Title: Interaction of urban stormwater runoff
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 Material Information
Title: Interaction of urban stormwater runoff control measures and receiving water response
Physical Description: xxiv, 298 leaves : ill. ; 28 cm.
Language: English
Creator: Medina, Miguel Angel, 1946-
Publication Date: 1976
Copyright Date: 1976
 Subjects
Subject: Hydrologic cycle   ( lcsh )
Urban runoff   ( lcsh )
Water quality management   ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Dissertations, Academic -- Environmental Engineering Sciences -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 291-296.
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Miguel Angel Medina, Jr.
 Record Information
Bibliographic ID: UF00098126
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000177764
oclc - 03096644
notis - AAU4264

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INTERACTION OF URBAN STORMWATER RUNOFF,
CONTROL MEASURES AND RECEIVING WATER RESPONSE













By

MIGUEL ANGEL MEDINA, JR.


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1976






















To My Parents, My Sister, Elena,

and My Fiancee, Margarita














ACKNOWLEDGEMENTS


The author is deeply indebted to Dr. Wayne C.

Huber for his undivided attention, valuable suggestions,

and overall guidance throughout this investigation.

The strong influence of Dr. James P. Heaney on

the direction of research, and his continued encourage-

ment, are especially appreciated. The author is grate-

ful to Professor Thomas deS Furman for his invaluable

advice and assistance in the early stages of doctoral

research.

Special thanks are due to Drs. William Morgan

and Daniel Spangler for their review of this manuscript.

The author also wishes to recognize the excellent draft-

ing of Mr. James Graham and professional typing of Pat

Whitehurst.















TABLE OF CONTENTS

Page


ACKNOWLEDGEMENTS ------------------------------------ iii

LIST OF TABLES -------------------------------------- vii

LIST OF FIGURES ------------------------------------- x

NOTATION -------------------------------------------- xiv

ABSTRACT ------------------------------------------- xxiii


CHAPTER

I INTRODUCTION -------------------------------- 1


II A UNIFIED PHYSICAL SYSTEM CONCEPTUALIZATION 11

2.1 Characterization of Urban Wastewater
Discharges and Polluted Surface Waters 11
2.2 A Unifying Conceptualization of the
Physical System ------------------------ 20


III DESCRIPTION OF THE STUDY AREA AND NECESSARY
MODELING TECHNIQUES ------------------------- 30

3.1 The Need for a Study Area -------------- 30
3.2 Des Moines, Iowa ----------------------- 31
3.3 Pollutant Loads ------------------------ 33
3.4 The Receiving Stream ------------------- 41
3.5 An Abstraction of the Physical System -- 42
3.6 Technique for Calculation of Urban
Runoff Quantity and Quality ------------ 49
3.7 Separate, Combined and Dry Weather
Loading -------------------------------- 50
3.8 Data Sources --------------------------- 56










Page


IV STOCHASTIC CHARACTERIZATION OF URBAN
RUNOFF ---------------------------------------- 59

4.1 Hydrologic Time Series ------------------- 59
4.2 Analysis of Time Series ------------------ 60
4.3 Definition of an Event ------------------- 74
4.4 Statistical Summaries of Deterministic
Mechanisms ------------------------------- 77

V MATHEMATICAL APPROACH TO STORAGE/TREATMENT
RESPONSE TO VARIABLE FORCING FUNCTIONS -------- 81

5.1 System Models and the Unifying Concept --- 81
5.2 Well-Mixed Constant Volume.Model --------- 85
5.3 Well-Mixed Variable Volume Model --------- 120
5.4 Dispersive Variable Volume Model --------- 157
5.5 Summary ---------------------------------- 193


VI STATISTICAL APPROACH TO STORAGE/TREATMENT
RESPONSE FOR WELL-MIXED CONSTANT VOLUME MODEL 199

6.1 Introduction ----------------------------- 199
6.2 Equalization of Concentration and Mass
Flow Rate --------------------------------199
6.3 Methodology ------------------------------ 201
6.4 Application to Des Moines, Iowa ---------- 209
6.5 Limitations of a Strictly Statistical
Approach --------------------------------- 219


VII RECEIVING WATER RESPONSE TO WASTE INPUT
COMBINATIONS ---------------------------------- 222

7.1 Introduction ----------------------------- 222
7.2 Initial Conditions ----------------------- 225
7.3 Oxygen Balance of Polluted Streams ------- 227
7.4 Critical Deficit and D.O. Levels --------- 230
7.5 Reaeration and Deoxygenation Coef-
ficients --------------------------------- 233
7.6 Special Problems ------------------------- 235
7.7 Application to the Des Moines River ------ 236


VIII SUMMARY AND CONCLUSIONS ----------------------- 248










Page

APPENDICES ------------------------------------------- 251

I WELL-MIXED AND DISPERSIVE VARIABLE VOLUME
DIGITAL COMPUTER MODEL --------------------- 252

II WELL-MIXED CONSTANT VOLUME AND RECEIVING
WATER DIGITAL COMPUTER MODEL ---------------- 273

REFERENCES ------------------------------------------ 291

BIOGRAPHICAL SKETCH --------------------------------- 297















LIST OF TABLES


Table Page


2-1 Constituents in Rainfall 13

2-2 Characteristics of Urban Stormwater 14

2-3 Characteristics of Combined Sewer
Overflows 15

2-4 Pollution and Contamination Indices 17

2-5 Treatment Potential of Various Com-
ponents of the Physical System 28

3-1 Pollutant Unit Loads for Drainage
Area Above Des Moines, Iowa 34

3-2 Summary of Pres'ent Annual Metro Area
Discharges 36

4-1 Divided Difference Table for Determi-
nation of Point of Maximum Curvature 76

5-1 Solutions to Equation (5.5) for Various
Forcing Functions of Concentration 89

5-2 Analytic Solutions to Equation (5.9)
for Various Forcing Functions of Con-
centration and Flow Rate 92

5-3 Required Basin Volume for Desired
Average Detention Time 109

5-4 Statistics for Well-Mixed Constant
Volume Model for Wet Weather Event
No. 52 114

5-5 Pollutant Removal Effectiveness of
Well-Mixed Constant Volume Model for
Wet Weather Event No. 52 115









Table Page

5-6 Statistics for Well-Mixed Constant Vol-
ume Model for All Wet Weather Events 125

5-7 Pollutant Removal Effectiveness of
Well-Mixed Constant Volume Model for
All Wet Weather Events 126

5-8 Integration of Equation (5.34) for Var-
ious Forcing Functions of Concentration
and Flow Rates 131

5-9 Average Storage Volumes Used for Given
Detention Times 138

5-10 Statistics for Well-Mixed Variable Volume
Model for Wet Weather Event No. 52 143

5-11 Pollutant Removal Efficiency of Well-
Mixed Variable Volume Model for Wet
Weather Event No. 52 144

5-12 Reduction in Peak and Mean Flow Rates
with Variable Volume Model for Wet
Weather Event No. 52 146

5-13 Statistics for Variable Volume Model
with Detention Time of 48 Hours for
Wet Weather Event No. 52 147

5-14 Statistics for Well-Mixed Variable
Volume Model for All Wet Weather Events .154

5-15 Pollutant Removal Efficiency and Outflow
Rate Attenuation of Well-Mixed Variable
Volume Model for All Wet Weather Events 155

5-16 Maximum Storage Volume Required for
Desired Detention Time 156

5-17 Statistics for Dispersive Variable
Volume Model for Wet Weather Event
No. 52 176
5-18 Pollutant Removal Efficiency of
Dispersive Variable Volume Model for
Wet Weather Event No. 52 177




viii











Table


5-19 Statistics for Dispersive Variable Vol-
ume Model for All Wet Weather Events 184

5-20 Pollutant Removal Efficiency of Disper-
sive Variable Volume Model for All
Wet Weather Events 185

5-21 BOD Concentration Statistics for All
Wet Weather Events for Various Peclet
Numbers 191

5-22 BOD Concentration Statistics for All Wet
Weather Events for Various Reaction Rate
Groups 192


6-1 Summary Statistics.for BOD Mass Rate
and. Fluid Flow Rate Inputs of the Urban
Runoff Time Series 210

6-2 Predicted System Response to Mass and
Fluid Flow Rate Inputs 214

6-3 Pollutant Removal Efficiency of the
Well-Mixed Constant Volume Model 216

7-1 Waste Input Combinations and Stream
Conditions 223

7-2 Percentage of Critical D.O. Loncentra-
tions Exceeding Given Stream Standard 245


Page














LIST OF FIGURES
Figure Page

2-1 A Generalized Component of the Physi-
cal System. 21

.3-1 Map of Des Moines Area. 32

3-2 Existing DWF Process Profile. 35

3-3 Location Map: River Sampling Points. 40

3-4 An Abstraction of the Physical System. 43

4-1 Point Rainfall for Des Moines, Iowa. 61

4-2 Lag k Autocorrelation Function of Des
Moines, Iowa, Hourly Rainfall, 1968. 68

4-3 Autocorrelation Function of Hourly Urban
Runoff for Des Moines, Iowa, 1968. 72

4-4 Definition of a Wet Weather Event for
Des Moines by Graphic Procedure. 75

5-1 Well-Mixed Constant Volume Model. 86

5-2 Discrete Inputs of Flow Rate and Concen-
tration at Equal Time Intervals. 94

5-3 BOD Removal from Sewage in Primary Sedi-
mentation Tanks. 101

5-4 Input Flow Rate for Wet Weather Event
No. 52. 106

5-5 Input BOD Concentration for Wet Weather
Event No. 52. 107

5-6 Input BOD Mass Rate for Wet Weather
Event No. 52. 108

5-7 Output Flow Rate for Wet Weather Event
No. 52. 111


__~










Figure Page


5-8 BOD Concentration Response for Wet
Weather Event No. 52. 112

5-9 BOD Mass Rate Response for Wet Weather
Event No. 52. 114

5-10 Frequency Distribution of Input BOD
Concentrations for All Wet Weather
Events. 117

5-11 Frequency Distribution of Output BOD
Concentration for All Wet Weather
Events. 118

5-12 Cumulative Frequency of BOD Concentra-
tions for All Wet Weather Events. 119

5-13 Frequency Distribution of Input BOD Mass
Rate for All Wet Weather Events. 121

5-14 Frequency Distribution for Output BOD
Mass Rate for All Wet Weather Events. 122

