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Geological Society of America Bulletin. \'. ,3, p. 1025-1046, ! I figs., Scptember 196~
1015
Quantitative Geomorphology of Some
Watersheds in the Appalachian Plateau
delayed by lack of quantitative methods andprocedures for measuring geomorphic charac~
terisrics. Much impetus, however, was givenfluvi31 morphometry by Horton's (1945) suggested methods of quantitative analysis of
IOH
1036
1039
1040
10331034
1035
10·;[
10·W
l().;Z
10H
10·H
TJl>lc
1_ G<:omurnhic char:lcteristics of 15 b:lSins studicdIII .\ol):llachun Pbtc:lu pro\'illce bv order
.. Conslant' ~r channel mairUe;lJlICC dctc'rmincdU\' three dilfcre/l[ mcdlOds
5. Correl:won coclliciC'nu (or re;;ressiolls of oneb:lsm property on anothcr for tot:tl bJsinson .\pp.1Iachi:ln Pbteau province
.,. Correlation ('ocllicients (or relationships o(dl:lr:JCteristies of first·ordcr basins o(.\pp:lbchi:J.Il Plateau province. , ....
5. R:ltios showing geolllemc:::d simibrity of watersheds in three sections of lhe ;\oD:lbchi:lnP!Jtl'au ..
6. Correlation eodlicil'nlS (or J;colllorphk charactcnSlies :Jlld hydrology of watersheds of.\opalachian Plarc:lU province .. , .. ,
Elfcct 'oi chJnge of Y.f:letor on SI:lndJrd errorS. StJnd:lrd error of estimates. correlation co-
diiciclHs. and signilieance for multiplere::.:rc:ssiollS on peak runoff
s. SucJm profib Jiang longcst length9..\\"erJ);c tOIJI relief plaited :lg:lillSt ordcr
10. Rc!Jtioli of basin arc:J. to strCJIll length within:I single I\':ltl'rshcd . . _ . . . . . . .
II. Lo~ mean ch:lnnel slope of :III b:l.Sins flolted:I£3inst are:l :lnd Slream lcngth 0 carre·sponding ordcr
Simple corrcl:llions of hydrologic and geomorphologic features provide the b:lsis for choice ofch:.r:.eteristics to lise in a multiple regression onpeak-runoff intensity. A regression of pC:lk in·tcnsin' of runoff on b:.sin :uea, r:linf:dl incensic\':l.nd f~equcncy, :lnd ropogr:lph}' has :l high correl~tion coefficient :lnd is signific:lnt :It thc 0.001 le\'c!.Qu:.ntitati\·e decermin:Hions 01 geomorphic proper·ties of dr:lin:lge basins thus hJ.\·c :l. pr:l.ct!c:l! usc inbasin hydrolog~"
1027101910301030
103110311032
1015101610161O~;
1015101SIOlS103S1039
1041IO,U10·'"10-15
CO:"TE:"TS
INTRODCCTION ANDACKNOWLEDGMENTS
Evaluation of geomorphic f3C[OrS and [heirm,:nhematic31 relationships to hydrology was
Abstract: Geometry of 15 watersheds in the Appabehi:!o Plateau province conforms to Honon'sbws of dr:lin:lge composition in horizont:ll, or pbni.metric. propcnies hut not in vcnic:l!' or relid.properties. Gcologic structure :llld varying lithology interact to ch:lnge vcnic:d form demenls :muCJuse dc\"ialions from Honon's bW5.
Gcolm:tric simibrirics :md dilfcn:nces in W:HC(
shed morphology provide both qu:wtil:tti\'c :lOdqualit:Hi\'c bases for grouping the regions studiediow three distinct sections. Dissimibritics, :.Ithoughdistinct. :::m: not gre:J(. ~
MARIE E. MORISA\VA Ro//te 202, Towaco, tV. j.
Introduclion .1Ild .1cknowled;';lllclllSGefH:f:JI dcscnpuon ot w:l[(;:rshcos
W:lIcnhcds smdicdCulkClion at Jata
List oi sYmbols and definitionsBasin m~rphomctry .
.\lorphometric ProfX·rtics .ReI:Hions wltlllll lint.order b:lsinsInlluellcc o( litllOlu;.:y on morphology.
Moroholot:ical simdatll\' o( w:lIersheJs bv physio.. J:ra~hi..: sections ~ .
Rl'1:Itions between ~elllllorpholog~'JIlJ hydrologyF:ll:tors cotHrolling runuli'.Gener;]1 correlation of geolnorphomeuy :md
hydrology:\luhiple correlalion with peak disch:lr~c
Summa(\' :lmj condmions.Selected 'bibliogr:lphy
Figure
I. Index mJO sho\\'ln~ loc:nion oi bJsins uuoied2. Strahler ~YUClll at stre:lm ordcfmg3. Log number of SlreJmS ploHed :tgJinst order,4. Log IneJn strc:Jm lcngth plottcd .1J;Jinst order5. Log mC:ln tot:ll stre:lrn length plotted agJinst
order6. Log me:ln basin :lrea plutted JgaillSt order7. Log rneJn slope plorred Jgainst order,
(FOR 1960)
FI:"ITtES. WOR:IotS. TR.\CE
):\ TOLOG Y
r:'R\I,\FROST•. \rthur I-r.
REF.' OR FOl'R·.\xIS LSI,
din:; H new species. fromiorm:u!uns of the Shcn:.n-
)\·ICI.\:" OSTR.\COD,\. fohn
S. FisherEI'OSITS IS' QUARTZ MosIDUTIl, MOST,\:-;A. Forbes
:. J. Sllbcrling :lIld R:liph
..:\bitre:unsORTHER:" \IISSISSIPI'! E:IoI-
:,\OLI:"ITtC CL,W DEPOSITS
;0 TilE PACIFIC yL,ltCIS OF
"OIl.SI.\, John H. Spottsarold E. :\l:tldc :loci Howard
; ISSUES
:5 SrRATA OF TilE WESTlOIO;
1026 M. E. ~IORIS:\Wr\-GEOMORPHOLOGY, APPALACIII ..\N PL>\TEAU W:\TERSHEDS
drainage features. Following Horton's lead,Strahler (1952; 1957; 1958), V. C. Miller(1953, unpub. ms, Columbia Univ.), Schumm(1956), and others developed quantitativemethods by adding new parameters and investigating regional variations in morphologyin a wide range of geologic and climatic envi·ronments.
Accurate prediction of stream flow undergiven precipitation conditions has been a goaltoward which hydrologists have struggled. Thisgoal seems impossible to obtain because of thecomplexity of factors (climate, vegetation, soilcharacteristics, and topography) which deteanine runoff. However, \Veather Bureau dataon frequency, duration, and intensity of rainfall have made it possible to draw up empiricalequations for rainfall-runoff relations. Soils research at many experiment stations has produced infiltration-runoff equations and quantitative determination of influence of type :lOdamount of vegetation. The geomorphologistcan conrr.ibute by determining the importanceof the topography of a drainage basin. Geomorphic characteristics must be measured andstudied to establish qU:l11titative relationships.
.Although it has been acknowledged thatgeomorphic characteristics of a watershed influence its discharge, this relationship has not beenstudied quantitatively until recently. Sherman(1932) illustrated that basins with differentshapes and slopes gave different unit hydrographs, but he did not quantify the relations.Langbein and others (1947) measured parameters of drainage basins and showed a mathematical relation of drainage area to discharge.Potter (1953) u,ed length and slope of prineipalwaterway as the geomorphic factor in a multipleregression on peak flow. ;"'[ore recently, Leopoldand ~[addock (1953) and Leopold and Miller(1956) have drawn up quantitative relationships of stream flow to width and depth ofstream channels. The present study was undertaken in an effort to establish mathematicalrelationships between quantitative geomorphicfactors of a watershed and stre3Jll-flow characteristics. In addition. this detailed analysis ofrepresentative basins will put the regionaldescription of the Appalachian Plateau prov~
ince on a quantitative basis.Fifteen basins, ranging from 1.5 to 550
square miles, were chosen for study. Basis forselection was fourfold: (I) Stream-flow recordswere a necessary part of the daraj therefore,only gaged basins were used. (2) Watershedswere chosen for which modern, large-scale
maps were available. (3) In an e£fore to minimize variables such as lithology, structure, andclimate, all basins were solected [rom withinthe Appalachian Plateau province. (4) Be·cause one of the main objectives of the studywas to relate stream flow to geomorphology,most of the basins smdicd arc among those usedby POlter (1953) to determine an empiricalregression for lO-year peak fiow.
This investigation was sponsored by theGeography Branch of the Onice of Naval Research, Project NR 389·042, under contractN 6 ONR 271-30 with Columbia University.The writer wishes to thank Prof..-\. N. Strahlerwho supervised the project. Professor Strahlerand members of the Scmin~r in Geomorphologyat Columbia University during the years1954-1955 offered valuable criticism and ad·vice. Amy M. Garthly assisted the author inthe field season during the summer of 1954 andj\'frs. D. :\. Norton assisted in the field 5<::lson
of 1955.
GENERA.L DESCRIPTIO\,OF W.HERSHEDS
fVat~,slz~di Stlldi~d
Drain::lge basins studied lie in three divisionsof the .-\ppalachian Plateau province (Fenneman, 1938): the Allegheny ~(ountain division,the Cumberland Phlteau division, ::lnd the unglaciated .-\llegheny Plateau (Fig. 1).
The Allegheny ~(ountain di\·ision is theeastern section of the plateau and extends in anarrow strip from northern Pennsylvania tocentral \Vest Virginia. The stfJra. are gentlyfolded; eroded remnants of Jnticlina.1 archesnow form ridges; synclines Jre represented bybroad plateaulike areas. BecJuse mJn)' basinsare eroded anticlines, steep SCJrps bound theouter divides, wher~s a more gendy rolling surface forms the center of rhe basin. Higher surfaces are dissected to maturity with great relief.Basins studied in this division include those ofGreen Lick Run, Pennsylvania: YoughioghenyRiver, Casselman River, and Big Pine~' Run,~'farvland; and Blackw3rer Ri\·er, \VestVirg~nia.
The unglaciated Allegheny Pbteau division,a westward continuation of the :\lIeghenyMountain section, is a shallow regional synclinein which beds are almost horizontal. [[ ismature and has fine texture and moderate-to'great relief. The surface is rugged; dividesare long and linear wich intermittent areas ofrolling upland. Valley flats are narrow and
confmcd to taltaries. Stream \slecp·sided. M,gradients dccrtdivides are bro.dJis region inchCreek, Beech (
Skin Creek andLittle Mahonin:Pennsylvania.
The Cumber!ward extensionPlateau, includ(Plateau whichKentucky Rive333). This sect:
Figure 1. Index map showing loc::uion of basins studied.Am-Allegheny .'vlountJin di\'ision: :\-:\llegheny PlatCJUdivision. ungbciJecd; G -.\llegheny PlJee:lU division,gbci:aed: C-Cumberbnd PlJteJu di\'ision; Cm-Cumberland )o'[ountJin division. BJsins arc numbered:ls follows:I. Green Lick Run. P::I.: 2. Pine\' Creek. ;vfd.: 3. Cassclm:lnRiver. )O[d.: 4. Youghioghcny River. )o(d.; 5. BbckwaterRiver. W. V:I.: 6, TJr Hollo\\'. Ohio: i, Home Creek. Ohio;S. Little )o'(ill Creek. Ohio: 9. Beech Creek. Ohio: 10. SkinCreek. W. \'::1.: II. Little )Obhoning River. P:I.: 12. )o'(iddleCreek, W. V:I.: 13..-\lIegheny Ri\'Cr. Pa.; 14-. DaddysCreek, Tenn.; 15, Emory Ri\'er, Tenn.
1027
Emory River and Daddys Creek, Tennessee.
