vvEPA
Unitt'i) St;m;s
Environmental Protect ion
Agency
Environmental Monitoring
nnil Support L.ibnr.Hory
P O Box 15027
Las Vf-y.is NV 891 14
EPA 600 7 78 169
Augusl 1978
cf, lirui Development
Evaluating the
Sampling Frequencies
of Water Quality
Monitoring Networks
Interagency
Energy-Environment
Research
and Development
Program Report
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad categories
were established to facilitate further development and application of environmental
technology. Elimination of traditional grouping was consciously planned to foster
technology transfer and a maximum interface in related fields. The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the INTERAGENCY ENERGY—ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the effort
funded under the 17-agency Federal Energy/Environment Research and Development
Program. These studies relate to EPA'S mission to protect the public health and welfare
from adverse effects of pollutants associated with energy systems. The goal of the Pro-
gram is to assure the rapid development of domestic energy supplies in an environ-
mentally-compatible manner by providing the necessary environmental data and
control technology. Investigations include analyses of the transport of energy-related
pollutants and their health and ecological effects; assessments of, and development of,
control technologies for energy systems; and integrated assessments of a wide range
of energy-related environmental issues.
This document is available to the public through the National Technical Information
Service. Springfield, Virginia 22161
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EFA-600/7-78-169
August 1978
EVALUATING THE SAMPLING FREQUENCIES OF
WATER QUALITY MONITORING NETWORKS
by
Robert C. Ward
Agricultural and Chemical Engineering Department
Colorado State University
and
Knud Strange Nielsen
Data Analysis Section
Water Quality Institute
Horsholm, Denmark
Contract Number CB-6-99-2530-A
Project Officer
Donald B. Gilmore
Monitoring Systems Design and Analysis Staff
Monitoring Systems Research and Development Division
Environmental Monitoring and Support Laboratory
Las Vegas, Nevada 89114
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL MONITORING AND SUPPORT LABORATORY
LAS VEGAS, NEVADA 89114
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DISCLAIMER
This report has been reviewed by the Environmental Monitoring and
Support Laboratory — Las Vegas, Nevada, U.S. Environmental Protection
Agency, and approved for publication. Approval does not signify that
the contents necessarily reflect the views and policies of the U.S.
Environmental Protection Agency, nor does mention of trade names or
commerical products constitute endorsement or recommendation for use.
ii
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FOREWORD
Protection of the environment requires effective regulatory actions
which are based on sound technical and scientific information. This infor-
mation must include the quantitative description and linking of pollutant
sources, transport mechanisms, interactions, and resulting effects on man
and his environment. Because of the complexities involved, assessment of
specific pollutants in the environment requires a total systems approach
which transcends the media of air, water, and land. The Environmental
Monitoring and Support Laboratory—Las Vegas contributes to the formation
and enhancement of a sound monitoring data base for exposure assessment
through programs designed to:
o develop and optimize systems and strategies for
monitoring pollutants and their impact on the
environment
o demonstrate new monitoring systems and technologies
by applying them to fulfill special monitoring
needs of the Agency's operating programs.
This report covers a procedure for evaluating sampling frequencies of
established water quality monitoring networks. This report is intended
to assist monitoring systems managers to more efficiently distribute
resources between sampling sites and laboratory facilities in an effort to
achieve better data at a lower cost. For further information contact the
Monitoring Systems Research and Development Division at this Laboratory.
^K
&
George B. Morgan
Director
Environmental Monitoring and Support Laboratory
Las Vegas
iii
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PREFACE
There is a large number of general water-quality management agencies
in the United States that are functions of state and local governments. The
agencies routinely manage water quality within political boundaries. To
support such management, the agencies operate a wide variety of monitoring
programs. One type of water-quality monitoring common to most agencies is a
routine fixed-station network. The purpose of such networks has, in the
past, often been poorly defined, especially from a statistical viewpoint.
However, there currently are several efforts being made to clarify the goals
of this type of monitoring. This, in turn, is resulting in the need to
evaluate the design of the network, particularly the sampling frequencies.
The sampling frequency evaluation procedures presented in this report
utilize a number of simplifying assumptions and basic statistical methods.
Hopefully, employing such a straightforward, simple approach will facilitate
use of the evaluation procedures and, therefore, set the stage for wider
understanding and use of more sophisticated approaches that may be developed
at a later date. Practical application has been an overriding consideration
in development of the evaluation procedures.
iv
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CONTENTS
Page
Foreword ii:L
Preface iv
Acknowledgements v*
I. Introduction -1-
II. Conclusions ^
III. Recommendations ^
IV. Statistical Basis 5
V. Procedure 9
VI. Application 15
VII. Discussion 25
00
References ^°
29
Appendix A
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ACKNOWLEDGEMENTS
The authors wish to acknowledge the assistance of Mr. Dennis Anderson
of the Water Quality Control Division of the Colorado Department of Health,
and Mr. Dale Trippler of the Minnesota Pollution Control Agency. Their
comments and discussions provided valuable insight into the practical aspects
of this work.
vi
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I. INTRODUCTION
During the past 10 years, a large number of water-quality monitoring
programs have been established by local, state and federal water-quality
management agencies in response to the Water Pollution Control Act of 1965
(PL 89-234), the Water Pollution Control Act Amendments of 1972 (PL 92-500)
and the Safe Drinking Water Act of 1974 (PL 93-523).
The legal purpose of these monitoring efforts is, in general, simply to
"monitor" water quality; however, the efficient operation of a monitoring
program requires a detailed definition of "monitor." Since water-quality
monitoring by definition is a statistical sampling operation, it is highly
desirable that the monitoring purpose be carefully defined in terms of the
statistical precision and confidence sought and the eventual use of the
results.
In order to comply with the law's requirement to "monitor" water
quality, most management agencies selected, on the basis of the experience
of their personnel, sampling sites and relevant parameters to be measured.
The sampling frequency was, in general, determined by the capacity of the
laboratory and, in turn, the samples were equally divided among the stations.
Over the years, these monitoring systems have been revised and modified
to reflect more specific monitoring objectives. A recent study by the
Environmental Protection Agency's Standing Work Group on Water Monitoring
(1977) points out that routine fixed-station monitoring determines trends in
water quality while intensive surveys should be used to obtain enforcement
information. The recommendations of the study emphasize the need to shift
monitoring resources from routine fixed-station monitoring to intensive
surveys.
To ensure that such shifts occur with a minimum impact on the trend-
detection ability of the fixed-station network, there needs to be a careful
statistical evaluation of a network's design. A complete and thorough
theoretical statistical evaluation of an agency's monitoring network is
often beyond the resources of an agency that is operating an active and
aggressive regulatory monitoring program.* It is possible, however, for
agencies to perform more basic statistical evaluations if such evaluations
can take advantage of existing personnel, programs, facilities, data and
Dunnette, David. Personal communication, Dunnette of the Water Quality
Division, Department of Environmental Quality, Portland, Oregon, to Robert C.
Ward, August 24, 1977.
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data handling procedures and if they do not require a large commitment of
the agency's resources.
Evaluation of the design of a regulatory water-quality monitoring
system, in general, involves examining: (1) sampling station locations,
(2) parameter coverage, and (3) sampling frequencies (where, what and how
often to sample). Evaluation of the first two design aspects requires the
collection of additional data between existing stations and on parameters
not currently measured. Collection of such data strictly for evaluation
purposes is often not economically feasible. However, if the evaluation of
these two points was carefully integrated into the recently emphasized
special surveys performed for enforcement purposes, the special survey data
could serve an additional purpose and result in better location of fixed-
stations and parameter coverage. The additional expense involved would be
small compared to the benefits gained by the fixed-station network.
Evaluation of the third aspect of network design, sampling frequencies,
can take advantage of other existing programs and procedures and be performed
at a reasonable cost. Development of an evaluation procedure which utilizes
existing personnel, data and data handling facilities, however, will require
compromises on theoretical completeness.
The purpose of this report, therefore, is to develop a simple and easy-
to-use procedure for evaluating sampling frequencies in a routine fixed-
station, water-quality monitoring network used for regulatory water-quality
management purposes. The procedure is based upon available data, utilizes
common STORET routines for a major part of the data analysis, and employs
simple, straightforward statistics via the use of several simplifying
assumptions.
More specifically, the procedure uses data currently in STORET and the
STORET inventory routine to compute the sample statistics for each station
on each parameter. These sample statistics, based on the assumption that
each parameter follows the normal distribution, are then assumed to repre-
sent the "population" parameters (i.e., they are not considered sample
statistics, but rather they are assumed to represent the actual population
being sampled). The population parameters are then used to examine the
uniformity and size of the precisions (confidence intervals) about the water
quality means.
If the precisions are not sufficiently uniform (each station supplying
a relatively equal amount of information), then the total number of samples
can be reallocated using a proportional sampling formula. If the precisions
are not small enough for management decision making, several alternatives
are presented. In addition, if there is to be a change in total samples
used in the network, the effects can easily be determined by examining the
effect on the precisions—both in uniformity and size.
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II. CONCLUSIONS
The sampling frequency evaluation procedure presented in this report is
a simple, straightforward method by which regulatory water-quality management
agencies can adjust the design of their routine fixed-station monitoring
networks to better meet their data and information needs. Since water
quality monitoring is a statistical sampling operation, the sampling fre-
quency evaluation procedure involves a number of statistical assumptions and
utilizes basic statistical techniques.
An agency that defines its routine monitoring network data expectations
in statistical terms (in this case, confidence in estimates of means) can
make better use of the evaluation procedure than an agency that does not.
In the latter case, however, the agency may want to use the evaluation
procedure to establish its data needs or expectations in statistical terms.
The statistical assumptions made to greatly simplify the procedure
should be clearly understood before the results of the evaluation are used.
