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Soil Science Society of America Journal 65:300-310 (2001)
© 2001 Soil Science Society of America

DIVISION S-1-SOIL PHYSICS

Particle-Size Distributions

Comparing Texture Systems, Adding Rock, and Predicting Soil Properties

Mostafa A. Shirazia, Larry Boersmab and Colleen Burch Johnsonc

a Western Ecology Division, NHEERL, U.S. Environmental Protection Agency, 200 SW 35th Street, Corvallis, OR 97333
b Dept. of Crop and Soil Science, ALS 3017, Oregon State Univ., Corvallis, OR 97331-7306
c OAO Corporation, 200 Sw 35th Street, Corvallis, OR 97333

Corresponding author (safa{at}mail.cor.epa.gov)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 METHODS AND MATERIALS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Conventional soil texture classification systems use different definitions of particle-size distributions (PSDs). For example, sand in the International Soil Science Society (ISSS) system equals the combined separate limits of coarse silt and sand in the USDA system. Because relationships between texture and other soil properties are affected by these differences, the ability to merge survey data in environmental studies is limited. Previous research calculated two PSD statistics, namely the geometric mean particle diameter (dg) and its standard deviation ({sigma}g), which do not depend on separate limits. We expanded the development of the PSD statistics dg and {sigma}g to compare the USDA and ISSS systems, develop relationships with soil properties, include rock fragments, and simplify the USDA texture classification to facilitate the use of soil survey data in environmental research. We found that (i) for equal clay and sand fractions, the texture of a soil sample as described by the USDA system has larger dg and {sigma}g values than in ISSS; (ii) for equal clay and sand fractions, soil samples have larger values of cation-exchange capacity (CEC) in the ISSS than in the USDA system; (iii) small differences between some of the traditional 12 USDA classes are reflected in the dg and {sigma}g values for samples containing rocks, thereby presenting a rationale for simplification; and (iv) with this rationale, the 12 USDA classes were aggregated into five classes.

Abbreviations: CEC, cation-exchange capacity • ISSS, International Soil Science Society • PSD, particle-size distribution • SC, soil characteristic • STATSGO, State Soil Geographic Data Base • WSPSD, whole soil particle-size distribution • USDA5, aggregated USDA classes • USDA12, original 12 USDA classes


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
METHODS AND MATERIALS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
PREDICTING PHYSICAL and chemical properties of soils from easily measured intrinsic soil characteristics such as PSD has long been a goal of soil science research. Recently, Arya et al. (1999) expanded upon the frequently studied relationship between PSD and soil water characteristics, and Skaggs et al. (1999) pointed out the need to estimate soil water retention from only the clay, silt, and sand separates. The research also found renewed impetus from efforts to define and characterize soil quality and to prescribe sustainable management of soils (Johnson et al., 1991, 1992; Droogers and Bouma, 1997). Shirazi et al. (2001a) developed relationships between the whole soil PSD and a suite of soil characteristics that influence water quality, and Shirazi et al. (2001b) used these relationships to extrapolate observed water property information across a region. The mathematical description of the whole soil PSD used by the authors is developed in the present paper. The investigation addresses several practical concerns when using soil survey data in environmental research.

First, many soil data bases exist but not all use the same cutoff points for spacing size fractions. For instance, in the State Soil Geographic Data Base, STATSGO (Soil Survey Staff, 1991), the lower cutoff point for sand is 0.074 mm, which is based on the American Association of Highway Officials (AASHO) system, rather than the conventional 0.05 mm used in the USDA system (Soil Survey Staff, 1993). The increased availability of technologies and data for research and the increased need for soil information in environmental management efforts around the world require the ability to convert texture information from one data set to another (e.g., from the USDA system to the ISSS system). Therefore, the description of the PSD statistics is expanded to allow for differences in cutoff points.

Second, because rocks (>2 mm) have been shown to have ecological significance in the landscape (Corti et al., 1998), we add rock to a soil sample and calculate the whole soil particle-size distribution (WSPSD) statistics to include clay, silt, sand, and rock.

Third, soil survey data bases often report only the texture class of a soil sample (for example, loamy sand), without specific information on the separates. We estimate the PSD statistics for the classes on the basis of the clay, silt, and sand fractions of each texture class centroid.

Fourth, after developing the mathematical basis for the above calculations, we develop relationships between the PSD statistics and other soil characteristics (SCs) of the sample.

We begin by reviewing soil texture terms used in this study. Mineral soil particles <2 mm in equivalent particle diameter are named the fine earth, and particles >2 mm are called rock separates. The PSD, or texture, of the fine earth is defined by the relative weight proportions in the clay, silt, and sand fractions (or separates) of the sample. These separates are the primary soil separates. Each separate is defined by a range of nonoverlapping mineral particle sizes, that is, separate limits that define the cutoffs. A soil sample that is classified as clay, silt, or sand, and consists of 100% of a single separate of the same class name, is called unimodal because only one separate contributes mass to the PSD. Soil samples of any texture class that are mixtures of two or three separates are named bimodal or trimodal, respectively.

