Page 1
O R I G I N A L P A P E R
Soil carbon saturation: concept, evidence and evaluation
Catherine E. Stewart
Æ
Keith Paustian
Æ
Richard T. Conant
Æ
Alain F. Plante
Æ
Johan Six
Received: 6 November 2006 / Accepted: 18 June 2007 / Published online: 3 August 2007
Ó
Springer Science+Business Media B.V. 2007
Abstract
Current estimates of soil C storage
potential are based on models or factors that assume
linearity between C input levels and C stocks at
steady-state, implying that SOC stocks could increase
without limit as C input levels increase. However,
some soils show little or no increase in steady-state
SOC stock with increasing C input levels suggesting
that SOC can become
saturated
with respect to C
input. We used long-term field experiment data to
assess alternative hypotheses of soil carbon storage
by three simple models: a linear model (no satura-
tion), a one-pool whole-soil C saturation model, and a
two-pool mixed model with C saturation of a single C
pool, but not the whole soil. The one-pool C
saturation model best fit the combined data from 14
sites, four individual sites were best-fit with the linear
model, and no sites were best fit by the mixed model.
These results indicate that existing agricultural field
experiments generally have too small a range in C
input levels to show saturation behavior, and verify
the accepted linear relationship between soil C and C
input used to model SOM dynamics. However, all
sites combined and the site with the widest range in C
input levels were best fit with the C-saturation model.
Nevertheless, the same site produced distinct effec-
tive stabilization capacity curves rather than an
absolute C saturation level. We conclude that the
saturation of soil C does occur and therefore the
greatest efficiency in soil C sequestration will be in
soils further from C saturation.
Keywords
Agroecosystems
Carbon saturation
Soil carbon sequestration
Soil carbon modeling
Tillage
Introduction
Soil organic C (SOC) constitutes a large pool of C in
the global C cycle representing a dynamic balance
between C inputs through photosynthesis and depo-
sition and losses via respiration, erosion and leaching.
In agroecosystems, the SOC balance is influenced by
management practices such as organic matter addi-
tions, tillage intensity, fertilization, irrigation, and
crop rotation. Soil organic C storage may be
increased directly by increasing C returns to the soil
C. E. Stewart (
&
)
K. Paustian
R. T. Conant
A. F. Plante
J. Six
A242 Natural Resource Ecology Laboratory, Colorado
State University, Fort Collins, CO 80523-1499, USA
e-mail: catherineestewart@gmail.com
K. Paustian
Department of Soil and Crop Sciences, Colorado State
University, Fort Collins, CO 80523-1170, USA
A. F. Plante
Department of Earth and Environmental Science,
University of Pennsylvania, Philadelphia, PA 19104, USA
J. Six
Department of Plant Sciences, University of California,
Davis, CA 95616, USA
123
Biogeochemistry (2007) 86:19–31
DOI 10.1007/s10533-007-9140-0
Page 2
as crop residue, manure, or other organic amend-
ments. Carbon inputs to the system also may be
increased indirectly by fertilization or irrigation
treatments that increase crop productivity, biomass
and root production.
Interest has grown in promoting C sequestration in
soils to help mitigate increasing CO
2
levels in the
atmosphere because most agricultural soils have been
previously depleted with respect to organic matter
(CAST
2004
). This interest is also coincident with the
desire to increase soil C contents to improve soil
sustainability (Follett and Delgado
2002
). Key ques-
tions include: what is the relative C storage efficiency
(i.e., C stock increase per unit C added) for different
soils and is there an upper limit to the capacity for
soils to store organic C?
Most current SOC models employ first-order
kinetics for decomposition processes, and therefore
the models predict linearity between C input level
and SOC level at equilibrium (i.e., steady-state;
Paustian et al.
1997a
). This linearity means that soil
C storage ‘efficiency’ (i.e.
D
SOC/
D
C input) is
constant and that equilibrium soil C levels could
increase continuously and without limit as steady-
state C input levels increase. Many long-term agro-
ecosystem field experiments, in which treatments
give different levels of C inputs, show soil C stocks
that appear linearly related to the average amount of
C returned to the system (e.g. Huggins et al.
1998b
;
Kong et al.
2005
; Paustian et al.
1997a
). This linear
relationship between steady-state C inputs and soil C
levels is consistent with the behavior predicted by
soil C models based on first-order kinetics.
However, some long-term agroecosystem experi-
ments show little or no change in SOC stocks in response
to varying C input levels. After 30 years of continuous
corn (
Zea mays
L.) at Morris, MN, neither varying levels
of fertilization nor removal of crop stover had a
significant effect on SOC content of the upper 20 cm
of soil (Reicosky et al.
2002
). At Lamberton, MN,
greater residue additions in corn versus corn-soybean
(
Glycine max
L.) crop rotations over 10 years (Huggins
et al.
1998a
) and differences in N-fertilizer rates and
residue inputs over 19 years (Huggins and Fuchs
1997
;
Huggins et al.
