EPA-600/5-76-012
December 1976
Socioeconomie Environmental Studies Series
HANDBOOK FOR THE ALLOCATION OF
COMPLIANCE MONITORING RESOURCES
Office of Air, Land, and Water Use
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1 Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6 Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the SOCIOECONOMIC ENVIRONMENTAL
STUDIES series. This series includes research on environmental management,
economic analysis, ecological impacts, comprehensive planning and fore-
casting, and analysis methodologies Included are tools for determining varying
impacts of alternative policies; analyses of environmental planning techniques
at the regional, state, and local levels; and approaches to measuring environ-
mental quality perceptions, as well as analysis of ecological and economic im-
pacts of environmental protection measures. Such topics as urban form, industrial
mix, growth policies, control, and organizational structure are discussed in terms
of optimal environmental performance. These interdisciplinary studies and sys-
tems analyses are presented in forms varying from quantitative relational analyses
to management and policy-oriented reports.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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fY OF EPA-600/5-76-012
December 1976
USER HANDBOCK FOR THE ALLOCATION OF COMPLIANCE
MOOT TOPING RESOURCES
by
G. Paul Grimsrud
E. John Finnemore
Wendy J. Winkler
Ronnie N. Patton
Arthur I . Cohen
Systems Control, Inc.
Palo Alto, California 94304
Contract No. 68-01-2232
Project Officer
Donald H. Lewis
Environmental Research Laboratory
Corvallis, Oregon 97330
OFFICE OF AIR, LAND, AND WATER USE
OFFI CE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, DC 20460
EPA-RTF LIBRARY
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DISCLAIMER
This report has been reviewed by the Office of Air, Land and Water Use,
U.S. Environmental Protection 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.
ii
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FOREWORD
A successful water quality management program requires not only
thorough problem definition and prudent implementation of effective
control methods, but also adequate monitoring and strict enforcement
of the ambient and effluent quality standards upon which the program
is based. The acquisition and analysis of adequate data for detection
and enforcement of standards violations is a complex and costly process,
and can be ineffective and inefficient unless due consideration is
given to the statistics and economics of the system, and the monitoring
program is designed and operated accordingly.
This report is the eighth in a series within the Environmental
Management Research Program which addresses the management aspects of
the design and operation of water quality monitoring and information
management programs at the state or regional level, and develops
user-oriented handbooks to assist personnel in program design and
management. The other seven reports are available from GPO or NTIS,
and are listed below:
"Design of Water Quality Surveilance Systems," 16090DBJ08/70,
August 1970
"Quantitative Methods for Preliminary Design of Water Quality
Surveilance Systems," EPA-R5-72-001, November 1972
"Data Acquisition Systems in Water Quality Management,"
EPA-R5-73-014, May 1973
"Michigan Water Resources Enforcement and Information System,"
EPA-R5-73-020, July 1973
"Design of Cost-Effective Water Quality Surveilance Systems,"
EPA-600/5-74-004, Janauary 1974
"Demonstration of a State Water Quality Management System,"
EPA-600/5-74-022, August 1974
"Quantitative Method for Effluent Monitoring Resource Allocation,"
EPA-600/5-75-015, August 1975
Thomas A. Murphy
Deputy Assistant Administrator
for Air Land and Water Use
ill
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ABSTRACT
This report is designed as a handbook specifically oriented to
environmental planners and managers. It presents the development and
successful demonstration of hand and computerized procedures for the
design of effluent compliance monitoring systems. The procedures may
help planners allocate compliance monitoring budgetary resources so as
to minimize environmental damage. The original technical development
of these procedures is given in a companion report, "Quantitative
Methods for Effluent Compliance Monitoring Resources Allocation,"
EPA-600/5-75-015. Both the computerized and hand calculation
procedures are demonstrated to function satisfactorily using data
supplied by the State of Michigan.
This report is submitted in fulfillment of Contract Kumber
68-01-2232, by Systems Control, Inc., under sponsorship of the Office
of Research and Development, Environmental Protection Agency.
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TABLE OF CONTENTS
Section Page
1. INTRODUCTION 1
2. DESCRIPTION OF COMPLIANCE MONITORING DESIGN PROCEDURES. 3
2.1 REVIEW OF GOVERNING LAWS AND REGULATIONS 3
2.2 COMPLIANCE MONITORING PROCEDURES 11
2.3 OVERVIEW OF RESOURCE ALLOCATION PROCEDURES .... 13
2.4 RESOURCE ALLOCATION CRITERIA 16
2.5 STATISTICAL CHARACTERISTICS OF EFFLUENT STREAMS. . 21
2.6 RESOURCE ALLOCATION PROBLEM 29
2.7 SIMPLIFIED EXAMPLE 34
3. GENERAL REQUIREMENTS FOR MANPOWER, DATA, AND COMPUTERS. 45
3.1 INPUT DATA REQUIREMENTS AND PROCEDURES 45
3.2 COMPUTER AND MANPOWER REQUIREMENTS 54
4. USER MANUAL FOR HAND CALCULATION APPROACH 58
4.1 INTRODUCTION 58
4.2 STEP-BY-STEP PROCEDURE 65
5. USER MANUAL FOR COMPUTER CALCULATION 145
5.1 MODE OF OPERATION 145
5.2 INPUT DESCRIPTION 150
5.3 SAMPLE INPUT DECK 176
5.4 OUTPUT DESCRIPTION 176
6. DEMONSTRATION OF PROCEDURES 197
6.1 DEMONSTRATION OF HAND CALCULATION PROCEDURES -
INITIAL ALLOCATION 198
6.2 UPDATE PROCEDURE 212
6.3 ALTERNATE DETERMINATION OF VIOLATION WEIGHTING
FACTOR 218
6.4 COMPARISON OF THE HAND CALCULATION AND COMPUT-
ERIZED RESULTS 221
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TABLE OF CONTENTS — Continued
Section Page
7 COMPUTER PROGRAM DOCUMENTATION 229
7.1 INTRODUCTION 229
7.2 PROGRAM DESCRIPTION 231
7.3 DESCRIPTION OF VARIABLES 252
REFERENCES 309
LIST OF SYMBOLS (For Section 4) 313
VI
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TABLES
Table
2.1 Constituents Recommended for Limitation by Industrial
Category 5
2.2 Recommended Minimum Sampling and Analysis Frequency
for Process Effluent 9
2.3 Municipal Wastewater Treatment Facilities Minimum
Sampling Frequency 10
2.4 Damage Functions 18
2.5a Self Monitoring Data for Source 1 35
2.5b Self Monitoring Data for Source 2 35
2.5c Self Monitoring Data for Source 3 35
2.5d Self Monitoring Data for Source 4, Pipe 1 36
2.5e Self Monitoring Data for Source 4, Pipe 2 36
2.6a Initial Statistics for Source 1 37
2.6b Initial Statistics for Source 2 37
2.6c Initial Statistics for Source 3 37
2.6d Initial Statistics for Source 4, Pipe 1 38
2.6e Initial Statistics for Source 4, Pipe 2 38
2.7 Expected Damage and Probability of Violation 40
2.8 Resources Needed to Sample 41
2.9 Priority List of Samples for Simplified Example .... 42
2.10 Final Allocation Given Monetary Budget 44
2.11 Final Allocation Given Maximum Allowed Cost of Un-
detected Violations 44
Vll
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TABLES — Continued
Table
3.1 Summary of Input Data Types 46
4.1 Statistical Distribution Types of Constituent
and Source 68
4.2 Effluent Standards 71
4.3 Conversion Factors 72
4.4 Data and Standards Conversion 73
4.5 Effluent Data, Statistics, and Probabilities 79
4.6 Compliance Monitoring Input Data 90
4.7 The Standard Normal Cumulative Distribution
Function, (x) 104
4.8 Ranges of Sampling Rates and Expected Extents of
Undetected Violations 108
4.9 Record of Task 10 Options and Calculations 119
4.10 Examples of Alternative Type of Weighting Factor
Functions (WFF) 120
4.11 The Standard Normal Probability Density Function, f(x) 121
4.12 Resources Needed to Monitor Each Source Once 127
4.13 Marginal Returns for Each Source 131
4.14 Sampling Priority List 135
4.15 Sampling Rates 143
5.1 EFFMON Inputs 151
5.2 pH/pOH Damage Function Breakpoints 171
5.3 Non-pH Damage Functions 172
VI11
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TABLES — Continued
Table Page
5.4 Constituent Identification Numbers and Input Units. . . 173
5.5 Input Units 174
5.6 Sample Input Data 177
6.1 Statistical Distribution Types by Constituent and
Source 199
6.2 Effluent Standards 200
6.3 Source Number 9: Raw Data 202
6.4 Data and Standards Conversion 203
6.5 Effluent Data, Statistics, and Probabilities 204
6.6 Worksheet for Task 8 206
6.7 Worksheet for Task 10 207
6.8 Record of Task 10 Options and Calculations - K = — . . 208
6.9 Ranges of Sampling Rates and Expected Extents of
Undetected Violation 209
6.10 Resources Needed to Monitor Each Source Once 211
6.11 Marginal Returns for Each Source 213
6.12 Sampling Priority List 214
6.13 Sampling Rates 215
6.14 Effluent Data, Statistics, Probabilities 217
6.15 Record of Task 10 Options and Calculations 219
6.16 Ranges of Sampling Rates and Expected Extents of Un-
detected Violations 220
6.17 Resources Needed to Monitor Each Source Once 220
IX
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TABLES — Continued
Table
6.18 Marginal Returns for Each Source 223
6.19 Sampling Priority List Using Hand Calculation
Procedure 224
6.20 Sampling Rates Using Hand Calculation Procedures. . . . 225
6.21 Priority List of Samples Using Computer Calculation
Procedure 226
6.22 Final Allocation Using Computer Calculation Procedure . 228
7.1 Description of Common Variables 253
7.2 Description of Local Variables 258
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ILLUSTRATIONS
Figure
2.1 Major Monitoring Activities 6
2.2 Flow of Resource Allocation Procedure 14
2.3 Example Damage Function 19
2.4 Initial Statistical Description Procedure 25
3.1 as a Function of Depth 50
3.2 Dissolved Oxygen Response as a Function of Water Body
Type and 51
3.3 Dissolved Oxygen Saturation Versus Temperature and
Chlorides 53
4.1 Example of Monitoring Sequence 60
4.2 Interrelationships of Comprising Tasks 63
4.3 Variation of Scaling Factor, G, with Sample Size for
Normal Distributions 85
4.4 Standard Deviation Estimated From the Mean and Maximum
of Lognormal Distributions, for Various Sample Sizes, n. 86
4.5 Variation of the Confidence Parameter for Standard
Deviation with Sample Size 87
5.1 Organization of Input Deck 170
5.2 Organized Print of Inputs 179
5.3 Organized Print of Inputs 180
5.4 Printout of Initial Resource Allocation 137
5.5 Printout of Sample Priorities 188
5.6 Printout of Sample Priorities Beyond Minimum Allocation. 139
XI
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ILLUSTRATIONS ~ Continued
Figure Page
5.7 Printout of Final Allocation Based on Budget Limit. . . . 190
5.8 Printout of Final Allocation Based on Maximum Acceptable
"Cost of Undetected Violations" 191
5.9 Print of Source Statistical Summaries 193
7.1 General Program Flow Diagram for EFFMON 232
7.2 Main Program 233
7.3 Function COMEXD 237
7.4 Subroutine DAMAGO 238
7.5 Subroutine EXPDAM 239
7.6 Subroutine ISTAT 240
7.7 Subroutine PARAMS 242
7.8 Function PHEXD 243
7.9 Subroutine PNVCOM 244
7.10 Subroutine PRIORT 245
Xll
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SECTION 1
INTRODUCTION
In response to increasing public awareness and concern for the
quality of the environment, government agencies at all levels are taking
steps to protect and enhance the quality of the nation's waters. Control
of wastewaters is essential to the success of this initiative toward
environmental quality. The Federal Water Pollution Control Act Amendments
of 1972 require the establishment of wastewater (effluent) limitations
for all joint sources by July 1, 1977. The Environmental Protection Agency,
or designated state agency, is required to establish monitoring programs
to ensure that the effluent sources are in compliance with the standards.
According to the Federal monitoring guidelines, there are three
ways the monitoring agency must obtain information concerning the com-
pliance of dischargers:
1. Self-Monitoring. The effluent dischargers are required to
sample their own effluent levels and periodically transmit
records of these samples to the monitoring agency.
2. Compliance Monitoring. The monitoring agency visits the
effluent dischargers to ensure that the self-monitoring is
being properly executed and reported.
3. Ambient Monitoring. The water quality of the receiving waters
monitored by state and/or local agencies.
The self-monitoring reports are the principal source of compliance in-
formation used by monitoring agencies since the agency expense to acquire
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these data is minimal. Some check is, however, needed on the reliability
of self-monitoring data. The compliance monitoring program is set up to
provide that check. The compliance program also has other purposes
associated with the permit program, such as verifying that the plant pro-
cesses described in the permit are correct, evaluating new waste removal
equipment, reviewing progress toward scheduled pollution control activities,
and monitoring to aid in preparing enforcement actions. The ambient
monitoring is primarily used to determine water quality, discern trends
in water quality, and evaluate the overall effectiveness of pollution
control in a region. Under certain conditions, however, ambient monitoring
may flag effluent irregularities unmeasured by other means. Through know-
ledge of the effluent sources that could contribute to the decline in
ambient quality, action can be initiated against possible violators.
This handbook is directed toward responsible monitoring agencies
on the local, state and Federal levels, and specifically to the design
of compliance monitoring programs. It is intended to extend the Resource
Allocation Procedure of a previous Research and Development report
[1] to include hand calculation procedures, and user oriented documentation.
The handbook provides simple and concise procedures for the preliminary
design of effluent compliance monitoring programs. It includes the option
of using hand calculation or computer calculation techniques. It is in-
tended to assist officials in developing efficient and effective compliance
monitoring programs using a relatively simple, yet meaningful approach.
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SECTION 2
DESCRIPTION OF COMPLIANCE MONITORING DESIGN PROCEDURE
This section presents a technical overview of the monitoring
Resource Allocation Procedure, and how it relates to the governing laws
and regulations.
2.1 REVIEW OF GOVERNING LAWS AND REGULATIONS
The Federal Water Pollution Control Act Amendments of 1972 shift
the emphasis of the law from water quality standards to effluent limitations,
These effluent limitations are asserted through the National Pollutant
Discharge Elimination System (NPDES) permits. The Federal Environmental
Protection Agency (EPA) or state agency designated by the EPA regional
administrator must issue NPDES permits to all dischargers based upon cer-
tain criteria outlined as follows.
The basic limitations are based upon known effluent control tech-
nology. Permits for 28 industrial categories [2] are set according to the
Best Practicable Control Technology Currently Available (by 1977), and
Best Available Technology Economically Achievable (by 1983). Municipal
sewage discharge permits are set according to the basic Secondary Levels
of Treatment (by 1977), and Best Practicable Waste Treatment Technology
*
(by 1983). However, in Water Quality Limited Segments the permits must
be based upon the level of additional treatment needed to assure maintenance
of acceptable water quality. It is the responsibility of the state or
regional administrators to set the permit levels in these areas based upon
*
Areas of receiving waters where acceptable water quality levels are not
always reached when the effluents of that area are held to the basic
limitations.
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studies such as those under Sections 303e and 208 of the Water Quality Act
[3]. Once the permits are specified, it is the responsibility of each
discharger to maintain their effluents within permit levels.
The Federal government has set out guidelines to officials issuing
NPDES permits in the form of Effluent Limitations Guidelines [2,4-20],
The important aspects of these guidelines are listed below.
1. Only constituents of major significance should be limited
and monitored. The full list of constituents recommended
for effluent limitations in the 28 industrial categories
is given in Table 2.1.
2. Limitations should be in terms of "production days," i.e.,
loads throughout a day.
3. Each permit should contain limitations on (monthly) average
and daily maximum.
4. Permits should be based upon gross loads, unless the discharger
has a strong argument to use limitations on net loads (i.e.,
outlet load minus the intake load). Where possible, the permits
should be in units of kilograms per day.
The enforcement of these NPDES requirements requires certain
specified monitoring procedures, as outlined in the next subsection.
Monitoring Guidelines
The Federal Water Pollution Control Act Amendments of 1972 and the
accompanying regulations and guidelines specify a comprehens'ive set of
monitoring programs for enforcement of the law. The major monitoring
efforts to be required are shown in Figure 2.1.
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Table 2.1 Constituents Recommended for Limitation by Industrial Category
INDUSTRY
2 BUILDFRS PAPHR AND BOARD
3. TIMBER PRODUCTS
4 SOAP .Via DETERGENTS
5 DAIRY PRODUCTS
6 ORGANIC CHEMICALS
7 PETROLEKI REFINING
8 LEATHER TAXNTSG i FISHING
o CANNED AN'J PSFSl'KVED
FRCITS ASD viCTABLEs
10 NONFERP.OUS HITALS
11 GRAIN HILLS
12 SUCAR PROCESSING
13 FERTILIZERS
14 ASDESTOS
IS MEAT PRODUCTS
16 FERROALLOYS
1 7 CLASS
18 ELECTROPLATING
19 PHOSPHATE MANUFACTURING
20 FEEDLOTS
21 CF.NENT MANUFACTURING
22 RUSHER PROCESSING
23 PI.ASTICS A[.U SYNTHETICS
24 INORGANIC CHEMICALS
25 UOH AND STEEL
26 TEXTILES
j; STEAM EI.F.CfSlC GENERATING
EQU 1 PMFJIT
28 SEAFOOD PROCESSING
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From References [2,4-20]
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DISCHARGER
SELF-MONITORING
STATE AND
FEDERAL
ENFORCEMENT
STATE MONITORING
REQUIREMENTS
(PL92-500, Section 106)
PRIMARY
AMBIENT WATER
QUALITY MONITORING
COMPLIANCE
MONITORING
GROUNDWATER
Figure 2.1
Major Monitoring Activities
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The effluent discharger under an NPDES permit must monitor his
effluent (self-monitor) at some minimum sampling frequency, maintain
records of sample results, and periodically transmit these records to the
state. In addition, state officials must have the authority to enter the
premises of a permittee at any reasonable time to inspect records and
instrumentation and to sample effluents, both to verify the quality of
self-monitoring reports and to check for compliance with permit conditions.
The States have a number of monitoring responsibilities (shown in
Figure 2.1) in order to be eligible for Federal wastewater control program
grants. These responsibilities are described in regulations developed
under Section 106e(l) of PL 92-500 [3]. In summary, these regulations re-
quire that monitoring systems include the following components:
• Compliance Monitoring to validate self-monitoring reports and
support enforcement actions. This monitoring must include
scheduled and random quality control inspection of permittees'
monitoring reports and equipment to establish the credibility
of self-monitoring reports, follow-up inspections Xv>hen there
is evidence of an effluent standard violation, and ad hoc in-
tensive surveys when there is evidence of a water quality
violation.
• Intensive surveys (scheduled in advance on a periodic basis)
conducted "before and after implementing pollution controls
in areas of significant pollution sources, clustered pollution
sources, localized nonpoint sources of pollution, and in major
bodies of water which are known or suspected to be accumulating
pollutants." These surveys may include monitoring of both
ambient and effluent levels.
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• Primary ambient monitoring designed to give the long-term
coverage necessary to describe trends in water quality and
to establish a macroscopic view of the effectiveness of
pollution control actions (see Section 305b, PL 92-500).
• Toxic pollutant monitoring including "studies and systematic
sample collection from surface waters, groundwaters, sediments
and biological communities" to define where toxic pollutants
are entering the States' waters and to provide basis for control
actions.
• Groundwater monitoring consisting of stations designed to
"determine baseline conditions and provide early detection of
pollution."
The procedures given in this handbook are concerned with the allocation
of monitoring resources for compliance monitoring.
Self-Monitoring Requirements
The NPDES permit program guidelines [2] give detailed requirements
for self-monitoring programs. They suggest that minimum self-monitoring
frequencies be set according to the discharge flows and constituent
nature for industrial and municipal effluents as given in Tables 2.2 and
2.3. Since the effluent standards must be set in terms of daily loads,
the monitoring guidelines strongly recommend the use of composite samples.
However, if it is only feasible to take grab samples, they can be used to
represent daily composite samples.
The self-monitoring data must be reported on standard forms giving
the maximum and minimum of production day loading samples over a month,
and the monthly average of these samples. The dischargers with more than
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Table 2.2 Recommended Minimum Sampling and
Analysis Frequency for Process Effluent
Effluent
Flow Volume (MGD)
Minimum Frequency
for
Major Constituents
Minimum Frequency
for
Other Constituents
< .05
.05-1.0
1.0-10.
10. - 50.
>50.
Once per month
Once per month
Once per week
Three times per week
Daily
Semi-Annually
Quarterly
Once per Month
Once per Month
Once per Month
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Table 2.3 Municipal Wastewater Treatment Facilities
Minimum Sampling Frequency
EFFLUENT
Plant Size (mgd)
Up to 0.99
1 - 4.99
5 - 14.99
15 and greater
•j
o
tH
fK
Once each
Wkday.2
Daily
Daily
Daily
^^
tH
60
8
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B
to
-O
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O
CO
-------
one discharge pipe are given the option of reporting on each discharge
separately, or on the combined discharges. The self-monitoring data must
be transmitted to the State at least quarterly — semi-annually for very
small industries.
2.2 COMPLIANCE MONITORING PROCEDURES
This handbook is concerned with the part of the compliance monitor-
ing program that determines whether effluent sources are in compliance
with the effluent standards. Since the state monitoring agency has limited
resources available for compliance monitoring, it is important that these
resources be used in an efficient manner. The procedure developed in the
first SCI study [1], and presented in this handbook,determines how often
to monitor each source in a region to obtain maximum benefit from the
compliance monitoring program. The procedure uses information from past
self-monitoring, ambient monitoring, and compliance monitoring reports.
As discussed earlier, an effluent source is in violation (i.e., does
not comply with standards) if either the value of a daily composite measure-
ment exceeds the maximum standard, or the average of the daily composites
over the month exceeds the average standard. In order to determine whether
an effluent source is in violation of the "average" standard, it is
necessary to take measurements over a large percentage of the month, while
to determine if the "maximum" standard is violated, it is only necessary
to determine if the standard was exceeded over a single day. Since com-
pliance monitoring is costly to the monitoring agency, and since most
regions will contain many effluent sources, it is not expected, in general,
that compliance monitoring resources will be available to determine whether
the "average" standard is violated. Additionally, the chronic, long-term
pollution effects resulting from the "average" violation can usually be
sensed in both the primary monitoring network, and through a compliance
11
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monitoring scheme designed for the "maximum" standard. Therefore, the
procedure given in this handbook is limited to determining whether the
"maximum" standard is violated.
The Resource Allocation Procedure sets priorities on which effluent
sources should be monitored and how often. The procedure determines the
sampling rates so that sources that have a high probability of violating
their standard, and (optionally) sources that may cause large environmental
damage will be sampled with high priority. The objective in allocating
monitoring resources then is to minimize the "cost" of undetected violations,
or equivalently, the expected environmental damage that would result from
undetected violations. The "cost" of undetected violations for a number
of effluent sources may depend on:
1. The expected number of undetected violations;
2. The expected "environmental cost" due to undetected violations;
3. The expected magnitude of undetected violations.
Any one of these three factors can be used as the criterion for the
allocation of monitoring resources.
The first allocation criterion depends on the probability that the
various violating sources in the monitoring region will not be caught in
violation once in the monitoring period (i.e., the probability of being
an undetected violator). This quantity in turn depends on the sampling
rates and single day probability that each of the sources will violate
one of their standards. The other two criteria are also a function of the
probability of being an undetected violator; however, they all depend on
other factors. The second criterion depends on the environmental damage
that is expected to result from a standard violation, while the third
criterion depends on the degree or amount by which the standard is ex-
pected to be exceeded. These criteria are defined in more detail in
Section 2.4.
12
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All the above criteria are functions of the discharges or loadings
from effluent sources. These effluent loads, due to their inherent vari-
ability, are modeled statistically by either a normal or lognormal prob-
ability density function. Allowing for two types of density functions
results in the ability to model a wide range of effluent loadings with
sufficient accuracy to determine sampling priorities. Both the normal
and lognormal density functions can be defined by two parameters, a mean
and a standard deviation. (For the lognormal case, the mean and standard
deviation are those of the logs of the effluent values.) These parameters
are obtained for each constituent of each source from historical data, in-
cluding self-monitoring and compliance monitoring data. The procedure
used to determine the statistical characteristics of the effluents is
described in Section 2.5.
2.3 OVERVIEW OF RESOURCE ALLOCATION PROCEDURE
The basic task flow for the Resource Allocation Procedure is given
in Figure 2.2. The various major functions of the procedure are briefly
described below, and described in more detail in Sections 2.4 through
2.6.
1. Initialize Statistical Description
Combine the raw self-monitoring and compliance monitoring
data to obtain an initial statistical description (distribution,
mean and standard deviation) for each pollutant of each source.
2. Calculate Probability and "Cost" of Violation (Allocation
Criteria)
Use the statistical description of the effluent loads, the
effluent standards, and the stream parameters to obtain the
13
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INITIALIZE
STATISTICAL
DESCRIPTION
RESOURCE ALLOCATION PROCEDURE
CALCULATE "COST" AND
PROBABILITY OF VIOLA-
TION (ALLOCATION
CRITERIA)
DETERMINE
PRIORITIES
UPDATE
STATISTICS
MONITORING
SCHEDULE
MONITORING \
PERIOD y~
1
MONITORING PROGRAM
Figure 2.2 Flow of Resource Allocation Procedure
14
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"cost" and probability of violation for each source. Use the
appropriate option in this calculation as described in Section
2.4.
3. Determine Priorities
Use the method of maximum marginal return to obtain the
monitoring rates.
4. Monitoring Schedule
Take the sampling rates obtained in the previous function and
determine which date to sample which sources.
5. Monitoring Period
This box represents the actual time spent monitoring the sources.
6. Update Statistics
Combine new self-monitoring and compliance data with the initial
statistics to obtain an updated statistical description of the
effluents.
Functions 1, 2, 3, and 6 are performed by the Resource Allocation Procedure
and will be described in Sections 2.4 through 2.6. The scheduling of the
sampling (Function 4) depends on a number of factors which are difficult
to quantify in an optimization framework, such as: the spatial location
of the various effluent sources, the size of the monitoring agency's
jurisdiction, and the availability of personnel. This scheduling is left
to the individual monitoring agency. Function 5 simply denotes the
passage of time.
15
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2.4 RESOURCE ALLOCATION CRITERIA
The procedures presented in this handbook give users several
optional criteria for resource allocation, as discussed in Section 2.2.
This section discusses the mathematical definitions of these criteria.
Those readers with non-mathematical background are encouraged to skip
this section.
Number of Undetected Violators (Criterion //I)
The objective of this allocation criterion is to minimize the
number of undetected violators, which is defined as the expected number
of effluent sources which will not be caught in violation given that the
i source is sampled s. times.
Now (p.) i-is the probability that the i source will not be caught
in violation, if it is sampled s. times, where p. is the probability that
it will not be caught in violation if it is sampled once. The number of
undetected violators is then
n
S Si
1=1
where ng is the number of sources. The calculation of p . is discussed in [1],
Equation 2.1 should more accurately be called the "Number of Undetected
Sources," since the probability that each source will be a violator is not
included. The expected number of sources which will violate a standard
but not be caught in violation given that the ith source is sampled s. times
during a monitoring period of N days is 1
n
s
Pi
Since this formula differs from Equation 2.1 only by a constant, the same
sampling rates, s will minimize both functions. Therefore, the simpler
formula has been presented.
16
-------
"Cost of Undetected Violations" (Criterion #2)
The objective of this allocation criterion is to minimize the
"environmental cost" of undetected violations, which is the damage to
water quality in receiving waters due to the effluent constituents of the
effluent sources. The environmental damage due to a given effluent con-
stituent is related to the concentration of the constituent (or correspond-
ing water quality indicator) in the receiving waters through a damage func-
tion. The damage function is defined as a piecewise linear function where
a numerical value is given to each "level of damage" - the values 0, 2, 4,
6, 8 and 10 correspond to "none", "excellent", "acceptable", "slightly
polluted", "polluted", and "heavily polluted", respectively. This type of
subjective damage function closely follows the approaches used by Prati [22],
Horten [23], and McCelland [24]. Using various references [22-27], appro-
priate damage function were specified for 26 water quality indicators as
shown in Table 2.4. The user of this procedure may optionally modify the
damage functions in this table based upon his own experience and particular
needs. Figure 2.3 gives an example, in graphical form, of a damage function;
the indicator considered is suspended solids. The computation of the cost of
undetected violations using this approach is given in [1].
Magnitude of Undetected Violations (Criterion #3)
This allocation criterion serves as an alternative to the very com-
plex "Cost of Undetected Violations" criteria. It accounts for severity of
environmental damages, and yet is simple enough to be included in the hand
calculation procedures. The "Magnitude of Undetected Violations" is defined
as the severity of undetected violations (i.e., the amount by which effluent
standards are exceeded). The degree of violation, for a loading M and a
standard T, is given by equation
(0 ; M < T
DV(M,T) = " (2.2)
( ct(M--c); M > T
17
-------
Table 2.4 Damage Functions
Constituent
name
Aluminum
Ammonia
Dissolved oxygen
Inorganic carbon
Chloride
Chloroform extract
Chromium
Coliforms-total
Coliforms- fecal
Copper
Cyanide
Fluoride
Iron
Lead
Manganese
Mercury
Nickel
Inorganic nitrogen
Oil-grease
pH-MIN
pH-MAX
Phenol
Phosphates
Solids-dissolved
Solids-suspended
Temp. diff.
Tin
Zinc
Units
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
MPN/lOOml
MPN/lOOml
mg/1
mg/1
mg/1
mg/1
Pg/1
mg/1
ug/1
mg/1
mg/1
mg/1
Ug/1
mg/1
mg/1
mg/1
°C
mg/1
mg/1
Level of damage
None
0
0
0
>9
<50
0
0
0
0
0
0
0
<0.7
0
0
0
0
0
<0.6
0
7
7
0
0
<100
0
0
0
0
Excellent
2
0.01
0.1
8.0
70
25
0.04
0.02
100
20
0.02
0.01
0.8
0.1
5
0.05
1
0.01
0.9
0.01
6.5
8.0
0.5
0.1
200
20
1.0
10
0.1
Acceptable
4
0.05
0.3
6.8
90
175
0.15
0.05
2000
200
0.10
0.02
0.9
0.3
50
0.17
5
1.0
3.0
0.10
6.0
8.4
1.0
0.2
500
40
2.5
40
1
Slightly
polluted
6
0.10
0.9
4.5
110
200
0.25
1.0
7500
800
1.00
0.05
1.2
0.9
100
0.50
10
3.0
4.5
5
5.0
9.0
20
0.5
1000
100
3.0
100
5
Polluted
8
.50
2.7
1.8
130
240
0.35
10.0
15,000
3,000
5.00
0.10
3.0
2.7
250
1.00
20
9.0
7.0
30
4.0
10.0
100
1.6
1500
280
4.0
300
15
Heavily
polluted
10
1.00
3.0
0.9
150
250
0.40
50.0
150,000
50,000
10.00
0.50
8.0
3.0
350
1.50
50
20.0
10.0
50
3.9
10.1
200
10
2300
300
10.0
1000
40
Reference*
7
2
5
5
3
3
6,7
3,6
4,5
6,7
6,7
7
2
6,7
2
7
7
5
67
, 1
6*7
»'
7
CD
*The references shown are those used to develop the damage function for each constituent.
-------
101-
w
o
PM
O
w
3
0 100 200 300 400
CONCENTRATION OF SUSPENDED SOLIDS, mg/1
Figure 2.3
Example Damage Function
19
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where a is a design constant discussed in detail in Section 4, Task 10.
The expected degree of violation for the j constituent of the
.th
i source is
(2.3)
DVr = / DV(M,tr) 4>1-(M)dM =/ ^.(M-T^) ^^
O T. .
13
The expected degree of violation from all the constituents of the
i source is then
DV = Max DV.. (2.4)
J 1J
where it is assumed that the user is interested in the worst degree of
violation from the source. The derivation of the Degree of Undetected
Violation now follows exactly the derivation of the "Cost of Undetected
Violation" given in [1]. The Degree of Undetected Violation is therefore,
n
s s.
DV = l>V.p. . (2.5)
i=l 1 1
where, for the i source, DV. is the expected degree of violation, p. is
the probability the source will not be found in violation if sampled once,
and s. is the number of times the source was monitored.
Summary of Resource Allocation Criteria
In examining the three optional resource allocation criteria, it
is seen that they are all a function of the number of Undetected Violations
given in Criteria #1. In fact, they are all of the form
n
s s .
Allocation Criteria = £ (weighting factor) (p.) 1 . (2.6)
i=l L
In Criterion //I, the weighting factor is simply set to 1. In Criterion #2,
the weighting factor is set to the expected "environmental cost" of un-
20
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detected violation. In Criterion //3, the weighting factor is set to the
relative severity or magnitude of undetected violations given by Equations
2.3 and 2.4
The manual calculation procedures presented in Section 4 gives the
option of using Criteria //I and //3. The computer calculation procedure
gives the option of using Criteria #1 and //2.
2.5 STATISTICAL CHARACTERISTICS OF EFFLUENT STREAMS
All three of the allocation criteria, discussed in the previous
section, require knowledge of the probability of violation for each
effluent source. Thus, the priority setting procedure for compliance
monitoring requires that the daily composite effluent loads, due to their
inherent variability, be modeled statistically. Among the questions that
must be addressed in developing a statistical model are:
• What probability distributions adequately model the
effluent data?
• What is the statistical correlation between the various
constituents of the effluent?
• What is the time-varying nature of the statistics?
It has been shown in [1], for several example sets of data, that
the normal and lognormal distributions adequately model the statistics
of the daily composite effluent loadings. In order to decide whether to
model a particular constituent by a normal or lognormal distribution, it
is necessary to process a large amount of daily data. It is not expected
that the individual monitoring agency will have the resources to analyze
the daily data of each source in its jurisdiction. It is only postulated
that the monitoring agency will have a monthly mean and maximum for each
constituent of each source. It is, therefore, necessary to determine,
using industry-wide studies of effluent characteristics, which distribution
can be associated with a given industrial process. Since this information
is unavailable at the publication of this report, several guidelines are
specified in Section 4, Task 1, on how to choose between the normal and
lognormal cases.
21
-------
The normal and lognormal distributions are defined by a mean and a
standard deviation. (For the lognormal distribution, the mean and standard
deviation are of the logs of the data.) Since it is only assumed that the
monthly mean and maximum, and not the sample standard deviation, are
available to the monitor, the standard deviation of the normal process
must be estimated using nonstandard estimation procedures. Approximate
maximum likelihood estimates of the mean and standard deviation from the
mean and maximum were developed in [1] for both the normal and lognormal
cases. These estimates were tested on real data and it was shown that they,
coupled with the associated distributions, adequately describe the statis-
tical variations.
There has been little study into the statistical correlation of the
constituents of an effluent. As with the problem of determining the
appropriate distributions, it is not expected that the monitoring agency
would be able to determine the correlation of the constituents of the
sources in its jurisdiction. It is therefore necessary that the correlation
coefficients be obtained from industry-wide studies. Since these are un-
available at the present time, it is assumed, unless other knowledge is
available, that the constituents from a source are uncorrelated. The
priority setting procedure also allows for the case where the constituents
are completely correlated. In [1] a correlation study for a single
municipal treatment plant was carried out. It is clear that no general
conclusions can be reached from the analysis of one water treatment plant.
The analysis has shown that variability in the correlation between con-
stituents exists from month to month, and that there are some'problems
inherent in choosing between the hypotheses of uncorrelated constituents
and correlated constituents.
The time-varying nature of effluent statistics comes from two
sources: (1) periodic variations due to weekly, monthly, or seasonal
22
-------
variations and (2) trends due to changes in the plant processes. The
weekly and monthly variations are averaged out in the input data (i.e.,
monthly mean and maximum). These variations, if known, should be taken
into account when determining when, in a monitoring period, to monitor
a particular source. The seasonal variations and trends are taken into
account in the statistical characterization by discounting appropriate
past information and updating the statistics as new data become available
(see Section A, Task 7).
The specific procedures used in the Resource Allocation Procedure
to obtain the initial statistical description of the effluent sources and
to update the statistics as new information becomes available are dis-
cussed below.
Initial Statistical Description
The monitoring agency will have two types of data available from
which it can initially determine the statistical characteristics of the
effluent discharges:
• Self-monitoring data
• Compliance data
The self-monitoring reports will typically be sent to the appropriate
regulatory agency on a monthly or quarterly basis. The reports will at a
minimum contain the monthly maximum and monthly sample mean of the daily
measurements (usually composite) of those constituents for which standards
have been set. The report will also state the number of samples which were
used to obtain the sample mean and maximum. Compliance data will also be
available on the sources the monitoring agency has inspected as part of
its compliance monitoring program.
23
-------
When using the Resource Allocation Procedure for the first time,
it is necessary to obtain an initial statistical description of all the
effluent source constituents. This statistical description will be a
function of self-monitoring data and compliance monitoring data gathered
over many months. The procedure required to obtain the initial statistical
description in the computer implementation is shown in Figure 2.4. The
changes made for the manual procedure are discussed at the end of this
section. The various components of this procedure will now be discussed.
Aggregate Data. The procedure to obtain estimates of the mean and
standard deviation from the sample mean and the maximum (given in Appendix
A of [1]) requires that the number of measurements used to obtain the
sample mean and the maximum be greater than three. If the number of
measurements is three or less, the data over several months can be
aggregated to obtain a sample mean and maximum based on more than three
measurements. In this way, the estimation procedures, which have been
shown to be applicable in describing the effluent statistics [1], can
still be used. A theoretical description of the aggregation procedure
is given in [1, Section 5].
Obtain Estimates of Mean and Standard Deviation From Monthly
Self-Monitoring Data. The estimation procedures to obtain estimates of
the mean and standard deviation for normal and lognormal processes are
given in Appendix A of [1],
Combine Self-Monitoring and Compliance Monitoring Data. At this
point in the procedure (see Figure 2.4), estimates of the mean and standard
deviation, based on self-tnonitoring data, are available for each month or
aggregated month. These will be combined with the compliance monitoring
data to obtain new improved estimates. Since the monitoring agency will
be collecting the compliance monitoring data, this data will be more
24
-------
MONTHLY JJATA
SELF-MONITORING:
MEAN, MAXIMUM
NO. OF MEASUREMENTS
COMPLIANCE MONITORING
MEASUREMENTS
AGGREGATE DATA
(if necessary)
FOR EACH MONTH, OBTAIN
ESTIMATE OF MEAN AND
STANDARD DEVIATION
FROM SELF-MONITORING
DATA
FOR EACH MONTH, COMBINE
SELF-MONITORING AND
COMPLIANCE MONITORING
DATA TO OBTAIN NEW
ESTIMATE OF MEAN AND
STANDARD DEVIATION
COMBINE ESTIMATES FROM
ALL MONTHS TO OBTAIN
ESTIMATES OF MEAN AND
STANDARD DEVIATION AT
START OF MONITORING
PERIOD
Figure 2.4
Initial Statistical Description Procedure
25
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reliable than the self-monitoring data. This should be taken into con-
sideration in the method of combination. The combination procedure is as
follows. Let
Z1'Z2' •"' Zc
be c daily composite values obtained in the compliance monitoring program
for a month. Let m and V be the estimated mean and variance (estimated
standard deviation square d) for that month based on the self-monitoring
data. Let n and v be the parameters which express the confidence in the
mean and variance respectively, n and v are constants representing the
*
equivalent number of measurements used to estimate m and V. The values of
n and v are set proportionally to the number of measurements, N, used to
calculate the monthly mean and maximum. That is,
n = h N (2.7)
n
and
v = h (N-l) (2.8)
where h and h are design parameters.
n v
The compliance data and the monthly estimates are combined sequen-
tially, using the updating formula described in Appendix E of [1], First,
the compliance data z from a given month are combined with the self-
monitoring estimates (m, n, V, v) for that month using the update formula
(E.3) of [1], yielding the posterior estimates (m , n , V v,). The second
compliance data z« for that month are then combined with this estimate to
yield a new estimate (m^, r\2, V^, V2). The process is repeated until all
the compliance data are used to obtain a final monthly estimate for each
month. In order to give the compliance monitoring data more weight (since
A discussion of these confidence parameters is given at the end of this
section. They are also discussed in [1]. For further information see
[28].
26
-------
they will, in general, be more reliable),the values of V and n-used in
(E.3a) and (E.3b) of [1] should be replaced by V/y and n/y where y >1 is
a design constant.
As an example, consider the case where the estimate of the mean,
from self-monitoring data, is m = 100, and the estimate of the standard
deviation is a = 25. The confidence parameters are assumed to be n = 15
and v = 10. Suppose compliance data for the month are also available with
values z = 115 and z« = 145. Let y be equal to 2. [Recall n' - 1 and y1 =• 0.]
Using (E.3), of [1], z can be combined with the estimates (m, n, V, v) to yield
(n/y)m + z
m1 = . N . = 101.8
1 (n/y) + 1
nL = n + 1 = 16
[(v/y) V + (n/y)m2] + z2 - ((n/y) + l)m2
vi = , , , , | -=543.7
1 (v/y) + 1
and
vn = v + 1 = 11. (2.9)
The new estimate of the standard deviation is a, = vv = 23.3. The process
is then repeated with (m.. , n , V , v ) replacing (m, n, V, v) and z? re-
placing z1 to yield
m = 106.6
n2 = 17
V2 = 715.27
and
v2 = 12. (2.10)
The new estimate of the standard deviation is a~ =26.7.
27
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Combine Estimates From Several Months. The final step in obtaining
an initial statistical description is to combine the estimates from several
months to obtain an estimate of the mean and standard deviation at the
start of the monitoring period. The estimates are combined by sequentially
using the Bayesian update formula (E.3) given in Appendix E of [1], If the mean,
m , and the variance, V , along with the confidence parameters, n£, and
v , are available for months t = 1,2, .... T, the final estimates would be
obtained by first combining (m,, n^ V^ v 2> and (ny n^, V2> v2> using (E.3) of [1]
yielding (mj, n£, V.J, vp . Then (m£, nj, Vj, vp would be combined with (raj
n3, V3, v3) to yield (mj, nj, Vj, vJ). This process would be repeated until
the estimate (m^,, n^, Vj,, vj,)is obtained, which is the estimate to use in the
priority setting procedure.
Confidence Parameters. In order to use the Bayesian update formula,
it is necessary to specify the confidence parameters n and v. These para-
meters describe one's confidence in the estimates of the mean and
variance. A discussion of how to obtain these parameters is given in
Section 5, of [1]. A detailed manual procedure for obtaining them is given
in Section 4, Task A.
Update of Statistics
In the previous section, a procedure was given to obtain the
statistical characteristics of the effluent sources at the commencement
of the use of the Resource Allocation Procedure. The Resource Allocation
Procedure will be used on a periodic basis to obtain the sampling frequencies
for the following monitoring period. At the same time the monitoring agency
will continue to receive self-monitoring and compliance data. The purpose
of this section is to describe how this data should be used to obtain an
updated statistical description.
28
-------
The update procedure is identical to the procedure for the Initial
Statistical Description with the small exception that the old statistical
characterization is used as a starting point in the procedure. To be
precise, the statistical update procedure follows the Initial Statistical
Description procedure (see Figure 2.2), in that first, the new monthly
data are aggregated, if necessary, to obtain sample sizes greater than 3;
estimates of monthly means and standard deviations based on the self-moni-
toring data are then obtained. The Bayesian update formulas (Appendix E of
[1]) are then used to combine the compliance monitoring data and the monthly
statistical description of the effluent and thus the new monthly statistical
descriptions based on the new data are available. These are combined
sequentially, starting with the original statistics, using the Bayesian
update formula, therby obtaining an updated statistical description.
Manual Procedure
The manual procedure described in Section 4 is the same as the
computer implementation except that the data from all the previous months
are aggregated in the "Aggregate Data" step. This eliminates the need
for computing the standard deviation for each month of data — they only
have to be estimated once per monitoring period — and the need for combin-
ing the monthly estimates using the update formula. The tremendous reduction
in computation far outweighs the loss of accuracy in the effluent statistics.
2.6 RESOURCE ALLOCATION PROBLEM
In Section 2.4, performance criteria for the procedure of allocating
monitoring resources were defined. This section defines the complete resource
allocation problem and describes the method of solution used in this hand-
book, the maximum marginal return method.
29
-------
Formulation of The Problem
There are three resource allocation problems that the monitoring
agency might want solved :
1. Given a certain amount of resources (i.e., budget), determine
how the monitoring resources should be allocated to minimize
the allocation criteria, (i.e., minimize the Probability of
Undetected Violations, Cost of Undetected Violations, or
Magnitude of Undetected Violations).
2. In setting up a monitoring program, determine what level of
resources is needed to insure that an allocation criterion
is below a given level.
3. Given an increment of monitoring resources, determine how to
allocate these additional resources and the resulting improve-
ment in the monitoring system performance.
In the remainder of this subsection, these problems are formulated math-
ematically.
The allocation criteria are all of the form
n
.
-------
no violation is observed at the i source, n is the number of sources,
. s
s^ is the number of times the i source is monitored, and C. is defined by
the criteria used as explained in Section 2.4. The total monetary cost to
monitor all the sources, where the i source is monitored s. times is
n
R(s) = £ rS (2.13)
where r. is the cost of monitoring source i once. r. is made up of man-
power, transportation, equipment and laboratory costs. The actual values
of these costs will vary from agency to agency and as a function of time.
Upper and lower bounds on s. may also be given, i.e.,
£. < s. < L. (2.14)
i - i - i
To see when a monitor may desire to specify bounds, consider the
case where, from ambient monitoring, it has been observed that in a certain
river section the level of a particular constituent is higher than usual.
Then, one might want to check at least once during the next period all the
effluent sources that might have caused this. In this case a lower bound
of one is set on the corresponding sampling rates. Also, consider the
case of an effluent having a small expected violation cost. Based upon
the existing information, it will have a low priority for being monitored.
In order to prevent information from becoming obsolete, one can stipulate
that it has to be monitored at least once during a certain period of time.
An upper bound might be desired if the monitor does not want to sample
any source more than a given number of times. This should be true, for
example, if the monitor were required to visit a certain number of sources.
Another situation can occur when there is a known polluter (e.g., one
against which there are sufficient data to initiate legal action or one
which is improving its treatment according to an approved long-term plan);
31
-------
the monitor may then decide not to survey this source frequently because
the result is predictable. In this case, the upper bound for s. would
be set to some specified value.
The three optimization problems can now be specified.
Problem 1: minimize C(s)
subject to R(s) £ B
I £ s £ L
where B is the monitoring agency's budget and £=(£,...,£ ) and
g
L = (L,, ..., L ) are upper and lower bounds.
1 ns
Problem 2: minimize R(s)
subject to C(s) < A
I a s i L
where A is the maximum "cost" of undetected violations allowed.
Problem 3 is of the same form as Problem 1, except B includes the
additional resources and L specifies the sampling frequencies under the
original allocation. The decrease in "cost" between when the original
budget is used and the new budget is used is the system improvement.
