Editing IPCC:AR6/SR15/Chapter-2 (section)

== 2.2 Geophysical Relationships and Constraints ==

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Emissions pathways can be characterized by various geophysical characteristics, such as radiative forcing (Masui et al., 2011; Riahi et al., 2011; Thomson et al., 2011; van Vuuren et al., 2011b) <sup>[[#fn:r33|33]]</sup> , atmospheric concentrations (van Vuuren et al., 2007, 2011a; Clarke et al., 2014) <sup>[[#fn:r34|34]]</sup> or associated temperature outcomes (Meinshausen et al., 2009; Rogelj et al., 2011; Luderer et al., 2013) <sup>[[#fn:r35|35]]</sup> . These attributes can be used to derive geophysical relationships for specific pathway classes, such as cumulative CO <sub>2</sub> emissions compatible with a specific level of warming, also known as ‘carbon budgets’ (Meinshausen et al., 2009 <sup>[[#fn:r36|36]]</sup> ; Rogelj et al., 2011; Stocker et al., 2013; Friedlingstein et al., 2014a) <sup>[[#fn:r37|37]]</sup> , the consistent contributions of non-CO <sub>2</sub> GHGs and aerosols to the remaining carbon budget (Bowerman et al., 2011; Rogelj et al., 2015a, 2016b) <sup>[[#fn:r38|38]]</sup> , or to temperature outcomes (Lamarque et al., 2011; Bowerman et al., 2013; Rogelj et al., 2014b) <sup>[[#fn:r39|39]]</sup> . This section assesses geophysical relationships for both CO <sub>2</sub> and non-CO <sub>2</sub> emissions (see glossary).

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=== 2.2.1 Geophysical Characteristics of Mitigation Pathways ===

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This section employs the pathway classification introduced in Section 2.1, with geophysical characteristics derived from simulations with the MAGICC reduced-complexity carbon cycle and climate model and supported by simulations with the FAIR reduced-complexity model (Section 2.1). Within a specific category and between models, there remains a large degree of variance. Most pathways exhibit a temperature overshoot which has been highlighted in several studies focusing on stringent mitigation pathways (Huntingford and Lowe, 2007; Wigley et al., 2007; Nohara et al., 2015; Rogelj et al., 2015d; Zickfeld and Herrington, 2015; Schleussner et al., 2016; Xu and Ramanathan, 2017) <sup>[[#fn:r40|40]]</sup> . Only very few of the scenarios collected in the database for this report hold the average future warming projected by MAGICC below 1.5°C during the entire 21st century (Table 2.1, Figure 2.1). Most 1.5°C-consistent pathways available in the database overshoot 1.5°C around mid-century before peaking and then reducing temperatures so as to return below that level in 2100. However, because of numerous geophysical uncertainties and model dependencies (Section 2.2.1.1, Supplementary Material 2.SM.1.1), absolute temperature characteristics of the various pathway categories are more difficult to distinguish than relative features (Figure 2.1, Supplementary Material 2.SM.1.1), and actual probabilities of overshoot are imprecise. However, all lines of evidence available for temperature projections indicate a probability greater than 50% of overshooting 1.5°C by mid-century in all but the most stringent pathways currently available (Supplementary Material 2.SM.1.1, 2.SM.1.4).

Most 1.5°C-consistent pathways exhibit a peak in temperature by mid-century whereas 2°C-consistent pathways generally peak after 2050 (Supplementary Material 2.SM.1.4). The peak in median temperature in the various pathway categories occurs about ten years before reaching net zero CO <sub>2</sub> emissions due to strongly reduced annual CO <sub>2</sub> emissions and deep reductions in CH <sub>4</sub> emissions (Section 2.3.3). The two reduced-complexity climate models used in this assessment suggest that virtually all available 1.5°C-consistent pathways peak and then decline global mean temperature, but with varying rates of temperature decline after the peak (Figure 2.1). The estimated decadal rates of temperature change by the end of the century are smaller than the amplitude of the climate variability as assessed in AR5 (1 standard deviation of about ±0.1°C), which hence complicates the detection of a global peak and decline of warming in observations on time scales of one to two decades (Bindoff et al., 2013) <sup>[[#fn:r41|41]]</sup> . In comparison, many pathways limiting warming to 2°C or higher by 2100 still have noticeable increasing trends at the end of the century, and thus imply continued warming.

By 2100, the difference between 1.5°C- and 2°C-consistent pathways becomes clearer compared to mid-century, not only for the temperature response (Figure 2.1) but also for atmospheric CO <sub>2</sub> concentrations. In 2100, the median CO <sub>2</sub> concentration in 1.5°C-consistent pathways is below 2016 levels (Le Quéré et al., 2018) <sup>[[#fn:r42|42]]</sup> , whereas it remains higher by about 5–10% compared to 2016 in the 2°C-consistent pathways.

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'''Figure 2.1'''

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'''Pathways classification overview.'''
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[[File:fe1759678dc9162b928227cb1f09fd14 figure-2.1-1024x995.png]]

(a) Average global mean temperature increase relative to 2010 as projected by FAIR and MAGICC in 2030, 2050 and 2100; (b) response of peak warming to cumulative CO <sub>2</sub> emissions until net zero by MAGICC (red) and FAIR (blue); (c) decadal rate of average global mean temperature change from 2081 to 2100 as a function of the annual CO <sub>2</sub> emissions averaged over the same period as given by FAIR (transparent squares) and MAGICC (filled circles). In panel (a), horizontal lines at 0.63°C and 1.13°C are indicative of the 1.5°C and 2°C warming thresholds with the respect to 1850–1900, taking into account the assessed historical warming of 0.87°C ±0.12°C between the 1850–1900 and 2006–2015 periods (Chapter 1, Section 1.2.1). In panel (a), vertical lines illustrate both the physical and the scenario uncertainty as captured by MAGICC and FAIR and show the minimal warming of the 5th percentile of projected warming and the maximal warming of the 95th percentile of projected warming per scenario class. Boxes show the interquartile range of mean warming across scenarios, and thus represent scenario uncertainty only.

