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ABSTRACT

THE PREDICTION OF RUNOFF FROM SMALL
DRAINAGE BASINS IN MICHIGAN

BY
John E. Plotkowski, Jr.

Highway Operation and maintenance disrupt naturally
occurring processes of the environment. The extent to
which highway construction affects the small drainage basin
environment is not well understood. This is apparent when
considering the hydrology of a wooded or wetland area.

With current runoff prediction formulae, the judgement in
selecting key hydrologic coefficients is considerable.
This work on runoff prediction outlines a simple and
practical approach to determine the peak discharge of flow
from synthetically produced runoff hydrographs for small,
rural, ungaged drainage basins in Michigan. The method

is based on an approach proposed by Chow (1962). In this
study, design charts and accompanying tables for climatic
and physiographic conditions in Michigan are presented.

Major phases of the study include historical
review of develOped runoff prediction methods, review of
hydrologic factors affecting runoff from small drainage

basins, collection and analysis of available hydrologic

John E. Plotkowski, Jr.

data for Michigan and the northern Mid-West vicinity,
presentation of the proposed discharge formulation,

compilation of data and graphs developing the various
formula components affecting small drainage basins in

Michigan, and a section outlining future studies.

THE PREDICTION OF RUNOFF FROM SMALL

DRAINAGE BASINS IN MICHIGAN

BY

John E. Plotkowski, Jr.

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Civil Engineering

1974

“To my parents and brother."

ii

Chapter

TABLE OF CONTENTS

I 0 INTRODUCTION 0 I I O O C I O O O O O O O C

II. HISTORICAL REVIEW OF DEVELOPED RUNOFF
PREDICTION METHODS . . . . . . . . . . . .

III. HYDROLOGIC PRINCIPLES, DATA AND ANALYSES .

A.

C.

Hydrologic Principles . . . . . . .
l. DevelOpment of Unit Hydrographs
2. Variations of Rainfall Intensity
in a Storm 0 O O O O O O O O O 0
Sources of Hydrologic Data . . . . .
1. Rainfall O O O O O O O O O 0 O I
2. RunOff O I O I O O O O O O O O O
3. Hydrologic Soil Types . . . . .

Rainfall Analyses . . . . . . . . .

IV. CHOW. S FORMULA O O O O O O O O O I O O O O

A.

C.

Runoff Factor X . . . . . . . . . .

1. Determination of Land Use,
Surface Condition and Antecedent
Ground Moisture Effects . . . .

2. Determination of Hydrologic
Soil Type . . . . . . . . . . .

3. Determination of Rainfall Excess

4. Determination of Runoff Factor X

Climatic Factor Y . . . . . . . . .
Peak-Reduction Factor Z . . . . . .

1. Verification of Factor 2 by Data

iii

Page

13
15
18
26
26
27
28
29
30
44

49

49
51
55
56
58
62

65

V.

APPENDIX .

BIBLIOGRAPHY

Design Criteria .

Design Procedure by the PrOposed
Method

Merits and Shortcomings of the

Proposed Method .

FUTURE STUDIES

iv

72

74

85
89
91

119

Table

II.

III.

II.

III.

IV.

VI.
VII.
VIII.

IX.

XI.

LIST OF TABLES

Rainfalls of Different Frequencies and
Maximum Rainfalls in Inches for Michigan
and ViCinj-ty O O O O O O O O O O O O O I 0

Selection of Runoff Number N for Antecedent

Moisture Condition Class II . . . . . . .

Computation of Lag Time and Peak—Reduction

Factor 2 for Michigan . . . . . . . . . .
APPENDIX TABLES

Maximum Recorded Point Rainfalls in Inches
For Michigan and Vicinity . . . . . . . .

Hydrologic Soil Groups . . . . . . . . . .

Comparison of Station Data with
Corresponding Climatic Division Data . . .

Classification of Antecedent Moisture

condition Class O O C O O O O O O O O O O
Computation of Runoff Factor for-—2 Year
Computation of Runoff Factor for--5 Year

Computation of Runoff Factor

Computation of Runoff Factor

X
X
X
Computation of Runoff Factor x for--25 Year.
X
X

Computation of Runoff Factor

Computation of Lag Time and Peak-Reduction
Factor Z (after Chow, 1962) . . . . . . .

for--10 Year.

for--50 Year.

for-—100 Year

Page

36

52

67

91

96

99

110
111
112
113
114
115
116

117

Figure

l.

11.

12.
13.
14.

15.

LIST OF FIGURES

Example of Design Discharge for a Small
Basin Using the California Method . . . . . . .

Derivation of Unit Hydrograph by the
S-Curve MethOd o o o o o o o o o o o o o o o o

The Ten Climatic Divisions of Michigan . . . .

Rainfalls of Different Frequencies and
Maximum Rainfalls . . . . . . . . . . . . . . .

24-Hour Maximum Precipitation Isohyetals,
Averages and Conversion Factors for Six
Climatological Sections of Michigan . . . . . .
Major Michigan Hydrologic Soil Associations . .

Relationship Between Rainfall and Rainfall
Excess for Various Runoff Numbers . . . . . . .

Runoff Factor X for 2- and 5-Year Frequencies .

Runoff Factor X for 10- and 25-Year Frequencies

Runoff Factor X for 50- and lOO-Year Frequencies.

Climatic Factor Y for Climatological
Sections in Michigan . . . . . . . . . . . . .

Determination of Lag Time, tp (after Chow, 1962).

Relationship Between z and t/tp . . . . . . . .
Chart for the Determination of Design
Discharge for Small Rural Drainage Basins

in Michigan . . . . . . . . . . . . . . . . . .

Predicted Runoff Hydrographs for the
Given Example . . . . . . . . . . . . . . . . .

vi

Page

10

23

31

37

38

54

57
59
6O

61

63

70

75

84

CHAPTER I

INTRODUCTION

In recent years, an increasing emphasis has been
placed on the 'ecological' aSpects of the many Federal,
state, county and municiple roadway projects. The effacing
of land along corridor routings has had a damaging effect
on some forest lands, marshes and wildlife preserves as
evidenced by severe tree kills along some sections of
Michigan's highways. Prolonged or permanent flooding has
inflicted permanent damage to many tree stands of black
spruce, tamarack, northern white cedar, white pine, black
ash, American elm, red maple, balsum, fir, hemlock and
white spruce species found in much of the lake state
regions of Michigan, Wisconsin and Minnesota. According
to a recent study (Stoeckler, 1965) some roads act like
low dams creating a backwater effect and raising water in
low lying, wetland areas one-half to two feet. Some
42.7 percent of these wetland crossings have dead or dying
trees adversely affected by road placement. Public outcry
has often accused sponsoring agencies of insensitiveness
for irrepairably damaging high value woodland and wetland

l

areas. Beyond public sentiment remains the unanswered
probings of how to better counter-balance the upsetting
of our natural environment. The problem of road construc-
tion is seemingly two-fold; controversy stemming from a
concerned viewpoint for environmental aesthetics on the
one hand and lack of adequate knowledge in assessing road
impact prior to its placement on the other.

As‘a result of the Environmental Policy Act of
1969 and the 1970 Highway Act, an effort to aid highway
planners in their attempt to assess an ecological impact
on woodlots and wetlands directly or indirectly attributable
to highway construction activities was undertaken. In
conjunction with the U.S. Department of Transportation,
Federal Highway Administration, a prOposal from the Depart-
ment of Resource DevelOpment, Michigan State University
entitled "Ecological Effects of Highway Construction Upon
Michigan Woodlots and Wetlands" wassubmitted to the
Michigan Department of State Highways and included in the
Federal Highway Planning and Research Program, Project
RFP-2l7 "Effects and Evaluation of Water Quality Resulting
from Highway Development and Operation." This study,
"Prediction of Runoff from Small Drainage Basins in
Michigan" relates the hydrological aspects of small drain-
age basins to arrive at a possible ecological impact on

woodlots and wetlands.

In a preliminary study of available literature,
several conclusions were reached concerning the key para-
meters in the prediction of runoff from small drainage

basins. These considerations included:

a) the major climatic conditions in the area

of the given drainage basin,

b) the major physiographic conditions of the

basin, and

c) the limiting design conditions or design

frequencies.

In Michigan, the empirical formula developed by
Talbot (1888) has been used to assess the design capacities
for culverts and primary drainage structure on a five to
twenty year flood frequency. This empirical approach is
dependent upon the personal knowledge and judgement of the
planner for use in hydrologic modelling and hydraulic
design. Parameters such as soil cover, land slope and
basin shape can be considered only in part through the use
of a weighted coefficient (c) which relates a series of
basin features in one factor. In this manner, the in-
fluence of dominant basin characteristics cannot be indi-

vidually studied. Therefore, this approach is limited to

the knowledge and experience of the designer about the
particular basin under consideration.

With an emphasis placed on environmental impact
statements, it was found that a weighted coefficient
approach as used in the Talbot formulation cannot assess,
in a scientific manner, the interrelationship of direct
and indirect physical impact of a highway upon the hydrology
of a wooded or wetland area. The difficulty in handling
the vast amounts of hydrologic data and the need for a
straight forward, logical exploration of key hydrologic
parameters was seen as the purpose of this study. Based
on a method develOped by Chow (1962), this study utilizes
the concept of unit hydrograph synthesis, basin geometry,
physical makeup, land use and cover as well as channel
characteristics to arrive at a simple, logical approach to
predict runoff from small drainage areas. This forecast
coupled with environmental considerations such as effects
to waterfowl and vegetation would enhance the total sc0pe
of highway planning and may reduce the possible ecological
damages.

This study consists of the following major phases:
(1) A review of available literature outlining the earlier

conclusions reached by hydrologists, highway and

agricultural engineers on runoff from small watersheds.

(2)

(3)

A collection and analysis of available hydrologic
data for small, rural drainage basins in Michigan

and the northern Mid-West.

A presentation of a scientific, simple and practical
method for the determination of waterway areas and
its application for practical design purposes as

prOposed by Chow (1962).

CHAPTER II

HISTORICAL REVIEW OF DEVELOPED

RUNOFF PREDICTION METHODS

Rainfall-runoff prediction techniques have been
developed for three major areas. The first involved flood
routing studies, the second, sewerage design, and the
third, railway and highway structure design. Late 19th
century, post World War I era saw the develOpment of the
more renowned flood-discharge formulae such as the Myers'
formula, Bfirkli-Ziegler formula, Talbot formula and the
Rational Method. Other flood-discharge formulae were
developed for the design of waterway openings for specific
areas of the continental United States. These included
formulae by Fanning for New England streams, Murphy for
the Northeastern United States and Cooley for the St. Louis
vicinity of the Mississippi River Valley (Pickels, 1925).

From the introduction of such methods, a series of
runoff curves were developed for use in railroads and
various drainage districts. These included the mountainous
regions of the West as well as those of swamp and peat bog
areas found in Minnesota and the Florida Everglades.

6

Runoff curves were developed by men such as James Dun,
former Chief Engineer for the Santa Fe Railroad, in his
presentation of the 'Dun Waterway Table' for design of
culvert Openings throughout the regions of Missouri,
Arkansas and Kansas, C. G. Elliott for swamp and other
wetlands of the Upper Mississippi Valley, John T. Stewart
for North Dakota, A. E. Morgan for northeastern Arkansas,
and F. C. Elliott for the Florida Everglades Drainage
District (Pickels, 1925).

Since then, variations and adaptations of various
rainfall intensity-duration-frequency relationships have
been utilized (Fair 32 31, 1958). Such work includes
contributions by Carl F. Izzard, U.S. Bureau of Public
Roads in modifying former design curves deve10ped for the
U.S. Department of Agriculture for use in highway culvert
design (Izzard, 1954). Izzard's method applies to water-
sheds of less than 1,000 acres, especially farmed or wooded
lands in the Eastern and Middle Western United States
(Woods, 1960).

The rational formula was first presented in
American literature in 1889 by Emil Kuichling. Through
observations of the volume of discharge from several large
sewers in the city of Rochester, New York, he concluded

that there existed a direct relationship between discharge

fluctuations and the intensity of rainfall, and also
between the size of the drainage area and the time required
for the peak discharge to occur. The rational formula is

expressed by the equation:

Q = ciA (1)
where Q = runoff (cfs)
c = coefficient representing the ratio
of runoff to rainfall
i = intensity of rainfall (inches/hr.)
A = drainage area (acres)

The initial step in the use of the rational formula
is to select the rainfall intensity that corresponds to the
frequency of the peak runoff storm which the structure is
to accommodate. A considerable amount of rainfall data has
been collected for a number of years and several sources of
intensity—duration-frequency curves are available (see
Chapter III-B-l).

