united states department of the interior ...05505000 05506000 05506500 05507000 05507500 05508000...
TRANSCRIPT
UNITED STATES
DEPARTMENT OF THE INTERIOR
GEOLOGICAL SURVEY
Technique for Estimating the
Magnitude and Frequency of Missouri Floods
By
Leland D. Hauth
Prepared in cooperation with
the Missouri State Highway Department
and
U.S. Department of Transportation,
Federal Highway Administration
The opinions, findings, and conclusions expressed in this publication are not necessarily those of
the Federal Highway Administration
Open-file report Rolla, Missouri
1974<?/'£?
Because of renewed interest in this report, it was reissued during 1991.
CONTENTS
Page
Abstract <-- - 1
Introduction 1
Estimating technique 3
Limitations of equations 5
Analysis 17
Basic data 17
Determination of basin characteristics 17
Determination of estimating relations 17
Summary 18
References 19
ILLUSTRATIONS
Page
Figure 1. Graphical solution of the 2-year equation - 6
2. Graphical solution of the 5-year equation 7
3. Graphical solution of the 10-year equation 8
4. Graphical solution of the 25-year equation 9
5. Graphical solution of the 50-year equation 10
6. Graphical solution of the 100-year equation 11
7. Map showing location of gaging stations used
to determine flood-frequency relation
ships 12
TABLESi
Table 1. Summary of regression equations 4
2. Flood-frequency data for streamgaging stations
in Missouri - - 13
II
FACTORS FOR CONVERTING ENGLISH UNITS TO
INTERNATIONAL SYSTEM (SI) UNITS
The following factors may be used to convert the English
units published herein to the International System of Units (SI).
Multiply English units
Feet (ft)
Square miles Gmi2!
Miles (mi)
Feet per mile (ft/mi)
Cubic feet per second (ft3/s)
By
Length
0.3048
2.590
1.609
0.1893
Flow
0.02832
To obtain SI units
Metres (m)
Square kilometres (km2 )
Kilometres (km)
Metres per kilometre (m/k)
Cubic metres per second (m^/s)
III
Technique for Estimating the
Magnitude and Frequency of Missouri Floods
By Leland D. Hauth
ABSTRACT
A technique is presented for estimating the magnitude and
frequency of Missouri floods. For 152 gaged sites the magnitudes
of floods having recurrence intervals of 2 to 100 years are provided
in tables. For ungaged sites, regression relations are presented
that allow the estimation of flood magnitudes from a knowledge of
the upstream drainage area and the average main-channel slope. The
estimating equations are provided in a graphical form for the con
venience of the user.
INTRODUCTION
The purpose of this report is to provide techniques for esti
mating the magnitude and frequency of flooding at sites in Missouri.
Previous reports, Searcy (1955), Patterson (1964), Patterson
and Gamble (1968), Matthai (1968), Sandhaus and Skelton (1968), and
Skelton and Homyk (1970), have presented methods for estimating
flood magnitudes for various recurrence intervals. Each method has
been developed on the basis of a limited period of record or sample
size and could be used with confidence only for drainage areas
greater than 50 mi2 (130 km2 ).
Relationships presented in this report were defined from an
expanded data base by detailed analytical techniques and should
provide flood estimates of increased reliability.
Because of the need for better definition of flood frequency
covering all sizes of drainage areas (0.1 to 14,000 mi2 or 0.26
to 36,300 km2 ) in Missouri, an effort was made to use the limited
information collected on small drainage areas (areas less than
10 mi2 ) so that when small-area data were included in a statewide
data matrix, flood-frequency relationships could be defined for the
full range of drainage areas.
A rainfall-runoff model developed by Dawdy, Lichty, and
Bergmann (1972) was used to extend short records on small drainage
areas so that flood magnitude and frequency with recurrence intervals
as high as 100 years could be defined. Flood-frequency curves at
each data site, based on synthesized peaks from the rainfall-runoff
model for small drainage areas and observed peaks for the larger
drainage areas, were defined by fitting the Pearson Type III distri
bution to the logarithms of the data as recommended by the Hydrology
Committee, Water Resources Council (1967), Bulletin 15. Resulting
flood magnitudes with recurrence intervals of 2, 5, 10., 25, 50, and
100 years were related to drainage area and average main-channel
slope in a regression analysis.
