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Ecological Studies at the Woodworth Study Area

Hydrologic and Sedimentation Simulation in the Prairie Pothole Region of North Dakota

Baxter E. Vieux1*, Gary E. Freeman2, Erwan LeDimet1 and Sylvain Guinepain1
1Environmental Modeling and GIS Laboratory, School of
Civil Engineering and Environmental Science, University of
Oklahoma, Norman, OK 73019; 2Hydraulics Laboratory,
U.S. Army Corps of Engineers Waterways Experiment Station,
Vicksburg, MS 39180


The objective of this project was to model the hydrologic transport of sediment in complex terrain in the Prairie Pothole Region (PPR) of North Dakota. The National Biological Service together with the U.S. Environmental Protection Agency and the U.S. Army Corps of Engineers, Waterways Experiment Station have undertaken the assessment of farming practices on accelerated erosion and sedimentation rates in the wetlands of this region. Various farming and land management practices with the drainage area draining to wetlands affect the rate at which soil is detached by raindrop impact and transported by the runoff. Tillage practices tend to conserve or destroy crop residues which protect soil from erosion. Depending on the application of conservation practices such as terraces, contour farming and crop residue management, erosion and sedimentation rates may be accelerated or reduced in the closed watersheds that drain to the wetlands.

Data have been collected to assess the different rates of sediment deposition resulting from drainage areas consisting of native prairie, Conservation Reserve Program land (CRP), buffered wetlands, and tilled watersheds. Characteristics of the sediment, statistical analysis of the sediment for 1993, and other data reported by the U.S. Environmental Protection Agency (EPA) (1) indicate that wetlands with drainage areas consisting of tilled cropland have a greater sediment deposition than CRP cropland.

Approaches to Sediment Transport Simulation

Transport of sediment is affected by the detachment of soil particles by raindrop impact and transport by the runoff, susceptibility of the soil to detachment, the presence of material such as crop residue that reduces the magnitude of eroding forces, and management of the soil such that it is less susceptible to erosion. The rate at which sediment may be carried by the runoff is termed the capacity-limited transport rate. The rate at which sediment becomes available for transport is the supply-limited transport rate. At a given location on a slope, if the amount of sediment made available for transport by rainfall detachment is less than the transport capacity, then the sediment load moving down slope will be limited by the supply of sediment. If, on the other hand, the available sediment by detachment is greater than the transport capacity, then the sediment load is limited by the transport capacity (2, 3). The following factors affect the capacity- and supply-limited transport rates.

Rainfall and Runoff

Rainfall and runoff provide the basic driving energy for the erosion and transport processes. In stream channels where the bulk of sediment transport relationships have been developed, particles are continuously exchanged between the bed and the flow. In upland erosion, this does not usually occur because the shear required to detach the particle is much more than that required for transport. Foster and Huggins (4) reported that the critical shear stress required to detach soil particles is around 2.9 N/m2 whereas transport only requires around 0.5 N/m2 for a sand of 342 Ám. Rainfall impact on the soil surface is necessary for the detachment of particles, and, therefore, the supply of sediment. Modeling of upland erosion requires the simulation of supply rates and transport to obtain an estimate of sediment transport at a particular location in the landscape.


Topography affects the rate of runoff through slope and the length of slope. As slope increases so does the transport capacity. As length increases at a given slope, more drainage area contributes more runoff volume and rates providing more transport capacity. As soil particles are detached in the upper reaches of the watershed and transported down slope to the wetlands, the relative magnitudes of supply and transport rates govern the amount of sediment transported. Slope of the landsurface plays a key role in this sub-process. As slope decreases closer to the wetlands, it is expected that the transport capacity will fall below the supply rate. In the near-wetland part of the landscape, deposition has been observed and is explained by the decrease in transport capacity due to flatter slopes.


Soils have different susceptibilities to erosion forces. Thus, soil type and the management of the soil influences the rate at which soil may be detached by rainfall impact (5). Soil transportability is the ease with which the detached soil particles are transported by the water. Soil is eroded as primary particles (e.g., sand, silt, and clay) or as aggregates of different particle sizes and organic matter. Continual, intensive tillage breaks down the soil structure and depletes organic matter enhancing erodibility. Sediment produced on uplands as opposed to sediment flowing in rivers is a mixture of primary particles and aggregates (6). The proportion of primary particles and aggregates depends on upslope sorting, soil properties, and the amounts coming from rill and interrill areas. Soil particle sizes affect transport and deposition rates. Clays, if they are primary particles, may never be deposited due to resuspension caused by turbulence; whereas silts and sands are the first to be deposited as transport capacity decreases below the supply rate.


