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UNITED STATES DEPARTMENT OF THE INTERIOR

TOPOGRAPHIC CHARACTERISTICS 

OF DRAINAGE BASINS

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 968-C
UNITED STATES DEPARTMENT OF THE INTERIOR 

J. A. Krug, Secretary

GEOLOGICAL SURVEY 

W. E. Wrather, Director

Water-Supply Paper 968-C

TOPOGRAPHIC CHARACTERISTICS 

OF DRAINAGE BASINS

BY WALTER B. LANGBEIN

AND OTHERS

Contributions to the hydrology of the United States, 1944 

(Pages 125-158)

UNITED STATES

GOVERNMENT PRINTING OFFICE 

WASHINGTON : 1947

For sale by the Superintendent of Documents, U. S. Government Printing Office, Washington 25, D. C.

Price 15 cents
NOTE. This report was prepared in 1941. Conditions arising out 

of the war have delayed its publication.
CONTENTS

Abstract__________________________.___________ 125

Introduction_____________________________________________________ 125

Cooperation and personnel_____________________________________ 127

Meteorologic factors affecting runoff _________________________________ 127

Differences in character of drainage basins____-___________-_____ __ 128

Previous studies _______________________________________________ 128

Purpose and scope of the present study____________________________ 130

Methods of work______ ________________ _ ________ 132

Maps._____________________________________ 132

Area of basins______________________________________________ 133

Stream density _______________________________________ 133

Area-distance distribution._________________________________ 134

Length of basin______.___________-__________________________ 135

Land slope______________________________________________ 135

Channel slope_________________________________________________ 138

Area-altitude distribution_______________________________ 140

Area of water surfaces________---_______-____---____________--_ 141

Summary of results_______________-.___________-______________-_ 142

Index_____________________________________ __ 157

ILLUSTRATIONS

Page 

PLATE 2. Topographic map of Little Androscoggin River Basin above

South Paris, Maine______________________________ In pocket

FIGURE 48. Hydrographs of two streams in New Jersey during flood of

June 1938_____________________________ 129

49. Relation between area of drainage basin and S al________ 136

50. Variation of computed slope of tributary streams with number

of subareas, West River at Newfane, Vt_________________ 139

51. Typical hypsometric curves of drainage basins___________ 140

52. Graph showing general variation in stream slopes and altitude

in relation to size of drainage basin__ _________________ 143

m
TOPOGRAPHIC CHARACTERISTICS OF DRAINAGE BASINS

By WALTER B. LANGBEIN and others

ABSTRACT

River floods are the result of many causes, and one of the primary 

objectives of scientific hydrology is the segregation and evaluation of the 

causative factors. The climatic factor and the soil-vegetation complex are variables that exercise their principal influence on the volume 

of runoff. The topography of drainage basins is a sensibly permanent 

characteristic which influences mainly the concentration or time 

distribution of the discharge from a drainage basin. River systems 

differ in their efficiency as agencies for collecting and conducting water. 

In some systems, surface waters are quickly assembled, and the discharge reflects somewhat sensitively the variations of the available 

supply. In others, the surface drainage is longer delayed and the 

discharge is released slowly.

As a basis for quantitative studies of these evident differences in 

behavior, selected topographic features for about 340 drainage basins 

in the northeastern United States were studied, using Geological Survey topographic maps. The data were compiled in cooperation with 

the Work Projects Administration of the Federal Works Agency and 

included information on drainage area, length of streams, stream 

density, land slope, channel slope, area-altitude distribution, and area 

of water bodies of basins that ranged in extent from 1.64 to 7,797 

square miles. Considerable effort was made to assure accuracy of 

the computations by appropriate checks, and the results are summarized in the table at the end of this report.

The results indicate that none of the topographic factors are unique, 

but each reflects a condition that also influences the olhers. For 

example, steep land slopes are generally associated with stpbp channel 

slopes and conversely. A significant variation of slope awd altitude 

with area of basin is found, and stream density tends to vary^with the

land slope.

INTRODUCTION

This report presents a compilation of topographic data on drainage 

basins in the northeastern United States. The configuration of the 

earth reflects the impact of many natural forces, and it in turn exercises profound influence upon man. Most of these influences are so

125
126 CONTRIBUTIONS TO HYDROLOGY, 1944

basic that they have shaped life and civilization into conformity with 

them. Mountains, plains, valleys, and rivers each favor or retard 

man's search for economic stability. Within human history the 

first three have remained unchanged. Rivers, on the other hand, 

fluctuate in size from day to day and from year to year. The amplitude and frequency of these fluctuations, so significant with respect 

to navigation, water power, irrigation, and such riparian developments 

as cities and highways, are largely determined by three separate, yet 

interdependent features, namely climate, physiography, and the soilvegetation complex. The interrelation of these three features with 

the behavior of rivers is imperfectly understood and is the subject of 

much investigation. This report singles out the physiography of 

the land for attention.

The relations between the rate, volume, and fluctuations of rivers 

and the topographic characteristics of the land they drain and through 

which they flow may be readily determined after discerning examination of the terrain and river developments, but expressing them in the 

quantitative terms necessary for the economic design of structures 

for river utilization or control requires first, topographic maps, and 

second, records of river flow of length adequate to define the behavior.

The stream-gaging program of the Geological Survey is Nationwide and now includes over 4,500 river-measurement stations, at 

which more than 65,000 station years of record were available in 

1942. These records furnish an adequate source of material concerning stream behavior. The mapping program of the Geological Survey, also Nation-wide, is in general not so complete. Although about 

50 percent of the country has been mapped, only States in the northeastern part have been completely covered; the scattered areas 

mapped in other States generally do not cover completely the areas in 

which stream-gaging has been carried OD, so that only a small fraction 

of them are suitable for use in comparisons of stream-flow characteristics or river morphology.

In the northeastern and north-central States the range hi topography is sufllcient to furnish a basis for studying its effect on stream 

flow. The^topographic characteristics compiled from the maps 

and summarized in this report can only be evaluated by a consideration of the hydrology of stream flow, the assembling of waters in a 

drainage system, and the hydraulic elements that regulate velocity of 

flow. Many stream-flow characteristics are related either directly or 

indirectly to topographic features. It would seem, however, that the 

factors most sensitive to topographic difference would be those 

relating to floods. In this study, therefore, particular although not 

exhaustive attention is given to the correlation of flood-flow characteristics with topography. This information will serve as a basis for
CHARACTERISTICS OF DRAINAGE BASINS 127

further study of such correlations and also of other characteristics, 

such as volume yield, erosion, and deposition of sediments. Similarly 

the topographic data offers basic material for studies of river morphology, as geologic evidence suggests that a significant portion of 

river-channel development takes place during flood.