The evaluation procedure is successfully demonstrated using data from
two state water-quality management programs.
The evaluation procedure was developed to serve as a basic or first
level of evaluation methodology. General acceptance and utilization of such
basic statistical, evaluation procedures sets the stage for use of more
advanced evaluation procedures when they are developed in the future.
Development of such procedures should proceed in a step-by-step manner
whereby one or two assumptions are removed each time. To do otherwise is to
develop a methodology that appears as a complex and impractical evaluation
procedure, to those who are not highly trained in statistics. This, in turn
tends to discourage use of such evaluation procedures and, consequently,
provides little direction to the attempts to make routine regulatory
monitoring more supportive of regulatory water quality management.
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Ill. RECOMMENDATIONS
The sampling frequency evaluation procedure is highly recommended for
water-quality management agencies that have not utilized statistics in the
design of their monitoring networks in the past. The procedure not only
provides considerable insight into the type of data a network generates, it
also introduces statistics to the agency at a level that can be easily
understood.
As an agency attempts to obtain more information from its network
(i.e., more statistically sound information), the assumptions used in the
evaluation procedure must be removed. More information could be gained from
a routine monitoring network if the types of probability distributions
generally applicable were known for the water-quality parameters. At a more
advanced level of statistics, more information might be gained if the exact
role of time-series analysis in regulatory monitoring were precisely known.
The rather low sampling frequencies in this type of monitoring obscure a
quantitative definition of the contribution time-series analysis may make.
Studies in the above two areas are recommended.
An overriding concern in this report has been practical utilization of
the results. As future research is performed in developing more thorough
evaluation procedures, it is recommended that the practical application not
be forgotten. This will require knowledge of the type and level of sta-
tistics being used on a practical basis by the many water-quality management
agencies and not greatly exceeding this level but carefully building upon
it.
Use of the Environmental Protection Agency's STORET system by water-
quality management agencies has greatly stimulated interest in data utiliza-
tion. It is recommended that future work in the areas of network design and
data analysis be closely coordinated with this major regulatory, water-
quality management data bank.
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IV. STATISTICAL BASIS
Since water quality monitoring is a statistical operation (analyzing a
part to obtain information on the whole), statistics will play the major
role in any attempt to evaluate how often one must sample. The level of
statistics one uses to perform such an evaluation depends upon many factors
(quality of data records, statistical training of personnel performing the
evaluation, confidence one wants to place on the information, use of the
information, etc.).
The level of statistics chosen for this evaluation procedure is more
basic due to the report's emphasis on practicality. Using a more basic
level of statistics involves making a number of simplifying assumptions.
There are a number of ramifications that result from making the assumptions.
A brief review of the assumptions will be presented below while a more
detailed discussion is presented at the end of the report.
ASSUMPTIONS
The data collected on each water-quality parameter is assumed to follow
a normal distribution. Making this assumption permits the evaluation pro-
cedure to utilize the existing STORET inventory routine results which include
the mean and standard deviation for each water-quality parameter at each
station. By assuming a normal distribution and using STORET, the evaluation
procedure avoids the need for laborious and costly analysis of the raw data
to determine the applicable statistical distribution for each parameter at
each station.
The effects on sampling frequencies of assuming the normal distribution,
rather than determining the distributions applicable, have not been evalu-
ated in this report or in the current literature. It has been noted,
however, by several authors (Beckers and Chamberlain, 1974; Lewis, 1976;
Montgomery and Hart, 1974; and Sherwani and Moreau, 1975) that, in general,
most water-quality parameters can be described by either the normal or log
normal distributions. Thus, any error introduced would stem from using the
normal distribution in a situation where the log normal was applicable.
Since the evaluation procedure requires that a selection of parameters be
made for inclusion in the analysis, a selection of those parameters more
disposed to normality would minimize the effect of the assumption. Beyond
this point, Lewis (1976) notes that "... the normal distribution remains
a sufficient representation of C(t) [concentration of water quality] for
purposes of developing monitoring network priority procedures."
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If the parameters that follow a log normal distribution are known or
determined, the original data for those parameters can be transformed into
logarithms (thus resulting in a normally distributed set of numbers) and the
evaluation procedure presented in the report can be followed. This is an
option, however, only for those that have the expertise and resources
available. Use of logarithms is not included in the evaluation instructions
presented later in order to: (1) keep the procedures as simple as possible;
(2) facilitate direct use of STORET; and (3) avoid the need to obtain and
analyze large amounts of raw data.
In order to develop a basis for evaluating sampling frequencies from
which rather straightforward statistics can be used, and from which compari-
son of alternative sampling policies can be made, the sample mean and stan-
dard deviation computed by STORET, or otherwise, are assumed to be population
parameters. Use of the word "population" implies that the mean and standard
deviation are known constants. Thus, from a statistical standpoint, the
standard deviation or variance (the standard deviation squared) computed or
estimated for each station is assumed to be the variance of the population
at that station and not the variance of a sample.
The variance is determined using past data from the monitoring network
(hopefully data stored in STORET in order to take advantage of STORET's
inventory routine to compute the variance). Data from any number of years
can be used to compute the variance, but in order to have the variance
represent current conditions, it is best to use the most recent year(s). If
known changes have occurred recently or are expected to occur in the near
future, their impact can be estimated and incorporated into the variance for
the station(s) affected. Once the variances are computed or estimated, they
are assumed fixed for the remainder of the analysis.
Water quality consists of a number of parameters; consequently,
determining the variance of water quality will involve determining the
variance of a number of different parameters. The parameters to be used in
a sampling frequency evaluation should be representative of the general
water-quality conditions encountered by the monitoring program. This point
will be discussed in more detail later.
PRECISION
One procedure for determining the effectiveness of a given level of
sampling in a routine fixed-station monitoring network is to compute the
precision of the estimate of the mean obtained from the number of samples
taken at each station. The precision refers to that value which, when added
and subtracted from the sample mean, establishes the range within which the
true mean can be expected to fall within a given level of confidence (this
range is also referred to as the confidence interval). The equation for the
precision is
BO
PRECISION -
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where e is the confidence coefficient, o^ is the standard deviation of
the water-quality population at station i , and n.^ is the number of sam-
ples taken at the ith station over the time period considered (a year is
considered as the time period in this report; therefore, n^ refers to the
number of samples taken per year).
The confidence coefficient is dependent upon the level of confidence
desired, but is not dependent upon the sample size since, in this situation,
o± is not a sample statistic. For a 90% confidence level e is 1.645, while
for a 95% confidence level B is 1.96. The e values for a range of
confidence levels appear in most basic statistical textbooks. The selection
of a confidence coefficient to use in the evaluation procedure is the respon-
sibility of the person doing the evaluation as there are no criteria that can
be used as a guide in its selection.
The precision of the estimates of annual means of the water quality
parameters (i.e., the confidence interval of each parameter's annual mean) at
the stations in the network gives a water-quality management agency an
indication of the worth of the data that it obtains from its routine moni-
toring efforts. A large precision (or wide confidence interval) makes it
difficult to speak very conclusively about a given parameter's average
quality over the past year. On the other hand, a small precision (or narrow
confidence interval) allows a much stronger statement to be made on the past
year's water quality.
In an ongoing routine monitoring operation, precisions often have had
little use in evaluating the monitoring effort because an agency has had a
given area to be covered, a given monitoring strategy and a given budget.
The sampling frequencies are set at the level permitted by the constraints.
In such situations, statistics have often played a small role.
When there is a change in the constraints (such as that proposed by
EPA's Standing Work Group on Water Monitoring) and an adjustment has to be
made in routine sampling frequencies, the effects on precisions can be used
as a basis for deciding which adjustments to make.
PROPORTIONAL SAMPLING
An evaluation of sampling frequencies and the resulting precisions
considers the uniformity of the precisions obtained from the stations and the
size of the precisions. Proportional sampling is introduced into the proce-
dure to serve as a technique for obtaining more uniform precisions from a
monitoring network.
By computing the precisions at all the stations in a network, different
levels of precision will be noted. Those stations with a low variation in
water quality will have relatively high precision for the estimate of the
mean. At the same sampling frequency, a station with high variation will
have low precision. By dividing the network into two or more groups and
allocating frequencies according to the group's general variation in selected
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water quality variables, more uniform levels of information can be obtained
across the network.
If this approach is carried a step further, each station can have its
sampling frequency determined by the variation in water quality that exists
at its location - a type of proportional sampling. In this case, adjustments
in sampling frequency are made such that each station is supplying approxi-
mately the same level of information as all the other stations (i.e., each
station has the same precision) .
To achieve equal precision, the following proportional allocation
equation is used
2
n, - -—• N (2)
Za±2
2
where n^ is defined as before, a^ is the variance at the ith station and
N is the total number of samples to be allocated. In a network with large
differences in variance, allocations according to equation 2 can be quite
extreme - some stations with almost no samples and some with a very large
number of samples.
This effect can be modified by basing the proportional sampling on the
standard deviation. In this case, the equation becomes
where the variables are defined as before. The result of using equation 3 is
not equal precisions at all stations, but precisions which are more uniform
than those obtained using equal sampling frequencies.
Since several water quality parameters will normally be involved in
evaluating sampling frequencies, a separate TI^ is computed for each. This
results in several sampling frequencies for each station - one for each
parameter considered. For practical scheduling of sample collection and
analysis, the frequencies must be compromised to arrive at one sampling
frequency. In this report, the compromise is achieved by simply averaging
the sampling frequencies at each station.
If it is possible to establish sample-collection schedules based on the
most frequently measured parameter, those parameters requiring less frequent
analysis could be analyzed in the laboratory on every other sample, every
fourth sample, etc. This, in effect, permits different parameters to have
different sampling frequencies and avoids the often large statistical impact
of compromising sampling frequencies among parameters.
