EPA-670/2-75-046
                                          May 1975
RAINFALL-RUNOFF RELATIONS ON URBAN AND RURAL AREAS
                        By

                 Ernest F. Brater
                 James D. Sherrill
              University of Michigan
            Ann Arbor, Michigan  48104
          Grant No. R-800941 (11040 DRS)
            Program Element No. 1BB034
                  Project Officer

                 David J. Cesareo
  Storm and Combined Sewer Section (Edison, N.J.)
   Advanced Waste Treatment Research Laboratory
      National Environmental Research Center
              Cincinnati, Ohio  45268
      NATIONAL ENVIRONMENTAL RESEARCH CENTER
        OFFICE OF RESEARCH AND DEVELOPMENT
       U.S. ENVIRONMENTAL PROTECTION AGENCY
              CINCINNATI, OHIO  45268

-------
               REVIEW NOTICE
The National Environmental Research Center—
Cincinnati has reviewed this report and approved
its publication.  Approval does not signify that
the contents necessarily reflect the views and
policies of the U.S. Environmental Protection
Agency, nor does mention of trade names or com-
mercial products constitute endorsement or recom-
mendation for use.
                       ii

-------
                           FOREWORD


Man and his environment must be protected from the adverse effects
of pesticides, radiation, noise and other forms of pollution, and
the unwise management of solid waste.  Efforts to protect the
environment require a focus that recognizes the interplay between
the components of our physical environment—air, water, and land.
The National Environmental Research Centers provide this multi-
disciplinary focus through programs engaged in

     o  studies on the effects of environmental contaminants on
        man and the biosphere, and

     o  a search for ways to prevent contamination and to recycle
        valuable resources.

As part of these activities, the study described here investigated
the factors which control the relationship between storm rainfall,
snow melt, and the resulting storm runoff, including the effects
of urbanization on the runoff process.
                                        A. ¥.  Breidenbach, Ph.D.
                                        Director
                                        National Environmental
                                        Research Center,  Cincinnati
                                iii

-------
                                 ABSTRACT
 A procedure was developed for estimating the frequency of storm runoff
 of various magnitudes from rainfall and/or snowmelt on small drainage
 basins in various stages of urbanization.   The study was based pri-
 marily on the analysis of storm runoff events on real basins varying
 in size from 0.02 to 734 sq mi.   The method is based on applying unit
 hydrographs to precipitations of various frequencies .after deducting
 infiltration and retention.   A concurrent  study with an analytical
 drainage basin model provided additional understanding of the effects
 of some parameters.   The unit hydrograph-infiltration capacity con-
 cept was selected as the most accurate practical method for predict-
 ing storm runoff.   It was found  that the form of the unit hydrograph
 could be related to  drainage basin size and degree  of urbanization  as
 measured by population density.   Other characteristics  of the drainage
 basin are much less  important.   The form of the unit hydrograph  stays
 relatively constant  for various  durations  and magnitudes  of input as
 long as  the duration of input is  smaller than a critical  time which
 can also be related  to the size  and population  density  of the basin.
 As  the population  increased  from rural to highly urbanized peak  dis-
 charges  for the same runoff  became as  much  as ten times greater.  In-
 filtration capacity was  found to vary  seasonally.  The prediction of
 flood frequency by this  procedure  is fully  operable  for Southeastern
 Michigan.   For application to other  areas some hydrograph  analysis
 must be  made.

 This  report was  submitted in  fulfillment of Project Number R-80ti941
 (formerly  11040  DRS), by The University of ffichigan, under the
 (partial)  sponsorship of the Environmental Protection Agency.  Work
was completed  as of July 1973.

-------
                                CONTENTS
Review Notice




Foreword




Abstract                           •     '       .




List of Figures




List of Tables




Acknowledgments




Sections




I     Conclusions




II    Recommendations




III   Introduction




IV    The State-of-the-Art




V     Collecting Data




VI    Hydrograph Analysis




VII   Infiltration Capacity




VIII  Unit Hydrographs




IX    Mathematical Model




X     Frequency Studies




XI    Time-Intensity Rainfall Patterns




XII   Predicting Flood Magnitudes and Frequencies




XIII  References
Page




 ii




iii




 iv




 vi




viii




 ix








 1




 4




 6




 7




 10




 19




 32




 38




 69




 71




 76




 85




 94
                                   v

-------
                            LIST OF FIGURES


No.                        .   .  .                    .                Page

 1    Atypical hyetographs and hydrographs.                           11

 2    Complex hyetograph and hydrograph.                             20

 3    Relation between slope and discharge on ground
      water depletion curve.                               .22

 h    Relation between slope and discharge on ground
      water depletion curve.                                   '•      23

 5    Surface runoff vs. precipitation.                              26

 6    Surface runoff vs. precipitation.                              27

 7    Surface runoff vs. precipitation.                              28

 8    Seasonal variation of infiltration capacity.                   33

 9    Five unit hydrographs from the same basin.               :      39

10    Reproduction of a complex hydrograph.                    :      ^1

11    Definition sketch.                                             h2

12    Unit hydrograph peaks vs.,area (original data).                k8

13    Unit hydrograph peaks vs. area with uniform slopes.            k-9

ih    Unit hydrograph peaks vs. population density.                  50

15    Significant period of rise vs. area.                           51

l6    Significant period of rise vs. area with uniform density.      52
                                   vi

-------
                      LIST OF FIGURES' (Concluded)
No.                  ,
17    Significant period of rise -vs. population density.

18    Period of rise vs. area.

19    Period of rise vs. area with uniform slope.

20  ,  Period of rise vs. population density.

21    Unit hydrograph peak vs. area-design curves.

22    Significant period of rise  vs. area-design  curves.

2J    Period of rise vs. area-design curves.

2k    Width at 75 percent of  peak vs.  area-design curves.

25    Width at 50 percent of  peak vs.  area-design curves.

26    Width at 25 percent of  peak vs.  area-design curves.

27    Width of base vs.  area-design curves.

28    The effect  of snowmelt  on frequency.

29    The effect  of length  of record  on frequency.

 JO    Final seasonal frequency curves.

 31    Precipitatidn-rduration expressed as percent
       of 2k-hr rainfall.

 32    Intensity-duration expressed as percent of 2k-br rainfall.

 33    Typical seasonal hyetographs expressed as
       percent of 2^-hr rainfall,,

 31).    Area-depth curves.

 35    Synthesized  and observed unit hydrographs  for Red Run.

 36    Predicted and observed flood frequencies for Red Run.
Page

 53
 55

 56

 62

 63

 6k

 65

 66

 67

 68

 73

 7^

 75


 77

 78


  82

  8k

  87

  92
                                    Vll

-------
                                  TABLES
 No.

  1

  2
  5

  6


  7

  8


  9

10


11
 Flood Runoff Data


 Computations of Surface Runoff and Unit Hydrograph
 Ordinates for Rain of Spril 1, 1959, on Plum Brook

 Computation of Infiltration Capacity

 Unit Hydrograph Parameters

 Legend for Figures 12-20

 Equations and Statistical Parameters for Lines
 on Figures 12,  13,  15,  16, 18, and 19

 Maximum Rainfall for Various Durations

• Hyetograph Ordinates in Percent of 2^-Hour Rainfall
 per Hour


 Twenty-Four Hour Rains  of Various Frequencies

 Computation of  Volume of Surface  Runoff for a
 50-Year Winter  Rain

 Computation of  Composite  Hydrograph for 50-Year
Winter Rain
Page

 12



 36

 37
 57

 79


 83

 86


89


91
                                 viii

-------
                            ACKNOWLEDGMENTS
The financial support of the Environmental Protection Agency is grate-
fully acknowledged.  The assistance of Messrs. Robert M. Buckley and
David J.. Cesareo> Project Officers, has been most appreciated.

The project was initiated in ~L96k by means of a small grant from the
University of Michigan Graduate School.  In 1965 a grant was obtained
from the National Institutes of Health.  This grant was continued to
this time under the sponsorship of FWQA and EPA.  During the period
1966-1971 additional support was provided by the Michigan Department of
State Highways and the U.S. Bureau of Public Roads.

Many graduate students worked on the project. •Their services made the
project possible.  Particular acknowledgment is made to Dr. Suresh K.
Sangal who not only worked on the project but contributed greatly to
the research through his Ph.D. dissertation.

-------

-------
                              SECTION I

                             CONCLUSIONS
The unit hydrograph-infiltration capacity method has been developed by
this research program to the point where it provides very satisfactory
estimates of peak discharge and if needed entire flood hydrographs, of
various frequencies for drainage basins of all sizes and all degrees
•of urbanization.  The procedure consists of forming runoff hydrographs•
of various frequencies by applying the unit hydrograph for that basin
size and population density to the precipitation excess.  The,precipi-
tation excess is precipitation plus snowmelt of a selected frequency
minus retention and infiltration on the permeable portions of basins
and minus retention on the impermeable portions.  The methods de-
scribed in this report provide the most accurate method of determining
required capacities of storm sewers, culverts, bridges and other flood
carrying structures known to the writers.

The specific  conclusions are summarized below:

1. The unit hydrograph peaks as well as their time  characteristics
such as their periods of rise and widths  at various fractions of the
peak discharge  can be correlated with watershed  areas  and population
density to provide statistically  significant relations which enable
hydrologists  to estimate the runoff characteristics of ungaged  areas.
These  relationships were derived  from the analysis  of  hundreds  of
flood  hydrographs  from 53  drainage basins from  five states.  The areas
of these basins vary  from  0.02  to ?4j sq  mi and the population  den-
 sities cover  a  range  from  less  than 100 to more  than 14,000 persons/
 sq mi.

 2.  The effect  of urbanization  is primarily  in  the  production  of flood
 hydrographs  of  much shorter duration  and  higher peaks.  For  example as
 the population  density changes  from 100 to 13,000 persons/sq mi the
 peak rate of surface runoff for a given total surface runoff becomes
 about 10 times  greater while the time parameters decrease to about one
 tenth of the values for rural areas.   For the same  population  increases

-------
the increase in total runoff due to increased impermeable area is only
about 10 percent in Southeastern Michigan.

3.  Tflien the 16 basins located in Southeastern Michigan* were studied
separately the correlations showed lower unit hydrograph peaks for low
population densities than the corresponding relation for all 53:ba-
sins.  It is suspected that the differences are related to the nature
of the drainage networks.  The use of local results improved the accu-
racy in Southeastern Michigan for low population basins over the use
of the general curves.

4.  Eleven basins located in Texast exhibited a tendency toward higher
peaks for given areas and populations then the trends of the other 53
basins which included many Texas basins at other locations.  Further
research will be required to determine the cause of this anamolous
behavior.  However, based on the behavior of the other basins it ap-
pears likely- that the drainage systems in these 11 basins have been
developed in advance of the population growth.

5.  Based on the analysis of about 200 flood hydrographs produced by
rains equal to or greater than >1 in., the average summer and .winter
infiltration capacities in Southeastern Michigan are O.kd and 0.10 in./
hr, respectively.

6.  The effect of the impermeable area was taken care of by developing
the concept of hydrologically significant impermeable area which was
found to vary linearly with population density from about 1 percent for
1000 persons/sq mi to about 10 percent for 7500 persons/sq mi.

7.  The maximum value of retention on the permeable portion of the
basins is about 0.2 in.  The average in summer is approximately! 0.15
in. and in winter 0.10 in.  An estimated retention of 0.05 in. on the
impermeable areas gave satisfactory results.

8.  An analysis of the frequency of one day' occurrences of winter
rain plus snowmelt gave values about 2 percent higher than the values
for the same frequency determined in the conventional manner from pre-
cipitation records, where snowfall is included along with rain.

9«  Typical large rainstorms in Southeastern Michigan have a nearly
symetrical time distribution with the maximum hour near the center of
*These 16 basins were part of the 53 basins which formed the basis
for the general relations.
tThese 11 basins were not among the 53 used for developing the gen-
eral relations.

-------
the rain storm.  In winter the maximum hour contains about 24 percent
of the rain and in summer the maximum hour usually provides about 55
percent of the total storm rainfall.  Information was obtained per-
mitting the formation of typical time-intensity precipitation patterns
from 2h-hr rains of any frequency.                •

-------
                               SECTION II
                            EECOMMEMDATIOHS
 The evidence provided by this research shows that storm runoff from
 most drainage basins behaves in a consistant manner when basin size
 and population density are taken into account.  However, there were a
 number of basins which did not follow this pattern.  It is believed
 that an investigation of these anomolies would be very productive in
 improving our knowledge of the runoff process.  The results to this
 time indicate that most differences could be explained if more were
 known about the density and efficiency of the drainage systems.  It
 is suspected that some drainage systems may be developed in advance
 of population increases whereas in other locations the drainage sys-
 tem may lag behind population increases.   Related to this same problem
 would be land use.   For example,  highly industrialized areas may not
 show population densities  which are consistant with their storm sewer
 system.   Perhaps in the future  s©me measures of drainage efficiency
 could be used in place of  population density as a measure of urbani-
 zation.

 Although there  is no substitute for field investigations  and the  use
 of real  rainfall and runoff records  to  find these  answers,  it is  be-
 lieved that  an  extension of the mathematical model to  more  complex
 drainage  networks would be of nearly equal value  in establishing  a
 better knowledge  of  this process.

 Research  should be continued to determine  more  accurately the  relation
 between point rainfall and average rainfall on  areas of various sizes
 for the same frequencies.  The form  of precipitation time-intensity
 pattern should also  be studied at other locations as should  the effect
 of including snowmelt with precipitation in frequency studies.  ;

 In general it is  strongly recommended that  hydrograph analysis be
 carried on systematically to determine the  various parameters such as
 infiltration capacities, retentions, hydrologically significant im-
permeable areas, and unit hydrograph characteristics for basins in

-------
various locations.  Population densities and'drainage patterns should'
also be determined.  These data will be needed to provide accurate de-
sign procedures even if in the future other methods are found to be
more satisfactory than the one suggested here.

-------
                              SECTION III

                              INTRODUCTION
 The objective of this project was  to gain a better understanding of
 the factors  which control the relationship between rainfall or  snow-
 melt and the resulting storm.runoff and to determine  the  effect of
 urbanization on this  runoff process.   The benefits would  include the
 prevention of flood damage by means of improved  design  of storm sewers
 and. waterways and would provide  the data needed  for the improved de-
 sign and operation of facilities for control of  pollution due to storm
 water and/or combined sewage.  A basic approach  was adopted which
 would provide a better understanding of the  surface runoff  process in
 rural and urban areas  while  concurrently examining and testing known
 methods  of predicting flood  peaks.   The  development of any  practical
 procedure  for predicting peak discharges  obviously needed to be  based
 on known surface runoff  events.  Therefore,  the  largest portion  of
 the  effort was  gathering and analyzing storm runoff events from' small
 drainage basins at  various stages of urbanization.  Data were gathered
 and analyzed  from 69 basins  located in five states and varying in size
 from 0.02  to  kj$ sq mi.  In  addition.to the testing and development of
practical  flood prediction procedures a simple mathematical model was
developed  in which runoff could be computed'for various rainfall inputs.
The model served to check and extend information derived from the study
of actual rainfall and runoff data.

-------
                              SECTION IV

                         THE STATE-OF-THE-ART
An intensive study of procedures and literature dealing with runoff
processes was carried out at the beginning of the research.  In Addi-
tion, to studying the literature, the Principal Investigator visxted
centers and researchers working on this phase of hydrology in the U.S.
and Europe.  The review of the subject included a reevaluation of
methods which had been used in the past as well as those in current
usage.  In a general way, these procedures can be separated into the
following categories; statistical methods, procedures utilizing em-
pirical equations or curves, storage-routing procedures and unit hydro-
graph procedures.  The later two categories refer to the way in which
the surface runoff hydrograph is formed;  the total volume  of runoff
being usually determined  by the use  of the infiltration capacity con-
cept.

