Focus on Cumulative Emissions, Global Carbon Budgets and the Implications for Climate Mitigation Targets

The Environmental Research Letters focus issue on 'Cumulative Emissions, Global Carbon Budgets and the Implications for Climate Mitigation Targets' was launched in 2015 to highlight the emerging science of the climate response to cumulative emissions, and how this can inform efforts to decrease emissions fast enough to avoid dangerous climate impacts. The 22 research articles published represent a fantastic snapshot of the state-or-the-art in this field, covering both the science and policy aspects of cumulative emissions and carbon budget research. In this Review and Synthesis, we summarize the findings published in this focus issue, outline some suggestions for ongoing research needs, and present our assessment of the implications of this research for ongoing efforts to meet the goals of the Paris climate agreement.

Recent years have witnessed unprecedented interest in how the burning of fossil fuels may impact on the global climate system. Such visibility of this issue is in part due to the increasing frequency of key international summits to debate emissions levels, including the 2015 21st Conference of Parties meeting in Paris. In this perspective we plot a timeline of significant climate meetings and reports, and against metrics of atmospheric greenhouse gas changes and global temperature. One powerful metric is cumulative CO₂ emissions that can be related to past and future warming levels. That quantity is analysed in detail through a set of papers in this ERL focus issue. We suggest it is an open question as to whether our timeline implies a lack of progress in constraining climate change despite multiple recent keynote meetings—or alternatively—that the increasing level of debate is encouragement that solutions will be found to prevent any dangerous warming levels?

Does the climate change signal emerge equally from internal climate variability across the globe? If not, are there particular locations where temperature extremes might disproportionately affect specific populations? The letter by Harrington et al (2016 Environ. Res. Lett. 11 055007) argues that people living in low latitude countries, which contain the majority of the world's poorest people, are—and will continue to be—disproportionately affected by increases in temperature extremes. Due to differences in expertise of climate scientists, and climate impact and adaptation scientists, few climate extreme event analyses are spatially disaggregated and linked to local populations' socio-economic characteristics. The research presented in this letter begins to bridge this gap by providing evidence of inequitable spatial impacts from climate extremes on the world's poorest people.

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

The transient climate response to cumulative carbon emissions (TCRE) is a highly policy-relevant quantity in climate science. The TCRE suggests that peak warming is linearly proportional to cumulative carbon emissions and nearly independent of the emissions scenario. Here, we use simulations of the Earth System Model (ESM) from the Geophysical Fluid Dynamics Laboratory (GFDL) to show that global mean surface temperature may increase by 0.5 °C after carbon emissions are stopped at 2 °C global warming, implying an increase in the coefficient relating global warming to cumulative carbon emissions on multi-centennial timescales. The simulations also suggest a 20% lower quota on cumulative carbon emissions allowed to achieve a policy-driven limit on global warming. ESM estimates from the Coupled Model Intercomparison Project Phase 5 (CMIP5–ESMs) qualitatively agree on this result, whereas Earth System Models of Intermediate Complexity (EMICs) simulations, used in the IPCC 5th assessment report to assess the robustness of TCRE on multi-centennial timescales, suggest a post-emissions decrease in temperature. The reason for this discrepancy lies in the smaller simulated realized warming fraction in CMIP5–ESMs, including GFDL ESM2M, than in EMICs when carbon emissions increase. The temperature response to cumulative carbon emissions can be characterized by three different phases and the linear TCRE framework is only valid during the first phase when carbon emissions increase. For longer timescales, when emissions tape off, two new metrics are introduced that better characterize the time-dependent temperature response to cumulative carbon emissions: the equilibrium climate response to cumulative carbon emissions and the multi-millennial climate response to cumulative carbon emissions.