The additional samples specify where to use the additional resources.
Method of Maximum Marginal Return - - Problem Solution
The optimization method used to solve the resource allocation
problems is the method of maximum marginal return. It is particularly
suited for these problems since it solves all of them in the same manner.
It is based on the following intuitive idea: the best place to allocate
32
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one unit of resource is where the marginal return (the decrease in damage
cost - in our case, undetected violation "cost" - accrued by using that
unit of resource) is greatest. Therefore, by ordering the marginal returns
in descending order, one obtains a priority list with the samples having
highest priority on top.
To be precise, the marginal return accrued when the sampling rate
on the i source is increased from s.-l to s. is
i i
VS.-D - c.cs.)
In view of the convexity of C., these marginal returns are monotonically
decreasing with s., i.e.,
The priorities of allocation are obtained by simply ordering these
marginal returns. If the ordering obtained is, for example
V2(l) > y1(l) > u2(2) > u3(D ...
then effluent source 2 is sampled with highest priority, then effluent
source 1, then again effluent source 2, then effluent source 3, etc. Following
this, a relation between the minimized "cost" of undetected violations and the
corresponding resource cost is obtained. Therefore, this method solves simul-
taneously the problem of minimizing the undetected violation "cost" subject to
the total budget and the minimization of the budget subject to a given "cost"
of undetected violations.
33
-------
The problem of allocating an increment of resources to maximize
the improvement in an existing monitoring system is solved as follows:
set up the priority list as described above, and remove from the list
those samples that have been allocated. The remaining items on the list
are, in descending priority, the ones that should be monitored with an
increase in resources.
2.7 SIMPLIFIED EXAMPLE
The performance of the Resource Allocation Program is demonstrated
in this section, using a simplified example. Initially, it is assumed
that there are four sources to be monitored, each having four months of
self-monitoring data available from which to obtain the initial statistics.
The initial self-monitoring data assumed are shown in Tables 2.5a through
2.5e. The data have been abstracted from real data that were used for the
demonstration case of [1] . Using the procedure outlined in Section 2.5 and
Section 2.3 of [1], Tables 2.5a through 2.5e present the initial statistics
obtained from the data. The estimated mean and estimated standard deviation
are the monthly estimates. For Source A, the sample size of the effluent
constituents for a single month is 2; therefore, the data in months 1 and 2
and months 3 and 4 have to be aggregated, as discussed in Section 2.5.
Thus, only two estimates of the mean and two of the variance are given in
Tables 2-,5d and 2.5e. Tables 2.6a through 2.6e also show how the estimates
of the mean and standard deviation are sequentially updated as the monthly
estimates are combined to obtain the estimates to be used in the Resource
Allocation Program. For this case the design parameters k and k , which
n V
determine the degree of the discounting of past information, have been set
to 3. The updated mean and variance for month 2 are therefore the combined
estimates derived from the 1st and 2nd monthly estimates. The updated
mean and variance for month 3 are the combination of the updated estimates
for month 2 and monthly estimate for month 3. The same process is repeated
for month 4, yielding the initial statistical description to be used in
the program.
34
-------
Table 2.5a SELF MONITORING DATA FOR SOURCE 1
Month
1
2
3
4
Mean
source
tlou.
Ml/day
0.90
1.10
1.20
0.85
Parameter: pH Max
Eff. stundnrJ: 9
Distribution: Normal
Mean
8.S
7.6
8.3
8.1
Max
10.6
9.0
9.B
9.5
Somile
size
20
22
22
20
Parnneter: pi! Mln
Eff. standard: 6
Distribution: Noranl
Me.in
8.5
7.6
8.3
B.I
Hln
6.0
5.4
6.4
6.4
San. Die
size
20
22
22
20
Parameter: Lead
Eff. standard:2 kg
Distribution: Noreal
Mean.
0.41
1.08
1.09
0.52
MAX.
kg
1.0
1.7
6.3
1.8
Sar-.ple
size
20
22
22
22
Table 2.5b SELF MONITORING DATA FOR SOURCE 2
Month
1
2
3
4
Mean
source
tlov.
Ml/day
0.80
0.78
0.87
0.65
Parameter: Chromium
Zff. standard: 0.45 kg
Distribution: Normal
Kcan,
kg
0.216
0.313
0.214
0.132
Max,
kR
0.808
0.867
0.620
0.255
Sanple
size
18
19
21
14
Parameter: Copper
Eff. standard: 1.5 kg
Distribution: Lognoreal
Mcant
V.R
0.524
0.374
0.364
0.110
Max
kg'
1.89
1.87
1.25
0.42
S.ir.ale
size
IB
19
22
14
Parameter: Fluoride
Eff. standard: 30 kg
Distribut lea: Noraa!
Mean
kg
24.4
25.4
24.7
14.0
Max .
kg
31.4
31.9
31.0
31.0
Sanple
size
18
19
22
11
Table 2.5c SELF MONITORING DATA FOR SOURCE 3
Month
1
2
3
4
Mean
source
t low,
Ml/day
105
110
109
108
r'jraraeter: BODj
Erf. standard: 3500 kf,
Distribution: Nomal
Mean ,
1165
900
1395
1060
Max i
kS
2115
2115
2880
2385
Sa-.?le
size
30
31
30
31
Pnr.iinetcr : Phosphate
Eff. st.iml.ird: 300 kg
Distribution: Loguomal
Moan ,
kv.
178
171
171
68
N.ix ,
658
338
500
275
SsT?ee
30
31
30
31
1'ar.imet rr : Sus. Solids
!'f f . Ft.indard: 4050 kg
Distribution: Logno rn.i 1
Mean .
ki:
2430
1665
3240
2160
Mnx ,
6030
5130
10935
4590
Sample
size
30
31
30
31
Parane ter :
Dissolved
oxygen
Me.in i
3.9
3.8
4.2
4.1
Sample
30
31
30
31
35
-------
Table 2.5d SELF MONITORING DATA FOR SOURCE 4, PIPE 1
Month
1
2
3
4
Mean
source(
tlov
Ml/day
0.35
0.26
0.29
0.30
Paraneter: Phosphates
EfC. 5car.ii.ird: 0.6 kg
Distribution: Normal
Mcjn,
kg
0.15
0.30
0.31
1.20
Max,
kg
0.24
0.36
0.36
2.56
Sample
size
2
Z
2
2
Parameter: Sue. Solids
Eff. standard: 25 kg
Distribution: Normal
Nca (i ,
kg
12.0
U.6
16.4
11.0
Max,
kg
18.9
18.9
18.0
15.3
Sample
size
2
2
2
2
Table 2.5e SELF MONITORING DATA FOR SOURCE 4, PIPE 2
Month
1
2
3
4
P/traoeter: Phosphates
Distribution: Normal
Est.
mean ,
kg
„
3.20
-
4.35
Esc.
at.dev. ,
kg
_
0.526
-
4.096
Updated
r.ean ,
kg
„
-
-
3.78
Updated
st. dev. ,
k«
_
-
-
2.719
Parameter: Suspended Solldfl
Distribution: Normal
Est.
mosn,
kg
_
88.0
-
62.0
Eat.
at . dev. ,
kg
_
156.3
-
62.3
Updated
neon ,
kg
„
-
-
75.0
Updated
St. dev. ,
kg
.
-
-
108.2
36
-------
Table 2.6a INITIAL STATISTICS FOR SOURCE 1
Month
1
2
3
4
Parameter: pH Max
Distribution: Normal
Est.
8.5
7.6
8.3
8.1
r.st.
1.12
0.73
0.78
0.74
Updated
_
8.03
8.12
8.12
Updated
„
1.06
0.98
0.92
Parnrofctrr: ' pH Min
Distribution: Normal
Est.
8.5
7.6
8.3
8.1
Esi.
1.33
1.15
0.99
0.90
Updated
8.03
8.12
8.12
Updated
1.33
1.22
1.14
Parameter: Lead
Distribution: Nonaal
Est.
0.41
1.08
1.09
0.515
Est. st.
0.31
0.32
2.72
0.67
Updated
mean, kg
0.76
0.87
0.78
Updated
St. dev., kg
0.51
1.62
1.45
Table 2.6b INITIAL STATISTICS FOR SOURCE 2
Month
1
2
3
4
Parameter: Chromium
Distribution: Normal
Est.
mean .
Vg
0.216
0.315
0.214
0.132
Est.
Bt. dev.,
Vg
0.321
0.297
0.214
0.070
Updated
dean ,
kg
.
0.266
0.247
0.218
Updated
st. dev. ,
kg
_
0.308
0.277
0.246
Parameter: Copper
Distribution: Lognoroal
Est.
log k.g
-0.437
-0.6S5
-0.570
-1.146
Est.
loE kg
0.369
0.474
0.337
0.404
Updated
log kg
_
-0.565
-0.567
-0.711
Updated
lofc kg
_
0.443
0.403
0.502
Parameter: Fluoride
Distribution: Normal
Est.
Kg
24.4
25.4
24.7
24.0
Est.
kg
3.79
3.49
3.29
4.17
Updated
kg
-
24.9
24.8
24.6
Updated
kg
-
3.62
3.46
3.61
Table 2.6c INITIAL STATISTICS FOR SOURCE 3
1
2
3
4
Pornmetcr: BOH.
Distribution: Norcval
Est.
oean,
kg
1165
900
1395
1080
Est.
st . dev. ,
kg
470
598
734
642
Updated
mean.
ks
1030
1150
1133
Updated
st .dev. t
kg
555
648
643
Parameter: rhnppli.-ite
Distribution: Loynorofll
Est .
ce.in ,
log kc
2.12
2.20
2.12
1.85
Est.
st .dev. ,
log kg
0.339
0.157
0.268
0.286
Updated
cr.e.in,
log kg
2.16
2.16
2,08
Updated
st .dev . ,
lor, kg
0.265
0.264
0.313
r.ir.irorter: Suspended Solids
Distribution: Lofinormjl
r.st.
jnc.1 n ,
log kp.
3.33
3.13
3.40
3.30
Kst.
st . dev. ,
IOR ke
0.218
0.282
0.312
0.175
Updated
irriin ,
IOR kS
3.23
3.29
3.29
Updated
:;t .dev. ,
log kg
0.277
0.302
0.274
P.ir.ine t cr :
oxycen
Est.
mean ,
Tf/\
3.90
3.80
4.20
4.10
V'pd.it ed
rean,
r.-./ 1
—
J.85
3.96
4.00
37
-------
Table 2.6d INITIAL STATISTICS FOR SOURCE A, PIPE 1
Month
I
2
3'
4
Parameter: Phosphates
Distribution: Normal
Esc.
oean ,
kg
-
0.225
-
0.755
Eet.
•t.dcv. ,
kg
-
0.101
-
1.356
Updated
mean ,
kg
-
-
-
0.490
Updated
St. dev. ,
kg
-
-
-
0.925
Parameter: Suspended Solids
Distribution: Normal
Ent.
mean ,
k£
-
13.3
-
13.7
Esc.
st .dev. ,
kg
-
4.21
-
3.23
Updated
mean ,
kg
-
-
-
13.5
Updated
at. dev.,
k&
-
-
-
3.3S
Table 2.6e INITIAL STATISTICS FOR SOURCE 4, PIPE 2
Month
1
2
3
4
Mean
source
!low,
Hi/day
0.90
1.01
1.09
1.00
Pjrancter: Phosphates
Eff. st.ino.ird: 3.5 kg
Distribution: Normal
Mean ,
2.9
3.5
2.9
5.8
Max i
kg
3.2
3.9
3.1
9.8
Sample
2
2
2
2
Parameter: Sufi. Solids
Eff. standard: 80 kg
Distribution: Norcal
Mean ,
kg
158
18
93
31
Max ,
296
26
145
33
Sarole
size
2
2
2
2
38
-------
The expected damage and probability of violation obtained from
the data are shown in Table 2.7, along with the estimated source flow
and the stream flow. For this case, the upstream concentration was
assumed to be at a level causing zero damage, and the distributions of
the various parameters were assumed uncorrelated. Certain of the
entries deserve some comment. Source 3 is a large sewage treatment
plant. From the table, the impact of BOD and phosphates is large; how-
ever, the standards are also large and therefore the probability of
violation for the parameters is small. Source 4 has a relatively small
impact on the stream (i.e., small expected damage); however, the standards
have been set so that the probability of violation is very large. The
resources required to sample the sources are given in Table 2.8, and the
priority list is given in Table 2.9. For the purposes of this example,
it was assumed that the sources could be sampled between 0 and 10 times.
From the table, one sees that sources 1 and 3 should be sampled with
higher priority than sources 2 and 4. This is due to the much larger
expected damage from the former sources. Source 4 appears relatively
early in the list, but most of the samples have low priority. This is
because the probability of violation is very large and therefore the
chances are that the source will be caught in violation after one or two
visits. Further sampling is therefore not necessary. Source 2 has a
small expected damage and a fairly large probability of no violation
resulting in a low sampling priority. Table 2.9 also gives the marginal
return, "cost" of undetected violations and resources used. The marginal
returns are decreasing (the list has been ordered in just this manner).
The "cost" of undetected violations is decreasing, and the resources
required are increasing as more sources are sampled.
If only, say $10,000 were available for monitoring, then only the.
sources with priority 1 through 17 would be monitored. The sampling
frequencies for this case are shown in Table 2.10. If, on the other
hand, a maximum allowed "cost" of undetected violations of say, 100 were
specified, then sources with priorities 1 through 10 would be sampled.
39
-------
Table 2.7 EXPECTED DAMAGE AND PROBABILITY OF VIOLATION
Source
1
2
3
4
Pipe
1
1
1
1
2
Esc. source
flow,
Ml/day
0.961
0.845
108
0.297
1.016
Stream
flow,
Ml/day
100
320
525
300
Parameter
PH
Lead
Chromium
Copper
Fluoride
Phosphate
Suspended Solids
Phosphates
Suspended Solids
Phosphates
Suspended Solids
Expected
damage
0.29
1.60
0.08
0.12
0.00
3.22
3.64
0.37
0.29
0.03
Probability
of no viola-
tion - P.,,%
80.0
80.0
82.6
96.1
93.1
100.0
97.6
87.8
100.0
51.8
54.4
46.0
Expected
damage for
source - C
1.60
0.12
3.64
0,29
Probability of
no violation
for source
64.0
74.0
85.6
13.0
-p-
o
-------
Table 2.8 RESOURCES NEEDED TO SAMPLE
Source
1
2
3
4
Field and
office costs
$525
$525
$525
$525
Laboratory
costs
$10.50
$23.00
$38.00
$30.00
Total Cost
-r .
i
$535.50
$548.00
$563.00
$555.00
41
-------
Table 2.9 PRIORITY LIST OF SAMPLES FOR SIMPLIFIED EXAMPLE
PRIORITY
SOURCE
COST OF
>'Al UrOETErTI
X100 VIOLATIONS
1
2
3
U
5
6
7
B
9
10
11
12
13
10
15
16
17
1ft
19
20
?1
22
23
2"
2.5
?b
27
28
29
30
31
32
33
31
35
36
37
3R
39
00
1
3
3
J
3
3
3
a
1
3
3
3
1
3
3
1
1
1
u
2
1
2
2
1
2
1
2
2
2
i\
2
2
2
3
,0231 5'-i9£
,01M1 1 U
. 8 0 '} ?. 6
,50^55
. « o i a i
.7997?
. 7992?
. 7991 T
, 799 1 tl
.799JU
7 Q Q \ /J
"T Q Q * •!
,7991'J
535.50
1095.50
1 f55 . 50
2191 , CO
?75 1 . f*0
3311.00
3*71 , f. ?
ca
-------
The sampling frequencies for this case are shown in Table 2.11. The
priority list in Table 2.9 also'shows when the return from monitoring
(i.e., the marginal return) starts becoming negligible; the return,
in this case, for monitoring more than 25 sources is very small.
43
-------
Table 2.10 FINAL ALLOCATION GIVEN MONETARY BUDGET
FT'AL ALLOCATION
BUDGET 11000.00
SOURCE
1
2
3
a
MJN; NO.
0
0
C
0
•nx NO.
SAMPLES
10
10
10
10
TITS
SAMPLED
7
0
10
i
COPT OF
RtSCU^CtS 0'\0':HCTHri
USEO VIOL ATI CVS
37U8,50 .07081
.00 ,U7i3
5600.00 .77376
55b,OC .03767
TOTAL ^ESOU^CFS ;JSEO 9903.50
Flk
-------
SECTION 3
GENERAL REQUIREMENTS FOR MANPOWER, DATA, AND COMPUTERS
3.1 INPUT DATA REQUIREMENTS AND PROCEDURES
The types of input data required by both the hand calculation
approach and the computer approach are indicated in Table 3.1. These
data types have been classified into categories in this table, which al-
so provides some indication of their relative availability. The data
needs, availability, adequacy, and preparation procedures required are
discussed below for each category.
Standards
Essentially, the same data on effluent standards is required by
both approaches. The computer approach is somewhat limited in the range
of units in which the data may be expressed (see Table 5.1). Therefore,
conversions into such units must be completed, where necessary, before
input to the computer, while the hand approach includes any needed con-
versions (units unlimited) as part of the procedure. The required data
should be readily available since they provide the basis and incentive
for the monitoring; the new National Pollutant Discharge Elimination System
(NPDES) required to be initiated by 1 July 1977, should provide a strong
added impetus to standard setting.
Data on ambient receiving water quality standards may be needed
only by the hand calculation approach, and then only when a certain option
is chosen. Under this option, the standard is only used to develop a
-------
Table 3.1
Summary of Input Data Types
Data Type
STANDARDS
Effluent
Receiving Water
EFFLUENT CHARACTERISTICS
Statistical Distribution Types
Constituent Correlations
MONITORING DATA
Self -Monitoring
Compliance Monitoring
ENVIRONMENTAL CHARACTERISTICS
Environmental Damage Functions
Upstream Constituent Concentrations
BOD-DO Transfer Coefficients
DO Saturation Concentrations
COMPLIANCE MONITORING COSTS
Sample Collection
Sample Analysis
DESIGN PARAMETERS
Discount Factors
Procedure
Requiring
Hand
A
/
/
/
Computer
/
/
/
J
/
/
Relative
Availability
High
High
Low
Low
High
Medium
Medium
High
High
High
Med ium
High
User
Determined
Need depends upon options selected
46
-------
weighting factor; therefore its value is less critical, and may be esti-
mated if not legally established. For this purpose, there is probably
sample information available on receiving water quality standards which
have been established or recommended by various government agencies. Any
preparation of the data needed will again be internal to the hand cal-
culation approach.
Effluent Characteristics
Needed effluent information includes a determination of the statis-
tical distribution types which best describe the daily constituent loading
rates, limited to normal and lognormal, and the correlations (full or none),
between the constituents at a given source. The requirements of both ap-
proaches are identical.
Very few determinations of such statistical distributions have
been made to date. Therefore, while this would appear to be an area
where availability could be greatly improved, the cost would clearly be
great and the benefits small, since analysis and sensitivity studies have
indicated that errors resulting from insufficient information will gen-
erally be quite small (see Section 4, Task 1: Discussion). Furthermore,
a good approximation method has been developed.
Little information is also likely to be available on the cor-
relations between the various constituents. A similar situation exists,
where the results are not very sensitive to error in this area, where it
would be very costly to reduce the errors, and where guidance for select-
ion is provided (see Section 4, Task 9: Procedure, Step 2).
The guidance provided in the hand approach (Section 4, Tasks 1
and 9) may also be used to help the user prepare this input data for the
computer approach.
47
-------
Monitoring Data
Self-monitoring and compliance monitoring data are required by
both the approaches. Self-monitoring data for the computer approach must
have been preprocessed to yield the maximum (or minimum), mean, and sample
size for each separate month of all data collected; data preprocessing is
optional for the hand approach, which does not require separate monthly
inputs, nor does it need to re-input data inputted to previous applic-
ations of this allocation procedure. Another difference between the two
procedures is that water discharge rates in receiving streams are required
only by the computer approach; effluent discharge rates are required in
the computer approach, and in the hand approach only to determine the
constituent loading rates.
Compliance monitoring data are entered only on an item-by-item
basis for both approaches. However, the month corresponding to each item
of data must be provided for the computer approach. With regard to up-
dating and effluent discharge rates, the same difference between the two
approaches apply as for self-monitoring data.
For both these types of data, the acceptable units of input data
are more limited in the computer approach (see Table 5.5), than in the
hand calculation approach; some preprocessing may be needed with the
computer approach, while unit conversions form part of the hand approach.
The availability of self-monitoring data should of course, be as
high as the surveillance agency wishes to make it, within reasonable
and justifiable limits. The availability of compliance monitoring data
will probably depend mostly upon the resources made available to the
surveillance agency.
48
-------
Environmental Characteristics
Receiving water data are required only by the computer approach,
since the impact of discharged effluent constituents upon the receiving
waters are considered directly only in that approach.
An estimate of streamflow immediately upstream of each effluent
source is needed. Streamflow data is usually available from the U.S.
Geological Survey on a daily basis. Since only one "design" streamflow
can be used, a single worst case, low streamflow is suggested. For design
purposes, the seven day, ten year low flow is often available, and is a
reasonable design flow for this procedure.
Information on environmental damage functions for each constituent
representing the variation of environmental damage with constituent con-
centration, has been collected and organized to a useful extent (see SCI's
first report [1], Section VI.2). When improved damage/water quality
information becomes available, and it is desired to input new damage
function data (i.e., override the program's default values in Tables 5.2
and 5.3), some preparatory re-scaling may be needed. Both the concentration
levels and the environmental damage values may be changed (input variables
"DMG", "DAMAGE", "S", and "SSPH").
Some idea of the upstream environmental damage (or corcp.rfration)
is necessary as input for the computer procedure. Since only one overall
value is used, the user must examine his damage functions and pick that
damage level which represents the "average" upstream damage for all con-
stituents of all sources (input variable "ICOPT").
The selection of the required BOD-DO transfer coefficient may be
readily achieved through the use of Figure 3.1 and Figure 3.2 (from [29]).
49
-------
Depth (fc)
Streamflow (ft /sec)
100.0
10.0
1.0
0.1
Creeks £
Shallow
Streams
10-20
1-10
Upstream
Feeders
2-5
10-100
Interme-
diate
Channels
5-10
100-1000
Main
Drainage
Rivers
10-20
1000-
10,000
Large
Rivers
20-30
>
10,000
Impounded
Rivers
30
1.0
10
DEPTH IN FEET
100
NOTE: H = Depth (ft.)
Q = Streamflow (ft /sec)
Figure 3.1 Assimulation Ratio () as a Function of Depth
50
-------
Figure 3.2 Dissolved Oxygen Response as a Function of Water Body Type and Assimulation
Ratio ()
-------
Likewise, the required dissolved oxygen saturation concentrations may be
obtained from Figure 3.3 (also from [29]) given the water temperature
and chlorides content (salinity).
Compliance Monitoring Costs
These costs are required in much the same way by both approaches;
one minor difference is that the computer approach lumps together travel
costs for samples taken from different pipes (outfalls) belonging to the
same source, while the hand approach does not. The development of these
cost data must remain the responsibility of the surveillance agency, which
should be able to extract the information from records hopefully kept on
past monitoring operations. Sample analysis costs for the various con-
stituents should be easily available from the water quality laboratory
which performs the analyses.
The hand approach (Section 4, Task 13) lists the various component
costs required. These must be combined together into separate analysis
costs (per constituent) and base costs (per number of pipes at a source)
before input to the computer approach.
Design Parameters
There are several design parameters used in combining monitoring
data for the computer procedure. First, there is a parameter used to
exponentially smooth the monthly effluent discharges at a source into a
single value. This parameter (input variable "ALPHA") should be between
0. and 1. where an ALPHA close to 0. represents the case where each new
piece of data is heavily weighted with respect to older data and an ALPHA
close to 1.0 represents the case where newer data is very lightly weighted
with respect to older data.
52
-------
§
M
H
Z
w
§
I— I
I
I
w
X
o
Q
W
O
CHLORIDES (ppm)
*^5
0&3
1.0
20 25 30
TEMPERATURE, °C
Figure 3.3
Dissolved Oxygen Saturation Versus Temperature and Chlorides
-------
A second design parameter is the discount factor used in in-
cluding compliance monitoring data. This factor, called "y", was ex-
plained in SCI's first report ([1], Section V.2). The corresponding
input variable is "GAMMA" and the value should be greater than 1. The
larger the input value of "GAMMA" is, the more weight that is given to
compliance monitoring data in comparison to self-monitoring data.
Other discount factors are "k " and "k " (from [1], Section V.2),
n v
where the corresponding input variables are "KETA" and "KNU". The larger
the values of these variables are, the more heavily weighted is past data
with respect to the current month's data in combining monthly constituent
self-monitoring data.
Finally, the values of "h " and "h " must be considered (from [1],
Section V.2). Since "h " is considered to be "1" and is not input, only
"h " need be considered. It was recommended that this be set according
to Table A.3.3 in [1] (use an "average" sample size for the source in
reading the table). The input variable is "ENU".
3.2 COMPUTER AND MANPOWER REQUIREMENTS
The requirements for manpower and hardware differ substantially
between the hand and computer calculation techniques. Generally, the
hand calculation option requires more person time to implement, but re-
quires only an inexpensive hand calculator. On the other hand, the
computer calculation option requires a large scale digital computer with
marginally less person time for programming and interpretation of results.
The computer calculation option becomes more cost-effective as the number
of effluent sources and constituents to be considered increase. If the
number of effluent sources is small, say less than 10, the hand calculation
technique becomes less tedious and more cost-effective.
54
-------
The hand calculation's efficiency depends more upon the efficiency
of the tester than does the computer.procedure. Numerous opportunities
exist for errors to creep into the early calculations. It would be quite
easy to carry these errors through the complete analysis only to discover
the necessity of repeating much of the analysis.
The same opportunities for error exist with the computerized pro-
cedure, but correction is a simpler process which would require substantially
less personnel time.
For the test case described in Section 6, seven effluent sources
and seven constituents were used in both the hand and computer calculation
options. Approximately 60 hours of professional man-time were spent per-
forming the hand calculations and determining the final allocation of
monitoring resources. Nearly half of this 60 hours was spent in initial
data extraction and tabulation, which must also be done to derive inputs
for the computer procedure. This was performed by an SCI staff member
previously unfamiliar with the Resource Allocation Program.
Other Differences Between the Computerized and Hand Procedures
The two major areas of difference between the hand calculation
approach and the computerized procedure (see Sections 5 and 7) are in the
resource allocation criteria used and in the methods of using the newly
entered self-monitoring and compliance monitoring data.
Among the resource allocation criteria used in the computerized
procedure is the total expected environmental damage from undetected
violation (see Section 2.4, Criterion Number 2). The expected environ-
mental damage computation is quite a lengthy procedure, more appropriate
for computers, based on the expected damage per source and the expected
damage per constituent. This in turn is computed from a "damage function"
for each constituent, which attempts to quantify environmental damage
55
-------
resulting from various concentrations of the constituent in the receiving
waters. Thus, the receiving water concentrations caused by each con-
stituent in an effluent must be determined, requiring a knowledge also of
the volume flowrates of both the source and the receiving stream. This
criterion is too complicated for use in the hand calculation procedures.
The resource allocation procedure is greatly simplified in the
hand calculation approach by the use of a different resource allocation
criterion: the total expected extent of undetected violation (discussed
in Section 2.4 as Criterion Number 3). The extent of violations is com-
puted from either the amount by which the effluent standards are exceeded,
or the number of times by which they are exceeded, at the user's option.
This has the effect of directing compliance monitoring towards those dis-
chargers with the more serious violations of the standard, whose conviction
is easier. It also eliminates all the calculations required to assess the
impact on the receiving waters, and in particular, prevents consideration
of the impact of BOD loads upon dissolved oxygen in the receiving waters.
Exclusion of the damage function criterion from the hand calculation
approach also enables the treatment of sources with multiple outfall pipes,
each with its own effluent standards, to be greatly simplified; the com-
puterized procedure requires many more involved computations to determine
the environmental damage caused by one source with multiple outfalls. For
the purposes of this entire hand calculation approach, a source is defined
as a separate outfall or discharge pipe, with its own set of effluent
standards. This differs from the computerized procedure, in which a source
may have a number of outfall pipes each with its own standards. The effect
of this difference appears in the resulting sampling rates, since with the
computerized approach, all pipes of one source would be sampled at the same
time (economizing on travel costs), whereas in the hand calculation approach,
each pipe will probably be assigned a different sampling rate (economizing
on compliance monitoring with low marginal returns). Since actual moni-
toring programs have historically been implemented on a source basis
rather than an individual pipe basis, this may be a slight deficiency in
the hand calculation procedure.
56
-------
Another major area of difference between, the hand and comput-
erized procedures is in the methods of using the newly entered monitor-
ing data. In the computerized procedure, the self-monitoring data are
entered monthly, aggregated across months if the number of data are too
small, and then used to estimate monthly statistics. The compliance
monitoring data are also entered monthly, incorporated into the monthly
statistics, which are then combined into cumulative statistics. In the
hand calculation approach the same general procedure is used, but the
data are not divided up into monthly subsets. Thus, the sample sizes
are much larger, and there is no need to aggregate across months or
combine monthly statistics. The principal effect of this difference is
in the time discounting of the data. In the hand procedure, only data
prior to the last monitoring period may be discounted, or down-weighted,
whereas, in the computerized procedure data as recent as that for the
month before last, may be discounted if desired.
57
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SECTION 4
USER MANUAL FOR HAND CALCULATION APPROACH
4.1 INTRODUCTION
Section 4 constitutes a stand-alone handbook for the hand applic-
ation of resource allocation methods for effluent compliance monitoring.
This handbook is intended for use in determining for an effluent
monitoring agency the rate (or frequency) with which it should sample
each effluent source within its jurisdiction. This sampling rate will
specify the number of samples to be taken at each source during a forth-
coming monitoring period, but it will not allocate their timing within
the period.
The criterion for determining the sampling rate is the "degree of
undetected violations". This is explained further in Section 2.2 and
Reference [1]. The sampling rate may be subject to constraints on the
total resources available for monitoring and on the maximum and minimum
sampling rates specified by the user for each source. The user may choose
to either:
1. Expend the remaining monitoring resources so as to minimize
the total degree of undetected violation from all sources; or
2. Bring the total degree of undetected violation from all sources
below some specified limit while minimizing the monitoring re-
sources spent.
58
-------
Since conditions in the jurisdictional region will undoubtedly
change with time, and since information on the dischargers may improve
with time as more data is collected, the rate allocation should be re-
designed from time to time in the future, each time incorporating all
new information available. The user therefore selects a suitable length
for the next compliance monitoring period, e.g., 3-, 6-, or 12-months.
Since some time is required to analyze the data and design the allocation
procedure for the next monitoring period, there must be a lag period be-
tween data collection and application of the new procedure. The timing
of the various monitoring and analysis functions is illustrated in an
example monitoring sequence in Figure 4.1. Some of the implications of
seasonal variations in effluents upon the selection of monitoring periods
are included in the discussion under Task 3.
The user may wish to apply this allocation procedure for any of
several reasons, such as:
A. For the preliminary design of a new effluent compliance
monitoring system.
B. To compare the effectiveness of an existing surveillance
system against that produced by this procedure.
C. For program planning, to evaluate (on the basis of the re-
source allocation criterion) the overall level of surveillance
required in a basin, region, or nation.
He may prefer the hand calculation procedure outlined in this Section to
the alternative computerized procedure (see Sections 5 and 7), for such
reasons as:
A. The lack of staff or facilities to operate the computerized
procedure.
B. The wish to become intimately familiar with the procedure, be-
fore implementing it on a computer. (However, there are some
differences, which will be discussed below.)
C. The small size of this surveillance operation does not justify
the use of a computer.
59
-------
Start Allocation Procedure
Start Compliance Monitoring Based on Allocation Procedure
1
2a
2b
3
Month
Collect
Compliance
Monitoring
Data Set Number
Update Compliance
Monitoring
Statistics
Through Set Number
Design
Compliance
Monitoring
Procedure Number
Apply
Compliance
Monitoring
Procedure Number
'OLD'
'OLD'
'OLD'
'C
1
'OLD'
Pl
)LD'
2
3
4
Dl
Pl
5
6
7
n
Ul
P2
8
9
10
D2
P2
11
12
13
n
U2
P3
cr>
o
Figure 4.1 Example of Monitoring Sequence. This assumes: (1) a six month compliance monitoring
period, and (2) a one month lag time to complete data analysis and to design the
procedure for the next monitoring period.
-------
The user should be familiar with basic engineering statistics and
mathematics up to, but not includin-g, calculus. He should also have
available a desk calculator or similar computational device. Once the
procedure is well understood, a programmable calculator could undoubtedly
be used to provide added convenience with the repetitive computations.
Many of the technical terms used are explained in the Glossary at
the back of this handbook.
Limitations
This hand procedure is limited to the preliminary design of effluent
compliance monitoring systems for which the primary goal is the minimization
of the total expected extent of undetected violations (or optionally,
minimization of the number of undetected violations). The methods require
that the effluent standards be expressed as simple thresholds for each
constituent (maximum or minimum values, or both).
This hand procedure does not include considerations of monitoring
system implementation costs, accessibility, maintainability, reliability,
and other similar practical engineering factors.
Assumptions
The methods employed in this hand procedure are based on the follow-
ing assumptions:
1. Only one set of effluent standards applies to each source.
2. Concentrations at various sampling times are independent.
3. The loading rates of the various constituents at one source
may be taken to be completely dependent (correlated) or
completely independent.
61
-------
4. The frequency distributions of daily loading rates of each
constituent may be represented by either a normal or a log-
normal distribution.
5. Effluent standard violations are the only concern. Therefore,
any damage to the receiving waters caused when source con-
stituents do not violate the effluent standards cannot be con-
sidered.
These assumptions are explained in more detail in the areas of
Section 4.2 where they are employed.
Other Requirements
Another requirement of the hand procedure employed here is that:
Data should be available on the component cost for transport-
ation, sampling, materials, labor, analysis, and reporting
which together comprise the total cost to take a 24-hour com-
posite (compliance monitoring) sample at each source within
the area of jurisdiction.
Overview of the Hand Calculation Approach
The quantitative preliminary design procedure used in the hand
calculation approach consists of a number of individual tasks. These
tasks are numbered, and their relationships indicated, in Figure 4.2.
Each task is relatively self-contained; the objective, outputs, inputs,
and procedure required for each are discussed separately in the following
subsection.
The 20 tasks have been grouped in Figure 4.2, into the four
principal activity areas identified in the original formulation of this
monitoring resource allocation procedure (see [1], p. 97). The first
three activities comprise the overall allocation procedure. The fourth
62
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INPUTS
Assign, conntit. distribs.
Effluent standards
New self-mon. data , *,
j
New cor.pli-rion. data T *"
Init. won. rss. alloc'n.
Cost/sample, ea. source
I
1
1
NHTF • TVi 0 niiml-\£}r- -in Kr\vQO -i
1
T
1 1
•t 1
* '
,a (-_
<
1
*• c
1
,
1
i r
•ta T
i
ir 1
i
i
i
\
r*
' 1
u i
- — < j_
L .
1 1
J 20 I
i i
t
)
f
0
<
0
f
6
8'
. j
91
1
. j
R
1 '
CALCULATIONS
Est. new self-mon. statistics
Combine, for improved
statistics
Cotabinc into cumulative
statistics
Prob. of non-viol'n/constit.
Violation wt. factor/source
Prob. of non-viol'n/source
Alt. exp. extents of undet.
viol'no.
Tabulate marginal returns
Preselect init. allocated '
samples
Priority order marg. returns
Det. sampling rates/source
Devel. monitoring schedule
Compliance monitoring
Self monitoring
.
H
to
M
<
) C°»H
r [ »—
ft <3
I-1
E-i
Q
pa .
O *
* >
5> c
to
bl
H
o:
o
)
w
M
Ul
H
w
LI
o
H
1
task numbers of the hand cal-
culation procedure as described
in Section 4.2.
Figure 4.2 Interralationships of Comprising Tasks (linking
areas in present flow of effluents)
63
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activity represents the remaining tasks to be executed by the monitoring
agency and the dischargers, which will provide additional inputs for the
next allocation.
Organization
Following this introduction, the objectives, outputs, inputs, and
the step-by-step procedure required for each task are discussed separately.
Examples of the computational tables required are provided. For user
convenience, each task begins on a fresh page. For clarification, task
numbers are placed in boxes similar to those in Figure 4.2.
Units
For computational efficiency, an attempt has been made to use a
consistent 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.
Symbols
To the extent possible, the symbols used herein have the same
meaning as they have in Section 2: Summary. The meanings are given in
the list of symbols at the back of this handbook.
64
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4.2 STEP-BY-STEP PROCEDURE
TASK.Q]: ASSIGN CONSTITUENT DISTRIBUTIONS
Objective
For each water quality constituent of interest in the surveillance
program and at each source where it occurs, assign a type of statistical
distribution which best represents the frequency distribution of the
daily loading rates of the effluent.
Output
The output for TaskQ] is the completed Table 4.1 with the name of
the frequency distribution type (must be either "Normal" or "Lognormal").
Inputs
Previous determinations of statistical distributions in the area
of interest, if available.
Information Sources
• Reference [1], Section V.I
• References [2,3]
Discussion
Very few determinations of statistical distributions have been
made to date (see [1], Recommendation 3). Sensitivity studies ([1],
Section 8.3) indicate that an error in the specification of a distribution
65
-------
type would be small (approximately 10 percent), if not negligible, in effect,
Therefore, the extensive studies of effluent data required to make a more
accurate determination do not seem to be justified, especially when a
good approximating alternative method is available (Alternative 2 of Step
6 below).
In the SCI first report [1], it was found that a large majority of
effluent loading rates could be accurately represented by either normal
or lognormal distributions. Therefore, candidate distributions are limit-
ed to these two.
Procedure
1. List all the sources of interest in the region and constituents
of interest at each source, in columns 1-3 of Table 4.1,
arranging them in source order (for convenience later). Choose
a convenient ordering which will be repeated in many subsequent
tasks. In column 1, assign a number to each source for con-
venient reference later.
2. At a given source, for a given constituent, assign constituent
distributions as follows: if this is the first time this
particular constituent at this source is being considered for
assignment, (determine this from Table 4.1 for the most recent,
previous application of this allocation procedure), then pro-
ceed to Step 4; otherwise go to Step 3.
3. Procedure has been applied previously. Copy the distribution
assignment from Table 4.1 for the previous application into
the new Table 4.1 for this application. (Note: Such assign-
ments must not be changed after the first application of this
procedure, since once "typed" normal or lognormal, the cumul-
ative statistics cannot be later converted from one type to
the other).
Go to Step 7.
66
-------
4. For first application of procedure. If the constituent is pH
or coliform bacteria, go to Step 5; otherwise skip to Step 6.
5. For pH and coliforms only. Because specific assignments are
the most reasonable for certain constituents, and they are
also of help in subsequent tasks, this overall hand calculation
procedure requires the following constituents, if present, to
be always assigned the following distributions:
Constituent Distribution
pH always Normal (N)
Coliforms always Lognormal (Lj
Indicate the distribution assignment in column 4 of Table 4.1,
and enter a dash in column 5 (not applicable).
Go to Step 7.
6. For all other constituents. Select one of the following two
alternative methods to assign a distribution type (see Taskf!),
Discussion):
Alternative 1: Where available, use previous determinations
of the statistical distribution type made
for this specific constituent and source.
Alternative 2: Assume a normal distribution for all cases.
(Note: This assumption may be modified
later in Step 4g of TaskQj]) .
Enter the assignment and selection into columns 3 and 4
respectively on Table 4.1.
7. Repeat Steps 2-6 (as appropriate) for each constituent of
interest at the same source.
8. Repeat Steps 2-7 (as appropriate) for each source of interest
in the region.
67
-------
Table 4.1
Statistical Distribution Types By Constituent and Source
Source
No.
(i)
Constituent
Name
Distribution
Type (N or L)
Task [I]
Alternative
Used (1 or 2)
(1)
(2)
(3)
Note: This table can be duplicated for use in the hand calculations.
68
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TASKQJ: INPUT EFFLUENT STANDARDS
Objective
For each source and each constituent, prepare a list of the effluent
standards.
Output
TaskQJ's output is Table 4.2 which lists by source the limiting
loading rates or concentrations permitted for each constituent.
• Effluent limitations stated on National Pollution Discharge
Elimination System (NPDES) discharge permits (required by
1 July 1977).
• Pending the establishment of the above, equivalent limitations
previously established by the responsible water quality control
agency.
Discussion
In some cases, effluent standards may alternatively be specified
as either (a) a maximum loading (e.g., kg/day, Ib/day, MPN/day), or (b)
a maximum concentration (e.g., mg/L, ppm) together with a maximum volu-
metric flow rate (e.g., ML/day, cfs, mgd). Assuming these maxima are
synchronous, (a) can be computed from (b). In the last analysis, it is
the loading rate which is the crucial quantity and which must be con-
trolled to prevent environmental damage. Furthermore, for Task |LOl.
Step 4 (see Subsection a), the allocation procedure requires that the
effluent standard S be prescribed in the form of a loading rate wherever
possible. pH is a special case, and is so treated in Task [iCJ, Step 4,
Subsection c.
69
-------
The same units used to specify these effluent standards will be
also specified for the monitoring data to be input in Tasks [3] and[3j, in
order to obtain consistency.
Procedure
Enter the applicable standards into Table 4.2, following the same
source and constituent order established in Table 4.1 (Task 1). Where-
ever possible, enter the standard in the form of a loading rate (e.g.,
kg/day, MPN/day - see Discussion); use Table 4.3 to assist in making the
conversions. Also, wherever possible, convert the units of the standard
to CGS units; use Table 4.4 to assist in making these conversions.
For pH standards, make two separate entries: for pH MAX and pH
MIN.
70
-------
Table 4.2
Effluent Standards
Source
Constituent
Name
Units
Standard
Value,
S
(1)
(2)
(3)
(A)
k
Specify in the form of a loading rate, preferably kg/day,
wherever possible (see TaskQ]Discussion). For concentrations,
only where unavoidable, preferably use mg/L.
Note: This table can be duplicated for use in the hand calculations.
71
-------
Table 4.3
Conversion Factors
MASS
1 pound (Ib)
1 kilogram (kg)
1 kilogram (kg)
1 kilogram (kg)
1 kilogram (kg)
.4536 kilograms (kg)
2.205 pounds (Ib)
1000 grams (g)
1,000,000 milligrams (mg)
1,000,000,000 micrograms
VOLUME
1 gallon (g)
1 gallon (g)
1 liter (L)
1 liter (L)
3
1 cubic foot (ft ) =
3
1 cubic foot (ft ) =
.13368 cubic feet (ft )
3.785 liters (L)
.2642 gallons (g)
.03532 cubic feet (ft3)
7.4805 gallons (g)
28.3161 liters (L)
TIME
1 day
1 second
86,400 seconds
.0000115741 days
NOTE: Parts-per-million (ppm) is approximately
equivalent to milligrams per liter (mg/L)
72
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Table 4.4
Data and Standards Conversion
Unconverted
Data or
Standard
Unconverted
Units
Conversion
Factor
Converted
Units
Converted
Data or
Standard
Note: This table can be duplicated for use in the hand calculations.
73
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TASK[5]: INPUT NEW SELF-MONITORING DATA
Objective
For each constituent, and for each source, tabulate summary infor-
mation on all the new self-monitoring data collected during the monitor-
ing period just completed.
Output
The output, to be recorded in columns 1-7 of Table 4.5, will
include:
• Listing of constituents of concern at each source in the
region.
• Self-monitoring summary data on these constituents for
the monitoring period just completed.
Inputs
Depending upon both the source and the constituents, the inputs
may be either raw, grab sample and daily composite measurements, or they
may be summaries for subintervals, such as monthly means, monthly maxima,
and the number of measurements made during each interval.
References
• [1], Section III
74
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Discussion
Input data from composite self-monitoring samples are clearly pre-
ferred to data from grab samples, because they are far more representative
of the total pollutant load and they relate directly to the NPDES daily
maximum effluent standard. However, there are likely to be many more
grab sample data available, due to their lower acquisition cost. Unless
there are ample composite sample data available, it is suggested that the
grab sample data should be included in the input self-monitoring data for
this task. The fact that the grab sample data are less reliable can be
accounted for later in the reliability factor, y> of Taskjjjj, Step 1.
Where fairly strong seasonal variations in effluents are known to
occur, as for example, in the food processing industry, possible measures
to reduce misallocation would be:
1. to design for a one-year-long compliance monitoring period,
and to then allocate the compliance monitoring samples to
suit the seasonal operations;
2. to treat data from "peak season" and "off season" periods as
though they came from two different regions, and to therefore
design separate compliance monitoring programs for each period,
Since the surveillance agency can specify the units in which the
self-monitoring data is to be reported, it is assumed in this task that
these units will be the same as those used to define the effluent standards
(see Taskfjj) • Therefore, no conversions of self-monitoring input data
should be needed; in the event they are needed, the user may refer to
Task[]2J, Procedure.
For the purposes of this entire hand calculation approach, a source
is defined as a separate outfall or discharge pipe, with its own set of
effluent standards. In the case of the constituent pH, pH Max and pH Min
are treated as separate constituents until TaskfSJ. The mean (m) of pH Max
and the mean (m) of pH Min (Table 4.5, Column 4) should be equal and re-
present the mean of all pH values.
75
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Procedure
1. For the first constituent at the first source (outfall) listed
in Table 4.1, enter the source name, constituent name and units
in the first three columns of Table 4.5 (Taskfjj) . The units to
be used will be those with which the effluent standards are
specified for this constituent (see Task("2}).
2. Using all the self-monitoring data collected for this consti-
tuent during the most recent monitoring period, find the sample
mean, maximum (and/or minimum), and sample size as described
below. If no processing of raw daily measurements (into means,
etc.) has been done, use Method A. If processing has been done,
use Method B. (Note: In allocation procedures for previous
monitoring periods, some data may not have been used because
its sample size was less than four (see TaskjTj, Steps 1 and 2).
This data can be conbined with data for the new monitoring
period in this step.
Method A: (for raw data)
sum of all values 1
mean, m
number of values
r=l
maximum, £ = maximum of the values = max (y )
n r
minimum, w = minimum of the values = min (y )
[for pH only] n r
sample size, n = number of values
where y is the r-th of n data values
76
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Method B; (for processed data)
Suppose the data for the last monitoring period was divided
up and summarized for R smaller reporting periods (e.g.,
months), and the input data consists of a mean, m , a
maximum, £ (or minimum, co ), and sample size, n , for
each reporting sub-period number r. Then for the entire
monitoring period:
R
£
m n
mean, m
maximum, £ =
minimum, w =
sample size, n =
maximum of the £ values = max (£ )
R
minimum of the co values = min (co )
R
R
f>
r=1 r
Enter the results in columns 4-7 of Table 4.5,
NOTE: When this Task Qj is being done in
a region for the first time, the
"data collected during the monitor-
ing period just completed," will in-
clude £ll_ the desired past self-monitor-
_
ing data collected.
3. Repeat the preceding Steps 1 and 2 for each constituent of
interest at the first source, following the constituent
order established in Table 4.1,
77
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4. Repeat the preceding Steps 1-3 for each source of interest
in the surveillance region, following the source order of
Table A.I.
