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a Western Ecology Division, NHEERL, U.S. Environmental Protection Agency, 200 S.W. 35th Street, Corvallis, OR 97333
b Dep. of Crop and Soil Science, ALS 3017, Oregon State Univ., Corvallis, OR 97331-7306
c 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 DISCUSSIONCONCLUSIONREFERENCES |
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Abbreviations: ANC, acid neutralizing capacity • 
g, geometric particle standard deviation • cr, coarse-textured soils • cstdv, conditional standard deviation • dg, geometric mean particle diameter • DOC, dissolved organic carbon • EMAPSW, Environmental Monitoring and Assessment Program of Surface Waters • fn, fine-textured soils • ir, index of relationship for 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 • 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 • WP, physical and chemical water property
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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Shirazi et al. (2001b) defined similar soils on the basis of relationships between 27 SCs of soil map units and two whole-soil particle size distribution (PSD) statistics. These statistics were calculated in Shirazi et al. (2001a) and were named the geometric mean particle diameter (dg) and the geometric particle standard deviation (g). The SCs for the map units were selected from STATSGO (Soil Survey Staff, Soil Conservation Service, 1991). Shirazi et al. (2001b) created mathematical models using SCs from one-half of the map units across the entire United States and found that grouping map units of similar dg and g values successfully predicted (i.e., spatially extrapolated) the SCs of map unit groups (MUGs) for the other half. By this modeling approach, the authors addressed the need for the appropriate spatial scale defined by Karlen et al. (1997). In summary, the fundamental concept of aggregating relatively homogenous spatial features in order to classify or predict attributes of a similar, but unstudied, area was applied to SCs by Shirazi et al. (2001b) using the whole-soil PSD statistics.
For the present paper, our objective was to apply the techniques to extrapolate water properties (WPs) such as dissolved organic carbon (DOC), nitrate (NO3), and turbidity to MUGs with similar whole-soil PSD statistics. Specifically, this includes obtaining the WPs and watershed–map unit overlap areas (intersections), assigning WPs to the intersected map units, developing models of WPs as functions of SCs in area-weighted map units, aggregating map units by texture classes, and testing the models. We emphasize the method, or process, for relating water and soil information at large spatial scales. A detailed examination of particular locations or mechanistic links is deferred to future studies.
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METHODS AND PROCEDURES |
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TOPABSTRACTINTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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During 1991–1994, EMAPSW collected water samples at 721 sites. The samples were analyzed for several chemical and physical properties including pH, DOC, base cations, nutrients, monomeric aluminum, Fe, Mn, Cl-, and turbidity. Detailed information on the sampling and analysis procedures can be found in USEPA (1987). Although most sites were sampled only once, a limited number of sites were sampled again during the same or subsequent years. We used 10 physical and chemical WPs to demonstrate our approach. The variable names and descriptions for the selected WPs are listed in Table 1.
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Soil Characteristics of Regional and Intersected Map Units
STATSGO contains information for soil layers and components of a map unit. This information includes clay, sand, and rock separates, soil depth, the high and low values of bulk density, cation exchange capacity, permeability, pH, and many other variables. We call this suite of variables the SCs. Shirazi et al. (2001b) aggregated the SCs of layers and components for each of the 10463 map units in the conterminous United States and Hawaii. Of these, 882 map units were in the EMAPSW study region. We named them the regional map units. Using geographic information system overlay techniques, we found that 400 regional map units had areas in common to the EMAPSW watersheds, and referred to them as intersected map units.
Model Development and Testing
Assigning Water Properties to Intersected Map Units
We assigned WPs to a map unit if it overlapped (intersected) one or more watersheds. The area-weighted average WP for the map unit equaled 
, A = 
ai, i = 1, 2,...n, where Qi is the water property of an intersected watershed, ai is the area of each intersection, A is the total intersected area, and n is the number of intersections. This produced a data matrix associating each WP to the SCs in each intersected map unit. The data matrix consisted of 400 columns, one for each intersected map unit, and one row for the weighted average WP, plus up to 25 additional rows for SCs (i.e., up to 26 rows, total).
To preserve the variability in measured water properties (WPs) and to remain consistent with the low and high range values for SCs in STATSGO, we partitioned each WP of intersected map units into low and high ranges. The low range included the mean and lower values, and the high range consisted of the mean and larger values. Separate models were developed from the data for each WP before partitioning, and one each after partitioning the WP into high and low ranges.
