WATER
RESOURCES RESEARCH,
VOL. 35, NO. 11, PAGES 3523-3530, NOVEMBER
Effects of sediment supply on surface textures
of gravel-bed rivers
1999
This file was created by scanning the printed publication.
Errors identified by the software have been corrected;
however, some errors may remain.
John M. Buffington• and David R. Montgomery
Departmentof GeologicalSciences,Universityof Washington,Seattle
Abstract. Using previouslypublisheddata from flume studies,we test a new approach
for quantifyingthe effectsof sedimentsupply(i.e., bed materialsupply)on surfacegrain
sizeof equilibriumgravelchannels.Textural responseto sedimentsupplyis evaluated
relativeto a theoreticalpredictionof competentmediangrainsize(D•0). We find that
surfacemediangrain size(Ds0) variesinverselywith sedimentsupplyrate and
systematically
approachesthe competentvalue (D•0) at low equilibriumtransportrates.
Furthermore,equilibriumtransportrate is a powerfunctionof the differencebetween
appliedand critical shearstressesand is therefore a power functionof the difference
betweencompetentand observedmediangrain sizes(D•0 andDs0). Consequently,
we
proposethat the differencebetweenpredictedand observedmediangrain sizescan be
usedto determinesedimentsupplyrate in equilibriumchannels.Our analysisframework
collapsesdata from different studiestoward a singlerelationshipbetweensedimentsupply
rate and surfacegrain size.While the approachappearspromising,we cautionthat it has
been testedonly on a limited set of laboratorydata and a narrow range of channel
conditions.
surfacetexturesof gravel-bedrivers.Althoughsurfacetextures
can also respond to changesin the size distribution of the
Laboratoryand field studiesdemonstratethat surfacetex- sedimentsupply[Jackson
and Beschta,1984;Plattset al., 1989;
tures and gravel-bedrivers respondto changesin the rate of Perkins,1989; Knighton,1991; Parker and Wilcock,1993; Posedimentsupply(i.e., bed material supply) [Leopoldet al., tyondyand Hardy, 1994],we concentratehere on textural re1964; Dietrich et al., 1989; Kinerson, 1990; Lisle and Hilton, sponseto alterred sedimentload of a fixedgrain-sizedistribu1992, 1999; Lisle et al., 1993; Rice, 1994; Nolan and Marron, tion. Furthermore,we focuson the specialcase of channels
1995].When deprivedof sediment,poorlysortedbed surfaces that are in equilibriumwith their sedimentsupply.
typically coarsen through size-selectivewinnowing of fine
1.
Introduction
grains,as is commonbelowdams[Leopoldet al., 1964] and
wood jams [Rice, 1994]. Winnowingresultsfrom transport
ratesin excess
of sedimentsupply.Conversely,
wheninundated
with sediment,bed load transportcapacitiesmaybecomeoverwhelmed,causingdepositionof bed load material (typically
fine-grainedparticles[Leopold,1992]) and consequentreduction of surfacegrainsize[Rice,1994;Nolan andMarron, 1995].
On the basisof observedrelationshipsbetween sediment
supplyand bed-surfacetexture, severalmethodshave been
proposedfor qualitativelyassessing
sedimentload (i.e., low,
medium, and high) from inspectionof surface grain size
[Dietrichet al., 1989;Lisle and Hilton, 1992].Lisle and Hilton
[1999] recently demonstratedquantitativerelationshipsbetween sedimentyield and both the size and volume of fine
sedimentin pools. However, the observedrelationshipsare
sensitiveto basinlithologyand associated
propensityfor productionof fine-grainedsediment.In this paper we use data
.frompreviouslypublishedflume studiesto test a new model
for quantitativelydeterminingrates of sedimentsupplyfrom
observedbed-surfacegrainsize.We alsousethe modelframework to further examine the effects of sediment supply on
2.
Theory
Here we developa theoreticalrelationshipbetween sediment supplyrate and bed-surfacegrain size of equilibrium
channels.For equilibriumconditionsthe bed load transport
rate is equalto the sedimentsupplyrate (qb = qs). We define
bed load transportrate as a power functionof the difference
betweenthe applied and critical shearstresses
qb = k(r' - rc)n-- qs,
(•)
where,' is the bed shearstress(that portionof the total shear
stressapplied to the bed and responsiblefor sedimenttransport) [EinsteinandBarbarossa,
1952;Nelsonand Smith,1989],
*c is the critical shearstressfor particle motion, and k and n
are empirical values [du Boys, 1879; O'Brien and Rindlaub,
1934; Meyer-Peterand Mtiller, 1948; Chien, 1956; Ashmore,
1988;Wathenet al., 1995].
