APR B01964

Channel Geometry of 

Piedmont Streams as 

Related to Frequency

of Floods SCRANTON I 

PUBLIC LIBRARY 

feom

GEOLOGICAL SURVEY PROFESSIONAL PAPER 422-E
Channel Geometry of 

Piedmont Streams as 

Related to Frequency 

of Floods

By F. A. KILPATRICK and H. H. BARNES, JR.

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 422-E

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1964
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEW ART 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

Glossary.._ ______________________

Abstract.. _ ______________________

Introduction. ____________________

The study area.__--__-__--__-____

General requirements__ _ _____

Characteristics of the Piedmont. 

Selection of sites._____________

Field surveys___________________

Observations on channel geometry _ _

Page

IV

El 

1 

1 

1 

1

1

2

2

Definition of bankfull stage._________________________

Section properties as criterion for bankfull stage.__.

Valley benches as criterion for bankfull stage...--.. 

Presentation of data. ___________---_-___--_-___--_-

Frequency of bankfull discharge._________-____-_--__

The effect of slope.______-_____-_____-__-_-___---__

Variation of water surface slope with depth.__________

Summary and conclusions....-.-..-_________________

References cited____________________________________

Page 

E4

4

5

9

10

10

10

FIGURE

ILLUSTRATIONS

1.

2.

3.

4

5.

6.

Page 

Location of the channel geometry sites in the 

study area ______ _ _ _ _ E2

Plan view of Stevens Creek near Modoc,

S.C. ____-.___-_---_.-_.______________ 3

View of rock outcrop below cross section 

11 at Stevens Creek__ __ 3

View from left bank looking upstream toward 

natural levee at cross section 1 1 at Stevens 

Creek ___ __________ _ 5

View of deposition on the natural levee below 

cross section 11 at Stevens Creek __ 5

FIGURE

1 

1

1

Formation of natural levee by deposition in 

the immediate vicinity of the stream bank 

at Murder Creek near Monticello, Ga____

Profiles of mean annual flood stage and 

various bench levels for Stevens Creek-.

9. Photograph indicating the existence of two 

prominent benches at Murder Creek. ____

10. Relation of bankfull depth to depth of mean 

annual flood for Piedmont streams. ______

Comparison of the data for 34 sites in the 

Piedmont with graph of equation 1 ______

Relationship between water surface slopes 

at low stage and at bankfull stage. ______

Page

E5

10

TABLES

TABLE 1. Channel-geometry sites near gaging stations._

2. Supplementary channel geometry sites..____

3. Data corresponding to the mean annual flood 

and various bench levels for streams in the 

Piedmont.______________ ________________

Page

E4

4
GLOSSARY

Bankfull stage. A river stage corresponding to the mean elevation of the predominant bench.

Bench. A relatively flat portion of land within a river valley.

Channel slope. A ratio of fall to length for a given reach of 

stream, usually expressed as feet per foot.

Control. A reach or section of channel downstream from a 

gaging station that determines the stage-discharge relation 

at the gage. A natural constriction of the channel, a sudden steepening of bed slope, or an artificial dam, is a section 

control; in the absence of a section control, a long reach 

of channel or a bend may be a channel control.

Depth. The difference between the average elevation of the 

bed of the main channel and the elevation of the water 

surface.

Flood plain. A relatively flat strip of land adjoining a river 

channel, which is associated with the stream in its present 

regime. This strip may or may not be the predominant 

bench in the valley.

Mean annual flood. The mean of the values in an array consisting of the highest momentary discharge dui'ing each year of 

stream flow record; it is the discharge of the stream which 

is equalled or exceeded once each 2.33 years on the average.

Natural levee. An alluvial ridge on the flood plain, usually 

adjacent to the channel.

Predominant bench. The widest bench in a river valley which 

can be traced throughout a reach of river channel, and 

which is flooded at intervals by the stream.

IV
PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

CHANNEL GEOMETRY OF PIEDMONT STREAMS AS 

RELATED TO FREQUENCY OF FLOODS

By F. A. KILPATRICK and H. H. BARNES, JR.