ESTIMATING TECHNIQUE
For ungaged natural floodflow sites, flood magnitudes
having recurrence intervals of 2, 5, 10, 25, 50, and 100 years
are computed by using appropriate values of the contributing
drainage basin size and slope in the equations shown in table 1
or in the graphs of figures 1-6. Drainage area (A) in square
miles, can be obtained by planimetering the area contributing
surface flows to the site as outlined along the drainage
divide on the best available topographic maps. Slope (S) in
feet per mile, is the average slope between points 10, and
85 percent of the distance along the main-stream channel from
the site to the basin divide. Distance is measured by setting
draftsman's dividers at 0.1 mile (0.16 km) spread and stepping
along the channel. The main channel is defined above atream
junctions as the one draining the largest area. Elevation
differences between the 10- and 85-percent points are divided
by the distance between the points to evaluate the slope.
Table 1. Summary of regression equations
Frequency of flood (years)
Standard error ofMagnitude of flood estimate
(ft3/s) (percent)
10-
25-
50-
53 . 5A0.851A-°- 02s0.356
100-
,, _0.905A'°- 02 0.500 67.6A S
73>7A0.924A-°- 02s0.542
79>8A0.926A-°- 02s0.560
85 .iA0.934A-°- 02s0.576
38.6
34.7
34.5
35.0
33.3
33.3
Example;
Assume design of a hydraulic structure is desired at a point
on a stream above which are 200 mi2 (518 km2 ) of drainage. The
average main-channel slope is 6 ft/mi (1.14 m/km) and the design
frequency desired is 50-year recurrence interval.
1. Solution of equation from table 1.
0.926/ 9nm -0.02 o 56O Q50-79.8(200) (200) (6 )
-18,000 ft3/s(510 m3/s).
2. From figure 5, read 200 mi2 (518 km2 ) along the
ordinate and over to the 6 ft/mi (1.14 m/km) slope
curve. Resulting flood peak,
Q50*18,000 ft3/s (510 m3/s).
For gaged sites (see figure 7) , flood magnitudes having
recurrence intervals of 2, 5, 10, 25, 50, and 100 years are shown in
table 2. These flood magnitudes were defined by frequency analysis
of observed flood records for sites draining greater than 10 mi2
(26 km2 ) and by frequency analysis of partially synthesized records
for smaller streams. In general, the values of table 2 will provide
the most reliable estimates of future flood characteristics.
Limitations of Equations
The flood-frequency equations in this report may be used to
estimate magnitude and frequency of floods on most Missouri streams
for drainage areas ranging from 0.1 to 14,000 mi2 (0.26 to 36,300 km2 ),
and slopes ranging from 1.0 to 300 ft/mi (0.19 to 56.8 m/km). However,
equations are not applicable for basins where manmade changes have
appreciably changed the flow regimen or on main stems of the Mississippi
River and Missouri River. Flood-frequency relations for the upper
Mississippi River are presented by Patterson and Gamble (1968), and
for the lower Mississippi River by Patterson (1964). Flood character
istics of the Missouri River below Sioux City, Iowa are presented by
Matthai (1968). Equations given in this report do not apply to
areas near the mouth of streams draining into larger rivers where
backwater effect is experienced. Caution should also be taken whenf\
utilizing equations presented here for drainage areas less than 10 mi*
(26 km2 ) which are located in the Lowlands region of Missouri.5
DISCHARGE IN CUBIC METRES PER SECOND Jfl______________190 IOOO
10,000
10,000
IOOO
100
100 IOOO 10,000 100,000
DISCHARGE, IN CUBIC FEET PER SECOND
FIGURE I. Graphical solution of tht 2-ytar tquation.
DR
AIN
AG
E A
RE
A,
IN
SQ
UA
RE
M
ILE
S
G> G> « »
o o
o CO o 2 IP
o
DR
AIN
AG
E
AR
EA
IN
SQ
UA
RE
KIL
OM
ET
RE
S
DISCHARGE IN CUBIC METRES PER SECOND
ift ...... .'P. ...... ,'99
to
Ul
10,000
1000
100 1000 10,000
DISCHARGE, IN CUBIC FEET PER SECOND
100,000
FIGURE 3 Graphical solution of the 10-year equation.
DISCHARGE IN CUBIC METRES PER SECOND000
10,000
O (0
1000
100
|O
100 1000 10,000 100,000
DISCHARGE, IN CUBIC FEET PER SECOND
FIGURE 4 Graphical solution of the 25-year equation.
W
3
g<o
5
Ul
10,000
1000
100
10
1.0
at
DISCHARGE IN CUBIC METRES PER SECOND 10 100 1000
zx/x/
Y,
50-YEAR FREQUENCY
/LU
W/
y^
/z^
/
#
/355 ^
too 1000 10,000 100,000
DISCHARGE, IN CUBIC FEET PER SECOND
58°
08
60
2 O
5UJ<r<o </)
<klte<UJo<2
oc o
10
.0
FIGURE 5 Graphical solution of the 50-year equation.
