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a Western Ecology Division, NHEERL, U.S. Environmental Protection Agency, 200 S.W. 35th Street, Corvallis, OR 97333
b OAO Corporation, 200 S.W. 35th Street, Corvallis, OR 97333
Corresponding author (safa{at}mail.cor.epa.gov)
Received for publication February 22, 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONREFERENCES |
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Abbreviations: 
g, geometric particle standard deviation • CEC, cation exchange capacity • comppct, component percent • cr, coarse-textured soils • cstdv, conditional standard deviation • dg, geometric mean particle diameter • fn, fine-textured soils • ir, index of relationship of a soil characteristic of a map unit • mecr, medium coarse-textured soils • mocr, moderately coarse-textured soils • mofn, moderately fine-textured soils • MUG, map unit group • MUID, map unit identification code • PSD, particle size distribution • SC, soil characteristic • STATSGO, State Soil Geographic Data Base • stdv, standard deviation • USDA12, conventional USDA texture classes • USDA5, aggregated USDA texture classes
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONREFERENCES |
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Hoag et al. (1998) used soil pH, organic matter, available water capacity, and bulk density to define soil quality and evaluate sustainability in crop production. Soil survey information was used by Droogers and Bouma (1997) to model the effects of different agricultural practices and by Johnson et al. (1991) and Church et al. (1989) to predict surface water acidification. Larson and Pierce (1994) investigated the chemical, physical, and biological roles of soils in the landscape, particularly for partitioning precipitation and regulating water flow. According to these authors, soil texture, depth, permeability, biological activity, capacity to store water and nutrients, and the amount of organic matter all play roles in the landscape. Hence, water quality is strongly linked with soil quality and soil quality must be maintained to preserve water quality.
In Shirazi et al. (2001b), we developed methods to extrapolate observed physical and chemical water properties, such as acid neutralizing capacity and dissolved organic carbon, across a region using relationships between the properties of soils and surface waters. That application is derived from the present investigation, which describes selecting, scaling, aggregating, modeling, and analyzing soil data.
We selected SCs for this study from STATSGO (Soil Survey Staff, Soil Conservation Service, 1991). The term soil characteristic implies an observed or inferred physical, chemical, or biological soil property or attribute (Soil Science Society of America, 1997). Table 1 lists the symbols for the selected SCs in this paper.
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The multiple scales for soil quality evaluation were defined by Karlen et al. (1997) based on research needs. For example, a point, a plot, a field, a watershed, and a continent, each may fulfill the respective spatial requirements of basic research, applied research, interdisciplinary research, interagency monitoring, and policy development. In the present paper, we use soil information at the STATSGO map unit scale (mean area = 742 km2, standard deviation [stdv] = 13000 km2), which is appropriate for monitoring needs on a multistate or national scale. However, the approach is scale independent and may be used in basic research at higher spatial resolutions.
Previous research by Shirazi et al. (2001a) developed two statistics of the whole-soil particle size distribution (PSD) as a common "language" for describing SCs of soil layers. These statistics where named the geometric mean particle diameter (dg) and the geometric particle standard deviation (g). We now add a spatial element to this description by analyzing relationships of these statistics with SCs of map units. Our objective is to develop whole-soil PSD–SC relationships in empirical models using STATSGO map units and to verify the use of the statistics dg and g as the basis for spatial extrapolation of SCs.
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METHODS AND PROCEDURES |
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TOPABSTRACTINTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONREFERENCES |
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g. The statistics form a new coordinate system to mathematically describe the texture of a soil sample consisting of clay, silt, sand, and rock. Shirazi et al. (2001a) simplified the conventional 12 USDA texture classes (which they named USDA12) to five texture classes (named USDA5). The USDA5 classes are: cr = coarse, mocr = moderately coarse, mecr = medium coarse, mofn = moderately fine, and fn = fine. In the dg and g coordinates, percent rocks can be plotted along with the centroids of the USDA5 texture classes. The lines connecting the centroid coordinates as percent rock increases from 0 to 100% were called trajectories (Shirazi et al., 2001a). In the present paper, we use this USDA5 system to model and summarize SCs of map units. We use the whole-soil PSD that includes rock rather than the fine earth (<2 mm) PSD, because of the potential influence of rocks on water quality. Corti et al. (1998) studied the physical and chemical roles of rock in the soil. In particular, they showed that rock is not an inert component of the soil, instead rock surfaces play an active role in soil chemistry.