COOPERATION AND PERSONNEL,

The cooperative project for the compilation of topographic data 

was undertaken in 1939 by the Works Progress Administration, which 

on April 25, 1939, became the Work Projects Administration under 

the Federal Works Agency. Their cooperation in organizing competent working groups is especially acknowledged. The Geological 

Survey sponsored the project and furnished technical direction, maps, 

and supplies. This work was carried on by W. B. Langbein, under 

the general direction of K. W. Davenport, chief of the Division of 

Water Utilization. The project at Boston, Mass., was under the 

supervision of H. B. Kinnison, district engineer, and his associates, 

particularly C. E. Knox, M. A. Benson, and B. R. Colby. The conduct of the work at Pittsburgh, Pa., was ably managed by Wm. S. 

Crozier, supervisor for the Works Projects Administration. Mr. 

Crozier died January 21, 1941, near the close of the project. H. M. 

Erskine, associate engineer of the Geological Survey at Pittsburgh, 

maintained close contact with the project there, and its continuity 

and efficiency may be largely credited to his competent administration.

METEOROL.OGIC FACTORS AFFECTING RUNOFF

River floods are the result of many causes, and one of the primary 

objectives of hydrologic study is the segregation of the causative 

factors and the evaluation of their effects on the resultant floods 

under various associated conditions.

Readily apparent is the source of the water, generally an unusual 

amount of rainfall, which may be characterized by great intensity 

and in many regions may be augmented by water from melting snow. 

Water in excess of that which can be absorbed by the ground or evaporated into the air directly or through vegetation collects in the 

stream channels that drain the area. Once in 'the stream system, the 

runoff flows to the mouth through channels which, as the trunk of a 

network of streams, progressively increase in size as contributions 

are received from tributary streams.

The quantity of rainfall or snow melt, its time distribution, and the 

associated soil, vegetal, and climatic conditions that determine the 

portion of the supply that becomes direct runoff are to a large extent 

variable characteristics of individual storms. These variable edaphic 

and climatic factors are separate phases of the rainfall-runoff relation.
128 CONTRIBUTIONS TO HYDROLOGY, 1944

The channel system, however, is a relatively permanent characteristic 

of a drainage basin. Some influential changes may take place in this 

system; for example, variations in seasonal vegetation along the banks 

may affect the hydraulic conveyance, floods may scour or deposit 

sediments, and old bends may be cut through and new ones created. 

Although the effect of thes.e changes on local flood stages may be 

considerable, it is assumed that the resultant effect on total discharge 

from a basin will tend to be compensating and that even the cumulative 

effect on flood-discharge characteristics during a period as short as 

the usual stream-gaging record would be minor.

DIFFERENCES IN CHARACTER OF DRAINAGE BASINS

River systems differ in their efficiency as agencies for collecting and 

conducting water. In some systems the surface waters are quickly 

assembled, and the discharge therefrom reflects somewhat sensitively 

the variations of the available supply. In others 'the surface drainage 

is longer delayed and the discharge is released slowly. This difference 

is illustrated in figure 48, which shows the hydrographs of two nearby 

streams, each draining about 50 square miles of coastal areas of New 

Jersey, during a flood in June 1938. The rainfall causing these floods 

and the volume discharged were nearly the same for both areas. The 

difference in behavior illustrated by the hydrographs is normal for 

these two basins and may be accounted for largely by the differences 

in physiographic characteristics, Manasquan River having about 

twice the gradient of Great Egg River and about one-fifth the swamp 

area.

PREVIOUS STUDIES

The fact of relationship between the time distribution of discharge 

during a flood and the size, shape, and gradient of a drainage system 

is widely recognized. Few attempts have heretofore been made to 

determine this relationship quantitatively, probably because of the 

volume of labor required to evaluate the topographic factors.

Horton 1 in 1926 and again in 1932 discussed the desirability and 

need for a quantitative rational procedure and proposed methods for 

evaluating certain pertinent physiographic factors.

Pettis 2 in 1927 presented a formula to compute the maximum flood 

discharge, in which the five-fourths power of the average basin width 

was used.

Gregory and Arnold 3 in 1932 developed in detail certain expressions

1 Horton, R. E., in Jarvis, C. S., Flood-flow characteristics: Am. Soc. Civil Eng. Trans., vol. 89, pp. 

1881-1086,1926; Drainage-basin characteristics: Am. Geophys. Union Trans., No. 13, pp. 350-361,1932.

8 Pettis, C. B., A new theory of river flood flow (published privately, copyrighted 1927).

* Gregory, B. L., and Arnold, C. E., Eational runoff formulas: Am. Soc. Civil Eng. Trans., vol. 96, pp. 

1038-1175, 1932.
CHARACTERISTICS OF DRAINAGE BASINS 129

1600

1400

1200

llOOO

Ul

£800

I

600

400

200

MANASQUAN RIVER AT 

SOUANKUM, NEW JERSEY

GREAT EGG RIVER AT 

FOLSOM, NEW JERSEY

26 27 28 29 30 I 23 4 5> 6 

JUNE JULY

FIGUEE 48. Hydrographs of two streams in New Jersey during flood of June 1938.

and procedures applicable to small drainage areas for translating rainfall into rates of stream flow in terras of basin characteristics.

Bernard 4 carried Gregory and Arnold's expressions somewhat 

further and presented formulas applicable to a few selected basins.

* Bernard, M. M., An approach to determinate stream flow: Am. Soc. Civil Eng. Trans., vol. 100, pp. 

347-395, 1935.

747049 47 2
130 CONTRIBUTIONS TO HYDROLOGY, 1944

Sherman 5 in 1932 presented unit hydrographs for four streams 

whose drainage areas and slopes differed widely. He explained how 

the unit hydrographs expressed these differences and suggested that 

basins having physical characteristics similar to the four types presented would have similar hydrographs.

McCarthy 6 in 1937 also used the unit hydrograph as an expression 

of the runoff characteristics of a drainage basin, stating further that 

"the agreements between graphs developed from May and November 

storms substantiate the contention that primarily the unit hydrograph 

is a function not of surface cover, which may be subject to seasonal 

change, but of topographic features of a watershed." From this 

postulate he derived a working relationship between the crest discharge and the length of base of unit hydrographs of 25 drainage 

basins* in the Connecticut River Basin, in terms of the area, mean 

slope, and stream pattern, determined by inspection and expressed 

as one-stem basin, two-stem basin, and so on, for application to floodcontrol design.

Morgan and Hullinghorst 7 in 1939 stated:

The factors which determine the discharge characteristics of any watersned 

are innumerable, some having a major bearing on those characteristics while 

others are of negligible consequence. It was determined by examination of nine 

gaged basins having complete unit hydrograph and watershed data, and corroborated by examination of a number of gaged basins with data ranging from 

almost complete to fragmentary, that the discharge characteristics can be attributed principally to three fundamental, definite watershed characteristics, 

namely,

a. Area of the watershed in square miles,

b. Mean length of travel in miles, and

c. Mean height of watershed above outflow station in feet.

On this basis, empirical relations between these three factors were 

established for nine streams tributary to the Chemung River in New 

York.