Original Creation for this Report using SR15 scenario database, public, 2018

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==== 2.2.1.1 Geophysical uncertainties: non-CO <sub>2</sub> forcing agents ====

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Impacts of non-CO <sub>2</sub> climate forcers on temperature outcomes are particularly important when evaluating stringent mitigation pathways (Weyant et al., 2006; Shindell et al., 2012; Rogelj et al., 2014b, 2015a; Samset et al., 2018) <sup>[[#fn:r43|43]]</sup> . However, many uncertainties affect the role of non-CO <sub>2</sub> climate forcers in stringent mitigation pathways.

A first uncertainty arises from the magnitude of the radiative forcing attributed to non-CO <sub>2</sub> climate forcers. Figure 2.2 illustrates how, for one representative 1.5°C-consistent pathway (SSP2-1.9) (Fricko et al., 2017; Rogelj et al., 2018) <sup>[[#fn:r44|44]]</sup> , the effective radiative forcings as estimated by MAGICC and FAIR can differ (see Supplementary Material 2.SM1.1 for further details). This large spread in non-CO <sub>2</sub> effective radiative forcings leads to considerable uncertainty in the predicted temperature response. This uncertainty ultimately affects the assessed temperature outcomes for pathway classes used in this chapter (Section 2.1) and also affects the carbon budget (Section 2.2.2). Figure 2.2 highlights the important role of methane emissions reduction in this scenario, in agreement with the recent literature focussing on stringent mitigation pathways (Shindell et al., 2012; Rogelj et al., 2014b, 2015a; Stohl et al., 2015; Collins et al., 2018) <sup>[[#fn:r45|45]]</sup> .

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<span id="changes-and-uncertainties-in-effective-radiative-forcings-erf-for-one-1.5c-consistent-pathway-ssp2-19-as-estimated-by-magicc-and-fair."></span>
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'''Changes and uncertainties in effective radiative forcings (ERF) for one 1.5°C-consistent pathway (SSP2-19) as estimated by MAGICC and FAIR.'''
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[[File:973385e9fbc985c7954e74a64d1ed321 figure-2.2-1024x975.jpg]]

The lines are indicative of the total effective radiative forcing from all anthropogenic sources (solid lines) and for non-CO <sub>2</sub> agents only (dashed lines), as represented by MAGICC (red) and FAIR (blue) relative to 2010, respectively. Vertical bars show the mean radiative forcing as predicted by MAGICC and FAIR of relevant non-CO <sub>2</sub> agents for year 2030, 2050 and 2100. The vertical lines give the uncertainty (1 standard deviation) of the ERFs for the represented species.

Original Creation for this Report using the SR15 scenario database

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For mitigation pathways that aim at halting and reversing radiative forcing increase during this century, the aerosol radiative forcing is a considerable source of uncertainty (Figure 2.2) (Samset et al., 2018; Smith et al., 2018) <sup>[[#fn:r46|46]]</sup> . Indeed, reductions in SO <sub>2</sub> (and NO <sub>x</sub> ) emissions largely associated with fossil-fuel burning are expected to reduce the cooling effects of both aerosol radiative interactions and aerosol cloud interactions, leading to warming (Myhre et al., 2013; Samset et al., 2018) <sup>[[#fn:r47|47]]</sup> . A multimodel analysis (Myhre et al., 2017) <sup>[[#fn:r48|48]]</sup> and a study based on observational constraints (Malavelle et al., 2017) <sup>[[#fn:r49|49]]</sup> largely support the AR5 best estimate and uncertainty range of aerosol forcing. The partitioning of total aerosol radiative forcing between aerosol precursor emissions is important (Ghan et al., 2013; Jones et al., 2018; Smith et al., 2018) <sup>[[#fn:r50|50]]</sup> as this affects the estimate of the mitigation potential from different sectors that have aerosol precursor emission sources. The total aerosol effective radiative forcing change in stringent mitigation pathways is expected to be dominated by the effects from the phase-out of SO <sub>2</sub> , although the magnitude of this aerosol-warming effect depends on how much of the present-day aerosol cooling is attributable to SO <sub>2</sub> , particularly the cooling associated with aerosol–cloud interaction (Figure 2.2). Regional differences in the linearity of aerosol–cloud interactions (Carslaw et al., 2013; Kretzschmar et al., 2017) <sup>[[#fn:r51|51]]</sup> make it difficult to separate the role of individual precursors. Precursors that are not fully mitigated will continue to affect the Earth system. If, for example, the role of nitrate aerosol cooling is at the strongest end of the assessed IPCC AR5 uncertainty range, future temperature increases may be more modest if ammonia emissions continue to rise (Hauglustaine et al., 2014) <sup>[[#fn:r52|52]]</sup> .

Figure 2.2 shows that there are substantial differences in the evolution of estimated effective radiative forcing of non-CO <sub>2</sub> forcers between MAGICC and FAIR. These forcing differences result in MAGICC simulating a larger warming trend in the near term compared to both the FAIR model and the recent observed trends of 0.2°C per decade reported in Chapter 1 (Figure 2.1, Supplementary Material 2.SM.1.1, Chapter 1, Section 1.2.1.3). The aerosol effective forcing is stronger in MAGICC compared to either FAIR or the AR5 best estimate, though it is still well within the AR5 uncertainty range (Supplementary Material 2.SM.1.1.1). A recent revision (Etminan et al., 2016) <sup>[[#fn:r53|53]]</sup> increases the methane forcing by 25%. This revision is used in the FAIR but not in the AR5 setup of MAGICC that is applied here. Other structural differences exist in how the two models relate emissions to concentrations that contribute to differences in forcing (see Supplementary Material 2.SM.1.1.1).

Non-CO <sub>2</sub> climate forcers exhibit a greater geographical variation in radiative forcings than CO <sub>2</sub> , which leads to important uncertainties in the temperature response <sub> </sub> (Myhre et al., 2013) <sup>[[#fn:r54|54]]</sup> . This uncertainty increases the relative uncertainty of the temperature pathways associated with low emission scenarios compared to high emission scenarios (Clarke et al., 2014) <sup>[[#fn:r55|55]]</sup> . It is also important to note that geographical patterns of temperature change and other climate responses, especially those related to precipitation, depend significantly on the forcing mechanism (Myhre et al., 2013; Shindell et al., 2015; Marvel et al., 2016; Samset et al., 2016) <sup>[[#fn:r56|56]]</sup> (see also Chapter 3, Section 3.6.2.2).

