May 1984
DETERMINATION
OF
EXCESSIVE/NONEXCESSIVE INFLOW RATES
Prepared By
Roy F. Weston, inc.
Designers-Consultants
Weston Way
West Chester, Pennsylvania 19380
EPA Contract No. 6 8-01-6737
Project Officer
Lam K. Lim
Municipal Technology Branch
MUNICIPAL CONSTRUCTION DIVISION
OFFICE OF WATER PROGRAM OPERATIONS
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
W.O. No. 0300-93-04
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1.0 INTRODUCTION
Roy F. Weston, Inc. has been retained by the U.S. Environmental
Protection Agency's (EPA) Municipal Technology Branch to evaluate
methods for determining excessive/nonexcessive inflow rates to
separate sanitary sewer systems.
EPA has streamlined the infiltration and inflow (I/I) program and
nas replaced detailed procedural requirements with simplified
screening procedures. The simplified procedures are anticipated
to reduce or eliminate the need for detailed Infiltration/Inflow
Analysis and Sewer System Evaluation Surveys routinely performed
in the past, and are expected to result in sewer rehabilitation
programs that remove the most serious inflow from sewer systems.
Under the simplified approach, inflow may be considered nonexces-
sive if the daily peak flow rate during a storm event does not ex-
ceed two and one-half times the average daily design flow rate.
The basis for the nonexcessive inflow rate has been questioned.
In view of this, an analysis of the rate has been undertaken.
The objectives of this wofk- assignment are to:
^[^Investigate whether specific storm frequency
/ and intensity guidance can be used or related
to inflow, conditions in a sewer systemy
^Develop a nonexcessive inflow rate based on
the storm frequency developed^ f
/£ ^Evaluate current EPA nonexcessive inflow rate
of less than "2.5 times the average design
flow during a rain stormV7(May 12, 1982 regula-
tions). ^
1-1
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2.0 LITERATURE SEARCH AND DATA COLLECTION
A selective literature search and phone contact activity were con-
ducted to review data and storm criteria selection methods rele-
vant to inflow analysis studies. Concurrently with this investi-
gation, individuals, agencies, and organizations familiar with in-
flow studies were contacted to gather input/data relative to the
current regulation value, adjustments in the value, and alterna-
tive nonexcessive inflow determination options.
Recent journals and periodicals were reviewed. Copies of approxi-
mately 3 5 related articles were compiled. (Appendix C provides
selected abstracts of these articles.) Additionally, follow-up
phone contacts were made. (Appendix D lists persons contacted. )
A single theme repeatedly expressed throughout the articles and
conversations is that each project certification is handled on a
case-by-case basis. Many states utilize additional criteria to
supplement the regulations when evaluating excessive or nonexces-
sive inflow, such as:
1) Storm frequency and intensity.
2) Frequency of bypasses/overflows.
3) Performance standards as opposed to design
standards.
As part of all phone conversations, data availability was investi-
gated. That is, requests were made for rainfall and I/I report
information available to use to verify alternative methods.
A database has been developed containing information from 45 sepa-
rate sanitary sewer systems, in which infiltration/inflow studies
have been completed. The system service areas range from 0.3 to
90 square miles. Populations served range from 350 to 200,000
people, with an average population of 19,600. For each system,
the following information was obtained:
• Service area in square miles.
• Population served.
• Average dry weather flow (influent to the
treatment plant).
2-1
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• Maximum wet weather flow (influent to the
treatment plant.
• Corrected maximum wet weather flow (total for
the system).
The corrected maximum wet weather flow is defined as the total
flow remaining after the maximum wet weather flow is reduced by
the amount of excess inflow that was determined in the I/I Study
to be cost effective to remove from each system.
Data were also collected and reviewed for several combined sewer
system studies. These data were not used in this evaluation be-
cause combined sewer systems are expected to handle a much larger
inflow component than separate sewer systems.
2-2
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3.0 EXISTING REGULATIONS
With the passage of ?ublic Law 92-500 in 1972, emphasis was
placed on sewer rehabilitation to reduce the hydraulic loads
placed on treatment plants from excessive I/I. If system flows
can be reduced through the removal of excess I/I, the lower hy-
draulic loading to collection and treatment facilities during wet
weather periods can allow the lowering of capital costs associa-
ted with oversized facilities, a reduction in operation and main-
tenance cost requirements, and a prolonged life-capacity of the
facilities.'
The initial EPA requirements for I/I analysis and sewer system
evaluation surveys required in conjunction with the preparation
of facility plans indicate the degree of emphasis placed on sewer
rehabilitation. They required a detailed step-by-step evaluation
of each existing sewer system. Implementation of these regula-
tions regarding study, operation, maintenance, and repair of
sewer systems, however, has been cumbersome in many cases.
The EPA evaluation of the success of sewer system rehabilitation
with respect to I/I indicated that correlation of the diverse
methods of pre-rehabilitation study and post-rehabilitation evalu-
ation was virtually impossible. Thus, the need for consolidated
and straightforward guidelines for use by professionals in the de-
velopment of comprehensive programs became evident.
Engineering practice in response to the I/I regulatory guidelines
has matured over the past ten years. This work assignment has at-
tempted to capitalize on the information gained by way of this
maturation process and to use this information to (1) evaluate
the guidance presently proposed for screening nonexcessive in-
flow rates in separate sewer systems (2.5 times average design
flow) and (2) develop alternative methods for screening non-exces-
sive inflow rates.
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4.0 EXISTING PRACTICE AND OPERATING EXPERIENCE
In formulating inflow guidance for separate sanitary sewer sys-
tems, existing practice and operating experience is reviewed and
analyzed. In particular, the impact of particular storm events
("design storms") must be addressed.
The practical realities of exceeding any reasonably conservative
storm event and the related issue of consistency/compliance with
the Clean Water Act statuatory requirements (i.e., no plant by-
passes) must be addressed. This can be accomplished by:
1) Preparing an update on practice and operating
experience.
2) Reviewing possible exceptions to the no by-
pass regulation.
3) Relating the possibility of by-pass to the op-
tions for EPA design storm guidance.
4.1 Existing Regulations
The existing regulation (May 12, 1982) states that a system is
not considered subject to excessive inflow if flow rates do not
exceed 2.5 times average design flow during a rain storm. This
regulation has been subject to criticism and comment such as the
following:
• It is an arbitrary number not relative to ac-
tual conditions.
• It does not recognize the design and operation-
al differences between small plants and large
plants.
• It does not recognize the possible impact of
storm frequency and intensity.
4.2 Alternative Methods/Approaches
WESTON was unable to directly identify supporting technical data
for selection of the "x2.5n rate used in the regulation through
literature search data collection activities. Consequently,
4-1
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several possible alternative approaches were developed to identi-
fy excessive inflow. WESTON analyzed and attempted to verify
these approaches, and utimately selected the approach which
appeared to have the greatest universal application. WESTON com-
pared the results of this approach to selection of nonexcessive
inflow rates determined using the existing regulations.
The following discussions present the pros and cons, cost-effec-
tiveness implications, and basis of each alternative evaluated.
4.2.1 Alternative 1 - Relate Peak Inflow to Rainfall
Intensity and Duration
Nogaj and Hollenbach (Reference 1, Appendix C) illustrated the
fact that projections for flow reduction through rehabilitation
programs developed from Sewer System Evaluation Surveys (SSES)
have been limited by the inability to accurately measure peak in-
flow in surcharged sanitary sewers. They developed a method to
correlate flow and peak rainfall intensity for durations of 15
minutes to 24 hours. Their method is based on the premise that a
separate sanitary sewer responds similarly to a storm sewer dur-
ing intense storm events. Consequently, flow rates in the system
can be analyzed using a modification of the Rational Method for
computing runoff. Inflow, if equated to runoff, would be a func-
tion of the runoff coefficient, the average rainfall intensity,
and the drainage area.
The technique provides a method for estimating peak system flows
during storm events, if systems are subject to surcharging. If
this technique could be generalized, criteria might be selected
to allow its use as a screening method for excessive or nonexces-
sive inflow. To utilize this technique, measured flow rates are
correlated with rainfall intensity. These data are then used to
develop system coefficients to use in the modified rational formu-
la.
The data required to use this technique were not available in the
SSES Studies collected for this work assignment. Also, extensive
flow and rainfall monitoring efforts would be required to gather
data required to apply this technique to a new study. For this
reason, its value as an initial screening method for excessive or
nonexcessive I/I is limited. The principle value of this tech-
nique is in estimating actual peak flows in a sewer system after
it has been determined the system is subject to surcharging and a
sewer system evaluation survey is necessary.
4-2
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4.2.2 Alternative 2 - Develop a Method of Wet Weather Flow
Management
The East Bay Municipal Utility District (EBMUD) (see Reference 2,
Appendix C) is responsible for the interception and treatment of
wastewater flows from a tributary area along the eastern shore of
San Francisco Bay. During periods of wet weather, portions of
the rainfall enter the sanitary wastewater collection system as
I/I. When this occurs, the additional flow exceeds the capacity
of existing conveyance and treatment facilities to cause over-
flows to San Francisco Bay.
The District was required to develop a program to reduce or elim-
inate its wet weather overflows. The District was also required
to develop alternative projects that coincided with the "mainten-
ance level" concept of treatment. The maintenance level concept
considers the beneficial uses of the water body that will be re-
ceiving the waste discharge and is based on frequency and degree
of impairment of the beneficial uses of the receiving body of
water. This maintenance level concept recognizes the importance
of the receiving water quality, and thus differs from the more
traditional "end-of-pipe" performance standards.
This concept was reviewed to assess its application as a screen-
ing method for excessive or nonexcessive inflow. It was determin-
ed that the concept is not applicable^aost situations, because
its application is very site specific andrrequires extensive rain-
fall, system flow, and receiving water quality data to properly
assess the impact of overflows or treated effluent discharges on
the receiving water body. Also, the concept of managing over-
flows is more appropriate to combined sewer systems than to sepa-
rate sewer systems.