We define *c as the critical shearstressof the median bedsurfacegrain size(*cso). The mediangrainsize(D5o) is related to its criticalshearstressby the Shields[1936] equation,
which is a force balancebetweenthe fluid stressesactingon a
bed-surfaceparticleandthe resistinggrainweightper unit area
•Nowat WaterResources
Division,
U.S.Geological
Survey,
Boul-
* = •'c5o/(Ps-p)gD5o,
der, Colorado.
T c50
(2)
Copyright1999by the American GeophysicalUnion.
where p and Ps are the fluid and sedimentdensities,respec-
Paper number 1999WR900232.
00.43-1397/99/1999
WR900232509.00
tively,g is gravitational
acceleration,
and **csois the dimensionlesscritical shearstressfor incipientmotion of Dso.
3523
3524
BUFFINGTON
AND
MONTGOMERY:
EFFECTS
OF SEDIMENT
SUPPLY
ON GRAVEL-BED
RIVERS
Becausethe Shieldsequationis a force balance,it can be propriateconservative
value for use with bed load transport
invertedto determinethe competentmediangrain sizefor a data in general.There is alsohistoricalprecedentfor choosing
given bed shear stressby definingthat stressas the critical this value.In their well-knownstudyof bed load transport,
Tc50
Meyer-Peter
andMtiller[1948,p. 54]propose
* = 0ß03 asa
value
D•o = z'/Z*cso(psp)g,
(3)
where D}o is the competentmedian grain size for z'. Consequently,(1) canbe rewrittenin termsof a differenceof median
grainsizes,ratherthan a differenceof shearstresses
qb= k•(z' - Zc)n = k2(D•0- D50)n = qs,
(4)
whereDso is the observedmediangrain size(proportionalto
*c) andTc50
* is assumed
constant.
Severaltestablehypothesesfor relating bed-surfacegrain
sizeto sedimentsupplyrate can be developedfrom (4). First,
we hypothesizethat if equilibriumtransportrate is a power
functionof excessshearstress(,' - *c), it alsoshouldbe a
functionof the differencebetweenD }o andDso (a surrogate
for excessshearstress).If verifiable,ratesof sedimentsupply
could be determined
from the difference
of observed and com-
petent median grain sizes.Second,we hypothesizethat for
givenvaluesof k, n, and ,', there shouldbe an inverserelationshipbetweensedimentsupplyrate and *c (and thusDso)
for equilibriumtransport.
3.
Data
Sources
and Methods
Becauseit is difficultto demonstratechannelequilibriumin
natural rivers,we testedthe abovehypotheses
usingdata from
flume studieswhere equilibriumtransportcould be verified.
We used previouslypublisheddata from laboratory studies
that met the following criteria: (1) Experimentswere con-
lower limit for transportof mixedgrain sizes.
Predictionof D}o from (3) alsorequiresestimationof the
bed shearstress(,', alsoknown as the skin friction stressor
fluid stressactingon the bed). The simplestand bestknown
methodfor determining,' is that developedbyEinstein[1934,
1942, 1950;seealsoEinsteinand Barbarossa,1952]. However,
the Einstein approachassumesa logarithmicvelocityprofile
whichis inappropriatefor channelswith grainsthat are large
relativeto the flow depth.Large grainscausesignificantparticle form drag [Andrews,1999]and developmentof a strongly
nonlogarithmicvelocityprofile, producingbed stressesmuch
smallerthan would be predictedfrom a logarithmicvelocity
profile[Wibergand Smith,1991].Relativeroughness
is a measure of potential particle form drag and is defined here as
D84/h, where D84 is the surfacegrain sizefor which 84% of
the particlesare smallerandh is flow depth.Valuesof D84/h
for the compiledlaboratorystudiesrangefrom 0.07 to 0.55,
with an averageof 0.28 (Table 1). Consequently,
the Einstein
methodis not justifiedfor the currentdata set.Instead,we use
a more appropriate,albeit more complex,approachbasedon
the work of Wibergand Smith [1991].
Wibergand Smith [1991] developeda model for simultaneoussolutionof the verticalvelocityprofileandthe form drag
due to bed-surfacegrains;simultaneoussolutionis required
because the two influence
one another.
