EPA-R5-72-001
November 1972
QUANTITATIVE METHODS FOR PRELIMINARY DESIGN
OF WATER QUALITY SURVEILLANCE SYSTEMS
By
Charles V. Beckers
Stanley G. Chamberlain
G. Paul Grimsrud
Contract No. 68-01-0144
Project 16090 HOJ
Project Officer
Dr. Roger D. Shull
Implementation Research Division
Environmental Protection Agency
Washington, D.C. 20460
Prepared for
OFFICE OF RESEARCH AND MONITORING
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price $2.75
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h!'A Ht-'vj_cw Noti_ce_
This report has been reviewed by the Environmental Pro-
tection Agency and approved for publication. Approval
does not signify that the contents necessarily reflect the
views and policies of the Environmental Protection
Agency, nor does mention of trade names or commercial
products constitute endorsement or recommendation for
use.
11
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ABSTRACT
This report presents the development and successful demonstration of quantita-
tive design methods for preliminary design of water quality surveillance systems.
It includes a comprehensive set of quantitative design procedures in handbook
form for use within the existing capabilities of governmental water quality agen-
cies. The quantitative methods are intended for use in design of monitoring sys-
tems that satisfy an abatement objective. Preliminary design is that portion of
the design process that deals solely with the interface between the surveillance
system and the monitored system, the river basin. The preliminary design
includes specification of station locations, sampling frequencies, and priorities.
Incorporation of such practical engineering concerns as cost, reliability and
maintainability, and computerization of the procedure are recommended areas
for additional development.
The methods are based on a systems approach, in which the performance of the
total surveillance system is evaluated as a whole. A new method for establish-
ing sampling frequency is developed, based on a unique formulation of the sam-
pling design problem. The development incorporates a "macroscopic" concept
that limits consideration of time and space dimensions to scales compatible with
an overview of the river basin. Data availability remains a constraint of the
method, even under the "macroscopic" concept; methods are developed for esti-
mation of required design data.
The quantitative preliminary design methods are demonstrated to function satis-
factorily on the Wabash River Basin. It is concluded that the methods incorpora-
ted in the User Handbook represent an acceptable method for use by governmental
water quality agencies under the existing constraints.
This report is submitted in fulfillment of Project Number 16090 HQJ, Contract
Number 68-01-0144, under the sponsorship of the Office of Research and Moni-
toring, Environmental Protection Agency.
111
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CONTENTS
Section Page
I Summary and Conclusions 1
n Recommendations 3
HI Introduction 5
IV Design of Water Quality Surveillance Systems 7
V Study Objective and Approach 13
VI Development of Quantitative Methods 17
Vn Demonstration of Quantitative Methods 49
VHI Discussion 79
DC Acknowledgements 81
X References 83
XI Glossary 87
XII Appendices 91
IV
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FIGURES
No, Page
1 General Systems Analysis Framework 9
2 fllustration of Stream Characterization for Conservative
Parameters 24
3 Illustration of Stream Characteristics for a Non-Conserva-
tive, Non-Coupled Parameter, Assuming Uniform Conditions 26
4 Illustration of Stream Characteristics for BOD-DO, Assuming
Uniform Conditions 27
5 Effect of Stream Segmentation 31
6 Probability of Violation (TTV) as a Function of P 36
7 Comparison of Probability of Violation (TTV ) for Varying
Parameter Means, with Standard Deviation Constant 39
8 Comparison of Probability of Violation (TT,,) for Varying
Standard Deviations, with Mean not in Violation of
Standard 39
9 Comparison of Probability of Violation ( TT ) for Varying
Standard Deviation, with Mean in Violation of Standard 39
10 Temporal Effectiveness Rating as a Function of T ,
T and A 45
11 Typical Pollutant Spectrum Showing Effect of Sampling 46
12 Wabash River Basin Overview (from [30] ) 51
13 Typical STORET Summary Data Retrieval for Wabash Basin 53
14 Typical STORET Data List Retrieval for Wabash Basin 54
15 Typical STORET Municipal Wastewater Inventory for Wabash
Basin 55
16 Typical Industrial Implementation Data for Wabash Basin 56
17 Typical USGS Stream Flow Data (from [34^ ) 58
18 Typical USGS Stream Gauge Calibration Data Sheet for
Wabash Basin 59
19 Basin Subset and Major Tributaries 60
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FIGURES
No. Page
20 Segmentation of Wabash River 70
21 Wildcat Creek and Tributaries in Segmented Form 71
VI
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TABLES
No. Page
1 Standards for Dissolved Oxygen and Fluorides Applicable to
the Wabash River and Wildcat Creek 52
2 Stream Flow Data During System Duration in Wabash Basin
Subset 62
3 Major Tributaries to the Wabash River 63
4 Major Tributaries on the Wildcat Creek Basin 64
5 Segmentation Computation Table for Wabash River 65
6 Segmentation Computation Table for Wildcat Creek—BOD-DO 68
7 Segmentation Computation Table for Wildcat Creek—Fluorides 69
8 Discharge Points on the Wabash River that are Grouped and
Considered Major Sources 72
9 Discharges on the Wabash River Ignored Due to Small Impact 72
10 Priority Computation Table for Wabash River 73
11 Priority Computation Table for Wildcat Creek—BOD-DO 74
12 Priority Computation Table for Wildcat Creek—Fluorides 75
13 Computation Table for Temporal Priority Rating for Wabash
Mainstem 78
VI]
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SECTION I
SUMMARY AND CONCLUSIONS
Quantitative methods for the preliminary design of water quality surveillance
systems are developed and demonstrated in this report. The quantitative
methods are organized into a User Handbook (Appendix G).
The quantitative methods are intended for use in preliminary design of sur-
veillance systems which satisfy the abatement objective. Abatement of water
pollution places more stringent requirements on a surveillance system than
prevention and planning goals [I] . The abatement objective requires that the
system detect an acceptable percentage of violations of the federal-state water
quality standards.
Preliminary design is that portion of the design process which deals solely
with the interface between the surveillance system and the monitored system,
the river basin. The surveillance system is characterized by ideal locations
of observation and by sampling frequency. A priority is assigned to the obser-
vation of each water quality parameter in each stretch of the river. The
priority is based on the probability that a violation of the standards will occur
for that parameter and on the existence of other observations of that parameter
in the vicinity. Sampling frequency is rated according to the expected per-
centage of violations detected. Such practical engineering concerns as cost,
accessibility, reliability, and maintainability are addressed during later
design stages, not during preliminary design.
A unique analytical approach to the selection of sampling frequency is taken,
based on the requirement that the system detect violations of the water quality
standards. The violations are defined in terms of threshold crossings, which
eliminates many established techniques of sampling design. The result of the
analysis of the time-sampling problem is a new approach to selection of
sampling frequency.
The development incorporates a "macroscopic" concept which limits consider-
ation of time and space dimensions to scales compatible with an overview of
the entire extent of the basin. This approach permits use of simplified mathe-
matical models in the characterization of the river basin. It also reduces the
level of detail required of input data.
However, data availability does remain a constraint. The quantitative methods
detailed in the User Handbook (Appendix G) incorporate approximations neces-
sitated by data limitations. Methods are included for estimation of some of the
required inputs from more readily available data, such as census information.
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The quantitative m- d? 'J^ developed are intended for use in a non-computer
environment. The emphasis is placed on compilation of tabular, nomographic,
and desk calculator approaches. The user, however, is assumed to be familiar
with basic engineering nvXhematics (up to, but not including, calculus). This
corr ' it repress a 1. -.do-off between the labor necessary to generate a
compui-. • ji •/*•'{- -\-n necessary for manual computation.
The a.*- ' • '•!' reliniinary design methods are demonstrated to function
saiisia i... • uie Wabash River Basin. Station locations, priorities, and
sampl'mi 'i .'.encies for the Wabash main stem are derived using the methods
on a^a: .(Hi iiafor biochemical oxygen demand and dissolved oxygen (BOD-
DO). The irothods are also applied to Wildcat Creek, a tributary to the Wabash,
for tv-.: ! sob--DO and fluorides. Reasonable results are derived for both the
main stern and its tributary.
It is concluded that the quantitative methods incorporated in the User Handbook
represent an acceptable method of preliminary design under the existing con-
straints. The limitations of the method are recognized and recommendations
for further development of the quantitative methods are offered in Section II.
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SECTION II
RECOMMENDATIONS
The present project has provided a number of opportunities to evaluate the var-
ious methods by which water quality surveillance systems are designed. The
following recommendations are made on the basis of observations made during
the course of the project.
The Environmental Protection Agency (EPA) should begin immediate implemen-
tation of the preliminary design procedure described in this report; it appears to
constx'.trte a significant improvement over previous methods.
The EPA should provide a mechanism for review and update of the preliminary
design procedure as experience is gained in its use, by monitoring applications
of the procedure to river basins. The procedure reflects the aggregate of years
of scientific research on the behavior of streams, filtered through the judgment
of environmental systems analysts. Although the procedure represents the best
professional judgment of its authors and has been demonstrated to perform in a
reasonable way for one river basin, its general applicability can only be deter-
mined by further evaluation and study. Review and update will also permit
incorporation of new information in such related areas as the characterization
of the effluent dynamics of wastewater treatment plants.
The manual procedures described in this report should be converted to computer
techniques. Computerization will benefit the user in two ways. First, the pro-
cedures lor preliminary design described in this report are laborious. Every
attempt has been made to minimize tedious hand computation, through use of
tables, graphs, and nomographs. The procedures still require extensive
detailed manual calculation, which may limit their usage. Second, by compu-
terizing, the user may take advantage of existing computerized models of river
basins- Such models are presently under development by EPA for a number of
river basins. Use of these models will provide even better estimates of stream
conditions than can be achieved by the manual computations.
The procedure described in this report should be extended to include both the
expected total cost of the surveillance system and the anticipated effectiveness
of the proposed system in achieving the surveillance goals. The quantitative
design procedure is limited to consideration of preliminary design factors. As
3'j > it yjirtially fulfills the intent of the recommendation on which this project
is based j_2J. Extension to include practical engineering factors would provide
a more complete system engineering tool, in line with that recommendation.
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The EPA should continue to proceed with their plans to incorporate intoSTORET
more detailed data on such properties as constituents and variability of individ-
ual outfalls. The lack of readily available data on outfalls has presented a major
obstacle to demonstration. It will present a similary obstacle to application of
the methodology under real conditions. Similarly, attention should be given to
improvement of available data on distributed pollution sources, such as farm-
land runoff.
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SECTION III
INTRODUCTION
In response to increasing public awareness and concern for the quality of the
environment in general, government at all levels is taking steps to protect and
enhance the quality of the public waters of the nation. The Federal Water
Pollution Control Act of 1956 and its successors, including the Water Quality
Act of 1965, are major landmarks in the drive to bring the full cooperative
efforts of state and federal governments to bear. The Act of 1956 clearly
recognizes the primary responsibilities and rights of the states to control
water quality[3]. The federal government assumes a primarily supporting role,
including financial aid, research and development, planning, coordination, and
technical assistance. The Water Quality Act of 1965 charges the states with
the establishment of water quality standards and the development of plans for
implementation and enforcement of those standards, under federal guidance.
Water quality surveillance is essential to the success of this initiative toward
environmental quality. William T. Sayers has recently pointed out that moni-
toring of "... the rivers, lakes, and coastal waters receiving wastes [is
required] to assure attainment and maintenance of desired water quality levels
consistent with criteria contained in state-federal water quality standards. "[3]
He further states the aims of water quality surveillance are ". .. to assess
existing water quality conditions, to determine long-term trends in water
quality and to evaluate compliance with state-federal water quality standards. "
In order to affect cost-effective monitoring of water quality, the Environmental
Protection Agency is supporting a program of technology development aimed at
providing standard methods for the further implementation of water quality
surveillance systems. This report is one of several recent studies undertaken
with EPA support to examine the question of design of water quality data
acquisition systems. Two of these studies are reviewed in Section IV to
establish the background for the present study.
The objectives of the present study are directed toward the development of
quantitative procedures for implementing the qualitative design methods of its
predecessors. A detailed discussion of the implications of the study objective
is presented in Section V, followed by a description of the approach taken in
achieving the objective.
The realization of the study goal required the development of quantitative means
for evaluating the priority of observing water quality, for determining preferred
locations for sampling, and for measuring the effectiveness of various sampling
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frequencies. Section VI is devoted to the development of the quantitative proce-
dures, supported by the detailed analyses presented in the Appendices. Appen-
dix G is a User Handbook intended to guide the surveillance-system designer in
the application of the quantitative procedure to the subject river basin.
For purposes of confirmation and illustration, the quantitative methods of the
User Handbook are applied to portions of the Wabash River Basin in Section VII.
A final discussion of the quantitative procedure and its relationship to the over-
all goals and objectives of water quality surveillance system design is contained
in Section VIII.
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SECTION IV
DESIGN OF WATER QUALITY STTTf* !
The present study is an outgrowth and continuei '«r. v . - ' ir in
the design of water quality surveillance system ,."-)'*
Design of Water Quality Surveillance Systems [ 2 [ proyjr" s <;" ;-;: •
tical framework within which the quantitative ir'^bfuL ! . /.,,_• ,-.
Data Acquisition Systems in Water Quality Mavu.u'''. " ; ' ' pro/ider~ a >;road
HML;\ fcis of the context in which surx'eil'ino, .:,./ ' _aj\vi< pi
I'l.-.^.e,!; r'-au;/' - ':•,' -. yrious system o^'tci
Design . .1 Water Quality Surveillance Systems [ ^ _; -'iu question of setting
up water quality surveillance systems throughout th- • ••••• ;ri response to the
rxcj.iirerrirnt" of tho Water Quality Ant of 19('.' hility of r»dni
dual sy:-5?"r.i> d».'vfloped by various federal, r,\. .MCS, si. ;; .^
analysis i.ci'iiniqucs are adapted to the design oj .*. -j stems. h,
analytical techniques are demonstrated in a qua'i;, I ..<.-. .,>u three rivt-,
basins by: 1) reviewing the literature associated \\; wa^er qualiK' c-hai-ao-
teristics; 2) on-site visits to the river-basin areas, "-ip.^?.tive r\ , :< „ <>'' she
interstate water quality standards and plans of imph r - ;: , \r,d ! . 1 Con-
siderations in surveillance program design. The latter investigations disclose
some very pertinent limiting aspects of the legal structure as it existed in 1970
and the report details a number of legal problems in the establishment of federal
water quality surveillance systems. A number of recommendations are advanced
to further development of the systems analytical methods. Among them is one
suggesting that "... the tasks, functions, and interrelationships as identified
in the systems analysis framework should be described in specific quantitative
relationships ..." and that "... a user handbook . . . should be developed
to describe these techniques and extend their utility. " The stated objectives of
the present study correspond, in part, to that recommendation. To show the
relationship between the prior EPA report and the present one, Figure 7 from
Design of Water Quality Surveillance Systems [2] is reproduced here as
Figure 1.
The figure summarizes an integrated analysis of all pertinent considerations in-
herent to the establishment of a water quality surveillance system. It presents
a generalized analysis which is compatible with any specific area of geographical
interest.
The logic represented in Figure 1 can be divided into two stages of system design
development. The first stage comprises those activities that analyze the relation-
ship between the surveillance system and the natural system that is to be moni-
tored. This preliminary design stage deals only with the establishment of water
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IDENTIFY AND QUANTIFY WATER
QUALITY AND ENVIRONMENTAL
PARAMETERS FOR SPECIFIC
AREAS OF EACH IASIN
IPDESENT VALUES AND VARIATIONS
IDENTIFYAND
QUANTIFY PRESENT
mOILEM CONDITIONS
AND SOURCES OF
POLLUTION
IDENTIFY AND QUANTIFY (PRESENT
VALUES) ADDITIONAL OESCRIP FACTORS
FOR SPECIFIC AREAS QF EACH
REVIEW DOCUMENTED
INFORMATION ON
FWPCA STATE*
LOCAL WATER
QUALITY STANDARDS
-LLXHINING
Trpft I.OCATIOM AMD E
CONTMOLI AMOtTMIAM
MAIMTENAMCf
ACQUIRE SUPPLEMENTAL
INFORMATION ON
THROUGH INTERVIEWS
I INSPECTIONS
LOCATION AMOOUAKTlUCATIOM
mLLUTIOM «>ATEMiMT f AClLITI
OENTIFY AND QUANTIFY PROJECTEC
FUTURE CHANGES IN THE
DESCRIPTIVE FACTORS FOR THE
SPECIFIC AREAS OF EACH IASIN
ALSO INCLUDE A CHRONOLOGICAL
SCHEDULE FOR THE PROJECTED
CHANGES.
FUTURE POLLUTIOK MOIL EMS
AND SOURCES
PRELIMINARY DESIGN
Figure 1. General Systems Analysis Framework (Sheet 1 of 2)
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SAMPLE COLUCTIDN
TECHNIQUES ANO
EQUIPMENT ALONG
WITH ASSOCIATED
FACILITIES
PERSONNEL AND
OTHER RESOURCES
REQUIRED FOR
REVIEW LEGAL
STATUS Of
METHODS
—
DENTiFY ALTERNAT VE
NALYTICAL TtCHNIOUE
AND EQUIPMENT
ALONG W TH
ASSOCIATED
MOLIT(ES PERSONNEL
REQUIRED FOR
OPERATIONS SUPPORT
TRANSMISS ON TECHNIQUES ALONG
OTHER RESOURCES REQUIRED
FOR OPERATIONS SUPPORT
IDENT fY THE DEGREE OF
HANOI NG FACILITIES
IDENTIFY ALTERNATIVE DATA
HANOUMG A OfSSCMfftAriO*
ALONG WITH A
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REQUIRED F
s
EXTEN
— •<
SSOCIATED FACILITIES
R OPERATION ANO
UPPORT
T OF GENERAL
MINATIONOF
DATA
— FORMATS Of
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ESTABLISH TIMES
IS NEEDED
/
DEFINE ALTERNATIVE SAMPLE
COLLECTION SYSTEMS FOR
MCN IASIN
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1
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CALCULATE VALUES FOR THE
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MER T
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Figure 1. General Systems A nalysis Framework (Sheet 2 of 2)
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quality sampling on the basis of scientific and social considerations. The second,
or final, design stage is composed of those activities which are aimed at the
selection of the "best" realization of the preliminary design. The practical con-
siderations of engineering, legal constraints, cost, reliability, and existing
surveillance are used, during the final design stage, to select a preferred im-
plementation of the surveillance system.
This report deals with the preliminary design stage of surveillance system
design. The quantitative methods developed and demonstrated in this document
deal with the question of how best to monitor a river basin from the perspective
of enforcement of water quality standards. Those activities related specifically
to preliminary design of water quality surveillance systems are shown within
the broken line in Figure 1.
The major outputs from the preliminary design stage are identified with three
blocks in Figure 1. One is a catalog of stretches of water according to the like-
lihood of need to monitor the segment. Need to monitor is determined in rela-
tionship to the existing or proposed water uses. Another is the specification of
locations for the observation of water quality. The third is the specification of
intensity of observation at the surveillance stations. Determination of each of
the three preliminary design outputs is based on a number of considerations, as
diagramed in the general systems analysis framework.
The natural system to be monitored must be carefully described. Factors
included in the description are geography, demography, and historical water
quality. A number of elements must be considered in each factor. Geography
includes not only the physical description of the river itself, but also such ele-
ments as the location of cities, towns, major industries, and farmlands border-
ing the streams. Population is a major indicator of potential for water quality
degradation. Methods for estimation of impact based on demographic data are
available [4]. Historical water quality provides information for evaluation of
the existing situation in the basin and for prediction of water quality variability
to be anticipated over the life of the surveillance system.
While the general systems analysis framework calls for analysis of desired
water uses, the procedures developed in this report do not specifically require
study of that aspect. The water quality standards of most states are based on an
established pattern of water use and reflect the state's determination of its water
quality needs (see Appendix B and Section VI).
Similarly, the procedures do not specifically require the identification of existing
surveillance networks. They do provide a mechanism for incorporation of such
data in the development of the preliminary design, should the user choose to
consider the additional factor.
10
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In summary, the contents of this report provide detailed quantitative procedures
for accomplishment of the first stage of the generalized design framework estab-
lished in Design of Water Quality Surveillance Systems [2] .
The design and operation of surveillance systems is carried on in the context of
water quality management. The EPA report Data Acquisition Systems in Water
Quality Management [l] identifies two general objectives for surveillance sys-
tems in that context: prevention and abatement. The information requirements
of the objectives are delineated in general terms and a procedure is developed
for designing a state water quality surveillance program. The program design
procedure has two major aspects: 1) the determination of the state agency's
strategy, and 2) characterization of the streams in the state so that sampling
locations and frequencies may be determined.
Again, the quantitative preliminary design methods developed in this report can
work within the state-wide program design procedure to provide numerical
priorities, preferred sampling locations, and a quantitative measure of sampling
frequency effectiveness for each river basin. The quantitative procedure is
intended for use in design of systems with the abatement goal, but it incorporates
the recommended prevention approach for stretches of river having low need for
monitoring. In general, systems designed to the abatement goal will satisfy the
data needs of prevention strategies as well [ 1J .
The methods for selection of state agency strategy [l] may be employed to deter-
mine applicability of the quantitative preliminary design methods to the needs of
the state agency. An emphasis on abatement goals in the agency's water quality
management program would indicate selection of the methods developed in this
report for use in system design.
A further discussion of the EPA report Data Acquisition Systems in Water
Quality Management [l] is presented in Section VIII of this report, where a
specific comparison of the methods developed in the two reports is presented.
11
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SECTION V
STUDY OBJECTIVE AND APPROACH
While the study reported in this document is an outgrowth and extension of
the previous developments described in Section IV, the scope of the present
project is narrower than that of its predecessors. In this section, the objec-
tive of the dtudy is prestnlec! an
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Study Approach
A number of potential technical approaches exist for the quantitative design of a
water quality surveillance system. Among the candidates are techniques based
on spectral analysis, quasi-deterministic analysis of water quality, ar.d ^la'Is-
tical analysis of random processes.
The study approach was aimed at the selection of the proper mix of technolo-
gies, based on a thorough analysis of the preliminary design problem "/Vriiie
some techniques, such as spectral analysis, could be eliminated rapiJi> based
on the constraints of available data or user capability, the correct utilization
of others needed detailed study.
Thus, the study approach called, first, for the analysis of the context in which
the procedures would be used. The analysis included an extensive examination
of STORET, and other data bases, from the viewpoint of sampling methodology.
The nature of the data contained in such systems was expected to fox 0.0. a
significant constraint on the preliminary design procedure. For example, the
general frequency of sampling found in STORET was known to be low enough to
effectively eliminate spectral analysis techniques. The analysis also included
a review of the federal-state water quality standards. As a central element in
the enforcement of water quality regulations, the form of the standards would
shape the quantitative preliminary design methods. Of particular interest was
the extent to which the standards had been quantified.
Having thus established the operational context of the quantitative procedures,
the next step was the theoretical development of the methods for establishing
priority, location, and sampling frequency. The objectives of the study >er>-
interpreted on the basis of the preceding EPA report [2] . Priority was
equated with the need to monitor a particular stretch of river. Location of
sampling stations was based on maximum priority conditions, while sampling
frequency was examined from the viewpoint of effectiveness.
The theoretical methods were then used to generate a handbook procedure for
application to actual design situations. The thrust was to provide a step-by-
step guide for use of the procedure. Particular attention was paid to mea:i£ of
estimating design quantities from the typically limited data available.
Selection of the demonstration case and application of the quantitative prelim-
inary design procedure followed its development. An important aspect of the
demonstration activity was the feedback provided to update the quantitative
procedure. Experience with application of the procedure could be expected to
disclose weaknesses and suggest improvements.
In the next section, the results of the quantitative methods development are
14
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presented. These are followed, in Section VII, by a description of the demon-
stration of those methods.
15
-------
SECTION VI
DEVELOPMENT OF QUANTITATIVE METHODS
This section of the report describes the supporting technical material, assump-
tions and decisions which resulted in the quantitative procedure detailed in the
User Handbook (Appendix G). Extensive use is made of accepted mathematical
models of stream processes, without detailed discussion or derivation of the
models. References are given where appropriate in the text. The reader may
wish to familiarize himself with Simplified Mathematical Modeling of Water
guality [4] before reading the section.
The section begins with a summary of the quantitative methods and the results
to be obtained from application to surveillance system design. Next some of
the fundamental concepts of system design are presented. The quantitative
methods for preliminary design are then developed around those concepts,
beginning with the priority of monitoring. Location of stations and the time
sampling design methods follow in that order. Additional concepts are intro-
duced as needed in the presentation.
The major portion of the development is given in terms of one parameter set,
biochemical oxygen demand-dissolved oxygen (BOD-DO). The limitation is made
for purposes of clarity. The BOD-DO case is selected for several reasons.
It is of general interest to the user community; it is one of the most commonly
cited parameters in the federal-state standards (Appendix B); and it is repre-
sentative of the general mathematical class of coupled parameters.
Summary of Quantitative Methods for Preliminary Design
Application of the quantitative preliminary design procedure contained in the
User Handbook (Appendix G) results in the computation of three sets of quanti-
tative design factors. One is a set of numerical priorities rating the need to
monitor each stretch of the river for each water quality parameter of interest
to the designer. The second set specifies the preferred location for sampling
each of these parameters in each stretch of the river. The third gives a quan-
titiative measure of the effectiveness of each candidate sampling rate, for each
To achieve these results, the procedure gives step-by-step directions, begin-
ning with the gathering of the data necessary to provide an adequate characteri-
zation of the river basin to be monitored. The river basin is then divided into
stretches of water (segments) based primarily on the identification of major
effluent sources (frequently groupings of smaller sources) and their regions of
17
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dominant influence. The expected behavior of each parameter of interest is
then characterized for each segment. Using this information, the preferred
station locations are identified, and the need to monitor each segment for each
parameter is computed. The final step is calculation of the set of values des-
cribing the effectiveness of alternate sample schedules in detecting water
quality standards violations. For very high quality segments, a method for
computing sampling frequency for long-term trend analysis is substituted.
Two features of the procedure may be noted. First, it incorporates a means of
re-assessing segment priority as samplinc; stations are established in the basin.
Second, while the procedure is intended primarily for design of surveillance
systems to detect violations of standards, it tends to identify high quality seg-
ments as well and includes methods for establishment of surveillance require-
ments for long-term treit'" analysis.
Concept of System Duration
Throughout the development of the quantitative preliminary design method,
an implicit concept of the anticipated system duration is used. System duration
is defined as that time over which the water quality surveillance system will
maintain a fixed configuration of spatial and temporal sampling. It is the time
over which average effectiveness of the system would be computed in a cost-
effectiveness ana]j sis.
Thus, all the system design f-iefors are ;n orage factors over the system
duration. The need to monitor a stretch of river is essentially the average
need to monitor for d>e pi::uv><\ syslor.i duration. Similarly, the measure
of time sampling effectiveness is essentially the average effectiveness for the
total span of the planned / ; ; , i" •-•. ,s!err operation.
For example, it should be rlrar that h. finite, possibly large, difference may
exist between the ti.ric ;,;!J,,piing rf1\vf iveness as estimated for an annual cycle
and the actual system performance based solely on the low-flow period. The
long sampling interval appropriate to provide an acceptable level of effective-
ness throughout the year ma" tend to miss n large percentage of those viola-
tions which occur ilur.ng ti_-; lev- -flow period. A sampling interval aimed at
maximizing the measure of effectiveness during the low-flow period will, of
course, yield an accepts Me level of effectiveness throughout a year period as
well, but the co?' •>'< • • ' ~- • l' 1 'T'C'-i could be prohibitive.
An essential input "<-> the preliminary design process is, therefore, the planned
or intended sy; < ""• .- • -. ? her factors are such that the sys-
tem may be changed during the annual cycle, the methods developed in this
report permit n : , ; - - , ions, as well as longer ones.
