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TEP: A Tillage Erosion Prediction model to calculate soil translocation rates from tillage.

ABSTRACT Soil movement by tillage is a function of slope gradient. Tillage direction performed upslope and downslope in opposing directions over alternate years results in a net downslope movement of soil. The objective of this study was to develop a simulation model to describe sail redistribution along a hillslope transect that can be used to explain observed erosion and deposition' patterns in cultivated fields that result from tillage action. A diffusion-based conceptual model was used to represent soil redistribution by tillage, whereby the regression coefficient for the relationship between translocation and slope gradient was described by a diffusion coefficient, k'. Soil redistribution was calculated over a 50-yr period on a measured topographic transect in west central Minnesota using published k' values for the moldboard plow. Additional simulations included the additive effects of secondary tillage (tandem disc) and an examination of hillslope segment lengths on soil redistribution rates. Results s howed that 14.7% of the area from the measured transect would experience a loss or gain in soil that exceed 10 t [ha.sup.-1] [yr.sup.-1] with moldboard plow using a k' value of 2.34 kg [m.sup.-1] slope width. The loss or gain in soil that exceed 10 t [ha.sup.-1] [yr.sup.-1] increased to 26% of the area with a k' value of 3.3 0 kg [m.sup.-1]. The addition of secondary tillage (two tandem disc operations) increased the area of excessive soil redistribution to 59%. The Tillage Erosion Prediction (TEP) model has the capability to identify areas based on landscape configuration of excessive soil loss (erosion) or gain (deposition) due to soil translocation by tillage.

Key words: Deposition, erosion, modeling, soil translocation, tillage erosion.

Soil translocation from tillage operations has been identified as a cause of soil erosion, which at specific landscape positions can be greater than soil loss tolerance levels (Lindstrom et al. 1992; Govers et al. 1994; Lobb et al. 1995; Poesen et al. 1997). Soil is not directly lost from fields by tillage translocation; rather, it is moved away from convex slopes and deposited in concave slope positions.

Tillage erosion, the net movement of soil downslope through the action of mechanical implements, has been observed for many years, but in most cases these observations have been qualitative. Papendick et al. (1983) reported that the original topsoil on most hilltops had been removed by tillage erosion in the Palouse region of eastern Washington state. The moldboard plow was identified as the primary cause of tillage erosion, but all tillage implements will contribute to this problem (Govers et al. 1994; Lobb et al. 1999).

Lindstrom et al. (1992) showed that soil movement on a convex slope in southwestern Minnesota could result in a sustained soil loss level of approximately 30 r [ha.sup.-1] [yr.sup.-1] from annual moldboard plowing. Lobb et al. (1995) estimated soil loss in southwestern Ontario from a shoulder position to be 54 r [ha.sup.-1] [yr.sup.-1] from a tillage sequence of moldboard plowing, tandem disc (double-pass), and a C-tine cultivator. In this case, tillage erosion was estimated through resident [Cs.sup.137] to account for at least 70% of the total soil loss from natural and tillage erosion. Poesen et al. (1997) measured annual soil loss rates on a convex hillslope using multiple passes with a sweep plow in southeast Spain to be 1.5 to 2.6 mm [yr.sup.-1] for contour tillage, and up to 3.6 to 5.9 mm [yr.sup.-1] for upslope and downslope tillage. These values were at least one order of magnitude larger than reported soil erosion rates caused by water erosion in similar environments. Thus, it can be inferred that t illage erosion can contribute significantly to soil degradation.

Govers et al. (1996) determined soil redistribution over a 35-yr period using [Cs.sup.137] techniques on two agricultural fields in the United Kingdom. Predicted patterns of soil redistribution from overland flow erosion were poorly correlated with observed patterns of soil redistribution. Good agreement was observed with diffusive redistribution, which included splash erosion, soil creep, and tillage. Govers et al. (1996) concluded that the magnitude of the diffusive coefficients required to explain the amount of soil redistribution observed could only be explained by tillage.

The distance that soil will move by tillage has been shown to be statistically correlated with slope gradient (Lindstrom et al. 1990; Lindstrom et al. 1992; Govers et al. 1994; Lobb et al. 1995; Poesen et al. 1997). The amount of soil loss or gain at any place on the landscape is governed by the change in slope gradients rather than the magnitude of the slope gradient. When slope gradients (gradients are considered positive in the upslope direction, negative in the downslope direction) are decreasing in the direction of tillage (convex slope), soil loss occurs. When slope gradients are increasing in the direction of tillage (concave slopes), soil deposition occurs. When slope gradients are equal or not changing, a net soil loss or gain will not occur even though there is a downslope soil flux that is based on the magnitude of the slope gradient.

