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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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Suggested Citation:"5. Wind Erosion." National Research Council. 1986. Soil Conservation: An Assessment of the National Resources Inventory, Volume 2. Washington, DC: The National Academies Press. doi: 10.17226/648.
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5 Wind Erosion Dale A. Gillette Although there was much interest in wind erosion of agricultural soils in the 1930s, research has not been extensive except in a few places including the Great Plains and Southern High Plains. In an effort to include wind erosion data with other kinds of soil erosion data for the entire United States, the Soil Conservation Service (SCS) estimated total wind erosion by using National Resources Inventory (NRI) data and a wind erosion equation that was described by Skidmore and Woodruff (1968). The equation for expressing expected wlna erosion IS : E = IKCf'(L')V, where I is expected erosion (tons/hectare/year) for a flat bare soil, K is the ridge roughness factor, C is a climatic factor, f'(L') is a function of the fetch length L', and V is the vegetative factor. The Wind Erosion Equation (WEE) was developed from wind tunnel work, laboratory experimentation, and field observations in the Great Plains and Southern High Plains. For the SCS application, the factor I was estimated from soil texture data that complemented other NRI data; C was obtained from maps; and f'tL'), K, and V were calculated using the field data of the NRI. Estimations based on Equation 1 and the NRI data proved, however, to be somewhat puzzling. For example, wind erosion for south central Minnesota and northwest Florida (see Table 1) show that wind erosion is of the same magnitude as rill and sheet erosion by water. Intuitively, given soil characteristics, climate, and vegetation in these regions, the results suggest an overestimate of the magnitude of wind erosion. For this 129 (1)

130 TABLE 1 Wind and Sheet and Rill Erosion for Four Major Land Resource Areas (MLRAs) Wind Sheet/Rill Erosion Erosion HLRA Location (106 Ton) (106 Ton) . 72 Western Kansas55 21 77 Western Texas330 27 103 South central67 57 Minnesota 154 Northwest0.7 0~9 Florida SOURCE: W. E. Larson, University of Minnesota, personal communication (1984). reason, an analysis was initiated of the wind erosion equation and the data used in it to see whether features of the equation or of the data would lead to overestima- t~ons of wind erosion for localities having soil charac- teristics and climate different from the area in which the equation was developed [western Kansas, Major Land Resource Area (MLRA) 72]. This paper includes an analysis of four of the five terms used in the WEE, a possible alternative WEE that would correct some perceived shortcomings of the original equation, a proposed provisional WEE (requiring more research for implementation) that may be used with data from the 1982 NRI, and a review of some work on the portion of the eroded soil (dust) that is carried far from the eroded field, to emphasize its importance and to urge that work be started to estimate the loss of this fine portion of the soil. It has potential impact not only on soil but also on atmospheric pollution. ANALYSIS OF TERMS OF THE WIND EROSION EQUATION Erodibility Term, I The cornerstone of the WEE in explaining variance is the soil erodibility term, I. It was derived from the

131 total annual erosion (mass/area/year) for fields located near Garden City, Kansas. certain farm Garden City, Kansan In the WEE, the I values are used as expected annual wind erosion for soils having a certain parameter. The soil parameter to which this total expected erodibility was related is the percentage of soil mass in aggregates smaller than 0.84 mm. Previous work on threshold velocities that included a regression with percentage of mass smaller than 1 mm (a size very close to 0.84 mm) allowed the expected annual soil loss per unit area (I') to be calculated and compared with the equivalent I factors of the original WEE. The expected total annual soil loss per unit area could be expressed as an expectation integral divided by field length. The proposed integral is composed of a function that expresses horizontal soil mass flux at the downwind edge of a field as a function of wind friction velocity, a probability density function for wind friction velocity at a given location, and a threshold friction velocity at which erosion starts. 00 I. = AT r q ( u* ) f(u*) du*/L/ u*t where AT is the sampling time It year for the WEE), L is field length, u* is a wind friction velocity, u*t is threshold friction velocity, q(u*) expresses total soil horizontal mass flux (i.e., soil movement) as a function of wind friction speed (u*), and f(u*) is the probability density of the wind friction velocity. H. Lettau (University of Wisconsin, personal communication, 1973) gives the horizontal mass flux [mass/(width · time)1 as: q(u*) = ku* (u* - u*t) where k is a constant. The fit of field data (Gillette, 1981) to this function is shown in Figure 1. Soils 1, 2, 3, 4, and 5 (sand and loamy sand) all have q versus u* data that fit Equation 3 quite well for threshold friction velocities u*t between 20 and 40 cm/s. These values of u*t for sand and loamy sand textures are quite consistent with outdoor wind tunnel tests for threshold friction velocities. The data points for soil 6 (a sandy loam soil) and soil 9 (a clay textured soil) (2) (3)

132 1o1 100 _ 10-1 In C) 10-2 - - ~r 'it 10-3 10-4 1 _ ./ 10-5 1 1 20 Soil x Soil 1 2 3 o Soil 4 o Soil 5 ~ Soil 6 O Soil 7 Soil 8 V Soil 9 ~1 1 1 1 1 ~1 40 60 u. (cm/s) 80 100 200 FIGURE 1 Plot of the function q(u*) = 4 x 10-7u* 2(u* - u*t) versus friction velocity, u*, and field data (Gillette, 1981). (Textures of soils 1-9 are plotted in Figure 8.) Threshold velocities (u*t) for the six curves (left to right) are 20, 30, 40, 50, 60, and 70 cm/s. fall close to the curve for u*t = 62 cm/s, which is also consistent with outdoor wind tunnel data for threshold friction velocities. The value for soil 7 (a loamy sand soil) falls on a curve for u*t = 45 cm/s. A probability density of wind speed, the Rayleigh distribution, which has been used by researchers in the wind energy field (see, for example, Corotis et al., 1978), was used in the expectation integral. Details of the Rayleigh distribution are given in Appendix A. For the parameter of the Ravleiah distribution data for Dodge City, Kansas _ _ (which is located near Garden City, Kansas) were used. Substitution into Equation 2 of the mass flux function of wind speed (Equation 3), the distribution of wind speeds, and the lower limit of wind speed at which the soil erodes gives an expression of expected wind erosion for a flat bare soil:

