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WATER QUALITY MONITORING
PROGRAMS
DEVELOPED BY
Stanley L. Ponce
WSDG Technical Paper
WSDG-TP-00002
December 1980
Watershed Systems Development Group
USDA Forest Service
3825 East Mulberry Street
Fort Collins, Colorado 80524
AD-33 Bookplate
NATIONAL
LIBRARY
917036
PREFACE
Recent legislation, such as Public Law 92-500 (the Federal Water
Pollution Control Act Amendments of 1972), RPA and NFMA, and public opinion
have forced water quality considerations to surface in many land and
resource decision processes. This has generated a need to provide
decision-makers with information about existing water quality and the
impacts of land management practices on water quality. In general, this
information is obtained through water quality monitoring.
Water quality monitoring, which is defined in the Forest Service
Manual as "the systematic evaluation of achievement of water quality
management goals, objectives, or targets," is usually the responsibility of
the forest hydrologist. The purpose of this Technical Paper is to help
forest hydrologists develop technically sound water quality monitoring
programs. The material presented here is the result of an extensive
literature review and personal experience.
It is intended that this paper be used as a technical guide, not a
"cook book." Every water quality monitoring program will be different. As
a result, each program will require that the hydrologist understand the
hydrologic system at hand as well as the interaction between land-use
activities and water quality. In my opinion, there is no substitute for
careful planning by the professional forest hydrologist when developing a
water quality monitoring plan of operation for a National Forest.
This paper was designed to be used in conjunction with Watershed
Systems Development Group (WSDG) Technical Paper 00001, "Statistical
Methods Commonly Used in Water Quality Data Analysis"; and WSDG Application
Documents 00001, "Statistical Analysis Using the Statistical Analysis
System (SAS) at the EPA National Computer Center"; an
APR I 1989
Analysis Using the Statistical Package for the Social Sciences (SPSS) at
the USDA Fort Collins Computer Center."
I would like to acknowledge all the following people who reviewed this
paper and provided many valuable suggestions for its improvement: Mr. John
Potyondy, USDA Forest Service; Dr. David W. Schindler, Fisheries and
Environment Canada; Dr. Robert C. Averett, USGS-WRD; Dr. Robert Beschta,
Oregon State University; Mr. Karl Gebhardt, BLM; Dr. Ken Brooks, University
of Minnesota; Mr. David Ryn, USDA Forest Service; Dr. Walt Hivner, Colorado
State University; Dr. David DeWalle, Pennsylvania State University; Dr.
Clarence Skau, University of Nevada; Mr. Ronald Russell, USDA Forest
Service; Mr. Owen Williams, USDA Forest Service; Mr. Rhey Solomon, USDA
Forest Service; Mr. Larry Schmidt, USDA Forest Service; Mr. Andrew Leven,
USDA Forest Service; Mr. Dallus Hughes, USDA Forest Service; Mr. Keith
McLaughlin, USDA Forest Service; Mr. Harry Parrott, USDA Forest Service,
Mr. Ted Beauvais, USDA Forest Service; Ms. Ann Puffer, USDA Forest Service;
and Mr. Warren Harper, USDA Forest Service.
TABLE OF CONTENTS
Page
1.0 Introduction 1
2.0 Types of Monitoring 2
Cause-and-effect 2
Compliance 3
Baseline 3
Inventory 3
3.0 Defining Problem Areas and Setting Study Objectives 4
4.0 Reviewing Past Work 8
5.0 Thinking About Data Analysis 11
6.0 Where, What and When 13
6.1 Guidelines for Locating Sampling Stations 14
6.1.1 Station Location as Influenced by the Type of Monitoring 14
6.1.2 Station Location as Influenced by the Water Type 21
6.2 Selecting Water Quality Constituents 34
6.3 Guidelines for Determining Sampling Frequency 36
6.3.1 Systematic Sampling 37
6.3.2 Simple Random Sampling 38
6.3.3 Stratified Random Sampling 47
7.0 Guidelines for Collecting and Handling of Water Quality
Samples 55
7.1 Types of Samples 56
7.1.1 Grab Samples 56
7.1.2 Composite Samples 56
7.2 Sample Collection 57
7.3 Sample Handling
59
TABLE OF CONTENTS
(conti nued)
8.0 Literature Cited
Appendi x
Page
64
LIST OF FIGURES
Page
Figure 1 - Example of Station Location for Cause-and-Effect
Monitoring Study Where the Treatment can be Readily
Isolated 15
Figure 2 - Hypothetical Rating Curves of Suspended Solids
(log Qss) versus flow (log Qw) for
Stations A and B. 16
Figure 3 - A Paired-station Plot for Suspended Solids
Concentration 17
Figure 4 - Sample Station Location for the Paired Watershed
Approach 18
Figure 5 - A Plane View of Sampling Station Location at a
Swimming Beach Along a Lake 20
Figure 6 - Sampling Station Location for Two Cases, I and II,
in Which a Point Source Effluent is Draining into
a Stream 20
Figure 7 - Example of Sampling Station Location for a Cause-
and-Effect Monitoring Study in Which a Tributary
is Involved 23
Figure 8 - An Illustration of Lateral Mixing 24
Figure 9 - Examples of Transect and Grid Sampling Schemes 26
Figure 10 - The Three Zones of a Temperature Profile in a
Stratified Lake 26
Figure 11 - Illustration of Sample Locations Along the
Depth Profile in a Stratified Lake 28
Figure 12 - Temperature Profile in a Lake or Reservoir
During the Period of Overturn, Either in the
Spri ng or Fal 1 29
Figure 13 - An Illustration of the Effect of Wind on the
Mixing of Water in the Epilimnion 29
Figure 14 - A Hypothetical Example of Where to Locate Sampling
Stations to Monitor Surface Water Quality on a
Multiple Use Lake 30
Figure 15 - Location of Sampling Stations Around a Solid Waste
Disposal Site
32
LIST OF FIGURES
(continued)
Figure 16 - Radial Design of Observation Wells Around a
Point Source
Page
33
LIST OF TABLES
Page
Table 1 - Indexes for Computerized Search of Water Resources
Literature 9
Table 2 - Activities and Concerns - Water Quality Matrix 35
Table 3 - Multiplier (M) of (sd/d2) to be Used in Paired
Comparitive Sample Size Calculations (After Potyondy,
1977) 46
Table 4 - Electrical Conductivity Data (ymhos/cm) collected
From a Rocky Mountain Stream 48
Table 5 - Summary of Special Sampling or Sample Requirements 60
'
LIST OF EXAMPLES
Page
Example 1 - Establishing Study Objectives from
Problem Definitions 7
Example 2a - Estimating Sample Size for the Simple Random
Sampling Method 41
Example 2b - Estimating Sample Size for Simple Random
Sampl i ng 43
Example 3 - Estimating Sample Size for a Stratified
Random Sample 53
WATER QUALITY MONITORING PROGRAMS
1.0 Introducti on
Designing a water quality monitoring program that will provide useful
information is an intellectual activity. It requires a great deal of
thought and careful planning. Thinking about the measurements you are
going to make and why you are going to make them leads to problem solving.
Just as a blood sample gives a physician insight into the functions of
the human body, a water sample can tell a hydrologist a great deal about
the complex system of a watershed. The quality of the water resource is
directly related to natural factors, such as climate, geology, soils and
terrestrial and aquatic vegetation; and man's land-use activities, such as
timber harvesting, road building, grazing, recreation and mining.
Consequently, to obtain useful information from water quality monitoring,
the sampling network for collection of data must be properly located in
both time and space and the constituents which are relevant to the
management objectives must be sampled. In addition, if the monitoring is
to be cost effective, the hydrologist needs to evaluate, at the outset of
the program, what can be accomplished with the resources that are
available.
The purpose of this paper is to (1) summarize the various types of
water quality monitoring commonly carried out on National Forest System
lands and (2) provide a series of guidelines to aid you with problem
definition, establishing study objectives, locating past work, data
analysis, locating sampling stations, selecting water quality constituents,
determining sampling frequency, and collecting and handling samples.
1
One final comment before we begin our discussion on developing water
quality monitoring programs. It is strongly recommended that you document
your program in the form of a water quality monitoring plan of operation
(see FSM 2542). A written monitoring plan serves several purposes. First,
it forces you to clearly define your problem and study objectives as well
as develop a logical approach to collecting data which will provide
information. Second, it provides your supervisor and other interested
parties with a statement of the problem you plan to address, how you will
do it, the type of data that will be obtained, how the data will be
analyzed, the expected knowledge to be gained, the financial commitment
required, and when reports are to be done. Finally, if you leave the
Forest before the project is completed, it provides the next hydrologist
with the proper framework to continue the study. In general, the structure
of a water quality monitoring plan varies from Region to Region. However,
the major components of most plans are the topics discussed in this paper.
2.0 Types of Monitoring
In general, the types of water quality monitoring performed on
National Forest System lands can be divided into four categories:
cause-and-effect , compliance, baseline, and inventory. A brief summary of
each follows.
Cause-and-effect (project) monitoring is performed to quantify the
impacts of specific land management activities on water quality. The
information obtained from this type of study is often used to evaluate the
effectiveness of "Best Management Practices," calibrate existing models
which were developed at different locations or under different conditions,
and develop and verify models designed specifically for the Forest.
2
Cause-and-effect monitoring is generally implemented on a project
level. The surveys are designed to deal with questions about what happened
and why. The monitoring is generally short-term, lasting three years or
less. Whenever possible, paired sampling is employed with samples being
collected before, during and after the treatment.
Comp! iance monitoring on National Forest System lands is performed
primarily to protect public health. It includes the monitoring of drinking
water and water used for primary contact recreation. The water quality is
generally compared with existing State water quality standards and when
these standards are not met, corrective action should be taken as soon as
possible.
Basel i ne monitoring is performed to provide land managers with
reliable information on water quality trends. The data are generally used
to determine if water quality maintenance and improvement criteria required
by law and/or policy are being met and for long-term trend assessment. If
the data indicate that water quality degradation is occurring as a result
of activities on the National Forest, corrective action may be evaluated
and appropriate action initiated. Water quality stations associated with
this type of monitoring program are usually located at strategic points
within the Forest and sampled on a routine basis for many years.
