Page 1
Biogeosciences, 21, 2759–2776, 2024
https://doi.org/10.5194/bg-21-2759-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research
ar
ticle
Soil carbon-concentration and carbon-climate feedbacks in
CMIP6 Earth system models
Rebecca M. Varney
1,2
, Pierre Friedlingstein
1,3
, Sarah E. Chadburn
1
, Eleanor J. Burke
4
, and Peter M. Cox
1,2
1
Faculty of Environment, Science and Economy, University of Exeter, Laver Building,
North Park Road, Exeter, EX4 4QE, UK
2
Global Systems Institute, University of Exeter, Laver Building, North Park Road, Exeter, EX4 4QE, UK
3
Laboratoire de Météorologie Dynamique/Institut Pierre-Simon Laplace, CNRS, Ecole Normale Supérieure/Université PSL,
Sorbonne Université, Ecole Polytechnique, Paris, 75231, France
4
Met Office Hadley Centre, FitzRoy Road, Exeter, EX1 3PB, UK
Correspondence:
Rebecca M. Varney (r.varney@exeter.ac.uk)
Received: 9 November 2023 – Discussion started: 15 November 2023
Revised: 4 April 2024 – Accepted: 24 April 2024 – Published: 12 June 2024
Abstract.
Achieving climate targets requires mitigation
against climate change but also understanding of the re-
sponse of land and ocean carbon systems. In this context,
global soil carbon stocks and their response to environmental
changes are key. This paper quantifies the global soil carbon
feedbacks due to changes in atmospheric CO
2
, and the asso-
ciated climate changes, for Earth system models (ESMs) in
CMIP6. A standard approach is used to calculate carbon cy-
cle feedbacks, defined here as soil carbon-concentration (
β
s
)
and carbon-climate (
γ
s
) feedback parameters, which are also
broken down into processes which drive soil carbon change.
The sensitivity to CO
2
is shown to dominate soil carbon
changes at least up to a doubling of atmospheric CO
2
. How-
ever, the sensitivity of soil carbon to climate change is found
to become an increasingly important source of uncertainty
under higher atmospheric CO
2
concentrations.
1
Introduction
Global soil carbon stocks contain at least twice as much car-
bon than is stored in the world’s vegetation, making soils the
largest active store of carbon on the land surface of Earth
(Canadell et al., 2021). In the absence of human disturbance
and land-use change (Jones et al., 2018), future changes in
soil carbon depend on the sensitivity to increases in atmo-
spheric CO
2
concentrations and the sensitivity to the associ-
ated impacts, such as increases in atmospheric temperatures
and changes in precipitation patterns (Varney et al., 2023;
Todd-Brown et al., 2014). The quantification of such carbon
cycle feedbacks is required to determine the overall response
of the climate system to given anthropogenic CO
2
emissions
and to help achieve Paris Agreement targets (Friedlingstein
et al., 2022; Gregory et al., 2009).
Previous studies have defined land carbon cycle feedbacks
within Earth system models (ESMs) from both CMIP6 and
CMIP5 ensembles (Arora et al., 2020, 2013). In general,
the overall response of carbon stores is separated into those
due to changes in atmospheric CO
2
(
1
CO
2
) and those due
to changes in global temperature (
1T
), with the latter as-
sumed to represent the overall impacts of climate change on
large spatial scales. These components of land carbon cy-
cle feedbacks are called carbon-concentration feedbacks (
β
L
)
and carbon-climate feedbacks (
γ
L
), respectively (Friedling-
stein et al., 2003, 2006). An advantage of using this formu-
lation is that it allows for the quantification of the feedbacks
for a given atmospheric CO
2
concentration, which can then
be used as a simplified measure to compare amongst ESMs
despite the increasing model complexities (Arora et al.,
2020, 2013; Gregory et al., 2009). For example, it provides a
consistent metric to measure land carbon feedbacks despite
the differing climate sensitivities amongst ESMs (Boer and
Arora, 2013).
In this study, soil-carbon-driven feedbacks in ESMs are
quantified using this
βγ
formulation (Friedlingstein et al.,
2006). Additionally, the
βγ
formulation is combined with
Published by Copernicus Publications on behalf of the European Geosciences Union.
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
the Varney et al. (2023) framework, which breaks down
future changes in soil carbon (
1C
s
) into individual pro-
cesses which drive this response. This paper makes use of
the latest generation of the Coupled Model Intercomparison
Project (CMIP6) used within the Intergovernmental Panel
on Climate Change 6th Assessment Report (IPCC AR6;
IPCC, 2021; Eyring et al., 2016). To do this, soil carbon-
concentration and carbon-climate feedback parameters are
presented for CMIP6 ESMs, named
β
s
and
γ
s
, respectively,
together with components which make up
β
s
and
γ
s
due to
associated processes. The aim of this paper is to (1) quantify
the sensitivity of soil carbon to increased atmospheric CO
2
concentrations and associated climate impacts by calculat-
ing
β
s
and
γ
s
for CMIP6 ESMs, (2) investigate the linearity
of future soil carbon change at higher levels of atmospheric
CO
2
increase, and (3) identify the fraction of the land carbon
response to climate change that is due to global soils.
2
Methods
2.1
C4MIP simulations
The Coupled Climate-Carbon Cycle Model Intercomparison
Project (C4MIP) was set up to provide a common frame-
work to allow for comparison and consistent evaluation of
carbon cycle feedbacks within ESMs (Friedlingstein et al.,
2006) and has been used across CMIP generations (Arora
et al., 2013, 2020). This framework includes a set of idealised
experiments to simplify and quantify the impact of increas-
ing atmospheric CO
2
on the climate system. In these exper-
iments, additional effects such as land-use change, aerosols
and non-CO
2
greenhouse gases are not included, and nitro-
gen deposition is fixed at pre-industrial values (Jones et al.,
2016).
The control simulation is known as the 1 % CO
2
run
(CMIP simulation
1pctCO2
), where a consistent 1 % in-
crease in atmospheric CO
2
per year is prescribed (referred
to in this study as the full 1 % CO
2
simulation), starting
from pre-industrial concentrations and running for 150 years.
Additional experiments were designed to enable the CO
2
and climate effects to be isolated, and these are known as
biogeochemically coupled (referred to here as the “BGC”
simulation) and radiatively coupled (referred to here as the
“RAD” simulation) runs. In the BGC runs (CMIP6 simu-
lation
1pctCO2-bgc
and CMIP5 simulation
esmFixClim1
),
the 1 % CO
2
increase per year only affects the carbon cy-
cle component of the ESM, while the radiation code con-
tinues to see pre-industrial CO
2
values. Conversely, in the
RAD runs (CMIP6 simulation
1pctCO2-rad
and CMIP5 sim-
ulation
esmFdbk1
), the 1 % CO
2
increase per year affects
only the radiation code, and the carbon cycle component of
the ESM continues to see just the pre-industrial CO
2
value
(285 ppm).
This study uses the full 1 % CO
2
, BGC and RAD
C4MIP experiments with 10 CMIP6 ESMs (Eyring et al.,
2016): ACCESS-ESM1-5, BCC-CSM2-MR, CanESM5,
CESM2, GFDL-ESM4, IPSL-CM6A-LR, MIROC-ES2L,
MPI-ESM1-2-LR, NorESM2-LM and UKESM1-0-LL (see
Table 1). For comparison, the soil carbon feedback pa-
rameters were calculated using six CMIP5 ESMs (Tay-
lor et al., 2012): CanESM2, GFDL-ESM2M, IPSL-CM5A-
LR, MPI-ESM-LR, NorESM1-ME and HadGEM2-ES (see
Table A2). The ESMs included were chosen due to the
availability of the data required at the time of analysis
(CMIP6: https://esgf-node.llnl.gov/search/cmip6/, last ac-
cess: 4 February 2024, CMIP5: https://esgf-node.llnl.gov/
search/cmip5/, last access: 6 February 2024).
2.2
Defining soil carbon feedbacks
2.2.1
Friedlingstein et al. (2006)
βγ
formulation
The standard formulation uses a linear approximation to
estimate carbon cycle feedbacks in a changing climate
(Friedlingstein et al., 2003, 2006). The change in land carbon
storage (
1C
L
, PgC) is approximated linearly using feedback
parameters which define separate sensitivities to changes in
atmospheric CO
2
(
1CO
2
, ppm) and changes in global tem-
peratures (
1T
, °C), defined as the land carbon-concentration
(
β
L
, PgC ppm
−
1
) and carbon-climate (
γ
L
, PgC °C
−
1
) (Eq. 1).
1C
L
≈
β
L
1
CO
2
+
γ
L
1T
(1)
The Friedlingstein et al. (2006) methodology uses time-
integrated fluxes, which represent the total change in the size
of the land carbon pool (
1C
L
). This is presented for the full
1 % CO
2
simulation (Eq. 2), BGC simulation (Eq. 3) and
RAD simulation (Eq. 4) below, where
1C
L
,
1C
BGC
L
and
1C
RAD
L
are the changes in global land carbon pools (PgC)
and
F
L
,
F
BGC
L
and
F
RAD
L
are the net carbon fluxes to the
land (PgC yr
−
1
) for each simulation.
1C
L
=
Z
F
L
d
t
≈
β
L
1
CO
2
+
γ
L
1T
(2)
1C
BGC
L
=
Z
F
BGC
L
d
t
≈
β
L
1
CO
2
+
γ
L
1T
BGC
≈
β
L
1
CO
2
(3)
1C
RAD
L
=
Z
F
RAD
L
d
t
≈
γ
L
1T
RAD
(4)
In these equations,
1
CO
2
(t )
(ppm) is consistent between
all the scenarios. Within the RAD simulation, however
(Eq. 4), the carbon cycle does not see an increased CO
2
,
so the
1
CO
2
is neglected and only found in the full 1 %
CO
2
and BGC simulations (Eqs. 2 and 3, respectively).
