Drainage Density 

and Streamflow

GEOLOGICAL SURVEY PROFESSIONAL PAPER 422-C

B
Drainage Density 

and Streamflow

By CHARLES W. CARLSTON

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 422-C

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1963

of

tt. 8. Geological Survey
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

Abstract__ _ ______________

Introduction. ______________

Previous studies ____________

Methods of study_________

The Jacob water-table model.

Page 

Cl

1

2

3

Application of the Jacob model to landform and streamflow characteristics.. ______________________________

The relation of base flow to recharge and drainage density. 

The relation of the mean annual flood to drainage density. 

Conclusions._______________________________________

References.__-________---__-___-_-_-__-___-___--_--

Page

C4 

6

6

7

8

ILLUSTRATIONS

FIGURE 1. Map showing location of drainage basins.__.__--_-.

2. Ground-water table base-flow model after Jacob...-.

3. Relation of drainage density to base flow and floods.

Page 

02

in

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

DRAINAGE DENSITY AND STREAMFLOW

By CHARLES W. CARLSTON

ABSTRACT

Drainage density, surface-water discharge, and ground-water 

movement are shown to be parts of a single physical system. 

A mathematical model for this system, which was developed by 

C. E. Jacob, can be expressed in the equation T= WD~2/8h0t in 

which T is transmissibility, W is recharge, D is drainage density, 

and h0 is the height of the water table at the water table divide. 

The rate of ground-water discharge into streams, or base flow 

(Qb), is dependent on and varies directly with transmissibility 

of the terrane. If W and ho are constant, Q& OC D~2 . Thirteen 

small, almost monolithologic basins, located in a climatic area 

in the eastern U.S. where recharge is nearly a constant, were 

found to have a relation of base-flow discharge to drainage density 

in the form of Qb per mi2 =14Z)-2 . The field relations, therefore, agree with that predicted by the Jacob model.

If transmissibility controls the relative amount of precipitation which enters the ground as contrasted with that which 

flows off the surface, surface-water or overland discharge should 

vary inversely with transmissibility. It was found that flood 

runoff as measured by the mean annual flood (Q2 .ss) varies with 

drainage density in the form of Q2 .ss per mi2 =1.3D2 . The close 

relation of mean annual flood to drainage density in 15 basins 

was not affected by large differences among the basins in relief, 

valley-side slope, stream slope, or amount and intensity of 

precipitation. It is concluded that drainage density is adjusted 

to the most efficient removal of flood runoff and that the mean 

annual flood intensity is due predominantly to terrane transmissibility.

INTRODUCTION

This report describes the results of an investigation 

of some of the relations between hydrology and geomorphology. The hydrology of a stream basin involves 

(1) the overland runoff from the basin, (2) the groundwater recharge rate, which is dependent upon the 

amount of precipitation in excess of evapotranspiration 

losses and upon the infiltration capacity of the soil 

mantle, and (3) the permeability of the bedrock, which 

affects the rate of yield of ground water to wells, to 

springs, and to the streams which drain the basin. 

Stream-flow characteristics were examined in terms of 

base flow and of height of flood peaks.

The geomorphic character of drainage basins, following techniques first suggested by Horton (1945),

689426 63 2

may be measured or described in a variety of ways. 

For example, Strahler (1958, p. 282-283) has listed 37 

such properties or parameters. In a general way these 

properties may be divided into four classes: (1) length 

or geometric properties of the drainage net, (2) shape 

or area of the drainage basin, (3) relation of the drainage 

net to the basin area, and (4) relief aspects of the basin. 

It has beer assumed by hydrologists and geomorphologists that certain relations must exist between 

runoff characteristics and topographic or geomorphic 

characteristics of stream basins. Much effort has been 

devoted to statistical correlation of these relations 

without a clear understanding of how runoff is related 

to the geomorphic and geologic character of the basins. 

This paper advances the theory that runoff and drainage density are genetically and predictably related to 

the transmissibility of the underlying rock terranes.