1998b
) did not significantly affect SOC
levels. Other field studies have shown decreased SOC
stabilization efficiency in high-C compared to low-C
soils under the same treatments. For example after
31 years of fertilizer and crop rotation treatments,
Campbell et al. (
1991b
) found that SOC content was not
significantly different as a function of C input level (1.4–
2.2 Mg C ha
1
year
1
) at Melfort, Saskatchewan,
whereas SOC increased as a function of C input level
(0.9–2.0 Mg C ha
1
year
1
) at Indian Head, Saskatch-
ewan. They attributed this difference in response of
SOC to carbon input, in part, to the lesser SOC content of
Indian Head (36–42 Mg C ha
1
) compared to Melfort
(61–67 Mg C ha
1
, 0–15 cm). After 11 years, Nyborg
et al. (
1995
) found less stabilization of new C in a Typic
Cryoborol (Ellerslie, Alberta) with a greater C content
(86.7 Mg C ha
1
, 0–15 cm) compared to a paired site at
Breton, Alberta (Typic Cryoboralf) (33.2 Mg C ha
1
,
0–15 cm) under straw addition and N-fertilization
treatments. This lack of response in SOC levels to
varying levels of C input, over many years, and the
apparent dependency between C stabilization efficiency
and soil C content, suggests the possibility of an upper
limit or ‘saturation level’ for soil carbon (Six et al.
2002
).
Saturation limits to individual SOC pools have
been proposed by other researchers, due to silt + clay
protection (Hassink
1996
,
1997
), soil structure (phys-
ical protection within aggregates), and the biochem-
ical complexity of the organic compounds (Baldock
and Skjemstad
2000
). Six et al. (
2002
) proposed a
whole-soil C saturation limit with respect to soil C
input levels at steady-state comprised of all the above
C pools, including a non-protected C pool. Soil C
saturation is then defined as a soil’s unique limit to C
stabilization as a function of C input levels (at steady
state) based on the cumulative behavior of these four
C pools (i.e., chemically-, physically-, biochemically-
protected, and non-protected pools). Across 11 agro-
ecosystems, Six et al. (
2002
) found that an asymp-
totic curve fit the SOC content and C input level data
better than a linear relationship. They suggested that
the smaller increase in SOC content with increased C
input level was due to the decreased capacity of a
high C soil to store added C. Their conceptual model
implies that the further a soil is from saturation (i.e.,
the greater the saturation deficit), the greater its
capacity and efficiency to sequester added C, whereas
a soil approaching saturation will accumulate a
smaller amount of SOC at a slower rate and
efficiency (Hassink and Whitmore
1997
).
As our ability to increase SOC stocks (even
beyond native levels) through greater C inputs and
improved management practices advances, it is
20
Biogeochemistry (2007) 86:19–31
123
Page 3
crucial to know what, if anything, limits the amount
and rate of SOC stabilization. Results from long-term
experiments are ambiguous, with many sites showing
a linear response of SOC to C input levels that is
consistent with first-order decomposition processes
and other experiments that suggest saturation dynam-
ics. Our objective was to analyze previously pub-
lished data to test three simple C accumulation
hypotheses: the common (first-order) ‘linear’ model,
a one-component whole-soil C saturation model
(representing a simplification of the Six et al.
(
2002
) hypothesis of C saturation), and a two-pool
mixed model with assumptions of C saturation of a
single C pool, but not the whole soil. The latter model
is analogous to Hassink and Whitmore (
1997
) where
the single saturated pool is represented by the silt and
clay associated C. We explored the steady-state
dynamics of each simplified model and using infor-
mation theory, we then ranked the performance of
models against experimental data from long-term
agroecosystems to test whether C saturation influ-
enced whole SOC accumulation.
Theory
The distinction between the concepts of equilibrium
soil C content and soil C saturation is illustrated in
Fig.
1
. Soil organic matter dynamics are typically
viewed in terms of changes in stocks over time. If
changes in agricultural management practices in-
crease (or decrease) C input levels, then over time,
soil C content will increase (or decrease) until a new
equilibrium
soil C content is reached. Multiple
equilibrium levels of C input will produce multiple
equilibrium SOC levels because equilibrium soil C
levels are achieved where C additions are balanced
by C losses—if C input rates are held constant, soil C
contents approach an equilibrium level over time
(Fig.
1
a, c). With no saturation, there is no limit to
soil C content as steady-state C input rates increase
(Fig.
1
b). The soil C saturation concept proposes that
there is a maximum equilibrium C level that will be
attained when C input is maximized (Fig.
1
d). Hence,
under the C saturation model, equilibrium SOC also
increases with greater C input rates, but the incre-
mental increase in SOC declines as the rate of C
addition increases (Fig.
1
c). Hence the storage effi-
ciency decreases towards zero as the soil C content
approaches the saturation level.
Complex simulation models for SOC, when ana-
lyzed at steady-state, can be simplified to mathemat-
ical expressions that illustrate general conclusions
(Bolker et al.
1998
). Here, we present the simplest
form of a linear (first-order decay) model which
forms the basis of simulation models such as Century,
RothC, and many others (Paustian et al.
1997
b) and
we compare this to simple models that include a C
saturation component. It is important to note that here
Fig. 1
Theoretical
relationship between C
input level and soil organic
C (SOC) contents at steady-
state, with and without C
saturation. Steady-state
SOC accumulation
dynamics expressed over
time (
a
) produces a linear
relationship when expressed
over C input level (
b
) Under
the conditions of C
saturation, SOC
stabilization with increasing
input rates (at steady state)
is not proportional (
c
)
resulting in an asymptotic
relationship when expressed
over C input level (
d
)
Biogeochemistry (2007) 86:19–31
21
123
Page 4
we use the models not to simulate the dynamic
behavior of SOM pool(s) over time, but rather to
evaluate the fundamental relationship between C
addition levels and soil C levels at steady-state.