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V. PROCEDURE
A general procedure can be outlined for incorporating the statistics
presented in the previous section into an evaluation of a water-quality moni-
toring network's sampling frequencies. However, before any evaluation is
undertaken, it is imperative that the network being evaluated be clearly
defined in terms of the stations included, the parameters important to the
network's agency, the purpose of the network, the role the evaluation results
will play in modifying the network's design, etc. Having a clear definition
of the network and the purpose of the evaluation will greatly enhance
utilization of the results of the evaluation.
The general evaluation procedure considers: (1) uniformity of preci-
sions and (2) size of precisions. In both cases, the procedure describes
alternative ways to handle conditions deemed inadequate; i.e., poor uniform-
ity and precisions that are too large (wide confidence intervals).
EVALUATION STEPS
The general sampling frequency evaluation procedure is outlined in
figure 1. The first step, numbered 1 in figure 1, involves establishing the
level of confidence an agency wants from its routine, fixed-station monitor-
ing network. This will be dependent upon the use to which the data are put
within the agency. As noted earlier, there are no criteria established to
assist in this determination.
The second step is selecting the water-quality parameters upon which the
evaluation will be based. Although it is not impossible to include all
parameters of concern, it is more economical to select representative param-
eters. For example, a parameter could be selected from major categories of
parameters: (1) biological, (2) chemical, (3) nutrient, (4) hydrological,
etc. The parameters selected should be those critical to water-quality
conditions within the area being monitored. For example, a representative
critical chemical parameter in a western United States monitoring network may
be total dissolved solids (TDS) or conductivity.
In the third step, the total number of samples (N) available for the
design period (one year is used in this report) is determined by noting the
number of samples that can be processed by the available monitoring resources
of the agency. Depending upon the purpose of the evaluation, either one
value of N is determined or a range of N values is selected for evalua-
tion. In the former case, the resources devoted to routine fixed-station
monitoring are fixed and the question is how to get the most information from
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DETERMINE CONFIDENCE
NEEDED IN THE NETWORK
LEVEL
SELECT WATER QUALITY PARAMETERS
TO INCLUDE IN THE EVALUATION
DETERMINE THE TOTAL NUMBER
SAMPLES (N) TO BE ALLOCATED
OF
COMPUTE THE VARIANCE OF EACH
PARAMETER FOR EACH STATION OVER
THE YEARS OF RECORD SELECTED FOR
THE EVALUATION
COMPUTE PRECISIONS USING PAST
SAMPLING FREQUENCIES
ARE
PRECISIONS
SUFFICIENTLY UNIFORM
7
YES
NO
COMPUTE NEW SAMPLING
FREQUENCIES USING EQ. 2 or 3
YES
ADJUST FREQUENCY CHANGES
UNIFORMLY OVER THE NETWORK
COMPROMISE THE FREQUENCIES
AMONG THE WATER QUALITY
PARAMETERS
COMPUTE PRECISIONS USING NEW
SAMPLING FREQUENCIES
EITHER:
1. LOWER CONFIDENCE LEVEL
Z, INCREASE NUMBER OF SAMPLES
3. REDUCE NUMBER OF STATIONS
REPEAT EVALUATION
ARE
PRECISIONS
ACCEPTABLE FOR MGT
PURPOSES
YES
I IMPLEMENT NEW FREQUENCIES
J
Figure 1. Flowchart of the sampling frequency evaluation procedure (numbers
refer to steos in the procedure).
10
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these resources. In the latter case, the exact amount of monitoring
resources devoted to sampling may depend upon the results of the evaluation.
The resources devoted to routine fixed-station monitoring may depend upon the
type of information that can be obtained versus that which is needed.
The fourth step involves computing means and variances for the selected
parameters at all stations included in the evaluation. It is at this step
where use of STORET can tremendously reduce the computational effort
required. The length of the historical record used for computing variances
may vary, depending upon the quality of the record, the preference of the
evaluator, and the tradeoffs between changes in quality over time versus more
data for more accurate estimates. The variances computed from the historical
record are assumed to be indicative of past and future quality conditions
and, therefore, are assumed to be population parameters. If there are rea-
sons to believe this is not the case, more accurate estimates of the expected
variances should be substituted. If such estimates are unavailable, the
station may have to be removed from the evaluation.
If, after the variances are computed, it is noted that one or two are
excessively large (e.g., greater than ten times the average of the vari-
ances) , these stations should be removed from the evaluation and treated
separately. Excessively large values distort the evaluation procedure, often
far beyond the importance of measuring the quality variation in question.
The fifth step takes the standard deviations (square root of the
variance), the confidence coefficient determined in step one and the past
sampling frequencies (for the past year) and computes the precisions being
obtained from the network as it now exists, using equation 1. A review of
these precisions gives an indication of past uniformity in the information
being obtained by the monitoring network. If the precisions are sufficiently
uniform for the needs of the management agency, then any adjustment in
sampling frequencies can be made uniformly over the network.
If the precisions are not sufficiently uniform for the needs of the
management agency, the evaluation proceeds to step six where the total number
of samples is now allocated to the sampling stations through the use of equa-
tion 2 or 3. The choice of equation depends upon the level of uniformity
sought. If the sampling frequencies were to be based on only one parameter,
equation 2 would yield exactly equal precisions at all the stations while
equation 3 would simply result in more uniform precisions than can be
achieved with uniform sampling frequencies. As noted earlier, if sample
collection could be geared to the parameter needing the most frequent sam-
ples, then through varying laboratory analyses the different frequencies
could be permitted, resulting in exactly equal precisions using equation 2
and more uniform precisions using equation 3 rather than uniform frequencies
for all parameters.
In compromising (step seven) the sampling frequencies of all the param-
eters at each station, the exactly equal precisions of equation 2 are lost
and the more uniform precisions of equation 3 are made less uniform. With
the compromising, however, the relative benefits of equation 2 versus equa-
tion 3 remains - equation 2 yields more uniformity in precisions, in general,
11
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than equation 3. Both equations could be used with the results dictating
which is more useful, given the constraints involved.
The frequency compromising used in step seven of the evaluation proce-
dure is simple averaging, although the parameters could be weighted to give
more emphasis to a parameter particularly critical in the area being
monitored.
New precisions are computed in step eight using the compromised sampling
frequencies from step seven. As noted above, using compromised frequencies
results in compromised precisions. If the frequencies have not been allo-
cated for uniformity, but rather allocated uniformly, the new precisions are
computed at this step. In either case, the new precisions must be reviewed
to determine if the precisions (confidence intervals) are sufficient for
management purposes.
PERCENTAGE CHANGE INDEX
At this point in the evaluation procedure, it may be quite helpful to be
able to compare average precisions over the entire network for the various
water-quality parameters rather than station by station. The effects on
average precisions of using one allocation method versus another (equation 3
allocations versus equation 2 allocations versus uniform allocations), or of
using one level of sampling versus another, will be much easier to visualize
on a total network basis if average network precisions are available.
One approach is simply to compute the mean and standard deviation of the
precisions across all the stations for each water-quality parameter. Thus,
if more uniformity of precisions across stations is being sought by a new
allocation procedure (equation 2 or 3), a comparison of the standard devia-
tion of the precisions obtained with constant sampling frequencies with those
obtained with equation 2 or 3 will reveal the amount of improvement that can
be achieved. Likewise, if tighter precisions are sought by increasing the
total number of samples available, comparing the mean of the precisions of
the old level of sampling with that of the new will indicate the amount of
improvement that can be obtained. If a reduction in sampling must take
place, the effect can be determined by comparing means of the precisions.
A further aggregation of the means and standard deviations of the preci-
sions, which includes all the water-quality parameters used for the evalu-
ations, will permit one overall number (index) to be developed which will
indicate the level of Improvement or degradation in the precisions when
changes in sampling frequencies are being evaluated. For example, what is
the overall Improvement In precisions when samples are allocated for uniform
precisions rather than for uniform frequencies?
Development of such an index is based on the sum of the percentage
changes that occur in each parameter's precision from one design to the next.
Thus, while a negative change may occur in one parameter and a positive
change In all the others considered, the percentage change index gives an
12
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overall indication of change, either negative or positive, depending upon the
magnitude of change of the parameters in the sum.
A percentage change index can be computed for the mean of the precisions
or the standard deviation of the precisions. The equation for the percentage
change index based on the mean of the precisions (PCI ) is
m
p 0PM - NPM.
i=l °PMi
PCIm = -± - p x 100 (4)
where OPM.^ is the old sampling-frequency precision mean for the ith
parameter, NPM.^ is the new precision mean, and p is the total number of
water-quality parameters included in the evaluation.
The equation for the percentage change index based on the standard
ions (PCI .) is
SQ
p OPSD - NPSD
deviations of the precisions (PCI .) is
SQ
_ i.
i-1 °PSDi
PCIsd -- p— ^ -
where OPSD.^ is the old sampling frequency precision standard deviation of
the ith parameter, NPSD^ is the new precision standard deviation, and p
is defined as above.
PRECISION IMPROVEMENT ALTERNATIVES
If, after comparing the individual precisions and the percentage change
indexes, it is decided that the precisions are adequate for management pur-
poses, then the sampling frequencies that generated these precisions are
implemented. However, if it is deemed that the precisions are not adequate,
then the monitoring data will not be sufficient to support the management
agency.
If this latter situation exists, the agency must either accept the data
limitations and organize its management strategy to match the information it
can afford, or it can do one of three things to improve the precisions:
(1) lower the confidence level, (2) increase the number of samples, or
(3) reduce the number of stations. Each of these actions would increase the
precision.
Reducing the confidence in the precision estimate is not recommended
unless the management program decides it can effectively operate with a lower
level of confidence in the estimates of quality obtained from its monitoring
system. Lowering the confidence level just shifts the data limitation rather
than corrects it.
