Network Design Factors For Assessing Temporal Variability In Groundwater Quality

600J89022
NETWORK DESIGN FACTORS FOR ASSESSING
TEMPORAL VARIABILITY IN GROUND-WATER QUALITY
MICHAEL J. BARCELONA,«A DENNIS P. LETTENMAIER,** and MICHAEL R.
SCHOCK,*
* Illinois State Water Survey, Aquatic Chemistry Section, 2204 Griffith Drive, Champaign,
IL 61820, U.S.A.
** University of Washington, Department of Civil Engineering, 164 Wilcox Hall, FX-10, Seattle,
WA 98195, U.S.A.
(Received August 1988)

Abstract. Benchmark major ions and nutrients data were collected biweekly for about two years at 12
wells at two sites in a shallow sand and gravel aquifer in west-central Illinois. The purpose of the study
was to explore the time series properties of ground-water quality data collected at a relatively high sampling
frequency. A secondary purpose was to determine the relative magnitudes of natural and sampling-related
sources of variance in ground-water quality time series. The absence of this kind of information has
severely hindered the design of ground-water sampling programs in the past.
An autocorrelation analysis showed that the median sampling frequency for which the predicted ratio
of effective independent sample size to total sample size was 0.5 (50% sampling redundancy) ranged from
6 to 14 samples per year. For a predicted ratio of effective independent sample size to total sample size
of 0.9 (10% sampling redundancy) the sampling frequency ranged from 3 to 6 samples per year. This
suggests that, for the wells sampled, sampling frequencies much higher than monthly can result in
considerable loss of information, and may not be cost effective. Care was taken in the design of the field
and laboratory sampling protocol to minimize the effects of measurement error. The data analysis
confirmed that this goal was accomplished. In most cases considerably less than five percent of the total
variability could be attributed to sampling and analytical error. Because of the relatively short duration
of the study (42 biweekly sampling occasions at most wells) it was not possible to identify the magnitude
of seasonal variations reliably.
Notice

Although the research described in this article has been supported wholly or in part
by the United States Environmental Protection Agency through cooperative agree-
ment CR812165-02 to the Illinois State Water Survey, it has not been subjected to
Agency review and therefore does not necessarily reflect the views of the Agency and
no official endorsement should be inferred. Mention of trade names or commercial
products does not constitute endorsement or recommendation for use.

1. Introduction

Ground-water quality monitoring networks are designed for a number of purposes,
including ambient resource studies, contaminant detection and assessment, contami-
nant source evaluation, litigation and research investigations. The effective design
of virtually any such network depends on knowledge of the hydrogeologic system
A = author to whom correspondence should be addressed.

Environmental Monitoring and Assessment 12: 149-179, 1989.
© 1989 Kluwer Academic Publishers. Printed in the Netherlands.

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150                       MICHAEL J. BARCELONA ET AL.

of interest, the presumed contaminants or water  quality indicators as well as the
statistical characteristics of the  data being collected.  Regardless of the network
objectives, the interpretation of the data inevitably involves distinguishing a 'signal'
from background 'noise* or natural variability.
  The design of an optimal sampling network requires that the relative contributions
of different sources of variability be known. In practice, of course, this is impossible.
Various authors (e.g., Todd et al.,  1976;  Sanders et al., 1983; Moss et al., 1978;
Liggett, 1984,  1985;  Gillham et  al., 1983) have suggested that the need for infor-
mation about relative sources of variability for sampling design can be accomplished
by supplementing background information with preliminary sampling results (e.g.,
pilot studies). In theory, this information could be used to refine the network design
progressively.  In many  cases,  however, there are insufficient background data to
accomplish a reasonable initial design. So-called literature values that might be used
for preliminary  sampling design are virtually nonexistent,  especially for the time
series properties of ground-water quality that are necessary for long-term sampling
design, such as is required by  the Resource Conservation and  Recovery Act,  1976
(RCRA)  and the Comprehensive Environmental Response, Compensation, and
Liability  Act,  1980 (CERCLA) regulations.
  Variability in  the time series of ground-water chemical concentrations may arise
due to  'natural'  causes,  physical-chemical  transport properties or sampling-related
variables. Examples of natural causes are inhomogenous spatial distributions of the
constituents superimposed on the local and regional ground-water flow field, tem-
poral variability in recharge, and inhomogeneities in aquifer properties (e.g., trans-
missivities). Physical-chemical transport properties may include dispersivities, sorp-
tive interactions or chemical reactions. Sampling-related variables are well design,
sampling  devices,  and  field sampling and laboratory  analysis protocols. Other
sources of temporal  variability in water-quality data which are often attributed to
natural effects include  hydrologic  transience,  the  time and  space variations in
contaminant source,  strength and composition, and the interactions between reactive
chemical, biochemical and mineral constituents in recharge or flowing ground water.
Our understanding of the interdependence of hydrologic, biological and chemical
processes in the  subsurface is limited. However, it is not necessary (or  possible) to
understand the relationship among  these processes  fully in order to design useful
monitoring programs. An alternate approach, which should be adequate for sam-
pling design purposes, is to treat most of  the physical-chemical processes as black
boxes,  and to  base the  sampling design on the statistical properties (e.g., relative
sources of variability) of the black boxes.
  In this view, a particular set of data is  regarded  as simply  one realization of a
stochastic process, which includes both determinate (i.e., systematic) and indetermi-
nate (i.e., random) error. Indeterminate error is the imprecision or irreproducibility
of a particular observation. In statistical terms it can be characterized by the variance
of the  observation.  Indeterminate error can be characterized by the  variance of
replicate  determinations. Determinate error is the inaccuracy  or bias between the

