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Carbon–concentration and carbon–climate feedbacks in
CMIP5 earth system models
Vivek Arora, George Boer, Pierre Friedlingstein, Michael Eby, Chris Jones,
James Christian, Gordon Bonan, Laurent Bopp, Victor Brovkin, Patricia
Cadule, et al.
To cite this version:
Vivek Arora, George Boer, Pierre Friedlingstein, Michael Eby, Chris Jones, et al.. Carbon–
concentration and carbon–climate feedbacks in CMIP5 earth system models. Journal of Climate,
American Meteorological Society, 2013, 26 (15), pp.5289-5314. �10.1175/JCLI-D-12-00494.1�. �hal-
03207457�
Carbon–Concentration and Carbon–Climate Feedbacks in CMIP5 Earth System Models
VIVEK K. ARORA,
a
GEORGE J. BOER,
a
PIERRE FRIEDLINGSTEIN,
b
MICHAEL EBY,
c
CHRIS D. JONES,
d
JAMES R. CHRISTIAN,
a
GORDON BONAN,
e
LAURENT BOPP,
f
VICTOR BROVKIN,
g
PATRICIA CADULE,
f
TOMOHIRO HAJIMA,
h
TATIANA ILYINA,
g
KEITH LINDSAY,
e
JERRY F. TJIPUTRA,
i
AND TONGWEN WU
j
a
Canadian Centre for Climate Modelling and Analysis, Environment Canada, University of Victoria, Victoria,
British Columbia, Canada
b
College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom
c
School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada
d
Met Office Hadley Centre, Exeter, United Kingdom
e
National Center for Atmospheric Research,
k
Boulder, Colorado
f
LSCE, IPSL, CEA, UVSQ, CNRS, Gif-sur-Yvette, France
g
Max Planck Institute for Meteorology, Hamburg, Germany
h
Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan
i
Uni Klima, Uni Research, Bergen, Norway
j
Beijing Climate Center, China Meteorological Administration, Beijing, China
(Manuscript received 24 July 2012, in final form 5 February 2013)
ABSTRACT
The magnitude and evolution of parameters that characterize feedbacks in the coupled carbon–climate
system are compared across nine Earth system models (ESMs). The analysis is based on results from bio-
geochemically, radiatively, and fully coupled simulations in which CO
2
increases at a rate of 1% yr
21
. These
simulations are part of phase 5 of the Coupled Model Intercomparison Project (CMIP5). The CO
2
fluxes
between the atmosphere and underlying land and ocean respond to changes in atmospheric CO
2
concen-
tration and to changes in temperature and other climate variables. The carbon–concentration and carbon–
climate feedback parameters characterize the response of the CO
2
flux between the atmosphere and the
underlying surface to these changes. Feedback parameters are calculated using two different approaches. The
two approaches are equivalent and either may be used to calculate the contribution of the feedback terms to
diagnosed cumulative emissions. The contribution of carbon–concentration feedback to diagnosed cumula-
tive emissions that are consistent with the 1% increasing CO
2
concentration scenario is about 4.5 times larger
than the carbon–climate feedback. Differences in the modeled responses of the carbon budget to changes
in CO
2
and temperature are seen to be 3–4 times larger for the land components compared to the ocean
components of participating models. The feedback parameters depend on the state of the system as well the
forcing scenario but nevertheless provide insight into the behavior of the coupled carbon–climate system and
a useful common framework for comparing models.
1. Introduction
Earth system models (ESMs) incorporate terres-
trial and ocean carbon cycle processes into coupled
atmosphere–ocean general circulation models (AOGCMs)
in order to represent the interactions between the car-
bon cycle and the physical climate system. Changes in
the physical climate affect the exchange of CO
2
between
theatmosphereandtheunderlyinglandandocean,
and the resulting changes in atmospheric concentration of
CO
2
in turn affect the physical climate. Aspects of the
behavior of the carbon cycle and its interaction with the
physical climate system are characterized in terms of
carbon–concentration and carbon–climate feedback pa-
rameters (Friedlingstein et al. 2006; Boer and Arora 2009;
Roy et al. 2011). Feedback parameters can be calculated
k
The National Center for Atmospheric Research is sponsored
by the National Science Foundation.
