Schumm_1956_Evolution of Drainage Systems and Slopes in Badlands of Perth Amboy

BULLETIN OF THE GEOLOGICAL SOCIETY OF AMERICAVOL. 67. PP. 697-646. 43 FIGS.. 6 PLS. MAY 1966

EVOLUTION OF DRAINAGE SYSTEMS AND SLOPES INBADLANDS AT PERTH AMBOY, NEW JERSEY

BY STANLEY A. SCHUMM

ABSTRACT

To analyze the development of erosional topography the writer studied geomorphicprocesses and landforms in a small badlands area at Perth Amboy, New Jersey. Thebadlands developed on a clay-sand fill and were morphologically similar to badlands andareas of high relief in semiarid and arid regions. A fifth-order drainage system wasselected for detailed study.

Composition of this drainage network conforms to Horton's laws. Within an area ofhomogeneous lithology and simple structure the drainage network develops in directrelation to a fixed value for the minimum area required for channel maintenance. Ob-served relationships between channel length, drainage-basin area, and stream-ordernumber are dependent on this constant of channel maintenance which is in turn depend-ent on relative relief, lithology, and climate of any area.

Other characteristics of the drainage network and topography such as texture, maxi-mum slope angles, stream gradients, drainage-basin shape, annual sediment loss perunit area, infiltration rate, drainage pattern, and even the morphologic evolution ofthe area appear related to relative relief expressed as a relief ratio, the height of thedrainage basin divided by the length. Within one topographic unit or between areas ofdissimilar but homogeneous lithology the relief ratio is a valuable means of comparinggeomorphic characteristics.

Hypsometric curves are available for a series of 11 second-order drainage basinsranging in stage of development from initial to mature. Relief ratio and stream gra-dients attain a constant value when approximately 25 per cent of the mass of the basinhas been eroded. Basin shape becomes essentially constant at 40 per cent of mass re-moved in accord with Strahler's hypothesis of time-independent forms of the steadystate.

Comparison of the drainage pattern as mapped in 1948 with that of 1952 reveals asystematic change in angles of junction and a shift of the entire drainage pattern ac-companying changes in the ratio between ground and channel slope.

Field observations and experimental studies suggest that badland slopes may re-treat in parallel planes and that the rate of erosion on a slope is a function of the slopeangle. The retreat of slopes may not conform to accepted concepts of runoff action as afunction of depth and distance downslope. Runoff occurs as surge and subdividedflow which may be closely analogous to surficial creep.

Rills follow a definite cycle of destruction and reappearance throughout the year underthe action of runoff and frost heaving.

At Perth Amboy, slopes are initiated by channel degradation and maintained byrunoff and by creep induced through frost heaving. Runoff or creep may form convexdivides, and both parallel and declining slope retreat are important in the evolution ofstream-carved topography.

Hypsometric curves reveal that the point of maximum erosion within a drainagebasin migrates upchannel and that the mass-distribution curve of any basin has asimilar evolution to that of the longitudinal stream profile.

Comparative studies in badland areas of South Dakota and Arizona confirm conclu-sions drawn at Perth Amboy and show the importance of infiltration of runoff on topo-graphic development and of subsurface flow in slope retreat and miniature pedimentformation.

597

598 S. A. SCHUMMBADLANDS, PERTH AMBOY, N. J.

CONTENTSTEXT

PageIntroduction 599Acknowledgments 600General description of the Perth Amboy

locality 600Characteristics of the drainage network 602

Components of the drainage network 602Limiting values of drainage components. . . . 607Form of the drainage basins 612Basin form related to geomorphic stage of

development 614Evolution of the drainage network 617

Effect of stage on angles of junction 617Evolution of the Perth Amboy drainage

pattern 620Field observations and experimental studies on

the development of badland topography. . 622Field-erosion measurements 622Experimental erosion measurements and

study of runoff 627Seasonal effects on erosion; the rill cycle... 632

Cycle of development of erosional topography. 634Relation of stream profiles to slopes 634Available relief and the development of land-

forms 636Hypsometric study of geomorphic stages of

development 638Comparative studies in badland regions of the

West 641Topographic forms and erosion processes. . . . 641Influence of regional upland slope on topog-

raphy 644Summary and conclusions 645References cited 646

ILLUSTRATIONSFigure Page

1. Grain-size distribution of Perth Amboy fill. 6012. Relation of number of streams of each order

to order number3. Relation of mean basin area, mean stream

length, mean stream gradient, to streamorder

4. Comparison of shape of basin and mamdrainage elements of three areas 605

5. Relation of mean basin area and meanstream length to stream order

6. Relation of mean stream length of eachorder to mean basin area of each order. .

7. Frequency-distribution histograms of thelogs of drainage-basin area 607

8. Frequency-distribution histograms of logsof stream-channel lengths 607

9. Position of interbasin area and method ofclassifying streams by order number

10. Frequency-distribution histograms of first-and second-order basin areas and inter-basin areas 609

11. Frequency-distribution histograms of first-and second-order channel lengths andmaximum interbasin lengths 610

12. Relation of drainage density to relief ratio. 61313. Relation of drainage density to relief ratio

of third-order basins 613

Page14. Relation of mean stream gradients to relief

ratio 61315. Relation of mean maximum-slope angles to

relief ratio 61316. Relation of elongation ratio to reh'ef ratio. . 61417. Relation of mean estimated sediment loss

to relief ratio 61518. Sequence of second-order hypsometric

curves 61519. Sequence of second-order hypsometric

curves 61520. Relation of mass removed within a basin to

relief ratio, gradient, elongation ratio,and drainage density 617

21. Frequency-distribution histograms ofyoung, mature and combines angles ofjunction 618

22. Drainage-pattern changes in selected basinsbetween 1948 and 1952 at Perth Amboy. 620

23. Possible development of angles of bifurca-tion 621

24. Suggested evolution of the Perth Amboydrainage pattern 621

25. Frequency-distribution histogram of anglesbetween tributaries and segments of themain channel 622

26. Typical Perth Amboy slope profiles 62327. Regression fitted to scatter diagram of

depth of erosion on per cent of distancefrom top of the straight slope segment. . 624

28. Regression line fitted to adjusted values ofFigure 27 625

29. Frequency-distribution histograms ofangles between stakes measured inSeptember superimposed on histogramof angles measured in June 625

30. Frequency-distribution histograms of max-imum-slope angles measured in 1949 and1952 626

31. Relation of erosion to sine of slope angle. . . 62732. Relation of the largest particle moved on a

slope to sine of slope angle 629603 33. Depth of erosion measured on slope profile

D during the summer of 1952 63034. Slope profile Din June and September 1952. 63135. Depth of erosion measured on an initially

straight slope during the summer of 1952 63236. Development of valley-side slopes 63537. Effect of direction of drainage of upland

slopes on slope-profile form 63638. Development of topography in areas of

high, moderate, and low relief 63739. Possible topographic differences, at a late

stage of development, between areas oforiginally high, moderate, and low rela-tive relief 638

40. Changes in longitudinal stream profiles atPerth Amboy 639

41. Method of dividing a drainage basin intofive equal areas and the system of num-bering each 20 per cent area 639

42. Relation of erosion within each 20 per centarea of a basin to total erosion during acomplete geomorphic cycle 640

43. Two longitudinal stream profiles surveyedin Badlands National Monument, SouthDakota 644

604

605606

60S

INTRODUCTION 599

Plate Facing page1. Topographic map of the Perth Amboy bad-

lands 5972. Perth Amboy badlands 6323. Rill cycle 633

Following page4. Rill cycle5. Badland slopes at Perth Amboy and

Badlands National Monument, South


steep sides, V-shaped cross section, and branchingenter most abundantly into his mental pictures ofan upland of homogeneous material or horizontalrocks that is undergoing dissection, especially whenerosion is vigorous."

ACKNOWLEDGMENTS

This investigation formed part of a quanti-tative study of erosional landforms sponsoredby the Geography Branch of the Office of NavalResearch as Project Number NR 389-042 underContract N6 ONR 271, Task Order 30, withColumbia University.

The writer wishes to thank Prof. A. N. Strah-ler, who sponsored the project, for the use ofdata collected at Perth Amboy before 1951, andfor the topographic map of the area (PI. 1). Pro-fessor Strahler and members of the Seminar inGeomorphology at Columbia University dur-ing the years 1952 and 1953 gave much valu-able criticism and advice. Messrs. J. T. Hack,L. B. Leopold, H. V. Peterson, and M. G. Wol-man of the U. S. Geological Survey, Prof. JohnMiller of Harvard University, and ProfessorStrahler read and offered valuable suggestionsfor improvement of the manuscript.

During the field season of 1952 Mr. IvenBennett of Rutgers University acted as fieldassistant. M. Rossics and A. H. Schumm alsohelped in the field. Mr. A. Broscoe kindly fur-nished the drainage map of the Chileno Canyondrainage basin.

GENERAL DESCRIPTION OF THE PERTH AMBOYLOCALITY

The Perth Amboy badlands, where most ofthe investigation was made, were located on thewestern boundary of Perth Amboy, New Jersey,on the north bank of the Raritan River be-tween the two highway bridges over the river.The area was conspicuous because it was anom-alous in the humid climate of New Jersey andresembled larger badlands of the more aridWest (PI. 2, figs. 1, 2, 3). The Perth Amboybadlands are not unique, however; badlandshave developed elsewhere in humid climates.Rapid badland erosion is occurring in the Duck-town Copper Basin of Tennessee where W}$square miles are devoid of vegetation becauseof destruction by smelter fumes. It is consideredthe largest bare area in any humid region of

the United States (Hursh, 1948, p. 2). Similarerosion occurs where volcanic ash covers thesurface sufficiently to destroy vegetation (Seger-strom, 1950).

