Quantitative Geomorphology of Some Watersheds in the Appalachian Plateau

22 Pages·2011·7.09 MB·English

; ISSUES
MARIE E. MORISA\VA Ro//te 202, Towaco, tV. j.
:5SrRATAOFTilE WESTlOIO;
;0TilE PACIFIC yL,ltCIS OF Quantitative Geomorphology of Some
S. Fisher
EI'OSITS IS' QUARTZ Mos Watersheds in the Appalachian Plateau
IDUTIl, MOST,\:-;A. Forbes
a"OroIll.dSI.E\,.J:o\lh:tnldcH:.loScipoHtotsward Abstract: Geometry of15 watersheds in theAppa Simple corrcl:llions of hydrologic and geomor
behi:!o Plateau province conforms to Honon's phologic features provide the b:lsis for choice of
bwsofdr:lin:lgecomposition in horizont:ll,orpbni. ch:.r:.eteristics to lise in a multiple regression on
:,\OLI:"ITtCCL,W DEPOSITS metric. propcnies hut not in vcnic:l!' or relid. peak-runoff intensity. A regression of pC:lk in·
properties. Gcologic structure :llld varying lithol tcnsin' of runoff on b:.sin :uea, r:linf:dl incensic\'
..:\bitre ogy interact to ch:lnge vcnic:d form demenls:mu :l.nd f~equcncy, :lnd ropogr:lph}' has :l high correl~­
:uns CJuse dc\"ialions from Honon's bW5. tion coefficient:lnd issignific:lnt :It thc 0.001 le\'c!.
ORTHER:" \IISSISSIPI'! E:IoI- Gcolm:tric simibrirics :md dilfcn:nces in W:HC( Qu:.ntitati\·edecermin:Hions01geomorphic proper·
shed morphology provide both qu:wtil:tti\'c :lOd ties ofdr:lin:lge basins thus hJ.\·c :l. pr:l.ct!c:l! usc in
qualit:Hi\'c bases for grouping the regions studied basin hydrolog~"
iowthreedistinctsections. Dissimibritics,:.Ithough
distinct. :::m: not gre:J(. ~
)\·ICI.\:" OSTR.\COD,\. fohn
din:; H newspecies. from CO:"TE:"TS
iorm:u!unsof the Shcn:.n-
Introduclion .1Ild.1cknowled;';lllclllS 1015 s. SucJmprofibJiang longcst length 1033
GefH:f:JIdcscnpuon otw:l[(;:rshcos 1016 9..\\"erJ);c tOIJI reliefplaited:lg:lillStordcr 1034
W:lIcnhcdssmdicd 1016 10. Rc!Jtioliofbasinarc:J. tostrCJIll length within
CulkClionatJata 1O~; :Isingle I\':ltl'rshcd . . _ . . . . . . . 1035
ListoisYmbolsand definitions 1015 II. Lo~ mean ch:lnnel slope of:III b:l.Sinsflolted
Basin m~rphomctry . 101S :I£3inst are:l :lnd Slream lcngth 0 carre·
.\lorphometric ProfX·rtics . IOlS spondingordcr 10·W
ReI:Hions wltlllll lint.order b:lsins 103S
Inlluellcc o(litllOlu;.:yon morphology. 1039 TJl>lc
REF.' OR FOl'R·.\xIS LSI, Moroholot:ical simdatll\'o(w:lIersheJsbv physio. 1_ G<:omurnhicchar:lcteristicsof15 b:lSinsstudicd
. J:ra~hi..: sections ~ . III.\ol):llachun Pbtc:lu pro\'illce bv order 1036
Rl'1:Itions between ~elllllorpholog~'JIlJ hydrology .. Conslant'~r channel mairUe;lJlICC dctc'rmincd
F:ll:torscotHrolling runuli'. U\' threedilfcre/l[ mcdlOds 1039
Gener;]1 correlation of geolnorphomeuy :md 5. Correl:won coclliciC'nu (or re;;ressiolls of one
hydrology 1041 b:lsm property on anothcr for tot:tl bJsins
:\luhiplecorrelalion with peakdisch:lr~c IO,U on .\pp.1Iachi:ln Pbteau province 1040
Summa(\':lmjcondmions. 10·'" .,. Correlation ('ocllicients (or relationships o(
r:'R\I,\FROST•.\rthur I-r. Selected'bibliogr:lphy 10-15 dl:lr:JCteristies of first·ordcr basins o(
.\pp:lbchi:J.Il Plateau province. , .... IOH
Figure 5. R:ltiosshowinggeolllemc:::dsimibrityofwater
I. Index mJO sho\\'ln~ loc:nion oi bJsins uuoied 1027 sheds in three sectionsoflhe ;\oD:lbchi:ln
:. J. Sllbcrling :lIld R:liph 2. Strahler ~YUClll at stre:lm ordcfmg 1019 P!Jtl'au .. 10·;[
