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 WellMixed Constant Volume.Model  85
5.3 WellMixed Variable Volume Model  120
5.4 Dispersive Variable Volume Model  157
5.5 Summary  193
VI STATISTICAL APPROACH TO STORAGE/TREATMENT
RESPONSE FOR WELLMIXED 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 WELLMIXED AND DISPERSIVE VARIABLE VOLUME
DIGITAL COMPUTER MODEL  252
II WELLMIXED CONSTANT VOLUME AND RECEIVING
WATER DIGITAL COMPUTER MODEL  273
REFERENCES  291
BIOGRAPHICAL SKETCH  297
LIST OF TABLES
Table Page
21 Constituents in Rainfall 13
22 Characteristics of Urban Stormwater 14
23 Characteristics of Combined Sewer
Overflows 15
24 Pollution and Contamination Indices 17
25 Treatment Potential of Various Com
ponents of the Physical System 28
31 Pollutant Unit Loads for Drainage
Area Above Des Moines, Iowa 34
32 Summary of Pres'ent Annual Metro Area
Discharges 36
41 Divided Difference Table for Determi
nation of Point of Maximum Curvature 76
51 Solutions to Equation (5.5) for Various
Forcing Functions of Concentration 89
52 Analytic Solutions to Equation (5.9)
for Various Forcing Functions of Con
centration and Flow Rate 92
53 Required Basin Volume for Desired
Average Detention Time 109
54 Statistics for WellMixed Constant
Volume Model for Wet Weather Event
No. 52 114
55 Pollutant Removal Effectiveness of
WellMixed Constant Volume Model for
Wet Weather Event No. 52 115
Table Page
56 Statistics for WellMixed Constant Vol
ume Model for All Wet Weather Events 125
57 Pollutant Removal Effectiveness of
WellMixed Constant Volume Model for
All Wet Weather Events 126
58 Integration of Equation (5.34) for Var
ious Forcing Functions of Concentration
and Flow Rates 131
59 Average Storage Volumes Used for Given
Detention Times 138
510 Statistics for WellMixed Variable Volume
Model for Wet Weather Event No. 52 143
511 Pollutant Removal Efficiency of Well
Mixed Variable Volume Model for Wet
Weather Event No. 52 144
512 Reduction in Peak and Mean Flow Rates
with Variable Volume Model for Wet
Weather Event No. 52 146
513 Statistics for Variable Volume Model
with Detention Time of 48 Hours for
Wet Weather Event No. 52 147
514 Statistics for WellMixed Variable
Volume Model for All Wet Weather Events .154
515 Pollutant Removal Efficiency and Outflow
Rate Attenuation of WellMixed Variable
Volume Model for All Wet Weather Events 155
516 Maximum Storage Volume Required for
Desired Detention Time 156
517 Statistics for Dispersive Variable
Volume Model for Wet Weather Event
No. 52 176
518 Pollutant Removal Efficiency of
Dispersive Variable Volume Model for
Wet Weather Event No. 52 177
viii
Table
519 Statistics for Dispersive Variable Vol
ume Model for All Wet Weather Events 184
520 Pollutant Removal Efficiency of Disper
sive Variable Volume Model for All
Wet Weather Events 185
521 BOD Concentration Statistics for All
Wet Weather Events for Various Peclet
Numbers 191
522 BOD Concentration Statistics for All Wet
Weather Events for Various Reaction Rate
Groups 192
61 Summary Statistics.for BOD Mass Rate
and. Fluid Flow Rate Inputs of the Urban
Runoff Time Series 210
62 Predicted System Response to Mass and
Fluid Flow Rate Inputs 214
63 Pollutant Removal Efficiency of the
WellMixed Constant Volume Model 216
71 Waste Input Combinations and Stream
Conditions 223
72 Percentage of Critical D.O. Loncentra
tions Exceeding Given Stream Standard 245
Page
LIST OF FIGURES
Figure Page
21 A Generalized Component of the Physi
cal System. 21
.31 Map of Des Moines Area. 32
32 Existing DWF Process Profile. 35
33 Location Map: River Sampling Points. 40
34 An Abstraction of the Physical System. 43
41 Point Rainfall for Des Moines, Iowa. 61
42 Lag k Autocorrelation Function of Des
Moines, Iowa, Hourly Rainfall, 1968. 68
43 Autocorrelation Function of Hourly Urban
Runoff for Des Moines, Iowa, 1968. 72
