Hickin:1968-1988
A statistical
analysisof bankerosionandchannel
migrationin westernCanada
GERALD C. NANSON Depanmentof Geogmphy,TheUniversityof Wollongong,P.O.Box I144, Wollongong,NewSouthWales,Australia2500
EDWARD J. HICKIN Departmentol Geography,SimonFraserUniversity,Burnaby,B.C. CanadaVsA 156
ABSTRACT
Mean laleral-migration rates for 18 meandering river channels in
weslern Canado are expluined statlslically in terms of hydraulic and
sedimentological vrriables. The volurne of sediment eroded from the
outer bont of a meander bend is shown to be largely a funclion of
river size and grain size of sedlment at lhe base of the outer bank.
These variablec erplain almosl 70% of lhe volurnetric migration rale
for thesc relalively large, sand- and gravel-bed strems. It would appear lhat brnk erocion snd channel migration are essentially problems
of sediment enlrairunenl which is dependent on total slream power
rnd sedlmcnl size. Vegetation on the order brnk h seen to hrve litlle
siErilicrnt cfrec{ in controlllng channel migratlon. Further refinements
of the type of data used here should permit the development of an
rccurale predictive model of regional channel migration. To this effect, it is most imporlrnl to develop r precise relationship between
ben& resistance and the slze of sedimenl at the base of the outer bank.
(r,r), channel width (I7), the force per unit area of the outer (concave)
bank which resistschannelmigration (16), the bank height (i), and the
bend radiusofcurvature (r). Further,we haveshown that 16 is largelya
functionof the sizeof sedimentat the baseof the channel(D5s),suchthat
M = f (a, Llt, D5s, h, r).
(l )
Sediment load (particularly bedload) is known lo be strongly correlatedto channelmigrationrate(Neil, 1984),but whetherthe relationship
is causal or dependent has not been clearly demonstrated.Almost no
sediment load data exist for the l8 rivers chosen;therefore,the role of
sedimentload cannot be independentlyevaluated.Bagnold(1980), however, has shown ihat bedload transport is largely a function of stream
power operating on particular sedimentsizes,and, as both of thesevariables are included in equation l, a bedload transportterm is implicit.
Previousresearchenhaveexaminedbank erosionand channelmigration from a number ofaspects.Planfsrm ofmeander bendshas long been
consideredan important variable.Ieighly (1936) showedhow changesin
INTRODUCTION
the position of the high-velocityfilament in a bend,from low to high stage,
could provide a mechanismto accountfor the evolution of meanderbends
Channel migration and associatedriver-bank erosion arc among the through a seriesof predictrbleplanforms.Daniel (1971) demonstrated
most dynamic geomorphologicalprrxessesand, thereftrre,of considerable that channel lenglh around a meanderloop increasesin proportion to the
rientific interest. Furthermore, man's intensive use of river valleys and magnitudeof the channel-formingdischarge,whereasHickin ( 1974) demfloodplains means that a detailed understandingof theseprocessesis of onstratedthat migration operatesto maintain a minimum curvature ratio
(bend radius to channel width: r/LV) ofslightly >2. From dendrochrono
considerableeconomic valuc and engineeringsignificance,
Numerousdescriptionsof particular casesof channel migration exist, logicalevidence,Hickin and Nanson(1975) showedthat bend migration
but, for the most part, thes!are restriaed to a few bends on one or two
reachesa maximum value as the curvature ratio approaches3 and declines
channels(see'lable lV in Hooke, 1980).A lack of accompanyingbasic rapidly on either sideof this ratio value.Indeed,Carey ( I 969) and Page
bydraulic garmorphologic, and sedimentologicdata makes it imposible
and Nanson( I 982) haveshown that, in very tightly curving bends,deposi
to combinc more than a few of theseobservationsin order to derive a tion will occur around the outer bank and erosionwill occur at the convex
:ereral model of channel migration for a range of environmentalcondi- bank.