The purpose of this research was not to develop a 

means of predicting stream-flow characteristics from a 

landform characteristic. It was to attempt to solve 

a complex geohydrologic problem by defining a physical 

system in terms of: (1) the elements of the system, 

(2) how it operates, and (3) why it operates in the 

observed fashion. The theory resulting from this type 

of analysis, if valid, illustrates the basic simplicity and 

rationality of natural processes.

During the progress of research, much effort was 

devoted to statistical analysis of the data. While very 

good correlation coefficients (0.96 to 0.98) were obtained 

the procedure shed no light on the physical cause and 

effects of the processes. The present theory, formed 

by inductive and deductive reasoning, is so basically 

simple that the correlation can be shown adequately 

in simple graph form and equations can be solved 

directly by graphical means.

The author appreciates Dr. Luna B. Leopold's 

penetrating and enlightening critical comments on 

earlier drafts of this paper. Mr. Frederick Sower, 

chemist and mathematician, greatly aided the author 

in the development of the equations.

Cl
C2 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

PREVIOUS STUDIES

Early studies of the relation of topographic character 

of drainage basins to basin-runoff characteristics have 

been described by Langbein (1947, p. 128-129). The 

topographic parameters considered important in these 

studies were: area, channel slope, stream pattern, 

average basin width, mean length of travel (channel 

length), and mean relief measured from gaging station.

In 1939 and 1940, Langbein (1947) and his coworkers, 

through assistance from the Works Project Administration of the Federal Works Agency, compiled a large 

variety of topographic measurements from 340 drainage 

basins in the northeastern United States. The basins 

ranged in area from 1.6 to 7,797 square miles. The 

parameters determined were drainage area, length of 

streams, drainage density, land slope, channel slope, 

area-altitude distribution, and area of water bodies.

No attempt was made to correlate these topographic 

measurements with streamflow properties. The measurements were compiled for future studies which would 

determine their effects on the runoff of streams.

Such studies have been carried on in the Water 

Resources Division of the U.S. Geological Survey by 

Benson (1959), who participated in the studies reported 

by Langbein in 1947. As a result of graphical correlation of several topographic parameters with flood 

flow for 90 New England drainage basins, Benson 

determined that basin area and channel slope were the 

most effective determinants of flood flow. These parameters were then statistically computed in correlation 

with records of 170 gaging stations.

Benson's studies were made entirely of streams in 

New England where the bedrock lithology, with the 

exception of the Triassic rocks of the Connecticut

EXPLANATION

1) INTERIOR LOW PLATEAUS 

I) APPALACHIAN PLATEAUS 

3) VALLEY AND RIDGE

BLUE RIDGE

PIEDMONT

COASTAL PLAIN

Base map by Geological Survey Physiography from Fenneman, 1946

FIGURE 1. Map showing location of drainage basins studied and discussed in this report. TJncircled numbers and letters

correspond to those in table and on graphs.
DRAINAGE DENSITY AND STREAMFLOW C3

basin and the Carboniferous rocks of the southeastern 

New England region, is largely a hydrologically homogeneous complex of igneous and metamorphic rocks. 

Glacial erosion has modified the land surface of the 

crystalline rocks, and glacial deposits mantle much of 

the area. Drainage density among the basins studied 

ranged from 1.1 to 2.35, as measured on 1: 62,500 scale 

maps by Langbein.

METHODS OF STUDY

The area of study comprises the central and eastern 

United States south of the Wisconsin glacial border. 

This area was chosen because the landscape is the 

product of normal denudational processes; landscapes 

shaped or modified by glacial erosion or deposition, 

such as those studied by Benson (1959) were thus 

excluded. The area is generally homogeneous in climate. Average annual precipitation ranges from about 

40 to 50 inches and average annual temperature ranges 

from 50 ° to 60 ° F. Four criteria were used in selecting 

basins having a variety of bedrock geology: (1) homogeneity of bedrock, (2) availability of l:24,000-scale 

topographic maps, (3) availability of discharge records, 

(4) lack of appreciable flow regulation of the streams. 