44 Definition of a Wet Weather Event for
Des Moines by Graphic Procedure. 75
51 WellMixed Constant Volume Model. 86
52 Discrete Inputs of Flow Rate and Concen
tration at Equal Time Intervals. 94
53 BOD Removal from Sewage in Primary Sedi
mentation Tanks. 101
54 Input Flow Rate for Wet Weather Event
No. 52. 106
55 Input BOD Concentration for Wet Weather
Event No. 52. 107
56 Input BOD Mass Rate for Wet Weather
Event No. 52. 108
57 Output Flow Rate for Wet Weather Event
No. 52. 111
__~
Figure Page
58 BOD Concentration Response for Wet
Weather Event No. 52. 112
59 BOD Mass Rate Response for Wet Weather
Event No. 52. 114
510 Frequency Distribution of Input BOD
Concentrations for All Wet Weather
Events. 117
511 Frequency Distribution of Output BOD
Concentration for All Wet Weather
Events. 118
512 Cumulative Frequency of BOD Concentra
tions for All Wet Weather Events. 119
513 Frequency Distribution of Input BOD Mass
Rate for All Wet Weather Events. 121
514 Frequency Distribution for Output BOD
Mass Rate for All Wet Weather Events. 122
515 Cumulative Frequency of BOD Mass Rates
for All Wet Weather Events. 124
516 WellMixed Variable Volume Model. 128
517 Output Flow Rate for Wet Weather Event
No. 52 for Varied Detention Time. 140
518 BOD Concentration Response for Wet
Weather Event No. 52 for Varied Deten
tion Time. 141
519 BOD Mass Rate Response for Wet Weather
Event No. 52 for Varied Detention Time. 142
520 Frequency Distribution of Output BOD
Concentration for All Wet Weather Events
for Variable Volume Storage/Treatment. 148
521 Frequency Distribution of Output BOD
Mass Rates for All Weather Events
for Variable Volume Storage/Treatment. 149
Figure Page
522 Cumulative Frequency of BOD Concentra
tions for All Wet Weather Events for
Variable Volume Storage/Treatment. 151
523 Cumulative Frequency of BOD Mass Rates
for All Wet Weather Events for Variable
Volume Storage/Treatment. 152
524 Advection and Dispersion in the Variable
Volume Model. 158
525 Discrete Convolution. 165
526 Flow Rate Response for Wet Weather Event
No. 52. 172
527 BOD Concentration Transient Response for
Wet Weather Event No. 52. 173
528 BOD Mass Rate Transient Response for Wet
Weather Event No. 52. 174
529 Frequency Distribution of Output BOD Con
centrations for All Wet Weather Events
for Dispersive Variable Volume Model. 178
530 Frequency Distribution of Output BOD
Mass Rates for All Wet Weather Events
for Dispersive Variable Volume Model. 179
531 Cumulative Frequency of BOD Concentra
tions for All Wet Weather Events for
Dispersive Variable Volume Model. 182
532 Cumulative Frequency of BOD Mass Rates
for All Wet Weather Events for Disper
sive Variable Volume Model. 183
533 System BOD Concentration Response for
Varied Longitudinal Dispersion Coeffi
cient. 187
534 BOD Concentration Response for a Reactor
Characterized by Peclet Numbers. 189
535 BOD Concentration Response for Various
System Models. 194
Figure Page
536 BOD Mass Rate Response for Various
Systems Models. 195
61 Lag k Serial Correlation Coefficients
for Input BOD Mass Rates. 212
62 Lag k Serial Correlation Coefficients
for Input Fluid Flow Rates. 213
63 Deterministic Model and Statistical
Approach Predictions for All Wet
Weather Events. 218
64 Lag k Serial Correlation Coefficients
for Fluid Flow Rate for Wet Weather
Event No. 52, Hourly. 221
71 Application to Des Moines, Iowa. 239
72 Minimum D.O. Frequency Curves for
Varied WWF Control and DWF Secondary
Treatment Versus No Treatment of
Urban Waste Sources. 242
73 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 crosssectional 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 crosssectional area due to a
variable depth, L2
B = benthal demand of bottom deposits,
mg/1hour
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 dryweather 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(I1)
Cl(T)
C1 (Ti).
