Journal of Wind Engineering and Industrial Aerodynamics, 36 (1990) 1415-1424 1415 Elsevier Science Publishers B.V,, Amsterdam - - Printed in The Netherlands

Windstorm Erosion and Soil Deposition Simulation

J. M. Gregory* J. Borrelli ** C. B. Fedler ***

ABSTRACT

A computer program, TEAM, designed to simulate windstorm erosion and soil deposition is described. Components of the simulation model are based on verified cause and effect relationships that match physical boundary conditions. Applications of the model were given. It is shown that the interaction of management or even placement of highways relative to railroads can have a major effect on wind erosion and soil deposition.

INTRODUCTION

Wind forces acting on soil surfaces can reduce land productivity, abrade surfaces of buildings, pollute the atmosphere, and reshape the landscape often covering highways and railways with deposits of sediment. Many problems in Agricultural, Civil, and Environmental Engineering are directly affected by wind erosion. For example in New Mexico, the number 2 state after Texas with severe wind erosion problems, it is estimated that damage of $358/person occurs each year because of wind erosion, much of which was due to sediment on roads and health-related problems which result from dust in the environment (Huszar and Piper, 1986).

Wind erosion research is only 40 to 50 years old, beginning primarily with the work of Bagnold (1945). In addition to Bagnold's work, USDA researchers have also performed research during the last two decades with emphasis on long-term soil loss. Over 230 technical papers, experiment station bulletins, and journal articles have been written by researchers at the USDA Wind Erosion Laboratory at Manhattan, Kansas (technically National Erosion Laboratory) and their associates. Yet, short-term or single-event research has been neglected. Ironically, single-storm erosion events are easy to detect visually and offer a major opportunity for field research, especially model verification. Single events also can be easily linked to off-site damage including abrasion, sedimentation, and movement of chemicals.

*Professor of Agricultural Engineering, **Professor and Chairman of Agricultural Engineering, ***Assistant Professor of Agricultural Engineering, Texas Tech University, Lubbock, TX 79409

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TEAM (Texas Erosion Analysis Model) is a computer program developed at Texas Tech University to simulate the wind profile development and soil movement over multiple land segments of variable length, soil erodibility, and clod, residue, and canopy cover. Predictions of soil movement and soil loss are made on an hourly basis for single events but can be extended to yearly loss for some limited conditions. Eventually, crop growth and soil tillage subroutines will be completed so complex yearly simulations can be performed. Since the user supplies specific site information, predictions of soil movement can be made for a variety of problems, such as agricultural fields, urban area, construction sites, or surface mine areas. TEAM is an extension of the Texas Tech Wind Erosion Model reported by Gregory and Borrelli (1986).

MODEL DEVELOPMENT

TEAM is made of several submodels, including soil detachment (Gregory and Borrelli, 1986), soil detachment with length (Gregory, 1986), erosion reduction with wind breaks (Borrelli et al., 1987), and determination of the wind velocity profiles (Abtew et al., 1988). The derived equations were verified using data reported in the literature in addition to data collection from wind tunnel studies at Texas Tech University.

Wind Profile

An understanding of wind velocity profiles near the surface is necessary to predict soil erosion by wind. The following equation is typically used to model the wind profile over a given surface:

U* Z - D U* = -- in(- )

k Z o

[1]

where U = the average velocity measured at height Z, U* = shear velocity, Z = height of velocity measured from a reference surface, D = displacement height, Z o = aerodynamic roughness, and k = Von Karman's constant which is 0.4 for neutral conditions

when air is neither rising or falling due to thermal gradients.

The estimation of the displacement height, D, and the aerodynamic roughness, Zo, has been a perplexing problem. Various researchers have defined these parameters differently and offered different equations to estimate them.

To remedy this problem, Abtew et al. (1988) developed relationships between the displacement height D and the height of

individual roughness elements H. Thus, for any type of roughness element ranging from individual sand particles to trees, the displacement height D can be calculated. The general equation for displacement height is given as follows:

D = F H [2]

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where F = fraction of surface covered with roughness elements, and H = average height of individual roughness elements.

The aerodynamic roughness was found to have the following

relationship:

Z o = 0.13 (H - D) [3]

This equation is based on 19 measured data points reported in the literature. It had an R 2 value of 0.92 and was significant at the 99.9 percent level (a = 0.001). This equation was also verified to work over five orders of magnitude of roughness heights with other data sets, which suggests that it is universal in nature except when the roughness elements are widely spaced.

