Models of soil organic carbon (SOC) storage and turnover can be useful tools to analyse the effects of soil and crop management practices and climate
change on soil organic carbon stocks. The aggregated structure of soil is
known to protect SOC from decomposition and, thus, influence the potential
for long-term sequestration. In turn, the turnover and storage of SOC
affects soil aggregation, physical and hydraulic properties and the
productive capacity of soil. These two-way interactions have not yet been
explicitly considered in modelling approaches. In this study, we present and describe a new model of the dynamic feedbacks between soil organic
matter (SOM) storage and soil physical properties (porosity, pore size distribution, bulk density and layer thickness). A sensitivity analysis was first performed to understand the behaviour of the model. The identifiability of model parameters was then
investigated by calibrating the model against a synthetic data set. This
analysis revealed that it would not be possible to unequivocally estimate
all of the model parameters from the kind of data usually available in field
trials. Based on this information, the model was tested against measurements
of bulk density, SOC concentration and limited data on soil water
retention and soil surface elevation made during 63 years in a field trial
located near Uppsala (Sweden) in three treatments with different organic matter (OM) inputs
(bare fallow, animal and green manure). The model was able to accurately
reproduce the changes in SOC, soil bulk density and surface elevation
observed in the field as well as soil water retention curves measured at the
end of the experimental period in 2019 in two of the treatments.
Treatment-specific variations in SOC dynamics caused by differences in OM
input quality could be simulated very well by modifying the value for the OM
retention coefficient ε (0.37 for animal manure and 0.14 for
green manure). The model approach presented here may prove useful for
management purposes, for example, in an analysis of carbon sequestration or
soil degradation under land use and climate change.
Introduction
As a consequence of intensive cultivation, most agricultural soils have lost
ca. 25 %–75 % of their antecedent store of SOC (Lal, 2013; Sanderman et
al., 2017). Apart from contributing to the increase in atmospheric CO2,
this has also degraded the inherent physical quality and productivity of
soil (e.g. Lal, 2007; Rickson et al., 2015; Henryson et al., 2018). This is
because many important soil physical and hydraulic (e.g. water retention and
hydraulic conductivity) properties are strongly influenced by soil organic
matter (SOM). For example, SOM increases porosity and reduces soil bulk
density (e.g. Haynes and Naidu, 1998; Ruehlmann and Körschens, 2009;
Jarvis et al., 2017). This is partly because the density of organic matter
is less than that of soil minerals, but more importantly, it is a
consequence of the aggregated soil structure induced by the microbial
decomposition of fresh organic matter (Tisdall and Oades, 1982; Young and
Crawford, 2004; Cosentino et al., 2006; Feeney et al., 2006; Bucka et al.,
2019). Changes in the SOM content may also affect the pore size
distribution, although the magnitude of these effects across different
ranges of pore diameter is still a matter of some controversy (e.g. Hudson,
1994; Rawls et al., 2003; Loveland and Webb, 2003; Minasny and McBratney
2018; Libohova et al., 2018).
The relationship between SOM and soil pore space properties can be
characterized as a dynamic two-way interaction. This is because, in addition
to the effects of SOM on soil pore size distribution and porosity,
decomposition rates of SOM are reduced within microporous regions of soil
that are poorly aerated and where the carbon is physically much less
accessible to microorganisms (e.g. Ekschmitt et al., 2008; Dungait et al.,
2012; Lehmann and Kleber, 2015). Whereas sorption interactions with mineral
surfaces are probably the dominant mechanisms protecting SOM from
decomposition in coarse-textured soils, the additional physical protection
afforded by microporous regions of the soil may lead to an enhanced
long-term storage of SOM in structured fine-textured soils (e.g. Hassink et
al., 1993; Chevallier et al., 2004; Souza et al., 2017; Dignac et al.,
2017). Thus, the turnover of both particulate and soluble SOM has been shown
to depend on its location in soil pore networks of different diameters and
connectivity and with contrasting microbial communities (e.g. Strong et al.,
2004; Ruamps et al., 2011; Nunan et al., 2017). Recent studies using novel
X-ray imaging techniques have also provided additional insights into how the
soil pore space architecture regulates the physical protection of SOM in
structured soil (Kravchenko and Guber, 2017). For example, Kravchenko et al. (2015) showed that the decomposition rates of intra-aggregate particulate
SOM were three to 15 times faster in the presence of connected networks of
aerated soil pores >13µm in diameter than in the absence
of such pores. Toosi et al. (2017) showed that plant residues decomposed
more slowly in soil microcosms dominated by pores 5–10 µm in diameter
than in those containing a significant proportion of pores >30µm in diameter. Quigley et al. (2018) showed that pores 40–90 µm
in size were associated with a fast influx of fresh carbon, followed by its
rapid decomposition, whereas soil pores <40µm in diameter
were associated with reduced rates of carbon decomposition. From the
foregoing, it follows that the turnover of SOM will be significantly
affected by any physical or biological mixing process which transfers SOM
between different pore regions in soil. For example, soil tillage may
promote decomposition by exposing SOM that was previously effectively
protected from microbial attack within microporous regions of the soil (e.g.
Balesdent et al., 2000; Chevallier et al., 2004). Physical protection of SOM
is also affected by the mixing resulting from the ingestion and casting of
soil by earthworms (e.g. Martin, 1991; Görres et al. 2001; Angst et al.,
2017).
Some widely used models of SOM turnover and storage attempt to implicitly
account for the effects of chemical and physical protection by introducing a
stable or inert pool (e.g. Falloon and Smith, 2000; Barré et al., 2010).
Other models have also been proposed that explicitly predict the effects of
soil structure on SOM storage and turnover by making use of the concept of
soil micro- and macro-aggregates (e.g. Stamati et al., 2013; Segoli et al.,
2013). An alternative approach would be to define soil structure in terms of
the soil pore space. The advantage of this is that it allows a
straightforward coupling to models of flow and transport processes in soil
(e.g. Young et al., 2001; Rabot et al., 2018). From a mathematical point of
view, soil structure can be concisely described by the volume and
connectivity of solids and pore space and the surface area and curvature of
their interface, all expressed as a function of pore diameter (Vogel et al.,
2010). Of these metrics, we focus here on the pore size distribution and its
integral, the total porosity, since these properties underlie widely used
soil hydrological models based on the Richards equation. Incorporating such a
pore-space-based approach to the interactions between SOM and soil structure
into a soil–crop model would enable explicit recognition of the feedback
links that exist between SOM dynamics, soil hydrological processes and plant
growth (Henryson et al., 2018). Kuka et al. (2007) earlier proposed a
pore-based model of SOM turnover carbon turnover in pore space (CIPS), although they did not account for
any feedbacks to soil physical properties and hydraulic functions.