A further assumption in the selection of the rain-
fall intensity corresponding to the frequency of the peak
runoff storm is that the design storm will be of a duration
great enough to allow water to arrive at the outlet of the
watershed simultaneously from all parts of the drainage
area. The minimum duration of the rainfall intensity
selected should be the time it takes for the farthermost

water in the drainage area to reach the structure site.

This is usually referred to as the time of concentration.

If this assumption is not satisfied, part of the basin area
will not have contributed to the peak flow at the outflow
site when the rainfall ceases. For this reason the rational
formula is constrained to basins of less than 1,000 acres.
Following this limitation, surface detention effects are

not as critical and a time of concentration factor can be
applied.

The next step in the rational method is to determine
the runoff coefficient (c). This coefficient value is
selected on the basis of various climatic conditions and
physiographic characteristics of the watershed. In assessing
the influences of drainage shape, vegetative cover, land and
channel slope, the judgement involved in estimating this
coefficient is considerable. For this reason it is difficult
to obtain uniform design recommendations between various
designers.

A number of states use the rational method in
design of waterway areas. California, for example, uses a
rational method based on expected rainfall intensities for
given regions across the state. The nomograph presented
in Figure 1 gives a graphical solution of the rational
method used to determine peak flow from drainage basins in

California.

10

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11

In Michigan, the rainfall-runoff method used to
determine the area of waterway Opening required for culverts
is expressed in the empirical Talbot formula. This method

is expressed by the equation:

4 3

a = C A (2)
where a = required waterway opening (ft2)

A = drainage area (acres)

C = runoff coefficient (varies from

1.0 to 0.2 or less, depending

upon the characteristics of the

drainage area)
The Talbot formula approximates the area of the culvert
Opening required without consideration for hydraulic and
hydrologic principles and various design frequencies.
Limited investigations have indicated that its use yields
a waterway Opening that is approximately adequate to
accomodate the ten year flood and a ten foot-per-second
velocity through culverts located in the Middle Western
United States (Woods, 1960).

Further studies utilizing statistical techniques
to estimate peak runoff rates from ungaged, small, rural
‘watersheds include the Highway Research Board (1972), the
Journal of the Hydraulics Divisi9g_(l973) and a multiple
regression analysis by Anderson (1949). Chow's investi-

gation (1962) utilizes a hydrograph synthesis approach for

12

runoff prediction for small watersheds in Illinois. A
series of reports by the U.S.G.S. Water Resource Division
for small drainage basins in Michigan include a multiple
regression analysis by Bent (1971) and a hydrograph
synthesis approach (Wiitala, 1961) to assess lag-time
variances of urbanized areas over rural basin areas.
Conclusions forwarded by Bent (1971) for drainage
basins in Michigan indicate that three basic factors affect
streamflow. These factors are drainage area, soil cover
and its permeability. From the study of Wiitala (1961),
land use modifications were found to increase runoff potentials
in suburban develOpments over rural districts for basins of
southeastern Michigan by a ratio of 2.7. From these reports,
drainage area, precipitation intensity and frequency, land
use and cover, soil index and channel slope seem to be the
key parameters affecting runoff from small drainage basins

in Michigan.

CHAPTER III

HYDROLOGIC PRINCIPLES, DATA AND ANALYSES

Naturally occurring hydrologic processes are, for
the most part, stochastic or probabilistically time-
dependent. Such processes include rainfall, evapotranSpi-
ration, infiltration and surface runoff. A simplification
is realized by analyzing stochastic processes as time-
independent events, i.e. assume that these processes follow
a definite law of certainty but not of probability (Chow,
1964). Ignoring the randomness of occurrence of the
variables comprising such a stochastic process, the re-
sulting model is said to be deterministic. For purposes
of analysis, this study is based both on a deterministic
and probabilistic approach. In order to investigate the
various hydrologic parameters comprising a deterministic
model, a review of the hydrologic principles is necessary.
Following this, probabilistic hydrologic data such as rain-
fall intensity, frequency, duration and distribution for
the study area will be presented. With this background
information, one may be capable of performing a logical
rainfall and runoff analyses.

13

14

The hydrologic principles which must be incorpo-
rated into any model include climatic and physiographic
factors, primarily peak expected rainfall amounts and basin

size. To understand this development, it is necessary to:

l) express the factors comprising the hydro-

logic cycle,

2) establish the type of rainfall common to

the northern Mid—West region,
3) explain rainfall frequency, and

4) define what is meant by a small watershed.

In order to utilize hydrologic data in a determin-
istic modelling approach, a discussion of unit hydrograph
theory is presented. Included is a derivation and applica-
tion of unit hydrographs as derived by the S-curve method.
Following the analysis presented by Chow (1962), the concept
of a unit hydrograph peak-reduction factor 2 is formulated.
Also, provision for the non-uniform distribution of rain-
fall intensity is studied.

The next step in this procedure involves the ac-
quisition of hydrologic data. Included is a list of Federal
and state agencies handling rainfall, runoff and hydrologic

soil data. Analysis of this data for Michigan and vicinity

15

will provide further insight into the various climato-
logical aspects of the state.

In the development of a rainfall analysis, it is
necessary to review the maximum recorded point rainfalls
at various locations across Michigan, Ohio, Indiana,
Illinois, and Wisconsin. From this information, isohyetal
patterns based on 24-hour maximum recorded point rainfalls
in inches can be mapped. Analyzing these isohyets, clima-
tological sections based on similar weather patterns across
the state can be assigned. Following this outline, the
conclusions forwarded in this analysis will be included in

Chow's formulation (see Chapter IV).

A. Hydrologic Principles

The factors comprising part of the hydrologic cycle
affecting runoff include two major areas: climatic and
physiographic. Climatic factors include the types of pre-
cipitation, rainfall intensities, durations and their
distribution, pattern of storm movements, antecedent soil
moisture conditions and other climatic conditions which
affect evaporation and transpiration. Following is a list
of some of the major climatic factors which should be

considered:

16

(a) Rainfall

(i) Intensity

(ii) Duration

(iii) Time distribution
(iv) Areal distribution
(v) Frequency

(vi) Geographic location

(b) Snow

(c) Evapotranspiration

Physiographic factors include basin characteristics such

as land use, soil type, area, shape, elevation, lepe and

the extent of direct, indirect and artificial drainage

influences. Some of the important physiographic factors

are:

(a) Basin characteristics

(i) Geometric factors
Drainage area
Shape
Slope

Stream density
(ii) Physical factors

Land use or cover

Surface infiltration condition

Soil type

Geological condition, such as the
permeability and capacity of
ground water resevoirs

Topographical condition, such as
the presence of lakes and swamps

(b) Channel characteristics

(i) Carrying capacity, considering size
and shape of cross section, slope,
and roughness

(ii) Storage capacity

17

The Mid-West areas of Ohio, Indiana, Illinois,
Wisconsin and Michigan usually experience high peak dis-
charges from small drainage basins. Thunderstorms are the
most common examples of high intensity-short duration
rainfalls common to this region. The Michigan Weather
Service (1971) reports that damaging or dangerous storms
do not occur as frequently in Michigan as in the states to
the south and west. This is due possibly to a '1ake effect'
imposed by three of the Great Lakes on Michigan's upper and
lower peninsulas moderating intense climate. Nevertheless,
in Michigan, the annual number of thunderstorms observed
ranges yearly from about forty in the south to around twenty-
five in the Upper Peninsula area with nearly 50 percent of
these recorded during the summer months, June through August.

For numerous small drainage structures and possible
ecological impact assessments, the determination of rainfall
frequency Offers a logical basis for establishing design
standards. The frequency of rainfall relates a particular
storm intensity for a given return period, usually 2, 5,

10, 25, 50 or 100 years. Frequency rationale would serve
the requirements for an economical design of the drainage
structure as well as provide guidelines for the assessment
of direct and indirect physical impact of a highway upon

the hydrology of a wooded or wetland area.

18

A major physiographic factor affecting runoff is
the size of the drainage basin. The following exerpt from
the American GeOphysical Union (1957) differentiates the
character of small versus large watersheds:

From the hydrologic point of view, a distinct
characteristic of the small watershed is that

the effect of overland flow rather than the

effect of channel flow is a dominating factor
affecting the peak runoff. Consequently, a

small watershed is very sensitive to high-intensity
rainfalls of short durations, and to land use.

On larger watersheds, the effect of channel flow

or the basin storage effect becomes very pro-
nounced so that such sensitivities are greatly
suppressed. Therefore, a small watershed may be
defined as one that is so small that its sensitivi-
ties to high-intensity rainfalls of short durations
and to land use are not suppressed by the channel-
storage characteristics. By this definition, the
size of a small watershed may be found from few
acres to 1,000 acres, or even up to 50 square miles.
The upper limit of the area depends on the condition
at which the above mentioned sensitivities become
practically lost due to the channel-storage effect.

Following the limit adopted by Chow (1962), this study used
a limit of 6,000 acres to distinguish between small and
largetwatersheds.

1. Development of
Unit Hydrographs

Runoff contributed by high intensity-short duration
rainfalls as defined in the previous exerpt is generally

composed of two parts:

19

l) BASE FLOW, contributed by phreatic water

recharge, and

2) SURFACE RUNOFF, contributed by overland

flow of excess water.

Surface runoff, influenced by climatic and physiographic
factors, is not steady but varies with time. The hydro-
graph, a plot of discharge (Q) versus time (t), patterns

a basin's storm runoff. The resulting graph is a curve
sloping upward to reach a peak discharge, then falling off.
This hydrograph reSponse is determined by the physiographic
and climatic conditions of each particular basin. The base
flow may be separated from the hydrograph using established
methods such as straight line approximations* (Wisler and
Brater, 1959; Chow, 1964). The remaining hydrograph is
called the direct runoff hydrograph. The area under the
direct runoff hydrograph represents the volume of runoff
obtained from a given rainfall. This runoff amount is in-
fluenced by both physiographic and climatic factors as dis-

cussed in Chapter III-A.

 

*

It should be noted that any procedure for base-
flow separation is arbitrary unless the exact amount of
the base flow can be determined. Fortunately, for most
hydrograph analysis in which the base flow is a small
percentage of the critical peak flow, any errors involved
in base-flow separation may be considered negligible.

20

Analyzing the pattern unique to a series of
direct runoff hydrographs, Sherman (1932) developed the
idea of the unit hydrograph or unit-graph. By definition,
a unit hydrograph is a hydrograph of direct runoff re-
sulting from one inch of rainfall excess precipitated uni-
formly over the basin area at a uniform rate during a
specified period of time (see Figure 2-D). Although the
unit hydrograph analysis was originally deve10ped for large
watersheds, studies by many investigators have substantiated
its application to small drainage basins as well (Brater,
1940; Hickok gt :1, 1959). The most important, practical
concept involved in the unit hydrograph theory is that all
unit hydrographs, regardless of their magnitudes, produce
nearly identical distribution graphs.

Unit hydrographs may be developed by several
established methods including the method of direct deri-
vation, the method of synthesizing and the method of building-
up. The method of direct derivation, discussed here, is a
method of unit hydrograph derivation whereby a unit hydro-
graph is produced from an observed hydrograph or a series
of hydrographs. Usually, a hydrograph resulting from an
isolated, intense, short-duration storm of nearly uniform
distribution in space and time is most desirable in this

analysis. It is then necessary to separate base-flow from

21

direct runoff by methods discussed previously. Once the
direct runoff hydrograph is derived, the ordinates of the
required unit hydrograph are simply equal to the corre-
sponding ordinates of the given direct-runoff hydrograph
divided by the total amount of runoff in inches. A general
method of derivation applicable to unit hydrographs of any
required duration may be found through the principle of
superposition, better known as the 'S-hydrograph' method
first suggested by Morgan and Hullinghors (1939).

Figure 2 shows graphically the derivation of the
unit hydrograph by the S-curve method. Figure 2-A depicts
the theoretical S-hydrograph produced by a continuous
effective rainfall at a constant rate for an indefinite
period. To arrive at the unit hydrograph for a given

duration (t hours) the following steps must be followed.

1) Assume that the S-hydrograph is produced
by a continuous effective rainfall at a

constant rate of x inches per hour (Figure 2-A).

2) Advance the position of the S-hydrograph for
a period equal to the desired duration Of t

hours (offset S-curve of Figure 2—B).

3) The difference between the ordinates of the

original and offset S-hydrograph is designated

22

as the A y-curve of Figure 2-C.

