SUPPLEMENTARY INFORMATION

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1 In the formt provided y the uthors nd unedited. SUPPLEMENTARY INFORMATION ARMOUR (7) :: SUPPLEMENTARY INFORMATION Energy udget constrints on climte sensitivity in light of inconstnt climte feedcks DOI:.3/NCLIMATE37 Kyle C. Armour School of Ocenogrphy nd Deprtment of Atmospheric Sciences, University of Wshington, Settle, WA 995 This document contins the following supplementry mteril: (i) Fig. S showing the clcultion of CO forcing nd equilirium climte sensitivity (ECS) within the CMIP5 models; nd Tle S, summry of CMIP5 results. (ii) Fig. S showing the ehvior of the energy lnce model (EBM) tht cptures the inconstnt ehvior of climte feedcks seen in CMIP5 models; Fig. S3 showing the EBM numericl simultions; Fig. S demonstrting tht the methods used for estimting ECS within the min text work well when pplied to synthetic dt; nd Tle S summrizing EBM prmeters. (i) CO forcing, ECS nd ECS infer for the CMIP5 models Model F (Wm ) ECS ( C) ECS infer ( C) ACCESS ACCESS cc-csm CnESM CCSM. 3.. CNRM-CM CSIRO-Mk GFDL-CM GISS-E-H GISS-E-R.5.3. HdGEM-ES inmcm 3... IPSL-CM5A-LR IPSL-CM5A-MR IPSL-CM5B-LR MIROC5...3 MIROC-ESM MPI-ESM-LR MPI-ESM-MR MRI-CGCM NorESM-M. 3.. Tle S Estimtes of F, ECS nd ECS infer for CMIP5 models. Forcing due to douling of tmospheric CO concentrtion (F ) nd equilirium climte sensitivity (ECS) for CMIP5 models (s estimted from rupt CO qudrupling simultions). Vlues of ECS infer re from yer of %/yr CO rmping simultions (clculted s 3-yer men over yers 5-5). NATURE CLIMATE CHANGE 7 Mcmilln Pulishers Limited, prt of Springer Nture. All rights reserved.

2 S - ARMOUR (7) :: SUPPLEMENTARY INFORMATION c ACCESS- ACCESS-3 cc-csm- ΔQ (Wm - ) ΔQ (Wm - ) ΔQ (Wm - ) d ΔQ (Wm - ) e f CnESM CCSM CNRM-CM5 ΔQ (Wm - ) ΔQ (Wm - ) g h i CSIRO-Mk3-- GFDL-CM3 GISS-E-H ΔQ (Wm - ) ΔQ (Wm - ) ΔQ (Wm - ) Figure S Regressions used to estimte CO forcing nd equilirium climte sensitivity for CMIP5 models. Chnge in glol-men top-of-tmosphere rditive imlnce ( Q) plotted ginst chnge in glol-men ner-surfce ir temperture ( T ) for rupt CO qudrupling simultion of ech CMIP5 model. Blue points show nnul mens, nd drk lue line shows -yer running verge. Red line shows liner regression through yers -5. Green line shows liner regression over yers -5. Blck line goes from the y-intercept of the red line (equl to F ) to the x-intercept of the green line (equl to ECS). The models consistently evolve long or elow the lck line, indicting tht climte sensitivity inferred vi eqution () under trnsient wrming (ECS infer ) is roustly smller thn ECS.

3 ARMOUR (7) :: SUPPLEMENTARY INFORMATION S - 3 j ΔQ (Wm - ) k l GISS-E-R HdGEM-ES inmcm ΔQ (Wm - ) ΔQ (Wm - ) m n o IPSL-CM5A-LR IPSL-CM5A-MR IPSL-CM5B-LR ΔQ (Wm - ) ΔQ (Wm - ) ΔQ (Wm - ) p ΔQ (Wm - ) q r MIROC5 MIROC-ESM MPI-ESM-LR ΔQ (Wm - ) ΔQ (Wm - ) s ΔQ (Wm - ) t u MPI-ESM-MR MRI-CGCM3 NorESM-M ΔQ (Wm - ) ΔQ (Wm - ) Figure S (continued).

