GEOSTATISTICAL OF P A L M E R T O N
THOMAS
ANALYSIS
SOIL SURVEY
DATA
H. STARKS
Environmental Research Center, University o f Nevada, Las Vegas, Las Vegas, N V 89154, U.S.A. ALLEN
R. S P A R K S
P.O. Box 15027, Las Vegas, NV89114, U.S.A. and KENNETH
W. BROWN
U.S. Environmental Protection Agency, Environmental Monitoring Systems Laboratory, P.O. Box 15027, Las Vegas, NV89114, U.S.A.
(Received 15 September, 1986) Abstract. This paper describes statistical and geostatistical analyses of data from a soil sampling survey. Soil sampling was performed, in October and November of 1985, to obtain information on the level, extent, and spatial structure of metal pollution of the soil in and around the Palmerton, Pennsylvania, N P L Superfund site. Measurements of the concentrations of cadmium, copper, lead, and zinc in the soil samples were obtained. An appropriate variance stabilizing transformation was determined. Estimation of variance components was performed. Generalized covariance functions for log-transformed concentrations were estimated for each metal. Block kriging was employed using the estimated spatial structure models to obtain estimated metal concentration distributions over the central part of Palmerton.
1. Introduction Soil samples were obtained to gather information about the level, extent, and spatial structure of concentrations of cadmium, lead, copper, and zinc in the soil in and around the Palmeton, Pennsylvania, NPL Superfund site (i.e., a site specified under CERCLA, the Comprehensive Environmental Response, Compensation and Liability Act of 1980). The sources of the metal contamination of the soil are alleged to be two zinc smelter operations, denoted herein as the East and West Plants, and a 4 km long slag pile located near Palmerton (see Figure 1). The West Plant started operations in 1898 and the East Plant began in 1914. The two plants underwent modification in 1980 that drastically reduced metal emissions. The purpose of the soil survey was to obtain information for use in planning a more definitive survey of the metal concentrations in the soil near Palmerton to be used in planning remedial actions. The sampling was performed in October and November of 1985, by the firm of R.E. Wright Associates, Inc. This firm also dried, mixed, and sieved the samples and split out subsamples sent for laboratory analysis. These subsamples were analyzed using analytical method EPA-600-4-79-520, Metals Environmental Monitoring and Assessment 9 (1987) 239-261. 9 1987 by D. Reidel Publishing Company.
240
THOMAS
H. STARKS ET AL.
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by Atomic Absorption Methods, by the Soil and Environmental Chemistry Laboratory of The Pennsylvania State University. The town of Palmerton lies in a narrow valley bounded on the south by Blue Mountain and on the north by large hills and ridges. It is approximately 25 miles north of Allentown, Pennsylvania. The soils in and around Palmerton consists of unconsolidated deposits of glacial outwash. These deposits are poorly sorted, stratified sandy gravels with some interbedded red clay. The purpose of this paper is to demonstrate how (and why) statistical and geostatistical techniques are combined in the analysis of soil survey data to locate, and estimate the size of important sources of variation, and to estimate spatial structure of pollutant concentrations in the soil. In particular, it is intended to show the need for variance stabilizing transformations, and for care in determining appropriate models for spatial structure so that the models will be consistent with the data and with the process that created the system under study.
