Yearly Variations in Runoff 

for the Conterminous 

United States, 1931-60

By MARK W. BUSBY

CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1669-S

A revision of a study by G. E. Harbeck, 

Jr., and ff^ B. Langbein covering the 

period 1921-45

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1963
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402
CONTENTS

Page

Abstract_____________________.________________ SI

Introduction_ _____________________________________________________ 1

Maps of annual runoff___________-_-_____-__-__---__-__-__--___---_ 5

Regional variations in runoff____________________________ 37

Monthly distribution of runoff._____________________________________ 38

Excessive and deficient runoff___________________-_______.___________ 44

Long-term trends in runoff_______________________________________ 49

References- ______--_________-__-________________--______---____--_ 49

ILLUSTRATIONS

Pare

FIGURES 1-30. Annual runoff for the water years 1931-60._______... S6

31. Location of gaging stations used in this report_._._____- 36

32. Regional divisions of the conterminous United States____ 39

33. Yearly regional variations in runoff.____________________ 40

34. Normal monthly distribution of runoff________________ 43

35. Maximum annual runoff for the period 1931-60_________ 46

36. Minimum annual runoff for the period 1931-60__-________ 47

37. Long-term trends in runoff__________-_-______-_-_-_-_ 48

TABLES

Page 

TABLE!. Gaging stations used in this report________________________ S2

2. Comparison of 30-year normals of runoff with other long-term

normals _______________________________________________ 5

3. Regional standard deviations of annual runoff for the conterminous United States._______-___-____________-_--__-_---_ 38

4. Average and standard deviation of mean annual runoff_______. 44

5. Percentage of conterminous United States with deficient and excessive runoff__________________________________--._-__- 45

m

CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

YEARLY VARIATIONS IN RUNOFF FOR THE CONTERMINOUS UNITED STATES, 1931-60

By MARK W. BUSBY

ABSTRACT

In the late 1950's the World Meteorological Organization proposed that all 

countries adopt standard reference periods. The countries chose 30-year periods, 

starting with 1901, that do not overlap: for example as 1901-30, 1931-60, and 

1961-90. The U.S. Geological Survey has adopted the period 1931-60 for use 

in its monthly Water Resources Review and has discontinued use of the period 

1921-45 formerly used.

This report brings up to date and revises "Normals and variations in runoff, 

1921-45," by G. B. Harbeck, Jr., and W. B. Langbein, issued in 1949 as supplement 2 of the Geological Survey's Water Resources Review.

A comparison of the mean annual runoff at 25 gaging stations selected at 

random throughout the conterminous United States showed no persistent difference between the periods 1921-45 and 1931-60.

INTRODUCTION

The accompanying maps and discussions show the year-to-year 

changes in runoff for the period 1931-60. This period was chosen, 

not because of any hydrologic significance, but primarily because it 

agrees with the climatological standard period of the World Meteorological Organization.

In the late 1950's the World Meteorological Organization (1956) 

proposed adoption by all countries of a standard reference period. 

They chose 30-year periods starting with 1901, that do not overlap: 

for example 1901-1930,1931-1960, and 1961-90. The U.S. Geological 

Survey has adopted the climatological standard period, 1931-60 for 

use in its monthly Water Resources Review.

This period is probably most noted for two droughts during the 

1930's and the middle 1950's. Although the wet years were not as 

noteworthy as the droughts, there were several in the middle 1940's, 

1951, 1952, and 1958. Many extremely high floods occurred during 

those years; and in almost every year, including the drought years, 

major floods took place somewhere in the conterminous United States. 

The runoff for the period 1931-60 is somewhat representative of the 

long-term runoff, although in some parts of the country the 1931-60 

average was less than the long-term average.

The 30 maps of the conterminous United States supplemented by 

other discussions show the annual runoff in a way similar to the maps

81
S2 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

and discussions published in the Water Resources Review. The section on "Regional variations in runoff" shows the year to year variations for the nine regions into which the country was divided. The 

section on "Monthly distribution of runoff" discusses the monthly 

variation for several stations. The section on "Excessive and deficient 

runoff" summarizes the map data in terms of percent of area of the 

country that was excessive or deficient each year. The last section discusses "Long-term trends in runoff."

This report brings up to date and revises the original study by 

Harbeck and Langbein (1949), which covered the period 1921-45. 

The findings are generally similar to those of the earlier report but 

with the benefit of 15 years of information added. Differences that 

may exist between the maps of the two reports for each year of the 

overlapping period 1931-45 are due to the use of different stations, 

to the use of arithmetic mean rather than the median for the normal, 

and to the use of different reference periods. Table 1 lists the gaging 

stations used in this report. For comparison, table 2 shows the mean 

annual runoff at selected gaging stations for the periods 1921-45 and 

1931-60, as well as for longer periods where records are available.

