Arora et al. (2020). Carbon–concentration and carbon–climate feedbacks in CMIP6 models and their comparison to CMIP5 models

Biogeosciences, 17, 4173–4222, 2020
https://doi.org/10.5194/bg-17-4173-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Carbon–concentration and carbon–climate feedbacks in CMIP6
models and their comparison to CMIP5 models

Vivek K. Arora

1

, Anna Katavouta

2,3

, Richard G. Williams

2

, Chris D. Jones

4

, Victor Brovkin

5,6

, Pierre Friedlingstein

Jörg Schwinger

, Laurent Bopp

, Olivier Boucher

, Patricia Cadule

, Matthew A. Chamberlain

10

,

James R. Christian

, Christine Delire

, Rosie A. Fisher

, Tomohiro Hajima

, Tatiana Ilyina

, Emilie Joetzjer

,

Michio Kawamiya

, Charles D. Koven

, John P. Krasting

, Rachel M. Law

, David M. Lawrence

,

Andrew Lenton

, Keith Lindsay

, Julia Pongratz

, Thomas Raddatz

, Roland Séférian

, Kaoru Tachiiri

,

Jerry F. Tjiputra

, Andy Wiltshire

, Tongwen Wu

, and Tilo Ziehn

1

Canadian Centre for Climate Modelling and Analysis, Environment and Climate Change Canada,

University of Victoria, Victoria, BC, Canada

2

School of Environmental Sciences, University of Liverpool, Liverpool, UK

3

National Oceanography Centre, Liverpool, UK

4

Met Office Hadley Centre, Exeter, UK

5

Max Planck Institute for Meteorology, Bundesstraße 53, Hamburg, Germany

6

CEN, Universität Hamburg, Hamburg, Germany

7

College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK

8

NORCE Norwegian Research Centre, Bjerknes Centre for Climate Research, Bergen, Norway

9

IPSL, CNRS, Sorbonne Université, Paris, France

10

CSIRO Oceans and Atmosphere, Hobart, Tasmania, Australia

11

CNRM, Université de Toulouse, Météo-France, CNRS, Toulouse, France

12

Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique, (CERFACS), Toulouse, France

13

Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

14

Climate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, USA

15

NOAA Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey, USA

16

CSIRO Oceans and Atmosphere, Aspendale, Victoria, Australia

17

Climate and Global Dynamics Laboratory, National Center for Atmospheric Research, Boulder, Colorado, USA

18

Ludwig Maximilian University, Department of Geography, Munich, Germany

19

Beijing Climate Center, China Meteorological Administration, Beijing, China

Correspondence:

Vivek K. Arora (vivek.arora@canada.ca)

Received: 2 December 2019 – Discussion started: 9 December 2019
Revised: 4 May 2020 – Accepted: 18 May 2020 – Published: 18 August 2020

Abstract.

Results from the fully and biogeochemically

coupled simulations in which CO

2

increases at a rate of

1 % yr

−

1

(1pctCO2) from its preindustrial value are ana-

lyzed to quantify the magnitude of carbon–concentration
and carbon–climate feedback parameters which measure the
response of ocean and terrestrial carbon pools to changes
in atmospheric CO

2

concentration and the resulting change

in global climate, respectively. The results are based on 11
comprehensive Earth system models from the most recent

(sixth) Coupled Model Intercomparison Project (CMIP6)
and compared with eight models from the fifth CMIP
(CMIP5).

The

strength

of

the

carbon–concentration

feedback

is

of

comparable

magnitudes

over

land

(mean

±

standard deviation

=

0.97

±

0.40 PgC ppm

−

1

) and

ocean (0.79

±

0.07 PgC ppm

−

1

), while the carbon–climate

feedback over land (

−

45

.

1

±

50.6 PgC

◦

C

−

1

) is about 3

times larger than over ocean (

−

17

.

2

±

5.0 PgC

◦

C

−

1

). The

strength of both feedbacks is an order of magnitude more

Published by Copernicus Publications on behalf of the European Geosciences Union.

4174

V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

uncertain over land than over ocean as has been seen in ex-
isting studies. These values and their spread from 11 CMIP6
models have not changed significantly compared to CMIP5
models. The absolute values of feedback parameters are
lower for land with models that include a representation of
nitrogen cycle. The transient climate response to cumulative
emissions (TCRE) from the 11 CMIP6 models considered
here is 1.77

±

0.37

◦

C EgC

−

1

and is similar to that found

in CMIP5 models (1.63

±

0.48

◦

C EgC

−

1

) but with some-

what reduced model spread. The expressions for feedback
parameters based on the fully and biogeochemically coupled
configurations of the 1pctCO2 simulation are simplified
when the small temperature change in the biogeochemically
coupled simulation is ignored. Decomposition of the terms
of these simplified expressions for the feedback parameters
is used to gain insight into the reasons for differing responses
among ocean and land carbon cycle models.

Copyright statement.

The works published in this journal are

distributed under the Creative Commons Attribution 3.0 License.
This license does not affect the Crown copyright work, which
is re-usable under the Open Government Licence (OGL). The
Creative Commons Attribution 3.0 License and the OGL are
interoperable and do not conflict with, reduce or limit each other.

1

Introduction

The Earth system responds to the perturbation of atmospheric
CO

2

concentration ([CO

2

]), caused by anthropogenic emis-

sions of CO

2

or any other forcing, via changes in its physical

climate. The changes in the globally averaged temperature
and the subsequent changes in other components of phys-
ical climate due to changes in radiative forcing associated
with [CO

2

] are larger than what would be expected from

the blackbody response alone. The reason for this is that the
positive feedbacks associated with various aspects of the cli-
mate system enhance the initial warming. These primarily
include changes in atmospheric water vapour, tropospheric
lapse rate, surface albedo resulting from ice and snow, and
clouds (Hansen et al., 1984; Gregory et al., 2009; Ceppi and
Gregory, 2017).

The biogeochemical cycling of carbon is also affected

by changes in [CO

2

] and the physical climate. In fact,

changes in both the physical climate and the biogeochem-
ical carbon cycle affect each other through multiple feed-
backs. The response of the Earth’s carbon cycle for both land
and ocean components has been characterized in terms of
carbon–concentration and carbon–climate feedback parame-
ters which quantify their response to changes in [CO

2

] and

the physical climate, respectively (Friedlingstein et al., 2006;
Arora et al., 2013). The carbon–concentration feedback (

β

)

quantifies the response of the carbon cycle to changes in
[CO

2

] and is expressed in units of carbon uptake or release

per unit change in [CO

2

] (PgC ppm

−

1

). The carbon–climate

feedback (

γ

) quantifies the response of the carbon cycle to

changes in physical climate and is expressed in units of car-
bon uptake or release per unit change in global mean temper-
ature (PgC

◦

C

−

1

). The changes in physical climate, in this

framework, are expressed simply in terms of changes in the
global mean near-surface air temperature although, of course,
the carbon cycle also responds to other aspects of changes
in climate (in particular precipitation over land and circula-
tion changes in the ocean). The assumption is that the effect
of other aspects of changes in climate on the carbon cycle
can be broadly expressed in terms of changes in near-surface
air temperature. These feedback parameters can be calcu-
lated from Earth system model (ESM) simulations globally,
separately over land and ocean, regionally, or over individ-
ual grid cells which makes somewhat more sense over land
than over ocean to investigate their geographical distribu-
tion (Yoshikawa et al., 2008; Boer and Arora, 2010; Tjipu-
tra et al., 2010; Roy et al., 2011; Friedlingstein et al., 2006;
Arora et al., 2013). The feedback analysis has shown that the
carbon–concentration feedback is negative from the atmo-
sphere’s perspective. That is, an increase in [CO

2

] leads to an

increased carbon uptake by land and ocean which leads to a
decrease in [CO

2

], thereby slowing CO

2

accumulation in the

atmosphere. The carbon–climate feedback, in contrast, has
been shown to be positive in ESM simulations (at the global
scale) from the atmosphere’s perspective since an increase
in temperature decreases the capacity of land and ocean to
take up carbon, thereby contributing to a further increase in
atmospheric CO

2

.

The carbon–concentration and carbon–climate feedback

parameters serve several purposes. First, these feedback pa-
rameters allow for the comparison of models in a simple and
straightforward manner despite their underlying complexi-
ties and different model structures. Intermodel comparisons
offer several benefits, including common standards and ex-
periment protocol, coordination, and documentation that fa-
cilitate the distribution of model outputs and the characteri-
zation of the mean model response (Eyring et al., 2016), as
has been shown for multiple model intercomparison projects
(MIPs). Second, they allow for the quantification of the con-
tribution of the two feedback processes to allowable anthro-
pogenic emissions for a given CO

2

pathway. For example,

Arora et al. (2013) and Gregory et al. (2009) showed that the
contribution of the carbon–concentration feedback to allow-
able diagnosed emissions is about 4–4.5 times larger than
that of the carbon–climate feedback. Third, they allow the
comparison of feedbacks between climate and the carbon cy-
cle to other feedbacks operating in the climate system as
was performed by Gregory et al. (2009). Fourth, the feed-
back parameters can be considered as emergent properties of
the coupled carbon cycle climate system which can poten-
tially be constrained by observations, as Wenzel et al. (2014)

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4175

attempted for the carbon–climate feedback parameter over
land.

Here, we build on the work carried out in earlier stud-

ies that compared the strength of the carbon–concentration
and carbon–climate feedbacks in coupled general circu-
lation models with land and ocean carbon cycle compo-
nents. Friedlingstein et al. (2006; hereafter F06) reported
the first such results from the Coupled Climate–Carbon
Cycle Model Intercomparison Project (C

4

MIP). Arora et

al. (2013) (hereafter A13) compared the strength of the
carbon–concentration and carbon–climate feedbacks from
models participating in the fifth phase of the Coupled
Model Intercomparison Project (CMIP5; https://pcmdi.llnl.
gov/mips/cmip5/, last access: 15 December 2019; Taylor et
al., 2012). The A13 study found that the strength of the two
feedbacks was weaker and the spread between models was
smaller in their study than in F06. However, the results from
these two studies are not directly comparable because of sev-
eral reasons. The results from the F06 study were based on
the Special Report on Emissions Scenarios (SRES) A2 emis-
sions scenario, while those in the A13 study were based on
the 1 % yr

−

1

increasing CO

2

experiment in which the atmo-

spheric CO

2

concentration increases from its preindustrial

value of around 285 ppm until it quadruples over a 140-year
period (referred to as the 1pctCO2 experiment in the frame-
work of the Coupled Model Intercomparison Project, CMIP).
The absolute values of the feedback parameters are known
to be dependent on the state of the system, the timescale
of forcing (i.e. underlying emissions and concentration sce-
nario), and the approach used to calculate them (Plattner et
al., 2008; Zickfeld et al., 2011; Hajima et al., 2014; Gregory
et al., 2009; Boer and Arora, 2010). The varying approaches
employed over the past decade have made the cross compari-
son of feedbacks among the studies and different generations
of Earth system models difficult.

In order to address the diversity of approaches to diag-

nose climate carbon cycle feedbacks and to promote a ro-
bust standard moving forward the C

4

MIP community has

endorsed a framework of tiered experiments (Jones et al.,
2016) that builds upon the core preindustrial control and
1pctCO2 experiments performed as part of the CMIP DECK
(Diagnostic, Evaluation and Characterization of Klima) ex-
periments (Eyring et al., 2016). Here, we compare carbon–
concentration and carbon–climate feedbacks from models
participating in the C

4

MIP (Jones et al., 2016) contribution

to the sixth phase of CMIP (CMIP6; Eyring et al., 2016).
To maintain continuity and consistency, feedback parame-
ters are derived from the 1pctCO2 experiments as they were
in A13. The 1pctCO2 experiment is a DECK experiment in
the CMIP6 framework. All participating modelling groups
are expected to perform DECK experiments to help docu-
ment basic characteristics of models across different phases
of CMIP (Eyring et al., 2016).

2

Feedbacks metrics in the coupled climate–carbon
system

We largely follow the climate carbon cycle feedbacks frame-
work presented in A13 (which in turn was built on F06) but
with some additional modifications that are explained below.
Only the primary equations are presented here, while the bulk
of the framework is summarized in the Appendix for com-
pleteness. We also provide some history of how the carbon
feedbacks analysis reached its current stage.

Carbon feedbacks analysis is traditionally based on simu-

lations run with fully, radiatively, and biogeochemically cou-
pled model configurations of an Earth system model. The ob-
jective of these simulations is to isolate feedbacks discussed
above. In a biogeochemically coupled simulation (referred
to here as the BGC simulation), biogeochemical processes
over land and ocean respond to increasing atmospheric CO

2

,

while the radiative transfer calculations in the atmosphere
use a CO

2

concentration that remains at its preindustrial

value. Small climatic changes occur in the BGC simulation
due to changes in evaporative (or latent heat) flux resulting
from stomatal closure over land (associated with increasing
[CO

2

]), changes in vegetation structure, and changes in veg-

etation coverage and composition (in models which dynam-
ically simulate competition between their plant functional
types, PFTs), all of which affect latent and sensible heat
fluxes at the land surface. In a radiatively coupled simulation
(referred to here as the RAD simulation) increasing atmo-
spheric CO

2

affects the radiative transfer processes in the at-

mosphere and hence climate but not the biogeochemical pro-
cesses directly over land and ocean, for which the preindus-
trial value of atmospheric CO

2

concentration is prescribed.

In a fully coupled simulation (referred to here as the COU
simulation) both the biogeochemical and the radiative pro-
cesses respond to increasing CO

2

.

Following the F06 methodology which uses time-

integrated fluxes (which are the same as the changes in car-
bon pool sizes), the changes in land (L) or ocean (O) carbon
pools (

1

C

X

, X

=

L,O) can be expressed using three equa-

tions corresponding to the BGC, RAD, and COU experi-
ments, as shown in Eq. (1) (see also the Appendix).

Radiatively coupled simulation

1

C

+

X

=

Z

F

+

X

d

t

=

γ

X

T

+

(1a)

Biogeochemically coupled simulation

1

C

∗

X

=

Z

F

∗

X

d

t

=

β

X

c

0

+

γ

X

T

∗

(1b)

Fully coupled simulation

1

C

0

X

=

Z

F

0

X

d

t

=

β

X

c

0

+

γ

X

T

0

(1c)

https://doi.org/10.5194/bg-17-4173-2020

Biogeosciences, 17, 4173–4222, 2020

4176

V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Here

F

+

,

F

∗

, and

F

0

are the CO

2

flux changes (PgC yr

−

1

);

1

C

+

X

,

1

C

∗

X

, and

1

C

0

X

the changes in global carbon pools

(PgC);

T

+

,

T

∗

, and

T

0

the temperature changes (

◦

C) in the

RAD, BGC, and COU simulations, respectively; and the sub-
script

X

=

LO refers to either the land or ocean model com-

ponents.

c

0

is the change in [CO

2

]. Here and elsewhere up-

percase C is used to denote pools and lowercase

c

is used to

denote atmospheric CO

2

concentration, [CO

2

]. All changes

are defined relative to a preindustrial equilibrium state repre-
sented by the preindustrial control simulation. In the context
of a specified-concentration simulation (the 1pctCO2 exper-
iment in our case),

c

0

is the same in BGC and COU simu-

lations. There is no

β

X

c

0

term in the RAD simulation since

the biogeochemistry sees the preindustrial value of [CO

2

] al-

though

T

+

is a function of increasing

c

0

that is seen only by

the radiative transfer calculations.

These equations assume linearization of the globally in-

tegrated surface–atmosphere CO

2

flux (for land and ocean

components) in terms of global mean temperature and [CO

2

]

change (compared to a preindustrial control run) and serve
to define the carbon–concentration (

β

X

) and carbon–climate

(

γ

X

) feedback parameters. A similar set of equations can

be written that defines the instantaneous values of the feed-
back parameters and is based on fluxes rather than their time-
integrated values (see Eqs. A4 and A5 in the Appendix). Both
the time-integrated flux and the instantaneous flux-based ver-
sions of the feedback parameters evolve over time in an ex-
periment as shown in A13.

There are several different ways in which the feedbacks

(

β

X

and

γ

X

) in a coupled climate and carbon cycle sys-

tem may be evaluated: (1) the experiments may use spec-
ified (concentration-driven) or freely evolving (emissions-
driven) [CO

2

], (2) any two of the three configurations of an

experiment (COU, RAD, and BGC) may be used to calculate
the two feedback parameters, and (3) the experiment may
be based on an idealized scenario (like the 1pctCO2 experi-
ment) or a more realistic emissions scenario. In addition, the
small temperature change in the BGC simulation,

T

∗

, may

be ignored, and other external forcings such as nitrogen (N)
deposition or land use change, which directly affect carbon
fluxes, may or may not be taken into account. The original
framework proposed by F06 used COU and BGC versions
(referred to as coupled and uncoupled in the F06 study) of an
emissions-driven simulation for the SRES A2 scenario. The
F06 framework assumed that the small temperature change
in the BGC simulation can be ignored. A13 used BGC and
RAD versions of the 1pctCO2 experiment in which the evo-
lution of [CO

2

] is specified and took into account the small

global mean temperature change in the BGC simulation.

With regard to the use of concentration-driven versus

emissions-driven simulations, Gregory et al. (2009) rec-
ommended the use of specified concentration simulations,
which ensures consistency of [CO

2

] across models, and this

recommendation has been adopted since CMIP5. C

4

MIP has

also adopted the use of the 1pctCO2 simulation; i.e. an ideal-

ized scenario is preferred over a more realistic scenario. The
1pctCO2 experiment provides an ideal experiment to com-
pare carbon–climate interactions across models as the ex-
periment does not include the confounding effects of other
climate forcings (including land use change, non-CO

2

green-

house gases, and aerosols) and is a CMIP DECK experiment,
as mentioned earlier.

Using Eq. (1) as an example, Table 1 shows how any two

combinations of the three configurations of an experiment
can be used to calculate the values of the two feedback pa-
rameters. The A13 study showed that under the assumption
of a linear system and if the conditions

F

0

=

F

+

F

∗

and

T

0

=

T

+

T

∗

are met, i.e. if the sum of flux and tempera-

ture changes in the RAD and BGC simulations is the same as
that in the COU simulation, then all approaches yield exactly
the same solution. However, this is not the case because of
the nonlinearities involved (Gregory et al., 2009; Zickfeld et
al., 2011; Schwinger et al., 2014).

The use of BGC and RAD simulations that have only bio-

geochemistry or radiative forcing responding to increases
in [CO

2

] to find the feedback parameters is attractive since

these simulations were designed to isolate the feedbacks.
In the RAD simulation (whose purpose is to quantify the
carbon–climate feedback,

γ

X

) the preindustrial global car-

bon pools for both land and ocean typically decrease in
response to an increase in global temperature (hence the
positive carbon–climate feedback and the negative value of

γ

X

). Consequently, negative values of

γ

X

(positive carbon–

climate feedback) are obtained when using the RAD–BGC
and RAD–COU approaches (see Table 1). If, however,

γ

X

is

determined using the BGC and COU simulations in both of
which the globally summed carbon pools for land and ocean
are increasing in response to increasing [CO

2

], the calculated

value of

γ

X

is different than that obtained using the RAD–

BGC and RAD–COU approaches. In the ocean, the RAD
simulation mainly measures the loss of near-surface carbon
owing to warming of the surface ocean layer (Schwinger et
al., 2014). The RAD simulation misses the suppression of
carbon drawdown to the deep ocean due to weakening ocean
circulation, because there is no buildup of a strong carbon
gradient from the surface to the deep ocean in contrast to the
BGC and COU simulations. Therefore, the absolute value
of

γ

X

for the ocean is smaller (less negative) when calcu-

lated using the RAD–BGC and RAD–COU approaches com-
pared to the BGC–COU approach (Schwinger et al., 2014).
Over land, in the RAD simulation carbon is lost in response
to increasing temperatures primarily due to an increase in
heterotrophic respiration. However, an increase in temper-
ature also potentially increases photosynthesis at high lati-
tudes, and this increase compensates for carbon lost due to
increased heterotrophic respiratory losses, especially in the
presence of continuously increasing [CO

2

] seen in the COU

configuration. Therefore

γ

X

value for land calculated using

RAD–BGC and RAD–COU approaches may be higher or
lower than that calculated using the BGC–COU approach.

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4177

Table 1.

The values of the carbon–concentration (

β

) and carbon–climate (

γ

) feedback parameters can be solved using results from any two

combinations of the RAD, BGC, and COU versions of an experiment as shown in Eq. (1). In addition, when using results from the BGC
and COU simulations, the effect of temperature change in the BGC simulation (

T

∗

) can be neglected, as it was in the F06 study, yielding

approximate values for

β

X

and

γ

X

.

Approach

γ

X

β

X

The RAD–BGC approach

γ

X

=

1

C

+

X

T

+

β

X

=

1

C

∗

X

c

0

−

γ

X

T

∗

c

0

The RAD–COU approach

γ

X

=

1

C

+

X

T

+

β

X

=

1

C

0

X

c

0

−

γ

X

T

0

c

0

The BGC–COU approach

γ

X

=

1

C

0

X

−

1

C

∗

X

T

0

−

T

∗

β

X

=

1

c

0

1

C

∗

X

T

0

−

1

C

0

X

T

∗

T

0

−

T

∗

The BGC–COU approach with

T

∗

=

0

γ

X

=

1

C

0

X

−

1

C

∗

X

T

0

β

X

=

1

C

∗

X

c

0

These are some mechanisms that lead to nonlinearities. Since
the ongoing climate change (predominantly caused by in-
creasing [CO

2

]) is best characterized by the COU simula-

tion, it can be argued that feedback parameters are more rep-
resentative when calculated using the BGC–COU approach.
Here, we propose to use the COU and BGC configurations
of an experiment as the standard set from which to calcu-
late the feedback parameters as recommended in the C

4

MIP

protocol (Jones et al., 2016). However, we also quantify the
values of feedback parameters when using the RAD simu-
lation for comparison. The calculated values of the carbon–
concentration feedback parameter (

β

X

), in contrast, are less

sensitive to the approach used as shown in A13.

There is no broad consensus on whether temperature

change in the BGC simulation should be assumed to be zero
(

T

∗

=

0) as standard practice when calculating the strengths

of the feedbacks, as it was in F06. While the globally aver-
aged value of

T

∗

is an order of magnitude smaller than

T

0

,

the spatial pattern of

T

∗

is quite different from that of

T

0

. The

spatial pattern of temperature change in the COU simulation
(

T

0

) is dominated by radiative forcing of increased [CO

2

]

with greater warming at high latitudes and over land than
over ocean. In contrast, the spatial pattern of temperature
change in the BGC simulation (

T

∗

) is determined primar-

ily by the reduction in latent heat flux associated with stom-
atal closure as [CO

2

] increases which reduces transpiration

from vegetation (Bounoua et al., 1999; Ainsworth and Long,
2005). This process leads to a much more spatially vari-
able pattern of temperature change (than

T

0

) and the asso-

ciated changes in precipitation patterns due to soil moisture–
atmosphere feedbacks (Chadwick et al., 2017; Skinner et al.,
2017). The difference in spatial patterns of temperature and
precipitation change in the RAD versus the COU simulation
is another reason that the values of the carbon–climate feed-
back (

γ

X

) depend on the simulation used, and this is another

pathway through which nonlinearities can occur. A complete
analysis of the effect of differences in spatial patterns of cli-
mate change and the carbon state on the calculated value of

γ

X

when using the RAD versus the COU simulation and de-

termining whether or not the assumption of

T

∗

=

0 should

be a standard practice are beyond the scope of this study but
remain topics for additional scientific investigation. In the
interim, we report here values of

β

X

and

γ

X

both by con-

sidering

T

∗

and by ignoring it (i.e.

T

∗

=

0) when using the

BGC–COU approach.

Following Table 1, when using results from the BGC and

the COU configurations of a specified-concentration experi-
ment, the values of the feedback parameters are written as

β

X

=

1

c

0

1

C

∗

X

T

0

−

1

C

0

X

T

∗

T

0

−

T

∗

,

(2)

γ

X

=

1

C

0

X

−

1

C

∗

X

T

0

−

T

∗

.

(3)

Equations (2) and (3) may be rearranged to explicitly calcu-
late the effect of the

T

∗

=

0 assumption on calculated values

of feedback parameters, as shown in Eqs. (4) and (5). Here,
the

T

∗

term is retained only in the second part of the equa-

tions, whose contribution becomes zero when

T

∗

is ignored.

β

X

=

1

C

∗

X

c

0

+

1

c

0

"

1

C

0

X

−

1

C

∗

X

T

∗

(T

0

−

T

∗

)

#

(4)

γ

X

=

1

C

0

X

−

1

C

∗

X

T

0

+

1

C

0

X

−

1

C

∗

X

T

∗

T

0

(T

0

−

T

∗

)

(5)

Finally, in regard to other external forcings such as nitrogen
(N) deposition that directly affect carbon fluxes, the C

4

MIP

protocol for CMIP6 (Jones et al., 2016) recommended per-
forming additional simulations for BGC and COU versions
of the 1pctCO2 experiment with time-varying N deposition
in addition to their standard versions which keep N depo-
sition rates at their preindustrial level. Simulations with N
deposition can only be performed for models that explicitly
model the N cycle and its interactions with the carbon (C)
cycle. The rationale for recommending increasing N deposi-
tion, in conjunction with temperature and CO

2

increases, is

to be able to quantify the response of feedback parameters to
this third forcing. However, here we restrict ourselves to the

https://doi.org/10.5194/bg-17-4173-2020

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

traditional analysis that considers the climate and CO

2

forc-

ings only. We do highlight, however, which models include
coupled C–N cycle interactions over land. The analysis of
runs with N deposition forcing is left for future studies.

2.1

Reasons for differences in feedback parameters
among models

As shown later in this paper, the contribution of the sec-
ond term involving

T

∗

in expressions for the carbon–

concentration (

β

X

) and carbon–climate (

γ

X

) feedback pa-

rameters (in Eqs. 4 and 5, when using the BGC–COU ap-
proach) is around 1 % to 5 %. This allows for the reasons
for differences in the feedback parameters to be investigated
across models as the expressions for the feedback parameters
can be simplified in terms of the changes in the sizes of car-
bon pools (

1

C

0

X

and

1

C

∗

X

), the temperature change in the

COU simulation (

T

0

), and the specified change in [CO

2

] (

c

0

)

as follows:

β

X

≈

1

C

∗

X

c

0

,

(6)

γ

X

≈

1

C

0

X

−

1

C

∗

X

T

0

.

(7)

2.1.1

Land

Over land, Eqs. (6) and (7) can be expanded to investi-
gate, firstly, the contributions, from changes in live vege-
tation pools (

1

C

V

) and dead litter plus soil carbon pools

(

1

C

S

) to the strength of the feedback parameters, since

1

C

L

=

1

C

V

+

1

C

S

. Secondly, Eq. (6) can be further decom-

posed to gain insight into the reasons for differences across
models, in a manner similar to Hajima et al. (2014).

β

L

≈

1

C

∗

L

c

0

=

1

C

∗

V

+

1

C

∗

S

c

0

=

1

C

∗

V

1

NPP

∗

1

NPP

∗

1

GPP

∗

1

GPP

∗

c

0

+

1

C

∗

S

1R

∗

h

1R

∗

h

1

LF

∗

1

LF

∗

c

0

=

τ

veg

1

CUE

1

GPP

∗

c

0

+

τ

soil

1

1R

∗

h

1

LF

∗

1

LF

∗

c

0

(8)

γ

L

≈

1

C

0

L

−

1

C

∗

L

T

0

=

1

C

0

V

−

1

C

∗

V

T

0

+

1

C

0

S

−

1

C

∗

S

T

0

(9)

The superscript

∗

in Eq. (8) implies that the terms are calcu-

lated here using the BGC version of the 1pctCO2 experiment.
In Eq. (8),

1

NPP and

1

GPP represent the change in net

primary productivity (NPP) and gross primary productivity
(GPP),

1

LF the change in litterfall flux, and

1R

h

the change

in heterotrophic respiration, compared to the preindustrial
control experiment. The multiplicative terms in Eq. (8) do
indeed have physical meaning although they are based on
change in the magnitude of quantities as opposed to their
absolute magnitudes. We note here explicitly that as such,
these terms cannot be compared directly to the terms which
are based on absolute magnitudes.

The term

1

NPP

1

GPP

(fraction) is the fraction of GPP (above its

preindustrial value) that is turned into NPP after autotrophic
respiratory losses are taken into account. We use the term
carbon use efficiency (CUE) but subscripted by

1

(CUE

1

)

to represent

1

NPP

1

GPP

. The subscripted

1

allows CUE

1

to be

differentiated from CUE as used in the existing literature
(Choudhury, 2000), which represents the fraction of abso-
lute GPP that is converted to NPP rather than its change over
some time period, as well as the point that we consider glob-
ally integrated rather than locally derived quantities. Sim-
ilarly, the term

1

C

V

1

NPP

represents a measure of turnover or

residence timescale of carbon in the vegetation pool (

τ

veg

1

,

years). The term

1

GPP

c

0

(PgC yr

−

1

ppm

−

1

) is a measure of the

strength of the globally integrated CO

2

fertilization effect.

However, in the models that dynamically simulate changes
in vegetation cover, the effect of changes in vegetation cov-
erage is implicitly included in this term. The term

1

C

S

1R

h

is a

measure of the average residence time of carbon in the dead
litter and soil carbon pools (

τ

soil

1

, years). However, as with

CUE, this quantity cannot be compared directly to the resi-
dence time of carbon in the litter plus soil carbon pool calcu-
lated using the absolute values of

C

S

and

R

h

. Nor can it be

compared to the changes in carbon residence time due to the
“false priming effect” associated with the increase in NPP in-
puts, as [CO

2

] increases, into the dead carbon pools (Koven

et al., 2015).

1R

h

1

LF

(fraction) is a measure of the increase in

heterotrophic respiration per unit increase in litterfall rate,
and

1

LF

c

0

(PgC yr

−

1

ppm

−

1

) indicates the global increase in

litterfall rate per unit increase in CO

2

, which in principle,

should be close to the change in net primary productivity

per unit increase in CO

2

,

CUE

1

GPP

c

0

. A comparison of

these terms across models can potentially yield insight into
the reasons for large differences in land carbon uptake across
models.

2.1.2

Ocean

Assuming changes in the biological organic carbon inventory
are small, the change in the ocean carbon inventory,

1

C

O

, is

defined by an integral of the change in the dissolved inor-
ganic carbon,

1

DIC, and density over the ocean volume:

1

C

O

=

12 gC mol

−

1

Z

V

1

DIC d

V

×

10

−

15

,

(10)

where

1

C

O

is in petagrams of carbon; the ocean dissolved

inorganic carbon, DIC, is in moles per cubic meter; the ocean
volume

V

is in cubic meters; and the multiplier 10

−

15

con-

verts grams to petagrams of carbon.

To gain insight into how the ocean carbon distribution is

controlled, the ocean dissolved inorganic carbon, DIC, may
be defined in terms of separate carbon pools (Ito and Follows,
2005; Williams and Follows, 2011; Lauderdale et al., 2013;

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4179

Schwinger and Tjiputra, 2018):

DIC

=

DIC

preformed

+

DIC

regenerated

=

DIC

sat

+

DIC

disequilib

+

DIC

regenerated

,

(11)

where the preformed carbon, DIC

preformed

, is the amount of

carbon in a water parcel when in the mixed layer at the time
of subduction and the regenerated carbon, DIC

regenerated

, is

the amount of dissolved inorganic carbon accumulated below
the mixed layer due to the biological regeneration of organic
carbon. The preformed carbon is affected by the carbonate
chemistry and ocean physics. To gain further insight into how
close the ocean is to an equilibrium with the atmosphere,
the preformed carbon, DIC

preformed

, is further split into satu-

rated, DIC

sat

, and disequilibrium, DIC

disequilib

, components.

The saturated component represents the concentration in sur-
face water fully equilibrated with the contemporary atmo-
spheric CO

2

concentration. The disequilibrium component

represents the extent that surface water is incompletely equi-
librated before subduction, which is affected by the strength
of the ocean circulation altering the residence time in the
mixed layer and the ocean ventilation rate. Each of these
components is affected by the increase in atmospheric CO

2

and the changes in climate.

The change in the global ocean carbon inventory,

1

C

O

,

relative to the preindustrial period may then be related to the
global volume integral of the change in each of these DIC
pools:

1

C

O

=

1

C

preformed

+

1

C

regenerated

=

1

C

sat

+

1

C

disequilib

+

1

C

regenerated

,

(12)

where

1

C

preformed

is the preformed carbon inventory,

1

C

sat

is the saturated carbon inventory,

1

C

disequilib

is the disequi-

librium carbon inventory, and

1

C

regenerated

is the regenerated

carbon inventory.

The simplified expressions for carbon cycle feedback pa-

rameters in Eqs. (6) and (7) based on the air–sea flux changes
to the ocean may then be approximated by the global ocean
carbon inventory changes, which may be expressed in terms
of these different global ocean carbon pools (Williams et al.,
2019):

β

O

≈

1

C

∗

O

c

0

=

1

C

∗

preformed

c

0

+

1C

∗

regenerated

c

0

=

1

C

∗

sat

c

0

+

1

C

∗

disequilib

c

0

+

1

C

∗

regenerated

c

0

,

(13)

γ

O

≈

1

C

0

O

−

1

C

∗

O

T

0

=

1

C

0

preformed

−

1

C

∗

preformed

T

0

+

1

C

0

regenerated

−

1

C

∗

regenerated

T

0

=

1

C

0

sat

−

1

C

∗

sat

T

0

+

1

C

0

disequilib

−

1

C

∗

disequilib

T

0

+

1

C

0

regenerated

−

1

C

∗

regenerated

T

0

.

(14)

The anomalies for each of these carbon pools are calculated
as

1

DIC

regenerated

= −

R

CO

1

AOU

+

1

2

(1

Alk

−

1

Alk

pre

−

R

NO

1

AOU

) ,

(15)

1

DIC

sat

=

f p

CO

atm
2

, T

o

, S

o

,

P

,

Si

,

Alk

pre

t

−

f p

CO

atm
2

, T

o

, S

o

,

P

,

Si

,

Alk

pre

t

=

0

,

(16)

1

DIC

disequilib

=

1

DIC

−

1

DIC

regenerated

−

1

DIC

sat

,

(17)

where

R

CO

and

R

NO

are constant stoichiometric ratios,

1

AOU is the change in apparent oxygen utilization from

its preindustrial value (where preformed oxygen is assumed
to be approximately saturated with respect to atmospheric
oxygen);

1

Alk is the change in alkalinity;

T

o

and

S

o

are

the ocean temperature and salinity, respectively; P and Si
are the phosphate and silicate concentrations; and

1

Alk

pre

is the change in preformed alkalinity (Ito and Follows, 2005;
Williams and Follows, 2011; Appendix of Lauderdale et al.,
2013). In Eq. (16),

1

DIC

sat

is calculated using the partial

pressure of CO

2

in the atmosphere (

p

CO

atm
2

) and preformed

alkalinity as represented by the function

f

following the it-

erative solution for the ocean carbon system of Follows et
al. (2006) and by considering the small contribution of mi-
nor species (borate, phosphate, silicate) to the preformed al-
kalinity, at time

t

, and the preindustrial values, at time

t

=

0.

In Eq. (16), the calculation uses the preformed alkalinity, the
alkalinity at the time of water subduction, instead of the to-
tal instantaneous alkalinity to remove the effect of CaCO

3

dissolution from the time the water parcel lost contact with
the atmosphere. The preformed alkalinity is estimated from
a multiple linear regression using salinity and the conserva-
tive tracer PO (PO=O

2

−

R

o2

:

P

P; Gruber et al., 1996), with

the coefficients of this regression estimated based on the up-
per ocean (first 10 m) alkalinity, salinity, oxygen, and phos-
phate in each model. Our diagnostics of the ocean feedbacks
and carbon pools depend primarily upon changes in DIC
and upon the preformed and regenerated pools, relative to
the preindustrial period, although differences in the prein-
dustrial ocean in our suite of models do affect the saturated
DIC changes relative to the preindustrial period by

∼

5 % or

less due to the nonlinearity of the carbonate chemistry.

3

Model descriptions

Table 2 summarizes the primary features of the 11 compre-
hensive ESMs that contributed results to this study. Brief
descriptions of land and ocean carbon cycle components
of these ESMs are provided in the Appendix. The 11
ESMs, in alphabetical order, are the (1) Commonwealth
Scientific and Industrial Research Organisation (CSIRO)
ACCESS-ESM1.5, (2) Beijing Climate Center (BCC) BCC-
CSM2-MR, (3) Canadian Centre for Climate Modelling
and Analysis (CCCma) CanESM5, (4) Community Earth

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Table 2.

Primary features of the physical atmosphere and ocean components and land and ocean carbon cycle components of the 11 partici-

pating models in this study.

Modelling group

CSIRO

BCC

CCCma

CESM

CNRM

GFDL

ESM

ACCESS-ESM1.5

BCC-CSM2-MR

CanESM5

CESM2

CNRM-ESM2-1

GFDL-ESM4

Atmosphere
resolution

1

.

875

◦

×

1

.

25

◦

,

L38

1

.

125

◦

×

1

.

125

◦

,

L46

2

.

81

◦

×

2

.

81

◦

,

L49

0

.

9

◦

×

1

.

25

◦

T127 (1

.

4

◦

×

1

.

4

◦

),

L91

Cubed sphere
C96
(

∼

100 km)

Ocean
resolution

1

◦

but finer

between 10

◦

S and

10

◦

N and in

the Southern
Ocean, L50

1

◦

but becoming

finer to 1

/

3

◦

within
30

◦

N–30

◦

S,

L40

1

◦

but becoming

finer to 1

/

3

◦

within
20

◦

N–20

◦

S,

L45

gx1v7 displaced
pole grid
(384

×

320

lat

×

long)

1

◦

but becoming

0.3

◦

in the tropics,

L75

0.5

◦

tripolar grid

Land carbon and biogeochemistry component

Model name

CABLE2.4 with
CASA-CNP

BCC-AVIM2

CLASS-CTEM

CLM5

ISBA-CTRIP

LM4.1

Number of live
carbon pools

3

22

6

Number of dead
carbon pools

6

8

2

7

4

Number of plant
functional types
(PFTs)

13

16

9

22

16

5

Fire

No

Yes

Dynamic vegetation
cover

No

Yes

Nitrogen cycle

Yes
(and phosphorus)

No

Yes

No (implicit,
derived from
Yin, 2002)

No

Ocean carbon and biogeochemistry component

Model name

WOMBAT

MOM4_L40;
ocean carbon
cycle follows
OCMIP2

CMOC
(biology);
carbonate
chemistry
follows OMIP
protocol.

MARBL

PISCESv2-gas

COBALTv2

Number of
phytoplankton
types

1

0

1

3

2

3

Number of
zooplankton
types

1

0

1

2

3

Explicit nutrients
considered

Phosphorus,
iron

Phosphorus

Nitrogen

Nitrogen,
phosphorus,
silica, iron

System Model version 2 (CESM2), (5) Centre National
de Recherches Météorologiques (CNRM) CNRM-ESM2-1,
(6) Institut Pierre Simon Laplace (IPSL) IPSL-CM6A-LR,
(7) Japan Agency for Marine-Earth Science and Technol-
ogy (JAMSTEC) in collaboration with the University of
Tokyo and the National Institute for Environmental Stud-
ies (team MIROC) MIROC-ES2L, (8) Max Planck Institute
for Meteorology (MPI) MPI-ESM1.2-LR, (9) Geophysical
Fluid Dynamics Laboratory (GFDL) NOAA-GFDL-ESM4,
(10) Norwegian Climate Centre (NCC) NorESM2-LM, and
(11) United Kingdom (UK) UKESM1-0-LL.

In contrast to the A13 study where only two of the eight

participating comprehensive ESMs had the terrestrial N cy-
cle implemented and coupled to their C cycle, in this study 6
of the 11 participating ESMs represent coupling of terrestrial
C and N cycles. These six models are the ACCESS-ESM1.5,
CESM2, MIROC-ES2L, MPI-ESM1.2-LR, NorESM2-LM,
and UKESM1-0-LL. Note that CESM2 and NorESM2-LM
employ the same land surface component – version 5 of
the Community Land Model (CLM5) – so we expect the
land carbon cycle to respond very similarly in the two mod-
els. Three of the ESMs have land components that dynam-
ically simulate vegetation cover and competition between

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4181

Table 2.

Continued.

Modelling group

IPSL

JAMSTEC

(team

MIROC)

MPI

NCC

UK

ESM

IPSL-CM6A-LR

MIROC-ES2L

MPI-ESM1.2-LR

NorESM2-LM

UKESM1-0-
LL

Atmosphere
resolution

2

.

5

◦

×

1

.

3

◦

, L79

2

.

81

◦

×

2

.

81

◦

, L40

T63, 1

.

8

◦

×

1

.

8

◦

, L47

1

.

9

◦

×

2

.

5

◦

, L32

1

.

875

◦

×

1

.

25

◦

, L85

Ocean
resolution

1–0.3

◦

in the

tropics L75

Almost 1

◦

but

becoming finer to
North Pole and
Equator (tripolar
system: 360

×

256),

L62

GR1.5 (1.5

◦

,

finer close to
Antarctica and
Greenland),
L40

1

◦

with

enhanced
meridional
resolution near
the Equator,
L53

1

◦

Land carbon and biogeochemistry component

Model name

ORCHIDEE,
branch 2.0

MATSIRO (physics)
VISIT-e (BGC)

JSBACH3.2

CLM5

JULES-ES-
1.0

Number of live
carbon pools

8

3

22

3

Number of dead
carbon pools

3

6

18

7

4

Number of plant
functional types
(PFTs)

15

13

22

13

Fire

No

Yes

No

Dynamic vegetation
cover

No

Yes

No

Yes

Nitrogen cycle

No

Yes

Ocean carbon and biogeochemistry component

Model name

PISCES-v2

OECO2

HAMOCC6

iHAMOCC

MEDUSA-
2.1

Number of
phytoplankton
types

2

2 (nondiazotroph
and diazotroph)

2

1

2

Number of
zooplankton
types

2

1

2

Explicit nutrients
considered

Nitrogen,
phosphorus,
silica, iron

Nitrogen,
phosphorus,
iron

Nitrogen,
phosphorus,
silica, iron

Nitrogen,
silica, iron

their PFTs – NOAA-GFDL-ESM4, MPI-ESM1.2-LR, and
UKESM1-0-LL.

