Soil Science Society of America Journal 67:425-436 (2003)
© 2003 Soil Science Society of America
DIVISION S-1—SOIL PHYSICS
Aggregate-Mean Diameter and Wind-Erodible Soil Predictions Using Dry Aggregate-Size Distributions
T. M. Zobeck*,a,
T. W. Pophamb,
E. L. Skidmorec,
J. A. Lambd,
S. D. Merrille,
M. J. Lindstromf,
D. L. Mokmag and
R. E. Yoderh
a Wind Erosion and Water Conservation Research Unit, Cropping Systems Research Lab., USDA-Agricultural Research Service, 3810 4th Street, Lubbock, TX 79415
b USDA-ARS, Stillwater, OK
c USDA-ARS, Manhattan, KS
d Univ. of Minnesota, St. Paul
e USDA-ARS, Mandan, ND
f USDA-ARS, Morris, MN
g Michigan State Univ., E. Lansing
h Univ. of Tennessee, Knoxville
* Corresponding author (tzobeck{at}lbk.ars.usda.gov)
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ABSTRACT
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Temporal estimates of surface soil dry aggregate-size distributions (DASD) are needed to evaluate soil management systems and estimate wind erosion. This study was conducted to determine the most accurate and precise DASD to estimate aggregate-mean diameter and amount of wind-erodible soil. Over 5400 surface samples of soil dry aggregates were collected at various times throughout the year for 2 to 4 yr at 24 locations in six states. The soils represented a wide range of management systems and intrinsic soil properties, including mineral and organic soils. We evaluated four DASDs: the log-normal determined by two methods, fractal and Weibull distributions, and compared estimates of the aggregate-mean diameter and amount of wind-erodible soil derived from the distributions. We evaluated log-normal distributions expressed as amount oversize (LNO) and undersize (LNU) and tested the effect of using different smallest and largest sieve openings sizes. The Weibull distribution is the most accurate because the ranges of error of the Weibull were generally smaller than all other distributions over the full range of sieve sizes tested, rarely exceeding 0.15. The Weibull distribution is the most precise because only the Weibull had an error mode of ±0.05 in all sieve-size classes tested. Using substantially different sizes for the smallest sieve-size openings had a great effect on estimates of aggregate-mean diameter and wind-erodible soil, but only when using LNO. Using substantially different sizes for the largest sieve size openings had a great effect on estimates of aggregate-mean diameter but little effect on estimates of wind-erodible soil.
Abbreviations: DASD, dry aggregate-size distribution • LNO, log-normal oversize • LNU, log-normal undersize
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INTRODUCTION
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MANY STATISTICAL METHODS have been proposed to describe the particle-size distribution of sediments (Cooke et al., 1993). These distributions include the conventional Gaussian or normal, log-normal (Shirazi and Boersma, 1984; Buchan, 1989), modified log-normal (Wagner and Ding, 1994), log-hyperbolic (Hartmann and Christiansen, 1988), bi- or multimodal (Pinnick et al., 1985), Rosin-Rammler (Kittleman, 1964), Weibull (Wohletz et al., 1989), and others. Soils form natural aggregations of particles called aggregates during soil formation. During tillage and other soil manipulations the soil is fractured along aggregate faces to create aggregates of various sizes. Large aggregates or pieces of aggregates have been called clods by some writers. Several attempts have been made to describe the distribution of these soil aggregates and clods.
Gardner (1956) studied more than 200 DASD in a search of a regular pattern to describe the DASD. He believed that most DASDs appeared to be log-normally distributed. The 2-parameter log-normal cumulative distribution function can be described by the form:
 | [1] |
where y is the predicted cumulative soil mass smaller than particle or aggregate size x and a and b are parameters. Gardner (1956) showed how DASDs could be plotted as a straight line on log-probability paper when percentage oversize was the independent variable and the logarithm of the aggregate diameter was the dependent variable. The geometric mean diameter is the size at which 50% of the aggregates' mass pass through the sieve.
Fractal theory also has been applied to determine DASD (Perfect and Kay, 1991; Tyler and Wheatcraft, 1992; Rasiah et al., 1993; Logsdon et al., 1996). Fractal relationships for particle-size distributions have been described relating number of particles of a defined size to the size using Eq. [2]
 | [2] |
where N(r > R) is the number of particles greater than size R and D is the fractal dimension (Mandelbrot, 1982; Turcotte 1986). The relationship of particle numbers and volume developed by Tyler and Wheatcraft (1989) was used by Perfect et al. (1992) to derive a rather simple model (Eq. [3]) of estimating D based on particle mass and diameter
 | [3] |
where M(x) is the cumulative mass smaller than diameter x (same as mass undersize), D1 is the fractal dimension and k is a constant. In this derivation, D1 is independent of aggregate geometry and density used in calculating the number of objects.
Tyler and Wheatcraft (1992) also derived an equation, Eq. [4], to estimate the fractal dimension based on particle mass rather than particle number. Their equation is typically reported in the form of a fraction of mass less than a size as
 | [4] |
where M(x < XL) is the cumulative mass smaller than diameter x, XL is the diameter of the largest particle, and MT is the total sample mass. This approach places limits on the fractal dimension (0 < D < 3) and requires an estimate of the largest grain size, XL. Rasiah et al. (1993) also applied this approach to aggregate-size distributions. They assumed scale invariant aggregate density and found a 1:1 relation between fractal dimensions computed using aggregate numbers and fractal dimensions using aggregate mass.
Recent studies have shown mathematically how the sequential fragmentation of materials may lead to a Weibull distribution of particles (Wohletz et al., 1989). The Weibull distribution was proposed to describe the distribution of soil strength (Perfect and Kay, 1995) and the distribution of airborne dust particles (Zobeck et al., 1999). In this paper, we test the use of the Weibull distribution to describe soil DASDs as
 | [5] |
where M(x < X) is the cumulative mass x smaller than diameter X, MT is the total sample mass, the b parameter is a scale factor and the c parameter is a shape factor.
Dry soil aggregate-size distributions can be used to derive specific important aggregate parameters and indexes useful in making soil management decisions and erosion predictions. The aggregate geometric mean diameter is commonly used in soil management studies to compare cropping systems (Campbell et al., 1993) and in wind-erosion prediction models such as the wind-erosion prediction system, WEPS (Zobeck, 1991). Winderodible soil was defined by Chepil (1942) as the amount of dry soil aggregates <0.84 mm in diameter. The amount of erodible soil is used in making estimates of wind erosion in wind-erosion prediction models such as the wind-erosion equation (Woodruff and Siddoway, 1965) and the revised wind-erosion equation (Fryrear et al., 1998). Although many different distributions have been proposed to estimate a soil DASD, little is known about how the distributions compare. In this study, we will compare four DASDs: the log-normal distribution determined by two methods, fractal, and Weibull distributions. We believe there are significant differences in DASD parameter estimates among distributions. To determine the most accurate and precise method to predict aggregate-size distribution, we compared estimates of cumulative soil fraction undersize by sieve size, estimates of the aggregate size at which 50% of the mass passes (known as the geometric mean diameter in the log-normal distribution), and estimates of the wind-erodible soil.
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MATERIALS AND METHODS
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This study was part of a larger investigation of soil surface physical and chemical properties measured throughout the year on a wide variety of soils in the USA (Zobeck et al., 1992). The purpose of this study was to determine the effects of climate and management on soil properties and to develop models to estimate temporal soil properties believed to affect wind erosion. The surface soil samples described herein were collected for the determination of DASD as part of the investigation. Approximately 2- to 5-kg samples of the upper 3 cm of the soil surface, collected with a spade, were used to determine DASD on 24 sites in six states representing the U.S. upper Midwest (Michigan and Minnesota), Northern (North Dakota), Central (Kansas), and Southern (Texas) Great Plains, and the Pacific Northwest (Washington). The classification, texture, organic C, and calcium carbonate contents of the soils are listed in Table 1. The texture, organic C, and calcium carbonate contents were measured using standard procedures described by the USDA, NRCS (1992).