Inventory monitoring is carried out to provide land managers with
reliable information of existing water quality conditions. The data are
generally used to provide information for the land management planning
process and to establish water quality goals. Usually the inventory data
are obtained from existing stations established for cause-and-effect,
compliance and baseline monitoring. However, if additional stations are
3
required, they are often located at strategic points within the Forest and
sampled intensively for a short period of time.
One of the keys to an effective water quality program is to integrate
the various types of monitoring so that they are complementary. Some of
each type of monitoring will generally be carried out on all Forests.
Enough of each type should be accomplished to characterize the quality of
the water resource, to assess the impacts of management activities on water
quality and to determine if water quality standards, goals and objectives
are being met.
Priorities for monitoring should be established because it is not
feasible to monitor the water quality of all management activities or all
water bodies within the Forest. Variation of priorities between Forests
will exist depending on the existing data base, management issues and
concerns, and water quality management objectives.
3.0 Defining Problem Areas and Setting Study Objectives
The first step in developing an effective water quality monitoring
plan is to define problem areas. Each problem definition must evolve from
the needs identified by the line officer for information which will aid in
making management decisions (Boynton, 1972). It is very important that the
needs of the line officer be clearly identified since water quality
monitoring can only be justified if it is done to address specific needs of
management for information. Furthermore, commitment by line officers to
monitoring programs is achieved through their involvement in problem
identification and setting specific study objectives.
The role of the hydrologist in the problem definition phase is to take
the lead in suggesting specific problem areas which are technically
4
feasible and satisfy the managers needs. The hydrologist has the technical
expertise and the familiarity with land use and water quality relationships
to make this linkage. Involvement of other functional specialists with an
interest in water quality, such as fishery biologists, is often appropriate
at this stage to coordinate common data needs. Interdisciplinary
involvement can avoid duplication of effort and address a multitude of
management needs at one time (Potyondy, 1980).
Problem definitions should be as specific as possible. A problem
definition, such as "What is the effect of land use on the quality of water
draining the Routt National Forest?" is too broad to be of much use. In
this case, the problem definition could be greatly improved if (1) the land
management activity of interest was identified (timber harvesting, mining,
recreation, etc.); (2) the water resource was specified (stream, lake
and/or ground water); and (3) the type of water quality was stated
(physical, chemical, biological and/or radiological). An improved problem
definition might read "What is the effect of cl earcutting on the sediment
regime of Trout Creek?" The problem definition is now very clear and
direct. Often times problem definitions will not be this specific. More
often they are as follows:
1. A reliable method to predict the effect of clearcutting on the
sediment yield for the various stream types found in the Forest
is needed.
2. A simple, reliable approach to classify lakes by water quality
within the Forest is needed.
These problem statements, broad as they may appear, are consistent with the
water quality information needed in the land management planning process
and still provide the hydrologist with sufficient guidance to formulate
study objectives.
5
Once the problem areas have been defined, the next step is to
establish study objectives. This process should also be a mixed effort
between the hydrologist and the line officer. The hydrologist's role,
because of his technical knowledge of the watershed system and land use/
water quality interactions, is to suggest specific monitoring objectives
while the line officer's role is to act as a sounding board, continually
asking why and making sure the objectives speak only to his needs and that
the plan fits within the available resources (Boynton, 1972). When the
objectives are agreed upon by the hydrologist and line officer, they should
be documented in written form.
Objectives should be specific statements of measurable results to be
achieved within a stated time period. In addition, they should be specific
enough so that the hydrologist can convert them into statistical hypotheses
which can be tested with the data obtained from the water quality
monitoring program (more about this in Section 5.0). Some illustrations of
problem definitions and related study objectives are given in Example 1.
Defining the problem and setting the study objectives phase of the
study may seem like a lot of work which will require a substantial amount
of your time. It is and it does. However, it is time very well spent.
The point is, if you have spent time defining your objectives and making
sure that they are compatible with management's needs, there is a very good
chance that your study will be successful and provide meaningful
imformation to the land manager.
6
Example 1
Establishing study objectives from problem definitions.
Case A.
Problem Definition:
Does the water at Public Beach A pose a health hazard to primary
contact recreationists?
Study Objective:
To determine if the water at Public Beach A meets the State
standards for swimming during the summer of 1980.
In this case, the strategy is to monitor the water quality at Swimming
Beach A over the summer and compare it with the State standards for primary
contact recreation.
Case B.
Problem Definition:
Is acid precipitation adversely affecting the productivity of
Agnes Lake?
Study Objectives:
1. To determine the pH of the precipitation on a seasonal
basis at Agnes Lake over the next five years.
2. To determine the seasonal trend of pH, alkalinity and
conductivity in Agnes Lake over the next five years.
3. To determine the biological significance of any change in
pH, alkalinity and conductivity in Agnes Lake that occurs
over the next five years.
In this case, the strategy is to quantify the seasonal input of acid
(hydrogen ions) to the lake from precipitation, to develop the trend of the
lake's response over the next five years, and determine if this response is
biologically significant.
4.0 Reviewing Past Work
After the objectives have been established, the next step is to
determine what has al ready been done. Several common sources of data of
interest to the wildland hydrologist are listed below:
1. Forest, District, and Regional Office resource reports.
2. U.S. Forest Service research, U.S. Geological Survey, U.S.
Environmental Protection Agency, Bureau of Land Management, Water
and Power Resources Administration, Corps of Engineers, National
Oceanic and Atmospheric Administration, and Soil Conservation
Service.
3. State Geological Survey, State Department of Health, State
Department of Engineering, and State Water Pollution Control
Agency.
4. State universities, especially the departments specializing in
watershed management, hydrology, geology, chemistry, aquatic
biology, limnology, and microbiology.
5. River basin commissions.
6. STORET.
In addition to the sources mentioned above, several of the Regions now
have agreements with Forest Service research libraries or other libraries
which provide computerized literature searches. The major indexes
presently available or soon to be available are summarized in Table 1.
Most of the time, you can expect that little if any data will be
available from your watershed of interest, or if they are, they often will
be the wrong kinds of data. You can sometimes circumvent this problem by
reviewing information available from tributary streams or adjacent
drainages. However, you must be cautious when transferring data from one
place to another.
Whenever data are available from your watershed of interest, they
probably will have been collected for another purpose and will not solve
your specific problem. Nevertheless, such data can provide you with
8
Table 1. Indexes for computerized search of water
resources literature (modified from Busby, 1980).
INDEX
SUBJECT AREA
AGRICOLA
Covers worldwide journal and monographic literature in
agriculture and related subject fields, including forestry,
natural resources, chemistry and water resources. Prepared
by the U.S. National Agriculture Library.
AQUALINE
Provides access to information on every aspect of water,
waste water, and the aquatic environment. Worldwide sources
cited are 400 periodicals, research reports, legislation,
conference proceedings and preprints, books, monographs,
pamphlets, dissertations, translations, standards and
specifications, and miscellaneous publications from
water-related institutions worldwide. Prepared by the Water
Research Centre.
B I OS IS
PREVIEWS
Includes contents of Biological Abstracts and Bio-Research
Index, covering the entire life sciences. Citations are
taken from approximately 8,000 serial publications, as well
as books. Prepared by Biological Sciences Information
Service.
CDI
Comprehensive Dissertation Index, containing all
dissertations accepted for academic doctoral degrees granted
by United States education institutions and some non-U. S.
universities. Prepared by University Microfilms
International .
COMPENDIX
Covers civil, environmental and geological engineering;
mining, metals, petroleum and fuel engineering; mechanical,
automotive, nuclear and aerospace engineering; chemical,
agricultural and food engineering; and industrial
engineering, management, mathematics, physics and
instruments. Prepared by Engineering Index, Inc.
GeoRef
Geological Reference file, covering geosciences literature
from 3,000 journals, plus conferences and major symposia and
monographs in such areas as environmental geology,
geochemistry, and fluvial geomorphology. Prepared by the
American Geological Institute.
NTIS
This is a broad and cross-disciplinary file containing
citations and abstracts of government-sponsored research and
development reports and other government analysis prepared
by Federal agencies on their contractors and grantees.
Prepared by National Technical Information Service of the
U.S. Department of Commerce.
9
INDEX SUBJECT AREA
POLLUTION
Covers non-U. S., as well as domestic reports, journals,
contracts, patents and symposia in the areas of pollution
control and research. Prepared by Pollution Abstracts, Data
Courier, Inc.
WATERLIT
Covers the water resources and water-related literature of
the world. WATERLIT topics include, but a^e not limited to,
water supply, reservoirs of all types, water utilization,
water standards, limnology, health aspects of water, water
law and water ecology. It is produced by the South African
Water Information Centre.
WRD
Water Resources Abstracts is a computerized version of
Selected Water Resources Abstracts, a semimonthly journal
published by the Office of Water Research and Technology.
It covers literature of water related aspects of the life,
physical and social sciences as well as related engineering
and legal aspects of the characteristics, conservation,
control, use, or management of water.
10
information about the interactions between land use, hydrology and water
quality and be very useful in the design of your sampling program.
5.0 Thinking About Data Analysis
This is the stage of your study design when you should begin thinking
about how the data will be analyzed. You should start by converting your
objective statements into null (H0) and alternative (Ha) hypotheses.
For example, consider the objective presented in Case A, Example 1. The
study objective is a very specific water quality concern which can be
readily converted into a set of null and alternative hypotheses. The
hypotheses to be tested could be stated as follows:
H0: The water at Public Beach A does not exceed the State water
quality standards for swimming during any portion of the summer
of 1980.
Ha: The water at Public Beach A exceeds the State water quality
standards for swimming at some time during the summer of 1980.