78
-------
Table 4.5 Effluent data, Statistics and Probabilities
Y(Task 6)
Discounting constant, h(Task 7) -
TASK Q]
Self-ironitorlng Input data (record in source sequence)
Source
(1)
Constituent
Name
(2)
Units
(3)
Mean
m
(4)
*
Max
c
(5)
Kin
CO
(6)
Sample
Size
n
(7)
TASKQ]
Self-monitoring statistics
Est'd
Mean
V
(8)
Est'd
Std.
Dcv.
O
(9)
Distrib-
uLicn
L or N
(1C)
n
(ID
M
(12)
TASK [5]
Self + compliance
V
(13)
O
(14)
n
(15)
•o
(16)
TASKH
New cum. statis.
V
(17)
e
(18)
n
(19)
0
(20)
TASK 1 31
Probabilities
Norm'd
Effl't
Std.
X
(21)
*(x)
(22)
I'r . non-
viol 'n./
const .
Pi.1
(23)
Not required for pH nin,
tk
Required only for pK rain.
Note: This table can be duplicated for use in the hand calculations.
-------
TASKJ4J: ESTIMATE SELF-MONITORING STATISTICS
Objective
To obtain for each constituent occurring at each source, an esti-
mate of the mean and standard deviation of the newly entered self-monitor-
ing data.
Output
Tabulation of the estimated means and standard deviations in columns
8-12 of Table 4.5
Inputs
• Distribution types (from Table 4.1, TaskQ})
• Self-monitoring input data (from Table 4.5, Task 0)
References
• [1], Appendix A
• [1], Section V.I
• [1], Section IX.1
• [4], for the preparation of Figure 4.5
Discussion
The procedure employed in this task to obtain estimates of the
source mean and standard deviation from the sample mean and the maximum
SO
-------
requires that the number of measurements (sample size) upon which these
are based be greater than three.
If the sample size for a constituent is greater than three, then
the estimation procedure to be used differs between normal and lognormal
distribution types.
Procedure
1. For the first constituent at the first source, determine from
column 7 of Table 4.5, Task[3], whether the sample size n is
less than 4.
If n is less than 4, go to Step 2, otherwise proceed to Stepfsl.
2. For n < 4. In Table 4.5 write "INSUFFICIENT DATA" under Task 3,
The insufficient data may be saved for incorporation with the
data from the next monitoring period. Return to Step 1 and re-
start the procedure for the next constituent.
3. Determine from Table 4.1, TaskQ] whether the constituent's
distribution type is Normal or Lognormal (N or L), and which
Task^ alternative was used for it (Alternative 1 or 2).
If the distribution type is Normal (N), go to Step 4; if
Lognormal (L), go to Step 5.
4. For normal distributions.
a. Use the sample mean, m, from column 4 of Table 4.5,
TaskQj, as the best estimate of the source mean, y.
b. Use the sample size, n, from column 7 of Table 4.5,
31
-------
Task[3|, to determine the scaling factor, G, from
from Figure 4.3.
c. Compute the estimated standard deviation for the source
a, from
£ — m m -
o = — — or a = —
where m, £, and w are obtained from columns 4-6 of
Table 4.5, TaskQL
d. If this task has been performed previously to design a
prior compliance monitoring program for this constituent
and source, go to Step 4f; if not, go to Step 4e.
e. If both the following are true:
A. Alternative 2 was used in Task[T| (see Step 6)
and
B. o > 1.5u
then go to Step 4g; otherwise go to Step 4f.
NOTE: The factor of 1.5 used in condition B
is somewhat arbitrary, but is near-best
based on the limited known information.
Even if it were sufficiently in error
to yield the wrong distribution, the
effect on the resource allocation would
still be small — see the TaskfT],
Discussion.
f. Enter the values of y and a obtained in Steps 4a and 4c
above, into columns 8 and 9 respectively of Table 4.5,
Task[4j. Enter an "N" in column 10 of Table 4.5, Task[5J.
Go to Step 6.
82
-------
g. Change the distribution type from normal (N) to log-
normal (L) in column 4 of Table 4.1. Go to Step 5
immediately following and redetermine y and o as for
lognormal distributions.
5. For lognormal distributions:
a. Compute the ratio of the maximum to the mean, p = —
rn
where m and E, are obtained from columns 4 and 5 of
Table 4.5, Task 3.
b. Knowing the ratio, p, and the sample size, n, from
column 7 of Table 4.5, determine the estimated standard
deviation (of the logarithms of the measurements), o,
from Figure 4.4; interpolate carefully between curves
for different sample sizes, where necessary.
c. Compute the estimated mean (of the logarithms of the
measurements), v, from
2
Vi = l°810m ~ 1.1513 o
d. Enter the values of y and o obtained in Steps 5c and 5b
above into columns 8 and 9 respectively of Table 4.5,
- Enter an "L" in column 10 of Table 4.5, TaskQJ
6. Knowing the sample size n (from column 7 of Table 4.5), determine
the confidence parameters. Prescribe n, the confidence parameter
for the mean, to be
TI = n
and obtain v, the confidence parameter for the standard deviation
from Figure 4.5.
Enter the results into columns 11 and 12 of Table 4.5, Task[4].
83
-------
7. Repeat the preceding Steps 1-6 (as required) for each additional
constituent of interest at the first source.
8. Repeat the preceding steps 1-7 (as required) for each source
of interest in the surveillance region.
84
-------
00
3.2,
3.0
2.8
2.6
e>
u
rt
oo
s
2.2
1.8
1.6
1.4
1.21 1 1 1—I—I—I-
10
J I I I I I I
50
Sample Size, n
100
500
Figure 4.3 Variation of Scaling Factor, G, with Sample Size
for Normal Distributions
-------
1.5
Figure A. A
2 34
Ratio of the Maximum to the Mean,
Standard Deviation Estimated from the Mean and Maximum of
Lognormal Distributions, for Various Sample Sizes, n
-------
200
00
—I
o
01
O
C
CB
n)
01
o
c
0)
-o
•H
U-i
c
o
2 _
10
100
500
1000
Sample Size, n
Figure 4.5 Variation of the Confidence Parameter for Standard Deviation with Sample Size
-------
TASKIJJ: INPUT NEW COMPLIANCE MONITORING DATA
Objective
For each constituent, and for each source, tabulate all the new
compliance monitoring data collected during the monitoring period just
completed.
Output
Data on the constituents monitored by the surveillance agency at
each source in the region.
Inputs
Daily composite data values obtained in the compliance monitoring
program during the last monitoring period.
Discussion
It is assumed that grab sample data will not be included in com-
pliance monitoring input data, since the objective of the surveillance
exercise is to identiy violators, and violations are defined (via the
NPDES daily maximum effluent standard) in terms of daily composite samples.
The computational procedure requires that the units of effluent
standards and self-monitoring and compliance monitoring data are con-
sistent for any one constituent at a given source. Therefore, it is
required that the compliance monitoring data be converted, if necessary,
before input, to have the same units as the corresponding effluent
standards specified in TaskQJ. Information which may aid such conversions
is provided in Tables 4.3 and 4.4.
88
-------
Procedure
1. Follow the same source order as was established in Table A.I,
TaskQ.
At a given source with compliance monitoring data, copy or
record all such data collected during the monitoring period
just completed into Table 4.6. Ensure that the units of this
data are the same as those specified for the effluent standards
in Taskjj?]; if they are not, convert them as necessary (see
Discussion above).
NOTE: When this task is being done for the
first'time, these input data will in-
clude all the past compliance monitor-
ing data of interest which has been
collected.
2. Repeat Step 1 for each source in the region having compliance
monitoring data.
89
-------
Table 4.6
Compliance Monitoring Input Data
Source
Constituent
Name
Units
Monitored
Value
z
(1)
(2)
(3)
(4)
Note: This table can be duplicated for use in the hand calculations.
90
-------
TASK 6: COMBINE SELF-MONITORING STATISTICS AND COMPLIANCE MONITORING
DATA
Objective
To obtain, for each constituent, and for each source, new improved
estimates of the means and standard deviations of the data.
Output
Tabulation of improved means, standard deviations, and confidence
parameters in columns 13-16 of Table 4.5.
Inputs
• Self-monitoring statistics from Table 4.5, Taskfgl.
• Compliance monitoring data from Table 4.6, TaskMSl.
References
• [1], Section V.2
• [1], Appendix E
Discussion
Compliance monitoring data are treated differently in this pro-
cedure from self-monitoring data, since the former may be considered more
reliable and weighted accordingly.
Procedure
1. If only self-monitoring data is used, skip this task and go
to TaskQj, and write the words "same as TaskQ," in columns
13-16 of Table 4.5. Otherwise, select for the region, a value
91
-------
for Y» always greater than 1, and probably in the range of
1.5-3, but possibly much larger. This y value will represent
the greater weight (due to greater reliability) given to the
compliance monitoring data than to the self-monitoring data.
Therefore, one consideration might be the ratio of composite
to grab sample data in the self-monitoring input data (see
L Discussion). Enter the chosen y value above Table 4.5,
NOTE: Once the user becomes familiar with the
intent and effect of y, there is no rea-
son why it could not be varied with the
constituent, source, etc., treated.
2. For the first constituent and source with a compliance monitor-
ing measurement, z, and with sufficient data from self-monitor-
ing statistics (see Step 2, TaskRl);
a. Compute the improved estimate of the process mean,
z + yn/Y
P 1 + n/Y
where z is obtained from Table 4.6, Task[31j and y and
n are obtained from Table 4.5, Taskpl.
b. Compute the improved estimate of the process standard
deviation
- = /z2 + (vo2 + ny2)/y - (1 + n/y)y2
° V 1 + v/Y
where o and v are also obtained from Table 4.5, TaskQ.
c. Compute the new confidence parameter for the estimated
mean
fj = 1 + n
92
-------
d. Compute the new confidence parameter for the estimated
standard deviation
v = 1 + v
3. If more than one compliance monitoring measurement, z, was
taken for the same constituent and source during the last
monitoring period, then successively combine them into the
statistics by repeating Step 2 above for each measurement.
4. Enter the final results for jl, d, n and v obtained from
Step(s) 2 (and possibly 3), into columns 13-16 of Table 4.5,
5. Repeat Steps 2-4 for each source and each constituent where
compliance measurements were taken during the most recent
monitoring period.
-------
TASK[TJ: COMBINE LATEST STATISTICS INTO CUMULATIVE STATISTICS FOR
COMPLIANCE MONITORING PERIOD
Objective
To obtain, for each constituent and each source, estimates of the
mean and standard deviation of the data based on all past measurements.
Output
Tabulation of cumulative means, standard deviations, and confidence
parameters in columns 17-20 of Table 4.5.
Inputs
Cumulative estimates (if any) of process statistics from previous
allocation period.
Latest improved estimates of process statistics from Table
4.5,
References
• [1], Section V. 2
• [1], Appendix E
Discussion
One or two of the formulas used in this task look rather complex.
However, only straightforward substitution and computation are required
to evaluate them, for which a hand calculator should be found very help-
ful. If the size of the formula is of concern to a user, it is suggested
94
-------
he develop a table for operating on the various terms in a step-by-step
procedure.
Procedure
1. Determine whether this compliance monitoring allocation pro-
cedure has been used previously. If it has, go to Step 3;
otherwise go to Step 2.
2. No previous statistical computations or monitoring allocations
have been made with this procedure. Therefore, the cumulative
statistics desired in this task will be derived entirely from
the "latest" (all previous) data, summarized in Table 4.5,
In columns 17-20 of Table 4.5 (Task 7), write "VALUES SAME
AS FOR TASKfU."
3. Keep at hand the cumulative statistics (in Table 4.5, Taskf7|)
from the most recent, previous application of this allocation
procedure. These previous cumulative statistics will be re-
presentative of all data preceding the latest monitoring data
used in Tasks 2-5.
Select a value for the data discounting constant, h, for the
region. This value will probably be in the range 1-3, but may
be less than one. It effectively discounts past data (relative
to new data) by limiting their sample size to h times the
size of the new sample. It should therefore be made smaller
for longer monitoring periods.
Enter the chosen h value over Table 4.5.
-------
NOTE: Once the user becomes familiar with
the intent and effect of h, there is
no reason why it could not be varied
with the constituent, source, etc.,
treated, or with the age of the data.
Update the cumulative statistics for one constituent at one
source as follows: Let a "-" indicate a new statistic for
the latest monitoring period (taken from columns 13-16 of
Table 4.5, TaskQJ); a "~" without & subscript will indicate
cumulative statistics obtained from the previous application of
this allocation procedure (see Step 3). A "A" with a subscript
"1" indicates statistics updated for this application. Then:
a. Compute the new cumulative estimate of the process mean,
ny + ny
y, - ~ -
i n + n
b. Compute the new cumulative estimate of the process
standard deviation
°1
ro 2 * A 2 " *2
/va + ny + va + ny
•N. A
V + V + 1
c. Compute the new confidence parameter for the cumulative
estimated mean,
r\ = min (n + n), hn I
d. Compute the new confidence parameter for the cumulative
standard deviation
A r ~ A ~~|
v, = min (v + v + 1), hv
96
-------
e. Enter the values of U-, , o , r\ and v obtained in
Steps 5a-d above, into columns 17-20 of Table 4.5,
TaskPTj.
6. Repeat Step 5 for each additional constituent of interest at
the same source.
7. Repeat Steps 5-6 for each source of interest in the surveil-
lance region.
97
-------
DETERMINE PROBABILITY OF NON-VIOLATION PER CONSTITUENT
Objective
To obtain, for each constituent at each source, its probability
of non-violation.
Output
A tabulation of the probabilities of non-violation in columns 21,
22, and 23 of Table 4.5.
Inputs
• Distribution types (from Table 4.1, TaskQ)
• The cumulative statistics for each constituent at each source
(from Table 4.5, TaskQJ) .
• The effluent standards (from Table 4.2,
References
[1], Appendix C, Sections C.2 and C.4
Procedure
For a given source, i, and a given constituent, j:
1. Determine from Table 4.5, Task[4] whether the constituent's
distribution type is normal (N) or lognormal (L). If it is
type -N, go to Step 2; if it is type -L, go to Step 5.
98
-------
2. Check whether or not the constituent is pH. If it ±s pH, go
to Step 3; otherwise go to Step 4.
3. For pH only. During this step, statistics for pH Max and pH
Min (columns 17-20 of Table 4.5) will be combined to produce
a probability of no violation of the overall pH standards.
Note that quantities such as o (standard deviation for pH Max)
and 5 (standard deviation for pH Miri) can both be required in
one calculation of joint probability. In this step, pH Min
and pH Max should be treated as one constituent.
Compare the estimated mean y (from column 17 of Table 4.5) with
the standards for maximum and minimum pH, S and £ respectively
(from column 4 of Table 4.2), and proceed as follows:
If u < S_, go to Section (i)
S^ < M < S, go to Section (ii)
u > S, go to Section (iii)
(i) For p < S (pH only).
Compute the normalized effluent standard
§ - y
X — =:
a
where
S = pH Min standard from column 4 of Table 4.2
y = estimated mean from column 17 of Table 4.5
~ = cumulative estimate of the standard devi-
° ation of pH Max, from column 18 of Table
4.5, Task]""
99
-------
Enter the result for x into column 21 of Table 4.5,
TaskQO.
Determine 0(x) from Table 4.7. Enter the result in-
to column 22 of Table 4.5, Task[8j.
Determine the constituent (pH) probability of non-
violation at this source
p±. = I ~ *(x)
Enter the result into column 23 of Table 4.5, Task[8].
Go to Step 6.
(ii) For S < y < S (pH only).
Compute the normalized upper and lower effleunt
standards
V - § _ g _ -
2 o
where
g is as above,
A
2 = cumulative estimate of the standard devi-
ation of pH Min, from column 18 of Table
4.5, Task[7].
Enter the results for x and x into column 21 of
Table 4.5, TaskQO, using a row for each and
identifying which is which.
Determine *(x) and *(x) from Table 4.7. Enter the
results into column 22 and the corresponding rows
of Table 4.5, TaskQO.
Determine the probability of non-violation of pH
at this source (overall, not separately for pH Max
and pH Min) from
100
-------
Enter the result into column 23 of Table 4.5,
TaskQQ.
Go to Step 6.
(iii) For y > S (pH only).
Compute the normalized effluent standard
f\ •—
x = u:s
n
where
2 is as above.
Enter the result for x into column 21 of Table 4.5,
Task|j).
Determine (x) from Table 4.7. Enter the result
into, column 22 of Table 4.5, TaskQO.
Determine the probability of non-violation of pH
at this source
Pij = ~2 ~ *^
Enter the result into column 23 of Table 4.5,
Task [8].
Go to Step 6.
4. For Normal Distributions (except pH). Compute the normalized
effluent standard
x =
where y and CT are taken from Table 4.5, TaskQJ. a^d S is taken
from Table 4.2.
101
-------
NOTE: v and a must have the same units as S, so check
column 3 of Table 4.5 against column 3 of Table
4.2.
Enter the result for x into column 21 of Table 4.5, TaskCsl
Determine (x) from Table 4.7. Enter the result into column 22
of Table 4.5, Task[8J.
Determine the constituent probability of non-violation at this
source
Pij - | + *<*)
Enter the result into column 23 of Table 4.5, Task[|J.
Go to Step 6.
5. For Lognormal Distributions . Compute the normalized effluent
standard
x =
losios -
where u, a, and S are obtained in the same way as for Step 4,
and the same check on their units should be made.
Enter the result for x into column 21 of Table 4.5, Taskf^J.
Determine 4>(x) from Table 4.7. Enter the result into column 22
of Table 4.5, TaskQi].
Determine the constituent probability of non-violation at this
source
I
P. . = ~r + $(x)
ij 2
Enter the result into column 23 of Table 4.5, Task[|].
Go to Step 6.
102
-------
6. Repeat Steps 1-5 (as appropriate) for each constituent j at
the same source i.
7. Repeat Steps 1-6 (as appropriate) for each source i in the
region.
103
-------
Table 4.7
The Standard Normal Cumulative Distribution Function, $(x)
X
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
0.00
.00000
.03983
.07926
.11791
.15542
.19146
.22575
.25804
.28814
.31594
.34134
.36433
.30493
.40320
.41924
.43319
.44520
.45543
.46407
.47128
.47725
.48214
.48610
.48928
.49.180
.49379
.49534
.49653
.49744
.49813
0.01
.00399
.04380
.08317
.12172
.15910
.19497
.22907
.26115
.29103
. 31859
.34375
.36650
.38686
.40490
.42073
.43448
.44630
.45637
.46485
.47193
.47778
.48257
.48645
.48956
.49202
.49396
.49547
.49664
.49752
,49819
0.02
.00798
.04776
.08706
.12552
.16276
.19487
.23237
.26424
.29389
.23121
.34614
.36864
.38877
.40658
.42220
.43574
.44738
.45728
.46562
.47257
.47831
.48300
.48679
.48983
.49224
.49413
.49560
.49674
.49760
.49825
0.03
.01197
.05172
.09095
.12930
. 16640
.21094
.23565
.26730
.29673
.32381
.34850
.37076
.39065
.40824
.42364
.43699
.44845
.45818
.46633
.47320
.47882
.48341
.48713
.49010
.49245
.49430
.49573
.49683
.49767
.49831
0.04
.01595
.05567
.09483
.13307
.17003'
.20540
.23891
.27035
.29955
.32639
.35083
.37236
.39251
.40988
.42507
.43822
.44950
.45907
.46712
.47381
.47932
.48382
.48745
.49036
.49266
.49446
.49585
.49693
.49774
.49836
0.05
.01994
.05962
.09871
.13683
.17364
.20884
.24215
.27337
.30234
.32894
.35314
.37493
.39435
.41149
.42647
.43943
.45053
.45994
.46784
.47441
.47982
.48422
.48778
.49061
.49286
.49461
.49598
.49702
.49781
.49841
0.06
.02392
.06356
.10257
.14058
.17724
.21226
.24537
.27637
.30511
.33147
.35543
.37698
.39617
.41309
.42786
.44062
.45154
.46080
.46856
.47500
.48030
.48461
.48809
.49086
.45305
.49477
.49609
.49711
.49788
.49846
0.07
.02790
.06749
.10642
.14431
.18082
.21566
.24857
.27(-x) = -4>(x)
104
-------
TASK[9]: DETERMINE PROBABILITY OF NON-VIOLATION PER SOURCE
Objective
To obtain, for each source, its probability of non-violation.
Output
A tabulation of the probabilities of non-violation in columns 1,
2, and 3 of Table 4.8.
Inputs
The probabilities of non-violation for each constituent at
each source (from Table 4.5, Taskf"8|) .
References
• [1], Section VI.3
• [1], Appendix B
• [1], Section VIII.3
Procedure
For a given source, i:
1. Indicate the source number in column 1 of Table 4.8.
2. Select whether the various constituents at the source as
a group are to be described as statistically dependent (SD)
or statistically independent (SI). If SD, all the constituents
105
-------
vary together in time in the same way (are completely cor-
related) maintaining the same ratios to one another; if SI,
there is zero statistical correlation between their variations,
NOTE: Since sufficient data to ascertain the
exact correlation between various con-
stituents are not readily available,
one of the above extremes must be as-
sumed. Appendix B of [1] suggests SD
is less likely to be true than SI. Sen-
sitivity studies (Section 8.3 of [1]
revealed that in many cases the resulting
compliance monitoring priorities will be
insensitive to this selection; however,
cases could clearly be devised where the
priorities would be very sensitive to the
correlation assumption.
Indicate the type of dependence (SD or SI) chosen in column
2 of Table 4.8, Task[9].
3. Accordingly, knowing the probabilities of non-violation,
p . . , of the various constituents at source i, from column
»'. 23 of Table 4.5, Task[&j, determine the source probability
of non-violation, P., from either a or b below.
.^ i
•' a. If dependent (SD) , then
f± = min(p )
3
! i.e., P. is the smallest of the constituent
probabilities at this source i.
b . If independent (SI) , then
106
-------
i.e., P. is the product of all the constituent pro-
babilities at this source i.
Enter the result for P. into column 3 of Table 4.8,
i
4. Repeat Steps 1-3 for each source i in the region.
107
-------
-*„ •««•. v
Table 4.8
Ranges of Sampling Rates and Expected Extents of Undetected Violations
Source
No.
i
(1)
Constitu-
ent Inter-
dependence
SD/SI
(2)
TASK GO
Prob. of
Non-
violation
Pi
(3)
TASK |OJ
Violation
Weighting
Factor
Ci
(4)
TASK jll|
Min . No .
Samples
Required
*i
(5)
Max. No.
Samples
Allowed
Li
(6)
TASK (lU
Alternative Expected Extents of
Undetected Violations, C. (s.), for
Various Sampling Rates, s.
V1
(7)
2
(8)
3
(9)
4
(10)
5
(ID
6
(12)
7
(13)
8
(14)
o
00
Note: This table can be duplicated for use in the hand calculations.
-------
TASK p.0|; DETERMINE THE VIOLATION WEIGHTING FACTOR PER SOURCE
Objective
To obtain, for each source, a quantitative factor representing the
significance attached to violations which might occur there.
Output
A tabulation of violation weighting factors in column 4 of Table
4.8. These factors are found by completing an interim Table 4.9.
Inputs
• Effluent standards, from Table 4.2, TaskfT].
• Constituent distribution type (normal and lognormal), from
Table 4.5. TaskQ.
• Cumulative estimates of constituent means and standard devi-
ations, from Table 4.5, TaskpTJ
• x (normalized effluent standard), 0(x) , and p (probability of
non-violation) for each constituent at each source, from
Table 4.5, TaskQJJ.
• Receiving water concentration standards for the region and
the constituents of interest (need depends upon options
chosen).
References
• [1] , Section VI - Introduction
• [1], Section 6.3
• [1], Appendix C, Section C.I
109
-------
• [1], Appendix C, Section C.2.1
• [1], Section VI.2
Discussion
The purpose of the Violation Weighting Factor is to make available
to the user alternative ways in which he can weight the allocation of his
surveillance resources. This is done by weighting the violations.
One obvious way to do this is to weight them in proportion to the
environmental damage caused in the receiving waters, through the use of
environmental damage functions (damage as a function of concentration)
for each constituent. While desirable, this approach necessitates much
detailed computation, and has therefore, been excluded from this hand
calculation procedure. It is included in the computerized procedure,
however. (See Sections 5 and 7 of this handbook, and [1], Section 6.)
Two simpler alternative weighting methods have been included in
this hand calculation approach. One gives all violations equal weights,
the other weights them by the amount by which the standards are exceeded.
With these simpler methods, the effects of the effluents on the receiving
waters are still taken into account indirectly, since the effluent stand-
ards should have been set with these effects in mind.
Since the second simpler method contains a number of options and
since different procedures are required for different constituents, it
has been necessary to break this task up into numerous components, many
of which may turn out to be skipped in any one application.
110
-------
Procedure
1. For the entire region, select one of the following two alter-
native methods for assigning violation weighting factors:
Method 1: Set all the weighting factors to be equal. This
has the effect that the sampling frequency then
depends only upon the probability of violation,
Task GO.
Method 2; Make the weighting factors increase with the extent
by which the standard is exceeded. This has the
effect of directing compliance monitoring towards
those dischargers with the more serious violations
of the standards, where conviction is easier.
Indicate the method selected above Table 4.9.
If using Method 1, go to Step 2; if Method 2, go to Step 3.
2. Method 1. For all sources, set the source violation weighting
factor, c. = 1.
Enter this result into column 4 of Table 4.8, Task jLO|.
Go to Task (Tl|.
3. Method 2. Copy, in the same order, the information from columns
1 and 2 (Task[3l) and 10 (TaskQj) of Table 4.5 into columns 1,2,
and 3 respectively of Table 4.9.
4. For each constituent at one source, select a weighting factor
function (WFF) type from the following three types, (A, B or C)
and select a WFF coefficient k for each:
111
-------
a, WFF Type A; (General, for Normal or Lognormal
constituents, excepting pH)
W
where
M
( k(M-S), M > S
10, M < S
constituent mass loading rate or concentration
in effluent, depending upon the form of S
applicable effluent standard for M
a WFF coefficient (see below)
With this type of WFF, the weighting factor, W, for a
constituent is proportional to the amount by which M
exceeds its standard.
The coefficient, k, may be chosen to specify the principle
upon which the WFF is preferred to operate, such as:
1. k a — for each constituent
8
where 6 is the receiving water concentration
standard for the constituent. This will result
in, W, varying as the magnitude of the exceed-
ance.
In the case of BOD, assume the in-stream standard
to be as follows :
1 2
e
15.0
10.0
5.0
Type of Streams
Fast flowing, shallow
streams
Slow flowing, shallow
streams and fast flowing,
medium to deep streams
Slow flowing, deep rivers
and estuaries
112
-------
2. k a — for each constituent at each source
O
This will result in W varying as the number
of times by which the standard is exceeded.
The difference between these two alternatives for k is
illustrated in Table 4.10. Alternative (1) is seen to
penalize the larger dischargers, and is therefore, gen-
erally preferred; alternative (2) penalizes the smaller
dischargers.
k may also be weighted to emphasize concern for any
particular constituent, regardless of its source.
WFF Type B; (For Lognormal constituents only, e.g.,
colifoons)
The concentrations (and hence loading rates) of certain
constituents, particularly coliform bacteria, vary so
rapidly that their orders of magnitude are of more
significance than their actual size. As a result, their
type of frequency distribution in Task[T], will usually
be lognormal (specifically required for coliforms), and
the following Type B WFF is a more appropriate measure
of standard exceedance.
/k(log M - log S), M > S
W 10, M s S
Here, k, would be either (1) I/log 9, or (2) I/log S.
W, M, S, and k are as defined in Subsection a above.
NOTE: A lognormal (L) distribution
in TaskQp, Table 4.1, is
specifically required for
constituents to be assigned
a Type B WFF.
113
-------
if*'
£; •
i*}
«:•
ji;
c. WFF Type C; (for pH only)
For pH, the logorithm of the hydrogen ion concentration
has already been taken, and the possible range of values
is very limited. With this constituent, therefore, the
weighting factor is the amount by which the pH standard
is exceeded (in either direction, since there are both
upper and lower standards).
W
w =
where
S
S
W
k(S - M), M < S
0, M > S
k(M - S) , M > S
0, M < S
minimum pH standard
maximum pH standard
weighting factor for pH (Min or Max)
and commonly, k = k * 1.
Record the type of WFF selected for this constituent in column
4 of Table 4.9. If the selection is Type B, check that the
corresponding distribution is lognormal (Type "L" in column 3
of Table 4.9) as is required. Record the magnitude chosen for
the WFF coefficient, k, (or k and k, identifying which is
which) in column 5 of Table 4.9.
5. Repeat Step 4 for each constituent at the same source.
6. For each constituent at the same source, compute the expected
extent of violation, D, from the appropriate section below,
114
-------
depending upon the WFF type as follows:
For WFF Type A, go to Section a
For WFF Type B, go to Section b
For WFF Type C, go to Section c
a. For WFF Type A; (W = k[M-S])
If the constituent distribution is normal (N) (from
column 3 of Table 4.9), go to Subsection (1); if
lognortnal (L), go to Subsection (2) .
1. For Normal Distribution (W = k[M-S])
D = kojf(x) - x [l-p]|
where
x = probability of non-violation per
constituent, from column 23 of
Table 4.5, Task Of]
o = cumulative estimate of the standard
deviation, from column 18 of Table
4.5, TaskQ]
f(x) is given by Table 4.11
k is recorded in column 5 of Table 4.9
2. For Lognormal Distribution (W = k[M-S])
D = k exp"' ' A °
2 /
2.
where
p, o, and k are as above, and
115
-------
y = cumulative estimate of the mean
from column 17 of Table 4.5,
Task(T|
S = effluent standard, from Table
log S = loglQS
A = InlO = 2.3026
$(x) is given by Table 4.7
Go to Step 7.
b. For WFF Type B (W = k[log M-log S]
NOTE: This may be used only for
constituents with distri-
bution type L in Table 4.5,
TaskQj.
."'' "'
•» . D = kajf(x) - x[l-p]j
«''.;, ' '
{(_ •• where
. * • ' (
' x, k, o, f and p are as above
-:!''.
ji •• Go to Step 7.
•• •'.
c. For WFF Type C (W = k[S-M], W = k[M-S]
, n
'. •' For pE only, compare the estimated mean, v (from
ii column 17 of Table 4.5, with the standards for
maximum and minimum and minimum pE, S and S re-
spectively (from column 4 of Table 4.2), and pro-
ceed as follows: if
/\
y < S, go to Subsection (i).
S < y < S, go to Subsection (ii).
y > S, go to Subsection (iii).
116
-------
(i) For u < S (pH only)
D = k
where
(o - a) S - u
2TT
+ alf(x) + x*(x)j
x = normalized effluent standard from
column 21 of Table 4.5, Task[jB)
/»
a = cumulative estimate of the standard
deviation of pH Min, from column 18
of Table 4.5, Taskft]
a = cumulative estimate of the standard
deviation of pH Max, from same
location
is obtained from column 22 of Table
4.5, Task QO
f(x) is given by Table 4.11
k is recorded in column 5 of Table 4.9
Go to Step 7.
(ii) For S < y < S (pH only)
D = kcr
f(x) + x[0.5-*(x)]
4 ko
f(x)
+ x[0.5-*(x)]
where
a, o, and f are as above, and
x and x are obtained from column 21 of
Table 4.5, TaskQO
$(x) and
-------
(iii) For p > S (pH only)
- k.
where
5 ^ u - s
27T ' 2
a, a, and f are as above, and
x and •' 8. Repeat Steps 6-7 for all constituents of interest at the same
V * *' ;
•'•" • "; source.
.T :•.',
£J j :
/j ••• 9. Of the expected extents of violation, D, for the various con-
'ttt stituents at this same source i, find the largest, to be the
^•i source violation weighting factor, c , i.e.,
M:-; i
i :' |
c. = max(D)
' ' ** r*^-m
.<*t Enter the result into column 4 of Table 4.8, Task (lOJ.
lil,'
10. Repeat Steps 4-9 (Method 2).for each source of interest in
the region.
118
-------
Table 4.9
Record of Task |10| Options and Calculations
Violation weighting factor assignment method (I or II):
Source
No.
i
(1)
Constituent
Name
(2)
Distri-
bution
L or N
(3)
Type of
WFF
A/B/C
(4)
WFF
Coefficient
k
(5)
Expected
Extent of
Violation
D
(6)
Note: This table can be duplicated for use in the hand calculations.
119
-------
Table 4.10 Examples of Alternative Type of Weighting
Factor Functions (WFF)
(Comparison for the same constituent, Q = 100)
Let S
Let M
Then (M-S)
(1) k = 1/9
W = (M-S)/ 9
(2) k = 1/S
W = (M-S)/S =
Source 1
100
600
500
5
5
Source 2
10,000
10,500
500
5
0.05
Source 3
10,000
12,000
2,000
20
0.2
120
-------
Table 4.11 The Standard Normal Probability Density Function, f(x)
ix
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
0.00
.3989
.3970
.3910
.3814
.3683
.3521
.3332
.3123
.2897
.2420
.2179
.1942
.1714
.1497
.1295
.1109
.0940
.0790
.0656
.0540
.0440
.0355
.0283
.0224
.0175
.0136
.0104
.0079
.0060
.0044
.0033
.0024
.0017
.0012
.0009
.0006
.0004
.0003
.0002
0.01
.3989
.3965
.3902
.3802
.3668
.3503
.3312
.3101
.2874
.2396
.2155
.1919
.1691
.1476
.1276
.1092
.0925
.0775
.0644
.0529
.0431
.0347
.0277
.0219
.0171
.0132
.0101
.0077
.0058
.0043
.0032
.0023
.0017
.0012
.0008
.0006
.0004
.0003
.0002
0.02
.3989
.3961
.3894
.3790
.3653
.3485
.3292
.3079
.2850
.2371
.2131
.1895
.1669
.1456
.1257
.1074
.0909
.0761
.0632
.0519
.0422
.0339
.0270
.0213
.0167
.0129
.0099
.0075
.0057
.0042
.0031
.0022
.0016
.0012
.0008
.0006
.0004
.0003
.0002
0.03
.3988
.3956
.3885
.3778
.3637
.3467
.3271
.3056
.2827
.2347
.2107
.1872
.1647
.1435
.1238
.1057
.0893
.0748
.0620
.0508
.0413
.0332
.0264
.0208
.0163
.0126
.0096
.0073
.0055
.0040
.0030
.0022
.0016
.0011
.0008
.0005
.0004
.0003
.0002
0.04
.3986
.3951
.3876
.3765
.3621
.3448
.3251
.3034
.2803
.2323
.2083
.1849
.1626
.1415
.1219
.1040
.0878
.0734
.0608
.0498
.0404
.0325
.0258
.0203
.0158
.0122
.0093
.0071
.0053
.0039
.0039
.0021
.0015
.0011
.0008
.0005
.0004
.0003
.0002
0.05
.3984
.3945
.3867
.3752
.3605
.3429
.3230
.3011
.2780
.2299
.2059
.1826
.1604
.1394
.1200
.1023
.0863
.0721
.0596
.0488
.0396
.0317
.0252
.0198
.0154
.0119
.0091
.0069
.0051
.0038
.0028
.0020
.0015
.0010
.0007
.0005
.0004
.0002
.0002
0.06
,3982
.3939
.3857
.3739
.3589
.4410
.3209
.2989
.2756
.2275
.2036
.1804
.1582
.1374
.1182
.1006
.0848
.0707
.0584
.0478
.0387
.0310
.0246
.0194
.0151
.0116
.0088
.0064
.0050
.0037
.0027
.0020
.0014
.0010
.0007
.0005
.0003
.0002
.0002
0.07
.3980
.3932
.3847
.3726
.3572
.3391
.3187
.2966
.2732
.2251
.2012
.1781
.1561
.1354
.1163
.0989
.0883
.0694
.0573
.0468
.0379
.0303
.0241
.0189
.0147
.0113
.0086
.0065
.0048
.0036
.0026
.0019
.0014
.0010
.0007
.0005
.0003
.0002
.0002
0.08
.3977
.3925
.3836
.3712
.3555
.3372
.3166
.2943
.2709
.2227
.1989
.1758
.1539
.1334
.1145
.0973
.0818
.0681
.0562
.0459
.0371
.0297
.0235
.0184
.0143
.0110
.0084
.0063
.0047
.0035
.0025
.0018
.0013
.0009
.0007
.0005
.0003
.0002
.0001
0.09
.3973
.3918
.3825
.3697
.3538
.3352
.3144
.2920
.2685
.2203
.1965
.1736
.1518
.1315
.1127
.0957
.0804
.0669
.0551
.0449
.0363
.0290
.0229
.0180
.0139
.0107
.0081
.0061
.0046
.0034
.0025
.0018
.0013
.0009
.0006
.0004
.0003
.0002
.0001
Note: f(-x) = f(x)
121
-------
TASK [Li]: ESTABLISH LIMITING SAMPLING RATES
Objective
To establish limits on the surveillance sampling rate desired at
each source.
Output
A tabulation of the minimum and maximum number of samples required
at each source listed in columns 5 and 6 of Table 4.8.
Inputs
Information on:
• Past sampling rates
• Established policy (if any), on minimum and maximum
sampling rates
• Suspected trouble spots, based on self-monitoring or
ambient receiving quality data
* Length of planned monitoring period
References
• [1], Section VII.1
Procedure
Based on the information provided by the inputs, assign a mininum
and maximum number of samples required at each source. Enter these into
columns 5 and 6 of Table 4.8.
122
-------
TASK |12J: DETERMINE ALTERNATIVE EXPECTED EXTENTS OF UNDETECTED VIOLATIONS
Objective
To obtain, for each source, expected extents of undetected violations
for various sampling rates.
Output
A list of expected extents of undetected violations for each can-
didate sampling rate recorded in columns 7-14 of Table 4.8.
Inputs
• Minimum and maximum sampling rates (from Table 4.8, Task [H])
• Violation weighting factors (from Table 4.8, Task (ic|)
• Probabilities of non-violation (from Table 4.8, Task{"9b
References
[1], Section VI.3
Procedure
1. For each source i:
In Table 4.8, Task J12], blank out spaces under s values
less than i. or greater than L..
NOTE: The user can extend the table for larger
values of s., if necessary. The sampling
rate limits, SL. and L., are given in columns
5 and 6 of Table 4.8.1 If £.=0, no column
is needed for s.=0 because this eventually
is considered later.
123
-------
I )
Hi.
2. For a given source i:
a. For the lowest s. value, compute the corresponding ex-
pected extent of undetected violation, C., from
C.(s.) = c.P. X
where
p. and c. are taken from columns 3 and 4 (Tasks (ITI
i i
and 0 of Table 4.8
Enter the result in Table 4.8 appropriate s. column
under Task |12|.
b. For the next s. value, compute C. by multiplying the
result of Step 2a again by p.. Enter the result in
Table 4.8, next column under Task (T2J.
c. Repeat Step 2b for all s values of interest, i.e., not
blanked out.
3. Repeat Step 2 for each source in the region.
124
-------
TASK [13J: DETERMINE COST TO SAMPLE EACH SOURCE ONCE
Objective
To obtain, for each source, the total cost of collecting, analyzing
and reporting a surveillance monitoring sample.
Output
A list of component costs and a total sampling cost for each source.
Output is recorded in Table 4.12.
Inputs
• Man-hours required to sample each source and process resulting
data
• Unit cost of labor
• Travel distance to sample each source
» Unit cost of field transportation
• Cost of expended field equipment
• Laboratory analysis charge for each constituent of interest
References
• [1], Section IX.1 (Table 9.2)
• [1], Appendix D
125
-------
Procedure
1. Enter names of constituents to be checked in headings of columns
10 through 15 in Table 4.12.
NOTE: The user can increase the number of
these columns as required by his list
of constituents
2. For a given source i:
a. Enter the above input information (input items a-e) into
columns 2-5 and 8 respectively of Table 4.12.
3. Multiply contents of column 2 by column 3, and enter results
in column 6 of Table 4.12.
4. Multiply column 4 by column 5, and enter the result in column
7 of Table 4.12.
,. ...... 5. Enter in columns 10-15 of Table 4.12, where appropriate, the
^;'••••• constituent analysis cost for each constituent to be analyzed
{•••;';' at an individual source. The constituents to be analyzed at
any given source are listed in Table 4.5, TaskQJ.
' • 'i'
i'/." NOTE: The analysis costs will probably be quite
!Ji. small by comparison with the cost of the
man-hours and travel, columns 6 and 7.
6. Add the contents of columns 6-8 to obtain total cost per
sample. Enter the results in column 9. Add the contents
of columns 9-14 in Table 4.12, to obtain the total cost of
a sample at an individual source; enter the result in the
last column.
7. Repeat Steps 2-6 for each source of interest in the region.
126
-------
Table 4.12 Resources Needed to Monitor Each Source Once
Source
No.
i
(1)
Man
Hours
Per
Sample
(2)
Cost
Per
Man
Hours
(3)
Travel
Miles
Per
Sample
(4)
Cost
Per
Mile
(5)
Per Sample Cost of:
Man
Hours
(6)
Travel
(7)
Expend .
Equip' t.
(8)
Total
Per
Sample
Cost
(9)
Laboratory Analysis
Charge/Constituent
(add constituent names)
#1
(10)
#2
(ID
//3
(12)
l?4
(13)
05
(14)
#6
(15)
Total
Cost
Note: This table can be duplicated for use in the hand calculations.
-------
TASK |14j; TABULATE MARGINAL RETURNS
Objective
To obtain, for each source, the marginal return from each additional
surveillance monitoring sample collected there.
Output
A tabulation of marginal returns for each sample to be taken at each
source-. Output is recorded in Table 4.13.
Inputs
• Alternative expected extents of undetected violations, C.,
P'^' from Table 4.8, Task [H]. 1
•" ;•'• • Costs to sample each source once, r., from Table 4.12, Task |13l.
j / ' S 1
"'!!! References
it'''
• [1], Section VII.2
, .-,. Discussion
The marginal return, \i. , at a source i, varies with the sampling rate,
s., there. As the source is sampled more frequently (s. increases), the
expected extent of undetected violations, C., decreases. Therefore, the
marginal return for a given sample, y.(s.), is defined to be the incremental
decrease in C , resulting from taking that single sample, divided by the
cost, r., to take that sample. The cost, r., includes the analysis of
all constituents of interest in the sample.
128
-------
Procedure
1. Enter the source numbers into Table 4.13, and for each source
blank out spaces under y. which correspond to those blanked
out in Table 3.8 under Task ^2J. In addition, for each source
also blank out in Table 4.13, the p. space under, s. = £. ,
where H. is given in column 5 of Table 4.8, Task O.
1 fc^^—*
2. For a chosen source, i, if the marginal return, u., for sample
s. = 1, has been blanked out, skip to Step 4, otherwise proceed
to Step 3.
3. For the same source, i, and for sample number 1 (s. = 1), compute
the marginal return
c. - C (1)
where c. and C.(l) are taken from columns 4 and 7 of Table 4.8,
and r. is taken from Table 4.12. Enter y.(l) into the second
column of Table 4.13.
4. For the next sample number, s., at the same source, if y has
been blanked out (i.e., if s. < H. ), then increase s. by 1
and restart this Step 4. Otherwise, compute the marginal return
C.(s.-l) - C.(s )
(\ 11 -LI
i Si) = rT
where the C's are taken from Table 4.8 and r. is taken from
Table 4.12. Enter the result, p.Cs..^), into the appropriate
s. column of Table 4.13.
i
129
-------
ti-
lt
5. Repeat Step 4 for each subsequent sample, s., not blanked out
(i.e., s± < L± ) in Table 4.13.
NOTE: The user can extend the table for larger
values of s., if necessitated by an ex-
tended Table 4.8.
6. Repeat Steps 2-5 for each source in Table 4.13.
130
-------
Table 4.13
Marginal Returns for Each Source
Source
No.
i
Marginal return, Uj(s.), from one additional sample, number s
V1
2
3
4
5
6
7
8
Note: This table can be duplicated for use in the hand calculations.
-------
TASK |15|: PRESELECT INITIALLY ALLOCATED SAMPLES
Objective
To preselect those samples needed to meet the previously established
minimum requirements for each source.
Output
A listing of the samples required to meet minimum requirements, with
the resulting degrees of undetected violation and monitoring resources re-
quired. Table 4.14 is utilized.
Inputs
: • Minimum sampling rates, &., desired at each source (from
Table 4.8, Task (ll|). *
• Violation weighting functions, c., for all sources (from
Table 4.8, Task (lOJ) . 1
i>. •'..., • Expected extents of undetected violations, C.(s.), for all
f! "• sources (from Table 4.8, Task J12|). 1 1
i • f * *
• Resources needed to monitor each source once, r., for all
sources (from Table 4.12, Task J13J) . """
"''•• Discussion
Since the initially allocated samples treated in this task must be
included to meet the minimum requirements established in Task (O, no choice
may be exercised as to whether or not they may be included. Therefore,
their marginal returns and ordering are of no consequence, and so these
computations have been omitted from this task to save labor.
132
-------
Procedure
1. Complete the first line of Table 4.14 for the case when no
surveillance monitoring samples would be collected. In that
case
Obtain this quantity Vc .), by summing all the entries in
column 4 of Table 4.8. Enter the result in both columns 5
and 6, row 1, of Table 4.14. Enter a "0" in column 8, row 1,
of Table 4.14.
2. Find the first source in Table 4.8 with JL > 0. If all £± = 0,
go to Task [l6j. In order to minimize the computations, all the
£ samples required as a minimum at that source, will be treated
together as follows:
a. Enter a "0" for the priority order in column 1, row 2,
Table 4,14.
b. Enter the source number, i, in column 2, row 2.
c. Enter the range of the number of samples, "1 to 8,." where
the value of I. is indicated, in column 3. Thus, if
£. = 3, we will write: 1 to 3.
d. Write a dash for the marginal return in column 4 (since
this quantity is not required subsequently).
e. Compute AC. for the 8,. samples from
AC. = C.(£.) - c.
i 11 i
133
-------
where C,(£.) is the first entry for source, i, under
Task |l2J in Table 4.8, and c. is obtained from column 4
of Table 4.8. Note that AC. will be negative. Enter
the result, AC., into column 5.
f. Add the latest AC.(s.) (from Step 2e above) into the
cumulative total, £^C.(s.) in the previous row. Note
thaty]C.(s.) should decrease, since the AC.(s.) being
added in is negative. Enter the new cumulative total
in column 6.
g. Multiply the number of samples, £., (see Step 2c) by
the cost per sample, r., (obtained from Table 4.10)
and enter the result in column 7.
h. Add the latest column 1 entry (Step 2g above) to the
previous total in column 8, and enter the resulting
. ,. new total in column 8.
5,
1 I
: 3. Repeat Step 2 for each subsequent source in Table 4.8, with
'' : H. > 0, entering the results into subsequent rows of Table 4.14.
}(-• . 4. Draw a line across Table 4.14, below the last entry, to indicate
';il the end of Task O.
