Impact of short-lived non-CO2 mitigation on carbon budgets for stabilizing global warming

Limiting global warming to any level requires limiting the total amount of CO2 emissions, or staying within a CO2 budget. Here we assess how emissions from short-lived non-CO2 species like methane, hydrofluorocarbons (HFCs), black-carbon, and sulphates influence these CO2 budgets. Our default case, which assumes mitigation in all sectors and of all gases, results in a CO2 budget between 2011–2100 of 340 PgC for a >66% chance of staying below 2°C, consistent with the assessment of the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Extreme variations of air-pollutant emissions from black-carbon and sulphates influence this budget by about ±5%. In the hypothetical case of no methane or HFCs mitigation—which is unlikely when CO2 is stringently reduced—the budgets would be much smaller (40% or up to 60%, respectively). However, assuming very stringent CH4 mitigation as a sensitivity case, CO2 budgets could be 25% higher. A limit on cumulative CO2 emissions remains critical for temperature targets. Even a 25% higher CO2 budget still means peaking global emissions in the next two decades, and achieving net zero CO2 emissions during the third quarter of the 21st century. The leverage we have to affect the CO2 budget by targeting non-CO2 diminishes strongly along with CO2 mitigation, because these are partly linked through economic and technological factors.


Introduction
A near-linear relationship between cumulative emissions of carbon dioxide (CO 2 ) and peak global-mean temperature increase is seen in many climate models, and the ratio between these two quantities is referred to as the transient climate response to cumulative emissions of carbon (TCRE). TCRE is defined as the global-mean surface temperature increase for an emission of 1000 PgC to the atmosphere, and applies for cumulative emissions up to about 2000 PgC until the time temperatures peak (Collins et al 2013). The Working Group I (WGI) contribution to the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) assesses TCRE to fall with greater than 66% probability-'likely' in the calibrated uncertainty language of the IPCC (Mastrandrea et al 2010)-within the range of 0.8-2.5°C (Collins et al 2013, Technical Summary in IPCC 2013.
As a consequence of the near-linear relationship between cumulative carbon emissions and peak temperature, a CO 2 budget can be computed that defines the emissions compatible with limiting peak warming to below a given temperature limit with a given probability. IPCC AR5 WGI computed that to limit CO 2 -induced warming to below 2°C with at least 33, 50, and 66% probability, the corresponding compatible carbon budgets would be 1570, 1210 and 1000 PgC, respectively 8 (Summary for Policymakers in IPCC 2013). With historical CO 2 emissions amounting to about 515 PgC ('likely' range 445-585 PgC) by 2011 (Friedlingstein et al 2014, Summary for Policymakers in IPCC 2013, this suggests that we have already emitted about half of the CO 2 emissions compatible with limiting warming to below 2°C with a greater than 66% chance. This interpretation would only be correct for the hypothetical case that all the warming is caused only by CO 2 . Many other, both cooling and warming, species influence the radiative balance of the Earth (Myhre et al 2013). As their resulting effect at the time of zero CO 2 emissions is projected to be net positive (i.e. to be a net warming effect), compatible CO 2 emissions budgets are smaller when taking into account all radiatively active species (Collins et al 2013, Clarke et al 2014, Knutti and Rogelj 2015, Technical Summary in IPCC 2013. For instance, IPCC AR5 WGI estimates that compatible CO 2 emissions from 2011 onward to limit peak global-mean temperature increase to below 2°C would be reduced to about 410, 355, and 275 PgC for having at least 33, 50, and 66% chance, respectively. Likewise, based on the Working Group III (WGIII) contribution to the IPCC AR5 (Clarke et al 2014, Summary for Policymakers in IPCC 2014, scenarios that have a 'likely' chance of limiting warming to below 2°C have a range of about 170-320 PgC for CO 2 emissions from 2011 to 2100. This is much lower than what would be estimated for a world in which only CO 2 -induced warming would play a role. In other words, half of the CO 2 emissions compatible with limiting warming to below 2°C (with a greater than 66% chance) have been emitted if we consider only CO 2 -taking also the influence of non-CO 2 species into account, however, about two thirds of 2°C-compatible CO 2 emissions have been emitted to date.