4.2.3 Alternative 3 - Modify Combined Sewer Overflow
Management Practice to Set a Standard for Control of
Inflow in a Separate Sewer System
The Onondaga County, New York Sewer System includes significant
areas of combined sewers. Based on preliminary estimates that a
total of several billion gallons of overflow passed through the
outlets in an average year, and based on apparent storm related
water quality problems, a Facilities Planning Study was under-
taken (See Reference 3, Appendix C). The recommended plan in-
cludes a long-range comprehensive abatement program and also pro-
vides for short-term, low-investment abatement projects that can
be readily accomplished to realize immediate improvements in
water quality.
4-3
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The methodology developed in this analysis was reviewed to assess
its application to developing a screening method, for excessive or
nonexcessive inflow. In the Onondaga County Study, an array of
abatement alternatives were developed through analysis of estab-
lished water quality criteria for Onondaga Lake and a review of
current CSO abatement technology. Screening of alternatives in-
volved analysis of interrelationships between dry weather flow,
storm patterns, runoff rates, and system constraints. The analy-
sis was facilitated by use of the SWMM and simplified SWMM Mo-
dels.
One conclusion reached in the computer simulation of the existing
sewer system was that various system modifications or improve-
ments would have a significant effect on the reduction of CSO dis-
charges. The concept of Best Management Practices (BMP) policy
offered an immediate means of optimizing the existing systems con-
veyance capacity, while aiding in the development of a long-term,
structurally intensive solution.
Cost estimates were prepared and the associated water quality im-
pacts were developed for several design storm conditions to estab-
lish a cost-effective design level of CSO abatement. Based on
this analysis, control of the "90% storm", defined as the storm
that is exceeded in total rainfall approximately 10% of the time,
was determined to provide optimum benefits to cost ratios.
To extend this concept to screening a separate sewer system for
excessive inflow, a standard storm must be selected. This stan-
dard storm must then be evaluated to determine its impact on sys-
tem inflow rates and possible effects of system overflows on re-
ceiving water bodies.
As in' Alternatives 1 and 2, the data required to extend this com-
bined sewer overflow evaluation technique is not readily avail-
aole in existing SSES Reports.
4.2.4 Alternative 4 - Analyze Inflow in Existing Separate
Sewer Systems to Develop Excessive or Nonexcessive
Inflow Relationships
As part of this work assignment, WESTON established a database
which includes flow, service area size, and population from 53 in-
dividual SSES studies in several regions of the United States.
The flow data collected includes average dry weather flow, maxi-
mum wet weather flow, and corrected wet weather flow (see Section
2).
4-4
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Inspection of the flow data indicated that inflow actually mea-
sured in separate sewer systems is a small fraction, less than
one hundredth, of the total quantity of rainfall actually falling
on the service area. This fact suggests that inflow rates in a
separate sewer system are not directly related to the actual rain-
fall intensity falling on a service area. Any precipitation or
runoff event heavy enough to cause ponding and runoff in the ser-
vice area can result in inflow to a separate sewer system.
Further inspection of the database indicated that inflow rates
may be proportional to both service area size and population.
WESTON concluded that if a statistical significant correlation
could be found between corrected maximunr flow and either service
area size or population, then WESTON could probably define the re-
lationship between these parameters. This relationship could
then be used as a screening mechanism to compare maximum flow
rates from an existing system with the standard "nonexcessive"
flow rates to determine if further study and analyses are re-
quired in the existing system.
WESTON has been able to demonstrate the statistical significance
of these relationships. The analysis and development of nonexces-
sive inflow rates is presented in Section 5.
4-5
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5.0 DATA EVALUATION
As noted, data from fifty-three (53) previously conducted SSES
studies representing seven EPA regions of the United States were
obtained. The information gathered consisted of the following
items:
• Population.
• Area.
Average dry weather flow.
• Maximum wet weather ,flow.
• Corrected flow.
The data listed above was then used to calculate the following
variables:
• Population density.
• Average dry weather flow rate per unit area.
• Maximum wet weather flow rate per unit.area.
• Corrected flow rate per unit area.
Table A-l in Appendix A presents the data for all variables
above.
An analysis of the data resulted in the descriptive statistics
presented in Table A-2, Appendix A. This table presents such
basic statistics as mean, variance, and standard deviation for
the following variables:
Corrected flow is defined as the maximum wet weather
flow minus the amount of inflow determined to be cost
effective to remove as per the I/I Analysis.
Rates were determined by dividing the respective flows
in million gallons per day by the area served in square
miles.
5-1
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• Population.
• Area.
• Corrected flow.
• Corrected flow rate
Additionally, scatter plots for each of these variables are pre-
sented in Appendix A, Figures A-l through A-4. A scatter plot is
produced by plotting each variable as a point versus observation
number. The result is an indication of how a variable is distri-
buted.
The next phase of the data evaluation involved a regression analy-
sis. Variables were compared two at a time utilizing eight (8)
mathematical models as follows:
The purpose of comparing the selected variables two at a time by
means of a regression analysis is to find and demonstrate a sta-
tistically valid relationship between the respective variables.
It was expected that one of the eight (8) mathematical models
would represent a "best fit" regression equation when fitted to
and compared with the database. The statistical programs used to
apply these models are described in Appendix B. The following
sections discuss comparisons of variables two at a time.
5.1 Population vs. Area
^.-.comparison table representing the eight (8) mathematical models
is presented in Table A-3, Appendix A. The comparison table pro-
vides the intercept (A), the slope (B), the standard error of re-
gression, and the maximum absolute error. Model #1 (Y = A + BX)
is the preferred model, because it has the least standard error
of regression. Figure A-5f Appendix A, represents a plot of the
selected model. When plotted, the slope (B) is a measure of the
dependency of one variable upon the other. As the slope (B) ap-
proaches zero, these Y-variables do not depend on X.
Model No
Equation
1
2
3
4
5
6
7
8
Y = A + BX
Y a A CEXP(BX)]
Y ¦ 1/(A + BX)
Y - A + B/X
Y a A + B (LOGX)
Y a AX
Y a X/(A + BX)
Y • BX
5-2
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Another measure of the strength of the relationship is the cor-
relation coefficient. With linear regressions, it is customary
to compute the Pearson Product Moment correlation coefficient de-
noted by r. The validity of the relationship is represented by
r . As r2 approaches 1.0 or -1.0, the relationship approa-
ches complete agreement or disagreement as well as strong depen-
dency between variables.
When plotting these data in terms of population versus area, r2
= 0.83. This indicates a strong relationship between the vari-
ables. The mean density is 2,640 people per square mile for the
grouped data.
5.2 Population vs. Corrected Flow
The comparison table representing the use of the eight (8) mathe-
matical models with regard to a comparison of population and cor-
rected flow is presented in Table A-4, Appendix A. As was the
case with population vs. area, this regression results in the se-
lection of Model #1 (Y *» A + BX) as that with the least standard
error of regression. For this relationship,' r = 0.87 which in-
dicates a very strong relationship between population and the cor-
rected flow. The relationship is projected to be 275 gpcd.
Note; 27 5 gpcd is 2.3 times the 120 gpcd set in the current
regulations as the flow rate representing average flow
plus nonexcessive infiltration. This is of interest in
remembering that the current regulations designate 2.5
times the average design flow as the cutoff for non-
excessive inflow.
5.3 Population and Corrected Flow Rate
As mentioned previously, it was decided that this data evalu-
ation would include a comparison of populations (and area) with a
rate similar to the inches per hour commonly used in hydrology.
Therefore, a corrected flow rate (mgd/mi ) was calculated util-
izing corrected flow and area served. Table A-5, Appendix A, re-
presents the comparison table for population vs. corrected flow
rate.
Models #1, 5, and 6 have the lowest standard errors of regres-
sion. The determination of which is best could be facilitated by
a residuals analysis. However, the correlation coefficient
(r ) is 0.0 4 using Model #1. This indicates a very weak rela-
tionship with regard to these variables. Therefore, the need to
determine the best model was eliminated. Figure A-7, Appendix A,
represents a plot of this model.
5-3
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5.4 Area vs. Corrected Flow
The regression analysis of area vs. corrected flow results in
Table A-6 , Appendix A. Model #1 (Y = A + BX) again provided the
least standard error of regression. Figure A-8, Appendix A, re-
presents a plot of Model #1. The correlation coefficient (r )
is 0.7 8 which represents a strong relationship between area and
corrected flow. The slope indicates a relationship of 0.613
mgd/mi .
5.5 Area vs. Corrected Flow Rate
For reasons explained previously (see Population vs. Corrected
Flow Rate), a comparison of area and corrected flow rate was in-
vestigated. Model #1 (Y = A + BX) was again the preferred model
in terms of standard error of regression. However, as was the
case with the comparison of population and corrected flow rate,
the correlation coefficient was very low. At r = 0.003, there
is essentially a totally independent relationship between area
and corrected flow rate.
5-4
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6 .0 SUMMARY AND CONCLUSION^ 'c-'
The database used in fernese studies, developed from 53 SSES Stu-
dies representing co/amunities in seven EPA regions, was suffi-
cient to develop natural guidance regarding excessive inflow
removal. The population and service area information reported in
each study is basic data obtained from generally available infor-
mation (census reports and area maps). The corrected flow infor-
mation, however, is more subjective. These values are based on a
combination of flow data interpretation and cost-effectiveness
evaluation. In this study, these parameters (developed for all
of the studies included in the database) were evaluated to deter-
mine if a statistical relationship exists between the data
points.
From the comparison of service area size with population, WESTON
concluded that 8 3 percent: of the variation in service area size
is due to the linear relationship between population and service
area size. The corresponding values obtained when comparing cor-
rected flow rate with population and service area size are 87 per-
cent and 76 percent, respectively. These correlation coeffi-
cients, when determined from data sets with more than forty de-
grees of freedom (data points), indicate a confidence level
greater than 99.9 percent.
If corrected flow is plotted against population, the resulting re-
gression line has a slope of 2 75 gallons per capita, per day.