Separate limits and the number of texture classes are fixed, by convention, in each classification system. Two soil texture classification systems, namely the ISSS and the USDA systems are the subjects of our study (Soil Survey Staff, 1975, 1993; Soil Survey Division Staff, 1993; Soil Science Society of America, 1997).

Textures of various weight proportions of the primary soil separates produce different PSDs. Shirazi and Boersma (1984) described the PSD statistics of a soil sample within a texture classification system. They started with the assumption that the logarithm of particle size within each primary separate is uniformly distributed and each separate makes an additive contribution to the PSD statistics of the sample. The results were the geometric mean particle-size diameter (dg) and the geometric particle-size standard deviation ({sigma}g). Shirazi et al. (1988) improved the accuracy of dg and {sigma}g calculations by using a lognormal distribution instead of the log-uniform distribution of their earlier approach. The lognormal curve of each separate in a sample was integrated between the separate limits and then summed to obtain the sample dg and {sigma}g. Shirazi et al. (1988) also added the rock separates and calculated the whole soil PSD statistics (dg, {sigma}g).

This mathematical process of changing a sample description from a conventional texture triangle and separate limits to a new system that uses dg and {sigma}g as coordinates is a coordinate transformation. The transformation has two distinct steps, the first defines the PSD, and the second mathematically integrates the PSD to calculate the statistics dg and {sigma}g. Because the transformation mathematically combines or unifies the description of separate fractions with defined limits in a texture classification system, the statistics (dg, {sigma}g) become independent of a particular system of classification. When the rock separate is included in these calculations, the results are the WSPSD statistics.

In summary, the transformation is a systematic tool that we use (i) to describe and compare the (dg, {sigma}g) statistics for the USDA and the ISSS Systems, (ii) to develop relationships of the WSPSD with other SCs, and (iii) to examine these SCs for both systems.


   METHODS AND MATERIALS
TOP
 ABSTRACT
 INTRODUCTION
 METHODS AND MATERIALS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Transformation of the USDA and ISSS Texture Systems
Coordinate Transformation
We present a brief outline of the steps taken by Shirazi et al. (1988) in calculating the PSD statistics dg and {sigma}g using the lognormal distribution. The lognormal density function f(s) is obtained from replacing the particle size s with log (s) in the normal function. That is,

(1)
where x = log(s), a = log(dg), and b = log({sigma}g). The parameters a and b can be estimated graphically using the distribution function F(s) = {int}f(s)dx, which produces a straight line when plotted on a log-probability scale. Because of symmetry, the intercept of this line with F(s) = 0.50 is the median diameter log(dg) = log(d50), or log(s) = log(d50) = a. The slope of this line represents particle sorting, which is expressed as standard deviations. Thus, the intercept with F(s) = 0.841 is at one standard deviation from the mean, or log(s) = log(d84). It follows that b = log({sigma}g) = log(d84) - log(d50), and {sigma}g = d84/d50. This explains the graphic procedure for estimating a and b.

Alternatively, we can use numerical integration with the help of statistical tables or a computer to estimate a and b. In this method, we use the inverse normal function Y = {Phi}-1[F(s)], which has a linear relationship with x = log(s). In other words, the log-arithmetic plot of the normal deviate Y is a linear function of x, the intercept at zero standard deviation (Y = 0) is log(s) = A + B(0), and A = a. The intercept at one standard deviation (Y = 1) is log(s) = A + B(1) = log(d84), or log(d84) = log(d50) + B and B = b.

We now demonstrate the method by using a numerical example. Consider a sample having 60% clay, 30% silt, and 10% sand. In the USDA system, these proportions are associated with the upper separate limits, which we name y = 0.002 mm, t = 0.05 mm, and d = 2.00 mm, respectively, representing the last letters for clay, silt, and sand. As in Shirazi et al. (1988), the lower limit for clay is set at s0 = 0.00005 mm with a probability = 0.0001. The probability for the sand limit, d = 2.00 mm is assumed to be 0.9999. The assumed probabilities are needed for graphical or numerical integrations.