Overview: Aggregation, Soil Characteristics Model, and Verification
The approach described in this section consists of four general steps: (i) Aggregating STATSGO SCs from layers and components into SCs of the map units, calculating the whole-soil PSD statistics (dg and g) for each map unit, and grouping the map units into five USDA5 texture classes. (ii) Developing mathematical models of relationships among SCs of map units in each texture class. (iii) Regrouping the map units of each texture class into six map unit groups (MUGs) based on rock content. (iv) Using the models to predict the mean SCs of the MUGs, which we called an interpolation test. The test shows how well the whole-soil PSD statistics (dg and g) can be used to recover spatially defined SCs. We also performed extrapolation tests by predicting the mean SCs of new MUGs. The latter were formed from map units not used in building the models. Therefore, an extrapolation test indicates how well the whole-soil PSD statistics (dg and g) produce new information for areas only indirectly defined by model data. Figure 1
shows a general overview of the steps.
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The data base lists a high and a low value, respectively, representing the maximum and minimum range in a SC. Each soil layer sample in the layer file is listed with a map unit identification code (MUID), a soil sequence number, and a soil layer number. The soil sequence number identifies the soil component in a map unit and links the layer and component files.
Each map unit may include up to 21 soil components but each component contributes only fractionally to the total area. This fraction is presented as a percentage in the data base and is named comppct. The data base provides rock fragment information as weights only. We calculated the volume of rock fragments by interpolating Exhibits 618-11 and 618-13 of the Soil Survey Staff, Soil Conservation Service (1993) documentation using bulk density of <2 mm and rock fragments as percent weight.
We used 317267 STATSGO layer samples from 109532 soil components that formed 10463 soil map units. The 27 map unit SCs listed in Table 1 were used in our study due to their potential relationship with water quality.
Aggregation of Soil Characteristics
Overview
This section illustrates the steps used in aggregating SCs of layers from STATSGO layers to components and then to SCs of a map unit. Our example includes only soil texture and permeability for one New Hampshire map unit (MUID = NH002). Map Unit NH002 contains 13 components and we aggregated SCs of Components 1 and 13. The steps and results are outlined in Table 2 for the layer to component stage, and in Table 3 for the aggregation from component SCs to a map unit SC. The USDA12 texture class, low and high layer depths, and low and high permeabilities listed in Table 2 were obtained from the data base. We calculated layer and component rock contents and component permeabilities as explained below.
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Rule 1. Assume n soil layers with permeabilities x1, x2,..., xn and layer depths d1, d2,..., dn. Let the aggregated component permeability be designated by X and its depth by D. We assume that layer permeabilities can be aggregated in the vertical direction to obtain a representative component permeability, analogous to resistors connected in series, by using the arithmetic operation:
 | [1] |
Rule 2. Let the aggregated map unit permeability and depth be designated by X and D = d1 + d2 + ... + dn. We assume that component permeabilities can be aggregated to obtain a representative map unit permeability by the analogy with resistors connected in parallel, that is, by using the arithmetic operation:
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We used Rule 1 for the aggregation from layer permeabilities to a component permeability and Rule 2 for all other SC aggregations from layers to a component and from components to a map unit.
The Whole-Soil Particle Size Distribution Statistics of a Soil Layer
After the rules for aggregation are specified, we examine the data needs for calculating whole-soil PSD statistics, noting that in STATSGO the PSDs for the fine earth are reported for the USDA12.
