EPA-600/2-77-168
September 1977
Environmental Protection Technology Series
Municipal Environmental Research Laboratory
Office ol Reearch and
fifcto
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U S Environmental
Protection Agency, have been grouped into nine series These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are'
1 Environmental Health Effects Research
2. Environmental Protection Technology
3 Ecological Research
4 Environmental Monitoring
5 Socioeconomic Environmental Studies
6 Scientific and Technical Assessment Reports (STAR)
7 Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL PROTECTION TECH-
NOLOGY series. This series describes research performed to develop and dem-
onstrate instrumentation, equipment, and methodology to repair or prevent en-
vironmental degradation from point and non-point sources of pollution This work
provides the new or improved technology required for the control and treatment
of pollution sources to meet environmental quality standards.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/2-77-168
August 1977
STORMWATER RUNOFF ON
URBAN AREAS OF STEEP SLOPE
by
Ben Chie Yen, Yen Te Chow and A. Osman Akan
Department of Civil Engineering
University of Illinois at Urbana-Champaign
Urbana, Illinois 61801
Contract No. 68-03-0302
Project Officer
Richard Field
Storm and Combined Sewer Section
Wastewater Research Division
Municipal Environmental Research Laboratory(Cincinnati)
Edison, New Jersey 08817
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
- >- -- -,t"l Protection Agency
,.irj (oPL-lS)
. .:orn Street, Room 1670
- -.i, 60604
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DISCLAIMER
This report has been reviewed by the Municipal Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for publica-
tion. Approval does not signify that the contents necessarily reflect the
views and policies of the U.S. Environmental Protection Agency, nor does
mention of trade names or commercial products constitute endorsement or
recommendation for use.
ii
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FOREWORD
The US Environmental Protection Agency was created because of in-
creasing public and government concern about the dangers of pollution
to the health and welfare of the American people. Noxious air, foul
water, and spoiled land are tragic testimony to the deterioration of
our natural environment. The complexity of that environment and the
interplay between its components require a concentrated and integrated
attack on the problem.
Research and development is that necessary first step in problem
solution and it involves defining the problem, measuring its impact,
and searching for solutions. The Municipal Environmental Research
Laboratory develops new and improved technology and systems for the
prevention, treatment, and management of wastewater and solid and
hazardous waste pollutant discharges from municipal and community
sources, for the preservation and treatment of public drinking water
supplies and to minimize the adverse economic, social, health, and
aesthetic effects of pollution. This publication is one of the pro-
ducts of that research; a most vital communications link between the
researcher and the user community.
For effective control of water pollution due to storm runoff, a
prerequisite is a reliable method to predict the quantity of the
runoff. The time distribution of storm runoff depends on the rain-
fall and physical characteristics of the drainage basin. One
important factor is the slope of the basin. Many cities have areas
with steep slopes. This publication reports the effect of steep
slope on storm runoff.
Francis T. Mayo
Director
Municipal Environmental Research
Laboratory
iii
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ABSTRACT
A research is conducted to investigate the applicability of commonly
used urban storm runoff prediction models to drainage basins with steep
slopes. The hydraulics of runoff on steep slope areas is first reviewed
and its difference from that for mild slope areas is discussed. Next the
difficulties in applying commonly used methods to steep slope basins are
presented. It appears that most engineers are not aware of the problems
associated with runoff from steep slope areas and they do not realize that
the numerical results given by the conventionally used methods, if ob-
tainable, may not be reliable. A simple approximate method specifically
for steep slope basins is proposed and an example is provided. The ex-
ample utilizes the data from the Baker Street Drainage Basin in San
Francisco.
This report is submitted in fulfillment of the extension part of
Contract No. 68-03-0302 by the Department of Civil Engineering, University
of Illinois at Urbana-Champaign, under sponsorship of the Office of
Research and Development, U.S. Environmental Protection Agency. Work was
completed as of October 25, 1976.
iv
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CONTENTS
Foreword Ill
Abstract iv
Figures vi
Tables viii
Abbreviations and Symbols ix
Acknowledgments x
I. Introduction 1
II. Summary and Conclusions 3
III. Recommendations 5
IV. Hydraulics of Runoff on Surface with Steep Slopes 7
1. Mathematical representation of surface runoff 7
2. Physical phenomena of runoff on steep slopes 10
V. Difficulties in Applying Existing Runoff Prediction Methods
to Steep Slopes 16
1. The rational method 19
2. Unit hydrograph method 21
3. Chicago hydrograph method 22
4. Transport and Road Research Laboratory Method 23
5. University of Cincinnati Urban Runoff Model 24
6. Dorsch Hydrograph-Volume-Method 25
7. Storm Water Management Model 26
8. Illinois Urban Storm Runoff Method 28
VI. Example Urban Area of Steep Slope Baker Street Drainage
Basin in San Francisco 30
1. General basin characteristics 30
2. Surface drainage pattern 34
3. Sewer system 46
4. Rainfall and runoff data 53
VII. Proposed Simplified Method for Runoff Flowrate Determination
for Areas of Steep Slopes 64
1. Surface runoff and inlet hydrograph determination ... 64
2. Sewer flow routing 68
3. Example: Baker Street Upper Basin 71
References 82
Appendix: Baker Street Drainage Basin Runoff Water Quality ... 86
v
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FIGURES
Number Page
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Definition sketch of open-channel flow
Sketch of roll waves passing down a steep slope
Depth- velocity diagram for six types of open-channel flows
Approximations of St. Venant equations hydraulic routing .
Location map of Baker Street Drainage Basin, . ,
Topograph of Baker Street Drainage Basin
Photographic views of Baker Street Drainage Basin ....
(a) Typical view of upper basin Jackson Street between
Maple and Spruce
(b) Baker Street looking north from Vallejo Street. . . .
(c) Typical view of lower basin Jackson Street between
Maple and Spruce
Baker Street surface drainage pattern
Details of typical sidewalk curb
Cross sections of typical curb and gutter
Typical view of sidewalk curb - Broderick Street
Semi- circular grate inlet,
Baker Street Drainage Basin sewer system ,
Typical cross section of egg-shape sewer ,
Typical sewer junction
(a) Circular sewers
(b) Egg-shape sewers
Hyetograph and hydrograph for rainstorm of 4-5 April, 1969
Hyetograph and hydrograph for rainstorm of 15 October,
1969
Hyetograph and hydrograph for rainstorm of 5 November,
1979
Hyetograph for rainstorm of 22 October, 1973
Cumulative rainfall and intensity for rainstorm of
22 October, 1973
Circular sewer flow cross section
Type C 10-min inlet unit hydrograph for Upper Basin . . .
8
12
13
17
31
33
35
35
35
35
36
38
39
45
45
47
49
50
51
51
55
56
57
62
63
70
73
vi
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FIGURES (Continued)
Number Page
23 Standard 5-min inlet unit hydrographs for Upper Basin ... 74
24 Hydrograph routing in sewer 80
25 Runoff from upper basin for rainstorm of 22 October, 1973 . 81
A-l Pollutographs for runoff on 4-5 April, 1969 88
A-2 Pollutographs for runoff on 15 October, 1969 89
A-3 Pollutographs for runoff on 5 November, 1969 90
vii
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TABLES
Number Page
1 Hydraulic Characteristics of Routing of Distributed Urban
2
3
4
5
6
7
8
A-l
A- 2
Land Slope Distribution of Baker Street Drainage Basin. .
Baker Street Drainage Basin Sewer and Gutter Data ....
Rainstorm Runoff Monitored for Baker Street Drainage
Typical Print Out of San Francisco Rainfall Data
Typical Print Out of Sewer Flow Water Level Record. . . .
Inlet Hydrograph Identification for Upper Basin
Hydrograph Computation for Sewer Between Nodes 288 and
250
Baker Street Drainage Basin Runoff Water Quality
Cumulative Net Mass Emission
Baker Street Drainage Basin Dry Weather Flow Quality. . .
18
34
40
54
60
61
77
78
91
92
viii
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ABBREVIATIONS AND SYMBOLS
A = area;
B = water surface width;
C = runoff coefficient; also, coefficient or constant;
D = hydraulic depth = A/B;
d = pipe diameter;
₯ = Froude number of flow = V//gD;
g = gravitational acceleration;
h = flow depth;
i = rainfall intensity;
K,K' = pressure distribution correction factors in Eq. 3;
L = length;
N = Kerby's coefficient in Eq. 7;
n = Manning's roughness factor;
Q = discharge;
Q = peak discharge;
q = lateral inflow per unit length of circumference a;
R = hydraulic radius;
E. = Reynolds number of flow = VR/v;
S = slope;
Sf = friction slope;
S = bed slope = sin9;
t = time;
t = time of concentration;
c
U = x-component of velocity of lateral flow;
X
V = flow velocity;
V = volume;
x = longitudinal direction;
3 = momentum flux correction factor;
6 = angle between ground surface or sewer invert and horizontal plane;
v = kinematic viscosity;
a = perimeter bounding flow area A; and
= central angle of water surface in sewer (Fig. 21).
IX
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ACKNOWLEDGMENTS
In an investigation on the methods for determination of volumes and
flow rates of urban storm water runoff, which led to the publication of
the report by Chow and Yen (1976) quoted in Reference, eight selected
representative methods were evaluated by using recorded data of the Oakdale
Avenue Drainage Basin in Chicago. In checking whether the recorded data
of the Baker Street Drainage Basin in San Francisco is suitable to test
these methods, it was realized that runoff from steep slope basins is a
unique problem which requires further research and deserves a separate
study. The recently developed sophisticated urban runoff prediction
methods which produce satisfactory results for mild-sloped urban areas
have great difficulties when applied to areas with very steep slopes
such as the Baker Street Basin. Nonetheless, considerable experiences
and insight of the problem of runoff on steep slope basins have been gained
through the investigation. The authors would like to thank Messrs. Richard
Field and Chi Yuan Fan of the U.S. Environmental Protection Agency for
their encouragement to report the experience gained in the Baker Street
study and for their granting an extension of the project so that the
preparation of this report become possible.
Many people have directly or indirectly contributed to the work re-
ported in this publication. The staff of the Division of Sanitary
Engineering of the Bureau of Engineering of the Department of Public
Works, City and County of San Francisco, particularly Mr. Robert T.
Cockburn, are extremely cooperative in providing data and information
concerning the Baker Street Drainage Basin. Mr. W. 0. Maddaus of
Engineering-Science, Inc. was also very helpful in providing data and
information. Their help is sincerely appreciated. The authors would
also like to thank Mrs. Norma Barton and Miss Hazel Dillman for their
typing of the manuscript.
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SECTION I
INTRODUCTION
Reflecting the public concern of the urban environment, recently con-
siderable attention and interest have been extended to stormwater control
and management. Many methods or "models" of various degrees of sophistica-
tion and reliability have been proposed to simulate urban rainstorm water
runoff (Chow and Yen, 1976; Brandstetter, 1976; Colyer and Pethick, 1976).
A few of these methods have been applied to field conditions. Some have
been evaluated using recorded rainfall and runoff data different from the
data that were used in developing the methods. Most of them have not
been tested beyond the conditions of the original data that were used to
develop the methods. Particularly, none of these methods was considered
specifically for the case of urban drainage areas of very steep slopes.
Since many cities are located along steep banks of rivers and coastal bays
and also in mountains, steep slope urban drainage basins are not uncommon.
Typical examples are San Francisco, Seattle, and a number of cities along
the Mississippi River.
The problem in simulating stormwater runoff from steep slope areas
stems from the failure of any existing mathematical model to represent
reliably very high velocity gravity flow, i.e., unstable transient super-
critical flow with roll waves which hydrodynamically is quite different
from subcritical flow. The existing storm runoff simulation methods
simply ignore the existence of the high velocity flow. When such a flow
indeed occurs, some of these methods produce numerical results without
any indication of the physical occurrence of the roll waves and provide
no assurance of the reliability of the results which are often mis-
leading if not in error. A few other methods, mostly the more reliable
and sophisticated ones, simply break down producing no results because
of the combination of numerical and hydrodynamic instabilities.
In a previous investigation Chow and Yen (1976) evaluated eight
prediction methods for urban rainstorm water runoff. The eight methods
are the rational method, unit hydrograph method, Chicago hydrograph
method, British Transport and Road Research Laboratory method,
1
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University of Cincinnati Urban Runoff method, Dorsch Hydrograph-Volume -
Method, EPA Storm Water Management Model, and Illinois Urban Storm Runoff
method. The comparison and evaluation of these methods were done by
using four recorded hyetographs of the Oakdale Avenue Drainage Basin in
Chicago to produce the predicted hydrographs by the individual methods
and the results were compared with recorded hydrographs. The Oakdale
Drainage Basin has rather flat slopes and the storm runoffs on the ground
and in the sewers are all within the subcritical flow regime. However,
when these methods were applied to the San Francisco Baker Street Drainage
Basin which is a steep slope urban area, considerable difficulties were
encountered.
The objectives of this report are (a) to alarm the engineers dealing
with the quantity and quality aspects of urban storm runoff the existence
of problems in evaluating the runoff from steep slope areas, (b) to point
out the sources and conditions of the problems for selected representa-
tive methods, thus providing useful information for practicing engineering
in their selection of the most appropriate simulation method or methods
for their particular cases involving steep slopes; and (c) to suggest a
possible alternative method to determine storm runoff from steep slope
areas. This report may be considered as a supplement to that by Chow and
Yen (1976). The reader is suggested to read Sections IX and X of the
latter in order to gain a more balanced view of the problem.