5-15 Cumulative Frequency of BOD Mass Rates
for All Wet Weather Events. 124

5-16 Well-Mixed Variable Volume Model. 128

5-17 Output Flow Rate for Wet Weather Event
No. 52 for Varied Detention Time. 140

5-18 BOD Concentration Response for Wet
Weather Event No. 52 for Varied Deten-
tion Time. 141

5-19 BOD Mass Rate Response for Wet Weather
Event No. 52 for Varied Detention Time. 142

5-20 Frequency Distribution of Output BOD
Concentration for All Wet Weather Events
for Variable Volume Storage/Treatment. 148

5-21 Frequency Distribution of Output BOD
Mass Rates for All Weather Events
for Variable Volume Storage/Treatment. 149










Figure Page


5-22 Cumulative Frequency of BOD Concentra-
tions for All Wet Weather Events for
Variable Volume Storage/Treatment. 151

5-23 Cumulative Frequency of BOD Mass Rates
for All Wet Weather Events for Variable
Volume Storage/Treatment. 152

5-24 Advection and Dispersion in the Variable
Volume Model. 158

5-25 Discrete Convolution. 165

5-26 Flow Rate Response for Wet Weather Event
No. 52. 172

5-27 BOD Concentration Transient Response for
Wet Weather Event No. 52. 173

5-28 BOD Mass Rate Transient Response for Wet
Weather Event No. 52. 174

5-29 Frequency Distribution of Output BOD Con-
centrations for All Wet Weather Events
for Dispersive Variable Volume Model. 178

5-30 Frequency Distribution of Output BOD
Mass Rates for All Wet Weather Events
for Dispersive Variable Volume Model. 179

5-31 Cumulative Frequency of BOD Concentra-
tions for All Wet Weather Events for
Dispersive Variable Volume Model. 182

5-32 Cumulative Frequency of BOD Mass Rates
for All Wet Weather Events for Disper-
sive Variable Volume Model. 183

5-33 System BOD Concentration Response for
Varied Longitudinal Dispersion Coeffi-
cient. 187

5-34 BOD Concentration Response for a Reactor
Characterized by Peclet Numbers. 189

5-35 BOD Concentration Response for Various
System Models. 194









Figure Page


5-36 BOD Mass Rate Response for Various
Systems Models. 195

6-1 Lag k Serial Correlation Coefficients
for Input BOD Mass Rates. 212

6-2 Lag k Serial Correlation Coefficients
for Input Fluid Flow Rates. 213

6-3 Deterministic Model and Statistical
Approach Predictions for All Wet
Weather Events. 218

6-4 Lag k Serial Correlation Coefficients
for Fluid Flow Rate for Wet Weather
Event No. 52, Hourly. 221

7-1 Application to Des Moines, Iowa. 239

7-2 Minimum D.O. Frequency Curves for
Varied WWF Control and DWF Secondary
Treatment Versus No Treatment of
Urban Waste Sources. 242

7-3 Minimum D.O. Frequency Curves for
Varied WWF Control and DWF Primary
Treatment Versus No Treatment of
Urban Waste Sources. 243


x i i i















NOTATION


A = wetted cross-sectional area in the
physical component, L2

A = area served by combined sewers, acres
c
At = total area of catchment, acres

AR = urban area runoff, inches per hour

A(t) = fluctuating cross-sectional area due to a
variable depth, L2

B = benthal demand of bottom deposits,
mg/1-hour

BOD = Biochemical Oxygen Demand

BODc = mixed BOD concentration in the combined
sewer, mg/l

BODCM = average field measured BOD concentra-
tion in combined sewer overflows,
mg/l

BODd = BOD concentration of dry-weather flow
treatment facility effluent, mg/l

BODf = BOD concentration of municipal sewage,
mg/l

BOD = mixed BOD concentration in receiving
water, mg/l

BOD = BOD concentration of urban stormwater
runoff, mg/l









BOD = mixed BOD concentration of urban runoff
from the separate storm sewer and com-
bined sewer flows, mg/l

BOD = hourly BOD concentration of total urban
runoff, mg/l

BOD = mixed BOD concentration from sources up-
ustream of urban area, mg/l

BOD = BOD concentration.of treated WWF storage/
treatment facility effluent, mg/.

C = concentration of water quality parameters
(pollutant), M/L3

C = concentration of D.O. in the stream,
mg/l

c. = value of input concentration from t.
I to (ti + At), M/L3

C min = concentration of D.O. at maximum deficit, .
mg/l

Cs = dissolved oxygen saturation, mg/1

c.v. = sample coefficient of variation of the
water quality parameter

C = constant influent concentration, M/L3

c1 = factor to convert mg/l to Ibs/cf

Cl = concentration of pollutant in the inflow,
dimensionless

c2 = factor to convert FF from Ib/hr to cfs.
mg/1

C2 = mean effluent concentration, M/L

CR = composite runoff coefficient dependent
on urban land use

C (I) = concentration of wastewater in the storage/
treatment system at t = 0, for storm event
I, M/L3









c2(I-1)



Cl(T)

C1 (Ti).

cl(t)


c2(t)


c2(ti)


c2(ti + 2)

c2(x, t- t )


C (x-Ut,
t 1)



D = C C

Dc

D 0

Du
u

D.O.

DWFSEP

DWFCMB


= concentration of wastewater in the system
during the last hour oa runoff of the pre-
vious storm event, M/L

= concentration forcing function, dimension-
less

Sdiscrete concentration forcing .function,
dimensionless

= concentration forcing function of material
in inflow, M/L3

= concentration of material in the tank and
outflow,as a continuous function of time,
M/LJ

= concentration value obtained by equation
(5.12) for the previous time step, M/L3

= time-averaged concentration for each time
step, M/L3

= pollutant concentration at distance x along
the flow axis and time t > t mass of
pollutant/mass of fluid, dimensionless


= initial concentration at a time x/U
earlier and a distance Ut upstream,
M/L3
= dissolved oxygen deficit, mg/l

= critical (maximum) D.O. deficit, mg/l

= initial D.O. deficit, mg/i

= D.O. deficit in receiving waters upstream
of inflow point, mg/l
= Dissolved Oxygen

= DWF contribution from separate sewer area,
cfs

= DWF contribution from combined sewer area,
cfs









DWH = number of dry weather hours preceding each
runoff event

DWT(I) = number of DWH preceding storm event I

E = longitudinal.dispersion coefficient, L2/T

f = K2/K1 = self-purification ratio, dimensionless

f = available urban depression storage, inches

FF = first flush factor, pounds/DWH-acre

f(t T) = system step response, dimensionless

g = exponent in solution to steady-state dif-
ferential equation.for dissolved oxygen
deficit, T-1

H = stream depth, feet

h = sampling interval =ti+1 t.= 1 hour

I(t) = system input function, M/L3

j = exponent in solution to steady-state dif-.
ferential equation for dissolved oxygen
deficit, T-1

K = first-order decay rate of pollutant in the
fluid medium, T-1

k = number of hourly lags

K = oxidation coefficient of nitrogenous BOD,
n hours-1
-1
K = first-order BOD decay constant, day-
1 and hours-I

K2- = atmospheric reaeration coefficient, hours-

L = length of the storage/treatment basin,
feet

L = remaining carbonaceous BOD concentration,
mg/l

(L ) = ultimate first-stage BOD demand, mg/l



L xvii
















m At
m-
At2

N


N


n

n

P


P
u

Pe

Q






Qd

Qi


Qs




Qt
Q.


QL \


= equalized variation of the flow, dimen-
sionless

Sexponent in the steady-state differential
equation for dissolved oxygen deficit,
L-1

Total number of increments desired per
time step

= remaining nitrogenous BOD concentration,
mg/l

= any desired upper bound, dimensionless
number

= total number of data points or observations

= total number of inputs

= oxygen production rate by algal photosyn-
thesis, mg/l-hour

= hourly rainfall/snowmelt in inches over
the urban area

= Peclet dispersion number

Svolumetric flow into and out of tank,
L3/T

= mean influent fluid flow rate, L3/T

= combined sewer overflow rate, cfs

= DWF treated effluent, cfs

= value of input flow rate from t to
(ti + At), L3/T 1

= .urban runoff carried by the separate
storm sewer, cfs

= total (storm plus combined) urban runoff,
cfs

= upstream flow, cfs

= .WWF storage/treatment effluent, cfs


xviii


I









QCOM = total flow generated by-the combined
sewer area, including DWF contribution,
for all periods of urban runoff, cf/yr

q"(T). = variable time rate of mass injection per
unit area at the plane source, M/L2T

Qo(I) = system outflow rate at t = 0, for storm
event I, L3/T

q = influent fluid flow rate per unit width,
L2/T

Q, = influent fluid flow rate, L3/T

Q2(I 1) = outflow rate from the storage/treatment
system during the last hour of runoff of
the previous storm event, L3/T

Q2 = outflow rate, L3/T

Q1(t) = fluid flow rate into tank, as a continuous
function of time, L3/T

Q2(t) = fluid flow rate out of the tank, as a
continuous function of time, L3/T

Q2(t=0) = initial outflow of the system, L3/T

Q2(ti) = outflow value at the end of the previous
time step, L3/T

Q2(ti + At) = output flow rate at the end of the time
step, L3/T

2(t + ) = time-averaged outflow rate for each time
2 i step, L3/T

r = total number of hourly runoff occurrences
during the year

R = fraction removal of BOD achieved by the
DWF treatment facility

R = algal respiration rate, mg/l-hour
S = sources or sinks of the substance C,
M/L3T









= standard deviation of observations of the
water quality parameter from its computed
mean

Unbiased estimate of the variance of ob-
served magnitudes of the water quality
parameter

= water temperature, C

= Time, T


= elapsed time at which the
occurs, hours

= detention time, T

= average detention time, T

= the beginning of the time
which the system response
uated, T


critical deficit


interval for
is being eval.-


Sany time t > t
1


= correlation time constant
fluid flow rates, hours

Correlation time constant
inputs, hours


for influent


for mass rate


= duration of injection, T

= total number of DWH in the year, DWH/yr

= tolerance limits at a 95% probability
level

= longitudinal velocity in the storage/
treatment system, or in the stream, L/T

= volume of tank, L

= time-varying volume of the basin, L3

value of input mass rate from t. to
(ti + At), M/T


tl

TDWH

TL (95%)


V

V(t)









W, = mean influent mass rate, M/T

- At
w2(t + ) = time-averaged output mass rate for each
time step, M/T

x = unbiased estimate of the mean value of
the water quality parameter

x. = discrete data series (observations) of a
i hydrologic process I, for i = 1, 2,
n

X = unbiased estimate of the flow-weighted
w mean value of the pollutant concentration
-1
a = time constant, T

aI = regression coefficient

a2 = regression coefficient
-B r = constant of integration

,l = regression coefficient

B2 = regression coefficient

At = length of time interval, say, 1 hour

v = coefficient of variation of the effluent
concentration, dimensionless

VCQ = coefficient of variation of the effluent
mass flow rate, dimensionless

Q = coefficient of variation of the influent
fluid flow rate, dimensionless

,W = coefficient of variation of the influent
mass rate, dimensionless

= U +4KE, has the dimensions of velocity,
L/T

p = density of the receiving fluid, M/L3

Q = standard deviation of the influent fluid
flow rate, L3/T

oW = standard deviation of the influent mass
rate, M/T










r2 = variance of the influent fluid flow rate,
L6/T2

02 = variance of the influent mass rate, M2/T2
W

S= dummy variable of integration

T. = iAt, dimensions of time, T

T = normalized detention time for fluid flow,
dimensionless

T = normalized detention time for pollutant
w mass input, dimensionless

Xi = data series of observed magnitudes of
the water quality parameter, for i = 1,
2, 3, . ., n


xxii











Abstract of Dissertation Presented to the.Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



INTERACTION OF URBAN STORMWATER RUNOFF,
CONTROL MEASURES AND RECEIVING WATER RESPONSE



By

Miguel Angel Medina, Jr.

