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Published in Soil Sci. Soc. Am. J. 67:1477-1486 (2003).
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

DIVISION S-5—PEDOLOGY

Spatio-Temporal Simulation of the Field-Scale Evolution of Organic Carbon over the Landscape

C. Walter*,a, R. A. Viscarra Rosselb and A. B. McBratneyb

a ENSA-INRA Rennes, 65 rue de St Brieuc, CS 84215, 35042 Rennes, France
b Faculty of Agriculture, Food and Natural Resources, The University of Sydney, NSW 2006, Australia

* Corresponding author (cwalter{at}roazhon.inra.fr).


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION AND CONCLUSION
 REFERENCES
 
The spatial or temporal variability of soil has been extensively considered in the literature using either experimental or modeling approaches. However, only a few studies integrate both spatial and temporal dimensions. The aim of this paper is to present a method for field-scale simulations of the spatio-temporal evolution of topsoil organic C (OC) at the landscape scale over a few decades and under different management strategies. A virtual landscape with characteristics matching part of Brittany (France) was considered for the study. Stochastic simulations and regression analysis were used to simulate spatial fields with known spatial structures: short-range, medium-range, and long-range variability. These were then combined using an additive model of regionalization. Agricultural land use was simulated considering four different land uses: permanent pasture, temporary pasture, annual cereal crops, and maize (Zea mays L.). Land use evolution over time was simulated using transition matrices. Evolution of soil organic matter was estimated each year for each pixel through a rudimentary balance model that accounts for land use and the influence of soil waterlogging on mineralization rates. This spatio-temporal simulation approach at the landscape level allowed the simulation of several scales of soil variability including within-field variability. Spatial variability decreased drastically over time when only the influence of land use was considered. This effect on soil variability over the landscape may have implications for site-specific soil management and precision agriculture. The presence of redoximorphic conditions was found to maintain soil spatial variability.

Abbreviations: DEM, digital elevation model • HI, hydromorphic index • OC, organic C • RF, random function • SOC, soil organic C • VQT, variance quadtree algorithm


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION AND CONCLUSION
 REFERENCES
 
IN RECENT YEARS, soil quality has received much less attention than water quality, especially in regions where soil degradation and reduced yields have not manifested themselves. Identifying soil degradation is usually based on observations of trends from historical soil data and on comparisons of projections that are made over time. In regions with intensive farming systems, concerns about reductions in organic matter, nitrate leaching, accumulation of P, or contamination by trace elements are much more justified by examining trends than by present indicators (Coppenet et al., 1993, Walter et al., 1997). The assessment of soil quality needs the spatial prediction of soil attributes under different management practices and over many decades. In doing so, both field and landscape scales should be considered.

Soil organic C (SOC) is of particular interest in agriculture because of its role in biochemical transformations that occur in soil (Baldock and Nelson, 2000). It is also of crucial consequence to the chemical, physical, and biological condition of soil (Oades, 1993; Stevenson, 1994). To maintain SOC in agricultural fields, we need to consider its local and global evolution. With respect to the latter, global warming and the potential release or sequestration of C into or from the atmosphere must be considered. Intermediate spatial scales such as variations along slopes are also important as they contribute to soil diversity, which impacts biodiversity (Ibáñez et al., 1995).

The spatial or temporal variability of soil organic matter has been extensively considered by experimental or modeling approaches (Balabane and Balesdent, 1995; Bernoux et al., 1998; Smith et al., 1997; Six et al., 1999; Collins et al., 2000; Arrouays et al., 2001), but only few studies integrate both spatial and temporal dimensions (Jolivet et al., 1997; Papritz and Webster, 1995). The ones that do, neglect short- and medium-range spatial variability and consider only mean values (Smith et al., 1997; Nieder and Richter, 2000). Thus the impact of management strategies on soil, at both the field and landscape scales, cannot be adequately evaluated. Furthermore, the design of soil monitoring networks cannot be tested a priori for their ability to detect the evolution of selected soil properties in a given region (Mol et al., 1998).

