TECHNIQUES FOR ESTIMATING MAGNITUDE

AND FREQUENCY OF FLOODS IN MINNESOTA

U. S. GEOLOGICAL SURVEY

Water-Resources Investigations 77-31

Prepared in cooperation with the

Minnesota Department of Transportation, Division of Highways

and

Minnesota Department of Natural Resources, Division of Waters

BIBLIOGRAPHIC DATA 1. Report No. 2. SHEET

4. Title and Subtitle

TECHNIQUES FOR ESTIMATING MAGNITUDE AND FREQUENCY OF FLOODS IN MINNESOTA

7. Author(s)

Lowell C. Guetzkow9. Performing Organization Name and Address

U.S. Geological Survey, Water Resources Division Room 1033 Post Office Building St. Paul, Minnesota 55101

12. Sponsoring Organization Name and Address

U.S. Geological Survey, Water Resources Division Room 1033 Post Office Building

St. Paul, Minnesota 55101

3. Recipient's Accession No.

5. Report Date

May 19776.

8. Performing Organization Rept.

No - USGS/WRI 77-3110. Project/Task/Work Unit No.

11. Contract/Grant No.

13. Type of Report & Period Covered

Final14.

15. Supplementary Notes Prepared in cooperation with Minnesota Department of Transportation, Division of Highways and Minnesota Department of Natural Resources, Division of Waters.________________________________________________

16. Abstracts Estimating relations have been developed to provide engineers and designers with improved techniques for defining flow-frequency characteristics to satisfy hydraulic planning and design requirements. The magnitude and frequency of floods up to the 100-year recurrence interval can be determined for most streams in Minnesota by methods presented. By multiple regression analysis, equations have been developed for estimating flood-frequency relations at ungaged sites on natural flow streams. Eight distinct hydrologic regions are delineated within the State with boundaries defined generally by river basin divides. Regression equations are provided for each region which relate selected frequency floods to significant basin parameters. For main-stem streams, graphs are presented showing floods for selected recurrence intervals plotted against contributing drainage area. Flow-frequency estimates for intervening sites along the Minnesota River, Mississippi River, and the Red River of the North can be derived from these graphs. Flood-frequency characteristics are tabulated for 201 paging statiqns having 10 or more years of record._________________________17. Key Words and Document Analysis. I7a. Descriptors

* Frequency analysis, * Regression analysis, * Regional analysis,* Flow characteristics, * Estimating equations, Design flow, Regional

flood, Small watersheds, Floods, Hydraulic design, Natural flow, Hydrologic data, Peak discharge, Probability, Statistical methods.

I7b. Identifiers/Open-Ended Terms

* Flood frequency, * Minnesota, Recurrence interval, Ungaged watersheds.

17c. COSATI Field /Group

is. Availability Statement NO restriction on distribution. This report may be purchased from:

National Technical Information Service ____Springfield. Virginia 22161__________

19. Security Class (This Report)

UNCLASSIFIED20. Security Class (This

Page ___ UNCLASSIFIED

21. No. of Pages

37

22. Price

FORM NTis-33 (REV. 10-73) ENDORSED BY ANSI AND UNESCO. THIS FORM MAY BE REPRODUCED USCOMM-DC 8205-P74

TECHNIQUES FOR ESTIMATING MAGNITUDE

AND FREQUENCY OF FLOODS IN MINNESOTA

By Lowell C. Guetzkow

U. S. GEOLOGICAL SURVEY

Water-Resources Investigations 77-31

Prepared in cooperation with the

Minnesota Department of Transportation, Division of Highways

and

Minnesota Department of Natural Resources, Division of Waters

May 1977

UNITED STATES DEPARTMENT OF THE INTERIOR

CECIL D. ANDRUS, Secretary

GEOLOGICAL SURVEY

V. E. McKelvey, Director

For additional information write to:

U.S. Geological Survey 1033 Post Office Building St. Paul, Minnesota 55101

CONTENTS

Abstract ...................... 1Introduction .................... 2

Purpose and scope ............... 2Previous reports ............... 3Gaging-station numbering system ........ 3Cooperation .................. 3Use of metric units .............. 3

Estimating flood frequency ............. 4Transfer of defined flood characteristics ... 4Regional analysis for ungaged sites ...... 13Illustrative examples ............. 18Main-stem streams ............... 20Accuracy and limitations ........... 24

Analytical techniques ............... 27Data used ................... 27Flow-frequency analysis at gaging stations . . 27Multiple-regression model ........... 28Basin characteristics investigated ...... 31

Summary ...................... 31References ..................... 33

ILLUSTRATIONS

Figure 1. Map of Minnesota showing location ofgaging stations and hydrologic regionsused in regression analysis ....... 16

Figure 2. Relation of flood magnitudes for selected recurrence intervals to drainage area, Minnesota River main stem ........ 21

Figure 3. Relation of flood magnitudes for selected recurrence intervals to drainage area, Mississippi River main stem ....... 22

Figure 4. Relation of flood magnitudes for selected recurrence intervals to drainage area, Red River of the North main stem .... 23

Figure 5. Graphical interpretation of standarderror of estimate for 10-year flood inRegion G ................ 25

Figure 6. Flood frequency curve for East BranchBlue Earth River near Bricelyn, Minnesota 29

111

TABLES

Table 1. Conversion factors ...........Table 2. Flood-frequency and basin characteristics

for gaging stations in Minnesota .... Table 3. Regional flood-frequency equations . . . Table 4. Standard error of estimates for

defined relations ........... 26

IV

TECHNIQUES FOR ESTIMATING MAGNITUDE AND FREQUENCY OF FLOODS IN MINNESOTA

By Lowell C. Guetzkow

ABSTRACT

The magnitude and frequency of floods up to the 100-year recurrence interval can be determined for most streams in Minnesota by methods presented in this report. By multiple regression analysis, equations have been developed for esti­ mating flood-frequency relations at ungaged sites on all natural flow streams which are not significantly affected by man-made regulation, diversion, or urbanization. Eight distinct hydro- logic regions are delineated within the State with boundaries defined generally by river basin divides. In a few instances the regional divides were based on topographic or geologic con­ siderations. Regression equations are provided for each region which relate the 2-, 5-, 10-, 25-, 50- and 100-year floods to significant basin parameters. In four regions, drainage area, slope, and storage are used as estimating variables; in two regions, drainage area and slope are used; and, in the remaining two regions, only the drainage area is used as the significant variable. Accuracy of resulting frequency estimates and limita­ tions on the use of the equations are discussed.

For main-stem streams, which traverse regional divides and which may be affected by regulation, graphs are presented show­ ing floods for selected recurrence intervals plotted against contributing drainage area. Flow-frequency estimates for inter­ vening sites along the Minnesota River, Mississippi River, and the Red River of the North can be derived from these graphs.

Flood-frequency characteristics are tabulated for 201 gag­ ing stations having 10 or more years of record. These frequency data may provide the best estimates of floods for the specified streams at sites in the vicinity of the gaging station.

INTRODUCTION

A reliable estimate of the magnitude and frequency of floods is essential to the efficient design of bridges, cul­ verts, dams, and other hydraulic structures. In more recent years, the need for flow-frequency estimates has greatly expand­ ed through implementation of the State Flood Plain Management program and the Federal Flood Insurance Act.

Purpose and Scope

The purpose of this report is to provide engineers and designers with improved techniques for estimating flow-frequency relations for most streams in Minnesota. Regression equations are presented for estimating the magnitude of floods having re­ currence intervals ranging from 2 to 100 years at ungaged sites on streams which are not -significantly affected by man-made reg­ ulation, diversion, or urbanization. The .equations apply to natural flow streams of all sizes with the exception of the main stems of the Minnesota River, Mississippi River and Red River of the North. Input to the equations requires only the measurement of selected basin characteristics which can be obtained from topographic maps of the basin under consideration.

Individual graphs are presented for the main-stem streams noted above from which selected frequency floods can be deter­ mined at ungaged sites on the basis of contributing drainage area. The effects of regulation were included in these analyses where applicable and no further adjustment is required if the degree of regulation remains unchanged.

Flood-frequency data for 201 gaged sites on natural flow streams are tabulated for use in defining flood-frequency char­ acteristics at upstream or downstream locations. These data may be transferred by drainage area ratio and can provide an alternative to computation of flood frequency by regression equation.

Recurrence interval is the average interval of time, in years, within which the given flood magnitude can be expected to be exceeded once. It is the inverse of probability; thus a flood having an exceedance probability of 5-percent would have a 20-year recurrence interval, and a flood having an exceedance probability of 1-percent would have a 100-year recurrence interval.

Flow-frequency estimating methods for Minnesota presented in this report supersede those in earlier publications of the U.S. Geological Survey and the Minnesota Department of Conser­ vation.

Previous Reports

Previous reports by Prior (1949) , Prior and Hess (1961) , Wiitala (1965), and Patterson and Gamble (1968), also provided flood-frequency estimating techniques-. Considerable flood data have become available since these analyses were prepared by the accumulation of additional years of record for established gaging stations, and by expansion of the gaging network through installation of crest-stage stations on small watersheds. The latter program made possible the definition of flood character­ istics over a larger range in drainage area size. The addi­ tional data base and improved analytical methods warrant greater confidence in the estimates derived from the techniques provided in this report than the estimates based on previous studies.