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==== 2.2.1.2 Geophysical uncertainties: climate and Earth system feedbacks ====

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Climate sensitivity uncertainty impacts future projections as well as carbon-budget estimates (Schneider et al., 2017) <sup>[[#fn:r57|57]]</sup> . AR5 assessed the equilibrium climate sensitivity (ECS) to be ''likely'' in the 1.5°–4.5°C range, ''extremely unlikely'' less than 1°C and ''very unlikely'' greater than 6°C. The lower bound of this estimate is lower than the range of CMIP5 models (Collins et al., 2013) <sup>[[#fn:r58|58]]</sup> . The evidence for the 1.5°C lower bound on ECS in AR5 was based on analysis of energy-budget changes over the historical period. Work since AR5 has suggested that the climate sensitivity inferred from such changes has been lower than the 2 × CO <sub>2</sub> climate sensitivity for known reasons (Forster, 2016; Gregory and Andrews, 2016; Rugenstein et al., 2016; Armour, 2017; Ceppi and Gregory, 2017; Knutti et al., 2017; Proistosescu and Huybers, 2017) <sup>[[#fn:r59|59]]</sup> . Both a revised interpretation of historical estimates and other lines of evidence based on analysis of climate models with the best representation of today’s climate (Sherwood et al., 2014; Zhai et al., 2015; Tan et al., 2016; Brown and Caldeira, 2017; Knutti et al., 2017) <sup>[[#fn:r60|60]]</sup> suggest that the lower bound of ECS could be revised upwards, which would decrease the chances of limiting warming below 1.5°C in assessed pathways. However, such a reassessment has been challenged (Lewis and Curry, 2018) <sup>[[#fn:r61|61]]</sup> , albeit from a single line of evidence. Nevertheless, it is premature to make a major revision to the lower bound. The evidence for a possible revision of the upper bound on ECS is less clear, with cases argued from different lines of evidence for both decreasing (Lewis and Curry, 2015, 2018; Cox et al., 2018) <sup>[[#fn:r62|62]]</sup> and increasing (Brown and Caldeira, 2017) <sup>[[#fn:r63|63]]</sup> the bound presented in the literature. The tools used in this chapter employ ECS ranges consistent with the AR5 assessment. The MAGICC ECS distribution has not been selected to explicitly reflect this but is nevertheless consistent (Rogelj et al., 2014a) <sup>[[#fn:r64|64]]</sup> . The FAIR model used here to estimate carbon budgets explicitly constructs log-normal distributions of ECS and transient climate response based on a multi-parameter fit to the AR5 assessed ranges of climate sensitivity and individual historic effective radiative forcings (Smith et al., 2018) <sup>[[#fn:r65|65]]</sup> (Supplementary Material 2.SM.1.1.1).

Several feedbacks of the Earth system, involving the carbon cycle, non-CO <sub>2</sub> GHGs and/or aerosols, may also impact the future dynamics of the coupled carbon–climate system’s response to anthropogenic emissions. These feedbacks are caused by the effects of nutrient limitation (Duce et al., 2008; Mahowald et al., 2017) <sup>[[#fn:r66|66]]</sup> , ozone exposure (de Vries et al., 2017) <sup>[[#fn:r67|67]]</sup> , fire emissions (Narayan et al., 2007) <sup>[[#fn:r68|68]]</sup> and changes associated with natural aerosols (Cadule et al., 2009 <sup>[[#fn:r69|69]]</sup> ; Scott et al., 2018) <sup>[[#fn:r70|70]]</sup> . Among these Earth system feedbacks, the importance of the permafrost feedback’s influence has been highlighted in recent studies. Combined evidence from both models (MacDougall et al., 2015; Burke et al., 2017; Lowe and Bernie, 2018) <sup>[[#fn:r71|71]]</sup> and field studies (like Schädel et al., 2014; Schuur et al., 2015) <sup>[[#fn:r72|72]]</sup> shows ''high agreement'' that permafrost thawing will release both CO <sub>2</sub> and CH <sub>4</sub> as the Earth warms, amplifying global warming. This thawing could also release N <sub>2</sub> O (Voigt et al., 2017a, b) <sup>[[#fn:r73|73]]</sup> . Field, laboratory and modelling studies estimate that the vulnerable fraction in permafrost is about 5–15% of the permafrost soil carbon (~5300–5600 GtCO <sub>2</sub> in Schuur et al., 2015) <sup>[[#fn:r74|74]]</sup> and that carbon emissions are expected to occur beyond 2100 because of system inertia and the large proportion of slowly decomposing carbon in permafrost (Schädel et al., 2014) <sup>[[#fn:r75|75]]</sup> . Published model studies suggest that a large part of the carbon release to the atmosphere is in the form of CO <sub>2</sub> (Schädel et al., 2016) <sup>[[#fn:r76|76]]</sup> , while the amount of CH <sub>4</sub> released by permafrost thawing is estimated to be much smaller than that CO <sub>2</sub> . Cumulative CH <sub>4</sub> release by 2100 under RCP2.6 ranges from 0.13 to 0.45 Gt of methane (Burke et al., 2012; Schneider von Deimling et al., 2012, 2015) <sup>[[#fn:r77|77]]</sup> , with fluxes being the highest in the middle of the century because of maximum thermokarst lake extent by mid-century (Schneider von Deimling et al., 2015) <sup>[[#fn:r78|78]]</sup> .

The reduced complexity climate models employed in this assessment do not take into account permafrost or non-CO <sub>2</sub> Earth system feedbacks, although the MAGICC model has a permafrost module that can be enabled. Taking the current climate and Earth system feedbacks understanding together, there is a possibility that these models would underestimate the longer-term future temperature response to stringent emission pathways (Section 2.2.2).