TABLE 1. Gaging stations used, in this report

Name

Piscataquis River near Dover-Foxcroft,

Pemigewasset River at Plymouth, N.H___. 

Quinebaug River at Jewett City, Conn____ 

Sacandaga River near Hope, N.Y_____ ___

South Branch Raritan River near High 

Bridge, N.J.. __ ____________________

Swatara Creek at Harper Tavern, Pa____-.

Seneca Creek at Dawsonville, Md__ _ _ _

Slate River near Arvonia, Va__ _______--_

Neuse River near Clayton, N.C___-__ - -

Yadkin River at Wilkesboro, N.C_ ____---

Lynches River at Effingham, S.C____ ._-_-

St. Marys River near Macclenny, Fla_____

Fisheating Creek at Palmdale, Fla__ ___ -

Ochlockonee River near Havana, Fla____-.

Chattahoochee River near Roswell, Ga____ 

Conecuh River at Brantley, Ala ____---_

Mulberry Fork near Garden City, Ala____-

Strong River at Dlo, Miss.- ___ _--__-_-

Little Beaver Creek near East Liverpool, 

Ohio.. ________________ ..__.-------

Hocking River at Enterprise, Ohio. . _ . _ .

Gauley River near Summersville, W. Va___ 

Blue River near White Cloud, Ind _______

Eel River at North Manchester, Ind ___

Skillet Fork at Wayne City, 111. __ __

Clear Fork near Robbing, Tenn __ __ _ _

Haroeth River at Belleview. Tenn. --_____

Station

1A-0315

1A-0765 

1A-1270 

IB-3210

IB-3965

IB-5730

IB-6450

2A-0305

2A-0875

2A-1120

2A-1320

2B-2310

2B-2565

2B-3290

2B-3355 

2B-3715

2B-4500

2B-4875

3A-1095

3A-1575

3A-1895 

3A-3030

3A-3280

3A-3805

3B-4095

3B-4335

Map 

No. 

(fig. 31)

1

2 

3 

4

5

6

7

8

9

10

11

12

13

14

15 

16

17

18

19

20

21 

22

23

24

25

26

Drainage 

area (square 

miles)

297

622

711 

491

65.3

333

101

235

1,140

493

1, 030

720

435

1,020

1,230 

492

368

429

505

460

680 

461

416

475

278

404

30-year 

mean 

(inches)

26.71

29.48 

24.49 

29.89

24.26

23.35

12.58

12. 92

14.37

20.54

12.32

11.46

8.76

12.35

24.46 

18.88

22.82

17.49

14.00

12.83

31. 14 

18.01

11.47

10.74

22.54

18.33
YEARLY VARIATIONS IN RUNOFF, 1931-60 S3 

TABLE 1. Gaging stations used in this report Continued

Name

Pigeon River at Middle Falls, below International Bridge, Minn.. ... __ _______

Oconto River near Gillett, Wis_______ ___

Huron River at Ann Arbor, Mich_ ________

Genesee River at Scio, N.Y... __ ___ ____

Chateaugay River near Chateaugay, N.Y__ 

Mustinka River above Wheaton, Minn____ 

Park River at Grafton, N. Dak ________ _ Wintering River near Karlsruhe, N. Dak__ 

Big Fork River at Big Falls, Minn_ _ _ _ _

Namekagon River near Trego, Wis_ _

Sugar River near Brodhead, Wis _ _ _ _

Ralston Creek at Iowa City, Iowa_-_.__ _

Lime Creek at Mason City, Iowa.---. ___

Money Creek at Lake Bloomington, Ill____ 

Big Muddy River at Plumfield, 111 __ __

Red Rock River below Lima Reservoir, 

near Monida, Mont___ _ _ .__ _ ___ .

Tenmile Creek near Rimini, Mont___

Judith River near Utica, Mont. ____ ___

Milk River at Milk River, Alberta _ _ _

Redwater Creek at Circle, Mont_ __-_ _ _

Clarks Fork Yellowstone River at Chance, 

Mont_.___ ___ _ _____ __ _____ __

Wood River at Sunshine (near Meeteetse), 

Wyo.__ _. __________ _____

Little Missouri River near Alzada, Mont__ 

Knife River near Golden Valley, N. Dak__ 

Rapid Creek near Pactola (below Pactola 

Dam), S. Dak __________ ______

South Fork White River near Rosebud, 

S. Dak. _____________________________

Floyd River at James, Iowa. ____._-___ _

Blue Creek near Lewellen, Nebr_ __ _____

Tarkio River at Fairfax, Mo___ __________

Frenchman Creek at Palisade (near Hamlet), Nebr _ __ ________ _ ______

Wakarusa River near Lawrence, Kans _ .

