Sustained accelerated soil erosion alters key soil properties such as nutrient availability, water holding capacity, soil depth and texture, which in turn have detrimental effects on crop productivity and therefore reduce C input to soils. In this study, we applied a 1-D soil profile model that links soil organic carbon (SOC) turnover, soil erosion and biomass production. We used observational data to constrain the relationship between soil erosion and crop productivity. Assuming no change in effort, we evaluated the model performance in terms of SOC stock evolution using published observational data from 10 catchments across Europe and the USA. Model simulations showed that accounting for erosion-induced productivity decline (i) increased SOC losses by 37 % on average compared to a scenario where these effects were excluded, and (ii) improved the prediction of SOC losses when substantial soil truncation takes place. Furthermore, erosion-induced productivity decline reduced soil–atmosphere C exchanges by up to 30 % after 200 years of transient simulation. The results are thus relevant for longer-term assessments and they stress the need for integrated soil–plant models that operate at the landscape scale to better constrain the overall SOC budget.
The soil system represents one of the most important carbon (C) pools by storing around 1417 Pg C in the upper first metre. As a result, its impact on the global C cycle and climate has been widely recognized and studied (Hiederer and Köchy, 2011; Houghton, 2007; Crowther et al., 2016). The terrestrial carbon cycle is mainly driven by soil–atmosphere exchanges; vegetation takes up carbon from the atmosphere and provides input into the soil in the form of root excretions and plant residues while biologic activity and in situ mineralization release carbon from soils back to the atmosphere (Houghton, 2007).
Through vegetation disturbance and agricultural extension, human activities have had an important impact on the soil system, not only by changing the soil C cycle, but also increasing soil erosion rates by up to 2 orders of magnitudes (Vanacker et al., 2013; Gregorich et al., 1998; Montgomery, 2007). Soil erosion affects vegetation growth and biomass production by changing soil physical and chemical properties related to soil fertility such as water holding capacity, nutrient status or soil depth (Bakker et al., 2004). Effects of soil erosion on crop productivity have been intensively studied during recent decades for a wide range of pedological and climatic conditions (Kosmas et al., 2001; Bakker et al., 2004; Fenton et al., 2005; Gregorich et al., 1998). In this study, we consider that crop productivity is directly proportional to the total amount of plant tissues produced (in kilograms) per unit of area. As a result, productivity is directly related to biomass productivity. Experimental studies have indicated that for a given agricultural management practice, crop productivity tends to decrease when soil is subject to erosion (Bakker et al., 2004; den Biggelaar et al., 2003; Larney et al., 2016). In the long term, this reduction is expected to result in an additional loss of SOC due to decreasing C inputs in the soils (Gregorich et al., 1998; Doetterl et al., 2016; Kirkels et al., 2014). Although large uncertainties remain about the strength and the form of the relationship between crop productivity and soil erosion, general tendencies and underlying mechanisms have been identified through data meta-analyses (e.g. Bakker et al., 2004; Chappell et al., 2012).
In addition to change in soil C inputs, human-induced soil erosion also resulted in lateral redistribution of soil particles across the landscape and subsequent SOC transfer to the fluvial system (e.g. Van Oost et al., 2005a). Soil redistribution by erosion affects SOC dynamics through changes in physical protection as a result of aggregate structure breakdown during transport from eroding sites to deposition sites, (partial) replacement of eroded C by new photosynthates at eroding sites and burial, and enhanced preservation in sediment depositional areas (Stallard, 1998; Harden et al., 1999; Van Oost et al., 2007b; Lal, 2003; Hoffmann et al., 2009; Wang et al., 2014). Although each of these three processes is individually relatively well understood, the result of their interactions at the landscape scale is still poorly constrained (Kirkels et al., 2014). A dynamic representation of the interaction between soil erosion, crop growth and SOC turnover is needed in order to better constrain C budgets in eroding landscapes (Chappell et al., 2015; Harden et al., 1999).
