Introduction

An important recent development in climate science is the finding that warming responds approximately linearly to cumulative CO2 emissions over time [1–3, 9, 26]. This proportionality between cumulative emissions and global temperature change opens new avenues for how we approach climate mitigation [27, 43], as well as our ability to predict the regional climate impacts associated with a given emission pathway [17]. Importantly, this allows us to estimate a global carbon budget, which represents the total quantity of CO2 that can be emitted if we want to avoid exceeding a desired level of global temperature increase [2, 3].

Setting a finite budget of allowable CO2 emissions is a simple and easily understood way of framing the global climate challenge and the national emissions pathways that would be consistent with international climate targets [7, 36]. However, there is a high level of confusion surrounding the use and estimates of carbon budgets in the scientific literature, which hampers their utility for climate policy development. The confusion stems from inconsistent methodologies and definitions among published carbon budget estimates, as well as from fundamental scientific uncertainties associated with estimating the climate response to a given quantity of emissions [38]. Furthermore, there has been virtually no research focussed on estimating carbon budgets for less than 2 °C of global warming; this is an urgent research gap that needs to be filled to support the Paris climate agreement’s goal of “holding the increase in the global average temperature to well below 2 °C above pre-industrial levels and to pursue efforts to limit the temperature increase to 1.5 °C” (Article 2 of the Paris Climate Agreement, available at: https://unfccc.int/resource/docs/2015/cop21/eng/l09r01.pdf).

In this paper, we review the scientific basis of carbon budget estimates, focusing on how the concept of allowable emissions can be inferred from known (though uncertain) geophysical constraints emerging from the climate response to cumulative CO2 emissions. We begin by discussing the climate response to CO2 emissions alone and the resulting carbon budget estimates associated with a given amount of CO2-induced warming. We then show how this CO2-only budget can be adjusted to account for the effect of non-CO2 greenhouse gas and aerosol emissions, which results in an “effective” estimate of the total CO2 emissions associated with a given climate target. Finally, we discuss the important contributors to uncertainty in carbon budget estimates, and the implications of this uncertainty for emissions targets. Throughout, we focus on the climate targets of 1.5–2 °C above pre-industrial, as stipulated in the Paris Climate Agreement.

Geophysical Basis for a Carbon Budget

The climate response to CO2 emissions is well characterized by a linear temperature response to cumulative emissions of CO2 over time [1–3, 9, 19, 20, 26]. The slope of this relationship—the temperature change per unit emission of CO2—has now been defined as the “Transient Climate Response to cumulative CO2 Emissions,” or TCRE [2, 9, 10]. Analyses of the climate response to cumulative emissions have shown that the TCRE remains approximately constant for total emissions up to several thousand giga-tonnes of carbon (GtC), and is highly path-independent in that the value of the TCRE shows only a small variation across a wide range of CO2 emission scenarios [16, 25, 41, 44].

Another important feature of the climate and carbon cycle system is the fast climate response to CO2 emissions [23, 37, 42]. This response time was recently quantified by Ricke and Caldeira [37] who showed that the peak warming occurs 10 years after a 100 GtC pulse emission of CO2. Zickfeld and Herrington [42] further showed that the climate response time varies as a function of the size of the emission pulse, such that larger pulse sizes as associated with a longer response time. By extension, the climate response to small changes in CO2 emissions should be effectively instantaneous [23].