In this report, the physical phenomena of runoff on steep slope
areas are described in Section IV. The applicability of the eight se-
lected prediction methods to steep slope areas is discussed in Section V.
A steep slope basin, the San Francisco Baker Street Drainage Basin, is
described in Section VI. A proposed approximate method together with an
example is presented in Section VII. Conclusions and recommendations
are given in Sections II and III, respectively. This investigation was
accomplished within a rather limited time and budget and hence limited
scope. The study is definitely not exhaustive and perhaps it is more
appropriately to be viewed as a peer of the state-of-the-art. Consid-
erable research is still needed to advance the technology of this aspect
of drainage problems.
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SECTION II
SUMMARY AND CONCLUSIONS
The major purpose of this report is to alert the engineers of the
possible difficulties that they may encounter when dealing with runoff on
steep slope areas. The hydraulics of gravity flow on areas with steep
slopes is first reviewed in Section IV and the sources of difficulties are
discussed. Physically and mathematically, the difficulties are the com-
bined result of four sources; namely, the incapability of the St. Venant
Equations to simulate the highly unsteady nonuniform flow, the numerical
instability, the hydrodynamic instability, and the lack of information
on flow resistance to unstable supercritical flow with roll waves.
Based on hydraulic considerations, the applicability of eight selec-
ted representative urban storm water runoff prediction methods to steep
slope areas as well as the associated difficulties for each of them is
discussed in Section V. The eight methods, roughly in ascending levels
of hydraulic sophistication, are: the rational method, unit hydrograph
method, Chicago hydrograph method, University of Cincinnati Urban Runoff
method, British Transport and Road Research Laboratory method (also ILLUDASX
Dorsch Hydrograph Volume method, Storm Water Management Model (both the
EPA and WRE versions), and Illinois Urban Storm Runoff method. Ironi-
cally, it is the less sophisticated methods having low level of hydraulic
considerations that can produce numerical results whereas the hydraulically
higher level methods have difficulty in providing results. The diffi-
culties normally occur when roll waves of the flow occur. However, it
should be cautioned that the results of the hydraulically low level
methods which take no consideration on roll waves may be inaccurate or
even misleading. Information on the applicability to steep slope basins
of other runoff prediction methods that are not specifically discussed in
this report can be deduced by identifying the level of hydraulic sophisti-
cation of the method of interest to that of one of the eight methods eval-
uated.
Clearly, there is a lack of research and information on runoff from
drainage basins with steep slopes. Meanwhile, in view of the flow travel
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time, detail and accuracy of available data and other hydraulic and hydro-
logic considerations, an approximate method that can be used for predic-
tion of runoff from steep slope areas is formulated and proposed in
Section VII. An example of the proposed method is also presented by using
the data from the San Francisco Baker Street Drainage Basin which is
described in Section VI.
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SECTION III
RECOMMENDATIONS
Based on the experience and results obtained in this investigation,
the following recommendations concerning the determination of stormwater
runoff from urban areas with steep slopes are made:
1. Engineers dealing with urban runoff problems should be aware of the
differences between runoff from steep slope drainage basins and those
from mild slope basins. Particularly, they should understand that
the sources of difficulties that would affect the accuracy of the
results are different for the two different cases.
2. The methods with low level of hydraulic consideration, when applied
to drainage basins with steep slopes, will produce numerical results.
However, the adequacy and reliability of these results have not been
established. Therefore, they may be considered only as rough approxi-
mations. These methods include the rational method (which gives only
the peak discharge), Chicago hydrograph method, University of
Cincinnati Urban Runoff model, and British Transport and Road Research
Laboratory method. The choice of these methods is more or less a
matter of convenient and personal preference since they are all rough
approximations.
3. The unit hydrograph method is directly applicable to steep slope
basins with adequate engineering accuracy provided the unit hydro-
graphs can be reliably established through measured data or synthetic
techniques. Therefore, this method is recommended to be used whenever
feasible. Nevertheless, the engineer should always keep in mind the
limitations such as linearity and time invariance of the basin that
are associated with the unit hydrograph theory.
4. Ironically, it is the methods with higher levels of hydraulic consid-
eration, namely the Dorsch Hydrograph-Volume-Method, Storm Water
Management Models, and Illinois Urban Storm Runoff method, that would
produce unreliable results or no results at all when applied to steep
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slope basins and when roll waves occur in the unstable supercritical
flow. Much more research has yet to be conducted before these advanced
level methods can be modified to produce reliable results for practical
uses. At present practicing engineers are recommended not to waste
their efforts trying to use these methods to produce useful results for
steep slope basins. It should be noted that this recommendation is in
reverse of the recommendation made for mild slope basins by Chow and
Yen (1976).
There is a lack of past investigation and information on runoff from
drainage basins with steep slopes. As a result, there is also a lack
of understanding of the physical and mathematical aspects of such
runoffs. Much effort and research is needed in the future to advance
this aspect of urban technology. Particularly, reliable, detailed
and coordinated measurements of rainfall and runoff from steep slope
basins are urgently needed. These measurements will be used to
evaluate the degree of approximation of the hydraulically low level
methods which can produce numerical results. They will also provide
invaluable information for the improvement of the hydraulically high
level methods.
The approximate method proposed in Section VII was developed for prac-
tical applications specifically to areas with steep slopes. It is
not meant to be theoretically sophisticated and its improvement is
possible and desirable. The method has not been verified by field
data because reliable and adequate measurements of runoff from steep
slope areas are not available at present to verify this or any other
methods.
Many drainage basins have both steep and mild slope areas. Therefore,
it is desirable to have a model that can be used in both types of
areas and yet sufficiently reliable. One possibility is to integrate
the proposed method into the existing simulation models after
it is adequately tested. Further research is needed to develop such
combined models as well as to develop more reliable models.
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SECTION IV
HYDRAULICS OF RUNOFF ON SURFACE WITH STEEP SLOPES
IV-1. MATHEMATICAL REPRESENTATION OF SURFACE RUNOFF
Storm runoff on urban land surface and in partially filled sewers
can be described mathematically by a pair of partial differential equations
of hyperbolic type commonly known as the St. Venant equations
3V 3V 3 1 T
IE + *k + 4^ COS6) = « + i (Ux-V)q da (2)
J a
in which x is the direction of the flow measured along the ground surface or
sewer invert (Fig. 1); t is time; A is the flow cross sectional area; B is
the width of the water surface; D = A/B is the hydraulic depth; V is the
cross sectional average flow velocity; h is the depth of the flow above the
ground or invert; 6 is the angle between the channel bed and the horizontal;
S = sin9 is the bed slope, Sf is the friction slope; a is the perimeter
bounding A; q is the lateral discharge per unit length of a having a velocity
component U along the x-direction when joining or leaving the flow, being
X
positive for inflow (e.g., rainfall) and negative for outflow (e.g., in-
filtration) ; and g is the gravitational acceleration. The first equation is
the equation of continuity and the second the momentum equation.
The St. Venant equations have often been referred to as complete
dynamic wave equations in the sense that they include all the influential
terms representing the gradually varied unsteady free surface flow. Un-
fortunately, many engineers misinterpret the word "complete" as "exact" and
subsequently attempt to apply the St. Venant equations to conditions
that they are not valid. Large Froude number supercritical open-channel
flow on drainage surfaces and sewers with steep slopes is one of such
invalid cases.
Rigorously speaking, the St. Venant equations are cross sectional
averaged one-dimensional equations and they are not exact (Yen, 1973b,
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Fig. 1. Definition sketch of open-channel flow
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Strelkoff, 1969). In the form of Eqs. 1 and 2 they are applicable to flow
of an incompressible homogeneous fluid of constant density and viscosity
in an essentially straight, non-deposit and non-erodible, prismatic channel
(Yen, 1973b, 1975), and the following additional assumptions are involved
in the derivation of Eq. 2:
(a) The pressure distribution over the flow cross sectional area A is
hydrostatic.
(b) The x-component of the point velocity is uniformly distributed
over A.
(c) The effect of spatial change of internal stresses on A is rela-
tively negligible.
Assumption (c) usually does not cause much error. Assumptions (a) and (b)
are valid for gradually varied flows including low Froude number super-
critical flow and subcritical flow. However, they are invalid for super-
critical flow with the Froude number greater than about two for which roll
waves occur. This is the type of flow that occurs for runoff on steep slope
areas. In a careful and detailed study on numerical solution of Eqs. 1 and
2 for transient supercritical flows, Zovne (1970) found that the solution
becomes unstable when roll waves occur.
In order to eliminate the constraint of Assumption (b), a momentum flux
correction factor 3 should be introduced. For uniform distribution of x-
component of velocity on A, 3 = 1. To eliminate Assumption (a), two
pressure distribution correction factors K and K' are introduced (Yen, 1973b,
1975). Both K and K' are equal to unity for hydrostatic pressure distribu-
tion. Accordingly, the more accurate momentum equation is
|^ + (23-D v|^ + V2 || + [(8-l)V2 + (K-K')gh cos0]-||^
a i f
+ g (Kh cosG) = g(S -S ) + Y (U -V)q da (3)
oX O -L A, I X
J a
With the introduction of the correction factors 3, K, and K1 and allow-
ing them to vary with both space and time, theoretically Eq. 3 together
with Eq. 1 can be applied to solve problems of unsteady open-channel flows,
including rapidly varied and supercritical flows with high Froude number,
-------
provided the friction coefficient S can be correctly represented. However,
in practice, two major difficulties arise. First, the values of the three
correction factors 3> K, and K' are known only for special cases (Yen, 1973b,
1975). Their spatial and temporal variations for high Froude number flows
with roll waves are at present unknown. Second, currently the knowledge on
the friction slope, S,-, is limited to steady uniform flow and a few special
cases of unsteady flows. No information exists on Sf for supercritical flow
with roll waves. In fact, many engineers do not realize the difference
between the friction slope and energy slope, using them indiscriminately and
incorrectly in solving problems (Yen, 1973b).
Mathematically, the St. Venant equations, which are a pair of quasi-
linear first order partial differential equations of hyperbolic type,
cannot be solved analytically, and they are difficult enough to be solved
numerically. Only in recent years have satisfactory numerical solution
techniques been developed using modern computers (Amein and Fang, 1969;
Baltzer and Lai, 1968; Chow and Ben-Zvi, 1973; Dronkers, 1964; Liggett and
Woolhiser, 1967; Price, 1974; Sevuk and Yen, 1973; Yevjevich and Barnes,
1970). A method to apply the St. Venant equations to storm sewer networks
with appropriate solution techniques has been proposed only recently for
subcritical flow and supercritical flow without roll waves (Sevuk et al.,
1973). So far there has been no attempt to solve Eqs. 1 and 3 for open
channel flow problems. In view of the difficulties in numerical solution
techniques and the variations of the correction factors and friction slope,
the chance of obtaining an acceptable solution for Eqs. 1 and 3 in the
immediate future is rather unlikely. Therefore, it is desirable to iden-
tify the various simplified forms of Eqs. 1 and 3 and to evaluate their
applicability in solving problems involving runoff on areas of steep slopes.
IV-2. PHYSICAL PHENOMENA OF RUNOFF ON STEEP SLOPES
Physically, stormwater runoff on urban areas of steep slopes is
characterized by fast moving water. The water flow is driven by the gravi-
tational force while resisted through the viscosity of the water by the
solid boundary at the bottom and air on the surface. Because the air re-
sistance is relatively small and usually negligible, the high velocity water
10
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is usually at or near the free surface. When the bottom slope is small,
the flow velocity is relatively low because of the small gravitational
driving force, and it is slower than the celerity of the wave generated by
a disturbance. Such a flow for small slope is called subcritical flow
which is characterized by the value of the Froude number, IF, less than
unity, where
3F=^- (4)
/go
As the bottom slope increases, the flow velocity also increases as a
result of increasing driving force. When the bottom slope is sufficiently
steep, the flow velocity exceeds the wave celerity (i.e., the Froude number
IF > 1) and the flow is called supercritical, analogous to supersonic motion
of a fast flying object. In supercritical flow disturbant waves are swept
downstream by the fast flow and they cannot travel upstream. In other
words, the backwater effect of a supercritical flow can only propagate
downstream but not upstream. This fact of no backwater effect from down-
stream for supercritical provides great advantages in solving mathemati-
cally urban storm runoff by using Eqs. 1 and 2 or 1 and 3 because the solu-
tion can be sought sewer by sewer or reach by reach of overland in sequence
toward downstream instead of simultaneous solution for a number of sewers
or reaches as for the case of subcritical flow.
However, complication arises when the bottom slope becomes even
steeper. With greater driving force associated with the steeper slope,
the water velocity near the free surface flows faster while that at the
bottom remains zero, creating an instability condition and roll waves
occur which completely changes the flow characteristics and increases
energy dissipation. Roll waves occur when the Froude number of the flow
exceeds approximately 1.5 to 2, depending on the geometry of the channel,
the bed roughness and the unsteadiness of the flow. Unstable super-
critical flow with roll waves associated with steep slopes rarely occur
in natural streams but it happens often in urban conditions.
Roll wave is a subject that only a few studies have been conducted and
only a little information is available. An idealized sketch of roll waves
passing down a steep slope is shown in Fig. 2. Iwasa (1954) proposed a
stability criterion for quasi-steady, uniform flow in a smooth rectangular
11
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Fig. 2. Sketch of roll waves passing down a steep slope
channel which was experimentally checked by Koloseus and Davidian (1966).