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=== 2.2.2 The Remaining 1.5°C Carbon Budget ===

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==== 2.2.2.1 Carbon budget estimates ====

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Since the AR5, several approaches have been proposed to estimate carbon budgets compatible with 1.5°C or 2°C. Most of these approaches indirectly rely on the approximate linear relationship between peak global mean temperature and cumulative emissions of carbon (the transient climate response to cumulative emissions of carbon, TCRE) (Collins et al., 2013; Friedlingstein et al., 2014a; Rogelj et al., 2016b) <sup>[[#fn:r79|79]]</sup> , whereas others base their estimates on equilibrium climate sensitivity (Schneider et al., 2017) <sup>[[#fn:r80|80]]</sup> . The AR5 employed two approaches to determine carbon budgets. Working Group I (WGI) computed carbon budgets from 2011 onwards for various levels of warming relative to the 1861–1880 period using RCP8.5 (Meinshausen et al., 2011b; Stocker et al., 2013) <sup>[[#fn:r81|81]]</sup> , whereas WGIII estimated their budgets from a set of available pathways that were assessed to have a &gt;50% probability to exceed 1.5°C by mid-century, and return to 1.5°C or below in 2100 with greater than 66% probability (Clarke et al., 2014) <sup>[[#fn:r82|82]]</sup> . These differences made AR5 WGI and WGIII carbon budgets difficult to compare as they are calculated over different time periods, are derived from a different sets of multi-gas and aerosol emission scenarios, and use different concepts of carbon budgets (exceedance for WGI, avoidance for WGIII) (Rogelj et al., 2016b; Matthews et al., 2017) <sup>[[#fn:r83|83]]</sup> .

Carbon budgets can be derived from CO <sub>2</sub> -only experiments as well as from multi-gas and aerosol scenarios. Some published estimates of carbon budgets compatible with 1.5°C or 2°C refer to budgets for CO <sub>2</sub> -induced warming only, and hence do not take into account the contribution of non-CO <sub>2</sub> climate forcers (Allen et al., 2009; Matthews et al., 2009; Zickfeld et al., 2009; IPCC, 2013a) <sup>[[#fn:r84|84]]</sup> . However, because the projected changes in non-CO <sub>2</sub> climate forcers tend to amplify future warming, CO <sub>2</sub> -only carbon budgets overestimate the total net cumulative carbon emissions compatible with 1.5°C or 2°C (Friedlingstein et al., 2014a; Rogelj et al., 2016b; Matthews et al., 2017; Mengis et al., 2018; Tokarska et al., 2018) <sup>[[#fn:r85|85]]</sup> .

Since the AR5, many estimates of the remaining carbon budget for 1.5°C have been published (Friedlingstein et al., 2014a; MacDougall et al., 2015; Peters, 2016; Rogelj et al., 2016b, 2018; Matthews et al., 2017; Millar et al., 2017; Goodwin et al., 2018b; Kriegler et al., 2018b; Lowe and Bernie, 2018; Mengis et al., 2018; Millar and Friedlingstein, 2018; Schurer et al., 2018; Séférian et al., 2018; Tokarska and Gillett, 2018; Tokarska et al., 2018) <sup>[[#fn:r86|86]]</sup> . These estimates cover a wide range as a result of differences in the models used, and of methodological choices, as well as physical uncertainties. Some estimates are exclusively model-based while others are based on observations or on a combination of both. Remaining carbon budgets limiting warming below 1.5°C or 2°C that are derived from Earth system models of intermediate complexity (MacDougall et al., 2015; Goodwin et al., 2018a) <sup>[[#fn:r87|87]]</sup> , IAMs (Luderer et al., 2018; Rogelj et al., 2018) <sup>[[#fn:r88|88]]</sup> , or are based on Earth-system model results (Lowe and Bernie, 2018; Séférian et al., 2018; Tokarska and Gillett, 2018) <sup>[[#fn:r89|89]]</sup> give remaining carbon budgets of the same order of magnitude as the IPCC AR5 Synthesis Report (SYR) estimates (IPCC, 2014a) <sup>[[#fn:r90|90]]</sup> . This is unsurprising as similar sets of models were used for the AR5 (IPCC, 2013b) <sup>[[#fn:r91|91]]</sup> . The range of variation across models stems mainly from either the inclusion or exclusion of specific Earth system feedbacks (MacDougall et al., 2015; Burke et al., 2017; Lowe and Bernie, 2018) <sup>[[#fn:r92|92]]</sup> or different budget definitions (Rogelj et al., 2018) <sup>[[#fn:r93|93]]</sup> .

In contrast to the model-only estimates discussed above and employed in the AR5, this report additionally uses observations to inform its evaluation of the remaining carbon budget. Table 2.2 shows that the assessed range of remaining carbon budgets consistent with 1.5°C or 2°C is larger than the AR5 SYR estimate and is part way towards estimates constrained by recent observations (Millar et al., 2017; Goodwin et al., 2018a; Tokarska and Gillett, 2018) <sup>[[#fn:r94|94]]</sup> . Figure 2.3 illustrates that the change since AR5 is, in very large part, due to the application of a more recent observed baseline to the historic temperature change and cumulative emissions; here adopting the baseline period of 2006–2015 (see Chapter 1, Section 1.2.1). AR5 SYR Figures SPM.10 and 2.3 already illustrated the discrepancy between models and observations, but did not apply this as a correction to the carbon budget because they were being used to illustrate the overall linear relationship between warming and cumulative carbon emissions in the CMIP5 models since 1870, and were not specifically designed to quantify residual carbon budgets relative to the present for ambitious temperature goals. The AR5 SYR estimate was also dependent on a subset of Earth system models illustrated in Figure 2.3 of this report. Although, as outlined below and in Table 2.2, considerably uncertainties remain, there is ''high agreement'' across various lines of evidence assessed in this report that the remaining carbon budget for 1.5°C or 2°C would be larger than the estimates at the time of the AR5. However, the overall remaining budget for 2100 is assessed to be smaller than that derived from the recent observational-informed estimates, as Earth system feedbacks such as permafrost thawing reduce the budget applicable to centennial scales (see Section 2.2.2.2).