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              ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY            151

observed and the 'true value', if known. In practice, determinate errors can only be
estimated and controlled by careful quality assurance/quality control measures. In
some cases, determinate errors, or biases, which might otherwise adversely affect the
decision process, can be transformed to random errors through a process of randomi-
zation in the sampling process. For instance, if it is known that a certain instrument
is susceptible to 'drift' in time, then it may be advisable to randomize the sequencing
of sample processing. Some determinate errors are unavoidable; for instance, distur-
bance of the subsurface is inevitable in  ground-water quality work. Identifying and
controlling these design-related errors have been the  focus of much of our recent
research (Barcelona et al., 1983, 1985, 1986; Barcelona and  Gibb, 1986).
  Statistical measures of  short-term temporal variability include: (1) Seasonality,
which is the tendency of some variables (for instance, near-surface hydraulic heads
and/or  temperatures)  to change systematically throughout the year; (2) Short-term
trends (e.g., consequences of anthropogenic contaminant sources, spills or pumping
effects); (3) Serial  correlation, which, if positive, is the tendency for large obser-
vations  to follow large observations and small observations to follow small obser-
vations. The reverse is true for negative correlation. However, this is virtually never
seen in  water quality time series. Long-term trends in data, on the other hand,  are
variations that occur over periods much longer than one hydrologic year (Porter and
Trautmann, 1984). This categorization  of temporal effects is  somewhat artificial in
that the combination  of seasonal, short-term trends, and serial dependence may
result in characteristics that cannot be differentiated quantitatively from long-term
trends (see, for example, Lettenmaier and  Burges,  1978).  In  this  respect, it is
important to recognize that the identification of short- or long-term trends in water
quality  is conditional on some knowledge of the proximity of the sampling point to
the location and time of chemical release, as well as the statistical characteristics of
ground-water quality variables. Water quality data which are not normally distribut-
ed pose particular  challenges to statistical trend detection. A recent review by van
Belle and Hughes (1984) describes some of the difficulties and recommends nonpar-
ametric tests for water quality trends.
  Statistical measures of  temporal variability in ground-water  quality have been
reviewed recently by Groeneveld and Duval (1985). In addition, Loftis et al. (1986),
Montgomery et al. (1987) and Harris et al. (1987) cite examples of both short- and
long-term temporal variability in water quality time series.  Earlier reviews by Porter
and Trautman (1984)  and Colchin  et  al. (1978)  take a statistical  approach to
ground-water quality assessment as well. Loftis et al. (1986) note in their review that
few long-term observation series exist at sufficiently high sampling frequency (i.e.,
more frequent than quarterly) to distinguish seasonal effects from serial dependence
or autocorrelation. Most water quality variables are positively skewed (nonnormal),
hence commonly used  parametric tests of significance to compare means or identify
trends may not be appropriate (Montgomery et al.,  1987; Helsel and Hirsch, 1988).
Transformations of variables such as logarithms are widely used to produce approxi-
mately normally distributed variates for hydrologic data.

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152                        MICHAEL J. BARCELONA ET AL.

  Transformation is difficult and often unsuccessful for water quality data which
may exhibit outliers  (infrequent values that lie far outside the range of the data). The
absence of benchmark ground-water quality observation series at high sampling
frequency (i.e., monthly or biweekly) for time periods in excess of one year has made
the determination of optimal sampling frequencies for ground-water quality moni-
toring difficult or impossible. Such data  may also prove useful for the testing of
statistical methods for trend analysis and for evaluation of background water quality
conditions (Harris et al., 1987).
  The primary purposes of this study were to assess the relative contributions of
variability and to identify methods to optimize sampling frequency within routine
monitoring network designs. The study design controlled sampling and analytical
variability to minimum values through a thorough  quality assurance and  quality
control program. The effects of hydrologic transience were minimized in the design
of the study by selection of wells drawing from water-table aquifers in both a pristine
environment and at  a site under the influence of a steady source of contamination.
The choice of sites was expected to enable the isolation of the effect of network design
variables from those due to natural or contaminant-related sources.  Shallow water-
table aquifers can be expected to show the greatest natural variability which enhances
the ability to distinguish between  natural  and sampling variability.  Further, many
sites at  which contamination problems exist affect or potentially  affect shallow
aquifers. This makes exploration of the statistical properties of water table aquifers
especially relevant.
                           2.  Experimental Design

2.1.  SITE DESCRIPTION
Two sites were selected on the eastern flank of the Illinois River Valley in the Havana
lowlands area of western Illinois. The coarse sand-and-gravel, unconfined aquifer
in the region has been described previously (Walker et al., 1965; Naymik and Sievers,
1983, 1985).
  The uncontaminated site is located in the Sand Ridge State Forest which is in a
pristine condition far removed from any sources of contamination. The area consists
of a mixed  hardwood and coniferous forest with prairie vegetation growing in a 20
to 30 foot (6-10 m) sequence of fine wind-blown sand. The fine dune sand overlies
a 90 to 120  foot (30-40 m) sequence of coarse sand and gravel terrace material. The
regional ground-water flow has a very stable directional component toward the river
and  is influenced by a production well field serving a state fish  hatchery.  Three
two-inch (five cm) o.d. polytetrafluoroethylene (PTFE-Teflon®, DuPont) monitor-
ing wells with five-foot screens were constructed at depths of 35, 50 and 65 feet (11,
15 and 21 m) by hollow-stem auger techniques in October of 1984. An additional
well was completed at 105 feet (32 m) in September of 1985.  The wells were  all
equipped with dedicated PTFE positive displacement bladder pumps (Well Wizard®,

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ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY
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QED Env. Systems, Ann Arbor, MI) with PTFE air and ground-water transfer lines
(Barcelona et al., 1986). The monitoring well nest was supplemented by an array of
shallow piezometers to monitor hydrologic conditions during the study.
The contaminated site is located on an industrial property in Beardstown, Illinois.
The site is in the southern lobe of the shallow unconfined aquifer in the Havana
lowlands adjacent to an anaerobic treatment impoundment for meat processing
wastes. After a preliminary hydrogeochemical survey, PTFE sampling wells were
constructed similarly to those at Site 1 at locations upgradient and downgradient
from the impoundments during October of 1985. The upgradient nest, consisting of
18 ft. (5.5 m) and 23 ft. (-7.0 m), two-inch (five-cm) o.d. PTFE monitoring wells
with five-foot screens, was located about 50 ft. (16 m) upgradient from the impound-
ment. Downgradient wells were located — 50 ft (16 m) from the impoundment at a
depth of 33 ft. (10 m) and in a nest approximately 200 ft. (-60 m) further down-
gradient at depths of 25, 30 and 35 feet (7.5, 9 and 10.5 m). The installation at
Beardstown was also supplemented with a number of piezometers for water level
measurements. The physical characteristics of the two sites are summarized in
Table I with the general condition of ground-water quality denoted in the left
margin. The four nested wells (i.e., wells 1, 2, 3 and 4) in the Sand Ridge State Forest
provide a vertical sequence to observe water quality variability with depth in a pristine
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ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY
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environment. The other sampling points include upgradient (i.e., wells 5 and 6) and
downgradient wells (i.e., wells 13, 8, 9, 10, 11, 12) along the general ground-water
flow path beneath the anaerobic impoundment at the contaminated site. The latter
two groups of wells are illustrated in plan view in Figure 1 which also shows the
location of the piezometers for water level measurements.