Global-mean temperature increase is roughly proportional to cumulative emissions of carbon-dioxide (CO₂). Limiting global warming to any level thus implies a finite CO₂ budget. Due to geophysical uncertainties, the size of such budgets can only be expressed in probabilistic terms and is further influenced by non-CO₂ emissions. We here explore how societal choices related to energy demand and specific mitigation options influence the size of carbon budgets for meeting a given temperature objective. We find that choices that exclude specific CO₂ mitigation technologies (like Carbon Capture and Storage) result in greater costs, smaller compatible CO₂ budgets until 2050, but larger CO₂ budgets until 2100. Vice versa, choices that lead to a larger CO₂ mitigation potential result in CO₂ budgets until 2100 that are smaller but can be met at lower costs. In most cases, these budget variations can be explained by the amount of non-CO₂ mitigation that is carried out in conjunction with CO_2, and associated global carbon prices that also drive mitigation of non-CO₂ gases. Budget variations are of the order of 10% around their central value. In all cases, limiting warming to below 2 °C thus still implies that CO₂ emissions need to be reduced rapidly in the coming decades.

Recent estimates of the global carbon budget, or allowable cumulative CO₂ emissions consistent with a given level of climate warming, have the potential to inform climate mitigation policy discussions aimed at maintaining global temperatures below 2 °C. This raises difficult questions, however, about how best to share this carbon budget amongst nations in a way that both respects the need for a finite cap on total allowable emissions, and also addresses the fundamental disparities amongst nations with respect to their historical and potential future emissions. Here we show how the contraction and convergence (C&C) framework can be applied to the division of a global carbon budget among nations, in a manner that both maintains total emissions below a level consistent with 2 °C, and also adheres to the principle of attaining equal per capita CO₂ emissions within the coming decades. We show further that historical differences in responsibility for climate warming can be quantified via a cumulative carbon debt (or credit), which represents the amount by which a given country's historical emissions have exceeded (or fallen short of) the emissions that would have been consistent with their share of world population over time. This carbon debt/credit calculation enhances the potential utility of C&C, therefore providing a simple method to frame national climate mitigation targets in a way that both accounts for historical responsibility, and also respects the principle of international equity in determining future emissions allowances.

An analysis of the climate impact of various forms of beef production is carried out, with a particular eye to the comparison between systems relying primarily on grasses grown in pasture ('grass-fed' or 'pastured' beef) and systems involving substantial use of manufactured feed requiring significant external inputs in the form of synthetic fertilizer and mechanized agriculture ('feedlot' beef). The climate impact is evaluated without employing metrics such as ${\mathrm{CO}}_{2}{\rm{e}}$ or global warming potentials. The analysis evaluates the impact at all time scales out to 1000 years. It is concluded that certain forms of pastured beef production have substantially lower climate impact than feedlot systems. However, pastured systems that require significant synthetic fertilization, inputs from supplemental feed, or deforestation to create pasture, have substantially greater climate impact at all time scales than the feedlot and dairy-associated systems analyzed. Even the best pastured system analyzed has enough climate impact to justify efforts to limit future growth of beef production, which in any event would be necessary if climate and other ecological concerns were met by a transition to primarily pasture-based systems. Alternate mitigation options are discussed, but barring unforseen technological breakthroughs worldwide consumption at current North American per capita rates appears incompatible with a 2 °C warming target.

International climate mitigation efforts are focused on limiting increase in global mean temperature, which has been shown to be proportional to cumulative CO₂ emissions. However, the ability of natural and human systems to successfully adapt to climatic changes depends on both the magnitude and rate of change, the latter of which will depend on how quickly a given level of cumulative emissions occurs. We show that cumulative CO₂ emissions of 4620 Gt CO₂ (reached in 2100 in RCP4.5 and 2057 in RCP8.5) produce globally averaged warming rates that are nearly twice as fast in RCP8.5 than RCP4.5 (0.34 ± 0.08 °C per decade versus 0.19 ± 0.05 °C per decade, respectively). Similarly, the globally averaged velocity of climate change calculated according to the 'nearest equivalent climate' is greater by a factor of ∼2 in RCP8.5 than in RCP4.5 (2.51 ± 0.67 km yr⁻¹ versus 1.32 ± 0.39 km yr⁻¹, respectively), despite equivalent cumulative emissions. These differences in the projected velocity of climate change represent uncertainty for ecosystems that may be unable to adapt to the faster changes. Particularly at risk are boreal forests, of which 48% are projected to experience rates of change beyond their expected adaptive capacity (i.e. >0.3 °C per decade) in RCP4.5, compared with 95% in RCP8.5. Thus, the same budget of cumulative carbon emissions may result in critically different impacts on natural and human systems, depending on the amount of time over which that budget is expended.