ABSTRACT

The relation of the height of valley benches to the height of 

water surfaces corresponding to floods of selected recurrence 

intervals was investigated at 34 sites in the Piedmont province, 

which lies in the southeastern part of the United States. The 

field investigation included surveys of the geometry of the 

channel and the measurement of water surface profiles during 

flood periods. The discharge-probability relation was established from records at gaging stations.

The heights of the valley benches were found to be significantly 

related to the depth of flow corresponding to the mean annual 

flood, and to the slope of the stream channel.

INTRODUCTION

Recent investigations have indicated that the geometry of a stream channel is related to the flow regime. 

Several investigators 1 (Wolman, 1955, p. 31; Wolman 

and Leopold, 1957, p. 89), have shown that the discharge 

at bankfull stage has a recurrence interval of 1 to 2 

years. However, bankfull stage as used in these studies 

was more of a concept than a precise topographic definition. It was recognized that where terraces or abandoned flood plains exist, the active flood plain associated 

with present stream regimen is often difficult to define.

The purpose of this investigation was to define bankfull stage in relation to topographic features and to 

relate it to some index of discharge. The data required 

for the study included detailed surveys of the channel 

geometry along reaches of streams for which the frequency of flood discharges was known from gaging-station records or areal studies.

Data used in this study were obtained in part from 

the district offices of the Geological Survey in Georgia, 

Alabama, North Carolina, and South Carolina. These 

offices also provided valuable assistance with the field 

work in obtaining the necessary profiles and cross sections at the study sites.

1 Walter B. Langbein (unpublished data) showed that the discharge 

at bankfull stage is roughly equal to the mean annual flood; this flood 

has a recurrence interval of 2.33 years.

THE STUDY AREA 

GENERAL REQUIREMENTS

The selection of a study area was governed by physiographic considerations. The study sites were selected 

within one broad area of generally similar physiographic or geomorphic characteristics, the southern 

part of the Piedmont province. Similarity of physiographic characteristics should imply similarity of 

stream channels. This area should provide a large 

degree of homogeneity among sites within the area.

CHARACTERISTICS OF THE PIEDMONT

The Piedmont province (see fig. 1) lies in eastern 

United States, bounded on the west by the Blue Ridge 

and on the east by the Coastal Plain. It extends southward from Maryland into Alabama, a distance of about 

700 miles.

The Piedmont is a nearly smooth undulating upland 

surface which slopes gradually southeastward. There 

are no ridges or peaks within the area that stand out 

conspicuously above the surrounding terrain. The 

crystalline rocks, which underlie the Piedmont, pass 

southeastward beneath the unconsolidated sediments 

of the Coastal Plain. The rocks have been subject to 

several profound deformations involving metamorphism, igneous intrusion, close folding, and overthrust 

faulting.

The Piedmont is a peneplain which has been only 

slightly dissected and in which strong and weak rocks 

do not show marked differences in resistance to erosion. 

In general, the rocks are deeply weathered. The uplands, therefore, tend to be smooth, have few outcrops of 

fresh rock, and exhibit broad and shallow valleys having long, gentle slopes. Rocks are exposed in many of 

the streambeds.

SELECTION OF SITES

Thirty-four sites were chosen for study from more 

than 200 stream-gaging stations currently maintained 

within the study area. These sites were selected priEl
E2

88°

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

86° 84° 82° 80°

U T H.--'' C A R 0 L I N A 

FIGURE 1. Location of the channel geometry sites in the study area. Site numbers correspond to those in tables 1 and 2.

marily on the basis of (1) adequacy of the stage-discharge relation to at least overbank stages, (2) freedom 

from regulation of floodflows, and (3) uniformity of 

the stream channel in or adjacent to the reach on which 

the gage is located. Drainage areas ranged from 1.6 

square miles to 630 square miles. The selected sites were 

also well distributed with respect to location and 

altitude.

FIELD SURVEYS

Detailed information on channel geometry was obtained at each of the 19 sites near gaging stations listed 

in table 1. Less detailed information was obtained at 

the 15 supplementary sites listed in table 2.

