Soil Science Society of America Journal 64:1733-1739 (2000)
© 2000 Soil Science Society of America
DIVISION S-6-SOIL & WATER MANAGEMENT & CONSERVATION
Modeling Translocation and Dispersion of Soil Constituents by Tillage on Sloping Land
K. Van Oosta,
G. Goversa,
W. Van Muysena and
T.A. Quineb
a Laboratory for Experimental Geomorphology, K.U. Leuven, Redingenstraat 16, B-3000 Leuven, Belgium
b Dep. of Geography, University of Exeter, Amory Building, Rennes Drive, Exeter EX4 4RJ, UK
kristof.vanoost{at}geo.kuleuven.ac.be
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ABSTRACT
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Recent studies clearly indicated that soil tillage is a major factor affecting soil redistribution on arable land. However, existing modeling studies of the redistribution of soil constituents by tillage are largely theoretical in nature due to the lack of sufficient experimental data. This paper describes the results of field experiments carried out with a moldboard plow on different slope gradients showing that an important net downslope translocation and dispersion of soil constituents is associated with soil tillage. Both translocation and dispersion are strongly affected by slope gradient. Available experimental evidence suggests that redistribution of soil constituents can be modeled by convoluting the displacement probability distribution with the spatial distribution of the soil constituent. The convolution model presented here was found to be superior to existing models because it accounts for dispersion, directionality of tillage, and topography. A comparison of soil property data with model simulations indicated that soil tillage is a major factor when assessing the effect of erosion processes on the variability of soil properties.
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INTRODUCTION
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VARIOUS STUDIES have shown that erosion processes can contribute significantly to the variability of soil properties in fields with complex topography (e.g., Stone et al., 1985; Kreznor et al., 1989). Most attention has been directed toward the effect of overland flow erosion on soil properties and soil productivity (e.g., Williams et al., 1984; Verity and Anderson, 1990; Weesies et al., 1994; Larney et al., 1995). However, recent studies have clearly indicated that, beside water, tillage is a major factor affecting soil redistribution on arable land (e.g., Kiburys, 1989; Lindstrom et al., 1990, 1992; Govers et al., 1994, 1996; Guiresse et al., 1995; Lobb et al., 1995; Quine et al., 1997).
Tillage erosion results from the spatial variation of soil translocation by tillage. The downhill displacement of soil during a downslope tillage operation is not entirely compensated for by the uphill displacement during the complementary upslope operation. Consequently, there is net downslope transport of soil on the field. The experimental data published recently clearly demonstrate that the average displacement distance, and therefore the unit soil transport rate, depends primarily on the slope gradient (e.g., Lindstrom et al., 1990, 1992; Govers et al., 1994; Poesen et al., 1997; Thapa et al., 1999; Van Muysen et al., 1999). Consequently, whether or not erosion or deposition occurs will depend on the change in slope gradient rather than its absolute value. Tillage will cause erosion on convexities or shoulders and will cause deposition in concavities or hollows. Govers et al. (1994) and Quine et al. (1997) proposed characterizing soil translocation by tillage as a single constant: the tillage transport coefficient (k value), which is a proportionality coefficient relating the unit soil transport rate to the slope gradient. This coefficient can then be used to assess the intensity of tillage erosion and allows prediction of soil redistribution rates by tillage (Govers et al., 1994; Quine et al., 1997; Lobb et al., 1995; Lobb and Kachanoski, 1999).
However, tillage erosion and the associated loss of fertile topsoil is not the only effect tillage has on the soil. Tillage will also redistribute soil constituents (e.g., phosphates, organic matter, disease organisms, stones) within the plow layer, affecting the spatial distribution of soil properties. Until now, the effect of tillage on the redistribution of soil constituents within the plow layer has not been studied in detail. Sibbesen et al. (1985), Sibbesen and Anderson (1985), and Sibbesen (1986) demonstrated the effect of tillage on soil substances inventories by predicting the rate and extent of cross-contamination of soil amendments in long-term field experiments. Yorston et al. (1990) studied the disturbance of archaeological material by cultivation. Lobb and Kachanoski (1999) used theoretical models to estimate the magnitude of translocation and the redistribution pattern of soil within the plow layer. These studies indicated that characterizing tillage solely by means of the tillage transport coefficient is not adequate for the examination of the redistribution of soil constituents within the plow layer. The tillage transport coefficient, which is based on the averaged displaced distance of the plow layer, suggests a uniform displacement of the plow layer, which is not in agreement with observations. In fact, a considerable variation in displacement distances occurs during tillage translocation (e.g., Govers et al., 1994). However, existing models only allow study of the effect of tillage on soil properties on horizontal surfaces. They do not account for variation of soil translocation with slope gradient, which is a basic characteristic of tillage, leading to the loss and accumulation of soil constituents on specific landscape positions. If this principle is not accounted for, one cannot predict changes in soil properties on sloping land. Furthermore, the existing studies of the dispersion of soil constituents by tillage are largely theoretical in nature due to the lack of sufficient experimental data.