Unlike
the Einstein
approach,the form of the velocityprofile is not specifieda
priori, allowingmore accuratedeterminationof fluid forcesin
conjunction
with site-specific
measuresof bed materialproperties. We modified the Wibergand Smith [1991] model to
ducted in sediment-feed flumes with surface textures, bed includeother sourcesof roughness
observedin the compiled
slope,and water surfaceslopeallowedto equilibratewith an studies.We calculatedthe bed shearstress(,') in (3) as a
imposeddischargeand sedimentfeed rate; (2) eachinvestiga- reach-averagedepth-slopeproduct correctedfor wall effects
tor conductedexperimentsat severalfeed rates,usinga con- [Houjouet al., 1990], particleform drag [Wibergand Smith,
stantsizedistribution;(3) experiments
were allowedto run to 1991], and bed form drag where present[Nelsonand Smith,
a stateof equilibriumtransport(definedasequalratesof input 1989]
andoutput);and (4) grain-sizedistributions
of the equilibrium
ß =
- [,w(Z) +
+ ,¾(z)],
(5)
bed surfacewere reported. We found only four studiesthat
met these criteria [Parkeret al., 1982;Kuhnle and Southard,
(equalto ,' at thebed),*r is the
1988, 1990;Dietrichet al., 1989;Lisleet al., 1993].In two of the where,f is the fluidstress
total
stress,
*w
is
the
stress
associated
withwallroughness,
,p
investigations
[Dietrichet al., 1989;Lisle et al., 1993],equilibis
the
stress
caused
by
particle
form
drag,
*of
is
the
stress
rium transportwas additionallydefinedby similarityof input
associated
with bed form drag,andz is heightabovethe bed.
and outputgrain-sizedistributions.
Furthermore,in thesetwo
A finite differencemodel is usedto simultaneously
determine
studiesthe channelevolvedin responseto a progressivedeeach of thesereach-averageshearstresscomponentsin concreasein sedimentsupplyrate. In contrast,the channelwas
junctionwith the reach-average
verticalvelocityprofile [Houresetfor eachrun in the experimonts
byParkeret al. [1982]and
jou et al., 1990;Wibergand Smith,1991].
Kuhnleand Southard[1988,1990].The compiledstudiescover
Followingthe approachof Wibergand Smith [1991], the
a broad range of channelslopes(0.0035-0.031),width/depth
vertical gradientof the downstreamvelocity(Ou/Oz) is exratios (2-23), mediangrain sizes(2.3-12.9 mm), equilibrium
pressedin termsof the abovestressesas
transport
rates(0.0028-1.07
kgm-• s-•), andbedform
mor-
phologies(planebed, dune,and alternatebar) (Table 1). The
primarysourcesof roughness
in thesestudiesare channelwalls
Oz L
•p
, (6)
and form drag due to bed-surfacegrainsand bed forms.
To test the relationshipsindicatedby (4), valuesof the whereL is the lengthscaleof turbulentmixing(as definedby
competentmediangrain size (D}o) were calculatedfrom (3) Wibergand Smith [1991]).Rearrangingtermsand integrating
Ou_
1(•)0.5
1[*r-(*w+
*p+
,¾)]0.5
with Tc50
* equalto 0.03,a conservative
valuefor visually
based yields
studiesof incipientmotion[Buffington
andMontgomery,
1997].
Moreover,, cSovaluesnear 0.03 are commonlyreportedfrom
studiesof bedloadtransport[e.g.,ParkerandKlingeman,1982;
Andrewsand Nankervis,1995], suggesting
that 0.03 is an ap-
u(z)
p
o
(7)
BUFFINGTON AND MONTGOMERY: EFFECTS OF SEDIMENT SUPPLY ON GRAVEL-BED RIVERS
3525
3526
BUFFINGTON
AND
MONTGOMERY:
EFFECTS
OF SEDIMENT
SUPPLY
ON GRAVEL-BED
RIVERS
whereZo is the roughnesslengthscaleof the bed and u = 0 at proximatesthat of spheresresting on a bed of like grains
z - Zo. Equation(7) is integratednumerically,with the stress [Coleman,1967].
Becausethe sizedistributionof the competentbed surfaceis
componentsdefinedin terms of u and z, allowingiterative,
simultaneoussolution of both the stressesand the velocity unknown,we approximatedCm using a lognormalgrain-size
distribution
profile [Wibergand Smith,1991].