Here, we propose and test a new model that describes the dynamic two-way
interactions between SOM storage and turnover, soil structure and soil
physical properties. We first performed a sensitivity analysis of the
proposed model and also investigated parameter identifiability using a
synthetic data set (e.g. Luo et al., 2017). This was done because the data
usually available from field experiments for testing models of SOM storage
and turnover may be insufficient to uniquely identify the parameters of even
the simplest models (Juston et al., 2010; Luo et al., 2017). Such problems
of parameter non-identifiability or equifinality (Beven, 2006) may
introduce considerable uncertainties into model predictions under changing
agro-environmental conditions (e.g. Sierra et al., 2015; Bradford, 2016; Luo
et al., 2017). Making use of the results of this sensitivity and uncertainty
analysis, we calibrated the model against field data obtained from two
treatments (bare fallow and animal manure) at the Ultuna long-term frame trial
in Uppsala, Sweden, using measurements of the temporal changes in SOC
concentrations and bulk density and limited data on both the soil pore size
distribution derived from water retention curves and surface
elevation. As a further test, we also compared predictions of the calibrated
model with independent observations made in a green manure treatment in the
same experiment.
Schematic illustration of the conceptual model with the soil pore
space comprising macropores (A), mesopores (thin lines; B) and micropores
(C) and with two qualities of organic matter, namely particulate organic matter (POM; e.g. decaying roots; green lines; D) and microbially processed organic matter (blue circles; E), both of which are stored either in contact only with micropores (and therefore partially protected from decomposition) or in contact with mesopores.
Description of the modelConceptual model
The model describes the dynamic two-way interactions between SOM storage and
turnover and soil porosity and pore size distribution. A simple conceptual
model is adopted to capture how the soil pore space changes as a result of
changes in soil organic matter concentration (Figs. 1 and 2). A list of
all variables and their symbols can be found in Table S1 in the
Supplement. We consider that the total pore volume, Vp,
comprises the sum of a constant textural pore volume, Vtext, defined as
the minimum value of the pore volume found in a purely mineral soil matrix
without SOM (e.g. Fies and Stengel, 1981; Yoon and Gimenéz, 2012) and a
dynamic structural pore volume comprising both macropores, Vmac, and an
aggregation pore volume, Vagg, generated as a consequence of the
microbial turnover of organic matter (OM). The biological processes underlying the generation
of aggregation pore space (Dignac et al., 2017) would be difficult to model
individually in a mechanistic way, so we make no attempt to do so in our
model. Instead, in our model approach, which is based on the dynamics of
soil pore space, the term aggregation is simply defined as the additional pore
space in soil associated with the presence of organic matter. Based on
empirical knowledge, we assume a linear relationship between this
aggregation pore volume, Vagg, and the volume of soil organic matter
(e.g. Emerson and McGarry, 2003; Boivin et al., 2009; Johannes et al.,
2017). Thus, individual soil aggregates are not considered as explicit
entities in this model. In addition to classifying the soil pore space in
terms of its origin, the model also considers three pore size classes
(Figs. 1 and 2). In addition to macropores, the soil matrix porosity is
partitioned into mesopores and micropores.
Schematic illustration of pore volumes and pore classes in the
model (for explanation of symbols, see text). In this example, macroporosity
has been neglected, and the total pore space is comprised of 80 % textural pores and 20 % aggregation pores induced by soil organic matter, with a maximum micropore diameter of 10 µm.
The model currently neglects the storage of SOM in macropores because we expect that SOM, per se, would have little direct influence on the properties of soil
macropore networks (e.g. Larsbo et al., 2016; Jarvis et al., 2017), but also
because it would most likely be a minor component of the long-term SOM
balance. The pore size distribution in the soil matrix influences SOM
storage and turnover in the model in two ways. First, the mineralization
rate of SOM in microporous regions is reduced due to physical protection.
Second, the partitioning of OM inputs derived from plant roots between the
two pore classes is determined by their relative volumes in an attempt to
mimic, in a simple way, how changes in soil structure affect the spatial
distribution of root proliferation in soil. SOM is transferred between the
two pore size classes using a simple mixing concept to reflect the
homogenizing effects of soil tillage and faunal bioturbation. In this sense,
the model has some conceptual similarities to the dual-pore region models
that are commonly used to quantify the effects of soil structure on water
flow and solute transport (e.g. Larsbo et al., 2005).
Schematic diagram of the structure of the organic matter model
showing storages and flows. For explanations of the symbols, see the text in
connection with Eqs. (1) to (6).
Soil organic matter storage and turnover
Four pools of organic matter (kg OM m-2),
comprising two types (qualities) of organic matter stored in the two pore
regions of the soil matrix (Figs. 1 to 3), are considered in the model. The model tracks two pools of
young undecomposed organic matter, with one stored in parts of the soil in
contact with well-aerated mesopore networks and the other stored in
microporous soil regions (MY(mes) and MY(mic) respectively).
Similarly, the model accounts for two pools of older microbially processed
organic matter stored in the mesoporous and microporous regions of soil
respectively (MO(mes) and MO(mic)). Both types of organic matter are
transferred between the two pore regions by biophysical mixing processes
such as tillage and bioturbation. The SOM fluxes and rates of change in
storage in the four pools of organic matter in the model are given by a
modified version of the ICBM model (Andrén and Kätterer, 1997;
Wutzler and Reichstein, 2013) extended to account for organic matter storage
in two pore regions, as follows:
1dMY(mes)dt=Im+ϕmesϕmes+ϕmicIr-kYMY(mes)+TY2dMO(mes)dt=εkYMY(mes)-1-εkOMO(mes)+TO3dMY(mic)dt=ϕmicϕmes+ϕmicIr-kYFprotMY(mic)-TY4dMO(mic)dt=εkYFprotMY(mic)-1-εkOFprotMO(mic)-TO,
where φmic and φmes are micro- and mesoporosity
(m3 m-3), kY and kO are the first-order rate
constants for the decomposition of fresh and microbially processed organic
matter (yr-1), Fprot is a response factor (–) varying from zero
to unity that reduces decomposition in the micropore region to reflect a
degree of physical protection, ε is an OM retention coefficient
varying from zero to unity (–), and Ir and Imare the below-ground
(root residues and exudates) and above-ground (litter and organic amendments, e.g. manure) inputs of organic matter (kg m-2 yr-1). It can be
seen from Eqs. (1) and (3) that the model assumes that root-derived organic
matter is added to the microporous and mesoporous regions in proportion to
their volumes, while above-ground litter and organic amendments are added
solely to the mesopore region. Finally, TY and TO are source–sink terms (kg m-2 yr-1) for the exchange of organic
matter (e.g. by tillage or earthworm bioturbation) between the two pore
classes given by the following:
5TY=kmixMY(mic)-MY(mes)26TO=kmixMO(mic)-MO(mes)2,
where kmix is a rate coefficient (yr-1) determining how
much of the stored organic matter is mixed annually, varying between zero
(no mixing) and unity (complete mixing on an annual timescale). It should
be apparent from Eqs. (1) to (6) that the effects of soil structure on SOM
turnover become weaker as kmix and/or Fprot tend to unity.
