Page 1
Biogeosciences, 20, 3767–3790, 2023
https://doi.org/10.5194/bg-20-3767-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research
ar
ticle
Simulated responses of soil carbon to climate change in CMIP6
Earth system models: the role of false priming
Rebecca M. Varney
1,2
, Sarah E. Chadburn
1
, Eleanor J. Burke
3
, Simon Jones
1,2
, Andy J. Wiltshire
2,3
, and
Peter M. Cox
1,2
1
Department of Mathematics and Statistics, 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
Met Office Hadley Centre, FitzRoy Road, Exeter, EX1 3PB, UK
Correspondence:
Rebecca M. Varney (r.varney@exeter.ac.uk)
Received: 2 March 2023 – Discussion started: 24 March 2023
Revised: 23 June 2023 – Accepted: 28 July 2023 – Published: 19 September 2023
Abstract.
Reliable estimates of soil carbon change are re-
quired to determine the carbon budgets consistent with the
Paris Agreement climate targets. This study evaluates pro-
jections of soil carbon during the 21st century in Coupled
Model Intercomparison Project Phase 6 (CMIP6) Earth sys-
tem models (ESMs) under a range of atmospheric compo-
sition scenarios. In general, we find a reduced spread of
changes in global soil carbon (
1
C
s
) in CMIP6 compared to
the previous CMIP5 model generation. However, similar re-
ductions were not seen in the derived contributions to
1
C
s
due to both increases in plant net primary productivity (NPP,
named
1
C
s
,
NPP
) and reductions in the effective soil carbon
turnover time (
τ
s
, named
1
C
s
,τ
). Instead, we find a strong re-
lationship across the CMIP6 models between these NPP and
τ
s
components of
1
C
s
, with more positive values of
1
C
s
,
NPP
being correlated with more negative values of
1
C
s
,τ
. We
show that the concept of “false priming” is likely to be con-
tributing to this emergent relationship, which leads to a de-
crease in the effective soil carbon turnover time as a direct
result of NPP increase and occurs when the rate of increase
in NPP is relatively fast compared to the slower timescales of
a multi-pool soil carbon model. This finding suggests that the
structure of soil carbon models within ESMs in CMIP6 has
likely contributed towards the reduction in the overall model
spread in future soil carbon projections since CMIP5.
1
Introduction
The response of soil carbon to human-induced climate
change represents one of the greatest uncertainties in de-
termining future atmospheric CO
2
concentrations (Canadell
et al., 2021). Global soil carbon stocks contain at least 3 times
more carbon than present atmospheric concentrations and are
the largest store of carbon on the land surface of Earth (Jack-
son et al., 2017). The land surface has been a carbon sink
throughout the 20th century and is estimated to be absorbing
about 30 % of current CO
2
emissions (Friedlingstein et al.,
2022). However, the long-term response of soil carbon is un-
certain due to large stocks which are known to be particu-
larly sensitive to changes in CO
2
and the subsequent global
warming (Cox et al., 2000). For example, permafrost thaw
under climate change has the potential to release significant
amounts of carbon into the atmosphere over a short period of
time with increased warming, representing a significant feed-
back within the climate system (Schuur et al., 2022; Hugelius
et al., 2020; Burke et al., 2017). Therefore, quantifying the
future response of soil carbon under future changes to cli-
mate is vital in determining the long-term potential land car-
bon storage.
Soil carbon storage in the future will be determined by
the net response of changes in land–atmosphere carbon ex-
change under increased anthropogenic CO
2
. The carbon
fluxes which control the fate of global soil carbon stocks
are known to be sensitive to changes in climate and there-
fore result in soil-carbon-driven feedbacks to climate change
Published by Copernicus Publications on behalf of the European Geosciences Union.
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
(Canadell et al., 2021). The overall effect of climate change
on soil carbon is not very well constrained due to compet-
ing feedbacks (Arora et al., 2020, 2013). These include both
the negative feedback due to the CO
2
fertilisation effect, re-
sulting in increased absorption of carbon by the land sur-
face (Schimel et al., 2015), and the positive climate feedback
due to increased carbon losses via soil respiration (Crowther
et al., 2016; Van Gestel et al., 2018). The balance between
these effects will determine the future response of soil car-
bon stocks under a changing climate (Friedlingstein et al.,
2006).
This study assumes that net primary productivity (NPP)
represents the input flux of carbon to the system and is de-
fined as the net rate of accumulation of carbon by vegetation
arising from photosynthesis minus the loss from plant respi-
ratory fluxes (Todd-Brown et al., 2014, 2013). In the absence
of nutrient and moisture limitations (Wieder et al., 2015b;
Green et al., 2019), NPP is projected to increase under in-
creased atmospheric CO
2
due to the CO
2
fertilisation effect,
which can result in increased soil carbon storage through in-
creased litter (Schimel et al., 2015). Heterotrophic respira-
tion (
R
h
) is assumed to represent the output flux of carbon
from the soil and is defined as the carbon losses due to de-
composition from microbes in the soil.
R
h
is projected to in-
crease under global warming due to an increased rate of mi-
crobial decomposition under warming (Varney et al., 2020)
in the absence of significant increases in soil moisture (Sierra
et al., 2015; Schmidt et al., 2011). Soil carbon turnover time
(
τ
s
) is defined as the ratio of soil carbon stocks to the output
flux of carbon (
R
h
). Global warming alone generally reduces
τ
s
, resulting in carbon residing in the soil for less time and a
release of carbon from the soil into the atmosphere (Crowther
et al., 2016). The effective soil carbon turnover time can also
reduce under increasing litterfall inputs (e.g. due to CO
2
fer-
tilisation of plant growth), because the faster components of
the soil increase more quickly than the slower components.
The net effect of this is that a higher fraction of the soil car-
bon flux is cycled in the fast pools under increasing litter-
fall, which reduces the effective soil carbon turnover time – a
transient phenomenon known as false priming (Koven et al.,
2015).
In this study, CMIP6 Earth system models (ESMs) are
used to predict changes to soil carbon stocks under future cli-
mate scenarios with differing magnitudes of climate change
(SSP126, SSP245, SSP585; Eyring et al., 2016; O’Neill
et al., 2016). The aim is to evaluate estimates of soil car-
bon change (
1
C
s
) during the 21st century to (a) quantify the
soil-carbon-driven feedback to climate change and (b) en-
able comparisons with the previous generation of CMIP5
ESMs (RCP2.6, RCP4.5, RCP8.5; Taylor et al., 2012; Mein-
shausen et al., 2011). Additionally, this study includes anal-
ysis of 21st century carbon fluxes to and from the soil, repre-
sented by changes in NPP and
τ
s
, and investigates how these
individual terms contribute to the net soil carbon response
projected by ESMs. Finally, a simple box model is used to
investigate soil carbon change, along with idealised simula-
tions (Coupled Climate-Carbon Cycle Model Intercompari-
son Project – C4MIP) which separately model the physio-
logical and climate effects of increasing atmospheric CO
2
.
Our aim is to distinguish more clearly between the direct and
indirect mechanisms of reduced soil carbon turnover times
by isolating the effects of false priming in models.
2
Methods
2.1
Earth system models
2.1.1
Future climate scenarios
This study uses output data from 10 CMIP6 ESMs
(Eyring et al., 2016): ACCESS-ESM1-5, BCC-CSM2-
MR, CanESM5, CESM2, CNRM-ESM2-1, IPSL-CM6A-
LR, MIROC-ES2L, MPI-ESM1-2-LR, NorESM2-LM, and
UKESM1-0-LL. For comparison between the CMIP genera-
tions, output data from nine CMIP5 ESMs are also used (Tay-
lor et al., 2012): BNU-ESM, CanESM2, GFDL-ESM2G,
GISS-E2-R, HadGEM2-ES, IPSL-CM5A-LR, MIROC-
ESM, MPI-ESM-LR, and NorESM1-M. 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 access: 8 April 2022; CMIP5: https://esgf-node.
llnl.gov/search/cmip5/, last access: 12 April 2022).
