\sum_{t=2023}^{2070} P_{country}(t)}{\sum_{t=2023}^{2070} P_{global}(t)} (2)

The cumulative emissions, CE_{country}, are estimated by creating simplified pathways towards an NZT for each country under the assumption that countries’ NDCs and NZTs are achieved. It should be noted that this may be an optimistic assumption. Rogelj et al.7 assessed whether the targets are legally binding if credible plans for implementation are in place, and near-term policies contribute to reducing emissions. If only realistic NZTs are accounted for, on top of current policies, “warming is projected to increase to 2.4°C by 2100 (range due to emissions projection uncertainties: 1.7–3.0°C)”7.

The simplified pathways develop linearly from the country’s 2022 emission level to its 2030 emission target, as reported in the country’s NDC and quantified by Climate Action Tracker (CAT)33, after which the pathway continues from 2030 until zero at the NZT year as communicated by the country (Fig. 1a). CAT gives a range of what the NDC means in greenhouse gas emission reductions, excluding land use, land-use change and forestry (LULUCF). Since we only analyse the fossil CO2 budget, we apply the same percentage reduction on fossil CO2 emissions as was observed for total greenhouse gas emissions. Note that other greenhouse gases are expected to form a large part of the residual greenhouse gas emissions when the net-zero target is reached. Hence, our assumption is not necessarily more ambitious than the stated NZT. Our study focuses only on CO2 emissions of CO2 and global warming2. However, the size of any global carbon budget depends on assumptions of future emissions of other greenhouse gases, see Table 5.

Since our calculations exclude emissions and removals by LULUCF, we deduct 25 GtCO2 (Table 5) for emissions occurring within LULUCF from 2023 up until 2058, when net emissions in LULUCF turn negative, based on the IPCC’s Illustrative Mitigation Pathway for renewables (IMP-Ren)34. When a range of emission reductions is given for an NDC, the mean value in the range is used. For countries with a conditional and unconditional definition of their NDC (i.e. where the country makes their emission reductions conditional on support from other countries), the unconditional one (higher emissions) is used. For countries without stated net-zero targets (i.e. Egypt, Iran, Kenya, Mexico, Morocco, Philippines and the United Arab Emirates), we assume 2070 as the targeted year. We assume that all definitions of net-zero targets result in zero emissions of fossil CO2 at the target year. For ‘Rest of the World’, including international aviation and shipping, we assume flat emissions until 2030, and a linear reduction from 2030 to net zero in 2070 (Supplementary Table 2).

The cumulative emissions for a country during the period 2023–2070 can be estimated using Eq. (3), where ET_{country}(2030) is the emission level in 2030 if the country’s NDC is achieved and t_{net-zero} denotes the communicated year for achieving net-zero emissions.

CE_{country} = \frac{E_{country}(2022) + ET_{country}(2030)}{2} \cdot (2030 - 2021) + \frac{ET_{country}(2030) + 0}{2} \cdot (t_{net-zero} - 2031) (3)

Again, we assume here that countries achieve both the NDC targets for 2030 and their NZT pledges; the additional national carbon accountability would be larger otherwise (for countries with a positive additional accountability).

The total excessive carbon claims, TECC_{country}, is the sum of a country’s carbon debt and excessive carbon claims, see Eq. (4).

TECC_{country} = Carbon debt_{country} + Excessive carbon claims_{country} (4)

In this study, calculations are conducted for carbon budgets for both 1.5°C with 50% probability and 2°C with 83% probability3, but our method can be used with any carbon budget.

Additional carbon accountability
We define additional carbon accountability as each country’s responsibility to mitigate CO2 emissions or remove CO2 in addition to its NDC and NZT pledges to stay within its share of a specific global carbon budget allocated based on equal cumulative per capita emissions and accounting for carbon debts based on the same method. The additional carbon accountability is conceptualised as follows. We allocate zero accountability to all countries whose total excessive carbon claim is negative, i.e. the sum of their carbon debt and future excessive carbon claims, as calculated in Eqs. (1–3). The emission allowances that these countries refrain from using together build up a global emission allowances pool, EAP, that reduces the global (net) excessive carbon claims. The global excessive carbon claims are therefore smaller compared to if all these low-emission countries were planning to emit according to an equal cumulative per capita allocation. The additional carbon accountability, ACA, is then estimated iteratively by redistributing those countries’ unused emission allowances until the pool of emission allowances is exhausted and no country is assigned a negative additional carbon accountability. The iterative process is mathematically described in Eqs. (5–7):

EAP_{n} = - \sum_{i \in \{all countries | ACA_{i,n-1} < 0\}} ACA_{i,n-1} (5)

EAP_{country,n} = EAP_{n} \cdot \frac{\sum_{t=2023}^{2070} P_{country}(t)}{\sum_{i \in \{all countries | ACA_{i,n-1} > 0\}} \sum_{t=2023}^{2070} P_{i}(t)} (6)

ACA_{country,n} = \begin{cases} ACA_{country,n-1} - EAP_{country,n} & \text{if } ACA_{country,n-1} > 0 \\ 0 & \text{if } ACA_{country,n-1} < 0 \end{cases} (7)

where n=1,2,3,... until the condition EAP_{n} = 0 is met. The additional carbon accountability, ACA, for a country is equal to its total excessive carbon claim in the first iteration, ACA_{country,n=0} = TECC_{country}. The additional carbon accountability is estimated by subtracting the equal cumulative per capita share of the emission allowances pool, EAP_{country,n}, from the country’s additional carbon accountability in the previous iteration, ACA_{country,n-1} (Eq. 7). The equal cumulative per capita share of the pool is estimated as in Eq. (2), but where the share of the cumulative future population is estimated based on the sum of countries that have positive additional carbon accountability in the previous iteration, see Eq. (6). Also similar to Eq. (2), the robustness of the choice of allocation principle to estimate a country’s share in the emission allowances pool, EAP_{country,n}, is tested by also using alternative principles for redistributing the EAP. The mathematic formulations for these alternatives are provided in Supplementary Note 1 and results are provided in Supplementary Figs. 4, 5, and 6. To calculate the additional carbon accountability per capita, we used the country’s average population for future years (2023–2070).