Soil physical properties
The model of SOM turnover and storage described by Eqs. (1)–(6) above
considers how the soil pore space influences SOM dynamics. We now derive a
simple model of the feedback effects of SOM on porosity and pore size
distribution. Our starting point is the fundamental phase relation for the
total soil volume, Vt (m3), as follows:
Vt=Vs+Vp=Vs(o)+Vs(m)+Vp=AxsMs(o)γo+Ms(m)γm+Vp,
where Vs, Vs(o), Vs(m) and Vp are the volumes (m3) of
solids, organic matter, mineral matter and pore space, γo and
γm are the densities (kg m-3) of organic and mineral
matter, Axs is a nominal cross-sectional area in the soil (=1 m2), Ms(m) is the mass of mineral matter (kg m-2), and Ms(o) is the total mass of organic matter (kg OM m-2) given by the following:
Ms(o)=MY(mes)+MO(mes)+MY(mic)+MO(mic).
The mineral mass, Ms(m), in Eq. (7) is assumed constant and is
obtained from user-defined values of a minimum matrix porosity, φmin (m3 m-3), and thickness of the soil layer, Δzmin (m), corresponding to the theoretical minimum soil volume,
Vmin (m3), attained when Ms(o)=0, as follows:
9Ms(m)=Δzminγm1-ϕmin10Vt(min)=AxsΔzmin.
The volume of organic matter, Vs(o), and thus the total soil volume, Vt, in Eq. (7) naturally changes as the stored mass of soil organic
matter, Ms(o), changes. The total soil volume is also affected by
changes in the dynamic soil pore volume, which comprises macropores,
Vmac and aggregation pore space, Vagg, induced by microbial
activity, whereas the textural pore volume linked to soil mineral matter,
Vtext (see Fig. 2), remains constant. For the sake of simplicity, we
assume here that the soil macroporosity is also constant, such that
Vmac is maintained in proportion to the total soil volume. With these
assumptions, the total pore volume, Vp, is given by the following:
Vp=Vagg+Vtext+Vmac=AxsfaggMs(o)γo+Δzminϕmin+Δzϕmac,
where fagg is an aggregation factor (m3 pore space m-3 organic
matter) defined as the slope of the linear relationship assumed between the
volume of aggregation pore space, Vagg, and the volume of organic
matter, Vs(o), φmac is the macroporosity (m3 m-3), and Δz is the layer thickness (m). The constant volume of
textural pores, Vtext (m3), is obtained by combining Eqs. (7), (9) and (10) with Ms(o)=0.
Temporal variations in Vs(o) and Vp induce changes in the total soil volume (and therefore the soil layer thickness), porosity and bulk density.
Combining Eqs. (7), (9) and (11), gives the soil layer thickness, as follows:
Δz=VtAxs=1+faggMs(o)γo+Δzmin1-ϕmac,
and the matrix porosity, φmat (m3 m-3), total
porosity, φ (m3 m-3), and soil bulk density, γb (kg m-3), are as follows:
13ϕmat=Vagg+VtextVt=faggMs(o)γo+ΔzminϕminΔz14ϕ=Vagg+Vtext+VmacVt=ϕmat+ϕmac15γb=Ms(o)+Ms(m)Vt=Ms(o)+Δzminγm1-ϕminΔz.
It is also helpful to derive expressions for porosity and bulk density as
functions of the soil organic matter concentration, fsom (kg kg-1),
rather than of Ms(o), since fsom is more often measured in the
field. The organic matter concentration is defined as follows:
fsom=Ms(o)Ms(o)+Ms(m).
Combining Eqs. (9) and (16) gives the following:
Ms(o)=fsomΔzminγm1-ϕmin1-fsom.
Substituting Eq. (17) into Eqs. (13)–(15) leads to the following
expressions for the matrix porosity and the soil bulk density:
18ϕmat=fsomγofagg+ϕmin1-fsomγm1-ϕmin1-ϕmacfsomγo1+fagg+1-fsomγm1-ϕmin19γb=1-ϕmacfsomγo1+fagg+1-fsomγm1-ϕmin.
In the absence of other governing processes, Eqs. (14), (18) and (19) enable
the identification of the upper and lower limits of porosity and bulk density
that occur at limit SOM concentrations of zero (i.e. a purely mineral soil)
and unity (i.e. organic soils). Setting fsom to zero defines the maximum and minimum values of bulk density and porosity respectively, as follows:
20γbfsom=0=γm1-ϕmin1-ϕmac21ϕfsom=0=ϕmin+ϕmac(1-ϕmin).
Conversely, bulk density and porosity attain minimum and maximum values
respectively in an organic soil when fsom=1 kg kg-1, such that, in the following:
22γb(fsom=1)=γo1-ϕmac1+fagg23ϕ(fsom=1)=fagg1+fagg(1-ϕmac)+ϕmac.
Finally, the matrix porosity, φmat, is partitioned
between micro- and mesoporosity as follows:
24ϕmic=Vagg(mic)+Vtext(mic)Vt=faggMY(mic)+MO(mic)γo+Ftext(mic)ΔzminϕminΔz25ϕmes=ϕmat-ϕmic,
where Vagg(mic) and Vtext(mic) are the volumes (m3) of
aggregation and textural micropores respectively (see Fig. 2), and
Ftext(mic) represents the proportion (–) of the textural pore space that
comprises micropores. It should be feasible to estimate Ftext(mic) from
data on soil texture, since pore and particle size distributions are similar
in the absence of structural pores (e.g. Arya et al., 1999; Yoon and
Gimenéz, 2012; Arya and Heitman, 2015).
Equation (19) fitted to data from three Swedish field sites. Ultuna
data taken from Kirchmann et al. (1994), Gerzabek et al. (1997), Kirchmann and
Gerzabek, (1999) and Kätterer et al. (2011). Måtteby data taken from
Larsbo et al. (2016), with the soil under grass. Offer data taken from Jarvis
et al. (2017); harrowed soil had been ploughed and harrowed (samples were
taken at 2–6 cm depth) and ploughed soil was only ploughed (samples were
taken at 13–17 cm depth). Data used in this study are highlighted in red
(fallow, animal manure and green manure). Soil organic matter content was
estimated from soil organic carbon by multiplying by two (Pribyl, 2010).
