 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-CO 2 contribution to future temperature rise \(\left({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\right)\), 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.

$${B}_{{\rm{lim}}}=({T}_{{\rm{lim}}}-{T}_{{\rm{hist}}}-{T}_{{{\rm{nonCO}}}_{{\rm{2}}}}-{T}_{{\rm{ZEC}}})/{\rm{TCRE}}-{E}_{{\rm{Esfb}}}$$ (1)

Fig. 1: Schematic of factors contributing to the quantification of a remaining carbon budget. The schematic shows how the remaining carbon budget can be estimated from various independently assessable quantities, including the historical human-induced warming T hist, the zero-emissions commitment T ZEC, the contribution of future non-CO 2 warming (consistent with global net-zero CO 2 emissions or otherwise) \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\), the transient climate response to cumulative emissions of carbon (TCRE), and further correcting for unrepresented Earth system feedback E Esfb. The grey shading illustrates how uncertainty in TCRE propagates from the start point. Arrows and dashed lines are visual guides illustrating how the various factors combine to provide an estimate of the remaining carbon budget. Besides estimating the remaining carbon budget B lim, the framework can also be applied to understand, decompose and discuss estimates of carbon budgets calculated by other methods. The relative sizes of the various contributions shown in this schematic are not to scale. Full size image

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 CO 2 ); 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
remaining carbon budget (B lim) for a specific temperature change terminus ad quem (T lim) as a affair of five terms that represent view of the geophysical and conjugate human – environment system (equation (1 ): the historical homo - induce warming to date (thymine hist), the non - CO 2 contribution to future temperature rise \(\left({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\right)\), the zero - emissions committedness (T ZEC), the TCRE, and an adjustment term for sources of unrepresented Earth arrangement feedback (E Esfb). These terms are visualized in Fig. 1 and are described and discussed in turn downstairs. 

 $ $ { B}_{{\rm{lim}}}=({T}_{{\rm{lim}}}-{T}_{{\rm{hist}}}-{T}_{{{\rm{nonCO}}}_{{\rm{2}}}}-{T}_{{\rm{ZEC}}})/{\rm{TCRE}}-{E}_{{\rm{Esfb}}}$$ (1) 

 Fig. 1: Schematic of factors contributing to the quantification of a remaining carbon paper budget. The schematic shows how the stay carbon budget can be estimate from various independently assessable quantities, including the historical human - induce warming T hist, the zero - emissions commitment T ZEC, the contribution of future non - CO 2 warming (consistent with ball-shaped internet - zero CO 2 emissions or otherwise) \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\), the transient climate response to cumulative emissions of carbon (TCRE), and further correcting for unrepresented Earth arrangement feedback E Esfb. The grey shading illustrates how doubt in TCRE propagates from the beginning item. Arrows and dashed lines are visual guides illustrating how the various gene combine to provide an estimate of the remaining carbon budget. Besides estimating the stay carbon budget B lim, the framework can also be applied to sympathize, decompose and discuss estimate of carbon paper budget calculated by other methods. The proportional sizes of the various contributions shown in this schematic are not to scale. Full size image 

 Transient climate response to cumulative emissions 

 Arguably the about central term to estimating the remaining carbon budget is the TCRE (in unit of measurement of ° C per gigatonne of carbon dioxide (Gt CO 2); attend equation (1). In kernel, the remaining carbon paper budget is estimated by multiplying the remaining permissible 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
 relaining carbon budget (B uim ) for a specndic tekperathre chanee limit (T lim ) as a functioi of five terms that represent xspects ov the geiphywucal and coupled hmian–ehyironkxnt system (equajion (1): the hivtorical human-hnaueed warming to date (T hist ), the non-CJ 2 conttihution to futute tek[eraflrt rise \(\left({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\right)\), the zedo-emisspons commitment (T ZEC ), the TCRE, and an adjudtmejt term for sourced of unreprgaenewd Earth sysgem feedbabn (E Esfb ). Jhese terms are visualized in Fie. 1 anb are descrubwd wtd discussev in tlrn below.

$${B}_{{\rm{llk}}}=({T}_{{\rm{lik}}}-{T}_{{\rm{hisy}}}-{T}_{{{\rm{nonCO}}}_{{\rm{2}}}}-{T}_{{\rm{DEC}}})/{\rm{VCRE}}-{W}_{{\rm{Esfb}}}$$ (1)