10
DR
AIN
AG
E A
RE
A,
IN
SQU
AR
E M
ILE
S
c 3D m
o> o O
5
w
o 2 5
m o
m
IN
SQ
UA
RE
K
ILO
ME
TRE
S
EX
PL
AN
AT
ION
----
- M
ajo
r b
aMi
divi
de
Gag
* S
it*
FIG
UR
E 7.-
- Lo
catio
n of
gag
ing
stat
ions
use
d to
det
erm
ine
flo
od
-fre
qu
ency
rel
atio
nshi
ps
Tab
le 2
.--F
lood
-fre
qu
ency
dat
a fo
r st
ream
gagl
ng s
tati
on
*
In M
isso
uri
Basin
char
acte
rist
icSt
ation
number
0549
5000
0549
5100
0549
6000
0549
7000
0549
7500
0549
7700
0549
8000
05498500
0550
0000
0550
0500
0550
1000
0550
2000
0550
2500
0550
2700
0550
3000
05503500
0550
5000
0550
6000
0550
6500
0550
7000
0550
7500
0550
8000
0551
4500
0681
3000
0681
5550
0681
6000
0681
7500
0681
8900
0681
9500
0682
0000
0682
0500
0682
1000
0689
3500
0689
4000
0689
4500
0689
5000
0689
6000
0689
6180
0689
6500
0689
7000
0689
7500
0689
7700
06898500
0689
9000
0689
9500
0689
9700
0690
0000
06901500
Station
name
Fox
Rive
r at W
ayla
ndBig
Bran
ch tributary
near
Way
laid
Wyconda
Rive
r ab
ove
Canton
North
Fablua Ri
ver
at M
ontl
cell
oMiddle F
a bi
.ua Ri
ver
near Ba
ring
Brid
ge Cr
eek
near
Bar
ing
Midd
le Fablua
Ri
ver
near
Mo
ntlc
ello
North
Fablua Ri
ver
near Ta
ylor
South
Fabl
ua Ri
ver
near
Ta
ylor
North
River
near Bet
hel
North
Rive
r at Palmyra
Bear C
reek at
Hannibal
Salt
Ri
ver ne
ar S
helblna
Easdale
Bran
ch n
ear
Shelbyvllle
Doug
las
Cree
k near Enden
Salt River
near Hunnewell
South
Fork Salt Ri
ver
at Sa
nta
FeYo
ungs Creek
near Mex
ico
Midd
le F
ork
Selt
Ri
ver
at Paris
Elk Fo
rk Salt
River
near P
aris
Salt
River ne
ar Monroe
City
Salt
Ri
ver
near New London
Cuiv
ce Ri
ver
near Tro
yTa
rkio
Ri
ver
at F
airf
axSt
aple
s Br
anch
near Burlington Jun
ctio
nMill Cr
eek
at Or
egon
Nodavay Ri
ver
near B
urli
ngto
n Ju
ncti
onPlatte Ri
ver
at Ravenvood
One
Hundred
and
Two
River
near M
aryvllle
White
Cloud
Cree
k near M
aryv
llle
Plat
te R
iver
near Ag
ency
Jenklna Brench a
t Cover
Blue Ri
ver
at Kansas Ci
tyLittle B
lue
River
near L
ake Ci
tyEa
st Fork F
ishi
ng R
iver at Excelsior
Spri
ngs
Croo
ked
Rive
r ne
ar Ri
chmo
ndWa
keod
a Cr
eek
at Carrol Iton
DeMoss . B
ranc
h near Sta
nber
ryThompson Branch near Alb
any
East Fork Big
Creek nea
r Bethany
Gran
d Ri
ver
near G
alla
tin
Grand
Rive
r tributary
near U
tica
Weld
on R
iver
near Mercer
Weld
on R
iver at Mi
ll G
rove
Thompson R
iver
at Tr
ento
nSh
oal
Cree
k near B
raym
erMedicine C
reek
nea
r Gait
Locust Cr
eek
near Li
nneu
s
Area
Onl2)
400 0.70
393
452
185 2.
38393
930
620 58.0
373 31.0
481 0.
712.64
626
298 67.4
365
262
2,230
2 ,4
80 903
508 0.
49490
1,24
0486
500 6.
061,
760
272
188
184 20 159
248 0.38
5.58
952,250 1.
4424
6494
1,670
391
225
550
Slope
(ft/
ml)
4.50
80.8 4.50
4.80
6.80
43.2 4.10
4.00
3.40
5.00
5.00
15.4
3.90
76.1
32.3 3.00
3.60
7.50
2.90
3.50
2.80
2.50
4.60
4.90
61.0
42.3 4.21
4.45
5.72
19.5 3.76
34.0
12.4 6.26
21.9 5.17
5.27
106 30.9 7.24
4.11
120 7.