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Temperature changes from 1850–1900 versus cumulative CO <sub>2 </sub> emissions since 1st January 1876.
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[[File:484c10d19c0ae148cbd2082ed4a2fcfe figure-2.3-1024x768.jpg]]

Solid lines with dots reproduce the globally averaged near-surface air temperature response to cumulative CO <sub>2</sub> emissions plus non-CO <sub>2</sub> forcers as assessed in Figure SPM10 of WGI AR5, except that points marked with years relate to a particular year, unlike in WGI AR5 Figure SPM.10, where each point relates to the mean over the previous decade. The AR5 data was derived from 15 Earth system models and 5 Earth system models of Intermediate Complexity for the historic observations (black) and RCP8.5 scenario (red), and the red shaded plume shows the range across the models as presented in the AR5. The purple shaded plume and the line are indicative of the temperature response to cumulative CO <sub>2</sub> emissions and non-CO <sub>2</sub> warming adopted in this report. The non-CO <sub>2</sub> warming contribution is averaged from the MAGICC and FAIR models, and the purple shaded range assumes the AR5 WGI TCRE distribution (Supplementary Material 2.SM.1.1.2). The 2010 observation of surface temperature change (0.97°C based on 2006–2015 mean compared to 1850–1900, Chapter 1, Section 1.2.1) and cumulative carbon dioxide emissions from 1876 to the end of 2010 of 1,930 GtCO <sub>2</sub> (Le Quéré et al., 2018) is shown as a filled purple diamond. The value for 2017 based on the latest cumulative carbon emissions up to the end of 2017 of 2,220 GtCO <sub>2</sub> (Version 1.3 accessed 22 May 2018) and a surface temperature anomaly of 1.1°C based on an assumed temperature increase of 0.2°C per decade is shown as a hollow purple diamond. The thin blue line shows annual observations, with CO <sub>2</sub> emissions from Le Quéré et al. (2018) and estimated globally averaged near-surface temperature from scaling the incomplete coverage and blended HadCRUT4 dataset in Chapter 1. The thin black line shows the CMIP5 multimodel mean estimate with CO <sub>2</sub> emissions also from (Le Quéré et al., 2018). The thin black line shows the GMST historic temperature trends from Chapter 1, which give lower temperature changes up to 2006–2015 of 0.87°C and would lead to a larger remaining carbon budget. The dotted black lines illustrate the remaining carbon budget estimates for 1.5°C given in Table 2.2. Note these remaining budgets exclude possible Earth system feedbacks that could reduce the budget, such as CO <sub>2</sub> and CH4 release from permafrost thawing and tropical wetlands (see Section 2.2.2.2).

Original Creation for this Report using Temperature observations, model results, and projections as a function of cumulative carbon emissions.

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<span id="co-2-and-non-co-2-contributions-to-the-remaining-carbon-budget"></span>
==== 2.2.2.2 CO <sub>2</sub> and non-CO <sub>2</sub> contributions to the remaining carbon budget ====

<div id="section-2-2-2-2-block-1"></div>

A remaining carbon budget can be estimated from calculating the amount of CO <sub>2</sub> emissions consistent (given a certain value of TCRE) with an allowable additional amount of warming. Here, the allowable warming is the 1.5°C warming threshold minus the current warming taken as the 2006–2015 average, with a further amount removed to account for the estimated non-CO <sub>2</sub> temperature contribution to the remaining warming (Peters, 2016; Rogelj et al., 2016b) <sup>[[#fn:r98|98]]</sup> . This assessment uses the TCRE range from AR5 WGI (Collins et al., 2013) <sup>[[#fn:r99|99]]</sup> supported by estimates of non-CO <sub>2</sub> contributions that are based on published methods and integrated pathways (Friedlingstein et al., 2014a; Allen et al., 2016, 2018; Peters, 2016; Smith et al., 2018) <sup>[[#fn:r100|100]]</sup> . Table 2.2 and Figure 2.3 show the assessed remaining carbon budgets and key uncertainties for a set of additional warming levels relative to the 2006–2015 period (see Supplementary Material 2.SM.1.1.2 for details). With an assessed historical warming of 0.87°C ± 0.12°C from 1850–1900 to 2006–2015 (Chapter 1, Section 1.2.1), 0.63°C of additional warming would be approximately consistent with a global mean temperature increase of 1.5°C relative to pre-industrial levels. For this level of additional warming, remaining carbon budgets have been estimated (Table 2.2, Supplementary Material 2.SM.1.1.2).

The remaining carbon budget calculation presented in the Table 2.2 and illustrated in Figure 2.3 does not consider additional Earth system feedbacks such as permafrost thawing. These are uncertain but estimated to reduce the remaining carbon budget by an order of magnitude of about 100 GtCO <sub>2</sub> and more thereafter. Accounting for such feedbacks would make the carbon budget more applicable for 2100 temperature targets, but would also increase uncertainty (Table 2.2 and see below). Excluding such feedbacks, the assessed range for the remaining carbon budget is estimated to be 840, 580, and 420 GtCO <sub>2</sub> for the 33rd, 50th and, 67th percentile of TCRE, respectively, with a median non-CO <sub>2</sub> warming contribution and starting from 1 January 2018 onward. Consistent with the approach used in the IPCC Fifth Assessment Report (IPCC, 2013b) <sup>[[#fn:r101|101]]</sup> , the latter estimates use global near-surface air temperatures both over the ocean and over land to estimate global surface temperature change since pre-industrial. The global warming from the pre-industrial period until the 2006–2015 reference period is estimated to amount to 0.97°C with an uncertainty range of about ±0.1°C (see Chapter 1, Section 1.2.1). Three methodological improvements lead to these estimates of the remaining carbon budget being about 300 GtCO <sub>2</sub> larger than those reported in Table 2.2 of the IPCC AR5 SYR (IPCC, 2014a) <sup>[[#fn:r102|102]]</sup> ( ''medium confidence'' ). The AR5 used 15 Earth System Models (ESM) and 5 Earth-system Models of Intermediate Complexity (EMIC) to derive an estimate of the remaining carbon budget. Their approach hence made implicit assumptions about the level of warming to date, the future contribution of non-CO <sub>2</sub> emissions, and the temperature response to CO <sub>2</sub> (TCRE). In this report, each of these aspects are considered explicitly. When estimating global warming until the 2006–2015 reference period as a blend of near-surface air temperature over land and sea-ice regions, and sea-surface temperature over open ocean, by averaging the four global mean surface temperature time series listed in Chapter 1 Section 1.2.1, the global warming would amount to 0.87°C ±0.1°C. Using the latter estimate of historical warming and projecting global warming using global near-surface air temperatures from model projections leads to remaining carbon budgets for limiting global warming to 1.5°C of 1080, 770, and 570 GtCO <sub>2</sub> for the 33rd, 50th, and 67th percentile of TCRE, respectively. Note that future research and ongoing observations over the next years will provide a better indication as to how the 2006–2015 base period compares with the long-term trends and might affect the budget estimates. Similarly, improved understanding in Earth system feedbacks would result in a better quantification of their impacts on remaining carbon budgets for 1.5°C and 2°C.