4 S - ARMOUR (7) :: SUPPLEMENTARY INFORMATION (ii) Energy lnce model results. Q (Wm - ) nger th eq/" ( spce eq eq +(" ) s steeper (more n c d.5.5 (F-Q)/F T/ECS Figure S Energy lnce model (EBM) response to rupt CO qudrupling., Glol-men surfce temperture nomly., Chnge in glol-men top-of-tmosphere rditive imlnce plotted ginst glol-men surfce temperture nomly. c, Glol-men surfce temperture nomly (normlized y ECS), plotted ginst glol energy imlnce sutrcted from rditive forcing (normlized y F ). d, The quntity λ/λ eq =. Blue points show nnul men vlues. Red line in, shows the slope λ over the first few yers (pproximtely equl to the liner regression through yers -5); green line shows the evolution of dq/dt s equilirium is pproched (pproximtely equl to liner regression over yers -5); lck line goes from the y-intercept of the red line (equl to F ) to the x-intercept of the green line (equl to ECS). EBM prmeter vlues (Tle S) re the ensemle men of vlues found y fitting the EBM to the response of suset of CMIP5 models to rupt CO qudrupling (from ref. 9) nd F = 3. Wm from ref.. EBM prmeter Description CMIP5 men nd rnge c s Upper ocen het cpcity. [. 9.7] W yr m K c d Deep ocen het cpcity 9 [5 7] W yr m K γ Ocen het uptke efficiency.7 [.9.] W m K ɛ Ocen het uptke efficcy. [.3.] Tle S EBM prmeter vlues. Vlues show men nd rnge of vlues fit to CMIP5 models (from ref. 9).

5 ARMOUR (7) :: SUPPLEMENTARY INFORMATION S c.5 d e under historicl forcing 3 3 under %/yr CO forcing Figure S3 EBM response to historicl forcing (left) nd %/yr CO rmping (right). Glol-men surfce temperture nomly reltive to -79 under historicl forcing. c, The quntity = λ/λ eq under historicl forcing., Glol-men surfce temperture nomly under %/yr CO rmping. d, The quntity = λ/λ eq under %/yr CO forcing. Thick lines show men nd thin lines show one stndrd devition cross ll EBM memers tht re consistent with the oservtions of T os, Q os nd F os over yers -9. e, clculted over the yers -9 of historicl forcing simultions plotted ginst clculted t yer of %/yr CO forcing; lue points show individul EBM ensemle memers, nd ll lie very ner on the one-to-one line (R =.99).

6 S - ARMOUR (7) :: SUPPLEMENTARY INFORMATION ECS ( C) Proility density ( C - )... ECS infer (eq. ) ECS (eqs.,5) true ECS ECS infer ( C) ECS ( C) Figure S EBM reltionship etween ECS nd ECS infer for individul ensemle memers (left) nd proility density functions of ECS infer, ECS nd true ECS (right)., Sctter plot of ECS ginst ECS infer for EBM ensemle (light lue points); ll points lie ner or ove the one-to-one line, indicting ECS > ECS infer on verge. The thick green curve through points shows λ/λ eq = clculted with eqution (5) using the EBM men vlue of λ /F, while thin green curves use ±σ of λ /F cross EBM ensemle memers. Curves on xes show schemticlly how the proility density function of ECS infer (lck curves on x-xes, clculted using eqution () over the s within historicl simultions) is mpped to ECS using equtions () nd (5) (green curve on y-xis)., Blck curve shows proility density for ECS infer clculted from eqution () over the s within historicl simultions. Green curve shows ECS clculted y pplying equtions () nd (5). Dshed green curve shows true proility density of ECS for the EBM ensemle memers. The proility densities re plotted s smoothed histogrms of the individul EBM ensemle memers, with wiggles result of the limited smple size.