Gasconade River near Hazelgreen, Mo _____

Wolf River at Rossville, Tenn_____

Little Red River near Heber Springs, Ark_

Little Arkansas River at Valley Center, 

Kans __ _ ___ _ _____

Council Creek near Stillwater, Okla_______

Rayado River at Sauble Ranch, near CiPetit Jean Creek at Danville, Ark_ _ ____

Little Wichita River near Archer City, Tex_ 

Washita River near Cheyenne, Okla_ _._.__

Mountain Fork River near Eagletown, 

Okla. _______ __ _____________________

Tensas River at Tendal, La__ __.._-__ ___

Station

4-0105

4-0710

4-1745

4-2215

4-2705 

5-0490 

5-0900

5-1205 

5-1320

5-3325

5-4365

5-4550

5-4595

5-5655 

5-5970

6A-0125

6A-0625

6A-1100

6A-1345

6A-1775

6A-2075

6A-2750

6A-3340 

6A-3395

6A-4115

6A-4495

6B-6005

6B-6465

6B-6870

6B-7105

6B-8130

6B-8340

6B-8915

6B-9015

6B-9280

7-0165

7-0305

7-0760 

7-1010

7-1442

7-1630

7-1870

7-2085

7-2605

7-3145 

7-3165

7-3390

7-3695

Map

No. 

fig. 31)

?,7

28

29

30

31 

32 

33

34 

35

36

37

38

39

40 

41

42

43

44

45

46

47

48

49 

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64 

65

66

67

68

69

70

71 

72

73

74

Drainage 

area (square 

miles)

600

678

711

309

112 

834 

742

675 

1,460

503

527

3.01

526

68.6 

753

570

32.7

331

1,104

534

1,340

194

780 

1,230

315

1,020

882

216

267

165

508

1,500

458

550

1,250

808

503

1,141 

2.00

1,327

31

410

65

741

481 

794

787

309

30-year 

mean

(inches)

11.39

10.31

8 4.9

17 24

20.87 

.71

QQ

 24

(J QQ

12.64

8. 10

6 99

5. 14

7.68 

12.04

2.85

6.02

1. 86

1.59

.41

9.09

7.53

1.04 

1.04

1. 67

1.39

2. 56

3.22

3.58

4. 11

4.78

.89

5.08

7.57

11.08

10.59

18.26

22.29 

5.66

2.61

3.61

11.91

2.67

16.01

2.35 

.69

23.64

14,65
S4 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES 

TABLE 1. Gaging stations used in this report Continued

Name

Tangipahoa River at Robert, La _________

Bayou des Cannes near Eunice, La _______

East Fork Trinity River near Lavon (near 

Rockwall), Tex _______________________

North Bosque River near Clifton, Tex __ _

Yegua Creek near Somerville, Tex. _______

Middle Concho River near Tankersly, Tex_ 

Guadalupe River near Spring Branch, Tex. 

Atascosa River at Whitsett, Tex _ _______

Conejos River near Mogote, Colo____ _ __

Bluewater Creek near Bluewater, N. Mex__ 

Alamito Creek near Presidio, Tex. ________

Rio Ruidoso at Hondo, N. Mex_ ______ __

Pinto Creek near Del Rio, Tex_ __________

Roaring Fork at Glenwood Springs, Colo__ 

New Fork River near Boulder, Wyo __ -_

Yampa River at Steamboat Springs, Colo__ 

Ashley Creek near Vernal, Utah __________

Animas River at Durango, Cblo_______ __

Silver Creek near Snowflake (near WoodBright Angel Creek near Grand Canyon, Ariz 

San Carlos River near Peridot, Ariz. ______

San Pedro River at Charleston, Ariz____._

Aqua Fria River at Lake Pleasant Dair», 

Ariz _ ____________________ ___

Big Cottonwood Creek neat Salt Lake City, 

Utah.... _________ _ _ _ _

Beaver River near Beaver, Utah _ _______

Palm Canyon Creek near Palm Springs, 

Calif... _______________________________

Convict Creek near Mammoth Lakes, Calif _ 

Cottonwood Creek near Olancha, Calif-___ 

Carson River near Fort Churchhill, Nev_ 

South Fork Humboldt River near Elko, Nev._ 

Martin Creek near Paradise Valley, Nev____ 

Silvies River near Burnes, Oreg _ ________

Arroyo Seco near Pasadena, Calif _ _ _ _ _

Miller Creek at Gerber Reservoir near 

Lorella, Oreg_----_-_- -.____ _._ _

Los Gatos Creek above Nunez Canyon, 

near Coalinga, Calif:..-..... _________

Bear Creek near Lockeford, Calif _____ ._--

Big Chico Creek near Chico, Calif . ,___--

Chehalis River near Grand Mound, Wash__ 

Swan River near Bigf ork, Mont ________

Coeur d'Alene River near Cataldo, Idaho_ 

Methow River at Twisp, Wash. ______..