After TCRE uncertainty, a major additional source of uncertainty is the magnitude of non-CO <sub>2</sub> forcing and its contribution to the temperature change between the present day and the time of peak warming. Integrated emissions pathways can be used to ensure consistency between CO <sub>2</sub> and non-CO <sub>2</sub> emissions (Bowerman et al., 2013; Collins et al., 2013; Clarke et al., 2014; Rogelj et al., 2014b, 2015a; Tokarska et al., 2018) <sup>[[#fn:r103|103]]</sup> . Friedlingstein et al. (2014a) <sup>[[#fn:r104|104]]</sup> used pathways with limited to no climate mitigation to find a variation due to non-CO <sub>2</sub> contributions of about ±33% for a 2°C carbon budget. Rogelj et al. (2016b) <sup>[[#fn:r105|105]]</sup> showed no particular bias in non-CO <sub>2</sub> radiative forcing or warming at the time of exceedance of 2°C or at peak warming between scenarios with increasing emissions and strongly mitigated scenarios (consistent with Stocker et al., 2013) <sup>[[#fn:r106|106]]</sup> . However, clear differences of the non-CO <sub>2</sub> warming contribution at the time of deriving a 2°C-consistent carbon budget were reported for the four RCPs. Although the spread in non-CO <sub>2</sub> forcing across scenarios can be smaller in absolute terms at lower levels of cumulative emissions, it can be larger in relative terms compared to the remaining carbon budget (Stocker et al., 2013; Friedlingstein et al., 2014a; Rogelj et al., 2016b) <sup>[[#fn:r107|107]]</sup> . Tokarska and Gillett (2018) <sup>[[#fn:r108|108]]</sup> find no statistically significant differences in 1.5°C-consistent cumulative emissions budgets when calculated for different RCPs from consistent sets of CMIP5 simulations.

The mitigation pathways assessed in this report indicate that emissions of non-CO <sub>2</sub> forcers contribute an average additional warming of around 0.15°C relative to 2006–2015 at the time of net zero CO <sub>2</sub> emissions, reducing the remaining carbon budget by roughly 320 GtCO <sub>2</sub> . This arises from a weakening of aerosol cooling and continued emissions of non-CO <sub>2</sub> GHGs (Sections 2.2.1, 2.3.3). This non-CO <sub>2</sub> contribution at the time of net zero CO <sub>2</sub> emissions varies by about ±0.1°C across scenarios, resulting in a carbon budget uncertainty of about ±250 GtCO <sub>2</sub> , and takes into account marked reductions in methane emissions (Section 2.3.3). If these reductions are not achieved, remaining carbon budgets are further reduced. Uncertainties in the non-CO <sub>2</sub> forcing and temperature response are asymmetric and can influence the remaining carbon budget by −400 to +200 GtCO <sub>2</sub> , with the uncertainty in aerosol radiative forcing being the largest contributing factor (Table 2.2). The MAGICC and FAIR models in their respective parameter setups and model versions used to assess the non-CO <sub>2</sub> warming contribution give noticeable different non-CO <sub>2</sub> effective radiative forcing and warming for the same scenarios while both being within plausible ranges of future response (Figure 2.2 and Supplementary Material 2.SM.1.1, 2.SM.1.2). For this assessment, it is premature to assess the accuracy of their results, so it is assumed that both are equally representative of possible futures. Their non-CO <sub>2</sub> warming estimates are therefore averaged for the carbon budget assessment and their differences used to guide the uncertainty assessment of the role of non-CO <sub>2</sub> forcers. Nevertheless, the findings are robust enough to give ''high confidence'' that the changing emissions of non-CO <sub>2</sub> forcers (particularly the reduction in cooling aerosol precursors) cause additional near-term warming and reduce the remaining carbon budget compared to the CO <sub>2</sub> -only budget.

TCRE uncertainty directly impacts carbon budget estimates (Peters, 2016; Matthews et al., 2017; Millar and Friedlingstein, 2018) <sup>[[#fn:r109|109]]</sup> . Based on multiple lines of evidence, AR5 WGI assessed a ''likely'' range for TCRE of 0.2°–0.7°C per 1000 GtCO <sub>2</sub> (Collins et al., 2013) <sup>[[#fn:r110|110]]</sup> . The TCRE of the CMIP5 Earth system models ranges from 0.23°C to 0.66°C per 1000 GtCO <sub>2</sub> (Gillett et al., 2013) <sup>[[#fn:r111|111]]</sup> . At the same time, studies using observational constraints find best estimates of TCRE of 0.35°–0.41°C per 1000 GtCO <sub>2</sub> (Matthews et al., 2009; Gillett et al., 2013; Tachiiri et al., 2015; Millar and Friedlingstein, 2018) <sup>[[#fn:r112|112]]</sup> . This assessment continues to use the assessed AR5 TCRE range under the working assumption that TCRE is normally distributed (Stocker et al., 2013) <sup>[[#fn:r113|113]]</sup> . Observation-based estimates have reported log-normal distributions of TCRE (Millar and Friedlingstein, 2018) <sup>[[#fn:r114|114]]</sup> . Assuming a log-normal instead of normal distribution of the assessed AR5 TCRE range would result in about a 200 GtCO <sub>2</sub> increase for the median budget estimates but only about half at the 67th percentile, while historical temperature uncertainty and uncertainty in recent emissions contribute ±150 and ±50 GtCO <sub>2</sub> to the uncertainty, respectively (Table 2.2).