2.2. SAMPLING
From March 1986 through the fall of 1987, sampling was conducted on a biweekly
basis at both sites for the range of major ionic, water quality, and geochemical
parameters shown in Table II. These parameters were supplemented by determi-
nations of methane, ferrous iron and sulfide to provide additional geochemical
information as well as for the other potential network design purposes noted in the
table. Water level measurements were made in all sampling wells in addition to the
numerous piezometers at each site on each sampling date. The wells were purged at
rates of 1 to 1.5 liter• min~', removing an average of ~ 5 well volumes until purging
indicator parameters stabilized prior to sampling. Stabilization was noted when the
pH, Eh and conductivity values changed less than 0.05 pH units, ±10rnv or
llOjiS-cm"1, respectively over successive well volumes (Garske and Schock,
1986). Samples for volatile organic compounds, TOC, and TOX were collected at
a flow rate of -100 mL-min"1, while other samples were collected at flow rates
of - 1 L-min~'. In-line filtration (0.4 nm Nucleopore®), relying on pump pressure,
was used for samples collected for determinations of trace metal and dissolved
inorganic species. The samples contacted only PTFE tubing and stainless steel
(fittings and filtration apparatus) prior to collection and preservation in appropriate
vessels. Measurements of the purging parameters (i.e., pH, Eh, and conductivity)
as well as temperature, total alkalinity, Winkler-titration and electrometric-probe
dissolved oxygen determinations, were made according to methods described prev-
iously (Barcelona et al., 1985). Sampling operations were conducted from a specially
outfitted sampling van equipped with a generator, refrigerator, air compressor for
bladder pump drive gas, and adequate bench space for maintaining the integrity of
the water samples and conducting preservation or analytical procedures. Appropriate
field blanks, standards and duplicate samples were included for each day of sampling
to insure data quality control. At least one sample from each site on each sampling
date was selected at random for processing as a duplicate.

2.3. ANALYSIS
Analytical procedures approved by the USEPA (1980) were used for most of the
ionic, water quality and geochemical parameters. Total dissolved metals were deter-
mined by the single-solution modification of the USEPA atomic absorption spectro-
photometry procedure developed by Smith et al. (1983). Sulfate determinations in
the contaminated water samples from the downgradient Beardstown wells were done
by potentiometric titration with Pb(NO3)2 after cation exchange, La(NO3)3 addition
to remove phosphate, and adjustment of ionic strength and pH. Analytical determi-
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ASSESSING TEMPORAL VARIABILITY iN GROUND-WATER QUALITY 157

nations were performed in duplicate for all parameters except for methane, sulfide
and the field electrometric determinations of pH, dissolved oxygen and temperature.
Eh values were recorded with two platinum -Ag/AgCl reference combination
electrodes calibrated each day and at each site relative to Zobell's solution (1946)
at the temperature of measurement.
3. Results and Discussion

3.1. WATER QUALITY COMPOSITION
It is useful to have an appreciation for the composition of the ground-water at the
two sites. Average chemical constituent concentrations for samples from selected
wells over the sampling period of the wells are shown in Table III. With the exception
of sodium, chloride, pH and alkalinity the major ionic composition of the ground-
water samples was similar. Comparison of the results for wells # 1 and #4 (i.e., the
shallowest and deepest wells, respectively, at the uncontaminated site) showed the
difference between fully oxidized and suboxic subsurface redox conditions (Barcel-
ona et al., 1989). There was a very strong gradient of oxygen concentration and redox
potential with depth in this unconfined sand and gravel aquifer, and the average
concentrations of ferrous iron mirror these changes. A chemical gradient in calcium
carbonate solubility from oversaturation towards equilibrium with increased depth
was also evident. These chemical gradients as well as the hydrologic gradient and
flow direction were very stable during the study, although regional water levels have
dropped at a rate of -1.2 ft (0.37 m) per year over this period. The steady rate of
water level decline has been observed since 1982 due to the well-field operations of
the fish hatchery downgradient from Site 1.
The results for the ground-water samples from the contaminated site clearly
showed the marked difference one would expect between locations upgradient and
downgradient from a leaking anaerobic treatment impoundment. The influent to the
treatment impoundment may be characterized as an organic-rich aqueous waste
stream with - 0.1 % dry volatile solids content. The effluent from the impoundments
reflects the products of anaerobic degradation processes, since it contains high levels
of alkalinity, methane, ammonia, total organic carbon and nonvolatile dissolved
solids. Ground-water flow rate and direction did not vary significantly from that
shown in Figure 1 during the study period. Dissolved oxygen levels at both locations
at the contaminated site (Table III) were consistently at or near the detection limit
for oxygen electrode measurements and below the corresponding limit for iodometric
titration by the Winkler method. Ground-water quality conditions were markedly
changed at downgradient locations by the leakage of leachate from the anaerobic
impoundment. The downgradient ground-water samples were generally much higher
in the major components of the impoundment effluent; dissolved solids, total
organic carbon, methane, alkalinity, ammonia, sulfide, iron, chloride, sodium and
potassium than were samples from upgradient positions. Time-series plots for the
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MICHAEL J. BARCELONA ET AL.