Consider, again, the silt separate in the above example. We want to obtain an equation of a straight line in the x and Y system that passes through the coordinates of the upper limits of clay and silt separates, that is (y, 60%) and (t, 60 + 30%). We are interested only in a segment of the line between these limits, but the entire line defines the lognormal function for silt in this soil sample. We consult a table of cumulative standardized normal distribution function to interpolate the normal deviates at probabilities 0.6 and 0.9 corresponding with the limits y and t. The deviates are 0.2533 and 1.2817, and the coordinates in the x and Y system are x = log(y) = -2.699, Y = {Phi}-1[F(y)] = 0.2533 and x = log(t) = -1.301, Y = {Phi}-1[F(t)] = 1.2817. Fitting a line to these two points yields x = a + bY = -3.043 + 1.359Y. This line is the desired lognormal function ft(s)(a, b) = ft(s)(-3.049, 1.359) for silt. Shirazi et al. (1988) calculated the lognormal parameters for the clay, silt, and sand separates and used them to estimate the parameters a and b representing the whole sample. Their method was to calculate the 0th, 1st, and 2nd moments of the segments of the lognormal curves for each separate and divide each by the total area (the sum of 0th moments), as follows

(2)


The subscripts y, t, and d refer to and define limits of integrations for the clay, silt, and sand separates, respectively. These calculations produced (a, b) = (-2.562, 0.747), dg = 0.00274 mm, and {sigma}g = 5.59 for the sample. In other words, the transformation reduces percentage clay, percentage silt, percentage sand, and three separate limits to two coordinates, dg and {sigma}g. The results of calculations for the 66 nodes at the intersections of 10% intervals of clay, silt, and sand and 16 vertices of texture polygons are reported in Shirazi et al. (1988).

Note that in the above, each f(s) is a unimodal symmetric function in which log(d50) = log(dg). The PSD of a multimodal sample is not symmetric and the whole sample dg and {sigma}g are estimated on the basis of a distribution having total probabilities equal to the contributions of several f(s) segments. Note also, that the above coordinate transformations estimate the statistics of a sample in the USDA classification system, but the same can be done for the ISSS system.

Precision of Numerical Integration
The systematic transformation process described above consists of three integrations, the 0th, 1st, and 2nd moments of the lognormal function. Each integration is performed for clay, silt, and sand fractions of a soil sample. Then, the results of the nine integrations are combined algebraically to produce estimates of dg and {sigma}g. The integration of the normal function can be carried out numerically to any desired precision. We considered the fourth-order Simpson rule combined with Newton's 3/8 rule (Hilderbrand, 1956; IBM, 1970) to offer adequate precision for our purpose. The integration of the standardized normal function was carried out between the limits of five deviates (-5 < x < 5) using h = 0.1 deviate as an increment in the Simpson rules. The lower limit (0.00001 mm) is selected below the smallest clay particle (0.00005 mm, after Shirazi et al., 1988) and is equal to the truncation error in the Simpson rule, which is on the order of h5. Spot checks of the integrated normal curve agreed with published tables, such as in Cramér (1945), which listed the values to five decimal places.

Texture Triangle and Tetrahedron
Shirazi et al. (1988) extended the traditional texture system, based on clay, silt, and sand, by including rock as a fourth primary soil separate. Using their method, the conventional soil triangles became tetrahedrons as shown in Plate 1A and 1B . The vertical dimension of the tetrahedron represents percentage rock, and the base is the customary texture triangle with 0% rock. At the apex of the tetrahedron, the sample consists of 100% rock. In each plane, or projection, parallel to the base, the distribution of the fine earth is in the same relative proportion as in the base triangle, but the absolute percentages are reduced in proportion to percentage rock. Although texture classes of both systems have similar names (abbreviated labels in each base triangle of Plate 1A and 1B), classes differ in number, definition, and symmetry.



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  		Plate 1. The (A) USDA and (B) ISSS texture class tetrahedrons show: triangles at 0% rock; projected triangles at 50% rock; apex (a) at 100% rock; and texture class labels: s = sand, ls = loamy sand, sl = sandy loam, l = loam, sil = silt loam, si = silt, scl = sandy clay loam, cl = clay loam, sicl = silt clay loam, sc = sandy clay, sic = silt clay, and c = clay. (C) Soil separates for clay, silt, and sand for the USDA and ISSS systems are compared

 
The separate limits that describe the USDA and ISSS systems differ in the cutoff for silt, which is 0.05 mm in the USDA and 0.02 mm in the ISSS (Plate 1C). We set the upper limit for rock for both systems to <3162 mm, (10 m)1/2 (Soil Survey Staff, 1993).

Each vertex of a tetrahedron defines unimodal samples of clay, silt, sand, or rock. For example, the apex a is 100% rock and the vertex m is 100% sand (Plate 1A or 1B). The six lines connecting the four vertices define six bimodal samples. Thus, samples consisting of mixtures of rock and clay are defined by aw in Plate 1A and 1B. The four faces of the tetrahedron each define trimodal samples. Samples containing mixtures of clay, sand, and rock are represented by wma (Plate 1A and 1B). Quatramodal samples are represented by points inside the tetrahedron that can be identified on planes parallel to the base. One projected plane, midway to the apex, is shown for each system in Plate 1A and 1B, and all the quatramodal samples on this plane have 50% rock and 50% fine earth.