PURPOSE AND SCOPE OF THE PRESENT STUDY

The present project was designed to provide basic material whereby 

investigations such as those outlined can be carried further, the range 

being limited, of course, to areas adequately mapped, which are 

mainly in the northeastern United States. Prior to this study, references to the subject were read with the view to determining which 

topographic factors were considered to have major influence upon

 Sherman, L. K., The relation of hydrographs of runoff to size and character of drainage basins: Am. 

Qeophys. Union Trans., No. 13, pp. 332-339, 1932.

 McCarthy, O. T., The unit hydrograph and flood routing (unpublished manuscript presented at conference of North Atlantic Division, Corps of Engineers, II. S. Army, June 24, 1938).

i Morgan, K., and Hullinghorst, D. W., Unit hydrographs for gaged and ungaged watersheds: U. S. 

Engineer Office, Binghamton, N. Y., July 1939. [Processed.]
CHARACTERISTICS OF DRAINAGE BASINS 131

discharge characteristics, and, so far as practicable, the suggestions 

thus obtained were incorporated in the project as proposed for cooperation to the Works Progress Administration (succeeded on April 25, 

1939, by the Work Projects Administration). The compilation was 

based upon the topographic maps of the Geological Survey covering 

areas tributary to gaging stations of the Geological Survey.

In the organization of a surface-water system, and of a large part 

of the ground-water system as well, the drainage basin is a natural 

hydrologic land unit. Surface runoff is divided into drainage basins 

by the watersheds, and within each basin it follows a system of water 

courses in which the flow undergoes retardation, acceleration, or other 

changes that are distinctly related to the physical characteristics of 

that basin. Similar conditions exist with respect to all or most of. 

the ground-water runoff. Essentially all the water within a given 

basin, except that which is lost by evaporation or transpiration, 

drains out through a common outlet or mouth.

For purposes of analysis, a major stream basin may be subdivided 

by considering the area tributary to the stream at any given point, 

for example, a gaging station, as a basin having its own characteristics. 

The separate characteristics of several contributory areas may then 

be combined to obtain the resultant for the major basin.

Geographic and topographic characteristics of drainage basins, 

based largely on certain horizontal and vertical dimensions, were 

selected for compilation and study. Geographic characteristics 

include water bodies, direction of stream flow, latitude, and longitude. 

Topographic characteristics include horizontal dimensions covering 

basin area, stream length, and area-distance distribution, and vertical 

dimensions covering land slope, tributary and principal stream slopes, 

and basin altitude.

In selecting basins for this study preference was given to those for 

which long-term stream-flow records are available and to those free 

from artificial regulation. In addition to areas in the northeastern 

States and the Ohio River Basin a few surveyed areas in Wisconsin 

and Kentucky were included to spread the range in geographic extent 

and topographic characteristics. Many basins in New York, Pennsylvania, and New Jersey that might otherwise have been included 

were not studied because of insufficient time.

Besides listing topographic and hydrologic data, the original records 

afford a gazetteer of streams and lakes. Maps were prepared showing 

the stream skeleton of each basin, with names of streams, length from 

confluence to confluence, and drainage areas and altitudes pertinent 

to the subdivisions. A list of lakes and ponds, giving names, locations, 

and approximate altitudes and areas was also prepared, much of the
132 CONTRIBUTIONS TO HYDROLOGY, 1944

data for basins in New York State being based on a gazetteer by 

E. M. Douglas.8

The summarized results of the compilation, covering about 340 

basins, are given in the table on pages 145-155. The original records 

are on file at the office of the Geological Survey in Washington, D. C., 

and the computations for basins in New England (except Maine) are 

on file also at the Boston -office of the Geological Survey.

METHODS OF WORK

MAPS

Quadrangle maps on the scale 1:62,500, are the basis of this compilation, except for a few areas in New Jersey where more detailed 

maps were available. On these maps the gaging stations were located 

and the tributary basins with sub-basin divisions were outlined. 

Generally, each basin was divided into 50 to 75 sub-basins. Care was 

taken that the sub-basins crossed the streams only at confluence 

points. To systematize the necessary tabulations, the sub-basins 

were numbered in accord with the following system, which is illustrated on plate 2.

The headwater basin farthest upstream (the one farthest removed 

from the gaging station along the main stream) is called no. 1; the 

sub-basin which it joins at the first confluence point is called no. 2; 

the sub-basin (or intervening area along the combined channel) below 

the confluence of sub-basins 1 and 2 is called no. 3; the next tributary 

sub-basin is called no. 4, and so on. Where a large tributary stream 

that has been subdivided joins the main stream, the next consecutive 

number is assigned to the farthest upstream sub-basin of this tributary. This constitutes the lowest number on such tributary, and the 

sub-basins of the tributary system are then numbered in the same 

manner as those of the main stream, down to the sub-basin immediately above the confluence of the tributary with the main stream. 

The succeeding number is assigned to the sub-basin along the main 

river immediately below the confluence, as before. The highest 

number in a basin is that of the sub-basin immediately above the 

mouth of the main stream; it indicates the number of sub-basins into 

which that drainage area is divided. As shown on plate 2 the number 

of each sub-basin is the large integer near its center; the smaller 

figures represent area, length of stream, and altitude.

8 Douglas, E. M., Gazetteer of the lakes, ponds, and reservoirs of the State of New York: Map Information Office, Board of Surveys and Maps, 44 pp., Washington, 1926. [Processed.]
CHARACTERISTICS OF DRAINAGE BASINS 133 

AREA OF BASINS

The total area of the basin within the watershed lines above the 

selected gaging station is the primary basin factor. In a humid climate 

the volume of discharge varies directly with the size of the tributary 

drainage area. Accordingly, the area in square miles was measured, 

not only of the main basin above the gaging station but also of a 

number of sub-basins (generally over 50). The size of the basins 

included in this compilation ranges from 1.64 to 7,797 square miles. 

In general, large streams were excluded because the size of sheets 

became unwieldy, because some contained unsurveyed areas, and 

because their stream-flow characteristics could best be determined by 

synthesis of their components.

STREAM DENSITY

The runoff from the several parts of the drainage basin is discharged 

by the streams, and, other factors being constant, the time required 

for the water to flow a given distance is directly proportional to the 

stream length. The stream or drainage density is-the ratio between 

the total length of all streams within the drainage basin and the total 

area of the basin and is an indication of the drainage development. 

Accordingly, the length of all streams down to the smallest shown on 

the topographic maps was measured to determine the stream density 

and the area-distance distribution.

The number of small headwater streams shown on the topographic 

maps would vary with the season and the wetness of the particular 

year during which the survey was made, as well as with the judgment 

of the topographer and cartographer as to the amount of detail to be 

shown on the map. These circumstances introduce a measure of 

inconsistency in stream-density results as determined from maps.

The ratio of stream density for the basins included in this compilation, all of which are in the humid region, ranges from 0.89 to 3.37 

miles per square mile and averages 1.65 miles per square mile. Other 

factors being equal,high drainage density indicates a more effective operation, of the agencies of stream incision. Greater incision, for example, 

would be associated with steep land slopes. Opportunity for incision 

would be greater also where most of the discharge occurs as surface 

runoff rather than through ground-water channels; such a condition 

exists in areas where the ground is sufficiently impervious to shed 

storm rainfall.. Drainage density is greater in humid regions than in 

arid regions; it would approach zero in flat, sandy desert regions and 

would approach a maximum in steep, rocky, humid regions.
134 CONTRIBUTIONS TO HYDROLOGY, 1944

The variation of stream density with'the land slope is shown by the 

following data derived from groups of basins in New England.