133 co I' = kcd AT I U U2(U - Ut) f(U) dU/L, t where cd equals (u*/U)2 (the drag coefficient), U is wind speed at 7 m, and f(U) is a Rayleigh probability density function. Therefore, as derived in Appendix A, I' = kcd 1.5 AT [U3Ftx) - U2UtG(x)]/L, _ _ where x equals Ut/U, U is the mean annual wind speed, Ut is threshold wind speed, and F and G are functions of x (evaluated in Appendix A). For this calculation, threshold velocities given by Gillette et al. (1980), shown in Figure 2 and corrected to the height of 7 m, were used. Actually, percentage of mass smaller than 1 mm is not the best predictor of threshold velocity, although it does allow us to compare the annual expected wind erosion with the I factor of the original WEE, which uses the common parameter, percentage of soil mass smaller than 0.84 mm. This comparison is shown in Figure 3. Both curves have been normalized by the expected erosion for all soil mass smaller than 0.84 mm. Thus, both curves represent a relative erosion as a function of percentage of soil mass smaller than 0.84 mm. The agreement is relatively good for high percentage values of soil mass smaller than 0.84 mm. But in the region of less than 70 percent, there is significant disagreement. However, as Chepil (1960) pointed out, this part of the I curve is doubtful: "In view of great inaccuracies in measuring relatively small annual soil losses from depth of soil removal, conversion of the relative field erodibility to annual soil loss based on the curve of [his] Figure 1 must be regarded only as highly approximate. n Use of an expectation integral appears justified because of the progress that has been made in the determination of wind speed probability distributions, of the horizontal flux of soil as a function of wind stress, and of threshold friction velocities for the onset of wind erosion. On the other hand, an examination of Chepil's data on which I versus percentage of soil mass less than 0.84 mm is based shows considerable scatter of the rather sparse data points from which this most important term of the (4) (5)

134 104 ,~5 %massd< lmm FIGURE 2 Threshold velocities versus percentage of soil mass smaller than 1 mm (Gillette et al., 1980). - o o A_ a) - - WEE was estimated. Data are also relatively sparse for the highest erodibility class. Therefore, Chepil's warning on the reliability of the I function for low erodibility cases should probably be heeded. Indeed, the significant differences of erodibility for the WEE and for the expectation integral based on threshold velocity would indicate an overestimation of erosion using the WEE if the integral method is more correct. Estimate of I Based on Wind Erosion Groups The TORI estimates of wind erosion used tables showing values of I for the various subsets of the soil texture domain wind erosion groups (WEG) rather than using dry sieving. (See Table 2 for a typical table of I versus

135 0.8 ._ ._ n ._ o 0.6 llJ o o ._ 0.4 0.2 ; 1 1 1 1 1 1 _ r u2 (u ut,p(u, du ~ Ut I .. i- [it~u2(u-ut)p(u)du] d ~- \ Hi, by,, ,, I // Imax \ '/ by/ /' 0 20 40 60 °/0 Mass <0~84 mm 80 100 FIGURE 3 Plot of the relative shapes for I curve used in the NRI calculations and the expectation integral of Equation 5 in this paper versus percentage of soil mass in aggregates smaller than 0.84 mm. WEG and for definitions of WEGs.) These "typical" data were obtained from Lyles (1976) but are not necessarily the same as those used for specific MLRA units to obtain wind erosion estimates (T. George, Soil Conservation Service, personal communication, 1984). When some of the threshold velocity data for sand- and clay-textured soils (Gillette et al., 1980) were examined, the variability of u*t from which expected erodibility may be calculated was striking. For disturbed sand-textured soils, the mean and standard deviation of threshold friction velocity for seven soils was 31.6 + 8.2 cm/s. For disturbed gravelly soils having sand textures, threshold friction velocity was 61 + 20 cm/s. Four clay-textured soils had a mean threshold friction velocity of 31.3 + 8.2 cm/s, i.e., practically the same

136 TABLE 2 Descriptions of Wind Erodibility Groups (WEG) and Corresponding Erodibility (I) Values WEG Predominant Soil Textural Class Dry Soil Aggregates 0.84 mm (Percentage) Soil Erodibility I [(T/Ha)/Yr] 1 Very fine, fine, and medium sands: dune sands 2 Loamy sands; loamy fine sands 3 Very fine sandy loams; fine sandy loams; sandy loams 4 Clays; silty clays; noncalcareous clay loams; silty clay loams with more than 35% clay content 4L Calcareous loams and silt loams; calcareous clay loams; silty clay loams with less than 35% clay content 5 Noncalcareous loams and silty loams with less than 20% clay content; sandy clay loams; sandy clay 6 Noncalcareous loams and silt loams with more than 20% clay content; noncalcareous clay loams with less than 35% clay content 7 Silts; noncalcareous silty clay loams 50 with less than 35% clay content 1 10 25 25 25 45 696 301 193 193 193 126 108 85 SOURCE: Lyles (1976). value as for the disturbed nongravelly, sand-textured soils. However, three of these four soils had very limited reservoirs of erodible material. Once a small amount of soil had eroded, their threshold velocities returned to high values, which rendered the soil virtually unerodible. The fourth clay soil, a vertisol, had a deep reservoir of erodible material and was capable of eroding as much as the sand-textured soils. Four other disturbed clay-textured soils had friction velocities well above 100 cm/s and were considered almost unerodible. The great variability of I values will not be explained solely by a relationship with soil texture. This unexplained variability will probably be greater for soil textures other than sand and loamy sand, although the latter may have considerable variability if gravel is a significant constituent of the surface soil layer.

137 Constancy of I The use of a constant value for I for an entire year seems inadvisable when considering the changes observed in dry aggregate size distribution for certain textures of soil during one 9-month period. For example, the histograms in Figure 4 show dry aggregate size distribu- tions of a clay-textured soil at the beginning of a drought season in West Texas and at the end of that season 9 months later. The aggregates show a disintegration that led to an increase in I by a factor of about 5. The value of threshold wind speed also changed during this time from 204 cm/s to 35 cm/s. C Term--Erodibility Corrected for Climate Effect of Mean Wind Speed Difference In correcting for areas having different wind speed and rainfall climates (using Garden City, Kansas, as the reference area), the WEE uses a correction based on mean quantities of wind speed and rainfall evaporation. In an attempt to elucidate the effect of this treatment, the climate factor C was simplified by assuming no soil moisture effects; only the effect of differing mean wind speeds in the same way as is done in the WEE was considered. The C value is used to correct the I value so that erosion can be estimated for an identical farm field located in a different climatic region. Thus, IC would estimate annual erodibility for a farm field that is flat and barren and that has a length and threshold velocity identical to those fields near Garden City, Kansas, where the I values were determined. Therefore, the question is asked, does a correction factor, U3/U 3 where the subscript GC stands for the Garden City value of the subscripted variable, properly correct for a change of the distribution for different geographical regions? Evaluation of Equation 5 for Garden City and another location using Appendix A and correcting the Garden City value with Equation 5 yields: (6)

go ~ o 200 180 160 140 120 1 80 00 40 20 o 200 180 160 140 o 100 80 60 40 20 o ~2 0~2 0~ d (mm) i I 1 2.0 20.0 ~2 0~ 0~ d (mm) 2.0 20.0 FIGURE 4 Size distributions of loose particles on the surface of a Randall Clay soil {upper) before a season of drought and (lower) after a season of drought.