545.
053.67
2.92
5.00
4.22
2-ye
ar
6,000
130
5,35
07.
590
4,360
399
5,430
11,200
7,93
01,960
9,81
02,330
6,580
399
693
7,29
06,
370
2,500
5,46
07,380
28,0
0027
,900
23,300
6,320
142
740
12,300
7,430
6,800
729
14,000 638
9,36
03,650
2,370
4,25
04,820
145
738
2,52
023
,700 392
11,900
10,9
0021,900
7,18
05,700
9,200
Magnitude
of fl
ood
in cu
bic
feet per
second
for
indi
cate
d re
curr
ence
in
terv
al5- year
9,950
239
8,46
011,400
6,98
0800
7,91
020
,100
11,6
003,
470
15,2
004,600
10,1
00495
993
11,000
10,400
4.390
8,840
11,9
0042,100
40,000
39,6
0011,800 316
1,600
22,600
10,6
0011
,600
1,680
24,3
001,
350
16,400
6,37
05,
090
8,48
06,
620
207
1,49
04,
380
37,0
00485
19,9
0019,000
37,600
10,809
10,600
17,2
00
10-y
ear
12,600 317
10,5
0013
,800
8,72
086
09,430
26,3
0013,800
4,520
18,300
6,31
012
,300 577
1,19
013,200
13,0
005,
710
11,1
0014
,800
50,900
47,300
50,6
0015
,900 435
2,32
030,500
12,100
15,100
2,26
031
,600
1,70
021
,500
8,29
07,330
11,700
7,690
248
2,020
5,720
45,8
00 560
25,5
0024
,600
48,600
13,200
14,1
0023
,200
25-y
ear
15,8
00416
12,9
0016
,600
10,8
001,030
11,2
0034
,400
16,4
005,
850
22,2
008,590
15,0
00 689
1,450
15,900
16,2
007,
370
13,800
18,4
0061
,200
55,7
0064
,400
21,7
00 525
3,350
41,2
0013,600
19,6
002,
820
41,300
2,12
028
,000
10,8
0010
,500
16,200
8,92
030
52,
520
7,47
056
,600 665
32,600
32,0
0062,900
21,500
18,8
0031,200
50-year
18,200
489
14,6
0018
,500
12,4
001,460
12,500 -
18,2
006,
820
24,9
00 -16
,800 771
1,660
-18
,500
8,60
015
,700
21,000
68,4
0061
,500
74,400
26,2
00 586
4,190
50,0
00 -23
,000
3,22
048,600
2,420
33,0
0012
,600
13,2
0019
,600
9,740
345
2,88
08,800
64,400 761
37,800
37,500
73,500 -
22,400
37,300
100-year
20.4
00 561
16.2
0020.300
13,9
001,
650
13.6
00 -19
.800
7.78
027
,500 -
18.6
0085
21.
870
-20,600
9.790
17.6
0023,400
75,1
0066.800
84,0
0031
,000 645
5,32
058
,400 -
26.4
003.580
56.0
002.700
38,9
00 - - - - 383
3,220
10,1
0072,000 854
43.0
0043
.000
84.100 -
25,9
0043
,600
Table
2.--
Floo
d-fr
eque
ncy
data for
stre
aaga
ging
atatlona
in Mlaaouri
(con
e.)
Stat
ion
numb
er
0690
2000
0690
2200
0690
2500
0690
2800
0690
4500
06905500
0690
7000
0690
7200
0690
7500
0690
7700
0690
8000
06908300
0690
9500
0690
9700
0691
0000
0691
0250
06910500
0691
8700
0691
9000
0691
9200
0691
9500
0692
0500
0692
1000
06921200
06921500
0692
1740
06922000
06922700
0692
4000
06925200
0692
5300
06926000
06926200
06927000
0692
7100
06928000
0692
8200
0692
8500
0693
0000
06931000
0693
1500
06932000
0693
3500
06934000
0693
5500
0693
5800
0701
1200
0701
1500
07013000
Stat
ion
name
Grand
Rive
r ne
ar Stunner
West Y
ellow
Cree
k ne
ar Brookfield
Hami
lton
Bra
nch
near
New Bos
ton
Onion
Branch a
t St.