4) Finally, this difference, A y, when divided
by the product of continuous effective rain-
fall (x) times the desired duration (t) should
result in the desired unit hydrograph (Figure

2—D).

This approach can be modified when a number of unit
hydrographs of various durations are obtained. Chow (1962)
indicates that the use of actual data in plotting such a
curve is better than derivation by theory, which assumes
the condition of linearity. Regarding this assumption,
linearity exists since the ordinates of the offset S-
hydrograph of Figure 2-C are mutually proportional. Because
the S-hydrograph method assumes the principle of superposition,
such ordinates can be added or superimposed numerically in
proportion to the total amount of direct runoff. This
assumption simplifies the analysis since actual hydrographs
for a drainage basin may be somewhat nonlinear in nature.
Further review and application of unit hydrograph methods
can be found in the studies done by Chow (1962); Wisler and
Brater (1959); and Chow (1964).

It can be shown that the discharge of the S-

hydrograph at the time of equilibrium is equal to 1.008 Ax

23

Deviation of unit liydtograpli by the S-Bum method (am: 0mm»

(A)

(B)

[C]

(D)

 

Discharge

Discharge

Discharge

Discharge

WWW/”II”

Continuous rainfall excess
at a rate of 'x’ inCheS/hr

   
   

 

(

 

G =1.DOBAX

1

Continuous rainfall
excess at a rate
of ‘x' inches/hour

 

   
  

 

 

W£:::Z:Z::Z::ZZ::ZZ-
[Position of initial 8- -Cu~ve

x1 /’I Ifi—-foset S— -Durve
I /

 

 

 

 

 

 

 

 

‘ I Ay=Difference in
m I /'.\S-Curve ordinates
1 inch Unit hyd‘ograph

for 't' hour citation
[Ay/xt.)= P

  

“-—-b -

 

 

 

 

Time

FIGURE 2

24

(see Chow, 1962). Provision for major physiographic
conditions in the basin could be included by a coefficient

c. Therefore the formula becomes:

Q = 1.008 ch (3)
where Q = discharge (cfs)
c = coefficient describing physiographic
conditions
x = rate of continuous rainfall excess
or rainfall intensity (in/hr.)
A = drainage area (acres)

or approximately Q = ch. This expression is identical to
that from Equation (1), Q = ciA, which is the well-known
rational formula (ref. Chapter II). From the definition of
unit hydrograph, the S-curve method assumes that a rate of
rainfall excess x equals one inch per t hours. Neglecting
physiographic constants (c) and substituting l/t for the
intensity of a rainfall, that is, one inch of precipitation

over a period of t hours, Equation (3) becomes:

Q 1.008 A/t (4)

where t - duration of rainfall excess (hours)

The unit hydrograph peak discharge, P, set equal to

Equation (4) is defined as the peak-reduction factor Z:

z = Pt/(1.008 A) (5)

25

where Z = peak reduction factor
P = unit hydrograph peak discharge (cfs)
t = duration of rainfall excess (hrs.)
A = drainage area (acres)

From Equation (5), Z can vary from 0 to 1 depending on the
selected offset period t (ref. Figure 2-B). Such offset
period t can range from zero, in which case the offset S-
curve will coincide with the initial S-curve and the Z
factor would equal to 0,to twice the time of rise of the
peak flow in an instantaneous unit hydrograph, in which
case Z would equal 1 (Refer to Chapter IV-C [Chow, 1962]).
Mitchell (1948) found that the unit hydrograph peak
discharges for basin areas of 80, 500 and 1200 square miles
could be computed from synthetic S-curves,* the abscissa
of which is eXpressed in terms of lag time.** From such
study it was found that the resulting Z versus t/tO curves
converged to a limiting position as the drainage area
decreased. Upon reviewing Mitchell's study for basins of
80 square miles, Chow (1962) concluded that such a peak

reduction factor Z would apply to basin considerations

outlined in this formulation.

 

*

A method of developing unit hydrographs for un-
gaged drainage basins by synthesizing a number of repre-
sentative unit hydrographs in a given region was first
proposed by Snyder (1938).

**

The lag time t as defined by Chow (1964) is
equal to the time intergal in hours from the center of mass
of rainfall excess to the center of mass of runoff.

26

2. Variations of Rainfall
Intensity in a Storm

A basic assumption of the unit hydrograph develop-
ment as presented in the S-curve method involves the
uniform distribution of effective rainfall over the entire
basin area within a specified period of time. Rarely does
the actual rainfall intensity follow a uniform 'time-area'
pattern. In a study of rainfall distribution patterns
(Soil Conservation Service, l957),rainfalls of six hour
durations were analyzed to account for the effects of an
average non-uniform rainfall distribution over a basin.
Recommendations included increasing the peak discharge for
a uniform distribution from 6 to 10 percent. Following
the analysis by Chow (1962), this study assumes the average
effect of non-uniform distribution of rainfall intensity to
increase an assumed uniform distribution peak discharge by

about 6.0 percent.

B. Sources of
Hydrologic Data

 

 

The data used in the present study include the
rainfall, runoff and other hydrologic data published for
the upper Mid-West vicinity. This includes Michigan, Ohio,
Indiana, Illinois and Wisconsin. The sources of these data

are as follows:

27

l. Rainfall

Perhaps the most widely known and used rainfall
intensity-duration-frequency curve in the past has been
U.S. Department of Agriculture Miscellaneous Publication
No. 204 (1935). More recent studies by the U.S. Weather
Bureau have resulted in a broader coverage of rainfall
relationships and utilize a longer period of record.
Further update includes U.S. Weather Bureau Technical
Papers No. 40 (1963) and NO. 57 (1966). Additionally,
maximum recorded point rainfalls at 207 first order stations
throughout the United States has been reprinted in the U.S.
Weather Bureau publication Technical Paper No. 2 (rev. 1963).
Various Federal and state agencies have published
material on rainfall in specific areas of the United States
(U.S. Weather Bureau, 1954, Agricultural Engineering
Department, Michigan State University, 1967, U.S. Geologic
Survey, 1972, Michigan Weather Service, 1971). The U.S.
Weather Bureau has designated a series of climatic divisions
based on a grouping of county jurisdictions for various
states. Figure 3 describes the ten climatic divisions of
Michigan as designated by the U.S. Weather Bureau. In the
U.S. Weather Bureau (1969) publication, probability data
by climatic division is presented for twenty-three eastern

states (see Chapter III-C).

28

For the State of Michigan, rainfall intensity-
duration-frequency curves are published in the U.S. Weather
Bureau Technical Paper No. 25 (1955) for the first-order
stations of Alpena, Detroit, Lansing, Marquette, Port
Huron, Sault Ste. Marie, Escanaba, Grand Haven, Grand
Rapids and Houghton. The maximum recorded point rainfalls
for Michigan and vicinity, Table I of the Appendix, are
available through the U.S. Weather Bureau Technical Paper
No. 2 (rev. 1963). Likewise, rainfalls for Michigan and
vicinity,* Table I, were compiled through these publica-
tions. Other records of the Northeastern region of the
United States can be obtained through the U.S. Department
of Agriculture, Beltsville, Maryland, and the U.S. Depart-
ment of Commerce, National Climatic Center, Asheville,

North Carolina.

2. Runoff

The runoff data for Michigan's rivers and tribu-
taries have been studied and analyzed by the U.S. Geologic
Survey (1972). Each volume of the 1960 series of the
U.S.G.S. Water-Supply Papers entitled "Surface Water Supply
of the United States" contains a listing of all areal

records of surface-water data. Information regarding

 

*
Period of record varies from station to station.

29

special reports on major floods, droughts, or other hydro-
logic studies for the Michigan area can be obtained through
any district office of the U.S.G.S. Water Resource Division.
In the present investigation, Observed data for runoff

from small drainage basins such as Plum Brook,.Red Run and
Rose Lake located in Michigan was provided by the U.S.G.S.
Water Resources Division, Lansing, Michigan and the U.S.

Department of Agriculture, Michigan State University.

3. Hydrologic Soil Types

The COOperative Extension Service, Agricultural
Experiment Station, Michigan State University has made a
comprehensive study on the types of soils in Michigan
(Whiteside g£_al, 1968). Hydrologic classification of
these soils by soil management group was also obtained
through this agency (Christenson gt El, 1972; Schneider
35 El, 1967). A major Michigan hydrologic soil association
map, Figure 6, was deve10ped through the use of a major
Michigan soil association map and hydrologic soil group
classifications (Table II of the Appendix) provided courtesy

of the Soil Science Department, Michigan State University.

30

C. Rainfall Analysis

In the rainfall analyses, two approaches are
presented. The first involves expected precipitation
probabilities on a monthly return basis for the ten
Climatic Divisions of Michigan. These eXpected monthly
rainfall amounts (Table III of the Appendix) could be
utilized in Chow's formulation (Chapter IV) if a more
detailed rainfall selection for ecological assessments
is desired. The second approach involves the analysis
of rainfall intensity-duration-frequency curves on a
return period of 2, 5, 10, 25, 50 and 100 years. These
curves are prepared for a selected base station and
regionally interpolated for other areas through a series
of conversion factors (after Chow, 1962). The rainfall
intensity-duration-frequency approach is adOpted in this
report.

The first approach requires an explanation of the
monthly expected precipitation probabilities for the ten
Climatic Divisions of Michigan shown in Figure 3. In this
develOpment, precipitation probability values were derived
by the gamma probability function (Thom, 1947). Table III
of the Appendix gives the precipitation probabilities for
each of the ten Climatic Divisions of Michigan by month as

obtained through U.S. Weather Bureau (1969). Further

31

THE TEN CLIMATIC DIVISIONS OF MICHIGAN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_fiLma_

as m

o 99 a
0000 h.*—

 

ain'- &'

V

I” “‘0 0

 

 

 

 

I!

 

 

 

 

 

 

 

 

 

 

 

Weather Bureau

U.S.

Source:

FIGURE 3

32

studies by Thom (1951, 1958, 1968), Friedman and Janes
(1957) and Barger at 21 (1959) have shown that the gamma
probability function gives a good fit for precipitation
in a climatological data series. The precipitation data
for the individual stations used in this study were taken
from annual summaries for each station and, in general,
cover the period 1931-1967. Included in these calculated
probability values are the monthly mean precipitation
amounts and the two parameters, gamma and beta of the gamma
probability function. The shape parameter, gamma, is in-
versely.related to the skewness. That is, a small gamma
indicates that a few large values cause positive skewness
and that the mean departs further from the median value.
A large gamma causes the probability function to approach
normality. Beta, the scale parameter, indicates range or
dispersion with a larger beta indicating a greater tendency
to deviate from either the mean or median.

These characteristics can be illustrated with data
from Michigan's Northeast Lower Climatic Division (p. 103)-
For example, in January, one finds the 50-percenti1e value
is 1.52 inches while in September it is 3.35 inches. In
general, this indicates that larger precipitation amounts
can be eXpected in September than in January. By comparing

the differences in the expected precipitation amounts-for

33

the high (95-percenti1e) and low (5-percentile) proba-
bilities for these two months, we can assess the dependa-
bility of the precipitation, that is, the variation of
expected rainfall amounts in any one month. For example,
in January, the range between the 5-percenti1e precipita-
tion amount and the 95-percenti1e amount is 2.21 inches.
In September, the range between the same probabilities is
5.19 inches. Thus, while a large amount of precipitation
can generally be expected in September, relative to January,
the September precipitation amounts over a period of years
will show greater variation.

This type of information can be valuable in plan-
ning for the expected monthly rainfall for water supplies,
irrigation needs and ecological impact assessments. It
indicates both the distribution of the potential supply
over the year and the probability of monthly excessive
rainfall amounts. It also emphasizes the inadequacies
inherent in using the average precipitation over an area
for planning.

The second approach, the study of rainfall intensity-

duration-frequency curves, involves:

l) acquisition of rainfall data,

2) comparison of rainfall point data to

predicted frequency curves,

34

3) analysis of maximum recorded point rainfalls

for the surrounding area,

4) develOpment of climatological sections based

on recorded precipitation isohyetal patterns,

5) establishment of the mean rainfall for each

climatological section,

6) selection of a base station whose predicted
frequency curves will be used as an index for

the other climatological sections, and

7) averaging of the mean recorded rainfall amount
for each climatological section against that

of the selected base station.

With this completed, gaged data can be reasonably applied
to expected rainfall amounts experienced by small, ungaged
watersheds. This outlined procedure can be applied to
areas ranging from a few square miles to a township, county
or state-wide region. For purposes of example, this study
applied the outlined procedure to the state of Michigan
using the frequency curves of Lansing, Michigan as a suit-
able index.