This fast climate response time to small changes in CO2 emissions supports a third important feature of the climate response to CO2 emissions: that the unrealized warming associated with past CO2 emissions is small [22]. The future warming associated with past emissions is defined as the “Zero-Emissions Commitment” (ZEC), which represents the amount of additional warming that occurs after CO2 emissions have been set to zero. Analyses of the ZEC across a range of different climate models suggest that there is little (if any) unrealized warming associated with past CO2 emissions, but rather that global temperature remains approximately constant for several centuries after CO2 emissions reach zero [8, 18, 22, 24, 25, 33, 40, 45]. This arises as a result of the near-cancellation of opposing inertial effects associated with ocean heat and carbon uptake. In the case of constant atmospheric CO2, ocean thermal inertia would lead to continued warming for decades to centuries; however, in the context of zero CO2 emissions, the continued uptake of CO2 by the ocean leads to declining atmospheric CO2 concentrations which largely cancels the effect of ocean thermal inertia and results in near-constant global temperature over time [23, 24]. This relative balance of ocean thermal and carbon cycle inertia does vary among models, though while some models show larger amounts of unrealized warming [4], the occurrence of substantial continued warming after zero emissions is generally restricted to simulations driven by very high (>2000 GtC) levels of cumulative emissions [5, 16, 32, 42]. This body of literature therefore suggests that the quantity of emissions produced to date is consistent with the CO2-induced warming that has already occurred, with little additional expected future warming commitment, and also little recovery from current levels of warming on centennial timescales.

The concept of a carbon budget—the total allowable CO2 emissions consistent with a given amount of global temperature increase—is therefore a robust measure of human-climate influence that emerges from these three properties of the climate-carbon cycle system: (1) that global temperature responds linearly to cumulative CO2 emissions, as defined by the TCRE; (2) that the climate response time to CO2 emissions is fast and (3) that the realized warming associated with total CO2 emissions to date is approximately the same as the centennial-scale legacy of these same emissions. As a consequence, the total amount of CO2 emissions as inferred from the TCRE is uniquely associated with remaining below a given level of CO2-induced warming on timescales of 10 to several hundred years. This quantity has been defined as the “CO2-only carbon budget” to represent the total allowable CO2 emissions associated with a given amount of CO2-only warming [38]. In the case of low temperature targets, the CO2-only budget is consistent with both meeting and also not exceeding the targeted amount of CO2-induced temperature change. That is, there is little difference here between the budgets associated with exceeding or avoiding 1.5–2 °C (i.e. the threshold exceedance or threshold avoidance budgets, as defined by [38]).

Estimates of CO2-Only Carbon Budgets

The CO2-only carbon budget can be understood simply as the inverse of the TCRE. While the TCRE equals ∆T/E T (where ∆T = global temperature change and E T  = cumulative emissions over time), the carbon budget per degree of warming = E T /∆T. The CO2-only carbon budget for a given climate target (T*) is therefore T*/TCRE. This simple relationship between the TCRE and the CO2-only carbon budget is shown in Fig. 1.

Fig. 1
figure 1

Relationship between the cumulative CO2 emissions and CO2-induced temperature change for two different estimates of the TCRE. CO2-only carbon budget ranges for 1.5–2 °C associated with this range of TCRE values are marked on the horizontal axis. The two values of the TCRE illustrated here are the median of the ensemble of CMIP5 Earth system models (1.6 °C/1000 GtC; blue line) and the observationally constrained best estimate (1.35 °C/1000 GtC; red line) [9]

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The TCRE can be estimated from either Earth system models (ESMs) that include a dynamic representation of the global carbon cycle, or from the observational record. Across the current generation of climate models, as represented by the ESMs included in the CMIP5 model ensemble, the TCRE varies from 0.8–2.4 °C/1000 GtC [9], with an median value of 1.6 °C/1000 GtC (calculated from CO2-only simulations with CO2 concentrations increasing by 1% per year).

Estimating the TCRE from the observational record requires first identifying the proportion of observed warming attributable to CO2 alone, and then calculating the TCRE as a function of observed CO2-induced warming and historical cumulative CO2 emissions from fossil fuels and land-use change. Applying this approach, Gillett et al. [9] estimated an observationally constrained (5–95%) TCRE range of 0.7–2.0 °C/1000 GtC, with a best estimate of 1.35 °C/1000 GtC.

