STATISTICAL TRENDS IN GROUND-WATER MONITORING DATA AT A LANDFILL SUPERFUND SITE: A CASE STUDY M I C H A E L R. S T O L I N E * , R I C H A R D N. P A S S E R O * * and M I C H A E L J. B A R C E L O N A * * * Dept. of Mathematics and Statistics, Western Michigan University, Kalamazoo, M1-49008, U.S.A. ** Institute for Water Sciences, Western Michigan University, Kalamazoo, MI-49008, U.S.A. (Received: October 1991; Revised: August 199211 Abstract. This paper describes the use of statistical regression models to characterize temporal trends in groundwater monitoring data collected between 1980 and 1990 on 15 wells and 13 parameters (195 cases in all) at the KL Avenue landfill site in Kalamazoo County, Michigan. This site was used as a municipal landfill prior to 1980, then was placed on the Superfund site list in 1982 after ground-water contamination was found. Six temporal regression trend models were defined using linear and quadratic regression models. These trends were used to classify each of the 195 cases as: improving, deteriorating, or stable over the 1980-1990 time period. Using these classifications it was determined that there were more than twice as many improving cases as deteriorating conditions at the KL site during this time period. These models provide a method for visualizing and interpreting trends in ground-water quality at individual well locations within the contaminant plume and for assessing the chemical trend behavior of the overall plume. The improving, deteriorating, and stable trend categories were developed for two purposes. The first purpose is to facilitate comprehension of information contained in large amounts of water quality data. The second is to assist communication among the many different groups of people who recommend actions, including remediation responsibilities at Superfund sites, like the KL site. A normal probability model was used in the trend classifications. This model contained provisions to accommodate nondetect data and other 'abnormal' laboratory determinations which can influence the trend selection process. The robustness of this classification procedure was examined using a lognormal probability model. The overall conclusions about the KL site using the lognormal model were similar to those obtained using the normal model. However, some individual trend indications were different using the lognormal model. The Shapiro-Wilk test was used to check the adequacy of both the normal and lognormal models. The lognormal model was found to be a somewhat more adequate model for fitting the KL site data, but was not found to be superior to the normal model for each case. The normal and lognormal models were both found to be suitable for determining overall trend conditions at this site. Both models are recommended for these purposes assuming an understanding of the statistical constraints and hydrochemical context. However, it is recommended that the search for more adequate trend models continues.
1. 1.1
Introduction
SITE BACKGROUND
The KL Avenue site was used as a landfill during the 1960s and 1970s. It was closed in 1979 after ground-water contamination was detected in nearby residential wells. Monitoring wells were then installed both on-and-off- site. Since then, either quarterly or semi-annual data have been continuously collected from these wells. In 1982 the site was added to the Superfund list. Additional information about the KL site is given in Section 2. Environmental Monitoring and Assessment 27: 201-219, 1993. (~) 1993 Kluwer Academic Publishers. Printed in the Netherlands.
202 1.2
MICHAEL R. STOLINE ET AL.
OBJECTIVES
The primary goal of this work was to illustrate how statistical regression procedures yield a comprehensive characterization of ground-water quality at the KL Avenue Landfill site within the time period 1980 to 1990. A secondary goal was the development of useful statistical summary methods. These were introduced so that hydrogeologists, engineers, and other decision-makers, as well as the general public, who are not necessarily technically trained in the practice of statistical science, could more easily understand the essential information contained in monitoring data. These summary methods are illustrated using the KL monitoring data. The basic question addressed in this paper is now posed. Has the ground-water quality at the KL site improved (IMP), remained stable (STA), or deteriorated (DET) over this eleven year period? 1.3
METHODS
To accomplish this objective, fifteen monitoring wells and thirteen parameters were selected at the KL site. The monitoring data analyzed from these 195 wellparameter cases provide a reliable characterization of ground-water quality trends at this site over the period of record. Six trend models were fit to the data for each of the 195 well-parameter cases using linear and quadratic regression procedures. The six trend models are characterized as: increasing; decreasing; increasing then decreasing; decreasing then increasing; constant; and zero (nondetect). A trend classification procedure was introduced in order to determine the single 'best-fitting' trend among these six for each of the 195 cases. A second trend summary method was then introduced and used to classify each case as improving (IMP), deteriorating (DET), stable (STA), or nondetect (ZERO). Details concerning these trend classification methods and their rationale are provided in Section 3. The regression models used in the classifications assumed a normal probability model (N) where laboratory non-detect data were coded at one-half the laboratory detection limit for each parameter. These trend models were also adapted to account for possible high and low outlying (or incorrect) laboratory determinations, which occur with monitoring data sets. The trend model selection procedure is described in Section 3.6. This procedure was used in the selection of the trend models and characterizations reported in Tables IV-VI for the KL site data given in Section 4. The robustness of the KL site trend conclusions obtained from these tables was then examined assuming a lognormal model. Gilbert (1987) stated that the lognormal is the probability model of choice for fitting environmental data. A reason for this choice is that environmental data are often observed to be right-skewed and the normal distribution is symmetric. It is well known that the lognormal is right-skewed. This provides a rationale for the use of the lognormal in preference to the normal in the trend models used in analyzing
TRENDS IN GROUND-WATER MONITORING DATA
203
environmental monitoring data, like those collected at the KL site. Other statistical methods were considered but not used in the analyses. BoxJenkins time series models are only applicable for equally-spaced monitoring data. These methods are not applicable here because the KL site monitoring data are not equally-spaced. Robust kriging, spatial, and other multivariate statistical methods are difficult to apply in circumstances like those at the KL site where data are only sparsely available in a spatial sense, and because of the presence of many nondetectable observations. Nonparametric methods were also not used because nonparametric quadratic trend analyses are not available. Trend classifications using the normal (N) model were applied to the KL data. The results are presented in Section 4 and conclusions are discussed in Section 5. Conclusions about ground-water trends can be key components in the actual determination of remediation plans at Superfund sites, like the KL site. Because of their potential importance in decision-making activities, it is important that the trend conclusions not be overly dependent upon model assumptions, like normality (N). For this reason the KL site trend classifications were also obtained using a lognormal (LN) model. These results are also presented and discussed in Sections 4 and 5. 2.
KL Site Characteristics
A brief description is given here of the history and hydrogeologic characteristics of the KL site. More details are provided in Kehew and Passero (1990). 2.1
SITELOCATION
The West KL Avenue Landfill site is located in Oshtemo Township in Kalamazoo County in southwest Michigan. The 90 acre landfill is about five miles west of the City of Kalamazoo (80000 population) in a rural residential area of rolling semiforested hills. Private wells are the source of drinking water for approximately 8000 people who live within a three-mile radius of the site. The closest residences are on KL Avenue (directly south and southwest), 4th Street (1/2 mile west of the site), and West Main Street (north and northwest). Figure 1 shows the locations of these residences. 2.2
SITE HISTORY
The site was operated as a landfill by Oshtemo Township prior to 1968, when it was acquired by Kalamazoo County. It was operated by the county as a landfill between 1968 and 1979. During this time it is estimated that five million cubic yards of primarily commercial refuse, bulk liquids, and chemical waste drums were deposited at the site (U.S. Environmental Protection Agency, 1989). In 1976, four residential wells on 4th Street, west of KL site, were found to be contaminated. Six onsite monitoring wells were installed in 1977. These test wells (TW) are labelled TW1-TW6 (Figure 1). In 1979, nine offsite monitoring wells
204
MICHAEL R. STOLINEET AL.
SAMPLING LOCATIONS 1'18o - - p ~ E S l E N T
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were installed. These are labelled M 1 - M 9 (Figure 1). In 1979, the site was closed by the Michigan Department of Natural Resources and, since then, the site has not received additional waste materials. A site closure plan was implemented by Kalamazoo County in 1980. As a result of this plan, a bentonite soil cap was placed over the area and nine methane gas vents were installed onsite. Deep wells were installed for nine residences and, later, a water main was extended to serve the residences near the site. The site was added to the Superfund site list in 1982. The following contaminant concentrations were recorded at TW4, the historically most contaminated monitoring well at the site, during the March, 1982 sampling period. The measured levels (in parts per billion) were: 240 (benzene) 1100 (1,1 dichloroethane), 340 (1,2 dichloroethane), 1100 (toluene), and 560 (phenol). These measurements are indicative of the levels of contamination at this site at the time it was added to the Superfund list.
TRENDS IN GROUND-WATER MONITORING DATA
2.3
205
SITE HYDROGEOLOGY
The ground-water flow is predominately to the northwest, and secondarily to the west of the site. The contaminant plume has expanded in a westerly direction from the landfill to an area near well M5 on the west. Offsite monitoring wells were purposely located in this west component of the contaminant plume. Another component of the plume extended to the northwest of the site. The 10 mg/1 contour of chloride in the contaminant plume is shown in Figure 1. Bonnie Castle Lake is a ground-water recharge lake abutting the site on the northeast. This lake has not been found to be adversely affected by ground-water flow from the KL site. Dustin Lake is a flow-through lake located 1/2 mile west and downgradient of the site, and has not been found to be contaminated by groundwater discharge from the site.