1T
,
1T
BGC
and
1T
RAD
(°C) are the changes in global temper-
atures in the full 1 % CO
2
, BGC and RAD simulations, re-
spectively. In Eq. (3),
1T
BGC
is assumed to be negligible,
following Friedlingstein et al. (2006). As the increased CO
2
within the BGC simulation does not affect the radiation code,
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
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Table 1.
The CMIP6 Earth system models included in this study and the relevant features of the associated land carbon cycle components:
simulation of interactive nitrogen, the inclusion of dynamic vegetation, representation of fire and the soil decomposition functions used
(Varney et al., 2022; Arora et al., 2020). Explanations of the temperature and moisture functions used within ESMs are given in Varney et al.
(2022) and Todd-Brown et al. (2013).
Earth system
Nitrogen
Dynamic
Fire
Temperature and
model
cycle
vegetation
moisture functions
ACCESS-ESM1.5
Yes
No
No
Arrhenius
and Hill
BCC-CSM2-MR
No
No
No
Hill
and Hill
CanESM5
No
No
No
Q
10
and Hill
CESM2
Yes
No
Yes
Arrhenius
and Increasing
GFDL-ESM4
No
Yes
Yes
Hill
and Increasing
IPSL-CM6A-LR
No
No
No
Q
10
and Increasing
MIROC-ES2L
Yes
No
No
Arrhenius
and Increasing
MPI-ESM1.2-LR
Yes
Yes
Yes
Q
10
and Increasing
NorESM2-LM
Yes
No
Yes
Arrhenius
and Increasing
UKESM1-0-LL
Yes
Yes
No
Q
10
and Hill
there is no direct increase in atmospheric temperatures within
the model. Arora et al. (2020) explain however that local
changes in the carbon cycle arising from increases in CO
2
affect latent and sensible heat fluxes at the land surface, in-
cluding changes to evaporative fluxes from stomatal closure
over land and changes in vegetation structure and coverage if
dynamic vegetation is included within the ESM (see Table 1).
This study assumes that the global temperature changes in
the BGC simulation are negligible in the context of the
βγ
formulation (Fig. A1).
2.2.2
Soil carbon-concentration and carbon-climate
feedbacks
Global
1C
L
can be written as the sum of the changes in veg-
etation carbon (
1C
v
) and changes in soil carbon (
1C
s
). Fol-
lowing the
βγ
formulation, a similar breakdown of the land
carbon-concentration and carbon-climate feedback parame-
ters can be derived, where
β
L
=
β
v
+
β
s
and
γ
L
=
γ
v
+
γ
s
(Eq. 5).
1C
L
≈
(β
v
+
β
s
) 1
CO
2
+
(γ
v
+
γ
s
) 1T
(5)
1C
v
≈
β
v
1
CO
2
+
γ
v
1T
(6)
1C
s
≈
β
s
1
CO
2
+
γ
s
1T
(7)
Therefore, an equation for
1C
s
can be obtained, with soil-
specific carbon-concentration (
β
s
) and carbon-climate (
γ
s
)
feedback parameters, which represent the sensitivity of
1C
s
to CO
2
and
T
, respectively (Eq. 7).
2.3
Processes driving soil carbon change and the
relation to the
βγ
formulation
To isolate the processes which make up each soil carbon
feedback, we follow the framework presented in Varney et al.
(2023). An equation for soil carbon (Eq. 8) is derived us-
ing the definition of soil carbon turnover time (
τ
s
=
C
s
/R
h
),
which is defined as the ratio of soil carbon storage (
C
s
) to
the carbon output flux from the soil (heterotrophic respira-
tion,
R
h
; Varney et al., 2020). Future soil carbon can then be
defined as initial soil carbon (
C
s
,
0
) plus a change in soil car-
bon (
1C
s
), as shown by Eq. 9, where the subscript 0 denotes
the initial state (decadal time average at the start of C4MIP
simulation). Equation (9) can be expanded to give Eq. (10),
which can be simplified to give Eq. (11), as shown below.
C
s
=
R
h
τ
s
(8)
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
C
s
,
0
+
1C
s
=
R
h
,
0
+
1R
h
τ
s
,
0
+
1τ
s
(9)
C
s
,
0
+
1C
s
=
R
h
,
0
τ
s
,
0
+
τ
s
,
0
1R
h
+
R
h
,
0
1τ
s
+
1R
h
1τ
s
(10)
1C
s
=
τ
s
,
0
1R
h
+
R
h
,
0
1τ
s
+
1R
h
1τ
s
(11)
To consider the above- and below-ground effects on soil
carbon separately, the effects due to changes in vegetation
productivity, represented by net primary productivity (NPP),
and effects due to changes in soil carbon turnover time due
to increased heterotrophic respiration (
τ
s
) are considered
(Todd-Brown et al., 2014). However, due to the difference
between the global fluxes NPP and
R
h
in a transient climate,
an additional term is included which is defined as net ecosys-
tem productivity (NEP
=
NPP
−
R
h
). Using the definition of
NEP, this can be substituted into Eq. (11) to give Eq. (12)
and expanded to give an equation for
1C
s
in terms of NPP,
NEP and
τ
s
(Eq. 13, where the subscript 0 denotes the initial
state).
1C
s
=
τ
s
,
0
1(
NPP
−
NEP
)
+
(
NPP
0
−
NEP
0
) 1τ
s
+
1(
NPP
−
NEP
)1τ
s
(12)
1C
s
=
τ
s
,
0
1
NPP
+
NPP
0
1τ
s
+
1
NPP
1τ
s
−
τ
s
,
0
1
NEP
−
NEP
0
1τ
s
−
1
NEP
1τ
s
(13)
The individual terms in Eq. (13) are the change in
soil carbon due to NPP changes (
1C
s
,
NPP
≈
τ
s
,
0
1
NPP),
the change in soil carbon due to the NEP transient term
(
1C
s
,
NEP
≈ −
τ
s
,
0
1
NEP), the change in soil carbon due to
τ
s
changes (
1C
s
,τ
≈
NPP
0
1τ
s
) and the transient effect on
τ
s
(
1C
s
,τ
NEP
≈ −
NEP
0
1τ
s
). The two additional terms are the
non-linear term between NPP and
τ
s
(
1
NPP
1τ
s
) and the
non-linear term between NEP and
τ
s
(
1
NEP
1τ
s
).
The NEP term is used to represent the transient state of
the system where NPP
6=
R
h
. However, it is noted that, if the
initial state is in equilibrium, then the initial NEP (NEP
0
)
will be approximately equal to zero. This would mean the
1C
s
,τ
NEP
term (representing the difference in
τ
s
from using
NPP or
R
h
in the definition) will be negligible. Despite ini-
tialising at the start of the C4MIP simulations (decadal time
average at the start of C4MIP simulation), this term is in-
cluded within the analysis for completeness to ensure exact
values of
1C
s
.
Following on from this Varney et al. (2023) framework,
the equation for
1C
s
(Eq. 13) can also be defined for the
change in soil carbon in both the BGC simulations (
1C
BGC
s
,
Eq. 14) and RAD simulations (
1C
RAD
s
, Eq. 15), where the
superscripts denote the BGC and RAD simulations, respec-
tively.
1C
BGC
s
=
τ
BGC
s
,
0
1
NPP
BGC
+
NPP
BGC
0
1τ
BGC
s
+
1
NPP
BGC
1τ
BGC
s
−
τ
BGC
s
,
0
1
NEP
BGC
−
NEP
BGC
0
1τ
BGC
s
−
1
NEP
BGC
1τ
BGC
s
(14)
1C
RAD
s
=
τ
RAD
s
,
0
1
NPP
RAD
+
NPP
RAD
0
1τ
RAD
s
+
1
NPP
RAD
1τ
RAD
s
−
τ
RAD
s
,
0
1
NEP
RAD
−
NEP
RAD
0
1τ
RAD
s
−
1
NEP
RAD
1τ
RAD
s
(15)
These equations can be used to investigate the sensitivity
of these isolated processes to changes in atmospheric CO
2
and global temperature (
T
), as shown by Eqs. (16) and (17).
This is done by the explicit differentiation of Eqs. (14) and
(15) with respect to CO
2
and
T
, respectively.
1C
BGC
s
=
∂
∂
CO
2
h
1C
BGC
s
i
1
CO
2
(16)
1C
RAD
s
=
∂
∂T
h
1C
RAD
s
i
1T
(17)
Equations (16) and (17) can be used to relate these CO
2
and
T
sensitivities to the
βγ
formulation, where
β
is used
to represent the sensitivity to CO
2
and
γ
is used to repre-
sent the sensitivity to
T
. Equation (7), which defines
1C
s
in terms of the soil carbon-concentration (
β
s
) and carbon-
climate (
γ
s
) feedback parameters, can be rewritten in terms
of partial derivatives, as shown by Eq. (18).
1C
s
=
∂C
s
∂
CO
2
1
CO
2
+
∂C
s
∂T
1T
where
, β
s
=
∂C
s
/∂
CO
2
and
γ
s
=
∂C
s
/∂T
(18)
Then, Eqs. (16) and (17) can be used together with Eq. (18)
to combine the
βγ
formulation with the Varney et al. (2023)
framework. In this case, therefore,
β
s
and
γ
s
can be defined as
the contributions to
1C
s
based on the individual sensitivities
of the soil carbon controls to CO
2
and
T
(by substituting
Eqs. (14) and (15) into Eqs. (16) and (17), respectively), as
shown by Eqs. (20) and (21).
1C
s
=
∂
∂
CO
2
h
1C
BGC
s
i
1
CO
2
+
∂
∂T
h
1C
RAD
s
i
1T ,
(19)
where
β
s
=
τ
BGC
s
,
0
∂
NPP
BGC
∂
CO
2
+
NPP
BGC
0
∂τ
BGC
s
∂
CO
2
+
∂1
NPP
BGC
1τ
BGC
s
∂
CO
2
−
τ
BGC
s
,
0
∂
NEP
BGC
∂
CO
2
−
NEP
BGC
0
∂τ
BGC
s
∂
CO
2
−
∂1
NEP
BGC
1τ
BGC
s
∂
CO
2
,
(20)
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
2763
γ
s
=
τ
RAD
s
,
0
∂
NPP
RAD
∂T
+
NPP
RAD
0
∂τ
RAD
s
∂T
+
∂1
NPP
RAD
1τ
RAD
s
∂T
−
τ
RAD
s
,
0
∂
NEP
RAD
∂T
−
NEP
RAD
0
∂τ
RAD
s
∂T
−
∂1
NEP
RAD
1τ
RAD
s
∂T
.