Mayer (1961) described the process of generation and propagation of roll
waves. The occurrence of roll waves makes Eq. 2 invalid to represent the
flow, whereas in Eq. 3, V, A, 3, K and K1 become highly variable while Sf
is modified and unknown at the present.
Urban stormwater runoff is a spatial and temporal varying process and
may cover all the six types of open channel flow classified on the basis of
relative importance of inertial, viscous and gravity forces. The six types
are: subcritical laminar flow, subcritical turbulent flow, supercritical
laminar flow without roll waves, supercritical turbulent flow without roll
waves, unstable supercritical laminar flow with roll waves, and unstable
supercritical turbulent flow with roll waves. A diagram of the depth-
velocity ranges for the different types of steady, uniform, wide open
channel flow was given by Robertson and Rouse (1941) and is modified to
include the roll wave cases as shown in Fig. 3. This diagram can be used
only as an approximation for urban storm runoff because the runoff is an
unsteady flow and often not with wide homogeneous channels. Nevertheless
urban storm runoffs seldom have depth less than one-tenth of an inch
(0.3 mm) because of surface unevenness. Therefore, from Fig. 3, it can
12
-------
Velocity, m/s
1000
(I ) Subcritical
Turbulent
Unstable
Supercritical
Turbulent
Supercritical
Laminar
Unstable
Supercritical
Laminar
- Subcritical
- Laminar
E
E
a.
a>
O
0.003
Velocity ,fps
Fig. 3. Depth-velocity diagram for six types of open-channel flows
13
-------
be postulated that urban storm runoff flow is rarely supercritical laminar
(stable or unstable), seldom subcritical laminar, often stable subcritical
or supercritical turbulent when the slope is not too steep, and is un-
stable supercritical turbulent flow with roll waves for steep slopes.
Inevitably any overland runoff due to rainstorm starts with subcriti-
cal flow of near zero velocity when the rainfall has satisfied the initial
abstractions and overcome the initial retention due to surface depression
and surface tension. For a steep slope as the flow velocity increases the
flow will soon become supercritical. The transition of a flow from sub-
critical to supercritical is called a hydraulic drop. This transition
from subcritical flow to supercritical flow occurs at different times for
different places within the drainage area. In other words, the hydraulic
drop is moving.
Likewise, as the rainfall ceases and the runoff is receding, the flow
will change back from supercritical to subcritical. This transition is
known as a hydraulic jump. Again, the occurrence time of the hydraulic
jump is different for different locations and the hydraulic jump is moving.
At the same instance there may exist more than one hydraulic jump or drop
of different speeds along the channel of runoff. Two hydraulic jumps (or
hydraulic drops) when they meet, do not compensate each other. They simply
pass each other by and continue on their own propagation.
The existence of moving hydraulic jumps or drops for unsteady flows
greatly complicate the solution method of Eqs. 1 and 2 or 3. Information
on moving jumps or drops is rather limited. Zovne (1970) proposed an
approximate technique to account for them in numerical solution of Eqs. 1
and 2.
It should also be mentioned that for a sewer for heavy rainstorms
during the peak flow period the discharge may exceed the sewer capacity and
the sewer may become surcharged. The transition from free surface flow to
full-conduit flow of the sewer, and later from full-conduit flow back to
free surface flow imposes both hydrodynamic and numerical instabilities.
Although now the physical and mathematical concepts of these instabilities
14
-------
are clear and reasonably well understood, there exists no numerical solu-
tion technique that involves no restrictive assumptions.
In view of the previously discussed mathematical difficulties in ob-
taining solutions of Eqs. 1 and 3 for unstable transient supercritical
flow with roll waves on steep slopes, together with the numerical diffi-
culties in dealing with the transitions between the supercritical and
subcritical flows and between the surcharged and free-surface flow sewers,
one can only conclude that considerable research has yet to be conducted to
develop a reliable solution method. At present from a practical viewpoint
it will probably be more fruitful to identify or develop approximate
methods (though unavoidably subject to limitations and criticisms) that
can be used for solving runoff problems on steep slopes.
15
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SECTION V
DIFFICULTIES IN APPLYING EXISTING RUNOFF
PREDICTION METHODS TO STEEP SLOPES
Because of the difficulties and computation costs involved in solving
the St. Venant equations, Eqs. 1 and 2, or the more complete form, Eqs. 1
and 3, for urban storm runoff problems, various simplifications of these
equations have been used in most of the existing storm runoff prediction
methods many of them were without realizing the assumptions and limita-
tions implicitly imposed. From a hydraulic viewpoint, these simplifica-
tions of the St. Venant equations can be classified as shown in Fig. 4
(Yen, 1973a). The physical significance of these simplifications has been
discussed elsewhere (e.g., Lighthill and Whitham, 1955; Sevuk, 1973; Zovne,
1970) and is omitted here.
The existing storm runoff prediction methods can be classified in
accordance with their respective levels of hydraulic simplifications (Fig.
4). As mentioned in Section I, INTRODUCTION, Chow and Yen (1976) eval-
uated eight runoff prediction methods which are listed in Table 1 except
the rational method. These methods are listed respectively for the over-
land, gutter, and sewer flows in regard to the simplifications given in
Fig. 4. Although many other methods have been proposed recently and
appeared in the literature, at present these eight methods can still be
regarded as representatives of the existing methods in terms of the various
levels of hydraulic sophistications. In this section the applicability of
these eight methods to urban areas of steep slopes is evaluated in view
of the hydraulic theories. The computational procedures and details of
each of these methods can be found in the references cited in Table 1 and
in Chow and Yen (1976) or Colyer and Pethick (1976); therefore, they are
not repeated here. However, a variation of Storm Water Management Model,
the WRE SWMM, is included in the discussion of SWMM because of its recent
publicity. A reader who is interested in methods other than those
discussed in this section may identify by using Fig. 4 the hydraulic level
of his chosen method to one of the eight methods discussed. He then can
utilize the evaluations and recommendations in this report accordingly
with appropriate modifications, if necessary.
16
-------
IV
at
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cose) - g(S -S ) - 7 f (U -V)q da
O I £\ I X
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Kinematic wave approximation
Diffusion wave approximation
Quasi-steady dynamic wave approximation
Dynamic wave model
Figure 4. Approximations of St. Venant equations hydraulic routing
All of the sophisticated methods to simulate storm runoff from urban
drainage basins consist of two parts: the surface runoff model and the
sewer system runoff model. The surface runoff routing techniques of
these methods are based on various approximations to the St. Venant equa-
tions (Fig. 4) because solution of the complete St. Venant equations is
not justifiable due to the computer time required and uncertainties on
the resistance coefficient, flow boundaries of the surface runoff and
data reliability. Contrarily, the information on sewer systems is usually
well defined. Moreover, from a stormwater management viewpoint, errors
in surface flow prediction are more tolerable than those in sewer flow
prediction. Consequently, almost all of these methods have a more so-
phisticated scheme for sewer routing than for surface flow routing. For
drainage basin with steep slopes, the occurrence of roll waves on street
pavements and overland surfaces, though more often seen, is less serious
than its occurrence in sewers. Also, for steep slope surfaces, usually
the initial abstractions from rainfall are smaller and less important as
compared to mild slope surfaces.
17
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V-l. THE RATIONAL METHOD
The rational method is a black box type lumped system method giving no
consideration to either surface or sewer routing. Discussions on applica-
tion of the rational method for urban storm drainage can be found in Yen
et al. (1974), Colyer and Pethick (1976), McPherson (1969), Chow (1964),
and Manuals and Reports on Engineering Practice No. 37 of ASCE and WPCF
(1969). The rational method gives only the peak discharge, Q , but not
the runoff hydrograph; i.e.,
Q = CiA (4)
in which C is the runoff coefficient; i is the rainfall intensity, and A
is the drainage area. The effects of the surface condition, antecedent
moisture condition and slope are adsorbed in the runoff coefficient C.
The value of i is assumed equal to the average rainfall intensity over a
duration equal to the so-called time of concentration which, for urban
area, is equal to the largest of the sum of overland flow time and sewer
flow time for the different possible flow paths.
The problems of the rational method, when applied to steep slopes,
come from the estimation of C and i, more seriously from the latter than
the former. The values of C given in the standard references are empir-
ical values from areas of relatively mild slopes with no or insignificant
effects of roll waves. For steep slopes C should be chosen as the higher
value of the range for the given condition.
The error due to i for steep slopes comes mainly from the overestima-
tion of the duration of the rainfall, which is due in turn mostly to the
overestimation of the overland flow time. Several methods have been
proposed for estimation of the overland flow time in urban areas. Izzard's
(1946) formula has the form
tc = C^i + C2i~2/3)(L/S)1/3 (5)
in which t is the time of overland flow; L is the length and S the slope
of the overland flow path; and C.. and CL are coefficients. This formula
19
-------
is useful only for small areas of less than 1 acre (0.4 ha) in size
because of the limitation that the nondimensional value of iL/v should not
exceed approximately 1000 (or iL<500 with i in in./hr and L in ft) where
L is the length of the flow path and v is the kinematic viscosity of the
water.
A formula to estimate the overland flow time that has been adopted by
the U.S. Department of Transportation Federal Aviation Administration
(1970) for airport drainage design is
t- r c i i r^T/^' f fi"\
L ~ V-*- ^ J_. X U / Lt / S V O /
in which t is in min; C is the runoff coefficient; and C, = 0.39 when L
c j
is in ft and C« = 0.69 when L is in m.
Another formula proposed by Kerby that is often used for urban over-
land flow, with t in min, is
in which N is a "retardance coefficient" ranging from 0.02 for smooth im-
pervious surface to 0.80 for conifer timberland or dense grass, and assumed
dimensionless here. The constant C, is equal to 0.83 for L in ft and 1.44
for L in m. The formula is applicable to L less than 1200 ft (365 m) .
Equations 5, 6, and 7 are all empirical formulas derived from data
from surfaces with relatively mild slopes. They overestimate the flow time
when applied to surface with steep slopes. Consequently, using any of
these three equations to estimate the rainfall duration for the rational
method will result in a lower intensity, and hence a lower Q .
By using the kinematic wave approximation (Fig. 4), it is possible to
establish a formula to estimate approximately the flow time. Ragan and
Duru (1972) proposed that for simple, homogeneous, constant slope overland
surface, and assuming constant Manning's roughness factor n, t is
(8)
20
-------
in which t is in min, C = 0.93 for L in ft and i in in./hr and C = 6.9
for L in m and i in mm/hr. Equation 8 provides a more reliable and
theoretically reasonable estimate of t than Eqs. 5, 6, or 7. Hence it is
recommended to use in estimating the overland flow time for the rational
method. However, one should realize that Eq. 8 is not without difficulties
in applications, and it is accurate only within the limitation of the
assumptions involved. For instance, a decision must be made in judging
the average condition of the overland surface in order to estimate the
representative slope S and Manning's roughness n, especially in the case
of sheet flow for which n varies considerably. Also, since the rainfall
intensity is a function of the rainfall duration, it may be necessary to
find t through trial-and-error for successive values of i, which in fact
is closer to the value of the rainfall excess averaged over the duration
than the corresponding average value of the rainfall.
With the proper estimation of the runoff coefficient and time of
concentration, and hence i, the rational method is equally applicable to
steep slopes as to flat slopes. It is suggested that Eq. 8 be used for
the estimation of the overland flow travel time until a better method
becomes available for the estimation. The sewer flow travel time may be
approximated by the steady uniform flow velocity of a half full pipe if
one is not willing to use any one of the slightly more reliably but more
complicated available techniques. It should be mentioned here that for
urban storm drainage in estimating the time of concentration normally an
accuracy of one or half a minute is sufficiently adequate. It is also
suggested that for steep slopes the runoff coefficient should be chosen
as the high value over the range for the given surface condition.
V-2. UNIT HYDROGRAPH METHOD
Any black box type lumped system method which takes no specific
consideration on how the water flows inside the drainage area would not
recognize explicitly whether the drainage area slope is steep or flat.
Hence the runoff prediction procedure of such a lumped system method is
21
-------
equally applicable to steep as well as flat slopes provided the appro-
priate values of the lumped system parameters are used. The rational
method discussed in the preceding subsection is an example. The unit
hydrograph is another example.
The unit hydrograph of a drainage basin is esentially a refer-
ence scale which is obtained through deduction of the past records of
rainfall and runoff. In application of this reference scale, the unit
hydrograph is simply re-applied to similar conditions to produce the
runoff hydrographs for the rainfalls being considered. In other words,
the deduced unit hydrograph already accounts for the effect of the slope.
Therefore, so long as the rainfall and runoff are within the range that
the linearity assumption that is basic to the unit hydrograph theory (Yen
et al. 1969, 1973) is valid, the unit hydrograph method is applicable to
drainage basins of flat slopes as well as steep slopes, and to basins
with simple as well as complicated drainage patterns. However, in many
urban areas the physical characteristics of the drainage basin change with
time, and there may exist no data to establish the unit hydrograph,
subsequently making the unit hydrograph method impractical.
Several techniques have been proposed to synthesize unit hydrographs.
One group is to transform the unit hydrographs from gaged to ungaged
drainage basins. This approach to establish synthetic unit hydrographs
have not been proven successful for urban areas. Contrarily, synthetic
unit hydrographs obtained through theoretical or semi-theoretical
techniques have proved feasible with limited degree of success. In fact,
this concept of synthetic unit hydrographs is adopted in the proposed
method for prediction of runoff from steep slope areas that will be
described in Section VII.
