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Climate and MorphometryAuthor(s): Richard J. ChorleyReviewed work(s):Source: The Journal of Geology, Vol. 65, No. 6 (Nov., 1957), pp. 628-638Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/30058827 .

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GEOLOGICALNOTESCLIMATE AND MORPHOMETRY

RICHARD J. CHORLEYBrown University

ABSTRACTAn analysis of the morphometry of three areas of similar gross lithology, structural effect, and stage ofdissection shows that there is a significant difference between each of the equivalent landscape unit forms.A climate/vegetation index (Ic) was obtained for each region, employing the mean annual rainfall, the meanmonthly maximum precipitation in 24 hours, and Thornthwaite's precipitation effectiveness index. It isfound that the climate/vegetation index bears a remarkably consistent relationship to the mean logarithmsof stream lengths, basin areas, and drainage densities.

INTRODUCTIONTheoretically, the local morphometry offluvially dissected landscapes may be con-sidered as a function of the following inter-acting variables:

1. Structurea) Rock type, in terms of resistance toerosion and permeabilityb) Attitude of the bedsc) Soil and mantle characteristics-size andshape of loose load, resistance to erosion,angle of internal friction, cohesion, andinfiltration capacity2. Processa) Amount of precipitationb) Rainfall intensityc) Vegetational cover, being a function ofprecipitation, temperature, evaporation,soil, and slope conditions, and havingquantitative significance in regard to thedegree to which it inhibits erosion3. Stage or time

In order that the relative effects of thesevariables in the production of landscapemay be studied quantitatively, it is neces-sary, first, that they be themselves suscep-tible to quantitative expression and, second,that it is possible to isolate one of these vari-ables in order to determine whether it bearsa consistent relationship to empirically ob-tained, quantitative measures of landscapemorphometry. The design of this paper,therefore, is to determine with varying con-

1Manuscript received January 19, 1956.

ditions of process, whether the theoreticallyassumed relationship between process andmorphometry holds empirically true underreasonably uniform conditions of structureand stage.STRUCTURE

Three areas were selected for study, all ofwhich have been subjected to completefluvial dissection and all of which are com-pletely underlain by sedimentary sequences,the predominant rock of which is sandstone.The Exmoor region of Somerset and De-von counties, England, is an elevated tractabout 30 by 12 miles in extent, rising fromsea level to a maximum of 1,706 feet (Bal-chin, 1952), the drainage basins studiedhaving a mean relief of 1,067 feet. It is un-derlain by some 20,000 feet of Devonianrocks, variously dipping to the south atangles averaging about 300 in the north(Dewey, 1935). The lithology is predomi-nantly arenaceous, although argillites arecommon (see Diagram A).

It is readily apparent that neither thedifferences in lithology nor the dip of thebeds has led to significant, mappable, mor-phometric variations and that the geometri-cal features of the landscape are broadlythose which are associated with structurallyand lithologically homogeneous uplands.Drainage density, drainage pattern, and re-lief bear little relation to major formationalvariations, and the main geologic contacts

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GEOLOGICALNOTESare indistinguishable topographically. Theonly gross structural influence exhibitedwithin the region is that the shapes of thethree basins paralleling the east-west strikeare more elongate than the rest, having amean value of k (Chorley, Malm, andPogorzelski, 1957) of 3.17, compared witha mean of 1.94 for the remaining ten basins.

1885; Moore, 1944; Ebright and Ingham,1951) (see Diagram B).The low regional dips are obscured by anti-clinal structures, four of which trend north-east to southwest across the area (Wharton-Cameron, New Bergen, Rattlesnake-KettleCreek, and Driftwood axes) and one cross-ing Cameron County from northwest toDIAGRAM A

Upper

DEVONIANMiddle

Lower

Lower and MiddlePilton bedsBaggy and MarwoodbedsPickwell Down bedsMorte slatesIlfracombe bedsHangman gritsLynton bedsForeland grits

