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Densmore, A.L. and Ellis, M.A. and Anderson, R.S. (1998) 'Landsliding and the evolution of normal
fault-bounded mountains.', Journal of geophysical research : solid earth., 103 (B7). pp. 15203-15219.
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Densmore, A. L. and Ellis, M. A. and Anderson, R. S. (1998) 'Landsliding and the evolution of normal fault-bounded
mountains.', Journal of geophysical research : solid earth., 103 (B7). pp. 15203-15219, 10.1029/98JB00510. To view the
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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. B7, PAGES 15,203-15,219,JULY 10, 1998
Landslidingand the evolutionof normal-fault-boundedmountains
Alexander
L. Densmore
Departmentof Geology,Trinity College,Dublin, Ireland
Michael
A. Ellis
Center for EarthquakeResearchand Information,Universityof Memphis,Memphis,Tennessee
Robert
S. Anderson
Institute of Tectonicsand Departmentof Earth Sciences,Universityof California,SantaCruz
Abstract. Much of the tectonicand climatichistoryin high-reliefregions,suchas the
mountains
of thewestern
U.S.BasinandRangeprovince,
is contained
in themort?holo
•
of hillslopes,
drainage
networks,
andotherlandforms
thatrangein scalefrom10-' to 10•
km. To understandhow theselandformsevolve,we havedevelopeda numericallandscape
evolutionmodel that combinesa detailedtectonicdisplacementfield with a set of
physicallybasedgeomorphicrules.Bedrocklandsliding,long recognizedas a significant
geomorphicprocessin mountainoustopography,is for the first time explicitlyincludedin
the rule set. In a seriesof numericalexperiments,we generatesyntheticlandscapes
that
closelyresemblemountainoustopographyobservedin the Basinand Range.The
productionof realisticlandscapes
dependscriticallyon the presenceof bedrocklandslides,
and landslidingyieldsratesof long-termerosionthat are comparablein magnitudeto
thoseof fluvial erosion.The erosiveefficiencyof bedrocklandslidingimpliesthat
hillslopesmay respondvery quicklyto changesin local baselevel and that fluvial erosion
is the rate-limitingprocessin steadystateexperimentallandscapes.
Our experiments
generatepower law distributionsof landslidesizes,somewhatsimilarto both field and
laboratoryobservations.
Thusevena simplemodelof bedrocklandsliding
is capableof
quantitativelyreproducingmountainoustopographyand landslidedistributionsand
representsa significantstep forward in our understandingof the evolutionof normal-faultboundedranges.
1.
Introduction
formationfrom the model results.In a high-resolutionmodel
like the one we develophere, geomorphic
rule setsmay be
Despite recent interest in the interplaybetweentectonics groundedin the physics
of specificprocesses.
Landformevoandtopography
[MerrittsandEllis, 1994,andreferencesthere- lutionmaythenbe linkedto measurablerelativeprocessrates.
in), the evolutionof mountainoustopographyat the landform Recent LEMs have proposedphysicallybasedalgorithmsfor
scaleremainspoorlyunderstood.
While the grossmorphology the processes
of hillslopesedimenttransport[Anderson,
1994;
of a particularmountainrangeor orogenmayreflectthe large- Rosenbloom
and Anderson,1994],fluvial sedimenttransport
scaleforcesthat have shapedit [Elliott, 1976;Suppe,1981; [Howard,1994],and bedrockchannelincision[Howardet al.,
Koons,1989;Beaumontet al., 1998],additionalinformationon 1994]. As yet, however,no LEM has incorporatedrealistic
the tectonicand climatic historyof the range is containedin algorithmsfor tectonicdisplacements
or bedrocklandsliding.
landforms that are one to several kilometers in extent, includ- We discuss
belowwhy suchalgorithmsare importantin gening individualhillslopesand catchments,faceted spurs,and erate and interpretingmountainouslandforms,and our reasonsfor applyingthe completedLEM to mountainoustopogdepositional
fans.
