Extending the relationship between global warming and cumulative carbon emissions to multi-millennial timescales

Thomas L. Frölicher1 and David J. Paynter2

1Environmental Physics, ETH Zürich, Switzerland, 2Geophysical Fluid Dynamics Laboratory, Princeton, USAthomas.froelicher@usys.ethz.ch

In a wide set of future carbon emissions scenarios,

Earth System Model (ESM) simulations and theoretical

arguments indicate an approximately linear relationship

between cumulative carbon emissions and projected

global mean temperature over the 21st century and

beyond. Any global temperature target therefore implies

a limited carbon emissions budget. On multi-millennial

Motivation(a) 1000 yr simulation of GFDL ESM2M, with prescribed atmospheric CO2 increasing at a rate

1 %/yr from 286 ppm to 745 ppm (year 99 of the simulation) when global warming is 2°C

above preindustrial levels, after which carbon emissions stop.

(b) Existing data from 12 CMIP5-ESMs and from 8 EMICs. The temperature in year 1000 for

the CMIP5-ESMs and EMICs are estimated using available 1% increasing CO2 experiments:

Methods

T1000[°C] = ECS[°C] ln((emis99[Gt C] af1000 / 2.12 Gt C ppm-1 + CO2,PI[ppm])/CO2,PI) / ln(2)

ECS: Equilibrium climate sensitivity; emis99: Cumulative carbon emissions in year 99; CO2,PI: Preindustrial CO2; af1000: Airborne fraction of anthropogenic carbon emissions

GFDL ESM2M simulates additional global warming of 0.5°C after carbon emissions are stopped at 2°C

Time (years)1000010001000

Phase I Phase II Phase III

Glo

bal m

ean

tem

pera

ture

cha

nge

(°C

)

0

1

2

3

4

5b)

Time (years)1000010001000

Com

patib

le c

umul

ativ

e ca

rbon

em

issi

ons

(Gt C

)

0

400

800

1200

1600

a)2000

Time (years)1000010000

N, R

, R-N

(W

m-2)

0

2

3

4

5

c)

Phase I Phase II Phase III

N

R - N

R

1

100

Equi

libriu

m te

mpe

ratu

re

CMIP5-ESMs also show a post-emissions increase in temperature, whereas EMICs suggest a decrease

Time (years)1000010001000

Glo

bal m

ean

tem

pera

ture

cha

nge

(°C

)

0

1

2

3

5

6

4

Phase I Phase II Phase III

a) CMIP5-ESMs

Time (years)1000010001000

Phase I Phase II Phase III

b) EMICs

Glo

bal m

ean

tem

pera

ture

cha

nge

(°C

)

0

1

2

3

5

6

4 T mean (simulated)

GFDL ESM2M

T max (estimated)

T min (estimated)

T mean + std (estimated)

T mean - std (estimated)T mean (estimated)

Individual models (simulated)

War

min

g af

ter c

arbo

n em

issi

ons

stop

page

T 1‘00

0 - T

99 (°

C)

-1.6

-0.8

0.0

1.6

2.4

0.8

0.90.80.60.4 0.5 0.7Realized warming fraction: T99 / ECS99

GFDL ESM2MCMIP5-ESMs

EMICs

r2 = 0.80

r2 = 0.24

a)

Glo

bal m

ean

tem

pera

ture

cha

nge

(°C

)

0.0

0.4

0.8

1.2

2.4

1.6

2.0T10‘000 = 2.1°C

T99 = 2.0°C

T1‘000 = 2.5°C

Cumulative carbon emissions (Gt C)16008000 400 20001200

Cumulative carbon emissions for 2°C global warming (Gt C)16008000 400 2000

GFD

LE

SM

2MC

MIP

5-E

SM

sE

MIC

s

TCRE ECRE MCREmean +std-std mean +std-std mean +std-std

b)

1200

1947

1558

1854

1388

1328

1465

1189

1590

1760

timescales when carbon emissions tape off, the coefficient relating global warming to cumulative

carbon emissions is assumed to be approximately constant or slowly decreases. This results out

of modeling studies with ESMs of Intermediate Complexity (EMICs) suggesting that global

mean temperature will either stabilize or decline post CO2 emissions. However, EMICs represent

relevant components of the Earth System, such as cloud feedbacks or ocean physics in a simpli-

fied manner and often at low resolution. Here we estimate the multi-millennial temperature re-

sponses to cumulative carbon emissions for wide a range of ESMs of different complexities. Re

f Frölicher, TL, Paynter, DJ, 2015, Extending the relationship between global warming and cumulative carbon emis-sions to multi-millennial timescales. Environ. Res. Lett, in press. Frölicher, TL, Winton, M, Sarmiento, JL, 2014, Continued global warming after CO2 emissions stoppage, Nature Climate Change, 4, 40-44.

20% lower quota on cumulative carbon emissions

0

1

2

3

4

51000 2000 3000 4000 5000 6000 7000 8000

Cumulative total anthropogenic CO2 emissions from 1870 (GtCO2)

Tem

pera

ture

ano

mal

y re

lativ

e to

186

1–18

80 (°

C)

0 500 1000 1500 2000Cumulative total anthropogenic CO2 emissions from 1870 (GtC)

2500

2050

2100

2100

2030

2050

2100

21002050

2030

2010

2000

1980

1890

1950

2050

RCP2.6 HistoricalRCP4.5RCP6.0RCP8.5

RCP range1% yr

-1 CO2

1% yr -1 CO2 range

Fig. 2: Time series of (a) compatible cumulative carbon emissions, (b) simulated (phase I and II) and estimated (phase III) global mean temperature changes and estimated equilibrium temperature changes, and (c) radiative forcing, ocean heat uptake and the difference between radiative forcing and ocean heat uptake. The radiative forcing has been calculated using the simplified expression R = 5.35 ln(CO2(t)/CO2(t=0) with CO2(t=0) = 286 ppm.

Fig. 3: Global mean temperature changes simulated (phase I) and estimated (phases II and III) by (a) 12 CMIP5 CMIP5-ESMs and (b) 8 EMICs. Fig. 4: Relationship between the realized warming fraction, T99/ECS99, in year 99 and the global temperature change over the period 99-1000 after carbon emissions tape off.

Fig. 5: (a) Relationship between global warming and cumulative carbon emissions in GFDL ESM2M. (b) Cumulative carbon emissions to remain below 2°C global warming as simulated and estimated by GFDL ESM2M, CMIP5-ESMs and EMICs for TCRE, for equilbirum climate responses to cumulative carbon emissions (ECRE), and multi-millennial climate responses to cumulative carbon emissions (MCRE).

Conclusions1. GFDL ESM2M simulates an increase in global mean surface temperature by 0.5°C after carbon

emissions are stopped at 2°C global warming, implying an increase in the coefficient relating

global warming to cumulative carbon emissions on multi-millennial timescales.

2. GFDL ESM2M also suggest a 20% lower quota on cumulative carbon emissions to achieve a

policy-driven limit on global warming.

3. CMIP5-ESMs qualitatively agree on these results. However, EMICs suggest a post-emissions

decrease in temperature, because of a smaller simulated realized warming fraction.

4. Two new metrics (ECRE and MCRE) are introduced that better characterize the long-term

temperature responses to cumulative carbon emissions.