Additional costs for mitigation and CDR
Finally, we estimate the cost for each country to deliver additional emission reductions or carbon dioxide removal (CDR) in line with their accountability. We used the ability to pay metrics GDP per capita, which is a common metric for capabilities16. We apply a least-cost principle and assume for simplicity that the average cost for cost-effective measures is 150 USD per ton of CO2 mitigated or removed; this is within the estimated cost range of most CDR methods (see paragraph C.3.5 by the IPCC35), when countries have already employed all low-cost measures for achieving their NDCs and NZTs. For example, one review concludes that the cost range is 100–200 USD/ton for BECCS and 100–300 USD/ton for DACCS36 while other assessments suggest lower cost ranges37. We assume the technologies for CDR to be internationally standardised and therefore choose to measure the ability to pay in current USD. However, since the global potential for BECCS is limited by area and DACCS is limited by scaling and costs38, a large part of countries’ additional carbon accountability may be met by mitigation.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is an interesting paper which can make a useful contribution to the literature on fair-share approaches to climate debt and climate mitigation obligations. However, several weaknesses need to be addressed before the manuscript is suitable for publication.\nThe main problem is that the author divides the assessment period between past (1990-2021) and future (2022-2070). For the former period (\"national carbon debts\"), national emissions are assessed against an equal per capita share of historical global emissions during the period. For the latter period (\"excessive carbon claims\"), nations' planned emissions are assessed against an equal per capita share of the remaining carbon budget for 1.5C. The method for the latter period is sound but I see no good justification for the approach taken for the former period, as the fair-shares are overdetermined by the scale of global emissions during the period, which are in turn overdetermined by the emissions of high-emitting countries. This approach seems inconsistent with the principle of the carbon budget and falls foul of the equity-based fair-shares principles established in previous literature (see below).\nInstead, it seems much more reasonable to use something like the latter method consistently across the whole assessment period. This can be done by taking the remaining carbon budget for 1.5C as of 2022, and adding observed emissions for 1990-2021, to derive a carbon budget for 1.5C for the period from 1990. Nations' observed emissions (and observed emissions plus planned emissions) should then be measured against equal per capita shares of the carbon budget from 1990 (in other words, using national population as a share of global population over the analysis period, as the authors have done).\nThis is the approach that was taken by Hickel (2020) and Fanning and Hickel (2023) (https://www.sciencedirect.com/science/article/pii/S2542519620301960; https://www.nature.com/articles/s41893-023-01130-8), the latter of which (in Nature Sustainability) represents what is to my knowledge the most recent contribution to the literature on carbon budget fair-shares and should be engaged. Fanning provides country-level results online here: https://goodlife.leeds.ac.uk/related-research/atmospheric-appropriation/, with a baseline option for 1992. With the 1992 baseline, it seems that results differ substantially from what is obtained in the present paper, with respect to the historical period. For instance, Fanning's website indicates that China is still within its fair-share of the 1.5C carbon budget (with emissions through 2019).\nA second major question has to do with the selection of the baseline year, 1990. This approach is justified, however I think it would be worthwhile to include an earlier baseline year for comparison - such as 1960, which is used in the papers cited above and others. The results of such an exercise should be mentioned in the main text and can be represented more fully in the SI.\n-In table 1, the colour coding does not seem necessary, as the countries are already ranked by GDP per capita. Perhaps better to use a \"traffic light\" colour coding, for instance to indicate those with carbon debt and excessive carbon claims in red, those with only one or the other in yellow, and those with neither (both negative) in green.\n-line 220, the $100 figure seems low, and the justification for selecting this figure seems weak. It seems to me that the price should be selected based on abatement costs in IPCC AR6 scenarios consistent with 1.5C. I believe these are considerably higher than $100. In Fanning and Hickel (SI table 3) they indicate $100-500 depending on the year.\n-the linear future pathways seem a bit odd when most studies use Raupach curves or similar. For robustness, at least one alternative pathway shape should be tested so that we know how sensitive the results are to the chosen pathways shape.\n-I feel that some important references are missing. For example:\nPickering, J. & Barry, C. On the concept of climate debt: its moral and political value. Crit. Rev. Int. Soc. Polit. Phil. 15, 667–685 (2012).\nNarain, S. & Riddle, M. in Reclaiming Nature: Environmental Justice and Ecological Restoration (eds Stanton, E. et al.) 401–414 (Anthem Press, 2007)\nFair Shares: A Civil Society Equity Review of INDCs (CSO Review, 2015); https://www.equityreview.org/\nFanning, A. L., O’Neill, D. W., Hickel, J. & Roux, N. The social shortfall and ecological overshoot of nations. Nat. Sustain. 5, 26–36 (2022).\nHolz, C., Kartha, S. & Athanasiou, T. Fairly sharing 1.5: national fair shares of a 1.5 °C-compliant global mitigation effort. Int. Environ. Agreem. 18, 117–134 (2018).\nSultana, F. Critical climate justice. Geogr. J. 188, 118–124 (2022).\nJayaraman, T. & Kanitkar, T. Deconstructing declarations of carbon neutrality. Third World Resurgence 347, 11–13 (2021).\nKlinsky, S. et al. Why equity is fundamental in climate change policy research. Glob. Environ. Change 44, 170–173 (2017).\nVanderheiden, S. Atmospheric Justice: A Political Theory of Climate Change (Oxford Univ. Press, 2008); https://doi.org/10.1093/acprof:oso/9780195334609.001.0001", "reviewer_2": "The paper studies the gap between countries’ targets (nationally determined contributions (NDCs) and net-zero targets) and a fair carbon budget computed from an equal cumulative emissions per capita approach. To measure this gap, the authors define the ‘Fair National Carbon Accountability Indicator’. The indicator measures for each country how much the carbon budget from countries’ targets deviates from the fair carbon budget. Some countries do not plan to use up their fair carbon budget, the excess is then also distributed to countries whose targets lack behind the fair budget and it is distributed in proportion to how much they deviate. In addition, the paper studies the ability to pay of countries for this accountability.\nThe paper is very well written, and the analysis of the defined indicator is very clear.\nHowever, while it can be important to define and study such indicators, it is not clear why the indicator is defined in this way:\n1) Why are only CO2 emissions considered?\n2) Why is the ‘Fair National Carbon Accountability Indicator’ discounted in proportion to the fair budget that is not used up by some countries. This means that countries with a larger gap between targets and the fair budget, get a higher discount, which seems flawed. It seems the ‘Total excessive claims’ (defined in the paper) would be a better indicator since it does not have this flaw.\n3) What is the novelty of the indicator especially compared to the ‘Total excessive claims’? The ‘Fair National Carbon Accountability Indicator’ of each country is related to the ‘Total excessive claims’ by the same factor for all countries, so what new information does it provide?\nOverall, the indicator should be explained and justified more.", "reviewer_3": "Key results\nThe study proposes a new approach to fair distribution of a remaining carbon budget and burden sharing of climate change mitigation, with the aim of linking top-down budget approaches to in their view bottom-up nationally determined contributions. The study combines an estimate of responsibility for past emissions and projected national emissions as compared to the budget under a cumulative equal per capita approach to determine the degree to which a country has used or will in the future use more than their fair share of remaining emissions to remain under a stringent climate target (1.5 degrees, with an additional analysis for 2 degrees found in extended data). The upshot is an indicator which tries to merge up to now somewhat separate but related concepts (fairness budgets vs NDCs) to provide an alternative approach to informing as to adequacy of national climate plans and need for additional mitigation and carbon removal. The indicator’s use in identifying groups of countries which can/cannot fully account for previous and future planned emissions via mitigation alone, versus requiring CDR is a novel application. Overall I think the concept is an interesting one, and to my knowledge represents a unique and novel approach to try to bridge NDCs and other budget allocation methods.\nI’d like to thank the authors for their work; it was an enjoyable read and I do think the idea is a novel one and could be a nice addition to the field. I have some comments which I hope can be helpful to the authors in further steps of refining the work for publication, which follow below.\nValidity\nIn terms of robustness of the data interpretation and conclusions, I think the point essentially hinges on the assumption that “differentiated national responsibility… is a more reasonable and fair principle for allocating accountability.” (Discussion, beginning line 250). The validity of the results relies on the NDCs being a “bottom-up approach to fairness” (line 67) but no argument is made to this effect. The study cited (Winkler et al. 2018) does not seem to support this, stating (in the abstract) “Broadly, we find that most claims to equity are either unsubstantiated or drawn from analysis by in-country experts.” The work asserts that the indicator is an improvement on previous fairness approaches, but one could argue (as one of the citations in the study (Williges et al, 2022) does) that many NDCs implicitly rely on grandfathering, which is inconsistent with fair allocation of remaining budgets. To the author’s credit, they do acknowledge this potential issue, but do not resolve it. The benefit of incorporating NDCs as in this work would seem more related to political acceptability or feasibility arguments, but the focus of the work is on the asserted Fair indicator. There are two other instances (more minor in nature) where the normative implications are referenced but not made clear. Line 263, and Methods line 349. Again these are less vital to the overall argument, but follow a theme of the work. The indicator is “Fair National Carbon Accountability”, but there is little argumentation in the study that it is in fact fair.