Transit-stadia surveys of a reach of channel were 

made at each site. An average of 12 cross sections were 

surveyed at sites near gaging stations, and 2 or 3 at 

the supplementary sites. The distance between cross 

sections was equivalent to about twice the width of the 

channel. A typical plan view of the location of cross 

sections is shown in figure 2.

Additional data obtained in the surveys included 

samples of bed and bank material, photographs, and 

profiles of highwater marks of one or more floods.

OBSERVATIONS ON CHANNEL GEOMETRY

Stream channels in the Piedmont follow a variety of 

courses that consist of rather sharp, short-radius bends, 

as well as long, gradually curving or almost straight 

reaches. Some of the reaches may extend for as much 

as a mile with only minor deviations from a straight 

line. In some places the benches are narrow and irregular, or almost nonexistent; in others, they are broad 

and flat.

The stream channels are deeply entrenched in many 

places, the present position being controlled by outcrops 

of rock. Even where the benches are broad and active 

meandering might be expected to occur, rock exposures 

are found in the streambed and along the channel banks 

(fig. 3).

This pattern is consistent with Lobeck's (1939, p. 223) 

suggestion of streams having alternating stretches of 

youth and maturity. The concept of temporary base 

levels may apply here.

The streambeds, in cross section, are nearly flat, and 

the bed materials range from fine sand to small boulders. 

Usually the streambed is highest near the center of the 

channel and deepest near the banks, which generally
CHANNEL GEOMETRY OF PIEDMONT STREAMS E3

 Cross sections 

Crest-stage gages 

Volley limits

-/ Limits of bench systems 

Different bench levels

Natural levees ' '

FIGUEE 2. Map of Stevens Creek near Modoc, S.C.

rise rather steeply. The banks are usually protected 

near the top by trees and healthy growths of vines and 

bushes.

Natural levees and a complex system of benches exist 

at all sites. For example, the cross section of Stevens 

Creek in figure 4 shows natural levees and three separate 

benches at different elevations. The benches are also 

delineated in figure 2. The photograph shown as 

figure 5 was taken on the left bank of cross section 11 

looking upstream. The mean annual flood corresponds 

to a stage about 4 feet above the top of the levee and 

6 to 7 feet above the bench.

Another phenomenon noted at Stevens Creek was 

the active deposition of mud and fine silt on the natural 

levees. The amount of deposition on the levee just below 

cross section 11 is easily discernible in figure 6. The 

trees stand in "sinkholes" formed by deposition occurring everywhere except in the immediate vicinity of 

the tree trunks, where local velocities are higher. The 

reach on Stevens Creek has a very flat slope, which may 

explain the large amount of deposition, but deposition 

also occurs on the immediate banks of many of the 

streams regardless of channel width, depth, or slopes.

FIGURE 3. View of rock outcrop below cross section 11 at 

Stevens Creek. These rock outcrops are typical of Piedmont 

streams.
E4 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

This was noted particularly at the site on Murder Creek 

near Monticello, Ga., immediately after the flood of 

June 2, 1959. Silt and sand were deposited adjacent to 

the banks of the creek and formed new levees or added 

to old ones. One of these deposits is shown in figure 7. 

The thick undergrowth may have increased the deposition.

TABLE 1. Channel-geometry sites near gaging stations

No. Station

Drainage 

area (sq. 

mi.)

Datum of 

gage above 

sea level

Alabama

1 

2 

3

Sofkahatchee Creek near Wetumpka__ 

Talladega Creek near Talledega _ _ _

Hillabee Creek near Hackney ville_

5. 1 

98.4 

196.0

440 

500 

558

Georgia

4 

5

6 

7 

8 

9 

10

Murder Creek near Monticello _ _

South Beaverdam Creek near Dewy

Etowah River near Dawsonville_____

Chattahoochee River near Leaf

Tobesofkee Creek near Macon

Middle Oeonee River near Athens. ___

24.0

35.8 

103.0 

134 

150 

182 

398

498

581 

1,050 

810 

1,219 

310 

556

South Carolina

11

12

13

South Tyger River near Reidville_

Little River near Mount Carmel

106.0 

217.0 

545

626 

354 

197

North Carolina

14

15 

16 

17 

18 

19

Eno River at Hillsboro

Second Broad River at Cliffside _ _ _

4.9 

28.8 

66. 5 

168 

211 

340

356 

1,212

487 

472 

670 

420

TABLE 2. Supplementary channel geometry sites

No. Station

Drainage 

area 

(Sq mi)