Corresponding author address: Vivek K. Arora, Canadian Cen-
tre for Climate Modelling and Analysis, Environment Canada,
University of Victoria, Victoria BC V8W 2Y2, Canada.
E-mail: vivek.arora@ec.gc.ca
V
OLUME 26 JOURNAL OF CLIMATE 1AUGUST 2013
DOI: 10.1175/JCLI-D-12-00494.1
Ó 2013 American Meteorological Society
5289
for global averages, separately over land and ocean, over
specific regions or for individual grid cells in order to
investigate their geographical distribution as in Boer
and Arora (2010). The carbon–concentration feedback
parameter is a measure of the response of the land and
ocean carbon pools to changes in atmospheric CO
2
concentration. It is a negative feedback from the per-
spective of the atmosphere, since the higher values of
atmospheric CO
2
that result from anthropogenic emis-
sions are partially offset by a loss of atmospheric carbon
to the underlying land and ocean. The carbon–climate
feedback parameter is a measure of the response to
changes in temperature and other climate variables.
The carbon–climate feedback parameter is generally
positive from the atmosphere’s perspective as higher
temperatures promote a flux of carbon from the land
and ocean into the atmosphere. The positive carbon–
climate feedback acts to reduce the capacity of the land
and ocean to take up carbon resulting i n a larger frac-
tion of anthropogenic CO
2
emissions remaining in the
atmosphere as temperatures warm. The first Coupled
Carbon Cycle Climate Model Intercomparison Project
(C
4
MIP) found that this positive carbon–climate feed-
back varied significantly across ESMs due mainly to the
differences in the behavior of terrestrial carbon cycle
components (Friedlingstein et al. 2006).
Both carbon–climate and, in particular, carbon–
concentration feedback parameters have been found
to be sensitive to the emission scenario, the state of the
system, and the approach used to calculate them (Boer
and Arora 2009, 2010; Plattner et al. 2008; Gregory et al.
2009; Zickfeld et al. 2011). As a result, values of feed-
back parameters from one scenario cannot be used, in
a quantitative way, to proje ct carbon cycle behavior
for a different emission scenario. The geographical pat-
terns of the feedback parameters are, however, found to
be reasonably robust across different emissions sce-
narios (Boer and Arora 2010) and the feedback pa-
rameters do serve to illustrate and quantify the carbon
feedback processes operating in the coupled carbon–
climate system. The dependence of the feedback pa-
rameters on emission scenario and system state means
that the comparison of the behavior of the coupled
carbon–climate system across models is more straight-
forwardly investigated for a common scenario.
The fifth phase of the Coupled Model Intercom-
parison Project (CMIP5; http://cmip-pcmdi.llnl.gov/cmip5/
forcing.html) (Taylor et al. 2012) provides a common
framework for comparing and assessing Earth s ystem
processes in the context of climate simulations. A 140-yr-
long simulation in which atmospheric CO
2
concentra-
tion increases at a rate of 1% yr
21
from preindustrial
values until concentration quadruples is a standard
CMIP experiment that serves to quantify the response
to increasing CO
2
. To isolate feedbacks, additional radi-
atively and biogeochemically coupled versions of this
‘‘1% increasing CO
2
’’ experiment are performed. In
radiatively coupled simulations increasing atmospheric
CO
2
affects the climate but not the biogeochemistry,
for which the preindus trial value of atmospher ic CO
2
concentration is prescribed. In the biogeochemically
coupled simulation the biogeoch emistry responds
to the increasing atmospheric CO
2
while the radia-
tive forcing remains at preindu strial val ues. The sim-
ulations do not inclu de th e con founding effects
of chan ges in la nd us e, non-CO
2
greenhouse gases,
aerosols, etc., and so provide a controlled experiment
with which to compare carbon–climate interactions
across models. Results from eight of the comprehen-
sive Earth system models participating in the CMIP5
intercomparison project are analyzed as well as results
from an Earth system model of intermediate com-
plexity (EMIC).