The use of CMIP allows for comparison between ESMs
in the different ensemble generations. Table 1 presents key
soil carbon ESM information from both CMIP6 and CMIP5
(adapted from Tables 1 and 2 in Varney et al., 2022). The
table can be used to identify key ESM updates between
CMIP6 and CMIP5, such as the simulation of interactive
nitrogen in CMIP6 (ACCESS-ESM1.5, CESM2, MIROC-
ES2L, MPI-ESM1.2-LR, NorESM2-LM, and UKESM1-0-
LL) compared to CMIP5 (NorESM1-M) and the number of
soil carbon pools (dead carbon pools). The ESMs where both
CMIP5 and CMIP6 generations are included in our analysis
are CanESM2 and CanESM5, GFDL-ESM2G and GDFL-
ESM4, IPSL-CM5A-LR and IPSL-CM6A-LR, MIROC-
ESM and MIROC-ES2L, MPI-ESM-LR and MPI-ESM1.2-
LR, NorESM1-M and NorESM2-LM, and HadGEM2-ES
and UKESM1-0-LL, respectively, where direct comparisons
can be made. It is noted that some land surface models within
ESMs share similarities (e.g. CESM2 and NorESM2-LM
both use the Community Land Model version 5; Arora et al.,
2020).
Within ESMs, specific soil carbon processes are modelled
using biogeochemical models which are used to simulate the
flow and storage of carbon within the soil. Since early mod-
els, both the litter and soil have been simulated using separate
carbon pools, which are used to represent differing sensitivi-
ties of carbon to decomposition. The allocation of carbon to
pools is often dependent on the molecular structure of the lit-
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
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Table 1.
The CMIP5 and CMIP6 Earth system models included in this study and the relevant features of the associated land carbon cycle
components: simulation of interactive nitrogen, the number of live carbon pools, and the number of dead soil carbon pools (Varney et al.,
2022; Arora et al., 2013, 2020).
Earth system
Nitrogen
No. of live
No. of dead
References
model
cycle
carbon pools
carbon pools
BNU-ESM
No
–
–
Ji et al. (2014); Dai et al. (2003)
CanESM2
No
3
2
Arora et al. (2009); Arora and Boer (2010)
GFDL-ESM2G
No
8
2
Dunne et al. (2012, 2013);
Shevliakova et al. (2009)
GISS-E2-R
No
7
5
Schmidt et al. (2014); Yue and Unger (2015)
HadGEM2-ES
No
3
4
Jones et al. (2011); Best et al. (2011);
Clark et al. (2011)
IPSL-CM5A-LR
No
–
7
Dufresne et al. (2013); Krinner et al. (2005)
MIROC-ESM
No
4
2
Watanabe et al. (2011); Ito and Oikawa (2002);
Sato et al. (2007)
MPI-ESM-LR
No
4
2
Raddatz et al. (2007); Knorr (2000)
NorESM1-M
Yes
13
7
Bentsen et al. (2013); Iversen et al. (2013);
Lawrence et al. (2011)
ACCESS-ESM1.5
Yes
3
6
Ziehn et al. (2020); Haverd et al. (2018);
BCC-CSM2-MR
No
3
8
Wu et al. (2019); Ji et al. (2008)
CanESM5
No
3
2
Swart et al. (2019); Melton et al. (2020);
Seiler et al. (2021)
CESM2
Yes
22
7
Danabasoglu et al. (2020); Lawrence et al. (2019)
CNRM-ESM2-1
No
6
7
Séférian et al. (2019); Delire et al. (2020)
GFDL-ESM4
No
6
4
Dunne et al. (2020); Zhao et al. (2018)
IPSL-CM6A-LR
No
8
3
Boucher et al. (2020); Cheruy et al. (2020);
Guimberteau et al. (2018)
MIROC-ES2L
Yes
3
6
Hajima et al. (2020); Ito and Oikawa (2002)
MPI-ESM1.2-LR
Yes
3
18
Mauritsen et al. (2019); Goll et al. (2017);
Goll et al. (2015)
NorESM2-LM
Yes
22
7
Seland et al. (2020); Lawrence et al. (2019)
UKESM1-0-LL
Yes
3
4
Sellar et al. (2020); Wiltshire et al. (2021)
ter and the long-term stability (Exbrayat et al., 2013). Early
examples of soil carbon models are the grass and agroecosys-
tems dynamic model (CENTURY; Parton et al., 1988) and
the Rothamsted carbon model (ROTH-C; Jenkinson et al.,
1991). Updated variants of these models are still widely
used to represent soil carbon decomposition in modern ESMs
within CMIP (Arora et al., 2020; Todd-Brown et al., 2018).
Table 1 presents the number of soil carbon pools (dead car-
bon pools) within both CMIP5 and CMIP6 ESMs, which can
be used to compare between the ESMs.
The analysis in this study considers three future climate
scenarios defined by CMIP, which are used to consider dif-
ferent levels of global warming and the associated climate
policies. The CMIP6 shared socioeconomic pathways (SSPs)
considered in this study are SSP126, SSP245, and SSP585,
which run from 2015 to 2100 (O’Neill et al., 2014, 2016).
These pathways are chosen to allow for comparison with
the CMIP5 representative concentration pathways (RCPs)
RCP2.6, RCP4.5, and RCP8.5, which run from 2005 to 2100
(Meinshausen et al., 2011). It is noted that the SSP and RCP
concentration scenarios are not identical, but they are sim-
ilar enough to enable helpful comparisons between CMIP5
and CMIP6 projections. For the reference period from which
change is calculated, the CMIP
Historical
simulation was
considered, where the simulation runs from 1850 to 2005
in CMIP5 and from 1850 to 2015 in CMIP6. A change (
1
)
was defined as the difference between the last decade of the
21st century (time-averaged between 2090 and 2100) and
the last decade of the CMIP5 historical simulation (time-
averaged between 1995 and 2005), which allows for consis-
tency between the CMIP generations. If a time series is con-
sidered, the historical reference period (historical simulation
time-averaged between 1995 and 2005) was subtracted from
the entire future climate simulation (e.g. SSP126 minus the
historical reference period).
2.1.2
C4MIP experiments
This study also uses model experiments set up by C4MIP
that are idealised experiments designed to separate the ef-
fects of CO
2
increases and associated climate changes on
land and ocean carbon stores. In these experiments addi-
tional effects such as land use change, aerosols, or non-CO
2
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
greenhouse gases are not included, and nitrogen deposition
is fixed at pre-industrial values (Jones et al., 2016). The
use of these experiments allows for a more focused eval-
uation of soil carbon and related fluxes by isolating sensi-
tivities to CO
2
and associated climate changes (e.g. global
temperature changes) and removing additional complica-
tions in the SSP simulations. The experiments included are
(1) a
full
1 % CO
2
simulation (CMIP6 simulation
1pctCO2
),
which is a simulation that sees a 1 % increase in atmo-
spheric CO
2
per year, starting from pre-industrial concentra-
tions (285 ppm) and running for 150 years (
full
1 % CO
2
);
(2) a biogeochemically coupled
BGC
simulation (CMIP6
simulation
1pctCO2-bgc
), where the 1 % CO
2
increase per
year only affects the carbon cycle component of the ESM
and the radiative code remains at pre-industrial CO
2
values
(CO
2
only); and (3) a radiatively coupled
RAD
simulation
(CMIP6 simulation
1pctCO2-rad
), where the 1 % CO
2
in-
crease per year affects only the radiative code and the car-
bon cycle component on the ESM remains at pre-industrial
CO
2
values (climate only). These simulations are used with
10 CMIP6 ESMs for further analysis: 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. Here, 2
×
CO
2
and 4
×
CO
2
are
defined as 70 and 140 years, respectively, into the simula-
tions.
2.1.3
Climate variables
Using ESM output variables, soil carbon (C
s
) is defined as
the sum of carbon stored in soils and surface litter (CMIP
variable
cSoil
+
CMIP variable
cLitter
). This allows for a
more consistent comparison between the models due to dif-
ferences in how soil carbon and litter carbon are defined.
For models that do not report a separate litter carbon pool
(
cLitter
), soil carbon is taken to be simply the
cSoil
variable
(UKESM1-0-LL in CMIP6, GISS-E2-R and HadGEM2-ES
in CMIP5). Spatial C
s
is given in units of kilogram per square
metre (kg m
−
2
), and global total C
s
is given in units of peta-
grams of carbon (PgC), which are calculated using an area-
weighted sum (using the model land surface fraction, CMIP
variable
sftlf
).
Additionally, ESM output variables were used to define
the soil-carbon-driven climate feedbacks. NPP (CMIP vari-
able
npp
) is defined as the net carbon assimilated by plants
via photosynthesis minus loss due to plant respiration and
is used to represent the net carbon input flux to the system.
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
): see Eq. (1).
τ
s
(years) is de-
fined as the ratio of mean soil carbon to annual mean het-
erotrophic respiration (where the mean represents an area-
weighted global average). Carbon fluxes (NPP and
R
h
) are
considered as area-weighted global totals (Pg C yr
−
1
).