Only limited attempts have been made to model the resultant effects of soil movement by tillage. Lindstrom et al. (1992) developed a simple spreadsheet accounting method to determine soil movement of individual soil blocks [11.5 m (5 ft) long, 0.46 m (18 in) wide, and 0.24 m (9 in) deep] as affected by slope gradients. Soil elevation change for an individual soil block was calculated based on the difference in soil movement between adjacent blocks. The moldboard plow was the only tillage tool considered with plowing simulated in opposite directions. Govers et al. (1994) introduced the concept that the net flux of soil that moves downslope as a result of tillage can be described by using a diffusion-type equation that contains a coefficient representing the net downslope displacement per unit slope width for each tillage tool. This study's objective has been to develop a model to simulate soil movement by tillage that can be used to explain observed erosion patterns resulting from tillage activities. The mode l was developed in [VisualBasic.sup.TM] and is available upon request from the authors.

Model development

The basic principle for development of the model is the distance soil moves as affected by slope gradients. Lindstrom et al. (1992) developed regression equations describing the distance soil moves, both parallel and perpendicular to the direction of tillage for the moldboard plow, that had the form:

M = [alpha] + [beta](S) [1]


M = soil movement (m);

S = slope gradient (m [m.sup.-1]), positive in upslope direction, negative in downslope direction;

[alpha] = constant (m); and

[beta] = regression coefficient (m).

Govers et al. (1994) developed similar equations for movement parallel to the direction of tillage with the moldboard and chisel plow. Poesen et al. (1997) developed regression equations for movement parallel and perpendicular to the direction of tillage for a sweep plow. However, Poesen et al. (1997) found that as slope gradients became greater than 45%, this relationship appeared exponential rather than linear. Turkelboom et al. (1997), working in northern Thailand, found a constant relationship in slopes ranging between 32 and 60% for manual tillage, but soil movement increased significantly on slopes greater than 70%.

Using the diffusion coefficient (k) concept introduced by Govers et al. (1994)

k= -D [rho]b [beta] [2]


k = tillage diffusion coefficient (kg [m.sup.-1]),

D = tillage depth (m),

[rho]b = soil bulk density (kg [m.sup.-3]), and

[beta] = regression coefficient representing soil displacement (m) at a slope gradient of 1.

Then, annual net flux downslope (kg [m.sup.-1]) for each tillage operation, assuming tillage in alternating directions, at any point on the landscape can be determined by:

[Q.sub.s] = -k(S) [3]


[Q.sub.s] = downslope flux (kg) of soil per unit width (m) of slope.

For simulation, Equation 3 was transposed to:

[Q.sub.s] = - k' ([theta]) [4]


k' = k/100, and

[theta] = slope gradient (S) expressed on a percent slope basis.

The TEP model is designed to calculate net soil movement for individual hillslope segments across a field transect for individual tillage operations. Inputs required to describe a hillslope segment include elevation, slope gradient, and segment length. The model can calculate the initial elevation for each hillslope segment if the slope gradient is known, or vice versa. If slope gradients are inputs into the model, then an initial elevation for the first soil segment is required.

Assumptions include a constant slope gradient within a hillslope segment, uniform loss or gain of soil within a hillslope segment, and negligible net soil movement perpendicular to tillage direction. The latter assumption is only valid if the cross-slope gradient is negligible. Any number of tillage operations in a year can be included in the model; however, to examine soil redistribution over time, the tillage operations must remain constant from year to year.

Other input variables required for each tillage operation include tillage depth, soil bulk density of the tilled zone, and respective k values. Tillage depth and bulk density are easily measured or estimated values. Selection of the appropriate k values is not as clear and will require more research information. Govers et al. (1994) showed k range values of 234 to 330 kg [m.sup.-1] for the moldboard plow for up- and downslope tillage. Lobb et al. (1999) determined k values for a wide variety of tillage implements. However, many factors will influence the k value for specific tillage operations, including soil texture, structure, and moisture content, along with equipment design, size, speed of operation, and tractor-implement match.

Simulation procedure

Starting with known elevation and slope gradients along a field 1 m (3.3 ft) wide, the soil flux difference ([delta][Q.sub.s]) in direction of tillage between adjacent hillslope segments is determined:

[delta][Q.sub.s(i)] = [Q.sub.s(i)] - [Q.sub.s(i-1)] [5]


i = individual hillslope segments, and

n = number of hillslope segments.