These limitations resulted in an unavoidably small 

sample. The basins, their geology, and their hydrologic 

and geomorphic parameters are listed in the following 

table, and their locations are shown in figure 1.

Drainage densities were obtained by sampling randomly distributed 1-square-mile plots, whose total area

is generally not less than 25 percent of the total basin 

area. Drainage density is a measurement of the sum 

of the channel lengths per unit area. It is generally 

expressed in terms of miles of channel per square mile. 

Horton (1945, pp. 283-284) and Langbein (1947, p. 

133) determined drainage density by measurement of 

the blue streamlines on topographic maps having a 

scale of 1:62,500. Langbein (p. 133) pointed out that 

the number of small headwater streams shown on these 

maps would vary with the season and wetness of the 

year in which the survey was made, as well as with the 

judgment of the topographer and cartographer.

The current practice, and the method used in this 

study, is to show drainage lines wherever a cusp or Vnotch of a contour line indicates a channel. By this 

method, the drainage densities of the basins, on topographic maps having a scale of 1:24,000, range from 

3.0 to 9.5. The measurements are believed to be of 

consistent accuracy because the maps used were all 

1:24,000 scale maps and the measurements were made 

by one operator, the author. Delineation of drainage 

lines was generally conservative; therefore, drainagedensity values, particularly in the higher values, may 

be lower than those ordinarily measured.

An accurate method of distinguishing the groundwater discharge component of streamflow from the surface- or overland-flow component has not yet been 

developed. Estimates of ground-water discharge of 

streams, or base flow, are usually made by assuming 

that all flood peaks are overland-flow discharge and

Locality 

(fig. 1)

!_.__. _ ___

2. _____ __

3__- 

4___ __

5. ----------

6 _ _ __

1. ----------

8--.. _ 

Q

10___ 

11_. ________

12.. --------

13. _________

A --------

B --------

Basin

Gaging station

Sawpit Run near Old town, Md__

Hancock, Md. 

South Fork Little Barren River

near Edmonton, Ky. 

Crabtree Creek near Swanton,

Md.

Va. 

Sawmill Creek near Glen Burnie,

Md.

burg, W. Va.

ton, W. Va.

Point, N.C. 

Pinev Run near Svkesville, Md

Beetree Creek near Swananoa,

N.C.

Catheys Creek near Brevard,

N.C.

Bedrock lithology

Shale. _________________ __ __

with sandstone.

Sandstone (60-80 percent) and

some shale.

coal.

coal.

Area

(sq mi)

5

16. 9

18. 1

16.7

6.0

5. 1

11. 3

55. 7

20. 9

14. 7

11. 4

31. 9

5. 5

10. 9

11. 7

Drainage

density

7.6

7.0

9. 5

4. 2

4. 7

3. 0

3. 6

6. 3

8.0

8.0

6.0

5. 0

5. 6

7. 4

8. 0

Average 

minimum

monthly 

flow (cfs 

per sq mi)

0. 13

. 29

. 26

. 61

.35

1. 22

. 80

. 27

. 10

. 36

. 84

. 83

. 91

1. 86

2. 45

Mean 

annual

flood (cfs 

per sq mi)

62

44

77

32

23

19

14

44

86

102

75

38

44

72

67

Mean 

annual

precipitation 

(inches)

38

38

49

42

45

45

40

44

43

46

45

47

49

62

63
C4 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

that the remaining lower flow segments of the hydrograph are base flow. Many surface-water hydrologists 

believe that the base flow of many streams is largely 

derived from bank storage, rather than from discharge 

from the ground water. On the other hand, there are 

large areas of highly permeable sand formations in the 

Atlantic Coastal Plain where there is never any discernible overland-flow runoff and where virtually all 

discharge, including flood peaks, is ground-water discharge. Because of this uncertainty in the definition 

and computation of base-flow or ground-water discharge, the author used as a measure of base flow average minimum monthly flow, computed by averaging 6 

years of monthly minimum discharge measurements.