139 ~(XGC) ~ Ut/UGC G(XGC) = F(x) Ut/ where x equals Ut/U and xGc equals U/UGc. In fact, the evaluation shows that the correction factor C will overestimate wind erosion when the ratio of wind velocity_at a particular site to wind velocity at Garden City (U/UGc) is less than one. Thus, the WEE would be expected to overestimate wind erosion for most parts of the United States because the ratio U/UGc is less than one for most parts of the United States. This analysis shows that C does not accurately correct the estimate for expected erosion in a different climatic region because mean values of wind speed to the third power do not equal the expectation of the third power of the wind speed. Indeed, a significant overestimation of wind erosion would be expected using C for mean wind speeds that were lower than those at Garden City, Kansas. Effect of Soil Moisture (7) According to Chepil (1956), the threshold velocity of soil following moistening is increased by an amount proportional to soil moisture content divided by soil moisture content at 15 bars tension. When the soil dries it will either return to its former physical state and recover its old (lower) threshold velocity or it will form a crust that will determine a new threshold velocity. Gillette et al. (1982) showed that soil crusts thicker than 1 cm and having a modulus of rupture greater than 1 bar prevent erosion for friction velocities smaller than about 150 cm/s (rarely exceeded by the atmosphere). Thus, until disturbance of the soil disintegrates the surface crust, the soil is for practical purposes unerodible by wind. Crust formation is not prevalent on sandy and sandy loam soils, but it is quite an important mechanism in preventing wind erosion on finer textured soils. Moreover, the author has observed that wind erosion recurred within minutes of a rainfall for sand and loamy sand soil textures. These observations suggest that crusting of finer textured soils may be more important than soil moisture to wind erosion prevention.

140 2 1 5 05 o , ' 1 - 1 1 1 ~ sphere 2, low speed · sphere 2, high speed o sphere 3, low speed · sphere 3, high speed ,i dig ~ ~ 1 1 . 0 1 1 0 40 80 120 160 £(cm) FIGURE 5 Nondimensionalized mass flux, using center-line wind speed as the speed parameter, versus length in a wind tunnel (Gillette and Stockton, 1985). L' Term--Fetch Length The wind fetch effect, named "soil avalanching" by Chepil (1957), is an increase with downwind distance of the horizontal flux of soil mass in wind erosion. Actually, avalanching is a misnomer because the increase of soil horizontal flux is not related to conversion of the potential energy of erodible soil particles into kinetic energy. For a constant wind stress and homo- geneous soil aggregate structure across a farm field, no increase of soil mass flux with distance should be expected because soil mass flux responds within 10 cm to a change in wind stress (Gillette and Stockton, 1985). An observed increase of particle saltation flux with distance in a wind tunnel has been ascribed to the effect of a feedback mechanism that increases wind stress with distance by increasing the effective aerodynamic roughness height (Owen and Gillette, 1985). Figure 5 shows the increase of particle flux (expressed as a nondimensional ratio) with distance downwind in a wind tunnel. This increase was accompanied by an increase of the ratio of friction velocity to center-line wind velocity with distance (Gillette and Stockton, 1985) such that the ratio of particle flux divided by friction velocity to the third power remained more or less constant.

141 The experiment from which Figure 5 was obtained showed that the particular fetch effect observed can be explained by a purely aerodynamic effect. Although it is true that length scales differ greatly between wind tunnel and farm field, this evidence suggests that Chepil's assumption that the wind stress is constant for a given eroding field and his representation of the increase of saltation flux as a function only of soil erodibility is incorrect. A correct treatment of the fetch effect must consider the roughness of the surface upwind of the eroding field, the height of the planetary boundary layer, the roughness of the eroding field, and the dry aggregate structure of the eroding soil, among other parameters. More work needs to be done on the problem of the fetch effect, especially in the light of recent findings on wind erosion in wind tunnels. K Term--Ridge Roughness Factor Ridges or furrows in farm fields affect the flux of eroding particles by establishing an aerodynamic roughness height and by trapping sand in the furrows. Sand trapping appears to be the dominating effect and a deep furrow would be very effective in limiting sand flow on a farm field. For this reason the K factor used in the WEE that expresses fraction of eroding material for a furrowed field to that in a flat field is puzzling. That is, the fraction, K, after a minimum for ridge roughness of about 88 mm, increases with increasing furrow depth (see Figure 6). The increase with increasing furrow depth (see Figure 6) after a minimum furrow is also puzzling. This increase would seem to be explainable only by increased roughness height and extremely erodible soil. The newer data of Fryrear (1984) (see Figure 6) do not show an upturn in the K factor curve when ridge roughness is greater than 88 mm. The differences in the curves are probably explained by the differences in experimental methods. Whereas Armbrust et al. (1964) set the base of their soil ridges even with the bottom of the wind tunnel and used highly erodible dune sand and gravel, Fryrear (1984) set his wind tunnel 20 mm below the peak of the ridges. Eryrear's method may have simulated field conditions better because it simulates the action of a boundary layer that has its point of zero mean wind speed not too far from the tops of the soil ridges. Substitu- tion of Fryrear's K factor in the WEE would lower the

142 10 o In 6 ~ 06 En En o 08 J J 04 En LL o . _ at\ I\ ~' _ \ An. - i_ - \ \ - - - - ,, _ _~ 1 1 1 1 0 50 100 150 RIDGE ROUGHNESS Kr (mm) 200 250 FIGURE 6 Ratio of soil loss from ridged surface to soil loss from a flat surface with the same soil versus ridge roughness. Data from Fryrear (1984) are a solid line; those from Armbrust et al. (1964), a dashed line. Results from Chepil and Doughty (1939) are marked Y; from Woodruff et al. (1968), X; and from Fryrear and Armbrust (1969), 0. (Entire figure from Fryrear, 1984.) total estimated erosion by lowering the estimates for deep-furrowed farm fields. The possibility that field furrow depth can change during the erosion season makes the approach of using only one value of K for the entire season a probable source of error. V Term--Vegetat Live Effect Nonerodible material on the surface acts to limit erosion in two ways. The first and most obvious way that the soil surface is covered and thus not exposed to erosive forces. Second, nonerodible elements partition the wind stress in such a way that a fraction of the