trons. Indeed, tbere appean to have been no attempt to systematically
The intermittent nature of channel migration has beendemonstrated
examineI rEngeof migration ratesfor a varicty of river types.The objec- by Brice (1973), who found that meanderloops along the samereach of
tive of this fnper is statisticallyto relate bend migration ratesto channel the White River do not evolvesequentiallyor simultaneously,
but interhydraulic, geomorphoklgic, and sedimentologic characteristicsfor l8
mittently,{irst in one part ofthe reachand then in another.tlickin (1974)
single-threedmeanderingriver reachesin westernCanadain an attempt to obtained similar lindings,and Nanson and Hickin (1983) showed thar
develop a predictive, empirical model of lateral migration. In the strictest migration can be very discontinuousin time as well as in distanc!along a
s!ns!,this model will have dircct application only for riven in physio
singlereach.Bendscan remain stationaryfor tensof years,therebymaking
graphic and climatic settings very similar to those in westem Canada. diflicult the estimate of long-term nrigration rates from short-term
More importantly, at this early stageof investigationinto channel migra- measurements.
tion, however, these empirical results identify at a general level those
A rather different approach to the problem ofchannel migration has
variablesthat are most infhrentialin determiningriver migrationrate.
beendevelopedby thosefocusingon the detailsof bank erosionwithout
In earlier work (Hickin and Nanson, 1984), we suggested
that the specificregardto channelplanform. The role of frost action and ground ice
rate of channel migration (ill) is likely to be dependenton stream power has been consideredby Wolman (1959), Walker and Arnborg (1966),
(essentially,the product of dischargeand slope) per unit area of the bed and Outhet (1974). Knighton (1973) found that bank erosionat a cross
Geological
Socictyof AmericaBulletin,v.97, p. 497-5M, 5 figs.,3 tabla, April 1986.
497
EJH:246
Hickin:1968-1988
NANSON AND HICKIN
sectionwas largcly determinedby the magnitudeand variability of dischargeand by thc degreeof asymmetryin thc velocityfiel4 bank wetting
More recentwork
beinga particularlyimportantpreconditioningprooess.
hasshown the importanceof basalsedimentsin compoite banks(nonwherein
sandysilt) in cases
sandandgravcloverlainby cohesive
cohesive
cantilevercollaFc brings down the cohesiveoverburden(Thorne and
thatremovalof boththe
Tovey,l98l). lmportantly,thiswslt rccognized
basd sedimentand thc mlla@ blocksis dependenton fluvial proc!ss!s
althoughthe predominanthilure mechanismis not directly lluvial (see
the role of
alsoThorneand [ewin, 1979).Their work alsoacknowledges
bankvegetationin limiting croaion,a problemexaminedquantitativelyby
Snith (1976).
Despitethesenumerousstudic of bank erosionand channelmigraOnly Hmke (1979,1980)
tion,theproblemremainslargelyunquantified.
basattemptedto developpredictivestatisticalrelationship. Most of thc
however,werenot sufficientlyindependent
ten variablestbat sheassessed,
results,andthey weres!lectedfrom
of oneanotherto allow unambiguous
a very restrictedrangeof river environmcnts.Hooke,however,did find, as
did Daniel (1971), that erosionrate is relatedto otchment area (disof silt and clay in the banls.
chargc)and the perc!ntage
Most of the above work on bank erosionhas been for relativcly
thresholdsare relow-energystrearns,but, becauselhe erosion-resistance
lated particularly to bank vegetationand fine-sedimentcohaion, thesc
operatingon
ohervations may not comparecloselyto similar processes
Greol Slove loke
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Hickin:1968-1988
ANALYSIS
OF BANKEROSION
AND CHANNEL
MIGMTION.CANADA
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COBBTES
Figure4. Thcrehdonbetweenthecoeffldentof rcdstrnccio htcnl Grodon(ra;,O / fri rE) rd 013medhndhmetcrof tlrebas6rcdlments
(Dsd ln theouler bmt" Horlzontdbnrsdefrnethe Wentwordrtertunldrs reprcsentrdve
of tbc hsrl grrln dze h c.ch dudy rcrch.Rlver
rcechesrre UeotfrcdIn Trblc 2.
rat!serceed!d5.5 channclwidtbspcr century,rnd thcrcwrs r urarimum
r&!eof - I channd width per decrde.