134
-------
Table 4.14
Sampling Priority List
Priority
Order
(1)
Source
No.
i
(2)
Sample
No.(s)
Si
(3)
Marginal
Return
y.(Si)
(4)
Degree of
Undetected
Violation
Incre-
mental
ACi(si)
(5)
Cumula-
tive
zc^)
(6)
Monitoring
Resources
Required
Per
Sample(s)
ri
(7)
Cumula-
tive
R=Zr
(8)
Note: This table can be duplicated for use in the hand calculations,
135
-------
»i:
TASK p|; PRIORITY ORDER MARGINAL RETURNS
Objective
To order the marginal returns from all optional samples at all
sources, in terms of their sizes.
Output
An ordered tabulation of marginal returns from each optional sample
collected at each source, together with the resulting degrees of undetected
violation and monitoring resources required. Output is recorded in Table
4.14.
Discussion
The term "optional sample" here refers to samples over and above the
minimum requirement and below the maximum limit (both established in Task
jll]), and therefore, in the range where choice may be exercised.
Inputs
• The results of the preselection of the initially allocated
samples (from Table 4.14, Task O) .
• The tabulation of marginal returns (not ordered) obtained in
Task [L3], Table 4.13.
• Resources needed to monitor each source once, r., for all
sources (from Table 4.12, Task |l3J). 1
136
-------
Procedure
1.
a. Locate the largest marginal return, y.(s.), in Table 4.13.
Enter its value into column 4 of the next available now in
Table 4.14. Enter its corresponding source number, i, and
sample number, s., into columns 2 and 3 of Table 4.14.
Enter its priority order, "1", into column 1. Check it off
in Table 4.13 as having been extracted.
b. Enter the cost, r., for this single sample (obtained from
Table 4.12) into column 7 of the same row of Table 4.14.
c. Add the latest column 7, cost entry (Step Ib above) to the
previous total cost in column 8, and enter the resulting
new total cost in column 8.
d. Compute the incremental degree of undetected violation from
either
(i) ACi(si) = Ci(s1) - Ci(si-l)
where the C.(s ) are obtained from Table 4.8, Task Ez] and
X 1 ^"""^
where C.(0) is defined to be, c., (also from Table 4.8) or
from
(ii) AC^s..) = -riPi(s.)
where the r. and p. are obtained from Steps Ib and la above
columns 7 and 4 of Table 4.14. Enter the result into
column 5 .
NOTE: AC.(s.) will be negative
e. Add the AC.(s.) from Step Id above, to the cumulative total
5jC.(s.) in column 6 of the previous now. Note that y^C . ( s . )
should decrease, since the AC.(s.) being added in is negative.
Enter the new cumulative total into column 6.
137
-------
2. Repeat Step 1 for the next largest marginal return, v^s ), in
Table 4.13, increasing its priority order (column 1 of Table
4.14) by 1.
3. Repeat Step 2 until all the entries in Table 4.13 have been ex
tracted, and entered in order in Table 4.14.
138
-------
TASK 17: DETERMINE SAMPLING RATES
Objective
To determine and summarize for the chosen constraint, the sampling
frequency for each source.
Output
A source-by-source tabulation of sampling rates, monitoring re-
sources required, and resulting degrees of undetected violations.
Inputs
• Limiting sampling rates (from Table 4.8, Task pjj) .
• Cumulative degrees of undetected violation and monitoring
resources required for individual samples, rank ordered by
marginal return (from Table 4.14, Task [l6j).
• Resources required to monitor each source once (from Table
4.12, Task (l^).
• Degrees of undetected violation per source for various
alternative sampling rates (from Table 4.8, Task JTJJ) .
• The constraint on the surveillance monitoring funds available,
or on the maximum acceptable degree of undetected violation.
Discussion
The two principal constraints most likely to limit the total number
of surveillance samples to be collected during a monitoring period are:
(i) the amount of funds (resources) available for surveillance monitoring,
or (ii) the maximum acceptable degree of undetected violation (compare
139
-------
with column 6 of Table 4.14). The former obviously increases with more
sampling, while a decrease in the latter requires more samples to be
taken.
It is expected that the dollar constraint (i) will most commonly
be used, particularly at first when the users of this allocation pro-
cedure are not very familiar with the concept of "degree of undetected
violation." However, as familiarity with both this concept and the
numbers which measure it grows, it is quite possible that improved effluent
control by dischargers could lead to a type (ii) constraint requiring
fewer surveillance samples than type (i).
When a compliance sample detects a violation during a monitoring
period, the compliance monitoring program could be said (depending upon
the extent of the violation) to have "achieved its objective" at the
source in question. If further samples had been scheduled at the same
source during the monitoring period, these may now be deemed unnecessary,
depending upon the surveillance agency's policy. The funds from these
saved samples, may be. applied to samples at sources next in priority order
(see Table 4.14) if the agency can reschedule in mid-period, or they may
be saved for use in the following monitoring period.
Procedure
1. Copy the contents of columns 1, 5, and 6 of Table 4.8 into
the first three columns of Table 4.15.
2. Determine which of the following two constraints will limit
the total number of samples to be collected in the proposed
monitoring (see Discussion above) period:
140
-------
(i) The maximum monitoring resources (funds) available;
or
(ii) the maximum acceptable degree of undetected violation.
3. Locate the position of the chosen constraint in relation to the
contents of column 6 or 8 of Table 4.14, whichever is appropriate.
Draw a second line across Table 4.14 immediately below the
largest entry smaller than the constraint. (To meet the con-
straint, the samples below this line cannot or need not be
taken.)
4. From the portion of Table 4.14 above, the cutoff line drawn
in Step 3, determine the total number of samples to be taken
at each source, and enter the results in column 4 of Table 4.15.
5. Determine the monitoring resources needed per source by (i)
adding the individual resources, r., for that source listed in
column 7 of Table 4.14 above the cutoff line, or by (ii)
multiplying the number of times to be sampled (column 4 of Table
4.15) by the resources, r., required to monitor each source
once (last column of Table 4.12). Enter the result for each
source in column 5 of Table 4.15.
6. Determine the degree of undetected violations per source by
finding the value of C.(s.) in Table 4.8, Task O, which cor-
i i ^"""^
responds to the sampling rate, s., specified in Table 4.15,
column 4. If s. = 0, for any source enter C., because C(0)=C..
Enter the result for each source into the last column of Table
4.15.
14.1
-------
7. Add up all the entries in columns 5 and 6 of Table 4.15 to
obtain the two respective totals and enter them below those
columns.
NOTE: The appropriate total should meet the
constraint specified above Table 4.15.
142
-------
Table 4.15
Sampling Rates
Maximum monitoring resources available, R = $
Maximum acceptable degree of undetected violations
Source
No.
i
(1)
Min. No.
Samples
Required
*i
(2)
Max . No .
Samples
Allowed
Li
(3)
No. of
Times
to be
Sampled
Si
(4)
Totals:
Monitoring
Resources
Needed
$
(5)
Degree of
Undetected
Violations
C^s.)
(6)
Note: This table can be duplicated for use in the hand calculations.
143
-------
... 'j
TASK J18J: DEVELOP MONITORING SCHEDULE (Discussion)
Objective
To develop a time schedule for monitoring the sources to be sampled
during the forthcoming monitoring period.
A surveillance monitoring time schedule, indicating on which days
which sources are to be sampled.
The sampling rate determined for each source in Task JITJ, Table A.15.
Discussion
The scheduling of the sampling depends on a number of factors which
are difficult to quantify in an optimization framework, such as: the
: , spatial location of the various effluent sources, the size of the monitoring
agency's jurisdiction, the availability of personnel, and the desire for
• '. "random" timing within the monitoring period, to combat possible "gamesman-
; ji ship" on the part of the dischargers. This scheduling must, therefore, be
the responsibility of the surveillance agency; it is not part of the re-
source allocation procedure provided in this handbook.
144
-------
SECTION 5
USER MANUAL FOR COMPUTER CALCULATION
5.1 MODE OF OPERATION
Purpose
The purpose of the Effluent Monitoring Program (EFFMON) is to aid
the user in scheduling future compliance monitoring visits to effluent
sources. The user of the program may specify up to 30 effluent sources
which are of interest, inputting information about the sources, including
up to two years of past self-monitoring and compliance monitoring data.
The program uses this information to compute a "priority allocation",
a listing of the effluent sources showing how often each should be sampled
during the upcoming monitoring period in order to minimize environmental
damage. The larger the amount of past effluent data which is input, the
better EFFMON will perform. Likewise, the quality of information is also
important.
Solution Technique and Model Usage
The algorithms used by EFFMON in the calculation of a priority
allocation are described in detail in Section 2 and also in Reference [1].
Briefly, the procedure is as follows: for each distinct constituent of
each effluent source, all given self-monitoring and compliance monitoring
data are combined to yield overall estimates of the mean and standard
deviation of the constituent loading. Using these statistics, and the
effluent standard, a probability of not violating the standard is found
for the constituent. From the constituent probabilities, a source prob-
ability of no violation is calculated.
145
-------
Next, an expected damage of an undetected violation is calculated
for each constituent of a source, which leads to the expected damage for
that source. Expected damage is defined as the average environmental
damage expected to be caused by the effluent; it is determined on the
basis of damage functions (see Section 2.4, Criterion #2 for details).
These damage functions relate environmental damage to constituent con-
centrations, and consist of six "breakpoints" (11 in the case of pH)
which are assigned increasingly larger "damage values" as shown in Table
2.4 and Figure 2.3. Damage values are numerical values which indicate
the relative environmental damage caused (i.e., 0, 2, 4, 6, 8 and 10)
corresponding to "none", "excellent", "acceptable", "slightly polluted",
"polluted", and "heavily polluted". The breakpoints are the associated
levels of concentration for the constituent. The specific damage values
and breakpoints used influence the determination of expected damages and
hence, the priority allocation. The user can rely on the default values
for these functions present in EFFMON, but should consult Section 3.1 for
advice on inputting his own values. The user can optionally set all ex-
pected damages at 1.0 and compute the priority allocation solely on the
basis of probabilities of no violation (as discussed in Section 2.4,
Criterion #1) and monitoring costs.
Finally, the program uses the information about expected damage
and probability of no violation for each source to compute monitoring
allocations for all effluent sources. Other factors important in deter-
mining the allocation which the user has input control are the monitoring
costs. Each source has a resource cost (cost to monitor) which is deter-
mined by adding a laboratory cost for each constituent of the source onto
a base cost determined by the number of pipes at the source. Default
values are present in the program, but these costs are highly variable,
and the user should input his own (see Section 3.1).
146
-------
As has been pointed out, the user has various ways of influencing
the program results given a particular set of monitoring data. There are
also other constants which affect the final results (i.e., the constants
used in the combination of data to find the mean and standard deviation
of each constituent). All such influential variables are marked by a "+"
in the input description, Table 5.1, and the user is referred to Section
3.1 for assistance in determing input values.
The program works in standard units which are the same as those
listed in Table 5.4. (Table 5.4 lists acceptable input units for com-
pliance monitoring data and effluent standards.) Data which is input in
other units is converted by the program.
General Model Inputs
The information which the user must have to input to the program
consists of:
1. A list of effluent sources to be considered and the minimum
and maximum number of samples for each, for the next monitoring
period. If the user specifies "zero" as the minimum, and a
large value as the maximum, the program makes the most optional
allocation; however, the user may need to meet certain con-
straints and thus, specify other values.
2. A list of the discharge pipes present at each effluent source
and the constituents to be considered from each pipe.
3. A decision for each constituent as to whether that constituent
loading is distributed normally or lognormally. Note that pH
is always considered to be distributed normally whereas coli-
forms are always considered to be lognormal (see Section 4,
Task 1 for assistance in making decisions on other constituents)
4. A decision for each effluent source as to whether or not the
various constituent loadings are correlated (see Section 3.1).
5. The stream flow immediately upstream of each effluent source.
147
-------
6. Self-monitoring data (effluent measurements taken by the dis-
charger and sent to the monitoring agency) for each constituent
and flows for each pipe.
7. Any compliance monitoring data (measurements taken by the
monitoring agency) which is available for the dischargers.
8. An effluent standard for each constituent (of each pipe of
each effluent source) except DO. The constituent DO is
different from all others in that it is only used to aid in
calculating expected damage due to BOD,, loads. No expected
damages or violation probabilities are calculated for DO it-
self. Therefore, whenever possible, DO effluent data should
be entered for sources containing BOD,.; in the event that no
DO data is input, default values are used.
9. The "permit effluent flow" (as registered with the monitoring
agency on a discharge permit) for each pipe of each source.
10. The saturation level of dissolved oxygen (DO) in the stream
for effluent sources where BOD,, is a considered constituent.
11. Various options and coefficients (as marked by a "+" in the
input list of Table 5.1 and explained in Section 3.1).
Restrictions and Requirements
1. The maximum number of effluent sources which can be considered
in the monitoring allocation procedure at one time is thirty.*
2. A maximum of four discharge pipes can be considered at each
source.
3. All discharge pipes at a single source are assumed to empty
into the same receiving water body.
4. No more than ten distinct constituents may be considered at
one effluent source (there may be forty constituents if the
same ten occur in each pipe).
5. The self-monitoring data must consist of measurements of the
effluent levels and pipe flow made once, on several days, or
daily during a calendar month. All self-monitoring data must
be reducible to a monthly mean of each constituent's loadings,
:
The limit of 30 sources was set for purposes of demonstration in this
project. This capability could easily be expanded in the computer pro-
gram by changing the appropriate numbers in the DIMENSION and COMMON
statements of the program.
148
-------
monthly maximum of each constituent's loadings, and a sample
size for the month (except for -the constituent pH, for which
a monthly minimum must also be available and a monthly mean
is not mandatory). The pipe flows must reduce to a monthly
mean of the measured daily flows.
6. A minimum of one calendar month of self-monitoring effluent
data must be available for each constituent of every pipe of
every source. More than the minimum one month's data is man-
datory if the sample size for that month is less than four;
in that case as many months as is necessary for the sum of
the monthly sample sizes to be four or larger is needed.
7. A maximum of twenty-four calendar months of self-monitoring
data may be input for any pipe of a source. The months need
not be consecutive months, but a monthly mean pipe flow and
data for each constituent of the pipe (or zeros if no data is
available for some of the constituents for a given month),
must be entered.
8. Compliance monitoring data may be entered for any constituent
for any month for which self-monitoring data (or zeros) was
entered. Compliance monitoring consists of a single measure-
ment, and a maximum of thirty of these compliance monitoring
points may be entered for a constituent for any given month.
9. Compliance monitoring data must be entered in units as specified
in Table 5.4. Likewise, self-monitoring data and effluent
standards must also be entered in units as specified in Table
5.4. The user must convert the data in all other cases;
assistance may be found in Section 4, Task 2.
10. The permit flow units must be Megaliters/day and a permit flow
must be entered for each pipe of each source. This value is
necessary for use in converting the effluent standards into
proper units; the program has standard units (generally Kg)
and does conversions of its own. The permit flow is also used
in cases where all monthly pipe flows are 0.0 (no pipe flow
data).
Preparation of Inputs
Before entering numbers on coding forms, the user should organize
his data. He should have a list of all his sources which he should number
as 1, 2, 3, 4 and so on (in whatever source order is convenient). The
149
-------
total number must be less than or equal to 30, He should number each
pipe of each source as 1, 2, 3, and 4 (for a 4-pipe source), in whatever
order is convenient. Finally, he should number each constituent of the
pipes as 1, 2, 3, 4, and so on (maximum of 10).
Next, he should examine each pipe of each source and all of its
constituents to find all months for which monitoring or flow data will
be entered. These months should be ordered chronologically and numbered
as 1, 2, 3, 4, and so on (to a maximum of 24). The numbers themselves
mean nothing; they serve only for identification. Therefore, it does not
matter if there are months skipped, or even larger gaps, so long as each
month is numbered sequentially, larger numbers indicating more recent
data. Even if some part of the data is missing for a particular month,
assign a number (i.e., if only two constituents for a particular month
have monitoring data and there is no flow data for the month, one can
enter the data for the two constituents for that month and enter 0.0 for
all other constituents and the flow) .
All of the numbers assigned should be carefully recorded. They
must be consistently used for identification throughout the input cards.
'V j •" •
--' 5.2 INPUT DESCRIPTION
The inputs required by EFFMON are described in Table 5.1. Any
variable marked by a "+" is discussed in Section 3.1 and the user should
refer to that Section for suggested input values. A sample input deck
is illustrated in Figure 5.1.
All variables which require a decimal point are specified, and the
user should be careful to insert a decimal point. For the other variables,
no decimal point is allowed. For a given variable, the numerical data
need not fill all the allowed columns, but the data must be placed in the
150
-------
Table 5.1 EFFMON Inputs
CARD
NUMBER
CARD
COLUMN(S)
DECIMAL
POINT?
VARIABLE
NAME
UNIT MUST
BE
DEFAULT
VALUE
DESCRIPTION
DAMAGE FUNCTION/RESOURCE COST OPTIONS
No
ICOSTS
No
IDMG
No
IDAMAG
0, Default values
for monitoring
costs (see
variables PIPCST
and CONCST)
0, Costs will be
inputted
0, Default pH and
pOH damage
function break-
points will be
used (see DMG)
1, Read in pH o_r
pOH damage
function break-
points
2, Read in both pH
and pOH damage
function break-
points
0, Default damage
function break-
points for non-
pH constituents
(see DAMAGE)
-------
• • :'.• : " ' '.•'•{ .1" "; JTC ':
CARD CARD DECIMAL VARIABLE UNIT MUST DEFAULT
NUMBER COLUMN(S) POINT? NAME BE VALUE
= X, Total number of
constituents
whose damage
function break
points will be
replaced with
inputted values
(530)
7 No ISS = 0, Default damage
function values
will be used
^ 0, Inputted damage
function values
will be used
(see S and SSPH)
*****Cards 2-6 are included only if ICOSTS^O************************************************^
*BASE COST TO MONITOR
* 2 1-10 Yes PIPCST(l) $ $ 525 Base cost to monitor
1-pipe source
* 16-25 Yes (2) $ 525 Base cost to monitor
2-pipe source
* 31-40 Yes (3) $ 857 Base cost to monitor
3-pipe source
* 45-54 Yes (4) $ 857 Base cost to monitor
4-pipe source
*LAB COSTS TO MONITOR
* 3 1-5 Yes CONCST(l) $ 8.50 Lab cost to analyze
aluminum
* 11-15 Yes (2) $ 10.00 Lab cost to analyze
ammonia
* 21-25 Yes (3) $ 20.00 Lab cost to analyze
BOD
-------
Table 5.1
Continued
Ul
OJ
CARD
NUMBER
*
*
*
*
*
* 4
*
*
*
*
*
*
*
* 5
*
*
*
*
CARD
COLUMN (S)
31-35
41-45
51-55
61-65
71-75
1-5
11-15
21-25
31-35
41-45
51-55
61-65
71-75
1-5
11-15
21-25
31-35
41-45
DECIMAL
POINT?
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
VARIABLE
NAME
CONCST (4)+
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
UNIT MUST
BE
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
DEFAULT
VALUE
0.00
10.00
0.00
5.00
15.00
7.50
15.00
15.00
7.50
15.00
8.00
7.50
7.50
7.50
15.00
7.50
10.00
10.00
DESCRIPTION
Not used-leave
columns blank
Lab cost to analyze
carbon
Not used-leave
columns blank
Lab cost to analyze
chloride
Lab cost to analyze
chloroform
Lab cost to analyze
chromium
Lab cost to analyze
total coliforms
Lab cost to analyze
fecal coliforms
Lab cost to analyze
copper
Lab cost to analyze
cyanide
Lab cost to analyze
fluoride
Lab cost to analyze
iron
Lab cost to analyze
lead
Lab cost to analyze
manganese
Lab cost to analyze
mercury
Lab cost to analyze
nickel
Lab cost to analyze
nitrogen
Lab cost to analyze
oil-grease
-------
Table 5.1
ContinueH
CARD
NUMBER
CARD
COLUMN(S)
DECIMAL
POINT?
VARIABLE
NAME
UNIT MUST
BE
DEFAULT
VALUE
DESCRIPTION
51-55
Yes
CONCST(22)
3.00
*
*
*
*
61-65
71-75
1-5
11-15
21-25
31-35
41-45
51-55
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
(23)
(24)
(25)
(26)
(27)
(28)
(29)
(30)
$
$
$
$
$
$
$
$
0.00
12.50
10.00
5.00
5.00
0.00
8.50
3.00
Lab cost to analyze
PH
Not used-leave blank
Lab cost to analyze
phenol
Lab cost to analyze
phosphorus
Lab cost to analyze
dissolved solids
Lab cost to analyze
suspended solids
Lab cost to analyze
temperature difference
Lab cost to analyze
tin
Lab cost to analyze
DO (dissolved oxygen)
******Cards 7 and 8 are included only if IDMG^O********************************************************************
* pH/pOH DAMAGE FUNCTION BREAKPOINTS IN UNITS OF ION CONCENTRATION
No
II
*
*
*
*
*
*
* 8
6-15
16-25
26-35
36-45
46-55
56-65
6-15
Yes
Yes
Yes
Yes
Yes
Yes
Yes
DMG(Il.l)
(11,2)
(11,3)
(11,4)
(11,5)
(11,6)
(11,7)
=1 for pH damage
function
=2 for pOH damage
function
See Table 5.2 See Table 5.2 1st damage function
breakpoint
" " 2nd damage function
breakpoint
" " 3rd damage function
breakpoint
" " 4th damage function
breakpoint
" " 5th damage function
breakpoint
" " 6th damage function
breakpoint
" " 7th damage function
breakpoint
-------
Table 5.1 Continued
CARD
NUMBER
*
*
*
*
CARD
COLUMN (S)
16-25
26-35
36-45
46-55
DECIMAL
POINT?
Yes
Yes
Yes
Yes
VARIABLE
NAME
DMG(I1,8)
(11,9)
(11,10)
(11,11)
UNIT MUST
BE
As in
Table 5.2
M
It
tl
DEFAULT
VALUE
See
Table 5.2
It
It
It
DESCRIPTION
8th damage function
breakpoint
9th damage function
breakpoint
10th damage function
breakpoint
llth damage function
breakpoint
*****Cards 9 and 10 are included only if iDMG=2******************!l:************************************************
* 9 Cards 9 and 10 correspond to 7 and 8 except that the other damage function must be inputted
10 (i.e., if 7 and 8 input pH, 9 and 10 must input pOH, or vice versa)
*****Card(s) 11 are included only if IDAMAG>0*********************************************************************
* NON-pH DAMAGE FUNCTION BREAKPOINTS
11 1-2 No II Damage function
* identification
number (i.e., 01
* for aluminum, 15
for iron, and so on -
* see Table 5.3)
* 6-15 Yes DAMAGE(I1.1)+ See Table 5.3 See Table 5.3 1st damage function
breakpoint for II
* 16-25 Yes (11,2) " " 2nd damage function
breakpoint for II
* 26-35 Yes (11,3) " " 3rd damage function
breakpoint for II
* 36-45 Yes (II.,4) " " 4th damage function
breakpoint for II
* 46-55 Yes (11,5) " " 5th damage function
breakpoint for II
* 56-65 Yes (11,6) " " 6th damage function
breakpoint for II
* Repeat card 11 as many times as specified by the value of IDAMAG (one card for each damage function,
in any order).
-------
Table 5.1
Continued
Ln
cr-
CARD CARD DECIMAL
NUMBER COLUMN(S) POINT?
VARIABLE UNIT MUST DEFAULT
NAME BE VALUE
DESCRIPTION
********Cards 12 and 13 are included only if iss^O**************************************************************
NON-pH BREAKPOINT DAMAGE VALUES +
* 1-5 Yes S(l) 0. 1st value of non-
*
*
*
*
*
*
*
*
*
A
*
*
*
*
*
*
*
6-10
11-15
16-20
21-25
26-30
pH BREAKPOINT DAMAGE VALUES
13 1-5
6-10
11-15
16-20
21-25
26-30
31-35
36-40
41-45
46-50
51-55
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
(2)
(3)
(A)
(5)
(6)
-I-
SSPH(l)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
2.
4.
6.
8.
10.
0.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
pH damage functions
2nd value of non-
pH functions
3rd value of non-
p-H functions
4th value of non-
pH functions
5th value of non-
pH functions
6th value of non—
pH functions
1st value of pH/
pOH damage function
2nd value of pH/
pOH damage function
3rd value of pH/
pOH damage function
4th value of pH/
pOH damage function
5th value of pH/
pOH damage function
6th value of pH/
pOH damage function
7th value of pH/
pOH damage function
8th value of pH/
pOH damage function
9th value of pH/
pOH damage function
10th value of pH/
pOH damage function
llth value of pH/
pOH damage function
-------
Table 5.1
Continued
CARD
NUMBER
CARD
COLUMN(S)
DECIMAL
POINT?
VARIABLE
NAME
UNIT MUST
BE
DEFAULT
VALUE
DESCRIPTION
OUTPUT OPTIONS
14 1
11
16
21
26-35
36-45
No
No
No
No
No
Yes
Yes
NOUT
IOUT1
IOUT2A
IOUT2B
I OUT 3
B
D
?fO, No tabled output
(as in Figure
5.7)
=0, Tabled output
5*1, No type 1 output
(as in Figure
5.2)
=1, Output type 1
^1, No type 2A output
(as in Figure
5.3)
=1, Output type 2A
^1, No type 2B output
(as in Figure
5.4)
=1, Output type 2B
^1, No type 3 output
(see Figures
5.5 and 5.6)
=1, Output type 3
Budget limit (used
if IOUT3=1)
Undetected-violation-
cost limit (used if
IOUT3=1)—for B and D,
one allocation is
made for each which
is not 0.
-------
f-y^ -* n S f
Table 5.1
Continued
CARD
NUMBER
CARD
COLUMN(S)
DECIMAL
POINT?
VARIABLE
NAME
UNIT MUST
•BE
DEFAULT
VALUE
DESCRIPTION
SOURCE CONSTANTS
15 1
oo
11-12
16-17
UPDATING CONSTANTS
16 1-10
11-20
21-30
31-40
41-50
No
ICOPT
No
IEXPD
No
No
Yes
Yes
Yes
Yes
Yes
NOSORS
NUSORS
ALPHA
GAMMA
KETA
KNU
ENU+
That damage function
breakpoint n (n=l,
2,3,4,5,or 6) which
represents the up-
stream concentration
of all non-coupled
constituents (by the
nth breakpoint of
their respective
damage function)
±0, All expected
damages in the
allocation are
set at .1.0
=0, All expected
damages are
calculated from
the data
Number of sources
for which data will
be read in
Number of sources
to be considered by
the program for
allocation (
-------
Table 5.1
Continued
CARD
NUMBER
CARD
COLUMN(S)
DECIMAL
POINT?
VARIABLE
NAM:;
UNIT :
-------
Table 5.1
Continued
CARD
NUMBER
SOURCES TO
20
CARD
COLUMN (S)
BE ALLOCATED
1-2
3-4
5-6
DECIMAL
POINT?
No
No
No
VARIABLE UNIT MUST D
NAME BE
INSORS(l)
(2)
(3)
ST DESCRIPTION
Sources to be considered
for priority allocation
in sequential order (i.e.,
by source number)
(NOSORS)
SOURCE DESCRIPTION
21 1-2
No
ID
For variable NAME only, data must begin in column 4 and need not fill all columns.
4-55 No NAME(I,J)
57-62
63-68
69-74
QU(I)
KBOD(I)
DOSAT(I)
Megaliters/
day
Mg/liter
Source number (between 1 and
30)
Source description as
desired (i.e., XYZ COMPANY,
RIVER CITY).
Upstream flow for sources
ID
BOD transfer coefficient
for source ID
Saturation level of DO for
source ID
-------
Table 5.1
Continued
CARD
NUMBER
CARD
COLUMN(S)
DECIMAL
POINT?
VARIALLE
NAME
UNIT MUST
BE
DEFAULT
VALUE
DESCRIPTION
77-78
79-80
PIPE DESCRIPTIONS
22 1-2
4-5
IONESD(1)
NPIP
NPPARS(l)
NMNTHS(l)
Fill in the following if there is a 2nd pipe, otherwise leave remainder of card blank
7-8 NPPARS(2)
10-11
NMNTI!S(2)
Fill in the following if there is a 3rd pipe, otherwise leave remainder of card blank
13-1A NPPARS(3)
16-17
NMNTHS(3)
= 0, if there is no
for source ID or if
for source ID has a
minimum and mean.
= 1, if pH data for
source ID consists of
only a maximum and
minimum (no mean)
Number of discharge
pipes for source ID
Number of constituents
discharged from 1st'
pipe to be entered as
data
Number of months of con-
stituent and flow data
from 1st pipe
Number of constituents
discharged from 2nd pipe
Number of months of con-
stituent and flow data
from 2nd pipe
Number of constituents
discharged from 3rd pipe
Number of months of con-
stituent and flow data
from 3rd pipe
-------
Table 5.1
Continued
CARD
NUMBER
CARD
COLUMN'(£)
DECIMAL
POINT?
VARIABLE
NAME
UNIT MUST
BE
DEFAULT
VALUE
DESCRIPTION
Fill in the following if there is a 4th pipe, otherwise leave remainder of card blank
19-20 NPPARS(A) Number of constituents
discharged from 4th pipe
22-23 MHHTHS(4) Number of months of con-
stituent and flow data
from 4th pipe
Cards 21 and 22 must be repeated for every source (i.e., 21 and 22 for the first souce, then 21 and 22 for the second
source, then 21 and 22 for the third). Note that the number of times NPPARS(i) and NMNTHS(i) appears on card 22 is
the number that was listed under NPIP on card 21; in counting constituents for NPPARS, pH (if present) must be counted
twice.
PIPE FLOW DATA
23
1-2
5-6
7-8
9-10
No
No
No
No
15-16
19-24
29-30
No
Yes
No
ID
PIPNO
IQS
QSUNIT(J)
MNTHQS(J.l)
QSMEAN(J.l) Megaliters/day or
million gallons/day
MNTHQS(J,2)
Source number (between
1 and 30)
Pipe number (between 1
and 4)
Enter "99" (signals com-
puter that this is a
flow card)
Units that pipe-flow will
be entered in (for this
source and pipe J=PIPNO),
= 8 for megaliters/day
= 3 for million gal/day
First month for which
pipe J-PIPNO flow will
be entered
Mean pipe flow for first
month, pipe J=PIPNO
Second month for which
pipe J=PIPNO flow will
be entered
-------
Table 5.1
Continued
u>
CARD CARD
NUMBER COL-UMAT(S)
33-38
43-44
47-52
57-58
61-66
71-72
DECIMAL
POINT?
Yes
No
Yes
No
Yes
No
VARIABLE
NAME
QSMEAN(J,2)
MNTHQS(J,3)
QSMEAN(J,3)
MNTHQS(J,4)
QSMEAN(J,4)
MNTHQS(J,5)
UNIT MUST DEFAULT
BE VALUE
Megaliters/day or
Million gallons/day
Megaliters/day or
Million gallons/day
Megaliters/day or
Million gallons/day
DESCRIPTION
Flow for second month
Third month for which
pipe J=PIPNO flow will
be entered
Flow for third month
Fourth month for which
pipe J=PIPNO flow will
be entered
Flow for fourth month
Fifth month for which
75-80
Yes
QSMEAN(J,5)
Megaliters/day or
Million gallons/day
pipe J=PIPNO flow will
be entered
Flow for fifth month
Repeat columns 15-80 on as many cards as needed (up to 4 additional cards) to enter more months and flows for this
pipe; at any point on any card when the end of the month/flows is reached, leave the remainder of the card blank
and proceed to card 24. Note that the months must be placed sequentially on the cards (i.e., 1,2,3,5,6,8,10, ...)
although some may be skipped if no data is available; but any month for which data is entered must appear. If for
a certain month flow data is not available, enter 0.for QSMEAN for that month.
SELF-MONITORING CONSTITUENT DATA
24 1-2
No
ID
Source number (must be
the same as on card 23)
-------
Table 5.1
Continued
CARD CARD
NUMBER COLU'-CT(S)
5-6
7-8
9-10
11-16
17-22
23-24
25-30
31-36
37-38
39-44
45-50
DECIMAL
FOIN'T?
No
No
No
Yes
Yes
No
Yes
Yes
No
Yes
Yes
VARIABLE
NAME
PIPNO
IPARM(J,K,I)
PRUNIT(J,K)
SMAX(J,K,1)
SMEAN(K,K,1)
NSIZE(J,K,1)
SMAX(J,K,2)
SMEAN(J,K,2)
NSIZE(J,K,2)
SMAX(J,K,3)
SMEAN(J,K,3)
UNIT MUST DEFAULT
BE VALUE
See Table 5.4
See Table 5.5
As in PRUNIT(J,K)
above
As in PRUNIT(J.K)
above
As in PRUNIT(J,K)
above
As in PRUNIT(J,K)
above
As in PRUNIT(J,K)
above
As in PRUNIT(J.K)
DESCRIPTION
Pipe number (must be
the same as on card 23)
Constituent identification
number (see Table 5.4)
for first constituent
of source ID, Pipe
J=P1PNO
Units this constituent's
data is in
Maximum of this con-
stituent samples for
first month
Mean of this constituent
samples for first month
Number of samples taken
from this constituent
for first month
Maximum for second month
Mean for second month
Sample size for second
month
Maximum for third month
Mean for third month
above
-------
Table 5.1
Continued
CARD CARD
NUMBER COLUMN (S)
51-52
53-58
59-64
DECIMAL
POINT?
No
Yes
Yes
VARIABLE
NAME
NSIZE(J,K,3)
SMAX(J,K,4)
SMEAN(J,K,4)
UNIT MUST DEFAULT
BE VALUE
As in PRUNIT(J.K)
above
As in PRUNIT(J,K)
DESCRIPTION
Sample size for third
month
Maximum for fourth month
Mean for fourth month
65-66
67-72
73-78
79-80
No
Yes
Yes
No
NSIZE(J,K,4)
SMAZ(J,K,5)
SMEAN(J,K,5)
NSIZE(J,K,5)
above
As in PRUNIT(J.K)
above
As in PRUNIT(J,K)
above
Sample size for fourth
month
Maximum for fifth month
Mean for fifth month
Sample size for fifth
month
Repeat columns 11-80 on as many cards as needed (up to 4 additional cards) to enter more months of data; at any point
on any card when the end of the data is reached, leave the remainder of the card blank and proceed to the next step as
detailed below. If no data is available for a constituent during a month, enter zeros for maximum, mean, and sample
size for that month. Note that a maximum, mean, and sample size must be entered for each month that was listed on
card 23 and that the maximum, mean, sample-size groups must be ordered as the months were. When the constituent being
entered is pH, card 24 must be repeated twice. The first time, pH must be entered as constitutent 23 (pll max) and means,
maximums, and sample sizes are listed as above. The second time, pH must be entered as constituent 22 (pH min) and the
same means and sample sizes are listed but instead of sample maximums, sample minimums are listed. If, as may be the
case for pH, no means are available, enter zeros in those columns.
After the first constituent has been completed, repeat card 24 for every other constituent of the pipe (that pipe listed
on card 23). Once all constituents have been done., repeat cards 23 and 24 for pipe 2, pipe 3, and then pipe 4 (if
they exist), of the source (that source listed on card 23). Then proceed to card 25.
-------
Table 5.1
Continued
CARD
NUMBER
CARD
COLUMN(S)
DECIMAL
POINT?
VARIABLE
NAME
UNIT MUST
BE
DEFA'JLT
VALUE
DESCRIPTION
EFFLUENT STANDARDS
25 1-2
4-5
7-12
13-14
15-20
22
No
No
Yes
No
Yes
No
ID
PIPNO
EFFLOW(J,I)
IP(D
Megallters/day
IUNIT(1)
As in IUNIT(1)
See Tables 5.4
and 5.5
Source number
Pipe number (1 to 4)
Permit flow for pipe
J=P1PNO
First constituent of
pipe PIPNO (use identifi-
cation number as in Table
5-4)
First constituents effluent
standard
Units that standard is
expressed in
23
25-26
27-32
No
No
Yes
IP(2)
Xl(2)
As In IUNIT(2)
Distribution of constituent
0 = Normal
1 = Lognormal
Second constituent
Second constituent's
effluent standard
34
No
IUN1T(2)
Units of standard
-------
Table 5.1
Continued
CARD CARD
NUMBER COLOMN(S)
35
37-38
39-44
46
47
49-50
51-56
58
59
61-62
63-68
70
71
DECIMAL
POINT?
No
No
Yes
No
No
No
Yes
No
No
No
Yes
No
No
VARIABLE
NAME
M(2)
IP(3)
Xl(3)
IUNIT(3)
M(3)
IP(4)
Xl(4)
IUNIT(4)
M(4)
IP(5)
Xl(5)
IUNIT(5)
M(5)
•JNiTM-iJST DvIlUET DESCRIPTION
Distribution of second
constituent (0 or 1)
Third constituent
As in IUNIT(3) Third constituent effluent
standard
Units of standard
Distribution of third con-
stituent (0 or 1)
Fourth constituent
As in 1UNIT(4) Fourth constituent effluent
standard
Units of standard
Distribution of fourth
constituent (0 or 1)
Fifth constituent
As in IUNIT(5) Fifth constituent effluent
standard
Units of standard
Distribution of fifth
constituent (0 or 1)
-------
Table 5.1
Continued
CARD
NUMBER
CARD
COLUMN (S)
DECIMAL
POINT?
VARIABLE
NAME
UNIT MUST
BE
DEFAULT
VALUE
DFSrRTPTTON
DESCRIPTION
00
Repeat columns 13-71 on another card, if necessary, to list all constituents and their standards for the pipe. Then
repeat card 25 for pipes 2, 3, and 4 of the source (if they exist). Once all pipes have been completed, repeat
cards 23, 24 and 25 for the next source. Proceed until all sources have been completed, being careful to enter the
sources in their proper order (source 1, source 2, source 3,...). Note that no standard is necessary if the con-
stituent is DO (enter "0." under XI).
COMPLIANCE MONITORING DATA
26
1-2
5
7-8
11-12
14-19
20-21
23-28
29-30
32-37
38-39
No
No
No
No
Yes
No
Yes
No
Yes
No
ID
J
IPAR
NUM
Xl(2)
M(2)
Xl(3)
M(3)
See Table 5.4
See Table 5.4
See Table 5.4
Source number
Pipe number ("0" if there
is no compliance monitoring
for this source)
Constituent identification
number (as in Table 5.4)
Number of compliance moni-
toring points to be entered
for this constituent
Value of first compliance
monitoring point
Month from which compliance
monitoring point was taken
Second CM point
Month of second CM point
Shird CM point
Month of third CM point
-------
Table 5.1
Continued
o\
VD
CARD CAK2
NUMBER COLUMN (S)
41-46
47-48
50-55
56-57
59-64
65-66
68-73
74-75
DECIMAL
POINT?
Yes
No
Yes
No
Yes
No
Yes
No
VARIABLE
NA.ME
Xl(4)
M(4)
Xl(5)
M(5)
XI (6)
M(6)
Xl(7)
M(7)
UNIT MUST DEFAULT DESCRIPTION
BE VALUE ULbLKli'l.U.N
See Table 5.4 Fourth CM point
Month of fourth CM point
See Table 5.4 Fifth CM point
Month of fifth CM point
See Table 5.4 Sixth CM point
Month of sixth CM point
See Table 5.4 Seventh CM point
Month of seventh CM point
Repeat columns 14-75 on as many cards as needed (up to 5 additional cards) to enter all compliance monitoring points
the constituent. At any point on any card when the last CM point is recorded, leave the remainder of the card blank
and proceed as below. Repeat card 26 for any other constituents in any of the pipes of the source for which there are
compliance monitoring points (any order is acceptable and the number of CM points may vary with constituents where
some constituents may not have any and need not be entered). Once a source has been completed, a final card for the
source must be added which contains the source number under ID and "0" for J before going on to the next source.
Repeat card 16 for all compliance monitoring data of the next source. Each source listed under variable INSORS
on card 20 must be represented, and in the same order; if a source has no compliance monitoring data, enter the
source number under ID and a "0" for J and proceed to the next source on the next card.
-------
Cards 21 through 26 are grouped for
each source/pipe/constituent. Refer
to Figure 5.1, "Organized Print of
Inputs," for and example. /
COMPLIANCE
MONITORING
DATA *
26
EFFLUENT"
STANDARDS
/
(SE
lew
ELF-MONITORING
CONSTITUENT
DATA
PIPE *
FLOW DATA
23
PIPE *
DESCRIPTION
SOURCE
DESCRIPTION
21
'SOURCES
TO BE
ALLOCATION
20
CONSTITUENT
CORRELATION
/SAMPLlT " 18
f ALLOCATION
'SAMPLE
ALLOCATION
MAXIMA
171
DAMAGE FUNCTION
BREAKPOINTS
AND VALUES
MONITORING
COSTS
Figure 5.1
Organization of Input Deck
170
-------
Table 5.2 pH/pOH Damage Function Breakpoints
BREAKPOINTS
Damage Function
Point
PH
Cone of H ions
pOH
Cone of OH~ions
10
11
1.00 x 10
-7
1.78 x 10
-7
3.16 x 10
-7
5.62 x 10
-7
1.00 x 10
-6
3.16 x 10
-6
1.00 x 10
-5
3.16 x 10
-5
1.00 x 10
-4
1.12 x 10
-4
1.26 x 10
-4
1.00 x 10
3.16 x 10
-7
1.00 x 10
-6
1.58 x 10
-6
2.51 x 10
-6
5.01 x 10
-6
1.00 x 10
~5
3.16 x 10
-5
1.00 x 10
-4
1.12 x 10
-4
1.26 x 10
-4
171
-------
--J
ro
Table 5.3 Non-pH Damage Functions
DFIN*
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Constituent
Name
Aluminum
Ammonia
Dissolved Oxygen
Not Used
Inorganic Carbon
Not Used
Chloride
Chloroform Extract
Chromium
Coliforms-Total
Col if orms-Fecal
Copper
Cyanide
Fluoride
Iron
Lead
Manganese
Mercury
Nickel
Inorganic Nitrogen
Oil-Grease
Not Used
Not Used
Phenol
Phosphates
Solids-Dissolved
Solids-Suspended
Temp. Diff.
Tin
Units
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
MPN/lOOml
MPN/ 100ml
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
C°
mg/1
1
0
0
>9
0
<50
0
0
0
0
0
0
0
0
<0.7
0
0
0
0
0
<0.6
0
0
0
0
0
<100
0
0
0
2
0.01
0.1
8.0
0.
70.
0.
25.
0.04
0.02
100.0
20.
0.02
0.01
0.8
0.1
0.005
0.05
0.001
0.01
0.9
0.01
0.
0.
0.0005
0.1
200.
20.
1.
10.
•— BTTGciicpoin t s~
3
0.05
0.3
6.8
0.
90.
0.
175.
0.15
0.05
2000.
200.
0.1
0.02
0.9
0.3
0.05
0.17
0.005
1.
3,
0.1
0.
0.
0.001
0.2
500.
40.
2.5
40.
4
0.1
0.9
4.5
0.
110.
0.
200.
0.25
1.
7500.
800.
1.
0.05
1.2
0.9
0.1
0.5
0.01
3.
4.5
5.
0.
0.
0.02
0.5
1000.
100.
3.0
100.
5
0.5
2.7
1.8
0.
130.
0.
240.
0.35
10.
15000.
3000.
5.
0.1
3.
2.7
0.25
1.
0.02
9.
7.
30.
0.
0.
0.1
1.6
1500.
280.
4.
300.
6
1.
3.
0.9
0.
150.
0.
250.
0.4
50.
150000.
50000.
10.
0.5
8.
3.
0.35
1.5
0.05
20.
10.
50.
0.
0.
0.2
10.
2300.
300.
10.
1000.
*Damage Function Identification Number
-------
Table 5.4 Constituent Identification
Numbers and Input Units
Number
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Constituent
Aluminum
Ammonia
BODj
-
Carbon
-
Chloride
Chloroform
Chromium
Total Coliforms
Fecal Coliforms
Copper
Cyanide
Fluoride
Iron
Lead
Manganese
Mercury
Nickel
Nitrogen
Oil-grease
pH-rain
pH-max
Phenol
Phosphorus
Dissolved Solids
Suspended Solids
Temperature Difference
Tin
DO
Acceptable Units for Self-
Monitoring Data and Effluent Standards
ug/1
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
mg/1
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Ibs/day
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Kg/day
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
°c
X
pH
X
X
MPN/day
X
X
Acceptable Units for
Compliance Monitoring Data
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
MPN/100 ml.
MPN/100 ml.
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
pH
pH
Kg/day
Kg/day
Kg/day
Kg/day
°F
Kg/day
mg/1
-------
Table 5.5
Input Units
Identification Number
Units
4
5
8
9
rog/1
Ug/1
MGD (Million Gallons/Day)
Ibs/day
pH
MPN/lOOml
Ml/day (Megaliters/day)
Kg/day
174
-------
right-most columns allowed (i.e., if the value 2 is to be placed in columns
60-62, specify "002" in columns 60-62 or simply place "2" in column 62).
If a decimal point number being entered as input data is too large
to fit into the allowed columns, scientific notation should be used (i.e.,
6,020,400 would be 6.02 x 10 , which is entered into the columns as 6.02E6
and likewise, .0000005 would be entered as 5.0E-7). Make sure in this
case also that the entry is in the right-most columns allowed, and has a
decimal point.
All self-monitoring or flow data which is read in as 0.0 is con-
sidered to be "missing data". Therefore, if a sample value really is 0.0,
a very small number (i.e., .00001) should be entered instead.
The variable INSORS on card 20 allows the user flexibility in
specifying which sources to consider in the priority allocation. All
sources must be numbered (1 to 30), their pipes numbered (1 to A), and
the months of data numbered (1 to 24) as described in Section 5.1. Sup-
pose that all data has been entered on cards and the user decides that
for some reason he wants to delete one or more sources. Rather than
having to renumber and retype all cards, he simply specifies exactly which
numbered sources he does want in his allocation and lists these under
INSORS. If he does not wish to delete any sources, he lists all source
numbers under INSORS.
Finally, the user should study the examples of input and output
presented in Sections 5.3 and 5.4. These examples should help in re-
solving any questions arising out of the table of inputs.
175
-------
5.3
SAMPLE INPUT DECK
Suppose that the available self-monitoring and compliance monitor-
ing monthly data for sources of interest is as in Table 5.6. The card
input would then resemble that of Figure 5.2, depending upon the rest of
the data and the options which the user chooses.
5.4
OUTPUT DESCRIPTION
The output generated by EFFMON is printer output. Except for an
initial printout of all the inputs which is always printed (see Figure
5.3), the output may consist of any or all of the following as desired
by the user (the theoretical background for the various outputs is dis-
cussed in Section 2.6).
Output Option 1 : An initial allocation, including the minimum
number of times each source must be sampled as
specified by the user (see Figure 5.4).
Output Option 2a;
Output Option 2b;
A priority list of the samples, 'including the
minimum required samples (see Figure 5.5).
A priority list of the samples, including only
samples to be taken beyond the minimum number
required for each source (see Figure 5.6).
Output Option 3 : A final allocation including the total number of
times each source is to be sampled and other
summary information based on a given budget
limit (see Figure 5.7).
Output Option 4 : A final allocation including the same information
as in 4 above, but based on a given maximum "cost
of undetected violations" as defined below (see
Figure 5.8).
