Source: pages 1109 - 1113, IPCC (WGI_AR5_all_final.pdf)

The total amount of anthropogenic CO2 released in the atmosphere since pre-industrial (often termed cumulative carbon emission, although it applies only to CO2 emissions) is a good indicator of the atmospheric CO2 concentration and hence of the global warming response. The ratio of GMST [Global Mean Surface Temperature] change to total cumulative anthropogenic CO2 emissions is relatively constant over time and independent of the scenario.

This near-linear relationship between total CO2 emissions and global temperature change makes it possible to define a new quantity, the transient climate response to cumulative carbon emission (TCRE), as the transient GMST change for a given amount of cumulated anthropogenic CO2 emissions, usually 1000 GtC (TFE.8, Figure 1).

TCRE is model dependent, as it is a function of the cumulative CO2 airborne fraction and the transient climate response, both quantities varying significantly across models.

Taking into account the available information from multiple lines of evidence (observations, models and process understanding), the near linear relationship between cumulative CO2 emissions and peak global mean temperature is well established in the literature and robust for cumulative total CO2 emissions up to about 2000 GtC. It is consistent with the relationship inferred from past cumulative CO2 emissions and observed warming, is supported by process understanding of the carbon cycle and global energy balance, and emerges as a robust result from the entire hierarchy of models.

Expert judgment based on the available evidence suggests that TCRE is likely between 0.8°C and 2.5°C per 1000 GtC, for cumulative emissions less than about 2000 GtC until the time at which temperature peaks (TFE.8, Figure 1a). {6.4.3, 12.5.4; Box 12.2}

CO2-induced warming is projected to remain approximately constant for many centuries following a complete cessation of emissions. A large fraction of climate change is thus irreversible on a human time scale, except if net anthropogenic CO2 emissions were strongly negative over a sustained period.

Based on the assessment of TCRE

• (assuming a normal distribution with a ±1 standard deviation range of 0.8 to 2.5°C per 1000 GtC),
• limiting the warming caused by anthropogenic CO2 emissions alone (i.e., ignoring other radiative forcings) to less than 2°C since the period 1861–1880
• with a probability of >33%, >50% and >66%, total CO2 emissions from all anthropogenic sources would need to be below a cumulative budget of about 1570 GtC, 1210 GtC and 1000 GtC since 1870, respectively.
• An amount of 515 [445 to 585] GtC was emitted between 1870 and 2011 (TFE.8, Figure 1a,b).

Source: pages 102 - 104, Thematic Focus Elements TFE.8 "Climate Targets and Stabilizaion", Technical Summary, CLIMATE CHANGE 2013, The Physical Science Basis, IPCC (WGI_AR5_all_final.pdf)

The uncertainty in TCRE is caused by the uncertainty in the physical feedbacks and ocean heat uptake (reflected in TCR) and uncertainties in carbon cycle feedbacks (affecting the cumulative airborne fraction of CO2).

Pages 1112 - 1113 in WGI_AR5_all_final

12.5.4.3 Conclusions and Limitations

One difficulty with the concepts of climate stabilization and targets is that stabilization of global temperature does not imply stabilization for all aspects of the climate system. For example, some models show significant hysteresis behaviour in the global water cycle, because global precipitation depends on both atmospheric CO2 and temperature (Wu et al., 2010). Processes related to vegetation changes (Jones et al., 2009) or changes in the ice sheets (Charbit et al., 2008; Ridley et al., 2010) as well as ocean acidification, deep ocean warming and associated sea level rise (Meehl et al., 2005b; Wigley, 2005; Zickfeld et al., 2013) (see Figure 12.44d), and potential feedbacks linking, for example, ocean and the ice sheets (Gillett et al., 2011; Goelzer et al., 2011), have their own intrinsic long time scales. Those will result in significant changes hundreds to thousands of years after global temperature is stabilized. Thermal expansion, in contrast to global mean temperature, also depends on the evolution of surface temperature (Stouffer and Manabe, 1999; Bouttes et al., 2013; Zickfeld et al., 2013).

The simplicity of the concept of a cumulative carbon emission budget makes it attractive for policy (WBGU, 2009). The principal driver of long term warming is the total cumulative emission of CO2 over time. To limit warming caused by CO2 emissions to a given temperature target, cumulative CO2 emissions from all anthropogenic sources therefore need to be limited to a certain budget. Higher emissions in earlier decades simply imply lower emissions by the same amount later on. This is illustrated in the RCP2.6 scenario in Figure 12.46a/b. Two idealized emission pathways with initially higher emissions (even sustained at high level for a decade in one case) eventually lead to the same warming if emissions are then reduced much more rapidly. Even a stepwise emission pathway with levels constant at 2010 and zero near mid-century would eventually lead to a similar warming as they all have identical cumulative emissions.