3. Log numberof SlreJmS ploHed :tgJinst order, 1030 6. Correlation eodlicil'nlS (or J;colllorphk charac
4. Log IneJn strc:Jm lcngth plottcd .1J;Jinstorder 1030 tcnSlies :Jlld hydrology of watersheds of
):\TOLOG Y 5. Log mC:ln tot:ll stre:lrn length plotted agJinst .\opalachian Plarc:lU province.. , .. , l().;Z
order 1031 Elfcct'oichJnge of Y.f:letor on SI:lndJrd error 10H
6. Logme:ln basin :lrea plutted JgaillSt order 1031 S. StJnd:lrd error of estimates. correlation co-
FI:"ITtES. WOR:IotS. TR.\CE
7. Log rneJn slope plorred Jgainst order, 1032 diiciclHs. and signilieance for multiple
re::.:rc:ssiollSon peak runoff 10·H
delayed by lack of quantitative methods and
INTRODCCTION AND
procedures for measuring geomorphic charac~
(FOR 1960) ACKNOWLEDGMENTS terisrics. Much impetus, however, was given
Evaluation ofgeomorphic f3C[OrS and [heir fluvi31 morphometry by Horton's (1945) sug
m,:nhematic31 relationships to hydrology was gested methods of quantitative analysis of
Geological SocietyofAmerica Bulletin. \'. ,3, p. 1025-1046, !I figs., Scptember 196~
1015
1026 M. E. ~IORIS:\Wr\-GEOMORPHOLOGY, APPALACIII..\N PL>\TEAU W:\TERSHEDS
drainage features. Following Horton's lead, maps were available. (3) In an e£fore to mini
confmcd to tal
Strahler (1952; 1957; 1958), V. C. Miller mize variables such as lithology, structure, and
taries. Stream \
(1953, unpub. ms, Columbia Univ.), Schumm climate, all basins were solected [rom within slecp·sided. M,
(1956), and others developed quantitative the Appalachian Plateau province. (4) Be·
gradients dccrt
methods by adding new parameters and in cause one of the main objectives of the study
divides are bro.
vestigating regional variations in morphology was to relate stream flow to geomorphology,
dJis regioninch
in a wide range ofgeologic and climatic envi· mostofthe basinssmdicdarcamong thoseused Creek, Beech (
ronments. by POlter (1953) to determine an empirical
Accurate prediction of stream flow under regression for lO-year peak fiow.
given precipitation conditions has been a goal This investigation was sponsored by the
towardwhichhydrologistshavestruggled.This Geography Branch of the Onice ofNaval Re
goal seems impossible to obtain because of the search, Project NR 389·042, under contract
complexity offactors (climate, vegetation, soil N 6 ONR 271-30 with Columbia University.
characteristics, and topography) which de Thewriterwishes to thankProf..-\.N.Strahler
teaninerunoff.However,\VeatherBureaudata who supervised the project. Professor Strahler
on frequency, duration, and intensity of rain andmembersoftheScmin~rinGeomorphology
fall have made it possible todraw up empirical at Columbia University during the years
equations for rainfall-runoff relations. Soils re 1954-1955 offered valuable criticism and ad·
search at many experiment stations has pro vice. Amy M. Garthly assisted the author in
duced infiltration-runoffequations and quanti the field seasonduring thesummerof1954and
tative determination of influence of type :lOd j\'frs. D. :\. Norton assisted in the field 5<::lson
amount of vegetation. The geomorphologist of 1955.
can conrr.ibute by determining the importance
ofthe topographyofadrainage basin. Geomor GENERA.L DESCRIPTIO\,
phic characteristics must be measured and OF W.HERSHEDS
studied to establish qU:l11titative relationships.