The validation of temporal modeling that also combines several spatial scales of variation is very difficult, if not impossible, on real soil landscapes. One reason for this is the trade-off between sampling density and the cost of the survey, that is, soil sampling is either too sparse or too expensive. Recent developments in simulation techniques (Hauhs, 1990; Philip, 1991; Goovaerts, 2000) enable alternative approaches that allow the creation of virtual soil landscapes with inherent spatial structures that are similar to those observed in reality. The virtual landscape can then be modified over time considering different management scenarios and the evolution of the spatial structures described.

The aim of this paper is to present a method for field-scale simulations of the spatio-temporal evolution of topsoil OC at the landscape scale over a few decades and under different management strategies. The aim is achieved by: (i) creating a virtual landscape; (ii) simulating an initial SOC content distribution with respect to the observed spatial structures; and (iii) modeling the temporal evolution of SOC over four decades, considering land use, the influences of soil waterlogging, and their combined effect.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION AND CONCLUSION
 REFERENCES
 
The overall methodology is shown in Fig. 1 . The study area consists of a virtual, 15 by 15 km, agricultural landscape with characteristics matching part of Brittany in north-west France. This area was represented by 90 600 pixels, each being 50 by 50 m in size.



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  		Fig. 1. Framework of the combination of stochastic and deterministic approaches to simulate the initial spatial field of soil organic C content over the landscape. DEM, digital elevation model; HI, hydromorphic index; OC, organic C.

 
The Initial State
We chose a small subregion of Brittany, for which we had a detailed digital elevation model (DEM) at an x,y resolution of 50 m and a z resolution of <1 m. Within this subregion, we had some information on field sizes, on land use and its change, and general relationships between soil and topography. Thus, we could ascertain certain landscape parameters such as topography and field sizes before simulation.

The Landscape of the Study Area
For each cell in the study area, the altitude was available from a DEM (Fig. 2a) . Landscape attributes such as slope, surface drainage (Wilson and Gallant, 2000), and a soil hydromorphic or redoximorphic index (HI) (Chaplot et al., 2000) derived from topographic attributes, were calculated for each cell.



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  		Fig. 2. (a) Topography of the virtual study area and (b) initial land use under (P) long-term pastures; (T) short-term pastures; (C) cereals and (M) maize. Simulations of land use was conducted over 4500 virtual fields.

 
Simulations of Land Use and Field Sizes in the Study Area
The land use types considered were: (i) permanent pastures (P), (ii) temporary pastures (T), (iii) cereals (C), and (iv) maize (M). Initially, land use was attributed to each field in defined proportions that were representative of agricultural land use in Brittany in the 1960s. That is, roughly equal proportions of permanent and temporary pastures and cereals (approximately 30–40%) and a much smaller proportion of maize fields (approximately 5%).

An adaptation of the variance quadtree algorithm (VQT) (McBratney et al., 1999) was used to define field sizes over the study area. The VQT algorithm was developed by McBratney et al. (1999) to maximize the efficiency of a sampling scheme while ensuring that the variability of the sampling area is characterized effectively. The authors designed the approach to sample sparsely where variation is low, and more intensively where variation is large. In this case, the algorithm provided us with a means of partitioning the variance of the DEM, thus permitting the allocation of smaller virtual fields to areas of more variable topography (steeper slopes) and conversely, larger virtual fields to areas of more homogeneous topography (Fig. 2b).

Simulations of Soil Organic Carbon At Different Spatial Scales
A combination of stochastic and deterministic approaches was used to simulate the initial state of SOC in the study area (Fig. 1). Semivariograms were used to describe the spatial variability of SOC at the short- and long-range scales and a deterministic model that relates variations in SOC to soil waterlogging was used to derive the medium range structure.

Short- and Long-Range Spatial Variability of Organic Carbon.
A semivariogram characterizing the short-range variability of SOC in the study area was derived using 360 samples from a nested survey conducted in the south of Brittany (Walter, 1990) (Fig. 3a) . Similarly, a semivariogram characterizing the long-range variability in SOC (i.e., that occurring at a regional scale, between 3000 and 35000 m+) was derived using 40000 samples from a regional study conducted in Brittany by Walter et al. (1997) (Fig. 3e).