Statistical methods  utilize flood records on a particular  basin.
Sometimes  they  are  applied regionally by assuming similar  rainfall,
snowmelt  and drainage basin characteristics.   These methods  are  usu-
ally limited  in accuracy because  of lack of sufficient  records  to  make
a significant  statistical analysis  as compared with methods  using  rain-
fall as  input  in which frequency can be  determined  from the  much longer
precipitation records.   They  lack the flexibility to determine the ef-
 fect of urbanization or other watershed changes.   The various  empirical
 methods also require a fairly long period of records to determine  the
 necessary constants in particular locations  and again they do not lend
 themselves to modification for changing conditions.

 Most of the attention was given to methods which combined the deter-
 mination of flood volumes by deducting .infiltration from precipitation
 and forming flood hydrographs by storage routing or unit hydrographs.
 These procedures provide models which attempt to represent the -actual
 runpff process.

 Peak flood discharges are controlled by  two independent processes.

-------
  One process determines the time rate of input to the system and the
  other establishes the response of the system which is the flood hydro-
  graph.  The system input is rainfall plus snowmelt minus infiltration
  and other minor retentions.  This process is dependent on the frequency
  and nature of the rain and snowmelt as well as the variations of the
  infiltration capacity of the soil.  Since the concept of infiltration
  capacity was first introduced1 a number of investigators have studied
  the variations of infiltration capacity with time during a rain2~5 as
  well as its seasonal variation.6-8  Its variation from place to place
  has also been noted.9,10  ^ factors which control infiitrati6n capa_
  city are quite well understood but quantitative  values  for any region
  must be obtained from the analysis of rainfall and surface runoff
  events  on drainage basins within the region.   For example,  previous
  work on this project  has  provided more  than 200  values  of infiltra-
  tion capacity  for Southeastern Michigan from which average  seasonal
  values  have been determined.5

  The  second process which  deals with  the response  of.the system and
  controls the shape of the flood hydrograph  is a function  of the input
  and  of the  physical characteristics  of the drainage basin.  Knowledge
  gained from this aspect of the runoff process is not limited to re-
  gional conditions but can be expected to be applicable to all loca-
  tions.  The important input parameters are intensity, duration and
 spacial distribution  of rain and snowmelt.  The physical characteris-
 tics are those of the flow system.  The flow system consists of a
 series of surfaces which receive the input and contribute to the
 stream system.   Throughout the system, flow is spatially variable and
 unsteady.  For simplified basins the flow can first be computed over
 the land surfaces1!-^ and then through the channels.15,16  combining
 the two phases  provides  a useful mathematical model.17,18  For prac_
 tical flood predictions  a simpler approach is essential.   Various
 methods  of routing input through storage have been proposed 19-21   The
 storage-discharge relation is  usually derived from the recession side
 or  a hydrograph.   In some  cases  the Input  is  transferred  to the outlet
 by  a convolution process after  estimating the time  of travel from  vari-
 ous segments of the drainage area.  All  of these procedures  have been
 explored  in this  research  program.  The  unit  hydrograph procedure has
 shown the best  results when considering simplicity  as well as sensi-
 tivity to urbanization and other physical parameters.

 The unit hydrograph idea was first ProPosed22,25 f   large watershed
 but it is also a useful tool for small watersheds.^  Many investi-
 gators have studied the effect of drainage basin characteristics on
unit hydrographs.25-32  previous research has shown'that drainage
basin size is one of the most important factors in influencing the

-------
shape of the unit hydrograph.?  This project has provided much more
evidence that the area is one of the most important factors0;*-(>n>
and has produced quantitative evidence that population density is  a
very important parameter.

-------
                                SECTION V

                             COLLECTING DATA
  It was  clearly recognized from the beginning of this research that any
  effort  that would provide a better understanding of surface runoff pro-
  cesses  and eventually lead to  a dependable method of predicting runoff
  from rainfall  would require the analysis of many rainfall and/or snow-
  melt and runoff events from many different.sizes and types of drainage
  basins.                                                             &

  A great deal of effort was devoted to searching for available runoff
  and rainfall records.   It became obvious early in the work that the
  effect of urbanization would be one of the most important factors in
  the relations dealing with hydrograph shape.   Many runoff records from
 urbanized areas are unpublished and must be obtained by copying from
 the original hydrographs where they are stored.   Many were not pub-
 lished in sufficient detail and therefore'it was  necessary to work from
 the original gage charts or tapes  in the U.S.G.S.  offices to  obtain the
 records.  £1 the case  of Red Run,  a highly urbanized basin in South-
 eastern Michigan,  it was also necessary to  combine  the  runoff from the
 gaging station with the  discharge  diverted  into the  sewer system.   An-
 other  part of the analysis consisted of the determination of  the
 weighted hourly precipitation for  each event and the  computation  of
 snowmelt when  it occurred.  Each event was  then plotted as  shown  in
 Figure 1.   It  is estimated that the  collection of data  along with the
 hydrograph analysis mentioned above required about 70 percent of the
 total effort.

 In Table 1  is presented a  list  of the watersheds that were studied
 The location, the  U.S.G.S. number, area, population density and the
 number of rain gages are also shown in the table. '  The number of drain-
 age basins studied was 69, varying in size from 0. 02 to 73^ sq mi with
54 basins having areas of  less  than 20 sq mi.  Population densities
vary from less than 100 to more than 36,000 persons/sq mi.  The num-
ber of hydrographs analyzed for each basin is also shown.  The total
number of hydrographs analyzed was 1620.
                                  10

-------
Q-
0.50




0.25




   0
       480
                                          PLL//W BROOK
          Figure 1.
                 2345



                      APRIL, 1959



              Typical hyetographs  and hydrographs.
                               11

-------
ID


CO
  >  <;  o  ra     FL,
       p>
                                                           CQ
                                                                            ON
                                                                                     OJ
                                                                                     t--
                                                                   8?
                                                                            NA
o
vo
VD
H
 I
                                                          o3

                                                                   0)
                                                                   0)
                                                                  •ri
                                                                  pq
                                                                       §
$t  O
                                                                               •H

                                                                               s
irmingh
            a
                    O
                    0\
                    KN
                    H
                                                                                               CO
                                                                                               oo
          IPv      CO


          ir\      oo




          -*      'ON
                                                                                              CO
                  H
                  VO
                  VO
                                                                           PM
                                                                           CVJ
                  a
                  
-------


"ON


"co

^

„ — .,
MD^
EH
P
O ' — -

rt ' ^
p
0
o


^ 2
CD
2
a
-p
o
o
1 — 1 ^-^

H
1



x — *
OJ
«*_*
x —
i —
v_
(3 w
O £l
•H O
-p CQ
o3 in
H eu
£ -rl


d a1
K M
tin
CQ
&
>H


CQ

*3
£
£4
•H
1
a
1



EH
CQ
"S
CJ
5-1



£^
<)H ^_j CO
° § g1
o ' — ^ m
^i ^~^ ^j

•^
.
CO
. 6
CO
[35




t-i
w
S
fl3
§•
to


*
o



x1 — s
fl
o
Drainage basil
fname and locati
s
X
1


O 0
rH in
t- MD
OJ rH

o o
CO -3-

s s
to, O
rH OJ
10 O
rH OJ

-* rH
H OJ






MD H
m oj



0 0
in c5
MD -d"
MD "M3
r~{ r~H
~3" -^"


• 	 .
C
^
Rouge Rr, Detroit, MI
Clinton Rr/ nr Fraser,
MD C-


o
o
o
rH

O
10,

1
OJ
OJ
OJ
OJ

rH
to






m



0
in
in
rH
i
_r}~





P
i
«\
g
.1
rH
O
CO


rH
rH

CO
in

: g
OJ

OJ


in







OJ
to



Ln
f
-3"





Clemens-, MI
McBride Drain nr
ON


o
MD

MD
CO

g
__,.

j-


m







OJ



in
OJ
MD
H
1
-^i~

H
S
^
•
0)
Macomb,, MI
Tupper Brook, Ray Cent
s


rS'^
OJ

in o
ON to
H

O O
MD OJ

MD OJ


ON in







O t-1
co _=r



0 O
OJ KA
MD J-
MD MD
rH rH
1 1
-^f -d"

y
^
f-r-)
H
Q)
•M •»
£< O
O O
CQ 0
0
O O
02 3
> 133
rH OJ
rH H


o
MD
in

O
"rH

g
K-N

to


in







KN



O
OJ
in
MD
H
-3~

•N
bO
3
o . '
d
H
1
o
-p
•H
P
0)
to


ON
OJ
H

m
rH

1 .
in .

m


ON







0



0
to
MD
MD
H
1
-^i"

•N
S
-p

a
Q)
W)
I
CL) H
!•*
s


O OJ
0 rH
m H
t>- rH

m co
MD C—
io, H

S g.
ON 10

ON KN


-4- CO
rH






H t-
ON to.



0
rH
H.
MD
rH
1
-^~


H
s
fl
PH ^H
M
fH CD
oi O
'H
^j i — 1
Q) 03
in MD
' H H


O
OJ
MD
ON
OJ
0


PR
PM
OJ

OJ


OJ







rH









ct3
cu
Heights, MI
Northwood Drainage Ar
Baltimore, MD
r7
13

-------
 0)
1
o
0)
"a




*•"•
OC
>*_
*••— •
t>
N^-


*~+,
VO

1 § a -gl
1 >H O a|
M 03 to gj1} VO §
§• rt $H ^ *
p< -a PI
•-f
I -3- O
5 8 a * * °
/ uj .3 I • •
Id c
<5 a
O W) £
• Q) *J"J^ ^J
t^ S\ "f"
EH a
3 S/*
* rrtl
« hfllEH
1£ •»
ll
£ fH
3
-3-


s

"aT
Jjfl
£
CQ
. 0
CQ &
•
'
Drainage basin
(name and location)
'~sl •
H o
*H &
r
i

PI-J ^q
f\ i p^|
H ^H

H H

-d- in

OJ H




Gray Haven, Baltimore, MD
Oakdale, Chicago, ILL
CO ON
H H
IS




CO O
IPv \f\
"
CQ
O O
 >
IfN H

ITv -*

VO -3-

ON VO
OJ rH

O IT\
KN O
1 1
KN CO
Boneyard Crk, ILL
Stoney Brook St Ditch,
Houston, T
O ,H
OJ OJ
VO
^



ON
OJ
^
CQ
^C
>
OJ

ir\

OJ

n

m
06
f
ob
Bintliff Ditch, Bissonet
St. , Houston, T
OJ
OJ
OJ
OJ



VO
OJ
KN
CQ
tfT
>
OJ

OJ

^

m
H

m
o
CO
•p
CQ
a
a
3
i*
ll
t?9
ga
m

OJ
H
VO
J-



j-
H

•rf*
>
j-

VO

v.

ON
H

C-
1
ob
CQ EH
2~ -P
p ra
II
If
-P O
g ON

OJ
ON O
CO N~N
CO iS



0 ^
H OJ
CQ CQ
S^ ^~^
> ^
OJ OJ

m j-

VD t—

81 Ed

m o
^ ^
is t-
0 0
oo ob
Hunting Bayou, Calvalcade
St. , Houston, T
Bering Ditch, Woodway
Drive, Houston, T

OJ OJ
VO
m
H



VO
00
-=?
CQ
Q ,
g
KN

VO

VO

H

O
O
CO
Berry Crk, Galveston Rd.
Houston, T -

OJ
VO
VO



OJ
•
CQ
Q
£
KN

m

VO

3

VO

CO
Hunting Bayou, Falls St. ,
Houston, T

c°
                                               14

-------


^
'

OO
•-'


^x_


<; ^0
S!- ~
Q
l=i
O '~N
B ^
per
«
o
§
• «
V
pi
5
4s
8
0 ^
>""^' ' K^
H "-'
H
,Q
cS
EH




"o



5
£{ 03 ,
O £H *S
•H O S
•P ra Cjl
I ! s
!*-
Q) pj S
^ 'H S"
 ^
>H

to
• 5 o3 ^
si &S 1
^!

CQ
C5 O

.



x — x
fl
*i
cS ?
•° 0
0) "^
SP|
ii


c


CO
OJ
H
H
H


<
>>
J-'

xt



\D




ON



ir\
•
\o

C--
cb


rrt
_W
r~j
o
43
S EH
^
g g"
•> 43
pi ra
0 2
^lS
pq
>» r
?H 43
3 m
pq
01


i^ H m o\ j- ir\ o
j- 01 J- 01 VO CO MD
3- O OJ UA VO .
7-1 H 01
uR oi UA o 01 tr\ t>-
rH rH 


CQ CQ CQ CQ CQ
> > > > > > >
VO 01 1TN 01 01 rov 01

SO ' -* VO 01 01 J- 01



VD t- VO VO 1T\ ' ITN A£>




Cr OH H UA 01 O
OJ OJ OJ H H H H



O, O ITN O O O ' CO
MD ON OJ OJ H CT\ t>-
lf\ _-^- ^f -^}- t1 — l^N |£"N
o o o o o o o
CO OO CO CO CO CO CO

EH
»\ o3 "^ •
•N ^Sn+3 lEHTJ 'O
r-f K rn T* i t, nj*^ , pfc fV^
1^ Q 1 *> flj CQ »N ^
o H^ «^ jj , «\ CQ J~
J3CQ SMp! -HEH ^ M _^C
J^ S d ° r tt ^ ^5 . g g g ^
O^H-'s 5D
>jp! j» i-^ i— i -^^
?, * • & -R .^ R- '^.


t— K>
o j-
OO Ol
[>- IPI
01 o
iA c^-



CQ CQ

KN ^

^f^ ir\



\0 vo




01 tr\
H H


0 0
• •
OJ H
^T 1^\
CO OO





f— J
h EH .
^ "§ iT ^
! CQ ,3
' ?T 5 ' S
! l>5 * ft
*' 3^ js!
rH CQ rH PH
c6 O
|^rj (^
t~ OO
^f>\ NA
15

-------
 o\
 CO
VO
m
I
1
o
K\
      d  w
      o  d -H
      •H  o a
      •P  W
      » Tn £>
      EH
           W
   -
                  o

                  CO
             s
                    VO
            K\

            P
            o

            CO
                    0)
                    Is
                    pq^

                                             •m
                                                                 oj
 CO







 OJ





 Cvl









VO
       s
                                 VO
 CO

 I



 lf\



vo
             1
                                                                        OJ
                          g  g  s
                                                                vo.. ir\
                                             H
                                             rH
                                                              VO
K>

^
o

CO
                          -p
                          CO
ir\
 •'
H

^
o

CO
CO
 *•
t-

£
o

CO
                   m
                   t-
                   ir\
                   H

                   CO
            &
            UA
            rH


            CO
                                                          m
                                                         CO
                                                                ooo
 I   I   I
CO  CO  CO
                                                                EH - EH  (D
                          pqw  ow
                                         s
                                            :$
                                  16

-------
jH tQ t
o c "3
•H O »
S 1 ft M
» - CD
O R o.
PH -rl '"
„, -H
^•^ ra S3
"co *" 3

"^ M
CM c!
0 g> 0
t — CD "Cn -p

rt W| PH

< s -«3 n
|j " P3 bfl| EH
fe % «o
fei fQ
° s~*. tQ ^

O
0
S w
• 2-" 9 M •"!
"•rf" *-' • 5 ° ^
CD g CHH ,§ s:

1 b
•H '^
+>
S
8 ^ - « .
	 to, C5 C
1 ' CQ
CD i-^
«
EH
(2)
Drainage basin
aame and location)
i~f
"H" c

t--


.-*'
VO




^
CM

OJ
H


CO




"oi





o
OJ
t-
0
1
CO
CD
rH
Rock Crk, Greenvil
. , Dallas , T
CD CD
-P >;
•H  > PS1 > > O O
OJ OJ H , OJ 10, OJ OJ

OJ CM H OJ to, CM OJ
,


rH rH H OJ OJ OJ H



t-- to, ITN ON vo co vo



-"


-3- OJ ITv ITS O .KA .
lA CO UA CO VO ITN
CO CO CO CO CO CO
? ? ' ? ? ? ^
CO CO C3D CO CO OO •
« - « s '• „ I
a , s^ 1 * IM
•g 5 -g cT EH r « o£fl
IH"SR-PM -p S EH •- 1=1 COI-H
OfnfH^CQ a PM
Is 13- ' ^ O •" it! »\ «\ »\ .ft
rQ^ISPf-PfclO ^S^J • -^2
•g-ss.pg'S'-aEH-fi-es s s ^
EHOPH^&'cJ ,2_ EH
for-HO CQ . S^ rJ>S H ixi^nrT
M «H ptj ^ CO fQ *tH "H I-M CQ pSn
^^CQ .'TH-P CQ-poJ ^^-P
O^W^CQ^ PPPn CQPn putE-t 0>5^
IOO r OOO PnO
CDUAP^OJ >5 pc| ^^ NN ^J^^^IS
PntO, COf-i SH ij^&S,
O CD Co^/SH^ CD-xgH^O-H-p
Co'&'.pjg'.rH.p O +3-P ,O COCUO
Of3 43j5SO >s|34 H^CQ I^IS OCQFc)
t>a -H CD PH -H PH l>j
CQ i-^ CQ ft J ft CQ
OJ to, J- IT\ VO C— OO
ITv IP, lf\ lf\ TV T\ UA
17

-------

2



CC

^?