2. Sample Design The samples were collected at 88 points on a square grid over a diamond shaped area at the center of Palmerton and at 119 points along eight transects emanating out from the center of the grid to locations as far as 9.5 km from the center of the grid (see
GEOSTATISTICAL
ANALYSIS OF PALMERTON
SOIL SURVEY DATA
241
Figure 1). (The transect to the west from Palmerton was bent to follow the Lehigh River valley). The designated distance between sample points on the square grid was 122 m (400 ft.). On the transects, the distances between sample points varied from 122 m up to 366 m (except where no samples were taken when a transect crossed smelter property). The original sampling plan called for 211 sample points, and only four points were not sampled. Failure to sample was either due to inability to get authorization from a land owner or to nature of terrain. Samples were not always taken at the designated sample point due to physical obstructions (i.e., rocks, highways, buildings, etc.). The field crew was allowed to move to the nearest unobstructed spot to take their sample provided that spot was within 61 m (200 ft.) of the designated point. The location where the actual sample was obtained was recorded and used in the spatial analysis of the data. The soil samples f r o m 30 sample points on the transects were archived without measurement. Hence, measurements of metal concentrations were obtained at 177 points. A discussion of the rationale for the design is given in Starks et al. (1986). At each sample point, a core was taken from each of the four major compass points on a 6 m diameter circle centered at the designated sample point. The depth of the core was 15 cm at all but 19 points where cores of 30 cm were obtained. The core diameter in each case was 1.9 cm (0.75 in). For all but ten sample points, the four cores from each sample point were composited. At ten sample points where 30 cm cores were taken, each core was cut into twelve 2.5 cm segments and the four segments from the same depth at a sample point were composited so that there were 12 samples to be analyzed from each of these ten sample points to provide information on how metal concentrations change with depth. For the other nine sample points where 30 cm cores were obtained, each core was cut into two 15 cm segments and segments from the same depth were composited to give two samples from each of these sample points for further investigation of depth effect. At ten sample points with 15 cm cores, the cores were not composited, but analyzed separately, so as to obtain information needed to estimate how much of the variation in metal concentrations between sample points was due to variation between core concentrations at individual sample points. For quality assurance purposes, duplicate pairs (co-located samples) were obtained at ten sample points. This was done by first taking the usual sample of four 15 cm depth cores and compositing them, and then taking and compositing another sample of four 15 cm cores at locations within 0.5 m of the cores in the first sample. Analyses were performed on both samples and the differences in the results are due to short range spatial variation of the metal concentrations in the soil and also due to variation in sample taking, handling, subsampling, and analytical techniques. Two subsamples (called splits) were taken, after drying, sieving, and mixing, from ten samples and sent separately to the laboratory for analyses. The results from splits gave information on the amount of variation in the results due to subsampling and analytical errors. Splits and duplicates were from different sample points.
242
THOMAS
H. STARKS ET AL.
3. Methods of Data Analysis
The first step in the data analysis consisted of plotting the measurements at their sample point locations on the map to visually inspect for trends, anomalies, and range of values. Next, quality assurance data from duplicate pairs were inspected to determine an appropriate transformation to stabilize the variance (i.e., to obtain data where the variance is not dependent on the mean concentration), After transformation, the variance of duplicates was calculated, to determine the contribution of short range spatial variation and variation in sample handling, subsampling, and analytical techniques to total variation between samples. Also, after transformation, variance between splits was obtained to determine the contribution of subsampling and analytical errors to total variance of the data. In addition, variance between cores within samples was estimated to find its contribution to total variance. The spatial structures of the transformed concentrations of the four metals were obtained using a method consisting of cross-validation and response surface analysis (see Starks and Sparks, 1987). This procedure uses the fact that if the spatial structure model is correct, point kriging gives unbiased estimators of (transformed) concentrations and their estimation standard deviations. The cross-validation involves point kriging at sample points using the measurements at nearby neighbors to obtain standardized residuals (i.e., [observed value - predicted value]/estimated standard deviation). A criterion that measures the difference between the set of standardized residuals and the expected results in a sample from a standard normal distribution is used to compare different models and to provide direction in the search for a 'best' model. Block kriging on 200' x 200' blocks with the estimated models for spatial structure using the BLUEPACK software package, yields plots and isopleths of the average metal concentrations over the blocks within the region covered by the square grid of sampling points within the City of Palmerton.
4. Results
Figures 2-9 give 'post plots' showing metal concentrations (in mg kg-1) measured at the various sample points for the top 15 cm. (in some cases, the measurements are averages from several analyses. For ease of reading, the measurements are shown at the design points rather than at the actual sample points). These plots make evident the high concentrations between and near the two smelter locations and the steady decline in concentrations as distance from the smelters increases. Table I gives the measured metal concentrations for the ten duplicate pairs of samples, the absolute values D of pair differences of the original measurements in mg kg-1 and the absolute values L of pair differences of the logarithms of the measurements. Note that the sample variance computed on a pair of observations is s 2 =/92/2. Hence, changes in D indicate how sample standard deviation is changing from pair to pair. In Table I, it is obvious that, for each metal, D increases as the
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THOMAS
ANALYSIS
SOIL SURVEY
DATA
H. STARKS
Environmental Research Center, University o f Nevada, Las Vegas, Las Vegas, N V 89154, U.S.A. ALLEN
R. S P A R K S
P.O. Box 15027, Las Vegas, NV89114, U.S.A. and KENNETH
W. BROWN
U.S. Environmental Protection Agency, Environmental Monitoring Systems Laboratory, P.O. Box 15027, Las Vegas, NV89114, U.S.A.