December, 1976

Chairman: Wayne C. Huber
Cochairmen:. James P..Heaney, Thomas deS Furman*
Major Department: Environmental Engineering Sciences


Pollutant transport within each phase of the

hydrologic cycle, and through the various components

of the physical system, is governed by the principle of

conservation of mass. Deterministic mathematical models

are derived.from this unifying concept.to represent the

movement, decay, storage, and treatment of stormwater

runoff pollutants and dry weather wastewater flows

through the urban environment and the receiving body of

water. The general one-dimensional, transient conserva-

tion of mass equation may be simplified for application

to the various pathways by retention of only the dominant

terms in each instance. The detention time and decay

coefficient are key parameters in establishing the final

form of the governing differential equation.


xxiii










The precipitation time series and the urban runoff

series generated by a continuous hydrologic simulation

model are characterized stochastically by autocorrelation

analysis to define independent wet weather events. The

transient response of storage/treatment systems to vari-

able forcing functions of flow and concentration is deter-

mined for completely mixed systems of constant and vari-

able volumes and for one-dimensional advective systems

with and without dispersion,.and results are compared.

Frequency analyses are performed on input and output

concentrations and mass rates for a single event and for

all wet weather events during-the year of record.

The unifying concept of continuity is extended

to determine the receiving water response to waste inputs

from (1) wet weather urban sources, (2) dry weather

urban sources, and (3) upstream sources. The results

are presented in terms of minimum dissolved oxygen cumu-

lative frequency curves. Interpretations are based on

established stream standards for the study area: Des

Moines, Iowa and the Des Moines River. The wet weather

flow storage/treatment .facility for the receiving water

analysis was represented by a well-mixed constant volume

model. The receiving water response was found to be

sensitive to the length of the detention time in the

storage/treatment device, during periods of urban runoff.


xxiv













CHAPTER-I

INTRODUCTION



Historically, scientific concepts have been modes of

reasoning rather than absolute realities. In this sense,

models are tools of thinking to formulate hypotheses which

must be verified by observations (Vollenweider, 1975). The

nature of the models themselves depends largely on points of

view and objectives. Problems involving physical phenomena

seem to fit naturally into three classes (Domenico, 1972):

(1) those studied from a scientific point of

view in order to promote a better de-

scriptionof physical phenomena,

(2) those studied from an engineering point of

view to achieve useful purposes, such as

prediction by using the laws of science,

and

(3) problems studied from a management and

planning point of view to achieve some

degree of control over the state of the

system.

Scientific studies are based on the premise that all natural

phenomena and processes are interrelated and interactions are

governed by certain laws, thus involving numerous subsystems.








The research problem addressed in this work is the interaction

of urban stormwater runoff, control measures, and receiving

water response. The water quality cycle is a dynamic system

interacting with each phase of the hydrologic cycle. The

amount of pollution entering or leaving a water body is

determined by the quantity of flow and concentration of

pollutants in each of the hydrologic components of the physi-

cal system. The retention of pollutants in the water body

is not a sole function of the quantity and quality of

hydraulic flows, since it also depends upon the location of

the pollutants within the water body. The pollutants exist

in the water, bottom sediments, and the aquatic life.

The engineering problem is finding analytical

relationships between the variables characterizing the inflow

and outflow processes and parameters defining the state of

the system. In principle, these analytic relationships are

provided in all cases by solution of the complete equations

of energy, mass, momentum, and state (Eagleson, 1970).

However,.it is seldom possible to formulate all of these

equations accurately (Eagleson, 1970) because of

(1) inadequate knowledge of physical behavior,

(2) unknown system heterogeneities and

anisotropies,

(3) unknown temporal variabilities of system

parameters, and

(4) numerical approximations introduced for

computational economy, or to obtain a










solution where direct mathematical analysis

is impossible.

Whereas state variables (density, volume, temperature, etc.)

define the condition of system components, decision vari-

ables act to modify the state. For example, storage and

treatment may modify the concentration of pollutants in an

accelerated manner to prevent damaging shock loadings from

entering receiving bodies of water. The degree of control

defines the management problem.

Urban hydrology, including water quality processes,

is a combination of concepts and parameters that pertain

to scientific, engineering, and management points of view.

The essence of a rational approach to water quality control

in the urban environment is the development of a conceptual

model, based on scientific principles, which has the pre-

dictive capabilities necessary to the decision-making pro-

cess. The high cost of pollution control facilities, in

terms of energy utilization, land requirements, engineer-

ing manpower, and long-term financial burden, obligates

the planning agency to select an optimum strategy for area-

wide wastewater management. Such a process must focus on

a systematic procedure that identifies and defines (1)

the cause/effect relationships of the physical environ-

ment, (2) the efficiency of control alternatives, and (3)

the benefits to be derived from implementation of these

controls. The mathematical models applied need not









incorporate all phenomena but rather should be relevant

to the problem under consideration.

Two philosophies have emerged in recent years to

provide decision perspectives on urban stormwater pollu-

tion: (1) the micromodeling approach, and (2) the macro-

modeling approach. The more complex urban hydrologic

simulation models typify the micromodeling philosophy,

where short time increment mathematical models are applied

to a specific catchment subjected to a known or synthetic

rainfall history. Unquestionably, as the degree of detail

increases, so does the difficulty to generalize the results

obtained. This is particularly true of sewer routing models,

where hydraulic computations depend on diverse sewer cross-

sections. For example, 13 different sewer cross-sections

are represented in the U. S. EPA Storm Water Management

,Model (Huber et al., 1975). Thus, varying shapes and

dimensions from urban area to urban area will modify the

runoff hydrographs. These models are invaluable in iden-

tifying problem areas in sewer networks. The Storm Water

Management Model can predict the elements where surcharging

will occur and, as an option, enlarges the downstream

conduit by standard amounts until capacity exists to accept

the flow (.Heaney et al., 1975). However, experience at

the University of Florida in applying the detailed simula-

tion models to large metropolitan areas suggests that the

data needs alone may be quite substantial and the









discretization for the mathematical abstraction of the

physical drainage system is time consuming (Medina, 1974).

At the other end of the mathematical modeling

spectrum is the macroapproach. The methodology is typi-

fied by a simplified version of the physical process to

compute a scalar quantity which ranks pollution severity

and also allows study of the scalar's sensitivity to the

interrelationships involved (Young, 1976). The approach

focuses on an aggregated receiving water pollutograph,

specifically the ultimate BOD concentration versus time.

This pollutograph is assumed to represent water quality

downstream from an urban area as a flow-weighted average

of concentrations from sewage residuals, urban storm

washoff and upstream sources. As computed, it is indepen-

dent of hydrologic rainfall-runoff features, and varies

with the receiving water streamflow and the public treat-

ment works of the urban system. Decision rules are based

on calculation of scalar pollutograph maxima for ranking

the control needs of the various urban areas studied.

This approach has considerable merit because of its sim-

plicity of application. However, there are several

limitations:

(1) estimates for design streamflow, urban

runoff quality, removal efficiencies,

and hydraulic capacity of interceptor

sewers are largely dependent on the

analyst's judgment and experience;









(2) independence of the methodology to vari-

ations in volume of runoff and associated

pollutants excludes the possibility of

evaluating realistically the relative

efficiency of control measures and the

receiving water response to these mea-

sures; and

(3) a single scalar index precludes obtaining

any information about the frequency of

occurrence of events that result in dele-

terious water quality conditions in the

receiving waterways.

There is a real need for.an approach which is

intermediate between the micromodeling and macromodeling

philosophies, provides for continuous hydrologic simula-

tion, and recognizes that pollutant transport through the

various components of the urban environment is governed

by the same principle that describes transport in the

natural environment--conservation of mass. The justifica-

tion for continuous hydrologic simulation in dealing with

problems of urban storm runoff and urban storm runoff

quality is the probability of occurrence of events of

various magnitudes (Linsley and Crawford, 1974). Conse-

quently, the research objectives are

(1) to present a unified physical system

conceptualization;









(2) to develop a model based on the unifying

concept which is representative of the land

use, hydrology, and climatology of the

drainage area while providing an analytical

framework to

-generate stormwater runoff pollutant loads

and dry weather sanitary flow pollutant

loads,

-simulate the pollutant removal capabilities

of various storage/treatment alternatives,

-simulate the conveyance system, including

mixing in combined sewers of wet and dry

weather pollutants,

-mix the various pollutant inflow combina-

tions with pollutants already in the re-

ceiving water (from upstream sources), and

-predict the oxygen balance of the polluted

waters downstream from the waste sources,

subject to the constraints imposed by the

quantity and quality of the data base; and

(3) to examine, in particular, the response of

storage/treatment systems to variable wet

weather flows by a detailed mathematical

application of the continuity equation.

Scientific principles derived from hydrologic

theory, chemical reactor engineering and process dynamics,









unit operations of wastewater engineering, and the mathe-

matics of diffusion are applied to characterize urban

runoff quantity and quality, evaluate control measures,

and determine receiving water response. A major portion

of this work is devoted to storage/treatment systems

because of their importance in reducing pollutant loads

to the receiving waters from highly variable wet weather

flows. These'systems, as stated in the objectives, are

represented by mass transport models satisfying continuity.