Is
n
1 s
8
2
K
^ 3"
tJ **— • '
1
a
0
o
"*"""'* *»/^
K*
H —
Q)
H
*§
^
"oT
3
1 la
•P 03 a
Si !•
o a S
fM -rl P
g g S
!' !
« -sj
Itt!
q S «
1 SP
« W) EH
0 M
CQ p;
^ S
ca

• » O *Zj
O ^""^ £>>
^
.
CQ
. •
cii o
CQ &
£)

_
Drainage basin
(name and location
6

8
iH


0.
H

^
CVJ
CVJ

H



1TN



CVJ
•
IfN
CO
o
CO

-p^
CQ »\
S5
si
-§1
to *>
0^:
Q) IfN
O
CQ
ON
ITN.

O
CVJ
H
i—l-


CVJ
H
CVJ

^
-d-

CVJ



vo



0
•
c**-
t**-
H
CO


OMos Crk, Dresden Dr. ,
San Antonio, T
o
VO

o
r-H
CVJ
KN


VO
CVJ
KN
CQ
S
CVJ
CVJ

CVJ



ON



O
•
fT*\
CO
^
OO

•\
Alazan Crk, St. Cloud St
San Antonio, T
H
vo

vo
IfN


VO
CVJ

CQ
1
H
H

CVJ



CO



ON
#
vo
CO
c-
H
l
CO

CQ
!M
-'











W.W. Trunk Sewer,
Louisville, KY
VD
VD

o
IfN
^^f-
H

^
CVJ

g
IfN

LfN



VD











W. Outfall Sewer,
Louisville, KY
t-
vo

0
IfN
ON


•5>
vo

1
ON
: ON

IfN



ON











S. Outfall Sewer,
Louisville, KY
oo
VD

I
vo


CVJ
LfN
IS-

1
VD

IfN



VO







S
»\
0)
•H
t>
S.W. Outfall Sewer, Louis
ON
vo
18

-------
                               SECTION VI
                          HYDROGRAPH ANALYSIS
Hydrograph analysis on perennial streams for.the purpose of determining
the surface runoff, infiltration capacity, the duration of precipitation
excess, and the form of the surface runoff hydrograph requires the sep-
aration of surface runoff from ground water discharge or base flow.-  The
method conventionally used was based to some extent on judgment.  Fur-
thermore, it has been commbn practice to neglect initial retention (the
portion of the rain which is intercepted by vegetation or the ground
surface and never becomes infiltration or surface runoff) and the ef-
fect of runoff from impervious areas on the computations 'of infiltra-
tion capacity.  Therefore, one of the initial goals of this project was
to develop objective methods of carrying out this operation including the
effect of retention and impermeable area.

SEPARATION OF GROUND WATER DISCHARGE FROM SURFACE RUNOFF

The first step in hydrograph analysis is to select lines such as b]_b2 in
Figures 1 and 2, to separate ground water discharge from surface runoff.
Various logical^subjective selections of this line could be made.  Usually
the range of reasonable locations where this line could be established  is
not great enough to create substantial differences in the computed values
of either the, infiltration capacity or the unit hydrograph ordinates.
However, in the interest  of better uniformity the following method was
derived.  There is little difficulty  in  selecting the point bL  where  sur-
face runoff begins, but locating the  point b2 where surface runoff ends
is more difficult.  Consequently,  it  was  decided to make use  of the ground
water  depletion curve  to  determine the location of such points.  The
ground water depletion curve  is the hydrograph  of river discharge during
a time of no precipitation  and it depicts a rate of decrease in discharge
that is much  smaller than that of  the recession side of  a  flood hydrograph
such as  sb2  in Figures 1  and  2.   If point b2  correctly  locates  the' end of
surface  runoff, then a ground water depletion  curve for  the basin  should
 closely  fit  the hydrograph to the  right  of b2 but  should depart from  the
hydrograph to the  left of b2.   This  is  illustrated by the ground water
                                     19

-------
o
to.
10
OJ
                                                       si
                                                    to
                                                    CD
                                                        o
                                                       -p
                                                       H


                                                       I
                                                       O
                                                       OJ

                                                       a;
                             NI 30yvHosia
 '03 dd
                           20

-------
depletion curves gdc in Figures 1 and 2.

The practice of deriving ground water depletion curves by graphically
fitting together portions of the curve permits the exercise of consider-
able judgment.  Consequently, a more objective procedure was sought.
The method selected is based on the idea that insofar as there exists a
consistent relationship between ground water discharge and storage on the
drainage basin, there* must also exist a consistent relationship between
discharge (Q,)> which is the ordinate of a point on the depletion curve,
and its slope  (AQ/AT), and that the equation for this relationship can
be solved to obtain the equation for the ground water depletion curve.
Values of Q and AQ/AT were read from only those portions of the hydro-
graphs preceded by a period of at least 3 days during which there was
neither rain nor snowmelt.  Examples, of plotted values of AQ/AT versus Q
are shown in Figures J. and k.  In all river basins for which this deri-
vation has been made, the relationship between AQ/AT and Q appeared to
be linear.  For example,.the numerical value of the linear correlation
coefficient (r) for the group  of points in Figure k is 0.93, which is
much greater than the value of 0.7 required to indicate that there is
only one chance in 1000 that linearity is a fortuitous occurrence.  The
equations relating AQ/AT to Q were derived by the method of least squares.
The equation for Plum Brook  (Figure k) is
          dQ/dT  =  0.102 + 0.12UQ

 Solution  of this differential  equation yields

                            -  1 PkT1
          Q   =   (Q  +  0.82)e     ^   -  0.82
(1)
(2)
 in which  Qo  is  the value  of Q selected for  T  =  0.  This  is  the  equation
 of the  ground water  depletion curve.   A segment of this  curve is plotted
 as line gdc  in  Figure  1.    •                         .•           ,

 A point of interest  regarding the  relation  between AQ/AT and Q  is  that
 none of the  straight lines  such as those in Figures  3 and k pass through
 the  0,0 coordinate.  There  seems to be no physical reason why they should.
 On the  other hand, the data are probably not  sufficiently accurate to give
 any  significance to  the location of the lower end points of these  lines.

 Having  eliminated most of• the subjectivity  from selecting point b2,  it
 remains to decide on the form of the line connecting b-j_  and b2.  Logical
 deduction would suggest that  the ground water discharge  would continue to
 recede  for a time beyond b-j_ and then rise in  an s curve  to  point b2.  How-
 ever, until this process is better defined quantitatively,  it was  decided
 to use  a  straight line connecting  points b]_ and b2.  The straight  line has
                                     21 .

-------
     1.0
     0.8
     0.6
o
Of
     0.4
     0.2
       0
        0
1	1	
 Rouge at
  Farmington
                                         I/
          4           6
            Q  INCFS
8
          Figure 3.  Relation between slope and .discharge
          on ground water depletion curve.
10
                              22

-------
    2.4
    2.0
>-

-------
 the advantage of providing a consistent method of making this separation
 and eliminating any imaginative approach,  even though' it is based on
 logic.
 Once the line bjbg is established,  the surface runoff may be computed by
 finding the area between this line  and the hydrographs.   The example shown
 in Figure 1 is complicated by the occurrence of a second rain before the
 surface runoff from the preceding one has ended.   In such cases,  a  reces- .
 sion line such as xy is drawn having the same form as the recession sbg.
 After the initial retention and the runoff from the impermeable area are
 taken into consideration,  the average value of infiltration  capacity (pav)
 is obtained by trial,  assuming that the precipitation excess (Pe) is equal
 to the surface runoff.
 RETENTION

 Before overland flow begins,  or during its  early stages,  a  small  portion
 of the initial rainfall is  stored and permanently abstracted from surface
 runoff by interception and  surface or depression storage.   The  intercep-
 tion^evaporates,  and the depression storage either evaporates or  infil-
 trates after  the end of rainfall.   The interception is  abstracted from
 the beginning of rainfall,  whereas depression  storage accumulates only
 after  the rain intensity exceeds the infiltration capacity.  However, for
 the purpose of flood prediction it is convenient to combine the two ab-
 stractions.   In this discussion,  the total  of  these .two abstractions will
 be referred to as retention (R).   There is  evidence1)- that interception
 continues to  accumulate until the rainfall  has reached  2  or more  inches,
 and it seems  logical to assume  that depression storage  may  also increase
 toward some top limit as the  rain continues at high intensities.   There-
 fore,  small rains are not likely to fulfill the  maximum possible  abstrac-
 tions.  The values of retention that have been estimatedQin the past
 presumably refer  to  the upper limit.   Tholin and Keif er  have suggested
 values of retention  of 1/16 in.  for pavements  and lA in. for grass land.
 For small paved areas,  values reported by Vies sman35 range from O.Ol)- to
 0.10 in.   Values  of  this order  of magnitude could be considered as in-
 consequential when dealing  with large floods.  However, for  smaller stream
 rises,  variations in the selected magnitudes of  this factor produce sig-
 nificant  differences  in the computed values  of infiltration capacity.
 For example,  for  the hydrographs  shown  in Figure  1, values  of fav  com-
 puted  first by neglecting this  abstraction  and then by  assuming .a value
 of  0.2 in. have the  ratio of  about 3  to 2,  respectively, for the .first
 stream rise and k to  1 for  the  second stream rise.

Although  quantitative  values  of depression  storage  cannot be determined
 directly  from the analysis  of individual hydrographs, it is possible to
                                    24

-------
gain a reasonably good idea, of the maximum values of retention by ar-
ranging the data for total precipitation and surface runoff in the manner
shown in Figures 5, 6, and 7.  In these figures Line A is drawn near the
left side to represent the condition of 100 percent surface runoff which
could only occur if there were no infiltration  (f = 0) and no retention
(R = 0).  If the vertical and horizontal coordinates were drawn to the  •
same scale this would be a ^-degree line.  Any points falling near Line
A represent stream rises which must have occurred when the infiltration
capacity on the permeable portion of the basin was very low.*

Another line, Line B, is then drawn through the points nearest to Line A
and above and to the left of the main body of points.  The magnitude of
the retention can be estimated by assuming that points falling on Line B
have zero infiltration and that all of the precipitation becomes either
surface runoff or retention.  Therefore the retention is the vertical
distance between Lines A and B.  It will be seen that for Plum -Brook and
Big Beaver Creek (Figures 5 and,6) nearly all of the points fall below
and to the right of the lines representing an R of 0.2 in., thus indi-
cating that the probable maximum value of R is slightly more than 0.2 in.
For Red Run (Figure 7) more points fall above the 0.2-in. line than in the
cases of Plum Brook or Big Beaver Creek.  However, it- may be noted that
most of these points are designated in Figure 7 by black circles which
represent winter rains which occurred within 15 hr after antecedent pre-
cipitation.  Therefore, the portion of the retention caused by intercep-
tion on vegetation was very low and there is also a good possibility that
there was residual retention from the previous rain.  The four summer
storms falling between Line A and" B in Figure 7, designated by triangles,
were very small rainstorms (P < 0.2 in.) for which the retention capacity
may not have been filled.  It may be inferred, therefore, that the value
of R on Red Run for summer rains greater than 0.2 in.' and not preceded by
a rain within 15 hr is approximately 0.2 in., but that it may be smaller
for winter rains.

Although the maximum value of R appears to be about 0.2 in., it is clear
that the average value during large rains is less.  The determination of
typical average values to be used in flood prediction was carried out
in the analysis of the runoff hydrographs by assuming several values of
R and computing the time of beginning of precipitation excess, recognizing
 *The  significance  of  the points  pn these  graphs which  lie toward the
 lower right,  near  the line  labelled  "SRO  from A±  only,"  is discussed  in a
 later section of this report.  The points in the  central portion of the
 graph represent  stream rises  during  which there occurred.both  surface
 runoff from and  infiltration  into the  permeable portion  of the basin.
                                    25

-------
CO
UJ

O
O
ID

UJ
O
s
oc
ID
CO
                                     Plum Brook
                         oNov.thru Apr. No Antec. Precip.
                                    „   Precip. within
                                          15 hrs.
                          May thru Oct.
                                        No Antec. Precip.
                         SRO from A; only, (A-,/A = 0.1)
      0
       .5        1.0       1.5       2.0

        STORM PRECIPITATION, INCHES

Figure 5.  Surface  runoff vs. precipitation.
                            26

-------
CO
LLJ
1C
O
UJ
O

-------
CO
LU
n:
o
uu
U_l   n
o  .3
CO
                                     Nov. thru April
                                      No Antec.  Precip. —
                                     Nov. thru April
                                      Precip. within 15hrs
                                     May thru October
                                      Precip. within 15hrs
                                     May thru October
                                      No Antec.  Precip.
               .5        1.0       1.5       2.0

                 STORM PRECIPITATION,  INCHES

         Figure 7-  Surface runoff vs. precipitation.
                             28

-------
that the initial precipitation excess would become retention.  For each
storm the value was selected which produced the best time relation be-
tween the beginning of precipitation excess and the beginning of surface
runoff.  For all rain storms over 1 in. in magnitude the values of R for
the permeable portion of the basins varied from zero to 0.2 in. and the
average value for summer was 0.15 in. and for winter 0.09 in.  The latter
value was rounded to 0.10 in. for practical application to flood predic-
tion. • For the impermeable portion of the basins a value of 0.05 in. gave
satisfactory results.