Interpolation of the rainfall intensity-duration-

*
frequency curves for Lansing, Michigan (U.S. Weather Bureau

 

*

The frequency curves prepared by the U.S. Weather
Bureau in Technical Paper No. 25 (1955) used the Gumbel
method of extreme values.

35

Technical Paper No. 25, 1955) provided the frequency data
used as the basis for this study. Rainfall amounts for
frequencies of 2, 5,10, 25, 50 and 100 years and durations
of from 5 minutes to 24 hours are shown in Table I and
presented graphically in Figure 4.

Comparing rainfall point data with the predicted
rainfall frequency curves for Lansing as found in Table I
and Figure 4 it can be seen that the maximum Lansing recorded
point rainfall falls within the 25-50 year predicted frequency
for a 5 minute to 6 hour period. From Figure 4 it is esti-
mated that the maximum recorded point rainfall for Michigan
and Michigan and vicinity may be in the order of a 100 year
frequency for durations of less than 40 minutes and approxi-
mately a 1000 year frequency or greater for longer durations.

The maximum recorded point rainfalls for Michigan
and vicinity as obtained from the U.S. Weather Bureau
Technical Paper NO. 2 (rev. 1963) were also studied and are
listed in Table I of the Appendix. These included 14 in-
state and 13 out-state rainfall stations. Out-of-state
stations were selected to reflect southern and western rain-
fall amounts to pattern isohyetal averages over Michigan's
upper and lower peninsula regions (Figure 5).

Mapping the 24-hour maximum precipitation for these

twenty-seven stations, the isohyetal patterns for the

36

 

 

 

 

 

 

m .02 ummmm .nowe swmusm umcummz .m.D «mousom
o 0 0 o 0 0 0 0 0 O %HHGHOH> can
cm m cm o mm o om v Hm v no m mm N 00 m ow H mm o cmmflnowz CH .xmz
vo.m oa.m Hm.v NH.v om.m mo.m vw.~ mm.H ov.a mm.o comacoaz ca .xmz
hv.m mo.v No.m om.m mm.m oo.~ mm.H m~.H mm.o o>.o Hz.osamcmq CH .xmz
.mm .02 momma .coms smousm Hocpmmz .m.c "mousom
mh.a mm.a om.H mm.a o~.H mo.d.mm~oimmso mm.o mm.o m
vm.m mm.m mm.a om.a vo.a O¢.H oa.a mm.o mm.o vv.o m
NH.m vo.m vm.~ oa.m om.H oo.H om.H mm.o mm.o Hm.o 0H
mv.m oo.m on.m mv.~ ov.m oo.m mm.a mH.H hm.o mm.o mm
vm.m om.m oo.m on.m oo.m oa.m on.a om.a mo.a mo.o om somanoaz
mm.v oo.m om.m vo.m oo.m ov.m om.H mv.H SH.H mh.o ooa .msamcmq
macaw
humongoum
«N NH o m m om (om ma ca m
mnsom mousse:

 

 

MBHZHUH> 02¢ ZfiUHmUHE mom mmmUZH ZH
mqqfimZHdm SDEHx4£ 02¢ mmHUZMDOMmm 92mmmthQ m0 mqqthHdm

H mqmdB

umnu

 

37

Iii-fall: cl diliomt (music: and Iain. nimll:

III 1510 30405000 2 34587.!II2 024 9
INN“; NIB
IUMHMISHIN

-————-= duration-frequency curves for Lansing, Mich.

----- = expected maximum duration-frequency curves
for Lansing, Mich., and Michigan and vicinity.

FIGURE 4

38

2441-: suin- mcipimiu isdyotals, average: and comm» (actor:
htflxdhnmfiuluflhquIHMu

\ \ \ IICIIIGAII

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(contour interval = 0.5 inches)

FIGURE 5

39

Michigan area were obtained. The sensitivity of isohyetal
patterns to sampling variation is remarkably great (Huff
and Neill, 1959). With insufficient data, therefore, the
orientation and distribution of the isohyets in Figure 5
is somewhat uncertain.

From a review of the isohyetal patterns arrived at
by these data, a division of the state into six climato-
logical sections is proposed (Figure 5). These climato-
logical sections include the upper peninsula, the northeast,
central, southeast central, west and south lower peninsula.
Subsequently, precipitation averages for each section were
computed through an isohyetal method of plainimetering the
areas between adjacent isohyets to assess a mean rainfall
average for each section. These averages are also shown in
Figure 5.

Lansing, Michigan, a first-order rain gaging station
located centrally in the state, is taken as the base station
in this analysis. Located in the lower peninsula, Lansing
is situated in the northern portion of-the south climato-
logical section. All frequency curves for Lansing pre-
sented graphically in Figure 4 appear to have a similar
trend of variation. Upon analysis of predicted rainfall
curves for other first-order stations in Michigan, a

similar frequency distribution for durations of from 5

40

minutes to 24 hours is apparent. Furthermore, a review

of rainfall intensity-duration-frequency curves used in

an Illinois study (Chow, 1962) shows a similar frequency
distribution. This similarity would indicate that a
possible correlation of frequency curves for various state
areas and northern Mid-West regions is reasonable. There-
fore, following the generalization made in Chow's study
(1962), a conversion factor relating various climatological
sections to a selected base station may be considered.

For the basis of comparison, the Lansing frequency data
found in Table I will be used as an index for other climato—
logical sections of the state.

To correlate this frequency analysis, the maximum
recorded point rainfall for Lansing obtained through the
U.S. Weather Bureau's Technical Paper NO. 2 (rev. 1963) is
used. The 24-hour maximum recorded point rainfall for
Lansing is 5.47 inches. The ratio of the average 24-hour
maximum recorded point rainfall for each climatological
section to that of the Lansing value is then computed.

This ratio is the conversion factor. The Lansing 24-hour
maximum recorded point rainfall times the conversion factor
for any climatological section will give the 24-hour average
maximum rainfall for that section. For example, from

Figure 5, the conversion factor for the central lower

41

peninsula section is 0.78. This conversion factor times
the index rainfall for Lansing (5.47 inches) gives an
average maximum rainfall for the central lower section of
4.26 inches.

The conversion factor for the south-lower section
where the Lansing index is based, is 0.92. Theoretically
this value should be 1.00. However, since sectional
conversion factors are averages and due to the uncertain
sampling variations described above, this difference may
be ignored for practical purposes. For any particular
basin location within a climatological section in Michigan,
an interpolated value of the conversion factor may be obtained
if so desired.

In reviewing this procedure, greater accuracy may be
gained by expressing the climatic factor by a series of
isocontours. These isocontours, relating the combined
affects of rainfall, snowfall and temperature patterns,
could then be mapped as shown for rainfall in Figure 5.

In this manner, the subdivision of the state into six
climatological sections from the analysis of rainfall
patterns throughout the state, could be further refined to
include other weather variations. This would provide
further insight on the factors contributing to waterway

area determinations and ecological impact assessments.

42

In this section, a study of hydrologic concepts
was presented. With a knowledge of deterministic modelling

from:

1) a description of factors comprising the

hydrologic cycle,

2) a discussion of unit hydrograph theory,

and

3) the develOpment of a rainfall analysis,

a method for the prediction of runoff from small drainage
basins in Michigan can be formulated. This procedure

should satisfy the following requirements:

1) It should consider the major climatic conditions

in the area of the given drainage basin.

2) It should consider the major physiographic
conditions in the area of the given drainage

basin.

3) It should consider either a definite design

frequency or a limiting design condition.

4) It should be based on sound and simple hydro-
logic principles so that the practicing
engineer can use it with confidence and under-

standing.

43

5) It should be simple and practical so that a

beginner can use it readily with ease.

6) It should depend less on personal judgment
and more on logical procedure so that the
result will be relatively consistent among

determinations by different individuals.

CHAPTER IV

CHOW'S FORMULA

The method of rainfall-runoff prediction deve10ped
by Chow (1962) utilizes the concept of unit hydrographs
and is based on unit hydrograph synthesis. It is an attempt
to arrive at a logical procedure such that results will be
relatively consistent among different individuals. It
incorporates the major climatic and physiographic conditions
and their influence on runoff in the area of the given-
drainage basin.

To develOp an equation relating the expected direct
peak runoff from a drainage basin, a series of variables

must be defined. These are as follows:
1) the excess precipitation (Re) in inches for a
given duration of t hours,

2) the unit hydrograph peak discharge (P) in cfs
per inch of direct runoff for the duration t

hours of rainfall excess,

3) the area of the given drainage basin (A) in

acres,.

44

45

4) the unit hydrograph peak-reduction factor (Z),
5) the runoff factor (X), and

6) the climatic factor (Y).

From the integration of these factors a design peak dis-
charge relationship (Qd) can be derived.

Following the analysis presented by Chow (1962),
the direct peak runoff from a drainage basin may be computed
as a product of the rainfall excess and the peak discharge

of a unit hydrograph:

0
ll

ReP (6)

where Q = direct peak runoff

rainfall excess in inches for a

given duration of t hours

P = unit hydrograph peak discharge
in cfs per inch of direct runoff
for the duration t hours of rain-
fall excess.

2:!
II

From the previous review of the hydrologic principles,
it was found that-the factors affecting the design peak dis-
charge can be categorized into two groups. The first group
affects directly the amount of rainfall excess or direct
runoff and it consists mainly of land use, surface condition,
soil type, and the amount and duration of rainfall. The
second group affects the distribution of direct runoff and

it includes the size and shape of the drainage basin, the

46

land slope, and a time measure of detention effect such as
the lag time. The distribution of direct runoff is expressed
in terms of the unit hydrograph.

There may be a certain interdependence existing
between the two groups of factors described above. However,
this interdependence is unknown, and for practical purposes
it may be assumed that it does not affect the relationship
between the direct runoff and rainfall excess. This assump-
tion forms the basis upon which Equation (6) is established.

A series of relationships may be utilized to further
expand Equation (6). These include the peak reduction
factor Z, the runoff factor X and the climatic factor Y.

Rewriting the peak reduction factor Z (Equation 5) as:

P = 1.008AZ (7)

t
and substituting into Equation (6) one obtains:
1.008 R AZ
e

Q = (8)
t

 

In Equation (8), the factor 1.008 Re/t may be expressed
as the product of two factors, X and Y. The factor X is a

'runoff factor,‘ eXpressed as:

47

R
x=-9-l-'- (9)
t
where ReL = rainfall excess at Lansing, Michigan

increased by 6% to account for the

average effects of non-uniform dis-

tribution of rainfall intensity in

the duration t

The factor Y is a 'climatic factor,‘ expressed as the ratio
of rainfall at the selected basin to that of Lansing,
Michigan. Assuming Re/ReL = R/RL, that is, the ratio of
rainfall excess of the selected basin to that of Lansing

is equal to the ratio of rainfalls of the selected basin

to that of Lansing, this factor is represented as:

Y = 1.008 R (10)

RL

where RL rainfall in inches at
Lansing, Michigan
R = rainfall in inches at
other location

Consequently, Equation (6) may be written as:
Q = AXYZ (11)

If the base flow (sustained or fair-weather runoff) at the
time of the peak discharge is Qb' then the design peak

discharge, Qd, can be expressed as:

Qd = Q + Qb (12)

48

To develOp Equation (11) the components defining
the factors x, Y, and Z must be analyzed. For convenience,
the following outline is presented.

In order to formulate a RUNOFF FACTOR X, we must

consider:

1) Land use, surface condition and antecedent
ground moisture effects through use of a run-

off number N,

2) Soil types based on a grouping of hydrologic

soil associations for Michigan, and

3) Rainfall excess (Re) and rainfall depth (R)

relationships.

To establish the CLIMATIC FACTOR Y, we must utilize

(from the analysis presented in Chapter III-C):

l) Climatological sections based on recorded

precipitation isohyetal patterns,

2) Predicted frequency curves from a selected
base station to be used as an index for the

other climatological sections, and

3) Rainfall distribution ratios for the selected

base station to that of other localities.

49

To apply a PEAK REDUCTION FACTOR Z, one must:

1) understand unit hydrograph peak discharge,

2) define a time measure of detention effect,

and

3) analyze channel length and channel slope

influences.

A. Runoff Factor X

 

1. Determination of Land Use,.
Surface Condition and
Antecedent Ground Moisture
Effects

In order to assess land use, surface condition and
antecedent ground moisture effects, it was found that the
data used in the method of hydrograph synthesis by the U.S.
Soil Conservation Service (1963) could be utilized in Chow's
analysis to evaluate the direct runoff. For the present
investigation, an average hydrologic condition of drainage
basins was assumed. This condition represents the average
condition of antecedent moisture content and groundwater
influence during the optimum time of the year. This is
classified as antecedent moisture condition Class II.