The boundaries of the proposed models are soil
organic matter rather than the soil itself (Fig.
2
). This
places an important distinction on how C inputs (
I
) to
the system are defined; they do not represent residues
entering the soil system as a whole, but rather organic
materials entering the pool of soil organic matter,
which is usually operationally defined as organic
materials <2 mm in size that are intimately associated
with the soil matrix.
Linear model
The simple first-order decay model (proposed by
Jenny (
1941
) and other early workers) assumes that
the amount of C entering a C pool is independent of
the pool size and that decomposition rates are directly
proportional to the size of the pool (Fig.
2
a).
dC
t
dt
¼
I
kC
t
ð
1
Þ
where the rate of change in SOC at time
t
(
dC
t
/
dt
) is
dependent on the level of C input (
I
) and losses
through first-order decomposition kinetics of the SOC
pool (
C
t
) with a specific decay constant (
k
).
1
If C
input level (
I
) added to the soil pool is increased by a
constant proportion (
n
) in the manner
I
n
= I
i
n
, SOC
will accumulate until a new steady-state level is
achieved (Fig.
1
a).
However, for the present analysis we are only
concerned with the relationship at steady-state (
dC
t
/
dt
= 0),
C
t
¼
I
k
ð
2
Þ
where SOC content (
C
t
*
) is directly proportional to C
input level (
I*
). If
I
is increased, SOC content at
steady-state will increase by the same proportion,
without limit (Fig.
1
b). Most current SOC models are
based on first-order decomposition kinetics and hence
show a linear relationship between C input levels and
SOC content at steady-state (Paustian
1994
; Paustian
et al.
1997c
). This relationship holds even for sim-
ulation models with multiple pools (and
k
’s) of SOC
(e.g. Bolker et al.
1998
; Jenkinson
1990
; Parton et al.
1988
) and simulation models where the specific
decomposition rates (
k
) is treated as a variable (e.g.
Bosatta and Agren
1999
) rather than a constant
(Paustian et al.
1997c
).
Carbon saturation model
The C saturation model has a whole soil saturation
limit (
C
m
) (Fig.
2
b) due to inherent physicochemical
limitations. In contrast to the linear model, the
fundamental relationship between C addition levels
and soil C levels at steady-state is asymptotic. While
I
k
C
t
a
I
C
t
C
m
k
⎟⎟⎠
⎞
⎜⎜⎝
⎛
−
m
t
C
C
1
b
I
k
2
)
α
−
1
(
k
1
α
k
1
⎟⎟⎠
⎞
⎜⎜⎝
⎛
−
m
C
C
2
2
1
C
2
C
m
2
C
1
c
⎟⎟⎠
⎞
⎜⎜⎝
⎛
m
t
C
C
Fig. 2
Graphical
representations of the linear
(no saturation) model
(
a
), the one-pool whole-soil
C saturation model (
b
) and
the two-pool mixed model
with C saturation of a single
C pool, but not the whole
soil (
c
)
1
For simplicity, losses via respiration are included in the term
k
, and losses through other pathways (e.g., leaching) are
assumed to be zero.
22
Biogeochemistry (2007) 86:19–31
123
Page 5
many first-order based simulation models use texture
to modify soil stabilization of C inputs between soils
of differing silt + clay content (e.g. CENTURY),
there is no explicit limit to soil C stabilization.
Another simulation model (Hassink and Whitmore
1997
) assumed C saturation of a single C pool, but
not the whole soil. Our simplified C saturation
expression differs from previous models in that the
stabilization of C input into soil organic matter is
explicitly limited
and the mechanism of physico-
chemical stabilization is implied rather than directly
modeled as a specific process.
Over time, the soil C saturation concept may be
expressed as a simple modification to the C input
term in Eq. 1:
dC
t
dt
¼
I
1
C
t
C
m
kC
t
ð
3
Þ
where
C
m
is the maximum amount of C that can be
stabilized by the soil. In this model, soil C storage is
limited by a saturation deficit (
sd
) which we define as:
sd
¼
1
C
t
C
m
ð
4
Þ
As a soil approaches C saturation level, the
proportion of new C input stabilized by physico-
chemical mechanisms is reduced by the proportion of
SOC present (
C
t
) to the maximum C level (
C
m
), i.e.,
the SOC stabilization efficiency decreases. The
remaining C inputs (
I*C
t
/
C
m
) are not stabilized as
soil organic matter. As in the non-saturated case, if
the amount of C added to the soil pool is increased by
a constant proportion
I
n
= I
i
n
, SOC will accumu-
late until a new steady-state level is achieved
(Fig.
1
c). However in the C saturation case, relative
SOC stabilization decreases with increasing
I
, rather
than remaining proportional as in the linear model
(Fig.
1
c vs. 1a).
Solving Eq. 3 for steady-state SOC concentration
(
C
t
*
) results in an asymptotic relationship between C
inputs (
I*
) and SOC (e.g., Fig.
1
d):
C
t
¼
I
k
þ
I
C
m
ð
5
Þ
The asymptotic relationship between C input
levels and SOC content at steady-state is a key
attribute to the C saturation model (Fig.
1
d vs.
1
b).