Gaging Station Numbering System

Each gaging station has been assigned a unique number in downstream order in accordance with the permanent numbering system adopted by the U.S. Geological Survey. Stations are numbered in a downstream direction along the main stream, and stations on tributaries between main-stream stations are num­ bered in the order they enter the main stream. Stations on other ranks of tributaries are treated in the same manner. The complete 8-digit station number, such as 05134200, includes the major basin part number "05" and a 6-digit station number.

Cooperation

The frequency analyses in this report were based on data collected and published by the U.S. Geological Survey as part of cooperative programs with various State and Federal agencies. The report was prepared as part of cooperative programs with the Minnesota Department of Transportation, Division of Highways and the Minnesota Department of Natural Resources, Division of Waters. Opinions, findings, and conclusions expressed in this publication are those of the U.S. Geological Survey and not necessarily those of any cooperating agency.

Use of Metric Units

The analyses and data compilations in this report are based on English units of measurement. Equivalent metric units (SI) are given in the text. Space limitations precluded the use of a dual system of units in the tables and only English units are shown. Metric units can be obtained by use of the conversion factors in table 1.

Table 1.--Conversion factors

The following factors may be used to convert English units published herein to the International System of units (SI).

Multiply English units By To obtain SI units

Feet (ft)

Miles (mi)

Square miles (mi 2 )

Cubic feet per second (ft 3 /s)

.3048

1.609

2.590

.02832

meters (m)

kilometers (km)

square kilometers (km2 )

cubic meters per second (m3/s)

Feet per mile (ft/mi) .1894 meters per kilometer(m/km)

ESTIMATING FLOOD FREQUENCY

It is generally accepted that the most reliable estimates of flood characteristics are those based on a frequency analysis of recorded floods at the site under consideration. Usually such records are not available and estimates must be obtained by transfer of flow-frequency data from gaged sites to the site being investigated, or must be computed from generalized flood- frequency relations.

Transfer of Defined Flood Characteristics

The flood characteristics defined by frequency analyses of gaging-station records listed in table 2 may provide the basis for satisfactory estimates at ungaged locations near the sta­ tion, particularly where long-term records are available. Location of gaging stations for which frequency relations are presented are shown in figure 1. Where the period of record is short, flow-frequency estimates based on regional relations would likely provide more reliable results. Transfer of defined flow-frequency data to upstream or downstream sites on the same stream should be accomplished by an adjustment factor derived from drainage area ratio. Frequency data can be transferred

Table

2.-

-Flo

od

-fre

qu

en

cy and

basin

ch

ara

cte

ristics f

or

gagin

g sta

tions

in M

inn

eso

ta

Map

No. 1 2 3 4 5 6 7 8 9 10

i I' 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Stat

ion

numb

er

04010500

04011370

04012500

0401

3100

04013200

04014500

04015150

04015200

04015300

04015360

0401

5370

0401

5400

0401

6500

0401

7000

0401

9000

0401

9500

0402

4100

0402

4110

0402

4200

0503

0000

0504

0500

0504

9000

0506

0800

0506

1000

05061200

0506

1400

0506

1500

0506

2000

0506

2280

0506

2470

Stat

ion

name

Pige

on Riv

er a

t Mi

ddle

Fa

lls,

ne

arGr

and

Port

age,

MN

Litt

le D

evil Tr

ack Ri

ver ne

ar G

rand

Mara

is,

MNPo

plar

Riv

er a

t Lu

tsen

, MM

Lake S

uperior

tributary near

Tac

onit

eHa

rbor

, MN

Caribou Ri

ver near L

ittl

e Marais,

MNBaptism

Rive

r near B

eave

r Bay, MN

Crow Cre

ek n

ear

Silv

er C

reek,

MNEn

camp

ment

Riv

er t

ributary a

t Silver

Creek, MN

Litt

le S

tewa

rt R

iver

near Two

Harbors, MN

Lake S

uper

ior

tributary

No.

2 at

French R

iver,

MMTalmadge R

iver

at

Dulu

th,

MNMiller C

reek

at

Dulu

th,

MMSt.

Loui

s Ri

ver

near Aur

ora,

MN

Emba

rras

s Ri

ver

at E

mbarrass,

MNWest Two

Riv

er near

Iron J

unction, MM

East

Swan River near T

oivo

la,

MMRock Cre

ek nea

r Bl

ackh

oof,

MN

Rock

Cre

ek t

ribu

tary

nea

r Bl

ackh

oof,

MMSo

uth

Fork N

emad

ji R

iver

nea

rHolyoke, MN

Otte

r Ta

il Ri

ver

near D

etro

it L

akes,

MNPe

lica

n Ri

ver

near F

ergus

Fall

s, M

NMustinka R

iver' ab

ove

Whea

ton,

MN

Buffalo

Rive

r near C

all away,

MNBuffalo Ri

ver ne

ar Haw

ley,

MN

Whis

key Creek

at B

arne

svil

le,

MMHa

y Cr

eek

abov

e Do

wner

, MN

Sout

h Br

anch

Buf

falo

Riv

er a

tSab i

n, MN

Buff

alo

Rive

r ne

ar O

il wo

rth, M

MMo

squi

to C

reek

nea

r Ba

gley

, MN

Marsh Cr

eek

trib

utar

y near

Mahnomen,

MN

Drainage

area

(mi2

)

600 7.

4911

4 1.56

22.7

140 1.

07

0.96

5.54

1.41

5.79

4.92

312 93.8

68.4

112 4.

94

0.20

19.4

270

482

834, 94.5

322 25.3 5.81

522

1,040 3.

98

11.9

Slop

e (ft/mi)

1310

51.4

25.0

226 52.6

57.6

108

183 53.8

144 92.7

28.0 9.8

4.9

10.8

11.2

41.7

90.9

36.8 3.4

3.1

0.7

6.03

8.1

18.6

16.0

13.8 9.7

11.4 4.01

Sto­

ra

ge %

14 10 7.9

7.7

7.0

4.4

19 0 3.2

0 3.1

7.5

29 28 2.1

42 0 0 7.6

22 248.5

27 5.2

8.7

2.2

1.7

2.5

3.0

4.8

Discharge, in

ftVs, for

indicated

recurrence

intervals

Q2 4,550

140

827 90 622

2,470 44 57 190

135

299

209

1,540

571

557

1,140

447 16 810

168

283

799

227

646

144 57

1,250

1,180 31 92

Q5 6,76

0

279

1,200

194

1,030

3,920 80 107

290

278

514

337

2,430

994

739

1,48

083

9 28

1,44

0

258

436

2,200

379

1,110

267

172

2,670

2,880 59 247

Q10

8,320

400

1,45

0

291

1,350

4,980

110

150

362

406

682

427

3,090

1,330

857

1,700

1,150 38

1,92

0

320

545

3,540

489

1,450

365

305

3,900

4,59

0 80 406

Q25

10,400 587

1,780

448

1,780

6,440

154

213

458

608

922

546

3,980

1,810

1,000

1,960

1,590 51

2,590

399

693

5,700

637

1,920

503

565

5,760

7,540

112

677

Q50

12,000 752

2,030

592

2,140

7,600

191

268

533

790

1,120

, 637

4,700

2,210

1,110

2,150

1,950 61

3,130

458

809

7,700

751

2,290

615

840

7,370

10,400 137

933

Q100

13,600 940

2,280

760

2,520

8,82

023

2

330

611

999

1,340

730

5,450

2,650

1,220

2,340

2,340 71

3,690

518

930

10,000 869

2,670

734

1,200

9,150

13,900 165

1,240

Year

s of

re

cord

46 14 31 11 14 39 15 15 15 11 11 15 28 22 14 15 13 14 14 34 30 36 15 26 14 14 26 40 14 14

Tab

le 2

. F

loo

d-f

req

ue

nc

y

an

d

ba

sin

ch

ara

cte

risti

cs f

or

ga

gin

g

sta

tio

ns

in M

inn

eso

ta C

on

tin

ued

Map

No. 31 32 33 34 35 36 37 38 39 40

, « 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

Station

number

0506

2500

0506

2700

05062800

0506

3200

0507

3600

0507

3750

0507

3800

0507

6000

0507

6600

0507

7700

0507

8000

0507

8100

0507

8180

0507

8200

0507

8400

0507

8500

0507

9000

05087500

0509

4000

05095500

05104500

05106000

05107000

0510

7500

0512

5500

0512

6000

0512

6500

0512

8500

0512

8700

Station

naae

Wild Ric

e Ri

ver

at T

win Va

lley

, MN

Wild Ric

e River

tributary

near

Twin

Val

ley,

MN

Coon

Creek near Twin Val

ley,

MN

Spri

ng C

reek

tri

buta

ry nea

r Ogema,

MNSouth

Branch B

attle

Rive

r at

Nort

home

, MN

Spring C

reek nea

r Bl

ackd

uck,

MN

Perry

Creek

trib

utar

y ne

arSh

ocks

, MN

Thief River

near Thi

ef River

Fall

s, MN

Red

Lake

River tributary ne

arTh

ief River

Falls, MN

Ruffy

Brook near G

onvick,

MNClearwater R

iver a

t Plummer, MN

Lost

River a

t Go

nvic

k, MN

Silv

er C

reek nea

r Cl

earb

rook

, MN

Silv

er C

reek tributary

atClearbrook,

MNClearwater Riv

er tr

ibut

ary

near

Plummer, MN

Clearwater Riv

er a

t Red Lake

Fall

s, MN

Red

Lake

Riv

er a

t Cr

ooks

ton,

MNMi

ddle

Riv

er at Arg

yle,

MN

South

Branch T

wo R

ivers

at La

keBronson, MN

Two

Rive

rs be

low

Hal lo

ck,

MNRoseau River b

elow South F

ork

near M

alun

g, MN

Spra

gue

Cree

k near S

prague,

Manitoba

Pine

Creek near

Pine C

reek

, MN

Roseau River a

t Ro

ss,

MNStony River

near

Isabella,

MNDunka

River

near B

abbitt, W

Bear

Is

land

Riv

er n

ear

Ely,

MN

Pike

River n

ear

Embarrass, MN

Pike

River tributary

near W

ahlsten,

MN

Drainage

area

(mi2)

888 4.