fVat~,slz~diStlldi~d
.Although it has been acknowledged that
geomorphiccharacteristicsofawatershed influ Drain::lge basinsstudied lie in three divisions
enceitsdischarge, this relationshiphasnotbeen of the .-\ppalachian Plateau province (Fenne
studied quantitatively until recently. Sherman man, 1938): the Allegheny ~(ountaindivision,
(1932) illustrated that basins with different the Cumberland Phlteau division, ::lnd the un
shapes and slopes gave different unit hydro glaciated .-\llegheny Plateau (Fig. 1).
graphs, but he did not quantify the relations. The Allegheny ~(ountain di\·ision is the
Langbein and others (1947) measured param eastern section of the plateau and extends in a
eters of drainage basins and showed a mathe narrow strip from northern Pennsylvania to
matical relation ofdrainage area to discharge. central \Vest Virginia. The stfJra. are gently
Potter(1953) u,ed lengthandslopeofprineipal folded; eroded remnants of Jnticlina.1 arches
waterwayasthegeomorphicfactorinamultiple now form ridges; synclines Jre represented by
regressiononpeakflow.;"'[orerecently,Leopold broad plateaulike areas. BecJuse mJn)' basins
and ~[addock (1953) and Leopold and Miller are eroded anticlines, steep SCJrps bound the
(1956) have drawn up quantitative relation outerdivides,wher~samoregendy rollingsur
ships of stream flow to width and depth of face forms the center of rhe basin. Higher sur
stream channels. The presentstudy was under facesaredissected tomaturity withgreat relief.
taken in an effort to establish mathematical Basins studied in this division include those of
relationships between quantitativegeomorphic Green Lick Run, Pennsylvania: Youghiogheny
factors ofa watershed and stre3Jll-flow charac River, Casselman River, and Big Pine~' Run,
teristics. In addition. this detailed analysis of ~'farvland; and Blackw3rer Ri\·er, \Vest
representative basins will put the regional Virg~nia. Skin Creek and
description of the Appalachian Plateau prov~ The unglaciated Allegheny Pbteau division, Little Mahonin:
ince on a quantitative basis. a westward continuation of the :\lIegheny Pennsylvania.
Fifteen basins, ranging from 1.5 to 550 Mountainsection, isashallow regionalsyncline The Cumber!
square miles, were chosen for study. Basis for in which beds are almost horizontal. [[ is ward extension
selection was fourfold: (I) Stream-flow records mature and has fine texture and moderate-to' Plateau, includ(
were a necessary part of the daraj therefore, great relief. The surface is rugged; divides Plateau which
only gaged basins were used. (2) Watersheds are long and linear wich intermittent areas of Kentucky Rive
were chosen for which modern, large-scale rolling upland. Valley flats are narrow and 333). This sect:
;\TE:\U WATERSHEDS CENER:\L DESCRIPTION OF WATERSlJEDS 1027
lble. (3) Tn an effore to mini con~ned to larger strt.:ams and major tribu generally flat orsltghtly rolling surface, incised
ehas lithology, structure, and
taries. Stream valleys arc generally narrow and by steep, youthful valleys. The undularory
15 were solected from within steep-sided. tvfany arc deeply incised but the summit indicates a peneplain correlated with
Plateau province. (-0 Be
gradients decrease ncar their heads, nnel rhe the Schooley, here called the Cumberland.
main objectives of the study divides are broadly rounded. Basinsstudied in Reliefis Iowan upland areas, but deep ravines
'e:lm flow. to geomorphology, this region include those ofTar Hollow, Home give total relief as great as 2000 feet. \Vater
sstudiedarc:among thoseused Creek, Beech Creek, and Mill Creek, Ohio; sheds studied in this region are those of the
.) to determine .an empirical
-year peak flow.
ltion was sponsored by the
ch ofthe Office ofNaval Re
\"R 389-042, under COntract
:0 with Columbia University.
stothankProf. A. N. Str.ahler
:he project. Professor Strahler
heSemin~rinGeomorphology
:niversity during the years
:d valuable criticism .:lod ad
Jar[hly assisted the author in
uring thesummerof1954and
:on assisted in the field season
SCRIl'TI01\
EDS
o.:d
1S studied lie in threedivisions
ian Plateau province (Fenne
.-\!Iegheny ~\'[ounrain division,
Pbteau division, and the un
:ny Plateau (Fig. I).