It is alsoapparenrfrom Figure3 thatduringthc 2l- to 3!yr pcriodof
record,- ?0%of thc bcndsdid oot move(Ml W = 0). Somcof thcscctses
may be tbc rcsult of an insuffcientlylong pcriod of timc havingcla@
betueenphotographsfor thc methodto detccl whst is, by its nature,an
interminent processof channclmigration (scc dctailcd evidcoccof this
point in Nansonand Hichn, 1983).If the pcriod of reoordwerc longcr,
mct of thesezcro valucsshouldmorc clccly onform to the long-tcrm
mcan migrationraa. Additional zcro valuesmty bc the rcutt of ocrtain
bcodsarrcstrngon unknowuobstructionswirhin cachlloodplain.In both
crscs,zcroshavebccnintcrpretcdasunreprcenLative
of thegeneratcondition for utrconfn!dmeandcnduring long periodsof time, and lherefore,
tbcc bcndshavebcenomittcd from themeanvalucsgivenin Trble 2 and
from the following strtisticalanatysc.Underthescconditions,themedian
migrationralc for thedlts setrs a wholc is -2 channelwidthsperoentury.
rametcn) from equationl, a sericsof rtcpwiscrcgrcssions
wasexecutcd.
To testfor statisticalrelatio"shipsamongthe variablcsin eqrution l, arithmctic meansof migration nrta(M ,) (ny-t) nachannel widrh (D (m)
werecalcrlatcdfor cachof tbe l8 river rcachcs.Thcc, aswell asdischarge
for the 5-y flood (0s.0) (m3s-l), cbannelstope(^9),outerbankleight lrry
(m), rod mcdiandiametcrof the bosalscdimcntsin the outcr bail (D50)
(mm), wcre usedto derivcthc puametcn of the maximumcrosionratcof
the brnts. Thcc paramctcnincludcvolumepcr unit lengthof channclat
thc pointof maximumlat!ru!displaccmcnt
perycar(l/r rl) (m3m-ly-l =
m2y-r), powerpcr unit areaof rhe bcd 1i = AQSF -tj 6ym+y, and
totrl power per unir lengrhof channel(O = pegs) (Wn-t) (Table 2).
Becauscall of thcc scc of dau rr! stronglypositivclyskewedtoward the
largestrivers, thcir distnbutioru wer!normalizedby obhining the log
(bascl0) ofeach variable.
The simple conelation matrix of transformedvariables(Table 3)
indicatesthat no singlemeasuredvariableaocountsfor >50%ofthe variancein thc meanmigration rst!; total stretm power, meanwidth, and
DATA ANALYSIS AND INTERPRETATION
dischargcprovide 48%,44%,tnd 34%,respectively.Usingstcpwiseregression,meanmigrationrate is rcgresodscqucntiallyagainstgroupcof inde.
In ordcr to estsblishthc respectivevariancecontributionsand bcnoe pendent variables introduccd in ordcr of thcir decreasingsimple
the prcdictivc valw ofeach iodcp!odentvariablc(and thcir dcrived pa- correlation. In this proccdurc,sdditionsl indcpcndcntvariablcswcrc
EJH:250
Hickin:1968-1988
fi2
NANSONAND HICION
T tt.s t. oonxE|. Ttol{ coEFftctFxts EETWEEN
AU. VATTASLES
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sddedto the rclationshiponly if, in combination,thcy explaincd>5% of
Ivtrr=0.45(D0.m
(l)
thc varianccin mern migntion and thenonly if thcir individualcontnbu20.3
20.3
tion wassignificrntst st lcastthc 10{6level.
10.0
10.0
If mean migration ratc is rqrcssed agrinst dischargqslope,bank
5.0
heighgaod mcdiangnin sizc,dischargerccouns for 34.1%of thevariance
and slopesmunts for 17.l%.Thc othcrshavcno significantoontnibution
Tbe totnl !rocivework accomplishcdby the river during the migra(eqution 2).