Linking Water Properties, Soil Characteristics, and Whole-Soil Particle Size Distribution
Models developed from the data matrices assume that water properties (WPs) co-vary with SCs, which in turn are related to the whole-soil PSD statistics (dg, g). Shirazi et al. (2001b)(Eq. [3] and [4]) used the whole-soil PSD statistics and the USDA5 texture classes to determine a conditional mean (Mq) and conditional variance (Vq) for each SC as a linear function of the remaining SCs. We extended these PSD–SC models to derive interrelationships between SCs of intersected map units and each WP, that is, to PSD–SC–WP relationships. Consequently, 50 equations (models) for Mq were generated from the 10 WPs in five texture classes. One difference between Shirazi et al. (2001b) and this study is the number of SCs used. With the data set for 49 states in the previous investigation, all 27 SCs could be used as model variables in all texture classes. However, the data set for this study was smaller, thus reducing the numbers of SCs to 8 for coarse, moderately fine, and fine; 18 for moderately coarse; and 25 for medium coarse texture classes.
Model Validation
The purpose of the tests described below was to verify the predictive capabilities of the models. Each test consisted of using SCs as predictors of WPs and comparing the resulting WP estimates with the observed WPs.
Regional and Intersected Map Unit Groups
We followed Shirazi et al. (2001b) and used the mean SC of MUGs rather than SCs of individual map units as predictors in the equations of WPs. Map unit groups (and associated WP groups) were based on the similarity of their whole-soil PSD statistics. The groups are constant for all WPs. Regional MUGs included all map units in the study area, whereas intersected MUGs contained only map units associated with EMAPSW watersheds. In all, there were 17 regional MUGs, 17 intersected MUGs, and 17 WP groups.
We conducted two types of tests on the WP models. The first were interpolation tests because values and relationships were estimated from within the data set. In this test, we used SCs of intersected MUGs as predictors of WPs. The statistical errors were calculated by comparing the interpolated WPs (estimates) with the previously defined observed WP groups.
The second type of test was an extrapolation test where the known models or values were projected beyond the data set. This test used SCs from the regional MUGs to predict (extrapolate) WPs. The statistical errors could not be calculated directly because no WP data were available for 482 of the 882 regional map units without EMAPSW watershed intersections. However, we estimated the error using similarities among the regional and intersected MUGs to assign WP groups, member-to-member, to the regional MUGs. This was a reasonable approach based on Shirazi et al. (2001b) and helps to test our WP–SC linkage.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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Relationships of Water Properties and the Whole-Soil Particle Size Distribution
Relationships of Water Properties within a Texture Class
Figure 1
is a series of nomograms that summarize observed mean WP groups based on the whole-soil PSD statistics (dg, g) of intersected MUGs. Each nomogram displays: (i) USDA5 texture class trajectory lines, (ii) (dashed) lines of equal rock separates in 10% intervals up to 60%, and (iii) 17 WP groups (colored markers placed at the mean MUG dg and g). The names and variable abbreviations for WPs are in Table 1. The range and distribution of WP values is reflected in the color scale of each legend. Patterns within and among texture class trajectories are discernable, as well as potential anomalies or points of interest. Because the models preserve all original data, these points can be fully investigated and we will describe some patterns and outliers below.
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In Fig. 1B–1K, each colored circle represents the mean WP value of a WP group. For example, Fig. 1B displays the mean acid neutralizing capacity (ANC) of EMAPSW-sampled lakes and streams. Mean ANC decreases from 2109 µeq/L at about 20% rock on the fn trajectory to 195 µeq/L at approximately 45% rock for the cr trajectory. As expected, the pattern of decrease is very similar to the pattern in pH (Fig. 1G). Figure 1C displays the mean chloride for each group. Note that the logarithm of measured values was used due to the extremely large range. The highest mean chloride is log (4.53) = 33884 µeq/L on the cr trajectory, and the lowest is on the fn trajectory, log (2.16) = 144 µeq/L. In general, the chloride means decrease as percent rocks increase along all trajectories. However, the highest mean is markedly different from the other groups and prompted further scrutiny. The highest chloride value came from a near-ocean environment where coarse, sandy soils were prevalent. Patterns in the nitrate and total N nomograms (Fig. 1E and 1F) are nearly identical with highest means along the fn and mofn trajectories at approximately 20 and 35% rock.
