Estimating and tracking the remaining carbon budget for stringent climate targets

An Author Correction to this article was published on 25 March 2020


Research reported during the past decade has shown that global warming is roughly proportional to the total amount of carbon dioxide released into the atmosphere. This makes it possible to estimate the remaining carbon budget: the total amount of anthropogenic carbon dioxide that can still be emitted into the atmosphere while holding the global average temperature increase to the limit set by the Paris Agreement. However, a wide range of estimates for the remaining carbon budget has been reported, reducing the effectiveness of the remaining carbon budget as a means of setting emission reduction targets that are consistent with the Paris Agreement. Here we present a framework that enables us to track estimates of the remaining carbon budget and to understand how these estimates can improve over time as scientific knowledge advances. We propose that application of this framework may help to reconcile differences between estimates of the remaining carbon budget and may provide a basis for reducing uncertainty in the range of future estimates.


Since the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC)1, the concept of a carbon budget has risen to prominence as a tool in guiding climate policy2. We here define the remaining carbon budget as the finite total amount of CO2 that can be emitted into the atmosphere by human activities while still holding global warming to a desired temperature limit. This is not to be confused with another concept, the historical carbon budget, which describes estimates of all major past and contemporary carbon fluxes in the Earth system3. The idea of a remaining carbon budget is grounded in well established climate science. A series of studies over the past decade has clarified and quantified why the rise in global average temperature increase is roughly proportional to the total cumulative amount of CO2 emissions produced by human activities since the industrial revolution4,5,6,7,8,9,10,11,12,13. This literature has allowed scientists to define the linear relationship between warming and cumulative CO2 emissions as the transient climate response to cumulative emissions of CO2 (TCRE). Once established, the appeal of this concept became immediately evident: the possibility that the response of an enormously complex system—such as the response of planet Earth to our emissions of CO2—could potentially be reduced to a roughly linear relationship would allow scientists to infer clear and easy-to-communicate implications. However, additional processes that influence and are influenced by future warming, such as the thawing of permafrost, have recently been included in models that simulate the Earth system. These additional processes add uncertainty and may change our understanding of this linear relationship. Moreover, global warming is not driven by emissions of CO2 only. Other greenhouse gases (such as methane, fluorinated gases or nitrous oxide) and aerosols and their precursors (including soot or sulphur dioxide) affect global temperatures. Estimating the remaining carbon budget thus also implies making assumptions about these non-CO2 contributions. This further complicates the relationship between future CO2 emissions and global warming.

Carbon budgets nevertheless have become a powerful tool for communicating the challenges we face in aiming to hold warming to 1.5 °C and to well below 2 °C—the limits of global average temperature increase set out in the United Nations Paris Agreement14,15,16,17,18. First, every tonne of CO2 emitted into the atmosphere by human activities adds to warming, and it does not matter whether this tonne of CO2 is emitted today, tomorrow or yesterday. This also implies that to limit temperature increase to any level, global CO2 emissions produced by human activities must be reduced to net-zero levels at some point in time and, on average, stay at net-zero levels thereafter. Furthermore, when aiming to limit warming to below a specific limit, a finite carbon budget also implies that the more we emit in the coming years, the faster emissions will have to decline thereafter to stay within the same budget—simple arithmetic. Finally, once net CO2 emissions are brought to zero, warming would stabilize but would not disappear or be reversed19,20,21. Any amount by which a carbon budget compatible with a desired temperature limit is missed or exceeded would thus have to be actively and permanently removed from the atmosphere in later years. This could be achieved through measures that result in net negative CO2 emissions, which come with their own technical and social complications22,23,24,25,26,27. Besides its role as a communication tool, the carbon budget concept also provides a way to exchange knowledge across disciplines. For example, such knowledge exchange is already happening for climate change mitigation requirements between the geoscience community and other disciplines that study climate change from a more societal angle28,29.

Diversity that may confuse

Unfortunately, all that glitters is not gold. Over the past five years, a plethora of studies have been published12,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44 further exploring and estimating the size of carbon budgets while in some way accounting for non-CO2 climate forcing. These studies most often focus on requirements for holding warming to the internationally agreed 1.5 °C or 2 °C limits14,15,16. Although all studies aim to evaluate the same quantity, the use of different definitions and non-CO2 climate forcing assumptions, as well as methodological and model differences, have led to a wide variety of reported carbon budget estimates that aim to achieve temperature goals that are nominally the same (see Box 1 for an overview of carbon budget estimation approaches). This variation seems to have decreased instead of increased the broader understanding of the remaining carbon budget and has thus tempered the initial enthusiasm about its usefulness as a guide for policy making and target setting45,46. This confusion is avoidable, however. Differences in remaining carbon budget estimates can be understood if a set of potential contributing factors are carefully taken into account.

Here we present a conceptual framework that allows one to track, understand, update and explain estimates of the remaining carbon budget over time. The framework’s structure enables the assessment of individual contributing factors, including historical warming, the TCRE, the zero-emissions commitment and non-CO2 contributions to future warming. It integrates suggestions made in earlier literature12,47 and is a generalization and extension of the framework used in ref. 48.

Remaining carbon budget framework

As discussed, the remaining carbon budget can be defined as the remaining amount of CO2 emissions that can still be emitted while keeping the global average temperature increase due to human activities to below a specific temperature limit. The framework set out below applies to a situation in which one aims to limit peak (or maximum) warming and its associated impacts. It can, however, also be extended to apply to a situation where temperature rise has temporarily exceeded an intended temperature limit, often referred to as a temperature overshoot (see Supplementary Text 1).

We present in equation (1) an estimate of the remaining carbon budget (Blim) for a specific temperature change limit (Tlim) as a function of five terms that represent aspects of the geophysical and coupled human–environment system (equation (1): the historical human-induced warming to date (Thist), the non-CO2 contribution to future temperature rise \(\left({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\right)\), the zero-emissions commitment (TZEC), the TCRE, and an adjustment term for sources of unrepresented Earth system feedback (EEsfb). These terms are visualized in Fig. 1 and are described and discussed in turn below.

Fig. 1: Schematic of factors contributing to the quantification of a remaining carbon budget.