All the erosion forms in this badlands areawere developed after 1929 when waste and over-burden from other pits backfilled the aban-doned clay pit at this site, producing a benchor terracelike deposit 40 feet high whose steepfront and gently sloping upper surface rapidlygullied. The terrace as a whole was still in ayouthful stage at the beginning of this study.Alluvial fans had been built along its base (PI. 2,fig. 1, 2). The easily eroded terrace might beconsidered the initial stage of landform develop-ment of the theoretical Davisian cycle, withthe elevated flat-terrace surface representing arapidly elevated peneplain. Similar small bad-lands have developed elsewhere in the areawhere removal of vegetation and Pleistocenedeposits have exposed the soft Cretaceous Rari-tan clays.

Plans for continued field studies to observethe cycle of development were unfortunatelyconcluded when the area was leveled for con-struction purposes in the summer of 1953.

Reports of the nearest weather station atNew Brunswick, New Jersey, 8J>^ miles north-west, reveal that erosion up to 1948 was accom-plished by a total of 844 inches of precipitationand that mean yearly precipitation was 43inches (U. S. Weather Bureau, 1929-1948).These figures contribute to a statement of gen-eral climatic conditions but not to a quantita-tive evaluation of the effect of rainfall, becausethere are no data on the local intensities of pre-cipitation during this period. Intensities hereare not low, however, compared with stormsin the badland regions of the West. The maxi-mum intensities of precipitation of any stormover periods of time ranging from 2 to 100 yearsmay be expected in the eastern portion of thehumid regions of the United States (Yarnell,1935). Undoubtedly the erroneous impressionof higher intensities in the arid West is due tothe destructive nature of runoff on sparselyvegetated slopes.

Temperatures during this period ranged from0 to 95F., indicating that frost heaving wasprobably important during the 5J

GENERAL DESCRIPTION OF PERTH AMBOY LOCALITY 601

west orientation of the major drainage chan-nels affects the microclimatic environment,subjecting the north- and south-facing slopesto different frequencies of freeze and thaw.

In spite of high precipitation the sterility ofthe fill and the rapidity of erosion prevented

It may be suspected that frost heaving prob-ably modifies the topography somewhat be-cause the soil has moderate to objectionablefrost-heaving characteristics and the low tem-peratures at Perth Amboy cause frequent freez-ing during the winter months.

PER

CEN

T_

en

c

0

o

c

6i

i -^ .

'0 20 6 2GRAVEL

\\

\x\

\x^'. 0.6 0,2 .06 .02 .006

SAND | SILT OR CLAYGRAIN S I Z E I N MM.

FIGURE 1.GRAIN-SIZE DISTRIBUTION or PERTH AMBOY FILL

the growth of vegetation within the basin stud-ied, except for one wild cherry tree and a smallpatch of poison ivy on the western drainagedivide.

The fill forming the terrace at Perth Amboyis essentially homogeneous and the topographyshows no persistent control by structure orlithology. Mr. Richard Chorley of ColumbiaUniversity made a grain-size analysis of thefill, showing that it is 67 per cent sand, 22 percent silt and clay, and 11 per cent gravel. Thealmost equal amounts of silt and clay weredetermined by the low plasticity of the finerfraction of the sediment (Burmister, 1952, p.102). A cumulative percentage curve was plot-ted for the sample (Fig. 1) and from this Ha-zen's "effective size", designated Dw by Bur-mister, was obtained. The quantity Dm is thegrain size in millimeters for which 10 per centof the material is finer. For the Perth Amboyfill Dia is 0.04 mm. Using this value the fillcharacteristics important to this study caneasily be determined using Burmister's charts:(1) the drainage of the fill is fair with a coeffi-cient of permeability approximately 0.004 cm/sec.; (2) the capillarity is moderate with anapproximate rise of 5.0 feet; (3) the frost-heaving characteristics are moderate to objec-tionable.

The importance of the values for capillarityand permeability are apparent from Burmister's(1952, p. 83) statement that, during excavation,slopes seldom need to be cut flatter than 45"in soils containing more than about 5% siltexcept where surface erosion of the slopes bythe rapid runoff of rainwater is excessive." The5 per cent silt causes enough capillary cohesionin the soil to maintain steep slope angles, andthe permeability is low enough to aid runoff.Thus, steep slopes are maintained, but erosionis rapid.

The effect of capillary cohesion within thePerth Amboy fill makes the mean maximumslope angle for the area 48.8, and thus theslopes are classified by Strahler (1950, p. 693)as high-cohesion slopes.

The drainage basin selected for intensivestudy was mapped in 1948 by Strahler andCoates of Columbia University on a scale of 1inch equals 10 feet (PI. 1). The contour intervalis 1 foot. The drainage pattern was mappedwith particular care so that all drainage-basincharacteristics could be measured; all channelspossessing recognizable drainage areas wereconsidered permanent drainage features andmapped as such.

The drainage basin mapped was that of afifth-order stream network. Streams are desig-


nated on the basis of orders; all unit or fingertipstream channels without tributaries are first-order streams (Horton, 1945, p. 281); the junc-tion of two streams of the same order forms astream of the next higher order.

In all the drainage basins studied the streamsare assigned order numbers following themethod outlined by Strahler (1952b, p. 1120)whereby the higher stream-order numbers arenot extended headward to include smaller tribu-taries, but refer to segments of the main chan-nel (Fig. 9). With the Horton classification, thehigher stream-order numbers include the small-est headward extension of the main stream.Using Strahler's method, the two major chan-nels joining at point H (PI. 1) are third-order;using Horton's method, the south tributarywould be the extension of the fifth-order chan-nel and would be eliminated from studies in-volving third-order channels. This method willbe referred to again in a discussion of channellengths.

The fifth-order basin mapped includes 3531feet of drainage channels within an area of31,027 square feet. The drainage density (Hor-ton, 1945, p. 283), equal to the sum of thechannel lengths in miles divided by the area ofthe drainage basin in square miles, is 602, indi-cating that within an area of this type 602miles of drainage channels occur for everysquare mile of drainage basin. This value is in-dicative of the fine texture of the area. Althoughthe density is high compared to a typical valueof 5 to 20 for humid regions, it is not high forbadland topography.

Within the mapped area the first-, second-,and third-order stream basins show a transitionfrom maturely developed topography near themouth of the main stream, where the mainchannel has widened the valley until small seg-ments of flood plain have developed, to pro-gressively more youthful basins toward its head,where the tributaries are eroding into portionsof the undissected surface of the fill.

The mean length of the first-order channelsis 10.1 feet, and the mean drainage area is 85.0square feet, indicating the small scale of thetopography. The hypsometric integral (Strah-ler, 1952b) for the entire fifth-order networkis 70 per cent, indicating that erosion has re-moved a minimum of 30 per cent of the total

mass of the basin. This figure is reasonablyaccurate because the upper surface of the ter-race into which the system developed is stillpreserved in the headwater areas. Although theterrace is not a natural deposit and the drainageis developing on a small scale, investigation ofprinciples of drainage-network development isaided by knowledge of several factors not avail-able in the study of the geomorphic evolutionof other areas.

The homogeneity of the fill aided develop-ment of an insequent drainage pattern on theterrace. The rapid erosion developed youthfulV-valleys with steep straight slopes descendingfrom convex or sharp-crested divides. The longi-tudinal profile of the main channel, typical ofstreams growing headward into an upland sur-face, had a concave lower segment and an upperconvexity where degradation was most rapid.Tributary profiles varied with stage from con-vex-up, where the streams were unable to main-tain themselves against the rapid degradationof the main channel in the headwater areas, toconcave-up where the main channel appearedto be at grade.

Stream-channel erosion with sheet and rillerosion on the slopes were the dominant geo-morphic processes observed. Wind erosion wasnegligible, but frost action became importantduring the winter months.

CHARACTERISTICS OF THE DRAINAGE NETWORK

Components of the Drainage NetworkMorphometric studies of drainage-network

components at Perth Amboy included measure-ments of all stream-channel lengths and drain-age-basin areas for all stream orders, so thateach component could be studied independ-ently. Stream-order analysis permits compari-son of the drainage network developed on thePerth Amboy terrace with patterns originatingunder natural conditions. Horton (1945) pro-posed certain laws of drainage compositionwhich assume an orderly development of thegeometrical qualities of an insequent drainagesystem. These laws were applied to data ob-tained from morphometric measurements onthe Perth Amboy map (PL 1) to determinewhether they conformed; if they did, conclu-sions from the Perth Amboy study might apply

CHARACTERISTICS OF THE DRAINAGE NETWORK 603

to other Jarger areas. Geometry of two otherfifth-order basins was measured for comparisonwith Perth Amboy basin (Table 2): ChilenoCanyon basin (Chileno Canyon, California,

500

100

zUlaui

I1UIEiolO

SiT

M

1 2 3 4 5STREAM ORDER NUMBER

FIGURE 2.RELATION OF NUMBER or STREAMS OFEACH ORDER TO ORDER NUMBER

(1) Perth Amboy, (2) Chileno Canyon, (3)Hughesville area

quadrangle) and Mill Dam Run basin (Hughes-ville, Maryland, quadrangle).