Relationships of Water Properties Among USDA5 Texture Classes
Another method for examining broad differences among WPs is to aggregate them by texture classes. Table 1 lists the 10 WPs by USDA5 texture class and related statistics, such as mean, standard deviation (stdv), and conditional standard deviation (cstdv). In general, the above statistics increase from low values in coarse-textured soils (cr) to high values in fine-textured soils (fn) for ANC, total N, silica (SIO2), nitrate, pH, and turbidity. No predictive relationship is evident for nitrate, total P, sulfate (SO4), and chloride. These WPs are extremely variable, as reflected in their high coefficients of variation (CVs).
In Table 1, the largest CVs are for chloride in mocr (476%) and cr (443%), sulfate in cr (422%) and mecr (278%), nitrate in mocr (335%) and mecr (196%), and total P in mecr (245%) and cr (186%). Although chloride in the water column naturally increases with proximity to coastal areas, high values also indicate human activities (e.g., road de-icing, fertilizer use, or industry) in the watershed (Herlihy et al., 1998). High concentrations of sulfate are often related to acid mine drainage, while total P, nitrate, or total N are associated with urban and agricultural areas or septic tanks.
The cstdv of a WP is smaller than its stdv because of the correlation between each WP and SC. The magnitude of this association is calculated by an index of relationship, ir = 100(1 - cstdv/stdv), as in Shirazi et al. (2001b). If no correlation exists, then cstdv = stdv and ir = 0. The index is listed in the last column of Table 1 and can be used to compare WP–SC relationships. For example, the average ir for the WPs with CV < 170% are DOC (46%), ANC (44%), total N (42%), silica (41%), pH (35%), and turbidity (29%). The correlation between DOC and SCs across the five texture classes is relatively strong, whereas turbidity has the weakest overall WP–SC relationship of these six properties. Because of the high variability in chloride, nitrate, total P, and sulfate, we did not include their ir averages in the above comparison.
Model Verifications
Model verification, or testing, involved using SCs from the intersected MUGs or regional MUGs as predictors to estimate the WP groups. These estimates were compared with WP groups derived from the observed data. The comparison between the estimated WPs and the observed WPs was made using linear regression models. When the regression coefficient and slope of the regression line both equal unity, then the average values for the observed and estimated WPs are identical for all texture classes. In our study, no slopes or regression coefficients were exactly unity, but several were close.
To facilitate the comparison as described above, all WPs were standardized (i.e., divided by the WP mean for all map units in the texture class). One set of regression equations included all 10 WPs together (n = 170). This approach was used to examine interpolation vs. extrapolation.
Interpolation Tests of Combined Lake and Stream Data
Results of the regression equations that included all ten WPs are listed in Table 2. The relative standard errors of predicting WP groups ranged from 14 to 21% for the combined lake and stream data (Fig. 2A)
. These standard errors indicate that whole-soil PSD statistics (dg, g) accurately classify and predict WPs within a data set (interpolation test). Shirazi et al. (2001b) used the statistics for predicting SCs, and the present finding extends the predictive role to physical and chemical water properties when WPs are related to watershed SCs.
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Analysis of Lake-Only Data
In our study, the lake site map units are located in the eight northeastern states and those of stream sites, with few exceptions, are in the five Mid-Atlantic states.
We assumed that lake and stream data could be used together in an analysis because: (i) the map units of lakes and streams do not overlap, (ii) the SCs of intersected map units are uniquely linked to WPs of either lakes or streams, and (iii) SCs control the prediction of WPs in the models. The assumption is tested by comparing the analyses of the lakes-only data with the combined data. In the interpolation test, the standard errors for lake-only data range between 17 and 29% (Table 2). For the extrapolation test, standard errors for the lake-only data range between 27 and 52% (Table 2). The large standard error of the high range lake-only data is due to some extreme outlier WP observations. The close agreements of results from lake-only data and combined lake and stream data substantially support the validity of our assumptions.