Direct corollaries of this asymptotic relationship are
that (1) the further a soil is from saturation (i.e., the
greater the saturation deficit), the greater its effi-
ciency in sequestering added C, and (2) as a soil
approaches saturation, the rate and amount of SOC
accumulation decreases due to a smaller saturation
deficit.
Mixed model
The C saturation model above assumes that the
amount of C that can be stabilized is limited and that
once saturation is reached any additional C input will
be not be stabilized but will be lost from the system.
Hence, we can visualize a mixed C saturation model
comprised of a labile residue C pool (
C
1
) that is not
saturatable and a second more stable C pool with
saturation behavior (
C
2
), (Fig.
2
c):
dC
t
dt
¼
dC
1
dt
þ
dC
2
dt
ð
6
Þ
where
dC
1
dt
¼
I
a
k
1
C
1
ð
1
a
Þ
1
C
2
C
2
m
k
1
C
1
ð
7
Þ
and
dC
t
dt
¼ ð
1
a
Þ
1
C
2
C
2
m
k
1
C
1
k
2
C
2
ð
8
Þ
with decomposition constants
k
1
and
k
2,
respec-
tively. The term
a
is a partitioning coefficient for
the losses from
C
1
between respiration (
a
) versus
the transfer of decomposition products to the more
stable pool (1
a
). We assign a value of 0.55 to
a
,
similar to respiration coefficients used in simula-
tion models for SOM dynamics (e.g. Parton et al.
1987
). The remaining microbial products that are
not
incorporated
into
the
stable
pool
(i.e.
ð
1
a
Þ
k
1
C
2
C
2
m
C
1
) are retained implicitly in
C
1
,
the labile fraction, and represent processed organic
materials unable to be protected due to the
saturation of the stable pool. Carbon stabilization
in
C
2
is limited by the saturation limit of
C
2
(
C
2
m
).
As
C
2
approaches
C
2
m
, the amount of decomposi-
tion products from
C
1
transferred into
C
2
decreases
Biogeochemistry (2007) 86:19–31
23
123
Page 6
until
C
2
reaches its saturation level (i.e.
C
2
=
C
2
m
).
At this point, C transfer into
C
2
ceases, and SOC
accumulation in
C
1
proceeds according to the
linear model (Eq. 1).
Solving Eqs. 6, 7 and 8 for steady-state expressed
as a function of a single C pool (with C
1
solved in
terms of
C
2
),
illustrates the relationship between C input level (
I
)
and whole-soil SOC (
C
t
). Although there are two
solutions, the only relevant one produces
C
t
in positive
space (positive root). At low to moderate C input
levels, this model produces slightly curvilinear whole
soil C accumulation dynamics, but under high C input
levels, SOC accumulation is linear. Theoretically,
SOC will increase indefinitely in this model as SOC
input levels are increased, however at a slower rate
than in the linear model. Assuming
k
1
>
k
2
, the
turnover rate of the total soil C increases as the
recalcitrant pool approaches saturation because C is
retained in the labile (unprotected) state, which is
subject to a faster rate of decomposition.
The three steady-state models described above
(Eqs. 2, 5 and 9) provide three contrasting scenarios,
or hypotheses of SOC accumulation: (1) no saturation
(i.e., linear, Eq. 2), (2) whole-soil C saturation (i.e., C
saturation model, Eq. 5), and (3) soil C saturation of a
stabilized C pool, but not the whole soil (i.e., mixed
model Eq. 9). By using likelihood-based methods and
information theory (small sample Akaike’s Informa-
tion Criterion, AIC
c
), we were able to quantify the
relative explanatory power of these models, given the
long-term agroecosystem (Anderson et al.
1998
;
Burnham and Anderson
2001
,
2004
).
Analysis methods
We compiled the most recent SOC contents and
average C input levels (as crop residues and organic
amendments) from a data set compiled from long-
term agricultural sites around the world (see Ogle
et al.
2005
). Required data included SOC stocks,
soil bulk density, depth of measurement, and C
input levels. We estimated crop residue C inputs
based on reported crop yield (and in some cases
total
aboveground
biomass
production),
using
regression models to estimate total C inputs from
roots plus aboveground residues (Table
1
) or
published values from the experiment. Long-term
agricultural sites were only included if the exper-
imental duration was greater than 12 years in age
and had been under conventional cultivation at least
10 years prior to the initiation of the current
treatment. This criterion was to exclude sites where
soil C stocks may be far from steady-state. Addi-
tionally, sites were required to have four or more C
input levels (e.g., differences in crop rotations or
organic matter addition treatments) on which to
base a regression line. Sites with multiple treatments
(e.g., tillage and crop rotation) were split as tillage
could confound the C input effect.
An additional factor in the analysis is that the long-
term experiments do not, strictly speaking, represent
a true steady-state condition with respect to SOM
levels as a function of C input level, because of the
very long residence time of some recalcitrant SOC
and the variability in carbon inputs. For example,
when C inputs are totally eliminated (e.g., bare fallow
experiments), a substantial fraction of the SOC
persists over many decades (Paustian et al.
1992
;
Plante et al.