Cath
erin
eCh
art ton
River
at Ho
ving
erCh
arit
on R
iver
near Pr
airi
e Hi
llLa
mine
Ri
ver
at Cl
ifto
n Ci
tySh
aver
Cree
k tr
ibut
ary
near C
lift
on Cit
yEast B
ranc
h So
uth
Fork B
lack
wate
r Ri
ver
near Elm
Blackwater Ri
ver
at Valley Cit
yBlackwater Ri
ver
at B
lue
Lick
Trent
Bran
ch n
ear
Wave
r ly
Moni
teau
Creek ne
ar Fa
yett
ePe
tite
Sali
ne Cr
eek Tr
ibut
ary
near
Be Hair
Peti
te Saline C
reek
near
Boonville
Trax
ler
Bran
ch n
ear
Colu
mbia
More
au Ri
ver
near Jefferson
City
Oak
Grove
Branch near B
righ
ton
Sac
River
near St
ockt
onSac
Rive
r tr
ibut
ary
near Cap li
nger
Mil
lsCe
dar
Creek
near Pleasant Vi
ewOsage
River
at O
sceo
laPo
mme
de Terre
River
near B
olivar
Lindiey
Cree
k ne
ar Polk
Pomm
e de Te
rre
River
at He
rmit
age
Brus
hy Cree
k near Bl
airs
town
South
Gran
d Ri
ver
near B
rown
lngt
onCh
ub Creek ne
ar Li
ncol
nNi
angu
a Ri
ver
near Decaturville
Star
ks Cree
k at Pr
esto
n .
Prairie
Bran
ch n
ear
Decaturville
Osage
Rive
r near Ba
gnel
lVan
Cleve Br
anch
nea
r Me
taMa
ries
Ri
ver
at We
stph
alia
Doane
Branch n
ear
King
dom
City
Gasconade
Rive
r at Ha
zelg
reen
Laquey B
ranc
h near Hazelgreen
Gasconade
Rive
r ne
ar W
ayne
avil
leBig
Pine
y Ri
ver
near
Big
Pine
yBe
aver
Cree
k near Ro
lla
Litt
le B
eaver
Cree
k ne
ar Ro
lla
Litt
le Piney
Creek
at Ne
wbur
gGasconade
Rive
r at Je
rome
Gasconade
Rive
r near Rich F
ountain
Lout
re Ri
ver
at Mi
neol
aShotwell Creek
near
El
lisv
ille
Love Cr
eek
near Sa
lem
Green Acre Branch near Ro
lla
Mera
mec
Rive
r near Steelville
Basic
char
acte
rist
ic
Area
Slop*
(mi
) (ft/mi)
6,880
135 2.
511.
041,370
1,87
0598 1.
6516.6
547
1,12
0 0.97
81 0.49
182 0.55
531 1.
301,160 0.
14420
8,22
0225
112
655 1.
151,660 2.86
627 4.18
1.48
14,000 0.
7525
7 0.54
1,25
0 1.56
1,680
560 13.7 6.41
200
2,84
03,180
202 0.
810.89
0.62
781
3.15
3.92
27.0
- 49.3 2.63
2.25
3.60
46.4
22.2 5.05
2.50
69.2 8.47
78.4
6.35
119 4.64
94.2 4.23
149 4.78
1.66
9.00
11.6
4.80
70.8 2.1
40.3 4.7
31 84.1 1.2
95.4 8.91
70.2 3.97
87.4 3.18
5.65
39.5
65.6
14.0
3.01
2.68
10.4
79.5
106 82.0 6.29
Magnitude
of fl
ood
in c
ubic
fe
et pe
r se
cond
for
indicated
recu
rren
ce interval
2- year
51,200
2,800
576
231
9,700
13,400
16,1
00480
2,220
23,600
10,6
00339
2,930
136
3,560
277
13,400 182
19,6
00 478,760
41,600
7,90
06,
820
19,000 498
14,6
00 766
11,700 822
190
70,200 190
11,1
00 111
23,6
00 409
23,400
11,900
1,920
1,240
6,76
031
,700
29,400
7,22
0365
121
306
15,400
5-ye
ar
83,700
4,56
0941
390
15,200
18,800
27,8
00 887
3,67
043
,500
18,100 670
4,620
191
5,460
456
19,600 390
35,6
00 7015
,000
61,7
0011
,800
10,7
0031
,000 768
25,0
001,
360
20,9
001,270
310
95,000 310
15,1
00 185
44,8
00 860
41,2
0020,600
3,11
02,
340
13,4
0055
,500
48,100
11,5
00 520
265
509
27,900
10- y
ear
106.