4

Results

4.1

Global surface CO

2

fluxes and temperature change

Figure 1 shows the simulated changes in temperature in the
three model configurations (COU, BGC, and RAD) of the
1pctCO2 experiment. Here and in subsequent figures, results
are also shown for the eight comprehensive ESMs that par-

ticipated in the A13 study. The eight models in the A13 study
are a subset of 11 models considered in this study although
they have been updated since CMIP5.

As expected, temperature change is higher in the COU and

RAD simulations than in the BGC simulation, since the ra-
diative forcing responds to increasing [CO

2

] in these simula-

tions. The small temperature change in the BGC simulation
is due to a number of not only contributing but also compen-
sating factors: (1) reduction in transpiration and hence latent
heat flux due to stomatal closure in response to increasing
[CO

2

] (Cao et al., 2010); (2) increase in vegetation leaf area

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Figure 1.

Temperature changes in the fully, biogeochemically, and radiatively coupled configurations of the 1pctCO2 experiment across

participating CMIP6

(a)

and CMIP5

(b)

comprehensive ESMs that participated in this and the A13 study, respectively. The model mean is

indicated by the solid lines, and the range across the models is indicated by shading around the solid lines. Individual CMIP6 model results
are shown in Fig. A1 in the Appendix.

index (LAI), which decreases land surface albedo and hence
increases absorbed solar radiation; and (3) increase in veg-
etation fraction in models that explicitly simulate competi-
tion between their plant functional types (PFTs) over land
(NOAA-GFDL-ESM4, MPI-ESM1.2-LR, and UKESM1-0-
LL), which also leads to reduced land surface albedo. As a
result, temperature change in the COU simulation is higher
than in the RAD simulation since these biogeochemical pro-
cesses are active and contribute to a small additional warm-
ing. This is seen in Fig. 1a for CMIP6 models and Fig. 1b for
CMIP5 models.

When comparing CMIP5 and CMIP6 models, the CMIP6

models are on average slightly warmer than CMIP5 models
in the COU and RAD simulations. In Fig. 1a, the globally av-
eraged near-surface temperature change at CO

2

quadrupling

in the COU simulation is 4.87

◦

C in CMIP6 models, com-

pared to 4.74

◦

C in CMIP5 models. The CMIP6 ensemble

considered here includes some high-climate-sensitivity mod-
els including CanESM5, CESM2, CNRM-ESM2-1, IPSL-
CM6A-LR, and UKESM1-0-LL. The globally averaged tem-
perature change at CO

2

quadrupling in the COU simulation

for the eight models that are common to this (CMIP6) and the
A13 (CMIP5) studies is 4.97 and 4.74

◦

C, respectively. The

temperature change in the BGC simulation in CMIP6 models
(0.21

◦

C) is, however, slightly lower than in the CMIP5 mod-

els (0.26

◦

C). The values in Fig. 1 for participating CMIP5

models are slightly different than those reported in the A13
study because those numbers also included the UVic Earth
System Climate Model (an intermediate complexity model),
which we have omitted here to keep the comparison consis-
tent between comprehensive ESMs. In addition, in contrast

to A13, the temperature at the end of the simulations in this
study is calculated after fitting a fourth-order polynomial in R
to the model mean values rather than using the actual model
mean value at the end of the simulation which can be higher
or lower than that calculated using the polynomial fit due
to interannual variability. A fourth-order polynomial fit has
been shown to yield a good estimate of the forced response
of the global mean temperature response and to minimize the
potential influence of internal variability (Hawkins and Sut-
ton, 2009).

Figures 2 and 3 show simulated model mean values and

the range across models for annual simulated atmosphere–
land and atmosphere–ocean CO

2

fluxes and their cumulative

values for participating CMIP6 and CMIP5 models from the
COU, BGC, and RAD configurations of the 1pctCO2 exper-
iment. The general results from CMIP6 models are broadly
similar in nature to those from CMIP5 models, as would
be expected, with higher annual and cumulative values of
atmosphere–land and atmosphere–ocean CO

2

fluxes in the

BGC simulation compared to the COU simulation in which
the radiative warming caused by increasing CO

2

weakens the

land and ocean sinks. In the RAD simulation, where land and
ocean carbon cycle components do not respond to increasing
[CO

2

], both components lose carbon, for reasons discussed

below.

Over land, the model mean rate of increase in atmosphere–

land CO

2

flux declines and even becomes negative in the

COU and BGC simulations as the terrestrial CO

2

fertiliza-

tion effect saturates and the carbon pools build up, which
increases the respiratory losses. The biggest difference be-
tween the CMIP5 and CMIP6 models is that the cumulative

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

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Figure 2.

Model mean values and the range across models for annual simulated atmosphere–land CO

2

flux

(a, b)

and their cumulative values

(c, d)

for participating CMIP6

(a, c)

and CMIP5

(b, d)

models from the fully, biogeochemically, and radiatively coupled versions of the

1pctCO2 experiment. Individual CMIP6 model results are shown in Fig. A1.

land carbon uptake in the COU simulation is about 25 %
higher in CMIP6 (635

±

258 PgC, mean

±

standard devia-

tion) models than in CMIP5 (505

±

297 PgC) models, al-

though this increase is not statistically significant across
the model ensemble (Mann–Whitney test). Here and here-
after, we use the sample (not population) standard deviation.
The cumulative value of carbon loss in the RAD simula-
tion is similar in both CMIP6 and CMIP5 models: 239

±

120

vs. 252

±

158 PgC, respectively. This carbon loss occurs due

to both increased heterotrophic respiration per unit carbon
mass and reduced GPP (and consequently NPP) in the RAD
simulation (not shown). While NPP declines globally in re-
sponse to increases in temperature, mid- to high-latitude net
primary production increases (Qian et al., 2010), so the re-
duction in global NPP comes largely from the reduction in
the tropics. The large spread across CMIP6 land carbon cy-

cle models, seen also in earlier F06 and A13 studies, has not
changed significantly compared to CMIP5 models, and its
implications will be discussed in more detail in Sect. 5. As
discussed later in Sect. 4.3, the standard deviation of land
carbon–climate feedback increases from CMIP5 to CMIP6
models, while it decreases somewhat for the land carbon–
concentration feedback.

Over the ocean, the response to increasing [CO

2

] and

changing climate remains fairly similar across CMIP5 and
CMIP6 models. The cumulative ocean carbon uptake in the
COU simulation is 593

±

54 and 611

±

50 PgC in CMIP6

and CMIP5 models, respectively. Unlike the land uptake,
however, the ocean carbon uptake does not saturate over the
length of the simulation in the BGC simulation (Fig. 3a, b);
it keeps on increasing albeit at a declining rate. The cumula-
tive ocean carbon loss in the RAD simulation is 23

±

19 and

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Figure 3.

Model mean values and the range across models for annual simulated atmosphere–ocean CO

2

flux

(a, b)

and their cumulative

values

(c, d)

for participating CMIP6

(a, c)

and CMIP5

(b, d)

models from the fully, biogeochemically, and radiatively coupled versions of

the 1pctCO2 experiment. Individual CMIP6 model results are shown in Fig. A1.

37

±

17 PgC in CMIP6 and CMIP5 models, respectively, and

is primarily associated with warmer temperatures which re-
duce CO

2

solubility (Goodwin and Lenton, 2009; Schwinger

et al., 2014).

As in F06 and A13, the range in cumulative atmosphere–

land CO

2

fluxes among models at the end of the COU sim-

ulation, in response to changes in atmospheric CO

2

concen-

tration and surface temperature, is 3 to 4 times larger than for
the atmosphere–ocean CO

2

fluxes. Figure A1 shows results

from individual CMIP6 models for which model means and
ranges were shown in Figs. 1, 2, and 3 and allows for the
identification of models which behave differently compared
to the majority of models.

4.2

Carbon budget terms

Figure 4a shows the carbon budget components of the diag-
nosed cumulative fossil fuel emissions at the end of the 140-
year period of the 1pctCO2 COU experiment when CO

2

con-

centration quadruples (

˜

E

4

×

CO

2

or simply

˜

E

), from CMIP6

models. Cumulative emissions can similarly also be calcu-
lated at 2

×

CO

2

(

˜

E

2

×

CO

2

). The term “carbon budget” in

this context refers to the accounting of carbon internal to in-
dividual ESMs. The sum of ocean (

1

C

0

O

) and land (

1

C

0

L

)

sinks and the resulting change in atmospheric carbon burden
(

1

C

0

A

) yield cumulative fossil fuel emissions which are con-

sistent with the specified CO

2

pathway (the 1pctCO2 sce-

nario in this case) as indicated in the Appendix (Eq. A6).
The corollary to this is that, in a specified emissions simula-
tion, if the respective fossil fuel emissions were to be used in

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

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Figure 4.

Components of the carbon budget terms in cumulative emissions from the 11 participating CMIP6 models based on Eq. (A6) in

(a)

and Eq. (A7) in

(b)

using results from the fully coupled 1pctCO2 simulation. The models are arranged in an ascending order based on

their cumulative emissions values. Results from participating CMIP5 models in the A13 study are shown in panels

(c)

and

(d)

. In addition,

ESMs whose land component includes a representation of the N cycle are identified by a red font colour for cumulative land carbon uptake

(a, c)

and fractional emissions taken up by land

(b, d)

. Model mean is shown not only for all models but also separately for models whose

land components include or do not include a representation of the N cycle.

their models, each model would yield CO

2

concentrations

that rise at a rate of 1 % yr

−

1

. The term “diagnosed” im-

plies that the cumulative fossil fuel emissions are calculated
from changes in atmosphere, land, and ocean carbon pools in
the specified-concentration 1pctCO2 experiment. Figure 4b
shows the terms of the budgets as fractional components for
atmosphere (A), land (L), and ocean (O) based on Eq. (A7),
where

f

A

is the airborne fraction of emissions and

f

L

and

f

O

are the fractions of emissions take up by land and ocean,

respectively. More details are provided in Sect. A1 of the Ap-
pendix.

1

C

0

A

+

1

C

0

L

+

1

C

0

O

=

Z

t

0

E

d

t

= ˜

E

(18)

f

A

+

f

L

+

f

O

=

1

(19)

All panels in Fig. 4 identify models whose land component
includes a representation of the N cycle – the cumulative land
carbon uptake (panels a and c) and fractional emissions taken
up by land (panels b and d) for these models are shown in red.

Consistent with Figs. 2 and 3, and CMIP5 results reported

in the A13 study, the differences among models are pri-
marily due to the diverse response of the land carbon cy-
cle components. While the model mean cumulative carbon
uptake by the ocean is fairly similar between participating
CMIP5 (611

±

50 PgC) and CMIP6 (593

±

54 PgC) models,

the land uptake is higher in CMIP6 (635

±

258 PgC) com-

pared to CMIP5 (505

±

297 PgC) models, as mentioned ear-

lier. This is the case even when the CanESM5, the model
with the largest land carbon uptake, is omitted from CMIP6
models (model mean land carbon uptake for the remain-

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Figure 5.

Carbon–concentration

(a)

and carbon–climate

(b)

feedback parameters over land from participating CMIP6 models calculated

using the approaches summarized in Table 1. The boxes show the mean

±

1 standard deviation range, and the individual coloured dots

represent individual models. Models which include a representation of the land nitrogen cycle are identified with a circle around their dot.
The model mean

±

1 standard deviation range of feedback parameters is also separately shown for models which do and do not represent the

land nitrogen cycle using the BGC–COU approach. Results from participating CMIP5 models in the A13 study are shown in

(c)

and

(d)

.

ing 10 models is 578

±

185 PgC). As a result, the model

mean cumulative diagnosed emissions from CMIP6 mod-
els (3031

±

242 PgC) are about 4 % higher than those from

CMIP5 models (2927

±

294 PgC). In Fig. 5a, the land car-

bon uptakes in the CESM2 (656 PgC) and NorESM2-LM
(652 PgC) models are very similar; as noted above these
models employ the same land component. Model mean es-
timates that are reported separately for models whose land
component does and does not include a representation of the
N cycle, for both CMIP5 and CMIP6 models, show that the
model mean land carbon uptake is lower for models that ex-
plicitly represent the N cycle. As a consequence, the airborne
fraction of emissions is also higher for models that repre-

sent the land N cycle and their diagnosed cumulative fossil
fuel emissions are lower (Fig. 4). Of the 11 CMIP6 ESMs
considered in this study, 6 represent the N cycle over land
compared to only 2 of the 8 considered in the A13 study
based on CMIP5 models. Yet, the model mean land carbon
uptake over land is higher in this study than in the A13 study.
This is partly because of the three models with the largest
land carbon uptake (CNRM-ESM2-1, BCC-CSM2-MR, and
CanESM5) which do not include land the N cycle (Fig. 4a).
In addition, inclusion of the N cycle does not universally im-
ply lower land C uptake. In Fig. 4a, IPSL-CM6A-LR and
NOAA-GFDL-ESM4, both of which do not include the land

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N cycle, yield lower land carbon uptake than four of the mod-
els that do include the land N cycle.

Figure 4a and c allow for the direct comparison of models

from the same modelling group. CanESM2, from the CC-
Cma, which had below-average land carbon uptake among
CMIP5 models, has evolved into CanESM5, a model with
the largest land carbon uptake among CMIP6 models. The
reason for this is an increase in the strength of its CO

2

fer-

tilization effect following the retuning of its photosynthesis
downregulation parameters, using carbon budget constraints
over the historical period, as explained in Arora and Scinocca
(2016). CESM1, which had one of the lowest land carbon
uptakes among CMIP5 models, because of its apparently ex-
cessive nitrogen limitation effect in CLM4, has evolved into
CESM2 (with the CLM5 land component) with near-average
land carbon uptake among CMIP6 models. The transition of
CLM from CLM4 to CLM5 on the one hand and the reduc-
tion in its nutrient constraints on photosynthesis and the para-
metric controls on fertilization responses on the other are
discussed in Wieder et al. (2019) and Fisher et al. (2019),
respectively. The land carbon uptake in MIROC-ESM in-
creased from the lowest among CMIP5 models to near av-
erage for MIROC-ES2L among CMIP6 models, due to a
new terrestrial biogeochemical component (Ito and Inatomi,
2012). Although the CO

2

fertilization effect in this new land

model is weaker likely due to the incorporation of the nitro-
gen cycle, the model yields relatively higher NPP (Hajima
et al., 2020), due to a higher CUE

1

(as confirmed later in

Sect. 4.4.1). The land carbon uptake in the IPSL-CM5A-LR
model decreased from being the second largest in CMIP5
models to below average for the IPSL-CM6A-LR model due
to the implementation of terrestrial photosynthesis downreg-
ulation, as a function of CO

2

concentration, which leads to a

decrease in GPP across all latitudes, with the largest decrease
in the tropics. For the MPI ESM, the decrease in land carbon
uptake in MPI-ESM-LR for CMIP5 and MPI-ESM1.2-LR
for CMIP6 is associated with the implementation of a nitro-
gen cycle model (Goll et al., 2017) and a new soil carbon
model Yasso (Goll et al., 2015). Compared to its predeces-
sor HadGEM2-ES, UKESM1-0-LL represents a prognostic
treatment of terrestrial nitrogen including its impact on car-
bon storage in vegetation biomass and soil organic matter. A
limitation on terrestrial productivity from available nitrogen
is likely also the main reason for reduced land carbon storage
in UKESM1-0-LL compared to in HadGEM2-ES.

The ocean carbon uptake in the IPSL model decreased

from being the largest among CMIP5 models in IPSL-
CM5A-LR to being lower than average for IPSL-CM6A-LR,
and this change is attributed to a greater ocean stratification
in the IPSL-CM6A-LR. The annual mean mixed-layer depth
is 46.7 and 40.2 m in IPSL-CM5A-LR and IPSL-CM6A-LR,
respectively. While NorESM1-ME was one of the CMIP5
models with the largest ocean carbon uptake, NorESM2-LM
has an ocean carbon uptake close to the CMIP6 model mean.
This change is a consequence of changes in the simulated

(shallower depth and weaker strength) Atlantic meridional
overturning circulation and reduced mixed-layer biases par-
ticularly at high latitudes (less deep winter mixing). Due to
these modifications, the efficiency of carbon export below the
mixed layer in NorESM2-LM is considerably reduced com-
pared to in NorESM1-ME. This, in turn, leads to less ex-
cess carbon stored in the North Atlantic Deep Water (below
2000 m) as well as in the Antarctic Intermediate Water.

Figure A2 in the Appendix shows a version of Fig. 4 but at

the time of CO

2

doubling (at year 70). Interestingly, the or-

dering of the models according to their diagnosed cumulative
emissions at 2

×

CO

2

is different from that at 4

×

CO

2

. As ex-

pected, however, the model mean fractional emissions taken
up by land and ocean at 2

×

CO

2

are higher than at 4

×

CO

2

,

because both land and ocean carbon sinks relatively weaken
as CO

2

continues to increase.

4.3

Feedback parameters

Figure 5a and b compare the carbon–concentration feedback
(

β

L

) and carbon–climate feedback (

γ

L

) parameters over land

from participating CMIP6 models, calculated using results
at the end of the BGC, RAD, and COU simulations. The
plots show not only feedback parameters from different mod-
els as coloured dots but also their mean

±

1 standard devia-

tion as a box. Three primary observations can be made from
Fig. 5. First and foremost, the spread in the magnitude of
the carbon–concentration and carbon–climate feedback over
land in CMIP6 models is of a similar magnitude to that in
CMIP5 models (Fig. 5c and d). Second, the carbon–climate
feedback (

γ

L

) is more sensitive to the approach used (and

hence the type of simulations used) to derive its value than
the carbon–concentration feedback (

β

L

). The absolute value

of

β

L

varies by around 7 %, while

γ

L

varies by up to 26 %,

depending on the approach used. Third, in the model mean
sense, the absolute strength of the feedback parameters is
weaker for models that include a representation of the N cy-
cle, for both CMIP5 and CMIP6 models. Both the carbon
gain due to an increase in atmospheric CO

2

concentration

and the carbon loss due to an increase in the global average
temperature in models with representation of the land N cy-
cle are much lower than in models that do not include the N
cycle. This response is most likely explained by the N limi-
tation of photosynthesis as CO

2

increases and the additional

release of N from dead organic matter as warming increases,
which boosts productivity, thereby compensating for carbon
lost due to increased respiratory losses, as also discussed in
A13. The values of the feedback parameters, however, over-
lap between models that do and do not include a representa-
tion of the N cycle, given the wider spread in the feedback
parameter values among models that do not include a repre-
sentation of the land N cycle compared to models that do.

Figure 6a and b compare the carbon–concentration feed-

back (

β

O

) and carbon–climate feedback (

γ

O

) parameters

over the ocean from participating CMIP6 models. For both

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Figure 6.

Carbon–concentration

(a)

and carbon–climate

(b)

feedback parameters over ocean from participating CMIP6 models calculated

using the approaches summarized in Table 1. The boxes show the mean

±

1 standard deviation range. Results from participating CMIP5

models in the A13 study are shown in

(c)

and

(d)

.

CMIP5 and CMIP6 models, the absolute spread in the mag-
nitude of the feedback parameters across the participating
models is an order of magnitude smaller for the ocean C cy-
cle component compared to the land C cycle component, as
was also seen in F06 and A13. Similar to the land, the calcu-
lated values of the ocean carbon–climate feedback (

γ

O

) are

more sensitive to the approach used (and hence the type of
simulations used) than the ocean carbon–concentration feed-
back (

β

O

). In agreement with Schwinger et al. (2014), the

absolute values of

γ

O

are 2–3 times larger when calculated

using the COU and BGC simulations, compared to cases
when RAD simulation is used, for reasons mentioned ear-
lier. Figures 5 and 6 show also that while the strength of
the carbon–concentration feedback is similar over land and
ocean, the strength of the carbon–climate feedback parame-
ter over ocean is much weaker than over land.

Figures 5 and 6 provide justification for using the BGC–

COU approach, over the RAD–BGC and RAD–COU ap-
proaches, in calculating the feedback parameters as discussed
below. In Fig. 6, the absolute magnitude of

γ

O

when using

the BGC–COU approach is about twice as large in CMIP5

models and more than 3 times larger in CMIP6 models com-
pared to its model mean value calculated using the RAD–
BGC and RAD–COU approaches. The reason for this is that
the RAD simulation misses the suppression (due to weaken-
ing of the ocean circulation) of carbon drawdown to the deep
ocean due to a lack of buildup of a strong carbon gradient
from the atmosphere to the deep ocean, as mentioned ear-
lier. This process is important when climate change is forced
by increasing atmospheric CO

2

, and therefore feedback pa-

rameters calculated using the BGC–COU approach are more
likely to include all processes relevant to application to real-
istic scenarios. In Fig. 6, the value of

γ

O

changes sign for the

CNRM-ESM2-1 model from positive when calculated using
the RAD–BGC or RAD–COU approaches to negative when
calculated using the BGC–COU approach, and this further
illustrates the sensitivity of feedback parameters to the ap-
proach used to calculate them. Section A2 discusses the rea-
sons for this sensitivity in the CNRM-ESM2-1 model.