A value of retention of 0.15 in. determined as described above represents the
weighted average of the retention on the impermeable portion of the basin
(R^) and the retention on the permeable portion of the basin (Rp)-  If a
value is assumed for Ri? then the value of Rp can be computed from- the
following equation:               *
          RA  =
R A
 P P
                                                                     (3)
in which A is the total area of the basin, and Ai and Ap are the areas of
the  impermeable and permeable portions, respectively.  The solution will
be illustrated for Red Run by assuming Rj_ = 0.05 in. and making use of
the  fact (demonstrated later) that ^ is 10 percent  of the total area.
Then
          0. 15A =  0.05A.
                          + R A
                             p p
 and
           0.15 ?=  0.05A./A + R A  /A
                        i      p p
Since A.J/A = 0.1 and A /A = 0-9,
 le is presented to illustrate t
                                     is  found to be  0. 16 in.   This  exam-
 ple  is  presented to  illustrate  that  even  for a basin  in which 10 percent
 of the  area  is  impermeable,  there  is only a small difference  between R
 and  Rp,  probably less  than the  uncertainty in the estimated value  of R.
 For  less urbanized areas  such as Plum Brook and Big Beaver Creek,  this
 difference would,  of course,  be even smaller.
 IMPERMEABLE AREAS
                                  .36
 Shortly after the time when Hortori'  recognized the now obvious  fact  that
 surface runoff is produced when precipitation intensity ex-ceeds the  infil-
 tration capacity of the soil,  studies  made by the senior author on storm
 runoff from small watersheds  seemed to indicate a flaw in this  concept. 2^"
 Typical flood hydrographs were being observed on watersheds  having such
 permeable soils that surface  runoff was assumed to be impossible.  It was
                                     29

-------
only after  surveys of the  stream  channel area were made that it became
clear that  the precipitation falling on the streams themselves and the
immediately adjacent banks produced unit hydrographs exactly similar to
those from  adjacent, less permeable areas.  This discovery indicated that
a thorough  study of the characteristics of infiltration capacity must
take into consideration the nearly 100 percent runoff from water surfaces
and other impervious areas.  Similar findings have since been reported
for other drainage basins.-^'

Hie extent  of the effectively impervious area is of particular interest
in this research, because  it appears obvious that this is one of the im-
portant factors whereby urbanization influences storm runoff.  It is rec-
ognized that the effectively impervious portion of the basin may be larger
during wet  seasons than during dry periods.  This might be caused by in-
creased area of water surfaces on the basin but also by portions of the
permeable portions of the basin that might become nearly impervious after
prolonged rainfall or snowmelt.   It was decided to approach the problem
by attempting to determine what portion of ,the drainage basin acted as an
impermeable area under all conditions.  This area, expressed as the per-
centage of the total area, has been called the 'hydrologically significant
impermeable area, ' (HSIA.).  (HSIA = 100 (A^A), where Ai is the imperme-
able area and A is the total area of the drainage basin).  It was reasoned
that this area could be computed from hydrographs produced during periods
of very high infiltration capacity when the entire hydrograph of surface
runoff can be attributed to the rainfall minus retention (P - R.^) on the
HSIA..
Although such hydrographs can be found from a search of the records, they
can also be isolated readily by plotting the surface runoff against pre-
cipitation for all stream rises of record, as shown in Figures 5, 6, and
7.  The hydrographs, which are of the type mentioned above, provide the
points on the lower right side of Figures 5, 6, and 7, near the line
labeled  'SRO from A$_ only. '  The slope of this line (Ai/A) multiplied by
100 gives the value of the HSIA..  The two drainage basins for which, such
data are plotted in Figures 5 and 6 are relatively unurbanized when com-
pared with highly populated areas.  They contain farm land, some scat-
tered housing along main roads, and several industrial parks.  The popu-
lation density of Plum Brook is about 700/sq. mi and that of Big Beaver
Creek approximately 800/sq. mi.  (Population density data were compiled by
the Detroit Metropolitan Area Regional Planning Commission.)  It may be
seen that the lines drawn for an HSIA of 1.0 percent of the basin area
and for an assumed value. of retention on the impermeable area (R^) of
0.05 in. form envelopes that include nearly all of : the lowest points.
(if RJ were assumed to be zero, the line for the same hydrologically
significant area would have the same slope but would pass through the
                                    30

-------
origin. )  A similar plotting for Red Run, shown in Figure J, reveals
an HSIA area of about 10 percent of the drainage basin.   The popula-
tion density of the Red Run basin is approximately 7500.   Thus, it is
indicated that, for these particular basins, the HSIA increases in
about!the same way as the population density.  As additional rainfall
and runoff data are analyzed for other drainage basins,  the relation of
the HSIA to other measures of the degree of urbanization, as well as to
natural physical characteristics of the drainage basin, will be examined.

The small amount.of HSIA in the Plum Brook and Big Beaver watersheds makes
little difference in the computed values of fav when there is a substan-
tial contribution of surface runoff from the pervious portions of a drain-
age basin.  However, even such small amounts of HSIA as 1.0 percent can,
if ignored, lead to the computation of meaningless values of fav for those
summer or autumn floods produced'entirely by runoff from impervious areas.
The importance of taking into consideration the runoff from even a small
percentage of impervious areas is illustrated by the stream rise for the
River Rouge at Birmingham shown in Figure 2.  It may be .seen that the sur-
face runoff started on October 6 at OJOO, whereas the rainfall excess did
not begin until 0600.  This is illogical, unless the runoff from the HSIA
is included as a separate item.  If the HSIA. were 1.8 percent, which is typi-
cal for that population density, then the rainfall occurring before 0600
would have produced a runoff from the impermeable area of the amount shown
by the hatched area in Figure 2.  The beginning of surface runoff from
precipitation excess on the permeable area would then be at 0700, or an
hour later than the beginning of rainfall excess, and the entire hydro-
graph becomes a reasonable output from the precipitation pattern.

Values of HSIA were determined for 12 basins in Southeastern Michigan.
TOien plotted against population density the trend of the points was
closely represented by the following equation

          HSIA  =  l-38Pd

where  Pfl  is the population density  in thousands  of persons  per square
mile and  HSIA  is  in percent  of  total area.         •
                                    31

-------
                              SECTION VII
                         niFILTRATION CAPACITY
 The prediction of the peak flow resulting from a,specific input from
 rainfall and/or snowmelt requires knowledge of the portion of the
 total input which will be abstracted as infiltration and surface re-
 tention.  Of these abstractions, infiltration is by far the most impor-
 tant.  Unlike the shapes of the unit hydrographs which depend primarily
 on the areas of the drainage basins and on other physical character-
 istics of the basins which are not related to a particular geographical
 region,  the* infiltration capacity(f) depends to a large extent on the
 soil in the particular location where flood predictions are to be made.
 Therefore one of the principle parameters sought from hydrograph ^analy-
 sis is the infiltration capacity and its seasonal variation.

 The determination of infiltration capacity for a runoff event may be
 described with reference to Figure  1.  The amount of surface  runoff
 which is the hatched area for each stream rise is computed first, then
 the average infiltration capacity during a storm is  computed  by trial
 by finding the value which makes the precipitation excess,  Pe on the
 rain intensity diagram,  eq.ua! to the surface  runoff,  after taking into
 consideration retention and runoff  from impermeable  portions  of the
 basin.   Sketching this  value of infiltration  capacity on the  hyeto-
 graph as shown in Figure 1,  then establishes  the  duration of  precipi-
 tation excess  which becomes  an important parameter in the formation
 of the surface runoff hydrograph.   Infiltration capacity decreases
 during rain storms as illustrated by the two  rains in Figure  1 and  it
 also varies  seasonally  as  shown in  Figure  8.

 Because  of the variation of  f with  time  during a  rain the  actual value
 during a particular rain depends  on whether there has  been recent ante-
cedent precipitation.  The  scatter of  points in Figure  8  is largely  due
 to this  factor.   The only  method of determining the average infiltra-
 tion capacity  of  a particular drainage basin  is by means  of hydrograph
 analysis.  This type  of analysis yields the average value  of infiltra-
 tion capacity  ( fay) for  each  stream rise.  The variation  of f with
                                   32

-------
       >
       CO
                                              -P
                                              •H
                                              t)
                                               o
                                               o
                                              •H
                                              •8
                                               !4.
                                              s
                                              •H
                                               o
                                               •H
                                               -P
                                               03
                                               •H
                                               o
                                               CQ
                                               03
                                               0
                                               CO
                                              CO
LCi
                           LPk
            'AllOVdVONOIlViiniJNI
                      33

-------
 time can be obtained from a closely spaced series of stream rises as
 shown by an example in the next section on "Unit Hydrographs." ,

 Each of the more than 200 points in Figure 8 was determined by hydro-
 graph analysis on the 16 basins in Southeastern Michigan.  These
 basins have quite similar soils and therefore the infiltration capacity
 did not vary greatly from one basin to. another.  The average value for
 summer which included June, July, August, and September was 0.^ in./hr
 and the average for winter, which included the other eight months, was
 0.10 in./hr.  The values should not be used in other regions.   Enough
 hydrographs must be analyzed in any region to establish the order of
 magnitude of infiltration capacity.  The computed value of infiltra-
 tion capacity depends to some extent on whether retention and runoff
 from impermeable areas are included in the computations.  The  latter
 factor becomes particularly important for highly urbanized areas where
 the impermeable area becomes large.  In the analysis,  the total sur-
 face runoff (SRO) is taken to be equal to the surface  runoff from im-
 permeable portion of a basin (SROj_) -plus that from the permeable portion
 (SROp).   These values  are defined by the following equations
                 =  p -
'(5)
           SRO   =  P -  F -  R
              P              P
where  P is  the  average  precipitation,  R.  is  the  retention on the  im-
permeable area, F  is  the  total infiltration  and  Rp is  the retention on
the permeable area.   A  detailed description  of the determination  of the
impermeable area and  the  retention has  been  presented  in the  section  on
Hydrograph  Analysis.

The computations for  determining the infiltration  capacity for the
first  stream rise  in  Figure 1  are  presented  here to illustrate the
procedure.

     Area of Drainage Basin, A = 22.9 sq mi
     Impermeable area, Aj_ = .02A                               '.
     Retention on  impermeable  area, R^  = 0.05  in.
     Retention on  permeable area, Rp =  0.15  in.
     Weighted average precipitation, P  = 1.35  in.

The first step is the computation of the surface runoff.  This requires
that a line separating surface runoff from gfoundwater discharge be drawn

-------
such as b^bg in Figure 1.  The procedure used to do this was explained
earlier in this report in the section on hydrograph analysis.  In the
example shown in Figure 1, it was also necessary to draw the line xy
to separate the hydrograph produced by the first rain from one resul-
ting from the second rain.  This is done by sketching a line having
the same form as sb2 which represents the same release of storage as
would have occurred at the end of the first hydrograph.  Ordinates from
the first hydrograph were tabulated for 2-hr intervals as shown in col-
umns 1 and 2, Table 2.  The surface runoff in inches on the basin is
then computed from the summation of column 2 by multiplying by the num-
ber of second in 2 hr dividing by the area of the basin and multiplying
by 12 as shown as follows.
          SRO  =
                         x 2 x 3^00
                  22.9 x 5280 x 5280
                           x 12  =  .^68 in.
The surface runoff from the  impermeable area (SROj_)  is computed using
Eg.. (5) and then converting  to  inches  on the entire  basin by multi-
plying by the ratio of the impermeable area to  the total area as follows
SRO   =  —
                                                                   (7)
                 = ' .02  (1.35  -  .05)   =  -026 in-,  on A
 The  surface  runoff from the  permeable  area (SROp)  is  then the  difference
 between the  total surface  runoff and SROi and is  (.1)68 -  .026)  = .¥)2.
 expressed in inches  on the total basin.   This value is converted to
 inches  on the permeable portion of the basin as  follows:
SRO   =  j-x(M2)  =
          P
                                                =  .1451 in.  on A
 The total precipitation excess on the permeable area (Pep)  is then ob-
 tained by adding the retention (Rp)  as follows:
              •  =  SRO  + R
            ep        P    P
                =  .14-51 + .15  =  .601 in. on A
                                               P
                                                                    (8)

-------
 Table 2.   COMPUTATIONS OF SURFACE RUNOFF AND UNIT HYDROGRAFH
      ORDIMTES FOR RAIN OF APRIL 1,  1959, ON PLUM BROOK
                 (Drainage Area = 22.9 sq mi)
Number of
2-hour
Intervals
1
2
3
4
5
6

7
8
9
10
11
12
15
14
15
16
17
18
19
20
21
22
23
2k
25
26
27
28

Average rate of
surface runoff,
cfs
28
116
230
294
308
320
(324)
320
308
280
240
190
148
120
96
80
66
56
48
4o
36
32
26
22
18
14
10
7
3
3456
aTypical computation of unit hydrograph
28 cfs


Unit hydrograph.,
cfs/sq. mi. /in.
2.6
10.8
21.5
27.4
28.8 .
29.9
(30.3) (peak)
29.9
28.8
26.1
22.4
17.7
13.8 :
13.8
9-0
7.5
6.2
5-2
4.5
3.7
3.4
3.0
2.4
2.1
1.7 '
1.3
0.9
0.7
0.3

ordinate :
in
22.9 SOL mi x 0.468 in.
                             36

-------
The infiltration capacity of the permeable area is now computed by
trial.  The final trial computations are shown in Table 3 in which
hourly precipitation is given in column 2, the assumed infiltration
capacity in column 3 and the precipitation excess in column 4.  The
total of column 4 multiplied by 60/60 to convert from inches per hour
to inches is 0.600 which agrees with the value of Pep computed above.
Therefore the infiltration capacity of the permeable portion of the
basin is 0.114 in./hr.  This procedure applies to simple hydrographs
which can readily be assigned to a particular, rain.  For more complex
storms the method involves an application of the unit hydrograph and
will be described later.
            Table  J.  COMPUTATION  OF INFILTRATION CAPACITY
Hours
17 •
18
19
20
21
22
23
24
25
26
2?
28
Precipitation
intensity,
±n./nr.
.00
.07
.26
.16
.18
.32
.25
.03
.ok
.01
.03
.00
Infiltration
capacity,
in./hr.
.114
.111*.
.114
,.114
.114
.114
.114
.114
.114
.114
.UL4
.114
Precipitation
excess,
in . /hr .
-
' -
0.146
0.046
0.066
o. 206
0. 136
-
-
-
-
-
                                                        0.600
                                 37

-------
                               SECTION VIII

                            UNIT HYDROGRAPHS
By far the major portion  of  the  research  effort was deyoted to  studying
unit hydrograph characteristics.   This procedure  in its  simplest form is
based  on the  assumption that the important characteristics of a surface
runoff hydrograph for  any basin  are  essentially constant  if the duration
of 'precipitation excess is less  than some critical value, that  the ordi-
nates  of this hydrograph  vary  linearly with the magnitude of rainfall
excess and that various complex  rainfall  or snowmelt  inputs can be trans-
formed into a complete hydrograph by a linear additive convolution
process.

The unit hydrograph is obtained  from a surface runoff hydrograph pro-
duced  by a precipitation  excess  having a  duration less than some critical
duration to be defined later by  taking the surface runoff ordinates for
successive arbitrarily selected  uniform time intervals and converting
them to cfs per square mile  per  inch of rainfall-excess.  This is done by
dividing the  ordinates in cfs by the area of the drainage basin in square
miles  and by  the rainfall excess  in  inches as illustrated in Table 2.
The ordinates of a unit hydrograph could  also be expressed in percentage
of total surface runoff.  In this  form the graph is often referred to as
a  distribution graph.  This  latter form is not used in this report.  The
example shown in Table 2  is  for the  first of the two hydrographs of Fig-
ure 1.  In Figure 9 are shown five unit hydrographs from this same basin.
These  five show typical variations for a basin.   It should be noted that
they are relatively consistent even  though the total  surface runoff for
the largest of the five was  about  four times the smallest as shown by the
values of surface runoff  tabulated in Figure 9.   The average unit hydro-
graph  is also shown in Figure 9.                                  ::

The most important characteristic  of a unit hydrograph is its peak be-
cause this is the value used to predict peak flood flows.  However, in
order to construct a complete flood hydrograph the entire set of unit hy-
drograph ordinates and abscissas must be known as  shown in tabular form
in columns 1 and 3 in Table 2 or graphically in Figure 9.  A very useful

-------
                                              PLUM  BROOK
                                              (Area 22.9 Sq-Ml.)
  40
  30
X
Z
•X
S
in
   20
   10
                                               SURFACE
                                    DATE     RUWOFF (IN-)
                             —O— April 29,1956    1.008
                             —A— MAY 6.1956     -283
                             —O— JULY 11.1957     -378
                             —0- April  1.1959     .468
                             —O— JUNE 16,1960    -423
                             	Ave. Unit Hydrograph
                                30       40        SO
                                  TIME  (Hrs.)
                                                    60
       10        20


Figure 9.  Five unit  hydrographs from the same,basin.
70
                                   39

-------
  application  of the unit hydrograph  is in determining the progressive vari-
  atipn of infiltration  capacity during a closely spaced series of storms.
  This process also provides a test of the accuracy of the unit hydrograph
  procedure by applying  the unit hydrograph for a drainage basin to a com-
  plex rain storm in which the contributions from various portions of the
  rainfall excess must be added taking into account the sequential time of
  occurrence of the periods of rainfall excess and comparing the computed
  hydrograph with the actual hydrograph.  A typical example is shown in
  Figure 10.  When a unit hydrograph  is applied to successive portions of.
  a long complex series  of rains such as those in Figure 10, the infiltra-
  tion capacity is computed for each  separate stream rise and adjusted by
  trial until the summation of the overlapping hydrographs fits the actual
 hydrograph.   The curve of infiltration capacity (fav) shown in Figure 10
  is based on five values of fav determined for the five bursts of rainfall.
 The volumes of precipitation excess (Pe) are shown by the hatched areas
 of the hyetograph above the infiltration capacity curve.   The derived hy-
 drograph shown by the dashed line was computed by applying the average  '
 unit hydrograph for that basin five times  to the five values of precipita-
 tion excess  (Pe)  and adding overlapping ordinates.   This  latter process is
 sometimes  called convolution.