tioo of a meandcrbeodis expresedby theannualvolumctricerosionrate
at the point of maximumbend migration@;b. Equations5,6, and 7
go.eE2
fr , = 1.63
So.36E
indicatcthat the useof M/r clearly increascsthe predictabilityof channel
e)
53.2
YJ
(% explainedvarianoe)
l7.l
migration from measurements
of channelwidth, discharge,slope,bank
1.0
1.0
(%significsoccof explained
2.5
heighgand bosalsedimenlsize.This improvementrcsultsbecause
channel
variaooe;F tat)
migrEtiooinvolvescrcion of a volumeof marcrialaroundtheoutsideof a
1.0
(% significanc that exponent
5.0
mcanderbend a factor not takeninto acooutrtif migrationis expresedas
doesnot eqtul zcro;t t!st)
a simplelinear mcasurcof benddisplacement
If the sameregressionis ancmpted,but dischargcis replacedby mean
width, almct thesamelevelof cxplanationis achicvedandgrainsizeand
bank hcightremainoonsignificant(eqrutioo 3).
fr. =0.301
54.1
1.0
Wos
43.7
1.0
0.1
902?l
10.4
10.0
10.0
!)
Equation:2 and 3 clearlyindicatcthat thesizeofthe river (exprcsed
as dischargeor width) and the river slope providc important statistical
explanationsof migratioo rarc. It is also evident thst in this form of
rnnlysis,the variaoceoontnbutionof bankmatcrialand heightarc negligible, althoughthey are likcly o provc strtisticrlly significantin a group of
riven larger thsn 18. In multiple rqrcssion, variablesthat cxplain relatively low proportionsof the total explainedvariancerequirelarge&ta
setsin order to be idendfid asstatisticallysigrifieanl The hct thtt width
s!ernsto be a bencrprcdictorthanis dischargeprobablyindicatesthat the
useof widtb intcgratesthc effecrof the long-tcrmflow record whereas
rclativcly short-tcrmdischargerccordsarc used!o calculate0s.0. This
mustbe of somecomfortto thcc wishitrgto esrimatcbendmigrationratcs
on ungaugedrivcrs
The product of dischargeand slope in cquation 2 \ essentialln
sueampower,and,if includedassuchin thc rcgression
analp\ it explains
48%of the migration rat!vsrisnc whcreasgnin sizeaod bant height
rcmain noasignificaolStrean power per uoit arcais a poor predicrorof
channelmigrationrstc, cxplaidng ooly 20%of the variaace,andgrainsize
and bsl* hcightdrop out of thc sodFb rs mignificant (cqrution 4).
M th = 25.06
69.1
1.0
90.78E
57.5
1.0
1.0
so.7a
2.6
2.5
5.0
M .tr = 2.089
62.6
t.0
W r.t6e
53.6
1.0
0.1
D;$.ozr
1.5
10.0
10.0
M ,h = 0.67
29.3
10.0
a0.823
I1.5
2.5
5.0
D*2vt
r7.8
10.0
10.0
D*.N
9.0
5.0
10.0
(5)
^S0.56s
7.4
10.0
10.0
(6)
e)
Equation5 providcsthe bestpredictivecapacityof theaboveset,
although
theunexplained
variance
remains
highat -30%.F4uation8 isan
sttemptto scalethemigrationrate(throughchannelwidth)to thesizeof
theriver.
4i'
tr
= o.ota @o.6oi Dfi.m
36.5
1.0
8.5
r.0
2.o
(8)
27.9
1.0
5.0
Here, the size of the basalsedimentsis shown to be imporunt in
explainingthe volumetric erocionralcs of rivcr bends.In other words,
EJH:251
Hickin:1968-1988
ANALYSF OF BANK EROSION AND CHANNEL MIGRATION. CANADA
Channel migration
503
lN
Low-water surface
Channel boundary
in stage 1 '---2-.....-...
deeoz;';lonat
?l
tl
l*
erosional
20ne
tl
Figure 5. A schematlcdiagram of a channelcross sectlon through lhe erosional axis (Hickin, l9l4) of a mesnderbend which shows lhe
lrrge exlenl ofboundrry shearoporatingon the outer bed(B) comparedto lhe ouler bank(A). Note that the root zoneincludesonly the upper
part of the nesr-yerdcd cuthnt and docs nol effect tlrc bed of the channel.
holding river scaleconstantrcsultsin variationsin the sizeof basalsedimeotsthathavea relativelyimportanteffecton migrationrate,anobcervation alsomadefor Britishriven by Hooke(1980).