143 stress is absorbed by those elements, leaving a residual wind stress to erode the erodible soil lying in between. The Wind Erosion Unit of the Agricultural Research Service has been using this conceptual framework of momentum partitioning in assessing the effect of vegetation and has made good progress, as described, for example, by Lyles and Allison (1976). The incorporation of this kind of work into the new WEE proposed in the next section would be beneficial. In this equation, the threshold velocity would be determined not only by the physical state of the exposed soil, but also by partitioning of momentum by nonerodible elements (for example, vegetation) and other effects (for example, soil moisture and trapping of particles by furrows and surface residues). The wind momentum flux available for wind erosion of soil would continue to be affected by nonerodible elements after threshold velocity is increased and that effect would be included in the drag coefficient Cd. Again, any change of the vegetative cover should be represented in the new wind erosion equation by a change of the threshold velocity and drag coefficient. Knoll Erodibility Increased flux of soil particles on an upslope may be explained by considering the physics of saltation. Saltation is a type of particle motion by which particles move through the air by jumps and return to the surface. An upalope probably causes the saltating particle to have a shorter flight length. A more detailed theoretical analysis of particle movement is needed to produce a better estimate of knoll erodibility. AN ALTERNATIVE WIND EROS ION EQUATION As this discussion indicates, the present WEE leads to possible overestimation of annual wind erosion loss by its structure and dependence on a limited data set. Recent work since the formulation of the equation by Skidmore and Woodruff (1968) suggests that many of the factors in the original equation need to be reevaluated. An approach using the expectation integral given in Equation 2 appears to be superior to the original wind erosion equation, Equation 1, because it more closely

144 follows the aerodynamics and physics of wind erosion. That is, it has as its basis verified distributions of wind speed, saltation flux as a function of wind stress, and wind threshold velocity, and it combines them in a way consistent with experimentation in the physics of wind erosion. A proposed alternative WEE is the sum of n expectations for n periods of time, which added together cover the per iOd of interest. i-1 ~ d; Jri bTi I U (U - Utilpi(U) dU/L (8) where each period of time bTi (in seconds) represents a period when the parameters remain relatively constant; pi(U) is the probability density of wind speed during i; Ut = u*t cd ~0 5, which is affected by soil aggregation, vegetation, soil moisture, and ridge roughness; ri is the fraction of ground not covered by vegetation or other nonerodible elements; c is the di drag coefficient for time period i (cd = [u*/U]2); L is field length (meters); k is a constant; and U is a wind speed at 7 m. Equation 8 is a version of the expectation integral given in Equation 2 and has as its variables the threshold wind speed, drag coefficient, fraction of surface covered, field length, and a constant coefficient. All the variables considered by the original WEE are implicit in the variables of this alternative. Standing vegetation and vegetative residue woula affect the fraction of surface covered and partitioning of wind stress by the nonerodible elements (the vegetation and vegetative residue), and the erodible soil would affect the threshold friction velocity. Threshold wind speed would also be affected by soil aggregate structure, crusting, and soil moisture. The field length effect, ridge roughness, ana vegetation-vegetative residue would affect the drag coefficient and sand trapping. The integral would be evaluated for every significant change of threshold velocity, drag coefficient, wind probability distribution, and fraction of surface covered. Such a formulation would be responsive to changes of soil conditions and would treat erosion in a manner consistent with experimental and theoretical work in wind

145 erosion. As experience was gained with the new wind erosion equation, changes could be easily incorporated and simplifications easily made. For example, improve- ments for such effects as field length, changing of the threshold velocity as a function of soil conditions, and possibly a revised knoll effect would probably improve the wind erosion estimates. A PROPOSED " PROVI S IONAL CORRECTED WEE n FOR COMPUTATION OF WIND EROSION FROM THE 1982 NRI In light of the above commentary on the original wind erosion equation and the proposed form for a new wind erosion equation (Equation 8), which will require much research to implement, an incomplete "provisional wind erosion equation" is suggested here for estimating wind erosion from the 1982 NRI data. The proposed provisional equation corrects some of the shortcomings of the original WEE but will not correct for many effects that will require much more research. Corrections include replace- ment of the I and C factors of the original wind erosion equation with the expectation formula given in Equation 4 and replacement of the old ridge roughness factor K with Fryrear's (1984) ridge roughness factor. The provisional corrected wind erosion equation does not use the series of values for cd, Ut, r, p, and AT as given in Equation 8 because these values are not in the 1982 NRI data, and research is lacking to complete formulation of the new wind erosion equation. Rather, one value for each parameter is used for the entire year, and the old field length formulation and old vegetation factors will be used e It will be noted that the soil moisture effect is also temporarily ignored. The soil flux function of Equation 3 is used along with the Rayleigh probability density of Appendix A. A value for cd of 0.002 is assigned based on a selection of field measurements on eroding soils. This value is consistent with drag coefficients given by Priestly (1959) for similar surfaces. The combined proposed provisional wind erosion equation for 1 year is given below: E' = 1,127 [U3~(x) - U2UtG(x)] Kf'(L')V/L [(t/ha)/yr], (9) where x equals Ut/U, V and f(L) are as in the original WEE (Equation 1), K is the ridge roughness factor of