2,000 feet Marine argillaceous and cal-careous sandstones1,200 feet Littoral shales and micaceoussandstones3,000 feet Brown, red, and purple sand-stones1,500 feet Marine shales, becoming are-naceous at the top3,990 feet Marine shales and sand-stones; some limestones3,600 feet Uniform, fine-grained, redsandstones2,000 feet Marine and littoral bluish-gray shales1,500 feet Continental quartzose coarsesandstones, shales inter-bedded

Pennsylvanian

Mississippian

Devonian

AlleghenyPottsville

Maunch Chunk

Pocono

CatskillChemung

A second group of drainage basins wasselected for study in Cameron and Pottercounties, north-central Pennsylvania, wheresome 1,500 feet of regionally horizontalDevonian and Carboniferous sedimentaryrocks have been maturely dissected by awell-integrated stream system. The litholo-gy here is even more predominantly arena-ceous than that of the Exmoor region, andthe following column is representative ofCameron County (Sherwood, 1880; Sheafer,

DIAGRAM B50 feet Coal measures and shales

400 feet Coarse sandstone, locally con-glomeratic, with thin, inter-bedded coals, fireclays, andlimestones50 feet Discontinuous shales which, inplaces, may represent argilla-ceous facies of the lower Potts-ville700 feet The upper 400 feet of massive,steel-gray sandstone are cappedby thin Mississippian limestone;the basal 300 feet are similar to,and gradational with, the Cat-skill formation500 feet Red sandstone350 feet Dark purple and red shales andsandstonessoutheast (Kinzua-Emporium-Crossaxis).Local dips are away from these axes andaverage less than 30, although restricted dipsof up to 70 occur on the north flank of theNew Bergenanticline.The thirdareais locatedin Winston,Cull-man, and Lawrence counties, Alabama,where 350-500 feet of the Pottsville forma-tion (Lower Pennsylvanian), dippingsouth-southwest at 20-50, have been dissected bythe headwaters of Sipsey Fork, giving a

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GEOLOGICALNOTESlocal relief of 370-492 feet (Adams, Butts,Stephenson, and Cooke, 1926; Semmes,1929). In this locality the Pottsville forma-tion consists of 0-160 feet of basal, white,siliceous sandstone and conglomerate, over-lain by thick to massively bedded arkosicsandstone, alternating with thinly beddedblack shales.

STAGEAll three localities have been completelydissected by streams, and remains of anyunconsumed, high-level, previous surfacesare not extensively evident, except in theform of some accordance of hilltops. The

mean hypsometric integrals (Strahler, 1952)for the drainage basins selected in each ofthe areas are 55.87, 59.21, and 57.46 percent, respectively, which would enable thebasins to be classified as in the equilibrium(mature) stage of Strahler (1952). An analy-sis of variance (Walker and Lev, 1953)shows that there is no significant differencebetween the mean hyposometric integralsfor the three regions, taking a critical levelof significance of Fo.95. As indicated byGlock (1932), the amount of relief is a poorindicator of stage, but if one wishes to con-sider stage on the basis of rate of dissectionrather than on the amount of bedrock re-moved from a basin, some measure involv-ing relief might be perhaps more appropriate(Schumm, 1955).

MORPHOMETRYIn Exmoor, Pennsylvania, and Alabama,

respectively, 13, 7, and 7 third-, fourth-, andfifth-order drainage basins were selected forstudy. The data for each basin were ob-tained from Ordnance Survey 1:25,000(nos. 21/43, 44, 53, 54, 63, 64, 73, 74, 83, 84,93, 94), U.S. Geological Survey 1:24,000(First Fork, Cameron, Wharton, and Em-porium quadrangles), and U.S. GeologicalSurvey 1:62,500 (Danville and Mount Hopequadrangles) maps, the latter being photo-graphically enlarged to 1:31,726 in order tofacilitate delimitation and measurement ofthe landscape features. Although the accu-racy of these maps may be open to question,there is no reason to suppose that the indi-vidual degrees of accuracy are of such a dif-

