Soil organic carbon (SOC) dynamics result from different interacting processes and controls on spatial scales from sub-aggregate to pedon to the whole ecosystem. These complex dynamics are translated into models as abundant degrees of freedom. This high number of not directly measurable variables and, on the other hand, very limited data at disposal result in equifinality and parameter uncertainty.

Carbon radioisotope measurements are a proxy for SOC age both at annual to decadal (bomb peak based) and centennial to millennial timescales (radio decay based), and thus can be used in addition to total organic C for constraining SOC models. By considering this additional information, uncertainties in model structure and parameters may be reduced.

To test this hypothesis we studied SOC dynamics and their defining kinetic
parameters in the Zürich Organic Fertilization Experiment (ZOFE) experiment, a > 60-year-old controlled
cropland experiment in Switzerland, by utilizing SOC and SO

The use of different model structures allowed us to explore model structural
uncertainty and the impact of

By varying the relative importance of total SOC and SO

The measurements and all model structures indicated a dramatic decline in SOC
in the ZOFE experiment after an initial land use change in 1949 from grass-
to cropland, followed by a constant but smaller decline. According to all
structures, the three treatments (control, mineral fertilizer, farmyard
manure) we considered were still far from equilibrium. The estimates of mean residence time (MRT) of the C pools defined by our models were sensitive to
the consideration of the SO

The simplest model structure performed the best according to information criteria, validating the idea that we still lack data for mechanistic SOC models. Although we could not exclude any of the considered processes possibly involved in SOC decomposition, it was not possible to discriminate their relative importance.

The dynamics of soil organic carbon (SOC) are directly linked to major soil
ecosystem services such as soil fertility, resistance to erosion, C
sequestration, and soil CO

However, the timescale of SOC decomposition, from years to millennia, makes it difficult to design experiments, and requires gathering indirect answers through analysis of monitoring programs, long-term experiments and SOC turnover models. Most of these models, for example among the most well-known RothC (Coleman et al., 1997), Century (Parton et al., 1993) and Yasso (Liski et al., 2005), are built around multiple conceptual pools decomposing with first-order kinetics. This basic structure works well to simulate decadal to centennial timescales, but shows problems with longer (when considering more protected organic matter; e.g., Trumbore and Czimczik, 2008) or shorter (when considering microbial dynamics; e.g., Schimel and Weintraub, 2003) timescales.

Formally, these models could be extended in complexity to represent more accurately all the processes involved in SOC decomposition that we are aware of. However, a purely mechanistic modeling approach often fails because the lack of data with respect to the complexity of the system limits the number of latent variables (all the variables that cannot be directly measured) that we can infer. A high system complexity, as characterized by multiple interactions between parameters, causes equifinality problems (Beven, 2006). Representing such interactions in a way that is both accurate and abstract enough to realistically consider the availability of data is termed the bias/variance dilemma (Briscoe and Feldman, 2011). This dilemma represents the most critical point in producing reliable estimates in SOC modeling.

The struggle of contemporary SOC models becomes more evident when including
SO

Methods for the inclusion of radiocarbon measurements in SOC models are
currently under active development. While most SOC models consider

Yet a few studies have considered SO

In order to consider the effect of

The three research questions driving this work are the following:

How will the inclusion of

What are the reasons for the observed discrepancy between modeled total SOC
and SO

Can we model SOC and SO

These research questions generated the following, partially concurrent,
hypotheses:

An underestimation of the age of slow C due to the presence of
recalcitrant C (e.g., black C, Leifeld, 2008) or C protected through some
other mechanisms is one possible reason for the observed discrepancy between
SOC and SO

An interaction between substrate pools is a process often neglected in C models but which can contribute the observed discrepancy. Representing this process in the model can improve model performances.

Is it possible to discriminate between the abovementioned processes?

The data utilized in this study have been collected in the ZOFE (Oberholzer et al., 2014), located in
Switzerland at the Agroscope premises in Reckenholz (Zürich), at
47

The treatments considered in this study.

The SOC data set comes from Oberholzer et al. (2014). For modeling, the
calibration error for both SOC and SO

In the SO

We took the atmospheric

The C inputs have been calculated with the C allocation coefficients proposed by Bolinder et al. (2007) and in case of potatoes by Walther et al. (1994). More details about the input calculations can be found in Oberholzer et al. (2014).