2. Feedbacks in the coupled climate–carbon system
We consider globally averaged and vertically inte-
grated carbon budget quantities. Following Boer and
Arora (2013) for the combined atmosphere–land–ocean
system the rate of change of carbon is written as
dH
G
dt
5
dH
A
dt
1
dH
L
dt
1
dH
O
dt
5 E , (1)
where the global carbon pool H
G
5 H
A
1 H
L
1 H
O
is
the sum of carbon in the atmosphere, land, and ocean
components (Pg C) and E is the rate of anthropogenic
CO
2
emission (Pg C yr
21
) into the atmo sphere. The
equations for the atmosphere, land, and ocean are
dH
A
dt
5 F
A
(T, C) 1 E,
dH
L
dt
5 F
L
(T, C), and
dH
O
dt
5 F
O
(T, C), (2)
where (F
L
1 F
O
) 52F
A
are the fluxes between the at-
mosphere and the underlying land and ocean, taken to
be positive into the components. The fluxes F are ex-
pressed as functions of surface temperature T and the
surface atmospheric CO
2
concentration C, following
Boer and Arora (2009, 2010). In the experiments ana-
lyzed here the CO
2
concentration is specified beginning
at the preindustrial value of ;285 ppm and increasing at
5290 JOURNAL OF CLIMATE VOLUME 26
1% yr
21
until concentration has quadrupled 140 years
later. The rate of change of atmospheric carbon dH
A
/dt
is specified in (1) and (2) and the loss or gain of CO
2
by
the underlying land and ocean yields an effective emis-
sion E, which serves to maintain the budget.
a. Direct/instantaneous feedback parameters
Following Boer and Arora (2009, 2010) and the ac-
companying paper by Boer and Arora (2013, hereafter
BA), the changes in atmosphere carbon budgets, from
the control simulation, in the differently coupled simu-
lations are represented as follows:
d
radiatively coupled
dH
0
A
dt
2 E
1
5 F
1
A
5G
A
T
1
, (3a)
d
biogeochemically coupled
dH
0
A
dt
2 E* 5 F
A
*
5G
A
T* 1 B
A
C
0
, and (3b)
d
fully coupled
dH
0
A
dt
2 E 5 F
0
A
52F
0
L
2 F
0
O
5G
A
T
0
1 B
A
C
0
, (3c)
which serve to define the carbon–concentration (B
A
)
and carbon–climate (G
A
) feedback parameters and as-
sume an approximately linear response of the globally
integrated surface–atmosphere CO
2
flux in terms of
global mean temperature and CO
2
concentration change.
The control simulation has no anthropogenic emissions
and a specified atmospheric CO
2
concentration C
0
of
;285 ppm. In Eq. (3), F
1
, F*, and F
0
are the flux changes;
T
1
, T*, and T
0
are the temperature changes in the radi-
atively, biogeochemically, and fully coupled simulations;
and E
1
, E*, and E are the resulting implicit emissions.
In the biogeochemically coupled simulation there is no
radiative f orcing because of increasing CO
2
so T*is
small, a lthough it is not zero. Changes in vegetation
biomass and transpiration as well as vegetation struc-
ture (e.g., changes in leaf area index and vegetation
height) and its spatial distribution (through competi-
tion between plant functional types) affect the surface
energy and wat er balance to some extent. Changes in
absorption of solar radiation can also affect climate
through changes in phytoplankton and chlorophyll al-
though phytoplankton growth parameterizations usu-
ally do not include a strong dependence on CO
2
.The
term H
0
A
5 mC
0
isthechangeinatmosphereCO
2
amount
(Pg C), which is the same for the biogeochemically, ra-
diatively, and fully coupled versions since C
0
is specified.