In the last years, several coupled soil erosion–C turnover models have been presented: some of them are point models that operate at the soil profile scale (e.g. Billings et al., 2010; Harden et al., 1999; Manies et al., 2001). Others are spatially explicit and focus on the representation of geomorphic processes and SOC turnover in a three-dimensional context (e.g. Dialynas et al., 2016; Fiener et al., 2015; Van Oost et al., 2005a; Wilken et al., 2017). They operate at timescales from single events (e.g. tRIBS-ECO, Dialynas et al., 2016; MCST-C, Wilken et al., 2017) to annual (Van Oost et al., 2005a) to long-term landscape evolution (e.g. Vanwalleghem et al., 2013; Rosenbloom et al., 2006; Yoo et al., 2006). The point models have a detailed representation of the soil–plant system and are typically based on ecosystem models assuming first-order decay (e.g. Harden et al., 1999; Liu et al., 2003; Lugato et al., 2016). For example, the CENTURY model simulates the dynamics of carbon, nitrogen, phosphorus and sulfur for different plant–soil systems (Parton, 1996) and can be modified to represent erosion-induced C losses or gains (e.g. Harden et al., 1999; EPIC, Izaurralde et al., 2001, 2007; Farina et al., 2011). The approach adopted in these studies have two key advantages as they allow the representation of management practices and simulation of how plant-derived C inputs evolve over time with ongoing erosion. Most models were developed as short-term decision-making tools for agricultural (or grassland) management. These models have not only allowed us to predict the consequences of specific management options – they also provided insights into the geomorphic soil plant-response at different spatial scales. However, most models were applied either to reproduce the temporal evolution of soil–atmosphere C exchange of a specific study site (Manies et al., 2001; Liu et al., 2003) or at larger spatial scales (e.g. Lugato et al., 2016) but without a thorough model validation due to the lack of observational data. To our knowledge, few modelling studies addressed how erosion-induced productivity decline influences C turnover and soil–atmosphere C exchange in detail in the long term. This study proposes a step in that direction by explicitly linking crop productivity, soil properties and SOC dynamics in a soil profile model to explore the longer-term (i.e. decades to centuries) effect of soil erosion on SOC stocks and fluxes. The model accounts for vertical soil–atmosphere C exchange, lateral SOC displacement and C inputs into the soil at the profile scale. Rather than using a process-based soil–plant model, which faces issues such as parameter estimation and model structure selection (e.g. Beven, 2007), we propose a parsimonious approach where relations are implemented based on observational erosion–productivity relationships. Our objectives are (i) to evaluate the performance of a parsimonious coupled model by confronting model simulations to available data and (ii) to investigate the longer-term (i.e. centennial) effect of erosion on crop productivity and SOC dynamics at the profile scale.
To represent the effect of erosion on crop productivity, we opted for an
empirical approach based on the dataset of 24 studies compiled by Bakker et
al. (2004). This dataset is one of the most comprehensive meta-analyses
available and evaluates crop productivity response to soil erosion for a
broad set of environmental conditions, crop growth constraints, soil
conditions and experimental methodologies. This approach compares plots with
different degrees of erosion but similar characteristics in terms of
landscape position, slope and management practices. Crop productivity
relative to non-eroding conditions was reported by Bakker et al. (2004),
where a relative crop productivity of 1 indicates that there is no
erosion-induced change in crop productivity, values smaller than one
represent crop productivity losses and values larger than 1 represent crop
productivity gains. In their meta-analysis, Bakker et al. (2004) discussed
three functional forms of erosion–crop-productivity relationships (Fig. 1):
a rapid and non-linear decrease in crop productivity, a continuous and
linear decrease, and a slow and non-linear decrease (Bakker
et al., 2004). Despite the small empirical basis, the individual studies
used by Bakker et al. (2004) clearly show that local environmental
conditions can strongly affect the form of the relationship between soil
loss and crop productivity. As a result, a generally applicable response
“model” does not exist. To tackle this issue, we use a broad range of
potential trajectories that cover the scatter observed. We explore the full
range of constraint forms of soil truncation on crop productivity using the
following equation:
Based on the analysis of the Bakker et al. (2004) data,
Relative crop productivity evolution as a function of
soil truncation based on paired-plot experiments. Observations are taken
from the data meta-analysis presented by Bakker et al. (2004). Values larger than 1 indicate a gain in crop productivity and
values smaller than 1 indicate a loss of crop productivity. The three
shaded areas represent the space of the relationships investigated in our
study. Dark blue, cyan and orange shades denote the concave
relationship (
Building on existing work, we used a SOC turnover model that is coupled to a
dynamic representation of the SOC and clay profiles in response to ongoing
erosion (Fig. 2). SOC cycling was represented by a depth explicit version of
the Introductory Carbon Fluxes Model (ICBM, Andren and Katterer, 1997)
which has been implemented in coupled models (e.g. Van Oost et al., 2005a).