Carbon allocation coefficients may differ between treatments. The potential error introduced by the nonlinear nature of the root/shoot factor (Bond-Lamberty et al., 2002) was considered negligible in our case due to conditions being close to optimal for plant growth at our site. The control treatment still stores as much SOC as treatments with full mineral fertilization (Oberholzer et al., 2014) and it was still considered to be far from causing extreme deviations from the selected root/shoot ratio. Another source of error in our estimate is inherent to extrapolating the original root–shoot relationship (Bolinder et al., 2007) to our soil. Such a relationship was built on 168 samples reviewed from the literature of typical agricultural soils, not different from our alluvial soil, and this error should therefore be small. Another possible error comes from the lack of estimates for C in the form of root exudates.

We considered the above uncertainties for the C allocation by introducing an error factor calibrated with a uniform prior distribution between 0.8 and 1.2.

The basic model (structure I) is the ICBM model developed by Andrén and Kätterer (1997). ICBM is a minimalist model of the general SOC decomposition theory built around two SOC pools decomposing with first-order kinetics. The simplicity of the model allows for a high degree of flexibility and makes it ideal for model structure explorations, hypotheses testing, and model development.

We used the model stepwise in its recursive form, as derived by Kätterer
et al. (2004), in order to follow the highly nonlinear shape of the
atmospheric

A first modification (i.e., model structure II), already suggested by
Juston (2012), adds a static pool representing SOC cycling at extremely slow
decomposition rates. This pool is virtually inert and does not interact with
the other pools or decomposes. Since the SOC age spectrum is likely
distributed according to a logarithmic function of age (Bosatta and
Ågren, 1999), this approximation may be reasonable for very slow SOC
atoms. Equation (4) can therefore be modified by adding an “inert” pool

A second modification, i.e., model structure III, introduces a decomposing third pool instead of a
static third pool. The dynamics of the

A third modification of structure I, i.e., model structure IV, modifies the
basic set of equations with a single, aggregated term to account for the
effect of “young” substrates on microbial dynamics and therefore on
decomposition rates. We modified Eqs. (1) and (2) by adding the term

This model structure adds one more unknown parameter (Table 2). Finally, model structure II was extended by a substrate control as in structure IV to make structure V. All model structures were run in annual time steps.

Summary of the model structures tested in this study (considered here in their basic forms for total C only and for the two isotopes together).

For model structures III and IV, with a substrate interaction term, an
alternative MRT could be defined as

Each model structure was extended by running a separate system of equations
for SO

The radiocarbon decay is considered by adding the term

We did not consider a time lag between C assimilation and release into the SOC cycle because we are considering an agricultural system with annual plants. These plants have a physiological time lag of few hours (Kuzyakov and Gavrichkova, 2010) and eventual storage compounds are released at the end of the cultural cycle, which is in most cases less than 1 year. The years during rotation where leys are present are few (Oberholzer et al., 2014). With the annual resolution utilized in this study the time lag could therefore considered being negligible.

The effect of the two data streams (SOC and SO

In order to better capture the effect of adding the information contained in
the SO

Since the two data streams are not homogeneous, this weighting term is
considered as an empirical evaluation of the sensitivity of the model. It is
an effective method for assessing the relative effect of the information
from either isotope and offers more detail compared to testing only for the
two options (SOC only and SOC

A possible differential loss of SO

The parameter

In this particular case we included proxies for soil temperature and soil
moisture and we selected the two climatic functions from the CENTURY model
(Parton et al., 2001; Bauer et al., 2008), since they adapted well to the
data available for this experiment. The temperature function was adopted as
follows:

Meteorological data were obtained from the Swiss Federal Research Station for Agroecology and Agriculture Zürich-Reckenholz (FAL), located at less than 100 m from the ZOFE experiment.

In order to maintain comparability of results with the original ICBM model,

Given the close interactions between the kinetic parameters a deterministic optimization algorithm might miss possible equifinality (Beven, 2008). We therefore relied on a Metropolis–Hastings algorithm (in the implementation of JAGS (Just Another Gibbs Sampler) Plummer, 2003). The likelihood function utilized was the default one in JAGS, which according to a formal Bayesian statistical framework utilizes a Gaussian shape.