3. 3.1
Statistical Design and Analysis
SELECTION OF THE MONITORING WELLS
Data from fifteen monitoring wells and residential wells were used in the study. These were chosen on the basis of available water quality data. Four monitoring wells were selected on-site. These are TW1, TW3, TW4, and TW6 (Figure 1). As mentioned elsewhere, TW4 has been historically the most contaminated well, and is located on the west edge of the KL site. The other three wells: TW1, TW3, and TW6 are located on the northwest, southern, and northeast areas of the site, respectively. Eight wells were selected in the plume off-site. These wells (labelled M 1 - M 8 in Figure 1) were chosen within the westerly ground-water flow gradient from the most contaminated areas just west of the KL site to the least contaminated areas at the western-edge of the plume. M3 and M4 are located less than 50 feet from TW4. Wells M1, M2, and M8 are a nest of wells at different depths in the central portion of the plume southwest of M3 and M4. Wells M6 and M7 are located south of KL Avenue and are south of the site. M5 is located at the western edge of the plume near Dustin Lake, nearly a mile west of the site. Three residential wells were also selected. These include two of the residential wells that were found to be contaminated in 1977. They are located at 710 S. 4th and 9033 W. KL, and are labelled 4TH and KL in the tables that follow. An uncontaminated upgradient well is also included. This well is located at 8383 W. Main and is labelled WM. Data from several other residential wells have also been collected since 1975, but were not included in this study due to the low observed levels (or lack) of contamination, or the erratic sampling history.
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MICHAEL R. STOLINE ET AL.
TABLE I Ground-water quality trend categories.
3.2
Model code
Temporal trend categories
Regression trend model
Model
Z
Non-detect or zero
No model
Zero (Z)
C
Constant
y t = c~
Constant (C)
I
Increasing
y t = c~ + f i t ,
/3 > 0
Linear (L)
D
Decreasing
y t = c~ + f i t ,
/3 < 0
Linear (L)
ID
Increasing initially, decreasing later
y t = c~ + / 3 t + "yt2 , 7 < 0
Quadratic (Q)
DI
Decreasing initially, increasing later
y t = c~ + f i t + ",/t2 , 3' > 0
Quadratic (Q)
SELECTION OF THE PARAMETERS
Thirteen parameters were selected for this study. These include the metals: chromium, iron, and lead. The organic compounds included were: benzene, chloride, 1,1-dichloroethane (1,1-DCA), 1,2-dichloroethane (1,2-DCA), phenol, toluene, and xylene. Three water quality parameters: pH, chemical oxygen demand (COD), and specific conductance (SC) were also included. Other elements such as calcium and sodium were also monitored, as were several organic compounds. These parameters were not analyzed here because either they were not contamination indicators, or were routinely observed at nondetect levels. 3.3
REGRESSIONTREND MODELS
It is convenient to let Yt denote the analytical (measurement) result of a groundwater quality parameter of interest measured at time t. The variable Yt is the 'dependent' variable and t is the 'independent' variable in the six trend models described in Table I. Models I and D are two linear (L) models and are characterized by either an increasing or decreasing trend across the time period. Models ID and DI are quadratic (Q) models. Model ID exhibits increasing values during the initial part of the time period, achieves a maximum level, and then decreases in the latter part of the time period. Model DI is the reverse of Model ID in that values decrease in the initial portion of the time period, achieve a minimum level, then increase in the later part of the time period. Model C is a constant model in which the level neither increases nor decreases throughout the time period. Model Z is a nondetect or zero-level model, which is applicable for cases with few detectable observations
TRENDS IN GROUND-WATERMONITORINGDATA
207
TABLE II Ground-water quality trend conditions. Trend condition
Trend categories
Definition
IMP DET STA ZERO
D, ID I, DI C Z
Improvement Deterioration Stabilization Nondetect or Zero
or where a C, L, or Q model can not be fitted. 3.4
GROUND-WATER QUALITY TREND CONDITIONS
Four general interpretive ground-water quality and trend conditions were also defined using the trend categories defined in Table I. These are labelled: IMP, DET, STA and ZERO to denote generally improving ground-water quality, generally deteriorating quality, unchanging (or stable) quality, and nondetectable levels of ground-water respectively (Table II). Those parameters which showed either a decrease in level throughout the sampling period (D) or showed an initial increase followed by a decrease in level during the latter part of the time period (ID) are considered indicative of generally improving (IMP) ground-water quality. Water quality parameters showing a persistent increase in concentration level during the sampling period (I), or those that showed an initial decrease in level, followed by an increase in level during the latter part of the sampling period (DI), are indicative of generally deteriorating (DET) ground-water quality. 3.5
DATA COLLECTION AND CODED TIME t VALUES
Ground-water quality data were collected at 27 sampling periods between March, 1980 and April, 1990. Quarterly data were obtained in 1980 and 1981. Semiannual data were obtained in 1982 and in each of the years in the period 1985-1989. Three observations were obtained in both 1983 and 1984. One sample is included from 1990. The samples were collected by Kalamazoo County Health Department personnel and were analyzed by a private laboratory. The 'independent' variable time value t was coded for each of the 27 sampling periods as the number of months from the first data collection in March, 1980 (where t = 1). The t value for the last sampling period (April, 1990) is t = 122. The t-values for the other 25 sampling periods were obtained similarly.
208 3.6
MICHAEL R. STOLINE ET AL. TREND MODEL SELECTION PROTOCOL
The trend model selection testing was performed according to the following hierarchy: quadratic models (first), linear models (second), constant models (third), and the zero model (fourth). The rationale for this model selection order is that constant models are a subset of linear models, and linear models are a subset of quadratic models. The procedure is as follows. First, the stage 1 tests determined if one of the quadratic models (ID, DI) could be fit. If yes, no further testing was done. If no, the stage 2 linear trend model testing was done to determine whether Model I or D could be fit. If yes, no further testing was done. If no, then an attempt was made to fit a constant C model in stage 3 testing. If the constant model C could not be fit, then the zero model Z was accepted. In the course of applying this procedure, one or two large (outlying) observations were observed in several instances to have unusual influence upon the testing results. In these situations the estimated standard errors were so high that no quadratic, linear, or constant model could be fit to the data. Under ideal conditions it is recommended that a data verification procedure be established to determine if these outlying observations represent incorrect analytical determinations (or coding errors), or if they are legitimate measurements. For the former cases, the data should be either corrected or deleted. In the latter case, the data should be used in trend model estimation processes that have been modified to accommodate the outlying observations. It was not possible to implement a data verification procedure to check the authenticity of the several outlying (large) observations identified in the KL data set. For this reason two additional constant trend models C1 and C2 were introduced to fit these cases. The C1 model is a constant model fitted with the largest observation removed. The C2 constant model is fitted with the two largest observations removed. The following constant trend model selection procedure was introduced to account for those cases where the presence of one or two outlying values could mask the acceptance of any but a zero Z model. This procedure was performed as follows: -
-
-
If model C was not fit, then model C1 was fit. If model C1 was not fit, then model C2 was fit. If model C2 was not fit, then model Z was accepted.
The model fitting procedure was not robust for cases containing many nondetect data values. For these cases a zero (Z) model was adopted. The cut-off value of m _< 3 was arbitrarily chosen, where m denotes the number of detectable measurements among the 27 possible monitoring events. No trend model was fit if m 4, then the following trend model hierarchy selection order was adopted. Trend selection order First Second Third
Fourth
Model Quadratic (ID, DI) Linear (I, D) Constant First (C) Second (C1) Third (C2) Zero (Z)
A significance level of c~ = 0.05 was chosen and all KL trend selections were performed using this level. More specific trend model selection details are provided in the Appendix section located at the end of the paper. 3.7
T R E N D MODEL SELECTION COMPUTER PROGRAM
An environmental monitoring regression analysis program (ENREG) was written which incorporates the trend model selection procedure described in Section 3.6 (and in the Appendix) for user-supplied o~significance levels. The p-values (probability values) associated with the quadratic, linear, and constant trend models, were calculated assuming Yt is normally distributed. This assumes that the (N) model is valid. Provisions are provided in ENREG so that the p-values are also calculated assuming a lognormal (LN) model. This was accomplished by letting zt = ln(yt) be the dependent variable in the trend selection model previously defined, where zt is assumed to be normally distributed. 4. 4.1
Statistical Analysis of the KL Site Data
TRENDMODELSELECTIONASSUMINGA NORMAL(N) MODEL
The results of the ENREG computer program are presented in Table IV for the KL site data using the o~ = 0.05 significance level with the normal (N) model. Table V contains a categorization of the KL site temporal trends summarized by monitoring well. Table VI contains a similar categorization summarized by parameter. Because of its inverse water quality relationship to other parameters used in this study, the I, DI, D, and ID trends for pH in Table IV are tabulated in Tables V and VI as D, ID, I, and DI trend frequency counts, respectively. The pH
210
MICHAEL R. STOLINEET AL.