At this point, we are ready to select a statistical model which will
allow an efficient test of the null hypothesis against the alternative
hypothesis. The statistical methods that you select, along with the
knowledge you have gained about the system through reviewing past work,
will influence where you sample, such as above or below a treatment or at
the mouths of paired watersheds offering impact and controlled data
comparisons; and when and how often you sample, such as once a season
without replication or diurnal ly with replication. If you do not feel
comfortable designing your statistical analysis, you should review in
detail WSDG Technical Paper 00001 ("Statistical Methods Commonly Used in
Water Quality Data Analysis", Ponce, 1980) and/or seek the aid of a
statistician.
11
There are a few principles that you should keep in mind when you begin
thinking about your data analyses. These have been summarized from Green
(1979).
1. Carry out some preliminary sampling to provide a basis for
evaluation of sampling design and statistical analysis options.
Those who skip this step because they do not have enough time or
money usually ending up loosing both time and money.
2. To test whether a condition (treatment) has an effect, collect
samples both where the condition (treatment) is present and where
it is absent but all else is the same. Remember, an effect can
only be demonstrated by comparison with a control.
3. If possible, take replicate samples within each combination of
time, space, and any other controlled variable. Differences
among can only be demonstrated by comparison to differences
within. For example, if you are comparing NO3 yield from a
clearcut area with a forested area, only if you take replicate
samples can you separate sampling error from differences due to
the treatment.
4. If the system to be sampled has a large-scale environmental
pattern, break up the system into relatively homogeneous
subsystems and allocate samples to each by some predetermined
weighting criteria. For example, if you are measuring TDS in the
northern Rockies, you could reduce the overall variance
substantially if you broke your sampling periods into three
strata; baseflow, snowmelt, and stormflow; and weigh each by
di scharge.
It is very important that you consider the statistical analysis at
this stage of the study design. As Averett (1979) states "problems almost
always arise when statistical methods become an afterthought of study
design and are used as a salvage operation. This 'afterthought'
application of statistical methodology leads to the deadliest data analysis
trap of all--the mathematical manipulation of non-related, non-correlated
data, into a probability function."
One final comment before we proceed; it is important that you keep the
role of statistical methods in proper perspective. Their primary use is to
reduce data and to help us make "yes" or "no" statements about the
12
relation of samples collected from different populations. While there is
much merit in designing water quality sampling studies around a statistical
framework, it must be emphasized that the statistical testing of data is
not interpretation of data (Averett, 1979). It is the responsibility of
the hydrologist to interpret the results of the statistical analysis and
provide the line officer with information which can be used in the decision
making process.
6.0 Where, What and When
At this stage of your study design, you are ready to select your
sampling stations (where) , choose the water quality constituents to be
sampled at each station (what), and determine the sampling frequency of
each constituent at each sampling station (when) . This phase of the study
design requires a sound understanding of the hydrologic system and how the
water quality relates to the beneficial uses of the water resource. If the
study objectives have been clearly stated and you have spent time thinking
about the interaction between land use, hydrology, and water quality in
your system, the determination of where, what, and when should be fairly
straightforward.
Throughout this section you should keep two points in mind. First,
where, what, and when you sample should be directly related to the needs
and objectives of the study. Remember, the line officer holds you
responsible for the water quality data collected and it is your job to see
to it that unnecessary data are not obtained. Second, station location,
parameter selection, and sampling frequency are all very important. You
cannot short cut one without affecting the others (Averett, 1976).
13
6.1 Guidelines for Locating Sampling Stations
There are two factors which strongly influence the location of
sampling stations: (1) the type of monitoring and (2) the type of water
body. Guidelines for locating sampling stations are discussed for each of
these factors separately.
6.1.1 Station Location as Influenced by the Type of Monitoring
As you recall, water quality monitoring on National Forest System
lands can generally be classified as (1) cause-and-effect, (2) compliance,
(3) baseline, and (4) inventory. Locating the sampling stations for
cause-and-effect monitoring is generally the easiest to carry out. The
strategy in this case is to isolate the treatment effects by (1) sampling
above and below the treatment and/or (2) sampling before and after the
treatment. Consider the example presented in Figure 1. There we have a
treatment which covers only a portion of a small stream. Stations A and B
have been placed immediately above and below the treatment, respectively,
to isolate it. Station A represents the control. Station B, in theory, is
assumed to be similar to Station A in all respects except that it includes
the effect of the treatment. Whenever the "above and below" approach is
used, you must be certain the above station is a satisfactory control.
The type of sampling design shown in Figure 1 readily lends itself to
two types of statistical testing: (1) comparison of the means of Stations
A and B and (2) comparison of the regression of Stations A and B. If the
variance of the water quality parameter of interest is not strongly
influenced by fluctuations in the stream flow, a simple comparison of the
means can be made to test for treatment effect. The hypotheses to be
tested are as follows:
14
Figure 1. Example of station location for cause and effect
monitoring study where the treatment can be readily isolated.
H0: = yB
Ha: PA i yB
where y/\ and yg denote the mean at Stations A and B, respectively. The
statistical method generally employed to make this comparison is the paired
t-test. However, if the variance is strongly influenced by discharge, it
is very likely that the treatment effects will be masked. If you develop a
regression of the water quality constituent versus discharge (commonly
referred to as a rating curve) you can remove or explain much of the
variance due to flow and make a stronger test of the treatment effect.
A suspended solids rating curve is illustrated in Figure 2. Note, a
log X transformation has been applied to the data to obtain a linear
15
log Qw
Figure 2. Hypothetical rating curves of suspended solids
(log Qss ) versus flow (log Qw) for Stations A and B.
regression. This is usually required since most water quality constituents
are best related to flow by a power function, which can be linearized with
a log X transformation. To test for the treatment effect, we would compare
the slopes of the regression lines and their intercepts. The hypotheses to
be tested are as follows:
H0: slope A = slope B H0: intercept A = intercept B
Ha: slope A t slope B Ha: intercept A / intercept B
Covariance analysis would be the statistical method employed to make these
comparisons.
If the above and below stations were established prior to the
treatment and a paired sample data base developed both before and after the
treatment, the opportunity exists to develop a paired-station plot. Such a
plot for suspended solids concentrations at Stations A and B, both before
and after treatment, is illustrated in Figure 3. In general, these
regressions have strong correlation coefficients because many of the
16
After treatment
Before treatment
<
SS (mg/I) at Station B
Figure 3. A paired-station plot for suspended solids concentration.
background variables that contribute to variance in the data, such as
climatic and hydrologic variables, have been normalized at both stations.
Consequently, this method enables us to make a better assessment of the
treatment effects than any of the methods previously described. The actual
statistical comparison is the same as that explained for the regression
curves.
In some cases, we cannot isolate a treatment by placing stations above
and below. Such an instance is illustrated in Figure 4. Here the
treatment, which could be a vegetative conversion on a grazing allotment,
covers an entire tributary system. There are two approaches to locating
sampling stations in this case. The first is to simply position a station
immediately below the treatment (such as Station A, Figure 4), and another
one (such as Station B, Figure 4) on a watershed which is similar to the
treated watershed in all respects (that is climate, geology, soils,
vegetation, land use, etc.) except it is not influenced by the treatment.
17
V
Figure 4. Sample station location for the paired watershed approach.
With either approach, a valid assessment of the treatment effect would
require sampling both before and after the treatment. If only one station
is established, the statistical comparison will be made using the before
and after means or regression lines. If two stations are established, the
comparisons can be made using the before and after means or paired-station
regressions. The paired station approach is recommended over the single
station approach because it allows you to account for year-to-year
variation in climate and hydrology.
Compliance monitoring is generally performed to protect public health
and to assure that waters draining from National Forest System lands meet
State water quality standards. In general, station location involves the
positioning of a single sampling station or a pair of stations. Consider
the situation where the drinking water in a campground needs to be tested.
18
In general, there is a single water source, such as a well or stream, from
which the water is collected and distributed through lines to various
locations within the campground. In this type of a situation, care should
be taken not to select a single water tap and designate it as the sampling
station, but instead each time a sample is required, select any one of the
water taps at random (not haphazardly) and then collect the sample.
In the case of a swimming beach, such as that illustrated in Figure 5,
you might have to establish several sampling stations. Because of the
shape of the lake, one sampling station may not be enough to provide a
representative sample. Consequently, the area of concern may have to be
divided into homogeneous strata, each of which is sampled separately. This
type of sampling design enables you to make a direct comparison with the
standard or compare the sample mean with the standard.
Sometimes compliance monitoring requires the surveillance of point
sources. Consider, for example, a sewage lagoon which treats the waste
from a campground and whose effluent drains into a perennial stream (Figure
6). There are two approaches to locating sampling stations in this
situation. If the State standards require the effluent to be of a fixed
quality or better, the station should be positioned to sample the effluent
directly, such as in Case I, Figure 6. If the State standards require that
the effluent not increase the stream's composite load by a certain
difference, such as temperature by 2°C, stations would have to be
positioned above and below the outfall (Case II, Figure 6).
Baseline monitoring is designed to provide information on water
quality trends. In general, stations are positioned strategically
throughout a Forest or District (such as at the mouths of major streams or
confluences of major tributaries) to obtain trend information for a wide
19
Figure 5. A plane view of a sampling station
location at a swimming beach along a lake.
Figure 6. Sampling station location for two cases, I and II,
in which a point source effluent is draining into a stream.
20
range of conditions, such as climate, topography, geology, soils,
vegetation and land use.
Inventory monitoring is designed to characterize the water quality of
a Forest on a broad scale. Sampling stations are usually located on major
streams at or near the Forest boundary or at other strategic locations
within the Forest. These stations are often positioned so that they
integrate several different land uses. As a result, the quality of water
at these stations often times represents the cumulative impacts resulting
from multi-resource management activities on the Forest.
6.1.2 Station Location as Influenced by the Water Type
In general, there are three types of water bodies of concern to the
forest hydrologist: (1) streams, (2) lakes and reservoirs, and (3)
groundwater. The establishment of sampling stations along or in any of
these water bodies is directly related to the character! sties that control
the movement of water and distribution of water quality parameters in that
water body.