In Fig. 5, although the carbon–climate feedback param-

eter over land (

γ

L

) is larger in absolute terms, it is com-

paratively less sensitive to the approach used than that over

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ocean, because over land an increase in temperature not
only increases the respiratory losses but also affects photo-
synthetic processes especially in conjunction with increas-
ing CO

2

. Warmer temperatures increase photosynthesis over

mid- to high-latitude regions where photosynthesis is cur-
rently limited by temperature and more so with increasing
CO

2

but decrease photosynthesis over tropical regions where

the temperatures are already too warm for optimal photosyn-
thesis. The net result of these compensating processes plays
out very differently in different models, and in the model
mean sense this results in less sensitivity over land than over
ocean of the calculated value of the carbon–climate feed-
back parameter (

γ

L

and

γ

O

, respectively) to the different ap-

proaches. This is seen in both CMIP5 and CMIP6 models.
Over land, photosynthesis is also affected by temperature
(with widely varying responses between models) in addition
to respiration, and the

γ

L

values vary widely between mod-

els between the RAD–BGC and RAD–COU approach and
the BGC–COU approach. This is seen, for example, for the
ACCESS-ESM1.5, IPSL-CM6A-LR, and CanESM5 models
in Fig. 5b.

Figures 5 and 6 also show that the effect of assuming

T

∗

(the temperature change in the BGC simulation) to be

zero is around 1 % for the calculated value of the carbon–
concentration feedback parameter (

β

X

;

X

=

LO) and around

5 % for the carbon–climate feedback parameter (

γ

X

;

X

=

LO). This small effect of

T

∗

on the calculated global val-

ues of the feedback parameter allows for the investigation of
the reasons for differences among model by using simplified
forms of

β

X

and

γ

X

as presented in Eqs. (6) and (7).

For completeness, Table A1 in the Appendix summarizes

the values of feedback parameters for both land and ocean
from CMIP6 and CMIP5 models (corresponding to Figs. 5
and 6) not only at 4

×

CO

2

but also at 2

×

CO

2

. Table A1

also shows the value of parameter

α

, the linear transient cli-

mate sensitivity to CO

2

, following F06 (their Eq. 6), which

is calculated using values at the end of the COU simulation
as

T

0

=

αc

0

.

(20)

4.4

Reasons for differences among models

4.4.1

Land

Equations (8) and (9) in Sect. 2.1.1 are used to gain in-
sight into reasons for differing responses of land models.
In the BGC–COU approach and assuming

T

∗

=

0 (Eq. 8),

the carbon uptake in the BGC simulation is used to calcu-
late the carbon–concentration feedback parameter (

β

L

). Fig-

ure 7 shows how this carbon uptake over land is separated
into vegetation and soil

+

litter components both in absolute

(panel a) and fractional (panel b) terms. Figure 7b shows that
models vary widely in terms of how the carbon uptake over

Figure 7.

Carbon uptake over land in the BGC simulation, used

to calculate land carbon–concentration feedback (

β

L

) and its parti-

tioning into vegetation and soil

+

litter carbon pools across the par-

ticipating CMIP6 models

(a)

. Panel

(b)

shows the fractional land

carbon uptake by vegetation and soil

+

litter carbon pools in the

BGC simulation. No partitioning is shown for the BCC-CSM2-MR
model because total land carbon uptake in this model exceeded the
sum of changes in the vegetation and soil

+

litter carbon pools by

more than 10 %. Total land carbon uptake in models which include
a representation of the N cycle is shown in red. The results from the
BCC-CSM2-MR model are not used in calculating the model mean
values.

land is split into vegetation and soil

+

litter components. The

model mean values indicate that slightly more of the car-
bon sequestered is allocated to vegetation (55 %) than to the
soil

+

litter pools (45 %).

Figure 8 shows the individual components of Eq. (8)

which contribute to terms corresponding to changes in veg-
etation (

1

C

V

) and soil

+

litter (

1

C

S

) carbon pools. Figure

7a is repeated in Fig. 8 for the easy matching of individ-
ual components of Eq. (8) with their corresponding models.
The model mean values of individual terms do not take into

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Figure 8.

Individual terms of Eq. (8) which contribute to changes in

vegetation (

1

C

V

) and litter

+

soil (

1

C

S

) carbon pools. Values from

the BCC-CSM2-MR model are not used in calculating the model
mean.

account the results from the BCC-CSM2-MR model as ex-
plained in the figure caption. In essence, the terms in Fig. 8
are emergent properties of the land models of the individual
ESMs and result from their multiple interacting processes.
The comparison of the individual terms of Eq. (8) provides
additional insight into the reasons for differences in land
models. For example, the CNRM-ESM2-1 model has the
highest land carbon uptake among all models in the BGC
simulation. However, this is not caused by a strong CO

2

fer-

tilization effect (the

1

GPP

c

0

term) but rather by the relatively

high

τ

veg

1

and

τ

soil

1

values. The CO

2

fertilization effect is

strongest for the three models that simulate vegetation cover
dynamically (NOAA-GFDL-ESM4, MPI-ESM1.2-LR, and
UKESM1-0-LL) since the

1

GPP

c

0

term also implicitly in-

cludes the effect of increasing vegetation cover as CO

2

in-

creases. The tree cover in the NOAA-GFDL-ESM4 model,
for example, increases in the BGC simulation – particularly
in dry, high-latitude regions above 50

◦

N (not shown). How-

ever, these models do not simulate the largest land carbon
uptake because of their lower-than-average

τ

veg

1

and

τ

soil

1

values. The

1

GPP

c

0

term is unable to capture the CO

2

fertil-

ization effect separately from increasing vegetation cover,
and this illustrates the challenge in comparing models that
do and do not simulate vegetation cover dynamically. The
CanESM5 model exhibits higher-than-average land carbon
uptake despite its near-average strength of the CO

2

fertiliza-

tion effect and

τ

veg

1

and

τ

soil

1

values. However, its CUE

1

is the highest, and therefore a much larger fraction of GPP
is converted to NPP. Although CUE

1

is not the same as

CUE, we found that CUE

1

and CUE (calculated at the end

of the 1pctCO2 simulation at 4

×

CO

2

) are strongly corre-

lated with a correlation of around 0.90 (not shown). Simi-
larly,

τ

veg

1

is strongly correlated, with a correlation of 0.96,

to

τ

veg

=

C

V

/

NPP calculated at the end of the simulation.

The ACCESS-ESM1.5 model exhibits the lowest land car-
bon uptake because of its weak CO

2

fertilization effect and

the lowest CUE

1

of all models. Finally, the

1R

h

1

LF

term shows

the least variability across models, which is reflective of the
fact that the magnitude of the heterotrophic respiration flux is
dominated by NPP inputs into the dead carbon pools (Koven
et al., 2015). Several of these individual terms are strongly
correlated. The

1

GPP

c

0

and

1

LF

c

0

terms have a correlation of

0.77, and CUE

1

GPP

c

0

and

1

LF

c

0

have a correlation of 0.94,

since a stronger CO

2

fertilization effect also implies a larger

litterfall flux per unit CO

2

. Surprisingly, CUE

1

and

τ

veg

1

are negatively correlated (correlation

= −

0

.

49) across mod-

els, indicating that models which retain a higher fraction of
GPP as NPP typically get rid of vegetation carbon sooner via
litterfall as indicated by a faster turnover of vegetation (lower

τ

veg

1

), thereby partially compensating for higher CUE

1

.

Figure 9 investigates the reasons for varying magnitudes

of the carbon–climate feedback over land (

γ

L

). In Eq. (9),

γ

L

is a function of change in land carbon (divided into veg-

etation and soil

+

litter components) in the COU relative to

the BGC simulation and the temperature change in the COU
simulation (

T

0

). Over land, the higher temperatures in the

COU relative to the BGC simulation affect not only both au-
totrophic and heterotrophic respiratory fluxes, from live and
dead vegetation pools, respectively, but also gross photosyn-
thesis rates. The primary effect of this temperature change in
COU versus the BGC simulation is the loss of carbon from
the soil

+

litter carbon pool (hence the negative sign of

γ

L

for most models; Fig. 6b and d), but changes in the vegeta-
tion carbon pool also occur. Although

γ

L

also depends on

T

0

,

Fig. 9 arranges models in order from the largest to smallest
loss of land carbon in COU relative to the BGC simulation to
illustrate the varying response of the models. This ordering
of models changes slightly if the carbon loss (or gain in the
CanESM5 model) is divided by the temperature change

T

0

in

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4191

Figure 9.

The changes in vegetation and soil

+

litter carbon pools

in the COU relative to the BGC simulation, as shown in Eq. (9),
which contribute to the calculation of the carbon–climate feedback
over land (

γ

L

) in the BGC–COU approach. The names of models

which include the N cycle are shown in a red font colour.

the COU simulation (yielding the value of

γ

L

which assumes

T

∗

=

0 as in Eq. 9).

As shown in Fig. 9, all models lose carbon from the

soil

+

litter carbon pool but with widely varying magnitudes.

Although typically smaller than the change in the soil

+

litter

carbon pool, the change in the vegetation carbon pool in the
COU relative to the BGC simulation is not of the same sign
across models. Of the 11 participating models, 6 lose car-
bon in the vegetation pool in the COU relative to the BGC
simulation, thereby contributing to increasing the absolute
magnitude of

γ

L

, while the remaining 5 exhibit an increase

in the vegetation carbon pool, thereby decreasing the abso-
lute magnitude of

γ

L

. The largest increase in the vegetation

carbon pool is seen in the CanESM5 model that more than
compensates for the carbon loss from the soil

+

litter carbon

pool, yielding a positive value of

γ

L

in contrast to other mod-

els. This case is one of the few times a positive value of

γ

L

is seen in an Earth system model. Thornton et al. (2009) re-
ported positive

γ

L

after their first attempt to include N cycle

in the CLM. Preliminary analysis of CanESM5 data shows
the increase in vegetation carbon in the COU relative to the
BGC simulation is caused by the increase in GPP and the
resulting vegetation growth at middle to high latitudes in re-
sponse to warming temperatures and increasing CO

2

. Inter-

estingly, this response is not seen at 2

×

CO

2

(see Table A1

in the Appendix), and

γ

L

is still negative for CanESM5.

The loss in land carbon in the COU relative to the BGC

simulation (except for the CanESM5 model that gains car-
bon), indicated by the dark orange bars in Fig. 9, is strongly
correlated with the carbon gain in the BGC simulation
(Fig. A1e; correlation is 0.59 for all models and 0.87 when
CanESM5 is excluded) but not with the absolute amount of
total land carbon. Figure A3 in the Appendix shows the ab-
solute amount of carbon in soil

+

litter and vegetation pools,

and their change from the beginning, for the BGC simula-

Table 3.

Correlation between carbon–concentration (

β

X

) and

carbon–climate (

γ

X

) feedback parameters over land and ocean

across comprehensive ESMs from the CMIP5 intercomparison in
the A13 study and CMIP6 intercomparison in this study. For the
land correlation it is also shown when CanESM5 is excluded from
CMIP6 models.

Land

Ocean

−

0

.

69

−

0

.

64

CMIP6

−

0

.

92 (excluding CanESM5)

(11 models)

−

0

.

82

−

0

.

75

CMIP5
(8 models)

tion. The models vary widely in terms of the absolute size of
the carbon pools, especially for the soil

+

litter pool. There

are two implications of models losing more carbon in the
COU relative to the BGC simulation when they take up more
carbon in the BGC simulation alone. First, the transient be-
haviour of a model is determined primarily by its response to
CO

2

and temperature perturbations and not by the absolute

amount of land carbon. Second, carbon–concentration (

β

X

)

and carbon–climate (

γ

X

) feedback parameters must be cor-

related as well. Indeed, this is not only the case over land for
both CMIP5 and CMIP6 models but also true for ocean feed-
backs although the correlations are somewhat weaker over
the ocean. These correlations are shown in Table 3 and are
negative since higher positive values of

β

X

are correlated

with higher negative values of

γ

X

, indicating that models that

take up more carbon with increasing CO

2

also release more

carbon when they “see” the associated higher temperatures.

4.4.2

Ocean

The time-integrated air–sea flux of carbon provides the dom-
inant contribution to the increase in global ocean carbon
through changes in the DIC inventory. However, the global
ocean carbon inventory is also affected by the land-to-ocean
carbon flux from river runoff and the carbon burial in ocean
sediments (see Table A2 in the Appendix).

Ocean carbon cycle feedbacks are defined in terms of

ocean carbon inventory changes for the COU simulation and
by the differences in COU relative to the BGC simulation. To
fully understand the ocean carbon cycle feedbacks, it is nec-
essary to understand the ocean carbon distributions for the
preindustrial period and then analyze the carbon anomalies
relative to the preindustrial period for these climate model
experiments.

Ocean carbon distribution

The ocean dissolved inorganic carbon, DIC, distribution is
controlled by a combination of physical, chemical, and bio-
logical processes. For the preindustrial period, there is less
DIC in the warmer waters of the upper ocean and more DIC

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Figure 10.

Meridional section of the dissolved inorganic carbon, DIC (mol m

−

3

), and constituent carbon pools in UK-ESM1-0-LL for

the zonally averaged Atlantic and Southern Ocean:

(a)

the preindustrial absolute concentrations and

(b–d)

the anomalies relative to the

preindustrial state at year 140 for

(b)

the COU configuration,

(c)

the BGC configuration, and

(d)

the COU minus the BGC configuration.

The DIC is separated into saturated carbon, DIC

sat

, the disequilibrium carbon, DIC

disequilib

, and the regenerated carbon, DIC

regenerated

. The

Atlantic and Southern Ocean domains are separated by a vertical black line.

in the colder mid-depth and bottom waters (Figs. 10a, 11a;
illustrated here for UKESM1-0-LL as a representative exam-
ple, and Figs. S1 to S7 show similar distributions for all the
diagnosed Earth system models). The vertical extent of the
low DIC follows the undulations of the thermocline, which
is defined by strong vertical temperature and density gradi-
ents, and is deeper over the subtropical gyres at 30

◦

N and

30

◦

S and shallower in the equatorial zone and at high lati-

tudes. The greater DIC at depth is a consequence of greater
solubility in colder waters and the accumulation of DIC from
the regeneration of organic matter.

To gain insight into how the ocean carbon distribu-

tion is controlled, the DIC is separated into three pools,
DIC

sat

, DIC

disequilib

, and DIC

regenerated

, as defined earlier.

The DIC distribution for both the preindustrial period and
after 140 years in the 1pctCO2 simulation reveal the follow-
ing key features for each of these carbon pools (Figs. 10a, b
and 11a, b):

–

The saturated carbon pool provides the dominant con-
tribution to the DIC, holding more than 2.15 mol C m

−

3

,

particularly within cooler waters below the thermocline.

–

The regenerated carbon pool enhances the carbon stored
below the surface waters, typically providing an addi-
tional 0.2 mol C m

−

3

within the Southern Ocean and

older waters spreading from the Southern Ocean into
the Atlantic and below the thermocline in the Pacific.

–

The disequilibrium carbon is small close to the sur-
face, representing waters close to an equilibrium with
the atmosphere. There is sometimes a positive disequi-
librium of up to 0.05 mol C m

−

3

in some surface waters,

which is associated with upwelling transferring carbon-
rich deeper waters to the surface. The disequilibrium
carbon is more strongly negative below the thermocline,
typically reaching

−

0

.

1 mol C m

−

3

in the Atlantic and

−

0

.

02 mol C m

−

3

in the Southern Ocean and Pacific. In

the preindustrial period, the undersaturation in carbon
below the thermocline is due to the subduction of cold

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Figure 11.

Meridional section of the dissolved inorganic carbon, DIC (mol m

−

3

), and constituent carbon pools in UK-ESM1-0-LL for

the zonally averaged Pacific and Southern Ocean:

(a)

the preindustrial absolute concentrations and

(b–d)

the anomalies relative to the

preindustrial state at year 140 for

(b)

the COU configuration,

(c)

the BGC configuration, and

(d)

the COU minus the BGC configuration.

The DIC is separated into saturated carbon, DIC

sat

, the disequilibrium carbon, DIC

disequilib

, and the regenerated carbon, DIC

regenerated

. The

Pacific and Southern Ocean domains are separated by a vertical black line.

waters at high latitudes that have not equilibrated fully
with the atmosphere, which then spread by advection
along density surfaces. In the model integrations reach-
ing year 140, the carbon below the thermocline becomes
further undersaturated relative to the contemporary at-
mosphere due to the rapid rise in [CO

2

].

Next we consider the anomalies in the DIC at year

140 in the COU configurations of the 1pctCO2 simulation
calculated relative to the preindustrial period. The carbon
anomaly,

1

DIC, in the COU configuration is positive over

the upper thermocline over the Atlantic and Pacific basins,
reaching

+

0

.

3 mol C m

−

3

, coinciding with regions that are

well ventilated. This gain in carbon is made up of an increase
in the saturated carbon over all depths due to higher atmo-
spheric CO

2

. There is a dipole in the disequilibrium anomaly

(Figs. 10b, c and 11b, c); it is generally weakly positive in
the upper ocean and more strongly negative in deeper waters
below the thermocline reaching up to

−

0

.

2 mol C m

−

3

. This

negative disequilibrium anomaly in deeper waters is small-
est in the relatively well-ventilated mid-depth waters of the

North Atlantic but extends over nearly all of the more poorly
ventilated mid-depth waters of the Pacific (Figs. 10b and
11b).

The regenerated carbon anomaly is relatively small in

magnitude, reaching less than 0.05 mol C m

−

3

, and varies re-

gionally, enhanced within much of the North Atlantic and the
thermocline of the Pacific but with little change in the deep
waters of the Pacific (Figs. 10b and 11b). The increase in
regenerated carbon is due to a weakening of ocean overturn-
ing leading to an increase in residence time and an associ-
ated accumulation of DIC from the regeneration of biologi-
cally cycled carbon (Bernardello et al., 2014; Schwinger et
al., 2014). The regenerated carbon signal does not change in
the mid-depths and deep Pacific as 140 years is too short an
integration timescale for any effect to be detected.

To diagnose the carbon cycle feedback parameters, the

ocean carbon response needs to be considered for the BGC
configuration where there is only limited warming from the
increase in atmospheric CO

2

and therefore limited change in

climate and ocean circulation. The resulting DIC anomalies

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

are generally very similar to those for the COU configuration
(Figs. 10b, c and 11b, c), which is to be expected as the dom-
inant effect for the ocean carbon response is the enhanced
ocean uptake of carbon in response to the increase in [CO

2

].

There is a weakening in ventilation in the COU configura-
tion due to the additional radiative forcing. In comparison, in
the BGC configuration, there is no change in the circulation
as there is no radiative warming effect, so there is slightly
more carbon uptake in the northern North Atlantic, such as
revealed at around 50

◦

N, compared with the COU configura-

tion. For the BGC configuration, the saturated carbon pool is
slightly greater at depth due to the water masses being cooler
than in the COU configuration, the disequilibrium anomaly
shows a less negative anomaly in the northern North Atlantic
because there is little or no change in ventilation, and there
are only slight differences in the regenerated pool.

The climate response to rising [CO

2

] is now considered

in terms of the difference in the COU and BGC configura-
tions, which includes the combined effects of warming and
circulation changes (Figs. 10d and 11d). The surface warm-
ing drives a decrease in solubility, an increase in stratifica-
tion, and a reduction in ventilation, which leads to an over-
all decrease in carbon uptake over the Southern Ocean and
Pacific basins and much of the Atlantic basin. There is a de-
crease in the saturated carbon pool associated with the warm-
ing acting to inhibit carbon uptake. The regenerated carbon
anomaly is enhanced in the deep northern North Atlantic and
in the Southern Ocean. The regenerated carbon anomaly for
this climate response is very similar to that for the COU con-
figuration, suggesting that the regenerated carbon anomaly is
mainly due to circulation changes: the gain in the regenerated
carbon anomaly is consistent with the expected longer resi-
dence time from weaker overturning and ventilation. There
is a more negative disequilibrium anomaly in the deep wa-
ters of the North Atlantic, which is a consequence of weaker
ventilation.

To gain more insight into the disequilibrium response, the

ocean DIC response is also considered for the radiatively
coupled integration (RAD), where the ocean biogeochem-
istry does not see the increase in [CO

2

]. The warming in

the RAD simulation leads to a weakening in the overturn-
ing, which enhances the residence time in the surface wa-
ters and so generally decreases the magnitude of the dise-
quilibrium anomaly in the North Atlantic (Fig. S8), making
the disequilibrium less negative relative to the preindustrial
period and so forming a positive disequilibrium anomaly at
year 140. In comparison the COU–BGC approach captures
the effect of the warming under rising [CO

2

], leading to the

disequilibrium anomaly instead becoming more negative at
depth, since the weakening in the ventilation leads to more
of the anthropogenic carbon remaining at the surface rather
than being transferred into the deeper ocean (Schwinger et
al., 2014).

Figure 12.