13
-------
Increasing a monitoring budget is often difficult, if not impossible.
Given the information from the evaluation, however, it may be easier to
justify an increase in a monitoring budget since the budget increase can be
directly related to an increase in the precision of the network. In this
situation, an average precision increase over the entire network may be more
readily understood.
If an increase in budget is not possible, a reduction in the number of
stations is the only remaining alternative for increasing the network's
precision. Such an action trades spatial coverage for more precision at the
remaining stations. The results (sampling frequencies) of the evaluation
procedure (step seven) indicate which stations have a low quality variation
(indicated by low frequencies) and which may, therefore, be eliminated from
routine monitoring, especially if the quality mean is well below water qual-
ity standards applicable at that station. In general, such a view of the
sampling frequencies allocated by variation permits the evaluation procedure
to identify stations that may be of questionable value. It cannot, however,
identify where stations are needed.
If any of the above changes are made, the evaluation procedure is
repeated. The exact portion of the procedure repeated depends upon the change
made. Through successive iterations around such changes, a large amount of
information can be obtained relative to tradeoffs between monitoring preci-
sion, spatial coverage, and monitoring budget.
Once the precisions are deemed acceptable, the computed sampling
frequencies must be implemented. This first involves rounding the frequen-
cies to integer values. Next the frequencies must be integrated into prac-
tical and economical sample collection routes and schedules, laboratory
analysis schedules, etc. In the process of working the computed frequencies
into an operational monitoring system, there will, no doubt, be further
compromises in the frequencies. Thus, the computed frequencies actually
serve only as a guide for establishing sampling frequencies in a regulatory
water-quality monitoring network.
14
-------
VI. APPLICATION
Applications of the sampling frequency evaluation procedure are
developed using data from the Water Quality Control Division of the Colorado
Department of Health and the Minnesota Pollution Control Agency. The appli-
cations are established only to illustrate the evaluation procedure and do
not relate to the practical design of either the Colorado or Minnesota
monitoring networks.
The Colorado application includes an evaluation of the effects of using
equation 2 versus equation 3 for allocating samples while the Minnesota
application includes a sensitivity analysis of the total number of samples
available for allocation. In addition, the Colorado application was per-
formed using a Hewlett-Packard programmable pocket calculator (Model 65)
while the Minnesota application was performed on an IBM computer using a
F0RTRAN program.
In initial tests of the evaluation procedure, it was noted that exces-
sively large values of variance (or standard deviation) tended to completely
dominate the allocation of samples in step six. Upon checking the large
values, it was noted that they were due to unusual situations which should be
treated separately. Consequently, limits on the variance were established
for the parameters involved in the applications. This resulted in one sta-
tion being excluded in each of the applications. To illustrate, in the
Colorado and Minnesota applications, conductance was limited to a variance of
1.0 x 10° micromhoe or a standard deviation of 10,000 micromhos.
By reviewing the variances or standard deviations prior to initiating
the evaluation, any highly unusual situations can be identified. Removal of
such stations from the evaluation prevents a distortion of the results and
allows the special stations to be treated in a manner which better deals with
the special nature of the pollution problem causing the condition.
COLORADO APPLICATION
Colorado operates a routine, fixed-station monitoring network that
consists of a primary set of stations and a secondary set - the distinction
being a sampling frequency of 24 samples per year for primary stations and 6
samples per year for the secondary stations. Since each sub-network has a
different information goal, each should be evaluated independently of the
other.
15
-------
Only the primary stations will be considered in this application. The
stations included in this application are not exactly those in Colorado's
network. Again, the use of Colorado's data is for demonstration purposes
only and is not intended to reflect actual conditions.
The Colorado evaluation application assumes that the same number of
total samples will be used in the next year as has been used in the past.
The purpose of the evaluation is to allocate the samples so that a more
uniform level of information is obtained from the stations in the network.
STEP 1 - A 90-percent confidence level was arbitrarily selected for this
application. The confidence coefficient (a) for a 90-percent confidence
level is 1.645. The implication of this is that the means of water quality
can, 90 percent of the time, be expected to lie within the confidence
interval computed from the precisions.
STEP 2 - Three water-quality parameters were arbitrarily chosen for the
Colorado application: (1) conductivity as a representative chemical param-
eter, (2) biochemical oxygen demand (BOD) as a representative biological
parameter, and (3) nitrate-nitrogen (tKL-N) as a representative nutrient
parameter.
STEP 3 - Since the purpose of the evaluation is simply to determine how
to reallocate the existing samples in a manner which yields a more uniform
level of information for the stations, the total number of samples will be
the same as in the past (576).
STEP 4 - Computation of variances and standard deviations was accom-
plished through use of the standard STORET inventory routine (PGM = INVENT).
The variances and standard deviations were computed by STORET using three
years of record (1973-1975). The statistics obtained from the STORET print-
out are assumed to be the population parameters as described in Section IV.
The means and standard deviations are presented in table 1; the means are for
reference only as they are not used in the evaluation procedures.
STEP 5 - The precisions obtained using the uniform, 24 samples per year
sampling frequency are computed using equation 1, the e value from step
one, and the standard deviations from step four. The precisions obtained for
the three water-quality parameters are presented in table 2.
The precisions vary over a wide range as did the standard deviations in
table 1. To see if the precisions can be made more uniform, the evaluation
proceeds to the next step.
STEP 6 - Allocation of samples is first computed for each parameter
using equation 3 and then using equation 2. The latter equation assures that
the precisions obtained for each parameter are equal while the former results
in more uniformity than constant sampling over the network, but not equal
precisions for each parameter. If, in using equation 2, the network had a
sampling frequency determined only by conductivity, the precision of con-
ductivity at all the stations would be 110.90 micromhos. Likewise, if only
BOD were used, the BOD precision at all stations would be 2.35 mg/1. For
16
-------
TABLE 1. ASSUMED POPULATION STATISTICS FOR COLORADO APPLICATION
(Means are presented for information only)
Conductivity BOD
Station
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Mean
(Micromhos)
4136.19
1431.43
759.39
723.75
1410.39
962.87
354.34
155A.15
1791.18
926.80
573.34
681.20
237.11
383.64
339.60
779.86
1068.69
692.58
523.77
993.68
1623.06
353.49
353.06
2263.76
Standard
Deviation
(Micromhos)
867.75
436.05
238.28
146.90
246.68
251.78
74.32
277.62
426.76
371.45
204.84
257.64
87.64
135.53
93.97
278.55
371.64
303.44
156.72
421.96
434.57
200.40
149.84
405.58
Mean
(mg/1)
2.25
4.02
4.29
19.96
10.35
15.69
2.21
11.37
8.68
10.34
6.88
7.32
2.32
2.87
1.38
1.64
1.94
1.49
1.42
1.84
2.06
1.97
3.66
13.32
N03 ~
Standard
Deviation
(mg/1)
1.28
1.81
2.82
14.77
12.66
9.16
1.25
12.34
8.21
9.91
3.32
3.81
1.28
1.27
0.63
1.05
1.04
0.80
0.66
0.77
0.99
1.18
2.69
18.31
Mean
(rag/1)
1.54
2.59
2.04
1.45
4.43
2.37
2.15
4.16
2.27
2.01
1.42
1.82
0.42
0.56
0.17
0.28
0.77
0.33
0.24
1.09
2.73
0.46
0.39
2.68
N
Standard
Deviation
(ms/1) .
0.59
0.96
0.97
1.74
1.44
2.42
1.86
1.55
1.15
1.14
1.10
1.71
0.34
0.92
0.19
0.38
0.30
0.37
0.17
0.60
1.05
0.37
0.38
1.37
17
-------
TABEE 2 SAMPLING FREQUENCIES AND PRFCISIONS FOR THE COLORADO NETWORK
Station
Number
1
2
3
it
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
TOTAL
Uniform
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
576
Sampling Frequencies
(Samples per Year)
Computed
by Eq. 3
31.45
23.37
19.57
43.96
40.62
42.92
19.73
41.88
35.67
36.88
20.61
27.99
7.48
13.66
5.33
12.79
14.46
12.98
6.94
18.12
22.67
10.75
11.98
54.19
576
Standard
Computed
by Eq. 2
57.64
20.27
11.29
56.22
43.64
54.87
22.22
45.62
32.70
34.25
12.43
25.42
1.55
6.90
0.94
6.78
10.76
7.72
2.05
15.37
20.91
4.04
3.74
78.67
576
Deviation
Conductivity
(Micromhos)
Uniform
291.38
146.42
80.01
49.32
82.83
84.54
24.96
93.22
143.30
124.73
68.78
86.51
29.43
45.51
31.55
93.53
124.79
101.89
52.62
141.69
145.92
67.29
50.31
136.19
95.70
57.25
Eq. 3
254.54
148.38
88.61
36.45
63.67
63.22
27.53
70.57
117.54
100.62
74.22
80.11
52.72
60.32
66.95
128.12
160.77
138.55
97.93
163.06
150.14
100 . 68
71.21
90.63
100.27
50.58
Eq. 2
188.02
159.32
116.66
32.23
61.43
55.91
25.94
67.61
122.76
104.41
95.57
84.06
115.80
84.88
159.43
175.97
186.37
179.65
180.05
177.05
156.33
164.01
127.63
75.22
120.68
51.60
Precisions
BOD
(mg/1)
Uniform
0.43
0.61
0.95
4.96
4.25
3.08
0.42
4.14
2.76
3.33
1.11
1.28
0.43
0.43
0.21
0.35
0.35
0.27
0.22
0.26
0.33
0.40
0.90
6.15
1.57
1.78
Eq. 3
0.38
0.61
1.05
3.66
3.27
2.30
0.46
3.14
2.26
2.68
1.20
1.18
0.77
0.57
0.45
0.48
0.45
0.37
0.41
0.30
0.34
0.59
1.28
4.09
1.35
1.21
Eq. 2
0.28
0.66
1.38
3.24
3.15
2.03
0.44
3.00
2.36
2.79
1.55
1.24
1.68
0.80
1.07
0.66
0.52
0.47
0.75
0.32
0.36
0.96
2.30
3.40
1.48
1.05
I
N03-N '
(mg/1)
Uniform
0.20
0.32
0.32
0.58
0.48
0.81
0.62
0.52
0.39
0.38
0.37
0.57
0.11
0.31
0.07
0.13
0.09
0.12
0.06
0.20
0.35
0.12
0.13
0.46
0.32
0.20
Eq. 3
0.17
0.33
0.36
0.43
0.37
0.61
0.69
0.39
0.32
0.31
0.40
0.53
0.20
0.41
0.14
0.18
0.12
0.17
0.10
0.23
0.36
0.19
0.18
0.31
0.31
0.15
Eq. 2 !