ICBM is a two-pool carbon model simulating SOC transfer from the plant
roots, residue and manure to a “young” C pool, transfer from the “young”
pool to an “old” C pool and C mineralization in both pools (Andren and
Katterer, 1997). The model time step is 1 year. SOC fluxes are described by
the following equations:
The humification factor is estimated as follows:
The climate factor
The model is depth-explicit and considers depth-dependent C inputs and
mineralization rates (Nadeu et al., 2015; Van Oost et al., 2005b; Wang et
al., 2014). While manure- and residue-derived C inputs only affect the
topsoil layers, the carbon input from plant roots is distributed throughout
the soil profile using the following relationship:
The turnover rates of the SOC pools as a function of depth are computed as
an exponential function:
The model starts with prescribed SOC and clay content profiles. Carbon
turnovers are coupled to the clay content profile through a depth-dependent
humification factor (Eq. 4). Crop productivity is updated each year following
Eq. (1), in relation to the cumulative soil truncation. Crop productivity
affects the SOC content by multiplying the
Schematic representation of the model. Black arrows depict processes included in published versions of the model (Nadeu et al., 2015) and red arrows represent the new processes included in this study. The humification coefficient is now updated each year according to the evolution of C input in response to soil erosion.
The soil profile has a constant thickness of 1 m and is represented by 100 layers of 1 cm, each layer being characterized by its own clay content, SOC content, C input and turnover rates. This very fine representation of the vertical soil profile and advection in response to soil erosion is required due to the sensitivity of the model to the vertical discretization as a coarse resolution typically results in substantial numerical dispersion and smoothing of the evolution of C fluxes between layers over time. Hence, to better account for time dependency of C flux evolution in response to soil erosion and changing C inputs, a very fine representation of soil layers was required. Test simulations showed that 100 layers represent a good compromise between computational efficiency and limited dispersion.
At the bottom of the profile, we assumed constant boundary conditions. Soil truncation was modelled as an upward advection of soil properties where the advection rate was proportional to the amount of soil removed by erosion at the surface. As we assumed a constant bulk density of the fine soil fraction, the amount of clay and SOC vertically transferred between layers was proportional to the amount of erosion (upward transfer). The SOC content in the profile was then updated each year in response to the vertical advection of matter, new C inputs at the surface and clay content evolution following erosion. The model tracks SOC and clay content per layer as well as the evolution of crop productivity over time.