North Carolina

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30

Uwharrie River near Eldorado.. _ _ _ _

South Fork Catawba River at Lowell _ _

Carroll Creek near Colletsville __ ___

Moon Creek near Yancy ville

21.7 

80.0 

93. 9 

347 

630 

1. 6 

2. 76 

3.26 

16.3 

29. 9 

77.0

Georgia

31

32 

33

34

Shetley Creek near Norcross_ _ __ _ _ 0. 98 

2.23 

26. 5 

126. 5

DEFINITION OF BANKFULL STAGE

One of the objectives of this investigation was to 

develop a consistent method for defining bankfull stage 

from the properties of the cross section or from topographic features which can be recognized in the field. 

The criterion for consistency is that the profile of bankfull-stage elevations should plot approximately parallel 

to the longitudinal profile of the water surface at some 

given discharge through the reach.

SECTION PROPERTIES AS CRITERION FOR BANKFULL 

STAGE

The relation between stage and section properties 

such as area, wetted perimeter, width or mean depth 

do not consistently denote the elevation of bankfull 

stage. In any single cross section a sharp break usually

25

20

15

§ 10

LiJ

O 

CD

<

-5

© Old bench

Q) Predominant bench

@ Minor bench

50 

I

100 FEET 

I

FIGURE 4. Cross section 11 at Stevens Creek.
CHANNEL GEOMETRY OF PIEDMONT STREAMS E5

FIGURE 5. View from left bank looking upstream toward natural levee 

at cross section 11 at Stevens Creek. The tape is stretched horizontally from the top of the levee toward the edge of the predominant 

bench.

- V-9^

FIGURE 6. View of deposition on the natural levee below cross section 

11 at Stevens Creek.

t*~« urfe ^

m^ ' ;>

-'SWf i

>^5 si^:^?l*s^^^f':^i^ fs&efc

FIGURE 7. Formation of natural levee by deposition in the immediate 

vicinity of the stream bank at Murder Creek near Monticello, Ga.

occurs in the relation of any two section properties, 

such as depth and width, but the elevations determined 

in this manner do not follow a regular pattern along 

a reach. These stage-property curves have erratic 

shapes that reflect the existence of several benches.

VALLEY BENCHES AS CRITERION FOR BANKFULL

STAGE

The problem of defining bankfull stage therefore is 

due directly to the difficulty in deciding which of the 

several valley benches are associated with present stream 

regimen. Since this problem could not be resolved 

within the time limitation of this study, the predominant bench was used in each case to determine bankfull 

stage.

A bench was considered predominant at a given site 

if it was the widest bench and could be traced for a 

considerable distance along the stream. The bench elevations were determined by field survey. Natural 

levees were ignored in computing the mean elevation of 

the benches. A profile of bankfull stage at each site 

was defined by plotting the elevations of the predominant bench against distance along the channel and
E6 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

CROSS SECTIONS

46 8 10 12 14 16 18 20 

DISTANCE DOWNSTREAM FROM CROSS SECTION 1, IN HUNDRED FEET

FIGUBB 8. Profiles of mean annual flood stage and various bench levels for Stevens Creek.

22 24

fitting the points with a line parallel to the known 

water-surface profile at about this stage.

When bankf ull stages so defined were plotted against 

distance along the channel, discontinuities were evident 

where there were major changes in the slope of the 

channel bed. This is illustrated in figure 8 by the profiles of benches 2 and 3 along Stevens Creek. In this 

instance benches 2 and 3 are clearly predominant in 

the respective upstream and downstream reaches. It 

should be noted that a higher and lower bench are 

identifiable but not prominent enough that either could 

be associated with bankfull stage. There is a drop of 

about 3 feet between the predominant benches where 

the slope of the channel bed flattens. Because the bench 

elevations appear to be associated with the slope of the 

channel, reaches were subdivided into lengths of reasonably constant slope.