A correction factor was developed to adjust Equation 3 for the condition of widely spaced roughness elements. Data from Kutzbach (1961) were analyzed and the following equation was obtained:

Z o = 0.13(H-D) (l-e -94(H W/$2)2) [4]

where w = width of roughness element, and s = spacing between roughness elements.

The correction factor has a value of 1.0 for most field applications and did not change the results by Abtew et al. (1988). The correction factor, however, is important for sparse cover conditions such as 5 or i0 percent clod cover. Equation 4 fit data from Kutzbach (1961) with an R 2 of 0.68 and was significant with an alpha of 0.001.

The above derived equations make it possible to estimate U* with only the measurement of velocity at one height. The equations also explain how surface roughness interacts with the wind profile. This is especially important for problems such construction and mining sites where surface roughness can be varied with management. This procedure was programmed into TEAM.

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D e t a c l ~ e n t

Gregory and Borrelli (1986) used dimensional analysis to develop the following equation to predict the mass of soil detached by a flowing fluid:

(~ - xc)U M - (a + b) tan Sf [5]

~S

where

(F/L2),

(L/T).

M = detachment (M/L2T), t fluid shear (F/L2),

~c = critical fluid shear required to initiate soil movement

U = fluid velocity at the top of the surface boundary

~s = soil shear strength (F/L2), Sf = soil friction angle, and

a & b = constants.

Gregory (1984A) defined a function S to estimate the energy transfer to the eroding surface. This function was combined with the above equations to produce a model for soil detachment by wind. The equation is as follows:

2 2 M = (S U* - U~ t) U*BI [6]

where M --

S =

B ~

U* =

U* t = I =

soil detachment per unit area per unit time (M/L 2 T), surface cover factor which expresses the amount of detachment energy at the top of the cover which is transferred to the soil, a constant to adjust for the units used for I, U*, and M, shear velocity (L/T), threshold shear velocity (L/T), and soil erodibility factor involving soil shear strength and shear angle.

Equation 6 is similar to published transport equations (Greeley and Iversen, 1985) in that it contains the variable U .3. It is unique, however, because it also contains the variable S to account for residue, vegetation, or clod cover effects. Equation 6 does not contain a length variable to account for the avalanching effect.

While Equation 6 may not appear to have a physical basis because of the development with dimensional analysis, it is an expression of detachment from kinetic energy input which is a documented physical relationship (Greeley and Iverson, 1985). This relationship between detachment and kinetic energy has been documented by Greeley and and

Iversen (1985) for erosion by wind, Hudson (1981) and Gregory (1984B) for erosion by water, and Gregory (1988) for erosion of metal from roller chains.

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Soil Detaclment with Length

On an erodible field, the windward edge generally will not erode due to the protection provided by vegetation or other barriers on the edge of the field. However, the rate of soil detachment and movement increases until, when the field is of sufficient length, the maximum rate of detachment and movement occurs. Gregory (1984B) developed a mathematical function which explains the length effect for soil erosion by wind and verified the relationship using published data. This mathematical function has been re-derived by Gregory (1986) and is defined as:

X = C(SU ~ - U~t)U* ( I - e-0"000169AalLf) [7]

where X = rate of soil movement at length Lf (M/L T), C(SU e - Uet)U* = maximum rate of soil movement (Lf = ~) which occurs when surface is covered with fine non-cohessive material, C = a constant which depends on width sampled and units used

for U ~ (MT2/L4), Lf = length of unprotected field in the direction of wind

movement (L), A a = abrasion adjustment term.

The term A a is:

A a = (I 0.23) (I e -0 0072e0"000791Lf) - - " + 0.23 [8]

Equation 7 was checked with wind erosion datapublished by Chepil (1957) and found to fit the data well (R 2 = 0.91 and a = 0.001). A second data set (Chepil and Milne, 1941), independent from the data used to develop the abrasion effect was used to also verify Equation 7. The overall R 2 value for the independent data set consisting of five fields was 0.79. When one field (with non-uniform field conditions) was eliminated from the data set, the R 2 increased to 0.87. Both values were significant with a 99.9 percent probability level (a = 0.001). Equation 7 couples four physical parameters (wind, cover, soil, and length) that affect soil detachment and movement by wind.