Modeled and Observed Water Property Variability on the Spatial Scale of a Map Unit
In Shirazi et al. (2001b), Eq. [3] is used to estimate the variance of each WP on the spatial scale of a map unit and the variance is used to estimate the mean in Eq. [4]. However, this mean WP value may be based on a MUG or an individual map unit, depending on which spatial scale is used as a predictor. The resulting standard errors are lower for MUGs than for map units. Figure 2C is based on lake-only data and shows four WPs predicted by interpolation for each intersected map unit rather than for the MUGs. Although clusters and trends are apparent, variability is relatively large. The standard error of this data set is 100% (last line in Table 2), which is considerably larger than the standard error of interpolation for lake data on the spatial scale of a MUG (17 to 29%, Table 2). Because the WPs have been averaged for MUGs, the variability is expected to increase at a finer spatial resolution where relatively less smoothing has occurred. In other words, the models realistically reflect the observed WP variabilities at various spatial scales.
Figure 2D is a bar graph comparing stdvs of the observed data with cstdvs from the models at the map unit scale. Both stdvs are divided by the overall mean values of each WP. The cstdvs (Table 1) were averaged over all USDA5 classes and represent average variability in interpolation. Note that the spatial variability of the observed data is within the predicted variability. Thus, retaining the high and low WPs of intersected map units as separate variables preserves variability in our models, as also illustrated in Fig. 2C.
Discussion of the Errors
EMAPSW Sampling
Differences between the SCs of intersected and regional MUGs were partly due to the EMAPSW sampling locations often being in uplands where soils tend to be shallow and rocky. The MUG differences, in turn, produce higher extrapolation errors than interpolation errors. If the 721 EMAPSW sampling sites were distributed among the map units, the probability of intersection would be 721/882 = 0.82. However, map units were not considered in the EMAPSW probability sampling, leading to the actual intersection probability of 400/882 = 0.45. An improved, larger probability of intersection can also result from sampling higher stream orders (>3), as is now done in EMAPSW studies.
Extreme Values of Water Properties
In addition to the underrepresentation of low-elevation map units, the presence of extreme outliers in the WP data contributed to large extrapolation errors. These extremes were often related to land use or local conditions that did not influence the broad-scale SCs in our models. However, our models are sensitive to data with high coefficients of variation and respond to these data with high extrapolation errors. We have used this feature of our model as a signal to examine site-specific influences.
We examined watershed land use and site-specific data for lakes or streams with extremely high nitrate, sulfate, or chloride values to identify potential local sources that could not be predicted by broad-scale SCs alone. For example, the highest nitrate level in our data came from a small, low-flow stream with a trash dump and >90% agricultural land in the watershed. Evidence of acid mine drainage was found in the stream with the highest sulfate value. The highest chloride value among the EMAPSW sites was from a brackish, shallow lake within 0.3 km of the Atlantic ocean, surrounded by about 38% urban and 29% agricultural lands. A complete and detailed analyses is deferred until future research, but these observations generally agree with other studies describing relationships between land use and water chemistry (Liegel et al., 1991; Mueller et al., 1995; Herlihy et al., 1998). For the present research, we note that the presence of extreme values and land use–water chemistry relationships increase the coefficients of variation and extrapolation errors in our models.
The Spatial Relationships of the Whole-Soil Particle Size Distribution and Water Properties
In the USDA5 system, unique whole-soil PSD statistics (dg, g) are defined by texture classes and percent rock, which can be used to portray the spatial distribution of the whole-soil PSD. For example, Fig. 3
is a map of the Mid-Atlantic portion of our study region with the boundaries of EMAPSW stream watersheds shown in bold lines. The lightest color on the map represents coarse (cr) soils with colors darkening through moderately coarse (mocr), medium coarse (mecr), moderately fine (mofn) and fine (fn) soils in the darkest shade. Within each texture class, the percent rock content is represented by markers of varying densities. The mapped texture classes and percent rock are also incorporated in each WP group on the nomograms of Fig. 1. Therefore, we can estimate a WP at a particular location by identifying the texture class and percent rock on the map then using the nomograms to determine the mean value for that group. In addition, we use Table 2 to assess the accuracy of the estimate. If the site is in an intersected MUG, the interpolation errors from Table 2 are used, whereas the extrapolation errors apply to other map units in the region.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMETHODS AND PROCEDURESRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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This article has been cited by other articles:
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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. [Abstract] [Full Text] [PDF]
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M. A. Shirazi, L. Boersma, P. K. Haggerty, and C. B. Johnson Spatial Extrapolation of Soil Characteristics Using Whole-Soil Particle Size Distributions J. Environ. Qual., January 1, 2001; 30(1): 101 - 111. [Abstract] [Full Text]
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