176
-------
Table 5.6
Sample Input Date
Source
& Pipe
Source 1
Pipe 1
Source 2
Pipe 1
Source 3
Pipe 1
Constituent
(or Pipe Flow)
Flow
pH-max
pH-min
Lead
Phosphorus
Cyanide
Flow
pH-max
pH-min
Flow
Self -Monitor ing
Monthly
Max. or
Min.
NA
NA
10.6
9.0
6.0
5.4
800.
510.
" .017
.066
.025
-
NA
NA
NA
10.0
9.9
9.2
7.6
7.4
7.6
NA
NA
NA
NA
NA
NA
NA
Monthly
Mean
.254
.148
-
-
-
-
760.
400.
.011
.025
.020
-
.04
.04
.05
9.0
9.2
9.0
9.0
9.2
9.0
.430
.437
.524
—
.491
.482
.554
Sample
Size
NA
NA
6
7
6
7
6
7
6
7
6
-
NA
NA
NA
10
12
12
10
12
12
Units
MGD
pH
pH
ug/1
mg/1
rag/1
MGD
PH
pH
Compliance
Monitoring
Points
NA
NA
10.0,9.0,9.5
8.0,7.1,6.8
Month
and Year
6/74
7/74
6/74
7/74
6/74
7/74
.461,. 202,. 371* 6/74
.051, .023
7/74
6/74
7/74
.052, .059,. 071 6/74
NA
NA
NA
8.5
9.1,8.9
8.3,8.4,8.3,
8.7,8.5
7.7
8.0,7.7
7.6,7.6,7.5
7.4,7.6
NA Megaliters/ NA
NA
NA
NA
NA
NA
NA
day
NA
NA
NA
NA
NA
NA
7/74
2/74
7/74
8/74
2/74
7/74
8/74
2/74
7/74
8/74
10/73
11/73
12/73
6/74
7/74
8/74
12/74
* Note that units are k.g as required.
NA-Not Applicable
177
-------
Table 5.6
Continued
Source
& Pipe
Pipe 2
Constituent
(or Pipe Flow)
Chloroform
Extract
Flow
Chloroform
Extract
Total
Colifonns
BOD.
J
DO
Self-Monitoring
Monthly
Max. or
Min.
24.0
8.0
23.6
45.0
56.8
16.8
13.2
NA
NA
NA
NA
NA
NA
8.4
19.2
15.6
20.0
28.0
19.2
-
1080.
-
1200.
1210.
1150.
-
-
7.8
13.0
18.0
11.0
-
-
-
5.7
7.0
8.0
6.7
-
5.4
"
Monthly
Mean
15.5
2.8
7.6
31.4
30.1
-
6.0
.121
.125
.131
.126
-
.133
3.5
5.8
7.1
8.1
6.2
8.9
-
1010.
-
-
1050.
1100.
-
-
6.3
5.0
12.0
7.7
-
-
-
5.0
6.7
7.0
6.3
-
5.2
*~
Sample
Size
2
2
3
5
7
2
1
Units
mg/1
Compliance
Monitoring
Points
NA Megaliters/ NA
NA
NA
NA
NA
NA
2
2
3
7
7
7
-
2
-
3
10
10
-
-
2
2
3
7
-
-
-
2
2
3
7
-
2
""
day
mg/1
MPN
mg/1
mg/1
NA
NA
NA
NA
NA
Month
and Year
10/73
11/73
12/73
6/74
7/74
8/74
12/74
10/73
11/73
12/73
2/74
3/74
8/74
10/73
11/73
12/73
2/74
3/74
8/74
9/74
10/73
11/73
12/73
2/74
3/74
8/74
9/74
10/73
11/73
12/73
2/74
3/74
8/74
9/74
10/73
11/73
12/73
2/74
3/74
8/74
9/74
178
-------
00*0
0 ' 1 I J 10000.
1 ° 3 3
.« 1.5 1
10100505
01020101
001
010203
01 JONES MANUFACTURING CO.
05 02
02 SAKE CHEMICAL CO.
02 03
05 SEWAGE TREATMENT
01 07 On 07
01 019903 01 ,25a 02
01 012306 10.6 0.0 6 9.0
01 012206 6,0 0.0 6 5.1
01 011602 POO, 760. b 510,
01 012501 .017 ,011 6 .066
01 011301 ,025 ,020 6 0.0
01 01 ,5?9?3 9.5 60 22 6.
02 oi^oi 01 ,na 02
02 012306 JO.O 9,010 9,9
82 012206 7.6 9.010 7.1
02 01 1,1323 9.5 60 22 6.
OJ 019903 01 .130 02
06 ,482 07
03 010801 2U.O 15.502 8.0
16,8 0.002 13,2
03 029908 01 ,121 02
06 .133
03 02^801 8.1 3.5fi2 J9.2
19,2 8,907
03 021007 1080, 1010,02 0.0
0,0 0.000
OJ 020301 7,8 6.302 13,0
0.0 0.000
03 023001 5,7 5.002 7,0
5.4 5,?02
03 01 2,0008 10. 11
03 0? ,16508 20, 11 10 1*500
01 23 03 10.0 1 9.0 1
01 22 03 P,0 1 7,1 1
01 16 03 ,061 1 .202 1
01 25 02 .051 1 ,0?3 1
01 13 03 ,052 1 ,059 1
01
02 1 23 08 8,5 1 9.1 t
8.5 3
02 1 22 08 7,T 1 8,0 2
7, A 3
02
03
M
.5
.118
0.0 7
0.0 7
«00, 7
.025 7
o.ooo
5 60 16
,0«
9,212
9.212
7 60
."37
.55U
2.602
6.001
.125
5,802
0.000
5.002
6,702
i 70 03
9.5 1
A.e i
.371 1
,071 1
fl.9 2
7.7 2
,25
.7
100, ft. 0. 0101
20.7 0. 0. 0001
525. .5 9.0 0002
.1 10 25 ?, 11 13 .25 11
03 .05
9,2 9.012
7,6 9.012
03 ,5?« 0« 0.0 05 ,«<>1
23.6 7.&03 U5.0 31.105 56.8 30.107
03 .131 01 ,126 05 0.0
15,6 7,103 20.0 8,107 ?8,0 6.207
1200, 0,003 1210. 1050,10 1150. 1100,10
18.0 12,003 11.0 7.707 0.0 0.000
8.0 7.003 6,7 6,307 0,0 0,000
15, 10 30 10
8,3 3 »,1 3 8,3 3 B.7 3
7.6 3 7.* 1 7,5 3 7.1 3
Figure 5.2 Organized Print of Inputs
179
-------
05/30/75 1?J56:0<> "INK 000373i)53
000573
S30 75
OATE
•THE INPJT CARv
oo
o
:CQSTS=O
PTPCSTC 15=
( 2) =
( 3) =
( ENPtD SOLIDS
Tf^PERATUKE DIPF
TIN
DO
Figure 5,3
Organized Print of Inputs
-------
OS/30/7S
WINK OOC373oS3
S30 75
OATE OS307S
PAGE
--POn
00
S(J)
NCijTiO
J)
V J •
.( l.J)
( 2.J)
( 3.J)
( . J)
(27. J)
(25. J)
(29. J)
(30? J)
)
J= 1 2
0000001 .0000002
0000001 .0000003
J= 1
.00000
.00000
9.00000 8
.00000
50.00000 70
.00009
3
.000000*
.OnOOOlO
2
.PlOoC
.10000
.00000
.00000
.00000
. 0 0 0 fl 0
.00000 25.00000
.00-^00
.00100
.00000 100
.00000 20
.00000
.ooooo
.70000
.00000
. fl o o r o
.00000
.00000
.00000
.6:000
.03UO
.ooooo
. 0 0 0 0 0
.00^00
. 0 3DOO
i o o . o :• o o .1 200
.0-3300 2 ;
.00?00 1
.00000 10
.00000
.00 ?.00
.00 1.00
I CUT 1 = 1
.C'iODO
.02000
11
.0000006
.0000016
3
.ObOOO
.30000
6.60000
.00000
90.00000
.OOUOO
175.06000
. 15000
.05000
.00000 2000.00000
.OOOoO
.02000
.01000
.SCCoO
. 10000
.00500
.&5000
.00100
.01000
.90000
.01000
.00000
.OOCOO
•00050
. 1 0 0 1) C
• a o o o o
. 0 0 C :) 0
. o c o o o
.00000
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1.00
2.00
IOLJT,
200.00000
. 10000
.02000
.90000
.30000
.05000
. 17000
.00500
1 .00000
3.00000
. 10000
.00000
.ooooo
.00100
.70000
SOD. ooooo
'10.00000
2.50000
40.00000
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6.00
3.00
2i=l
1 lEXKCsJ NOSORS= 3
•
OiJRCE 1 =
I)
(I)
.10 GAIL*.
1 2 3
10 10 5
1 2 1
5
.0000010
.0000025
'I
. 10000
.90000
4.SOCOO
.OOCOO
1 10.00000
.00000
200.00000
.25000
1 .00000
7500.00000
600-00000
1.00000
.05000
1 .20000
.90000
. 10000
.50000
.01000
3.00000
1.50000
5.00000
,00000
.00000
.02000
.50000
100 D. OOOOO
100.00000
3.00000
100.00000
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A. 00
:ouT2s=]
NUSJRS=
00 KETA= l.SO K,NU =
6
.0000032
.0000050
s
.50000
2.70000
1.80000
.00000
130.00000
.00000
210.00000
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10,00000
1SOOO. OOOOO
3000.00000
5.00000
. 10000
3.00000
2.70000
.25000
1.00000
.02000
9.00000
7.00000
30.000UO
.00000
,00000
. 10000
1.60000
1500.00000
280,30000
4.00000
200. OOOOO
.00000
10.00
5.00
I
3
1.50
7
.0000100 .OOOC
.0000100 .OOOC
6
1.00000
3.00000
.90000
.00000
150.00000
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250.00000
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5 0 . u 0 0 0 0
150000. OOOOO
SOOOO. OOOOO
10.00000
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8.00000
3.00000
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1 .50000
.05000
20.00000
10.00000
50.00000
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10. OOOOO
2300.00000
300.00000
10 .00000
1000.00000
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6.00 7.00
IOU13S1
ENU= ,ro
.0001000
.0001000
10
.0001120
.0001120
11
.0001260
.OOOU60
ALPHA=
ISFUP(i)
ISFLO(I
1C3PCI) 0 0
F3R 1 = 1 TO NjSQSSA 1, £. I.
8.00 9.00 1J.OO
3s 10000.00 0= .3
ic
QU
KBOD DOSAT
IONESD NPIP NPPAKS(J) ,iiMNTnSU) J=l TO NPIP
Figure 5.3
— Continued
-------
05/1-0/75 12:56109 >>INK
1 JONES MAMUFACTUKlNG CO.
2 SAFE CHEMICAL CO,
3 SEWAGE TREATMENT
00047J
75
100.000
ao.7oo
sas.ooo
OATF
.00
.00
.50
, Oo
.00
9,00
It 7
oo
NJ
Figure 5. 3
i— Continued
-------
05/30/75 12156109
000373D53
000^73
S30 75
DATE
PIPF FLO* AND SELK-MONlTo"P'G
(SO"RCt> (PIHF)
ID HlPNO IOS GSuN'lT
1 1
-------
0^/30/75 12|56IO<> "ij1^ QOC-573.-5? <>OM'/t 530
PIPE FLO* ANd SEUF-HONlTilRING CONSTITUENT
(50'iRCE) CrlPE)
ID PlPNO IOS (3SUf;iT MNTnOSiQS;-.EA>:--fOH ALL MONTHS
2 t 99 3 t. .0'* / ?t ,0« / 3, .05 /
ID PjPNO IFAUM PKH's'TT S'^AX tS^E AN »NS iZf-FOP ALL MONTHS
2 t 23 6 10.00. '
-------
05/30/75 I2l5i:09 X
G00373Q53
000373
S30 75
DATE 053075
PAGE
;• ;PF FLO* AND SELF-MONITORING CONSTITUENT DATA
(SOURCE) (PIPE)
10 PlPNO JOS OSuNjT MMTnOSt CSMEAN--KOH ALL MONTHS
3
10
3
PIPP FLOn
(S2I'SC£)
10
3
10
3
3
3
i— j
oo 3
Ln
1 99
8
PlPNO IPARM PRUNIT
1
AND SELF-
(P1PE)
PIPNO ICS
Z 99
PIPNO IP
i
2
Z
2
8 1
MONITORING
OSUNlT
a
ARM PRUMT
6 I
10 7
3 1
30 1
1, .£3
5, .49
/ 2, .'11
/ b, .'16
SMAX,SMEAN,USIZE--FOR
211.00,
5b.8o,
CONSTITUENT
15.50, 2/
30.10, 7/
DATA
/ 3,
/ 7,
ALL MONTHS
a. oo,
16.80,
.52 / 4
.55 /
2.80,
.00,
f
Zf
^t
.00 /
23.60,
13.20,
7.60,
6.00,
3/ 45,00,
I/
31.40, 5/
M(vThjOS«()Sr1EAI>.--f OS ALL MONTHS
1, .12
5, ,00
SMAX.S,
8.40,
28.00,
ICBO.OO,
1150.00,
7. 60,
.00 ,
5.7n,
.00,
/ 2, .13
/ 6, .13
i£AN>f.SIZE--FOR
3,50, 2/
6.20, '//
1C10.00. 2/
1 100.00, 10/
6.30, 2/
.00, O/
5.00, 2/
.00, O/
/ 3,
/ 0,
ALL MONTHS
19,20 ,
19.20,
.00,
.00,
13.00,
.00,
7.00,
5.40,
.13 / 4
.00 /
5.60,
8.90,
.00,
.00,
5.00,
.00,
6.70,
5.20,
,
2/
7/
O/
O/
2/
O/
2/
2/
.13 /
15.60,
.00,
1200.00,
.00,
18.00,
.00,
8.00,
.00,
7.10,
.00,
.00,
.00,
12.00,
.00,
7.00,
.00,
3/ 20.00,
O/
3/ 1210.00,
O/
3/ 11,00,
O/
3/ 6.70,
O/
8.10, 7/
U50.00.10/
7.70, 7/
6.30, 7/
EFFLUENT
(SOURCE) (PIPE)
ID PIF-0 E?FLO^ IP,x:.IUNlT,K—FOR ALL CONSTITUENTS CF PIPE
3 I 2.Co 6, lO.OOn.l. 1
."6
b,
10,
3,
30,
20.000,1, 1
1500.000,7, 0
15.000,1, 0
.0001 1, 0
CO-.PLlANCE «ONITCR1NG
(PIPE)
1C
1
1
1
1
1
2
J IP/"
1 23
1 22
1 1*
1 25
1 1 J
1 23
Nj«
3
3
3
2
3
8
X) (K) ,-"(K)--F3R *=1 TO
10.000,
8.000,
.461,
.051,
.052,
P. 500,
6.300,
NlH
1
I
I
1
1
1
3
C* POINTS
9.
7.
,
,
,
9.
8.
000,
100,
202,
023,
059,
100,
700,
1
1
I
1
1
2
3
9.500,
6.800,
.371,
.071,
8.900,
8.500,
1
1
1
1
2
3
Figure 5.3 — Continued
6.300, 3
8.400, 3
-------
OS/30/75
2
b3u
0!>307b
23
7.70"r I
3
8.000* 2
7.«00* 3
7.700t a
7,600i 3
7.600* 3
7.600* 3
Figure 5.3
— Continued
-------
05/30/75 [2J56J09 WjNX Oflrt37.'5c.53 «On.?/J S30 75 OATE 05307S
1MTIAL ALLOCATION
SCHftCt TIMES JiAPPLED RESOUKCtS USED
t i 560.50
2 2 1050.00
3 1
TOTAL RESOURCES USED 3309,SO
M COST OF UNDETECTED VIOLATIONS .32322
Figure 5.4 Printout of Initial Resource Allocation
-------
05/?0/7S 12»S6«09
000i73
S3u
75
DATE 053075
tiST OF SAf.Pt.tS
COST Of-
oo
oo
PRIOHITY
1
?.
J
17
16
19
20
21
as
23
;:u
25
SOURCE
SAMPLED
3
1
1
2
Z
2
2
2
2
2
?
2
2
1
1
1
1
1
1
3
1
1
3
3
3
MARGINAL
RETUKN XJOO
,308i7G(3
.012^1636
.008C.SS93
,OQ7i«7338
.00*) '15239
,00557088
,00060981
.OP'115270
,003'J3S37
.OOJ09SS5
.00267265
.002J0752
,00062all
.ouooiue
,00000157
,00000006
,00000000
.00000000
,00000000
.00000000
.00000000
.00000000
.00000000
.00000000
UNOETtCTEu
VIOLATIONS
1.810B2
,«0fl38
.3S»«23
.29253
.25307
.21900
.18958
.lt>
-------
05/30/75 12;56:09 WINK
Sit)
75
UATE OSJ075
LISI OF SiMPLtS
sousct MARGINAL
'''UIKITY SAMPLED KffURN XJOO
\
<>
3
1 ,0l25lb3o
2 .Oo6'l7nJ3V
? ,OOSb70«8
'1 ? . 0 0
9 2 ,00
-------
(15/7,0/75 I2s56»0<> WINK 000373l>S3
75
FINAL ALLOCATION
8'IOGET 10UOO.OO
DATE 053075
MIN MO. MAX NO. COST OF
SAMPLES SAMPLES TIMES RESOURCES UNDETECTED
SOURCE KEOl'JPEO ALLOWED SAMPLED USED VIOLATIONS
1
a
*
I 10 7 3923. bO
£ 10 10 5aao.OO
1 5 I 593.00
.00000
.07700
.00000
TOTAL RESOURCES USED 9796.50
rINAL COST OF UNDETECTED VIOLATIONS .07700
Figure 5.7 Printout of Final Allocation Based on Budget Limit
-------
OV30/75
"On.*73 S30 7'J
Ftt-*L
MAXIMUM Al.l P*l'0 COST OK UNDETECTED VIOLATIONS
OATE 053075
,25000
MIN MO, MAX NO.
SAclPLES SAMPLES
SOURCE REUUiPtO ALLOv-TD
COST OF
TIMES RESOUHCLS UNOETtCTtD
SAMPLED USED VIOLATIONS
1
2>
5
\ 10
?. 10
1 S
2
3
1
1121.00
15BI4.00
593.00
.00369
.21530
.00000
TOTAL RESOURCES USED 3296.00
FINiL COST OF UNUCTFCTEO VIOLATIONS .21900
Figure 5,8 Printout of Final Allocation Based on Maximum
Acceptable "Cost of Undetected Violations"
-------
Output Option 5 : Statistical summary tables for each source
(see Figure 5.9).
All of the values under "Resources Used" or "Resources Required"
in the output are dollar values. They are derived from the base cost to
monitor each effluent source given: (1) its number of pipes (input vari-
able PIPCST), and (2) the cost to analyze each of the constituents of each
pipe of an effluent source (input variable CONCST).
The "Cost of Undetected Violations", as listed in the output, re-
fers to the expected value of the damage caused by the pollutants (assuming
Resource Criterion #2 is used) for those days when violations go undetected
(see Section 2 of this handbook, and Section VI of Reference 1 for a more
complete description of the term). The "Marginal Returns" listed are
simply the decrease in the cost of undetected violations per unit of re-
sources expended as each sample is taken.
In the statistical summary tables, the means, standard deviations,
and standards are in units of Kg/day. For lognormal distributions ('L'
under 'DIST'), the mean and standard deviation are of the log values of
the loadings.
In some cases, a series of '***' will be printed out in the sta-
tistical summary tables. This occurs when a constituent is discharging
from more than one pipe; only one value of expected damage and probability
of no violation (for the combined loadings) is possible, and so when the
constituent is printed more than once '***' replaces the numerical value.
Similar output occurs for pH, since pH is always printed out under pH MIN
and pH MAX.
192
-------
05/^0/75 l2!S6tO<> WINK 0003731)53
00(1.473
S30 75
OATE 053075
» » » 4 * * f * * * *
sonnet i
DISCHARGE (MLXOAY)c
.7207
UPSTREAM FLOw (ML/DAY)=
100,0000
CONSTITUENT
LEAD
PHOSPHORUS
CYANIDE
STANDARD
Q.5000
A. 5000
.OS29
1 .OS80
.1322
DIST
N
N
N
L
L
EST. MEAN
8,0'137
7.M12
.'Ii67
-1.9153
-1.5S15
EST. SIGMA
l.fa3bH
1.4335
.2788
.3106
.2849
EXPECTED
DAMAGE
*»****»*
.5626
1.U763
,0031
.0687
PROB. UF NO
VIOLATIUN
**»»»******
,S
-------
e ;r-
os/30/75
WINK
000373
S30 75
DATE OS3075
SOUKCt 2
DISCHARGE (ML/r>AY)3
UPSTREAM FLUW (HL/DAY)a
20.7000
PH-MIN
STAV04
-------
05/30/75 12:56!09 *1
00u373i;5j
S30 75
DATE 053075
»FIN
SOUKCE 3
PJPt = 1 UFA!.
MEAN DO CONCENTRATION'
,52-b5
UHS1KEAM FLOW CML/DAYJs
52S.OOOO
EXPECTED PKOfl, OF NO
COr.'STlT'-'c'^T
ChLOROFORf' EXTRACT
PTPE = 2 MF
MEAN 00 CQNCF.NiTRA
C 0 »• S T I T u f. >; T
CHLOkOFORl EXTRACT
CJUIFOKXS-- TOTAL
0005
STANDARD
tO.OOOO
AM niScwARf,E (ML/OAY
1 1 0 N ( r< r, / L ) = 11 .
STA^-Df^D
P. 3000
1500.0000
6.97'JO
OlST
L
J =
1M2
DIST
L
N
N
ESI. MEAN
1.1335
.1305
EST. MEAN
-.0380
1069.0909
1.0201
EbT. SlbMA
.5262
UPSTREAM f-LOW
EST. SIGMA
.3944
^7307
DAMAGE
1.8286
(ML/OAY)=
EXPECTED
DAMAGE
.0267
.0090
V10LAIION
.624^
S25.0000
PROB. OF NO
VIOLATION
.9907
1.0000
1.0000
Figure 5.9
— Continued
-------
Error Messages
The program performs a careful check on the input data and should
an error be found, a series of 'XXX1 followed by an error message will be
printed and the program will stop. The error message will include infor-
mation such as the card number (Column 1 in Table 5.1) or source and pipe
number so that the user can locate his mistake; the error message will
also include a brief diagnosis of the problem. In most cases, an obvious
error such as a transposition of data or a misspecification of an option
can be easily found and the reader need only refer to Section 5.2 (Input
Description) to correct the error. In certain instances, a sequencing
mistake will have been made—a card may have been deleted or identifying
numbers rearranged. In this case the error message may not point directly
to the source of the error but to some point downstream and the user will
need to carefully compare the preceding part of the input deck against
Section 5.2 to find the error.
Sometimes an error may not be detected until processing of the data
has begun. If sample minimum loadings and mean or maximum loadings have
been transposed, for a sample in the input stream, the program will auto-
matically delete the incorrect sample and print out a message specifying
the details but processing is continued. However, should the total number
of valid samples during the sampling period for any constituent be too
small (less than 4) or too large (larger than 40 for pH or 365 for other
constituents) an error message will be printed specifying the source and
the constituent and the program will stop. Also, should the ratio of the
combined maximum to the combined mean, during the sampling period for any
constituent too large (greater than 6.0), or too small (less than 1.25),
the program will print the details and stop. In the cases mentioned above,
a decision will .have to be made to correct data that was incorrectly enter-
ed or to delete constituents which cannot be tolerated by the program.
196
-------
SECTION 6
DEMONSTRATION OF PROCEDURES
This section demonstrates results of tests of both hand and com-
puter calculation procedures. The tests were performed using data supplied
by the State of Michigan, Department of Natural Resources. The data was
obtained on seven effluent sources which are a subset of the data used in
the previous SCI demonstration of the computerized procedure [1] . The
effluent sources used were those computed to give the highest environmental
damage in the first SCI report (see Section 9 of [1]). The constituents
used in this demonstration are high and low pH, biological oxygen demand
(BOD, total suspended solids (SS), chromium, phosphorus, and oil-grease.
In Section 6.1, data from the year 1972 is used in the hand cal-
culation procedure to determine the initial allocation of monitoring re-
sources. Section 6.2 shows how the more recent 1973 data is used to
illustrate the update of statistics procedure. Section 6.3 shows an
alternate method of evaluating the magnitude, or severity, of violations
in hand calculations. Finally, Section 6.4 gives results of the computer
calculation method applied to the same test problem, and compares these
with the hand calculation results.
Although there are minor discrepancies between the hand and com-
puter calculation results, due primarily to the different allocation
criteria used (described in Section 2), they are in general agreement.
In all cases, results were found to be reasonable.
CAVEAT
The objective of this section is the demonstration of the hand
calculation approach. The selection of the Grand and Saginaw Rivers to
197
-------
further this objective should not be construed as an expression of opinion
concerning the status of these rivers or their tributaries. The results of
the demonstration are based on a careful application of the procedure to
the data available. The authors have made every attempt to assure that
the data used is exhaustive and representative, but they recognize the
possibility that relevant information may have been overlooked. To this
extent, the results of the demonstration may be considered directly appli-
cable to evaluation of water quality surveillance on the Grand and
Saginaw Rivers.
6.1 DEMONSTRATION OF HAND CALCULATION PROCEDURES - INITIAL ALLOCATION
The hand calculation approach was successfully demonstrated using
the Section 4, User Manual. Self-monitoring data from seven effluent
sources on the Grand and Saginaw Rivers in Michigan were used to determine
resource allocations for effluent compliance monitoring. Four sources
are automobile and chemical industries, typical of the area, while the
other three effluent sources are municipal waste treatment plants located
on the same rivers. All are major effluent sources whose discharges
historically have been significant. The presentation here follows the
order of tasks found in the User Manual (Section 4). The reader is en-
couraged to use this section as a step-by-step illustration of the hand
calculation procedure.
TASKS 1 and 2
The procedures are self-explanatory. Tables 6.1 and 6.2 represent
the output from these tasks. All seven sources, their constituents, and
relevant standards are shown, although subsequent tasks generally will
illustrate the technique only for one source in order to reduce repetitive
calculations.
198
-------
Table 6.1 Statistical Distribution Types by
Constituent and Source
Source
9
10
12
18
22
25
27
Constituent
pH Max
pH Min
BOD
SS
CHR
pH Max
pH Min
SS
phos
Oil - Gr
pH Max
pH Min
BOD
SS
BOD
SS
BOD
SS
phos
BOD
SS
BOD
SS
ph'os
Distribution
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
Task 1
Alternate Used
1 or 2
_
-
2
2
-
-
-
2
2
2
-
-
2
2
2
2
2
2
2
2
2
2
2
2
199
-------
Table 6.2
Effluent Standards
Source
(1)
9
10
12
18
22
25
27
Constituent
Name
(2)
pH Max
pH Min
BOD
SS
CHR
pH Max
pH Min
SS
Phos
Oil - Gr
pH Max
pH Min
BOD
SS
BOD
SS
BOD
SS
Phos
BOD
SS
BOD
SS
Phos
Units
(3)
Kg/day
Kg/day
Kg/day
Kg/day
Kg/ day
Kg/day
Kg/ day
Kg/day
Kg/ day
Kg /day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/ day
Kg/day
Kg/day
Standard Value S
(*)
9.5
6.5
189.27
473.2
5.7
10.5
6.5
46.4
1.35
19.9
9.0
6.0
41.6
104.1
3000.0
4445.2
1360.8
907.2
378.5
4535.9
3628.7
272.2
272.2
58.3
200
-------
TASK 3
Table 6.3 presents raw data for source 9 and illustrates the cal-
culation of the mean, m. Data for other sources are similar and are not
included in this example.
All constituent data except pH are expressed as concentrations,
but must be converted to loading rates (Kg/day) in order to compare data
to the standards in Table 6.2. Table 6.4 shows typical conversions.
Finally, all converted data is entered in columns 1-7 of Table
6.5.
TASK 4
Task 4 is concerned with the calculation of self-monitoring
statistics. The hand calculation procedure is illustrated below for pH
Max.
M = m = 8.39
' G = 2.735 (Figure 4.3)
Distribution is normal (N)
N = n = 249
v = 50 (Figure 4.5)
Although formulas may differ, the procedure for the remaining
four constituents of source 9 is virtually identical. The calculated
statistics are entered in columns 8-12 of Table 6.5.
201
-------
Table 6.3
Source Number 9: Raw Data
Jan, 72
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec, 72
Sn
Lnx
m=^
Z_»n
Min=io
Max=C
PH
Avg Max Min n
8.67 9.95 7.52 17
8.9 10.3 7.8 20
9.21 10.43 7.9 20
9.7 10.9 7.7 20
8.4 10.4 6.4 22
6.2 7.8 4.4 22
8.4 10.6 6.1 19
8.5 10.8 7.3 23
9.1 10.2 7.8 21
8.2 9.0 7.2 22
7.8 9.4 7.5 22
7.9 9.0 7.3 21
249
2089 -
8.39
4.4
10.9
BOD (mg/fc)
Avg Max n
115.6 155.4 15
95.5 168.9 20
179.1 279.2 20
126.5 295. 20
101.9 234. 22
92.1 134. 22
60. 84. 19
46.2 100.4 18
70.8 198. 17
94. 358. 22
80. 150. 22
86.5 208. 19
236
22670
96.06
_
358.
SS (mg/SO
Avg Max n
6.03 15.2 17
6.8 16.8 20
5.0 12.2 20
3.1 9.0 20
9.9 44.6 22
10.6 47. 22
3.8 16. 19
4.7 13.8 23
3.9 8.0 21
6.3 12.2 22
4.4 8.1 22
3.5 6.0 21
249
1423
5.713 - 0
_
47.
CHS (ug/Jl)
Avg Max n
3.53 30. 17
0. 0 20
35.5 320. 20
2.0 20. 20
.91 10. 22
4. 20. 22
5.21 70. 19
0. 0. 23
0. 0. 21
59. 400. 22
0. 0. 21
0. 0. 21
248
2315
9.335
_
400.
Effluent
Flow
Avg (mgd)
1.14
1.21
1.27
1.18
1.17
1.19
1.0
1.1
1.3
1.4
1.49
1.5
-
-
1.25
-
-
NJ
O
to
-------
Table 6.4
Data and Standards Conversion
Unconverted
Data or
Standard
96.06
358
5.713
47
9.335
400
Unconverted
Units
mg/1
mg/1
mg/1
mg/1
mg/1
mg/1
Conversion
Factor
3.783*1.250
3.783*1.250
3.783*1.250
3.783*1.250
3.783*1.250
*10~3
Converted
Units
kg/day
kg/day
kg/day
kg/day
Converted
Data or
Standard
454.4
1693
27.02
222.3
.04416
.1892
BOD
SS
Chr
Note: This table can be duplicated for use in the hand calculations.
203
-------
Table 6.5
Effluent Data, Statistics, and Probabilities
Y(Task 6)
Discounting constant, h(Task 7) -
Self-nor.iroring input data (record in source sequence)
Source
(1)
9
10
12
18
22
25
27
Constituent
Kar.e
(2)
pH Max
pH Min
SOD
SS
Chr
pH Max
pH Min
SS
Phos
Oil - Gr
pH Max
pH Min
BOD
SS
BOD
SS
BOD
SS
Phos
BOD
SS
BOD
SS
Phos
Units
(3)
_
-
Kg/day
Kg/day
Kg/day
_
-
Kg/day
Kg/day
Kg/day
-
-
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Kg/day
Mean
m
(4)
8.39
8.39
454.4
27.02
.04416
8,11
8.11
29.86
1.614
0
7.64
7.64
64.25
67.50
252.98
1815.1
2140
2094
132
5197
5942
3639
2849
295.3
Max
^
(5)
10.9
-
1693
222.3
1.892
10.1
-
91.63
15.71
0
9.91
-
300.1
617.9
1673.5
6945.5
6105.4
9616.3
453.6
11958
17452
7838.2
8291.8
476.28
Mln
u)
(6)
_
4.4
-
-
-
_
7.0
-
-
-
-
6.68
-
-
_
-
-
-
-
_
-
_
-
-
Sample
Size
n
(7)
249
249
236
249
248
285
285
285
285
0
248
248
215
247
21
21
349
351
347
295
297
142
149
128
1 TASK 4 |
Self-monitoring statistics
Est'd
Mean
V
(8)
8.39
8.39
454.4
1.2466
-.8227
8.11
8.11
29.86
-.005
0
7.64
7.64
64.25
1 . 6204
2.073
1815.01
2140
2094
132
5197
5942
3639
2849
295.3
Est 'd
Std.
Dcv,
0
(9)
.9177
1.459
455.37
.401
.68
.7176
.4003
22.276
.43
-
.8300
.3510
87.742
.426
.549
2681.9
1396.3
2648.7
113.24
2429.4
4135.8
1643.5
2117.8
68.87
Distrib-
ution
L or N
(10)
N
N
N
L
L
N
N
N
L
-
N
N
N
L
L
N
N
N
N
N
N
N
N
N
n
(ii)
249
249
236
249
248
285
285
285
285
0
248
248
215
247
21
21
349
351
347
295
297
142
149
128
V
(12)
50
50
49
50
50
53
53
53
53
-
50
50
47
50
13.8
L3.8
58
58
58
54
54
39
40
43
Self •*• conpliance
U
(13)
SAMI
SA>
a
(14)
AS '
E AS
n
(15)
ASK
TASK
V
(16)
4
6
TASK 7
N'ev cue*
U
(17)
VAL
TAS
e
(18)
;cs ;
; 6
statis.
n
(19)
utr '
0
(20)
s
Probabilities
Norsi'd
Effl't
Std.
X
(21)
1,2954
x =•
1.2954
-5822
3.5622
2.3288
2.0220
X
3.3905
.7425
.31473
-
1.639
x =
4.632
-.25314
.93204
2.5576
.9807
-.5580
-.4481
2.1768
-.27212
-.55934
-2.0486
-1.2167
-3.4413
4(x)
(22)
.38676
.4024
-21978
.4997
.49007
.4996
.4998
.27111
.12352
-
.4494
.4999
-.1018
.32434
.49473
.33663
-.2115
-.1729
.48525
-.1072
-.2120
-.4798
-.3882
-.4993
Pr . non-
viol 'r../
const.
Pij
(23)
7892
.2802
.9997
.99007
.9994
.7711
.6235
-
.9593
.39815
.82434
.9947
.8366
.2584
.3271
.9853
.3928
.2880
.0203
.1119
.0003
K)
O
.p-
Not required for pH nin.
Required only for pH rain.
Note: This table can be duplicated for use in the hand calculations.
-------
TASKS 5,6, and 7
These tasks do not apply in this calculation.
TASK 8
Task 8 is illustrated in Table 6.6, where values for x,
-------
Table 6.6 Worksheet for Task 8
pH (Max and Min considered simultaneously)
y = 8.39 (Table 4.5)
S = 9.5 (Table 4.2)
S = 6.5 (Table 4.2)
S < \i < S, SO
u - S
x = —;— = 1.2954
x = 2—-*- = 1.2095
a
*(x) = 0.38676 (Table 4.7)
*(x) = 0.4024 (Table 4.7)
P. . = *(x) + $(x) = 0.7892
206
-------
Table 6.7 Worksheet for Task 10
Method B is chosen for each source
pH (Max and Min considered simultaneously)
k = k = 1
U = 8.39
S = 9.5
S = 6.5
S i y ^ S, SO
D = k a j f(x) + x[0.5-*(x)]|+ k aj=(x) + x[0.5-*(x)]j
= (1) (0.9177) j 0.192 + 1.2095[0.5-0.38676]'
+ (1) (1.459) JO.1725 +1.2905[0.5-0.4024] = .7373
207
-------
Table 6.8
Record of Task 10 Options and Calculations - K
Violation weighting factor assignment method (1 or 2 ); 2,1
Source
No.
i
(1)
9
10
12
18
22
25
27
Constituent
Name
(2)
pH Max
pH Min
BOD
SS
CHR
pH Max
pH Min
SS
Phos
Oil - Gr
pH Max
pH Min
BOD
SS
BOD
SS
BOD
SS
Phos
BOD
SS
BOD
SS
Phos
Distri-
bution
L or N
(3)
N
N
N
L
L
N
N
N
L
-
N
N
N
L
L
N
N
N
N
N
N
N
N
N
Type of
WFF
A/B/C
(4)
C
C
A
A
A
C
C
A
A
A
C
C
A
A
A
A
A
A
A
A
A
A
A
A
WFF
Coefficient
k
(5)
.1
.1
.2
.025
.20
.1
.1
.025
.10
.10
.1
.1
.2
.025
.2
.025
.2
.025
.10
.2
.025
.2
.025
.10
Expected
Extent of
Violation
D
(6)
0.7373
68.84
0.003
1.1767
0075
.0740
6.9984
-
.1555
9.498
.4196
1.9724
5.790
228.57
43.86
6.12
267.10
86.10
657.78
67.29
5370.
Note: This table can be duplicated for use in the hand calculations,
208
-------
Table 6.9
Ranges of Sampling Rates and Expected Extents of Undetected Violation
Source
No.
i
(1)
9
10
12
18
22
25
27
Constitu-
ent Inter-
dependence
SD/SI
(2)
SI
SI
SI
SI
SI
SI
SI
TASK 9
Prob. of
Non-
violation
Pi
(3)
.2189
.4805
.3149
.8322
.1054
.1131
.000001
TASK 10
Violation
Weighting
Factor
c .
(4)
68.84
6.9984
9.498
5.970
228.57
267.1
2370.
TASK 11
Min . No .
Samples
Required
SL.
i
(5)
0
0
0
0
0
0
0
Max. No.
Samples
Allowed
Li
(6)
3
3
3
3
3
3
3
TASK 12
Alternative Expected Extents of
Undetected Violations, C .(s .) , for
Various Sampling Rates, s.
SrL
(7)
15.1
3.36
4.99
4.97
24.1
30.2
.002
2
(8)
3.30
1.62
.942
4.13
2.54
3.42
0
3
(9)
.722
.776
.300
3.44
.268
.386
0
4
(10)
-
-
-
-
-
-
-
5
(11)
-
-
-
-
-
-
-
6
(12)
-
-
-
-
-
-
-
7
(13)
-
-
-
-
-
-
-
8
(14)
-
-
-
-
-
-
-
to
o
Note: This table can be duplicated for use in the hand calculations.
-------
TASKS 11 and 12
Limiting sampling rates are established and entered in Table 6.9,
columns 5 and 6.
For source 9, the expected extent of undetected violations,
C.., is calculated below.
Sg = C9(l) = (68.84)(0.2189) = 15.07
C9(2) = 3.2986
C9(3) = 0.7221
TASKS 13 and 14
Component per sample costs were not obtained for this demonstration.
As in the computerized procedure, total cost per sample was assumed to be
$525 for each source. This figure and the laboratory charges per con-
stituent are entered into Table 6.10.
The marginal return for source 9 and sample 1 is computed using
the formula:
. 0.09593
For sample 2 and 3, the following calculations are made:
210
-------
Table 6.10
Resources Needed to Monitor Each Source Once
Source
No.
i
(1)
9
10
12
18
22
25
27
Man
Hours
Per
Sample
(2)
Cost
Per
Man
Hours
(3)
Travel
Miles
Per
Sample
(4)
Cost
Per
Mile
(5)
Per Sample Cost of:
Man
Hours
(6)
Travel
(7)
Total
(8)
525
525
525
525
525
525
525
Total
Per
Sample
Cost
(9)
Li
ri
0
#L,
•PH
Max
(10)
3
3
3
-
-
-
-
iboratory Analysis
large/Constituent
idd constituent names)
92
pH
Min
(11)
0
0
0
-
-
-
-
ff'J
BOD
(12)
20
-
20
20
20
20
20
#4
S9
(13)
5
5
5
5
5
5
5
f/5
Chr
(14)
750
-
-
-
-
-
-
ffb
Phos
(15)
-
10
-
10
-
10
Total
Cost
560.5
543
553
550
560
550
560
Note: This table can be duplicated for use in the hand calculations.
-------
r9
- 15.07 - 3.2986
P9
yg(3) = 0.0046
These values are entered in Table 6.11.
TASKS 15, 16, and 17
There are no mandatory samples, so Task 15 does not apply. Tasks
16 and 17 are self explanatory and are illustrated by Tables 6.12 and
6.13.
6.2 UPDATE PROCEDURE
The preceding initial allocation of resources (given in Section 6.1)
utilized data from 1972. This section incorporates self-monitoring data
from 1973 to illustrate the hand calculation update procedure. Tasks 3
through 7 are illustrated because only these tasks are directly concerned
with the update procedure.
The other tasks do not change, although Tasks 8 through 20 are
repeated during the update procedure.
Only one source (27) is used to illustrate the update procedure,
but all sources are handled similarly.
212
-------
Table 6.11
Marginal Returns for Each Source
Source
No.
i
9
10
12
18
22
25
27
Marginal return, u.(s.), from one additional sample, number s
V1
.09593
.00670
.01177
.00182
.36514
.43071
4.2321
2
.02100
.00322
.00371
.00153
.03848
.04871
.000004
3
.00460
.00155
.00117
.00125
.00406
.00551
0
4
_
-
-
-
-
-
5
_
-
-
-
-
-
6
_
-
-
-
-
-
7
„
-
-
-
-
-
8
„
-
-
-
-
-
ho
h-'
LO
Note: This table can be duplicated for use in the hand calculations.
-------
Table 6.12
Sampling Priority List
Priority
Order
(1)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Source
No.
i
(2)
27
25
22
9
25
22
9
12
10
25
9
22
12
10
18
10
18
18
12
27
S ample
No. (3)
s .
i
(3)
1
1
1
1
2
2
2
1
1
.3
3
3
2
2
1
3
2
3
3
2
Marginal
Return
V8i>
(4)
4.2321
.43071
.36514
.09593
.04871
.03818
.02100
.01177
.00670
.00551
.00460
.00406
.00371
.00322
.00182
.00155
.00153
.00125
.00117
.000004
Degree of
Undetected
Violation
Incre-
mental
Aci(Si)
(5)
2957.
-2370
-236.9
-205.5
-53.8
-26.8
-21.6
-11.8
-6.5
-3.6
-3.0
-2.6
-2.3
-2.0
-1.7
-1.0
-8.4
-8.4
-.69
-6.5
-.002
Cumula-
tive
tt^s,)
(6)
295.7
587
350.1
145.6
91.8
65.0
43.4
31.6
25.1
21.5
18.5
15.9
13.6
11.6
9.9
8.9
8.06
7.22
6.53
5.88
5.878
Monitoring
Resources
Required
Per
Sample(s)
ri
(7)
560
550
560
560.5
550
560
560.5
553
543
550
560.5
560
553
543
550
543
550
550
553
560
Cumula-
tive
R=Er .
i
(8)
0
560
1110
1670
2230.5
2780.5
3340.5
3901
4454
4997
5547
6107.5
6667.5
7220.5
7763.5
8313.5
8856.5
9406.5
9956.5
10509.5
11069.5
Note: This table can be duplicated for use in the hand calculations.
214
-------
Table 6.13 Sampling Rates
Maximum monitoring resources available, R = $ 5000
Maximum acceptable degree of undetected violations =
Source
No.
i
(1)
9
10
12
18
22
25
27
Min. No.
Samples
Required
*i
(2)
0
0
0
0
0
0
0
Max. No,
Samples
Allowed
Li
(3)
3
3
3
3
3
3
3
No. of
Times
to be
Sampled
Si
(4)
2
1
1
0
2
2
1
Totals:
Monitoring
Resources
Needed
$
(5)
1121
543
553
0
1120
1100
560
4997
Degree of
Undetected
Violations
Vs.)
(6)
3.2986
3.3530
2.9910
5.9700
2.5390
3.4170
.0024
21.5810
215
-------
TASK 3
New self-monitoring data is entered in columns 1-7 of Table 6.14
TASK 4
The following values for a are calculated for each constituent
*nn . „ - 5892 - 3780 Q ,,
iSUJJ • 0 — '-•••"• •• = o»3D
cc 8868 - 3236
SS : ° = ~2756
T>U 984 - 318
Phos: 0 m 2i5Q -
TASKS 5, 6, and 7
Tasks 5 and 6 are not applicable to this update, but calculations
for Task 7 are shown below
Source 27, BOD
,
n + n
(144) (3780) + (142) (3639) =
144 + 142 J/J-
va + nu + va + ny -
v + v + 1
(39.5)(825)2+(144)(3780)2-f(39)(1643.5)2+(142)(3639)2-(144+142)(3710)2
39.5 +39+1
1297
216
-------
y(Task 6) •
Table 6.14 Effluent Data, Statistics, and Probabilitico
Discour.tiag constant, h(Task. 7) - _2
TASK 3
Self-aonitorir.g input data (record in source sequence)
Source
(1)
27
Constituent
Xa-.e
(2)
BOD
SS
Phos
Units
(3)
kg/day
kg/day
kg/day
Mean
01
(4)
3780
3236
318
Max*
(5)
5892
8868
894
Min
(J
(6)
-
-
-
Sample
Size
n
(7)
144
145
120
TASK 4
Self-monitoring statistics
Est'd
Mean
V
(S)
3780
3236
318
Est'd
Std.
Dev.
0
(9)
825
2200
230
Distrib
ution
L or N
(10)
N
N
N
n
(ii)
144
145
120
V
(12)
395
395
36
TASK 6
Self +• compliance
y
(13)
o
(14)
amc
tas
n
(15)
as
4
M
(16)
TAS<< 7
New cum. statis.
V
(17)
371
304
30
8
(18)
L297
L'177
165
„
(19
286
290
240
V
(20)
79
79
72
!
Norm' c
Std.
X
(21)
TAS:-; i
•Xx)
(22)
Pr . ncn-
vial'r../
ccr.sc .
(23)
I
1
1
i
1
Not required for pH nin.
Note: This table can be duplicated for use in the hand calculations.
-------
n = min|(n+n), hnj
= 286
v1 = min | ( v+v+1 ) , hv | = 79
A A
Updated values of the process mean (p.), standard deviation (o ) ,
and confidence constants (n and v, ) for the cumulative estimated mean
and standard deviation have been calculated for the constituent BOD for
source 27. Calculation for other constituents and other sources are
similar. The updated values were entered in columns 17-20 of Table 6.14
(Update of Table 6.5). It can be noted that these updated numbers are
somewhat, but not drastically, different from the prior statistics given
in columns 8-12 of Table 6.5.
6.3 ALTERNATE DETERMINATION OF VIOLATION WEIGHTING FACTOR
The initial hand calculation calculated a weighting factor function
(WFF) with a coefficient k which varied with the reciprocal of the re-
ceiving water concentration standard, — . An alternative is to vary k
1 0
with — where S is the constituent effluent standard for a particular
O
source. Task 10 discusses the differences in these representations.
This section illustrates the alternative where k = — . Tasks 10-
£>
17 are completed and the results are summarized in the following tables.