After a model spin-up without erosion allowing the C pools to reach
equilibrium, we performed transient simulations where the soil profile was
modified by erosion. During the simulations, erosion rates are assumed to be
constant through time. We presented the results in terms of the total SOC
content evolution for the 1 m profile and the net vertical C fluxes
exchanged with the atmosphere. The annual net vertical flux of C between the
soil and the atmosphere, integrated over the 100 soil layers at a time
This study is divided into two main parts: a model evaluation in which model parametrization and runs were based on site-specific environmental characteristics and a second part addressing the long-term effect of crop productivity decline on the SOC budget. The first part is based on the environmental data and empirical results of SOC loss presented by Van Oost et al. (2007) and assesses the model performance with and without the erosion–crop-productivity link against these empirical results. The second part is a numerical exploration of the effect of the erosion–crop-productivity functional form on long-term SOC loss and cumulative vertical C fluxes, over a wide range of parameter combinations, compared to a situation without the erosion–crop-productivity link.
To explore a wide range of environmental conditions, we parametrized and
calibrated the SOC profile for 10 study sites across Europe and the US
based on the published data reported by Van Oost et al. (2007). Eight sites
were located in Europe and two sites in the US. The European sites represent
a broad range of soil and climate conditions. Belgian, English and Danish
sites were located in temperate regions and mainly varied from each other by
their erosion rates and soil properties: from loamy soils with relatively
high erosion rates in Belgium toward more clay–loam soils and slightly lower
erosion rates for the Danish and English sites (Table 1) (Quine and
Zhang, 2002; Heckrath et al., 2005). The US sites were located in Iowa and
characterized by fine-textured loamy to silty soils and a temperate
continental climate (Ritchie et al., 2007). Mediterranean sites
were characterized by a warm and dry climate, clayey soils, high erosion
rate (except for the Greek site), and similar cultivation periods (Table 1).
Based on information reported in the original studies, we tried to estimate
the local erosion–productivity relationship for each site. Clearly, the
erosion–productivity relationships are generally poorly constrained and we
therefore used a range for the
Model calibration and parametrization were done only on the parameters
describing the initial SOC profile (i.e. SOC profile for stable areas). The
parametrization procedure considered the three model parameters that control
the shape of the SOC depth profile: C inputs from crops (
We used the RRMSE metric to parametrize the SOC profiles as it ensures that both the SOC content in the topsoil and in the subsoil (i.e. the profile shape) are accurately captured by the model. This is a crucial element, as these attributes will control both the C loss intensity and timing.
Observed characteristics of the study sites used for the model evaluation. Site selection observed range of relative SOC loss and cumulative vertical fluxes are from Van Oost et al. (2007).
This part aims at comparing the model performance with and without the
erosion–productivity link in terms of SOC losses compared to results
available in the literature. We performed a model evaluation based on data
on SOC losses obtained by Van Oost et al. (2007) from 10 catchments. In
their study, data on SOC profiles at different geomorphic positions (stable,
eroding, deposition), climate parameters, soil texture, period of
cultivation and erosion rate were gathered. Based on a space for time
substitution for ca. 1400 soil profiles and the use of fallout radionuclides
as a tracer for lateral SOC loss, Van Oost et al. (2007) derived both mean
annual vertical and lateral C fluxes for the period under consideration
(i.e. 1954 to
In a second step, we ran the model presented in this study for each site
using the environmental parameters reported in Van Oost et al. (2007) and
the site-specific model parameters obtained by inverse modelling (see
Sect. 2.4). To account for the uncertainty related to the estimation of
the initial SOC profiles and site conditions, we created for each of the 10 sites a set of 1000 scenarios for which parameter values were randomly
chosen in a range around their optimal (for initial SOC status) and reported
values (for site specific conditions) in Van Oost et al. (2007). Therefore,
each of the site-specific parameter sets combines fixed values (for
temperature) and randomly generated parameter values inside a prescribed
range assuming a uniform distribution:
Measured (blue) and optimized (red) SOC profiles that were used to initialize the model.
