Supporting Information: The integrated Global Temperature change Potential (igtp) and relationships between emission metrics

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1 Supporng Informaon: Te negraed Global Temperaure cange Poenal (GTP) and relaonsps beween emsson mercs Glen P. Peers *, Borgar Aamaas, Tere Bernsen,2, Jan S. Fuglesved Cener for Inernaonal Clmae and Envronmenal Researc Oslo (CICERO), PB 29 Blndern, 38 Oslo, Norway 2 Deparmen of Geoscences, Unversy of Oslo, Norway * Correspondng Auor, glen.peers@ccero.uo.no Insananeous response of a susaned emsson versus e negraed response of a pulse emsson Impulse response funcons can be used o caracerse e response of a sysem (suc as radave forcng or emperaure) o an arbrary npu (suc as emssons or radave forcng) (-3), RF ( ) E ( s) R ( s) ds (SI) were, n s example, e npu s an arbrary emsson E and e response s e radave forcng RF. Emsson mercs are ofen consruced for a pulse emsson, E =E P =δ (Drac dela funcon) and Equaon (SI) becomes, P RF ( ) R ( ) (SI2) wc as e mpulse response funcon as e response. I s no uncommon o consruc emsson mercs for a susaned emsson, E =E S =H (Heavsde sep funcon), RF S ( ) H ( s) R ( s) ds (SI3) A propery of a convoluon and Heavsde sep funcon s a RF S P ( ) H ( s) R ( s) ds R ( s) ds RF ( s) ds AGWP ( ) (SI4)

2 wc sows a e nsananeous forcng of a susaned emsson (lef and sde) s equal o e negraed forcng of a pulse emssons (AGWP, rg and sde). By drec analogy, e same olds for e emperaure response, T S S ( ) RF ( s) RT ( s) ds AGWP ( s) RT ( s) ds AGTP( ) (SI5) so a e nsananeous emperaure perurbaon o a susaned emsson s equal o e negraed emperaure perurbaon o a pulse emsson. Analycal Expressons for e AGWP, AGTP, AGTP, and AOHP We derve analycal expressons for AGWP, AGTP, and AGTP based on e layered EBM. For a layered EBM, R T s a sum of exponenals as n Equaon (5) n e man arcle K g R T ( ) exp (SI6) and as e propery a K g (derved by negrang o nfny w a sep forcng). Te varables g represen e gans and e decay mes of e equvalen conrol sysem analogue (4). Te AGWP are derved by subsung Equaons () and (2) no (3) all from e man arcle. Te AGWP for CO 2 s AGWP ) A K a a exp (SI7) 2 CO ( 2 CO2 and for a speces w a sngle adusmen me, AGWP ( ) A exp (SI8) Smlarly, e AGTP can be found by subsung Equaons (), (2), and (SI6) no (4). Te AGTP for CO 2 s AGTP ) A CO ( CO2 J J K a g a g exp exp exp 2 2 and for a speces w a sngle adusmen me, (SI9) 5 J g AGTP ( ) ACO exp 2 exp (SI) 5 More deals and dscusson of e AGWP and AGTP can be found n Fuglesved e al. (5).

3 We derve analycal expressons for e AGTP by negrang Equaons (SI9) and (SI). 52 Te AGTP for CO 2 s, exp ) ( 2 2 J CO CO g a A AGTP 54 J K g a 2 exp exp... (SI) 55 and for speces w a sngle adusmen me 56 J g A AGTP exp exp ) ( (SI2) 57 We calculae AOHP as e dfference n Equaon (2) n e man arcle

4 6 Paper Hasselmann e al 993 Sne e al (25) Hasselmann e al 993 Hasselmann e al 993 Bernsen and Fuglesved (28) Boucer and Reddy (28) L and Jarvs (29) Reference (2) (6) (2) (2) (7) (8) (4) Model Scenaro A Analycal ECHAM, 2xCO 2 GFDL, 2xCO 2 Analycal HadCM3 HadCM3 (yr) (yr) (yr) 476. g (K/W/m 2 ) g 2 (K/W/m 2 ) g 3 (K/W/m 2 ).483 λ (K/W/m 2 ) c (W/K/m 2 ) c 2 (W/K/m 2 ) c 3 (W/K/m 2 ) 3.4 (m/yr) (m/yr).6 Table SI : Te parameers of e dfferen emperaure IRFs (Equaon SI6) used o es e robusness of our resuls. 64