7250.8 4.99

2.80

7.96

1.14

959 2.

3345.2

512 53.6 4.96

6.02

6.51

1,370

5,28

026

5

444

644

573

169 74.6

1,220

180 53.0

68.5

115 1.

93

Slop

e (ft/mi)

7.2

17.9

15.2

20.2 9.72

13.1

10.5 1.0

5.71

13.0 4.4

12.2

39.6

36.4 8.31

4.6

2.2

7.5

3.2

5.4

5.3

6.9

11.0 3.7

12.6

18.8 2.6

12.1

18.1

Sto­

rage

% 7.0

3.0

1.5

21 14 15 51 31 0 24 12 18 15 8.8

1.5

7.3

24 7.5

8.3

8.5

6.5

20 1.3

12 19 32 26 23 36

Disc

larg

e, in

ft'

/s,

for

indi

cate

d recurrence

inte

rval

sQ2 1,170 76 630 59 49 84 33

1,34

0 74 216

1,39

0136 51 59 62

2,83

06,650

843

1,14

0906

1,590

595

279

1,540

835

348

199

802 40

Q5 2,37

0

189

1,30

0 83 88 167 56

2,450

121

374

2,34

025

010

0

101

125

5,08

012,300

1,770

2,420

1,84

0

3,21

01,

220

531

2,720

1,33

049

8326

1,31

0 70

Q10

3,37

0

298

1,77

0 98 118

240 73

3,300

154

492

3,030

338

139

132

176

6,81

016,700

2,570

3,530

2,610

4,340

1,680

730

3,62

01,670

595

417

1,67

0 92

Q25

4,86

0

475

2,43

0

117

160

350 95

4,60

0

199

654

3,970

463

196

174

252

9,210

22,600

3,770

5,21

03,760

5,73

02,280

1,010

4,85

02,130

715

539

2,14

0

122

Q50

6,11

0

637

3,00

0

131

194

447

113

5,550

233

781

4,69

056

3243

207

316

11,100

27,000

4,80

0

6,65

04,730

6,690

2,77

01,240

5,84

02,470

803

632

2,510

146

Q100

7,48

0

826

3,55

0

145

229

555

131

6,70

0

269

914

5,450

670

294

240

385

13,2

0031,000

5,94

0

8,24

05,790

7,59

03,250

1,480

6,87

02,820

889

728

2,88

0

171

Year

s of

record

49 14 13 12 15 15 15 59 13 10 32 13 15 15 12 44 67 21 33 11 41 42 25 42 12 11 10 12 14

O\

Tab

le 2

.~F

loo

d-f

req

uen

cy

an

d

basin

c

ha

rac

teri

sti

cs

fo

r g

ag

ing

s

tati

on

s

in M

inn

eso

ta C

on

tin

ued

Map

No. 60 61 62 63 64 65 66 67 68 69 70 71 72 73

, 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89

Stat

ion

nunber

0512

9000

0513

0300

0513

0500

0513

1000

0513

1500

0513

2000

0513

4200

0513

9500

0514

0000

0514

0500

0521

0200

0521

6980

0521

7000

0521

7700

0524

4000

0524

4100

0524

4200

0526

7800

0526

7900

0527

0300

0527

0310

05270500

05271800

0527

2000

0527

2300

05273700

05274200

0527

5000

0527

6000

0527

6100

Station

name

Verm

ilio

n Ri

ver be

low Ve

rmil

ion

Lake

, near Tower,

MMBoriin Cre

ek n

ear

Chisholm,

MNSt

urge

on Riv

er nea

r Ch

isho

lm,

MVDark R

iver nea

r Ch

isho

lm,

MNLittle Fo

rk R

iver a

t Littlefork,

MMBig

Fork R

iver a

t Bi

g Falls, MM

Rapi

d River near B

audette, MN

War r

oad River near War

road

, MN

Bulldog Run near War

road

, MM

East

Branch Wa

rroa

d Ri

ver near

Warr

oad,

MN

Smit

h Cr

eek ne

ar Hil

l Ci

ty,

MNSw

an R

iver tributary

at W

arba

, MN

Swan

River near Wa

rba,

MN

Bluff Cr

eek near Jac

obso

n, MN

Crow Wing

Rive

r at N

imro

d, MN

Kitten C

reek

nea

r Sebeka,

MNCat

River near N

imrod, MN

Big

Mink Cre

ek tributary near

Last

rup,

MN

Hillman

Cree

k near P

ierz,

MNSa

uk R

iver t

ributary a

t Spring

Hill

, MN

Sauk R

iver

tributary N

o.

2 near

St.

Mart

in,

MNSauk R

iver near

St.

Cloud, MN

Johnson Creek

tributary

atLu

xemb

urg,

MN

Johnson

Cree

k tributary

No.

2 near

St.

Augu

sta,

MM

John

son

Cree

k near S

t. Au

gust

a, MN

Otsego C

reek n

ear

Otse

go,

MMStony

Brook

tributary near F

oley,

MMElk

River ne

ar B

ig L

ake,

MM

North

Fork

Crow

Rive

r near R

egal ,

MMNo

rth

Fork C

row Ri

ver

tributary

near P

ayne

svil

le,

MM

Drai

nage

ar

ea(«i2

)

483 13.7

187 50.6

1,730

1,46

0543

162 11.1

45.8 8.00

3.95

254 1.

501,

010 14.7

49.2 1.53

46.7 7.06

0.24

925 3.

82

13.4

46.7 3.11

2.26

615

215 0.

55

Slope

(ft/mi)