The reach-averagetotal shear stressis written as a depthslopeproductthat variesas a linear functionof height above
Cm=
exp (12)
the bed
(8)
where co is the maximumconcentrationof bed-surfaceparticles (set equal to 0.6), 4)rnand 4%0are the componentand
median grain sizes,respectively,expressedin 4• units (4• =
-log 2D, whereD is in millimeters[Kmmbein,1936]) and rr is
where ro is the total boundaryshearstress(p#hS) and h and
S are the reach-averageflow depth and water surfaceslope, the standard
deviationof particlesizesin 4•.We chose'the
respectively.
smallestreportedvalue of rr in eachinvestigationas a conserForm drag causedby bed-surfacegrains,bed forms,or any vative estimatefor the competentbed surface,with the range
other objectin the flow can be expressedas
of grain sizeslimited by thoseusedin eachstudy.Here 4%0is
determinedthroughsimultaneous
solutionof (3) and (5) (disP
cussedfurther below).
Fd= 5 Cd(lg2)Ax'
(9) Similarly, the stress associatedwith drag due to twodimensionalbedformsis definedbyNelsonand Smith[1989]as
where F a is the drag force that resultsfrom pressuredifferencesacrossthe object, Ca is the drag coefficient,Ax is the
flow-perpendicular
areaof theobject,and(u2) isthesquare
of
PCd(U
2)•;
gx
Tbf(Z)
=5
(13)
the referencevelocityaveragedoverAx. The referencevelocity
is definedas the velocitythat would existin the absenceof the
objectof interest.Dividing the drag force by the flow-parallel
area of the object(Ab) yieldsthe associated
drag stress
p
2 Ca•Ax
p
fzb• z¾
u2dz/(
- Zo)
,
•Z0
whereZbSis the heightof thebedform.Here the dragcoeffi-
Ax
Td:5Cd(lg2)
Ab'
=-
(IO) cientis 0.21 if flow separatesaroundthe bed form and is 0.84
The stressdue to grain form drag is defined accordingto
Wibergand Smith[1991]asthe particledragforceper unit area
summedover all grainsizes(smallestto largest,D i to D3•) at
each level of z
M
if flow remainsunseparated[Smithand McLean, 1977].
Wall effects include both momentum diffusion causedby
proximityof walls(i.e., width-to-deptheffects)[Leighly,1932;
Parker,1978]and differencesbetweenbed andwall roughness
[Einstein,1934; 1942; Houjou et al., 1990]. Using data from
Houjouet al.'s [1990]studyof planarrectangularchannels,the
ratio of wall to bed stress(rw/r') canbe expressed
asa power
functionof the width/depthratio (w/h) andthe ratio of bedto
wallroughness
( zob/Zow)
PZ Cd{
112) C
rn--t
(lib)
Tw
ZOb
ZOw/
r-7= 2.55
2
R = 0.99'
(14)
rn
where all valuesare cross-sectional
and reach averages.Rearranging(14) yieldsan expressionfor r w as a functionof r',
P2
.
Izm ]
tg2 dz/(z m- Zo) ,
(11c)
w/h, andZofZow
o
where ½mis the concentrationof a componentgrain size and
Zm is the vertical height of that particle above the bed. We
assumeellipticalgrainswith a Corey[1949]shapefactor of 0.6
(a reasonablevalueboth for naturalsedimentsand thoseused
in the laboratorystudiesinvestigated
here).The shapefactoris
definedas D s/V'D•Dz•, wherethe subscripts
S, I, and L
ßw= 2.55'
ZOw/
.
Theeffective
roughness
of thebedin planarchannels
isz%•
0.1D84 [•iting
and DietHch, 1990; Wibergand Smith, 1991].
Thisdefinition
of Zo•includes
bothgrainskinfrictionand
particleform drag [Wibergand Smith,1991].The effectivebed
roughness
in channelswith bed formsis foundby matchingthe
inner and outer veloci• profilesat the height of the bed form
indicate short, intermediate, and long axes,respectively.We
assumethat the grainsare orientedwith their short axesver- (z•f) [Nelson
andSmith,1989],yielding
tical and that the intermediateand longdiametersare equalto
one another (D s = 0.6D• - 0.6Dz•). Using the nominal
graindiameter
((DsD•rDt)•/3),
Cdm
isapproximated
bythe
drag coefficientfor a sphere,which is a function of particle
Reynolds number [e.g., Rouse, 1946]. While developedfor
isolatedsphereswell awayfrom channelboundaries,this relationshipbetween drag coefficientand Reynoldsnumber ap-
(
.