Table 6.15 shows the WFF constant k and the expected extent of
violation D for each constituent. These results are utilized in Table
6.16 to calculate c. and C (s ) for each source. In all instances,
218
-------
Table 6.15
Record of Task 10 Options and Calculations
Violation weighting factor assignment method (1 or 2 ):
Source
No.
i
(1)
9
10
12
18
22
25
27
Constituent
Name
(2)
pH Max
pH Min
BOD
SS
Chr
pH Max
pH Min
SS
Phos
Oil - Fr-
pH Max
pH Min
BOD
SS
BOD
SS
BOD
SS
Phos
BOD
SS
BOD
SS
Phos
Distri-
bution
L or N
(3)
N
N
N
L
L
N
N
N
L
-
N
N
N
L
N
N
N
N
N
N
N
N
N
N
Type of
WFF
A/B/C
(4)
C
c
A
A
A
C
C
A
A
A
C
C
A
A
A
A
A
A
A
A
A
A
A
A
WFF
Coefficient
k
(5)
.00528
.00211
.1754
.1
.1
.00216
.7471
t
1
1
.0240
.0961
.00033
.00022
.00073
.00110
.00264
.00022
.00028
.00367
.00367
.01715
Expected
Extent of
Violation
D
(6)
.73733
1.8186
.0002
.01032
.0075
-
.07974
.5184
—
.1555
-
1.1415
.16123
.00329
.05210
.83984
1.9339
.001617
.29443
.94910
12.0827
9.8883
4.0652
Note: This table can be duplicated for use in the hand calculations.
219
-------
Table 6.16
Ranges of Sampling Rates and Expected Extents of Undetected Violations
Source
No.
i
(1)
9
10
12
18
22
25
27
Constitu-
ent Inter-
dependence
SD/SI
(2)
SI
SI
SI
SI
SI
SI
SI
TASK 9
Prob. of
Non-
violation
Pi
(3)
.2189
.4805
.3149
.8322
.1054
.1131
.000001
TASK 10
Violation
Weighting
Factor
c .
i
(4)
1.8186
.5184
1.1416
.0521
1.9339
.94910
12.0927
TASK 11
Min . No .
Samples
Required
i.
i
(5)
0
0
0
0
0
0
0
Max. No.
Samples
Allowed
Li
(6)
3
3
3
3
3
3
3
TASK 12
Alternative Expected Extents of
Undetected Violations, C. (s .) , for
Various Sampling Rates, s.
V1
(7)
3981
2491
3595
0434
2038
.1072
00001
2
(8)
.0871
.1197
.1132
.0351
.0215
.0121
*•"
3
(9)
.0191
.0575
.0356
.0300
0023
0014
"""
4
(10)
-
• -
-
-
-
-
5
(11)
-
-
-
-
-
-
~~
6
(12)
-
-
-
-
-
-
~*
7
(13)
-
-
-
-
-
-
'
8
(14)
-
-
-
-
-
-
'
NJ
o
-------
calculations for each constituent are identical to those performed in the
initial allocation.
Table 6.17, the same as Table 6.10 in the initial allocation procedure,
is used in conjunction with Table 6.16 to calculate the marginal returns y.(s )
found in Table 6.18. Finally, the sampling priority list (Table 6.19) and
the sampling rates (Table 6.20) are formed by allocating resources in the
order of diminishing marginal returns.
6-4 COMPARISON OF THE HAND CALCULATION AND COMPUTERIZED RESULTS
The data in the hand calculation procedure was used in the computer
allocation program to obtain the results shown in Tables 6.21 and 6.22.
In general, the agreement between the two procedures was quite good, how-
ever results were not identical. Each assesses potential damage differently,
so disagreement - particularly in the realm of marginal returns - is reported.
Priorities may be expected to differ, although monitoring frequencies for a
fixed budget are remarkably close. Refer to Section 3.2 which discusses the
major technical differences between the two approaches.
PRIORITIES
Similarities In the hand calculation and computerized results are
observed in Tables 6.19 and 6.21. Both procedures have determined source 27
to be the most injurious to the environment, and consequently both procedures
assign top priority to monitoring that source. Furthermore, the probability
of uncovering a violation of standards for source 27 was sufficiently high in
both procedures so that repeat monitoring was unnecessary.
Sources 9, 22, and 25 were given, the next three priorities in both
cases, however, their relative positions differed. This is attributed to
the different methods of calculating marginal returns.
221
-------
Table 6.17
Resources Needed to Monitor Each Source Once
Source
No.
i
(1)
9
10
12
18
22
25
27
Man
Hours
Per
Sample
(2)
Cost
Per
Man
Hours
(3)
Travel
Miles
Per
Sample
(A)
Cost
Per
Mile
(5)
Per Sample Cost of:
Man
Hours
(6)
Travel
(7)
Total
(8)
525
525
525
525
525
525
525
Total
Per
Sample
Cost
(9)
L
(
#1
(10)
3
3
3
-
-
-
-
aboratory Analysis
large/Constituent
add constituent names)
if 2
(11)
0
0
0
-
-
-
-
ff3
(12)
20
-
20
20
20
20
20
f> ^
(13
5
5
5
5
5
5
5
ffi>
(14)
750
-
-
—
-
-
—
//fa
(15
-
10
-
—
10
-
10
Total
Cost
560.5
543
553
550
560
550
560
Note: This table can be duplicated for use in the hand calculations.
-------
Table 6.18 Marginal Returns for Each Source
Source
No.
i
9
10
12
18
22
25
27
Marginal return, u.(s ), from one additional sample, number s
V1
.00253
.00050
.00141
.00002
.00309
.00153
.02158
2
.00055
.00024
.00045
.000011
.00033
.00017
0
3
.00012
.00011
.00014
.00001
.00003
.00002
0
4
-
-
-
-
-
-
-
5
-
-
-
-
-
_
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
NJ
N>
U>
Note: This table can be duplicated1' for use in the hand calculations.
-------
Table 6.19
Sampling Priority List Using Hand Calculating Procedures
Priority
Order
(1)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Note:
Source
No.
i
(2)
27
22
9
25
12
9
10
12
22
10
25
12
9
10
22
25
18
18
18
27
27
Sample
No. (a)
Si
(3)
1
1
1
1
1
2
1
2
2
2
2
3
3
3
3
3
1
2
3
2
3
Marginal
Return
u.Csp
(4)
.02158
.00309
.00253
.00153
.00141
.00055
.00050
.00045
.00033
.00024
.00017
.00014
.00012
.00011
.00003
.00002
.00002
.00001
.00001
0
0
Degree of
Undetected
Violation
Incre-
mental
ACi(Si)
(5)
18.4964
-12.0827
- 1.7301
- 1.4205
- .8418
- .7821
- . 311
- .2314
- .2463
- .1823
- .1294
- .0952
- .0776
- . 068
- .0622
- .0192
- .0107
- .0087
- .0073
- .0061
- .00001
0
Cumula-
tive
DC^s,)
(6)
18.4964
6.4137
4.6836
3.2631
2.4213
1.6392
1.3282
1.0968
.8505
.6685
.5388
.4436
.3660
.2980
.2358
.2166
.2059
.1972
.1899
.1838
.1838
.1838
Monitoring
Resources
Required
Per
Sample (s)
ri
(7)
560
560
560.5
550
553
560.5
543
553
560
543
550
553
560.5
543
560
550
550
550
550
560
560
Cumula-
tive
R=Er.
i
(8)
560
1120
1680.5
2230.5
2783.5
3344.
3887.
4440.
5000.
5543.
6093.
6646.
7206.5
7749.5
8309.5
8859.5
9409.5
9959.5
10509.5
11069.5
11629.5
This table can be duplicated for Use in the hand calculations.
224
-------
Table 6.20 Sampling Rates Using Hand Calculation
Procedures
Maximum monitoring resources available, R = $ 5000
Maximum acceptable degree of undetected violations =
Source
No.
i
(1)
9
10
12
18
22
25
27
Min. No.
Samples
Required
*i
(2)
0
0
•o
0
0
0
0
Max. No.
Samples
Allowed
Li
(3)
3
3
3
3
3
3
3
No. of
Times
to be
Sampled
Si
(4)
2
1
2
0
2
1
1
Totals:
Monitoring
Resources
Needed
$
(5)
1121
543
1106
0
1120
550
560
5000
Degree of
Undetected
Violations
Ci(si}
(6)
.0871
.2491
.1132
0.
.0215
.1073
.00001
.57821
225
-------
Table 6.21 Priority List of Samples Using Computer
Calculation Procedure
t, i n ;• I i v
SOU&LE
S A f. P L E C
k F: f i Ik M Vino
COST OF
UNOfTtCTEG
VIOLATIONS
RESOURCES
7
o
I"
1 1
1?
IS
IS
17
Q
e1?
1 0
Q
2?
10
.1 J 'J 2 6 H U 6
. 1 0 r> b 3 S 0 6
.0 7626479
,0o
. n M 5 7 u a 3
. n 1 u o fc 6 P 0
,o13bO 756
. 0 0 Q <* 1 f 10 u 0 0 0 (.1
. nooooooo
20.
1 o , 9 7 0 a 5
.1 I5a3
a . 2 e 0 7 o
5.71670
3.69072
"5,6b8u7
b60.00
1 123.00
2233.bO
279U.OO
3357,00
3910.00
0060,00
S 0 1 0 . 0 0
55*0.00
6110.00
6653.00
7213,bO
7766.50
9672.bO
996b.bO
lOSlB.bO
1 1078.bO
11636,bO
226
-------
SAMPLING RATES
Although discrepancies may be found in the priority ordering for
each procedure, relatively little disagreement should be found in sampling
rates for a sufficiently large budget. Different marginal returns may
suggest different priorities, but both procedures should be able to sense
in general terms, those sources that require high monitoring priorities.
It was seen, for instance, that both procedures recognize the need to
monitor source 27 first, but found repeat monitoring unimportant.
Table 6.20 and Table 6.22 present sampling rates for each procedure
assuming a fixed budget of $5,000 and the results are close. In both al-
locations sources 9 and 22 are monitored twice and sources 12 and 27 once.
Small differences are found in the number of samples required for sources
18 and 25. The computerized procedure would monitor both sources once,
but the hand procedure monitors source 25 twice. Another difference be-
tween the two methods can be seen for source 10 which is monitored once
by the hand procedure, but is not monitored by the computer method. This
difference is largely due to the different sequences in which the budget
is spent. Using the hand procedure, it was possible to spend $4,997 to
monitor 9 times, but using the computerized procedure it was only possible
to monitor 8 times for a cost of $4,460. Had the hand calculation run in-
to similar budetary limits during allocation number 9, source 10 would not
have been monitored, and both procedures would agree.
The disagreement in the sampling rates appear quite small. Both
procedures tend to monitor the seven sources at about the same frequency
but may accomplish these tasks in different sequences. Both procedures
recognize the necessity to assign a high monitoring priority to potentially
harmful sources and to give lower priority to situations where additional
effect would yield relatively little new information.
227
-------
Table 6.22 Final Allocation Using Computer
Calculation Procedure
. T 5000.00
fM'-i Nfl. ?'AX M\ CUM OF
SAIL'S S^PLES Tires Ptsnunces
bi.K'QCt Kuj'UWfcD all.'Wo bArPL^D USbO
TniflL wtbni.iPCF. S i.iStO oiJftO.OO
l-T'.&l C^ST OF U'4/^TfCTLQ VIOLATIONS
0 03
in n .i
\? 0 }
IM 03
^? 0 j
2^ n 3
<=7 U 3
c?
0
1
1
I
1
I
U?l
b53
550
ll?b
550
560
.00
.00
.00
.00
.00
.00
.00
,?.3376
.3d 3<*2
.250bl
^.2^'Jio
.0^031
. 3 0 0 0 P
.00000
228
-------
SECTION 7
COMPUTER PROGRAM DOCUMENTATION
7.1 INTRODUCTION
The Effluent Monitoring Program (EFFMON) computes a priority al-
location used to schedule future monitoring visits to discharge sources,
having been given past information about those sources. For a description
of the solution technique and restrictions on the model, the reader should
consult Sections 2 and 5. This section will present documentation for
EFFMON including general requirements for implementation, descriptions
of the main program and subprograms (flow charts included) and, finally,
definitions of program variables.
The EFFMON code conforms to ASA Standard FORTRAN V and has been
successfully run on a UNIVAC 1108. The average size of the program on
the UNIVAC 1108 is about 42K words. Along with the use of logical units
5 and 6 as card reader and line printer, two auxiliary mass storage units
are utilized by the program for temporary storage. Logical unit 11 is
referenced in the main program only, and is used to sequentially store
discharge data for all sources; the data is then read back one source at
a time as needed to compute initial statistics, probability of no violation
and expected damage for that source. Logical unit 12 is called in the main
program to sequentially store certain computed statistics for each source
until the time such statistics have been computed for all sources; then,
if these statistics are to be written out, subroutine OUTPUT is called,
and the statistics are read back andprinted source by source (see Figure
5.7 for an example). Note that if NOUT (the flag variable which controls
this putput option) is non-zero, OUTPUT is not called and unit 12 is not
used.
229
-------
One machine-dependent feature of the program which might need
to be changed occurs in subroutines PNVCOM and EXPDAM. In those two
routines, variables labelled as "WENDTA(7,J,-)" and "WENDTA(6,J,-)" are
set equal to extremely large numbers. The reason for doing this is so
that an overflow condition will exist when printing out certain terms.
The UNIVAC 1108, which the program was run on, prints out the desired
asterisks in this case. Adjustments may have to be made on another
machine. Note that these asterisks are printed in the (optional) sta-
tistical summaries in place of a value for expected damage and prob-
ability of no violation when duplication (in multiple pipes) of any
constituent at a source occurs.
One other item requiring attention is the function RNORM. Re-
ferenced within Function XNORM, RNORM(X) computes a rational function
approximation to the standard normal distribution function with argument
X:
,X
RNORM(X) = -±- f exp(-t2/2)dt
RNORM is a library function available through the UNIVAC 1108 STAT-PACK
(statistical library). The method for computation as described by STAT-
PACK is:
RNORM(X) =
f; X < 0
1-f; X > 0
where
i~|-16
Li=o
1
230
-------
and where the a.'s are taken from Hastings' Numerical Approximations for
Digital Computers (Princeton, 1955). .The user must accommodate EFFMON
by supplying a suitable reference for RNORM.
7.2 PROGRAM DESCRIPTION
The EFFMON main program and subprograms are described in the suc-
ceeding pages. Figure 7.1 demonstrates the linkages between the main
program and subprograms. Simplified flow charts of major individual
routines are presented in Figures 7.2 through 7.10. All equations
labelled therein are located in Reference [1].
Main Program
The main program reads all input data and echo prints all inputs.
The constituent data are converted where the units are inappropriate
(standard units for the program are the same as those listed in Table 5.4),
The only other calculations done in the main program are those for es-
timating an average pipe flow for each pipe. The rest of the calculations
and output are carried out by subroutines coordinated by the main program.
For each source to be considered, the main program calls ISTAT, PNVCOM,
and EXPDAM to determine initial statistics, calculate the probability of
no violation, and find the expected damage of undetected violations re-
spectively. The priority allocations and corresponding output are then
created by calling PRIORT. Additional output of the statistics of the
individual sources is obtained by calling OUTPUT.
Subroutine ABEF
Subroutine ABEF computes the coefficients used in calculating
the expected damage for pH/pOH.
231
-------
MAIN
PROGRAM
K)
CO
to
ISTAT
PARAt-IS
PNVCOM
OUTPUT
MAJOR ROUTINES
Figure 7.1
I 1
•
IL,
I ILINAO,
I ILINFA,
| ILINFB,
| IN,
^ ININFA,
" ININFB,
I RILBT1,
I DIFF,
J DNORM,
XNORM
I I
SUPPORTING
-FUNCTIONS.
General Program Flow Diagram for EFFMON
-------
GENERAL
INPUTS
PIPD FLOWS
SELF-MONITORING
DATA
EFFLUENT
STANDARDS
c
START
I
/READ PRO-
JGRAM CONSTANTS
AND OPTIONS
READ SOURCE
(DESCRIPTIONS
AND CONSTANTS
REPEAT FOR EACH SOURCE I
REPEAT FOR EACH PIPE J AT
READ MONTHS,i
(PIPE FLOWS &
UNITS
SOURCE I
ARE
FLOW UNIT
GALITERS/DAY
CALCULATE SINGLE ESTI-
MATE OF PIPE FLOW (EX-
PONENTIAL SMOOTHING OF
ALL DATA FOR THAT PIPE)
/READ ALL SELF-MONITOR-
[ING CONSTITUENT DATA &
UNITS FOR ALL MONTHS
PIPE LOOP
FIND LIST OF DISTINCT
CONSTITUENTS FOR
SOURCE I
REPEAT FOR EACH PIPE
/READ ALL
[STANDARDS &
UNITS FOR PlPt
LL
Figure 7.2 Main Program
ARK
STANDARDS
IN CORRECT
SITS2
233
-------
CONVERSION OF DATA
INTO USABLE UNITS
COMPLIANCE
MONITORING
IS
SOURCE I
TO BE USED IN
ALLOCATION
REPEAT FOR EACH PIPE J AT SOURCE I
IS
CONSTITUEN
DATA IN PROPER
UNITS
STORE
FLOW AND
CONSTITUENT
DATA FOR SOURC
I TEMPORARILY
(UNIT 11)
SOURCE LOOP
REPEAT FOR EACH SOURCE I THAT
/READ SOURCE I
COMPLIANCE MON-
ITORING (ASSUM-
ED IN CORRECT
UNITS')
IS TO BE IN THE ALLOCATION
READ
SOURCE I
DATA BACK
FROM UNIT 11
Figure 7.2 — Continued
234
-------
INITIAL STATISTICS
SOURCE
PROBABILITY OF
NO VIOLATION
SOURCE
EXPECTED
DAMAGE
PRIORITY
ALLOCATION
AND TABLES
/ CALL 1STAT
/ (CALCULATE
\ INITIAL
\STATISTJCS)
/CALL PNVCOM
/ (COMBINE PIPE DATA
\A
AND CALCULATE PROB.
F NO VIOLATION)
SHOULD
XPECTED DAM-
GES BE CALCUI
ATED
CALL EXPDAM
(CALCULATE EX-
ECTED DAMAGE)
ARE
TABLES OF
SOURCE STATISTICS T
BE PRINTED
STORE
OUTPUT
STATISTICS
EMPORAR1LY
ON TAPE
/CALL PRIORT
/(ALLOCATE
\ PRIORITIES)
Figure 7.2
— Continued
-------
SUMMARY TABLES
ARE
TABLES OF SOU-^ NO
CE STATISTICS TO BE
PRINTED
9
ACALL OUTPUT
/ (PRINT SUHM-
\ARY TABLES BY
SOURCE)
c
END
Figure 7.2
— Continued
236
-------
CONSTITUENT
EXPECTED
DAMAGE
( ENTRY J
^C.2.8
CALCULATE AND
ADD SIX INTEGRAL
TERMS FOR EXPECT
ED DAMAGE
CALCULATE AND
ADD DELTA FUNC-
TION TO EXPECTED
DAMAGE
CALL DAMAGO\
(CALCULATE \
DAMAGE AT 0-LOAD/
y
JNG
(RETURN J
Figure 7.3
Function COMEXD
237
-------
ZERO-LOAD
CONSTITUENT
EXPECTED
DAMAGE OR
DELTA
FUNCTION
COEFF1CIENT
TO
CALCULATE 0 -
OADING DAMAGE
RESET 0-LOAD-
ING TO FIND
DELTA FUNCT-
ION COEFFIC-
IENT
LOCATE 0-LOAD-
IHG WITH RESPEC1
TO DAMAGE FUNC-
TION BREAKPOINTS
LOCATE 0-LOADING
WITH RESPECT TO
DAMAGE FUNCTION
BREAKPOINTS
CALCULATE EXACT
0-LOADING
DAMAGE
CALCULATE EXACT
0-LOADING DAMAGE
( RETURN )
\^ RETURN J
Figure 7.4 Subroutine DAMAGO
238
-------
CONSTITUENT
EXPECTED DAMAGE
FUNCTION COMEXD\
(CALCULATE EX-
PECTED DAMAGE
OG NORMAL)
REPEAT FOR EACH DISTINGUISHABLE
CONSTITUENT M AT SOURCE
YES
FUNCTION PIIEXD
(CALCULATE F.X'i'KCTEU
.DAMAGE FOR pli AND
C.2.40
CALCULATE
TEMPERATURE
CONSTANTS
CALCULATE
CONSTANTS FOR
NON-COUPLED
CONSTITUENTS
DETERMINE UP-
STREAM DAMAGE
LEVEL
WHAT
IS CONSTITU-
ENT DISTRIBUTION
/FUNCTION' COMEXD
/ (CALCULATI-: EX-
\ PECTKI) DAMAGE
\IORMAL)
-*r«
SOURCE
EXPECTED
DAMAGE
CONSTITUENT LOOP
SOURCE EXPECTED DAMAGE
= LARGEST OF CONSTI-
TUENT EXPECTED DAMAGES
(RETURN^
Figure 7.5
Subroutine EXPUAM
239
-------
Check of Self-
Monitoring Data
Aggregate
Months
c
ENTRY
REPEAT FOR EACH PIPE L
REPEAT FOR EACH CONSTITUENT J OF PIPE L
REPEAT FOR EACH MONTH K OF PIPE L
REMOVE ANY ERROR DATA-
DATA ENTERED AS 0. OR
DATA WHERE THE MAXIMUM
: MEAN OR MINIMUM > MEAN
MONTHS LOOP
CHECK SAMPLE SIZE FOR
EACH MONTH AND COMBINE
SAMPLE SIZES FOR MONTHS
IF SAMPLE SIZE < 4
IS
THE TOTAL
AMPLE SIZE
1A1 (IB
Figure 7.6
Subroutine ISTAT
240
-------
ESTIMATE MEAN
AND STANDARD
DEVIATION
INCLUDE
COMPLIANCE
DATA
(BAYESIAN UPDATE
IN APPENDIX E,
REFERENCE 1)
COMBINE MONTHLY
ESTIMATES
REPEAT FOR EACH MONTH (OR COMBINATION OF
IS
THIS A
COMBINATION OF
MONTHS
COMBINE MEANS
AND MAXIMUMS/
MINIMUMS
-------
ESTIMATE 0 AND 6
OF CONSTITUENT
LOADING
WHAT
IS CONSTITU-
ENT DISTRIBUTIO
ESTIMATE PARAMETERS FOR
FUNCTIONAL MODEL* GIVEN
MAXIMUM (OR MINIMUM)
AND MEAN OF SAMPLE
ESTIMATE PARAMETERS FOR
FUNCTIONAL MODEL* GIVEN
MAXIMUM (OR MINIMUM)
AND MEAN OF SAMPLE
A.3.1
ESTIMATE
AND 8
CALCULATE 0
AND 8
( RETURN J
*FUNCTIONAL MODELS WERE DEVELOPED AS APPROXIMATIONS TO THE EXACT
METHODS FOR FINDING p AND 3 IN APPENDIX A OF REFERENCE 1.
Figure 7.7
Subroutine PARAMS
242
-------
( ENTRY )
EXPECTED DAMAGE FOR
CONSTITUENT pH/pOH
FIND UPSTREAM
DAMAGE LEVEL
MEAN OF pOH=
14-MEAN OF pH
CALL PHDMGO
(CALCULATE 0-
DAMAGE:
REMOVE 0-LOAD-
ING DAMAGE FROM
EXPECTED DAMAGE
C.2.28
CALCULATE AND SUM 11
INTEGRAL TERMS FOR
EXPECTED DAMAGE OF pH
OR pOH-WHICHEVER IS
SIMPLf'R
C.2.32
CALCULATE AND ADD
INTEGRAL TERMS FOR pH
OR pOH-WHICHEVER WAS
NOT DONE
( RETURN )
Figure 7.8 Function PHEXD
243
-------
REPEAT FOR EACH PIPE CONSTITUENT K
N0
COMBINE STATISTICS
AND DETERMINE
CONSTITUENT
PROBABILITIES OF
NO VIOLATION
REPEAT FOR EACH DISTINGUISHABLE
CONSTITUENT M OF SOURCE
REPEAT KOR EACH SOURCE PIPE J
C.3.6,C.3.7,C.2.3.5,C.2.3.6
COMBINE C's AND
8's AND CALCU-
LATE P(NO VIOL)
C.3.2.C.3.3.C.2.10
COMBINE O's AND
d's AND CALCU-
LATE P(NO VIOL)
C.3.6,0.3.7
COMBINE C's AND 8's
AND CALCULATE P(NO
VIOLATION)
C.3.8.C.3.9
CONSTITUENT LOOP
PIPE LOOP
FINISH CALCULATING
COMBINED 0 AND 8
FOR M
DETERMINE SOURCE
PROBABILITY OF
NO VIOLATION
C. 3. 11, C. 3. 12
SOURCE P(,\'0 VIOLA-
TION) ^PRODUCT OF ALL
CONSTITUENT PROBAB-
ILITIES (EXCEPTING
DO)
SET DO COEFFICI-
ENT USING P (DE-
IFAULT is 0.)
SOURCE CONSTITUENT LOOP
C. 3. 11, C. 3. 12
SOURCE P(NO VIOLA-
TION') =PRODUCT OF THE
MINIMUM CONSTITUENT
PROBABILITY OF EACH
PIPE (EXCEPTING DO)
RETURN
Figure 7.9 Subroutine PNVCOM
244
-------
(
ENTRY
REPEAT FOR EACH SOURCE I
DETERMINE
RESOURCE COST
TO MONITOR
CALCULATT ON
OF MARGINAL
RETURNS
SOURCE LOOP
REPEAT FOR EACH SOUKGE I
CALCULATE MARGINAL
RETURNS (MR's)
FROM LOWER TO UP-
PER SAMPLING LIMIT
SOURCE LOOP
7.8
COMBINE ALL MR's
AND SORT INTO
DECREASING ORDER
DETERMINE TOTAL RESOURCE COST
AND TOTAL COST OF UNDETECTED
VIOLATIONS (EACH SOURCE MONI-
TORED MIN. KG. OF TIMES)
PRT NTI NG
OPTI ONS
YES
PRINT
"INITIAL
ALLOCATION;
7.6
7.8
Xi.
OUT!
OPT]
^
NO
\
5\
>UT
ON
•Jx
'X. YES
FOR EACH SOURCE:
CALCULATE MR's FROM
0 TO MINIMUM NUMBER
OF SAMPLES
PRINT "PRIO-
RITY LIST OF ^_
SAMPLES"
U->-
DETERMINE CUMU-
LATIVE RESOURCE
COST AFTER EACH
SAMPLE
b
d _,
COMBINE WITH PREVIOUS
MR's AND SORT INTO
DECREASING ORDER
I
DETERMINE TOTAL COST
OF UNDETECTED VIOLA-
TION COST AFTER EACH
SAMPLE
o
Figure 7.10
Subi-outiiie PRIORT
245
-------
USING FIRST SET OF
ORDERED MR'S: DETERMINE
VIOLATIONS COST AND
TOTAL RESOURCE COST AT
EACH SAMPLE
PRINTING
OPTIONS
CONTINUED
PRINT
"PRIORITY LIS
3F SAMPLES"
IS OUTPUT
OPTION 211=1?
IS OUTPUT
OPTION 3=1?
IS
THE BUDGET
CONSTRAINT
NON-ZERO?
LOCATE FIRST SAMPLE FOR
WHICH TOTAL COST OF UN-
DETECTED VIOLATIONS
< DESIRED COST
LOCATE THE LAST SAMPLE
OF WHICH TOTAL RESOURCE
COST i BUDGET
REPEAT FOR EACH SOURCE
COUNT THE NUMBER OF
TIMES SOURCE I IS TO BE
SAMPLED (PRIOR TO LIMIT
DETERMINE TOTAL RESOURCJ
REQUIRED TO SAMPLE
SOURCE I THAT MANY TIME!
DETERMINE SOURCE I COST
OF UNDETECTED
VIOLATIONS
Figure 7.10
246
— Continued
-------
DETERMINE TOTAL
RESOURCE COST AND
VIOLATIONS COST
OVER ALL SOURCES
PRINTING
OPTIONS
CONTINUED
PRINT
"FINAL
ALLOCATION"
HAS COST
CONSTRAINT BEEN
ALLOCATED?
LOCATE FIRST SAMPLE FOR
WHICH TOTAL COST OF
UNDETECTED VIOLATIONS
< DESIRED COST
IS THE
COST CONSTRAIN
NON-ZERO?
NO
Figure 7.10
— Continued
247
-------
Function COMEXD
Function COMEXD calculates the expected damage of any non-pH con-
stituent with the use of IN, IL, ININFB, ILINFB, ILINAO, and XNORM.
DAMAGO is used to calculate the damage which would occur under zero load
and this damage is subtracted from the expected damage.
Function DAMAGO
DAMAGO calculates the damage for a given constituent that would
occur under zero load (damage caused by the upstream concentration of
the given constituents). This value is also used as the delta function
coefficient.
Function DIFF
Function DIFF is used in conjunction with function XNORM in order
to obtain greater accuracy in taking the difference of two values of the
standard normal distribution functions.
Subroutine EXPDAM
Subroutine EXPDAM determines the expected damage for a single
source using functions PHEXD (constituent pH/pOH) and COMEXD (non-pH
constituents), and sets the source expected damage equal to the maximum
of the constituent expected damages.
ft
The delta function concept is used in the case of normally distributed
constituents. The normal distribution curve includes loading values
from -°° to +°°. Since actual loading values cannot be less than 0.0,
the delta function accounts for this fact by lumping all negative values
together and adding them into the 0.0 loading value when calculating
expected damage.
248
-------
Functions IL, ILINAO, ILINFA, ILINFB, IN, ININFA, ININFB
These functions (along with the entry point RILBTl in IL) all
compute variations of the integral (C.2.9 in Reference [1]).
I (e,f,a,e,p,a) = / (ex + f)4» (x)dx ,
2
where is the normal density function with mean y and variance 0 if
Y = normal, and where $ ^s lognormal, with mean and variance of the
Y 2
corresponding normal distribution being y and a , if y = lognormal. All
of the above functions beginning with the letters "IN" are normal, while
those containing "IL" are lognormal.
Subroutine ISTAT
Subroutine ISTAT calculates the initial statistics for a single
source. ISTAT combines all given data to find an estimated mean and
standard deviation for the loading of each constituent of each discharge
pipe. First, these estimates are made for each month (or group of months
if any sample size is less than 4) by calling PARAMS, then compliance
monitoring data is used to improve the monthly estimates, and finally,
the estimates for all the months are combined into a single mean and
standard deviation for the constituent.
Subroutine ORDER
ORDER organizes a given array of values into descending order.
Called by PRIORT, ORDER is used to rearrange the marginal returns so that
a priority allocation can be made.
249
-------
Subroutine OUTPUT
This subroutine prints one table for each source being considered
(see Figure 5.8 for an example). The table summarizes the source statistics
for the monitoring period by listing average source flows as well as stand-
ards, means, standard deviations, expected damages, and probabilities of
no violation for each of the constituents, and also source expected
damage and source probability of no violation. OUTPUT is called by the
main program only if the user has specified that he desires such tables.
Subroutine PARAMS
PARAMS estimates a mean and standard deviation for the loading of
a single constituent given a sample mean, sample maximum, sample size,
and distribution specification (normal and lognormal). PARAMS uses two
functional models (one for the normal case, the other for the lognormal
case), which were developed from the methods of Appendix A of Reference
[1]. PARAMS will also yield estimates of mean and standard deviation for
the constituent pH/pOH given a mean and maximum, or mean and minimum, or
maximum and minimum.
Subroutine PHDMGO
PHDMGO is analogous to DAMAGO in that it calculates the damage
caused by zero loading (the upstream damage) or, equivalently, the delta
function coefficient. PHDMGO specifically treats pH/pOH, and DAMAGO is
called for all other constituents.
Function PHEXD
Function PHEXD calculates the expected damage for a pH constituent.
250
-------
Calling ABEF to compute coefficients, PHEXD uses IL, RILBT1, and ININFA.
PHEXD also calls PHDMGO to calculate'zero-loading damage which is sub-
tracted from the total expected damage.
Subroutine PNVCOM
PNVCOM, for a source with multiple discharge pipes, combines con-
stituent loads when the same constituent occurs in more than one pipe of
an effluent source. That is, PNVCOM creates a single mean and single
standard deviation for each distinguishable constituent of a multi-pipe
source. PNVCOM also calculates probabilities of no violation (with the
use of IN, ININFA, and ILINFA) for all constituents and combines these
into a source probability of no violation. In addition, PNVCOM calculates
the total effluent source flow and sets the combined DO concentration if
DO data has been provided.
Subroutine PRIORT
PRIORI calculates the total cost to monitor each source. PRIORT
also calculates marginal returns for each source and calls ORDER to sort
these into descending order. Depending upon which print options are
specified by the user, PRIORT uses this sorted list to determine the
sampling allocation and prints tables giving the sampling frequencies,
monitoring costs, and costs of undetected violations.
Function XNORM
XNORM finds the value F(x) of the standard normal distribution
function with argument x. If x < 4.0, XNORM calls RNORM (see Section
5.1, Introduction, for an explanation of RNORM) to find this value.
251
-------
For |x| > 4.0, XNORM uses its own approximation formula (for greater accuracy)
XNORM contains entry point DNOKM, used when calculating l-F(x).
7.3 DESCRIPTION OF VARIABLES
Variables residing in common blocks within the program will be
described in Table 7.1. Then in Table 7.2, local variables are defined
according to their respective subprograms. Note that the variable I,
defined under COMMON/UPDATE, is used consistently throughout both tables
to refer to that effluent source which is currently being worked on by
the program.
A complete program listing follows Table 7.2.
252
-------
Table 7.1
Description of Common Variables
VARIABLE
DEFINITION
COMMON/BIJ/
—Refer to Equation C.2.22 in Reference 1—
Al
B(2)
COMMON/BODDMG/
TQS
QU
CS
IBOD
COMMON /BRKPTS/
S(J)
*J ~"i 5 • • • y O
SSPH(J)
COMMON/CONST/
Parras (J,K)
COMMON/DMG1/
DAMAGE (J,K)
K= JL 5 • • • 5 b
COMMON/DMG2/
DMG (J,K)
J=l and
K=l,...,11
J=2 and
Mass loading coefficient of downstream
concentration for pH or pOH constituent, a
iJ
Downstream concentration factor for pH, b
iJ
iJ
Downstream concentration factor for pOH, b
Total flow for effluent source I
Upstream flow at effluent source I
Mean of DO concentration for source I
Internal flag for BOD to indicate the
calculation of either zero load damage or
delta function coefficient
Damage value of the J point of the non-
pH/pOH damage functions
Damage value of the J point of the pH/pOH
damage functions
Alphanumeric description (J=l,...,5
alphanumeric words) of constituent
identified as K (see Table 5.4)
The Kth breakpoint of the Jth function
where J is the damage function identifica-
tion number (see Table 5.3)
The K breakpoint of the pH damage function
The K breakpoint of the pOH damage
function
253
-------
Table 7.1
Continued
VARIABLE
DEFINITION
COMMON/EXP/
NPPARS (J,I)
COMMON/FLAGD/
ID
COMMON/IST/
MNTHQS (J,K)
K=l,...,24
NSIZE (J,K,L)
SMEAN (J,K,L)
SMAX (J,K,L)
NOCPTS (J,K)
MNTHSZ (J,K,L)
Z(J,K,L)
DELTA
GAMMA
KETA
Number of constituents discharged from pipe
J of effluent source I
Distribution of constituent being examined
(0 for normal, 1 for lognormal)
Sequentially numbered months (in the range
1-24) for which data was entered for pipe J
of source I
Sample size for data on the K constituent
of pipe J, month L of source I
Sample mean of the K constituent of pipe J
month L of source I
Sample maximum (or minimum in the case of pH)
of the K'-h constituent of pipe J, month
L of source I
Number of compliance monitoring points for K
constituent of pipe J of source I
th
Numbered month (in the range 1-24) corres-
poinding to the Lth compliance monitoring
point (Z(J,K,L)), Kth constitutent of pipe
J, source I
L compliance monitoring point (maximum 30
points) for the Kth constituent of pipe J
of source I
Not used
Coefficient used in Bayesian update in
Subroutine ISTAT
Coefficient used in Bayesian update in
Subroutine ISTAT
254
-------
Table 7.1
Continued
VARIABLE
DEFINITION
KNU
ENU
IPARM (J,K,I)
ISTATS (I,J,K,L)
L=l
L=2
L=3
L=4
COMMON/ISTPNV/
MU (J,K)
SIGMA (J,K)
COMMON/OUT/
WSRC(l)
WSRC(2)
WSRC(3)
UPFLW
DO
NPTSW
WEND(1,J)
Coefficient used in Bayesian update in
Subroutine ISTAT
Coefficient used in Bayesian update in
Subroutine ISTAT
Constituent identification number of the
Kch constituent of pipe J of source I (see
Table 5.4)
Combined mean of the K constituent of
source I, pipe J (for the monitoring period)
Combined variance of the KC constituent of
source I, pipe J (for the monitoring period)
Lf
Combined confidence in the mean of the K
constituent of source I, pipe J (for the
monitoring period)
Combined confidence in the variance of the
Kth constituent of source I, pipe J (for the
monitoring period)
Combined mean of the K constituent pipe
J, of source I (equal to ISTATS (I,J,K,1)
Combined standard deviation of the K
constituent pipe J, for the monitoring
period for source I (equal to ISTATS
Identification number for effluent source I
Expected damage for effluent source I
Probability of no violation for effluent
source I
Upstream flow at effluent source I
Mean of DO concentration for source I
Number of pipes for source I
Mean discharge flow of pipe j, source I
255
-------
Table 7.1
Continued
VARIABLE
DEFINITION
WEND(2,J)
WENDTA(J,K,L)
J=l
J=2
J=3
J=4
J=5
J=6
J=7
COMMON/PCOPT/
ICOPT
Number of constituents of pipe J, source I
For L constituent of pipe K of source I:
Constituent identification number (see
Table 5.4)
Constituent effluent standard
Constituent distribution code
Estimated constituent loading mean for the
monitoring period
Estimated constituent loading standard
deviation for the monitoring period
Constituent expected damage
Constituent probability of no violation
Damage function point (1,2,3,4,5, or 6)
whose corresponding damage value is
closest to the upstream concentration for
a non-coupled constituent (the same point
is used for all non-coupled constituents of
all sources)
COMMON/PNVEXP/
—For this common block, constituents present in more than one pipe of an
effluent source have been combined and each of the J constituents is
distinct—
DIST(J)
TMU(J)
TSIG(J)
COMMON/PRI/ (as listed in MAIN)
NOPIPS (I)
NOPARS (I)
Distribution of the J constituent of source I
specified as 0 or 1 for normal or lognormal
Mean loading of the J constituent
Standard deviation of loading of the J
constituent
th
Number of pipes at effluent source I
Number of distinct constituents of effluent
source I (constituents present in more than
one pipe are only counted once)
256
-------
.Table 7.1
Continued
VARIABLE
DEFINITION
INDPAR(J.I)
ISFUP(I)
ISFLOW(I)
EXPDM(I)
PNV(I)
IOUT1
IOUT2A
IOUT2B
IOUT3
NAME (I,J)
B
D
NUSORS
INSORS(I)
PIPCST(J)
CONCST(J)
COMMON/UPDATE/
I
QS(J,I)
Index of distinct constituents (J=l,...,10)
of effluent source I
Upper sampling limit of effluent source I
Lower sampling limit of effluent source I
Expected environmental damage due to
effluent source I
Probability of no violation of effluent
source I
Output option 1 (a value of "1" signals to
print)
Output option 2A (a value of "1" signals to
print)
Output option 2B (a value of "1" signals
to print)
Output option 3 (a value of "1" signals
to print)
Source identification for source I (J=l,...,13
alphanumeric words)
Budget limit for the monitoring agency during
the next monitoring period
Desired limit to the undetected violation cost
Number of effluent sources actually included in
the allocation procedure(out of all those
entered in input)
Index of effluent sources actually included
in the allocation procedure.
Cost to monitor an effluent source with
J pipes
Laboratory cost to analyze a sample
containing constituent J (see Card Groups
3-6 in Table 5.1)
Effluent source currently being examined
Calculated estimate of pipe flow for pipe
J of effluent source I
257
-------
Table 7.2
Description of Local Variables
VARIABLE
DEFINITION
MAIN PROGRAM
— See Section 5.2 for a description of input variables —
Subroutine ABEF
Function COMEXD
TMU
TSIG
M
FUNGI
aiJ
biJ
— Refer to Equation C.2.27 in Reference 1 —
Dl
D2
A
B
KD
ALPHA
BETA
E
F
L
where k is KD below
where k is KD below
(from C.2.222b)
(from C.2.22c)
aiJk
BiJk
eiJk
fiJk
Internal flag indicating if ALPHA and
BETA are both outside of limits (where
the limits are
.0000001 < ALPHA < BETA < 1.)
L=l if ALPHA and BETA are within limits,
2 if not
Combined mean of the loading of con-
stituent M (defined below) for the
entire monitoring period and all pipes
of an effluent source where M occurs
Combined standard deviation of con-
stituent M for the entire monitoring
period and all pipes of an effluent
source where M occurs
Constituent identification number as
defined in Table 5.4
External function — IN or IL
258
-------
Table 7.2
Continued
VARIABLE
DEFINITION
Function COMEXD Continued,..,
FUNC2
A
B
E
F
ALPHA
BETA
DJB
Subroutine DAMAGO
DJB
M
B
BBOD
Subroutine EXPDAM
IPARAM (J)
KBOD
EXPDM
NOPARS
IPARM(J,K,I)
NOPIPS(I)
External function — ININFB or ILINFB
a. (See equation C.2.4b, Reference 1)
bij (See equation C.2.4c, Reference 1)
(See equation C.2.7d)
(See equation C.2.7e)
(See equation C.2.7b)
(See equation C.2.7c)
Delta function coefficient or zero-loading
damage for constituent M
Delta function coefficient or zero—loading
damage for constituent M
Constituent identification number (as
defined in Table 5.4}
Coefficient B of COMEXD
Coefficient B adjusted (if the constituent is
BOD)
Constituent identification number (as defined
in Table 5.4) for Jc^ distinct constituent
of source I
Coefficient 1^ (C.2.16)
Expected damage due to effluent source I
Number of distinct constituents of
effluent source I
Constituent identification number for K
constituent of pipe J of effluent source I
Number of discharge pipes for effluent
source I
Effluent source number
259
-------
Table 7.2
Continued
VARIABLE
DEFINITION
EXPD(J)
A
B
COPT
Expected damage for each distinct
constituent of effluent source I
a. (as in COMEXD)
bi> (as in COMEXD)
Upstream concentration of a non-coupled
constituent
Functions IL. ILINAO. ILINFA. ILINFB. IN. ININFA. ININFB
—Refer to equations for the normal integral (C.4.1) and lognormal
integral (page 197) in Reference 1—
A
B
a
b
ALPHA a
BETA B
MU
SIGMA
u
a
Subroutine ISTAT
NOPIPS
NPPARS(J)
NMNTHS(J)
DIST(J.K)
QU
EMEAN(L,J,K)
ESIGMA(L,J,K)
ETA(L,J,K)
NU(L,J,K)
certain of the above functions use constants
in place of a, b, a or 3 in order to
calculate commonly used integrals
Number of discharge pipes for effluent source I
Number of constituents of pipe J
Number of months of constituent and flow data
for pipe J
Distribution of constituent K of pipe J
Streamflow just upstream of effluent source I
Estimated mean of loading
Estimated standard deviation
(or at some points, variance)
Confidence in the estimated
mean
Confidence in the estimated
variance
Pipe L, Jth
constituent,
month K
260
-------
Table 7.2
Continued
VARIABLE
DEFINITION
Subroutine ORDER
XMR(M)
ISORC(M)
Subroutine OUTPUT
NUSORS
Subroutine PARAMS
SSIZE
SMEAN
SMAX
SMIN
IONESD
DIST
EMEAN
ESIGMA
IPRM
Subroutine PHDMGO
DJB(l)
DJB(2)
Function PHEXD
TMU(J)
TSIG(J)
TQS
QU
Array of M marginal returns to be organized
into decreasing order
Array of effluent source numbers
corresponding to marginal returns in XMR,
which is organi^ed exactly as XMR
Number of elements in XMR and ISORC as
calculated by the program
Number of effluent sources included in the
allocation procedure, (see definition
of INSORS in Section 5.2)
Sample size of constituent loadings
Sample mean of constituent loadings
Sample maximum (or minimum for pH) of
constituent loadings
Sample minimum (for pH) of constituent
loadings
Flag to indicate pH data in maximum/
minimum form (no mean)
Constituent loading distribution
Estimated mean of constituent loading
Estimated standard deviation of
constituent loading
Constituent identification number (as in
Table 5.4)
Expected damage for zero-loading of pH
Expected damage for zero-loading of pOH
A monthly mean for constituent j=l=pH, j=2=pOH
A monthly standard deviation for J=l=pH, J=2=pOH
Total flow for effluent source I
Streamflow just upstream of source I
261
-------
Table 7.2
Continued
VARIABLE
DEFINITION
Function PHEXD continued
A
B(J)
PSI
Subroutine PNVCOM
NOPIPS
NPPARS(J)
NOPARS
IPARM(J.K)
INDPAR(M)
DISTYP(J,K)
EFST(J.K)
QU
PNV
IGOR
TQS
DO
CS
TMU(M)
TSIG(M)
TEMPNV
TEMPM
SUMM
a.j (from C.2.22b, reference 1)
b , where J=pH=l or J=pOH=2 (from C.2.22c,
reference 1)
Delta function coefficient for pH and pOH
Number of discharge pipes, effluent source I
Number of constituents discharged from pipe J
Number of distinct constituents, effluent
source I
Constituent identification number for K
constituent of pipe J
Index of constituent identification numbers
containing each distinct constituent
Distribution of K constituent of pipe J (0
or 1 for normal or lognormal)
Effluent standard of K constituent of pipe J
Streamflow just upstream of effluent source I
Probability of no violation of effluent
source I
Flag indicating if the constituents of source
I are correlated (1=1) or not (I?4!)
Total effluent source flow
Dissolved oxygen concentration
Dissolved oxygen concentration (CS=DO)
Mean of M distinct constituent (all pipes
of effluent source I combined)
Standard deviation of M distinct constituent
(all pipes of effluent source I combined)
Probability of no violation for a single
constituent
m in equation C.3.4, reference 1
m in equation C.3.4, reference 1
262
-------
Table 7.2
Continued
VARIABLE
Subroutine PN'VCOM continued
TEMPV
SUMV
Subroutine PRIORI
IPARM(J,K,I)
NPPARS(J,I)
RESRCE(I)
XMR(M)
ISORC(M)
TMR(Ml)
ISORCT(Ml)
NUM(I)
DEFINITION
v in Equation C.3.5, Reference 1
v in Equation C.3.7, Reference 1
Constituent identification number for
the Kt" constituent of pipe J, effluent
source I
Number of discharged constituents of
pipe J, effleunt source I
Total resource cost to monitor source I
Marginal returns array where number of
elements in array XMR =
NUSORS
E
1=1
(ISFUP (I) - ISFLOW(I))
(see COMMON/PRI/ for definition of other
variables)
Effluent array containing the sources
which correspond to the marginal returns
in XMR above
Marginal returns array containing XMR
plus marginal returns for the 1st through
minimal number of samples for each source
where number of elements in array TMR =
NUSORS
E.