Reservoir management models have been proposed using

inventory theory (Sobel, 1975), but these models are best

suited to formulate release policies which are a function*:

of the quantitative demand for water supply. It is diffi-

cult to foresee their application in a context where water

quality and interaction between the urban environment and

the receiving water are important.

Chapter II discusses the characterization of urban

wastewater discharges and polluted surface waters, and

presents a unified physical system conceptualization. An

oxygen demand parameter is selected to characterize the

strength of all waste sources in the system. The principle

of conservation of mass is shown to be equally applicable

to pipe segments of a sewer system, storage/treatment

devices, and receiving bodies of water.

Chapter III describes the study area, including

the receiving stream, and presents the necessary modeling









techniques. Typical pollutant loads are summarized and

pertinent water quality standards are defined. Data

sources are also identified.

Chapter IV presents a stochastic characterization

of urban runoff. Techniques of time series analysis are

discussed, as well as an approximate graphic procedure, to

define a wet weather event.

Chapter V addresses the response of storage/treat-

ment systems to variable inputs of wet weather flows, and

their associated pollutant concentrations and mass rates.

Storage/treatment units are modeled as well-mixed constant

volume systems, well-mixed variable volume systems, and

variable volume systems where nonideal mixing is repre-

sented by advection and dispersion. Numerical applications

are shown for each type of system for various residence

times, and statistical summaries of the results are pre-

sented.

Chapter VI introduces a statistical approach to

storage/treatment response for the case where the system

is assumed to be represented by a well-mixed constant

volume model. The results are compared to those obtained

from solution of the continuity equation in Chapter V. A

discussion of the concentration and mass flow rate equali-

zation provided by the well-mixed constant volume model

is included.


~





10



Chapter VII discusses the methodology adopted for

the receiving water analysis. The receiving water response

to waste input combinations is presented in the form of

minimum dissolved oxygen frequency curves. The interpre-

tation of these results is based on established water

quality standards.

Finally, Chapter VIII summarizes the conclusions

drawn from this work and the recommendations made for

further research.















CHAPTER II

A UNIFIED PHYSICAL SYSTEM CONCEPTUALIZATION



2.1 Characterization of Urban Wastewater Discharges
and Polluted Surface Waters


Urban areas represent only 3 percent of total land

use in the United .States (U. S. Dept. of Agriculture,

1968), yet they constitute the centers of most intense

human activity. Point discharges resulting from com-

mercial, industrial, and residential wastes generally

enter the receiving stream within relatively short dis-

tances of each other, and in some cases all such wastes

are processed by municipal facilities and discharged to

the water body at one location. Thus, these continuous

waste products are concentrated within a relatively small

volume of the receiving water. Intermittent precipitation

falling on urban areas becomes contaminated as it enters

and passes through or within the man-made environment.

The first quality degradation occurs when the rainwater

comes into contact with pollutants in the air. The

Cincinnati Water Research Laboratory of the Robert A.

Taft Sanitary Engineering Center started rainfall sampling









in August 1963 (Weibel et al., 1966). Constituents found

in the rainfall from August 1963 to December 1964 are

listed in Table 2-1. The concentrations represent average

values from 35 storms.

Next, the surface runoff passes over ground and

building surfaces, carrying suspended sediment from ero-

sion sites and dissolving other impurities. Table 2-2

summarizes typical ranges of pollutant concentrations

found in urban stormwater runoff (Field and Tafuri, 1973).

Finally, the stormwater runoff comes into contact with

(1) solid residues deposited from earlier storms through-

out the conveyance system and appurtenances, and (2) dry

weather flow (DWF) in combined sewer systems. This storm

runoff is well mixed with sanitary sewage under condi-

tions of turbulent flow in a combined sewer system, and

it eventually discharges to the receiving stream. Table

2-3 lists ranges of pollutant concentrations found to be

typical of combined sewer overflows (Field and Tafuri,

1973). From an examination of Tables 2-1, 2-2, and 2-3,

it can be verified that the degradation undergone by

urban stormwater passing through the surface runoff phase

of the hydrologic cycle (including the collection system)

can be several orders of magnitude greater than that

experienced by rainwater during the precipitation

phase.












Table 2-1

Constituents in Rainfall
(Weibel et al., 1966)




Constituent Concentration



Suspended solids, mg/l 13


COD, mg/l 16


Total N, mg/1 (N) 1.27


Inorg. N, mg/l (N) 0.69


Hydrolyzable P04,
mg/l (PO4) 0.24


Org. Chlorine*, mg/l 0.28


*From pesticides in the air.


---









Table 2-2

Characteristics of Urban Stormwater
(Field and Tafuri, 1973)


Constituent


Concentration Range


BOD5

COD

TSS

Total Solids

Volatile Total Solids

Settleable Solids

Organic N

NH3-N

Soluble PO4 (as PO4)

Total PO4 (as P04)

Chlorides

Oils

Phenols

Lead

Total Coliform

Fecal Coliform

Fecal Streptococci


: 1

5

2

450

12

0.5

0.1

0.1

0.1

0.1

2

0

0

0

200

55

200


700 mg/1

3,100 mg/l

11,300 mg/i

14,600 mg/1

1,600 mg/1

5,400 mg/l

16 mg/l

2.5 mg/l

10 mg/l

125 mg/l

25,000 mg/l*

110 mg/l

0.2 mg/l

1.9 mg/l

146x106/100 ml

112x106/100 ml

1.2x106/100 ml


*With highway deicing.





15




Table 2-3

Characteristics of Combined Sewer Overflows
(Field and Tafuri, 1973)


Constituent


Concentration Range


BOD5

TSS

Total Solids

Volatile Total Solids

pH

Settleable Solids

Organic N

NH3-N

Soluble PO4 (as P04)

Total Coliform

Fecal Coliform

Fecal Streptococci


30

20

150

15

4.9

2

1.5

0.1

0.1

20,000

20,000

20,000


- 600 mg/l

- 1,700 mg/l

- 2,300 mg/l

- 820 mg/l

- 8.7

- 1,550 mg/l

- 33.1 mg/l

- 12.5 mg/l

- 6.2 mg/1

- 90x106/100 ml

- 17x106/100 ml

- 2x106/100 ml










The various constituents listed so far represent

a large and diverse number of chemical, physical, and

bacteriological indicators of water quality. The most

common parameters measured are listed in Table 2-4 under

their appropriate categories. The bacteriological pro-

cedures are designed to detect potential health hazards

from contamination of the water with human or animal

feces. The sampling technique, frequency of sampling, and

method of preservation should be tailored to the indicators

chosen for measurement. Field observations are extremely

valuable for verification of mathematical models. Greater

precision may be obtained in the laboratory, but if the

sample is unrepresentative, greater accuracy will be

achieved by in situ procedures.

The wastewater constituents that affect the dis-

tribution of dissolved oxygen (D.O.)in a natural water

system are well documented. The oxygen demand of sewage,

sewage treatment plant effluent, polluted stormwater run-

off or industrial wastes is exerted by three types of

materials (American Public Health Association, 1971):

1. carbonaceous organic matter oxidized by
heterotrophic bacteria for energy and cell
synthesis;

2. organic nitrogen compounds hydrolyzed into
ammonia-nitrogen (NH3-N), then oxidized by
autotrophic bacteria (Nitrosomonas europaea)
to nitrite-nitrogen (NO2-N), further oxidized











Table 2-4

Pollution and Contamination Indices




Physical Parameters:

Temperature
Turbidity
Color


Chemical Parameters:

Oxygen Demand

Biochemical Oxygen Demand (BOD)
Chemical Oxygen Demand (COD)
Total Organic Carbon (TOC)

Nitrogen Compounds

Organic
Nitrite
Nitrate

Phosphorus Compounds

Ortho Phosphorus
Poly Phosphates

Total Solids

Dissolved
Suspended
Volatile and Fixed
Settleable

Chlorides
Sulfates
pH
Alkalinity
Hardness










Table 2-4 continued




Chemical Parameters continued:

Heavy Metals

Lead
Copper
Zinc
Chromium
Mercury

Biological Parameters:

Plankton
Periphyton
Macrophyton
Macroinvertebrates
Fish Bioassays


Bacteriological Parameters:

Total Coliform Count
Fecal Coliform
Fecal Streptococci
Total Plate Count










by Nitrobacter winogradskyi to nitrate-nitrogen
(NO3-N); and

3. certain chemical reducing compounds (ferrous
iron, sulfite, and sulfide) which will react
with molecularly dissolved oxygen.

This oxygen demand is the response of aquatic biota

to an adequate food supply and is commonly referred to as

the biochemical oxygen demand (BOD). The laboratory BOD

technique is an empirical bioassay-type procedure: the

D.O.consumed by microbial life in an incubated bottle is

measured with respect to time at a specified temperature.

The actual environmental conditions of temperature changes,

biological population, water movement, sunlight, and zones

of aerobic and anaerobic processes cannot be faithfully

reproduced in the laboratory. Thus, the "bottled" system,

on a kinetic comparison, is completely accurate in repre-

senting itself but may be relatively unreliable as a

representation of the source from which the sample was

taken. The basic assumption that consumption of .D.O. is an

absolute and complete parameter of biological decomposition

in the BOD bottle constitutes a simplification of complex

interactions (Liptak, 1974).

Other laboratory methods have been developed to

measure the oxygen.demand exerted by organic matter. The

chemical oxygen demand (COD) and total organic carbon

(TOC) tests are more precise chemical methods, but the









analytical results are not accurate if the organic ma-

terial measured is not equivalent to the organic matter

actually being utilized by the microorganisms in the

stream. Much can be done to improve the accuracy of the

BOD test by using dilution water from the receiving stream,

thus introducing a natural "seed" of diverse organisms

into the bottle system. With all of its limitations, the

BOD procedure is still considered to be the best method

for evaluating the effect of waste inputs on the oxygen

balance of a stream (Nemerow, 1974).


2.2 A Unifying Conceptualization of the Physical System


The principle of conservation of mass may be

applied universally throughout the urban and natural

environments to describe the transport of pollutants.

Figure 2-1 represents a generalized component of the

physical system, which may characterize (1) a pipe

segment of the sewer system, (2) a storage/treatment

device, or (3) a reach of the receiving body of water.

