Stephen E. Schwartz

April 4, 2018

https://www.bnl.gov/envsci/schwartz/ ses@bnl.gov

HOW LONG DOES ANTHROPOGENIC COSTAY IN THE ATMOSPHERE?

2

Environmental and Climate SciencesSeminar Series

OUR COLLECTIVE ENERGY USE

Equivalent to 100 watts

Standard diet US adult: 2000 Calories (k cal) per day

Equivalent to 100 people!

Per capita energy US use: 10,000 watts

And all these “people” are exhaling CO !2

100 100-watt light bulbs, 24 – 7

10,000 5000 0Time, yearsbefore 2005

Mix

ing

ratio

, ppm

1800 1900 2000Year

1960 20101985Year

350

300

250

200

400

50,000100,000150,000Time, years before 1950

Mixing ratio, ppm

350

300

250

200

400

CARBON DIOXIDE OVER TIME

ContemporaneousAnthropoceneHoloceneLast glacial cycle

Mauna LoaAntarcticaAntarctica

Lüthi (2008)Etheridge (1996)

Monnin (2001, 2004)Siegenthaler (2005)

MacFarling Meure (2006)Keeling (1995),updated

Dlugokencky (2018)

Antarctica, Cape Grim

GlobalAntarctica

Mauna Loa

Preindustrial

12

10

8

6

4

2

0

CO

2 em

issi

on, P

g yr

-1

200019501900185018001750

Total Fossil + cement Land use change

(Linear ramp 1750-1850)

ANTHROPOGENIC CARBON DIOXIDE EMISSIONS

Houghton and Nassikas, 2017Boden et al., 2017

700

600

500

400

300

200

100

0Cum

ulat

ive

CO

2 em

issi

on, P

g

200019501900185018001750

600

550

500

450

400

350

300

CO

2 , ppm

Total Fossil + cement Land use change

CUMULATIVE ANTHROPOGENIC CO2 EMISSIONS2

700

600

500

400

300

200

100

0Cum

ulat

ive

CO

2 em

issi

on, P

g

200019501900185018001750

600

550

500

450

400

350

300

CO

2 , ppm

Total cumulative emissions

CUMULATIVE ANTHROPOGENIC CO2 EMISSIONS2

Antarctica, Cape Grim Global CO2 in air

Nature’s “subsidy” of our carbon dioxide emissions

AND ANTHROPOGENIC ATMOSPHERIC STOCK

Motivation for this study

DECAY OF EXCESS ATMOSPHERIC CO2 AFTER CESSATION OF EMISIONS

Calculated and redrawn from recent publications

2

ses - in review

Frac

tion

rem

aini

ng in

atm

osph

ere

Time after cessation, years

Abrupt Cessation

Convolution of IRF

Matthews 08 2000 PgC Plattner 08 CLIMBER2 Cao 10 Matthews 08 500 PgC Zickfeld 12 Solomon 09 Knutti 12 Gillett 11 Frölicher 10

Hare 06

Allen 09 Zickfeld 13 Ensemble RCP6

Joos 13 Bern3D LPJ Ref Matthews 08 Pulse 2000 PgC Joos 13 CLIMBER2 LPJ Joos 13 Multimodel mean Matthews 08 Pulse 500 PgC Joos 13 NCAR CSM1.4 Joos 13 MPI ESM

Raupach 14

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2100806040200

This study

∞

50

70

100

150

200

500

Lifetime (~54 yr) is much shorter than given in prior studies.

The amount of time it takes until the CO2 concentration in the air recovers substantially toward its original concentration [in the absence of emissions]

2

0 200 400 600 800 1000

Original CO2 noitartnecnoc

300

400

500

600

700

CO2 (ppm

v)

0

20

40

60

80

100

Emis

sion

s re

mai

ning

(%)

Present model

1000 Pg pulse

11 Pg pulse

Archer et al., 2009

CO2 DECAY, MULTIPLE MODELS2Response to pulse emission

DEFINITIONS

Turnover time: Ratio of Stock to Flux out

ito = Si

j Fij

Requires a budget. Need to specify which stock, which fluxes.

Adjustment time: Inverse of fractional removal rate

iadj =

SidSidt

, Qant = 0

Requires a model.

Lifetime: Time required, in absence of anthropogenic emissions, until the CO2 concentration in the air recoverssubstantially toward its original concentration.Qualitative.

The global CO budget2

CO2 STOCKS, FLUXES, AND ANNUAL CHANGE2

ses, in review

Preindustrial

3700 – 420

Surface sediment150

119.4120

Respiration

Gross primaryproductivity

70.670

Stock, PgFlux, Pg yr -1

Mixed-layer ocean906.1 + 32.2

100 m

3583 m

2034 + 73

Deep ocean35,917 + 124

44.750

5.3 ± 1.855.149.8

Concentration, µmol kg-1

2250 + 9

0.6Ftm

Sd

FmaFam

FmdFdm Fpc

Sm

FtaFat

Marine biota3

3700 – 422Fossil fuels & cement

Total ocean36,823 + 156

589.4 + 269.2AtmosphereSa

2300 – 228 + 219

Terrestrial vegetation,soil, and detritusSt

Surface sediment150

Steady state

Do nothing cycleDisequilibrium!