V-3. CHICAGO HYDROGRAPH METHOD
Any storm runoff simulation model that hydraulically is of the level
of kinematic wave or lower is incapable of reflecting the dynamic effect
of the flow. Therefore, the model cannot faithfully predict the flow when
the dynamic effect becomes important. Lighthill and Whitham (1955)
22
-------
suggested that for simplified cases of unidirectional wide-channel flow the
dynamic effect becomes important when the Froude number approaches about
2. This, of course, does not take into consideration of the rapidly
varied flow conditions such as hydraulic jumps. Actually, for storm
runoff on heterogeneous urban land surface and in sewers, the dynamic
effect becomes significant for flow having the Froude number as low as
0.8. However, in the kinematic approximation because the dynamic effect
is not reflected, the calculation will produce numerical results which
differ from the true solutions. Whether the numerical result can be con-
sidered as an acceptable approximation depends on the physical conditions
of the flow and the solution accuracy required.
Chicago hydrograph method, by using modified Izzard's (1946) method
for overland flow computations and storage routing with Manning's for-
mula for gutter and sewer flow computations (the time-offset procedure is
hydraulically much less desirable) is essentially a linear kinematic wave
approximation incapable of accounting for the dynamic effect due to steep
slopes. Moreover, the method was developed based on the conditions of
flat land which is typical in Chicago. Presumably, the linear kinematic
wave routing scheme used in the gutter and sewer flows may be used as an
approximation for steep slope areas, provided the overland runoff routing
is modified and the applicability is verified with field data. Therefore,
before such verification is done, the Chicago hydrograph method in its
present form is inappropriate to be used for steep slope areas despite
the fact that it could produce numerical results.
V-4. TRANSPORT AND ROAD RESEARCH LABORATORY METHOD
The British TRRL method, commonly known as RRL method in the
United States, is another hydrograph routing method that hydraulically is
of a level lower than the linear kinematic wave approximation. The flow
from impervious surface is estimated by a flow-time area method and the
sewer flow by reservoir routing with the hydrographs lagged by the time
of travel computed based on steady uniform full pipe flow velocity. Since
23
-------
the dynamic effect of the flow cannot be accounted for, there is no compu-
tational stability problem when applied to steep slopes and the method will
produce numerical results of undetermined reliability. However, the method
was developed based on British data of less intense rainfall and relatively
mild ground slope with roofs draining directly into sewers. Therefore, it
is inappropriate to apply the TRRL method to steep slope areas in the
United States without modifications and without sufficient testing to es-
tablish its adequacy and reliability.
Based on their experience in applying the TKRL method to rainfall-
runoff data from American watersheds, Terstriep and Stall (1974) proposed
a model called ILLUDAS which is a modification of the TRRL method. The
major differences between the ILLUDAS and TRRL are that the former con-
siders also the runoff contribution from pervious areas by applying the
same flow time-area method to both the pervious and impervious areas, and
that it uses Manning's formula instead of Colebrook-White formula as in
the TRRL method to compute the sewer flow.
Realizing the inadequacy of the TRRL method when applied to outside
of the Great Britain and based on their experience in Kenya, the TRRL
method developers also proposed a modified version to account for the
runoff contribution from pervious areas. They used a linear reservoir
model instead of time-area method to represent the runoff from pervious
areas. It appears that this linear reservoir model would work well if
the abstractions follow an exponential decay function of the type of
Horton's infiltration formula.
Neither the ILLUDAS nor the modified version of TRRL method has
changed the hydraulic level of the original TRRL method. Therefore,
they share the same conclusions as the TRRL method for their applicabil-
ity to areas of steep slopes.
V-5. UNIVERSITY OF CINCINNATI URBAN RUNOFF MODEL
The University of Cincinnati Urban Runoff (UCUR) model is in-
cluded here, despite its lack of popularity, merely because it was evalu-
ated previously (Chow and Yen, 1976). Hydraulically it differs from other
24
-------
methods in that it has a higher level and more sophisticated routing
scheme for the overland surface flow than for both gutter and sewer flows.
The overland flow routing is a simplified kinematic wave approximation
whereas the gutter flow is routed simply by using the continuity equation
and the sewer flow by lagging the hydrograph without modification.
Being hydraulically a relatively low level method, the UCUR model
will give numerical results when applied to steep slope drainage basins.
However, the reliability of the results is in doubt. As mentioned in Sub-
section V-3, for a flow on a steep slope the dynamic effect becomes im-
portant and the kinematic wave approximation that is used for overland
flow routing may not be adequate. But this inadequacy is relatively in-
significant when compared to the gutter flow routing of the TJCUR model
which uses only the continuity equation of steady spatially varied flow.
No geometric or hydraulic characteristics of the gutter are required
except the gutter length. For two gutters having different gutter slopes
but identical length and overland flow conditions, the TJCUR model will
give identical inlet hydrographs although in fact the gutter with steeper
slope will give a hydrograph with higher and earlier peak discharge.
Hydraulically, the UCUR, TRRL, and Chicago methods are of simi-
lar level which will produce numerical results when applied to drainage
basins with steep slopes. However, one has to be extremely careful in
accepting these results even as an approximation because of their doubtful
reliability inherent with the simplicity of the methods. Particularly,
the UCUR model is inferior to the other two methods and yet it is much
more complicated in application.
V-6. DORSCH HYDROGRAPH-VOLUME-METHOD
The Hydrograph-Volume-Method (HVM) proposed by the German firm,
Dorsch Consult, is a method that has been widely misunderstood and mis-
interpreted in the United States. Similar to the TRRL method, the
surface flow is treated without considering separately the overland flow
and gutter flow. The surface runoff is routed by using a linear kinematic
25
-------
wave approximation. As discussed previously, the kinematic wave approxi-
mation will impose no computational difficulty when applied to steep slope
surface but its reliability is questionable.
The sewer flow is routed by using a simplified diffusion wave
approximation. The simplification is made through an assumption on the
ratio between friction slope and sewer slope (Vogel and Klym, 1973). This
assumption substitutes the specification of one of the two boundary con-
ditions required in solving the differential equations. For subcritical
flow this eliminates the need of the downstream boundary condition, en-
abling the solution to proceed towards downstream sewer by sewer in a cas-
cading manner, and consequently it eliminates the need to solve many
simultaneous algebraic equations to obtain the solution. It also elimi-
nates the means to realistically account for the downstream backwater
effect for subcritical flow. However, for supercritical flow, the two
boundary conditions are normally specified at the upstream end of the sewer.
Therefore, this assumption on friction slope is merely an unnecessary con-
dition that further jeopardizes the reliability of the solution.
Moreover, for unstable supercritical flow with roll waves, diffu-
sion wave approximation offers no mechanism to realistically account for
the dynamic effect of the flow. Therefore, a true nonlinear diffusion wave
model will not adequately represent the flow and yet poses considerable
computational difficulties. However, in the Dorsch HVM, the assumption on
the ratio of friction and channel slopes may have reduced or even elimi-
nated the computational difficulties, and thus provide numerical results.
Nevertheless, the significance and accuracy of the computed results, if
obtainable, has yet to be evaluated and is not investigated in this
study because of the limitation in budget and manpower of this project
and the proprietary nature of the method.
V-7. STORM WATER MANAGEMENT MODEL
An evaluation and comparison of the EPA SWMM for mild slope drainage
areas has been reported previously (Chow and Yen, 1976). Recently
another version of the model, WRE SWMM, has become nonproprietary and avail-
able to the public under the support of U.S. EPA. Therefore its applica-
bility to areas of steep slope is also discussed here.
26
-------
As shown in Table 1, the EPA SWMM uses linear kinematic wave
routing for overland and gutter flows and an improved nonlinear kinematic
wave routing for sewer flow. Therefore, the model could provide numerical
results if the numerical solution scheme and the computational time inter-
val are properly chosen. In the EPA SWMM a four-point implicit finite
difference scheme is used in solving the nonlinear kinematic wave approxi-
mation to sewer flow. For supercritical flow no iteration is performed
(Metcalf 5. Eddy et al., 1971, Vol. 1, p. 127, Vol. 3, pp. 127 and 128).
When the downstream backwater effect is insignificant, the pipe flow may
also be approximated by using the linear kinematic wave model of gutter
flow (Metcalf & Eddy et al., 1971, Vol. 1, p. 76 and Vol. 3, p. 52).
When the sewer is connected at its downstream end to a large storage ele-
ment from which the backwater effect is important, the water surface is
assumed to extend horizontally upstream until it intercepts the sewer
invert (Metcalf & Eddy et al., 1971, Vol. 1, pp. 129-132 and Vol. 2,
pp. 160-162). The sewer flow above this interception point is calculated
by using the kinematic wave approximation. For supercritical sewer flow
this backwater assumption precludes the consideration of the formation
of hydraulic jump which may actually occur in such flow condition.
Moreover, as discussed in Subsection V-3, the kinematic wave
approximation does not account for the dynamic effect of the flow and is
inaccurate for supercritical flow with roll waves. Of course, whether an
approximation is acceptable depends on the required accuracy. However, it
is beyond the scope of the present study to investigate the accuracy of the
kinematic wave model to approximate flow in steep slope areas. Since, un-
like the subcritical flow and stable supercritical flow cases, theoretical
solutions are not yet available for unstable supercritical flow with roll
waves, such an accuracy verification can only be accomplished by using lab-
oratory or well controlled field data from small, well defined drainage
areas, which unfortunately are also unavailable. The EPA SWMM developers
applied the model to the San Francisco Baker Street Drainage Basin (which
will be described in the following section) to simulate the runoff from re-
corded rainstorms (Metcalf & Eddy et al., 1971, Vol. 2, pp. 27-28). The
27
-------
agreement between the computed and measured results is far from satis-
factory. It cannot be identified whether the discrepancies are due mainly
to the data deficiency or the model inadequacy.
The WRE version of SWMM has identical overland and gutter flow routing
schemes as the EPA SWMM. However, the sewer routing is a dynamic wave
scheme solving the St. Venant equations using an explicit finite difference
scheme. Explicit scheme is easy to formulate, easy to understand, and easy
to program. Thus, it is a logical first trial for anyone who is not fa-
miliar with numerical solution techniques for the St. Venant equations.
Unfortunately, the explicit scheme is also notoriously known for its poor
computational stability and efficiency (e.g., see Gunaratnam and Perkins,
1970; Price, 1974; Sevuk and Yen, 1973; Yevjevich and Barnes, 1970). From
a practical viewpoint it can be used only for sharp flood waves of short
durations which would restrict the applicability of the explicit scheme
to a small drainage basin of only a few sewer pipes under a short duration
heavy rainfall. Moreover, as discussed in Section IV, the St. Venant
equations cannot adequately represent the unstable supercritical flow and
stability problems will develop in the solution process. Therefore, WRE
SWMM is not applicable to steep slope areas without further restrictive
assumptions as in the EPA SWMM.
V-8. ILLINOIS URBAN STORM RUNOFF MODEL
Hydraulically the Illinois Urban Storm Runoff (IUSR) model is prob-
ably the most sophisticated of all the existing urban storm runoff pre-
diction models. As summarized in Table 1, the overland runoff is routed
by using a nonlinear kinematic wave approximation (Eq, 1 and Fig. 4) with
the friction slope S,. computed by using Darcy-Weisbach's formula (Chow
and Yen, 1976). This is because for overland sheet flow Manning's
roughness factor n is no longer a constant. Gutter flows are routed
also by using a nonlinear kinematic approximation but the friction slope
is estimated by using Manning's formula with constant n which is simpler
than Darcy-Weisbach's and yet provides adequate accuracy under the normal
conditions of gutter flows. Similar to the linear kinematic wave approxi-
mation that is used in SWMM in routing surface flow, the nonlinear
28
-------
kinematic wave approximations for surface runoff in the IUSR model when
applied to steep slopes will produce numerical results but the accuracy
has not been verified.
The sewer flows of the IUSR model are routed by using a nonlinear
complete dynamic wave model with a first-order method of characteristics
numerical scheme. Both the upstream and downstream backwater effects
from the sewer junctions are accounted for. The more complicated routing
scheme for sewer flows than for surface flows is justified by the fact
that in terms of their effects on the accuracy of the sewer outflow hydro-
graphs, approximation of surface flows is more tolerable than that for
sewer flows, and that sewer flows have much better definite boundary con-
ditions. Moreover, for combined sewer systems, dry weather flows are
confined in the sewers while no surface flow computation is needed. The
consideration of backwater effects at junctions and manholes makes a
model such as the IUSR method hydrodynamically superior to other sewer
routing techniques. The sewer routing technique of the IUSR method is
efficient and stable for subcritical and stable supercritical flows.
However, when applied to unstable supercritical flow with roll waves,
the computation becomes unstable and usually no solution can be obtained.
The instability comes both from numerical and hydrodynamic causes. The
hydrodynamic instability is particularly serious when the roll waves grow
and tend to overtop and break. As mentioned previously the St. Venant
equations cannot adequately represent the unstable supercritical flow
with roll waves. Conversely, investigation on the possible solution
techniques for Eq. 3 together with Eq. 1, which can represent mathemati-
cally the supercritical flow with roll waves, has never been conducted.
In this research project the IUSR model was applied to the Baker
Street Drainage Basin which is a steep slope basin as will be described
in the Section VI. Several futile attempts were made trying to overcome
the stability problems to produce some meaningful results. The effort
was soon given up because it was a very difficult task far beyond the
time and financial limitations of the project. Thus, in its present
form the IUSR model is inapplicable to steep slope areas where roll waves
would occur.