Variation of stream density with land slope

Range in stream Average land

density slope

(miles per square (feet per

mile) mile)

1.00 to 1.25.__.__._._______.____._-_-_-_____ 290 

1.26 to 1.50____________--._._-----________ 550 

1.51 to 2.00.____.___---._._.______-_.____ 600 

2.01 to 2.25________________________________ 700

The mean land slopes for basins in New England having drainage 

densities within the ranges indicated in the above data were averaged, 

and the results indicate that, in general, in a given region the higher 

drainage densities are associated with the steeper land slopes. The 

reciprocal of the drainage density is the average distance between 

streams, and half the reciprocal of drainage density is the average 

horizontal distance between the streams and appurtenant watershed 

lines, measured at right angles to the streams. Drainage density 

appears to be inversely related to the distance of overland flow as 

distinguished from flow in stream channels. However, hi basins 

sufficiently permeable so that all rainfall can be taken directly into the 

soil through infiltration, the drainage density approaches zero and is 

associated with zero, overland flow.

AREA-DISTANCE DISTRIBUTION

The concentration of runoff from drainage basins of equal size may 

be greatly affected by the distribution of the area with respect to distance from the gaging station or outlet. Other factors being equal, 

the runoff from areas close to the gaging station should reach it 

sooner than water from remote areas. Accordingly, a drainage basin 

whose tributaries are compactly organized, so that water from- all 

parts of the basin has a comparatively short distance to travel, will 

discharge its runoff more quickly and reach greater flood crests than 

one in which the larger part of the area is remote from the gaging 

station or outlet. This basin characteristic is expressed in the summary table by the quantity Sal, computed by multiplying each partial 

area in the basin (a) by the channel distance from the midpoint of the 

mam stem serving it, downstream to the gaging station (1). Distances 

along the stream channels were measured in 0.1 mile chords.

In a sense this quantity is also a measure of the volume of channel 

storage in the basin. For example, if under a given regime of flow 

the cross-sectional area of a river at a given place varies directly as 

the drainage area above, then the volume in any given reach would 

vary as the product of a coefficient by mean drainage area above the
CHARACTERISTICS OF DRAINAGE BASINS 135

reach by the length of the reach. The coefficient would be a function 

of the stage of the regime selected, the slope of the reach, friction al 

resistance, and other hydraulic factors. No method is proposed for 

evaluating the coefficient. However, the sum of the products of 

mean drainage area and length of reaches for a given basin is equal 

to the product Sal which was derived by both methods of computation.

The most compact drainage basin would be a glory-hole inlet, and 

the product. Sal for such a basin is 0.375 A 1>6° where A represents 

total area; for an equilateral triangle, with reference to an outlet at 

one of the vertices, the product is 0.94 A. 1 -50 ; and for a square, with 

reference to a corner, it is 0.76 A 1 -50 . Figure 49 shows the results of 

plotting the products Sal against the corresponding drainage area. 

Only enough points are shown to define the line of regression, whose 

equation is 0.90 A 1 - 56, or more approximately 1.2 A 1 -50, within the 

range shown. Natural basins are generally less compact than any 

of the geometric shapes mentioned.

Additional subdivision of a basin beyond the 50 to 75 sub-basins 

generally used would tend to increase the value of the product Sal. 

However, a study of West River Basin, above Newfane, Vt., indicates 

that the product Sal for 20 sub-basins was 6,620, for 50 sub-basins 

6,810, and for 100 sub-basins 6,860. The values given in this report 

may therefore be considered essentially correct limiting values.

Points on the right of the trend line (fig. 49) represent basins less 

compact than the average, and those on the left the more compact. 

The regression line therefore furnishes a standard for comparing the 

relative compactness of different basins.

LENGTH OF BASIN

The table «(pp. 145-155) lists the length of longest watercourse in 

each basin measured in 0.1-mile chords to the source of the most 

headward stream. This length, when divided by the mean velocity 

of flow will give the time of concentration as used in the rational 

formula for the computation of flood discharge.

The mean length of travel of runoff or the distance to the center of 

gravity of the drainage system may be found by dividing the quantity 

Sal by the drainage area in square miles. This quotient is commonly 

identified by the symbol Lca . The table also lists the length of principal streams as defined under "Channel slope."

LAND SLOPE

Rainfall or snow melt which becomes direct runoff flows over the 

surface of the ground or, where the surface soil is shallow and permeable, immediately beneath it over the bedrock. The average 

distance water travels before entering a stream channel may be
136 CONTRIBUTIONS TO HYDROLOGY, 1944

Y

Efll. I betw

V

gsmw aavnbs KE '
CHARACTERISTICS OF DRAINAGE BASINS 137

expressed in terms of stream density. (See p. 133.) The rapidity 

with which the water travels to the streams likewise depends on the 

slope of the land.

The contours on the topographic maps provide a basis for determing 

the slope of the land by the intersection-line method outlined by 

Horton 9 as follows:

The intersection-line method. In order to reduce the labor of computation of 

slope of large areas the author has utilized the following method. An area the 

slope of which is to be determined is subdivided into squares of equal size by lines 

forming the boundaries between adjacent squares. The number of contours 

crossed by each subdividing line is counted and the lengths of the lines are scaled. 

Then the average scale-distance I' between contour crossing in the subdivision 

lines is v

F-5

1 N

where N is the number of contours crossed and 2i is the total length of the subdividing lines. If a is the horizontal angle at which each of two parallel contours 

crosses an intersection line, then I' sin a is the horizontal distance between the two 

contours measured normal to the contours. Contours may cross the intersection 

lines at all angles from 0° to 90°. The mean value of sin a for angles from 0° to 

90° is

yJ o

If D is the contour interval or difference in elevation in feet, and L is the average 

normal horizontal distance between contours, then

L= 0.6366 V 

and the mean slope Sg of the area is

0.6366 =.

= t 1.571 * » -gIn applying this method it is assumed that each contour crossed represents a 

difference of elevation along the subdivisional line equal to the contour interval. 

Of course it may happen that two adjacent contours are at the same elevation and 

are separated by land only a little higher or lower. On an average, however, the 

elevations of summits or depressions between equal contours will differ from that 

of the adjacent contours by an amount equal to one-half the contour interval, and 

it can readily be seen that the average declivity between a pair of contours of equal 

elevation is nearly the same as if the contours were separated by the contour 

interval D, so that the method gives nearly correct results even where the subdivision lines cross adjoining contours of equal elevation, as in the case of summits 

and depressio'ns.

 Horton, R. E., Drainage-basin characteristics: Am. Geophys. Union Trans., No. 13, pp. 350-361, 1932. 