This rate can be used to predict a corrected maximum flow for a
study area, when the population is known. Similarly, comparison
of area against corrected flow yields a corrected flow rate of
0.613 M6D per square mile.
The corrected flow rate of 0.613 mgd per square mile is equiva-
lent to the flow volume resulting from 0.035 inches per day over
a square mile. This is a small fraction of the total rainfall
that would occur over a service area during a significant rain-
fall event. He therefore conclude that any precipitation or run-
off event of sufficient intensity to cause ponding and runoff in
the service area can produce maximum nonexcessive inflow rates in
a separate sewer system.
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Either 275 gallons per capita per day or 0.613 MGD per square
mile can be used in screening data from existing separate sewer
systems for excessive or nonexcessive inflow rates. The two
figures will not provide identical results. WESTON recommends
use of 27 5 gallons per capita per day, because the comparison of
corrected flow rates with service area populations yielded a high-
er linear correlation coefficient than comparison of corrected
flow rates with area.
The flow rates used in this study are average daily flows, not
instantaneous flow rates. Average daily flows should be com-
pared to the proposed nonexcessive inflow rates when screening
data from existing sewer systems. If the average daily flow dur-
ing a rainstorm is less than 275 gallons per capita times the ser-
vice area population, it can be assumed that the system is not
subject to excessive inflow.
The factor of 275 gallons per capita represents a peaking factor
of approximately 2.3 times average daily flow if we assume the
following:
1. Average daily flow is assumed to be 120 gal-
lons per capita per day and includes waste-
water flow plus nonexcessive infiltration.
2. Maximum inflow conditions occur during the
same season as maximum infiltration condi-
tions.
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APPENDIX A
STATISTICAL ANALYSIS
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TABLE A-1
USEPA INFLOW GUIDANCE/REGULATIONS
1
2
3
A
5
o
7
8
9
10
Variable labels
POPULATION*1 0f 4
AREA, 111 *fl I
DENSITY(PEOPLE/ni*ni
AVERAGE DRY WEATHER FLOW,MCD
riAxinun wet weather flow.mgd
CORRECTED FLOW,MCD
CORRECTED INFLOW,riGD
AVE. DRY WEATHER RATE, HGD/niTfll
HAX. WET WEATHER RATE,MGD/niI
CORRECTED FLOW RATE, riCD/MI*MI
Observe t i on
n 1 ,
« A
(1-3)
0.752
1 .8
(4-6)
1 .21
1 .8
(7-9)
0.23
0.67
(10)
0.77
Observat i on
• 2.
(1-3)
0.035
1 . 1
(4-6)
0.07
0.5
(7-9)
0.09
0.06
(10) :
0.32
Observe! i on
*3.
(1-3)
0.894
0.8
(4-6)
0.66
0.88
(7-9)
0. 15
0.83
(10)
0.76
Observe;i on
#4 :
(1-3)
0.546
0.6
(4-6)
0.48
0.63
(7-9)
0. 13
0.8
(10)
0.67
Observe:i on
«5:
(1-3) :
0.364
0.5
(4-6)
0.18
0.27
(7-9)
0. 1
0.36
(10)
0.2
4180
1 .4
1
320
0.35
0.45
11 180
0.61
1 . 1
9100
0.4
1 .05
7280
0.1
0.54
-1-
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TABLE A-l
(Continued)
Observa t i on a 6 :
(1-3) 0.77S
(4-6) 0.5
(7-9) 0.29
(10) 0.44
I .6
1 .2!
0.31
4850
0.71
0.76
Observat i on a 7 •.
(1-3) 0.33
(4-6) 0.23
(7-9) , 0.06
(10) . 0.21
Observat ion #8-.
(1-3) 0.31
(4-6) 0.27
(7-9) 0.12
(10) 1.2
0.33
0.21
0.3
0.57
0.9
3000
0.23
0.3
10330
0.36
1 .9
Observer i on «9:
(1-3) 1.155
(4-6) 1.32
(7-9) 0.19
(10) 0.57
Observat i on « 1 0 •.
(1-3) 1.3
(4-6) 1.02
(7-9) 2.28
(10) 0.8
Observar i on all:
(1-3) 5.5124
f 4-6) 14.14
(7-9) 5.47
(10) 6.09
Observer ion a 12•.
(1-3) 5.5411
(4-6) 6.87
(7-9) 2.51
(10) 3.4
2.2
1 .59
0.6
2.8
6.24
0.36
3.3
29.7
4.28
2.7
13.57
2.54
4800
1 .25
0 .72
4640
2.24
2.23
16700
20. 1
9
20520
9.17
5.03
ObservaT ion «13:
(1-3) i -0.29
(4-6) 0.39
(7-9) » 0.38
(10) : 0.46
2.3
1 .74
0. 17
1260
1 .05
0.76
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TABLE A-l
(Continued)
ObservoT i on
#14:
(1-3)
1 .83
18.5
990
(4-6)
2.5
5.7
3.4
(7-9)
1 .31
0.14
0.31
(10)
0.18
ObservoT i on
# 1 5!
(1-3)
0.43
0.7
61 40
(4-6)
0.3
1.5
0.6
(7-9)
0.51
0.43
2.14
(10)
0.86
Observo t i on
#16;
(1-3) :
0.72
1 .7
4240
(4-6)
0.7
2.6
1 . 3
(7-9)
0.74
0.41
1 .53
(10)
0.76
Observat i on
#17:
(1-3)
0.7
1 .6
4375
(4-6)
0.5
0.9
0.6
(7-9)
0.17
0.31
0.56
(10)
0.38
Observe"? i on
#18
(1-3) :
0.298
0.5
5960
(4-6)
0.4
1 .2
0.7
(7-9)
0.29
0.8
2.4
(10) >
1 .4
Observation #19-.
M-3) 0.46 0.8 5750
C4-6) 0.4 1,5 0.9
C7-9) 0.34 0.5 1.88
(10) 1.13
ObservoTion «20:
(1-3) 1.4 2 7000
14-6) 1.2 5 2.1
(7-9) 1.65 0.6 2.5
(10) 1.05
ObservoT i on #21:
fl-3) 0.38 4.7 810
f4-6) 0.66 • 0.88 0.73
(7-9) 0.09 0.14 0 19
(10) 0.16
-3-
-------
TABLE A-l
(Continued)
Observaii on
«22:
(1-3)
4.63
6.6
7015
(4-61
5.24
24 .77
14.51
(7-9)
5-85
0.79
3.75
(101 :
2.2
ObservaT i on
*23:
(1-3)
0.4
2
2000
(4-6)
0.5
1 .3
0 . 74
(7-9)
0.32
0.25
0.65
(10) :
0.37
ObservaT i on
»24 :
(1-3) :
0.375
2.3
1630
(4-6)
0.76
1 .9
0 ..85
(7-9)
0.6
0.33
0.83
(10)
0.37
ObservaT i on
• 25
U-3) :
'0.16
1 .5
1070
(•4-6)
0.16
0.41
0.24
(7-9)
0.1
0.11
0.27
(10)
0.16
ObservaT i on
*26
(1-3)
' 1 .45
1 .7
8530
(4-6)
1 .85
4
2.25
(7-9) :
1
1 .09
2.35
(10)
1 .32
ObservaT i on
«27
(1-3) :
0.51
2
2550
(4-6)
1 .01
1 .9
1 .34
(7-9)
0.32
0.51
0.95
(10) :
0.67
ObservaT i on
"28
(1-3)
' 1 .28
5.8
2220
(4-6)
2.3
7.2
4.4
(7-9)
1 .6
0.4
1 .24
(10) :
0.76
ObservaT i on
«29
i
(1-3)
2
4.7
4255
(4-6)
2.5
5.7
3.9
(7-9)
1 .03
0.53
1 .21
(10)" !
0.83
4
-------
TABLE A-l
(Continued)
Observeri on
s30
:
CI-3)
0.27
1 .9
1420
(4-6)
0.27
0.87
0 .45
(.7-9)
0.24
0.14
0.46
rial
0.24
Observof i on
«31
(1-3) s
*0. 75
2.2
34 10
(4-6)
0.79
2.01
1 .33
(7-9)
0.39
0.36
0.QI
(10)
0.6
Observat ion
* 32
(1-3)
*0.45
3
1500
(4-6)
0.58
0.74
0.67
(7-9)
0 .04
0.19
0 .25
(10)
0.22
Otoservat ion
«33
fl-3)
2.7
10.9
2480
(4-6)
7.28
12.5
9.61
(7-9)
1 .66
0.67
1 . 15
(10)
0.88
Observati on
«34
(1-3) :
0.88
2.9
3030
(4-6)
2.3
9.52
7.03
(7-9)
1 .42
0.79
3.28
(10) :
2.42
Observat ion
#35
(1-3)
*0.22
1 .3
1690
(4-6)
0.33
2.52
1 .72
(7-9) ,
0.46
0.25
1 .94
(10) .
1 .32
Observat i on
«36
(1-3)
0.11
0.4
2750
(4-6) .
0. 1
0.83
0 .56
(.7-9)
0.15
0.25
2.08
f'10) :
1 .4
Observat ion
837:
fl-3)
0.912
3. 1
2940
(4-6)
0.57
0.75
0.63
(7-9)
0.07
0.18
0.24
(10)
0.2
-------
TABLE A-l
(Continued)
Observa t i on
#38
(1-3)
0.2275
0.7
3250
(4-6)
0.3
0.33
0.33
(7-91
0
0.43
0 .47
(10)
0.47
Observat i on
#39
(1-3)
0.2
0.5
4000
(4-6)
0.21
0.38
0.23
(7-9)
0.09
0.42
0.76
(10)
0.46
Observaii on
#40
(1-3)
*0.17
4
4250
(4-6 3
0.2
0.32
0.29
(7-9)
0.02
0.5
0.8
(10)
0.73
Observat i on
#41
(1-3) :
*2.72
1 .9
14315
(4-6)
5.84
6.74
5.93
(7-9)
0.46
3.07
3.55
(10)
3.12
Observcii on
#42
(.1.-3)
8.2437
1 1 .7
7045
C'4-6)
16.02
23.72
19.82
(-7-9) .