(Received 15 September, 1986) Abstract. This paper describes statistical and geostatistical analyses of data from a soil sampling survey. Soil sampling was performed, in October and November of 1985, to obtain information on the level, extent, and spatial structure of metal pollution of the soil in and around the Palmerton, Pennsylvania, N P L Superfund site. Measurements of the concentrations of cadmium, copper, lead, and zinc in the soil samples were obtained. An appropriate variance stabilizing transformation was determined. Estimation of variance components was performed. Generalized covariance functions for log-transformed concentrations were estimated for each metal. Block kriging was employed using the estimated spatial structure models to obtain estimated metal concentration distributions over the central part of Palmerton.
1. Introduction Soil samples were obtained to gather information about the level, extent, and spatial structure of concentrations of cadmium, lead, copper, and zinc in the soil in and around the Palmeton, Pennsylvania, NPL Superfund site (i.e., a site specified under CERCLA, the Comprehensive Environmental Response, Compensation and Liability Act of 1980). The sources of the metal contamination of the soil are alleged to be two zinc smelter operations, denoted herein as the East and West Plants, and a 4 km long slag pile located near Palmerton (see Figure 1). The West Plant started operations in 1898 and the East Plant began in 1914. The two plants underwent modification in 1980 that drastically reduced metal emissions. The purpose of the soil survey was to obtain information for use in planning a more definitive survey of the metal concentrations in the soil near Palmerton to be used in planning remedial actions. The sampling was performed in October and November of 1985, by the firm of R.E. Wright Associates, Inc. This firm also dried, mixed, and sieved the samples and split out subsamples sent for laboratory analysis. These subsamples were analyzed using analytical method EPA-600-4-79-520, Metals Environmental Monitoring and Assessment 9 (1987) 239-261. 9 1987 by D. Reidel Publishing Company.
240
THOMAS
H. STARKS ET AL.
North
••.
Lehlgh ~ River"
Eas-t
.. West " .
~ 9
.
~
S(a9
P4.e
.
Ptant / ~ . _ ~ \ ~ Aquc~shico[a .......
H-----H 4000
f'•
Fig. 1. Palmerton and designated sample point locations.
by Atomic Absorption Methods, by the Soil and Environmental Chemistry Laboratory of The Pennsylvania State University. The town of Palmerton lies in a narrow valley bounded on the south by Blue Mountain and on the north by large hills and ridges. It is approximately 25 miles north of Allentown, Pennsylvania. The soils in and around Palmerton consists of unconsolidated deposits of glacial outwash. These deposits are poorly sorted, stratified sandy gravels with some interbedded red clay. The purpose of this paper is to demonstrate how (and why) statistical and geostatistical techniques are combined in the analysis of soil survey data to locate, and estimate the size of important sources of variation, and to estimate spatial structure of pollutant concentrations in the soil. In particular, it is intended to show the need for variance stabilizing transformations, and for care in determining appropriate models for spatial structure so that the models will be consistent with the data and with the process that created the system under study.