We assumed that the parameters defining the SOC pools (namely,

Priors for the rates (

Priors for the initial distribution of the SOC pools were considered
uniformly distributed between 0 and 100 % of initial SOC but constrained
by the mass balance, i.e., the sum of SOC mass in all pools should add up to
100 % of initial SOC. Priors for the initial distribution of the pools
for SO

Following the same principle of simplicity maximization on which we built
the whole study, we selected the Akaike information criterion (

Average of the

The use of the

The choice of the

In general the addition of the SO

The introduction of the SO

Average of the RMSE among all the three treatments for the five
model structures with the variation of the relative weight of SO

Overall, the “best” model structure indicated by the

The average RMSE was similar for all model structures, but there were small differences. Unexpectedly, structure III did not present the lowest average RMSE among all structures (Fig. 2), although it has the highest number of parameters. Structure II was the one that performed the best in terms of RMSE.

We also compared these five structures through DIC, which was 591.9 for
structure I, 579.9 for structure II, 593.8 for structure III, 603.1 for
structure IV, and 591.9 for structure V. Also the DIC indicated better
performances of simpler structures and it indicated structure II as the best
model. However, it did not indicate any difference between the second and
third best choice (structure I and V) and differences were not as evident as
when using

The MRT (Fig. 3) of the old pool, according to structures I and II, were
95.09

MRT of the young pool

Effect of the SO

Effect of the SO

The estimated size of the initial pools did not vary much among the selected
model structures (Fig. 9). The amount of carbon in the young pool ranged from
15.37

Effect of the SO

Simulation of SOC pools

Simulation of SOC pools

All the tested model structures, and within all the tested values of the weighting parameter, inferred a change right after the land use change in the ZOFE trial. In all treatments without amendments, the young pool decreased rapidly within a few years after conversion from grassland to FYM and mineral fertilization. In structures I this decrease was more dramatic, while more complex models (II, III, IV, and V) could describe the observed trends as more gradual thanks to the additional number of parameters.

During calibration, all model structures seemed to react to the SO

Probability distribution of the initial size of the C pools
(Y: Young, O: Old, R: Recalcitrant) in structure I

None of our tested model structures could represent consistently both data
streams at the same time. For the SO

The use of the radiocarbon bomb peak to constrain SOC turnover models,
although in use for decades (Trumbore, 1989), has often raised similar
controversies. The implicit inclusion of

One of the possible reasons for the recorded discrepancies in the estimates
from models conditioned with and without SO

In our study we focused on the optimal utilization of the information
contained in SO

A generalizable and detailed mechanistic understanding of SOC stabilization is not yet available, and SOC models are still facing a deep parametrical and structural uncertainty. According to some authors (e.g., Beven, 2002) such uncertainty is inherent to the nature of ecosystem modeling, and needs to be accepted and considered in developing new methodologies. In this perspective we adopted a pragmatic approach to determine the optimal weighting factor, which turned out to be a crucial step with a large impact on modeling results.

All the model structures indicated a rapid decrease in the young pool following the conversion from grassland to cropland. This means that the annual inputs under the new management were too small to replenish the C in the former young pool while most of the material is either decomposed or humified in the old pool. This is not unlikely since also by-products, like straw, are removed, and the inputs from the cropland management are greatly reduced compared to a low-intensity grassland (Rumpel et al., 2015), where a lot of the net primary productivity is either retained or returned in form of excrements. Furthermore, the disruption of the soil structure that formed under permanent grassland caused by the conversion may have released and subsequently mineralized largely undecomposed organic matter, such as particle or light fractions previously protected inside aggregates (Six and Paustian, 2014). After this re-equilibration of the young pool, the slower but constant decrease in the total SOC was explained by all the models with a slow but constant decrease in the old pool, missing the inputs previously received from a bigger young pool. All our model structures indicated that the considered treatments in the ZOFE experiment are all still far from a new SOC equilibrium.