The objective of this study was to assess the effect of soil tillage on the redistribution of soil constituents on sloping land. The results of a tillage experiment, conducted on different slopes, are discussed. More specifically, analysis of available experimental data is used (i) to demonstrate the deficiencies of existing tillage models and (ii) to present a new model for simulating redistribution of soil constituents on complex slopes. Finally, model results are compared with field data and implications of the experimental and theoretical findings for changes in soil constituent inventories, and consequently soil quality, are analyzed.
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Materials and methods
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The experiments were conducted in Huldenberg, Belgium, on a basically convex slope 40 of m long. The maximum slope gradient is 0.22 m m-1 or 12.5°. A detailed map of the study area was constructed using an automatic theodolite (Fig. 1)
. Soils on the experimental field varied from a Typic Hapludalf on the plateau position over a Typic Eutrochrept on the mid-slope to a Typic Udorthent on the lower part of the slope. As the previous tillage operation had been carried out more than 12 mo before, the plow layer was rather compact, the mean bulk density being 1570 kg m-3 (SD = 110 kg m-3; n = 41). Average gravimetric soil moisture content of the plow layer was 0.18 g g-1 (SD = 0.04 g g-1; n = 41), and organic matter content according to the Walkley-Black method was 0.42% (SD = 0.2%; n = 35).
Two series of six plots 1.5 m wide were delineated perpendicular to the tillage direction and on varying slopes (Fig. 1). On each strip, 100 aluminum cubes with an edge length of 15 mm were inserted in the soil following the hole drilling method as developed by Govers et al. (1994) and Van Muysen et al. (1999), and their position was accurately recorded. Both series were tilled with a mounted, four-bladed, reversible, 45-cm-wide moldboard plow in alternate directions: Series U in the upslope direction and Series D in the downslope direction. During tillage, the tractor speed and tillage depth were maintained as constant as possible (Table 1)
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After the tillage operation, the tracers were carefully excavated and the translocation of each tracer was recorded. For every plot, a recovery rate of tracers in excess of 95% was obtained. Individual horizontal displacement distances of the tracers as well as descriptive statistics of displacement distances for each strip were calculated (Table 1). Positive values are given to tracers moving in the tillage direction, negative values to tracers moving in the opposite direction. Only those tracers that were situated in the plow layer were used in these calculations as these were the only ones subject to movement during a tillage pass. Tracers that were situated below the plow layer were excluded from the analysis.
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Results and discussion
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Dispersion Effect
Figure 2
shows a boxplot of displacement distances in the tillage direction calculated for each strip plot. Most tracers are displaced in the range of 0.2 to 0.8 m, while some are displaced more than 2 m. For upslope tillage operations, some tracers moved downslope and therefore have negative displacement distances. These tracers were considered to reflect real tillage conditions and were therefore included in the analysis.
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Fig. 2 Boxplot of displacement distances for each strip. The box indicates the 25th and 75th percentile; the whiskers indicate the 10th and 90th percentile. The median is drawn in a full line and the mean in a dotted line
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In order to describe the data in mathematical terms for modeling, the probability distributions of displacement distances were estimated. A statistical analysis based on the Kolmogoroff-Smirnoff test (SAS Institute, 1996) indicated that a skewed normal distribution gives a good fit with the experimental data. The probabilities were calculated by transforming the skewed distribution in a standard normal distribution (Nicks and Lane, 1989):
 | (1) |
where x is the standard normal variate; X is the raw variate; and u, s, and g are the mean, standard deviation, and skew coefficient of the raw variate, respectively.