(21)
Equations (20) and (21) can be rewritten by defining the
β
s
and
γ
s
contribution terms, where each component of the
equations makes up the total
β
s
and
γ
s
sensitivities, as shown
below for
β
s
(Eq. 22) and
γ
s
(Eq. 23):
β
s
=
β
NPP
+
β
τ
+
β
1
NPP
1τ
−
β
NEP
−
β
NEP
τ
−
β
1
NEP
1τ
,
(22)
γ
s
=
γ
NPP
+
γ
τ
+
γ
1
NPP
1τ
−
γ
NEP
−
γ
NEP
τ
−
γ
1
NEP
1τ
,
(23)
where
β
NPP
and
γ
NPP
are the
βγ
contributions due to
1
NPP,
β
τ
and
γ
τ
are the
βγ
contributions due to
1τ
s
,
β
NEP
and
γ
NEP
are the
βγ
contributions due to the transient NEP term,
including
β
NEP
τ
and
γ
NEP
τ
representing the
βγ
contributions
due to the transient NEP term on
1τ
s
, and then
β
1
NPP
1τ
,
β
1
NEP
1τ
,
γ
1
NPP
1τ
and
γ
1
NEP
1τ
are the non-linear effects
on
βγ
.
2.4
Calculation of feedback parameters
2.4.1
Defining climate variables
For each of the CMIP6 ESMs, the CMIP output variables
cSoil
,
cLitter
and
cVeg
are considered in the land carbon stor-
age analysis. Soil carbon (
C
s
) is defined as the sum of carbon
stored in soils and the carbon stored in the litter (CMIP vari-
able
cSoil
+
CMIP variable
cLitter
), allowing for a more con-
sistent comparison between the models despite differences
in how soil carbon and litter carbon are simulated (Varney
et al., 2022; Todd-Brown et al., 2013). For models that do
not report a separate litter carbon pool (CMIP variable
cLit-
ter
), soil carbon is taken to be simply the CMIP variable
cSoil
(UKESM1-0-LL). Land carbon (
C
L
) is defined as the sum of
carbon stored in soil
+
litter (
C
s
) plus the carbon stored in
vegetation (
C
v
, CMIP variable
cVeg
). Global total values for
C
s
and
C
L
(PgC) are calculated using an area-weighted sum
(using the model land surface fraction, CMIP variable
sftlf
).
In the breakdown analysis of the
βγ
feedbacks, NPP
(CMIP variable
npp
) is defined as the net carbon assimilated
by plants via photosynthesis minus loss due to plant respira-
tion and is used to represent the net carbon input flux to the
system. Heterotrophic respiration (
R
h
, CMIP variable
rh
) is
defined as the microbial respiration within global soils and is
used to define an effective global soil carbon turnover time
(
τ
s
).
τ
s
(years) is defined as the ratio of mean soil carbon to
annual mean heterotrophic respiration, given as
τ
s
=
C
s
/R
h
(where the mean represents an area-weighted global aver-
age). Carbon fluxes (NPP and
R
h
) in the calculation of feed-
back contributions are considered area-weighted global to-
tals (PgC yr
−
1
, using the model land surface fraction, CMIP
variable
sftlf
).
Increases in global temperatures (
1T
) are considered us-
ing CMIP variable
tas
, which is defined as the change in
near-surface air temperature (°C). To calculate changes in at-
mospheric CO
2
(
1
CO
2
) in the C4MIP 1 % CO
2
simulations,
initial pre-industrial CO
2
concentrations are assumed to be
285 ppm and then cumulatively increased by 1 % each year
for 70 years (approximately 2
×
CO
2
) or 140 years (approx-
imately 4
×
CO
2
).
2.4.2
Carbon-concentration feedback parameter (
β
)
To calculate the soil carbon-concentration feedback parame-
ter (
β
s
), the BGC run was used. For each ESM, the change
in soil carbon in the BGC run (
1C
BGC
s
, PgC) was divided
by the change in CO
2
concentration (ppm) up to that point
in time (expressed in units of carbon uptake or release per
unit change in CO
2
, PgC ppm
−
1
). For this study,
β
s
was cal-
culated at the time of 2
×
CO
2
and 4
×
CO
2
. To calculate
the land carbon-concentration feedback parameter (
β
L
), the
same method was used but replacing
C
BGC
s
with
C
BGC
L
.
2.4.3
Carbon-climate feedback parameter (
γ
)
To calculate the soil carbon-climate feedback parameter (
γ
s
),
the RAD run was used. For each ESM, the change in soil
carbon in the RAD run (
1C
RAD
s
, PgC) was divided by the
change in temperature
T
(°C) up to that point in time (ex-
pressed in units of carbon uptake or release per unit change in
temperature, PgC °C
−
1
). For this study,
γ
s
was calculated at
2
×
CO
2
and 4
×
CO
2
. To calculate the land carbon-climate
feedback parameter (
γ
L
), the same method was used but re-
placing
C
RAD
s
with
C
RAD
L
.
2.4.4
Feedback parameter contributions
To calculate the isolated contributions which make up
β
and
γ
, as shown in Eqs. (22) and (23), the BGC and RAD simula-
tions are again used for each CMIP6 ESM. To calculate gra-
dients with respect to CO
2
and
T
, the methodology presented
above is used but with the relevant component against CO
2
or
T
, such as NPP or
τ
s
. The
β
s
contributions are expressed
in units of carbon uptake or release per unit change in CO
2
(PgC ppm
−
1
) and the
γ
s
contributions are expressed in units
of carbon uptake or release per unit change in temperature
(PgC °C
−
1
), using the definitions presented in Eqs. (22) and
(23).
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
Figure 1.
Time series of projected changes in soil carbon (
1C
s
) in CMIP6 ESMs for the
(a)
idealised 1 % CO
2
,
(b)
biogeochemically
coupled 1 % CO
2
(BGC) and
(c)
radiatively coupled 1 % CO
2
(RAD) simulations. This figure has been adapted from Fig. A2 in Varney et al.
(2023).
3
Results
3.1
Projections of soil carbon change
Projections of soil carbon change in CMIP6 ESMs for the
full 1 % CO
2
(
1C
s
), BGC (
1C
BGC
s
) and RAD (
1C
RAD
s
)
simulations are presented in Fig. 1. Soil carbon is pro-
jected to increase in the full 1 % CO
2
simulation amongst
CMIP6 ESMs (ensemble mean 88.2
±
40.4 PgC at 2
×
CO
2
and 177
±
141 PgC at 4
×
CO
2
). However, the magnitude
of the increase varies amongst the ESMs, with a range
of 38 PgC (NorESM2-LM) to 145 PgC (BCC-CSM2-MR)
at 2
×
CO
2
and a range of 15 PgC (ACCESS-ESM1-5)
to 502 PgC (CanESM5) at 4
×
CO
2
. Six of the ESMs
(CanESM5, CESM2, GFDL-ESM4, MIROC-ES2L, MPI-
ESM1-2-LR, NorESM2-LM) see an increased
1C
s
value
with increasing climate forcing. However, the remaining four
ESMs (ACCESS-ESM1-5, BCC-CSM2-MR, IPSL-CM6A-
LR, UKESM1-0-LL) see a saturation in the rate of increase
or even a turning point where carbon starts to decrease again,
from 70 years (
≈
2
×
CO
2
) in the simulation (Fig. 1a).
The projected increase in soil carbon can be approximated
by the increases projected in the BGC run (
1C
BGC
s
; ensem-
ble mean 132
±
66.5 PgC at 2
×
CO
2
and 348
±
203 PgC at
4
×
CO
2
, Fig. 1b) and the decreases projected in the RAD
run (
1C
RAD
s
; ensemble mean
−
45.5
±
22.9 PgC at 2
×
CO
2
and
−
170
±
94.7 PgC at 4
×
CO
2
, Fig. 1c). The responses
due to increases in atmospheric CO
2
(BGC simulation) are
found to dominate the overall response (full 1 % CO
2
simula-
tion) in the majority of the models, where greater magnitudes
of change are seen compared with the RAD simulation (ex-
ception ACCESS-ESM1-5). The BGC simulation also sees a
greater spread in projected
1C
s
, with ranges of 218 PgC at
2
×
CO
2
and 603 PgC at 4
×
CO
2
(
1C
BGC
s
) compared with
ranges of 68 PgC at 2
×
CO
2
and 312 PgC at 4
×
CO
2
in the
RAD simulation (
1C
RAD
s
).
Figure 2 shows patterns of soil carbon changes at 4
×
CO
2
for the full 1 % CO
2
(
1C
s
), BGC (
1C
BGC
s
) and RAD
(
1C
RAD
s
). In the BGC simulation, increases in
1C
BGC
s
are
seen across the majority of regions within CMIP6 ESMs,
though exceptions are found at the northern latitudes for
two ESMs (CanESM5 and NorESM2-LM). Across the en-
semble, the projected increases in
1C
BGC
s
have spatially
varying magnitudes, where generally the greatest increases
are seen in the tropical regions. Conversely, the RAD sim-
ulation generally sees reductions in
1C
RAD
s
globally, with
the greatest reductions seen in the tropical regions. How-
ever, disagreement is seen at the northern latitudes, where
four models (ACCESS-ESM1-5, CanESM5, MIROC-ES2L,
UKESM1-0-LL) see an increased
1C
RAD
s
and three models
(BCC-CSM2-MR, CESM2, NorESM2-LM) see a decreased
1C
RAD
s
. The overall
1C
s
values seen in the full 1 % CO
2
simulation are again found to be mostly dominated by the
BGC simulation (Fig. 2), though exceptions are seen where
the RAD simulation is shown to dominate the response for
certain regions. Specifically, the reduced
1C
s
within the
RAD simulation dominates the net response at the north-
ern latitudes of three ESMs (BCC-CSM2-MR, CESM2 and
NorESM2-LM, the only models where decreases were seen)
as well as in the tropical regions of three different ESMs
(ACCESS-ESM1-5, GFDL-ESM4 and UKESM1-0-LL).