747049-47 3
138 CONTRIBUTIONS TO HYDROLOGY, 1644

By making the subdivision lines sufficiently frequent, the average slope of an 

area may be determined with whatever degree of accuracy is required.

This method has been tested by comparison of slope for the same area computed 

from the measured total lengths of contours, with, in general, good agreement.

In carrying out this computation, the slope along the meridian lines 

is computed separately from the slope along the parallels of latitude. 

Where there is a great difference between the land slope in the two 

directions, the orientation of the basin is determined by the axis of 

least slope. Where the east-west slope and the north-south slope are 

nearly the same, the line of orientation may be approximately midway 

between the two, or it may not be clearly defined in either direction 

in a cup-shaped or fan-shaped basin. Land slopes listed in the table 

range from 1,598 feet per mile for the upper Pemigewasset River 

Basin in New Hampshire to 55 feet for Great Egg River in Coastal 

New Jersey.

Paulsen 10 found, during the flood of September 1938 in the North 

Atlantic States, that the infiltration index tends to increase with 

decrease in mean land slope. He states that "although the slope of the 

land itself might influence the retentive capacity of the ground, this 

tendency may be due to other factors related to slope, such as depth 

of soil cover."

CHANNEL SLOPE

Upon leaving the land the runoff enters the channel system, through 

which it flows in channels that increase progressively in size with the 

entrance of additional water. Channels in a drainage basin are classified for study as principal and tributary. The principal streams of 

a basin are defined as those that drain 10 percent or more of the total 

area of the basin; tributaries are defined as those that drain less than 

10 percent of the area of the basin. The average slope of the tributaries and of the principal streams is computed separately as the 

quotient of the total fall divided by the corresponding total length 

and is reported in the summary table.

In computing the slope of the stream channels, only the largest 

stream in each sub-basin is considered. Thus, if a basin is divided 

into 75 sub-basins only 75 stream lengths and falls are measured. 

These stream lengths are classified as principal or tributary, and the 

average slope of each is computed. As only one stream in each subbasin is included in the classification, many minor headwater streams 

are excluded from consideration; consequently, the reported slope of 

the tributary stream is affected by the number of subareas into which 

the basin is divided. The reported mean slope of the tributary

"" Paulsen, C. G., Hurricane floods of September 1938: U. S. Qeol. Survey Water-Supply Paper 867, pp. 

440-441, 1940.
CHARACTERISTICS OF DRAINAGE BASINS 139

streams increases as the number of subareas becomes larger, thus 

embracing more steep minor headwater streams. This is illustrated 

in figure 50, which shows the result of a comprehensive study of the 

slope of tributaries of West River at Newfane, Vt. The asymptote 

resulting from that study is about 225 feet per mile, whereas the 

channel slope obtained with 53 subareas (see table, No. 1-354) is 

200 feet per mile.

The slope information for the several drainage basins listed in the 

table discloses that a steep land slope is generally associated with

zo 30 40 50 60 70 80 90 100

NUMBER OF SUBAREAS

FIQPEB 60. Variation of computed slope of tributary streams with number of subareas, West River at

Newfane, Vt.

steep tributary and principal channel slopes and conversely, as might 

be expected. There is, however, no systematic variation; moreover, 

according to geometric analysis by Horton, 11 the ratio between 

principal channel slope and average land slope is a measure of the 

horizontal angle that the lateral slope makes relative to the stream 

slope. A low slope ratio indicates that the laterals tend to enter the. 

streams at right angles, whereas the angle of inflow into the stream 

becomes more acute as the channel slope approaches equality with 

the ground slope. This slope ratio tends to decrease with increase in 

drainage area, but varies considerably between drainage basins of 

equal size.

» Horton, R. E., op. cit., p. 360.
140 CONTRIBUTIONS TO HYDROLOGY, 1944-47

AREA-ALTITUDE DISTRIBUTION

Another method of expressing the slope of the basin is by means of 

the altitude of the several parts with reference to sea level. This is 

best expressed through the hypsometric curve, as a graph showing the 

area-altitude distribution is called. Although the area-altitude distribution was derived for each basin, only the maximum, mean, and 

minimum altitudes as determined from the topographic maps are 

shown in the table. From this information, however^ the areaaltitude distribution curve can be readily approximated. Figure 51 

shows the hypsometric curves for several basins plotted in terms of 

percent of range in altitude and percent of area above the indicated 

altitude. The variations are wide, but in general the mean altitude

100

20 30 40 50 60 70 80

PERCENT OF AREA 

FIGTTBB 51. Typical hypsometric curves for drainage basins.

1-104. Swift Biver near Eoxbury, Maine.

1-153. East Branch of Pemigewasset Eiver near Lincoln, N. H.

1-175. Lake Winnipesaukee outlet at Lakeport, N. H.

1-435. Quinnipiac Eiver at Wallingford, Conn.

1-464. Leadmine Brook near Thomaston, Conn.

3- 18. Brokenstraw Creek at Youngsville, Pa.

4-250. Otter Creek at Center Rutland, Vt.

90
CHARACTERISTICS OF DRAINAGE BASINS 141

*

of a basin is located at 0.34 of the range between the minimum and 

maximum; thus a basin is comparable to the surface of a cone.

The area-altitude distribution curve has several applications. For 

example, snow surveys generally show an increase hi depth of cover 

and water equivalent with increase in altitude; the area-altitude relation provides a means for estimating the mean depth of snow or its 

water equivalent over a drainage basin. Barrows 12 describes a significant variation in annual precipitation and runoff in the Connecticut 

River Basin with respect to altitude. The obvious variation in 

temperature with change in altitude is further indication of the utility 

of the area-altitude distribution curve.

The mean altitude of the basin above the altitude at the outlet or 

gaging station represents the potential head of a uniform depth of 

water over the basin with respect to the outlet or gaging station, and 

as such is a factor in determining the rate at which the waters are 

collected and discharged. The data in the summary table shows 

that, hi general, the land slopes and channel slopes vary with the mean 

altitude of the basin above the outlet. Thus steep slopes are associated with a high altitude above the outlet, and conversely. A rough 

average relation between slope and mean altitude is as follows:

where Ki=0.31

K2 ranges from 0.97 at 50 square miles to 3.0 at 1,000 square miles.

KZ ranges from 3.5 at 50 square miles to 23.4 at 1,000 square miles.

<Si=mean land slope, in feet per mile.

St= slope of tributary streams, in feet per mile.

S9 slope of principal streams, in feet per mile.

AREA OF WATER SURFACES

The effect of storage in retaining flood runoff and prolonging its 

discharge until the flood^in channels farther downstream^has 'begun 

to subside tends to reduce flood peaks and increase the time lag between rainfall and its consequent runoff. Natural storage in lakes 

and ponds and artificial storage in reservoirs aids this retardation. 