A numericalmodelof landscapeevolutionprovidesoneway raphyin the Basinand Rangeprovinceof the westernUnited
to explorethe sensitivityof differentlandformsto tectonicand States.
climaticprocessesand may be used to comparethe relative
1.1. Models of Tectonic Displacements
rolesof variousprocesses
in shapingthe landscape.
Most landCoseismicand aseismictectonic displacementsgenerate
scapeevolutionmodels(LEMs) have focusedon orogenicstructural
relief and createthe templateon whichgeomorphic
scalelandscapes
andhavereasonably
ignoredthe finer details
act. The degreeof realismrequired in the tectonic
of the topography[Koons,1989;Anderson,
1994;Gilchristet al., processes
field usedby an LEM dependson the desired
1994;Kooiand Beaumont,1994;Tuckerand Slingerland,
1994, displacement
realism
and
spatial
resolutionof the model. Simple wedge1996].A disadvantage
of theseorogen-scale
LEMs is that they
shaped
[Kooi
and
Beaumont,
1996], sinusoidal[Tuckerand
require coarsespatialresolutionsand lumpedparameterrule
Slingerland,
1996],
or
Gaussian
[Anderson,
1994]upliftpatterns
sets,which limit the extractionof tangibleor measurableinmaybe sufficientto simulateorogenic-scale
tectonicdisplaceCopyright1998by the AmericanGeophysicalUnion.
ments.At higherresolutions,
permanenttectonicdisplacement
Paper number98JB00510.
0148-0227/98/98JB-00510509.00
fieldsgenerally
displaysignificant
structure
at lengthscalesof
a few kilometers[e.g.,Kinget al., 1988;Steinet al., 1988].If
15,203
15,204
DENSMORE
ET AL.: EVOLUTION
OF MOUNTAINOUS
TOPOGRAPHY
topography
isgenerated
byrepeated
applications
of thatdis- [Pearceand Watson,1986;Blodgettet al., 1996;Hoviuset al.,
placementfield, simulatingthe effectsof multipleearthquakes 1997].
on a particularset of faults,then a high-resolutionLEM must
to the BasinandRangeProvince
include a tectonicfunction that accuratelyreproducesstruc- 1.3. Application
ture in the displacementfield at thoselength scales.
The primary motivation behind the developmentof our
LEM is to explorethe evolutionof mountainoustopographyin
1.2.
Models of Bedrock Landsliding
the Basinand Range provinceasa functionof both surfaceand
Bedrocklandslidinghasbeen shownto be a significantgeo- tectonic processes.The dramatic ranges of the Basin and
morphicprocessin a varietyof landscapes
[Kelsey,1980, 1988; Range are consequences
of late Cenozoicextensionand have
Pearce and Watson, 1986; Schmidt and Montgomery,1995; inspiredeloquentexplanationsfor the origin of mountainsin
Blodgettet al., 1996;Burbanket al., 1996;Densmoreet al., 1997; general.The structureof theserangesis due to time-integrated
Hoviuset al., 1997].Blodgettet al. [1996]calculatedshort-term tectonicdisplacements,and consequently,their structuralgeerosionratesdue to landsliding
of 10-14 mm yr-• in the ologyhasreceivedthe mostattentionin resolvingissuesabout
BolivianAndes,whileHoviuset al. [1997]derivederosionrates their origin. In contrast,their topographyhas receivedlittle
of 5-12 mmyr-• in the Southern
Alpsof New Zealand.De- attention since the turn of the century [Gilbert, 1928] (see
spite these observationsthe long-termrole of bedrockland- Sharp[1939,1940]and Wallace[1978]for notableexceptions).
slidesin landscapeevolution is poorly understood,and no This is partly becausemountainoustopographyis often conLEM has yet incorporated a realistic bedrock landsliding sideredthe remnantof the more activeprocessof geological
mechanism.ExistingLEMs treat hillslopeprocesseseither as mountainbuilding, the insignificantremainsof the day. Even
diffusive[e.g.,Kooi and Beaumont,1994, 1996], or as a "buzz whentopographyis acknowledgedto containvaluabletectonic
saw" that instantaneouslylowers unstable slopes [Howard, information,it is recognizedthat thisinformationis convolved
1994; Tuckerand Slingerland,1994].Anderson[1994] argued with the effectsof surfaceprocesses.