2.8

13.8 9.6

16.2 2.2

1.9

2.7

6.3

8.0

6.2

41.9

15.9 5.1

12.7 3.8

15.4 6.90

24.9 9.53

16.8

78.4 2.3

7.38

16.6

15.4

24.1

10.7 4.7

5.1

48.1

Sto­

rage %

23 20 11 10 17 19 78 59 9.0

47 20 24 15 27 11 4.5

15 10 20 2.4

2.5

4.3

14 4.3

2.4

2.3

8.8

1.3

7.9

1.6

Disc

harg

e, in f

t*/s

, for

indi

cate

d recurrence

inte

rval

sQ2 1,10

021

81,090

343

9,210

5,18

02,930

603

161

386

111 34 718 33

1,26

011

8258 13 766

166 19

1,400 31 71 222 78 40

1,630

825 16

Q5 1,57

037

41,

630

550

13,900

8,960

4,82

01,230

334

753

234 50 949 53

1,91

0223

404 32

1,76

0

254 34

2,920 58 133

404

176 84

3,300

1,260 35

Q10

1,88

0491

2,02

070

417

,200

11,8

006,

100

1,770

482

1,050

328 60

1,090 67

2,350

306

506 49

2,55

0

315 47

4,230 79 182

546

266

121

4,65

0

1,55

0 51

Q25

2,260

649

2,520

917

21,200

15,6

007,

700

2,56

070

2

1,48

045

3 741,260 83

2,91

0424

638 76

3,640

392 64

6,20

0

110

251

744

406

177

6,60

0

1,93

0 77

Q50

2,540

774

2,920

1,090

24,3

0018

,700

8,80

03,230

890

1,84

054

7 831,

380 94

3,330

521

738

101

4,47

0

450 78

8,00

0

135

308

904

529

224

8,20

0

2,210

100

Q100

2,82

0904

3,330

1,27

027

,400

21,8

0010

,000

3,960

1,10

0

2,23

0640 93

1,49

010

43,740

625

839

129

5,31

0

509 93

10,000 161

368

1,07

0669

276

10,0

00

2,490

125

Year

s of

reco

rd

48 16 28 24 50 45 14 25 10 13 14 14 16 14

-45 14 14 14 11 15 14 44 11 10 11 11 15 46 11 15

Tab

le 2

. F

loo

d-f

req

uen

cy a

nd

b

as

in

ch

ara

cte

risti

cs f

or

ga

gin

g s

tati

on

s in

Min

ne

so

ta ~

Co

nti

nu

ed

Map

No. 90 91 92 93 94 95 96 97 98 99 100

oo 101 102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

Station

number

0527

8000

0527

8350

05278500

0527

8700

0527

8750

0527

8850

0527

9000

05280000

0528

0300

0528

4100

0528

4600

0528

4620

0528

4920

05286000

05289500

0529

0000

0529

1000

05293000

05294000

05299100

05300000

05301200

0530

2970

0530

3450

05304500

0530

5200

0531

1200

Station

name

Middle F

ork

Crow

River nea

r Spicer,

MNFo

unta

in C

reek

near

Montrose,

MNSouth

Fork

Cro

w River

at Cosmos,

MNOt

ter

Creek

near L

ester Pr

airi

e, MN

Otte

r Creek

tributary ne

ar L

este

rPr

airi

e, MN

Buffalo

Creek

tributary near

Brown t

on,

MNSouth

Fork

Crow Ri

ver ne

ar M

ayer,

MNCrow R

iver a

t Ro

ckfo

rd, MN

School Lake C

reek

tri

buta

ry nea

rSt

. Mi

chae

l, MN

Mille

Lacs

La

ke tr

ibut

ary

near

Wealthwood,

MNRo

bins

on B

rook n

ear On

amia

, MN

Rum River

trib

utar

y near Ona

mia,

MN

Stan

chfi

eld

Creek

trib

utar

y near

Day, VK

Rum

River near S

t. Francis, MN

Minnehaha

Creek

at Minnetonka

Mills, W

Litt

le M

inne

sota

River near

Peever,

SDWhetstone

River

near

Big

Stone C

ity,

SDYe

llow Ban

k River near Odessa, MN

Pomme

de T

erre R

iver

at Ap

plet

on,

MNLa

zaru

s Creek

tributary near C

anby,

MNLa

c qui

Parl

e River ne

ar Lac q

uiParle, MN

Minn

esot

a River

tributary near

Montevideo,

MNOutlet C

reek tr

ibut

ary near

Starbuck,

MNHassel Creek

near

Clontarf

, MN

Chip

pewa

River nea

r Milan, MN

Spring C

reek n

ear

MDntevideo,

MNNorth

Bran

ch Yel

low Medicine R

iver

near

Iv

anho

e, MN

Drainage

area

(m

i2)

179 6.

7322

1 30.2 1.54

9.45

1,17

02,520 2.

04

0.58

4.79

2.37

1.26

1,36

0

130

447

389

398

905 2.

97

983 0.

40

0.47

7.53

1,870 16.0

14.8

Slop

e (f

t/mi

)

2.6

3.49

1.1

3.27

14.5 2.90

3.1

3.3

10.6

33.9 9.48

13.1

34.9 3.7

0.14

3.2

10.9

17.7 2.5

67.9

12.7

10.3

51.2

40.4 4.1

5.68

11.8

Sto­

rage %

10 12 8.6

4.1

2.6

14 3.9

4.6

6.4

6.9

24 20 8.7

37 30 1.1

1.5

1.3

5.4

2.0

0.9

5.0

0 2.1

5.2

1.2

2.7

Disc

harg

e, in f

t3/s, for

indi

cate

d recurrence

inte

rval

sQ2

160 52 328

130 32 31

2,030

3,010 44 12 94 68 32

3,920 57 817

941

1,240

730

138

1,48

0 7 7 621,560

110 96

Q5

284 76 722

264 49 60

5,170

6,920

109 32 199

143 76

6,59

0

149

2,05

0

2,730

3,020

1,710

410

3,78

0 27 20 117

3,440

255

324

Q10 379 93

1,10

0376 60 82

8,260

10,500 171 50 289

208

116

8,30

0'v 243

3,250

4,650

4,71

02,

620

671

6,150 53 33 162

5,100

388

594

Q25 510

113

1,67

0542 75 115

13,100

16,300 273 81 426

305

180

10,7

00 402

5,23

0

8,060

7,450

4,100

1,080

10,300 103 55 231

7,650

597

1,11

0

Q50 615

129

2,20

068

1 86 141

17,700

21,800 365

109

543

388

236

12,2

00 551

7,050

11,400

9,940

5,30

0

1,420

14,300 157 77 291

9,88

078

4

1,65

0

Q100 72

514

42,800

834 97 170

22,500

28,000 472

142

672

480

301

14,0

00 728

9,17

0

15,4

0012

,800

6,70

0

1,78

0

19,300 228

102

357

12,400 996

2,33

0

Year

s of

reco

rd

22 13 20 14 13 14 37 49 11 12 15 15 14 41 11 30 43 31 40 15 43 15 13 13 34 16 15

Tab

le 2

. F

loo

d-f

req

ue

nc

y

an

d

basin

c

ha

rac

teri

sti

cs

fo

r g

ag

ing

sta

tio

ns

in M

inn

es

ota

Co

nti

nu

ed

Map

No.

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

Stat

ion

number

0531

1250

05311300

05313500

05313800

05314900

05315000

0531

5200

05316500

0531

6550

0531

6700

0531

6800

0531

6850

05316900

05317000

0531

7850

05318000

05318100

05318300

05320000

05320200

0532

0300

0532

0400

05320440

05320500

05330150

0533

0200

05330300

Station

name

North

Branch Yellow Me

dicine

River

trib

utar

y near Wilno,

MNNorth

Branch Yellow Me

dici

ne R

iver

tributary

No.

2 ne

ar P

orter, MN

Yellow Med

icin

e Ri

ver near G

rani

teFa

lls,

MN

Kand

iyoh

i Co

unty

dit

ch 16

near

Bl ra

nkes

t, MN

Redw

ood River

at R

uth to

n, MN

Redw

ood River

at M

arsh

al 1

, MN

Prai

rie

Ravi

ne n

ear

Mars

hal

1 , MM

Redwood Ri

ver

near R

edwood F

alls

, MM

West F

ork

Beaver Cre

ek near Olivia,

MNSp

ring

Cre

ek near

Sleepy E

ye,

MMCo

tton

wood

River tr

ibut

ary near

Balaton, MN

Meadow Creek tributary

near

Marshal

1 , MM

Dry

Creek

near J

effers,

MNCottonwood Riv

er n

ear New

Ulm,

MM

Fost

er Cre

ek n

ear Al

den,

MN

East

Branch

Blue

Earth

River

near

Bric

elyn

, MM

East B

ranch

Blue

Earth R

iver

trib

utar

y ne

ar B

lue

Earth, MM

Wato

nwan

River n

ear

Delft, MN

Blue

Ear

th R

iver

near

Rapidan, MN

Le Sueur

River

trib

utar

y ne

arMankato, MM

Cobb

River tr

ibut

ary near

Mapl

eton

, MN

Maple

Rive

r tr

ibut

ary ne

arMapleton,

MNJu

dici

al di

tch

49 near Amb

oy,

MNLe

Sueur

River near R

apid

an,

MMSand Cre

ek tr

ibut

ary near

Montgomery,

MNRi

ce L

ake

trib

utar

y ne

arMontgomery,

MNSa

nd Creek near Ne

w Pr

ague

, MM

Drainage

area

(mi

2) 0.33

3.70

653 0.

836.

1830

7 5.63

697 12.2

31.3 0.91

0.54

3.13

1,280 2.

26

132 9.

2013.0

2,430 0.

07

7.25

6.22

18.0

1,10

0 0.36

3.16

62.4

Slope

(ft/mi)

87.7

30.9

12.4 7.75

42.4

17.0

11.4

11.0 4.57

2.88

42.8

57.0

61.4 6.0

20.1 3.2

10.5

15.7 2.7

158 4.

02

9.30

8.82

8.1

68.7

10.0 5.97

Sto­

rage %

0 0.5

0.5

0 0.2

1.7

0.4

0.4

3.7

4.2

0 0 0 0.7

0 5.3

0 1.9

0.8

0 3.6

0.1

0.9

2.7

5.6

12 11

Disciiarge,

in f

t3/s, fo

r in

dica

ted re

curr

ence

in

terv

als

Q2

22 91

1,160 32 148

647 31 811 71 185 22 17 131

2,97

0 82 332

147

121

7,150 20 161

137

204

4,19

0 21 50 255

Q5

49 148

3,650 64 369

1,760 81

2,71

0

163

399 55 55 321

7,42

016

8

755

271

361

14,7

00 38 285

309

395

9,000 30 101

541

Q10 70 189

6,46

0 88 583

2,850

131

5,100

246

586 87 100

503

11,7

00 236

1,14

0

369

624

21,400 53 380

463

558

13,7

00 36 144

788

Q25 98 243

11,700 118

936

4,60

021

410

,000 377

871

138

185

798

18,800 332

1,74

0

506

1,100

32,000 73 510

704

807

20,800 43 206

1,16

0

Q50 119

284

16,9

00 141

1,26

06,

200

292

15,500 493

1,120

185

273

1,070

25,400 409

2,27

0

617

1,57

041

,800 90 614

915

1,02

027,300 48 259

1,48

0

Q100 14

1

327

23,400 163

1,640

8,200

383

22,900 624

1,390

239

384

1,38

033,000 488

2,87

0

735

2,140

54,000 107

722

1,15

01,270

34,600 53 316

1,840

Years

of

record

15 15 39 14 16 31 16 45 16 16 16 12 14 44 16 20 15 15 28 16 16 16 14 27 14 15 15

Tab

le 2

.~F

loo

d-f

req

uen

cy

an

d

basin

ch

ara

cte

risti

cs fo

r g

ag

ing

sta

tio

ns

in

M

inn

es

ota

C

on

tin

ue

d

Map

No.