146 Fryrear (1984), F(x) and G(x) are given in Appendix A, and the remaining variables are as designated for Equation 5. Since the last three factors of this new provisional WEE are either equal to or evaluated similarly to those in the original WEE, and field length is already measured in the 1982 NRI, only the variables U and Ut and their ratio Ut/U must be determined to use this provisional WEE. Values for U are given in Table 3 for selected locations in the United States. Values for Ut are given in Table 4 for seven WEGs as defined in Table 2. These values were simply based on the percentage of soil mass smaller than 0.84 mm as given for the seven WEGs by Lyles (1976) in Table 2, and the values of U*t given in Figure 2 corrected for height to give Ut. Functions F(x) and G(x) are given in Appendix A. Table 5 gives some sample results for the proposed provisional WEE before the Kf(L)V correction factors are applied. Values for erodibility, I' = {1,127 [U3F(x) - U{U G(x)]}/L (10) for 1,127-m-long flat bare fields (somewhat longer than those used by Chepil in his 1960 work) are given in Table 5 along with WEGs for Dodge City, Kansas (near the location of Chepil's data source), and for Minneapolis, Minnesota (a location where it was felt that the old wind erosion equation could be overestimating wind erosion). A comparison of the erodibility values (I') for Dodge City in the present work with the I values versus WEG given by Lyles (1976) shows moderately good agreement for the low numbered WEGs but large disagreement for WEGs 6 and 7. However, comparison of erodibility values (I') for Minneapolis with Dodge City values (R · I') corrected by (uMinneapolis/uDodge City) (i e ~ the kind of correction i used by the original wind erosion equation) shows that the R · I' is larger by a factor of 2 for WEGs 1 and 2; by a f actor of 5 for WEGs 3, 4, and 4L; and by about a factor of 10 for WEGs 5 and 6. The substitution of Fryrear's (1984) ridge roughness factor for the K factor of the original WEE will give lower estimates for fields having deep furrows. It is not known how important the neglect of soil moisture will be, although it can reasonably be said that the estimates will be a bit high.

147 TABLE 3 Mean Wind Speed (U) for Selected U. S. Stations U U Station State (M/S) Station State (M/S) Birmingham AL 3.3 Detroit MI 4.6 Montgomery AL 3.0 Grand Rapids MI 4.5 Tucson AZ 3.7 Lansing MI 4.6 Yuma AZ 3.5 Sault St. Marie MI 4.3 Fort Smith AR 3.4 Duluth MN 5.1 Little Rock AR 3.6 Minneapolis MN 4.7 Fresno CA 2.8 Jackson MS 3.4 Red Bluff CA 3.9 Columbia MO 4.4 Sacramento CA 3.7 Kansas City MO 4.6 San Diego CA 3.0 St. Louis MO 4.2 Denver CO 4.1 Springfield MO 5.0 Grand Junction CO 3.6 Billings MT 5.1 Pueblo CO 3.9 Great Falls MT 5.9 Hartford CT 4.0 Havre MT 4.5 Washington DC 3.4 Helena MT 3.5 Jacksonville FL 3.8 Missoula MT 2.7 Tampa FL 3.9 North Platte NE 4.6 Atlanta GA 4.1 Omaha NE 4.8 Macon GA 3.5 Valentine NE 4.8 Savannah GA 3.6 Ely NV 4.7 Boise ID 4.0 Las Vegas NV 4.0 Pocatello ID 4.6 Reno NV 2.9 Chicago IL 4.6 Winnemucca NV 3.5 Moline IL 4.4 Concord NH 3.0 Peoria IL 4.6 Albuquerque NM 4.0 Springfield IL 5.1 Roswell NM 4.1 Evansville IN 3.7 Albany NY 4.0 Fort Wayne IN 4.6 Binghamton NY 4.6 Indianapolis IN 4.3 Buffalo NY 5.5 Burlington IA 4.6 New York NY 5.5 Des Moines IA 5.0 Rochester NY 4.3 Sioux City IA 4.9 Syracuse NY 4.4 Corcordia KS 5.4 Cape Hatteras NC 5.1 Dodge City KS 6.3 Charlotte NC 3.4 Topeka KS 4.6 Greensboro NC 3.4 Wichita KS 5.6 Wilmington NC 4.0 Louisville KY 3.8 Bismarck ND 4.7 Shreveport LA 3.9 Fargo ND 5.7 Portland ME 3.9 Cleveland OH 4.8 Baltimore MD 4.2 Columbus OH 3.9 Boston MA 5.6 Dayton OH 4.6

148 TABLE 3 (Continued) U U Station State (M/S) Station State (M/S) Toledo OH 4.2 Dallas TX 4.9 Oklahoma City OK 5.7 E1 Paso TX 4.2 Tulsa OK 4.7 Port Arthur TX 4.5 Portland OR 3.5 San Antonio TX 4.2 Harrisburg PA 3.4 Salt Lake City UT 3.9 Philadelphia PA 4.3 Burlington VT 3.9 Pittsburgh PA 4.2 Lynchburg VA 3.5 Scranton PA 3.8 Norfolk VA 4.7 Huron SD 5.3 Richmond VA 3.4 Rapid City SD 5.0 Quillayute WA 3.0 Chattanooga TN 2.8 Seattle WA 4.1 Knoxville TN 3.3 Spokane WA 3.9 Memphis TN 4.1 Green Bay WI 4.6 Nashville TN 3.6 Madison WI 4.4 Abilene TX 5.4 Milwaukee WI 5.3 Amarillo TX 6.1 Cheyenne WY 5.9 Austin TX 4.2 Lander WY 3.1 Brownsville TX 5.3 Sheridan WY 3.6 Corpus Christi TX 5.4 Elkins WV 2.8 SOURCE: Department of Commerce (1977). LONG-1)ISTANCE LOSS OF SOIL MATERIAL It would be a worthy goal for estimates of soil removal to be made for that portion of the eroded soil that is carried far from the location of erosion. Eroded soil moving in saltation and creep (movement having lower trajectories than saltation) is removed from a particular farm field, but it is often deposited in a nearby licks t i On . . . ~ _. It may even be restored to the original field should an equally strong wind from the opposite direction happen to erode the deposited material. Fine soil material that is carried in suspension, however, has the potential of being carried great distances from the eroding field and being lost to an entire agricultural region. Because this fine soil material is associated with field soil moisture capacity and with important nutrients, its loss may be far more

149 TABLE 4 Selected Values of Threshold Wind Speed Ut Versus Wind Erosion Group (WEG) WEG Ut (M/S) 2 3 4 4L 5 6 7 6.6 7.7 11.1 11.1 11.1 13.3 17.7 19.9 NOTE: See Table 2 for a description of wind erosion groups. SOURCE: Based on Lyles (1976) important than the loss of the coarser particles that are moved in saltation and creep. The fine-grained sediment carried from fields represents a potential offsite impact as an air pollutant, and upon settling onto surfaces it may have damaging offsite effects. The original WEE refers to total soil loss to a farm field and not to the loss of the fine portion of the soil. This loss of fine soil carried in suspension by the air may approach in magnitude the loss of saltation/ creep-transported soil, but it cannot be simply cal- culated as a constant fraction of the estimated soil loss given by the wind erosion equation. Rather, it must be considered as a function of wind erosion fluxes over the entire field and in individual erosion events. As the proposed WEE is constructed, it would be suitable for use in estimating the long-distance loss of soil material. Particles that are carried great distances have fall velocities that are a small fraction of the friction velocity (an approximate scale for the root-mean-square vertical velocity fluctuations of the air). Thus, for a given wind speed and drag coefficient, the maximum size of particle that may be lost to an agricultural region can be calculated (see Figure 7). 1