The schematic shows how the remaining carbon budget can be estimated from various independently assessable quantities, including the historical human-induced warming Thist, the zero-emissions commitment TZEC, the contribution of future non-CO2 warming (consistent with global net-zero CO2 emissions or otherwise) \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\), the transient climate response to cumulative emissions of carbon (TCRE), and further correcting for unrepresented Earth system feedback EEsfb. The grey shading illustrates how uncertainty in TCRE propagates from the start point. Arrows and dashed lines are visual guides illustrating how the various factors combine to provide an estimate of the remaining carbon budget. Besides estimating the remaining carbon budget Blim, the framework can also be applied to understand, decompose and discuss estimates of carbon budgets calculated by other methods. The relative sizes of the various contributions shown in this schematic are not to scale.

Transient climate response to cumulative emissions

Arguably the most central term to estimating the remaining carbon budget is the TCRE (in units of °C per gigatonne of carbon dioxide (Gt CO2); see equation (1). In essence, the remaining carbon budget is estimated by multiplying the remaining allowable warming with the inverse of the TCRE, where the magnitude of the remaining allowable warming is the result of various contributions shown in Fig. 1 and discussed below. The TCRE can be estimated from several lines of evidence, including the observational record10,12,49,50,51, CO2-only simulations10 and multi-gas simulations12,31,49,50,51,52,53 with Earth system models of varying complexity. In its latest assessment54, the IPCC reported the TCRE to fall within the range of 0.2–0.7 °C per 1,000 Gt CO2 with a probability of at least 66%. TCRE, and hence the linear proportionality of warming to cumulative emissions of CO2, has also been found to be robust up to about 7,300 Gt CO2 of cumulative emissions54,55 and probably more56. This domain of application easily spans the range of carbon budgets consistent with warming limits of 1.5 °C and 2 °C.

Historical and maximum temperature increase

After TCRE, the combined remaining allowable warming (represented by TlimThist \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\) − TZEC) is the next key determinant for estimating the remaining carbon budget. Its first term is the specific temperature limit of interest relative to preindustrial levels (Tlim, in units of °C), and its second term represents the historical human-induced warming (Thist, in units of °C); see equation (1). Thist is the amount of human-induced warming since preindustrial times until a more recent reference period, such as the 2006–2015 period.

The estimation of Thist is a central factor affecting the size of the remaining carbon budget, because it determines how far we currently are from policy-relevant temperature limits (1.5 °C or 2 °C). The assessment of Thist should adequately isolate the human-induced warming signal from the effects of natural forcing and variability57,58. The same is true for Tlim, and if Tlim is intended to represent an internationally agreed climate goal in line with the Paris Agreement it should do so by definition15. Two additional choices play an important role in determining or setting Thist and Tlim: the choice of the preindustrial reference period and the temperature metric for determining global average temperature increase. Neither the preindustrial reference period nor the specific warming metric are explicitly defined by the Paris Agreement and recent literature has explored the implications and interpretations of this ambiguity34,35,59.

The 1850–1900 period is often used as a proxy for preindustrial levels because observational temperature records stretch back to the beginning of that period60, and key scientific reports that fed into the Paris Agreement also used this proxy1,59,61,62 (see Supplementary Text 2 for more details). Other periods have been suggested63,64,65, but ultimately the crux lies in that Thist and Tlim should always be expressed relative to the same preindustrial reference period to avoid introducing erroneous changes to the remaining allowable warming and therewith the remaining carbon budget. Besides defining an appropriate preindustrial reference period, the choice of metric by which warming is estimated from that period is also important. Studies analysing climate model simulations or observational products can use different metrics to estimate global mean temperature change (see Supplementary Text 2). The impact of this metric choice has been highlighted recently with studies34,59 showing that this choice can result in variations in the estimated global warming of the order of 10% (Supplementary Fig. 1), leading to a potential variation in remaining carbon budget estimates of more than 400 billion tonnes of CO2 (ref. 59). The IPCC has typically specified carbon budgets based on global area-averaged change in surface air temperature48,66. Other studies, however, have used different metrics and at times have even changed metrics between observations and projections (Supplementary Table 1, Fig. 2). This limits the comparability of these budget estimates59—a situation this new framework attempts to avoid.

Fig. 2: Comparison of recent remaining carbon budget estimates for limiting global warming to 1.5 °C (blue) and to 2 °C (red) relative to preindustrial levels, and overview of factors affecting their variation.

Estimates are shown for a 50% probability of limiting warming to the indicated temperature levels (additional estimates for a 66% probability are provided in Supplementary Table 2). Several studies do not report formal probabilities, but report the frequency distribution across model simulations instead. The latter estimates are marked N in the ‘Formal TCRE uncertainty distribution’ column. Estimates shown with dashed lines indicate carbon budget estimates with an imprecise level of implied global warming, for example, because they were reported for a radiative forcing target instead. TEB means threshold exceedance budget37; TAB means threshold avoidance budget37 (see Box 1). Data are taken from the IPCC Special Report on Global Warming of 1.5 °C (ref. 48), ref. 39 (with values for 1.5 °C based on our own calculations using the same method), the IPCC Fifth Assessment Report (ref. 28) and refs 12,30,31,32,36,41,43. The latest IPCC assessment of the remaining carbon budget48 assumes 0.97 °C of historical warming until 2006–2015, whereas other estimates assume either higher or lower warming for that period (Supplementary Table 1). The background and values for all studies are provided in Supplementary Tables 1 and 2. The assumptions made for each study are coloured (right-hand side of figure) for ease of visual grouping: N, no; Y, yes; SAT, global near-surface air temperatures; BT, blended temperatures (surface air temperature over land and sea-ice regions combined with sea surface temperature over open ocean); RCP, Representative Concentration Pathway; CMIP5, Phase 5 of the Coupled Model Intercomparison Project.

Non-CO2 contribution to future warming

Another term affecting the remaining allowable warming is the non-CO2 contribution to future global temperature rise (\({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\), in units of °C) (see equation (1) and Fig. 1). Current and future warming depends on both CO2-induced warming and warming due to non-CO2 forcing. Future non-CO2 warming might be considerable, given that reducing emissions of cooling sulphur dioxide causes warming67 and the knowledge that no obvious mitigation options have been identified that can completely eliminate several important sources of non-CO2 greenhouse gases68,69. To include \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\) in the remaining carbon budget framework, the non-CO2 warming contribution between a recent reference period (for example, the same period as Thist) and a specific time in the future has to be estimated. We suggest that this non-CO2 contribution to future temperature rise should be estimated from scenarios with an internally consistent evolution of greenhouse gases and other climate forcers36,70,71,72,73,74 and at the moment at which global CO2 emissions reach net zero48. Estimating the non-CO2 warming contribution at that moment in time reflects a situation in which global cumulative emissions of CO2 are effectively capped and hence allows us to directly inform the question of how much CO2 can be emitted while keeping warming to a given temperature level. If non-CO2 warming were to be estimated at other moments in time, its usefulness for informing mitigation requirements would potentially be strongly reduced.