The mean annual flood is determined by plotting 

annual maximum-flood discharges on modified probability graph paper in which the discharge peaks are 

plotted against recurrence interval. Gumbel (1958, p. 

177) has pointed out that the return or recurrence interval for the mean annual flood is 2.2328 years, the 

median annual flood is 2 years and the most probable 

annual flood is 1.582 years. The U.S. Geological Survey 

has adopted the mean annual flood ($2.33) as its standard reference value. According to Wolman and Miller 

(1960, p. 60) most of the work of stream erosion is 

done by frequent flows of moderate magnitude with a 

recurrence interval of 1 to 2 years. The use of the 

(>2.33 flood in the present correlation study is, therefore, 

generally in scale with the magnitude and frequency of 

floods which Wolman and Miller have demonstrated to 

be most important in geomorphic processes.

THE JACOB WATER-TABLE MODEL

Models depicting the relation of the ground-water 

table to ground-water drainage have been made by 

Horton (1936) and Jacob (1943, 1944).

Horton (1936, p. 346) considered the shape of the 

water table as a parabola. He stated that the elevation 

of the water table (A.) at any point X distance from the 

draining stream is:

equation is shown in figure 2. 

equation states:

In this equation, h0 is the elevation of the draining 

stream, Kt is the transmission capacity of the soil, L0 is 

the distance from the stream to the ground-water 

divide, and a is the rate of accretion of recharge to the 

aquifer, with a being equal to or less than the infiltration 

capacity.

In 1943 and 1944, Jacob developed a parabolic-type 

equation for ground-water flow in a homogeneous aquifer of large thickness and having uniform accretion 

from precipitation (1943, p. 566). The model for this

In a simplified form the

L and surface

FIGURE 2. Ground-water table base-flow model after Jacob (1943).

, _a*W fh- 2T (2)

where h0 is the height of the water table 'above the draining 

stream, as measured at the ground-water divide, a is 

the distance from the water-table divide to the stream, 

Wis the rate of accretion to the water table (recharge), 

and T is the transmissibility (the volume rate of flow 

through a vertical strip of the aquifer of unit width 

under a unit hydraulic gradient). Thus, according to 

equation 2, the height of the water table at the watertable divide is proportional to the square of the distance 

of the divide from the drainage stream and to the rate 

of ground-water recharge. The value h0 is also inversely proportional to transmissibility.

APPLICATION OF THE JACOB MODEL TO LANDFORM 

AND STREAMFLOW CHARACTERISTICS

Jacob (1944, p. 938-939) computed the transmissibility 

of the M ago thy sand aquifer of Long Island from a 

water-table contour map of the island and estimated 

recharge as about 60 percent of the average annual 

precipitation. He used the following equation for his 

computation:

T==W (3)

The Jacob ground-water model can be related to a 

landform model by assuming that the land surface is 

also a parabola coincident with the water table. Then, 

the symbol a is equal to LQ or length of overland flow. 

Thus:

T= 2h0

(4)

Horton (1945, p. 284) pointed out that the average 

length of overland flow (Z0) is, in most cases, approximately half the average distance between the stream
DRAINAGE DENSITY AND STREAMFLOW C5

channels and is therefore approximately equal to half 

the reciprocal of drainage density (D), or

2D (5)

Substituting equation 5 in equation 4 the equation 

becomes:

T W f(\\ -'-"oriSA W

or

(7)

Jacob's water-table model as used on long Island, 

simulates an aquifer having parallel boundaries at a 

constant head (the sea level on both sides of the island). 

Jacob pointed out, however, that a serious weakness of 

the Long Island study was the impracticability of 

measuring the ground-water discharge along the 

northern and southern shores of the island. He 

suggested (1944, p. 939) that the model could be tested 

more effectively under field conditions where the parallel 

shores would be replaced by streams draining the water 

discharged from the water table aquifer. This model 

is shown in figure 2. The ground-water discharge into 

such streams would be dependent upon the transmissibility of the aquifer, and this discharge could be 

measured by the gain in flow per unit length of stream.