The CO2-only carbon budget estimates associated with these TCRE values are summarized in Table 1. The model-average TCRE of 1.6 °C/1000 GtC suggests a global carbon budget of 625 GtC per degree, or 940 GtC and 1250 GtC for 1.5 and 2 °C of CO2-induced warming, respectively. [Note: all carbon budget values are rounded to the nearest 5 GtC]. By contrast, the observationally based TCRE of 1.35 °C/1000 GtC suggests a larger carbon budget of 740 GtC per degree, or 1110 GtC and 1480 GtC for 1.5 and 2 °C of CO2-induced warming. It is clear that differences in the sensitivity of the climate system to CO2 emission, as illustrated here by the difference between model- and observationally-based TCRE estimates, can have a large effect on the size of the CO2-only carbon budgets for 1.5–2 °C.

Table 1 Best estimates of the Transient Climate Response to cumulative CO2 Emissions (TCRE) from climate models and observational data, with corresponding estimates of the CO2-only carbon budgets associated with a given amount of CO2-induced global temperature increase. Italicized values in parentheses are in units of CO2 rather than C, where 1 tonne of C = 3.67 tonnes of CO2, and all carbon budget values are rounded to the nearest 5 Gt
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Influence of Non-CO2 Greenhouse Gases and Aerosols

The CO2-only carbon budget is well grounded in the science of the climate system response to cumulative CO2 emissions, and can be easily estimated from the TCRE. However, the real climate system is also influenced by non-CO2 greenhouse gas and aerosol emissions, as well as changes in surface albedo due to land-use. The effect of non-CO2 emissions is complicated by the large number of individual forcing agents, which have widely varying atmospheric lifetimes that are in general considerably shorter than that of CO2. While the climate response to CO2 is well characterized by the TCRE, and similar relationships have been proposed for other long-lived greenhouse gases [39], there is no simple linear scaling factor that can be applied to all non-CO2 emissions. Although scientifically robust, the CO2-only carbon budget is not by itself enough to inform efforts to meet climate targets, as it does not account for the additional net warming expected from these other emissions. It is important therefore to adjust the CO2-only carbon budget to account for non-CO2 emissions and related warming.

According to the IPCC forcing estimates, non-CO2 forcing—including the combined effect of all non-CO2 greenhouse gases and aerosols—currently accounts for 23% of the total anthropogenic forcing [31]Footnote 1 Using the simplifying assumption that this ratio of forcings approximately represents the ratio of contributions to historical warming, we infer that about 77% of the observed warming up to the year 2015 can be attributed CO2 forcing, with the remaining observed warming attributable to non-CO2 emissions. We can then define an “effective TCRE” which represents the global temperature response to cumulative CO2 emissions, adjusted to implicitly include the effect of non-CO2 forcing.

The effective TCRE can be estimated from observations as: TCREeff = ∆T obs / E T , where ∆T obs is the observed human-induced global temperature change and E T represents the cumulative historical CO2 emissions from fossil fuels and land-use change. To represent the human contribution to observed warming, we use the “Global Warming Index” (GWI) [11, 34], which allows us to remove the effect of particularly warm or cold individual years on the estimate of human-induced climate change. When updated to the end of 2015, the GWI gives an observed human-induced temperature increase of 0.99 °C, relative to the 1861–1880 average [11]. Total historical CO2 emissions between 1870 and 2015 are 555 GtC [15], which gives a TCREeff of 1.78 °C/1000 GtC.

The effective TCRE is therefore an estimate of the warming caused by a given quantity of CO2 emissions, scaled upwards to account for the additional warming from non-CO2 emissions. The ratio of TCRE to TCREeff should therefore be equal to the ratio of CO2 to total anthropogenic forcing. Using the observationally-based best estimate for the TCRE of 1.35 °C/1000 GtC, we can see that the ratio of TCRE to TCREeff is 1.35/1.78 = 0.76, which is consistent with the current ratio of CO2 to total anthropogenic forcing taken from the IPCC forcing estimates (see Fig. 2). Updated estimates of the year 2015 anthropogenic warming, CO2 emissions and anthropogenic forcing therefore support Gillett et al.’s [9] observationally constrained TCRE of 1.35 °C/1000 GtC, and a corresponding TCREeff of 1.78 °C/1000 GtC.