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Computer Program Code

The computer code for TEAM was designed to allow the user to input the number of length segments and the associated data with each segment. Data for each segment is then entered. Data entered includes height and fraction of cover of plant canopy, residue, and clods, location and height of barriers, and soil erodibility. Separate segments allow an erosive segment such as a sandy soil to be placed up wind to the soil segment in question. The abrasion caused by the sand particles will accelerate the detachment on the section in question. By varying the erodibility and cover conditions on up- wind segments, both the abrasion and deposition effects on erosion are simulated. TEAM also evaluates the surface area of the soil in motion divided by the surface area of the initial soil to estimate chemical enrichment. A discussion of the program is given by Gregory et al. (1988).

If the up-wind segment has a movement rate larger than the maximum transport capacity for the new segment, deposition will occur. The deposition rate is computed by subtracting the new maximum transport rate from the movement off the previous segment. All deposition is assumed to occur at the leading edge of the new segment. This assumption is reasonable compared to the 3 m strip width requirement suggested by Lyles et al. (1973) and the results of Hagen et al. (1972). Three meters is negligible when compared to segment lengths of i00 m or larger.

TEAM was also programmed to estimate the average rate of soil loss from the given area on an hourly basis. This calculation is performed by dividing the total movement of material by the total length from which the material is derived.

APPLICATION EXAMPLI~

The first application example is for soil movement from bare soil. Figure i shows simulated results from TEAM. These results match measured results of Chepil (1957) with an R 2 of 0.91.

Farmers and employees of SCS in West Texas are aware that soil clod management is a key way to reduce soil erosion by wind. Predictions for various fractions of 3 cm diameter clod cover are plotted in Figure 2 for the wind conditions at Amarillo, Texas. Because clods affect the wind profile as well as protect the finer soil from erosion, TEAM predicted little change in soil loss as clod cover was increased from 0 to i0 percent. A 20 percent clod cover, however, produced some reduction in erosion from the bare soil condition. An increase in clod cover to 30 percent, however, was very effective and resulted in a soil loss reduction of over one order of magnitude. From these predictions, it appears that farmers must be careful to achieve at least 20 and preferably a 30 percent clod cover.

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300 L

~ 2 5 0

200 W

w i ~ o

x

lOO

w

50 H

w

0 0

o E40 & V - t 5 + E30 & V - t 5 * E20 & V - J 5

m

• u I I I

t 0 0 400 500 200 300 FIELD LEN6TH (m)

Figure I. Predicted soil movement as a function of field length and soil erodibility for a wind velocity of 15 m/s at a height of 10 m.

(!,1 f_ {_1l Io

t- o 4J

o3 o3 0 _1

_1 H 0 or)

1000

800

600

400

200 W NO TREATHENT o WITH TREATHENT

/ ==!

200

!

0 400 600 800 1000 LENGTH ( f t )

Figure 2. Example use of predicted results for analyzing conservation treatments next to highway.

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Another example is for the interaction of an agricultural field field with two different soil types and a highway. In this example, the first three segments are sandy with an erodibility of 50 t/ha and the next five segments have a much lower erodibility of i0 t/ha. Down wind from the field is a I0 m wide road ditch and grassed area with 50 percent cover of 15 cm tall grass. Next to the grass is a highway with zero erodibility. The predicted results are shown in Figure 3. The grassed strip protects the highway from drifts of sediment, but the soil in the road ditch will eventually have to be removed with cost to the taxpayer. If a I0 m grassed strip were located on the last strip of sandy soil, both the farmer, the highway department, and the taxpayer would benefit because of the reduced soil movement. This treatment is also shown in Figure 3. Predictions of this nature should be of value in determining both estimates of future cost and selection of least cost alternatives.

1200

~ . 1 0 0 0

8 0 0

m 600

0 J

4 0 0

0 m 2 0 0

o No clods + I O X * 2 0 X O 3 0 Z

0 I i i i

0 t 0 0 2 0 0 3 0 0 4 0 0 5 0 0 LENGTH (m)

Figure 3. Effect of clod cover on total soil loss.