All sites were cropped or maintained in a fallow condition during the study. The management systems and crops grown varied widely (Table 1). Aggregate samples were collected at various times throughout the year from 1.5 to about 3 yr, depending on the site. Soil samples were air-dried before sieving through a rotary sieve (Chepil, 1942; Chepil, 1962). The size of the holes used in the rotary sieves varied somewhat among sites (Table 2). All sites used at least five sieves. The sieves with the smallest diameter holes varied from 0.42 to 0.60 mm. All sites with the exception of the Kansas sites had either 12- or 19-mm wide holes as the largest sieve openings size. The largest holes in the sieves used to determine DASD for the 10 Kansas sites were 44 mm in width.
In this study, we calculated the log-normal distribution using two different methods of expressing the data: (i) the cumulative fraction of aggregate mass passing through each sieve (fraction undersize = LNU) and (ii) the cumulative aggregate mass retained on each sieve (fraction oversize = LNO). We used the normal probability functions (PROBIT and PROBNORM) of SAS Institute (1990) to determine the normal probability of the cumulative mass fraction oversize and undersize by sieve size. The SAS PROBIT(p) function returns the pth quantile from the standard normal distribution. The probability that an observation is less than or equal to the returned quantile is p. We regressed the logarithm of the sieve size on the normal probability of that cumulative mass fraction (expressed as the cumulative quantile) by sieve size to derive a straight line defining the aggregate-size distribution (Fig. 1)
. The mean diameter was defined as the anti-log of the sieve size where 50% of the aggregate mass passed. This is analogous to the geometric-mean diameter described by Gardner (1956). In this manuscript, the term aggregate-mean diameter is used to indicate the aggregate and particle diameters at 50% (0.50 fractionally) undersize for all methods described. Particle diameters are included with aggregates because we did not attempt to separate discrete particles from aggregates when measuring soil mass.
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Fig. 1. Representative log-normal, Weibull, and fractal soil aggregate-size distributions from an Acuff (fine-loamy, mixed, superactive, thermic Aridic Paleustolls) fine sandy loam.
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Since the SAS probability functions determine results for values less than or equal to the given p value, we used fraction undersize calculated as 1 - fraction oversize for probability calculations of the log-normal distribution of mass fraction oversize. The net result of this manipulation was to increase the number of data points (sieves) used in the regression as illustrated in Table 3. Table 3 represents the sieves used in the Kansas sites, Sites 1 through 10 in this study. The smallest sieve had 0.42 mm in diameter openings. Regressions of the LNU data had the same number of data points as sieves used in the sieving process, six (Sieve Numbers 2–7 in Table 3). The smallest sieve size used in LNU regressions was the smallest sieve used in sieving, 0.42 mm in this case. Regressions of LNO data had one more data point. This occurred because the smallest fraction must be identified to calculate fraction oversize. Since the log (0) is undefined, we initially (arbitrarily) set the smallest sieve size as a very small number (10-8 mm). We then tested setting the smallest sieve at 10-4 mm and compared the results of setting the smallest sieve at 10-8 and 10-4 mm to evaluate the effect of variations in the smallest sieve size. Table 3 lists the cumulative fractions undersize, oversize, and the cumulative quantile for the standard log-normal distribution as determined by the PROBIT function of SAS. We regressed the log of the sieve size on the cumulative quantile (PROBIT[fraction undersize or oversize]) to represent the log-normal distribution.
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Table 3. Representative sieving statistics used in the calculation of the log–normal soil dry aggregate-size distribution.