150 TABLE 5 Soil Wind Erodibilitya (I') near Dodge City, Kans., and Minneapolis, Minn., for 1,127-m-Long Flat Bare Fields, Compared with I Values from Lyles (1976) I' I' for Dodg e C i ty Minneapol i s (T/Ha)/Yr R Times I' (T/Ha)/Yr I New for Dodge New (Lyres, Provisional Cityb Provisional WEG 1976) Equation (T/Ha) /Yr Equation 1 696 434 180 111 2 301 354 147 73 3 193 137 57 10 4 193 137 57 10 4L 193 137 57 10 5 126 57 24 2 6 108 5 2 0.01 7 85 1 0.5 0.001 aErodibility (I') = 1,127 [U F(x) - U UtG(x)1 [ (t/ha)/yr] bR = [ UMinneapolis ] 3 (a simple correction factor for U. . using Dodge City erosion to Dodge City estimate Minneapolis erosion). At a given point in an eroding field, the horizontal mass flux q' of saltating particles and creeping par- ticles moving through a surface perpendicular to the ground and to the wind greatly exceeds the vertical mass flux F.a of particles carried in suspension that may be transported great distances from the farm field (see Figure 8). Considering, however, that the loss of total soil mass for a given width of eroding field is the horizontal mass flux at the downwind boundary of the field, and that the suspended material portion of this flux is approximately equal to the integrated vertical flux of fine material over the entire area of the eroding field, the loss of fine material clearly becomes a much larger fraction of the total loss of soil mass.

151 Particle ~ I | w' Air Parcel Al I I iw t vsed For long time suspension Vsed < `~ = 0w ~ A u. - 10-2 C- 1 1 ~ 1 1 1 ~10 I I ~ 1 ~ ~1 >~1102 - 1 1 1 -T 1 :: 10-7 10 5 10-3 lo~1 1 10 SIZE OF PARTICLES, IN MILLIMETERS 1.0 z o ~ 0.8 J 11 a: ~ 0.6 cn at o a: 6 0.4 0.2 o 1 1 1 ~ \ \ \ 0 1 2 Vsed/U * 3 4 FIGURE 7 Clockwise from upper left: sedimentation velocity Vsed compared to vertical velocity fluctuation w'; upward motions divided by downward motions for a particle having a sedimentation velocity Vsed in air having vertical velocity fluctuations with mean zero and standard deviation u*; sedimentation velocity versus particle size. (This part of figure from Bagnold, 1941; entire figure from Gillette, 1981.) The vertical suspension mass flux is probably strongly related to the horizontal saltation flux. This relation- ship seems to arise because the kinetic energy flux to the surface by saltating particles is related to the horizontal mass flux of saltating particles (Gillette and Stockton, 1985) and because the production of fine particles by sandblasting is related to the flux of kinetic energy to the surface (Hagen, in press). Indeed, some of the measurements shown in Figure 8 show a striking (though admittedly noisy) constancy between horizontal mass flux of saltating and creeping soil and the vertical flux of particles carried in suspension (Figure 8, bottom). This relationship suggests a method for estimating total loss of fine material for long distances; however, development of the method will require fundamental research.

152 DUST GENERATION WIN D D IR ECTION - 100 ~ 90A ~ : :~\ ::: ~ WEG 0 1 2 3 14 and 4L 1= 5 1 l6 ~`V 60j~o ~ -~ }~ " ~' '\ :~ ~'~:~:~:~:f ~:\ 50 % C~ 50 k-~ ~--~:--~-~-~--\ ~ ~ 40 /·~ , ,: ~ ~ '} ~ ~C~ 60 '^ 6 ~A· · ~/'.~ ,%~ ·~- ~ ---~-- - _~_ ~QA-M_ k70 ~,~; . ,Y.L,,OA.M/,~ ~ '~) ~ ~ 2 .' ' - . v ~ ~ ~ ~- V . .r, ~ ~ . . /. . . ,` · ~ , . . , . ~ ~ . ~ . ~ ., . \. , ,. ^, ., . 7 .~- ~ ·LOAM'~.~.-.-}'t'.SILT LOA~' ·,'- · ~ go ,2 ~;LOAH~.·.~.·7~,~·.·,^. ~. 3lLT.\ 4- ~AND~.~ .'.~,y. ~.-.-} ~\,100 ~N N \ N \ \ \ \ \ ~ 100 90 \ 80 70 eo so 40 30 20 10 7,8 PERCENT SAND '°-F 6 10-7 CR 10-9 lo-lo 101 10° 10 10-2 103 o" 10 10-° 1~6 10 2 Xo X O . _ ~o O 10-4 _ 10-5 1 _ X O X ~ X.~0~ · . .0 ~ 1 i4 x 10-7 u2 (U*~25) 0c, x ,+ 0 S + o 0 e0 ° ~D V ~o v ~_ °c, , _ · 1 1 1111il · Soil I + Soil 2 x Soil 3 0 Soi! 4 O Soil 5 Soil 6 O Soil 7 0 Soil 8 v Soil 9 1 1 1 1 1 1 1 1 1 1 1 1 0 100 u*, cm/see FIGURE 8 Clockwise starting with triangle: sampled soils; illustration of horizontal flux q' and vertical flux Fta total soil movement versus wind frictzon velocity; vert~cal flux of particles smaller textures of than 0.02 mm versus wind friction velocity; ratio of vertical flux of particles smaller than 0.02 mm to total soil movement per unit area per time versus wind friction velocity (from Gillette, 1981). The vertical flux of fine soil material that is subsequently carried great distances may be estimated by using some of the variables in the NRI data set. However, this estimate will probably be rough and will need much fundamental research to have the same validity as do those for sheet and rill erosion. - 1000