In STATSGO, different particle sizes are reported as weight percents in relation to different benchmarks such as the whole-soil or particular sieve sizes. Thus, we needed to standardize all values to the whole soil. For example, for Map Unit NH002, Component 13, Layer 3, the low range sample has the following categories listed: (i) Materials >76.2 mm = 15% (relative to whole-soil sample), that is, material <76.2 mm = 85% (relative to whole-soil sample). (ii) Materials <2 mm = 20% (relative to <76.2 mm), and therefore, 20 (85/100) = 17% (relative to whole-soil sample). The rock content relative to the whole-soil sample is 100 - 17 = 83% (Table 2). This standardizing procedure was repeated for all other layers.
Aggregating Texture from Layers to Components
NH002, Component 1. We determine the depth variables needed to complete component aggregations (Rule 1 or 2) from Table 2 by subtracting the low from the high depth values. For Component 1, the Layers 1, 2, 3, and 4 have depths of 20.32, 25.38, 50.82, and 68.58 cm, respectively.
The centroids of clay and sand percentages are 12.45 and 21.64%, respectively, for the silt loams (USDA12 sil) of Layers 1 and 2 whereas the values are 32.94 and 10.00% for the silty clay loams (sicl) of Layers 3 and 4 (Shirazi et al., 2001a). These are the "x" values needed, along with the depth data described above, to complete Rule 2 for aggregating texture from layers to a component. In this example, Component 1 has a clay content of 
= 
= 27.27%. Likewise, the percent sand for Component 1 is 2182.95/165.10 = 13.22%. These clay and sand values are listed for Component 1 of Table 3. The same methods were used to aggregate rock contents and repeated for all 13 components of Map Unit NH002 (Table 3).
Permeability of a Soil Component
To illustrate Rule 1 (used only for aggregating the layer permeabilities), we refer to Table 2 and note substantially different permeabilities for each layer of Component 1 but identical values for Component 13. When we apply Rule 1 to the high range of permeabilities for Component 1, the results are: 
= 
= 0.29 cm/h. This value is also listed on the first line of Table 3. In order to avoid dividing by zero while aggregating permeabilities based on the low values of Component 1, we inserted the nominal value of 0.00254 cm/h (i.e., 0.001 in/h). Thus, the resulting low permeability value is <0.004 (rounded to 0.00 cm/h in Table 3). Because the permeabilities of all layers in Component 13 are equal, the aggregation based on Rule 1 produces the same values. Any component having a surface layer classed as "muck" or any "non-soil" designation was omitted from these calculations (NH002, Component 7).
Texture and Permeability of a Soil Map Unit
The next steps aggregate component data to the map unit level, again using data from NH002. Refer to Table 3 for the percent of map unit area occupied by each component (comppct) and its depth. Map unit depth is calculated from the relative contribution of each component depth. Specifically, each component depth is multiplied by comppct, the products are added together, and the resulting sum is divided by the sum of all comppct values (i.e., 95). Thus, total depth (D) for NH002 is derived from the following simplified equation: 
= 130.96 cm.
Map unit depth is used to calculate the whole-soil PSD statistics for texture and to calculate map unit permeability. For the map unit texture, we use the aggregated percent clay, percent silt, percent sand, and percent rock of the components to derive the coordinates dg and g. To calculate the total percent clay or sand for NH002 from the component separates, each percent clay or percent sand value is multiplied by comppct and component depth. The sum of these values becomes the numerator in Rule 2. The denominator of Rule 2 is the product of the map unit depth and the sum of comppct values, or 130.96 x 95 = 12441.20 in this example. Completing the Rule 2 equation reveals that Map Unit NH002 contains 14.64% clay and 51.22% sand, and therefore is classified as loam (l) in the USDA12 system or mecr (medium coarse) in USDA5. By repeating this process for rocks, we obtain 3.6 and 14.96% rocks as the low and high values of NH002. Finally, we use the above percentages to interpolate Table 2 of Shirazi et al. (2001a) to determine the coordinates (dg and g), which are (-1.339, 17.62) and (-1.696, 8.651) for the high and low rock percentages, respectively.