There are several factors that you should consider when you are
locating sampling stations in streams: (1) tributaries, (2) mixing
characteristics, (3) suitability for discharge measurements, (4)
accessibility, and (5) suitability for biological monitoring. Tributaries
should always be considered in locating sampling stations because of the
effect they can have on the receiving water. The question, however, is
whether or not a specific tributary should be included in the monitoring
program. In general, tributaries involved in cause-and-effect and
compliance monitoring studies should be monitored. If they are not
included, it is very difficult to isolate constituents of concern and
21
minimize variability. An example of station location for a
cause-and-effect study in which a tributary is involved is presented in
Figure 7. By placing sampling stations above and below the clearcuts
(treatment of concern) on both the mainstem and tributary allows us to
assess the effect of logging on stream quality and to exclude the effects
of the pasture and the mountain home development.
The problem lies with baseline, inventory, and mixed monitoring
studies where large areas are involved. It is not practical to include
every tributary in our monitoring network, yet, how do we decide which ones
to include? Ideally, the best way to make this assessment is to carry out
a preliminary reconnaissance and sample all the tributaries at least once.
However, most of the time this is not possible because of constraints
in manpower, time, and money. The hydrologist, therefore, must consider
each tributary separately and develop a list of potential tributaries to
sample. Averett (1976) suggests you consider the following guidelines when
performing this task.
1. Be thoroughly familiar with the physical characteristics of the
system you are studying. Consider such things as drainage area,
geology, soils, vegetative type and land use. A large variation
of any of these factors in a tributary from the conditions of the
mainstem calls for the tributary to be included in the sampling
network.
2. Consider the dissolved solids concentration or the electrical
conductivity of the tributary. If during low flow periods
electrical conductivity or dissolved solids are higher or lower
when compared to the mainstem flow, then you have strong reason
to consider monitoring the tributary.
3. Look for sediment plumes and sand and gravel bars near the mouth
of tributaries. The presence of these features is an indicator
of erosion upstream and is reason to consider monitoring the
tributary.
4. If a tributary provides a proportionately large volume of flow to
the mainstem, you should consider establishing a monitoring
station at its mouth. An upstream tributary may be small
compared to the downstream mainstem. However, in its upstream
22
Figure 7. Example of sampling station location for a cause-and-effect
monitoring study in which a tributary is involved. Stations A and C lie on
the mainstem while Station B is on the tributary.
location, the tributary may contribute substantially to the
mainstem both in quantity and quality. In other words, you
should not select tributaries for sampling based upon volume of
flow alone, but rather based on their volume relative to the
mainstem at the confluence.
5. If a tributary is of sufficient volume and different water
quality to influence the mainstem, it may be useful to establish
some stations on the tributary other than at its mouth.
How well -mixed a water quality constituent is in a stream is dependent
upon the physical and chemical nature of the constituent as well as the
physical characteristics of the stream. The physical characteristics of
the stream which affect mixing include temperature, depth, velocity,
turbulence, slope, changes in direction, and roughness of the bottom.
In general, if the sampling point of interest is some distance
downstream from a tributary or other point source, such as a sewage outfall
or irrigation return flow, the water quality is usually fairly well mixed
across the cross section. Most sampling problems involve mixing below
tributaries and other point sources. Vertical mixing (from surface to
bottom) is usually quite rapid due to the turbulence of mountain streams.
Lateral mixing (from one side to the other), on the other hand, may not be
23
complete until the stream has passed through several sharp bends. Consider
the example presented in Figure 8. The water from the tributary "hugs" the
bank until the first bend has been entered. In this bend, the tendency of
the water is to continue in a straight line and, as a result, mixing
begins. By the time the water enters the third bend, the lateral mixing is
nearly complete. Consequently, when you are positioning stations below a
tributary or other point source, make sure that you thoroughly consider the
mixing effects. If you do not, your sample may not be representati ve of
the system.
When establishing sampling stations in the field, it is important that
you consider the suitability of each station for discharge measurements.
Many water quality studies on streams have been of little use because
discharge measurements were not made and most water quality constituents
are flow dependent. Without discharge measurements, you cannot perform a
mass balance or determine mass yield, both of which are important water
quality data analysis techniques.
Another concern when locating stations is accessibility. If a
sampling station is located a substantial distance from a road, make sure
time and manpower costs of sampling are considered. In many cases, bridge
24
locations are selected for sampling stations. They provide ready access to
the entire cross section, even during high flows. Bridges are, however,
not without their disadvantages. Their purpose is to move traffic and, as
such, may not be positioned properly for water quality monitoring purposes.
Bridges may influence the water flow and quality at a site.
If biological sampling is to be involved in the study, you should
consider the physical substrate (boulders, rubble, sand, and mud), velocity
of flow, exposure to the sun and the width and depth of the stream. In
general, aquatic biological sampling in streams involves systematic
resampling of (1) a transverse or longitudinal transect or (2) a grid or
quadrant system. Transect sampling consists of collecting samples either
along a section of stream length of in a line across the stream (Figure 9).
Samples may be collected at uniform intervals along the transect line or at
random. If the transect line is along the stream length and includes pools
and riffles, each habitat is usually considered separately and sampled
equally. A sampling grid or quadrant consists of an imaginary or physical
rectangular arrangement of lines, covering all or part of a given habitat
(Figure 9). A grid or quadrant sampling scheme should, as with the
transect scheme, give equal consideration to the various habitat types.
When locating sampling stations in a lake or reservoir, you need to
consider the (1) thermal stratification, (2) circulation of the water, and
(3) morphology of the basin. Each of these factors strongly influences the
spatial distribution of the water quality parameters throughout the lake or
reservoir.
In temperate regions, lakes and reservoirs deep enough to stratify
will typically develop a temperature profile similar to that in Figure 10.
This profile consists of three zones, the epilimnion, the metalimnion, and
25
Depth
Figure 9. Examples of transect and grid sampling schemes.
A illustrates longitudinal and transverse transects while
B illustrates a grid of nine sampling sites (after Averett, 1977).
Temperature
Figure 10. The three zones of a temperature
profile in a stratified lake.
26
the hypolimnion , each defined by the rate of change in temperature with
depth. In general, the epilimnion is a fairly wide zone consisting of warm
water which has a moderate temperature gradient. The metal imnion is
commonly a narrow zone characterized by a very rapid temperature change in
depth. The hypolimnion spans from the base of the metal imnion to the
bottom of the lake or reservoir and has a slight to moderate temperature
gradient. Density differences of the water, which are related to the
temperature, effectively isolate the hypolimnion from the zones above
except for particle exchange due to gravity or movement of fish. If
bacterial respiration is excessive in the hypolimnion, which is usually the
case when the water body is in a eutrophic or enriched state, the dissolved
oxygen can be depleted and anaerobic conditions may develop. If this
condition occurs the dissolution of phosphorus, iron, manganese and other
trace metals from the sediments can be expected.
The epilimnion and metal imnion are warmer than the hypolimnion and are
the zones of phytoplankton production. As a result, the water quality in
these zones may be substantially different than that of the hypolimnion.
The point to remember here is that the thermal zones in a lake or
reservoir can have water quality quite different from one another. When a
surface site is selected you must consider the thermal zones below it and
make certain that the samples you obtain are representative of the system
you think you are sampling. In many studies, you will find it necessary to
establish several sampling stations along a depth profile (Figure 11).
Temperature, dissolved oxygen, specific conductance, and pH are very useful
measurements to make when deciding where to locate sampling stations along
a depth profile.
27
V
Epilimnion
Metalimnion
Hypolimnion
• = Sampling station
Figure 11. Illustration of sample locations along the
depth profile in a stratified lake.
Circulation of the water is another factor that you need to consider
when locating stations in lakes and reservoirs. During the spring and
fall, the water mass overturns, due to a density change derived from the
seasonal cooling or warming, and the water obtains a uniform temperature
throughout the entire depth profile (Figure 12). At this time, the water
quality is generally uniform throughout the depth of the lake and a single
sample collected at 0.5 to 1.0 meters depth may be representative of the
water column.
Wind will generally cause the water in the epilimnion to circulate and
facilitates the mixing of water quality constituents throughout this zone
(Figure 13). In the case of a circular lake where wind mixing has
occurred, a sample collected at the lake's outlet would probably be as
representative of the water quality of the epilimnion as a sample collected
at the center of this zone.
28
Temperature
Q.
CD
Q
' r
Figure 12. Temperature profile in a lake or reservoir during the
period of overturn, either in the spring or fall.
Figure 13. An illustration of the effect of wind on the
mixing of water in the epilimnion.
If the morphology of a lake or reservoir is irregular, the mixing
patterns of the epilimnion by the wind may vary substantially. As a
result, several sampling stations may be required to characterize the water
quality of the lake. For example, consider the lake illustrated in Figure
14. Here we have several land uses located around a lake which is
irregularly shaped. The area around the recreational home development is
shaped like an hour glass and should probably have each "bulb" sampled
29
Prevailing winds
Figure 14. A hypothetical example of where to locate sampling stations
to monitor surface water quality on a multiple use lake.
30
separately. The island isolates a cove which would require that it be
sampled separately. The other coves and the center of the lake may or may
not have to be sampled, depending on the mixing caused by the wind. The
swimming beach area, which is divided by a peninsula, would require at
least two sampling stations. However, the actual number of sampling
locations and intensity of sampling would depend upon the original
objectives of the monitoring plan.
When locating sampling stations in lakes and reservoirs, be careful
not to overlook the areas of sediment deposition (Averett, 1976). These
are often areas of potential enrichment and may have a substantial
influence on the water quality of the lake or reservoir in the future as
well as give insight to past conditions of the water body. You may need to
obtain some grab samples or dredge hauls of the bottom sediment in your
sampling program to delineate these areas. You also may wish to further
delineate your stations with a bathymetric map of the lake or reservoir if
one is not available.
Most groundwater quality problems confronting the forest hydrologist
involve the contamination of unconfined or water table aquifers from point
sources, such as solid waste disposals or leach fields below sewage
treatment facilities. When locating your sampling stations for this type
of problem, you need to consider the soils and geology of the area, flow
direction of the ground water and accessibility. Consider the example
illustrated in Figure 15 where we have a solid waste disposal site.