Essentially, all of these subsystems may be approximated

by the one-dimensional version of the convective-dispersion

equation,


ac 3 E3c UC] + ES
at 3x ax


(2.1)


































ss^


bC b Es 1 + U
-- E- --UC -/ S
bt Zx






Figure 2-1. A Generalized Component of the Physical
System.





22


where C = concentration of water quality parameter
(pollutant), M/L3,

t = time, T,

-E0- = mass flux due to longitudinal dispersion
ax along the flow axis, the x direction,
M/L2T,

UC = mass flux due to advectionn by the fluid con-
taining the mass of pollutant, M/L2T,

S = sources or sinks of the substance C,
M/L3T,

U = flow velocity, L/T, and

E = longitudinal dispersion coefficient, L2/T.


The source/sink term accounts for biochemical processes

(e.g., decay, photosynthesis, algal respiration), bound-

ary losses such as stream benthic deposits, and boundary

gains (e.g., reaeration, and point or distributed waste

discharges). Assuming that the longitudinal dispersion

coefficient and the advective velocity are constant along

the flow axis, equation (2.1) may be expanded for the

generalized component in Figure 2-1 to


C_ E C U
at ax2 ax



KC + (C C) (2.2)



where K = first-order reaction rate coefficient,
1/T,









q1 = influent fluid flow rate per unit width,
L2/T,

Cl = concentration of water quality parameter
in the inflow, M/L3, and

A = wetted cross-sectional area in the com-
ponent, L2.


In equation (2.2) the influent fluid flow rate per unit

width, influent concentration, and the wetted cross-

sectional area may all be variable functions of time.

For a nondispersive pipe segment, equation (2.2)

may be reduced to the form for simple advection.



C + U -C + KC = 0 (2.3)
at 9x


The solution to equation (2.3) is given by



C(x,t) = C (x-Ut, t )exp[-Kt] (2.4)


where Cl(x-Ut, t -) = initial concentration at a
time x/U earlier and a dis-
tance Ut upstream, M/L3.


Equation (2.4) states that the reactive, nondispersive

advective system has an instantaneous response which

travels downstream at a velocity U, and the magnitude

of the response decreases exponentially because of

first-order decay. Chemical engineers refer to a system

governed by equation (2.3) as a plug flow reactor. If








there is no decay, or if it can be assumed that it is

negligible because the travel time in the system is very

short (a large U), then equation (2.4) reduces to


C(x,t) = C1(x Ut, t 2) (2.5)


This is a reasonable assumption to make for most sewer

systems when the study objectives are not design-oriented.

Extensive studies have been conducted by chemical

engineers concerning the kinetic analysis, flow charac-

teristics, and dispersion characteristics of chemical

process reactors. Danckwerts (1953) studied the residence-

time distribution of continuous-flow systems. The basic

differential equation for a continuous-flow reactor is

given as


E a2C U B-C KC = 0 (2.6)
x2 ax


for a first-order reaction. Equation (2.6) is obtained

from equation (2.2) for steady-state conditions (DC/3t =

0). Wehner and Wilhelm (1956) solved equation (2.6)

analytically. Their solution has been recommended by

Thirumurthi (1969) for the design of large waste stabili-

zation ponds, aerated lagoons, and activated sludge aera-

tion tanks.

For completely mixed storage/treatment systems

(3C/ax = 0), equation (2.1) reduces to








aC
=t E (2.7)


which may be rewritten, for the sources and sinks of the

generalized component in Figure 2-1, as the ordinary dif-

ferential equation


dC
V d 1t. 1 2C KC V (2.8)


where Q1 = influent fluid flow rate, L 3/T,

3
Q2 = outflow rate, L3/T, and

V = volume of the fluid mass in the-component,
L3.


Solutions to equation (2.8) are presented in Chapter V

for the constant volume and variable volume cases, for

time-varying influent flow rates and concentrations. In

chemical engineering texts (e.g.,-Cooper and Jeffreys,

1971), the design equation for a continuous-flow stirred

tank reactor is given as



C 1 (2.9)
CO 1 + KtD

3
where- C = constant influent concentration, M/L ,
o and


tD = detention time in the reactor, T.
D









This equation is used by Eckenfelder (1966) in designing

aerated lagoons for industrial water pollution control.

It should be noted that equation (2.9) predicts the

steady-state value of the general solution to equation

(2.8) for a constant volume system. A methodology is

also presented in Chapter V to obtain solutions to equa-

tion (2.1) for the more difficult case of-a dispersive

variable volume system.

A receiving body of water, such as a.river reach

or an estuary, is goverened by equation (2.1). Whereas

C represented the BOD concentration of wastewaters in

the urban environment, equation (2.1) is usually solved

to obtain the dissolved oxygen concentration in the

natural system. The BOD inputs from the urban area be-

come oxygen sinks, along with benthal demand, respira-

tion by aquatic plants, and others. An oxygen concen-

tration gradient is developed between the atmosphere

and the waterway, leading to reaeration as a dissolved

oxygen source. This process is supplemented by algal

photosynthesis. A steady-state analysis of equation

(2.1) is presented in Chapter VII.

As noted in Figure 2-1, all of the systems

described by the generalized component are essentially

characterized by

(1) a flow velocity U,

(2) a reaction rate coefficient K,









(3) a residence time tD, and

(4) a longitudinal dispersion coefficient E,

all of which are a function of the system geometry. (vol-

ume V, cross-sectional area A, length x). Velocities in

the sewer systems tend to be much higher than in either

the storage/treatment devices or the receiving waters.

In a receiving stream reach, lake or bay the detention

time is much longer than in the other systems due to the

large volume of the fluid mass relative to the wastewater

inflows. From performance-time curves of activated sludge

units, an overall BOD first-order decay coefficient of

0.2 per hour (4.8/day) may be obtained for the biologi-

cal waste treatment process (Fair, Geyer and Okun, 1968).

For tidal rivers and estuaries a first-order decay rate

for BOD not much higher than 0.02 per hour (0.5/day)

can be expected (Hydroscience, 1971). In lakes, K may

vary from 0.01/day for the dry season to 0.02/day for

the wet season (Huber et al., 1976), and the detention

time is on the order of months. By contrast, a deten-

tion time of 10 to 11 hours is common design practice

for conventional activated sludge plants (American

Society of Civil Engineers, 1959). Estimates of K, tD'

and the product KtD are summarized for various systems

.in Table 2-5. The reaction rate group KtD provides a

rough idea of treatment potential.









Table 2-5

Treatment Potential of Various Components
of the Physical System


Selected Decay Selected Detention
Coefficient Time, tD KtD
Component K at 200


Pipe Segmenta
of Sewer System 0.005/hour 0.56 hours 0.003

Activated-Sluge
Plant for Dry
Weather Flow 0.2/hr 11 hours 2.20

Waste Stabili-
zation Pondb
for Raw Sewage 0.061/day 39.8 days 2.40

Wet Weather
Flow Storage/
Treatment
System 0.005/hour 24 hours 0.12

Kissimmee
River 0.3/day 9 days 2.70

Lake Tohod 0.015/day 5 months 2.25
(150 days)

Tidal River
or Estuary 0.5/day 5 to 50 days 2.5 to 25.0


aSegment length 10,000 feet (3 km) with mean velocity of
5 ft/sec (1.5 m/sec).
bAverage of five ponds in Fayette, Missouri (Thirumurthi,
1969).

CKissimmee River, Florida for a length of 90 (144 km)
from Huber et al., 1976; and Hydroscience, 1971.
dLake Toho, Florida, decay rate for total phosphorus,
from Huber et al., 1976.









Comparisons based on the reaction rate group

KtD in a dispersive system must be qualified. For ex-

ample, the longitudinal dispersion coefficient in the

aeration tank of an activated sludge process may be ex-

pected to be around 1.6 ft /sec (Murphy and Timpany,

1967). For a tidal river or estuary, about 300 ft /sec

represents the lower limit of the longitudinal dispersion

coefficient. The differences in. mass flux due to advec-

tion (U) and dispersion (E) will vary the system response

considerably. Additional discussion of the importance

of these parameters is presented in Chapter V. Further-

more, bays and lakes may be treated in a detailed manner

by a multi-dimensional form of equation (2.1), namely,

a 2-dimensional or .3-dimens.ional expression of the con-

vective diffusion equation. Crude approximations may

be obtained by simply applying equation (2.8), which

assumes completely mixed systems,













CHAPTER III

DESCRIPTION OF THE STUDY AREA AND
NECESSARY MODELING TECHNIQUES



3.1 The Need for a Study Area

Pitt and Field (1974) applied available informa-

tion on urban runoff pollution to a hypothetical test area,

subjected to a worst-case storm event, to demonstrate

potential problems and their solutions. However, it has

already been established.that there is a need for contin-

uous hydrologic simulation to assess the frequency with

which runoff events cause adverse effects in the receiving

waters. It would be quite difficult to generate a realis-

tic pollutant distribution for a long sequence of synthetic

flows. There are other important reasons that justify

selection of a real study area. The only way to estab-

lish the necessary validity which renders a mathematical

model of water quality useful for planning purposes is

to conduct verification procedures and calibrate against

field-measured data (Hydroscience, 1971). Furthermore,

when evaluating the effectiveness of proposed control mea-

sures it is important to base comparisons against existing

conditions in the study area.









3.2 Des Moines, Iowa

The city of Des Moines, Iowa is located at the

confluence of the Des Moines River and the Raccoon River

as shown in Figure 3-1. Within its limits are approximately

200,000 people out of a total of 288,000 for the metro-

politan area. The mean annual precipitation is about 31

inches (787 mm), approximately equal to the State of Iowa

average and the United States average (Waite, 1974).

The urban area covers 49,000 acres (19,830 ha) of land

which has gently rolling terrain. Most of the area,

45,000 acres, is served by separate sewers, while 4,000

acres are served by combined sewers.

Selection of the study area was based primarily

on data availability. Davis and Borchardt, of Henningson,

Durham & Richardson, Inc., Omaha, Nebraska, conducted an

extensive sampling program of combined sewer overflows,

stormwater discharges, and surface waters in the Des Moines,

Iowa Metropolitan Area for the U. S. Environmental Pro-

tection Agency. The objective was a combined sewer

overflow abatement plan for the metropolitan area. The

sampling program was conducted from March 1968 to October

1969. Other considerations revolved around the fact that

Des Moines, Iowa is somewhat typical of many urban centers

throughout the country.

(1) it has a medium-sized population;

























































VICINITY MAP


Figure 3-1. Map of Des Moines Area (Davis and Borchardt,
1974).