Transformation of the Texture Triangle
Soil samples with 0% rock are represented by conventional triangles that have texture class polygons based on defined separate limits. These texture classes are transformed to the dg, {sigma}g coordinate system and plotted in Plate 2A and 2B , respectively, for the USDA and ISSS systems. The texture class labels are placed near the centroid symbols in Plate 2A and 2B and are consistent with labels used in Plate 1A and 1B. After transformation, the vertices of the triangle are lined up along the dg (horizontal) axis. Note that the unimodal clay at w has the smallest dg and the unimodal sand at m has the largest dg. Straight lines from the triangle are transformed as curved lines. For example, the three curved lines wt, tm, and mw in Plate 2A are the loci of the bimodal samples that are represented by the sides of the base triangle in Plate 1A. The trimodal samples are defined within the areas wmt and wmu in Plate 2A and 2B for the USDA and ISSS triangles, respectively. The graphic overlay of the two transformed systems is shown in Plate 2C.



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  		Plate 2. Transformed soil texture triangles for the (A) USDA and (B) ISSS systems show relationships of particle-size distribution statistics. (C) The two systems are superimposed for comparisons. Round and triangular symbols show the location of the centroid for each texture class polygon

 
Transformation of Texture Tetrahedron
Next, we calculate the WSPSD statistics (dg, {sigma}g) for samples that also include rocks. The transformations of USDA and ISSS tetrahedrons are plotted in Fig. 1A and 1B . After transformation, points representing the unimodal clay, silt, sand, and rock are aligned along the dg axis. The unimodal clay at w has the smallest dg, and the unimodal rock at a has the largest dg. The loci of bimodal samples containing rock and sand, rock and silt, or rock and clay are transformed into the curved lines am, at, and aw in Fig. 1A. The base planes wmt and wmu in Fig. 1A and 1B are the loci of trimodal samples at 0% rock and are identical to Plate 2A and 2B, respectively. Note the 0% labels for these planes near the w vertices in Fig. 1A and 1B. The projections of the base triangle for 25, 50, and 75% rocks are shown in Fig. 1 and are labeled at points corresponding with the clay vertex. The planes awtm and awum, respectively, in Fig. 1A and 1B circumscribe the coordinates of the quatramodal samples represented by the interior of the tetrahedrons in Plate 1A and 1B.



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  		Fig. 1. Transformed soil texture tetrahedrons for (A) the USDA and (B) the ISSS systems show relationships of projected planes at 25, 50, and 75% rock with the base plane at 0% rock. The sides of the tetrahedrons are labeled as in Plate 1. The dashed line (c) in (A) is the trajectory that connects the centroids of the clay texture class polygons from 0 to 100% rock

 
The path that the centroid coordinates of a texture class traverses as the rock content increases from 0 to 100% is referred to as the trajectory of that class. For example, the dashed line plotted in Fig. 1A (marked as c) defines the clay trajectory in the USDA system.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 METHODS AND MATERIALS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Comparison of the USDA and ISSS Texture Systems
The USDA soil texture classification system (Plate 1A) differs from the ISSS system (Plate 1B) in the number of texture classes and separate limits (Plate 1C). The influence of these differences on the WSPSD statistics (dg, {sigma}g) varies with the modality of the sample. Recall that modality, in our discussion, refers to the number of separates in a soil sample that contribute mass to the WSPSD. For example, a unimodal clay sample contains only clay separate that contributes 100% of the mass.

Unimodal Sample
The unimodal samples are influenced by the choice of separate limits, which are reflected in the WSPSD statistics (dg, {sigma}g). For example, a lognormal curve fitted for sand in the USDA system at the lower limit log(0.05) = a + b(-3.71) and the upper limit log(2.0) = a + b(+3.71) obtains a = [log(2.0) + log(0.05)]/2 = -0.5, dg = 0.316 mm, b = 0.801/3.71, and {sigma}g = 1.64 (point m in Plate 2A). The limits in the ISSS system generate dg = 0.2 mm and {sigma}g = 1.86 (point m in Plate 2B). The difference in the sand separate limits produces a smaller mean diameter but a larger standard deviation in the ISSS system. Because the clay separates are identical in the USDA and ISSS, the statistics are the same in both systems for the 100% clay sample (dg = 0.000316 mm and {sigma}g = 1.64, points labeled w in Plate 2A and 2B).