Precipitation leaches through the disposal, picks up metals and other
contaminants and transports them to the water table. The soil and geology
of the area influence the rate at which leachate moves toward the water
table. Depending on the nature of the contaminant, the soil and geology
31
CROSS-SECTION VIEW
j Precipitation
* 1
Water table
PLANE VIEW
Contamination boundary
Figure 15. Location of sampling stations around
a solid waste disposal site.
32
may act as a filter and reduce the concentration of the contaminant
reaching the water table. If a clay lens is present, a perched water table
may develop. The movement of the ground water strongly influences where
the observation wells are placed. In many cases, wells are simply located
above and below the source to quantify the effect of the treatment. In
other cases, the concern might lie with the rate and extent of
contamination which would require a more extensive monitoring program
(Figure 15). Sometimes, we are not even sure which way the ground water
flows and must position our observation wells in a radial pattern around
the source (Figure 16).
Figure 16. Radial design of observation wells around a point source.
33
If the groundwater problem involves a confined aquifer, it is
important that you obtain knowledge of the aquifer in question. At a
minimum this should include the areal extent of the aquifer, its width and
its transmissibility. Walton (1970) and Freeze and Cherry (1979) present
several excellent illustrative examples of groundwater monitoring.
In general, access is limited to existing wells and as a result, we
can only obtain sketchy information about the system. The cost of drilling
new wells is usually prohibitive. However, if the opportunity arises to
establish a well for monitoring purposes, you should consult a geologist
about placement.
6.2 Selecting Water Quality Constituents
Every water quality constituent you monitor represents an investment
in time, energy and money. When designing your water quality program be
sure that each constituent carries its own weight and will contribute data
that help solve the problem or question at hand.
Table 2, which is an Activity and Concerns - Water Quality Matrix, has
been developed to provide you with some guide! i nes for water quality
constituent selection. The left margin of the table consists of pertinent
hydrologic and water quality constituents. The hydrologic constituents
have been included because measurement of water flow and/or volume is
essential for most water quality studies and it is important that they are
not overlooked. At the top of the table is a series of activities and
concerns. This series of activities and concerns is not all encompassing,
but does include the major ones of interest to the forest hydrologist.
Each activity and concern, in turn, has been subdivided by water type:
stream (S), lake or reservoir (L), and ground water (G). For each
34
ACTIVITIES AND CONCERNS
a- F- c/i
'S f5 1
• *
CD U
g Vi
*1-0 I
35
combination of activity or concern, water quality type, and constituent,
there is one of four priority codes: 1, 2, 3 or blank. A primary code, 1,
suggests that it is very important that the constituent be monitored.
Sampling these constituents will provide information which is necessary to
meet study objectives. A secondary code, 2, suggests that it is important
that a constituent be monitored, however, if funds are restricted, these
constituents should be considered a lower priority than those coded by a 1.
These constituents usually supply supporting information which address the
study objectives. A tertiary code, 3, means that this constituent probably
will contribute little direct information to the study objectives, but may
be useful for other purposes. A blank suggests there is no need to monitor
the constituent.
Please keep in mind that these priority codes are presented only as
guide! ines. The specific needs and objectives of your study objectives of
your study may require more emphasis be placed on certain constituents and
less on others.
For individuals interested in a review of the various water quality
constituents, their significance to beneficial uses and land use-water
quality interactions, the following literature is suggested: Brown (1972),
U.S. EPA (1977, 1976a, 1976b, 1973 and 1971), U.S. Forest Service (in
press), Greeson, et al (1977), Guy (1970), Hem (1970), Krygier and Hall
(1971), McKee and Wolf (1963), McNeely, Neimans and Dwyer (1979), and
Thatcher, Janzer and Edwards (1977).
6.3 Guidelines for Determining Sampling Frequency
The frequency of sample collection should be designed to provide the
data necessary to (1) calculate an estimate of a specific population
36
parameter, such as the mean, and/or (2) develop a regression relationship.
In either case, we want our parameter and regression estimators to fall
within some pre-established bound of reliability. As a result, sampling
frequency should be directly related to the variance of the water quality
constituent of concern. In other words, the more variable a constituent is
in time and space, the more frequently it must be sampled to achieve a
given level of reliability.
In this subsection, guidelines for determining sampling frequency for
several different sampling methods are presented. It should be noted that
emphasis has been placed on application of the methods opposed to the
intricacies of the underlying statistical theory. For a more detailed
discussion of each method, including the underlying theory, two references
are suggested: Mendenhall, Ott, and Schaeffer (1971) and Cochran (1963).
Much of what follows in this subsection has been taken from Freese (1962),
with minor modifications.
6.3.1 Systematic Sampling
Systematic sampling is easily carried out and under some circumstances
is a useful method. It consists of randomly selecting the first time of
sampling and then selecting the remaining samples at some pre-determined
interval, such as weekly, biweekly or monthly. While this simple method
can be easily used in most water quality studies, it has serious
limitations in that the data may be biased. If the data are biased, the
statistical analysis may lead to erroneous inferences about the water body
being examined.
37
6.3.2 Simple Random Sampling
The fundamental principle in simple random sampling is that, in
choosing a sample of "n" observations, every possible combination of "n"
observations should have an equal chance of being selected. For example,
if you plan on collecting 25 daily samples over a period of one year, you
must choose the 25 days of sample collection in a random manner.
The question of interest here is. How do we determine "n"? More often
than not, "n" has been arbitrarily selected by a sampler basing the
decision of what "looks right." Fortunately, a simple, objective procedure
exists for determining "n" when using the simple random sampling method.
The procedure is based on the level of risk the sampler is willing to take
when estimating the mean. The level of risk, in turn, is directly related
to the beneficial use of water. Obviously, if you are dealing with a
drinking water supply you would be more concerned with the accuracy of
your estimate than if you were dealing with a stock watering tank.
In planning a water quality survey, we might state that unless the
l-in-20 chance (a= 0.05) occurs, we would like our sample estimate of the
mean to be within some specified error range of the population mean such as
mg/1. Since the small sample confidence limits are computed as
X = ± t„Sx (1)
where X is the mean, t denotes the Student's t value for a specified a and
sj( is the standard error of the mean, this is equivalent to stating that
we want E = t„ s* (2)
For a simple random sample the standard error of the mean can be determined
^ = Vn (’ -S) (3)
where s^ is the sample variance, "n" the number of units sampled and N is
the total number of units in the population. Substituting equation (3)
38
into equation (2) and solving for "n" yields equation (4).
n
+
N
(4)
To determine "n", we must have some estimate of the population variance,
the absence of this information, a small preliminary survey might be made
in order to obtain an estimate of the variance. When, as often happens,
neither of these solutions is feasible, a very crude estimate can be made
using equation (5) where R is the estimated range from the smallest to the
largest concentration (mass) likely to be encountered in sampling. This
approximation procedure should be used only when no other estimate of the
variance is available and the observations are approximately normally
di stributed.
Having specified a value of E and obtained an estimate of the
variance, the last piece of information required is the value of t. Here
we hit a circular problem. To use t we must know the number of degrees of
freedom. However, the number of degrees of freedom is "n-1" and "n" is not
known and cannot be determined without knowing t.
An iterative approach can be used to solve this problem. The
procedure is to guess at a value of "n," use the guessed value to get the
degrees of freedom for t and then substitute the appropriate t value into
the sample-size formula (equation 4) and solve for a first approximation of
n. Selecting a new "n" somewhere between the guessed value and the first
approximation, but closer to the latter, we compute a second approximation.
The procedure is repeated until successive values of "n" are nearly the
same; usually three trials will suffice.
s** . Sometimes the information is available from previous surveys. In
(5)
39
If the sampling fraction is likely to be small (f[ < 0.05)
n . ,
the term 1-|[ of the standard error formula (3) can be ignored and
the sample size formula (4) simplifies to
Examples 2a and 2b illustrate the estimation of sample size for the
simple random sampling method.
40
Example 2a
Estimating Sample Size for the Simple Random Sampling Method
Problem:
Blue Spruce Reservoir, which is underlain by gypsum bearing rock
formations, drains into Camp Creek. There is some concern by downstream
users that the sulfate concentrations are excessively high. The Forest
Supervisor would like an estimate, within 15 mg/1 , of the mean annual SO4
concentration passing the stream gage immediately below the outlet spillway
with a fairly high degree of reliability (a= 0.05). There is little
fluctuation in the discharge from the dam, therefore, simple random
sampling can be applied. Assume the SO4 concentration varies between 20
and 100 mg/1 during the year. Estimate the necessary sample size, n.
If the sample size is less than 18, then we may use the simplified
formula since 18/365 = 0.049 < 0.05.
We know from the problem that E = 15 mg/1, a= 0.05 and R = 80 mg/1. The
variance can be estimated as follows.
To determine t we can use as a first approximation n = 18 which yields 17
d.f. and t. 05(17) = 2.110 (See Appendix Table A, Values of t). The first
estimate on n can now be calculated.
The correct solution is somewhere between 7.91 and 18, but much closer to
7.91. For our second trial we select n = 8. The value of t now becomes
2.365.
Solution:
(2.1 10)2 (400)
n = 7.91
n
(2.365)2 400
(15)2
n = 9.94
41
We now know the correct solution lies between 8 and 9.94. Repeated trials
will give values between 9.1 and 9.94. Since the sample size, n, must be
an integral value and, because 9 is too small, a sample of n = 10
observations would be required for the desired precision.
42
Example 2b
Estimating Sample Size for Simple Random Sampling
Problem:
A preliminary sample (10 observations) of electrical conductivity in
the epilimnion of Elk Lake yielded the following statistics.
X = 187 s = 35
What sample size would be required to estimate the mean EC in the
epilimnion of Elk Lake within plus or minus 10 percent, with a l-in-20
chance of being wrong in the conclusion that y^u have done so. Assume
simple random sampling is to be employed and ^-is less than 0.05.