3.2
Soil carbon-concentration and carbon-climate
feedback parameters
The calculated
β
s
and
γ
s
values for CMIP6 ESMs are pre-
sented in Table 2. Values for
β
s
are found to be positive
amongst the CMIP6 ESMs, which is consistent with in-
creased
C
s
with increasing CO
2
, and values for
γ
s
are found
to be negative, which is consistent with decreased
C
s
with
increasing temperature (Fig. 3). The magnitudes of the feed-
back parameters (
β
s
and
γ
s
) are found to vary amongst the
CMIP6 ensemble, suggesting uncertainty in the magnitude of
the soil carbon response to climate change. Generally, mod-
els with higher sensitivities to CO
2
(
β
s
) also have higher
sensitivities to temperature (
γ
s
), where
r
2
values of 0.64
(2
×
CO
2
) and 0.60 (4
×
CO
2
) are found between the
β
s
and
γ
s
values (Table 2). The ranges in projected
β
s
param-
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
2765
Figure 2.
Maps showing the changes in soil carbon (
1C
s
) at 4
×
CO
2
in CMIP6 ESMs, for the
(a)
idealised simulation 1 % CO
2
(left
column),
(b)
biogeochemically coupled 1 % CO
2
(BGC, middle column) and
(c)
radiatively coupled 1 % CO
2
(RAD, right column).
eters are found to be relatively consistent between 2
×
CO
2
and 4
×
CO
2
(where a small decrease is seen), with a range
of 0.704 PgC ppm
−
1
and a range of 0.636 PgC ppm
−
1
, re-
spectively. Conversely, the ranges of calculated
γ
s
param-
eters are found to be less consistent between 2
×
CO
2
and
4
×
CO
2
(increasing range with increased global warming),
with ranges of 42.7 and 68.0 PgC °C
−
1
, respectively (Ta-
ble 2).
The linearity of future soil carbon changes can be in-
vestigated by comparing the 2
×
CO
2
and 4
×
CO
2
lines
for
β
s
and
γ
s
in Fig. 3. A future linear response is shown
to be a good approximation. However, the figure suggests
a slight non-linearity in the soil carbon response to both
CO
2
(
1C
BGC
s
) and temperature (
1C
RAD
s
) in the majority
of ESMs. The BGC simulation generally sees greater con-
sistency between 2
×
CO
2
and 4
×
CO
2
β
s
values, for ex-
ample in the CESM2 and NorESM2-LM models. However,
the majority of ESMs (ACCESS-ESM1-5, BCC-CSM2-
MR, GFDL-ESM4, IPSL-CM6A-LR, MIROC-ES2L, MPI-
ESM1-2-LR and UKESM1-0-LL) see a reduction in
β
s
and a
saturation in the sensitivity with greater CO
2
levels (Fig. 3a).
In the RAD simulation, generally inconsistencies are seen
between 2
×
CO
2
and 4
×
CO
2
(exception MPI-ESM1-2-
LR), and an increased sensitivity of
C
RAD
s
to temperature (
T
)
with increased climate forcing is suggested by the majority of
CMIP6 ESMs (Fig. 3b). As an example, in CESM2, where
one of the lowest sensitivities to
T
at 2
×
CO
2
is seen, the
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
Figure 3.
Time series plots used to calculate the soil feedback parameters.
(a)
Soil carbon in the BGC simulation (
C
BGC
s
, PgC) vs. CO
2
(ppm) for the carbon-concentration feedback parameters (
β
s
, PgC ppm
−
1
) and
(b)
soil carbon in the RAD simulation (
C
RAD
s
, PgC) vs.
temperature (
T
, °C) for the soil carbon-climate feedback parameters (
γ
s
, PgC °C
−
1
), for each CMIP6 ESM. The lines show the gradients at
2
×
CO
2
(lighter line) and 4
×
CO
2
(darker line), respectively.
ESM sees an approximate 50 % increase in
γ
s
by 4
×
CO
2
(Table 2).
The
β
s
and
γ
s
values were also calculated for CMIP5
ESMs (Table A3), which can be compared with a subset
of generationally related CMIP6 ESMs considered in this
study (Fig. A3). The CMIP6 ensemble means for both
β
s
and
γ
s
parameters are found to be lower compared with the
CMIP5 ensemble means (Tables 2 and A3). The relation-
ship of
β
s
and
γ
s
values between CMIP5 and CMIP6, how-
ever, is not found to be consistent amongst the ensembles.
For
β
s
, reductions are seen in four ESMs (GFDL-ESM2M
vs. GFDL-ESM4, IPSL-CM5A-LR vs. IPSL-CM6A-LR,
MPI-ESM-LR vs. MPI-ESM1-2-LR and HadGEM2-ES vs.
UKESM1-0-LL) compared with increases in the remain-
ing two (CanESM2 vs. CanESM5 and NorESM1-ME vs.
NorESM2-LM). For
γ
s
, a greater value (closer to 0) is seen
in four ESMs (CanESM2 vs. CanESM5, GFDL-ESM2M
vs. GFDL-ESM4, IPSL-CM5A-LR vs. IPSL-CM6A-LR and
MPI-ESM-LR vs. MPI-ESM1-2-LR) compared with a lower
value (greater negative) seen in the remaining two ESMs
(NorESM1-ME vs. NorESM2-LM and HadGEM2-ES vs.
UKESM1-0-LL).
3.3
Breakdown of the feedback parameters into soil
carbon drivers
In this section,
β
s
and
γ
s
are broken down into the individ-
ual sensitivities of drivers of soil carbon change which make
up the net response. As shown in Fig. 4, the total soil carbon
sensitivities (
β
s
and
γ
s
, blue bars) can be considered as the
sum of the sensitivity due to
1
NPP (
β
NPP
and
γ
NPP
, green
bars), the sensitivity due to
1τ
s
(
β
τ
and
γ
τ
, red bars) and ad-
ditional terms due to the transient land carbon sink, such as
NEP (
β
NEP
and
γ
NEP
, light green bars) and the NEP effect on
τ
s
(
β
τ
NEP
and
γ
τ
NEP
, pink bars). Additionally, there are non-
negligible contributions due to non-linear sensitivities be-
tween NPP and
τ
s
(
β
1
NPP
1τ
and
γ
1
NPP
1τ
, black bars) and a
small contribution from non-linear sensitivities between NEP
and
τ
s
(
β
1
NEP
1τ
and
γ
1
NEP
1τ
, grey bars).
Investigating the sensitivity of soil carbon to
1
NPP,
β
NPP
is found to be positive amongst CMIP6 ESMs (Fig. 4). At
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
2767
Figure 4.
Investigating the contribution of individual soil carbon drivers to the soil carbon-concentration (
β
s
, top row) and carbon-climate
(
γ
s
, bottom row) feedback parameters, for each CMIP6 ESM, for
(a)
2
×
CO
2
and
(b)
4
×
CO
2
. The figure shows soil carbon feedback
parameter contributions from NPP (
β
NPP
and
γ
NPP
),
τ
s
(
β
τ
and
γ
τ
), the non-linearity in NPP and
τ
s
(
β
1
NPP
1τ
and
γ
1N P P 1τ
) and the
effect from the non-equilibrium term NEP (
β
NEP
,
β
τ
NEP
,
β
1
NEP
1τ
and
γ
NEP
,
γ
τ
NEP
,
γ
1
NEP
1τ
).
2
×
CO
2
,
β
NPP
ranges from 0.567 PgC ppm
−
1
(ACCESS-
ESM1-5) to 5.62 PgC ppm
−
1
(BCC-CSM2-MR), with an
ensemble mean of 2.37
±
1.37 PgC ppm
−
1
. There is some
evidence of a saturation of global NPP at higher CO
2
,
with the sensitivity of NPP to CO
2
(
β
NPP
) decreasing at
4
×
CO
2
to an ensemble mean of 1.44
±
0.933 PgC ppm
−
1
.
The sensitivity of NPP to global temperature changes (
γ
NPP
)
is found to be more variable in the ensemble. The ma-
jority of models find
γ
NPP
to be negative. However, it is
found to be positive in two ESMs (CanESM5 and MPI-
ESM1-2-LR). The sensitivity of NPP to temperature (
γ
NPP
)
is found to be more consistent with climate change than
the sensitivity to CO
2
(
β
NPP
), where the
γ
NPP
ensemble
mean changes from
−
29.4
±
40.1 PgC °C
−
1
at 2
×
CO
2
to
−
35.3
±
33.1 PgC °C
−
1
at 4
×
CO
2
(Fig. 4). At 4
×
CO
2
, the
lowest sensitivity of NPP to temperature is seen in CanESM5
(3.95 PgC °C
−
1
) and the highest sensitivity in BCC-CSM2-
MR (
−
90.8 PgC °C
−
1
).
Investigating the sensitivity of soil carbon to
1τ
s
, negative
β
τ
and
γ
τ
values are mostly found amongst the CMIP6
models (Fig. 4). An anomaly is found where
τ
s
is found to
increase with temperature in the ACCESS-ESM1-5 model,
where the reason for this is unclear (Fig. A2). The sensitivity
of
τ
s
to
T
(
γ
τ
) is also found to be more consistent with
increasing climate change than the sensitivity to CO
2
,
where an ensemble mean of
−
25.2
±
27.9 PgC °C
−
1
at
2
×
CO
2
and
−
20.5
±
29.5 PgC °C
−
1
at 4
×
CO
2
is seen.
At 4
×
CO
2
, the greatest sensitivity of
τ
s
to temperature
is seen in the MIROC-ES2L model (
−
54.6 PgC °C
−
1
)
and the lowest sensitivity is seen in the NorESM2-
LM model (
−
2.80 PgC °C
−
1
).