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ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY 159

five preliminary and thirty-nine sequential biweekly runs are shown in Figure 2 for
well-head temperature, total organic carbon, ferrous iron and sulfide for wells # 1
through #4 at the Sand Ridge site. Corresponding plots for the wells along the flow
path at the contaminated site are shown in Figure 3. There were no obvious temporal
trends for these constituents at the pristine Sand Ridge site (Figure 2).
The well-head temperature measurements (Figure 3a) for the upgradient wells
(i.e., #5 and #6) at the contaminated site, however, show evidence of periodic
variability. The trends were not directly related to known periods of recharge. The
same relative hydraulic head differences between wells 6, 13 and 10 were maintained
throughout the study. The temperatures from the downgradient wells did not show
periodic variability presumably due to the 5 to 8 °C temperature increase down-
gradient which was a consequence of high microbial activity in the leachate-impacted
ground water. The remaining portions of Figure 3 contain similar time series for a
major component of the leachate, TOC (3b) and indicators of geochemical con-
ditions, ferrous iron (3c) and sulfide (3d) for the wells at the contaminated site. The
ferrous iron series for well #6 upgradient reflects some periodic variability which
precedes the apparent maxima in temperature noted in 3a. It should be noted that
the major specific constituents in the contaminated ground water are inorganic
species and contaminant indicators or surrogates like TOC. Levels of volatile
halocarbons or other purgeable contaminants were observed to be below 1 j/g-L"1
and these determinations were stopped early in the study period.
The major waste constituents observed at the contaminated site are common
components of landfill leachates (Zenone et al., 1975; USEPA, 1977) coal gasifi-
cation wastes (Humenick and Mattox, 1988), sewage and septic waste ponds or
disposal operations (USEPA, 1977; Kehew et al., 1983), and bear some similarity
to the soluble constituents of livestock feedlot waste streams (USEPA, 1977). The
results of the present study therefore have relevance to many subsurface hydrogeo-
chemical situations.

3.2. DATA QUALITY
During the course of the study more than 55 000 analytical determinations were made
on blanks, standards and samples. The final dataset was 96% complete, that is, a
recovery of 96% of the maximum possible number of samples and subsequent
analytical determinations were successfully completed. Outliers were screened suc-
cessively at ± 3 and ± 2 standard deviations from the mean levels. In most cases,
this screening revealed apparent errors in calculations, calibration or data entry
which were corrected prior to data analysis. For all wells and constituents, the
maximum number of samples which were identified as possible outliers and for which
no documented error was identified was four percent of the total. No adjustment
was made to apparent outliers for which no documented error could be identified.
It should be noted that very few (<5%) of the chemical constituent results for any
of the wells showed any clear tendency towards normality judging from the results
of the Shapiro-Wilk W statistic test (1965).
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Analyses were performed on the Quality Assurance/Quality Control data to
determine if there was evidence of temporal variability in the blanks and standards
or field standard recoveries and to determine if there was a concentration-related
dependence in the accuracy or precision of these datasets. A time series was
constructed for the field and laboratory QA/QC samples (i.e., field and laboratory
standards and blanks). Missing values were removed to create a complete series of
reduced sample size. A linear regression was then fit to the series, with time as the
independent variable. The significance of the slope (time coefficient) was tested at
the 0.05 significance level. No cases were found in which the slope was significant.
This result in itself was somewhat surprising, since the expected number of rejections
of the null hypothesis (that the slope is zero) is 0.05 times the number of analyses,
or approximately seven. This result may be explained by the discrete nature of some
of the data (especially blanks) and perhaps by nonnormality or outliers, all of which
may make the true significance level less than the nominal value of 0.05, and hence
reduce the number of rejections. The test should be powerful enough, however, to
detect large time trends in the laboratory and field procedures, and the absence of
significant trends may be taken as evidence that there was no significant temporal
variability in the blank and standards which might bias the sample dataset over time.
The procedure outlined above was also applied to the sample percent recovery data
for three groupings of the wells: (1) the uncontaminated Sand Ridge site (wells
# l-#4), (2) the upgradient wells at the Beardstown contaminated site (#5& #6)
and (3) the downgradient wells at this site (wells # 8-# 13). Time series were formed
for each of two sets of analytical determinations for each chemical for each group
of wells. The first reflects laboratory error only (i.e., two replicate determinations
were made on samples spiked within the laboratory) while the second incorporates
both laboratory and field error (two replicate determinations were performed on
actual samples). Separate time series also were constructed from the mean, median,
and standard deviation of the percent recovery data. No significant trends were
found for any of the chemical constituents for either field or laboratory recoveries
in the Sand Ridge wells. Significant increasing recovery trends with time were
observed for the mean, median, and standard deviation of the percent recoveries of
NH3 (laboratory and field), SO4 = (field only), Fe2+ (laboratory only) and MnT
(laboratory only) for the Beardstown wells. The apparent recovery trends were due
largely to difficulties encountered in the five preliminary sampling runs of the study
between November 1985 and March of 1986 when the biweekly sampling began.
When these early samples were eliminated, the time trends were no longer statistically
significant. As in the blank and standards analysis, the number of significant trends
was less than would be expected based on chance.
The average overall sampling and analytical accuracy and precision values for the
chemical constituents are shown in Table IV. The levels of overall accuracy and
precision routinely achieved during the project were routinely within acceptable
limits for the laboratory analytical methods (USEPA, 1980). Exceptions to this level
of performance were noted for constituents which were consistently present at or near
-------
ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY 163

TABLE IV

Average overall accuracy and precision for the chemical constituents determined in the study
Param.
NH3
T-PO4
Fe*2
NO2-
S =
NOj-
SiO2
o-PO4
cr
so4-
Ca
Mg
Na
K
Fe
Mn

Ace.
95.90
99.64
96.07
82.17
NA
100.35
99.47
103.44
105.78
95.77
98.36
99.15
101.69
97.85
99.22
101.04
Overall
Prec.
23.49
8.60
18.80
36.29
NA
10.27
5.03
15.38
32.59
21.85
3.88
8.70
12.17
5.17
5.80
6.46
Sand Ridge
Ace.
91.99
100.95
NA*
81.07
NA
98.85
100.21
106.54
112.01
94.73
98.65
99.90
103.51
99.10
100.34
101.28
Prec.
29.80
9.28
NA
35.00
NA
7.82
2.97
20.77
46.55
6.58
3.76
10.72
16.16
5.15
7.20
8.17
Beardstown
Ace.
100.09
98.24
96.07
83.27
NA
101.97
98.71
100.12
100.18
97.24
98.07
98.42
99.95
96.63
98.04
100.79
Prec.
12.54
7.56
18.80
37.50
NA
12.17
6.41
2.32
1.52
33.07
3.98
6.03
5.87
4.89
3.46
3.92
NA indicates that the number of observations for which accuracy and precision could be determined
was less than five, principally due to a larger number of below detection limit results.
analytical detection limits (e.g., Cl~, Fe(II), S=). The QA/QC data analyses
demonstrate that the sampling and analytical protocols employed in the study were
in control.