Equation (19) was fitted by non-linear least-squares regression, assuming a
priori that γm=2.7, γo=1.2 g cm-3 and ømin=0.35 cm3 cm-3.
The model described by Eq. (19) was first derived by Stewart et al. (1970), albeit in a simpler form in which macroporosity is neglected and
γo and fagg are lumped into one parameter, i.e. the bulk density
of a purely organic soil given by Eq. (22) with φmac=0.
This simple model has been shown to accurately represent the observed
relationships between organic matter concentration and bulk density in
forest soils in Wales (Stewart et al., 1970; Adams, 1973) and northeastern
USA (Federer et al., 1993) and agricultural soils in Australia (Tranter et
al., 2007). More recently, this function has been incorporated into the Jena
model (Ahrens et al., 2015; Yu et al., 2020). The validity of the extended
model approach presented here, which explicitly incorporates macroporosity
and soil aggregation, is confirmed by Fig. 4, which shows that Eq. (19)
gives reasonably good fits to measurements of bulk density and organic
matter concentration made at three agricultural field sites in Sweden,
including the Ultuna frame trial.
Plots of Eq. (19) for contrasting values of the aggregation
factor, fagg, with γm=2.7 g cm-3, γo=1.2 g cm-3ømac=0.1 and
ømin=0.35 cm3 cm-3.
Figure 5 shows the relationship between bulk density and organic matter
concentration predicted by Eq. (19) for values of fagg lying between
zero and four. A comparison of the curves for values of fagg, similar to
those obtained in the model fitting to the data (ca. 2–4; see Fig. 4), with
that of fagg=0 (i.e. when no additional pore space is generated due
to the presence of organic matter) demonstrates that aggregation dominates
the effects of organic matter on soil bulk density, while the different
densities of organic and mineral matter (γo and γm) only have a minor effect. It should be noted that the composition
of OM sources may affect the extent of soil aggregation generated by
microbial activity (e.g. Bucka et al., 2019). In this respect, each of the
four OM pools could have been characterized by a different value of the
aggregation factor. However, we have assumed here that the two qualities of
organic matter modify the pore space to the same extent in both the
micropore and mesopore regions so that only a single aggregation factor,
fagg, is required in the model. As we will see later, this is because
unequivocal parameterization of a more detailed model would be difficult to
achieve given the amount and kinds of data normally available from field
experiments. Alternatively, a model of intermediate complexity can be
envisaged in which fagg would take different values in micropore and
mesopore regions. Such a model would only introduce one additional parameter
compared with the simplest case assumed here, but even this modest increase
in complexity could cause difficulties with parameter identifiability.
Soil hydraulic properties
Equations (13), (24) and (25) describe a partitioning of the matrix pore space
into two size classes as a dynamic function of soil organic matter storage.
This partitioning can also be used to estimate continuous model functions
for soil hydraulic properties (water retention and hydraulic conductivity) to
enable a straightforward coupling to hydrological models based on Richards'
equation. Most commonly used models of soil water retention employ two shape
parameters to characterize the pore size distribution. Thus, one requirement
of this approach is that one of these two parameters must be assumed to
remain constant. We illustrate this approach, taking the widely used van
Genuchten (1980) equation as an example. If residual water is negligible,
the water content θ (m3 m-3) is given by the following:
θ=ϕmat1+αψn1n-1,
where ψ (centimeters) is the soil water pressure head, and α (cm-1)
and n (–) are shape parameters that reflect the pore size distribution. We
assume that n can be held constant, since it is known to be strongly
determined by soil texture (e.g. Wösten et al., 2001; Vereecken et al.,
2010), while α is allowed to vary, as it is more influenced by the
nature of the structural pore space in soil (Assouline and Or, 2013). In this case, α (cm-1) is given by the following:
α=ϕmicϕmat-nn-1-11/nψmic/mes,
where ψmic/mes is a fixed user-defined pressure head (centimeters)
defining the size of the largest micropore in soil. This model only
considers the two pore size classes comprising matrix porosity. However, it
is possible to extend this model to account for macropores by making use of
dual-porosity concepts (Durner, 1994; Larsbo et al., 2005).
Application of the modelSensitivity analysis
We performed a Monte Carlo sensitivity analysis to better understand the
behaviour of this new model. We ran 500 simulations with parameter values
obtained by Latin hypercube sampling from uniform distributions. The
simulations were run for 2000 years to make the outputs independent of the
assumed initial conditions. Organic matter was added solely from
below-ground residues at a rate (0.02 g cm-2 yr-1) that gave a
final organic matter concentration of 0.03 kg kg-1 for the mean
simulation. The sensitivity of the model parameters was quantified by the
Spearman rank partial correlation coefficients for three target output
variables, namely the final values of bulk density, γb, soil organic
matter concentration, fsom, and the micropore fraction of the matrix
porosity, fmic (=φmic/φmat), as a measure
to characterize the soil pore size distribution (see Eq. 27). Parameter
ranges of Fprot and Ftext(mic) (0.05<Fprot<0.2; 0.5<Ftext(mic)<0.9; see Table 1) were selected
to represent a well-structured loamy to fine-textured soil, assuming a
maximum pore size of the micropores of 5 µm (i.e. ψmic/mes=-600 cm). Our analysis focuses on matrix pore space properties and SOM,
so the macroporosity was fixed at a constant value in these simulations. The
sampled ranges for the remaining model parameters shown in Table 1 were
selected to approximately match their expected variations based on previous
modelling experience.
Sampled parameter ranges and the Spearman rank partial correlation
coefficients (r) between parameters and target outputs. Values marked in
bold show a significant correlation (p<0.01). Note: fsom – soil organic matter concentration, γb – bulk density and fmic – fraction of micropores.