τ
s
is found to decrease
non-linearly with increasing CO
2
(
β
τ
). At 2
×
CO
2
,
β
τ
ranges from
−
0.329 PgC ppm
−
1
(ACCESS-ESM1-
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
Table 2.
The soil carbon-concentration (
β
s
, PgC ppm
−
1
) and
carbon-climate (
γ
s
, PgC °C
−
1
) feedback parameters for 2
×
CO
2
and 4
×
CO
2
for the CMIP6 ESMs.
Earth system
2
×
CO
2
4
×
CO
2
model
β
s
γ
s
β
s
γ
s
ACCESS-ESM1.5
0.242
−
29.2
0.127
−
37.3
BCC-CSM2-MR
0.861
−
50.5
0.763
−
83.1
CanESM5
0.544
−
21.4
0.620
−
31.8
CESM2
0.175
−
7.67
0.183
−
15.1
GFDL-ESM4
0.397
−
25.0
0.371
−
31.4
IPSL-CM6A-LR
0.357
−
11.9
0.222
−
15.3
MIROC-ES2L
0.684
−
49.4
0.630
−
63.1
MPI-ESM1-2-LR
0.494
−
14.4
0.375
−
15.6
NorESM2-LM
0.157
−
12.0
0.161
−
19.5
UKESM1-0-LL
0.351
−
24.7
0.307
−
32.7
Ensemble mean
0.426
−
24.6
0.376
−
34.5
Ensemble SD
±
0.213
±
14.2
±
0.212
±
21.3
5)
to
−
1.90 PgC ppm
−
1
(BCC-CSM2-MR),
with
an
ensemble
mean
of
−
0.900
±
0.574 PgC ppm
−
1
.
Due
to
the
non-linearity,
a
reduced
ensemble
mean
of
−
0.450
±
0.359 PgC ppm
−
1
is found at 4
×
CO
2
com-
pared with 2
×
CO
2
(Fig. 4).
It is apparent from Fig. 4 that the sensitivities of NPP and
τ
s
to both CO
2
and
T
must be accounted for to understand
and quantify the sensitivities of soil carbon. The magnitude
of
β
τ
is found to be approximately one-third of the magni-
tude of
β
NPP
at both 2
×
CO
2
and 4
×
CO
2
but with coun-
teracting signs of change. Models with the lowest
β
NPP
sen-
sitivities also see the lowest
β
τ
sensitivities (e.g. ACCESS-
ESM1-5) and vice versa. The magnitude of
γ
NPP
is generally
found to be greater across the ensemble compared with
γ
τ
,
with however a greater range of sensitivities. Additionally,
the apparent sensitivity of soil carbon to CO
2
is less than the
individual sensitivities of NPP and
τ
s
, due to a cancellation
effect from opposing signs, leading to a lower apparent
β
s
.
The magnitudes of
β
NPP
and
β
τ
are lower at 4
×
CO
2
than
2
×
CO
2
, which means a reduced sensitivity of NPP and
τ
s
to
CO
2
at greater levels of climate change. However, due to this
cancellation effect, the same reduced sensitivity is not seen in
β
s
. Conversely, a reduced sensitivity of NPP and
τ
s
to tem-
perature is not suggested under increasing climate forcing.
No clear relationship between
γ
NPP
and
γ
τ
is seen amongst
the CMIP6 ESMs (Fig. 4).
The contribution of the non-linearity between NPP and
τ
s
to the net soil carbon sensitivity is also investigated
(
β
1
NPP
1τ
and
γ
1
NPP
1τ
). Figure 4 suggests that the non-
linearity between NPP and
τ
s
is more robustly projected to
result from increasing CO
2
(
β
s
). However, non-linearities
in
γ
s
are also seen in the models with the greatest
temperature sensitivities. The ensemble mean predicted
β
1
NPP
1τ
is found to be
−
0.462
±
0.462 at 2
×
CO
2
and
−
0.463
±
0.468 PgC ppm
−
1
at 4
×
CO
2
. As expected from
Fig. 4, predicted
γ
1
NPP
1τ
is found to have a low sensitiv-
ity, where the ensemble means of
−
0.374
±
3.12 at 2
×
CO
2
and
−
0.0478
±
7.42 PgC °C
−
1
at 4
×
CO
2
are found. Addi-
tionally, the NEP terms (
β
NEP
and
γ
NEP
) are shown to con-
tribute to both CO
2
and
T
sensitivities (Fig. 4), due to the
disequilibrium of land carbon changes under 1 % increasing
CO
2
.
3.4
Investigating the robustness of the
1C
s
approximation
Projections of
1C
s
in ESMs in the full 1 % CO
2
simu-
lation were compared with the estimated
1C
s
derived us-
ing Eq. (7), which uses the derived
β
s
and
γ
s
feedback
parameters together with model-specific
1T
and estimates
for
1
CO
2
(Fig. 5). This investigates the approximation that
changes in the full 1 % CO
2
simulation are equal to the sum
of changes in the BGC and RAD simulations. At 2
×
CO
2
,
the approximation is found to predict
1C
s
within 20 % of the
actual projected values in the 1 % CO
2
simulation for 7 out
of the 10 CMIP6 ESMs (BCC-CSM2-MR, CESM2, GFDL-
ESM4, IPSL-CM6A-LR, MIROC-ES2L, MPI-ESM1-2-LR
and UKESM1-0-LL). At 4
×
CO
2
, the robustness of the as-
sumption between the BGC and RAD simulations decreases
for future changes in soil carbon. However,
β
s
1
CO
2
+
γ
s
1T
is within 20 % of the projected
1C
s
for 5 out of the
10 ESMs (GFDL-ESM4, IPSL-CM6A-LR, MIROC-ES2L,
MPI-ESM1-2-LR and UKESM1-0-LL). The models where
the approximation is the least consistent with projected
1C
s
are ACCESS-ESM1-5 and BCC-CSM2-MR, where at
4
×
CO
2
the greatest non-linearities are present between
BGC and RAD simulations (Fig. 5).
3.5
Comparisons between soil and land feedback
parameters
The contribution of the sensitivity of soil carbon stocks (
C
s
)
to the total sensitivity of land carbon stocks (
C
L
) was inves-
tigated by comparing the
β
and
γ
feedback parameters for
land (Table A1) and soil (Table 2) for both 2
×
CO
2
and
4
×
CO
2
in CMIP6 ESMs (Fig. 6). Here, the assumption
from Eq. (5) is followed that the land sensitivity is made up of
the sum of the soil and vegetation responses. For the carbon-
concentration feedback (
β
), the portion of the land sensitiv-
ity to CO
2
(
β
L
) that is due to global soils (
β
s
) ranges from
19 % (NorESM2-LM) to 53 % (BCC-CSM2-MR), with a
mean of 38
±
11 % seen across the CMIP6 ESMs at 2
×
CO
2
(Fig. 6a). Similar proportions are found at 4
×
CO
2
, ranging
from 22 % (NorESM2-LM) to 58 % (MIROC-ES2-L), with a
mean of 42
±
12 % seen across the CMIP6 ESMs (Fig. 6b).
The portion of
β
L
due to
β
s
is estimated to be close to half of
the total land response. For the carbon-climate feedback (
γ
),
the portion of the land sensitivity to climate (
γ
L
) that is due to
global soils (
γ
s
) ranges from approximately 42 % (CESM2)
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
2769
Figure 5.
Comparison of
1C
s
(PgC) in the full 1 % CO
2
simulation (
x
axis) against the estimated
1C
s
using the calculated
β
s
and
γ
s
feedback parameters (
y
axis), where estimated
1C
s
≈
β
s
1
CO
2
+
γ
s
1T
for each CMIP6 ESM at
(a)
2
×
CO
2
and
(b)
4
×
CO
2
.
to 147 % (MPI-ESM1-2-LM), with a mean of 75
±
30 %
seen across the CMIP6 ESMs at 2
×
CO
2
(Fig. 6a), and
at 4
×
CO
2
the range is from 48 % (ACCESS-ESM1-5) to
157 % (MPI-ESM1-2-LM), with a mean of 75
±
31 % seen
across the CMIP6 ESMs (Fig. 6b). Therefore, the portion of
γ
L
due to
γ
s
is estimated to be the majority of the sensitivity,
suggesting that soil dominates the response of land carbon to
climate. Note that the MPI-ESM1-2-LR model sees a greater
γ
s
value compared with
γ
L
, resulting in the percentage of
the land response attributed to soil being greater than 100 %.
This suggests a positive
γ
v
response in this model, meaning
a predicted increased vegetation carbon globally with global
warming.
4
Discussion
Quantifying the future sensitivity of global soil carbon stocks
to anthropogenic CO
2
emissions and their role in future land
carbon storage is vital in order to understand future changes
in the Earth’s climate system (Canadell et al., 2021). Global
changes in soil carbon (
1C
s
), in the absence of human dis-
turbance and land-use change, will result from responses due
to changes in atmospheric CO
2
and the associated changes in
global temperatures (
T
), which are used to represent climate
effects on a global scale. By separating the sensitivities due
to increasing CO
2
and
T
, the idealised C4MIP ESM simu-
lations allow for these effects on soil carbon to be examined
individually, and the use of the
βγ
formulation allows these
sensitivities to be quantified and compared for CMIP6 ESMs
(Jones et al., 2016; Friedlingstein et al., 2006). Further, com-
bining the
βγ
formulation with the Varney et al. (2023)
1C
s
framework allows us to isolate the sensitivities of soil carbon
processes which influence
β
s
and
γ
s
within models.
Across CMIP6 ESMs, soil carbon is projected to increase
in the BGC simulation (“CO
2
-only”) and decrease in the
RAD simulation (“climate-only”), consistent with projec-
tions of the overall land carbon response (Arora et al., 2020).