Fig. 2
figure 2

Ratio of CO2 to total anthropogenic forcing from the IPCC forcing estimates (dotted line) and the CMIP5 model ensemble (solid lines). IPCC forcing data is calculated according to Myhre et al. [31], updated to the year 2015. CMIP5 forcing data is approximated here using forcing data from Meinshausen et al. [28], which gives forcing estimates using the MAGICC model, scaled to match the mean response of the CMIP5 model ensemble

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An alternate method to estimate the TCREeff would be to scale the CMIP5 model-based TCRE according to the ratio of CO2 to total forcing as simulated by this model ensemble, again assuming that temperature response is approximately proportional to forcing. As plotted in Fig. 2, CO2 makes up about 86% of total anthropogenic forcing at the year 2015 in the CMIP5 models; this value is consistent with the ensemble average for RCP scenarios 8.5, 4.5 and 2.6, noting that there is some variation in the ratio of CO2 to total forcing among scenarios, and also among individual CMIP5 models for a particular RCP scenario [28]. Using the CMIP5 TCRE of 1.6 °C/1000 GtC, this results in a TCREeff of 1.6/0.86 = 1.86 °C/1000 GtC. This model-based TCREeff suggests an observed warming of 1.03 °C at the end of 2015 (1.86 °C/1000 GtC * 555 GtC) which, while slightly higher than the GWI best estimate of 0.99 °C for this date, is well within the 5–95% uncertainty range of the GWI (0.85 to +1.21 °C) [11]. It is worth noting that the difference between the model-based and observationally-based estimate of the TCREeff (1.86 vs. 1.78 °C/1000 GtC) is smaller than the difference for the CO2-only TCRE (1.6 vs. 1.35 °C/1000 GtC). This smaller TCREeff difference is explained by a smaller total anthropogenic forcing (about 0.3 W/m2) in the CMIP5 ensemble compared to the IPCC forcing estimate, which in turn reflects an overall larger negative aerosol forcing in the CMIP5 models compared to the IPCC forcing data. As a result, the ratio of CO2 to total forcing is larger in the CMIP5 models than the IPCC forcing data, as can be seen in Fig. 2. This highlights the important role of aerosol forcing uncertainty in particular as a constraint on our ability to validate TCREeff estimates against the observational record.

These estimates of the TCREeff can be used to estimate an effective carbon budget, which represents the total quantity of CO2 emissions that is consistent with a given climate target, while allowing for additional non-CO2 warming. Using the observationally-based TCREeff of 1.78 °C/1000 GtC suggests an effective carbon budget of 560 GtC per degree, or 845 GtC for 1.5 °C and 1125 GtC for 2 °C. Using the model-based TCREeff of 1.86 °C/1000 GtC results in an effective carbon budget of 540 GtC per degree, or 805 GtC for 1.5 °C and 1075 GtC for 2 °C (see Table 2).

Table 2 Best estimates of the TCREeff (“effective TCRE,” representing the climate response to cumulative CO2 emissions, scaled upwards to account for additional non-CO2 warming) from climate models and observational data, with corresponding estimates of the effective carbon budgets associated with a given amount of global temperature increase resulting from all human emissions. Italicized values in parentheses are in units of CO2 rather than C, where 1 tonne of C = 3.67 tonnes of CO2, and all carbon budget values are rounded to the nearest 5 Gt
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These effective carbon budgets, as derived either from models or from historical data, are therefore a first-order estimate of the quantity of CO2 that would be consistent with 1.5 or 2 °C of global warming, allowing for a portion of this warming to come from additional non-CO2 emissions. This calculation implicitly assumes that the ratio of CO2 to total anthropogenic forcing will remain approximately constant as we approach these targets. There are important caveats to this assumption, however, that limit the utility of this simple TCRE-based derivation of effective carbon budgets.