2.22
1 .37
2.03
(10)
1 .69
Observat i on
#43 i
f 1 -31
20
90
2220
(4-6)
20.91
76.83
63. 12
(7-9)
7.81
0.23
0.85
(10)
0.7
ObservaT ion
#44 :
(1-3)
10.34
40
2585
(4-6)
8.5
17.55
12.52
(7-9)
2.87
0.21
0.44
(10)"
0.31
Observat i on
#451
(1-3)
5.2
27
1925
(4-6)
5.8
17.96
9.88
(7-9)
4.61
0.21
0.67
f 10)
0.37
-6-
-------
TABLE A-l
(Continued)
Observaii on »46:
(1-3) 0.146
(4-6) 0.15
(7-9) , 0.02
(10) : 1.11
0.55
0.67
0.27
2654
0.62
1 .22
Observation *»47
(1-3)
(4-6)
(7-9)
(10)
Observcn
(1-31
(4-6)
(7-9)
(10)
Observat
(1-3)
(4-6)
(7-9)
(10)
on »48:
on »49
1 .498
1 .61
0.21
1 .28
0.663
0.9
0.11
2.41
2.703
3.03
0.37
1 .3
4. 15
5.83
0.39
0.75
2.05
1 .2
6.95
9.9
0.44
3610
5.33
1 .4
88-40
1 .81
2.73
3890
9.05
1 .42
Observation «50»
(1-3) « 1.554
(4-6) 3.03
(7-9) « 0.92
(10) ; 1.88
3.7
9.09
0.82
4200
6.96
2.46
ObserverI on *51>
C1-31 : 0.378
(4-61 , 0.52
17-9) : 0.61
(10) t 2.01
1 .4
4.24
0.37
2700
2.81
3.03
ObservoTion *52:
(1-3) . 1.705
f4-6) . 1.Q3
£7-9) 3.33
(10) i 1.84
Observa tI on « 531
d-3) , 0.169
(4-6) , 0.17
(7-9) , 0.03
M0) , 1,14
8.95
24.2
-0.22
0.65
0.82
0.26
1905
16.5
2.7
2600
0.74
1 .26
-7-
-------
TABLE A-2
USEPA INFLOW GUIDANCE/REGULATIONS
DESCRIPTIVE STATISTICS
Variable t. POPULATION*10t4
TOTAL NUMBER OF OBSERVATIONS 53
NUMBER OF OBSERVATIONS WITH MISSING VALUES 0
NUMBER OF OBSERVATIONS WITH VALID VALUES 53
MEAN 1.831
VARIANCE 10.780
STANDARD DEVIATION 3.283
STANDARD ERROR OF THE MEAN 0.451
COEFFICIENT OF VARIATION. X 179.330
SKEWNESS 3.808
KURTOSIS 19.669
MINIMUM VALUE 0.035
MAXIMUM VALUE 20.000
RANGE 19.965
MEDIAN 0.720
-1-
-------
TABLE A-2
(Continued)
USEPA INFLOW GUIDANCE/REGULATIONS
DESCRIPTIVE STATISTICS
Variable 2. AREA,MI*111
TOTAL NUMBER OF OBSERVATIONS
NUMBER OF OBSERVATIONS WITH MISSING VALUES
NUMBER OF OBSERVATIONS WITH VALID VALUES
53
0
53
MEAN
5.789
VARIANCE
STANDARD DEVIATION
STANDARD ERROR OF THE MEAN
185.915
13.635
1 .873
COEFFICIENT OF VARIATION, X
235.547
SKEWNESS
KURTOSIS
4 .947
29.434
MINIMUM VALUE
MAXIMUM VALUE
RANGE
0.300
90.000
89.700
MEDIAN
2.000
-2-
-------
TABLE A-2
(Continued)
USEPA INFLOW GUIDANCE/REGULATIONS
OESCRIPTIVE STATISTICS
Variable 6. CORRECTED FLOW,MGD
TOTAL NUMBER OF OBSERVATIONS
NUMBER OF OBSERVATIONS WITH MISSING VALUES
NUMBER OF OBSERVATIONS WITH VALID VALUES
53
0
53
MEAN
4.801
VARIANCE
STANDARD DEVIATION
STANDARD ERROR OF THE MEAN
92.472
9.616
I .321
COEFFICIENT OF VARIATION, X
200.283
SKEWNESS
MJRTOSIS
4.507
26.854
MINIMUM VALUE
MAXIMUM VALUE
RANGE
0. 100
63.120
63.020
MEDIAN
1 .300
-------
TABLE A-2
(Continued)
USEPA INFLOW COIDANCE/REGULATIONS
DESCRIPTIVE STATISTICS
Vorloble 10. CORRECTED FLOW RATE.MGO/M1*111
TOTAL NUMBER OF OBSERVATIONS
NUMBER OF OBSERVATIONS WITH MISSING VALUES
NUMBER OF OBSERVATIONS WITH VALID VALUES
53
0
53
MEAN
1 .068
VARIANCE
STANDARD DEVIATION
STANDARD ERROR OF THE MEAN
1 .059
1 .029
0.1-41
COEFFICIENT OF VARIATION, X
96.358
SKEVNESS
KURTOSIS
2.630
12.255
MINIMUM VALUE
MAXIMUM VALUE
RANGE
0. 160
6.000
5.930
MEDIAN
0.760
-4-
-------
TABLE A-3
USEPA INFLOW GUIDANCE/RECULAT IONS
COMPARISON TABLE
STD ERROR OF MAXIMUM
MODEL
A
B
REGRESSION
ABSlERROR 3
®Y=A+B*X
-I.133
3.701
5.606
18.334
Y=A#EXP(B*X)
1 .419
0.262
25.188
176.260
Ys1/(A+B¥X)
0.886
-0.083
13.735
91.208
YsA+B/X
7.423
-0.630
13.512
82.600
Y=A*B*LOGIX)
7.370
6.331
11.138
63.665
Y=A#XTB
2.739
0.714
10.699
66.734
Y=X/CA+B*X)
0.056
0.590
14.395
88.312
Y=B*X
0.000
3.632
5.784
18.239
6Model currently selected
-------
'j. ttoiiE ft~ i
POPULATION vs. CORRECTED FLOW
USEPA INFLOW CUIDANCE/REGULATIONS
COMPARISON TABLE
STD ERROR OF MAX IMUM
MODEL
A
B
REGRESSION
ABStERROR J
6Y=A+B*X
-0.200
2.731
3.504
15.524
Y=A*EXP(B*X)
0.033
0.310
55.303
393.678
Y=l/(A+B*XI
1 .635
-0.171
10.779
63.682
Y=A+B/X
6.292
-0.574
9.407
56.857
Y=A+B*LOG(XO
6. 105
5.217
7.057
41.388
Y=A*XtB
2. 100
0.977
4.475
23.920
Y=X/CA+B*X)
0. Ml
0.958
10.450
62.084
Y=B*X
0.000
2.705
3.508
15.452
©Model currently selected
-------
TABLE A-5
POPULATION VS. CORRECTED FLOW RATE
USEPA INFLOW GUIDANCE/REGULATIONS
COMPARISON TABLE
STO ERROR OF MAXIMUM
MODEL
A
B
REGRESSION
ABSt ERROR 3
§Y=A-»B*X
0.056
0.061
1 .010
4 . 797
Y=A*EXP(B*X)
0.695
0.041
1 .077
5.219
Y=1/(A+B*X)
2.003
-0.066
1 . 168
5.480
Y=A+B/X
1 . 197
-"0.050
1 .018
4 .902
Y-A+B*LOG CXI
1 . 142
0.298
0.967
4 .439
Y=A*XtB
0.792
0.220
1 .023
4 .938
Y=X/(A+B*X)
0.066
1.710
1 . 160
5.509
Y=B*X
0.000
0. 187
1 .326
5.060
©Model currently selected
-------
imBLE h-6
AREA vs. CORRECTED FLOW
USEPA INFLOW GUIDANCE/REGULATIONS
COMPARISON TABLE
STD ERROR OF MAX I MUM
MODEL
A
B
REGRESSION
ABSt ERROR]
8Y=A+B*X
1 .237
0.616
4.735
16.831
Y=A*EXPCB*X)
1 . 173
0.058
23.386
162.926
Y=1/CA+B*X)
1 .490
-0.030
10.663
63.930
Y=A+B/X
8.451
-4.968
9.029
54.725
Y=A+B*LOG(X)
0.220
5.524
7. 120
38.044
Y=A*XtB
0.758
0.935
4.950
17.787
Y=X/tA+B*X)
1 .281
0.382
10.088
60.597
Y=B*X
0.000
0.649
4.874
17.959
SModel currently selected
-------
TABLE A-7
AREA vs. CORRECTED FLOW RATE
USEPA INFLOW GUIDANCE/REGULATIONS
COMPARISON TABLE
STD ERROR OF MAXIMUM
MODEL
A
B
REGRESSION
ABSCERROR]
QY=A+B*X
1.110
-0.007
1 .034
5.004
Y=A*EXP(B*X)
0.775
-0.006
1 .084
5.330
Y=1/(A+B3X)
1 .847
0.006
1 . 172
5.554
Y=A+B/X
1 . 123
-0.075
1 .037
4.990
Y=A+B*LOC(X)
1 .070
-0.003
1 .039
5.023
Y=A*XtB
0.780
-0.048
1 .089
5.354
Y=X/(A+B*X)
-0.239
2.057
1 . 175
5.586
Y=B*X
0.000
0.022
1 .467
6.016
©Model current]/ selected
-------
figure a-i
USEPA INFLOW GUIDANCE/REGULATIONS
SCATTER PLOT
*
**
~ * *
* * * * * *
***** ** *,** «
** ft . * * **.* *** * * * tx **» * ¦* *
9 10 20 30 40 50 80
OBSERVATION NUMBER
-------
FIGURE A-2
A
R
E
A
M
I
#
M
I
00
80
70
60
50
40
30
20
10
USEPA INFLOW GUIDANCE/REGULATIONS
SCATTER PLOT
0
0
»»«««»«,<***» «**«** ***** ?** *******
*
* *
* * .* *
10
20 30
OBSERVATION NUMBER
40
50
60
-------
FIGURE A~3
70
USEPA INFLOW GUIDANCE/REGULATIONS
SCATTER PLOT
60
C
0
R
R
E
C
T
E
D
50
40
F
L
0
U
M
G
0
30
20
10
0L
0
* *****!* ***
**
** *** *
*«» "*»***
10
20 30
OBSERVATION NUMBER
40
50
60
-------
FIGURE A-4
USEPA INFLOW GUIDANCE/REGULATIONS
SCATTER PLOT
*
* *
*
* * ** * * *
** * *
* ** * ** ***** * *
* * * * ** * ** **
* * * * ***** *
i i i —i 1
9 10 20 30 40 50 60
OBSERVATION NUMBER
-------
FIGURE A-5
USEPA INFLOW GUIDANCE/REGULATIONS
POPULATION*I0t4
-------
FIGURE A-6
r
USEPA INFLOW GUIDANCE/PECULATIONS
MODEL . Y = A+B*X
POPUAHOmIi
*
*
# * m
* **
J
0.5
I J .5
POPULATION*10T4
2,5
-------
FIGURE A-7
3.^r
USEPA INFLOW GUIDANCE/REGULATIONS
ttODEL . Y = A+B*X
C
0
R
R
E
C
T
E
D
F
L
0
U
R
A
T
E
II
G
D
/
M
]
*
M
1
2.5
1.5
0.5
* *
*
**
**
*** *
* *
**
*
0L
0
_L
0.5
1 1 .5
POPULATION*10t4
f0PU.AVI0M«llt4
25
-------
c
0
R
ft
E
C
T
E
D
F
L
0
V
$
n
c
o
18
16
14
12
10
8
0
FIGURE A-8
USEPA INFLOW GUIDANCE/REGULATIONS
MODEL . Y = A+B*X
*
0
10
AREA
15
20
-------
FIGURE A-9
3.5
USEPA INFLOW GUIDANCE/REGULATIONS
MODEL i Y = A+B*X
C
0
R
R
E
C
T
E
D
F
L
0
V
R
A
T
E
$
n
c
D
/
M
1
*
M
1
2.5
I .5
49 ••
AtfA.nitni
0.5
0
0
10
AREA.MI*M
15
20
-------
APPENDIX B
STATISTICAL PROGRAMS
-------
Section 4
THE PROGRAMS
OVERVIEW
This section describes the programs listed on the Tests And Distributions menu (except
for Program 19 DATA MANAGEMENT UTILITIES, described in Section 5).
PLOT 98 STATISTICS:
DATA ENTRY
DATA FROM KEYBOARD 1
DATA FROM DISC 2
DESCRIPTIVE STATISTICS 3
EXPLORATORY PLOTTING
HISTOGRAMS 4
STEH-AND-LEAF DISPLAY S
BOX-AND-UNISKER PLOT 6
SCATTER PLOT 7
PROBABILITY PLOTS AMD
DISTRIBUTION ANALYSIS 8
ONE SAMPLE t-TEST AND
CONFIDENCE INTERVALS 9
**
TESTS AND DISTRIBUTIONS
fCNU t*
TUO SAMPLES
T-TEST,EQUAL VARIANCE 10
T-TEST, UNEQUAL UARIANCE 11
T-TEST, PAIRED 12
F TEST 13
SIMPLE REGRESSIONS 14
CONTINGENCY TABLES
2X2 15
R X C 16
RANDOM NUMBER GENERATION 17
PROBABILITY DISTRIBUTIONS
(TABLES) 18
DATA MANAGEMENT UTILITIES 19
Please choose one of the above:
NOTE
Algorithms and References for these programs are available in Appendix A.
The first program, DATA FROM KEYBOARD, is used to enter a data file into the System.
The file is entered from the keyboard and automatically stored on the disc.
The second program, DATA FROM DISC, is used to recall a data file stored on the disc.
The third program, DESCRIPTIVE STATISTICS, is used to generate a table of basic
statistics for any variable in the current file.
The next four programs. HISTOGRAMS. STEM-AND-LEAF, BOX-AND-WHISKER, and
SCATTER PLOT are used to discover how a variable is distributed or how two variables
are related.
STATISTICS: TEST AND DISTRIBUTIONS
-------
THE PROGRAMS
Program 8 PROBABILITY PLOTS AND DISTRIBUTION ANALYSIS is used to draw
probability plots of a variable and to compare these plots to an ideal distribution.
Programs 9 through 13 provide various tools for testing hypotheses about a data sample:
one and two-variable t-tests and the F-test.
Program 14 offers nine models for doing simple regression analysis, including the
resistant line model.
Programs 15 and 16 are used to do contingency table analysis where expected and
actual frequencies are compared.
Program 17 is used to generate a random sample from one of two distributions: the
normal distribution and the uniform distribution.
Program 18 provides a list of 15 routines which are used to calculate the value of the
distribution function or inverse distribution function. These are calculated using various
probability distributions.
Program 19 provides 15 data management utilities. These are discussed separately in
Section 5.
Each program description is divided into the following subheadings:
• Purpose — tells you-what the program is used for.
• Running The Program — gives you a step-by-step procedure for running the
program.
• Options — lists and describes any options associated with the program.
• Restrictions — defines any limitations of the program.
4-2
STATISTICS: TEST ANO DISTRIBUTIONS
-------
THE PROGRAMS
PROGRAM 3 DESCRIPTIVE STATISTICS
PROGRAM 3 DESCRIPTIVE STATISTICS
Purpose
Run DESCRIPTIVE STATISTICS to get a table of the statistics describing a variable
(column of data). The table includes the:
coefficient of kurtosis
(See Appendix E, Glossary, for definitions of these terms.) The table also displays the title,
variable label, total number of observations, number of missing values, and number of
observations with valid values.
Running The Program
Obtain the menu, select Program 3, and press RETURN. The program starts with the
following:
mean
minimum
range
standard deviation
coefficient of variation
median
maximum
variance
standard error of the mean
coefficient of skewness
tX DESCRIPTIVE STATISTICS tt
Enter variable lumber: 2
Enter the number of the variable. The following message appears:
There nay be delays in interaction. Please stand by
STATISTICS: TEST AND DISTRIBUTIONS
4-13
-------
THE PROGRAMS
PROGRAM 3 DESCRIPTIVE STATISTICS
This appears while the program is computing the descriptive statistics for the variable
entered. When finished, the program displays the results as a table:
UATER QUALITY DATA
DESCRIPTIVE STATISTICS
Uariablc 2: BOD
TOTAL NUMBER OF OBSERVATIONS 26
NUMBER OF OBSERVATIONS WITH HISSING VALUES 0
NUMBER OF OBSERVATIONS HITH VALID VALUES 28
MEAN
3.937
IIQDTQUPP
STANDARD DEVIATION
STANDARD ERROR OF TW MEAN
0.949
0.221
a. 042
COEFFICIENT OF VARIATION
3.628
SKEHNESS
KURTOSIS
0.238
2.866
MINIMUM VALUE
MAX IHUM VALUE
RANGE
3.609
4.400
0.800
MEDIAN
3.903
Press SOLVE to compute statistics for another variable. Otherwise, press any other
function.
Options
This program has no options.
Restrictions
The variable number entered must correspond to a variable in the data file.
Some statistics may not be calculated, for example, in cases where calculations would
involve a denominator equal to zero.
4-14 STATISTICS: TEST AND DISTRIBUTIONS
-------
Appendix A
EQUATIONS, ALGORITHMS,
AND REFERENCES
PROGRAM 3 DESCRIPTIVE STATISTICS
Equations
The descriptive statistics are computed from the following equations:
n
1 • 7 = mean = —^ Xt
i-1
n
1 /
2. V- variance
3. s = Standard Deviation « Vv
s
4. Standard Error of the Mean « ^="
5. Coefficient of Variation = 100 y
Vn(^X,3 - 3x23x,2 + 2n
6. Skewness - ——^— —
[V(n—1)!372
7. Kurtosis:
n (2x'4 - 4XS *1®+ ex2I2xi2 -3n*4)
M-1 i-1 1-1 '•
[V(n-1)]2
where n ¦ number of values of the variable.
STATISTICS: TEST AND DISTRIBUTIONS
-------
the programs
PROGRAM 7 SCATTER PLOT
PROGRAM 7 SCATTER PLOT
Purpose
A scatter plot is produced by pairing two variables and plotting each pair of observations
as a point. The plot of all pairs is called a scatter plot.
Run SCATTER PLOT to produce a scatter plot of two variables from the current file.
Running the Program
Obtain the menu, select program 7, and press. RETURN. The program starts with the
following:
tt SCATTER PLOT SS
Enter variable nanbar for x-axis* (8 for observation number>: A
Enter the number of the variable to be plotted on the horizontal axis.
NOTE
To obtain an index plot, enter a zero. In an index plot, the data is plotted
against the observation numbers which are plotted along the x-axis.
The next message is:
Enter variable nunber for y-axis: 3.
Enter the number of the variable to be plotted on the vertical axis.
STATISTICS: TEST AND DISTRIBUTIONS
4-35
-------
THE PROGRAMS
PROGRAM 7 SCATTER PLOT
The program then pairs the variables and displays them as a scatter plot.
A
n
it
0
M
1
A
2j.
1.8-
1.6
1.
1.2
1.
8.8.
e.d-
0.
8.21
8
MATER QUALITY DATA
SCATTER PLOT
* *
* * t t *
t .
t » t t t *
ITION liSlBER
28
23
38
Options
This program has no options.
Restrictions
There are no restrictions to this program.
4-36
'A.N0V1
STATISTICS: TEST AND DISTRIBUTIONS
-------
THE PROGRAMS
PROGRAM 14 SIMPLE REGRESSIONS
PROGRAM 14 SIMPLE REGRESSIONS
Purpose
Run SIMPLE REGRESSIONS to fit one of nine models to your data. The models are:
1. Y= A+ B*X
2. Y»A»EXP(B»X)
3. Y= 1/(A+ B*X)
4. Y=* A+ B/X
5. Y« A+ B*LOGX
6. Y-A^X
7. Y=* X/(A+ B»X)
8. Y= B*X
9. Y= A+ B*X(resistant line).
The resistant line is not affected by outliers as much as the least-squares line is affected.