0.13 1
0.35
0.47
0.38 !
0.36 '
0.54
0.-65
0.38
0.33
0.32
0.51
0.56
0.45
o.ss :
n."!3 '
0.24 ,
0.14 ;
0.22 I
0.19
0.25 j
0.38 !
0.30
0.32
0.25
0. 36
0.14
CO
-------
NOj-N, the precision would be 0.38 mg/1. These, iti other words, are the
precisions that would be obtained if there were no compromising. Varying
analytical determinations in the laboratory would help approach these
precisions.
It Is- possible to collect different frequencies, for different parameters,
but often', this is not practical in routine monitoring; therefore, the
frequencies for the parameters will be compromised in this example. By
compromising the sampling frequencies and equal precisions gained by use of
equation 2, unequal precisions for the parameters result. Also, the more
uniform precisions gained by use of equation 3 are reduced in uniformity by
compromising.
STEP 7 - The frequencies computed for the individual parameters are com-
promised, by simple averaging, to yield one frequency at each station. These
compromised frequencies are presented in table 2 for allocations made by both
equations 3 and 2. In both cases, the total samples allocated sum to 576 as
established in step three since there is no change in the number of samples
to be allocated in the next year.
STEP 8 - The new, more uniform precisions for the water quality param-
eters are computed using the new sampling frequencies, equation 1, the confi-
dence coefficient established in step one and the standard deviations from
step four. The precisions for both equation 3 and 2 allocations are
presented in table 2.
A review of the individual station results in table 2 reveals that, in
general, the sampling frequencies computed by equation 3 result in slightly
more uniform precisions than the uniform frequency while those computed by
equation 2 have more of the large precision extremes brought back into line
with the other precisions (conductivity at station 1 and BOD at station 24).
In both cases, there is a general tendency for the large precisions to be
reduced and the small precisions to be expanded. As would be expected, this
tendency is greater when equation 2 is used to allocate samples. The sam-
pling frequencies also reflect this, as those computed by equation 2 are more
extreme than those of equation 3 - these extremes are needed to bring the
precision at high variation stations more into line with the other
precisions.
To further compare the improvements in uniformity, the standard devia-
tions of the precisions are computed and presented in table 2. The standard
deviations of equation 2 and 3 precisions are better for all parameters than
the constant frequency precisions. Thus, there is more uniformity when
samples are allocated by equations 2 or 3.
To measure exactly how much overall improvement there is, the standard
deviation percentage change index will be used. The PCIgd for equation 3
frequencies over uniform frequencies is 23 percent. For equation 2 frequen-
cies over uniform frequencies the PCIg
-------
changing from a constant frequency can only be decided by the agency using
the data.
The results in table 2 can also be used in deciding which stations
should be removed, if the precisions are not adequate. The frequencies
computed by equations 2 and 3 yield a common basis for comparison of the
water-quality variability among the stations. Those stations with really low
frequencies have a relatively low variability in all the parameters. If the
mean quality is not near the water-quality standard, the results in table 2
may be sufficient justification for a station's removal from the network.
Stations 13, 15 and 19 in table 2 have very low frequencies compared to the
average of 24 samples per station.
MINNESOTA APPLICATION
Minnesota, as defined for purposes of this application, operates a
routine fixed-station monitoring network of 80 stations, each of which is
sampled 12 times per year. The Minnesota sampling frequency evaluation
application assumes that there is a desire to know what effect an increase or
decrease in sampling frequency would have on the network. The application
will include a reallocation of samples for more uniformity (equation 2 will
be used).
STEP 1 - As with the previous application, the 90 percent confidence
level is used.
STEP 2 - Three water quality parameters selected for the application
are: (1) conductivity as a representative chemical parameter, (2) dissolved
oxygen (DO) as a representative "biological" parameter, and (3) organic
nitrogen (ON) as a representative nutrient parameter.
STEP 3 - Since the purpose of the evaluation is to examine the effects
of any increases, or decreases in sampling frequencies, a range of total
samples will be considered. The range will consider reductions to an average
of 6 and 9 samples per station per year and increases to an average of 15,
18, 21 and 24 samples per year. Of the 80 stations used in this application,
one station was eliminated for having an excessively large organic nitrogen
variance; therefore, the corresponding total number of samples considered is
474, 711, 948 (for the average 12 samples per year), 1,185, 1,422, 1,659, and
1,896.
STEP 4 - Again the variances and standard deviations are computed via
STORET. Rather than printing it, the output is instead placed in a data set.
The data set is then edited to delete unwanted parameters, summary tables,
etc. The data are placed in a data set to permit the use of a F0RTRAN
program to perform the computations involved in the application.
The variances and standard deviations are computed using three years of
record (1974-1976). Again, these statistics are assumed to be the population
statistics.
20
-------
STEPS 5-8 - These four steps are performed by the F0RTRAN program. In
addition, a number of "checks" are added to the program to ensure that the
proper data are used. A listing of the program is presented in Appendix A.
The program is designed to handle this particular application and, although
the program is general in most aspects, certain portions would have to be
changed for other applications.
In table 3, the results of the F0RTRAN program are presented for the
allocation of the same total number of samples (948) as in the past. The
comparison is between the constant sampling frequency among stations (12
samples per year per station) and the proportional allocation which results
in more uniform precisions using equation 2. The improvement in uniformity
of the precisions is 31 percent.
Data similar to that in table 3 were obtained for each of the other
sample totals considered. In each case, the proportional allocation was used
to allocate the samples and these results were then compared with the results
of the 12 samples per year per station presented in table 3.
To illustrate the general effect of changing the level of sampling from
the 948 samples per year level with a constant 12 samples per year per sta-
tion, the percentage change index on the means (PCl^) is computed for each
level of sampling considered. The PCI^'s are presented in table 4, Thus, if
the sampling level is reduced by one-half and if the 474 samples are propor-
tionally allocated to achieve more uniform precisions, a reduction in the
precision means of 37.02 percent can be expected. If 237 samples are added
to the present 948 samples and the resulting 1,185 samples are proportionally
allocated to achieve more uniform precisions, an improvement in precision
means of 13.34 percent is achieved over the current 948 samples, allocated
uniformly to the stations.
To examine changes in the sampling level only, the PCl^'s can be sub-
tracted from each other. This results in a measure of effect of a change per
237 samples (the samples are assumed to be allocated proportionally at all
sampling levels). These percent changes are presented in the third column of
table 4. Thus, if the current sampling level (948) is reduced by one-half,
reduction in the precision means is 40.13 percent (25.14 + 14.99). An addi-
tion of 237 samples to the current 948 samples would improve the precision
means by 10.23 percent.
The changes in precision means per 237 samples, presented in table 4,
illustrate the principle of diminishing returns. At a low level of sampling
(474 samples per year) , the addition of 237 samples yields an improvement of
25.14 percent while at a higher level of sampling (1,659 samples per year),
the addition of 237 samples yields an improvement of only 4.73 percent.
It is only a short step from the information in table 4 to a cost-
benefit analysis. A cost is associated with collecting and processing each
group of 237 samples. This cost can then be associated with the additional
benefit or effectiveness gained by adding the 237 samples. Such information
can be extremely useful in water-quality management program planning.
