ARTICLESPUBLISHED ONLINE 18 SEPTEMBER 2017 | DOI 10.1038/NGEO3031Emission budgets and pathways consistent withlimiting warming to 1.5 CRichard J. Millar1,2*, Jan S. Fuglestvedt3, Pierre Friedlingstein1, Joeri Rogelj4,5, Michael J. Grubb6,H. Damon Matthews7, Ragnhild B. Skeie3, Piers M. Forster8, David J. Frame9and Myles R. Allen2,10TheParisAgreementhasopeneddebateonwhetherlimitingwarmingto1.5 Ciscompatiblewithcurrentemissionpledgesandwarming of about 0.9 C from the mid-nineteenth century to the present decade. We show that limiting cumulative post-2015CO2 emissions to about 200GtC would limit post-2015 warming to less than 0.6 C in 66 of Earth system model membersof the CMIP5 ensemble with no mitigation of other climate drivers, increasing to 240GtC with ambitious non-CO2 mitigation.We combine a simple climate–carbon-cycle model with estimated ranges for key climate system properties from the IPCCFifth Assessment Report. Assuming emissions peak and decline to below current levels by 2030, and continue thereafteron a much steeper decline, which would be historically unprecedented but consistent with a standard ambitious mitigationscenario RCP2.6, results in a likely range of peak warming of 1.2–2.0 C above the mid-nineteenth century. If CO2 emissionsarecontinuouslyadjustedovertimetolimit2100warmingto1.5 C,withambitiousnon-CO2 mitigation,netfuturecumulativeCO2 emissions are unlikely to prove less than 250GtC and unlikely greater than 540GtC. Hence, limiting warming to 1.5 C isnotyetageophysicalimpossibility,butislikelytorequiredeliveryonstrengthenedpledgesfor2030followedbychallenginglydeep and rapid mitigation. Strengthening near-term emissions reductions would hedge against a high climate response orsubsequent reduction rates proving economically, technically or politically unfeasible.The aim of Paris Agreement is ‘holding the increase in globalaverage temperature to well below 2 C above pre-industriallevels and pursuing e orts to limit the temperature increaseto 1.5 C’ ref. 1. The Parties also undertook to achieve this goal byreducingnetemissions‘toachieveabalancebetweenanthropogenicsources and removals by sinks of greenhouse gases in the secondhalf of this century’, and hence implicitly not by geo-engineeringplanetary albedo. Under what conditions is this goal geophysicallyfeasibleHuman-induced warming reached an estimated 0.93 C 0.13 C; 5 95 percentile range above mid-nineteenth-centuryconditions in 2015 and is currently increasing at almost 0.2 C perdecade2. Combined with the e ects of El Nio and other sourcesof natural variability, total warming exceeded 1 C for the first timein 2015 and again in 20163. Average temperatures for the 2010sare currently 0.87 C above 1861 80, which would rise to 0.93 Cshould they remain at 2015 levels for the remainder of the decade.With a few exceptions4,5, mitigation pathways that could achievepeak or end-of-century warming of 1.5 C have thus far receivedlittleattention.Eventhe‘Paris,increasedambition’scenarioofref.6results in CO2 emissions still well above zero in 2100, and hence alow chance of limiting warming to 1.5 C.Long-term anthropogenic warming is determined primarily bycumulativeemissionsofCO2 refs7 10theIPCCFifthAssessmentReport IPCC-AR5 found that cumulative CO2 emissions from1870hadtoremainbelow615GtCfortotalanthropogenicwarmingto remain below 1.5 C in more than 66 of members of the5th Coupled Model Intercomparison Project CMIP5 ensemble ofEarth system models ESMs11 see Fig. 1a. Accounting for the545GtC that had been emitted by the end of 201412, this wouldindicate a remaining budget from 2015 of less than seven years ofcurrentemissions,whilecurrentcommitmentsundertheNationallyDeterminedContributionsNDCsindicate2030emissionsclosetocurrent levels13.The scenarios and simulations on which these carbon budgetswere based, however, were designed to assess futures in the absenceof CO2 mitigation, not the very ambitious mitigation scenariosand correspondingly small amounts of additional warming abovepresent that are here of interest. Furthermore, many mitigationscenariosbeginreductionsin2010andarealreadyinconsistentwithpresent-day emissions, complicating the comparison with pledgesfor 2030.Carbon budgets and scenarios for ambitious climate goalsThe black cross on Fig. 1a shows an estimate of human-inducedwarming, which excludes the impact of natural fluctuations such asElNio,in20150.93 0.13 Crelativeto1861 80;5 95 percentilerange and pre-2015 cumulative carbon emissions 545 75GtCsince 1870; 1 s.d.. Although both quantities are individuallyconsistent with the CMIP5 ensemble, in the mean CMIP5 responsecoloured lines cumulative emissions do not reach 545GtC untilafter 2020, by which time the CMIP5 ensemble-mean human-induced warming is over 0.3 C warmer than the central estimateforhuman-inducedwarmingto2015.Inestimatingtheoutstanding1College of Engineering, Mathematical and Physical Sciences, University of ter, ter EX4 4QF, UK. 2Environmental Change Institute, University ofOxford, South Parks Road, Oxford OX1 3QY, UK. 3Center for International Climate and Environmental ResearchOslo CICERO, PO Box 1129, Blindern,0318 Oslo, Norway. 