Besides the future evolution of non-CO2 emissions, the non-CO2 warming contribution also depends on estimates of the corresponding radiative forcing, including potential changes in surface albedo43. Non-CO2 forcing and warming can be estimated with the help of simple climate models43,75,76, inferred from more complex climate model runs77, or taken from the literature37,48. Importantly, non-CO2 emissions would continue to affect warming levels after the time when net CO2 reaches zero, which creates uncertainty in methods that estimate budgets by integrating changes over time and after an overshoot (for example, see refs 36,43 and Box 1). These uncertainties are reduced in the framework proposed in this Perspective by focusing on the time of reaching net-zero CO2 emissions and by considering internally consistent non-CO2 emissions. Under these assumptions, non-CO2 emissions are projected to result in a constant or declining forcing and warming after the time of net-zero CO2 (refs 48,73). However, if under alternative assumptions one would project non-CO2 warming to continue to increase irrespective of the level of CO2 emissions78, this further increase should also be accounted for within \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\) because it would add to future peak warming.

Zero-emissions commitment

The zero-emissions commitment, TZEC (in units of °C) is the next term in the remaining carbon budget framework represented by equation (1). TZEC is defined as the additional contribution to peak warming that is still to be expected after a complete cessation of CO2 emissions79,80, and hence provides a correction term for the instantaneous linearity postulated by the concept of the TCRE. TZEC can be positive, negative or zero. For estimates of the remaining carbon budget, the TZEC when CO2 emissions approach net-zero levels is of particular interest. In more general terms, this could also be formulated as an assessment of the lag in CO2-induced warming at current and declining emissions rates50,79. When TZEC is positive, not all warming will have been experienced by the time global CO2 emissions reach net zero. The estimated additional warming would hence also have to be reduced from the allowable remaining temperature increase. At present, TZEC is frequently neglected in carbon budget studies (see Supplementary Table 1, with exceptions only hypothesizing the effect of its contribution37) and is hence implicitly assumed to be zero or negative. Several studies suggest, however, that there might be a smaller79,80,81,82 or larger83,84 lag between the time when CO2 emissions have ceased and the time of maximum warming caused by those emissions. Instead of being accounted for as a separate term, the TZEC could also be integrated within the assessment of TCRE, although a dedicated methodological framework to do so is currently lacking.

Unrepresented sources of Earth system feedback

Finally, reductions in emissions due to unrepresented Earth system feedback mechanisms (EEsfb, in units of Gt CO2), are the last term in the proposed remaining carbon budget framework (equation (1)). Any Earth system feedback that is not yet incorporated in estimates of the TCRE or that would reduce the applicability of TCRE should be assessed, and accounted for and communicated as part of EEsfb. These feedback processes have typically been related to permafrost thawing40,41,42,85 and the associated long-term release of CO2 and CH4. However, other Earth system feedback sources that can affect remaining carbon budgets have been identified42, including changes in vegetation CO2 uptake linked to nitrogen availability86,87,88. If unrepresented feedback results in a direct CO2 emission from an ecosystem, the translation to the EEsfb term is direct. However, because of the diverse nature of Earth system feedback42, accounting for it through an adjustment in CO2 emissions is not always straightforward. For example, if a feedback system results in the release of other greenhouse gases or affects the Earth system through changes in surface albedo, clouds or fire regimes, for example, its contribution needs to be translated into an equivalent CO2 correction term (see refs 89,90 for example). Because most Earth system feedback is either sensitive to rising CO2 or to variations in climate parameters, it is expected that these contributions are scenario-dependent, nonlinear, and in some cases realized over longer timescales only40,41,85,91,92,93,94,95,96,97,98. This adds to the complexity of the translation into a CO2-equivalent correction term, and makes EEsfb an uncertain contribution. EEsfb could be estimated either for the time at which global net CO2 emissions become zero or until the end of the century or beyond, assuming anthropogenic CO2 emissions are kept at net-zero levels but feedback mechanisms continue to change over time41,85,92,93,97. Finally, scenario-independent Earth system feedback that scales linearly with global average temperature increase could also be incorporated by adjusting the TCRE, as long as it is not double-counted in both EEsfb and TCRE.

Tracking and explaining scientific progress

We are of the opinion that through conscientious and rigorous application of the framework we propose in this Perspective, much of the confusion surrounding the size and variation of remaining carbon budget estimates can be avoided. Our proposed framework allows scientists to identify, understand and track how the progression of science on multiple fronts can affect budget estimates. It also allows us to identify and discuss key uncertainties and choices related to each respective term (Table 1). Together, these two improvements can contribute to a more constructive and informed discussion of the topic, and better communication across the various disciplines and communities that research, quantify and apply estimates of the remaining carbon budget.

Table 1 Key choices or uncertainties of terms affecting estimates of the remaining carbon budget

The road from the geosciences to climate policy is long and winding. However, carbon budgets provide one of the simplest and most transparent means of connecting geophysical limits imposed by the Earth system to implications for climate policy. For example, they provide the geophysical foundation for setting global net-zero targets6,99, which have recently been picked up by policy scholars as being potentially more effective in guiding policy towards a more actionable climate change mitigation goal100. When combined with models that simulate possible transformations to a low-carbon society101, they can also help inform other, more specific, climate change mitigation targets.