Solution:
The confidence limits on the mean are given by
X
± to
s
v"n
Therefore:
1 87 ± t Q5
35
\fn
The 95 percent confidence limits of plus or minus 10 percent of the
mean gives
18.7
t 05
35
\fn
Solving for "n" yields
n
t os2 (35)2
(18.7)2
For our first trial we select n = 25 which gives us 24 d.f.; therefore
*05(24) = 2.064.
_ (2.064)* (35)2
" (18.7)*
n = 14.9
43
We know the correct solution lies between 14.9 and 25, but closer to 14.9.
For our second trial n is set at 16.
_ (2.131)2 (35)2
(18.7)2
n = 15.9
From repeated trials we find little difference in the calculated n,
therefore we select 16 as the sample size.
44
In some cases you may want to determine your sample size based on a
pre-established estimate of the magnitude of change (difference) in the
concentration or mass of a water quality constituent between paired
stations. As with other procedures used to estimate sample size when
simple random sampling is employed, this method is also based on a good
estimate of the sample variance. The method outlined below is discussed in
detail by Snedecor and Cochran (1967) and has been summarized by Potyondy
(1977).
The procedure requires you to select a value, d, which represents the
size of difference between the paired stations that is regarded as
important. If the difference is as large as d, we would like the
monitoring program to have a high probability (probabilities of 0.80 and
0.90 are common) of showing a statistically significant difference between
the paired stations. In statistical jargon, the calculation allows the
selection of the confidence level of the test (1 - a) as well as the power
of the test (1-3) and combines these two elements in determination of the
sample size.
The following example taken from Potyondy (1977) is used to illustrate
the mechanics of this procedure. Consider the following sample statistics
from a set of turbidity data collected on the East Fork Smiths Fork
Barometer Watershed in Utah and Wyoming: X = 4.5 JTU; s = 2.83. (It
should be noted that an underlying assumption of this procedure is that the
data are normally distributed.) The standard deviation, s, can be
expressed as a percent of the mean, referred to as the coefficient of
variation, C V. Therefore:
CV = (s/X)100 = (2.83/4.5)100 = 63% (7)
45
(8)
The standard deviation of the difference, s^, is estimated as:
sd = 2 vCv = 2 v(63) = 89%
Suppose we wish to detect a difference of 5 JTU's between the paired
stations of interest. Expressed as a percent of the mean, the difference
to be detected, d, is determined as follows:
d = (5.0/4.5)100 = 111% (9)
Assume that we want to be 90 percent certain of showing a statistically
significant difference between means in a two-tailed t-test at the a = 0.05
level of significance.
The following formulas apply:
(10)
where M(o.90,0.05) 1S a multiplier from Table 3 which is equal to 10.5.
Substituting and solving for n-j yields:
ni = (89^/11 1 2 ) (10.5) = 6.75
which is rounded up to the next highest integer
ni = 7
Degrees of freedom, v, are determined as follows:
v = 2ni - 2 = (2) (7) - 2 = 12 (11)
The required sample size, n, can now be determined.
Sample size = n = (v+ 3) n-j/(v+ 1) = (15)(7)/(13) = 8.08 (12)
The sample size to use is rounded to 8.
ni = (sd/d2) M(l-e,a)
Table 3
•
Multi pi ier
• (M)
of ( sd%d^ ) t0 be
used
in paired comparitive
sample
si;
ze calculations
(after Potyondy,
1977)
•
Two-l
tailed Tests
One-
tailed
Tests
(i
- 3)
a 1 evel
a level
0.01
0.05 0.10
0.01
0.05
0.10
0
.80
11.7
7.9 6.2
10.0
6.2
4.5
0
.90
14.9
10.5 8.6
13.0
8.6
6.6
.95
17.8
13.0 10.8
15.8
10.8
8.6
46
Although simple random sampling has its place in water quality
monitoring, it is limited because the watershed system under investigation
is too variable with regard to its component parts. Fortunately the
component parts of most watershed systems vary within a definite and
repeated pattern and their variability can be reduced and better understood
using stratified random sampling methods (Averett, 1976).
6.3.3 Stratified Random Sampling
Stratified random sampling is a commonly used sampling method in water
quality studies. This method allows the hydrologist to take advantage of
prior knowledge concerning the mechanisms and processes controlling the
water quality in a watershed system. In stratified random sampling, the
units of the population are grouped together on the basis of similarity of
some characteristic, such as flow regime (that is baseflow, stormflow,
snowmelt runoff, etc.) or temperature in a lake, such as the epilimnion and
the hypolimnion. Each group or stratum is then sampled and the stratum
estimates are combined to give a population estimate.
Stratified random sampling offers two primary advantages over simple
random sampling. First, it provides separate estimates of the mean and
variance of each stratum. Second, for a given sampling intensity, it
generally gives more precise estimates of the population parameters than
would a simple random sample of the same size. For this latter advantage,
however, it is necessary that the strata be established so that the
variability among sample values within the strata is less than the
variability in the population as a whole.
Some drawbacks of stratified random sampling are that: (1) each unit
in the population must be assigned to one and only one stratum; (2) the
47
size of each stratum must be known; and (3) a simple random sample must be
taken in each stratum. The most common barrier to the use of stratified
random sampling is lack of knowledge of the strata sizes.
To illustrate the computational procedures required to determine the
mean and its confidence limits from a stratified random sample consider the
electrical conductivity data tabulated in Table 4. The flow regime was
divided into three periods (strata): (1) winter baseflow (November 1/
April 15); (2) snowmelt runoff (April 16/July 15); and (3) summer runoff
(July 16/October 30). Grab samples were collected ten times during winter
baseflow, 25 times during snowmelt runoff and 15 times during summer
runoff. Only one sample was collected per day and each sample day was
selected at random.
Table 4. Electrical conductivity data (ymhos/cm) collected from a Rocky
Mountain stream.
Stratum
Observations
I. Winter Baseflow
110
100
112
119
Total = 1087
105
113
X = 108.7
115
106
s = 6.25
107
100
II. Snowmelt Runoff
89
73
51
41
57
72
54
43
47
69
Total = 1505
43
50
49
51
77
X = 60.2
51
62
68
63
81
s = 14.6
68
74
39
48
85
III. Summer Runoff
156
172
191
145
164
210
Total = 2476
129
178
139
X = 165.1
187
154
145
s = 21.78
159
167
180
48
The mean EC of the stratified sample is computed by the general
equation
(13)
Where Xy$ is the mean of the stratified sample, L the number of strata,
Nh is the total size (number of possible observations) of stratum h, and
N is the total number of observations in all strata. Using the data
presented in Table 2, the mean can be calculated as follows:
L = 3
Nj = 166 Xj= 108.7
Nn = 91 Xu = 60.2
N i i i = 108 Xjjj = 165.1
N = 365
_ 166(108.7) + 91(60.2) + 108(165.1)
365
ECts = 113 Mnnhos/cm
The mean EC computed here is basically a time weighted average which is the
average daily EC of the water passing the point of measurement.
The standard error of the mean of a stratified random sample is
calculated by the general equation
where n^ is the number of observations in stratum h, s^ is the
variance of sample from stratum h and the other terms are as previously
49
defined. If the sampling fraction within a particular stratum (n^/Nh)
is small (that is less than 0.05), the term (l-n^/N^) can be omitted
for that particular stratum when calculating the standard error of the
mean. For the electrical conductivity example the standard error can be
calculated as follows:
SyT
>4
/l
[(166)2 (6.25)2 / 10 \ (91)2 (14.6)2 /
(108)2 (21.78)2
(l - J5
(365)2
L 10 \ 166/ 25 \
91/
15
\ 108/J
Svx = 188
A rough estimate of the 95% confidence interval about the mean can be
obtained using equation (15).
XST ± 2(SxT). (15)
For our electrical conductivity example, the confidence interval would
range from 109 to 117 ymhos/cm.
Before an estimate of the total sample size can be made, the
hydrologist must select the method of sample allocation. Basically, there
are two methods of sample allocation: proportional and optimal. In the
proportional allocation procedure, the proportion of the sample that is
selected in the hth stratum is made equal to the proportion of all units
in the population which fall in that stratum. If a stratum contains half
of the units in the population, half of the samples would be collected in
that stratum. In equation form, if the total number of sample units is to
be "n," then for proportional allocation the number to be observed in
stratum "h" is
nh = ^n)" (16)
In optimum allocation the observations are allocated to the strata so
as to give the smallest standard error possible with a total of "n"
50
observations. For a sample size "n," the optimum allocation is
2 N„sh
n
(17)
The best way to allocate a sample among the various strata depends on
the study objectives and our information about the population. The optimum
allocation is preferable if the objective is to get the most precise
estimate of the population mean for a given cost. If we want separate
estimates for each stratum and the overall estimate is of secondary
importance, we may want to sample heavily in the strata having high-value
information. Then we would ignore both optimum and proportional allocation
and place our observations so as to give the degree of precision desired
for the particular strata.
The procedure for estimating the total size of sample (n) needed in
stratified random sample can now be addressed. Basically three pieces of
information are required:
2
(1) a reasonably good estimate of the variance (s ^ ) or standard
deviation (s^) among individuals within each stratum.
(2) the method of sample allocation.
(3) a statement of the desired size of the standard error of mean,
symbolized by D.
Some preliminary sampling is generally required to determine the
desired size of the standard error of the mean. The estimate of D in the
sample size equations is generally taken to be some portion, such as
two-thirds or one-half, of the standard error calculated from the
preliminary sample.
51
Given this hard-to-obtain information, the stratified random sample
size can be estimated by the following equations.
For proportional allocation:
t„2 N £ N„s„2
(18)
h = 1
n
L
N2D2 + t„2 ^ N„s„2
h = 1
For optimum allocation:
n
ta2
(19)
L
N2D2 + t„2 £n„s„2
The value "2" is commonly used as an estimate of the Student's t
value. When sampling fractions (n^/N^) are likely to be very small for
all strata, the second term of the denominators of the above equations
may be omitted leaving only N^D^.