In general, CO2 forcing will continue to increase until the point that global CO2 emissions drop below the level of natural sinks; at the point that we reach 1.5 or 2 °C of global warming, the level of CO2 in the atmosphere will therefore necessarily be higher than today. The assumption of a constant ratio of CO2 to total forcing would only be consistent with a scenario of a net increase in non-CO2 forcing, at a rate comparable to the rate of increase in CO2 forcing. This is a plausible assumption for the next decade or two, as expected decreases in global aerosol emissions (and associated negative forcing) are likely to result in a near-term increase in net non-CO2 forcing. However, it is unlikely that non-CO2 forcing will continue to increase, given that efforts to curb greenhouse gas emissions are unlikely to be applied only to CO2 and not also to other non-CO2 greenhouse gases. We therefore argue that in the context of ambitious mitigation scenarios that are consistent with 1.5–2 °C climate targets, it is very likely that by the time we reach 1.5 or 2 °C of climate warming, net non-CO2 forcing will be smaller than today, and consequently that the ratio of CO2 to total anthropogenic forcing will increase over time (as is the case for the RCP2.6 scenario, as shown in Fig. 2).

This in turn means that the effective carbon budget for 1.5–2 °C will likely increase over time, becoming larger than the values given in Table 2; for example, if we were successful in mitigating non-CO2 emissions rapidly enough such the ratio of CO2 to total forcing were to increase to 0.93 (the maximum value in RCP2.6), this would imply an effective carbon budget of 580 GtC per degree (870 GtC for 1.5 °C; 1165 GtC for 2 °C) based on the model-based TCRE of 1.6 °C/1000 GtC and the resulting TCREeff of 1.72 °C/1000 GtC at the time that we reach 1.5 or 2 °C. We suggest therefore that the TCREeff, and associated effective carbon budget, be treated as quantities that will change over time in response to our own climate policy decisions regarding non-CO2 mitigation. This time and scenario dependence of the effective carbon budget is plotted in Fig. 3, which shows that the range of non-CO2 mitigation across the RCP scenarios results in an effective carbon budget range of 90 GtC per degree, or about 17% of the estimate based on the year 2015 forcing ratios.

Fig. 3
figure 3

Effective carbon budget estimates (per 1 °C), based on a constant CO2-only budget scaled using the ratios of CO2 to total anthropogenic forcing shown in Figure 2. Both model-based (solid lines) and observationally-based (dashed line) estimates of the effective carbon budgets are shown, calculated using their respective CO2-only budget estimates from Table 1 (horizontal lines). Values in Table 2 correspond to the year-2015 values taken from these time-series (where the model-based estimate for 2015 is consistent with the RCP2.6, RCP4.5 and RCP8.5 scenarios, rather than with RCP6 which shows a slightly higher year 2015 effective carbon budget)

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Key Contributions to Carbon Budget Uncertainty

The values given above represent best estimates of the TCRE and associated TCREeff based on currently available model output and observational data. While the observationally - constrained estimates are arguably the more reliable of the two [9], the model-based estimates are also consistent with the range of uncertainty associated with observed temperature changes and should therefore be considered to be a similarly plausible representation of the climate response to cumulative human CO2 emissions. We therefore suggest here that the range of values between the observationally and model-based estimates shown in Table 2 should be taken as a range of best estimates of the effective carbon budgets for 1.5–2 °C. These values are considerably larger than most previous carbon budget estimates [3, 13, 38], though are consistent with a recent reassessment of CMIP5 model results in light of observed temperature changes [30]. We also note that the effective carbon budgets reported in the IPCC Fifth Assessment Report [13] were estimated using RCP8.5 simulations only, which include larger non-CO2 warming compared to the other scenarios; as shown in Fig. 3, our estimate of the mean effective carbon budget based on RCP8.5 would be smaller over the entire twenty-first century than the budgets provided in Table 2 that are derived from the year 2015 forcing estimates.