The resistant line is discussed in Paul R. Velleman and David C. Hoaglin's book:
"Applications, Basics, and Computing of Exploratory Data Analysis."
Running the Program
Obtain the menu, select program 14, and press RETURN. The program starts with the
following message:
tt SIMPLE REGRESSIONS t*
Enter variable mutter for independent variable (x-axis): _1_
Enter the variable number. The next message is:
Enter variable nuftber for dependent variable (y-axis): 2
STATISTICS: TEST AND DISTRIBUTIONS
4-65
-------
THE PROGRAMS
PROGRAM 14 SIMPLE REGRESSIONS
Enter the variable number.
The program then displays nine regression models.
MODELS
1. Y«A+B*X
Z* Y-A*EXP
3. Y-1/
4. Y-A+B/X
5. Y-A*B*L0C
6. Y-ASXtB
7. Y«X'U*B*X>
8. Y"B*X
9. Y»A+B*X (Resistant tine)
Please choose one of the above: 1
Choose a model. The program then displays the following:
4.4r
HATER QUALITY DATA
HODEL : Y • A+fitX
B
0
0
4.3.
4,2
4.1
3.9-
3.8
S t
3.7
** *
3.6*
-4 •-
HILE
4-66
STATISTICS: TEST AND DISTRIBUTIONS
-------
THE PROGRAMS
PROGRAM 14 SIMPLE REGRESSIONS
You can change the display's scale by turning SELECT GRAPH on. In this case the
System Plotting parameters are displayed.
SYSTEM PLOTTING PARAMETERS:
X nininun • 0. Y ninimin » 3.6
X noximin ¦ 6. Y naximin ¦ 4.4
X tick interval « 1. Y tick interval ¦ 8.1
Do you wish to change any of the X paraneters (Y/N; def: N>?
Do you wish to change any of the Y parameters ? _Y
Enter new ninimin (default: no change): 2.8
Enter new naximin (default: no change): 6.8
Enter new tick interval (default: no change): .2
Do you wish to print observation labels (first N characters)
along the points* (All* Sonc or HoneI default: None)?
Changing the Y-axis scale and tick interval, then pressing SOLVE produces the following:
UATER QUALITY DATA
HOOEL : Y - A+BSX
B
0
D
NILE
STATISTICS: TEST AND DISTRIBUTIONS
4-67
-------
THE PROGRAMS
PROGRAM 14 SIMPLE REGRESSIONS
Options
This program has five options. These are:
tt SIMPLE REGRESSIONS tt
OPTIONS
1. PRINT PARAMETERS
2. LIST RESIDUALS
3. SAVE X, Y. PREDICTED Y AND RESIDUALS ON DISC
4. SAVE RESIDUALS ONLY ON DISC
5. PRINT COMPARISON TABLE (Not OMlicable to nodcl 9>
Please choose one of the above:
OPTION 1 PRINT PARAMETERS
Select option 1 to list the variable labels of the independent (X) and dependent (Y)
variables. Also listed are the coefficients (A and B) of the regression model.
WATER QUALITY DATA
MODEL : Y • A+BSX
X • NILE
Y - BOO
A » 3.829
B - 0.048
OPTION 2 LIST RESIDUALS
Select option 2 to list residuals, observed values of X and Y, predicted values of X and Y,
and observation number and labels.
STATISTICS: TEST AND DISTRIBUTIONS
-------
THE PROGRAMS
PROGRAM 14 SIMPLE REGRESSIONS
WATER QUALITY DATA
HODEL : Y ¦ A+BSX
OBSERVATION
LABEL
NO.
X
OBS
1
1
8.888
OBS
2
2
8.288
OBS
3
3
8.488
OBS
4
4
8.688
OBS
5
5
8.888
OBS
6
6
1.888
OBS
7
7
1.288
OBS
8
8
1.488
OBS
9
9
1.688
OBS
18
18
1.888
OBS
11
11
2.888
OBS
12
12
2.288
OBS
13
13
2.488
OBS
14
14
2.688
OBS
15
15
2.888
OBS
16
16
3.888
OBS
17
17
3.288
OBS
18
18
3.488
OBS
19
19
3.688
OBS
28
28
3.888
OBS
21
21
4.888
OBS
22
22
4.288
OBS
23
23
4.488
OBS
24
24
4.688
OBS
25
25
4.888
PREDICTED f RESIDUAL
3.680
3.698
4.208
3.698
4.228
4.888
4.818
3.988
3.888
3.888
3.788
3.688
4.178
4.888
4.848
4.878
3.918
3.848
3.688
3.718
4.188
4.388
3.988
3.818
3.888
3.829
3.837
3.845
3.853
3.861
3.869
3.877
3.885
3.893
3.981
3.989
3.917
3.923
3.933
3.941
3.949
3.957
3.965
3.973
3.981
3.989
3.997
4.883
4.813
4.821
•8.149
-8.147
8.335
-8.163
8.339
8.131
8.133
8.815
-8.893
-8.181
-8.289
-8.317
8.245
8.867
8.899
8.121
-8.847
-8.125
-8.373
-8.271
8.111
8.383
-8.185
-8.283
-8.221
HATER QUALITY DATA
moo. : y ¦ a+bsx
OBSERVATION
LABEL HO.
OBS 26 26
OB$ 27 27
OBS 28 28
3.888
3.288
3.488
4.188
4.288
4.488
PREDICTED Y RESIDUAL
4.829
4.837
4.845
8.871
8.163
8.355
OPTION 3 SAVE X, Y, PREDICTED Y. AND RESIDUALS ON DISC
Select option 3 to save the output of option 2 on the disc. The option starts with the
following:
Enter filcnanc for savins residuals: RES ID
Enter a filename. The option responds, storing the X, Y, predicted Y, and residual values
on disc. When this is finished, the following message appears:
Residuals saved!
STATISTICS: TEST AND DISTRIBUTIONS
4-69
-------
THE PROGRAMS
PROGRAM 14 SIMPLE REGRESSIONS
OPTION 4 SAVE ONLY RESIDUALS ON DISC
Select option 4 to store the residuals in a disc file. The option starts with the following:
Enter filename for saving residuals: rcsidonly
Enter a filename. The option responds, storing the residuals on disc. When finished, the
following message appears:
Residuals saved!
OPTION 5 PRINT COMPARISON TABLE
Select option 5 to display a table comparing all the models. The table lists the coefficients
of the regression equations, the standard error of regression, and the maximum absolute
error.
HQDEL
8Y-ft*BSX
A
B
STD ERROR OF HAXXHUH
REGRESSION ABSCERR0R3
3.829
3.826
8.262
8.848
8.219
8.219
8.373
Yf*EXP
Y-l'CfrtttX)
Y»A*BSLOGCX>
Y-ASXtB
Y-X/
Y-6SX
8.818
-8.883
8.219
8.367
8.367
nay net be calculated
nay net be calculated
nay net be calculated
nay not be calculated
8.888
1.884
2.892
3.766
The @ sign designates the model currently being used.
Restrictions
For model 9, The Resistant Line, the maximum number of data pairs is 280.
4-70
STATISTICS: TEST AND DISTRIBUTIONS
-------
EQUATIONS. ALGORITHMS. AND REFERENCES
PROGRAM 14 SIMPLE REGRESSIONS
PROGRAM 14 SIMPLE REGRESSIONS
Method
If one of the first eight models is selected, the model is linearized and a least-squares
regression is performed on the transformed data. For the plot of the line and for all
subsequent options, the model and estimates are transformed back to the original units.
If the ninth model is selected, a line is fit by the resistant line method (same method as
used by Program 8).
The standard error of regression equals the sum of the squares of the residuals divided
by (n-2). The im residual equals (y(i)-Y(i)) where y(i) equals the ith value of the y variable
and Y(i) equals the predicted value. The maximum absolute residual is the residual with
the largest absolute value.
Algorithm
The algorithm for fitting the resistant line is the same as that for Program 8.
STATISTICS: TEST AND DISTRIBUTIONS
A-13
-------
Appendix E
GLOSSARY
NOTE
This glossary contains definitions of some PLOT SO terms unique to
Tektronix. /nc„ and some of the more common statistical terms. For a
discussion of more complicated statistical concepts, see a standard
statistical text such as Mood, Graybill, and Boes (References, *7).
ADJACENT VALUE: The furthest data value from the median, but still inside the inner
fence.
COF: See Cumulative Distribution Function.
CENSORED DATA: Data falling outside the interval of measurement
COEFICIENT OF KURTOSIS: A measure of departure from normality. It is given by the
average value of (x-p.)4 divided by a*.
COEFFICIENT OF SKEWNESS: Indicates the direction and degree of the lack of
symmetry. Skewness may be given as:
3 (mean-median)
Standard Deviation
/Variance\
COEFFICIENT OF VARIATION: V-100(— )
STATISTICS: TEST AND DISTRIBUTIONS
-------
GLOSSARY
CONFIDENCE INTERVAL: The distance between the edges of the critical areas (see
Figure E-1).
CRITICAL AREA
CONFIDENCE INTERVAL M3i.i«
Figure E-1. Confidence Interval.
CONFIDENCE LEVEL The probability that the t-statistic does not fall into the critical area
when the hypothesis is true (see Figure E-2). It is expressed in percent. The confidence
level »100(1 -Significance level).
CONFIDENCE LEVEL (%) - CONFIDENCE AREA X 100
~ CONFIDENCE AREA
CRITICAL AREA
Figure E-2. Confidence Level.
E-2 STATISTICS: TEST AND DISTRIBUTIONS
-------
GLOSSARY
CUMULATIVE DISTRIBUTION FUNCTION (CDF): A function which gives the probability
that a random variable is less than or equal to the independent variable of the function.
CUMULATIVE HISTOGRAM: A histogram in which successive sums of frequencies are
displayed. It tells you how many observations fall below a certain point.
DISTRIBUTION PARAMETERS: Numbers that characterize populations.
ENDPOINTS: The first few and last few values in a column of data.
EXPONENTIAL:
FAR OUTSIDE VALUE: A data value lying beyond the outer fence of a boxplot.