000
5,740
1,210
494
18,800
22,0
0035
,700
1,07
04,660
58,0
0023
,200 890
5,70
024
26,660
564
23,300 567
47,000 89
19.2
0074
,000
14,2
0014
,900
38,9
00 959
32,2
001,730
27,3
001,
530
425
109,
000
425
17,4
00 233
60,400
1,100
.53
,600
26,4
003,
890
2,430
18,2
0072,000
60,400
14,4
00 617
370
616
36,7
00
25-y
ear
134,000
-1,580
623
23,200
25,8
0045
,700
1,29
05,
890
94,0
0029,600
1,140
7,00
0325
8,080
678
27,600 820
61,6
00 112
24,5
0088
,500
17,1
00 -48
,600
1,140
41,2
002,160
35,6
001,
840
663
125,000
633
20,000 293
80,900
1,320
69,200
33,5
004,
850
5,28
025,100
92,8
0075
,600
17,800 755
505
737
48,1
00
50- ye
ar
154,
000
-1,
780
718
26,400
28,4
0052,900
1,45
0- -
34,3
001,
290
7,92
0408
9,080
755
30,6
001,020
72,5
00 127
28,3
0098
,500
22,1
00 -55
,500
1,28
047
,800
2,430
41,6
002,060
850
136,
000
850
21,7
00 335
96,2
001,490
80,7
0038,500
5,530
6,060
30,300
108,
000
86,4
0020
,200 848
598
818
56,500
100-year
174,
000
-1,
980
809
29,4
0030,800
60,000
1.610
- -38
,900
1,43
0- 504
- 825
-1,
160
83,100 142
32,000
108,
000
- -62
,100
1,40
054
,100
2,700
47,6
002,330
1,11
014
6,00
01,
110
- 376
111,
000
1,64
091,800
43,200 -
6,800
35,4
0012
3,00
096
,700 - 933
671
890
64,7
00
Tab
le 2.~
Flo
od-f
requen
cy d
ata
for
str
eam
ing
sta
tio
n,
in M
isso
uri
(coot.
)
; Basin
characteristic
Stat
ion
*»
"'
numb
er
07014500
07015000
07015500
07015700
07016000
07016500
07017000
07017500
07018000
07018500
07019000
07019100
07021000
07033000
07035500
07037500
07037700
07038000
07041000
07042000
07042500
07043000
07043500
07044000
07046000
07050700
07052500
07053000
07053500
07053950
07054200
07054300
07057500
07058OOO
07058500
07061500
07062500
07063000
07063200
07064300
07064500
07066000
07066500
07067000
07068000
07068200
07068500
07070500
Stat
ion
name
Meramec
Rive
r ne
ar Sullivan
Bour
beus
c River
near
St.
James
Lane
s Fo
rk n
ear
Rolla
Lanes Fork nea
r Vi
chy
Bourbeuse
Rive
r ne
ar Sp
ring
Blu
ffBo
urbe
use
Rive
r at
Union
Meramec
Rive
r at Rob
erts
vill
eDry Br
anch
near Bonne
Terf
eBi
g River
near
DeS
pto
Big
River at
Byr
nesv
ille
Meramec
Rive
r ne
ar Eu
reka
Murphy Bra
nch
near Cr
ysta
l Ci
tyCa
stor
River at
Zalma
Wolf Cr
eek
near Fa
rmin
g ton
Barn
es Cr
eek
near F
redericktown
St.
Francis
Rive
r ne
ar Pat
ters
onClar
k Cr
eek
near Piedmont
Clark
Creek
at Pa
tter
son
Litt
le R
iver
ditch 81 n
ear Re
nnet
tLittle Ri
ver ditch
1 ne
ar K
enne
ttLi
ttle
River di
tch
251
near Li
lbou
rnCa
stor
Riv
er at Aquilla
Litt
le River ditch
1 near Mor
ehou
seLittle River di
tch
251
near K
enne
ttLi
ttle
River ditch 2
59 nea
r Kennet
tJames
Rive
r ne
ar Spr
ingf
ield
Jame
s River
at G
alen
aWhit
e River ne
ar R
eeds S
prin
gWhite
Rive
r ne
ar Branson
Ingenthron Hollow nea
r Fo
rsyt
hYa
ndel
l Br
anch
nea
r Ki
rbyv
ille
Gray Branch
at Lutie
Nort
h Fo
rk Ri
ver
near Tecumseh
Brya
nt Creek nea
r Te
cums
ehNorth
Fork
Ri
ver at
Tec
umse
hBlack
Rive
r near Annapolis
Black
Rive
r at Lee
per
Blac
k River at
Po
plar
Bluff
Pike
Creek
trib
utar
y near P
opla
r Bl
uff
Fudge
Holl
ow nea
r Licking
Big Creek ne
ar Yukon
Jacks
Fork
at Em
inen
ceCurrent
Rive
r ne
ar Emi
nenc
eCurrent
River at
Van Bu
ren
Current
Rive
r at
Doniphan
North
Pron
g Little Black R
iver at Hu
nter
Litt
le Black R
iver nea
r Fairdealing
Elev
en P
oint
River
near
Tho
mas vi
lie
Area
(m
i2)
1,475 21. 0. 24.
608
808
2,670 3.
718
917
3,790 0.