The law of stream numbers, first of Horton'slaws of drainage composition, is stated as fol-lows (Horton, 1945, p. 291): "The numbers ofstreams of different orders in a given drainagebasin tend closely to approximate an inversegeometric series in which the first term is unityand the ratio is the bifurcation ratio." If ageometric series exists, a straight-line series ofpoints results where the numbers of streams ofeach order are plotted on a logarithmic scaleon the ordinate against order numbers on anarithmetic scale on the abscissa. This has been

done in Figure 2, in the manner of Horton'sgraphs. All three sets of points show a markedup-concavity at the lower end, suggesting thatthe geometric progression is not closely ob-served in the higher orders, but the Perth Am-boy data show general similarity with the rest

TABLE 1.METHOD op DERIVING WEIGHTEDMEAN BIFURCATION RATIO

1Streamorder

1

2

3

4

5

2Number of

streams

214

45

8

2

1

3Bifur-cationratio

4.78

5.63

4.00

2.00

4No. ofstreamsinvolvedin ratio

259

53

10

3

sProducts ofcolumns 3

and 4

1238.0

298.4

40.0

6.0

Total number of streams used in Col. 4 = 325.Sum of products of Col. 5 = 1582.4.. . . . . . , ., . . 1582.4weighted mean bifurcation ratio = 325

4.87.

and there is no reason to believe that any fun-damental dissimilarity exists.

The weighted mean of the Perth Amboy bi-furcation ratio is 4.87. Bifurcation ratio is theratio of the total number of streams of one orderto that of the next higher order (Horton, 1945,p. 280), e.g., a basin with 20 second-order chan-nels and 60 first-order channels would have abifurcation ratio between these two orders of 3.Because of chance irregularities, bifurcationratio between successive pairs of orders differswithin the same basin even if a general observ-ance of a geometric series exists. To arrive at amore representative bifurcation number Strah-ler (1953) used a weighted-mean bifurcationratio obtained by multiplying the bifurcationratio for each successive pair of orders by thetotal number of streams involved in the ratioand taking the mean of the sum of these values(Table 1).

The second law stated by Horton (1945, p.291) concerns stream lengths: "The averagelengths of streams of each of the different orders


in a drainage basin tend closely to approximatea direct geometric series in which the first termis the average length of streams of the firstorder."

lengths although the value of the length of thefifth-order stream is low in two cases Becauseinteger values only are used for order numberscontinued channel development might be ex-

UJaoco

- 5


"There is a fairly definite relationship betweenslope of the streams and stream order, whichcan be expressed by an inverse geometric serieslaw." The Perth Amboy stream slopes appearto conform (Fig. 3). In this case the gradient isobtained by dividing stream length measuredfrom mouth to headwaters by the elevationdifference.

Horton's laws may require revision becausehe obtained his data from old maps of smallscale on which he measured as stream channelsonly the blue drainage symbols, thus omittinga large part of the first- and second-order chan-net network. His statements are sound, how-ever, in the light of investigations made onmodern topographic maps, either mapped forthe purpose (Perth Amboy basin) or selectedbecause of their large scale and detailed repre-sentation of topography (Hughesville and Chi-leno Canyons quadrangles). These undoubtedlyafford data more precisely representative of thenatural development of drainage systems thanthe old maps.

The writer compared the Hughesville and

HUGHESVILLE

CHILENO CANYONFIGURE 4.COMPARISON or SHAPE OF BASIN AND

MAIN DRAINAGE ELEMENTS or THREE AREASNumbers indicate order of main drainage

channels

J j 100

1000

100 1 2 3 4STREAM ORDER NO. ?. 3 4 5

FIGURE 5.RELATION OF MEAN BASIN AREA AND MEAN STREAM LENGTH TO STREAM ORDER


TABLE 2.DRAINAGE-NETWORK CHARACTERISTICS

Basin

PerthAmboy

ChilenoCanyon

Hughes-vule

Ordernum-ber

123451234512345

S 11 !"

21445821

296661631

15037821

Meanlength(ft.)

10.140.4

24216603530482

25601140051100

25400014206860

28400180000397000

Meanarea(sq. ft.)

85.0343

23601460031000

167000872000

38900001810000086100000

7810002540000

1200000078800000

154000000

Meangra-dient(%)59.940.633.718.211.1

length of channels close to the maximum value,perhaps obtainable only by detailed remappingin the field.

Further investigations included map meas-urement by polar planimeter of all drainage-basin areas. Horton (1945, p. 294) inferred thatmean drainage-basin areas of each order shouldform a geometric series. A plot of the meanareas of stream basins of each order for thethree basins compared above (Figs. 3, 5) revealsthis relationship. A fourth law of drainage com-position may therefore be formulated in thestyle set by Horton: the mean drainage-basinareas of streams of each order tend to approxi-mate closely a direct geometric series in whichthe first term is the mean area of the first-ordertasins. It could be assumed that such a rela-tionship would exist if there were any connec-tion between the length of a stream and thesize of its drainage basin.

AREA 1,000,000 ft2(HUSHESVILLE 8 CHILENO CANYON)

FIGURE 6.RELATION OF MEAN STREAM LENGTH OF EACH ORDER TO MEAN BASIN AREA OF EACH ORDER

Chileno Canyon maps with aerial photographsso that the blue drainage lines could be ex-tended to what appeared to be the correctlength and small tributaries were also added tothe drainage pattern. This method brought the

In Figures 3 and 5 the parallelism of the plotsof mean stream length and mean drainage-basinarea is striking and suggests a directly propor-tional relationship between the two. Figure 6shows a plot of the mean drainage-basin areas


and mean stream-channel lengths for the threeareas. The scatter of the Perth Amboy datais slight around a regression line fitted by themethod of least squares and is described by theregression equation Yc = 56.8 + S.TJX. Theratio between mean area and length values isthus approximat?ly 9. The calculated ratio forthe Chileno Canyon basin is 339 and for theMill Dam Run basin 388.

The significance of the ratio is that it repre-sents in square feet the area required to main-tain 1 foot of drainage channel. It is the quan-titative expression of one of the most importantnumerical values characteristic of a drainagesystem: the minimum limiting area requiredfor the development of a drainage channel.This value, the constant of channel maintenance,is a measure of texture similar to drainage den-sity; it is in fact, equal to the reciprocal ofdrainage density multiplied by 5280 (becausethe channel-maintenance ratio is expressed insquare feet while drainage density is expressedin miles). Along with drainage density this con-stant is of value as a means of comparing thesurface erodibility or other factors affectingsurface erosion and drainage-network develop-ment. A related texture measure is Morton's(1945) length of overland flow, the distanceover which runoff will flow before concentratinginto permanent drainage channels. The lengthof overland flow equals the reciprocal of twicethe drainage density.

The discovery of the above relationship per-mits statement of a fifth law of drainage com-position: the relationship between mean drain-age-basin areas of each order and mean channellengths of each order of any drainage networkis a linear function whose slope (regression co-efficient) is equivalent to the area in square feetnecessary on the average for the maintenanceof 1 foot of drainage channel. This law requiresan orderly development of any drainage net-work, for the extension of any drainage systemcan occur only if an area equal to the constantof channel maintenance is available for eachfoot of lengthening drainage channel.

Limiting Values of Drainage ComponentsIn addition to a lower limiting area necessary

for channel maintenance there may be expectedupper limits to basin areas and stream lengthsof each order beyond which new tributaries orbifurcation occurs, forming new basins. These

AREA (SQ.FT.)5 10 80 100 500 1000

"o .e i:eAREA (LOG FT. SO.)

FIGURE 7.FREQUENCY-DISTRIBUTION HISTO-GRAMS OF THE LOGS OF DRAINAGE-BASIN ABEA

CHANNEL LENGTH (FEET)5 10 5p 100 500 IQOO

2.4LENGTH

FIGUREGRAMS

1.6CHANNEL

(FEET)8. FREQUENCY-DISTRIBUTION HISTO-ag THE LOGS or STREAM-CHANNEL

LENGTHS

relationships would appear in frequency-dis-tribution histograms of the basin areas andstream lengths of each order and further con-firm the principle of a channel-maintenanceconstant.

Frequency-distribution histograms of thestream lengths and basin areas show a markedright skewness, which appears to be correctedby plotting log values on the abscissa (Figs. 7,8; Tables 3, 4). All measurements are made on atopographic map and are therefore taken fromthe horizontal projection of the drainage-basinelements rather than from true lengths and sur-face areas. Frequency-distribution study islimited to the first two orders by the small


number of streams in the third and higher or-ders. A study of the first- and second-orderbasin areas and interbasin areas may be ade-

TABLE 3.FREQUENCY DISTRIBUTIONS or LOGSOF CHANNEL LENGTHS*

Sample j lengths in feet

First orderchannels

Second-orderchannels

n.,s

11

0.5

17

0.7

45

0.9

45

1.1

58

1.3

30

41 7

1.5

6

14

1.7

2

14

1.9

5

7.1

1

X

.92

1.54

s

.302

.21

N

214

45* In this and all following tables and figures, ^ is the

arithmetic mean, 5 is the standard deviation, and N is thenumber of items in each sample.

irregular, wider than long, or were on roundedspurs where the divergence of orthogonalsdownslope prevents the concentration of run-off. From this investigation alone it is difficultto set limiting area above which channel de-velopment may be expected on the interbasinareas, especially since the comparison of tri-angular interbasin areas with elliptical first-order basins is questionable.

Areas of first-order basins rise sharply at the10-square-foot class limit. Two first-order basinsof less than 10 square feet were mapped byStrahler and Coates, but a field check revealedthat these did not contain permanent drainagechannels. The fact that areas of less than 10square feet are remarkably free of drainagechannels coincides with the concept of a con-

TABLE 4.FREQUENCY DISTRIBUTIONS or LOGS OF DRAINAGE-BASIN AREAS

Sample

First-order areasSecond-order areas

Class mid-values in logs of area in square feet0.3 0.5

2

0.7

2

0.9

6

1.1

17

1.3

34

1.5

45

1.7

50

1.9

342

2.1

127

2.3

811

2.5

112

2.7

17

2.9

15

3.1

1

'

1.792.45

s

.19

.284

ff

21445

quate, however, to determine if a transitionphase exists between orders.