Other distribution types like normal or exponential functions are less suitable for describing displacement distances (Table 2) . Thus, all tracer populations are characterized by a unimodal skewed distribution with a tail in the tillage direction. It must be stressed that these density functions are merely a description of the observed displacement distances and do not seek to explain individual particle movements. However, this approach is preferred since characterizing the redistribution of soil particles within the plow layer using deterministic approaches is difficult due to the complexity of the tillage process (Lobb and Kachanoski, 1999). Since the density functions are based on experimental data, they reflect the displacement distances under these particular tillage and soil conditions.
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Table 2 Kolmogorov statistic for different distribution types as a measure of the discrepancy between empirical and parametric (based on sample estimate) cumulative distribution function
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The existence of a specific statistical distribution implies that not all soil particles will be transported over the same distance. This is due to the fact that the displacement of any given soil particle depends on its initial position within the plow layer relative to the tillage tool. Similarly to the movement of contaminants in groundwater, this leads to a dispersion effect (Wang and Anderson, 1982). Thus, characterizing tillage solely by means of the average displaced distance of the plow layer, which suggests a uniform displacement, is not adequate for the examination of soil redistribution within the plow layer.
Slope Effect
The results of the experiments were analyzed by plotting the relationship between the average displacement distance in the tillage direction and the slope gradient, using negative slope gradients for downslope tillage and positive for upslope tillage (Fig. 3)
. The mean displacement distance is significantly related to slope gradient, which is in agreement with other authors (e.g., Lindstrom 1990, 1992; Govers et al., 1994; Van Muysen et al., 1999). The standard deviation of displacement distances is significantly related to the mean displacement distance. On the other hand, the skew coefficient shows no significant relationship with displacement distance or slope and has a mean value of 1.59 m (SD = 0.36 m). The effect of slope on the redistribution of soil particles within the plow layer is best visualized by plotting the probability density functions for different slopes (Fig. 4)
. It can be seen that the peak of the distribution during a downslope tillage operation is shifted to the right in comparison with the uphill displacement during the complementary upslope operation. However, not only the location of the distribution, but also the shape is slope dependent. This is because both average and standard deviation of displacement distances are significantly related to slope (P < 0.001 in both cases).
Modeling
These results raise the question as to how the rate of soil redistribution within the plow layer by tillage can be modeled. Various authors used a modification of the soil transport model proposed by Govers et al. (1993, 1994) for predicting soil redistribution rates. The unit soil transport rate per tillage operation in the direction of tillage for a specific point on the slope is
 | (2) |
where Qs is the unit soil transport rate (kg m-1), 
b is the soil bulk density (kg m-3), 
is the average displacement distance of the plow layer in the tillage direction (m), and D is depth of tillage (m).
If an elementary slope element of unit width is considered, the erosion rate Es (kg m-2) due to tillage can then be calculated by calculating the difference between the amount of soil leaving (Qs,out) and the amount of soil entering (Qs,in) the slope element, or
 | (3) |
where 
x is the longitudinal length of the elementary slope segment under consideration.
These equations can be modified to calculate the redistribution of soil constituents within the plow layer. It is assumed that the unit transport rate of a soil constituent at a specific point on the hillslope equals
 | (4) |
where Qc is the unit transport rate of a soil constituent (kg m-1) at a specific point with concentration C (kg m-3).
Similar to erosion rates, rates of change in concentration (Ec) can then easily be calculated for an elementary slope element of unit width by calculating the difference between the amount of soil constituent leaving (Qc,out) and the amount of soil constituent entering (Qc,in) the slope element, or
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The ability of this model to describe the redistribution of soil constituents by the tillage process is limited. Soil transport rates are calculated using only the average displacement distance of the plow layer so that the dispersion of soil constituents during transport is not accounted for. However, due to the numerical implementation of the model, soil constituents will nonetheless be dispersed as with each tillage operation soil is transferred toward a neighboring grid cell wherein it is assumed to be homogeneously distributed. Consequently, the displacement distance of soil particles, and thus the predicted concentration of soil constituents, depends largely on the grid resolution chosen. In the literature, this effect is known as numerical dispersion (e.g., Wang and Anderson, 1982). The effect of numerical dispersion is illustrated in Fig. 5
, where it can be seen that an increasing grid resolution results in a larger numerical dispersion.