(2) its domestic and industrial dry weather

flows receive secondary treatment;

(3) its wastewaters are discharged into a non-

tidal receiving stream; and

(4) the urban area receives a mean annual pre-

cipitation equal to the national average.

The mean annual temperature.is 50C (100C), vary-

ing from an average of 210F (-6C) in January to an average

of 750F (24C) in July.


3.3 ..Pollutant Loads

Annual pollutant unit loads upstream from the city

are summarized in Table 3-1, as determined by Davis and

Borchardt (1974). From data gathered by wastewater treat-

ment plant personnel during the period August to October,

1969, the average daily flow was estimated at 35.3 mgd

(133,600 cu m/day) with an organic load from domestic

and industrial sources of 85,800 pounds of BOD (43,450 kg

BOD per day). The high-rate trickling filter facility

achieved 84 to 85 percent BOD removal, producing an

effluent BOD concentration of 49 mg/l (Office of Water

Planning and Standards, 1974). A simplified profile of

the DWF treatment facility is shown in Figure 3-2. The

estimated annual loading from the urban area's separate

and combined sewer systems is presented in Table 3-2.








Table 3-1

Pollutant Unit Loads for Drainage Area*
Above Des Moines, Iowa
(Davis and Borchardt, 1974)


Des Moines Raccoon
River River Total

Drainage Area, acres 3,738,000 2,202,000 5,940,000
(ha) (1,512,769) (891,149) (2,403,918)
Unit Average Annual
Runoff, acre-ft/acre 0.42 0.40 0.41
(ha-m/ha) (0.13) (0.12) (0.12)
Unit BOD, Ibs/acre 13.40 6.93 11.01
(kg/ha) (15.02) (7.77) (12.34)
Unit NO3, Ibs/acre 3.75 3.74 3.75
(kg/ha) (4.20) (4.19) (4.20)
Unit P 04, lbs/acre 0.54 0.42 0.50
(kg/ha) (0.61) (0.47) (0.56)


*On an annual basis.























C>
cn










;2
C)





co


0

--










0
0)









U3


'C


CQ


OCO O-
COC OC


r-00 UtD
Co co) C











C0 o r
O'oi Or-.

cO-- o r
.0 co 0 C








0 00
Din oCn
10 CO f

oC- I.oCO

COD CMC




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Taking the total upstream drainage area for the

Raccoon and Des Moines Rivers, the pollutant contributions

are 65,225,000 pounds of BOD (29,586,000 kg); 22,222,000

pounds of NO3 (10,080,000 kg); and 2,940,000 pounds of

PO4 (1,334,000 kg). The urban area loadings (when added

to upstream values) represent, respectively, 15 percent,

3 percent and 51 percent of the total BOD, NO3, and PO4

mass loadings to the Des Moines River below the metropoli-

tan area. The Davis and Borchardt estimates, made from

river sampling data taken below Des Moines, indicate

the following average annual river loadings: 70,000,000

pounds of BOD (31,851,466 kg); 25,400,000 pounds of NO3

(11,521,250 kg), and 7,950,000 pounds of PO4 (3,606,059

kg). These figures reveal that (1) 6,610,000 pounds of

BOD (2,998,246 kg) are "lost" in transit through the urban

section of the stream, and (2) by contrast -2,474,360

pounds of NO3 (1,122,351 kg) and 1,917,400 pounds of PO4

(869,718 kg) are gained in addition to the measured urban

sources.

The authors of the report offer some explanations.

The 'sometimes' decreases in organic
load through the metro area may be attribu-
table to treatment realized in the low
head impoundments at Scott and Center
Streets on the Des Moines River and just
below Fleur Drive on the Raccoon. To some
extent these impoundments may be serving
as intermittent sedimentation and stabili-
zation units.
All BOD data, including those used
from the two other studies, were obtained









from unfiltered samples. However, since
the analytical technique was the same for
all samples, the relative magnitude of the
data should not be affected.
There has been some speculation that
treated wastewater effluents may exert an
antagonistic or retardant effect on the
BOD exertion rate of the receiving stream.
If true, this may be due to surfactants or
to the expected lower exertion rate of the
effluent. In this regard, the decreased
BOD in 4 or 5 measurements between R-5
and R-6 is of interest. Increased loads
between the summation of R-4 and R-9 ver-
sus R-5 are likely due to raw and combined
sewage bypassing the intervening area.
Another, and probably the most prac-
tical, possibility for the discrepancies
is the fact that the data are biological
and biochemical in nature and such data
do not always provide predictable compara-
tive summations. (p. 108)

The river sampling stations (R-4, R-5, R-6 and

R-9) are shown in Figure 3-3. It is possible that inter-

vening creeks, such as Beaver Creek which carries nutrient

loads of 2,860,000 pounds of NO3 per year (1,297,274 kg

per year) and 390,000 pounds of PO4 per year (176,900 kg

per year), may answer observed differences in the nitrate

loads. However, the phosphate totals remain unbalanced

and the cause unresolved.

Combined sewer overflows were monitored at five

locations and stormwater discharges at three locations.

The average BOD concentration of stormwater was reported

as 53 mg/l, while the average BOD concentration in com-

bined sewer overflows was 72 mg/l.









NNEo 0ST" No.- N-


NN.2 / NNo 1.








N I '^N.
o o iNo.6
No.?


Na4Na0



oI I












So zor ws Stoa e University
Sngineearng Resotc atotu


i State Hyionic Lob.ratory
Thls ProJec
USGS Streamidow Sttlon

Figure 3-3. Location Map: River Sampling Points (Davis
and Borchardt, 1974).
S-^^ ''^^ S? 063 ^^^ ^
^^^_;L ?^ ^ i--^--
-^rr ,-^ c'











and Borchardt, 1974).


A1









3.4 The Receiving Stream


From Figure 3-3, it is clear that although the

Raccoon River receives urban stormwater discharges from

parts of the urban area, the ultimate recipient is the.

Des Moines River. All stormwater discharges, combined

sewer overflows, and wastewater treatment plant effluent

are assumed to enter the Des Moines River at its con-

fluence with the Raccoon River. The Des Moines River

stretches for 200 miles (322 km) from the City of Des

Moines to its junction with the Mississippi River and, in

general, the river is wide and swift with occasional deep

holes and a broad flood plain. According to.. the State

Hygienic Laboratory (1974) bottom material is composed of

silt deposits, sand, gravel and rubble providing numerous

habitats for fish and other aquatic life. Recreational

activities such as fishing and boating are quite heavy.

The entire reach is classified as warm water "B" stream

by the Iowa Water Quality Standards, such that the absolute

minimum dissolved oxygen level specified is 4.0 mg/l. The

Iowa Standards also require a minimum of 5.0 mg/l during

at least 16 hours per day (State Hygienic Laboratory,

1970).

For the heavy precipitation months of June, July.

and August, 1968, Da.vis and Borchardt reported the follow-

ing nutrient concentrations at a point approximately 5.5


\1








miles (9.0 km) downstream from the confluence of the Raccoon

and Des Moines Rivers:

(1) total organic nitrogen ranged from 1.6

to 3.7 mg/1,

(2) nitrate nitrogen ranged from 0.2 to 7.8

mg/l, averaging 3 to 4 mg/1, and

(3) orthophosphate (0-PO4) ranged from 0.6 to

1.8 mg/l, averaging slightly over 1.0 mg/l.

Davis and Borchardt also observed high algal densities in

both the Des Moines and Raccoon Rivers, and state that

nutrient concentrations are almost always present at levels re-

ported by Sawyer (1966) to be sufficient for nuisance algal

growths: 0.3 mg/l for inorganic nitrogen (NH3, NO2, NO3)

and 0.015 mg/1 of inorganic phosphorus.


3.5 An Abstraction of the Physical System

To study the interaction of urban runoff,.control

measures, and receiving water response, an analytic frame-

work is sought that describes the key elements of the physi-

cal system. Conceptual models are normally expressed in

mathematical terms (Vollenweider, 1975). A conceptual

model is derived from an abstraction of the physical system,

and such an image is presented in Figure 3-4.

The urban community served by a separate sewer

system will convey stormwater runoff and municipal sewage

through conduits which are not connected together. The













SEPARATE SEWER SOURCE









URBAN RUNOFF MUNICIPAL WASTEWATER
------------------------------------tL______

COMBINED SEWER SOURCE









URBAN RUNOFF -l Ks F: MUNICIPAL WASTEWATER


UPSTREAM REWCEIVINr WATER
SOURCES
Q, BOD, y FLOW


Figure 3-4. An Abstraction of the Physical System.









BOD concentration of the storm sewer runoff is mixed with

the dry weather flow (DWF) and accumulated sewer solids.

An interceptor carries the sanitary design flow to the

municipal sewage treatment plant. Since complete mixing

is assumed, the BOD concentrations of the combined sewer

overflow and the flow intercepted for treatment by the DWF

plant are identical. The combined sewer overflow and the

separate storm sewer flow are both processed through a

central wet weather flow (WWF) storage/treatment facility

before discharge to the receiving body of water.

An examination of Figure 3-4 from top to bottom

reveals three distinct phases of the water quality cycle

within the urban environment. At the top level is the

pollutant build-up phase, represented by surface runoff

generated within the separate and combined sewer areas as

well as industrial and domestic wastewater. Estimation

of DWF sanitary loads is a relatively simple task. The

design flow for a sanitary wastewater treatment plant is

based on water consumption within the urban area, and the

organic waste load is a function of population density and

data obtained from industrial and commercial establishments.

However, the estimation of surface runoff quantity and

quality is more complex.

Urban runoff is a direct result of precipitation

over an urban area. However, due to temporal and spatial

variabilities associated with atmospheric motions, all









hydrologic processes are more or less stochastic (Chow,

1964). If a deterministic system receives a random input,

output from the system will also be random. A single time

history representing a random phenomenon is referred to as

a sample record when observed over a finite time interval

(Bendat and Piersol, 1971)., By selecting a sample record

of point precipitation, a random element in the hydrologic

process is eliminated: chance of occurrence. The precipi-

tation time series may then be fed into an urban hydrologic

simulation model ito generate the urban runoff series. The

spacing and sizing of individual events in the sequence,

however, is probabilistic (Eagleson, 1970). Therefore,

a combination of probabilistic and deterministic methods

must be used. At this stage, analysis of time series, a

classical statistical technique, is applied to define a

minimum interevent time and-group runoff occurrences into

independent storm events. A detailed presentation is made

in Chapter IV.