The term m is the mass of the atmosphere multiplied
by the ratio of molecular weight of carbon to the mean
molecular weight of air.
1
Although the feedback param-
eters are dependent on the approach used to calculate
them and also if they are determined from emissions-
or concentration-driven simulations (Gregory et al. 2009;
Zickfeld et al. 2011; Boer and Arora 2013), the as-
sumption made in Eq. (3) is that the feedback parame-
ters are the same in the three cases. It is a reasonable
assumption for the 1% CO
2
simulations considered here,
as is shown later.
Carbon budget changes for the land component par-
allel (3) but without the emissions terms as
d
radiatively coupled
dH
1
L
dt
5 F
1
L
5G
L
T
1
, (4a)
d
biogeochemically coupled
dH
L
*
dt
5 F
L
*
5G
L
T* 1 B
L
C
0
, and (4b)
d
fully coupled
dH
0
L
dt
5 F
0
L
5G
L
T
0
1 B
L
C
0
, (4c)
and similarly for the ocean component. Since F
A
5
2(F
L
1 F
O
), it follows that G
A
52(G
L
1G
O
) and
B
A
52(B
L
1 B
O
).
The feedback parameters G and B represent averaged
rates of change of the CO
2
flux F with respect to tem-
perature and concentration and indicate how the sys-
tem responds to temperature and CO
2
concentration
changes [see section 3d in Boer and Arora (2013)].
There are no terms involving C
0
in the radiatively cou-
pled simulation [Eqs. (3a) and (4a)] since the pre-
industrial value of atmospheric CO
2
concentration is
prescribed for the biogeochemistry components so
C
0
5 0 and does not affect the flux. Changes in the flux
in the radiatively coupled simulation are driven by
changes in temperature alone.
b. Integrated flux-based feedback parameters
The flux-based BA approach in section 2a differs
from the integrated flux approach of Friedlingstein
1
m 5 5:1 3 10
18
3 (12:01/28:93) ’ 2:12 3 10
18
kg 5 2:12 3 10
6
Pg,
where 5.1 3 10
18
kg is the mass of the atmosphere: 12.01 and 28.93
are the molecular weights (g mol
21
) of carbon and air, respectively,
and 1 ppmv CO
2
(1 3 10
26
volume mixing ratio) in the atmosphere
is thus equivalent to 2.12 3 10
12
kg C (or 2.12 Pg C).
1A
UGUST 2013 A R O R A E T A L . 5291
et al. (2006), who express time-integrated flux changes
(i.e., change in pool or reservoir sizes) as functions of
temperature and CO
2
concentration changes (referred
to as the FEA approach) with
d
radiatively coupled
ð
F
1
A
dt 5 g
A
T
1
, (5a)
d
biogeochemically coupled
ð
F
A
*
dt 5 g
A
T* 1 b
A
C
0
, and (5b)
d
fully coupled
ð
F
0
A
dt 5 g
A
T
0
1 b
A
C
0
(5c)
and similarly for the land and ocean components. The
connection between g and b in (5) and G and B in (3) is
g
A
5
ð
t
0
G
A
T
1
dt
T
1
(6a)
from the radiatively coupled cases (3a) and (5a); for
small T* the biogeochemically coupled simulations (3b)
and (5b) give
b
A
5
ð
t
0
(G
A
T* 1 B
A
C
0
) dt 2 g
A
T
*
C
0
’
ð
t
0
B
A
C
0
dt
C
0
.