29
-------
SECTION VI
EXAMPLE URBAN AREA OF STEEP SLOPE BAKER STREET
DRAINAGE BASIN IN SAN FRANCISCO
The Baker Street Drainage Basin in San Francisco is selected as an ex-
ample to illustrate problems involved in storm runoff simulation for urban
areas having steep slopes. The basin is located at the north shore east of
the Golden Gate Bridge and the Presidio Military Reservation in the City of
San Francisco (Fig. 5). Because of the time and financial limitations of
this research project, neither an instrumental nor a photographic survey was
undertaken to collect the drainage basin physical data. Most of the informa-
tion presented in this section was obtained from the city maps and drawings
provided by the Engineering Bureau of the Department of Public Works of the
City and County of San Francisco. A detailed visual survey was also con-
ducted to supplement and to confirm the data.
VI-1. GENERAL BASIN CHARACTERISTICS
The Baker Street Drainage Basin has a combined sewer system, draining a
mostly residential area with steep slopes. The outlet of the basin is the
diversion structure located at Baker Street and Marina Boulevard at which
point dry weather flow (including the sanitary sewage from the Presidio)
and runoff from light rainfall is intercepted and transported through the
Marina Pumping Station to the North Point Sewage Treatment Plant. The inter-
ceptor was designed to carry the dry weather flow plus the runoff from a
rainfall of 0.02 in./hr (0.5 mm/hr) with a rational formula runoff coeffi-
cient C = 0.65. Outflow from the basin exceeding the capacity of the inter-
ceptor is discharged directly north into the San Francisco Bay through the
outfall structure at about 250 ft offshore at the Outer Marina Beach.
The size of the Baker Street Drainage Basin above the diversion struc-
2
ture as shown by the heavy solid line in Fig. 6 is 180 acres (0.73 km ).
30
-------
Boy
N
c
o
1)
u
o
Baker St.
Drainage
Basin
Presidio
Military
Reservation
Office Bldg.
San Francisco City and County
San Mateo County
Fig. 5. Location map of Baker Street Drainage Basin
31
-------
The population within the drainage basin is of the order of eight thousand,
excluding that from the Presidio Military Reservation. The basin is actually
divided into two parts: an upper basin and a lower basin. The upper
(southern) basin is bounded approximately at its east by Lyon Street, north
by the earth embankment of the Presidio, west by Cherry and Maple Streets,
2
and south by Clay Street. The size of the upper basin is 68 acres (0.27 km ),
mostly medium to high income dwellings with a significant amount of trees and
shrubs. The streets are well maintained with one or more litter boxes in
almost every block. The gutters and inlets are reasonably clean. The lower
(northern) basin is bounded at its west from the Presidio by Lyon Street,
south by Pacific Street, east by Devisadero and Broderick, and north by
Jefferson, Marina, Lyon, Baker and Bay as shown by the solid line in Fig. 6.
The size of the lower basin above the basin outlet (interceptor) is 112 acres
2
(0.45 km ), consisting of medium to above medium housing, with some community
commercial activities, most of which are on or immediately below Lombard
Street. The residential houses in the lower basin have small lawns with
little or no shrubs and trees. The streets surrounding the commercial area
are generally more littered than the residential area.
The runoff from the upper basin is drained into an egg-shaped sewer off
Pacific between Locust and Laurel Streets. The egg-shaped sewer which is
buried diagonally in the Presidio, connects the upper basin to the lower
basin at Lyon and Union Streets.
The most noticeable physical feature of the basin is its steep slope,
particularly in the southern (upper) portion of the lower basin, where in a
five-block distance, the elevation rises along Lyon Street from 90 ft at
Filbert to 370 ft at Pacific, and along Baker from 60 ft at Filbert to 340 ft
at Pacific. In fact the portion of Baker Street between Broadway and Vallejo
is so steep (a grade of 35%) that the street has long been closed and grass
and weeds are full grown on the surface. The percentage of the total basin
area for different ranges of land slope is listed in Table 2 based on the in-
formation given in a report by Engineering-Science, Inc. (1971). The topog-
raphy of the basin is shown in Fig. 6. The numbers at the corners of the
blocks are the elevations in feet at the intersections. The highest ground
32
-------
San Francisco Bay
MARINA
JEFFERSON
All Elevations Are In Feet
Numbers At Corners Are Elevation
At Intersections
FRANCISCO
CHESTNUT
ZOO m 400 m 600 m
Basin Boundary
PRESIDIO
MILITARY
RESERVATION
275
WASHINGTON
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Fig. 6. Topograph of Baker Street Drainage Basin
33
-------
TABLE 2. LAND SLOPE DISTRIBUTION OF BAKER STREET DRAINAGE
BASIN (Engineering-Science, Inc., 1971)
Land slope, %
Percent of Basin Area
<2
18.1
2-5
9.9
5-10
33.7
10-15
24.7
15-20
6.5
>20
7.1
in the basin is 370 ft above the mean sea level at the intersection of Lyon
and Pacific which is also the dividing point between the upper and lower
basins. Typical photographic views of the basin are shown in Fig. 7.
VI-2. SURFACE DRAINAGE PATTERN
The surface drainage pattern of the land surface of the Baker Street
Basin is shown in Fig. 8. In general the rainwater that falls on the land
surface is collected through gutters into inlet catch basins which in turn
are connected to sewers. There are four types of land surface; namely,
roofs, lawns and yards, paved sidewalks, and street pavements. Some of the
roof and yard runoffs are drained directly into the combined sewers without
flowing through the gutters. The relative percentages of size of the four
different types of land surface vary from block to block. Detailed data on
the distribution of these four types of surfaces for each block of the Baker
Street Basin is unavailable. It has been estimated (Engineering-Science, Inc.,
1971) that the land use of the entire drainage basin consists of 80% resi-
dential, 8% commercial, the remaining 12% of land being vacant or belonging
to governmental agencies, and there is no industry. About 60% of the basin
area is impervious, including nearly 9 miles (14 km) of streets.
The standard nominal width of the roadway pavement of most of the
streets is 68.8 ft (21 m). The exceptions are Broadway (82.5 ft or 25 m) ,
Marina, Richardson, and most of Lombard, which have a width of about 100 ft
(30 m). All the streets are paved with asphalt or concrete. Most streets
have gutters and sidewalks on both sides. The sidewalks are paved, usually
9 ft (2.7 m) to 12 ft (3.7 m) wide. As shown in Fig. 7c, many houses in the
34
-------
(a) Typical view of upper
basin Jackson Street
between Maple and Spruce
(b) Baker Street looking
north from Vallejo
Street
(c) Typical view of
lower basin
Fig. 7. Photographic views of Baker Street Drainage Basin
35
-------
Son Francisco Bay
1. Diversion Structure
2. Semi -Automatic Water
Sampling Station
3. Flow Measurement
4. Dye Injection For Flow
Measurement
5. Raingage
U
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X
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Fig. 8. Baker Street surface drainage pattern
36
MARINA
JEFFERSON
WASHINGTON
CLAY
-------
lower basin are built adjacent to the sidewalk without separation by a lawn
or yard. In the upper (southern) part of the lower basin and in the upper
basin, many houses were built 6 ft (2 m) to 10 ft (3 m) away from the side-
walk, separated by a lawn or paved yard. In general the sizes of the lawns
and yards in the Baker Street Basin are much smaller than those in standard
American suburban houses. The standard block size excluding the roadway
pavement is 412.5 ft (126 m) by 255.4 ft (78 m) in the upper basin and
412.5 ft (126 m) by 275.0 ft (84 m) in the lower basin, respectively. How-
ever, blocks adjacent to Presidio Avenue in the upper basin and to Lyon,
Broadway, Lombard, and Richardson in the Lower basin differ from the
standard sizes.
All the roadway pavements of the streets are crowned, except a few
streets which have steep lateral slope so they incline only to one side.
According to the standards of the City of San Francisco the crown is 1.0, 0.8
or 0.6 percent of the roadway width between curbs, when the street grade is
respectively 0 to 0.03, greater than 0.03 to 0.06, and greater than 0.06.
All the street gutters are formed by the sidewalk curb connected to the
roadway pavement. Most of the gutters are approximately triangular in cross
sectional shape and with the gutter bottom set to fit the crown or super-
elevation of the adjacent roadway. The concrete curbs are built with a
slope of 1:4 with vertical, and the curb height is 6 in. (15 cm) or 8 in.
(20 cm) as shown in Fig. 9. Most of the gutters and curbs in the drainage
basin are as those shown in Fig. 10. A typical view of the curb and gutter
is illustrated in Fig. 11. (Note that the piece of white paper is 11" x
8-1/2" in size). However, many curbs and gutters are interrupted by the
driveway of the houses which is a rather common phenomenon in urban resi-
dential areas.
The length and slope of the gutters are listed in Table 3. In the
table the streets that have a gutter at only one side or unequal gutter
lengths at both sides of the street are specified. Otherwise it is under-
stood that each street has one gutter at each side with identical length
and slope. The values of gutter slope are taken from a map supplied by
the Bureau of Engineering of the City and County of San Francisco. They
37
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Fig. II, Typical view of sidewalk curb Broderick Street
Fig. 12. Semi-circular grate inlet
45
-------
are approximately equal to the difference between the intersection eleva-
tions given in Fig. 6 divided by the corresponding gutter length.
Runoffs in gutters are collected at the downstream end through gutter
inlets into catch basins. Three types of inlets are used in the Baker
Street Basin: semi-circular grate inlet, rectangular grate inlet, and
curb inlet. Most of the inlets are semi-circular grate which is made of
steel, consisting of a semi-circle of 2 ft (0.6 m) diameter and a 2 ft
(0.6 m) by 1 ft (0.3 m) rectangle as shown in Fig. 12. There is only one
rectangular grate inlet in the Baker Basin. The curb inlets are usually 2
ft (0.6 m) long with little or no depression. The type of inlet at the
downstream end of each gutter is also given in Table 3. The first letter
before the dash identifies the inlet for the north or west gutter of the
street, the second letter (after the dash) identifies the inlet for the
south or east gutter of the street. The distribution of the inlets are
shown in Fig. 8. Also shown by arrows in the figure is the direction of
street gutter flow according to the topographic condition.
Obviously, because of the shallow gutters and relatively small inlet
openings, on a street with steep longitudinal slope a significant part of
the fast moving storm water may flow on the roadway pavement, not getting
into the gutters, and bypassing the inlets. It is not difficult to
conceive that under heavy rainfall streets such as the southern portion of
Broderick, Baker, and Lyon become a channel for the storm runoff. Fortu-
nately the short duration rainfall intensity at San Francisco is much
smaller than those at the eastern half of the nation. Hence, the chance
of occurrence of having the major part of storm water runoff on surface
instead of in the sewers is rather small.
VI-3. SEWER SYSTEM
The layout of the sewer system of the Baker Street Drainage Basin is
shown in Fig. 13. The detailed information on the length, size, and slope
of the sewers is given in Table 3. The sewer layout and sizes is obtained
from a map provided by the Engineering Bureau of the City and County of
San Francisco and it differs considerably in both the layout and sizes given
in an earlier blueprint map which was also supplied by the Engineering Bureau.
46
-------
IV
Presidio
Sanitary Sewer *o
7
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Fig. 13. Baker Street Drainage Basin sewer system
47
-------
The node numbers used in Fig. 13 and Table 3 to identify the beginning
and end of the sewers are approximately the ground elevations at the respec-
tive nodes, except Nodes 501 and 502. Different nodes having the same
elevation are differentiated by a letter (a,b,c, etc.) following the number.
Nearly all of the sewers are buried under the roadway pavement of the corre-
sponding streets.
As shown in Fig. 13, the sewer system can be divided into three parts:
the upper basin system, the main-line, and the lower basin system. The main-
line starts at Node 170 at the junction of Locust and Pacific, draining the
flow from the upper basin northward in a tunnel at the southeast corner of
the Presidio Military Reservation to the lower basin at Node 120 at the
junction of Lyon and Union, from where it runs eastward under Union for one
block and then turns north under Baker Street, heading north to the diver-
sion structure at the junction of Baker and Marina. The Presidio Military
Reservation has a separated storm sewer system and supposedly no sewer
connection is made to the main-line in the tunnel or anywhere else except
at Node 5a at the junction of Baker and Bay where the Presidio sanitary
sewer is connected to the Baker Street main-line.
The combined-flow sewers of the main-line are all egg-shape concrete
pipes except the last 1720 ft (520 m, 5 blocks) which are circular concrete
pipes. A typical cross section of an egg-shape sewer is shown in Fig. 14.
The sizes of the egg-shape sewers are 2'-6" x 3'-9" from Node 170 (Locust
and Pacific) to Node 120 (Lyon and Union), followed by 2' x 3' size to
Node 31 (Baker and Lombard) and then 2'-6" x 3'-9" to Node 7a (Baker and
Francisco). For the last five blocks from Node 7a to the diversion
structure at Baker and Marina the diameters of the circular concrete pipes
are 5 ft (1.5 m) for the first four blocks and 5.5 ft (1.6 m) for the last
block. The slope of the main-line sewers obtained from the information
supplied by the city of San Francisco is given in Table 3.