ferent order of magnitude as to prohibit thecomparison of results, particularly as thedrainage densities of all these regions maybe classed as coarse or medium-coarse(Smith, 1950). It should be noted that, inthe locality having the most suspect maps(Alabama), mean stream lengths and basinareas are the smallest and drainage densityis the highest of the three regions (figs. 1-3)and that more accurate maps would tend toincrease, rather than decrease, this differ-ence with respect to the other two localities.Strahler (1950, p. 690-693) has defended theuse of recent maps on a scale of 1:25,000 and1:24,000 for morphometric work in regionsof coarse texture of erosion.For each of the twenty-seven basins,lengths of streams of various orders (Lo),areas of stream basins of various orders(Ao), drainage densities (Dd), relief (H), andhyposometric integrals were measured, ac-cording to the methods outlined by Horton(1945), as modified by Strahler (1953) andMiller (1953). The lengths of first-orderstreams were found to be generally toosmall to be measured individually with sat-isfaction on maps of this scale, particularlythose of Alabama, and often it was foundimpossible to delimit areas of first-orderbasins with any accuracy. Consequently,they have been omitted from the followingdiscussion.

The first step was to determine whetheror not similar morphometric features are ofsignificantly different magnitude in thethree regions. The analysis of variance isbased on the assumption that the individualsamples are representative of normally dis-tributed populations having equal vari-ances, but it has been demonstrated (Miller,1953) that the frequency distributions in-volving the actual values of stream lengthand basin area present a characteristic right-skewness. If the logarithms of the individualvariates are employed, however, the result-ing frequency distributions appear morenearly normal. In accordance with this ob-servation, the frequency distributions of thelogarithms of one hundred times the indi-vidual stream lengths and basin areas (toavoid negative logarithms) were constructedas histograms (figs. 1 and 2), together with

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500 50~=L9l 0~4-42S395

20

0 I 2 3

1.640=18-440 X~I.86P>.50

20

0 1 23 0 0 1 2 3

507=1.342- N=I5ILSAMPS=.302

20

0 0 I 2 3LOG 100L~tMILES]F=20.84!~$ ao~

0~0 1 2 3LOG100L3[MILESJFz2 548F,5~3.04

0~~0 1 2 3LOG IOOL1JMILESJF: asi~;3. 7

FIG. 1 -Histograms of the logarithmic values of stream lengths

631

~l.569~%J~/97S =~392

20

X=2.34 IN=14S~.544X=6 3.40PSOOI

00

20

2 3 00

50 X~'I.460N-89S=~3I4

x

1 23

~o* ~2.303J,~7~jt 38

20 20'

00 1 2 3

50

20

50X:1.379N=181&335I.803N=37S=A72

I)~=10.93P>.50 ~20

%FREQUENCY

%

FREQUENCY

%FREQUENCY

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50 50'X'2. 208N=42S=. 331

20 200

00

50-

200

0

50

02 3 0

50X"I.231N=89S=.318

I 2

1.893 _N=18S".3 52

3 0

50

I20' X4.96P>.050

I 2 3

>~~.9I9N- 37 [SAMF~jS~.2 97x

20~

0

50

20'

0~'1 2 3 0

50

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100 X=3.012N 13S127

50

1.0

100 - 8N=7S=.049

1.0

10000 X.934N=7S=.04 950'

X=2.622S=t049

50

00 .5LOG DF= 199.52Fa 3.40

1.0 02.5 3.0LOG HF=5.35F, 3.40

3.5

FIG.3.-Histograms of the logarithmic values of drainage densities and reliefs633

100 X .510N* I3S=.048

50'

0 0 .5 3.022.5

100

3.5

50

X=3.125N=7S=.04950

0 .5 02.5 3.0 3.5

XI

%FREQUENCY

%FREQUENCY

%FREQUENCY

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GEOLOGICAL NOTESthose employing the logarithm of the drain-age density and relief for each of the majordrainage basins (fig. 3). This resulted inmore symmetrical distribution of the samplevariates and in a close correspondence of thestandard deviations between the three re-gions for equivalent morphometric features(e.g., second-order stream lengths). In orderto test the normality of the distributionsrepresented by the samples, chi-square testswere made for each of the four sampleswhich still appeared most skewed (lengthsof third-order streams for Pennsylvania,lengths of fourth-order streams for Exmoor

tempt to determine whether they presentsignificantly different characteristics. Theresults of these tests are given in figures 1,2, and 3, indicating that the means of thelogarithms of equivalent morphometricmeasures are significantly different in eachinstance.