Nevertheless, adequately characterizing and communicating the uncertainties that surround carbon budget estimates is a challenge that will remain. These uncertainties are not unfathomable, however, and language exists to describe the nature of the various uncertainty contributions102 (Table 1, Fig. 2). In some cases, uncertainties exist because of our imprecise knowledge of certain processes or lack of precise measurements. This uncertainty is applicable to all terms in our framework except for Tlim, and will only gradually be reduced over time. In other cases, terms are not used consistently throughout the literature, resulting in confusion and inconsistency between carbon budget estimates (Table 1, Supplementary Table 1, Fig. 2). This is the case for the choice of global temperature metric or for the time period over which remaining carbon budgets are computed. For increased comparability and flexibility, it would be useful if global surface air temperature values were routinely estimated for observational products and if climate model projections were to report both metrics. Some uncertainties represent policy choices44. An example of such uncertainty is the estimate of the non-CO2 emissions contribution to future warming. Future non-CO2 emissions depend on future socio-economic developments and deployment of mitigation measures, and these are influenced by policy and societal choices today, for example, regarding how much the emission of non-CO2 greenhouse gases is penalized or which sectors are targeted when promoting innovation for climate change mitigation. These policy-driven uncertainties and ambiguities can be understood, quantified and explained using a scenario-based approach. For sources of Earth system feedback that are not fully represented in models, a quantification of their impact remains difficult. Expert judgment can be applied in this case to provide an estimate of its importance.

The overview of assumptions made in carbon budget studies (Fig. 2 and Supplementary Tables 1 and 2) can already provide a first step in understanding the relative differences between estimates. For example, except for the most recent IPCC report48, none of the estimates available in the literature simultaneously apply consistent global warming metrics for historical and projected temperatures together with a non-CO2 warming contribution reflecting a future that is in line with the Paris Agreement (Fig. 2, Supplementary Tables 1 and 2). Several estimates also infer the chance of limiting warming to 1.5 °C from ad hoc frequency distributions of model results, instead of from a formal representation of the uncertainty in TCRE. In addition, studies typically do not include all currently identified Earth system feedback, although the impact of some has been described in dedicated studies40,41,42,85.

Comparing estimates that are the same in all but their inclusion of some of the unrepresented Earth system feedback mechanisms (from refs 41,48) suggests that the inclusion of additional Earth system feedback could consistently reduce estimates of the remaining carbon budget—something to bear in mind when future studies that use the latest generation of Earth system models become available103. A further insight is that estimates that apply temperature metrics other than global surface air temperatures (Fig. 2 and Supplementary Text 2) consistently suggest remaining carbon budgets that are larger than estimates that use surface air temperature only. The reasons underlying this perceived shift are well understood (see Supplementary Text 2) and can be identified as an artefact of a methodological choice. To be sure, although estimates using temperature metrics other than global averaged surface air temperature usually suggest a larger remaining carbon budget, they also come with clear climate change consequences: a relatively hotter Earth, inconsistent with the long-term temperature goal of the Paris Agreement59. A sound rationale therefore needs to accompany the choice of temperature metric. We strongly recommend using global average surface air temperature as the temperature metric because it is computed from invariable fields across models, model runs and over time. More detailed comparisons between published estimates of remaining carbon budgets are complicated or impossible at this stage because the quantifications of the various contributing factors by the original studies are lacking. Hence, we suggest that future studies should provide a quantitative discussion of assumptions and factors contributing to their remaining carbon budget estimates (Supplementary Text 3), without which it is often virtually impossible to determine them later.

In the future, this framework could play a part in contextualizing new estimates, even if such estimates are obtained using alternative methods. In addition, this framework can be used in combination with expert judgment to anticipate potential changes in the remaining carbon budget. Finally, application of the framework presented here also allows us to make a more independent assessment of remaining carbon budgets by drawing on multiple lines of evidence. A simplified version of this framework has also already been applied in ref. 48 (see Box 2).

Towards more robust carbon budget estimates

Decomposing the remaining carbon budget into its contributing factors also allows one to identify a set of promising avenues for future research. An area of research that could advance this field is a closer look at TCRE. Future research is anticipated to narrow the range of best estimates of TCRE as well as to clarify the shape of the uncertainty distribution surrounding this value, the influence of a potential lag of CO2 warming on estimating TCRE, and the validity of the TCRE concept for annual emission rates approaching net zero or during episodes of global net CO2 removal. For example, at present there are no studies dedicated to explicit analysis of the uncertainty distribution surrounding TCRE, resulting in limited evidence to support the choice of a particular formal distribution (be it normal, lognormal, or otherwise10,31,54) when estimating the remaining carbon budget (see Fig. 2 and Supplementary Table 1).

Another promising area of research is the study of the interdependence between factors and their uncertainties, for example, between uncertainties in Thist and \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\). This could be pursued through the development of methods that allow robust estimates of recent levels of human-induced warming and allow us to link them to internally consistent projections of future non-CO2 warming. For example, methodological developments with reduced-complexity climate models could be useful57,75,104, because such models can flexibly and promptly incorporate most up-to-date observations and forcing estimates. This also ties into a larger question of trying to understand the overall, combined uncertainties affecting remaining carbon budgets. At present, each factor of the presented framework comes with its own uncertainties, and a method of formally combining these uncertainties is lacking.

Finally, an important uncertainty in determining the remaining carbon budget continues to be the quantification of uncertain and ill-constrained Earth system feedback processes that feed into the assessment of TCRE or EEsfb. Besides affecting carbon budgets that are consistent with limiting maximum warming to a specific temperature threshold, such feedback could help to inform the risks that would be incurred by exhausting and exceeding a specific carbon budget and temperature limit, and attempting to return warming afterwards to lower levels through global net CO2 removal (see the definition of the threshold return budget in Box 1). Challenges here lie in covering the full range of responses of these highly uncertain components, including high-risk, low-probability outcomes.

Advancements in any of these areas would improve our understanding of carbon budget estimates, and would be invaluable in the on-going assessment of carbon budgets for the forthcoming Sixth Assessment Report of the IPCC. A systematic understanding of remaining carbon budget estimates is possible if studies improve their reporting. We recommend that future studies estimating the remaining carbon budget report the factors considered within this framework (see Supplementary Text 3 for a checklist): the surface temperature measure and historic warming used, what is assumed for TCRE, and how non-CO2 warming and Earth system feedback sources are accounted for. A systematic understanding of remaining carbon budget estimates and how they could evolve as science advances will be essential for effective target setting and for communicating the challenges of climate change mitigation.


  1. 1.

    Intergovernmental Panel on Climate Change (IPCC) Climate Change 2013 : The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge Univ. Press, 2013).

  2. 2.

    Messner, D., Schellnhuber, J., Rahmstorf, S. & Klingenfeld, D. The budget approach: a framework for a global transformation toward a low-carbon economy. J. Renew. Sustain. Energy 2, 031003 (2010).