The total permeability of Map Unit NH002 is also calculated by applying Rule 2. For this example, we use the component high value permeabilities (units = cm/h) listed in Table 3. Component permeabilities are multiplied by comppct and depth, then summed to become the numerator of Rule 2. The denominator is the product of map unit depth (D) and the sum of comppcts (i.e., 
= 22.42 cm/h). For NH002, the low value permeability is 6.60 cm/h.
In summary, Map Unit NH002 has an aggregated depth of 130.96 cm, is in the USDA12 loam texture class, with 14.64% clay, 51.22% sand, 3.6 to 14.96% rock, and a permeability of 6.60 to 22.42 cm/h. The whole-soil PSD coordinates, dg and g, are (-1.339, 17.62) for the high percent rock values and (-1.696, 8.651) for low percent rock values. We repeated the entire aggregation procedure, from layers to components to map units, for all 27 SCs and all 10463 map units of the USA.
Map Unit Groups of Similar Whole-Soil Particle Size Distribution Statistics
STATSGO map units are the smallest spatial scale of SCs but are too numerous for our purposes. We needed broader-scale delineations in order to summarize the data in a tabulated form, prepare the data for producing a map, and test our models by extrapolating similar SCs from known areas to unknown areas. Map unit groups were created by aggregating map units of similar whole-soil PSD statistics. The resulting MUGs are also easily depicted using USDA5 texture classes and rock limits. Within each texture class (n = 5), we defined six categories of percent rocks: 0 to 10, 10 to 20, 20 to 30, 30 to 40, 40 to 50, and 50 to 100%, to obtain 5 x 6 = 30 MUGs. These delineations are equivalent to whole-soil PSD, but are in familiar terms, and were used in Shirazi et al. (2001b) to produce a whole-soil PSD map.
Soil Characteristic Models
The next major step is to use the map unit information to develop conditional SC models. Thus, a SC model is a method for relating a SC, q (hereafter, SCq) to all remaining SCs of the same map unit. We denote a data point (or sample) as xij where i is any SC belonging to map unit j. The matrix X containing these data has p = 27 rows, one for each SC, and n = 10463 columns for the map units (see center box of Fig. 1).
First, we partitioned the matrix X into the USDA5 texture classes, which consisted of 570, 2393, 4152, 1875, and 1473 map units for the cr, mocr, mecr, mofn, and fn classes, respectively. Within each class, the sample mean µ (a 1 x p matrix) and the sample variance–covariance 
were calculated. The sample variance–covariance is a p x p symmetric matrix with p variances on the diagonal and covariances between any two SCs as off-diagonals.
Next, we split each matrix , belonging to a USDA5 texture class, to relate the conditional variance (Vq) of each SCq to the respective sample variance 11 (subscripts refer to the number of rows and columns):
 | [3] |
1x(p-1), -1
, and (p-1)x1 are respectively (p - 1) row, (inverse) square, and column matrices that define the SCq variance. This variance is applicable to all points along the USDA5 trajectory because it is not associated with any particular "conditioning" SC (Johnson and Wichern, 1982, p. 136).
The conditional mean (Mq) of each SCq was also related to its sample mean µ11 (Johnson and Wichern, 1982) and it is modified by, and dependent on, the relationships with other SCs, as follows:
 | [4] |
In essence, this equation estimates the conditional average of a SCq for an individual map unit, relative to the other 26 SCs of the map unit. Note that 1x-1, which represents correlation terms, is the same term as in Eq. [3]. The constant, µ(p-1)x1, represents the mean vector of the remaining 26 SCs. The matrix x(p-1)x1 on the right hand side of Eq. [4] defines assigned or "conditioning" values of one or more of the remaining 26 SCs. In our analysis, we select the mean SCs of MUGs as conditioning variables in interpolation and extrapolation tests of the model in Eq. [4].