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Fig. 5 Comparison of predicted concentrations using an analytical diffusion equation, a convolution model, or MST-model (grid resolution 0.5, 1, or 2 m). Ten tillage operations are simulated in opposing directions (i.e., five each way) on a labeled plot 2 m wide (dashed line). Parameter values are based on equations in Fig. 3 for a zero slope
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Sibbesen et al. (1985) and McGrath and Lane (1989) described the redistribution of soil constituents on an experimental plot by means of the solution of the diffusion equation:
 | (6) |
where C(x,t) is the concentration of a soil constituent after t tillage operations (n), x is the distance from the center of the plot, C0 is the initial concentration within the plot before tillage, b is the width of the plot (m), Dc is the diffusion coefficient that characterizes the dispersivity of the tillage implement (m2 n-1), and erf is the error function or cumulative normal distribution:
 | (7) |
This approach allows us to take account of the dispersivity of tillage, but it has some restrictions. The underlying assumptions are that (i) the initial concentration of the constituent is homogeneously distributed along a plot of width b, (ii) tillage translocation occurs in opposing directions simultaneously at equal rates, and (iii) the probability distribution is symmetrical in both tillage directions. Under these assumptions, the distribution density of the soil constituent will approach a Gaussian normal distribution as t increases. This follows from the central limit theorem in probability theory. It is then clear that the application of the diffusion model is limited since (i) the initial distribution can be of any form, (ii) tillage patterns are not limited to the simple case of opposing directions, and (iii) the necessary assumption of symmetrical probability distributions in both tillage directions is only fulfilled on nonsloping land.
A more complex modeling approach that explicitly deals with these aspects is therefore needed. Consider a soil constituent with concentration C1 where the initial spatial distribution consists of just a single point x1 in a one-dimensional space. The resulting spatial distribution of the soil constituent P(x) after one tillage operation equals:
 | (8) |
where G(x - x1) is the probability distribution of displacement distances evaluated at a distance of (x - x1).
When the initial distribution is a continuous function S(y), the resulting spatial distribution equals the integration of Eq. [8] over -
to +
 | (9) |
Equation [9] is simply an instance of the standard convolution integral (Bracewell, 1986). Consequently, the effect of tillage on the redistribution of soil constituents can be described by convoluting the displacement probability distribution with the spatial distribution of a soil constituent (e.g., Yorston et al., 1990). The effect of various tillage operations can be simulated by repeating the convolution. The convolution and diffusion models produce similar results when tillage is conducted in opposing directions on nonsloping land (Fig. 5). Unlike diffusion models, the convolution model is not restricted to symmetrical probability distributions in both tillage directions and allows simulation of soil redistribution when tillage is conducted in a single direction. We can conclude that the convolution model is superior to the diffusion model and MST-model because it accounts for dispersion, the directionality of tillage, and has no restrictions on the form of the initial concentration or displacement distribution. Thus, the convolution model can be used to simulate redistribution of soil constituents on sloping land.
In order to extend the convolution model for use on complex slopes, it is implemented in a grid by using a discrete approximation to the convolution equations. The displacement probability distribution can then be changed according to the slope gradient of a grid cell. Furthermore, this approach makes the convolution model more amenable to complex situations that cannot be solved by analytical solutions. For example, the problems of transfers between plow and sub-plow layer and additional soil constituents leaving or entering the plow layer are more easily handled.
Implications
From our experimental data, it follows that soil redistribution by tillage is characterized by a slope-dependent dispersion effect. The implication of dispersion can be illustrated by a simple example. Consider a horizontal area where labeled soil material is inserted into a 0.4-m-wide plot and where tillage direction is alternating in opposite directions perpendicular to the plot boundary (Fig. 6)
. Although no net soil displacement will occur, the labeled soil material will spread further and further when the number of tillage passes increases. It continues to spread out as long as the disturbing influence is present (Yorston et al., 1990). On sloping land, the initial distribution will also undergo a net downslope translocation. Moreover, the dispersion in the downslope direction will be greater than in the upslope direction, leading to an asymmetric dispersal of the labeled soil material. When tillage is carried out in one direction, the translocation and dispersion are more pronounced.