Cover, including plant canopy, mulches, plant residue, or densely growing plants, has a greater influence on erosion than any other factor. Cover, in contact with the soil, greatly reduces rill erosion by cushioning raindrop impact and reducing the shear stress exerted by flowing water. Strips of dense mulches or grasses can induce deposition and filter sediment from the runoff. Tillage type, frequency, and elapsed time between tillage and a runoff event affect the detachment of soil particles.

Given these factors that affect the detachment of soil particles (supply) and transport of sediment, the overall goal of simulation is not only to adequately represent the processes but to provide realistic estimates of the impacts of anthropogenic effects on wetlands. We were interested in both the capacity and the supply-limited rates because as runoff from the watershed divide traverses the topography, either control may dominate the transport of sediment. From preliminary analysis of sediment taken from the wetlands, CRP treated watersheds yield less sediment than those that were tilled (1). This indicates that the rate of sediment deposition is dependent on the supply which in turn is affected by tillage and land management practices.

Supply Limited Sediment Transport

Kilinc described a formula that includes the effects of slope and runoff on sediment transport (7). This equation was modified by Julien (8) to account for the soil erodibility, cropping and tillage effects, and conservation practices. The mass transport rate in metric tons per second per meter of width, qt, is

where, qt is the mass transport rate in metric tons per meter of width and seconds; So is the land surface slope; and q is the unit width flow rate in m2/s. This equation can be further modified (8) to account for the soil erodibility, cropping and tillage effects, and conservation practices as follows

where, K is the soil erodibility, C is the crop management factor, and P is the conservation practice factor. The factors K, C, and P are readily available for specific soils, crop management, and conservation practices. Further, K, C, and P represent the supply-limiting characteristics of the watershed.

Capacity Limited Sediment Transport

When sediment transport is controlled by the capacity of the flow, there exist several equations for predicting the transport capacity. Total load formulas applicable to upland erosion conditions include the formulas of Ackers and White (9), Foster (2), Yang (10), Laursen (11), and Einstein (12). Bed load formulas include Meyer-Peter and Muller (13), Bagnold (14), and Yalin (15). Alonso et al. (16) compared these formulas against field and laboratory experiments concluding that no formula satisfactorily represented the spectrum of sediment transport conditions or characteristics. Further, it was observed that equation by Yang (10) best estimated streamflow carrying fine to coarse sands; and that the Yalin (15) equation is best suited to overland flow, particularly on concave slopes.

Foster and Meyer (17) compared the sediment transport predicted by the Yalin equation to laboratory and erosion plot studies and found excellent agreement. Erosion of natural agricultural soils has been observed to occur by detachment and saltation of soil aggregates due to lifting forces induced by the flowing water. The Yalin equation assumes that sediment motion begins when the lift force of flow exceeds a critical lift force. The particle is transported downstream until the particle weight forces it out of the flow and back in the bed. The number of particles in motion at a given time is a linear function of an excess shear parameter, . The required hydrodynamic parameters are energy slope, and the hydraulic radius, R. The transportability of the soil is determined by the particle (aggregate or primary) specific gravity, the diameter, and the critical lift force, Ycr, given by the Shields diagram which defines incipient motion based on particle and fluid characteristics. The Yalin equation defines a dimensionless transport rate, (equation 3), in which Ws is transport rate in Newtons per second per unit width; SG is the specific gravity; w is the mass density of the water; d is the diameter in meters; g is the acceleration of gravity in m/s2; the shear velocity; V* is as in equation 4;

The excess shear parameter, in equation (3) is

where the lift force, Y is

The critical lift force Ycr is defined as a function of a dimensionless particle diameter, D*

The Shields diagram, usually presented in graphical form, may be expressed as a piece-wise continuous set of functions:

In equation (3) the value of = A * where A is

This defines each of the terms in equation 3. The resulting value of is dimensionless, whereas, the value of Ws computed with parameters in the Meters-Kilogram system, yields the capacity-limited transport rate in units of Newtons per second per unit width [N/(m s)].

Simulation of Sediment Transport in the Prairie Pothole Region

We applied the principles outlined above to sediment transport in wetland drainage areas in the PPR study area. Specific characteristics of sediment and topography in this region are important in the selection of appropriate transport equations and the correct application. Further, the overall goals of the project must be recognized so that model results are useful to decision makers.

Coupled Hydrodynamics and Sediment Transport

The complex terrain associated with the PPR must be adequately represented so that the simulated flow depths, velocities, and unit flow rate are predicted. The hydrodynamic module produces flow depth and velocities which are used to compute the unit flow rate, q. This flow rate was then used to compute transport rates and load.