ParameterSampled rangePartial correlation coefficients, rfsomγbfmicFirst-order rate coefficient, ky (yr-1)0.1–1.0-0.540.37-0.10First-order rate coefficient, ko (yr-1)0.01–0.05-0.820.700.32Physical protection factor, Fprot (–)0.05–0.20-0.460.28-0.08Organic matter retention coefficient, ε (–)0.1–0.50.92-0.82-0.30Mixing coefficient, kmix (yr-1)0–0.2-0.680.50-0.60Fraction of textural micropores, Ftext(mic)(–)0.5–0.90.24-0.160.96Density of mineral matter, γm (g cm-3)2.6–2.7-0.090.370.01Density of organic matter, γo (g cm-3)1.1–1.4-0.030.33-0.01Minimum porosity, φmin (cm3 cm-3)0.3–0.40.162-0.850.02Aggregation factor, fagg (–)2–40.0-0.500.02
The partial rank correlation coefficients are shown in Table 1. Not
surprisingly, the organic matter concentration fsom was most affected by
parameters regulating SOM turnover, especially the OM retention coefficient,
ε, and the first-order rate coefficient for the
microbially processed OM pool, ko. As expected, the physical protection
factor, Fprot, was also highly significantly (and negatively) correlated
with fsom. Parameters controlling organic matter turnover also strongly
affected the simulated bulk density, γb, along with soil
physical parameters, especially the aggregation factor, fagg, and the
minimum (i.e. textural) porosity, φmin. The pore size
distribution, as expressed by the fraction of micropores, fmic, was most
sensitive to changes in the micropore fraction of the textural pore space,
Ftext(mic) (Table 1). This is encouraging because it is well known that
soil texture exerts the most important control on the pore size distribution
in soil. The fraction of micropores was also highly significantly (and
negatively) correlated with the mixing coefficient, kmix, presumably
because this mixing transferred root-derived OM from micropores to
mesopores. This is also the reason why the bulk density, γb, and
fsom are also strongly correlated with kmix (Table 1), given that OM
decomposition rates differ between the pore regions.
Parameter identifiability
The fact that model parameters are sensitive does not imply that they will
be identifiable in a calibration procedure, since their effects on the
target outputs may be correlated (e.g. Luo et al., 2017). We therefore
investigated the identifiability of the model parameters using synthetic
data generated by 50-year forward simulations of the model for two scenarios
with different OM inputs, namely a bare fallow scenario with no OM inputs and a
scenario with a constant OM input of 0.06 g cm-2 yr-1. As
initial conditions, the organic matter pools were set to values in
equilibrium with a constant OM input of 0.02 g cm-2 yr-1, giving
an initial fsom of 0.03 kg kg-1. Simulated bulk density, γb, soil organic matter concentration, fsom, and the soil
microporosity, φmic, were used as target output variables in
the calibration. The SOM concentration was assumed to have been sampled
every fifth year, while data for bulk density and microporosity were
assumed to be available only at the start of the experiment and on two
subsequent occasions (after 20 and 50 years). Errors were added to the model-simulated values for all three target output variables to represent
measurement and sampling uncertainties due to spatial variability. We
calculated these errors assuming 10 replicates per sampling occasion and
normally distributed errors with a coefficient of variation of 10 %. The
parameter values used to generate the synthetic data are listed in Table 2.
Parameter values used to generate the synthetic data and the
sampled range in the model calibration.
ParametersValue used for dataSampled rangegeneration (true value)during calibrationFirst-order rate coefficient, ky (yr-1)0.400.1–1.0First-order rate coefficient, ko (yr-1)0.020.005–0.1Mixing coefficient, kmix (yr-1)0.050–0.3Microbial efficiency, ε (–)0.30.1–0.6Physical protection factor, Fprot (–)0.30.05–1.0Fraction of textural micropores, Ftext(mic) (–)0.50.2–0.8Density of mineral matter, γm (g cm-3)2.7Density of organic matter, γo (g cm-3)1.2Minimum layer thickness, Δz(min) (centimeters)16Minimum porosity, φmin (cm3 cm-3)0.4a/ 0.41bAggregation factor, fagg (–)5.0a/ 4.92b
a Used for data generation. b Estimated by regression (Fig. 4) and fixed during calibration.
The model was calibrated against the synthetic data using the Powell
conjugate gradient method (Powell, 2009), within given parameter ranges
defined by minimum and maximum values (Table 2), and using the sum of squared
errors as the goal function. The analysis was repeated 100 times for
different initial starting values for the parameters in order to assess the
uniqueness of the optimized parameter estimates. Two relatively insensitive
parameters, γo and γm (Table 1), were assumed to be
known and fixed at their true values (Table 2). Two further parameters were
excluded from the calibration, namely the aggregation factor, fagg, and
minimum porosity, φmin. Instead, they were fixed a priori by a
non-linear least squares regression on the synthetic data generated for bulk
density and fsom using Eq. (19; with φmac=0) and
known values of γo and γm (Table 2). Optimized
parameter sets with goal function values less than 10 % larger than the
global optimum (n=36) were considered acceptable (Beven, 2006). Figure 6
shows that the best simulation with the calibrated model closely matched the
synthetic data for bulk density, SOM and microporosity. Nevertheless, only
three of the six parameters (ε, ko and Ftext(mic)) were
identifiable, with values for the 36 best parameter sets limited to narrow
ranges around the true values (Fig. 7). This was not the case for the
three remaining parameters; optimized values of kmix and ky covered
almost the whole tested range, while optimized Fprot values were
restricted to roughly half of the sampled range (Fig. 7). As can be seen
in Table 3, the mixing coefficient kmix correlated strongly with
ky, ko, Fprot and Ftext(mic) but not with ε. The strongest correlations were found between the rate constants
ky and ko (r=0.95) and ko and Fprot (r=-0.91). A
strong correlation was also found between ε, ky and ko and Fprot.
Correlation matrix for parameter estimates for the 36 best
parameter sets of 100 calibration runs against synthetic data for soil bulk
density, SOC and microporosity (Fig. 6). Values highlighted in bold show a
significant correlation (p<0.01).
Synthetic data (symbols; bars show standard deviations) for
microporosity, bulk density and soil organic matter concentration and model
simulations (lines) after calibration.
Model evaluation with data from a long-term field trialField measurements at the Ultuna frame trial
The model was tested against data from the Ultuna long-term soil organic
matter experiment in Uppsala, Sweden (59.82∘ N, 17.65∘ E; Kirchmann et al., 1994; Witter, 1996; Herrmann and Witter, 2008;
Kätterer et al., 2011). The climate is cold temperate and subhumid, with
an annual mean air temperature of 6.3 ∘C and a mean annual
precipitation of 554 mm (1981–2014). The experiment was started in 1956 at
the Swedish University of Agricultural Sciences in order to investigate the
long-term effects of mineral N fertilizers and different organic amendments
on crop yields, soil organic matter concentrations and soil physical
properties. The soil texture in the uppermost 20 cm is clay loam (37 %
clay, 41 % silt and 22 % sand).
Of the 15 treatments included in the experiment, the following three were chosen for model
testing: a bare soil treatment (bare fallow) that has received neither mineral N fertilizer nor any organic amendments since the beginning of the experiment and two other treatments receiving no mineral N fertilizer but 4 t ha-1 C as organic amendments every second year in the form of green manure and animal manure respectively. All three treatments receive P and K fertilizer (20 and 38 kg ha-1 yr-1) and are annually dug by hand,
with the organic amendments mixed into the soil to a depth of 20 cm. The
organic amendments were added irregularly at the beginning of the experiment,
i.e. in 1956, 1960 and 1963, but have since been supplied every second year.