Carbon uptake over the ocean in the biogeochem-

ically coupled simulation, used to calculate the ocean carbon–
concentration feedback and its partitioning into saturated, dise-
quilibrium, and regenerated carbon pools across the participating
CMIP6 models (left) using Eq. (12). No partitioning is shown for
models for which 3D ocean fields were not available, and the results
of these models are not used in calculating the model mean values
(right). The sum of the partitions does not exactly match the total
ocean uptake diagnosed from the air–sea fluxes due to land–ocean
interactions involving storage in sediments and river inputs.

Changes in ocean carbon pools for diagnosing feedback
parameters

The ocean carbon–concentration feedback parameter,

β

O

, is

diagnosed from the changes in the ocean carbon inventories
for the BGC configuration, which does not include radiative
warming due to increasing [CO

2

] (Eq. 13). There is a consis-

tent increase in ocean carbon storage across all models with
a model mean value of around 670 PgC (Fig. 12, turquoise
bars). This increase in ocean carbon storage is made up of an
increase in the saturated carbon inventory,

1

C

sat

, by about

3100 PgC from the increase in [CO

2

] (Fig. 12, red bars). This

increase is partly offset by a more negative disequilibrium
carbon,

1

C

disequilib

, of typically

−

2500 PgC (Fig. 12, blue

bars), representing how the ocean carbon uptake cannot keep
up with the rate of [CO

2

] increase. There is relatively lit-

tle change in the regenerated carbon inventory,

1

C

regenerated

.

The resulting

β

O

is positive and mainly explained by the

chemical response involving the rise in ocean saturation with
no significant biological changes, although the physical up-
take of carbon within the ocean is unable to keep pace with
the rise in [CO

2

].

The ocean carbon–climate feedback parameter,

γ

O

, is di-

agnosed from the difference between the COU model con-
figuration and the BGC configuration and so includes the
effect of an increasing surface warming under rising [CO

2

]

(Eq. 14). There is a broadly consistent response across mod-

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4195

els, with a model mean decrease in carbon inventory of
around 80 PgC due to the additional warming in the COU
configuration relative to the BGC configuration (Fig. 13,
turquoise bars). The effect of this additional warming and
the associated climate change leads to a decrease in both the
saturated carbon and disequilibrium carbon of typically

−

60

and

−

70 PgC (Fig. 13, orange and blue bars), representing

the decrease in solubility and decreased ocean ventilation.
There is an increase in the regenerated carbon of typically
50 PgC (Fig. 13, green bars), which is due to a weaker circu-
lation leading to a longer residence time of thermocline and
deep waters, so there is more time for the accumulation of
regenerated carbon below the mixed layer. The resulting

γ

O

is negative, indicating that the ocean takes up less carbon in
response to the combination of surface warming and a weak-
ening in ocean ventilation. This response involves a combi-
nation of chemical, physical, and biological changes where
the warming reduces the solubility of the carbon in the ocean
and a weakening in the circulation decreases the disequilib-
rium pool but lengthens the residence time and so increases
the regenerated pool.

Overall, the ocean carbon inventory increases in the BGC

configuration by 666

±

53 PgC (model mean

±

standard

deviation) and decreases in COU relative to BGC by

−

80

±

15 PgC. The resulting

β

O

is very similar across all

the models (0.78

±

0.06 PgC ppm

−

1

), reflecting not only the

strong control of carbonate chemistry by rising atmospheric
CO

2

(Katavouta et al., 2018) but also the use of similar

carbonate chemistry schemes and bulk parameterizations of
air–sea CO

2

fluxes across marine biogeochemical models

(Séférian et al., 2020). The dominant contributions are com-
posed of a positive contribution from the saturated carbon
(3.66

±

0.16 PgC ppm

−

1

) and a negative contribution from

the disequilibrium carbon (

−

2

.

98

±

0.16 PgC ppm

−

1

; see

Table A3 in the Appendix); these intermodel differences are
relatively small with ratios of the standard deviation to model
mean of only 0.05 and 0.06, respectively. The regenerated
contribution is over 2 orders of magnitude smaller than the
sum of the saturated and disequilibrium contributions and so
may be neglected for evaluating

β

O

.

The values of

γ

O

differ more strongly across the models

(

−

16

.

95

±

5.62 PgC

◦

C

−

1

) and arise from differences in the

extent of the surface warming and the dynamical changes
in the ocean circulation and resulting changes in ventila-
tion, residence time, and biological regeneration (Table A3).
The contributions to

γ

O

include negative contributions from

the saturated (

−

12

.

78

±

2.50 PgC

◦

C

−

1

) and disequilibrium

(

−

16

.

36

±

5.31 PgC

◦

C

−

1

) components, which are partly op-

posed by a positive contribution from the regenerated com-
ponent (12.25

±

8.53 PgC

◦

C

−

1

). The largest intermodel dif-

ferences are in the regenerated and disequilibrium responses
and a relatively small spread in the saturated response, with
the ratios of the standard deviation to the model mean being
0.70, 0.33, and 0.20, respectively (Table A3).

Figure 13.

Change in saturated, disequilibrium, and regenerated

carbon pools in the fully coupled minus the biogeochemical sim-
ulation using Eq. (14), which contributes to the calculation of the
carbon–climate feedback over the ocean. The sum of the partitions
does not exactly match the total ocean uptake diagnosed from the
air–sea fluxes due to land–ocean interactions involving storage in
sediments and river inputs.

4.5

Transient climate response (TCR) and transient
climate response to cumulative emissions (TCRE)

The idealized 1pctCO2 simulation is also routinely used for
calculating two other climate metrics. The first is the tran-
sient climate response (TCR), which is defined as the tem-
perature change relative to the preindustrial state at the time
of CO

2

doubling (

1T

2

×

CO

2

), which occurs at 70 years after

the start of the simulation. The second is the transient climate
response to cumulative carbon emissions (TCRE), which is
defined as the ratio of the TCR to cumulative fossil fuel emis-
sions also at the time of CO

2

doubling (

˜

E

2

×

CO

2

; Matthews

et al., 2009), typically expressed in units of degrees Celsius
per exagram of carbon (EgC

−

1

; 1 EgC

=

1000 PgC).

TCRE

=

1T

2

×

CO

2

˜

E

2

×

CO

2

(21)

It has been shown that the TCRE is approximately constant
over a wide range of cumulative emissions and emission
pathways (MacDougall, 2016). Although non-CO

2

green-

house gases and other climate forcings (e.g. aerosols and land
use change) also affect the realized warming, the TCRE is
considered to be a straightforward measure of peak warming
caused by anthropogenic CO

2

emissions. The TCRE metric

has gained significant policy relevance (Frame et al., 2014;
IPCC, 2014; Millar et al., 2016), and it is a central compo-
nent of frameworks used to calculate the remaining allowable
carbon emissions to reach a specified temperature change tar-
get above the preindustrial level (Millar et al., 2017; Rogelj
et al., 2018, 2019).

Table 4 lists the TCR,

˜

E

2

×

CO

2

, and TCRE from the 11

CMIP6 models considered in this study. We calculate the

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Table 4.

Transient climate response (TCR;

1T

2

×

CO

2

), diagnosed

cumulative emissions at 2

×

CO

2

(

˜

E

2

×

CO

2

), and transient climate

response to cumulative emissions (TCRE) for the 11 CMIP6 models
considered in this study.

CMIP6 model

TCR

Cumulative

TCRE

(

◦

C)

diagnosed

(

◦

C EgC

−

1

)

emissions

(PgC)

ACCESS-ESM1.5

2.15

1064

2.02

BCC-CSM2-MR

1.70

1291

1.32

CanESM5

2.54

1214

2.09

CESM2

2.29

1073

2.13

CNRM-ESM2-1

1.84

1124

1.63

IPSL-CM6A-LR

2.36

1107

2.13

MIROC-ES2L

1.58

1135

1.39

MPI-ESM1.2-LR

1.86

1127

1.65

NOAA-GFDL-ESM4

1.55

1066

1.45

NorESM2-LM

1.42

1075

1.32

UKESM1-0-LL

2.42

1054

2.30

Mean

1.97

1121

1.77

Sample SD

0.39

72.9

0.37

TCR, following the standard approach, as the average tem-
perature of 20 years (years 60–79) centered on the year
when CO

2

doubles (year 70). The mean

±

standard deviation

for the TCR,

˜

E

2

×

CO

2

, and the TCRE from the 11 CMIP6

models considered here is 1.97

±

0.39

◦

C, 1121

±

73 PgC,

and 1.77

±

0.37

◦

C EgC

−

1

, respectively. For 15 CMIP5

models, Gillett et al. (2013) calculated the TCRE to be
1.63

±

0.48

◦

C EgC

−

1

and a 5 %–95 % range for its observa-

tionally constrained value as 0.7–2.0

◦

C EgC

−

1

. The CMIP5

and CMIP6 mean values quoted are not statistically differ-
ent given the small sample size of available models, some of
which duplicate processes or components.

The uncertainties in the TCRE stem from uncertainties in

both the TCR and

˜

E

2

×

CO

2

which is directly affected by land

and ocean carbon uptake. A large fraction of uncertainty in

˜

E

2

×

CO

2

comes from the diverse response of land carbon cy-

cle models. Inclusion of the N cycle helps to reduce this un-
certainty in terms of the spread across the land models (both
the strength of their feedback parameters and diagnosed cu-
mulative emissions). Cumulative diagnosed emissions for
models with the land N cycle total 1088

±

34 PgC compared

to 1160

±

91 PgC for models without the N cycle (from Ta-

ble 4). For the results reported here from 11 CMIP6 models,
however, the uncertainty in the TCR (mean

±

standard de-

viation

=

1.97

±

0.39

◦

C), as indicated by standard deviation

normalized by the mean, is 3 times as big as the uncertainty
in

˜

E

2

×

CO

2

(1121

±

73 PgC). As a result, the TCR contributes

about 90 % of the total variance in the calculated TCRE value
(1.77

±

0.37

◦

C EgC

−

1

; see Sect. A6 in the Appendix).

The TCRE may also be expressed in terms of a product of

a thermal contribution from the dependence of surface warm-

ing on radiative forcing and a carbon contribution from the
dependence of radiative forcing on cumulative carbon emis-
sions (Williams et al., 2016; Katavouta et al., 2018), as

TCRE

=

1T

2

×

CO

2

1R

2

×

CO

2

1R

2

×

CO

2

˜

E

2

×

CO

2

,

(22)

where

1R

2

×

CO

2

is the change in radiative forcing relative

to the preindustrial period. For a suite of 10 CMIP5 mod-
els, Williams et al. (2017) show that the intermodel spread
in the TCRE calculated from the 1pctCO2 experiment has
a larger contribution from the intermodel differences in the

thermal contribution,

1T

2

×

CO2

1R

2

×

CO2

, due to climate feedback and

ocean heat uptake over the first few decades, but the inter-

model differences in the carbon contribution,

1R

2

×

CO2

˜

E

2

×

CO2

, due

to land and ocean carbon uptake become of comparable im-
portance after 80 years.

Thus we conclude, as shown by Jones and Friedling-

stein (2020), that the contributions to TCRE uncertainty have
changed since CMIP5 from being of similar magnitudes due
to carbon feedbacks and climate feedbacks to now being
dominated by climate feedbacks. The reduction in the spread
of land carbon model feedbacks which we are beginning to
see in CMIP6 has led to a reduction in the spread of the
TCRE implying that a large fraction of uncertainty in the
TCRE is now contributed to by physical climate system pro-
cesses that determine the TCR. More CMIP6 models include
a complete treatment of important processes – notably the
terrestrial nitrogen cycle – that determine the airborne frac-
tion and hence

˜

E

2

×

CO

2

. Reducing the uncertainty in land and

ocean carbon uptake across models remains a priority and
will contribute to further reducing the uncertainty in the esti-
mates of the TCRE on centennial timescales.

5

Summary and conclusions

Model intercomparison projects offer several benefits includ-
ing the calculation of the model mean response, the quantifi-
cation of the uncertainty based on the spread across mod-
els, and showing how this uncertainty changes over time.
The carbon feedback analysis presented here based on the
C

4

MIP protocol of experiments (Jones et al., 2016) allows

us to investigate how feedback strengths have evolved since
CMIP5 and also to attempt to understand the reasons behind
the spread in models.

The carbon uptake over land and ocean, in re-

sponse to increasing atmospheric CO

2

concentration, is

well known to be dominated by the positive contri-
bution from the carbon–concentration feedback (Gre-
gory et al., 2009; Arora et al., 2013). The strength of
this feedback is of comparable magnitudes over land
(mean

±

standard deviation

=

0.97

±

0.40 PgC ppm

−

1

) and

ocean (0.79

±

0.07 PgC ppm

−

1

) although the feedback is

much more uncertain over land as indicated by the standard

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4197

deviation across the 11 models considered here. This dom-
inant positive contribution from the carbon–concentration
feedback is, however, opposed by the weaker negative
carbon–climate feedback that is associated with the cli-
mate change that results due to increasing atmospheric
CO

2

. The absolute magnitude of this weaker negative feed-

back is about 3 times larger and an order of magnitude
more uncertain over land (

−

45

.

1

±

50.6 PgC

◦

C

−

1

) than

over ocean (

−

17

.

2

±

5.0 PgC

◦

C

−

1

). Model estimates of the

ocean carbon–concentration feedback are consistent with
each other, reflecting the strong control of how carbon-
ate chemistry alters with rising atmospheric CO

2

. There

is a relatively wider range in the model estimates of the
ocean carbon–climate feedback, particularly in terms of how
changes in ocean circulation alter the disequilibrium and
regeneration terms. Over land, however, since the carbon–
concentration and carbon–climate feedbacks are determined
entirely by biological process, which are much less under-
stood, the resulting uncertainty is much higher across the
land models than across the ocean models. This uncertainty
in the strength of carbon–concentration and carbon–climate
feedbacks over land is well known (Friedlingstein et al.,
2006; Arora et al., 2013). The inclusion of the N cycle re-
sults in lower absolute strength of the feedback parameters
over land. In addition, the land models that include a rep-
resentation of the N cycle exhibit a reduced spread in their
feedback parameters, despite the additional complexity, com-
pared to when all models are considered. This suggests that
if all models were to include the N limitation of photosyn-
thesis, the spread across them will potentially reduce.

The additional analyses that we have performed provide

insight into the reasons for the diverse responses among mod-
els, especially for land models. Over land, the diverse re-
sponse of models is found to be primarily due to the wide
range of the strength of the CO

2

fertilization effect, the frac-

tion of GPP that is converted to NPP, and the residence times
of carbon in the live (vegetation) and dead (litter plus soil)
carbon pools across models. There is more consistency in
the response of the ocean models, although intermodel differ-
ences arise from differences in the ventilation and residence
time, altering the ocean disequilibrium and regenerated car-
bon.

In regard to the TCRE, while its uncertainty is dominated

by physical processes affecting the thermal response involv-
ing climate feedbacks and heat uptake on decadal timescales,
a reduction in the uncertainty in land and ocean carbon up-
take across models will reduce the uncertainty in the TCRE
on centennial timescales.

Finally, the decision to use fully and biogeochemically

coupled configurations of the 1pctCO2 experiment as the
standard simulations from which to diagnose carbon cycle
and climate system feedbacks should provide consistency
and continuity for future versions of Earth system models
that can be compared against their predecessors.

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Appendix A: The climate carbon cycle feedbacks
framework

The rate of change in carbon in the combined atmosphere–
land–ocean system is written as

dC

G

d

t

=

dC

A

d

t

+

dC

L

d

t

+

dC

O

d

t

=

E,

(A1)

where the global carbon pool C

G

=

C

A

+

C

L

+

C

O

is the sum

of carbon in the atmosphere, land, and ocean components
(PgC) and

E

is the rate of anthropogenic CO

2

emissions

(PgC yr

−

1

) into the atmosphere. The equations for the atmo-

sphere, land, and ocean are

dC

A

d

t

=

F

A

(T , c)

+

E,

dC

L

d

t

=

F

L

(T , c) ,

dC

O

d

t

=

F

O

(T , c) ,

(A2)

where

(F

L

+

F

O

)

= −

F

A

is the fluxes between the atmo-

sphere and the underlying land and ocean, taken to be posi-
tive into the components. The fluxes

F

are expressed as func-

tions of surface temperature

T

and the surface atmospheric

CO

2

concentration

c

. Here and subsequently, uppercase C

denotes carbon pools and lowercase

c

denotes atmospheric

CO

2

concentration.

In the fully, biogeochemically, and radiatively coupled ver-

sions of the 1pctCO2 experiments analyzed here, the rate
of change in atmospheric carbon dC

A

/ d

t

is specified in

Eqs. (A1) and (A2). The uptake or release of CO

2

by the un-

derlying land and ocean yields an effective emission

E

which

serves to maintain the budget.

The changes in atmosphere carbon budgets, from the

preindustrial control simulation, in the differently coupled
simulations are represented as

radiatively coupled

dC

0

A

d

t

−

E

+

=

F

+

A

= −

F

+

L

−

F

+

O

=

0

A

T

+

,

(A3a)

biogeochemically coupled

dC

0

A

d

t

−

E

∗

=

F

∗

A

= −

F

∗

L

−

F

∗

O

=

0

A

T

∗

+

B

A

c

0

,

(A3b)

fully coupled

dC

0

A

d

t

−

E

=

F

0

A

= −

F

0

L

−

F

0

O

=

0

A

T

0

+

B

A

c

0

,

(A3c)

which

serve

to

define

the

instantaneous

carbon–

concentration (

B

A

) and carbon–climate (

0

A

) feedback

parameters and assume linearization of the globally inte-
grated surface–atmosphere CO

2

flux in terms of global mean

temperature and concentration change. In Eq. (A3),

F

+

,

F

∗

, and

F

0

are the flux changes and

T

+

,

T

∗

, and

T

0

the

temperature changes in the radiatively, biogeochemically,
and fully coupled simulations, and

E

+

,

E

∗

, and

E

are

the resulting implicit emissions.

c

0

is the specified CO

2

concentration change above its preindustrial level in the
1pctCO2 simulations. In the biogeochemically coupled
simulation there is no radiative forcing due to increasing
CO

2

, so

T

∗

is small, although not zero, and exhibits a

distinct spatial pattern. The assumption made in Eq. (A3) is
that the feedback parameters are the same in the three cases.

Carbon budget changes for the land component parallel to

Eq. (A3) but without the emissions terms as

radiatively coupled

dC

0

L

d

t

=

F

+

L

=

0

L

T

+

,

(A4a)

biogeochemically coupled

d

C

∗

L

d

t

=

F

∗

L

=

0

L

T

∗

+

B

L

c

0

,

(A4b)

fully coupled

dC

∗

L

d

t

=

F

0

L

=

0

L

T

0

+

B

L

c

0

,

(A4c)

and similarly for the ocean component. Since

F

A

=

−

(F

L

+

F

O

, )

it follows that

0

A

= −

(0

L

+

0

O

)

and

B

A

=

−

(B

L

+

B

O

)

. There are no terms involving

c

0

in the ra-

diatively coupled simulation (Eqs. A3a and A4a) since the
preindustrial value of atmospheric CO

2

concentration is pre-

scribed for the biogeochemistry components, so

c

0

=

0 and

does not affect the flux.

The instantaneous feedback parameters (

B

L

and

0

L

) dif-

fer from those in the integrated flux approach of Friedling-
stein et al. (2006), who express time-integrated flux changes
(i.e. change in pool or reservoir sizes) as functions of tem-
perature and CO

2

concentration changes with

radiatively coupled

Z

F

+

L

=

1

C

+

L

=

γ

L

T

+

,

(A5a)

biogeochemically coupled

Z

F

∗

L

=

1

C

∗

L

=

γ

L

T

∗

+

β

L

c

0

,

(A5b)

fully coupled

Z

F

0

L

=

1

C

0

L

=

γ

L

T

0

+

β

L

c

0

,

(A5c)

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4199

Figure A1.

Individual model values from CMIP6 models for globally averaged surface temperature change

(a–c)

, cumulative atmosphere–

land CO

2

flux

(d–f)

, and cumulative atmosphere–ocean CO

2

flux

(g–h)

from the fully, biogeochemically, and radiatively coupled versions

of the 1pctCO2 experiment.

and similarly for the ocean component, with the assumption
that the

1

C

0

O

term includes changes in the carbon amount of

ocean sediment as well.

The

units

of

instantaneous

and

integrated

flux-

based parameters are different (

0

–PgC yr

−

1

◦

C

−

1

,

B

–

PgC yr

−

1

ppm

−

1

and

γ

–PgC

◦

C

−

1

,

β

–PgC ppm

−

1

). Arora

et al. (2013) show how the instantaneous and integrated
flux-based feedback parameters are related to each other

Integrating Eqs. (A1) and (A2) from initial time to

t

gives

1

C

0

A

+

1

C

0

L

+

1

C

0

O

=

Z

t

0

E

d

t

= ˜

E.

(A6)

Here

1

C

0

A

=

2

.

12

(c(t )

−

c(

0

))

is the change in atmospheric

carbon burden (the factor 2.12 converts atmospheric CO

2

concentration from parts per million to atmospheric burden
in petagrams of carbon) and

1

C

0

X

=

R

t

0

F

0

X

d

t, X

=

L, O is

the cumulative flux equal to the change in the land or ocean
carbon pool for the fully coupled simulation. The terms in
Eq. (A6) indicate the contribution of changes in atmosphere,
land, and ocean carbon pools to cumulative emissions

˜

E

. Fi-

nally, division by the cumulative emissions term in Eq. (A6)

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

Figure A2.