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  		Fig. 3. (a) Short-range semivariogram of organic carbon (OC) from 360 samples of a nested survey in southern Brittany and (b) its corresponding random function (RF) [Y1(x)]; (c) representation of a linear model of OC as a function of the redoximorphic index (HI) used to derive (d) the medium-range spatial field [Y3(x)]; (e) long-range semivariogram of OC based on 40 000 regional samples in Brittany, and (f) its simulated RF [Y2(x)].

 
Simulations of the Short- and Long-Range Spatial Patterns.
Geostatistical simulations of SOC at these scales were conducted over the landscape to derive respective random function (RF) models that may be representative of the study area (Fig. 3). The simulations were conducted in two stages (Fig. 1). First, two independent random fields were generated by stochastic simulation at 3249 locations on a 300-m grid using the covariance functions for short- and long-range variability respectively, that were described above. For each case, this involved forming the covariance matrix C, and multiplying a z vector of uncorrelated random variables with zero mean and unit variance by the Cholesky decomposition of C (C = XX'), to obtain the simulations of the random process S over the landscape. That is:

[1]
where µ is the expectation of S, E{S}, and X is the lower triangular n x n matrix of the decomposition of C. For more details, the Cholesky decomposition method is described in Cressie (1991). Second, sequential Gaussian simulations of the SOC content over the landscape were made onto the finer 50-m grid. These simulations, conditioned on the 300-m grid data resulting from the previous simulations, were made to reproduce the short- and long-range RF models onto a 50-m grid. Such simulations can produce an infinite number of realizations that reproduce the global statistics (histogram and semivariogram), thus it may be important to note that there is not a unique solution. In this instance, we used a single realization of the process for the study. Goovaerts (1997) and Deutsch and Journel (1998) provide the details of the sequential Gaussian simulation algorithm used.

Deterministic Derivation of the Medium-Range Spatial Pattern.
The medium-range spatial field was derived from a linear model that describes the impact of redoximorphic conditions (measured by the HI) on the soil's OC content (Fig. 3c). The relationship was derived from experimental data at different landscape positions (Chaplot et al., 2001). A semivariogram of the SOC estimates was also produced.

Combination of the Spatial Fields Characterizing the Different Spatial Scales.
To derive a permissible description of the overall spatial variability in the study area, the two random functions that describe the short- and long-range variability of SOC were combined with the medium-range spatial field using a linear model of regionalization (Goovaerts, 1997) (Fig. 1). The combined spatial field S(x) was derived from a linear combination of the two independent RFs [Yi(x)] and the deterministic spatial field Yi(x), so that:

[2]
where each RF and spatial field Yi(x) has zero mean and semivariogram {gamma}i(h). Therefore, the combined permissible semivariogram was described as a linear combination of each of the three semivariogram models {gamma}i(h), so that:

[3]
where the positive coefficient bi is the variance contribution of the respective standardized semivariogram models {gamma}i(h).

The Dynamic (Temporal) Model
Land Use Evolution
The temporal evolution of land use was simulated using transition matrices (Cressie, 1991), which allow us to model change as a probabilistic Markov chain. The transition matrix describes the probability of going from one land use (P, T, C, and M given above) in year (y) to the same or another land use in subsequent year (y + 1). Our best knowledge is that in this area, where the slopes do not exceed 10%, slopes are not limiting to the cultivation and preparation of crops. So we have not enough evidence of a significant link between topography and land use evolution to justify a more complex model. Therefore, we assume that the land use in any field in year (y + 1) is simply a function of the land use in that field in year (y). The land use in any given year may be described using the vector By = (Py, Ty, Cy, My)Y. The following matrix Ly describes the land use evolution between y and (y + 1):

[4]
where the ayij correspond to the transition probability with which land use j in Year y transits to land use i in Year (y + 1). Therefore aypp is the probability that land use P does not evolve in Year y and remains as P to (y + 1); ayTP is the probability that land use P changes to land use T in (y + 1), etc. The advantages of this technique are that it avoids having to determine the successions in land use of each field for the duration of the study, and also that the matrix is easily modifiable so that different land use evolution scenarios may be considered with ease.