We showthat despitethis,
that bedrock landslidesare necessaryto produce the linear the topographyof activelyformingmountainsmayyield quanhillslopesoften observedin real landscapes,
and simulatedthe titative insightsinto both setsof processes.
landslideprocesswith a hillslopesedimentflux that increased
In this paper, we describea numeric landscaleevolution
sharplyas a critical slope angle was approached.These ap- model and demonstratethe role of bedrocklandslidingin the
proacheshave been shownto producerealistic-lookingland- evolution
of synthetic
landscapes
at lengthscales
of 102-104
m.
scapesand may be sufficientif the modelinggoal is simplyto Sincethis is, to our knowledge,the first LEM to incorporatea
L.,•
L•,la•,•l,Xlally.
reproducethe grossshapeo•t ,h•.,
.......
h,, However,they
CtAIOg,lk lCtll•1311•llllg l HIC• WC ½•Ulllpi:11C UHI 111ULII•I pll•LlllJtlUllb
UI
are ultimatelylimited by their relianceon parametersthat have topography,landslideerosionrates,and landslidedistribution
no physicalmeaning:a "landscape-scale"
diffusivityin the case with existingfield data from active-fault-bounded
mountainsin
of the diffusionmodel,and a criticalslopethresholdin the case the Basin and Range.
of the buzz saw model. In addition, such deterministic models
ignore the potentially important and time-dependentrole
playedby largebedrocklandslidesin landscapeevolution.For
example,large landslidesmay form natural damswhosecreation and eventualfailure have drasticimpactson the downstreamgeomorphology
of the river system[Costaand Schuster,
1988].The sizeof the landslidedam determinesboth howlong
it persistsand how large the eventualoutburstflood is, which
in turn determinethe amountof geomorphicchangeeffected
by the presenceof the dam [Costaand O'Connor, 1995]. Finally, suchdeterministicmodelscannotbe usedin testingfrequency-magnitude
distributionsof landslides,despitethe fact
that these distributionsprovide a distinctivefingerprint of
mountainousregions and are increasinglyeasy to acquire
throughremote sensing[e.g.,Hoviuset al., 1997].
A variety of studieshave addressedeither the short-term
behavior of bedrock landslidesor their spatial and temporal
distribution.Selby[1980]recognizedthe importanceof discontinuitiesin controllingand materialpropertiesof bedrockand
devised a landscape-scalebedrock strength index. Kirkby
[1987] producedone-dimensionalnumericalmodels of hillslope evolution by landslidingusing a steady state reaction
model.Schmidtand Montgomery[1995]usedthe observedrelief in landslide-dominatedregions to infer landscape-scale
bedrockstrength,and Miller and Dunne [1996] predictedthe
two-dimensional density of fracturing within bedrock hillslopes.Compilations of spatial landslide distributionshave
generallybeen limited to small spatial and temporal scales
[e.g.,Megahanet al., 1978;Noever,1993],althougha numberof
recent studieshave used remote-sensing
techniquesto determine landscape-scale
landslidescalinglaws and erosionrates
2.
The Landscape Evolution Model: ZSCAPE
ZSCAPE
is a three-dimensional
numerical
model
that acts
on a finite-differencegrid [Elliset al., 1995].We use a 100-m
spacingbetweengrid pointsas a compromisebetweenspatial
resolutionand computationtime. This is comparableto the
resolution
of theU.S. Geological
Survey(USGS)3-arcsec
digital elevationmodels(DEMs), andwe testour numericallandscapesagainstthosedigital data. The model processescan be
divided into two distinct groups:a tectonic rule set, which
generatesa bedrockdisplacement
field, and a geomorphicrule
set,which attacksthe resultingbedrocktopographyand rearrangesmassat the surface.