τ = 589/(120 + 70) ≈ 3 yr

τ = 36000/55 ≈ 600 yr

Nearlyequal Nearly equal

Near equilibrium

Detailed balance

Measured

Universal deposition velocity

Universal piston velocity

CO2 STOCKS, FLUXES, AND ANNUAL CHANGE2

ses, in review

Preindustrial

Anthropogenicperturbation

9.9 ± 0.51.4 ± 0.7

3700 – 420

Surface sediment150

119.4120

Respiration

Gross primaryproductivity Land

sinkLand use change 70.670

Stock, PgFlux, Pg yr -1

Mixed-layer ocean

1.8 ± 0.6

Annual change, Pg yr -1

906.1 + 32.2+0.55100 m

3583 m

32.0 29.8

2034 + 73

Deep ocean35,917 + 124

44.750

5.3 ± 1.855.149.8

Concentration, µmol kg-1

2250 + 9

0.2

4.0 ± 1.1

+1.6

0.6Ftm

Sd

FmaFam

FmdFdm Fpc

Sm

QluFtaFat

QffFat

Fam Fma

Fmd Fdm

Marine biota3

3700 – 422Fossil fuels & cement

+2.1 ± 0.6

Total ocean36,823 + 156

+5.2 ± 0.4589.4 + 269.2AtmosphereSa

2300 – 228 + 219

Terrestrial vegetation,soil, and detritusSt

Surface sediment150

± 0.6

± 0.061.2 ± 0.1

µmol kg yr-1 -1

τ = (269 + 32)/[(9.9 + 1.4) – (5.2 + 0.55)] = 54 ± 10 yr

τ = 32.2/29.8 ≈ 1 yr

Turnover time = Stock / [Emissions – Growth]

Global CO model2

Preindustrial

TRANSFER COEFFICIENTS FOR ANTHRO CO22

kam = Fam,pi / Sa,pi; global mean deposition velocity

kmdzm = kdmzd = vp; global mean piston velocity, 5.5 m yr-1

k By differenceat Q tot - dSa/dt( )/Sa,ant ] 2016= [ - dSm/dt - dSd/dt

From obs’d global heat uptake rate

UniversalAcid dissocchemistryKam = (dSa/dSm)eq , a known function of Sa, 5–10kma = kamKam;

Transfer coefficients, yr-1-1 Anthropogenic

emissions3700 – 420

Surface sediment150

0.6

Flux, Pg yr -1

Mixed-layer ocean100 m

3583 m Deep ocean

5.3

5.35.3

0.6Ftm

Sd

Fma,net

Fdm,net

Fpc

Sm

QluQ ffkat

kam kma

kmd kdm

Marine biota

Fossil fuels & cement

AtmosphereSa

St

at,netF0.6

0.01480.119 0.6–1.2

0.055 0.0015

2018-1218

9.9 ± 0.51.4 ± 0.7

Terrestrial vegetation,soil, and detritus

AssumptionAlert!

Assumed sink to terrestrial biosphere plus deep ocean agrees with sink based on measured increase in atmospheric stock and inventoried emissions.

Uncertainty fromuncertainty in emission

and variation in atmospheric growth rate

8

6

4

2

0

-2300250200100500

From observations and emissions Law Dome, Cape Grim Global CO2 in air

τ = 54.3 yr

+ Smant(Sa

ant ), Pg

Qan

t+

S mant

– d

(Saan

t)/d

t, Pg

yr-1

SINK RATE INTO TERRESTRIAL BIOSPHERE PLUS DEEP OCEAN

THE DIFFERENTIAL EQUATIONS

Four coupled ordinary differential equations.

dSadt

= kamSa + kmaSm kat Sa Spi( ) Ftmpi +Qant (t)

dSmdt

= kamSa kmaSm kmdSm + kdmSd +Ftmpi

dSddt

= kmdSm kdmSd +Fpc

dStdt

= kat Sa Spi( )

Fpc

Slightly nonlinear because kmidepends weakly on Si.

kmaSm

Atmospheric CO2 decreases exponentially with same time constant irrespective of time of cessation of emissions.

2

MODELED CO2 MIXING RATIO2Abrupt cessation at three start times

440

420

400

380

360

340

320

300

280

CO

2, pp

m

215021002050200019501900185018001750278

Model emissions

Law Dome, Cape Grim Global CO2 in air

Historical Zero

Observations

= 53.8 yr

exp(-t/ )

53.5 yr

53.1 yr

CO2 can be stabilized by reduction of emissions to present removal rate into terrestrial biosphere and deep ocean, about half of current emissions (nature’s subsidy).