At Murder Creek two benches of about equal width

exist, and two equally valid bankfull profiles were 

determined. The two benches are indicated in figure 

9. The water-surface profile existing at the higher 

bench level was much steeper than the water-surface 

profile at the level of the lower bench. The two benches 

are thus associated with different slopes an unusual 

occurrence where a section control is effective up to an 

extreme stage.

PRESENTATION OF DATA

Data corresponding to the mean annual flood and the 

various bench levels at the 34 stream sites are listed in 

table 3. The definition and source of the data in each 

numbered column in the table are given below: 

1. The numbers corresponding to the various bench 

levels in the valley reach. Bench levels are numbered from highest to lowest in the manner illustrated in figures 2,4 and 8.
CHANNEL GEOMETRY OF PIEDMONT STREAMS E7

FIGURE 9. Photograph indicating two prominent benches at Murder

Creek.

2. The discharge corresponding to the various bench 

levels as determined from the stage-discharge 

relationship.

3. The recurrence interval of the discharges in column 

2 determined from an analysis of gaging-station 

records for sites 1-19 and from a regional floodfrequency analysis for sites 20-34.

4. The slope of the water surface for the particular 

bench level.

5. The mean depth, determined as the difference between the stage corresponding to the average 

bench elevation and the stage corresponding to the 

mean elevation of the channel bed.

6. The number of cross sections used to define the characteristics of the reach. The highest and lowest 

benches were seldom identifiable throughout a 

reach.

7. The relative size of the benches at a given site are 

shown by numbers from 1 to 3. Number 1 indicates the predominant bench; number 2, a prominent but narrower bench; and number 3, a lesser 

bench.

8. The discharge corresponding to the,mean annual 

flood, determined from the information on flood 

frequency described for column 3.

9. The depth of the mean annual flood, determined as 

the difference between the stage of the mean annual flood (from the stage-discharge relationship) 

and the stage corresponding to the mean elevation 

of the channel bed. An average value of the 

reach is listed.

TABLE 3. Data corresponding to the mean annual flood and various bench levels for streams in the Piedmont

Bench level

Site

1

2____. _ ._ _

3___________.

4__ _ ___ _

5__ __________

6___ ___ _

7__ __ _______

1

Bench 

(highest 

to lowest)

1

2 

3 

1

2 

3 

4 

1

2 

3 

4 

1

2 

3 

1

2 

3 

4 

1

2 

3 

1

2

2

Q

(cfs)

890

760 

620 

7,700

6,600 

5,050 

1,950 

5,950

4,500 

3, 450 

1,660

2,000 

580 

2,000

1, 300 

1, 240 

630 

3,700

3, 170 

2,900 

7,500

4,200

3

Recurrence 

interval 

(years)

2.90

2. 33 

1.90 

2.90

2. 18 

1.82 

1. 10 

2. 30

1.65 

1. 38 

1. 12

23. 1 

1. 55

9.7

2.55 

2. 33 

1. 14 

5. 2

3. 0 

2. 33 

12. 2

3. 5

4

Slope 

(ft per ft)

0. 0039

. 0039 

. 0039 

.0023

.0017 

. 0009 

. 0007 

. 00068

. 00078 

. 00085 

. 00052

. 0044 

.0018 

. 0017

. 0018 

. 0028 

. 0040

. 00088 

. 00068 

.0012

.0012

5

Mean 

depth 

(feet) 