If the optimum allocation formula indicates a sample (n^) greater
than the total number of units (N^) in a particular stratum, n^ is
usually made equal to N^. The previously estimated sample size (n)
should then be dropped, and the total sample size and allocation for the
remaining strata recomputed omitting the and s^ values for the
offending stratum, but leaving N and D unchanged.
Example 3 illustrates how to estimate the sample size for a
stratified random sample.
52
Example 3
Estimating Sample Size for a Stratified Random Sample
Rrobl em:
The mean daily electrical conductivity is to be determined at the
mouth of Cabin Creek which is located in the northern Colorado Rockies.
Estimate the sample size that would be required and distribute the samples
over a one year period.
Sol ution:
The flow regime can be divided into three periods (strata): winter
baseflow (November 1/April 15); snowmelt runoff (April 16/July 15); and
summer runoff (July 1/ October 30). Data collected on a nearby stream
provided information about the variance.
Stratum (h)
Nh
sh
1 (WB)
166
8
2 (SM)
91
24
3 (SRO)
108
41
An estimate of the standard error of the mean, sx, was made from past
data.
sx = 5.05
The desired D is set equal to one-half of sj(. Therefore, D = 2.53. In
addition, the optimal allocation method is selected to allocate the
samples .
The sample size, n, can now be determined using the optimal allocation
method.
n
296
2.15
138
The determined n is the sample size necessary to estimate the sample mean
with a standard error of 2.53. However, because of budgetary constraints,
it may not be possible to sample the stream 138 times. If that is the
case, then we would have to lower the reliability constraint on the
estimate of the mean. If we set D = sx the required sample size becomes
n ~ 58.
53
In this hypothetical problem assume that n = 58 is accepted. The next
step is to allocate the sample by strata. This is achieved as follows
[from equation (19)].
Strata 1.
(wi nter)
Pi = (166) (8) (58) „1Q
7940
Strata 2.
(snowmelt runoff) n. _ (91) (24) (58) ~ 16
7940
Strata 3.
(summer) n = (108) (41) (58) s 33
7940
At this point you should look at the allocation and ask yourself if it
looks right. In this case, most of the samples are allocated to the summer
runoff period. This is the period of greatest variation in the water
quality and, hence, the period that should be sampled most intensely. On
the other hand, the water quality is fairly stable during baseflow and
requires the least amount of sampling. Snowmelt varies twice as much as
baseflow but occurs over a period equal to two-thirds of the period for
baseflow. As a result, the sampling of snowmelt looks about right. It is
decided that the allocation is acceptable.
54
7.0 Guidelines for Collecting and Handling of Water Quality Samples
Obtaining representative samples and then maintaining the integrity of
the constituents is an integral part of any wildland water quality program.
If the samples are not collected and handled properly the data will be of
little value no matter how well the sampling program was designed.
Although analytical techniques have been standardized to a very high
degree (American Public Health Association (APHA) 1976), at this time,
there are no established standards for USDA-Forest Service hydrologists to
follow when collecting and handling water quality samples even though the
National Handbook of Recommended Methods of Water Data Acquisition (USGS,
1977) exists. As a result, collection methods may differ between
hydrologists. When analyzing data, it is generally taken for granted that
the data are representative of the water body from which the sample was
obtained. However, this assumption can result in erroneous inferences
about the quality of water body being studied, especially if several
different individuals were involved in the collection of the samples.
Before you compare data collected by different individuals, satisfy
yourself that the samples were collected and handled properly and that the
data are truly representative of the water body from which they were
collected. The methods of sample collection and handling as well as the
analytical methods used to measure each constituent, should be clearly
documented in the Water Quality Monitoring Plan of Operation.
The purpose of this subsection is to discuss the types of sampling and
to present guidelines for collecting and handling water quality samples.
55
7.1 Types of Samples
7.1.1 Grab Samples
A grab sample is a sample collected at a particular time and place.
Strictly speaking, a grab sample can represent only the composition of the
water body at that time and place. However, when a water body is known to
be fairly constant in composition over a considerable period of time or
over substantial distances in all directions, then a grab sample may be
said to represent a longer time period or a larger volume, or both, than
the specific point at which it was collected (APHA, et al , 1976). When a
water body is known to vary with time, grab samples collected at suitable
intervals and analyzed separately can be of great value in documenting the
extent, frequency and duration of these variations. Sampling intervals
should be selected on the basis of the frequency with which changes are
expected.
7.1.2 Composite Samples
In most cases, the term "composite sample" refers to a mixture of grab
samples collected at the same sampling point at different times or to a
sample formed by continuously collecting a portion of the flow. The
formation of a composite sample serves as an alternative to the separate
analysis of a large number of grab samples, followed by computation of the
average. Composite sampling can represent a substantial saving in
laboratory effort and funds; however, it should be noted that this savings
in energy and money is sometimes obtained at the expense of data
resol ution.
Composite samples can only be used for constituents that do not change
appreciably in character during the interval from collection to analysis.
56
Under no circumstances should microbiological samples be composited. If
preservatives are used, add them to the sample bottle initially so that all
portions of the composite are preserved as soon as collected.
7.2 Sample Collection
When samples are collected from a stream, the sampler must consider
the variability of constituent concentration with streamflow, depth, water
velocity, distance from the bank and distance from one bank to the other.
It is very important that samples be collected during representati ve flows
over the time period of interest. If storm flows occur, it is important
that they are sampled. In some cases, such as suspended solids, the
majority of mass transport will occur during storm flow and/or snowmelt
runoff. In some cases, data resolution will require sample collection on
both the rising-limb and falling-limb of the hydrograph.
If equipment is available, it is best to take an "integrated" stream
sample from the water surface to the stream bottom at selected intervals
across the channel in such a way that the sample is made composite
according to flow. If only a grab sample can be collected, it is best to
take it in the middle of the stream at the 0.6 depth. Brown and others
(1970), Guy (1970) and Greeson and others (1977) discuss the various types
of sampling equipment in detail.
Lakes and reservoirs are subject to considerable variations in water
quality from normal causes, such as seasonal stratification, precipitation,
runoff and wind. The choice of location, depth and frequency of sampling
will depend on local conditions and the purpose of the investigation. A
detailed discussion of sample collection methods in lakes and reservoirs
57
and equipment used to collect the samples is presented by Lind (1979),
Schwoerbel (1970) and Welch (1948).
The chemical quality of ground water at a sampling point may vary in
response to changes in rate of water movement, to pumpage, or to
differences in rate and chemical composition of recharge from precipitation
and from the surrounding area (Brown and others, 1970). Although
concentrations of dissolved constituents in ground water from any one well
may vary widely, sometimes several fold, in general the changes take place
much slower than those commonly associated with surface water. Usually, it
is safer to assume that the quality of the water from a well fluctuates
rather than that it is uniform for long periods of time. Changes in ground
water quality usually can be described satisfactorily by a monthly,
seasonal or annual sampling schedule. For more information about sampling
ground water, see Hem (1970), Walton (1970) and Freeze and Cherry (1979).
Samples should be collected from wells only after the well has been
pumped sufficiently to insure that the sample represents the ground water
that feeds the well. Before samples are collected from distribution
systems, such as water lines in a campground, flush the lines sufficiently
to insure that the sample is representative of the water supply and
sterilize the water tap.
In all cases, sampling points should be fixed by detailed description,
by maps, or with the aid of stakes, buoys or landmarks in such a manner as
to permit their identification by other persons without reliance upon
memory or personal guidance.
7.3 Sample Handling
A record should be made of every sample collected and every sample
container should be identified, preferably by attaching an appropriately
inscribed tag or label (APHA, et al , 1976). The record should contain
sufficient information to provide positive identification of the sample at
a later date as well as the name of the sample collector, the date, hour
and exact location, the water temperature, how the sample was handled (that
is refrigeration, acidification, degassing, etc.), and any other data
which may be needed in the future for correlation, such as weather
conditions, water level, stream flow, or the like.
After the sample has been collected, care must be exercised to protect
the integrity of the sample to assure at the time of analysis that it is
representative of the water body from which it was collected. In general,
the shorter the time that elapses between collection of a sample and its
analysis, the more reliable will be the analytical results. For certain
constituents, such as pH, immediate analysis in the field is required to
obtain dependable results because the sample composition may change before
it arrives at the laboratory.
It is impossible to state exactly how much time may be allowed to
elapse between collection of a sample and its analysis; this depends on the
character of the sample, the particular analyses to be made and the
conditions of storage. Changes caused by the growth of organisms are
greatly retarded by keeping the sample in the dark and at a low temperature
until analysis. Where the interval between sample collection and analysis
is long enough to produce changes in either the concentration or the
physical state of the constituent to be measured, follow the preservation
59
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62
practices outlined in Table 5. Record the time elapsed between sampling
and analysis, and which preservati ve, if any, was added.
Stainton and others (1977) suggest several special precautions when
sampling for nutrient elements. The usually low levels of these elements
in upland water resources make contamination a significant problem. While
the need for clean samples and sample containers is obvious, there are
several other contamination sources which must be avoided. Small amounts
of tobacco ash, dandruff and perspiration contributed by field personnel,
or plant pollen and other atmospheric particulates all can introduce
significant errors into nutrient element analysis. Field personnel must be
made aware of these and other possible sources of contamination.
The foregoing discussion is by no means all inclusive. It is
impossible to prescribe absolute rules for the prevention of all possible
changes. Some advice will be found in the discussions of methods of
determination of various constituents in Standard Methods (APHA and others,
1976) and The Chemical Analysis of Fresh Water (Stainton and others, 1977).
However, to a large degree, the dependability of water quality data must
rest on the experience and good judgement of the samples and analyst.
63
&.0 Literature Cited
American Public Health Association, Inc. and others 1976. Standard methods
for the analysis for water and waste water. 13th ed. Am. Public
Health Assoc. 874 p.
Averett, R.C. 1979. The use of select parametric statistical methods for
the analysis of water quality data. Presented at the USGS-BLM
Conference on Water Quality in Energy Areas. January 10-11, Denver,
Colorado. 16 p.