Bimodal Samples
The WSPSD statistics (dg, {sigma}g) of bimodal samples are affected by separate limits and the proportion of each separate, or sample location along any one of six edges of the tetrahedrons (Plate 1). Recall that these six straight lines on a tetrahedron transform into six curved lines connecting two unimodal samples. Also, each curved line attains a peak value near the middle where the {sigma}g has its maximum value (Fig. 1). The maximum standard deviation of a bimodal sample results from mixing equal proportions of the two separates. For bimodal samples without rock, mixing clay with increasing amounts of sand continuously increases the dg of the sample, but the {sigma}g of the sample begins to decrease after reaching a maximum value at 50% sand and 50% clay (curves wm in Plate 2A and 2B). The (dg, {sigma}g) coordinates for this 50–50% sample are (10 µm, 11.86) for the USDA and (6.97 µm, 8.57) for the ISSS systems. Again, the ISSS system's smaller coordinates reflects the difference in the lower separate limit for sand (Plate 1C). Because both systems use identical separate limits for clay and rock, the transformed curves for bimodal samples of clay and rock are identical (wa, Fig. 1A or 1B). Like the example of clay and sand, the bimodal clay and rock sample also attains maximum standard deviation at 50% of each separate and the (dg, {sigma}g) coordinates for this sample = (93.75 µm, 113.65) for both systems (Fig. 1A or 1B).

Trimodal Samples
Trimodal samples are formed for USDA or ISSS systems by mixing any three of the four separates. The loci of all trimodal samples are the inclined surfaces of the tetrahedron and are represented in Fig. 1B as uam for mixtures of silt, rock, and sand; wam for clay, rock, and sand; and uwa for silt, clay, and rock.

The centroids of texture class polygons in the USDA and the ISSS triangles are listed in Table 1 as examples of trimodal samples with no rocks. For example, the centroids of clay polygons are defined by 60.76% clay, 19.36% silt, and 19.87% sand in the original 12 USDA classes and by 82.41% clay, 9.04% silt, and 8.55% sand in ISSS. This comparison ignores the difference in separate limits between the two systems. For an equitable comparison, we must transform the centroids to obtain (dg, {sigma}g) = (3.53 µm, 7.54) for the USDA and (1.28 µm, 4.09) for the ISSS systems (Table 1). This pattern of smaller dg and {sigma}g for the ISSS system than the USDA system is consistent for all transformed texture class centroids, shown also in Plate 2C.


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  		Table 1. Texture class centroids in the (dg, {sigma}g) and triangular coordinates of USDA12, ISSS, and USDA5 systems

 
Quatramodal Samples and Trajectories
Quatramodal samples are defined by projected triangles containing >0 to <100% rock. Examples of these projections are plotted for 25, 50, and 75% rock in Fig. 1A and 1B. We described the concept of a trajectory when discussing Fig. 1A. Points along a trajectory describe the path of all quatramodal samples that pass through the centroid of a texture class in projections between 0 and 100% rock. Clearly, there are infinite numbers of paths that do not pass through the texture class centroids which we do not name as trajectories. Figures 2A and 2B display, respectively, 12 USDA trajectories and 10 ISSS trajectories. Because the ISSS centroids represent finer soil samples than USDA centroids, the ISSS trajectories exhibit higher {sigma}g values. Finally, trajectories in the ISSS system are relatively evenly spaced, unlike those of the USDA, a difference that suggests simplifying the USDA classes.



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  		Fig. 2. Centroid trajectories of texture classes for (A) the USDA and (B) the ISSS systems with triangular markers at projected texture class centroids at 20% rock intervals

 
Applications of the Whole Soil Particle-Size Distribution Statistics (dg, {sigma}g)
Application 1: Aggregating USDA Texture Classes
In Fig. 2A, the USDA trajectories depicting clay loam and sandy clay nearly merge together, and loam, silt loam, silt, and sandy clay loam form a compact cluster. Even though an entire texture polygon is represented by a single mathematically defined point, the clusters of trajectories suggest the need for additional simplification. The USDA has developed a generalized texture system with five classes (Soil Survey Division Staff, 1993, p. 140) that we analyzed in relation to trajectories incorporating percentage rock. For convenience, we refer to the original 12 USDA classes as USDA12 and the aggregated classes as USDA5.

The five USDA5 classes are: cr = coarse, mocr = moderately coarse, mecr = medium coarse, mofn = moderately fine, and fn = fine. They each comprise one to three USDA12 classes and the calculated centroid characteristics are listed in Table 1. For example, mocr includes USDA12 sl and the fn consists of sc + sic + c.

USDA5 Tetrahedron and Texture Class Trajectories
A tetrahedron based on the USDA5 system is plotted in Plate 3A showing five lines that connect the tetrahedron coordinates of texture class centroids as rock content increases from 0 to 100%. These lines define trajectories. Transformations of the five trajectories are plotted in Plate 3B. The trajectories are intersected by lines of constant rock percentages (dashed lines), which are labeled at 20% rock intervals. We also constructed Table 2 using intervals of 5% rock to define the trajectories in greater detail.