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To determine the fractal DASD, we used the log-transformed and rearranged form of Eq. [4] as described by Rasiah et al. (1993):
 | [6] |
The linear best fit of Eq. [6] produced estimates of k1 and k2, where the fractal dimension D = 3-k1. We also attempted to determine the fractal DASD using nonlinear regression of Eq. [3]. Since we did not know the largest aggregate size, we could not accurately determine the midpoint of the largest sieve size. We used the actual sieve size of the largest sieve to determine the fractal dimension and k parameter but the equation performed very poorly when estimating aggregate-mean diameter and wind-erodible fraction.
The Weibull DASD was determined by nonlinear regression provided by SAS Institute (1990), using Eq. [5]. Examples of log-normal, fractal, and Weibull distributions are illustrated in Fig. 1. Differences in the dependent and independent variables among the figures arise because of differences in the original definitions of the distributions as described above. The DASD for all methods were fitted separately for each soil sample.
The DASD described above was used to determine the aggregate-mean diameter, the wind-erodible soil as a percentage of erodible soil (diameter <0.84 mm), and the fraction of soil passing at each sieve size used at each site (Table 2). Aggregate-mean diameter was determined by substituting 0.50 as the fraction undersize or oversize and solving for the aggregate size. Similarly, wind-erodible soil was determined by substituting 0.84 as the aggregate size in each distribution equation.
To determine which distribution was the best predictor of aggregate size, we examined differences in observed versus predicted values by distribution type over the entire range of the data. The observed data were the amounts of soil measured during sieving. The aggregate-mean diameter and wind-erodible soil were derived from the distributions but represent two points of each distribution curve. For example, the predicted mean diameter using the LNU, Weibull, and fractal distributions for a representative soil sample is shown on Fig. 1. To examine how each distribution performed over the entire range of observed aggregate size, we calculated the differences in the observed and predicted cumulative soil undersize or oversize (called errors in this analysis) by sieve and distribution type for each location.
Statistical analyses were performed using SAS Institute (1990). All statistical significance was tested at the P = 0.05 level.
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RESULTS AND DISCUSSION
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The soils used in this study consisted of twelve different surface soil textures, including marl and muck surfaces (Table 1). These sites were selected because they represent a wide range of conditions where wind erosion poses a significant hazard. The sand content varied from 7 to 92%, clay varied from 1 to 42%, and organic matter varied from 2 to 500 g kg-1. A total of 5462 observations were made over the 2- to 3-yr study period (Table 1). The number of samples per site varied because of the diverse experimental designs and sampling times used in this study.
Differences Among Dry Aggregate-size Distribution Types
Estimated aggregate-mean diameter and wind-erodible soil for each site and DASD type are listed in Table 4 and Fig. 2
, respectively. Since the methods of fitting the distributions did not assume the same distribution of errors, it is not possible to make statistical comparisons among methods. The reason for the differences among sites is unclear. No trends related to physical or chemical properties of the soil are evident. Differences among sites may be due to seasonal differences caused by the effects of temporal climatic factors such as rainfall, freezing and thawing, etc. One study has explored the cause of the variation in DASD at the North Dakota site (Merrill et al., 1999) but more work is still needed to explain the temporal variation in DASD for the other sites.
Although it is not possible to make statistical comparisons among distributions, some general trends are evident. The aggregate-mean diameters seem very large for some of the Kansas sites (Sites 1–10) and for the North Dakota site (Site 18). Site 6 had an unusually large aggregate-mean diameter and standard error (Table 4). In addition, for these sites differences in aggregate- mean diameter among distributions seem quite large. For all other distributions the aggregate-mean diameters appear comparable. Determination of the reason and other details about these differences is beyond the scope of this study. These data are presented to demonstrate the unusual results possible when applying DASD to some aggregate samples. Some of the differences among distributions may be explained by specification of the smallest sieve size as discussed below.
Comparisons of the distributions with respect to accuracy and precision of computed values relative to actually observed values provides the best measure of performance as models of DASD. Accuracy is the closeness of a measured or computed value to its true value; precision is the closeness of repeated measurements of the same quantity to each other (Sokal and Rohlf, 1995). In this study, the true value is the mass of soil measured by sieving. Figure 3 and 4
show the range of errors for each distribution type and the frequency of errors by sieve size class for all sites combined, respectively.