Inasmuch as ground-water discharge into streams 

would vary directly with the transmissibility, groundwater discharge or base flow (Qt) should also vary 

according to equation 7 or:

(8)

W and h0 remaining constant, base flow should be related to drainage density in the form:

(j/ftQC-L/ (y)

It may be deduced that as transmissibility decreases, 

the amount or rate of movement of ground water 

passing through the system decreases and a proportionately greater percentage of the precipitation is forced 

to flow directly into the streams in flow over the land 

surface. Streamflow, therefore, would be derived from 

ground-water discharge plus overland flow. Both 

components of discharge should vary inversely in their 

relative contribution to stream discharge in a regular 

and predictable system controlled by the transmissibility of the water-table aquifer. As T increases, 

ground-water discharge into streams increases and surface^discharge decreases. As T decreases, there would

be a corresponding decrease in base flow and increase 

in surface discharge.

Equation 6, which was derived from Jacob's basic 

equation, states that transmissibility varies inversely 

with drainage density squared. Thus as transmissibility increases, drainage density would decrease, and 

as transmissibility decreases, drainage density would 

increase.

This relationship may be examined from two different 

viewpoints. Horton (1945, p. 320) has stated that 

erosion will not take place on a slope until the available 

eroding force exceeds the resistance of the surficial 

materials to erosion. This eroding force increases 

downslope from the watershed line to the point where 

the eroding force becomes equal to the resistance to 

erosion. He named this distance the "critical distance," and the belt of land surface within the critical 

distance was termed the "belt of no erosion." One of 

the most important factors in determining the width 

of the belt of no erosion is the infiltration capacity of 

the soil. Simply stated, the greater the infiltration 

capacity, the less will be the amount of surface runoff. 

As infiltration capacity increases, the critical distance 

also increases because a greater slope length is required 

to accumulate overland flow of sufficient depth and 

velocity to start erosion. Thus the infiltration capacity 

is chiefly responsible for determining the width of the 

belt of no erosion and the width of the spacing of 

streams or channels which carry away surface runoff.

The infiltration capacity of the soil may be regarded 

as one part of the general capacity of a terrane to 

receive infiltering precipitation and to transmit it by 

unsaturated flow through the vadose zone above the 

water table and by saturated flow through the aquifer 

to the streams draining the ground water. This 

capacity is here termed "terrane transmissibility." It 

is recognized that this extends the strict meaning of 

transmissibility, which is a measure only of saturated 

flow.

Another way of regarding the relation of transmissibility to drainage density is to consider that as 

T decreases, a concurrent progressive increase in surface 

flow will occur. Increase in proliferation of drainage 

channels would provide a more efficient means of 

transporting the water off the land, and as the water 

to be so removed increases (with decreasing T) the 

proliferation and closeness of spacing of the drainage 

channels would increase. The channel spacing or 

geometry should operate at peak efficiency during 

periods of flood runoff. Since flood runoff (Qf) of 

streams varies in magnitude inversely with the magnitude of their base flow runoff (Qb ), (Q^/Qf), and 

according to equation 9 QbccD~2, then flood runoff
C6 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

should vary with the positive second power of drainage 

density, or

(10)

100 1000

Chorley and Morgan (1962) have compared the 

morphometry of two areas of crystalline and metamorphic rocks: the Unaka Mountains of Tennessee and 

North Carolina, and Dartmoor, England. Morphometric characteristics which were measured included 

number of stream segments, mean stream lengths, 

mean basin areas, mean stream-channel slopes, mean 

relief of fourth-order basins, mean basin slopes, and 

mean drainage density. Relief and drainage density 

were the only parameters which showed significant 

differences between the two areas. The difference in 

drainage density between the two areas (Dartmoor, 

Z>=3.4; Unakas, J9=11.2) was ascribed to differences 

in runoff intensity caused by more intense rainfall and 

greater mean basin slopes. They concluded that the 

channel system is geared to conditions of maximum 

runoff. These conclusions are only partially in agreement both with the theoretical and observed relations 

described in the present paper.