v ~[ountain division is the
t
the plateau and extends in a
1m northern Pennsylvania to
[ginia. The strata ;re gently
Figure 1. Index map showing loc::uion of basins studied.
remn3.nts of anticlinal arches
Am-Allegheny .'vlountJindi\'ision: :\-:\llegheny PlatCJU
;synclines are represented by
division. ungbciJecd; G-.\llegheny PlJee:lU division,
e Jre:J.s. Bec;lUse many basins gbci:aed: C-Cumberbnd PlJteJu di\'ision; Cm-Cum
:Iines. steep SC3rps bound the berland )o'[ountJindivision. BJsinsarcnumbered:lsfollows:
ll':re3S:J.moregently rollingsur I. GreenLick Run. P::I.: 2. Pine\'Creek.;vfd.:3.Cassclm:ln
:nterofthe basin. Higher sur River. )O[d.: 4. Youghioghcny River. )o(d.; 5. Bbckwater
d tomaturitywithgrC.:J.t relief. River. W. V:I.:6, TJrHollo\\'.Ohio: i, HomeCreek.Ohio;
1this division include those of S. Little )o'(ill Creek. Ohio:9. BeechCreek. Ohio: 10.Skin
Creek. W. \'::1.: II. Little)Obhoning River. P:I.: 12. )o'(iddle
. Pennsylvania; Youghiogheny
Creek, W. V:I.: 13..-\lIegheny Ri\'Cr. Pa.; 14-. Daddys
n River, and Big Pine>' Run,
Creek, Tenn.; 15, Emory Ri\'er, Tenn.
Blackwater River, \Vest
Skin Creek and ~liddle Fork, West Virginia; Emory River and Daddys Creek, Tennessee.
:d :\Hegheny Plateau division, Little ~fahoningCreek and Allegheny River,
ltinu3.tion of the Allegheny Pennsylvania. Collection ojData
11,isashallow regionalsyncline Th~ Cumberland Plateau division, a south yfc3suring stream geometry and other geo
arc almost horizontal. It is ward extension of the unglaeiated Allegheny morphic features in the field is laborious and
fine texture and moderate-to Plateau, includes that part of the Appalachian time-consuming. \Vork in quantitative geo
le surface is rugged; divides Plateau which lies within and south of the morphology would progress more rapidly if
e:J.r with intermittent areas of K.entucky River basin (Fenneman, 1938, p. me3Surements could be taken directly from
VaHcy flats are narrow and 333). This section is a broad upland with a topographic maps. However, an investigation
1028 M. E. MORISAW,-\-GEOMORPHOLOGY, :\PPAL-\CHIAN' PLATEAU WATERSHEDS
in Figure 2. -I
of accuracy of topographic maps (~loris.1.wa. miles ofall stre:uTIS in a basin to arca oE ample, is c1aSSt.
the basin insquare miles
1957) indicated discrep:mcics between stream c constantofchannel maintenance,arca in though notcon.
lengthsor numberofstreamsdetermined from feet required tomainmin I fOOLofdrain upstream from
topographic mapsand those determined in the agechannel; reciprocalofD, in feet segment.
field. Hence, all maps were checked by field frequcncy ordensity, ofstream oforder
I
measurements, and stream networks were in 0/; number of streams of a given order
serted from field scudy. Air photographs were per unit arca
also used [or checking stream networks and basin circularity, ratio of the. area of a
suearn heads. In the field, stream lengths were basin [Q the area of a circle with the
measured with rape, and slopes were deter perimeterofthegi\'cn basin
mined widl Brunton compass or Abney hand channel gradient of order ti, tangent of
the vertical anglc at point of measurc
·, level. Forcomparisonwith map measurements, ment;or ratio offall infeet to length of
lengthswerecomputedforhorizontaldistances.
channel in feet
Areas and perimeters were taken from coc R. slope ratio. ratio of me:ln gradient of
eened topographic sheets by planimeter and Streams of order u to me:lll gradiem of
chartomcter.