TABLE IV Temporal trends in ground-water quality by monitoring well and by parameter: March, 1980-April, 1990 - (N) model. Trend category ID DI I D C Cx
Description Increasing, then decreasing Decreasing, then increasing Increasing Decreasing Constant Constant with largest observation eliminated Constant with two largest observations eliminated Non-detect or zero
C2 Z Monitoring well Substance
M1 M2 M3 M4 M5 M6 M7 M8 TW1 TW3 TW4 TW6 4TH KL WM
Benzene COD Chloride Chromium 1,1-DCA 1,2-DCA Iron Lead pH Phenol SC Toluene Xylene
D C C
I C I
I ID D
DI C C
Z C C
Z C DI
Z C D
D D D
DI D Z DI I I ID DI C Z
C C Z DI I I D C C I
C C D D C DI C C DI C
C C D C C DI D C C Z
D Z Z C1 C I C DI Z Z
D Z Z DI C I C D Z Z
DI Z Z C C I C D Z Z
C D C2 Z DI Z C C C C DI I C C D C D Z C Z
Z C DI
Z C C
I ID C
Z C C
C D D
Z Z D
Z C ID
C C1 C D C I Z C Z Z
C ID D D C I D ID ID ID
D Z Z C ID I ID D Z Z
Z ID C DI Z ID D C C1 Z
D Z Z C I I Z D Z Z
C Z Z DI C C Z ID Z Z
parameter is the only one summarized in this manner. A code is introduced to identify the first and second most frequent trend conditions for a given well (Table V) or parameter (Table VI). For example, the classification STA/IMP designates a well or parameter whose most frequent trend condition was stable (STA) and whose second most frequent trend was improving (IMP). The code (IMP, STA) designates cases where IMP and STA were equally the most frequent category. Finally, the code IMP indicates situations for which IMP trends are the most numerous, and DET and STA are equal as the second most frequent condition. The ZERO trend condition was not used in these classification designations. The following general observations and overall conclusions can be obtained
TRENDS IN GROUND-WATERMONITORINGDATA
211
TABLE V Number of water quality parameters with IMP, DET, STA and nondetect trends by monitoring well - (N) model.
Well
DET (I, DI)
Frequencies IMP STA (D, ID) (C)
Nondetect (Z)
Well classification (IMP, DET) (STA, DET) (IMP, STA) STABMP STA/IMP (IMP, STA) STA/IMP (IMP, STA) STA/IMP STA/IMP IMP/STA IMP/STA (IMP, STA) IMP STA/IMP
M1 M2 M3 M4 M5 M6 M7 M8 TW1 TW3 TW4* TW6 4TH KL WM**
4 5 1 1 1 2 1 1 1 0 1 0 2 1 1
4 2 6 3 2 3 3 6 2 2 9 5 4 4 2
3 5 6 8 5 3 4 6 5 7 3 3 4 1 4
2 1 0 1 5 5 5 0 5 4 0 5 3 7 6
Totals %
22 11.3%
57 29.2%
67 34.4%
49 25.1%
* Most contaminated well ** Upgradient well
f r o m an e x a m i n a t i o n o f the s u m m a r i e s c o n t a i n e d in Tables V and VI. (1) T h e r e w e r e m o r e than twice as m a n y I M P c h e m i c a l p a r a m e t e r trends (29.2%) as D E T trends (11.3%). (2) T h e r e w e r e nearly as m a n y I M P c h e m i c a l p a r a m e t e r trends (29.2%) as S T A trends (34.4%).
(3)
T h i r t e e n o f the fifteen wells exhibited m o r e e v i d e n c e o f overall trend i m p r o v e m e n t than deterioration i.e., m o r e I M P than D E T c h e m i c a l p a r a m e t e r trends. O n l y one well (M2) s h o w e d m o r e e v i d e n c e o f trend deterioration.
(4) N i n e o f the thirteen parameters exhibited m o r e e v i d e n c e o f trend i m p r o v e m e n t than deterioration. T h r e e parameters (benzene, iron, and lead) s h o w e d m o r e
212
MICHAEL R. STOLINE ET AL.
TABLE VI Number of wells with IMP, DET, STA and nondetect trends by water quality parameter - (N) model. Frequencies IMP STA (D, ID) (C)
Parameter
DET (I, DI)
Benzene COD Chloride Chromium 1,1-DCA 1,2-DCA Iron Lead pH Phenol SC Toluene Xylene
4 0 3 2 0 1 5 3 1 0 2 0 1
2 4 6 5 3 3 3 1 13 6 7 3 1
1 10 6 7 5 2 7 10 1 6 6 4 2
8 1 0 1 7 9 0 1 0 3 0 8 11
22
57
67
49
Totals
Nondetect (Z)
Parameter classification DET/IMP STA/IMP (IMP, STA) STA/IMP STAJIMP IMP/STA STA/DET STA/DET IMP (IMP, STA) IMP/STA STA/IMP STA
evidence o f trend deterioration than trend improvement. Two of these, iron and lead, showed more evidence of stabilization than deterioration. (5) The above evidence supports the general conclusion that ground-water quality has generally been stable or has improved overall in the K L site plume. 4.2
EXAMPLE - TREND MODEL SELECTION FOR PHENOL
The trend selection method used in obtaining the results in Table IV can be illustrated for a specific case in which the adequacy of the normal (N) model is questionable. The phenol data for T W 6 were chosen to graphically illustrate the trend model selection procedure in this study. Figure 2 shows computer-generated plots o f the phenol concentrations, and the best-fitting quadratic, linear and constant regression models for these data, assuming the (N) model is valid. As noted in Table IV, the quadratic ID model was selected by the r e c o m m e n d e d method at -- 0.05 for this case. An examination of the visual evidence presented in Figure 2 corroborates the choice o f the quadratic model as the 'best' fitting trend model. This data set is typical of many of the other K L site data sets which contain some nondetect data with several large, possible outlying, detectable observations. Such data sets are difficult to analyze properly because there exist wide fluctuations both in level and variability across the time period. For these reasons there may exist
213
TRENDS IN GROUND-WATER MONITORING DATA
PHENOL 5~00
DATA AND TRENDS:
TW6
1
O 4000 N
C E 3000 N
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,
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.
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.
.
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.
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1988
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some reasonable doubt about the robustness of the normal model in determining trend characteristics for cases like these. Hence, an alternative lognormal (LN) model was used to examine the KL site data. The results of the application of the (LN) model are reported in Section 4.3, and the adequacy of both the (N) and (LN) models is explored in Section 4.4. 4.3
T R E N D MODEL SELECTION ASSUMING A LOGNORMAL
(LN) MODEL
The p-values used in the selection of the trend models reported in Tables IV-VI were calculated assuming the normal model. The counterparts to Tables IV-VI were obtained for the KL site data using a trend model selection process assuming a lognormal distribution. These are not reproduced here. However, several tables are provided in this section which can be used to compare the results of the trend model selection processes for the normal (N) and lognormal (LN) models. Table VII shows the frequencies of the trend models (DI, ID, I, D, C, C1, C2, Z) for both the (N) and (LN) models for the KL site data. Table VIII shows the frequencies of selection of various trend conditions (IMP, DET, STA, ZERO) for both models. The (N) and (LN) models are compared using the results presented in Tables
214
MICHAELR. STOLINEET AL.
TABLE VII (N) and (LN) temporal trend model selection frequencies for the KL site.
Trend model DI ID
Frequency of selection (N) (LN) 14 16
D C CI C2 Z
41 63 3 1 49
16 27 16 38 50 0 0 48
Total
195
195
I
8
TABLE VIII (N) and (LN) temporal trend condition selection frequencies for the KL site. Trend condition
(N)
%
(LN)
%
IMP STA DET ZERO
57 67 22 49
29.2% 34.3% 11.3% 25.1%
65 50 32 48
33.3% 25.6% 16.4% 24.6%
195
99.9%
195
99.9%
Total
V I I and VIII: (1) The two outlier models C1 and C 2 w e r e not selected for any case using the (LN) model. (2) Relatively m o r e linear (I, D) and quadratic (ID, DI) trends were selected by the (LN) m o d e l (49.7%) as c o m p a r e d to the (N) model (40.5%). (3) Relatively f e w e r trends were judged STA by the (LN) model (25.6%) as c o m p a r e d to the (N) m o d e l (34.3%). (4) Relatively m o r e trends were j u d g e d I M P by the (LN) model (33.3%) as c o m pared to the (N) m o d e l (29.2%).