\nSignificance\nAs mentioned previously, I do think the new indicator is interesting and could be a potential way to bridge NDCs and top-down fairness budget allocations. I think in it’s current form, the study would be of interest to the field, but I struggle to assess to what degree it would be significant, and the relevance to related fields. I think the authors could improve upon the significance by placing their new indicator in context – as it is, the Carbon Debts and Excessive Carbon Claims section presents a lot of results, but doesn’t really contextualize how their indicator performs relative to other means of allocating budgets. The study would do well to help the reader understand that beyond the method being new and better, it leads to different conclusions. As it is the reader would have to determine this on their own, comparing to recent works on similar topics etc. It would be helpful to make the case of significance and novelty if the authors illustrate their method is an improvement in terms of fairness as discussed above (or minimize the fairness argument and focus on more practical considerations) and drive home the novelty of results.\nData and methodology\nValidity of the approach: The calculations of national carbon debt, excessive carbon claims etc. are all based in previous allocation approaches. As mentioned previously, there are some value judgements made in e.g. Step 1 calculating national carbon debt (line 349, and also the choice of using Robiou du Pont’s approach and not Matthews (line 343-344) but these can be justified. (It would benefit the reader if the authors would clarify why steps were taken, e.g. when they state it’s a ‘value judgement’ etc. Not a long argument, but perhaps a sentence or two of elaboration.\nIn terms of data quality: Limiting the study to the countries of the CAT database seems fine, but I would caution the authors to recheck their data, perhaps it is out of date. I did not have time to check all countries, but when looking at Argentina, in the extended data .xls file (sheet “2030 emission estimates”) the climate action tracker estimate is given as 315.9 MtCO2e in 2030; the 2030 estimate as of January 2024 appears to be 398 Mt, unless I’ve found a different set of scenario estimates.\nQuality of presentation: Here I think some improvements could be made, Particularly w.r.t. Figure 1 and all Tables.\nAll figures: Improve readability – text is quite small.\nFigure 1: Panel labels missing; 1b is difficult to gain any meaning from, since I have to work hard to figure out which countries correspond to which lines. Better would be to do similar to panel A and include the country names on the left, in between the axis and the start of the line. Panel B is meant to illustrate highest carbon claims per capita for high-income countries – perhaps keep the income level coloration from panel A. Caption of Figure 1: why do you only show countries with claims higher than 15,000 Gt (Gt? This must be a different unit)? It seems an arbitrary number, try and justify differently perhaps.\nTable 1: This table seems far too big and busy – I can understand wanting to convey all results for readers, but they run the risk of getting lost in the table and details. I would recommend trying to trim down the number of countries you list here, tied to the countries you discuss at more length in the text. Colors to divide into income groups – what is the rationale for the divisions? Instead of colors, probably best to try and separate them with a row of merged cells, indicating e.g. “High income”, “upper middle” etc. to avoid readability issues if/when printing. Explain the rationale for the division more specifically in the table caption text.\nFigure 2: I quite like this figure and think it is helpful to convey your results and get an idea of where all the countries stand etc. It may be helpful to emphasize the zero lines, and perhaps label the quadrants / areas indicating as you say in the paper groups of high-income countries where their accountability is higher than their planned emissions, and conversely the larger emissions than accountabilities (so different ways to fulfill their obligations) – the reader could already spot that from your chart. The colors could be more helpful (yellow is hard to read on my screen at least). Would it help your scaling issue (e.g. China) if you put everything in per capita terms? This may then make the comparison of claims and debt impossible though, given the different numbers, so maybe not. While the exploded view (left panel) is useful, it seems a shame to waste so much space on the right panel, as its quite hard to read the country names. But, I can understand the necessity, and the way the exploded view is done is quite helpful for the reader.\nTable 2: Needs a more descriptive table caption (at least a full sentence) but I wondered as to the value of this table when reading the paper. It is only referred to once or twice, in two sentences discussing G7 and BRICS, but the disaggregated results do not seem so interesting – I as reader can check in the main table if I want the details. Or if there’s further importance of this breakdown, it needs more elaboration in the table caption and text.\nAnalytical approach\nStrength of analytical approach – I believe my comments above have generally covered this area as well.\nSuggested improvements\nAgain, see my above comments, but two main improvements:\n1. Strengthen the discussion of fairness, and make an argument that the proposed indicator is indeed fair (as per discussion in Validity above)\n2. Provide a means of comparison for the new indicator – place it in related / relevant literature / estimates. It is hard to judge the impact of the indicator and this study without some reference for reader to compare with.\nClarity and context\nSee above – the study, while referencing previous work that provides overviews as to fairness considerations, and the need to address normative aspects of carbon budgets explicitly, does not do so to a large degree, and the work could be improved by adding this additional context (as well as the context in terms of how the results compare).\nReferences\nNo major issues."}, "author_response": "Our response\nThanks for many valuable comments and for highlighting that our approach differs\nfrom previous studies in the field. We have made substantial revisions and enclose\na separate document with track changes. We see our estimates of both past and\nfuture emissions as important and in doing so, we consider the approach to be\nconsistent “with the principle of the carbon budget” and being grounded in\n“equity-based fair-shares principles”. On Line 430-442 we added:\nIn line with Matthews (2016), we argue that countries accumulate a carbon debt\nover time that is equal to the difference between the country’s historic emissions\nand a per-capita allocation of global historic emissions. Since the adoption of the\nUNFCCC in 1992, all countries have agreed to limit global warming and reduce\nemissions. Hence, we further argue that the comparatively higher emissions\nallocation to the historic period in our method is reflecting the joint failure of the\nparties to the UNFCCC, since this is what has happened. If we calculate the equal\nshare 1990-2070, then future populations are given the right to (and responsibility\nfor) past emissions.\nAn added benefit of our approach is enabling a disaggregated analysis that can\nhighlight the interplay between a country’s carbon debt and excessive carbon\nclaims (e.g., Table 3)\nWith that said, we agree with the reviewer that the methods used in previous\nstudies should be tested and compared with our new approach. We have included\nthe equal cumulative emissions per capita during 1990-2070 in our sensitivity\nanalysis, see Supplementary Figures 7 and 8. We note that shifting to this\napproach has a fairly low impact on the results (below ±10%), except for Chile and\nThailand whose accountability increases notably but from low levels per capita.\nFurther, shifting to this approach would result in reduced additional carbon\naccountability for many high-income countries (see Line 265-281).\nIn regards to the comparison with Fanning and Hickel (2023), they use consumption-\nbased emissions, and assume reductions of “emissions at a constant rate using a\nsimple exponential function” from 2020 to 2050, implying the same net-zero year for\nall countries. Hence, it is not relevant for their study to account for territorial targets\nsuch as the NDCs and NZTs. This means that our results, which use territorial emissions\naccounting and estimate the additional accountability on top of achieving a country’s\nNDC and NZT, are not comparable with their study.\n------------------------------------------------------------------\nA second major question has to do with the selection of the baseline year, 1990. This approach is\njustified, however I think it would be worthwhile to include an earlier baseline year for comparison -\nsuch as 1960, which is used in the papers cited above and others. The results of such an exercise\nshould be mentioned in the main text and can be represented more fully in the SI.\nOur response\nThanks for raising this. We agree that an analysis of how sensitive the results are to\nthe choice of baseline year is missing. Hence, we have added a sensitivity analysis in\nSupplementary Figure 6, where we show the impact of assuming a baseline year of\n1960, 1980, or 2000 in comparison to the main case, where 1990 is assumed.\nGenerally, we note that an earlier baseline year increases the Additional Carbon\nAccountability for high-income countries and the opposite for a later baseline. To\nhighlight two examples, the United States has an Additional Carbon Accountability of\n180, 155, and 120 GtCO for baseline years of 1960, 1980 and 2000, respectively,\n2\nwhich can be compared to 140 GtCO in the main case. China has an Additional Carbon\n2\nrespectively, which can be compared to 175 GtCO in the main case. (Line 252-263)\n2\n---------------------------------------------------------------\n-In table 1, the colour coding does not seem necessary, as the countries are already ranked by GDP\nper capita. Perhaps better to use a \"traffic light\" colour coding, for instance to indicate those with\ncarbon debt and excessive carbon claims in red, those with only one or the other in yellow, and those\nwith neither (both negative) in green.\nOur response\nWe have removed the colour codes in Table 1 as suggested and instead indicate the\neconomic development categories in the table, as suggested by the Reviewer 3.\n--------------------------------------------------------------------------\n-line 220, the $100 figure seems low, and the justification for selecting this figure seems weak. It\nseems to me that the price should be selected based on abatement costs in IPCC AR6 scenarios\nconsistent with 1.5C. I believe these are considerably higher than $100. In Fanning and Hickel (SI\ntable 3) they indicate $100-500 depending on the year.