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Fig. 3. Difference in observed- and estimated-aggregate size (error) by sieve size for all data combined.
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Fig. 4. Frequency of errors in predicting observed values by sieve size class using fractal, log-normal, and Weibull distributions.
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The Weibull distribution appears to be the most accurate of the distributions tested. The width of the vertical lines in Fig. 3 indicates the range of error of estimated values from observed values. The ranges of error are generally centered at 0 (no error in the estimate) for the Weibull distribution across all sieve sizes, with the exception of the smallest sieve size. In all other distributions, the range of values appear centered above or below the 0 line in several of the sieve sizes. Comparison of the frequency of occurrence of errors by sieve-size class may be a better method to evaluate accuracy and is shown in Fig. 4. The bar centered at 0 represents an error of ±0.05. Each subsequent bar represents errors in classes of 0.10. For the Weibull distribution, the mode (indicated by the tallest bar) of the frequency distribution was ±0.05 for all sieve size classes, meaning it most frequently estimated within ±0.05 of the true value. In all other distributions, the mode was >0.05 in at least one sieve class. The mode was >0.05 in only one sieve size class in the LNU and LNO distributions. The fractal distribution seems to be the least accurate, with the mode of observations often greater than the observed value (Fig. 4).
The Weibull distribution also appears to be the most precise distribution tested. The ranges of error of the Weibull, a measure of the closeness of the estimated values to one another, over all sieve sizes is generally smaller than all other distributions (Fig. 3). The distribution of frequency of errors also describes how precisely the distribution estimated the observed value by considering the spread of the error bars from the mode in Fig. 4. The precision varied among distributions by sieve size class. The LNO and Weibull made the most precise predictions of the wind-erodible fraction found in sieve-size class 
2.0mm (Fig. 4). All distributions performed well in predicting the 2.0- to 4.0-mm size class. The Weibull performed better than all other distributions in predicting the 4.0- to 6.0-, 6.0- to 8.0-, and >12.0-mm sieve size classes. The LNU performed the best in predicting the 8.0- to 10.0-mm class and the LNO performed the best in predicting the 10.0- to 12.0-mm size class. Over all, the fractal distribution seems to be the least precise, with no clear advantage for any size class and poor precision for the larger size aggregates (Fig. 4).
Effect of Varying Smallest Sieve Opening Size
The specification of the smallest sieve opening size only created difficulty in the LNO distribution calculation because of limitations in the calculation procedure. To determine the LNU, Weibull, and fractal distributions, the smallest sieve size was used explicitly in the calculations because it indicated the size through which the soil passed (undersize). To determine the LNO distribution, the amount retained on the pan (oversize) was used in the calculation and serves as the ‘sieve’ with the smallest openings. However, the pan has no holes, in this case the smallest sieve opening size is zero. Thus, the smallest sieve opening size must be specified in the LNO calculation as some small number because the LNO calculation requires the natural log of the sieve size and the log of zero (sieve size of the pan) is undefined. We hypothesized that differences in parameter estimates based on LNO will occur when substantially different sizes are used to estimate the smallest sieve size. To test the hypothesis we calculated the LNO for all sites using 10-8 and 10-4 mm as the size of openings of the smallest sieve. Hereafter, ‘Size 1’ refers to tests when 10-8 mm was used, and ‘Size 2’ refers to tests when 10-4 mm was used as the size of openings of the smallest sieve. The effect of the specified smallest sieve size on estimated aggregate-mean diameter and wind-erodible soil statistics are shown in Table 5.
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Table 5. Effect of variation in specification of the smallest sieve size on estimated aggregate mean diameter and wind erodible soil statistics for the log-normal oversize distribution.