However, in the context of setting emissions targets for a given level of global temperature increase, these best estimates are only consistent with a 50% chance of remaining below the desired level of global warming. Given the large uncertainty in the climate response to emissions, increasing the confidence level associated with meeting a climate target (e.g. to a 67% chance) can result in a substantial decrease in allowable emissions. For example, if the model-based range of TCRE is assumed to represent a Gaussian distribution with 5th and 95th percentiles of 0.8 and 2.4 °C/1000 GtC, this would mean that the TCRE has a 67% chance of being less than 1.8 °C/1000 GtC and a 90% chance of being less than 2.2 °C/1000 GtC. The increase in confidence from a 50 to 67% chance in remaining below the desired climate target requires decreasing the carbon budget for a given climate target by about 11% (i.e. by 70 GtC per °C of target). Similarly, increasing the confidence from 50 to 90% decreases the carbon budget by about 27% (170 GtC per degree). For comparison, the difference between the model-based CO2-only and effective carbon budgets (reflecting the effect of accounting for non-CO2 warming) is 85 GtC per degree of warming (Table 1 vs. Table 2).

This idea of assigning a likelihood of meeting a climate target given some carbon budget has been used in most previous assessments of carbon budgets associated with different levels of climate change [3, 38]. However, the method accounts for only one source of quantified uncertainty: the uncertainty associated with the climate response to CO2 emissions. This implicitly includes the contribution of climate sensitivity (or more precisely, transient climate response) uncertainty, as well as the uncertainty associated with the uptake of anthropogenic CO2 by land and ocean carbon sinks (which further includes the uncertainty associated with climate-carbon feedbacks that govern how carbon sinks are affected by CO2 (or non-CO2)-induced warming). It also indirectly accounts for uncertainty associated with observed temperature change and the present-day strength of non-CO2 forcing, in that a higher TCRE would have to be associated with smaller net non-CO2 forcing (e.g. due to stronger negative aerosol forcing) in order to remain consistent with the observational record.

These above likelihood values do not, however, account for the uncertainty associated with future non-CO2 emission pathways, and therefore do not account for the critical question of how strong non-CO2 forcing will be at the time that we are approaching 1.5–2 °C of climate warming. Given that the majority of the non-CO2 forcing is the result of gases and aerosols with short atmospheric lifetimes—so-called short-lived climate forcers or SLCFs—the strength of non-CO2 forcing is primarily determined by the annual rate of emissions, rather than (as is the case for CO2) the total accumulated emissions over time [39]. Consequently, the level of non-CO2 emissions several decades from now will have a very large influence on the effective carbon budget associated with 1.5–2 °C of climate warming. And unlike the likelihood values associated with the climate response uncertainty above, there are no equivalent likelihood values that have been estimated for future non-CO2 emissions pathways. Previous analyses have therefore considered the range of non-CO2 forcing strengths across the RCP scenarios as a plausible range, and have used these values to estimate a range of effective carbon budgets, without assigning any additional likelihood values to this range [3, 38]. This has resulted in a very large range of “likely” (i.e. 67% chance of remaining below the target) carbon budgets, which limits their usefulness to climate policy.

While there is no immediate solution to the problem of how to apply likelihood values to the mitigation decisions that will determine future non-CO2 forcing, we here attempt to clarify what these human decisions mean for carbon budget estimates. First, for any climate target in the range of 1.5–2 °C it seems highly unlikely that non-CO2 emissions will follow a business-as-usual trajectory, with human mitigation effort concentrated solely on decreasing CO2 emissions. This then suggests that the lower end of the RCP non-CO2 forcing range (which makes up between 7 and 15% of total forcing during the second half of this century as shown in Fig. 2) is much more likely than the higher non-CO2 forcing in RCP8.5. This in turn implies that effective carbon budgets based on the current strength of non-CO2 forcing (as in Table 2) should be taken as conservative estimates with a high likelihood that the eventual effective carbon budget will be closer to (but lower than) the CO2-only carbon budgets listed in Table 1. Second, the implication that emerges here for climate mitigation decision-making is that while the size of CO2-only carbon budget is governed entirely by geophysical constraints, the difference between CO2-only and effective carbon budgets depends primarily on human decisions. If we decide to aggressively mitigate non-CO2 emission such that non-CO2 forcing at the time we reach 1.5–2 °C is small, then this will enlarge the effective carbon budget, thereby increasing the amount of cumulative CO2 emissions that would be consistent with the desired target.