Components of the carbon budget terms in cumulative emissions from the 11 participating CMIP6 models based on Eq. (A6) in

(a)

and Eq. (A7) in

(b)

, using results from the fully coupled 1 % yr

−

1

increasing CO

2

simulation at 2

×

CO

2

(year 70) in contrast to Fig. 4

which showed these results at 4

×

CO

2

. The models are arranged in ascending order based on their cumulative emissions values. Results from

participating CMIP5 models in the A13 study are shown in

(c, d)

. In addition, ESMs whose land component includes a representation of the

N cycle are identified by a red font colour for cumulative land carbon uptake

(a, c)

and fractional emissions taken up by land

(b, d)

. The

model mean is shown not only for all models but also separately for models whose land components include or do not include a representation
of the N cycle.

gives all the terms in a fractional form as

f

A

+

f

L

+

f

O

=

1

,

(A7)

where

f

A

is the airborne fraction of cumulative emissions

and

f

L

and

f

O

are fractional emissions taken up by the land

and ocean. These components are evaluated at the time of
CO

2

quadrupling.

A1

Reasons for nonlinearity in the ocean C cycle
response in the CNRM-ESM2-1 model

In Fig. 6 the value of

γ

O

changes sign for the CNRM-ESM2-

1 model from positive when calculated using the RAD–BGC
or RAD–COU approaches to negative when calculated us-
ing the BGC–COU approach. This nonlinear behaviour for
a previous version of the CNRM model was documented
in Schwinger et al. (2014) and is caused by the large in-
crease in regenerated DIC in the RAD simulation, similar to
the increase in the COU relative to the BGC simulation, as

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4201

Figure A3.

Absolute amounts and the change from the beginning of the BGC simulation for carbon in soil

+

litter

(a, b)

and vegetation

(c, d)

pools.

shown in Fig. 13 for the CNRM-ESM2-1 model. This non-
linear behaviour is stronger in CNRM-ESM2-1 compared to
CNRM-ESM1, its previous version (Séférian et al., 2016),
most likely due to a new parameterization for N fixation
which increases ocean NPP and a revised parameterization
for organic matter remineralization (in PISCESv2-gas). A
contribution to a positive

γ

O

is also made by declining sea

ice in the RAD simulation which leads to changes in the sign
of the air–sea carbon exchange in the Southern Ocean. The
vertical profile of dissolved inorganic carbon in the Southern
Ocean in BGC and COU simulations (with rising [CO

2

]) is

different from that in the RAD simulation (for the preindus-
trial [CO

2

]), and this leads to additional nonlinearities.

A2

Additional figures and discussion

Figure A1 shows results from individual CMIP6 models for
which model means and ranges were shown in Figs. 1, 2, and
3 and allows for the identification of models which behave
differently compared to the majority of models. In Fig. A1a
and c, CanESM5 shows the largest temperature increase and
NorESM2-LM and MIROC-ES2L the smallest in response

to increase in [CO

2

] for the COU and RAD simulations, re-

spectively. For cumulative atmosphere–land CO

2

flux in the

COU simulation (panel d), CanESM5 simulates the largest
land carbon uptake and ACCESS-ESM1.5 the smallest. This
is not the case for the BGC simulation (panel e) where land
carbon uptakes from BCC-CSM2-MR and CNRM-ESM2.1
are the largest among all models, while land carbon uptake
from ACCESS-ESM1.5 is the lowest. Finally, in the RAD
simulation (panel f) the loss of carbon from land in response
to increasing temperatures is lowest in MPI-ESM1.2-LR and
largest in BCC-CSM2-MR. Over the ocean, while most mod-
els behave very similarly, the carbon uptakes in BCC-CSM2-
MR, ACCESS-ESM1.5, and NOAA-GFDL-ESM4 are larger
than in most models in the COU and BGC simulations. In the
RAD simulation, almost all models simulate a loss of carbon
from the ocean, but CNRM-ESM2.1 shows a small uptake.

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

A3

Additional tables

Table A1.

Values of carbon–concentration and carbon–climate feedback parameters for land and ocean calculated using the BGC–COU

approach (using results from the BGC and COU simulations) and the linear transient climate sensitivity to CO

2

, from CMIP6 and CMIP5

models at 4

×

CO

2

(i.e. at the end of the 1pctCO2 simulation) and 2

×

CO

2

.

CMIP6 models at 4

×

CO

2

Land

Ocean

Carbon–climate

Carbon–concentration

Carbon–climate

Carbon–concentration

Climate

feedback,

γ

L

feedback,

β

L

feedback,

γ

O

feedback,

β

O

sensitivity,

α

PgC

◦

C

−

1

PgC ppm

−

1

PgC

◦

C

−

1

PgC ppm

−

1

◦

C ppm

−

1

ACCESS-ESM1.5

−

21

.

1

0.37

−

23

.

75

0.9

0.00546

BCC-CSM2-MR

−

163

.

1

1.81

−

19

.

94

0.92

0.00485

CanESM5

15.95

1.28

−

14

.

72

0.77

0.00751

CESM2

−

21

.

6

0.9

−

10

.

85

0.71

0.00637

CNRM-ESM2-1

−

83

.

11

1.36

−

9

.

38

0.7

0.00632

IPSL-CM6A-LR

−

8

.

67

0.62

−

12

.

97

0.76

0.00687

MIROC-ES2L

−

69

.

57

1.12

−

22

.

25

0.73

0.00436

MPI-ESM1.2-LR

−

5

.

17

0.71

−

20

.

11

0.77

0.00512

NOAA-GFDL-ESM4

−

80

.

06

0.93

−

21

.

65

0.84

0.00430

NorESM2-LM

−

20

.

95

0.85

−

19

.

64

0.78

0.00410

UKESM1-0-LL

−

38

.

4

0.75

−

14

.

07

0.75

0.00721

Model mean

−

45

.

07

0.97

−

17

.

21

0.78

0.00568

Sample SD

50.59

0.40

4.95

0.07

0.00123

CMIP6 models at 2

×

CO

2

Land

Ocean

Carbon–climate

Carbon–concentration

Carbon–climate

Carbon–concentration

Climate

feedback,

γ

L

feedback,

β

L

feedback,

γ

O

feedback,

β

O

sensitivity,

α

PgC

◦

C

−

1

PgC ppm

−

1

PgC

◦

C

−

1

PgC ppm

−

1

◦

C ppm

−

1

ACCESS-ESM1.5

−

12

0.75

−

11

.

72

1.06

0.00750

BCC-CSM2-MR

−

132

.

84

2.22

−

12

.

38

1.09

0.00592

CanESM5

−

6

.

22

1.42

−

7

.

71

0.9

0.00950

CESM2

−

12

.

76

0.98

−

4

.

24

0.84

0.00789

CNRM-ESM2-1

−

44

.

51

1.37

−

3

.

58

0.81

0.00650

IPSL-CM6A-LR

−

12

.

24

1.11

−

7

.

37

0.87

0.00876

MIROC-ES2L

−

63

.

36

1.45

−

10

.

44

0.85

0.00530

MPI-ESM1.2-LR

−

0

.

81

1.08

−

11

.

4

0.88

0.00636

NOAA-GFDL-ESM4

−

50

.

69

1.08

−

8

.

97

0.97

0.00543

NorESM2-LM

−

15

.

61

0.94

−

9

.

34

0.88

0.00509

UKESM1-0-LL

−

24

.

01

1

−

7

.

35

0.88

0.00885

Model mean

−

34

.

10

1.22

−

8

.

59

0.91

0.00701

Sample SD

38.39

0.40

2.90

0.09

0.00157

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4203

Table A1.

Continued.

CMIP5 models at 4

×

CO

2

Land

Ocean

Carbon–climate

Carbon–concentration

Carbon–climate

Carbon–concentration

Climate

feedback,

γ

L

feedback,

β

L

feedback,

γ

O

feedback,

β

O

sensitivity,

α

PgC

◦

C

−

1

PgC ppm

−

1

PgC

◦

C

−

1

PgC ppm

−

1

◦

C ppm

−

1

BCC-CSM1-1

−

109

.

7

1.4

−

17

.

4

0.85

0.00511

CanESM2

−

64

.

9

0.99

−

11

.

28

0.7

0.00623

CESM1-BGC

−

6

.

39

0.24

−

12

.

16

0.74

0.00481

IPSL-CM5A-LR

−

46

.

65

1.13

−

17

.

6

0.89

0.00559

MIROC-ESM

−

86

.

82

0.75

−

20

.

94

0.82

0.00660

MPI-ESM-LR

−

89

.

64

1.49

−

18

.

36

0.85

0.00582

NorESM1-ME

−

4

.

3

0.22

−

18

.

72

0.87

0.00441

HadGEM2-ES

−

54

.

94

1.24

−

21

.

88

0.82

0.00607

Model mean

−

57

.

92

0.93

−

17

.

29

0.82

0.00558

Sample SD

38.24

0.49

3.78

0.07

0.00075

CMIP5 models at 2

×

CO

2

Land

Ocean

Carbon–climate

Carbon–concentration

Carbon–climate

Carbon–concentration

Climate

feedback,

γ

L

feedback,

β

L

feedback,

γ

O

feedback,

β

O

sensitivity,

α

PgC

◦

C

−

1

PgC ppm

−

1

PgC

◦

C

−

1

PgC ppm

−

1

◦

C ppm

−

1

BCC-CSM1-1

−

57

.

61

1.75

−

11

.

06

1.03

0.00676

CanESM2

−

48

.

13

1.05

−

6

.

64

0.85

0.00830

CESM1-BGC

−

5

.

02

0.25

−

4

.

41

0.86

0.00603

IPSL-CM5A-LR

−

37

.

28

1.58

−

8

.

88

0.99

0.00609

MIROC-ESM

−

64

.

79

1.04

−

12

.

36

0.94

0.00778

MPI-ESM-LR

−

62

.

52

1.86

−

11

.

24

0.99

0.00686

NorESM1-ME

1.02

0.24

−

9

.

53

1

0.00506

HadGEM2-ES

−

21

.

78

1.43

−

11

.

27

0.92

0.00836

Model mean

−

37

.

01

1.15

−

9

.

42

0.95

0.00690

Sample SD

25.48

0.63

2.70

0.07

0.00118

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

A4

Model descriptions

A4.1

Commonwealth Scientific and Industrial
Research Organisation (CSIRO)
ACCESS-ESM1.5

The Australian Community Climate and Earth System Sim-
ulator ACCESS-ESM1.5 (Ziehn et al., 2020) is comprised
of a number of component models. The atmospheric model
is the UK Met Office Unified Model version 7.3 (Martin et
al., 2010, 2011) with their land surface model replaced with
the Community Atmosphere Biosphere Land Exchange (CA-
BLE) model (Kowalczyk et al., 2013). The ocean component
is the NOAA GFDL Modular Ocean Model (MOM) version
5 (Griffies, 2014) with the same configuration as the ocean
model component of ACCESS1.0 and ACCESS1.3 (Bi et al.,
2013). Sea ice is simulated using the LANL CICE4.1 model
(Hunke and Lipscomb, 2010). Coupling of the ocean and sea
ice to the atmosphere is through the OASIS-MCT coupler
(Valcke, 2013). The physical climate model configuration
used here is very similar to the version (ACCESS1.3) that
contributed to the Coupled Model Intercomparison Project
Phase 5 (CMIP5; Bi et al., 2013). The carbon cycle is in-
cluded in ACCESS through the CABLE land surface model
and its biogeochemistry module, CASA-CNP (Wang et al.,
2010), and through the World Ocean Model of Biogeochem-
istry and Trophic-dynamics (WOMBAT; Oke et al., 2013).

The WOMBAT model is based on an NPZD (nutrient, phy-

toplankton, zooplankton, and detritus) model with the addi-
tions of bioavailable iron limitation, dissolved inorganic car-
bon, calcium carbonate, alkalinity, and oxygen. Productiv-
ity drives uptake and formation of carbon and oxygen that
are exchanged with the atmosphere. The sinking and rem-
ineralization of detritus carries biogeochemical tracers to the
deep ocean. Iron is supplied by dust deposition, continental
shelves, and background ocean values.

The Australian community model CABLE simulates the

fluxes of momentum, heat, water, and carbon at the surface.
The biogeochemistry module CASA-CNP simulates the flow
of carbon and nutrients such as nitrogen and phosphorus be-
tween three plant biomass pools (leaf, wood, root), three litter
pools (metabolic, structural, coarse woody debris), and three
organic soil pools (microbial, slow, passive), plus one inor-
ganic soil mineral nitrogen pool and three phosphorus soil
pools.

In the CABLE configuration applied here the land sur-

face is represented by 10 vegetation and 3 nonvegetation
land cover types. CABLE calculates gross primary produc-
tion (GPP) and leaf respiration at every time step using a two-
leaf canopy scheme (Wang and Leuning, 1998) as a function
of the leaf area index (LAI). This set-up uses a simulated
(prognostic) LAI based on the size of the leaf carbon pool
and the specific leaf area. Daily mean GPP and leaf respi-
ration values are then passed onto CASA-CNP to calculate
daily respiration fluxes and the flow of carbon and nutrients

between the pools. Similar to the previous version, ACCESS-
ESM1 (Law et al., 2017; Ziehn et al., 2017), the model is run
with nitrogen and phosphorus limitation enabled.

A4.2

Beijing Climate Center (BCC) Climate System
Model version 2 with medium resolution
(BCC-CSM2-MR)

BCC-CSM2-MR (Wu et al., 2019) is the second generation
of the BCC model with medium resolution that was released
to run CMIP6 simulations. It is a fully coupled global cli-
mate model and updated from its previous version of BCC-
CSM1.1 used for CMIP5 (Wu et al., 2013). The atmospheric
component of BCC-CSM2-MR is the BCC Atmospheric
General Circulation Model version 3 (BCC-AGCM3-MR;
Wu et al., 2019). The land component is the BCC Atmo-
sphere and Vegetation Interaction Model version 2.0 (BCC-
AVIM2; Li et al., 2019) with the terrestrial carbon cycle. The
oceanic component is the Modular Ocean Model version 4
with 40 levels (hereafter MOM4-L40). The sea ice compo-
nent is the NOAA GFDL Sea Ice Simulator (SIS). These
components are physically coupled through fluxes of mo-
mentum, energy, water, and carbon at their interfaces. The
coupling was realized with the flux coupler version 5 de-
veloped by the National Center for Atmosphere Research
(NCAR).

The atmospheric component of BCC-CSM2-MR has a

T106 horizontal resolution of approximately 1.125

◦

and 46

vertical levels in a hybrid sigma–pressure vertical coordinate
system with the top level at 1.459 hPa. The ocean component
resolution of BCC-CSM2-MR is 1

◦

longitude by 1

/

3

◦

lati-

tude between 30

◦

S and 30

◦

N which increases to 1

◦

latitude

at 60

◦

S and 60

◦

N and nominally 1

◦

polarward with tripolar

coordinates, and there are 40

z

levels in the vertical plane.

The atmospheric component model BCC-AGCM3-MR in

BCC-CSM2-MR is developed from its previous CMIP5 ver-
sion (Wu et al., 2008). The main updates include a modifica-
tion of deep convection parameterization, a new scheme for
cloud fraction, indirect effects of aerosols through clouds and
precipitation, and the gravity wave drag generated by deep
convection (Wu et al., 2019). Atmospheric CO

2

concentra-

tion in BCC-AGCM3-MR for this work is a prognostic vari-
able and calculated through a budget equation which con-
siders advective transport in the atmosphere, anthropogenic
CO

2

emissions, and interactive CO

2

fluxes at the interfaces

with land and ocean. But chemical processes are not taken
into account. The terrestrial carbon cycle in BCC-AVIM2
(Li et al., 2019) operates through a series of biochemical
and physiological processes acting on the photosynthesis and
respiration of vegetation and takes into account carbon loss
due to turnover and mortality of vegetation and CO

2

release

into the atmosphere through soil respiration. The vegeta-
tion litter on the ground surface and in the soil is divided
into eight terrestrial carbon pools (surface structural, surface
metabolic, surface microbial, soil structural, soil metabolic,

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4205

Table A2.

Estimate of the change in the ocean carbon inventory (PgC) expected from a time integral of the global air–sea carbon flux into

the ocean versus the volume integral of the change in the dissolved inorganic carbon, together with the small residual. The time integral of
the air–sea carbon flux provides the dominant contribution to the change in the ocean carbon inventory, although there is a small mismatch
due to the land-to-ocean carbon flux from river runoff and the ocean-to-land carbon flux from carbon burial in ocean sediments.

Model

Time integral of the

Global ocean volume

Residual

global air–sea carbon

integral of

1

DIC (PgC)

(PgC)

flux into the ocean

(PgC)

ACCESS-ESM1.5

763

736

27

CanESM5

656

651

5

CNRM-ESM2-1

597

658

−

61

MIROC-ES2L

625

632

−

7

MPI-ESM1.2-LR

657

621

36

NOAA-GFDL-ESM4

720

759

−

39

NorESM2-LM

671

628

43

UKESM1-0-LL

637

609

28

Model mean (

x

)

666

662

Sample SD (

σ

x

)

53

55

Coefficient of variation (

σ

x

/

|

x

|

)

0.08

Table A3.

Carbon cycle feedback parameters for the ocean,

β

O

and

γ

O

, diagnosed from the air–sea carbon fluxes and separately diagnosed

for the ocean carbon inventory and its separate ocean saturated, disequilibrium, and regenerated DIC pools for the subset of eight CMIP6
models for which 3D ocean data were available; their sum does not exactly match the diagnostics from the air–sea fluxes due to land–ocean
interactions involving storage in sediments and river inputs.

Carbon–concentration

Carbon–climate

feedback (PgC ppm

−

1

)

feedback (PgC

◦

C

−

1

)

β

O

β

sat

β

dis

β

reg

γ

O

γ

sat

γ

dis

γ

reg

ACCESS-ESM1.5

0.90

3.54

−

2

.

69

0.005

−

23

.

75

−

13

.

60

−

20

.

47

11.52

CanESM5

0.77

3.83

−

3

.

06

−

0

.

001

−

14

.

72

−

10

.

72

−

8

.

62

4.29

CNRM-ESM2-1

0.70

3.75

−

3

.

01

0.03

−

9

.

38

−

14

.

56

−

17

.

66

29.27

MIROC-ES2L

0.73

3.76

−

3

.

01

−

0

.

001

−

22

.

25

−

16

.

48

−

25

.

50

21.08

MPI-ESM1.2-LR

0.77

3.34

−

2

.

62

0.002

−

20

.

11

−

14

.

37

−

15

.

37

8.40

NorESM2-LM

0.78

3.67

−

2

.

92

−

0

.

004

−

19

.

64

−

12

.

91

−

14

.

44

9.19

UKESM1-0-LL

0.75

3.62

−

2

.

88

−

0

.

02

−

14

.

07

−

8

.

87

−

11

.

04

6.56

NOAA-GFDL-ESM4

0.84

3.77

−

2

.

93

0.05

−

21

.

65

−

10

.

75

−

17

.

77

7.7

Model mean (

x

)

0.78

3.66

−

2

.

89

−

0

.

003

−

18

.

20

−

12

.

78

−

16

.

36

12.25

Sample SD (

σ

x

)

0.06

0.16

0.009

4.95

2.50

5.31

8.53

Coefficient of variation (

σ

x

/

|

x

|

)

0.08

0.05

0.06

3.00

0.27

0.20

0.33

0.70

soil microbial, slow, and passive carbon pools) according to
the timescale of the decomposition of carbon in each pool
and the transfers between different pools. Allocation to and
from the three vegetation biomass pools (leaf, stem, root)
leads to dynamic vegetation that in turn produces litterfall
and which ultimately transfers carbon to soil organic mat-
ter. The allocation of carbon to the three vegetation biomass
pools is dependent on light availability, water stress, and the
phenology stages of the canopy and follows the formulations
of Arora and Boer (2005).

The biogeochemistry module to simulate the ocean car-

bon cycle in MOM4_L40 is based on the protocols from the

Ocean Carbon-Cycle Model Intercomparison Project Phase 2
(OCMIP2; http://ocmip5.ipsl.jussieu.fr/OCMIP/phase2/, last
access: 15 December 2019). The OCMIP biogeochemistry
module parameterizes the process of marine biology in terms
of geochemical fluxes, without explicit representation of the
marine ecosystem and food web processes, and includes five
prognostic variables: phosphate, dissolved organic phospho-
rus, dissolved oxygen, dissolved inorganic carbon, and al-
kalinity. Ocean carbon cycle processes in BCC-CSM2-MR
follow OCMIP, except for in parameterizing the export of or-
ganic matter from surface waters to deep oceans (Wu et al.,
2013).

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

A4.3

Canadian Centre for Climate Modelling and
Analysis (CCCma) fifth-generation Earth System
Model, CanESM5

CanESM5 has evolved from its predecessor CanESM2
(Arora et al., 2011) that was used in the Coupled Model Inter-
comparison Project phase 5 (CMIP5). CanESM5 represents a
major update to CanESM2 and is described in detail in Swart
et al. (2019). The major changes relative to CanESM2 are
the implementation of completely new models for the ocean,
sea ice, and marine ecosystems and a new coupler. The res-
olution of CanESM5 (T63 or

∼

2

.