21
-------
TABLE 3. EXAMPLE OF SAMPLING FREQUENCIES AND PRECISIONS FOR THE MINNESOTA
NETWORK (NEW N EQUAL TO PAST N). (continued)
NJ
STATION
NO. STATION DESCRIPTION
1 CEDAR RIVER 2.5 MI. w. OF LVLE
9. CEDAR RIVER 3 Ml S. OF AUSTIN
3 FOUNTAIN L-USH-16 AT AlBERT LEA
4 SMELLROCK R. W OF GOROONSV1LLE
5 OES MOINES R.-W FORK.PETERS8URG
6 RAINY RIVER BRIDGE AT BAUDETTE
7 RAINY R. AT INTERNATIONAL FALLS
8 RAINY R.PUBLIC ACCESS.INT FALLS
9 LAKE SUPERIOR »T SILVER BAY
10 5T LOUIS R. SM-23 AT FOND OU LAC
11 ST. LOUIS R. USM-Z 8Y BROOKSTON
12 PIPESTONE CREEK S M OF PIESTONE
13 ROCK P-IVER S OF LUVERNE
14 4LUC EARTH RIVER N OF WINNEBAGO
15 COTTONKOOD R. SM-16 AT NEK ULM
16 LAC oui P*RLE R.BY LAC out PARLE
17 MINNESOTA RtSH-36 IN BLOOMINGTON
18 NINNESOTA R. SH-19 AT HENDERSON
19 MINNESOTA R. SM-22 AT ST. PETER
20 NINNESOTA P.CSAH-Z4 AT COURTLAND
21 MINNESOTA R. USH-71 AT NORTON
22 MINN R. CS4M-40 BRIDGE AT MILAN
23 PONME OE TERRE R. AT APPLETOI*
24 WATONWAN R. M. OF GARDEN CITY
25 YELLOW MEDICINE R.-GRANITE FALLS
26 CANNON R. USH-61 M OF RED MING
27 CROW RIVER CSAH-36 AT OAYTON
28 CROW R« SH-22 1 MI N» OF BISCAY
29 CROW WING R. USM-210 BY PILLAGER
30 O'BRIEN BROOK CAR-12«PENGJLLY
31 RUN RIVER USH-10 AT ANOKA
3? RUM RIVER CAR-5 AT ISANT1
33 ROOT RIVER SH-26 E. OF HOKAH
34 SAUK RIVER CSAH-1 SAUK RAPIDS
35 STRAIGHT RIVER bY CLINTON FALLS
36 MISSISSIPPI R. AT SAUK RAPIDS
37 MISSISSIPPI R. AT LA CROSSE
38 MISSISSIPPI R. AT HASTINGS
39 MISSISSIPPI R. AT FRIOLFY
40 MISSISSIPPI R. AT CLEARWATER
41 MISSISSIPPI R. BY ROYAUTON
42 MISSISSIPPI R. AT CAMP RIPLEY
43 MISSISSIPPI RIVER AT JAC08SON
44 MISSISSIPPI R. S.W. OF COHASSET
45 MISSISSIPPI R. EAST OF BEMEOJI
OLD
FREO
12.00
12.00
12.00
12.00
12.00
12.00
IZ.OO
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
IZ.OO
IZ.OO
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
iz.on
IZ.OO
IZ.OO
12.00
12.00
IZ.OO
12.00
12.00
12.00
IZ.OO
1?.00
iz.oo
12.00
12.00
12.00
12.00
12.00
NEW
FREO
12.02
14.07
14.12
23.60
19.59
8.30
5.15
16.27
4.00
8.17
8.00
25.02
15.53
15.52
11.57
16.09
12.43
12.6ft
12.65
12.79
11.10
14.03
12.89
12.72
10.93
11.30
10.00
16.83
7.36
7.53
8.54
8.4*
15.59
9.64
10.63
7.98
7.65
11.60
8.09
7.19
6.47
6.77
6.43
6.48
5.44
CNOUCTVY
010 PREC NEW PREC
50.874 50.838
60.647 56.013
51.646 47.612
90.449 64.50Z
224.924 176. 03Z
64.635 77.714
5.644 8.614
30.261 25.984
0.683 14.896
27.580 33.422
66.125 76.857
249.663 172.916
90.610 79.666
125.368 110. Z3Z
00.937 82.442
166.717 143.975
70.770 69.532
72.758 70.040
05.315 03.104
•T.320 04.586
99.009 101.892
02.911 76.681
90.052 86.901
79.034 73.640
07.376 91.545
46.118 47.357
48.708 51.335
141.952 136.733
27.842 35.554
45.094 56.925
29.15Z 34.557
34.394 40.907
19.248 16.888
39.050 43.566
75.911 80.667
32.180 39.469
18.647 23.350
45.315 46.085
35.037 42.671
35.8*2 46.313
29.799 40.571
27.166 36.171
32.183 43.951
23.855 32.461
19.183 28.502
0
OLD PREC
1.127
1.053
2.174
2.091
1.Z50
0.909
1.068
1.163
0.540
1.420
1.162
1.740
1.887
1.484
0.976
1.332
1.130
1.257
1.070
1.452
1.002
1.715
1.113
1.345
0.909
1.229
1.016
1.304
1.266
1.101
1.264
1.222
0.961
1.115
1.135
1.144
1.290
1.209
1.223
1.060
1.083
1.047
1.003
1.186
0.968
0
NEW PttEC
1.126
0.972
2,004
1.441
0.978
1.093
1.630
0.998
0.926
1.731
1.351
1.205
1.659
1.304
0.994
1.150
1.110
1.224
1.050
1.407
1.042
1.586
1.074
1.306
0.952
1.262
1.071
1.101
1.617
1.390
1.499
1.453
0.843
1.2*4
1.207
1.403
1.616
l.?29
1.4*9
1.370
1.475
1.394
1.370
1.614
1.438
O
OLD PREC
0.390
0.509
0.306
0.822
0.305
0.148
0.046
0.7?9
0.177
0.149
0.128
0.480
0.334
0.307
0.296
0.244
0.3*3
0.335
0.332
0.256
0.206
0.296
0.325
0.311
0.248
0.342
0.341
0.314
0.1?8
0.119
0,202
0.191
0.761
0.274
0.217
0.141
0.172
0.364
0.163
0.115
0.102
0.1 SB
0.109
0.100
0.09?
KU *
NEW PREC
0.390
0.470
0.282
0^239
0.178
0.146
0.626
0.217
0.180
0.149
0.332
0.294
0.270
0.302
0.211
0.347
0.326
0.323
0.248
0.214
0.274
0.314
0.302
0.260
0.351
0.359
0.265
0.164
0.150
0.240
0.227
0.668
0.306
0.231
0.222
0.216
0.370
0.148
0.174
0.139
0.184
0,149
0.136
0.137
-------
TABLE 3. (continued) EXAMPLE OF SAMPLING FREQUENICES AND PRECISIONS FOR
THE MINNESOTA NETWORK (NEW N EQUAL TO PAST N).
NJ
CO
46 MISSISSIPPI R. BY LAKE ITASC*
»T OTTERTA1L RIVER *T BRECKENRIDGE
*f) PEO LAKE RIVER-EAST GRAND FORKS
44 WED R. CSAH-18 8R AT 8RUSHVALE
so WATERWORKS INTAKE GR. FORKS, NO
51 RED H. CSAM-39 0R * OF PEBLEY MM
5;» RED R» MAI* & FIRST A/ HR. FARGO
•ji BOISE OE SIOUX ".MR HRECKENHIDGE
5* BUFFALO R. USH-T5 «T GEORGETOWN
55 WILD RICE R. USH-7S N OF HENDKUM
56 KETTLE R. CSAH-48 E OF HINCLEY
57 ST. CROIX R. RR BH NEAR HUDSON
58 ST CROIX R. AT TAYLORS FALLS
59 ST. CROIX P. H OF DAN81M»Y. »S
60 MISS R, 5 II SE OF GRAND RAPIDS
61 SKAH RIVER AT JAC08SON
62 LON6 PRAIRIE R. OSH-10 S MOTLEY
63 BEAVER R. «t OF BEAVER BAY
64 ST LOUIS BAY AT OULUTH-SOPERIOR
65 SAUK R. CSAH-31 S OF NEX MUNICH
66 BUFFALO CR. USM-212 H OF PLATO
67 CENTER CR, 1 MI N OF FAIRMONT
68 COTTONWOOD R, SE OF SPRIN6FIELO
69 CHIPPEHA R. SH-40 EAST OF MILAN
70 REDWOOD «, CSAH-I01 AT N REDWOOD
71 LE SUEUR R, 5 MI SW OF WASECA
72 WHITEWATER », CR-I NW OF OTICA
73 VERHILLION R, N OF FABMINSTON
7* OKABENA CR. CSAH-9 OR AT OKA8ENA
75 MISS R, AT L * D 5 N OF WINONA
76 RAINY R. AT OUTLET OF RAINY LAKE
77 ST LOUIS R. CSAM-27 * OF ZIM
78 E SWAN R, CR-*** SE OF HIBBING
79 CANNON RIVER AT RANDOLPH
80 ZUMBRO R, CSAH-1* N OF ROCHESTER
POECISION MEANS
PPECISION STANDARD DEVIATIONS
12.00
12.00
12.00
12.00
12.00
12.00
12.00
0.0
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
12.00
948.00
ONS
6.89
13.38
8.71
11.77
12.06
13.80
1 1 .23
0.0
28.57
12.53
7.72
7.72
5.78
5.74
6.95
6.20
9.67
6.79
8.01
9.41
48.05
16.38
12.99
12.01
19.64
14.84
9.37
9.65
47.05
8.07
4.93
7.25
9.67
12.17
11.92
948.00
27.788
68.604
26.489
104.329
75.983
119.158
85.3*6
o.o
416.395
74.507
2?. 6*9
23.363
18.553
13.185
31.103
30.401
37.054
25.224
23.723
54.936
683.858
181.103
107.49*
91.731
237.694
152.334
25.64*
67.073
422.327
16.950
4.121
4*. 871
75.3*2
52.935
80.108
81.16*
101.91*
36.683
64.970
31.085
105,361
75.782
110.164
88.210
0.0
269.866
72.923
28.237
29.13*
26.727
19.057
40.873
*Z.277
41.284
33.539
29.033
62.021
341.755
154.99*
103.310
91.688
185.785
136.972
29.026
74.79*
213.285
20.663
6.*?7
57.740
83.91*
52.565
80.371
71.562
57.3*9
1.205
1.40A
1.299
1.278
1.51*
1.264
l.*77
0.0
1.512
1.369
1.37*
1.093
0.938
1.079
1.1*7
1.006
1.720
1.173
1.476
1.271
1.91*
1.292
1.358
1.259
1.198
1.376
1.257
0.792
2.*8*
1.313
0.979
0.932
0.976
1.014
0.847
1.235
0.338
1.590
1.331
1 .524
1.291
1.510
1.178
1.526
0.0
0.9BO
1.3*0
1.713
1.363
1.351
1.559
1.508
1.399
1.917
1.559
1.80V
1.434
0.957
1.106
1.298
1.258
0.938
1.237
1.423
0.883
1.255
1.608
1.528
1.199
1.087
1.007
0.858
1.299
0.245
0.110 (
0.36* (
0.215 '
0.171 (
0.232 (
0.264 <
0.155 (
0.0 <
0.228 '
0.297 »
0.1*6 (
0.203
0.124
0.109
0.116
0.099
0.155
0.119
0.1*0
0.176
0.568
0.276
0.22*
0.231
0.281
0.199
0.269
0.253
1.219
0.201
0.105
4.117
0.190
0.417
0.349
0.260
0.183
1.1*6
1.345
1.252
1.173
1.231
1.2*6
1.160
1.0
1.1*8
1.291
1.182
.253
.178
.157
.152
.138
.173
.158
.172
.199
.284
• 193
.217
.231
.219
.179
9.305
9.283
9.616
9.2*4
9.164
1. 176
9.211
0.414
9.350
0.253
D.116
-------
TABLE 4. IMPACT OF CHANGING THE SAMPLING FREQUENCY —
MINNESOTA APPLICATION
Total Number
of Samples to
be Allocated
474
711
948
1,185
1,422
1,659
1,896
(Change over the current
constant sampling frequencies)
-37.02
-11.88
3.11
13.34
20.89
16.76
31.49
Percent Change
per 237 Samples
25.14
14.99
10.23
7.55
5.87
4.73
24
-------
VII. DISCUSSION
The applications have illustrated how the sampling frequency evaluation
procedure can be used to obtain more uniform levels of information from a
network and to provide quantitative information on the effects of changes in
sampling frequency. Considerable insight can be gained on a network by
simply reviewing the precisions computed in the initial phases of the
evaluation.