Between adjacent drainage basins are inter-basin areas, those roughly triangular areaswhich have not developed a drainage channel(Fig. 9), but which drain directly into a higher-order channel. The histograms of first- andsecond-order basin areas and interbasin triangu-lar areas are superimposed in Figure 10 (Ta-ble 5); the histograms of first- and second-orderstream lengths are compared with maximuminterbasin-slope lengths in Figure 11 (Table 6).Figures 7 and 8 compare the histograms of thelogarithms of basin area, channel length, inter-basin areas, and interbasin maximum lengths.The discussion of limiting values of drainagecomponents may be followed on either set offigures.

An overlap between the areas of each histo-gram suggests that transformation from first tosecond order takes place within a wide rangeof values. In Figure 10 interbasin areas show asharp decrease in frequency for areas above 50square feet, which is well below the mean of thefirst-order areas. Of the 27 interbasin areas over50 square feet, 12 seemed capable of developinga channel at any time; the remaining 15 were

FIGURE 9.POSITION OF INTERBASIN AREA AN0METHOD OF CLASSIFYING STREAMS BY ORDER

NUMBER

stant of channel maintenance of about 9 (8.77).Thus, no permanent channel will develop with-out a drainage area of about 10 square feet,while the channel can lengthen only with theaverage increment of 9 square feet of area foreach additional foot of length.

Most of the overlap between the first- andsecond-order areas falls between 50 and 150square feet, although some first-order areasrange up to 650 square feet. Again an inspection


X49.3 (INTERBASIN AREAS)

X-343.0(SECOND ORDER)

200 400 600AREA (SQ.FT.)

FIGURE 10.FREQUENCY-DISTRIBUTION HISTOGRAMS OF FIRST- AND SECOND-ORDER BASIN AREAS ANDINTERBASIN AREAS

TABLE 5.FREQUENCY DISTRIBUTIONS OF FIRST- AND SECOND-ORDER DRAINAGE-BASIN AREAS ANDINTERBASIN AREAS

Sample

Mid-valuesFirst-order

areas

Mid-valuesSecond-order

areas

Mid-valuesInterbasin

areas

Class mid-v&lues in square feet

3091

1006

12.551

8073

20014

37.528

13026

3007

62.57

18010

4006

87.55

2303

5005

112.55

2807

6003

137.53

3300

7002

162.54

3802

8000

187.53

4300

9001

212.51

4800

10000

237.51

5300

11001

5801

6301

385

343

49.3

i80

218

49

N214

45

108

610 S. A. SCHUMMBADLANDS, PERTH AMBOY, N. J,

of individual basin characterstics within thezone of histogram overlap is profitable. Of the46 first-order areas greater than 110 squarefeet, 29 are of very youthful basins including

basins it seems a fair generalization that first-order channels with areas greater than 100square feet are unstable and ready for subdivi-sion.

CHANNEL LENGTH (FEET)FIGURE 11.FREQUENCY-DISTRIBUTION HISTOGRAMS OF FIRST- AND SECOND-ORDER CHANNEL LENGTHS

AND MAXIMUM INTERBASIN LENGTHS

broad, gently sloping surfaces with only tracesof channels on the flat undissected divide areas.With further development these would evolveto a higher order, for their longitudinal profilesare still essentially convex-up, retarding rapidtributary extension into their headwater areas.Thirteen of the 46 are narrow almost rill-likebasins unable to broaden because of adjacentmore aggressive basins. The remaining 4 of the46 first-order basins larger than 110 square feethave no obvious reason for not developing intosecond-order channels. Although it is difficultto explain peculiarities of individual drainage

The smallest second-order channel area is 65square feet. The class limits of the second-orderareas within the overlap are 50 and 150 squarefeet (Fig. 10). Within this size range are sixsecond-order basins which have developed trib-utaries recently and are capable of enlarging byheadward extension so that the lowest-fre-quency class of the second-order area histogramwould disappear unless replaced by new unitscreated by bifurcation of first-order channels.Youthfulness of the entire system at Perth Am-boy prevents the recognition of narrow transi-tion zones between orders. A similar study in a

CHARACTERISTICS OF THE DRAINAGE^NETWORK 611

fully extended mature drainage system mightshow sharper distinctions.

In accordance with the fifth law of drainagecomposition, stream-length frequency distribu-tions are similar to the area distributions. Maxi-mum interbasin-slope lengths cannot be di-

streams have an upper limiting length between9 and 17 feet and an upper limiting area be-tween 65 and 110 square feet. The limited num-ber of stream orders considered and the subjec-tive evaluation of parts of the data make itmore appropriate to set a lower limit below

TABLE 6.FREQUENCY DISTRIBUTIONS OF FIRST- AND SECOND-ORDER CHANNEL LENGTHS ANDINTERBASIN LENGTHS

Sample

Mid-valuesFirst-order lengths

Mid-valuesSecond-order lengths

Mid-valuesInterbasin lengths

Class mid-values in feet

342

18.513

13

770

35.518

316

518

1140

52.56

721

923

1530

68.55

115

138

1919

86.51

155

175

236

103.51

192

210

275

120.51

230

311

252

351

X10.1

40.4

8.06

s6.08

23.4

4.17

ff214

45

108

rectly compared to actual stream lengths be-cause a channel developing on the interbasinsurface will not extend the entire length of theslope. Nevertheless, a sharp drop in frequencyat 10 feet suggests that at lengths above thisrunoff surfaces are unstable in form and willtend to develop channels (Fig. 11). Twenty-sixinterbasin areas with lengths greater than 10feet had no channels. Seven were very narrowwith little drainage area. The remaining 19, aspreviously noted under the discussion of inter-basin areas, are irregular or on rounded spurs,while 4 seem capable of developing channels.

The lower values for first-order streamlengths are not significant because all channelsmust originate from a point and then lengthen.The region of transition between first- and sec-ond-order stream lengths lies between 9 and 17feet, but 17 feet is not the upper limit of first-order lengths. Of 27 streams longer than 17 feet,20, within basins considered previously underthe discussion of areas, were in very youthful ornarrow basins; the remaining 7 seemed capableof change. All but 1 of the 12 second-order chan-nels between 10 and 17 feet will continue todevelop, eliminating these streams from the fre-quency class. Youthfulness of the area probablymasks a more distinct transition zone.

Within the Perth Amboy drainage networkthere are recognizable limits to the areas andlengths of streams of each order. First-order

which higher orders cannot exist. The first-orderstreams require more than 10 square feet fordevelopment; second-order streams will notnormally evolve from first orders until thedrainage area is equal to 65 square feet and thefirst-order channel is longer than 10 feet.

The writer remapped the drainage patternin 1952 and compared it with the patternmapped in 1948, aiding the study of channelalterations within the zones of transition. Inall cases the addition of channels occurred onlyin basins above the size limits set from the fre-quency-distribution analysis. No channels de-veloped on areas less than 10 square feet. Fournew channels developed on interbasin areas,all but one (46.5 sq. ft.) greater than 50 squarefeet. Twelve new tributaries developed on first-order channels, forming several new second-order basins. Each new basin was youthful (de-veloping headward into the as yet undissectedfills), and almost all exceeded 110 square feet.Four were within the transition zone betweenfirst- and second-order areas. The newer fieldstudy, therefore, seems to confirm the existenceof the zones of transition and upper limitingvalues of development related to the constantof channel maintenance. The constant of chan-nel maintanence, therefore, may be applied tothe as yet undissected portions of a drainagesystem to aid in the prediction of areas of futuresediment loss.


Form of the Drainage BasinsIn addition to indices of drainage-network

composition based on stream orders other im-portant geomorphic characteristics are shapeof the basins, relief, surface slope, drainage den-sity, and stage of geomorphic development.Geomorphic development can be evaluated bymeans of the hypsometric integral (Strahler,1952b). If each characteristic had a numericalvalue, comparisons could be made between top-ographic units. It may be appropriate to set upstandards of comparison from the available in-formation which can be modified later or re-jected if unacceptable.

Relief is analyzed by a relief ratio, defined asthe ratio between the total relief of a basin(elevation difference of lowest and highestpoints of a basin) and the longest dimension ofthe basin parallel to the principal drainage line.This relief ratio is a dimensionless height-lengthratio equal to the tangent of the angle formedby two planes intersecting at the mouth of thebasin, one representing the horizontal, the otherpassing through the highest point of the basin.Relief ratio allows comparison of the relativerelief of any basins regardless of differences inscale of topography. Recent field studies, how-ever, reveal that residuals or abnormally highpoints on the divide should be ignored whenobtaining the total relief of a basin (Hadley andSchumm, In preparation).

The shape of any drainage basin is expressedby an elongation ratio, the ratio between thediameter of a circle with the same area as thebasin and the maximum length of the basin asmeasured for the relief ratio. This ratio is thesame as the Wadell sphericity ratio used inpetrology (Krumbein and Pettijohn, 1938, p.284), where the ratio approaches 1 as the sedi-ment grain, or in this case the shape of thedrainage basin, approaches a circle. Miller(1953, Ph.D. dissertation, Columbia Univer-sity) used a similar measure, the circularityratio, which is the ratio of circumference of acircle of same area as the basin to the basinperimeter.

Table 7 compares Strahler's data (1952b, p.1134) on five mature drainage basins with thewriter's data obtained from the more youthfulPerth Amboy and Hughesville areas and theChileno Canyon area.