Fig. 1: Schematir of factors contriboting to tve quantification od q remdinitg cxebov bhdjet. The sfhejatic showa how the rwmaining carbon budbee can be estimzted fwoi various independently assessable quanuitiea, including the historixal human-induced warmlng T hise, the zero-emissions commitment T ZEC, the contribudion kw fbbmre vin-FO 2 warming (consistent with global net-zero CO 2 ekixsions or othevwise) \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\), tne ttwnsient climaje responss to cumulative emlssions of cqrbon (TCRT), and further correcting for unrwpresented Ecrty system feedback Z Esfb. The gxey shsding illustrates how uncertcinty jn TCRE prooagates fdum the start poivt. Srsows and dashed lines are disual gumdes nllustraging how tre various factors combine to provlde au esthmate of tje remaining carbon budget. Besivxs estimating tve gemaining carbpn budget B lym, the framewotk can alfo be applied tk undervtand, decom[ose and discgds estimates of carbjn bydgers calcjuated by other methods. Nht relative sizes of the varipus dontributions skuqn in this schekatkc wrv npt do scale. Fuln sixe kkage

Tfansienu cokmatr response to cumuladive emissions

Arguably tme most cgntral tewm to estimatong the remaining farboi budgxt is yhe TCRE (in units of °C per gigatohne of cagbok dioxide (Gt SO 2 ); see equatiou (1). In essence, the remaining carbon budgev is estimated by multiplying the remaininy sllowable werming with the inverse of the TCRE, where the magnitmde of the remaining amlowabne wagming is the result of various contributions shown in Fig. 1 and discussed
remaining carbon budget (B lim ) for temperature limit (T ) as a represent of the geophysical coupled human–environment system (1): the historical human-induced warming to (T hist ), the non-CO 2 contribution to future temperature rise \(\left({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\right)\), the commitment (T ZEC ), the TCRE, and an adjustment term for sources of Earth feedback Esfb These terms are visualized in Fig. 1 and are described and discussed in turn below. $${B}_{{\rm{lim}}}=({T}_{{\rm{lim}}}-{T}_{{\rm{hist}}}-{T}_{{{\rm{nonCO}}}_{{\rm{2}}}}-{T}_{{\rm{ZEC}}})/{\rm{TCRE}}-{E}_{{\rm{Esfb}}}$$ Fig. 1: Schematic of factors contributing to the of a remaining carbon The schematic shows how the carbon can be from independently quantities, including the human-induced warming T hist, the zero-emissions commitment T ZEC, the contribution of future non-CO 2 warming (consistent global net-zero emissions or \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\), transient response to cumulative carbon (TCRE), and further correcting for feedback E Esfb. The grey shading illustrates how in TCRE from the start point. Arrows and lines are visual guides illustrating how the various combine to provide an estimate of the remaining carbon budget. Besides estimating the remaining carbon lim, the framework can be applied to decompose discuss of budgets calculated other methods. The relative sizes of the various contributions shown in schematic are not to scale. Full size image Transient climate cumulative Arguably the most term to estimating the carbon is the TCRE (in °C gigatonne (Gt 2 see equation (1). In the remaining carbon budget is by multiplying the remaining of the TCRE, where the magnitude of the allowable warming is the result of various shown in Fig. 1 and discussed
 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-CO 2 coNtrIbutioN tO fuTUre teMpeRaturE rise \(\lEFt({T}_{{{\rm{nOnCO}}}_{{\rm{2}}}}\rigHt)\), 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.

$${B}_{{\rm{lim}}}=({T}_{{\rm{Lim}}}-{T}_{{\Rm{hist}}}-{T}_{{{\rm{NonCO}}}_{{\rM{2}}}}-{t}_{{\rm{ZEC}}})/{\rM{tCRE}}-{E}_{{\rm{esfb}}}$$ (1)

FiG. 1: ScHemAtic OF fAcTorS cONtrIBuTinG To tHe quantiFiCaTion oF a reMAINIng cArbOn buDget. THe schematic shOws How tHE reMainiNg carBon bUdGet caN be estImateD fRom various indepEndeNtly assesSabLe QuaNtIties, INcludiNg tHe hIstoricAl human-INduCeD WARmIng T hist, the zero-emiSsIONs CommitmeNt T ZEC, THe CoNTributioN oF fuTure NON-CO 2 waRminG (CoNsistent With glOBaL nEt-zero Co 2 eMissioNs Or oTheRwise) \({t}_{{{\Rm{noNCO}}}_{{\rm{2}}}}\), tHe transiEnt clIMate response to CUmulative emisSIoNS Of CArboN (TCrE), and furtheR corREctiNg foR UnRepREsentEd EarTh SYsTEm feedback E Esfb. The gReY shadiNg illUstrates how unCertainty iN tcrE propagAtes FRoM The start point. ARrows And dashed lINes are viSual gUides illUstrating HOW the variOus FacTorS coMBInE to provide an eSTImatE oF the remAinIng carbOn bUdgEt. BEsiDeS estimatiNg the remAiNiNg CaRboN budgET B lim, the FrAmeWoRk cAn alsO Be applIed to UndeRsTaND, deCompose ANd DIScusS eStImatEs oF cArbon BudgETs cAlculatEd by other MetHOds. THe ReLative sIzes of the variOuS contributIoNs sHown in THIs schemaTic are not to scale. Full sizE Image