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Fig. 6 Dispersion and translocation of a labeled plot 0.4 m wide (A) on a flat surface and (B) on a slope of 0.22 m m-1 after n tillage passes in opposing directions (dotted line) or in one direction (solid line)
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The analysis presented above indicates that soil tillage can have important implications for spatial patterns of soil properties on sloping land. This can be illustrated using data collected on the Huldenberg experimental site (Govers, 1987). Here, the sand content (0.063–2.0 mm fraction) was measured for the plow and sub-plow layer along a slope profile using the wet-sieving method. Most of the slope profile is covered by wind-blown loess deposits, but a sandy outcrop occurs at the uppermost part (Fig. 7)
. The boundary of this outcrop is well represented in the subsoil by a sharp decrease in sand content between 10 and 12 m. This sharp boundary is absent in the plow layer: here, the sand content is found to decrease gradually from 
55 to 10% over a distance of 45 m. The sand content to be expected in a loess-derived topsoil is between 5 and 10%. Therefore, it could be assumed that the excess sand present in the topsoil between 12 and 40 m is not in situ and results from the downslope movement of the sandy material by water and tillage processes after the experimental site was brought into cultivation 130 yr ago (Govers et al., 1993). The gradual decrease of the sand content over a distance of 45 m suggests that important dispersion took place while the sandy material was transported over the silty loamy subsoil.
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Fig. 7 Measured sand content of plow layer (squares) and sub-plow layer (triangles) on the Huldenberg field. The measured sand content is compared with three model predictions where only water (diamonds), only tillage (exes), and water and tillage (circles) processes are taken into account
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In order to investigate the relative role of tillage and water in the genesis of the observed pattern, the convolution model, as described above, was extended with a water erosion component which is based on the model of Govers et al. (1993). The water model describes rill and interrill erosion as a function of slope gradient and slope length on a one-dimensional slope. Another factor, which may be of relevance to soil and soil constituents budgets on cultivated land, is the loss of soil with the harvest of root crops. A harvest routine was therefore implemented that assumes a uniform soil loss of 0.6 Mg ha-1 yr-1. Soil redistribution by diffusive processes like soil creep and rain splash is ignored since their intensity is much lower than water and tillage erosion (Govers et al., 1993, 1996). Transfers between plow and sub-plow layer due to erosion or deposition are also accounted for. The model is implemented with the following assumptions: (i) the sandy outcrop was already present when the field was tilled for the first time and the sand content of the plow layer in this area has remained constant (55%); (ii) the silty loam has an initial sand content of 10% for the plow layer and 3% for the sub-plow layer; (iii) tillage depth was constant and equaled 0.15 m; and (iv) for the water erosion component of the model, the parameter values proposed by Govers et al. (1993) were used.
Tillage conditions during the last 130 yr are unknown; therefore, tillage parameters are optimized by adjusting the slope of the relations between (i) slope gradient and average displacement and (ii) average and standard deviation of displacement. Variations in the parameter values of the tillage erosion model did not significantly affect the predicted spatial pattern.
Table 3
and Fig. 7 show that the agreement between observed sand content and model output is poor when only water processes are considered (Simulation 1). Overland flow reduces the sand content of the plow layer in the silty loam area because eroded soil particles are transported downslope until the transport capacity is exceeded. As in our case the slope is convex, all material eroded by water is simulated to leave the slope at the bottom end. Due to the lowering of the surface by erosion, subsoil poor in sand is continuously mixed into the plow layer. When only tillage is taken into account (Simulation 2), the correspondence between predicted and observed values of sand content is better and a clear downslope movement of sand-rich topsoil over the silty subsoil is simulated. However, the simulated sand content is always above the observed values. Apparently, dispersion due to tillage alone does not lead to the very gradual decrease of sand content observed in the field. In Simulation 3, tillage and water are combined, resulting in a much better correlation between observed and predicted redistribution patterns. The transition between sandy and silty topsoil is now much more gradual due to the combination of two processes: (i) soil tillage continuously moves sand downslope and (ii) at the same time, dilution of the sand occurs due to the mixing of subsoil poor in sand with the plow layer as a result of surface lowering by both water and tillage erosion. Optimal linear regression coefficients for the tillage erosion model are given in Table 3 and are in close agreement with the experimentally derived data in combination with four tillage operations per year. These values correspond with a k value of 324 kg m-1 yr-1, which is higher, but in the same order of magnitude, than the k value of 133 kg m-1 as found by Govers et al. (1994), based on height differences.
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Table 3 Comparison of measured and predicted sand content using only water, only tillage, and a combination of both processes
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It is recognized that the procedure used here is not a rigorous model validation. However, this exercise merely seeks to point out the typical characteristics of tillage and water processes and the assumptions made are adequate for this purpose.
Further validation of the model is therefore necessary, and the effect of other tillage implements and conditions needs to be studied. Furthermore, a two-dimensional version of the model needs to be developed for applications on complex landscapes.