2004
). The true steady-state condition
for all three models under the condition of zero C
inputs, however, is zero SOC. An intercept term (
R
)
was added to the linear model in Eq. 2 to account for
the residual SOC that is not affected over the course
of the agroecosystem experiment:
C
t
¼
I
k
þ
R
ð
10
Þ
Due to the composite nature of the mixed model, there
is no unique steady-state solution in terms of
C
t
,
so a
sensitivity analysis was performed to determine the
C
t
¼
I
C
m
2
k
1
ð
C
m
2
C
2
þ
a
C
2
Þ
þ
ð
a
1
Þ
I
k
2
C
m
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðð
a
1
Þ
I
k
2
C
m
2
Þ
4
Ik
2
C
m
2
ð
a
1
Þ
2
q
2
ð
k
2
a
k
2
Þ
ð
9
Þ
24
Biogeochemistry (2007) 86:19–31
123
Page 7
sensitivity of the proportions of C
1
and C
2
on the model
parameter estimates. To determine the effect of the
proportion of
C
1
versus
C
2
on the steady-state solution,
we ran the model iteratively with fixed proportions of
C
2
(0.1–0.9). We found that the parameter estimates varied
only slightly across all proportions of
C
2
and produced
less than nine percent variation in AIC
c
value.
Traditional statistics lack a formal method of incor-
porating the uncertainty of the data into the model.
However, information-theory integrates model-selection
uncertainty by penalizing models with poor predictor
choice, errors in structure, or poor explanation of the
given data. Information theory also allows a set of
competing models to be tested and a ‘‘best’’ model or
models (if there is high uncertainty) to be determined
based on the data (Anderson et al.
1998
). Akaike
information criterion (AIC) is an estimate of the relative
distance between the fitted model and the unknown true
equation (or process) that produced the observed data
(Burnham and Anderson
2001
).
AIC
¼
2 log
L
[(
h
i
j
Y
Þ þ
2
K
ð
11
Þ
with
L
(
h
i
j
Y
Þ
as the maximized likelihood, a function of
the unknown parameters
h
i
, given the data
Y
and the
model. However, to account for the extremely small
sample sizes, we used small sample Akaike information
criterion (AIC
c
) for model selection which is modified by
the number of parameters (
K
) and sample size (
n
), i.e.,
AIC
c
¼
AIC
þ
2
K
*(
K
þ
1)
n
K
1
ð
12
Þ
An advantage of AIC
c
is that models may be
ranked according to best-fit. To compare models,
AIC
c
values were rescaled as differences (
D
i
)
between the AIC
c
of model
i
and the best approxi-
mating model (
D
i
= AIC
ci
AIC
c min
). The relative
likelihood of a model, given the data and the set of
models, or its ‘probability’, is expressed by weights.
w
i
¼
e
1
=
2
D
i
P
i
e
1
=
2
D
i
ð
13
Þ
We used this method to test the likelihood of the
linear (Eq. 10), C saturation (Eq. 5), and mixed (Eq.
9) models given the C input level and SOC data. All
models were fit using PROC NLMIXED in SAS/
STAT (SAS Institute, Cary NC) to normalize for the
treatment of variance in model fits, and to obtain AIC
and AIC
c
values. A model was considered to be best
fit if differences in
D
i
< 2 (Burnham and Anderson
2001
).
Results
We found that by incorporating a simple proportional
C saturation limit 1
C
t
C
m
to the C input term of the
first-order decomposition model, that steady-state
SOC versus C input level produced an asymptotic
function and allowed us to explicitly estimate the
value C saturation for a given soil. The expression in
the two-pool model, incorporating C saturation of a
single pool, produced a slight curve at low to
moderate C input levels but produced linear SOC
accumulation under high C input levels. The 2-pool
model is analogous to the Hassink et al. (
1997
)
hypothesis of C saturation of the silt + clay protective
Table 1
Regression equations for above- and belowground C input from grain dry weight (GDW) for common crops in long-term
agroecosystems experiments based on long-term crop yield data from US agroecosystem experiments (IPCC Guidelines
2006
)
Aboveground residue (AGR) (Mg dry wt. ha
1
)
Belowground residue (BGR) (Mg dry wt. ha
1
)
Alfalfa
0.325 * GDW
0.43 * (GDW
+ AGR)
Oat
1.09 * GDW + 0.387
0.26 * (GDW + AGR)
Soybean
1.712 * GDW + 0.795
0.24 * (GDW + AGR)
Corn
1.03 * GDW + 0.610
0.21 * (GDW + AGR)
Wheat
Winter
1.61 * GDW + 0.389
0.21 * (GDW + AGR)
Spring
1.29 * GDW + 0.715
Barley
0.95 * GDW + 0.625
0.20 * (GDW + AGR)
GDW = grain dry wt. (Mg ha
1
); for alfalfa GDW = aboveground biomass dry weight
Biogeochemistry (2007) 86:19–31
25
123
Page 8
capacity, but not the whole soil. This occurs because
C is retained in the labile (unprotected) state, which is
subject to a faster rate of decomposition as the
recalcitrant pool approaches saturation. This model
does not simulate whole-soil saturation because SOC
will increase indefinitely in this model as SOC input
levels are increased.
We found 14 sites that matched our criteria from a
variety of temperate agroecosystems in the U.S. and
Canada (Table
2
). They varied in SOC contents from
7.7 to 121.9 Mg C ha
1
and C input levels from 0.17
to 7.42 Mg C ha
1
year
1
. To assess the relative
support in the compiled agroecosystem data for non-
saturating (linear) versus C saturating (asymptotic
relationship) behavior between C input level and
SOC content, we ranked the models by
D
i
< 2
(Burnham and Anderson
2001
). Using this criterion,
only five sites had a clear best-fit model (Table
3
); the
linear model for Lancaster 2, Pendleton, Sanborn CT,
and Sterling, and the C saturation model for Sanborn
NT (Fig.