The writer compared relief ratio and drainagedensity for fourth- and fifth-order channels(Fig. 12, Table 7) and found a definite positivetrend in the mature basins. Points for theyouthful Hughesville and Perth Amboy basinsdisplace upward to positions well above the

TABLE 7.DRAINAGE-BASIN CHARACTERISTICS

Area

1. Gulf Coastal Plain2. Piedmont3. Ozark Plateau4. Verdugo Hills5. Great Smoky Mts.6. San Gabriel Mts.7. Hughesville8. Perth Amboy

K?

il

&lp

4.66.9

13.826.214.215.613.6

602.0

toS

1

.008

.025

.062

.245

.267

.220

.006

.117

O+3SG.2bo1

.975

.935

.692

.594

.760

.675

.730

.602

ga

1o

0.331.133.52

22.4612.3317.20.22

11.1

1,.||19O M'**'

5.917.553.799.086.773.47.0

110.8

trend line. When the values for the individualthird-order basins of each of the two youthfulareas are plotted (Fig. 13), the points show apositive trend similar to the plot of the maturebasins. Thus, within homogeneous areas ofsimilar development the drainage density is apower function of the relief ratio.

In Figure 14 the relief ratio shows a closecorrelation with stream gradient. The gradientvalues are means for the entire stream lengthand thus would approach the value of the reliefratio if the stream length was measured to thedrainage divide. In general, the gradient someasured will be less than the relief ratio, formeandering or the usual lack of straightness of achannel will increase the stream length beyondthe drainage-basin length.

Valley-side slope angles are also clearly re-lated to the relief ratio. In Figure 15 threevalues would lie well to the right of a line fittedto the other points. This may be the result ofobtaining the mean slope values from topo-graphic maps in these cases; all the data werenot measured in the field, and slopes measuredon maps usually are lower than field measure-ments (Strahler, 1950, p. 692).

In Figure 16 the shape of the drainage basinis plotted against relief. The trend is negative


and may indicate that as the relief ratio in-creases the drainage basin becomes more elon-gate. The data are not conclusive, but thesteeper the slope on which small basins develop

5.

.01 O.IRELIEF RATIO 1.0FIGURE 12.RELATION OF DRAINAGE DENSITY TO

RELIEF RATIONumbers refer to basins described in Table 7

RELIEF RATIOas 1.0100

(PERTH AMBOY)5.0

10.005 0.1100.01 .05

RELIEF RATIO (HUGHESVILL6)FIGURE 13.RELATION OF DRAINAGE DENSITY TO

RELIEF RATIO OF THIRD-ORDER BASINS

the more closely spaced are the drainage chan-nels, resulting in more elongate basin shapes.

One practical application of the relief ratio isin estimation of sediment loss. Figure 17 showsthe direct relation between mean relief ratio forseveral areas in Utah, New Mexico, and Ari-zona and mean annual sediment loss as esti-mated from sedimentation in small stock reser-voirs. Once the characteristic regression trendhas been established for a region the investi-gator may select areas of high potential sedi-ment production from topographic maps(Schumm, 1955).

Various interrelationships among drainage-

basin characteristics have been previously de-termined. Langbein (1947, p. 125) states thatsteep land slopes are generally associated withsteep channel slopes and fine texture, and that

.01RELIEF RATIO

FIGURE 14.RELATION OF MEAN STREAMGRADIENTS TO RELIEF RATIO

Numbers refer to drainage basins described inTable 7

$100I

\5i10

10

-7.

.2

- -3

.001 .01RELIEF RATIO

8 46

O.I 1.0

FIGURE 15.RELATION OF MEAN MAXIMUM-SLOPEANGLES TO RELIEF RATIO

Numbers refer to drainage basins describedin Table 7

altitude of a basin above its outlet increaseswith steepening land and channel slopes. Paul-sen (1940, p. 440) found that infiltration in-creases with decrease in mean land slope, ex-plaining in part the increase of sediment losswith the relief ratio. Strahler (1952b, p. 1136)observed that the hypsometric integral de-


creased as basin height, slope steepness, gra-dient, and drainage density increased.

Although more data are desirable the rela-tionships observed suggest that the geomorphiccharacter and even rates of erosion may be pre-

maturity and old age. A unique opportunityto study stage changes was afforded by thedevelopmental sequence of drainage basinstributary to the main channel at Perth Amboy.Eleven second-order drainage basins forming a

1.0

oj^ao

zo

1oIII

Ol

9 7

1B

1^_?

1 1- M1

* 8

56 - 1

4VMM

.005 .01 O.I.05RELIEF RATIO

FIGURE 16.RELATION OF ELONGATION RATIO TO RELIEF RATIONumbers refer to drainage basins described in Table 7.

0.5

dieted from the relief ratio, although it is onlya geometrical element which is probably relatedto lithology, structure, stage, vegetation, andclimate.

The above relationships when considered inthe light of recent discussions of the quasi equi-librium between the hydraulic and geomorphiccharacteristics of stream channels (Leopold andHaddock, 1953; Wolman, 1955; Leopold andMiller, in press) suggest that when more in-formation becomes available this concept ofquasi equilibrium in graded and ungradedstream channels may extend to the landformsadjacent to the stream channels, and close in-terrelationships may be found among the geo-morphic, hydrologic, and hydraulic character-istics of a topographic type.

Basin Form Related to Geomorphic Stage ofDevelopment

During geomorphic development basin formschange with time. According to the classicDavisian analysis, relief, slope of valley walls,stream gradients, and drainage density increaserapidly during youth to a maximum in earlymaturity, then decline slowly throughout later

sequence from earliest youth to late maturitywere selected for map study and a comparisonof hypsometric integrals. The hypsometric in-tegral is a measure of stage (Strahler, 1952b)because it expresses as a percentage the mass ofthe drainage basin remaining above a basalplane of reference.

Figure 18 shows hypsometric curves plottedfor each basin in the sequence. Data are ob-tained from the topographic map by measuringthe total area of each basin with a planimeter,then measuring the area between each contourand the basin perimeter above it. Each areais converted into a percentage of total basinarea, so that a cumulative percentage curvecan be plotted, each area value correspondingto a percentage of the total height of the basin.Using this hypsometric curve it is possible toread the percentage of total basin area aboveany percentage of total height. The area-alti-tude relations of the basin are thus revealed bya curve illustrating in dimensionless co-ordi-nates the distribution of mass within the drain-age basin (Langbein, 1947, p. 140; Strahler,1952b). Area under the hypsometric curve isthe hypsometric integral, expressed as per cent.


An integral of 60 per cent indicates that erosionhas removed 40 per cent of the mass of thebasin between reference planes passing throughsummit and base. Strahler (1952b) discussedin more detail the hypsometric curve and itsuse in geomorphic research.

tion may be obtained by plotting percentage ofarea against percentage of total elevation ofthe terrace at Perth Amboy rather than against

~ 5ad

XHu.1uK0FIGURE 18.SEQUENCE OF SECOND-ORDER HYPSO-

METRIC CURVESFrom Perth Amboy.Numbers increase from youthful to mature

basinsORIGINAL TERRACE SURFACE

FIGURE 19.SEQUENCE OF SECOND-ORDER HYPSO-|; METRIC CURVESPer cent area is plotted against per cent of total

relief at Perth Amboy. Numbers increase fromyouthful to mature basins and are the same areasas shown in Figure 18.

total relief within each basin. This method(Fig. 19) is more satisfactory because the squarein which the curves are plotted may be visual-ized as a vertical section through the entireterrace at Perth Amboy. Each curve occupiesits true relative vertical position within thatmass and reveals the degradational history of


the basin. The 100 per cent elevation lineshould be visualized as the upper surface of theterrace, the base as the level of the mainstream's mouth. The right edge of the chart isthe locus of points of junction of second-ordertributaries with some higher-order stream. Each

TABLE 8.DRAINAGE-BASIN CHARACTERISTICS orTHE SECOND-ORDER SEQUENCE

Basinnumber

123456789

1011

Per centmass

removed

2.44.95.69.5

17.223.539.8SO. 860.864.677.0

Reliefratio

.049

.121

.158

.156

.330

.575

.590

.660

.710

.620

.690

Elonga-tionratio

.993

.648

.595

.645

.783

.725

.507

.473

.474

.478

.530

Gradi-ent(%)

4.014.418.621.842.052.058.367.565.551.550.7

Drainagedensity(mi./sq.mi.)

553504270241672560610895

123011501320

line represents the distribution of mass withina second-order basin at a different stage of de-velopment, the position of its mouth controlledby the degrading stream to which it is tributary.

To determine the nature of basin-formchanges with time, or stage of evolution, animportant index is the percentage of mass re-moved at each position in the sequence ofbasins. This value, obtained by measuring thearea above each curve and comparing it to thetotal area of the diagram, is a measure of themass removed in relation to the total availablefor removal.

Percentage of mass removed, relief ratio,stream gradient, basin shape, and drainagedensity were determined for each of the 11basins whose curves are drawn in Figure 19.The data for each basin in the sequence (Table8) are plotted against corresponding per cent ofmass removed (Fig. 20). The plot of relief ratiowith per cent removed (A) reveals that withinitial dissection the relative relief rapidly in-creases. A sharp break in the continuity of theplot occurs when approximately 25 per cent ofthe mass of the basin is removed, after whichthe relief ratio remains almost constant to 80

per cent of mass removed; beyond 80 per cent,data are lacking.

The stream-gradient plot (B) shows a similarform. The rapid increase in gradient is checkedat approximately 25 per cent of mass removed;a decrease in gradient sets in at the upper partof the plot after a maximum value reached at50 per cent removal. This agrees with the typicaldescriptive concept of stream development, but,in comparison to the rapid early increase ingradient, the portion of the plot above 25 percent is essentially constant.

Maximum slope angles were not obtained foreach basin, but, because these values clusterclosely about a mean value for any homogeneousarea (Strahler, 1950, p. 685), and because theclose relationship between stream gradients andmaximum slope angles has been established(Strahler, 1950, p. 689), any plot of slope anglesand mass removed would be expected to ap-proximate the gradient curve.