The error in the simulated SO

Another possible reason for the error in model predictions might be the
nature of the error in the SO

Our results for the kinetic parameters are in general in the same order of
magnitude as what was reported in the literature (Andrén and
Kätterer, 1997), although the introduction of the SO

The estimation of MRT strongly depends on all the assumptions in the model structure, and the high uncertainty around what might be the “best” structure is pointed out by the disagreement of the different criteria used for selection, which highlights the fact that there is no true model (or that “all models are wrong”, Box, 1976). The combination of several structures, although difficult to perform in practice (Refsgaard et al., 2006), might therefore represent a reasonable option and deserves further attention.

The MRT estimates (Fig. 3) depend on the introduction of a substrate control
term in the model structure, but once this was accounted for it seemed quite
robust. We must consider here that the introduction of a substrate control
term as described by Eq. (8) modifies the definition of the decomposition
constants, and therefore the MRT calculated accordingly. When introducing
also the term

Model initialization seemed quite robust, with values substantially not differing between models with the same number of pools.

As suggested by the multiple structures evaluated in this study, the conceptual nature of SOC pools makes their definition volatile. Each pool is a theoretical construction defined specifically by assumptions at the level of model structure as well as model calibration.

Some attempts have been made to reconcile a definition of C pools with real measurements. For example the well-established forest model Yasso (Liski et al., 2005) bases its calibration on data from chemical litter fractionation, which gives the initialization values for the different C pools. But the fractionation behind Yasso might seem questionable in agricultural soils where inputs are often homogenized with the mineral fraction and less, if at all, identifiable. In more homogenized mineral topsoils the main obstacle to this approach is that available fractionation methods do not reflect precise stabilization processes (von Lützowet al., 2007). One of the most promising recent attempts to develop a non-theoretical quantification of SOC pools in agricultural/mineral soils is the one by Zimmermann et al. (2007), which tried to develop a measurement standard for RothC (Coleman et al., 1997) pools. All these methods share in common the risk that correlations between the measurements and the theoretical pools might be strongly localized (or difficult to reproduce, Poeplau et al., 2013). This is not surprising given the complexity of SOC stabilization mechanisms (Kleber et al., 2011). Indications are that stability should be considered as an intrinsic property of the soil ecosystem (Schmidt et al., 2011) and thus local. It is therefore problematic to generalize a fractionation methodology that reflects in detail SOC stabilization processes, which would in turn define SOC pools.

Hence, we still need to aggregate the available information in a theory of SOC decomposition that is simple enough to be generalizable. This way the model structure represents the SOC decomposition processes in an aggregated (and simplified) way that is compatible with the amount of knowledge at disposal. The challenge of conciliating predictive power, and therefore practical value of our models, with accuracy is the formulation of the bias/variance trade-off as found in modern soil science.

As suggested from our data set, which although not perfect is already relatively rich in information and not far from the best possible conditions available for soil carbon modeling, the information available for inverse modeling discrimination still seems insufficient to validate models that are too mechanistic. A possible improvement could be the inclusion of data from deep soil layers, and the extension of the model to represent spatial processes. In general, we would expect a better resolving power of the data by adding new constrains to the model, although this would be also dependent on the additional assumptions needed to include another dimension. Testing this approach was however out of the scope of the present study, but foreseeable in the near future.

The SOC in the ZOFE experiment underwent a profound decrease after the initial land use change from grass- to cropland. This decrease was described in the first years by all our model structures as a fast re-equilibration of the young pool, which decreased rapidly after a reduction of the inputs and/or an increased mineralization and caused in consequence a slower but constant decrease in the older pools. In the long term, treatments not receiving organic fertilization were still losing C even more than 60 years after land use change. The estimates of the MRT in the ZOFE experiment were robust once accounted for differences inherent to the model structures. Comparable model structures (in particular I, II, and III) were relatively in agreement, and the influence of the number of pools on MRT was instead quite limited.

The introduction of SO

In our data set, the best model performances were achieved by the two simpler models, pointing out that the data available do not allow for a more detailed mechanistic SOC modeling. Although processes based on interactions of part of the substrate with the decomposition kinetics might explain the observations, recalcitrance inherent to the substrate (corresponding to the adoption of a slower additional decomposing C pool) remains a valid alternative in explaining the data.

All the data on which this study is based are published in previous studies and the sources are cited in the text.