Snake River at Moran, Wyo ____________

Trapper Creek near Oaklev, Idaho..-- -.

Big Wood River at Hailey, Idaho _ _ ._

Grande Ronde River at La Grande, Oreg- _ 

Lochsa River near Lowell, Idaho _____ -

Klickitat River near Glenwood, Wash_ 

McKenzie River at McKenzie Bridge,

Orpnr

South Fork Coquille River at Powers, 

Oreg.---.-- _ -_ _ _ _

Station

7-3755

8-0100

8-0610

8-0950

8-1100

8-1285 

8-1675 

8-2080

8-2465

8-3420 

8-3740

8-3880

8-4550

9-0850 

9-2010

9-2395 

9-2665

9-3615

9-3935

9-4030 

9-4685

9-4710

9-5130

10-1685

10-2345

10-2585

10-2652 

10-2860 

10-3120 

10-3205 

10-3295 

10-3935

11A-0980

11A-4835

1 IB-2245

11B-3120

1 IB-3840

L2-0275 

fi-3700

12-4135 

12-4495

13-0110

13-0830

13-1395

13-3190 

13-3370

14-1100 

14-1590

14-3250

Map 

No 

fig. 31)

75

76

77

78

79

80 

81 

82

83

84 

85

86

87

88 

89

90 

91

92

93

94 

95

96

97

98

99

100

101 

102 

103 

104 

105 

106

107

108

109

110

111

112 

113

114 

115

116

117

118

119 

120

121 

122

123

Drainage 

area (square 

miles)

646

131

779

971

990

1,280 

1,282 

1 171

282

235 

1,504

290

236

1,460 

552

604 

101

692

886

98.4 

1,027

1,219

1,459

48.5

82

94

18.7 

39. 9 

1,450 

1,150 

172 

934

16.4

220

95.5

47.6

67.9

895 

671

1,220 

1,330

824

53.7

640

678 

1, 180

360 

345

169

30-year 

mean 

inches)

22.67

25.96

7.67

3.09

3.88

.50 

3.02 

1.70

15.05

16.92 

.20

.81

1.59

11.70 

9. 13

9.67 

12.17

14.85

.35

5.01 

.60

.64

.51

17.86

8.39

.70

17.54

7. 2S 

3.30 

1.40 

2.52 

2.4.

7.08

437

.7e 3. 2e

28.71

43.21 

21. 81

28.7^ 

14.6,

22.35

3.4'

9. 11

7. 4( 

31.7'

30.8, 

65.0'

65. I!
YEARLY VARIATIONS IN RUNOFF, 1931-60 S5

TABLE 2. Comparison of 30-year normals of runoff with other long-term normals,

in inches

Name

East Branch Penobscot River at Grindstone, Maine.. .. ____________

Sudbury River at Framingham Center, 

Mass _________ ________

North Bald Eagle Creek at Beech Creek 

Station, Pa _ ____________

Yadkin River at Wilkesboro, N.C.... __

St. Regis River at Brasher Center, N.Y _

Mississippi River at Winnibigoshish

Madison River below Hebgen Lake, near

Clear Creek near Golden, Colo __ _____

Logan River above State Dam, near

N6rth Fork Kaweah River at Kaweah, 

Calif...................................

North Fork Feather FJver near PrattviUe, 

Calif.. ___ . ... . _________ .

McKenzie River at McKenzie Bridge, 

Oreg-.._._ _________ . __ _ ....

Map 

No. 

(fig. 

31)

10

29

121 

122

Mean annual runoff

1931-60

23.73 

20.38

18.82 

20.54 

18.59 

26.93 

9.62 

8.42 

22.15

4.29 

7.03

13.42 

7.65 

9.35 

8.31 

2.57

12.64 

4.62 

8.56

11.24

23.27

29.58 

22.32 

30.85

65.07

1921-45

22.51 

19.34

18.05 

20.52 

18.65 

27.70 

10.48 

6.98 

22.74

3.47 

6.35

12.69 

8.00 

10.37 

9.82 

3.10

14.56 

5.87 

9.28

11.06

21.03 

25.93 

21.06 

29.45

59.98

1911-60

23.79 

19.46

19.40 

 20.58 

19.60 

28.15 

10.41 

8.51 

23.20

4.36 

6.92

14.26 

8.07 

10.69 

9.56 

2.98

15.27 

6.66 

8.81

10.62

23.23 

28.07 

23.11 

31.73

64.78

1901-60

19.59

20.01 

29.20 

10.44

4.78 

7.46

9.61

16.36

5.82

1886-60

20.50

4.85

1876-60

20.48

140 years (1921-60).