Class I and Class III antecedent moisture conditions signify

below and above average rainfalls respectively. Condition

50

classes are based on recorded precipitation amounts over

a 5-day period for two seasonal conditions, dormant and
growing. Generally, in Michigan, this growing season may
last from late March, early April through October, depending
upon ground frost conditions. This frost condition is
reflected in the lower precipitation amounts necessary for

a greater amount of expected runoff to occur. From Table IV
of the Appendix for example, a 5-day total antecedent rain-
fall of 1.2 inches would be placed in antecedent moisture
condition Class I for the normal growing season but would

be modified to Class III for the dormant season.

The hydrologic soil-cover complex numbers used by
the Soil Conservation Service (1963) were modified after
Chow and renamed the 'runoff number' N. Table II contains
various runoff numbers, N, on the basis of land use, surface
condition and soil type for a Class II antecedent moisture
condition. Such soil-cover complex numbers are based on a
5-day total antecedent rainfall as outlined at the tOp of
Table IV of the Appendix. Runoff numbers can be modified

from Class II to either Class I or Class III by:

1) referring to the 5-day antecedent moisture

condition class (top of Table IV of the Appendix),

2) selecting the Class II runoff number based on

51

land use, surface condition and soil type

(Table II), and

3) interpolating the modified runoff number for
either Class I or Class III (bottom of Table IV
of the Appendix) against that specified for

antecedent moisture condition Class II.

For example, a sparsly forested region with a
Class II runoff number N of 46 (refer to Table II) would
have a modified runoff number N equal to 27 for Class I
or N equal to 66 for Class III (refer to Table IV of the
Appendix). The final selection of the runoff number N
would of course depend on the season and the 5-day total
antecedent rainfall amount.

2. Determination of
Hydrologic Soil Type

To analyze the effect of soil types on runoff,
Table II of the Appendix classifying soil types from well-
drained (Group A series) to poorly-drained (Group D series)
was prepared for Michigan. These soil series are divided
into four hydrologic soil groups based on work conducted
by the Soil Conservation Service of the U.S. Department of
Agriculture, the COOperative Extension Service, and the

Michigan Agricultural Experiment Station. These rankings

52

TABLE II

SELECTION OF RUNOFF NUMBER N FOR ANTECEDENT MOISTURE

CONDITION CLASS II

 

 

-'

 

 

 

Land Use or Cover Surface Condition Soil Type
A B C D
Fallow Straight Row 77 86 91 94
Row Crops Straight Row 70 80 87 90
Contoured 67 77 83 87
Contoured & Terraced 64 73 79 82
Small Grains Straight Row 64 76 84 88
Contoured 62 74 82 85
Contoured & Terraced 60 71 79 82
Legumes (closed- Straight Row 62 75 83 87
drilled or broad- Contoured 60 72 81 84
cast) or rotation Contoured & Terraced 57 70 78 82
meadow
Pasture or Range Poor 68 79 86 89
Normal 49 69 79 84
Good 39 61 74 80
Contoured, Poor 47 67 81 88
Contoured, Normal 25 59 75 83
Contoured, Good 6 35 70 79
Meadow (Permanent) Normal 30 58 71 78
Woods (Farm wood Sparse/Low transpiration 45 66 77 83
lots) Normal 36 60 73 79
Dense/High transpiration 25 55 70 77
Farmsteads Normal 59 74 82 86
Roads Dirt 72 82 87 89
Hard Surface 74 84 90 92
Forest Very Sparse/Low 56 75 86 91
transpiration
Sparse/Low transpiration 46 68 78 84
Normal 36 60 70 76
Dense/High transpiration 26 52 62 69
very De“?e/H?gh 15 44 54 61
transpiration
Impervious Surface .- 100 100 100 100

 

Source: U.S. Soil Conservation Service (1963).

53

are established through basic interpretive soil groupings.
They are based on properties of the soil profile to a depth
of from 3.5 to 5.5 feet. Table II of the Appendix was
further subdivided to show the predominence of particular
soil types throughout northern and southern Michigan

(after Michigan State Highway Department, 1960) and should
be used in conjunction with Table II.

For the convenience of identifying the major hydro-
logic soil types in Michigan and their general locality,
Figure 6 was prepared through use of hydrologic soil group
classifications and a major Michigan soil association's map
(Whiteside 32 El, 1968). Figure 6 represents the different
hydrologic soil types of Michigan. A predominence of group
B and C soil series (moderate well-drained to moderate
poorly drained) is noticed in the thumb region of Michigan.
This could well be the result of a lack of glacial morains,
till plains and outwash plains in the area. Such glacial
drifts carry the well drained gravel and sand materials as
deposited by the last Ice Age termed the 'Wisconsin Glacial
Surge.‘ Northern regions of the southern peninsula show
a predominence of well drained sand and gravel materials.

With the variability of soil types and soil groups
in any one general locality, a composite runoff condition

should be evaluated. This can be done through use of a

54

 

 

FIGURE 6

55

weighted runoff number N. For example, assume a basin has
a 5-day total antecedent rainfall (dormant season) of 2.5
inches. From Table IV of the Appendix, this basin is
classified as belonging to antecedent moisture condition
Class III. If this basin contains 22.3 percent impervious
area and the remaining area is densly forested over soil
types of Group C soil series, the weighted runoff number

is computed as follows:

 

(Appendix
(Table II) Table IV)
Runoff No. Runoff No.
Cover Percentage Class II Class III Product
(a) (b) (C) (b x C)
Impervious
Surface 22.3% 100 100 22.3
Dense
Forested 77.7% 62 79 61.4
Area
Sum = 83.7

The weighted runoff number N is 83.7 for this example.

3. Determination of
Rainfall Excess

After the runoff number (N) is determined, the
rainfall excess (Re) for a given rainfall depth (R) can
be computed from the following formula:

(3 - 200/14 + 2)2
(R + BOO/N - 8)

 

R

e (13)

56

This formula is used to calculate the direct runoff (Re)
as a function of the rainfall (R) for different runoff
numbers (N). It was derived by the U.S. Soil Conservation
Service from various plots of storm rainfall versus direct
runoff for observed storms and correlated using the runoff
number N.

A chart deve10ped by the U.S. Soil Conservation
Service (1963) uses Equation (13) to formulate design
curves based on rainfall (R) and runoff number (N). These
curves are presented in Figure 7. A value for direct run-
off can be obtained through direct computation of Equation
(13) or interpolation of Figure 7. For example, with N
equal to 83.7 and R equal to 2.5 inches, the direct runoff
from either the chart or Equation (13) is Re = 1.10 inches.

4. Determination of
Runoff Factor X

After the runoff number N is determined, the rain-
fall excess (Re) for a given rainfall can be computed from
Equation (13) or through the curves of Figure 7. Knowing
Re*’ the runoff factor X for the duration t of the rainfall

can be computed by Equation (9).

 

*

Computed as the rainfall excess at Lansing,
Michigan (R ) since the rainfall R of Equation (13) is
that of LangIng used as an index.

57

Iclatiuship hum nimll and rainfall aces: in mice: mail was:

a
_ aoo )
(Fl —-—N +2,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

flmvnub: Pb1=
FI-l- 8&0 - a

Re = rainfall excess in inches

R = rianfall in inches

N = hydrologic soil-cover complex number

7

.471; /

i / , / 1
i ////
.2 Q // /,
g ’/,//// [j/
5 4 . i////:// 1//'
an / /
E 3% // )9! / 1 __
c 1/ I’
a?” / I / /

a / / A

/,’////t// 4’
1 ’//;;;// A/
/ /;4/ ,i/ /
22; fi
D 1 2' 3 4 5 B 7 B 9 1D

RJ%#falhifljEB

Source: U.S. Soil Conservation Service (1963).

FIGURE 7

58

The computation of the runoff factor X for frequencies
of 2, 5, 10, 25, 50 and 100 year frequencies may be found in
Appendix Tables V through X. Columns one and two of these
tables assign the rainfall duration, column three, the rain-
fall frequency amount for Lansing, Michigan as presented in
Table I, column four, the Lansing rainfall amount increased
by 6 percent to account for the effects of non-uniform distri-
bution over a basin, and columns five through twelve, the
corresponding runoff factor X in 5 unit increments for runoff
numbers N of 100 to 65 inclusive. It should be noted that
the curves of Figures 8, 9, and 10 which graphically relate
the runoff factor X for the above mentioned computed tables
have been fitted to accomodate a smooth curve. It is
suggested that interpolation of the curves be used rather
than Equation (9) directly for computation of a runoff factor
X of less than 1 hour because of the above mentioned curve

fitting technique.

B. Climatic Factor Y

The climatic factor Y is represented in Equation (10)
as the ratio of rainfall at a selected basin location to
that of the selected base station increased by 1.008. In
the present analysis, to establish a climatic factor Y for

each of the six climatological sections of Michigan (as

59
Runoff facts x in: 2- and s-mr frequencies

———-— = 5 yr. frequency

..... = 2 yr. frequency

X. runoff factor (in/hr)

/
/

 

0.01
5 101520304080 234568
hours

minutes
15. duration as shown

FIGURE 8

60
llnnoil iactu X lot 1o-anil 25—ynar frequencies

————— = 25 yr. frequency

_____ = 10 yr. frequency

 

T.‘
.C
\
.5
(3
.8
Q-
“6
C
3
L
X
CJCQE 13 1E§EI3 EIDAKD EID 2 3 ‘4 558 (B
rnkLmes VIKFS

txirafion assymen

FIGURE 9

61
Runoff factor X for 50- and 1oo-year frequencies

-——-—-= 100 yr. frequency

_____ = 50 yr. frequency

 

T
.C
\
£1.
E
a;
X 0.1
C1015 101520304060 2 34568
minutes hou‘s

tidunamon as shomri

FIGURE 10

62

obtained through the rainfall analysis of Chapter III-C)

the areal conversion factor is used. The conversion factors
found in Figure 5 represent the rainfall distribution ratio,
that is, the ratio of rainfall of each climatological
section to that of the established Lansing base station.
Through this conversion ratio, the predicted frequency
curves for Lansing as outlined in Table I and Figure 4 can
then be modified to serve as an index for the six climato-
logical sections of the state. The sectional conversion
ratios multiplied by 1.008 establish the representative
climatic factor Y for that section. Figure 11 outlines

the climatological sections of Michigan as obtained from
Figure 5 and their respective climatological factors Y.

I

C. Peak-Reduction
Factor Z

 

The peak-reduction factor Z represented by Equation
(5) is equal to the ratio between the peak discharge of a
unit hydrograph due to the rainfall of a given duration t
and the equilibrium runoff or the runoff of the same rain-
fall intensity continuing indefinitely. From Mitchell's
study (1948) this ratio is shown to be a function of the

ratio between duration t and lag t In Chow's analysis

0.
(1962) the value Z is to be represented by a function of

63

Eli-afie fatter 1 far ell-atelegieal sections in lieligan

IICIIIGAI

 

 

 

 

 

 

 

 

 

\. J%/’ 031

\</ \
firwub: \(

\
( ;\ 0.79
_ 1.DDBFI \ 'x

/
y

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Y- ‘ a
Y = climatic factor \ i/
. . _ QED )3
R = rainfall in inches /
at other locations / \\ 73.81
RL= rainfall in inches l / \l
at Lansing, Mich. // \F
/ 093 \.
/ \
/
/

FIGURE 11

64

the ratio between duration t and lag time tp. For the
purpose of develOping the proposed method, Chow analyzed

a time measure of detention effect to relate tp, the time
of rise of the peak flow in an instantaneous unit hydro-
graph, to to, the lag or time interval from the center of
mass for rainfall excess to that of the center of mass for
runoff. Such analysis is desired to achieve a suitable
comparison between small drainage basins (6000 acres) and
basins of 80 square miles (51,200 acres). From the concept
of instantaneous unit hydrographs, a relationship between
the lag t

0
is expressed as:

and the lag time tp was formulated. This equation

tp = 0.47 to (14)

The implications of this formula will be discussed later in
this analysis.