(Db}

5. 1

4.6 

3.6 

12. 6

10.7 

8.6 

6.7 

11.9

11. 1 

9.5 

7.6 

12. 0

6. 1 

4.4

8. 2

5.9 

5.6 

4. 1 

12.4

10. 9 

11. 1

18.8

13. 5

6

Identifiable at 

sections

1-8

4-8 

2-3 

1, 2, 4, 6, 8

1-4 

1-11

3,7,9 

1, 5-8

1-4, 6-9 

4-8 

1-2, 6-8 

5-6,8

1-4, 6-8 

1-4, 7-8 

4,6-7

1-5 

6-9

7-8 

2-3, 6-9

1-5 

6-11 

4, 9, 12

1-12

7

Relative 

size

1

2 

3 

2

3 

1 

3 

2

1 

2 

3 

3

2 

2 

3

1 

1 

3 

2

1 

1 

3

1

8

QMAF

(cfs)

760

6, 400

6, 000

870 

870

1, 240 

1, 240

2,900 

2,900

3, 500

9

' Mean 

depth 

(feet) 

(£>/>

4.

9.

12.

4. 

4.

5. 

5.

10. 

11.

9,

Mean annual flood

3. 2
E8 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

TABLE 3. Data corresponding to the mean annual flood and various bench levels for streams in the Piedmont Continued

Bench level

Site

8____ __

9---_--------

10_. ____-__._

!!___ _ _ _ .

12___ _ _____

13__---_- -__

14_ __ _

15___ _ ___ -

16_-_- _______

17-_- __ _-_

18____- -----

1Q

20-------- __

21_____--___.

22_ __ _ __

23-__ __ __

24_ _

25__ _____ ..

26___ ____ .

27--_ ____ .

28----------

29.- __ . . .

30_ __ ._- .

31___ __ . _

32___ _ _ __ _

33_._ . ._. _

34__ _________

1

Bench 

(highest 

to lowest)

1

1 

2 

3 

1 

2 

3 

1 

2 

1 

2 

3 

1 

2 

3 

4 

1 

2 

3 

1 

2 

3 

4 

1 

2 

3 

1 

2 

1 

2 

1 

2

2

Q

(cfs)

8,350 

5,850 

3, 780 

2, 570 

12, 300 

7, 000 

4,480 

7, 400 

4, 160 

5,700 

2,500 

2,020 

10, 200 

6,900 

5,400 

2,560 

1, 150 

700 

185 

10, 900 

5,200 

1,580 

1, 150 

2,350 

1,250 

575 

2, 170 

1,040 

8,000 

2,350 

12, 300 

7,750 

1, 120 

6, 100 

4,250 

9, 100 

14, 300 

465 

370 

410 

1, 150 

320 

3,500 

310 

300 

.345 

2,650

3

Recurrence 

interval 

(years)

2.60 

4. 5 

2.65 

1.75 

23.0 

3.0 

1. 45 

23 

6. 5 

2.45 

1. 19 

1. 08 

1. 75 

1.28 

1. 16 

1.04 

14.0 

5.3 

1. 24 

90.0 

13.7 

3.20 

1.80 

2. 10 

1. 10 

1. 01 

3. 90 

1. 32 

6.0 

1. 09 

2. 40 

1. 15 

2. 9 

4.5 

2. 5 

2. 6 

4.0 

7.5 

10. 0 

1.8 

2. 2 

1. 01 

48 

5. 2 

2.0 

1. 05 

1. 71

4

Slope 

(ft per ft)

.0014

. 0007 

. 0007 

. 00045 

. 00047 

. 00060 

. 0017 

.0019 

. 00044 

. 00030 

. 00020 

. 00043 

. 00038 

. 00025 

. 00026 

.0150 

.0090 

.0120 

.0034 

.0044 

.0042 

.0019 

. 0004 

. 00042 

. 00048 

. 00086 

. 00086 

. 0021 

.0031 

. 00054 

. 00062 

. 0023 

.0018 

.003 

.0011 

. 00060 

.0087 

.0150 

.0035 

.0017 

. 00046 

.0014 

. 0059 

. 0067 

. 00075 

.0058

5

Mean 

depth 

(feet) 

(£>&)