 For the  purpose  of relating unit  hydrograph  shape  to basin characteristics
 the average unit hydrographs  for  each basin  was  defined  in terms  of  the
 peak (q-pA.), the period of rise  (Tr), the significant period of rise  (tr),
 the width of  the graph at  the base  (W0)  and  at 25, 50, and 75 percent  of
 the peak discharge  (W25, ¥50, and ¥75).  These parameters  are defined
 graphically in Figure  11.   The average values of. these parameters for  53
 of the basins* are presented in Table k.  The numbers in column 1 of Table
 k provide a convenient  method of  identifying each watershed by reference
*Sixteen of the 69 basins listed in Table 1 are not included in Table 4.
Basins l£ and 59 had not experienced enough large rains to define the unit
hydrograph.  Basins 5, 16, and k2 were omitted because the flood hydro-
graphs were double peaked thus making it difficult to define their shape.
The double peaks appear to be caused by highly urbanized areas in the
lower reaches of an otherwise less urbanized basin.  Eleven basins in the
Austin (kk-k6), Dallas (Vf-5l), and San Antonio (60-62) regions were
omitted because they displayed runoff characteristics which indicated high
urbanization even though their values of Pd are very low.   It is suspected
that the storm drainage systems of these eleven basins may have been de-
veloped in advance of anticipated urban growth.   As with the double peaked
basins, a detailed study of the drainage system is expected to reveal the
causes of the anomolous behavior.   This additional research was beyond the
scope of this project.
                                   40

-------
                                      29
                               April 1956
Figure 10.  Reproduction of a  complex hydrograph for the flood
of April 27-50, 1956 on Plum Brook (area = 22.9 sq mi).
                              41

-------
 CO
 LU
 u
 I

 <
 o:
 u_
 o
CO

UJ
                         Centroid of Precipitation
                         Excess

                         Precipitation  Excess

   0.75qDA	
0 0.50qDA
or      MPA
                             Lag


                             Duration of Precipitation
                             Excess

                             Period  of Rise
                                Significant Period
                                of Rise

O.IOqeA	
        'PA
        L
                                -W0
                              TIME

                Figure 11.  Definition sketch.
                           42

-------
  cu
      ~  a1 ft ca
         CO     -i-l

••  _ -  '^-•S  h
CQ  a1 c!  co  c!
ca  ca  O  CH  <8- CH
as     .H  o  o  .o
   C  -P     •<-!
   •H  O"   '  "
       a
      •r)

       0)
       CO

      J!
                     -    b-
    O tov H O- .OJ IfN U>i H    H


    OJCDOOOHHO    d





       VD OJ tf\          IT\    MD
    ot~-o\oo-*ifNir\oj    oj









    OOJOOOOJlf>OK>i    f~
    HHOJK\t-CT\OJOO    K>







          8VO O

          H ° S       °    R

    K^ooo-=^^^\VD^f^    H
    OJ             H H

-PJ
•H
ca
u
o;
t3   _  rr\ (TV p o       p    t—



s  3i^:^^'7d    3





i           _
ft      IfN N^\ C*- VD       K^\    C*-
     ~  oj p H H ir\ ir\ tov

"Eb
•H   OJOOOOrHHO    O
                                                   OOOVO
                                                   t~-HIAQ>
                                                   tr\OCO-*

                                                   b~ |0v OJ
                                                                o
                                                                OJ
                                                    8O O O O ON VD  O
                                                    OJVD OOOOOJONO
                                                 IPvVD^XO ONrH C^-ITNCQ  O

                                                 E— ON CO VD GO CO VOiIf\^+,  CQ

                                                       (Ov 10,        '"^ -^
                                                 VD
                                                   -4- VO

                                                   o  c9  o

                                                   o  o  o
                                                                      1T\
                                                 HHrHHOJOJOJlfN
                                                               CO


                                                                o
                                                                            ir\
                                43

-------
PM
K

1
O
I
EH
        •p
         ^
        ^
        PM
                  vo o  o vo t- KN



                  o o  o o o  o
                 *.  |^_ *-v  |Si__    ^-*

                 -*  KN VO  H  H C-

                 O  O O  H  H O
                                                 ^IS^rr0   tITNCVIVO  H-*  HVO
                                                 iH  r- 1  OJ           rH
                                                    i-l -=r rH
                                              OJCOiHOONCO
                                                                     rHrH
                                                                                      rHH

                 O  0  O H  H  H
                 t— C— KN  t—
                 VO CO CO  H


                 OJ  O H  KN
                 KN H CO H  H CO
                 KN OJ -3- -*  ON in


                 O  O O O  O* O
                                                           Si
                                                                     iR
                 O t- CV1 CVJ
                 ir\ vo -=)- -*
                 OJ H  [Ov ^r^
                                  o

                                  KN

                 O  O  O O  O O
                                         •H
                                         CO
                                         fl
                                         0)
                                         •O
                                         aj
                                        H


                                         I
                                         ft
                                              
-------






1
1
5J
 O IT\
O • C- IS- CO N"\ C—
ir\ ir\ H o oj H

tc\ O ,O
tc\ H o r^\ vo vo
ON ON fTN. H KN OJ
ir\ b- ir\ ir\
CO 00 OJ O\ O\ OJ
vo ir\ ipv H tr\ -=*•
rH i — 1

VD
O O 00 H O O
IOv -4" O -* CO H
hO\ K"\ H H H





N^\
o ITS ir\ ^r^ o ipi
OJ O OJ CO ON C-
tf\ vo ro\ o OJ OJ




o o o x~\ t<~\ ir\
O lf\ O CO CO OJ
-* -* t^v O H OJ


t- vo.. .
CO VD t- VO t--*
lf\ ITN VO OJ N^\ O>
H -* H H



CT\ VO IA O -* O
K% t- CO rH ON H

O\ -H- CO -*
OJ ON VO O N^ ON
O -* IT\ iH OJ H
OJ H
S3RRK®
H O
OJ fe1^
H H
0^
SJ^
O O
ir\ H
«-\ J-


o
-P ON. O
ca H
pj
d)
Q

a
0
•H
-P O O
S H OJ
Pi
O
P^
0
•s
•H If N O
<3) H H
a H oj
0)
43
^
O O
VD O
OJ OJ



SN.S
»OJ

0
CO CO
H
-H-VO
C~-
lfNOHH-4-HHOJHOJH o

^wss&sswz®
oo o cvj i^*\ co cvi OJ K^\ cvj ^c\ OJ i — 1
\c\ o^ ^^ ^? ^5 o c^ ^\ ^\ oo
"H"IA^^""""CUH
•0
fl ITN o ir\ ir\
•HOlS-OOOirNOirNOlf\OJOJ
Si^^ ^o}^. SI o7^
OONVO -f}"^Q CO ITNKA
IT\ IT\ OJ OJ -=T t— OO H 1P\ IP\ r— 1 N~N.
f^O-^3^^O.H
r^oJOJOJOJOJOJOJK^^f^lr^vo
45

-------
 to Table 1.  All of the parameters  are  used to define, the  shape  of  a unit
 hydrograph.  However,  tr is  also  the  critical time  characteristic which  is
 related to the  maximum duration of  rainfall excess  which will produce  a
 single  unit hydrograph.                                          •

 It was  previously discovered that for a group of watersheds  from within
 the same large  watershed system there was  a relatively consistant rela-
 tionship between the two most important unit hydrograph characteristics,
 their peaks and periods of rise,  and  the areas of the  drainage basins.9
 The research reported  here provided an  opportunity  to  determine  if  such
 relationships, exist for a wide variety  of  watersheds from  different re-
 gions.   The relations  between unit  hydrograph peak and area and between
 the various time parameters  and area  were  found to  be  quite  consistant
 for all watersheds if  the degree  of urbanization was accounted for.  At
 this stage in the research the population  density (Pd)  seems to  be  a very
 significant factor in  expressing  the  degree of urbanization.   Satisfactory
 practical relationships  were developed  for varying  population densities.
 This factor appears to be much more important than  such factors  as  water-
 shed shape, channel slope, or roughness.

 The investigation of the effect of  population density was  carried out by
 arranging the basins in  the  three groups shown in Table ij-.   The  first
 group "High Population Density" consists of 15 basins having population
 densities  greater than 5,590 persons/sq mi.   The average value of Pa for
 this group of 13,300 persons/sq mi.   The second group  in Table if- "Low
 Population Density" consists of 23  basins  having population  densities
 less than  1,200 persons/sq mi, the  average for this group  being  539
 persons/sq. mi.  Finally  Table It- shows 15 watersheds under  the heading
 "Intermediate Population Density" for which values  of  Pd were  in the range
 1,400-4,700 and the  average  Pd was  2,689 persons/sq mi. ,

 The  unit hydrograph peaks  are shown plotted against Pd  in  Figure 12.  The
 symbols used in Figures  12-20 are explained in Table 5.  Best fit equa-
 tions based on the use of a  least squares  analysis were derived  for the
 three groups of points representing three  degrees of urbanization in Fig-
 ure  12.  These are  Eqs.  (9),  (15),  and  (13)  in Table 6  and the straight
 lines represented by these equations are shown in Figure 12.  Table 6 also
 shows the  number  of  points used to  derive  each equation, the average P,
 for  each graph and  the linear correlation  coefficient  (r).   All values of
 r are well above  the value needed to  indicate  a one percent  chance that
 the  linear relationship  is accidental.  Also  shown in Figure 12  is a
 dashed line which represents  Eq.   (ll).  In  the  derivation  of Eq.;(ll) two
points representing basins 25 and 28,  both  from the Huntington Bayou area'
 of Houston, were  omitted.  These points fell well below the other high Pd
points as  can be  seen  in Figure 12.   It might  therefore be inferred that
                                    46

-------
Symbol
  A

  D
   O
   A
   0

    0
     Table 5.   LEGEND FOR FIGURES 12-20

Pd*? 5590, Pd Av. =  13300
All basins
Pd g 1200, Pd Av. =  539
All basins
1400 ?  Pd § 4700, Pd Av.  = 2763 or 2689
All basins
Pd g 1200, Pd Av. =  610
.Michigan basins
Pd =£ 1200, Pd  Av. = 488
All  basins except Michigan
 1400 S Pd S  2700,  Pd Av. = 2038
Michigan basins
 1400 =S Pd ^ 4700, Pd Av. = 2926
All  basins except Michigan
 Michigan basins
 All basins except Michigan
 Values obtained from Figures 13,
   16 and 19 at A =  10 sq. mi
   for all drainage  basins.
 Values obtained from Figures 13,
   16 and 19 at A =  10 sq mi
   for Michigan basins only.
  Figures
12, 13, 15, 16,
18, 19
12, 15, 18  .

12, 15, 16, 13,
19
13, 16, 19

13, 16, 19

13

13

14,  17,  20
14,  17,  20
14,  17/20 ~

14,  17,  20
    *P,,  = Population density in persons/sq. mi.
                                    47

-------
                                  CS

                                  •8
                                  •d
                                  bo
                                  •H
                                  03
                                  Q)
                                  03
                                  0)
                                  P)
                                  s-
                                 I


                                 I
                                 OJ
                                 .§
   Vd
'(    b) >|V3d
                    1INP
48

-------
                                           oo
                 v/d
•uiniAfbsrSJD -'(   b)>iv3d
ilNfl
                         49

-------
                                       O
                                       CD
                                       O_
                                          t
                                           W
                                           a
                                  d
                                  o
                                  •H

                                  •8
                                  H


                                  I
                                  ft
                                           0)
                                       ID  -0
                                       Q_  +D


                                       £  s
                                       D_  ta
                                           0)
                                          •H
•U|/'!W*S/'SJO
  °wd

'   V
>|V3d
                             UNfl
             50

-------
                                05
                                0>
                                0>
                                w
                                o
                                •H
                                JH
                                (D
                                A
                                O
                                •H
                               •H
                               ra
                               H

                               0)
'(
jo aomd INVOIJINOIS
    51

-------
'( J
dO
  o
1NVOHIN9IS
   52

-------
'(
3SId JO
  1NVOWN9IS
53

-------
sjnoH'(Jl)  3SIH  JO
                54

-------
'(Jl) 3SIH  dO
            55

-------
                                 05
                                     -p
                                     ra
                                     a
                                     §
                                     -H
                                 —•   to
                                 00   >

                                 Z   a)
                                 LoJ   co
                                 f~\   -rl
                                     S~i
                                     8
                                     0)
  °WJ
'(   1) 3Siy dOQOI^d
          56

-------
Table 6.  EQUATIONS AND STATISTICAL PARAMETERS FOR LIKES
         ON FIGURES 12, 13, 15, 16, 18, AND 19

           N  = Number of drainage basins
           Pd = Population density in persons
                per square mile
           r  = Linear correlation coefficient
(1)
Eq. No.

9
10
11
12
13
14
15
16
17
18
19

20

21
22.
23
24
25
26

27
28
29
30



V
V
V
V
V
V
V
V
t
r
t
r
t
r
t
r
t
r
t
r
t
r
t
r
T
r
T
r
T
r
T
r
T
r
T
r
(2)
Equation
- 448
= 834A >445
= 835A"'400
= 1032A~*
= 1034A~*
= 184A-458
- 400
= 162A * '
= 375A-558
- 4OO
= 269A 'w
= . .274A
= .274A'457
= .325A
. „
= .325A'^'
486
= 1.292A
= 1.447A'457
= .572A'655
= .849A'457
= .383A'425
= .384A-457
.446
= .449A
= . Vi8A
= 1.688A'504
- 1.968A'457
(3)
N

15
15
13
13
23
23
15
15
13
13
15

15

23
- 23
14
14
13
13

. 15
15
23
23
(4)
Av. Pd

13,300
13,300
14,250
14,250
539
539
2,689
2,689
14,250
14,250
13,300

13,300

539
539
• 2,763
2,763
14,250
14,250

13,300
13,300
53.9
539
(5)
r

-0.81

-0.92
-0.77
-0.95

0.87

0.81



0.75

0.90

0.91


0.85

0.78

                            57

-------
Table 6  (concluded).  EQUATIONS AND STATISTICAL PARAMETERS FOR
         LINES  ON FIGURES,  12, 13,  15,  16,  18,  AND 19
(1)
(2)
(3)
(4)
(5)
31
32

33
34
35
36

37
38
39
40
Tr = .835A'655
T = 1.196A'457
r
Michigan Basins
= 65. OA~'25
q^ = 112A"400
q^ = 159A"'595

-.
Pfi
tp - 3.78A'26
t = 2.18A'457
I* . *
Tr - 4.18A'54
T ,= 3.06A'457.
14
14
Only
9
9
4
4

9
9
.9
9
2,763
2,763

610
610
2,038
2,038

610
610
610
610
: 0.88


0.95

0.99


0.90

0.88

                             58

-------
some unusual conditions exist on these two basins which can only be de-
termined from more detailed investigation.  If these two points are •jgmit-
ted the average population density of this group of points becomes ll|.,25Q
persons/sq mi.