TRENDS IN GROUND-WATER MONITORING DATA
215
(5) Relatively more trends were judged DET by the (LN) model (16.4%) as compared to the (N) model (11.3%). Upon closer examination, it was found that the primary reasons that the (N) and (LN) trend condition frequencies differed is that some trends classified as STA by the (N) model tended to be classified as IMP or DET by the (LN) model. This occurred in nearly 70% of the cases of (N) and (LN) model disagreement. Using the (LN) model, there were relatively more cases judged improving and deteriorating than when using the (N) model. One-third (33.3%) of the cases were classified as improving by the (LN) model compared to (29.2%) for the (N) model. Similarly, (16.4%) of the cases were classified as deteriorating by the (LN) model compared to (11.3%) for the (N) model. An important interpretation question arises. Would the use of the (LN) model substantiate the overall conclusions at the KL site obtained using the (N) model? It was found that ten of the fifteen wells showed more trend improvement than deterioration using the (LN) model. This is compared to thirteen of fifteen wells using the (N) model. Also, eight of thirteen parameters showed more evidence of trend improvement than deterioration using the (LN) model, as compared to ten of thirteen parameters using the (N) model. The (LN) trend analyses also supported the overall conclusion that ground-water quality has been generally improving at the KL site with twice as many improving as deteriorating trends. However, as noted above, there were basic differences between the (LN) and (N) models. 4.4
W H I C H MODEL IS RECOMMENDED: N O R M A L OR LOGNORMAL?
In the previous section it was observed that the overall conclusions obtained were essentially the same using either the (N) of (LN) models. However, specific interpretations for particular well and parameter cases may depend upon which model was used. The following questions arise. Is either model adequate? Which model is generally more adequate? Which model, if either, is recommended for general usage? These questions were addressed by an examination of the fitted residuals of the selected trend models using the Shapiro-Wilk (SW) test of normality. The results of the use of the (SW) procedure on the estimated residuals for both the (N) and (LN) models are presented in Table IX. The results in Table IX are presented by parameter and contain the proportion of wells for each parameter which were adequately fit by the stated model for two levels of significance: c~ = 0.01 and o~ = 0.05. Using the 0.01 significance level results given in Table IX, it is observed that 66% of the cases were adequately fit by the (LN) model as compared to 56% using the (N) model. Using a 0.05 significance level, 53% and 43% were adequately fit by the (LN) and (N) models. The 'preferred model' in Table IX is determined by designating the model which
2]6
MICHAEL R. STOLINEET AL.
TABLE IX Shapiro-Wilk tests of normality for the (N) and (LN) trend models at c~ = 0.01 and 0.05. c~ = 0.01 c~ = 0.05 Preferred Parameter N LN N LN model Benzene
43% (3/7)
57% (4/7)
43% (3/7)
43% (3/7)
LN
COD
57% (8/14)
50% (7/14)
43% (6/14)
29% (4/14)
N
Chloride
67% (10/15)
93% (14/15)
47% (7/15)
93% (14/15)
LN
Chromium
0% (0/14)
7% (1/14)
0% (0/14)
7% (1/14)
Neither
1,1-DCA
67% (4/6)
38% (3/8)
50% (3/6)
38% (3/8)
N
1,2-DCA
67% (4/6)
17% (1/6)
67% (4/6)
17% (1/6)
N
Iron
50% (7/14)
73% (11/15)
36% (5/14)
73% (11/15)
LN
Lead
36% (5/14)
79% (11/14)
21% (3/14)
43% (6/14)
LN
pH
100% (15/15)
100% (15/15)
67% (10/15)
73% (11/15)
Both
Phenol
50% (6/12)
69% (9/13)
33% (4/12)
54% (7/13)
LN
SC
100% (15/15)
87% (13/15)
87% (13/15)
73% (11/15)
N
Toluene
17% (1/6)
57% (4/7)
17% (1/6)
57% (4/7)
LN
Xylene
50% (2/4)
100% (4/4)
50% (2/4)
50% (2/4)
LN
80/142 (56%)
97/147 (66%)
61/142 (43%)
78/147 (53%)
Total
TRENDS IN GROUND-WATER MONITORING DATA
217
TABLE X KL site trend classification summaries using the (N) and (LN) models. Trend classes
Frequencies (N)
(LN)
IMP - Improving
57
65
STA - Stable
67
50
DET - Deteriorating
22
32
Z E R O - Nondetect
49
48
195
195
Total
adequately fits more wells for each parameter case using the 0.01 significance level SW test results. Using this criteria, it is determined that the (LN) model was preferred for 7 parameters and the (N) model was preferred for 4 parameters. Both models were adequate for the pH parameter. Neither model was preferred for chromium cases, which had 80.7% nondetect observations.
5. 5.1
Summary and Future Work
SUMMARY
Table X contains the results of the trend classifications using the normal (N) and lognormal (LN) models for the 195 cases discussed in Section 4. The results in Table X indicate that there were more than twice as many improving as deteriorating trends, and that there were nearly as many improving as stable trends. These observations (and others discussed in Section 4) support the overall conclusion that ground-water quality trends at the KL site are generally improving or stable. There are essential differences between the (N) and (LN) model results given in Table X. There were relatively more trends classified as either improving or deteriorating and fewer classified as stable using the (LN) model than for the (N) model. However, it is noted that the overall conclusion is the s a m e using either model, i.e., there were roughly twice as many improving and stable trends than deteriorating trends at the KL site. Finally, the adequacies of both the (N) and (LN) models were examined in Section 4 using the Shapiro-Wilk test applied to the fitted residuals of the nonZERO trend models. The results of applying this test are summarized in Table XI for two significance levels: c~ = 0.01 and 0.05. From Table XI it is observed that the (LN) model fitted 66% of the cases at a
218
MICHAEL R. STOLINE ET AL.
TABLE XI Shapiro-Wilk (N) and (LN) model adequacy tests for the KL site data. Level of significance 0.01 (N) and (LN) model acceptance
0.05
(N)
(LN)
(N)
(LN)
Frequency
80/142
99/147
61/142
78/147
Percentage
56%
66%
43%
53%
0.01 level of significance compared to 56% for the (N) model, a difference of 10%. This difference was observed for the 0.05 cases, too. The above results support the conclusion that the (LN) model is a somewhat more adequate trend model overall than is the (N) model. However, the (LN) model was not uniformly preferred for every parameter case. Finally, as could be seen with the phenol data in Section 4.2, the challenge remains to find more reliable models and methods for selection of the most appropriate trend models to characterize these 'messy' (but typical) cases. 5.2
FUTURE WORK
The results of this study indicate that additional effort is needed in the development of more adequate models to characterize ground-water quality trends at landfill sites. However, the (N) and (LN) models appear to be reasonably adequate for this purpose, and both are recommended. In addition, the (LN) model is slightly preferred to the (N) model for this purpose. The trend classification models in this study were used for the purpose of characterizing changes in ground-water quality over time at a particular site. These same trend classification models can also be used to quantitatively assess the magnitude of change at a particular site over time, or to compare an upgradient site to a downgradient site for a specified time period. The quantitative assessments and comparisons will be the subject of a future paper (under development).
Appendix: Trend Model Selection Method: s-level The specific details are given here describing the trend model selection procedure used in the analysis of the KL site data. STAGE 1 - QUADRATIC TREND MODEL SELECTION (ID, DI) Model:
Yt = c~ + / 3 t + 7t 2
219
TRENDS IN GROUND-WATERMONITORINGDATA
Estimate:
;y
Test:
H 0 : 7 = 0 vs. HI" " y ¢ 0 with p-value pl
Decision:
- if (Pl < o~ and + < 0), then accept model ID; -
-
if (Pl < o~ and ;y > 0), then accept model DI; if (Pl _> o0, then go to Stage 2 testing.
STAGE 2 - LINEAR TREND MODEL SELECTION (I, D)
fit
Model:
Yt = oz +
Estimate:
/~
Test:
Ho:/3 = 0 vs. H1:/3 ¢ 0 with p-value P2
Decision:
- if (P2 < c~ and ¢) > 0), then declare model I; - if (P2 < c~ and ¢) < 0), then accept model D; -
if (P2 > o~), then go to Stage 3 testing.
STAGE 3 - CONSTANT TREND MODEL SELECTION (C, C1, C2) Model:
Yt = o~
Test:
Ho: c~ = 0 vs. H i : ct ¢ 0 with p-values P3, P4, and P5 for models C, C1, and C2 respectively.
Decision:
-
-
-
if (P3 < c~) then declare model C; if (P3 > o~ and P4 < ct), then declare model C1; if (P3 > oz and P4 > ct and P5 < c~), then declare model
C2;
- if (503 > o~ and P4 > ct and P5 > oO, then declare model Z.