THE RELATION OF BASE FLOW TO RECHARGE AND 

DRAINAGE DENSITY

Figure 3A shows the relation of drainage density to 

base flow per square mile for 13 basins previously 

described. As previously stated, average annual precipitation in the 13 basin areas ranges from about 40 

to 50 inches and average temperatures range from 50° 

to 60° F. Recharge (W] is dependent upon the amount 

of precipitation less the amount of evapotranspiration 

losses, which is dependent largely on temperature. 

The variations in rainfall and temperature among the 

13 basins are within a sufficiently small range that 

recharge can be considered to be approximately a constant for the 13 basins. The relation of base flow per 

unit area to drainage density can be delineated by 

a regression line which has a slope and intercept such 

that:

Qb per mi2=14Z>~2

Equation 8 states that base-flow rate is also directly 

proportional to recharge. Two basins at the southern 

tip of the Blue Ridge province were examined to 

determine qualitatively the effect of significantly higher 

precipitation or recharge on base flow. In this area 

annual precipitation is more than 60 inches. The two 

basins are those of Crab Creek near Penrose, N.C. 

(A), and Catheys Creek near Brevard, N.C. (J5). (See 

figs. 1, 3.) Their position on the diagram in figure 3A 

shows a much higher rate of base flow which may be 

due to the higher recharge rate. The gaging stations 

for both basins are, however, located in alluvium-filled

I 5 10 

DRAINAGE DENSITY, D

5 10 

DRAINAGE DENSITY, D

FIGURE 3. The relation of drainage density to base flow and floods. A, Base flow 

(Qi). B, Mean annual flood (Qj.ss).

valleys; therefore, the higher base flow discharges may 

be due in part to higher transmissibility of the alluvium. 

The relation of drainage density to the 10-day base 

flow recession coefficient (ri0) was also investigated. 

It was found that this relation could be expressed 

quantitatively by the equation: Log r:0= 0.008/>2.

THE RELATION OF THE MEAN ANNUAL FLOOD TO 

DRAINAGE DENSITY

In the preceding discussion of the theoretical relation 

of drainage density to flood runoff it was concluded that 

flood runoff should vary directly with the second power 

of drainage density. Flood runoff for the basins studied 

was computed in terms of the mean annual flood per 

square mile ($2.33 per mi2 ). A regression line having a 

slope of D2 was plotted on this graph and the best fit 

gave an intercept with unit drainage density of about 

1.3. This gives the equation:

#2.33 per mi2=1.3Z>2.

The departures from this mean trend line were compared graphically with average annual precipitation
DRAINAGE DENSITY AND STREAMFLOW C7

and average maximum rainfall intensities as given by 

the U.S. Weather Bureau. There was no apparent 

correlation. Graphical correlation was also made between mean annual flood and total relief, local relief, 

the ruggedness number (the product of relief and drainage density), stream slope, and valley-side slope. If 

significant correlation of flood peaks with these parameters exists, it is not apparent in the graphical plots.

The apparent lack of correlation between rainfall 

amount or intensity and flood intensity and between 

relief and flood intensity may be briefly illustrated by 

reference to points plotted in figure 35. Basins A and 

B are located in the region of highest mean annual 

rainfall and rainfall intensity in the eastern U.S. In 

addition, the relief (1,500 ft) in these basins places 

them among those with the highest relief in the total 

sample, yet they plot on and below the average for the 

basins. Basin 10 has the highest mean annual flood 

(102 cfs per mi2), but its relief is only 200 feet. Basin 

13 has a relief of 2,600 feet and a high average annual 

precipitation (49 in.), but departure of its mean flood 

intensity from the average is not significantly high.