Hie lowest group of points in Figure 12 is for drainage basins having pop-
ulation densities less than 1,200 persoris/sq mi, and with an average den^" -
sity of 539 persons/sq mi.  These points are plotted with a distinguishing
symbol which may be identified in Table 5- '

It is significant to note that the slopes of these lines as determined by
a least squares analysis, are -Q.kkS and - .kl.6 for the upper two lines
which represent highly populated basins and -O.lf-58 for the lowest line
which was derived for low values of P^.  -A similar set of unit hydrographs
peaks derived from the mathematical model (discussed in the next section)
produced a slope of -O.k when plotted in the same fashion.

The center group of points representing an average population density of
2,689 when fitted by least squares (Eq. (15)) produced a somewhat steeper
line having a slope of -0.558.  One explanation for this difference in
slope is that the development of a -drainage system is probably not always
a gradual process related directly to gradual changes in population den-
sity but it may lag behind or jump ahead of population increases thus
creating anomolous situations.  Because of the fact that there is so much
evidence that the slopes of these lines should, be about -0.il-, the least
squares method was applied again to find the best fit with a slope of -O.U.
Five curves for which this was done, are shown in Figure 1J.  Three of
these represent the upper three groups of points from Figure 12, the
fourth and fifth lines represent the low population basins (average popu-"
lation density is 610) and intermediate population basins (average popu-
lation density is 2,038) in Southeastern Michigan.  The line representing
Eq. (llj-) for all of the low population basins coincides with the line rep-
resenting Eq. (36) for the intermediate population basins in Southeastern
Michigan.  The equation numbers are shown in Figure 13 to enable the
re'ader to locate the corresponding equations in Table 6.  The average pop-
ulation densities are also shown on the graphs.  The lines for Southeastern
Michigan were included' in order to provide for the most accurate applica-
tion to that region.  These lines fell somewhat below lines representing
all of the low population basins.  The difference between'the more general.
lines and the one for Southeastern Michigan will be discussed in the next
portion of the report.

Although interpolation between the lines showing unit hydrograph peaks for
various population densities might be carried out on Figure 13, a new pa-
rameter q    which eliminates area as a variable was found more useful
                                     59

-------
for this purpose-.  This factor is defined by the following equation
                        .40
                            V
in which qp^ is the unit hydrograph peak for any area A in cfs/sq' mi/in.
and QpAo is the corresponding unit hydrograph peak for a selected: base
area AQ.  The value <3pA0 ^s obtained for any basin from its value of q_^
by means of Eq. (kl} or by following along a line such as those in Figure
13 to the base area A .  In this case AQ was chosen as 10 sq mi but any
other size of basin could be selected for this purpose.  The resulting
points may then be plotted against population density as shown in Figure
14.  It will be seen that the trend is quite clear and that the basins
from Southeastern Michigan (white diamonds) follow a slightly different
trend than those from other areas (black triangles).  Also shown in Figure
J.h are values of P^ vs. qpA0 read from the six straight lin'es in Figure
13, two of which are coincident.  The symbol 0 is used for the four points
derived from all 53 basins and the symbol 0 for the points from the two
lines representing the 16 Southeastern Michigan basins.

The solid curve shown in Figure lit- is drawn to best represent Southeastern
Michigan.  A more general curve such as the dashed line represents all
basins.  The curve in Figure li)- was used to derive design curves for South-
eastern Michigan.

The relation of the unit hydrograph time parameters to area and population
density were analyzed and correlated in the same manner as the peak dis-
charges.  The values of tr, the significant period of rise (see Figure
11), are plotted against area in Figure 15.  The top line represents
the "Low Population Density" basins and the lower two lines represent
"High Population Density" basins.  These lower two lines differ only in
the omission of two data points from the dashed line as previously de-
scribed.  Equation numbers are shown to aid in identifying the correspon-
ding equations and statistical parameters in Table 6.

The slopes of these lines are 0.^22, O.kk^, and 0'. hQ6, respectively,
•which are again similar to the slope derived from unit hydrographs de-
veloped by the model which was 0.^37-  Also, as in Figure 15 the inter-
mediate population basins showed a different trend.  Figure 16 shows
the best fit lines converted to a common slope of 0.^37 and Figure 17
gives the relation of
                           with population density.  The correlation
coefficients and equations for the regressions are shown in Table 6.
Similar correlations for Tr are presented in Figures 18, 19, and 20.
The equations and statistical parameters are shown in Table 6.  The
                                     60

-------
corresponding derivations for WQ, Wgc, ¥,-Q, and ¥7^ are not presented
in this report but the final results are -given as described in the
following paragraph.

In order to provide a more convenient way of deriving the form of the
unit hydrograph for any area and population density curves such as those
shown in Figures lU, 17, and 20 were used to provide values of qpA, tr,
Tr, ¥75* ¥50* W25> and W0 for an area of 10 scl mi for various population
densities.  Lines with the proper slope were then constructed as shown
in Figures 21-27 for round numbered values of population density.  These
curves make interpolation much easier than in the original graphs.  Re- .
suits from streams in Southeastern Michigan were given the most weight
in deriving these curves.  Therefore the curves apply more accurately
there than elsewhere.  The use of these curves will be demonstrated in
the section titled Predicting Flood Magnitudes and Frequencies.
                                    61

-------
                                                      P
                                                      o


                                                      s,
                                                      •H
                                                      W


                                                      ?
                                                      cs
                                                      O)

                                                      &



                                                      g


                                                      «
                                                      (L)
                                                      ft



                                                      I
                                                     OJ


                                                      0)
                                                     •H

                                                     fe
62

-------
                                                                 f-l
                                                                 3
                                                                 O
                                                                 •H
                                                                 ra
                                                                 03
                                                                 
-------
sjnoH'(Jl)3SI*HO
             64

-------
'(SiM)>IV3d dO %$L IV Hid I'M- HdVHDOdCIAH IINP
                       65

-------
raM))IV3d dO %05 IV HldlM
iiNn
                   66

-------
                                o

                                a
                                (3D
                                •H
                                ra
                                0)
                                "d

                                n5
                                (U

                                a
                                •a
                                IV3d JO
IV H1QIM HdVHOOaaAH IINH
     67

-------
SJPOH TM)>IV3d JO %0 IV HldlM
                1INH
68

-------
                              SECTION IX
                          MATHEMATICAL MODEL
It became apparent early in the work that an analytical approach to the
surface runoff problem would be an exceedingly valuable goal if it could
be developed well enough to simulate natural watershed responses from
precipitation inputs.  Consequently, a mathematical model was constructed
which fulfills these requirements to a certain point..(the next step is
to incorporate more complex drainage networks into the model).  The model
simulates the runoff process in a conceptual watershed consisting of a
plane rectangular basin with a stream flowing in the middle.  The model
performs a two phase transformation on the rainfall excess input.  For
the first or land phase, the kinematic wave theory is used to transform
the precipitation excess into an overland flow hydrograph.  For the
second or channel phase, the complete equations of motion are used to
transform the overland flow hydrograph, which is now taken as the lat-
eral inflow, to the main channel, into the output from the watershed.
These equations are formulated in a direct implicit method using a
fixed rectangular grid, and the resulting system of simultaneous non-
linear finite difference equations is solved using the generalized
Newton-Raphson procedure on an IBM 360-67 digital computer.    The model
functions well even in the difficult conditions of very low  initial
flows (less than 1 percent of peak flow).  The results are independent
of any reasonable downstream boundary conditions imposed.

The model was investigated first to determine the effect of  the dura-
tion of  rainfall excess ('tQ) on the peak discharge (Qp) and  on  such time
parameters as Tr, t  , W5Q, ¥?5 (Figure  11) which define the  form  of the
unit hydrograph.  This was done by running the model for various  values
of t  with the total  input (D) held constant.  These  runs  indicated
that the form of the  unit hydrograph varies  little when t0 < tp/2 and
for t  < t  the variation is small for  practical purposes.   The.meaning of
t  is  shown-in Figure 11.  These results agree with  those  obtained from
natural  watersheds where tr was used  instead of t  .   The values of tr  and .
t-n were  found to be  nearly the  same  in  natural watersheds  and tr  is more
useful and  easier  to  obtain.
                                     69

-------
 The second set of runs was made holding to to constant at a value less than
 tp and varying the input D.  It was found that the relation between peak
 discharge.and input was expressed by the following equation
                  CD
                    G
 If G is  unity the relation between peak and volume  is  linear.   For
 trapezoidal channels  the  value of G was found to be about  l.h whereas
 for parabolic channels with the sides concave downward  G was  about 1.2.
 It is  believed that this  latter shape tends to simulate natural rivers
 and flood  plains  much more clearly than does a trapezoidal channel.
 If the roughness  is allowed to increase with increasing depth natural
 conditions are simulated  even more closely and the  value of  G in the
 model  was  reduced to  1.05-   These findings helped explain  why many natu-
 ral basins have a linear  relation between  peak and  total input.  The
 effects  of roughness, slope,  and  channel length on  the  value of ;G were
 found  to be much  less important than changing the shape of the  channel.

 In addition to providing  a better understanding of  the  storm runoff
 process  as  described above,the  model provides  qualitative  information
 on the effect  of  certain  parameters which  are  likely to have only a
 limited  range  in  gaged natural watersheds.  For example, under  urban
 conditions  some watersheds  are  changed  artificially so  that they are
 much more  slender than typical natural  basins.   The model  enables one
 to  determine how  such parameters  as  unit hydrograph peak vary as, the
 shape  of the model watershed is changed from nearly square to very
 slender.  Such results can  be used to indicate what trends can be ex-
pected for  the same parameters in real watersheds.  Specific refer-
ences to comparisons of specific  phases of the runoff process in the
model and in natural watersheds are given at appropriate places  in
this report.
                                  70

-------
                              SECTION X

                          FREQUENCY STUDIES
The determination.of the winter rainfall frequency is complicated in
Michigan by the fact that recorded precipitation may be snowfall rather
than rainfall and should therefore be excluded.  Furthermore, rapidly
melting snow whether or not accompanied by rainfall produces precipi-
tation excess and such events should be included in the frequency anal-
ysis.  Fortunately, including snowfall tends to compensate for leaving
out snowmelt in the frequency analysis of precipitation, however, the
extent to which they do so needed .to.be determined.  The frequency in-
vestigation was made by analyzing 535 station-years of records from
16 stations in Southeastern Michigan.  The recorded daily precipita-
tion and average temperature were determined from records of the
U.S. Environmental Data Service.  For each winter season at each
weather station a continuous record was developed of the water equiva-
lent of snow on the ground by adding snowfalls and deducting daily
snowmelt.  The recorded precipitation was considered to be snowfall
when the average of the daily maximum and minimum temperature was 32°
or lower.  Snowmelt from rain was computed by means of Eq.     "
                 P (T  -32)
           M  =
 and snowmelt resulting from atmospheric  heat was  computed by the degree-
 day method using the  following equation
           M  =  0-05 (T -3*0
                        9*
 In these equations M is the water derived from melt in inches  per day,
 T  is the average of the daily maximum and minimum temperature and P
 is the 2U-hr rainfall.  Examination of these two equations will show
 that melt due to rainfall tends to be very small compared with that
                                    71

-------
  caused by atmospheric heat.  Although Eq. (W) only indirectly includes
  the significant amount of heat transferred to the snow by condensation
  it has given satisfactory results in accounting for snowmelt in Michigan
  based on the analysis of several hundred hydrographs from many drainage
  basins.                                                       .  .   •

  The recorded daily rainfalls used in this analysis have been corrected
  to a 2U-hr basis by adding half of the largest rain which occurred on
  an adjacent day.  This procedure is based on the  fact that the maximum
  2k hr of rain could have included an amount recorded for an adjacent
  day varying from zero to the full recorded value.   Shown in Figure 28
  are winter frequencies for rainfall plus  snowmelt,  for rainfall  plus
  snowfall (conventional recorded precipitation)  and,  for comparitive
  purposes,  the  values  for rainfall alone are  also  shown.   In the  lower
  frequencies, up  to  about 30 years,  the curve of rainfall plus  snowmelt
  is  about 2 percent  above the curve  for rainfall only.   The  fact  that
  the correct curve (rainfall plus  snowmelt) falls  only  2  percent  above
  the conventional precipitation  curve  is accounted for  by the fact  that
  including snowfall while  excluding  snowmelt  nearly equals the effect
  of  including snowmelt while  excluding snowfall.  This  is  fortunate  be-
 cause a  great deal of  time and  expense is involved in  computing snow-
 melt for a large number  of years.   It is, of course, not known, whether
 the error would be this small in other latitudes or at other geographi-
 cal locations at the same latitude.  A frequency study was also niade
 for 1950 station-years of conventional rainfall to determine if 535
 station-years was long enough to provide a good estimate of frequency.
 The 535 station-years used in the snowmelt studies are included in the
 longer period of records and all stations  are in a meteorologically
 homogeneous area in Southeastern Michigan and Northwestern Ohio.   The
 longer period of record included enough larger rains to raise the! curve
 an average of 2 percent for recurrence intervals up to 30 years.  : The
 two curves are  shown in Figure 29.                          '     ;

 It can then be  assumed that the  best estimate of the  frequency  of 'winter
 rain plus snowmelt can be obtained by drawing a curve about  2 'percent
 higher than the conventional curve for the 1950 station-years of  record.
 This corrected  curve  is shown in Figure 30 along with the curve giving '
 frequencies  of  summer  rains  as determined  from the  1950 station-years
 of record.   The winter  curve  of  Figure 30  differs from  the winter curve
 in Figure 29 in that after adding  2  percent for  snowmelt  the month  of
 October has  been  included with the winter  months and  eliminated from'
 the  summer months.  This was  done because  infiltration  capacities (dis-
 cussed previous^) and  time-intensity  rainfall patterns (discussed  in
next section) in October were found  to be more like the winter months
than the summer months.
                                   72

-------
                                                  a
                                                  (U
                                                  §
                                                  s
                                                  -P
                                                  O
                                                  0)
                                                  CX3
                                                  CM
S3HONI  Nl INnOIAIV
                 73

-------
                                                    0)
                                                    g.
                                                    fn
                                                    o
                                                    O
                                                    0)
                                                    H

                                                    
-------
                                O
                                I
                                a
                                o
                                ra
                                cd
                                0)
                                02
                               O
                               h
-------
                                SECTION XI
                     TIME-INTENSITY RAINFALL PATTERNS
 The analysis of rainfall and runoff for natural drainage basins smaller
 then about 100 sq mi as well as for all sizes of urbanized basins  requires
 the use of rain intensities for time intervals smaller than 2k hr.   The
 unit hydrograph-infiltration capacity method of flood frequency prediction
 requires the use of time intervals as small as one hour on natural basins
 of about 0.2 sq mi, and for urbanized drainage basins of about 10  sq mi.
 When drainage basins are smaller than about 0.2 sq mi for rural areas  or
 about 10 sq mi for densely populated areas  the rainfall intensities must
 be broken down to smaller than hourly time  intervals.   Although fre-
 quency studies can be made for durations less than 2k hr there is  much
 less information available for these shorter durations.   Therefore,
 greater accuracy can usually be achieved by determining frequencies  for
 24-hr rains and then finding relationships  between shorter duration
 rains and 24-hr rains.   This was done in two ways.38   One  method was to
 find the values of maximum continuous precipitation of various durations.
 The other method was to determine the chronological time distributions  of
 rain storms about the maximum hour of rain.                      •

 The maximum continuous accumulated rainfall was  determined for durations
 from 1 to 24 hr for 80 summer rains  and for 44 winter  rains.   The' rains
were selected from a rain  gage network located in  Southeastern Michigan
maintained by the Detroit  Metropolitan Area Planning Cpmmission and  the
U.S.  Environmental Data  Service.   Only rains  having a  24-hr rainfall equal
to or greater than 1.5 in. were used,  and the same  rain  storm was not used
twice even though it may have covered more  than  one of the rain gages.'
The period covered was the thirteen years from I960 through 1972.'  The re-
sults  expressed in percent of 24 hr rains along with the standard devia-
tions  for each  duration  are  shown  in Table  7.  The  rather  large standard
deviations  indicate  the  considerable variations among  individual values
for each  duration.   The  values  of  P versus  t  are plotted in Figure 31.
Also shown  in Figure 31  are values of  P derived from U.S. Weather: Bureau39
frequency studies.   In Figure 32 the same data are shown as'P/t versus t.
In  this form the ordinates are percentage of 24-rain divided by the
                                    76

-------
sf
CM

CM
CM

O
CM

go


CD
£


CM

O

CO

CD

sr
CM
/~\









*"*"

*-^
CO
a:
o
IE

2
~"
O
i 	
£
o:
•3
Q











d
<
u.