    Google Scholar 

  3. 3.

    Le Quéré, C. et al. Global carbon budget 2017. Earth Syst. Sci. Data 10, 405–448 (2018).

    Google Scholar 

  4. 4.

    Zickfeld, K., Eby, M., Matthews, H. D. & Weaver, A. J. Setting cumulative emissions targets to reduce the risk of dangerous climate change. Proc. Natl Acad. Sci. USA 106, 16129–16134 (2009).

    ADS  CAS  PubMed  Google Scholar 

  5. 5.

    Matthews, H. D., Gillett, N. P., Stott, P. A. & Zickfeld, K. The proportionality of global warming to cumulative carbon emissions. Nature 459, 829–832 (2009).

    ADS  CAS  PubMed  Google Scholar 

  6. 6.

    Matthews, H. D. & Caldeira, K. Stabilizing climate requires near-zero emissions. Geophys. Res. Lett. 35, (2008). This was the first paper to highlight the importance of global net-zero CO 2 emissions for limiting global warming.

  7. 7.

    Meinshausen, M. et al. Greenhouse-gas emission targets for limiting global warming to 2 °C. Nature 458, 1158–1162 (2009). This seminal study reports carbon budgets up to the recent past and enabled the broad uptake of the carbon budget concept in climate policy discussions by linking it to the amount of carbon available in proven economically recoverable oil, gas and coal reserves.

    ADS  CAS  PubMed  Google Scholar 

  8. 8.

    Allen, M. R. et al. Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature 458, 1163–1166 (2009).

    ADS  CAS  PubMed  Google Scholar 

  9. 9.

    MacDougall, A. H. & Friedlingstein, P. The origin and limits of the near proportionality between climate warming and cumulative CO2 emissions. J. Clim. 28, 4217–4230 (2015). This paper provides a decomposition of the various factors contributing to the near-linear proportionality underlying TCRE.

    ADS  Google Scholar 

  10. 10.

    Gillett, N. P., Arora, V. K., Matthews, D. & Allen, M. R. Constraining the ratio of global warming to cumulative CO2 emissions using CMIP5 simulations. J. Clim. 26, 6844–6858 (2013). This study discusses the shape and observational constraints of the TCRE.

    ADS  Google Scholar 

  11. 11.

    Zickfeld, K. et al. Long-term climate change commitment and reversibility: an EMIC intercomparison. J. Clim. 26, 5782–5809 (2013). This multi-model study quantifies the warming commitment after a cessation of CO 2 emissions.

    ADS  Google Scholar 

  12. 12.

    Matthews, H. D. et al. Estimating carbon budgets for ambitious climate targets. Curr. Clim. Change Rep. 3, 69–77 (2017).

    Google Scholar 

  13. 13.

    Williams, R. G., Goodwin, P., Roussenov, V. M. & Bopp, L. A framework to understand the transient climate response to emissions. Environ. Res. Lett. 11, 015003 (2016).

    ADS  Google Scholar 

  14. 14.

    The United Nations Framework Convention on Climate Change (UNFCCC) Paris Agreement (UNFCCC, 2015).

  15. 15.

    Rogelj, J., Schleussner, C.-F., & Hare, W. Getting it right matters: temperature goal interpretations in geoscience research. Geophys. Res. Lett. 44, 10662–610665 (2017).

    ADS  Google Scholar 

  16. 16.

    Schleussner, C.-F. et al. Science and policy characteristics of the Paris Agreement temperature goal. Nat. Clim. Chang. 6, 827–835 (2016).

    ADS  Google Scholar 

  17. 17.

    Knutti, R. & Rogelj, J. The legacy of our CO2 emissions: a clash of scientific facts, politics and ethics. Clim. Change 133, 361–373 (2015).

    ADS  CAS  Google Scholar 

  18. 18.

    Matthews, H. D., Solomon, S. & Pierrehumbert, R. Cumulative carbon as a policy framework for achieving climate stabilization. Phil. Trans. R. Soc. Lond. A 2012, 4365–4379 (1974).

  19. 19.

    Matthews, H. D. & Solomon, S. Atmosphere. Irreversible does not mean unavoidable. Science 340, 438–439 (2013).

    ADS  CAS  PubMed  Google Scholar 

  20. 20.

    Solomon, S., Pierrehumbert, R., Matthews, D. & Daniel, J. in Climate Science for Serving Society—Research, Modeling and Prediction Priorities (eds Hurrell, J. & Asrar, G.) 506 (Springer, 2013).

  21. 21.

    Solomon, S. et al. Persistence of climate changes due to a range of greenhouse gases. Proc. Natl Acad. Sci. USA 107, 18354–18359 (2010).

    ADS  CAS  PubMed  Google Scholar 

  22. 22.

    Minx, J. C. et al. Negative emissions—Part 1: research landscape and synthesis. Environ. Res. Lett. 13, 063001 (2018).

    ADS  Google Scholar 

  23. 23.

    Fuss, S. et al. Negative emissions—Part 2: costs, potentials and side effects. Environ. Res. Lett. 13, 063002 (2018).

    ADS  Google Scholar 

  24. 24.

    Nemet, G. F. et al. Negative emissions—Part 3: innovation and upscaling. Environ. Res. Lett. 13, 063003 (2018).

    ADS  Google Scholar 

  25. 25.

    Williamson, P. Emissions reduction: scrutinize CO2 removal methods. Nature 530, 153–155 (2016).

    ADS  CAS  PubMed  Google Scholar 

  26. 26.

    Bellamy, R. Incentivize negative emissions responsibly. Nat. Energy 3, 532–534 (2018).

    ADS  Google Scholar 

  27. 27.

    The Royal Society Greenhouse Gas Removal (The Royal Society, 2018).

  28. 28.

    Intergovernmental Panel on Climate Change (IPCC) Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC, 2014).

  29. 29.

    Hallegatte, S. et al. Mapping the climate change challenge. Nat. Clim. Chang. 6, 663–668 (2016).

    ADS  Google Scholar 

  30. 30.

    Millar, R. J. et al. Emission budgets and pathways consistent with limiting warming to 1.5 °C. Nat. Geosci. 10, 741–747 (2017).

    ADS  CAS  Google Scholar 

  31. 31.