9.3 

14.0 

10.4 

7.7 

17.8 

12.4 

11. 5 

14 1 

8.8 

16. 8 

9.8 

8.4 

16. 4 

14.6 

15. 1 

12. 1 

5.8 

4.3 

2.3 

8.4 

5.6 

4.6 

3. 7 

10.4 

7.9 

5.9 

9.9 

6.4 

9.3 

4. 5 

17. 8 

12.5 

6. 5 

10.4 

7. 1 

11.9 

13.2 

4 5 

2.6 

4.6 

6.4 

4.7 

10.4 

2. 7 

3.2 

42 

8. 0

6

Identifiable at 

sections

3-9 

1-2, 8-10 

1-17 

1,4,6, 10-12- 

1,3-5,8,13 

1-4, 5-13 

5,8 

2,4-5,7 

1-11 

1,3,5,8 

2-6, 8 

1-2, 4, 6-7 

4-6, 8-11 

1-6 

8-11 

1-3, 5,7, 9-11 3-5 

6-8 

3, 5-7 

1, 9-10 

1-4 

1-3 

8-10 

1-6, 11 

1-11 

1-3, 5 

1-7, 9 1-7 

1-2, 8-9 

2-4, 8-9 

1-2, 4-5, 7-9 

1-9 

1-4 

1-2 

1-2 

1-2 

1-2 

1-2 

1-2

1-2

1-2

1-2 

1-2 

1-5

1-3 

1-3

1-4

7

Relative 

size

1 

2 

1 

3 

2 

1 

3 

2 

1 

3 

1 

3 

3 

1 

1 

3 

1 

1 

3 

2 

1 

3 

1 

2 

1 

3 

2 

1 

1 

3 

2 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1

Mean annual flood

8

QMAF 

(cfs)

7, 800 

3,300

6, 270

2,300 

5, 500

12, 500 

12, 500

380 

380

1,350 

1,350 

2,560

1,700 

5,000

12, 200 

1,020 

4,500 

4, 150 

8, 750 

11, 000 

270 

190 

500 

1,220 

1,300 

2,500 

210 

340 

1,400 

3,300

9

Mean 

depth 

(feet) 

(£/)

9.0 

10.0

11.8

6.8 

16.4

16. 1

18. 3

2.7 

3.3

3.9 

4.6 

10.7

7.8 

7.4

17. 5 

6.2 

8.7 

7.0 

11.7 

12.0 

2.7 

2. 2 

4.9 

7.0 

6.6 

8.2 

2. 1 

3. 5 

6.6 

9.5

FREQUENCY OF BANKFULL DISCHARGE

Wolman and Leopold (1957) found that with only 

a few exceptions the frequency of overbank flooding 

was remarkably uniform on many small and large 

rivers. Their study indicates that many flood plains 

are subject to inundation at approximately yearly intervals ; that is, the recurrence interval of bankfull stage 

is between 1 and 2 years. The uniformity of the relation between the channel and flood plain was attributed 

to the lateral migration of the channel across the flood

plain with no change in width. However, there is some 

implication in their data (p. 88) that on streams with 

steep slopes, the recurrence interval of bankfull stage 

may be quite high.

Inspection of table 3 of this report indicates much 

the same tendency, if the elevation of the predominant 

bench is considered to be bankfull stage. Generally on 

streams of relatively mild slope, the recurrence interval 

of bankfull stage lies bet\veen 1 and 2 years. The recurrence interval tends to increase with steepening slope.
CHANNEL GEOMETRY OF PIEDMONT STREAMS E9

Some of the lower benches on these steeper streams have 

recurrence intervals between 1 and 2 years. It is doubtful, however, that these benches can be considered the 

"flood plains," because these lower benches are not 

prominent and the streams do not meander and aggrade 

or degrade rapidly in this region.

THE EFFECT OF SLOPE

The effect of channel slope on the character of the 

benches and the frequency of their inundation is illustrated in figure 10. This graph which is based on data 

for the 34 reaches as given in table 3 shows the relation 

between bankf ull depth, the depth of mean annual flood, 

and slope. The data for streams on which the higher 

bench was predominant tend to plot to the r^ght of the 

equal depth line, and data for streams on which a lower 

bench was predominant plot to the left. The mean annual flood on streams having steep slopes is contained 

within the channel, but on streams of mild slope it covers 

the predominant bench to a considerable depth.