The level of non-CO 2 emissions could thus play an important role in determining the size of the CO 2 budget. Here we explore if, and by how much, the targeted mitigation of various, both cooling and warming, non-CO 2 species would influence CO 2 emissions budgets during the 21st century consistent with limiting warming to below specific temperature thresholds. We explore the potential impact of methane (CH 4 ), soot (or black carbon-BC), sulphate (SO 2 ), and hydrofluorocarbons (HFCs), and do so by accounting for possible linkages between sources of emissions of CO 2 and non-CO 2 species (see section 2).
Emission mitigation actions discussed in the framework of the United Nations Framework Convention on Climate Change (UNFCCC) focus on the so-called Kyoto-basket of greenhouse gases (GHGs). This basket contains CO 2 , as well as CH 4 , N 2 O, HFCs, perfluorocarbons, sulphur-hexafluoride (SF 6 ), and nitrogen trifluoride (NF 3 ) (UNFCCC 1998(UNFCCC , 2012. Actions to reduce BC and sulphates are thus not explicitly pledged under the UNFCCC. Recently, however, initiatives have been launched by other forums that focus on limiting socalled short-lived climate pollutants (SLCPs). These SLCPs consist of CH 4 and HFCs, (both controlled under the UNFCCC), the tropospheric ozone arising from CH 4 , NMVOC, CO and NO x emissions, and BC (UNEP 2011). The cooling sulphates, although also being air and climate pollutants, are not considered under the group of SLCPs.
It is well-established that, unlike for CO 2 , the annual rate rather than the cumulative emissions of SLCPs have the strongest effect on peak warming (Smith et al 2012, Bowerman et al 2013, Pierrehumbert 2014, Rogelj et al 2014c. Moreover, despite not being directly covered by actions undertaken under the UNFCCC, also some SLCPs (including BC) will be strongly reduced by mitigation measures to limit cumulative CO 2 emissions (figure 1; Rogelj et al 2014b, Rogelj et al 2014c). This is because CO 2 and some SLCPs are emitted by common sources. For example, many combustion processes, like diesel engines, release both CO 2 and BC. If diesel engines are phased out because CO 2 emissions are limited, the BC emissions that originally originated from these engines disappear.

Methods
Based on an initial scenario set of almost 200 scenarios (Rogelj et al 2011), we construct a set of cases that allow an assessment of the influence of SLCP mitigation on CO 2 budgets. Each of the original scenarios contains an internally consistent set of both CO 2 and non-CO 2 emission trajectories over the 21st century. We here use a set of earlier published methods (Rogelj et al 2014b, Rogelj et al 2014c to recalculate new, internally consistent baseline emissions for CH 4 , BC, co-emitted species like organic carbon (OC), and SO 2 , and compare these to stringent emission mitigation pathways. These new baselines are required to allow an assessment of the maximum effect of non-CO 2 mitigation on CO 2 budgets: the difference between a mitigation path and a baseline in absence of mitigation targeting a specific non-CO 2 forcer. CH 4 , BC, and SO 2 are affected differently by CO 2 mitigation (figure 1). For BC, OC, SO 2 and other coemitted pollutant emissions, we use a tool provided by Rogelj et al (2014b) that allows to calculate consistent global relationships between CO 2 and these air-pollution species. Default baseline emissions for these air pollutants assume that current air-pollution legislation is fully implemented and that global airquality standards converge in line with regional economic development. This baseline also assumes that with increasing economic development an increasingly larger share of the population will get access to clean sources of energy (Pachauri et al 2012, Rogelj et al 2014c. The mitigation path for BC and its coemitted species mimics the 'all measures' case developed by the UNEP SLCP report (UNEP 2011) until 2030 and is further projected throughout the century as described by Rogelj et al (2014c). The mitigation path for SO 2 assumes that stringent air-pollution controls are implemented over the 21st century (see Rogelj et al 2014b).