Collection oj Data
yfc3suring stream geometry and other geomorphic features in the field is laborious andtime-consuming. \Vork in quantitative geomorphology would progress more rapidly ifme3Surements could be taken directly fromtopographic maps. However, an investigation
generally flat or sltghtly rolling surface, incisedby steep, youthful valleys. The undularorysummit indicates a peneplain correlated withthe Schooley, here called the Cumberland.Relief is Iowan upland areas, but deep ravinesgive total relief as great as 2000 feet. \Vatersheds studied in this region are those of the
CENER:\L DESCRIPTION OF WATERSlJEDS
Skin Creek and ~liddle Fork, West Virginia;Little ~fahoning Creek and Allegheny River,Pennsylvania.Th~ Cumberland Plateau division, a south
ward extension of the unglaeiated AlleghenyPlateau, includes that part of the AppalachianPlateau which lies within and south of theK.entucky River basin (Fenneman, 1938, p.333). This section is a broad upland with a
con~ned to larger strt.:ams and major tributaries. Stream valleys arc generally narrow andsteep-sided. tvfany arc deeply incised but thegradients decrease ncar their heads, nnel rhedivides are broadly rounded. Basins studied inthis region include those of Tar Hollow, HomeCreek, Beech Creek, and Mill Creek, Ohio;
;\TE:\U WATERSHEDS
lble. (3) Tn an effore to minieh as lithology, structure, and15 were solected from within
Plateau province. (-0 Bemain objectives of the study
'e:lm flow. to geomorphology,s studied arc: among those used.) to determine .an empirical-year peak flow.ltion was sponsored by thech of the Office of Naval Re\"R 389-042, under COntract:0 with Columbia University.s to thank Prof. A. N. Str.ahler:he project. Professor Strahlerhe Semin~r in Geomorphology:niversity during the years:d valuable criticism .:lod adJar[hly assisted the author inuring the summer of 1954 and:on assisted in the field season
SCRIl'TI01\EDS
o.:d
1S studied lie in three divisionsian Plateau province (Fenne.-\!Iegheny ~\'[ounrain division,Pbteau division, and the un
:ny Plateau (Fig. I).v ~[ountain division is thet the plateau and extends in a1m northern Pennsylvania to
[ginia. The strata ;re gentlyremn3.nts of anticlinal arches; synclines are represented bye Jre:J.s. Bec;lUse many basins:Iines. steep SC3rps bound thell':re3S:J. more gently rolling sur:nter of the basin. Higher surd to maturity with grC.:J.t relief.1 this division include those of. Pennsylvania; Youghioghenyn River, and Big Pine>' Run,
Blackwater River, \Vest
:d :\Hegheny Plateau division,ltinu3.tion of the Allegheny11, is a shallow regional synclinearc almost horizontal. It isfine texture and moderate-tole surface is rugged; dividese:J.r with intermittent areas ofVaHcy flats are narrow and
1028 M. E. MORISAW,-\-GEOMORPHOLOGY, :\PPAL-\CHIAN' PLATEAU WATERSHEDS
taking logs of bo
log .vu
substituting
lac
But equation (l~
sion of the regr l
which the (og:Hiplotted aga.inst I
we obtain
.od
~13XweIl (1955)can be equatedslope of {he regrlon order. EquJtl
y
Horton (194:number of sue:basin form :tn ill'the first term ibifurcation ratio.ffi3cicJUy :15:
Figure 2. 'stream on
\
in Figure 2. -Iample, is c1aSSt.though not con.upstream fromsegment.
relief ralio, ratio of tot:11 relief of:1. basinto its longest dimension parallel to theprincipal drainage linemean dischargc in cfs for :t basinpeak discharge in C£s for a basin
H.higher order. n--
n .. .,.l
aVer.:lgc toG11 relief of basin of order II
total relief ratio. ratio of relief of a b:1sinof order 11 to total relicf of basin of next
Sstreams of ncxt higber order,~
.') .. _1
miles of all stre:uTIS in a basin to arca oEthe basin in square milesconstant of channel maintenance, arca infeet required to main min I fOOL of drainage channel; reciprocal of D, in feetfrequcncy I or density, of stream of order0/; number of streams of a given orderper unit arcabasin circularity, ratio of the. area of abasin [Q the area of a circle with theperimeter of the gi\'cn basinchannel gradient of order ti, tangent ofthe vertical anglc at point of measurcment; or ratio of fall in feet to length ofchannel in feetslope ratio. ratio of me:ln gradient ofStreams of order u to me:lll gradiem of
_\!orpllOm~lric Prop~rli~s
~[orphome[ric properties were analyzed forconformity of these watersheds to the laws ofdrainage composition. In this paper Streams areordered .ftcr Str.hlers (1952. p. 1120) .d.p·[ntion of the Horton (1945. p. 281) scheme ofclassification (Fig. 2). Small finger-tip tribu·taries are designated as order I. Two first-orderstrcams unite to form :l sccond-order segment..-\ third-order segment is formed by junctionof twO second-order streams, but may be joinedby additional first· or second-order segments.Two third-order segments join to form afourth-order segmcm, and so on. The masterstream is always a segment of highest order. :\basin is designated as of the same order as themaster-stream segment.
The placement of stream·gaging stationsproduced complications. These stations :Ire not.in general, loc~lted at the end of a stream segment and therefore the gage does not measurea complete basin of a given order. In all watersheds studied gauges were located as indicated
B.\SI:\ ~IORPHO~IETRY
R.
c
f . d L.streams 0 next higher or er,::r--LJ,..,.1
h· 1 d ::t.next Ig ler or er, =-.-1. .. +1
D drainage density, ratio of total length in
~ L.. towl cumubli"e length of :111 streamu = I segments of :'Ill orders contained in basin
of order II
RL stre:1.m-length ratio, ratio of mean lengthof Stre:1.ffiS of order tt to mean length of
7:... me:m length of stre:tm channel seg;mc:ntsof order u
~L.. total length of all stre:lffi segments oforder 11
::r.. mc:m area of b:lSin of order tt
R,I basin-area ratio, ratio of mean arca ofbasin of order tI to mean area of basin of
,V..of next higher order, -,,-
I .. + I
of accuracy of topographic maps (~loris.1.wa.
1957) indicated discrep:mcics between streamlengths or number of streams determined fromtopographic maps and those determined in thefield. Hence, all maps were checked by fieldmeasurements, and stream networks were inserted from field scudy. Air photographs werealso used [or checking stream networks andsuearn heads. In the field, stream lengths weremeasured with rape, and slopes were determined widl Brunton compass or Abney handlevel. For comparison with map measurements,lengths were computed for horizontal distances.Areas and perimeters were taken from coceened topographic sheets by planimeter andchartomcter.
Runoff data were obtained from C. S.Geological Survey \Vater-Supply papers. Datagathered from the rime of establishment ofgaging station to 1955 were used to determinemean annual runoff and peak How. Periods oftime covered bv these records varv from basinto basin, the sh~rtesr period being' 8 years, thelongest 34 years.
LIST OF SYMBOLS .~:\D DEFII'ITIOI'S/I order of basin or stream segment de
noting level of magnitude in dr:1.inagenetwork hierarch,'
i highest order within :t drainage networkN.. number of streams of order !I
R~ bifurcation ratio. ratio of branching in :tdrainagc nctwork: ratio of number ofStre:tffiS of ordcr !/ to number of streams
I.~,
·,
BASIN MOIU'IIO_\IETR Y
(2,)
1029
ratio is the antilog of the slope of the regressionrelating log number of streams to order. :\1though the basins arc not complete 10 thehighest order, the points ploued neverthelesslie on :t straight line. Bifurc::J.tion ratios wcrecalculated by melhod of least squares, ::J.nd regression lines werc fined by eye.
For the Skin Creek, Blackwater River, and~liddlc Fork basins, only randomly selectedthird-order basins were measured. If the bifurcation r:ttio of a watC'fshed is constallt, thebifurcJ.tion ratio of a smaller watershed withina larger one should not differ significandy fromthat of the tot:d basin. This inferellce wasverified by a paired [-test (Croxton, 1953, p.240) of difl"erences between bifurcation ratiosof tOl:t1 basins and mean bifurcation ratios ofthird orders in e:tcll basin. Dara from thcseb.1Sins. then, indicatc rh:tt the number ofstreams of each order above any point on amJin stre:tm forms :t geomerric series wirhorder, :lnd th:H the bifurcJ.tion r:l[io for a givenwatc:rshed tends (0 be const:Jnt.
:herage stream length conforms lO the lawof stre:lll1 lengths (Honon, 1945, p_ 291): The:t\"crage length of stre:lms of erich of thedifferent orders in :1 drainagc b:1sin tends roc1osd~' approxim:llc a direct geometric seriesin which tht: first term is [he average length ofStreams of the first order.
which is the regression equ:ltion of log me:1I1stream length on order. Hence. length r:ttio istht: .:Jntilogarithm of the slopt: of the regressionof log me:ll1 stream length on order (Fig. 4)_The length of the highest-order segment w:tsnot plotted because this leng th to g:lge is lessthan the actual length of the complete seg·men£. :\ paired [-test showcd no significantdifference between length r:l[ios obrained fortot:ll basins and thosc obrained for randomh'selected third-order basins in rhe 5:lme wate;·sheds. Length ratio, then, rends to be constantfor an individual b::J.sin.
Figure 5 shows log cumulative stream lengthsof c:lch order in :t basin plotted against order.Straight lincs. fitted by eye. seem to bcstdescribe the regressions. Hence, log totalcumulative srream lengths, from first through
Csing the same method of mathem:ttic:tl:tnah-sis :ts that [or bifurcation ratio. we obt:lin
(I)
(1:1).Y,... Roo
raking logs ot" borh sides
log.Y~ .. i log Ro -!l log RI>, (ib)
and
substituting
b-logR,.
i\faxwdl (1955) showeu that bifurc:llioll ratiocan be equalt:u to the :lluilog:lridlll1 of b. theslope of the regression of log number of srreamson order. Equ::J.tion (I) can be \Hittcn
we obtain
Horron (1945, p. 186) suggcstcd th:n thenumbt:r of stre:lms of e:lch order in a 2i\'cnbasin form an inverse geometric series in \~hichthe first term is unitv and the ratio is thebifurc:ttion r:llio. Horron's law is stJ,tcJ m:Hhe'm~Hicalh- :IS:
,: .. i log Ri>
rigurt:~. Slr:Jhkr's (1952) syS[t:m ofSUt:lIl1 ordering
in Figure 2. Therefore, Tar Hollow, for ex:llllplc, is classed as a fOllrth-order basin, although nOl c.omplere because the g:tge is pbcedupstream from the end of the fourth-ordersegment.
log N. s a - bll . (Ie)
But equ:Hion (Ic) is also the cmpirical expres·sion of the regression shown in Figure 3, inwhich the logarithm of number of streams isplotted against order. Hence rhe bifurcation
J W:\TERSHEDS
h· h d S.t 'lg cr or cr,~.')~ - I
::lief of b.1sin of order II
10. ratio of rdief of a basinotal rdicf of bJsin of ncxt
Ti~
it" _ I
_lO ()[ tot,d relief of:J basindimcnsion paf:llld to the
l:l2C line': 70 ,is for J bJ.Sin: in cis fOf :l bJsin
Hio of mcan gradient of.cr II to mcan gradient of
[yo ratio of the area of 3
:rca of :J. circle with the1e gi\'cn b:lsin'm of ord~r II, tangent of19!C :1( POlOt of mC:lSUrc_ot f:lll in fcet to length of
calllS in a b:lsin [0 3re:t o!u:J.rc milcsIOnd m:limClI:lll'CC, arca ino maintain I foor of drain_:ciprocal of D, in feetlensity, of Slre:lln of orders[re:lIns or :J. given order
ETRY
erric.:s were :1I1alned for·.1lCrshcus to the' laws ofIn this paper streams arc·s (1952, p. 1120) adap'1945. p. 281) scheme ofSmall finger·tip tribu-
,order I. Two first-order:I .second·order segmenr.[ IS formed by junction·cams. but may be joined
second-order segments.me:l1(S join to form :t:lnd so on. The master
TIcnt of highest order. .-\of lhe 5:lme order as rhet.
sue:tm·gaging stationsIS. These srations are nor,the end of a stream segIe gage: does not measure!i\'cn order. In all warervere locHed as indica red
;;
,~ z-> I00
" ,.
oL~_..,:~"
~L .. • I
Figure: 6. Log nlisted in Table
'I• Is: 4-
~
"•,
Figure 5. Log meanlisted in Table 1.
where the anrilog of
R,P • R;,log-I" ~ RL - Rb •
Hence, the slope of the regression relating logcumulative stream length and order is a constant equ~d to the length ratio minus bifurcarion ratio.