3.
Tectonic
Rule
Set
CurrentLEMs usea kinematictectonicforcingfunctionthat
prescribesa relativelysimplepattern of uplift assumedto be
appropriate at the temporal and length scale of interest. In
most cases,these LEMs have been aimed at very long-term
(-->106years)andlonglengthscale(->105m) orogens
in which
the detailsof tectonicdisplacements
dueto uppercrustalfaulting are likelyto be irrelevant.Our levelof interest,however,is
at the mountainrange scaleand below,whichrequiresa more
realistictectonicdisplacementfunction.
We assumethat patternsof deformationare derivedprimarily from the sum of repeatedearthquakesacrossfaults within
the upper crust [Steinet al., 1988;King et al., 1988], and we
assumethat such displacementfields may be derived from
planar dislocationswithin an isotropicelastic half-space.A
DENSMORE ET AL.: EVOLUTION
OF MOUNTAINOUS
TOPOGRAPHY
15,205
(cm)'
'0
Uplift
400
•
Figure 1. Tectonicdisplacement
field usedin the modelexperiments,
corresponding
to a singleearthquake
(Mw '" 7.0). The fault is drivenby a pure shear,extensional
displacement
gradienttensor(shownschemat-
icallybythelargearrows)
at a strainrateof -"10-7 yr-•. Notethatthefaultextends
alongstrikebeyond
the
edgesof the 20 by 20 km displacement
field.The ZSCAPE experiments
useonlythe central10by 10km region
of the displacement
field shownhere.The insetshowsa crosssectionthroughthe centerof the displacement
field, as well as the 45ø-dippingfault plane.
number of studieshave demonstratedthat simple elasticdis- tion acrossour 10 by 10 km model spaceis smallfor geologilocationmodelsreproduceat least the first-orderfeaturesof cally reasonablevaluesof crustalelasticthickness.Flexurally
real tectonic displacementfields from a variety of geologic derivedtilting, which couldpotentiallyinfluencethe geomorsettings[e.g.,Steinet al., 1988;Massonnet
et al., 1993;Gomberg phic evolutionof the modelspace,is thusrelativelyunimportant.
and Ellis, 1994;Andersonand Menking,1994].
We calculate displacementsusing the three-dimensional
The accumulationof tectonicdeformationimportantlyinboundary-elementalgorithm of Gombergand Ellis [1993, volvesboth horizontalandverticaldisplacements.
Many three1994], based on the three-dimensionalGreen's function of dimensionalLEMs incorporateonly vertical displacements,
Okada [1992]. The boundaryelement method [Crouchand but we employ the full three-dimensionalfield. We use an
Starfield,1983]providesanalyticalsolutionsfor displacements Eulerian description of the deformation that amounts to
within a material that is subjectto internal displacements watching material move through the fixed finite-difference
acrossone or more planar dislocationelements.Solutionsare grid.
obtainedby minimizingstrainenergywithin the materialwhile
satisfyingstress,strain, or displacementboundaryconditions.
The Gomberg-Ellisalgorithmallowsin additionthe specifica- 4. Geomorphic Rule Set
tion of a remote or far-field boundaryconditionthat provides
Erosion and depositionwithin the model are dictated by
the drivingforcefor displacements
acrossmodelfaultsthat are
conservationof mass,which relatesthe rate of changeof the
constrainedby stressconditions.