144

145

146

147

148

149

150

151

152

153

±154

o

155

156

157

158

159

160

161

162

163

164

165

166

167

168

Stat

ion

number

05330550

05330600

05336200

05336300

05336550

05336600

05338200

05338500

0534

0000

05345900

0535

2700

05352800

0535

5100

05355150

0535

5200

0535

5230

0537

3000

0537

3350

0537

3700

0537

3900

0537

4000

0537

4500

0537

5800

0537

6500

0537

7500

Stat

ion na

me

Raven

Stream t

ribu

tary

nea

r New

Prag

ue,

MNSa

nd Cre

ek tributary

No.

2 ne

arJo

rdan

, MN

Glaisby Br

ook

near K

ettl

e River, NN

Moos

e River

tributary

at Moose

Lake,

MNWolf Cre

ek t

ributary n

ear

Sandstone,

MMKe

ttle

River

trib

utar

y at

Sa

ndst

one,

MMMission

Creek near Hinckley, MN

Snake

River

near P

ine

City,

MMSu

nris

e Ri

ver

near S

tacy,

NNVermill io

n River

trib

utar

y near

Hast

ings

, MN

Turt

le C

reek

tributary N

o.

2 near

Pratt, MN

Turt

le C

reek

tributary ne

ar S

teel

eCe

nter

, MM

Litt

le C

anno

n River

tributary

near

Kenyon,

MMPine C

reek near

Cannon F

alls

, MS

Cann

on R

iver

at We

lch,

MM

Cann

on R

iver

tributary ne

ar Welch,

MNSo

uth

Fork Zumbro R

iver n

ear

Rochester, MM

Zumbro R

iver

tributary ne

ar S

outh

Troy,

MMSp

ring

Cre

ek n

ear

Wana

ming

o, MM

Trout

Brook

tributary

near

Go

odhu

e,MN

Zumbro R

iver at Zu

mbro

Fa

lls,

MN

Zumbro R

iver at

Theilman, MN

East

In

dian

Cre

ek tributary

near

Weav

er,

MNSouth

Fork

Whi

tewa

ter

Rive

r near

Altu

ra,

MMWh

itew

ater

River a

t Be

aver

, MN

Drainage

area

(mi2)

22.1 2.62

24.2 1.23

5.46

0.65

3.84

958

167 14.3 1.26

5.01

2.20

20.2

1,320 0.

05

304 0.

169.93

0.40

1,13

01,320 0.

22

76.8

288

Slop

e (f

t/mi

)

10.0

30.9

11.5

30.4

12.4

32.4

12.7 5.3

1.9

5.53

36.2

16.4

53.4

12.8 4.2

140 9.

3

156 20.7

88.9 7.7

6.4

604 22.3

15.5

Sto­

rage *

10 6.1

17 3.3

58 28 20 43 47 16 0.8

0.8

0 1.3

2.4

' 0 0.2

0 0 0 0.1

0.1

0 0 0

Discharge, in

ft3

/s,

for

indicated

recurrence

inte

rval

sQ2 17

9 68 427 81 57 17 76

4,96

0307 28 64 105

194

131

5,880 23

4,41

0 23 417 88

10,400

12,600 12

1,750

4,67

0

Q5

324

138

742

157

128 34 137

8,280

466

134

135

201

412

394

11,0

00 42

8,830 50 843

161

17,400

19,400 27

3,52

08,

100

Q10 443

194

979

219

192 49 184

10,900 574

295

196

279

600

683

15,300 57

12,500 73

1,20

0

220

22,500

24,000 40

4,99

010

,800

Q25 616

274

1,300

309

291 72 249

14,300 712

665

287

391

884

1,200

21,700 77

17,900 109

1,73

0

306

29,400

30,0

00 61

7,160

14,500

Q50 763

340

1,56

0

383

377 91 302

17,000 815

1,110

365

483

1,13

01,

720

27,200 94

22,400 140

2,170

380

34,7

0034,500 79

8,98

017,500

Q100 92

5

413

1,83

0

464

475

112

357

20,000 918

1,740

451

Year

s of

re

cord

15 15 15 15 15 15 15 24 17 13 .i:i

582

15!

1,400

2,35

034,000 111

27,500 175

2,66

0

461

40,200

39,100 99

11,000

21,000

15 15 43 15 19 13 15 15 49 19 13 31 20

Ta

ble

2. F

loo

d-f

req

uen

cy

an

d

ba

sin

ch

ara

cte

risti

cs fo

r g

ag

ing

s

tati

on

s

in M

inn

eso

ta C

on

tin

ued

Map

No.

169

170

171

172

173

174

175

176

177

178

179

- 18

0J1

81 182

183

184

185

186

187

188

189

190

191

192

193

194

195

Station

nurc

ber

05378300

05379000

05383600

05383700

05383720

0538

3850

0538

4000

05384100

05384150

0538

4200

05384300

05384400

05384500

05385000

05385500

05386000

05457000

05457080

05474750

05474760

0547

5400

0547

5800

0547

5900

0547

6000

0547

6010

0547

6100

0547

6900

Stat

ion name

Stra

ight

Valley

Cree

k ne

arRoll ings to

ne,

MNGi

lmor

e Creek

at Win

ona,

MN

North

Bran

ch R

oot

River

trib

utary

near

Stewartville, MN

Mill

Creek

tributary near

Chat

fiel

d, MN

Mill Cr

eek ne

ar C

hatfield,

MNSouth

Fork

Bea

r Cr

eek near Gr

and

Mead

ow,

MNRo

ot R

iver near

Lanesboro, MN

Duschee

Creek near L

anes

boro

, MN

Root

River tributary near Wha

lan,

MMGr

ibbe

n Creek near Wha

lan,

MN

Big

Spri

ngs

Creek near Are

ndah

l , MN

Pine

Creek n

ear Ar

enda

hl ,

MNRush C

reek

near

Rushford,

MNRoot R

iver near

Hous

ton,

MN

South

Fork

Roo

t Ri

ver near H

oust

on,

MNRo

ot R

iver

bel

ow S

outh F

ork ne

arHo

usto

n, MN

Cedar

River

near Aus

tin,

MN

Rose

Cre

ek tributary near D

exte

r,W

Beaver C

reek t

ribu

tary

No. 2 near

SI ay t

on,

MNBeaver C

reek tributary

abov

eSI

ay t

on,

MNWarren L

ake

tributary near Windom,

MNDe

s Mo

ines

River tributary

near

Jack

son,

MN

Des

Moin

es R

iver tr

ibut

ary

No.

2ne

ar L

ake fi

eld,

MN

Des

Moin

es Ri

ver

at J

acks

on,

MNNelson Cre

ek a

t Ja

ckso

n, MN

Story

Brook near P

etersburg, MN

Four

mile

Creek nea

r Dunnell, MN

Drainage

area

(mi2) 5.16

8.95

0.73

2.36

22.4

14.0

615 3.

85

0.08

7.80

0.14

28.1

129

1,270

275

1,56

042

5 1.17

3.53

2.20

1.39

1.52

5.18

1,22

0 6.19

25.8

14.0

Slope

(ft/mi)

113

109 47.3

80.8

50.4

14.5 7.5

70.8

243

101

100 18.3

28.0 6.5

7.6

6.4

4.0

37.9

43.7

38.8

17.4

20.6

12.1 2.6

46.3

23.2

17.2

Sto­

rage

* 0 0 0 0.4

0 0 0 0.2

0 0.1

0 0 0 0 0 0 0.7

0 0 0.3

0 0.7

0 4.5

0 0 0

Discharge, in f

t3/s

, fo

r in

dica

ted recurrence

intervals

Q2

258

370 59

406

1,24

0

622

8,43

026

5 23 738 17 776

2,670

10,2

00

2,67

0

13,3

003,

860 79 61 40 54 26 67

1,47

033

566

3310

Q5

578

1,04

0

176

603

2,80

0

1,230

15,5

00 605 52

1,760 41

1,82

06,

440

18,700

5,10

0

22,200

7,090

146

116 77 109 71 136

3,720

667

1,360

743

Q10 866

1,750

297

735

4,200

1,73

020,400 914 79

2,730 65

2,79

09,590

25,500

7,20

0

28,900

9,620

199

162

108

158

118

193

6,00

0941

1,95

01,

150

Q25

1,310

2,99

0

499

901

6,39

0

2,46

026,700

1,400

121

4,270

104

4,340

14,000

34,900

10,000

38,400

13,200 273

232

156

233

197

279

10,000

1,34

02,830

1,800

Q50

1,710

4,18

0

686

1,02

08,

310

3,070

31,100

1,830

159

5,67

014

25,

730

17,500

42,6

00

12,7

00

46,1

0016

,100 333

293

197

301

273

351

14,0

001,

680

3,58

02,

390

Q100

2,15

05,

620

900

1,15

010,500

3,730

35,400

Year

s of

re

cord

16 25 17 16 13 13 382,320

' 16

202

7,27

018

87,

310

21,100

51,500

15,5

00

55,500

19,100 396

360

243

378

363

430

19,000

2,04

04,400

3,070

16 16 16 16 29 49 18 24 31 13 15 15 14 15 15 45 12 13 15

Tab

le 2

.--F

loo

d-f

req

ue

nc

y

an

d

ba

sin

ch

ara

cte

risti

cs f

or

ga

gin

g

sta

tio

ns

in M

inn

eso

ta C

on

tin

ued

Map

No.