Because of nonzero correlations between SCq and each (p - 1) SC, Eq. [3] and [4] are adjusted (i.e., corrected) by the expression 1x-1. For each conditional mean (Mq), the correction is in reference to the conditioning (or predictor) SCs. When no correlation exists between the SCq and any remaining (p - 1) SCs, the correction term (1x-1) for Eq. [3] becomes zero. Hence, the SCs used as predictors do not explain any variance and the sample and conditional variances (or stdvs and cstdvs) are equal.
Model Verification
Using Soil Characteristics of Map Unit Groups in Model Verification
Equation [4] estimates the conditional average of any SC in relation to the remaining 26 SCs of a map unit. The equation also applies to MUGs. Recall that MUGs were defined, in advance, based on similar whole-soil PSD statistics of the map units and will be listed in tabular format. Thus, conditional averages obtained by using Eq. [4] for a MUG pertain to SC means from its map units, relative to the other 26 SC means. The comparison of this estimate with tabulated values determine the errors related to the MUGs. Because map units of MUGs all have similar whole-soil PSD statistics, the errors indicate how well the groups differentiate SCs in the landscape. These tests are described below for models (in each USDA5 class) built from all map units in a class (Test 1), or only from the odd-numbered map units (Test 2).
Errors of Interpolation
The mean SCs of MUGs are derived from the same data as the mean SCs of the texture classes, or odd-numbered map units, in Test 1. Therefore, differences between these means are called interpolation errors and indicate the accuracy of MUGs as predictors of known SCs.
Errors of Extrapolation
Test 2 is used to evaluate how well the MUGs predict SCs outside the original model (i.e., the even-numbered map units) and is called an extrapolation test. Associations between known landscape areas, defined by SCs of odd-numbered map units, and the unknown areas of even-numbered map units were based on similarities in their respective MUGs.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONREFERENCES |
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= -2.406, g = 7.65. Thus, dg is 0.0039 mm and the g is 7.65. If this sample is mixed with 20% rock, the diameter increases to log = -1.651 or dg = 0.0223 mm and the g to 40.50. Adding rock fragments increases the mean diameter and also increases the stdv. The largest g occurs when the sample contains 50% rock 
. Increasing the rock percentages above 50% decreases the g while the mean diameter continues to increase.
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g increasingly less (Shirazi et al., 2001a).
Trajectories in Fig. 2A also display the MUGs. Colored dots are placed along each trajectory at the dg and g coordinates of MUGs at their mean percent rock values (Shirazi et al., 2001a). The colors vary from yellow to magenta along a continuous scale in relation to the frequency distribution of map units. The legend provides benchmarks of the range rather than categorical divisions to indicate relative differences along and between trajectories. For example, the MUGs with the lowest numbers of map units are on the bottom line (cr trajectory) between the rock limits of 40 and 60%. In contrast, the MUG on the third line (mecr trajectory), between 0 and 10% rocks, consists of 1771 map units and the MUG at 0 to 10% rocks at the topmost line (fn trajectory) includes 910 map units.
Next, we used the USDA5 trajectories to display the distribution of SCs of MUGs with respect to the whole-soil PSD statistics (dg and g). Figure 2B displays the distribution of the available water holding capacity. Two color-coded lines are plotted along each of the five trajectories, the upper line displays the high range of the available water holding capacity and the lower line represents the low range. Available water holding capacity generally increases from coarse- to fine-textured soils (cr and fn, respectively) but decreases with percent rock along each texture class trajectory. Likewise, Fig. 2C displays the variation of soil cation exchange capacity (CEC) in the trajectory system. The low and high CEC generally increase as expected from cr to fn, reflecting in part the increased clay in the soil. We also observe variations of the CEC (Fig. 2C) due to the rock content. In Fig. 2B and 2C, rocks are included in the description of the whole-soil PSD statistics, but in STATSGO, the available water holding capacity and CEC are reported on the basis of the fine earth (<2 mm) soil only, presuming the rock as an inert component of the soil. The observed variation in available water holding capacity and CEC with rock reflects statistical associations.