3
). The linear and C saturation models were
indistinguishable at 11 sites, but both had better fits
than the mixed model. The large
D
i
for the mixed
model at all sites indicated that it is the worst-ranked
of the three proposed models and reflected the
penalty of additional parameters (versus the other
two models) on AIC
c
. There was no evidence in the
Morrow corn-soybean rotation data to distinguish
between any of the models (Table
3
).
To overcome the small sample size within sites
and minimize the effect of the AIC
c
penalty term, we
also fit our three models against the combined site
data. Combining site data could confound the C
saturation analysis if C input level (
I
) co-varied with
decomposition rate (
k
), resulting in an apparent
saturation response of less SOC accumulation at high
input levels because of faster decomposition rates due
to optimal temperature and moisture conditions. We
Table 2
Long-term agroecosystem sites selected for use in comparative model analyses
Site
Treatment duration (years)
Treatments
Reference
Breton, AB
51
Crop rotation
Izaurralde et al.
2001
Fertilizer addition
Manure addition
Indianhead, SK
30
Crop rotation
Campbell and Zentner
1997
Lamberton, MN
22
Fertilizer addition
Darmody and Peck
1997
Lancaster2, PA
14
Tillage
Karlen et al.
1994
Lancaster1, PA
14
Residue management
Vanotti et al.
1997
Mandan, ND
12
Tillage
Halvorson et al.
2002
Fertilizer addition
Melfort, SK
30
Crop rotation
Campbell et al.
1991c
Morrow, IL
27
Crop rotation
Darmody and Peck
1997
Pendleton, OR
17
Tillage
Rasmussen and Albrecht
1997
Sanborn, MO
CT 96
Tillage
Buyanovsky et al.
1998
NT 25
Manure addition
Sterling, CO
12
Crop rotation
Sherrod et al.
2003
Topographic location
Stratton, CO
12
Crop rotation
Sherrod et al.
2003
Topographic location
Swift Current, SK
13
Crop rotation
Campbell et al.
1999
Fertilizer addition
Walsh, CO
12
Crop rotation
Sherrod et al.
2003
Topographic location
Conventional tillage = CT and no-tillage = NT. Equations are based on IPCC Guidelines (
2006
)
26
Biogeochemistry (2007) 86:19–31
123
Page 9
found no significant relationship, however, between
decomposition (
k
calculated using the linear model
fit) and C input level (
I
) (data not shown). Although
there is great variability in the data, when the three
models were tested against all the sites combined, the
C saturation model had greater support (
D
i
= 0) in the
data than either the linear (
D
i
= 8.78) or the mixed
model (
D
i
= 6.3) (Fig.
4
and Table
3
). Combining
Akaike weights (
w
i
) as an estimation of probability,
that there is a 99% probability either the C saturation
or mixed model is the best approximation of these
data.
Discussion
Of our three hypotheses of SOC accumulation: no
saturation limit (i.e., linear), whole-soil C saturation
(i.e., C saturation model), and soil C saturation of a
stabilized C pool, but not the whole soil (i.e., mixed
model), the C saturation model best fit the combined
site data, supporting the hypothesis that whole soil C
accumulation is limited with respect to C input level.
Fig. 3
Linear, C saturation, and mixed model fits of soil organic C
content (Mg C ha
1
) as a function of C input levels (Mg C ha
1
year
1
) in the manure plots at Sanborn in no- (NT) and conventional-
tillage (CT) treatments (25 and 96 years, respectively)
Table 3
Model fit statistics of the linear model (no saturation), whole-soil C saturation model (CSAT) and the two-pool mixed
model (C saturation of a single C pool, but not the whole soil)
Site
n
AIC
AICc
D
i
w
i
linear
CSAT
Mixed
linear
CSAT
Mixed
linear
CSAT
Mixed
linear
CSAT
Mixed
Breton, AB
6
31.3
32.8
33.7
43.3
44.8
93.7
0.0
1.5
50.4
0.68
0.32
0.00
Indianhead, SK
7
29.2
30.2
29.9
37.2
38.2
92.0
0.0
1.0
54.8
0.63
0.37
0.00
Lamberton, MN
4
23.6
23.4
27.4
47.6
47.4
87.4
0.1
0.0
40.0
0.48
0.52
0.00
Lancaster2, PA
4
26.6
29.5
30.0
50.6
53.5
90.0
0.0
2.8
39.4
0.81
0.19
0.00
Lancaster1, PA
5
34.0
34.3
38.3
58.0
58.3
98.3
0.0
0.0
40.0
0.50
0.50
0.00
Mandan, NE
17
74.7
75.5
78.2
76.5
77.4
83.6
0.0
0.8
7.1
0.59
0.39
0.02
Melfort, SK
8
37.2
37.2
41.1
43.2
43.2
71.2
0.2
0.0
28.0
0.47
0.53
0.00
Morrow, IL
Corn
4
28.0
29.0
31.2
52.0
53.0
71.2
0.0
1.0
39.5
0.62
0.38
0.00
Corn–soybean
4
27.3
29.1
13.2
51.3
53.1
91.6
0.0
1.7
38.7
0.70
0.30
0.00
Corn–oat–hay
4
26.1
27.5
27.5
50.1
51.5
90.1
0.0
1.5
39.1
0.67
0.33
0.00
Pendleton, OR
4
9.4
15.5
7.5
33.4
39.5
89.2
0.0
6.1
46.7
0.95
0.05
0.00
Sanborn, MO
Conventional-till
6
34.8
38.8
33.8
46.8
50.8
80.1
0.0
3.9
46.9
0.88
0.12
0.00
No-till
5
32.7
29.6
22.7
56.7
53.6
93.7
14.9