(16)
)-4(•'+•)/(•'+•+•)
z¾
z0•= z¾ 0.1D84
We definethewall roughness
fromNikuradse's[1950]equation
for hydraulicallysmoothflow, appropriatefor the smoothwalled flumes studied here,
BUFFINGTON AND MONTGOMERY: EFFECTS OF SEDIMENT SUPPLY ON GRAVEL-BED RIVERS
1
•
Parker et al. [1982]
[]
Kuhnleand Southard[1988]
3527
[]
ß Dietrich
etal.[1989]
A LiMeetal. [1993]
o.
1 //.4•
•
.
0.01
_
y=0.009 x1.3550.19,
R2=0.82
•
I ....
I ' '
0.001
0
5
10
15
D5O'- D5O(mm)
Figure 1. Equilibriumtransportrate (q•, -- qs) asa function
1
of thedifference
between
competent
mediangrainsize(D }o)
andthe observed
value(Dso).
10
Reach-averagebed stress(z', Pa)
Zow
= v/9u*w,
(17)
wherev is thekinematic
velocityandu* is the shearvelocity
w
at thewall(rX/-•w/p).
The competent
mediangrainsize(D}o) is determined
from
simultaneous,
iterativesolution
of (3), (5), (8), (11), (13), and
Figure2. Observed
mediansurfacegrainsize(D so) versus
bed shearstress(r') for experiments
by Parkeret al. [1982]
(diamonds),
KuhnleandSouthard
[1988](squares),
Dietrichet
al. [1989](circles),
andLisleetal. [1993](triangles).
The data
are stratifiedby equilibriumtransportrates(q•, = qs) of
<0.01,<0.1, and>1 kgm-• s-• shown
asopen,shaded,
and
solid,respectively;
specific
equilibriumtransportratesfor each
datapointarelistedin Table1. The dashedlinesarepredic-
(15). BecauseD }o is a functionof bed shearstress,whichis,in tionsof Dso for equilibriumtransportratesof 0.01,0.1, and 1
onthecurve
fitofFigure1, assuming
Tc50
* --turn, a functionof the surfacegrain-sizedistributionand con- kgm- • s-• based
0.03
and
Ps
-2650
kg
m
-3.
The
bold
solid
line
is
the
sequentparticleform drag,the competentmediangrainsize
prediction
of competent
mediangrainsize(D•o,
andthe bedshearstressmustbe solvedtogether.We empha- theoretical
seeequation(3)).
sizethat the competentmediangrainsizeis a hypothetical
value,theoccurrence
of whichdepends
onthelocalsupplyand
caliber of sediment. Channel characteristics and calculated
averagemediansurfacegrainsize,(3) caliberof suppliedsedvaluesfor the compiledstudiesare presentedin Table 1.
iment,and(4) sortingof suppliedsedimentin the four studies
(Table1). Previous
methods
for assessing
texturalresponse
to
sedimentsupplyresultedin a familyof curvesthat were de4. Use of Surface Grain Size to Infer Sediment
Supply
pendenton study-specific
ratiosof bed shearstressto critical
shearstressof thebedloadmaterial[Dietrichetal., 1989;Lisle
Data fromthe compiledlaboratorystudiessupportthe form et al., 1993].The generalcollapse
of the datatowarda single
of (1) quitewell, demonstrating
that equilibriumtransport functionsuggests
that the analysis
frameworkusedherepro(q•, = q•) is a powerfunctionof the differencebetweenthe videsa unifying
relationship
betweensediment
supplyrateand
appliedandcriticalshearstresses.
The equilibriumtransport surfacegrain sizein equilibriumchannels.
equation
for thesedataisq•, = 0.025(r' - %)•.3•___o.•9
with
R: = 0.82.Although
theexponent
of thisequation
iswithin
the rangeof typicallyreportedvalues(1.3-1.8 [O'Brienand 5.