cl(t)
c2(t)
c2(ti)
c2(ti + 2)
c2(x, t t )
C (xUt,
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
= timeaveraged 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 = selfpurification ratio, dimensionless
f = available urban depression storage, inches
FF = first flush factor, pounds/DWHacre
f(t T) = system step response, dimensionless
g = exponent in solution to steadystate dif
ferential equation.for dissolved oxygen
deficit, T1
H = stream depth, feet
h = sampling interval =ti+1 t.= 1 hour
I(t) = system input function, M/L3
j = exponent in solution to steadystate dif.
ferential equation for dissolved oxygen
deficit, T1
K = firstorder decay rate of pollutant in the
fluid medium, T1
k = number of hourly lags
K = oxidation coefficient of nitrogenous BOD,
n hours1
1
K = firstorder BOD decay constant, day
1 and hoursI
K2 = atmospheric reaeration coefficient, hours
L = length of the storage/treatment basin,
feet
L = remaining carbonaceous BOD concentration,
mg/l
(L ) = ultimate firststage 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 steadystate differential
equation for dissolved oxygen deficit,
L1
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/lhour
= 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 bythe 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 + ) = timeaveraged 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/lhour
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
= timevarying 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 + ) = timeaveraged 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 flowweighted
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 onedimensional, 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 onedimensional 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 duringthe 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 wellmixed 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
CHAPTERI
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 decisionmaking pro
cess. The high cost of pollution control facilities, in
terms of energy utilization, land requirements, engineer
ing manpower, and longterm 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 crosssections
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 flowweighted average
of concentrations from sewage residuals, urban storm
washoff and upstream sources. As computed, it is indepen
dent of hydrologic rainfallrunoff 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 environmentconservation 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 wellmixed constant
volume systems, wellmixed 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 wellmixed 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 wellmixed 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 manmade 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 21. 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 22
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
23 lists ranges of pollutant concentrations found to be
typical of combined sewer overflows (Field and Tafuri,
1973). From an examination of Tables 21, 22, and 23,
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 21
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 22
Characteristics of Urban Stormwater
(Field and Tafuri, 1973)
Constituent
Concentration Range
BOD5
COD
TSS
Total Solids
Volatile Total Solids
Settleable Solids
Organic N
NH3N
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 23
Characteristics of Combined Sewer Overflows
(Field and Tafuri, 1973)
Constituent
Concentration Range
BOD5
TSS
Total Solids
Volatile Total Solids
pH
Settleable Solids
Organic N
NH3N
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 24 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
ammonianitrogen (NH3N), then oxidized by
autotrophic bacteria (Nitrosomonas europaea)
to nitritenitrogen (NO2N), further oxidized
Table 24
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 24 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 nitratenitrogen
(NO3N); 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 bioassaytype 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 21 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 onedimensional version of the convectivedispersion
equation,
ac 3 E3c UC] + ES
at 3x ax
(2.1)
ss^
bC b Es 1 + U
 E UC / S
bt Zx
Figure 21. 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 21 to
C_ E C U
at ax2 ax
KC + (C C) (2.2)
where K = firstorder 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 crosssectional 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 (xUt, t )exp[Kt] (2.4)
where Cl(xUt, 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
firstorder 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 designoriented.
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 continuousflow systems. The basic
differential equation for a continuousflow reactor is
given as
E a2C U BC KC = 0 (2.6)
x2 ax
for a firstorder reaction. Equation (2.6) is obtained
from equation (2.2) for steadystate 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 21, 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 thecomponent,
L3.
Solutions to equation (2.8) are presented in Chapter V
for the constant volume and variable volume cases, for
timevarying influent flow rates and concentrations. In
chemical engineering texts (e.g.,Cooper and Jeffreys,
1971), the design equation for a continuousflow 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
steadystate 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 ofa 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 steadystate analysis of equation
(2.1) is presented in Chapter VII.
As noted in Figure 21, 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, crosssectional 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 performancetime curves of activated sludge
units, an overall BOD firstorder 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 firstorder 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 25. The reaction rate group KtD provides a
rough idea of treatment potential.
Table 25
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
ActivatedSluge
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 multidimensional form of equation (2.1), namely,
a 2dimensional or .3dimens.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 worstcase 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
fieldmeasured 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 31. 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 mediumsized population;
VICINITY MAP
Figure 31. 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 31, 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 highrate 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 32. The
estimated annual loading from the urban area's separate
and combined sewer systems is presented in Table 32.