Hydrologists have found that the delay time (and 

hence the attenuation) of flood peaks is composed of 

two parts; the inlet or overland-flow time, and the 

channel-transit time. The present study deals with 

inlet times of monolithologic terranes. The writer's 

analysis of flood runoff per unit area at gaging stations 

in the Appalachian Plateaus of eastern Kentucky (a 

basically monolithologic terrane) suggests that inlet 

time is dominant over channel transit time up to about 

75 to 100 square miles in drainage area; however, because the channel transit time increases continuously, 

for larger basins it tends to become the dominant 

component of the flood-peak lag.

CONCLUSIONS

This paper has presented evidence that drainage 

density, surface-water runoff, and the movement of 

ground water are parts of a single hydrologic system 

controlled by the transmissibility of the bedrock and 

its overlying soil mantle. A mathematical model of 

such a system, constructed by Jacob (1943; 1944), has 

been adapted to show that transmissibility (T) is related 

to ground-water recharge (W), to drainage density (D) 

and to the height of the water table at the water table 

divide (ho). The equation for this relation is:

T=WD

If W and h0 are constant, the equation may be simplified to T=KD~2 . Inasmuch as the rate of base flow

or ground-water discharge into streams varies with 

and is controlled by transmissibility, Qb ccD~2 . A total 

of 13 small, basically monolithologic stream basins were 

selected in the eastern United States where rainfall 

and temperature are such that recharge can be considered to be a constant. It was found that the relation 

of base flow of the 13 streams to drainage density can 

be expressed by the equation Qb per mi2 =14Z>~2 . The 

observed relation therefore is the same as that predicted by the Jacob model. Two stream basins in the 

southern Blue Ridge province, where rainfall is much 

higher than that of the 13 basins, have much higher 

base flows than comparable streams in the lower 

rainfall region.

Flood runoff as measured by mean annual flood ($2.33) 

was found to be closely related to drainage density; 

the equation may be expressed as $2.33 Per nii2 = 

1.3D2. It is concluded that the terrane transmissibility 

controls the amount of precipitation which passes 

through the underground system. The rejected or 

surface-water component increases with decreasing 

transmissibility. As surface-water runoff increases, an 

increase in the proliferation of stream channels is required for efficient removal of the runoff. The close 

relation of drainage density to mean annual flood per 

unit area indicates that the drainage network is adjusted to the mean flood runoff. Among the 15 

basins in which flood runoff was correlated with 

drainage density, there are large and significant 

differences in relief, in valley-side and stream slopes, 

and in amounts and intensities of precipitation. These 

factors, however, have no discernible effect on the 

relation of the magnitude of the floods to drainage 

density. Transmissibility of the terrane appears to be 

the dominant factor in controlling the scale of drainage 

density and the magnitude of the mean annual flood 

for basins up to 75 to 100 square miles in area.

The research reported here should be of interest to 

geomorphologists in that it provides a quantitative 

physical model for the origin of one of the most important elements of landform characteristics, drainage 

density. In addition, it appears that surface-water 

hydrologists and ground-water hydrologists have far 

more in common in their hydrologic studies than is 

generally realized. Transmissibility or permeability 

is the most important aquifer characteristic in groundwater studies. The results reported in this paper 

indicate that the transmissibility or permeability of 

terranes drained by streams is also important in the 

study of surface-water hydrology. It is hoped that 

this study provides a theoretical physical basis for 

interdisciplinary hydrologic studies.
C8 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

REFERENCES

Benson, M. A., 1959, Channel slope factor in flood frequency 

analysis: Am. Soc. Civil Eng. Proc., Jour. Hydraulics Div., 

v. 85, pt. 1, p. 1-9.

Chorley, R. J., and Morgan, M. A., 1962, Comparison of morphometric features, Unaka Mountains, Tennessee and North 

Carolina, and Dartmoor, England: Geol. Soc. Am. Bull., v. 

73, p. 17-34.

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