The total of all strC:3.m lengths of a givenorder (and that order alone) is also empiricallyrelated to order by the regression
log ~ L.. = a T btl.
Taking the logs of both sides and substituting3S in equ3tions (I) and (2), we find th3t (3.)equals equation (3) and t~at t.he an.tllog 0.£ bin ~qua[ion (3) is length ratio mulUS bifurc3CionratiO,
(3)
(3.)
(3b)
L w - a + bll .
RLw - R"w R".---R~ Rt.-R,,·
log
·~0,·"z~
,E•~z0
3
z
Figure 4. Log mean stream length plotted against order. Letters along abscissa representbasins listed in Table I.
, r----,--r-......--,,.-...,.....--,--,---,--------,-,.----,----,
o 11 0 E R
Figure 3. Log number of streams ploned against order. Letters along abscissa represembasins listed in Table l.
•o.;z
or, where u = i and p
:. - I
Horton (1945, p. 293) states that
a given order within a basin, are directlylated to order by a line:J.r regression,
1030 M. E. MORISAWA-GEOMORPHOLOGY. ,\PPALt\CHIA!\" PLATEAU WATERSHEDS
1031
J
1
!
" ...Q'~U
This. In turn, is equi\':llent to the regression
The !:Iw of basin areas is stated by Schumm(1956, p. 606) as follows: d1C mean drainageb:lsin areas of strcams of cach ordl:r tend toclosely approximatc a direct geometric sericsin which the first tcrm is the mcan arC:l of firstorder b.:lsins:
ORO E 11..
BASIN 1I.10RPtIO~IETRY
! '
. // .
1';/~. . I /. /
/
"~ ,- .,
///" / /2
zJ- !'/!I/j<
: /:, .,
'j:/ / ////J; ,-u I>
I/II//I/!• j" "~
./,-
01 , , , ," " H "' .. " .. .. '"o Fl 0 f:" 'M
QI~er
Figure 6. Log mCJn bJsin :lreJ. ploltcd :lgJinSI order. Lettcrs along Jbsciss3 represent b:lsinslistcd in Table I.
Figure;. Log me:Jn rOlJI Slre:lln length ploued Jg:liost order. Letters :lIang :lbscissJ. reprcsent basinslisted in TJblc J.
"· •;•~"> ,<
"•••" ,L~~
I; !o.· />
•
J.I~ , .I
whl.:rl.: the :lntilo~ of b is Horton's p f:tetor,
,".
This follows from :l mathcmatic:ll :Illalysis ofHorton's equality (1945. p. 191):
:::'L., _ LR.:-"R,.',-I . (-b)
wherc. ;lg:lin. equation (-b) C:1I1 bl.: reduced lO
equ:ltiOll (4).
,j
/
JOscissJ represent
j
cam It.:llgths of :l gi\'enllont:J i~ :11,,0 empiric:llly
(cgrl.:"'loll
go. - g...
: I.. '" .1 - h,.
le re~rcssioll rc!:lting logIgth :lntl orde.:r is a congrh ralio minus bifurca-
th sides :lnd substituting,J (2), \\'c lintl that (3a)nJ th:n the.: :llltilog of bIt [alia minus bifurcation
:\U W.\TERSI-IEDS
19 ;)OscisSJ represcm
1032 r-.·L E.. MORISAWr\-GE.OMORPI-IOLOGY, APP:\LACHIAN PLATEAU WATERSHEDS
shown in Fis plotled a:
Hence, art.{he rcgrcssi
I{is cviu,
lines [0
strcamcloselyPlateau.
Chanlistic of .geomciitangentmeasure
J WATERSIlEDS
POCONO
C:.TSKIL!..
1033
Mill Creek
ALLEGHENY
~LE
Daddys Creek
CATSKILL
::mory R.
CONEMAUGH
Youghiogheny R.
?iney Creek
bw. Some watersheds swdicd show tha[ archuionship of rnc:m channel gr:ldicm andorder can be expressed by :l straight line. Insuch cases (Fig. 7) rhe regression of log me::mchannel gradient on ordcr is
log 5" "" II - /III . (6)
:\lso we can formulate a law of slopes: dlC meanchannel gr:ldien[s of c:lch order form:ln inverse
ALLEGHENY
with a tapc and clinomc[cr. or hand level.Channel gmdicm is the average slope of theentirc segmenc \Vhen [aken from a map, fall infeet was di\'idcd by horizont:d leng[h of stre:lmin ft:cl.
Horton (1945, p. 295) infers ,hat the relationship of strc:lrn-channcl gr:ldicn[ and ordercan be expressed by an inverse geome[ric series
\....CATSI(~LL
-----:HEMUNG
--~~'--
ALLEGHENY
Home Creek
CONEMAUGH
~L.L.EGHENYCL.ARION
8eech Creek
BASIN MORPI-IO~IETKY
6"lCEVILLE
_____ CATSKILL
\:CHE~UNG POTTSVILLE~
;>OTTSVILLE
ALLEGHENY
Casselman R. MAHONING
VINTONJ.LLENSVlLLE
" BYER",---CUYAHOGA
Tor Hollow
CONE "lAUGH - :C:'~o:s:s:v~'L::L::'=- _MAHONlNG
:.LLEGH(NY
-:;:-----:C~L~.~'~'~O~N ...::.2!'2'~'F.~,...,c;:;::c::::_=__;:_:_POTTSVILLE "OTiSVILLELittle \tononlnq Cr.
FIb' \;onSYM<l MAUCH CHUNK
500 POTTSVlLLE
Green Lick
Figure S. Strc:lI11 profiles along longest length
FEET
o 20.000 Allegheny R.,
~ '_O_C_K_C_"_·_'L_' -"~::.:~::.'~ _SCOTT CROSSVILLE
WART3UOlG
lines [0 the preceding d:H:l th:l[ the bws ofsuearn numbers, lengths, :lI1d :trc:l.S :lpplyclosely to w:Hersheds of the .\ppabchi:mPla[(~:lu.
Channel gradicn[ is an impon:llH ch:lracteristic of the vertical aspen of dr:linagc-nc[workgeometry. Ch:lnnd gradien[ here refers [Q therangcll[ of the vertical :Ingle .H the poim ofmcasurcmCIl[. In dlC field. slopes were measured
Hence, arc;;! ratio is the ::1I1tilog of the slope ofthe regression of log basin are:l :lod order.
It is evident from the excellent fi[ of suaiglH
shown in Figurt.: 6, where log mcan b:lsin :lrcais plotted against order:
}"!og=--a+hll.
:11
=
=
0::
W
o0::
o
1034 I\f. E. MORIS;\WA-GEOMORPHOLOGY, APPALACHIAN PLATE,\U WATERSHEDS
Figure 9. Average cotal relief plolCcJ against order. Lctters along each abscissarepresent basins lisced in Table I.
geoffilterm:md d
Th.log to.\vcr:form~
firstbasin.
The l
slopeordercontrline i,~ grl~ prwe:u!faces.
B~press l
basinordetnon.'in fl
SISt::1l
~ral\
the UIpected
,Is ,that I
IifredBreakbeamomllowerreJuVl
Fig1
of StH
ugraprelatilseen. Iprofil,laredand Igradil'part 0
law heg.r.1d.ilt1nult
there:gradilhomochann
,.
lONE
ORDER~-
ER
bcen established in streams of Virginia andMaryland (Hack, 1957, p. 89). Differentialresistance to erosion of horizontal rock byersmay well account for these brcaks in the slopecurve. r\ stream segment flowing through athick, resistant stratum may be stcepened
although the gradient may bc less upstre:lmon the stratum. Also, wcathering and slopewash may more easily reducc slopes on highersurfaces, whereas lower slopes may be prmcctedby more resistant layers. This helps [0 naw~n
(6a)
~.
ORDER
LM DCy
151 I
2.0
15 A CR
2.0
2.5
2." ////1/
3.0
S.. .. "S,R/- tl•
MC3.01 TH HC BC GL PC f
Howevcr. aU basins studied do not form a
geometric scries with order, where the firstterm is gradient of the first-order segment andthe slopt:: of the curve is the slope ratio, or
straight-line ploe of stream gradient on ordcr.The deviations from a straight line may beexplained by one cause or a combination ofcauses. The close relationship between lithology, structure. and stream gradient has
I
il,~I I-
wWll..
ll..-
W--.1W0::
-.1<J:I-0I-
190-.1
(8)
(9)
1035
Logc+dZ,I.og X
LogY .. Logll +bZ
Creek watersheds show benching in topogr.:lphycorrcsponding to breaks in the relief r~ti()-order
cur\"C where rcsist~nt 5..'lndstones occur. Ingeneral, resistant laycrs decrease [he rdicf r:ltioby disproportionately decreasing height andincreasing lenglh. Huwcver, relief ratio docsdecrease with incrensing order :1I1d, if a b.:lsin islithologic:llly homogeneous, log rdid ratiotends to form a straight linc when plottedagainst order.
Basin-shape factors h;l\'C been formulatedfor use in quantit:ni\"c geomorphology. Circularity was chosen for this study as the mostuseful shape measure in correlation with streamflow (\f~risa\\'a_ 1958, p. 591). Circularitywithin a basin seems to be indepcndl.:nt ofordcr (T.:lble 1)_ Ho\\,e\'cr, Ile:trlless of circu"bril\' tends to incre:l.')C to third order and thendccr~asc. so thJt higIH:r-order b:lsins arc generalh- kss ne:lfh- circular than lower-order b:lsins.It -seems un~e:lson;lblc that in a rcgion oftkndritic drainage, large. higher-ordcr basins~hould hc le~s m::trh- circular in outlinc. :\<:\'erthdcss this is so bel::lll~e of thc dclll1ition ofb:t'iin circul:trity. Length of the perimeter de"pcnLls upon crcllulations in basin outlinc. orupon {I.:xturl.:. In gcncral. smaller basins ha\"I.:It:ss crclllll:ltcd outlines than larger OIlCS. Thus.cirl:ld:Jrit y docs not gi\'e a true picturc or basinsh:lpt.'. but rathcr of an incre:lSC.: in crcllul:uionof pcrimctcr. This is \\'hy circu!:lrity of higherorders appC:lrs (0 dccre:lsc.
Dr:nllage dcnsity reprcsents Icngth or streamdunnd pcr unit area in the warcrshl.:d. Dr:lin:I~I.: dcnsity docs nO{ scem to changl.: regubrl~'
with order within ba"ins. Howc\·er. draimgcJCllsitv or (Ot.:ll b:lsins tenus to ~pproximate them('":l11 -dr:lil1:.lgc dcnsil\' 0' 'rst=Or r basins inthe w.:ltcrshe~1. Hack' ( 57, p. 66 suggested[h:1[ Jrain:tgc density or - r b3.Sins :1I1Uthal or highest order in the S:.lme watershedarl.: cqu:tl..\ paired {-[('"st comparing wtal drainage densiry with first-order density in theseb:lsins showed no significant difference betweenthe two \':1Iues anu supports H;1ck's obscr\"ation.
Since number of streams, length, and are::J.within a basin arc all exponentially rcl:Hed toorder they ought co be rela[ed [0 each other.:\ny twO exponential equations expressing therelationship of properties X :tnd Y to Z are of[he type
(,)
BASIN ~IORPIIO\IETRY
the upper part of the profile lIlorl.: than expected.
As·a CJuite Jin"erenl causc, m.: ll1ay postulatethat the i\ppalachian Plaleau has been up·liftcd and thc streams thereby rejuven:lted.Bre.:lk-in-slope curves may thus conceivablybe a result of rejun:nation, slarting ;1t themouth :1l1l1 progressing 1l(:aJ\\'ard_ Hencc,lower-ord('r scgmellls may not yet have beenrejuvenated.