R
e
f
e
r
e
n
c
e
s
Gilbert, R.O.: 1987, Statistical Methods for Environmental Pollution Monitoring, Van Nostrand Reinhold, New York. Kehew, A.E. and Passero, R.N.: 1990, 'pH and Redox Buffering Mechanisms in a Glacial Drift Aquifer Contaminated by Landfill Leachate', Ground-water 28, 728-737. U.S. Environmental Protection Agency: 1989, 'Final Remedial Investigation Report for West KL Avenue Landfill - Kalamazoo, Michigan - May, 1989 - Emergency and Remedial Response Branch, Region V, 230 South Dearborn Street, Chicago, Illinois, 60604.
1. 1.1
Introduction
SITE BACKGROUND
The KL Avenue site was used as a landfill during the 1960s and 1970s. It was closed in 1979 after ground-water contamination was detected in nearby residential wells. Monitoring wells were then installed both on-and-off- site. Since then, either quarterly or semi-annual data have been continuously collected from these wells. In 1982 the site was added to the Superfund list. Additional information about the KL site is given in Section 2. Environmental Monitoring and Assessment 27: 201-219, 1993. (~) 1993 Kluwer Academic Publishers. Printed in the Netherlands.
202 1.2
MICHAEL R. STOLINE ET AL.
OBJECTIVES
The primary goal of this work was to illustrate how statistical regression procedures yield a comprehensive characterization of ground-water quality at the KL Avenue Landfill site within the time period 1980 to 1990. A secondary goal was the development of useful statistical summary methods. These were introduced so that hydrogeologists, engineers, and other decision-makers, as well as the general public, who are not necessarily technically trained in the practice of statistical science, could more easily understand the essential information contained in monitoring data. These summary methods are illustrated using the KL monitoring data. The basic question addressed in this paper is now posed. Has the ground-water quality at the KL site improved (IMP), remained stable (STA), or deteriorated (DET) over this eleven year period? 1.3
METHODS
To accomplish this objective, fifteen monitoring wells and thirteen parameters were selected at the KL site. The monitoring data analyzed from these 195 wellparameter cases provide a reliable characterization of ground-water quality trends at this site over the period of record. Six trend models were fit to the data for each of the 195 well-parameter cases using linear and quadratic regression procedures. The six trend models are characterized as: increasing; decreasing; increasing then decreasing; decreasing then increasing; constant; and zero (nondetect). A trend classification procedure was introduced in order to determine the single 'best-fitting' trend among these six for each of the 195 cases. A second trend summary method was then introduced and used to classify each case as improving (IMP), deteriorating (DET), stable (STA), or nondetect (ZERO). Details concerning these trend classification methods and their rationale are provided in Section 3. The regression models used in the classifications assumed a normal probability model (N) where laboratory non-detect data were coded at one-half the laboratory detection limit for each parameter. These trend models were also adapted to account for possible high and low outlying (or incorrect) laboratory determinations, which occur with monitoring data sets. The trend model selection procedure is described in Section 3.6. This procedure was used in the selection of the trend models and characterizations reported in Tables IV-VI for the KL site data given in Section 4. The robustness of the KL site trend conclusions obtained from these tables was then examined assuming a lognormal model. Gilbert (1987) stated that the lognormal is the probability model of choice for fitting environmental data. A reason for this choice is that environmental data are often observed to be right-skewed and the normal distribution is symmetric. It is well known that the lognormal is right-skewed. This provides a rationale for the use of the lognormal in preference to the normal in the trend models used in analyzing
TRENDS IN GROUND-WATER MONITORING DATA
203
environmental monitoring data, like those collected at the KL site. Other statistical methods were considered but not used in the analyses. BoxJenkins time series models are only applicable for equally-spaced monitoring data. These methods are not applicable here because the KL site monitoring data are not equally-spaced. Robust kriging, spatial, and other multivariate statistical methods are difficult to apply in circumstances like those at the KL site where data are only sparsely available in a spatial sense, and because of the presence of many nondetectable observations. Nonparametric methods were also not used because nonparametric quadratic trend analyses are not available. Trend classifications using the normal (N) model were applied to the KL data. The results are presented in Section 4 and conclusions are discussed in Section 5. Conclusions about ground-water trends can be key components in the actual determination of remediation plans at Superfund sites, like the KL site. Because of their potential importance in decision-making activities, it is important that the trend conclusions not be overly dependent upon model assumptions, like normality (N). For this reason the KL site trend classifications were also obtained using a lognormal (LN) model. These results are also presented and discussed in Sections 4 and 5. 2.
KL Site Characteristics
A brief description is given here of the history and hydrogeologic characteristics of the KL site. More details are provided in Kehew and Passero (1990). 2.1
SITELOCATION
The West KL Avenue Landfill site is located in Oshtemo Township in Kalamazoo County in southwest Michigan. The 90 acre landfill is about five miles west of the City of Kalamazoo (80000 population) in a rural residential area of rolling semiforested hills. Private wells are the source of drinking water for approximately 8000 people who live within a three-mile radius of the site. The closest residences are on KL Avenue (directly south and southwest), 4th Street (1/2 mile west of the site), and West Main Street (north and northwest). Figure 1 shows the locations of these residences. 2.2
SITE HISTORY
The site was operated as a landfill by Oshtemo Township prior to 1968, when it was acquired by Kalamazoo County. It was operated by the county as a landfill between 1968 and 1979. During this time it is estimated that five million cubic yards of primarily commercial refuse, bulk liquids, and chemical waste drums were deposited at the site (U.S. Environmental Protection Agency, 1989). In 1976, four residential wells on 4th Street, west of KL site, were found to be contaminated. Six onsite monitoring wells were installed in 1977. These test wells (TW) are labelled TW1-TW6 (Figure 1). In 1979, nine offsite monitoring wells
204
MICHAEL R. STOLINEET AL.
SAMPLING LOCATIONS 1'18o - - p ~ E S l E N T
-
soo
o
,ooo
ft"
~
" - -~----~
SCott I~l rtzT I~ONN~E CAST e3~ e
e2s
25QI
J~el
ItTW ~1
%
KL AVENU~ lANDFill
%',
/ '" "st Kt * * F . ~
.
oe~-=e
.... ,
g ,~n~
•
,~lallOW I:)oml~lli¢ Well
O
Deep Oomtstlc We~l (next to well if ~eplsced)
•
~ a l l o w Monitoring Well
•
Test Well
~m-~
..... ,os, e•
.~'~"4s
~B~o
- - ~ I I ~ /
mue
wM~
N ..... %
"i"
_
jf
2"
/ z L r -.-. , , , s ~ s /
Deep Monitoring Well
Fig. 1. Monitoring wells, sampled residential wells, and the 10 mg/1 contour of chloride in the contaminant plume at the KL site.
were installed. These are labelled M 1 - M 9 (Figure 1). In 1979, the site was closed by the Michigan Department of Natural Resources and, since then, the site has not received additional waste materials. A site closure plan was implemented by Kalamazoo County in 1980. As a result of this plan, a bentonite soil cap was placed over the area and nine methane gas vents were installed onsite. Deep wells were installed for nine residences and, later, a water main was extended to serve the residences near the site. The site was added to the Superfund site list in 1982. The following contaminant concentrations were recorded at TW4, the historically most contaminated monitoring well at the site, during the March, 1982 sampling period. The measured levels (in parts per billion) were: 240 (benzene) 1100 (1,1 dichloroethane), 340 (1,2 dichloroethane), 1100 (toluene), and 560 (phenol). These measurements are indicative of the levels of contamination at this site at the time it was added to the Superfund list.
TRENDS IN GROUND-WATER MONITORING DATA
2.3
205
SITE HYDROGEOLOGY
The ground-water flow is predominately to the northwest, and secondarily to the west of the site. The contaminant plume has expanded in a westerly direction from the landfill to an area near well M5 on the west. Offsite monitoring wells were purposely located in this west component of the contaminant plume. Another component of the plume extended to the northwest of the site. The 10 mg/1 contour of chloride in the contaminant plume is shown in Figure 1. Bonnie Castle Lake is a ground-water recharge lake abutting the site on the northeast. This lake has not been found to be adversely affected by ground-water flow from the KL site. Dustin Lake is a flow-through lake located 1/2 mile west and downgradient of the site, and has not been found to be contaminated by groundwater discharge from the site.