Soil elevation and slope gradients for the first and last soil segment in the transect are held constant for ease in calculation. The difference in flux is then converted to a soil volume using the assigned soil bulk density. A new elevation and slope gradient are then recalculated for each hillslope segment.

The field transect is now ready for one or more secondary tillage operations, if desired. Secondary tillage bulk density values should be chosen to reflect the appropriate values at the time of secondary tillage. The decision in this study was to simulate each tillage operation within a tillage sequence individually rather than summing k' values for all tillage operations within an annual sequence. Summing k' values over an annual tillage sequence had the potential to produce excessive rates of soil movement that are not physically possible for a single mass movement of soil and could result in program failure. After simulation of all tillage operations conducted in one year, the program begins the entire process again and continues for the number of years selected when the program was initialized.

Output from the model includes graphical displays of elevation of the original transect and concluding elevation. Tabular outputs include yearly summation of elevation changes for each hillslope segment. Graphical displays of average annual soil redistribution rates along the transect also can be displayed.

Materials and methods

Applications of the Tillage Erosion Prediction (TEP) model are shown by analyzing soil redistribution from a measured field transect located in Stevens County, west central Minnesota. Site selection was based on curvature of the shoulder, backslope gradient (17.4% maximum), and evidence of prior erosion. Prior erosion was identified by exposure of calcareous subsoil (Cca horizon) material in the upper shoulder position. Prior analysis by Schumacher et al. (1999) on a similarly configured transect showed that the observed erosion in the upper shoulder position was the result of tillage erosion rather than water erosion. Elevation points were measured every 5 m (16.4 ft) using a survey-grade Differential Global Positioning System (DGPS). Elevations and slope gradients on 1-m spacing were determined by simple linear interpolation. The topography of the measured transect and surrounding area is shown in Figure 1. Soil series within the landscape included a Blue Earth (fine-silty, mixed, calcareous, mesic Mollic Fluvaquents) in the footslope position; a Barnes (fine-loamy, mixed, Udic Haploborolls)-Buse (fine-loamy, mixed, Udic Calciborolls) complex in the footslope, backslope, and shoulder-slope positions; and a Doland (fine-loamy, mixed, Udic Haploborolls) in the summit position.

Simulations were set up to show soil redistribution rates from annual mold- board plowing over a 50-yr period with k' values of 2.34 and 3.30 kg [m.sup.-1], the range in k' values reported by Govers et al. (1994). A third simulation was set up to show the additive effects from secondary tillage operations. In this case, the tillage sequence included an annual moldboard plowing (k' = 3.30 kg [m.sup.-1]) and two spring tandem disc operations (k' = 1.94 kg [m.sup.1]) over a 50-yr period. A soil bulk density of 1,350 kg [m.sup.-3] for moldboard plowing and 1,100 kg [m.sup.3] for discing was assumed. The k' value of 1.94 kg [m.sup.-1] for each tandem disc operation was obtained from published values reported by Lobb et al (1999).

Results and discussion

The comparison between k' values for annual moldboard plowing over the 50-yr period is shown in Figures 2, lines a and b. As the k' value increased, the magnitude of soil redistribution increased. For annual moldboard plowing with a value of 2.34 kg [m.sup.-1], 14.7% of the area of the transect was experiencing a soil loss or gain that averaged [greater than] 10 t [ha.sup.-1] [yr.sup.1]. When the k' value was increased to 3.30 kg [m.sup.-1], soil loss or gain at a rate [greater than] 10 t [ha.sup.-1] [yr.sup.1] occurred on 26% of the area. Average soil loss for a 20-m section of the shoulder position (distance = 101 to 120 m, Figure 2) was 6.9 t [ha.sup.-1] [yr.sup.1] when the k' value was 2.34 kg [m.sup.-1] and increased to 9.8 t [ha.sup.-1] [yr.sup.1] with a k' value of 3.30 kg [m.sup.-1].

The additive effect from secondary tillage (discing twice) is shown in Figure 2, line c. Area of the transect that was experiencing a loss or gain in soil [greater than] 10 t [ha.sup.-1] [yr.sup.-1] over the 50-yr period increased to approximately 60%. Average soil loss in the shoulder position increased to 24.1 t [ha.sup.-1] [yr.sup.-1] Simulated soil loss in the shoulder position increased linearly as k' values increased from 2.34 to 7.18 kg [m.sup.-1].