A measure of the amount of storage available for such modification 

of flood discharge can be derived from the surface area of the water 

bodies shown on the topographic map. (See table.) The computations at Boston included the determination of swamp areas, which had 

been part of an earlier project carried on hi 1936 in cooperation with 

the Works Progress Administration; this covered compilations for the 

Merrimac and Connecticut River Basins, both in square miles and

i' Barrows, H. K.( Precipitation and runoff and altitude relations for Connecticut River: Am. Geophys 

Union Trans., 14th Ann. Meeting, pp. 396-406, 1933.
142 CONTRIBUTIONS TO HYDROLOGY, 1944

in drainage percent.13 The computations made at Pittsburgh did 

not include swamp areas.

The areas of swamps as reported would be affected by the hydrologic conditions under which the topographic surveys were made. 

Surveys made in spring or early summer would probably show a 

greater swamp area than those made in late summer or fall, and 

surveys in a wet year would show marked contrast with those made 

in a dry year. It is not known to what extent the results given in 

the table were affected by hydrologic conditions.

It should be pointed out that the area of water surfaces is only 

one measure of their effect on the time distribution of flood discharge. 

The position of the water bodies in the river system is also important; 

thus a large pond near the headwaters would affect but a small 

part of the runoff, whereas one of the same size farther downstream 

would affect a larger part of the runoff.

In addition to the effect of storage in modifying the shape of flood 

waves or the time distribution of runoff, the total volume of runoff may 

be influenced by evaporation from lakes, reservoirs, and swamps. 

The loss of water by evaporation from water surfaces in the northeast 

is about twice that from land surfaces, per unit of area. Accordingly, 

basins with a large proportion of water and swamp surfaces may be 

expected to yield less runoff than those with a small proportion.

In many of the basins listed in the table the proportion of lake and 

swamp areas exceeds 10 percent, and in a few, especially in New England, it approaches 20 percent; doubtless the effect on water losses is 

significant. The percentage of lake area is highest in New England 

and northern New York and generally in the glaciated portions of 

the areas studied.

SUMMARY OF RESULTS

The summary table that follows gives the results of measurements 

on topographic maps on a scale of 1:62,500. It includes about 22,000 

areas covering 145,000 square miles. A total of 240,000 miles of 

stream length was measured, and nearly a million contours on the 

topographic maps were counted and translated into land and channel 

slopes.

Reference has already been made to general relationships between 

the topographic factors listed in the table. Each item is not necessarily unique, but it may reflect a condition that also influences the 

others, consequently other relationships between them may be found. 

For example, figure 52 shows that, in general, larger drainage areas 

are associated with flatter stream slopes; but average land slopes and

» Grover, N. O., The floods of March 1936, pt. 1: U. S. Geol. Survey Water-Supply Paper 798, pp. 335-338, 

1937.
CHARACTERISTICS OP DRAINAGE BASINS 143

mean altitudes of drainage basins above outlets or gaging stations 

show a tendency to increase with drainage area. The points shown 

on figure 52 correspond to averages of groups of drainage basins within 

limited ranges in size. If individual basins were plotted on figure 52, 

material scattering of points would result, the basins plotting on the 

left being relatively flatter than those on the right. The average 

curve therefore provides a means fdr comparing the slopes and altiSUOPE OF TRIBUTARY STREAMS 

<FE£T PER MILE)

SLOPE OF PRINCIPAL STREAMS 

(FEET PER MILE) \

POINTS SHOWN ARE FOR

AVERAGES OF GROUPS WITHIN

LIMITED RANGE IN DRAINAGE AREA \

\

MEAN LAND SLOPE 

(FEET PER MILgl

;

IEAN ALTITUDE OF BASIN i 

>BOVE GAGING STATION/ 

(FEET) /

2 K> | 100 1000 

SLOPES. IN FEET PER MILE AND ALTITUDES, IN FEET

FIGURE 52. Graph showing general variation in stream slopes and altitude in relation to size of drainage

basini

tudes of basir»s of different size, the

showing principal channel slope and 

the slope ratio of the basins analyzed 

in drainage area.

A principal shortcoming of the c 

istics may be that it was not practicable 

distribution of stream and land sloj 

within every area. Steep slopes on 

average slope considerably, yet thess 

flood-peak discharges. Moreover,

divergent trends of the lines 

average land slope indicate that 

tends to decrease with increase

omputations of physical characterto determine in detail the 

es and of lake and swamp areas 

i few tributaries may increase the 

slopes may have little effect on 

1,he course of a river in a given
144 CONTRIBUTIONS TO HYDROLOGY, 1944

length may be characterized either by uniform slope or by a series of 

pools with intervening rapids or perhaps cataracts. The velocity in 

a stretch of uniform slope would probably be the greater if other factors were constant, as pools have a detention storage effect and the 

fall at rapids or cataracts imparts but little horizontal velocity to the 

water. A lake on the headwaters of a stream may have no noticeable 

effect, whereas a lake of the same size on the main channel near the 

lower reaches of an otherwise flashy stream may greatly modify flood 

discharges. Also, steep slopes or abnormally high elevations in the 

part of a drainage basin upstream from a lake may affect considerably 

the average land slope and the mean elevation of a basin, but the lake 

may decrease the flood discharges so much that the outflow from the 

lake would differ little from that of a basin in which the slopes and 

elevations were much less.

Storage capacity was not computed, as topographic maps furnish 

no information'from which channel and lake cross sections at different 

stages can be determined, except that they might be crudely correlated with the stream slopes.
^CHARACTERISTICS OF DRAINAGE BASINS 145

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CMOO CMO CO

1 1 1 1 1
Summary of drainage basin topographic characteristics Co

No.

1-213.5.----

1-216 

1-218 

1-220A. -

1-222 

1-223 

1-225 

1-227 

l-230 

1-232A. 

1-232B. 

1-237A J

1-249A1-264 

1-267 

1-272 _.

1-275 

1-279A _ 

1-282 ___

1-284 

1-289 . ...

1-294A. 

1-295.5 

1-298 . 

1-301 _

1-329A. 

1-332... 1 

1-334 

1-336.8A.... 

1-339A -

Name of gaging station

Charles River at Charles River Village, Mass.

Quinsigamond River at North Grafton, Mass.

Willimantic River near South Coventry, Conn. 

Shetucket River near Willimantic, Conn __ .

Ammonoosuc River at Bethlehem Junction, 

N. H 

Mascoma River at West Canaan. N. H... 