153 CONCLUSIONS Analysis of the WEE reveals that it probably over- estimates wind erosion for values of M smaller than 65 percent where ~ is percentage of soil mass in aggregates smaller than 0.84 mm. Since small values of M often correspond to the higher numbered wind erosion groups, a systematic error probably exists in erosion estimates for these soils. The method of correcting for mean wind speed also probably leads to an overestimation of wind erosion for most locations in the United States where mean wind speed is less than at Garden City, Kansas. Because soil aggregation can change during the season, the assignment of only one value to potential erosion for an entire season is questionable. New evidence shows that increase of soil mass flux with field length is related to a feedback mechanism that increases aerodynamic roughness height with field length. An alternative WEE is proposed that would correct for perceived shortcomings of the original WEE. Unfor- tunately, insufficient data exist to implement this equation, so a provisional WEE is proposed that would improve some of the features of the original equation but still retain some formulation that should be replaced when sufficient research becomes available. Suspended soil material (dust) also constitutes an important product of erosion. A version of the new WEE may be used to estimate dust emission, but only after several problems relating dust emission and saltation flux are solved. REFERENCES Armbrust, D., W. Chepil, and F. Siddoway. 1964. Effects of ridges on erosion of soil by wind. Soil Sci. Soc. Am. Proc. 28: 5S7-560. Bagnold, R. A. 1941. The Physics of Blown Sand and Desert Dunes. London: Methuen. Chepil, W. S. 1956. Influence of moisture on erodibility of soil by wind. Soil Sci. Soc. Am. Proc. 19:288-292 Chepil, W. S. 1957. Width of Field Strips to Control Wind Erosion. Agricultural Experiment Station Technical Bulletin No. 92. Manhattan: Kansas State University. Chepil, W. S. 1960. Conversion of relative field erodibility to annual soil loss by wind. Soil Sci. Soc. Am. Proc. 24:143-145.

154 Chepil, W. S., and J. L. Doughty. 1939. Wind tunnel experiments on soil drifting. P. 19 in Report Regional Commission on Soil Drifting, Swift Current, Saskatchewan, July 11. Corotis, R. B., A. B. Sigl, and J. Klein. 1978. Probability models of wind velocity magnitude and persistence. Solar Energy 20:483-493. Department of Commerce. 1977. Local Climatological Data--Annual Summaries for 1977. Asheville, N.C. National Climatic Data Center. Fryrear, D. W. 1984. Soil ridges--clods and wind erosion. Trans. ASAE 27:445-448. Fryrear, D. W., and D. V. Armbrust. 1969. Cotton gin trash for wind erosion control. Texas Agricultural Experiment Station, MP-928. Gillette, D. A. 1981. Production of dust that may be carried great distances. Pp. 11-26 in Desert Dust: Origin, Characteristics, and Effect on Man, T. Pewe, ed. Special Paper 186. Boulder, Colo. Geological Society of America. Gillette, D. A., and P. H. Stockton. 1985. Mass, momentum and kinetic energy fluxes of saltating particles over eroding particle deposits of varying lengths in a wind tunnel. Unpublished. Gillette, D. A., J. Adams, A. Endo, and D. Smith. 1980. Threshold velocities for input of soil particles into the air by desert soils. J. Geophys. Res. 85(C10):5621-5630. Gillette, D. A., J. Adams, D. Muhs, and R. Kihl. 1982. Threshold friction velocities and rupture moduli for crusted desert soils for the input of soil particles into the air. J. Geophys. Res. 87:9003-9015. Hagen, L. In press. Soil aggregate abrasion by impacting sand and soil particles. Trans. ASAE 27:805-808. Lyles, L. 1976. Wind erosion: Processes and effect on soil productivity. Paper presented at Annual Meeting of the American Society of Agricultural Engineers, Lincoln, Nebr., June 1976. Lyles, L., and B. Allison. 1976. Wind erosion: The protective role of standing stubble. Trans. ASAE 19:61-64. Owen, P. R., and D. A. Gillette. 1985. The wind tunnel effect on wind erosion. Unpublished. Priestley, C. H. B. 1959. Turbulent Transfer in the Lower Atmosphere. Chicago: University of Chicago Press.

155 Skidmore, E. L., and N. P. Woodruff. 1968. Wind Erosion Forces in the United States and Their Use in Predicting Soil Loss. Agriculture Handbook No. 346. Washington, D.C.: U.S. Government Printing Office. Woodruff, N. P., B. L. Schmidt, E. L. Skidmore, J. D. Dickerson, R. L. Meeker, and L. M. Feusner. 1968. A Study of Wind Erosion in Northwestern Ohio. Wind Erosion Unit, U.S. Department of Agriculture, Manhattan, Kans.

156 APPENDIX: DERIVATION OF EXPECTATION FORMULA Equation 4 may be rewritten as 00 I. = kc bT r u (u - u ) f(U) dU/L d U t t co co = kc~ AT [! U3 f(V) dU - U. J u2 f(U) dU]/L ut t U I' = kcd1 5 hT [I1 - I2]/L. t Now, let us evaluate I1, which is given as ~ 3 I1 = ~ U f(U) dU. U By substituting t f(U) = (nU)/(2U2) exp[-nU2/4U2] (the Rayleigh density function) and letting t = [n U/(2U)] , we get (A-1) I = (4/~)1~5U3 J tl-5 -tat (A-2) 1 z where z equals (~/4) (Ut/U)2 This has the solution (Abramowitz and Stegun, 1970) . I1 = (4/~)1 5U3 r(2~5, z), (A-3)

157 2.0 1.5 r _ ~ ~ _ - 10 0.5 o - F(y) tends to 1.91 as y tends to zero y=0.8s6x x UtlU - \ See approximation for larger values of y 0 0.5 1.0 1.5 2.0 y FIGURE A-1 Function F(0.886x) versus 0.886x, where y equals 0.886x (Cowherd et al., 1984). where f(2.5, z) is an incomplete gamma function. The function F(y) = (4/~)1 5 [(2.5, ~X2/4) (A-4) - where x equals Ut/U and y equals 0.866x is plotted in Figure A-1 (after Cowherd et al., 1984). For values of x greater than 1.6, the approximation given by Abramowitz and Stegun (1970) is used: F(x) = 1.44[(0.70 x3 + 1.33 x) exp(-nx2/4)] . (A-5)

158 Now, the second integral, co I2 = Ut ~ u2 f(U) dU, ut becomes, after substituting for f(U) and changing variables as above, I2 = 4 U2 Ut/n a, ~ t e~tdt. After the integral is evaluated, the equation may be rewritten I2 = u2 UtG(x), where G(x) (4/~) exp(-nx2/4) Thus, equation A-1 may be rewritten (A-6) (A-7) [(nX2/4) - 1]. I' = kc~ AT [U3 F(x) - u2 Ut G(x)~/L (A-8) where x equals Ut/U. REFERENCES Abramowitz, M., and I. A. Stegun. 1970. Handbook of Mathematical Functions. New York: Dover Publications. Cowherd, C., G. Muleski, P. Engelhart, and D. A. Gillette. 1984. Rapid Assessment of Exposure to Particulate Emissions from Surface Contamination Sites. Report to Environmental Protection Agency. Contract No. 68-03-3116, Project No. 7972-L MRI. Kansas City, Mo.