Because choice ol t«"> p^ >- v. dUi-atjon depends on factors specifically
-------
excluded from consideration in this study (such as cost), system duration
must be treated as an input factor, based on a decision external to the quan-
titative preliminary design process.
In the design methods detailed in the User Handbook (Appendix G), selection of
aprvonriate estimators for various system design factors is based on the cho-
S'Ti v is tha characterization of the processes to be monitored.
The objective of characterization is to sufficiently restrict the range of new
information necessary from the surveillance system, so that it may be speci-
fically designed to respond only in the range of interest. If nothing were known
of the natural system to be monitored, it would be necessary to establish a
finely spaced, intensely sampled surveillance system to assure a high prob-
ability of observing the property cr event of interest. As the level of initial
information on the monitored system is improved, the surveillance system
may be more carefully designed to monitor only that which is of interest.
This line of reasoning leads to the interesting paradox that design of the true
optimum surveillance system requires perfect, advance knowledge of the be-
havior of the monitored system, which obviates the need for surveillance.
Since such perfect advance knowledge is not found in practical design situations,
it is desirable to strive for the best available characterization within planning
budgets, in order to improve the expected surveillance-system performance.
In order to achieve this goal in preliminary system design, it is necessary to
rely on generalized models of stream processes, which are fit to the subject
river basin through use of existing historical data.
The level of detail achievable in the characterization of river basins through
use of mathematical models for planning purposes is limited primarily by the
availability of data and by the effort expended in calibrating and exercising the
model. Knowledge of the anticipated data availability and intended level of
preliminary design effort can be used to select appropriately detailed mathe-
matical models for use in surveillance system design.
The mathematical models used for characterization of river basins in prelim-
inary design of surveillance systems have been selected on the basis of their
general acceptance, their relative simplicity, their compatibility with available
watei quality data, and their compatibility with the available data base. A
review of some aspects of the models concludes the discussion of characteri-
zation.
19
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The "Macroscopic" Concept
In the development of the quantitative preliminary design methodology,
scopic" time and space scales have been employed. An initial understanding
of the "macroscopic" concept may be gained by imagining the appearance of a
river basin as seen from high altitude (a manned earth satellite, fur example).
Major cities reduce to points and the river network itself assumes a one-
dimensional appearance, a line f;onnoct^rjj; fh" fil> "ju.-iril:..
The objective in assuming a "macroscopic" viewpoint is the development of a
model of the stream system which is comjmtiHo v-ijh tin5 Irvel nl which the
surveillance system will operate. The surveillance system will be employed
to ascertain the status of the river basin as a whole and the overall water
quality of stretches of river, in particular. It is not intended that the sur-
veillance system be used to determine the px-ecise cause and extent of water
quality degradation. Definition of detailed local problems is not a monitoring
function; it requires, in general, the implementation of a special-purpose,
intensive water quality survey of a stretch of water. Furthermore, it is
anticipated that the operational constraints, such as personnel, equipment and
financial support, would restrict implementation of a high-intensity sampling
network, even if one were desired.
In practice, the "macroscopic" concept restricts the spatial scales of interest.
The stream is treated as a one-dimensional flow, with depth and width entering
only as they influence the values of coefficients and other input variables, such
as velocity. Outfalls located in "close" proximity to each other are grouped and
treated as a single source, based on a quantitative measure of closeness.
Cities, in particular, are treated as point sources of effluents.
Commensurate with the space scale, the time scale is restricted to very slow
variations, those taking place over days. Computation of spatial factors is
based on time-averaged inputs. Specification of sampling rates is constrained
to integer days and the inputs to compulation are comparably scaled,
In addition to the conceptual requirements, there are practical reasons for the
use of the "macroscopic" concept. Refinement of the level of system-design
detail requires a comparable refinement of the data on which the design is
based. The data required by the "macroscopic" approach is generally avail-
able, although gaps have been noted. The quantity and quality of data useful
to more fine-scaled planning is severely limited.
Review of Data Base
The database necessary for characterization of the natural system may be
divided into three categories:
20
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1) stream data
2) discrete pollution source data
3) distributed pollution source data.
Stream data is the aggregate of historical records on the quality of the water in
the stream bed. Some 700 plus individual descriptors of the stream water
quality (water quality parameters) have been identified, including stream flow,
other physical properties, and chemical and biological properties [5] .
Discrete pollution source data refers to data on the nature of effluents entering
the stream from discrete outfall sources. Distributed pollution source data
refers to information on such pollution sources as mine drainage, benthic
demand, natural sources, and farm and feedlot runoff. These occur along
a length of stream and are not readily identified with a single location.
A survey of the stream data expected to be available to the user of the quan-
titative design procedure was conducted. The detailed results are presented
in Appendix A. In summary, water quality data may be expected to be gen-
erally available, but the spatial and temporal intensity tends to be low. Thus,
it is necessary to the quantitative design procedure that mathematical models of
stream processes be used to extrapolate and interpolate these data for stream
characterization. Specific data sources include STORET, U.S. Geological
Survey stream flow records and state agency files; a comprehensive listing
is given in the User Handbook (Appendix G).
Detailed data on discrete waste outfalls is not generally available, and in
many cases even precise location of outfalls is not known [ 1] . The level of
information on municipal wastewater treatment plant outfalls is better, typ-
ically, than that on industrial sources, due to the impact of financial assistance
and regulation programs on wastewater treatment plants. The cataloguing of
industrial outfalls under the Refuse Act Permit Program may be expected to
bring improvement in this category.
However, detailed data on the composition and variability of discrete source
effluents, both municipal and industrial, is expected to remain a problem.
For example, existing data on municipal treatment plants is frequently limited
to three days per week. Methods for estimating the necessary inputs on these
sources have, therefore, been incorporated into the User Handbook (Appendix
G), for use when good information is lacking. These methods include a means
to estimate wastewater treatment plant impact based on population and type of
treatment [4] . Use of standard textbook values for typical effluents based on
Standard Industrial Codes [6, 7, 8 ] , and estimates based on the professional
experience of the project staff and consultants (for example, use of 2 mg/1 as
the typical DO of wastewater treatment plant effluents). These techniques are
21
-------
necessarily gross estimates; the availability of better methods remains an
area for improvement in the quantitative design procedure.
Improvement in the status of distributed pollution source data is not as easily
foreseen as improvement in discrete pollution source data, although it is as
necessary. While discrete sources may be readily identified and analyzed,
distributed sources are less tractable. It cannot be expected that detailed
descriptions of specific distributed sources in every reach of a river basin
will become commonly available. An alternative is research aimed at des-
cribing the typical characteristics of such sources. Even this type of data is
not presently available for the majority of water quality parameters mentioned
in the federal-state standards (Appendix B). Appropriate guidelines have been
incorporated in the User Handbook (Appendix G), based on the investigation of
the project team and available reference material [9, 10, 11 ]. In most cases,
the guidelines call for analysis of the stream quality in relatively remote
stretches of river to ascertain the distributed source loads to be assumed
throughout the basin. In some cases, such as BOD-DO, tables are provided
based on source literature [4 j, (Another alternative, of course, is the use of
more complex mathematical models than may be conveniently employed in a
non-computer setting. That alternative is not available in the context of this
study.)
Mathematical Modeling for Stream Characterization
Because of the limited availability of stream data, it is necessary to turn to
generalized models of stream water quality for purposes of stream characteri-
zation. The most useful models for this purpose are those which describe the
desired water quality parameter in terms of available data through use of an
analytical (mathematical) relationship.
The mathematical models selected for use in the quantitative preliminary de-
sign method are those typified by Simplified Mathematical Modeling of Water
Quality [4 ]. They were chosen on the basis of their wide-spread acceptance
and long usage, compatibility with the "macroscopic" concept, and minimal
demands on input information [ 11, 12, 13, 14, 15, 16],
The mathematical models may be described as one-dimensional, steady-state
models. That is, or-ly one linear stream dimension is considered, longitu-
dinal distance along tae stream bed, and it is assumed that changes in the
system take place at a rate which does not significantly affect the description
of the system. Properties of the stream (such as width and depth) and of the
water quality parameters enter the equations in the form of coefficients.
Effluents are assumed to mix with the stream immediately at the point of
discharge.
22
-------
It should be noted that use of one- dimensional models limits the consideration
of reservoirs and lakes. While this does not constitute a severe limitation,
care must be used in application of the models. In particular, it is necessary
to re-initialize the models downstream of such bodies, through use of either
stream data or assumed conditions.
For the purposes of quantitative preliminary design, the steady-state conditions
correspond to the mean conditions in the stream over the system duration.
The validity of this approach is confirmed in Stochastic Modeling for Water
Q uality M anagem e nt [ 17 ] . (See also [ 18 ] . ) The bars over some of the sym-
bols indicate use of the mean value over system duration.
The mathematical models used in Appendices D, F, and G for synthesis of
the quantitative procedure may be classified as either:
1) Conservative
2) Non-conservative, non-coupled
3) Non-conservative, coupled.
Conservative mathematical models describe processes in which the property
does not decay with time; the intensity (concentration) of the parameter is
reduced only by dilution. Such non-interacting parameters as salinity, total
dissolved solids, and the total nitrogen are described with conservative models
[4], Figure 2 diagrams the spatial characteristics of a conservative param-
eter, with three sources entering the stream. One of the sources indicated is
a tributary stream. This is done to illustrate the broad meaning of the term
"source" when used in mathematical modeling. The only factors affecting the
concentration of the conservative parameter in the stream are the flow in the
stream (Q) and the concentration of the sources (Cg), including the initial
concentration in the stream (C (0)). The flow in the stream at any point may
be written as
Q(x) = Q (0) + £ Q (x.) , x.
-------
x = 0
x = X? - -
x = x-j - -
CIO)
0(0)
d
_
"5s(x1) = Q(0)
Cs (x2)
'Qs(x2)
Cs(x3)»C(x2)
Qj (x3) «Q(x2)
C(x)
X2
X3
Q(x)
X1
X2
X3
Figure 2. Illustration of Stream Characterization
For Conservative Parameters
24
-------
the physical characteristics of the stream. Since these factors vary along the
length of the stream, the decay coefficients are (strictly) functions of location
on the stream.
The non-conservative models can be divided into two classes, non-coupled and
coupled. The non-coupled models describe parameters which are modified
solely by their own decay (and by dilution), such as temperature and BOD.
The coupled models are applied to those parameters which are influenced by
the behavior of other parameters. For example, dissolved oxygen is affected
not only by exchange with the atmosphere but also by the oxygen uptake of BOD.
Figure 3 illustrates the case of a non-conservative, non-coupled parameter.
It assumes that the physical characteristics of the stream are uniform over the
distance shown, so that the decay coefficient (k), and the stream velocity (U)
are constant. The equation describing the steady-state spatial characteristics
of a non-conservative, non-coupled parameter with one source, under uniform
conditions, is:
(" -kx/U _ -'
C (x) = J- C (0) Q(0) e + C(x ) QJ (x ) e"k (X"X1)7 U
Q(x) [ s 1 s 1
(3)
The non- conservative, coupled case is the most general mathematical form of
the three categories of models. It can be reduced to either of the other two
categories by appropriate choice of zero coefficients.
Because of the importance of dissolved oxygen to the quality of streams, the
BOD-DO equations are used here to illustrate the non- conservative, coupled
case. Figure 4 diagrams a case in which there is one new source of BOD
and the stream conditions are uniform (i.e. , the decay coefficients and stream
velocities are constant). To simplify the model, distance is measured from
the source in this illustration. The total BOD concentration (L (0)) in the
stream immediately below the source (assuming immediate mixing, as before)
is:
LQ (OMLQ-
The dissolved oxygen is treated as a deficit concentration (D) referenced to the
saturation concentration (C ):
sat
D (x) = C . (x) - C (x) (5)
sat
25
-------
x = 0
x =
C(0)
0(0)
C(x)
Q(x)
Figure 3. Illustration of Stream Characteristics for a Non-Conservative,
Non-Coupled Parameter, Assuming Uniform Conditions
26
-------
L0
-------
Thus, the DO deficit in the stream immediately below the source is:
D Q (0) + D Q
D(0) = -«_•_-•_! ,6,
And the equation giving the spatial characteristics of the DO deficit, under
conditions of the one source, steady-state and constant coefficients, is:
kx\i — ( k x
D
(7)
where k = the oxygen reaeration rate coefficient
a
k = the BOD de-oxygenation rate coefficient.
It should be readily apparent from Equations (2), (3), and (7) that the down-
stream effect of any single source can be isolated from that of others influ-
encing the concentration at that point. For example, the downstream effect
of the BOD source alone (Figure 4) would be computed by:
_ L Q
L' (0) = -1-1 (8)
VQs
D Q
D' (0) - S * (9)
Q +Q
^0 s
r- i v
[exp (-^-)-
k x v /kx\-i /kx
and its relative effect ( R ) at any point could be computed as :
R (x) = 1^ (11)
D (x)
where D (x) is obtained from Equation (7). This relationship is used later in
the discussion of "ultimate segment priority. "
Estimation of Stream Characteristics
Estimation of the stream characteristics using Equations (2), (3) and (7)
requires estimation of the various rates and coefficients. Information on
stream flow (Q), for example, may be gained directly from statistical analysis
28
-------
of the U.S. Geological Survey stream flow records. In contrast, estimates
of velocity (U) must be computed from the stream flow and a knowledge of the
hydraulic cross-section of the stream. The rate coefficients for non-conser-
vative parameters must be estimated from historical water quality data and
a knowledge of stream velocity, by solving Equation (3) under carefully selected
conditions. For example, the BOD decay rate coefficient (k^) could be esti-
mated by
where the L's are BOD concentrations in the stream and it is assumed there
are no BOD discharges in the interval (x^, Xg). The values for U, x-p Xp,
and the L's are derived from historical water quality data. Methods for esti-
mation of the necessary inputs to stream characterization are incorporated in
the User Handbook (Appendix G) .
Stream Segmentation
The application of the simple mathematical models used in quantitative pre-
liminary design requires that the stream be divided into a number of segments.
The stream segments are stretches of river along which the conditions which
affect stream quality may be assumed to remain constant. Mathematically,
this assumption means that the coefficients and certain of the independent
variables (such as stream velocity and stream flow) are taken as constant
throughout the segment.
Segmentation of the stream is done by isolating the geographical location of
those stream features which modify stream conditions . The features may be
either man-made or natural, ranging from industrial outfalls to the confluence
of tributaries with the main stem. An identification of features requiring
stream segmentation is contained in the User Handbook (Appendix G).
Use of the "macroscopic" concept in quantitative preliminary design requires
that groupings of effluent sources be considered as point sources. This usage
tends both to preserve the basin-level of design activity and to reduce the
number of stream segments (reducing computational effort).
Establishment of outfall groupings is arbitrary, since the meaning of "a point
source" is not precisely defined by the "macroscopic" concept.
However, any arbitrary rule employed in establishing groupings must be uni-
formly used throughout the basin. To promote uniformity of application, a
quantitative rule should be used.
29
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The User Handbook contains one such arbitray quantitative rule. The rule
groups together all sources within a distance along the stream called the
"tolerance length" (x, •,). The tolerance length is defined as the distance
required for the parameter with the greatest rate of decay to reduce its
concentration by 10%. (Another percentage could be selected by the system
designer.)
The grouping rule is applied in a sliding fashion, beginning at the upstream end
of the river. As groups are identified, the group impact on the stream is
computed and compared with an arbitrary threshold. The threshold is set by
the system designer at a level which defines a "major source". A decision
that a group constitutes a major source defines the upstream end of a new
stream segment (and, therefore, the downstream end of the previous segment).
It should be noted that the source grouping is done for all sources, regardless
of water quality parameter affected by the source. While other computational
steps in the quantitative preliminary design procedures are done for individual
parameters, grouping considers all parameters.
The result of stream segmentation is that the mathematical models typified by
Equations (2), (3) and (7) may be applied to each segment independently. The
segment is considered to have two source inputs at its upstream end, one due
to the preceding segment and the other due to the major source group which
defines its beginning (Figure 5). All computations are, thus, performed with
longitudinal distance (x) measured from the upstream end of the segment. If
the length of the segment is XE, then for conservative parameters, Equation
(2) becomes:
C C3 +~C Q
)= Q ° g g (13)
Qo+Qg
where ~cT = the mean concentration at the end of the preceeding segment
"C~ = the equivalent mean concentration of the group effluent
_g
Q = the mean stream flow at the end of the preceeding segment
"o" = the total mean flow added by the source group.
g
In the case of non-conservative, non-coupled parameters, Equation (3) becomes:
k
, 0
-------
x = 0
S
E
G
A/1
E
N
T
X = X£
S
E
G
M
E
N
T
LO-DO-
CO-QO
u = CONST.
k = CONST.
L'0-D'o-
~r
u' = CONST.
k' = CONST.
MAJOR ) JV Lg- Dg
'SOURCE ) Qn
MAJOR
SOURCE
f CV LV D'g
(Q'g
C'0 = t (XE) AND Q'0 = Q (XE) = Qg
Figure 5. Effect of Stream Segmentation
31
-------
The BOD-DO equation (Equation (7)) remains as it was, because of the defin-
itions used in writing it:
d a
kx
k x
D(0) expl-JL-
(15)
where L{0) =
Vo
(16)
DO + D Q
00 £T
and D (0) - —_U _g
(17)
Q +Q
0 g
Concept of Need to Monitor
The concept of need to monitor a particular segment is based on a judgment of
the total benefit to be accrued from monitoring that segment. The total benefit
has two components, one based on the worth to society of the information and
the other based on the magnitude of new information to be gained. Each of
these is discussed in the following paragraphs.
The establishment of the worth of information on water quality requires at
least a qualitative judgment on the part of society which has not generally
been made. Quantification of the worth is even less common. The problem
of establishing the worth of information is not unique to water quality and
various methods have been developed for establishing worth in specific cases.
(See, for example, the development of "relative worth"curves based on "quan-
tified expert judgment" described in [19] and [20] . See also [21].)
For the purposes of preliminary design of water quality surveillance systems,
it is assumed that society has expressed its judgment of worth in terms of the
federal-state water quality standards. The adopted standards are frequently
referred to as "stream standards, " because they apply to the waters con-
tained in the open stream bed, rather than to effluents entering the stream .
Typically, each stretch of a state's rivers is classified according to society's
desired use of that stretch. Standards are then established for each stretch,
based on scientific knowledge of the minimum water quality necessary to sup-
port the desired use. Where multiple uses are assigned, standards are based
on the most sensitive use. Thus, it is taken that, in society's judgment,
32
-------
knowledge of any violation of the stream standards is a requirement of stream
surveillance.
Since the use of such judgments in a quantified preliminary design procedure re-
quires that they also be quantitative, a review of the existing federal-state water
quality standards was undertaken. The objectives of the review were: 1) to de-
termine the extent to which the stream standards were quantitative, and 2) the
mathematical form of those standards which had been quantified. The latter
objective was necessary in order to evaluate the impact of the standards on the
mathematical formulation of the preliminary design procedure.
The detailed results of the review of stream standards are presented in Appen-
dix B.
In summary, the level of quantification in stream standards varies widely from
state to state, but standards for four of the water quality parameters are nearly
always quantified. The parameters dissolved oxygen, coliform bacteria, pH,
and temperature are consistently given in quantitative form, while the others
are occasionally given numerical values. Of those standards which are quanti-
fied, the majority fall into the category described as "simple threshold."
Examples of simple threshold are "temperature not to exceed 78° F at any
time" and '^dissolved oxygen not less than 5 mg/1 at any time. " The coliform
bacteria standard was nearly always of the form "not to exceed a median of
1000 per 100 ml nor more than 2400 in more than 20% of samples collected."
Based on the dominance of the simple threshold in the existing standards, it
can be expected that future quantification of standards will be in that form pre-
dominantly. For example, individual chemical parameters are quantified in-
frequently in the present standards, but when quantified they are in simple
threshold form. It may be expected that development of quantitative standards
will continue to be in simple threshold form.
Thus, the stream standards constitute an acceptable quantified expression of
society's judgment of the worth of information on the status of a stream seg-
ment. The standards reflect society's desired uses of the stream, its inter-
est in protecting those uses, and its understanding of the minimum conditions
necessary to support those uses. It may be assumed that it is highly important
to have knowledge of those occasions when the stream fails to meet those mini-
mum conditions.
The way in which the stream standards are used to compute the priority (the
need for measurement) of a stream segment is detailed in the development of
the priority rating procedure, which is found later in this section.
The priority rating procedure is based solely on the simple threshold form of
the standards. This choice is made because of the dominance of that form in
33
-------
the standards. Existing standard procedures may be used to establish monitor-
ing for the case of coliform bacteria [22, 23, 24], For purpose of system
design, other forms of the standards can be reduced to the simple threshold
form.
The other factor affecting the need to monitor a particular segment of a stream
is the expected net gain of information. The net gain in information is the
amount of new information to be acquired by establishing surveillance of the
segment. Net gain can be minimized by the existence of stream surveillance
in the vicinity of the location specified by the quantitative procedure. Such
stream surveillance may be associated either with a previous monitoring net-
work which will continue to function, or with the system under design. In the
latter case, a decision to establish surveillance in one segment of the stream
may reduce the relative need to monitor neighboring segments. Detection of
a violation in an upstream segment may provide a warning of impending viola-
tion in a segment downstream, or it may indicate worsening conditions further
upstream.
Thus, the need to monitor a particular segment must be weighted by the likeli-
hood that sufficient information on the segment may be available from other
sources. The weighting is based on the relative dependence of water quality in
the segment on conditions at stations already being monitored.
Segment Priority
The quantitative measure of need to monitor a stream segment for a parameter is
called, in general, the "segment priority. " For purposes of discussion, seg-
ment priority has been separated into two portions, one associated with the
absolute worth of information on the stream segment, the other associated with
the relative worth of the information, as discussed above. The priority asso-
ciated with absolute worth is termed the "initial segment priority." When con-
sideration of the relative worth is included, the combined measure is called
"ultimate segment priority."
Initial Segment Priority
The initial segment priority (P) is a function of the expected condition of the
stream segment and the desired condition of the stream , as expressed by the
applicable water quality standards.
The definition of initial segment priority is based on the concept of probability of
violation. The need to monitor a segment may be measured by the maximum
probability that a violation will occur in the segment under consideration (TT ).
However, as shown below, it is not necessary to carry out the computation of
probability in order to establish the initial segment priority. For the purposes
34
-------
of quantitative preliminary design of water quality surveillance systems, (see
Appendices C and D) the initial segment priority (P) may be defined as:
C - C"
— — for NLT thresholds (18)
P =
0"
c
C -C
—— for NTE thresholds
cr
C
where C = the expected worst case (maximum or minimum) value of the
parameter concentration in the segment.
C = the standards threshold in the segment
cr - the expected standard deviation of the parameter concentration
in the segment
NLT - "not less than"
NTE = "not to exceed"
The properties of this formulation are shown in the appendices to constitute a
sufficiently good representation of TT . In summary, the priority has a possible
range of -o>to +&, but the range is somewhat limited in practice by physical
properties such as saturation values and zero concentration. The lowest priority
segments may have negative priorities, corresponding to probability of violation
less than 0.5. A positive priority implies a relatively high need, with a prob-
ability of violation greater than 0.5. See Figure 6 for a graphical interpretation
of the relationship between P and TT . Computation of actual segment priorities
is based on the estimation of Cm and o"c. Methods for estimation of these quan-
tities are explored in Appendix D. The average (expected) worst case value of
the parameter may be estimated from knowledge of the average source load,
stream flow and contribution from the upstream segment. For dissolved oxygen,
for example, the estimator for Cm derived from Equations (5) and (15) is:
C" = C~(x ) = C~ -~D(x ) =C" -~L(0)A (x )-D(0)A (x )
m m sat m sat 1m 2m
(19)
kH T / kHX™\ / k«Xm \1
where
2 m
35
-------
TT - erf (a.)
-p
Figure 6, Probability of Violtation (nv) as a Function of P.
36
-------
As before, estimates of L, D. U, k_j and k are obtained from the available
historical data. Estimation of the location (xm) of the maximum probability
of violation is discussed below. Estimation of the standard deviation is handi-
capped by a general lack of available data on the variability of source loads.
For dissolved oxygen, for example, analysis of Equation (15) yields the rela-
tionship:
1/2
] ff __ | (20)
c
T2 2 2 2/2—2 2 — 2\ 2 "1
= A rr + A o •+ [A L + A D ) or
LlL0 2D0 \10 2 0 / U J
Evaluation of this equation requires a knowledge of
-------
Figure 9. These relationships are preserved in the use of the quantity P to
represent the segment priority.
However, computation of P is accomplished by use of fixed cr in each segment.
The rationale for this choice has been discussed above.
Under this circumstance, it can readily be seen that the location of maximum
violation probability coincides with the location of maximum (or minimum,
depending on the type of threshold) temporal mean parameter concentration.
For conservative parameters, the time-average concentrations is takenas con-
stant throughout each segment (Equation (13)). Computation of the segment
priority may be based on the value of mean concentration, without regard for
location.
Non-conservative, non-coupled parameters typically have a maximum concen-
tration at the upstream end of each segment, closest to the source (Equation (14)).
Computation of segment priority is, thus, based on the value at the upstream
end of the segment, for non-conservative, non-coupled parameters.
The case of non-conservative, coupled parameters requires some attention.
These parameters may have an extremum anywhere in the segment, with the
location dependent on a number of factors (Appendix D). For the BOD-DO case
typical of this category of parameters, the point of minimum concentration
(since it is a NLT parameter) is found by:
0 for x <0
c
x =
m
where
x for 0< x < x
c c E
for
Xc>XE
(21)
U in
k - k ln
a d
k
a
kd
(ka-
k
k.) k D
d' a 0
4 Lr^
(22)
Ultimate Segment Priority
Ultimately, the need to monitor a particular segment is a function not only of
the likelihood of a violation occuring in the segment, but also of the information
available from monitoring neighboring segments. If the occurence of violations
in two segments is highly correlated, then it is possible to monitor only one
of them without significant loss of information on the others.
38
-------
p(C)
MEAM
VALUE
,-—j~
TriP.FiHOLu
(NtTi
Figure 7. Comparison of Probability o} I :<>}'.•> >'>u
Parameter Means, with Standaiti !>• :'.v//-
PARAMETER
CONCENTRATION
, ; 'or Varying
P(C)
p(C)
MEAN
VALUE
AREAS PROPORTIONAL
TOn.,
STANDARDS
THRESHOLD
(NLT)
PARAMETER
CONCENTRATION
Figure 8. Comparison of Probability of Violation frv) for Varying
Standard Deviation*, with Mean not in Violation of Standard
MEAN
VALUE 1
AREAS PROPORTIONAL
TOiT
STANDARDS
THRESHOLD
(NLT)
PARAMETER
CONCENTRATION
Figure 9. Comparison of Probability of Violation (TTV) for Varying
Standard Deviation, with Mean in Violation of Standard
39
-------
Theoretically, it is possible to compute the statistical cross-correlation between
every pair of segments in the river basin and to adjust the segment priority
accordingly.
Practically, however, it is not feasible to compute the ultimate segment priority
according to the theoretical approach. Computation of the true statistical corre-
lation is limited by the lack of information necessary to its calculation. Even if
sufficient information were available, the use of P as the segment priority does
not require direct application of the true statistical correlation.
It should also be noted that the calculation requirements for computation of ul-
timate priority are extreme. For a basin containing n segments the re are (n -n/2
cross-correlations. If m of those segments were included in existing surveill-
m
v^
ance, the number of adjustments of segment priority would be .2-i (n-i), each
involving numerous individual steps, since the priority of every remaining seg-
ment must be adjusted as each new station is added.
An estimation method has been developed to facilitate the actual computation of
the ultimate segment priority. The estimation method has been incorporated in
the preliminary design procedure detailed in Appendix G. Its development is
described next.
Estimation of Ultimate Segment Priority
There are two aspects to the estimation of the ultimate segment priority.