The second phase in the urban water quality cycle

is at the middle level in Figure 3-4, represented by the.

man-made conveyance and pollutant control systems. Since

travel times in the sewer system are usually relatively

short, it has been assumed that no pollutant decay occurs

in the conduits. The BOD concentration of the DWF treat-

ment plant effluent is given by









[BODf DWFSEP + BOD DWFCMB] (l-Rd)
BOD -d (3.1)
d DWFSEP + DWFCMB



where BODf = BOD concentration of municipal sewage,
mg/l,

BOD = mixed BOD concentration in the combined
c sewer, mg/l,

DWFSEP = DWF contribution from separate sewer
area, cfs,

DWFCMB = DWF contribution from combined sewer
area, cfs, and

Rd = fraction removal of BOD achieved by the
DWF treatment facility.

Treatment of the DWF facility is accomplished

S in a single time step. That is, a mass of pollutant

entering the DWF plant at a particular time step is treated

and released during that time step, with no effects extend-

ing beyond the discrete time interval. The effects of

storage/treatment in the WWF facility are dynamic and

extend beyond the time step length, depending on the de-

* tention time primarily. The BOD concentration of the

input to the WWF unit is given by



BOD Q + BOD Q
BODsc = s Q + BO (3.2)
sc QS + Q


where BOD = mixed BOD concentration of urban runoff
s from the separate storm sewer and com-
bined sewer flows, mg/l,









BODs = BO concentration of urban stormwater
runoff, mg/l,

Qs = urban runoff carried by the separate
storm sewer, cfs, and

Qc = combined sewer flow below the inter-
ceptor, and to the WWF storage/treatment
units, cfs.


To characterize the response of the WWF storage/

treatment system, mass transport models derived from the

concepts of continuity presented in Chapter II are applied

to the wet weather quantity and quality inputs. The

complete mathematical analysis is presented in Chapter V.

Frequency analyses are performed on concentration and

mass rate inputs, and outputs from selected models of the

storage/treatment system.

At the bottom level of Figure 3-4 is the third

phase of the water quality cycle in the urban environment:

the natural pollutant control system provided by the waste

assimilation capacity of the receiving body of water. An

analogy has been drawn in Chapter II between the man-made

storage/treatment system discussed above and the receiving

water. Both systems are governed by the same principles

of conservation of mass. The mass of pollutant entering

either body is subjected to

(1) mixing with the impurities already present

in the system within a specified volume;

(2) first-order decay of nonconservative sub-

stances;









(3) mass flux due to longitudinal dispersion

along the flow axis; and

(4) mass flux due to advection along the flow

axis by the fluid containing the pollutant.

The concentration of the combined BOD inputs in the re-

ceiving water is given by



BOD Q + BOdQd + BOD Q
BODm = Qu + Qd + Q (3.3)



where BOD = mixed BOD concentration in receiving water,
Smg/1,

BOD = mixed BOD concentration from sources up-
u stream of urban area, mg/l,

BODd = BOD concentration of dry weather flow
treatment plant effluent, mg/l,

BOD = BOD concentration of WWF storage/treatment
facility effluent, mg/l,

Q = upstream flow, cfs,

Qd = DWF treated effluent, cfs, and
Q = WWF storage/treatment effluent, cfs.

The initial conditions of BOD in the river are

defined by equation (3.3), and the hypothetical impact on

the oxygen balance of the receiving stream is estimated

using simplified mathematical modeling approaches. Criti-

cal D.O.deficits are computed as a function of several

stream parameters: temperature, flow, oxygen concentration,









deoxygenation and reaeration rates, BOD concentrations,

velocity, and the longitudinal dispersion coefficient.

Minimum DO's are calculated subsequently and frequency

analyses are performed.


3.6 Technique for Calculation of Urban Runoff Quantity
and Quality


This section briefly describes the methods used

to generate storm runoff and pollutant concentrations.

The Hydrologic Engineering Center model, STORM, is

utilized to obtain hydrographs and pollutographs for

Des Moines for the year 1968 on an hourly time step.


Urban Runoff Quantity


STORM computes urban runoff as a function of land

use and rainfall/snowmelt losses (Hydrologic Engineering

Center, 1975.).


AR = CR (P f (3.4)
u U U u


where AR = urban area runoff, in/hr,
u

CR = composite runoff coefficient dependent
u on urban land use,


P = hourly rainfall/snowmelt in inches over
u the urban area, and









f = available urban depression storage,
in.


A maximum depression storage of a hundredth of

an inch (0.25 mm) is assumed for Des Moines, Iowa. The

hourly urban runoff values, expressed in cfs, are saved

in a file for later recall by the simplified mathematical

model.


Urban Runoff Quality


The basic water quality parameters modeled by

STORM are suspended and settleable solids, BOD, total

nitrogen (N), and total phosphate (P04). It is important.

to emphasize that the BOD values are expressed in terms of

the standard BOD5 test: incubation at a temperature of

200C for five days. These values represent most of the

carbonaceous oxygen demand exerted by organic matter

present in the urban runoff, and include the BOD contri-

bution from suspended and settleable solids. The BOD

loading rates generated by STORM are based on land use

and other factors such as number of dry days without

runoff since the last storm and the street sweeping.intervals.



3.7 Separate, Combined and Dry Weather Loading

All of the following methodology can be used,

regardless of the technique employed.to generate storm









runoff and quality, as long as these values pertain to the

entire area being modeled.

Separate Flows and Loadings


Apportionment of the total flow and BOD loading is

made on the basis of the relative area served by separate

and combined sewers. Runoff from separate sewered areas

is thus (refer to Figure 3-4)


A
Q Qt (3.5)
s At t


where Qs = stormwater flows from separate sewered areas,
cfs,

As = area served by separate sewers, acres,


Qt = total (storm plus combined) urban runoff,
cfs, and

At = total area of catchment, acres.


The concentration of BOD in separate storm sewers,

BODs, is simply the hourly value computed by STORM, BODt

.(mg/l), for the total urban runoff.


Dry Weather Flow and Loadings


Dry weather flow and BOD loadings are assumed known

from data on point sources in the area. Thus, Qd represents









the flow (cfs) into receiving waters of treated wastewater,

and BODd represents the BOD concentration at 680F (200C)

for five days, mg/l. The amount of treatment can be

varied in the analysis.


Combined Flows and Loadings


Dry weather flow is assumed to cause only a negli-.

gible increase in flow in a combined sewer during a storm

event. However, two factors related to DWF may increase

significantly the BOD concentration of the combined sewer

storm water.


(1) The BOD strength of the municipal sewage with

which it mixes, and

(2) the BOD exerted by sediment accumulation in

each section of the sewer under DWF conditions

which is subject to the "first flush" effect

induced by the initial runoff.


Data collected at various combined sewer overflow

sampling stations in Des Moines, Iowa, support the first

flush theory (Davis and Borchardt, 1974). BOD and total

suspended solids (TSS) concentrations decreased with time

with little dr no relation to the flow pattern. Further-

more, pollutographs (BOD vs. time and TSS vs. time) for

these stations seem to indicate that the flushing occurs










mostly during the first hour of runoff generated by the

storm event. A model based on shear stress considerations

was developed to predict dry weather flow deposition for

30 combined sewer collection systems in Dorchester,

Massachusetts (Pisano, 1976). The overall percentage of

DWF suspended solids.loadings depositing daily in the sys-

tems was estimated at 10.3 percent.

To incorporate the first flush effect, it is assumed

that the hourly in-sewer sediment build-up is constant over

consecutive dry weather hours (DWH). This assumption is

reasonable although particle size and specific gravity,

depth of flow and the slope of the conduit are important

factors affecting deposition. The computation of combined

sewer flows, as with separate sewer flows, is accomplished

by apportionment of the total hourly flow predicted by

the urban hydrologic model on the basis of relative area

served.

A
Qc Qt (3.6)



where A = area served by combined sewers, acres, and
C

Qc = combined sewer overflow rate, cfs.


The BOD load contributed from accumulation of

sewer solids during consecutive DWH is lumped into









the first hour of.a runoff sequence, .and is estimated

by

FF = FFLBS DWH (3.7)


where FF = first flush BOD load, Ibs,


FFLBS = first flush factor, Ibs/DWH, and

OWH = number of dry weather hours preceding
each runoff event.


The first flush factor is site-dependent and must

be determined from (1) the total flow generated by the

combined sewer area, including the DWF contribution, for

all periods of urban runoff during the year; (2) the total

number of DWH during the year; and (3) the average field

measured BOD concentration in the combined sewer overflows.

For Des Moines, Iowa, it was estimated from digital computer

simulation that about 14 percent of the average BOD load

in combined sewer overflows may be attributed to first

flush effects. Thus, the first flush factor, in pounds of

BOD per DWH, may be obtained from


0.14 BODCM QCOM cl
FFLBS = TOWH (3.8)


where BODCM = average field measured BOD concentration
in combined sewer overflows, mg/l,









QCOM = total flow generated by the combined sewer
area, including DWF contribution, for all
periods of urban runoff, cf/yr,

TDWH = total number of DWH in the year, DWH/yr,
and

c = factor to convert mg/l to Ibs/cf

= 0.000062435.

The total flow generated by the combined sewer area

is obtained from

r
QCOM = E (Q + DWFCMB) .(3.9)
i=1


where i = 1, 2, 3, ..., r, and

r = total number of hourly runoff occurrences during
the year.

Finally, the mixed BOD concentration in the combined

sewer, BOD (mg/1), is computed by the following expression:



BOD ODt Qc + BOD' Qd (Ac/At + FF c2
cBOD BQc + d (Ac/At)


(3.10)


where c2 = factor to convert FF from Ib/hr to cfs
mg/l = 4.45.









The first flush factor, FFLBS, is computed in

the next section from available data sources. Further

research is necessary to develop a mathematical relation-

ship that predicts the first flush BOD load, independent

of calibration to measured data, with a reasonable degree

of accuracy.


3.8 Data Sources


Numerous agencies provided the information required

to meet the substantial data needs for mathematical model-

ing of urban runoff, storage/treatment systems, and receiv-

ing water effects. All land use classifications, population

density figures, area, curb lengths, etc., were obtained

from data prepared by the American Public Works Associa-

tion for specific use in STORM simulations. Precipitation

records for 1968, collected at the Des Moines, Iowa

Municipal Airport, were obtained from the National Weather

Records Center at Asheville, North Carolina. Receiving

water upstream flows, temperatures, BOD and DO levels

were taken from the Davis and Borchardt report; however,

supportive material which provided considerable insight

on the characteristics of the Des Moines River was obtained

from the State of Iowa Department of Environmental Quality.