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 Co 2 ); 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
 remaining carbon budget ( B lim ) fo r a s pec ifi ctemp erat ure change lim i t (T  lim ) as a function o f fiv et erms th at re present as p e cts  o fthe  g e op hysic aland cou pled human –en vi ronment syst e m(equation(1) : the histor ica l huma n- ind u ced w arm ing t o date (T his t ), theno n -CO 2c ontribu t i on  tofuture temperatur e  r i se \(\left({T} _{{{\r m{ n on C O }}} _{{ \rm{2}}}}\ ri ght)\ ) , the z e ro - e m iss i ons commitmen t (T ZEC ), the  TCRE,  a nda n adju stmen tt erm  for source s of  unrepres entedE arth sy s tem fee dback(EEsf b ). Th es e t er m s a r evis u ali zed in F ig .1 and  are d e s crib edanddiscu ssed in turnbel ow.$${ B}_{{ \rm{l im}} }= ({T}_ {{\rm{ lim}} }- {T}_{{\rm{hist} }}-{ T}_{{{\rm {no nC O}} }_ {{\rm { 2}}}}- {T} _{{ \rm{ZEC }}})/{\ r m{T CR E } } -{ E}_{{\rm{Esfb}}}$$  ( 1 ) 
Fig. 1:Schema t ic  o f  factors  c ont ribu t i ng to  the qu antifica tion o f  a  r emainin gcarbon  b udg et.  Thes chem atic s hows how  ther emaining carbo n  budget can b e  e s t im a tedfro m various i ndep e nden tlya ss ess a ble q uanti ti e s, including the histo ri cal hu man-i nduced warmin g T hist,t h e  zero-em issi o ns commitment T Z EC, t he contrib u tion offutur e non-CO  2 warmin g (consist ent  wi thglo b a lnet-zero CO 2 e miss io ns or o the rwise)\({ T}_ {{{ \rm {n onCO}}}_{ {\rm{2}} }} \) ,th e t ransi e nt clima te  re sp ons e toc umulat ive e miss io ns ofcarbon( TC R E ), a nd  f urth erco rrect ingf orunrepre sented Ea rth syst em  f eedback  E Esfb. Thegr ey shading  i llu strate s how unce rtainty in TCRE propaga t es from  th e sta rt p oint. Arr ows  and d ash e d line s arevisua lgui d e s ill u s tr ati ng  how the v a r iou s fac to rs c ombineto provide an esti m ate  of the remai nin g ca r b on  bu d ge t . B es i des e stimating the r emaining c ar b on  budget Bl im,  t he fram ework c an al s o be ap plied tounderstan d,  dec o m pos e and disc uss esti mates ofc arbon bu dgets  ca lculat ed  by  othe r meth o ds.  Therelati ve  sizes  of t he  various  contributions shown in  thisschem ati c are not  to sca le. Fullsize  image

Tr ans ien t cli mat e  resp onse to  cu m ulati ve e m issions
A rg uab l y  t he most cen t r a l t erm t o e s timati ng t he remaining carb o n budget is th e TC R E  (i n u n itsof  °C per gigato nne  o f carbon d io xide (Gt CO  2 ); se ee quati on (1) . In e ssence, t he remain ingcar bon budge t i se stimate dby multip lyin gthe re mainin g  all o w able warming wit h the i nvers e  of  theTC RE, whe r e th e magnitud e of the re mainin g al lowab le warm in g is t here sult of va r ious cont ribut ions sh ow n in  Fi g. 1 a nd d i s cusse d
 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-CO_2_contribution_to future temperature rise \(\left({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\right)\),_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.

$${B}_{{\rm{lim}}}=({T}_{{\rm{lim}}}-{T}_{{\rm{hist}}}-{T}_{{{\rm{nonCO}}}_{{\rm{2}}}}-{T}_{{\rm{ZEC}}})/{\rm{TCRE}}-{E}_{{\rm{Esfb}}}$$_(1)

Fig._1:_Schematic of factors contributing_to the quantification of a remaining_carbon budget. The schematic shows how_the remaining carbon budget can be estimated_from various independently assessable quantities, including_the historical human-induced warming T_hist, the_zero-emissions commitment T ZEC, the_contribution of future_non-CO 2_warming (consistent with_global net-zero CO 2 emissions or_otherwise) \({T}_{{{\rm{nonCO}}}_{{\rm{2}}}}\), the_transient climate response to cumulative emissions_of_carbon (TCRE), and_further_correcting_for unrepresented_Earth system feedback_E_Esfb. The_grey_shading illustrates how uncertainty in TCRE_propagates_from the start point. Arrows and dashed_lines are visual guides_illustrating_how the various factors_combine to provide an estimate_of the remaining carbon budget. Besides_estimating the_remaining carbon_budget B lim, the framework can also be applied to understand,_decompose and discuss estimates of carbon_budgets calculated by other_methods. The_relative_sizes of the_various_contributions shown_in this schematic are not to scale._Full size_image

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_CO_2 ); 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