3.3. ESTIMATION OF SOURCES OF VARIATION
In order to insure that monitoring resources are optimally allocated, it is important
to identify the sources of natural (i.e., spatial and temporal) and sampling and
analytical variance.
The general statistical approach to reducing the effect of any source of variation
is to randomize and collect replicates. Therefore, the effects of natural variability
can only be reduced by increasing the sample size (that is, either the sampling
frequency or the length of the data collection series). Increasing the sample size has
the effect of reducing the component of the variance of, for instance, the long-term
mean attributable to field and lab errors as well. In addition, if the component of
the total variance due to laboratory and/or field errors is large, it can be reduced
by taking more than one field or laboratory replicate at each sampling occasion.
Whether or not collection of laboratory or field replicates is cost effective depends
on the fraction of the total variance attributable to each source. The conceptual
model used to estimate sources of variation was:
-------
164 MICHAEL J. BARCELONA ET AL.

where
a2, = total variance
crj; = natural variance
a} = laboratory analytical
a} = field sampling variance

Generally, the natural variations in water quality time series are of interest. For
instance, the difference between the time series of a given contaminant at a down-
gradient and an upgradient well may give an indication of whether contaminant
release has occurred. However, the difference series is inevitably corrupted by errors
in the field data collection and laboratory analysis procedures, both of which
introduce what may be considered 'noise' into the time series. Each of these noise
processes has a variance, and the total variance is the sum of the three variance terms.
This model assumes that the three sources of variation are statistically independent,
which is a reasonable assumption because the sources are physically independent.
A possible exception is that the magnitude of the field and laboratory errors may
depend on the true value of the chemical concentration. This consideration is
addressed below.
The sources of variation were estimated as follows. First, the laboratory analytical
variance was estimated by taking the difference of the laboratory calibration stan-
dards series, since each standard was subjected to two replicate analytical determi-
nations. Each difference was normalized by dividing it by the (known) true value
of the standard. Then, a normalized standard deviation was computed using the
inner-quartile differences (i.e., 75th minus 25th percentiles) multiplied by an adjust-
ment factor appropriate to the normal distribution. The use of the adjustment factor
for the normal distribution does not imply that the distributions were in fact normal
(most were not), it is only a convenience. Next, a similar procedure was applied to
the field replicate series. Because the field replicates include the effect of laboratory
analytical variability as well, the analysis of the field replicates provided estimates
of the sum of the normalized laboratory and field sampling variance. The normalized
field sampling variance was then estimated by subtraction. This subtraction oc-
casionally gave negative values, which were reported as 'NA'. An alternative proce-
dure would be to simply set these values (i.e., the normalized field variance) to zero.
Finally, the normalized total variance was estimated from the entire time series at
each well, and for each chemical constituent where the normalization was by the
median for the given well. The normalized natural variance was then estimated by
subtraction.
The results are summarized in Table V for the three groups of wells. For almost
all of the groups, and for almost all of the chemical constituents, a high fraction
of the total variation was natural. This is consistent with the QA/QC data analyses,
which showed that the data collection errors were generally quite small. The entries
in the table have been separated into water quality parameters and chemical parame-
ters of geochemical interest. The results confirm that if careful sampling and
-------
ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY 165

analytical protocols are used, the natural variability in the major ion chemistry of
the system can be identified. For TOC and TOX it is clear that 'natural' sources of
variability are greater than the combined lab and field variance. However, the level
of overall variability in TOX results was quite large in comparison to the mean values
for each well. The significance of these determinations at the microgram per liter
level is doubtful.
A similar attempt to estimate sources of variations in ground-water quality data
was performed by Summers et al. (1985). They analyzed data from two sources on
related ground-water samples collected in the vicinity of power plant waste disposal
impoundments. They reported that, in general, combined sampling and analytical
variability was less than the natural variability. Summers et al. (1985) noted that
TABLE V
Percentage of variance attributable to laboratory error, field error, and natural variability by chemical
and site
Type of Sand Ridge
lab field nat
Beardstown (upgradient) Beardstown (downgradient)
lab field nat lab field nat
Water quality
N03- 0.0 00.0 100.0 0.1 NA« 99.9 0.2 NA 99.8
SO4 = 0.0 0.0 100.0 0.2 NA 99.8 1.4 0.1 98.6
SiO2 0.0 NA 100.0 0.0 20.0 80.0 0.0 6.8 93.2
o-PO4- 1.2 1.2 97.6 0.0 0.0 100.0 0.0 0.0 100.0
T-PO4- 0.0 NA 100.0 2.8 NA 97.8 0.9 NA 99.1
Cr 7.2 NA 92.8 0.0 3.3 96.1 0.0 17.2 82.8
Ca 0.0 45.7 54.3 0.0 2.3 97.7 0.0 3.6 96.4
Mg 0.0 20.0 80.0 0.0 2.2 97.8 0.0 2.8 97.2
Na 0.0 NA 100.0 0.0 0.3 99.7 0.0 7.1 92.9
K 0.0 NA 100.0 33.9 NA 66.1 87.1 NA 12.9

Geochmical
NH,
NO2-
S =
Fe*2
F«T
MnT
0.0
NA
NA
NA
0.0
0.0
Contaminant
indicator
TOC
TOX

15.4
0.0
0.0
NA
NA
NA
NA
NA
lab +

100.0
NA
NA
NA
100.0
100.0
field"

84.6
100.0
0.0
0.1
NA
0.0
0.0
0.0

29.9
12.5
0.0
NA
NA
0.1
0.0
40.1
lab -t-

100.0
99.9
NA
99.9
100.0
59.9
field

70.1
87.5
0.0
0.3
NA
0.0
0.0
0.0

40.6
24.6
0.0
NA
NA
5.9
NA
73.6
lab +

100.0
99.7
NA
94.1
100.0
26.4
field

59.5
75.4
* NA indicated that the number of observations on which the estimated variance was based was less
than 5, or the estimated variance was negative.
*• True field spiked standards no available for these constituents demanding combined estimates of
laboratory and field variability.
-------
166 MICHAEL J. BARCELONA ET AL.