2. Sample Design The samples were collected at 88 points on a square grid over a diamond shaped area at the center of Palmerton and at 119 points along eight transects emanating out from the center of the grid to locations as far as 9.5 km from the center of the grid (see
GEOSTATISTICAL
ANALYSIS OF PALMERTON
SOIL SURVEY DATA
241
Figure 1). (The transect to the west from Palmerton was bent to follow the Lehigh River valley). The designated distance between sample points on the square grid was 122 m (400 ft.). On the transects, the distances between sample points varied from 122 m up to 366 m (except where no samples were taken when a transect crossed smelter property). The original sampling plan called for 211 sample points, and only four points were not sampled. Failure to sample was either due to inability to get authorization from a land owner or to nature of terrain. Samples were not always taken at the designated sample point due to physical obstructions (i.e., rocks, highways, buildings, etc.). The field crew was allowed to move to the nearest unobstructed spot to take their sample provided that spot was within 61 m (200 ft.) of the designated point. The location where the actual sample was obtained was recorded and used in the spatial analysis of the data. The soil samples f r o m 30 sample points on the transects were archived without measurement. Hence, measurements of metal concentrations were obtained at 177 points. A discussion of the rationale for the design is given in Starks et al. (1986). At each sample point, a core was taken from each of the four major compass points on a 6 m diameter circle centered at the designated sample point. The depth of the core was 15 cm at all but 19 points where cores of 30 cm were obtained. The core diameter in each case was 1.9 cm (0.75 in). For all but ten sample points, the four cores from each sample point were composited. At ten sample points where 30 cm cores were taken, each core was cut into twelve 2.5 cm segments and the four segments from the same depth at a sample point were composited so that there were 12 samples to be analyzed from each of these ten sample points to provide information on how metal concentrations change with depth. For the other nine sample points where 30 cm cores were obtained, each core was cut into two 15 cm segments and segments from the same depth were composited to give two samples from each of these sample points for further investigation of depth effect. At ten sample points with 15 cm cores, the cores were not composited, but analyzed separately, so as to obtain information needed to estimate how much of the variation in metal concentrations between sample points was due to variation between core concentrations at individual sample points. For quality assurance purposes, duplicate pairs (co-located samples) were obtained at ten sample points. This was done by first taking the usual sample of four 15 cm depth cores and compositing them, and then taking and compositing another sample of four 15 cm cores at locations within 0.5 m of the cores in the first sample. Analyses were performed on both samples and the differences in the results are due to short range spatial variation of the metal concentrations in the soil and also due to variation in sample taking, handling, subsampling, and analytical techniques. Two subsamples (called splits) were taken, after drying, sieving, and mixing, from ten samples and sent separately to the laboratory for analyses. The results from splits gave information on the amount of variation in the results due to subsampling and analytical errors. Splits and duplicates were from different sample points.
242
THOMAS
H. STARKS ET AL.
3. Methods of Data Analysis
The first step in the data analysis consisted of plotting the measurements at their sample point locations on the map to visually inspect for trends, anomalies, and range of values. Next, quality assurance data from duplicate pairs were inspected to determine an appropriate transformation to stabilize the variance (i.e., to obtain data where the variance is not dependent on the mean concentration), After transformation, the variance of duplicates was calculated, to determine the contribution of short range spatial variation and variation in sample handling, subsampling, and analytical techniques to total variation between samples. Also, after transformation, variance between splits was obtained to determine the contribution of subsampling and analytical errors to total variance of the data. In addition, variance between cores within samples was estimated to find its contribution to total variance. The spatial structures of the transformed concentrations of the four metals were obtained using a method consisting of cross-validation and response surface analysis (see Starks and Sparks, 1987). This procedure uses the fact that if the spatial structure model is correct, point kriging gives unbiased estimators of (transformed) concentrations and their estimation standard deviations. The cross-validation involves point kriging at sample points using the measurements at nearby neighbors to obtain standardized residuals (i.e., [observed value - predicted value]/estimated standard deviation). A criterion that measures the difference between the set of standardized residuals and the expected results in a sample from a standard normal distribution is used to compare different models and to provide direction in the search for a 'best' model. Block kriging on 200' x 200' blocks with the estimated models for spatial structure using the BLUEPACK software package, yields plots and isopleths of the average metal concentrations over the blocks within the region covered by the square grid of sampling points within the City of Palmerton.
4. Results
Figures 2-9 give 'post plots' showing metal concentrations (in mg kg-1) measured at the various sample points for the top 15 cm. (in some cases, the measurements are averages from several analyses. For ease of reading, the measurements are shown at the design points rather than at the actual sample points). These plots make evident the high concentrations between and near the two smelter locations and the steady decline in concentrations as distance from the smelters increases. Table I gives the measured metal concentrations for the ten duplicate pairs of samples, the absolute values D of pair differences of the original measurements in mg kg-1 and the absolute values L of pair differences of the logarithms of the measurements. Note that the sample variance computed on a pair of observations is s 2 =/92/2. Hence, changes in D indicate how sample standard deviation is changing from pair to pair. In Table I, it is obvious that, for each metal, D increases as the
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