One is replacement of the cross-correlation with a method which is both cal-
culable from the available information and compatible with the use of P to repre-
sent segment priority. The other aspect is the limitation of the total number of
computational steps required to calculate ultimate segment priority. Both
aspects are satisfied by the method incorporated in the User Handbook (Appen-
dix G).
It is shown above (see, for example, Equations (8), (9), (10) and (11))that the
impact of individual sources can be isolated from that of others influencing the
water quality at a point. Thus, it is possible to eliminate from the computation
of P that portion of Cmwhich is due to the water quality in a segment under sur-
veillance. Defining P* as the ultimate segment priority gives:
C - C~*
m- for NLT thresholds
P* =
°c
c* - c
— for NTE thresholds
-------
where C * = C (1-R;J
m m !Q
The quantity R. is an estimator for the cross-correlation between the ith seg-
ment and the qth segment, which is under surveillance. For adjacent segments,
the quantity R^ is computed as in Equation (11):
Rn= IT2- ' ^J-1 (24)
J C
m
where the superscript i indicates the portion of C which is due to the up-
stream segment. As a result of defining R^ in this way, it can be shown that,
for most cases:
R = R.. R., , i = j - 1 = k - 2 (25)
ik ij jk
Equation (25) holds exactly for conservative parameters and for non-conserva-
tive non-coupled parameters. It also holds for some cases of the non-conserva-
tive, coupled parameters for example, when one of the two terms in Equation
(10) dominates. For purposes of preliminary design, it is taken that the re-
lationship is at least approximately true for all cases.
Thus, use of the above relationship reduces the computation of (n2 - n)/2 cross-
correlations to computation of (n- 1) values of R;. (i = j - 1) and calculation of
O ^-J
(n - 1)^/1 products R^ R.^ (i = j-l = k-2). Furthermore, it can be seen that
Rj,- is very nearly zero for all but the closest segments. This significantly
reduces the number of actual adjustments of priority which must be made, as
selection of segments to be monitored progresses.
Station Location
Under the preceeding analysis, the selection of the location for monitoring
each parameter in each segment becomes a trivial task. Since the objective
of the surveillance system is the detection of water quality violations, obser-
vations should be taken at the point of maximum probability of violation in the
segment. The preferred station location for each parameter in a segment,
thus, coincides with the point at which the segment priority is computed. Con-
servative parameters may be sampled anywhere within the segment. Stations
near the upstream end of the segment are established for non- conservative,
non-coupled parameters. Because this location typically is an outfall location,
the practical application of most standards requires the station be located out-
side of, but immediately adjacent to, the mixing zone (Appendix B). For non-
conservative, coupled parameters, the preferred station location may vary
41
-------
along the length of the segment and is identified by use of Equations (21) and (22).
Again, when the station is near the upstream end of a segment, cognizance must
be given to the mixing-zone requirement.
Development of the Procedure for Selection of Sampling Frequency
The procedure for establishing appropriate sampling frequencies differs from
the procedure for establishing segment priority in that it yields a priority mea-
sure describing the relative "goodness" of sampling frequencies. It does not
tend to select a preferred frequency, since the measure continuously improves
with increasing frequency of observation.
Because of this feature of the sampling frequency priority measure, it is ideally
used in conjunction with a cost-effectiveness analysis. Used in that way, it
tends to measure the effectiveness of the sampling scheme. Balancing effective-
ness against cost may be expected to yield a unique preferred sampling fre-
quency.
In the following paragraphs, the development of the priority measure used to
rate candidate sampling frequencies is summarized. The surveillance system
objectives are reviewed and the priority measure defined in relation to those
objectives. A mathematical expression for the measure is given and the limit-
ing forms of the expression examined. The measure is contrasted with more
traditional sampling theory. Based on these discussions and an analysis of the
practical aspects of computation, a procedure for rating candidate sampling
frequencies is presented.
Definition of Priority Measure for Sampling Frequency
The priority measure for sampling frequency (M) is defined as the expected
percentage of violations of water quality standards that are detected, or more
precisely:
Expected Number of Violations Detected
M = —
Expected Number of Violations
The definition is stated in terms of only one of the major objectives of water
quality surveillance systems, abatement, but the resulting sampling schemes
are sufficient to the other major goal, planning (or prevention, [ 1 ] ).
The necessity for this measure to be quantitative is clear. It is intuitively ob-
vious that, by increasing the sampling frequency, more surveillance informa-
tion is obtained, so that higher frequencies should be rated better than lower
frequencies. It is not obvious how much better a higher frequency is. Thus,
a priority measure is needed which is a quantitative measure of sampling
effectiveness.
42
-------
Mathematical Expression for Sampling Frequency Priority Measure
An expression of the priority measure M in terms of the sampling interval, A,
(the reciprocal of the sampling frequency), the expected average duration of
a violation, T , and the expected average interval between violations, T , is
M
where:
, TX> = -^ [CQ
C =
T n-1 n
(26)
c =
i-l rp n
n = 1 0 1
" n k-1
/ „ a A
rTo
T
k=l ' L 0
r T
" n k-1 ( C
> h A 1
i ,
-v
T
1 -
- T
1
k-1
(2n - k -
(n-k)! (n-1)! (k-1)!
and A < T is assumed.
Equation (26) is based on consideration of the probability of sampliag a viola-
tion event under the assumption that such events are Poisson processes. The
detailed derivation of this expression is presented in Appendix E.
The expression can be approximated by a less complex form, for A
-------
The condition under which this approximation holds, A < TQ + T,, is the case
of most interest. It states that the sampling interval is less than the expected
average time between violation incidence. The condition is true for all cases
in which a high percentage of violations are to be detected, i.e. M >50%.
The expression M* (A, TQ, Tjj is plotted in Figure 10 as a function of relative
sampling interval (A/T^) for several values of TQ/T^. As A/T-^ becomes
small, M* approaches unity, as expected, since the probability of at least one
sample being taken during each violation is close to one when A is small rela-
tive to T^. Also, as TQ/TI, becomes large, corresponding to a small prob-
ability of violation, the measure M* becomes dependent solely on A/T, (and
independent of TQ), as would be expected.
The curves shown in Figure 10 constitute the essential element in the procedure
for rating candidate sampling frequencies. Using the curves, the quantitative
improvement in sampling effectiveness can be found for any sampling interval
(frequency). A graphical procedure is feasible, because M* is a function only
of the two parameters A/T-^ and TQ/T^.
Contrast with Spectral Methods
The sampling theory presented here and in Appendix E contrasts with the spec-
tral methods which are commonly used to establish sampling frequencies [25] .
In the spectral approach, the designer bases selection of the sampling frequency
on an estimate of the power spectrum of the process and the maximum accep-
table error [26] . Nyquist sampling theory indicates that variations at fre-
quencies greater than the Nyquist frequency (fN) will appear as an "error" at
lower frequencies. Since a direct relationship exists between the Nyquist fre- .
quency and the sampling frequency (f^r = 1/2 fg), the designer may select the
sampling frequency to reduce the expected "error" to an acceptable level
(Figure 11). The spectral approach can provide information about the "good-
ness" of a particular sampling rate at portraying the original process. It
cannot provide information about the ability of a sampling scheme to detect
particular conditions of that process, such as a violation condition. This limi-
tation is due to the elimination of phase information in the computation of the
power spectrum.
Thus, while the spectral approach is an excellent means of designing sampling
systems to protray the full variation of the original process, it is not useful in
designing sampling systems to detect only discrete states of the original pro-
cess.
A sampling scheme designed on the basis of spectral methods may detect vio-
lations, of course. There is, however, no way of measuring the likelihood
44
-------
13
§
a
o
c
•
to
a
•
CO
o
UJ
M
CC
O
5
o
I
I
•Sf>
k,
(IN) DMlVb SS3N3All03dd3
45
-------
SPECTRUM
OF POLLUTANT
CONCENTRATION
AREA PROPORTIONAL
TO "ERROR" VARIANCE
w/////////.»
fN ' fS/2
FREQUENCY
Figure 11. Typical Pollutant Spectrum Showing Effect of Sampling
of such detection using the spectral method. Even if sufficient water quality
data were available to allow system design based on spectral methods, applica-
tion of those methods to design of systems solely to detect water quality viola-
tions is not a preferred approach.
Estimation of the Sampling Frequency Priority Measure
Estimation of the sampling frequency priority measure (M) is dependent on esti-
mation of the expected durations, TQ and T^. Obtaining estimates of TQ and Tj_
requires relatively detailed data on the historical stream quality and waste load
characteristics, at least daily observations over a number of years. Such high
frequency data on both stream and effluent characteristics is not generally avail-
able. Long records of daily stream flow are available through the U.S. Geologi-
cal Survey for every minor river basin in the country. A method of estimating
TQ and TI based on the streamflow records is presented in Appendix F and
incorporated in the User Handbook (Appendix G).
46
-------
It should be noted that the estimation method is inappropriate in low priority
segments. This is due to failure of the available data records to meet the mini-
mum sample size requirement when the probability of violation is low. Under
conditions of low probability of violation, the chance of actually observing a
violation condition in the data record becomes extremely small. Estimation of
the TQ and Tj_ requires observation of at least one violation event.
Establishment of Sampling Frequency in Pristine Waters
Establishment of sampling frequency in segments with very low priority should
be based on prevention objectives, not abatement objectives. Satisfaction of
prevention objectives requires observation of long-term trends to detect degra-
dation of high quality water. Ward[l] has explored standard statistical techni-
ques for establishing sample size and developed a method of determining sampl-
ing frequency effectiveness under the prevention goal. Ward's method assumes
that all samples are drawn from a normally distributed population. Using this
assumption, he then computes the number of samples necessary to yield an esti-
mate of the parameter value to within predetermined confidence limits. By
assuming these samples are to be obtained over a known period of time, he
arrives at a sampling rate. These methods have been incorporated into the
User Handbook (Appendix G), without further development.
Multiple Parameter Design
Until this point in the development, the discussion has been directed toward
establishing the priority, station location and sampling frequency for a single
parameter. In application, the user will probably be concerned with design of
a surveillance system for more than one parameter [27, 28, 29, 30] . The
application of the design procedure to the multi-parameter case should be done
in the context of a cost-effectiveness trade-off. It can be seen from the pre-
ceeding discussion that segment priority, station location and sampling fre-
quency are dependent on the parameter under consideration. A given segment
may have as many preferred station locations and priorities as there are param-
eters of interest to the designer. The decision as to which of these to implement
is a function not only of the priority, but also of the expected cost of implementa-
tion and the anticipated benefit. For example, collection of a grab sample for
analysis of a high priority parameter may permit additional analysis for low
priority parameters. Alone, the low priority parameters might not justify
acquisition of the sample, but in conjunction with a high priority parameter they
may become cost-effective.
However, for purposes of preliminary design, it may be of interest to consider
only the comparative weights of the various parameters. To further such com-
parison, the following points are made:
47
-------
1) Because of the inherent normalization, the segment priority for each
parameter may be directly compared with that for other parameters.
A more positive (or less negative) segment priority indicates a propor-
tionally higher probability of violation than the parameter to which it is
being compared.
2) The computation of correlations is performed on a parameter by param-
eter basis, just as the initial segment priority is. When a station is
established, the computation of new ultimate segment priority is done
only for the parameters to be sampled at that station.
3) An aggregate segment priority can be computed for each segment as the
average of the individual segment priorities for each parameter in the
segment. It should be recognized that such aggregate segment priorities
must be re-computed by re-averaging as each new station is established,
since the application of correlations is on a parameter-by-parameter
basis.
4) The comparison between sampling frequency for each parameter is also
direct, due to the inherent normalization. The effectiveness of a given
sampling frequency is a function not only of the frequency, but also of
the parameter. Thus, two parameters sampled at the same frequency
may have significantly different effectiveness ratings.
Use of Available Data
Finally, it is emphasized that the methods of estimation developed in this sec-
tion are founded on the requirement that they be generally applicable. Such a
constraint tends to produce methods which may be used with the minimum data
available.
The user should make every effort to include the best data available in his pre-
liminary design. Where the existing procedures detailed in the User Handbook
do not accommodate higher quality data, modifications should be made compati-
ble with the general theoretical basis for the method, as described in this sec-
tion and Appendices A through F.
48
-------
SECTION VII
DEMONSTRATION OF QUANTITATIVE METHODS
The major features of the quantitative preliminary design procedure are suc-
cessfully demonstrated on portions of the Wabash River Basin in this section.
The procedure is demonstrated for BOD- DO on both the Wabash River and its
tributary, Wildcat Creek. It is also demonstrated for a conservative param-
eter, fluorides, on Wildcat Creek alone.
The Wabash River Basin was selected by the EPA as the basin on which the
quantitative preliminary design procedure would be demonstrated. It was sti-
pulated that the procedure would be demonstrated on the Wabash mainstem and
one of its tributaries. Wildcat Creek was selected as the tributary on the basis
of the recognized degradation of water quality in the stream.
Following some introductory remarks concerning the validity of the demonstra-
tion results and an overview of the Wabash River Basin, the presentation follows
the order of activity found in the User Handbook (Appendix G). The reader may
use this section of the report as a step-by-step illustration of the application of
the quantitative preliminary design procedure.
The preliminary design of the surveillance system is aimed at providing a moni-
toring capability on only the Wabash River and Wildcat Creek. Thus, these two
streams compose the basin subset, as defined in the User Handbook (Appendix G).
Caveat
The objective of this section is the demonstration of the quantitative procedures
for preliminary design of water quality surveillance systems. The selection
and use of the Wabash River Basin to further this objective should not be con-
strued as an expression of opinion concerning the status of the Wabash River
or its tributaries. The results of the demonstration are based on a careful
application of the design procedure to the data available. The authors have
made every attempt to assure that the data used is exhaustive and representa-
tive, but they recognize the possibility that relevant information may have been
overlooked. To this extent then, the results of the demonstration may be con-
sidered directly applicable to evaluation of water quality surveillance on the
Wabash Rjvej.- and Wildcat Creek.
The Wabash River Basin lies predominantly in the states of Indiana and Illinois,
encompassing approximately 2/3 of Indiana and approximately 1/6 of Illinois
49
-------
(Figure 12). The mainstem of the Wabash forms the southern portion of the
boundary between the two states. A much smaller area of the basin (approxi-
mately 319 square miles) lies in Ohio, where the Wabash River originates.
The total area drained is approximately 33,100 square miles. A population of
about 3.1 million lived in the basin in 1960. Principal industrial centers in the
basin include Indianapolis, Champaign-Urbana, Terre Haute, Kokomo, and
Muncie [30].
The Wabash River is a major tributary of the Ohio River, normally adding
about 30, 000 cubic feet per second to the flow in the Ohio. Major tributaries
to the Wabash include theSalamonie, theMississinewa, the White, the Patoka,
the Embarras, and the Little Wabash Rivers [31] . While the Wildcat is not
usually considered a major tributary, it is significant and drains the industrial-
ized area surrounding Kokomo, Indiana.
Task One Activities
The first task in preliminary design of water quality surveillance systems is
primarily organizational. Included in the task are map gathering, standards
identification, data organization, and selection of constraints that will guide
subsequent activity.
The federal-state standards for the Wabash River and Wildcat Creek are estab-
lished by Indiana, Illinois, and Ohio. Those applicable to the demonstration
are contained in Table 1, which is derived from those standards [32, 33, 34] .
Data on the Wabash River and Wildcat Creek were obtained from several
sources. The EPA STORET system provided a number of types of data,
including:
• Summaries of all data in STORET for the Wabash River Basin (Figure 13
is typical).
• Detailed listings of individual data entries on specific water quality
parameters (Figure 14 is typical).
• Inventories of municipal wastewater treatment facilities for the Wabash
Basin (Figure 15 is typical).
• Inventories of industrial wastewater treatment implementation plans for
the Wabash Basin. These include the SIC codes and planned effluent
flows (Figure 16 is typical).
The U. S. Geological Survey (USGS) provided data on stream flows through
their publications "Water Resource Data for Indiana," "Water Resource Data
50
-------
DAYTCW
CINCINNATI
LOUISVILLE
SHAWNEETOWN i
MT. VERNON
72. Wabash River Basin Overview (from [31])
51
-------
Table 1. Standards for Dissolved Oxygen and Fluorides Applicable to the
Wabash River and Wildcat Creek
State
Classi-
fication
Dissolved Oxygen
Fluorides
Ohio
PWS
IWS
AL(A)
AL(B)
REC
AG
No Standard.
Not less than 2. 0 mg/1 as a daily
average, nor less than 1.0 mg/1 at
any time.
Not less than an average of 5.0 mg/1
per calendar day and not less than
4. 0 mg/1 at any time.
Not less than 3. 0 mg/1 as a daily-
average value, nor less than 2. 0
mg/1 at any time.
No Standard.
No Standard.
(Not Applicable)
(Not Applicable)
(Not Applicable)
(Not Applicable)
(Not Applicable)
(Not Applicable)
Indiana
PWS
IWS
AL
REC
AG
No Standard.
Not less than 2. 0 mg/1 as a daily
average value, nor less than 1.0
mg/1 at any time.
Average at least 5. 0 mg/1 per calen-
dar day and shall not be less than
4. 0 mg/1 at any time.
No Standard.
No Standard.
Not to exceed 1. 0
mg/1 at any time
No Standard
No Standard
No Standard
No Standard
Illinois
Not less than 6. 0 mg/1 during at
least 16 hours of any 24-hour
period, nor less than 5. 0 mg/1 at
any time.
(Not Applicable)
KEY:
PWS - Public Water Supply
IWS - Industrial Water Supply
AL - Aquatic Life
REC - Recreation
AG - Agriculture
52
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for Illinois, " and "Water Resource Data for Ohio" [35, 36, 37] . These docu-
ments include daily stream flow data for each of the stations in the Wabash
Basin, in a format typified by Figure 17. The USGS also supplied copies of
the detailed data sheets on stream flow cross-sections (USGS Form 9-207), as
shown in Figure 18. Additional data were provided by direct access to data
files of the Indiana Stream Pollution Control Board and the Illinois Environ-
mental Protection Agency, and by an advance copy of Appendix F to the
'Wabash River Basin Comprehensive Study" prepared by the Lower Ohio Basin
Office of the EPA [38].
Charts and maps of the Wabash Basin are available from the USGS, the U. S.
Army Corps of Engineers, and state sources. The Corps of Engineers charts
are navigation charts and cover the Wabash River from the mouth to Huntington,
Indiana, the White River, and the Eel River. Such navigation charts are
extremely useful, since river mileage, bottom contours, and river grade are
included. The EPA Water Quality Surveillance Section provided aperture cards
of the USGS 15' topographic maps of the basin. Printed copies of the USGS
1:250, 000 scale maps of the basin proved extremely useful in gaining an over-
view of the basin. Other sources of basin maps include the basin maps
supplied by the USGS Office of Water Data Coordination w th their "Catalog of
Information on Water Data—Index to Water Quality Section" [39] and the Rand
McNally Road Maps [40] , both extremely useful in locating stations.
The so-called "Basin Subset, " those streams in the river basin to be included
in the monitoring network, is specified to be the Wabash mainstem and Wildcat
Creek. The basin subset is mapped in Figure 19. Several tributaries of Wild-
cat Creek are not included in the basin subset, because no significant effluent
sources were located on the tributaries.
A system duration of two months, specifically August and September, was
selected. The data on the Wabash indicate few problems on the river during
most of the year. During the low flow period of the year (August and Septem-
ber), the number of problem areas increases, requiring abatement-type
monitoring at that time.
The water quality parameters selected for system design consideration were
BOD-DO for both streams and fluorides on the Wildcat. BOD-DO is repre-
sentative of the nonconservative, coupled parameters, is a parameter of great
interest in water quality evaluation and has a generally high level of data.
Fluorides are representative of the conservative class of parameters, has a
moderate level of data available for Wildcat Creek, and appears to constitute
a potential problem in the creek. The STORET data indicate observed values
in excess of the NTE standard for public water supply use.
-------
UMASH RIVER BASIN
033*t2000 Wabash River at Rlverton, Ind.
LOCATION.-L.t 39°OI'I3", Ions Br^'OT", in NEfcSW* s.c.30, T. 7 N., R.IO W., Sullivan County, on left bank «t downstream sl,950
13 lit 100
I* 19,200
15 22,700
16 24,600
17 25,200
18 23,200
19 19,100
20 15,700
21 lUU
18,200
304,700 175,910
9,829
20,700
5,690
.75
1 .87
i 350 MEAN
,430 MEAN
5,675
19,500
2,930
.43
.50
14,440
12.230
19,800
21,800
22,500
20,000
18,200
19,100
19,000
18,200
17,900
16,000
14,600
12,800
10,900
9,950
9,500
8,740
7,960
7,330
8,390
B, 840
9,300
9,530
10,200
10,800
10,300
9,290
8,250
8,040
367,720
13, 130
22,500
7,830
1.00
1.04
PAX 96
MAX 71
7,930
7.670
7,750
9,240
10.600
11,300
12,900
15,100
16,000
15,600
13,900
12,300
11.000
9,610
8,680
7,980
7,610
7,380
7,370
7,830
8,360
8,630
9,290
10,400
10,900
11 ,600
14,800
19,300
22 , 500
2^ *700
24,500
372,730
12,020
24,700
7,370
.92
1.06
,600 MIN
,900 MIN
21,400
18,700
16.800
19,000
22,700
24,100
24,600
22,900
19,600
16.400
14,100
12, 500
11,500
11, 300
11,600
11.900
11,500
11.200
11,700
21, 300
28,600
3O.900
35,000
48,200
62, 100
68,900
71.400
71,900
66,600
60 • 500
879,100
29,300
71.SOO
11,200
2.24
2.50
2,540
2,100
55,300
50,000
45,100
40.600
36,700
33,400
30,500
27,900
25,100
21,000
16,900
14,800
15,700
18,100
23,300
27,400
28.600
30,100
31,900
33, 300
33,700
31,800
27,900
23,300
21,100
22,700
24,500
23,600
19,800
16 »000
13,500
863,600
27,860
55,100
13,500
2.13
2.45
CFSM 1.10
CFSM .93
12,100
11,300
11,600
11.700
11,300
10,800
10,200
9,920
9,530
9,190
9,160
8,840
8,950
8,410
8,310
8,070
8,440
B.740
8,500
8,650
8,760
7,850
6,900
6,420
6,330
6.12O
5,960
5,720
5,290
5 , 260
258,320
8.611
12.100
5,260
.66
.73
IN 14
IN 12
5,590
5.800
5,770
5,720
5,580
5,690
5.770
5,350
4,880
4,520
4,340
4,280
4,20O
4.320
4.380
4.190
4.OOO
4,000
3,920
3,740
4,420
5,750
6,410
6,250
5.42O
4,610
5,460
4,550
4.020
3. 720
4,740
151.390
4,884
j,4lo
3.720
.37
.43
.97
.68
7,110
9,670
10,000
9,130
8.580
8.150
7,960
7,800
7,610
6,790
6,010
5,130
4,310
3,880
3,540
3,320
3, LOO
2,930
2,800
2,810
3,860
4,200
5,240
4.620
3,860
3,700
3,410
3,170
3.000
2, 870
2,660
161.220
5.201
10,000
2,660
.40
.46
2,500
2,390
2,380
2.J30
2,180
2.100
2,470
2.420
2.360
2.440
2,520
2,440
2,380
2,440
2,540
2.780
2.960
3,400
4,380
4,860
5,080
5,080
5,100
5,240
7.720
10,200
11,100
10,100
8,170
7, 510
129,570
4,319
11,100
2.100
.33
.37
Figure 17. Typical USGS Stream Flow Data (from 135])
-------
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- LITTLE RIVE.!?
E.E.L. RjVER
TIPPE.CAWQE.
(2.IVE-R.
VE.R.MIUUIOM
Rivee.
.--^ ^-^SALAJHOWlE.
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R,ive:e
•'OHIO RIVER
Figure 19. Basin Subset and Major Tributaries
60
-------
Task Two Activities
During Task Two, the system designer is concerned with conditioning the data
collected in Task One for use in later tasks.
Stream flow data from USGS stream gauging stations on the basin subset were
analyzed for arithmetic mean values over the system duration. The resultant
information is summarized in Table 2.
The major tributaries (in the context of system design) were identified using the
arbitrary standard described in Activity 2 of this task. Table 3 presents a tabu-
lation of the major tributaries, with the associated river miles and average flow
added to the Wabash over the system duration. Most of the flows used to identify
major tributaries were computed directly from USGS stream gauge data. In a
few cases, the values were estimates based on drainage area. Table 4 contains
a similar tabulation of tributaries to Wildcat Creek.
Much of the data developed during the remaining activities of Task Two eventu-
ally find their way onto the computation table assembled during stream segrneta-
tion (Task Three).
In preference to duplicating these data in several intermediate tables, they are
presented once in the computation tables (Tables 5, 6, and 7). The effluent
flow rates derived from Activity 3 of this task are listed there as the Q's, along
with a characterization of each source. Similarly, the concentrations of BOD,
DO and fluorides in the discharges are tabulated concentrations.
The background parameter concentrations due to distributed soiirces were esti-
mated through an examination of the historical water quality records, since
direct information was not available. For BOD-DO, a background DO deficit
of 1 mg/liter was used as representative of BOD runoff. This value is at a
moderate level, as indicated in Table G-2, of Appendix G.
The background value for fluorides was set at 0. 1 mgAiter, based on inspec-
tion of historical data from relatively unaffected parts of Wildcat Creek and its
tributaries.
The BOD data for tributaries found in the computation tables are adjusted from
5-day BOD values to ultimate BOD load through multiplication by 1. 21. This is
based on the BOD decay relationship:
-k (5 days)
LOe =
when k(j is taken as 0. 35 day (a typical value for lab BOD analysis) [41]
Equation (2 8) is then solved for ultimate BOD (L ):
(28)
61
-------
Table 2. Stream Flow Data During System Duration in Wabash Basin Subset
Position
Wabash River
New Corydon, Ind.
Linn Grove, Ind.
Huntington, Ind.
Wabash, Ind.
Peru, Ind.
Logansport, Ind.
Delphi, Ind.
Lafayette, Ind.
Covington, Ind.
Montezuma, Ind.
Terre Haute, Ind.
Riverton, Ind.
Vincennes, Ind.
Mt. Carmel, Ind.
Wildcat Creek and
Tributaries
Jerome, Ind.
Kokomo, Ind.
Owasco, Ind.
(South Fork) near
Lafayette
Lafayette, Ind.
Average
Depth
(ft)
0.5
0.35
0.7
0.80
1.0
1.3
1.6
2.5
3.1
10.1
6.3
3.3
4.0
8.2
0.48
1.05
1.10
0.90
1.40
Average
Flow Velocity
(ft/sec)
0.9
0.5
0.97
1.10
0.90
0.76
1.7
1.10
1.25
0.57
0.74
1.55
1.3
0.75
0.25
0.90
1.50
0.50
0.90
Stream Flow
(liters/sec)
193
198
334
1,981
5,099
10,312
15,015
36, 829
46, 745
57,510
75, 641
67, 992
73,658
151,565
180
785
1,100
650
1,950
Temperature
(°C)
23
23
23
23
22
21
22
23
23
22
22
23
25
27
24
30
22
20
21
62
-------
Table 3. Major Tributaries to the Wabash River
Tributary Name
Beaver Creek
Little River
Salamonie River
Mississenewa River
Pipe Creek
Eel River
Deer Creek
Tippecanoe River
Wildcat Creek
Big Pine Creek
Vermillion River
Sugar Creek
Racoon Creek
Embarras River
White River
Patoka River
Little Wabash River
Wabash
River Mile
468
406
394
375
363
354
329
322
317
288
257
245
238
122
96
93
15
Stream Flow
(liters/sec)
85
261
737
850
198
3,966
850
9,066
2,266
623
1,841
1,700
1,445
1,983
56,660
1,417
850
63
-------
Table 4, Major Tributaries on the Wildcat Creek Basin
Tributaries to
Wildcat Creek
Mud Creek
Kokomo Creek
Honey Creek
South Fork Wildcat Creek
Tributaries to
South Fork of Wildcat Creek
Prarie Creek
Kilmore Creek
Middle Fork Wildcat Creek
Wildcat Creek
River Mile
81
64
53
7.5
South Fork Wildcat
Creek River Mile
36
29
3.9
Stream Flow
(liters/sec)
70
20
25
760
Stream Flow
(liters/sec)
150
180
170
L = 1.21 L
0 5-day
(29)
There is only one reservoir in the basin subset on Wildcat Creek approximately
70 river miles above the Wabash. Since the quantitative methods are restricted
to use in situations which may be represented as one-dimensional, the reservoir
must be excluded from consideration in the system design. A STORET station
at river mile 69. 8 on the Wildcat was used to estimate the quality of water
flowing into the Wildcat below the reservoir.