\nOur response\nThanks for raising this issue. We agree that the figure seems low and have changed it\nto 150 USD/ton. This is within the estimated cost range of most CDR methods (IPCC\nAR6 WG3). The following text has also been added in the Methods section:\n“For example, one review concludes that the cost range is 100-200 USD/ton for BECCS\nand 100-300 USD/ton for DACCS (Fuss et al. 2018).” (Line 547-548)\nFuss, S.et al. (2018). Negative emissions—Part 2: Costs, potentials and side effects.\nEnvironmental research letters, 13(6), 063002.\n---------------------------------------------------------------------\n-the linear future pathways seem a bit odd when most studies use Raupach curves or similar. For\nrobustness, at least one alternative pathway shape should be tested so that we know how sensitive\nthe results are to the chosen pathways shape.\nOur response\nWhile we understand the reviewer’s concern about a linear pathway not being a\nplausible development, we argue that a linear pathway is more transparent and\nrepresentative of the targets set by policy-makers than a Raupach curve. A Raupach\ncurve is based on the emission levels of the base year and two parameters: a rate of\nincrease in emissions in the short-term (r), and a rate of decrease in emissions in the\nlong-term (m) (Raupach et al. 2014).\nThe two parameters can be estimated based on an assumption of the increase of\nemissions in the short-term and a carbon budget, but this is not how countries’ policy\ntargets generally are formulated. Hence, assumptions in addition to the targets set by\npolicy-makers need to be made by us researchers, and it would be difficult to fit the\ncurve to the 2030 emission target and the year for reaching zero. Using a Raupach\ncurve would therefore reduce the useability of our method for practitioners\n(governments, NGOs, etc.). In fact, a Raupach curve never reaches zero and is\ntherefore not useful for representing the policy targets that we analyze.\nFurthermore, we are primarily interested in the cumulative emissions and due to the\nassumptions needed to form a Raupach curve, it could easily be manipulated to result\nin equal cumulative emissions as the linear curve (e.g., the linear curve for planned\nemissions for the US results in cumulative emissions of 62.7 GtCO over 2023-2070\n2\nand by assuming r = 0.04 and m = 0.17295 we can achieve that same level of\ncumulative emissions. Hence, there is no added benefit of using Raupach curves.\n-------------------------------------------------------------------\n-I feel that some important references are missing. For example:\nPickering, J. & Barry, C. On the concept of climate debt: its moral and political value.\nCrit. Rev. Int. Soc. Polit. Phil. 15, 667–685 (2012).\nNarain, S. & Riddle, M. in Reclaiming Nature: Environmental Justice and Ecological\nRestoration (eds Stanton, E. et al.) 401–414 (Anthem Press, 2007)\nFair Shares: A Civil Society Equity Review of INDCs (CSO Review, 2015);\nhttps://www.equityreview.org/\nFanning, A. L., O’Neill, D. W., Hickel, J. & Roux, N. The social shortfall and ecological\novershoot of nations. Nat. Sustain. 5, 26–36 (2022).\nHolz, C., Kartha, S. & Athanasiou, T. Fairly sharing 1.5: national fair shares of a 1.5 °C-\ncompliant global mitigation effort. Int. Environ. Agreem. 18, 117–134 (2018).\nSultana, F. Critical climate justice. Geogr. J. 188, 118–124 (2022).\nJayaraman, T. & Kanitkar, T. Deconstructing declarations of carbon neutrality. Third\nWorld Resurgence 347, 11–13 (2021).\nKlinsky, S. et al. Why equity is fundamental in climate change policy research. Glob.\nEnviron. Change 44, 170–173 (2017).\nVanderheiden, S. Atmospheric Justice: A Political Theory of Climate Change (Oxford\nUniv. Press, 2008); https://doi.org/10.1093/acprof:oso/9780195334609.001.0001\nOur response\nThank you for these references! We have included two of them in the manuscript\n(Holz et al. 2018 and Klinsky et al. 2017):\n“Such a two-step approach to fairness is not unique. For example, Holz et al.24 have\nsuggested “dual obligations\" for countries by first meeting their own national targets\nand then allocating additional obligations to countries with excessive emissions (large\ncumulative emissions) and high capacity (economic wherewithal).” (Line 349-352)\n“ Governments’ perceptions of what is “fair enough” are manifested in negotiations\nand commitments like NDCs (Klinsky et al. 2017)16“ (Line 77-78)\n--------------------------------------------------------\nReviewer #2 (Remarks to the Author):\nThe paper studies the gap between countries’ targets (nationally determined contributions (NDCs)\nand net-zero targets) and a fair carbon budget computed from an equal cumulative emissions per\ncapita approach. To measure this gap, the authors define the ‘Fair National Carbon Accountability\nIndicator’. The indicator measures for each country how much the carbon budget from countries’\ntargets deviates from the fair carbon budget. Some countries do not plan to use up their fair carbon\nbudget, the excess is then also distributed to countries whose targets lack behind the fair budget and\nit is distributed in proportion to how much they deviate. In addition, the paper studies the ability to\npay of countries for this accountability.\nThe paper is very well written, and the analysis of the defined indicator is very clear.\nHowever, while it can be important to define and study such indicators, it is not clear why the\nindicator is defined in this way:\n1) Why are only CO2 emissions considered?\nOur response\nThank you for your many valuable comments. We have made substantial revisions and\nenclose a separate document with track changes. The reason for focusing on CO\n2\nemissions is the close-to-linear relationship between cumulative emissions of CO and\n2\nlong-term global temperature change - a relationship called the transient response to\ncumulative carbon emissions (TCRE).\nThis relationship is what enables cumulative emissions to be a proxy for a country’s\ncontribution to global warming and without it the concept of carbon budgets is not\nrelevant. Other greenhouse gases of course also impact the global temperature and\nare important to reduce over time, but is harder to be described in terms of an explicit\nbudget. Instead, the global carbon budget is adjusted to account for projected future\nemissions of other greenhouse gases.\nIn our case, the budgets applied for CO imply “reductions in other greenhouse gases\n2\nbetween 2020–2050, such as CH (50 %) and N O (25 %).” (see caption of Table 5). To\n4 2\nclarify this, we have now added under Method:\n“Our study focuses on only CO emissions given the TCRE - the close-to-linear\n2\nrelationship between cumulative emissions of CO and global warming. However, the\n2\nsize of any CO global carbon budget depends on assumptions of future emissions of\n2\nother greenhouse gases, see Table 5.” (Line 479-482)\n------------------------------------------------------------\n2) Why is the ‘Fair National Carbon Accountability Indicator’ discounted in proportion to the fair\nbudget that is not used up by some countries. This means that countries with a larger gap between\ntargets and the fair budget, get a higher discount, which seems flawed. It seems the ‘Total excessive\nclaims’ (defined in the paper) would be a better indicator since it does not have this flaw.\nOur response\nIf we had used “total excessive carbon claims” as indicator we would assume that\nequal cumulative per capita emissions 1990-2070 is the “correct” interpretation of\nfairness. However, equating fairness with equal is only one possible normative choice.\nOur ambition is not to assert what is fair per se but to allocate additional\naccountability on top of what countries have already agreed to. Countries should of\ncourse restrain themselves from emitting more than they express in their own plans.\nThis does not exclude reasons for high capability countries to assist developing\ncountries in their goal achievement, on the contrary, which we discuss in relation to\nchallenges illustrated in Table 4:\n“We acknowledge the need to “provide financial resources to assist developing\ncountry Parties” (Article 9) and such assistance may be needed also for some middle-\nincome countries, which have considerable Additional Carbon Accountability for the\n1.5°C budget on top of the challenges to achieve their national targets (Table 4).” (Line\n374-377)\nIn their NDCs and NZTs, high income countries have generally committed to faster\nphase-out of CO (by 2050) than low or middle-income countries, which is the norm in\n2\nthe Paris Agreement. Our ambition is to build on and stimulate dialogue on how to\nimprove the implementation of the Paris Agreement, not to replace it with a\nhypothetical norm. We have deleted “discount” in the text since we realise this was\nmisleading:\n“The sum of only positive total excessive carbon claims is 789 GtCO2 but the global net\nsum of excessive carbon claims is 576 GtCO2, since 14 countries plan to emit less than\nwhat follows from an equal cumulative per capita emission approach for 1990-2070.\nThis corresponds to 213 GtCO2 or 27% of the large emitters’ total excessive carbon\nclaims.” (Line 184-188)\n-----------------------------------------------------\n3) What is the novelty of the indicator especially compared to the ‘Total excessive claims’? The ‘Fair\nNational Carbon Accountability Indicator’ of each country is related to the ‘Total excessive claims’ by\nthe same factor for all countries, so what new information does it provide?\nOverall, the indicator should be explained and justified more.\nOur response\nThank you for this comment which catalysed lots of discussions. First, we have\nchanged the name of the indicator from “Fair” to “Additional” to clarify that this is\nadditional to the accountability of achieving nationally determined targets. This also\nclarifies that the aim with the article is not to propose a “fair” allocation per se but to\nimprove the fairness of the existing institution, the Paris Agreement.\nSecond, the novelty is our ambition to combine a bottom-up analysis of countries’\nclimate targets with a top-down allocation of accountability to close the mitigation\ngap.\nWe have clarified and justified the indicator and the aim of the article;\n“This Additional Carbon Accountability indicator operationalises the CBDR-RC principle\nand complements previous research by combining bottom-up estimations of country\nemission pathways, based on pledges made by governments, with a top-down equal\ncumulative per capita approach. The ambition is to build on the Paris Agreement,\nbeing the internationally agreed climate treaty, and improve the fairness of its\nimplementation by acknowledging common but differentiated responsibilities for past\nand future emissions.” (Line 103-108).