Effects of SedimentSupply on SurfaceGrain
Rindlaub, 1934; Meyer-Peterand Maller, 1948; Chien, 1956; Size
Ashmore,1988]), both the coefficientand exponentof the
Figure2 comparesthe observedmediangrainsizeto the
relationship
are sensitiveto investigator
choiceof (1) the predictedcompetentvalueasa functionof bed shearstressand
methodfor determining%, (2) the characteristic
grain size sedimentsupplyrate. The data are stratifiedby equilibrium
represented
by % (i.e., the particulargrain-size
percentileand transport
ratesof <0.01,<0.1, and>1 kg m-1 s-1, withspe-
thepopulation
it isdrawnfrom(surface,
subsurface,
or load)), cificvalueslistedin Table 1; contours
of predictedgrainsize
and (3) the methodof correctingr' for channelroughness. for thesetransportratesalsoare shownbasedon the curvefit
Depending on the above choices,valuesof the coefficientk of Figure 1. The data of Lisleet al. [1993]andKuhnleand
varybyanorderof magnitude
(0.003-0.06),whilevaluesof the Southard[1988]showa wide rangeof mediansurfacegrain
exponentn vary from 1.2 to 2.1 for this data set [Buffington, sizesfor a relativley
smallrangeof bedshearstresses,
withD so
19981.
varyinginversely
with sedimentsupplyas hypothesized
from
Becauseequilibriumtransportis a powerfunctionof excess
shearstress,it followsthat it is alsoa powerfunctionof the
competent
andobserved
mediangrainsizes(surrogates
for the
appliedand criticalshearstresses,
(4)), as demonstrated
by
Figure 1. Plottedin this fashion,the data collapsetowarda
singlefunctiondespitediffering(1) bedshearstress,
(2) reach-
(4). Furthermore,the compileddatashowthat mediansurface
grain sizesystematically
approaches
the competentvalue at
low equilibrium
transportrates,as predictedfrom (4). This
equationindicatesthat the observed
surfacegrainsizeshould
approach
thetheoreticalcompetent
valueasequilibriumtransport rates go to zero.
3528
6.
BUFFINGTON
Discussion
AND
MONTGOMERY:
EFFECTS
OF SEDIMENT
and Conclusions
Our analysisdemonstratesthat surfacetexturesrespondto
changesin sedimentsupplyrate, as documentedby Dietrichet
al. [1989] and Lisle et al. [1993]. Imbalancesbetweenrates of
sedimentsupplyand bed load transportcausesize-selective
depositionor erosionthat altersbed roughness
which,in turn,
likely alters both the critical shear stressfor grainstraveling
over the bed [Kirchneret al., 1990; Buffin•on et al., 1992;
Johnstonet al., 1998] and the effectivebed shearstress[Naot,
1984; Wibergand Smith, 1991]. These responsesfeed back on
one another,partiallycounteractinglocal imbalancesbetween
sedimentsupplyand transportcapacity[Dietrichet al., 1989;
Lisle et al., 1993]. For example, transport capacitiesoverwhelmedby highsedimentsuppliesshouldcausefine-sediment
deposition,creating smootherbed surfaceswith lower intergranularfriction anglesand higherbed stresses,
both of which
will promote increased transport rates acrossthat surface
(equation(1)), reducingthe differencebetweensupplyand
transport rates.
Parkerand Klingeman[1982,p. 1422]hypothesizedthat surfacetextureand degreeof armoringin gravel-bedchannelsare
controlledby the ratio of bed stressto criticalstress(an alternativeexpression
for excessshearstress).They suggested
that
"when stressesare well above critical stress,mobility differenceson a grain-by-grainbasis are reduced;the differences
disappearasymptotically.
Thus a coarsepavementshouldnot
form. The low-stressrange for which pavementis required is
typical of gravel bed streams;the high-stressrange where it
shouldnot occuris typicalof sandbed streams."Subsequent
laboratory and field studies corroborate their hypothesis
[Parkeret al., 1982;Wilcockand Sourhard,1989;Pitlick,1992].
We further suggestthat bed-surfacetexturerepresentsa feedback between rates of both sediment supply and bed load
transport(the latter being a functionof surfaceroughness,
excessshearstress,and availabilityof transportable
sediment).
Althoughbed-surfacetexturemay respondto rates of both
sedimentsupplyand bed load transport(i.e., excessshear
stress),our use of equilibriumconditionsrendersthesetwo
factorsequal and inseparable,allowinginterpretationof equilibrium rates of sediment supply from inspectionof bedsurfacegrain size.The analysispresentedhere extendsprevious studiesof the relationshipbetweensedimentsupplyrate
and surfacegrain size [Dietrichet al., 1989;Lisle et al., 1993]
and showsthat there may be a singlerelationshipwhen sediment supplyis relatedto the differencebetweenD •o andD5o.
We find that this difference
is an indirect
measure
of excess
shearstress(z' - z½) and is well correlatedwith rates of
equilibriumtransportacrossdifferentstudies(Figure 1). Althoughthere are investigation-specific
trendswithin the data,
our analysisframeworkproducesa reasonablecollapseof the
compileddata.