3. 3.1
Statistical Design and Analysis
SELECTION OF THE MONITORING WELLS
Data from fifteen monitoring wells and residential wells were used in the study. These were chosen on the basis of available water quality data. Four monitoring wells were selected on-site. These are TW1, TW3, TW4, and TW6 (Figure 1). As mentioned elsewhere, TW4 has been historically the most contaminated well, and is located on the west edge of the KL site. The other three wells: TW1, TW3, and TW6 are located on the northwest, southern, and northeast areas of the site, respectively. Eight wells were selected in the plume off-site. These wells (labelled M 1 - M 8 in Figure 1) were chosen within the westerly ground-water flow gradient from the most contaminated areas just west of the KL site to the least contaminated areas at the western-edge of the plume. M3 and M4 are located less than 50 feet from TW4. Wells M1, M2, and M8 are a nest of wells at different depths in the central portion of the plume southwest of M3 and M4. Wells M6 and M7 are located south of KL Avenue and are south of the site. M5 is located at the western edge of the plume near Dustin Lake, nearly a mile west of the site. Three residential wells were also selected. These include two of the residential wells that were found to be contaminated in 1977. They are located at 710 S. 4th and 9033 W. KL, and are labelled 4TH and KL in the tables that follow. An uncontaminated upgradient well is also included. This well is located at 8383 W. Main and is labelled WM. Data from several other residential wells have also been collected since 1975, but were not included in this study due to the low observed levels (or lack) of contamination, or the erratic sampling history.
206
MICHAEL R. STOLINE ET AL.
TABLE I Ground-water quality trend categories.
3.2
Model code
Temporal trend categories
Regression trend model
Model
Z
Non-detect or zero
No model
Zero (Z)
C
Constant
y t = c~
Constant (C)
I
Increasing
y t = c~ + f i t ,
/3 > 0
Linear (L)
D
Decreasing
y t = c~ + f i t ,
/3 < 0
Linear (L)
ID
Increasing initially, decreasing later
y t = c~ + / 3 t + "yt2 , 7 < 0
Quadratic (Q)
DI
Decreasing initially, increasing later
y t = c~ + f i t + ",/t2 , 3' > 0
Quadratic (Q)
SELECTION OF THE PARAMETERS
Thirteen parameters were selected for this study. These include the metals: chromium, iron, and lead. The organic compounds included were: benzene, chloride, 1,1-dichloroethane (1,1-DCA), 1,2-dichloroethane (1,2-DCA), phenol, toluene, and xylene. Three water quality parameters: pH, chemical oxygen demand (COD), and specific conductance (SC) were also included. Other elements such as calcium and sodium were also monitored, as were several organic compounds. These parameters were not analyzed here because either they were not contamination indicators, or were routinely observed at nondetect levels. 3.3
REGRESSIONTREND MODELS
It is convenient to let Yt denote the analytical (measurement) result of a groundwater quality parameter of interest measured at time t. The variable Yt is the 'dependent' variable and t is the 'independent' variable in the six trend models described in Table I. Models I and D are two linear (L) models and are characterized by either an increasing or decreasing trend across the time period. Models ID and DI are quadratic (Q) models. Model ID exhibits increasing values during the initial part of the time period, achieves a maximum level, and then decreases in the latter part of the time period. Model DI is the reverse of Model ID in that values decrease in the initial portion of the time period, achieve a minimum level, then increase in the later part of the time period. Model C is a constant model in which the level neither increases nor decreases throughout the time period. Model Z is a nondetect or zero-level model, which is applicable for cases with few detectable observations
TRENDS IN GROUND-WATERMONITORINGDATA
207
TABLE II Ground-water quality trend conditions. Trend condition
Trend categories
Definition
IMP DET STA ZERO
D, ID I, DI C Z
Improvement Deterioration Stabilization Nondetect or Zero
or where a C, L, or Q model can not be fitted. 3.4
GROUND-WATER QUALITY TREND CONDITIONS
Four general interpretive ground-water quality and trend conditions were also defined using the trend categories defined in Table I. These are labelled: IMP, DET, STA and ZERO to denote generally improving ground-water quality, generally deteriorating quality, unchanging (or stable) quality, and nondetectable levels of ground-water respectively (Table II). Those parameters which showed either a decrease in level throughout the sampling period (D) or showed an initial increase followed by a decrease in level during the latter part of the time period (ID) are considered indicative of generally improving (IMP) ground-water quality. Water quality parameters showing a persistent increase in concentration level during the sampling period (I), or those that showed an initial decrease in level, followed by an increase in level during the latter part of the sampling period (DI), are indicative of generally deteriorating (DET) ground-water quality. 3.5
DATA COLLECTION AND CODED TIME t VALUES
Ground-water quality data were collected at 27 sampling periods between March, 1980 and April, 1990. Quarterly data were obtained in 1980 and 1981. Semiannual data were obtained in 1982 and in each of the years in the period 1985-1989. Three observations were obtained in both 1983 and 1984. One sample is included from 1990. The samples were collected by Kalamazoo County Health Department personnel and were analyzed by a private laboratory. The 'independent' variable time value t was coded for each of the 27 sampling periods as the number of months from the first data collection in March, 1980 (where t = 1). The t value for the last sampling period (April, 1990) is t = 122. The t-values for the other 25 sampling periods were obtained similarly.
208 3.6
MICHAEL R. STOLINE ET AL. TREND MODEL SELECTION PROTOCOL
The trend model selection testing was performed according to the following hierarchy: quadratic models (first), linear models (second), constant models (third), and the zero model (fourth). The rationale for this model selection order is that constant models are a subset of linear models, and linear models are a subset of quadratic models. The procedure is as follows. First, the stage 1 tests determined if one of the quadratic models (ID, DI) could be fit. If yes, no further testing was done. If no, the stage 2 linear trend model testing was done to determine whether Model I or D could be fit. If yes, no further testing was done. If no, then an attempt was made to fit a constant C model in stage 3 testing. If the constant model C could not be fit, then the zero model Z was accepted. In the course of applying this procedure, one or two large (outlying) observations were observed in several instances to have unusual influence upon the testing results. In these situations the estimated standard errors were so high that no quadratic, linear, or constant model could be fit to the data. Under ideal conditions it is recommended that a data verification procedure be established to determine if these outlying observations represent incorrect analytical determinations (or coding errors), or if they are legitimate measurements. For the former cases, the data should be either corrected or deleted. In the latter case, the data should be used in trend model estimation processes that have been modified to accommodate the outlying observations. It was not possible to implement a data verification procedure to check the authenticity of the several outlying (large) observations identified in the KL data set. For this reason two additional constant trend models C1 and C2 were introduced to fit these cases. The C1 model is a constant model fitted with the largest observation removed. The C2 constant model is fitted with the two largest observations removed. The following constant trend model selection procedure was introduced to account for those cases where the presence of one or two outlying values could mask the acceptance of any but a zero Z model. This procedure was performed as follows: -
-
-
If model C was not fit, then model C1 was fit. If model C1 was not fit, then model C2 was fit. If model C2 was not fit, then model Z was accepted.
The model fitting procedure was not robust for cases containing many nondetect data values. For these cases a zero (Z) model was adopted. The cut-off value of m _< 3 was arbitrarily chosen, where m denotes the number of detectable measurements among the 27 possible monitoring events. No trend model was fit if m 4, then the following trend model hierarchy selection order was adopted. Trend selection order First Second Third
Fourth
Model Quadratic (ID, DI) Linear (I, D) Constant First (C) Second (C1) Third (C2) Zero (Z)
A significance level of c~ = 0.05 was chosen and all KL trend selections were performed using this level. More specific trend model selection details are provided in the Appendix section located at the end of the paper. 3.7
T R E N D MODEL SELECTION COMPUTER PROGRAM
An environmental monitoring regression analysis program (ENREG) was written which incorporates the trend model selection procedure described in Section 3.6 (and in the Appendix) for user-supplied o~significance levels. The p-values (probability values) associated with the quadratic, linear, and constant trend models, were calculated assuming Yt is normally distributed. This assumes that the (N) model is valid. Provisions are provided in ENREG so that the p-values are also calculated assuming a lognormal (LN) model. This was accomplished by letting zt = ln(yt) be the dependent variable in the trend selection model previously defined, where zt is assumed to be normally distributed. 4. 4.1
Statistical Analysis of the KL Site Data
TRENDMODELSELECTIONASSUMINGA NORMAL(N) MODEL
The results of the ENREG computer program are presented in Table IV for the KL site data using the o~ = 0.05 significance level with the normal (N) model. Table V contains a categorization of the KL site temporal trends summarized by monitoring well. Table VI contains a similar categorization summarized by parameter. Because of its inverse water quality relationship to other parameters used in this study, the I, DI, D, and ID trends for pH in Table IV are tabulated in Tables V and VI as D, ID, I, and DI trend frequency counts, respectively. The pH
210
MICHAEL R. STOLINEET AL.