The upper basin sewer system can again be divided at Laurel Street
into the east and west subsystems as shown in Fig. 13. All the sewers in
the upper basin are circular vitrified clay pipes. The sewers in the
eastern subsystem most likely have steeper slopes than those in the western
48
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(b) Egg-shape sewers
51
-------
subsystem. Since data on sewer slopes (except for the main-line) were not
supplied in the information provided by the Engineering Bureau of the City
and County of San Francisco, it is assumed that for the sewers in the
upper basin as well as those in the lower basin the sewer slopes are equal
to the corresponding average ground slopes, which is computed as difference
of the elevations at the intersections (given in Fig. 6) divided by the
distance between the intersections. The average ground slope is smaller
than the corresponding street-gutter slope because of the relatively flat
street surface at the intersections. The sewer slopes for both the upper
and lower basins are listed in Table 3.
The lower basin consists of two major subsystems and 18 minor sub-
systems, each subsystem draining directly into the main-line. The two
major subsystems are the Baker Street line which starts at the junction
of Lyon and Pacific and joins the main-line at the junction of Baker and
Union, and the Broderick line which starts at Node 58 (Baker and Pacific)
and joins the main-line at Node 7a (Baker and Francisco). In general the
sewers in the southern part of the lower basin have steeper slopes than
those in the northern part, and those running from south to north have
steeper slope than those running in the east-west direction. All the
sewers in the lower basin are circular vitrified clay pipes, except the
last three sections of the Broderick line, for which from Node 22
(Broderick and Lombard) to Node 7c (Broderick and Francisco) are 2' x 3'
egg-shape concrete pipes, and from Node 7c to Node 7a (Baker and Francisco)
are 2'-6" x 3'-9" egg-shape concrete pipes.
The sewers receive storm water from connecting upstream sewers and
inlet catch basins. There is no unusually large catch basins, manholes,
or sewer junctions. Their storage volume is small in comparison to the
storm runoff volume when overflow at the diversion structure occurs.
Typical junctions for circular and egg-shape sewers are illustrated in
Fig. 15.
For the purpose of monitoring the quality of the sewer flow, a semi-
automatic water sampling station was installed in the sewer system at
the junction of Baker and Jefferson. The drainage area of the basin above
52
-------
2
this point is 175 ac (0.71 km ). Sewer flow measurements were made by in-
jecting dye at the junction of Baker and Northpoint and taking the measure-
ments at Baker and Beach. The area of the basin upstream of Node 3a (Baker
?
and Beach) is 171 ac (0.69 km ).
VI-4. RAINFALL AND RUNOFF DATA
The U.S. National Weather Service has two official precipitation
gauging stations near the Baker Street Drainage Basin: one at the Federal
Office Building about 1.7 mi (2.5 km) to the southeast, and the other at
the Richmond-Sunset Water Pollution Control Plant in the Golden Gate Park
about 3 mi (5 km) to the southwest. Good records have been kept for these
stations. However, it is well known that considerable spatial variability
of the weather exists in the San Francisco Bay region because of the
special topographic and climatic characteristics of the area. It has yet
to be investigated how reliable the precipitation records of the above
mentioned two stations are to represent the rainfall in the Baker Street
area. During the 1969-70 winter season the Bureau of Engineering of the
City and County of San Francisco installed a network of 13 recording
rain gages, one of which is in the lower part of the Baker Street basin
(Fig. 6). An analysis of the data from these rain gages and those from
the National Weather Service stations confirmed that there exists sig-
nificant spatial and temporal variations of rainfall within the city.
In 1969 the Bureau of Engineering of the city monitored the runoff
from three rainstorms (April 4-5; October 15; and November 5) to investi-
gate the quantity and quality of storm water runoff from the Baker Street
Drainage Basin. The data were used in the verification of the Storm
Water Management Model (SWMM) (Metcalf & Eddy, Inc. et al., 1971) and
also in a project on treatment of combined sewer overflows by the
dissolved air floatation process (Engineering-Science, Inc., 1971). The
data as reported in the latter report are summarized in Table 4 and the
corresponding hyetographs and hydrographs are shown in Figs. 16, 17, and
18 respectively for the three rainstorms. The discharge measurements
were made by injecting dye at the junction of Northpoint and Baker
Streets and taking concentration samples at the junction of Beach and
Baker Streets. The hydrographs shown in Figs. 16 to 18 are the "due to
53
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storm" hydrographs which are the measured discharges deducted by the
3
average dry weather flow of 2.64 cfs (0.074 m /s) which was determined
by the dry-weather-flow measurements on 19-20 May, 1969. Runoff water
quality samples were taken at the junction of Jefferson and Baker Streets.
The pollutographs of COD, BOD, total and volatile suspended solids,
grease, floatable materials, and conductivity for the runoff from these
three rainstorms are shown in Appendix as Figs. A<-1, A-2, A-3 and
Table A-l. Detailed information on sampling techniques, dye injection
flow measurement and data can be found in the report by Engineering-
Science, Inc. (1971).
The rainfall intensity data for the rainstorms of April 4-5, 1969
and October 15, 1969 used in the verification of SWMM (Metcalf & Eddy, Inc.
et al., 1971, Vol. 2, pp. 27 and 28) are also plotted in Figs. 16 and 17
since they differ from those presented by Engineering-Science, Inc. (1971).
The total amount of rainfall in Fig. 16 is 0.31 in. (7.8 mm) under the
hyetograph by Engineering-Science, Inc. and 0.35 in. (8.9 mm) by Metcalf &
Eddy Inc. et al., and in Fig. 17 is 0.44 in. (13.4 mm) and 1.73 in. (52.5
mm), respectively. Presumably both sets of hyetographs were derived from
the same rainfall depth record at the Federal Office Building gauging
station at downtown San Francisco and should agree at least in terms of
total rainfall volume. A check of these hyetographs against the official
rainfall record at the Federal Office Building was not done In this in-
vestigation partly because it was felt that this record is not a true
representation for the Baker Street Drainage Basin and partly due to the
time and expenses in acquiring the record from the NOAA Environmental
Data Service, National Climatic Center.
With the installation of a recording rain gage and a sewer flow
level monitor within the drainage basin by the City Bureau of Engineering,
a large amount of good quality data on rainfall and runoff becomes avail-
able. These data are available from the Division of Sanitary Engineering
of the Bureau of Engineering, Department of Public Works, City and County
of San Francisco. The rain gage is a tipping bucket automatic recording
rain gage and the record is transmitted directly into a digital computer
58
-------
system in the central office of the Bureau of Engineering to record on
magnetic tape and printout. The tipping buckets have a standard capac-
ity of 0.01 in. (0.25 mm). During rainfall whenever the bucket tips a
signal indicating the tipping time to the nearest second is transmitted
to the computer and recorded. A typical printout is shown in Table 5.
The rain gage for Baker Street is identified as gage No. 12. The value
in the table under this column of No. 12 indicates, to the nearest second,
the occurrence of 0.01 in. (0.25 mm) rainfall. For example, the first
value, 43, in the column indicates a bucket of rainfall on the 295th day
of the year (i.e., October 22), at the time 19 hr 18 min 43 sec. The
hyetograph of the rainfall on October 22, 1973 is plotted in Fig. 19 using
a 10 min interval. However, it is probably more reliable to obtain the
hyetograph by first computing the cumulative rainfall as shown in Fig. 20.
The slope of the cumulative curve represents the rainfall intensity and
from which the hyetograph can be plotted.
The sewer runoff water level was monitored by an automatic level
recording gage at Baker and Francisco Streets. A typical printout of
the recorded data is shown in Table 6. The readings were taken at every
15 sec and the number for level indicates water level of flow in inches.
For example, the number 3 circled in the table indicates that on Day 295
(October 22) at 18 hr 55 min 15 sec the flow water stage is 3 in. (76 mm)
above the reference data. The stage can be converted into discharge if
a proper rating curve is available.
59
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63
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SECTION VII
PROPOSED SIMPLIFIED METHOD FOR RUNOFF FLOWRATE
DETERMINATION FOR AREAS OF STEEP SLOPES
As discussed in Sections IV and V, ironically it is the supposedly
more reliable, higher level of hydraulic sophistication runoff prediction
models that have more difficulties in producing results when applied to
areas having steep slopes. In fact, the model with the highest level of
hydraulic sophistication, the Illinois Urban Storm Runoff Model, is simply
unable to produce numerical results. Presumably the WRE SIMM will also
be unable to produce any results if the computation is carried out by
using the dynamic wave equations with an explicit numerical scheme.
Moreover, even if a technique is developed that will be able to produce
results, the computer cost to obtain such solutions would probably be
prohibitively high and the accuracy cannot be guaranteed.
Conversely, from an engineering viewpoint, by considering the fact
that the time of travel of the fast flowing runoff water on a steep slope
surface, gutter, or sewer is relatively short, it is possible to develop
simplified approximate methods that can be used for flow rate determina-
tion producing results that are within acceptable engineering accuracy.
One such method which was developed in this project is described in this
section.
The method is developed on the basis of the fact that the water
travel time for the surface runoff and sewer flow in a block with
steep slope is short relative to the computational time interval
used in routing and hence accurate determination of the travel time
becomes unnecessary. The simplified method consists of the development
and utilization of the inlet unit hydrographs for surface runoff and a
modified linear kinematic wave routing of the sewer flow.
VII-1. SURFACE RUNOFF AND INLET HYDROGRAPH DETERMINATION
The method described below for the determination of inlet hydro-
graphs is applicable to steep slope areas as well as to mild slope areas.
64
-------
(A) Determination of Inlet Unit Hydrographs
The first step is to classify the surface areas of the drainage basin
into typical groups. For example, the Baker Street Drainage Basin can be
classified into three groups; namely, the blocks of the Upper Basin and
southern Lower Basin which are characterized by residential blocks with
steep slopes; the blocks of the Lower Basin which are semi-residential
blocks with some commercial and with medium slopes; and the blocks of the
northern Lower Basin which are characterized by relatively densely built
residential blocks with flat slopes.
For each group, for each block of identical size a typical unit hydro-
graph for each of the inlets of the block is established. Any method that
is generally acceptable to produce unit hydrographs can be used to estab-
lish the inlet hydrographs. It can be determined as the average of a
number of hydrographs measured at the inlet or identical inlets, exactly
in the same manner as normally done to obtain unit hydrographs for larger
natural watersheds. Or it can be determined by using any one of the
synthetic methods. However, measured data of runoff at city block inlets
are normally unavailable and unreliable. Also, past data may represent
the runoff for a physical condition that is different from the present or
future conditions. Under such circumstances the inlet unit hydrographs
can only be derived based on synthetic methods.
One synthetic method that has been applied to the Baker Street
Drainage Basin to establish inlet unit hydrographs is the Illinois Surface
Runoff (ISR) model (Chow and Yen, 1976). For each block the surface is
divided into rectangular strips. Within each strip the physical proper-
ties of the land surface as well as abstractions are assumed to be homo-
geneous. Each strip flows into a gutter which in turn flows into the
inlet at its downstream end or turns the block corner into the next
gutter. No more than 10 rectangular strips are allowed for each gutter.
The flow directions of the strips and gutters are determined by the topo-
graphic conditions. Both the overland flow and gutter flow are simu-
lated by the one-dimensional nonlinear kinematic wave approximation,
e.g., Eq. 1 and from Fig. 4,
- Sf + ^
-------
with all the symbols defined before and listed in Notation. For overland
flow the friction slope Sf is computed by using Darcy-Weisbach's formula
with Weisbach's resistance coefficient estimated by a simplified Moody
Diagram (Chow and Yen, 1976). For gutter flow Sf is computed by using
Manning's formula. The reason to use the computationally more compli-
cated Darcy-Weisbach formula for overland flow is because under sheet
flow conditions Manning's n is no longer a constant. However, it should
be reminded here that even by using Darcy-Weisbach formula the resistance
coefficient used in routing is nothing but a representative average con-
dition of the surface of the strip and it does not necessarily repre-
sent the actual surface roughness. The lateral flow q in Eqs. 1 and 9
is the rainfall rate or the infiltration rate. Infiltration is estimated
by using Horton's formula. For gutter flow q may also represent the
input from overland flow.
The nonlinear kinematic wave equations, Eqs. 1 and 9, are solved by
using a four-point noncentral semi-implicit numerical scheme. Details of
the ISR model and the computer program have been reported elsewhere (Chow
and Yen, 1976). Inlet hydrographs for the block for several rainfalls of
different durations are generated if necessary. For each rainfall dura-
tion the intensity is uniformly distributed over the duration and over
the entire block. To avoid inaccuracy due to small rainfalls preferably
the intensity used in the computation is about 1 to 3 in./hr (25-75 mm/hr).
Finally, the computed hydrographs are converted into unit hydrographs for
the respective inlets by the standard linear proportional technique of
unit hydrograph theory. If possible, preferably several rainfalls of
the same duration but different intensities would be used to generate
several unit hydrographs of the same duration and the average of these
unit hydrographs would be used as the inlet unit hydrograph.
In this development of the inlet unit hydrographs, in addition to
the assumptions and reliability limitations of the kinematic wave
approximation and the unit hydrograph theory, it is also assumed that
the surface runoff takes place only around each individual block and no
cross-block flow occurs. The flow is assumed completely intercepted by
the inlets of the block.