(6b)
The FEA parameters are temperature (T
1
) and CO
2
concentration change (C
0
) weighted versions of the BA
feedback parameters. As shown in appendix A, Eqs. (3)
and (5) with two unknowns each are consistent pro-
vided that the system is linear (i.e., F
0
5 F
1
1 F*and
T
0
5 T
1
1 T*), so t hat the fully coupled case is the sum
of the radiatively and biogeochemically coupled cases
for seven of the nine models considered. For the com-
parison of feedback parameters among models, we use
results from the radiatively and biogeochemically cou-
pled simulations that have only one component, either
radiation or biogeochemistry, responding to increasing
CO
2
and that are designed to isolate the two feedbacks.
c. Feedback contributions
Integrating Eqs. (1) and (2) from initial time to t gives
H
0
A
1 H
0
L
1 H
0
O
5
ð
t
0
Edt5
~
E, (7)
where H
0
A
5 H
0
A
(t) 2 H
0
A
(0) is the change in atmospheric
carbon burden and H
0
X
5
Ð
t
0
F
0
X
dt, where X 5 L, O is the
cumulative flux equal to the change in the land or ocean
carbon pool for the fully coupled simu lation. The terms in
Eq. (7) indicate the contribution of cumulative emissions
~
E to the atmosphere, la nd, and ocean carbon pools.
As discussed in the accompanying manuscript by Boer
and Arora (2013), the different units for the feedback
parameters G (Pg C yr
21
8C
21
), B (Pg C yr
21
ppm
21
),
g (Pg C 8C
21
), and b (Pg C ppm
21
) mean that their re-
spective contributions to the atmospheric carbon bud-
get are not immediately obvious. Following Eq. (3) and
the assumed linearization of the globally integrated
surface–atmosphere CO
2
flux in terms of global mean
temperature and CO
2
concentration, these contribu-
tions may be estimated by decomposing the flux
changes into components as sociated w ith the carbon–
concentration (F
C
) and carbon–climate (F
T
) feedbacks
using F
0
A
5 F
C
1 F
T
5 B
A
C
0
1G
A
T
0
and writing
H
0
A
1 H
0
C
1 H
0
T
5
~
E
e
5
~
E 1 d
~
E, (8)
where H
0
C
52
Ð
t
0
B
A
C
0
dt 5
Ð
t
0
(B
L
1 B
O
)C
0
dt 52b
A
C
0
5
(b
L
1 b
O
)C
0
and H
0
T
52
Ð
t
0
G
A
T
0
dt 5
Ð
t
0
(G
L
1G
O
)T
0
dt 5
2g
A
T
0
5 (g
L
1 g
O
)T
0
are the cumulative flux changes
associated with the carbon–concentration and carbon–
climate feedbacks, respectively. The term d
~
E is the
difference between
Ð
t
0
F
0
A
dt and its approximation
as H
0
C
1 H
0
T
52
Ð
t
0
(B
A
C
0
1G
A
T
0
) dt 52(b
A
C
0
1 g
A
T
0
).
With B
A
52(B
L
1 B
O
)andG
A
52(G
L
1G
O
), Eq. (8)
can be further decomposed to obtain land and ocean
components of the feedbacks as
H
0
A
1 H
0
TL
1 H
0
CL
1 H
0
TO
1 H
0
CO
5
~
E
e
5
~
E 1 d
~
E, (9)
where H
0
TL
5
Ð
t
0
G
L
T
0
dt 5 g
L
T
0
and H
0
CL
5
Ð
t
0
B
L
C
0
dt 5
b
L
C
0
and similarly for the ocean terms. Finally, division
by the respective cumulative emissions term in Eqs.
(7)–(9) gives all the terms in a fractional form as
f
A
1 f
L
1 f
O
5 1 and (10)
f
A
1 f
C
1 f
T
5 f
A
1 f
CL
1 f
CO
1 f
TL
1 f
TO
5 1, (11)
where f
A
is the airborne fraction of cumulative emissions
and f
L
and f
O
are the fractions of emissions taken up
by the land and ocean, respectively. The terms f
C
and f
T
are the fractional contributions to diagnosed cumulative
emissions associated with carbon–concentration and
carbon–climate feedbacks and f
CL
, f
TL
, f
CO
, and f
TO
are
their land and ocean components. These components can
be calculated using either the BA or the FEA approach
and are evaluated at the time of CO
2
quadrupling.
5292 JOURNAL OF CLIMATE VOLUME 26