This part aims at numerically exploring the behaviour of the model by
running long-term simulations (200 years) where we focused on the effect of
crop productivity, comparing the effect of the link and its shape, on the C
budget over longer timescales. To this end, we built two sets of 1000 scenarios in which model parameters values were randomly generated, assuming
a uniform distribution, in an extended range (see Table 3). We took the
maximum and minimum value of each parameter reported in the site
characteristics compilation of Van Oost et al. (2007) to set the limits of
these extended ranges. Selected parameters include the distribution with
depth of root density (
We performed a SOBOL procedure based on the Fourier Amplitude Sensitivity Test (FAST) to assess the contribution of each individual parameter to the global variance of the results (Cukier et al., 1973, 1975). Finally, using the set of 1000 randomly generated scenarios with variable erosion rate (analysis A), we evaluated the impact of the erosion–crop-productivity link on the SOC content and vertical fluxes after 200 years by comparing the results produced by the model in FB configuration (including the effect of erosion on productivity) and in CTL configuration (no effect of erosion on crop productivity). Note that in these long-term simulations, the reference productivity does not change as we assume constant agricultural practices. We discuss the implication of this assumption in the discussion.
In this section, we first assess the performance of the model in reproducing the observed initial SOC profiles of each site based on the calibration procedure (Fig. 3). As Fig. 3 shows, the static adjustment of parameters governing the SOC profile shape for each site resulted in a good representation of observed SOC profile. All estimated initial SOC profiles were close to the observations for each of the sites, with a RRMSE ranging between 0.01 and 0.09 (Fig. 3). In a second step, we evaluated the model presented in this study by comparing the predicted SOC losses to those reported by Van Oost et al. (2007).
RRMSE of CTL (control dataset, no effect of erosion on crop productivity assumed) and FB (feedback dataset, effect of erosion on productivity included) dataset for each location and as well as the RRMSE of each dataset, including all observations (all). RRSME is calculated over the whole 1 m profile between observed and optimized SOC profile.
Hereafter, the C loss will be reported as a fraction of the initial SOC
content. The observed relative amount of eroded SOC at the end of the
simulations varied between
Including the erosion–crop-productivity relationship (scenario FB) increased
SOC losses by 14 % on average and improved the overall accuracy, albeit
slightly, with an RRMSE of 0.27 for FB compared to 0.33 for CTL when all
sites are were considered (Table 1). The predictive power of the model was
highly site-dependent: as opposed to the results for Belgium and the USA,
the Greek and Spanish sites did not exhibit a substantial increase in SOC
losses (
Modelled against observed relative SOC losses. Colours denote the different datasets: control dataset (CTL, red) and the dataset including the effect of erosion on productivity (FB, blue). Error bars represent 1 standard deviation from the mean for both observed and modelled values.
We performed a model sensitivity analysis to explore the model behaviour.
The results of the FAST procedure are reported in Table 3. A sum of the
contribution to the global variance may exceed 1 when two or more variables
are correlated, which is the case here between erosion rate and the crop
productivity response. In analysis A (i.e. erosion is included), the
relative SOC loss was almost entirely controlled by the soil erosion rate
(70 % of the total variance) and the effect of erosion on crop
productivity (18 % of the total variance) (Table 3a). Similar
observations are valid for the cumulative vertical C fluxes, although
vertical fluxes were more sensitive to crop productivity reduction than to
the erosion rate. The factor controlling the depth attenuation of C turnover
was the third major factor influencing SOC losses and the cumulative C
fluxes, accounting for 12 % to 14 % of the variability. It should be noted
that clay content and root depth distribution only played a minor role in
our analyses. When the variability due to erosion was excluded from the
analysis (analysis B), both SOC loss and the vertical carbon fluxes were
mainly sensitive to the functional form of the link between erosion and crop
productivity (
Selected parameters, range of tested values and results of the FAST analysis. The FAST analysis results can be interpreted as the relative contribution of each parameter variability to the total variance of the selected output, i.e. the relative SOC loss compared to the initial SOC content and the cumulative vertical C fluxes at the end of the 200-year transient simulations. Table 3a represents analysis A where erosion intensity was allowed to vary while Table 3b represents analysis B where a constant erosion rate was used; “ns” stands for “non-significant”. The sum of the contribution to the global variance may exceed 1 when two or more variables are correlated.