The BGC simulation has been used to quantify the sensitiv-
ity of soil carbon to
1
CO
2
(
β
s
), where positive
β
s
values
were defined according to the projected increase in soil car-
bon with increased atmospheric CO
2
(Fig. 1b). The positive
β
s
has been shown here to mostly be a result of a positive
β
NPP
term (Fig. 4), which represents the increased CO
2
fer-
tilisation effect describing increased vegetation productivity
under higher atmospheric CO
2
concentrations, which leads
to an increased input of litter carbon into soil carbon pools
(Schimel et al., 2015; Koven et al., 2015). A negative contri-
bution of
β
τ
to
β
s
is also shown (Fig. 4). Previously, Varney
et al. (2023) presented a transient reduction in
τ
s
in CMIP6
ESMs due to an increased rate of carbon input into the soil
(i.e. negative
β
τ
due to positive
β
NPP
), a phenomenon known
as false priming (Koven et al., 2015). However, it can be seen
that the magnitude of this effect is small compared with the
CO
2
fertilisation effect across the ESMs (
β
τ
vs.
β
NPP
, Fig. 4).
Despite agreement on a net increase in soil carbon stocks
globally (positive
β
s
), this study highlights uncertainty in the
projected magnitude of this sensitivity amongst the CMIP6
models, which is seen to be driven by uncertainties in
β
NPP
(Fig. 4).
The RAD simulation has been used to quantify the sensi-
tivity of soil carbon to changes in climate (
1T
;
γ
s
), where
negative
γ
s
values were defined due to the projected decrease
in soil carbon with global warming (Fig. 1c). The negative
γ
s
term has been shown here to be a result of negative
γ
τ
and, in
many cases, negative
γ
NPP
(Fig. 4). The negative sensitivity
of
τ
s
to global warming (negative
γ
τ
) is known to be due to
an increased rate of heterotrophic respiration (
R
h
) at warmer
temperatures as a result of increased microbial activity (Var-
ney et al., 2020; Crowther et al., 2016). The global sensitiv-
ity of NPP to climate changes (
γ
NPP
) is less certain where
both negative and positive values are seen across the CMIP6
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
Figure 6.
Comparisons of the land carbon-concentration (
β
L
) feedback parameters with the soil carbon-concentration (
β
s
) feedback param-
eters (top row) and the land carbon-climate (
γ
L
) feedback parameters with the soil carbon-climate (
γ
s
) feedback parameters (bottom row),
for
(a)
2
×
CO
2
and
(b)
4
×
CO
2
.
ESMs (Fig. 4). This is likely due to more spatially varying
responses, where the resultant
1C
s
can be seen in Fig. 2. For
example, increased temperatures at northern latitudes could
result in the northward expansion of boreal forests (Pugh
et al., 2018), which would increase forest productivity and
subsequently carbon storage in these regions. However, fu-
ture changes in precipitation patterns could lead to regions
with reduced soil moisture, which would conversely lead to
reduced vegetation productivity and carbon uptake (Green
et al., 2019). The uncertainties associated with projected spa-
tial changes (
γ
NPP
), together with the uncertainties in the
magnitude of carbon turnover times within the soil (
γ
τ
; Var-
ney et al., 2020; Koven et al., 2017), result in uncertainties in
the sensitivity of soil carbon to climate changes (
γ
s
) amongst
the CMIP6 models.
This paper highlights the importance of soils within the
land carbon response to global warming (Fig. 6). Despite the
1C
s
sensitivity to CO
2
dominating net soil carbon changes
(
β
s
), it could be argued that the significance of the
1C
s
cli-
mate sensitivity (
γ
s
) will increase under more extreme lev-
els of climate change. This is suggested by both a projected
saturation of
β
s
and an increase in
γ
s
between 2
×
CO
2
and
4
×
CO
2
shown in the CMIP6 ensemble means (Table 2). The
saturation, or reduced rate of increase, in
β
s
seen in CMIP6
is likely due to a limit of the CO
2
fertilisation effect, based
on the reduced
β
NPP
values between 2
×
CO
2
and 4
×
CO
2
(Fig. 4). The rate of CO
2
fertilisation in the future is ex-
pected to be limited by nutrient availability (Wieder et al.,
2015), which in CMIP6 is now more explicitly represented
by the inclusion of an interactive nitrogen cycle in multi-
ple models (see Table 1). This implementation is expected to
limit the increased productivity from CO
2
fertilisation within
ESMs (Davies-Barnard et al., 2020) and has previously been
found to lower the magnitude of the land feedback param-
eters (Arora et al., 2020). However, it is noted that warm-
ing within the soil could accelerate nutrient mineralisation,
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
2771
which could result in a liberation of nitrogen due to increased
microbial breakdown of plant litter, alleviating the nutrient
limitation in plants (Todd-Brown et al., 2014).
Unlike the
β
s
parameter, the sensitivity of soil carbon to
climate changes (
γ
s
) has been shown to increase with global
warming in CMIP6. The greater
γ
s
values at 4
×
CO
2
com-
pared with 2
×
CO
2
found here imply an increased rate of
soil carbon loss under increased amounts of global warming
(Table 2). Additionally, it could be hypothesised that limita-
tions within CMIP6 ESMs in the representation of soil car-
bon and related processes could lead to a potential under-
estimation of
γ
s
. In Fig. 2, reductions in soil carbon stocks
at the high northern latitudes are only seen in three models
for the full 1 % CO
2
simulation (BCC-CSM2-MR, CESM2
and NorESM2-LM). Varney et al. (2022) find that these
CMIP6 models represent quantities of northern-latitude car-
bon stocks most consistently with observational estimates,
which could imply an increased likelihood of soil carbon loss
from the northern latitudes based on consistency with obser-
vations. It is noted however that CESM2 and NorESM2-LM
contain the same land surface model and so are expected to
show similar results (Lawrence et al., 2019). Furthermore,
the majority of ESMs do not include explicit representation
of permafrost carbon (Burke et al., 2020). Including per-
mafrost within ESMs would result in increased quantities of
carbon within the soil known to be especially sensitive to
global warming (increased
γ
s
), which currently are not in-
cluded in the calculation of these feedbacks (Schuur et al.,
2015).
The
βγ
formulation has many benefits in allowing the
quantification and comparison of land and soil carbon feed-
backs amongst ESMs. However, one limitation is due to
1C
s
not being consistently linear with increasing CO
2
and tem-
perature (Fig. 3), so the parameter values depend on the point
in time at which they are calculated (for example, 2
×
CO
2
or
4
×
CO
2
). This has been shown to be due to non-linearities in
the processes driving soil carbon feedbacks (Fig. 4), such as
the discussed saturation of the CO
2
fertilisation effect (
β
NPP
;
Wang et al., 2020) and additionally a known Q
10
dependence
of heterotrophic (soil) respiration on temperature (
γ
τ
; Zhou
et al., 2009).
Non-linearities between CO
2
and
T
responses are also
known and have previously been shown within ESMs in
the future land carbon responses (Schwinger et al., 2014;
Zickfeld et al., 2011; Gregory et al., 2009). Zickfeld et al.
(2011) suggest that the non-linearity in the land response is
due to significantly differing vegetation responses which de-
pend on whether or not climate effects are combined with
the CO
2
fertilisation effect, e.g. forest dieback (Cox et al.,
2004). However, this is model-dependent, as not all models
within CMIP6 simulate dynamic vegetation (Table 1). The
spatial variations in the response of soil carbon to CO
2
and
climate that are seen in Fig. 2 could also contribute to the
non-linearity. For example, a different spatial pattern of soil
carbon under elevated CO
2
could lead to a different over-
all temperature response, e.g. if more carbon is at the high
latitudes where greater temperature changes are seen. Arora
et al. (2020) find that climate responses in the BGC simula-
tion account for a difference of 1 %–5 % in the calculation
of the feedbacks, suggesting a small but non-negligible ef-
fect of climate in the BGC runs. This response was shown
to be dependent on the representation of vegetation within
the model, as with the non-linearities found in Zickfeld et al.
(2011). Despite this, isolating and quantifying the key sensi-
tivities with the
βγ
method provides a useful benchmark for
feedbacks within CMIP.
5
Conclusions
The Friedlingstein et al. (2006) methodology adapted in this
study suggests that
β
s
and
γ
s
linearity is a valid assumption
for projected soil carbon changes in ESMs up until a dou-
bling of CO
2
. However, under more extreme levels of climate
change, the results here suggest the need for the non-linearity
in feedbacks to be further investigated. Soil carbon is found
to have a greater impact on carbon-climate feedbacks than
vegetation carbon responses, which means that the sensitivity
of soil carbon to changes in global temperature is the dom-
inant response of the land carbon cycle when considering
climate effects. Therefore, further understanding and quan-
tifying the sensitivity of global soils under global warming is
necessary to quantify future changes in the climate system.
Moreover, the sensitivity of soil carbon to temperature in-
creases with increasing climate forcing, suggesting that soil
carbon is particularly important in the long-term land carbon
response under extreme levels of global warming.
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
Appendix A
Figure A1.
Time series of projected global mean temperature changes (
1T
) in CMIP6 ESMs for the idealised simulations 1 % CO
2
(a)
,
biogeochemically coupled 1 % CO
2
(BGC,
b
) and radiatively coupled 1 % CO
2
(RAD,
c
).
Figure A2.
Time series of projected changes in net primary productivity (
1
NPP, top row) and soil carbon turnover time (
1τ
s
, bottom row)
in CMIP6 ESMs for the idealised simulations 1 % CO
2
(a)
, BGC
(b)
and RAD
(c)
. This figure has been adapted from Fig. A2 in Varney
et al. (2023).
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
2773
Figure A3.
Comparison of the soil carbon-concentration (
β
s
) feedback parameters (top row) and the soil carbon-climate (
γ
s
) feedback
parameters (bottom row) from generationally related ESMs from CMIP5 and CMIP6, for
(a)
2
×
CO
2
and
(b)
4
×
CO
2
.
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
Table A1.
The land carbon-concentration (
β
L
, PgC ppm
−
1
) and
carbon-climate (
γ
L
, PgC °C
−
1
) feedback parameters for 2
×
CO
2
and 4
×
CO
2
for the CMIP6 ESMs.