Task Three Activities
The results of source grouping and stream segmentation are presented in Tables
5, 6, and 7, and diagrammed in Figures 20 and 21. The segment numbering
scheme has been set up to consider Wildcat Creek independently from the Wabash
River.
The tolerance lengths, on which source grouping and segmentation is based, vary
from fractions of a mile to upwards of 5 miles.
Table 8 lists those sources tributary to the Wabash which were grouped together
during the Task Three analysis and which were considered major sources. Each
of these groups defines the upstream end of a stream segmert in Table 5,
A number of single and grouped discharges into the Wabash were ignored during
the preliminary design process. In addition to those so small that they escaped
64
-------
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LITTLE RIVER.
MARICLE
BLUFFTOM
4.
BIG PIKJE
WILLIAMSPOET
VERMILLIOM
R.IVEE.
RA.COOU
HUTSOWVIL.LE
VINCE.MMES
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J"
ST FRAMCISWILLE.
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PA.TOK.A RIVE.E.
• COFFEE BA.VOU
-SRA-TVII-L.E.
OHIO R1VE.R.
Figure 20. Segmentation of Wabash River
-------
MULBERRY
Figure 21. Wildcat Creek and Tributaries in '•ie^nn-.tu-d Fo,-m
notice completely, Table 9 presents a tabulation of those sources that were
intentionally eliminated from consideration, based on their minimal impact.
It should be noted that the Little Wabash River (Q = 850 liter/sec) is eliminated
from consideration, while the Mississinewa River (Q = 850 liter/sec) is not.
This is due to the relative impact of the two streams. The Mississinewa River
enters the Wabash at a point where the total flew is approximately 1/20 of the
flow at the confluence of the Little Wabash with the Wabash.
In several cases on Wildcat Creek, segments are determined not by the pre-
sence of major pollutant sources, but by significant changes in stream charac-
teristics. These changes are associated with additional flow from relatively
"clean" tributaries,
Group characteristics are computed as weighted averages of the individual
source loads. For example, the D computed for segment 6 in the Wildcat
subbasin is:
^ , ^ „ t (0)(172) + (0)(14. 5)+ (0)(0.4)+ (5. 5)(598)
Dg (segment 6 ) -_ ^+ ^ ^"+±-L->L-J
- 4.19 mg/liter
Tasks Four and Five
The results of stream characterization and rating of segment priorities are
presented in Tables 10, 11, and 12.
-------
Table 8. Discharge Points on the Wabash River that are Grouped and Considered Major Sources
Discharge Points
Associated
River Mile
Salamonie River—Largo
Eel River—Logansport (town)
Delphi—Deer Creek
Wildcat Creek—Burnetts Creek
Big Pin Creek—Attica (town)—Williamsport
(town)
Montezuma (town)—Little Racoon Creek-
Racoon Creek
Hutsonville—Turmans Creek
St. Francisville—Poker Creek
White River—Mount Carmel (town)—Patoka
River
Bonpass Creek
394
354
329
317
287
239
172
115
95
65
Table 9. Discharges on the Wabash River Ignored Due to Small Impact
Discharge
Associated
River Mile
Andrews
Rock Creek
Little Pine Creek
Mill Creek—Little Vermillion River
Brouillets Creek
Lost Creek
Honey Creek
Prairie Creek
Busseron Creek
New Harmony (town)—Black River
Little Wabash River
401
341
296
249
226
218
204
180
142
51
15
72
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75
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The computation of the characteristics of each segment is performed using the
grouped source loads found in Tables 5, 6, and 7.
The standard deviations are estimated from historical water quality records.
There were insufficient data on the variability of effluent sources to permit use
of mathematical models in characterizing parameter variability. In the case of
fluorides, the estimate is extremely poor, due to the small number of fluoride
observations during the system duration period.
The standard threshold (Cf) used for BOD-DO (5 mg/liter) is the value set by
Indiana for use of the waters to support aquatic life. The standard threshold
selected for fluorides (1 mg/liter) is the standard for public water supplies and
food processing, a use to which the Wildcat is put.
The initial segment priorities (P) computed for BOD-DO range from +0.178 to
-2. 44 in the Wabash and+ 3. 48 to -2.45 in the Wildcat. Thus, if only priority
were considered in establishing surveillance in a segment, the first station in
the basin subset should be implemented in the headwaters of the Wildcat, where
the priority of 3. 48 is found. It should be noted that, over the system duration
(the annual low flow period), the priorities in the Wildcat tend to be positive,
while those in the Wabash are predominantly negative. This indicates a gener-
ally higher probability of violation in the Wildcat than in the Wabash, a situation
documented in the STORET data.
In the case of fluorides on the Wildcat, the initial segment priorities are seen
to range from + 1. 33 to -2. 9, with the maximum in the segment just below
Kokomo (segment 5).
To illustrate several points about the relationship between initial segment
priority and ultimate segment priority, three separate cases have been exa-
mined.
In the first case, it is assumed of interest to establish a surveillance system
to detect DO violations on the Wabash. Considering only priority as a criterion
for station implementation, the first station would be in segment 25, below
Terre Haute, where the initial segment priority is + 0.178. Computation of the
ultimate segment priority, based on a station in segment 25, gives the values
in the column labeled PI* (Table 10). It can be seen that the priorities in seg-
ments 24 and 26 are radically lowered, while those in segments 15 through 23
and 27 through 33 are somewhat lower. Upstream of segment 15 there is no
change, due primarily to the low correlation between segments 14 and 15.
(The column labeled R gives the correlation with the upstream segment, RJJ
for i - j - 1.) Following computation of ultimate segment priority, segment
2 has the highest ultimate priority of those remaining (f 0.122). This may be
compared with the ultimate segment priority of segment 24 (-2. 30). The initial
76
-------
segment priority in segment 24 was 0.167, nearly equal to that of segment
25. Thus, consideration of intersegment correlation is an important feature
of the system design process.
In the second case, it is assumed of interest to set up a monitoring system for
DO on the Wildcat and its tributaries. Using priority as the sole criterion for
establishment of surveillance in a segment, the station in the headwaters of the
Wildcat would be established first (P = 3. 48). In this case, the intersegment
correlations are predominantly zero, leading to no change in the order of seg-
ment priority after computation of PI*. Similarly, there is no change after
implementation of surveillance in segment 5, just below Kokomo. It should
be noted that the reason for the initial high priority of the headwaters segment
during the system duration is the low stream flow at that point, not the magni-
tude of the source.
In the final case, a monitoring system for fluorides on the Wildcat and its tri-
butaries is assumed. Comparing this system with that on the Wildcat for BOD-
DO, it can be seen that system design based solely on priority considerations
can lead to widely differing configurations for different parameters. In the case
of fluorides, the first station to be implemented would be in segmeit 5. After
computing ultimate priorities based on that monitoring station, it can be seen
that the next station would go in the headwaters of the Wildcat, the first choice
in the case of BOD-DO.
Turning to the location of stations in the segments, the column labeled xm gives
the distance of the preferred station location below the upstream segment bound-
ary. Thus, the surveillance station for monitoring DO in segment 25 on the
Wabash would be at the upstream end of the segment, river mile 196. It should
be noted that any station established to monitor DO in segment 24 would pre-
ferrably be 18 miles below its upstream boundary, or river mile 196. This
interesting result may be attributed to the interaction of the large impact on the
stream at Terre Haute and the slight improvement due to dilution at the down-
stream segment boundary. In the case of fluorides, the monitoring may be
carried out anywhere within the segment, since fluorides are a conservative
water quality parameter.
Tasjc Six_Activj.ti.es
The procedure for determining time-sampling ratings was exercised for two
cases of interest on the Wabash River. The cases are the two segments with
highest ultimate segment priority, segment 25 and segment 2. The design
parameter is BOD-DO. Four candidate sampling frequencies are considered:
daily, weekly, monthly, and quarterly. The base data are for the period of
system duration {August and September) over the years 1961 through 1965.
77
-------
Table 13 is the computation table for the two demonstration cases. It can be
seen that, for some purposes, a weekly sampling rate might be appropriate in
segment 25, below Terre Haute, since M is 0. 7 under that sampling scheme.
In contrast, a daily sampling rate would be required to obtain a comparable M
in the headwaters of the Wabash. A weekly sampling rate at the headwaters
yields a very poor M = 0.17. The result is intuitively satisfactory; the volume
of flow in segment 2 is 0. 2% of the flow in segment 25 and subject to greater
variability over short periods of time. A higher frequency of observation should
be anticipated under those circumstances. The quantitative procedure provides
a numerical measure of precisely how much higher the frequency must be to
achieve the same results.
N1
L Implementation
Sequence No.
1
2
3
4
5
6
7
8
9
N
Segment
Number
25
2
Q(n-l)
Stream
Flow (I/sec)
36307
85
Qg
"U~
1
1 1
£ 1
. 70
.17
A
Sampling
Period (days)
30
30
M
£ !'
.. n
- ca
.33
.03
A
r Sampling
Period (days)
90
90
M
>i
It
I- rt
0. «
.10
<. o:
Table 13. Computation Table for Temporal Priority Rating for Wabash Mains tern
78
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SECTION VIII
DISCUSSION
Having developed a procedure for quantitative preliminary design of water quality
surveillance systems and successfully demonstrated it in one case, it is worth-
while to discuss the procedure in the general context of governmental water
quality programs.
The procedure has been successfully demonstrated on portions of the Wabash
River Basin. Based on this demonstration, it is believed the essential concepts
of the procedure are sound. The determination of segment priority provides a
realistic measure of need to monitor, with adequate resolution for clear separation
of low- and high-need segments. The inclusion of a measure of intersegment
correlation provides a clearly useful means of reassessing priority as stations
are implemented. The rules for location of stations are consistent with our
understanding of river processes and the method of analyzing sampling frequency
provides a quantitative assessment of the "goodness" of a given sampling scheme.
The procedures developed here are applicable to the design of surveillance sys-
tems that have abatement as their primary objective. Other surveillance objectives
include prevention and program control. A method has been developed by Ward
[l]to analyze the emphasis of a state's water quality policy with respect to the
three surveillance objectives. If that method is applied and abatement is found to
be an important objective, then the quantitative procedures developed here provide
definitive numerical methods for performing each of Ward's design tasks, up to
the point of cost considerations. It is of interest to note that the quantitative
procedure described in this report provides an analytical method for evaluating
sampling frequency, in contrast to the computer simulation method of Ward[l].
Where comparisons could be made between the two methods, the results
indicate general agreement. As sampling interval becomes small (i.e.,
frequency increases), both methods indicate an asymptotic approach to 100%
detection, with fixed pollution event characteristics. Similarly, for fixed
sampling interval both indicate approach to 100% detection as the average
violation duration approaches the system duration.
That the quantitiative procedures are useful in one demonstration and that the
results are similar to those achieved by independent analysis does not constitute
proof of generality. The general applicability of the quantitative procedure can
only be confirmed by its successful use in a number of river basins. It may be
anticipated that such application may locate insufficiencies in the User Handbook
and detailed implementation. The recommendations of Section II have suggested
a means of dealing with such problems as may be encountered. It is not anticipated
that such application will find fault with the overall theoretical structure of the
method.
79
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There is some concern that the shear volume of the User Handbook may limit its
application by appearing unwieldy, in spite of the fact that every effort has been
made to simplify and limit the effort required by the handbook procedure. Real-
istically, the user must anticipate that application of the method requires the
commitment of manpower resources. While the commitment is justified by the
resulting minimization of risk in system implementation, the demands on man-
power can be substantial. The experience of the Wabash demonstration indicates
that the system designer may wish to give careful thought to his work plan before
beginning preliminary design activities.
The recommendation to computerize the quantitative design procedure is based
on the experience of the demonstration. A major portion of the quantitative pro-
cedure is devoted to organizing water quality data and using it in stream charac-
terization. The mathematical models to be used by the EPA in establishing
computerized basin models (for example [lO]) for planning purposes [42, 43, 44]
can provide these data directly. Thus, the laborious stream characterization
portion of the quantitative procedure can be eliminated and the remaining portions
more rapidly computed.
While it is clear that the quantitative preliminary design procedure permits a
useful analysis of the requirements for water quality surveillance, they do not
provide a complete tool for design of water quality surveillance systems.
Extension of the procedure to include cost and performance factors, as recom-
mended in Section II, will equip the user with a means for evaluating realizable
systems against the requirements of preliminary design.
80
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SECTION IX
ACKNOWLEDGMENTS
The authors wish to acknowledge the contributions of a number of individuals
and organizations to the development of quantitative methods for preliminary
design of water quality surveillance systems. Particular recognition must go
to the Project Officer, Dr. Roger D. Shull of the Implementation Research
Division, Office of Research and Monitoring, for his valued guidance and sup-
port. Mr. C. Robert Home, Chief, and Mr. F. Paul Kapinos, Sanitary Engi-
neer, of the Water Quality Surveillance Section, Office of Water Programs,
generously provided the project with the user's viewpoint, aided in selection of
the Wabash River Basin for demonstration, and provided direct assistance in
STORET data retrieval. Mr. William T. Sayers, now of the Coordination and
Support Division, Office of Research and Monitoring, gave the project initial
direction based on his experience as Chief of the Water Quality Surveillance
Section.
The EPA Region I personnel at Needham Heights, Massachusetts supported the
project through use of their STORET terminal and contribution of their experi-
ence in surveillance. Mr. Paul Cummings, Systems Analysis Branch, and
Mr. David Stonefield, Surveillance Branch, are thanked for their cooperation.
During the Wabash River Basin demonstration, the project was supported by a
number of individuals in regional organizations. Within the EPA, there were
Mr. Max Noecher and Mr. Donald Hook, both of the District Office, Evansville,
Indiana, and Mr. Robert Bowden of the Region V Office, Chicago. The U. S.
Geological Survey provided data on stream flow through Mr. Joseph D. Camp
(Illinois District, Champagne) and Mr. James Swing (Indiana District, Indian-
apolis). Mr. Daniel Goodwin, of the Illinois Environmental Protection Agnecy,
and Mr. Oral Hert, of the Indiana Stream Pollution Control Board, are thanked
for their cooperation and assistance.
81
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SECTION X
REFERENCES
1. Robert C. Ward, Data Aquisition Systems in Water Quality Management,
Report No. 16909 FUO 12/71 (Environmental Protection Agency, Washington,
D.C., 1971).
2. NUS Corporation, Design of Water Quality Surveillance Systems, Report No.
16090 DBJ 08/70 (U.S. Department of the Interior, Federal Water Quality
Administration, Washington, D. C., 1970).
3, William T. Sayers, "Water Quality Surveillance", Environmental Science &
Technology, 5^(2), February 1971.
4. Hydroscience, Inc., Simplified Mathematical Modeling of Water Quality
(Report to Environmental Protection Agency, Washington, B.C., March,
1971).
5. Joint Committee on Water Quality Management Data, Water Quality Manage-
ment Data Systems Guide (published by the Pennsylvania Department of
Health, May 1967).
6. U.S. Army Corps of Engineers, Permits for Work and Structures in, and
for Discharges or Deposits into Navigable Waters Handbook (Washington,
D.C., 1971).
7. W.W. Eckenfelder, Water Quality Engineering for Practicing Engineers
(New York, 1970).
8. H. F. Lund, Industrial Pollution Control Handbook (New York, 1971).
9. W. E. Dobbins, "BOD and Oxygen Relationships in Streams", ASCE Jour.
Sanitary Engineering Division, 90 (SA3), June 1964, pp. 53-78.
10. Texas Water Development Board, Simulation of Water Quality in Streams
and Canals, Theory and Description of QTJAL-1 Mathematical Modeling
System (Austin, Texas, May 1971).
11. TRACOR Inc., Estuarine Modeling: An Assessment, Report No. 16070-
DZV 02/71 (Environmental Protection Agency, Washington, D. C., 1971).
12. Quirk, Lawler and Matusky Engineers, Systems Analysis for Water
Pollution Control (for Commonwealth of Massachusetts, June 1971).
13. Enviro Control Corp., Systems Analysis for Water Quality Management—
Survey and Abstracts Report No SD1 09/71 (Environmental Protection
Agency, 1971).
83
-------
14. R. V. Thomann, Systems Analysis and Water Quality Management (New
York, 1972).
15. R.V. Thomann, "Mathematical Model for Dissolved Oxygen", ASCE Jour.
Sanitary Engineering Division, 89 (SA5) October 1963, pp. 1-30.
16. D. J. O'Conner, "Oxygen Banance in an Estuary", ASCE Jour. Sanitary
Engineering Division, 8§ (SA3), May 1960, pp. 35-55.
17. Stochastics, Inc., Stochastic Modeling for Water Qua!iiy Management,
Report No. 16090 DUH 02/71 (Environmental Protection Agency,
Washington, D.C., 1971).
18. D.M. DiToro and D. J. O'Conner, "The Distribution of Dissolved Oxygen
in a Stream with Time-Varying Velocity", Watej^ Re sources Research,
June 1968, pp. 639-646,
19. G.M. Northrup, "Cost Effectiveness Methodology for Environmental
Monitoring Systems", NEREM 71 RECORD, Part 1: Technical Papers
(Institute of Electrical and Electronics Engineers, 1971).
20. G.M. Northrup, et al, "Cost Effectiveness of National Data Buoy Systems",
Proceddings of the Marine Technology Society 6th Annual Conference &
Exposition (Washington, D.C. 1970).
21. T. W. Bilhorn and J. M. Sharp, "An Analytical Procedure for Coastal
Zone Allocation Decisions", Preprints, 7th Annual Marine Technology
Society Meeting, (August, 1971), pp. 453-471.
22. U.S. Public Health Service, Public Health Service Drinking Water
Standards Revised 1962 (Washington, D. C., 1969).
23. U. S. Public Health Service, Manual for Evaluating Public Drinking Water
Supplies (Cincinnati, Ohio, 1969).
24. Environmental Protection Agency, A Guide to the Inter-State Carrier Water
Supply Certification Program (Washington, D. C., 1971).
25. T.A. Wastler, Spectral Analysis Applications in Water Pollution Control
(Federal Water Pollution Control Administration, Washington, D. C. 1969).
26. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra
(New Yrok, 1958).
27. L. Prati, R. Pavanello and F. Pesarin, "Assessment of Surface Water
Quality by a Single Index of Pollution", Water Research, 5, 1971, pp.
741-751.
84
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28. Syracuse University Department of Civil Engineering, Benefits of Water
Quality Enhancement, Report No. 16110 DA J 21/70 (Environmental Pro-
tection Agency, 1970).
29. Mitre Corp., Monitoring the Environment of the Nation, Report No. MTR-
1660 (Council on Environmental Quality, Washington, D.C., April 1971).
30. R.M. Brown, N.I. McClelland, R.A. Deininger, R. G. Tozer, "A Water
Quality Index—Do We Dare?" Proceddings National Symposium on Data
and Instrumentation for Water Quality Management (University of
Wisconsin, 1970).
31. Wabash Valley Interstate Commission, The Wabash River Basin-Water
Resources Planning (Terre Haute, 1971).
32. Illinois Pollution Control Board, Proposed Water Quality Standards
Revisions — #R71 -14 (1971).
33. Indiana Stream Pollution Control Board, Water Quality Standards for
Waters of Indiana (September 18, 1970).
34. Water Pollution Control Board, Ohio Department of Health, Resolution
Establishing Amended Criteria of Stream-Water Quality for Various Uses
Adopted by the Board on April 14, 1970.
35. U. S. Geological Survey, Water Resources Data for Indiana (Indianapolis,
Indiana, 1970).
36. U.S. Geological Survey, Water Resources Data for Illinois (Champaign,
Illinois, 1971).
37. U. S. Geological Survey, Surface Water Supply of the United States 1961-
1965, Part 3. Ohio River Basin (Wahsington. D.C., 1971).
38. Lower Ohio Basin Office, Environmental Protection Agency, Wabash River
Basin Comprehensive Study, Vol, VII, Appendix F (for Wabash River
Coordinating Committee, 1971).
39. U.S. Geological Survey, Catalog of Information on Water Data, Index to
Water Quality Section (Washington, D.C., 1970).
40. Rand McNally Road Atlas (New York, 1971).
41. G.M. Fair, J.C. Geyer, D. A. Okun, Elements of Water Supply and
Wastewater Disposal (New York, 1971).
42. Environmental Protection Agnecy, Schuylkill River Basin Model Project,
RFP WA 72A-8 (Washington, D.C., February 9, 1972).
85
-------
43. Environmental Protection Agency, South Platte River Basin Model Project.
RFPNo. WA 72A-14 (Washington, B.C., February 28, 1972).
44. Environmental Protection Agency, Chattahooche - Flint River Basin
Mathematical Computer Model Project, RFPNo. WA 72A-23 (Washington,
D.C. , March 22, 1972).
45. A.M. Mood and F.A. Graybill, Introduction to the Theory of Statistics
New York, 1963).
46. C.W. Helstrom, Statistical Theory of Signal Detection (New York, 1960)
47. A. Papoulis, Probability, Random Variables, and Stochastic Processes
(New York, 1965).
48. R. V. Thomann, "Systems Analysis and Simulation in Water Quality
Management1', Proceddings IBM Scientific Computing Symposium—Water
ajid Air Resources Management (1967), pp. 223-233.
49. D. P. Loucks and W. R. Lynn, "Probabilistic Models for Predicting Stream
Quality", Water Resources Research, 2 (3), September, 1966, pp. 593-605.
50. J. C. Arnold, "A Markovian Sampling Policy Applied to Water Quality
Monitoring of Streams", Biometrics, December, 1970, pp. 739-747.
86
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SECTION XI
GLOSSARY
TERMINOLOGY
Background Parameter Concentration—The concentration assumed in the
stream due to distributed sources.
Basin Subset—That portion of a river basin which is under consideration in
preliminary design.
BOD—Biochemical Oxygen Demand.
Design Parameters—Those water quality parameters being considered in the
preliminary design.
DO—Dissolved oxygen.
"Macroscopic" Concept—The overview approach to system design which limits
the spatial and temporal scales.
NLT—Not less than.
NTE—Not to exceed.
Preliminary Design—That stage of surveillance system design which deals
solely with the relationship of the surveillance system to the natural system.
Source Group—A group of effluent outfalls considered as a single source for
design purposes.
System Duration—That time over which the water quality surveillance system
will maintain a fixed configuration of spatial and temporal sampling.
USGS—United States Geological Survey.
USPHS-United States Public Health Service.
MATHEMATICAL NOTATION
A^—A function defined by equation (19).
A£—A function defined by equation (19).
a^1—A function defined by equation (29).
b^—A function defined by equation (29).
C—In general, concentration.
87
-------
C — A function defined by equation (29).
C — A function defined by equation (29).
C —The expected worse case value of the parameter concentration in the
m
segment.
C — The standards threshold in the segment.
C —Concentration of parameter at source.
s
C —Saturation concentration of DO.
sat
C —Equivalent mean concentration due to a source group.
&
D—DO deficit concentration.
D —Initial DO deficit concentration at upstream end of segment.
D —Initial DO deficit concentration at upstream end of segment due to
upstream segment.
D —Initial DO deficit concentration at upstream end of segment due to source.
s
E—The mathematical expectation (or expected value).
exp—The exponential function.
e—The exponential function.
f —A function defined by equation (29).
On
f —A function defined by equation (29).
in
f —Sampling frequency.
s
f —Nyquist frequency.
N
G—degradation variable
I—parameter index
k—Decay rate coefficient.
k — BOD deoxygenation rate coefficient.
88
-------
k — Reaeration rate coefficient.
a
L—Concentration of BOD.
L —Initial concentration of BOD at upstream end of segment.
L —Initial concentration of BOD at upstream end of segment, due to upstream
segment.
L —Concentration of BOD in source effluent.
s
In—The natural logarithm.
M—Priority measure for temporal sampling.
M*—Estimator for M.
N—Segment index.
n —Average number of detection pulse strings.
d
n—Dummy variable of summation.
n —Average number of violations.
Pr—Probability.
P—Initial segment priority.
P *—Ultimate segment priority of a segment resulting from n implementations.
n
p—Probability density function.
Q—Stream Flow.
Q —Stream flow at upstream end of segment due to upstream segment.
E
Q —Flow at upstream end of segment due to source.
fa
Q —Stream flow at upstream end of segment.
Q —Total flow due to source group.
g
Q —Stream flow threshold.
R —Estimator for p .
ij ij
R—Relative effect of upstream segment (equation (11).
S—Sampling process, a function of time.
89
-------
s—Dummy variable of integration.
T —Average interval between violations.
T —Average duration of violation.
t—Time—an independent variable.
T—A dummy variable of integration.
U—Stream velocity (positive downstream).
v—Magnitude of a water quality parameter (a function of time).
V —Threshold value of parameter as defined by standards. (Used in time sampling
analysis.
W —BOD discharge rate at source.
S
x—Linear distance from upstream end of a segment (positive downstream).
x —Linear distance of minimum (or maximum) parameter value, with respect
to upstream end of segment.
x —The length of a segment.
E
x —Critical distancejlocation of minimum in DO sag curve.
c
y—The violation process, a two-state variable.
y —The sampled violation process.
s
z—A variable defined as y(t) - y(t -A).
+
z —A variable defined as the positive pulses of z.
z+—z (t) S (t).
S
a—Sufficient statistic for P (equation (C-4)
A —The sampling interval.
TT — Probability that y is in state i at time t, given that it was in state i attimet=0.
TT —Probability of violation.
v
TT—Ratio of circumference of a circle to its radius.
p..—Cross-correlation between segments i and j.
o" —The expected standard deviation of the parameter in the segment.
c
4j —Parameter of the Rayleigh distribution.
-------
SECTION XII
APPENDICES
Page No.
A. Characterization of Stream Water Quality Data Base ... 93
B. Analysis of Federal-State Water Quality Standards . . . .115
C. Derivation of Segment Priority Rating 127
D. Estimation of the Segment Priority 137
E. Derivation of Priority Measure for Sampling Frequency . . . 141
F. Derivation of Estimators for T and T 147
o 1
G. Users Handbook 151
91
-------
APPENDIX A
CHARACTERIZATION OF STREAM WATER QUALITY DATA BASE
This appendix reports a review of the water quality data base available for use
in preliminary design of water quality surveillance systems. This review sub-
stantially corroborates and updates a similar review published by Sayers [3] ,
based on data from 1968.
The objective of the review was the determination of the level of data which the
user might typically expect to find in the application of the quantitative design
procedure. By determining the level in advance, methods for characterization
of the natural system could be developed which accommodated the available data
and which contained means for circumventing inadequacies in the data base.
The stream data base is composed of all the historical records of the charac-
teristics of the stream. Some 700 individual descriptors of stream water
quality characteristics (parameters) have been identified [5] .
A survey of the available data on stream water quality parameters was made by
a statistical anarysis of a representative sample drawn from the U.S. Geological
Survey publication Catalogue of Information on Water Data [39] , This approach
was taken, in preference to a direct survey of STORET, to minimize the lev el of
effort required. The USGS Office of Water Data Coordination publication already
contained a level of summarization which was not immediately available through
STORET. The set of stations described in the USGS publication is not strictly
identical to the set of stations in STORET. There is sufficient overlap, however,
to conclude that the USGS data set is representative of the STORET stations.