Averett, R.C. 1977. Biological sampling and statistics. In methods for
the collection and analysis of aquatic biological and microbiological
samples: U.S. Geol . Survey Techniques Water-Resources Inv., Book 5,
Chap. A4, p. 3-19.
Averett, R.C. 1976. A guide to the design of data programs and
interpretive projects. U.S. Geological Survey, Water Resources
Division, Central Region, Lakewood, Colorado 80225. 100 p.
Brown, G. 1972. Forestry and water quality. Oregon State University. 74 p.
Brown, E., M.W. Skougstad and M.J. Fishman. 1970. Methods for collection
and analysis of water samples for dissolved minerals and gases. U.S.
Geol. Survey Techniques Water -Resources Inv., Book 5, Chap. Al,
160 p.
Boynton, J.L. 1972. Managing for quality - A plan for developing water
quality surveillance programs on National Forests in California. In
the Proceedings of a Symposium on "Watersheds in Transition" held at
Fort Collins, Colorado, June 19-22. AWRA Proceedings series No. 14.
p. 84-90.
Busby, J.F. 1980. The design and execution of a groundwater geochemical
study. A class handout, U.S. Geological Survey, Water Resources
Division, Northern Great Plains Aquifer System Assessment, Mail Stop
418, Denver Federal Center, Lakewood, Colorado 80225. 52 p.
Cochran, W.G. 1963. Sampling techniques. John Wiley and Sons, Inc., New
York, New York. 413 p.
Freese, F. 1962. Elementary forest sampling. Agricultural Handbook No.
232. USDA-Forest Service. 91 p.
Freeze, A.R. and J.A. Cherry. 1979. Groundwater. Prentice-Hall, Inc.
604 p.
Greeson, P.E., et al . 1977. Methods for the collection and analysis of
aquatic biological and microbiological samples: U.S. Geol. Survey
Techniques Water-Resources Inv., Book 5, Chap. A4, 165 p.
Guy, H.P. 1970. Fluvial sediment concepts: U.S. Geol. Survey Techniques
Water Resources Inv., Book 3, Chap. Cl, 55 p.
64
Guy, H.P. and V.W. Norman. 1970. Field methods for measurement of fluvial
sediment: U.S. Geol . Survey Techniques Water-Resources Inv., Book 3,
Chap. C2, 59 p.
Hem, J.D. 1970. Study and interpretation of the chemical characteri sties
of natural water. U.S. Geol. Survey Water Supply Paper 1473. 363 p.
Huibregtse, K.R. and J.H. Moser. 1976. Handbook for sampling and sample
preservation of water and waste water. U.S. Department of Commerce,
National Technical Information Service. PB-259-946. 257 p.
Kennedy, V.C., E.A. Jenne and J.M. Burchard. 1976. Backflushing filters
for field processing of water samples prior to trace-element analysis.
U.S. Geological Survey, Open file report 76-126. 11 p.
Krygier, J.T. and J.D. Hall. 1971. Proceedings of a symposium forest land
uses and stream environment. Oregon State University. 252 p.
Lind, O.T. 1979. Handbook of common methods in limnology. Mosby Company,
St. Louis, Missouri. 199 p.
McKee, J.E. and H.W. Wolf. 1963. Water quality criteria. California
State Water Resources Control Board. Publication No. 3-A. 548 p.
McNeely, R.N., V.P. Neimanis and L. Dwyer. 1979. Water quality sourcebook
- a guide to water quality parameters. Inland Water Directorate,
Water Quality Branch, Ottawa, Canada. Cat. No. En 37-541 1979. 89 p.
Mendenhall, W., L. Ott and R.L. Schaeffer. 1971. Elementary survey
sampling. Wadsworth Publishing Company, Inc., Belmont, California.
247 p.
Ponce, S.L. 1980. Statistical methods commonly used in water quality data
analysis. WSDG Technical Paper WSDG-TP-00001 . WSDG, USDA - Forest
Service, 3825 E. Mulberry St., Fort Collins, CO 80524. 152 p.
Potyondy, J. 1977. Guidelines for water quality sampling. Determination
of detection limits and sample sizes. WQ-3 East Fork Smiths Fork
Barometer Watershed, Wasatch National Forest, Intermountain Region,
USDA Forest Service, Ogden, Utah. 8 p.
Potyondy, J. 1980. Guidelines for water quality monitoring plans. Draft
USDA-Forest Service, Intermountain Region, Soil and Water Management,
324 25th Street, Ogden, UT 84401 49 p.
Schwoerbel , J. 1970. Methods of hydrobiol ogy. Pergamon Press, Limited.
Oxford, England. 200 p.
Snedecor, G.W. and W.G. Cochran. 1967. Statistical methods, 6th ed., Iowa
State Univ. Press, Ames, Iowa. 593 p.
65
Stainton, M.P., M.J. Capel , and F.A.J. Armstrong. 1977. The chemical
analysis of freshwater. Fisheries and Environment Canada. Fisheries
and Marine Service. Misc. Spec. Pub. No. 25. Winnipeg, Manitoba
180 p.
Thatcher, L.L., V.J. Janzer and K.W. Edwards. 1977. Methods for
determination of radioactive substances in water and fluvial
sediments: U.S. Geol . Survey Techniques Water Resources Inv., Book
5, Chap. A5. 95 p.
U.S. EPA. 1971. Studies on effects of watershed practices on streams.
Prepared Oregon State University School of Forestry. 13010 EGA
02/71. 173 p.
U.S. EPA. 1973. Processes, procedures and methods to control pollution
resulting from silvicultural activities. EPA 430/9-73-010. 91 p.
U.S. EPA. 1976a. Forest harvest, residue treatment, reforestation and
protection of water quality. EPA 910/9-76-020. 273 p.
U.S. EPA. 1976b. Quality criteria for water. Washington, D.C. 256 p.
U.S. EPA. 1977. Silvicultural chemicals and protection of water quality.
EPA 910/9-77-036. 224 p.
U.S. Forest Service. 1980. An approach to water resources evaluation
non-point sources silviculture. Produced under USFS-EPA amended
interagency agreement EPA-IAG-D6-0660. 816 p.
USGS. 1977. National handbook of recommended methods for water-data
acquisition. U.S. Department of Interior. Reston, Virginia.
Walton, W.C. 1970. Groundwater resource evaluation. McGraw-Hill. N.Y.,
N.Y. 664 p.
Welch, P.S. 1948. Limnological Methods. McGraw-Hill. N.Y., N.Y. 381 p.
66
APPENDIX
Table A-l.
Values of t (Steel
and Torrie, 1960).
Probability of a larger value of t, sign ignored
df
0.5
0.4
0
.3
0
.2
0
.1
0
.05
0
.02
0
.01
0.001
1
1.000
1.376
1
.963
3
.078
6
.314
12
.706
31
.821
63
.657
636 619
2
.816
1 .061
1
.386
1
.886
2
.920
4
.303
6
.965
9
.925
31.598
3
.765
.978
1
.250
1
.638
2
.353
3
182
4
.541
5
.841
12.941
4
.741
.941
1
190
1
.533
2
132
2
.776
3
.747
4
.604
8.610
5
.727
.920
1
.156
1
.476
2
.015
2
.571
3
.365
4
.032
6.859
6
.718
.906
1
.134
1
.440
1
.943
2
.447
3
143
3
.707
5.959
7
.711
.896
1
.119
1
.415
1
.895
2
365
2
.998
3
.499
5 . 405
8
.706
.889
1
.108
1
397
1
.860
2
306
2
.896
3
.355
5.041
9
.703
.883
1
100
1
.383
1
833
2
262
2
821
3
.250
4.781
10
.700
.879
1
.093
1
372
1
812
2
228
2
.764
3
.169
4.587
11
.697
.876
1
088
1
363
1
796
2
201
2
718
3
.106
4.437
12
.695
.873
1
083
1
356
1
782
2
179
2
681
3
.055
4.318
13
.694
.870
1
079
1
350
1
771
2
160
2
650
3
012
4.221
14
.692
.868
1
076
1
345
1
761
2
145
2
624
2
977
4.140
15
.691
.866
1
074
1
341
1
753
2
131
2
602
2
947
4.073
16
.690
.865
1
071
1
337
1
746
2
120
2
583"
'2
921
4.015
17
.689
.863
1
069
1
333
1
740
2
110
2
567
2
898
3.965
18
.688
.862
1
067
1
330
1
734
2
101
2
552
2
878
3.922
19
'.688
.861
1
066
1
328
1
729
2
093
2
539
2
861
3.883
20
.687
.860
1
064
1
325
1
725
2
086
2
528
2
845
3.850
21
.686
.859
1
063
1
323
1
721
2
080
2
518
2
831
3.819
22
.686
.858
1
061
1
321
1
717
2
074
2
508
2
819
3.792
23
.685
.858
1
060
1
319
1
714
2
069
2
500
2
807
3.767
24
.685
.857
1
059
1
318
1
711
2
064
2
492
2
797
3.745
25
.684
.856
1
058
1
316
1
708
2
060
2
485
2
787
3.725
26
.684
.856
1
058
1
315
1
706
2
056
2
479
2
779
3.707
27
.684
.855
1
057
1
314
1
703
2
052
2.
473
2
771
3.690
28
.683
.855
1
056
1
313
1
701
2
048
2.
467
2.
763
3.674
29
.683
.854
1
055
1
311
1
699
2.
045
2.
462
2.
756
3.659
30
.683
.854
1
055
1
310
1.
697
2.
042
2.
457
2.
750
3.646
40
.681
.851
1
050
1
303
1
684
2.
021
2.
423
2.
704
3.551
60
.679
.848
1
046
l
296
l.
671
2.
000
2
390
2.
660
3.460
120
.677
.845
1
041
1
289
1.
658
1.
980
2.
358
2.
617
3.373
00
. 674
.842
1
036
1
282
1.
645
1.
960
2.
:52f>
i
2.
576
3.291
0.25
0.2
0
15
0.
1
0
05
0.
025
0.
01
0
005
0.0005
df
Probability of a larger value of t, sign considered
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