combined sampling and analytical variability was usually less than -15% of the total
variability which is consistent with the results of the present study. They did,
however, report exceptions in the cases of NO3~~, silicate and Zn where the combined
sampling and analytical variance exceeded 30% of the total variance. The potential
sensitivity of these constituents to well construction and sampling errors was not
discussed in their report.
The implication of the results of this study and that of Summers et al. (1985) is
that network design optimization efforts should focus primarily on the natural
variability. The use of field and laboratory replication for purposes other than
QA/QC will be difficult to justify as long as the sampling and analytical protocols
are in control. This conclusion must be qualified, however. The chemical constituents
present at appreciable concentrations (i.e., mg-L"1) at either site are the major
cations and anions and general water quality indicators. The analytical and sampling
variances for trace organic contaminants would be expected to be higher and their
analytical recoveries are frequently found to be a function of concentration. In this
case the field and laboratory variations may not be independent, which would violate
a basic assumption in this model. Nonetheless, particular care should be given to
establishing acceptable performance levels for the accuracy and precision of field and
laboratory operations. The field and analytical data were collected with very careful
QA/QC in the course of this research project. It is unlikely that combinations of
different laboratories and field sampling crews would be able to achieve and maintain >
such low levels of error. Further, the sites were picked specifically to provide stable 3
hydrologic conditions of ground-water flow and direction as well as a steadily leaking <
source of contamination. The effect of these conditions would be to minimize natural
variability which makes the degree of sampling and analytical control all the more
critical.

3.4. TEMPORAL VARIATIONS IN GROUND-WATER QUALITY
There are numerous examples of both short- and long-term variability in ground-wat-
er quality in the literature. Recent reviews by Loftis et al. (1986) and Montgomery
et al. (1987) pointed out the need for very careful selection of statistical methods and
for qualified interpretations of existing datasets. The well-documented cases of both
short- and long-term temporal variability in ground-water quality have been tabulat-
ed in Tables VI and VII, respectively. These observations cover temporal variability
caused by agricultural and nonagricultural sources in high-volume water supply
production wells, observation, monitoring, and shallow private wells from a variety
of hydrogeologic settings. The concentration variations are noted mainly as multiples
above and below an arbitrary baseline or background concentration. In a few
instances, where the trends were clearly very long-term or cyclic (i.e., due to alternate
pumping and nonpumping conditions), the variations have been entered in concen-
tration units.
Although the details of purging, sampling, filtration/preservation, and analysis
were frequently lacking in the reports, very substantial variability has been docu-
-------
ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY
167

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ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY 169

mented over time-frames ranging from minutes to decades. Significant short-term
temporal concentration variability has been observed in low yield wells (i.e., monitor-
ing and observation wells) largely resulting from purging effects (Wilson and Rouse,
1983; Barcelona and Helfrich, 1986). Similar variations of one to ten times the initial
or background concentrations have been noted in samples from high-volume pro-
duction wells due to pumping rate, initial pumping after periods of inactivity or due
to cone of depression development (Schmidt, 1977; Eccles et al., 1977; Colchin et
al., 1978; Keely and Wolf, 1983; McReynolds, 1986). The magnitude of short-term
concentration variations noted in the literature strongly suggests that the analysis of
ambient resource water quality datasets must be undertaken with careful attention
to the pumping procedures used in purging and sample collection. This observation
is particularly critical in relatively sparse datasets where annual 'mean* concen-
trations may be determined from programs with low sampling frequency (i.e., less
frequently than quarterly).
Similar cautions in interpretations of long-term datasets apply in the analysis of
trends at varying or unequal sampling frequencies due to the relatively short duration
of the records in comparison to the length of apparent annual to multi-year
variations. It was expected that the high sampling frequency (i.e., biweekly) and fp>
consistent purging and sampling procedures employed in this study would permit the
identification of optimal frequencies for monitoring water quality variations under
stable hydrologic and contaminant source conditions. For this reason, field sampling
and laboratory analytical protocols were carefully controlled. |

3.5. SAMPLING FREQUENCY *
The primary purpose of the project was to investigate the optimal sampling frequency —
for ground-water quality monitoring. Strictly speaking, there is no required or
minimum sampling frequency. However, there is a relationship between the infor-
mation content of the data and the sampling frequency. The term 'information' is
sometimes used loosely, but in a statistical context, it can be given a more precise
definition, depending on the use of the data. The most common definition of
information (e.g., in the Fisher sense) is in terms of the variance of the mean,
Var(;t) = a2//!, where x is the sample mean, n is the sample size, and a2 is the variance
of the data (Matalas and Langbein (1962)). The reciprocal of the variance of the mean
is a measure of the information content of the data. If the a2 is large, or the sample
size small, the information content is low. While this definition of information
applies to estimation of the mean, the power of trend detection (in space or time) -jfc
is related to the variance of the mean as well.
As noted in the previous section, the total variance is made up of the natural
variance and the variance attributable to the sample collection process (field sampling
and laboratory error). Most monitoring programs are intended to discriminate some
effect (e.g., the long-term mean in the case of baseline sampling, or the difference
in the mean between upgradient and downgradient wells in the case of RCRA
sampling) from the total variation in the time series. The effect of sample collection
-------
170 MICHAEL J. BARCELONA ET A.L.