Maize has been grown exclusively on all the cropped plots since 2000. Before
2000, the crop rotation included a sequence of barley, oats, beets (excluded
after 1966) and occasionally rape. Samples for the measurement of SOC were
taken after the harvest of the crops every second year. The three selected
treatments show contrasting temporal trends in SOC during the 63 years of
the experiment. While SOC concentrations have decreased steadily in the bare
fallow treatment, they are still increasing in the plots fertilized with
animal manure. The addition of green manure led to a slight increase in SOC
concentrations during the first 10–15 years of the experiment, followed by a
period of approximately steady-state conditions and then a slight decline in
SOC concentrations on the most recent sampling occasions. Soil bulk density
was measured occasionally, i.e. in 1956, 1975, 1991 (Kirchmann et al.,
1994), 1993 (Gerzabek et al., 1997), 1997 (Kirchmann and Gerzabek, 1999),
2009 (Kätterer et al., 2011) and in 2019 (this study). Kätterer et
al. (2011) also reported measurements of relative surface elevation in 2009,
which we utilize as additional validation data. Of the three treatments, the
bare fallow plots show the largest bulk densities and the animal manure
treatments the smallest. Information on the soil pore size distribution was
provided by the water retention curves measured on samples taken in the
uppermost 10 cm of soil on three different sampling occasions. As soil water
retention was not measured at the start of the experiment, we made use of
measurements made in 1969 (13 years later) on samples taken from just
outside the experimental plots (Wiklert et al., 1983) to initialize the
model. Soil water retention was also measured on four replicate undisturbed
core samples taken from the three treatments in 1997, 41 years after the
start of the experiment (Kirchmann and Gerzabek, 1999), and on eight
replicate samples taken in 2019, although on this occasion they were only sampled from the
animal manure and bare fallow treatments.
Cumulative frequency distributions of parameter estimates for the
36 best parameter sets of 100 calibration runs against synthetic data for
soil bulk density, SOC and microporosity. The grey lines mark the true
values used to generate the synthetic data.
Parameterization and calibration
The model was simultaneously calibrated against data from the bare fallow
and animal manure treatments using the measurements of average soil bulk
density and SOC concentrations in the uppermost 20 cm of soil and
the microporosity estimated from soil water retention curves, assuming a
value for the maximum pore diameter of micropores of 5 µm (equivalent
to a pressure head ψmic/mes of -600 cm). A factor of 0.5 (Pribyl,
2010) was used to convert simulated SOM to measured SOC concentrations. We
simulated a soil profile consisting of five soil layers, each initially 4.5 cm in thickness. The model equations were solved explicitly by Euler
integration at an annual time step. A spin-up phase of 5000 years with
constant root-derived OM input was included to initialize the four SOM pools
at a steady-state condition. During the 63-year experimental period, annual
average OM inputs from roots and above-ground crop residues were used in the
model. Following Kätterer et al. (2011), these were calculated for each
treatment from annual yield data and the crop-specific root allocation
coefficients reported by Bolinder et al. (2007). The root-derived input of
OM to the simulated soil profile was calculated from an assumed root
distribution estimated with a Michaelis–Menten-type function (Kätterer
et al., 2011) and distributed uniformly among the soil layers. The organic
amendments (8 t OM ha-1 every other year in both the animal and green
manure treatments) were assumed to be uniformly distributed within the 20 cm
depth of soil hand dug by hand. This means that some of this added OM
becomes incorporated into the subsoil below 20 cm (i.e. the depth of
digging) if soil layer thicknesses increase (and bulk density decreases)
due to an increase in SOM concentration (see Eq. 12).
Fixed parameters and range of parameter values included in the
calibration, and the final parameter estimates after calibration. The
range of the best fit parameter values for the calibration runs with goal
function values no more than 5 % larger than the value for the best
simulation (n=85) is given within parenthesis.
a Andrén and Kätterer (1997), b Kravchenko et al. (2015), c Nimmo (2013) and d Fig. 4.
Based on the results of the sensitivity analysis and model calibration
against the synthetic data, we decided to calibrate only the following four parameters,
namely the ones that we expected to be clearly identifiable: the input of
organic matter during the spin-up period, the fraction of micropores in the
textural pore region Ftext(mic), the OM retention coefficient
ε and the first-order rate coefficient for
microbially processed organic matter, ko (Table 4). Values for φmac and fagg were estimated using
Eq. (19) from non-linear regression between bulk densities and SOM
concentrations, assuming a value of φmin of 0.35 cm3 cm-3 (Nimmo, 2013), and including data from all three of the treatments
(i.e. bare fallow, animal and green manure; Fig. 4). Similarly, van
Genuchten's n was fixed to a value (=1.073) obtained from a
simultaneous fit of Eq. (26) to the water retention data measured in 2019
in the fallow and animal manure treatments. The remaining parameters were
determined a priori because they were less well identified in the calibration
against the synthetic data. Given that the micropore region comprises pores
smaller than 5 µm in diameter, we set the physical protection factor
Fprot to 0.1, a value which lies within the range observed in the
experiments described by Kravchenko et al. (2015). Following Andrén and
Kätterer (1997), we assumed ky=0.8 yr-1.
Estimating the mixing coefficient kmix is problematic because it is
highly sensitive for all target outputs (Table 1) but not identifiable by
calibration (Fig. 7). From preliminary simulations, we also concluded that
kmix must be set to a much smaller value in the spin-up period than
during the 63-year experimental period in order to avoid obtaining
unrealistically large calibrated estimates of the OM input prior to the
experiment. A smallerkmix value during the spin-up period presumably
reflects the crop rotation practised at the site prior to the experiment,
which included frequent grass leys, so that the soil was tilled less often.
For the sake of simplicity, we set kmix to zero during the spin-up period
and to 0.05 yr-1 during the experiment. This gave a calibrated value
of the OM input during the spin-up period (0.0064 g cm-2 yr-1;
Table 4) that is similar to the root OM input estimated for the green manure
and animal manure plots during the experiment (0.0061 and 0.0071 g cm-2 yr-1 respectively).