FILE HEADER INFORMATION: Information that summarizes the file. It includes: title,
number of variables, number of observations, and missing value.
FILE LABELING INFORMATION: Information about how the data file is labeled. It
includes: title, variable labels, observation labels, and missing value designator.
HISTOGRAM: A display of data showing how the data falls into various classes.
INDEX PLOT: A plot produced by plotting the values of a variable against its observation
numbers (that is, the values in a column by row number). The observation (row) number is
plotted along the x-axis.
INNER FENCE: A distance that is 158 Q-spreads from either quartile.
inner fence» upper quartile + 1.58 Q-spreads
lower quartile — 1.58 Q-spreads
LEAF: The final digit of a data value; e.g, 2 in 4562.
LEAF UNIT: A factor used to preserve the location of the decimal point when a data value
is split into a stem and leaf.
LEFT-CENSORED POINT: Data falling below the range being measured.
STATISTICS: TEST AND DISTRIBUTIONS IK NOV 1 E-3
1
f(x) ""Je * 0 )
B>0
X^A
-------
GLOSSARY
LOG NORMAL:
1
2 V ?
t ^
1 -i( iogx-M^2
,(X)= (Js/2n * 8
LOGISTIC:
0.eA+0X
f(x) =
(1 + e
i-i
n
where 7 is the mean and is the sum of n data values.
i-1
MEDIAN: The middle value in an ordered column of data. It is the data value halfway
between the top and bottom.
MINIMUM VALUE: The smallest value appearing in a column of data.
MISSING VALUE: A numeric constant used as a place holder for data missing from the
data set.
MODE: The value that occurs most often in a data set.
NOTCHED BOXPLOTS: A boxplot displaying special intervals (notches). These notches
are at 155 Q-spreads/(N E.5)
OBSERVATION: A row of data in a data file.
OBSERVATION LABEL: The label for one particular observation, e.g„ some date such as
12 JAN BO.
OUTER FENCE: A distance that is 3j0 Q-spreads from either quartile.
outer fence «¦ upper quartile + 3.0 Q-spreads
lower quartile — 3.0 Q-spreads.
E-4 STATISTICS: TEST AND DISTRIBUTIONS
-------
GLOSSARY
OUTLIERS: Data values occuring within a data set that may or may not be valid data
points, but fall outside the range of most of the data.
OUTSIDE VALUE: A data value lying between the inner and outer fences of a boxplot.
PLOT 50 STANDARD FILE: See Appendix C.
POPULATION PERCENTILE: The value of the inverse distribution function for a selected
probability.
PROBABILITY LEVEL: The smallest significance level that leads to rejection of the
hypothesis.
PROBABILITY LINE: Values of the theoretical distribution plotted on "probability paper."
PROBABILITY PLOT: Values of a variable plotted on "probability paper." The degree to
which the data lies on a straight line indicates the closeness of fit of the sample
distribution to the theoretical distribution.
Q-SPREAD: The distance between the quartiles.
QUANTILES: The quantiles for each data point on a probability distribution consists of:
the value of the variable, the value of the sample CDF. the value of the theoretical CDF,
and the difference between the-two.
QUARTtLE: When a data column is split in two by a median, the median of each half of the
data is the quartile.
RANGE: The maximum value minus the minimum value.
REGRESSION COEFFICIENT: The coefficients of the equation used in a regression
model.
RELATIVE FREQUENCY HISTOGRAM: A histogram showing the number of data values
falling into various classes, expressed as a percentage of the total.
RESIDUALS: The difference between actual data values and the data values predicted by
a regression line.
RESISTANT LINE: A line fitted through the data by resistant techniques rather than least
squares. The resistant line is more resistant to the effects of outliers, especially when the
outliers fall near the endpoints of the data.
STATISTICS: TEST AND DISTRIBUTIONS
E-5
-------
GLOSSARY
RIGHT-CENSORED POINT: Data falling above the range being measured.
SCATTER PLOT: A scatter plot is a graphical display showing how two variables are
related to each other.
SIGNIFICANCE LEVEL: The probability that the t-statistic falls into the critical area (see
Figure E-3) when the hypothesis is true.
Figure E-3. Significance Laval
STANDARD DEVIATION: The square root of the variance.
STANDARD ERROR OF THE MEAN: The standard deviation of a set of sample means.
STATISTICS: Random variables whose values are determined by sample data.
STEM: The initial digits of a data value; e.g., 456 in 4562.
TITLE: The title for or name of a set of data having one or more variables.
TOTALS: The sum of the expected frequencies in a contingency table:
UNIFORM DISTRIBUTION:
f(x)" Fa a
-------
GLOSSARY
VARIANCE: The average of the sum of the squares of the deviation of each observation
from the mean of the variable.
y*] x,2 — nx2
Variance = j_ 1
(n-1)
WEiBULL:
f(x)=j ABx^e-"8 A>0 B>0 x>0
[O xs=0
STATISTICS: TEST AND DISTRIBUTIONS
/A, NOV 1
E-7
-------
GLOSSARY
VARIANCE: The average of the sum of the squares of the deviation of each observation
from the mean of the variable.
n
Variance = j. 1
2 *? ~n*2
(n-1)
WEIBULL:
f(x)= f ABx^e-"8 A>0 B>0 x>0
1
0 x^O
STATISTICS: TEST AND DISTRIBUTIONS
REV A. NOV 1
E-7
-------
APPENDIX C
SELECTED ABSTRACTS
-------
APPENDIX C
SELECTED ABSTRACTS
"One Technique for Estimating Inflow with Surcharge Conditions."
R.J. Nogaj, A.J. Hollenbeck JWPCF, 53,491 (1981)
The determination of peak inflow by sanitary sewer flow monitor-
ing is an important element in a sewer system evaluation survey.
Flow measurements are often limited by surcharge conditions in
the sewer system and unpredictable weather conditions that may
not produce a desired storm event. A technique based on develop-
ing a relationship between peak inflow and rainfall intensity and
duration is presented for determining peak inflow for any desired
storm event. Data from five northern Illinois municipalities are
used to develop a correlation between flow and peak rainfall in-
tensity for various durations of 15 minutes to 24 hours. Based
on the premise that during intense storm events, a separate sani-
tary sewer responds similarly to a storm sewer, a modification of
the rational formula is used in the analysis. The highest corre-
l'ation occurs at storm duration periods betweenTS minutes and 9*0"
minutes. The results confirm the premise that inflow in a sepa-
rate sanitary sewer system is an exponential function of the in-
tensity of the storm event.
"Relation of Inflow/Infiltration Costs to Varying Policy Require-
ments." JWPCF, 54,1361 (1982)
D.I. Wilkowsky, C.T. Hay, D.L. Tucker,
D.S. Parker
The East Bay Municipal Utility District is responsible for inter-
ception and treatment of wastewater flows from a 215-km (83
sq. mile) tributary area along the east shore of San Francisco
Bay. During periods of intense wet weather, rainfall entering
the sanitary wastewater collection system as excessive infiltra-
tion and inflow exceeds the capacity of existing conveyance and
treatment facilities. Consequently, overflows of wastewater
mixed with storm water are diverted into San Francisco Bay 10 to
12 times per year. Storage and treatment alternatives to reduce
-1-
-------
pollutants being discharged are currently being investigated by
the District. Extensive computer simulations of flow and quality
within, the interceptor system and in San Francisco Bay are being
conducted. The regulatory framework, within which wet-weather
facilities planning is being developed, is based on a comprehen-
sive regional planning effort (The San Francisco Bay Basin Plan)
that addressed water qualilty considerations in the Bay in the
early 1970s and developed a maintenance-level concept for protec-
ting beneficial uses. The planning effort is ideal, in that,
rather than specifying facilities to meet arbitrary standards, it
provides the framework for a dialogue with regulatory agencies.
This paper highlights the policy dialogue and the costs of policy
requirements allowed by this flexible planning framework.
COST-EFFECTIVE PROGRAM FOR COMBINED
SEWER OVERFLOW ABATEMENT
Robert C. Ganley, Gary N. Kirsch, Arthur J. Okiver,
John M. Karanik, Randy R. Ott.
Onondaga County is located in central upstate New York
(Syracuse). The urbanized areas of Onondaga County, including
the City of Syracuse, discharge their wastes to Onondaga Lake.
The service area tributary to the county's Metropolitan Sewage
Treatment Plant (Metro) includes a population of nearly 300,000
in and around Syracuse and contains 1,125 km (700 miles) of
sewers, of which approximately 50 percent are combined.
A County Comprehensive Sewerage Study, published in 1968, identi-
fied a total of 87 combined sewer overflow (CSO) outlets that
discharge significant quantities of pollutants to Onondaga Lake
during rainfall events. The overflows were constructed along the
creeks at various times over the last 80 years to provide hydrau-
lic relief in the trunk and intercepting sewer systems wherever
necessary. Based on preliminary estimates that a total of sev-
eral billion gallons of overflow passed through the outlets in an
average year, and on apparent storm-related water quality prob-
lems in Onondaga Lake, a facilities planning study sponsored by
the U.S. Environmental Protection Agency (EPA) was undertaken
-2-
-------
by Onondaga County. The goal of the study was -to develop a
long-range plan directed toward improvements of water quality in
Onondaga Lake and the protection of downstream waters, including
Lake Ontario.
It is the purpose of this paper to present the approach utilized
in assessing magnitude of the CSO-related problems and in develop-
ing an achievable abatement program that allows for staged con-
struction of program elements. The recommended master plan,
which was submitted to EPA in June 1979, not only includes a
long-range comprehensive abatement program, but also provides for
short-term, low-investment abatement projects that can be readily
accomplished to realize immediate improvements in water quality.
An EPA grant has been awarded to Onondaga county to provide final
design funding for the first stage of the master plan.
Several primary objectives were established to give overall direc-
tion to the CSO abatement program:
• To minimize the wet weather discharge of com-
bined sewer overflow to receiving streams;
• To maximize the effective utilization of exist-
ing facilities;
• To develop a solution having an optimal
cost/benefit ratio; and
• To develop an approvable facilities plan.
