Estimating and tracking the remaining carbon budget for stringent climate targets.

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 Agreement^{14,15,16,17,18}. 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 reversed^19,20,21. 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 complications^{22,23,24,25,26,27}. 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 angle^28,29.

Diversity that may confuse

Unfortunately, all that glitters is not gold. Over the past five years, a plethora of studies have been published^{12,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44} 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 limits^14,15,16. 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 setting^45,46. 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 literature^12,47 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 (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-CO₂ contribution to future temperature rise (TnonCO2)(TnonCO2), 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.

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 record^{10,12,49,50,51}, CO₂-only simulations¹⁰ and multi-gas simulations^{12,31,49,50,51,52,53} 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 emissions^54,55 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 − TnonCO2TnonCO2 − 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 variability^57,58. 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 ambiguity^34,35,59.

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 proxy^1,59,61,62 (see Supplementary Text 2 for more details). Other periods have been suggested^63,64,65, 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 studies^34,59 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 temperature^48,66. 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.