S
Runoff data were obtained from C. S. streamsofncxt higberorder, ~
Geological Survey \Vater-Supply papers. Data .').._1
gathered from the rime of establishment of
gaging station to 1955 were used to determine aVer.:lgc toG11 reliefofbasin oforderII
total reliefratio. ratioofreliefofa b:1sin
mean annual runoffand peak How. Periods of
I oforder 11 to total relicfofbasin ofnext Figure 2. '
time covered bv these records varv from basin streamon
.~, to basin, the sh~rtesrperiod being'8 years, the H.
higherorder. n--
longest 34 years. n ...,.l
Horton (194:
reliefralio, ratiooftot:11 reliefof:1. basin
LIST OF SYMBOLS .~:\D DEFII'ITIOI'S to its longest dimension parallel to the number of sue:
basin form:tnill'
/I order of basin or stream segment de principal drainage line
noting level of magnitude in dr:1.inage mean dischargc in cfs for :t basin the first term i
network hierarch,' peak discharge in C£s for a basin bifurcationratio.
i highest order within :tdrainage network ffi3cicJUy :15:
NR~.. nbuifmurbceartioonfsrtaretiaom.sraotifooordfebrra!Inching in:t B.\SI:\ ~IORPHO~IETRY
drainagc nctwork: ratio of number of _\!orpllOm~lric Prop~rli~s ~13XweIl (1955)
Stre:tffiSofordcr!/ to number ofstreams ~[orphome[ric properties were analyzed for can be equated
,V.. slopeof{he regrl
ofnext higherorder, -,,- conformity of these watersheds to the laws of
I ..+I drainage composition. In this paperStreamsare on order. EquJtl
7:... me:m length ofstre:tm channel seg;mc:nts ordered .ftcr Str.hlers (1952. p. 1120) .d.p· y
oforder u [ntion of the Horton (1945. p. 281) scheme of
~L.. total length of all stre:lffi segments of classification (Fig. 2). Small finger-tip tribu· taking logs ofbo
order11 tariesare designated asorder I. Two first-order log.v
u
strcams unite to form :lsccond-ordersegment.
~ L.. towl cumubli"e length of :111 stream .-\ third-order segment is formed by junction substituting
u = I segments of:'Illorders contained in basin oftwOsecond-orderstreams, but may bejoined
oforder II
by additional first· or second-order segments.
RL stre:1.m-length ratio, ratioofmean length
ofStre:1.ffiS oforder tt to mean length of Two third-order segments join to form a .od
fourth-order segmcm, and so on. The master
streams 0fnext hi.gher order,::rL-.- stream is always a segment ofhighest order. :\
LJ,..,.1 basin is designated as of the same order as the
we obtain
::r.. mc:m area ofb:lSin oforder tt master-stream segment.
R,I basin-area ratio, ratio of mean arca of The placement of stream·gaging stations lac
basin oforder tI to mean areaofbasinof producedcomplications. Thesestations:Irenot. But equation (l~
in general, loc~ltedat the end ofa stream seg
next h·Ig1ler order, =::-t. ment and therefore the gage does not measure sion of the regrl
which the (og:Hi
.-1...+1 a complete basin ofa given order. In all water
plotted aga.inst
D drainage density, ratiooftotal length in sheds studied gauges were located as indicated I
\
BASIN MOIU'IIO_\IETRY 1029
J W:\TERSHEDS
calllS in a b:lsin [0 3re:to! in Figure 2. Therefore, Tar Hollow, for ex ratiois theantilogoftheslopeofthe regression
u:J.rc milcs :llllplc, is classed as a fOllrth-order basin, al relating log number of streams to order. :\1
IOnd m:limClI:lll'CC,arca in though nOl c.omplere because theg:tge is pbced though the basins arc not complete 10 the
omaintain I foorofdrain_ upstream from the end of the fourth-order highest order, the points ploued nevertheless
:ciprocalofD, in feet segment. lie on :t straight line. Bifurc::J.tion ratios wcre
lensity, ofSlre:llnoforder calculated by melhod of least squares, ::J.nd re
s[re:lIns or :J. given order gression lines werc fined by eye.
For the Skin Creek, Blackwater River, and
[yo ratio of the area of 3 ~liddlc Fork basins, only randomly selected
:1recgai\o'cfn:J.b:lcsiirncle with the third-order basins were measured. Ifthe bifur
'm oford~r II, tangent of cation r:ttio of a watC'fshed is constallt, the
19!C :1( POlOt of mC:lSUrc_ bifurcJ.tion ratio ofa smaller watershed within
otf:lll infcet to length of alargeroneshould notdiffersignificandy from
that of the tot:d basin. This inferellce was
Hio of mcan gradient of verified by a paired [-test (Croxton, 1953, p.