Also three alternative baselines are constructed for a sensitivity analysis: two with air-pollution legislation frozen at its 2005 levels throughout the 21st century for BC and SO 2 /NO x , respectively. In these two baselines, no improvements for BC or SO 2 /NO x air-pollution legislation are assumed to have occurred over the last decade and the stringency of air-pollution control is frozen at its 2005 levels throughout the 21st century for BC and SO 2 /NO x , respectively. These assumptions represent a counterfactual evolution of air-pollution control over the past decade, and a failure to effectively implement any additional air-pollution measures in the future. A third alternative baseline includes no targeted energy access policies (see table 1 and Rogelj et al 2014b for details). Under the latter assumption, large shares of the global population remain without access to clean energy until the end of the century. The use of traditional biomass for cooking and heating is currently a major source of anthropogenic BC emissions globally (Pachauri et al 2012).
For CH 4 , we follow the method presented in Rogelj et al (2014c) to create CH 4 baselines consistent with each respective CO 2 emission trajectory. This method applies no common carbon price to CO 2 and CH 4 , but only to CO 2 . Because CO 2 and CH 4 have few common sources, CH 4 baseline emissions do not vary much across a wide range of CO 2 emission pathways (figure 1). These CH 4 baseline emissions are then compared to a very stringent CH 4 mitigation path, derived from a model with particularly strong CH 4 reduction response to, for example, increasing carbon prices (van Vuuren et al 2011). Also a case assuming a 20-year delay of these stringent CH 4 measures is constructed.
For HFCs, we use updated HFC baseline estimates (Velders et al 2009) and assess their influence relative to earlier estimates (Nakicenovic and Swart 2000) as described in Rogelj et al (2014c). These estimates are the high end of the literature (Gschrey et al 2011). The 'reference case' of our study includes internally consistent baseline evolutions for air pollutants that all follow an extrapolation of current policies, as well as the original CH 4 and HFC pathways from Rogelj et al (2011). Note that carbon-price or policy effects are typically included in the CH 4 and HFC 'reference case' pathways which are found in the literature. To explore the maximum range, these carbonprice effects are excluded in our CH 4 and HFC baselines. However, CH 4 baselines still change as a function of CO 2 mitigation, not due to a carbon price but because some sources of CH 4 are phased out together with CO 2 mitigation (figure 1).
Comparing the various baseline, sensitivity and reference cases will provide us with an estimate of the potential effects of a set of policy interventions, which are, however, rarely fully independent from CO 2 mitigation. While BC and SO 2 emissions are coupled to CO 2 mitigation by co-emission from economic activities and technologies, CH 4 and HFCs are coupled to CO 2 mitigation by multi-gas carbon-price/policy effects, resulting from multilateral agreements under the UNFCCC and/or national policies.
The temperature outcome of each scenario variation is assessed with the reduced-complexity carboncycle and climate model MAGICC, version 6 (Meinshausen et al 2011a), in a probabilistic setup that is consistent with the IPCC AR5 WGI climate sensitivity assessment (Meinshausen et al 2009, Rogelj et al 2012, Rogelj et al 2014a. Temperature increase is computed relative to preindustrial levels (1850-1875). Globalmean temperature projections and assessing associated uncertainties are a key application for which MAGICC has been extensively vetted (Meinshausen et al 2011b). For each scenario, the 50%, 66% or other percentiles are computed out of a sample of 600 climate model runs; a cubic smoothing spline (smoothing parameter: 5 × 10 −9 ) is computed to show the general dependence of maximal target temperature versus cumulative CO 2 emissions (figure 2(A)). Alternative appropriate values for either smoothing parameter or fit type do not change our main conclusions.