a rationallyderivodrelationIn anotherpaper,we havedemonstrated
ship betweengrain sizeand the derivedshearstr!ngthof the sediments
(HickinandNanson,1984).Sediment
rangedin sizefromclayto bouldcrs
in a complexerosionrelationship
similarto thatof theHjulstromsediment
entr&ioment
curve(Hjulstrom,1935;Shields,1936)rn4 therefore,was
In the prcsentpaper,
not amenable
to descriptionusinglinearregression,
however,the l8 river reaches
werepurposefully
selected
to lie within the
fine-sandto cobble rangeand therebyto exhibit an essentiallylinear
relationshipbetweenD5gof the basalsediments
and river bank resistance
to erosion.As shownin equations2, 3, 5, and 6, river sizeis the most
importantcontributorto channelmigration.If volumeric erosionrate
(M *h) wereto be scaledby streampower,however,it couldprovidea
on the
basisfor examiningtherelativelysmallinfluence
of basalsediments
rateof latenl erosion,usingtheequation
DISCUSSION AND CONCLUSIONS
Theseresultsdemonstrste
thatmeanbankerosionandmeanchannel
migrationare predictablefrom channelllow and geomorphological
and
power,or evenchannelwidth explain
data.Discharge,
sedimentological
>45%of thevariancein volumetricerosionof theouterbank.Thismaybe
related to the physicsof flow, such as the developmentof large-scale
turbulencein the form of helicoidalflow, but of over-ridingimportance
mustbe the total erosiveenergyavailableto largerivers.In combination
with measurements
of sedimentsizeat the baseof the outerbank,river
scaleexplainsalmost70%of thetotal variance.Indeed,if estimates
of the
power,and sedimentsizecould bc
independent
variablesof discharge,
determinedmorepreciselythan waspossiblefor this study,then the level
of explanation
wouldbe evenhigher.
Holdingriverscaleconstant,
equations
8 and9 showthesizeofbasal
sedimentin the outer bank to be particularlyinllueotialin determining
erosionrate.The work of Smith (1976) and Zimmermanand others
(1967)suggess,
however,that vegetation
is dso importantin controlling
Mrh =
bank erosion.Variationsin floodplainand bank vegetation
may explain
x"-50'
-nsomeof thescatterin Figure4, but we did not havesufticientdatato test
For the followingreasons,
Furlhernrore,
if thedependent
variablewereto be inverted,it would this possibilitystatistically.
it doesnot appear,
(equation9), a parameter
which however,thatvegetation
is of greatimportance
in limitingbankerosionon
becomean expression
of bankresistance
(force/area;
in tact,hasthedimensions
Nm-f (Hickinand theserelativelylarge,perennial,sandand gravelrivers.Newly exposed
of shearstress
sandandgravelis not a suitablesubctrate
for rapidandeffectiveestablishNanson,1984).
mentof vegetation.Evenif present,vegetationprotectsonly thesubaerial
(e) portionof a bank,leavingthesubaqueous
185.78DS'zes;,"t.r.;ft"= tu
portionfully exposed
to boundMrh
ary shear.Furthermore,
on forestedfloodplains(asmostoftheseare),the
6l.l
6l.t
root zonedoesnot extendmorethanI to 2 m in depth,leavingthelower
1.0
1.0
by thisformof riprap. MurgatroydandTernan(1983)
strataunprotected
0.1
haveshownthatafforestation
of floodplainsleadsto greaterbankerosion
of thick grassturf on the banks.Smith's
Equation 9 shows s strong positive correlation between the size of as a resultof the suppression
work on the roleof rootsin retardingbankerosion
basal sediments and bank resistance(r5) for basal sediments coarser than ( I 976) experimental
alluviumbelowboth the root
silt (Fig. 4). Although 15 has the dimensioru of force/area, it is a coefti- did not tekeinto accountthe unvegetated
cient of resistanceto lateral migration, presumablydependentlargely on zoneandthewaterline.
Numerous
cros sections
surveyed
in meander
bendsshowthatlateral
bank strengthbut also absorbingall the other facton, including the statisti
erosionof thelaterallyslopingbed
cal variability in stream power and migration rates. In this regard it is channelmigrationinvolvessubstantial
analogous to Manning's n, s coemcient of total flow resistance,but not in the outerpart of the channelas well as erosionof the ncarlyvertical
upperpartof thebank(Fig.5) (alsoseeThomeandlrwin, 1979;Thorne
directly measurable.
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