Long-term climate experiments up to the year 2300 have been conducted using two full-scale complex Earth system models (ESMs), CESM1(BGC) and MIROC-ESM, for a CO₂ emissions reduction pathway, termed Z650, where annual CO₂ emissions peak at 11 PgC in 2020, decline by 50% every 30 years, and reach zero in 2160. The results have been examined by focusing on the approximate linear relationship between the temperature increase and cumulative CO₂ emissions. Although the temperature increase is nearly proportional to the cumulative CO₂ emissions in both models, this relationship does not necessarily provide a robust basis for the restriction of CO₂ emissions because it is substantially modulated by non-CO₂ forcing. CO₂-induced warming, estimated from the atmospheric CO₂ concentrations in the models, indicates an approximate compensation of nonlinear changes between fast-mode responses to concentration changes at less than 10 years and slow-mode response at more than 100 years due to the thermal inertia of the ocean. In this estimate, CESM1(BGC) closely approximates a linear trend of 1.7 °C per 1000 PgC, whereas MIROC-ESM shows a deviation toward higher temperatures after the emissions peak, from 1.8 °C to 2.4 °C per 1000 PgC over the range of 400–850 PgC cumulative emissions corresponding to years 2000–2050. The evolution of temperature under zero emissions, 2160–2300, shows a slight decrease of about 0.1 °C per century in CESM1(BGC), but remains almost constant in MIROC-ESM. The fast-mode response toward the equilibrium state decreases with a decrease in the airborne fraction owing to continued CO₂ uptake (carbon cycle inertia), whereas the slow-mode response results in more warming owing to continued heat uptake (thermal inertia). Several specific differences are noted between the two models regarding the degree of this compensation and in some key regional aspects associated with sustained warming and long-term climate risks. Overall, elevated temperatures continue for at least a few hundred years under zero emissions.

Development and climate goals together constrain the carbon intensity of production. Using a simple and transparent model that represents committed CO₂ emissions (future emissions expected to come from existing capital), we explore the carbon intensity of production related to new capital required for different temperature targets across several thousand scenarios. Future pathways consistent with the 2 °C target which allow for continued gross domestic product growth require early action to reduce carbon intensity of new production, and either (i) a short lifetime of energy and industry capital (e.g. early retrofit of coal power plants), or (ii) large negative emissions after 2050 (i.e. rapid development and dissemination of carbon capture and sequestration). To achieve the 2 °C target, half of the scenarios indicate a carbon intensity of new production between 33 and 73 g CO₂/$—much lower than the global average today, at 360 g CO₂/$. The average lifespan of energy capital (especially power plants), and industry capital, are critical because they commit emissions far into the future and reduce the budget for new capital emissions. Each year of lifetime added to existing, carbon intensive capital, decreases the carbon intensity of new production required to meet a 2 °C carbon budget by 1.0–1.5 g CO₂/$, and each year of delaying the start of mitigation decreases the required CO₂ intensity of new production by 20–50 g CO₂/$. Constraints on the carbon intensity of new production under a 3 °C target are considerably relaxed relative to the 2 °C target, but remain daunting in comparison to the carbon intensity of the global economy today.

Policy makers have called for a 'fair and ambitious' global climate agreement. Scientific constraints, such as the allowable carbon emissions to avoid exceeding a 2 °C global warming limit with 66% probability, can help define ambitious approaches to climate targets. However, fairly sharing the mitigation challenge to meet a global target involves human values rather than just scientific facts. We develop a framework based on cumulative emissions of carbon dioxide to compare the consistency of countries' current emission pledges to the ambition of keeping global temperatures below 2 °C, and, further, compare two alternative methods of sharing the remaining emission allowance. We focus on the recent pledges and other official statements of the EU, USA, and China. The EU and US pledges are close to a 2 °C level of ambition only if the remaining emission allowance is distributed based on current emission shares, which is unlikely to be viewed as 'fair and ambitious' by others who presently emit less. China's stated emissions target also differs from measures of global fairness, owing to emissions that continue to grow into the 2020s. We find that, combined, the EU, US, and Chinese pledges leave little room for other countries to emit CO₂ if a 2 °C limit is the objective, essentially requiring all other countries to move towards per capita emissions 7 to 14 times lower than the EU, USA, or China by 2030. We argue that a fair and ambitious agreement for a 2 °C limit that would be globally inclusive and effective in the long term will require stronger mitigation than the goals currently proposed. Given such necessary and unprecedented mitigation and the current lack of availability of some key technologies, we suggest a new diplomatic effort directed at ensuring that the necessary technologies become available in the near future.