MAPS OF ANNUAL RUNOFF

The maps of figures 1-30 show the annual runoff, in percent of the 

1931-60 normal, in the conterminous United States for each year from 

1931 to 1960.

Records at 123 stations (table 1) were used to define the areas of 

normal, excessive, and deficient runoff; the locations of these stations 

are shown in figure 31. The criteria used to select the 123 stations 

were as follows:

1. The drainage areas must range between 1 and 1,500 square miles.

2. Diversions are less than 10 percent of the flow or irrigation consumptive use is less than 10 percent of the annual runoff.

3. The downstream station must have a drainage area of more than 

twice that of an upstream station on the same stream.

In addition, records of two stations on the same stream were combined, if the drainage areas differ by less than 15 percent.

For this report, however, no two stations on the same stream and 

no station with regulated flow where the storage would affect the 

annual runoff by more than 10 percent were selected. Several station

(Text continues on p. 837.)

690-148 O - 63 - 2
S6 CONTRIBUTIONS TO THE HTDROLOGY OF THE TJNTTED STATES

o

I
YEARLY VARIATIONS IN RUNOFF, 1931-60

1I

!

ST
S8 CONTRIBUTIONS TO THE HYDROLOGY OF THE TOnTED STATES

^..

ooco 
YEARLY VARIATIONS IN RUNOFF, 1931-60 S9

fT^X'XtX'X-XvX'X'V-X'IsX'X'X f

u ''x:x:x::::::::::<::x:'' i 'xjxi:y':!x /s .f..-^.-.® / cvj ."."."L".*.".". o,p." / \ _ "."."l'.*.S*."^ .".*.". .". . .".". * - '' mm<y/^ i q$mmg&& ' - f i ( °r ^ - -H-t-:-:-:-:-:-x-:-:-::x-.Y --i-±i s , v i x :-xt;-;c-x-x-.-:-:-.-:-:-- / « ^
S10 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

cr>

COITi 
YEARLY VARIATIONS IN RUNOFF, 1931-60 S1I

8 -;iiiiili|::, J:,il ~m+m^& s ! - -.-. . R.O-.-.-.- .-. .[ .-. i;.S-. . .-. . .[. .-. R. .:>. . v.-^.. 5I
Streamflow among 24

,\VX lowest 25% of record 

SUeamflow among 

highest 25% of record 

E Estimated 1937

FIGURE 7. Annual runoff, In percent of normal, for tbe water year 1937.
YEARLY VARIATIONS IN RUNOFF, 1931-60 S13

oo

OO 

sp

a

00

tf

a 

690-148 O - 63 - 3
S14 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES
YEARLY VARIATIONS IN RUNOFF, 1931-60 S15

o>

-mA':

j|l P
Streamflow among 

lowest 25% of record 

Streamflo* among 

highest 25% of record 

Estimated 1941

FIGURE 11. Annual runofl, In percent of normal, for tbe water year 1941.
YEARLY VARIATIONS IN RUNOFF, 1931-60 S17

a 3

I 

53
S18 CONTRIBUTIONS TO THE HYDBOLOGY OF THE UNITED STATES

CO
YEARLY VARIATIONS IN RUNOFF, 1931-60 S19
S20 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

to
YEARLY VARIATIONS IN RUNOFF, 1931-60 S21

to

690-148 O- 63-4
S22 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES
YEARLY VARIATIONS IN RUNOFF, 1931-60 S23

00
S24 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

cn
YEARLY VARIATIONS IN RUNOFF, 1931-60 S25

En

s

I
S26 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES
YEARLY VARIATIONS IN RUNOFF, 1931-60 S27

. ...

j-JV.'.'.'.'.'.'. . ..-.V,,

IB" a
Nomal

Norm;

19 / :-:-:-37:-j-. 15 .] : : : :

/ 33 XvXfXv.-.v.vXyXv

 -^.. ::#.;:!fc;:;:!:;:;:>::;:!:j:|:!:;:;

GC

" v.&__>o:-::-!r:**''i

X.-.;.;

'.'.'." Streamftew among \\'t 

''.'.''. '. lowest 25% of record V''t/'"~'

Streamflow among 

P^w highest 25% of record \

1953

B 

w

1

» 

O

a

1

GO

FIQUBE 23. Annual runoff, in percent of normal, for the water year 1953.
YEARLY VARIATIONS IN RUNOFF, 1931-60 S29

:-:->«Xv : : :« x-r.v-.-Xvv
S30 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

A .*^.- I ~V--fcV> *">-/ ; - i K ^.-"r.
YEARLY VARIATIONS IN RUNOFF, 1931-60 S31
S32 CONTraBUTIONS TO THE HYDROLOGY OP THE TOOTED STATES

S

I 

I
YEARLY VARIATIONS IN RUNOFF, 1931-60

Ii

I

i
Normal . .'.'.'.\, . .'.'.' ^ ^/^r

E Estimated 1959

o 

o

i

en

FIOUBE 29. Annual runoff, In percent of normal, for the water year 1959. \

GO
YEARLY VARIATIONS IN RUNOFF, 1931-60 S35
S36 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES
YEARLY VARIATIONS IN RUNOFF, 1931-60 S37

records that did not span the entire 1931-60 period were extended 

by using the required record from a nearby station on the same stream 

if the drainage areas at the two sites differed by less than 15 percent. 