Figure S shows profiles plotted ;llong lengthof SlrC;lm channel from head to mouth. Stratigr.:lphy is indicated on each profile so th:][ [herebtion of lithology to ch:1l1ncl slope can beseen. In each watershcu. change in longitudinalprofile or in gradicnt oruer cun'c can be reI:lteu to change in litholog~·. HO\\"C\'c.:r. aho\'e:llld bclU\\· thc brc:lk in curve. log strC:llllgrauicnt and ordcr form a slfaightlinl.: for lh:][part of thc basin. Thus_ thc rd:ltion or til(: slopelaw holds ror that part of tilc (un'e whcre thcgr:ldiellt is 011 hOlllogt:lleous rOl:k. Tllc discontilluity on:urs :ll :1 ch:lnge in lithology. \\·cthcrdon: lluxliC\· thc bw ul stn:al11-dl:llllld~r:ldicnts to n::IJ": In .1 w:llcrshcd de\·doped onhomngcllcClll'i lithcllllgy and SlrUl:turc. stn::ll11,halllld gradil.:nts or c31'h order form .Ill ill\':r~c
!.:co/llctrit.:: scrics with ortlcr. whcn.: thc lIrstlefln is the gr:ll,.iiclH of the lirst-oflkr ~Cgl11ClHJIH.I thc slopt: of tllc ..::ur\"e is thc slope r:ttiu.
That :1 lilll.::lr rd:ltionship :dso cxist'i bctwccillog t(Hal rdid :Illd ordcr is ~hO\\"ll by Figurc 9..\\"t:r:lgc tol:d rdid' of ha,ill'i or C:lI:h ordcrrorms a dircl:t ~colllctric ~crit:~ ill whidl thctirst tcrlll I' ;l\·Cr:I~C rdid of lhc tirsl-onlt:rh;lsin: .
Thc Wt:Jl relid rallO. Ru. is lhe antilog of theslope of the rcgre'sioll or log total rdief onordcr. .\!though lithology I.:viuently CXl.:rts acamrol. :lS 'ihowl1 by tleparturcs rrom;) straightline in scvt:r:ll of lhe basins. ils inl1uencc is notas ~re:lt 3S in thc casc or strC:IlTI ~r:tuil.:nl. Thisis prob:lbly cJused by the adJeo clrect ofweathering and nl.:lSS grad3lion on basin surfaces.
B\' contrasr. rdid ralio. which IS an exprcs~ion or heisht-Iength rebtiollship of :l
basin. shows the same dC\-i:llions 3S gradientoruer. .\gain, lithologic control is the explan:tlion. Green Lick basin shows:1 striking changein relief ratio [rom low-ordl.:r basins 011 resislanl Pottsville to higher oruers cuc all\buch Chunk Shall.:. Emory River:mu Daudys
ilent ll1:lV be less upstre3m\60. \\T~lthering JnJ slope
ISI!y reduce slopl.:s on higherI\\"(:r ~Iopes may be protected!:l~T:S. This helps to llallen
ONEOROER~-
In stre3rns o[ Virgini3 :lud1957, p. 89). Differenti,1
)11 of horizontal rock byersfur these bre3ks in lhe slopese,g1ll1.:1H !lowing through atratulll may be stcepened
l"E:\U W.\TERSIIEDS
1036 M. E. i\IORISAWA-GEOMORPHOLOGY, APPAL:\CI-IIAN PLATE,IU \V:\TERSI-IEDS
TMil.E I. Gf.O'-IORPHIC CII,\!'t.\CTEIUS ncs 0' 15 B.\SI:-:S
S"rUDlf.D IS ,\PI'ALAeIIfA:- PL,\TEAU PltOVISCE " OROEn.
(Su Figure I for loc:ation of basins.)
Avenge i\vcr:tgcstream b:lSin Ciccu-
No. of length :teea Dr.linasc lacil)' Channel Relief
Order strc:tffiS (mi.) (sq. mi.) density r:nio slope: ratio Little ~13honins lP,.
Tar Hollow, Ohio I 74 O.OIS 0.011 2.93 .762 .419 .In2 IS a.OH O.OH -1.82 .671 .369 .150
3 5 O.li3 0.268 2.65 .n-l .113 .OSO; I 0.671 1.500 2.799 ,70-1 .015 .0-18
Home Creek, Ohio I ,0 0.0-19 O.OH 5592 .705 .ISI .149 Allegheny Ri\"cr,
2 Ii 0.115 0.0-11 i.076 .no .087 .IIS
3 6 0.292 0.189 5.897 .786 .025 .070
; 2 0.590 0.555 5.913 .67S .009 .058
5 1.053 1.6-10 5.1"56 .701 .005 .035
Mill Creek. Ohio 10; 0.069 0.025 ;.HO .603 .396 .14822 O.ISS 0.121 i.020 .i39 .113 .105
3 5 0.650 0.551 6.061 .6S0 .039 .065 Skin Cre::k. \\.. '
; I 1.190 1.6S0 5.660 .155 .010 .030
Green Lick, P:t. ,9 0.051 O.Oli 3.7H .590 .134 .07S
" 0.153 O.OSI 5.649 .649 .111 .Oi6 Bbckw:w:r Rive
3 3 0.981 0.690 3.533 .6S4 .076 .07-1 W. \':1.
; I 1.534 3.070 3.645 .6S5 .0-19 .06i
Bccch Creek, Ohio 1 IS6 0.110 0.06i 1.960 .6)2 .031 .029 ~IIJdk Fork, \\
2 55 0.246 0.109 3.S;"6 .114U .020 .021
3 13 0.710 0.819 1.759 .')')5 .011 .013; 3 l.;"fl I 3.ISS 1.1S3 .564 .1)05 .010
5 5.019 18.n 1.838 .500 .003 .00i
Pincy Creek. \lJ. lil 0.104 0.035 3.105 .1)3S .OS4 .1\0 50 that
i7 0.16i fl. Iii .67 -I .0-19 .OS63 19 0.75S 0.761 .6S1 .u13 .060; ; 1.::!19 1.417 .(dl .011 .033
5 I 5.0-1') 1-1.500 3.03S .5')') .005 .011
C:J.ssdlll:ln Rl\·cr. \IJ. 653 O.HO n.o-ll 3.19 j .SIIS .090 .090190 0.167 0.IS1 .61fi .OflS .OS4
3 ;6 0.555 O.SOt) .().. 1 .lH5 .062; \I 1.501 1.559 51 I .030 .045; 3 5.366 11.1.30 .31'J .005 .0206 I 5.492 62.500 3.319 .464 .001 .013
E.mory Ri,·cr. Tenn. 1936 O.06fi O.OIS 6.135 .6";1 .175 .1952 69S f).liS 0.076 5.659 .;"01 .111 .1453 209 0.49S 0.379 6.114 .iOi .0;5 .10i; 38 1.-i2:' 1.-130 5.069 .6-16 .031 .OS9; 9 3.S51 10.-131 .019 .0-42 Hence, 5ub~6 2 3.S-l I :18.396 .005 .019
1.06i 83.1 5.57"; .416 .00; Jnd Jnother
Youghioghcny Rinr. li95 O.LH 0.038 3.-17-1 .594 .051 .090powcr equa
\Id. 2 -152 0..3-10 0.11:1 .S25 .03; .05-1 bolh vJriJI
3 62 0.951 1.005 .60S .01S .]);S herence to:l; 13 1.572 i.079 .565 .00-1 .025 to order.5 ; 5.644 40.S5 3.-169 .H3 .002 .012 Figure 116 1 5.300 134. 3.6i6 .35-1 .001 and ~umul:
D::tddys Creek. Tenn. I 1181 0.116 0.052 -1.066 .663 .Oil .056 lof the reg rl
2 28H 0.2tS 0.1-19 6.207 .681 .041 .0..9 tlve·sUf:;11ll3 68 0.518 0.501 5.620 .692 .028 .027 The rdatio; 16 1.180 3.002 3.974 .634 .013 .023 isessellti:l15 ; 2..301 21.810 .602 .001 .01\6 I 5.612 93.50 2.S74 .513 .0002 .005 inlcrccp[ i·
S[:1n[ of cit
., C
1037
eirell-l:J.rit\' Ch;Il\l\C! Reliefrati~ slope ratio
.6% .140 .160
.690 .074 .107
.822 .01-1 .070
.655 .OOS .028.004 .015
.341 .002 .011
.646 .IS5 .162
.716 .091 .134
.602 .054 ,074
.595 .022 .026.OOS .015.0013 .009
.457 .0002 .OOi
.352
.243
.123
.192
.065
.028
.271
.134
.078
p. 60,). Bl:causc the slope of the regression3ctualh- \'arics somcwhat from 1, const:J.nt ofch:lIlnc'l maintcnancc. taken as the antilog ofthe intercept at log channel length =0, will\'3[\' from C as defincd. Table 2 shows thecon~t:mt of channel mailHenance obtained inthree ways: (1) By definition. constant ofchannel maintc!l:J.ncc is :J.rc:J. in square feet required to maint3in 1 foot of channel length .This is. therefore, the reciproc:t1 of drainagcdensity. (2) .-\milog ot the inrercept of the logcumulative stream length-log area curve :J.t logstream length =0. (3) :\ straight line withslope of 45° was drawn through log totalstream length of highest order, and the antilogof the imcrccpt of this line at log stream lcngth= 0 \\·:J.S taken as C. Table 2 shows that C obtained by method (2) oftcn differs greatly fromC obtained as inverse of drainage density,whereas rcsults of mcthod (3) are in closeagreement with those of (1). lvfethod (3) thuspro\'ides a quick. accurate method of obt::tiningC.
lf a watershed is homogeneous lithologically:lnd structurally. then area and gradient. aswell as length :lI1d gradient. C:ln be substitutedin pairs for.'( and )1 in equation (10). Figure IIshows combined plots for all watersheds of log
( to)
B:\SIN l\(ORPH01\IETK Y
T.\lILE I. Confimm/
:\\'crage :\n:rngcstream basin
:":0. of lellgth arca Dr:l.iu:l.gestrc:lIns (mi.) (sq. mi.) density
1055 0.064 0.028 .~.5H
291 0.209 0.139 4.23075 0.565 0.560 3.95 ..IS 1.351 2.6064 2.825 12.390I 14.987 37.36 2.576
5966 0.057 0.050 3.4891529 0.303 0.152 3.41337S 0.798 0.862 3.309
68 2.475 6.10413 7.045 33.980; 19.950 241.740
~.091 ,550. 2.913
1.3 .03420 .U546 .105
51 .IH514 .109, .!40
511 .o2.sI• .102
.3;2
Order
56
3
Little \bhoning Creek,Pa.
r .\~ i
\liJJle Fork, \\'. \'.1.
ubck\\'alC:r KI\·er.W. \':1. !
Skin Creek. W. \'.1.
5r,
3
)'" .\Lo<,- - • Lo.. -
.... ,1 (, ;:: C
rI.u:;- b Z
"
3
so th:lt
Hence, substituting one basin propt:rty for )'and :J.nothl:r for .Y, we may expect :l scrit:s ofpower equations. pro\'iding, of course. thatboth \':J.ri:J.bles cxhibit consistently good :J.d·herence to all cxponential function with respectto order.
Figure 10 is an examplc of the plms of mean:J.nd cumubti\'e stream lengths on area. Slopeof the regression line relating log-total clImub·tive·streamlcnglh and log area is dosl: to unity .The rdation betwccn thesc two bctors. then .is csscntially lincar. and thc antilog of theimcrcept in the regression equation is the cowstant of channel maintenance (Schumm. 1956.
fE.\U WATERSHEDS
\Sl:-:S
JIU>ER
Ci:.:u·brity Channel ReliefrJtio slope ratio
.:-62 .429 .1i2
.6;1 .369 .150
.77';' .113 .050
.7(}; .015 .0~8
.70; .ISI .149
.130 .05; .115.7SO .025 .070.6;5 .009 .0;5.,1)1 .005 .035
.6lH .396 .HS
.jjl) .125 .105
.6;)0 .039 .06;
.;';; .010 .030
.59/) .13~ .0iS.6":9 .111 .0,6.6;';' .0:6 .074.boll) .0..9 .067
.6;~ .03! .029
.0":0 .020 .on
.5·}) .011 .013
.5...~ .005 .010
.500 .003 .007
.'d~ .OS.. .110
.":-": .0..1) .OS6
.0'1 .1l!3 .01)0
.',';1 .011 .033
.;:::;9 .00; .02l
~I;~ .09Q .090.616 .06S .OS4.(1 .. 2 .04; .062.:::;1 .030 .048 I.3~ci .005 .020.":(j": .001 .013
I.r,":1 .1;::; .195.~f}1 .Ut .14;.;'0;- .0;; .10;.:>":lJ .0;2 .089
.019 .O..!