Recently, assessments have robustly linked stabilization of global-mean temperature rise to the necessity of limiting the total amount of emitted carbon-dioxide (CO₂). Halting global warming thus requires virtually zero annual CO₂ emissions at some point. Policymakers have now incorporated this concept in the negotiating text for a new global climate agreement, but confusion remains about concepts like carbon neutrality, climate neutrality, full decarbonization, and net zero carbon or net zero greenhouse gas (GHG) emissions. Here we clarify these concepts, discuss their appropriateness to serve as a long-term global benchmark for achieving temperature targets, and provide a detailed quantification. We find that with current pledges and for a likely (>66%) chance of staying below 2 °C, the scenario literature suggests net zero CO₂ emissions between 2060 and 2070, with net negative CO₂ emissions thereafter. Because of residual non-CO₂ emissions, net zero is always reached later for total GHG emissions than for CO₂. Net zero emissions targets are a useful focal point for policy, linking a global temperature target and socio-economic pathways to a necessary long-term limit on cumulative CO₂ emissions.

Efforts to mitigate and adapt to long-term climate change could benefit greatly from probabilistic estimates of cumulative carbon emissions due to fossil fuel burning and resulting CO₂-induced planetary warming. Here we demonstrate the use of a reduced-form model to project these variables. We performed simulations using a large-ensemble framework with parametric uncertainty sampled to produce distributions of future cumulative emissions and consequent planetary warming. A hind-cast ensemble of simulations captured 1980–2012 historical CO₂ emissions trends and an ensemble of future projection simulations generated a distribution of emission scenarios that qualitatively resembled the suite of Representative and Extended Concentration Pathways. The resulting cumulative carbon emission and temperature change distributions are characterized by 5–95th percentile ranges of 0.96–4.9 teratonnes C (Tt C) and 1.4 °C–8.5 °C, respectively, with 50th percentiles at 3.1 Tt C and 4.7 °C. Within the wide range of policy-related parameter combinations that produced these distributions, we found that low-emission simulations were characterized by both high carbon prices and low costs of non-fossil fuel energy sources, suggesting the importance of these two policy levers in particular for avoiding dangerous levels of climate warming. With this analysis we demonstrate a probabilistic approach to the challenge of identifying strategies for limiting cumulative carbon emissions and assessing likelihoods of surpassing dangerous temperature thresholds.

The international community has set a goal to limit global warming to 2 °C. Limiting global warming to 2 °C is a challenging goal and will entail a dramatic transformation of the global energy system, largely complete by 2040. As part of the work toward this goal, countries have been submitting their Intended Nationally Determined Contributions (INDCs) to the United Nations Framework Convention on Climate Change, indicating their emissions reduction commitments through 2025 or 2030, in advance of the 21st Conference of the Parties (COP21) in Paris in December 2015. In this paper, we use the Global Change Assessment Model (GCAM) to analyze the near versus long-term energy and economic-cost implications of these INDCs. The INDCs imply near-term actions that reduce the level of mitigation needed in the post-2030 period, particularly when compared with an alternative path in which nations are unable to undertake emissions mitigation until after 2030. We find that the latter case could require up to 2300 GW of premature retirements of fossil fuel power plants and up to 2900 GW of additional low-carbon power capacity installations within a five-year period of 2031–2035. INDCs have the effect of reducing premature retirements and new-capacity installations after 2030 by 50% and 34%, respectively. However, if presently announced INDCs were strengthened to achieve greater near-term emissions mitigation, the 2031–2035 transformation could be tempered to require 84% fewer premature retirements of power generation capacity and 56% fewer new-capacity additions. Our results suggest that the INDCs delivered for COP21 in Paris will have important contributions in reducing the challenges of achieving the goal of limiting global warming to 2 °C.