    Goodwin, P. et al. Pathways to 1.5 °C and 2 °C warming based on observational and geological constraints. Nat. Geosci. 11, 102–107 (2018).

    ADS  CAS  Google Scholar 

  32. 32.

    Tokarska, K. B. & Gillett, N. P. Cumulative carbon emissions budgets consistent with 1.5 °C global warming. Nat. Clim. Chang. 8, 296–299 (2018).

    ADS  CAS  Google Scholar 

  33. 33.

    Tokarska, K. B., Gillett, N. P., Arora, V. K., Lee, W. G. & Zickfeld, K. The influence of non-CO2 forcings on cumulative carbon emissions budgets. Environ. Res. Lett. 13, 034039 (2018).

    ADS  Google Scholar 

  34. 34.

    Richardson, M., Cowtan, K. & Millar, R. J. Global temperature definition affects achievement of long-term climate goals. Environ. Res. Lett. 13, 054004 (2018).

    ADS  Google Scholar 

  35. 35.

    Schurer, A. P. et al. Interpretations of the Paris climate target. Nat. Geosci. 11, 220–221 (2018).

    ADS  CAS  Google Scholar 

  36. 36.

    Rogelj, J. et al. Scenarios towards limiting global mean temperature increase below 1.5 °C. Nat. Clim. Chang. 8, 325–332 (2018).

    ADS  CAS  Google Scholar 

  37. 37.

    Rogelj, J. et al. Differences between carbon budget estimates unravelled. Nat. Clim. Chang. 6, 245–252 (2016).

    ADS  Google Scholar 

  38. 38.

    Rogelj, J., Meinshausen, M., Schaeffer, M., Knutti, R. & Riahi, K. Impact of short-lived non-CO2 mitigation on carbon budgets for stabilizing global warming. Environ. Res. Lett. 10, 075001 (2015).

    ADS  Google Scholar 

  39. 39.

    Friedlingstein, P. et al. Persistent growth of CO2 emissions and implications for reaching climate targets. Nat. Geosci. 7, 709–715 (2014).

    ADS  CAS  Google Scholar 

  40. 40.

    Comyn-Platt, E. et al. Carbon budgets for 1.5 and 2 °C targets lowered by natural wetland and permafrost feedbacks. Nat. Geosci. 11, 568–573 (2018).

    ADS  CAS  Google Scholar 

  41. 41.

    Gasser, T. et al. Path-dependent reductions in CO2 emission budgets caused by permafrost carbon release. Nat. Geosci. 11, 830–835 (2018). This paper provides an overview of recent estimates of the impact of permafrost thawing on remaining carbon budgets.

    ADS  CAS  Google Scholar 

  42. 42.

    Lowe, J. A. & Bernie, D. The impact of Earth system feedbacks on carbon budgets and climate response. Phil. Trans. R. Soc. A 376, (2018).

  43. 43.

    Mengis, N., Partanen, A.-I., Jalbert, J. & Matthews, H. D. 1.5 °C carbon budget dependent on carbon cycle uncertainty and future non-CO2 forcing. Sci. Rep. 8, 5831 (2018).

    ADS  PubMed  PubMed Central  Google Scholar 

  44. 44.

    Rogelj, J. et al. Mitigation choices impact carbon budget size compatible with low temperature goals. Environ. Res. Lett. 10, 075003 (2015).

    ADS  Google Scholar 

  45. 45.

    Geden, O. Politically informed advice for climate action. Nat. Geosci. 11, 380–383 (2018).

    ADS  CAS  Google Scholar 

  46. 46.

    Peters, G. P. Beyond carbon budgets. Nat. Geosci. 11, 378–380 (2018).

    ADS  CAS  Google Scholar 

  47. 47.

    Kriegler, E. et al. Pathways limiting warming to 1.5 °C: a tale of turning around in no time? Phil. Trans. R. Soc. A 376, (2018).

  48. 48.

    Rogelj, J. et al. in Global Warming of 1.5 °C: An IPCC Special Report on the Impacts of Global Warming of 1.5 °C Above Pre-Industrial Levels and Related Global Greenhouse Gas Emission Pathways, in the Context of Strengthening the Global Response to the Threat of Climate Change, Sustainable Development, and Efforts to Eradicate Poverty (eds Flato, G., Fuglestvedt, J., Mrabet, R. & Schaeffer, R.) 93–174 (IPCC/WMO, 2018). This special report by the IPCC applied a forerunner of the framework described in this Perspective.

  49. 49.

    Millar, R. J. & Friedlingstein, P. The utility of the historical record for assessing the transient climate response to cumulative emissions. Phil. Trans. R. Soc. A 376, (2018).

  50. 50.

    Tachiiri, K., Hajima, T. & Kawamiya, M. Increase of uncertainty in transient climate response to cumulative carbon emissions after stabilization of atmospheric CO2 concentration. Environ. Res. Lett. 10, 125018 (2015).

    ADS  Google Scholar 

  51. 51.

    Steinacher, M. & Joos, F. Transient Earth system responses to cumulative carbon dioxide emissions: linearities, uncertainties, and probabilities in an observation-constrained model ensemble. Biogeosciences 13, 1071–1103 (2016).

    ADS  CAS  Google Scholar 

  52. 52.

    Ehlert, D., Zickfeld, K., Eby, M. & Gillett, N. The sensitivity of the proportionality between temperature change and cumulative CO2 emissions to ocean mixing. J. Clim. 30, 2921–2935 (2017).

    ADS  Google Scholar 

  53. 53.

    MacDougall, A. H., Swart, N. C. & Knutti, R. The uncertainty in the transient climate response to cumulative CO2 emissions arising from the uncertainty in physical climate parameters. J. Clim. 30, 813–827 (2017).

    ADS  Google Scholar 

  54. 54.

    Collins, M. et al. in Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds Stocker, T. F. et al.) 1029–1136 (Cambridge Univ. Press, 2013). This report by the IPCC provided the first assessment of TCRE.

  55. 55.

    Leduc, M., Matthews, H. D. & de Elia, R. Quantifying the limits of a linear temperature response to cumulative CO2 emissions. J. Clim. 28, 9955–9968 (2015).

    ADS  Google Scholar 

  56. 56.

    Tokarska, K. B., Gillett, N. P., Weaver, A. J., Arora, V. K. & Eby, M. The climate response to five trillion tonnes of carbon. Nat. Clim. Chang. 6, 851 (2016).