variance might be reduced by replicate sampling. Although, the sample collection
variance made up such a small fraction of the total variance that this probably would
not be worthwhile for data similar to that described here. The effect of natural
variation can only be reduced by increasing the number of samples (increased
sampling frequency or length of sample collection). Increasing the number of
samples also reduces the effect of the sampling variance. Seemingly, the information
content of the data could be increased arbitrarily, since it depends linearly on the
sample size. In practice, though, the data are correlated in time (autocorrelated), and
the autocorrelation increases with the sampling frequency. When the data are
autocorrelated, the variance of the mean can be reexpressed as Var(x) = a2/nef,
where nef is an effective independent sample size, which depends on the autocorre-
lation (Bayley and Hammersley, 1946). The value of fle/is always less than n, the
actual sample size, if the autocorrelation is positive, as it usually is in practice. If
the model that describes the autocorrelation is the lag-one Markov process, nef
approaches an upper limit as the sampling frequency increases, regardless of how
large n becomes (Lettenmaier, 1976). Lettenmaier found that the lag-one process
provided a reasonable description of many water quality time series. It is often
difficult to extend the analysis of water quality data beyond lag-one because the
autocorrelation function becomes excessively noisy.
The ratio nej/n can be considered to be a measure of the loss of information due
to autocorrelation in the data. Although nef always increases with n for positive
autocorrelation, ne/may increase quite slowly if the autocorrelation is high. For this
reason, one of the analyses conducted was to estimate a model of the serial
dependence (i.e., autocorrelation) in the observed chemical series. The procedure
used was as follows: First, all missing values were removed, to form a series with
no missing values. This procedure is straightforward, but has the disadvantage that
the interval between observations is not constant (i.e., is greater than two weeks)
when there are missing observations. The effect of this approach, as compared to
a much more laborious procedure that would concurrently estimate the missing data
and the time series model (e.g., Lettenmaier, 1980) is to bias the autocorrelation
estimates down slightly. The practical effect is minimal so long as the number of
missing observations is small, which was usually the case for the chemical con-
stituents determined in this study.
Second, an outlier screening test was applied, as described in Section 3.2. Finally,
a lag one autoregressive (lag one Markov) model was fit to the data. Diagnostic
procedures described in Box and Jenkins (1970) were applied to check the model fit.
Specifically, the diagnostic checks used were Portmanteau's test and Anderson's test
applied to the estimated model residuals. The number of cases in which the diagnostic
tests were failed was only slightly larger than would be expected by chance. In most
of those cases that failed the diagnostic test, there was apparent strong seasonality
in the data, as described below. In all cases, the estimated lag one correlation was
retained, and averaged with the other estimates for the same chemical in the given
well group.
-------
ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY
171
Seasonality and long-term trends in the data presented a major complication in
the analysis. There are well-structured methods for handling seasonality in time
series, but none are applicable to the relatively short (i.e., in terms of total duration)
chemical time series that were available for analysis. The problem is that, to properly
estimate a seasonal model, a relatively large number of seasonal cycles (e.g., at least
10) are required; this corresponds to, say, ten years of data, which greatly exceeds
the length of the sampling horizon. Ignoring the seasonality tends to inflate the
estimate of the autocorrelation coefficient, as does the existence of trends in the data.
There is no completely satisfactory solution to this problem. Our approach was to
identify series with apparent strong seasonality or long-term trends subjectively.
TABLE VIII
Subjective estimate of strength of seasonality or trend in variables by location
Sand Ridge Beardstown Beardstown Number of
(1-4) (upgradient) (downgradient) violations
PH
Cond
Temp C
Temp W
Eh
Probe O2
Wink O2
Alk
NH3
NO, N
NO,NO2 N
HS-
SO4
SiO2
o-PO4
T-PO4
cr
Fcr*
Ca
Mg
Na
K
F
-------
172
MICHAEL J. BARCELONA ET AL.
(Seasonality in some variables, such as temperature, is apparent, and can be argued
from first principles.) Table VIII identifies those series for which there was apparent
strong seasonality, as well as the number of violations of the diagnostic checks for
each variable and well group. The maximum possible number of violations for each
variable was twice the number of wells in the group, since two tests were applied.
Subsequent results for series showing a high number of rejections, or for which there
was strong apparent seasonality or long-term trends, should be interpreted with
caution. However, these problems were not an issue for a large number of series.
By summarizing the results over well groups, and to a more limited extent, over
chemical constituents, it is possible to give a general picture of the sampling
frequency dependence of the effective independent sample size, which is relatively
unaffected by the peculiarities of individual variables or sites.
Table IX gives the average lag one correlation for each variable and well group,
ordered by the sum of the ranks over all well groups. Variables at the top of the list

TABLE IX
Ranking of average lag one correlation over all sites, from smallest to largest

NO2- N
Fe/
PH
s-
NH3
SiO2
MnT
Probe O2
T-PO4"
O-PO4-
Eh
NO3NO2-N
TOC
SO4=
Per
K
Ca
Mg
cr
Na
Alk
Ion balance
Temp C
VOC
Cond
TOX
Temp W
NVOC
Sand Ridge
(1-4)
0.27
0.01
0.51
0.16
0.29
0.37
0.51
0.41
0.06
0.10
0.46
0.75
0.46
0.59
0.21
0.31
0.45
0.49
0.19
0.47
0.73
0.73
0.54
0.54
0.80
0.80
0.66
0.66
Beardstown
(5-6)
0.42
0.86
0.47
0.36
0.82
0.76
0.47
0.66
0.20
0.19
0.60
0.35
0.60
0.53
0.90
0.89
0.92
0.91
0.%
0.95
0.69
0.92
0.92
0.92
0.94
0.94
0.97
0.97
Beardstown
(8-13)
0.37
0.56
0.20
0.67
0.26
0.24
0.20
0.44
0.86
0.91
0.60
0.42
0.60
0.52
0.66
0.71
0.66
0.65
0.75
0.65
0.76
0.79
0.79
0.79
0.75
0.75
0.78
0.78
Summed rank
17
18
25
26
28
28
28
30
32
33
34
36
37
39
40
46
50
50
54
56
62
69
69
70
73
74
76
77
Average (over
all three well
groups) (rho)
0.35
0.48
0.39
0.40
0.46
0.46
0.39
0.51
0.37
0.40
0.55
0.51
0.55
0.55
0.59
0.64
0.68
0.68
0.63
0.69
0.73
0.75
0.75
0.75
0.83
0.83
0.80
0.80
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ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY 173