196

197

198

199

200

201

Station

number

06482950

0648

2960

06483050

0648

3200

06603520

06603530

Stat

ion name

Moun

d Creek

near Har

dwic

k, NN

Moun

d Creek

trib

utar

y at

Hardwick,

NNRo

ck R

iver tr

ibut

ary near L

uverne,

WKa

nara

nzi

Creek

trib

utar

y near

Lismore,

^f>I

Judicial di

tch

28 tr

ibut

ary

near

Spaf

ford

, NN

Litt

le Si

oux

River

near S

pafford,

VK

Drai

nage

ar

ea(m

i2)

2.47

0.19

0.21

0.14

2.66

41.1

Slop

e (ft/mi)

25.3

112

100 66.0

14.5 6.39

Sto­

rage % 0.3

0 0 0 0.1

0.3

Discharge, in ftV

s, fo

r indicated re

curr

ence

in

terv

als

Q2

33 38 34 89 48 217

Q5 106

115

103

162

111

738

Q10 190

201

179

219

169

1,36

0

Q25 349

358

317

298

261

2,560

Q50 511

514

454

363

343

3,80

0

_Q100 714

707

622

431

436

5,390.

Year

s of

reco

rd

16 16 14 16 14 13

most reliably by the following relation which is applicable to most areas in Minnesota.

where: Q is the flood- frequency estimate for the ungaged site

Q is the flood-frequency value for the gaged site g (from table 2)

A is the drainage area for the ungaged site

A is the drainage area for the gaged site g (from table 2)

Local conditions may warrant a slight increase or decrease of the 0.6 exponent, which must be based on engineering judgment. Use of the transfer relation should be limited to sites which differ in drainage area size by no more than 40 percent from the gaged site.

Regional Analyses for Ungaged Sites

Equations derived from multiple regression analyses can be used to obtain flood- frequency estimates for ungaged sites on natural flow streams. Peak discharges for the selected recurrence intervals can be computed from these mathematical equations tabulated in table 3, which relate flood magnitude to basin characteristics. A set of equations to estimate flood peaks for the 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals (identified as Q 2 , Qs , Qio> etc.) are provided for each of the hydrologic regions into which the State has been divided. The eight regions are outlined on figure 1. The regional boundaries cannot be defined precisely; therefore, where the estimating site falls close to a regional divide, consideration should be given to averaging the results obtained by computation of the flood magnitudes from the equations for the two adjoining regions. Particular care should be exercised when the site in question has a large value for a basin char­ acteristic that is not used in the regression relation for both regions. If a flood-frequency estimate is to be made downstream from a regional divide which the stream crosses, the discharge at the site should be determined by weighting the regression estimates computed from both regional relations according to drainage area.

Due regard should be given to the limitations of these equations as discussed in a following section (Accuracy and Limitations) .

13

Table 3. Regional flood-frequency equations

Region A

Q =29.2 A« 622

Q =54.2 A» 625

Q =73.8 A» 62 10

Q =101 A- 6225

Q =124 A- 6250

Q =149 A. 62100

Region B

Q =5.71 A- 860 S. 1* 07 Sf- 0272

Q =16.1 A- 61* 8 S.* 52 Sf- 2315

Q =26.8 A- 642 S-* 73 Sf- 333 10

Q =46.5 A- 636 S- 1* 92 Sf- 1"* 325

Q =65.2 A- 631* S- 505 Sf « 51350

Q =88.4 A« 631 S- 516 Sf 575100

Region C

Q =10.5 A- 76 * S» 3752

Q =15.9 A- 736 S-5

Q =19.8 A 10

722

708 * 76Q =24.5 A. 708 S25

Q =28.1 A- 699 S.* 9550

Q =32.0 A« 690 S« 512100

Region D

Q =7.90 A* 65 * S» 3562

Q =25.1 A« 668 S« 288 Sf « 175

Q =44.8 A- 673 S- 252 Sf « 265 10

Q =79.7 A- 882 S- 217 Sf 3S *25

Q =115 A- 688 S- 19 " Sf-* 1150

Q =157 A- 695 S- 175 Sf * 60100

Region E

Q =1.91 A« 913 S« 8892

Q =5.76 A- 852 S» 77 *5

Q =9.83 A- 821 S« 725 10

Q =17.0 A« 790 S« 67 *25

Q =23.9 A- 770 S«50

Q =32.4 A^ 759 S- 616100

Region F

Q =83.8 A-* 72

Q =208 A> 9

Q =322 A- 50 10

Q =487 A^ 5125

Q =580 A« 5250

Q =762 A«100

52

Region G

Q =15.8 A- 687 S« 259 Sf « 1152

Q s =32.1 A- 723 S- 291* Sf- 212

Q =45.6 A- 7 * 1 S- 913 St'- 258 10

Q =66.3 A« 761 S« 329 St"- 90625

Q =83.5 A- 77 " S- m Sf- 39750

Q =102 A- 788 S« 3lf9 Sf « 369100

Region H

Q =23.2 A« 787 S- 31* 8 St"« 753

Q =55.0 A« 753 S« 32% St"

Q =86.4 A- 735 S- 309 Sf- 581* 10

Q =135 A- 718 S- 295 Sf- 52025

Q =183 A- 701* S- 283 Sf - 1* 8150

Q =236 A- 69 " S- 27lf Sf-100

14

Variables used for the equations in table 3 have the following measurement units:

Q-p - Peak discharge for T-year recurrence interval, in cubic feet per second.

A - Drainage area, in square miles.

S - Average main channel slope, between 10 and 85 percent points, in feet per mile.

St - Area of lakes, ponds and swamps, expressedas percentage of drainage area and increased by 1 percent.

Values for the basin characteristics used in the regression analyses were determined by the methods outlined below. Re­ quired independent variables used for estimated flood character­ istics at ungaged sites should be determined in a like manner.

1. Drainage area.- Trace contributing drainage-areaoutline on topographic maps along divides indicated by contour elevations, starting at point on stream where frequency characteristics are to be defined. U.S. Geological Survey topographic maps, 7^-minute or 15-minute quadrangles, should be used for basins smaller than 150 square miles. For larger basins, the 1:250,000 scale topographic maps may be used. Planimeter the outlined area to obtain drainage area (A) in square miles.

2. Main channel slope.- Determine the main channel of the stream on the drainage area map, from the point selected for the frequency estimate, to the extreme rim of the basin. Extension of the main channel to the basin divide, beyond the upstream end of the defined stream., should be made as indicated by contours. Upstream from each stream junction, choose the main channel as the fork which drains the larger area. Measure the total length by dividers set at appropriate intervals, such as 0.1 mile for 7%-minute quadrangles, 0.25 mile for 15-minute quadrangles, and 0.5 mile for the 1:250,000 scale maps. Locate points 10 and 85 percent of the main channel length upstream from the point of interest, and determine the elevation of these points by interpolation between contours. The average main channel slope (S) is computed as the dif­ ference in elevation, in feet, divided by the length, in miles, between the 10 and 85 percent points.

15

97° 95° 94° 93° 92 C 91 °

1

: / "~>

0 ,.i/ ~. \

P48* r 'stFTT " -

48°

47'

4$°

45°

44 s

; N 5i_T n w - ~ ,........r:............... ._

» i .----,..: ^SUK M "LlytX \ v-4:/ 4» 'p iit_i >«n ^ V°i ^- v ,. '

..._)

' 5)'

f- *'. ,,"' y^ : '"!li£.'.^, : : [

66

,....._!_..

SCALE

10 0 10 20 30 40 50 100 MILES

100 KILOMETERS

Figure 1. Map of Minnesota showing location of gaging stations and hydrologic regions used in regression analysis.

3. Storage.- Measure the area of lakes, ponds and swamps in the drainage basin on topographic maps. Storage areas can be measured by planimeter or by using a transparent grid. The grid is placed over the water and swamp areas and the number of squares, and esti­ mated fractional parts of squares, are summed up and multiplied by the area of each square, as calculated for the scale of the map being used. The total area of lakes, ponds and swamps is expressed as a percentage of the total contributing area. This percentage is then increased by 1 percent to obtain the storage pa­ rameter (St) used in the equations.

A transparent grid suitable to most map scales is enclosed in a packet at the back of this report.

Illustrative Examples

The following examples illustrate use of the relations to compute flow frequency estimates.

Example 1.- Estimate the 50-year flood on the Sauk River at Cold Spring, an ungaged site.

Solution:

1) Inspection of figure 1 and table 2 indicate the avail­ ability of gaging-station data for the Sauk River in close proximity to Cold Spring. The station is iden­ tified as Sauk River near St. Cloud, map no. 81 (Station No. 05270500).