.005 .019· ~26 .004
.5:)..: .0;1 .090·~~5 .037 .08...M::; .01S .O~S';0; .00.. .025.S-; j .002 .012· is'': .001
.6", .Oil .056
.n.; I .04l .049
.olJ! .02~ .027
.1I''': .013 .023
.',02 .001 .011
.51 j .OOO! .005
resistant bed ealstream which is rcut through it. Iil harder laver Ul
total relier" incrtsandstone formaldiminishes as dlsistant bed slope.increases wherelaver. This resultm'rio and breakgradient on ordein most forms OleThe propertieschancres are theverti~al to horiigradient.
MORPHOLOGOF WATERSPPHYSIOGRW
\krhod 2 is antilength-log oosin 3rt
\lcrhod 3 is 3nu;of -15° rhrough {Or3!
1886916898
14-191861lil51591ISI5HOS180:!9-1i
20-19
,D
T.\IILE 2. Co:-osDI:.'ER:l.lISED II
Olles. We can alrnenlS tend to h.marc nearly cin
lrJjlllcnce oj Lith
W:Hcrsheds idemonstrate thlbasin morphologbe easay seen onof basins. Althostraight line oflength against 01
In the past, re~
"'0
'Within first-order unit basins, then, largerwatersheds are characterized by longer streamlengths. gentler gradients. lower relief ratio,and they are less nearly circular than smaller
lv, means of first-order basin propcnies for aU15 watersheds were correl3ted with each other.Regression coefficients," whcn testcd for probability that.B = O. wcre significant at the 0.05level. Results (Table -1-) suggest that propertiesof first-order basins are relatcd. cach to each,as power functions, just as those in higher-orderbasins:
the first-order basin. Also, we have secn thatmathematical laws of drainage compositiondepend upon parameters of first-ordcr basins.The relationships among properties of firstorder unit bas~ns. arc of in~erest, as comparingthese would c1unlllate any lOhercnc correlationresulting [rom ordering procedure. According-
, ," , ,
lOG AREA (Sq.ft,)
Figure 10. RcI:Hion of basin area to stre:lln length\.... ithin :J. single watershed
,';----i'------:;.'---..;-----'r------i'
stream gradicllt against log basin area and logstream length of each order. Both adhere \\·e11to a straight line. Correlation coefficients weredetermined for the rcgressions shown, and rcgression coefficients pro\'cd significantly dincr~
ent from zero.Simple correlation coefficients for one geo-
..., =~ ~
~
~ ~ 2f---------------/------1~ "z~
"
morphic characteristic on another are shownin Table 3. :\11 regressions with high correlationcoefficients (0.50 or above) were tested forprobability that {j = o. and all were significantat the 0.05 le\-e! of probabilitv. Table 3 showsthat there is a high correlatj~n of basin areawith stream length. channel gradient, andfirst-order stream frequency in these watershedson the Appalachian Plateau, so that largerb3si~s tend to have longer streams with gentlergradients and fewer first*order streams.
Relations within First-Orda Basins
The basic unit in watershed morphology is
1038 ~'1. E. l'o'IORISAWA-GEOMORPHOLOGY, APPALACHIAN Pw\TEAU WATERSHEDS
BASIN ~IORPHOl\IETRY\TERSHEDS
we have seen thatmage compositionf first-oruer basins.Jropcrtics of first.~res(. as comparingnhercnt correlationceduce. :\Ccording_
Ofoocrtics for Jil'wir'h cJeh mher.rested for Droba·iCJnt Jt th'c 0.05;t [h~H properries:0. e3ch [0 each.,c in higher-order
lOS, theil, largerJy longer streamwee relief fatio.Ibe chJn sffiJller
J
onCS. We catl also 5.1Y thal shoft stream segments lend to have steeper gradients and fOfmOlorc nc:uly circular basins.
Inj/uence of Lithology all .\forphology
\V~Hcr5hcds in the ;\ppalachi:lIl Pbteaudemonstrate the elTeets of rcsist:mr beds onbasin morphology_ Ch:mgc in form factOrs (:inbe easily seen on graphs and related to lithologyof basins. Although 5m311, variations from astraight line of points ploned for log streamlength against ordcr indicate that a fbt-Iying,
T"\BLt 1. CoSST,\ST OF CIl,\SSEL ~f.-\I."TESASCt
DF.TER.\Il."ED BV THREE DIFH:RE:>-. ~IETIlODS
1 ~lcdloJ "\kdIOUD 2 3
IS86 3:;60 1990916 1650 97SS9X 3110 10::;0
1449 ltilO 16301861 iS60 20501715 1690 16301591 HUO 1550IS 15 ~4lJl) 1.'i60HOS 1:-20 HSOISO~ 3:-60 H2O94i II~O 10iO
2049 25:;0 2090
_'lethol! 2 is :IOCl]og of intercept of log totJI stre:1mlength-log b:1sin :1re:a CUt\"C :1t log stre:am kngth .. O.
~lcthoJ 3 is :antilol; oi intl"rccDt of:1 line with slopeof 4jo thrOllhh tot:al SlCe:1m kn:;til oi highest nrder,
resistant beo causes an increase in length of astrC:lm which is tlowing on it but which h:J.s notcut through it. Basin area also increascs wherea harder layer unoerlies the surface_ .-\!thoughtotal relief incrc3ses Jespite appear,:lllce of asandstone form.:uion. rate of increase of reliefdiminishes as does rdid r:uio. "\bo\"c .:l resistant bed slopes decre~se. but the gradientincreJ.Scs where a stream cuts through a hardlayer. This results in a sudden inCieasc in sloperatio and break in the cur\"e of log stre.:lmgr:ldient on order. Thus slight devi.:ltions occurin most forms according to ch:lllging lithology.The properties most sensiti\"c to lithologicch.:lnges arc those which express .J. r:ltio ofverric.J.l to horizomal measurements. such ::1Sgr.J.dicm.
:VIORPHOLOGIC.-\L SI:VllURITYOF W.-\TERSHEDS BYPHYSIOGR.WHIC SECTIO!'\S
[n the past. regional geomorphic chssific:ltion
1039
has been b:lscd etllircly on descriptive andqualit.J.tive criteria. Fenneman (l93S) andothers have divided the United Stares intoph)'siographic pro\"inccs on the basis of struc·ture, denud:ttional process, and stage of ero-.sion. BJ.Sins studied in this report lie in threeregions of the t\pp::1lachian Plate:tu province: asdivided by Fcnnem:lll's principles: ungl::1ciatcdAllegheny Plateau, Allegheny Mountain section, ::1nd Cumberland Plateau. Is the separationof these three sections justified morphologicall)'? Arc qualitati\"c differences upheld byquantit.J.tive analysis? Description in quantirative values allows objecti\"e comparison ofsimilarities Jnd differences be[\\,een watershedsand rcgions in which they ::1re located.
Drainnge basins th.J.t differ in sizc, can begeometrically similar. Strahler (l958, p. 292)st::1tes that twO land forms arc geometric::1l1ysimil.:tr if corresponding elements with lengthdimensions arc in the S::1I1lC scale ratio. Tlmt is,if the geometry of two regions is similar, them.:nhematic.:d l.J.ws €If similarity apply, :lnd,hence, aU corresponding properlies with thedimension length, L. must have the S::1me r;Hio.For example. if the ratio of first-order strc;J,mlengths in tWO geomctric::dly similar basins is1.2, thcn the r:ltio of all stre:un lengths of agiven order of the twO basins ought to equal1.2. If the r.:ttio of third-order basin :1((:a of thefirsl \\'atcrsheJ to third-ordcr basin area of thesecoml watershed is 1.-1-4. then the ratio of:lllothcr corresponding basin arC3S in the tWOwatershcds should be 1.14. Th.J.t is,.J.1I r:llios ofcorresponding elements with dimension L~ inthe two similar w.J.tcrshcds should ha\·c thev.:Jlue 1.1"!. FUrlhermore. the ratio of all\"property which has the dimension L-1, such ;sdrainage density. when calculated for corresponding parts of the twO watersheds, will beequal to 1 1.2.
Dimensionless elements such as gradienr.circularitv. :lnd relief ratio. which ~lfe independent of scale. c.J.n also be compared in thetWO simibr basins. These should have approximately the S::1me \"J.lue for corresponding c1cments. For example, if gradient of third-orderstreams in a watershed is 0.082, then thegradient of third-order streams in a w.J.tershedgeomctric.J.lIy similar should .J.lso be 0.082.However, this is the ideal situation. In comp.J.ring real watersheds for sLmibrity, one mustrt'.J.lize that ratio values wiU noc be absolucelyequal.
V.J.lucs [or r:ltios and dimensionless numbersused to compare the sections of rhe .-\ppalachi.J.n
T.\IIL
MORPI-IOU
:\rcaLengthGr.1die:otCircubrit,·Relief ratioDrainage: d
D
"I
many fcatures, tThe)' are [hen di
In comparing[ion with the Cunequal ratio valalthough not veresult in geometrof ratios, L, L~,
within the groupnumbers are alS(similaritv seemsregions.
Unglaciated r\unlike the .-\lleghwidc lange of ,corresponding eIccpt for drainag'consistent in va
"
considerablv. The U, or area ratios, are closenumeric::dl~;. but L-I, or drJinage density,ratios are different from cach other. Dimensionless numbers correspond well and show geomctrical similarity in these propenies. Thusthese two sections are similar to each other in
.'
..I.' .
..
/
, , ,LOG M(.lH !lAsiN 4RE':', SQ. ,r. I to.,)
0,o2
~
°3
,.,
,00~
"•3'•,~,0'3
0,
,
Figure It. Log me:m ch3nnd slope oi 311 b3sins plotted3g3inst are:t and stre3m length of corresponding order
LOG MEAN STR(,l,M LENGTH, FEET
0 1 Io 2 3 4 c
,
T,\BLE 3. CoRREL-\T10:" Co£FFICIE:"o"TS FOR R£cR£sslo:"s OF O:"E BASI:"
PROPERTY 0:" A:"OTHER FOR TOTAL BASI:"s OS ApP.\[,.\eIllAX PLATEAU PROVISCE
10·10 M. E. MORIS:\WA-GEO:\IORPHOLOGY. APPAG\CHIAN PLATEAU W:\TERSHEDS
TotalB:J.Sin stre:lm First-order
'''' length Stre:lm Circubrity Relict strc:1m(sq. m;.) (m;.) gr:ldient ratio rano frequency
Total stream length +.9916Gr.1dienr -.8112 -.6928Circubrirv rario -.6831 -.6498 +.24i6Relief r.u[o - .5750 -.8132 +.1949 +.3579First.order stream freque:nc)' -.8136 -.i545 +.3612 +.5720 +.6406
Plateau studied are given in Table 5. R:nios ofcorresponding elemencs of the ungbciatcd.-\Ilegheny Plateau [0 the Cumberland Platcauare close but nOt identical. Ratios for corresponding basin relief are almost the same, butratios for corresponding stream lengths difler
.-'\TEAU WATERSIIEDS
I~ ?iun::tllH': oruer
I
numbcrs arc also generally unequal, we cansav dut these t\\'o divisions arc not similar andrepresent distinct regions.
QUJnti[3ti\'c morphology of watershedsstudied, then, indic30tes that these duel" regionsare \'ery different. Stream lengths arc longer inthc .\lIeghcny ~lountail1 section, bec':l.Usefolded structure results in long linc:J.r outcropsupon which dr.:tin.:tge is developed. Basins in[his region arc less circubr for the 5.1me reason.There is good correspondence in scale of reliefin the three sections. :\5 onc might expect, theCumbcrbnJ and ungl.:tci:lled :\lIegheny pia·tC:lUS arc more similar then either arc [Q
.\lleghl:llY \(ountain region. Howc\"Cr, qU:llHi·t:ltiq:: col11parison of watersheds supports scpa.rati<:>n of these rcgions into distinct geomorphicsections.