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  		Plate 3. (A) Five general texture classes (USDA5), labeled at the base of tetrahedron, were created from 12 classes. The USDA5 and corresponding USDA12 classes are: cr = coarse = s + ls, mocr = moderately coarse = sl, mecr = medium coarse = l + sil + si, mofn = moderately fine = cl + scl + sicl, and fn = fine = sc + sic + c. (B) Coordinates of the USDA5 class trajectories (lines connecting centroids from 0 to 100% rock) in (A) were transformed to WSPSD statistics coordinates (curved lines). The broken lines connect texture class centroids at constant 10% rock intervals

 

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  		Table 2. Coordinates of five USDA5 trajectories listed at 5% rock separate intervals.{dagger}

 
Consider the trajectory for fine textured soils (fn), which is the topmost line in Plate 3B. The sample with 0% rock is at log(dg) = -2.406, {sigma}g = 7.65 (Table 2). In other words, the geometric mean diameter (dg) is 0.0039 mm and the geometric standard deviation ({sigma}g) is 7.65. If this sample is mixed with 20% rock, the WSPSD statistics (dg, {sigma}g) increases to log(dg) = -1.651 or dg = 0.0223 mm, and the standard deviation becomes {sigma}g = 40.50 (Plate 3B and Table 2). Continuing to add rock separates increases the mean diameter and the standard deviation until it reaches the maximum at 45 to 50% rock ({sigma}g = 67.19, Table 2). In summary, increasing the rock percentages above 50% decreases the standard deviation, while the mean diameter for texture classes continues to increase. As the categories become increasingly coarse textured (top to bottom), the addition of rocks changes the standard deviation progressively less (Plate 3B and Table 2).

Application 2: Conversion between USDA and ISSS Systems
Converting a Separate.

Samples with equal clay, silt, and sand separates have different whole sample PSDs in the ISSS and the USDA systems, and the difference persists after conversion. Because each lognormal segment defines the PSD of one separate, it is convenient to solve this lognormal function to estimate probabilities associated with any particle size within separate limits. This approach is adopted for conversion here, and it contrasts an alternative approach (below) that converts the PSD of the whole sample. Here, we convert sand from the ISSS to the USDA system by solving the equation for sand at the cutoff point for coarse silt, because: sand (ISSS: 0.02–2 mm) = coarse silt (USDA: 0.02–0.05 mm) + sand (USDA: 0.05–2 mm). To convert from USDA to ISSS, we solve the equation for silt at the cutoff point for coarse silt using the relationship: silt (USDA: 0.002–0.05 mm) = silt (ISSS: 0.002–0.02 mm) + coarse silt (USDA: 0.02–0.05 mm). Notice that in the conversion from the ISSS to USDA system, the percentage of silt in the sample increases with a concomitant decrease in the sand. When converting from USDA to ISSS, percentage sand increases while silt decreases.

We will illustrate this shift again using the USDA sample having 60% clay, 30% silt, and 10% sand. The PSD statistics produced dg = 0.00274 mm and {sigma}g = 5.59. The lognormal segment fitted to the silt separate of the sample was derived in the Coordinate Transformation section above. We obtained x = -3.043 + 1.359Y, which evaluated for Y at log(0.02 mm) = -1.699, yields Y = (-1.699 + 3.043)/1.359 = 0.989. The Y value is the number of standard deviations on the particle-size axis from the mean diameter (or the origin). We can use any standard table of the integrated normal distribution to invert Y to a probability estimate of 0.8386, which indicates the probability that the particle size is <=0.02 mm. Therefore, the total percentage clay and silt in this example is 83.86%, and percentage sand is 100(1 - 0.8386) = 16.14% in the ISSS system, vs. 10% in the USDA system. Applying these procedures to a range of samples produced Plate 4 , which can be used for converting percentage sand to or from the USDA and ISSS systems.



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  		Plate 4. Conversion nomograms for percentage sand (A) from the ISSS to USDA and (B) from the USDA to ISSS systems. For each texture triangle, the dashed lines are the percentage sand being converted, and the solid lines represent values after conversion. Conversion of percentage sand from the ISSS to USDA system is independent of the clay content of a sample, thus the dashed lines in (A) are linear. Because conversion of percentage sand from the USDA to ISSS system is a function of clay content, the dashed lines in (B) are curved and concentrated together at low percentage clay values

 
Conversion Nomograms
Although the clay percentage is unchanged when converting between the USDA and ISSS systems, nomograms are a convenient method to convert either sand or silt percentages. The nomograms in Plate 4 use triangular coordinate system to convert sand percentages. Only the clay and sand data are necessary because the percentage of silt can be calculated from silt = 100 - clay - sand. The coordinates for the system being converted are dashed lines, whereas the coordinates after conversion are the solid lines. As in the conventional nomenclature, the solid clay lines are horizontal and parallel to the base, but their values, unlike the conventional system, are marked on the right-hand side of the triangles. The sand lines are angled and marked at the base of the triangle.