159 Discussion Klaus ~ Flach The Wind Erosion Equation (WEE) was developed in the 1950s and 1960s primarily as an operational tool for soil conservationists to evaluate the effects of alternative erosion control practices. For this it has been useful. Despite difficulties cited in Gillette's paper, the formula has been useful in the National Resources Inventory (NRI) to identify those parts of the country-- the Great Plains--where erosion by wind is the pervasive soil conservation concern. As pointed out, NRI data suggesting that erosion by wind for parts of Minnesota and Florida exceeds that by water may be questioned. The equation had never been tested in these areas and local Soil Conservation Service (SCS) personnel are relatively . . . · . nexper~encec In its use. In any case, values for erosion by wind in these areas slightly in excess of erosion by water do not present the picture of an all-important problem related to wind erosion, although adding tons of soil loss by wind and water may result in high assessment of the areas' overall erosion problems. Although all soil erosion processes deal in principle with the same phenomenon--namely, the movement of soil in response to applied energy--there are major differences between air and water as the source of energy. These differences determine the conditions under which erosion occurs, the accuracy with which it can be measured, and the mechanisms through which erosion influences the quality of soil as a medium for plant growth. Some of these differences are described later herein in a very simplistic way to illustrate that erosion by wind is a much more complex process than that by water, and that equations to predict it will be less precise and results more difficult to interpret until a major research effort is made. Water is heavier than air and only runs downhill, carrying soil with it. It is relatively simple to measure the amount of soil carried by water. The Universal Soil Loss Equation (USLE) was developed and verified with thousands of such measurements. Wind, on the other hand, carries eroded soil in one direction on one day and in another direction on another day. The best part of the soil is carried as dust into the air and may move thousands of miles. Some may be

160 blown to the next field and replace some of the soil that has been lost there. There is no easy way to measure the amount of soil moved other than measuring soil thickness before and after the erosion event. This is a very crude measurement that, as Gillette's paper points out, can be used to measure the loss of 1 to 2 inches of soil (150 tons/acres), not the loss of 5 to 10 tons/acre that concerns soil conservationists. Because air is much less dense than water, a higher fluid velocity is required to move soil by wind. Various particle sizes and aggregates of different densities are moved selectively. Hence, there is a strong winnowing effect of wind, at least at relatively low velocities. As discussed, the deterioration of soil quality because of the preferential loss of fine soil particles may be a more appropriate measure of the effects of erosion by wind than the total amount of soil lost. Very intense wind storms, on the other hand, can remove the entire plow layer of whole fields within hours. Once again, "tons of soil loss" seems an inadequate way to describe such events. Since soil is always wet when it is being eroded by water, properties that are important for predicting erodibility are relatively constant during the process. On the other hand, a wet medium- or fine-textured soil is virtually immune to erosion by wind until it dries. And when it dries, it commonly forms a crust that protects the soil from further erosion. The WEE tries to account for this in a very simplistic way that, in the days before computers in field offices, was perhaps the only way. For evaluating conservation alternatives for an individual field this correction may have been reasonably adequate, but for a national assessment it is not. [To comment on a Point made in this paper, sandy loams and even loamy sanas In soles with xeric (Mediterranean climate) moisture regimes can form extremely strong crusts.] To be truly reliable, the equation must take into account that similar textures may behave quite differently in various soils. At this time no good measure or national data base exists to incorporate the propensity of soils to form crusts into an equation. Erosion by both water and wind have ephemeral effects on standing crops. Sediments moved by water can damage crops in relatively small areas in the bottom of fields and cause severe damages to streams and lakes. Windblown soil can destroy crops over large areas, form dunes that

161 block roads, and carry pollutants to waterways over large distances. In parts of the United States where erosion by wind is important, many farmers pay as much or more attention to these ephemeral effects as they do to the damage that wind erosion does to the potential productive capacity of the soil. To assess the total damage of erosion, these ephemeral effects must be fully considered. Wind erosion research has received relatively little attention since 1935, when the problems of the Dust Bowl region awakened the United States to the dangers of soil erosion. Low priorities for research on soil erosion by wind are even reflected in the terminology and agenda for this convocation, "Physical Dimensions of the Erosion Problem," which implies Baby water" when using the term erosion. The equation for predicting erosion by water is called the Universal Soil Loss Equation, yet the universe does not include erosion by wind. It is, of course, not wind that erodes, but soil. The difficulty of conducting research on erosion by wind probably has been a major factor in the low interest of researchers in this subject. Yet HRI data, imperfect as they may be, suggest that erosion by wind may be an extremely important component of the U.S. soil erosion problem. Gillette's paper provides some excellent suggestions for new directions in research on erosion by wind. The technology is now available to make meaningful measure- ments of erosion by wind in the field and, through microcomputers and computerized data bases, to provide soil conservationists with the wherewithal to use even a complicated equation in conservation planning. The difficulties of predicting with current technology the amount and impact of erosion by wind probably preclude the suggestion in this paper to modify the WEE as used with the 1982 NRI. There are essentially no experimental data available for those parts of the country, such as the northern Corn Belt or Florida, where erosion by wind may be significant but is not the dominant form of erosion. Yet these are the areas where the use of the WEE in the NRI is most suspect. Rather, it is worth emphasizing the sensible use of NRI data as far as erosion by wind is concerned. The NRI confirms the Great Plains as the major area of wind erosion concern, but it should not be used to assess the relative importance of the two forms of erosion where both are relatively minor. Tons of erosion by water cannot be added to tons of soil eroded by wind, and only

162 in a very general way can the relative impact of the two forms of erosion on the potential productivity of U.S. soils be assessed. Still, the NRI can provide evidence that erosion by wind is of major national concern and that more research on this is desperately needed if a complete assessment of the dangers of erosion is ever to be available.

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Soil Conservation: An Assessment of the National Resources Inventory, Volume 2 Get This Book
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Written by the foremost authorities in the field, this volume brings together the technical papers from which Volume 1 is drawn. The 10 papers and discussion from a National Research Council symposium cover such topics as soil erosion classification, evaluating how soil erosion damages productivity, calculating soil erosion, understanding ephemeral gully erosion, wind erosion, and the impact of range erosion on land use.

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