Drainage area 

(square miles)

23.3 

183 

251 

35.2 

260

42.2 

31.3 

139.2 

417 

26.1

27.8 

93.3 

199.8 

121 

401

76.2 

169 

93.8 

157 

331

711 

27.7 

58.7 

83.5 

88.6

88.5 

395 

241 

30.5 

80.5

Stream density (miles persquare 

mile)

2.34 

1.27 

1.37 

1.27 

1.28

1.20 

1.69 

1.36 

1.32 

1.57

1.14 

1.47 

1.51 

1.69 

1.62

1.61 

1.63 

1.46 

1.57 

1.55

1.56 

1.62 

 1.61 

1.51 

1.67

1.72 

1.53 

2.09 

1.99 

1.60

S al(cubic miles)

97 

3,638 

8,126 

202 

3,738

327 

164 

1,861 

8,184 

139

117 

966 

3,416 

1,775 

6,815

707 

2,320 

993 

2,362 

6,332

22, 477 

141 

617 

723 

738

968 

8,575 

4,272 

172 

622

Land slope (feet 

per mile)

$

H

359 

270 

273 

200 

129

158 

458 

414 

370 

374

293 

323 

298 

471 

414

377 

424 

579 

549 

478

420 

449 

355 

319 

351

1,225 

1,034 

1,378 

1,168 

734

i

z

257 

210 

223 

159 

105

129 

308 

279 

262 

248

275 

213 

228 

312 

293

303 

280 

330 

319 

291

261 

274 

237 

220 

271

1,056 

855 

1,236 

693 

486

Average

301 

236 

244 

176 

116

141 

371 

337 

307 

301

283 

260 

258 

378 

344

334 

341 

436 

415 

369

328 

348 

285 

262 

305

1,130 

931 

1,295 

890 

588

Channel 

slope (feet 

per mile)

Tributary

49.6 

22.6 

20.7 

35.3 

13.5

24.0 

77.9 

58.7 

41.5 

101

97.6 

59.0 

55.6 

91.4 

61.7

114

79.9 

60.2 

56.1 

51.0

42.1 

76.6 

70.9 

68.7 

64.0

575 

274 

350 

375 

234

Principal

12.8 

4.24 

3.57 

19.2 

3.28

11.6 

41.5 

12.5 

12.3 

20.0

46.1 

21.6 

15.1 

25.1 

13.3

20.7 

22.0 

8.97 

12.2 

13.7

12.1 

37.4 

26.2 

24.3 

24.9

75.8 

35.9 

21.8 

119.0 

39.2

Longest watercourse 

(m

8

38

59

1

26

15

1

26

44

9

7

1

27

25

32

1

2

1

2

3

6

1

1

1

2

5

3

1

1
1 «ijrt

1-346 

1-347-.. .-

1-350. 

1-352A......

1-354

1-356 .

1-358 ..

1-359 

1-362. 

1-363........

1-363A1-365 ....

1-367 

1-368.. 

1-371. 

1_?79

1-375 

1-376A _ ...

1-380A 

1-380.4A..... 

1-383.2......

1-384

1-387.. 

1-389 

1-390 .

1-394 

1-396.8-. 

1-399 

1-402 

1-406........

1-407 

1-410 ...

1-413 

1-416 

1-431- ...-

Ottauquechee River at North Hartland, Vt 

South Branch Ashuelot River near Marlboro,

N.H.. . _... 

Deerfleld River, excluding Somerset Reservoir,

Deerfleld River, excluding Harriman ReserGreen River above mouth at Greenfield, Mass. 

Mill River at Northampton, Mass. ...........

Westfleld River at Knightville, Mass... ......

Westfleld River near Westfleld, Mass ___ ..

Westfleld River, excluding Westfield Little 

River, near Westfleld, Mass. 

Middle Branch of Westfleld River at Goss

Heights, Mass. 

West Branch of Westfleld River at Huntington, Mass. 

Westfleld Little River near Westfleld, Massnear New Boston, Mass. 

Hoekanum River near East Hartiord, Conn....

153

221

269

158

72.2

308

71.2

420

41.8

36.4

83.8

186

370

19.0

18.7

49.9

12.2

362

332

178

663.5

88.4

89.4 

53.3

100

201

702

188

149

34.1

162

497

448 

62.6

93.7

48.5

98.4

92.0

75.3

74.5

1.57

1.76

1.59

1.45

1.69

1.53

2.17

2.21

2.32

2.17

1.72

1.90

1.97

1.82

1.73

2.00

1.96

1.71

1.72

1.94

1.85

1.64

1.75 

1.94

1.67

1.52

1.50

1.59

1.56

1.06

2.05

1.77

1.84 

2.24

1.95

1.12

1.58

1.34

1.36

1.64

1.912

4,562

5,211

2,733

666

6,812

751

11, 9^2

274

204

664

2,236

8,025

74

109

344

46

9,838

8,389

2,418

24,550

890

1,125 

446

919

4,017

22, 677

2,998

2,413

216

2,562

12,258

11, 266

544

1,051

352

1,129

' 758

582

749

756

1,215

707

969

1,073

879

665

710

700

630

376

370

479

392

376

537

768

884

914

1,022

821

699

726 

760

4fl4

402

519

628

461

232

722

678

698 

794

795

476

485

580

639

403

512

994

548

792

823

753

520

544

630

444

282

265

320

278

271

317

508

702

722

850

649

600

527 

494

246

281

318

ld.7

301

151

458

485

487 

555

620

422

303

411

446

292

614

1,090

615

868

932

806

580

614

660

522

322

310

387

328

314

409

778

803

922

721

642

610 

608

313

357

404

468

371

186

570

567

577 

655

 695

446

381

482

526

339

157

241

157

227

238

200

175

110

193

246

63.9

50.4

65.4

85.5

126

120

173

168

180

205

144

245

192 

218

69.3

66.5

52.2

98.5

70.5

49.7

125

115

111 

276

208

150

105

113

130

106

23.8

30.0

28.4

26.4

53.6

42.9

40.5

22.1

67.4

59.2

17.9

16.4

17.4

31.1

24.2

37.2

61.3

32.3

31.0

56.5

26.5

75.8

53.1 

59.3

22.9

16.0

12.3

12.1

17.4

11.7

50.7

30

29.8 

94.9

87.6

71.4

20.4

61.5

67.7

28

2

3

3

3

3

2

6

1

1

2

3

1

1

5

7

1

2

1

1

3

5

2

2

1

3

5

5

1

2

1

2

1

2
Summary of drainage basin topographic characteristics Co

No.

1-432 

1-435 

1-438 

1-444 . .

1-446 

1-460 .

1-453 

1-455. 

1-458 

1-459 - 

1-462 .

1-463 

1-464 .

1-466 

1-471 

1-476 

1-482 

1-485 

1-488 .

1-492 

1-496 

1-499 

1-501 

1-506 

1-508 _

1-510 

Name of gaging station

Housatonic River near Great Barrington,

Mass.

Naugatuck River near Thomaston, Conn..... 

Naugatuck River near Naugatuck, Conn. . ...

Hudson River near Newcomb, N. Y __ ......

Hudson River at Hadley, N. Y.. .............

Cedar River below Chain Lakes near Indian 

Lake, N. Y.... ..... ....

Schroon River at Riverbank, N. Y ............

East Branch of Sacandaga River at Griffin, 

N. Y ........ ... ... ... ..... .... ... ...

Batten Kill at Arlington, Vt. __ __ .

Kayaderosseras Creek near West Milton, 

N. Y-- .... ........ ... *...... .... ....

Hoosic River, excluding Hoosic Lake, at

North Branch of Hoosic River at North

Walloomsac River near North Benninston. Vt.