The relationships of basin shape and drainagedensity to stage (Fig. 20C, D) are less clear, butafter early variations in which the basin isclose to a circular shape the influence of in-creased relief is felt and the elongation ratiodecreases to a constant of about 0.5 at 40 percent mass removal, indicating that the basinmaximum length is twice the diameter of acircle of the same area. The drainage-densityplot is not regular, probably because of a highdegree of length variability in the low order ofthe streams used. Nevertheless, the plot sug-gests rapid early increase in drainage density,followed by a decreasing increment. Probablycontinued headward development of the drain-age channels continues until late in the erosioncycle, lagging behind the early stability ofother basin characteristics. If other series ofbasins could be studied similarly, the additionaldata might lead to the establishment of ageneral system of basin evolution.

In summary, the form of the typical basin atPerth Amboy changes most rapidly in theearliest stage of development. Relief andstream gradient increase rapidly to the point atwhich about 25 per cent of the mass of the basichas been removed, then remains essentiallyconstant. Because relief ratio elsehwere hasshown a close positive correlation with streamgradient, drainage density, and ground-slopeangles, stage of development might be expected


to have little effect on any of these values oncethe relief ratio has become constant.

The Perth Amboy data thus support theconcept of a steady state of drainage-basin de-velopment as outlined by Strahler (1950, p. 676)

establish major drainage divides; the reliefratio then reaches a fixed value, but changes inchannel network continue until a large portionof the basin mass is removed. Thus, the reliefratio becomes fixed before other network charac-

100

80

0 60bls111C

10

z

20

O

(B) GRADIENT


equals the ratio of the tangent of the mainchannel gradient to the tangent of the gradientof the tributary stream or of the ground slopeover which the tributary flows. It follows that

30

20

10.

30

20

I0

UJ3O111IE

S

20

10

A) YOUNG 55 = 65.25=15.3

_ N 33

8) MATUREAin X 46.2S.14.9N'26

C) A 8 B COMBINEDX

L^L

X 56.8S 17.6N59

I 40 80ANGLES (DEGREES)

120

FIGURE 21.FREQUENCY-DISTRIBUTION HISTO-GRAMS OF YOUNG, MATURE, AND COMBINED

ANGLES OF JUNCTION

during the early part of basin development,stream-entrance angles change with streamgradients.

Thus, a tributary will develop with an ini-tially large angle of junction; then as the ratiobetween the two gradients increases the angleof junction decreases. Horton notes that as theratio increases from 0.3 to 0.9 angles decreasefrom 72.3 to 25.5. The decrease is accom-plished by lateral migration of the tributarytoward the main channel and down-valley shiftof the junction.

The writer measured 61 entrance angles onthe 1948 Perth Amboy map. The frequency-distribution histogram is broad and flat-

topped with angles ranging from 24 to 90(Fig. 21C; Table 9).

If the assumed changes occur, then by classi-fying all entrance angles according to stage ofdevelopment of their tributary drainage basinsa significant difference should occur between

TABLE 9.FREQUENCY DISTRIBUTIONS or ANGLESor JUNCTION

Sample

Combinedangles

Matureangles

Youngangles

Class mid-values in degrees25

4

3

1

35

8

7

1

45

8

S

3

55

14

7

7

65

8

2

6

75

10

1

9

85

7

1

6

X

56.8

65.2

46.2

S

17.6

IS. 3

14.9

N

59

26

33

the means of youthful and more mature basins.The basins were separated into two groups onthe basis of the existence of flat, undissectedareas within the drainage areas, classifying asyoung basins capable of headward extension orhaving undissected areas within their drainageareas. The frequency-distribution histograms ofeach group (Fig. 21) show an expected overlap,but the means of the two groups are signifi-cantly different as judged by a t-test. The meanof the youthful class is 65, that of the oldergroup 46. The probability that such a differ-ence or greater would occur by chance alone isabout 1 in 10,000. A reasonable explanation ofthe observed difference in angles is the shiftingof tributary channels in response to changes inthe gradient ratio.

A similar test was applied to angles of bi-furcation, denned as the angles between twoapproximately equal first-order branches. Inthis case, the stream has bifurcated at its upperend, whereas in the tributary junction referredto above a branch has grown from the trunk ofan existing major drainage line. Twenty anglesof bifurcation were measured from youthfuldrainage basins having undissected areas. Themean is 62.1, compared with the mean of theyouthful angles of tributary junction, 65.2.The frequency distributions of both sampleshave such great dispersions that this observeddifference in means is not significant.

EVOLUTION OF THE DRAINAGE NETWORK 619

Remapping of the drainage pattern revealedchanges in the values of tributary entranceangles and angles of bifurcation. Table 10 showsdata for mean entrance angles and angles ofbifurcation measured from the 1948 and 1952drainage maps. There is a decrease of 5.3 in the

TABLE 10.ANGLES OF BIFURCATION AND ANGLESOF JUNCTION

Angles ofbifurca-tion

Angles ofjunction:TotalYoungMature

Mean angles(degrees)1948

62.1

56.865.246.2

1952

53.3

53.659.943.0

Standard devia-tion (j)

1948

13.4

17.615.314.9

1952

17.5

18.517.114.9

Number insample (N)1948

20

593326

1952

12

462917

mean of the youthful tributary-junction angles,but the standard deviation of each distributionis so large that a statistical test of the signifi-cance of difference between the means showsthat such a difference would be expectedthrough chance alone 20 per cent of the timeand is not significant. This is true also of thedifference between the mature angles, 3.2.

The means of the young angles in both 1948and 1952 are significantly different from thoseof the mature angles. It is interesting to notethat the means for the total, youthful andmature angles decreased by several degreesduring the 4-year period. The difference in eachcase is not statistically significant but suggeststhat with more time a significant change mightoccur.

Only the angles of bifurcation showed a sig-nificant reduction, 8.8, between 1948 and 1952.Only 12 of the 20 original angles could berecognized and measured in 1952. The extremeyouthfulness of the newly formed drainagebasins, with rapid lowering of channel gradientsin progress, is the cause of the great change inbifurcation angle.

A comparison of the drainage patternsshowed marked drainage changes. Twelve newtributaries were added to the drainage systembetween mappings. Coincidentally, 12 others

were eliminated, 6 by abstraction or lateral ex-pansion of a more competent neighbor, 2 byangle reduction to the minimum with collapseof the divide and union of the streams, while theremaining 4 were in small, shrinking basinssurrounded by headward-growing channels.Two of these channels were originally near thelower limiting area of channel formation, 11.8and 15.3 square feet. It is interesting to notethat both stages of Clock's (1931) drainage-de-velopment series are represented here: exten-sion and integration, with abstraction as themajor process of integration. Capture occurredin two other instances. Examples of thestraightening of the stream channels werenumerous.

One other change of pattern noted is thelateral shift of the major tributaries toward thecenter of the basin. This migration toward acommon axis within the system is gradual, butthe asymmetry of all high-order transverse-valley profiles testifies to its presence.

A series of drainage patterns traced from the1948 and 1952 maps (Fig. 22) illustrates someof the changes during that period. The basinsillustrated have steep channel gradients, anderosion would be rapid. In addition, the fill iseasily eroded and presents few structuralobstacles to drainage-channel modifications.

The following generalizations summarizechanges in the drainage network at PerthAmboy: A tributary to a channel of higherorder develops with an entrance angle de-pendent on the ratio between channel andground slope. Because of relatively slower de-gradation of the main channel, a downstreammigration of the point of junction occurs withlessening of the entrance angle. If the ratiobetween main-channel gradient and tributarygradient remains constant (steady state), nochanges in junction will occur except thosecaused by chance structural irregularities in thefill. As channel gradation spreads throughoutthe entire system the main-channel gradientwill first reach an essentially constant value,but the tributary gradient will continue tolower, with a lessening of the junction angle.When the junction angle becomes very small,lateral planation removes the interveningdivide, and the junction migrates upstream.Comparable evolution of stream-entrance


angles and drainage patterns in other regionsmay occur only in youthful areas with a highrelief ratio, but similarities between PerthAmboy and other areas in other aspects ofdrainage-basin morphology suggest that similar

In the initial stage the steep front of the ter-race was probably strongly rilled. Because theupper surface of the terrace drained toward thefront the rills quickly advanced across the lip ofthe terrace onto the essentially flat upper

FIGURE 22.DRAINAGE-PATTERN CHANGES IN SELECTED BASINS BETWEEN 1948 AND 1952 AT PERTH AMBOYBasins A, C, and D are steep gradient streams. Basin B is a youthful basin on the upper surface of the

terrace. Drainage changes are indicated by numbers on the figures:1 Angle of junction change 5 Angle of bifurcation change2 Migration of junction 6 Channel straightening3 Bifurcation 7 Elimination of tributary4 Addition of tributary

changes although perhaps less obvious, arenevertheless slowly occurring in all expandingdrainage systems.

Because the observed drainage-patternchanges were occurring mainly as the streamchannels were rapidly downcutting, any upliftof a land surface might initiate the samechanges. Studies of drainage patterns on thePleistocene terraces of the Atlantic Coast, forexample, might indicate that height above baselevel and stage are correlatable with angles ofjunction.

Evolution of the Perth Amboy Drainage PatternFrom the observed systematic drainage

changes at Perth Amboy and the known de-velopment of a network within the limitingvalues of basin area, it may be possible todeduce from the existing pattern the initial andfuture patterns.

surface. The channels most favored by chanceencounter with weak patches of fill deepenedand grew rapidly toward the divides of the indi-vidual small watersheds. These deeply cutpermanent channels followed the path of initialdrainage concentration manifested as faultchannel traces on the upper surface. Channeltraces of this type were observed at PerthAmboy in areas of headward channel develop-ment. The permanent channels follow thesefaint swales on the original surface becausethere the discharge of runoff is concentratedfrom the entire watershed. A headward de-veloping incised channel is hydrophilic, ad-vancing always toward maximum water supply.