The near proportionality between cumulative CO₂ emissions and change in near surface temperature can be used to define a carbon budget: a finite quantity of carbon that can be burned associated with a chosen 'safe' temperature change threshold. Here we evaluate the sensitivity of this carbon budget to permafrost carbon dynamics and changes in non-CO₂ forcings. The carbon budget for 2.0 ${}^{\circ }{\rm{C}}$ of warming is reduced from 1320 Pg C when considering only forcing from CO₂ to 810 Pg C when considering permafrost carbon feedbacks as well as other anthropogenic contributions to climate change. We also examined net carbon budgets following an overshoot of and return to a warming target. That is, the net cumulative CO₂ emissions at the point in time a warming target is restored following artificial removal of CO₂ from the atmosphere to cool the climate back to a chosen temperature target. These overshoot net carbon budgets are consistently smaller than the conventional carbon budgets. Overall carbon budgets persist as a robust and simple conceptual framework to relate the principle cause of climate change to the impacts of climate change.

We analyzed a dataset from an experiment of an earth system model of intermediate complexity, focusing on the change in transient climate response to cumulative carbon emissions (TCRE) after atmospheric CO₂ concentration was stabilized in the Representative Concentration Pathway (RCP) 4.5. We estimated the TCRE in 2005 at 0.3–2.4 K/TtC for an unconstrained case and 1.1–1.7 K/TtC when constrained with historical and present-day observational data, the latter result being consistent with other studies. The range of TCRE increased when the increase of CO₂ concentration was moderated and then stabilized. This is because the larger (smaller) TCRE members yield even greater (less) TCRE. An additional experiment to assess the equilibrium state revealed significant changes in temperature and cumulative carbon emissions after 2300. We also found that variation of land carbon uptake is significant to the total allowable carbon emissions and subsequent change of the TCRE. Additionally, in our experiment, we revealed that equilibrium climate sensitivity (ECS), one of the 12 parameters perturbed in the ensemble experiment, has a strong positive relationship with the TCRE at the beginning of the stabilization and its subsequent change. We confirmed that for participant models in the Coupled Model Intercomparison Project Phase 5, ECS has a strong positive relationship with TCRE. For models using similar experimental settings, there is a positive relationship with TCRE for the start of the period of stabilization in CO₂ concentration, and rate of change after stabilization. The results of this study are influential regarding the total allowable carbon emissions calculated from the TCRE and the temperature increase set as the mitigation target.

Global surface warming projections have been empirically connected to carbon emissions via a climate index defined as the transient climate response to emissions (TCRE), revealing that surface warming is nearly proportional to carbon emissions. Here, we provide a theoretical framework to understand the TCRE including the effects of all radiative forcing in terms of the product of three terms: the dependence of surface warming on radiative forcing, the fractional radiative forcing contribution from atmospheric CO₂ and the dependence of radiative forcing from atmospheric CO₂ on cumulative carbon emissions. This framework is used to interpret the climate response over the next century for two Earth System Models of differing complexity, both containing a representation of the carbon cycle: an Earth System Model of Intermediate Complexity, configured as an idealised coupled atmosphere and ocean, and an Earth System Model, based on an atmosphere–ocean general circulation model and including non-CO₂ radiative forcing and a land carbon cycle. Both Earth System Models simulate only a slight decrease in the TCRE over 2005–2100. This limited change in the TCRE is due to the ocean and terrestrial system acting to sequester both heat and carbon: carbon uptake acts to decrease the dependence of radiative forcing from CO₂ on carbon emissions, which is partly compensated by changes in ocean heat uptake acting to increase the dependence of surface warming on radiative forcing. On decadal timescales, there are larger changes in the TCRE due to changes in ocean heat uptake and changes in non-CO₂ radiative forcing, as represented by decadal changes in the dependences of surface warming on radiative forcing and the fractional radiative forcing contribution from atmospheric CO₂. Our framework may be used to interpret the response of different climate models and used to provide traceability between climate models of differing complexity.