<
o:
a:
Z)
o
X
sr
CJ
u_
o
i—
z
LJ
CJ
(T
UJ
CL-
OT
Q.





•
H
i — 1
ce
a
•H
03
fn
^
OJ

O
+5
fl
a;
o
a>
ft
to
03
(U
CO
/1\
UJ
(U
a
o
•H
•P
03
1
O
•H
• 3
o

-------
                                   •d-
                                   CM


                                   CM
                                   CM


                                   O
                                   CVS
                                          _
                                          _J
                                   co  4-  S

                                   sj- O  x
                                   __ ^*  «••»•«••
                                   — X  sr
                                          CSJ
                                 — CM
                                   o  ?  z
                                   ~  O  W
                                      <
                                — co Q
O   O
co   to
          O    O    O   O
          sJ*    ro    CM   —
                                   CM



                                   O
                                               H
                                               •H
                                                e
                                               •H

                                                In



                                               &
                                               
                                               p.

                                               CQ
                                               cS
                                               0)
                                               TO
                                               CQ
                                               0)


                                               I
                                              I
                                              CO

                                              C
                                              OJ
                                              tov


                                              0)
U/d) A11SN31NI
                     78

-------
I
H
CQ
 0)
H
£>
            0)
            •s

            CQ
                         O
                         •H
                                 LOv
                                        VDJ-  OJ
                                                      t- KN t- OO t-
O  J-  "3   _d-  ON IT\ KN. OJ
   OJ  3   OJ  H  rH rH  rH








    g

       p,    VO  C^  CO OO -^i" OO OJ CO
       ^^   U~\  NA ON KA O'X i—I  KS t"~

            KA  O\ OO ON ON ON t— -J" OJ  t"— O
            rHrHrHrHrHHrHrHH








^.i-j,-,   moot-vDr-it-voir\t£Nqo
SleS   -J-VO,cOC— rHvOt—OJOHO
Q)  __-j-  t*j j    ...•••••••
POJ  S3-3-COC— irNOJt-irNrHVOlTN
^      -H   OJKNJ-irNVOVOt— OOOOON_
   «H  Cl3                                      rH
    O








            LOvHOOKAVO KAt—OJ D-O  D—
            O  C— D^-OVO OVO iTNO  lT\rH


            LfN  KN OJ OJ rH rH  rH








    «

            J-1T\OOOOOOJ ONO-*rH
            OJ  ITN rH t—J- O OJ CO ON KA

    >°   H^OOIOKAOJCPOOVOKAO

05 .§







            O-*l^rHCVICVjK^-rHOOOO

            LfNKNO-d-OOCJ KNiTN\£)ONO
;,;     -n   LfNt— COOOOOONONO\ONONO
-  
-------
 duration  in hours  and the  curves have the  form  of the commonly used
 intensity-duration curves.  The equations  for these curves have the fol-
 lowing form
           P/t
                   (t•+ B)
                         n
(WO
 in which A,  B and n  are  constants.   If this equation  is expressed in
 logarithmic  form (Eq.  45)  it  can be  reduced to a straight
           log P/t  =   log A  - n log (t + B)
(45)
line by the proper  selection of B.  The optimum value of B was determined
by applying the method of  least squares to derive linear equations for a
series of values of B and  selecting the equation for which the linear cor-
relation coefficient was a maximum and -the standard deviation from the
regression was a minimum.

The resulting equations are, for summer,
          P/t
and for winter
                       112.0
                   (t + 1.0)
                           1.026
(46)
          P/t  =
                       68..0-
For each of these equations the linear correlation coefficient was very
near unity thus indicating a highly linear relationship.  The correspond-
ing standard deviation from the regression indicated deviations ifrom the
derived equations of less than 2 percent.  Among the individual values the
most interesting item of information determined from this analysis is that
for summer rains the maximum hour of rain included on the average 55 per-
cent of the 24-hr total while for winter the rainfall during the maxi-
mum hour was about 24 percent of the 24-hr rainfall.   Separate analyses
by months indicated that this change takes place quite abruptly at the
ends of the two seasons.  Additional analyses made by dividing the rains
into two groups according to size indicated that the intensity patterns
were independent of magnitude of rainfall.
                                    80'

-------
Typical hyetograph ordinates (P^/t) can be derived from these curves or
from Equations (k6) and (kj} by assuming that the rain for any duration
is the maximum for that duration and also contains all of the maximum
shorter durations.  A convenient way to do this is to express time (t) in
terms of uniform time intervals (At).  Then the rain expressed as percent
of 2^-hr rain for a duration NAt is NAt (P/t)jj-.  If one subtracts the
rain for a duration which is smaller by the amount At ((H-t)At (P/t)    ),
the difference is the rain during the Nth time intervals,  ((P^/At )jj A t ).
In equation form this relationship becomes
           (Ph/At)NAt  =  NAt (P/t)N -  (N -  l)At
Values of (P/t) are computed from Equations (ij-6) and (^7), (P/t)N being
the value of (P/t) at time t = NAt and (P/t)u_i being the value at time
t = (N-l)At.  Then, dividing by At the following simple' relationship is
obtained
(PhAt)H
                     =  N(P/t)N- (N- 1) (P/t)
 Computed values  of P/t and Ph/At are .shown in Table 8.   These values
 are plotted as typical hyetographs  in  Figure 53-   In order to change
 the ordinates to rain-intensity in  in./hr it is  only necessary to
 multiply each one by the 2k/hr rainfall of the desired frequency.

 The order in which the various intensities are arranged in Figure 33  is
 important if the period of rainfall excess is longer than can be, converted
 to runoff with a single application of the unit  hydrograph.   Therefore the
 nature of typical time-intensity patterns was studied.   This was done by
 arranging the 80 summer rains and kk winter rains previously described in
 tabular form so  that the maximum hours coincided.  It was found that  on
 the average the  rainfall patterns tended to be symmetrical.   The actual
 volumes of precipitation were about equal before and after the maximum .
 hour when averaged for all the rains.   The-second largest hour occurred
 somewhat more often after the peak hour than before for the summer rains
 and an equal number of times before and after the maximum hour for the
 winter rains. Based on this study, the hyetographs shown in Figure 33 may
 be considered as typical for Southeastern Michigan.  The use of these
 curves will be demonstrated in the section on Predicting Flood Magnitudes
 and Frequencies.

 All'rainfall frequency data discussed so far in  this section are from in-
 dividual rain gages and are usually referred to.as .point rainfall. Before
                                    81

-------
                                           iH
                                           H
                                           • 03


                                           •H
                                           03



v- »- •
*^* fll 1
E £ |
e § i
* \ $
\ , , rr
\ 1!

v 1
l~l
I"»L_
i 1
i
i
i
1.
•


i i r i i i
c
*^,^
^mmm
Q.
Q.
0) &
CC T3
ID S^
0 -g

x ^ Q
T""h, 8
i jj ••J
? ^
j— ^
>\
Z3
O
X
CD
CP
O
fe
ooooooo 5
CD in 
(D
^
^
•^
£

N-

or
LU
o
CC
' V —
, •••
o
X
CM
O
iC
o
X-
Q.
»
•^
g
0
CO
(U
CO
03
0
•H

N-\
(4V/Md) A1ISN31NI
a)
                     82

-------
 Table 8.   HYETOGRAEH ORD MATES IN PERCENT OF 24-HOUR RAINFALL PER HOUR
Duration
In hours
(t)
1
2
3
4
5
6
7
8
9
• 10
11
12
13
1H.'
15
Summer
P/ta,

-------
                                           W
                                        ;=, h
                                        ^  §
                                        o- xj
                                        00  "&
                                        <' •?
                                        UJi S3,
                                          ! (U
llVJNIVUlNIOd
                 84

-------
                             SECTION XII
             PREDICTING FLOOD MAGNITUDES AND FREQUENCIES
The procedure presented in this report is based on the idea that rainfall
and/or snowmelt can be determined for any.desired duration and frequency
and that peak surface runoff rate or, if needed, the entire surface run-
off hydrograph can be constructed by use of the unit hydrograph taking
into account infiltration, the contribution from impermeable areas and
retention.  For perennial streams this predicted hydrograph must be
superimposed on a typical base flow.  This procedure has been worked out
and is presented here for Southeastern Michigan.  The information
dealing with precipitation frequency, infiltration capacities, base flows
and HSIA are derived from the large group of basins for which hydro-
graphs were analyzed in Southeastern Michigan.  The design curves for
estimating unit hydrograph form were derived from basins located in many
locations including Southeastern Michigan.  However, as discussed in Sec-
tion VIII more weight was given to results from Southeastern Michigan
for low values of population density.  The curves based on the average
data for all basins would therefore give slightly different results for
rural areas.  In presenting the steps used in predicting flood peaks for
a given watershed a numerical example will be presented.  The example
selected is Red Run, a 36.5 sq mi basin located in Southeastern Michigan
on which the population density is 7500 people/sq mi.  It is assumed that
a knowledge of a range of flood magnitudes is desired.  Therefore a num-
ber of solutions are made in order to provide a set of points through
which a curve relating flood magnitude to frequency may be plotted.

1.  A number of values of 2^--hr summer point rainfall and winter point
rainfall plus snowmelt of various frequencies are determined from Figure
30 and tabulated in Table 9-

2.  Also shown in Table 9 are the corresponding values of average pre-
cipitation on 36.5 sq mi.  The conversion factors for changing point
rainfall to average values were determined from Figure 3*4- for an area of
36.5 sq mi and for durations which were arbitrarily selected to cover the
time required for 95 percent of the rain to fall.  Reference to Table 8
                                    85

-------
         Table 9.   TWENTY-HOUR HOUR RAINS OF VARIOUS FREQUENCIES
WINTER
Frequency
inyr
1
2
5
10
25
50
100
At a
point
1.52
1.86
2.29
2.62
3-13
3-39
3-71
On 36.5
sq mi
1.1*5
1-77
2.18
2.50
2.98
3.23
3-53-
SUMMER
At a
point
1.6p
2.01
2.55
2.97
3.62
IK 02
^.57
On 36.5
sq mi
1.5U
; 1.93
: 2,11-5
2.85
3.^8
I 3.86
4.38
 and Eqs.  (5)  and (7)  shows that the duration would be 10 hr for summer
 rains  and 18  hr for winter rains.   Then the  conversion factors  from Fig-
 ure 3^ are .960 for summer and .953 for winter.

 3.   A  typical unit hydrograph is derived for the  basin.   The unit  hydro-
 graph  characteristics  determined from Figures 21-27 for an area of 36.5
 sq,  mi  and a population density of  7500  people/sq  mi are as follows:

                           2
          q,pA = 138 cfs/mi/in.
          tr   =
          T    =
          W0  =
 2.6 hr
 3-7 hr
 2.8 hr
 If.l hr
 6.9 hr
22.0 hr
The unit hydrograph shown in Figure 35  is constructed by first placing the
peak at the time of rise (Tr).  Then the significant period of ri;se (tr)' is
used to sketch in the rising side  of the hydrograph.  Next, the hydrograph
widths at 75 percent, 50 percent,  25 percent  of peak plus the base width
are used to complete the recession side of the hydrograph.  Minor modifi-
cations may be necessary to form a unit hydrograph having an area of  1 in.

Also shown in Figure 35 is the average unit hydrograph derived from run-
off records on Red Run.  The close approximation of the actual unit hydro-
graph by the one synthesized from  generalized curves should not always be
expected.  It happens that the Red Run unit hydrograph characteristics
                                    86

-------
    140  -
    120  -
    100  -
cr
co
CO

&  80
LU
O
%  60
    40
    20
     0
       0
                         Unit Hydrograph Obtained
                         From Rainfall and
                         Runoff Records

                         Synthesized Unit
                         Hydrograph
                                       1
                 10         20
                    TIME,  Hours
Figure 35.  Synthesized and observed unit hydrographs for Red Run.
                            87

-------
fall near the best fit lines for the highly urbanized basins.

k.  A typical hyetograph of hourly precipitation is derived for summer
and winter rain using the arrangement shown in Figure 33 and numerical
values from Table 8.  An example computation is shown in Table 10 for a
50-yr winter rain.  The numerical values of the ratio of 1-hr rain to
2^-hr rain are arranged in a typical time sequence in the top line of
Table 10.  Line 2 shows the corresponding values of hourly precipitation
obtained by applying the ratios in row 1 to the 50-yr 2l<-hr winter rain.
The magnitude of the rain was. given as 3.23 in. in Table 9.

5«  The precipitation excess (Pe) is then computed for each hour by de-
ducting the average hourly winter infiltration which was found to be
0.10 in. for Southeastern Michigan.  (See Figure 8.)  These values are
given in line 3 of Table 10.

6.  In line h, the winter retention (0.10 in.) is deducted from the first
2 hr of Pe.  The values in line h are in inches on the permeable area.
In line 5 these are converted to inches on the entire basin by multiply-
ing by (l - HSIA/100).  The value of HSIA is obtained from Eq. (50).  This
          HSIA  =  1.38 Pd
(50)
equation was derived for basins in Southeastern Michigan.  HSIA is ex-
pressed in percent of total area and Pd in thousands of persons/sq mi.