\nFinally, we justify the indicator with a new sensitivity analysis, where different\nallocation principles for the remaining carbon budget are compared. (Line 243-281)\n--------------------------------------------------\nReviewer #3 (Remarks to the Author):\nKey results\nThe study proposes a new approach to fair distribution of a remaining carbon budget and burden\nsharing of climate change mitigation, with the aim of linking top-down budget approaches to in their\nview bottom-up nationally determined contributions. The study combines an estimate of\nresponsibility for past emissions and projected national emissions as compared to the budget under\na cumulative equal per capita approach to determine the degree to which a country has used or will\nin the future use more than their fair share of remaining emissions to remain under a stringent\nclimate target (1.5 degrees, with an additional analysis for 2 degrees found in extended data). The\nupshot is an indicator which tries to merge up to now somewhat separate but related concepts\n(fairness budgets vs NDCs) to provide an alternative approach to informing as to adequacy of\nnational climate plans and need for additional mitigation and carbon removal. The indicator’s use in\nidentifying groups of countries which can/cannot fully account for previous and future planned\nemissions via mitigation alone, versus requiring CDR is a novel application. Overall I think the concept\nis an interesting one, and to my knowledge represents a unique and novel approach to try to bridge\nNDCs and other budget allocation methods.\nI’d like to thank the authors for their work; it was an enjoyable read and I do think the idea is a novel\none and could be a nice addition to the field. I have some comments which I hope can be helpful to\nthe authors in further steps of refining the work for publication, which follow below.\nValidity\nIn terms of robustness of the data interpretation and conclusions, I think the point essentially hinges\non the assumption that “differentiated national responsibility… is a more reasonable and fair\nprinciple for allocating accountability.” (Discussion, beginning line 250). The validity of the results\nrelies on the NDCs being a “bottom-up approach to fairness” (line 67) but no argument is made to\nthis effect. The study cited (Winkler et al. 2018) does not seem to support this, stating (in the\nabstract) “Broadly, we find that most claims to equity are either unsubstantiated or drawn from\nanalysis by in-country experts.” The work asserts that the indicator is an improvement on previous\nfairness approaches, but one could argue (as one of the citations in the study (Williges et al, 2022)\ndoes) that many NDCs implicitly rely on grandfathering, which is inconsistent with fair allocation of\nremaining budgets. To the author’s credit, they do acknowledge this potential issue, but do not\nresolve it. The benefit of incorporating NDCs as in this work would seem more related to political\nacceptability or feasibility arguments, but the focus of the work is on the asserted Fair indicator.\nOur response\nThank you for this important comment. We have made substantial revisions and\nenclose a separate document with track changes. First, we have changed the name of\nthe indicator from “Fair” to “Additional” to clarify that this is additional to the\naccountability of achieving nationally determined targets. Hence, the title rhymes\nbetter with our ambition to combine feasibility and fairness. See also our answer to\nthe comment above by Reviewer 2.\nWe do not argue that the future claims (NDCs and NZTs) are fair, on the contrary, the\nlarger future carbon claims a high-emitting country has, the larger becomes its\nadditional carbon accountability. However, we argue that the Paris Agreement is the\ninternationally agreed climate institution and therefore it is a reasonable endeavour to\nimprove the fairness of its implementation. We agree with Winkler, bottom-up\napproaches to fairness concern what the governments perceive as fair and that is only\na start, although important in international negotiations (we added a ref on that, Line\n77-78).\nIndeed, our indicator allocates much more accountability to high-income countries\nthan any other allocation principle (see new sensitivity analyses in Supplementary\nFigures 7+8), because we account for historical emissions. (Line 265-281)\nWe do acknowledge the risk that NDCs are similar to grandfathering but when the\nyears for net-zero are considered, another pattern emerges:\n“On the contrary, many large developed countries take the lead in mitigation, hence\nrespecting Articles 4.4 of the Paris Agreement. Indeed, we found that three middle-\nincome countries in the BRICS+ group – Iran, Russia and China – have larger carbon\nclaims (planned emissions) per capita than any of the G7 countries (Table 3;\nSupplementary Table 1).” (Line 232-236)\n------------------------------------------------------------------------\nThere are two other instances (more minor in nature) where the normative implications are\nreferenced but not made clear. Line 263, and Methods line 349. Again these are less vital to the\noverall argument, but follow a theme of the work. The indicator is “Fair National Carbon\nAccountability”, but there is little argumentation in the study that it is in fact fair.\nOur response\nWe no longer make claims of the indicator being fair per se. It’s unavoidable though to\nmake normative choices and we have changed the passage around Line 263 to:\n“The ambition of this article is to help enhance climate fairness in the real world. The\ncalculations assume that countries are accountable to the mitigation targets they have\nvoluntarily committed to within the frames of the Paris Agreement, regardless if these\ncommitments are more ambitious than what a particular theoretical allocation\nprinciple would suggest is fair. This is of course, like all assumptions of fair allocations\nof carbon budgets, a normative assumption31. Another normative point of departure is\nthe suggestion that the countries with an Additional Carbon Accountability are\ncollectively responsible to meet the global target. Such a two-step approach to\nfairness is not unique. For example, Holz et al.24 have suggested “dual obligations\" for\ncountries by first meeting their own national targets and then allocating additional\nobligations to countries with excessive emissions (large cumulative emissions) and\nhigh capacity (economic wherewithal).” (Line 342-352)\nLine 349 has been changed to:\nSimilar to Fyson et al.20 and Ganti et al.18, we choose to estimate the carbon debt from\n1990, when the first IPCC assessment report signified an emerging global scientific\nconsensus and the negotiations on the UNFCCC started. However, this assumption is\nnormative10,19,20 and we have therefore also included other starting years – 1960,\n1980, and 2000 – in the sensitivity analysis.” (Line 444-448)\n----------------------------------------------------------------------------\nSignificance\nAs mentioned previously, I do think the new indicator is interesting and could be a potential way to\nbridge NDCs and top-down fairness budget allocations. I think in it’s current form, the study would\nbe of interest to the field, but I struggle to assess to what degree it would be significant, and the\nrelevance to related fields. I think the authors could improve upon the significance by placing their\nnew indicator in context – as it is, the Carbon Debts and Excessive Carbon Claims section presents a\nlot of results, but doesn’t really contextualize how their indicator performs relative to other means of\nallocating budgets. The study would do well to help the reader understand that beyond the method\nbeing new and better, it leads to different conclusions. As it is the reader would have to determine\nthis on their own, comparing to recent works on similar topics etc. It would be helpful to make the\ncase of significance and novelty if the authors illustrate their method is an improvement in terms of\nfairness as discussed above (or minimize the fairness argument and focus on more practical\nconsiderations) and drive home the novelty of results.\nOur response\nThanks for this comment which inspired us to include a more detailed section on the\nimpact of different assumptions on allocation principles.\nFirst, we clarified the two-step nature of our analyses (accountability to achieve\nnational targets and then additional accountability to stay within the global carbon\nbudget).\nSecond, we have added a section on the robustness of the indicator, where we test\ndifferent assumptions that have been made. We keep the framework that countries\nare first accountable for achieving their targets and that the indicator shows additional\naccountability for each country also for this sensitivity analysis, but change the\nallocation principle, the temperature target being achieved, and the assumed starting\nyear for the historic responsibility. See Lines 245-291)\nThe results are presented in Supplementary Figures 6-8 and methods further\ndescribed in Supplementary Notes.\nData and methodology\nValidity of the approach: The calculations of national carbon debt, excessive carbon claims etc. are all\nbased in previous allocation approaches. As mentioned previously, there are some value judgements\nmade in e.g. Step 1 calculating national carbon debt (line 349, and also the choice of using Robiou du\nPont’s approach and not Matthews (line 343-344) but these can be justified. (It would benefit the\nreader if the authors would clarify why steps were taken, e.g. when they state it’s a ‘value\njudgement’ etc. Not a long argument, but perhaps a sentence or two of elaboration.\nOur response\nWe have elaborated the text where we acknowledge that some choices are necessarily\nnormative, see answers above.\nThe following text was added on the choice of using Robiou du Pont et al.’s\nformulation:\n“However, in contrast to Matthews’17 and van den Berg et al. who use an annual per\ncapita allocation for historic emissions, we use equal cumulative per capita emissions\nalso for the historic period. This choice is made to reduce the impact of individual\nyears on the results given the close-to-linear relationship between cumulative\nemissions of CO and global warming – the transient response to cumulative CO\n2 2\nemissions (TCRE”\nAnd:\n“...the comparatively higher emissions allocated to the historic period in our method is\na joint failure of the parties to the UNFCCC. While one could argue that this is not\nobjectively fair, the alternative – to calculate the equal share for a carbon budget that\ncovers all years over the period 1990-2070 – would result in future populations being\ngiven the right to (and responsibility for) historic emissions. Indeed, we included this\nmethod in our sensitivity analyses, see Supplementary Note 1 for details on the\nmethodological choices tested and Supplementary Figures 6, 7 and 8 for the results.”\n----------------------------------------------------------------\nIn terms of data quality: Limiting the study to the countries of the CAT database seems fine, but I\nwould caution the authors to recheck their data, perhaps it is out of date. I did not have time to\ncheck all countries, but when looking at Argentina, in the extended data .xls file (sheet “2030\nemission estimates”) the climate action tracker estimate is given as 315.9 MtCO2e in 2030; the 2030\nestimate as of January 2024 appears to be 398 Mt, unless I’ve found a different set of scenario\nestimates.\nOur response\nWe have updated the data with the latest assessments from CAT (Feb 2024).\n----------------------------------------------------------------------\nQuality of presentation: Here I think some improvements could be made, Particularly w.r.t. Figure 1\nand all Tables.