PROCESSProcess may be considered as a functionof climate, acting mainly through the hydro-logical considerations of amount and inten-sity of precipitation and through the agencyof vegetational cover. All these three factors

MEAN MONTHLY

Years of recordJanuaryFebruaryMarchAprilMayJuneJulyAugustSeptemberOctoberNovemberDecemberMean annualMean

Ilfra-combe30+3.172.652.772.011.98

2.082.453.462.594.403.764.6535.97

PRECIPITATION(INCHEs)Empor-

ium ]203.232.983.983.134.654.474.923.703.383.102.883.5343.95

TABLE 1CLIMATIC DATAMAXIMUM 4-Houxl

PRECIPITATIONSt.

Bernard235.534.816.005.615.624.644.974.352.933.483.955.7457.63

Ply-mouth30+1.51.41.51.11.6

2.21.81.91.52.22.21.7

(INCHES)Empor-

ium611.662.062.262.565.852.387.672.512.412.431.801.81

St.Bernard424.474.053.805.304.254.495.515.843.676.155.225.02

Ilfra-combe30+43.343.344.448.254.058.760.961.358.753.348.545.3

MEAN MONTHLYTEMPERATURES(F.)Empor-ium B2026.224.835.547.359.267.270.768.262.250.139.429.9

St.ernard2343.045.952.460.867.675.478.077.073.461.450.643.7

1.72 2.95 4.81 51.3 48.4 60.8and Alabama, and areas of third-orderbasins for Pennsylvania), using a criticallevel of significance (P) of 0.05. The resultsof these tests are given appropriately in fig-ures 1 and 2, indicating that only the fourth-order stream lengths for Exmoor are non-representative of a normal distribution,probably because one variate represents arelatively large percentage of a small totalsample.Arbitrarily choosing a critical level ofsignificance of Fo.9s, analyses of variance(Walker and Lev, 1953) were made to com-pare the mean logarithmic values of lengthsand areas of second-, third-, and fourth-order streams and basins in each of thethree regions, together with the logarithmsof drainage densities and reliefs, in an at-

are capable of quantitative expression andvary between the limited localities selectedfor study, for each of which meteorologicalstations were selected as representative(Ilfracombe and Plymouth, Devon; Em-porium, Pennsylvania; and St. Bernard,Alabama).Amount of precipitation may be con-veniently indexed by the mean annual pre-cipitation (British Rainfall, 1939; U.S.Weather Bureau, 1939) and average inten-sity of precipitation by the mean monthlymaximum precipitation in 24 hours (Bil-ham, 1938; U.S. Weather Bureau, 1952).These data are given in table 1, togetherwith mean monthly temperatures.As an index of vegetative growth, Thorn-thwaite's (1931) precipitation effectiveness

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GEOLOGICAL OTES 635index (P-E index) (I) has been employed,where

I= E 115 P /9HereP and T arethe meanmonthlyprecipi-tation and temperature igures,respectively.That this index may be used in this connec-tion was inferred by Thornthwaite (1931,p. 641) when he showed the close relation-shipwhich it bearsto Weaver's(1924)plantgrowth ndex,which is a quantitativeexpres-

sion of the dry weight of vegetation perunitarea.Using the mean monthly precipitationsand temperaturesgiven in table 1 for the

Exmoor,Pennsylvania,and Alabama locali-ties, P-E indexes of 78, 126, and 111, re-spectively, were obtained.TABLE 2

Locality Ic 1/IcExmoor........ 1.2607 0.7932Pennsylvania.... 0.9718 1.0290Alabama ....... 0.4004 2.4975

2.4

2.2

2.0

0..1.2

-- r x?z Iz 000

1.0.0 .2 .4 .6 .8 L.O 1.2 1.4-e

FIG. 4.-Plots of the arithmetic mean values of the logarithms of stream length versus the climate/vegeta-tion index.