7.  The surface runoff from impermeable area is the total precipitation
given in line 2 converted to inches on the total area by multiplying by
HSIA/100.  These values are shown in line 6 of Table 10.  The retention
on the impermeable area, 0.05 in., was accounted for by the first several
hours of precipitation which are not included in Table 10.      '

8.  Line 7 is the sum of the hourly contributions to surface runoff from
the permeable area (line 5) and from the impermeable area (line 16).   These
are combined into success 2-hr inputs to the drainage system in :line 8.
This was done because it was shown earlier that the effective period of
rise (tr) is 2.6 hr and therefore the unit hydrograph can be applied to
inputs having durations as long as 2.6 hr.  The use of 2-hr increments
is therefore convenient and reduces the computation time over that re-
quired if 1-hr intervals were used.                              '

9-  The next step is to convert the 2-hr increments of surface runoff
                                    88

-------




£.
H
«
1 .
«
pj •
^ '
iR

<;4
PH
O
13
0
w
f^l
y
CQ
fa
O
g
fcj '
g
>
fa
O
s
g •
i
0
o

d
r-4
CD
r-l
3



IfN
NA
O
d
.1
d

o
d
VO
H
d

H

OJ
d
o
H
*
o


ON
UA
O
d

ITN
O
3
d


o1
NA
O
d
f

OJ
>> o •
2 • O
" O ft 0)
4-! "f^ ?"*
O ft
ft 43
O
•H
-P
,cd
PS
^
ON
O
r-l
d
r-l
IfN
r-l
d

IfN
OJ
d
H
5"
d

CO
N 	
t-
d
OJ
NA
d


IfN
.9
d


c-
H
d



o
d

	 ^
PL.
ft
•rf
•'8
ft
, — \
1
OJ
ON
O
d
r-H
lf\
O
d

IfN ,
NA
H
d
K
NA
d

CO
N 	
VO
d
VO
OJ
OJ
d


•§
d


t-
0
* . '
o



o




CQ
CQ 1
O PM
d II
0)
ft PW

0
1
NA
ON
O
O
d
H
°
d

UA
NA
•H
d
r-l
NA
d

CO
^ —
VO
d
VD
OJ
OJ
d


OJ
rH
o
d



o




o


.
CO
a a
•H to
. ] CO
pi rl
CQ C CO
O
II 
-------
 input to hydrographs by means of the unit hydrograph.   This  is  illustrated
 in Table 11 for the 50-yr winter rain.   The first two  columns  in Table  11
 show the coordinates of the unit hydrographs as  read from Figure 35.  At
 the top of columns 3>  ^-> 5> and 6 are shown the  successive 2-hr incre-
 ments to surface runoff derived in Table 10.  The values  of  surface run-
 off rates shown in these four columns are obtained by  multiplying by
 corresponding unit hydrographs ordinates and by  the area,  36.5  sq mi.
 Column 7 is the summation of Column 3>  ^-, 5, and 6 and represents the
 predicted surface runoff hydrograph with a peak  of 6631 cu ft/sec.

 10.   The actual peak discharge is obtained by adding a typical  ground
 water discharge.   This value is obtained from Eq.  (51)  in which Q,™ is
 ground water discharge in cfs and A is  the area  of the drainage basin in
            GW
               =   .6A
                                               (51)
square miles.  This equation was derived  from a  study of typical ground
water discharge in Southeastern Michigan.   The value for Red Run which
has an area of 36.5 sq mi  is 22 cfs thus  making  the estimated total peak
discharge 6653 cfs.

11.  The operations described  in steps  (ll)  and  (12) are then repeated
for all of the rains  shown in  Table 9.  The results are plotted in Figure
56.

12.  A curve for total frequency is then  obtained by combining the summer
and winter curves and is shown in Figure  36.  This is done by adding the
probabilities which are the reciprocals of  the frequencies for floods of
selected magnitudes as shown by the following equation in which T^, Tg and
          T.
           T
_!_
Ts
                                                                     (52)
TT are the winter, summer, and total frequencies, respectively.  The
total frequency is then computed by rearranging Eq. (52) to obtain Eq.
(53)«  Such values of Trp then form the final frequency curve.
                                                                     (53)
                                    90

-------


H
K
H
0
in
M
g
E .
C5
s-
M
CQ
O
o
!=)
O
1
EH
1
O
O
H
H
0)
H
1







in


to




CM






H

O 0
K -
                t^-NAO     H      ON    ONCMin
                CO \D CO     CM      NA    KN H
                -in vo VD     NA     H
                co
          t—     O '' O  "   IfN     t^-
          OCJOOCO     O     to1
                         -
                       -
                    ir\ -=!•     cu
          H   •  rH
          D^-
          ON
                     N~N
8
in CO  CO 1TNKN-4-  f -- *  H
                        COON
                                          rH H
                            i — I  i — !  i — 1  i — I  i — I  i — i
                                                             in

                                                             vd


                                                              x
                                                             V£)
                                                             vo
                                                             
-------
12,000 —
Figure 36".
  2        4     6   8 10        20          50
                FREQUENCY IN YEARS
Predicted and observed flood frequencies for Red!Run.
                                                                   100
                               92

-------
The frequency- curve for Red'Run computed from Eq. (53) is shown in Figure
36.  Also plotted on this figure are the observed frequencies from Ik yr
of records for Red Run.  The higher values of frequency in this series are
not reliable due to the shortness of the period of records but the lower
values should be reasonably correct and serve as a check with lower por-
tion of the total frequency curve derived from precipitation and snow-
melt.  Such remarkable agreement cannot always be expected.  It stems in
part from the fact that the unit hydrograph characteristics of Red Run
fall near to the average lines for high population densities in Figures
1^ 17, and 20.  However, the close agreement serves to verify the concept
that rainfall frequency can be used to predict flood frequency if a sound
hydrological approach,is used in computing runoff from rain and snowmelt.
                                    93

-------
                          SECTION XIII

                           REFERENCES
 1.
 2.
 3-
Horton, R. E.,  "Surface Runoff Phenomena," Publ.  101, Edwards Bros.,
Ann Arbor, Michigan,  1935-

Horton, R. E.,  "An Approach Toward a Physical Interpretation on In.
filtration Capacity," Soil  Sci.  Soc. Proc.,  19^0. '         I

Swartzendruber,  D. and M. R.  Huberty,  "Use of Infiltration Equation
Parameters to Evaluate Infiltration Differences in the Field," Trans.
Am. Geophys. Union, v.  39,  February 1958,  p. 84.

Betson, R. P.,  "What  is Runoff?," J. Geophys. Res., v. 69, April 15,
      p.
 5.


 6.
 8.
 9.
10.
Thames,  J. L.  and S.  J. Ursic,  "Runoff as a Function of Moisture-
Storage  Capacity,  J.  Geophys.  Res.,  v.  65,  February I960, p. 651.

Horner,  W. W.  and C.  Leonard Lloyd,  "Infiltration-Capacity Values
as Determined  from a  Study of  an Eighteen-Month Record at Edwards -
ville, 111., Trans. Am.  Geophys.  Union,  Part II,  19^0, pp. 522-5^1.

Wisler,  C. 0.  and E.  F.  Brater,  "Report on Floods on the Rouge
River,"  Report to Wayne  County Board of Road Commissioners, .August
1957.                                                        I

Brater,  E. F.  and J.  D.  Sherrill,  "Prediction of Magnitudes and
Frequencies of Floods in Michigan,"  Report to Michigan Department of
State Highways and U.S.  Bureau of Public Roads,  1971.

Wisler,  C. 0.  and E.  F.  Brater,  "Hydrology," John Wiley & Sons, Inc.,
New York, 2nd  Ed.,  1959.

Ursic, S. J. and  J. L. Thames,  "Effect  of Cover Types and Soils on
Runoff in Northern Mississippi,"  J.  Geophys. Res., v.  65, February
I960, p. 663.
                               94

-------
11.  Kueligan, G. H. , "Spatially Variable Discharge Over a Sloping Plane,"
     Trans. Am. Geophys. Union, Part VI, 19^-.

12.  Izzard, C. F., "The Surface Profile of Overland Flow," Trans. Am.
     Geophys. Union, Part VI, 19^-.

13.  Woo, D. C. and E. F. Brater,  "Spatially Varied Flow from Controlled
     Rainfall," J. Hydraulics Div. , ASCE, v.  88,  November 1962, p. 51.

lU.  Woolhiser, D. A. and J. A. Liggett, "Unsteady One-Dimensional Flow
     Over a Plane — The Rising Hydrograph, "•  Water  Resources Research,
     v. J., no. 3, 1967.

     Lin, P. N. , "Numerical Analysis of Unsteady  Flow in Open Channels,"
     Trans. Am. Geophys. Union, v.  33,  April 1952, p. 226.

     Lin, P. N. and Ching Seng Fang, "Streamflow  Routing with Application
     to North Carolina Rivers," rReport  No.  -17,  University of North
     Carolina, Chapel Hill  (January 1969).

     Sangal, S. , "The Surface Runoff Provess During Intense Storms,"
     Doctoral Dissertation, Department  of  Civil Engineering, The Univer-
     sity of Michigan, 1970.

     Tholin, A. L. and C.  J. Keller,  "Hydrology of Urban Runoff," Trans.
     ASCE,  v. 125, I960, p. .1308.

     Holtan,  H. N. and D.  E. Overton,  "Storage-Flow Hysteresis in Hydro-
     graph  Synthesis,"  J.  Hydrology,  v. II, No. h, April 1965, PP-  309-
     323.

     Crawford, Norman H.  and Ray K. Kinsley, "Digital Simulation  in
     Hydrology:   Stanford Watershed Model IV," Technical Report, No. 39,
     Department  of Civil Engineering,  Stanford University, 1966.

    . Laurenson,  E.  M. ,  "A Catchment Storage Model  for Runoff Routing, "
     J.  Hydrology,  v.  II,  196^,  p.
15.


l6.



17.



18.


19.



20.



21.


22.


23.


2k.
      Sherman, • L.  K. ,  "Stream Flow from Rainfill by the Unit Hydrograph
      Method,"  Eng. News-Record, v.' 108, 1932, p. 501.

      Bernard, 'Merrill M. , "An Approach to Determinate Stream Flow,"
      Trans.  ASCE, v. ' 100, 1935, P-
      Brater,  E. F., "The Unit Hydrograph Principle Applied to  Small
      Water-Sheds," Trans. ASCE, v. 105, 19^0, p. 1151+.
                                     95

-------
 25.


 26.



 27-



 28.



 29.


 50.


 31.


 32.
 Snyder, Franklin F. "Synthetic Unit-Graphs,"  Trans. Am.  Geophys.
 Union, Part I, 1938, p.
 Taylor, A. B. and H. E. Schwartz, "Unit Hydrograph  Lag and; Peak
 Flow Related to Basin Characteristics," Trans. Am. • Geophys.  Union,
 v. 33, no. 2, 1952, p. 235.                                i

 O'Kelley, J. J. "The Employment of Unit Hydrographs to Determine
 the Plans of Irish Arterial Drainage Channels," Proc.  Inst.  Civil
 Engrs., v. k, Part III, 1955, p. 365.         '             ;

 O'Kelley, J. J., "A Unit Hydrograph Study with Particular Reference
 to British Catchments," Proc. Inst. Civil Engrs., v. 1?, 1960,
 p.
33.
35.


36.


37.
 Gray,  Don M. ,  "Synthetic Unit Hydrographs for Small Watersheds,"
 J.  Hydraulics  Div., ASCE, July 196l, pp. 35-5^.            j

 Eagleson,  Peter S., "Unit Hydrograph Chacteristics for Sewered
 Areas, " J.  Hydraulics Div. ,  ASCE, Marcy 1962, pp. 1-25.

 Wu,  I.  Pai,  "Design Hydrographs for Small Watersheds in Indiana, "
 J.  Hydraulics  Div., ASCE, November 1963, p.  35.

 Espey,  William H.,  Jr.,  Carl W. Morgan, and Frank D. Masch, "A Study
 of  Some Effects of Urbanization on Storm Runoff from a Small Water-
 shed, "  Center  for Research in Water Resources, Department of Civil
 Engineering, The University of Texas (1965).

 Brater,  E. F.,  "Steps Toward a Better Understanding of Urban, Runoff
 Processes," Water Resources  Research,  v. k,  no.  2,  April 1968, pp.
 335-3^7.

 Brater,  E. F. and S.  Sangal,  "Effects  of Urbanization on Peak Flows,"
 University of Texas,  Water Research Symposium on the Effects of
Watershed Changes on Streamflow,  University  of Texas Press, Austin
 1969.

 Viessman, W. , Jr.,  "The  Hydrology of Small Impervious Areas!," Water
Resources Research,  v. 2,  no.  3,  1966,  p.
Horton, R. E., "The Role  of Infiltration in the Hydrological Cycle,"
Trans. Am. Geophys. Union,  v. 1^,  1933,  p.  kk6.             ;

Betson, R. P., "What is Runoff?,"  J.  Geophys.  Res.  v.  69,  April 15
    , p. 15ln.
                                    96

-------
38.  Brater, E. F., S. Sangal,  and J.  D,  Sherrill,  "Seasonal Effects on
     Flood Synthesis/' Water  Resources Research,  A. G.U., v. 10, no. 3,
     June 1971)-.

39-  U.S. Weather Bureau,  "Rainfall Frequency Atlas  of the United States
     for Durations from 30 Minutes to  2k  Hours and Return Periods from 1
     to 100 Years,," Technical Paper Wo. bo,  Washington, B.C., May 1961.
                                    97

-------
                                    TECHNICAL REPORT DATA
                             (Please read Instructions on the reverse before completing)
  I. REPORT NO.
  	EPA-670/2-75-046
2.
                             3. RECIPIENT'S ACCESSION-NO.
  4. TITUE AND SUBTITLE

   RAINFALL-RUNOFF RELATIONS ON URBAN AND  RURAL AREAS
                             5. REPORT DATE
                              May  1975;  Issuing Date
                             6. PERFORMING ORGANIZATION CODE
  r. AUTHORfS)

   Ernest F. Brater and James D. Sherrill
                             8. PERFORMING ORGANIZATION REPORT NO.
 9, PERFORMING ORGANIZATION NAME AND ADDRESS

   Department of Civil Engineering
   University of Michigan
   Ann Arbor, Michigan  48104
                             10. PROGRAM ELEMENT NO.
                              1BB034;  ROAP 2;1ATB; TASK 008
                             11.-J6®WF-RAGWGRANT NO.
                                                             11040 DRS
 12. SPONSORING AGENCY NAME AND ADDRESS
   National Environmental Research Center
   Office of Research  and Development
   U.S. Environmental  Protection Agency
   Cincinnati, Ohio  45268
                             13. TYPE OF REPORT AND PERIOD COVERED
                              Final          |
                             14. SPONSORING AGENCY CODE
 10. SUPPLEMENTARY NOTES
 16. ABSTRACT
   A procedure was developed for estimating the .frequency of storm runoff of various
   magnitudes from rainfall and/or snowmelt on small  drainage basins in various stages
   of urbanization.  The study was based primarily on the analysis of storm runoff
   events on real basins varying in size from 0.02 to 734 sq mi.   The method is based
   on applying unit hydrographs to precipitations of  various frequencies after deducting
   infiltration and retention.   A concurrent study with  an analytical drainage basin
   model provided additional understanding of the effects of some parameters.  The unit
   hydrograph-infiltration  capacity concept was selected as the most accurate practical
   method for predicting storm runoff.   It was found  that the form of the;unit hydro-
   graph could be related to drainage basin size and  degree of urbanization as measured
   by population density.   Other characteristics of the  drainage  basin are much less
   important.  The form of  the unit hydrograph stays  relatively constant for various
   durations and magnitudes  of input as long as the duration of input is smaller than a
   critical time which can  also be related to the size and population density of the
   basin.   As the population increased  from rural to  highly urbanized,  peak discharges
   for the same runoff became as much as ten times greater.   Infiltration capacity was
   found to vary seasonally.   The prediction of flood frequency by this procedure is
   fully operable for Southeastern Michigan.  For application to  other  areas some
   hydrograph analysis must  be  made.	
 7.
                                KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
                                              b.lDENTIFIERS/OPEN ENDED TERMS
                                          c.  cos AT I Field/Group
  *Watersheds
  *Mathematical models
  *Runoff
  *Urban areas
  *Surface water runoff
   Rural areas
                Unit hydrograph
                Southeastern Michigan
                Hydrograph analysis
                Infiltration/retention
                Infiltration capacity
13B
   DISTRIBUTION STATEMENT
  RELEASE TO PUBLIC
                                              19. SECURITY CLASS (ThisReport)'
                                                    UNCLASSIFIED
                                          21. NO. OF PAGES
                                                 108
               20. SECURITY CLASS (This page)
                     UNCLASSIFIED
                                                                         22. PRICE
EPA Form 2220-1 (9-73)
                                             98
                                                    U. S. GOVERNMENT PRINTING OFFICE: 1975-657-593/538't Region No. 5-11

-------