The most vigorously developing initial rillchannel thus dominated its less effective neigh-bors and established itself as the axis of abroadening ovate drainage basin. Its perma-nence was decided initially by a favored po-

EVOLUTION OF THE DRAINAGE NETWORK 621

sition in line with the axis of a shallow water-shed on the terrace surface from which it wassupplied with more runoff than its competitors.It may also have struck zones of weaker ma-terial in its bed. The added runoff allowed

(I)

(2)

(3)

FIGURE 23.POSSIBLE DEVELOPMENT OF ANGLESOF BIFURCATION

(1) Angle remains unchanged; (2) One channelbecomes dominant; (3) On steepest slopes anglesdecrease and channels unite.

deepening of the drainage channel with cor-responding oversteepening and collapse of itsvalley-side slopes. As soon as lateral expansionof the drainage basin produced sufficiently longslopes, tributary development set in on theseslopes.

As the channel outstripped its neighbors theexpanding drainage area permitted its bifurca-tion. The comparison of angles of bifurcationon the 1948 and 1952 maps suggests threepredictions of possible future development of abifurcated channel: (1) both segments of thebifurcated channel continue to grow headwardunchanged in angle (Fig. 23, 1); (2) one seg-ment becomes dominant and straightens itschannel, while the other segment becomestributary (Fig. 23, 2); (3) on steep slopes theangle of bifurcation reduces in accordance withthe Sc/Sg ratio, and the two segments becomeone (Fig. 23, 3).

It is postulated that (2) occurred in the early

stages of the Perth Amboy development, thusforming the first major tributary (Fig. 24, 1, 2).The tributary end grew normal to the mainchannel until it came under the influence of theforward slope of the terrace when its growth

LIMIT OF HEADWARD EXTENSION1 T1 1y\ ] / TERRACEil/

1FIRST

BIFURCATION

1 1 I1 1 11 ' ' \

1J 11\\/ FRONT

N

ZDOMINANCE SEC

OF ONE BIFURI

11

/

5OND;ATION

\\4

HEADWARDGROWTH PRESENTPATTERN

\ \6FUTURE

PATTERNFIGURE 24.SUGGESTED EVOLUTION OE THE PERTH

AMBOY DRAINAGE PATTERN

direction altered and its upper segment de-veloped parallel to the main channel (Fig. 24,3). Perhaps the next permanent bifurcation wasas indicated in Figure 24, 3, followed by head-ward growth (Fig. 24,4) and other branches andbifurcations to yield the major elements of thepresent pattern (Fig. 24, 5; PL 1).

As these streams incised their channelssecondary tributaries formed on the slopes ofthe valley walls. These tributaries were underthe influence of the rapidly degrading mainchannels; many still are in the youthful head-water areas. Figure 25 is a frequency-distribu-tion histogram of the angles measured betweentributaries and the segments of the main chan-nel (Table 11). The modal class lies betweenlimits of 90 and 100, indicating a right-anglepattern in accordance with a low Sc/Sg ratio.The earliest-formed of these tributaries becamethe most important and hindered the develop-ment of younger neighbors on adjoining slopes.This is borne out by the fact that the meandistance separating first-order streams along the


main channel (4.3 feet) is smaller than the meandistance separating first- and second-orderstream channels (7.6 feet). Order number thusprovides a rough means of classifying channels

so

4O

50i0(E20

10

o

*

X-9T.6SM0.3n. 96

TO 90 110ANGLES (DEGREES)

130

FIGURE 25.FREQUENCY-DISTRIBUTION HISTO-GRAMS OF ANGLES BETWEEN TRIBUTARIES

AND SEGMENTS OF THE MAIN CHANNEL

TABLE 11.FREQUENCY DISTRIBUTION OF ANGLESBETWEEN TRIBUTARIES AND MAIN CHANNEL

Sample

Angles ofjunction

Mid-values in decrees75

2

85

20

95

40

105

19

115

13

125

2

X

97.6

.?

10.3

FT

96

according to age; the oldest tributary channelshave the higher order number.

The present faintly trellised pattern of theprincipal large-order channels (Fig. 24, S;PI. 1) is not considered permanent. It is sup-posed that the angles of junction become smallerwith the increased Sc/Sg ratio, and the lateralshifting of the larger tributaries toward themain channel would result in the acute-angleddendritic drainage pattern that is typical ofmature areas of simple structure. This changewould involve considerable lateral planationand channel straightening, with a modified finalpattern perhaps like that in Figure 24, 6.

If, as previously noted, a positive relationshipexists between stream gradients, maximumslopes, and relative relief (expressed as the relief

ratio), it follows that the Sc/Sg ratio shouldvary as the relief ratio. Because entranceangles, and therefore the total drainage pattern,are dependent on this Sc/Sg ratio, similar areasdiffering only in relative relief probably haverecognizable differences in drainage pattern, atleast in the early stages of development.

FIELD OBSERVATIONS AND EXPERIMENTALSTUDIES ON THE DEVELOPMENT OF

BADLAND TOPOGRAPHY

Field-Erosion Measurements

Field and experimental work at Perth Amboywas designed both to verify conclusions de-rived from map analysis and to obtain new in-sight into processes operative in the develop-ment of erosional landforms of the badlandtype.

Many recent geomorphic studies have beenstrongly influenced by the work of W. M. Davisand Walther Penck. Each approached the studyof landforms with a separate purpose. Davisconsidered description of landforms for geo-graphical purposes the aim of the geomorpholo-gist, whereas Penck attempted to use the de-velopment of landforms as a key to the Earth'srecent structural history and the nature of thediastrophic forces.

A chief point of controversy between Davisand Penck is the manner of retreat of slopes.Penck (1953) maintained that on a stable massinitial stream incision produces steep, straightslopes which retreat at a constant angle, thatupwardly convex slopes indicate accelerateduplift, and upwardly concave slopes decreasingrate of uplift. Davis (1909, p. 268) imaginedthat the angle of valley-side slopes normallydeclines with time and reduction of relief.

Erosion on slopes at Perth Amboy was meas-ured to clarify the basic geomorphic problem ofslope retreat under the limited conditions ofbadland erosion.

The measurement of erosion on the badlandslopes was accomplished by simple and inex-pensive means. Wooden dowels J4 inch thick and1J feet long were driven into the slopes at1-foot intervals on downslope profile lines,orthogonal to the contours from crest to base ofeach slope (Fig. 26), and normal to the slopeuntil flush with the surface.

OBSERVATIONS AND STUDIES ON DEVELOPMENT OF BADLAND TOPOGRAPHY 623

Stake profiles were placed on 16 diverselyoriented slopes, some with sharp crests andothers with convex divides. On Plate 1, shortlines labeled "P" locate profile lines. All slopeswere composed of similar material; all had a

measurable exposure of the stakes. The lengthof stake exposed, measured to the nearesttenth of an inch, indicated the depth of erosionat that point on the slope. The last measure-ment was made on September 10, 1952, when

A "-4.

W

FIGURE 26.TYPICAL PERTH AMBOY SLOPE PROFILESTicks on profiles show position of stakes; numbers indicate depth of erosion in inches. Profiles A, B, and

C are typical of the area; profile D shows a basal convexity.

youthful, degrading, intermittent gully channelat the base. Slopes were selected, however, thatshowed no severe effects of rilling and offered noproblem in the determination of a straight,downslope profile line. Slopes ranged from 6 to14 feet long. The 16 profiles were installed onJune 15 and July 1, 1952, but because a negligi-ble amount of erosion occurred between thosedates, they are treated as a group.

Slope angle and distance between successivestakes were measured at the time of installation,and the original slope profiles thus plotted. Allprofiles are remarkably straight except for thosesegments forming convex divides or whereminor irregularities occur (Fig. 26). Thestraightness of profiles is characteristic ofmaturely dissected regions of steep slopes ofwidely differing scales of length, formed undervarious climatic and geologic conditions (Law-son, 1932, p. 711; Strahler, 1950, p. 681).

Measurement of erosion on the slopes beganafter the first runoff sufficient to produce a

the measurement of slope angle and distancebetween successive stakes was repeated. Duringthe 10 weeks of observation the depth of erosiondiffered both from slope to slope and from pointto point on each slope. Erosion depth wasgreatest on sharp-crested divides and least onconvex divides, but seemed to be essentiallyuniform along the straight segments of eachslope, where a mean of 0.9 inch of material wasremoved.

Only two of the slopes investigated showed ameasurable change of angle. Both had steep-ened, but neither had a simple, straight profileat the starting date in June. Slight convexitiesinitially existing at the slope base caused in-creased erosion at those points so that, by theend of the observation period, the characteristicstraight profile had been restored. Slope D(Fig. 26) shows thissteeperbasal segment causedby rapid channel undercutting. To determinesignificant increase or decrease of slope angle,only the straight parts of the profiles were used.


Erosion depth obtained from stakes on theconvex divides, on sharp-crested divides, and inchannel bottoms were eliminated by discardingall values of stakes at the crest or base of the

ZA2.01.61.2.8.40

'

7

Yc

. *

.

".. '

= .92 + .00s=.34"

' -

025X

.

f-

-

!

3 20 40 60 80 10Distance (%)

FIGURE 27.REGRESSION FITTED TO A SCATTERDIAGRAM or DEPTH or EROSION ON PER CENT

OF DISTANCE PROM TOP OF THE STRAIGHTSLOPE SEGMENT

erosion depths fall between 0.4 and 1.6 inches.On a given profile the depth of erosion wasgenerally highly uniform for all stakes, whereasthe mean depth differed considerably from oneprofile to another. Because absolute values forerosion are plotted on the ordinate the broadscatter zone produced (Fig. 27) fails to revealthe uniformity of erosion depth on a singleslope. The marked differences in average fromone profile to the next may be explained byvariations in microclimatic environment, degreeof compaction and permeability of the clay fill,or by slight compositional variations from slopeto slope. For example, mean erosion on oneslope was 0.6 inch but on another 1.3 inches.Consequently, when all readings are combinedon one diagram, the scatter of points is wide.