\nAll figures: Improve readability – text is quite small.\nOur response\nThank you for pointing out the small text. All figures have been improved with larger\nfont sizes to improve readability.\n-------------------------------------------------------------------\nFigure 1: Panel labels missing; 1b is difficult to gain any meaning from, since I have to work hard to\nfigure out which countries correspond to which lines. Better would be to do similar to panel A and\ninclude the country names on the left, in between the axis and the start of the line. Panel B is meant\nto illustrate highest carbon claims per capita for high-income countries – perhaps keep the income\nlevel coloration from panel A. Caption of Figure 1: why do you only show countries with claims higher\nthan 15,000 Gt (Gt? This must be a different unit)? It seems an arbitrary number, try and justify\ndifferently perhaps.\nOur response\nThank you for these remarks. Both panels of the figure have been redone. Labels have\nbeen added to the left of each line to make it easier to see which country corresponds\nto which line. In the background, the historic development has been added to show\nhow emissions have developed over time, but please note that it’s future emissions\nthat we focus on here, which is why the historic emissions are more transparent and\nbehind the labels. We have also made a new selection of countries representing the\nfour income levels considered in the tables. The same color coding is now used in all\nfigures. We find it more interesting to highlight the differences between selected\ncountries in different income groups than to just plot the top-ten emitters or countries\nwith claims higher than a certain number.\n---------------------------------------------------------------\nTable 1: This table seems far too big and busy – I can understand wanting to convey all results for\nreaders, but they run the risk of getting lost in the table and details. I would recommend trying to\ntrim down the number of countries you list here, tied to the countries you discuss at more length in\nthe text. Colors to divide into income groups – what is the rationale for the divisions? Instead of\ncolors, probably best to try and separate them with a row of merged cells, indicating e.g. “High\nincome”, “upper middle” etc. to avoid readability issues if/when printing. Explain the rationale for\nthe division more specifically in the table caption text.\nOur response\nThanks for the excellent suggestion to indicate “high-income countries” in Table 1. We\nhave changed accordingly and removed colours. The table provides empirical data for\na vast number of countries representing about 90% of global territorial emissions. The\nvalue would be reduced if the table had fewer countries. However, we have reduced\nthe number of columns from seven to five.\n----------------------------------------------------------------\nFigure 2: I quite like this figure and think it is helpful to convey your results and get an idea of where\nall the countries stand etc. It may be helpful to emphasize the zero lines, and perhaps label the\nquadrants / areas indicating as you say in the paper groups of high-income countries where their\naccountability is higher than their planned emissions, and conversely the larger emissions than\naccountabilities (so different ways to fulfill their obligations) – the reader could already spot that\nfrom your chart. The colors could be more helpful (yellow is hard to read on my screen at least).\nWould it help your scaling issue (e.g. China) if you put everything in per capita terms? This may then\nmake the comparison of claims and debt impossible though, given the different numbers, so maybe\nnot. While the exploded view (left panel) is useful, it seems a shame to waste so much space on the\nright panel, as its quite hard to read the country names. But, I can understand the necessity, and the\nway the exploded view is done is quite helpful for the reader.\nOur response\nThank you for these suggestions. We agree that showing these results per capita is\nindeed more valuable for the reader. We have redone the figure based on the average\npopulation during the respective periods for the carbon debt and the excessive carbon\nclaims, i.e., 1990-2022 and 2023-2070. A graph with absolute levels is also provided in\nSupplementary Figure 1. Lines have been added to emphasize the zero lines and the\ncolor palette has been changed to the batlow-palette that optimizes readability and\navoids colors that are problematic for color blind people\n(https://www.nature.com/articles/s41467-020-19160-7).\nWhen it comes to labeling the quadrants, we have decided not to do it since the\ninterpretation for the additional carbon accountability is tricky when the data is shown\nin average per capita terms. Hence, this graph should be used for illustrative purposes\nsince the method uses cumulative population. Nevertheless, illustrating a low or high\ncarbon debt per capita and excessive carbon claim per capita (as given by the axes)\ndo suggest how the carbon debt and excessive carbon claims influence the\nadditional carbon accountability.\n-----------------------------------------------------------------------------------------------------\nTable 2: Needs a more descriptive table caption (at least a full sentence) but I wondered as to the\nvalue of this table when reading the paper. It is only referred to once or twice, in two sentences\ndiscussing G7 and BRICS, but the disaggregated results do not seem so interesting – I as reader can\ncheck in the main table if I want the details. Or if there’s further importance of this breakdown, it\nneeds more elaboration in the table caption and text.\nOur response\nIn Table 3 (former Table 2) we only show G7 and BRICS+ countries to illustrate\ngeopolitical challenges. Here we added a column (Carbon claims per capita 2023-2070)\nand show that some developing countries within BRICS+ make very large carbon\nclaims. We have extended the analysis because the results suggest that NDCs and\nNZTs do not perpetuate inequalities like grandfathering:\n“On the contrary, many large developed countries take the lead in mitigation, hence\nrespecting Articles 4.4 of the Paris Agreement. Indeed, we found that three middle-\nincome countries in the BRICS+ group – Iran, Russia and China – have larger carbon\nclaims (planned emissions) per capita than any of the G7 countries (Table 3;\nSupplementary Table 1).” (Lines 232-236)\n-----------------------------------------------------------------------\nAnalytical approach\nStrength of analytical approach – I believe my comments above have generally covered this area as\nwell.\nSuggested improvements\nAgain, see my above comments, but two main improvements:\n1. Strengthen the discussion of fairness, and make an argument that the proposed indicator is indeed\nfair (as per discussion in Validity above)\nOur response\nSee above, we no longer claim that the indicator is fair per se. We have changed the\ntext to:\n“The ambition is to build on the Paris Agreement as the internationally agreed climate\ninstitution and improve the fairness of its implementation by acknowledging common\nbut differentiated responsibilities for past and future emissions.”\n2. Provide a means of comparison for the new indicator – place it in related / relevant literature /\nestimates. It is hard to judge the impact of the indicator and this study without some reference for\nreader to compare with.\nOur response\nSee above, we have made extensive sensitivity analysis under the sub-heading\n“Robustness of the Additional Carbon Accountability” and in Supplementary Figures\nand Notes.\nClarity and context\nSee above – the study, while referencing previous work that provides overviews as to\nfairness considerations, and the need to address normative aspects of carbon budgets\nexplicitly, does not do so to a large degree, and the work could be improved by adding\nthis additional context (as well as the context in terms of how the results compare).\nOur response\nUnder the subheading “Robustness of the Additional Carbon Accountability” we have\nrun our models using other fairness principles than the default equal cumulative per\ncapita.\nAlso see Supplementary Note 1 for details on the methodological choices tested and\nSupplementary Figures 6, 7 and 8 for the results.\n-------------------------------------------------------------"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed many of my concerns and made substantial improvements to the\nmanuscript.\nUnfortunately in my first reading I did not assess the use of the emissions concept. I understand now\nthat the authors are using territorial emissions rather than consumption-based emissions. This presents\na bit of a problem, because the literature on climate justice overwhelmingly supports the use of\nconsumption-based emissions. I understand that consumption-based emissions cannot easily be used for\nthe future period in this study, as the analysis is based on NDCs which (if I am not mistaken) deal with\nterritorial emissions. However, there is no reason that consumption-based emissions could not be used\nfor the historical period, as this data is readily available. I strongly recommend that the authors should\nuse this approach in the main analysis. If not, then at at minimum such an approach should be deployed\nas part of the sensitivity analysis and results should be discussed in the main text.\nThe price has been adjusted to $150, which I think is better and quite reasonable, but the rationale for\nthis needs further clarity. The reference to Fuss et al is fine, but if the range is 100-200 USD/ton for\nBECCS and 100-300 USD/ton for DACCS, if the distribution is equal it would seem that the correct\naverage is (150+200)/2 = 175. Unless Fuss et al indicate that the prices are distributed more toward the\nbottom of the range? Or unless you are assuming more BECCS than DACCS? Please specify briefly.\nOne significant issue remains. There is now a substantial literature indicating the limits of NETs. For\ninstance, scaling up BECCS means pressures on land use, water use and biodiversity (particularly in the\nglobal South where most of the necessary land would be obtained), which may run against other social\nand ecological objectives. As for DACCS, it is very energy intensive and therefore deployment at scale\nwould substantially increase energy demand and make decarbonization of the energy system more\ndifficult to achieve. If we account more fully for the limitations faced by NETs, the implication is that\n\"climate debtors\" need to scale down emissions faster than they are presently planning with their NDCs.\nIf these limitations cannot be included in the analysis they should at least be discussed.", "reviewer_2": "Thanks for your answers to my previous comments. In the previous review I mentioned one issue which\nin my opinion hasn't been addressed sufficiently. I wrote: \"Why is the ‘Fair National Carbon\nAccountability Indicator’ discounted in proportion to the fair budget that is not used up by some\ncountries. This means that countries with a larger gap between targets and the fair budget, get a higher\ndiscount, which seems flawed.