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GEOLOGICAL NOTESTHE CLIMATE/VEGETATION INDEX

Assuming, then, a reasonable constancy oflithology and stage between the three re-gions, one might expect that quantitativevariations in process, expressed in terms ofprecipitation characteristics and vegetativecover, should theoretically find sympatheticand consistent variations in the correspond-ing morphometric features between thelocalities.Theoretically, linear and areal aspects oflandscape morphometry are directly relatedin magnitude to the amount of vegetativecover and inversely to the amount (P) andintensity (Q,) of precipitation, whereasdrainage density is directly related to theamount and intensity of precipitation and

inversely to the amount of vegetative cover.An index of climate and vegetation (Ic) cantherefore be derived, in which_I = _ Vegetation amount

Precipitation X precipitation intensityI

P XQ, "Thus mean logarithms of lengths of streamsand areas of stream basins of various ordersshould, theoretically, be directly related toIc, whereas mean logarithms of drainagedensity should be inversely related to Ic.With the P-E indexes and the values ofP and Q, (table 1), Ic and 1/Ic were calculat-ed for each of the three localities (table 2).

3.2

2.8

24

20

1.6

1.2

.80 .2 .4 .6 .8 1.0 1.2 1.4Ic

FoIG..-Plots of the arithmetic mean values of the logarithms of basin area versus the climate/vegetationindex.

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GEOLOGICALNOTESThe plots of log 100 Lo and log 100 Aoversus Ic (figs. 4 and 5) and of log Dd versus1/Ic (fig. 6) yield remarkably consistent re-sults, which support, in every instance, theassumed theoretical relationships. It is ofnote that the respective increases (drainagedensity) and decreases (stream lengths andbasin areas) of the morphometric measureswhich, as has been suggested, might be ex-pected to appear with the use of more accu-rate maps of Alabama would, in every in-stance except one, tend to increase the de-gree of correlation.More striking than the general constancybetween the theoretical and quantified rela-

tionships is the fact that analyses of covari-ance (Walker and Lev, 1953) show that, atthe Fo.95 evel of significance, there is no sig-nificant difference between the regression co-efficients in figure 4 and a coefficient of 3.18(i.e., log-1 0.503) (F = 1.08 < F0.95) and nosignificant difference between those in figure5 and a coefficient of 7.94 (i.e., log-1 0.900)(F = 4.88 < F0.95). It is therefore possible

to derive the following general relationshipsfor these three regions:log 100 Lo = KL + 0.503 Ic,log 100 Ao = KA + 0.900 I,,

where KL and KA are constants, dependingon the stream order.CONCLUSION

Because of the controversial nature ofseveral basic assumptions, the questionableaccuracy of two of the maps used, the ar-bitrary selection of the precipitation factors,and the generalized nature of the vegetativeindex employed, the value of the foregoingwork in absolute terms is obviously limited.It is for precisely the same reasons, however,that the consistency of the results obtainedand the harmony between theoretical con-siderations and empirical measurements areall the more noteworthy. This reasoning as-sumes, of course, that the means about

1.6

1.2

.8

.4

0.5 1.0 1.5 2.0 2.5

IcFIG. 6.-Plots of the arithmetic mean values of the logarithms of drainage density versus the reciprocalof the climate/vegetation index.