Records extended in that way were adjusted on the basis of the ratio 

of their drainage areas to make them comparable.

The normals used in this report are arithmetic means. The arithmetic mean allows the use of the map of mean annual runoff in conjunction with these maps. A study was made comparing the mean and 

median at the 123 stations. For almost two-thirds of the country the 

difference between the mean and median is small, and hi only about 

one-sixth of the country is the difference greater than 25 percent. 

Either, therefore, could have been used with only little difference in 

the results, but the mean allows mathematical computations when compared with the map of annual runoff.

The lines of normal runoff separate the regions in which runoff was 

above normal from those in which runoff was below normal. In 

accordance with the procedures in the Water Resources Review, runoff for any given year was defined as excessive if among the highest 25 

percent of record and deficient if among the lowest 25 percent of 

record. To determine the years excessive and deficient in runoff at 

any gagging station used for this report, the 30 annual events were 

ranked at follows: The highest 7 were called excessive and the lowest 7 

were called deficient. The runoff at any gaging station, therefore, is 

called normal for 50 percent of the years, excessive for 25 percent, and 

deficient for 25 percent. The areas of excessive runoff are shown on 

the maps by dark shading and the areas of deficient runoff by light 

shading;.

In order to have a full set of 30 values for each gaging station, 

it was necessary to estimate some annual runoff figures. At most stations, where estimates were needed, only 1 or 2 years were estimated. 

Seventy stations did not require estimates and 26 needed only one. 

Only 4 percent of the total 3,690 station years were estimated.

REGIONAL. VARIATIONS IN RUNOFF

The country was divided into nine regions (fig. 32), which were 

delineated by gaging stations having similar patterns of annual runoff. The number of such stations within each region ranged from 9 to 

20. The mean discharge for the period 1931-60 was computed for each 

station, and the yearly discharges, expressed in percent of the 30-year 

mean, were averaged within each region. These averages are plotted 

in figure 33 to depict the yearly variation in runoff within each region. 

An interesting fact shown by figure 33 is the variability of the runoff 

from year to year. For example, in the Lower Plains the percentages 

range from 18 percent to 211 percent.
S38 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

Table 3 gives the average standard deviations of the percentage of 

annual runoff for each region. Because these percentages are approximately normally distributed, about two-thirds of the annual discharges will be within one standard deviation on each side of the mean. 

For example, the standard deviation for the Midwest region is 35 

percent, or about two-thirds of the annual discharges within the 

region are within 35 percent of the mean. Figure 33 also shows how 

few prolonged periods of either above or below normal runoff there 

are for several of the regions. The Northeast, South, and Northwest 

regions alternate above and below the mean almost each year. The 

Upper Plains region, however, has basically only three different 

periods, 2 below and 1 above the mean. The Southwest has been below 

the mean almost continuously since 1945.

Several years are of special interest. Both 1931 and 1940 were below 

the mean for all regions; and 1934, 1939, 1954, 1955, and 1959 were 

below the mean for all but one region. There were no years when all 

regions were above normal; but in 1938,1943,1951,1952, and 1958 all 

but two regions were above normal. For the country as a whole, 1934 

had the lowest average percentage, only 56 percent, and 1942 had the 

highest, 129 percent; 1934 had the least variation and 1941 had the 

most variation. The whole period from 1941 through 1952 was above 

normal and the period from 1953 through 1956 was below, the wettest 

and dryest periods, respectively, between 1931 and 1960. Table 4 gives 

the average and the standard deviation for each year for the conterminous United States. These are the averages of the regional figures.

MONTHLY DISTRIBUTION OF RUNOFF

Figure 34 shows the normal distribution of runoff by months at 

selected gaging stations. The monthly percentages were computed 

by averaging the discharges for each month and then expressing them 

as a percentage of the mean annual flow for the period 1931-60. These

TABLE 3. Regional standard deviations of annual runoff for the conterminous

United States, in percent

Region

Northeast

South. ___ ._ _ ... ___ ... ___ .. __ ...