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Conclusions
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The experiments clearly indicate that tillage not only causes soil translocation, but also important dispersion of soil constituents. The available data suggest that displacement distances in the tillage direction for a moldboard plow are best described by a skewed normal distribution. Furthermore, translocation and dispersion are both slope dependent. Topography is thus an important control on the redistribution of soil constituents by tillage.
Redistribution of soil constituents can be modeled by convoluting the displacement density function with the spatial distribution of a soil constituent. The slope effect can be incorporated by linking the displacement distribution with slope gradient. The convolution model presented here is superior to the existing analytical diffusion model and MST-model. The MST-model is unsuitable for simulating soil redistribution within the plow layer because it characterizes tillage solely by means of an average displaced distance. As such, this model does not account for the dispersion of soil particles. The limitation of the diffusion model is the necessary assumption that tillage is occurring in opposing directions at equal rates on nonsloping land. The convolution model accounts for dispersion, directionality of tillage (i.e., tillage occurring in one direction or in opposing directions at unequal rates), and topography.
A first model test showed that the spatial variation of sand content in the plow layer at the Huldenberg field site can only be explained by considering the effects of both water and tillage erosion, whereby dispersion by tillage has to be taken explicitly into account. Thus, soil tillage, and the associated translocation and dispersion of soil constituents, contributes significantly to the spatial variation and evolution of soil properties on arable land.Guiresse Revel 1995; Sibbesen Andersen 1985
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ACKNOWLEDGMENTS
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The research for this paper was carried out as part of the TERON collaborative project, funded by the European Commission (project no. FAIR-CT96-1478). Additional funding from the Flemish Government (Belgium) under project no. VIS/95/03 is gratefully acknowledged.
Received for publication August 31, 1999.
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REFERENCES
|
|---|
- Bracewell R.N. The Fourier Transform and its applications, 2nd ed New York: McGraw-Hill, 1986.
- Govers G. Spatial and temporal variation in rill development processes at the Huldenberg experimental site. In R. Bryan (ed.) Rill erosion: Processes and significance. Catena Suppl. 1987;8:17-34.
- Govers G., Quine T.A., Desmet P.J.J., Walling D.E. The relative contribution of soil tillage and overland flow erosion to soil redistribution on agricultural land. Earth Surf. Processes Landforms 1996;21:929-946.
- Govers, G., T.A. Quine, and D.E. Walling. 1993. The effect of water erosion and tillage movement on hillslope profile development: A comparison of field observations and model results. In S. Wicherek (ed.) Proc. of the Int. Symp. on Farm Land Erosion in Temperate Plains Environments and Hills. Saint-Cloud, Paris, France. May 1992. Elsevier, Amsterdam.
- Govers G., Vandaele K., Desmet P., Poesen J., Bunte K. The role of tillage in soil redistribution on hillslopes. Eur. J. Soil Sci. 1994;45:469-478.
- Guiresse M., Revel J.C. Erosion due to cultivation of calcareous clay soils on hillsides in south-west France. II. Effect of plowing down the steepest slope. Soil Till. Res. 1995;35:157-166.
- Kiburys B. Divozemio mechanine erozija (Mechanical soil erosion). Vilnius, Lithuania: Mokslas, 1989.
- Kreznor W.R., Olson K.R., Banwart W.L., Johnson D.L. Soil, landscape and erosion relationships in a northwest Illinois watershed. Soil Sci. Soc. Am. J. 1989;53:1763-1771.[Abstract/Free Full Text]
- Larney F.J., Izaurralde R.C., Janzen H.H., Olson B.M., Solberg E.D., Lindwall C.W., Nyborg M. Soil erosion–crop productivity relationships for six Alberta soils. J. Soil Water Conserv. 1995;50:87-91.
- Lindstrom M.J., Nelson W.W., Schumacher T.E. Quantifying tillage erosion rates due to moldboard plowing. Soil Till. Res. 1992;24:243-255.
- Lindstrom M.J., Nelson W.W., Schumacher T.E., Lemme G.D. Soil movement by tillage as affected by slope. Soil Till. Res. 1990;17:255-264.
- Lobb D.A., Kachanoski R.G. Modelling tillage translocation using step, linear-plateau and exponential functions. Soil Till. Res. 1999;51:317-330.
- Lobb D.A., Kachanoski R.G., Miller M.H. Tillage translocation and tillage erosion on shoulder slope landscape positions measured using Cs137 as a tracer. Can. J. Soil Sci. 1995;75:211-218.