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GEOLOGICAL NOTESwhich the climates of the three areas havebeen deviating bear a relationship to oneanother not significantly different from thatrelationship expressed by the modern cli-matic data employed here. What this studydoes provide, perhaps, is stimulus for furtherwork along the same lines of reasoning, to-gether with some indication that the quan-titative aspects of landscape morphometrymay have such an ultimately rational basis

that they may soon be placed within therealm of prediction.ACKNOWLEDGMENTS.-Thisnvestigationformedpart of a quantitative study of erosional

landforms sponsoredby the Geography Branchof the Officeof Naval Research as Project no.NR 389-042, Technical Report no. 14, underContract N6 ONR 271, Task Order 30. Thewriterwishes to thank ProfessorA. N. Strahler,of Columbia University, project director, forhis help and advice.REFERENCES CITED

ADAMS,G. F., BUTTS,C., STEPHENSON,J. W., andCOOKE,W., 1926, Geology of Alabama: Ala.Geol. Survey, Special Rept. 14, p. 25-27 and 40-230.BALCHIN,W. G. V., 1952, The erosion surfaces ofExmoor and adjacent areas: Geog. Jour., v. 118,p. 453-476.BILHAM,E. G., 1938, The climate of the BritishIsles: New York, Macmillan Co.British rainfall: London, H.M. Stationery Office,1939.CHORLEY,R. J., MALM, D., and POGORZELSKI,H.,1957, A new standard for estimating drainagebasin shape: Am. Jour. Sci., in press.DEWEY, H., 1948, South-west England: BritishRegional Geology, 2d ed., London, H.M.Stationery Office.EBRIGHT,. R., and INGHAM,. I., 1951, Geology ofthe Leidy gas field and adjacent areas, ClintonCounty: Pa. Geol. Survey, 4th ser., Bull. M34.GLOCK,W. S., 1932, Available relief as a factor ofcontrol in the profile of a land torm: Jour. Geol-ogy, v. 40, p. 74-83.HORTON,R. E., 1945, Erosional development ofstreams and their drinage basins: Geol. Soc.America Bull., v. 56, p. 275-370.MILLER, V. C., 1953, A quantitative geomorphicstudy of drainage basin characteristics in theClinch Mountain area, Virginia and Tennessee:Tech. Rept. no. 3, Dept. of Geology, ColumbiaUniversity, New York.MOORE,R. C., 1944, Correlation of Pennsylvanianformations of North America: Geol. Soc. AmericaBull., v. 55, p. 657-706.ScHUMM,., 1955, The relation of drainage basin re-lief to sediment loss: Pub. no. 36 de l'Association

Internationale d'Hydrologie (Assembl6e generalede Rome, v. 1), extrait.SEMMES, . R., 1929, Oil and gas in Alabama: Ala.Geol. Survey, Special Rept. 15, p. 34-68, 76, and126-138.SHEAFER,A. W., 1885, The township geology ofCameron County, Pa.: Pa. 2d. Geol. Survey,Rept. R2.SHERWOOD,., 1880, The geology of Potter County,Pa.: Pa. 2d Geol. Survey, Rept. G3.SMITH,K. G., 1950, Standards for grading textureof erosional topography: Am. Jour. Sci., v. 248,p. 655-668.STRAHLER,.N., 1950, Equilibrium theory of ero-sional slopes approached by frequency distribu-tion analysis: Am. Jour. Sci., v. 248, p. 673-696and 800-814.--- 1952, Hyposometric (area-altitude) analysisof erosional topography: Geol. Soc. AmericaBull., v. 63, p. 1117-1142.--- 1953, Revisions of Horton's quantitativefactors in erosional terrain: paper read beforeHydrology Section of American GeophysicalUnion, Washington, D.C., May, 1953.THORNTHWAITE,. W., 1931, The climates ofNorth America according to a new classification:Geog. Rev., v. 21, p. 633-655.U.S. Dept. of Commerce, Weather Bureau, 1939,Climatological data, Pennsylvania and Alabamasections.--- 152, Maximum 24 hour precipitation in theU.S.: Tech. Paper no. 16.WALKER, . M., and LEV,J., 1953, Statistical infer-ence: New York, Henry Holt & Co.WEAVER,. E., 1924, Plant production as a measureof environment: Jour. Ecology, v. 12, p. 205-237.

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