It is worth commenting briefly on a third source of uncertainty, which is associated with the climate response time to emissions. As argued above, there is evidence to suggest that the climate response time to CO2 emissions is small [37], implying that CO2-induced temperature change remains relatively stable once emissions are stopped [24]. For non-CO2 agents, however, global temperature does change after the elimination of emissions, leading to non-negligible positive or negative ZECs associated with current emissions of different short-lived species. This is well illustrated by the case of aerosols emissions, which include a range of individual aerosol types that both warm and cool the climate. On balance, aerosols currently produce a net negative forcing, and decreased emissions would therefore warm the climate, though this effect would of course vary depending on the relative effectiveness of mitigating different aerosol types. In the case of short-lived greenhouse gases (such as methane or tropospheric ozone), decreased emissions would result in cooling in response to declining forcing. Matthews and Zickfeld [25] estimated the ZEC associated with both CO2 and non-CO2 emissions, showing that an abrupt elimination of all emissions would lead to a warming of a few tenths of a degree over about a decade, followed by a gradual cooling that returned global temperatures to close to present-day levels over the course of about two centuries. This result implies that complete elimination of current non-CO2 emissions would likely cause a small initial warming as aerosol forcing abruptly dissipates, and would then gradually reverse in line with eventually declining non-CO2 greenhouse gas forcing. Again, however, this potential warming response depends primarily on human mitigation decisions, and not on any inherent geophysical constraints.

A final source of uncertainty relates to the potential effect of important processes that are still missing from, or poorly represented in, the current generation of Earth system models. For example, accounting for CO2 release from thawing permafrost would decrease the size of the CO2-only carbon budget, though like other carbon cycle feedbacks, the effect of permafrost melt does not invalidate the concept of a carbon budget and the associated linear relationship between warming and cumulative CO2 emissions [21]. Changing fire dynamics could also have important consequences for the carbon cycle [14] and therefore for carbon budget estimates. In general however, the uncertainty surrounding human decisions has much greater bearing on future warming estimates than do these geophysical uncertainties [6, 12]. And as outlined above, human decision uncertainty is also an important direct contributor to the differences in effective carbon budget estimates, which emphasizes the critical importance of effective climate mitigation decision-making that reflects and accommodates for fundamental geophysical uncertainty.

Conclusions

Despite the large uncertainty range on any estimate of a carbon budget for a given climate target, the idea that there is a finite amount of CO2 that is allowed to be emitted remains an appealing way of framing the climate mitigation challenge. CO2-only carbon budgets represent a simple and robust quantity that emerges from a set of increasingly well-understood processes that govern the climate response to cumulative CO2 emissions. Effective carbon budgets, which define the allowable CO2 emissions for a given climate target while allowing for additional warming from non-CO2 emissions, are less robust because they are less governed by geophysical constraints. This means that the eventual size of the effective carbon budget will be highly influenced by human decisions and in particular by our ability to mitigate emissions of short-lived greenhouse gases and aerosols.

This responsiveness of the size of effective carbon budgets to human decisions implies the need for climate mitigation strategies that are able to adapt to new information about the climate response to emissions [29], as well as to our success or failure at aggressively mitigating emissions of short-lived species. It may therefore be less important to precisely estimate the size of the effective carbon budget now, as it is to implement strong non-CO2 emission mitigation policies that would enlarge the carbon budget, in parallel with efforts to mitigate emissions of CO2 themselves. However, it is also crucial that efforts to curb non-CO2 emissions do not replace mitigation of CO2, as this would increase both peak and long-term warming [35]. While the CO2-only budget represents a firm (if uncertain) upper limit on total allowable emissions, the smaller effective carbon budget is a quantity that will become more clear only as we move forward with ambitious climate mitigation efforts aimed at limiting climate warming to the 1.5–2 °C range committed to in the Paris Climate Agreement.