From acquired data for small drainage basins
located in the northern Mid-West vicinity, Chow (1962)

formulated a lag time relation expressed as:

tp = 0.00236 (LA/‘5)0'54 (15)
where t = the time of rise of the peak flow

P in an instantaneous unit hydrograph

L = channel length in feet

S = channel slope in percent

65

Equation (15) represents a best fit curve of lag time tp
to a factor K. K is the ratio of channel length L in
feet to channel slope S in feet per foot for the basins

under study (Chow, 1962). This relationship is defined as:

K = L,</ s (16)

From Equations (15) and (16), a lag time relationship has
been correlated to channel length and slope characteristics.
This is reasonable in our analysis since we are considering
small drainage basins with simple drainage patterns. From
Equation (14) it is possible to correlate a peak-reduction
factor Z based on a t/t0 relationship (after Mitchell, 1948)
to that of a t/tp relationship (after Chow, 1962). For
practical applications, Equation (15) is shown by a chart
in Figure 12.

1. Verification of
Factor Z by Data

In order to verify the analysis presented by Chow
for small drainage basins of Illinois, Ohio, Missouri,
Wisconsin, Indiana, Iowa and Nebraska to that of Michigan,

a procedure similar to one presented by Chow (Table XI of
the Appendix) was followed. Table III presents a series
of stoms, durations, lag times and unit hydrograph peak dis-

charges. These data were used to arrive at a peak-reduction

tp. lag time (hr)

66

armin- a In. (in, t, (after ennui)

formula: cp- corneas(1.481054

 

L.|ength of eternal (ft)

FIGURE 12

67

 

 

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lava mhv.o mm.mmqm 4am.o mo.m v~.m mama .HN so:
Amen aqm.o mm.mmo¢ ~m.¢ aw.a snag .o uusmsa
mommssm you voucsooua loom ~om.o am.soam amm.o ma.m H~.H mmma .oN Adan
suns: scan uounwum N nvm.a ma.maoe ~am.~ oo.~ ma.a smma .«H nonso>oz
lava mmm.c mm.veom Hav.~ mo.~ oo.o nmma .vN nonouoo
mxmoa «Hansen: Lava oas.o ca.amah own.o mm.~ oo.~ omma .H nonso>oz
suns: can» “museum N oao.d oom~m smm.o ha.~ H~.H omma .sa case
Luc~ «cm.o mm.mmnm omv.o ma.~ o~.H omma .HH so:
.ncm o~m.o mm.mo~m ama.a as.m om.s omen .m an:
suns: cusp umumoum N mma.a oa.~aon mmm.~ mm.n ov.a swag .mm Hanna
suns: amen noumoum N mm..a mn.mnoh moa.~ oH.~ No.4 umma .h~ sauna
Loom ovo.H m~.momm wnH.H ~4.~ ma.~ wmafl .m none: can»: name
suns: nuns umumoum N «NO.H oomv mam.n ~m.~ om.m mmafl .N uonse>oz cam pom .coaz m
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lava nma.o mm.mooa maa.o NO.HH om.~ mmmfl .mH some:
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Luca oma.o cmm maa.o o~.HH GH.~ mmma .4 none:
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lace ~m~.o ma.mam «Ha.° mm.e~ oa.o vmma .mN noun: www.ca xooum asap .noa: a
OCHUUOHA Q mMflOZ NHSO:
Hoe Amoco a seam w u u «whoa
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HHH mqm¢8

z¢UHmUH2 mom N moaodm ZOHBUDQmmfxémm 02¢ mZHB Odd mo ZOHB<BDmeD

68

factor Z for two drainage basins in Michigan. This factor

Z when plotted against the ratio t/tp will allow correlation
and further comparison with Chow's data (Table XI of the
Appendix).

The first of these drainage basins, Plum Brook,
exemplifies a rural basin having a natural watercourse
throughout its length. The Plum Brook basin, for the most
part, lies on a lake plain of low relief. Land elevations
range from about 605 feet above mean sea level at the gaging
station to about 850 feet on the western rim of the basin.
Soils are loams, silt loams, and clay loams over compact and
retentive clay.

The second Of_these drainage basins, Red Run, is
completely sewered. Urban and suburban develOpment is
intensive although a number of parks, cemeteries, golf
courses, wooded areas and Open industrial sites are randomly
distributed over the basin. Approximately 25 percent of
the basin area is composed of impervious surface. Land
elevations range from about 610 to 710 feet above mean sea
level. Soils are finely textured sands, silts and clays.

In this analysis, an attempt to study runoff effects
of rural versus suburban develOpment for the two Michigan
basins to that of basins utilized in Chow's study (1962)

was made. This was established through use of a legend

69

as found at the tOp of Figure 13. For convenience, results
of Table III and Table XI of the Appendix make use of this
notation and are plotted in Figure 13 for comparison with
Chow's data.

In general, the plotting of computed data points
for Michigan basins against those of the out-state vicinity
(refer to Table XI of the Appendix) showed good correlation
to the fitted curve presented in Chow's analysis (refer to
Figure 13). Suburban development found in the Red Run
basin led to an increase in the peak-reduction factor Z.
This was expected since channelization of waters through
storm sewers would decrease the lag time tp and increase
the peak reduction factor Z.

Theoretically, t should not be greater than 2 tp.
Otherwise the peak discharge would occur before the end of
the rainfall excess Re‘ At t = th and greater, the unit
hydrograph should reach and maintain a maximum value. In
other words, Z equals 1 at t/tP = 2. The upper portion of
Figure 13 was therefore drawn to satisfy this condition
(after Chow, 1962).

This theoretical limit of Z = l at t/tp greater
than or equal to 2 could not be strictly upheld in the
Red Run analysis owing to the effects of channelization.

From Table III for example, the April 29, 1956 storm had

1.0

0.10

Z = Pt/1.CDBA

0.01

0.001

”at“ ”I" l I“ III,

.8
‘8
0:

70

Red FIun, Michigan
Plum Brook. Michigan
Dut State Vicinity after ChowB data

 

0.01

0.10

1.0
tub

FIGURE 13

10

 

 

71

a t/tP ratio less than 2 (1.883) but a peak reduction
factor Z greater than 1 (1.135). This occurrence appeared
in cases where a long storm duration was encountered with
a sufficiently short lag time period resulting owing to
channelization. From the Red Run data of Table III, no
attempt was made to analyze the results in cases of Z
greater than unity. The remainder of the Red Run results
showed good correlation to the fitted curve of Figure 13.
Data points of the Plum Brook basin also showed
good correlation to the fitted curve. Data points fell
below those of the Red Run basin since lag times were
markedly increased in the Plum Brook area over those of
the Red Run area. This could be explained in light of
natural drainage patterns present in the Plum Brook basin.
Equation (14) deve10ped by Chow (1962) was used to
compare the fitted curve for small drainage basins of
Michigan to that of Mitchell's study (1948). This con—
verted curve, based on the unit hydrograph for drainage
basins of an average size of eighty square miles in Illinois
is also plotted in Figure 13 for comparison. Upon review
of Figure 13, it is seen that the plotted data do not fit
this converted curve fitted by Chow for basins of an average
area of eighty square miles but are shown above the latter.

Basins of an average of 6000 acres would generally have a

72

shorter lag time than those of 80 square miles (51,200
acres). The result is a greater Z factor owing to a
reduced t/tp lag time ratio. Therefore, the average
curve fitted for small drainage basins of Michigan and

out-state vicinity appears justifiable in this analysis.

D.. Design Criteria

 

From a review of design practices in Michigan it
was found that adequate design criteria concerning the
climatic and physiographic conditions of drainage basins
for hydrologic and hydraulic considerations is needed.

In the prOposed method it is suggested that adequate hydro-
logic design criteria be considered and established as a
first step towards an environmental impact assessment of
highway placement. For this purpose, a definition (Chow,
1962) of the design discharge to be used by the proposed
method is given as follows:

The design discharge is the maximum discharge

that would occur under an average physiographic

condition of the drainage basin due to rainfall

of a given frequency and various durations and

due to base flow.
In view of the lack of a universal criterion for the design
frequency in assessing an environmental impact, values of

runoff factor X for frequencies of 2, 5, 10, 25, 50, and

100 years were prepared for use in the prOposed method.

73

From the rainfall analysis of Chapter II the maximum
recorded rainfall at Lansing, Michigan was found to have

a frequency of the order of 25-50 years (Figure 4). It
may appear reasonable to set frequency criteria in this
range as a practical upper limit for use of this procedure
in design applications.

The definition of the design discharge signifies
it as the maximum discharge due to rainfall of various
durations and due to base flow (Equation 12). Accordingly,
different rainfall durations must be assigned in order to
assess the maximum value of discharge. This maximum value
is then taken as the design discharge. For ecological im-
pact assessments, the predicted monthly rainfall amounts
(Table III of the Appendix) could be used if a more detailed
analysis is required or desired.

It is important to point out that the duration
referred to in the determination of runoff factor X is the
time interval within which the maximum depth of rainfall
of a given frequency would occur. This duration is not
necessarily the actual duration of rainfall excess or the
duration of the entire storm. Unless the true duration of
rainfall excess is available and used in the analysis of

rainfall frequencies, we can only assume that the maximum

74

rainfall depth occurs uniformly within the designated
duration. Since thunderstorms of high intensities and
short durations usually are the cause of the peak flows
from small drainage basins in Michigan, this assumption
is conservative and reasonable for the prediction of run-

off from these areas.

E; Design Procedure By
The~Pr9posed'Method

 

For the convenience of applying the proposed method,
a design chart is presented in Figure 14. For a drainage
basin of given size, runoff condition, and location in
Michigan, the procedure of computing the design discharge

is outlined as follows:

(1) From the soil type map in the design chart,
Figure 6 or Table II of the Appendix, determine

the soil type.

(2) From the runoff number table (or Table II),
determine the runoff number N for the soil
type and the given cover and surface condition.
If the drainage basin has composite soil types
and cover and surface conditions, a weighted

runoff number should be computed. If a more

 

STEP
(1)
(2)

(3)

(h)
(5)
(6)
(7)
(8)

PROCEDURE

Read soil type from (a)

With cover. surface condition. and soil type read
the runoff number. N. from (b) (pg- 76)

With N. frequency. and assigned t. read factor X
from (0) or (0) (pp. 77, 78)

Read the climatic factor, Y, from (a) (pg- 76)

With drainage basin data, read tp from (f) (pg. 77)

Compute the ratio t/tp

With t/tp read the beak reduction factor. 2. from (51 Cpg. 78)

Compute the discharge by Equation 11: Q I AXYZ
(Q s discharge in cfs) (A I drainage area in acres)

FIGURE 14

 

 

(b)

(e)

76

3mm 0 mo" '00!!! l POI! MID"? I018”!!!

Land the or cover

COIDITIOI CLASS 11
Surface Coalition

’

 

Pence
lce crepe

Sean Grains

Lego-cc (closed-
drilled or broad-
cast) or rotation
aeadoe

Pasture or huge

loada- (Per-amt)

Woods (hr- need
lots)

Iapervicua Surface

FIGURE 14 Con' t.

Straight Ice
Straight Io!
Contoured
contoured a Terraced
Straight Ice
Contoured
contoured e Terraced
Straight Ice
33W

toured e hrraced
Poor
Sci-Ia].
Good
Contoured. Poor
Contoured. loreai
Contoured. Good
lcraal

Sparse/Lee tranacireticn
lcrlal
Deuce/ugh transpiration

loreal

Dirt
hr! Surface

Very Scarce/Lee
traaa oi ration

Sparse/Lo- transpiration

lcraal

Dean/Sigh trageciratioa

Very Dense/Ii
traneciraticn

 

G 885%. 33 3 38.: ‘5 «25338 388 33‘? $33 3

Soil Type
S c
06 91
00 S7
77 83
73 79
76 at
7‘ 02
71 79
75 83
72 Si
70 78
67: 86
6, g2
67 i
59 75
35 70
50 71
66 77
60 73
55 70
7t 82
02 87
St 90

£33883:
$3338

833 833 333 838 3

OD
U0

338338§3

$33 3

61

100 100 100 100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/
/

 

 

(C)

X. muff factor (in/hr]

 

taxation as dbwn

(f)

 

D
L.length of m (ft)

FIGURE 14 Con't.

 

 

E

(d) .5

x'

C1015 ‘0 1533334363 2 34568
m'rucea rare
g
t‘
(g) g
N
0001
C101 Qt) 1O 1O
CIcp

FIGURE l4 Con' t.

(3)

(4)

(5)

(6)

(7)

(8)

79

detailed runoff number is needed, review

the monthly precipitation probabilities as
presented in Table III of the Appendix,
establish the antecedent moisture condition
class as presented in Table IV of the Appendix
(refer to the outlined example of Chapter IV-
A-l), then, from the runoff number table (or
Table II), the antecedent moisture condition
Class and the conversion table (Table IV of

the Appendix), determine the runoff number N.
Assign a certain rainfall duration t.