4Energy Program, International Institute for Applied Systems Analysis IIASA, 2361 Laxenburg, Austria. 5Institute for Atmosphericand Climate Science, ETH Zurich, Universittstrasse 16, 8006 Zurich, Switzerland. 6Institute for Sustainable Resources, University College London, LondonWC1H 0NN, UK. 7Concordia University, Montreal, Qubec H3G 1M8, Canada. 8School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK.9New Zealand Climate Change Research Institute, Victoria University of Wellington, PO Box 600, Wellington, New Zealand. 10Department of Physics,University of Oxford, Oxford OX1 3PJ, UK. *e-mail richard.millarouce.ox.ac.ukNATURE GEOSCIENCE | VOL 10 | OCTOBER 2017 | 741 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.ARTICLES NATUREGEOSCIENCE DOI 10.1038/NGEO30310123451,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000Temperature change relative to 1861−1880 CCumulative total anthropogenic CO2emissions from 1870 GtCO22090s2090s2090s2090s2000sTotal human-induced warmingCO2-induced warming430−480480−530530−580580−720720−1,000BaselinesRCP2.6RCP4.5RCP8.5RCP6.01.5 C TEB budget, 66 of models−101234Temperature change relative to 2010−2019 CCumulative total anthropogenic CO2emissions from 2015 GtCO2Cumulative total anthropogenic CO2emissions from 2015 GtC00 1,000 2,000 3,000 4,000 5,000 6,000 7,000−1,000−500 500 1,000 1,500 2,0002090sCO2-induced warming2090s2090s2090s2010sTotal human-induced warming0.6 C TEB budget, 66 of models0 500 1,000 1,500 2,000Cumulative total anthropogenic CO2emissions from 1870 GtC2,500abFigure1| Warming as a function of cumulative CO2 emissions in the CMIP5 ensemble. a, Cumulative emissions since 1870 and warming relative to theperiod 1861–80, adapted from figure 2.3 of ref. 11. The red and grey plumes show the 5–95 range of model response under the RCPs and 1 annual CO2increase scenarios, respectively. Thick coloured lines show ensemble-mean response to the RCP forcing scenarios. Ellipses show cumulative emissions andwarming in 2100 for dif_ferent categories of future emissions scenario. Black cross shows uncertainty in 2015 human-induced warming and observedcumulative emissions. b, As for a, but with cumulative emissions given since January 2015 and warming relative to the period 2010–2019. Dashed verticalgrey lines show the threshold-exceedance budgets TEBs below which over 66 of models have warmed less than 1.5 C above 1861–80 in a, and lessthan 0.6 C above 2010–19 in b.carbon budget for 1.5 C, this is an important discrepancy. IPCC-AR5 also calculated the percentiles of the CMIP5 distributionthat exceeded given thresholds of warming relative to the averageof 1986 2005 Table 12.3 of ref. 14, adding a further 0.61 Cto express these relative to 1850 1900. However, this referenceperiod and the GCM ensemble used in this table are not identicalto the ESM ensemble used to derive estimates of the carbonbudget, for which a volcano-free reference period is preferred, tofocusonhuman-inducedwarming.Moreover,sincethediscrepancyin warming between ESMs and observations emerges only after2000, expressing warming relative to the 1986 2005 referenceperiod does not entirely resolve it and also does not address thesmall underestimation of cumulative emissions to date. Figure 1bshows an alternative analysis of the CMIP5 ensemble to assessthe remaining carbon budget for an additional 0.6 C of warmingbeyond the current decade, a possible interpretation of ‘pursuinge orts to limit the temperature increase to 1.5 C’ in light ofestimatedhuman-inducedwarmingtodate.Themedianresponseofthe CMIP5 models indicates allowable future cumulative emissionsthreshold-exceedance budget or TEB15 of 223GtC for a further0.6 C warming above the 2010 2019 average, and a 204GtCremaining TEB from 2015 to keep warming likely below thisvalue meaning, by the time cumulative emissions from 2015 reach204GtC,66ofCMIP5modelshavewarmedlessthan0.6 Cabovethe present decade, consistent with the ology for assessingthe 2 C carbon budget in IPCC-AR516. Given uncertainty inattributable human-induced warming to date, di erences betweenobservational products and true global surface air temperature17,and the precise interpretation of the 1.5 C goal in the ParisAgreement for example, the choice of pre-industrial referenceperiod which temperatures are defined relative to18, budgetscorresponding to a range of levels of future warming should also beconsidered see Table 1 and the Supplementary Ination.TEBs are useful because peak CO2-induced warming is afunction shown by the grey plume in Fig. 1 of cumulativeCO2 emissions and approximately independent of emission path,although threshold