0.0
29.0
0.00
1.00
0.00
Sterling, CO
12
60.3
62.8
62.1
63.3
65.8
82.5
0.0
2.6
9.2
0.78
0.22
0.01
Stratton, CO
12
66.6
65.0
69.0
69.6
68.0
72.5
1.5
0.0
10.9
0.32
0.68
0.00
Swift Current, SK
7
33.6
34.4
36.2
41.6
42.4
78.9
0.0
0.8
55.3
0.59
0.41
0.00
Walsh, CO
10
59.8
60.5
64.5
63.8
64.5
96.9
0.0
0.7
15.8
0.59
0.41
0.00
Combined Sites
119
1057.3
1048.5
1052.5
1057.5
1048.7
1055.0
8.8
0.0
6.3
0.01
0.95
0.04
AIC = Akaike Information Criterion, AICc = Akaike Information Criterion corrected for small sample size,
D
i
= AIC
ci
-AIC
c min
,
and
w
i
is the relative weight given each model based on AICc
Biogeochemistry (2007) 86:19–31
27
123
Page 10
This corresponds to the 11 site analysis of Six et al.
(
2002
) who found an asymptotic model explained
more variability than a linear model. C saturation of a
whole soil, presumably including a non-protected
pool, suggests that even relatively labile soil C
approaches a maximum level.
This best fit of the whole soil C saturation model is
only corroborated by the single C saturation best
model fit in the individual site data of Sanborn.
Namely, the NT treatment at Sanborn (including
grass cover crops) had substantial support for the C
saturation model. However, the penalty of adding
parameters to the model is illustrated by the good fit
of the mixed model’s AIC value in both tillage
treatments, but lack of substantiation when compared
by AIC
c
to the linear and C saturation models
(Fig.
3
).
The observed best linear model fits as well as the
lack of model differentiation may be due to the small
sample size within a site (
n
of four input levels in six
sites). The Akaike value for small sample sizes
(AIC
c
), greatly penalizes models with both small
sample size and a larger number of parameters. The
additional parameter in the mixed compared to the
linear and C saturation models greatly increased the
AIC
c
value and subsequently decreased support for
the model given the small amount of data.
According to the C saturation concept, an asymp-
totic relationship would better fit the data than the
linear model, but if C input levels are low, the
asymptotic trend in SOC accumulation will not be
evident. The conjecture that C input levels were too
small to exhibit C saturation dynamics within a given
site is supported by three of the four linear best-fit
models (Lancaster, Pendleton, and Sterling), where
inputs were less than 3.5 Mg C ha
1
. Furthermore,
smaller sections of an asymptotic curve can appear
linear in the range being observed. Within each site, a
small range of C input levels will not necessarily
capture the full range of linear to asymptotic behav-
iors expected from a soil subject to C saturation. In
our data set, differences between the highest and
lowest input levels were <2 Mg C ha
1
at eight sites.
Soil C saturation versus effective C stabilization
capacity
Evidence of C saturation has been suggested using
data from long-term agroecosystem experiments that
show little response in SOC accumulation to increas-
ing C input level (e.g. Campbell et al.
1991a
; Solberg
et al.
1997
). Data from the Sanborn experiment
suggest that saturation behavior does occur, but that
tillage influences the level of effective soil C
stabilization that can be attained (Fig.
3
). According
to the original C saturation concept, each soil has a
single, unique C saturation level dictated by, for
example, textural and mineralogical properties. How-
ever, the conventional (CT) and no-tillage (NT)
treatments imposed at Sanborn fit two distinct curves.
How can the same soil appear to be approaching two
apparently distinct C stabilization levels with increas-
ing C input level? The C saturation model in Eq. 5
shows that the SOC content (
C
t
) is dependent on both
C input level (
I
) and decay constant
k
. Within a site,
k
is influenced by micro-environmental and disturbance
factors such as tillage-induced changes in porosity,
water retention, heat flux, etc. The factor
k
alters the
slope of the SOC and C input level relationship in the
models. Factors that influence decomposition rate
thus also influence SOC storage and its relationship to
C input level at steady-state. Consequently, a soil
under a management regime with an increased
inherent decomposition rate (e.g., CT) may therefore
show a different asymptotic SOC response to C input
levels at steady-state (CT curve in Fig.
5
). At the
greater addition levels, the soil may appear to be
approaching SOC saturation due to little or no SOC
accumulation as C input levels are increased further
(Fig.