τ
s
=
C
s
R
h
(1)
2.2
Breaking down the projected changes in soil carbon
From Eq. (1), soil carbon (C
s
) can be defined as shown by
Eq. (2). Future soil carbon stocks can be defined as initial soil
carbon (C
s
,
0
) plus a change in soil carbon (
1
C
s
) as shown by
Eq. (3), where the subscript 0 denotes the initial state (his-
torical simulation time-averaged between 1995 and 2005).
Equation (3) can be expanded to give Eq. (4), which can be
simplified to give Eq. (5).
C
s
=
R
h
τ
s
(2)
C
s
,
0
+
1
C
s
=
(R
h
,
0
+
1R
h
)(τ
s
,
0
+
1τ
s
)
(3)
C
s
,
0
+
1
C
s
=
R
h
,
0
τ
s
,
0
+
τ
s
,
0
1R
h
+
R
h
,
0
1τ
s
+
1R
h
1τ
s
(4)
1
C
s
=
τ
s
,
0
1R
h
+
R
h
,
0
1τ
s
+
1R
h
1τ
s
(5)
To isolate the above- and below-ground effects on soil car-
bon, the separate effects due to changes in NPP and changes
due to
τ
s
are considered (Todd-Brown et al., 2014). For car-
bon to be conserved, however, the difference between the
global fluxes NPP and
R
h
in a transient climate must be
taken into account, where the difference is defined as the net
ecosystem productivity (NEP), as shown in Eq. (6).
NEP
=
NPP
−
R
h
(6)
Equation (6) can be substituted into Eq. (5) to obtain an
equation for
1
C
s
in terms of NPP, NEP, and
τ
s
(Eq. 7).
1
C
s
=
τ
s
,
0
1(
NPP
−
NEP
)
+
(
NPP
0
−
NEP
0
)1τ
s
+
1(
NPP
−
NEP
)1τ
s
(7)
If the initial state is a steady state, the initial NEP (NEP
0
)
will be approximately equal to zero. However, as our initial
state is defined as the end of the historical simulation, NEP
0
will be non-zero as a result of the contemporary global land
carbon sink. ESMs may also include additional carbon fluxes
that cause changes to the resultant soil carbon inputs, such
as grazing, harvest, land use change, and fire (Todd-Brown
et al., 2014). The
1
NEP terms in Eq. (7) implicitly include
these effects.
Finally, Eq. (7) can be expanded to give Eq. (8), and the
individual responses which make up the total change in soil
carbon (
1
C
s
) can be broken down into six components:
1
C
s
=
τ
s
,
0
1
NPP
−
τ
s
,
0
1
NEP
+
NPP
0
1τ
s
−
NEP
0
1τ
s
+
1
NPP
1τ
s
−
1
NEP
1τ
s
.
(8)
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
3771
Figure 1.
Projected future change in soil carbon (
1
C
s
) in CMIP5
(a–c)
and CMIP6
(d–f)
ESMs for future climate scenarios RCP2.6 and
SSP126, RCP4.5 and SSP245, and RCP8.5 and SSP585, respectively. The dashed lines represent ESMs which include the representation of
interactive nitrogen in these simulations.
Equation (7) is exact for given time-varying values of NPP,
NEP, and
τ
s
. The individual terms in Eq. (8) are defined as
given below:
1
C
s
,
NPP
≈
τ
s
,
0
1
NPP
,
(9)
1
C
s
,
NEP
≈ −
τ
s
,
0
1
NEP
,
(10)
1
C
s
,τ
≈
NPP
0
1τ
s
,
(11)
1
C
s
,τ
NEP
≈ −
NEP
0
1τ
s
,
(12)
where
1
C
s
,
NPP
is the change in soil carbon due to changes in
NPP,
1
C
s
,
NEP
is the change in soil carbon due to changes in
NEP, and
1
C
s
,τ
is the change in soil carbon due to changes in
τ
s
(with
1
C
s
,τ
NEP
accounting for non-equilibrium). 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
).
3
Results and discussion
3.1
Projected changes in soil carbon
A reduced spread in projected end-of-21st-century estimates
of
1
C
s
is seen in CMIP6 compared to CMIP5 (Fig. 1). This
reduced spread is shown in Fig. 1, where projections of
1
C
s
by 2100 in CMIP6 are compared with those from CMIP5
across the different future scenarios. The reduced range of
projected changes is seen across all future scenarios (SSP126
and RCP2.6, SSP245 and RCP4.5, SSP585 and RCP8.5),
with the range in CMIP6 consistently less than 50 % of the
equivalent range in CMIP5 (Fig. 1). The standard deviation
of projections about the ensemble mean
1
C
s
is also reduced
in CMIP6 compared with CMIP5 by 50 %, consistent across
all future climate scenarios (Tables 2 and A1, bottom rows).
It is noted that the large range in CMIP5 estimates is mostly
a result of large increases in C
s
in HadGEM2-ES and MPI-
ESM-LR together with the large C
s
losses in GISS-E2-R
(Fig. 1). An updated CMIP6 version of the GISS-E2-R model
is not included in this analysis of this study, which could
contribute to the reduced uncertainty from CMIP5. However,
the updated equivalent CMIP6 models UKESM1-0-LL (from
HadGEM2-ES) and MPI-ESM1-2-LR (from MPI-ESM-LR)
have projected estimates of
1
C
s
which are more consistent
with the other models in the CMIP6 ensemble.
Nearly all of the ESM projections in CMIP6 suggest an in-
crease in C
s
by 2100; however, CMIP5 models project both
increases (positive
1
C
s
) and decreases (negative
1
C
s
) in soil
carbon during the 21st century (Fig. 1). In CMIP5 projec-
tions, the future responses of soil carbon range from an in-
crease of 23.2 % (HadGEM2-ES) to a decrease of 6.50 %
(GISS-E2-R) in RCP8.5, where across all future scenarios
approximately half of the models show increases and half
show decreases in
1
C
s
(Table A1). In CMIP6, the future
responses of soil carbon range from an increase of 12.5 %
(MPI-ESM1-2-LR) to a decrease of 2.25 % (ACCESS-
ESM1.5) in SSP585; however, the majority of the models
predict an increase in
1
C
s
across all the future scenarios (Ta-
ble 2).
Despite more consistent projections of increased
1
C
s
in
CMIP6 compared with CMIP5, it is apparent that greater
CO
2
forcing (i.e. SSP585 compared with SSP126) does not
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
Table 2.
Table presenting the absolute (Pg C) and relative (%) changes in 21st century soil carbon (
1
C
s
) for each CMIP6 model and the
ensemble mean
±
standard deviation for each future SSP scenario.
Earth system model
Absolute
1
C
s
(Pg C)
Relative
1
C
s
(%)
SSP126
SSP245
SSP585
SSP126
SSP245
SSP585
ACCESS-ESM1.5
3.44
−
0.98
−
23.4
0.38
−
0.108
−
2.55
BCC-CSM2-MR
31.8
22.3
−
35.2
1.76
1.23
−
1.95
CanESM5
50.6
66.7
97.7
3.41
4.49
6.59
CESM2
32.7
38.3
32.4
1.77
2.08
1.76
CNRM-ESM2-1
126
145
132
6.79
7.85
7.11
IPSL-CM6A-LR
57.6
55.0
35.5
8.86
8.45
5.46
MIROC-ES2L
87.3
118
126
5.88
7.94
8.5
MPI-ESM1-2-LR
86.2
97.9
123
8.79
9.98
12.5
NorESM2-LM
44.1
52.0
48.7
1.81
2.13
1.99
UKESM1-0-LL
52.3
46.9
17.5
2.96
2.65
0.988
Ensemble mean
55.4
58.3
50.3
4.53
4.24
3.67
±
standard deviation
±
31.8
±
44.3
±
57.8
±
2.95
±
3.51
±
4.50
always imply a greater magnitude of increased C
s
. In con-
trast to what is seen in CMIP6, the majority of CMIP5 mod-
els project an increased magnitude in estimated
1
C
s
with
increased CO
2
forcing (Fig. 1). In CMIP6, half the mod-
els (CESM2, CNRM-ESM2-1, IPSL-CM6A-LR, NorESM2-
LM, and UKESM1-0-LL) estimate less soil carbon accu-
mulation by 2100 (i.e. a smaller increase or a greater de-
crease) in SSP585 when compared with SSP126. This ef-
fect is most prominent in BCC-CSM2-MR and UKESM1-0-
LL, where a turning point from increasing to decreasing soil
carbon is seen in the mid-century of the SSP585 projections
(Fig. 2). This is contrary to an estimated increase in soil car-
bon storage with increased forcing, which is generally seen
in CMIP5 and the remaining CMIP6 models (CanESM5,
MIROC-ES2L, and MPI-ESM1-2-LR). This finding is likely
due to a saturation of the CO
2
fertilisation effect compared
with no saturation of increased respiration with warming in
these ESMs. This finding suggests a potential limit to
1
C
s
increase and a reduced likelihood of a carbon sink under
more extreme levels of climate change.
The spatial pattern of estimated
1
C
s
(Fig. 3) is quite vari-
able between CMIP6 ESMs in the tropical regions, where in-
creases in soil carbon can be seen in six of the CMIP6 ESMs
(BCC-CSM2-MR, CanESM5, CESM2, MIROC-ES2L, and
NorESM2-LM) but decreases are seen in the remaining four
(ACCESS-ESM1-5, CNRM-ESM2-1, IPSL-CM6A-LR, and
UKESM1-0-LL). There is a lack of agreement in the high
northern latitudes amongst the CMIP6 ESMs (Fig. 3), where
it is known that the uncertainty surrounding the fate of soil
carbon stocks in these regions is particularly important due
to the large magnitude of carbon stored (Burke et al., 2020;
Jackson et al., 2017). It has previously been found that a high
accumulation of northern-latitude C
s
is predicted amongst
CMIP5 ESMs; however, this C
s
response has not been sug-
gested in empirical studies based on observational findings
(Todd-Brown et al., 2014). The results here suggest that
Figure 2.
Time series of projected future soil carbon (C
s
) in CMIP6
ESMs for future climate scenarios SSP126, SSP245, and SSP585.
this accumulation (increased
1
C
s
) remains in the majority
of CMIP6 ESMs (Fig. 3), although reductions in northern-
latitude soil carbon stocks were found in three CMIP6 ESMs
(BCC-CSM2-MR, CESM2, and NorESM2-LM, with BCC-
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
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Figure 3.
Map plots showing the change in soil carbon (
1
C
s
) in SSP585 for each CMIP6 ESM.
CSM2-MR seeing reductions in a greater area). These ESMs
which predicted northern-latitude C
s
reductions were previ-
ously found to simulate historical northern-latitude soil car-
bon stocks which are more consistent with the observational
estimates seen in these regions (Varney et al., 2022).
3.2
Future changes to land–atmosphere fluxes
The projected
1
C
s
is a result of the changing input and
output land–atmosphere fluxes under climate change. To a
first order, the response of soil carbon will be determined by
changes to NPP and to
τ
s
(see Eq. 7). In this section, future
projections of these fluxes are analysed in both CMIP6 and
CMIP5 ESMs.
3.2.1
Net primary productivity
NPP is projected by CMIP6 ESMs to increase during the
21st century, with a greater increase with increasing cli-
mate forcing (across SSP scenarios). This result is consis-
tent with the projections of
1
NPP amongst the CMIP5 mod-
els (Fig. 4; Todd-Brown et al., 2014). Projections amongst
ESMs, however, show disagreement in the magnitude of
1
NPP by 2100 across all future climate scenarios, where a
projected CMIP6 ensemble increase of 24.6
±
16.9 Pg C yr
−
1
is seen in SSP585. The largest projections of
1
NPP amongst
the CMIP6 models are seen in CanESM5 and BCC-CSM2-
MR, where increases of 65.8 Pg C yr
−
1
(47 % increase) and
39.4 Pg C yr
−
1
(43 % increase), respectively, are projected by
2100 under SSP585. This is compared to ACCESS-ESM1-5,
which has the lowest projected changes amongst the CMIP6
models, with an increase of only 4.07 Pg C yr
−
1
(10 % in-
crease) by 2100 under SSP585 (Table 3).
The CMIP6 ensemble sees a slightly increased range in
end-of-century
1
NPP compared with CMIP5 across all fu-
ture scenarios (Tables 3 and A2). Figure 4 suggests that
the increased range is mostly due to outlying projections of
1
NPP (CanESM5), where greater increases are seen com-
pared to the majority of models within the ensemble. It is
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
Figure 4.
Projected future change in net primary productivity (
1
NPP) in CMIP5
(a–c)
and CMIP6
(d–f)
ESMs for future climate scenarios
RCP2.6 and SSP126, RCP4.5 and SSP245, and RCP8.5 and SSP585, respectively. The dashed lines represent ESMs which include the
representation of interactive nitrogen in these simulations.
Table 3.
Table presenting the change in 21st century NPP and
τ
s
for each CMIP6 model as well as the ensemble mean
±
standard deviation,
for each future SSP scenario.
Earth system model
1
NPP (Pg C yr
−
1
)
1τ
s
(years)
SSP126
SSP245
SSP585
SSP126
SSP245
SSP585
ACCESS-ESM1.5
1.66
3.58
4.07
−
0.828
−
1.69
−
2.35
BCC-CSM2-MR
8.37
19.7
39.4
−
4.53
−
8.52
−
14.0
CanESM5
17.4
35.4
65.8
−
3.09
−
5.01
−
7.10
CESM2
6.46
13.7
24.5
−
5.05
−
8.63
−
14.1
CNRM-ESM2-1
2.28
7.96
14.3
−
1.624
−
4.19
−
8.05
IPSL-CM6A-LR
8.40
13.9
16.2
−
0.938
−
1.81
−
2.83
MIROC-ES2L
4.90
13.9
29.0
−
1.52
−
3.37
−
6.23
MPI-ESM1-2-LR
7.84
14.3
25.9
−
0.555
−
1.27
−
2.30
NorESM2-LM
6.33
12.6
23.3
−
7.16
−
11.0
−
18.9
UKESM1-0-LL
8.08
15.2
28.1
−
2.37
−
4.52
−
8.25
Ensemble mean
7.44
13.6
24.6
−
2.30
−
4.55
−
7.65
±
standard deviation
±
4.01
±
8.71
±
16.9
±
2.047
±
3.35
±
5.65
noted that a cluster of ESMs which have similar projec-
tions of
1
NPP is seen within CMIP6 (CESM2, MIROC-
ES2L, MPI-ESM1-2-LR, NorESM2-LM, and UKESM1-0-
LL). The cluster is found to be made up of ESMs which in-
clude the simulation of an interactive nitrogen cycle (shown
by the dashed lines throughout this study), which is a
common addition within CMIP6 ESMs (ACCESS-ESM1.5,
CESM2, MIROC-ES2L, MPI-ESM1-2-LR, NorESM2-LM,
and UKESM1-0-LL; Davies-Barnard et al., 2020). ACCESS-
ESM1-5 is the only model within CMIP6 which simulates in-
teractive nitrogen, but it does not predict a similar
1
NPP to
the other nitrogen ESMs in CMIP6. However, the projections
of
1
NPP in ACCESS-ESM1-5 are similar to the projections
of NorESM1-M in CMIP5, which is the only CMIP5 model
considered here to simulate interactive nitrogen (Table 1).
3.2.2
Soil carbon turnover time
Future
τ
s
is projected by CMIP6 ESMs to decrease by 2100
across all future SSP scenarios (Fig. 5). A greater reduc-
tion in
τ
s
is seen with the increased climate forcing sce-
nario, where a reduced
τ
s
is a faster soil carbon turnover
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
3775
Figure 5.
Projected future change in soil carbon turnover time (
1τ
s
) in CMIP5
(a–c)
and CMIP6
(d–f)
ESMs for future climate scenarios
RCP2.6 and SSP126, RCP4.5 and SSP245, and RCP8.5 and SSP585, respectively. The dashed lines represent ESMs which include the
representation of interactive nitrogen in these simulations.
time and implies that carbon is cycled back to the atmo-
sphere in less time due to an increased carbon output from
the soil (increased
R
h
; see Eq. 1). This result is consis-
tent with the projections of
1τ
s
amongst the CMIP5 models
(Fig. 5; Todd-Brown et al., 2014). However, it is found that
greater variation exists amongst the CMIP6 ESMs’ end-of-
century estimates, where a projected CMIP6 ensemble
1τ
s
value of
−
7.65
±
5.65 years is seen in SSP585 compared to
−
6.13
±
3.03 years for CMIP5 ESMs in RCP8.5 (Tables 3
and A2).
The CMIP6 ESMs with the greatest reductions in effective
global
τ
s
by 2100 are seen in BCC-CSM2-MR, CESM2, and
NorESM2-LM, where global carbon turnover in the soil is
at least 14 years faster at the end of the SSP585 simulation
compared to the start of the 21st century (historical refer-
ence). The CMIP6 models with the least change in effective
global
τ
s
are ACCESS-ESM1-5, IPSL-CM6A-LR, and MPI-
ESM1-2-LR, where global carbon turnover in the soil is only
around 2 years faster at the end of the SSP585 simulation
(Table 3). The increased range in CMIP6 from CMIP5 is pri-
marily due to the large
τ
s
reductions seen in the CMIP6 mod-
els NorESM2-LM, CESM2, and BCC-CSM2-MR (Fig. 5).
3.3
Breaking down the projected changes in soil carbon
To understand the projected end-of-century changes in soil
carbon storage (
1
C
s
) in ESMs, the individual responses of
soil carbon due to changes in NPP (
1
C
s
,
NPP
; see Eq. 9)
and the response due to changes in
τ
s
(
1
C
s
,τ
; see Eq. 11)
were diagnosed for both CMIP5 and CMIP6 as shown in
Fig. 6. Future
1
C
s
(blue bars) is found to be mostly a re-
sult of the net effect of the linear terms
1
C
s
,
NPP
(dark-green
bars) and
1
C
s
,τ
(red bars). However, there are also non-
negligible contributions from the non-linear term
1
NPP
1τ
s
(black bars) and a small addition due to the non-equilibrium
terms
1
C
s
,
NEP
(light-green bars),
1
C
s
,τ
NEP
(pink bars), and
1
NEP
1τ
s
(grey bars).
The importance of investigating the individual processes
which contribute to the net
1
C
s
in ESMs can be seen (Fig. 6).
In Fig. 6 it is seen that the net
1
C
s
is relatively small com-
pared to the individual changes from the derived compo-
nents, where especially large magnitudes are seen in the
increased C
s
due to increased
1
NPP (
1
C
s
,
NPP
) and the
decreased C
s
due to reduced
1τ
s
(
1
C
s
,τ
). For example,
in SSP585 there is a range of approximately 170 Pg C in
net
1
C
s
, from an increase of 132 Pg C (CNRM-ESM2-1)
to a reduction of 35 Pg C (BCC-CSM2-MR). However, the
1
C
s
,
NPP
contribution has a much larger range of 1442 Pg C,
from an increase of 95 Pg C (ACCESS-ESM1-5) to an in-
crease of 1517 Pg C (NorESM2-LM). Similarly,
1
C
s
,τ
has
a range of 756 Pg C, from a decrease of 115 Pg C (ACCESS-
ESM1-5) to a decrease of 871 Pg C (NorESM2-LM).
The magnitude of change seen from the individual feed-
backs (
1
C
s
,
NPP
and
1
C
s
,τ
) is not obviously related to the
resultant magnitude of soil carbon change (Fig. A1). For ex-
ample, NorESM2-LM projects large
1
C
s
,
NPP
and
1
C
s
,τ
val-
ues (1517 and
−
871 Pg C in SSP585, respectively) but a rel-
atively small net change in soil carbon (49 Pg C in SSP585).
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
Figure 6.
A bar chart showing the contributions of NPP and
τ
s
to end-of-21st-century changes in soil carbon (
1
C
s
) in CMIP5
(a–c)
and
CMIP6
(d–f)
ESMs for future scenarios RCP2.6 and SSP126, RCP4.5 and SSP245, and RCP8.5 and SSP585, respectively. The included
terms are the linear term representing changes in soil carbon due to the changes in NPP (
1
C
s
,
NPP
), the linear term representing changes in
soil carbon due to the changes in
τ
s
(
1
C
s
,τ
), the non-linear term (
1
NPP
1τ
s
), and then additional terms to account for the non-equilibrium
climate in 2100 (
1
C
s
,
NEP
,
1
C
s
,τ
NEP
, and
1
NEP
1τ
s
).
Conversely, CNRM-ESM2-1 projects smaller
1
C
s
,
NPP
and
1
C
s
,τ
values (667 and
−
413 Pg C in SSP585, respectively)
but a larger net soil carbon change (132 Pg C in SSP585).
Within ESMs, it is found that the change in soil carbon is
determined by the relationship between all the contributing
terms to the net
1
C
s
response, as opposed to the absolute
size of a given contribution (Fig. 6).
Surprisingly, a very strong correlation is found amongst
the ESMs in CMIP6 (
r
2
value of 0.97) between the linear
terms
1
C
s
,
NPP
and
1
C
s
,τ
(Fig. 7a). This leads to the partial
cancelling of the terms, with a relatively small resultant net
1
C
s
. When comparing with the CMIP5 ensemble, a lower
correlation between
1
C
s
,
NPP
and
1
C
s
,τ
is seen (
r
2
value
of 0.084, Fig. 7a). This correlation amongst CMIP6 ESMs
results in net
1
C
s
being more clustered in CMIP6 com-
pared to CMIP5 (Fig. 1) despite a similarly large variation
in the individual contributions (Fig. 6). The strong CMIP6
correlation (
r
2
=
0
.
97) remains when the fractional changes
(
1
C
s
,
NPP
/
C
s
,
0
and
1
C
s
,τ
NPP
/
C
s
,
0
, where C
s
,
0
is initial soil
carbon stocks) are plotted instead (Fig. 7b).
Figure 6 also shows that the differences in ESM pro-
jections of
1
C
s
are partly due to differing magnitudes
of the non-linear term (
1
NPP
1τ
s
). A linear assumption
is commonly used which would allow these cross-terms
to be neglected (
1
NPP
/
NPP
1 and
1τ
s
/τ
s
1; Koven
et al., 2015). However, the ESM-projected magnitudes of
1
NPP
1τ
s
are found to be relatively large, especially in the
more extreme climate scenarios (Fig. 6). In SSP585, a range
from a decreased C
s
of 11 Pg C (ACCESS-ESM1-5) to a de-
creased C
s
of 599 Pg C (BCC-CSM2-MR) is found amongst
the CMIP6 models due to only the
1
NPP
1τ
s
term, and
in some cases values greater magnitudes are seen than the
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
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Figure 7.
Scatter plot comparing the relationship between
1
C
s
,
NPP
and
1
C
s
,τ
for CMIP5 (top row) and CMIP6 (bottom row) ESMs in
future scenarios RCP2.6 and SSP126, RCP4.5 and SSP245, and RCP8.5 and SSP585, respectively, for
(a)
absolute changes and
(b)
fractional
changes.
net
1
C
s
(BCC-CSM2-MR, CanESM5, CESM2, NorESM2-
LM, and UKESM1-0-LL). The term is greater when there
are large and counteracting magnitudes of
1
NPP and
1τ
s
,
which results in a non-negligible product.
Additionally, to obtain the overall change in soil carbon
seen in the models, contributions from the non-equilibrium
terms (
1
C
s
,
NEP
,
1
C
s
,τ
NEP
, and
1
NEP
1τ
s
) must also be in-
cluded (Fig. 6). The
1
C
s
,
NEP
term represents the change in
soil carbon due to the net carbon sink during the 21st cen-
tury, which exists while the climate is in a transient state due
to continuous climate change. By definition, the magnitude
of
1
C
s
,
NEP
is negative if
1
NEP is positive, which implies a
greater or faster increase in NPP with respect to
R
h
seen in
the majority of ESMs. The contribution from these terms is
found to be relatively small in most models but not in all. In
SSP585, projections of
1
C
s
,
NEP
amongst the CMIP6 models
range from a reduction of 333 Pg C (NorESM2-LM) to a gain
of 8.74 Pg C (ACCESS-ESM1-5). In CMIP5, there are ex-
ceptions where greater
1
C
s
,
NEP
terms are found in the GISS-
E2-R and MPI-ESM-LR models, implying that the models
are far from equilibrium at the end of the 21st century. The
change in soil carbon due to the change in NEP (
1
C
s
,
NEP
)
is often found to be greater in the models, which see greater
magnitudes of
1
C
s
,
NPP
and
1
C
s
,τ
.
3.4
Investigating the emergent relationship between
1
C
s
,
NPP
and
1
C
s
,τ
In this sub-section, the emergent relationship between
1
C
s
,
NPP
and
1
C
s
,τ
present across the CMIP6 ensemble
is investigated using the idealised C4MIP simulations (see
Methods). This enables investigation of the apparent nega-
tive correlation without additional complex processes which
are included in the SSP simulations. By isolating the sensi-
tivities to CO
2
and climate, we can more easily identify the
processes, which results in the apparent coupling between
NPP and soil carbon turnover time in CMIP6 ESMs. Fig-
ure 8 presents the relationship between
1
C
s
,
NPP
and
1
C
s
,τ
for each CMIP6 ESM as in Fig. 7 but for the
full
1 % CO
2
,
BGC
(CO
2
only), and
RAD
(climate only) simulations. It is
found that
1
C
s
,
NPP
and
1
C
s
,τ
are strongly correlated in the
full
1 % CO
2
simulation at both 2
×
CO
2
(
r
2
value of 0.925)
and 4
×
CO
2
(
r
2
value of 0.839). The correlation is found to
remain in the
BGC
simulation, where
r
2
values are found to
be 0.838 and 0.708 for 2
×
CO
2
and 4
×
CO
2
, respectively.
A correlation is also seen in the
RAD
simulation at 2
×
CO
2
(
r
2
value of 0.601); however, the correlation in the
RAD
sim-
ulation does not hold at 4
×
CO
2
, where the
r
2
value reduces
to 0.265. The reduced correlation in the
RAD
simulation at
4
×
CO
2
suggests a reduced relationship between NPP and
τ
s
at the more extreme temperature changes that are projected
at high levels of atmospheric CO
2
(without the direct effects
of CO
2
in this run).
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
Figure 8.
Scatter plots showing the relationship between
1
C
s
,
NPP
and
1
C
s
,τ
for each CMIP6 ESM in the
full
1 % CO
2
simulation (top
row),
BGC
simulation (middle row), and
RAD
simulation (bottom row) for
(a)
2
×
CO
2
and
(b)
4
×
CO
2
.
For each CMIP6 ESM, NPP and
τ
s
are found to be strongly
inversely correlated in the
full
1 % CO
2
simulation (Fig. 9).
The
r
2
values between NPP
/
NPP
0
and
τ
s
,
0
/τ
s
(where the
subscript 0 denotes the historical state) are found to be
greater than 0.95 in all the models, except for ACCESS-
ESM1-5 (where an
r
2
value of 0.65 is found due to a
breakdown at high CO
2
levels). In the
BGC
simulation, a
similar relationship between NPP
/
NPP
0
and
τ
s
,
0
/τ
s
is seen
up until approximately 2
×
CO
2
in all the ESMs (approx-
imately 50 % of the simulation). However, how the rela-
tionship between NPP
/
NPP
0
and
τ
s
,
0
/τ
s
changes through-
out the
BGC
simulation (between 2
×
CO
2
and 4
×
CO
2
)
varies between the models. A greater rate of NPP
/
NPP
0
in-
crease compared to
τ
s
,
0
/τ
s
is seen at greater levels of cli-
mate forcing for the majority of CMIP6 ESMs (BCC-CSM2-
MR, CanESM5, GFDL-ESM4, IPSL-CM6A-LR, MIROC-
ES2L, MPI-ESM1-2-LR, and UKESM1-0-LL), where the
τ
s
changes appear to saturate and a limit to the increase is seen.
In these ESMs, the changes seen in the
full
and
BGC
simula-
tions differ due to a climate effect (shown by the
RAD
simula-
tion), which appears to negate the apparent limit or saturation
seen in the
τ
s
,
0
/τ
s
increase in the
BGC
simulation (Fig. 9). In
CESM2 and NorESM2-LM (containing the same land sur-
face model component), a consistent relationship is seen in
both the
full
1 % CO
2
and
BGC
simulations, suggesting that
the changes in NPP and
τ
s
are primarily driven by changes in
CO
2
concentrations or that the climate affects cancel out to
a resultant net zero change. In ACCESS-ESM1-5, a consis-
tent relationship is seen in the
full
1 % CO
2
,
BGC
, and
RAD
simulations, suggesting a greater sensitivity of NPP to en-
vironmental climate changes compared to the other CMIP6
ESMs (Fig. 9).
It has been shown in this sub-section that the correlation
between
1
C
s
,
NPP
and
1
C
s
,τ
, as seen in the SSP simulations
(Fig. 7), is also evident in the
full
1 % CO
2
C4MIP simu-
lation (Fig. 8). This suggests that the relationship is not a
result of additional processes included in the SSP simula-
tions compared to the C4MIP experiments, such as land use
change (Jones et al., 2016). An additional explanation for the
coupling could be similarities in the modelled sensitivities
of NPP and
R
h
to changes in climate (i.e. temperature and
moisture changes). For example, if NPP and soil respiration
rate both increased with warming, a negative correlation be-
tween
1
C
s
,
NPP
and
1
C
s
,τ
would be seen. However, under
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
3779
Figure 9.
Scatter plots showing the correlation between NPP
/
NPP
0
and
τ
s,
0
/τ
s
for each CMIP6 ESM in the
full
1 % CO
2
simulation
(blue) and the
BGC
simulation (green) up to 4
×
CO
2
.
these circumstances, the negative correlation would not be
seen in the CO
2
-only runs (
BGC
simulation), as there is no
global warming in these simulations (see Methods). Instead,
a reduction in the effective soil carbon turnover time is seen
in the CO
2
-only runs (
BGC
simulation; Fig. A2), which im-
plies a non-climate response in
τ
s
and results in a NPP–
τ
s
negative correlation under changing atmospheric CO
2
alone
(Fig. 9). Figure 10 shows that the change in the effective soil
carbon turnover time in the CO
2
-only simulation (
BGC
sim-
ulation) accounts for at least 50 % of the total change in the
effective soil carbon turnover time in the
full
1 % simulation
across CMIP6 ESMs.
3.5
The role of false priming
Koven et al. (2015) present the concept of false priming as
a reduction in effective soil carbon turnover time (
τ
s
) due
to increases in productivity (NPP). It was defined as “false
priming” due to the impact being similar to the “true prim-
ing” process, but it occurs without simulating the priming
mechanisms, where priming is defined as the stimulation of
decomposition of soil carbon (reducing
τ
s
) due to input of
carbon to the soil (Liu et al., 2020). The false priming reduc-
tion in effective
τ
s
is a transient phenomenon that arises in
soil models that represent multiple carbon pools with differ-
ent turnover times. Under continually increasing NPP, pro-
portionally more of the additional input litter carbon is put
into the faster soil carbon pools than the slow ones, which
brings down the global average effective
τ
s
value of the soil.
In this sub-section, false priming is explored as a possible ex-
planation for the negative correlation seen between NPP and
τ
s
, which are seen even in the
BGC
simulations (CO
2
only),
where the climate does not change significantly (Fig. 10).
Koven et al. (2015) demonstrate false priming with a sim-
ple three-box soil carbon model, which has been adapted here
to use notation consistent with the rest of this study:
dC
s
,
1
d
t
=
NPP
−
C
s
,
1
τ
s
,
1
,
(13)
dC
s
,
2
d
t
=
e
1
C
s
,
1
τ
s
,
1
−
C
s
,
2
τ
s
,
2
,
(14)
dC
s
,
3
d
t
=
e
2
C
s
,
2
τ
s
,
2
−
C
s
,
3
τ
s
,
3
,
(15)
R
h
=
(
1
−
e
1
)
C
s
,
1
τ
s
,
1
+
(
1
−
e
2
)
C
s
,
2
τ
s
,
2
+
(
1
−
e
3
)
C
s
,
3
τ
s
,
3
,
(16)
C
s
=
C
s
,
1
+
C
s
,
2
+
C
s
,
3
,
(17)
τ
s
,
1
=
1
, τ
s
,
2
=
10
, τ
s
,
3
=
100
,
(18)
e
1
=
0
.
3
, e
2
=
0
.
3
, e
3
=
0
,
(19)
where C
s
,
1
, C
s
,
2
, and C
s
,
3
represent the carbon stored in soil
carbon pools 1, 2, and 3 and make up the total soil carbon
(C
s
). Similarly,
τ
s
,i
are the respective soil carbon turnover
times, which are given defined values of increasing turnover
times in years: fast (1 year), medium (10 years), and slow
(100 years). NPP represents the carbon input into the system,
where carbon is inputted into pool 1 (C
s
,
1
) and then flows to
pools 2 (C
s
,
2
) and 3 (C
s
,
3
). The coefficient
e
i
represents the
fraction of carbon that is passed to the next pool rather than
outputted as heterotrophic respiration (
R
h
).
At equilibrium, the change in the soil carbon pools will
be zero (dC
s
,i
/
d
t
=
0), so the amount of soil carbon present
within each pool depends on the input carbon and turnover
time of the pool (
τ
s
,i
). Under increasing NPP, the three-box
model can be used to investigate the subsequent changes to
soil carbon in the three carbon pools (C
s
,
1
, C
s
,
2
, C
s
,
3
) based
on changing input alone, due to each pool having a fixed
τ
s
,i
value. This removes the
1τ
s
from changing environmental
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
Figure 10.
Changes in soil carbon turnover (
1τ
s
) in C4MIP runs for the CMIP6 ESMs, with and without direct climate effects on
τ
s
.
(a)
Time
series of
1τ
s
in the
full
1 % CO
2
simulation (climate and CO
2
changes),
(b)
time series of
1τ
s
in the
BGC
simulation (CO
2
changes only),
and
(c)
bar chart showing the fraction of total
1τ
s
due to the changes in CO
2
at 4
×
CO
2
for each model.
and microbial conditions (Koven et al., 2015; Wieder et al.,
2015a; Exbrayat et al., 2013). The effective
τ
s
of the system
is calculated by definition (using Eq. 1).
Figure 11a shows a simulation of the response of this
three-box model to an NPP input flux that increases at
0.3 % yr
−
1
and where the soil carbon boxes are initialised at 0
(reproducing Fig. 12 in Koven et al., 2015). The greater frac-
tion of
1
C
s
in the fast soil carbon pool compared to the slow
one can be seen, which results in a decline in the effective
τ
s
of the system. This decline in effective
τ
s
with increas-
ing NPP is clear and demonstrates false priming (Fig. 11a).
Figure 11b again demonstrates that false priming is a tran-
sient effect associated with the distribution of soil carbon be-
tween the three pools, which emerges from the differences
in the mass-weighted and flux-weighted responses. It shows
results from the same model but for a step increase in global
NPP from 50 to 70 Pg C yr
−
1
at year 100. The fast soil carbon
pool reaches equilibrium before the slower soil carbon pool,
resulting in the instantaneous decline in
τ
s
of about 10 %,
which eventually reduces to return the soil to the original
τ
s
.
This transient effect occurs on the timescale of the slowest
carbon pool and therefore may take many centuries.
The same three-box model can also be used to investigate
the relationship between the contributions of changes in NPP
(
1
C
s
,
NPP
) and
τ
s
(
1
C
s
,τ
) with net soil carbon change that
was noted in both Figs. 7 and 8. Figure 12 plots
1
C
s
,
NPP
against
1
C
s
,τ
from the three-box model after 70 years of
runs that assume different rates of increase in NPP (0 % yr
−
1
to 0.8 % yr
−
1
in increments of 0.05 %). A clear relationship
between
1
C
s
,
NPP
and
1
C
s
,τ
is seen, with greater false prim-
ing (more negative
1
C
s
,τ
) when the NPP increase is larger
(more positive
1
C
s
,
NPP
). The similarity of Fig. 12 to both
Figs. 7 and 8 is clear, suggesting that false priming and the
structure of the soil carbon models within the ESMs are
likely contributing to these correlations in CMIP6 (and to a
lesser extent in CMIP5).
It is noted that the influence of false priming was stronger
in the
full
1 % CO
2
and
BGC
(CO
2
only) simulations com-
pared to the
RAD
(climate only) simulation (Fig. 8). This is
likely due to the
RAD
simulation not seeing sufficient NPP
change and therefore sufficient input of soil carbon for the
false priming effect to be significant (see Fig. A2). Addition-
ally, the direct effect of temperature changes on
τ
s
in the
RAD
simulation (in the absence of atmospheric CO
2
changes) is
likely to dampen the correlation with NPP changes, due to
both direct and indirect
1τ
s
influences in this case (Varney
et al., 2020).
False priming refers to a reduction in the effective turnover
time when the input of carbon into the soil increases. It was
named “false priming” as it can look like the increase in het-
erotrophic respiration that occurs when a soil microbial com-
munity is stimulated by the addition of labile carbon or nutri-
ents (“true priming”). However, false priming is arguably a
misleading term because it is a real effect. It arises as a result
of a change in the relative quantities of carbon turning over
at different rates, which occurs transiently in response to an
increase in the input of carbon into the soil. In the context
of our three-box model, for example, the turnover rates of
each individual box do not change. However, because each
box responds differently to the increase in NPP, a difference
in the average or effective turnover (i.e. as defined in Eq. 1)
is seen. The effective soil carbon turnover time is a measure
of how long carbon remains in the soil. However, it cannot
necessarily be assumed that all carbon will take exactly the
same amount of time to be re-released. Different types of lit-
ter input (e.g. lignin vs. carbohydrate) take different amounts
of time to decompose (Krishna and Mohan, 2017). Simi-
larly, vertical gradients in temperature throughout the soil re-
sult in variations of turnover time within the system (Koven
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
3781
Figure 11.
Time series plot showing the results from the simple three-box model.
(a)
For normalised changes in NPP,
R
h
,
τ
s
, and C
s
as well
as the fractional change in each of the three soil carbon boxes and in the total soil carbon (recreation of Fig. 12 in Koven et al., 2015).
(b)
For
an abrupt change in global NPP from 50 to 70 Pg C yr
−
1
at year 100.
Figure 12.
Relationship between
1
C
s
,
NPP
and
1
C
s
,τ
derived from
the three-box model. Each dot represents the results at the end of
a 70-year run with a different assumed rate of increase in NPP
(
∼
0.0 % yr
−
1
to 0.8 % yr
−
1
in increments of 0.05 %).
et al., 2017). The effective carbon turnover time is an aver-
age of these distributions of turnover times, and an increase
in the amount of fast turnover carbon in the system relative
to slower turnover carbon results in it decreasing. As it has
been shown here, this effect can be significant and must be
accounted for when attributing soil carbon change to differ-
ent environmental drivers (Georgiou et al., 2015).
This study has highlighted how false priming has con-
tributed to a reduced spread in
1
C
s
ESM projections in
CMIP6, due to a cancellation effect seen between increases
due to
1
NPP (
1
C
s
,
NPP
) and decreases due to
1τ
s
(
1
C
s
,τ
).
The extent of false priming within ESM projections will de-
pend on the distribution of carbon within soil carbon pools
and how litter carbon is allocated between pools with fast
and slow turnover times (Koven et al., 2015). Figure 10(c)
shows the fraction of
1τ
s
due to
1
CO
2
, which can be used
as a proxy to estimate the contribution of false priming to
the overall projected
1τ
s
in CMIP6 ESMs, which varies be-
tween approximately 50 % (CanESM5 and MIROC-ES2L)
and 90 % (CESM2 and NorESM2-LM). A more apparent
false priming affect within CMIP6 could suggest an im-
proved representation of the slower components of soil car-
bon since CMIP5, commonly by including more dead car-
bon pools within the ESM (Table 1). Based on observational
radiocarbon estimates, it has been found that CMIP5 ESMs
underestimate carbon age within the soil (He et al., 2016; Shi
et al., 2020), suggesting that ESMs underestimate the amount
of carbon in the slow carbon pools. It has been shown that
representing soil carbon ages more in line with radiocarbon
estimates leads to a reduced potential for soil carbon seques-
tration in the future (He et al., 2016), which agrees qualita-
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
tively with the projected 21st century soil carbon changes as
predicted by CMIP6 compared to CMIP5 found in this study.
On top of the role of false priming, additional factors in-
fluence the magnitude of predicted
1
C
s
within ESMs. Gen-
erationally related ESMs between CMIP5 and CMIP6 al-
low us to highlight some key changes between the CMIP
generations and to suggest potential model developments
which may have contributed to the projected differences in
future C
s
seen here. For example, within CMIP5, the mod-
els HadGEM2-ES and MPI-ESM-LR predicted the great-
est increases in soil carbon within the ensemble; however,
within CMIP6, the updated versions UKESM1-0-LL and
MPI-ESM1-2-LR predict reduced increases (Fig. 1). Both
updated variants of these ESMs include the representation of
interactive nitrogen in CMIP6 simulations (Table 1), which
could limit carbon sequestration by limiting the magnitude
of CO
2
fertilisation. Depending on the ratio of carbon to ni-
trogen within the soil, however, accelerated decomposition
due to soil warming can increase nitrogen mineralisation and
alleviate the nutrient limitation in plants (Wiltshire et al.,
2021). Additionally, MPI-ESM1-2-LR (CMIP6) sees an in-
creased number of dead or soil carbon pools compared with
MPI-ESM-LR (CMIP5), whereas UKESM1-0-LL (CMIP6)
from HadGEM2-ES (CMIP5) sees no change in the number
of carbon pools. The increased number of dead carbon pools
could contribute to the decrease in
1
C
s
by either a transient
reduction due to false priming or longer soil carbon turnover
times that result in carbon being stored in slower pools within
the soil. It is noted that an investigation into the role of soil
carbon pools in future soil carbon projections will require
data for projections and allocation of C
s
in individual soil
pools within ESMs, which is beyond the scope of this study
(Koven et al., 2015).
4
Conclusions
In this study, future projections of soil carbon change (
1
C
s
)
have been analysed using ESM output from the latest CMIP6
ensemble and have been investigated under differing levels
of climate change (future scenarios SSP126, SSP245, and
SSP585). The future projections made by CMIP6 ESMs were
also compared against equivalent projections made by the
previous generation of ESMs in the CMIP5 ensemble (fu-
ture scenarios RCP2.6, RCP4.5, and RCP8.5) to investigate
whether recent model improvements have reduced the uncer-
tainty surrounding the future soil carbon response. Addition-
ally,
1
C
s
was broken down into the individual components
which contribute to the net change within ESMs, with a spe-
cific focus on increases due to increases in NPP (
1
C
s
,
NPP
)
and decreases due to reductions in turnover (
1
C
s
,τ
). Below,
the key conclusions from this study are listed.
1. An apparent reduction in the uncertainty of end-of-21st-
century
1
C
s
projections is suggested in CMIP6 com-
pared to CMIP5.
2. However, the same reduction in projection uncertainty
is not suggested surrounding the soil carbon controls:
net primary productivity (NPP) and the effective soil
carbon turnover time (
τ
s
=
C
s
/R
h
) as well as the sub-
sequent effects on future soil carbon storage (
1
C
s
,
NPP
and
1
C
s
,τ
, respectively).
3. The derived linear terms which contribute to net soil car-
bon change, the response of soil carbon due to changes
in NPP (
1
C
s
,
NPP
), and the response due to changes in
τ
s
(
1
C
s
,τ
) are found to have a strong relationship in
CMIP6, with a more significant correlation than what
was seen in CMIP5. This correlation is likely to be
a cause of the reduction in the
1
C
s
projection spread
across the CMIP6 ensemble.
4. False priming was found to likely be contributing to the
apparent emergent relationship between
1
C
s
,
NPP
and
1
C
s
,τ
in CMIP6 ESMs, which describes a transient re-
duction in effective soil carbon turnover time due to in-
creased input of carbon to the soil. The net effect of false
priming is a coupling affect between
1
NPP and
1τ
s
and
results in a reduced range of future
1
C
s
predictions in
CMIP6.
5. Our study highlights the significant role that false prim-
ing can play under transient changes in atmospheric
CO
2
and climate. We advise caution in the interpretation
of changes in the effective soil carbon turnover time in
terms of climate effects alone. Idealised C4MIP simula-
tions, which can be used to separate the effects of CO
2
and climate on the effective soil carbon turnover time,
are very useful for assessing the role of false priming
in models. Understanding these factors will be key to
predicting soil carbon changes over the next 100 years.
Understanding and quantifying soil carbon feedbacks un-
der anthropogenic emissions of CO
2
is critical for calculating
an accurate global carbon budget, which is required if Paris
Agreement targets are to be met (Friedlingstein et al., 2022).
This study highlights the importance of considering the in-
dividual soil-driven carbon feedbacks under climate change
when determining the overall response of global soil carbon
storage, and it suggests the need for constraints on the mag-
nitudes of these feedbacks in CMIP6 to reduce uncertainty in
projections of future land carbon storage.
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Appendix A
Figure A1.
Scatter plot comparing the relationship between
1
C
s
,
NPP
,
1
C
s
,τ
,
1
NPP
1τ
s
, and
1
C
s
,τ
NEP
, each against
1
C
s
for CMIP5 (top
row) and CMIP6 (bottom row) ESMs for future scenarios SSP126 and RCP2.6, SSP245 and RCP4.5, and SSP585 and RCP8.5.
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R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
Figure A2.
Time series of projected changes in soil carbon (
1
C
s
, top row), net primary productivity (
1
NPP, middle row), and soil carbon
turnover time (
1τ
s
, bottom row) 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
).
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3785
Table A1.
Table presenting the absolute (Pg C) and relative (%) changes in 21st century soil carbon for each CMIP5 model and the ensemble
mean
±
standard deviation, for each future RCP scenario.
Earth system model
Absolute
1
C
s
(Pg C)
Relative
1
C
s
(%)
RCP2.6
RCP4.5
RCP8.5
RCP2.6
RCP4.5
RCP8.5
BNU-ESM
81.4
99.7
100
11.6
14.2
14.3
CanESM2
−
25.4
−
32.7
−
53.5
−
1.65
−
2.12
−
3.47
GFDL-ESM2G
19.9
47.9
0.278
1.40
3.37
0.020
GISS-E2-R
−
43.1
−
122
−
146
−
1.92
−
5.43
−
6.50
HadGEM2-ES
154
174
258
13.9
15.6
23.2
IPSL-CM5A-LR
42.5
57.1
28.4
3.14
4.22
2.10
MIROC-ESM
−
39.9
−
1.53
−
80.0
−
1.55
−
0.059
−
3.11
MPI-ESM-LR
211
277
219
6.94
9.09
7.19
NorESM1-M
−
3.94
−
7.60
−
17.7
−
0.723
−
1.40
−
3.26
Ensemble mean
44.1
54.7
34.3
3.45
4.17
3.38
±
standard deviation
±
84.2
±
111
±
127
±
5.66
±
6.97
±
9.24
Table A2.
Table presenting the changes in 21st century NPP and
τ
s
for each CMIP5 model and the ensemble mean
±
standard deviation, for
each future RCP scenario.
Earth system model
1
NPP (Pg C)
1τ
s
(years)
RCP2.6
RCP4.5
RCP8.5
RCP2.6
RCP4.5
RCP8.5
BNU-ESM
4.52
11.7
21.9
−
0.165
−
1.36
−
3.42
CanESM2
6.94
8.73
20.4
−
2.95
−
2.71
−
6.23
GFDL-ESM2G
9.47
16.4
40.13
−
1.53
−
3.31
−
6.38
GISS-E2-R
11.5
13.6
51.4
−
2.26
−
3.88
−
8.03
HadGEM2-ES
10.4
18.2
45.5
−
0.40
−
1.24
−
3.66
IPSL-CM5A-LR
10.4
16.9
37.0
−
1.50
−
2.91
−
5.31
MIROC-ESM
0.350
9.98
14.4
−
2.66
−
8.32
−
12.4
MPI-ESM-LR
–
26.6
43.0
−
0.280
−
5.00
−
8.17
NorESM1-M
−
0.388
2.25
6.94
−
0.151
−
0.645
−
1.55
Ensemble mean
5.32
12.4
28.1
−
1.26
−
3.26
−
6.13
±
standard deviation
±
4.74
±
7.42
±
16.8
±
1.13
±
2.21
±
3.03
https://doi.org/10.5194/bg-20-3767-2023
Biogeosciences, 20, 3767–3790, 2023
Page 20
3786
R. M. Varney et al.: Simulated responses of soil carbon to climate change in CMIP6 ESMs
Code availability.
Code is available on GitHub (https://github.com/
rebeccamayvarney/CMIP6_dCs, last access: 28 July 2023).
Data availability.
The CMIP data analysed during this study are
available online: CMIP6 (https://esgf-node.llnl.gov/search/cmip6/,
last access: 8 April 2022) and CMIP5 (https://esgf-node.llnl.gov/
search/cmip5/, last access: 12 April 2022).
Author contributions.
RMV, SEC, and PMC outlined the study.
RMV completed the analysis and produced the figures. All the co-
authors provided 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 in published maps and
institutional affiliations.
Acknowledgements.
This research has been supported by the Eu-
ropean Research Council’s Emergent Constraints on Climate–
Land feedbacks in the Earth System project (ECCLES; grant
no. 742472) and Climate–Carbon Interactions in the Current Cen-
tury project (4C; grant no. 821003) (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). Simon Jones was supported by the Brazilian
ecosystem resilience in net-generation vegetation dynamics scheme
(CSSP Brazil; project no. P109647). Andy J. Wiltshire and Eleanor
J. Burke were supported by the Joint UK BEIS/Defra Met Office
Hadley Centre Climate Programme (grant no. GA01101). We thank
the World Climate Research Programme’s Working Group on Cou-
pled 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 H2020 European Research Council (grant
nos. 821003 and 742472).
Review statement.
This paper was edited by Martin De Kauwe and
reviewed by three anonymous referees.
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