Midwest.. ____________ _____ _____ ____ _ ___

Upper Plains __ --___-__.__-____-_______--- __

Lower Plains _ _ _______________ _______________

Rocky Mountains____--___________._______- ___

Southwest -__-_____.-___-..__._.--.._...______-

Great Basin __ __ _____________________________

Northwest.. __ ________ _ _ __ _ __ _ ___ __._

Average-.-.--..-- ___ ___-__-__ _.____--

Number of stations in region

12

20

17

13

12

17

12

11

9

123

Standard deviation (percent)

20

35

35

70

75

35

75

35

25

50

S40 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED

1931 1935 1940 1945 1950 1955

140

Note:-Ordinate 

shows percent 

of the 30-year 

mean annual 

runoff for each 

year

20

1931 1935 1940 1945 1950 1955

FIGURE 33. Yearly regional variations in runoff.
YEARLY VARIATIONS IN RUNOFF, 1931-60 

1931 1935 1940 1945 1950 1955

Note:-Ordinate 

shows percent 

of the 30-year 

mean annual 

runoff for each 

year

i r

1931 1935 1940 1945 1950 

FIGURE 33. Continued.

1955 1960
Ordinate shows percent of 

the annual runoff that normally occurs in each month 

of the year

Abscissa shows monthly runoff for a 12-month period 

beginning in October and 

ending in September

FIGURE 34. Normal monthly distribution of runoff.
g
S44 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES 

TABLE 4. Average and standard deviation of mean annual runoff, in percent

Year

1931.---.

1932_. _

1933--.-

1934__-_-

1935-.--

1936---.

1937.-__.

1938-.--

1939..-..

1940.. _

Average

61

111

98

56

110

91

106

117

79

78

Standard deviation

31

50

39

26

49

49

49

61

23

28

Year

1941__-_-

1942.--.-

1943..---

1944..---

1945.---.

1Q4R

1Q47

1948----

1Q4Q

inert

Average

122

129

121

103

117

101

110

106

112

117

Standard deviation

80

72

50

54

37

33

41

55

42

71

Year

195J----

1952--.-

1953-.--

1954--.-

1955 _ .-

1956.-.--

1957---.

1958----

1959----

1960 .--

Average

111

127

87

73

73

83

105

122

80

100

Standard deviation

65

54

35

42

30

44

46

53

26

38

graphs show some patterns of runoff but may not represent what 

happens at any stream in the area. Many other patterns could be 

shown, such as the high flows in the fall and low flows hi the spring 

in the Florida Peninsula or the extremely uniform flows hi the 

Sand Hills of Nebraska.

It is interesting to note the seasons in which the maximum monthly 

discharge occurs. Starting in the Southeast where most of the high 

flows occur in February and March and progressing north and west 

to the Rocky Mountains where the high flows occur in May and June, 

there is a tendency for most of the flow to occur within progressively 

shorter periods. The shortest period of maximum flow occurs in 

the northern Great Plains. In the Park River in North Dakota more 

than 60 percent of the flow occurs in 1 month. Also worth noting are 

the high winter flows along the Pacific Coast, as shown by the Chehalis River in Washington, and the two high-water periods in the 

southern intermountain region as shown by the San Pedro River in 

Arizona.

EXCESSIVE AND DEFICIENT RUNOFF

Table 5 shows the percentage of area of the conterminous United 

States that was classified excessive or deficient in runoff each year. 

This table is another way of indicating the variation in runoff. There 

are no years when runoff was neither excessive nor deficient. The 

averages for the country as a whole for the period 1931-60 are: 18 

percent deficient, 16 percent excessive, and 66 percent normal. These 

figures are exactly the same as for the period 1921-45 (Harbeck and 

Langbein, 1949), even though the individual years varied greatly.

Noteworthy deficiencies in runoff occurred in the years 1931 and 

1934. More than two-thirds of the country was deficient in runoff in 

1934, and more than one-half was deficient in 1931. There is no out-
YEARLY VARIATIONS IN RUNOFF, 1931-60 S45

standing wet year, although in 1952 more than one-third of the 

country had excessive runoff. Two years, 1939 and 1946, were notable 

because of the small amount of excessive and deficient runoff; the 

runoff was classified as normal over 80 percent of the country for 

both years.

Local variations from the nationwide pattern can be seen on almost every map. For example, in 1934 the Pacific Northwest had excessive runoff in contrast to most of the rest of the country, which had 

deficient runoff. The excessive and deficient runoff areas for 1932 

and 1957 are intermixed and therefore are examples of no large 

regional pattern.

TABLE 5. Percent of area of the conterminous United States with deficient and

excessive runoff

Year

1931-------------

1932.. ._....___..

1933.. .---._._. -.

1934.. --._._.._..

1935_--------_..

1936__. --..._._..