Table 31
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, acreft/acre 0.42 0.40 0.41
(ham/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
r00 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
0 CO
C) O
ko .4
Cn o0ci :
C C 
OC ON
r'm LO n
Ln0 o
00( O
CON N0
00 00
cO',c
O0 OC C
O(CO C)
r"0 Ci I
oC n m
00 00
tC CO
V
0 O
C,
* 0 0
Co i
n
.Ln C, N CO C
CM
'n
01
S
L
U
VI
S
01
or
4
0'
>0
SE
4 EO
U,>
5
4U
E
fcO
C C
1;0
E E
LO 'LO
E E
c C
o o
S00
n n
o c
Oi 
iCO C c' UO 
cO CXLO CO C C
C 3 COO CJO 0 0
CM 10 r C'Jr
O C
0
On C
C t
0 ^l
c c
'r '*
E E
E E
n co
(.0 r0
c C
N LO
N e
41. S
4
 'C
4
1 C
p s
U)
2
0^
0
av
0C
c,
C3
0
02
C0 00 0: M3
00 00
002 0(0
rL 020
c) O COi
tc
o 0I
0o
0 i
NN
cuJ O
 L CM 0
CM
OD
0C0
0 UO
00
0)
0 N.
om
o o
0o l
CO CT
'0 'E '0
E E E
in L n
r r r
) o L
oCn o 00
mmCNN
Cff LA CM C)
LO oC
00 0 0
Lo 0 LO
(0 0
LA no
o r i
CM
0
30
4
0 a
D '
4
o C
4
s<
C 0
en <
L0 01
r ) o
m
L C
S E
4 o
4 ). 0 '0
to 10 u 5.
c a)
0) E 00
o0 r0 0
'0 >oL > s
S0 A
L ,'0 4 U,
'0 '00) U) 'O
2 02 S Cr CO
L3 2 U X*
0 0
0 m
.r0 02
N.t en
U,
3
0
V
0
1.
0
5
a>
0)
3
t
0
5/,
0r
0)
C
2
E
0
a) o
c a)
.4) 3
'0CE
0).r
:3.4)
C
.4 0
:3
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 R5
and R6 is of interest. Increased loads
between the summation of R4 and R9 ver
sus R5 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 (R4, R5, R6 and
R9) are shown in Figure 33. 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 33. 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 33, 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 (0PO4) 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 34.
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 34. 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 34 from top to bottom
reveals three distinct phases of the water quality cycle
within the urban environment. At the top level is the
pollutant buildup 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 andgroup 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 34, represented by the.
manmade 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] (lRd)
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 34 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 manmade
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) firstorder 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 34)
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 insewer sediment buildup 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 sitedependent 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 insewer solids buildup, 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 41.
The abscissa represents the 10month 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,
NU0q.

5
 '
C.,
u0 0
u NOli1Vi13dm d
63
00
o 0 0 0
_. 0
 "i
,2
I
a
'C
o
:0
m D
Q3
O
I
ro 
In
0u
OI
C.
10
U
64
U13 o
1
r)
0
U)
io
*,
00

.L
lh
. it
10)
.,L
PI L
65
U 13
o 0 o o0
in N 
to
= n
r
N
',
to
Y
U0
N
in
IO
r i
r
cc
N
L!.I
to
n 
"U! 'NOIJ.VLl13dl a~
J
1
.== 4
0t;0" 0 I
U*! 'NOIlVlldIOBUd0
a)
01
C)
LI
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.
nk rnk 1
E .xix+k k E x x
Si= i=l i=k+
r(k) = 0.5 0.5
nk2 nk ) [ 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 lagk 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 (nk) long is used for xi. and the
last part of the series (nk) long is used for xi+k.
Equation (4.1) provides an unbiased and efficient estimate
of the lagk autocorrelation coefficient, which is also
referred to as the sample estimate of the lagk 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 41
results in the curve shown in Figure 42. 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 42. 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 42 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 42 suggests a significantly nonzero
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)
Nk
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 42.
Similarly, autocorrelation analysis was performed
on the sequence of hourly runoff values generated by STORM
from the rainfall input. The lagk serial correlation
coefficients, rQ(k), are plotted against the number of lags
in Figure 43. The analytic technique establishes that
the minimum interevent time of consecutive DWH that separates
independent runoff events is nine hours. Examination of
Figure 43 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 42 and 43. 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 43. 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 43 continued
L1 zzVhZZIT7\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 41) is sufficient. A
plot of the number of wet weather events obtained by vary
ing the minimum interevent time is shown in Figure 44.
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 41, 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