.cr II to mcan gradient of 240) of difl"erences between bifurcation ratios
of tOl:t1 basins and mean bifurcation ratios of
t 'hl·ghcrordcr,~S. third orders in e:tcll basin. Dara from thcse
.')~- I b.1Sins. then, indicatc rh:tt the number of
::liefofb.1sinoforder II streams of each order above any point on a
10. ratioofrdiefofa basin mJin stre:tm forms :t geomerric series wirh
otal rdicfofbJsin ofncxt rigurt:~. Slr:Jhkr's (1952) syS[t:m of order,:lnd th:H the bifurcJ.tion r:l[iofor agiven
Ti~ SUt:lIl1 ordering watc:rshed tends (0 be const:Jnt.
:herage stream length conforms lO the law
it" _
I ofstre:lll1 lengths (Honon, 1945, p_ 291): The
_lO()[tot,d reliefof:J basin Horron (1945, p. 186) suggcstcd th:n the :t\"crage length of stre:lms of erich of the
dimcnsion paf:llld to the numbt:r of stre:lms of e:lch order in a 2i\'cn different orders in :1 drainagc b:1sin tends ro
l:l2C line basin form an inverse geometric series in \~hich c1osd~' approxim:llc a direct geometric series
':70 ,is for J bJ.Sin the first term is unitv and the ratio is the in which tht: first term is [he average length of
:in cis fOf :l bJsin bifurc:ttion r:llio. Horron'slaw is stJ,tcJ m:Hhe' Streamsof the first order.
m~Hicalh-:IS:
ETRY
(I)
Csing the same method of mathem:ttic:tl
i\faxwdl (1955) showeu that bifurc:llioll ratio
:tnah-sis:ts that [or bifurcation ratio. we obt:lin
erric.:s were :1I1alned for can be equalt:u to the :lluilog:lridlll1 ofb. the
·.1lCrshcus to the' laws of slopeofthe regression oflog numberofsrreams
(2,)
In this paperstreamsarc on order. Equ::J.tion (I) can be \Hittcn
·s (1952, p. 1120) adap'
.Y,... Roo (1:1)
1945. p. 281) scheme of which is the regression equ:ltion of log me:1I1
Small finger·tip tribu- raking logs ot"borh sides stream length on order. Hence. length r:ttio is
,order I.Twofirst-order tht: .:Jntilogarithmofthe slopt: ofthe regression
:I.second·ordersegmenr. log.Y~ .. i log Ro -!l log RI>, (ib) of log me:ll1 stream length on order (Fig. 4)_
[ IS formed by junction substituting The length of the highest-order segment w:ts
·cams. but may bejoined not plotted because this length to g:lge is less
second-order segments. ,: .. i log Ri> than the actual length of the complete seg·
me:l1(S join to form :t men£. :\ paired [-test showcd no significant
and
:lnd so on. The master difference between length r:l[ios obrained for
TIcnt ofhighest order. .-\ b-logR,. tot:ll basins and thosc obrained for randomh'
of lhe 5:lme order as rhe selected third-order basins in rhe 5:lme wate;·
we obtain
t. sheds. Length ratio, then, rends to be constant
sue:tm·gaging stations log N. s a - bll . (Ie) for an individual b::J.sin.
IS.Thesesrationsare nor, Figure5showslogcumulativestreamlengths
the end ofa stream seg But equ:Hion (Ic) is also the cmpirical expres· ofc:lch order in :t basin plotted against order.
Iegage: does not measure sion of the regression shown in Figure 3, in Straight lincs. fitted by eye. seem to bcst
!i\'cnorder. In all warer which the logarithm of number of streams is describe the regressions. Hence, log total
vere locHed as indicared plotted against order. Hence rhe bifurcation cumulative srream lengths, from first through
1030 M. E. MORISAWA-GEOMORPHOLOGY. ,\PPALt\CHIA!\" PLATEAU WATERSHEDS
•
o
.;
z
" ;;
•,
o 11 0 E R
Figure 3. Log number ofstreams ploned against order. Letters along abscissa represem
basins listed in Table l.
a given order within a basin, are directly Taking the logs of both sides and substituting
lated toorder by aline:J.r regression, 3S in equ3tions (I) and (2), we find th3t (3.) Figure 5. Logmean
equals equation (3) and t~at t.he an.tllog 0.£b listed in Table 1.
log Lw - a +bll . (3) irnati~Oq,ua[ion(3) islength ratiomulUSbifurc3Cion where the anrilogof
:. - I R,
Horton (1945, p. 293) states that log-I" ~ RL - Rb • P • R;,
Hence, the slope of the regression relating log
(3.) cumulative stream length and order is a con
stant equ~d to the length ratio minus bifurca
rion ratio. ~L.. • I
or, where u = i and p The total of all strC:3.m lengths of a given
order (and that order alone) is also empirically
RLw - R"w .--R"- (3b) related toorder by the regression ' I
R~ Rt.-R,,· log ~ L.. = a T btl.