The asterisk denotes parameters contributing to at least 20 % of the global variance.
Simulated relative SOC loss after 200 years ranged between 0.02 and 0.67 of
the initial content, depending on the erosion rate and the
erosion–productivity relationship used. In FB, the average SOC loss equalled
0.38 with a standard deviation of 0.13 (Fig. 5 and Table 4). When erosion
rates were lower than 0.5 mm yr
Although the mathematical form of the relationship between erosion and crop
productivity remains uncertain, it is worth analysing its impact on SOC
losses and cumulative vertical C fluxes. Owing to its high sensitivity to
soil erosion, the concave relationship (
The net cumulative carbon flux between the soil and the atmosphere after 200 years of transient simulations is represented in Fig. 7. Provided that C
inputs remained constant and unaffected by erosion (CTL), a higher erosion
rate resulted in an increased net C uptake into soils due to the enhanced
dynamic replacement (Fig. 6). For CTL, vertical carbon fluxes increased
almost linearly by 0.28 kg C m
Our study is based on several assumptions which are related to (i) the
modelling framework and (ii) external factors such as agricultural
practices. The first category of assumptions is mainly related to the
simplifications made in linking crop productivity to C dynamics as we
assumed a linear relationship between C inputs and crop productivity. This
relation may vary due to biological adaptation of plants to stress.
In particular, in shallow-soil environments or in a presence of a soil
horizon limiting the growth, plants tend to adapt their root morphology and
increase their root density in response to limited rooting depth, leading to
a slower decline of both C inputs and C stocks over time (Bardgett and
van der Putten, 2014; Bardgett et al., 2014; Jin et al., 2017; Kosmas et
al., 2001). This implies that our assumption about a constant root-depth
density may result in an underestimation of soil C inputs and hence an
overestimation of the C stock losses. Crop productivity reduction impacts on
SOC and vertical carbon fluxes (Fig. 5) should be carefully interpreted.
SOC content and cumulative vertical fluxes are much more sensitive to
concave (
Furthermore, in our model C enrichment and preferential detachment were set
to unity and we did not consider C leaching and bioturbation through the
profile. The first process has been recognized as an important factor when
evaluating lateral C fluxes, and particularly C export (Wilken et al.,
2017). Gerke et al. (2016) and Herbrich et al. (2017) highlighted that
environmental conditions and soil erosion had an impact on (i) tissues
growth and allocation, (ii) C leaching and, hence, on (iii) the vertical
distribution of C input in the profile. Our model does not take these
biological parameters into account as the root-depth density is kept
constant over time. Soil C leaching and bioturbation are two important
factors of SOC dynamics: Gerke et al. (2016) and Herbrich et al. (2017)
showed that eroded soils are more prone to C leaching than non-eroded soil
due to interactions between soil truncation, biomass production, soil
horizontation and porosity characteristics. These profile characteristics
affect the vertical transfer of water as well as the evapotranspiration rate,
which alter in turns C distribution and fluxes. In our simulations, the
vertical distribution of SOC is not affected by soil C leaching and
bioturbation but the measured C fluxes (
Given the relatively large uncertainty in the simulated vertical C fluxes, it can be argued that site-specific relationships are required to improve the predictive power of the model. This is particularly the case for concave relationships where our model overestimated the C loss and underestimated C uptake. Even if we treated the different forms of crop productivity responses to soil erosion as separate cases, these three relationships are not mutually exclusive under real conditions. Depending on soil erosion rates and soil properties, an eroding profile could experience different crop productivity responses over time: in the first phase, productivity may primarily respond to the alteration of topsoil properties by soil erosion. After several decades of soil erosion, soil depth limitations may exert a growing constraint on crop productivity, surpassing the initial topsoil-related constraints.