TABLE IV Temporal trends in ground-water quality by monitoring well and by parameter: March, 1980-April, 1990 - (N) model. Trend category ID DI I D C Cx
Description Increasing, then decreasing Decreasing, then increasing Increasing Decreasing Constant Constant with largest observation eliminated Constant with two largest observations eliminated Non-detect or zero
C2 Z Monitoring well Substance
M1 M2 M3 M4 M5 M6 M7 M8 TW1 TW3 TW4 TW6 4TH KL WM
Benzene COD Chloride Chromium 1,1-DCA 1,2-DCA Iron Lead pH Phenol SC Toluene Xylene
D C C
I C I
I ID D
DI C C
Z C C
Z C DI
Z C D
D D D
DI D Z DI I I ID DI C Z
C C Z DI I I D C C I
C C D D C DI C C DI C
C C D C C DI D C C Z
D Z Z C1 C I C DI Z Z
D Z Z DI C I C D Z Z
DI Z Z C C I C D Z Z
C D C2 Z DI Z C C C C DI I C C D C D Z C Z
Z C DI
Z C C
I ID C
Z C C
C D D
Z Z D
Z C ID
C C1 C D C I Z C Z Z
C ID D D C I D ID ID ID
D Z Z C ID I ID D Z Z
Z ID C DI Z ID D C C1 Z
D Z Z C I I Z D Z Z
C Z Z DI C C Z ID Z Z
parameter is the only one summarized in this manner. A code is introduced to identify the first and second most frequent trend conditions for a given well (Table V) or parameter (Table VI). For example, the classification STA/IMP designates a well or parameter whose most frequent trend condition was stable (STA) and whose second most frequent trend was improving (IMP). The code (IMP, STA) designates cases where IMP and STA were equally the most frequent category. Finally, the code IMP indicates situations for which IMP trends are the most numerous, and DET and STA are equal as the second most frequent condition. The ZERO trend condition was not used in these classification designations. The following general observations and overall conclusions can be obtained
TRENDS IN GROUND-WATERMONITORINGDATA
211
TABLE V Number of water quality parameters with IMP, DET, STA and nondetect trends by monitoring well - (N) model.
Well
DET (I, DI)
Frequencies IMP STA (D, ID) (C)
Nondetect (Z)
Well classification (IMP, DET) (STA, DET) (IMP, STA) STABMP STA/IMP (IMP, STA) STA/IMP (IMP, STA) STA/IMP STA/IMP IMP/STA IMP/STA (IMP, STA) IMP STA/IMP
M1 M2 M3 M4 M5 M6 M7 M8 TW1 TW3 TW4* TW6 4TH KL WM**
4 5 1 1 1 2 1 1 1 0 1 0 2 1 1
4 2 6 3 2 3 3 6 2 2 9 5 4 4 2
3 5 6 8 5 3 4 6 5 7 3 3 4 1 4
2 1 0 1 5 5 5 0 5 4 0 5 3 7 6
Totals %
22 11.3%
57 29.2%
67 34.4%
49 25.1%
* Most contaminated well ** Upgradient well
f r o m an e x a m i n a t i o n o f the s u m m a r i e s c o n t a i n e d in Tables V and VI. (1) T h e r e w e r e m o r e than twice as m a n y I M P c h e m i c a l p a r a m e t e r trends (29.2%) as D E T trends (11.3%). (2) T h e r e w e r e nearly as m a n y I M P c h e m i c a l p a r a m e t e r trends (29.2%) as S T A trends (34.4%).
(3)
T h i r t e e n o f the fifteen wells exhibited m o r e e v i d e n c e o f overall trend i m p r o v e m e n t than deterioration i.e., m o r e I M P than D E T c h e m i c a l p a r a m e t e r trends. O n l y one well (M2) s h o w e d m o r e e v i d e n c e o f trend deterioration.
(4) N i n e o f the thirteen parameters exhibited m o r e e v i d e n c e o f trend i m p r o v e m e n t than deterioration. T h r e e parameters (benzene, iron, and lead) s h o w e d m o r e
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MICHAEL R. STOLINE ET AL.
TABLE VI Number of wells with IMP, DET, STA and nondetect trends by water quality parameter - (N) model. Frequencies IMP STA (D, ID) (C)
Parameter
DET (I, DI)
Benzene COD Chloride Chromium 1,1-DCA 1,2-DCA Iron Lead pH Phenol SC Toluene Xylene
4 0 3 2 0 1 5 3 1 0 2 0 1
2 4 6 5 3 3 3 1 13 6 7 3 1
1 10 6 7 5 2 7 10 1 6 6 4 2
8 1 0 1 7 9 0 1 0 3 0 8 11
22
57
67
49
Totals
Nondetect (Z)
Parameter classification DET/IMP STA/IMP (IMP, STA) STA/IMP STAJIMP IMP/STA STA/DET STA/DET IMP (IMP, STA) IMP/STA STA/IMP STA
evidence o f trend deterioration than trend improvement. Two of these, iron and lead, showed more evidence of stabilization than deterioration. (5) The above evidence supports the general conclusion that ground-water quality has generally been stable or has improved overall in the K L site plume. 4.2
EXAMPLE - TREND MODEL SELECTION FOR PHENOL
The trend selection method used in obtaining the results in Table IV can be illustrated for a specific case in which the adequacy of the normal (N) model is questionable. The phenol data for T W 6 were chosen to graphically illustrate the trend model selection procedure in this study. Figure 2 shows computer-generated plots o f the phenol concentrations, and the best-fitting quadratic, linear and constant regression models for these data, assuming the (N) model is valid. As noted in Table IV, the quadratic ID model was selected by the r e c o m m e n d e d method at -- 0.05 for this case. An examination of the visual evidence presented in Figure 2 corroborates the choice o f the quadratic model as the 'best' fitting trend model. This data set is typical of many of the other K L site data sets which contain some nondetect data with several large, possible outlying, detectable observations. Such data sets are difficult to analyze properly because there exist wide fluctuations both in level and variability across the time period. For these reasons there may exist
213
TRENDS IN GROUND-WATER MONITORING DATA
PHENOL 5~00
DATA AND TRENDS:
TW6
1
O 4000 N
C E 3000 N
T R A 2000~T [ ] X
\ ~
\\ /
,
~---'~\
\
°
0
.
1979
.
.
1 9 8 0 19~
.
1 9 8 2 1983 19~ 1985 1986 YEAR
1987
1988
1989 1~0
concentration units (ugll, ppb) Trends - Constant - A Linear - [] - - Quadratic - ~> Fig. 2. Phenol data and fitted quadratic, linear and constant trends for TW6.
some reasonable doubt about the robustness of the normal model in determining trend characteristics for cases like these. Hence, an alternative lognormal (LN) model was used to examine the KL site data. The results of the application of the (LN) model are reported in Section 4.3, and the adequacy of both the (N) and (LN) models is explored in Section 4.4. 4.3
T R E N D MODEL SELECTION ASSUMING A LOGNORMAL
(LN) MODEL
The p-values used in the selection of the trend models reported in Tables IV-VI were calculated assuming the normal model. The counterparts to Tables IV-VI were obtained for the KL site data using a trend model selection process assuming a lognormal distribution. These are not reproduced here. However, several tables are provided in this section which can be used to compare the results of the trend model selection processes for the normal (N) and lognormal (LN) models. Table VII shows the frequencies of the trend models (DI, ID, I, D, C, C1, C2, Z) for both the (N) and (LN) models for the KL site data. Table VIII shows the frequencies of selection of various trend conditions (IMP, DET, STA, ZERO) for both models. The (N) and (LN) models are compared using the results presented in Tables
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MICHAELR. STOLINEET AL.
TABLE VII (N) and (LN) temporal trend model selection frequencies for the KL site.
Trend model DI ID
Frequency of selection (N) (LN) 14 16
D C CI C2 Z
41 63 3 1 49
16 27 16 38 50 0 0 48
Total
195
195
I
8
TABLE VIII (N) and (LN) temporal trend condition selection frequencies for the KL site. Trend condition
(N)
%
(LN)
%
IMP STA DET ZERO
57 67 22 49
29.2% 34.3% 11.3% 25.1%
65 50 32 48
33.3% 25.6% 16.4% 24.6%
195
99.9%
195
99.9%
Total
V I I and VIII: (1) The two outlier models C1 and C 2 w e r e not selected for any case using the (LN) model. (2) Relatively m o r e linear (I, D) and quadratic (ID, DI) trends were selected by the (LN) m o d e l (49.7%) as c o m p a r e d to the (N) model (40.5%). (3) Relatively f e w e r trends were judged STA by the (LN) model (25.6%) as c o m p a r e d to the (N) m o d e l (34.3%). (4) Relatively m o r e trends were j u d g e d I M P by the (LN) model (33.3%) as c o m pared to the (N) m o d e l (29.2%).