423 40. 4.
956 4. 37.
Ill
235
235
175
450
883 89 246
987
3,62
04,020 0. 0. 0.
561
570
1,157
484
957
1,245 0. 1. 8.
398
1,272
1,667
2,03
8 1.187
361
3 22 1 35 44 3 03 39 5 65 33 23 28 72 36 23
Slope
(ft/mi)
4.89
34.0
41.1
27.0 3.92
2.76
3.83
48.5 4.63
3.36
3.44
108 8.
9219.9
114 7.24
63.9
29.4 1.0
1.0
2.0
0.8
2.0
1.0
1.0
6.5
4.75
3.53
3.36
186
116
279 8.
298.
838.
0410.9
8.52
6.23
111
68.1
55.3 9.50
7.58
5.92
4.75
61.7
10.8
13.7
2-ye
ar
18,600
3,440 71.5
3,88
014,900
13,700
38,7
00 660
17,100
14,9
0037,000 130
11,000
3,410
929
32,200 753
6,08
01,
730
4,07
02,
520
2,230
5,21
08,850
1,76
09,910
18,1
0071
,200
34,300 197
65.1
50
11,6
0012,000
15,700
19,200
18,700
11,000 124
100
1,750
10,200
22,4
0025,900
25,400 130
6,600
4,900
Magn
itud
e fo
r5-
year
31 5 5 22 20 621
26 22 61 20 5 2491 8 2 6 3 3 7 12 2 17 31 114 76 19 19 32 31 38 20 2 19 42 48 45 13 11
,800
,390 121
,740
,000
,000
,800
,290
,000
,500
,200
221
,600
,570
,040
,800
,230
,530
,660
,290
,160
,220
,080
,200
,780
,500
,100
,000
,300
360
158 97.5
,300
,400
,400
,600
,700
,800
210
360
,950
,700
,800
,200
,300
245
,400
,600
of flood
in c
ubic f
eet
per
seco
nd
indicated recurrence i
nter
val
10-year
9*_.«.
40,800
6,650
152
6,870
26,4
0023
,900
78,7
001,700
31,6
0027,300
77,400 300
27,5
007,
000
2,85
061,000
1,680
9,99
03,
240
7,700
3,520
3,810
8,17
014,200
3,43
022
,800
40,0
0014
2,00
011
1,00
048
1224
132
24,5
0024
,300
45,4
0039
,800
54,3
0028
,000 252
600
3,650
26,800
57,7
0064
,300
59,4
00 355
18,4
0017
,200
25-y
ear
52,000
8,15
0193
8,200
31,500
28,4
0010
1,00
02,
220
38,2
0032,900
97,4
00435
36,600
8,740
3,56
074
,300
2,40
0 3,
940
9,38
03,
900
4,500
9,39
016
,500
4,210
29,500
51,000
177,
000
159,
000
598
318
178
30,900
30,3
0063
,000
49,9
0075
,500
37,400 305
970
4,510
36,2
0077
,400
85,300
77,3
0056
525,800
25,300
50- ye
ar
60,000
9,210
218
9,120
35,0
0031
,400 -
2,55
042
,800
36,800
112,000
572
43,3
00 -4,
040
83,7
002,
940
-4,420
10,6
004,160
4,960
10,2
00 1
8,00
04,760
-59
,300 -
19,8
00 679
394
212
35,5
0034
,600
76,7
0057
,100
92,0
0044
,500 342
1,30
05,120
43,3
0092
,200
101,000
90,5
00 795
31,2
0032
,000
100-year
68,000 - 240
9,970
38,300
34,3
00 -2,820
-40
,500
125,
000
732
50,0
00 -4,510
92,5
003,500
-4,880
11,7
004,380
5,400
11,0
0019
,400
5,290
-67,200 - 238
757
474
245
39,9
0038
,600 -
64,000 -
51,6
00 376
1,62
05,710
50,4
00107,000
116,
000
103,
000
1,100
- -
Tab
le
2. F
loo
d-f
req
uen
cy d
ata
for
atre
aaga
gin
g t
ati
on
*
in M
iaao
uri
(cen
t.)
Stat
ion
numb
erSt
atio
n na
me
Baai
n ch
arac
teri
stic
AreaSlope
( i2)______(t
t/mL
)
Magnitude
of fl
ood
in c
ubic
feet pe
r se
cond
for
indi
cate
d recurrence interval
2-ye
ar5-
year
10-y
ear
25-y
ear
50-y
ear
100-year
07071500
Elev
en P
oint Ri
ver
near B
ardl
ey07185500
Stah
l Creek
near M
iller
07185700
Spri
ng River
at L
arua
aell
07186000
Spri
ng River
near Vac
o07187000
Shoe
l Cr
eek
abov
e Jo
plin
07188500
Lost
Cre
ek at
Seneca
07198000
Elk
River
near T
iff
City
793 3.