STATISTICAL ASSUMPTIONS
Correct interpretation of the results of the evaluation procedure
requires a clear understanding of the assumptions. The assumption that past
means and standard deviations are population parameters is the most impor-
tant. This assumption permits the evaluation procedure to proceed in a
rather straightforward manner. Implications of the assumption are that
future water-quality conditions will be similar to past conditions.
Beyond assuming that past sample statistics are acceptable population
parameter estimates, the water-quality parameters used in the evaluations are
assumed to follow a normal distribution. In the absence of more detailed
data, this is not an unreasonable assumption (Lewis, 1976). Normal statis-
tics are easy to use and can be readily understood by users of the evaluation
procedure, thus greatly facilitating the incorporation of statistics into
monitoring efforts where few statistics have existed in the past.
There are studies dealing with specific situations that have shown that other
distributions may be more applicable, but these findings are not generalized
enough to justify using a distribution other than normal in all cases. As
more conclusive information on water-quality parameter frequency distribu-
tions is obtained, it can be incorporated into the procedure.
In addition to assuming the normal distribution, it is assumed that the
sampling has been performed in a "random" manner and that the samples are
"independent." Since the "population" being sampled is a time series, a true
evaluation of the random sample and independent observation assumptions is
difficult unless a large amount of data is taken and carefully examined.
Since a general purpose network, such as is being dealt with here, covers a
large area and has relatively low sampling frequencies, it is not practical
to perform the detailed analysis on every station.
Variation in water quality over a year's time frame is, in general, a
function of several factors: (1) long term trends, (2) seasonal changes, and
(3) random variations. No attempt has been made to break the overall
25
-------
variation into the above components. Thus, the evaluation procedure included
non-random variation as well as random variation. This fact results in
higher frequencies than would normally be used to measure only random
variation.
The above aspects of statistics and water-quality monitoring have been
discussed by several authors. Perhaps the more practical of the discussions
have been presented by Montgomery and Hart (1974) and Sherwani and Moreau
(1975). Sanders (1974) and Steele (1971) present somewhat more theoretical
discussions that also point out the impact of the above statistical assump-
tions. Ward, Nielsen and Bundgaard-Nielsen (1976) summarize a number of the
above discussions and also present a detailed review of proportional and
stratified sampling as it is related to the design of water-quality moni-
toring systems.
When the evaluation applications were setup with the Colorado and
Minnesota data, 3 years of past records were used to compute the standard
deviations. The standard deviations could be computed with only the latest
year's record, if this were deemed necessary.
UNIFORM INFORMATION LEVELS
The goal of uniform levels of information from stations in a monitoring
network may be desirable, but the use of uniform (constant) sampling fre-
quencies is often more practical. Any compromise between the two competing
objectives may be easier to resolve following an evaluation as proposed
herein.
The goal of uniform information levels has rarely been used in regula-
tory water-quality monitoring in the past. The concept of equal information
from stations in a water-quantity network has been discussed by several
authors (e.g., Matalas, 1968; and Yevjevich, 1972). Sherwani and Moreau
(1975) discuss the role of equal "information content" as it relates to
water-quality monitoring.
In using the uniform (or equal) information goal in a regulatory
monitoring network, several philosophical questions are raised. Most of
these can be dealt with by first carefully defining, in statistical terms,
exactly what is expected of a monitoring network. If the expectations
involve obtaining statistically sound information, then it is possible that
the monitoring network design can benefit from the evaluation procedure. If
not, the evaluation procedure will produce information that does not match
the manner in which the goals are stated.
More consideration of the uniform information goal in the future will
necessitate the incorporation of statistics into regulatory monitoring to a
larger extent than in the past. In general, any attempt to gain more infor-
mation, as well as more uniform information, will require the use of statis-
tics to a much larger extent. Too often in the past, regulatory water-
quality monitoring has not been viewed as a statistical sampling program. It
is a statistical sampling effort and should be treated as such.
26
-------
MONITORING SYSTEM EVALUATION
The evaluation of sampling frequencies is only one aspect of monitoring
network design which is, in turn, only one aspect of a total monitoring
system. Thus, the subject of this report covers a very small part of the
total system.
Evaluating sampling frequencies and ensuring that they are reflective of
agency policy and management goals can not imply that the total system is
meeting management and policy goals.
For example, if the data are not properly handled, analyzed and
utilized, then the data may not reach the decision-making levels of the
management agency. Thus, any attempt to evaluate sampling frequencies should
be accompanied by evaluations of: (1) the other aspects of network design,
(2) sample collection procedures, (3) laboratory analyses, (4) data handling
operations, (5) data analysis techniques and (6) information utilization
procedures.
Unfortunately, there are few evaluation procedures available to assist
in the evaluation of the monitoring system or its parts. As more emphasis is
placed upon the need for well defined and operated routine monitoring systems
for regulatory water-quality management, hopefully the needed evaluation
guidelines will be developed.
27
-------
REFERENCES
1. Becker, C. V., and S. G. Chamberlain. 1974. Design of cost-effective
water quality surveillance systems. U. S. Environmental Protection
Agency, Socioeconomic Environmental Studies Series Report No. EPA-600/
5-74-004, January.
2. Lewis, D. H. 1976. Optimization of state water quality monitoring
systems. Computers and Operations Research, Vol. 3, pp. 127-143.
3. Matalas, N. C. 1968. Optimum gaging station location. In the Pro-
ceedings of the IBM Scientific Computing Symposium on Water and Air
Resource Management, Form No. 320-1953. IBM Data Processing Office,
White Plains, New York. pp. 85-94.
4. Montgomery, H. A. C., and I. C. Hart. 1974. The design of sampling
programs for rivers and effluents. Journal of the Institute of Water
Pollution Control, Vol. 33(1):77-101.
5. Sanders, T. G. 1974. Rational design criteria for a river quality
monitoring network. Ph.D. Thesis, Civil Engineering Department, Univer-
sity of Massachusetts, August.
6. Sherwani, J. K., and D. H. Moreau. 1975. Strategies for water quality
monitoring. Report No. 107, Water Resources Research Institute of the
University of North Carolina, 124 Riddick Bldg., North Carolina State
Univers ity, Raleigh, N.C., June.
7. Standing Work Group on Water Monitoring. 1977. Basic water monitoring
program. Environmental Protection Agency Report No. EPA-440/9-76-025.
8. Steele, T. D. 1971. The role of network design in the management and
control of streamflow water quality. Published in Systems Approach
to Hydrology (V.M. Yevjevich, ed.), Water Resources Publications, Fort
Collins, Colorado, pp. 395-423.
9. Ward, R. C., K. S. Nielsen and M. Bundgaard-Nielsen. 1976. Design of
monitoring systems for water quality management. Contributions from the
Water Quality Institute, Danish Academy of Technical Science, No. 3,
Horsholm, Denmark, December.
10. Yevjevich, V. M. 1972. Probability and Statistics in Hydrology.
Water Resources Publications, Fort Collins, Colorado.