An array of abatement alternatives was developed through analysis
of established water quality criteria for Onondaga Lake and a re-
view of current CSO abatement technology. New York State has
classified Onondaga Lake as Class C in its southern portion and
Class B in its northern portion. These standards define specific
requirements in terms of bacterial counts, dissolved oxygen, and
other parameters. In addition, the state has proposed supplemen-
tal standards for CSO treatment, expressed as functions of bacter-
ial kill and removal of floatable and settleable solids. As part
of the CSO program, a storms impact study was conducted to deter-
mine effects of CSO on water quality in the lake and to define
abatement requirements more precisely. The storms impact study
demonstrated that there was an increase in bacterial counts in
all portions of the lake following CSO discharges. These
increased counts are sufficient to impair future recreational use
of the lake.
-------
"Major Infiltration Inflow Study to Break New Ground."
The Washington Suburban Sanitary Commission, one of the largest
pollution management agencies in the United States has awarded a
multiyear contract for a sewer system evaluation survey in select-
ed areas of its jurisdiction. RJN Environmental Associates of
Wheaton, IL will conduct the innovative study. The project con-
sists of developing and implementing new approaches for identifi-
cation, quantification, evaluation and rehabilitation of infiltra-
tion and inflow sources for approximately 2.5 million lin. ft. of
sanitary piping. The firm's Computer Assisted Sanitary Sewer
(CASS) programs with database management system techniques will
be used to process flow monitoring and field inspection data, per-
form hydraulic flow routing and cost-effectiveness analysis, and
establish a basis for a management control plan. One part of the
study will include investigation of migration if infiltration/in-
flow and its effect on sewer rehabilitation. Another object will
be to determine a streamlined approach to sewer system evaluation
and rehabilitation to serve as a basis of a new national level
alternative.
"Statistical Approach to Infiltration/Inflow Analyses."
W.E. Nute
Jour. Water Poll. Control Fed., 52,2500 (1980)
This paper describes statistical methods used to prepare infiltra-
tion/inflow analyses for 12 sewer systems in Marin County, CA.
The analyses conform to the State Basin Plan for San Francisco
Bay that established three possible maintenance levels for con-
trol of wet weather flows. The concept allows for violation of
secondary treatment standards for unusually severe rain storms
of certain return frequencies where the receiving waters are de-
termined not to be sensitive to such wintertime discharges. An
analogy is drawn between the prediction of wet weather wastewater
flows and the frequency analyses used in hydrology for the predic-
tion of flood flows. This depends on the recognition that wet
weather flows are more complex than represented by the infiltra-
tion and inflow components defined by the O.S. Environmental
Protection Agency. Also discussed are wet weather flow treat-
ment strategies for flow return frequencies used in defining
4-
-------
the three maintenance levels. Estimates are given of the
probability of violation of secondary treatment standards.
"Management and Control Technology for Urban Stonnwater Pollu-
tion. "
E.J. Finnemore, W.G. Lynard JWPCF, 54,1099 (1982)
Proven and promising approaches for managing and controlling
water pollution caused by urban runoff and combined sewer over-
flows are summarized for planners and designers. Best management
practices used to control urban runoff are emphasized because of
their great potential. They include institutional approaches,
land use planning, street cleaning, erosion controls, percolation
ponds, and detention/sedimentation basins, with the major empha-
sis on source storage. Structural measures - including in-line
and off-line storage, sedimentation, and biological treatment
lagoons - are used primarily to control combined sewer overflows.
Integrated systems, with storage again the most important ele-
ment, hold great promise for areawide control. More information
on cost-effectiveness and receiving water quality benefits is
acutely needed by local decision makers.
"Five Years of Sewer System Evaluation."
Allowances; Costs; Economic Analysis; Evaluation; Inflow;
Manholes; Optimization; Rehabilitation; Sewer Collection Systems.
Abstract: Twenty-eight wastewater collection systems spread over
the south-central and southeast region of the United States were
surveyed and evaluated for infiltration/inflow in a systematic
manner. After a brief description of the planning and executions
of the sewer system evaluation surveys, the findings are presen-
ted in five tables. Table 1 covers the infiltration/inflow char-
acteristics. Tables 2, 3, and 4 cover recommended rehabilitation
work broken down into the three major components of a collection
system: collection lines, manholes, and service lines. Table 5
covers rehabilitation costs and expected savings that will result
from the elimination of excessive infiltration/inflow.
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Reference: Gutierrez, Alberto F., and Rowell, J. Harry,
"Five Years of Sewer System Evaluation" Journal of the Environ-
mental Engineering Division ASCEf Vol. 105, No. EE6, Proc. Paper
15039, Decemoer, 1979, pp. 1149-1163.
"SWMM and Combined Sewerage in New Haven."
Combined Sewers: Field Tests, Models; Sewers, Storms; Storm
Water, Water
Abstract: Storm Water Management Model (SWMM) of EPA was calibra-
ted to predict runoff flows in the central portion of the city of
New Haven, CT. The study area is served by combined sewers and
overflow structures to divert excess wet weather flow into the ad-
jacent receiving waters. For application of SWMM, the project
area was divided into 23 subcatchments and two of them were selec-
ted for model calibration. During storm events, the rainfall
hydrographs, the runoff hydrographs, and combined sewage quality
parameters were measured in each of the two subcatchments. Using
these data, in SWMM calibration and verification of flow quanti-
ties , was accomplished successfully. However, problems were en-
countered in the quality calibration. The calibrated model
(quantity portion only) was subsequently used to predict runoff
flows for the design storm in each of the 23 subcatchments. A
two-year storm was selected as a design storm from the available
35-year or rainfall record. Literature values of BOD and SS
were used to predict wet weather waste loads.
Reference: Cermola, Joseph A., DeCarli, Sergio, Sachdev, Dev R.,
and El-Baroudi, Hassan M., "SWMM Application to Combined Sewerage
in New Haven." Journal of the Environmental Engineering Divi-
sion, ASCE, Vol. 105, No. EE6, Proc. Paper 15042, December, 1979,
pp. 1035-1048.
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COST-EFFECTIVE COMBINED SEWER
OVERFLOW POLLUTION ABATEMENT PLANNING
H.L. Kaufman, Fu-hsiung Lai
Clinton Bogert Associates, Fort Lee, NJ
Combined sewer systems serve about one quarter of our population.
Their untreated discharges may occur every 5 to 10 days on the
average, depending on rainfall patterns, and can reduce the effi-
ciency of biochemical oxygen demand (BOD) removal from about 90
percent, for secondary treatment, to perhaps 15 to 25 percent dur-
ing the period of discharge. Determination of economic methods
for the abatement of pollution requires exploration of nonstruc-
tural alternatives, such as sewer flushing and street sweeping,
and a systematic analysis of the interaction of various elements
in a sewer system, such as collection lines, trunk and intercep-
tor sewers, storage, and treatment works. The tools required for
this analysis use two mathematical models, the Environmental
Protection-Agency's (EPA) Storm Water Management Model (SWMM) and
the Corps of Engineers' (COE) Storage, Treatment, Overflow, and
Runoff Model (STORM). These models provide normalized hydro-
graphs that simplify flow routing through the many alternatives
that should be considered in design, and use a synthetic rainfall
hydrograph that reproduces probable rainfall volumes for stated
durations and return intervals rather than probable peak rainfall
rates.
These models use input which is correlated with actual storms.
They can: evaluate the effects of differing rainfall patterns,
intensities, and volumes on pollutant discharge characteristics,
quantify not only the long-term pollution discharges from combin-
ed sewer overflows, but also the effects of varying interceptor
and treatment capacities on pollutants discharged, and the econo-
mics of peak flow equalizing through storage for different treat-
ment capacities; and evaluate the effect on overflow pollution of
source control by varying the amount of upstream storage and com-
pare the effect of source control with downstream storage.
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"Calculating Overflows from Combined Sewer Systems."
Kirke E. Larson, A.M. ASCE
Analyzing the effects of storage and flow capacity on annual over-
flows from a combined sewer system is necessary so that the im-
pact of overflows on receiving waters can be evaluated and mea-
sures can be implemented to reduce these impacts. This paper ex-
plains one approach to solving the problem. The method supplies
practical answers to questions such as, "Which Sewer District in
the city has the most overflow?" "How much combined sewage over-
flow is there from a certain District?" "How many times a year
does an overflow occur?" Also related questions are answered,
such as, "How much additional sewage must be treated at the treat-
ment plant because overflows are reduced?"
"State Variable Model for Sewer Network Flow Routing."
Larry W. Mays, A.M. ASCE and Yeou-Koung Tung
Journal of the Environmental Engineering Division
The disposal of stormwater runoff is one of the major problems in
urban water management. This problem has become even more severe
due to the rapid rate of urbanization coupled with the increase
in quality of life that urban residents expect to enjoy. Large
amounts of money and resources are involved in the proper dispo-
sal of storm runoff in order to maintain present standards, not
to mention the needed improvements in the near future. The
rational method and the Chicago method are the most commonly used
in practice for designing storm sewer networks. These methods
are unable to account for the unsteady nature of sewer flow and
the mutual backwater effects among sewers. From an engineering
viewpoint, the storm drainage problem can be divided into two as-
pects; flow prediction and system design. Recently, there have
been several improved models developed for each of these aspects.
The flow prediction models essentially compute the time varia-
tion of storm runoff in storm sewer networks for known or assumed
designs (i.e., layouts, slope, length, and size of the sewer
pipes). These flow prediction models are useful from an opera-
tional (real-time) viewpoint for regulating storm runoff for pol-
lution control, design of storage facilities and treatment
plants, and other management purposes.
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APPENDIX D
PERSONS CONTACTED
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APPENDIX D
PERSONS CONTACTED
Mike Liebman
Foth & Van Dyke
Green Bay, WI
Gerald Novotry
WI Department of Natural Resources
Madison, WI
Frank Wellstein
Milwaukee Metropolitan Sewage District
Milwaukee, WI
National Weather Service
Asheville, NC
Brij Garg
Pennsylvania Department of Resources
Harrisburg, PA
John Kennedy
Pennsylvania Department of Resources
Norristown, PA
Garry Alden
City of Des Plaines Engineering Dept.
Des Plaines, IL
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