A final example, Figure 4, shows the interaction of a wind barrier with 50 percent porosity upwind to a railroad right-of-way which is upwind to a highway. Most of the sediment deposited behind the barrier on the railroad right-of-way. A small but final amount was deposited on the highway right-of-way which was simulated to have 30 percent vegetative cover.

SUMMARY AND CONCLUSIONS

A computer program, TEAM, has been developed to simulate the interaction of surface conditions of the wind profile and soil movement. Further development of TEAM is planned; never the less, the present program is capable of simulating many combinations for

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400 L = 350

300

250

200 Z W i 150 W

o 100 X

j 50 H O 0

0

J

I I I I

i 0 0 200 300 400 LENGTH (m)

I

500 600

Figure 4. Soil movement to and through wind barrier of 50% porosity with deposition on road bed.

single wind storm events and some average annual conditions. Example simulations were presented. From these examples, it appears that farmers must be careful to maintain at least a minimum fraction of clod cover if clods are to be used to control wind erosion. It is also obvious that the cost of highway maintenance is highly dependent on management of areas upwind to highways. It appears that a computer program such as TEAM could help engineers, city planners, and mine managers find least cost solutions to the problem of wind erosion.

~ C E S

Abtew, Wossenu, James M. Gregory, and John Borrelli. 1988. Wind Profile: Estimation of Displacement Height and Aerodynamic Roughness. TRANSACTIONS of the ASAE (Accepted for publication).

Bagnold, R. A. 1945. The Physics of Blown Sand and Desert Dunes. William Morrow and Company, New York.

Borrelli, John, J. M. Greogry and Wossenu Abtew. 1987. Wind Barriers: A Reevaluation of Height, Spacing, and Porosity. Presented at the Summer Meeting ASAE, Baltimore, MD.

Chepil, W. S. 1957. Width of Field Strip to Control Wind Erosion. Kansas Agricultural Experiment Station Technical Bulletin 92. Kansas State University. Manhattan, Kansas.

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Chepil, W. S., and R. A. Milne. 1941. Wind Erosion of Soils in Relation to Size and Nature of the Exposed Area. Science of Agriculture. 21:479-487.

Greeley, Ronald and J. D. Iversen. 1985. Wind as a Geological Process on Earth, Mars, Venus, and Titan. Cambridge University Press. New York.

Gregory, J. M. 1984A. Prediction of Soil Erosion by Water and Wind for Various Fractions of Cover. Trans. ASAE 27(5):1345-1350, 1354.

Gregory, J. M. 1984B. Analysis of the Length Effect for Soil Erosion by Wind. Paper presented at the 1984 Winter Meeting of ASAE. New Orleans, Louisiana.

Gregory, J. M. 1986. Analysis of the Length Effect for Soil Erosion by Wind. Unpublished Research. Department of Agricultural Engineering. Texas Tech University. Lubbock, Texas.

Gregory, J. M. and J. Borrelli. 1986A. Physical Concepts for Modeling Soil Erosion by Wind. Paper presented 1986 Southwest Region Meeting of the American Society of Agricultural Engineers. Louisiana State University. Baton Rouge, LA.

Gregory, J. M. and J. Borrelli. 1986B. The Texas Tech Wind Erosion Equation. Presented at the Winter Meeting of the American Society of Agricultural Engineers. Chicago, Illinois. Paper No. 86-2528.

Gregory, J. M., J. Borrelli, and C. B. Fedler. 1988. TEAM: Texas Erosion Analysis Model. Presented at the Summer Meeting ASAE, Rapid City, SD.

Hagen, L. J., E. L. Skidmore and J. D. Dickerson. 1972. Designing Narrow Strip Barrier Systems to Control Wind Erosion. Journal of Soil and Water Conservation. 27(6):269-272.

Huszar, P. C. and S. L. Piper. 1986. of Wind Erosion in New Mexico. Conservation. 41(6):414-416.

Estimating the Off-site Costs Journal of Soil and Water

Kutzbach, J. E. 1961. Investigations of the Modifications of Wind Profiles by Artificially Controlled Surface Roughness. Annual Report, Department of Meteorology, University of Wisconson- Madison. pp. 71-113.

Lyles, Leon, N. F. Schmeidler, and N. P. Woodruff. 1973. Stubble Requirements in Field Strips to Trap Windblown Soil. Kansas Agricultural Experiment Station Research Publication 164. Kansas State University. Manhattan, Kansas.