\" I still see this as the main issue with your indicator. In the definition of\nyour indicator, the total excessive claims are reduced for all countries with positive total excessive claims\nby multiplication with a factor that is the same for all, thus countries with higher excessive claims receive\na higher reduction. Could you explain why you chose to define the indicator that way? An alternative\ncould be to distribute the excessive claims of countries with negative excessive claims to countries with\npositive excessive claims in proportion to the cumulative population of the country. In that way again the\nequal cumulative per capita principle would come into play.", "reviewer_3": "I would like to thank the authors for addressing the concerns I raised in my first review of the work. My\nmajor issues having to do with fairness I find have been well addressed, and the what I felt maybe too\nambitious claims on fairness have been moderated. I appreciate the detailed responses to my concerns\nin the responses to reviewers document, and the inclusion of robustness checks etc. which move\ntowards my concern of setting the research in the field / highlighting novelty, along with the addition of\nthe new Robustness section and the additional results / methods in the Supplementary file.\nFinally, the figures are overall greatly improved, and easy for the reader to understand (along with\nthe captions).\nI think these changes do well to address all my previous concerns.\nThere were some minor issues I noted throughout the paper:\nLine 85: Carbon debt is discussed, but not really defined until Table 1 on line 130; it may be that some\nreaders more broadly interested aren't clear what's meant by carbon debt here.\nLine 130 - Table 1: You call it \"historic carbon debt\" only here, everywhere else its just carbon debt (or\ncarbon debts). An extremely minor issue of consistency.\nLine 229: I'm not sure I see a connection between your analysis showing that large developed countries\ntake the lead in mitigation, and grandfathering in NDCs providing legitimacy for status quo levels.\nCouldn't both be true, your results do indeed show that, but the NDCs also attribute legitimacy to status\nquo? I suppose it could be that your results do still address the second portion of your statement, in that\nthe risk of perpetuating inequality may not be as high as others would fear.\nLine 414, 460, 507, 537 - \"Carbondebt\" \"Excessivecarbonclaims\" in the equations without spaces, its\nquite minor but distracting for the reader\nSupplementary information, Line 113: shouldn't \"integrate\" be \"integrates\" and line 114 allocation\nOF not allocation FOR?\nRegarding detail in methods section and reproducibility of results:\nThe methods section does describe the approach in enough detail that one should be able to reproduce\nthe results, as the data are also all supplied by the authors. I did not try and do so from scratch, but\nchecked how the provided R code corresponded to the methods section.\nI can confirm that the code provided does reproduce the results in the paper, and that the data\nsources etc. all correspond to those specified in the manuscript. I did have some difficulty actually\nreconciling your methods equations and your R code. I am confident now that the method specified\nin the text is carried out in your code, but it took a bit of time to read.\nE.g. a quick early example from line 43 -> why are you multiplying the variable EmissionsMtCO2 by\n44/12?\n- I know it is because the data was actually Mt carbon, and you need to multiply it by 3.664 to get to\ntonnes CO2, but its not clear from the code.\nAdditionally, as mentioned the equations from methods were difficult to actually identify in the code,\nbut everything is all there, sometimes quite hidden. In the end, there is enough detail for work to be\nreproduced, and it does not affect the manuscript, so perhaps is not relevant for me as a reviewer to\ncomment on, but it would probably in the future make it easier for other reviewers to verify validity of\nresults if code were clearer or more thoroughly commented when necessary (as code can also be written\nto be understandable without comments of course).\nThank you for the well-written and interesting paper!"}, "author_response": "Answers to Reviewers’ Comments\nReview Round #2\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nThe authors have addressed many of my concerns and made substantial improvements to the\nmanuscript.\n1. Unfortunately in my first reading I did not assess the use of the emissions concept. I understand\nnow that the authors are using territorial emissions rather than consumption-based emissions. This\npresents a bit of a problem, because the literature on climate justice overwhelmingly supports the\nuse of consumption-based emissions. I understand that consumption-based emissions cannot easily\nbe used for the future period in this study, as the analysis is based on NDCs which (if I am not\nmistaken) deal with territorial emissions. However, there is no reason that consumption-based\nemissions could not be used for the historical period, as this data is readily available. I strongly\nrecommend that the authors should use this approach in the main analysis. If not, then at at\nminimum such an approach should be deployed as part of the sensitivity analysis and results should\nbe discussed in the main text.\nAnswer: The Paris Agreement is designed around national policies focused on emissions and\nremovals within each country, hence, the NDCs and net-zero targets concern territorial emissions.\nConsumption-based emissions are certainly relevant when analysing fairness and could also be\nrelevant to strengthen the implementation of the Paris Agreement by targeting emissions beyond\nthose covered by the territorial scope of the NDCs (see for example\nhttps://www.nature.com/articles/s43247-023-01012-z for a discussion on how the two perspectives\ncan be combined within the scope of the Paris Agreement). However, given the aim of this study to\nestimate the Additional Carbon Accountability for countries, defined as each country's responsibility\nto mitigate or remove CO , in addition to achieving its NDC and NZT pledges, we consider it\n2\nreasonable to use an accounting framework based on what countries have agreed on, i.e. territorial\nemission reductions. Further, we find it illogical to use different accounting frameworks for past and\nfuture emissions. On line 99-101 we clarify that “The ambition is to build on the Paris Agreement,\nbeing the internationally agreed climate treaty, and improve the fairness of its implementation by\nacknowledging common but differentiated responsibilities for past and future emissions.” Given that\nthe aim and ambition of this study concern improvements of the existing political framework and its\nmetric we believe it’s reasonable to use territorial emission accounting.\nWe’ve added a further clarification on our approach in Methods, on lines 366-370, with references\nto Hickel 2020 (32), Fanning & Hickel 2023 (33) and Morfeldt et al. 2023 (34):\n“Some studies32,33 advocate for using consumption-based emission accounting as a basis for\nfair allocations of the remaining carbon budget. Our analysis uses territorial emission\naccounting since the Paris Agreement is designed around national policies focused on\nemissions and removals within each country and consumption-based emission accounting is\nnot easily incorporated into the Paris Agreement’s transparency framework34.”\nFurther, we’ve made estimations of the carbon debt based on consumption-based emission\naccounting that are compared to equivalent estimates using territorial accounting (see\nSupplementary Figure 9). However, given that the Global Carbon Project only has consumption-\nbased emissions for a subset of the countries analysed in the study and for a smaller number of\nyears (no data is available for 2022 for all countries and full time series are lacking for Norway and\nGambia), a sensitivity analysis would need to be designed in a different way from the main analysis\nwhich would make comparisons difficult. This comparison is highlighted in the Method, lines 414-\n417, stating:\n“We also provide estimates of countries’ carbon debts using consumption-based emission\naccounting in comparison to territorial emission accounting (Supplementary Figure 9) based on\navailable data (i.e., for 1990-2021 and excluding Norway and Gambia).”\n------------------------------\n2. The price has been adjusted to $150, which I think is better and quite reasonable, but the\nrationale for this needs further clarity. The reference to Fuss et al is fine, but if the range is 100-200\nUSD/ton for BECCS and 100-300 USD/ton for DACCS, if the distribution is equal it would seem that\nthe correct average is (150+200)/2 = 175. Unless Fuss et al indicate that the prices are distributed\nmore toward the bottom of the range? Or unless you are assuming more BECCS than DACCS?\nPlease specify briefly.\nAnswer: 150 USD is used to estimate mitigation costs, encompassing both removals and mitigation\nthat could be financed in other countries. If we assumed that the additional accountability would be\nmet by only BECCS and DACCS, in similar proportions, then we could have used this single reference\nand assumed 175 USD/ton. However, we acknowledge the uncertainty of both scale and cost of CDR\nand we have added a few references. Still, it is not an aim of the article to analyse the future costs of\nmitigation and carbon removal, it clearly says: “We assume for simplicity that the average cost for\ncost-effective measures is 150 USD per ton CO2 mitigated or removed; this is within the estimated\ncost range of most CDR methods (see paragraph C.11.1 and Table TS.7 by the by the IPCC).” (line.\n525-528). The cost ranges estimated by IPCC AR6 WGIII are larger than in Fuss et al. We also cited\nanother study suggesting lower costs (line 531), this study concludes: “The model results show that\nDACCS in Europe 2050 could cost between 160 €/tCO2 and 270 €/tCO2 with very conservative\ntechno-economic assumptions and between 60 €/tCO2 and 140 €/tCO2 using more progressive\nparameters.” In our manuscript we use 150 USD/ton only for illustrating the magnitude of the costs\nand compare it with equally uncertain future military spending.\n—----------------------------\n3. One significant issue remains. There is now a substantial literature indicating the limits of NETs.\nFor instance, scaling up BECCS means pressures on land use, water use and biodiversity (particularly\nin the global South where most of the necessary land would be obtained), which may run against\nother social and ecological objectives. As for DACCS, it is very energy intensive and therefore\ndeployment at scale would substantially increase energy demand and make decarbonization of the\nenergy system more difficult to achieve. If we account more fully for the limitations faced by NETs,\nthe implication is that \"climate debtors\" need to scale down emissions faster than they are presently\nplanning with their NDCs. If these limitations cannot be included in the analysis they should at least\nbe discussed.