The results of the statistical survey are presented in Tables A-l through A-19.
The statistics contained in these tables represent: 1) the number of stations
measuring each parameter at each frequency, 2) the total number of stations
measuring each parameter, and 3) the total number of measurements at each
frequency. Each of the first 18 tables contains data on 80 stations selected at
random in a particular geographical area of the country. The 15 parameters
listed are those most pertinent to enforcement of federal-state water quality
standards. Table A-19 presents a summary of the preceding tables, for a total
of 1440 stations nation-wide (approximately a 31 sample of the STORET inven-
tory of about 45, 000 stations, and 6% of the stations reported in the USGS publi-
cation).
To summarize the tables in qualitative terms, given a river with several (at
least 3) stations on it:
-------
• Water temperature is measured on at least one station
• There is a 0. 9 probability that dissolved solids, common ions, hardness,
and pH are measured at least at one point
• Data on turbidity, color, chlorides, nutrients, dissolved oxygen, and
coliforms have a high probability (0. 7) of availability
» Odor, suspended solids, and radioactive chemical observations are each
performed in less than 20% of the stations in the sample
• The dominant frequency of measurement nationwide is monthly, but the
frequency of measurement is highly variable from geographical area to
geographical area.
A property of the existing data base not portrayed in the tables is the station
density. The data base survey indicates that rivers may be grouped into three
major categories, according to station density:
• Rivers in or near major metropolitan areas
• Rivers supporting significant, but less than urban, populations
• Creeks and remote streams.
Four major rivers in metropolitan areas were reviewed and the average separa-
tion between adjacent stations was computed:
• Maximum observed separation—4. 00 miles
• Minimum observed separation—1. 23 miles
• Mean observed separation—2. 7 miles.
These stations are often located adjacent to or downstream of major outfalls.
A survey of 38 streams in Category 2 disclosed the following station separation
statistics:
• Maximum observed separation—96. 0 miles
• Minimum observed separation—7.1 miles
• Mean observed separation—17. 9 miles
• Standard deviation—15.1 miles
Review of streams in Category 3 indicates a very sparse monitoring network.
Typically streams of this type have no station at all. When one is located on
the stream, it is typically at the mouth.
94
-------
In conclusion, the user can anticipate having stream water quality data available
on the parameters of interest under most circumstances, but the data may be
expected to have a low spacial and temporal intensity.
Note
All numbers in Table A-l through A-19 are taken out of a total of 80
sample stations. For example, there are a total of 60 stations out of
80 in the sample measuring temperature of Table A-l. Twenty-five
of them take monthly measurements.
95
-------
Table A-l. Occurrence of Parameter Measurement and Frequencies in the Northeast
(Sample Includes Streams in Connecticut, New Hampshire, Vermont, Maine, and New York]
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Ois. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
60
47
37
12
23
11
30
32
23
14
41
41
33
17
45
466
Frequencyt
*
1
5
7
7
10
3
2
3
7
5
3
2
2
57
1
6
1
7
2
3
1
1
2
4
7
4
10
3
2
2
1
1
8
38
5
25
28
7
7
7
7
14
17
10
11
21
23
1
12
13
203
6
19
10
11
2
9
2
4
10
9
9
10
26
1
21
143
7
2
2
2
2
2
2
3
15
8
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
96
-------
Table A-2. Occurrence of Parameter Measurement and Frequencies in the Northeast
(Sample Includes Streams in New Jersey)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
80
62
78
62
78
9
46
20
78
50
19
19
27
76
62
766
Frequencyt
*
1
1
1
1
1
1
1
1
1
9
1
2
3
7
1
3
6
1
18
4
4
3
1
1
1
1
1
3
15
5
22
22
25
25
22
3
3
25
3
3
22
22
175
6
36
36
36
36
36
9
27
1
36
34
27
34
36
384
7
8
10
15
15
15
15
15
15
15
15
12
142
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
97
-------
Table A-3. Occurrence of Parameter Measurement and Frequencies in the Northeast
(Sample Includes Streams in New York, New Jersey, and Pennsylvania)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
77
31
60
21
64
28
64
43
31
42
70
69
25
25
25
675
Frequencyt
*
2
2
4
1
13
1
4
18
2
3
2
1
3
4
5
2
2
2
2
2
2
2
19
5
15
7
9
14
7
12
17
14
11
18
18
10
1
153
6
21
21
21
21
23
21
24
2
6
22
24
23
21
21
271
7
2
2
8
20
26
26
26
25
9
9
26
26
9
1
203
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
98
-------
Table A-4. Occurrence of Parameter Measurement and Frequencies in the Southeast
(Sample Includes Streams in North Carolina and South Carolina)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
80
20
57
1
78
5
57
21
56
57
77
72
2
30
27
640
Frequencyt
*
1
2
2
2
3
21
15
3
1
21
19
15
21
116
4
2
2
5
3
1
1
1
1
2
2
3
1
3
3
21
6
16
7
7
7
7
7
7
5
7
5
75
7
35
2
35
35
2
35
1
35
35
35
35
2
19
1
307
8
3
3
11
J4
3
14
12
12
13
13
14
3
2
117
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
99
-------
Table A-5. Occurrence of Parameter Measurement and Frequencies in the Southeast
(Sample Includes Streams in Florida)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
79
3
78
78
77
73
78
78
78
76
3
78
2
781
Frequencyt
*
1
1
1
1
1
1
6
1
1
J
2
3
4
1
5
4
5
6
7
29
2
53
53
53
51
52
51
53
51
2
66
510
8
45
1
23
24
24
22
26
26
24
25
11
2
253
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
100
-------
Table A-6. Occurrence of Parameter Measurement and Frequencies in the Southeast
(Sample Includes Streams in Florida and Georgia)
Parameter
Temp.
Turb.
Color
Odor
PH
Sus. Solids
Ois. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
65
42
53
46
35
53
54
53
53
55
53
1
56
50
669
Frequencyt
*
1
3
1
1
2
7
2
3
3
1
1
1
6
4
12
12
12
12
12
12
12
12
12
12
12
12
12
156
5
18
16
16
16
15
16
17
17
16
17
17
17
30
228
6
8
8
8
8
8
8
8
8
8
8
8
8
96
7
14
14
14
14
13
13
14
14
13
11
134
8
3
3
3
3
3
3
3
3
3
1
2
30
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
101
-------
Table A-7. Occurrence of Parameter Measurement and Frequencies in the Central South
(Sample Includes Streams in Alabama and Mississippi)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
79
27
45
11
70
39
29
26
19
67
58
20
41
20
551
Frequencyt
*
1
10
18
30
29
18
1
107
1
6
1
7
2
2
2
3
14
13
13
1
12
3
2
10
10
2
3
1
9
10
103
4
1
1
1
1
1
1
1
1
8
5
40
6
18
28
21
21
6
1
22
14
1
22
2
202
6
1
2
2
1
1
1
1
9
7
7
7
8
9
7
12
11
12
4
8
8
12
10
7
6
106
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
102
-------
Table A-8. Occurrence of Parameter Meaa>ut '-ir
Kentucky , Indiana, Arkansas, Missouri,
(tad ,-'i • ;<
Parameter
Temp.
Turb.
Tot.
56
37
Color i 35
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
21
.39
9
39
39
19
34
42
33
12
42
39
496
Freqv i'tyt
*
9
2
1
I
3
2
1
3
11
3
3
1
40
1
2
3 4
5
5
n ?
i , :
i
T V
\
L
18
- .
J -r
-
j>^
- - : 7. .
" "., 1 i i
."'
7 1
j
a
] f'
19
19
1 18
19
; j
19
2J L' 14 T 2 [
2
2
1
2
2
23
' 3
i
1
3
3
3
2
27
8
8
8
4
15
10
110
19
H ; 2
<;
7
7
3
5
61
18
19
2
1
16
1
19
207
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
103
-------
Table A-9. Occurrence of Parameter Measurement and Frequencies in
Ohio, Kentucky, West Virginia, and Indiana
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
28
39
40
28
63
6
55
63
12
31
67
46
8
15
39
540
Frequencyt
*
3
1
4
1
2
2
1
14
1
5
1
3
9
2
3
7
3
3
3
1
1
4
3
2
27
4
3
4
2
2
2
4
2
2
4
2
4
31
5
7
6
8
11
7
10
4
2
12
11
1
7
7
93
6
3
3
3
3
3
3
3
3
5
8
3
3
5
3
3
54
7
1
22
22
21
22
22
110
8
22
22
22
22
3
20
24
1
19
22
3
22
202
t Frequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
104
-------
Table A-10. Occurrence of Parameter Measurement and Frequencies in the Mid East
(Sample Includes Streams in Ohio, West Virginia, and Pennsylvania)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
47
40
22
19
46
25
41
37
31
33
53
53
10
38
45
540
Frequencyt
*
1
1
2
2
6
1
6
2
8
2
1
1
1
1
1
5
3
5
10
8
1
7
10
4
45
4
6
5
2
2
5
3
2
2
6
10
14
8
65
5
7
3
3
10
4
11
14
14
8
10
9
5
9
107
6
21
21
17
17
17
21
21
14
14
24
21
18
8
16
22
272
7
6
6
6
6
6
2
32
8
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
105
-------
Table A-l 1. Occurrence of Parameter Measurement and Frequencies in the Mid West
(Sample Includes Streams in Minnesota, Wisconsin, and Illinois)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Ois. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
69
20
18
1
41
28
35
47
53
46
27
23
13
36
34
491
Frequency!
#
2
2
2
2
8
1
21
21
2
1
1
3
4
1
1
1
1
4
5
30
5
18
1
25
17
17
19
11
5
6
15
2
18
21
210
6
13
16
16
17
4
10
13
89
7
1
1
8
15
15
16
11
15
15
25
24
1
2
5
13
157
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
106
-------
Table A-12, Occurrence of Parameter Measurement and Frequencies in the Mid West
(Sample Includes Streams in Montana, South Dakota, Minnesota, and Wisconsin)
Parameter
Temp.
Turb.
Color
Odor
PH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
75
45
63
35
30
37
24
62
44
62
59
62
43
50
53
744
Frequencyt
#
1
1
1
1
1
1
7
1
1
1
2
1
1
3
3
1
1
5
4
3
3
5
67
43
48
35
18
35
12
47
37
43
43
48
13
48
48
585
6
3
3
3
3
5
8
3
3
31
7
8
8
8
8
8
8
8
27
83
8
4
2
2
2
3
2
2
3
2
2
2
26
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
107
-------
Table A-13. Occurrence of Parameter Measurement and Frequencies in the Mid West
(Sample Includes Streams in Nebraska, Iowa, North Dakota, South Dakota, and Montana)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
59
23
29
5
36
3
43
34
41
42
46
47
12
37
25
482
Frequencyt
*
2
2
4
1
8
2
2
1
1
1
15
2
1
1
4
4
5
5
4
5
1
29
3
8
1
2
3
2
1
3
1
2
23
4
5
1
2
2
2
1
1
1
1
3
2
21
5
29
18
13
3
17
3
25
22
24
24
26
30
8
16
16
274
6
5
10
6
6
6
5
5
6
6
4
3
62
7
1
1
1
1
1
1
1
2
8
17
8
3
3
3
3
2
3
3
5
2
2
5
2
36
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
108
-------
Table A-14. Occurrence of Parameter Measurement and Frequencies in the Southwest
(Sample Includes Streams in Texas and Oklahoma)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chern.
D.O.
Coliform
Totals
Tot.
51
4
3
55
70
9
12
28
61
36
2
f\
1
r
338
Frequencyt
*
1
1
1
8
1
13
1
2
2
30
1
4
4
2
3
33
3
1
29
32
3
11
30
17
159
4
1
5
8
3
1
8
9
1
1
37
5
13
1
20
22
3
8
2
22
8
3
102
6
7
8
2
2
2
6
tFsequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
109
-------
Table A-15. Occurrence of Parameter Measurement and Frequencies in the Southwest
(Sample Includes Streams in Texas, New Mexico, and Arizona)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
71
10
13
8
52
53
36
33
17
58
43
11
19
11
435
Frequencyt
*
1
1
3
2
5
1
13
1
5
1
1
1
1
1
10
2
3
20
9
9
9
9
1
9
9
75
4
3
2
2
2
6
1
1
3
2
1
23
5
18
1
2
1
16
16
14
15
4
17
16
3
9
8
140
•
13
3
5
3
12
14
2
4
3
14
9
3
85
--
1
1
1
1
!
B
11
3
3
3
1 < 12 :
•j
I i
1
1
1
2
t
1
i
13
5
10
2
R
12~|
5
1
4 i
8
i
!
76
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly .
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
110
-------
Table A-16. Occurrence of Parameter Measurement and Frequencies in the West
(Sample Includes Streams in California)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
74
15
6
6
50
6
53
34
28
19
53
20
48
20
432
Frequency!
*
2
4
4
4
4
4
4
4
30
1
10
10
2
8
8
4
8
8
36
3
4
1
5
4
5
23
3
6
6
20
3
17
14
20
10
18
11
27
17
195
6
6
1
5
1
1
1
5
1
6
27
7
13
13
13
13
16
0
O
71
8
8
7
1
3
15
6
3
3
2
4
7
58 '
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
111
-------
Table A-17. Occurrence of Parameter Measurement and Frequencies in the Northwest
(Sample Includes Streams in Oregon and Washington)
Parameter
Temp.
Turb.
Color
Odor
PH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
76
22
7
13
12
4
8
15
11
13
2
25
3
211
Frequencyt
*
1
1
1
1
2
2
1
1
10
1
23
23
2
3
17
2
2
2
23
4
10
10
2
1
2
1
6
4
2
9
47
5
21
4
4
7
6
4
4
3
5
6
12
2
78
6
7
8
5
5
1
4
3
2
2
4
1
2
8
37
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
112
-------
Table A-18. Occurrence of Parameter Measurement and Frequencies in the Northwest
(Sample Includes Streams in Washington)
Parameter
Temp.
Turb.
Color
Odor
PH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
77
24
24
4
51
24
19
45
36
53
21
2
39
34
453
Frequencyt
*
3
3
3
3
3
3
12
4
3
1
3
4
45
1
8
1
9
2
1
1
1
1
1
1
1
1
8
3
6
3
3
3
3
3
3
3
1
28
4
17
15
1
1
2
3
2
2
1
3
15
62
5
10
8
9
4
9
4
5
9
6
9
5
9
8
95
6
4
7
7
7
7
7
7
7
7
6
66
7
3
3
3
9
8
26
24
4
19
17
24
17
170
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
113
-------
Table A-19. Occurrence of Parameter Measurement and Frequencies
(Totals Based on 1440 Stations from the Index to Water Quality)
Parameter
Temp.
Turb.
Color
Odor
pH
Sus. Solids
Dis. Solids
Chloride
Nutrients (N)
Nutrients (P)
Com. Ions
Hardness
Radio Chem.
D.O.
Coliform
Totals
Tot.
1191
502
666
234
910
202
836
661
660
664
942
763
208
672
542
9653
Frequencyt
*
23
13
19
10
38
0
34
8
17
43
63
59
40
10
10
387
1
118
5
0
0
2
0
1
1
1
2
1
1
1
13
1
147
2
13
1
1
0
13
0
9
1
7
7
15
6
1
10
0
84
3
160
52
22
9
93
0
51
22
22
25
81
63
2
19
44
665
4
78
61
40
6
31
12
63
25
29
17
44
56
1
54
62
579
5
366
176
195
83
253
94
212
242
228
156
260
243
33
256
217
3011
6
153
108
133
82
131
69
133
85
121
142
135
107
79
101
125
1704
7
102
5
116
1
156
4
155
117
101
103
162
139
40
105
6
1312
8
178
81
140
43
193
23
178
160
134
169
181
89
11
104
77
1761
tFrequency
Code: * Not Periodic 3 Daily 6 Quarterly
1 Continuous 4 Weekly 7 Annually
2 Seasonal 5 Monthly 8 Other Periodic
114
-------
APPENDIX B
ANALYSIS OF FEDERAL-STATE WATER QUALITY STANDARDS
This appendix reports a review of the federal-state stream water quality stan-
dards.
The objectives of the review were: 1) to determine the extent to which the
strerurr standard^ were quantitative, and 2) the mathematical form of those
standards which had been quantified. A secondary objective of the review was
the identification of factors in the stream standards which would provide con-
jtrti ;. - v , J.'t way parameters were sampled. It was recognized that the stan-
dards might, in fact, already specify sampling schemes.
Copies of the currently approved federal-state water quality standards were re-
quested from 20 states by telephone in July, 1971. Additionally, copies of
current standards were solicited by mail from the remaining 30 states, the
District of Columbia and several of the territories, in November, 1971.
Responses were received from 44 of the 50 states, the District of Columbia,
and Guam*
The results of the survey are presented in Table B-l. The states which re-
sponded are listed along the left- and right-hand margins of the table. Most
states classify their waters according to the desired use of the water, and the
appropriate water use classification is listed in the column next to the state
name. Each subsequent column corresponds to a water quality parameter
identified in the standards. Not all the parameters mentioned in the standards
are listed in Table B-l; those listed are the most common. The standards are
categorized into eight groups. The number designating the proper category is
listed in the parameter column for each state. If no category is listed, the
parameter is not mentioned in that state's standards.
The categorization of the standard is a matter of judgment on the part of the
reviewer. Some errors may exist in Table B-l due to lack of knowledge of the
specific interpretations used in individual states. The judgments are based on
the standards as supplied to us by the states in July and November, 1971. No
attempt should be made to interpret the results summarized in Table B-l as a
measure of the "goodness" of a particular state's standards, due to varying
interpretations, implementations, and legal structures in the states. The
meaning of each category is given below, followed by a summary discussion.
•Category 1 indicates a general narrative standard, not keyed to a particular
.juantitative value of the parameter.
Category 2 indicates a simple upper limit, a "not-to-exceed" (NTE) threshold;
e.g., "temperatures not to exceed 78° F at any time. "
115
-------
Category 3 indicates a simple lower limit, a "not-less than" (NLT) threshold;
e.g. , "dissolved oxygen not less than 5 mg/1 at any time. "
Categories 4 and 5 indicate the parameter is keyed to a statistical value; e.g.,
"temperatures not to exceed an average of 72° F,11 with 4 assigned to the NTE
condition and 5 assigned to NLT.
Category 6 indicates the threshold is referenced to ambient natural conditions;
e.g., "temperatures not to exceed 2° F above that expected due to natural
causes."
Category 7 indicates a threshold with an associated duration; e.g., "dissolved
oxygen not less than 75% saturation, 16 hours/day, and not less than 5 mg/1
at any time. "
Category 8 indicates the kind of complex statistical threshold typified by the
coliform standard; e.g., "coliform bacteria not to exceed a median of 1000 per
100 ml nor more than 2400 in more than 20% of the samples collected. "
A number of conclusions may be drawn from the information in Table B-l.
The water quality standards in force at the time of the survey most generally
apply to a limited number of water quality parameters. Those most fre-
quently cited are:
Dissolved oxygen
Coliform count
PH
Temperature
Radioactivity
Toxicity
Sludge deposits
Color
Turbidity
Taste
Odor
Floating materials and debris
Of those, only the first four:
• Dissolved oxygen
• Coliform count
• pH
• Temperature
are consistently given in quantitative form, although the others are occasionally
given numerical values.
116
-------
LEGEND FOR TABLE B-l
DOM - Domestic
REC - Recreational
F&W - Fish and Wildlife
AG - Agriculture
PWS - Public Water Supply
IWS - Industrial Water Supply
AL - Aquatic Life
FW - Fresh Water
TYP - Typical
SF - Shellfish
NAV - Navigation
INTER - Intermittent Streams
MAX - Most Stringent Case
* - According to U.S. Public Health Service Drinking Water Standards
1 - Narrative
2 - "NTE" Threshold
3 - "NLT" Threshold
4 - Statistical "NTE" Threshold
5 - Statistical "NLT" Threshold
6 - Threshold Referenced to Ambient
7 - Threshold with Duration
8 - Complex Statistical Threshold
117
-------
LU
s
ALASKA
ARIZONA
COLORADO
CONNECTICUT
FLORIDA
IDAHO
INDIANA
IOWA
KENTUCKY
MAINE
MARYLAND
MASSACHUSETTS
MICHIGAN
MONTANA
NEVADA
S
O
8«
C
D
E
F
G
DOM
RFC
AG
A
a
c
D
A
B
C
D
1
(I
IN
IV
V
TYP
PWS
IW
AL
REC
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WS
AL
REC
PWS
IWS
AL
REC
AG
A
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|
II
in
IV
V
VI
c
D
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AG&JWS
NAV
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D1
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F
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INTER
TVP
1 DISSOLVED
OXYGEN
3
3
3
3
3
3
3
3
3
3 7
3 7
3 7
3
3
3
3
3
5
3
3 5
3 5
3, 7
3 7
3
3 6
3
3
3
3
8
3
3
3 7
3
1
1
3
3
1
3
3
3
3
3
3
3
3 5
3
3 5
I CQLIFQRM
I BACTERIA
8
8
B
1
B
B
a
B
e
e
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8
a
i
3
B
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8
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8
2
2
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B
2
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CONSTITUENTS
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CHLORIDE
4
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I CHROMIUM
2
2
2
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COPPER
2
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CYANIDES
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FLUORIDES
2
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Table B-l. Analysis of Federal—State Water Quality Standards (Sheet / of 6)
118
-------
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Table B-l. Analysis of Federal-State Water Quality Standards (Sheet 2 of 6)
119
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NEW HAMPSHIRE
NEW JERSEY
NEW MEXICO
NEW YORK
R
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OKLAHOMA
OREGON
PENNSYLVANIA
RHODE ISLAND
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UTAH
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WISCONSIN
DISTRICT OF COLUMBIA
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/?-/. Analysis of Federal-State Water Quality Standards (Sheet 3 of 6)
120
-------
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Table B-l. Analysis of Federal-State Water Quality Standards (Sheet 4 of 6)
121
-------
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Table B-l. Analysis of Federal-State Water Quality Standards (Sheet 5 of 6)
122
-------
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123
-------
Chemical parameters are infrequently cited (18 states of the 46 shown) and are
given in quantitative form only when listed separately by ion or compound.
Toxicity, cited by 26 of the 46 states listed, may be taken to include chemical
constituents, but is quantified for one or more water uses in only 15 of those
states.
Of those standards which are quantitative, 80% fall into the simple threshold
categories (Categories 2 and 3), either alone or in combination with another
category. Another 10% of the quantitative standards are in Category 8 (complex
statistical threshold), accounting for a total of 90% in categories 2, 3, and 8.
Category 8 appears only in the coliform parameter column, comprising 80%
of the quantified standards for that parameter. Another 15% of the quantitative
coliform parameter standards are Category 2 type.
The significance of these observations to the development of the quantitative
procedure lies in several areas.
First, it appears that the simple threshold case should be the focus for the
development of the quantitative preliminary design procedure. It is the
form most commonly found in the quantitative standards. The evidence
of Table B-l indicates that the simple threshold will dominate the stan-
dards for chemical constituents, as more states augment their standards
in that area.
Second, it may be anticipated that a number of parameters listed as having
predominantly narrative standards may become commonly quantitative (again
in Category 2 form). The observation is based on the occasional mention of
quantitative standards for these parameters:
• Toxicity
• Color
• Turbidity
• Taste
• Color
A number of observations affecting the formulation of quantitative preliminary
design methods based on water quality standards are not summarized in Table
B-l.
In general, the standards give no details of the sampling procedure to be used,
even when the standards clearly imply sampling. Use of Category 4, 5, 7 and
8 standards sets a requirement for sampling, but the length of time over which
averages were to be computed were rarely stated. The Category 8 coliform
standards are obviously based on the IJSPHS Drinking Water Standards [22] .
The drinking water standards have an establish*1'! rule for sampling, but rarely
was this rule explicitly cited.
-------
All the states gave cognizance to the mixing-zone requirement, and this factor
must be included in procedures for establishing station locations.
In addition, nearly all the states' standards contained a "nondegradation clause. "
The clause requires the preservation of stretches or bodies of water which
presently have very high quality. This presents a requirement for long-term
monitoring of these regions.
A number of the states gave standards which varied seasonally, monthly, or
in some other fashion. Temperature was one parameter which was frequenly
given in this way. Use of these standards in the quantitative preliminary design
procedure will require some flexibility in the procedure.
In summary, it is believed that a quantitative procedure designed to meet the
requirements of Category 2 and 3 standards will find the most general appli-
cability now and in the future. No attempt need be made to deal with Category
8 standards, since procedures for drinking water sampling are already well
established [22, 23, 24]. The standards do not, in general, form a constraint
on the detailed sampling procedures employed.
125
-------
APPENDIX C
DERIVATION OF SEGMENT PRIORITY RATING
In this appendix, the theoretical development of the segment priority rating is
presented. The development is given in terms of the BOD-DO case, which is
a nonconservativo, coupled process. The class of parameters which may be
described as nonconservative coupled is limited, but it constitutes the most
difficult and most general mathematical form found in Simplified Mathematical
Modeling of Water Quality [4]. The other two classes of parameters (noncon-
servative noncoupled and conservative) may be thought of mathematical subsets
of the nonconservative, coupled class.
For this development, the basin is assumed to be segmented as described in
Section VI and Appendix G. The discussion is in terms of a single segment
and a single parameter in that segment.
The theoretical rating of need to monitor a particular segment for a particular
parameter is based on the likelihood (or probability) of a violation of the water
quality standard for the parameter within that segment. If a particular
segment has a probability of violation higher than that of another segment, it
will have a higher priority rating than the other segment. The probability of
violation associated with the segment is the greatest probability found any-
where within the segment.
It is assumed that, at a given point x below the upstream end of the segment,
the DO concentration (C) will be a random variable which is Gaussianly
distributed. This assumption is made for two reasons: 1) for mathematical
tractability, and 2) on a general appeal to the central-limit theorem [45] .
The Gaussian assumption is analyzed in detail later in this appendix. This
assumption allows the distribution of DO concentration (p(C)) to be described
in terms of only the first two moments, the mean (C) and the standard devia-
tion (trc).
The probability of violation (TT ) under the Gaussian assumption is:
?
TT^ - Pr(C < CT) = J p(C) dC
— CO
"1 y* i- o r>
= ._ / exp - (C-C) /2 cr ] dC
./STT o- y L C
V ^ -en J
(C-l)
127
-------
where
C = the threshold standard for dissolved oxygen concentration
See Figure C-l for a graphical interpretation of the integral. If a change of
variables is made, such that
C - C
(C-2)
Equation (C-l) becomes:
TT =
V ./2lT
-s2/2 .
e ds
where:
= erf (a)
C - C
(03)
(C-4)
Figure C-i. Probability of Violation ( TT ) Under Gaussian Assumption for NL T Standard
128
-------
The probability of violation, TT , is a mono tonic ally increasing function of a,
and ranges from zero to unity (Figure C-2).
figure C-2. Probability of Violation (TTV) as a Function of a
Thus, probability of violation is a suitable measure of the need to monitor a
segment. It satisfies all the conceptual requirements for such a measure.
It ranges from 0 to 1 and it is monotonically increasing. It is a function of
the expected concentration of the water quality parameter, of the physical
variability of the parameters, and of the threshold value established by the
standards.
Because of the monotonic relationship between TT and G-, a is a "sufficient
statistic" [46] for rating segment priority. It is obvious that its range does
not satisfy the conceptual requirement of running from 0 to 1. However, it
does preserve the order of ranking and it tends to provide additional resolution
at the high- and low-priority ends of the scale.
Thus, a is a suitable representation of TTV as a measure of the need to monitor
a segment. It has the advantage of direct computation without table-lookup
or need of integration.