S":Jk:DllllcnSlOli rJ.l:tJ~ 3
I.I/I.I 0.;; 1.-13 1.:;6l:::.iL'!. 1.02 U! 1.39
L b:l/LJ 0.01 0.:-5 I..1S!ill II I 1.10 1.0; 0.9-4/-1-:./ If'2 l.00 1.09 1.09H31 11J 0.97 1.26 UO
1 Cllt, OJ 1.61 1.52 0.94
L IhlDJ 1.12 1.2.; 1.10
)1,/1, 1.04 n.9; 0.93L' J,!I.lz I.H I.~O 1.05
.b/.b I.I~ l.40 1.23
L"nd:IciJ.tedDUll\:lls:on!css .\flef!neny .\lIcghcny Cumbcrbnd
numOcrs P!alcau ~lounlJlll P!J.lcau.inJ o!!!t'r I~ c .709 0.653 0.700
~3 .045 0.040 0.051
U. 3.969 4.210 3.954;rd order R" .060 0.061 0.067
Area Lenglh Relief(sq. mi.) (l\1i.) Slope Clrcul:trity r:ltio
..\rea +.7H7 -.6814 -.5610 -..5429Length -:-.7H7 -.7961 -.6843 -.5103GrJ.dicnt -.6814 -.7961 +.3535 +.8183Circubrit\' -.SOlO -,68-13 +.3535 +.2085Relief ral[o -.5429 -.5103 +.8183 +.2085Drainage density +.3957 +.0023 +.4027
1\·tORPI-IOLOGICi\l. SIMILARITY OF W:\TERSHEDS UY PHYSIOGR,\PI-IIC SECTIONS 1041
many fearures, bur are nor similar in orhers.They are d1cn disrinct regions.
In comparing the :\lIcghcny ~lountain section with the Cumberland PI.:1te3U, we findunequal rJlio v:llues throughout. Total r:mge,:!Ithough not \'cry great, is gre:!t enough toresult in geometrical dissimibrity. E::ach groupof ratios, L, L'!, :lI1d L-I, din'ers cOl1siderabhwithin the group. Corresponding dimcnsionle~snumbers arc also uncqual. Little geomctricJIsimilarity scel11S [0 cxist bctween thcse tworegIOns.
Cngl:J.ciated _\lIegheny Pbte:.lu is .liso \'eryunlike thc .\lIcgheny \(oulHain section.:\ verywide l:lnge of \'alues exists for all ratios orcorresponding dCl11eIHS in all dimensions ex·cept for Jrain3gc density. which is sol11twh:uconsistcnt in \·alue. :\nd sincc dimensionless
T.\lIl.t: 5. R.\ nos SIlO\\ ISG GI,U~ILTlI.lC.\L SI.\llL.\llln· 01' \\·.\T1:IlSIII;OS IS
TIlIlI:E S£CTlOS5 UI' TILE ;\pr',\L.\CItI.\S PL\TI:.\U
T.\lu.r.: 4. COItItf.L.\TIOS COI!f'I'ICIf.ST5 I'OR REL>.T10SSIlII'S OF CIIARACTEItI:>TICS
OF FIRST·ORDER B,\SISS 01' AI·J·ALACIII .... S PL\Tf.AU PltOnSCE
rmt-on.icrSHC:lm
frcquency](l:!icitJ.tio
. J
~o
ht: L:_ or .lrc:.l i.::nios. .:lre closeIt L-', or dr:lin.:tgc densitv,nl from t::lch other. Dimensio;lIrrespond well .:lnci show oeo-. 0
ny 1I1 thesc propenies. Thus11:1 30re similar [0 c:lch other in
')F O:"F. BASI:"
PL\7!:.\(; PaO\·ISCr.:
":lJbr:I~':;1110
_.ji;'()
-. ;7~IJ
I. L"ngl:J.ciatcd .\llegheny PlaJc:J.u/Cunlbcrl:lllJ PI:ltc:IU., Allcgheny ~loun[:lins/CumbcrlandPbtc:lu3..\lIc:;heny ~lountJ.ins,unglJ.ciatcd .\lle:;heny P!J.te:lu
1042 M. E. MORI$AWA-GEOMORPI [OlOGY, :\PP;\Lt\CHIAN PLATEAU Wt\TERSHEDS
RELATIONS BETWEEN GEO~IOR·
PHOLOGY AND HYDROLOGY
Q
have a cloS<.drainage demaintenanceareater chanl,compensatesbigh·drainag
Thus, hyddirectly relaarea, and firinversely retariry, and rlbe expressedpbology of a
j\llultiple Cor
Runoff inthe combimclimate, veg l
raphy. Hencously takingconsideratiol(1953, p. 69discharge u~
and rainfall.basins in thetion fac tor \been testedin these basi
Tbe rainIP'rano, is dtrainfall imeJcurrence intto similar v;
. fall records1953, p. 68).the S-ratio, !
of the prod.of excessiverecurrence rvalues deri,·for Columb.
The [opo~
by Porrer isstream to s'!
MeanPe::ak ~lc::an ::annualflow runoff discharge(d,.) (in.) (,k)
:\rea .9480 .7828 .9865Tot::allength .9574 .7484 .9838Circu!::ariIY -.5378 -.6590 -.6997Relief r:llio -.5724 -.~52S -.3475Dr::ain::agc density -.2496 -.2992 -.2032COIIS[::ant of channel
In::aintcnancc .2498 .3022 .213lSUC:lffi frequency -.58il - ..;496 -.6132First.order
frequtney -.i214 -.6214 - .8386Bifurc::ation r:ttio .2630 .2064 .1000GrJdienr -.0327 -.;470 -.7912
determined for regressions on e3ch hydrologicfactor (Table 6). Regressions were tested forthe probability that {3 = 0, and were found tobe significant 3t the 0.05 level. :\rca and stream_length [actors, as expect~d. are ~e~y closelyrelated to stream flow. Baslll shape IS Influentialin determining discharge and runoff intensity.Close correlation with stream frequency reflects the fact that more streams per unit areaenable runoff to proceed bster, because thestream network can carry a brge amOunt ofwater and can discharge it quickly. Numerous
T.\Bl.E 6. CoRRELATIO:-: COEFFICIE:-"S FOR GEOMOR_
['lIIe CH.,\Ro\CTERISTICS A:-."D HYDROLOGY OF \VATtR_
SHEDS OF AI'['AL\CIlIA.S' PL.\TE.\U PROV1:-."CE
first-order tributaries conduct stream flow outof a basin in a short time. :\ large number ofchannels also means more rainfall conductedout of the watershed bv stream flow, ratherthan by infiltration t1lfo~gh the soil.
Correlation coefficienrs for regressions ofstream gradient on runoff are negative. This isexplained by the fact that streams with steepgradients are shorrer and carry less water thanstreams with low gradients which are long anddeep, and thus h:lve greater channel storage.Leopold and Maddock (1953, p. 15) showedthat incre:l.Se of depth in channel overcompensates for decreased gradient and tends topro"ide a net increase in stream velocity atmean annual discharge stations, Hence, ifprecipitation conditions are equal, a streamwith steeper gradient will ha,·e a smaller meanannual runoff and lower peak flow than astream with low gradient.
Relief ratio seems closely related ro peakdischarge and to runoff· rainfall ratio, but not tomean-discharge or runoff-intensity figures.Other parameters which might be expected to
(11)Q - f(·;)
Factors Controlling Runoff
Stream flow depends upon those factorswhich determine amount of rainf:lll excess andthose which influence length of rime for rainfallto travel through the basin. R:linfall excess isdetermined prim~rily by clirn:lte,vegetarion,infiltration capacity, and surface S[omge. Geo·morphic factors such as suearn lengths, basinshape, and ground slope. as well as geologiccharacteristics such as rock type and structure,influence runoff intensity and discharge.
If other factors remain the S:lIne. dischargeis proportional to the are:l of a w:ltershed.Average discharge as well as peak disch:lrge hasa direct relation to size of w:ltershed (Hack,1957, p. 5~; Eisenlohr, 1952, p. 143), averageand peak discharge increasing with increasingarea.
Sherman (1932, p. 339) concluded there wasa definite relation between basin ourline andthe unit hydrograph. Jarvis :lnd others (1936,p. 34) review ma...ximum·discharge formulaswhich use basin shape as a [actor. Morisawa(1958, p. 590) found regressions of circularityon runoff to be significant.
Stream density and bifurcntion ratio affectdischarge, as closely spaced, numerous tribu·rnries would result in rapid runoff and probablya large volume of flow. Longer stream lengthwould mean a longer lag [rom time of onset ofrainfall excess to flood peak. However, as allthese factors are hard to isolate and rebte todischarge in a qualitative way, quantitativeanalyses must be carried our.
General Carrdation ofGeamorpllOm(lry and Hydrology
?vIany geomorphic characteristics arc relatedto area, inasmuch as they change systematicallywith area. If discharge or runoff intensity arcfunctions of area,
and if
A - f' (L. ~ L, .V, S. H. R) , (12)
then Q will also be a function of the samemorphologic elements in (12). Correlations ofdischarge and runoff intensitv with those aeomorpillc properties that are ~learly related towatershed area should be high.
Correlation coefficients for each morpho·metric property of all 15 total basins were
1043
I; .04-1 _ ~.l;; I()~.-l - !.30.! log P_ 6.%4 log S - (;.bS! lug h 11;)
-u.5';; _ 1I.lh:") lu~ .1 - U·:;~ .11):. P_ tl.lj51o,.: _, _11.2;;10;; R, \:;,
log q",:u. '"'
Circtl'lrit,\" T,uio
!o~ ""':>1 '" _-Ltlh2 - I).n;; lu;.: .1 - ~ ..i\) In,.: l'~ . _ O.':tH In,.: S _l).lIn~ In;.:. Rc f It. I
Rt'!ic/ Ttl/if}
.-l .. :UC:l in ;lcn:S,T • T-bctor (topogr:tphy).P "" P-r;ltiO (r;lil\blllOtcnsit~). ;lndS • S-r:ltio (frcqucncy of r:linbll).
:\nah"sis of co\'ariancc sho\\"eJ all inl!cpendt:nc\.ari~;bks to be signilicilll beyond the O.OOlle\.d. :lllcl :l\·cr:lge stand;lrJ error \\":lS \8.1 per
cent. .The writc.:r h:1S sub::.tituled other gl:omorplm:
qu;mtitil:s for Pulter> T-i:u:t~r in :Ul dfort to.e~pbin e\"l"ll more 01 the \·:~n.:IIH:e. B.t:cal1se otthcir hi.,h (Orrdation codilLlent" \\·Ilh pc:,krunolf i~tt:1l:.it\·. ;Lnd beC1USl.' by r:ltion:ll dl:dUl:tions Il1e\· ;t:t:11\ to h:I\'c :1 rdation to peakIHten::.il\' ol ~unolr. cin:ubriIY, rdid r;ltio. :111l1rreql1t:n~y of lir::.t .o_r~l~r 'tre:.ullS if e:lc.h \\"ere,ubSlitllletl .1::' the !.L\(wr III :1 1l\ul ll ple re~n.:s:-iun on Pl,:,k inlCn~ll~· ot" runolf. \Ollt: ot"~11l.: len~th or s\011e mt:.\"l1rt:m~llts. \\"crt: l~-:cd:lS Pout:r h:ld (omidernl Iht:'l: III hiS cqu:HlOIl .
.\5 10 of lhe b:l::.ins dW'l:!l for this study wert:among tlH)~t: inclulkd 11\ PUller's study. hl'\.:t1ut:-: lor pt:':lk-rUlItlll" t1ltcll"ity. ':Ht::.l. .P-ratlo.:lml S-r:1I10 wt:rl: u"cd in dt:ternHll111~ tht:multipk re:.::re""ion. Till: :Iuthor's \':II11t:S forrdiet' r:1t in. ~(1 n:u!:mn·. .Illli !i. r:-l -ordcr ,trt::1111frt:qllency wt:[I.: -:Ub'U'tlllnllH ~':,ch c;l:-e (or theT.l":lcwr. :\"l:W re~re:-'II111 (IKlhclcnt$ wcn: de-Icrminnl b\· the "Do(llllde mcthod o( -:olutionof nurmal c~lu:ltinll<; for lin: \':H1ahkS (E1.t:klel.