1=1
ISFUP (I)
(see COMMON/PRI/ for definition of
variables)
Array containing the sources which cor-
respond to the marginal returns in TMR
above
Number of monitoring visits allocated
to effluent source I
Function XNORM
X
Argument of the standard normal dis-
tribution function, F(x)
263
-------
Program Listings
264
-------
M A I N C 1 )
DATE 021676
PACE
1 .
2.
3.
o.
5.
6.
7.
8.
9.
1 0.
11.
12.
13.
10.
15.
16.
17.
18.
73.
23.
?9.
JO.
5! .
32.
IS.
3fc.
37,
03.
.i5..e.,7.5.7.5»7.5,l5.,7.5,10,,10.t3.t0.ti2.5tl0.iS.i5.»
*n.,?.S,.s./
Dirt
DATA
DATA
DATA
DAT 4
DiTt
DATA
DATA
, fe) XO. » .01 t .05, . 10» .50, 1 ./
,fe)/o.,. 1, .3, .<»»2.7,3.X
, b) /9. , 8 . ,O.B,0.,ii0.tl30.il50.X
,6) XO. »0, ,0. ,0. » 0. » O.X
,b)/0. .35. t 175. . 200. ,240. ,250.X
,o)Xo., .00. .15«.25f .35, .aX
,6)XO. , .02, .05, t ., 10.? 50.X
i , fa) /O., 100., 2000. » 7500., 15000. ,150000. X
l,6)XO., 20. ,200. ,800. ,3000. ,50000.X
1 1 1>) /O , . . 02 , . 1 , ! . , 5. , 1 0 . X
i ,6) /o, , . o i , ,o2, . 05. . l , .SX
l .61 /.7, .B, .9, 1 ,2t 3. ,8.X
1 »o)/0. , .J «.j», 9,2. 7,3.X
! !>t«AGt ( 1 , Jl , J=l
fDi«4t;t.(2. J) ,J-i
(r>iMAGt f 3, jj , j=j
( QiMfiGt f u . J) , J= l
(OA «AGi.(S,J)«J=l
(,OAMAGE(6» J) . Jsl
c^*M4Gt(7, j) ,j=]
rC'-MAGr (S, J) . J=i
rPiw-iPtf V. J) , J=l
( D*MA&t' f 10, J) . Js
(OiM6Gt(ll,J),J=
( D.SMAGE O2 . J) , J=
c OA^r-t < i 3 , j) . j=
(OivAGEuu , J) , J=
(O^xAGt.^, J) ,J=
OATA ( PAM^Gt Cl 7 , J) , J= l ,6) /O . , . OS, . 1 7. .5, I . , 1 .SX
OiTAfDt^AGF(I8,J),Jsl,«>jXO.».001,.005,.01,.02».05/
OAT* (PAMiGEn«, J) , J=l .65 XO. , ,01 , 1 . i3.,9. ,20.X
DATA ( O^MAGL t 20 , J) , J=t .6) X .6, .9, 3. , o . 5, 7 . , l 0 .X
PAT/ (OA«Ar,Ef 21 , j; , j=i ,b)/0. , .01 . . 1 ,5, ,30. ,SO.X
OiTi cD4»iG:.f 22, J) , J=l •&)/b*0./
OATA t PA Mir,c ( 23 , J j , j= j , &) /6* o . X
00000 100
00000200
00000300
oooooaoo
00000500
00000500
00000700
00000800
00000900
OOOOlOOO
00 001 100
00001200
0000130C
0000l«00
00001500
OOOClfcOO
00001700
00001800
00001900
00002000
00002100
00002200
OOOU2300
00002UQO
0000?500
00002600
00002700
00002300
00002900
00003000
00003100
00003200
00003300
00003«00
00003SOO
00003600
00003700
00003600
00003900
0000«100
00000200
00000300
00000000
00000500
0000^600
OOOOU700
00000800
00000900
-------
5! .
S2.
S3.
5a.
«=5.
56.
57.
•56.
59.
£0 .
61 .
62.
63.
6J.
fc5.
fo.
.
07.
OAT.,
OATA
DATA
DATA
DATA
I
DATA
DATE 02187t>
00005000
00005100
00005200
00005300
oooosuoo
00005500
00005600
tDwG(l.J)»J=1.1 I)/.0000001..000000178*.000000316..0000005600005700
PAGE
(DA HAGc(26,J),J=l,o)/100..200..500..1000.ilSOO.i2300./
(DAMAGt(27,J),J=l,6)/0..20.,40..100.,280..300./
(Oi'-1AGcCce,J),J=i,6)/0.,1..2.5»3.,4.,10./
(r>AMAGfc(29,j),j = 1,6)/o.,10.,UO.,100.,300..1000./
(DAMAGE. (-3 0,J),J=1,0)/0,,0.,0.,0.,0.»0./
C *«*
C ***
*?..9000.11,.00000316,.00001..0000316.,0001,.000112*.000126/ OOOOiBOO
-2 00005900
DATA (DMCf2>J)•Js1,1 I)/.O000001..0000003l6..000001..00000158,.000006000
* '10 0 0 ?:'. ! • . '10 0 p 0 5 o 1 , . 00001. .0000316, .0001. .000112, .000126/ 00006100
**«xt*tx«.***«x*».********
C pEAD IN UsF.^-sPF.ClFlED DAMAGE FUNCTIONS AND MONITORING COSTS
C (PPOG^AM HAS PPESfcT FUNCTIONS AND COSTS IF NONE ARE READ IN)
C
"Etncs.'W) ICOSTS.ID^G.IOAHAG.ISS
9000 FOBvATfJfIl'lX))
».'pTTEf6.<>oo) ICOSTS.IDMU.IPAMAG.ISS
900 FCRMAT( ! \ i,i0('-'),'THE INPUT CARO'DATA FOLLOWS I»10('- I),/ I 0'.
1 'TCo5TS=i»Ii»T21, iJDMGsifill Tili"IDAMAG=I111fT611IISS=I111
IFI-TCOSTS.FO.O) GO TO 7
9100 FOP"4T(Jfrli).i,5x).a(/8(FS.2fSX)))
7 IFfTOsG.fd.O) GO TO 9
IFf innG.Nt.1.AND.IDMG.NE.2) GO TO 200
no OP:10 i oun = i. i oMr;
9200 OfAp(S. 9300) I 1 , (OMG( II.J),Js1,11)
930.-) FOP"Ar(i,,ux,6Fio.3./5x.5FlC.3)
9 IFClC'AMi&.eg.o) GO TO 11
IFf iniMiG.LT.l.0".I01MAG.GT.30) GO TO 200
00 00 )0 IOUM=1•IDAMAG
9UOO SF.iQf S. ^500) I 1 . (DAMAGE ( I 1 , J) , J=l ,6)
9500 FORMAT(I?,SA»6F10.3)
11 IFflSS.EQ.O) GO TO 13
R£0(S.*600) (S(Jj,J=i,6),(SSPH(J)fJ=i,n}
960^ rOPvAT(oF5.2.XJiFS.2)
1 I=1,30).(J»J=1.11)*((^HG(I.J)»J=1»11)»I=1.2),(J.
2 J=1.6)*(I.(OAMAGECI.J).J=l.6)fI=l»30))
910 FOR>;ir( ! 0't 'PIPCSTfi , 12,")= ' ,F 10.2, 10x,'**IF PIPCST. CONCST, OR'.
l - DAMAGE FUNCTIONS AND BREAKPOINTS WE.RE NOT READ IN.i./i '
2 oV. ' C' ,1?, ')=' .F10.2, 17X. iVALUES PRINTED ARE THOSE EXISTI.
3 'ING IN THE PROGRAM) ,2(/i i ,bX , 1( ' , 12 • ') = ',F 1 0.2)./ I 0 ' .
« lCoNCSTC',I2il)=i.F10.2.lOX,5Aa.29c/' '.6X,i(i,I2»
5 ' )='.Fio.2«10X,5AC),/' 1 ' ,T18, ' J=' ,10(12.9X).I2./I L
6 i..PHI,/i ),IOMG(!,J)i.2x.1 IF 1 1.7•/ ' '»l--HOH',/ ' I*
7 '!?(-'GC2.J)'»2x,llF11.7,/"0',Tl8.iJ=i,6(2XfI2«9X),/iOl
00006400
00006500
00006600
00006700
00006800
OOOO&VOO
00007000
00007100
)00007200
00007300
00007«oo
00007^00
00007600
00007700
00007800
00007900
00008000
00008100
00008200
00008300
00008UOO
ooooesoo
00008600
00008700
00008800
00008900
00009000
00009100
00009200
»00009300
00009400
00009500
00009600
00009700
00009600
,00009900
-------
M A I N C 1 ) DATE 021676 PACE
IOC. 9 'DAHAGECi»12t' »J) ' . 1X?°F 1 3 . S , 29C/ ' ' t6X i I C' . I 2 , • , J) ' .00010000
101. 9 1X.6F13.5J) 00010100
00010200
t3X.ll(3X«F5.2»3X00010300
l oa. i)) oooioaoo
1(15. C OOOlObOO
in6. C REAO TN CONSTANTS AND OPTIONS 00010600
J07. C 00010700
108. PEiOfSiI) NOuT«IOUTl»lOUT2AiIOUT2BiIGUT3fBiDiICOPTiIEXPD?NOSORSi 00010600
10*. * KUSORS 00010900
110. 1 FOPMIT {5 r 11 f ax } , 2F i o.2»/2d 1 •''X) » 2 (12 »3x )) 00011000
111. K(RnEf6t925) NCUT»IOUTliIOUT2A,IOUT2e.IOUT3.BfDfICOPTtIE.XPDtNOSORS00011100
112. 1 .NUSORS 00011200
113. 92S FoRM4TClOl.lKOOT=l.Il»T2l.'IOUTl=I.Il,TaitlIOUT2A=i.Il,T61.lIOUT2'00011300
115. 2 /i ' . i ICQPTsi,11,T21.'lEXPOsI.II»T>;^lTF('>TQU7)CICOR(I).lsltl>;0&ORS) 00013400
au? FOPwiTC1 ' » ' ICORfI) i , 7Xt30CIX,12)) 00013500
Jo. W(ou9) 00013600
30. 9a
-------
M A I N ( 1 ) DATE 021876 PAGE
UB.
145.
ISO.
151.
1S2.
153.
ass!
156.
1*7.
155.
159.
160.
161 .
162.
163.
1^4.
lf.5.
1 60.
167.
168.
169.
170.
a> 171.
00 172.
173.
17U.
175.
176.
177.
178.
179.
1 ?. 0 .
1 ?1 .
1 ?2.
•183.
1 S4 .
165.
1 "6.
1P7.
1*8.
189.
190.
1 9 I .
1°2.
193.
10-4.
195.
«; FORMAyf. I?. 1 X, 13A«» 1X.3E6.0.2X.212. / U ( 12 . 1 X . 12. 1 X) )
u--MTE(fc'<>'^)10»CNA«ECI»J)»J=l»iS)»QUCl) »KBOO( I)»OOSAT(I)»IONESOCI)
1 , NpIP,(NPPAftSf,JfI),NMNTHS(JfI).J=l»NPIP)
95o FOPMiTf ' ' .12, 2x,13A4fix,F12.3. lX,Fb.2i2Xf F6.2.6X» 11 »5X» I2.5X'i
1 4(12,',' ,12, IX))
NO0 IPS f I ) =NP JP
IFflC.NE.I) GO TO 205
20 CO^Tl^'UE.
C
C RCAD FLO'* CARL) FOR ALL SOURCES AND CONVERT FLOWS IF NECESSARY
C
DO 75 I = i«MJSi)KS
"•1 R I T f. ( 6 • 9 5 1 3
9Si FOPMAT C ' 1 ' )
Jl = MfjpTpS( I)
DO US J=l • Jl
'V(*lTr(6»955)
955 FOCKATt '0 ' . lp!pE FLOW AND SELF-MONITORING CONSTITUENT DATA'f/i l»
1 "(SOURCE) (PIPE)'t/1 I «3X» ' ID1 .4X. IPIPNO IQS QSUNIT I,
2 ' MNTHQS.QSMEAN-.FOR ALL MONTHS')
MUrM^NlTHSCj. I)
9tAp(s.2S) Ip«PlPNO,IQS.OSU'v'lT(J)«fMNTHQS(J.K),QSMEAN(J,K),K = l,S)
2S FOcMAT(I?«2x«3I2»5(yx,I2»2X»Efc.O)3
IF(NM.GT^>) R£AD(5,32) (MN^HOsCJiK) »3Si*F.AN(J,K) »K = 6.NM)
32 FOPMAT(10X.4Xrl2t2x.E6.0t4X(I2l2X,E6.0,'I2f2XtEb.C
* . JX.I2.2X.E6.0)
00014600
00014900
00015000
00015300
00015400
00015500
00015600
00015700
00015800
00015900
00016000
00016100
00016200
00016300
00016400
00016500
00016600
00016700
00016600
00016900
00017000
00017100
00017300
WRITE C6»9«)OnO»PIP NO, IQS'OSUN IT CJ)tCMNTHQs(J»K),QSMEAN(J»K),K31,NM 00017400
1 )
960 FOP^ATC ' «2I6f4x, 213, 6X,6(T30t 4(12, i , I ,Fio.3.1Xi '/") i/1' •))
Ir CTO.Nfc .I.UR.PJPNO.NE.J) GO TO 220
IFf IOs.NF.99) GO TO 210
CNvRTsl .
IF(GSL'NIT(J).EQ.8) GO TO 381
IF(oS|iNlT(-J).NE.3) W»ITE(6,380) I , J » QS|jN 1 T C J 1
33n FOOMATC '0 ' . !QS ERROR--SOURCE '.I2,i PIPE l»I2t' UNITS ARE 1,12.1
* RATHE1? T»*N 3 (MGO) OR 8 ( ML/CAY) --PROGRAM ASSUMES MGD")
00 3*00 KS ) , NM
3800 QSWEAMCJ»'<)=3.785306*QSMEAN(J,K)
c ESTIMATE & SIMPLE MONTHLY PLOW FOR SOURCE/PIPE
i&l aS(J,I)=QSMEAN(J,l)
IFf.QS(.JiT) .LE.O) OS(J,I)=EFFLOW(J,I)
00 332 Ks2.NM
IFf r,SrF.A.s.'(J,K) .LE.O.) GO TO 382
OSfJ.I)s(l-ALPHA)*QSMEAN(J,K)+ALPHA*QS(JtI)
332 CONTINUE
C
C SEAD CONSTITUENT DATA FOR ALL SOURCES
C
00017500
0001770C
00017800
00017900
00016000
00018100
00018200
00018300
00018400
000185QO
00018600
00018700
00018800
00018900
00019000
00019100
00019200
00019300
00019400
00019500
-------
M 4 I N C 1 )
199.
200.
201.
2m.
203.
20".
2C-7.
210.
211.
2t2.
213.
21«.
2)5.
2li.
217.
2l&.
2]9.
2?0.
2?i.
2?U.
225.
226.
2?8.
2?9.
230.
23«.
23h.
237.
238.
2U1.
2'J2.
2fl3.
9fc5
(6.9E40C5,390)(SMAXCJ»K«L)«SMEAN(J»K»L)»NSIZECJiKiL)fl=6»00020500
00020600
00020700
ooo2oeoo
00020900
00021000
lOX.2E6.Oi !2i2E6.0t I2.2£6.0iI2f 2t6.0, I2t 2E6.0t 12)
AT c
wHlTt(b.970)IO.PTP'JO.lPARMCJ.K.l5tP«UNlT(J»K)t(SMAX(JtKfL)»
1 SMEANCJ,K,L) tNSIZtC J.K.L) .L=1|NM)
97o FORM4!*' ' «2Io.SX. !«.4X.I2t3Xf6(T30f «(P10.2i t i I ,F10,2i ' t I f 12?
1 /' ' ) )
TF(iD.Nt.I.OR.PjPNo.NE.J) GO TO 230
C FIND LIST OF DISTI\CT CONSTITUENTS FOR SOURCE I
KISMPPAKSC 1 « I)
DO
363
iFt
, I) .NE.22) GO TO 383
«i , I) .NE.23) GO TO 2«0
I )=
IF(jl.F(5.1J GO TO 386
00 58^ J=2,J1
KIs.sjPpiftsC J. I)
C>0 ^B"? Ksl.M
Po in« LslrNO
33a TFf jPaP'U J,K, n .EQ.INDpAR(L. I) ) GO TO 385
NJ 0 = N; 0 4- 1
MO?4cSf I) ="'.0
TNOPAxf '-'fit I) = IPA«?M(J.Kt I)
IF( r^D^ARC^U, J) .tvE.23) GO TO 385
IFf TMo°APt^O-l, n .NE.23) GO TO 240
^n-l • I)=22
O. I)=23
535 COMTlfjlIt"
COMsTlluENT
STANDARDS
33*, W
1
00021300
0002UOO
00021SOO
00021600
00021700
00021800
00021900
00022000
00022100
00022200
00022300
00022^00
00022500
00022600
00022700
00022800
00022900
00023000
00023100
00023200
00023300
00023400
00023500
00023600
00023700
00023800
00023VOO
0002«000
0002«100
0002«200
t 3X. iPIPNO" • '
rXI l»3Xf
EFFLOW" .SXi ' IPfXlt IUNIT,M.-FOR ALL CONS I 0002«500
-------
M A I N C 1 ) DATE 021876 PACE
206. I »'TITt'E^TS OF PIPEI) 00024600
2u7. 00 72 J=1»J1
NPSNPP4.95(J»I) 00024800
pf.*OC5.50) IO.PlPNofEFFLOHCJfl).CIPrS.Sn CIPCK) tXl CK) .IUMT(K) rM(K) tK = 6tNP) 00025100
252. Si FQRMATC12X.l2.Eb.0.lx»2M.lX»12*E6.0tlXf211?lX»I2»E6.0tlXi2Il»lXt 00025200
253. * I2,tfc.0.1X.2Il.lX,l2.E6.0,lX,2Il)
254. WRITE(6.995)ID»PJPNO•tFFUOWCJiI)»ClPCK)iXlCK)fIUNITCK).MCK)»K=l,NP00025400
255. 1) 00025500
256. 985 FORM^TC.' ' «2I6. 1X.F12.2, 10CT29,12, ' » ' »F12.3» ' t ' ill» ' » I i12,/ I D)
257. IFflO.Ne.I.GS.PIPNO.NE.J) GO TO 250 00025600
255. c HATCH i/p STANDARDS *ITH PIPE CONSTITUENTS 00025900
259. iNSsO 00026000
260. 00 5^00 Ilsl.NUSORS 00026100
2M. IF {IMSCRSCI1) .NE.I) GO TO 5300 00026200
262. iNSsl 00026300
GO TO 53pl 00026400
5300 rnWTlwl t 00026500
265. GO TO 72
266. 5301 DO 70 K=}.^P 00026700
267. ICHNHrO 00026800
266. 00 55 Lsl?*? 00026900
f° 2fe9. IFCIP(L) ,NE.IPARM(J,K,I)) 60 TO 55 00027000
O 270. ICHMGsl 00027100
271. C N V R T =i , 00027200
272. IF{TP(Ll.NE.23.ANO.IP(L).KiE.22.ANO,lP(L).NE.23.ANO.IP(L,) ,NE. 1 0 . AND000273CO
273. * .IPCU.Nt.ll) GO TO 5302- 00027400
27«. IFripCL).E0.28.ANO.IUNlTCU.NE.5) GO TO 260 00027500
275. If t ( IPCI.I .EU.22.0R.IPCU .EQ.23) . AND. IUNIT (L) .NE.6) GO TO 260 OOC27bOO
276. IFffIPCL).Etf.10.0R.IP(U.EO.ll).ANO.IuNlTCU.NE.7) GO TO 260 00027700
277. GO TO 54 00027800
273. 530? TFCIiJ.MIT(U) .EQ.9) GO TO 54 00027900
279. IF(lUNlTrU) .NE.«) GO TO 530 00028000
280. CMV3T=.a53592 00028100
281. GO TO 5« 00028200
282. 530 IFCIUMIT(U).NE.2) GO TO 531 00028300
283. CNVRTsEFFuOMfJtI)*.001 00026400
284. GO TO 54 00028500
285. 531 IFCIUMIT(U).NE.I) GO TO 260 00028600
266. CNVkT=fFFLC«CJ»I) 00026700
267. $u FFSTCJ,K,I)=X1CL)*CNVRT 00028800
2"«i OISTYPCJ.i
-------
M A I N C 1 )
72
DATE 021876
00029SOO
00029600
PAGE
00 S303 Ilsl.NUSOSS
TFC t*SO*sni).NE.I) GO TO 5303
U'Ssl
300.
301.
302.
in3.
30( J ,K, I )
TFf jP9.',T.i .OH.lPR.EO.a.OR.IPR.EQ.6.0R.IPR.GT,30)
IPflP9.fr. 30) Go TO 721
It- '(P9gMT( J«k ) .NE. 1) GO TO 290
GO Tl 7500
I(-(I?'^,Mt:.2c!,ANJo.lPR..%E.22.A'S|O.IPR.'vE.23.ANO.IPR.I
* It) GO TO 725
IFf jiap.co.Sa.AND.PRUNlTCJfK) .NE.5) GO TO 290
lF((I»9.E0.22.0R.lPR.E.Q.23).AND.PRUNIT(JfK).NE,6)
TFfpRUs'lT(J.K) .tO. 9) GO TO 7300
If f P0ij"« IT( J iK) .EO.U) GO TO 726
U'f p«jMIT( Jf-<) .NE.2) GO TO 72fc
CMV«T=..JOI
GO TO 726
IFcP^jNlTCJ.Kj.NE.l) GO TO 29Q
CMU^TS i .
DO 7?7 Lrl.NM
75M=C.Sv'i4^fJ»L)
S"iFlf;(J.KfL) = S^EAN(JiKiL)*CNvRT*OSM
CONTl'i'Jc
C-G TO 7^00
00 7?Q u a 1 . li M
5'.'AxfJi-
-------
3«5.
3«6.
346.
5u9.
3SO.
'3S1.
352.
353.
354.
3S5.
357.
358.
3 = 9.
3feO.
361.
362.
363.
364.
365,
366.
367.
368.
369.
J7Q.
571.
372.
373.
37«.
375.
37fc.
377.
373.
379.
3*0.
361.
382.
303.
3B«.
3«5.
3«6.
337.
3«6.
3*9.
300.
331.
C Rt*D JM cnwPLlAMCE MONITORING DAJA
c FOR SOURCES R&ING USED CINSORS)
C
A i N ( i ) DATE 021876
00033800
00033900
00034000
00034100
00034200
990 F03-&T('0't"COMPLIANCE MONITORING DATA't/t Ifi(SOURCE) (PIPE) »?00034300
1 /' i,3vt'IQI,8Xt'Jif4X»IIPAR NUM X1CK)«M(K)--FOR K=l TO 'f00034400
2 iNi.iM CM POINTS') 00034500
DO 120 il=l»MUSoRS 00034600
TsTNSOSSCU) 00034700
00 96 Njijlsl «SO 00034800
REAOC5.79) 10. J.IPAR.NUM, (XKK) .M(K) ,K=li7) 00034900
79 FORKAT(I3«2X.II.IX.I?,2x»I2.IX•7Cfc.6 .0112.IX)) 00035000
IFcin.Mt.I) GO TO 295 00035100
IFfJ.EQ.O) GO TO 100 00035200
IF(MU«.GT,7) REAO(5,800)(X1(K).M(K)tK;8»NUM) 00035300
800 ropMATn3X.E6.0,l2,lxrE6.C.I2flX.E6>Otl2flXfE6*OtI2flXtE6.0tI2»lXt00035400
00035500
0003S600
00035700
00035800
00035900
CO 90 K=1.Kl 00036000
PAGE
*E6.0.I2.lX.E6.0,:2,lX)
WRlTE(6.99S)IOtJ,IPARf
995 FQP"AT<' 'tI5»bx.I3»«Xtl3,3X.12.50(/' !iT«0i5(Pi2.31 I i I 112)))
C
c
c
IK( IpA".N£.lPARM(J,K»n) GO TO 90
ICHvG=l
00 95 L=1 .MUM
Z(JiK.L)=Xl CD
W!^THS2(J.K'D=MCD
85 CONyTNUE
NOCPTSf J,K)=Nu^
GO TO 9o
?0 CONTINUE
Iff ifHMG.EO.O) GO TO 297
96 COMTIMUE
100 Jls.^jOPIPSC I )
R£AD(ltM(f)SME*NCJ,t<)tHNTriOS(J,K),J=l,Jl),K=l,2«).CCCSMAXCJtK,L).
* s-JfANtJ«K.L3.MS!ZE(J»K.L).J=l»jn.K=1.10).L=l«24)
CALL TSlATfNiOPIPSCl)»NPPARSCl»I)fNMHTHS(lrI)tDISTYP(rfl?I)tQU(I)t
* lONEsD(I))
11^ CALL PNVCOM[NOPlPStI) .NPPARSd ,1) .NOPARS(l) ,1PARM( 1, 1,1) .
* TNDpAhrl.n .OISTvPtJ.lf I)iEFST(lil?I)iQUCI)»PNVCIl)t ICOR(I))
117 IF(IEXPO.EO.O) GO TO 118
EXD0"CI 1) = 1 •
GO TO 1 1«0
IIP CALL t:xPOAM(iN,DPARtl.I)fKBOO{I)fDOSAT(I),EX?OM(Il)tNOPARS(I)i
* IPA8M.NQPIP5. I)
LOADING FnK SPECIAL OUTPUT
00036100
00036200
00036300
00036400
00036SOO
00036600
00036700
00036800
00036900
00037000
00037100
00037200
00057300
00037*400
00037500
00037600
00037700
00037800
00037900
00038000
00038100
00038200
00038300
00038400
00038500
00036600
-------
NJ
--J
M A r N C 1 ) DATE 021876
3«o.
39S.
396.
397.
308.
399.
400.
401 .
40?.
unj.
000.
005.
006.
007.
408.
"09.
1180 IF(WOuT
Iu,( hsl
WSRcC?)
WS»CC3)
UPFi>' = 0
NPTS^rN
DO 1 1*
wE*Of 1 •
ITF-'P1 =
J«ff.'f 2-
DO 119
I*E*r>T(
wENnTA f
iwEf.;Or(
VfENOTA C
ViENDTAC
,wE..O) GO TO 120
= PXP!)M(Ii)
=pNv(in
ij ( I )
opipscn
J=l ,NPTSw
Ji=nscj« i)
N?pi;-K(j,n
JISITC^PI
K=l »ITEMP1
1 , J.K) = IPARM( J, K, I)
2. JiMsEFSTdJtKfl)
3,J.K)=DlSTvp(J.K,l5
O.Jf K) = ISTATS(I»J'K, 1)
5,J,K)rsQRTf IST*TSCI«J«K,2))
410. 11 "5 CONTINUE
Oil.
412.
013.
010.
4t.5.
WRITEf 1
120 CONTlMM
CALL PR
iF(.%iOuT
RE wj MO
2) DUMMY
K
10RT(IPARM,MPPARS)
.NE.Ol GO TO 150
12
tj6. CALL OUTOUTCNUSQRS)
"17.
013.
419.
J?0 .
421 .
022.
«?3.
U?4 .
0?5.
o?b.
"27.
026.
429.
030.
031.
«?2«
053.
b\ii.
4Ti5.
OJ6.
4?7.
038.
039.
U40.
«ai.
4
-------
4U3. ?3o WRITF(6,?3U ID,PIPNO,I,J 00043600
uuii. 231 PORwATCO' ,10C'«" ), 'SEQUENCING OR SPECIFICATIONS ERROR—If/I 1,15X00043700
UU5, 1 , iSt'LF-MONlTORlNG CONSTITUENT DATA CARD READ AS SOURCE I » 13 , 0 0043800
tiuo. 2 'PlPE'fI3»l WHEN IT SHOULD HAVE BEEN SOURCE'»I3»' PIPE I 113)00043900
HUT'. wPiTF.c6.p990) 00044000
iius. STOP ooouaioo
Jii9. 2JO b,-RITEC6.;>4t) ItJ 00044200
4SO. 2'J1 FQRMATC'0', 10('*') ,'SOUKC£i,I3, ' ,PIPE',I3,'—PH MUST BE INPUTTED ' f 0004U300
451. 1 'WITH PH MAX (23) PRECEDING PH MIN (22)') 00044400
452. STOP 00044500
9. ?70 W«ITEc6»?7l) I,J, IPAHMf JtK.I) 00046200
"7o. ?7i FORHATC'o1loti*'>.ISOURCEI,is,i pjp£.iti3,i CONSTITUENT'fi3ii sTANiooo«63oo
"71. 1 ,'DARD NOT ENTEHEDl) 00046400
u7^. STOP OOOU6500
"73. 2Sft wRITE(b,?3n I.J.IPR OOOU6600
U7U. 281 F-OP^ATCO'.IOC'*') , iSOURCEi ,I3t ' PIPE",13,' CONSTITUENT SPECIFIED ' OOOU6700
U75. 1 'ASI,I3,i—RECHfc'CK LIST OF ALLOWABLE CONST ITUENTS I } 00046800
^76. STOP 00046900
"77. 2«0 WR!TE(6,29t) ItJ.IPR OOOU7000
"78. 29i FORMATC'o1.IOC'*').'SOURCEi,13,• PIPE',13," CONSTITUENTi,13,' SELI00047100
U7
-------
095.
095.
096.
097.
1
2
3
0
STOP
END
'0'.'CHECK CARDS TO BE SURE THAT* DSOURCE AND PIPE NUMBER'00008600
,iS ARE AS INTENDED"f'' 'i20X«•2)CAROS ARE IN PROPER StQUEI 00006700
lNCfci,/i I.20X,I3)NU«8ER OF MONTHS OF DATAt NUMBER OF PIPI00008800
'. lESiETC. AND OTHER DATA ARE CORRECTI,/' 't22Xi'FOR SOURCE' 00008900
tl3?' AND PRECEDING SOURCES 00009000
00009100
00049200
—I
Ln
0.
7.
8.
9.
10.
11.
12.
13.
1 0.
15.
16.
17.
18.
SUBROUTINE ABEFCD1,1)2'
A B E F
BETA»E»F»U
C COMPUTE COtFMCIENTS ALPHA,BET A.E.F F0R PH INTEGRALS
cjMHn"aBKPTS/S(fc),5SPhCll)
L=l
ALptJi = (Hi -B) /A
BtTA= CD2-")/4
DSS=SSPH(KD+1)-SSPH(KO}
F-pSS»(B.Dl)/OD+S5PH(KD)
ys.OOOOOOl
I'F(4LPHA.LT.X)
IFf ALpHA.GT.l.) L=2
IFCBETA.GT.l.) BETA=1.
RETURN
END
DATE 021876
00000100
00000200
00000300
00000000
00000510
00000600
00000700
00000600
00000900
00001000
00001 100
00001200
00001300
ooooiooo
00001500
00001600
00001700
00001SOO
PAGE
-------
1.
•2.
3.
4.
5.
6.
7.
8.
9.
10.
1 U
52.
13.
14.
15.
16.
17.
IS.
19.
20.
21.
?2.
23.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
ilO.
01.
02.
«3.
44.
45.
Ufa.
47.
48.
C 0 M E X 0
FUMCTlON COMF.XDCTMU»TSIGt M.FUNCl-FUNC2»At8)
c CO^E*D CALCULATES EXPECTED DAMAGE FOR ANY NON-PH CONSTITUENT
PEAL II.IMAO
COMxO"J/0>iGl /DAMAGE (JO. fa)
C ID CONTAINS DISTRIBUTION SPEC IF 1CAT ION —0 IS NORMAL AND 1 IS
COMMON/FLAGD/ID
CO*MON/BRKPTS/S(6).SSPH(ll)
CO*MON/BnODMG/TQS,QutCS»I BOD
c FIPST FIVE TEK*S Qf EXPECTED DAMAGE SUMMATION
DO 10 KDsl.5
E:OS*A/OD
' )-S(KD)
IF CRETA.L&.0.) GO TO 10
IF (ALPHA. GT.Ot) GO TO 7
r IO.FO.O) GO TO 7
EXO=C
GO TO 10
10 CONTINUE
L
c SI*TH TERM OF EXPECTED DAMAGE SUMMATION
T.Oi) GO TO 12
IFf lO.F.B.n GO TO 15
12 COuExO = CnMExO + F,jNC2CALPHA,'
TFCIO.Ea.l) GO TO H
C COMPUTE DELTA FUNCTION FOR NORMAL CASE
C
IFf.EQ.3) 1800=1
CALL OAM4&0(DJB,M,6)
TF(M,f0.3) CAUL DAMAGOCDJBtM,8)
15 CC
11 CALL
R E TU R N
END
DATE 021876
00000100
00000200
00000300
00000400
ooooosoo
UOGNORMAUOOOOOfaOO
00000700
oooooaoo
00000900
ooooiooo
00001100
00001200
00001300
00001400
00001500
0000)600
00001700
ooooiaoo
00001900
00002000
00002100
00002200
00002300
00002400
00002500.
00002600
00002700
00002600
00002900
D0003000
00003100
00003200
00003300
00003400
00003SOO
00003600
00003700
00003800
00003900
00004000
00004100
00004200
00004300
00004400
00004500
00004600
00004700
00004800
00004900
PACE
-------
0 A M A G 0 DATE 021876 PAGE
1. SUBROUTINE DAf"AGO(DJBiM,B3 00000100
2. C 00000200
3] C SUBROUTINE D4MAGt-ZERO DETERMINES DAMAGE FC« LEVEL 0 OF PARAMETER M 00000300
Uf C 00000400
5* CO^MON/DMtJl/OAMAGEfSO.b) 00000500
6. COM«.ON/BRKPTS/S(6),SSPH(113 00000600
7. CO""0"l/?ODOMG/TQS.r)U.CS.IBOD 00000700
8. IFCM.E^.33 GO TO 41 00000800
9. IFfB.GE.OAMAGEtMtt)) GO TO 15 00000900
10. Djo=0. 00001000
1. RETl'RN 00001100
2. 15 Do 20 *0rli5 00001200
3. IF(04HAGE(M,KD3.LE.B.AND.8.LT.DAMAGE(M,KD*133 GO TO 30 00001300
«. 20 CONTINUE 00001400
5. DJR = S(*>3 00001500
16. GO TO «0 00001600
17. 30 DJp-(S(KDtl)-S{KD))*(B-DAMAGE(M,KD)3/(OAMACE(MtKD+l)-DAMA6E(MtKO))00001700
18. »+5(KO) 00001600
tq. 40 RETURN 00001900
?Qt c 00002000
21! c BOD ROUTINE 00002100
22. C 00002200
?3* M BBOD=8 OOOQ2300
jy C 00002UOO
?sl C ISODrO FOR n-LEvEL DAMAGE DETERMINATION 00002500
30. C =1 FOR DELTA FACTION COEFFICIENT DETEKMINATION 00002600
J7> C 00002700
23^ IFCIROD.EQ.O) BBOD=B+T°S*C9..Cs3/(Qu+TQS3 00002800
2<». ISOD = 0 00002900
30. IFtR«cO.LE.OAMAGE(3,1)3 GO TO 42 00003000
11. DJPr.O. 00003100
32. RETURN 00003200
33. 4? 00 a? KD=lt5 00003300
3U. ir(0*"4GP(3tK03.GE.B800.AND.8BOD.GT.DAMAGE(3iKD+l33 GO TO 430 00003UOO
•55. 43 CO^TIMJE 00003SOO
36. OJB=S(63 00003600
37. RETURN 00003700
38. 430 DJ8=(S(KDtl)-S(KD))*CBBOD.DAMAGE(MfKD)3/(DAMAGE(M,KD+13-DAMAGE(M, 00003800
39. *K033+SfKO) 00003900
aO. RETURN 00004000
«1. END 00004100
-------
0 I F F DATE 021876 PAGE
1. FUNCTION DIFFCX.Y) OOOOOiOO
2. C OOOOOIOO
i. C Dlf-'F CALCULATES THE DIFFERENCE QF TWO STANDARD NORMAL DISTRIBUTION FUN00000300
a. C 00000^00
5. IF(y.GT.«..AND.y.CT.O.) GO TO 10 00000500
6. GO TO 2S 00000600
7. 10 niFF=4BStO^ORMtX)-DNORM(Y)5 00000700
8. RETURN ooooosoo
t>. 2? DIFF = XNORM(X)-XNOKMCY) 00000900
10. RETURN ooooiooo
11. END ooooiioo
-------
E X P D A H
D*TE 021676
PAGE
1.
2.
3.
«.
5.
6.
7.
8.
9.
10.
1 1.
12.
13.
1«.
15.
16.
17.
13.
t Q
I ^ .
20.
21'.
22.
?3.
24.
?5.
?fa.
27.
26.
29.
30.
31.
32.
33.
34.
35.
36.
37.
33.
39.
40.
41.
42.
11 1
u J •
44.
45.
46.
47.
48.
49.
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
SUBPOIJTIME EXPDAM(IPARAM.«BOD.DOSAT»EXP
EXPDAM pt'rERMlNts EXPECTED DAMAGE FOR A SOU
OIKENsIOM lPARAM(NOpARS)tEXPD(10),IPARM
COw.MON/O^Gl/DAMAGt(30t6)
COuvOM/D'«U2/DNG(2t 11 )
COMMON/PL AGD/IO
CO"MON/8PKPTS/S(6),SSPH(H)
COMMOM/BnODMr./TOSiOUtCS,I60D
COMMON/PMVEXP/DIST(lO)iTMU(iO)iTSI6(10)
CO--"Mn,N/PcOPT/lCOPT
COMMOM/EyP/NPPARS(4,303
I^CL'JOf PltLIST
INTEREP oIST
RE*L KROD
RE^L !>•'• JUt JLl^FRr ININFB
ExTF«K*L IMtlLiILlNFBilNlNFB
F j D rt M u f
tXPDM-0 .
DO 100 M-l.NQPARS
ID=nIST(M)
IF f JPAPAM(M) .EQ.30) GO TO 100
IFnPAfiAy(M) .E0.23) GO TO 100
Iff rPAEAM(H) .NE.22) GO TO 10
EXPECTFo OAMAGE FOR PH
DARAM p p s P H
PAPAM ?J=PGH
EyPD(M)=PMExD(TMU(M)fTSIGCM),TOS,QU) .
GO TO 60
10 IF(lpA"AM(Hj .ME. 28) GO TO 20
TEMpERATUfiE
AsnS/CGU + TQS)
P=0.
IP^r?6
GO T° ?5
20 IFt lPARAw(Mj .NE..3) GO TO 30
300
4 ixQ/^n///"!ll^TnC\
z-KrfOIJ/fvJU+TQo)
B=(i./(JU + TQS))*fCS*TQStOOSAT*OL1)
IP^ = 3
GO TO 55
NON-COi.iplED CONSTITUENT
00000100
00000200
00000300
OOOOOUOO
OOOOObOO
OU000600
00000700
00000600
00000900
00001 000
00001100
00001200
00001300
ooooiaoo
00001500
0000 1600
00001700
00001800
00001900
00002000
00002100
00002200
00002300
00002«00
00002500
00002600
00002700
00002800
00002900
00003000
00003100
00003200
0000X300
00003400
00003500
00003600
00003700
00003800
00003900
00004000
ooooaioo
00004200
0000^300
00004&00
00004500
0000^700
00004600
00004900
-------
N3
00
O
50.
51.
52.
53.
sa.
55,
56.
57.
58.
59.
60.
61.
63.
63.
64.
65.
66.
67.
66.
69.
70.
71.
72.
73.
70.
75.
30 4=i ./(CU+TGS)
E X P D A M
IFftPH.EO.10.OR.IPM.EO.il) AsA«TQS
CGPT=DAMAGECIPM, ICOPT)
IFf JCOPT.EQ.i. AND. COPT. GT.O.) COPTsO.
B=COPT*OU*A
55 IFfJO.EO.l) GO TO 56
DATE 021676
PAGE
GO TO 60
56
C Stt OP sPfcClAL OUTPUT
60
00 bl J=1 »NP
NPP-MPPA»S( J, I)
00 65 Klrl.NPP
!FfiPARM(J.Kt,I).NE.IPARAMCM)) GO TO 65
IF(iPARAM(HJ.EQ,a2) WENOT A ( 6. J,KL1) = 10000000.
IFtlCHVG.GT.l) «ENDTA(6iJ,Kl)slOOOOOOO.
65 CONTINUE
!F(FXPO(M).GT.EXPDM)
100 CONTINUE
END
00005000
00005100
00005200
00005300
GOOOS400
00005500
OOOOSoOO
00005700
00005600
00005900
00006000
00006100
00006200
00006300
00006400
00006500
00006600
00006700
00006800
00006900
00007000
00007100
00007200
00007300
00007400
00007SOO
-------
NJ
00
1.
a.
3.
a.
5 .
6.
7.
8.
9.
10.
11.
12.
13.
I I I N F B
FUNCTION lLINFB(ALPHAiHU»SIGMA)
c CO«PUTTKG iLro«s(6) .ALPHA, INFINITY»MU»SIGMA)
c
a E A L M "J
ALPMA]=CALOGlO( ALPHA) -MU5/SIGMA
IF (ALPHit .GT.«.) GO 'TO 20
ILTNFB=S(6)*(1.-XNORM(ALPHA1))
20 ILIMFB=S(6)*DNORM(ALPHA1)
RETI.IRN
END
DATE 021876
00000100
oooooaoo
00000300
00000000
ooooosoo
00000600
00000700
00000800
00000900
00001000
00001 100
00001200
00001300
PAGE
-------
oo
1 .
2.
3
*•
4.
5.
6.
7.
I L I N F A
REAL FUNCTION iLiNrA(BETA,MUf3iGMA)
C1UCULATING lL(Oilt-lN!FlNlTYiB£TA.MU»SlGMA)
END
DATE 021676
00000100
00000200
00000300
OOOOOilOO
00000500
00000600
00000700
PAGE
-------
I L I N A 0
DATE 021876
PAGE
N3
CD
LJ
1.
2.
3.
u.
5.
6.
7.
8.
9.
10.
11.
REAL ^UNCTION ILINAO c *i
Mfi tl. f A, b,0, BETA, Mg, SIGMA)
RCiL MU
8tTAl=(4LOGlO (BETA). MU) /SIGMA
C USING LNf 10)=2.ioaS851
BETA 3 = BE TAJ. SIGH A*2. 3025651
lL!NAo=A*EXP(CSIGMA*2. 3025851)**?.
*B*XNOP'<(8ETA1)
oooooioo
00000200
00000300
OOOOOUOO
00000500
00000600
00000700
+2. 3025851*MU)*XNORM(BETA2)+ 00000800
00000900
ooooiooo
00001100
-------
I L DATE 021876 PAG£
1. R£*L Fl'MCTlON JL(A,BiALPHA.aETA,MU,SIGMA) 00000100
2. c 00000200
3. C CQ'SIGMA OOOOOsoo
7. PET*TsCALdGlOCtETAj-MlO/SIGMA 00000700
8. C USING |.N( ] 0)r2.3025851 00000800
9. ALPH42=ALPHAj.siG^A*2.3025851 00000900
K> 10. BETA2 = Bt'T.Al-SIGMA»?.3025851 00001000
3° 11. IL=»»EXPC(SIGK,A»2.3025851)**2./2.+2.3025851*MU)*DIFF(BETA2.AUPHA2)00001100
i?. **e*oiFF(RETAi.ALPHAD 00001200
13. RETIJ'N 00001300
1". C OOOOlUOO
15. C ILCOiSffa).ALP^A. 1,MU,SIGMA) 00001500
16. EMTpY RlLCTl(ALPHA,MU»SlGMA) OOOOlbOO
17. ALPHAjs(ALOGlO(ALPHA)-Mu)/SIGMA 00001700
18. 3ET4l=-MU/SIGMA 00001800
19. IL=S(6)*OIFF(BETA1,ALPHA1) 00001900
20. RETURN 00002000
2t. END 00002100
-------
00
1.
a.
3.
a.
5.
6.
7.
1 N I N F A
FUNCTION lNlNFA(8ETA,MUiSIGMA)
C CALCULATING IN C 0 , 1 i . INF INIT Y » Bt'J A »
REAL MU
RF.TURM
END
DATE 021676
OOOOOiOO
00000200
00000300
00000400
00000500
00000600
00000700
PAGE
-------
I N
DATE 031876
PAGE
CO
1.
a.
3.
a.
5.
6.
7.
6.
9.
10.
tl.
12.
13.
14.
15.
16.
17.
JO.B.£0.1.) CO TO 10 00000700
C USING Fls3.1fll5«>27 00000800
C AKD i./SQRT(2*PI) = .59e9«22 00000900
INrA*SlKMA*,3989«22*ffc-xPC»(ALPHAN**2.)/2.)-£XP(-(B£TAN**2.>/2.»+ 0000 I 000
*(MU*AtB)*L>IFF(BETAN|ALPHAN> 00001100
RETU°N 00001200
C 00001300
C IN(0,l.Al.pHA,bETAtMU'SlGMA) 00001400
10 INsOIFF(BETANt ALPMAN) 00001500
RETURN 00001600
END 00.001700
-------
ro
CO
1.
2.
3.
u.
5.
6.
7.
8.
ej
*» •
10.
11.
12-
13.