8

◦

in the atmosphere and

∼

1

◦

in the ocean) remains similar to CanESM2 and is at

the lower end of the spectrum of CMIP6 models. The atmo-
spheric component of CanESM5 is represented by version 5
of the Canadian Atmospheric Model (CanAM5) and has sev-
eral improvements relative to its predecessor, CanAM4 (von
Salzen et al., 2013), including changes to aerosol, clouds, ra-
diation, land surface, and lake processes. CanAM5 uses a tri-
angular spectral truncation in the model dynamical core, with
an approximate horizontal resolution of 2

.

8

◦

in latitude and

longitude. It uses a hybrid vertical coordinate system with 49
levels between the surface and 1 hPa, with a vertical resolu-
tion of about 100 m near the surface. Relative to the 35 lev-
els used in CanESM2 most of the additional 14 levels were
added in the upper troposphere and stratosphere.

The land surface in CanESM5 is modelled using the Cana-

dian Land Surface Scheme (CLASS; Verseghy, 2000) and
the Canadian Terrestrial Ecosystem Model (CTEM; Arora
and Boer, 2005, 2010), which together form the land com-
ponent of CanESM5. CLASS and CTEM simulate the physi-
cal and biogeochemical land surface processes, respectively,
and together they calculate fluxes of energy, water, CO

2

, and

wetland CH

4

emissions at the land–atmosphere boundary.

Over land, three permeable soil layers are used with default
thicknesses of 0.1, 0.25, and 3.75 m for which liquid and
frozen soil moisture and temperature are prognostically cal-
culated. The depth to bedrock is specified on the basis of
the global dataset which reduces thicknesses of the perme-
able soil layers where soil depth is less than 4.1 m. Snow
is represented using one layer, whose snow water equiva-
lent and temperature are modelled prognostically. The intro-
duction of dynamic wetlands and their methane emissions
is a new biogeochemical process added since the CanESM2
(Arora et al., 2018). The nitrogen cycle over land is not rep-
resented but the parameterization of photosynthesis down-
regulation as CO

2

increases is included. The magnitude of

the parameter representing this downregulation is increased
in CanESM5 compared to CanESM2, following Arora and
Scinocca (2016), who found the best value of this param-
eter that reproduced various aspects of the historical car-
bon budget for CanESM4.2 (a model version more similar
to CanESM2 than CanESM5). Other than wetlands and the
changes to the strength of the CO

2

fertilization effect, the

remaining terrestrial ecosystem processes are represented in
the same way as in CanESM2.

The physical ocean component of CanESM5 is based on

Nucleus for European Modelling of the Ocean (NEMO) ver-
sion 3.4.1. It is configured on the tripolar ORCA1 C grid with
45

z

-coordinate vertical levels, varying in thickness from

∼

6 m near the surface to

∼

250 m in the abyssal ocean. The

horizontal resolution is based on a 1

◦

Mercator grid, varying

with the cosine of latitude, with a refinement of the merid-
ional grid spacing to 1

/

3

◦

near the Equator. Two modifi-

cations have been introduced to the NEMO mesoscale and
small-scale mixing physics in CanESM5, and these are de-
tailed in Swart et al. (2019). Sea ice is represented using the
LIM2 sea ice model (Fichefet and Morales Maqueda, 1997;
Bouillon et al., 2009), which is run within the NEMO frame-
work.

The ocean carbon cycle is represented using the Canadian

Model of Ocean Carbon (CMOC), which was developed for
earlier versions of CanESM (Christian et al., 2010; Arora et
al., 2011), and includes carbon chemistry and biology. The
biological component is a simple nutrient–phytoplankton–
zooplankton–detritus (NPZD) model, with fixed Redfield
stoichiometry, and simple parameterizations of iron limita-
tion, nitrogen fixation, and export flux of calcium carbonate.

A4.4

Community Earth System Model version 2
(CESM2)

CESM2 (Danabasoglu et al., 2020) contains substantial im-
provements on CESM1. The resolution remains the same
as in CESM1 (0

.

9

◦

latitude

×

1

.

25

◦

longitude for the atmo-

sphere and land with 32 vertical atmospheric levels and 25
ground levels and

∼

1

◦

for the ocean). The Community At-

mosphere Model version 6 includes many changes to the rep-
resentation of physical processes with the primary change be-
ing the inclusion of the Cloud Layers Unified By Binormals
(CLUBB) unified turbulence scheme.

The CESM2 ocean component (Parallel Ocean Program

version 2, POP2) is largely the same as that used in CESM1
except with a new parameterization for mixing effects in
estuaries along with several other numerical and physics
improvements. The sea ice model is CICE version 5.1.2
(CICE5; Hunke et al., 2015) . Ocean biogeochemistry is rep-
resented by the Marine Biogeochemistry Library (MARBL).
MARBL represents multiple nutrient colimitations (N, P,
Si, and Fe). It includes three explicit phytoplankton func-
tional groups (diatoms, diazotrophs, and picophytoplankton
and nanophytoplankton), one implicit phytoplankton group
(calcifiers), and one zooplankton group. MARBL includes
prognostic carbonate chemistry and simulates sinking partic-
ulate organic matter. Major updates relative to CESM1 in-
clude a representation of subgrid-scale variations in light and
variable C

:

P stoichiometry. The atmospheric deposition of

iron is computed prognostically in CESM2 as a function of
dust and black carbon deposition simulated by CAM6. River-

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4207

ine nutrient, carbon, and alkalinity fluxes are supplied to the
ocean from a dataset.

The land component is the Community Land Model ver-

sion 5 (CLM5; Lawrence et al., 2019) which simulates
land water, energy, momentum, and carbon and nitrogen cy-
cling. CLM5 includes an extensive suite of new and up-
dated processes and parameterizations that collectively im-
prove the model’s hydrological, biogeochemical, and eco-
logical realism and enhance the representation of anthro-
pogenic land use activities on climate and the carbon cycle.
The primary updates are as follows with details, references,
and additional updates described and listed in Lawrence et
al. (2019): (1) updated parameterizations and structure for
hydrology and snow (spatially explicit soil depth, dry sur-
face layer, revised groundwater scheme, revised canopy in-
terception and canopy snow processes, updated fresh snow
density, and inclusion of the Model for Scale Adaptive River
Transport); (2) a plant hydraulics scheme to more mecha-
nistically represent plant water use and limitation; (3) verti-
cally resolved soil biogeochemistry with base organic mat-
ter decomposition rates varying with depth and modified
by soil temperature, water, and oxygen limitation and ni-
trification and denitrification updated as in the CENTURY
model; (4) a methane production, oxidation, and emissions
model; (5) improved representation of plant N dynamics to
address deficiencies in CLM4 through the introduction of
flexible plant carbon

:

nitrogen (C

:

N) stoichiometry which

avoids the problematic CLM4 separation of potential and ac-
tual plant productivity, explicitly simulating the photosyn-
thetic capacity response to environmental conditions through
the Leaf Utilization of Nitrogen for Assimilation (LUNA)
module and accounting for how N availability affects plant
productivity through the Fixation and Uptake of Nitrogen
(FUN) module which determines the C costs of N acqui-
sition; methane emissions and oxidation from natural land
processes; (6) a global active crop model with six crop types
and time-evolving irrigated areas and industrial fertiliza-
tion rates; (7) updated canopy processes including a revised
canopy radiation scheme and canopy scaling of leaf pro-
cesses, colimitations on photosynthesis, and updated stom-
atal conductance; (8) a new fire model that includes repre-
sentation of natural and anthropogenic ignition sources and
suppression along with agricultural, deforestation, and peat
fires; and (9) inclusion of carbon isotopes.

A4.5

Centre National de Recherches Météorologiques
(CNRM) CNRM-ESM2-1

CNRM-ESM2-1 is the second-generation Earth System
model developed by CNRM and Centre Européen de
Recherche et de Formation Avancée en Calcul Scientifique
(CERFACS) for CMIP6 (Séférian et al., 2019).

The atmosphere component of CNRM-ESM2-1 is based

on version 6.3 of the global spectral model ARPEGE-Climat
(ARPEGE-Climat_v6.3). ARPEGE-Climat resolves atmo-

spheric dynamics and thermodynamics on a T127 triangu-
lar grid truncation that offers a spatial resolution of about
150 km in both longitude and latitude. CNRM-ESM2-1 em-
ploys a “high-top” configuration with 91 vertical levels that
extend from the surface to 0.01 hPa in the mesosphere; 15
hybrid

σ

–pressure levels are available below 1500 m.

The surface state variables and fluxes at the surface–

atmosphere interface are simulated by the SURFEX mod-
elling platform version 8.0 over the same grid and with the
same time step as the atmosphere model. SURFEX v8.0
encompasses several submodules for modelling the inter-
actions between the atmosphere, the ocean, the lakes, and
the land surface. Over the land surface, CNRM-ESM2-1
uses the ISBA-CTRIP land surface modelling system (http:
//www.umr-cnrm.fr/spip.php?article1092&lang=en, last ac-
cess: 15 December 2019) to solve energy, carbon, and water
budgets at the land surface (Decharme et al., 2019; Delire
et al., 2019). Its physical core explicitly solves the one-
dimensional Fourier’s and Darcy’s laws throughout the soil,
accounting for the hydraulic and thermal properties of soil
organic carbon. It uses a 12-layer snow model of interme-
diate complexity that allows for separate water and energy
budgets for the soil and the snowpack. It accounts for a dy-
namic river flooding scheme in which floodplains interact
with the soil and the atmosphere through free-water evap-
oration, infiltration, and precipitation interception and a two-
dimensional diffusive groundwater scheme to represent un-
confined aquifers and upward capillarity fluxes into the su-
perficial soil. More details on these physical aspects can be
found in Decharme et al. (2019).

To simulate the land carbon cycle and vegetation–climate

interactions, ISBA-CTRIP simulates plant physiology, car-
bon allocation and turnover, and carbon cycling through
vegetation, litter, and soil. It includes a module for wild
fires, land use and land cover changes, and carbon leach-
ing through the soil and transport of dissolved organic car-
bon to the ocean. Leaf photosynthesis is represented by the
semiempirical model proposed by Goudriaan et al. (1985).
Canopy-level assimilation is calculated using a 10-layer ra-
diative transfer scheme including direct and diffuse radia-
tion. Vegetation in ISBA is represented by four carbon pools
for grasses and crops (leaves, stem, roots and a nonstruc-
tural carbohydrate storage pool) with two additional pools
for trees (aboveground wood and coarse roots). Leaf phenol-
ogy results directly from the carbon balance of the leaves.
The model distinguishes 16 vegetation types (10 tree and
shrub types, 3 grass types, and 3 crop types) alongside desert,
rocks, and permanent snow. In the absence of nitrogen cy-
cling within the vegetation, an implicit nitrogen limitation
scheme that reduces specific leaf area with increasing CO

2

concentration was implemented in ISBA following the meta-
analysis of Yin (2002). Additionally, there is an ad hoc rep-
resentation of photosynthesis downregulation. The litter and
soil organic matter module is based on the soil carbon part
of the CENTURY model (Parton et al., 1988). The four litter

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

and three soil carbon pools are defined based on their loca-
tion aboveground or belowground and potential decomposi-
tion rates. The litter pools are supplied by the flux of dead
biomass from each biomass reservoir (turnover). Decompo-
sition of litter and soil carbon releases CO

2

(heterotrophic

respiration). During the decomposition process, some car-
bon is dissolved by water slowly percolating through the soil
column. This dissolved organic carbon is transported by the
rivers to the ocean. A detailed description of the terrestrial
carbon cycle can be found in Delire et al. (2019).

The ocean component of CNRM-ESM2-1 is the Nucleus

for European Modelling of the Ocean (NEMO) version 3.6
(Madec et al., 2016) which is coupled to both the Global
Experimental Leads and ice for ATmosphere and Ocean
(GELATO) sea ice model (Salas Mélia, 2002) version 6 and
also the marine biogeochemical model Pelagic Interactions
Scheme for Carbon and Ecosystem Studies version 2 gas
(PISCESv2-gas). NEMOv3.6 operates on the ORCA1L75
grid (Mathiot et al., 2017) which offers a nominal resolution
of 1

◦

to which a latitudinal grid refinement of 1

/

3

◦

is added

in the tropics; this grid describes 75 ocean vertical layers us-
ing a vertical

z

∗

coordinate with partial step bathymetry for-

mulation (Bernard et al., 2006).

The atmospheric chemistry scheme of CNRM-ESM2-1 is

Reactive Processes Ruling the Ozone Budget in the Strato-
sphere version 2 (REPROBUS-C_v2). This scheme resolves
the spatial distribution of 63 chemistry species but does
not represent the low-troposphere ozone nonmethane hydro-
carbon chemistry. CNRM-ESM2-1 also includes an inter-
active tropospheric aerosol scheme included in the atmo-
spheric component ARPEGE-Climat. This aerosol scheme,
named Tropospheric Aerosols for ClimaTe In CNRM (TAC-
TIC_v2), represents the main anthropogenic and natural
aerosol species of the troposphere.

The ocean biogeochemical component of CNRM-ESM2-

1 uses the PISCESv2-gas model, which derives from
PISCESv2 as described in Aumont et al. (2015). PISCESv2-
gas simulates the distribution of five nutrients (from
macronutrients nitrate, ammonium, phosphate, and silicate
to the micronutrient iron) which regulate the growth of two
explicit phytoplankton classes (nanophytoplankton and di-
atoms). Dissolved inorganic carbon (DIC) and alkalinity
(Alk) are involved in the computation of the carbonate chem-
istry, which is resolved by routines to model the ocean car-
bonate system version 2 (mocsy 2.0; Orr and Epitalon, 2015)
in PISCESv2-gas. The use of mocsy 2.0 enables a better and
faster resolution of the ocean carbonate chemistry at ther-
modynamic equilibria. Oxygen is prognostically simulated
using two different oxygen-to-carbon ratios, one when am-
monium is converted to or mineralized from organic matter
and the other when oxygen is consumed during nitrification.
Their values have been set to 131

/

122 and 32

/

122, respec-

tively.

At the ocean surface, PISCESv2-gas exchanges carbon,

oxygen, dimethylsulfide (DMS), and nitrous oxide (N

2

O)

tracers with the atmosphere using the revised air–sea ex-
change bulk as published by Wanninkhof (2014). PISCESv2-
gas uses several boundary conditions which represent the
supply of nutrients from five different sources: atmospheric
deposition, rivers, sediment mobilization, sea ice, and hy-
drothermal vents.

A4.6

Institut Pierre Simon Laplace (IPSL)
IPSL-CM6A-LR

IPSL-CM6A-LR is the coupled climate model of the Institut
Pierre Simon Laplace. It results from the integration of the
following components: the LMDZ atmospheric general cir-
culation model (version 6A-LR; Hourdin et al., 2019), the
NEMO oceanic model (version 3.6; Vancoppenolle et al.,
2009; Aumont et al., 2015; Rousset et al., 2015; Madec et
al., 2016), and the ORCHIDEE land surface model (version
2.0).

The atmospheric general circulation model LMDZ6A-LR

builds onto its previous version that has notably incorporated
advances in the parameterization of turbulence, convection,
and clouds. More specifically, LMDZ6A-LR includes a tur-
bulent scheme based on the prognostic equation for the tur-
bulent kinetic energy that follows Yamada (1983), a mass
flux representation of the organized structures of the convec-
tive boundary layer called the thermal plume model (Hour-
din et al., 2002; Rio and Hourdin, 2008; Rio et al., 2010),
and a parameterization of the cold pools or wakes created
below cumulonimbus by the evaporation of convective rain-
fall (Grandpeix and Lafore, 2010; Grandpeix et al., 2010). It
is based on a regular horizontal grid with 144 grid points reg-
ularly spaced in longitude and 142 in latitude, corresponding
to a resolution of 2

.

5

◦

×

1

.

3

◦

, and 79 vertical layers.

IPSL-CM6A-LR further includes NEMO (Nucleus for Eu-

ropean Models of the Ocean), which is itself composed of
three major building blocks: the ocean physics NEMO-OPA
(Madec et al., 2016), the sea ice dynamics and thermodynam-
ics NEMO-LIM3 (Vancoppenolle et al., 2009; Rousset et al.,
2015), and the ocean biogeochemistry NEMO-PISCES (Au-
mont et al., 2015). The grid used has a nominal resolution of
1

◦

in the zonal and meridional directions with a latitudinal

grid refinement of 1

/

3

◦

in the tropics. Vertical discretization

uses a partial step formulation (Bernard et al., 2006), which
ensures a better representation of bottom bathymetry, with 75
levels. The initial layer thicknesses increase nonuniformly
from 1 m at the surface to 10 m at 100 m depth and reach
200 m at the bottom and are subsequently time-dependent.
NEMO-PISCES (Aumont et al., 2015) models the lower
trophic levels of the marine ecosystem (phytoplankton, mi-
crozooplankton, and mesozooplankton) and the biogeochem-
ical cycles of carbon and of the main nutrients (P, N, Fe, and
Si). This model also computes air–sea carbon fluxes.

Finally, IPSL-CM6A-LR includes ORCHIDEE, a global

process-based terrestrial biosphere model (Krinner et al.,
2005) that calculates carbon, water, and energy fluxes be-

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4209

tween the land surface and the atmosphere. Photosynthesis
and all components of the surface energy and water budgets
are calculated at a 15 min resolution, while the dynamics of
the carbon storage (including carbon allocation in plant reser-
voirs, soil carbon dynamics, and litter decomposition) are
resolved on a daily basis. Photosynthesis depends on light
availability and CO

2

concentration, soil moisture, and tem-

perature and is parameterized based on Farquhar et al. (1980)
and Collatz et al. (1992) for C

3

and C

4

plants, respectively.

In the absence of an explicit representation of the nitrogen
cycle, this latest version of ORCHIDEE includes a down-
regulation capability that models a reduction in the terres-
trial photosynthesis rates as a function of CO

2

concentration.

While the N and C cycles interact in multiple ways, a key
aspect of these interactions is the limitation of carbon up-
take by nitrogen availability, especially under increasing at-
mospheric CO

2

concentrations. The downregulation param-

eterization models a reduction in the maximum photosyn-
thetic rate as the atmospheric CO

2

concentrations increase

using a logarithmic function of the CO

2

concentration rel-

ative to 380 ppm (Sellers et al., 1996). The PFT-dependent
parameters of this parameterization are chosen to broadly re-
produce the change in GPP observed at the free-air CO

2

en-

richment (FACE) experiment sites (Norby and Zak, 2011).
In ORCHIDEE, the spatial distribution of vegetation is rep-
resented using 15 plant functional types (PFTs; Prentice et
al., 1992; Cramer, 1997; Wullschleger et al., 2014). More
precisely these PFTs are decomposed into three groups ac-
cording to their physiological behaviour under similar cli-
mate conditions: tall vegetation (forests) represented by eight
PFTs, short vegetation (grasses and crops) represented by
six PFTs, and bare soil. The fractional coverage of these
PFTs varies geographically. A soil type is associated with
each one of these three PFT groups. This three-group par-
titioning allows for the dividing of each grid box into three
tiles for which an independent hydrological budget is calcu-
lated, using the 11-layer physically based hydrology scheme.
In ORCHIDEE the wood harvest product from the LUHv2h
database is used in addition to the annual land cover maps.

A4.7

Team MIROC (Japan Agency for Marine-Earth
Science and Technology, the University of Tokyo,
the National Institute for Environmental Studies)
MIROC-ES2L

MIROC-ES2L (Hajima et al., 2020) is based on the global
climate model MIROC5.2 (Tatebe et al., 2018), which is a
minor updated version of MIROC5 used for CMIP5 (Watan-
abe et al., 2010). The physical core shares almost the same
structure and characteristics with the latest model MIROC6
(Tatebe et al., 2019), except for the atmospheric spatial res-
olution and treatment of cumulus clouds. This model inter-
actively couples an atmospheric general circulation model
(CCSR-NIES AGCM; Tatebe et al., 2019) including an
on-line aerosol component (SPRINTARS; Takemura et al.,

2000), an ocean general circulation model (GCM) with a sea
ice component (COCO; Hasumi, 2015), and a land physical
surface model (MATSIRO; Takata et al., 2003). The land and
ocean biogeochemical components are represented by VISIT
(Ito and Inatomi, 2012) and OECO2 (Hajima et al., 2020),
respectively, which are interactively coupled to the atmo-
spheric component. There exists another branched version
that has an atmospheric chemistry component with a finer
atmospheric grid (MIROC-ES2H), but it was not used in this
study.

The atmospheric grid resolution is approximately 2.81

◦

with 40 vertical levels between the surface and about 3 hPa.
For the ocean, the model employs a tripolar coordinate sys-
tem with 62 vertical levels. To the south of 63

◦

N, the ocean

model has longitudinal grid spacing of about 1

◦

, while the

meridional grid spacing varies from about 0.5

◦

near the

Equator to 1

◦

in the midlatitudes. Over the Arctic ocean the

grid resolution is even finer following the tripolar coordinate
system. The physical terrestrial component resolves the ver-
tical soil profile with six layers down to a 14 m depth, with
two types of land use tiles (agriculture and nonagriculture).
Terrestrial biogeochemical component considers two layers
of soil organic matter (the upper litter layer and the lower
humus layer), with five types of land use tiles (primary veg-
etation, secondary vegetation, urban, crop, and pasture).