A regression line fitted to the points of thescatter diagram by the method of least squares

TABLE 12.EROSION MEASURED ALONG THE SLOPE PROFILES

StakeNo.

ProfileAlA2A3BlB2CDlD2ElFGHIJKL

Erosion at each stake in inches1

1.6*.8*.8*.7*.3*.3*

1.3*1.3*1.5*1.0*

.3*

.4*

.8*

.8*

.7*

.7*

2

.71.71.11.1

.5

.5*

.8

.9

.8

.9*

.61.1

.9*1.0

.7*

.9

3

.71.41.11.0.9.7.6

1.01.2

.7

.81.31.0.9.8.8

4

.71.11.01.4.8.8.7.4

1.2.7.4

1.2.8.9

1.6.7

5

.71.11.41.2.8.6.7.4

1.8.6.5

1.4.9.6

1.4.9

6

.51.11.01.2

.61.0.8

1.01.9

.4

.71.0.7.6

1.6.8

7

1.01.1

.5

.8

.9

2.6.8.5

1.01.0

1.6.5

8

.71.4

.61.0

.7

.81.0

.9

1.5

9

.6

.6

.8

.91.4

1.0

.6

10

2.3*1.2

.7

1.3

ll

.6

12

.9

13

.8

14

.6

* Reading eliminated from regression Figure 27.

slope profile which deviated by 10 or morefrom the straight segment. These values arenevertheless listed (Fig. 27; Table 12) with the113 readings of erosion depth that remained.These remaining values were combined into onescatter diagram by the use of a dimensionlessparameter: per cent of distance from upper tolower end of the straight slope segment. Most

(Croxton and Cowden, 1939, p. 655-657) hasthe equation

Yc = 0.92 - .00025X.A 2-test, to determine the validity of the nullhypothesis that the deviation from zero slope,shown by the regression equation, can be at-tributed to chance sample variations alone


when sampling from a population with zeroslope, reveals a probability greater than 0.65.Thus at least 65 times in 100 this great atrend or greater would occur. Lack of significanttrend suggests that erosion is uniform alongthe straight segment of the slopes.

24

C~l.6I l22kl B

A0

.

^ "

Yc'

.

.'.- '

^ * *

.92 -.000s= .ZZ"

.:.:

'

';

1


erosion varied from slope to slope. The aboveevidence sustains the hypothesis that, with anactively degrading stream at its base, the bare,unconsolidated, highly cohesive slopes of bad-land topography retreat in parallel planes whenadjusted to the controlling conditions of theirenvironment.

The effect of rilling and frost heaving onslopes are discussed below, but the importanceof these processes does not invalidate the dis-cussion of slope retreat under the action ofrunoff alone, for during the measurement oferosion depth on the slopes no frost heavingoccurred and there was no important rilling.

Channel erosion was also checked by re-peated surveying of the main channel. Duringthe year of observation this showed slight ag-gradation in the lower sections of the channeland degradation in the headwater areas.

Experimental Erosion Measurements and Studyof Runoff

Success of the use of wooden dowel rods tomeasure erosion during a short period of thestudy suggested the use of simulated rainfallon the slopes to study in more detail the proc-esses of erosion and to measure the amount oferosion produced by measured amounts ofprecipitation. A 2J.-gallon hand pump wasused to simulate rainfall. A horizontal cir-cular motion of the pump nozzle delivered anapproximately uniform intensity of fine sprayto an area of 36 square inches. Investigationswere thus limited to areas of this size.

The following technique gave consistentresults: The hand pump was filled with waterto within 6 inches of the top and 50 full strokesof the pump provided constant initial pressures.When the nozzle was held 18 inches above thesurface and moved in a circular motion for 5minutes about 640 cc were delivered to thearea.

Six hundred and fifty cc of water delivered toa 36 square inch area was equivalent to 1inch of precipitation, a far greater intensity(12 inches per hour) than all but the mostsevere natural rains. Because the aim of theexperiment was to determine the relation be-tween slope angle and erosion, the high in-tensity of precipitation is not thought to in-

validate it. On a slope several feet long a heavyrain would produce cumulatively an equivalentrunoff intensity over a small area of the slopebase, although this flow would enter the areawith considerable sediment entrained.

ii 100

/

.2 .4 .6 .8 1.0 12SINE OF SLOPE ANGLE (GRAVITY FUNCTION)

FIGURE 31.RELATION or EROSION TO SINE orSLOPE ANGLE

Eroded material collected after ten minutes ofspraying (2 in. of ppt.)

Attempts to measure erosion in the field byspraying the surface upslope from metal sedi-ment traps set in the slope failed because winddeflected the spray. Field trials were discon-tinued in favor of laboratory studies.

Sheet metal containers 6 inches square wereconstructed to hold sediment from a com-posite sample collected at Perth Amboy, andadjustable wooden stand was made to supportthe containers at the required angles (PI. 2,fig. 4). The sediment in the container approx-imated field conditions: size components ofthe sediment were roughly equally distri-buted; surface was smooth and level andsealed by clogging of the pores by clay par-ticles after wetting (Hendrickson, 1934).

The container and sediment were placedon the wooden stand, and spray was directedonto the sediment surface for 5 minutes. Theeroded sediment and runoff were taken fromthe collecting pan and weighed.

Figure 31 shows the results of four trialswhere sediment loss in grams is plotted againstsine of slope angle, termed the gravity function


(Strahler, 1952a, p. 928) because it representsthat proportion of the acceleration of gravityacting parallel with the slope and producingshear. The regression line representing eachexperiment reveals clearly that erosion on theslope is well described as an exponential func-tion of the sine of slope angle. A similar rela-tionship results if erosion is plotted directlyagainst slope angle, changing only the con-stants of the regression equations. The totalvolume of runoff from the slopes remainedessentially consant during each experiment.These results appear to agree with those ofBorst and Woodburn (1940) and Duley andHays (1932) although their values for erosionincrease more rapidly with increased slope,probably because of the greater length of thetrial plots and the loose plowed surfaces onwhich the water was sprayed.

The variation in amount of erosion fromexperiment to experiment is attributed in partto unrecognized variations in water deliveredby the spray; experiment 4 was performed on aday noticeably colder than the days the otherexperiments were performed. The lower tem-perature may have decreased the pressuresufficiently to cause decreased water deliveryand lessening of erosion.

Although many sources of error existed, aconsistent relationship within each seriessuggests that, with better equipment, quan-titative determination of the relations be-tween slope angle, amount and intensity ofprecipitation, soil type, and erosion wouldnot be difficult. The Department of Agriculturemade numerous studies of this type, dealingprimarily with surfaces representing fallowor cultivated plots and rarely with slopesgreater than 20. A large field remains forfurther experimentation.

The effect of increased slope angle on thegrain size of the eroded sediment was deter-mined by sieving the collected samples. Thesamples were arbitrarily separated on the 0.5mm (Wentworth's greater than mediumsand) and 2.0 mm (greater than coarse sand)sieves. It was supposed that with increasedslope the percentage of larger sizes wouldincrease, but instead the percentage by weightof sediment greater than 2.0 mm varied onlyslightly from 27 per cent of the total (Table

14). The runoff, therefore, had removed a pro-portionally equal amount of each grain-sizecomponent as the slope steepened.

Although the percentage of each componentdid not change appreciably, the size of thelargest particle transported increased with

TABLE 14.PEE CENT BY WEIGHT OF ERODEDSEDIMENT GREATER THAN 2 MM

Slope angle(degrees)

102030405060

Experiments1 and 2

27.026.826.722.034.827.5

Experi-ment 3

29.031.027.5

26.030.0

Experi-ment 4

27.0

26.018.026.026.0

Mean"ofall experi-

ments

27.728.926.720.028.927.8

slope angle. Weight of the largest grain trans-ported in experiments 3 and 4 (Fig. 32) is di-rectly proportional to the sine of slope. Datafrom experiment 2 is not linear and data fromexperiment 1 showed no consistent relation-ship. Deviation from a straight-line relation-ship may be due to pump variations, but ingeneral the increase of maximum gram sizetransported with slope is attributed to themore rapid uncovering of the larger sizes onsteeper slopes of the originally smoothed plots.Therefore, if by chance the largest grain pos-sible of transport was not uncovered, the rela-tionship would not appear to exist simply be-cause of the absence of the larger particles.

Erosion was greatest on the steepest slopes,and even on slopes of the lowest angle used(10 per cent), all components of the sedimentmoved in approximately the same proportion,but more slowly. The size of the largest particlestransported on any slope appears to be di-rectly proportional to the gravity function.

Perhaps the most interesting part of thestudy was the observation of the action ofrunoff on the slopes of varying inclination. Ona 10-degree slope, exposure of the coarsergrains, as the fine sediment is carried away,gave a sandy appearance to the surface. On a30-degree slope the medium-sized particlesmoving downslope jam between larger grains,forming miniature dams which check the flowof the runoff and pond the water on the slope


until the weight of water and sediment is greatenough to burst this tiny dam. When the damis broken a pulse of water and sediment movesdownslope with energy enough to move eventhe larger grains. The characteristic arcuateridges of sediment left by check dams on aslope can be recognized. Horton (1945, p.312-313) discusses surge-flow transport wheredebris on a slope causes the same checkingand temporary ponding of runoff. Large grainson this 30-degree slope are loose on the surfaceand appear ready to move when the force ofrunoff is great enough. The large pebbles areundermined. Activity on the SO-degree slopeis marke

Documents

Schumm_1956_Evolution of Drainage Systems and Slopes in Badlands of Perth Amboy