surfaceelevationto spatialgradientsin sedimentflux:
In the present experiments,we drive displacementsacross
normalfaultsby specifyinga regionalpure shearin whichcrust
oz/Ot = (l/p) V-qs
(1)
is horizontally extended at twice the magnitude that it is
thinned vertically and shortened horizontally. For a 45ø- Here Oz/Ot is the rate of elevationchangewith time, p is the
dippingfault of 40-kmlengthand 15-kmwidth (downdip),this bulk densityof the material in question,and qs is the mass
incrementof pure shearyieldsdisplacements
that correspond sedimenttransportrate per unit width. (Theseand other symto an earthquakeof moment magnitude7.0 (Figure 1). We bolsare depictedin the notationsection.)In determiningnurepeat these earthquakesat 500 year intervals,which corre- mericalexpressions
for qs, mostsurfaceprocesses
modelshave
sponds
to a strain-rate
of 10-7 yr-• overa lengthof 100km. distinguished
betweenhillslopeand fluvialsedimenttransport
These figures are within an order of magnitude of current processes
[Anderson,1994;Howard, 1994;Tuckerand Slingerestimatesof strainacrossthe Basinand Rangeprovince[Sav- land, 1994;Kooi and Beaumont,1996].We take a similarapageet al., 1995;Dixon et al., 1995].
proach,identifyingfour keygeomorphicprocesses
activein the
Surfacedisplacements
due to the model earthquakerange Basinand Range:regolithproduction,regolithtransport,bedfrom 140 cm of subsidenceto 30 cm of uplift. We neglect rocklandsliding,and fluvialsedimenttransport.The first three
second-orderdisplacements
due to postseismic
processesthat processes
occuron hillslopes,while the last is confinedto the
result from the viscous relaxation of stresses in lower crustal
fluvialchannelsystem.To accommodatethisbasicdichotomy,
material. At present, the model does not allow for flexural we divide the landscapeinto hillslopeand channelnodesand
isostaticelevationchangesthat resultfrom differentialloading apply the appropriatealgorithmsto each set of nodes.While
and unloading.These changeshave been shownto be signifi- we recognizethat valleyglaciershavebeenimportantgeomorcantin extensional
settings[e.g.,Weissel
andKarner,1989;King phic agentsin parts of the highestrangesof the Basin and
and Ellis, 1990;Small and Anderson,1995].We demonstrate Range[e.g.,Stewart,1980],we ignoretheir effectsin our curbelow,however,that the differentialflexuralchangein eleva- rent experiments.
15,206
DENSMORE
Faulting
Hillslopes
.
ET AL.: EVOLUTION
Channels
Ot, up to a regolith thicknessR,, beyondwhich the rate declinesexponentially(Figure 2):
OR
(OR)[
(OR/Ot)*
-(OR/Ot)ø]
Q,I
Transport
Rate
ii•ion
(2)
o
R, Thickness
QR
TOPOGRAPHY
Sediment
Regolith
Regolith
OF MOUNTAINOUS
Slope
O _<R _<R,
Bedrock
Bedrock
Incision
andslides
IDiffusion,
--=
0t
, exp
•
Rscale
R>R
*
(3)
Here R is the regoliththickness,
(0R/0t)o is the barebedrock
regolithproductionrate, (0R/0t), is the maximumproduction
R ,, andRscal
c is the exponentialdecaylength
Figure 2. Schematicdiagramof the tectonicandgeomorphic rate at thickness
scale
(Table
1).
Regolith
production
rateson barebedrockin
componentsof the ZSCAPE rule set.Topographyis produced
radioby faulting in responseto an applied displacementgradient the westernUnited States,determinedby cosmogenic
tensor.Regolith is producedat all nodesin the model space nuclideconcentrations,
are typically10-50 x 10-6 m yr-1
and is transportedvia a linear diffusionlaw that accountsfor [e.g.,Bierman,1994;SmallandAnderson,1996].
shallowmassmovements.Bedrocklandslidingis controlledby
a stochasticlaw that dependsupon the maximumstablehill- 4.2. Regolith Transport
slopeheight,whichin turn is determinedby the rock cohesion
Hillslopetransportof regolithtypicallyoccursby processes
and friction angle.Channelnodesare definedon the basisof
suchas creep,slopewash,rain splash,and downslopemotion
excessstream power, which also dictatesthe rate of alluvial
due to animalactivity[Selby,1993].Sincethe transportrates
sedimenttransportand the rate of bedrockincision.