SUPPLY
ON GRAVEL-BED
RIVERS
responseto eliminationof sedimentsupply.Temporalchanges
in bed-surfacegrain size and sortingwill also affect friction
angledistributions
andconsequent
valuesof z*•[Kirchner
etal.,
1990;Buffingtonet al., 1992;Johnstonet al., 1998].Our constant
valueof Tc50
* = 0ß03 is generallyappropriate
for nonimbricatedplanebeds,but highervaluesof z*eare advisedfor
channelswith more copmlexbed materialstructures(e.g.,imbricatedgrains,particle clusters,or stone cells) that reduce
particlemobility[Churchet al., 1998].
Despitetheuseof a constant
valueof z *½50we find a strong
relationshipbetweensurfacegrain size and equilibriumtransport rate for the data examined here. On the basis of our
findingswe suggest
that ratesof sedimentsupplyin equilibrium
channels can be determined
from the difference
between
ob-
servedmedian grain size and the predictedcompetentvalue
(Figure1). Regardless
of whetherthe caliberof the observed
surfacegrain size reflects textural responseto excessshear
stress,sedimentloading(Figure 2), or the particularsizedistribution of the supply,the differencebetweenpredictedand
observedgrain sizeis a measureof excessshearstressand is
therefore a measureof both q•, and qs for equilibriumchannels.
Assessingrates of sediment supply in natural gravel-bed
rivers using our approach requires conditions of quasiequilibrium. For equilibrium channelswith well-developed
floodplainsandself-formedbeds(i.e., all sizesmobileat typical
high flows),D•o shouldbe predictedfrom the bank-fullbed
stress.An expedientapproachfor applyingFigure 1 is to confine its use to hydraulicallysimple,plane-bedreacheswhere
correctionfor bank effectsand particleform drag may be the
only roughness correction needed. Hydraulically simple
reachesare recommendedbecausethe grain-sizeresponseto
sedimentsupplyobservedin our analysisis fairly small(-17
mm over3 ordersof magnitudeof sedimentloading)andmay
be overwhelmedby parameter uncertainty in formulas for
stresscorrectionof hydraulicallycomplexreaches.Lisle and
Hilton [1999] also report fairly small magnitudesof textural
responseto sedimentloadingin gravel-bedriversof northern
California and southernOregon.They found that the D5o of
fine pool materialdecreases
approximately9 mm over3 orders
of magnitudeof sedimentyield. The sensitivityof equilibrium
transportratesto smallchangesin grainsizealsohighlightsthe
importance of accurategrain-sizesampling,insuring a high
degreeof confidencefor the grain-sizestatistics(further discussionof sedimentsamplingproceduresand accuracyis given
by Churchet al. [1987],Riceand Church[1996],andBuffin•on
and Montgomery
[1999]).
While Figure 1 may proveusefulfor assessing
ratesof local
bed load sedimentsupply,it is cautionedthat our resultsare
based on a limited set of flume data with small grain sizes
(D5o < 13 mm) andchannels
not entirelyself-formed;
except
for the studyof Lisle et al. [1993] the laboratorychannelsused
However,ouranalysis
assumes
a constant
valueof To50
* and in our compilationwere constrainedto specificwidths. Furso doesnot fully describetexturalresponseto alteredratesof thermore,the caliberof sedimentsupplywasheld constantin
equilibrium
transport.
Dimensionless
criticalshearstress
(
eachexperiment,and althoughthe data collapsefairlywell into
will vary with site-specificdifferencesin bed material proper- a singlefunction despite differing size distributionsof sedities (e.g., grain shape,rounding,protrusion,imbrication,and ment supply,the limited amount of availabledata does not
distribution
of intergranular
frictionangles).