Evolution of Organic Carbon
The annual evolution of SOC in each pixel was estimated yearly over a 50-yr period. The model was based on the Henin and Dupuis (1945) two-compartment model described by:

[5]
where f is the isohumic coefficient, A is the annual input of fresh plant and animal C, r is the mineralization rate, and OC is the initial C content. The integration of this model over time leads to the following equation (Molina and Smith, 1998):

[6]
where C(y) is the C content at Year y and OC0 is the initial C content at y = 0.

Evolution of Soil Organic Carbon Based on Land Use.
Considering the evolution of land use previously described, the rudimentary C balance model was applied by accounting for only land use, that is, the annual inputs of C (fA) differ between land uses but the mineralization rate (r) remains constant. Initially, the annual input of C for each land use P, T, C, and M (see above) was estimated to be 0.57, 0.48, 0.37, and 0.13 kg C m-2, respectively (Balesdent, 1996).

Evolution of Soil Organic Carbon Based on Land Use and Soil Waterlogging.
Soil waterlogging affects the C balance in soil by causing changes in the mineralization rate (r). The temporal simulations of SOC accounted for such changes using an equation similar to that given by Remy and Marin-Laflèche (1974). First, r was estimated for well-drained soils (rwd) with 20% clay and no carbonates. Soil waterlogging was considered through the HI, so that the mineralization rate decreased linearly with increasing redoximorphism:

where HImax is the maximum value of HI.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION AND CONCLUSION
 REFERENCES
 
The Initial State
Simulation of land use and field sizes over the landscape of the study area
The landscape of the virtual portion of agricultural Brittany over which the study was conducted is shown in Fig. 2a. Its topography could be said to be representative of that occurring in Brittany, with elevation ranging from 20 to 100 m. Initially, land use in the study region consisted primarily of permanent or temporary pastures and cereal or maize. With the exception of permanent pastures that were, based on the HI, preferentially allocated to waterlogged areas and wetlands, the remaining land use types were randomly allocated to each field (Fig. 2b). Indeed, in this landscape, we have no known relationship between land use and topography, except for the permanent pastures, which is the only possible land use in the bottom lands without drainage; artificial drainage developed in this area from 1960 and enabled introduction of different crops. Field sizes in the study area ranged from approximately <1 to 12 ha. Smaller fields were allocated to areas with steeper slopes and larger fields to areas of more even topography (Fig. 2b).

Simulations of Soil Organic Carbon at Different Spatial Scales
The spatial variability of SOC in Brittany is assumed to occur at three different spatial scales: within fields due to topography and agricultural management (short-range); between fields because of differences in land use or topographical position (medium-range); and between regions due to differences in climate and production systems (long-range). The semivariograms for the short- and long-range structures are shown in Fig. 3a and 3e, and realizations of their simulated RF models Y1(x) and Y2(x) are shown in Fig. 3b and 3f, respectively. The medium-range spatial field was derived from a deterministic relationship that equates the OC of the study area as a function of the soil HI derived from a DEM (Fig. 3c). The resulting medium-range spatial field Y3(x) is shown in Fig. 3d.

Combination of the Random Functions Characterizing the Three Different Spatial Scales
The combined spatial field S(x) that characterizes the spatial variability of SOC at short-, medium-, and long-range spatial scales is shown in Fig. 4a . The resulting additive spatial field has some important features: (i) short-range variability between neighboring pixels; (ii) higher values of OC in areas with high HI values, which are generally riparian areas at the bottom of valleys; (iii) a large trend of increasing SOC content from the south-west to north-east portions of the study area. These features can also be recognized in the additive experimental semivariogram (Fig. 4b), which shows a relatively high variance between pixels 50 m apart (the first point on the experimental variogram), as part of an initial steep increase in semivariance to a distance of 300 m, then a moderate increase to 2000 m and finally an asymptotic increase to distances greater than 6000 m.