From the curves for runoff factor X (or
Figures 8 to 10) determine the value of x
for the assigned duration, the given frequency

and the runoff number.

From the chart for climatic factor (or Figure

11) determine the value of Y.

From the chart for lag time (or Figure 12)
determine the value of tp for the given length

and slope of the stream.
Compute the ratio t/tp.

From the curve for factor Z (or Figure 13)
determine the value of Z for the computed t/tp

ratio.

80

(9) Compute the discharge by Equation 11 or

Q = AXYZ.
(10) Repeat the steps for other assigned durations.

(11) Plot the computed discharges against assigned
durations. The largest computed discharge is

the design discharge Qmax'

(12) If the stream is perennial, the base flow Qb
should be estimated and added to the discharge
determined in step 10. The design discharge

from Equation 12 is then Qd = Qmax + Qb'

The above procedure is illustrated by the following

example:

Example. Determine the effect of road placement
on the design discharge from the following data:

(a) Location: Interstate I-75
Roscommon County
Section 34, T 23 N, R 2 W
Wetland Site No. 5

(b) Land Use: Before

Acres

Meadow 22.96 26%
Dense Forest 10.57 12%
Dense Forest 54.62 62%

After
Acres
Meadow 18.80 21.33%
Meadow 5.78 6.56%

Dense Forest 9.90 11.23%
Dense Forest 51.16 58.04%
Road, Hard

Surface 2.48 2.81%

81

(c) Basin Area: 88.15 acres

(d) Channel Length: Before After
1400 feet 2200 feet

(e) Channel Slope: Before After
0.29% 0.23%

(f) Frequency: 25 years

(9) Base Flow: None

(h) Soil Type: Rubicon Group A
Saugatuck Group C
Roscommon Group C
Saugatuck Roscommon Complex Group C
Peat Marsh Group D

(i) Predicted Seasonal Rainfall Amount:

Located in the Northeast Lower
Climatic Section

Growing Season (March-October) 2.72 inches
therefore Class III

Dormant Season (November-February) 1.77 inches
therefore Class III

(j) Climatic Factor: Y = 0.79

(k) Before:
Hydrologic Class Class

 

 

Land Use Percentage Soil Group» II III Product
Meadow 26% D 78 90 23.4
Dense Forest 12% A 26 45 5.4
Dense Forest 62% C 62 79 49.0
Sum N = 77.8
say 78
After:

Hydrologic Class Class
Land Use Percentage Soil Group_ II III Product

Meadow 21.33% D 78 90 19.20
Meadow 6.56% A 30 50 3.28
A
C

 

 

Dense Forest 11.23% 26 45 5.05
Dense Forest 58.04% 62 79 45.85

82

After Con't.

 

 

Hydrologic Class Class
Land Use Percentage Soil Group_ II III Product
Road, Hard
Surface 2.81% A 74 88 2.47
Sum N = 75.85
say 76
(1) Before:
For L = 1400 feet and S = 0.29%, the lag time curves
give tp = 0.36 hour

Now assign t = 15 minutes. Since the design frequency
is 25 years and the runoff number is 78, the curve for

runoff factor X gives X = 0.5 in/hr.

Since t = 15 minutes (0.25 hours) and tp = 0.36 hour,
then t/tp = 0.69. The curve for peak reduction factor
Z gives Z = 0.55. Thus the discharge at t = 15 minutes

is Q = AXYZ, or Q

88.15 acres x 0.5 x 0.79 x 0.55

Q 19.15 cfs

The following Table is computed in like manner:

 

 

 

 

Duration t t hour t/t X Y Z Q
____._P___._.
10 minutes 0.167 0.464 0.25 0.79 0.37 6.44
15 minutes 0.250 0.694 0.50 0.79 0.55 19.15
20 minutes 0.333 0.925 0.56 0.79 0.68 26.52
30 minutes 0.500 1.389 0.62 0.79 0.81 34.97
40 minutes 0.667 1.853 0.62 0.79 0.95 41.02
50 minutes 0.833 2.313 0.60 0.79 1.00 41.78
60 minutes 1.000 2.778 0.58 0.79 1.00 40.39
2 hours 2.000 5.555 0.40 0.79 1.00 27.86
3 hours 3.000 8.333 0.32 0.79 1.00 22.82
4 hours 4.000 11.111 0.25 0.79 1.00 17.41

 

83

 

After:
For L = 2200 feet and S = 0.23%, then tp = 0.52 hour.
Duration t t hour t/t X Y Z Q
10 minutes 0.167 0.321 0.09 0.79 0.26 1.63
15 minutes 0.250 0.481 0.21 0.79 0.38 5.56
20 minutes 0.333 0.640 0.34 0.79 0.51 12.08
30 minutes 0.500 0.962 0.42 0.79 0.70 20.47
40 minutes 0.667 1.283 0.47 0.79 0.82 26.84
50 minutes 0.833 1.602 0.48 0.79 1.00 33.43
60 minutes 1.000 1.923 0.45 0.79 1.00 31.34
2 hours 2.000 3.846 0.35 0.79 1.00 24.37
3 hours 3.000 5.769 0.27 0.79 1.00 18.80
4 hours 4.000 7.692 0.21 0.79 1.00 14.62
(m) Refer to Figure 15.
(n) Design Discharge:
Before: Qd = 41.78 + 0 = 41.78 cfs
After: = 33.43 cfs

Qd = 33.43 + 0

 

From the analysis of this example it can be seen
that the design discharge is lowered after road placement.
This can be eXplained in light of the alteration of soil
type used as road backfill material and the increase in
effective channel length due to the creation of drainage
ditches. From step (1) of the example problem, the peak
discharge can be computed. The plotting of the design dis—
charge Q versus the duration t from step (1) results in the
maximum predicted 25 year hydrograph of Figure 15. The
area under this hydrograph represents the predicted volume

of direct runoff. It should be noted that the total volume

84

Predicted rum" hymgtaphs to: the given example

 

SC)

 

 

 

 

[megahent

 

 

 

 

 

 

 

 

(3.decnagpflncfis

20—
\’ .

 

 

4C1

 

 

 

 

 

 

 

 

O)
C) SID EKD £2 :3 A)
ranmes rxxrs

ckmafion t

 

 

FIGURE 15

85

of rainfall before and after road placement is theoreti-
cally the same. Physiographic changes due to road place-
ment may alter the volume of direct runoff from the
original basin condition as seen in the curves of Figure
15. This information could be useful in the design of
storm water retention areas such as drainage ditches and

holding basins.

F. Merits and Shortcomings
of the ProposedCMetHOd

 

 

There are several major merits that can be stated

for the prOposed method. They are as follows:

(1) The method has an analytical basis since it
is developed from sound hydrologic principles.
Therefore, the method is rational and the user,
if he wishes, can follow through the procedure
of the development and thus develop an insight

to the underlying hydroloqic principles.

(2) The method is based on the available data
which are adequate to the local conditions

under consideration.

(3) The criterion for the determination of a

design discharge is clearly defined.

86

(4) Although the result obtained by the method

(5)

(6)

(7)

may still require some professional supervision
or review for final adOption in a design, the
method will provide a unique solution or produce

close answers by different individuals.

The procedure of the method is simplified by a
design chart so that designers can use it with

greater ease.

The method can be readily improved by further
verification with the accumulation of rainfall
and runoff data and the field experience for
Michigan and the Mid-West area. Since the method
is based on analytical principles, the improve-
ment will not change the basic scheme, but will
involve only the modification of the curves and
charts which depend on the quantitative part of

the data.

This method, incorporating parameters such as
drainage area, precipitation intensity and
frequency, land use and cover, soil index and
channel slope, could be used as a first step in
developing a hydrologic impact assessment toward

the environmental effects of road placement.

87

Like most methods in scientific and engineering
works, the proposed method has shortcomings, particularly
in the area of rainfall intensity—duration-frequency
predictions. Such curves are probabilistic in nature.

They are based on previously recorded rainfall records

and computed for various return periods. Since the analysis
of Figure 4 showed good correlation between Lansing maximum
recorded point rainfall amounts and projected frequency
curves of Table I for a 25-50 year return period, this
condition might be offset if a 25 year maximum design
frequency is used.

The sensitivity of the isohyetal patterns presented
in Figure 5 to sampling variation is remarkably great.

These isohyetal patterns, therefore, are somewhat uncertain.
This limitation might be overcome by increasing the assumed
uniform distribution of peak discharge by about 6.0 percent.

From the areal conversion factor of Figure 5 for
the Central Lower climatological section, a 21 percent
deviation from the theoretical limit of l is noted. This
is explained in light of the averaging technique used to
establish a mean rainfall amount for each section. Greater
accuracy could be obtained through the selection of a base
station located within each climatological section. Also,

further accuracy might be gained if the size of the

88

climatological sections were reduced and more detailed
rainfall data became available. In this manner, frequency
curves would be more characteristic for the area under
study. The resulting areal conversion factors for the
various subdivisions in a climatological section might
therefore be in better agreement with the above mentioned
theoretical limit.

The major disadvantage in this analysis is the
fact that the design discharge thus determined is based on
a given frequency of rainfall instead of runoff. This and
other rainfall shortcomings mentioned previously are due
in part to the lack of suitable data of runoff frequency
for small drainage basins. Further study and analysis of
a large quantity of suitable runoff data may overcome this

problem in the future.

CHAPTER V

FUTURE STUDIES

The present investigation has outlined a practical
procedure for the prediction of runoff from small, ungaged
drainage basins in Michigan. It is primarily a modification
of the Rational Method, analyzing in detail various climatic
and physiographic factors contributing to storm runoff.

When suitable rainfall data becomes available, a further
study on rainfall variables should be undertaken. The lack
of hydrologic data for small drainage basins limited further
refinement of Chow's analysis. Future study might include
the analysis of combined effects of weather phenomenon such
as rain, wind, snow and frost. The improvement of rainfall
variables might include such items as the frequency range

of variation of the effect of antecedent moisture condition
upon runoff, the relationship between the durations of gross
rainfall and rainfall excess, and the areal and time distri-
butions of rainfall.

Because of the shortage of runoff data pertaining
to the small drainage basin environment, the design pro-
cedure is based on rainfall intensities for given return

89

'90

periods.. When more runoff data becomes available, there
will be the need to assess a design frequency on the
analysis of runoff data. Also, the recommended design
criterion would have to be revised on the basis of runoff
frequencies if such work was integrated into this analysis.
The family of curves for the runoff factor X would also
have to be modified accordingly, but the general concept
of the prOposed method would remain the same.

This procedure is based on both a deterministic
and probabilistic approach. Natural processes are neither
deterministic or probabilistic but are stochastic. Only
recently (Chow and Kareliotis, 1970) has mathematical model-
ling simulated the phenomenon of the stochastic hydrologic
system. Such modelling techniques involve a greater under-
standing of the theory of time series to stochastic hydro-
logic processes. Stochastic modelling techniques have not
as yet been well introduced in the practical design and
planning of hydrologic projects because such methods have
not been fully developed. In future studies, the application
of a stochastic modelling technique might foreseeably be the
answer to a true assessment of environmental impact on small,
ungaged drainage basins found in wooded and wetland areas

of Michigan.