Statistical Properties of Soil Characteristics
Table 4 contains two parts, left and right, and we discuss the variables on the left first. The 27 SCs in Table 4 are identified by their symbols (Column 1), but complete names and units can be found in Table 1. The statistical summaries are listed by USDA5 texture classes and include sample mean, sample stdv, and the conditional standard deviation (cstdv). The mean and stdv are calculated for each SCq independently of relationships with other SCs in a map unit. Because map units are spatial entities, stdv and cstdv represent the spatial variability of SCq in each USDA5 texture class. The cstdv is calculated using Eq. [3], and cstdv is less than stdv because of relationships of SCq with the remaining 26 SCs in a map unit. The 95% conditional confidence interval (95% cci) may be calculated by multiplying the cstdv by the square root of the chi-square for 0.05 probability and one degree of freedom, that is, 95% cci = 1.960 (cstdv). For example, the soil depth (dept) of the coarse texture class (cr) is cstdv = 0.228 m and the 95% cci = 1.960 (0.228) = 0.447 m. Therefore, we estimate the mean soil depth = 1.496 ± 0.447 m when considering its relationships with other SCs belonging to map units of the cr texture class.
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Index of Soil Characteristic Relationship
Relationships among SCs of map units reflect spatial associations. For example, relatively high percent clay, CEC, available water holding capacity, and plasticity index all tend to occur together in map units of fine-textured soils in the landscape. Our analysis produces a quantitative index of this spatial relationship of SCs from the conditional and sample stdvs of each SC. When several SCs are cross-correlated, the cstdv of any one SC is reduced, relative to its own sample stdv.
The amount of reduction depends on the strength of correlations with other SCs and is expressed as a correction term in Eq. [3]. Based on this concept, we defined an index of relationship as ir = 100(1 - cstdv/stdv). Thus, if the stdv of a map unit SC is interpreted as an absolute measure of its spatial variability, its cstdv is its variability because of correlations with other SCs, and its ir value is a measure of the relationship between the two stdvs.
Among the SCs we studied, the smallest ir index is 100(1 - 6.5/8) = 19% for percent sand in fine-textured soils (fn), which means that in map units of fine-textured soils, the spatial association of percent sand with other SCs is not strong. However, the index increases to 61% for percent sand in cr soils where, for example, high permeability and low CEC occur together in map units. Low mean ir values are between 31 to 48% for soil depth, loss tolerance factor (tfac), percent sand, percent clay, low permeability (perl), and erodibility factor (kfac). Relatively high mean indexes are between 76 and 81% for depth to water table (wtdl, wtdh), liquid limit (liql, liqh), and the bulk density (blkl, blkh). The remaining index values are between 48 and 76%.
Map unit attributes that have little or no spatial association with SCs have very small or zero value of ir. As an extreme example, the average index for map unit area, which is not a SC, per se, and is highly variable (stdv/mean = 1.77), is ir = 3%.
Soil Characteristics of Map Unit Groups
Soil characteristics of MUGs were formed within each USDA5 texture class with respect to percent rock limits as described in the Methods section. For testing purposes, we created three separate sets of MUGs from the data, one using all map units, and second and third sets from the odd- or even-numbered map units alone. Correlation coefficients of the mean SCs were 0.990 when comparing MUGs of Sets 1 and 2, 0.995 for Sets 1 and 3, and 0.975 between Sets 2 and 3. Thus, the MUGs are consistent with respect to these different groupings.
The MUG SCs derived from the whole data set were displayed in Fig. 2A and their mean values are listed in the right hand columns of Table 4. As before, we can examine differences among the USDA5 texture classes or summarize a particular MUG. In addition, we can use the table to calculate the conditional confidence interval of a MUG SC. Consider as an example the MUG in the fn texture class between 0 and 10% rock, which consists of 910 map units (Fig. 2A). In Table 4, its mean soil depth (dept) is 1.439 m and its conditional confidence interval is estimated as 1.439 ± 0.291 
= 1.439 ± 0.570 m.