• I
,r----,--r-......--,,.-...,.....--,--,---,--------,-,.----,----,
s:
4-
·
~
~
·,0
"
z , ,
~
E• >~ z- I
0
~ 0
" ,.
z
0
3
z
oL~_..,:~"
Figure 4. Log mean stream length plotted against order. Letters along abscissa represent
Figure:6. Logn
basins listed in Table I. listed in Table
:\U W.\TERSI-IEDS
BASIN 1I.10RPtIO~IETRY 1031
! ' /
.
·"
• /
; .
•
~ 1';/~
" ,
>
<
•"
•
•
" ,L
~
~
I
·; !o. . . I /
> /
•~ J,.I .I . /
19 ;)OscisSJ represcm
./.
...
"
th sides :lnd substituting
ORO E11 Q'~U
,J (2), \\'c lintl that (3a)
Figure;. Log me:Jn rOlJI Slre:llnlength ploued Jg:liost order. Letters:lIang:lbscissJ. reprcsent basins
nJ th:n the.: :llltilog of b
listed in TJblc J.
It[aliaminusbifurcation
whl.:rl.: the :lntilo~ofbis Horton'sp f:tetor, The !:Iw of basin areas is stated by Schumm
(1956, p. 606) as follows: d1C mean drainage
go. - g...
b:lsin areas of strcams of cach ordl:r tend to
le re~rcssioll rc!:lting log closely approximatc a direct geometric serics
Igth :lntl orde.:r is a con This follows from :l mathcmatic:ll :Illalysis of in which the first tcrm is the mcanarC:l offirst
grh Horton's equality (1945. p. 191):
ralio minus bifurca- order b.:lsins:
:::'L., _ LR.:-"R,.',-I . (-b)
cam It.:llgths of :l gi\'en
llont:J i~ :11,,0empiric:llly wherc. ;lg:lin. equation (-b) C:1I1 bl.: reduced lO
equ:ltiOll (4). This. In turn, is equi\':llent to the regression
(cgrl.:"'loll
,
:I.. '" .1 - h,. ,j ".
., J
" /
,-
~
///"
2 /
! ' / ! I / j
z< J- 1
:: /
, ., ////J !
'j:/ /
; ,-
>u I
• j" " I / I I / / I / !
~
,- ./
/
j
.. .. ..
01 , , , ,
" " H o"'Fl0f:" " '" 'M
JOscissJ represent QI~er
Figure6. Log mCJn bJsin:lreJ. ploltcd:lgJinSIorder. Lettcrsalong Jbsciss3 represent b:lsins
listcd in Table I.
1032 r-.·L E.. MORISAWr\-GE.OMORPI-IOLOGY, APP:\LACHIAN PLATEAU WATERSHEDS
shown in F
is plotled a:
Hence, art.
{he rcgrcssi
I{iscviu,
lines [0
strcam
closely
Plateau.
Chanl
istic of.
geomcii
tangent
measure
1033
BASIN MORPI-IO~IETKY
J WATERSIlEDS
shown in Figurt.: 6, where log mcan b:lsin :lrca with a tapc and clinomc[cr. or hand level.
Channel gmdicm is the average slope of the
is plotted against order:
entircsegmenc\Vhen [aken from a map, fall in
}" feet wasdi\'idcd by horizont:d leng[hofstre:lm
!og=--a+hll.
:11 in ft:cl.