Assumptions related to external factors include those made with respect to changes in agricultural practices. To build the relationships between erosion and crop productivity, we used data derived from comparative analyses of eroding soils and their stable non-eroding counterparts (same slope position) that have received the same management and external inputs rather than manipulation experiments, which ensured some real-world relevance. On the one hand, practice evolution such as mechanization and increased usage of amendments and fertilizers may compensate for crop productivity loss as a result of continued erosion (Gregorich et al., 1998; Doetterl et al., 2016). Therefore, SOC content and crop productivity evolution may be partially decoupled whereby, without soil depth constraints, soil erosion does not substantially affect productivity. Erosion may still be an important driver for SOC losses in eroding landscapes (Meersmans et al., 2009; Bakker et al., 2007; Fenton et al., 2005). In intensively managed systems, fertilizer application compensates for erosion-induced nutrient losses. Hence, nutrient loss (i.e. topsoil limitation) may not be the most important effect of erosion, whereas rooting space and water availability are more likely to be key issues as soil depth limitation constitutes a physical limit which could not easily be overcome by agricultural practices adaptations. On the other hand, our range of functional forms allowed for a representation of a wide variety of cases. In our simulations, we did not consider the increase in productivity that did occur during the last decades. It should be noted that this study focussed on the impact of erosion, relative to non-eroding conditions (e.g. Van Oost et al., 2005). In the light of these limitations, our results on simulated C loss and soil–atmosphere fluxes could be overestimated as higher C inputs allow for higher C stocks and this would reduce C losses.
Our results showed that the erosion effect on crop productivity increased SOC losses by 3 % to 17 % relative to CTL. This relative increase depends primarily on the cumulative amount of soil truncation and the functional form of the relationship between erosion and productivity. Model evaluation indicated that our model predictions were close to the observations for sites that are characterized by relatively small soil truncation (i.e. short cultivation period or low erosion rates) (Fig. 4). FB resulted in an overall better prediction because it was able to predict the large relative SOC losses for the environments where intensive erosion took place. However, the addition of the erosion-induced productivity decline in the model led to contrasting results. On the one hand, SOC losses were higher for sites where productivity was more sensitive to erosion (concave or linear erosion–crop-productivity relationships) and FB exhibited an increase in model performances when SOC losses were important (Table 2, Fig. 4).
Comparison of the cumulative vertical C fluxes (kg C m
On the other hand, linear and convex crop productivity evolutions in
response to soil erosion had little effect on the model results (Figs. 4,
6). The differences between FB and CTL model simulations were
relatively similar except for (i) environments characterized by a concave
relationship between crop productivity and soil erosion (
The use of longer simulation periods (200 years) further exemplified the link between erosion–crop productivity SOC losses and vertical fluxes. The sensitivity analysis highlighted a strong influence of the soil erosion rate and crop productivity reduction rate, while the C profile shape (as determined by the clay content), the mineralization rate and the root depth distribution were less influential (Table 3).
Relative SOC loss and cumulative C fluxes (kg C m
When the effect of erosion on productivity is not accounted for, the SOC stock follows a non-linear evolution over time that can be divided into two phases. Given the exponential form of the SOC depth profile, a quick initial decrease in the SOC content is followed by a stabilization of SOC content to a steady-state level due to an equilibrium between C inputs, C uptake from the atmosphere, lateral C export and C mineralization (Bouchoms et al., 2017; Kuhn et al., 2009; Liu et al., 2003). Under continuous erosion, the rate of C export from a profile is decreasing over time owing to the differential SOC distribution between subsoil and topsoil (Kuhn et al., 2009; Liu et al., 2003). Hence, the fast initial decrease in the SOC stock is linked to the erosion of a SOC-rich topsoil, whereby a small sediment flux may carry a relatively large amount of SOC (Kirkels et al., 2014). In the later stages of the transient simulation, i.e. where the SOC-poor subsoil is exposed to erosion, the SOC loss is smaller for a similar amount of soil truncation (Kirkels et al., 2014), the impact of the erosion–crop-productivity effect becomes more important and drives the SOC stock decline. Depending on the erosion rate, the first phase could last for several decades before a steady state is reached. The impact of declining productivity on the SOC losses depended on the form of the response: concave or linear responses to soil erosion tended to amplify the SOC losses in the first decades while the effect of the convex relationship may initially be partially masked and become more stringent only in the later stages of the transient simulations when compared to C loss evolution without an effect of erosion on productivity.