C
C
c
c
I N I N F B
REAL FUNCTION ININFBCALPHA»MU»SIGMAJ
,AUPHA, INFINITY. H
REAL MU
ALDHAN=
IF C ALPHAS. G7 .«. ) GO TO 20
20 INlNjFB = Sf 6)*CNORM(ALPHAN)
RETURN
END
DATE OH1876
00000100
00000200
00000300
00000«00
00000500
00000600
00000700
oooooeoo
00000900
00001000
00001100
00001200
00001300
00001400
PAGE
-------
I 3 T A T DATE 021876 PAGE
*• SUBROUTINE ISTATCNoPIPSfNPPARStNMNTHStDlSTfQUtIONESO) 00000100
2. C 00000200
3. c s'iBsouTiME ISTAT COMPUTES THE INITIAL STATISTICAL DESCRIPTION GIVEN INOOOOOSOO
4. C DATA FROM 4 SINGLE SOURCE 00000400
5. C 00000500
.6. REAL NU(4,10t22. * GAMMAtKETA.KNUtENUiIPARMUi10fJO)tISTATSC30»4»10»4) 00001200
13. CO^'MON/lsTP'l. C 00002600
27. C 00002700
28. IF(lONF.s".NE.i.oR.(IPARM(L,Jf I).NE.22.AND,IPARM(L»J»I),NE,23)) GO 00002600
29. V TO 100 00002900
30. C CHECK PH DATA WHERE ONLY MAx/MIN ARE GIVEN 00003000
31. IFnPA«H(L.J,I).EQ.22) G0 T0 H13 00003100
32. 00 90 K=t»NM 00003200
33. IFfNSIZEtL.J.K).GT.O.AND.SMAX(LiJ»K).GT.O.) GO TO 90 00003300
34. NS!ZECL..7f K) = 0 00003400
35. SMAxfL»Jt*)S0. 00003500
36. NslzECL»J+l»K)*o 00003600
37. PMAX CL.' J*l tK)sO. 00003700
3?. 90 CONTINUE 00003800
39. no 9^. «=iiNM 00003900
40. NSl7E(L.J*l»K)=NSIzE(L»J»K) 00004000
41. IF(NSJZEfLtJ+l.K).GT.O.AND.SMAx(L»J-HtK).GT.O.) GO TO 98 00004100
42. NSIZc(L•J+1»K)*0 00004200
43. SM*XCL'J+l»Kl=0. 00004300
44. MSI7E(L»J»K)=0 00004400
45. SHAx(L•JtK)=0. 00004500
46. 9fl TF(gMAX(Lf J^lfK) .LE.S,^AX(Lt JtK))GO TO 99 0000<»600
47. WRITE (61101) MN-rHQstL t *) »Lf I 00004700
"8. 101 FCRMATt>0't'MIN.MAX ERROR FOR *ONTHI.I3»' OF PlPEitlS.i OF SOURCE 100004800
-------
T Q T A T •».*•*-
1 " ' A ' DATE O2itj7t> PAGE
a9- 1 »l3t/' '.'CONSTITUENT 22 MINIMUM IS GREATER THAN CONSTITUEI 0000^900
50. 2 .'NT 23 MAXIMUM--DATA DELETED') oooosooo
51. NST?S(LtJ+liK)=o 00005100
52. SMAy(LFJ+ltK)=0. 00005200
53. NSTzE(L«JfK)=o 00005300
5«. S M A X ( I. • o F * ) = 0 . 00005UOO
55. 99 CONTINUE 00005500
56' G0 TO 1113 00005600
57. C CHECK F03 REGULAR CONSTITUENTS (INCLUDING PH WITH MEAN) 00005700
59. 100 DO 1M2 K=IFK'M 00005800
59. IFfN,SlztrL.J.K).GT.O.AND.SMEAN(L,J,K).GT.O..AND.SMAXCL»JiK).GT.O.)00005900
60. * GO TO 1110 00006000
61. N5TzE{Li..'fK)50 00006100
62. SM*xfL•Jt^)=0. " 00006200
63. S •• F A M (L t.! F K ) = 0. 00006100
63. 1110 !K((TPA^M(LFj|I).NE.22.ANO.SMAv;(L.J.K).GE,SMEAN(L.JFK)).OR.(lHARM(00006i400
65. *l ..J, I) .tn.22.AND.SMAX(Lf J»K) ,LE ,S;-1EAN(L« J»K) )) GO TO 1112 00006500
66. WHTTF. (6t t Hi) MNTHQSCL.K) tLf lf IPARMCL, Jf I) 00006600
67. 1111 FC»MAT('0'•"MAX.MEAN OR MIN-MtAN REVERSED FOR MONTH"tI3.l OF PIPE I 00006700
68. * tT3.' OF SOURCE'113.'t CON$TITUENT'»13•'"»OATA DELETED') 00006600
69. VSTZECL».I«K)sO 00006900
70. S'xAv(L'J«K)=0. 00007000
71. 5" FA*(U«JfK) = 0. 00007100
72. 1112 CONTINUE 00007200
73. 1113 Klrfl 00007300
74. ]"MTH=0 00007000
75. DC 1=1 Ksi.l^M 00007^00
7b. IFtKJ.GE.K) GO TO 15 00007600
77. KI=K 00007700
754 l!5zrgsT7t-(L.JtK) 00007600
79. 12 IFn-iS.GE.3. GO TO 160 00009300
90. C 00009000
95. C FIND ESTIMATES FOR *LL MONTHS FOR GIVEN PIPE/PARAMETER 00009500
°6. C 00009600
-------
I S T A T
CO
vo
O
97.
X 1 =KO ?K2
i JfKj)*SMEAN(Lf J»K1)
IFf JPARM(U»J»J).NE.22) SO TO 18
IFfNSlzEcUt J.K1 ) ,£0.0) GO TO IS
TF(sHAX(L»J»K).6T.SMAX(LtJ,Kl)) SMAX (L » J . K)=SMAx (L • J.K1 )
GG TO 19
19 lc(s*iAX(|_»J»K) .GT.SMAxCL'Jf K1J) GO TO I1?
19
200 JFf irwKSO.^E.l) GO jO 21
IFf I"AR^(Li J, I) .^E.23) GO TO 21
IFfK.jn,K2) r,o TO 202
00 20: »
1 EMEAN(LfJfK)ttSIGKA(LfJ»K) , O.tlPARMCL, J, I)ilt IONESD)
22 ET4(L,J,Kj=NSIZefL, J,K)
Ni."'L.Jt^) = (;-'
220 EsTG>''AtL,Jf!<)
i JtK)
(L t J t
C ADE> in 4Ny COMPLIANCE pOINTS FOR MONTH(s) BEING DONE
C
IF(MCP.cn.D) GO TO 28
DATE 02J876
00009700
00009800
00009900
00010000
00010100
00010200
00010300
00010400
00010SOO
00010600
00010700
00010800
00010900
0001 1000
0001 1100
00011200
00011300
00011400
00011500
00011600
00011700
00011800
00011900
00012000
00012100
00012200
00012300
00012400
00012500
00012600
00012700
000]2600
00012900
00013000
00013100
OOC13200
00013300
00013400
00013500
00013600
00013700
00013800
00013900
0001UOOO
00014100
00014200
0001 U300
00014UOO
00014500
PAGE
-------
I S T A T
NJ
VO
1U7.
150.
153.
1SU.
155.
156.
157.
155.
159.
160,
161.
162.
163.
168.
169.
170.
171.
172.
173.
I7a.
175.
1 76.
177.
178.
179.
1P2.
lea.
IBS.
1P7.
IPo .
1QO,
192.
193.
19U.
00
Ki=KiK2
23 DO 2" M = HLO>I.NCP
TFfHNTH5z(l» J, *} .EQ.M.MTri) GO TO 25
25
GO Tn
fjij'sNij (U t Jt K) /GAMMA
TFfOIST(Lt J) .EQ.l) 2CL»JiM)sALCG10(ZCLtJtM))
r.M-c &'•"('.! J»K)
S!G=SQBT(ESIGMA(L»JiK))
1F{"LQW.GT .NCR) GO TO 2d
GC> TO ?5
C REsEf?uEf.iCF.--.s£T UP f (111 ASRAYs BY SEQUENTIAL INDEX OF 'MONTHS!
C INCLUDE COMBINATIONS OF MONTHS rtHERE DATA WAS INSUFFICIENT
N.jfL* Jf Nl)=NU(Lt JtK)
EotGk'A(l-.J.Nl)=ESlGMACLfJt
f '• F. A '•' ( L f J t * 1) = E M E A W ( L » J « K )
lr CM.MF . I'lNTW) GO TO 30
IF f TFLAG.f 5.0) GO TO
SIGMACLtJ)sESlGMA(LtJtl)
TMPFTAsETA(Li J t 1)
TN.P'..'J = NU(Lf Ji 1)
r,0 TO U7
KJ 1 = N + j
GO TP 17
C
C
3? ^u(
SIC-"4fL..n=£SIGM4(LiJ,l)
ESTIMATES
DATE 021676
0001«600
0001«700
0001
-------
195.
106.
107.
lo*.
199.
200.
201.
202.
2P3.
204.
205.
206.
207.
208.
209.
210.
211.
212.
213.
214.
215.
216.
217.
21<5.
219.
220.
221.
222.
I.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
t3.
14.
15.
16.
17.
18.
19.
20.
21.
PC o 0 K = K 1 •
TFfT"PNJ.G1
IFf T^PETi.C-T .KETA»FTACLf JtK )) TMPETA=KETA*ETACL«J•K)
(Lt
*.K)*F;TA(U'J|K)*fc^EAN(L'J«K)*E^EANCL»JfKJ-(TMPETA*£TA(L«JtK))
»Jn
u o C 0 '-• T I' i Ll E
47 ISTAT.SCl «Lt J, 1)=MU(L. J)
ISTiTS(I.LtJi2)=SlGMA(L»J)
ISTATs(I,LtJ.3)=TMPETA
.J)=SIG
-fJ)=0
SO COWTTNUE
C
9999
10000
wRTTE(6»10000) ItIPARM(LtJrl)
FC-PMATC *0 '• 10( !* ') t ' INSUFFICIENT DATA (COMBINED SAMPLE SIZE
1 ,i THAN a) FOR SOURCE'«I3»i CONSTITUENT I«13)
SVPP
LESS
ORDER
OSOER(XMRtlSORCtM)
C
C B!
RLR SO=>T
DO 70 1=1.
DO
IF
65t65»64
64
( J)
XhR(..T+
65 CONTINUE
IFCKFLiG.EO.O) RETURN
70 CONTINUE
RETURN
END
00019SOO
00019600
00019700
00019800
00019900
00020000
00020100
J00020200
*MUCLi00020300
00020400
00020500
00020600
00020700
00020800
00020900
00021000
00021 100
00021200
00021300
00021400
00021500
00021600
00021700
00021800
00021900
00022000
00022100
00022200
OAFt 02187fe
00000100
00000200
00000300
00000400
00000500
00000600
00000700
00000800
00000900
ooooiooo
00001 100
00001200
00001300
00001400
00001500
00001600
00001700
00001800
00001900
00002000
00002100
PAGE
-------
OUTPUT
DATE 021876
PAGE
1.
^.
3.
a.
5.
6.
7.
S.
9.
1 0.
1 1 .
12.
13.
14.
15.
16.
17.
16.
19.
?0.
21 .
?2.
23.
au.
25.
26.
?7.
2*.
29.
30.
31 .
32.
33.
3".
•T C
S3.
36.
37.
38.
3".
UO.
"1 .
02.
U3.
uu.
SUBpnuTlNc OUTPUT(NUSORS)
C
C OUTPUT ;> S
C
If'CU,1
00000100
00000200
IMS source STATISTICS SUMMARY TABLES 00000300
CE Pl.LIST
OIMFMSION DISTC2)
CO-MMn\.vCO^SI/P4RMS(5,30)
DATA
DATA
OAT 4
DATA
DATA
DATA
DATA
DATA
DATA
OAT4
DATA
DAT4
DATA
DATA
OATA
DATA
DATA
DATA
OATA
DiTA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
r> « T *
U •* ' A
DATA
PATA
DATA
C
c OUTPUT r!'-<
00 ill
PEinc
« R ! T F
S FQP.HA
OT JT{ 1 ) f DISTC?)/' N I , i L
( P A o .", s C L » 1
(PAOMSU. 2
(FAPM.SCL ,
CPAPMSU.
( P A P M S ( L •
(PAQ:'.S(L.
(PASMSCL,
(PARMSf U t
C P t R .« S ( L •
:°ARMS(L. 1
( ° 4 P ". S ( L ' 1
(OAp'-iSCLt 1
(pARMSCLt 1
(PA3^S(L. 1
) «L=1 »5>/ ' AUUKi ,
) »Lsl t 5) / ' AMMO i ,
3) .L=1.5)/iBOD5'
1) tL=l .5)/5* '
5) »L=1 f5)X ICAR6"
6) .L=1.5)/5*'
7) .1=1 .5) / ' CnLO
8) .U=l .5)/ iCHLO
9) «L = lt 5) / ' CMRO
0) .L=1.5)/'COL1
n ,L=i »5)/ ICOLI
2) »L=1 .5) / ICOPP
3) tL = l i5) / 'CYAN,
u) .L = 1.5)/'FLUO
(PAPfS(l.t 15) iU = 1 tS)/ ' ISO
000001*00
00000500
0 0 0 0 0 6'0 0
00000700
'/ 00000600
i INUMI » l 1 t 1 ' . 1 1 / 00000900
"NIAII l»l '»' I/ 00001000
f i ,' ' » 1 l » 1 '/ 00001 100
'/ OOOC1200
.ION . ' if" ' t l " / 0 0 0 0 1 i 0 0
I/ 00001400
, IRIOE
, i ROFO
i ' WIUM
f ' FOKM
. 'FORM
, 'fcR
. i IDE
, IRIOE
, IN
(PAP.MS(L,16) .1 = 1 i5)/'LEAC ,'
f BA9-S(L, I
r' = A*<"SU. , 1
( P i = y- 3 ( L i 1
f P4PMSU ,2
-PARMSCL .2
fPiOMSCL,2
7) .1=1 ,5)/IHA,M(j
6) t L = i • •>) / ' MERC
<9).L=ltS)XiNICK
0) tL=t i5) / INITR
1) .L=liS)/l01L-
2) »L=1 .5) / ' PH-M
fPARr-iS(L,23)»L=l.S)/iPK-K
(PAPMsa,2a) tL = 1.5)/'PH£N
CP'«MS(L»25) »L=l«5)/iPHOS
( P A a M S C t » 2
*Q«.r3Mcf| p
«•) .1 = 1 «5)/i DISS
7>.i -i_c;iyiCiiCU
;*xafc'1^ol,UfC//»t-*"lB-J'' 'vwvji
(PAP.MS(L«28)tL=lt5)/'TE»'pi
(PAPMSC1..29) .1=1 .S)/'TIN 1
CPiRMS CL . 30) .1=1 .5) / i DO l
f TAPUH. FOP EACH SOURCE
!= 1 f^uSOR
; P ) o U * « y
r6«S) Ih( 15
T ( ' 1 i . T60«
S
1 1 C I* ' ) ./ ' ' »T61
a5. C h'LAOI^r, FQR EACH PIPE
U6.
•i f
U 7 .
ue.
U9.
DO 37
w ^ T T c
IP FCB-MA
» , ' lipS
J = 1 , N P T s «
(6t10) Ji1^
T r ' 0 ' • T ! 1 f
TREAH FLO'''
CKlA^I T^ 1 1 D P 1 LJ
, I ANtS
» >uRy
. ' tL
, 'OGEN
, 'GREA
, 'IN
, IAX
. "OL
. ' PHQR
, 'OLVE
• i f-' KJ n r
V ' L. "i U U.
, IERAT
, 1
. I
1
IRM E
S.-T
S--F
E
SE
US
0 SO
r> sn
V O U
URE
t ' »
, XTRAI,
. ' .
. OTAL't
. ECAL't
t ' .
t ' •
. ' »
. ' t
. ' .
« ' .
. ' .
. ' .
T '•
• ' •
t ' «
. ' t
« ' .
. ' .
. LIDS' .
t LIDS'.
T I. 4 W V »
. OIFF'.
i ' .
. ' «
CT
/ 00001500
/ 00001600
/ 00001700
/ 00001600
/ 00001900
/ 00002000
/ 00002100
/ 00002200
/ 00002JOO
/ 00002aoo
/ 00002500
/ 00002600
/ 00002700
/ 00002800
/ 00002900
/ 00003000
/ 00003100
/ 00003200
/ 00003300
/ 00003UOO
/ 00003SOO
/ 00003600
/ 00003700
/ 00003800
00003900
OOOOUQOO
OOOOU100
0000^200
OOOOU300
i 'SOURCE'»I3,/i l .TfeOilK I*')) 0000**aoO
0000^500
0000«600
t.NU[ I *JJ fU'^^L.'*'
|PIP£= i t 12. 1 OXt (MEAN DISCHARGE (ML/DA Y) • i ,M 2.4 1 1 1 X
(MtXOAY)s 1 ,F 12.
«) OOOOU900
-------
OUTPUT DATE 021876
SO. IFfDC|.GT.O)wPlTEC6,15)00 00005000
SI. IS FOPn*T(' '.TlSt'HEAN DO CONCENTRATION (MC/L)»'«F12,4) 00005100
52. wanE(6t?0) 00005200
53. 20 FOPMA-J-C i o'»T89t'EXPECTED PROS. OF f.'O I / ' ' » T 16» ' CONSTITUENT ' • T38t 00005.400
Sfl. *'STANDARD'.T52.iDIST'tT60.'tST. MEAN IfT75» I EST. SIGMA I . T90f I DAMAGE00005«00
55. *>tTiOl.'VlOLATlONi/i i,Tll.20C«-')»T36tl3(l.l)»T52»«(l"l)»T5''fl2C|00005500
56. *-') ,T7at 12('.I)|T69»6('-')«T100tU('-'}) 00005600
57. NP = IWE»J(2» J) 00005700
S8. C DATA FOR EACH PARAMETER ooooSeoo
59. 00 ^0 Ks)iWp 00005900
60. IP=IWF>OT(I•J»Kj 00006000
41. C DOM'T OUTPUT 00 AS REGULAR VARIABLE 00006100
•62. IFfTP.PG.30) GO TO 30 00006200
63. in=I*'fMOT( 3> Jt K) 11 00006300
fa. *RTTF(o,?5)(PARMS(L.IP)fL=l,5)tWENOTA(2.J,K),DISTCID)rWENQTA(«»JtK00006UOO
*5. *)fWEKDTA(5tJtR)TKENDTA(6.J.K)»WENOTA(7»JfK) 00006500
66. 25 FORMATC1 ' iT1l'5Aa,T36.F13t4iT52iAUiT59iFl2,a»T7a»F12.4fT89,F8.a» 00006600
67. *TIOO.FII.«) 00006700
68. 30 CO^TlMJE 00006800
69. WRIjECoF^b) 00006900
70. 36 FOPV.ATC'0't/iO') 00007000
71. 37 COMTO.'Mt: 00007100
72. WHTTE(6,?5)^S«C(2)tWSRC(3j 00007200
73. 3S FORvATCQ1tTll»50(i*f)t/l ' tT12•'SOURCE EXPECTED DAMAGE"iT«6fF12.400007300
74. *,/' i,112,"SOURCE PROBABILITY OF NO VJOLATlONIiT«6fFIZ.It/I ItTUi00007400
75. *50fi*D) 00007500
76. «0 CONTINUE 00007600
77. RETuRN 00007700
7?. END 00007600
-------
p A R A M DATE 021676 PAGE
i. PI pent oooooioo
2. COMMON/OUT /I-.SRCC3) 'UPFLWtDOfNPTSW^WENDCZia) »WENDTAC7i«i 10} 00000200
vo >. DlfF.NSlOM DUMMV(29«j) , jw(3) • IWEN(2»4) t IWtNDTC 7»0i 10) OOOOOiOO
01 u. EQuIVALfcMCk' ( Iw,ws»C) f C IWENi WtND) i ClWtNCTf WENDTA) t CwSRC»DUMMY) 00000400
5. E^O 00000500
-------
P A R A M S
DATE 021876
PACE
1.
2.
3.
o .
5.
6.
7.
8.
9.
10.
1 1 .
1 2-
1 3.
!«.
15.
t 6.
17.
'.8.
t 9.
2 0 .
' 1 .
r '
22.
?3.
?o.
?5.
?6.
27.
26.
?9.
30.
31.
32.
33.
•i(J),J=l, 00) /!.,!. 126, 1.693, 2, 059, 2*326.2.530, 2. 7oai2.8a7i
* ?. o?0. 3. 073, 3. 173, 3. 253,3.336,3. 007, 3. 072,3. 532, 3. 588,
* 3. frOO, 3. 6P9. 3. 735, 3- 778. 3. 819, 3. 658, 3. 89 5, 3. 930. 3. 960,
* J. 997, o.O 27, 4. 0^7,0,086,0.113,0, 139, 0.165.0. l69,
* a, ji3,0. 236, 0,e'59,0.23o,0. 301,0, 322/
iMFGpe nIST , SSIZF
DATA CHfCKS
If t SSI7E.GT.36S) GO TO 350
IF(lONE5o.F.Q.l.AND. (1PRM.EQ.22.0R.IPRM.EQ.23)) GO TO 325
IftDlST.E'J. 1 ) f-0 To 100
EST!MATI.MG PnR NORMAL CASE
•C=fALOG(SS!zE/1.525l7)/2.9l5U6)tl.
ESIGMAr(SMAX.SMEAN)/C
E "••• F i ^ s S ."> f A N
RETU^;,
ESTIM4TT-J fpf- LnG'-oRH4L CASE
100 HATIOrSM4!'/iMEAN
IF f WATIO.LT. 1 . 25. OR. RATIO. GT. 6, 00) GO TO 365
IFfBATTO.GT.2.3) Go TO 200
*LPHi=l . Q
-------
p * R A K S DATE 021876 PAGE
50. IFCSSlze.LT.25) 8ETA = a.963a2-(SSlzE-5.J*C . 021 11"CSSIZE-10.)*( 00005QOO
51 . l.on 522
-------
P H 0 M G 0
DATE 021876
PACE
VO
00
1 .
2.
3.
u.
5.
fe.
7.
8.
-------
P H £ X 0
DATE 021876
PACE
1.
2.
3.
4.
5.
6.
7.
a.
9.
1 0.
11.
I 2.
[3.
I 4.
IS.
16.
7.
I 6.
[9.
?0.
21.
22.
?3.
34 .
?s.
26.
30.
31 .
32.
33.
34.
?5.
3o.
37.
36.
39.
40.
4! ,
42.
43.
to.
45.
"6.
07.
lie.
09.
50.
CALCULATES ExpEClEO DAMAGE FOR CONSTITUENT PH (AND POHJ
C 0 M M 0 >J / 6 I J / A . B ( 2 )
1 i 1C)
COPT?=DA^AGE(2t 1C)
TMUC?)= 1 O.-TMUC 1 )
PM i = crvTl
?C2)-COPf2'
20 IFCT'HH 1 ) .GT.7 . ) GO TO 24
w"ci
-------
H H E X 0 DATE 021876 PAGE
SI. 39 00 00 KD=ltlO 00005100
52. CALL A«EF(DAMAGE(I.KD) iDAMAGEdfKD*!) .AtB(Z) »KDtA|.PHA,BETAiE»F»U 00005200
?3. TF(L.Erj«2) GO To *»0 00005300
5U. IF (iLPrtA.Lt.T.AND.T.LT.BETA) GO TO 50 00005400
•S5. PHE-xOiPhEXO+ILCEtF.ALPHAtBETA.-TMuCD »TSIG(J)) 00005500
56. UO COMTlNUE 00005600
57i C ALPHAf l D=BETA( 10J 00005700
58. C LI=11 00005800
59. PHFXD=oHexO*IL(O..SSPH(ll).BETAtTf-THU(I)iTSIG(J))+RILBTl(Ti-TMU(100005900
60. *)tTSlG(I)) 00006000
61. RETURN 00006100
(,2. C 00006200
O *3« C LI = 1 TO <5 00006300
o t,u. 50 PHFyO=PHPxO+IL(EiFtALPHA»T»-TMU(I)»TSIGCJ))+IL(EtF»T»BETA|-TMUCI)f00006UOO
6S. *TSIR(in 00006500
f,6. LI = +1)tA»B(I)»KD»ALPHAtBETAtE»F»L) 00006900
70. TFCL.fc'O.?) GO TO 55 00007000
72. 55 CONTINUE 00007200
7J. CALPHA(Ji) = E?ETA(10) 00007300
75. RETURN 00007500
76. END 00007600
-------
P N V C 0 M DATE 021876 PACE
1. SUR9PUT1ME PMVCQMlNOPlPS»NPPARS«NCPARS»IPARM. INQPARf DISTYPiEFSTf 00000100
2. * nu»PNV,ICUP) 00000200
3. C 00000300
U. C pNvCol"- r 'LC'JLATLS PROBABILITY OF NO VlQL*TlON FOR A SOURCE. AND COMBINOOOOOUOO
5. C P«RMG/T(JS«TQU.C$. IBQD 00001300
u. COMMOM/IsTP'-'V/^Uf «• 10) tSlGMACU, 10)' 00001UOO
5. COMMOv/P.M^Exfr/OISTdO) fTMUCIO) .TSIGC10) 00001500
6. COM-/P-.VUPOATE/I tOS(«.30) 00001600
7. INCLUDE PI. LIST 00001700
8. C 00001300
9. C FIND ALL PlpF LOCATIONS OF SAME PARAMETER FOR SOURCE I 00001900
?0. C AND COM8INE DATA 00002000
21 . C 00002100
•>2. 00 = 0. 0000c200
?3. CS=0. 00002300
?u. TQitr^u 00002UOO
?5. TQSrO. 00002500
?6. DO 10 0 = '..^OOIOs 00002600
?7. 10 T(3SrTQS + -?S(J,I) 00002700
38. PMVsl. 00002800
29. no 80 ^sitMOPAPS 00002900
30. S'JMMsQ. 00003000
31. SUMV=0. 00003100
J2. TM|i(V)=o. 00003200
33. T s I G C K- ) = 0 . 00003300
3". MSAMgrO 00003aoO
?S. 00 t>0 J51.NOPIPS 00003500
36. MP=MPP4«s( J) 00003600
?7. 00 60 " = 1.N-P 00003700
76. IFfiPiPi( J.KI ,NE. INDPAR(M) ) GO TO 60 00003800
? 0000«900
-------
P N V C 0 H
DATE 021876
PACE
50.
51.
52.
53.
51.
55.
56.
57.
«?8.
59.
60.
M .
ft2.
f>3.
6 J .
65.
*-6.
67.
6S.
69.
70.
71 .
72.
73.
7U.
75.
76.
77.
78.
79.
1=0 .
61 .
82.
?3.
«'J.
«5.
»e.
a?.
B5.
P9.
00.
91 .
°2.
9 ? .
9u .
"5.
96.
o 7
° ' .
«6.
GO TO 52
C
C--LCGK>'OPlliV=TE'«PM»TEMPM* (10.** (2. 3025851 *SIGMA ( J, K) *SIGMA ( J, K) ) -1
SilMiy = 5|.iMV» TEMP V
Si Tt^P'VvilL 1N?« CEFgTf J.K5 »M0(J«K) «5IGMA(J,K))
C SET ViDTA^.Lt POrt OUTPUT OPTION
5? A'EfnTc. C /i J «K) = T£MPK'V
1Tf-!ji'*iDAOf*M r(j ??> toFKjDTAf7*,I«K*1^s1nfiOnnfi
f | ^ m 1 1 K « K ^ -J # t, W , C C J VNC'^Wl **(, / fWfr\^iJ«»lUUVUvV#
IF(TNnP4P(K) ,EO,30) GO TO 60
IF('Cf..R.F5.1) GO TO 60
p^!V = P^:V*Tt.MPNV
GO TC 60
C
C
C PH/pOrl
53 Tf^pM=iO.«:*C.Mu(J.K}*1.15l2925*SIGMA(J,K)*SlGMA(JtK))
SUWi-rsU^MtTt^PM
TE^PV=Tf"Pf*TEMPM*{io.**(2. 3025851*51 GMA(JiKJ*SlGMACJ»K))-l,
Si/'-o 100 KK= i » 2
KPCt^+1-KK
k-
-------
OJ
o
OJ
•50.
100.
1M.
102.
103.
10".
1P5.
int>.
107.
109.
109.
110.
111.
112.
113.
ll«.
SIS.
1 16.
117.
lie.
119.
1?0.
121.
p N V C 0 M
TSTG f«i}s.
69
70
= .
S! . 151?<»25*TSIG(H)-ALOG10(SUMM)
(TSIG(M))
.NE.30) GO TO 80
CO'iT INUT
JFClC05.Nt.n GO TO 90
CO Si J=ltNOPIPS
00 ft5 X
IFrwF-ND
JS eC-Ml^1
.LT.TE.MPNV)
9o IF(PI»V1.'UT. .0000000001) PNVs.0000000001
END
DATE 021676
00009900
000100CO
00010100
00010200
00010300
00010UOO
00010500
00010600
00010700
00010800
00010900
00011000
00011100
00011200
00011300
00011UOO
00011SOO
00011600
0001 1 700
00011800
00011900
00012000
00012100
PAGE
-------
PRIORI
DATE 021876
PAGE
o
*-
1.
2.
3.
6.
7.
8.
9.
10.
1 1 .
'.2.
13.
13.
15.
16.
17.
18.
19.
pi.
23.
2s!
29.
29.
30.
31 .
32.
33.
33.
?5.
36.
37.
36.
39.
30.
3! .
32.
33.
33.
35.
46.
37.
39.
SUBROUTINE PRIORTClPARMt NPPARS)
P=IO"T D£TFRMIM£S PRIORITY MONITORING ALLOCATION AND PRINTS TABLES
« THS=900
RtSnCECSO). XMH ( MKS) • ISORC (MRS ) , RESCST (MRS) t
* PeQRF.S(TPS)fCOSTCTRS)»NUM(M«S)«IPARMCU.«10,30)tNPPARS(4f30)
DIMENSION THR ( TRS) , ISORCT(TRS)
COMMON /PRl/NOPlPS(30)fNOPARSC3b)flNL>PARC10t30).ISFUPC30)t
* I$FLOw(30)t£XPD(30)»PNVC30)tIOUTl»10UT2AtIOUT2BiIOUT3«
* N/.M(3o.l3),e,D,NUSORS,ISLlST(30)f PIPCST (4) » CONCST £ 30)
l=ISLI5T(IJ
DETERMINE RESOURCE NEED TO MONITOR SOURCE I
NPzNOPIPSC II)
RESPCff I)=PIPCSTCNP)
00 ^ J-\ »NP
K1=MFPA»SC J- II)
DC ^ K=) .Kl
IPslPi^MfJ.K, II)
RESRCt Cl)=RESRC£(I)i.CONCST(IP)
55 CONTINUE
CALCULATE MARGINAL RETURNS FOR EACH SOURCE
M=0
DO b? iM
Kl=ISFUP( I)
00 60 KslSFL.Kl
M = »+l
XHRcM)=(exPD(I)*(PKlv(I)**£K.i))»(l..PNv(I)))/RESRCECI)
60
6?
ARRAMGF MARGINAL RETURNS IN DESCENDING ORDER
CALL .OROERCX^Rt ISORC»M)
C
C
c
c
C--OPTIOM i..
NECESSARY COSTS
FOR OESIRF.O OUTPUT OPTIONS AND WRITE OUTPUT
TGTCST=0.
PO PO 1 = 1 .K-USORS
00000100
00000200
00000300
ooooo«oo
ooooosoo
00000600
00000700
00000800
00000900
00001000
00001100
00001200
00001300
ooooiuoo
00001500
00001600
00001700
00001800
00001900
00002000
00002100
00002200
00002300
00002UOO
00002500
00002oOO
00002700
00002600
00002900
OC003000
00003100
00003200
00003300
00003*400
00003SOO
00003600
00003700
00003800
00003900
00004000
000041QO
00004200
00004300
0000^400
00004500
00004600
00004700
OOOOUdOO
OOOOU900
-------
50.
•51 .
53.
Si.
55.
57.
5 8
59.
60.
M.
62 .
e>3 .
6" .
65 .
66.
67.
68 .
S9 .
70.
71 .
1-0 7?
g 73 :
T /j
75.
7c.
77.
76.
79.
eo.
M.
SP .
*3.
"i .
*5.
*>6 .
"7.
a52( i- ')./' 0' rT50» 'TOTAL RESOURCES USED ' »F1 0 .2 » / i
*TSO,'r.OST OP UNDETECTED V I OL AT IONS ' « f 1 2 . 5)
£
C - - 0 P T I 0 " ? A - -
91 IF f TOijTZ&.NE., 1 ) GO TO 104
«c;jT^f(3il05;
Ml = 0
T 0 T C = 0
OQ <5 5 ! = 1 .NUSORS
T 0 T r. rTnTC-'EXPOCI)
IF f ISFLO'-C I ) .£0.0) GO TO 93
TSsISFLO-^CT)
00 ^? *st • IS
T^p("l) = f£xpOCl)*CPNv(I)**Ci<.l))*(l..PNv(I)))/RESRCECI3
ISORCTCM1 )=I
92 C 0 '-• T T N ' ) t
93 CO Mr P.'.iE
T F f •< . c -1 . 0 ) (i 0 TO 1 0 0 0
o o nti>'~Y£ 1 1
»EQOr S( 1)=KLSKC££ IS)
CO?T(l.i = TC'|TC.(T'"<8(i)*HESRCE£IS))
11 = 1 ^LTST( IS)
T[p'MO''PsTM'
-------
OJ
o
0\
QP..
100.
101 .
102.
103.
1 04.
105.
106.
107.
108.
1 l«J.
110.
111.
112.
li*.
1 1 a.
115.
116.
1(7.
lie.
119.
125.
l?*.
l?9.
no
131.
us
133.
13"
137
138.
140.
143.
107
1001
PRIORI
If IlfTEHPMR,COST(I),REORESU)
)
104 IS=ISUBC(1)
n = TOTCST.(XMR(l)*RESRCE(IS))
TFrMjcO.1) GO TO 1002
00 110 Isc tM
TS=lSO»Cf I)
Co?T(I)=CCST(l-l)-(XHRCI)*pESRCt(ISJJ
100? Cc,":fTf.-.lE
TF muTaT«0
*"ITY i , T5a. ' SAMPLEDI iTb«» 'HETURN X100 VIOLATIONS KEOUIREDi
00 1)2 Irl.M
75=fSORCt I)
T.lrlSLISTUS)
TE^PfS=X"«f15*100.
11? kRlTFJc-n n5J I. Il.TEMPHRfCOST(I) . REURESCI)
MS FoPnAyC ' . (T«3,13,155.I3,T60,Fl3.8. 1 X» F 12.5.2X , F 10 .2) )
wPITE(*»tl8)
tiff FOR^ATcio'fT40.56C i-' j)
c
C--C°TION 3--
120 IF(IOUT3.ME.J) RETURN
TF (R)1?0f170.125
12S Ici'T^sO
wplTr. ( 6 • 126) 3
126 F0r.-K.AT c i i < .760. 'FINAL ALLoCATloNi/iOI.T60t I BUDGET i « 1X»F9.2)
nn )35 I=I.M
TF' P-oEoocs(I)) 130.135.1J5
130 LI»=1-1
GO TO 1 4()
13S C0MTIN11E
W P I T E(6 • 137}
)37 FO°KATC'0 I»69(I* ' ),/I lfl6UDGET CONSTRAINT CANNOT BE REACHED
•CHRKENT M&XIMUH SAMPLE SIZES IN EFFECT'f/l tt69( I * I ) , / I 0 I )
00 1^5 Iai
no i5o 1=1.
DATE 02187&
OOOOV900
00010000
00010100
00010200
00010300
00010400
00010500
00010600
00010700
00010800
OG010SOO
00011000
00011100
00011200
00011300
00011400
0001 1500
If 00011600
"PKI000011700
/I It 00011800
0001 1900
OC012000
00012100
00012200
00012300
00012400
00012500
00012600
00012700
00012800
00012VOO
00013000
00013100
00013200
00013300
00013^00
0001 3500
OOOlJoOO
00013700
00013800
00013900
0001UOOO
WITH 0001U100
OC01U20Q
0001^300
0001««00
0001«SOO
00014600
00014700
0001U800
OOOJU900
PACE
-------
P R 1 0 R T DATE 021676 PAGE
ISO. 150 CONTINUE 00015000
1 c. 1 . WPTTF. (*>«<5U) 00015100
1S2. 15U FOPMAJ ( ' 0 ' t T«8, "Mlto NO. MAX NO. ifT89t'COST OF ' / I '»T«8,ISAMPLESO00 I 5200
1^3. * i f T5". iS4i'-5LfSi r T68» ITJMES' t «X« "RESOURCES UNDETECTED • ? / i "«T40i 00015300
15a. *iSOllcc^'.Tue.'PEOUIHFD'tTSS.'ALLOWED!,T68.1SAMPLED Ii5X.iUSEDI»«Xf 00015400
IS5. *'VIOLATIONS'/' >?TUO»58(I.i)/i0') 00015500
1S6. 00 ifrO I = l»NijSORS 00015600
1S7. PP?S = ??S^Ct ( I ) *,\UMC I) 00015700
15H. CSTsExPOfl)+f?NV(I)**(NUM(j))) 0001580Q
IS". DrlSLISTfl) 00015900
UO. w»lTEfo,i55) II i ISFLOi«(I) iISFUP(I) tNUM(I) iRREStCSJ 00016000
161. 155FOSM1T,'' ' .Tu2t l2fT5«,I2.T61il2tT71«I2.T77.F9.2,T88tF10.5) 00016100
if.2. 160 ru^TiM.it 00016200
1*>3. ^HITE(6» t e5) REORESCLIM) ,cOST(L I") 00016500
lea. 16S PO?''AT f ' o ' .TiiOi58( l-' ) / ' 0 i .Tao, i TOTAL RESOURCES USEDl.F9.2i/i i»T400016ETP CT£C VICLATTOMS ' • iXtF'.S) 00017100
172. D01P01=1«M 00017200
17J. TF fcr>ST( n-l>) 176'176,180 00017300
174. 176 LT'sl 000l7aoo
175. GC in l<4p 00017500
176. I6o Cr^'TTvijt 00017600
177. wRTrEch»1&00) 00017700
17(i. leOO FOPKtT( '0' f37C'»')./' ' ( 'UNDETECTED-V I OLAT ION-COST CONSTRAINT CANN0001780Q
179. *OT 151 P£4O£D ^'ITh CURRENT MAXIMUM SAMPLE SIZES IN EFFECT'f/' l» 00017900
180. *«7f i*i ),/ ' 0') 00018000
1«1. LI«=H 00018100
182. GO TO 14.0 00018200
193. 181 RETURN 00018300
END ooo;8«oo
-------
X N 0 R M
DATE 021876
PAGE 1
OJ
o
00
1,
2.
3.
u.
5.
6.
7.
e.
9.
10.
1 i.
12.
13.
t i.
IS.
1 6.
17.
16.
19.
20.
T*E
F0° v.rjT." UB X.LT.-U
•OS" CiLc"LATfc-S l-F(X)
f A:
CX,
TF
K 20 TO OUT
Sf A) .LE.y.j GO TO
GT ,u. ) GO TO 10
2s TO OUT
NORMAL DISTRIBUTION FUNCTION FCX)
AMD INFERENCES FUNCTION RNORM TO FIND A VALUE
X+ AND FCX) FOR X-
10
10
r 1 ./( A*X)
y2
TO
"•= CFy/xj*( 1 ..
}UT
2 n
END
00000100
00000200
00000300
ooooouoo
00000700
00000800
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REFERENCES
1. Cohen, A.I., Y. Bar-Shalom, W. Winkler and G.P. Grimsrud.
"Quantitative Methods for Effluent Compliance Monitoring
Resource Allocation," EPA-600/5-75-015, September 1975.
2. Environmental Protection Agency, Office of Enforcement. Effluent
Limitations Guidelines for Existing Sources and Standards of
Performance for New Sources. EPA National Field Investigations
Center, Denver, Colorado, August, 1974.
3. 92nd Congress. Federal Water Pollution Control Act Amendments
of 1972. Public Law 92-500, Washington, D.C., October, 1972.
4. Environmental Protection Agency. Notice of Proposed Rulemaking;
Effluent Limitations Guidelines for Existing Sources and Standards
of Performance and Pretreatment Standards for New Sources,
Federal Register, Vol 38, No. 173, Washington, B.C., September 7,
1973.
5. Environmental Protection Agency. Proposed Rules; Effluent Limit-
ations Guidelines and Standards of Performance and Pretreatment
Standards for Electro-plating Point Source Category, Federal
Register, Vol 38, No. 193, Washington, D.C., October 5, 1973.
6. Environmental Protection Agency, Proposed Rules; Effluent Limit-
ations Guidelines and Standards of Performance and Pretreatment,
Federal Register, Vol 38, No. 196, Washington, B.C., October 11,
1973.
7. Environmental Protection Agency, Glass Manufacturing; Effluent
Limitations Guidelines, Federal Register, Vol 38, No. 200,
Washington, B.C., October 17, 1973.
8. Environmental Protection Agency, Proposed Guidelines and Standards;
Ferroalloy Manufacturing Point Source Category. Federal Register,
Vol 38, No. 201, Washington, B.C., October 18, 1973.
9. Environmental Protection Agency, Proposed Effluent Limitations
Guidelines for Existing Sources and Standards for New Sources;
Meat Products Point Source Category, Federal Register, Vol 38,
No. 207, Washington, D.C., October 29, 1973.
309
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10. Environmental Protection Agency. Proposed Rules; Effluent Limit-
ations Guidelines for Asbestos Manufacturing Point Source
Category. Federal Register, Vol 38, No. 208, Washington, B.C.,
October 30, 1973.
11. Environmental Protection Agency. Proposed Effluent Limitations
Guidelines for Existing Sources and Standards for New Sources;
Canned and Preserved Fruits and Vegetables Processing Industry
Category. Federal Register, Vol 38, No. 216, Washington, B.C.,
November 9, 1973.
12. Environmental Protection Agency. Proposed Effluent Limitations
Guidelines; Nonferrous Metals Manufacturing Point Source Category.
Federal Register, Vol 38, No. 232, Washington, D.C., November 30,
1973.
13. Environmental Protection Agency. Grain Mills, Effluent Limitations
Guidelines, Federal Register, Vol 38, No. 232, Washington, B.C.,
December 4, 1973.
14. Environmental Protection Agency, Fertilizer Industry Leather
Tanning and Finishing Industry Sugar Processing Industry; Effluent
Limitations Guidelines and New Source Performance Standards.
Federal Register, Vol 38, No. 235, Washington, B.C., Becember 7,
1973.
15. Environmental Protection Agency. Proposal Regarding Minimizing
Adverse Environmental Impact; Cooling Water Intake Structures.
Federal Register, Vol 38, No. 239, Washington, B.C., Becember 13,
1973.
16. Environmental Protection Agency. Effluent Limitation Guidelines
and New Source Standards; Petroleum Refining Point Source
Category. Federal Register, Vol 38, No. 240. Washington, B.C.,
Becember 14, 1973.
17. Environmental Protection Agency. Organic Chemicals Manufacturing
Industry; Proposed Effluent Limitations Guidelines. Federal
Register, Vol 38, No. 241, Washington, B.C., Becember 17, 1973.
18. Environmental Protection Agency, Bairy Products Processing Industry;
Proposed Effluent Limitations Guidelines. Federal Register, Vol 38,
No. 244, Washington, B.C., Becember 20, 1973.
310
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19. Environmental Protection Agency, Proposed Effluent Limitations
Guidelines and New Source Standards; Soap and Detergent Manu-
facturing Point Source Category. Federal Register, Vol 38, No. 246,
Washington, B.C., December 26, 1973.
20. Environmental Protection Agency. Effluent Limitations Guidelines;
Builders Paper and Board Manufacturing Point Source Category.
Federal Register, Vol 39, No. 9, Washington, D.C., January 14,
1974.
21. Environmental Protection Agency. NPDES Self-Monitoring Require-
ments - Program Guidance. Attachment C of Memorandum from Don
Lewis, Project Officer, Office of Research and Development, EPA,
Washington, D.C., October 23, 1973.
22. Prati, L., et al. "Assessment of Surface Water Quality by a
Single Index of Pollution," Water Reserach, (GB), Vol 5, pp. 741-
751, 1971.
23. Horton, R.K. An Index-Number System for Rating Water Quality.
Water Pollution Control Federation Journal, 37, pp. 300-306,
March, 1965.
24. McClelland, N.I., Water Quality Index Application in the Kansas
River Basin, Report No. EPA-907/9-74-001, U.S. Environmental
Protection Agency, Kansas City, February, 1974.
25. Dee, N., et al. Environmental Evaluation System for Water
Resource Planning. Battelle Columbus Labs, January 1972.
26. McKee, J., and Wolf, H., (Eds.), Water Quality Criteria, Second
Edition, State Water Resources Control Board, California,
Publication No. 3-A, 1963.
27. Water Quality Criteria, Report of the National Technical Advisory
Committee, U.S. Department of Interior, Washington, D.C., 1968.
28. Raiffa, H. and Schlaiffer, R. Applied Statistical Decision Theory,
The M.I.T. Press, Cambridge., Mass., 1961.
29. Hydroscience, Inc. Simplified Mathematical Modeling of Water
Quality. Report to EPA, Washington, D.C., March, 1971.
311
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30. Hann, Jr., R.W. , et al. Evaluation of Factors Affecting Discharge
Quality Variation. Environmental Engineering Division, Civil
Engineering Department, Texas A&M University, September, 1972.
31. Tarazi, D.S., et al. Comparison of Waste Water Sampling Techniques.
J. Water Pollution Control Federation, 42, (5), 1970.
32. Budenaers, D. and A. Cohen. Relative Efficiency of Range Versus
Standard Deviation for Large Sample Sizes. Systems Control, Inc.,
(Technical Memorandum 5112-01), Palo Alto, California, May 14,
1975.
312
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LIST OF SYMBOLS (for Section 4)
Symbol Meaning
A A constant (in 10)
C. Expected extent of undetected violations
c. Violation weighting factor per source
D Expected extent of violation, per constituent
f The standard normal probability density function
G Scaling factor
h Data discounting constant
i Source number
j Constituent number
k Weighting factor function (WFF) constant
L Lognorraal distribution
L. Maximum number of examples required at source i
£ Minimum number of examples required at source i
M Constituent mass loading rate (or concentration)
m Sample mean
N Normal distribution
n Sample size
P. Probability of non-violation per source
p . Probability of non-violation per constituent
R Total compliance monitoring cost
313
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Symbol Meaning
r. Compliance monitoring cost per source
S Effleunt standard, for a constituent
S Lower effleunt standard for pH
S Upper effluent standard for pH
s. Sampling rate
W Weighting factor
x Normalized effluent standard
y Any data value (general)
z Compliance monitoring data point
a Reliability weighting factor
A An increment of
n Confidence parameter for u
6 Receiving water concentration standard
U. Marginal return
v Confidence parameter for a
5 Sample maximum
PI Product of
p Ratio of sample maximum to sample mean
Sum of
a Estimated standard deviation
$ The standard normal cumulative distribution function
u Sample minimum
314
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing!
1. REPORT NO.
EPA-600/5-76-012
3. RECIPIENT'S ACCESSION»NO.
4. TITLE AND SUBTITLE
USER HANDBOOK FOR THE ALLOCATION OF COMPLIANCE
MONITORING RESOURCES
5. REPORT DATE
December 1976 (Issuing date)
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
G. Paul Grimsrud, E. John Finnemore, Wendy J. Winkler,
Ronnie N. Patton, Arthur I. Cohen
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Systems Control, Inc.
1801 Page Mill Road
Palo Alto, California 94304
10. PROGRAM ELEMENT NO.
1HC619
11. CONTRACT/GRANT NO.
68-01-2232
12, SPONSORING AGf N£Y NAME AND ADDRESS
Office of Air, Land and Water Use - Wash., DC
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460
13. TYPE OF REPORT AND PERIOD COVERED
JEinal
14. SPONSORING AGENCY CODE
EPA/600/16
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This report is designed as a handbook specifically oriented to environmental
planners and managers. It presents the development and successful demonstration
of hand and computerized procedures for the design of effluent compliance
monitoring budgetary resources so as to minimize environmental damage. The
original technical development of these procedures is given in a companion report,
"Quantitative Methods for Effluent Compliance Monitoring Resources Allocation,"
EPA-600/5-75-015. Both the computerized and hand calculation procedures are
demonstrated to function satisfactorily using data supplied by the State of Michigan.
This report is submitted in fulfillment of Contract Number 68-01-2232, by Systems
Control, Inc., under sponsorship of the Office of Research and Development,
Environmental Protection Agency.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATl Field/Group
Wastewater
Effluents
Water Quality
Statistical Analysis
Cost Effectiveness
Monitors
Resource 'Allocation
Program, Effluent
Standards Compliance,
Effluent Monitoring
14A
8. DISTRIBUTION STATEMENT
UNLIMITED
19. SECURJTY CLASS (ThisReport)
TTNCT.ASSTFTF.n
21. NO. OF PAGES
327
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
315
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PENALTY FOR PRIVATE USE, $300
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