In41. p. 46111.The f(}Il()Wlll~ cl\ll.ltlllll~ re'ultl:d:
where• pt::lk intensity of runoff. cubic fecl pcr
second. per ;len::. for a IO-yc;lr recurrence
intcr\':I\,
from head to moulh. Poncr's cqu:'lion forreorcssion of lhese bClors on lO-year peak in·
olensilY of runon· is
logq",:u • _1.42\ + .liO log A - .554 log T+.929ln g P + .449 log S , (14)
RELxno:-.:s
BETWEEN GEO\\ORPHOLOGY AND 11YOROLOGY
rc 0 C:ln be ':lser:l0 C or pcak disch:trgt:. ory be- replaced by r;nolf-r:,inf:tll r:llio_ Since.dient and relid r~llio :lrl: both tne:lsures 01'0 of rdid to length. or nrtietllO horiwl\t:l1
urcnll: nts• we C:1I1 dimin:lle onc of themthl: equation. Stn::1m ltow. lhen. is geo
rphologic:llly rdated ll~ dr:lin:lgt: arc:I .111 lengd1. frcql1t:ncy 01 ,trl':11l1 (\l:lnn:.:!s.
'n shapt:. :\lld basin rdicf.
Jut/ipf" Currd'llioTl with Pok Ui.I(-!hw;c·Runolr inlensit \. :Inti lii~(h:lr~l: roull from
the c01l1bint:J act\on uf :1 11l1l1lbt:r of 1:lclOr":
dimau:. \·t:"ct:ttion. soil conditions..lIlt! topog·t3phy. HCI;Ct: :1 Illultipk n.:;;rt:ssiun .. )il1\ull~l1l':IJUSly taking a nU1l1bt:r at thoe 1:lctor" Intoronsider:ttion. should be Jr:IWIl tip. poltl:r(1953. p. 69) compu(eJ :1 .rt:~rcs-:ion fur pc:,kdischarge lISin~ f:lLtlHS til lopogr:lphy ...Ire~l.md r:linf:tll. delermim:d cmpiric,lly lor ) 1basins in the .\pp.ll:Khi:lIl Pbtl.':I1..l. The \ C~l"l:t·lion lactor \\.:1" not introduccd bt:C:ll1~t: 11 h:IJbeen teslt:J and found to be of no 'l:;miiclllCC
in these basin-:.The r:tinf:llI·illlef'1:-:il\· f:lCwr. Je~i~Il:ltnl tht:
P-ratio. is ddll1ed :IS .:... the .l\"l"r:~~e r:llla ofrainfall inten"il\" for 10·. ~5- .1Ild 50-\"l":Ir recurrence int::C'·;lh for :lny parucubr ·Ioc:ltlunto similar \·:11ues dcri\·eJ from long-It:rll\ r:unfail rccoros for Columhus. Ohio·' (POllt:r.1953, p. 6S). Frequency of i:uniJ.lI. de'l~natcdthe S'ratio. i::. ddi.nnl:iS ..... the :I\"er:l~e ralioof the product oi :lnnu:tl r:tinf:tll .1I1J numberof cxcessi,'c storms for thc 10-. ~5-. 50-\,e:1£recurrence rt:cords for :tIlY 10CHIon to Sil~librvalues dcri\·cJ from lono··tt:rm r.unf:.l!1 recordsfor Columbus. Ohiu" (i~omr. lQ53. p. 69).
Thc topogr:lphic factor. or "[-factor. cho::.enby Poncr is [:llia of longt:st ll:ngth o( principalstream to squ:He root of .1\·t:r:lgt: channd slop:
rel:t tiOI1 to hydrology, such as
age density and. co.nstanr of ch:lIlncltcnance. do nor. n\lS may be because
ter channel storage do\\ nstream more thaot1pcnsates for high disch:uge resulting from
h-drainage density.. .us, hydrology of :l basll1 C:lll be 5.'11d to ~eIiy rdated to total stream kngth, b:tSI~l
, and first-order SHean) frequency, :tnd ISrsdy related to strC:Il11 gr:lllient. circll
'ty, and rdid ralio. Stream ~ow, then, cane~prcsscd as :t gcncr:ll funcllon of gcolllOrlogy of a w:trcrshcd :\$ follo\\"s:
1 I I I) (13)Q - J(,'/' ~ L. -I'" -S -R -R .
, • ~, 1\
'C.lk \kJni\'fcanannual
1,,\\ runol1" discharge.r,.) (in.) (,".)
.9 .. '10 .iS2S .9865
.f)):"4 ::4:>4 .9838
.B:-S -.6i90 -.69975;~4 -.2525 -.3,475.24')1; - ..2992 -.2032
.~~.,,, .jO.!.! .1iJl~·c~ -.4496 - .6132
.i214 -.6114 -.8386
.2ei ill .206, .1000
.n ;2:- -.54:-0 -.i912
\lj \\":\TERSHEDS
sions on each hyd I .. rOog1grcsslOns were tCSt dr = 0, and were [ol~ndfo05 Ic\·c1. Are:t and Str ro
dcam-
Pl"Cl~ • are ~ery cI I. BaSin shape IS influe: Y.rgl: :tnl! runoff inre . latnSlty.h stre~lIn frequenc)' re~
ort strtams per unit area(ccd faster. because thcar~y a ~arge amount oerge It qUIckly. ::\i'umcro~COt:FFICI[~"TS FOR CEO
\:o,:U HYUROLOCY OF w)lOt."nlII.\S PLHE.\t) PRO"I:SC£
(ondtlct stream Row au[lime..\ brge number ofmon.: r:linf:lll conducted
Ii hy stream Ilo\\". ratheriHllU;.:h dH: ~oll.
Cit:lll~ for regressions ofunoli :Irc ncgali\·e. This is: Ihat S[re:lIllS with steepJnJ (;Hn· h:~s water than
dic!lls wliich :IfC long and: ~rt::I[t:r chonnd storage.Kk 11953. p. 15) showedmh til channel o\"crcomc-J ~r:lJient :lnd tends to3_'t: In ~[fe:lm \·c!ocity at:ugt: stJtions. Hence, iflOllS 3rt: equal. :l stre::uDi uill ha\'c :l 'imaller me:ut~~\\"er pt.'"ak lIo\\" than a
U1ent.<; .d()~dy related to pe$)Ii·raillfall r:ltio. bur not [0
rUllolj"-intellsit\" filJurcs., . . ~
nll:h 111lglu be ex!X'cted to
1044 M. E. MORISt\WA-GEOi,,{ORPHOLOGY, APPALACIII/\N PLATEAU WATERSHEDS
T.\BLE 8. ST.\:"O,\RO ERROR OF £STl:loI.\Tf.S, COI!.ItEL.\TIO:'" COEFFICIF.:"TS,
A:"'D $IGSIFIC.\:"'CI! FOR ~fULTH'LE REGRESSIO:"S OS PE" .. RU:"OFF
larger basins tendeots with gentll
circular, and havea homogeneous re~
slopes will .have a sstreams, will be In
¥~ve a greater relicgentle stream gra~:stream-length rarl(
tio are conservaconstant for basinHowever, as geolocontrols exert a ch:1in lithology will gl'wbole basin morphresults in basins wilstream gradient, :II
({minage density.creasing, docs so atof drainage compobasin, the basin i~
may look for the ilQuantitative ml
c'omparison of simwatersheds to dereforms as a basis forphysiographic pro'ties and differencein regions traditiosections shows th:1geometrically, but
• particular, the Cm
Amsden, T. W., 19Geology Bull. I
Ashley, G. H., 1925Pa. Geo!. Survl
Butts, C., and NelscDiv. Geology B
Croxton, F. E., 195~
3i6 p.Eisenlohr, W. S., Jr
Water Supply rEzekiel, M., 1941. ~
Fenneman, Nevin j\
Ine., 691 p.Hack,John T., 1957
Prof. Paper 294Hayes, C. W., 1894 .
. - 1895, PikevilleHickok, W.O., and
Survey Bull. C:
SUI:d.\RY ..\:\D CO:-:CLCSIO:\S
:\nalysis of quantitJ.tin: geomorphic chuac·teristics of watersheds in the :\ppalachian Pia·(e~ll tends to confirm Horton's laws of drainagecomposition for stream numbers, lengths, andJ.rcas. Propenies rebting ,"Crtied to horizontalmeasurements. that is, heighr-lenglh rariossuchlS relief ratio or stream gradient. for the mostpart do not sho,," an expoll(;ntial decreJ.se withoruer. This indicJ.tes thal horizontal or plani·metric aspeClS conform [Q Honon's bws, butcontrol by structure and lithology governsvertical or gr~dient aspl~ctS. Relief ratio andstream gradients do. ho\\'c,"(r, decrease con'sistelllly with increasing order. BecJ.use eachis J.n exponential function of order, the area,total streJ.m length. longest It:ngth. :llld meanstream length arc related to each other as powerfunClions.
In ~I region of horizontally uniform lithology,
combination of all oughl to be a determininfactor of the hydrologic charJ.cter of a Wate ~shed. Accordingly, a T~facwr of the product ~fthese three properties ,vas subslituted inmultiple regression with A, S, and P on peakintensily of runofl". Using the same figures fo.A, S, P, :\I~d qmu, and a new T factor, r
T .. F1 • R e • R!> ,
a new regression equation WJ.S solved by theDoolinlc method:
log qlll"1. = -8.958 or 0.542 log d or 4239 log p- 0.290 log 5 +0.723 log T (18)
The standard error of estimatc for this regression was 0.064 and the multiple correlationcoefficient equal to 0.9478, which J.n F testshowed to be significant. The pJ.niaJ correla.tion coefficient was 0.9071 and was significantTilt: usc, then, of a T-[Jcwr which is tbe expression of relief. shJ.pe, and network composi.tion of a watershed considerably reducesstanlbrd error and results in a high correlation",ith peak intcnsity of runoff.
18.211.612.19.1
StJndard ~"ult. Partialerror correlation correlation
T·factor of estimates coefficients SigllifiC:l.lIt .: coefficient Significantl-F, .099 -.9378 yt·s -.7816 ~'es
R, .201 -.7120 yes -.1072 noR, .194 .i381 yes .1758 no
FIReR!> .064 .9740 ycs .9071 yes
Qp vs .-l,P,S, :lnd TQp \·s .-I,P.S, :Iud R h
Qp \'s A,P,S, :lnd R e
Qp vs A,PS, :llld Fl
..\ \'cr:lgc st::md:uderror
V:lriables per celll
T,\Bl.E 7. EFFECT OF CII":"'GE OF T-F.\CTon
OS ST.\:"'IMltO EnRon
Circularity gives a multiple correlation coefficient of 0.7120 and standard error of 0.101;relief ratio gi\'es 0.7381 for corrd~llion coefficient and 0.194 for standard error. :\n F lestof multiple regression cocJncients showcd onlythe regression of first-order strC:llll frequencyto be significant. .-\ test of panial correbtioncoefficients J.lso showed onl\- the correlationcoefficient for first-order i"requcncy to bcsignificJ.nt.
Since relief ratio, circubrit\', :lOd first-orderstream frequency vary indep~ndently of c:lchother :lnd of area, they do not duplicate :lllYother geomorphic fJ.cwr. Together they showthe shape, relief or steepness, and networkcomposition of a dr:linagc basin. Hence, the
where qm,.,,;, A, P, and S are the same factorsas in Potter's equation and
R h relid ratio,Re = circularity ratio,F, = frequency of first-order streams.
Poner calculated the effect of addition ofeach independent variable as a per cent error.This is shown in Table 7, with per cent errorfor each substituted T·facror. Each variablesubstituted reduced the per cent error. Table8 presents standard error of estimate andmultiple and partial correlation coefficients andstates whether regression coefficients are significant. Use of first-order stream fr::quencygives highest correlation coefficient, 0.9378,and lowest st<tndard error of estimate at 0.099.
I'L\TEI\U WATERSHEDS
Y .I.'\D CO.'\CLl·SIO.'\S
III
.1
I
II
II'
Ij:
. !)
Ii:
rli:
jI)
~
10·15
and the unglaci:llt.::d r\llt:gheny Plateau section;Ire simibr cxcept for scale r:uio of Slre;lI11lengths ;lnd dr:linage densily. The Allcgheny-' jOlllltain region is morc distinctly diOcrentfrom lhcse other [\\'0 sections in all form clcmenlS.