The terrestrial biogeochemical component covers major

processes relevant to the global carbon cycle, with vegeta-
tion (leaf, stem, and root), litter (leaf, stem, and root), and
humus (active, intermediate, and passive) pools and with a
static biome distribution. Details on carbon cycle processes
in the model can been found in Ito and Oikawa (2002). The
N cycle is simulated with N pools of vegetation (canopy and
structural), organic soil (litter, humus, and microbe), and in-
organic nitrogen (ammonium and nitrate). The model consid-
ers two major nitrogen influxes into the ecosystem (biologi-
cal nitrogen fixation and external nitrogen inputs). Fluxes out
of the land ecosystem in the model are N

2

or N

2

O emissions,

leaching, NH

3

emissions, and other emission-like volatiliza-

tion from land use product pools. For installing into MIROC-
ES2L, the terrestrial ecosystem processes were modified
such that photosynthetic capacity is controlled by leaf N con-
centration. Processes associated with land use change are
also modified to take full advantage of the CMIP6 LUC forc-
ing dataset. Further details can be found in Hajima et al.
(2020).

The new ocean biogeochemical component model,

OECO2, is a NPZD-type model and modified from the pre-
vious model (Watanabe et al., 2011). The biogeochemical
compartments of OECO2 are nitrate, phosphate, dissolved
iron, dissolved oxygen, two types of phytoplankton (nondia-
zotroph and diazotroph), zooplankton, and particulate detri-
tus. There exist other compartments of dissolved inorganic
carbon (DIC), total alkalinity, calcium, calcium carbonate,
and N

2

O. All organic materials have an identical elemental

stoichiometric ratio. The model considers external nutrient

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

inputs (atmospheric N and Fe deposition, inorganic N and P
from rivers, biological N fixation, Fe input from ocean bot-
tom and shelf) and nutrient loss (denitrification for N and loss
into sediment for N, P, and Fe). The emission, transportation,
and deposition processes of iron are explicitly simulated by
the atmospheric aerosol component.

A4.8

Max Planck Institute for Meteorology (MPI)
MPI-ESM1.2-LR

The MPI-ESM1.2-LR model (Mauritsen et al., 2019) con-
sists of ocean, atmosphere, land, and sea ice components
which are connected via a coupler analogous to the pre-
decessor MPI-ESM versions (Giorgetta et al., 2013). The
atmosphere model, ECHAM6.3, at the LR resolution has
a spectral truncation at T63 or approximately 200 km grid
spacing with 47 vertical levels. It is directly coupled to
the land model, JSBACH3.2, through surface exchange of
mass, momentum, and heat. The ocean general circulation
model, MPIOM1.6 in MPI-ESM1.2-LR, runs on a bipolar
grid GR1.5 and has 40 unevenly placed levels. It computes
transport of tracers of the ocean biogeochemistry model
HAMOCC6 (Ilyina et al., 2013; Paulsen et al., 2017). The
MPI-ESM-LR configuration computes 45–85 model years
per physical day enabling new simulations which were not
feasible previously, such as for instance, large ensemble sim-
ulations (Maher et al., 2019) or millennial-scale simulations
with an interactive carbon cycle (Brovkin et al., 2019).

Terrestrial vegetation in JSBACH includes vegetation dy-

namics which interacts with land use changes (Reick et al.,
2013), accounting for the latest changes in the land use har-
monization dataset by Hurtt et al. (2006). The new SPITFIRE
model simulates burned area and carbon emissions to the at-
mosphere due to wildfires and anthropogenic fires (Lasslop
et al., 2014), replacing the old global fire parameterization
used in the CMIP5 model. The soil carbon model Yasso sim-
ulates the dynamics of four fast soil carbon pools, which are
different for leaf and woody litter types, plus a slow humus
pool (Goll et al., 2015). Nitrogen and carbon pools are cou-
pled based on CO

2

-induced nitrogen limitation (Goll et al.,

2017).

The ocean biogeochemistry model HAMOCC6 has been

extended compared to the previous version described in
Ilyina et al. (2013) to explicitly resolve nitrogen-fixing
cyanobacteria as an additional prognostic phytoplankton
class (Paulsen et al., 2017). This allows for the capture of the
response of N

2

fixation and ocean biogeochemistry to chang-

ing climate conditions. Additionally, updates of existing pro-
cesses have been performed. This includes for instance the
addition of a vertically varying settling rate for detritus fol-
lowing the formulation by Martin et al. (1987). Finally some
empirical relationships in the parameterized processes have
been updated to follow recommendations of the C

4

MIP and

OMIP protocols (Jones et al., 2016; Orr et al., 2017). The full

overview of changes in HAMOCC is given in Mauritsen et
al. (2019).

A4.9

Geophysical Fluid Dynamics Laboratory (GFDL)
NOAA-GFDL-ESM4

GFDL-ESM4.1 is a comprehensive, fully coupled Earth sys-
tem model developed by NOAA’s Geophysical Fluid Dy-
namics Laboratory with a fully interactive carbon cycle and
interactive atmospheric chemistry (Dunne et al., 2020) that
builds on previous-generation modelling efforts of the car-
bon cycle (ESM2 series; Dunne et al., 2012, 2013) and at-
mospheric chemistry (CM3; Donner et al., 2011) along with
increased resolution and improved numerics and physics,
akin to the GFDL’s fourth-generation coupled climate model
(CM4.0; Held et al., 2019), and representation of additional
Earth system processes.

The atmospheric component, GFDL AM4.1, is based on

the third-generation finite-volume cube-sphere dynamical
core (FV3; Lin, 2004) with a

∼

100 km horizontal resolution

and 49 vertical levels. The model top is located at

∼

0

.

01 hPa

to resolve the stratosphere. AM4.1 shares the critical de-
velopments in model physics with the AM4.0 model (Zhao
et al., 2018), including radiation, convection, and clouds.
AM4.1 differs from the AM4.0 model in its enhanced ver-
tical resolution and its more explicit representation of at-
mospheric chemistry that motivated a separate radiative and
gravity wave tuning.

AM4.1 includes interactive tropospheric and stratospheric

gas-phase and aerosol chemistry represented through 77
prognostic (transported) tracers and 41 diagnostic (nontrans-
ported) chemical tracers. The tropospheric chemistry in-
cludes reactions for the oxidation of methane among other
volatile organic compounds. The stratospheric chemistry ac-
counts for the major ozone loss cycles and heterogeneous re-
actions on liquid and solid stratospheric aerosols.

Land hydrology and ecosystem dynamics are represented

by the GFDL Land Model version 4.1 (LM4.1, Shevliakova
et al., 2020) and build on the previous-generation LM3.1
model (Milly et al., 2014). Soil carbon dynamics and biogeo-
chemistry are represented through the CORPSE model (Sul-
man et al., 2019) with an explicit treatment of soil microbes.
LM4.1 also includes a new fire model FINAL (Rabin et al.,
2018). Vegetation dynamics are represented by the second-
generation age–height-structured approach, the perfect plas-
ticity approximation (PPA; Weng et al., 2015; Martinez Cano
et al., 2020). Allometric constraints and competition enable
the simulation of size structure and carbon fluxes in dynamic
vegetation. There are six carbon pools in LM4.1 representing
leaves, fine roots, heartwood, sapwood, seeds, and nonstruc-
tural carbon. Litter is broken into leaf, fine roots, and coarse-
wood categories. Soil has 20 vertical levels each with its own
prognostic state for energy, water, and soil carbon variables.
There are five types of vegetation in LM4.1 representing C

3

grass, C

4

grass, tropical trees, temperate deciduous trees, and

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4211

cold evergreen trees. A combination of these vegetation types
could coexist. The model also includes a new treatment of
stomatal conductance and plant hydraulics. The vegetation
state is used to drive a dust emission model that is coupled
with the atmosphere for transport. The ESM4 implementa-
tion of LM4.1 does not include an interactive nitrogen cycle.

The ocean biogeochemical component of ESM4 is version

2 of the Carbon, Ocean Biogeochemistry and Lower Troph-
ics (COBALTv2) model (Stock et al., 2014b). COBALTv2
uses 33 tracers to represent carbon, alkalinity, oxygen, ni-
trogen, phosphorus, iron, silica, calcite, and lithogenic min-
eral cycling within the ocean. Relative to previous-generation
ocean biogeochemistry models developed at the GFDL,
COBALTv2 includes an enhanced representation of plankton
food web dynamics to resolve the flow of energy from phyto-
plankton to fish (Stock et al., 2014a) and enhance the model’s
capacity to resolve linkages between food webs and biogeo-
chemical cycles. COBALTv2 explicitly includes small, large
(split into diatoms and nondiatoms), and diazotrophic phy-
toplankton groups; three zooplankton groups; bacteria; and
three labilities of dissolved organic matter. Other updates
include a temperature dependence for sinking organic mat-
ter remineralization (Laufkötter et al., 2017), the addition of
semilabile dissolved organic material and carbonate chem-
istry calculations based on the open-source mocsy 2.0 (Orr
and Epitalon, 2015).

Data from the NOAA-GFDL-ESM4 model used in the

analysis presented in this paper are accessible via the Earth
System Grid Federation (ESGF) for the 1pctCO2 (Krasting
et al., 2019b) simulation and for its radiatively and biogeo-
chemically coupled configurations (Krasting et al., 2019a).

A4.10

Norwegian Climate Centre (NCC)
NorESM2-LM

The NorESM2-LM (Seland et al., 2020) is based on the latest
release of the Community Earth System Model (CESM2.1),
whose development is supported by the National Center for
Atmospheric Research in the United States. NorESM2 keeps
the original land and sea ice components of CESM2.1 (i.e.
CLM5 and CICE5, respectively). The atmospheric compo-
nent is CAM6 (as in CESM) but with modifications regarding
the energy and angular momentum conservation. Further, the
atmospheric aerosol module of CAM6 has been replaced by
the scheme developed by the Norwegian Meteorological In-
stitute. The ocean physical and biogeochemical components
of NorESM2 are the isopycnal ocean circulation and carbon
cycle components updated from NorESM1 version (Tjiputra
et al., 2013; Schwinger et al., 2016)

The CLM5 (Community Land Model version 5) prognos-

tically simulates the carbon and nitrogen cycles, which in-
clude natural vegetation, crops, and soil biogeochemistry.
The carbon and nitrogen budgets comprise leaf, live-stem,
dead-stem, live-coarse-root, dead-coarse-root, fine-root, and
grain pools. Each of these pools has short-term and long-term

storage of nonstructural carbohydrates and labile nitrogen. In
addition to the vegetation pools, CLM includes a series of de-
composing carbon and nitrogen pools as vegetation succes-
sively breaks down into coarse woody debris and/or litter and
subsequently into soil organic matter. Details on the CLM5
models are available in Lawrence et al. (2019).

Similar to the earlier version, the ocean carbon cycle com-

ponent in NorESM2 is based on the Hamburg Ocean Carbon
Cycle (HAMOCC; Maier-Reimer et al., 2005) model, which
has been coupled to an isopycnic ocean general circulation
model. The current version includes new processes and re-
fined parameterizations, as well as new diagnostic tracers.
The ecosystem model is based on an NPZD-type model with
multinutrient limitation in its phytoplankton growth formula-
tion. Riverine fluxes of inorganic and organic carbon as well
as nutrients are now implemented. Unlike the earlier ver-
sion, the sea-to-air dimethyl sulfate (DMS) fluxes alter the
atmospheric radiative forcing and hence the climate–carbon
cycle feedback. More details on the ocean carbon cycle of
NorESM2 are available in Tjiputra et al. (2020).

A4.11

The United Kingdom Community Earth System
Model, UKESM1-0-LL

UKESM1-0-LL (Sellar et al., 2019) is based upon the
HadGEM3-GC3.1 (Williams et al., 2018) global climate
model which includes coupled ocean, atmosphere, land, and
sea ice components. The atmosphere component is the Uni-
fied Model with a resolution of 1.875

◦

by 1.25

◦

with 85 ver-

tical levels up to a model top of 90 km (Walters et al., 2019)
and includes a modal aerosol scheme (Mann et al., 2010).
The ocean component uses the NEMO dynamical ocean at 1

◦

resolution with 75 vertical levels (Storkey et al., 2018). The
sea ice component uses CICE on the same grid as the ocean
with five ice thickness categories (Ridley et al., 2018). The
land component uses the JULES land surface model (Wilt-
shire et al., 2020); however, the land surface configuration is
substantially updated for UKESM. The primary differences
between the physical and Earth system models are the in-
clusion of a terrestrial carbon and nitrogen cycle (Wiltshire
et al., 2020), ocean biogeochemistry (Yool et al., 2013), and
a tropospheric–stratospheric chemistry model. Atmospheric
chemistry in UKESM1 is simulated by the UKCA chem-
istry and aerosol model with the specific configuration being
a combination of tropospheric (O’Connor et al., 2014) and
stratospheric chemistry (Morgenstern et al., 2009, 2017).

Terrestrial biogeochemistry is represented by the JULES-

ES model (Wiltshire et al., 2020). The land surface is rep-
resented by 13 plant functional types (PFTs) including 4
managed crop and pasture land types. The height, leaf area
index, and spatial distribution of the PFTs are dynamically
simulated by the TRIFFID dynamic global vegetation model
(DGVM; Cox, 2001). Soil carbon is represented by the four-
pool RothC scheme (Coleman and Jenkinson, 1999). Terres-
trial carbon uptake may be limited by the availability of ni-

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V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

trogen. Nitrogen does not directly affect photosynthetic ca-
pacity through leaf N concentrations but acts indirectly by
controlling the biomass and leaf area index within the TRIF-
FID DGVM. A second mechanism acts through soil carbon
by limiting the decomposition of litter into soil carbon in the
RothC model. The vegetation model includes the retranslo-
cation of nitrogen during the senescence of leaves and roots
into a labile pool to supply nutrients for the following sea-
sonal leaf-out. The soil model simulates mineralization and
immobilization with mineralized nitrogen becoming avail-
able for plant uptake and ecosystem loss. Inorganic nitrogen
is represented by a single grid box pool to which all PFTs
have equal access. Nitrogen deposition is prescribed from an-
cillary data.

Land use change is represented by the application of time-

varying fields of crop and pasture to the DGVM, which allo-
cates space dynamically to C

3

and C

4

, and crop and pasture

types. Pasture is represented as natural grass, whereas crops
include a harvest parameterization and are fertilized. Bio-
genic volatile organic compound (BVOC) emissions from
vegetation are simulated and affect the formation of sec-
ondary organic aerosols. Mineral dust is emitted from bare
soil and acts as both an aerosol and a fertilizer to the ocean.

Ocean biogeochemistry is represented by MEDUSA-2

(Yool et al., 2013), which resolves a dual size-structured
ecosystem of small (nanophytoplankton and microzooplank-
ton) and large (microphytoplankton and mesozooplankton)
components. This explicitly includes the biogeochemical cy-
cles of nitrogen, silicon, and iron nutrients as well as the
cycles of carbon, alkalinity, and dissolved oxygen. Large
phytoplankton are treated as diatoms and utilize silicic acid
in addition to nitrogen, iron, and carbon. Like the living
components, the detrital components are split into two size
classes. At the seafloor, MEDUSA-2 resolves five reservoirs
to temporarily store sinking organic material reaching the
sediment. The model’s nitrogen, silicon, and alkalinity cy-
cles are closed and conservative (e.g. no riverine inputs),
while the other three cycles (carbon, iron, oxygen) are open.
The ocean’s iron cycle includes aeolian (land-derived dust)
and benthic sources, and is depleted by scavenging. The
ocean’s carbon cycle exchanges CO

2

with the atmosphere.

The ocean’s oxygen cycle exchanges oxygen with the at-
mosphere, and dissolved oxygen is additionally created by
primary production and depleted by remineralization. Ocean
biogeochemistry also feeds back on the atmosphere through
the production of marine DMS and marine organic aerosols.

A5

Contribution of uncertainties in

1T

2

×

CO

2

and

E

2

×

CO

2

to the TCRE.

The uncertainty in the TCRE, as indicated by its standard
deviation (

σ

TCRE

), can be represented in terms of the stan-

dard deviation of

1T

2

×

CO

2

(

σ

1T

), the standard deviation

of

˜

E

2

×

CO

2

(

σ

E

), and their means

1T

and

E

across the 11

CMIP6 models. Since

1T

2

×

CO

2

and

˜

E

2

×

CO

2

are nearly in-

dependent (correlation between these two quantities is only
0.02 across the 11 CMIP6 models considered here), we can
write

σ

TCRE

=

TCRE

s

σ

1T

2

+

σ

E

2

,

(A8)

which allows us to calculate contributions of

σ

1T

2

and

σ

E

2

to

σ

TCRE

.

Biogeosciences, 17, 4173–4222, 2020

https://doi.org/10.5194/bg-17-4173-2020

V. K. Arora et al.: Carbon–concentration and carbon–climate feedbacks

4213

Data availability.

The data used here are from the CMIP6 simula-

tions performed by the various modelling groups and available from
the CMIP6 archive (https://esgf-node.llnl.gov/search/cmip6).

The following variables were used from the models reported in

Table 2 and for the three experiments (1pctCO2, 1pctCO2-bgc,
1pctCO2-rad). Over land tas, co2, netAtmosLandCO2Flux, gpp,
npp, rhSoil, rhLitter, cVeg, cSoil, and cLitter were used. Over ocean
fgco2, dissic, so, thetao, talk, po4, no3, si, o2, areacello_Ofx, vol-
cello_Ofx, basin_Ofx, and sftlf_fx were used.

At the CMIP6 archive site (https://esgf-node.llnl.gov/search/

cmip6) searching for a given model, a given experiment, and a given
variable name will yield the link to the dataset that can be down-
loaded. Although annual values are used for analysis in this paper,
the CMIP6 data archive typically provides monthly values for most
variables.

Supplement.

The supplement related to this article is available on-

line at: https://doi.org/10.5194/bg-17-4173-2020-supplement.

Author contributions.

VA wrote the majority of the manuscript and

performed the analysis over land. AK and RW performed the anal-
ysis over the ocean and wrote sections related to the ocean and
TCRE. VA, CDJ, PF, VB, TI, RW, JS, and LB attended the Bern
Carbon Cycle Workshop in April 2018 where the extended frame-
work for analyzing land and ocean carbon cycle feedbacks was de-
veloped. CDJ reviewed and contributed to various sections of the
paper. VB, JS, JT, JC, and RS reviewed various sections of the
paper and provided revised text for those sections. Model descrip-
tions were provided by co-authors who represent the various climate
modelling groups. These co-authors were also responsible for pro-
cessing output from their respective models and providing data in
ready-to-use format.

Competing interests.

The authors declare that they have no conflict

of interest.

Acknowledgements.

The framework analysis outlined in this pa-

per was developed at the workshop held in Bern, Switzerland, in
April 2018, officially endorsed by the Grand Challenge “Carbon
Feedbacks in the Climate System” of the World Climate Research
Programme (WCRP) in cooperation with the Analysis, Integra-
tion and Modeling of the Earth System (AIMES) project of Fu-
ture Earth. The paper contributes to the Coupled Climate Carbon
Cycle Model Intercomparison (C4MIP) project of Coupled Mod-
els Intercomparison Project Phase 6 (CMIP6). The C4MIP website
(http://c4mip.net/) is supported by the Max Planck Society.

We also thank one anonymous reviewer and Kirsten Zickfeld for

their helpful comments on our paper and the handling editor Alexey
Eliseev for taking on this paper.

Financial support.

CDJ and AJW were supported by the Joint

UK BEIS/Defra Met Office Hadley Centre Climate Programme
(GA01101). CDJ, VB, PF, RS, CD, and EJ acknowledge funding
from the European Union’s Horizon 2020 CRESCENDO project

(grant agreement no. 641816). PF acknowledges funding from the
European Union’s Horizon 2020 “4C” project (grant agreement
no. 821003). RS, CD, and EJ also acknowledge the H2020 CON-
STRAIN under the grant agreement no. 820829. RGW and AK ac-
knowledge support from the UK Natural Environmental Research
Council, NE/N009789/1 and NE/T007788/1. CDK acknowledges
support by the Director, Office of Science, Office of Biological and
Environmental Research of the U.S. Department of Energy under
contract DE-AC02-05CH11231 through the Regional and Global
Model Analysis Program (RUBISCO SFA) and the Early Career
Research Program. TH, MK, and KT acknowledge the support from
TOUGOU, the Integrated Research Program for Advancing Climate
Models (grant number JPMXD0717935715), through the Ministry
of Education, Culture, Sports, Science, and Technology of Japan.
JS and JT acknowledge support from The Research Council of Nor-
way through projects KeyClim (grant no. 295046) and COLUMBIA
(grant no. 275268) as well as support from the Bjerknes Centre for
Climate Research through the project LOES.

Review statement.

This paper was edited by Alexey V. Eliseev and

reviewed by Kirsten Zickfeld and one anonymous referee.

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