ISSS to USDA
We convert percentage sand from the ISSS to the USDA classification system using Plate 4A. The blank area on the left side of Plate 4A represents the USDA PSDs that are not included in the ISSS system. This nonoverlap area is bounded by the 0% silt lines of the ISSS and USDA systems, which are both labeled wm in Plate 2C.

To demonstrate a percentage sand conversion from the ISSS system to the USDA, refer to the triangular marker in Plate 4A, located at the intersection of the 30% clay line (right axis) and the dashed 40% ISSS sand line from the left axis. Next, follow the dashed line to the horizontal axis to obtain the USDA value of {approx}17% sand. Note that any sample with 40% sand in the ISSS system contains 17% sand in the USDA system, regardless of percentage clay. In other words, the ISSS percentage sand values remain constant when converting to USDA; therefore, the dashed lines in Plate 4A are linear. However, the same is not true when converting samples from USDA to ISSS.

USDA to ISSS
A sample with 40% sand and 30% clay in the USDA system is marked with a triangle in Plate 4B. By following the solid line to the horizontal axis, we obtain a value of {approx}49% sand in the ISSS system. Observe that a USDA sample of 40% sand and 5% clay (not marked on figure), converts to {approx}61% sand in ISSS. Because the ISSS sand definition includes coarse silt, the conversion from the USDA to ISSS shifts (or reclassifies) sample textures towards higher percentage sand values. The effect is greater when the clay and sand contents are initially small, as evident in the convergence of lines in Plate 4B.

Converting Separates vs. the Entire Particle-Size Distribution
In this paper, we used the PSD of individual texture separates for conversion rather than the PSD of the soil sample. Recall that converting a soil separate involves mathematically inverting a lognormal function, which can be done with accurate results. Although this simple approach provides a first step toward converting the entire PSD, it does not address relationships between the sample dg and {sigma}g before and after conversion. Because the dg and {sigma}g of the whole sample are numerically independent of a particular classification system, Shirazi and Boersma (unpublished data, 2000) developed an approach that keeps the dg and {sigma}g of the sample constant before and after conversion. This approach was also used to convert sand and clay percentages to and from the ISSS and USDA systems. The standard errors of the differences between conversions by separates and by sample PSD were ±2.21% for clay conversion and ±4.14% for sand. However, the errors vary, and the highest errors are about twice the standard error. For the conversion from ISSS to USDA, the highest errors are generally bounded by 6 to 80% clay, 0 to 35% silt, and 20 to 95% sand. The highest errors for the USDA to ISSS conversion were between 6 and 80% clay, 20 and 50% silt, and 20 and 70% sand.

Effect on Classification of Soil Layer
Layer texture in the STATSGO data base is given in the USDA system, except that the silt upper limit is at 0.074 mm instead of 0.05 mm. To use it in the conventional USDA or ISSS systems, we needed to convert it first. Textures from 314975 soil layer (horizon) samples from STATSGO were converted to USDA and ISSS systems using the methods of this paper. Figure 3 shows the frequency distributions of soil layers with respect to the sand separate in the USDA and the ISSS systems after conversion. The number of layers with 0 to 10, 20 to 30, and 40 to 50% sand are 25000, 53300, and 37700 in the USDA system, or 2400, 44700, and 59800 respective layers in the ISSS system. Thus, Fig. 3 illustrates the consequence of the shift to increased percentage sand after conversion from the USDA to ISSS system.



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  		Fig. 3. Frequency distribution curves show the number of soil layers in the STATSGO data base relative to percentage sand in a sample for the USDA12 (solid line) and the ISSS (dashed line) systems. Due to its conversion from the USDA system, the ISSS frequency curve reflects higher sand separates

 
Application 3: Relationship between PSD or WSPSD and Soil Characteristics
Next, we used information from STATSGO to demonstrate relationships between PSD or WSPSD and a SC, namely, the CEC. The CEC is reported in STATSGO for 314975 samples with high and low ranges for each soil layer (horizon). We averaged the layers. Changes in CEC with respect to clay and sand in the ISSS and USDA systems are listed in the body of Table 3. The mean and standard error of CEC with respect to clay are listed in the last column, and with respect to sand in the last row for each system. Note that the mean distribution of CEC in clay is identical in the two systems (see last column). The table also shows that soil CEC varies directly with the clay but inversely with the sand separates in a sample.