- McGrath S.P., Lane P.W. An explanation for the apparent losses of metals in a long-term field experiment with sewage sludge. Environ. Pollut. 1989;60:235-256.[Medline]
- Nicks, A.D., and L.J. Lane. 1989. Weather generator. p. 2.1–2.19. In L.J. Lane and M.A. Nearing. (ed.) WEPP Hillslope Profile Model Documentation. NSERL Rep. 2. USDA-ARS National Soil Erosion Res. Lab., West Lafayette, IN.
- Poesen J., van Wesemael B., Govers G., Martinez-Fernandez J., Desmet P.J.J., Vandaele K., Quine T.A., Degraer G. Patterns of rock fragment cover generated by tillage erosion. Geomorphology 1997;18:183-197.
- Quine T.A., Govers G., Walling D.E., Zhan X., Desmet P.J.J. Erosion processes and landform evolution on agricultural land-new perspectives form caesium-137 measurements and topographic-based erosion modelling. Earth Surf. Processes Landforms 1997;22:799-816.
- SAS Institute. SAS/insight user's guide. Version 6, 2nd ed Cary, NC: SAS Inst, 1996.
- Sibbesen E. Soil movement in long-term field experiments. Plant Soil 1986;91:73-85.
- Sibbesen E., Andersen C.E. Soil movement in long-term field experiments as a result of cultivations. II. How to simulate the two-dimensional movement of substances accumulating in the soil. Explor. Agric. 1985;21:109-117.
- Sibbesen E., Andersen C.E., Andersen S., Flensted-Jensen M. Soil movement in long-term field experiments as a result of cultivations. I. A model for approximating soil movement in one horizontal dimension by repeated tillage. Explor. Agric. 1985;21:101-107.
- Stone J.R., Gilliam J.W., Cassel D.K., Daniels R.B., Nelson L.A., Kleiss H.J. Effect of erosion and landscape position on the productivity of piedmont soils. Soil Sci. Soc. Am. J. 1985;49:987-991.[Abstract/Free Full Text]
- Thapa B.B., Cassell D.K., Garity D.P. Assessment of tillage erosion rates using small granitic stones on steepland Oxisols in the humid tropics. Soil Till. Res. 1999;51:233-243.
- Van Muysen W., Govers G., Bergkamp G., Poesen J., Roxo M. Effects of initial soil conditions and slope gradient on soil translocation by tillage. Soil Till. Res. 1999;51:303-316.
- Verity G.E., Anderson D.W. Soil erosion effect on soil quality and yield. Can. J. Soil Sci. 1990;70:471-484.
- Wang H.F., Anderson P.A. Introduction to groundwater modeling: Finite difference and finite element methods. San Francisco: W.H. Freeman and Co, 1982.
- Weesies G.A., Livingston S.J., Hosteter W.D., Schertz D.L. Effect of soil erosion on crop yield in Indiana: Result of a 10 year study. J. Soil Water Conserv. 1994;49:597-600.
- Williams J.R., Jones C.A., Dyke P.T. A modeling approach to determining the relationship between erosion and soil productivity. Trans. ASAE 1984;1:129-144.
- Yorston R.M., Gaffney V.L., Reynolds P.J. Simulation of artefact movement due to cultivation. J. Archaeol. Sci. 1990;17:67-83.
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S. Li, D. A. Lobb, M. J. Lindstrom, S. K. Papiernik, and A. Farenhorst
Modeling Tillage-Induced Redistribution of Soil Mass and Its Constituents within Different Landscapes
Soil Sci. Soc. Am. J.,
January 11, 2008;
72(1):
167 - 179.
[Abstract]
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K. Van Oost, G. Govers, S. De Alba, and T. A. Quine
Tillage erosion: a review of controlling factors and implications for soil quality
Progress in Physical Geography,
August 1, 2006;
30(4):
443 - 466.
[Abstract]
[PDF]
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Y. Li, G. Tian, M. J. Lindstrom, and H. R. Bork
Variation of Surface Soil Quality Parameters by Intensive Donkey-Drawn Tillage on Steep Slope
Soil Sci. Soc. Am. J.,
May 1, 2004;
68(3):
907 - 913.
[Abstract]
[Full Text]
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TOP
ABSTRACT
INTRODUCTION
. The relation between standard deviation (S) and mean is given by a functional relationship assuming proportional errors. The corresponding line is the reduced major axis.
, r2 = 0.78***