The greatest rates of simulated soil translocation were observed at a distance centered around 75 m where an irregularity in slope gradients occurred. This irregularity is the remnant of a fence line that was removed 3 yr prior to elevation measurements. Soil had accumulated around the fence line through wind and water deposition and deposition from tillage. Slope gradients rapidly changed in an irregular manner above and below the fence line.

Equations 3 and 4 describe the rate of soil movement at any point on the land-scape as a function of slope gradient, i.e., as slope gradients increase, downslope soil movement will increase. However if slope gradients are equal between adjacent hillslope segments, then downslope soil movement will be equal between these hillslope segments and there will be little or no net loss or gain in soil. When adjacent hillslope segments have different slope gradients, then the differences in soil movement will result in a net loss or gain in soil. The degree of curvature (change in slope gradients between adjacent slope segments) determines the rate of loss or gain. The slope gradient irregularity observed at the removed fence line, in effect, contained short segments of both convex and concave slopes with a high degree of curvature. This condition resulted in a high rate of soil redistribution (erosion and deposition) adjacent to the fence line as shown in Figure 2.

Changing the length of the slope segments had an effect on the simulated soil redistribution over the transect (Figure 3). The magnitude of soil redistribution rates was reduced as increment length increased, but in general the overall effects were similar. For example, the total area of the transect exhibiting a soil redistribution rate [greater than]10 r [ha.sup.-1] [yr.sup.-1] was 60, 60, and 59% for the corresponding 10-, 5-, and 1-m increment lengths. Average soil loss in the shoulder position (distance = 101 to 120 m) for the 10-, 5-, and 1-m increments lengths were 22.3, 22.8, and 24.1 t [ha.sup.-1] [yr.sup.-1].

However, the maximum rate in annual soil translocation near the former fence line area was substantially reduced as increment length increased from 1 m (Figure 3, line a) to 10 m (Figure 3, line c). These differences in annual soil translocation rates, observed with a change in hill-slope segment length, raises the question of appropriate hillslope segment length for the model. Given that Lobb and Kachanoski (1999) have reported soil translocation distances of 2 to 4 m per annual tillage sequences, and that the size of tillage implement frames can span 2 to 3 in, then analysis of hillslope segment by 1-m lengths may not be appropriate. In effect, soil redistribution rates at the 1-, 5-, and 10-m hillslope segment lengths were comparable, except at landscape segments where slope curvature was rapidly changing, i.e., removed fence line and upper shoulder slope position. In the situations where slope curvatures were rapidly changing, the magnitude of soil redistribution rates for individual hillslope segments c an change as increment lengths change, but the net effect of soil redistribution over the landscape will remain the same.


The TEP model explains the apparent loss of soil on landscape positions that may not be accounted for by water erosion models, i.e., convex shoulder positions. The distance soil moves by tillage is a function of the tillage tool and slope gradient. When tilling on sloping land in opposing directions, the net annual downslope movement of soil can be characterized by a single value for the diffusion coefficient (k). Soil loss or gain for individual hillslope segments is determined from differences in soil movement between individual soil segments as affected by soil gradient. A net soil loss occurs on convex slopes, soil deposition takes place on concave slope positions, and little net change takes place on linear slopes with a uniform slope gradient between soil segments.

The database requirements to run the model are not complicated, although additional research is required to obtain appropriate k values for the wide variety of tillage equipment and modes of operation. The locations where soil was lost or gained did not change with magnitude of the k values, but the rate of loss or gain did increase linearly with an increase in k-value. Soil redistribution rates within individual hillslope segments changed as hillslope segments lengths changed from I to 10 in, but the overall effects were comparable, except in situations where slope gradients were changing rapidly. This was especially evident in situations where slope gradients changed rapidly in an irregular fashion.

The TEP model used in combination with water erosion models will allow better identification of areas of excessive soil loss (erosion) or gain (deposition) from rillage and cropping system management. Upon identification of potential problem areas and recognition of the causal process, better conservation management systems can be developed to maintain long-term soil sustainability.

M.J. Lindstrom is a soil scientist with the U.S. Department of Agriculture's

Agricultural Research Service (USDA-ARS), at the North Central Soil Conservation Research Laboratory, Morris, Minn.; J.A. Schumacher is a research associate, and T.E. Schumacher is a professor, Department of Plant Science, South Dakota State University, Brookings, S.D. This paper is a joint contribution of the North Central Soil Conservation Research Laboratory, USDA-ARS, and South Dakota Experiment Station.


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Author:Lindstrom, M. J.; Schumacher, J. A.; Schumacher, T. E.
Publication:Journal of Soil and Water Conservation
Geographic Code:1USA
Date:Jan 1, 2000
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