Results
We here look at how CO 2 budgets consistent with limiting warming to below a specific temperature limit by 2100 are influenced by the mitigation of short-lived non-CO 2 species. As introduced earlier, to first order, annual emissions of short-lived non-CO 2 species leading up to the time of the peak play the most important role for peak warming (Smith et al 2012). Therefore mitigation actions on these species are only important insofar as they effectively reduce the annual emission burden of short-lived non-CO 2 species around the time of peak (or maximum) warming during the 21st century. In most temperature stabilisation scenarios, peak warming is reached by the last quarter of the 21st century. Scenarios with little CO 2 mitigation reach their maximum warming during the 21st century only by 2100, and are still increasing afterwards. Any scenario that does not reach zero or lower annual CO 2 emissions by 2100, will exhibit further warming after the 21st century.
Results are reported as relative changes to the 'reference case' (tables 1 and 2). Absolute values are reported in table S1. Table 1. Overview and description of cases and sensitivity cases assessed in this study. Accompanying references can be found in the main text.

Case Description
Reference case Case with internally consistent evolutions of air pollutants at the level of current legislation. This implies that global air-pollution control converges, along with regional economic development, to current best levels of air-pollution control. Also along with regional economic development, rural populations gradually gain access to clean forms of energy. Reductions in CH 4 are driven by the same carbon price as reductions in CO 2 . No CH 4 mitigation As reference case, but no carbon-price-induced reductions of CH 4 . CH 4 emissions are only reduced to a small degree as a result of technical linkages to CO 2 mitigation (see figure 1). Stringent CH 4 mitigation As reference case, but CH 4 emissions follow a very stringent mitigation path (from RCP2.6) which is situated at the very low end of the CH 4 mitigation literature range. Delayed stringent CH 4 mitigation As stringent CH 4 mitigation case, but with a 20-year delay of reduction. BC measures As reference case, but with BC and co-emitted species reduced very stringently, in line with the 'all measures' case of UNEP/WMO (2011). This impacts emissions from BC, OC, NMVOC, and CO. Frozen BC baseline As reference case, but instead of assuming the level of current legislation, BC and co-emitted species are subject to air-pollution controls frozen at their 2005 levels throughout the entire 21st century. No energy access policies As reference case, but instead of assuming no specific energy access policies at all during the entire 21st century, resulting in large populations still lacking access to clean sources of energy by the end of the century. SO 2 measures As reference case, but SO 2 is subjected to stringent air-pollution controls in the future. Frozen SO 2 and NO x baseline As reference case, but instead of assuming the level of current legislation, SO 2 and NO x are subject to air-pollution controls frozen at their 2005 levels throughout the entire 21st century. Updated HFC projections As reference case, but with updated HFC projections for the 21st century which represent the high-end of the literature.
Earlier literature has shown that mitigation measures of BC and its co-emitted species only have a limited effect on maximum 21st century temperatures (≪0.1°C) when compared to a baseline which already includes current and planned legislation (Rogelj et al 2014c). In the context of this study, this limited effect on maximum 21st century temperatures translates into virtually no effect (<2.5%) of 'BC measures' on CO 2 budgets (figure 2(B) and table 2, relative shifts of CO 2 budgets are rounded to the nearest 5%). This limited impact is robust across all temperature levels assessed here.
These findings are sensitive to the air-pollutant baseline evolution. Therefore sensitivity cases were created (table 1). First, when assuming a baseline without explicit energy access policies, CO 2 budgets decrease by about 5% for 2°C-compatible budgets (table 2). For higher temperature levels, this relative effect becomes smaller. Second, we assume a frozen BC baseline, representing a roll-back of future air-pollution controls over the 21st century from today's levels. In this case, maximum 21st century temperature is affected by 0-0.4°C, depending on the concurrent CO 2 mitigation. This translates in a 0-5% smaller CO 2 budget compatible with 2°C and 3°C, and 5-10% smaller CO 2 budgets compatible with 4°C by 2100 ( figure 2(B)). The lower end of these ranges corresponds to higher probabilities of limiting warming to below these temperature levels. This is a logical result as to achieve higher probabilities of staying below a given temperature limit, increasingly lower CO 2 pathways are required. A discussion of the robustness and adequacy of these values is provided in the following section.
The 'BC measures' assumed in the previous paragraph only tackle sources of air pollutants that have a net warming effect. However, other air pollutants (like SO 2 ) exist which have a net cooling effect. SO 2 emissions are strongly linked to emissions of CO 2 , and in addition, technology shifts lead to a projected steady phase-out of these emissions over the 21st century. Therefore, stringent emission reductions of SO 2 are projected to influence maximum 21st century warming to a very limited degree compared to our reference case which includes a 'current legislation' baseline, and their influence on CO 2 budgets consistent with particular temperature limits is therefore assessed to be virtually zero. Assuming that SO 2 controls are frozen at their 2005 levels, however, would increase the CO 2 budget for limiting median globalmean temperature to below 2, 3, and 4°C, by 10, 15, and 25%, respectively. For higher probabilities, this effect is smaller (table 2).
In the CH 4 pathways of our 'reference case' typically a multi-gas mitigation approach was pursued (e.g., Clarke et al 2009). This means that CH 4 , and other gases of the Kyoto-GHG basket, are targeted together with CO 2 by means of a common carbon price and a metric translating non-CO 2 emissions into CO 2 -equivalent emissions (for example, 100-year Figure 2. Dependence of carbon budgets consistent with a particular temperature limit during the 21st century. Panel A shows the distribution of global-mean temperature outcomes per scenario and smoothing splines for the outcomes at the 50, 66 and 75% probability level. Panel B shows how the median outcome would change when assuming alternative mitigation of non-CO 2 airpollutant species. Panel B shows smoothing splines for the medium temperature outcome for each case, respectively. The shaded ranges are visual guides. Note that the full range is to be considered highly hypothetical (see section 4 in main text). Moreover, only scenarios with a temperature increase in 2100 of about 2°C and less are stabilizing temperatures by 2100. When year-2100 temperatures are higher, temperatures continue to increase past 2100 and the provided carbon budgets are thus not holding warming to below the here reported year-2100 warming in the long term.
Global-Warming-Potentials, as currently under the UNFCCC). By contrast, in our baselines for CH 4 , we decoupled CH 4 from CO 2 mitigation by assuming that the carbon price is only applied to CO 2 . When switching CH 4 pathways in all scenarios to this hypothetical baseline, CO 2 budgets for limiting warming to specific temperature levels during the 21st century are reduced across all scenarios, but with important variations. For limiting warming to below 2°C, CO 2 budgets consistent with a 50, 66, and 75% chance of success are reduced by 35, 40, and 50% respectively (table 2). For higher temperature limits, this change is smaller ( figure 3(A), table 2), because for higher CO 2 budgets the 'reference case' includes higher reference CH 4 emissions due to a lower (implied) common carbonprice pressure in the original scenarios. Table 2. Carbon budgets between 2011 and 2100 in line with limiting warming to specific temperature limits with a particular probability level during the 21st century, and their relative changes (rounded to the nearest 5 PgC and nearest 5%). Note that all cases are not equally plausible across the various temperature levels (see section 4 in main text). Absolute emission values are in PgC (=GtC). Corresponding values in GtCO 2 are obtained by multiplying the reported values by a factor of 3.66. Note that only for the 1.5°C and 2°C temperature limits the results reflect the change in peak warming budgets. For both the 3°C and 4°C limit, CO 2 emissions are not at or below zero by 2100 and temperatures are thus not yet stabilized. In the latter case, the budget shifts are driven by changes in transient warming in 2100 rather than peak warming during the 21st century.
Carbon budgets between 2011-2100 Alternatively, if CH 4 pathways are all switched to a very stringent mitigation path (van Vuuren et al 2011) CO 2 budgets for limiting warming to below 2°C are increased by 20, 25, and 35%, for achieving a probability of 50, 66, and 75%, respectively. These relative shifts are similar for higher temperature limits, yet become increasingly less plausible (see discussion). When delaying this shift towards a stringent CH 4 mitigation path by 20 years, CO 2 budgets for 2°C are increased by about 5% less.
Finally, the high end of recent projections of HFCs are significantly higher than earlier estimates. Not tackling this projected increase strongly reduces the CO 2 budgets consistent with 50% probability of keeping warming to below 2, 3, and 4°C, by 20-45%, 10-15%, and 5-10%, respectively (table 2, figure 3(B)). In some cases, the highest updated HFC projections would push the achievability of staying below low temperature levels with high probability (66 or 75%) beyond the here assessed scenario literature. Given that our HFC assumptions are based on the highest available literature estimates and also lowerequally plausible-estimates are available, our results should also be read as upper-limit estimates.

Comparison to IPCC AR5 ranges
To situate our analysis within the wider literature, we compare our results with the transformation pathway assessment of the IPCC AR5 (table 6.3 in Clarke et al 2014). IPCC AR5 WGIII provides ranges of cumulative CO 2 emissions for limiting warming to specific temperature levels with a given probability (table SPM.1 in IPCC 2014). For several temperatureprobability combinations, a comparison with the data of this study can be made (table 2), which shows that our results are broadly consistent with the WGIII scenario assessment of the IPCC AR5.
In our 'reference case', limiting warming to below 2°C relative to preindustrial levels with 75, 66, or 50% chance would imply cumulative carbon emissions between 2011 and 2100 to be limited to 260, 340, and 460 PgC. This compares to IPCC ranges of assessed cumulative CO 2 emissions over the same period for limiting warming to below 2°C of 170-320, 260-390, and 270-420 PgC, for a >66%, >50%, and 33-66% probability, respectively. Our 2011-2100 CO 2 budget estimates for the higher probabilities (for instance, 340 and 260 PgC for 66% and 75% chance, respectively), both fall well within the IPCC ranges for a >50% and >66% probability, respectively. Our estimate for a >50% probability is slightly larger than the IPCC's 33-66% range. This is consistent with the understanding that the IPCC AR5 WGIII assessment of transformation pathways does not just use the direct model output of the MAGICC model but also further accounts for uncertainties of the temperature projections which are not covered by climate models (and which were assessed by WGI). In other words, the Figure 3. Dependence of carbon budgets consistent with a particular temperature limit during the 21st century. Vertical lines represent the 5th to 95th percentile range around the 'reference case' (see text). Panel A shows how the median outcome would change when assuming alternative levels of CH 4 mitigation. Panel B shows how the median outcome would change when taking into account updated baseline projections for HFCs. Note that accounting for common carbon-price signals already brings our 'reference case' at low CO 2 budgets down towards the stringent CH 4 reduction case (panel A), while at high carbon budgets the opposite is true. Not all cases are equally plausible across the various temperature levels (see section 4 in main text). Only scenarios with a temperature increase in 2100 of about 2°C and less are stabilizing temperatures by 2100. When year-2100 temperatures are higher, temperatures continue to increase past 2100 and the provided carbon budgets are thus not holding warming to below the here reported year-2100 warming in the long term.
IPCC conservatively interpreted the raw output numbers of their probabilistic model setup when translating them into the calibrated IPCC uncertainty language. This results in budget estimates that tend to be lower than what would be derived directly from model output. Finally, also 2011-2100 CO 2 budgets consistent with limiting warming to higher temperature levels over the 21st century, for example a 3 or 4°C warming, are found to be consistent with the IPCCagain, taking into account that the results and numbers in this paper reflect the direct probabilistic output of the MAGICC model simulations, while the IPCC further assessed these probabilities in light of possible limitations in our current understanding of the climate response.

Applicability and limitations
The magnitude of the effect of non-CO 2 mitigation on CO 2 emission budgets across 2°C and 4°C scenarios is strongly affected by the expected baseline range of the non-CO 2 emissions in these scenarios. These emissions may vary to a much larger extent in a 4°C scenario where CO 2 emissions are relatively high by the end of the century (figures 2 and 3). This is because even when not specifically targeted, non-CO 2 emissions can still be reduced by CO 2 mitigation. Emissions of air pollutants like BC can be emitted by the same sources as CO 2 . Hence, in a world with stringent CO 2 mitigation, air-pollution baseline emissions (in absence of any targeted air-pollution control) will already be much lower than in a world with high CO 2 emissions (Rogelj et al 2014b). Therefore, measures that target air-pollution species would allow a larger absolute amount of air pollution to be removed in a 4°C world compared to a 2°C world, where the baseline air pollution levels are much lower because sources common with CO 2 have been phased out.
Likewise, emissions of CH 4 by 2100 would be much higher in scenarios that reach high end-of-century warming, and the effect of policies targeting CH 4 specifically would be larger. This is because of two reasons. First, CH 4 emissions are to a limited degree coupled to technologies that also emit CO 2 , and are thus slightly reduced through mitigation targeting CO 2 only. Second, price signals like carbon prices lead to CH 4 emissions being reduced along with CO 2 . It is important to note that the inclusion of this price signal linkage in our 'reference case' pushes CH 4 emissions at low CO 2 budgets down towards the stringent CH 4 reduction case, while at high carbon budgets a lack of price signals results in CH 4 emissions towards the high no-mitigation baseline ( figure 3(B)).
Emission (reductions) of CO 2 and other species are often coupled because of physical/technological links (a certain technology emits both CO 2 and a host of other species), or an economic and policy link (an entire basket of gases is made subject to a single carbon price, e.g. in the UNFCCC). Taking into account these links, we find that the effectiveness of targeting non-CO 2 species individually is reduced in stringent CO 2 mitigation scenarios. In other words, initiatives that target individual species provide less additional benefits (or have a decreased 'additionality') when CO 2 emissions are stringently reduced. Furthermore, our results also provide an indication of how much displacement (in terms of cumulative CO 2 ) can be tolerated without exhausting the CO 2 budget benefits of, for example, stringent early CH 4 abatement (supple mentary table 1).
An important limitation of our estimated effects of non-CO 2 mitigation on CO 2 budgets is that for temperature levels higher than 2°C, global-mean temperature is not yet stabilized by 2100, as annual CO 2 emissions in 2100 in such scenarios are not yet at or below zero. Only for the lowest temperature levels (<2°C), scenarios thus actually represent realistic pathways towards keeping warming to below the levels indicated in the long term. For higher temperature levels, the estimated effects of non-CO 2 mitigation are to be considered transient and impermanent. This also explains the larger effect of non-CO 2 mitigation on CO 2 budgets for higher temperature levels-in some sense an artefact of the limited time horizon of this study, which only extends until the end of the 21st century. A second aspect, which works in the opposite direction, is the simple fact that CO 2 budgets consistent with higher temperature limits are larger and absolute changes therefore translate in smaller relative changes. If the time horizon would extend beyond 2100, the relative influence of non-CO 2 mitigation on CO 2 budgets for temperature limits higher than 2°C is expected to decline.