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Different smallest sieve sizes produced mixed results in the estimation of aggregate-mean diameter. In 11 of the sites, specifying Size 1 produced significantly larger aggregate-mean diameter than Size 2. No significant difference in aggregate-mean diameter was found in 11 of the other sites (Table 5). In most cases, the standard error of the estimates of aggregate-mean diameter with Size 1 was much larger than with Size 2. Overall, Size 2 seems to be better than Size 1 in estimating mean diameter because the values for many sites seem reasonable and less error was produced in making the estimates. However, on several sites even using Size 2 produced very large estimated mean diameter. Using Size 1 to estimate mean diameter generally produced very large and unreasonable estimates. For example, the mean diameter of Site 6 was estimated to be 43 km.
This difference in estimation of aggregate mean diameter is caused by shifting of the regression line used to estimate LNO (Fig. 5)
. The Size 1 regression line tends to have a steeper slope and higher intercept (cumulative quantile = 0) than the Size 2 line. In the example in Fig. 5, the resulting aggregate mean diameters were 38.5 and 21.5 mm for Size 1 and Size 2 regressions, respectively. The aggregate-mean diameter is defined in the normal distribution as the quantile value of zero. Figure 5 shows that, in this example, estimates of aggregate size will be underestimated by some quantile values and overestimated for other quantile values when using the Size 1 regression rather than the Size 2 regression to estimate aggregate size. The precise amount of over or underestimation will vary for other soil samples as differences occur in DASD among samples.
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Fig. 5. Effect of varying smallest sieve size on regressions used to determine log-normal oversize distributions.
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The same regressions were used to determine the wind-erodible soil by rearranging the equations to estimate the amount of soil undersize based on the aggregate size of erodible soil, 0.84 mm. The wind-erodible soil was significantly greater at every site when Size 1 was used for the regression calculation (Table 5). This result shows clearly that specification of the smallest sieve size opening is very important when estimating amount of wind-erodible soil.
Effect of Varying Largest Sieve Opening Size
Although specifications for the design of rotary sieves have been suggested (Chepil, 1942; Chepil, 1962), not all sieves used in this study had the same number and sizes of sieves (Table 2). Most locations used 19 or 12 mm as the size openings for the largest sieve; however, the Kansas location also included one larger sieve with 44-mm openings. We hypothesized that differences may occur in estimates of aggregate-mean diameter and wind-erodible soil when an additional sieve with 44-mm size openings is used rather than estimates made when the largest sieve size openings are 19 mm. We tested this hypothesis by calculating the aggregate-mean diameter and wind-erodible soil for all DASD types for two test conditions using the data collected in Kansas (Sites 1–10). For test condition one, we used all sieving data in the analysis as previously discussed and presented in Table 4 and Fig. 2. For test condition two, we recalculated the amount of soil retained on the 19-mm sieve as the sum retained on both the 19- and 44-mm sieves. We performed an analysis of variance to determine significant differences in aggregate-mean diameter and wind-erodible soil by site number, within DASD types (Table 6).
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Table 6. Effect of combining 19- and 44-mm diameter opening sieves on aggregate-mean diameter (mm) and amount of wind-erodible soil.
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Combining the soil retained on the two sieves with the largest opening sizes (19 and 44 mm) produced significant differences in aggregate-mean diameter in all DASD tested. However, the results were variable. No site had significant differences in aggregate-mean diameter in all DASD types. In most cases, when significant differences in aggregate-mean diameter occurred among the DASD types, the largest aggregate-mean diameter was produced when the largest sieve opening size was 44 mm. The notable exception was the LNO distribution type where the largest sieve opening size of 19 mm produced the largest aggregate-mean diameter. The LNO distribution was the least affected when the 44-mm sieve opening size was used, with only two sites showing significant increases in aggregate-mean diameter (Table 6). The fractal distribution was most affected with significant decreases in aggregate-mean diameter when the 19-mm sieve opening size was used in nine out of ten sites. Although combining the soil retained on the two sieves with the largest opening sizes did produce significant differences in aggregate mean diameter among DASD types, substitution of the aggregate-mean diameter data from Table 6 into Table 4 would not change the overall conclusions in the comparisons of DASD types discussed above.