The calibration method was the same as described earlier for the synthetic
data set. The calibrated model was then applied to the green manure
treatment by running a forward simulation, using the calibrated parameter
values and the treatment-specific OM inputs. Again, a spin-up period of 5000 years was run in order to bring the SOM pools and total organic matter
concentration to an initial steady-state condition. The goodness of fit of
the model simulations was evaluated by three criteria, i.e. the Pearson
correlation coefficient r, the root mean squared error (RMSE) and the mean
absolute error (MAE; Eqs. 28 to 30). While r is a measure of the strength
of the relationship between the observations and simulations, with a value of 1 showing a perfect positive linear relationship and a value of -1 showing a
perfect negative linear relationship, RMSE and MAE measure the average
magnitude of the error between observations and simulations. Both of them
vary from zero to unity, with smaller values representing a better agreement.
However, for the RMSE the errors are squared before averaging, which gives
comparatively greater weight to larger errors.
28r=cov(y,y^)σyσy^29RMSE=1n∑i=1nei230MAE=1n∑i=1n|ei|,
where y and y^ represent the observations and simulation results
respectively, cov is the covariance, σy and σy^
are the standard deviations of y and y^, e is the model error,
i.e. y-y^, and n is the number of observations. The analyses
were carried out with R (version 3.5.1; R Core Team, 2018) using the
openxlsx (Walker, 2019) and plyr (Wickham, 2011) packages.
Goodness of fit of the model simulations to observed bulk density
and soil organic carbon concentration. Note: r – correlation coefficient, RMSE – root mean squared error and MAE – mean absolute error.
ParameterrRMSEMAECalibrationFallow Bulk density (g cm-3)-0.200.050.04Soil organic carbon (kg kg-1)0.950.00050.0004Animal manure Bulk density (g cm-3)0.990.040.04Soil organic carbon (kg kg-1)0.890.00090.0007ValidationGreen manure (ε=0.37) Bulk density (g cm-3)0.940.080.07Soil organic carbon (kg kg-1)0.040.0040.004Green manure (ε=0.14) Bulk density (g cm-3)0.980.060.05Soil organic carbon (kg kg-1)0.370.00080.0007
Observed (symbols; bars show standard deviations) and simulated
(lines) microporosity (cm3 cm-3), bulk density (g cm-3) and
soil organic carbon concentration (kg kg-1) for the fallow and animal
manure treatments.
Figure 8 and Table 5 show that the calibrated model accurately matched the
trends observed in soil organic carbon in the bare fallow and animal manure
treatments. The data suggests that the soil bulk density increased in the
bare fallow treatment during the experiment, whereas it decreased in the
animal manure treatment. These trends were also reasonably well described by
the model (Fig. 8; Table 5). As the soil organic carbon content was
accurately simulated, the somewhat poorer match sometimes found between the
model predictions of bulk density and the measurements reflects, to a large
extent, the unexplained variation in the relationship between γb
and fsom (Eq. 19). In this respect, it is likely that the
macroporosity, and therefore the bulk density, at the time of sampling in autumn may vary from year to year, depending on the way the topsoil was dug and the
soil conditions at the time of cultivation. Kätterer et al. (2011) found
that the elevation of the soil surface in the plots treated with animal
manure was 2.6 cm higher relative to the bare fallow plots in 2009. In
comparison, the model predicted a difference in the elevation of the soil
surface of 2.7 cm between the two treatments in the same year (2009). The
optimized values of the four calibrated parameters (Table 4) are very well
constrained and also appear reasonable. The calibrated value of
Ftext(mic) (i.e. the fraction of textural pores smaller than 5 µm)
was 0.85 (Table 4). Calculations with the Arya and Heitman (2015) model,
based on particle size distribution data from the site (Kirchmann et al.,
1994), give a predicted value for Ftext(mic) of 0.9, which is in
excellent agreement with the estimate from model calibration.
Observed (symbols; bars show standard deviations) and simulated
(dashed and dotted lines) soil water retention curves in the fallow and
animal manure treatments using Eqs. (26) and (27). (a) Measurements taken in 1997, and (b) the measurements taken in
2019. The measurements used as the initial condition in 1956 are also shown,
together with a fitted curve. Van Genuchten's n was fixed at 1.073 for all
water retention curves.
Figure 9 shows a comparison of the water retention curves measured in 1997
and 2019 and the corresponding model predictions using Eqs. (26) and (27),
alongside the measurements utilized as an initial condition in 1956. The
model accurately matched the data in 2019 for both treatments (Fig. 9).
However, although the shapes of the water retention curves measured in 1997
were also successfully reproduced, the measured matrix porosity differed
significantly between the treatments in 1997, and this difference could not
be matched by the model (Fig. 9). It is unclear whether this discrepancy
can be attributed solely to model error. Spatial variability in the field
may also have played a significant role, since only four replicate core
samples were taken in 1997. Regardless of the reason for the discrepancy,
the results suggest that it should be a reasonable assumption to hold the
parameter n in van Genuchten's (1980) equation constant in dynamic models of
soil matrix hydraulic properties. Figure 9 shows that whilst n is fixed, van
Genuchten's (1980) α increased in the manure
treatment, reflecting an improvement in structure, and decreased in the bare
fallow, indicating structural degradation. The soil microporosity apparently
decreased during the experiment in both treatments, while the mesoporosity
remained largely unchanged in the fallow plots and only increased slightly
in the manured treatment (Figs. 8 and 9). The model simulations suggest
some possible explanations for these results, which are surprising at first. In the case of the bare fallow plots with no OM input, we might
expect physical protection to lead to a slower decline in the organic matter
stock in the micropore region compared with the mesopore region (and thus an
increase in the proportion of micropores). However, the bare fallow soil was
tilled every year. The simulation results (Fig. 10) suggest that this
leads to a homogenization of the OM distribution in soil, with a net
transfer of OM from the micropore region to the mesopores at a rate that
exceeds the difference in decomposition rates between the pore regions. In
the case of the manured plots, the stock of OM in the micropore region
decreases in the model as a result of the significant increase in tillage
intensity at the onset of the experiment, despite the large increase in the
OM input as the manure is input solely to the mesopore region (Fig. 10).
Furthermore, a successively smaller proportion of the root OM is added to
the micropores as the aggregation mesopore volume increases (Eq. 3).
Simulated temporal development of young undecomposed (Y) and
older microbially processed (O) organic matter (kg m-2) stored in meso-
and microporous regions in the bare fallow (a) and manure (b) treatment.
Observed (symbols; bars show standard deviations) and simulated
(lines) microporosity (cm3 cm-3), bulk density (g cm-3) and
soil organic carbon concentration (kg kg-1) for the green manure
treatment for two different values of the OM retention coefficient,
ε.
Model testing using data from the green manure treatment
The model predictions for the green manure treatment tended to underestimate
bulk density, whilst clearly overestimating SOC concentrations (Fig. 11).