2) Contributing drainage area at Cold Spring is planim- etered on topographic maps as 832 mi .

3) Reduction in drainage area at Cold Spring is only 10 percent from the 925 mi 2 listed in table 2 for the St. Cloud gaging station. Therefore, a transfer of flood characteristics by drainage area ratio is appropriate.

4) From table 2, Q = 8,000 ft 3 /s for 50-year flood.o

5) By substitution into transfer equation:

QU = Qg (VV

. Q 50 = 8,000 (832/925) 0 - 6

Q 50 = 8,000 x 0.938

Q 50 = 7,500 ft 3 /s (212 m 3 /s)

18

Example 2.- Estimate the 25-year peak discharge for an ungaged site on Spring Creek in Swift County, at the crossing of State Highway 9, 3^ miles west of Sunburg.

1) Inspection of figure 1 and table 2 indicate that no gaging-station data are available on this stream, therefore, flow-frequency estimates must be derived from regional equations.

2) Site is identified from figure 1 as being in Region D. Applicable equation for 25-year flood is located in table 3.

3) Drainage area is outlined on topographic map, De Graff SE 7-i- minute quadrangle.

4) Drainage area (A) is planimetered as 1.28 mi 2 , and main channel length is measured as 1.49 mi to the watershed divide.

5) The main channel slope is computed by dividing the difference in elevations at mile 0.15 (0.10 x 1.49) and mile 1.27 (0.85 x 1.49) by 1.12 (1.27 - 0.15), the distance between the two points.

Elevation at mile 1.27 is 1235 ft

Elevation at mile 0.15 is 1212 ft

Main channel slope (S) = (1235 - 1212)/1.12 = 20.5 ft/mi

6) Total lake, pond and swamp area is determined from the map by the grid system described in the discussion on storage preceding example 1. Fifteen of the small grid squares are counted as storage area.

15 squares x 0.00144 mi 2 = 0.02 mi 2

Storage = 0.02 x 100 = 1.6 percent 1.28

Storage index (St) = 1.6 + 1.0 * 2.6 percent

7) Region D equation for 25-year flood from table 3:

Q 25 = 79.7 A- 682 S- 217 St-- 35 "

8) By substitution of the variables:

Q 25 = 79.7 (1.28)- 682 (20.5)- 217 (2.6)'- 351*

19

9) Solving the equation:

Q25 = 130 ft 3 /s (3.68 m 3 /s)

Plotting points to define a frequency curve for the site can be obtained by solution of equations for other recurrence intervals.

Main-stem Streams

Estimating relations given previously do not apply to the main stem of the Minnesota River, Mississippi River and Red River of the North. The effects of regulation, interregional character of the streams and (or) the large drainage areas involved, require unique definition of the flood character­ istics for these streams. Individual relations between flood magnitude and contributing drainage area were prepared based on interpolation between gage sites on the main stems. Flood- frequencies indicated for regulated reaches of the main-stem streams are based on the assumption that past records represent homogeneous regulation patterns and are applicable only if such regulation patterns remain unchanged in the future.

The 100-year flood estimates for the Minnesota River, Red River of the North, and Mississippi River (between Aitkin and St. Paul) have been coordinated under an interagency agreement. Agencies involved in this coordination process, with limita­ tions imposed by their area of interest or jurisdiction, are as follows: St. Paul District-Corps of Engineers, Soil Conserva­ tion Service, U.S. Geological Survey, Minnesota Department of Natural Resources, and North Dakota Water Commission (Red River of the North Regional Flood Analysis, 1971).

Graphs showing flood estimates for selected recurrence intervals versus contributing drainage area for the Minnesota River, Mississippi River, and Red River of the North are pre­ sented in figures 2-4, respectively. When using the frequency graph for the Red River, it should be recognized that plotting positions of drainage areas from Halstad to Emerson have been corrected by subtracting 3,800 mi 2 (9842 km 2 ) for closed basins in the Sheyenne River basin in North Dakota.

Definition of flood characteristics for the main stem of the St. Croix River from St. Croix Falls to Prescott, Wisconsin is very complex owing to regulation of flows and the backwater effect from the Mississippi River, which affects elevation- frequency relations through a large part of this reach. Such analyses are outside the scope of this report. Frequency data for this section of the St. Croix River can be obtained from the report "St. Croix River Regional Flood Analysis" (Wiitala, 1973).

20

150,000

100,000

o oLLJCO

ccUJQ_

CJ

COZ3 CO

CDCC<3:CO CO

50,000

30.000

10,000 -

5000 -

3000

10001000 3000 5000

DRAINAGE AREA, IP10,000

SQUARE MILES

30,000

Figure 2.~Relation of flood magnitudes for selected recurrence intervals to drainage area, Minnesota River main stem.

21

300,000

100,000az: oLUCO

50,000

« 30,000CO

CJ

LJJCD OC

CJ CO

10,000 -

5000

30003000 5000 10,000 30,000 50,000 100,000

DRAINAGE AREA, IN SQUARE MILES

Figure 3. Relation of flood magnitudes for selected recurrence intervals to drainage area, Mississippi River main stem.

22

300,000

100.000

oCJ LLJGO

£ 50,000o_

oCO

CD GC

CJ CO

30,000

10,000

5000

30003000 5000 10,000

DRAINAGE AREA,30,000

SQUARE MILES50,000

Figure 4. Relation of flood magnitudes for selected recurrence intervals to drainage area, Red River of the North main stem.

23

Accuracy and Limitations

In general, estimates of future flood occurrences over a long time period become more reliable with greater length of record (Hardison, 1969). The standard error of estimate decreases with increasing years of available record, but at a decreasing rate. At or near gage sites (excluding main-stem streams), flood characteristics may be based on analysis of actual records collected at the site (from table 2), or may be computed from regional estimating relations. As noted previ­ ously, regional estimating relations will probably provide/more reliable results than the use of on-site gaging-station data if the period of record is short. It is recommended that use of tabulated gaging-station data for estimating flood character­ istics at on-site, or by transfer to nearby locations, be restricted to those frequency relations based on more than 20 years of record.

The reliability of a regression equation may be judged by the standard error of estimate, which is a measure of the dis­ tribution of the observed data about the regression equation. The standard error, given in percent, is the range of error to be expected two-thirds of the time. That is, the difference between the computed and the observed discharge for two-thirds of the frequency estimates will be within plus or minus one standard error of estimate. Because the variables used in these analyses were expressed in logarithmic form, standard errors are larger in the positive direction. A graphical interpreta­ tion of the standard error for the 10-year frequency relation in Region G is shown in figure 5. Table 4 lists the average standard errors of estimate for the defined relations in each region, except for Region F. Relations for that region were adapted from regression equations developed by Becker (1974) for the adjacent area in South Dakota.

Flood-frequency relations expressed in this report may be used to estimate magnitude and frequency of floods on most Minnesota streams. Applicability and reliability of these rela­ tionships is dependent on the basin characteristics at the site under consideration being within the range of characteristics used to define the frequency relations. The range in sampled basin parameters is large enough to allow use of the frequency relations at virtually all sites where streamflow is not sig­ nificantly affected by regulation, diversion, or urbanization. Exceptions will occur in those instances where the site, for which estimates are required, falls immediately below a lake or ponding area where large storage capacity, in relation to total drainage area size, could seriously alter the outflow flood characteristics. In such cases, the frequency relations may be used as an aid in developing an inflow hydrograph for use in routing through the storage area.

24

ESTI

MAT

ED 1

0-YE

AR P

EAK

DIS

CH

ARG

E,

IN

CU

BIC

FEE

T PE

R SE

CO

ND

tn

O

x: G)

Tl

co'

c (0 P1

0

o 1°

S "5

Q.

-i

-%

0>

(Q o'

3

3

Q.

0> n a a> ~\ ^ o -^ o -*1

(D

0)

^- 3' 21 (D

az

co

c-j

^cC

D

3D

I

C3

-O ^

3

00

CO

J

>

"5

H

a

-n 3D

m

O -<

CT5

Table 4. Standard error of estimates for defined relations

Recurrence interval (years)

Region A

2

5

10

25

50

100

Region B

2

5

10

25

50

100

Region C

2

S

10

25

50

100

Region D

2

5

10

25

50

100

Standard error of estimate (percent)

45

38

39

42

45

49

36

34

36

38

41

43

34

34

35

37

39

41

46

44

47

52

56

61

Recurrence interval (years)

Region

2

5

10

25

50

100

Region

2

5

10

25

50

100

Region

2

5

10

25

50

100

Standard error of estimate (percent)

E

56

54

54

55

55

55

G

47

37

37

39

42

46

H

37

28

28

32

35

39

26

ANALYTICAL TECHNIQUES

Data Used

Flood-frequency data used in the regression analysis were derived from records of 10 or more years length collected at 219 gaging stations located on natural flow streams. Stations operated by the Minnesota district consisted of 78 sites classi­ fied as continuous-record stations and 123 as partial-record stations. Records for 18 sites in adjoining states were also included. Annual peak data through the 1974 water year were considered for the Minnesota partial-record stations, through the 1972 water year for stations in adjoining states, and through the 1970 water year for Minnesota continuous-record stations. Frequency data for many of the continuous-record stations are the result of interagency coordination of 100-year flood estimates required for numerous studies conducted in Minnesota. Where such coordination occurred, frequency curves developed by individual participating agencies were adjusted to provide a uniform peak discharge at the 100-year recurrence interval.