producedby theseprocessesare slope-dependent,
we model
regolithtransportas a linear diffusiveprocess(Figure2):
SlopeSc•t
StableHeight
•"•excess
qs- -kV .z
Becauseof constraintson computationtime, LEMs in general are incapableof resolvingthe effectsof geomorphicprocessesbelow somecutoff length scale.The magnitudeof this
length scale dependson the particular numerical algorithm
used to represent the processin question.ZSCAPE is not
immune to this cutoff, but we have tried to representthe key
geomorphicprocesses
with algorithmsthat allow us to extend
the cutoff down to length scalesof the order of 100 m. In this
way we are able to examine the landscapeat the scale of
individual landforms. Our experimentsare not intended to
reproducethe fine-scaledetailsof the topography,suchasthe
detailedmorphologyof a streambed or the effect of jointing
on an individualbedrocklandslide[Weisseland Seidl, 1997].
Rather, they are designedto bridgethe gapbetweenorogenicscale simulations,in which geomorphicprocessesare only
crudely represented,and landform-scaleanalyses,which ignore the larger spatial and temporal framework.
4.1.
Sedimenttransportrequiresthe presenceof a mobile layer
of regolith,distinctfrom the bedrock.The regoliththicknessis
defined
as the difference
wherek is a diffusioncoefficient.Combiningequations
(1) and
(2) yieldsa diffusionequationfor topography:
Oz/Ot= •:V2z
between
the surface
and bedrock
elevations.Regolithis producedby in situweatheringof bed-
(5)
Here Oz/Otis the rate of changeof the surfaceelevationand K
is the topographic
diffusivity(equivalentto k/p). Typicallandform-scale
diffusivities
calculated
for semiarid
to arid land-
scapes
in thewestern
UnitedStatesare0.01m2yr-i [Hankset
al., 1984;Rosenbloom
andAnderson,1994].While someLEMs
haveuseddiffusionalalgorithms,with dramaticallygreaterdiffusivities,to produce realistic-lookingtopography[Koons,
1989;Kooi and Beaumont,1994],we note againthat diffusion
is properlyappliedonlyto transport-limitedprocesses
[Ander-
Table
1.
Model
Parameters
Parameter
Regolith Production
(4)
Value
Reference
•3crit
34ø
...
C
6 x 104kgm-l s-2
(2 x 107in experiment
5)
1
At
10 years
...
Ax
100 m
...
),
2.7 X 104 kg m-2 s-2
-..
•(
0.01m2 yr-•
2.3
the regolith thickness.Sinceweatheringprocessesare partly
ka
1.6X 10-4 m2 s2 kg-l
visualinspection
dependenton the presenceof water at the bedrocksurfacefor
kt,
1.2 x 10-7m s2 kg-l
4; visualinspection
significantperiodsof time, peak regolithproductionrateshave kw
8.0 x 10-4
visualinspection
120
4 x l0s kgs-3
visualinspection
been hypothesizedto occurbeneath some finite thicknessof
1 myr -l
...
regolith,rather than on bare bedrock[Ahnert,1970]. Recent P
0
17ø (40ø in experiment5)
1
studiesusing cosmogenicradionuclide concentrationshave
(OR/Ot)o
1 x 10-s m yr-•
5
confirmedthat weatheringis faster beneathregolith than on
(OR/Or),
5 x 10-s m yr-•
6
bare bedrock[Small and Anderson,1996] and that regolith rr
500 years
.-.
productionratesdeclinerapidlybeneaththickerregolith [HeReferencesare as follows: 1, Schmidtand Montgomery[1995]; 2,
imsathet al., 1996].The exactdependenceof the production Hankset al. [1984];3, Rosenbloom
andAnderson[1994];4, Stockand
rate curveon regoliththicknessis poorlyknown.
Montgomery[1995];5, Small andAnderson[1996];and 6, E. E. Small
We adopt a linear increasein regolithproductionrate, OR/ (unpublisheddata, 1996).
rock, which lowers the bedrock surface elevation and increases
DENSMORE
ET AL.: EVOLUTION
OF MOUNTAINOUS
son and Humphrey,1989] and that its efficacyin shapingthe
landscapeis contingentupon the availabilityof regolith.