The model predicted a steady increase in SOC throughout the experiment,
which was not observed in the field. As the animal and green manure
treatments only differ slightly in the amount of C provided by roots and
straw, the significant difference in SOC concentrations must be related to
differences in the quality of the organic amendments. We therefore
recalibrated ε using the data from the green manure treatment,
keeping all other parameters fixed at the values obtained from the
calibration against the other two treatments. The resulting calibrated value
for ε was 0.14, which significantly improved the fit of the
model to the data for both SOC and bulk density (Fig. 11; Table 5). The
difference in the elevation of the soil surface between the green manure
plots and the bare fallow plots measured by Kätterer et al. (2011) in
2009 (=1.4 cm) was also accurately simulated by the model (=1.6 cm).
The smaller value of ε in the green manure treatment implies
that less of the supplied OM is retained in the soil compared to the organic
matter added to the soil as animal manure. This finding is supported by
several previous studies that have analysed data from this experiment with
different approaches (e.g. Witter, 1996; Paustian et al., 1992; Hyvönen
et al., 1996; Andrén and Kätterer, 1997; Herrmann, 2003). Many
studies have shown that the quantity and quality of organic amendments can
strongly affect SOC turnover rates by altering the biomass, composition and
activity of the soil microbial community (e.g. Blagodatskaya and Kuzyakov,
2008; Dignac et al., 2017). Herrmann et al. (2014) showed that, despite
similar levels of microbial activity measured by heat dissipation, the soil
from the green manure treatment had a significantly larger CO2
production for the same energy input than the soil from the plots receiving
animal manure.
Discussion and conclusions
We presented a new model that describes, for the first time, the dynamic
two-way interactions between SOM, soil pore space structure and soil
physical properties. In this study, we tested the model against data taken
from plots with contrasting OM inputs in a long-term field trial in Ultuna,
Sweden. In a bare fallow treatment, the bulk density increased and soil
profile thickness decreased as the SOC concentration decreased during the
experiment, while the opposite trends were observed in plots amended with
animal manure. Small changes were also detected during the experiment in the
matrix pore size distribution (i.e. the shape of soil water retention
curve). Our relatively simple model concept to couple organic matter storage and turnover with soil pore space structure was able to satisfactorily
simulate these changes in SOC stocks and soil properties resulting from the
contrasting OM inputs.
A form of the simple two-pool ICBM model (Wutzler and Reichstein, 2013) is
obtained if the interactions between organic matter and soil structure are
removed from our model. Successful applications of the ICBM model to the
data from the Ultuna frame trial have already been published by Juston et
al. (2010), for data available until 2007, and by Poeplau et al. (2015), for
data until 2013. Although we do not show the results here, ICBM matches the
SOC data until 2019 for the manure and bare fallow treatments almost as well as the model described here (RMSE values are slightly larger than those
shown in Table 5), albeit with different parameter values. The retention
efficiency ε is similar (0.35 vs. 0.37) but ko is much
smaller (0.015 vs. 0.036 yr-1), since physical protection is not
modelled explicitly. However, in principle, for the same parameterization,
the predictions of our model must diverge from those of ICBM for treatments
with contrasting organic matter input rates. This is because ICBM is
strictly a first-order kinetic model, such that steady-state soil organic
matter contents are linearly dependent on the input. In contrast, in a
similar way to earlier models based on concepts of carbon saturation (e.g.
Hassink and Whitmore, 1997; Stewart et al., 2007), the extended model
described and tested here, which explicitly incorporates two-way soil
structure–SOM interactions, does not show such a linear response. This
non-linearity of the response of steady-state OM contents to OM inputs becomes
stronger as the mixing between the pore regions becomes weaker.
Even though it may be possible to satisfactorily calibrate a simple OM model
such as ICBM to the time series of OM measurements at one particular site, a
model that explicitly incorporates soil structure–OM feedbacks has some
important advantages. For example, it potentially enables direct
(forward) simulations of the effects of soil structure and physical
protection on OM turnover in contrasting soil types (e.g. sand vs. clay)
without having to resort to recalibrating model parameters describing OM
turnover for each soil, as was done, for example, by Poeplau et al. (2015).
In our model, some of the key parameters controlling physical protection
can, in principle, be determined a priori from measurements. Thus,
ømin and fagg can be derived from paired data on soil organic matter
contents and bulk density (Eq. 19), while Ftext(mic) can be
calculated from particle size distributions (e.g. Arya and Heitman, 2015).
In principle, our model also has a broader range of potential management
applications. For example, it could be used to simulate the effects of
contrasting tillage systems or faunal bioturbation on SOM dynamics and
sequestration potential.
The model currently neglects some processes that may be important for
determining the long-term storage of organic carbon in soil under changing
environmental conditions, such as the interactions of organic carbon with
mineral phases in soil and the regulation of decomposition rates by both
abiotic factors (i.e. soil temperature and moisture) and the biomass and the
community composition and activity of microbial populations (Dignac et al.,
2017). Moreover, organic matter inputs to the macropores, either by root
ingrowth (Pankhurst et al., 2002) or the incorporation of surface litter by
earthworms (e.g. Don et al., 2008), and its subsequent turnover are not
considered in the model. Extending the model to account for these processes
would be feasible, but it would require more comprehensive data to ensure
effective and reliable results from model calibration. The model described
here could also be further developed towards a more complete coupled model
of soil structure dynamics and soil processes by accounting for the dynamic
effects of other physical (e.g. tillage and/or traffic and swelling and shrinkage) and
biological processes (e.g. root growth and faunal activity) on soil
pore space properties and OM turnover. It should also be worthwhile to
incorporate our model approach into more comprehensive models of the
soil–crop system that integrate descriptions of hydrological processes,
carbon and nutrient cycling and crop growth. Such a next-generation
soil–crop modelling tool should prove useful in supporting a wide range of
analyses related to the long-term effects of land use and climate change on
SOM dynamics, soil hydrological processes and crop production.
Data availability
The model and the data will be made available upon request.
The supplement related to this article is available online at: https://doi.org/10.5194/bg-17-5025-2020-supplement.
Author contributions
NJ set up the project and developed the model based on discussions with EC, KHEM, AMH, TKä, CC and TKe. KHEM analysed the data. DNS ran the sensitivity analysis, and KHEM ran the calibrations. NJ and KHEM wrote a first draft of the paper. CC, EC, AMH, TKe, TKä and DNS reviewed and edited the paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This work was funded by the Swedish Research Council for Sustainable
Development (Formas) as part of the “Soil structure and soil degradation: improved model tools to meet sustainable development goals under climate and land use change” project (grant no. 2018-02319).
Financial support
This research has been supported by the Swedish Research Council for Sustainable Development (Formas; grant no. 2018-02319).
Review statement
This paper was edited by Andreas Richter and reviewed by three anonymous referees.
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