1937-.-. __._.___.

1938-------------

1939-----------..

1940--------.----

1941------.-_-_.

1942___--_-_____

1943. ----._-_-__.

1QAA.

1945--__--______

1946.. .---_-_._-_

1947.. _._.__-.---

Deficient

53

8

12

67

8

17

8

4

17

36

29

5

1 q

4

7

8

Excessive

1

1Q

14

3

16

8

22

18

1

1

24

27

27

IO

24

12

22

Year

1948.__----------

1Q4-Q

1950. __ ---------

1951. ..----------

1952.. __-___.-_--

1953____---------

1954 __ ------ _ -

1 Qi^

IQKfi

1957--.- _ --_.--

1958 ___ --------

1Q5Q

IQfift

1931-60

average __ _.

Deficient

12

6

7

18

11

16

39

qi

38

13

8

30

10

18

Excessive

16

18

25

27

35

9

5

1

15

15

27

6

13

16

Figures 35 and 36 show the maximum and minimum annual runoff, 

in percent of normal, for the 30-year period. The maximum annual 

runoff ranges from 115 percent of normal in Nebraska to more than 

700 percent of normal in North Dakota and is more than 600 percent 

of normal in the Southwest. The minimum annual runoff ranges 

from 75 percent of normal in Nebraska to zero in Montana, Minnesota, 

and California.

The regions of greatest maximum percent of normal flow are the 

Upper Plains, the Southwest, and Southern California, whereas the 

regions of lowest minimum percent of normal flow include almost 

all the Plains States and Southern California. The maps are similar 

in pattern but opposite in values. The regions of highest maximum 

percent of normal runoff are generally the regions of lowest minimum 

percent of normal runoff and vice versa.


S48 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

OO

01 01 0)

30

20> \J/k\

\J

^

^

A

Sudbury River at Framingham Center, Mass.

40

30

20

V

Hiwassee River above Murphy, N. C.

Mississippi River at Winnibigoshish Dam, 

near Deer River, Minn.

2.0

1.0 

0.8

0.6 

0.4

12

10

8

6

Little Missouri River near Alzada, Mont.

Rio Grand* near Del Norte, Goto,

00 0) 0) 0) 0) 0) 0)

San Pedro River at Charleston, Ariz.

Logan River above State dam, near 

Logan, Utah

Santa Ana River near Mentone, Calif.

Kachess River near Easton, Wash.

8

0 o o o o o o

O «- CM <*) ^ If) iO

00 wt O* O* O* O* Ot O1*

Noter-Ordinate shows the inches o 

runoff that occurred each year

FIGURE 37. Long-term trends In mnoff.
YEARLY VARIATIONS IN RUNOFF, 1931-60 S49

The maximum annual discharge is less than twice the mean for most 

of the conterminous United States east of the Mississippi Kiver and in 

a broad band from Colorado and Nebraska to the Pacific Northwest, 

The minimum annual discharge is at least one-half the mean for a 

much smaller area in the Northeast, Southeast, Upper Midwest, and 

scattered areas in Nebraska, Colorado, Idaho, and the Pacific 

Northwest.

LONG-TERM TRENDS IN RUNOFF

The runoff during the period 1931-60 agrees with that from the 

50-year period 1911-60, except in .the Central and Lower Plains and 

in the Southwest, where at places it has been considerably less (fig. 

37). For most of the conterminous United States, except the Central 

and Lower Plains and the Southwest, the runoff during the 30-year 

period is slightly more than that during the previous base period, 

1921-45. Table jafshows the comparison of the 1931-60 period with 

the 1921-45 and the 1911-60 periods for 25 selected long-term stations 

and comparisons with the 60-year, 75-year and 85-year periods for a 

few stations. A comparison of the mean annual runoff for the base 

periods 1931-60 and 1921-45 shows no persistent difference between 

them. Furthermore, although the mean annual runoff during the two 

base periods was a little less than during the 50-year period 1911-60 

at most of the 25 stations used in the comparison, neither base period 

seems to have a marked advantage over the other with respect to being 

more representative, nationwide, of the longer-term period.

REFERENCES

Harbeck, 6. E., Jr., and Langbein, W. B., 1949, Water resources review, supp. 2, 

Normals and variations in runoff 1921-1945: U.S. Geol. Survey, Water 

Resources Div.

U.S. Geological Survey, and Canada Dept. Northern Affairs and National Resources, issued monthly, Water resources review: U.S. Geol. Survey, Water 

Resources Div.

World Meteorological Organization, 1956, Technical regulations, General, 1st ed. 

Geneva, Switzerland, Secretariat, World Meteorol. Organization, v. 1, 

WMO-49.

U. S. GOVERNMENT PRINTING OFFICE : 1983 O - 690-148