Estimates of the amount of wind-erodible soil were generally unaffected by the size of the openings of the largest sieve. No significant difference in wind-erodible soil was found for the log-normal and fractal distributions when comparing test conditions. For the Weibull distribution, the wind-erodible soil was significantly greater when the sieve with the largest opening size was 44 mm at Sites 6 and 7 (Table 6).
These results underscore the importance of using a standard set of sieves for comparable estimates of some DASD parameters, particularly aggregate-mean diameter, regardless of the DASD used for parameter estimation. On the contrary, the effect of the largest sieve opening size was not critical for estimates of wind-erodible soil. Even for the limited number of sites with significantly different wind-erodible soil results using the Weibull method, the differences only occurred when the wind-erodible soil was very low; below the level wind erosion may be expected. Wind tunnel tests have shown that soil is not eroded until the wind-erodible soil exceeds about 20% (Chepil, 1958).
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CONCLUSIONS
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Many different soil dry aggregate-size distributions have been used in the past to describe sieving results and estimate selected parameters believed meaningful in soil management and erosion control. For some aggregate parameters the specific distribution used may not be important, as when only relative rankings among tests are needed. However, if accuracy and precision in the measurement of aggregate size or the amount of aggregates of a certain size are needed, the DASD used in the calculation may be very important. For example, accurate estimates of the amount of erodible soil may be needed if decisions on costly farm management alternatives are based on the amount of erodible soil measured from field samples.
In this study, we evaluate three DASDs: the log-normal, fractal, and Weibull distributions and compare estimates of two useful parameters, the aggregate-mean diameter and amount of wind-erodible soil derived from the distributions. We also evaluated two different methods of expressing the log-normal distribution, LNO and LNU, and tested the effect of using different smallest and largest sieve openings sizes.
These results suggest the Weibull distribution is the most accurate and precise of all distributions tested. The Weibull distribution is the most accurate because only the Weibull had a mode of ±0.05 in all sieve size classes. The Weibull distribution is the most precise because the ranges of error of the Weibull were generally smaller than all other distributions over the full range of sieve sizes tested, rarely exceeding 0.15. The fractal distribution had the lowest accuracy and precision of the distributions tested.
Since the LNO distribution is based on the amount of soil greater than a given sieve size (oversize), it is necessary to specify the smallest sieve size for the calculation of this distribution. We found that the value of estimates of the smallest sieve opening size had a great effect on estimates of aggregate-mean diameter and wind-erodible soil. Specifying a very small sieve opening size (10-8 mm) produced significantly larger and much more variable estimates of aggregate-mean diameter than when a larger sieve opening size (10-4 mm) was used. The precise effect of the specification of the smallest sieve opening size will vary with DASD compared. This result supports the identification of a ‘standard’ smallest sieve size to produce comparable results. The results of this study support specifying 10-4 mm as a suitable standard for the smallest sieve opening size. The sieve size of 10-4 mm produced aggregate-mean diameter results for LNO comparable with the other distributions that did not require specification of the smallest sieve size.
An examination of the effect of varying the size of the openings of the sieve with the largest openings demonstrated a clear effect of sieve opening size on aggregate mean diameter but no effect on wind-erodible soil. These results suggest that for estimates of aggregate-mean diameter, care should be exercised to ensure sieve opening sizes used in sieving analyses are comparable, regardless of the DASD used for aggregate-mean diameter estimation.
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ACKNOWLEDGMENTS
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The authors thank Dr. Bob Grossman, Research Soil Scientist, USDA-NRCS for assistance with physical and chemical soil analyses. We are grateful to Drs. Bobbie McMichael, Weldon Laird, and Jerry Winslow for helpful comments on early drafts of the manuscript and three anonymous reviewers for excellent comments that served to strengthen the presentation and inspire further development of the manuscript.
Received for publication February 5, 2002.
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ABSTRACT
INTRODUCTION