TRENDS IN GROUND-WATER MONITORING DATA
215
(5) Relatively more trends were judged DET by the (LN) model (16.4%) as compared to the (N) model (11.3%). Upon closer examination, it was found that the primary reasons that the (N) and (LN) trend condition frequencies differed is that some trends classified as STA by the (N) model tended to be classified as IMP or DET by the (LN) model. This occurred in nearly 70% of the cases of (N) and (LN) model disagreement. Using the (LN) model, there were relatively more cases judged improving and deteriorating than when using the (N) model. One-third (33.3%) of the cases were classified as improving by the (LN) model compared to (29.2%) for the (N) model. Similarly, (16.4%) of the cases were classified as deteriorating by the (LN) model compared to (11.3%) for the (N) model. An important interpretation question arises. Would the use of the (LN) model substantiate the overall conclusions at the KL site obtained using the (N) model? It was found that ten of the fifteen wells showed more trend improvement than deterioration using the (LN) model. This is compared to thirteen of fifteen wells using the (N) model. Also, eight of thirteen parameters showed more evidence of trend improvement than deterioration using the (LN) model, as compared to ten of thirteen parameters using the (N) model. The (LN) trend analyses also supported the overall conclusion that ground-water quality has been generally improving at the KL site with twice as many improving as deteriorating trends. However, as noted above, there were basic differences between the (LN) and (N) models. 4.4
W H I C H MODEL IS RECOMMENDED: N O R M A L OR LOGNORMAL?
In the previous section it was observed that the overall conclusions obtained were essentially the same using either the (N) of (LN) models. However, specific interpretations for particular well and parameter cases may depend upon which model was used. The following questions arise. Is either model adequate? Which model is generally more adequate? Which model, if either, is recommended for general usage? These questions were addressed by an examination of the fitted residuals of the selected trend models using the Shapiro-Wilk (SW) test of normality. The results of the use of the (SW) procedure on the estimated residuals for both the (N) and (LN) models are presented in Table IX. The results in Table IX are presented by parameter and contain the proportion of wells for each parameter which were adequately fit by the stated model for two levels of significance: c~ = 0.01 and o~ = 0.05. Using the 0.01 significance level results given in Table IX, it is observed that 66% of the cases were adequately fit by the (LN) model as compared to 56% using the (N) model. Using a 0.05 significance level, 53% and 43% were adequately fit by the (LN) and (N) models. The 'preferred model' in Table IX is determined by designating the model which
2]6
MICHAEL R. STOLINEET AL.
TABLE IX Shapiro-Wilk tests of normality for the (N) and (LN) trend models at c~ = 0.01 and 0.05. c~ = 0.01 c~ = 0.05 Preferred Parameter N LN N LN model Benzene
43% (3/7)
57% (4/7)
43% (3/7)
43% (3/7)
LN
COD
57% (8/14)
50% (7/14)
43% (6/14)
29% (4/14)
N
Chloride
67% (10/15)
93% (14/15)
47% (7/15)
93% (14/15)
LN
Chromium
0% (0/14)
7% (1/14)
0% (0/14)
7% (1/14)
Neither
1,1-DCA
67% (4/6)
38% (3/8)
50% (3/6)
38% (3/8)
N
1,2-DCA
67% (4/6)
17% (1/6)
67% (4/6)
17% (1/6)
N
Iron
50% (7/14)
73% (11/15)
36% (5/14)
73% (11/15)
LN
Lead
36% (5/14)
79% (11/14)
21% (3/14)
43% (6/14)
LN
pH
100% (15/15)
100% (15/15)
67% (10/15)
73% (11/15)
Both
Phenol
50% (6/12)
69% (9/13)
33% (4/12)
54% (7/13)
LN
SC
100% (15/15)
87% (13/15)
87% (13/15)
73% (11/15)
N
Toluene
17% (1/6)
57% (4/7)
17% (1/6)
57% (4/7)
LN
Xylene
50% (2/4)
100% (4/4)
50% (2/4)
50% (2/4)
LN
80/142 (56%)
97/147 (66%)
61/142 (43%)
78/147 (53%)
Total
TRENDS IN GROUND-WATER MONITORING DATA
217
TABLE X KL site trend classification summaries using the (N) and (LN) models. Trend classes
Frequencies (N)
(LN)
IMP - Improving
57
65
STA - Stable
67
50
DET - Deteriorating
22
32
Z E R O - Nondetect
49
48
195
195
Total
adequately fits more wells for each parameter case using the 0.01 significance level SW test results. Using this criteria, it is determined that the (LN) model was preferred for 7 parameters and the (N) model was preferred for 4 parameters. Both models were adequate for the pH parameter. Neither model was preferred for chromium cases, which had 80.7% nondetect observations.
5. 5.1
Summary and Future Work
SUMMARY
Table X contains the results of the trend classifications using the normal (N) and lognormal (LN) models for the 195 cases discussed in Section 4. The results in Table X indicate that there were more than twice as many improving as deteriorating trends, and that there were nearly as many improving as stable trends. These observations (and others discussed in Section 4) support the overall conclusion that ground-water quality trends at the KL site are generally improving or stable. There are essential differences between the (N) and (LN) model results given in Table X. There were relatively more trends classified as either improving or deteriorating and fewer classified as stable using the (LN) model than for the (N) model. However, it is noted that the overall conclusion is the s a m e using either model, i.e., there were roughly twice as many improving and stable trends than deteriorating trends at the KL site. Finally, the adequacies of both the (N) and (LN) models were examined in Section 4 using the Shapiro-Wilk test applied to the fitted residuals of the nonZERO trend models. The results of applying this test are summarized in Table XI for two significance levels: c~ = 0.01 and 0.05. From Table XI it is observed that the (LN) model fitted 66% of the cases at a
218
MICHAEL R. STOLINE ET AL.
TABLE XI Shapiro-Wilk (N) and (LN) model adequacy tests for the KL site data. Level of significance 0.01 (N) and (LN) model acceptance
0.05
(N)
(LN)
(N)
(LN)
Frequency
80/142
99/147
61/142
78/147
Percentage
56%
66%
43%
53%
0.01 level of significance compared to 56% for the (N) model, a difference of 10%. This difference was observed for the 0.05 cases, too. The above results support the conclusion that the (LN) model is a somewhat more adequate trend model overall than is the (N) model. However, the (LN) model was not uniformly preferred for every parameter case. Finally, as could be seen with the phenol data in Section 4.2, the challenge remains to find more reliable models and methods for selection of the most appropriate trend models to characterize these 'messy' (but typical) cases. 5.2
FUTURE WORK
The results of this study indicate that additional effort is needed in the development of more adequate models to characterize ground-water quality trends at landfill sites. However, the (N) and (LN) models appear to be reasonably adequate for this purpose, and both are recommended. In addition, the (LN) model is slightly preferred to the (N) model for this purpose. The trend classification models in this study were used for the purpose of characterizing changes in ground-water quality over time at a particular site. These same trend classification models can also be used to quantitatively assess the magnitude of change at a particular site over time, or to compare an upgradient site to a downgradient site for a specified time period. The quantitative assessments and comparisons will be the subject of a future paper (under development).
Appendix: Trend Model Selection Method: s-level The specific details are given here describing the trend model selection procedure used in the analysis of the KL site data. STAGE 1 - QUADRATIC TREND MODEL SELECTION (ID, DI) Model:
Yt = c~ + / 3 t + 7t 2
219
TRENDS IN GROUND-WATERMONITORINGDATA
Estimate:
;y
Test:
H 0 : 7 = 0 vs. HI" " y ¢ 0 with p-value pl
Decision:
- if (Pl < o~ and + < 0), then accept model ID; -
-
if (Pl < o~ and ;y > 0), then accept model DI; if (Pl _> o0, then go to Stage 2 testing.
STAGE 2 - LINEAR TREND MODEL SELECTION (I, D)
fit
Model:
Yt = oz +
Estimate:
/~
Test:
Ho:/3 = 0 vs. H1:/3 ¢ 0 with p-value P2
Decision:
- if (P2 < c~ and ¢) > 0), then declare model I; - if (P2 < c~ and ¢) < 0), then accept model D; -
if (P2 > o~), then go to Stage 3 testing.
STAGE 3 - CONSTANT TREND MODEL SELECTION (C, C1, C2) Model:
Yt = o~
Test:
Ho: c~ = 0 vs. H i : ct ¢ 0 with p-values P3, P4, and P5 for models C, C1, and C2 respectively.
Decision:
-
-
-
if (P3 < c~) then declare model C; if (P3 > o~ and P4 < ct), then declare model C1; if (P3 > oz and P4 > ct and P5 < c~), then declare model
C2;
- if (503 > o~ and P4 > ct and P5 > oO, then declare model Z.
R
e
f
e
r
e
n
c
e
s
Gilbert, R.O.: 1987, Statistical Methods for Environmental Pollution Monitoring, Van Nostrand Reinhold, New York. Kehew, A.E. and Passero, R.N.: 1990, 'pH and Redox Buffering Mechanisms in a Glacial Drift Aquifer Contaminated by Landfill Leachate', Ground-water 28, 728-737. U.S. Environmental Protection Agency: 1989, 'Final Remedial Investigation Report for West KL Avenue Landfill - Kalamazoo, Michigan - May, 1989 - Emergency and Remedial Response Branch, Region V, 230 South Dearborn Street, Chicago, Illinois, 60604.