Notice, the definition of a used here is specific to processes which have a
lower limit threshold, such as DO. The integration in Equation (C-l) would be
done between CT and positive infinity for cases in which the threshold constitutes
an upper limit. For the "not-to-exceed" cases:
C - C
a
NTE
(05)
129
-------
and, as before, for the "not-less-than" cases:
a
c -
T
NLT o- (C-6)
c v '
Methods for estimation of o are explored and developed in Appendix D.
It has been assumed in the foregoing development that the water quality para-
meters under consideration behave according to the Gaussian probability
density function. The assumption is made for mathematical tractability,
because the Gaussian is a familiar form. It is also made by appeal to the
central-limit theorem. Due to the physical properties of most water quality
parameters, the assumption is not entirely accurate. It is the purpose of the
following to assess the magnitude of the errors occurring from use of the
Gaussian assumption.
One of the essential physical properties of most water quality parameters is
that they are concentrations of constituents. Even pH and temperature may be
thought of in those terms, one as the concentration of hydrogen ions and the
other as the concentration of heat. Hence, each parameter possesses a fixed,
absolute physical lower limit of concentration, in most cases equal to zero.
(Temperature is unique in this regard, due to the definition of the fahrenheit
and celsius temperature scales. Effectively, its lower limit may be taken as
the freezing point, approximately 0° celsius.) In addition, there is typically a
variable upper limit of concentration equal to the saturation concentration,
which is at least a function of temperature. (Again, water temperature is
unique; with a physical limit at the boiling point. Experience indicates a
somewhat lower practical limit in streams.)
Therefore, a correct distribution for water quality parameters would have
zero value for values of the parameter less than zero or greater than the
saturation value (except where the finite probability of super-saturation is
considered). The Gaussian clearly does not fit these requirements, since it
has a finite value over the range -°° to o>. As the mean value approaches zero,
the error could become large, unless the variance becomes proportionately
smaller.
A probability density function which more closely resembles that required by
the physical properties is the Rayleigh distribution.
The Rayleigh distribution is defined as:
~ exp (- — ) , C > 0
-------
where ^ is the parameter of the Rayleigh distribution.
The mean and standard deviation of the Rayleigh distribution are, respectively:
cr =
(C-8)
(C-9)
The distribution is shown in Figure C-3, along with a Gaussian distribution,
for comparison. Although the Rayleigh distribution may not entirely accurately
portray the actual physical properties, it is used here for comparison because
it is more representative than the Gaussian for cases of C «
RAV \_E\GH
X=C/,
Figure C-3. Comparison of Gaussian and Rayleigh Distributions
With Equal Mean and Standard Deviation
The comparison between the Rayleigh distribution and the Gaussian is typical
of the kinds of errors which may be expected from use of the Gaussian in the
quantitative procedure. The comparison is made in Figures C-4 and C-5.
In Figure C-4 it can be seen that the maximum error between the two distribu-
tions is approximately 0.1 o- (assuming the two distributions have the same mean
and standard deviation). The maximum error in probability of violation is
even smaller, less than 0.05, as shown in Figure C-5.
131
-------
Figure C-4. Difference Between Gaussian (PQ) and Rayleigh
Distributions for Equal Mean and Standard Deviations
ERROR
-1-0.05--
-O.OS--
Figure C-5, Error hfnv Resulting from Use of Gaussian in Place of Rayleigh Distribution
132
-------
Another factor affecting the validity of the Gaiibsiau assumption is the
periodicity of many of the water quality parameters. The periodicity may be
due either to the direct influence of annual cyclic variation in rainfall and solar
radiation to the direct influence of seasonal variability in industrial production
or population, or to short-term changes, such as weekly industrial cycles.
In this case, the concentration of the parameter may be thought of as the
superposition of two processes, one Gaussian random arid the other periodic.
Graphically, this superposition may be shown as a sequence of Gaussian
distributions, with time-varying mean (Figure C>6). Since the concept of
system duration (Section VI) requires that the segment priority be computed
as the average segment priority over the system duration:
Priority = AVE [ TI ] - AVE [erf(o)J (C-10)
where AVE = the temporal average.
It can be shown [45] that:
CO
E [f(x>] = J f(x) p(x) dx (C-ll)
— CO
where
E = expected value (or ensemble average)
x = a random variable
p(x) = the probability density function of x
f(x) - any function of x
It can also be shown that, for stationary processes [47] :
AVE [f(x>] = E [f(xi] 'C-12)
If f(x) is a linear function of x, then, from Equations (C-ll) and (C-12)
AVE [f(x>] - f(x)
where
x = AVE [x] .
-------
Figure C-6. Concept of Periodically Varying Gaussian Distribution
An examination of Figure C-2 indicates that TT is approximately a linear
function of a for large sections of the range of a. Thus, it may be concluded
that, to a good approximation:
Priority = AVE [TT ] ^erf (a)
Using the same arguments, it can be shown that:
(C-13)
a =
CT-AVE [c]
(Notice, it has been tacitly assumed that standard deviation does not vary
significantly with time of year.)
Thus, <* remains a suitable measure of the segment priority under conditions
of periodic fluctuation.
It is concluded from these comparisons that the Gaussian distribution is a
sufficiently good estimate of the probability density functions of the water
quality parameters.
134
-------
It is also concluded that a is a sufficiently good measure oi se^mtnt priority.
Therefore, the segmenty priority (P) is defined as:
P = o-
for NLT thresholds
for NTE thresholds.
(014)
135
-------
APPENDIX D
ESTIMATION OF THE SEGMENT PRIORITY
Determination of the segment priority requires the estimation of P (see Appen-
dix C) from known quantities that describe the mean river water quality (C) and
the variability of that quality (°~c). Appendix A and the discussion in Section VI
indicate the generally limited usefulness of direct data on water quality. Since
data on stream flow and effluents are somewhat better (albeit still poor), mathe-
matical models of water quality may be used to evaluate the stream characteris-
tics, and coefficients descriptive of the physical processes. Using BOD-DO as
an example, relationships for evaluating C and a- are developed and discussed
in this appendix. While the relationships for C prove useful, further approxima-
tions are shown to be necessary for evaluating
-------
k L
— = d o I"
k -k, L
exP (~
a d
~ exP (~k x
a
/u) + D exp (-k x/u
Jo a
The expected DO profile, found using Equation (D-5), is:
(D-5)
(D-6)
where C is the mean DO at saturation.
oA 1
Of the three parameters needed to evaluate P, C is found from Equation (D-6)
and CT is established by the standards, leaving only the standard deviation crc
to be found.
An expression for
-------
kdL
D (x) = - •— exp (-k x/u) - exp (-k x/u) + D exp (-k x/u)
K - K L a ajo a
a d
= A (u,x) L + A (u, x) D
J. O & O
and o- = A (u, x) cr
D 1 LQ
Let Do(t) be a stochastic process with_mean DQ and standard deviation cr-p , and
let LQ and u be constants with values L0 and u, respectively. Then, by a pro-
cedure similar to that in [47] :
D (x) = A (u, x) L + A (u, x) D
1 o
-------
The standard deviation of the dissolved oxygen Is then found by noting that Equa-
tion (D-6) relates C and D through a constant. Under that condition the variation
in C (x, t) has the same magnitude as variations in D (x, t) and:
f . 2 22 222 222 l1/2
C= LA1 'L +A2 *D +(A1 Lo +A2 Do^u J
00 J
(D-12)
with the right-hand side evaluated at the point in the stream where TT is maxi-
mum (see Section VI).
Clearly, P can be partially evaluated by use of Equations (D-5) and (D-6) for
computation of C, but complete evaluation depends on the ability to derive
-------
APPENDIX E
DERIVATION OF PRIORITY MEASURE FOR SAMPLING FREQUENCE
This appendix presents the detailed derivation of the priority measure for
sampling frequency (M) discussed in Section VI, (Equations (26) and (27)). It is
based on the definition of the measure given in that section:
M =
Expected Number of Violations Detected
Expected Number of Violations
(E-l)
Let v(t) represent the time-varying magnitude of a water quality parameter, as
shown in Figure E-l. If the quantitative threshold level defined by the water
quality standards is VQ, a violation occurs when the parameter magnitude ex-
ceeds the threshold [v(t) >V0] . (In some cases, such as dissolved oxygen, the
violation occurs when v(t) < V0 but this does not change the mathematical anal-
ysis, as will be seen). A normalized two-state process can be defined which
equals unity during a violation and which equals zero when there is not a
violation. Such a process is shown graphically in Figure E-l as v(t).
Figure E-L Conversion of Parameter Process into Violation Process
To describe the stochastic process y(t), probabilities of transition from one
state to the other are needed. In general, these probabilities are functions of
the threshold level VQ (the normalizing factor) and the past history of y(t). As
a first-order simplifying assumption, it is taken that the transition probabilities
are explicitly dependent only on the present state (0 or 1) and on the length of
time that x(t) has been in that state and implicitly on the threshold level VQ [49].
For the simplified case, sufficient descriptors of the stochastic process y(t) are:
ir.(t) = Pr[y(t) = i|y(0) = i] i = 0, 1 (E-2)
141
-------
which are probabilities that, for time t>0, y is in state i, given that it entered
state i at time t - 0. Another way of stating it is that no transition occurs in
time t, given that a transition occurred at time 0.
To further simplify the mathematics, it is assumed that y(t) is a Poisson pro-
cess, a well-known process which satisfactorily describes many natural
processes. This assumption reduces the probabilities in Equation (E-2) to the
form:
TT (t) = exp(-t/T.) i = 0, 1
(E-3)
where T., i = 0, 1, is the mean time in state i before a transition occurs, and
depends on the threshold level VQ.
These assumptions produce a simple mathematical description of the violation
process in terms of two natural descriptors, the mean duration of a violation
(Ti) and the mean interval between violations (To). Also, the probability of a
violation (TTV) can be easily expressed in terms of the descriptors:
\ = T + T (E~4:'
1 o
Notice that computation of these probabilities for a real case requires the
estimation of the descriptors TQ and T .
To derive Equation 29, define the sampling process S(t) in Figure E-2 as the
periodic function:
S(t) =
1/e nA 0
(E-8)
0 for z(t) < 0
142
-------
+
= z(t) S(t)
(E-9)
Since the pulses in z(t) are of length A or less, at most one sample will be taken
during their existence. Hence, z+ contains only the first sample in any string
of samples associated with a single violation. The average number of detection
pulse strings (denoted by n^) is:
T
vit! f *>*
-------
Now:
mi f
-« J
E [S(t>] = lim i / S(t) dt
(E-13)
and
But:
and
- y(t-A)] }= Pr[y(t)-l, y(t-A)=0] (E-14)
= Pr[y(t-A)=0] Pr[y(t)=l y(t-A)=0]
Pr[y(t-A)=0] = °
1 o
(E-15)
Pr [y(t) = l|y(t-A)=0] = Pr [odd-number transitions in (0, A) (y(0) -OJ
CO
= 2 Pr[(2n-l) transitions in (0,A) y(0)=0] (E-16)
The probability of one transition in (0, A) can be found by:
A
Pr [1 transition in (0, A) Jy(0) = 0] = f Pr[no transition in (0,s)|y(0) = 0]
0
•Pr[transition in (s,s+ds)]
•Pr[no transition in (s+ds,A)jy(s+ds)=l]
/-s \ds
exp\T IT exp
\ o/ o
(A-s)
1 J
exp -
(E-17)
144
-------
In a similar manner, it can be shown that:
Pr [(2n-l) transitions in (0, A ) | y(0)=0] =
(T -
2n-l On
exP
ft)
(E-18)
where
n
n k=l
a. A
T -T,
o 1
,
o 1
k-l
k -k-l
EK n k-lTT=Tn
b A 0 J
k •-_ _ '
k=l
i
n (~l) (n--
\ (n-k)! (n-1)! (k-l)!
n
k n
\
By substituting Equations (E-17) and (E-18) into Equation (E-16):
Pr[y(T) = l y(T-A) = 0] = C exp (-•—-)+(
A
MM*>
T,
(E-19)
where
T T.
c_ = >^.-2 3L_f
2n-l
On
n-1 n
T T
c. =
n=l
2n-l In
145
-------
Then, using Equations (E-19), (E-15), (E-14), and (E-13), the expression for
(Equation (E-12)) can be evaluated:
exp(-
The average number of violations (n ) is:
(E-20)
(E-21)
Using Equation (E-20) and (E-21) in the definition of the priority measure yields:
n,
+ CL exp(~^r-)l (E-22)
M
-------
APPENDIX F
DERIVATION OF ESTIMATORS FOR T AND T,
o 1
In this appendix, the assumptions and rationale employed in developing the pro-
cedure for rating sampling frequei cy are described. Since the procedure
depends strongly on estimation of the descriptors TQ and Tj_, derivation of the
estimators is emphasized. The need for a description of the dynamics of
water quality variations is identified first, then the quasi-steady-state descrip-
tion of those dynamics is presented. Next the application of the quasi-steady-
state description is given, followed by the procedure for estimation of the
average violation duration (T^) and average interval between violations (T0).
In Appendix E, the quantitative priority measure for rating sampling frequency
is developed in terms of the dynamics of water quality violations at a point in
the stream. The descriptors To and T^ are used to describe the dynamics at
the point. To obtain estimates of T0 and T]_, either the dynamics of water
quality in the stream must be known or they must be describable in terms of
known processes which cause them, such as stream flow and waste discharges.
Since data on streamflow and discharges are either currently available or soon
to be available (through the Refuse Act Permit Program or its replacement),
the latter approach was selected, requiring the use of time-varying stream
quality equations.
Equations which describe the time-varying water quality parameters along a
stream are well known for all three classes of water quality parameters. They
are described here in the most complex form, that of the nonconservative,
coupled class represented by BOD-DO. Neglecting diffusion, the equations are:
9L 9L , T
_ = -u_-kdL (F-l)
_|P=_U12 -kD + k.L (F-2)
81 3x a d
where L = BOD concentration
D = DO deficit concentration
u = stream velocity
k , k = reaeration and deoxygenation rate coefficients, respectively.
a d
If LQ = LQ (t) (F_3)
D = D (t) (F_4)
147
-------
are sufficiently slowly-varying BOD and DO deficit concentrations at the up-
stream end of a segment (x = 0), then the solutions to Equations (F-l) and
(F-2), with initial conditions represented by Equations (F-3) and (F-4), are:
L (x, t) = L (t) exp (-k x/u)
(F-5)
D (x, t)
k -k
a d
L (t) exp (-k x/u) - exp (-k x/u)
o L d a J
D (t) exp (-k x/u)
o a
(F-6)
These quasi-steady-state expressions are identical in form to steady-state
expressions discussed in Section VI, except for the time-varying L0 and D0.
Using Equations (F-5) and (F-6), the dynamics of the deficit, D(xm, t), at the
point xm in the segment can be related to the dynamics of LQ(t) and Do(t) at
the upstream end of the segment. The Lo(t) and D0(t) can then be expressed
in terms of the BOD and DO deficit concentrations due to the upstream segment
(Le and De), the stream flow from the upstream segment (Qe), the BOD dis-
charge rate at the source (Ws), the flow from the source (Qs), and DO deficit
of the source (Ds). See Figure F-l. The relationships may be written as:
(t) =
Q L +W
e e s
Q +~Q
(F-7)
X»0
X- X
m
E,
Figure F-l. Segment BOD-DO Situation Diagram
148
-------
Q D + Q D
D (t) = -V+QS S (F-8)
o Q + CJ
e s
In many cases, the temporal variations in Qe are larger than the variations in
the other parameters on the right-hand side of Equations (F-7) and (F-8). Also,
the variations in W , Dg, and Qg are generally not well known. Hence, it will
be assumed here that the dynamics of LQ(t) and Do(t) are due entirely to the
dynamics of Qe(t). Average values of Wg, Dg, Qg, Le, and De are used in
evaluating these two equations.
For computational purposes, it is assumed that We = Qe Le (the initial waste
load due to the upstream segment) and Q,,D0 are constant; the values used in
C &
establishing segment priority and spatial locations are assigned. In this case:
_ ... Constant
L
o Q(t)+Q
e s
_ Constant
Do «> = oT^oI (
It can be seen that L (t) and D_(t) vary in identical ways, as Q0(t) varies.
O (J N?
Therefore, D(x, t) varies with Q0(t) in the same way.
"
Furthermore, it follows that
D (x, tx) D (x, tg)
Q (t)+Q = Q (tJ+Q (F~n)
els e 2 s
From Equation (F-ll), it can be shown that there is a threshold value of
stream-flow (Qt) that is associated with the threshold value of DO deficit derived
from the water quality standards. The relationship can be written as:
~D(Xm,t)-
°T
[Q w
L e
+ Q
s
where D = the DO deficit threshold derived from the standards value for
minimum DO
The descriptors TQ and T-^ may be estimated directly from statistics of Q ,
specifically the time Qe spends above and below Qrp, respectively. Since a
violation occurs if D >DT, a violation occurs if Q < QT, from Equation (F-ll).
The time D spends at values greater than DT is equal to the time Qe spends
149
-------
at values less than QT. Thus, TI can be estimated by statistical examination
of daily streamflow records, such as those available from the U.S. Geological
Survey. Similarly, T may be estimated by statistics on the time Q > QT.
O c J-
Since there may be more stream segments than stream gauging stations along
a river, the nearest upstream or downstream station must be used. Selection
should be made on the basis of which station can be expected to represent the
segment best, for example, in the vicinity of a confluence point. It is possible
to interpolate values between two stations, but it becomes impractical for the
manual methods to be used in the procedures under consideration.
Once the estimates of T0 and T-^ have been found for each segment, the priority
measure for sampling frequency may be evaluated using the methods derived in
Appendix E.
150
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APPENDIX G
USER HANDBOOK
This appendix constitutes a stand-alone handbook for the application of quantita-
tive methods to the preliminary design of water quality surveillance systems.
Usage
The User Handbook is intended for use in determining the following water quality
surveillance system design factors:
1) A numerical priority (P) for the measurement of each water quality
parameter of interest in each stretch of the stream
2) A preferred location (xm) for the measurement of each water quality
parameter of interest in each stretch of the stream
3) A numerical rating of merit (M) for each candidate sampling frequency
at the preferred location for measurement of each water quality param-
eter in each stretch of the stream.
The user may wish to determine these design factors for any of several reasons,
such as:
1) The preliminary design of a new water quality surveillance system
2) Comparing an existing surveillance system against the recommendations
of the procedure
3) Program planning to evaluate the overall level of surveillance required
in a basin, region or nation.
Limitations
The User Handbook is limited to preliminary design of water quality surveillance
systems which have abatement as the primary goal. It is intended that the result-
ing system detect violations of water quality standards. The methods require that
the standards be expressed as a simple threshold, either directly or, indirectly,
by arbitrary choice of the user.
The methods are limited to those cases in which the "macroscopic" concept
holds. That is, the stream is considered as one-dimensional and periods of
less than a day are ignored.
The user should be familiar with basic engineering mathematics up to, but not
including, calculus. He should also have available a desk calculator or similar
151
-------
computational device. It is not necessary to have access to an automatic digital
computer.
The User Handbook does not include consideration of cost, accessibility, main-
tainability, reliability and other similar practical engineering factors.
Overview of the Quantitative Procedures
The quantitative preliminary design procedure consists of a number of indivi-
dual activities which have been grouped into six tasks. The six tasks are per-
formed sequentially, beginning with Task 1 and proceeding to Task 6 (Figure
G-l). The activities within each task may occur in either iterative or sequen-
tial patterns; flow charts have been provided with each task to guide the user.
In Task 1, the user will be concerned with gathering necessary data, organizing
information and determining certain guidelines for his particular application.
Task 2 is devoted to the development of specific items of information which
characterize the river basin. This is accomplished by manipulation of the data
collected in Task 1.
In Task 3, the user begins the actual preliminary design by establishing stream
segments, which are stretches of the stream which may be dealt with as uniform
units.
The primary output of Task 4 is the location of preferred monitoring stations,
although a number of other factors are computed for use in Tasks 5 and 6.
The priority of each parameter of interest to the user in each segment is estab-
lished in Task 5.
Task 6 is concerned with the computation of a rating of the merit of various
sampling frequencies proposed by the user.
Stream Quality Parameters
The design procedures are based on stream quality profiles of (water quality)
design parameters of interest. Design parameters from three basic classes of
parameters, including non-conservative coupled, non-conservative uncoupled
and conservative, can be used in the procedures. Most stream quality parame-
ters of interest are included in one of these classes, given in Table G-l. In the
handbook procedures, the most general class (coupled) is presented in terms of
the important doublet, BOD-DO.
Illustration
For computational efficiency an attempt has been made to use a consistent
152
-------
TASK1
GATHER DATA
SET GUIDELINES
\
TASK 2
DEVELOP
INPUT DATA
\
TASK 3
SEGMENT
STREAM
TASK 4
CHARACTERIZE
SEGMENTS
PREFERRED
SAMPLING
LOCATIONS
TASK 5
COMPUTE
PRIORITY
RATING
OF
MERIT
SAMPLING
FREQUENCIES
Figure G-l. Handbook Task Flow Diagram
153
-------
Table G-l. Parameter Model Characterization
Parameter
Characterization
Dissolved Oxygen
Coliforms
Temperature
Nitrogen (organic, ammonia,
nitrite, nitrate)
PH
Radioactivity
Cyanides
Phosphates
Chloride
Sulphate
Heavy metals
Fluorides
Phenols
CaCO (hardness)
O
Sludge
Color
Turbidity
Taste
Odor
Petrochemicals
Foaming materials
Coupled, Non-conservative
Non- cons ervati ve
Non- cons ervati ve
Coupled, Non-conservative
Non-conservative
Non-conservative
Non-conservative
Non- cons ervati ve
Conservative
Conservative
Conservative
Conservative
Non- cons ervati ve
Non- cons ervati ve
Non-conservative
Non-conservative
Non-conservative
Non-conservative
Non-conservative
Non-conservative
Non-conse rvati ve
-------
system of units throughout. The system used is the metric system (specifically,
the CGS system). It is recognized that this system does not always reflect
common practice and tables have been provided for rapid conversion from more
common units.
Longitudinal dimensions are measured in two ways in the procedure. For ini-
tial location of major features of the stream, the traditional river mile system
is used. The river mile system measures all distances upstream from the
mouth of the river. For computation purposes, attention may be focused on
individual stretches of the river basin. Under these circumstances, distances
(symbolized by an "x", frequently with a subscript) are measured downstream
from the upstream end of the river segment. It will become clear to the user
which system is being used by the context of usage.
Data Inputs
The procedures contained in this handbook assume a relatively low level of
information on the historical quality of the river basin. The user should make
every effort to employ the best data available in his design. Should the handbook
procedures appear incompatible with the existing data the user may be guided by
reference to the development contained in Section VI of this report.
155
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TASK 1
COLLECTION OF PERTINENT DATA AND DETERMINATION OF
SYSTEM DESIGN GUIDELINES
The initial task in surveillance system design of a river basin involves collec-
tion of various pertinent data on the basin and setting up system design guide-
lines based on the data. The activities in this task should be performed in
sequential order as described in Figure G-2.
DETERMINE
STANDARDS
THRESHOLDS
COLLECT
PERTINENT
DATA
1
3
COLLECT
MAPS
DETERMINE
GEOGRAPHICAL
SCOPE
I
DETERMINE
SYSTEM
DURATION
LIMIT
DESIGN
PARAMETERS
GOTO
TASK 2
Figure G-2. Task I Activity Flow Diagram
156
-------
TASK 1, ACTIVITY 1—DETERMINE STANDARD THRESHOLDS
Objective
Determine the specific threshold level at which a violation is considered to have
occurred. This must be done for each parameter of interest to the designer.
Output
• Index of standard thresholds by parameter and geographical region of
applicability.
Information Source
• EPA— Technical Assistance Branch of Office of Water Programs has
state-federal water quality standards.
• Individual States— The most up-to-date standards are available directly
from the states.
Procedure
• Obtain from the listed information sources all parameter water quality
standards for the basin.
• From these standards define a standards threshold for each parameter
included in the documents and for all sections of the river. Or, if no
standard exists for the parameter of interest, select an arbitrary thres-
hold.
• Go to Task 1, Activity 2
TASK 1, ACTIVITY 2—COLLECT PERTINENT DATA
Objective
The objective of this activity is to bring together and organize the data required
for surveillance system preliminary design.
Output
• Index of all water quality stations and locations in the river basin
• Index of all U.S. Geological Survey stream flow gauging stations and
their locations on the river basin
157
-------
• Index of municipal and regional sanitary outfalls and their locations
• Index of industrial waste outfalls, their locations, and SIC codes.
Information Sources
• EPA—STORET inventory, municipal waste inventory, industrial imple-
mentation data.
• U.S. Geological Survey—'Water Resources data for (state)," Parts 1
and 2; detailed data on stream flow cross-sections (Form 9-207) from
regional offices.
• U.S. Army Corps of Engineers—"Refuse Act Permit Program" data from
regional offices.
• State Agencies
• Local Agencies
• Universities
Procedure
• Obtain a STORET Statistical Summary retrieval for all parameters of
interest to the designer, from all stations of the river basin, over a
period of at least two years.
• Obtain the "Water Resources Data for (state)," from U.S. Geological
Survey over the same time period as the retrieval of STORET, for all
USGS stations on the basin.
• Obtain the "Form 9-207" data from the U.S. Geological Survey basin
regional office for stations of the basin.
• Obtain Industrial and Municipal Effluent data from STORET for the entire
river basin.
• Obtain any additional, federal, state or local inventoried data which may
be available.
• Index these data in a form which may be easily accessed.
• Go to Task 1, Activity 3.
TASK 1, ACTIVITY 3-MAP COLLECTION
Objective
The objective of this activity is to provide the preliminary design program with
the appropriate base material for consideration of geographical relationships.
158
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Output
• An overall basin map with river mileage reference points, and, if
available, a complete set of detailed maps for the river basin.
Information Sources
• EPA— The Surveillance Branch maintains a complete aperture card file
of U.S. Geological Survey 15' quadrangle maps.
• U.S. Geological Survey—Topographic maps—7-1/2', 15' and 30'
(1:250,00) maps available without woodlands overprint. Also frequently
available as special printings, without contours.
• NOAA-NOS— Coastal navigation charts (including charts of tidal rivers
such as the Hudson River), Great Lake navigation charts, Aeronautical
charts.
• U.S. Army Corps of Engineers—Navigational charts of inland rivers.
Procedure
• Derive an overall basin map which is most convenient for the user.
• If river mileages are not available on the map at hand, use STORET data
giving river mileages and mark these data points as milestones with the
appropriate river mile. The river miles between milestones may be
approximated with a Map and Blueprint Measure (for example, Charrette
Catalogue No. 4719, Charrette Co., New York, N.Y., 1971).
• Go to Task 1, Activity 4.
TASK 1, ACTIVITY 4—DETERMINE GEOGRAPHICAL SCOPE
Objective
Identify the extent of the river basin to be included in the surveillance system
design ("BASIN SUBSET"), and prepare a "situation map" of this basin subset.
Output
• "Situation Map" of the basin subset.
Inputs
• Task 1, Activity 2
159
-------
Discussion
It may be desirable to limit the extent of the streams considered in design to a
portion of the river basin. Reasons for exclusion from the basin subset are:
1) Arbitrary exclusion for reasons external to the preliminary design pro-
cess
2) Any tributary which has no effluent sources on it will be excluded.
Procedure
• On the overall basin map, define those streams to be included in the
basin subset.
• Prepare (for example, by tracing) a map of the basin subset.
• On this map ("situation map") mark all effluent source points and tribu-
tary input points on the basin subset.
• Mark all points on the basin subset where stream flow data is available
from U.S. Geological Survey.
• Go to Task 1, Activity 5.
TASK 1, ACTIVITY 5—IDENTIFY SYSTEM DURATION
Objective
Specify the duration in which surveillance system design factors are to be com-
puted.
Output
• System duration (days).