The diffusionequation ignoresany potential for advective
transportof regolith, for exampleby shallowlandsliding.To
addressthis,we followAnderson[1994] in simulatingregolith
massmovementby allowingthe sedimenttransportrate qs to
increaseexponentiallyas a critical topographicslope /•cr•tis
approached(Figure 2; Table 1). While this is an approximate
solution,we showbelow that rates of weathering-limitedprocessessuch as diffusion are dwarfed by rates of fluvial and
landslidingprocessesin the arid landscapesin which we are
interested.
TOPOGRAPHY
15,207
pography from several mountain ranges in the Basin and
Range. We thus generate syntheticchannel networkswhose
spatial extent dependson 12oand whose rates of sediment
transportand bed incisiondependupon k, and k t,. By comparing these resultswith observedchannelnetworksand typical transport and incisionrates,we can determine reasonable
valuesof these parameters.Sensitivitytestsdemonstratethat
our experimentalresultscannot discriminatebetween values
that differ by lessthan an order of magnitude.
Finally, we note that our chosenprecipitationrate (1.0 m
yr-•) is considerably
higherthan measuredhistoricalrates
fromthe BasinandRange(typically<0.5 m yr-l). Precipita-
tion rates during the last glacialmaximumare estimatedto be
30-100%
higher than present,althoughthere is considerable
4.3. Fluvial Sediment Transport
disagreementover the magnitude of the change [SpauMing,
We distinguishbetweenalluvialandbedrockchannelbehav1985]. We stressthat our chosenvalue is somewhatarbitrary,
ior dependingon the availabilityof mobile materialwithin the
sinceprecipitationis linearlyrelated to sedimenttransportand
channel.Potential fluvial sedimenttransportflux is assumedto
bed incision through the empirical parameters k a and k•,,
be proportionalto the availablestream power per unit bed
which are chosenon the basisof landscapeform. While absoarea, 12 [Bagnold,1977], approximatedhere as
lute valuesof precipitationare relativelyunimportantfrom this
perspective,
relative temporal changesin precipitation may
•/APCrS
12:
(6) play an important role in landscapeevolution;we do not exw
plore this issuehere.
where 3/is the flow unit weight,A is the contributingdrainage
area,P is the precipitationrate, Cr is the runoff coefficient,S 4.4. Bedrock Landsliding
is the channelbed slope,andw is the flowwidth (Table 1). The
The final geomorphiccomponentof the model is a bedrock
precipitation
rate is setto 1 m yr-• andis bothspatiallyand landslidingalgorithm, which determinesthe distribution of
temporallyconstantin theseexperiments(Table 1). Sinceour landslidesin both spaceand time. In natural settings,landslide
grid spacing(100 m) is muchgreaterthan typicalflow widths, occurrenceis stronglystochastic,and we argue that a realistic
we use an empiricalrelation betweenflow width and contrib- algorithmmust reflect this stochasticcharacter.Discrete beduting drainagearea,
rock landslides deliver large and highly spatially variable
amountsof sediment to the channel network, affecting the
(?) pattern of erosionand depositionwithin the channeland thus
its geomorphicevolution.The frequencyand magnitudeof the
wherekw is the empiricallydeterminedconstant(Table 1).
landslide events control this evolution [Wolman and Miller,
The channel network is defined as the set of nodes for which
12>- 12o,where 12ois the thresholdstreampower necessaryfor 1960], as does the sequence in which the events occur
channelinitiation[BagnoM,1977].We followBagnoM[1977]in [Densmoreet al., 1997]. Accurate simulationof the landscape
relating alluvial sedimenttransportflux to excessstreampow- requiresa representationof the landslideprocessthat captures
theessence
of theobserved
long-term
behavi6r.
er:
Qs= ka' (12 - 120)
(8)
where Qs is the potential volumetricsedimenttransportrate
per unit bedwidth andka is an empiricalproportionalityconstant (Figure 2; Table 1). Spatialgradientsin sedimenttransport dictatethe rate of changeof the bed elevation,asgivenby
equation(1). Any excess
streampower,definedasthe available
power beyond that required to transport all sedimentin a
particularnode, erodesthe bedrockchannelbed [e.g., Seidl
and Dietrich, 1992] at a rate givenby
Ozb
Ot= k6'12......