In eroding landscapes, several studies have highlighted that a fraction of the erosional SOC loss is replaced by new photosynthates, thereby creating a local atmospheric carbon sink (Harden et al., 1999; Berhe et al., 2007; Van Oost et al., 2007). Although much smaller than the C release rate from land cover conversion or SOC lateral export, this erosion-induced atmospheric sink term operates on long timescales and can be sustained as long as (i) new C-depleted subsoil material is exposed to the surface and (ii) new C inputs, mainly from plants, are available (Doetterl et al., 2016; Wang et al., 2017; Naipal et al., 2018). Both conditions can be questioned here, particularly for landscapes having experienced intense cultivation, and hence erosion, for several centuries. The first condition requires deep soils without depth-limiting factors. The second condition requires continued C inputs via roots and plant residues.
In their meta-analysis, Bakker et al. (2004) highlighted that deeply truncated soils exhibit a large reduction in crop productivity. Our results showed that reducing C inputs in response to long-term erosion actually decreased the SOC stocks by 5 % to 67 % for the sites where intense erosion takes place (Fig. 5) and were consistent with observed SOC losses (see above and Fig. 4). As Harden et al. (1999) and Doetterl et al. (2016) reported, taking into account the erosion effect on productivity leads to a better estimation of the C budget. Hence, the dynamic replacement is likely to be overestimated when ignoring the erosion–crop-productivity relationship, particularly when considering longer timescales. Our study supports these assertions: when comparing FB and CTL, the cumulative vertical C fluxes decreased on average by 15 % to 65 % after 200 years depending on the nature of the relationship between erosion and productivity (Figs. 6 and 7). Simulations pointed out that intense sustained erosion combined with a strong reduction in soil C inputs can turn the soil into a net C source for the atmosphere when the soil C input becomes smaller than the mineralization rate due to decreasing productivity.
Based on the observations compiled in a meta-analysis, we derived a range of possible functional relationships linking soil truncation and crop productivity. We implemented the effect of soil erosion on crop productivity in a simple but depth-explicit model of SOC turnover. The integration of the erosion–productivity relationships allowed us to represent the effect of erosion on SOC evolution induced by a decrease in soil C inputs as well as from lateral SOC exports. By confronting model simulations with published, and independently derived, data on lateral SOC losses and erosion-induced soil–atmosphere exchange, our results suggest that introducing erosion constraints on soil C input improves estimates of SOC losses, compared to a model approach where the effect of erosion on productivity is not included, if (i) soil truncation is substantial and (ii) the erosion–productivity relationship is accurately representing local conditions.
A sensitivity analysis showed that the erosion rate, the form of the
erosion–productivity relation and the depth attenuation of the SOC
mineralization rate are the key factors controlling SOC losses and
soil–atmosphere C exchange. Long-term simulations showed that both SOC
content and the cumulative soil–atmosphere C exchange were largely
influenced by soil truncation and productivity decrease due to erosion. The
inclusion of the erosion effect on crop productivity in model simulations
leads to higher SOC losses (an additional SOC loss of 3 % to 17 %,
relative to simulations where no link is considered) and less C uptake on
eroding sites (
The model output data are available upon request.
SB adapted the model, produced and analysed the results, and wrote the paper. ZW developed the model and contributed to the data interpretation. KVO and VV helped and advised throughout the process of research and reviewed and revised the paper.
The authors declare that they have no conflict of interest.
This paper was edited by Peter Fiener and reviewed by two anonymous referees.