    ADS  CAS  Google Scholar 

  57. 57.

    Haustein, K. et al. A real-time global warming index. Sci. Rep. 7, 15417 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  58. 58.

    Huber, M. & Knutti, R. Natural variability, radiative forcing and climate response in the recent hiatus reconciled. Nat. Geosci. 7, 651–656 (2014).

    ADS  CAS  Google Scholar 

  59. 59.

    Pfleiderer, P., Schleussner, C. F., Mengel, M. & Rogelj, J. Global mean temperature indicators linked to warming levels avoiding climate risks. Environ. Res. Lett. 13, 064015 (2018). This paper quantified the impact on remaining carbon budgets of switching between global warming definitions.

    ADS  Google Scholar 

  60. 60.

    Morice, C. P., Kennedy, J. J., Rayner, N. A. & Jones, P. D. Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: the HadCRUT4 data set. J. Geophys. Res. Atmospheres 117, (2012).

  61. 61.

    UNFCCC Report on the Structured Expert Dialogue on the 2013–2015 Review. FCCC/SB/2015/INF.1 (UNFCCC, 2015).

  62. 62.

    The United Nations Environment Programme (UNEP) The Emissions Gap Report 2014. (UNEP, 2014).

  63. 63.

    Schurer, A. P., Mann, M. E., Hawkins, E., Tett, S. F. B. & Hegerl, G. C. Importance of the pre-industrial baseline for likelihood of exceeding Paris goals. Nat. Clim. Chang. 7, 563–567 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  64. 64.

    Hawkins, E. et al. Estimating changes in global temperature since the preindustrial period. Bull. Am. Meteorol. Soc. 98, 1841–1856 (2017).

    ADS  Google Scholar 

  65. 65.

    Meinshausen, M. et al. The RCP greenhouse gas concentrations and their extensions from 1765 to 2300. Clim. Change 109, 213–241 (2011).

    ADS  CAS  Google Scholar 

  66. 66.

    Stocker, T. F. et al. in Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds Stocker, T. F. et al.) 33–115 (Cambridge Univ. Press, 2013).

  67. 67.

    Samset, B. H. et al. Climate impacts from a removal of anthropogenic aerosol emissions. Geophys. Res. Lett. 45, 1020–1029 (2018).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  68. 68.

    Smith, P. et al. in Climate Change 2014: Mitigation of Climate Change. Contribution of Working Group III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds Edenhofer, O. et al.) 811–922 (Cambridge Univ. Press, 2014).

  69. 69.

    Gernaat, D. E. H. J. et al. Understanding the contribution of non-carbon dioxide gases in deep mitigation scenarios. Glob. Environ. Change 33, 142–153 (2015).

    Google Scholar 

  70. 70.

    Meinshausen, M. et al. Multi-gas emission pathways to meet climate targets. Clim. Change 75, 151–194 (2006).

    ADS  CAS  Google Scholar 

  71. 71.

    Clarke, L. et al. in Climate Change 2014: Mitigation of Climate Change. Contribution of Working Group III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds Edenhofer, O. et al.) 413–510 (Cambridge Univ. Press, 2014).

  72. 72.

    Riahi, K. et al. The shared socioeconomic pathways and their energy, land use, and greenhouse gas emissions implications: an overview. Glob. Environ. Change 42, 153–168 (2017).

    Google Scholar 

  73. 73.

    Huppmann, D., Rogelj, J., Kriegler, E., Krey, V. & Riahi, K. A new scenario resource for integrated 1.5 °C research. Nat. Clim. Chang. 8, 1027–1030 (2018).

    ADS  Google Scholar 

  74. 74.

    Huppmann, D. et al. IAMC 1.5 °C Scenario Explorer and Data hosted by IIASA (Integrated Assessment Modeling Consortium and International Institute for Applied Systems Analysis, 2018).

  75. 75.

    Smith, C. J. et al. FAIR v1.3: a simple emissions-based impulse response and carbon cycle model. Geosci. Model Dev. 11, 2273–2297 (2018).

    ADS  CAS  Google Scholar 

  76. 76.

    Meinshausen, M., Raper, S. C. B. & Wigley, T. M. L. Emulating coupled atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6—Part 1: model description and calibration. Atmos. Chem. Phys. 11, 1417–1456 (2011).

    ADS  CAS  Google Scholar 

  77. 77.

    Myhre, G. et al. in Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (eds Stocker, T. F. et al.) 659–740 (Cambridge Univ. Press, 2013).

  78. 78.

    Kriegler, E. et al. Fossil-fueled development (SSP5): an energy and resource intensive scenario for the 21st century. Glob. Environ. Change 42, 297–315 (2017).

    Google Scholar 

  79. 79.

    Ehlert, D. & Zickfeld, K. What determines the warming commitment after cessation of CO2 emissions? Environ. Res. Lett. 12, 015002 (2017).

    ADS  Google Scholar 

  80. 80.

    Gillett, N. P., Arora, V. K., Zickfeld, K., Marshall, S. J. & Merryfield, W. J. Ongoing climate change following a complete cessation of carbon dioxide emissions. Nat. Geosci. 4, 83–87 (2011).

    ADS  CAS  Google Scholar 

  81. 81.

    Ricke, K. L. & Caldeira, K. Maximum warming occurs about one decade after a carbon dioxide emission. Environ. Res. Lett. 9, 124002 (2014).

    ADS  Google Scholar 

  82. 82.

    Zickfeld, K. & Herrington, T. The time lag between a carbon dioxide emission and maximum warming increases with the size of the emission. Environ. Res. Lett. 10, 031001 (2015).

    ADS  Google Scholar 

  83. 83.

    Frölicher, T. L. & Paynter, D. J. Extending the relationship between global warming and cumulative carbon emissions to multi-millennial timescales. Environ. Res. Lett. 10, 075002 (2015).

    ADS  Google Scholar 

  84. 84.

    Frölicher, T. L., Winton, M. & Sarmiento, J. L. Continued global warming after CO2 emissions stoppage. Nat. Clim. Chang. 4, 40–44 (2014).

    ADS  Google Scholar 

  85. 85.

    MacDougall, A. H., Zickfeld, K., Knutti, R. & Matthews, H. D. Sensitivity of carbon budgets to permafrost carbon feedbacks and non-CO2 forcings. Environ. Res. Lett. 10, 125003 (2015).