APPENDIX

91

 

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92

 

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93

 

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94

 

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95

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96

TABLE II

HYDROLOGIC SOIL GROUPS

 

 

Southern Michigan

 

Group A--Soil Series

 

 

 

Abscota East Lake Landes Perrin
Ahmeek Eastport Lapeer Plainfield
Alcona Elmdale Leelanau Posen
Allouez Elo Longlois Randville
Alpena Emmert Lorenzo Rodman
Armada Emmet Marenisco Rousseau
Au Train Fox Marlette Rubicon
Baraga Gagetown McBride Sauble
Barker Genesee Metea Seward
Bark River Gogebic Miami Shelldrake
Berrien Graycalm Montcalm Sisson
Blue Lake Grayling Morley Sparta
Bohemian Guelph Munising Spinks
Boyer Hagener Nekoosa St. Clair
Bronson Hiawatha Nester Sumner
Broughton Hillsdale Nunica Sunfield
Cadmus Hodunk Oakville Superior
Casco Huron Oakley Thackery
Cedina Ionia Omega Trenary
Chatham Iron River Omena Tuscola
Chelsea Isabella Onaway Vilas
Coloma Johnswood Ontonagon Volinia
Constantine Kalamazoo Oshtemo Waiska
Deer Park Kalkaska Ottawa Wakefield
Dowagiac Kendallville Ottokee Wallace
Dresden Kent Owosso Warsaw
Dryden Keweenaw Parma Watton
Group B--Soil Series

Au Gres Detour Metamora Selfridge
Blount Eben Morocco Selkirk
Bowers Eel Moye Skanee
Brady Fabius Nappanee Sleeth
Brimley Firesteel Nestoria Teasdale
Capac Fulton Otisco Tedrow
Charlevoix Kawkawlin Perth Tula
Coldwater Kibbie Redridge Twining
Conover Locke Richter Wainola
Coral London Rimer Wasepi
Crosby Mackinac Roselms

Croswell Macomb Rudyard

Del Rey Matherton Sanilac

TABLE II Continued

 

Group B--Soil Series

 

 

 

Allendale Detour Missaukee Sigma
Arenac Eben Moye Skandia
Arvon Ensign Nestoria Skanee
AuGres Firesteel Nisula Spirit
Belding Ford River Otisco Sundell
Bowers Gladwin Palo Traunik
Brimley Glengary Pennock Tula
Capac Ingalls Perth Twining
Channing Iosco Redridge Tyre
Charlevoix Kawbawgam Richter Wainola
Cheneaux Kawkawlin Rudyard Watersmeet
Coral London Sanilac Wiggens
Croswell Mackinac Saverine Winegars
'Dafter McGregor Selkirk Winterfield
Group C--Soi1 Series
Angelica Epoufette Ogontz Satago
Bach Essexville Parkhill Saugatuck
Bergland Evart Pelkie Sims
Breckenridge Gay Pickford Tabico
Brevort Gormer. Pinconning Tappan
Bruce Hessel Pinora Thomas
Burleigh Hettinger Pleine Tolfree
Charity Kerston Rapid River Tonkey
Chassell Kinross Ronald Trout Lake
Deford Lacota Roscommon Wheatley
Diana Mangum Ruse Wisner
Edmore Munuscong Saganing Witbeck
Ensley Ogemaw Sand River

 

AL

Group-B--Soil Series

Northern and Southern Michigan

 

Carbondale
Carlisle
Cohoetah
Glendora
Greenwood
Houghton
Kerston
Loxley
Lupton

Rifle
Saranac
Sloan
Spalding

Tahquamenon

Wallkill
Wastenaw

over sands,

Adrian
Dawson
Markey
Tawas

over loams ,

Cathro
Linwood
Palms

over clays,
Ogden
Willette

over marl,
Edwards
Rollin

over limestone,
Chippeny

 

Source: ”Taxonomic Classification Chart for Michigan Soils."
Soil Science Department, Michigan State University.

TABLE II Continued

 

Group C--Soil Series

 

 

 

 

Adolph Deford Mangum Tappan
Algansee Diana Maumee Thomas
Angelica Dillon Mussey Tobico
Bach Edmore Newton Toledo
Barry Ensley Ogemaw Tolfree
Bergland Gay Parkhill Tonkey
Berville Gilford Paulding Waldenburg
Bono Granby Pewamo Warners
Brookston Hessel Pickford Wauseon
Bruce Hettinger Pleine Westland
Ceresco Hoytville Roscommon Wisner
Charity Jeddo Saugatuck Witbeck
Colwood Kinross Sebewa
Corunna Kokomo Shoals
Danby Lenawee Sims

Northern Michigan
Group A-—Soi1 Series
Ahmeek Dryburg Karlin Onaway
Alberta Duel Kent Onota
Alcona . East Lake Keweenaw Ontonagon
Allouez Eastport Kiva Pence
Alpena Echo Leelanau Posen
Amasa Elo Longrie Randville
Au Train Emmert Mancelona Rousseau
Baraga Emmet Manistee Rubicon
Barker Ewen Marenisco Sauble
Bark River Froberg Marlette Shelldrake
Bentley Gagetown McBride Stambaugh
Blue Lake Gilchrist Mecosta St. Ignace
Bohemian Gogebic Melita Summerville
Brule Goodman Menominee Superior
Champion Graycalm Montcalm Traverse
Chatham Grayling Moran Trenary
Chocolay Guelph Munising Ubly
Coventry Hiawatha Negaunee Vilas
Crivitz Huron Nester Waiska
Crystal Falls Iron River Newaygo Wakefield
Deer Park Isabella Nunica Wallace
Deerton Johnswood Ocqueoc Watton
Dighton Kalkaska Omena Yalmer

99

 

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mommaacoo aaa mamas

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sommm>mo um3oq Hmnudoo smmmsomz

101

 

 

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102

 

 

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103

 

 

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104

 

 

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105

 

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106

 

 

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107

 

 

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108

 

 

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BIBLIOGRAPHY

BI BLIOGRAPY

Anderson, H. S. "Flood Frequencies and Sedimentation
From Forest Watersheds," Trans. Am. Geophys. Union,
Vol. 30, No. 4, August, 1949, pp. 567-586.

Barger, G. L., Shaw, R. H. and Dale, R. F. "Gamma Distri-
bution Parameters from 2 and 3-Weed Precipitation
Totals in the North Central Region of the United
States," A ricultural and Home Economics Experiment
Station, Iowa State University, 1959, 183 pp.

Bent, Paul C. "Influence of Surface Glacial Deposits on
Streamflow Characteristics," Open-file report,
U.S. Geological Survey, Water Resources Division,
Lansing, Michigan, 1971.

Brater, E. F. "The Unit Hydrograph Principle Applied to
Small Watersheds," Transactions,_American Societ
of Civil Engineers, Vol. 16g: 1940, pp.1153-1178.

Chow, V. T., as Chairman, and others. Report of the
Committee on Runoff, 1955-1956, Transactions!
American Geophys. Union, Vol. 38, No. 3, June, 1957,
p. 379.

 

Chow, V. T. "Hydrologic Determination of Waterway Areas
for the Design of Drainage Structures in Small
Drainage Basins," University of Illinois Engineering
Experiment Station Bulletin No. 462, 1962.

 

Chow, V. T., editor-in-chief. Handbook of Applied Hydrology,
Section 14. McGraw-HilI Book Company, 1961?

Chow, V. T., Kareliotis, S. J. "Analysis of Stochastic
Hydrologic Systems," Water Resources Research,
Vol. 6, No. 6, December, 1970.

Christenson, D. R.; Lucas, R. E.; Doll E. C. "Fertilizer
Recommendations for Michigan," Extension Bulletin
E-550. Cooperative Extension Service, Agricultural
Experiment Station, Michigan State University,
November, 1972.

119

120

"Climate of Michigan by Stations," Michigan Department of
Agriculture, Michigan Weather Service, December,
1971.

"Design Discharge for Small Basins," California Division
of Highway§y_Highway Design Manual, 1972.

 

"Estimating Peak Runoff Rates from Ungaged Small Rural
Watersheds," National COOperative Highway Research
Program Report, Highway Research Board, 1972.

Fair, Geyer, Okun. Elements of Water Supply and Waste-
water Disposal, 2nd editiOn. JOhn Wiley & Sons,
1958' pp. 53-590

Field Manual of Soil Engineerig%, 4th edition. Michigan
State Highway Departmen , Lansing, Michigan,
July, 1960.

Friedman, D. G. and Janes, B. E. "Estimation of Rainfall
Probabilities," University of Connecticut, Agri-
cultural Experiment Station Bulletin 332, 1957,

22 pp.

Hickok, R. B.; Keppel, R. V.; Rafferty, B. R. "Hydrograph
Synthesis for Small Aridland Watersheds," A ri-
cultural Engineering, Vol. 40, No. 10, Octo er,

Huff, F. A.; Neill, J. C. "Frequency Relations for Storm
Rainfall in Illinois," Illinois State Water Survey
Bulletin No. 46, 1959.

"Hydrodynamic Modeling of Two-Dimensional Watershed Flow,"
Journal of the Hydraulics Division, November, 1973.

Izzard, Carl F. "Peak Discharges for Highway Drainage
Design," Transactions A.S.C.E., Paper 2709, 1954.

"Maximum Recorded United States Point Rainfall for 5
Minutes to 24 Hours at 207 First Order Stations,"
U.S. Weather Bureau Technical Paper No. 2, re-
vised 1963.

Mitchell, W. D. "Unit Hydrographs in Illinois," U.S.
Geological Survey and Illinois Division of Water-
ways, 948.

121

"Monthly Precipitation Probabilities by Climatic Divisions,"
U.S. Department of Agriculture and U.S. Department
of Commerce, Miscellaneous Publication No. 1160,
November, 1969.

Morgan, R., and Hullinghors, D. W. Unit Hydrographs for
Gaged and Ungaged Watersheds (unpublished manuscript)
U.S. Engineers Office, Binghamton, New York, July,
1939.

National Engineering Handbook, Section 4, Supplement A,
Hydrology. U.S. Soil Conservation Service, 1957,
3rd. edition, 1963.

 

"Normal Monthly Number of Days With Precipitation of 0.5,
1.0, 2.0, and 4.0 Inches or More in the Conterminous

United States," U.S. Weather Bureau Technical Paper
No. 57, 1966.

Pickels, George W. Draina e and Flood-Control Engineering,
1st edition, New York and London: McGraw-Hill
Book Company, Inc., 1925.

"Rainfall Frequency Atlas of the United States for Durations
from 30 Minutes to 24 Hours and Return Periods From
1 to 100 Years," U.S. Weather Bureau Technical Paper
No. 40, 1963.

"Rainfall Intensities for Local Drainage Design in the
United States," U.S. Weather Bureau Technical Paper
No. 24, 1954.

"Rainfall Intensity-Duration-Frequency Curves," U.S. Weather
Bureau Technical Paper No. 25, 1955.

Schneider, I. F.; Johnson, R. W.; Whiteside, E. P. "Tenta-
tive Placements of Michigan Soil Series in the New
Soil Classification System," Soil Science Department,
Michigan State University, March, 1967.

"Selected Low, Normal, High Monthly Precipitation Probabili-
ties by Climatic Divisions for Michigan," Agri-
cultural Engineering Department, Cooperative Extension
Service, Michigan State University, May, 1967.

Sherman, L. K. "Stream Flow From Rainfall by the Unit-
Graph Method," Engineering News-Record, Vol. 108,
April, 1932, pp. 01-505.

 

122

 

Snyder, F. F. "Synthetic Unit-Graphs," Transactionsy
American Geophysical Union, Vol.'l9, 1938, pp. 447-
454.

 

Stoeckler, Joseph H. "Drainage Along Swamp Forest Roads--
Lessons From Northern EurOpe," Journal of Forestry,
Vol. 63, No. 10, October, 1965, pp. 772-77 .

 

Talbot, A. N. "The Determination of Waterway for Bridges
and Culverts," Selected Papers of the Civil
Engineers' Club, Technograph No. 2, University of
Illinois, 1887—1888, pp. 14-22.

"Taxonomic Classification Chart for Michigan Soils," Soil
Science Department, Michigan State University,
East Lansing, Michigan.

Thom, H. C. S. "A Note on the Gamma Distribution,"
Statistical Laboratory, Iowa State College, 1947
(manuscript).

"A Frequency Distribution for Precipitation,"
Abstract in Bulletin Amerigan Meteorological
Society, Vol. 32, No. 10, December, 1951.

"A Note on the Gamma Distribution," Monthl
Weather Review, Vol. 86, No. 4, April, 1958,
pp. 117-122.

. "Direct and Inverse Tables of the Gamma Distri—
bution," Technical Re ort No. 2. Environmental
Data SerVice, ESSA, ApriI, I968, pp. 1—30.

"Water Resources Data for Michigan," U.S. Department of

the Interior, Geological Survey, Part I, Surface
Water Records, 1972.

Wiitala, S. W. "Some ASpects of the Effect of Urban and
Suburban Development Upon Runoff," Open-file
report, U.S. Geological Survey, Water Resources
Division, Lansing, Michigan, 1961.

Whiteside, E. P.; Schneider, I. F.; Cook, R. L. "Soils
of Michigan," Extension Bulletin E-63g. Co-
operative Extension ServIEe, Agricultural Experi-
ment Station, Michigan State University, 1968.

123

Wisler, C. O., and Brater, E. F. H drolo , 2nd edition.
John Wiley & Sons, Inc., 19E9, pp. 28-30.

Woods, Kenneth B. Highway Engineerin Handbook, lst edition.
McGraw-Hill Book’Company, 196 .

Yarnell, David L. "Rainfall Intensity-Frequency Data,"
U.S. Department of Agriculture, Miscellaneous
Publication 204, 1935.

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