66
-------
Once the unit hydrographs are established for the inlets, they will
be used repeatedly like a scale for different rainfalls having the same
duration as the unit hydrograph and for any blocks that have similar
physical characteristics as the one used to establish the unit hydro-
graphs. For example, if in an urban area there are ten blocks of identi-
cal size having similar land usage and surface slopes, and each has three
inlet catch basins, one at each of three of the four block corners, for a
given rainfall duration it is necessary to establish only three unit
hydrographs, one for each of the inlets. These three inlet unit hydro-
graphs can then be applied to all the ten blocks and to all other rain-
falls having the same duration to produce the corresponding inlet runoff
hydrographs.
(B) Determination of Inlet Hydrograph by Using Unit Hydrographs
The inlet hydrographs are obtained by linear combination of unit
hydrographs as specified in the standard procedure of unit hydrograph
theory. The procedures include:
(a) Obtain the hyetograph that is to be considered The hyetograph
can be obtained from past record or from assumed future rainfall
as the objective of the project dictates. The hyetograph is
represented as block diagram rainfall depth over equal time
intervals, mostly through digitization of rainfall data. For
instance, the standard hourly rainfall data available from the
U.S. National Oceanic and Atmospheric Administration Environ-
mental Data Service are given in terms of depth over one hour
interval. For inlet hydrograph determination block diagrams of
rainfall depth over 10, 5, 2, or 1 min are more useful.
(b) Select the appropriate unit hydrographs - From the set of inlet
unit hydrographs of different durations for different typical
city blocks, select the ones with the appropriate duration and
that represent the block being considered. For example, if the
hyetographs are rainfall depth or intensity over equal time
intervals of 10 min, then the 10-min unit hydrographs should
be used.
67
-------
(c) Obtain the component hydrographs For each inlet multiply the
inlet unit hydrograph by the depth of rainfall for each time
interval of the hyetograph. For example, if the hyetograph
consists of 0.8 in. (20 mm) of rainfall in the 10-min time in-
terval followed immediately by 1.1 in. (28 mm) of rainfall in
the next 10-min interval, the ordinate (discharge) of the 10-
min unit hydrograph is multiplied by 0.8 for the first rain-
fall interval and by 1.1 for the second. These component hydro-
graphs should be listed or plotted in accordance with their time
sequence.
(d) Summation of component hydrographs to obtain inlet hydrograph
The component hydrographs obtained in (c), after listing or
plotting the discharges (ordinates) at the appropriate time ac-
cording to the time sequence of the rainfall, are summed up to
produce the inlet hydrograph.
(e) Procedures (c) and (d) are repeated for each inlet and for all
the blocks within the basin under consideration.
It should be emphasized that the most difficult part of this method,
the establishment of the inlet hydrographs, need to be determined only
once. After established they are used again and again. Once the inlet
unit hydrographs are established, Step (A) on p. 65 is no longer needed.
Contrarily, the inlet hydrographs need to be computed every time a rain-
storm is considered. The ISR Model is too costly to be used for computing
surface runoff in drainage basins of any significant sizes. Conversely,
the proposed method of a combination of the ISR model together with the
unit hydrograph theory applied to representative blocks considerably
simplify the computations and yet preserve sufficiently the accuracy as
required in practical applications.
VII-2. SEWER FLOW ROUTING
With all the inlet hydrographs determined as described in the prece-
ding section, the input into the sewer system is known. The sewer system
can be described by the node-link representation as discussed elsewhere
68
-------
(Sevuk et al., 1973; Chow and Yen, 1976). The inflow hydrographs are then
routed sewer by sewer towards downstream using a simplified kinematic wave
approximate technique. In this technique the inflow hydrograph at the
upstream end of a sewer is transferred into the outflow hydrograph at its
downstream with distortion reflecting approximately the sewer flow travel
time and sewer storage. The sewer flow velocity is approximated by using
Manning's formula and from the sewer geometry shown in Fig. 21,
C 2/3 1/2
in which the constant C = 1 for SI units and C =1.49 for English units.
n n 6
The flow central angle <(> is given by noting that from Q = AV, one obtains
. . 5/3 n -8/3 -1/2
ta.iHt, ,20.1 ^d SQ (11)
n
The travel time is computed by
t = L/V (12)
in which L is the sewer length. The volume of sewer storage, A-V-, during
a time interval At = t_ - t1 is approximately equal to (B..+B_)Ah/2 where
the surface width B = d sin(<{>/2) and the depth h = (d/2) [l-cos(/2) ] .
In the hydrograph routing, an inflow discharge Q which occurs at
time t? is shifted to the downstream outflow hydrograph at the time
t_ + (L/V) and with the magnitude (discharge) reduced by A₯/At. This pro-
cedure is repeated until the entire hydrograph is routed. From a theo-
retical viewpoint, this simple routing technique is a very rough approxi-
mation. However, from a practical viewpoint, its accuracy is quite
acceptable despite its simplicity. Normally, in routing of rainstorm
runoff in actual drainage basins, the computational time interval is of
the order of one min, if not much longer. In a sewer having a steep
slope, the flow velocity is higher than 5 fps (1.5 m/s) except at the
very beginning and very end of the runoff, and probably in most of the
time faster than 10 fps (3.0 m/s). The length of a sewer between
junctions is normally less than 1000 ft (300 m) , and usually between
69
-------
-B
Flow area A = «- ($ - sin $)
Hydraulic radius R = j- (1 - ^
d f^ $>
Depth h = y (1 - cos )
Water surface width B = d sin
Fig. 21. Circular Sewer Flow Cross Section
70
-------
300 ft (90 m) to 500 ft (150 m) in American cities. Thus the flow travel
time in a sewer with a steep slope is usually less than 2 min. Thus, in
view of a computational time interval of 1 min or longer, an error in
travel time on the order of 10 sec would not cause significant error in
the results of routing. Moreover, when the driving force of the flow is
predominant , as in the case of the gravitational force for flow on
steep slopes, the flood peak attenuation is relatively insignificant in
comparison to the flood discharge. Therefore, the proposed scheme provides
a reasonable simple approximation. This is particularly significant since
at present a theoretically sound solution of the equations representing
the unstable supercritical flow with roll waves cannot be obtained. Never-
theless, it should be reminded here that the proposed technique has not
been adequately tested because of the lack of available data, and modifi-
cations may be desirable if verification with field data, when available,
indicates so. This simple sewer routing technique, of course, is appli-
cable to mild slope as well. However, presumably it is much less accurate
when applied to mild slope sewers and, hydraulically, it is of the same
level as Chicago hydrograph, TRRL, and UCUR methods. But its reliability
in comparison to these three methods when applied to mild slope cases has
not been investigated.
VII-3. EXAMPLE: BAKER STREET UPPER BASIN
The proposed simple method for storm runoff flow rate determination
for steep slope areas is applied to the upper basin of the Baker Street
Drainage Basin. The physical characteristics and drainage pattern of
the Upper Baker Street Basin have been described in detail in Section VI.
The reason for choosing only the Upper Basin as an example is due partly
to the project computational economics and partly to the relatively flat
land of the northern part of the lower basin. At any rate, the existing
runoff data for the entire Baker Street Drainage Basin is inadequate to
verify the accuracy of the proposed method even if the runoff for the
entire basin is computed. Moreover, it does not seem to be difficult to
install a measurement device in the egg-shape sewer in the tunnel to
record the runoff from the upper basin.
71
-------
(A) Establishment of Inlet Unit Hydrographs
A typical block of the Upper Baker Street Basin is shown at the upper
right corner of Fig. 22. The rectangular block has three inlets and four
gutters of different slopes. In this example the block is arbitrarily
subdivided into four isosceles triangles with their common apex at the
center of the block (Fig. 23). Each triangle drains into the adjacent
gutter which in turn drains into an inlet. The half street roadway width
is 34.4 ft (30.4 m). The four gutters all have different slopes. The
Illinois Surface Runoff (ISR) computer program of the IUSR model is
applied to this typical block for a rainfall of 1 in./hr (2.5 mm/hr)
intensity uniformly over a 10-min duration for three different sets of
slopes given in Fig. 22. The computed hydrographs are then converted
into unit hydrographs by multiplying the ordinate scale by 6 (=60 min/10
min). The computed unit hydrographs for the lowest inlet of the block,
called Type C inlet in Fig. 23, are shown in Fig. 22 for the three sets
of gutter slopes. An average Type C inlet unit hydrograph is then
obtained and used as the standard 10-min unit hydrograph for this inlet.
In applying the ISR program to the typical block to produce the inlet
unit hydrographs such as those shown in Fig. 22, no infiltration is con-
sidered, i.e., infiltration is assumed equal to zero. Thus, these unit
hydrographs are actually direct runoff unit hydrographs. Therefore,
later in applying these hydrographs the abstractions should be first
taken off from the rainfall before the unit hydrograph application. Each
of the isosceles triangular overland area of the block is approximated
by a number of rectangular strips of equal width. The gutters are
assumed 2 ft (0.61 m) in width with Manning's n = 0.013. The inlets are
assumed to be rectangular grate inlets of 2 ft by 2 ft (0.61 m by 0.61 m)
in size with an opening ratio of 0.60. It has been found that hydrauli-
cally this assumed rectangular grate inlet behaves similar to the semi-
circular grate inlet that is popular in the Upper Basin. The two inter-
mediate inlets (Types A and B in Fig. 23) each receives water from a
gutter and carryover to the downstream gutter is allowed if the inlet
capacity is exceeded. The lowest inlet, Type C inlet, receives water
from both gutters joining to it, and there is no carryover from this
inlet.
72
-------
(O
«^-
u
10
8
*-" 6
(2)
(I)-
-(2)
Type C
Inlet
Sit
412.5'-
m
m
CO
fs3
\urve
Slope\
Si
S2
S3
S4
1
0.114
0.082
O.I 10
0.082
2
0.125
0.142
0.0078
0070
3
0.129
0.0073
0.125
0.0048
For 1 in
(25mm)
rainfall
(3) excess
Average Curve
0.3
0.2
n
c>
L_
O.I
10 15
Time , min
20
25
Fig. 22. Type C 10-m±n inlet unit hydrograph for Upper Basin
73
-------
Type C (o
Inlet
X
/ \
s' 412.5'
/
/
10
to
CM
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Type A |£ __ _«
Type B
1/12
L
Rainfall
-12.11
Jrk
E
E
_c
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o
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Time , min
Fig. 23. Standard 5-min inlet unit hydrographs for Upper Basin
74
-------
Similarly, inlet unit hydrographs for other durations can be estab-
lished. The average 5-min unit hydrographs for inlets A, B, and C are
shown in Fig. 23 and will be used for the rest of the example.
(B) Determination of Rainfall
The rainstorm used in this example is the October 22, 1973 rainfall
between the clock hour 18:00 and 20:30 (Fig. 20). The reason for adop-
tion of this rainstorm as an example is because of its good quality
detail data in comparison to the rainstorms shown in Figs. 16-18. From
the time variation of the rainfall intensity shown in Fig. 20, it is
clear that a 10-min duration is too long to represent the rainfall. Con-
trarily, a 1-min or 2-min duration would require a large amount of compu-
tations. By observation it seems that a 5-min duration would be ade-
quately faithful in representing the rainfall without resulting in a
large amount of computation. In order to preserve the peak rainfall rate
occurred at the time between 19:34 to 19:39, the durations are taking as
successive 5 minutes start from 18:19.
(C) Application of Inlet Unit Hydrographs
The 5-min inlet unit hydrographs are then applied to each 5-min
duration intervals in succession for each inlet in the block. For ex-
ample, for the Type C inlet shown in Fig. 23, for the October 22, 1973
rainstorm there are 20 hydrographs between the time 19:39 and 20:19, each
lagged to the other by 5 minutes in succession, and each produced by a rain-
fall of 5-min duration. The ordinates of each of these hydrographs are
equal to the corresponding ordinates of the 5-min Type C inlet unit hydro-
graphs shown in Fig. 23 multiplied by the depth of rainfall in the re-
spective 5-min interval. These hydrograph ordinates with appropriate
successive 5-min time shifting are then added arithmetically to produce
the Type C inlet hydrograph for this particular rainstorm. This Type C
inlet hydrograph can subsequently be applied to all the Type C inlets
in the basin.
Inlet hydrographs for the October 22, 1973 rainstorm for Types A and
B inlets can be similarly established. The identification of the types
of inlet hydrographs for the Upper Baker Street Basin is shown in Table 7.
75
-------
It should be noted here that such identification needs to be done only
once, just like the inlet unit hydrographs, and once identified, the
table can be used for other rainstorms.
(D) Determination of Sewer Inflow Hydrographs
The inlet hydrographs are transformed into sewer inflow hydrographs
assuming there is no time lag. In reality this lag time is of the order
of magnitude of seconds and hence can be neglected. If a sewer receives
water from more than one inlet catch basin or also from upstream sewers,
the hydrographs from these inlets and sewers are summed up arithemati-
cally at their respective appropriate time to produce the inflow hydro-
graph for the sewer under consideration.
(E) Hydrograph Routing in a Sewer
The inflow hydrograph of a sewer is transformed into the outflow
hydrograph by using the method and equations described in Subsection
VII-2. The procedure can be illustrated in Table 8 and Fig. 24 using
the sewer on Laurel Street between Clay and Washington (Nodes 288 to
250) as an example. The inflow has been determined as described in (D)
and is listed in the second column of Table 8. The sewer diameter is 12
in. (30 mm) and the sewer slope S = 0.0117 (Table 3). Thus, with
Manning's n = 0.013, Eq. 11 can be reduced to
-_, 5/3
Q in cfs
f }
= 18.2Q Q in m /s
The corresponding equation to compute the reference velocity V is
_, 2/3
v v1 - * > (14)
where
C = 15.5 for V in fps
v v
C = 4.7 for V in m/s
The computed § and V are given as the third and fourth columns in Table 8.