Sediment Characteristics

The sediment characteristics in relation to the hydraulic regime was important in characterizing the type of sediment transport mechanisms. The sediment particle size distribution gives an indication of the potential sizes of sediment transported. The term potential was used since it is unknown whether the soil particles were transported as primary particles or aggregates or a combination. However, it was instructive to consider what the sediment size ranges are and the influence this has over the transport mechanisms. Sediment analyses taken from EPA (1) indicate that the sediment sizes, using logarithmic interpolation for the d50 , range from 15 Ám to 73 Ám. Figure 1 shows the ranges of particle sizes for selected potholes near Woodworth, North Dakota. The d50 for the W13E1 pothole was taken as 33 to 50 Ám. This places the median grain size in the range of a coarse silt (31 to 61 Ám).

Hydrodynamic Simulation

The hydrodynamic simulation was performed for a segment taken from the Digital Elevation Model (DEM) for the W13E1 pothole. The slope in this segment was 2% over a length of 80 meters. The rainfall intensity was taken at the higher end of the expected rainfall intensities, 18.97 cm/hr lasting for the duration of 360 seconds. The hydrodynamic module simulates flow depth and velocities for maps of topography (DEM), hydraulic roughness, and applied rainfall intensities.

Sediment Transport Rates

Supply-Limited Transport

To illustrate the transport computations for the W13E1 watershed, assumed conditions with respect to the supply-limited conditions (parameters K, C, and P) are made. Two conditions were modeled for CRP and tilled treatments with the following parameters. The resulting sediment transport is supply-limited and was the maximum amount that could be transported from the drainage area. So= 0.02 K= 0.42 Silt Loam with 2% OM CCRP= 0.24 No canopy and 20% cover by undecayed residues. Ctilled= 0.45 No canopy and 0% cover by undecayed residues. PCRP= 0.5 Farming on contour Ptilled= 1 No conservation practices.

The parameters chosen are typical values but should be modified for each soil mapping unit, land use/management, and cropping plan in each drainage area.

Capacity-Limited Transport

The Yalin equation defines the sediment transport limited by the capacity of the flow. This equation is independent of sediment source, and as such, simply represents the capacity of the flow to carry a particular sediment size. Natural sediments are comprised of a range of sizes. Capacity-limited transport equations often over-predict the total sediment load when applied to sediment size fractions and then summed by the percentage represented by each size. Thus, the Yalin equation was applied to the median grain size to compute the sediment load. The constants used to compute the sediment transport rate using equation 3 ff were:


g= 9.80 m/s2 vm 8.94e-07 m2/s Pw= 1000.00 kg/m3 Y= 9800 N/m3

Sediment Characteristics:

d_50= 3.30e-05 m Sg= 2.65 D*= 0.90 Ycr= 0.27 A= 0.86 The time-dependent supply-limited transport rate is shown in Figure 2 with the time-dependent capacity-limited transport rate. Note that the capacity-limited transport rate is less than both the CRP and tilled treatment transport rates. This indicates that the capacity-limited transport rate governs. The estimated transport rate is, therefore, the lesser of the two (capacity versus supply); the capacity-limited transport rate. Meyer and Wischmeier (3) found from erosion plot studies that for slopes of less than 3%, transport capacity was the limiting rate. The segment modeled in this example has an average slope of 2%.


The sediment transport associated with upland erosion is controlled by either the supply-limited or the capacity-limited transport rate. Depending on storm characteristics, topography, soils, land use, and management, either rate may dominate. The supply of sediment may be limited by crop residue which reduces soil detachment by rainfall. As the detached sediment becomes entrained in the runoff, it is transported as suspended or bed load depending on flow depth, velocity, and soil particle/aggregate size and specific gravity.

Under the conditions analyzed for the W13E1 pothole, both supply-limited and capacity-limited transport may dominate the sediment transport rate. Particularly on flat slopes encountered near the emergent vegetation of the wetland, sediment begins to drop out due to reduced transport capacity. The supply of sediment is also affected by the land treatment. CRP treated watersheds show less sediment transport than tillage without conservation treatment. Supply-limited transport rates for CRP conditions are 33% of the tilled conditions shown in Figure 2. The capacity-limited rate using the Yalin equation shows that it is controlling at all times during the storm for the flow rates encountered at 75 meters downslope from the watershed divide. Further analysis is needed to determine if this is true along the land surface profile from the watershed divide to the edge of the wetland.


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