28
-------
APPENDIX A
F0RTRAN Program Used for Analysis of
Minnesota Network
29
-------
FORTRAN IV 6 LEWFi 21 MAIN DATE • 771*9 14/50/26 PAGE 0001
C TITLE'TITtE FOP THE EVALUATION BEIMG DONE THIS RUN
C ANALVMYPE OF ANALYSIS BEING DONE THIS RUN - FOR PRINTING PURPORSES ONLY
C MS=*UMB£R OF STATIONS IK THE KETtfORK
C MP=NU*8ER OF PARAMETER^ INCLUDED IN THE EVALUATION
C Pl.P2.P3.P4=LlMlTS ON THE PARAKETEP STANDARD DEVIATIONS
C sTAUSIeDESCPIPTION OP STATION IS
C PDESC(IP)=DESCPIPTION OF PARAMETER IP
C OFUS.IP)=NUM9ER Of SAMPLES ALLOCATED TO STATION IS FOR THE IP PARAMETER
C FOR THE PAST THREE VEARS
C VP(IS»IP)»VARIAMCE OF PARAMETER IP AT STATION IS
C I YB< IS) 'BEGINNING YEAR OF RECORD
C IYE» IS) 'ENDING YEAR OF RECORD
C OFYUS.IP)sNUMBER OF SIMPLES ALLOCATED. ANNUAL AVERAGE* TO CTtTION IS FOR
C IP PARANLTEn IN THE "AST
C AOF I IS > -COMPROMISED OLD FREQUENCY
C KSOUT'STATIONS BEIMG EvCLUOCD
C TN.TOTAL NUMBER OF SAMPLES fO BF ALLOCATED
C AN ( IS< IP) -NUMBER OF SAMPLES ALLOCATED TO STATION IS FOR THE IP PARAMETER
C »V< IS) 'COMPROMISED NEW FREQUENCY
C DFO(ISfIP)*DE«REES OF PfcEEOOM FOR OLD PRECISION CALCULATION
C OFN C IS. IPI 'DEGREES OF FFEEDOM FOR NEn PRECISION CALCULATIONS
C OP (IS* IP) 'OLD PRECISION OF EACH PARAMETER AT EACH STATION
C EP(IStIPI«NE* PRECISION OF EACH PARAMETER AT EACH STATION
C »OPIIP»-OLO PRECISION MEANS
C AEP(IP)*NEn PRECISION MEANS
c SDOP«OLD PRECISION STANDARD DEVIATION
C *OEP(IP>»NEb PRECISION STANDARD DEVIATION
C PERIM*PERCENT INPROVCMFNT
0*01 DIMENSION SUM(«l«STA(ZO«>«)*POESC(A)*OF(20(t4)tVPIZOa>4|
00*2 DIMENSION ANI20l.4l.l2««)tAVtZOaitb1IMO(?«0>tOFY(2ee.4>
00«3 DIMENSION »OF(2Ctl.O«>(?»e.*>.FP|4),SOOP<4),SOEP<4)
••«• DIMENSION "SOOT(*e».TITLEC2«)
••B9 DIMENSION DFOI20D<4>.DFN(?oa>
•010 DIMENSION ANALVI2A)
C
C 3E4D IN INITIAL VALUES
C
gall READ(S.229> «TITLE(K)*K'I«20)
0012 2?9 FO»MAT(20A4>
••13 aE»OC5,2?*l (ANALYIfl .K9l<20)
• 014 2?S FOl
C
C INITIALI7E SUM TO 7EPO
C
0019 ' DO 2 I.l.MP
oo?o ? suMtn«o.o
c
C CALL STATION AND PARAMfTED DESCRIPTIONS
C
•021 MS»0
30
-------
FORTRAN IV Q LEVEL 21
MAIN
DATE « 771*0
14/50/26
PAGE oooa
8022
002?
0024
00 ?5
00?7
0028
0029
0030
0431
003Z
0033
043*
0035
0036
0037
0031
0039
0040
9041
0042
0043
0044
0045
9046
0047
0048
00*9
0050
0051
0052
0053
0054
0055
0056
•057
0058
0059
0060
0061
0068
0063
0064
0065
0066
00*7
400 RE*D(8.11) LINEC'5»
11 FOPMAT8>
7 FOHMAT
RE«D( 60 TO *0fl
IF(IE.NE.76) 60 TO 400
IF(IEM.LT.ll) 60 TO 400
MS=MS»1
00 40? K=l,a
40? STAIMS.K)sSTA(199tK>
WRITE (ft. 410) MS.(STA(HS,K) ,KM,9>
410 FORMAT(5XtI2»Sx,BA4>
401 IFK'l
-------
FORTRAN IV 6 LEVFL 21
MAIN
DATE • 77140
14/50/?6
PAGC 0003
0068
0049
0070
00T1
0072
OOT3
697*
0075
007*
007T
007S
0079
0000
00*3
00»*
0046
0087
00*0
oo»9
0090
0091
0092
0093
0094
0095
0096
0097
0098
00*9
0100
0101
0102
0103
0104
0105
0196
0107
0108
0109
0110
IF.GT.P1>GO TO 222
IF(VP3).6T.P3I6O TO 222
GO TO 221
2?2 KOU*KOu»l
KSOUTLlNG FnEOUENCIES
231 CONTINUE
<*EAD(5.230t TN
230 FORMAT IF10. 01
IFlTN.LT.O.OI STOP
00 102 IP-l.MP
00 102 JS-1.WS
102 »N(IS.IP»««VPIIS.IP»/SU«UP»»T..
AVERA6E SAMPLING FRCOUENCIES AT EACH STATION
00 99 IS*I<4S
99
DO 103 IS>1>NS
DO 104 IP-l.MP
1D4 SUHP(tS)-SUHPIIS)*«N(IS>IP)
103 AVIISI»SUMP*0.0
Iflfl CONTINUE
PRINT RESULTS
HHITE(6>20SI
205 FOtlMATOHll
WRI-Tt(6t20«-llTlTLE(K>tK«1.20l
2H6 FORMAT<30>«20A*/>
UHITE<6«232> (ANALV(KI tK*l<20)
232 FORMAT <35»,20A4/i
32
-------
FORTRAN IV G LEVEL 21
MAIN
DATE « 771*9
14/SO/2S
PAGE 0004
0111
0112
01J3
on*
ons
0116
0117
0118
0119
0120
0121
0123
0123
012*
0135
0126
0127
0128
0129
0130
0131
0132
0133
013*
0135
0136
0137
0118
0139
0140
01*1
0142
0143
014*
0145
0146
0147
01*8
0149
0150
0151
0152
0153
01S4
0155
0156
0157
0158
0159
WRITE (6. 233) TN
233 FOR«AT(35Xt< TOTAL NUHBEP OF SAMPLES CONSIDERED THIS RUN -»,F6.0I
MRITE(iSt207)IYB(l)
207 FORKAT|/30X.'OATA RECORD USED IN THE EVALUATION IS F»OM».13t« THRO
MOH',13)
WRITE <*»20fl) (KSOUTIK)
208 FOCMAT(/3nx. 'STATIONS EXCLUDED - '.15I*t
wRITE(f-.lO) (POESC(K).PDESCIIK) .K = 1.HP)
10 FORMAT (///.lX.«STATION',JflX,'OLD',»X. "NEW ' ,9X»2A4, 13X.2A4,l*X»2A*i
111X>2A4>
C
C
C
12 FOUMAT C3X.I NO. «.8X« 'STATION DESCRIPTION' , 1 3Xt >FREQ* .3X. *FREQ> •
XIX.'OLD PREC'
1 .2X.«NEX PR£C'.3X,»OLO PPEC" »2Xf >NE» PR£C«»2X« «OLO
2'NEW PtJEC'/l
DO 109 IS"=1,MS
*'»ITE(6«3)ISi (STA(IStKtl,8).AOF(IS>>AV(tSt<
3 FOR»«AT(lX«I*.4X»8A*.?X,2F7.2»lX.8F10.3/»
109 CONTINUE
COMPUTATION OF MEAN -MO STO. DEW. OF PRECISIONS
00 201 IP=1.MP
SUMOP< IP 1*0.0
SUHEP(IP)«0.0
SUHOPS(IPI<«.*
201 SUMEPSftPI'0.0
DO 200 IP«1,MP
00 200 IS*1.MS
SUMOP t IP » =SU»4Of»( IP> «nl>l IS . IP)
SOHOPSt IP1 "SOHOPS I IP» *OP( IS, IPf»«2
200 SimEPSfIPI>SUMEPSUPI*EPIIS.IP>»*2
00 2«2 IP-l.MP
AOP C IP) *SUMOP I IP ) XSI
«EP(IP)*SUMEP(IP)/SI
SDOP(IP)»SORH{SUMOPS(IP)-(1./S1)»SUKOP(IP)»»2»/(SI-1.))
202 SOEPCtPl*SQRT(CSUMEPS/(St-l.U
SMSN>0.0
00 210 IS=I,MS
SN50-SNSO*AOF!IS)
210 SNSN=SNSN«AVIIS>
MRI TE (6,21 1 ) SNSOt SNSN
211 FORMATc/isx. -TOTAL MUHBER OF SAMPLES '•i«»2Fg.2)
WRITE(6<203) (AOPdPI .AEP(IP) ,IP«1»MP)
203 FOPHAT(/18«, 'PRECISION MEANS ' .?5X»SF Id. 3)
MR!TEf*,204) (SOOP(IP| ,SD£P(If>),IP=l,MP)
2P4 FOKHAT(/lfiX,'PRECISI1N STANDARD DEVI ATIONS' t 11X, 8F10.3I
SUMAP=0.0
DO 213 IPil.MP
DP=ERlM=(SUMAP/PA(()»inn.
KRITE(6,215)PERIH
815 FORHATC/XlftX. 'PERCENT IMPROVEMENT OVER PAST POLICY' tFH. 2)
00 TO 231
EM)
33
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/7-78-169
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
EVALUATING THE SAMPLING FREQUENCIES OF WATER
QUALITY MONITORING NETWORKS
5. REPORT DATE
August 1978
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Robert C. Ward
Knud Strange Nielsen
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Colorado State University
Agriculture and Chemical Engineering Department
Fort Collins, Colorado 80523
1O. PROGRAM ELEMENT NO.
1NE624
11. CONTRACT/GRANT NO.
CB-6-99-2530+A
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency-Las Vegas, NV
Office of Research and Development
Environmental Monitoring and Support Laboratory
Las Veeas, Nevada 89114
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/07
15. SUPPLEMENTARY NOTES
EMSL-LV Project Officer for this report is Donald B. Gilmore.
(702) 736-2969, X241 or FTS 595-2969, X241
Commercial telephone
16. ABSTRACT
Sampling frequency evaluation procedures presented utilize a number of simplifying
assumptions and basic statistical methods. Employing such an approach will
facilitate use of these procedures and, therefore, set the stage for wider under-
standing and use of more sophisticated approaches that may be developed at a later
date. Practical application has been an overriding consideration in development
of these procedures.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b-IDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
Design criteria
Water monitoring
14A
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
TTNrT.ASSTFIED
21. NO. OF PAGES
40
2O. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
A03
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION is OBSOLETE
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