Moreover,
•*•val- allow a full explorationof the effectsof theseparameters.For
ues will covary with changesin bed-surfacegrain size and example,everythingelsebeing equal,bed surfaceresponseto
sorting that occur in responseto altered rates of bed load a supplyof fine-grainedsedimentmaybe very differentthan to
transportor sedimentsupply.For example,Churchet al. [1998] a supplyof coarser-grained
material.Use of a constantvalueof
observed
temporalchanges
in effective
valuesof ß*½5oas bed Tc50
ß alsomaycauseerrorsin calculated
valuesof D 5o
• and
surfacescoarsenedand as bed material structurechangedin corresponding
estimatesof equilibriumtransportrate (as dis-
BUFFINGTON
AND
MONTGOMERY:
EFFECTS
OF SEDIMENT
cussedabove).Becauseof theseconcerns,
furtherinvestigation
of our findingsis warrantedbefore they are appliedas a land
managementtool. Moreover, the condition of near-equilibrium transportmay not be a realisticassumptionfor actively
disturbedlandscapes,such as watershedsthat have been intenselyclear-cutand are experiencinghigh sedimentloadsdue
acceleratedlandslidefrequency,road runoff, or destabilized
river banks.Where it is knownthat channelsare aggrading,our
proposedmethodprovidesa minimumestimateof local sediment supplyrate; the difference between predicted and observedD5o can providean estimateof the bank-fullqb, which
must be lessthan qs for an aggradingsystem.
The requirementof equilibrium transport for use of our
approach motivates an interesting question about natural
channels:What is the time for bed-surfaceadjustmentto perturbationsof sedimentsupplyor transportcapacity?That is,
how long doesit take for surfacegrain sizeto equilibratewith
imposedchannel hydraulicsand sedimentload? Gravel-bed
channelsoccurin a wide rangeof environmentsthat are characterizedby different magnitudesand frequenciesof discharge
eventsand sedimentinputs,offering a range of timescalesfor
channeladjustmentto theseperturbations[Pitlick, 1994]. In
arid regions,channelsexperienceinfrequent,intensefloodsof
short duration (on the scaleof severalhours) that may not
offer sufficienttime for morphologicadjustmentto the imposeddischarges
and sedimentloads[LaronneandReid, 1993].
In mountaindrainagebasinsof the westcoastof North America, hydraulic dischargeis typically perennial, with rainfalldriven flood eventsoccurringone or more times a year and
having durationsof the order of one or more days,allowing
significantly
more time for morphologicadjustments.In intermontaine regionsof the United States,flood flows typically
result from spring snowmeltand are characterizedby long,
graduallyvaryingdischargesthat occurof the order of tens of
days to months and allow even more time for morphologic
adjustmentsand attainmentof quasi-equilibrium.To put these
environmentaldifferencesin context,the 100 year flood may
be less than 2 times the mean annual flow in snowmelt basins,
while it can be more than 10 times the mean annual flow in
watershedswith flashy, storm-drivenhydrographs[Pitlick,
1994].
The likelihoodof channelmorphologyequilibratingwith the
imposedhydrologyand sedimentload dependson the shape
and durationof the localhydrograph,aswell asthe timescale
of adjustmentfor the morphologicfeature of interest.Moreover, alluvialchannelsare nonlineardynamicsystemsthat can
exhibit a variety of responsesto perturbationsof hydraulic
dischargeor sediment supply. For example, many alluvial
channelsare free to adjusttheir width, depth,slope,bed form
morphology,channelpattern, and bed-surfacetexture in responseto changesin dischargeand sedimentsupply(see review by Montgomery
and Buffington[1998]). Severalmorphologic adjustments may occur simultaneously for a given
perturbation,with many responsesfeeding back on one another. The specificmorphologicresponseto a particularchannel perturbationdependson localchannelcharacteristics,
geomorphic setting,and historicaleventswithin the watershed.
Nevertheless,changesin bed-surfacetexturesmay be an active
and potentiallyrapid, first-orderresponseto alteredsediment
supply or hydraulic discharge. Consequently, observing
changesin bed-surfacetexture may be a more sensitiveand
effective means of monitoring channel responseto altered
sedimentsupplyand hydraulicdischargeover shorttimescales.
SUPPLY
ON GRAVEL-BED
RIVERS
3529
Over longer timescales,other morphologicfeatures may be
better indicatorsof channelresponse,particularlywhere textural changesare short-livedor counteractedby subsequent,
larger-scalemorphologicadjustments.
Acknowledgments. Financial supportwas provided by the WashingtonStateTimber, Fishand Wildlife agreement(TFW-SH10-FY93004, FY95-156), the PacificNorthwestResearchStationof the USDA
Forest Service(cooperativeagreementPNW 94-0617),and the National ResearchCouncil(USGS ResearchAssociateship).
We thank
Mike Church,Rob Ferguson,JohnPitlick, Jim Pizzuto,Peter Wilcock,
and an anonymousreviewerfor insightfulcriticismsof earlier draftsof
this work.
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(ReceivedApril 12, 1999;revisedJuly 19, 1999;
acceptedJuly22, 1999.)