Calculating carbon budgets from the TCRE requires the assumption that the instantaneous warming in response to cumulative CO <sub>2</sub> emissions equals the long-term warming or, equivalently, that the residual warming after CO <sub>2</sub> emissions cease is negligible. The magnitude of this residual warming, referred to as the zero-emission commitment, ranges from slightly negative (i.e., a slight cooling) to slightly positive for CO <sub>2</sub> emissions up to present-day (Chapter 1, Section 1.2.4) (Lowe et al., 2009; Frölicher and Joos, 2010; Gillett et al., 2011; Matthews and Zickfeld, 2012) <sup>[[#fn:r115|115]]</sup> . The delayed temperature change from a pulse CO <sub>2</sub> emission introduces uncertainties in emission budgets, which have not been quantified in the literature for budgets consistent with limiting warming to 1.5°C. As a consequence, this uncertainty does not affect our carbon budget estimates directly but it is included as an additional factor in the assessed Earth system feedback uncertainty (as detailed below) of roughly 100 GtCO <sub>2</sub> on decadal time scales presented in Table 2.2.

Remaining carbon budgets are further influenced by Earth system feedbacks not accounted for in CMIP5 models, such as the permafrost carbon feedback (Friedlingstein et al., 2014b; MacDougall et al., 2015; Burke et al., 2017; Lowe and Bernie, 2018) <sup>[[#fn:r116|116]]</sup> , and their influence on the TCRE. Lowe and Bernie (2018) <sup>[[#fn:r117|117]]</sup> used a simple climate sensitivity scaling approach to estimate that Earth system feedbacks (such as CO <sub>2</sub> released by permafrost thawing or methane released by wetlands) could reduce carbon budgets for 1.5°C and 2°C by roughly 100 GtCO <sub>2</sub> on centennial time scales. Their findings are based on an older understanding of Earth system feedbacks (Arneth et al., 2010) <sup>[[#fn:r118|118]]</sup> . This estimate is broadly supported by more recent analysis of individual feedbacks. Schädel et al. (2014) <sup>[[#fn:r119|119]]</sup> suggest an upper bound of 24.4 PgC (90 GtCO <sub>2</sub> ) emitted from carbon release from permafrost over the next forty years for a RCP4.5 scenario. Burke et al. (2017) <sup>[[#fn:r120|120]]</sup> use a single model to estimate permafrost emissions between 0.3 and 0.6 GtCO <sub>2</sub> y <sup>-1</sup> from the point of 1.5°C stabilization, which would reduce the budget by around 20 GtCO <sub>2</sub> by 2100. Comyn-Platt et al. (2018) <sup>[[#fn:r121|121]]</sup> include carbon and methane emissions from permafrost and wetlands and suggest the 1.5°C remaining carbon budget is reduced by 116 GtCO <sub>2</sub> . Additionally, Mahowald et al. (2017) <sup>[[#fn:r122|122]]</sup> find there is possibility of 0.5–1.5 GtCO <sub>2</sub> y <sup>-1</sup> being released from aerosol-biogeochemistry changes if aerosol emissions cease. In summary, these additional Earth system feedbacks taken together are assessed to reduce the remaining carbon budget applicable to 2100 by an order of magnitude of 100 GtCO <sub>2,</sub> compared to the budgets based on the assumption of a constant TCRE presented in Table 2.2 ( ''limited evidence, medium agreement'' ), leading to overall ''medium confidence'' in their assessed impact. After 2100, the impact of additional Earth system feedbacks is expected to further reduce the remaining carbon budget ( ''medium confidence'' ).

The uncertainties presented in Table 2.2 cannot be formally combined, but current understanding of the assessed geophysical uncertainties suggests at least a ±50% possible variation for remaining carbon budgets for 1.5°C-consistent pathways. By the end of 2017, anthropogenic CO <sub>2</sub> emissions since the pre-industrial period are estimated to have amounted to approximately 2200 ±320 GtCO <sub>2</sub> ( ''medium confidence'' ) (Le Quéré et al., 2018) <sup>[[#fn:r123|123]]</sup> . When put in the context of year-2017 CO <sub>2</sub> emissions (about 42 GtCO <sub>2</sub> yr <sup>-1</sup> , ±3 GtCO <sub>2</sub> yr <sup>-1</sup> , ''high confidence'' ) (Le Quéré et al., 2018) <sup>[[#fn:r124|124]]</sup> , a remaining carbon budget of 580 GtCO <sub>2</sub> (420 GtCO <sub>2</sub> ) suggests meeting net zero global CO <sub>2</sub> emissions in about 30 years (20 years) following a linear decline starting from 2018 (rounded to the nearest five years), with a variation of ±15–20 years due to the geophysical uncertainties mentioned above ( ''high confidence'' ).

The remaining carbon budgets assessed in this section are consistent with limiting peak warming to the indicated levels of additional warming. However, if these budgets are exceeded and the use of CDR (see Sections 2.3 and 2.4) is envisaged to return cumulative CO <sub>2</sub> emissions to within the carbon budget at a later point in time, additional uncertainties apply because the TCRE is different under increasing and decreasing atmospheric CO <sub>2</sub> concentrations due to ocean thermal and carbon cycle inertia (Herrington and Zickfeld, 2014; Krasting et al., 2014; Zickfeld et al., 2016) <sup>[[#fn:r125|125]]</sup> . This asymmetrical behaviour makes carbon budgets path-dependent in the case of a budget and/or temperature overshoot (MacDougall et al., 2015) <sup>[[#fn:r126|126]]</sup> . Although potentially large for scenarios with large overshoot (MacDougall et al., 2015) <sup>[[#fn:r127|127]]</sup> , this path-dependence of carbon budgets has not been well quantified for 1.5°C- and 2°C-consistent scenarios and as such remains an important knowledge gap. This assessment does not explicitly account for path dependence but takes it into consideration for its overall confidence assessment.