There are also general patterns of relationships between MUG SCs and the whole-soil PSD statistics (dg and g), that is, percent rock along a trajectory (read across right side of Table 4). Soil depth generally decreases with increasing percent rock, and the deepest soils have cr texture with low percent rock (1600 m, for 0–10% rock). However, mean percent clay, percent sand, and permeability values change relatively little along the trajectory of a single texture class (Table 4). The CEC and the plasticity index generally decrease with increasing percent rock along a texture trajectory.
Smoothing Effects of Aggregation
Aggregation from Layer to Map Unit
We use the term smoothing to describe the loss of variability in SCs resulting from averaging. We compared SCs of non-aggregated layers with SCs of components and map units after aggregation to estimate the magnitude of smoothing of SCs. Because the mean and the stdv both change in each aggregation step, we compared the sum (mean + stdv) of SCs. We denote this sum as DL for non-aggregated layers, DP after aggregation from layers to a component, and DM after aggregation from layers through components to a map unit. Smoothing from layers to a component was designated by DLP and from layers through components to a map unit by DLM. Then, DLM and DLP were expressed as percentages of the mean layer SCs, such that DLM = 100(|DL - DM|)/DL and DLP = 100(|DL-DP|)/DL. The DLP and DLM were calculated for 22 SCs (Table 5). On the average, SCs undergo 6.04% smoothing in the step from layers to a component, and an additional 11.77 - 6.04 = 5.73% from components to a map unit (Table 5). However, smoothing varies considerably among SCs. For example, organic matter undergoes maximum smoothing in both steps (33.76 and 42.27%). On the other hand, bulk density and the available water holding capacity are smoothed mainly in the step from components to a map unit (Table 5). There is no smoothing in the step from layers to a component for the loss tolerance factor (DLP = 0) because this factor pertains to the top layer of the soil only. Clay and sand undergo very little smoothing in the step from layers to a component because they both describe the centroid values of texture classes. A detailed analysis of clay and sand in STATSGO is found in Shirazi et al. (2001a).
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Additional comparisons summarized CEC, organic matter, percent rock, and plasticity index and revealed that our approach preserved, respectively, 30, 47, 14, and 35% more of the variabilities. Therefore, by retaining the low and the high SCs as separate variables, we attain a compensatory advantage that does not cancel, but substantially reduces, smoothing effects in each aggregation step. The compensatory action of our analysis addresses, in part, the concerns of Lammers and Johnson (1991), who noted that certain environmental problems are affected disproportionately to the area of a soil in a map unit.
Model Verification
Model verification consisted of using Eq. [4] to estimate each of the mean MUG SCs listed in the right side columns of Table 4, and then comparing the estimates to the actual values. The estimated and actual values each were divided by the mean SC for the texture class to produce relative values. Then linear regressions were performed using the actual relative SCs as the independent variables and the estimated values as the dependent variables. Table 6 lists the relative standard errors for 27 SCs. The relative standard error in the interpolation test based on the entire data set was (mean = 3.69%, stdv = 4.56%), and for the odd-numbered map units it was (mean = 3.99, stdv = 4.58%). The error in the extrapolation test was (mean = 5.85, stdv = 5.22). In summary, the extrapolation errors for 15 SCs were below 5%, seven SCs were between 5 and 10%, and five SCs were below 22.4%. The largest errors were associated with soil slope and percent rock, and the smallest errors were associated with bulk density, soil pH, and the depth to ground water level.
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ACKNOWLEDGMENTS |
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TOPABSTRACTINTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONREFERENCES |
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M. A. Shirazi, L. Boersma, C. B. Johnson, and P. K. Haggerty Predicting Physical and Chemical Water Properties from Relationships with Watershed Soil Characteristics J. Environ. Qual., January 1, 2001; 30(1): 112 - 120. [Abstract] [Full Text]
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