The total hourly urban runoff (Qt) and its BOD

concentration (BODt) are obtained from the STORM simulation









of Des Moines, Iowa. BODs, Qs, BODd, Qd' BODc, and

Q are computed from input data and the appropriate mix-
ing equations presented earlier. BODw is obtained from

the mathematical models of the storage/treatment process,

discussed in Chapter V. The first flush factor is ob-

tained from calibration of the digital computer model to

measured data.

(1) From rainfall records,

TDWH = 6,993 DWH/yr

(2) From equation (2.10),

QCOM =156,530,672 cf/yr

(3) From Davis and Borchardt (1974),

BODCM = 72 mg/l

(4) From digital computer simulation, disre-

garding in-sewer solids build-up, the

average BOD concentration in the combined

sewers = 61.92 mg/l

From the observed difference between items (3)

and (4) above,

BOD difference = 10.08 mg/l


= 0.0006293 Ibs/cf









BOD load = (0.0006293 lbs/cf)(156,530,672)

= 98,511.76 Ibs/yr (44,684 kg/yr)
that can be attributed to first
flush effects

FFLBS 98,511.76 1bs/yr
6,993 DWH/yr


= 14.09 Ibs BOD/DWH

= 6.39 kg BOD/DWH


This factor is then used in equation (3.7) to

estimate the first flush BOD load, FF, during the first

hour of runoff generated by each storm event. First

flush effects account for 14 percent of the average BOD

load in the combined.sewer overflows.















CHAPTER IV

STOCHASTIC CHARACTERIZATION OF URBAN RUNOFF



4.1 Hydrologic Time Series

Before the unifying concept can be applied to

wet weather and dry weather flows, it is important to

examine and analyze the hydrologic time series. A time

series is a sequence of values, arranged in order of their

occurrence, which may be characterized by statistical

properties. Data representing a purely random physical

phenomenon, or even a physical process that contains a

random element, cannot be described by an explicit mathe-

matical relationship. A hydrologic time series may be

considered to be the sum of two components: a random

element and a nonrandom element. For a hydrologic time

series, the occurrence of an event is not necessarily

independent of all previous events (Dawdy and Matalas,

1964). In fact, when known deterministic components are

removed (e.g., annual cycles) the dependence between hydro-

logic observations decreases with an increase in the time

base. For example, the dependence between monthly obser-

vations is less than between daily observations (Dawdy

and Matalas, 1964).








As stated previously, rainfall input to STORM is

prepared as a sequence of consecutive hourly values (in-

cluding zeros for no measurable precipitation). These

inputs are used by STORM to generate the corresponding

series of hourly urban runoff. The basic approach to de-

fine a wet weather event is to analyze the hydrologic time

series and establish the minimum number of consecutive dry

weather hours (DWH) that separates independent storm events.

The independence of these storm events is not strictly

climatological and is discussed later. The dry weather

hours refer to periods during which no runoff was produced.

Thus, depression storage and evaporation rates must be

satisfied before any runoff is generated by STORM.

The precipitation time series for Des Moines, Iowa

for the year of record 1968 is presented in Figure 4-1.

The abscissa represents the 10-month period, in hours, from

March 1 to December 30. An examination of the rainfall

record provides considerable insight as to storm groupings,

their intensity and duration, and frequency of occurrence.

The broken line on the abscissa indicates dry weather

periods at least nine hours in length. The annual pre-

cipitation total is 27.59 inches (701 mm), producing

10.28 inches (261 mm) of urban runoff as predicted by the

urban hydrologic model.


4.2 Analysis of Time Series

The analysis of the hydrologic time series is

performed at two levels: (1) an analytic approach,



































































































































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autocorrelation, and (2)an approximate, graphic procedure.

The results of the analytic approach are subjected to a

parametric test of significance for serial dependence.

Two approaches may be used to compute sample

autocorrelation coefficients: a circular series approach

or an open series approach. In the circular series approach

the end of a sample series is assumed to continue with its

beginning (Yevjevich, 1972). For both continuous and

discrete series in hydrology, the use of the circular

series approach is not recommended because the first and

the last part of the series may be independent, but cor-

responding adjacent parts may be highly dependent. The

circular series approach may decrease the degree of de-

pendence, thus introducing bias into the computation

(Yevjevich, 1972). Thus, it is preferable to estimate the

autocorrelation coefficients by an open series method.




n-k rn-k 1
E .xix+k -k E x x
Si= i=l i=k+
r(k) = 0.5 0.5
nk2 n-k ) [ i1 n )2]
E x A -n E
=1 1 n- 1 J i=k+ 1i=k+1


(4.1)


where ri(k) = sample estimate of lag-k autocorrelation
coefficient for hydrologic process I,









x = discrete data series (observations) of
S hydrologic process I, for i = 1, 2, ..., n,


n = total number of data points or observations,
and


k = number of hourly lags.


In the open series approach described by equation (4.1), the

first part.of the series (n-k) long is used for xi. and the

last part of the series (n-k) long is used for xi+k.

Equation (4.1) provides an unbiased and efficient estimate

of the lag-k autocorrelation coefficient, which is also

referred to as the sample estimate of the lag-k serial

correlation coefficient (Fiering and Jackson, 1971).

A plot of the serial correlation coefficients,

r(k), against the number.of lags, k, is called a corre-

logram. The technique of autocorrelation analysis is es-

sentially a study of the behavior of the correlogram of the

process under investigation (Quimpo, 1968). The correlogram

shape, or curve joining each point to the next, is hence-

forth referred to as the autocorrelation function. An

analysis of the precipitation time series of Figure 4-1

results in the curve shown in Figure 4-2. At a lag of

of zero hours, the correlation of the discrete open series

is unity because this point on the curve represents the

linear dependence of the data series on itself. The

number of observations (including zero values) totals















































20 30 40 50 60 70 80 90 100
LAG Ki hours


Figure 4-2. Lag k Autocorrelation Function of Des Moines,
Iowa, Hourly Rainfall, 1968.





69






0.2




o.I


95% T.L.

.0-
95% T.L.

-0.1



-0.21 -

300 310 320 330 340 350 360 370 380 390 400

hours

0.2








0.0 j
>% 95% T.L.'
S9 3% T. L.


-0.1
I


-0.2 ------- -
400 410 420 430 440 450 460 470 480 490 500
LAG K, hours


Figure 4-2 continued









7,372 consecutive values, and lags up to 720 hours were

investigated. The first minimum of the autocorrelation

function occurs at a lag of 10 hours, and the value of the

function is also zero at this point. The physical in-

terpretation is that periods without rainfall for at least

10 hours separate uncorrelated, and therefore independent,

storm events.

Actually any point of the autocorrelation function

which lies outside of the 95 percent tolerance limits

indicated in Figure 4-2 suggests a significantly non-zero

correlation between storm events at that particular time

lag. The Des Moines rainfall record obviously exhibits

nonrandom behavior at lags of 377 hours (% 16 days) and

421 hours (, 18 days) in particular. The tolerance

limits for a normal random time series of N values,-and

an open series approach at a 95 percent probability level,

are given by Yevjevich, 1972.



TL (95%) = -1 1.645 /Nkl (4.2)
N-k


where TL (95%) = tolerance limits at a 95% probability
level.


As the number of lags, k, increases, the tolerance

limits diverge. However, the divergence is not noticeable

for large N. Values of the autocorrelation function between









lags of 100 to 300 hours and 500 to 720 hours fell between

the 95 percent tolerance limits and are not shown in

Figure 4-2.

Similarly, autocorrelation analysis was performed

on the sequence of hourly runoff values generated by STORM

from the rainfall input. The lag-k serial correlation

coefficients, rQ(k), are plotted against the number of lags

in Figure 4-3. The analytic technique establishes that

the minimum interevent time of consecutive DWH that separates

independent runoff events is nine hours. Examination of

Figure 4-3 reveals that the runoff time series is not

purely random either. Linear dependence is observed at...

time lags of 377 hours (n 16 days) and 436 hours (% 18

days), as expected, because of the high correlation between

rainfall and runoff processes.

Slight differences are observed between the correlo-

grams of Figure 4-2 and 4-3. These are due to the fact that

depression storage and evaporation rates must be satisfied

before runoff is generated by STORM. Thus, the digital

simulation of the runoff process by STORM acts as a filter

and has a slight smoothing effect.

The graphic procedure requires the number of dry

weather hours immediately preceding each hourly runoff

occurrence. These values are determined directly by the

chronological record provided by STORM of all the runoff

events it generates from the input rainfall. If a hydrologic

















































10 20 30 40 50 60 70 80 90 100
LAG k


Figure 4-3. Autocorrelation Function of Hourly Urban Runoff
for Des Moines, Iowa, 1968.

















95 % T.L.____
---------- A 77 A ^ -- -- l--------


95% T.L.



I


300 310


320 330 340 350 360 370 380 390 4
hours


400 410 420 430 440 450 460 470 480 490 500
LAG K, hours


Figure 4-3 continued


-L1 z-zVhZZIT7\Z\%.J


-0,1-









model such as STORM is not.available, a close approximation

may be obtained by assuming that the same numbers of DWH

precede the rainfall and runoff events. Thus, the infor-

mation provided .by the precipitation records or the rain-

fall time.series (such as Figure 4-1) is sufficient. A

plot of the number of wet weather events obtained by vary-

ing the minimum interevent time is shown in Figure 4-4.

It is evident that a time value exists after which an

increase in the minimum interevent time does not result

in a correspondingly significant reduction in the number

of storm events. By the graphic procedure, a period of

eight consecutive DWH is obtained as the minimum inter-

event time. This result may be checked by constructing

a divided difference table. From Table 4-1, the first

minimum second difference occurs after the point of maxi-

mum curvature, at about 8 hours. These results indicate

that the graphic procedure yields an approximate solution.

Whenever possible, the analytic approach that defines a

correlation should be applied to investigate the sequen-

tial properties of.the hydrologic series.


4.3 Definition of an Event

Based on the above analyses, a wet weather event

and its duration are defined in the mathematical model

as follows:































a

0
0



ou





>U-
0o






ow


I--
m-


W








a .


I D
. --'---* I


u


r
.d


O


- -
a,
0i)




cO c


w 4o








4-
0



C1 0
0z





- -






0

N S
4.


o
0 c


WV3A M3d SIN3A3 a3HV3M A3M JO 'ON


V


-- r I 1


I


O/l




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