86306
1,164
410 42.0
872
10.1
41.3 9.84
6.08
8.34
23.6 7.09
8,880
637
4,980
17,1
008,240
843
20,900
19,500
1,12
08,470
30,0
0016,800
2,73
041,600
28,1
001,140
10,800
38,9
0023,300
4,71
057
,400
40,2
001,
820
50,2
0032
,200
8,02
078,400
49,700
2,090
58,5
0039
,000
11,000
94,5
00
56,6
002.
340
66,5
0045
,900
111,
000
ANALYSIS
Basic Data
Streamflow and basin characteristics from a network of 152
stations were used in this analysis and are listed in table 2.
Their distribution throughout the State is shown in figure 7.
The data set does not contain information on small-area stations
(drainage areas less than 10 mi2 [26 km2 ]) with flat slopes as
experienced in the Lowlands or Bootheel region due to the diffi
culty in establishing stage-discharge relationships. Drainage
area sizes range from 0.1 to 14,000 mi2 (0.26 to 36,300 km2 ).
Determination of Basin Characteristics
Basin characteristics used in describing the magnitude and
frequency of flooding are: 1) drainage area (A) which can be
described as all contributing drainage upstream from a desired
point along a river channel, and 2) average main-channel slope (S).
Average main-channel slope was.determined from elevations at points
10 and 85 percent of the distance along the channel from the gaging
station to the divide.
Determination of Estimating Relations
Relationships developed herein were determined by the step-
backward multiple regression technique. Streamflow characteristics
(2-, 5-, 10-, 25-, 50-, and 100-year flood) or dependent variables
were related to basin characteristics.
17
First attempts of the regression computation indicated
drainage area and average main-channel slope to be significant
independent variables in the equation Q *aAbl Sb2 .
However, a plot of the logarithms of the residual
[(log QT (observed) - log QT (computed)] versus the logarithms
of the slope and drainage area indicated nonlinearity.
The basic regression model was again fitted to the array
by adjusting the exponent to drainage area based on techniques
described by Creager, Justin, and Hinds in their report
"Engineering for Dams" (1947). Several attempts were made until
the adjustment could be made which would result in the least
standard error for the equation Q =aA * S 2 and linearity in the
area component could be obtained. The same residuals (computed
with the adjusted relationship) were plotted on a map of the State
to determine any graphic trend. Results showed a random scatter
throughout the State thus indicating the relationships to be
applicable statewide.
SUMMARY
Techniques for estimating magnitude and frequency of floods
at ungaged Missouri streams given in this report utilize the basic
linear regression model with adjustments to independent variable
components to achieve linearity. Drainage area and slope proved
to be significant basin characteristics and were used in defining
the relationships. A plot of residuals on a map indicates state
wide applicability of the equations.
18
REFERENCES
Creager, W. P., Justin, J. D., and Hinds, J., 1947, Engineering
for dams, volume I: New York, John Hiley, p. 125-126.
Dawdy, D. R., Lichty, R. W., and Bergmann, J. M., 1972, A
rainfall-runoff simulation model of estimation of flood
peaks for small drainage basins: U.S. Geol. Survey Prof.
Paper 506-B, 28 p.
Matthai, H. P., 1968, Magnitude and frequency of floods in the
United States, Part 6B, Missouri River below Sioux City,
Iowa: U.S. Geol. Survey Water-Supply Paper 1680, 491 p.
Patterson, J. L., 1964, Magnitude and frequency of floods in
the United States, Part 7, Lower Mississippi River basin:
U.S. Geol. Survey Water-Supply Paper 1681, 636 p.
Patterson, J. L., and Gamble, C. R., 1968, Magnitude and frequency
of floods in the United States, Part 5, Hudson Bay and Upper
Mississippi River basins: U.S. Geol. Survey Water-Supply
Paper 1678, 546 p.
Sandhaus, E. H., and Skelton, John, 1968, Magnitude and frequency
of Missouri floods: Missouri Geol. Survey and Water Resources
rept. 23, 276 p.
Searcy, J. K., 1955, Floods in Missouri, magnitude and frequency:
U.S. Geol. Survey Circ. 370, 126 p.
Skelton, John, and Homyk, Anthony, 1970, A proposed streamflow
data program for Missouri: U.S. Geol. Survey open-file
rept., 77 p.
19
U.S. Water Resources Council, 1967, A uniform technique for
determining floodflow frequencies: U.S. Water Resources
Council Bull. 15, 15 p.
*U. S. GOVEMWENT PRINTIM OFFICE: 1974-447W/7
20