As discussed, the remaining carbon budget can be defined as the remaining amount of CO 2 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 (B lim ) for a specific temperature change limit (T lim ) 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 (T hist ), the non-CO 2 contribution to future temperature rise \(\left({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\right)\), the zero-emissions commitment (T ZEC ), the TCRE, and an adjustment term for sources of unrepresented Earth system feedback (E Esfb ). These terms are visualized in Fig. 1 and are described and discussed in turn below.

$${B}_{{\rm{lim}}}=({T}_{{\rm{lim}}}-{T}_{{\rm{hist}}}-{T}_{{{\rm{nonCO}}}_{{\rm{2}}}}-{T}_{{\rm{ZEC}}})/{\rm{TCRE}}-{E}_{{\rm{Esfb}}}$$ (1)

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 T hist , the zero-emissions commitment T ZEC , the contribution of future non-CO 2 warming (consistent with global net-zero CO 2 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 E Esfb . 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 B lim , 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. Full size image

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 CO 2 ); 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, CO 2 -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 CO 2 with a probability of at least 66%. TCRE, and hence the linear proportionality of warming to cumulative emissions of CO 2 , has also been found to be robust up to about 7,300 Gt CO 2 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 T lim − T hist − \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\) − T ZEC ) 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 (T lim , in units of °C), and its second term represents the historical human-induced warming (T hist , in units of °C); see equation (1). T hist 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 T hist 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 T hist should adequately isolate the human-induced warming signal from the effects of natural forcing and variability57,58. The same is true for T lim , and if T lim 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 T hist and T lim : 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 T hist and T lim 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 CO 2 (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. Full size image

Non-CO 2 contribution to future warming

Another term affecting the remaining allowable warming is the non-CO 2 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 CO 2 -induced warming and warming due to non-CO 2 forcing. Future non-CO 2 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-CO 2 greenhouse gases68,69. To include \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\) in the remaining carbon budget framework, the non-CO 2 warming contribution between a recent reference period (for example, the same period as T hist ) and a specific time in the future has to be estimated. We suggest that this non-CO 2 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 CO 2 emissions reach net zero48. Estimating the non-CO 2 warming contribution at that moment in time reflects a situation in which global cumulative emissions of CO 2 are effectively capped and hence allows us to directly inform the question of how much CO 2 can be emitted while keeping warming to a given temperature level. If non-CO 2 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-CO 2 emissions, the non-CO 2 warming contribution also depends on estimates of the corresponding radiative forcing, including potential changes in surface albedo43. Non-CO 2 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-CO 2 emissions would continue to affect warming levels after the time when net CO 2 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 CO 2 emissions and by considering internally consistent non-CO 2 emissions. Under these assumptions, non-CO 2 emissions are projected to result in a constant or declining forcing and warming after the time of net-zero CO 2 (refs 48,73). However, if under alternative assumptions one would project non-CO 2 warming to continue to increase irrespective of the level of CO 2 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, T ZEC (in units of °C) is the next term in the remaining carbon budget framework represented by equation (1). T ZEC is defined as the additional contribution to peak warming that is still to be expected after a complete cessation of CO 2 emissions79,80, and hence provides a correction term for the instantaneous linearity postulated by the concept of the TCRE. T ZEC can be positive, negative or zero. For estimates of the remaining carbon budget, the T ZEC when CO 2 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 CO 2 -induced warming at current and declining emissions rates50,79. When T ZEC is positive, not all warming will have been experienced by the time global CO 2 emissions reach net zero. The estimated additional warming would hence also have to be reduced from the allowable remaining temperature increase. At present, T ZEC 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 CO 2 emissions have ceased and the time of maximum warming caused by those emissions. Instead of being accounted for as a separate term, the T ZEC 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