    ADS  Google Scholar 

  86. 86.

    Zaehle, S. et al. Evaluation of 11 terrestrial carbon–nitrogen cycle models against observations from two temperate free-air CO2 enrichment studies. New Phytol. 202, 803–822 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  87. 87.

    Wenzel, S., Cox, P. M., Eyring, V. & Friedlingstein, P. Projected land photosynthesis constrained by changes in the seasonal cycle of atmospheric CO2. Nature 538, 499–501 (2016).

    ADS  PubMed  Google Scholar 

  88. 88.

    Arneth, A. et al. Terrestrial biogeochemical feedbacks in the climate system. Nat. Geosci. 3, 525–532 (2010). This review presents an overview of terrestrial Earth system feedback mechanisms that could further affect TCRE and estimates of remaining carbon budgets.

    ADS  CAS  Google Scholar 

  89. 89.

    Carrer, D., Pique, G., Ferlicoq, M., Ceamanos, X. & Ceschia, E. What is the potential of cropland albedo management in the fight against global warming? A case study based on the use of cover crops. Environ. Res. Lett. 13, 044030 (2018).

    ADS  Google Scholar 

  90. 90.

    Allen, M. R. et al. A solution to the misrepresentations of CO2-equivalent emissions of short-lived climate pollutants under ambitious mitigation. npj Clim. Atmos. Sci. 1, 16 (2018).

    Google Scholar 

  91. 91.

    Burke, E. J. et al. Quantifying uncertainties of permafrost carbon–climate feedbacks. Biogeosciences 14, 3051–3066 (2017).

    ADS  CAS  Google Scholar 

  92. 92.

    Schneider von Deimling, T. et al. Observation-based modelling of permafrost carbon fluxes with accounting for deep carbon deposits and thermokarst activity. Biogeosciences 12, 3469–3488 (2015).

    ADS  Google Scholar 

  93. 93.

    Schneider von Deimling, T. et al. Estimating the near-surface permafrost-carbon feedback on global warming. Biogeosciences 9, 649–665 (2012).

    ADS  Google Scholar 

  94. 94.

    Schuur, E. A. G. et al. Climate change and the permafrost carbon feedback. Nature 520, 171–179 (2015).

    ADS  CAS  PubMed  Google Scholar 

  95. 95.

    Schaefer, K., Lantuit, H., Romanovsky, V. E., Schuur, E. A. G. & Ronald Witt, R. The impact of the permafrost carbon feedback on global climate. Environ. Res. Lett. 9, 085003 (2014).

    ADS  Google Scholar 

  96. 96.

    Koven, C. D. et al. A simplified, data-constrained approach to estimate the permafrost carbon–climate feedback. Phil. Trans. R. Soc. A 373, (2015).

  97. 97.

    MacDougall, A. H. & Knutti, R. Projecting the release of carbon from permafrost soils using a perturbed parameter ensemble modelling approach. Biogeosciences 13, 2123–2136 (2016).

    ADS  Google Scholar 

  98. 98.

    Schwinger, J. & Tjiputra, J. Ocean carbon cycle feedbacks under negative emissions. Geophys. Res. Lett. 45, 5062–5070 (2018).

    ADS  CAS  Google Scholar 

  99. 99.

    Rogelj, J. et al. Zero emission targets as long-term global goals for climate protection. Environ. Res. Lett. 10, 105007 (2015).

    ADS  Google Scholar 

  100. 100.

    Geden, O. An actionable climate target. Nat. Geosci. 9, 340 (2016).

    ADS  CAS  Google Scholar 

  101. 101.

    Weyant, J. Some contributions of integrated assessment models of global climate change. Rev. Environ. Econ. Policy 11, 115–137 (2017).

    Google Scholar 

  102. 102.

    Smith, L. A. & Stern, N. Uncertainty in science and its role in climate policy. Phil. Trans. R. Soc. A 369, 4818–4841 (2011).

    ADS  MATH  Google Scholar 

  103. 103.

    Eyring, V. et al. Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev. 9, 1937–1958 (2016).

    ADS  Google Scholar 

  104. 104.

    Meinshausen, M., Wigley, T. M. L. & Raper, S. C. B. Emulating atmosphere–ocean and carbon cycle models with a simpler model, MAGICC6—Part 2: Applications. Atmos. Chem. Phys. 11, 1457–1471 (2011).

    ADS  CAS  Google Scholar 

  105. 105.

    Zickfeld, K., MacDougall, A. H. & Matthews, H. D. On the proportionality between global temperature change and cumulative CO2 emissions during periods of net negative CO2 emissions. Environ. Res. Lett. 11, 055006 (2016).

    ADS  Google Scholar 

  106. 106.

    Allen, M. R. et al. Framing and context. In Global Warming of 1.5 °C. An IPCC Special Report on the Impacts of Global Warming of 1.5 °C Above Pre-Industrial Levels and Related Global Greenhouse Gas Emission Pathways, in the Context of Strengthening the Global Response to the Threat of Climate Change (eds Masson-Delmotte, V. et al.) 47–92 (IPCC/WMO, 2018).

Download references


We acknowledge support from the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement number 641816 (CRESCENDO) and grant agreement number 820829 (CONSTRAIN), and from the UK Natural Environment Research Council (NERC) under project NE/N006038/1 (SMURPHS). We thank J. Cook and colleagues contributing to the IPCC Special Report on Global Warming of 1.5 °C (ref. 48) for comments.

Reviewer information

Nature thanks Edward Parson, Nathan Gillett and Pierre Friedlingstein for their contribution to the peer review of this work.

Author information




J.R. coordinated the paper. All authors contributed substantially to the development of the framework, its description and presentation, and the writing of the paper. C.J.S. produced Supplementary Fig. 1. J.R. carried out the comparison of remaining carbon budgets, produced Figs. 1 and 2, and led the writing of the paper.

Corresponding author

Correspondence to Joeri Rogelj.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains Supplementary Texts 1-3, Supplementary Figure 1, Supplementary Tables 1 and 2 and Supplementary References.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rogelj, J., Forster, P.M., Kriegler, E. et al. Estimating and tracking the remaining carbon budget for stringent climate targets. Nature 571, 335–342 (2019).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing