Climate forcing from carbon emissions

Philip Goodwin1

Thanks to:Ric Williams1,Mick Follows2, Andy Ridgwell3, Stephanie Dutkiewicz2

1University of Liverpool2Massachusetts Institute of Technology, USA3University of Bristol

Rising atmospheric carbon dioxide (PCO2):Anthropogenic projection

Aims:

A) Relate emissions to ‘steady state’ PCO2

B) Consider radiative forcing

C) Consider feedbacks

– Ignore carbonate and silicate rock weathering

[IPCC 2007]

∆FPCO2

The rise in partial pressure of atmospheric CO2 (PCO2)

causes a radiative forcing (∆F) which alters climate

RELATING EMISSIONS TO PCO2

For the same ∆Iem, eventually same steady state PCO2

0

500

1000

1500

2000

2500∆I

em (

Gt C

)

0 500 1000 1500280

480

680

880

Time (years)

PC

O2 (

ppm

)

(a)

(b)

∆PCO2

Air-sea model response to a ∆Iem= 2000GtC EMISSION: Same steady state

RELATING EMISSIONS TO PCO2

Carbon in the atmosphere and ocean

Atmospheric carbon inventory:

IA=VatmxPCO2

Ocean carbon inventory:

IO=VoceanxCDIC

CO2 (Partial pressure, PCO2)

CO2 H2CO3 HCO3- CO3

2-

ATMOSPHERE

OCEAN

CDIC= CO2 + H2CO3 + HCO3- + CO3

2-

• A steady state is reached when:

oceanCO COP ][ 22 ∝

RELATING EMISSIONS TO PCO2

Emissions without ocean chemistry

OI∝

)(2 AOCO IIP +∝

ACO IP ∝2

( )OA

OA

CO

CO

IIII

PP

++

=δδ

2

2

OA

emCO II

IP+

=δδ 2ln

][ 22 COPCO ∝Steady state when:

Therefore:

Thus PCO2 proportional to total air-sea carbon:

And:

We can make a ratio:

Change in air-sea carbon is emission,δIem =δ(IA+IO):Therefore we can write:

)(2 AOCO IIP +∝δδ

PCO2

[CO2]

Special case;

IO=Voceanx[CO2]

Emissions with ocean chemistryRELATING EMISSIONS TO PCO2

][ 22 COPCO ∝

PCO2

[CO2] [H2CO3] [HCO3-] [CO3

2-]

OACO IIP +∝/2

At steady state:

But:

CDIC= CO2 + H2CO3 + HCO3- + CO3

2-

We must define a new inventory, IB [Goodwin et al, 2007], that accounts for the dissociation of CO2 in seawater

NO OCEAN CHEMISTRY : OCEAN CHEMISTRY

BIII O

AB +=OA II +2

2

CO

DIC

DIC

CO

PC

CPB

δδ

=WHERE:

B

emCO I

IP δδ =2lnOA

emCO II

IP+

=δδ 2ln

GCM experiment: how PCO2 links to carbon emissionRELATING EMISSIONS TO PCO2

MIT GCM

• Realistic circulation

• Realistic carbon cycling

• Monthly mean forcing

SURFACE

TEMPERATURE

(OC)

200

400

600

800

1000

1200

1400

0 1000 2000 3000 4000 5000

Carbon emission (GtC)

pCO

2 (p

pm)

MITGCM

CURRENT

EMISSIONS

CONVENTIONAL RESERVES

• Add carbon to atmosphere over ~500years

• Integrate for ~3000 years for steady state

• Measure final PCO2

RELATING EMISSIONS TO PCO2

Testing the independent analytical equation• Evaluate IB at pre-industrial steady state for MITGCM

• integrate by assuming IB remains constant [Goodwin et al, 2007]:

B

emCO I

IP ∆=∆ 2ln

200

400

600

800

1000

1200

1400

0 1000 2000 3000 4000 5000

Carbon emission (GtC)

pCO

2 (p

pm) MITGCM

Our method

CURRENT

EMISSIONS

CONVENTIONAL RESERVES

Compare to model results:

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆=

B

emif I

IPP exp

ANALYTICALEQUATION

NUMERICAL SOLUTION

RELATING PCO2 TO ∆F

How can CO2 affect climate?

Add CO2 Radiation imbalance, ∆F Temperature increases, ∆T

2ln COPF ∆=∆ α

How do PCO2 levels affect ∆F (and so ∆T)?

[Myhre et al, 1998]

Why logarithmic?

• CO2 only absorbs at certain wavelengths

• Amount of those wavelengths in atmosphere reduces with increasing PCO2

• An increase in PCO2 absorbs set fraction of what is left in the atmosphere

Therefore, write equations in log form.

RELATING EMISSIONS TO ∆F

How about Radiative forcing?

2ln COPF ∆=∆ α

0

1

2

3

4

5

6

7

8

9

0 1000 2000 3000 4000 5000

Carbon Emissions (GtC)

F (W

/m2)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

ln [p

CO

2]

GCM

Equation

27.1 −=∆ WmF per 1000Gt C

Using IPCC [2001] α, we find for MITGCM:

• The contribution of today’s emissions to the climate from 1000 to 5000 years

• cf current forcing ~1.6Wm-2 in transient state

• Possibly rising to ~7.5Wm-2 lasting for thousands of years

2ln COB

em PII

∆=∆

emB

II

F ∆=∆α

From:

We get:

Climate sensitivity of the past

Evaluate IB of GENIE model forced with palaeoconstraints from Ridgwell (2005)

The present day has a high climate sensitivity

CLIMATE SENSITIVITY

Years BP (Ma)

PCO2

(1000ppm)

∆F for a 1000GtC emission

(Wm-2)

⎟⎟⎠

⎞⎜⎜⎝

⎛=

Bem IIF α

δδ

CONSIDERING CARBON CYCLE FEEDBACKSFeedbacks from carbon cycles changes

Surface ocean

Deep ocean

Terrestrial carbon store,

AtmospherePCO2

Biological organic carbon

drawdown

Biological CaCO3

drawdown

Many factors affect PCO2 in addition to anthropogenic emissions

RELATING OTHER CARBON CYCLES TO PCO2

Testing the independent analytical relationsEvaluate IB at pre-industrial steady state and plot:

0 1000 2000 3000 4000 50000

500

1000

1500

δIem

−δIter

(GtC)

−0.1 −0.05 0 0.05 0.1 0.150

200

400

600

δCbio

+δCdis

(global average mol m3)

PC

O2 (

ppm

)

−0.02 −0.01 0 0.01 0.02 0.03250

300

350

δCCaCO3

(global average mol m3)

(a)

(b)

(c)

Terrestrial

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆−=

B

terif I

IPP exp

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆−=

B

bioif I

CVPP exp

ANALYTICAL EQUATION

NUMERICAL SOLUTION

Soft tissue

CaCO3( )

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆−

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∆−= −

−

−

B

CaCOCAOA

CaCOCAO

CAOif I

CIICVI

IPP 3)(

3)(

)( exp

CONSIDERING CARBON CYCLE FEEDBACKS

Feedbacks from carbon cycles changesPCO2 over time for: i) 2000GtC emission,

ii) Change in soft tissue biology,

iii) Change in biological CaCO3 production

PCO2

(ppm)

Time (yrs)

220

320

420

520

620

720

820

0 500 1000 1500 2000

CONSIDERING CARBON CYCLE FEEDBACKS

Feedbacks from carbon cycles changesFeedbacks combine in a non-linear way to alter PCO2

( ) ( ) ( ) ( ) 32222 CaCOCOTISSUESOFTCOEMISSIONCOoverallCO PPPP ∆+∆+∆≠∆ −

Time (yrs)

220

320

420

520

620

720

820

0 500 1000 1500 2000

PCO2

(ppm)

CONSIDERING CARBON CYCLE FEEDBACKS

Feedbacks from carbon cycles changes

30

2

0

2

0

2

0

2

CaCO

CO

TISSUESOFT

CO

EMISSION

CO

overall

CO

PP

PP

PP

PP

⎟⎟⎠

⎞⎜⎜⎝

⎛×⎟⎟

⎠

⎞⎜⎜⎝

⎛×⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛

−

Maths predicts:

280

380

480

580

680

780

880

0 500 1000 1500 2000

PCO2

(ppm)

Time (yrs)

Conclusions• Analytical link to numerical models: insight into non-linear

feedbacks

• Can compare future steady state forcing to present transient levels:

• Present climate sensitivity to carbon perturbations is large: 1.7Wm-2 per 1000Gt C for thousands of years

0

1

2

3

4

5

6

7

8

9

0 1000 2000 3000 4000 5000

Carbon Emissions (GtC)

F (W

/m2)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

ln [p

CO

2]

GCM

Equation

30

2

0

2

0

2

0

2

CaCO

CO

TISSUESOFT

CO

EMISSION

CO

overall

CO

PP

PP

PP

PP

⎟⎟⎠

⎞⎜⎜⎝

⎛×⎟⎟

⎠

⎞⎜⎜⎝

⎛×⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛

−

Why should we assume IB remains constant?

0

1000

2000

3000

4000

5000

6000

7000

0 5000 10000 15000 20000

EMISSIONS (GtC)pC

O2

(ppm

)

02468101214161820

B

pCO2B

DIC

DIC

CC

COCOB

δδ

][][

2

2=

BIII O

AB +=

IB can be expressed in terms of a carbon ‘buffer factor’, B:

By writing:

While B increases as PCO2increases; they have opposing effects on the value of IB. Causing: ∆IB<<IB

0

4000

8000

12000

16000

0 5000 10000 15000 20000

EMISSIONS (GtC)

Ib (G

tC) IbIB

VALID UNTIL ~ 5000GtC