Flow-frequency Analysis at Gaging Stations

A flood-frequency curve for each gaging station was pre­ pared by fitting a log-Pearson Type III frequency distribution to observed annual peaks, using regionalized coefficients of skewness. The log-Pearson Type III method is documented in U.S. Water Resources Council Bulletin No. 15 (1967).

Analysis of frequency characteristics, in connection with interagency coordination activities, had indicated a developing pattern to the variation of computed skew coefficients. Log- Pearson computations based on records starting in the early 1930 f s generally had large negative skew values while computa­ tions based on longer term records produced skew coefficients more nearly approaching zero. Large negative coefficients of skewness were also prevalent at sites where streamflow was sig­ nificantly affected by natural storage. Skew coefficients generated from records which commenced in the early 1930's, a sustained period of severe widespread drouth in Minnesota, apparently are affected to a varying degree by one or more low outliers. With extension of the record, low outliers are no longer evident.

Adoption of generalized coefficients of skewness applicable to a region was found to significantly improve the fit of the computed frequency curves as the effect of outliers (both high and low) is greatly diminished. Based on analysis of long-term

27

records, adjusted plotting position of outstanding floods recorded at short-term record sites, and extension of some records by correlation, generalized skew coefficients ranging from zero to -0.2 were selected for the log-Pearson analysis of Minnesota gaging-station records.

A later publication by the Water Resources Council, Bulletin 17 (1976) , recommends virtually the same procedures for log-Pearson Type III frequency analyses of gaging station records as were used in this report. Differences as they would apply to Minnesota streams are mostly in the regionalized skew- ness coefficient and in the treatment of historical peaks. Recommendations for generalized (regional) coefficients of skewness in Bulletin 17 range from -0.1 to -0.4 in Minnesota, which differ only slightly from the assigned skew coefficients used in this study. Historical peak adjustments would have only a minor effect on the regression analysis as historical peak data is available at only about 6-percent of the sites analyzed for this report.

Frequency analyses for each gaging station were developed by computer using standard U.S. Geological Survey programs. A computer printed plot of the frequency curve was obtained to visually compare the fit of the computed frequency curve to the observed annual peaks. Modification of the initial frequency curve, by graphical interpretation or use of a different coef­ ficient of skewness, was made in a few instances as dictated by the available data. A sample frequency curve is shown in figure 6.

From the frequency analyses, peak discharges for recurrence intervals of 2, 5, 10, 25, 50 and 100 years, listed as Qa, Qs, Qio, etc. in table 2, were selected for the regression analysis.

It should be noted that changing analytical methods, inter- agency coordination activities, and increasing length of record will undoubtedly result in variations from the frequency esti­ mates listed in table 2.

Multiple-regression Model

Relations between peak discharge (dependent variable) and a set of basin characteristics (independent variables) were developed by multiple-regression techniques. Past experience has shown that peak discharges are linearly related to most basin characteristics if the log transformations of the variables

28

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Figure 6. Flood frequency curve for East Branch Blue Earth River

near Bricelyn, Minnesota.

29

are used. The regression model then is of the form:

Log Q = log a + x log A + y log B + z log C

or it's equivalent:

QT = a Ax B^ C z

where:

QT is the peak discharge for T-year recurrence interval

a is a constant

x, y, and z are regression coefficients

A, B, and C are basin characteristics

The step-forward method of multiple-regression analysis was used wherein the regression equation is generated by adding the independent variables in the order of greatest significance to the estimating relation. The variable added for each step is the one which makes the greatest reduction in the standard error of estimate. Only those independent variables statisti­ cally significant at greater than the 95 percent confidence level are included in the equations. The analysis defines the regression constant and coefficients, standard error of esti­ mate, and other statistical data for each frequency relation.

In a few instances, independent variables were added or deleted from the equations in order to standardize, on a region­ al basis, the variables to be considered at the various recur­ rence intervals. Original equations, in such cases, resulted in frequency curves that were irregularly shaped. Continuity of the frequency curves was vastly improved by addition or deletion of such variables with little effect on the standard error of estimate.

Hydrologic regions shown on figure 1 were defined by plot­ ting residual values on a map. The residual errors from the regression analysis are the differences between observed and computed flood magnitudes and can be expressed in terms of ratios. The plot of residual ratios illustrated the geograph­ ical bias inherent in statewide frequency relations. The 8 regions were delineated by removal of successive areas from the regression, based on groupings of the residual values. As each area was removed, new regression relations were computed utiliz­ ing the remaining input data, and the residuals again plotted to define the remaining areal bias.

Inter-regional comparisons of the regression equations were made by computing flood magnitudes, at selected recurrence intervals, using constant basin characteristics for each region­ al relation. These tests showed considerable variability in computed flood characteristics across the State for a fixed set of independent variables.

Regional boundaries outlined on figure 1 generally follow basin divides. The following exceptions based on topographic or geologic features are: 1) in the southwestern part of the State, where the regional boundary follows the break in slope along the Coteau des Prairie and crosses the upper end of the Redwood, Yellow Medicine and Lac qui Parle River basins; and 2) in the northwestern part, where the regional boundary follows an upper beach ridge of glacial Lake Agassiz and crosses the upper end of the Wild Rice, Marsh, Sand Hill, and Clearwater River basins.

Basin Characteristics Investigated

A precondition established for this report was that the number of basin characteristics used in the regression be limited in number, and be readily determined from available maps, to eliminate the necessity for on-site measurements. Independent variables investigated in addition to area, slope and storage, were forest cover and soil type. Forest cover index was used as the percentage of the drainage area covered by forests increased by 1 percent. The soil index was deter­ mined by averaging residuals from an initial regression accord­ ing to different soil types. The soil index was tested separately on a multiple regression analysis of small basins where soil homogeneity was more probable. Neither basin characteristic improved the estimating relations.

SUMMARY

Basin characteristics and peak flows for 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals were tabulated for 201 gaging stations ranging in size from 0.05 to 5,280 mi 2 . The data from these 201 stations were grouped according to eight distinct hydrologic regions and equations were developed for each region by relating peak flows to basin characteristics. The resulting equations provider method for estimating flood- frequency relations for ungaged sites on all natural streams. In addition, graphs are presented for determining floods of selected recurrence intervals for large streams which may be significantly affected by regulation.

31

The equations developed by multiple regression for esti­ mating peak flows at ungaged sites determined that drainage area, slope, and storage are significant basin parameters for estimating 2-, 5-, 10-, 25-, 50-, and 100-year floods. Drainage area, slope, and storage were significant in 4 of the 8 regions, drainage area and slope in 2, and only drainage area in the remaining 2 regions. Accuracy of estimates obtained by using the equations are discussed and the standard error of estimate is given for each equation. Standard errors ranged from 28 to 61 percent.

Analytical techniques are discussed for determining flow frequency at gaging stations and for making estimates at ungaged sites. The regional regression equations provide more reliable results than frequency relations defined for gaging stations if the period of record is short. For sites at or near gaging stations having 20 or more years of record, the tabulated station data are considered more accurate than estimates from the regression equations.

32

REFERENCES

Becker, L. D., 1974, A method for estimating magnitude andfrequency of floods in South Dakota: U.S. Geol. Survey Water-Resources Inv. 35-74, 78 p.

Hardison, C. H., 1969, Accuracy of streamflow characteristics: in Geological Survey Research, U.S. Geol. Survey Prof. Paper 650-D, p. D210-214.

Patterson, J. L., and Gamble, C. R., 1968, Magnitude andfrequency of floods in the United States, Part 5: U.S. Geol. Survey Water-Supply Paper 1678, 546 p.

Prior, C. H., 1949, Magnitude and frequency of floods in Minnesota: Minnesota Dept. of Conservation, Div. of Waters Bull. 1, 128 p.

Prior, C. H., and Hess, J. H., 1961, Floods in Minnesota,magnitude and frequency: Minnesota Dept. of Conservation, Div. of Waters Bull. 12, 142 p.

Thomas, D. M., and Benson, M. A., 1970, Generalization ofstreamflow characteristics from drainage-basin character­ istics: U.S. Geol. Survey Water-Supply Paper 1975, 55 p.

U.S. Water Resources Council,, 1967, A uniform technique fordetermining flood flow frequencies: Hydrology Committee Bull. 15, 15 p.

___ 1976, Guidelines for determining flood flow frequency: Hydrology Committee Bull. 17, 196 p.

Wiitala, S. W., 1965, Magnitude and frequency of floods inthe United States, Part 4: U.S. Geol. Survey Water-Supply Paper 1677, 357 p.

___ 1971, Red River of the North regional flood analysis:North Dakota State Water Commission and Minnesota Dept. of Natural Resources, 19 p.

___ 1973, St. Croix River regional flood analysis (St. Croix Falls, Wis. to mouth): Minnesota Dept. of Natural Resources and Wisconsin Dept. of Natural Resources, 19 p.

33

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