5 65 66 Addonal Fgures Fgure SI : Te IRFs of e speces consdered n e man arcle sowng a e adusmen mes cover fve orders of magnude: a very sor adusmen me (blac carbon, BC,.2yr or wee), sor adusmen me (meane, CH 4, 2yr), medum adusmen me (nrous oxde, N 2 O, 4yr), and long adusmen me (sulpur exafluorde, SF 6, 3,2yr). We also sow e mulple amosperc responses for CO 2 demonsrang a CO 2 as componens a approxmae e amosperc response of CH 4 (8.5 years CO 2, 2 years CH 4 ) and N 2 O (72.9 years, 4 years). One-ff of e CO 2 remans permanenly n e amospere. Noe a a log scale s used w a mnmum value of. years so a only a par of e amosperc response of BC can be vsualzed

6 Fgure SI 2: Te AGTP for RF and RF (CO2) w an addonal spl no e conrbuon from e fas and slow me scales of e EBM sowng were e dfferences n e mercs arse, see Equaon (SI2)

7 Fgure SI 3: Te AOHP for a pulse emsson of and for a pulse emsson of CO 2 -equvalen of. Te oal AOHP s sown as well as e AOHP n e op and boom ocean layers. For early mes, e pulse emsson of e CO 2 equvalen of pus energy no e ocean layers dfferenly and for laer mes (wen e me-orzon s greaer an e adusmen me of ), CO 2 connues o pu energy n e sysem leadng o a more perssen AOHP for CO 2 - equvalen emssons. 93

8 Fgure SI 4: Te emperaure n e dfferen layers from a pulse emsson of and a pulse emsson of CO 2 -equvalen of, compare w Fgures SI4. 97

9 98 99 Fgure SI 5: Te energy flux ou of e frs layer bac o space (T /λ) and no e deeper ocean ((T -T 2 )) for a pulse emsson of and a pulse emsson of CO 2 -equvalen of, compare w Fgure SI4, Fgure SI5, and Equaon (8). 2

10 3 4 5 Fgure SI 6: Te GTP values for e dfferen IRFs (Table SI) normalzed relave o e Boucer and Reddy IRF sowng relave smlary n e values. 6 7

11 8 9 Fgure SI 7: Te GTP values for e dfferen IRFs (Table SI) normalzed relave o e Boucer and Reddy IRF sowng large varaons relave e GTP values (Fgures SI3).

12 References. Enng IG (27) Laplace ransform analyss of e carbon cycle. Envronmenal Modellng & Sofware 22(): Hasselmann K, Sausen R, Maer-Remer E, & Voss R (993) On e cold sar problem n ransen smulaons w coupled amospere-ocean models. Clmae Dynamcs 9(2): Wgley TML (99) A smple nverse carbon cycle model. Global Bogeocem. Cycles 5(4): L S & Jarvs A (29) Long run surface emperaure dynamcs of an A-OGCM: e HadCM3 4 CO 2 forcng expermen revsed. Clmae Dynamcs 33(6): Fuglesved JS, e al. (2) Transpor mpacs on amospere and clmae: Mercs. Amosperc Envronmen 44: Sne KP, Fuglesved JS, Halemaram K, & Suber N (25) Alernaves o e global warmng poenal for comparng clmae mpacs of emssons of greenouse gases. Clmac Cange 68: Bernsen T & Fuglesved JS (28) Global emperaure responses o curren emssons from e ranspor secors. Proceedngs of e Naonal Academy of Scences 5: Boucer O & Reddy MS (28) Clmae rade-off beween blac carbon and carbon doxde emssons. Energy Polcy 36: