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Causes of variation in soil carbon simulations from CMIP5 Earth
system models and comparison with observations
K. E. O. Todd-Brown
1
, J. T. Randerson
1
, W. M. Post
2
, F. M. Hoffman
1,6
, C. Tarnocai
4
, E. A. G. Schuur
5
, and
S. D. Allison
1,3
1
Department of Earth System Science, University of California, Irvine, CA 92697, USA
2
Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831–6335, USA
3
Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92697, USA
4
Research Branch, Agriculture and Agri-Food Canada, Ottawa, Ontario, Canada K1A 0C6, Canada
5
Department of Biology, University of Florida, Gainesville, FL 32611, USA
6
Computer Science & Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831–6335, USA
Correspondence to: K. E. O. Todd-Brown (ktoddbro@uci.edu)
Received: 28 September 2012 – Published in Biogeosciences Discuss.: 18 October 2012
Revised: 7 February 2013 – Accepted: 13 February 2013 – Published: 13 March 2013
Abstract. Stocks of soil organic carbon represent a large
component of the carbon cycle that may participate in cli-
mate change feedbacks, particularly on decadal and centen-
nial timescales. For Earth system models (ESMs), the abil-
ity to accurately represent the global distribution of exist-
ing soil carbon stocks is a prerequisite for accurately pre-
dicting future carbon–climate feedbacks. We compared soil
carbon simulations from 11 model centers to empirical data
from the Harmonized World Soil Database (HWSD) and
the Northern Circumpolar Soil Carbon Database (NCSCD).
Model estimates of global soil carbon stocks ranged from
510 to 3040 Pg C, compared to an estimate of 1260 Pg C
(with a 95 % confidence interval of 890–1660 Pg C) from the
HWSD. Model simulations for the high northern latitudes
fell between 60 and 820 Pg C, compared to 500 Pg C (with
a 95 % confidence interval of 380–620 Pg C) for the NC-
SCD and 290 Pg C for the HWSD. Global soil carbon varied
5.9 fold across models in response to a 2.6-fold variation in
global net primary productivity (NPP) and a 3.6-fold varia-
tion in global soil carbon turnover times. Model–data agree-
ment was moderate at the biome level (
R
2
values ranged
from 0.38 to 0.97 with a mean of 0.75); however, the spa-
tial distribution of soil carbon simulated by the ESMs at the
1
◦
scale was not well correlated with the HWSD (Pearson
correlation coefficients less than 0.4 and root mean square er-
rors from 9.4 to 20.8 kg C m
−
2
)
. In northern latitudes where
the two data sets overlapped, agreement between the HWSD
and the NCSCD was poor (Pearson correlation coefficient
0.33), indicating uncertainty in empirical estimates of soil
carbon. We found that a reduced complexity model depen-
dent on NPP and soil temperature explained much of the 1
◦
spatial variation in soil carbon within most ESMs (
R
2
values
between 0.62 and 0.93 for 9 of 11 model centers). However,
the same reduced complexity model only explained 10 % of
the spatial variation in HWSD soil carbon when driven by
observations of NPP and temperature, implying that other
drivers or processes may be more important in explaining
observed soil carbon distributions. The reduced complexity
model also showed that differences in simulated soil car-
bon across ESMs were driven by differences in simulated
NPP and the parameterization of soil heterotrophic respira-
tion (inter-model
R
2
=
0.93), not by structural differences
between the models. Overall, our results suggest that despite
fair global-scale agreement with observational data and mod-
erate agreement at the biome scale, most ESMs cannot re-
produce grid-scale variation in soil carbon and may be miss-
ing key processes. Future work should focus on improving
the simulation of driving variables for soil carbon stocks and
modifying model structures to include additional processes.
Published by Copernicus Publications on behalf of the European Geosciences Union.
Page 2
1718
K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
1
Introduction
Soil organic carbon is the largest carbon pool in the ter-
restrial biosphere (Jobbagy and Jackson, 2000), and losses
of soil carbon due to climate change could contribute to
rising atmospheric CO
2
concentrations. Loss rates for soil
carbon through heterotrophic respiration depend on tem-
perature (Davidson and Janssens, 2006; Lloyd and Taylor,
1994), moisture (Orchard and Cook, 1983; Ryan and Law,
2005), and disturbance regimes such as land use change
(Post and Kwon, 2000) and fire (Harden et al., 2000). The
sensitivity of many of these drivers to climate change cre-
ates the potential for feedbacks that may accelerate or de-
celerate the buildup of greenhouse gases in the atmosphere
(Young and Steffen, 2009).
Although field studies and atmospheric–ocean carbon
measurements suggest that the terrestrial biosphere is cur-
rently a net sink for carbon dioxide (Houghton, 2007; Lund
et al., 2009; Le Qu´er´e et al., 2009), it is unclear if this sink
will persist as climate changes. Projections from recent Earth
system models (ESMs) suggest that the magnitude of the sink
is likely to decline in response to climate change over the
21st century (Cramer et al., 2001; Friedlingstein et al., 2006;
Koven et al., 2011). However, this response is highly uncer-
tain (Friedlingstein et al., 2006) and depends, in part, on the
strength of feedbacks from the nitrogen cycle (Thornton et
al., 2009) and the impact of drought stress on net primary
production (NPP), tree mortality, and fires (Goulden et al.,
2011; Huntingford et al., 2008; Phillips et al., 2009).
In northern ecosystems, permafrost soils contain large
stocks of carbon (Tarnocai et al., 2009) that are particularly
vulnerable to loss with climate change (Schuur et al., 2008;
Zimov et al., 2006), given the large temperature increases ex-
pected for the region (Giorgi, 2006). Models of permafrost
soil carbon have only recently been integrated into ESMs
(Koven et al., 2011) and further improvements in the rep-
resentation of thermokarst dynamics, peat accumulation, and
soil hydrology are needed to reduce uncertainties related to
climate–carbon feedbacks in northern biomes.
Because future climate projections depend on the carbon
cycle, ESMs must be capable of accurately representing the
pools and fluxes of carbon in the biosphere, particularly in
soils that store a large fraction of terrestrial organic carbon.
However, there have been few quantitative assessments of
ESM skill in predicting soil carbon stocks, contributing to
uncertainty in model simulations. To help reduce this uncer-
tainty, we analyzed simulated soil carbon from ESMs par-
ticipating in the 5th Climate Model Intercomparison Project
(CMIP5). If ESMs can accurately represent current soil car-
bon stocks, then we might have more confidence in their
ability to predict future stocks under a changing climate
(Luo et al., 2012).
Our analysis had three specific goals: (1) quantify the vari-
ation in ESM representation of soil carbon stocks, (2) under-
stand the driving factors regulating soil carbon distribution in
ESMs, and (3) compare the ESM soil carbon stocks to em-
pirical data. We conducted these analyses at grid (1
◦
×
1
◦
),
biome, and global scales across models to assess spatial
variability in the data and model simulations. We compared
model outputs to the global Harmonized World Soil Database
(FAO/IIASA/ISRIC/ISSCAS/JRC, 2012) and the Northern
Circumpolar Soil Carbon Database (Tarnocai et al., 2009).
We used an additional data set at high latitudes because these
areas contain a large percentage of global soil carbon but
are difficult to model and to measure empirically. We ex-
pected ESMs to represent high latitude soils poorly because
many of the terrestrial decomposition models were devel-
oped for mineral soils, as opposed to the organic soils found
in many high latitude ecosystems (Koven et al., 2011; Neff
and Hooper, 2002; Ping et al., 2008). More generally, we ex-
pected that the global distribution of soil carbon in the ESMs
would be primarily driven by NPP, soil temperature, and soil
moisture. We also anticipated that ESMs with more soil car-
bon pools would be capable of representing a wider range
of soil carbon dynamics, and thus would yield more accurate
simulations when compared to observations.
2
Materials and methods
We examined soil carbon stocks in 16 ESMs (Tables 1 and
S1 in Supplement) from the 5th Climate Model Intercom-
parison Project (CMIP5). The model simulations were com-
pared with the Harmonized World Soil Database (HWSD)
(FAO/IIASA/ISRIC/ISSCAS/JRC, 2012) and high latitude
soil carbon stocks from the Northern Circumpolar Soil Car-
bon Database (NCSCD) (Tarnocai et al., 2009). We analyzed
the underlying drivers of soil carbon variability with a set of
reduced complexity models.
2.1
Earth system models
ESMs from CMIP5 use common simulation and output pro-
tocols, enabling direct comparisons between models. One of
the goals of CMIP5 is to facilitate benchmarking of ESMs
through the historical simulation protocol, which has a pre-
scribed time series of atmospheric CO
2
mixing ratios and
land use change (Taylor et al., 2011). ESMs were selected
from the CMIP5 repository based on the availability of soil
carbon and other key output variables for the historical sim-
ulation, as well as consultation with modeling centers.
The model structure for soil carbon across ESMs was rel-
atively uniform (Table 1). The soil carbon sub-models in all
ESMs represented decomposition as a first-order decay pro-
cess involving 1–9 dead (soil or litter) carbon pools. The tem-
perature sensitivity of decomposition in most ESMs was de-
scribed by the
Q
10
or Arrhenius equations, which are func-
tionally similar (Davidson and Janssens, 2006; Lloyd and
Taylor, 1994). In the
Q
10
form of the temperature sensitiv-
ity function, the decomposition rate is modified as a function
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
1719
Table 1. Summary of soil carbon models including Earth system model names, history of model development, number of litter and soil pools,
temperature and moisture functions, and representation of nitrogen cycling.
Model name
Soil model history
Litter
Soil
Temperature
Moisture
Nitrogen
BCC-CSM1.1
AVIM2; Huang et al. (2007), Ji et al. (2008)
2
6
Hill
a
Hill
Yes
Wu et al. (2013)
CEVSA; Cao and Woodward (1998)
CENTURY; Parton et al. (1987, 1993)
CanESM2
CTEM1; Arora and Boer (2005),
1
b
1
b
Q
c
10
Hill
No
(CMIP5 output)
Arora (2003), Arora et al. (2011)
CCSM4
CLM4; Oleson et al. (2008)
3
3
Arrhenius
Increasing
Yes
Gent et al. (2011)
CN; Thornton et al.(2007)
Biome-BCG 4.1.2 Kimball et al. (1997),
Thornton and Rosenbloom (2005), Thornton (1998),
Thornton et al. (2002), Olson (1963),
Veen and Paul (1981), Veen et al. (1984)
GFDL-ESM2G
LM3 (LM3p7 cESM, M45)
–
2
Hill
Increasing
No
(CMIP5 output)
Shevliakova et al. (2009)
ED; Moorcroft et al. (2001),
Bolker et al. (1998)
CENTURY; Parton et al. (1987)
GISS-E2-H
NCAR-CSM1.4; Doney et al. (2006)
–
9
Increasing
Increasing
No
GISS-E2-R
NASA-CASA; Potter et al. (1993),
(N. Kiang,
Randerson et al. (1997)
personal communication, 2012)
HadGEM2-ES
Martin et al. (2011), Collins et al. (2011)
–
4
Q
10
Hill
No
HadGEM2-CC
TRIFFID; Cox (2001)
Jones et al. (2011)
INM-CM4
Volodin (2007)
–
1
b
Q
c
10
Hill
No
Volodin et al. (2010)
LSM; Bonan (1995, 1996), Bunnell et al. (1977)
IPSL-CM5A-LR
ORCHIDEE (http://orchidee.ipsl.jussieu.fr/)
3
4
Q
10
Increasing
No
IPSL-CM5B-LR
STOMATE; Krinner et al. (2005)
(http://icmc.ipsl.fr, 2012)
CENTURY; Parton et al. (1988)
MIROC-ESM
SEIB-DGVM; Sato et al. (2007)
–
2
Arrhenius
Increasing
No
MIROC-ESM-CHEM
Roth-C; Coleman and Jenkinson (1999)
Watanabe et al. (2011)
DEMETER-1; Foley (1995)
CENTURY; Parton et al. (1987, 1992)
MPI-ESM-LR
JSBACH; Raddatz et al. (2007)
1
1
Q
10
Increasing
No
(CMIP5 output)
BETHY; Knorr (2000)
CENTURY; Parton et al. (1993)
NorESM1-ME
CLM4; Oleson et al. (2008)
3
3
Arrhenius
Increasing
Yes
NorESM1-M
CN; Thornton et al. (2007)
Tjiputra et al. (2012)
Biome-BCG 4.1.2; Kimball et al. (1997),
Thornton and Rosenbloom (2005),
Thornton (1998), Thornton et al. (2002),
Olson (1963), Veen and Paul (1981),
Veen et al. (1984)
a
We define a hill function as a function that increases to a maximum and then decreases.
b
Turnover parameterization dependent on biome or vegetation type.
c
Q
10
value
dependent on temperature.
of temperature (
T
) relative to a baseline (
T
0
)
, such that
f (T )
=
Q
(T
−
T
0
)/
10
10
. In this equation the
Q
10
value is often
set to between 1.5 and 2.5 based on estimates inferred from
ecosystem flux measurements (Mahecha et al., 2010; Raich
and Schlesinger, 1992) or the annual cycle of atmospheric
CO
2
(Kaminski et al., 2002; Randerson et al., 2002). In some
of the models, the temperature sensitivity of decomposition
follows neither a
Q
10
nor Arrhenius relationship. For ex-
ample, in BCC-CSM1.1 and GFDL-ESM2G, decomposition
rate increases up to some optimal temperature and then de-
creases (Ji et al., 2008; Parton et al., 1987; Shevliakova et
al., 2009). For the GISS-E2 model, the soil respiration re-
sponse to temperature is a linear fit to data from Del Grosso
et al. (2005) up to 30
◦
C, with a plateau above 30
◦
C. In all
of the models, decomposition either increases monotonically
with increasing soil moisture or increases up to some opti-
mum moisture level and then decreases. Three ESMs include
nitrogen interactions with soil carbon: CCSM4, NorESM1,
and BCC-CSM1.1.
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
We downloaded soil organic carbon, litter carbon, annual
NPP, 2 m air temperature, soil temperature, and total soil wa-
ter from the historical simulation, where available, for each
ESM (cSoil, cLitter, npp, tas, tsl, and mrso, respectively,
from the CMIP5 variable list). The monthly means for all
variables from 1995–2005 were averaged for each grid cell
to generate an overall mean for comparison to the HWSD and
to use as drivers for our reduced complexity models (see be-
low). We combined litter and soil carbon for our analysis and
refer to the sum as soil carbon. Coarse woody debris (cCwd
from the variable list) was not included in the sum since there
is no respiration from this pool in the two models that report
it (CCSM4 and NorESM1). Global turnover times for soil
carbon were calculated by dividing total soil carbon by to-
tal terrestrial NPP from each ESM. INM-CM4 did not report
NPP directly, so we derived NPP from gross primary produc-
tion and autotrophic respiration (gpp and ra from the variable
list). Soil temperatures were reported for each soil layer, but
only the top 10 cm mean was used in this analysis. Land area
was calculated from the grid area modified by the land cover
for each model (areacella and sftlf from the variable list, re-
spectively). All ensemble members were averaged for each
model; however, not all variables were available for each en-
semble member. For example, GISS-E2-R reported cSoil but
not tsl for ensemble member r1i1p1 at the time of download.
We performed a hierarchical cluster analysis and found
that ESMs from the same climate center generated very sim-
ilar distributions of soil carbon for 1995–2005 (see Supple-
ment Fig. S1). Clusters were constructed using complete
linkage of the Euclidian distances between the global 1
◦
-
gridded soil carbon distributions for each model. Models
from the same climate center always showed more than 90 %
relative similarity and included the following pairs: GISS-
E2 H and R, HadGEM2 ES and CC, IPSL-CM5 (LR) A
and B, MIROC-ESM and MIROC-ESM-CHEM, and finally
NorESM1 ME and M. As a result, these model pairs were
averaged. We were left with 11 independent simulations, one
representing each modeling center, that were evaluated using
the approaches described below.
ESMs do not report the depth of carbon in the soil pro-
file to CMIP5, making direct comparison with empirical es-
timates of soil carbon difficult. Although many soil models
were originally constructed to represent C dynamics at an ap-
proximate depth range of 0 to 20 cm (e.g., Kelly et al., 1997),
we assumed that all simulated soil carbon was contained
within the top 1 m to simplify comparison with data sets.
We recommend that future model intercomparison projects
request soil carbon output from model simulations with spe-
cific depth ranges (for example, soil carbon above 1 m and
below 1 m) to allow for more accurate and direct comparison
to survey data.
Fig. 1. Carbon density [kg m
−
2
] in the top 1 m of soil from the
Northern Circumpolar Soil Carbon Database (NCSCD) (Tarnocai
et al., 2009) and Harmonized World Soil Database (HWSD)
(FAO/IIASA/ISRIC/ISSCAS/JRC, 2012).
2.2
Data sets
2.2.1
Soil carbon
The HWSD provided empirical estimates of global soil
carbon stocks to validate ESM simulations. The HWSD
is a product of the Food and Agriculture Organization of
the United Nations and the Land Use Change and Agri-
culture Program of the International Institute for Applied
Systems Analysis. The HWSD aggregates data from the
European Soil Database (ESDB, 2004), the Soil Map of
China (Shi et al., 2004), regional soil and terrain databases
(Sombroek, 1984), and the FAO-UNESCO Soil Map of
the World (FAO/UNESCO, 1981). Soil carbon stocks were
calculated from bulk densities and organic carbon con-
centrations given in the HWSD for the top 1 m of soil
at a 0.5
◦
×
0.5
◦
resolution (Fig. 1). Bulk density esti-
mates in the HWSD were derived from soil texture; how-
ever, this approach is not appropriate for high carbon
soils (FAO/IIASA/ISRIC/ISSCAS/JRC, 2012; Saxton et al.,
1986). Therefore, we replaced Histosol and Andisol bulk
densities with values from the World Inventory of Soil Emis-
sion Potentials (Batjes, 1996).
Because high latitude soils contain a large fraction of
global soil carbon, we also validated ESM simulations of soil
carbon in high latitudes with the NCSCD, which is an inde-
pendent survey of soil carbon (Tarnocai et al., 2009). The
NCSCD covers 18.8
×
10
6
km
2
, including areas with differ-
ent geological histories and stages of soil development. We
used the 1
◦
×
1
◦
soil carbon data product for the first meter
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
1721
of soil (Fig. 1). The spatial and soil data used to develop this
database were collected during the last 60 yr and originated
from a variety of sources.
Quantitative uncertainty analyses for the HWSD and NC-
SCD have not been performed and would be a challenge to
construct because of the diverse data sources involved. How-
ever, some estimate of uncertainty was essential to enable
quantitative comparisons with the CMIP5 models. To gen-
erate such a range for total soil carbon from both data sets,
we constructed preliminary 95 % confidence intervals (CI
95
)
using a qualitative approach. These estimates must be inter-
preted with caution because they are not based on formal er-
ror propagation methods. Furthermore, these estimates only
apply to database totals, and uncertainties for individual grid
cells are likely to be larger.
For the HWSD, the major sources of error were related
to analytical measurement of soil carbon, variation in car-
bon content within a soil type, and mapping of soil types.
Analytical measurements of soil carbon concentrations are
generally precise, but measurements of soil bulk density are
more uncertain and may contribute to CI
95
values that are
±
15 % of the mean carbon content for a given soil profile.
Soil types in the HWSD are defined based on Food and Agri-
culture Organization soil taxonomic units that are assumed
to experience similar histories of soil forming factors such as
climate, vegetation, disturbance, topography, and parent ma-
terial. Batjes (1997) reported quartiles of soil carbon content
for 23 soil taxonomic units based on 18 to 1270 soil profiles
per unit. These quartiles suggest that soil carbon content is
approximately log-normally distributed, allowing for calcu-
lation of CI
95
values for each soil unit following log transfor-
mation. When back transformed, CI
95
ranged from 6 to 33 %
below the median to 6 to 48 % above the median, with an av-
erage CI
95
of 14 % below to 17 % above the median across
all 23 units.
Another major source of HWSD uncertainty was related
to the mapping of soil units and scaling of soil maps to
0.5
◦
. Soil taxonomic units and associated carbon contents
were spatially extrapolated using expert knowledge informed
by topography, geology, and vegetation (usually based on
aerial photography). Original soil maps were scaled up in
the HWSD by classifying each 0.5
◦
grid cell according to
its dominant soil unit. We assumed that the uncertainty as-
sociated with mapping and scaling was similar in magnitude
to measurement error and spatial variation, with a CI
95
of
approximately
±
15 % of the mean. To estimate an overall
CI
95
for the HWSD, we assumed that variation in soil carbon
content within soil taxonomic units already included analyt-
ical error, and that median carbon content within a soil unit
is extrapolated by multiplying by the area of the unit. Thus
the CI
95
values representing variation in soil carbon content
and mapping uncertainty were summed to yield an overall
CI
95
of 29 % below the mean to 32 % above the mean, or a
range of 890 to 1660 Pg C with a mean of 1260 Pg C. This es-
timate is broadly consistent with other empirical estimates of
global soil carbon (Eswaran et al., 1993; Jobbagy and Jack-
son, 2000; Sombroek et al., 1993).
For the NCSCD, the uncertainties varied by geographic re-
gion. The North American portion of the data set was based
on analysis of 1169 pedons producing a medium to high con-
fidence rating (66–80 %). Thus we estimated the CI
95
for the
North American portion of the NCSCD to be 165
±
17 Pg C,
corresponding to
±
10 % of the mean. In Eurasia, soil car-
bon estimates were based on fewer pedons (591) plus 90
peat cores, producing a low to medium confidence rating
(33–66 %). Therefore we estimated the CI
95
for the Eurasian
region to be 331
±
99 Pg C, or
±
30 % of the mean. Car-
bon in Yedoma deposits and river deltas was estimated inde-
pendently using surveyed depth information where available.
This deeper soil carbon had the lowest confidence rating but
contributed only
∼
1 % or 5 Pg of the database total; there-
fore we allowed for a CI
95
of 5
±
5 Pg C on this estimate.
Together, these uncertainty estimates yielded an overall CI
95
of roughly 500
±
120 Pg C for the first meter of soil.
2.2.2
Net primary productivity and temperature
To assess model skill in simulating key driving variables that
could affect soil carbon stocks, we compared ESM outputs
to temperature data from the Climate Research Unit (CRU)
and to NPP data from a literature synthesis and from the
Moderate Resolution Imaging Spectrometer (MODIS). The
CRU and MODIS data also were used in parameter estima-
tion for the reduced complexity models (Eqs. 1–2) to explain
the spatial variation in observed global soil carbon with ob-
served temperature and NPP. We used a 0.5
◦
×
0.5
◦
gridded
air temperature data set from the CRU, specifically the 1995–
2005 mean of the tmp variable from CRU TS 3.10 (Jones
and Harris, 2008). For NPP, we used the 0.008
◦
×
0.008
◦
gridded MODIS product MOD17A3 from 2000–2011 (Zhao
and Running, 2010). We also compared ESM-simulated NPP
to Ito’s (2011) value of 54
±
11 Pg C yr
−
1
(mean
±
stan-
dard deviation). This estimate was based on empirical models
that used environmental parameters to extrapolate field mea-
surements of NPP to the global scale. We considered ESM-
simulated NPP values to be consistent with empirical data if
they fell within 2 standard deviations of Ito’s (2011) estimate.
2.2.3
Biome map
To evaluate ESM soil carbon across biomes, we aggre-
gated HWSD estimates and model simulations of soil carbon
within biomes. The biome map was based on the MODIS
land cover product MCD12C1 (Friedl et al., 2010; NASA LP
DAAC, 2008) (Fig. S2). We assigned one of 16 land cover
types to each 1
◦
×
1
◦
grid cell by taking the most common
land cover from the original underlying 0.05
◦
×
0.05
◦
data.
Each 1
◦
×
1
◦
grid cell was assigned to one of 9 biomes: tun-
dra, boreal forest, tropical rainforest, temperate forest, desert
and shrubland, grasslands and savannas, cropland and urban,
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
Table 2. Soil carbon totals across all grid cells in each ESM, grid cells present in the HWSD and ESM, and grid cells present in the NCSCD
and ESM. Database totals include 95 % confidence intervals based on qualitative uncertainty analysis, shown in brackets. Values are rounded
to the nearest 10 Pg C.
Soil carbon [Pg C]
Original
Number of
Ensembles
HWSD
NCSCD
Database or
grid size
model
per
and ESM
and ESM
model name
◦
lat.
×
◦
long.
versions
version
Global total
shared
shared
HWSD
0.5
×
0.5
–
–
1260
1260
290
[890, 1660]
NCSCD
1
×
1
–
–
500
480
480
[380, 620]
CCSM4
0.94
×
1.25
1
6
510
510
60
NorESM1
1.89
×
2.50
2
3, 1
550
530
60
BCC-CSM1.1
2.81
×
2.81
1
3
1050
990
240
HadGEM2
1.25
×
1.88
2
1, 2
1120
1090
200
IPSL-CM5
1.89
×
3.75
2
5, 1
1310
1250
390
GFDL-ESM2G
2.01
×
2.50
1
1
1410
1360
690
CanESM2
2.79
×
2.81
1
5
1540
1460
370
INM-CM4
1.50
×
2.00
1
1
1680
1630
280
GISS-E2
2.00
×
2.50
2
15, 16
1900
1820
520
MIROC-ESM
2.79
×
2.81
2
3, 1
2570
2490
810
MPI-ESM-LR
1.86
×
1.88
1
3
3040
2930
340
snow and ice, or permanent wetland. Details for the biome
construction can be found in Fig. S2 in the Supplement.
2.3
Regridding approach
All model outputs and data sets were regridded to 1
◦
×
1
◦
for
biome- and grid-scale comparisons. Our regridding approach
assumed conservation of mass and that a latitudinal degree is
proportional to distance for close grid cells. Regridding the
outputs to 1
◦
×
1
◦
downscaled the models while upscaling
the data (Table 2).
2.4
Assessing driving variables for soil C stocks
We developed several reduced complexity models to evalu-
ate the drivers of simulated soil carbon variability and facil-
itate comparisons between ESMs. These reduced complex-
ity models consisted of a single pool of soil carbon at each
grid cell driven by locally varying NPP, soil temperature, and
soil moisture (Figs. S3, S4, S5 in Supplement) and globally
uniform parameters including a decomposition rate constant,
Q
10
value, and moisture coefficient. By applying the same
simple model, we were able to compare parameters across
ESMs and assess which variables had the strongest control
over soil carbon. Driving variables for the reduced complex-
ity models were taken from ESM annual means of NPP, soil
temperature (
T
, top 10 cm mean), and total soil water content
(
W
) over the period 1995–2005.
Our reduced complexity models assumed that the soil car-
bon pool (
C
) in grid cell
i
was at steady state, such that NPP
inputs equaled outputs from heterotrophic respiration (
R)
:
0
=
d
C
i
d
t
=
NPP
i
−
R
i
.
Carbon pools were not expected to be exactly at
steady state for 1995–2005, and mean grid differences be-
tween NPP and
R
across the ESMs ranged from 0.01 to
0.12 kg m
−
2
yr
−
1
, or between 1 % and 20 % of the mean grid
NPP for this period. Thus the ESMs were close to steady
state, and we assumed steady state to simplify our analysis.
For the simplest reduced complexity model, we assumed that
soil heterotrophic respiration was directly proportional to the
soil carbon pool with a spatially uniform decomposition rate
constant
k
(Olson, 1963; Parton et al., 1987):
R
i
=
kC
i
.
Combining the two above equations yielded the simplest
reduced complexity model, Eq. (1), in which soil carbon was
proportional to NPP and inversely proportional to a global
decomposition rate (
k)
:
C
i
=
NPP
i
k
.
(1)
We formulated a second reduced complexity model, Eq.
2, in which soil respiration in each grid cell also depended
on soil temperature (
T )
according to a
Q
10
function with a
baseline temperature of 15
◦
C (Lloyd and Taylor, 1994):
C
i
=
NPP
i
kQ
(T
i
−
15
)/
10
10
.
(2)
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
1723
A third reduced complexity model, Eq. (3), included a mois-
ture modifier that increased with total soil water content (
W
i
)
normalized to maximal soil water content for each ESM (
W
x
)
according to an exponential function, where
b
was a positive
scaling exponent:
C
i
=
NPP
i
kQ
(T
i
−
15
)/
10
10
W
i
W
x
b
.
(3)
The parameters
k, Q
10
, and
b
in each reduced complex-
ity model were optimized using ESM soil carbon and driv-
ing variables across all grid cells. We used a constrained
Broyden–Fletcher–Goldfarb–Shanno optimization algorithm
(Byrd et al., 1995), a quasi-Newtonian method, as imple-
mented in R 2.13.1 (R Development Core Team, 2012). This
algorithm was selected for parameter fitting because of its ro-
bust convergence and short run time. We ran the optimization
with the following constraints:
k
∈
10
−
4
,
10
, Q
10
∈
(
1
,
4
)
,
and
b
∈
(
0
,
3
)
. The initial parameter estimates were
k
=
0
.
1,
Q
10
=
1, and
b
=
0. We used the root mean square error
(RMSE) as the measure function. The optimization was per-
formed only on grid cells with non-zero soil carbon values.
We conducted an additional analysis to assess the causes
of variation in simulated soil carbon across ESMs (Eqs. 4–
7). For this analysis, we used a modified version of Eq. (2) to
predict total global soil carbon (
C)
for each ESM:
C
=
X
i
NPP
i
kQ
(T
i
−
15
)/
10
10
,
(4)
where the
Q
10
and
k
parameters were derived from fitting
Eq. (2) to the spatial distribution of soil carbon (at 1
◦
reso-
lution) from each ESM as described above. Grid-scale NPP
outputs (NPP
i
)
and soil temperatures (
T
i
)
from each ESM
were used as drivers in Eq. (4) to calculate soil carbon in
each grid cell
i
. Soil carbon was then summed across all
grid cells in each ESM to calculate the global soil carbon
pool (
C
). Thus Eq. (4) represents the contribution of both
model parameterization (
Q
10
and
k
) and soil carbon drivers
(NPP
i
and
T
i
)
to the global soil carbon pool. To isolate the
effect of ESM parameterization on
C
, we substituted multi-
model mean values for NPP (NPP
i
)
and temperature (
¯
T
i
)
into
Eq. (4) for each grid cell
i
:
C
=
X
i
NPP
i
kQ
(
¯
T
i
−
15
)/
10
10
.
(5)
To isolate the effect of ESM driving variables on
C
, we
substituted multi-model mean values for
Q
10
(
¯
Q
10
)
and
k
(
¯
k)
into Eq. (4):
C
=
X
i
NPP
i
¯
k
¯
Q
(T
i
−
15
)/
10
10
.
(6)
Finally, we substituted only the multi-model mean tempera-
ture into Eq. (4) to isolate the effect of NPP on inter-model
variation in
C
:
C
=
X
i
NPP
i
kQ
(
¯
T
i
−
15
)/
10
10
.
(7)
Using regression analysis, we compared the predicted
C
from Eqs. (4)–(7) to the totals simulated by the ESMs.
These regressions measure the contribution of parameteriza-
tion (Eq. 5) versus driving variables (Eqs. 6 and 7) to varia-
tion in soil carbon totals across ESMs. We excluded GISS-E2
from this inter-model analysis because Eq. (2) could not be
fit to this model, and therefore
Q
10
and
k
were not available.
2.5
Statistical analyses
ESM simulations were compared to data sets using Pear-
son correlation coefficients, RMSE, and Taylor scores in
R 2.13.1 (R Development Core Team, 2012). The Tay-
lor score (
T
S
)
combines the Pearson correlation coefficient
(
r)
and standard deviation (
σ )
of the model results (
m
)
compared to the data (
d
):
T
S
(d, m)
=
4 [1
+
r (d, m)
]
h
σ ( m)
σ (d)
+
σ (d)
σ ( m)
i
2
[1
+
r
max
]
,
where
r
max
is the maximum correlation attainable, assumed
to be 1 in this case (Taylor, 2001). Biome-aggregated totals
were compared to observations using linear regression.
3
Results
3.1
Global soil carbon stocks and turnover times
The mean (
±
SD) global soil carbon reported across all ESMs
was 1520
±
770 Pg, whereas the global soil carbon in the
HWSD was 1260 Pg with a CI
95
of 890 to 1660 Pg (Table 2,
Fig. 2). CCSM4 reported the lowest total at 510 Pg C and
MPI-ESM-LR the highest at 3040 Pg C. Examining only the
area shared by all ESMs and the HWSD reduces the global
carbon totals but does not substantially change the rank or-
der of the models (Table 2). CCSM4 and NorESM1 under-
estimated global soil carbon stocks by about 50 %, whereas
GISS-E2, MIROC-ESM, and MPI-ESM-LR overestimated
global soil carbon stocks anywhere from 50 % to 140 %. The
other models predicted global soil carbon totals that were
within 35 % of the HWSD global mean and fell within its
preliminary CI
95
.
Soil carbon in the high northern latitudes (as defined by
grid cells in the NCSCD) was underestimated by most ESMs
relative to the NCSCD (Table 2, Fig. S6). In addition, the
rank order of ESM soil carbon totals in this region differed
from the rank order based on global totals. CCSM4 and
NorESM1 simulated just over 10 % of the total soil carbon
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
Fig. 2. Global soil carbon (top), net primary production (middle), and soil carbon turnover times (bottom) for observations and ESMs.
Turnover times were calculated as HWSD carbon divided by MODIS NPP for the observations, and simulated global soil carbon divided by
simulated global NPP for the ESMs. The gray hashed area on the top panel represents the 95 % confidence interval for global soil carbon
in the HWSD based on a qualitative uncertainty analysis (see text). The hashed area on the middle panel represents
±
2 standard deviations
around the mean global NPP estimate from Ito (2011) based on empirical models. The hashed area on the bottom panel indicates the range
of turnover times for global soil carbon found in the literature (Amundson, 2001; Raich and Schlesinger, 1992). For soil carbon and NPP,
each global estimate is separated into individual biome components according to the legend shown in the top panel.
observed in the NCSCD. HadGEM2, BCC-CSM1.1, INM-
CM4, MPI-ESM, and CanESM2 also simulated soil carbon
totals below the preliminary CI
95
for the NCSCD. In con-
trast, GFDL-ESM2G and MIROC-ESM overestimated high
latitude soil carbon stocks by 45–60 %. Only IPSL-CM5 and
GISS-E2 soil carbon fell within the CI
95
for the NCSCD.
Variation in global soil carbon stocks simulated by ESMs
could be driven by variation in modeled NPP, and we found
that global terrestrial NPP varied by a factor of 2.6 across the
models (Fig. 2). CCSM4, BCC-CSM1.1, CanESM2, INM-
CM4, GISS-E2, and MIROC-ESM all predicted global NPP
values within 2 standard deviations of the Ito (2011) estimate
of 54 Pg C yr
−
1
, ranging from 46 to 73 Pg C yr
−
1
, whereas
the remaining 5 models fell outside this range. NPP from
MODIS was similar to Ito (2011) at 52 Pg C yr
−
1
. At high
northern latitudes, NPP estimates from the ESMs were more
variable (1.7 to 10.1 Pg C yr
−
1
)
, compared to a MODIS esti-
mate of 4.7 Pg C yr
−
1
(Fig. S6 in Supplement).
Turnover times for global soil carbon from the ESMs var-
ied by a factor of 3.6, between 10.8 and 39.3 yr, using global
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
1725
Table 3. Goodness-of-fit measures by grid cell for each ESM including soil carbon versus the HWSD, soil carbon versus NCSCD, soil carbon
versus HWSD without NCSCD grid cells (HWSD
−
NCSCD), NPP versus MODIS NPP, and land 2 m air surface temperature versus CRU
2 m air temperature.
T
S
=
Taylor score;
r
=
Pearson correlation coefficient; RMSE
=
root mean square error. RMSE has units of kg C m
−
2
for the soil carbon comparisons, kg C m
−
2
yr
−
1
for NPP, and
◦
C for temperature.
HWSD
NCSCD
HWSD
−
NCSCD
MODIS NPP
CRU temperature
T
s
r
RMSE
T
s
r
RMSE
T
s
r
RMSE
T
s
r
RMSE
T
s
r
RMSE
HWSD
NA
NA
NA
0.60
0.33
20.0
NA
NA
NA
NA
NA
NA
NA
NA
NA
CCSM4
0.21
0.18
11.3
0.05
−
0.04
27.7
0.29
0.26
9.1
0.87
0.75
0.25
0.98
0.96
3.8
NorESM1
0.24
0.17
11.2
0.05
−
0.07
27.7
0.33
0.25
9.1
0.81
0.71
0.28
0.97
0.96
4.3
BCC-CSM1.1
0.51
0.33
9.4
0.21
0.03
22.2
0.53
0.34
8.0
0.85
0.71
0.25
0.97
0.95
4.4
HadGEM2
0.56
0.31
9.7
0.18
−
0.03
23.5
0.63
0.31
8.6
0.71
0.73
0.35
0.97
0.95
4.5
IPSL-CM5
0.68
0.38
9.7
0.33
0.19
18.1
0.67
0.39
8.1
0.77
0.64
0.34
0.97
0.95
4.7
GFDL-ESM2G
0.50
0.26
16.0
0.51
0.04
23.6
0.61
0.22
10.1
0.79
0.64
0.32
0.97
0.95
4.4
CanESM2
0.62
0.25
12.3
0.50
0.03
22.6
0.62
0.25
10.2
0.75
0.56
0.34
0.97
0.94
4.6
INM-CM4
0.65
0.29
11.3
0.34
−
0.10
23.4
0.66
0.36
10.3
0.81
0.74
0.28
0.96
0.95
4.9
GISS-E2
0.34
0.06
20.7
0.46
−
0.07
25.0
0.29
0.01
19.4
0.72
0.48
0.36
0.97
0.93
4.8
MIROC-ESM
0.48
0.39
19.8
0.52
0.06
27.7
0.54
0.37
14.3
0.77
0.55
0.30
0.95
0.93
5.1
MPI-ESM-LR
0.41
0.06
20.7
0.44
−
0.03
23.2
0.34
0.10
22.0
0.70
0.67
0.39
0.97
0.94
4.5
stocks and NPP estimates from each model (Fig. 2). Using
MODIS NPP, we calculated a turnover time of 24 yr for soil
carbon in the HWSD. This estimate is consistent with the
range of 18 to 32 yr reported in other studies (Amundson,
2001; Raich and Schlesinger, 1992). However, CanESM2
and INM-CM4 were the only two ESMs with turnover times
that also fell within this range (Fig. 2). At high northern lat-
itudes, 5 of the 11 models had turnover times that were con-
siderably lower than the observations, whereas only 2 of the
models had turnover times exceeding observational estimates
(Fig. S6 see Supplement). Turnover times for high northern
latitudes were 101.2 yr for the NCSCD and 60.8 yr for the
HWSD.
3.2
Spatial distribution of soil carbon
The spatial distribution of soil carbon stocks varied widely
among the ESMs (Fig. 3). CCSM4 and NorESM1 had the
lowest overall soil carbon densities, but showed relatively
high densities in northern South America, central Africa,
eastern Asia, and eastern North America. HadGEM2, BCC-
CSM1.1, and INM-CM4 showed a broader range of soil car-
bon densities with high densities in North America, western
South America, central Africa, Southeast Asia, and north-
central Eurasia. HadGEM2 also showed elevated soil carbon
in southeastern South America. CanESM2 predicted high
soil carbon in northeastern North America, northern Europe,
northeastern Asia, central Africa, and eastern South America.
GFDL-ESM2G and MIROC-ESM showed uniformly high
carbon densities across all high northern latitudes and around
the Tibetan Plateau. GISS-E2 predicted a region of high soil
carbon across the northern latitudes of North America and
Europe, as well as another area of high soil carbon from
northeastern to southwestern Asia. MPI-ESM-LR showed
an inverse pattern compared with the other ESMs; soil car-
bon peaked in the mid-latitudes across Asia, western North
America, eastern Africa, southern South America, and south-
ern coastal Australia.
There was generally poor agreement between the ESMs
and the HWSD soil carbon distribution at the 1
◦
scale (Ta-
ble 3). Compared to the HWSD, ESMs had Pearson correla-
tion coefficients between 0.06 and 0.39, RMSE between 9.4
and 20.7 kg C m
−
2
, and Taylor scores ranging from 0.21 to
0.68. Omitting the high latitude portion of the HWSD that
overlapped with the NCSCD modestly improved these per-
formance metrics for most but not all ESMs (Table 3). Model
agreement with NCSCD soil carbon was poor with Pearson
correlation coefficients between
−
0.10 and 0.19, RMSE be-
tween 18.0 and 27.7 kg C m
−
2
, and Taylor scores between
0.05 and 0.52. Agreement between the HWSD and NCSCD
also was also low in the areas where the two data sets over-
lapped (Pearson correlation coefficient of 0.33, RMSE of
20.0 kg C m
−
2
, and Taylor score of 0.60), although better
than the agreement between any individual ESM and the NC-
SCD.
ESM agreement with the HWSD generally improved at
the biome level (Fig. 4). BCC-CSM1.1 and CanESM2 stood
out as being highly correlated with the HWSD (
R
2
>
0.90,
p <
0
.
01), though CanESM2 overestimated soil carbon in
boreal forests and grasslands and savanna. Biome simula-
tions from HadGEM2, IPSL-CM5, INM-CM4, and MIROC-
ESM also had relatively high levels of agreement with the
HWSD (0.90
> R
2
>
0.75,
p <
0
.
01), but most regression
slopes and intercepts diverged from 1.0 and zero, respec-
tively (Fig. 4). HadGEM2 overestimated soil carbon in grass-
lands and savanna. IPSL-CM5 generally overestimated tun-
dra but underestimated desert and shrublands. INM-CM4
overestimated grasslands and savanna, boreal forests, crop-
lands, and urban. MIROC-ESM overestimated all biomes ex-
cept wetlands. Both CCSM4 and NorESM1 were moderately
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
Table 4. Coefficients of determination (
R
2
)
and global-scale parameters (1
/ k
and
Q
10
)
from reduced complexity models of ESM soil
carbon distributions. Eq. (1): dependence on NPP; Eq. (2): dependence on NPP and soil temperature; Eq. (3): dependence on NPP, soil
temperature, and soil moisture. Parameters are shown from Eq. (2) with 1
/ k
analogous to turnover time. HWSD-MODIS-CRU represents
reduced complexity models based on observational data. The reduced complexity model for CanESM2 was the only one improved by
including soil moisture and had a turnover time (1
/ k
) of 8.20 yr,
Q
10
of 1.48, and moisture exponent of 0.46 based on Eq. (3). All
R
2
values
were statistically significant (
R
2
>
0
.
05,
p <
0
.
01
)
unless otherwise indicated (NS).
C
=
NPP/(
k Q
(T
−
15
)/
10
10
)
R
2
Eq. (2)
C
=
NPP/
k
C
=
NPP/
k
(T)
C
=
NPP/
k
(T, W)
1
/ k
Model name
Eq. (1)
Eq. (2)
Eq. (3)
(yr)
Q
10
HWSD-MODIS-CRU
NS
0.10
–
16.0
1.75
CCSM4
0.65
0.88
0.88
11.5
1.55
NorESM1
0.61
0.88
0.88
14.9
1.65
BCC-CSM1.1
NA
0.89
0.89
16.8
2.05
HadGEM2
0.27
0.79
0.85
13.5
1.52
IPSL-CM5
NS
0.93
0.93
13.2
1.61
GFDL-ESM2G
NS
0.85
0.89
10.9
2.61
CanESM2
NS
0.56
0.73
22.5
1.74
INM-CM4
NS
0.72
0.72
20.7
2.19
GISS-E2
NS
NS
NS
–
–
MIROC-ESM
NS
0.62
0.62
37.1
1.98
MPI-ESM-LR
NS
0.32
0.32
29.8
1.45
correlated with the HWSD (0.70
> R
2
>
0.65,
p <
0
.
01), but
consistently underestimated biome totals particularly in tun-
dra, boreal forest, and desert and shrubland. Biome totals
from MPI-ESM-LR were also moderately correlated with
the HWSD (
R
2
=
0
.
62,
p <
0
.
01), but this model overes-
timated most biome totals, particularly grasslands and sa-
vanna. GFDL-ESM2G and GISS-E2 were weak to moder-
ately correlated with the HWSD on the biome level (
R
2
=
0
.
38 and
R
2
=
0
.
51, respectively). GFDL-ESM2G overes-
timated biome totals from tundra and boreal forests while
underestimating the other biomes. GISS-E2 overestimated
biome totals in desert and shrublands, grasslands and sa-
vanna, tundra, and boreal forests while underestimating trop-
ical rainforests.
3.3
Drivers of soil carbon distributions and
global stocks
The spatial variability in 8 of the 11 ESMs was well ex-
plained by the reduced complexity model driven by NPP
and soil temperature (Eq. 2) with
R
2
values between 0.72
and 0.93 (Table 4). Consistent with our global-scale calcula-
tions (Fig. 2), the turnover times (1
/ k
) for global soil carbon
inferred from Eq. (2) (at a baseline temperature of 15
◦
C)
varied from 11 to 37 yr, and
Q
10
values ranged from 1.5 to
2.6 (Table 4). The reduced complexity model for CanESM2
was the only one significantly improved by the addition of
soil moisture (Eq. 3), with the
R
2
value increasing from 0.56
to 0.73. Soil carbon outputs from GISS-E2 (
R
2
<
0.01) and
MPI-ESM-LR (
R
2
=
0
.
32) were not well explained by any
of the reduced complexity models.
Given the strong relationships between soil carbon, tem-
perature, and NPP illustrated by our reduced complexity
models, model skill in simulating driving variables could
strongly influence simulated soil carbon stocks (Table 3).
ESMs varied in their ability to capture the observed 1
◦
spatial
distribution of NPP (Pearson correlation coefficients from
0.48 to 0.75, biome regression
R
2
values from 0.86 to 0.99;
Table 3, Fig. S7 in the Supplement). In contrast, models
performed better at simulating surface air temperature ob-
servations (correlations from 0.93 to 0.96, biome regression
R
2
values from 0.93 to 0.97; Fig. S8 in the Supplement).
Although air temperature is not directly comparable to soil
temperature, particularly in areas with thick organic soils,
the biome level correlation between soil and air tempera-
ture was high across all ESMs (
R
2
values higher than 0.97;
Fig. S9). INM-CM4, GISS-E2, BCC-CSM1.1, CCSM4, and
NorESM1 all showed warmer soil temperatures compared to
air temperatures in northern biomes (Fig. S9). In contrast
to the strong relationships we found between soil carbon,
NPP, and temperature in the ESMs, the 1
◦
spatial distribu-
tion of soil carbon from the HWSD was not well explained
by MODIS NPP and CRU surface air temperature data using
the same reduced complexity model (
R
2
value of 0.10 for
Eq. (2); Table 4).
The reduced complexity models that explained within-
model spatial variation of soil carbon also captured most
of the variation in global soil carbon totals across ESMs
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
1727
Fig. 3. Soil carbon densities [kg m
−
2
] from Earth system models. These soil carbon densities represent 1995–2005 means from the historical
simulations of the Climate Model Intercomparison Project 5.
(Fig. 5). Reduced complexity models using ESM-specific
values for
k
and
Q
10
and ESM-derived driving variables
were able to explain 98 % the variation in total soil carbon
across ESMs (Fig. 5a). Most of the variation in soil carbon
across ESMs could be attributed to differences in parameter-
ization as represented by Eq. (5) (
R
2
=
0
.
64, Fig. 5b). There
was no significant cross-ESM variation due to differences in
driving variables alone as represented by Eq. (6) (Fig. 5c).
However, driving variables must interact with parameters,
since the variances explained by drivers alone (13 %, not sig-
nificant) and parameters alone (64 %) did not sum to 98 %
(Fig. 5a–c). NPP was likely the main driving variable in this
interaction, since using the multi-model mean temperature at
each grid cell (Eq. 7) still allowed us to explain 93 % of the
variation in global soil carbon across ESMs (Fig. 5d).
4
Discussion
Accurate models of the soil carbon cycle are essential for pre-
dicting carbon–climate feedbacks in the future because soil
carbon stocks are sensitive to climate change and large rel-
ative to the atmospheric CO
2
reservoir. As far as we know,
our analysis is the first to benchmark soil carbon outputs
from ESMs against empirical data at the global scale, and
the first to explore the possible factors contributing to differ-
ences among models. We found that although some models
simulated reasonable global soil carbon totals, fewer were
able to match biome totals, and none were able to reproduce
grid-scale distributions of soil carbon. There are a number of
factors that may have contributed to the divergence between
ESM simulations and observational data. These factors in-
clude (1) uncertainties in the data, (2) incorrect representa-
tion of environmental drivers in the models (e.g., NPP, tem-
perature, and soil moisture), and (3) incorrect model structure
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
0
50
100
150
200
250
0
50
100
150
200
250
CCSM4
●
●
●
●
●
●
●
●
y
=
0.46
x
−
6.3
R
2
=
0.68
(
p
<
0.01
)
0
50
100
150
200
250
0
50
100
150
200
250
NorESM1
●
●
●
●
●
●
●
●
y
=
0.48
x
−
4.6
R
2
=
0.69
(
p
<
0.01
)
0
50
100
150
200
250
0
50
100
150
200
250
BCC−CSM1.1
●
●
●
●
●
●
●
●
y
=
0.86
x
−
2.66
R
2
=
0.95
(
p
<
0.01
)
0
50
100
150
200
250
300
0
50
100
150
200
250
300
HadGEM2
●
●
●
●
●
●
●
●
y
=
0.99
x
−
11.48
R
2
=
0.88
(
p
<
0.01
)
0
50
100
150
200
250
0
50
100
150
200
250
IPSL−CM5
●
●
●
●
●
●
●
●
y
=
1.05
x
−
0.22
R
2
=
0.85
(
p
<
0.01
)
0
100
200
300
400
0
100
200
300
400
GFDL−ESM2G
●
●
●
●
●
●
●
●
y
=
1.04
x
+
9.77
R
2
=
0.38
(
p
=
0.03
)
0
100
200
300
0
100
200
300
CanESM2
●
●
●
●
●
●
●
●
y
=
1.28
x
−
6.25
R
2
=
0.91
(
p
<
0.01
)
0
100
200
300
400
500
0
100
200
300
400
500
INM−CM4
●
●
●
●
●
●
●
●
y
=
1.53
x
−
21.68
R
2
=
0.87
(
p
<
0.01
)
0
100
200
300
400
0
100
200
300
400
GISS−E2
●
●
●
●
●
●
●
●
y
=
1.4
x
+
13.94
R
2
=
0.51
(
p
<
0.01
)
0
100
200
300
400
500
600
0
100
200
300
400
500
600
MIROC−ESM
●
●
●
●
●
●
●
●
y
=
2.11
x
−
7.66
R
2
=
0.87
(
p
<
0.01
)
0
200
400
600
800
1000
0
200
400
600
800
1000
MPI−ESM−LR
●
●
●
●
●
●
●
●
y
=
2.91
x
−
55.87
R
2
=
0.62
(
p
<
0.01
)
HWSD soil carbon [Pg C]
ESM soil carbon [Pg C]
●
●
●
●
●
●
●
●
Permanent wetlands
Tundra
Boreal forest
Temperate forest
Grasslands and savanna
Desert and shrublands
Cropland and urban
Tropical rainforest
Fig. 4. Linear regression of ESM versus HWSD soil carbon totals [Pg C] for the 8 major biomes. The gray line indicates a 1
:
1 relationship
and the black line is the linear regression.
or parameterization of the decomposition response to driv-
ing variables. Better performance at the global and biome
scales may be due to aggregation of environmental variation
that was not captured by the models at finer spatial scales.
For instance, topographic controls on soil texture, moisture,
and anoxia regulate soil carbon accumulation in peatlands
and other organic soil types (e.g., Fan et al., 2008) but are
poorly represented in many ESMs. Addressing these issues
will be essential for increasing confidence in ESM simula-
tions of terrestrial carbon in the future.
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
1729
C
N
B
H
I
G
c
i
M
m
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
2000
2500
3000
and drivers
(A) ESM−specific parameters
C
N
B
H
I
G
c
i
M
m
CCSM4
NorESM1
BCC−CSM1.1
HadGEM2
IPSL−CM5
GFDL−ESM2G
CanESM2
INM−CM4
MIROC−ESM
MPI−ESM−LR
y
=
1.09
x
−
70.54
R
2
=
0.98
(
p
<
0.01
)
C
N
B
H
I
G
c
i
M
m
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
2000
2500
3000
with multi−model mean drivers
(B) ESM−specific parameters
y
=
1.12
x
−
7.34
R
2
=
0.64
(
p
<
0.01
)
C
N
B
H
I
G
c
i
M
m
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
2000
2500
3000
with ESM−specific drivers
(C) Multi−model mean parameters
y
=
0.8
x
+
339
R
2
=
0.13
(
p
=
0.17
)
C
N
B
H
I
G
c
i
M
m
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
2000
2500
3000
with multi−model mean temperature
(D) ESM−specific parameters and NPP
y
=
1.02
x
+
70.88
R
2
=
0.93
(
p
<
0.01
)
ESM soil carbon [Pg C]
Reduced complexity model soil carbon [Pg C]
Fig. 5. Relationship between global soil carbon totals from ESMs and global soil carbon totals predicted by reduced complexity models
(Eqs. 4–7). The reduced complexity model in (A) used ESM-specific parameters and drivers (Eq. 4); (B) used ESM-specific parameters with
multi-model mean NPP and soil temperature (Eq. 5); (C) used multi-model mean parameters and ESM-specific NPP and soil temperature
(Eq. 6); (D) used ESM specific parameters and NPP but multi-model mean soil temperature (Eq. 7). The gray line indicates a 1
:
1 fit and the
black line is the linear regression.
4.1
Data uncertainties
Our ability to evaluate model performance relies on high
quality empirical data with associated estimates of uncer-
tainty. Whether model simulations diverge from the data is
difficult to assess without a formal analysis of uncertainty
in the data. Despite their comprehensiveness, the HWSD and
NCSCD lack quantitative uncertainty estimates, thereby con-
straining our ability to use these data sets for benchmarking
ESMs. Our preliminary analyses based on a qualitative as-
sessment indicated that the uncertainty in empirical estimates
of soil carbon stocks could exceed 770 Pg C at the global
scale, an amount similar to the entire pool of atmospheric
carbon.
At high northern latitudes, there was substantial disagree-
ment between the two data sets. NCSCD estimates of CI
95
were between 380 and 620 Pg C, whereas the corresponding
HWSD estimate was only 290 Pg C. However, the HWSD did
not include regional uncertainty information, meaning that
the two estimates may agree once a formal uncertainty anal-
ysis has been performed. Such an analysis requires quantifi-
cation of uncertainty in both measurement and scaling pro-
cesses used to construct the spatial distribution of soil car-
bon. Uncertainty in the measurement of soil properties such
as bulk density and carbon concentration must be integrated
with errors involved in extrapolating data from individual soil
profiles to the regional scale. Detailed analysis of the accu-
racy of soil maps will likely be essential for quantifying the
uncertainty in this extrapolation process.
4.2
Driving variables
Accurate observational data are important but will not re-
solve the differences in simulated soil carbon that we ob-
served among the ESMs. These differences must be due
to differential model skill in simulating soil carbon drivers
or in representing the response of soil carbon to drivers
through model parameterization and structure. Our reduced
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
complexity models showed that differences in NPP con-
tributed significantly to differences in soil carbon across
ESMs (Fig. 5). NPP was also a significant driver of soil car-
bon within ESMs (Table 3), suggesting it should be a focal
variable for improving soil carbon estimates. Given the large
range of global NPP across ESMs (Fig. 2) and the low Taylor
scores observed for some models in comparison to MODIS
NPP (Table 3), it may be possible to improve soil carbon
simulations by revising photosynthesis and autotrophic res-
piration algorithms in some of the ESMs so that NPP is more
consistent with contemporary observations.
In contrast to NPP, differences in soil temperature did not
contribute significantly to differences in soil carbon stocks
across ESMs (Fig. 5). However, our reduced complexity
models indicated that soil temperature was important for
explaining soil carbon variation within models (Table 4).
Therefore, simulation of soil temperature could also be a fo-
cal area for model improvement, especially since other stud-
ies suggest that soil temperature is not consistently well rep-
resented in ESMs. For example, the physical coupling be-
tween surface air temperature and soil temperature at high
latitudes differs considerably across ESMs, which influences
the spatial distribution of permafrost (Koven et al., 2012;
Slater and Lawrence, 2013). Even if ESMs can simulate av-
erage air temperatures consistent with observations (Table 3,
Fig. S8), fine-scale differences in the ability to represent
soil temperatures (Fig. S9) and permafrost could have con-
sequences for soil carbon distributions.
Soil moisture did not play an important role as a driv-
ing variable for soil carbon in our reduced complexity mod-
els, indicating that for most models this variable did not
strongly control spatial patterns in soil carbon stocks (Ta-
ble 4) or differences among models (Fig. 5). This result
was unexpected because soil moisture affects decomposition
rates in all ESMs (Table 1). Furthermore, other studies have
shown that soil carbon stocks depend on the response of het-
erotrophic respiration to soil moisture in global models, al-
though NPP and soil temperature were also important drivers
of soil carbon (Falloon et al., 2011). It is possible that soil
moisture influences soil carbon stocks in ESMs, but our re-
duced complexity model was unable to statistically distin-
guish the soil moisture effect from the NPP effect because
these two drivers often covary.
Alternatively, the exponential form of the moisture func-
tion in our reduced complexity model might have been inap-
propriate if decomposition rates decline at high soil moisture.
Based on empirical data, a substantial fraction of global soil
carbon likely resides in areas where poor soil drainage im-
pedes organic matter oxidation (Gorham, 1991). It is likely
that the interaction of topographic controls and soil texture
with soil moisture is not well represented in the current gen-
eration of ESMs. New approaches may be needed to deter-
mine which grid cells are poorly drained, and the rate at
which organic soils form in these area (Ise et al., 2008). We
also recommend that future CMIP archives require soil mois-
ture information for different soil layers to facilitate bench-
marking studies on the response of carbon to moisture in the
soil profile.
Although our reduced complexity models indicated that
soil carbon simulated by ESMs was driven primarily by NPP
and temperature, this relationship was much weaker with ob-
servational data. According to the same reduced complex-
ity model used for the ESMs, MODIS NPP and CRU sur-
face air temperatures were only able to explain 10 % of
the spatial variation in HWSD soil carbon stocks. Thus the
variables that drive soil carbon stocks in ESMs may differ
from those that determine observed carbon stocks. For ex-
ample, soil temperatures in organic-rich soils may be weakly
coupled to air temperatures (Koven et al., 2011; Slater and
Lawrence, 2013), in contrast to the strong coupling predicted
by most ESMs (Fig. S9). Alternatively, the mathematical
form of our reduced complexity model may have been in-
appropriate for the observational data, even though it was
appropriate for most ESM outputs. Regardless, our results
imply that ESMs may need to incorporate a broader range
of environmental drivers and processes to improve model–
data agreement. Even if simulations of NPP and soil temper-
ature can be improved in ESMs, these drivers have a limited
ability to explain spatial patterns in global soil carbon with
current model structures.
4.3
Parameterization and model structure
We found that parameterization was a major source of varia-
tion in ESM soil carbon simulations (Fig. 5). In some of the
ESMs such as CCSM4, soil carbon turnover may be too fast,
whereas in other models such as MIROC-ESM, turnover may
be too slow (Fig. 2). To address these issues, ESMs could
use terrestrial radiocarbon observations (both the total in-
ventory and vertical distribution of
14
C in different biomes)
to help constrain rates of soil carbon turnover (Torn et al.,
1997; Trumbore, 2009). Another avenue of improvement for
ESM parameterization could focus on processes that operate
on fine spatial scales. Differences in soil texture and topog-
raphy may lead to non-linear effects on soil carbon storage
that are not well described by the average characteristics of
a grid cell. For instance, relatively small-scale topographic
variations are associated with peatland formation, and it is
unclear how to scale these effects globally (Gorham, 1991;
Koven et al., 2011). A multi-scale approach is required to
determine which processes are important at the global scale
and how to represent them.
Improving empirical data sets, model driving variables,
and model parameterization could substantially increase
model–data agreement for present-day soil carbon stocks.
However, matching current soil survey data is a necessary but
not sufficient condition for validating the accuracy of Earth
system models. In order to have confidence in future simu-
lations, the models must correctly represent the mechanisms
and drivers of soil carbon change, such that they are right for
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
1731
the right reasons. For example, models with incorrect mech-
anisms or drivers could be tuned to correctly simulate current
soil carbon stocks, but might incorrectly simulate soil carbon
stock changes in the future.
We initially hypothesized that models with more pools
would have greater flexibility and capture more of the spa-
tial variation in soil carbon. However, the structural fea-
tures that we examined did not clearly relate to differences
in ESM agreement with empirical data (Tables 1, 3). We
saw no pattern in ESM-data agreement with respect to num-
ber of soil carbon pools, temperature and moisture sensitiv-
ity functions, or presence of a nitrogen component. Further-
more, our reduced complexity model (Eq. 3) explained most
of the spatial variation within 9 of 11 models (0
.
62
< R
2
<
0
.
93). This result confirmed that, despite different simulated
stocks of soil carbon, most of the models share a similar
underlying structure. Such similarity means that the mod-
els likely make similar assumptions about the mechanisms
regulating soil carbon cycling. If these underlying assump-
tions are incorrect or incomplete, the resulting errors will be
present in all of the models.
CanESM2, MPI-ESM-LR, and GISS-E2 are three excep-
tions that were not well explained by our reduced complexity
model (Eq. 2) driven by NPP and soil temperature (Table 4),
and thus may be examples of models with structural differ-
ences. CanESM2 was the only model in which soil water
content contributed to the explanatory power of the reduced
complexity model (
R
2
value improved from 0.57 to 0.74).
This dependency on soil water content may be partly ex-
plained by the biome-specific turnover time in CanESM2.
Since biomes are partially determined by precipitation and
soil moisture status, biome-specific turnover times might
have resulted in a tighter relationship between soil carbon
and moisture in our reduced complexity model. Outputs from
MPI-ESM-LR were only moderately explained by our re-
duced complexity models (
R
2
value 0.32). We do not have
a good explanation for the poor fit since there was no signif-
icant deviation in documented model structure, and driving
variables were roughly in line with other model simulations.
GISS-E2 outputs were not explained at all by the reduced
complexity model (
R
2
value less than 0.01). Unlike other
models, GISS-E2 showed a unique disconnect between NPP
and soil carbon which could be due to differences in the way
plant biomass is allocated to litter in the model. However, we
cannot offer a definitive explanation for the poor fit.
All ESMs may be missing key processes governing long-
term carbon storage that affect model–data agreement. De-
composition models currently used in all ESMs are built on
the assumption that carbon substrates have intrinsic chemi-
cal decomposition rates (Parton et al., 1993). However, there
is an emerging consensus that key abiotic and biotic factors
have a stronger governing role in decomposition than the
carbon compounds themselves (Schmidt et al., 2011). These
key governing components may include aggregate interac-
tions (Six et al., 2000), microbial dynamics (Todd-Brown et
al., 2012), cryoturbation (Koven et al., 2011), syngenetic
soil formation (Fan et al., 2008; Shur et al., 2004), extra-
cellular enzyme dynamics (German et al., 2011), and rare
substrate formation (Allison, 2006). Representing these pro-
cesses in the structure of soil carbon models remains a ma-
jor challenge. However, smaller-scale decomposition mod-
els have begun to explore several of these mechanisms
(Manzoni and Porporato, 2009).
Recent advances in the theory of microbial decomposi-
tion could provide a foundation for major changes in the
structure of soil carbon models used in ESMs. Schimel and
Weintraub (2003) proposed a model in which decomposition
was mediated by soil enzymes and microbial biomass. Later
models expanded this framework to include microbial func-
tional groups that preferentially decompose specific substrate
types (Moorhead and Sinsabaugh, 2006). In contrast to cur-
rent substrate pool models used in ESMs, biomass-mediated
decomposition models would likely include non-linear pro-
cesses such as Monod uptake or Michaelis–Menten enzyme
kinetics. These non-linear effects could produce very dif-
ferent behaviors at daily, annual, and centennial timescales.
Compared to substrate pool models, models driven by mi-
crobial biomass predict smaller losses of soil carbon under
warming due to declines in microbial growth efficiency with
higher temperature (Allison et al., 2010).
5
Conclusions
Overall, we found that some ESMs simulated soil carbon
stocks consistent with empirical estimates at the global and
biome scales. However, all of the models had difficulty rep-
resenting soil carbon at the 1
◦
scale. Despite similar overall
structures, the models do not agree well among themselves or
with empirical data on the global distribution of soil carbon.
Differences across ESMs are primarily due to differences in
the representation of NPP and the parameterization of soil
decomposition sub-models, not due to differences in model
structure. However, all model structures may have serious
shortcomings since NPP and temperature strongly influenced
soil carbon stocks in ESMs but not in observational data.
Fully reconciling this disagreement will require a range of
approaches, including better prediction of soil carbon drivers,
more accurate model parameterization, and more compre-
hensive representation of critical biological and geochemi-
cal mechanisms in soil carbon sub-models. There is also a
need for better quantification of the uncertainty in empiri-
cal estimates of soil carbon stocks that are used to bench-
mark ESMs. If this uncertainty is too high for rigorous model
comparison, additional measurements of soil carbon stocks
may be required in some regions of the world. Addressing
these issues will improve our ability to predict the response
of the carbon cycle to climate change and inform policymak-
ers about the potential impacts of carbon emissions.
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Biogeosciences, 10, 1717–1736, 2013
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K. E. O. Todd-Brown et al.: Soil carbon drivers and benchmarks in Earth system models
Supplementary material related to this article is
available online at: http://www.biogeosciences.net/10/
1717/2013/bg-10-1717-2013-supplement.pdf.
Acknowledgements. We thank Shishi Lui and Yaxing Wei for as-
sistance with the HWSD, as well as Yufang Jin for assistance with
the NCSCD data set. This research was funded by grants from
the NSF Advancing Theory in Biology program, the Decadal and
Regional Climate Prediction using Earth System Models (EaSM;
AGU-1048890) program, and the Office of Science (BER), US De-
partment of Energy.
We acknowledge the World Climate Research Programme’s Work-
ing Group on Coupled Modeling, which is responsible for CMIP,
and we thank the climate modeling groups (listed in Table S1) for
producing and making available their model output. For CMIP, the
US Department of Energy’s Program for Climate Model Diagno-
sis and Intercomparison provided coordinating support and led de-
velopment of software infrastructure in partnership with the Global
Organization for Earth System Science Portals.
The authors have no potential conflicts of interest to declare.
Edited by: U. Seibt
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