Drainage area 

(square miles)

104.7 

109 

57.1 

280

632

1, 545 

204 

68.5 

133 

75.3

71.9 

245.8 

24.0 

77.5 

192

1,664

160 

527 

491

114 

152

90 

46.2

31.4 

510

39.1 

111

Stream density (miles persquare 

mile)

1.62 

1.66 

1.91 

1.52

1.35

1.57 

1.34 

1.81 

1.98 

2.29

2.21 

2.05 

2.15 

1.84 

2.21

1.68

1.77 

1.58 

1.60

1.37 

1.51

1.68 

1.77

1.79 

1.68

1.92 

1.74

S al(cubic miles)

821 

1,323 

405 

6,841

21,092

81, 138 

3,497 

820 

2,431 

710

822 

4,483 

121 

710 

2.282

89, 931

2,503 

13,054 

9,640

1,258 

1,552

894 

268

142 

11, 036

210 

1.057

Land slope (feet 

per mile)

H

433 

452 

567 

607

621

666 

736 

593 

574 

624

644 

598 

552 

614 

1,148

973

684 

1,100 

1,022

1,275 

1,120

494 

842

844 

1,047

1,005 

950

CQ

1

fc

286 

274 

486 

513

487

477 

480 

407 

388 

366

475 

399 

334 

368 

1,010

882

883 

998 

961

1,074

827 

390

144

533 

795

719 

653

Average

349 

351 

521 

553

543

557 

537 

487 

465 

474

546 

483 

424 

474 

1,091

920

800 

1,040 

987

1,157 

953 

432

669 

900

841

777

Channel 

slope (feet 

per mile)

£

74.6 

91.2 

165 

135

79.8

54.2 

113

85.2 

88 

153

175 

103 

147 

92.6 

250

127

159 

118 

124

183 

314 

163

3Q7

414 

181

479 

271

Principal

40.2 

9.42 

78.6 

13.1

8.45

10 

17.1 

17.1 

31.4 

33.4

41 

17.5 

72.3 

32.2 

13.0

12.37

32.61 

16.54 

35.7

42.5 

52.7 

24.36

77

113

17.7

146 

80.2

&

8

OJ 

-JJ 

|

S

a 

o 

i-l

17

23

12

43

63

11

33

19

34

17

21

40

10

19

24

93

35

47

35

22

22

19

11

46

9

18
CHARACTERISTICS OF DRAINAGE BASINS 149

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150 CONTRIBUTIONS TO HYDROLOGY, " 19 4 4

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CHARACTERISTICS OF DRAINAGE BASINS 151

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? s
152 CONTRIBUTIONS TO HYDROLOGY, 1944

Continued Summary drainage topographic characteristics of basin 

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Shenango River Sharpsville, at Pa.__._ _____ Shenango River GreenvDle, Little Pa.... near 

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3-163 

3-166 

3-167 

3-169 ..

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3-206 

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Ohio. 

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466

27.5

140

672

386

913

460

438

540

1,357

236

1,315

128

150

287

281

1,145

393

267

587

762

1,226

389

1,225

2,150

198

209

255

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387

438

195

544

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331

808

286

76.5

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477

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2.29

2.03

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1.42

1.46

1.56

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1.26

1.56

1.80

1.87

2.12

1.59

2.10

2.12

2.09

2.17

1.77

1.64

1.64

1.39

1.16

1.37

1.37

1.42

1.32

1.37

1.62

1.05

1.64

2.09

2.17

1.62

1.73

1.44

12, 196

129

1,891

16, 414

10, 822

35, 364

10, 582

40,234

15, 130

17,475

91, 988

5,597

74, 848

2,041

1,569

7,542

11,004

88, 456

12, 726

4,740

23, 203

32, 960

91, 646

15, 246

56, 421

149, 121

5,436

6,708

5,373

967

9,778

13, 733

3,533

17, 090

5,060

21, 339

9,800

31,960

6,271

551

60,323

16, 837

13,509

421

882

650

368

1,661

1,677

546

737

1,345

1,534

1,431

1,317

1,344

1,257

1,334

1,212

1,764

1,832

2,260

2,294

802

2,013

2,098

2,594

2,343

2,281

2,495

2,113

103

64

96

97

147

132

136

110

83

227

1,059

811

214

199

136

414

731

667

358

1,610

1,670

532

746

1,332

1,606

1,474

1,349

1,302

1,373

1,481

1,133

1,774

1,722

2,149

2,169

853

1,993

2,061

2,511

2,268

2,211

2,077

2,496

100

56

102

118

134

130

116

107

226

983

802

218

162

118

417

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660

363

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1,673

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1,338

1,575

1,455

1,335

1,321

1,318

1,414

1,183

1,768

1,770

2,218

2,244

830

2,002

2,077

2,563

2,302

2,242

2,325

2,339

102

60

100

110

140

131

146

114

96

227

1,016

806

216

183

126

39.5

127

74.5

26.4

76.6

54.6

32.7

29.5

108

154

114

275

148

347

259

130

285

145

140

198

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118

171

113

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59.9

64.5

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17

3.01

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6.99

3.97

4.97

2.44

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27.19

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44.12

72.76

18.59

35.41

11.56

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2.28

11.26

7.01

18.06

13

8.02

7.79

7.30

2.19

4.8

5.4

4.85

12.04

6.47

6.75

5.28

7.32

7.51

7.07

7.06

6.72

8.5

2.52
154 CONTRIBUTIONS TO HYDROLOGY, 1944

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INDEX

Abstract .-.... . -. . 125

Area-altitude distribution curve, expressing

slope of basin by._ _______ 140-141

Channel slope, computation of. _ ______ 138-139

variation of with number of subareas.. _ 139

Channel storage, measurement of volume of 134

Connecticut, drainage basins in..___ 146,147-148

Drainage basins, differences in character of. 128,129 

relation of slope and altitude to size of._ 143 

summary of topographic characteristics

of-_ 145-155 

typical hypsometric curves for_,____ 140 

use of maps in tabulating data on__ 132; pi. 2

Iowa, drainage basin in. ... __________ 155 

Kentucky, drainage basins in_________ 153

Land slope, intersection-line method for determination of.. .- --._.. 137-138

Maine, drainage basins in.--_________ 145 

Maryland, drainage basins in________ 150,151

Page 

Massachusetts, drainage basins in.. 145-146,147,148

New Hampshire, drainage basins ha _ 145,146-147

New Jersey, drainage basins in 149,150

New York, drainage basins in 148,

149,150,151,154-155

Ohio, drainage basins in.. 152-154

Pennsylvania, drainage basins in 150,151,152 

Previous studies._.__ . - 128-130 

Purpose and scope of present study. 130-132

Rhode Island, drainage basins in. ..._ 146 

Runoff, effect of area-distance distribution

on i . 134-135,136 

effect of area of water surfaces on. ___v 141-142 

Meteorologic factors affecting. ___ 127-128

Stream density, features of._____-___ 133-134 

Vermont, drainage basins in.- 146,147,148,155

West Virginia, drainage basins in______ 152,153 

Wisconsin, drainage basins in.. 154,155

157

O