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  		Table 3. The cation-exchange capacity of STATSGO soil layers for varying percentages of sand and clay separates in USDA12 and ISSS systems. Blank spaces in the table indicate no data or impossible combinations of separate percentages

 
Cation-Exchange Capacity in Soil Samples without Rock
We combined information from Table 3 with the PSD statistics (dg, {sigma}g) from Plate 2A and 2B to produce Plate 5A , for USDA12, and 5B for the ISSS systems. Each figure displays constant percentage clay and percentage sand lines in the dg and {sigma}g coordinate system. The clay lines in Plate 5A and 5B are overlaid with interpolated CEC values from Table 3. This interpolation was obtained by separately fitting the CEC for constant clay values to a linear function of dg and {sigma}g. A linear equation was used because of the limited number of data points. The standard errors listed for discrete points in Table 3 also apply to the interpolated curves in Plate 5A and 5B. The colors vary from yellow to magenta along a continuous scale of CEC values. The legend shows benchmarks of the CEC rather than categorical divisions. These figures display the predictive potential of the coordinates (dg, {sigma}g). For example, the 70% constant clay line in Plate 5B corresponds with the 60 to 80% clay (ISSS) in Table 3. Estimates of CEC can be obtained from the nomograms or table based on predictable relationships with texture data.



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  		Plate 5. Relationship of particle-size distribution statistics and soil cation-exchange capacity (CEC) in (A) the USDA12 and (B) the ISSS systems. Note that (A) and (B) display only the fine earths with 10, 30, 50, and 70% clay intervals and sand from 0 to 90%. (C) The relationship of CEC with soil samples that contain rock separates are presented in the USDA5 trajectory system

 
Note that CECs in USDA12 (Plate 5A) have larger coordinates of dg and {sigma}g than CECs in the ISSS (Plate 5B). Because smaller particle sizes (which are reflected in smaller coordinates for the ISSS system) have larger surface areas (Petersen et al., 1996), CEC values are slightly larger in the ISSS than the USDA12 system.

The CEC of a soil sample for a constant percentage clay decreases with increasing percentage sand in USDA and ISSS. However, the increased sand in a sample also increases the geometric mean particle diameter of the sample. This inverse relationship between CEC and increasing sand or dg are displayed simultaneously in Plate 5A and 5B. These analyses demonstrate that the PSD statistics (dg, {sigma}g) can be used as a common language to describe soil CEC in different systems.

Cation-Exchange Capacity in Soil Samples with Rock (USDA5 Trajectories)
The relationships between STATSGO soil CEC and USDA5 texture classes are listed in Table 4 for rock contents from 0 to 100%. The mean CEC and the standard errors are rounded off to the nearest unit values. The CEC increases from coarse to fine soils and generally decreases with rock content. We combined the CEC from Table 4 with the USDA5 trajectories of Plate 3B by separately fitting the CEC for each texture class to a linear function of dg and {sigma}g. The interpolated function is plotted in Plate 5C, which graphically illustrates that soil CEC decreases from the finest texture class (fn) to the coarsest (cr). Moreover, the CEC decreases with increasing percentage rock within the majority of texture classes because of the statistical association of small CEC and large rock content in the whole soil sample.


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  		Table 4. The cation-exchange capacity of STATSGO soil layers along USDA5 trajectories.{dagger}

 
The above relationship of the WSPSD statistics (dg, {sigma}g) with CEC in samples containing rock further demonstrates that dg and {sigma}g are predictors of CEC. This predictive capability was investigated for a wide range of soil characteristics in Shirazi et al. (2001a) and was applied to water quality in Shirazi et al. (2001b).


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 METHODS AND MATERIALS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
The WSPSD statistics (dg, {sigma}g) mathematically define soil textures independently of classification systems. We used the statistics to illustrate differences between the USDA and ISSS systems and to convert textures between systems. Further, plotting the WSPSD centroids of the 12 USDA texture class polygons with rock contents increasing from 0 to 100% revealed several clusters, indicating the need and rationale for aggregating classes. Because soil texture is related to other soil characteristics, such as CEC, the WSPSD statistics retain these relationships. In summary, the WSPSD statistics form a common language for basic soil texture research and have several applied benefits.


   ACKNOWLEDGMENTS
 
Dr. Paul Schaffer of Dynamac International, Inc. reviewed the manuscript and provided helpful comments. Suggestions from the reviewers of SSSAJ significantly improved the clarity of our presentation. The EPA through its Office of Research and Development, funded the research. It has been subjected to EPA review and approved for publication.

Received for publication February 22, 2000.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 METHODS AND MATERIALS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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M. A. Shirazi, C. B. Johnson, J. M. Omernik, D. White, P. K. Haggerty, and G. E. Griffith
Quantitative Soil Descriptions for Ecoregions of the United States
J. Environ. Qual., March 1, 2003; 32(2): 550 - 561.
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