However, several aspects related to the concept of a cumulative carbon emission budget should be kept in mind. The ratio of global temperature and cumulative carbon is only approximately constant. It is the result of an interplay of several compensating carbon cycle and climate feedback processes operating on different time scales (a cancellation of variations in the increase in RF per ppm of CO2, the ocean heat uptake efficiency and the airborne fraction) (Gregory et al., 2009; Matthews et al., 2009; Solomon et al., 2009). It depends on the modelled climate sensitivity and carbon cycle feedbacks. Thus, the allowed emissions for a given temperature target are uncertain (see Figure 12.45) (Matthews et al., 2009; Zickfeld et al., 2009; Knutti and Plattner, 2012). Nevertheless, the relationship is nearly linear in all models. Most models do not consider the possibility that long term feedbacks (Hansen et al., 2007; Knutti and Hegerl, 2008) may be different (see Section 12.5.3). Despite the fact that stabilization refers to equilibrium, the results assessed here are primarily relevant for the next few centuries and may differ for millennial scales. Notably, many of these limitations apply similarly to other policy targets, for example, stabilizing the atmospheric CO2 concentration.

Using a best estimate for the TCRE would provide a most likely value for the cumulative CO2 emissions compatible with stabilization at a given temperature.

• However, such a budget would imply about 50% probability for staying below the temperature target.
• Higher probabilities for staying below a temperature or concentration target require significantly lower budgets (Knutti et al., 2005; Meinshausen et al., 2009; Rogelj et al., 2012).
• Based on the assessment of TCRE
• (assuming a normal distribution with a ±1 standard deviation range of 0.8- 2.5°C per 1000 PgC),
• limiting the warming caused by anthropogenic CO2 emissions alone (i.e., ignoring other radiative forcings) to less than 2°C since the period 1861–1880
• with a probability of
• >33%, total CO2 emissions from all anthropogenic sources would need to be below a cumulative budget of about 1570 PgC (5762 GtCO2)
• >50%,    " 1210 PgC (4441 GtCO2)
• >66%,    " 1000 PgC (3670 GtCO2)

since 1870.

• An amount of 515 [445 to 585] PgC (1890 [1633 to 2147) GtCO2) was emitted between 1870 and 2011.
• Accounting for non-CO2 forcings contributing to peak warming, or requiring a higher likelihood of temperatures remaining below 2°C, both imply lower cumulative CO2 emissions.
• A possible release of GHGs from permafrost or methane hydrates, not accounted for in current models, would also further reduce the anthropogenic CO2 emissions compatible with a given temperature target.




When accounting for the non-CO2 forcings as in the RCP scenarios, compatible carbon emissions since 1870 are reduced to about

• 900 PgC (3303 GtCO2) with a probability of >33%
• 820 PgC (3009 GtCO2) with a probability of >50%
• 790 PgC (2899 GtCO2) with a probability of >66%

to limit warming to less than 2°C since the period 1861–1880 .

• These estimates were derived by computing the fraction of CMIP5 ESMs and EMICs that stay below 2°C for given cumulative emissions following RCP8.5, as shown in TFE.8 Figure 1c. The non-CO2 forcing in RCP8.5 is higher than in RCP2.6.
• Because all likelihood statements in calibrated IPCC language are open intervals, the provided estimates are thus both conservative and consistent choices valid for non-CO2 forcings across all RCP scenarios.

There is no RCP scenario which limits warming to 2°C with probabilities of >33% or >50%, and which could be used to directly infer compatible cumulative emissions.

• For a probability of >66% RCP2.6 can be used as a comparison. Combining the average back-calculated fossil fuel carbon emissions for RCP2.6 between 2012 and 2100 (270 PgC) with the average historical estimate of 515 PgC gives a total of 785 PgC, i.e., 790 PgC when rounded to 10 PgC.
• As the 785 PgC estimate excludes an explicit assessment of future land-use change emissions, the 790 PgC value also remains a conservative estimate consistent with the overall likelihood assessment.
• The ranges of emissions for these three likelihoods based on the RCP scenarios are rather narrow, as they are based on a single scenario and on the limited sample of models available (TFE.8 Figure 1c).
• In contrast to TCRE they do not include observational constraints or account for sources of uncertainty not sampled by the models.
• The concept of a fixed cumulative CO2 budget holds not just for 2°C, but for any temperature level explored with models so far (up to about 5°C; see Figures 12.44 to 12.46), with higher temperature levels implying larger budgets.