behaviour, such as sudden carbon release fromthawingpermafrost,mightcomplicatethisrelationship19.Thisdoesnotapplytonon-CO2 forcing,whichisrelativelymoreimportantforambitious mitigation scenarios. The rapid warming from the 2000sto the 2030s in CMIP5 arises partly from strong increases in netnon-CO2 forcing over this period in the driving RCPscenarios, dueto simulated rapid reductions in cooling aerosol forcing. It remainsunclear whether this increase in non-CO2 forcing will be observedif future reductions in aerosol emissions occur because present-daye ective non-CO2 forcing is still highly uncertain20. Table 2 showsbudgets for thresholds of future warming in the CMIP5 ensembleunder an RCP2.6 scenario, a stabilization scenario in which non-CO2 forcing across the rest of the century remains closer to the2010 2019 average than in the RCP8.5 scenario. This allows moreCO2-induced warming for the same total, increasing the medianTEB of the CMIP5 distribution for an additional 0.6 C to 303GtCand the 66th percentile to 242GtC.In many current ambitious mitigation scenarios for example,RCP2.6 ref. 21, dark blue lines in Fig. 2, substantial CO2emission reductions begin in 2010, such that both emissions andforcing are already inconsistent with observed climate state andemission inventories to date. The thick dark green lines in Fig. 2show an amended version of RCP2.6 that is more consistent withcurrent emissions and estimated present-day climate forcing. Thisscenario, hereafter referred to as RCP2.6-2017, assumes the sameproportional rates of change of both CO2 and other anthropogenicforcing components as in the standard RCP2.6 scenario from2010, but with the mitigation start date delayed by seven years to2017 following the RCP8.5 scenario22 between 2010 2017. This ismore representative of a possible mitigation pathway from todaymany nations are already planning on policy action to reduceemissions over the 2015 2020 period, in anticipation of achievingtheir NDC commitments in the future. Total anthropogenicradiative forcing peaks in 2050 at 3.41Wm 2 in RCP2.6-2017, asopposed to in 2043 at 3.00Wm 2 under RCP2.6. The grey linesrepresentemissionspathwaysfromtheIPCC430 480ppmscenariocategory23,24 butwithproportionaldecreasesinradiativeforcingalsodelayed by seven years to start in 2017.Figure 2c shows the implications of these scenarios for futurewarming, uated with a simple climate model that reproducesthe response of the CMIP5 models to radiative forcing underambitious mitigation scenarios Supplementary s. Likeother simple climate models, this lacks an explicit physical linkbetweenoceanicheatandcarbonuptake.Itallowsaglobalfeedback742 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.NATURE GEOSCIENCE | VOL 10 | OCTOBER 2017 | 10.1038/NGEO3031 ARTICLESTable 1 | Future cumulative budgets GtC from January 2015for percentiles of the distribution of RCP8.5 simulations ofCMIP5modelsandvariouslevelsoffuturewarmingabovethemodelled 2010–2019 average.Warming above2010–2019 average CPercentiles of CMIP5 models90 66 50 33 100.3 80 106 119 142 1890.4 107 133 155 172 2420.5 137 168 186 209 2990.6 164 204 223 250 3330.7 199 245 256 289 3870.8 231 279 301 333 4380.9 274 321 348 376 5051.0 306 358 382 421 5791.1 332 395 416 464 653Percentiles correspond to the percentage of CMIP5 models that have greater cumulativeemissions for the given level of warming.between temperature and carbon uptake from the atmosphere, butno direct link with net deforestation. It also treats all forcing agentsequally, in the sense that a single set of climate response parametersis used in for all forcing components, despite some evidence ofcomponent-specific responses25,26. We do not, however, attempt tocalibrate the model directly against observations, using it instead toexploretheimplicationsofrangesofuncertaintyinemissions12,andforcing and response derived directly from the IPCC-AR5, whichare derived from multiple lines of evidence and, importantly, donotdependdirectlyontheanomalouslycooltemperaturesobservedaround 2010. Non-CO2 forcing and the transient climate responseTCR co-vary within AR5 ranges to consistently reproducepresent-day externally forced warming s, and as inFig. 1b, we quote uncertainties in future temperatures relative tothis level.The limits of the green plume in Fig. 2c show peak warmingunder the RCP2.6-2017 scenario is likely between 1.24 2.03 C1.12 1.99 C for 2100 warming given a 2015 externally forcedwarming of 0.92 C. The IPCC-AR5 did not propose a ‘best-estimate’ value of the TCR, but using a central value of 1.6 Cthemedianofalog-normaldistributionconsistentwithIPCC-AR5likely ranges, the typical shape of most reported TCR distributionsin ref. 16, RCP2.6-2017 gives a median peak warming of 1.55 Cabove pre-industrial 1861 1880 mean and 1.47 C in 2100,approximately consistent with as likely as not 50 probability ofwarming below 1.5 C in