Recent research has shown evidence of a linear climate response to cumulative CO₂ emissions, which implies that the source, timing, and amount of emissions does not significantly influence the climate response per unit emission. Furthermore, these analyses have generally assumed that the climate response to land-use CO₂ emissions is equivalent to that of fossil fuels under the assumption that, once in the atmosphere, the radiative forcing induced by CO₂ is not sensitive to the emissions source. However, land-cover change also affects surface albedo and the strength of terrestrial carbon sinks, both of which have an additional climate effect. In this study, we use a coupled climate-carbon cycle model to assess the climate response to historical and future cumulative land-use CO₂ emissions, in order to compare it to the response to fossil fuel CO₂. We find that when we isolate the CO₂-induced (biogeochemical) temperature changes associated with land-use change, then the climate response to cumulative land-use emissions is equivalent to that of fossil fuel CO₂. We show further that the globally-averaged albedo-induced biophysical cooling from land-use change is non-negligible and may be of comparable magnitude to the biogeochemical warming, with the result that the net climate response to land-use change is substantially different from a linear response to cumulative emissions. However, our new simulations suggest that the biophysical cooling from land-use change follows its own independent (negative) linear response to cumulative net land-use CO₂ emissions, which may provide a useful scaling factor for certain applications when evaluating the full transient climate response to emissions.

Recent research has demonstrated that global mean surface air warming is approximately proportional to cumulative CO₂ emissions. This proportional relationship has received considerable attention, as it allows one to calculate the cumulative CO₂ emissions ('carbon budget') compatible with temperature targets and is a useful measure for model inter-comparison. Here we use an Earth system model to explore whether this relationship persists during periods of net negative CO₂ emissions. Negative CO₂ emissions are required in the majority of emissions scenarios limiting global warming to 2 °C above pre-industrial, with emissions becoming net negative in the second half of this century in several scenarios. We find that for model simulations with a symmetric 1% per year increase and decrease in atmospheric CO₂, the temperature change (ΔT) versus cumulative CO₂ emissions (CE) relationship is nonlinear during periods of net negative emissions, owing to the lagged response of the deep ocean to previously increasing atmospheric CO₂. When corrected for this lagged response, or if the CO₂ decline is applied after the system has equilibrated with the previous CO₂ increase, the ΔT versus CE relationship is close to linear during periods of net negative CO₂ emissions. A proportionality constant—the transient climate response to cumulative carbon emissions (TCRE)− can therefore be calculated for both positive and net negative CO₂ emission periods. We find that in simulations with a symmetric 1% per year increase and decrease in atmospheric CO₂ the TCRE is larger on the upward than on the downward CO₂ trajectory, suggesting that positive CO₂ emissions are more effective at warming than negative emissions are at subsequently cooling. We also find that the cooling effectiveness of negative CO₂ emissions decreases if applied at higher atmospheric CO₂ concentrations.

Understanding how the emergence of the anthropogenic warming signal from the noise of internal variability translates to changes in extreme event occurrence is of crucial societal importance. By utilising simulations of cumulative carbon dioxide (CO₂) emissions and temperature changes from eleven earth system models, we demonstrate that the inherently lower internal variability found at tropical latitudes results in large increases in the frequency of extreme daily temperatures (exceedances of the 99.9th percentile derived from pre-industrial climate simulations) occurring much earlier than for mid-to-high latitude regions. Most of the world's poorest people live at low latitudes, when considering 2010 GDP-PPP per capita; conversely the wealthiest population quintile disproportionately inhabit more variable mid-latitude climates. Consequently, the fraction of the global population in the lowest socio-economic quintile is exposed to substantially more frequent daily temperature extremes after much lower increases in both mean global warming and cumulative CO₂ emissions.