:\ "aluable pr:lctical application of qU:lIltit;1li\"c geomorphology is dcmonslr:Hed by correlation of topographic f:lcwrs wirh hydrology ofbasins. Disch:trgc and runoO- inlensity in lhcse\\':Hershcds of the Appabchi:lI1 PI:HeJu arcclosely correia led \\'ith scrcam lenglh, :l.rca, andfrequcncy of tirst-order streams and in\"crselyrcblcd LO Slre:l.m gradient, relief ratio, ,::lI1dcircularity r:Hio..\n:dysis of simple correlationsof hydrology :InJ geomorphic (c:llures pro\"idc:da h:lsis for dlOicc of properties for use inmulti pic rcgres,iolls on peak intensity of runolr. Sub~litution of first·ordcr stre:lm fre'qucncy. relict r:uio. ;lnd circubrilY ralio, cadl:IS LUpugraphil: qU:llHities in Potter's regressionor arc:!. r:linf.lll and IOpography on pcak flo\\'.:Illd C:lkubllUn or ne\\' rcgrc!lSion codlicictHSprU\'idnl ctjll:ltiol1s greatly reducing a\'cclge)t:ll1lbrd l..'rror. _\n cqu:ltiol1 substiruting aproduct uf thl')e: thrl:e factors lFt R.· Rio)fur T re'lJ!tnl in:l rcgres::oion \\'ilh high correla·lion. "ignilicllll :It tht.:: 0.00 i le\"L·1. :\ multiplen::grl·'\!oion. thell. of :lCea. r:Jinf:I11. ,lI1d topography un pelk intellsil~' or runoll" prm'ides .1
ml.::lll~ of prnlit:"ting rUllolf intcJlsity for w:ltcr',hed" on thl' .\pp:lbchian Pbte:tu.
SU;...I~IAH.Y ;\~O Ctl~CLUSIO~S
Amsden. T. W.• ltlH. Gcolo~\' :md !:round 1\ .Ht'f rCSIJurccs uf C,lfft·U Cuunt \'. \ l:irdJlltl: \ td. Dt·nr.Geology Bull. 13..;";9 p. ~. ~ ...
AshJey, G. H., 1915. TopogrJphlC Jnt! gcolfl~i( .ltbs of Pt'ltns~·h-JIl!:J. :-\0. 65, PUllx,:U':l\nlcy qUJorJnglc:Pa. Geol. Sur\'c\', -ilil scr.. 1-!5 n.
Butts, C., and Ndso·n. W. Au 19~5: Gcolog~' .mJ mlllCf:!1 rcsources of the Crossville qu::uJrJngle: Tenn.Div. Geology Bull. 33·D. 4\ p.
Croxton, F. E., 1953. EJemcnt:tr\' st:ltl~tl":S WI[h :lllolic:ltiollS illltlcdi..:!nc: ):C\\· York. [')rcnticc·HJIl, Inc.,3i6 p. . , .
Eisenlohr, W. S.. Jr.. \951. Flootl\ of JlIly IS. 19-!1 in north·celler:J1 PcnllsylvJnia: C. S. Geol. SurveyWater Supply PJpcr 1134·S. 158 p.
Ezekiel, MOl 1941. _\lcthoJs of correbuon :m:llysis: ):C\\· York. Juhn \\'iley :lOd Sons. Inc.. 531 p.Fenneman, Nevin :\1.. 1938. PIl\'slo~r:JDh\' of e:IStern Cnilcd StJtcs: ):ew York. ~IcGra\\'-Hill Book Co"
Inc.. 691 p.' . - ..
Hack,John T., 1957. Stuuies ofIOlH!itlJdin:l1 StrC:Ull prolill..'s in \'ir!::!lll:l ,lItU \f:Jr\"bnd: C. S. Geol. Sun'cvProf. Paper 294-8. p. 45-97 - . ~, .
Hayes, C. \V., loS94. Kingston qlJ:tdr:lnglc. Tenn.: L:. S. Geol. SUf\'cy Geo!. :\rl:ts. Folio 4-:- 1895. Pikcvtllc qu:ltlrJl1glc. Tenn.: C. S. Geol. Sllf\'CY Ceo\. .\tbs. Folio::!!Hickok, W.O., and :vIO\·t(. F. T .• 1940. Gcolo~" :toll mineral resources of Fa\'cuc CoUnt\·, P:J.: P:l. Gco!.
Survey Bllil. C26. ~[h ·SCL. 530 p. . . .,
>F.LECTED BIBLIOGR.II'IIY
"Jarger basins ll'nd lO h:\\'(:: longl'r stream segments with gentler gr:ldieuts, :m::: less nearlybrcular, and have a sm:dlcr relief ralio. Or, inia homogl'neous rcgion, a w:ttershed with slecplslopes will havc :l sm:llll.:r drainagl.: arc;}, shortcrscreams, will be more nearly circular, and willhave a greater relief r:ttio than a watcrshed withgende scream gradil:IHs. Dcrin::d ratios such :IS
'stream·lenglh ralio, bifurc:uion ratio, anti :In::l
:(3tio are conscrv:ni,'c ;Inti rcm:lin essenriallyconS[:illr [or basins or the Pbtcau province.Howcvcr, :IS geologic (aelDrs ch:J.llgc. geologiccontrols excrt a change in these r:ltios.. \ changein lirhology will generally C:lUSC changes in thewhole b;lsin morphology. :\ more resistalH bcd
·resulrs in basins wirh incrc:lscd arc:l.lcngrh. andscream gr:ldicnt. and decrC:lSl.:J rdid ratio :lnddrainagt.:: density. Tuul rclid. while still in·creasing, Jocs ~ :Il J lowcr r:lre. f-knce. if bwsof drainage composition do not hold within :I
basin, the basin i!l nul homogene:om .1I1J \\'emay look for lhe indic:Hcd gtOologic dl:lngc.
Quanli[:lIin morpholugy permils objl'ctl\'ecomp;lfisol1 of "imibrit~· of form dClllenls ofwaccrsheds to de(crmillC hOll1ogl.·lleity uf bnd·forms ~s a ba~is fur l:bssiticltlUll widull.1 ~ill,gle
physiographic !)fU\·llKC.. \11 .1l1:d~·,i" uf ,illliLtrities and diJ1<:rcnccs in geometry uf \\';tter"hcd"in regions rr:u.lilion:llIy con~idcrcd .IS dislinl:tseaions shows thaI tht: re.;;iol1s :In: ditrt:rt'lltgeomctrically. but nUL (ollspicuou~ly "o. Inparricular. tht: CUll1bcrbnd -'!C1ul1t:lill ~t'ctioll
Signif!c:lOlf
-.;816- .lOi~
.1 ;5S
.90;\
Parllal(orn.:l:JllollcocJiiclcnt
on of horizontall~'uniform Ii chology,
of :tll oughc to be a delcrmininghydrologic ch~r:lctcr of a warer_
ingl)',;1 T-f:Ictor of lhe producr ofpropcrties was subsliluted in a
ressiun wilh A, S. alld P on peakrlmon·. Csing lhe samc figures forq...u., and a new T factor,
T - F1 • R• . Rio ,
;sion equ:nion W:lS sokcd by the:thoJ:
·8.958 + 0.542 log .·1 + 4.239 log p- 0..290 log 5 +0.723 log T. (IS)
-d error of e:Slimatc for lhis reo0.064 :lI1d lhl: multiple: correlarion
:qu:Il to 0.9478. which an F test)C signifiC:lIH. Thl: panial correlatill was 0.9011 and was significant.ell. of;l T·f:lctor which is rhe exrdief. shape. :IIlJ nctwork composi-
waterslu:d eonsiderabl,' rcducrsror Jntl re:sults in :l high ~orrelationlltCnSilV oC runOli'.
of (IU:llllit:ulve ge:omorphic characw:ltershcds ill the. \pp:llacbian Pia·:0 confirm I-Iorton's bws of drainage1 lor stre::llll !lumbers. lengths, ande:rties n:l:lting H'nic:d to horizonral!lIS. that is. helglll·k·ngth I.lliossuchio or ~tre:101 gr:ldienL for lhe most
[ ,huw :Ill c:,\poul'IHi:l1 dccreasc with, !ndicHe~ t1;at hOCizont:11 or plani·:cts .::onfurm to I-forton's bws, but
suucture :1I1d lithology govcrnsgr:llJie:nl as!}(:cts. Relief r3tio and
,Jicnls Jo. hmn:,·cr. decrease con'ith incrc:lsing urdcr. Bec:luse eachnCllti31 fUllction of orucr, the area,11 Icngth, long(..'~t length. :lIld mean;tl1 arc related to e:;Kh od1t::r as power
lilt:
,EL.\r1US C,JI.HIClr.:-TS,
, us PE,\~ Rl':>:OfF
ycsnono)·cs
---------
I.
\
1046 M. E. MORlSAW;\-GEO:\IORPHOLOGY, APP..\LACHIAN PUTE:\U WATERSHEDS
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-- 19-+5, Erosional development of streams :md their dr:linagc basins; h)'droph)'sic:ll approach to quanti.(alive morphology: Geo!. Soc. i\mcrica Bull., v. 56, p. 275-370
Hyde, J. E., 1921, Geology of Camp Sherman CJuadr:tnglc: Ohio Geol. Sur\'cy Bull. 23, 4th ser., 190 p.Ingham, A. 1., 1951, Geological structure of northern plateau region of P:l.: P;L Geol. Survey 4th sec
Progress Repr. 138 ",
Jarvis, C. S., and others, 1936, Floods in the United States, magniwde and frequency: U. S. Geo!. SurveyWater Supply Paper 771, 497 p.
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-- 1897, Wartburg quadrangle, Te:.nn.: U. S. Ge:ol. Survey Ge:ol. Atlas, Folio 40
Lamborn, R. E., 1954, Geology of Coshocton County: Ohio Dept. Nar. Res" Div. Geol. Sci. Bull. 53245p. '
-- 1956, Geolog)' of Tuscarawas County: Ohio Dept. Nat. Res., Di\,. Geol. Sci. Bull. 55, 269 p. !.t
Langbein, Walter, and others, 1947, Topographic characteristics of drainage basins: U. S. Ceol. Sur\"tJWater Supply Paper 968-C, p. 125-255
Leopold, Luna, and Maddock, Thomas, Jr., 1953, The hydraulic geometry of stream channels and somephysiographic implications: U. S. Geol. Survey Prof. Paper 252. 56 p.
Leopold, Luna, and Miller, J. P., 1956. Ephemeral strcams-hydraulic factors and their relation to thedrainage net: U. S. Geol. Survey Prof. Paper 282·:\, 36 p. .
Linsley, R. K., Jr., Kohler, M. A., and Paulhus,J. L. H., 1949, Applied hydrology: New York, McGraw_Hill Book Co., Inc., 689 p.
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Martin, G. C., 1908, Accident·Grantsville quadrangles, Md.·Pa.·W. Va.: U. S. Geol. Survey Folio 160
Maxwell, J. C., 1955, The bifurcation rario in Honon's law of stream numbers (Abstract): Am. Geoph}"s.:Union Trans., v. 36, p. 520 '
Morisawa, Marie E., 1957, Accuracy of determination of stream lengths from topographic maps:Geophys. Union Trans., v. 38, p. 86-88
-- 1958, MC3suremenr of drainage basin outline form: Jour. Geology, \'. 66, p. 587-591Poner, W. D., 1953, Rainfall Jnd topographic factors that affect runoiT: Am. Gcophys. Union Trans,
v. 34, p. 67-i3 .Schumm, S. A., 1956, Evolmion of drainagc systems and slopcs in badlands :l.t Perth Amboy. N. J.
Geol. Soc. America BuLL, \'.67, p. 597-646Shaffner, M. N., 19-16, Topographic and geologic atlas of the Smicksburg quadranglc, ~o. 55: Pa. GroL
Survey, 252 p.
Sherman, L. K., 1932. The rdation of hydrographs of runoff to size and character of drainage basins: AmGeophys. Union Trans., no. 13, p. 332-339
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Strahler, A. N., 1952. Hypsometric (area-altitude) analysis of erosional topography: Geol. Soc. AmenBull., v. 63, p. 1117-1142
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Bull. no. 4, 338 p.U. S. Geological Survey, 195i, Surface water supply of the Unitcd States: Ohio Ri ...·er basin. U: S. G
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MA:"'USCRIPT RECEIVE.D BY THE SECRETARY OF THE SOCIETY, OCTOBER. 25. 1960