76
-------
Table 7. INLET HYDROGRAPH IDENTIFICATION FOR UPPER BASIN
At Intersection of
Maple
Maple
Maple
Jackson
Jackson
Clay
Spruce
Spruce
Washington
Maple
Pacific
Pacific
Locust
Pacific
Clay
Locust
Clay
Washington
Washington
Locust
Locust
Jackson
Jackson
Pacific
Lyon
Jackson
Presidio Av
Presidio Av
Pacific
Pacific
Jackson
Washington
Walnut
Walnut
Walnut
Clay
Laurel
Laurel
Washington
Jackson
Laurel
Pacific
Pacific
Pacific
Clay
Washington
Jackson
Cherry
Spruce
Maple
Clay
Washington
Maple
Jackson
Maple
Spruce
Pacific
(Laurel)
Spruce
Clay
Laurel
Spruce
Laurel
Washington
Jackson
Spruce
Laurel
Lyon
Pacific
Lyon
Jackson
Washington
Presidio Av
Walnut
Walnut
Walnut
Clay
Washington
Jackson
Walnut
Clay
Washington
Walnut
Walnut
Jackson
Laurel
Node
284a
281
244
280c
221
284b
280a
275
282
243
233
187
170
186
280b
278
287
274
249
248
215b
220
218
370c
370a
330b
312
315
300
228
311
314b
304
284c
252
303
288
250
283
251
219
188
501
502
Type of
Inlet Hydrograph
A
-
2
-
1
-
2
1
-
-
-
-
-
-
2*+2
-
-
-
1*4-1
1*
-
-
-
-
-
2*
-
-
_
-
-
-
2*
1*
-
2
1
-
-
1
-
-
-
B
«.
1*
2
-
-
-
-
-
1*
-
1*
-
-
1*
-
-
-
-
1
-
-
1
1
-
-
2
1*
-
1*
1*
1*
-
-
1*
-
-
-
1
1
-
-
-
-
C
-
-
-
1
-
-
1
-
-
1*
2
-
-
-
-
-
-
2
2
-
-
-
-
-
-
1
1*
-
-
-
-
1*
-
-
1
-
-
1
1
-
-
Upstream
Sewer Flow
from Nodes
284a
281, 280c
244, 275
284b
280a, 282
243
233, 221
187, 215b, 186
280b, 287
249, 274, 278
248, 220, 218
370a
330b, 315
312, 370c
300, 252
31 4b, 304
284c, 311
303
288, 283
251, 250
219, 228
188
501, 170
*Special inlet unit hydrographs because of block size or flat slope.
77
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The nominal sewer flow travel time is computed as L/V where the length
L = 324 ft (99 m). The change of sewer storage in time interval
At = t~ - t , in cu ft is
1 *1 *? *1 *?
AV = | (sin ~ + sin -f) (cos -y - cos -y-) (15)
The time interval At used in the computation is At = 1 min. Therefore, the
average discharge reduction due to the sewer storage is A₯/At and the com-
puted values are given in the seventh column of Table 8. It can be seen
from the values in Table 8 that the discharge reduction due to sewer
storage is relatively small and usually can be neglected, consequently re-
ducing about 20% of the computations.
The sewer outflow can now be computed as 0. ,-, - A₯/At and is at
xinflow
the time on the outflow hydrograph equal to the clock time of the inflow
plus the sewer flow travel time. This computed time of the outflow hydro-
graph usually is at odd numbers not coinciding with the time intervals
used for the general computation. For instance, the inflow of 0.126 cfs
3
(0.0035 m /s) at 19:01 entering through the upstream end of the sewer
(Nodes 288 to 250) shown in Fig. 24a and Table 8 becomes the outflow of
3
0.126 cfs (0.0035 m /s) at 19:02.07 at the downstream end of the sewer,
shown as a cross point in Fig. 24b. A linear interpolation is then used
to obtain the outflow discharge at the time intervals of computation,
e.g., 0.126 - [(0.126 - 0.040) (2.07 - 2.00)7(2.07 - 1.52)] - 0.115 cfs
3
(0.0009 m /s) for the outflow at time 19:02 in Fig. 24b and Table 8.
(F) The above procedures are repeated sewer by sewer in sequence until
all the sewer flows are routed and the basin outflow hydrograph is
obtained. The computed runoff hydrograph for the October 22, 1973 rain-
storm for the Upper Baker Street Drainage Basin is shown in Fig. 25.
The proposed method would be as tedious as the Chicago Hydrograph
or TRRL methods if the computations are done by hand calculations. How-
ever, it is relatively easy to program for digital computers and requires
very little computation time. In fact, the computation can be done with
reasonable efficiency on a programmable pocket calculator providing the
geometric and rainfall data are hand loaded requiring no storage loca-
tions and the surface and sewer flows are computed separately.
79
-------
0.5
0.4
W
H-
u
a," 0.3
o>
Inflow at upstream end
of sewer
19:00
01 02
Clock Time, min
03
(A
IO
04
to
*u
«
Q>
O
.C
U
O
U.O
0.4
0.3
0.2
O.I
Q
i I i i
~ Outflow at downstream end
of sewer A ~
- X"
r\^^
. *J
"
/
/°
1 -*-^ *" 1 1
0.010 K?C
«»
o>
o>
w
O
0.005 ^
0
n
18-59 19:00 01 02 03 04
Clock Time, min
Fig. 24. Hydrograph routing in sewer
80
-------
6
w
.c
V.
-E 4
150 w
^
100 E
50 *~
o
« OCL
150
£ 100
o
*
a>
o
(O
50
1900
T r
Clock Time , Hour
D>
0>
O
CO
2000
Fig. 25. Runoff from upper basin for rainstorm of 22 October, 1973
81
-------
REFERENCES
Amein, M. , and C. S. Fang. Streamflow Routing with Applications to North
Carolina Rivers. Report No. 17, Water Resources Research Institute,
University of North Carolina, January 1969.
American Society of Civil Engineers, and Water Pollution Control Federation.
Design and Construction of Sanitary and Storm Sewers. ASCE Manual No.
37, New York, 1969.
Baltzer, R. A., and C. Lai. Computer Simulation of Unsteady Flows in
Waterways. Jour. Hyd. Div., ASCE, 94(HY4):1083-1117, July 1968.
Brandstetter, A. Assessment of Mathematical Models for Storm and Combined
Sewer Management. Environmental Protection Technology Series,
EPA 600/2-76-175a, U.S. EPA, August 1976.
Chow, V. T., and B. C. Yen. Urban Stormwater Runoff: Determination of
Volumes and Flow Rates. Environmental Protection Technology Series,
EPA 600/2-76-116, U.S. EPA, May 1976.
Chow, V. T., ed. Handbook of Applied Hydrology, McGraw-Hill Book Co.,
New York, 1964.
Chow, V. T., and A. Ben-Zvi. Hydrodynamic modeling of two-dimensional
watershed flow. Jour. Hyd. Div., ASCE, 99(HY11):2023-2040, November
1973.
Colyer, P. J., and R. W. Pathick. Storm Drainage Design Methods: A
literature review. Report Int 154, Hydraulics Research Station,
Wallingford, England, 1976.
Dronkers, J. J. Tidal Computations in Rivers and Coastal Waters. John
Wiley & Sons, New York, 1964.
Engineering-Science, Inc. Dissolved Air Floatation, Appendix A, July
1971.
Federal Aviation Administration. Airport Drainage, 1970.
Gunaratnam, D. J., and F. E. Perkins. Numerical Solution of Unsteady
Flows in Open Channels. Report No. 127, Ralph M. Parsons Laboratory
of Water Resources and Hydrodynamics, Massachusetts Institute of
Technology, Cambridge, Mass., July 1970.
Heaney, J. P., W. C. Huber, H. Sheikh, J. R. Doyle, and J. E. Darling.
Storm Water Management Model: Refinements, Testing and Decision-
Making. Report, Dept. of Environmental Eng. Sci., University of
Florida, Gainsville, Florida, June 1973.
82
-------
Huber, W. C., J. P. Heaney, M. A. Medina, W. A. Peltz, H. Sheikh, and
G. F. Smith. Storm Water Management Model User's Manual Version II.
Environmental Protection Technology Sew. No. EPA-670/2-75-017, U.S.
Environmental Protection Agency, 1975.
Iwasa, Y. The Criterion for Instability of Steady Uniform Flows in Open
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Izzard, C. F. Hydraulics of Runoff from Developed Surfaces. Proc.
Highway Res. Board, 26:129-146, 1946.
Kerby, W. S. Time of Concentration for Overland Flow. Civil Engineering,
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Kibler, D. F., J. R. Monser, and L. A. Roesner. San Francisco Stormwater
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Klym, H., W. Koiger, F. Mevius, and G. Vogel. Urban Hydrological Pro-
cesses. (Paper Presented in the Seminar Computer Methods in Hy-
draulics at the Swiss Federal Institute of Technology, Zurich,
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-------
Ragan, R. M., and J. 0. Duru. Kinematic Wave Nomograph for Times of
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1969.
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84
-------
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the Rational Method. Water & Sewage Works, 121(10):92-95, 121(11):
84-85, 1974.
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Parts I to IV. Hydrology Papers No. 43-46, Colorado State Univer-
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Zovne, J. J. The Numerical Solution of Transient Supercritical Flow by
the Method of Characteristics with a Technique for Simulating Bore
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Institute of Technology, Atlanta, Ga., 1970.
85
-------
APPENDIX
BAKER STREET DRAINAGE BASIN RUNOFF WATER QUALITY
The runoff water quality data of dry weather flow and the rainstorms
of 4-5 April, 15 October, and 5 November, 1969 for the Baker Street
Drainage Basin are taken from the report by Engineering-Science, Inc.
(1971). The combined sewer flow cumulative pollutant discharges for each
of the three rainstorms are summarized in Table A-l and the corresponding
pollutographs are shown in Figs. A-l to A-3. The dry weather flow
quality is summarized in Table A-2. More detailed data as well as des-
cription on the sampling technique can be found in the original report.
86
-------
CONDUCTIVITY
//mho/cm
TOTAL AND
VOLATILE
SUSPENDED
SOLIDS
mg//
FLOATABLE
MATERIAL
mg//
FLOW
cfs
4 APRIL
5 APRIL
J_
22OO
2400
02OO O400
CLOCK TIME,hours
06OO
0800
Fig. A-l. Pollutographs for runoff on 4-5 April, 1969
87
-------
CONDUCTIVITY
//mho/cm
TOTAL AND
VOLATILE
SUSPENDED
SOLIDS
mg//
FLOATABLE
MATERIAL
mg//
GREASE
mg//
COD AND BOD
mg//
FLOW
cfs
300i-
200
100
0
250
2OO
150
100
50
0
I 0
0.5
0
5
4
3
2
I
0
2OO
150
IOO
50
0
15
10
5
3-o...
TSS
15 OCTOBER
I
I
O300
0400
O7OO
05OO O6OO
CLOCK TIME,hours
Fig. A-2. Pollutographs for runoff on 15 October, 1969
88
0800
-------
CONDUCTIVITY
^mho/cm
TOTAL a VOLATILE
SUSPENDED SOLIDS
mg//
FLOATABLE
MATERIAL
GREASE
COD AND BOD
FLOW
cfs
300
200
100
0
250
200
150
100
50
0
3
2
I
0
100
75
50
25
0
600
TSS
O400 05OO 0600
CLOCK TIME, hours
0700
08OO
Fig, A-3, Pollutographs for runoff on 5 November, 1969
89
-------
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO.
EPA-600/2-77-168
3. RECIPIENT'S ACCESSION"NO.
4. TITLE AND SUBTITLE
STORMWATER RUNOFF ON URBAN AREAS OF STEEP SLOPE
5. REPORT DATE
September
1977 (Issuing Date
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
Ben Chie Yen, Ven Te Chow and A. Osman Akan
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Civil Engineering
University of Illinois at Urbana-Champaign
Urbana, Illinois 61801
10. PROGRAM ELEMENT NO.
1BC611
11. CONTRACT/GRANT NO.
68-03-0302
12. SPONSORING AGENCY NAME AND ADDRESS
Municipal Environmental Research LaboratoryCin., OH
Office of Research and Development
US Environmental Protection Agency
Cincinnati. Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
Final, 9/75-12/76
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
Richard Field, Storm and Combined Sewer Section, Edison, NJ
Tel. (201) 321-6674, FTS 340-6674
08817
16. ABSTRACT
A research is conducted to investigate the applicability of commonly used
urban storm runoff prediction models to drainage basins with steep slopes.
The hydraulics of runoff on steep slope areas is first reviewed and its
difference from that for mild slope areas is discussed. Next the difficulties
in applying commonly used methods to steep slope basins are presented. It
appears that most engineers are not aware of the problems associated with
runoff from steep slope areas and they do not realize that the numerical
results given by the conventionally used methods, if obtainable, may not be
reliable. A simple approximate method specifically for steep slope basins
is proposed and an example is provided. The example utilizes the data from
the Baker Street Drainage Basin in San Francisco.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Drainage
Rainfall
Runoff
Storm sewers
Surface drainage
Computer programs
Mathematical models
Hydrographs.
Steep Slope.
Baker Street Basin.
San Francisco.
13B
13. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
102
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
92
^U S GOVERNMENT PRINTING OFFICE. 1977-757-056/6516 Region No. 5-11
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