Earth system
2
×
CO
2
4
×
CO
2
model
β
L
γ
L
β
L
γ
L
ACCESS-ESM1.5
0.624
−
64.5
0.312
−
77.7
BCC-CSM2-MR
1.63
−
62.1
1.39
−
98.0
CanESM5
1.34
−
21.6
1.27
−
36.9
CESM2
0.839
−
18.3
0.787
−
30.1
GFDL-ESM4
1.00
−
42.3
0.891
−
57.3
IPSL-CM6A-LR
1.05
−
18.4
0.614
−
24.5
MIROC-ES2L
1.34
−
56.7
1.08
−
74.0
MPI-ESM1-2-LR
1.03
−
9.81
0.699
−
9.98
NorESM2-LM
0.811
−
22.2
0.740
−
35.3
UKESM1-0-LL
1.00
−
35.6
0.746
−
52.4
Ensemble mean
1.07
−
35.2
0.854
−
49.6
Ensemble SD
±
0.281
±
19.1
±
0.304
±
26.0
Table A2.
The CMIP5 Earth system models included in this study
and the relevant features of the associated land carbon cycle compo-
nents: simulation of interactive nitrogen, the inclusion of dynamic
vegetation and the soil decomposition functions used (Varney et al.,
2022; Arora et al., 2013; Anav et al., 2013; Friedlingstein et al.,
2014). Explanations of the temperature and moisture functions used
within ESMs are given in Varney et al. (2022) and Todd-Brown et al.
(2013).
Earth system
Nitrogen
Dynamic
Temperature and
model
cycle
vegetation
moisture functions
CanESM2
No
No
Q
10
and Hill
GFDL-ESM2M
No
Yes
Hill
and Increasing
IPSL-CM5A-LR
No
No
Q
10
and Increasing
MPI-ESM-LR
No
Yes
Q
10
and Increasing
NorESM1-ME
Yes
No
Arrhenius
and Increasing
HadGEM2-ES
No
Yes
Q
10
and Hill
Code availability.
Code is available on GitHub (https://github.com/
rebeccamayvarney/CMIP6-soil-beta-gamma, last access: 10 Jan-
uary 2024) and Zenodo (https://doi.org/10.5281/zenodo.10927091,
Varney, 2024).
Data availability.
The CMIP6 and CMIP5 data analysed during
this study are available online (CMIP6: https://esgf-node.llnl.gov/
search/cmip6/, ESGF, 2024a, CMIP5: https://esgf-node.llnl.gov/
search/cmip5/, ESGF, 2024b).
Table A3.
The soil carbon-concentration (
β
s
, PgC ppm
−
1
) and
carbon-climate (
γ
s
, PgC °C
−
1
) feedback parameters for 2
×
CO
2
and 4
×
CO
2
for the CMIP5 ESMs.
Earth system
2
×
CO
2
4
×
CO
2
model
β
s
γ
s
β
s
γ
s
CanESM2
0.413
−
39.4
0.463
−
54.2
GFDL-ESM2M
0.421
−
36.7
0.326
−
73.5
IPSL-CM5A-LR
0.511
−
28.3
0.410
−
39.5
MPI-ESM-LR
1.02
−
35.7
0.937
−
63.6
NorESM1-ME
0.0281
−
3.76
0.0287
−
7.80
HadGEM2-ES
0.745
−
12.9
0.729
−
18.0
Ensemble mean
0.522
−
26.1
0.482
−
42.8
Ensemble SD
±
0.306
±
13.3
±
0.290
±
23.7
Author contributions.
RMV and PMC outlined the study. RMV
completed the analysis and produced the figures. All the co-authors
provided useful guidance on the study at various times and sug-
gested edits to the draft manuscript.
Competing interests.
The contact author has declared that none of
the authors has any competing interests.
Disclaimer.
Publisher’s note: Copernicus Publications remains
neutral with regard to jurisdictional claims made in the text, pub-
lished maps, institutional affiliations, or any other geographical rep-
resentation in this paper. While Copernicus Publications makes ev-
ery effort to include appropriate place names, the final responsibility
lies with the authors.
Acknowledgements.
We thank the World Climate Research Pro-
gramme’s Working Group on Coupled Modelling and the climate
modelling groups for producing and making their model output
available.
Financial support.
This research has been supported by the Euro-
pean Research Council’s Climate–Carbon Interactions in the Cur-
rent Century project (4C; grant no. 821003) (Rebecca M. Var-
ney, Peter M. Cox and Pierre Friedlingstein) and the Emer-
gent Constraints on Climate–Land feedbacks in the Earth system
project (ECCLES; grant no. 742472) (Rebecca M. Varney and Pe-
ter M. Cox). Sarah E. Chadburn was supported by a Natural Envi-
ronment Research Council independent research fellowship (grant
no. NE/R015791/1). Eleanor J. Burke was supported by the joint
UK BEIS–Defra Met Office Hadley Centre Climate Programme
(grant no. GA01101).
Review statement.
This paper was edited by Daniel S. Goll and re-
viewed by Ben Bond-Lamberty and one anonymous referee.
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R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
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References
Anav, A., Friedlingstein, P., Kidston, M., Bopp, L., Ciais, P., Cox, P.,
Jones, C., Jung, M., Myneni, R., and Zhu, Z.: Evaluating the land
and ocean components of the global carbon cycle in the CMIP5
Earth System Models, J. Climate, 26, 6801–6843, 2013.
Arora, V. K., Boer, G. J., Friedlingstein, P., Eby, M., Jones, C. D.,
Christian, J. R., Bonan, G., Bopp, L., Brovkin, V., Cadule, P.,
and Hajima, T.: Carbon–concentration and carbon–climate feed-
backs in CMIP5 Earth system models, J. Climate, 26, 5289–
5314, 2013.
Arora, V. K., Katavouta, A., Williams, R. G., Jones, C. D., Brovkin,
V., Friedlingstein, P., Schwinger, J., Bopp, L., Boucher, O., Cad-
ule, P., Chamberlain, M. A., Christian, J. R., Delire, C., Fisher,
R. A., Hajima, T., Ilyina, T., Joetzjer, E., Kawamiya, M., Koven,
C. D., Krasting, J. P., Law, R. M., Lawrence, D. M., Lenton,
A., Lindsay, K., Pongratz, J., Raddatz, T., Séférian, R., Tachiiri,
K., Tjiputra, J. F., Wiltshire, A., Wu, T., and Ziehn, T.: Carbon–
concentration and carbon–climate feedbacks in CMIP6 models
and their comparison to CMIP5 models, Biogeosciences, 17,
4173–4222, https://doi.org/10.5194/bg-17-4173-2020, 2020.
Boer, G. and Arora, V.: Feedbacks in emission-driven and
concentration-driven global carbon budgets, J. Climate, 26,
3326–3341, 2013.
Burke, E. J., Zhang, Y., and Krinner, G.: Evaluating permafrost
physics in the Coupled Model Intercomparison Project 6
(CMIP6) models and their sensitivity to climate change, The
Cryosphere, 14, 3155–3174, https://doi.org/10.5194/tc-14-3155-
2020, 2020.
Canadell, J., Monteiro, P., Costa, M., Cotrim da Cunha, L., Cox,
P., Eliseev, A., Henson, S., Ishii, M., Jaccard, S., Koven,
C., Lohila, A., Patra, P., Piao, S., Rogelj, J., Syampungani,
S., Zaehle, S., and Zickfeld, K.: Global Carbon and other
Biogeochemical Cycles and Feedbacks, Cambridge University
Press, Cambridge, United Kingdom and New York, NY, USA,
https://doi.org/10.1017/9781009157896.007, 2021.
Cox, P. M., Betts, R., Collins, M., Harris, P. P., Huntingford, C., and
Jones, C.: Amazonian forest dieback under climate-carbon cycle
projections for the 21st century, Theor. Appl. Climatol., 78, 137–
156, 2004.
Crowther, T. W., Todd-Brown, K. E., Rowe, C. W., Wieder, W. R.,
Carey, J. C., Machmuller, M. B., Snoek, B. L., Fang, S., Zhou,
G., Allison, S. D., and Blair, J. M.: Quantifying global soil carbon
losses in response to warming, Nature, 540, 104–108, 2016.
Davies-Barnard, T., Meyerholt, J., Zaehle, S., Friedlingstein, P.,
Brovkin, V., Fan, Y., Fisher, R. A., Jones, C. D., Lee, H., Peano,
D., Smith, B., Wårlind, D., and Wiltshire, A. J.: Nitrogen cy-
cling in CMIP6 land surface models: progress and limitations,
Biogeosciences, 17, 5129–5148, https://doi.org/10.5194/bg-17-
5129-2020, 2020.
ESGF: CMIP6, ESGF [data set], https://esgf-node.llnl.gov/search/
cmip6/, last access: 4 February 2024a.
ESGF: CMIP5, ESGF [data set], https://esgf-node.llnl.gov/search/
cmip5/, last access: 6 February 2024b.
Eyring, V., Bony, S., Meehl, G. A., Senior, C. A., Stevens, B.,
Stouffer, R. J., and Taylor, K. E.: Overview of the Coupled
Model Intercomparison Project Phase 6 (CMIP6) experimen-
tal design and organization, Geosci. Model Dev., 9, 1937–1958,
https://doi.org/10.5194/gmd-9-1937-2016, 2016.
Friedlingstein, P., Dufresne, J.-L., Cox, P., and Rayner, P.: How pos-
itive is the feedback between climate change and the carbon cy-
cle?, Tellus B, 55, 692–700, 2003.
Friedlingstein, P., Cox, P., Betts, R., Bopp, L., von Bloh, W.,
Brovkin, V., Cadule, P., Doney, S., Eby, M., Fung, I., and
Bala, G.: Climate–carbon cycle feedback analysis: results from
the C4MIP model intercomparison, J. Climate, 19, 3337–3353,
2006.
Friedlingstein, P., Meinshausen, M., Arora, V. K., Jones, C. D.,
Anav, A., Liddicoat, S. K., and Knutti, R.: Uncertainties in
CMIP5 climate projections due to carbon cycle feedbacks, J. Cli-
mate, 27, 511–526, 2014.