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  		Fig. 4. (a) Block diagram of the additive spatial field that combines the short-, medium-, and long-range fields, and (b) the additive semivariogram model for soil organic C in the study region and the semivariograms of its three spatial components. The additive semivariogram was fitted with a triple exponential model.

 
The Dynamic (Temporal) Model
Temporal Land Use Evolution
The transition matrix that was used to simulate the temporal evolution of land use over time is given in Table 1. The transition matrix produced a rapid evolution of land use over a relatively short period of time (Fig. 5) . Much like in Brittany, maize cropping increased rapidly while the area in permanent pastures decreased. The proportions of temporary pastures and cereals remained constant throughout the simulation period (Fig. 5), however their allocation over the landscape is assumed to have varied. The proportion of maize cropping in the study area increased from 5 to 25% in 15 yr, while the proportion of permanent pastures decreased from 30 to 10% in approximately 30 yr (Fig. 5). The final land use proportions are approached asymptotically: if Ly is the transition matrix, then Lpy, as p tends to infinity, has columns that are identical and represent the final proportions that each of the land use types reaches. For our transition matrix (Table 1), asymptotically, the amount of permanent pastures is 5.7%, temporary pasture is 28.8%, cereal is 36.3%, and maize is 29.1%. Asymptotically, these final proportions are independent of the initial state. Figure 5 shows the evolution of the proportions over time and indicates that we have not reached the final proportions of the asymptote, but we are not far from it. The maps shown in Fig. 6 illustrate the evolution of land use over the landscape at different dates after the start of the simulation.


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  		Table 1. Transition probability matrix used to drive the land use evolution over time.

 


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  		Fig. 5. Simulations of land use over time driven by the transition matrix given in Table 1, for maize (M), cereals (C), temporary pastures (T), and permanent pastures (P).

 


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  		Fig. 6. Block diagrams of land use evolution at (a) the start of the simulation, (b) 10 yr after, (c) 20 yr after, and (d) at the end of the simulation: permanent pastures (P), temporary pastures (T), cereals (C), and maize (M).

 
Evolution of Soil Organic Carbon
Simulated maps of SOC content produced under the assumption that land use is the only factor affecting its evolution are shown in Fig. 7 . The most apparent features are the disappearance of the drainage pattern and long-range spatial trends, and the rapid development of medium range field patterns with an associated loss of short-range variation within fields (Fig. 7).



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  		Fig. 7. Maps of organic C content at different dates considering simulations that account only for land use.

 
Maps of SOC content simulated with the assumption that both land use and soil waterlogging affect its evolution are shown in Fig. 8 . In this instance, mineralization rates decreased with increasing HI value. The most apparent features of the simulations in Fig. 8 are the development of land use patterns and the disappearance of long-range spatial trends. The network of redoximorphic areas associated with the medium-range structure shows that higher amounts of SOC remained throughout the simulation period (Fig. 8).



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  		Fig. 8. Maps of organic C content at different dates considering simulations that account for land use and the influence of soil waterlogging.

 
Evolution of the Spatial Variability of Soil Organic Carbon
Considering land use as the only factor affecting the evolution of SOC, a strong systematic decrease in its semivariance was apparent over the first 20 yr of the simulation (Fig. 9a) . For the remaining period, the semivariograms were relatively similar (Fig. 9a). Figure 9a also shows that the evolution of SOC based on solely land use produces a simpler semivariogram structure with a lower nugget variance and a single range at 400 m. This suggests that an increase in maize cropping and a decrease in permanent pastures over time have resulted in loss of SOC variability.



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  		Fig. 9. Evolution of the organic C semivariograms at different dates considering simulations that (a) account for only land use, and (b) account for land use and the influence of soil waterlogging.