5
). However, a change in management (e.g.,
Fig. 4
Soil organic C content (Mg C ha
1
) expressed as a
function of C input levels (Mg C ha
1
year
1
) for the 14 long-
term agroecosystem experiments reported in Table 1
28
Biogeochemistry (2007) 86:19–31
123
Page 11
reduction or elimination of tillage) can decrease
decomposition and thereby increase steady-state SOC
content over the same range of C input levels. We
propose the term ‘‘effective stabilization capacity’’ to
denote these asymptotic relationships between SOC
content and C inputs at levels smaller than the soil C
saturation level, due to factors other than the
physicochemical properties of the soil. If disturbance
dominates SOC content such as in tilled agroecosys-
tems, a soil cannot achieve the saturation level, but
could reach an effective stabilization capacity com-
mensurate with the input level. Although these soils
are not approaching C saturation level, the asymptotic
relationship between C input level and SOC content
in these soils is indicative of C saturation dynamics.
The theoretical distinction between effective sta-
bilization capacity and C saturation level explains
why, over similar ranges of C additions, the different
treatments established on the same Sanborn soil can
be approaching two asymptotes even though they
have the same theoretical C saturation level. This also
implies that none of the soils included in our present
analyses are approaching their absolute saturation
level, but rather are approaching their effective
stabilization capacity because of tillage-induced
disturbances.
Summary
Soils that show no increase in SOC stock with
increasing C input levels as well as high C content
soils having decreased C stabilization efficiency
suggest an upper limit, or saturation limit to whole-
soil C. This hypothesis is contrary to the models that
assume linearity between C input level and C stocks
at steady-state. We used hypothesis-based model
testing to assess the relative support in long-term
agroecosystem data for C saturating (asymptotic)
versus non-saturating (linear) behavior between C
input level and SOC content at steady state. The C
saturation model was the best approximation of the
data pooled across all sites, suggesting that across a
wide range of C input levels, C stabilization
efficiency decreased in soils with high SOC content.
Given our data, there was less than 1% ‘‘probability’’
that the linear model was the best. However, within
individual sites, only Sanborn showed a C saturation
best-fit, whereas four sites had a linear model best-fit.
All other sites had both a small range in C input
levels and a small sample size, which greatly
penalized AIC
c
support for the model given the small
amount of data. These results underscore a lack of
range in C input level as well as a general scarcity of
data with which to explicitly test these hypotheses.
The fact that the C saturation model fits the pooled
site data suggests that not only the silt + clay pool
saturates with respect to C, but other, less-protected C
pools (i.e. the non-protected pool) do as well.
However, we do suggest, based on data from
Sanborn, that agroecosystems under disturbance
may never approach an absolute C saturation level,
due to the effects of tillage disturbance accelerating
SOC decomposition although within treatments,
asymptotic SOC dynamics are observed. We propose
the term effective stabilization capacity, which
defines the maximum C sequestration possible with
increasing C input level under a particular manage-
ment scenario.
The true soil C saturation level may be of small
practical importance, as large organic C inputs must
be maintained over long time periods to sequester
large quantities of C. Of more practical interest is the
behavior of soils as they approach their effective
stabilization capacity as well as the influence of C
saturation deficit on the efficiency of SOC accumu-
lation in non-saturated soils. Although current
n
o
i
t
a
z
il
i
b
a
t
s
e
v
i
t
c
e
f
f
E
T
C
-
y
t
i
c
a
p
a
c
SOC at
steady-state
e
t
a
t
s
-
y
d
a
e
t
s
t
a
s
t
u
p
n
i
C
T
N
T
C
n
o
i
t
a
z
il
i
b
a
t
s
e
v
i
t
c
e
f
f
E
T
N
-
y
t
i
c
a
p
a
c
l
e
v
e
l
n
o
i
t
a
r
u
t
a
S
+
e
v
i
t
a
N
n
o
i
t
i
d
d
a
C
Fig. 5
Soil C accumulation dynamics under theoretical
decomposition regimes produced by management scenarios.
Since no-tillage (NT) has a reduced specific decomposition rate
compare to conventional tillage (CT), steady-state SOC content
will be greater under the same C input level. Effective
stabilization capacity is the upper limit to C storage as a
function of differing specific decomposition rates (i.e., CT vs.
NT). These systems may appear to illustrate soil C saturation,
but are not considered saturated due to C decomposition
conditions dominating C stabilization. Soil C saturation is
imposed by physical and chemical properties of a soil under
conditions when C input levels are maximized and disturbance
minimized
Biogeochemistry (2007) 86:19–31
29
123
Page 12
simulation models are fairly successful in explaining
SOC accumulation in degraded agricultural soils, the
validity of these models need to be further examined
under scenarios of increasing C input levels and
increasing SOC contents, where decreasing SOC
stabilization efficiency due to saturation effects will
be manifested. However, additional research is
needed to firmly establish the validity of the satura-
tion concept and better quantify the controls on SOC
kinetics for C-rich soils.
Acknowledgements
The authors would like to thank Steve
Williams, Mark Easter, and Stephen Ogle for assistance with
long-term agroecosystem data compilation. We would also like
to thank Gabriela Bucini and Gabe Olchin for many helpful
discussions and Jim Graham for mathematical assistance. This
project was supported by the Office of Research (BER), U.S.
Department of Energy Grant No. DE-FG03-00ER62997 and
Grant No. DE-FG02-04ER63912 and by the Cooperative State
Research, Education, and Extension Service, U.S. Department
of Agriculture, under Agreement No. 2001-38700-11092.
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