\nAnswer: We fully agree with this. We realise that by only referring to BECCS and DACCS in the\nMethods section the article gives the wrong impression that we believe these technologies will be\nmost important for countries to meet their additional accountabilities. We have therefore added the\nfollowing after line 533:\n“However, since the global potential for BECCS is limited by area and DACCS is limited by scaling and\ncosts41 (also see Table TS.7 by the IPCC38), a large part of countries’ additional carbon accountability\nmay be met by mitigation.”\nWe have also emphasised the importance of additional mitigation (sharper NDCs and NZTs) under\nDiscussion: “Such negative carbon budgets are however not an argument for abandoning national\nallocations of the carbon budget. On the contrary, it reveals that every ton of future emissions must\nbe accompanied by at least one ton of removal, or additional reductions financed in countries with\nremaining budgets in the near future, which in turn provides strong incentives for faster mitigation”\n(lines 319-324).\nReviewer #2 (Remarks to the Author):\n4. Thanks for your answers to my previous comments. In the previous review I mentioned one issue\nwhich in my opinion hasn't been addressed sufficiently. I wrote: \"Why is the ‘Fair National Carbon\nAccountability Indicator’ discounted in proportion to the fair budget that is not used up by some\ncountries. This means that countries with a larger gap between targets and the fair budget, get a\nhigher discount, which seems flawed.\" I still see this as the main issue with your indicator. In the\ndefinition of your indicator, the total excessive claims are reduced for all countries with positive total\nexcessive claims by multiplication with a factor that is the same for all, thus countries with higher\nexcessive claims receive a higher reduction. Could you explain why you chose to define the indicator\nthat way? An alternative could be to distribute the excessive claims of countries with negative\nexcessive claims to countries with positive excessive claims in proportion to the cumulative\npopulation of the country. In that way again the equal cumulative per capita principle would come\ninto play.\nAnswer: We agree that this was a weak point in our methodology and would like to thank you for\nfurther highlighting it and suggesting an alternative approach. We have decided to incorporate this\nalternative for redistributing the emission allowances that are not used by countries with negative\ntotal excessive carbon claims and we have redistributed this “emission allowance pool” based on\nequal cumulative per capita access. Hence, amendments have been made to the methodology by\nredesigning the equation that estimates the Additional Carbon Accountability for each country. Two\nequations have been added in order to do this: equation 5, which estimates the unused emission\nallowances and pools them for redistribution among countries that are assigned an Additional\nCarbon Accountability, and equation 6, which makes the redistribution based on an equal\ncumulative per capita approach similar to the one used for the carbon budget. Equation 7 is also\nadjusted accordingly. The equations are solved iteratively to avoid countries being assigned a\nnegative Additional Carbon Accountability. All results have been updated accordingly along with the\nsensitivity analysis.\nReviewer #3 (Remarks to the Author):\n5. I would like to thank the authors for addressing the concerns I raised in my first review of the\nwork. My major issues having to do with fairness I find have been well addressed, and the what I felt\nmaybe too ambitious claims on fairness have been moderated. I appreciate the detailed responses\nto my concerns in the responses to reviewers document, and the inclusion of robustness checks etc.\nwhich move towards my concern of setting the research in the field / highlighting novelty, along with\nthe addition of the new Robustness section and the additional results / methods in the\nSupplementary file.\nFinally, the figures are overall greatly improved, and easy for the reader to understand (along with\nthe captions).\nI think these changes do well to address all my previous concerns.\nAnswer: Thank you for taking the time to review our manuscript.\n6. There were some minor issues I noted throughout the paper:\nLine 85: Carbon debt is discussed, but not really defined until Table 1 on line 130; it may be that\nsome readers more broadly interested aren't clear what's meant by carbon debt here.\nAnswer: We have moved all definitions to Table 1, we think the text benefits from that. On line 78\nwe explain the concept: ” The carbon debt, and with it the responsibility for historical emissions…”\nand only in Table we specify that we used equal cumulative per capita 1990-2022 for the calculation.\nLine 130 - Table 1: You call it \"historic carbon debt\" only here, everywhere else its just carbon debt\n(or carbon debts). An extremely minor issue of consistency.\nAnswer: Thanks for noticing. We have deleted ”historic” in the text and in the Table caption.\nLine 229: I'm not sure I see a connection between your analysis showing that large developed\ncountries take the lead in mitigation, and grandfathering in NDCs providing legitimacy for status quo\nlevels. Couldn't both be true, your results do indeed show that, but the NDCs also attribute\nlegitimacy to status quo? I suppose it could be that your results do still address the second portion of\nyour statement, in that the risk of perpetuating inequality may not be as high as others would fear.\nAnswer: We agree that NDCs attribute legitimacy to the present unequal levels of emissions and this\nis why we allocate additional carbon accountability to high-emitters. However, we find weak support\nthat NDCs perpetuate inequality since many large developed countries with large carbon debts (e.g.\nEU) have much more ambitious plans than other developed countries (e.g. Saudi Arabia) and upper\nmiddle-income countries. Like grandfathering, NDCs start from the present emission levels, but\nunlike grandfathering, NDCs do not allocate the global remaining carbon budget to nations based on\ncurrent emission shares (ref 10 in manuscript). We have changed the text to (lines 190-196):\n“Our analysis suggests that the statement above, that the grandfathering characteristic of NDCs and\nNZTs attributes legitimacy to the present unequal levels of emissions and risks perpetuating\ninequality11, is only partially true. The timing of countries’ NZTs play a large role in future\ncumulative emissions. For example, if we assume that a country choose 2070 as NZT over 2050 and\nthat their emissions pathway is linear from 2023 onwards towards the target, then choosing net-\nzero by 2070 implies 71% higher cumulative emissions compared to choosing 2050 (48/28 years).”\nLine 414, 460, 507, 537 - \"Carbondebt\" \"Excessivecarbonclaims\" in the equations without spaces, its\nquite minor but distracting for the reader\nAnswer: We don’t know why spaces were lost in these equations; now it’s corrected, and we will\nmake sure to monitor this issue when reviewing the proofs.\nSupplementary information, Line 113: shouldn't \"integrate\" be \"integrates\" and line 114 allocation\nOF not allocation FOR?\nAnswer: Thanks, we have corrected this now.\n7. Regarding detail in methods section and reproducibility of results:\nThe methods section does describe the approach in enough detail that one should be able to\nreproduce the results, as the data are also all supplied by the authors. I did not try and do so from\nscratch, but checked how the provided R code corresponded to the methods section.\nI can confirm that the code provided does reproduce the results in the paper, and that the data\nsources etc. all correspond to those specified in the manuscript. I did have some difficulty actually\nreconciling your methods equations and your R code. I am confident now that the method specified\nin the text is carried out in your code, but it took a bit of time to read.\nE.g. a quick early example from line 43 -> why are you multiplying the variable EmissionsMtCO2 by\n44/12?\n- I know it is because the data was actually Mt carbon, and you need to multiply it by 3.664 to get to\ntonnes CO2, but its not clear from the code.\nAdditionally, as mentioned the equations from methods were difficult to actually identify in the\ncode, but everything is all there, sometimes quite hidden. In the end, there is enough detail for work\nto be reproduced, and it does not affect the manuscript, so perhaps is not relevant for me as a\nreviewer to comment on, but it would probably in the future make it easier for other reviewers to\nverify validity of results if code were clearer or more thoroughly commented when necessary (as\ncode can also be written to be understandable without comments of course).\nAnswer: Thank you for taking the time to read the R-code. We are grateful for these comments since\nwe want to make our method easily accessible for other users (both researchers and technical\nexperts). Therefore, we decided to include working calculations in both Excel (only main case) and R\n(with full reproducibility of main case calculations as well as sensitivity analyses). We have gone\nthrough the code and added comments to explain what the purpose of each section is and what the\ncode does on individual lines as well as added references to the corresponding equations in the\nmanuscript. We hope that this will make it easier to read and use.\nThank you for the well-written and interesting paper!\nReviewer #3 (Remarks on code availability):\nAs I wrote to the authors - I was able to reproduce the results of the paper quite easily, in that I\ncould download their github repository and run the R script using all their provided files. All results\nseen in the manuscript and supplementary files can be reproduced exactly.\nThere was not a README file with installation instructions as such, and one would be quite easy to\nwrite up for the authors, but it was very straightforward for anyone with an introductory knowledge\nof R.\nAs for a usable resource for the community - the code was quite difficult to read in some cases, and\nperhaps does not lend itself to easy use by third parties.\nAnswer: Thanks again for reviewing the R-code. We have now added a README-file to make it\neasier for users to install the program, which we hope will make it even more straightforward to\nmake use of the code. In addition, the R-code has been thoroughly commented to assist users’\nunderstanding of what it does and what the purpose of different sections is.\nREVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nThe authors engaged with my concerns even if I believe they did not implement my suggestions in the\nway I would have liked to see (e.g., they relegated consumption-based accounting to the SI, and stuck\nwith the original price level). These would not be my preferred choices, but at the same time they are\nnot invalid\nReviewer #2 (Remarks to the Author):\nI am very happy with the changes now, all my concerns have been addressed. Therefore I would\nrecommend this article for publication."}]

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