Inputs
• Data from Task 1, Activity 2
• Decision based on factors external to this procedure.
Discussion
System duration is that period of time which the designer anticipates that the con-
figuration of the surveillance system will remain fixed. Although it is called a
duration, it is important to determine the time of year as well, when the system
duration is less than one year.
160
-------
Procedure
• Using judgment based upon a knowledge of the external constraints,
identify the system duration. All the data used in this procedure must
be based on averages over the system duration identified in this activity.
• Go to Task 1, Activity 6.
TASK 1, ACTIVITY 6—LIMIT PARAMETERS TO BE USED IN SYSTEM DESIGN
Objective
Specify which of the parameters of interest may be used in surveillance system
design.
Output
• Design parameters names and units.
Inputs
• Task 1, Activity 1
• Task 1, Activity 2
• Task 1, Activity 5.
Procedure
• Identify all water quality parameters which are included in the regional
stream standards.
• Identify those parameters of interest for which there is data meeting the
following criteria:
1) concentration data in some form for each effluent outfall. (General
textbook data may be sufficient.)
2) at least two measurements of that parameter in the stream during
the system duration at most of the STORET stations.
• Identify which parameters may be of particular interest in surveillance
system design due to their high risk in violating the standards.
• Specify the parameters selected for surveillance system design.
• Go to Task 2.
161
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TASK 2
CATALOGING AND CONVERSION OF INPUT DATA
In this task pertinent input data will be selected, based on its quality, and con-
verted to a form which is directly usable in the procedure. The activities in
this task should be performed in sequential order, as shown in Figure G-3.
( START \
1
CATALOGUE
U.S.G.S. STREAM
FLOW DATA
I
IDENTIFY
MAJOR
TRIBUTARIES
2
COMPUTE
EFFLUENT
FLOW RATES
I
IDENTIFY
PARAMETER
BACKGROUND LEVELS
I
COMPUTE
EFFLUENT
CONCENTRATIONS
I
DETERMINE
CONCENTRATION OF
INCOMING TRIBUTARIES
I
IDENTIFY DAMS
AND ASSOCIATED
WATER QUALITY DATA
U
GOTO
TASK 3
Figure G-3. Task 2 Activity Flow Diagram
162
-------
TASK 2, ACTIVITY 1-CATALOGUE GEOLOGICAL SURVEY STREAM FLOW
DATA
Objective
Find stream velocity, depth, stream flow and temperature during the specified
system duration at all available stations in the basin subset.
Output
• Stream velocity (U), depth (H), stream flow (Q) and temperature.
Inputs
• Task 1, Activity 2: U.S. Geologic Survey Intensive Studies (Form 9-207)
• Task 1, Activity 5: system duration.
Procedure
Perform the following tasks for each station using the U. S. Geological Survey
Form 9-207, identify all measurements within the system duration specified in
Task 1, Activity 5. Use at least two years of data.
• Using the identified measurements compute the average flow velocity
over the system duration.
cross sectional area
• Compute average depth (H) = — over the system dura-
width
tion.
• Compute average stream flow over the system duration.
• Compute average temperature over the system duration.
• Check the "situation map" to see if all stream flow data points are pro-
perly located.
• Go to Task 2, Activity 2.
TASK 2, ACTIVITY 2-IDENTIFY MAJOR TRIBUTARIES
Objective
Find flow rates of all tributaries of the basin subset and select the major tribu-
taries.
163
-------
Outputs
* Tributary flow rates in liters/second
• List of major tributaries.
Inputs
* Task 1, Activity 2
• Tributary drainage area from maps.
Discussign
This activity is to be performed on all tributaries which flow directly into the
basin subset.
Procedure
The logic shown in Figure G-4 is used in treating each tributary to the basin
subset.
TASK 2, ACTIVITY 3-COMPUTE EFFLUENT FLOW RATES
Objective
Select the most reliable data available for each effluent outfall in the basin sub-
set and convert effluent flow rates, Qg, to liters/sec.
Output
« Effluent flow rates (liters/sec).
Input
• Task 1, Activity 2.
Procedure
• For each outfall identify the most reliable data from the following sources:
1) Refuse act permit program data
2) STORET data
3) State and local data
• Convert this data to liters/sec using Table G-2.
• Go to Task 2, Activity 4.
164
-------
-I
165
-------
Table G-2. Conversion Factors for Flow
Input Data
Units
Multiply data
number by the
following to give
units (liters /sec).
ft /sec
28.33
c
gal x 10 /day
43.80
g
meters /sec
1 x 10"3
gal/day
4.38 x 10~5
TASK 2, ACTIVITY 4-DETERMINE BACKGROUND LEVEL OF EACH DESIGN
PARAMETER
Objective
For each of the design parameters, identify the characteristic background con-
centration for the basin subset (C^ (I)).
Output
Background levels in units defined in Task 1, Activity 6.
Inputs
• Task 1, Activity 2: Historical Water Quality Data
• Task 1, Activity 6: Design Parameters.
Procedure
• Determine the background concentrations for each design parameter.
For DO and total coliforms, the value may be determined from Table
G-3. For all parameters including DO and coliform, a more general
approach is to use STORET data and:
1) Determine the lowest values of parameter concentration found within
the basin subset.
2) Check to see if the value may be associated with a source.
3) If not associated with a source, let the background concentration
C^bk (I) equal that value.
4) If associated with a source, let C^ (I) = 0.
• Go to Task 2, Activity 5.
166
-------
Table G-3. Background Parameter Concentrations
Range
Low
Moderate
High
Region
Sparse Vegetation
Grass, Woodlands
Organic, Swampy
Areas
D.O. Deficit
(mg/1) (Dbk)
0.5
1.0
2.0
Coliforms
(MPN/100 ml)
10
100
1,000
Source: Simplified Mathematical Modeling of Water Quality,
Report to Environmental Protection Agency, March 1971
TASK 2, ACTIVITY 5-DETERMINE THE PARAMETER CONCENTRATIONS
AND FLOWS OF EACH EFFLUENT
Objective
For each design parameter and each effluent outfall, determine the parameter
concentration and the flow of the effluent.
Output
• Parameter concentrations in units defined in Task 1, Activity 6.
• Effluent flow in liters/sec.
Inputs
• Task 1, Activity 1
• Task 1, Activity 2
• Task 1, Activity 6
• Task 2, Activity 4.
Discussion
For dissolved oxygen both BOD and DO concentrations are needed. For other
parameters only the concentration of the parameters themselves are needed.
The units of the concentrations should be consistent with the units established
in Task 1, Activity 6.
167
-------
Procedure
The analysis is performed as shown in Figure G-5 for all parameters, except
DO (Figure G-5 applies to the BOD case). Figure G-5 references use of Table
G-4. If effluent data are not available, either of two methods can be used: one
for industrial effluents and one for municipal treatment plant effluents.
• Method 1: For industrial sources, it may be possible to estimate effluent
concentrations based on standard textbook data. Recommended sources
for such information are:
1) Eckenf elder, W. W. , Water Quality Engineering for Practicing Engi-
neers, Barnes & Noble, New York, 1970.
2) Eckenfelder, J.R., Industrial Water Pollution Control, McGraw-
Hill, New York, 1966.
3) Lund, H. F. , Industrial Pollution Control Handbook, McGraw-Hill,
New York.
4) Nemerow, N. L. , Theories and Practices of Industrial Waste Treat-
ment, Addison-Wesley, Boston, 1963.
Table G-4. Conversion Factors for Concentration
Input Data
Units
Multiply
Data by
the follow-
ing to give
units mg/1
gm
liter
.001
Pounds
Gallon
5
1.2x 10
Pounds
liter
5
4.54x 10
Pounds
Million Gals.
2
1.2 x 10
Parts Per
Million (ppm)
1
• Method 2: For municipal waste water treatment, the following estima-
tion technique, modified from Simplified Mathematical Modeling of Water
Quality (Environmental Protection Agency, 1971)
Q = f,_ P I/sec
s 5 0
,
L =
s
V
Q
mg/1
where the f-factors may be obtained from Tables G-5, G-6 and G-7, and
P. is the present population of the municipality.
168
-------
REFUSE ACT
PERMIT PROGRAM
DATA AVAILABLE
STATE
OR LOCAL DATA
AVAILABLE
MUNICIPAL
NOTE ANY INDUSTRIES
DUMPING INTO
MUNICIPAL SEWERS
CONVERT TO
PROPER UNITS.
USE TABLE G-4
TO CONVERT TO
MG/L
STORET
PARAMETER CONC
DATA AVAILABLE
STATE
OR LOCAL DATA
AVAILABLE
COMPUTE PARAMETER
CONCENTRATIONS PER
METHOD 1
GO TO TASK 2,
ACTIVITY 6
COMPUTE PARAMETER
CONCENTRATIONS AND
FLOW PER METHOD 2
Figure G-5. Logic Flow for Task 2, Activity 5 for all Cases Except DO
169
-------
Table G-5. Population Growth Factors (fj)
Area Growth
Description
Established Static
Low to Moderate
Moderate to High
Kapidly Developing
Growth Factor
1.10
1.50
2.00
2.50
Increase Range
0-25
25 - 75
75 - 125
125 - 375
Table G-6. Per Capita Waste Flow (f5) and Quantities (f3)
Low
Average
High
Flow
\Cap-sec i
4.4
7.8
13.1
Ultimate
/ r \
V Cap- sec/
C N
0.63 0.37
1.32 0.79
2.10 1.47
Solids
/ mg \
^Cap-secy
0.79
1.58
2.63
Nutrients
/ mg \
^ Cap-secy
N P
0.079 0.016
0.184 0.031
0.290 0.053
Coliforms
(MPN 3\
\Cap-sec y
58
116
174
Table G-7. Estimated Efficiency of Treatment Levels on Carbonaceous BOD (fj)
Treatment Level
Primary Treatment
Marginal Secondary
Treatment
High Rate Biological
Treatment
Secondary Treatment
with Nitrification
Advanced Treatment
Ultimate Treatment
% Removal
50
70
85
90
95
99
#/Capita/BOD
Remaining
0.125
0.075
0.037
0.025
0.013
0.025
£4 fraction
BOD Remaining
0.50
0.56
0.44
0.12
0.5
0.1
170
-------
For DO, Figure G-6 gives the logical analysis. Another method of evaluation
may be required in the DO analysis:
• Method: For DO in the case of industrial flushing water, obtain the
average concentration of dissolved oxygen from the nearest upstream
set of historical data (C(DO)). Then assume the effluent source concen-
tration CS(DO) is equal to C(DO).
TASK 2, ACTIVITY 6-DETERMINE PARAMETER CONCENTRATION OF EACH
INCOMING TRIBUTARY
Objective
Find the concentrations of each design parameter at the points where major tri-
butaries flow into the basin subset.
Output
• Parameter concentrations in appropriate units.
Inputs
• Task 1, Activity 2—Pertinent Data
• Task 1, Activity 6—Design Parameters
• Task 2, Activity 2—Tributary Identification
• Task 2, Activity 4—Background Levels.
Discussion
If historical data is used it should be obtained from a point as close to the tri-
butary mainstem confluence point as possible, still being on the tributary and
the background level for that parameter should be subtracted from historical
data concentrations.
Procedure
Perform the logic in Figure G-8 to compute the concentrations of each design
parameter at the confluence points of major tributaries with the basin subset.
171
-------
REFUSE ACT PERMIT
PROGRAM EFFLUENT
DATA ON D.O.
MUNICIPAL
OR INDUSTRIAL
OUTFALL
EFFLUENT
MAINLY DUE TO
FLUSHING OF INDUSTRIAL
PROCESSES. OR
SEWAGE
Figure G-6. Logic Flow for Task 2, Activity 5, DO Case
172
-------
o
o
UJ
cc
5
•w
I
I
•S-
i
•
I
1
1
SJ
a
I?
Bui- NOIiVUiN33N03 NOIlVUniVS W3DAXO
173
-------
Figure G-8. Logic Flow for Task 2, Activity 6
174
-------
TASK 2, ACTIVITY 7-IDENTIFY DAMS AND ASSOCIATED WATER QUALITY
DATA
Objective
Identify all reservoirs on the Basin Subset and obtain flow and design parameter
concentration data from the nearest stations below their respective dams.
Output
• Dam outflow and concentration data.
Inputs
• Task 1, Activity 2—Field Data
• Task 1, Activity 4—Situation Map
• Task 1, Activity 6—Design Parameters.
Procedure
• Identify all reservoirs on the situation map.
• Identify the nearest field data station downstream from dam.
• Extract flow and typical design parameter concentrations taken during
system duration at this station.
• Convert this data to the appropriate units.
• Go to Task 3.
175
-------
TASK 3
SEGMENTATION AND COMPUTATION OF
SEGMENT INPUT VARIABLES
The procedure for segmenting a river basin consists of a number of activities
which must be performed in sequence, beginning at the headwaters of the main-
stem and continuing to the river mouth. When a confluence point of a tributary,
which must be segmented, is encountered, the activities are again commenced
at the headwaters of the tributary until reaching the main stem confluence point.
The procedure then continues along the main stem.
After an effluent group is identified as significant and segmentation is performed,
a number of variables describing the segment are computed and entered into a
computational table. To avoid confusion one computational table should be set
up for each parameter. Tables G-8 and G-9 illustrate the typical table formats
for BOD-DO and uncoupled parameters. The index letter N is used to identify
the segments on the computational table. The index NN is used to indicate when
the task is to end. Both of these indexes are initially zero. The logical flow of
activities in this task is described in the following flowchart (Figure G-9).
176
-------
aoaatibag
73
bO
'U9OUO3
(l/Sra)
bC
aoa
bD
AVOJJ
9UIBM—
I
I
c
•
I
o
(l/Sui)
(00)
O1
(oas) (y)
ffi
(sajiui)
1JU
f ^ S
$1 5.
en CM
c
D
s
bo
0)
Cfi
IUB3J1SUMOCI
pu;j
177
-------
eoaanbag
0
be
s
2
•5
I
bC
dnoao
(00)
I
-
2
cK
(oas/y) Aji
ffi
(sajTUi)
Segment
Position
(RMI)
pug
Segment
apoo
178
-------
f START J
_x_
IDENTIFY MOST
UPSTREAM OUTFALL
THAT HASN'T ALREADY
BEEN GROUPED
1
IF
NOT
END
FIND PARAMETER
DECAY RATE (Kd) OF
THAT OUTFALL
GOTO
TASK 4
END
11
FINDD.O.
SATURATION
LEVEL
I
COMPUTE GROUPING
TOLERANCE LENGTH
MTOL
10
FIND SEGMENT
REAERATION
COEFFICIENT
I
GROUP OUTFALLS
WITHIN TOLERANCE
LENGTH
I
COMPUTE SEGMENT
DECAY COEFFICIENT
i
I
DETERMINE STREAM
CHARACTERISTICS IN
UPSTREAM SEGMENT
DON'T
SEGMENT
COMPUTE EFFLUENT
GROUP IMPACT AND
MAKE SEGMENT, DON'T
SEGMENT DECISION
1
SPECIFY RIVER
MILE OF GROUPED
DISCHARGE POINT
7
SEGMENT
COMPUTE FLOW RATE
AND CONCENTRATIONS FOR
THE EFFLUENT GROUP
Figure G-9. Logic Flow for Task 3
179
-------
TASK 3, ACTIVITY 1-IDENTIFY MOST UPSTREAM OUTFALL
Objective
Find, using the situation map, the most upstream effluent outfall or major tri-
butary input which has not already been grouped in Task 3, Activity 4,
Output
• Discharge (effluent outfall or tributary) identification.
Inputs
• Task 1, Activity 4—Situation Map
• Task 2, Activity 7—Reservoir identification
• Task 3, Activity 4—Grouping
Procedure
• In the initial pass through this loop identify the outfall which is furthest
upstream on the main stem (primary stream). If there is a tributary
whose confluence point is above any outfalls on the main stem, and which
contains an outfall, start segmentation at this outfall, on this "upper-
most" tributary which contains an outfall.
• If this activity is entered from Task 3, Activities 5 or 11 identify the next
discharge downstream from the previously considered discharge group.
If the point of confluence with a tributary in the basin subset is reached,
identify the outfall furthest upstream on the tributary and begin segmenta-
tion of the tributary at this outfall.
• If a reservoir is encountered before the next outfall or tributary ignore
the stretch of reservoir by
a) ending the upstream segment at the top end of the reservoir.
b) beginning the next segment at the dam.
• If there are any other major changes in physical characteristics, break
the river into "subsegments" for more accurate computation of the stream
profile. The stream characteristics and reaeration coefficients must be
specified for these "subsegments, " however they are not to be rated
themselves since they do not represent independent pollution threats.
• If the lower end of the main stem is reached let NN = 1, and go to Task
3, Activity 8; if not, go to Activity 2.
180
-------
TASK 3, ACTIVITY 2—FIND OUTFALL k VALUE
Objective
Find a length decay coefficient which corresponds to the outfall identified in
Task 3, Activity 1.
• k j, in days , for the outfall, and for each design parameter at the out-
fall.
Inputs
• Task 1, Activity 2—Stream data.
• Task 2, Activity 1—Stream flow data.
Discussion
The decay coefficients of all design parameters must be found and compared in
this activity. All conservative substances such as fluorides have decay coeffi-
cient kj of zero, by definition. In the case of coupled BOD-DO, the decay coef-
ficient of BOD is used in determining the length scale. From Fair, Geyer, and
Okun the following BOD kj values are assumed.
Municipal Effluent (No Treatment).
Industrial Effluent. d
= .4
Stream
depth
greater Municipal Effluent (Primary Treatment) k = . 35
than rt
10 feet
Municipal Effluent (Secondary Treatment) k(j " '2
Procedure
• Identify the effluent discharge type for that outfall described in Task 3,
Activity 1.
• Find the decay coefficients, kd, for all design parameters. To do this
for BOD:
1) Find k(j depth = 10 feet usmS tne appropriate assumption above and
identify the corresponding line of Figure G-10.
2) Follow this line laterally until appropriate depth is reached on
abscissa.
3) Read the corresponding k^ value on the ordinate.
181
-------
I I I
I I I I I I I 1 1 I I
I
«J
I
5?
a
5
3 0OZ ® (AVQ/L)
182
-------
• If general text information on a certain decay coefficient of the para-
meter is not available but concentrations at two locations, x-^ and x2,
are known and it can be assumed that there are no discharges between
xi and X£T the compute:
II C(X1)
k = E In i
d (x2-Xl) C(x2)
where U = stream flow velocity at the nearest U. S. G. S. station
C (x ) = parameter concentration at x
C (x ) = parameter concentration at x > x .
2 z l
• Specify the highest kj value of the design parameters and assign that
k,j to the outfall.
• Go to Activity 3.
TASK 3, ACTIVITY 3-COMPUTE GROUP TOLERANCE LENGTH
Objective
Compute the distance (x^0i) from the effluent outfall identified in Task 3, Activity
1, within which other outfalls may be "lumped" together with it and considered
one outfall.
., , in miles.
tol
Inputs
• Task 3, Activity 2—Outfall decay coefficient k^
• Task 2, Activity 1—Stream velocity (U).
Discussion
The tolerance length is defined as the distance from the effluent source in which
10% of the parameter with the highest k^ has decayed.
With this definition,
(1.72)*U ..
x , = -—~ miles
tol k,
d
183
-------
Procedure
• Locate the nearest U.S.G. S stream flow station from the discharge
identified in Task 3, Activity 1, and find its flow velocity (U).
• Compute
• Go to Activity 4.
TASK 3, ACTIVITY 4-GROUP OUTFALLS WITHIN TOLERANCE LENGTH
Objective
Group all discharges lying within x^i of the discharge identified in Task 3
Activity 1.
Output
• Discharge Grouping
Inputs
• Task 1, Activity 4— Situation map
• Task 3, Activity 3— Tolerance length
Procedure
• Locate all other discharges along stream which fall within X(-oi distance
of the discharge identified in Task 3, Activity 3.
• If a reservoir is encountered within x^o treat as that given in Task 3,
Activity 1, procedure step 3.
• Go to Activity 5.
TASK 3, ACTIVITY 5-COMPUTE EFFLUENT GROUP IMPACT AND MAKE
INCLUDE/DON'T INCLUDE DECISION
Objective
Compute the summed impact of the group of outfalls identified in Task 3
Activity 4 and decide whether to neglect this impact or include it in priority
rating.
Output
• Include/Don't Include Decision.
184
-------
Inputs
• Task 2, Activity 2—Tributary flow rates
• Task 2, Activity 3—Effluent flow rates
• Task 2, Activity 5—Effluent concentrations
• Task 2, Activity 6—Tributary concentrations
Procedure
Perform the following steps for each parameter
• For each source in the group, compute the mass loads
W (I) = Q * (C )
s s s
where: I = parameter identifier
C = parameter concentration of the source.
s
• Compute the sum of mass loads, for all sources in the group
W (I) = £w (I)
g s s
• Compute the total impact of the effluent group (Impact (I)), on the stream
concentration.
W (I)
Impact (I) = -2—
(al
where Q = approximate average flow during system duration from nearby
U.S.G. S. station.
• Decide at what threshold T(I) the impact should be considered negligible.
(As a guide line, for this study a 0.1 mg/1 impact change of DO or BOD is
set as the threshold.)
• If Impact (I) is less than or equal to T(I), neglect the effluent group and
go to test of the next parameter. If all design parameters have been
tested, ignore outfall group and go to Task 3, Activity 1.
• If Impact (I) is greater than T(I), include effluent group in segmentation,
let N = N + 1 denote the index number corresponding to the segment
with this effluent group at its upstream end, and go to Task 3, Activity
6.
185
-------
TASK 3, ACTIVITY 6-COMPUTE FLOW RATE AND CONCENTRATIONS FOR
THE EFFLUENT GROUP
Objective
Compute the total flow rate [Q£(N)j and concentration [C (I, N)] of each
pertinent parameter for the effluent group.
Outputs
• Q (N) in I/sec
&
• Cg (I, N) in mg/1.
O
Inputs
• Task 2, Activity 2— Tributary flow rates
• Task 2, Activity 3— Effluent flow rates
• Task 2, Activity 5— Effluent concentrations
• Task 2, Activity 6— Tributary concentrations.
Procedure
• Compute the sum of effluent flows from all effluents in group N:
Qg (N) = Z Qg
• Compute the summed concentrations for each effluent parameter (I).
£ C (I) * Q
• Enter flow rate Qg(N), and parameter concentrations C™(I, N) in
appropriate Computation Table, (E.g., Tables G-8, G-9).
• Go to Activity 7.
TASK 3, ACTIVITY 7-SPECIFY RIVER MILE OF GROUPED DISCHARGE
POINT
Objective
Assign a point river mileage to the location of effluent group N, segment N.
186
-------
Output
• Location in river miles of discharge group point.
Inputs
• Task 1 Activity 4—Situation Map.
Procedure
• Find the arithmetic mean of the river miles of the group using the
expression
R.M. = - > R.M. _
mean n *^> L
Lr-1
where n = number of outfalls in the group.
R. M. = river mile of Lth outfall as given in Situation Map
R. M. = the upper end of segment N and is also the grouped
mean „_ L . \.
effluent source location.
• Enter R.M.mean into the Computation Tables (i.e. , Tables G-8, G-9)
as both the end of the previous, upstream segment N-l, and the beginn-
ing of the new segment N.
• Go to Activity 8.
TASK 3, ACTIVITY 8-DETERMINE STREAM CHARACTERISTICS
Objective
Determine the average values of stream depth [H(N-l)] , flow velocity [U(N-l)] ,
stream flow [Q(N-l)] and water temperature [Temp (N-l)] over the system
duration for segment N-l.
Outputs
• Stream Depth—H(N-l) in feet
• Flow Velocity—U(N-l) in ft/sec
• Stream Flow—Q(N-l) in liters/sec
• Water Temperature—Temp (N-l) in °C.
187
-------
Inputs
• Task 2, Activity 1— Stream Flow Data
• Task 3, Activity 7— Segment Bounds
Discussion
The physical characterization is now performed on segment N-l because the
identification of discharge group N defines the downstream end point of segment
N-l. This characterization is to be made using available Geological Survey
data. In general the resolution of this data is larger than the segment size.
Therefore, one physical characterization per segment is usually made.
However, if stream data with finer resolution is available, the physical
variables may be given for a much finer resolution,
Procedure
• Identify the nearest Geological Survey stations from segment N-l.
• Specify the segment stream parameters (average flow velocity (U),
depth (H), stream flow (Q), and temperature) by
1) linearly interpolating the data over the system duration from the
stations identified above
2) averaging this data over the system duration.
• Enter output in Computation Tables, (Tables G-8, G~9) on row N-l.
• Go to Activity 9.
TASK 3, ACTIVITY 9— COMPUTE SEGMENT DECAY COEFFICIENT
Objective
Find the decay coefficients [k(j(I, N-l)] for each design parameter in segment
N-l.
Output
• Parameter Decay Coefficients k(I, N-l) in days
Inputs
• Task I, Activity 2— Effluent Types
• Task 2, Activity 1— Stream Data
IMP
-------
• Task '.\, A.rtivitv '•' - -nd "'!*»>--' '
• Task. .1, .'VtlvJ'v v' •-'!.••"'•. > 'li-irs' i .-i-i -"1 ' •
Procedure
For oacli design parameter perform the following stops:
* Fain tUf ii", :ur<-.--! .'-•; ^ • • ->! ' ; ,., •:;••• '^!i i'r,:!, f<; of ?V>
gj oup according t" its U- .'} and 'h' -: • "'s'i.sKP pr n.'-pTitrd in Task -J-,
• Compute the conjJjitjed dfctiv f-oeSli.-i^iits f-n oa''h parameter (I):
Enter k,(~s, N-1| in (lie °-*.i}>r'>t-rj'-iir (V>rripu)atic>r> Table nf»bl^ r, -8 o
(j -9 on 1 ov/ N.
CrO to A^fivilv 10.
TASK .1, AC'i JVIYY H) MNJ) ^FuMhiN'T RK-\KRATfON ''OF' ! !"' !!;<>-r'
(Note: Skip f"his p^tivitv i«" [i'> i-j n'-S" f>f r!i>f jjr»i inrc-ropi . ;
Objective
Vind the reaeratir.'n "oefficicnf I'<(;W 1; for scgiher'f N-3.
Outp_ujL
* Re?ierat i<*<•• ffi"- '*•? f i .jTJ I1 HI ..'-•',
inpy.S
* Task 3, A(/tivit\ ^ ;'U: <•=,.) i«pp*i>
* ^'isifl P P/-- 1 1
•. -,)'•, value.
* "i \ <>.< '• \Li"-\< .•/' •
( f'i ' ) =ltl f.TU1 V> !<>•
* Trace (i-''vi7.ont;dl\
(M ^ ) vfibjf1 of k...
-------
o
°0
CM
LU
QC
.2
DEPTH IN FEET
Figure G-l 1. Reaeration Coefficient (ka) as a Function of Depth
190
-------
• Enter ka(N-l) on the Compulation Table, Table G-9 on segment Row
(N-l).
• Go to Activity 11.,
TASK 3, ACTIVITY 11-FIND THE DO SATURATION LEVEL
(Note: Skip this activity it DO is not of design interest.)
Objective
Find the DO saturation level, C j-(N-l) for segment N-l.
Output
• DO Saturation Level Cgat(N-l) in mg/L
Inputs
• Task 3 Activity 8—Stream Temperature
• Task 2 Activity 5—Figure G-7.
Procedure
• Using the stream temperature for segment N-l and Figure G-7 find
csat directly.
• Enter Csa£ in Computational Table, Table G-9, on segment row N-l.
• If NN=1, go to Task 4; If NN=0, go to Activity 1.
191
-------
TASK 4
CHARACTERIZE SEGMENTS
The procedure for computation of a stream parameter profile is dependent on
the behavior of that design parameter. The three basic physical systems
which will be dealt with here are non-conservative coupled, non-conservative
uncoupled and conservative uncoupled. The first category, descriptive of
complex systems such as the BOD-DO system, is dealt with in Task 4A. The
latter two parameter types are handled in Tasks 4B and 4C, respectively.