The regression equation which expresses the relation 

of depth of mean annual flood (Df), bankful depth, 

(/>(,), and slope, (&), is:

n _ D (1)

The standard error is 12 percent and the regression coefficients are significant to the 0.001 level. The data for 

the predominant benches are compared with equation 1 

in figure 11. The data based on extensive surveys at the 

gaging-station sites display less scatter than the data for 

the supplementary sites. This difference emphasizes 

the accuracy needed in determining the predominant 

bench and thus the bankf ull stage.

Stream slope appears to play an important role in 

determining the elevation of valley benches. Streams 

having steep slopes are deeply entrenched in the valley 

floor and, as compared with streams of mild slope, otter 

a greater capacity in the main channel for water conveyance. The character of the bed material also varies 

with slope and offers more resistance to the lateral migration of stream channels where the slope is steep. It 

thus appears that the importance of deposition as an 

agent in the formation of flood plains may be related to 

stream slope.

50

-.10

5 10 

BANKFULL DEPTH, IN FEET

50

FIGUKE 10. Relation of bankfull depth to depth of mean annual flood 

for Piedmont streams.

afar

Gaging station sites 

Supplement sites

o.oooi 0.0005 0.001 0.005 

SLOPE (S), IN FEET PER FEET

0.01 0.05

FIGURE 11. Comparison of the data for 34 sites in the Piedmont with the graph of equation 1.
E10 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

VARIATION OF WATER SURFACE SLOPE WITH DEPTH

The water surface slope as used in this report is for 

bankfull stage. It is recognized that the slope of the 

water surface in a particular reach will vary with an 

increase in depth or discharge, as the pools and riffles 

which control low water flows are no longer individually 

effective. A comparison of the slope at low stage, and 

at bankfull stage, for the 34 reaches is given in figure 

12. The plot indicates that the slope at low stage may be 

considerably greater or less than the slope at bankfull 

stage, if the channel slope is less than 0.002 ft per ft. 

On streams of greater slope, the low water slope may 

be used in lieu of the slope at bankfull stage in the ap0.05

o.oooi

0.0001 0.0005 0.001 0.005 0.01 0.05 

SLOPE AT LOW-WATER STAGE, IN FEET PER FEET

FIGDRE 12. Relationship between water surface slope at low stage 

and at bankfull stage. Solid dot, data from table 1 ; open dot, data 

from table 2.

plication of equation 1. On any stream the two slopes 

tend to converge as the length of the reach increases.

SUMMARY AND CONCLUSIONS

A complex system of benches and natural levees exists 

along stream channels in the Piedmont province. At a 

given site, several benches at different elevations are subject to flooding at recurrence intervals of less than 50 

years. At most sites the active flood plain associated 

with the present stream regime cannot be distinguished 

in a survey of the stream channel.

The slope of the channel appears to be a major factor 

in determining the character of the benches. The mean 

annual flood is contained within the channel on streams 

of steep slope, but may inundate the highest bench to a 

considerable depth on streams of mild slope.

The depth of flow corresponding to the mean annual 

flood has been related to bankfull depth and the slope 

of the water surface. Bankfull depth was defined by 

the average elevation of the widest bench which could 

be traced along a considerable reach of stream channel.

o

The consistency of this relation for the 34 study sites 

in the Piedmont demonstrates that the elevation and 

slope of valley benches are significantly related to the 

frequency of flood discharge. This relationship should 

prove useful in flood plain zoning studies and in establishing the correlation between stage and discharge for 

ungaged streams in the Piedmont.

REFERENCES CITED

Lobeck, A. K., 1939, Geomorphology: 1st ed., New York and

London, McGraw-Hill Book Co., 731 p. 

Wolman, M. G., and Leopold, L. B., 1957, River flood plains;

some observations on their formation: U.S. Geol. Survey Prof.

Paper 282-C, 22 p. 

Wolman, M. G., 1955, The natural channel of Brandywine Creek,

Pennsylvania: U.S. Geol Survey Prof. Paper 271, 56 p.

U.S. GOVERNMENT PRINTING OFFICE : 1964 O - 717-122