This assessment finds a larger remaining budget from the 2006–2015 base period than the 1.5°C and 2°C remaining budgets inferred from AR5 from the start of 2011, which were approximately 1000 GtCO <sub>2</sub> for the 2°C (66% of model simulations) and approximately 400 GtCO <sub>2</sub> for the 1.5°C budget (66% of model simulations). In contrast, this assessment finds approximately 1600 GtCO <sub>2</sub> for the 2°C (66th TCRE percentile) and approximately 860 GtCO <sub>2</sub> for the 1.5°C budget (66th TCRE percentile) from 2011. However, these budgets are not directly equivalent as AR5 reported budgets for fractions of CMIP5 simulations and other lines of evidence, while this report uses the assessed range of TCRE and an assessment of the non-CO <sub>2</sub> contribution at net zero CO <sub>2</sub> emissions to provide remaining carbon budget estimates at various percentiles of TCRE. Furthermore, AR5 did not specify remaining budgets to carbon neutrality as we do here, but budgets until the time the temperature limit of interest was reached, assuming negligible zero emission commitment and taking into account the non-CO <sub>2</sub> forcing at that point in time.

In summary, although robust physical understanding underpins the carbon budget concept, relative uncertainties become larger as a specific temperature limit is approached. For the budget, applicable to the mid-century, the main uncertainties relate to the TCRE, non-CO <sub>2</sub> emissions, radiative forcing and response. For 2100, uncertain Earth system feedbacks such as permafrost thawing would further reduce the available budget. The remaining budget is also conditional upon the choice of baseline, which is affected by uncertainties in both historical emissions, and in deriving the estimate of globally averaged human-induced warming. As a result, only ''medium confidence'' can be assigned to the assessed remaining budget values for 1.5°C and 2.0°C and their uncertainty.

<div id="section-2-2-2-2-block-2"></div>

<span id="table-2.2"></span>
<!-- START TABLE -->
'''Table 2.2:'''

<span id="the-assessed-remaining-carbon-budget-and-its-uncertainties."></span>
'''The assessed remaining carbon budget and its uncertainties.'''

The assessed remaining carbon budget and its uncertainties. Shaded blue horizontal bands illustrate the uncertainty in historical temperature increase from the 1850–1900 base period until the 2006–2015 period as estimated from global near-surface air temperatures, which impacts the additional warming until a specific temperature limit like 1.5°C or 2°C relative to the 1850–1900 period. Shaded grey cells indicate values for when historical temperature increase is estimated from a blend of near-surface air temperatures over land and sea ice regions and sea-surface temperatures over oceans.
<!-- TABLE -->
{| class="wikitable"
|-
! Additional Warming since<br />
2006–2015 [°C] <sup>(1.)</sup>
! Approximate Warming since<br />
1850–1900 [°C] <sup>(1.)</sup>
! colspan="3"| Remaining Carbon Budget<br />
(Excluding Additional<br />
Earth System Feedbacks <sup>(5.)</sup> )[G t CO <sub>2</sub> from 1.1.2018] <sup>(2.)</sup>
! colspan="6"| Key Uncertainties and Variations <sup>(4.)</sup>
|-
|
| colspan="3"| Percentiles of TCRE <sup>(3.)</sup>
| Earth System Feedbacks <sup>(5.)</sup>
| Non-CO <sub>2</sub> scenario variation <sup>(6.)</sup>
| Non-CO <sub>2</sub> forcing and response uncertainty
| TCRE<br />
distribution uncertainty <sup>(7.)</sup>
| Historical temperature uncertainty <sup>(1.)</sup>
| Recent emissions uncertainty <sup>(8.)</sup>
|-
|
| 33rd
| 50th
| 67th
| [GtCO <sub>2</sub> ]
|-
| 0.3
|
| 290
| 160
| 80
| rowspan="15"| Budgets on the left are reduced by about –100 on centennial time scales
|
|-
| 0.4
|
| 530
| 350
| 230
|
|-
| 0.5
|
| 770
| 530
| 380
|
|-
| 0.53
| ~1.5°C
| 840
| 580
| 420
| ±250
| –400 to +200
| +100 to +200
| ±250
| ±20
|-
| 0.6
|
| 1010
| 710
| 530
|
|-
| 0.63
|
| 1080
| 770
| 570
|
|-
| 0.7
|
| 1240
| 900
| 680
|
|-
| 0.78
|
| 1440
| 1040
| 800
|
|-
| 0.8
|
| 1480
| 1080
| 830
|
|-
| 0.9
|
| 1720
| 1260
| 980
|
|-
| 1
|
| 1960
| 1450
| 1130
|
|-
| 1.03
| ~2°C
| 2030
| 1500
| 1170
|
|-
| 1.1
|
| 2200
| 1630
| 1280
|
|-
| 1.13
|
| 2270
| 1690
| 1320
|
|-
| 1.2
|
| 2440
| 1820
| 1430
|
|}
<!-- END TABLE -->

# Chapter 1 has assessed historical warming between the 1850–1900 and 2006–2015 periods to be 0.87°C with a ±0.12°C likely (1-standard deviation) range, and global near-surface air<br />
temperature to be 0.97°C. The temperature changes from the 2006–2015 period are expressed in changes of global near-surface air temperature.
# Historical CO <sub>2</sub> emissions since the middle of the 1850–1900 historical base period (mid-1875) are estimated at 1940 GtCO <sub>2</sub> (1640–2240 GtCO <sub>2</sub> , one standard deviation range) until end 2010. Since 1 January 2011, an additional 290 GtCO <sub>2</sub> (270–310 GtCO <sub>2</sub> , one sigma range) has been emitted until the end of 2017 (Le Quéré et al., 2018).
# TCRE: transient climate response to cumulative emissions of carbon, assessed by AR5 to fall likely between 0.8–2.5°C/1000 PgC (Collins et al., 2013), considering a normal distribution consistent with AR5 (Stocker et al., 2013). Values are rounded to the nearest 10 GtCO <sub>2</sub> .
# Focussing on the impact of various key uncertainties on median budgets for 0.53°C of additional warming.
# Earth system feedbacks include CO <sub>2</sub> released by permafrost thawing or methane released by wetlands, see main text.
# Variations due to different scenario assumptions related to the future evolution of non-CO <sub>2</sub> emissions.
# The distribution of TCRE is not precisely defined. Here the influence of assuming a lognormal instead of a normal distribution shown.
# Historical emissions uncertainty reflects the uncertainty in historical emissions since 1 January 2011.

<span id="overview-of-1.5c-mitigation-pathways"></span>