tended to have the lowest autocorrelation, while variables at the bottom were most
highly autocorrelated. Also given is the average autocorrelation over all three well
groups. Autocorrelations tended to be stronger at the Beardstown wells than at Sand
Ridge, and were higher at the Beardstown upgradient wells than at the downgradient
wells. The latter effect may be due to randomness introduced by the release,
migration and transformation of the contaminants. It is of interest that the autocor-
relations for almost all variables, even those with no apparent trends or seasonality,
were quite high, suggesting that there was considerable redundancy in the data at
a biweekly sampling frequency.
To illustrate the effect of the autocorrelation on sampling frequency, we solved
for the sampling interval, in weeks, that would result in ratios nef/n=0.5, 0.8, and
0.9 using Equation 13 of Lettenmaier (1976). Alternatively, these can be interpreted
as relative losses of information due to autocorrelation in the data of 50, 20, and
10%. The results are given in Table X. At Sand Ridge, the implied loss of infor-
mation is about 50% for many variables at a weekly sampling frequency, 20 percent
for many variables at sampling intervals in the range of 4-8 weeks, and 10% for the
majority of variables at a sampling interval of 8 weeks of more. At the Beardstown
wells, the loss of information at high sampling frequencies was much greater. At the
upgradient wells, which had the highest autocorrelation, the inferred loss of infor-
mation of 50% occurred for several variables at a sampling interval of over 26 weeks.
Information loss of between 20 and 10% was inferred for some variables at sampling
intervals exceeding one year. This effect is particularly evident for Na"1", Cl~ and
well temperature (TEMPW) which showed a consistent increasing trend over the
study period.
The results of the study indicate that, for the major chemical constituents (i.e.,
water quality or contaminant indicator), quarterly sampling represents a good
starting point for a preliminary network design. This frequency, of course, must be
evaluated with respect to the purpose and time-frame over which the network will
be conducted. Under the conditions of this study, sampling four to six times per year
would provide an estimated information loss below 20% and minimize redundancy.
The results for reactive, geochemical constituents suggest that bimonthly sampling
frequency would be a good starting point if chemical reactivity and transformation
are of concern.
Caution must be exercised in interpretation of the results due to the effects of
seasonality and long-term trends. However, it should be clear that there is consider-
able redundancy in the data at the two-week sampling interval used, and that, at
similar sites and for most of the variables studied, operational sampling programs
would be inefficient at sampling frequencies in excess of bimonthly. The practical
implication of this is that, for many operational monitoring programs, a relatively
long time horizon (e.g. on the order of ten years) may be required to obtain adequate
information for decision-making purposes, given that high frequency sampling will
not yield much increase in information. It is important to emphasize that the
information from sampling depends on the effective independent sample size, not
-------
174 MICHAEL J. BARCELONA ET AL.

TABLE X

Sampling intervals in weeks for given ratio of effective to independent sample size, based on the estimated
lag one markov model

Sand Ridge
NO;' N
Fe;:
PH
s-
NHj
SiO2
MnT
Probe O2
T-PO4'
O-P
-------
ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY
175
TABLE X
(Continued)

K
Ca
Mg
ci-
Na
Alk
Ion balance
Temp C
VOC
Cond
TOX
Temp W
NVOC
Beardstown dovmgradient
NO2- N
Fe2*
PH
s-
NH,
SiO2
MnT
Probe O2
T-PO4-
O-PO4-
Eh
NO3NO2-N
TOC
SO4 =
Per
K
Ca
Mg
cr
Na
Alk
Ion balance
Temp C
VOC
Cond
TOX
Temp W
NVOC

0.5
19
26
23
53
42
6
6
26
26
35
35
71
71

3
4
2
6
2
2
2
3
15
23
5
3
5
4
6
7
6
5
8
5
8
8
10
10
8
8
9
9
n,f/n
0.8
38
53
47
107
85
12
12
53
53
71
71
143
143

5
8
3
11
4
4
3
6
29
47
9
6
9
7
11
13
11
11
16
11
16
16
19
19
16
16
18
18

.9
51
71
62
144
114
16
16
71
71
95
95
192
192

6
11
4
15
5
5
4
8
39
62
12
7
12
9
15
18
15
14
21
14
22
22
25
25
21
21
24
24
-------
176 MICHAEL J. BARCELONA ET AL.

just the ratio nef/n. Therefore, if the autocorrelation is large so that a relatively low
sampling frequency is necessary to avoid sampling redundancy, the total length of
the sampling period must be increased to achieve sufficient information return. Our
results cannot simply be interpreted to mean, for instance, that quarterly sampling
is adequate, unless that interpretation is couched in terms of the time horizon of the
sampling program.

4. Conclusions

For the data analyzed, the fraction of the total variance attributable to sampling error
was less than 10% for almost all constituents. These low sampling variance fractions
are attributable to consistent, detailed protocols for sampling and analysis employed
in connection with a strict QA/QC program. The sampling variance fractions
achieved in this study are probably near the lower limit of what can be expected in
practice. For trace organic compound determinations, the sampling variance
fractions would likely be much higher. For the relatively low sampling variance
fractions indicated, field and laboratory replication would likely not be cost effec-
tive, except as required for the QA/QC program.
Apparent levels of temporal variability in ground-water quality noted in the
literature are very sensitive to pumping rate and duration during well purging and
sample collection operations. These effects may be large compared to long-term
temporal variability attributable to 'natural' causes. Purging and pumping effects
on ground-water chemical results must be better understood and controlled to
properly focus on natural or contaminant source-related variability.
In agreement with the results of previous studies, distributions of all ground-water
quality variables were most often nonnormal (positively skewed). In addition, most
constituents were strongly autocorrelated at the biweekly sampling frequency.
Because of the relatively short length of the data collection program, it was difficult
to quantify seasonality or time-trends even under stable hydrologic and steady
contaminant source release conditions. The potential implications for the design of
source detection and contamination assessment monitoring systems may be serious.
Sampling at high frequencies for background conditions may entail considerable loss
of information due to redundancy. Depending on monitoring objectives, much longer
sampling periods may be required than are common at this time to achieve adequate
information for decision-making. A relatively long time data collection horizon of
the order of five to ten years may be necessary for temporally variable constituents
since high sampling frequencies may not yield significant increases in information.

Acknowledgements

The authors thank Joseph Karny, Edward Garske, Allen Wehrmann, Mark Sievers
and the analytical support group of the Aquatic Chemistry Section for their dedicated
effort to high quality field and laboratory data collection efforts. Greg George, Carl
-------
ASSESSING TEMPORAL VARIABILITY IN GROUND-WATER QUALITY 177

Lonnquist, Pam Beavers, the cooperation of the Illinois Department of Conser-
vation, and that of our industrial collaborators made critical aspects of the project
possible. The support of the staff of the USEPA Environmental Monitoring Systems
Laboratory - Las Vegas, NV, especially Jane Denne and Ann Pitchford is appreciat-
ed. The support of the Campus Research Board of the University of Illinois and
QED, Inc., Ann Arbor, MI, is gratefully acknowledged. Much of the statistical data
analysis was performed by Eric Wong, a graduate student in the Department of
Biostatistics, University of Washington.
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