 
The combined effect of land use and soil waterlogging on the evolution of SOC was less dramatic (compare Fig. 9a and 9b). Initially, only a moderate decrease of the semivariance occurred up to 10 yr of the simulation period, after which the sill variance increased to a value similar to that of the initial state (Fig. 9b). After 50 yr of simulation, the nugget variance decreased and only one clear range near 800 m was apparent (Fig. 9b).

Figure 10 illustrates the average field evolution of SOC as well as the loss of within-field variation resulting from the two scenarios. Under the assumptions of the study, the simulation showed that changes in land use toward more maize cropping and a reduced area in permanent pastures resulted in a progressive decrease in the mean field SOC and its within-field variability (Fig. 10a and 10b). In this case, between-field variability is the unique variability component of the landscape after approximately 50 yr of simulation (Fig. 10b). Considering the influence of both land use and soil waterlogging, the temporal evolution of the spatial variability of SOC was quite different (Fig. 9). Lowering the mineralization rate by introducing the effects of redoximorphic conditions preserved the mean field SOC content and the within-field variability to levels found at the start of the simulations (Fig. 10).



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  		Fig. 10. Evolution of soil organic carbon (SOC) content (a) field mean values and the (b) mean within-field variability.

 

   DISCUSSION AND CONCLUSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION AND CONCLUSION
REFERENCES
 
A modular simulation approach was designed to build a virtual, dynamic soil landscape that has several important features similar to real landscapes. It has different scales of spatial variation, resulting from natural and artificial processes that underlie the data. It contains uniformly treated management zones that exhibit changing land use conditions and topographical variations. These are identified within the landscape as small to large fields that comprise within-field variation of soil organic matter and soil waterlogging. Also, changes in land use may occur over a few decades, modifying the spatial structure of SOC at both local and landscape scales.

Two main assumptions form the basis of the approach presented in this paper: first, the initial spatial variability of the soil property may be described by a simple additive model of two stochastic components derived from the structural analysis of existing data and of a deterministic component attributed to influence of soil waterlogging on the soil C cycle. This simple additive approach neglects potential interactions between the components but enables the combination of spatial processes with different spatial ranges. Second, the initial spatial state may be defined independently from the modeling of the temporal evolution. This latter assumption was very useful, as most existing experimental data consider either the spatial or temporal variation, not both. Some of the discrepancies that are apparent, particularly the fast decrease of the semivariance observed at the beginning of the simulation whatever the land use evolution scenario (Fig. 8), may nevertheless be attributed to the simplified representation of the system.

Modeling intends to capture the essentials of a system and leave out what is considered secondary or relatively unimportant. In a regular modeling procedure, the accuracy of the model should be validated by comparing its predictions to experimental data. However, in this case, validation of the predicted temporal evolution of SOC content at the landscape scale is almost impossible as a whole and only parts of the model may be compared with experimental data. Monitoring of different fields over time could be used to validate the apparent reductions in the spatial variability of SOC resulting from different land use and uniform management. Also, comparing areas differing by the proportion of redoximorphic soils could test the impact of soil waterlogging on the SOC variability of the landscape. The procedures considered in this work attempt to simulate some features of the SOC balance in a region, while attempting to reproduce similar spatial structures and temporal evolutions that occur in real landscapes.

A primary interest of simulating soil processes over time at the landscape scale is to assess soil management practices or sampling designs before their effective implementation. Management practices may be evaluated by their potential impact on both local and regional scales integrating evolutions over a few decades. For instance, different strategies to increase C sequestration in soils may be tested including a comparison between site specific (e.g., as permitted by precision agriculture) or uniform management. Another major interest of this simulation approach is to test sampling strategies for their ability to monitor the evolution of the landscape components over time without bias and with minimal estimation errors. With our approach, such a predictive approach of the sensitivity of a planned sampling strategy appears particularly useful as monitoring networks of soil quality are initiated in several countries (Mol et al., 1998). Different spatial configurations of the monitoring networks can easily be implemented and the estimated parameters compared with the "true" values of the virtual soil-landscape; the time interval between successive sampling campaigns can also be optimized.

Received for publication February 26, 2002.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION AND CONCLUSION
 REFERENCES
 




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