Because assumptions of socio-economic scenarios become increasingly uncertain when going more than 100 years into the future, our analysis is limited to the 21st century and therefore provides results for maximum 21st-century warming only. This maximum 21st-century warming either occurs at peak warming in case of stringent mitigation scenarios which keep warming to below 2°C, or in 2100 for scenarios that do not stabilise temperatures during the 21st century. However, the trade-offs that were quantified between CH 4 mitigation and CO 2 budgets also have to be seen in a longer-term context. Over longer timescales and for the same global warming in 2100, cases with larger CO 2 budgets and more stringent CH 4 abatement have more committed, irreversible long-term warming, than cases with lower CO 2 budgets and higher CH 4 . In the latter case, the possibility of bringing down temperature by later action on methane beyond 2100 is left open.
Most of these scenarios assume global mitigation action to start at a time point that lies in the past (2005 or 2010). Recently, many studies have provided scenarios that start mitigation at later points in time and thus explicitly delay near-term mitigation (Kriegler et  . While such delays strongly impact the technology feasibility and costs of scenarios, as well as transient temperature levels (Rogelj et al 2013a, Schaeffer et al 2013, the anticipated impact on CO 2 budgets consistent with limiting warming to below 2°C is anticipated to be small. Our cases have been developed to span the widest range of conceivable sensitivity cases. However, not all combinations remain equally plausible. For instance, given the already existing and operational policy instruments under the UNFCCC for mitigating the entire Kyoto-GHG basket, it is already counterfactual today to assume that no CH 4 mitigation occurs when CO 2 is reduced. Also for the future, it is thus plausible that CO 2 and CH 4 mitigation will be linked. Likewise, given that our assumed CH 4 mitigation path is extremely ambitious (Smith and Mizrahi 2013, Rogelj et al 2014c, Smith et al 2014, it is highly unlikely that it can be achieved if CO 2 emissions rise to levels in line with 3°C and higher. Finally, both our sensitivity BC and SO 2 frozen legislation baselines are highly hypothetical. It is difficult to conceive a future in which local policymakers strongly target air pollution from soot, but at the same time keep sulphate controls frozen at historical levels, or vice versa. As figure 2(B) indicates, freezing air-pollution legislation across the board (both BC and SO 2 ) would result in an overall cooling.

Conclusion
In conclusion, we have quantified the possible influence of short-lived non-CO 2 mitigation on CO 2 budgets consistent with limiting warming to various levels during the 21st century. The most meaningful findings are for 2°C, as for this level temperatures are actually stabilized by 2100, and peak warming has thus been reached. Our study looked at warming during the 21st century. If 21st-century reductions of short-lived climate forcers are traded with reductions in CO 2 , warming during the 21st century might be the same, but the multi-century warming commitment would still be larger due to larger cumulative CO 2 emissions.
We find that mitigation of air-pollution species (both warming and cooling) barely affects consistent CO 2 budgets. That is largely because a phase-out of CO 2 emissions would lead to reductions of co-emitted emissions as their sources disappear.
Very stringent CH 4 mitigation can markedly influence 2°C-consistent budgets, at the expense of a higher post-2100 CO 2 warming commitment. However, this influence depends strongly on the realism of the very low CH 4 scenario that was used here, or on the hypothetical case in which no CH 4 mitigation would be undertaken at all. Delaying stringent CH 4 mitigation by 20 year still yields a comparably large benefit as immediate stringent CH 4 mitigation. Similarly, updated HFC baseline projections could trigger substantial extra warming that would constrain the remaining CO 2 budget. However, for both CH 4 and HFCs, mitigation options and policy instruments are readily available.
Although our results indicate relatively large hypothetical variations of the remaining CO 2 budget, the real-world effects of more or less stringent mitigation action on CH 4 are likely much more limited. Thus, our results can be seen as an exercise to sketch the boundaries of the sensitivity. Even in case of very stringent CH 4 mitigation, the CO 2 budget's increase would not in any way change the fundamental necessity to limit the cumulative amount of CO 2 emissions and hence to phase-out unabated fossil-fuel emissions to net zero or below, likely earlier rather than later in the second half of the 21st century.