Hence, arc;;! ratio is the ::1I1tilog of the slope of Horton (1945, p. 295) infers ,hat the rela
the regression oflog basin are:l:lodorder. tionship ofstrc:lrn-channcl gr:ldicn[ and order
Itisevident from theexcellent fi[ofsuaiglH can beexpressed by an inversegeome[ric series
CONEMAUGH ALLEGHENY
VJ.ILNLTEONNSVlLLE ~L.L.EGHENY ~LE
CL.ARION
" BYER
",---CUYAHOGA
Home Creek
Tor Hollow Mill Creek
FIb' \;onSYM<
ALLEGHENY
l
8eech Creek
MAUCH CHUNK
\....CATSI(~LL
500 POTTSVlLLE -----:HEMUNG
Green Lick --~~CA'TSKI-LL -
?iney Creek
;>OTTSVILLE
ALLEGHENY
Casselman R. MAHONING
CONEMAUGH
0::
_____ CATSKILL
W \:CHE~UNG
o POTTSVILLE ALLEGHENY
~
Youghiogheny R.
0::
o = ~ '_O_C_K_C_"_·_'L_' -"~::.:~::.'~ _
SCOTT CROSSVILLE
WART3UOlG
Daddys Creek
6"lCEVILLE
L::L::'=- _
CONE"lAUGH - :C:'~o:s:s:v~'
MAHONlNG ::mory R.
:.LLEGH(NY
-:;:-----:C~L~.~'~'~O~N ...::.2!'2'~'F.~,...,c;:;::c::::_=__;:_:_
= POTTSVILLE "OTiSVILLE
Little \tononlnq Cr.
POCONO
C:.TSKIL!..
o, 20.000 Allegheny R.
FEET
FigureS. Strc:lI11 profilesalong longest length
lines [0 the preceding d:H:l th:l[ the bws of bw. Some watersheds swdicd show tha[ a
suearn numbers, lengths, :lI1d :trc:l.S :lpply rchuionship of rnc:m channel gr:ldicm and
closely to w:Hersheds of the .\ppabchi:m order can be expressed by :l straight line. In
such cases (Fig. 7) rhe regression of log me::m
Pla[(~:lu.
Channel gradicn[ is an impon:llH ch:lracter channel gradient on ordcr is
istic of the vertical aspen ofdr:linagc-nc[work log 5" "" II - /III . (6)
geometry. Ch:lnnd gradien[ here refers [Q the
rangcll[ of the vertical :Ingle .H the poim of :\lsowecan formulate alawofslopes: dlC mean
mcasurcmCIl[. In dlCfield.slopesweremeasured channelgr:ldien[sofc:lch order form:ln inverse
1034 I\f. E. MORIS;\WA-GEOMORPHOLOGY, APPALACHIAN PLATE,\U WATERSHEDS
geometric scries with order, where the first bcen established in streams of Virginia and
the UI
term isgradient of the first-ordersegment and Maryland (Hack, 1957, p. 89). Differential
pected
theslopt::ofthe curve is theslope ratio, or resistance to erosion of horizontal rock byers ,Is,
S.. .."S,R/-tl • (6a) cmuaryvew.erl\l asctcreoaumntsfeogrmtheenste fblrocwaiknsginthtrhoeusglhopea ItihfraetdI
Howevcr. aU basins studied do not form a thick, resistant stratum may be stcepened Break
bea
MC moml
3.01 TH HC BC GL PC f lower
reJuVl
Fig1
ilI / / / / 1 / of StH
,
ugrap
relatil
2."
seen. I
profil,
lared
~I and I
I-
w 2.0 gradil'
W part0
ll.. law he
g.r.1d.il
ll..-
I t1nult
W- 151 there:
-.1 gradil
W homo
0::
chann
geoffil
-.1 3.0
<J: term
I- :md d
0 Th.
I- ~.
log to
19 2.5 .\vcr:
0 form~
-.1 first
basin.
2.0
,.
The l
slope
ONE order
ORDER contr
~-
15 A CR y LM DC ER linei,
l ~ grl
~ pr
ORDER
we:u!
faces.
Figure9. Average cotal relief plolCcJ against order. Lctters along each abscissa
represent basins lisced in Table I. B~
pressl
basin
straight-line ploe ofstream gradient on ordcr. although the gradient may bc less upstre:lm ordet
The deviations from a straight line may be on the stratum. Also, wcathering and slope non.
explained by one cause or a combination of wash may more easily reducc slopes on higher 'in fl
causes. The close relationship between li surfaces, whereas lowerslopesmay beprmccted
thology, structure. and stream gradient has by more resistant layers. This helps [0 naw~n S~IrSat:l:1\l