Friedlingstein, P., O’Sullivan, M., Jones, M. W., Andrew, R. M.,
Gregor, L., Hauck, J., Le Quéré, C., Luijkx, I. T., Olsen, A., Pe-
ters, G. P., Peters, W., Pongratz, J., Schwingshackl, C., Sitch, S.,
Canadell, J. G., Ciais, P., Jackson, R. B., Alin, S. R., Alkama, R.,
Arneth, A., Arora, V. K., Bates, N. R., Becker, M., Bellouin, N.,
Bittig, H. C., Bopp, L., Chevallier, F., Chini, L. P., Cronin, M.,
Evans, W., Falk, S., Feely, R. A., Gasser, T., Gehlen, M., Gkritza-
lis, T., Gloege, L., Grassi, G., Gruber, N., Gürses, Ö., Harris, I.,
Hefner, M., Houghton, R. A., Hurtt, G. C., Iida, Y., Ilyina, T.,
Jain, A. K., Jersild, A., Kadono, K., Kato, E., Kennedy, D., Klein
Goldewijk, K., Knauer, J., Korsbakken, J. I., Landschützer, P.,
Lefèvre, N., Lindsay, K., Liu, J., Liu, Z., Marland, G., Mayot,
N., McGrath, M. J., Metzl, N., Monacci, N. M., Munro, D. R.,
Nakaoka, S.-I., Niwa, Y., O’Brien, K., Ono, T., Palmer, P. I., Pan,
N., Pierrot, D., Pocock, K., Poulter, B., Resplandy, L., Robert-
son, E., Rödenbeck, C., Rodriguez, C., Rosan, T. M., Schwinger,
J., Séférian, R., Shutler, J. D., Skjelvan, I., Steinhoff, T., Sun, Q.,
Sutton, A. J., Sweeney, C., Takao, S., Tanhua, T., Tans, P. P., Tian,
X., Tian, H., Tilbrook, B., Tsujino, H., Tubiello, F., van der Werf,
G. R., Walker, A. P., Wanninkhof, R., Whitehead, C., Willstrand
Wranne, A., Wright, R., Yuan, W., Yue, C., Yue, X., Zaehle, S.,
Zeng, J., and Zheng, B.: Global Carbon Budget 2022, Earth Syst.
Sci. Data, 14, 4811–4900, https://doi.org/10.5194/essd-14-4811-
2022, 2022.
Green, J. K., Seneviratne, S. I., Berg, A. M., Findell, K. L., Hage-
mann, S., Lawrence, D. M., and Gentine, P.: Large influence of
soil moisture on long-term terrestrial carbon uptake, Nature, 565,
476–479, 2019.
Gregory, J. M., Jones, C., Cadule, P., and Friedlingstein, P.: Quanti-
fying carbon cycle feedbacks, J. Climate, 22, 5232–5250, 2009.
IPCC: Climate Change 2021: The Physical Science Basis, Con-
tribution of Working Group I to the Sixth Assessment Report
of the Intergovernmental Panel on Climate Change, Cambridge
University Press, Cambridge, UK and New York, NY, USA,
https://doi.org/10.1017/9781009157896, 2021.
Jones, A. D., Calvin, K. V., Shi, X., Di Vittorio, A. V., Bond-
Lamberty, B., Thornton, P. E., and Collins, W. D.: Quantifying
human-mediated carbon cycle feedbacks, Geophys. Res. Lett.,
45, 11–370, 2018.
Jones, C. D., Arora, V., Friedlingstein, P., Bopp, L., Brovkin, V.,
Dunne, J., Graven, H., Hoffman, F., Ilyina, T., John, J. G.,
Jung, M., Kawamiya, M., Koven, C., Pongratz, J., Raddatz,
T., Randerson, J. T., and Zaehle, S.: C4MIP – The Coupled
Climate–Carbon Cycle Model Intercomparison Project: experi-
mental protocol for CMIP6, Geosci. Model Dev., 9, 2853–2880,
https://doi.org/10.5194/gmd-9-2853-2016, 2016.
https://doi.org/10.5194/bg-21-2759-2024
Biogeosciences, 21, 2759–2776, 2024
Page 18
2776
R. M. Varney et al.: Soil carbon-concentration and carbon-climate feedbacks
Koven, C. D., Chambers, J. Q., Georgiou, K., Knox, R., Negron-
Juarez, R., Riley, W. J., Arora, V. K., Brovkin, V., Friedlingstein,
P., and Jones, C. D.: Controls on terrestrial carbon feedbacks by
productivity versus turnover in the CMIP5 Earth System Models,
Biogeosciences, 12, 5211–5228, https://doi.org/10.5194/bg-12-
5211-2015, 2015.
Koven, C. D., Hugelius, G., Lawrence, D. M., and Wieder, W. R.:
Higher climatological temperature sensitivity of soil carbon in
cold than warm climates, Nat. Clim. Change, 7, 817–822, 2017.
Lawrence, D. M., Fisher, R. A., Koven, C. D., Oleson, K. W., Swen-
son, S. C., Bonan, G., Collier, N., Ghimire, B., van Kampenhout,
L., Kennedy, D., and Kluzek, E.: The Community Land Model
version 5: Description of new features, benchmarking, and im-
pact of forcing uncertainty, J. Adv. Model. Earth Sy., 11, 4245–
4287, 2019.
Pugh, T. A. M., Jones, C. D., Huntingford, C., Burton, C., Arneth,
A., Brovkin, V., Ciais, P., Lomas, M., Robertson, E., Piao, S. L.,
and Sitch, S.: A large committed long-term sink of carbon due to
vegetation dynamics, Earth’s Future, 6, 1413–1432, 2018.
Schimel, D., Pavlick, R., Fisher, J. B., Asner, G. P., Saatchi, S.,
Townsend, P., Miller, C., Frankenberg, C., Hibbard, K., and Cox,
P.: Observing terrestrial ecosystems and the carbon cycle from
space, Glob. Change Biol., 21, 1762–1776, 2015.
Schuur, E. A., McGuire, A. D., Schädel, C., Grosse, G., Harden,
J. W., Hayes, D. J., Hugelius, G., Koven, C. D., Kuhry, P.,
Lawrence, D. M., and Natali, S. M.: Climate change and the per-
mafrost carbon feedback, Nature, 520, 171–179, 2015.
Schwinger, J., Tjiputra, J. F., Heinze, C., Bopp, L., Christian, J. R.,
Gehlen, M., Ilyina, T., Jones, C. D., Salas-Mélia, D., Segschnei-
der, J., and Séférian, R.: Nonlinearity of ocean carbon cycle feed-
backs in CMIP5 earth system models, J. Climate, 27, 3869–3888,
2014.
Taylor, K. E., Stouffer, R. J., and Meehl, G. A.: An overview of
CMIP5 and the experiment design, Bull. Am. Meteorol. Soc.,
93, 485–498, 2012.
Todd-Brown, K. E. O., Randerson, J. T., Post, W. M., Hoffman, F.
M., Tarnocai, C., Schuur, E. A. G., and Allison, S. D.: Causes
of variation in soil carbon simulations from CMIP5 Earth system
models and comparison with observations, Biogeosciences, 10,
1717–1736, https://doi.org/10.5194/bg-10-1717-2013, 2013.
Todd-Brown, K. E. O., Randerson, J. T., Hopkins, F., Arora, V.,
Hajima, T., Jones, C., Shevliakova, E., Tjiputra, J., Volodin,
E., Wu, T., Zhang, Q., and Allison, S. D.: Changes in
soil organic carbon storage predicted by Earth system mod-
els during the 21st century, Biogeosciences, 11, 2341–2356,
https://doi.org/10.5194/bg-11-2341-2014, 2014.
Varney, R.: Soil carbon-concentration and carbon-climate feed-
backs in CMIP6 Earth system models, Zenodo [code],
https://doi.org/10.5281/zenodo.10927091, 2024.
Varney, R. M., Chadburn, S. E., Friedlingstein, P., Burke,
E. J., Koven, C. D., Hugelius, G., and Cox, P. M.: A
spatial emergent constraint on the sensitivity of soil car-
bon turnover to global warming, Nat. Commun., 11, 5544,
https://doi.org/10.1038/s41467-020-19208-8, 2020.
Varney, R. M., Chadburn, S. E., Burke, E. J., and Cox, P. M.: Eval-
uation of soil carbon simulation in CMIP6 Earth system models,
Biogeosciences, 19, 4671–4704, https://doi.org/10.5194/bg-19-
4671-2022, 2022.
Varney, R. M., Chadburn, S. E., Burke, E. J., Wiltshire, A. J.,
and Cox, P. M.: Simulated responses of soil carbon to climate
change in CMIP6 Earth System Models: the role of false priming,
EGUsphere [preprint], https://doi.org/10.5194/egusphere-2023-
383, 2023.
Wang, S., Zhang, Y., Ju, W., Chen, J. M., Ciais, P., Cescatti, A., Sar-
dans, J., Janssens, I. A., Wu, M., Berry, J. A., and Campbell, E.:
Recent global decline of CO
2
fertilization effects on vegetation
photosynthesis, Science, 370, 1295–1300, 2020.
Wieder, W. R., Cleveland, C. C., Lawrence, D. M., and Bonan,
G. B.: Effects of model structural uncertainty on carbon cy-
cle projections: biological nitrogen fixation as a case study,
Environ. Res. Lett., 10, 044016, https://doi.org/10.1088/1748-
9326/10/4/044016, 2015.
Zhou, T., Shi, P., Hui, D., and Luo, Y.: Global pattern of temperature
sensitivity of soil heterotrophic respiration (
Q
10
) and its impli-
cations for carbon-climate feedback, J. Geophys. Res.-Biogeo.,
114, G02016, https://doi.org/10.1029/2008JG000850, 2009.
Zickfeld, K., Eby, M., Matthews, H. D., Schmittner, A., and Weaver,
A. J.: Nonlinearity of carbon cycle feedbacks, J. Climate, 24,
4255–4275, 2011.
Biogeosciences, 21, 2759–2776, 2024
https://doi.org/10.5194/bg-21-2759-2024
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