2

MODELED CO2 MIXING RATIO2Abrupt reduction of emissions

440

420

400

380

360

340

320

300

280

CO

2, pp

m

215021002050200019501900185018001750278

Model emissions

Law Dome, Cape Grim Global CO2 in air

Historical Reduced

Observations

Usefully defined as sum of anthro atmospheric and mixed-layer stocks upon sum of net fluxes to deep ocean and terrestrial biosphere.

Virtually constant (52 – 54 yr) over Anthropocene, increasing to ~ 65 yr as flux into deep ocean decreases.

TURNOVER TIME OF ANTHROPOGENIC CO22

Agrees with multiple measures of life time.

=Sa +SmFat +Fmd,net

AM

70

65

60

55

50

45

40

Adju

stm

ent t

ime

, yr

21002050200019501900185018001750

Time of cessation or reduction of emissions

Reduction CessationHistorical AM

AM

Cessation AAM

Exponential fits Sa + Sma m Sma

BudgetAnalyticalNumerical

toant ant

NEAR EQUILIBRIUM BETWEEN ATMOSPHERE AND OCEAN MIXED LAYER

40353025201510

50

-5

Mix

ed la

yer s

tock

, Pg

C

215021002050200019501900185018001750

Anthropogenic Mixed-Layer Stock

Equilibrium Model Difference

Time constant for equilibration of atmosphere and ocean mixed layer is short, ~ 1 yr.These two compartments are thus in near equilibrium and are usefully considered a single compartment.

Assumed sink to terrestrial biosphere plus deep ocean agrees with sink based on measured and modeled increase in atmospheric stock and inventoried emissions.

Uncertainty fromuncertainty in emission

and variation in atmospheric growth rate

8

6

4

2

0

-2300250200100500

Historical Cessation

From observations and emissions Law Dome, Cape Grim Global CO2 in air

τ = 54.3 yr

+ Smant(Sa

ant ), Pg

Qan

t+

S mant

– d

(Saan

t)/d

t, Pg

yr-1

SINK RATE INTO TERRESTRIAL BIOSPHERE PLUS DEEP OCEAN

Comparison withObservations and

Other Models

Prescribed Land Use EmissionsModeled Land Use EmissionsPrescribed Land Use Emissions

with modeled nitrogen cycle

400

380

360

340

320

300

280

CO

2, pp

m

2000196019201880

Present model

Law Dome, Cape Grim Global CO2 in air

COMPARISON WITH OBSERVATIONS AND OTHER MODELSCO Mixing Ratio in Air2

Friedlingstein et al., 2014

COMPARISON WITH OBSERVATIONS AND OTHER MODELS

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

ObservationMean of 13 modelsPresent model

Net

oce

an u

ptak

e Pg

yr-1

20402000196019201880

Gruber

Wang

Net Ocean Uptake Rate

15 CMIP5 models; observational data from Wang et al. (2016), Gruber et al. (2019)

4

3

2

1

020502000195019001850

Terre

stria

l upt

ake

Pg y

r-1 Present model

Gruber

COMPARISON WITH OBSERVATIONS AND OTHER MODELSTerrestrial uptake rate

Gruber et al. (2019) Difference of emissions and ocean uptake rateModels from Friedlingstein et al. (2006)

CONCLUSIONS AND IMPLICATIONS

Atmospheric CO2 could be stabilized at its present value by halving current emissions.

2

The lifetime of excess atmospheric CO2 is found to be about 54 years by multiple measures.

2

This lifetime is much shorter than present estimates.

All this would be good news for strategies to meet climate change targets.

The simple model with 3 observationally determined parameters does a very credible job!

DECAY OF EXCESS ATMOSPHERIC CO2 AFTER CESSATION OF EMISIONS

Calculated and redrawn from recent publications

2

ses - in review

Frac

tion

rem

aini

ng in

atm

osph

ere

Time after cessation, years

Abrupt Cessation

Convolution of IRF

Matthews 08 2000 PgC Plattner 08 CLIMBER2 Cao 10 Matthews 08 500 PgC Zickfeld 12 Solomon 09 Knutti 12 Gillett 11 Frölicher 10

Hare 06

Allen 09 Zickfeld 13 Ensemble RCP6

Joos 13 Bern3D LPJ Ref Matthews 08 Pulse 2000 PgC Joos 13 CLIMBER2 LPJ Joos 13 Multimodel mean Matthews 08 Pulse 500 PgC Joos 13 NCAR CSM1.4 Joos 13 MPI ESM

Raupach 14

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2100806040200

This study

∞

50

70

100

150

200

500

Lifetime (~54 yr) is much shorter than given in prior studies.