The solution of parameter profiles in each of these sections consists of a num-
ber of activities which should be performed in the sequence shown in the flow
chart in Figure G-12. For each design parameter the activities are performed
iteratively for each segment, beginning with the headwaters and continuing to
the river mouth.
The computed values to be evaluated in Task 4 should be tabulated in a com-
putation table for ease in later use. Table G-10 illustrates a format for the
BOD-DO case to contain values found in Tasks 4 and 5.
TASK 4, CONTROLS: SELECT PARAMETER PROFILE COMPUTATION
Objective
Select a pertinent design parameter and choose the proper profile computation.
Output
• Specification of a design parameter and which subtask of Task 4 to use.
Inputs
• Task 1, Activity 2 — Field Data
• Task 1, Activity 6 — Design Parameters
Procedure
• Select Design Parameter.
• Initialize segment sequence index by letting N = 1.
• If the design parameter is dissolved oxygen, go to Task 4A.
• If the design parameter is non-conservative uncoupled go to Task 4B.
• If the design parameter is conservative uncoupled, go to Task 4C.
192
-------
ELEC
PARAMETER
AND DETERMINE
BASIC PROPERTY
Figure G-I2. Logic Flow for Task 4
193
-------
I
•Si
•c
I
a
* ^
(X
* rH
O
* ^
Q
K
(X
4-J
O
b
W
hJ
W
p
d*
e
u
e
Q
X
o
Q
o
H-l
W
X
Segment
Position
£
T# SUHBH -jotjd
a}Bun;in
{[/gui) -ouoo OQ
pg^snfpv
(l/Sui) -jaa OQ
pa;snfpy
uo;;Bpaaoo
§ag-ao;ui
§ui}Ba
A^]ao]j(j ^Bi^]U7
(l/Sui) ppqsajqx
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(t/§Ul) UOHB1A3Q
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(t/Sui) -ouoo dOH
pug ^uauiSag
(l/Sui) -jaa OQ
pug }U9Ui39g
•jsa oa
punoaSipBg
(l/Sui) -ouoo
DO XT3JM
(t/Sui) ;io?j9a
Oa XBW
(saijtu) aouB;s]Q
•DUOO XBH
d/3ui) ;ioijaa oa
T^mui
(I/STU) -ouoo aoa
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(sa^iui) q^SuaT
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P«3
£5 UIB9J}SUMOQ
^
£. pug
UIB9J}Sdf}
jgquinM
}U9UiSag
-
rH(MCO^irj^Ot~QOO5
194
-------
TASK 4A, ACTIVITY 1 - COMPUTE LQ(N)
Objective
Compute BOD concentration at upstream end of the N segment [Ly(N)].
Output
• L0(N) in mg/1.
Inputs
• Computation Table G-8—Q (N), Lg(N)
O
• Computation Table G-10 - L (N-l)
.L
Procedure
• For the segment under consideration (Segment "N"), compute:
L (N) a Qg(N)Lg(N) + Q (N-l) LE(N-1)
° Q(N-l) + Q (N)
g
Except: for N=l, assume L (N-l) = 0
E
• Enter L (N) on Computation Table G-10.
• Go to Activity 2.
TASK 4A, ACTIVITY 2 - COMPUTE D (N)
Objective
Compute initial DO deficit at upstream end of the N segment [D (N)].
Output
D (N) in mg/1.
Inputs
Computation Table G-8 - Q (N), D (N), Q(N-l), C (N)
g g sat
Computation Table G-10 - D_(N-1)
E
195
-------
if >b- "OMirdV'i-.! I'U f once ni ran UM i:s difrtj ru., in £•*,,••, ,,u1b I< I yinl N, the DO
deficit ai Juf, eiid of ilic u>.bUeam s^pTnein i-,<>;,st he cor'ipen^ated for., (Note:
step 1 oi j/T'icud':.!<.-,).
Pf uOfc-cm 11;
» i;'.,r It"' .:«..grr.»-<; '
if (N) - C
ftn! sat
if O' (N'-J • < it ivi D* (N 1) - 0
!• ' h
* ilu/nt' utj
,,, % Q fN)*L» (N) i-Q(l\-i)*D» (N-l)
if N -J dh'-iii.Mie i;! (ii- 1) - 0
* Dnlfcr iJ^N) on C/oiiifiaiafion fdhje './-
* Ge to Acti\ ily 3.
TASK 4 A, ACIiVaY ^ -• i:-h:'l RUJ'.'L? Ju ^, ;
<":)
jJbjjietrvt
» X ,-'•; tl
III
inputs
• C'omputatjoii Table C -H - iMTj) k (N- k (r<'}<
(i' d
• Computation Table (j— Mt - i (i-l), D (N), x ^ (1^),
J9fi
-------
Procedure
There are two alternate procedures for this activity. The first uses direct
computation of the values through use of equations. The second replaces
direct computation with a nomograph.
Alternative 1
For the segment of interest (segment N) compute
D (N)* k (N) - k (N)
Zj - -0- * d
LQ(N)*kd(N)
Compute Z = a (1-Z )
• Find Z - ln(Z ) using a table of natural logrithms.
3 £
U(N)* [16.36] *Z
* Compute Xc(N) = j^_— -
3. d
• Compare x (N) with x (N).
C/ .Cj
If x (N) is greater than x (N), set x (N) = x (N).
c E m E
If x (N) is less than x fN), set x (N) = x (N).
c E m c
Enter x (N) on Computational Table G-10.
m
• Go to Activity 4.
Alternative 2
Note: the condition for use of the nomograph method is that k must be less
a -
than 10.
• Refer to Figure G-13 through G-15. Figure G-16 is provided as a key
to these figures.
• Enter Figure G-13 on the abscissa with D (N). Trace vertically to the
isopleth corresponding to L (N). Trace horizontally to read D (N)/L (N).
197
-------
o
_J
.01
Figure G-13. DO Nomograph-Part I
198
-------
I I I I I 1 I I I 1
.1 -
.01
...].
Figure G-14. DO Nomograph—Part 2
199
-------
2.0
In 4>[l-D,,/L0 (-1)
Figure G-15. DO Nomographs-Part 3
200
-------
D0/L0 D0/L0
Figure G-16. Nomograph Key
201
-------
• Compute
= k (N)/k
Enter Figure G-14 on the ordinate with D /L . Trace horizontally to
the isopleth corresponding to^(N). Trace vertically downward to
abscissa to read
A (N) = In0[l - 0 (0- 1)]
Lo
Compute
U/k - U(N)* [16.36]
• Enter Figure G-15 on the abscissa with A (N). Trace vertically down-
ward to the isopleth corresponding to U/k . Trace horizontally to
13,
read x (N) on the ordinate.
c
• Compare x (N) with x (N)
c e
If x (N) is greater than x (N), set x (N)=x (N)
c Cj m. -tv
tfx (N) is less than x (N), set x (N)=x (N)
c E m c
• Enter x (N) on Computational Table G-10.
m
• Go to Activity 4).
TASK 4 A, ACTIVITY 4 — COMPUTE D (N)
m
Objective
Compute the magnitude of the maximum expected DO deficit for the N segment
[D <»].
202
-------
Output
• D (N) in mg/1.
m
Inputs
• Computation Table G-8 - U(N), k (N), k (N).
Q 3.
• Computation Table G-10 LQ(N). D0(N)> xm(N)'
Discussion
To compute D , we must evaluate the equation.-
m
(-k x /U -k x /U \ -k x
dm am I ^ a r
/+ D0e
k_ | **. .Tk. / W 1*. -TX / ^ m — JLV .<-*./ U
= do a m I ~ a m
m :—:—
k -k
a d
The following procedure is a step-by-step order of computation.
Procedure
k (N) x (N)
• Compute A (N) = — —
P 1 U(N) (16.36)
-A (N)
t Compute B (N) = e 1 using exponential tables in a math handbook.
k (N) x (N)
• Compute A (N) = — m
U(N)*(16. 36)
• Compute B (N) = e 2 using exponential tables
£
• Compute
D (N) = d 0 /B (N) - B (N)\ + D (N) *B (N)
m k (N) - k (N) I 2 I ° 1
3, d ^ /
203
-------
• Enter D (N) on Computation Table G-10.
• Go to Activity 5.
TASK 4A, ACTIVITY 5 - DETERMINE C (N)
m '
Objective
Compute the minimum expected oxygen concentration for the N segment
iCm(N)] .
Output
C (N) in mg/1.
m
Inputs
• Task 2, Activity 4 — D., .
bk
• Computation Table G-8 — C (N).
sat
• Computation Table G-10 — D (N).
m
Procedure
• Compute for segment N
Enter C (N) and D, , (N) on Computation Table G-10.
m bk
Go to Activity 6.
TASK 4A, ACTIVITY 6 - COMPUTE D^(N).
E
Objective
Compute the DO deficit at the end of the N segment [ D (N) ]
Output
D (N), DO deficit at end of segment in mgA.
E
204
-------
• Computation Table G-8 — U(N), kJN), k (N).
a a
* Computation Table G-10 ~ L (N), D (N), x (N).
0 0 E
Procedure
a K x (Nv - * (N), then set D ,(N)-^D (N) and go to Step 7. Otherwise,
-I i i. -s-j> jj HI
proceec to Step 2,
• Compu te
U(N) * (16.36)
• Compute
B'^N) =exp[-A'1(N)]
• Compute
A- (N, = VUV'L
U(N) * (16.36)
* Compute
B' (N) =exp[-A« (N)]
Zi £
• Save the value of B1 (N) for the next Activity.
• Compute
D
k ,(N)L (N)
,
E
k (N) -k (N)
a d
B'2(N) -B'^N)
• Enter D (N) on Computation Table G-10.
lii
• Go to Activity I.
TASK 4A, ACTIVITY 7 - COMPUTE L
E
Objective
.th
DQ(N)*BI1(N).
Compute the BOD load at the downstream end of the N segment [L (N)]
E
205
-------
Output
• L (N) in mg/1.
Inputs
• Computation Table G-8 — U(N), k (N).
a
• Computation Table G-10 — L (N), x (N).
0 E
• Task 4 A, Activity 6 — B' (N).
Discussion
To compute L , we must evaluate the equation
Hi
LE(N) = LQ(N) exp [-kd(N)xE(N)/U(N)] = LQ(N)*B'2(N)
Procedure
« Compute L (N) = L (N)*B»(N).
E 0 i
• Enter L (N) in Computational Table G-10.
E
• If end of last segment reached, go to Task 4, start, if not, increment N
by one and go to Task 4 A, Activity 1.
TASK 4B, ACTIVITY 1 — COMPUTE C (I, N) FOR EACH SEGMENT
m
Objective
Compute the maximum concentration of the no n- conservative parameter in the
th
N segment [C (I, N)].
m
Output
• C (I, N) in units appropriate to standards.
m
Inputs
• Task 2, Activity 4 - C (I)
bk
206
-------
• Computation Table G-9 - Q (N), Q(N-l), C (N).
g g
• Computation Table G-10 - C_(N-1)
Discussion
The maximum concentration of a non-conservative parameter occurs at the
effluent group point of discharge (i.e. , x (I, N) = 0).
m
Procedure
• Compute using data from Table 3
C (I,N-1)*Q(N-1) +C (N)*Q (N)
C0(I)M) = Q(N-1)+Q (N)
at the most upstream discharge of any tributary assume C (I, N-l) = 0.
E
• Add the background parameter concentration C (I, N).
m 0 bk
« Enter C (I, N) and C , (I, N) in the computational table (e. g. Table G-10).
m bk
• Go to Activity 2.
TASK 4B, ACTIVITY 2 - COMPUTE C (I, N) FOR EACH SEGMENT
E
Obi ective
Compute the concentration of non-conservative parameter at the end of the N
segment [(C (I,N)] .
XL
Output
• C (I, N)
E
Inputs
• Computation Table G-9 - U(N), k (I,N).
• Computation Table G-10 - C (I, N), x (N).
m E
207
-------
Procedure
k (I,N)*x (N)
• Compute A' (I, N) =
2,
• Compute
-A1 n N1!
C'E(I,N) = Co(I,N)*e 2U }
• Allowing the probability that
Q(N)^Q(N-1) +Q
g
due to small flow additions within segment N,
C< (I,N)*[Q(N-1) 4- Q (N)]
C(I,N) = — S
Ex Q(N)
• Enter C (I, N) in computation table (e.g., Table G-10)
E
• If C has been computed for all parameters, go to Task 5; if not, go to
E
Task 4 Start.
TASK 4C, ACTIVITY 1 - COMPUTE C FOR EACH SEGMENT
m
Objective
Compute the maximum concentration of the conservative parameter in the N
segment [C (I, N)] .
m
Output
C (I. N) in units appropriate to standards.
m
Inputs
• Task 2, Activity 4 - C (I)
bk
• Computation Table G-9 — Q (N), Q(N-l), C (N).
g g
• Computation Table G-10 — C (I, N-l)
E
208
-------
Procedure
Compute using data from Table 3
C (I,N-1)*Q(N-1) + C (N)*Q (N)
_ ,,
'
' ~ Q(N-1)+Q (N)
o
at the most upstream discharge of any tributary assume C (I,N) = 0.
ili
• Add the background parameter concentration, C (I, N)
DlC
C (I,N) = C (I,N) +C (I,N)
m 0 bk
• Enter C (I,N) and C (I) on the computational table (e.g. , Table G-10).
in DK
• Goto Activity 2.
TASK 4C, ACTIVITY 2 - COMPUTE C (I, N) FOR EACH SEGMENT
Jii
Objective
Compute the concentration of conservative parameter at the end of the N
segment C (I, N) .
E
Output
CE(I,N).
Inputs
• Computation Table G-9 — Q(N), Q(N-l), Q (N).
g
• Task 4C, Activity 1 — C (I, N).
Procedure
• Allowing the probability that
Q(N) 4 Q(N-l) 4Q
o
due to small flow additions within segment N,
C (I,N)*|Q(N-1) +Q (
r /T Nv _ _0 L g
CE(I>N)- Q(N)
209
-------
• Enter C (I,N) in computational table (e.g. , Table G-10).
E
• If C has been computed for all parameters, go to Task 5; if not, go to
E
Task 4, Start.
210
-------
TASK 5
DETERMINATION OF SEGMENT PRIORITY RATINGS
The ultimate priority ratings of a segment (N) are functions of the maximum
parameter degradations, standard deviations, and inter-s>egment correlations
for each parameter (I). In this task these factors are found and combined in
the direct computation of the ultimate priority ratings. The logical flow of
this task is given below in Figure G-17.
( START \
IDENTIFY
-------
TASK 5, ACTIVITY 1— IDENTIFY cr(I,N)
Objective
For each design parameter (I) and segment (N) find the parameter standard
deviation [o-(I,N)],
Output
Input
• Task 1, Activity 2— STORET Data.
Procedure
• Obtain a STORET Statistical Summary Retrieval:
1) for all stations of the basin subset
2) for the design parameters
3) retrieval by fixed date interval over the system duration.
NOTE: It is best to retrieve ovef the system duration (a particular
season), but for several different years.
The parameter standard deviations for each parameter are printed on thie
retrieval.
• Locate the nearest STORET station to segment N which has at least 2
parameter measurements, over the system duration, of parameter (l!r
• Enter this station's
-------
Inputs
• Task 1, Activity 1— Standards Thresholds
• Computation Table G-10 - C (I,N), cr(I,N).
Procedure
• Find the difference between expected concentration and the threshold
concentration:
1) For the case of dissolved oxygen, compute
G(I,N)=CT(I,N)-Cm(I,N).
NOTE: When this value increases, the degradation of the stream
increases.
2) In the not to exceed the threshold parameters, compute
G(I,N)= Cm(I,N)- CT(I,N)
NOTE: Again the value increases with increasing degradation.
. Compute P(I,N)=
• Enter P(I,N) in Computation Table G-10.
• Go to Activity 3.
TASK 5, ACTIVITY 3— COMPUTE INTER-SEGMENT CORRELATIONS
Objective
For each design parameter (I) and segment (N) compute the effect of immediate
upstream segment, as measured by the Inter-Segment Correlation R(I,N).
Output
• R(I,N) dimensionless.
Inputs
Task 2, Activity 4— C (I)
bk
Computation Table G-8— k,(I,N), k (I,N), U(N), Q(N), Q (N).
da g
213
-------
Computation Table G-10—L (N-l), D_(N-1), x (N), D (N), C_(I,N),
JD E m in E
Cm(I,N).
Procedure
For the coupled BOD- DO case:
1) Take Lg(N-l) and Dg(N-l) and compute their dilution due to the
effluent source in segment N, using the equations:
LE(N"1) =
LE(N-1)*Q(N-1)
&
(N)
Q(N-l) = stream flow in segment N-l
Q (N) = effluent group flow in segment N.
g
D' (N-l) =
Hi
Q(N-1)+ Q (N)
g
2) Compute the deficit at x (N) due only to L'(N-l) and D' (N-l)
m E E
using the equations,
D
xm(N)
L'E(n-l)kd(N)
jexp [-kd(N).xm(N)/U(N)j
k (N) - k (N)
- exp f-k (N) • x (N)/U(N)1\
La m Jl
+ D' (N - 1) • exp I -k (N) • x (N)/U (N)
£-i L 8, m —'
3) Compute R(N) as
R(DO, N) =
D (N)
x v '
m
Dm(N,
214
-------
For all uncoupled parameters simply compute
CE (I, N-l)
V^-V"
• Enter R(I,N) in Computational Table G-10.
• Go to Activity 4.
TASK 5, ACTIVITY 4—COMPUTE ULTIMATE SEGMENT PRIORITY RATINGS
Objective
Compute the ultimate segment priority ratings [P*(I,N)j for a phased imple-
mentation of sampling stations, as a function of the probability of violation and
the information available from segments already being monitored.
Inputs
Ultimate segment priorities, P *(I,N).
Computation Table G-10—R(I,N), C (I,N), D (N), C (N)
m m T
Discussion
The priority of each segment must be re-computed as phased implementation
of a surveillance system takes place, or is imagined to take place.
The uncoupled case will be presented first, then a modification of the procedure
will be identified for the coupled BOD-DO case.
Procedure
• Based on the implementation (selection) of segment q as a sampling
station, perform the following:
a) Compute the cross-correlations R (I,N,q) between segment q and
segments N, for all segments N / q whose waters eventually flow in
segment q, or vice versa, using:
R(I, N).- R(I, N 4- 1) • -R(I, q-1) if N< q
R(I,N,q)=R(I,q).R(I,q-l). -R(I, N-l) if N> q
1 if N = q.
215
-------
If the waters from segment q never flow with segment N, or vice
versa, then R(I,N,q) = 0.
b) Compute
C*(I,N) = Cm(I,N) [l-R(I,N,q)J .
c) Compute the ultimate priority ratings for all segments N:
C (I,
P * (I, N) =
,- ,
* =
where the subscript on Panel C* and a* denotes the number of stations
already implemented (selected).
• Based on the selection of segment r as the second stations to be imple-
mented, perform the following:
a) Compute the cross-correlations R(I,N,r) between segment r and
all other segments, using the above definition of R(I, N, g).
b) Compute:
c) Compute:
C*(I,N) = C*, (I,
C* (I, N) - C (I, N)
P * (I, N) - _S * .
2 o- (I, N)
Assuming the nth implementation takes place on segment s, for all
segments N which have not yet been selected for monitoring, perform the
following computations for all values of n of interest:
a) Compute:
C*(I,N) = C* (I, N) [l-R(I, N, s)J
n n-1
* (I, N)
For the BOD-DO case, for the nth implementation in segment s, n- 1, 2
. . . . for all segments N which have not yet been selected for monitoring,
perform the following:
a) Compute:
R(I,Ns)
b) Compute:
D*(N)= D* ,
n n-1
216
-------
C (DO.N) ~C (DO,N)
C * (DO, N)--=— —'
n (DO,N)
c) Compute:
C (DO.N)- C* (1)0, N)
P * (DO, N)= —- 2
n ' (DO,N)
• Enter P* (I,N) in Computation Table G--1i»,
• Go to Task 6.
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TASK 6
DETERMINATION OF TEMPORAL PRIORITY RATINGS
The actual temporal rating is performed on all segments which are implemented.
The ratings are based on two basic sampling objectives—prevention and abate-
ment. All segments in which the probability of violation is very close to zero
shall be rated on the basis of the prevention philosophy which is developed in
reference [1], In all segments with a finite probability of violation, the temporal
rating shall be based on the abatement philosophy which was developed in this
project.
Much of the input information needed for this procedure is developed in the
spacial rating procedure. In the Task 6 procedure a computation table,
illustrated in Table G-ll for the BOD-DO case, should be filled out sequentially
from left to right for each segment which is implemented. The logical flow
of this Task is illustrated for a single design parameter flow chart in Figure
G-18.
218
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c
START
1
SETUP
COMPUTATION TABLE FOR
IMPLEMENTED SEGMENTS
COMPUTE
STREAM FLOW
THRESHOLD
IDENTIFY
STREAM FLOW
STATION
3
FIND PREVENTION
PRIORITY RATING
FIND ABATEMENT
PRIORITY RATING
ALL
IMPLEMENTED SEGMENTS
TEMPORALLY
RANKED
SELECT NEXT
IMPLEMENTED SEGMENT
Figure G-18. Logic Flow for Task 6
220
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TASK 6, ACTIVITY 1— SET UP COMPUTATION FOR TEMPORAL PRIORITY
RATING
Objective
Enter information pertinent to the temporal rating procedure in the 7'ask 6
Computation Table for implemented segments.
» Task 6 Computation Table containing values of Q(I, N-l), Qg(N),
Cm(l,N), C(I,N) and C^C^N) for each implemented segment N.
(For BOD case, Cgat(N) also.)
Inputs
• Computation T able G- 8 — Q(N), Qg(N), Cgat(T).
• Computation Table G- 10 — Cm (I, N), CT(I,N), Cbk(I).
Procedure
• For each design parameter, determine which segments are to be
implemented and set up a computation table, such as Table G-.1! with a
row for each segment. (Table G-ll, for BOD-DO, is used here as the
prototype. )
• In the segment row, N, fill in the information from Tables G-B and G-10
Cm(I,N), G(N-l), Qg(N), Cgat(N), CT(I,N), Cbk(I,N), corresponding to
parameter I.
• Go to Activity 2.
TASK 6, ACTIVITY 2 — COMPUTE Qt FOR EACH SEGMENT
Objective
Compute the stream flow threshold values
Outgut
• Qt(T,N) in ft3 /sec,
Computation Table G-ll--Cm(I,N), Q(N), Qg(N), CT(I,N), Cbk(I,N),
Csat(N).
221
-------
Procedure
• Compute Qf.(I, N) for design parameter I:
C (I, N)* [Q(N-l) +Q (N)l
Q(L, N) = ~ 1 _!—J _ Q (N)
t' Ct(I, N) Cbk(I, N) ^gUN)
For DO compute:
JQ(N-l) + Qg(N)J
Qt(DO, N) CDO, N) - C (DO, N) - C (DO, N) " Qg (N)
• Convert Qt(I,N) from I/sec to ft3 /sec using Table G-l.
• Enter Qt(I,N) in Computation Table G-ll.
• Go to Activity 3.
TASK 6, ACTIVITY 3 — IDENTIFY STREAM FLOW DATA STATION WITH
EACH SEGMENT
Objective
Identify the USGS stream gauging station associated with each segment.
Output
• USGS Station Identification and Q(N).
Inputs
• Task 1, Activity 4 — situation map with gauging stations and river miles
• Computation Table G-8 — Q(N)
• Computation Table G-10 — x^I, N).
Procedure
• Identify the stream flow stations nearest to xm (I,N) of each segment N.
• Associate the stream flow station which has the average (over the system
duration) stream flow closest to that of the segment N, (Q(N)).
• Find the difference in average stream flow between the specified
segment (N), and the gauging station and call it AQ(N).
222
-------
• Enter the stream flow station and AQ(N) in Computation Table G-ll.
• Go to Activity 4.
TASK 6, ACTIVITY 4—'COMPUTE TQ AND T^ FOR EACH SEGMENT
Objective
Compute the average number of consecutive days TQ(!,N) the stream flow
is above Qt(I, N), and the average number of consecutive days |T^(I,N) the
flow is below Qt(I, N). *- -*
Outpjut.
• T0(I,N), T1(I,N) in days.
Inputs
• Task 1, Activity 2— Geological Survey 'Water Resources Data"
• Computation Table G-ll — Qt, AQ.
Procedure
• Extract USGS daily stream flow data for several years over the system
duration on the station identified in Task 6, Activity 3.
« Compute the average number of consecutive days T0(I,N) the stream
flow, from the previous step, is above Q^ + AQ.
• Compute the average number of consecutive days T..(I,N) the stream
flow is below Qt+ AQ.
• Enter TQ(I,N), T^N) in Computation Table G-ll.
• If there are no crossings below Q, + AQ, then go to Activity 5.
• If there are crossings below Q- + AQ, then go to Activity 6.
TASK 6, ACTIVITY 5—FIND TEMPORAL PRIORITY RATINGS BASED ON
PREVENTION OBJECTIVES
Objective
Determine the priority rating of sampling frequencies in segments with very
low probability of violation (based on prevention, rather than abatement
objectives).
223
-------
* Effectiveness ratings of sampling frequencies.
Tnprtj-;
e Computation Table G- 10 —
-------
Effectiveness
L-10% C(l, N)
-r 20%
±;nr?.
± 50f;{
± 60%
±70%
±909?
i 100%
Number of samples
per year, i,
'2'.i
1
4
2
1
1
j
i
• If, for each parameter, the effectiveness rating has been found for ail
implemented segments, end the procedure; if not, go back to Task 6,
Activity 2.
TASK 6, ACTIVITY 6 —FIND TEMPORAL PRIORITY RATINGS BASED ON
ABATEMENT OBJECTIVES
Objectives
Determine the priority rating of sampling frequencies in segments with finite
probability of violation (based on abatement objectives).
Effectiveness ratings of given sampling frequencies, or sampling
frequencies for given effectiveness ratings.
• Computation Table G-ll —TO, T-^nd either M or A.
Procedure
• Using Figure G-19 find the effectiveness M, as a function of T,, TQ and
the sampling period, A(which is I/frequency). (This figure may also be
used for the inverse case: find the sampling period (frequency) for a
given effectiveness rating.
• Enter M in Computation Table G-ll.
• If, for each parameter, the effectiveness rating had been found for all
implemented segments, end the procedure; if not, go back to Task 6,
Activity 2,
225
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226
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A rt'f-sMon Number
w
~ Subject Field & Group
06A 07A 07C
06B 07B
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Raytheon Company
Environmental Systems Center
Portsmouth, Rhode Island 02871
Tillf
QUANTITATIVE METHODS FOR PRELIMINARY DESIGN OF WATER QUALITY
SURVEILLANCE SYSTEMS
10
Authors)
Beckers, Charles V.
Chamberlain (Ph.D.),
Stanley G.
Grimsrud, G. Paul
_22j
l z Project Designation
EPA Project No. 16090 HOJ
21
\Note
EPA Contract No. 68-01-0144
May 1972
Citation
Environmental Protection Agency report
number EPA-R5-72-001, November 1972.
23
Descriptors (Starred First)
*Network Design,
^Monitoring, *Mathematical Models, *Systems Analysis,
*Data Collection, Water Quality, Markov Processes, River Basins, Pollution
Abatement, Standards, Ohio, Indiana, Water Pollution, Water Measurement,
Water Quality Control, Time Series Analysis, Water Quality Act, Analytical
Techniques
OC l-tent/fierl, (Starred First)
i *Monitoring Network Design, *Wabash River Basin, *Wabash River,
*Wildcat Creek, Surveillance, Ohio River Basin, Space Time Sampling,
Priority Measures
_?ZJ JS
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