We investigate the extent to which global mean temperature, precipitation, and the carbon cycle are constrained by cumulative carbon emissions throughout four experiments with a fully coupled climate–carbon cycle model. The paired experiments adopt contrasting, idealised approaches to climate change mitigation at different action points this century, with total emissions rising to more than two trillion tonnes of carbon (TtC). For each pair, the contrasting mitigation approaches—capping emissions early versus reducing them to zero a few decades later—cause their cumulative emissions trajectories to diverge initially, then converge, cross, and diverge again. We find that global mean temperature is linear with cumulative emissions across all experiments, although differences of up to 1.5 K exist regionally when the trajectories of total carbon emitted during the course of the two scenarios coincide, for both pairs of experiments. Interestingly, although the oceanic precipitation response scales with cumulative emissions, the global precipitation response does not, due to a decrease in precipitation over land above emissions of around one TtC. Most carbon fluxes are less well constrained by cumulative emissions as they reach two trillion tonnes. The opposing mitigation approaches have different consequences for the Amazon rainforest, which affects the linearity with which the carbon cycle responds to cumulative emissions. The average Transient Climate Response to cumulative carbon Emissions (TCRE) is 1.95 K TtC⁻¹, at the upper end of the Intergovernmental Panel on Climate Change's range of 0.8–2.5 K TtC⁻¹.

Scenarios from integrated assessment models can provide insights into how carbon budgets relate to other policy-relevant indicators by including information on how fast and by how much emissions can be reduced. Such indicators include the peak year of global emissions, the decarbonisation rate and the deployment of low-carbon technology. Here, we show typical values for these indicators for different carbon budgets, using the recently compiled IPCC scenario database, and discuss how these vary as a function of non-CO₂ forcing, energy use and policy delay. For carbon budgets of 2000 GtCO₂ and less over the 2010–2100 period, supply of low carbon technologies needs to be scaled up massively from today's levels, unless energy use is relatively low. For the subgroup of scenarios with a budget below 1000 GtCO₂ (consistent with >66% chance of limiting global warming to below 2 °C relative to preindustrial levels), the 2050 contribution of low-carbon technologies is generally around 50%–75%, compared to less than 20% today (range refers to the 10–90th interval of available data).

Previous studies have shown that global mean surface air temperature remains elevated after cessation of CO₂ emissions. However, studies differ in whether the temperature continues to increase, slowly decreases, or remains constant after cessation of emissions. An understanding of this committed warming is of importance because it has implication for the estimation of carbon budgets compatible with temperature targets. Here, we investigate the effect of the state of thermal and bio-geochemical equilibration at the time emissions are set to zero on the committed warming as the latter is determined by the balance of these two equilibration processes. We find that the effect of thermal equilibration, expressed as fraction of realized warming, dominates over the bio-geochemical equilibration, expressed as ratio of the airborne fraction to the equilibrium airborne fraction. This leads to a positive warming commitment, and a commitment that declines the later emissions are zeroed along a trajectory of constant atmospheric CO₂ concentration. We furthermore show that the scenario prior to zeroed emissions has the strongest effect on the warming commitment, compared to the time of zeroed emissions and the time horizon over which the commitment is calculated.

Cumulative CO₂ emissions are near linearly related to both global and regional changes in annual-mean surface temperature. These relationships are known as the transient climate response to cumulative CO₂ emissions (TCRE) and the regional TCRE (RTCRE), and have been shown to remain approximately constant over a wide range of cumulative emissions. Here, we assessed how well this relationship holds for seasonal patterns of temperature change, as well as for annual-mean and seasonal precipitation patterns. We analyzed an idealized scenario with CO₂ concentration growing at an annual rate of 1% using data from 12 Earth system models from the Coupled Model Intercomparison Project Phase 5 (CMIP5). Seasonal RTCRE values for temperature varied considerably, with the highest seasonal variation evident in the Arctic, where RTCRE was about 5.5 °C per Tt C for boreal winter and about 2.0 °C per Tt C for boreal summer. Also the precipitation response in the Arctic during boreal winter was stronger than during other seasons. We found that emission-normalized seasonal patterns of temperature change were relatively robust with respect to time, though they were sub-linear with respect to emissions particularly near the Arctic. Moreover, RTCRE patterns for precipitation could not be quantified robustly due to the large internal variability of precipitation. Our results suggest that cumulative CO₂ emissions are a useful metric to predict regional and seasonal changes in precipitation and temperature. This extension of the TCRE framework to seasonal and regional climate change is helpful for communicating the link between emissions and climate change to policy-makers and the general public, and is well-suited for impact studies that could make use of estimated regional-scale climate changes that are consistent with the carbon budgets associated with global temperature targets.