(9)
wherek•, is an empiricalproportionalityconstantand 12...... is
the excessstreampower (Figure 2; Table 1).
The behavior
of alluvial and bedrock channels in our model
is thus prescribedprimarily by the empirical parametersk a,
k•,, and 12o.While someeffort hasgone toward generalcharacterizationsof theseparameters[e.g.,BagnoM,1977;RosenbloomandAnderson,1994;Stockand Montgomery,1995],differencesin the algorithmsusedby differentworkersmake such
generalizationdifficult. We have chosenparametervaluesby
letting ZSCAPE operateon DEM representations
of real to-
A bedrocklandslidingalgorithmmust addressfour central
issues:where landslidesbegin,when they occur,how large they
area, and where the landslide material ends up after failure.
We usethe termsbedrocklandslideand landslideinterchangeably to denote a massmovementthat involvesintact or unweathered bedrock rather than being confined to a mobile
regolith layer.
In the absenceof strong tectonic and climatic variations,
landslidesin natural settingsare concentratedon hillslopes
that experiencea fall in local baselevel. This base level drop
maybe due to verticalmotionacrossa fault, to the occurrence
of a separatelandslidelower on the hillslope[Densmoreet al.,
1997], or to incision by a glacier [Harbor, 1992] or stream
[Megahanet al., 1978; Kelsey,1980, 1988; Seidl et al., 1996;
Densmoreet al., 1997].Landslidesare often observedto cluster
near the toes of hillslopes[Megahanet al., 1978;Kelsey,1988;
Densmoreet al., 1997].Megahanet al. [1978] found that most
landslides in the Northern Rocky Mountain physiographic
province occurred on the lower one third of the hillslope.
Kelsey [1988] found that most landslides along Redwood
Creek, California, initiated at the baseof the slope,leadingto
the formation of a steeptoe or inner gorgealongthe channel.
Densmoreet al. [1997] observedthat all slideson a granular
model hillslopeinitiated at the toe and that 90% involvedonly
15,208
DENSMORE ET AL.: EVOLUTION
OF MOUNTAINOUS
TOPOGRAPHY
where p is rock density,# is gravitational acceleration,/3 is
surfaceslope,andH is the hillslopeheight.The derivativeof C
with respectto 0 is
0C
i
sin (/3 - 20 +
O0= 7pgHsin(/3)cos
(qb)
(13)
so that C is maximizedat Oc = 1/2 (/3 + qb).Substituting0c
in (12) and solvingfor H providesthe maximumstableheight
of the hillslopeHc:
Hc =
4C
sin/3 cos qb
pg [ - cos (t3 - 4,)]
(14)
Sinceby definitionthe hillslopeheightH is alwayslessthanor
equal to Hc, we can calculatea probabilityof failure
H
PfailHc
(15)
Figure 3. Topographyfrom the Humboldt Range, Nevada,
from USGS 3-arcsecDEM data, and the syntheticchannel thatvariesbetween0 and 1 (Figure4). We take the true failure
network generatedon that topographyby ZSCAPE. Nodes probabilityto be the baseprobabilityplusa term thatincreases
designatedas channelsby ZSCAPE are shownin black. The linearly throughtime at a rate dictatedby the time sincethe
extent and interconnectedness of the channel network are dilast landslide at that node. This crudely accountsfor timerectly dependenton the thresholdchannelpower•o usedin dependentweakeningof the failure plane and rock mass.
the experiment(Table 1).
The potentialsize of a bedrocklandslideis a functionof
local topography and relief, topographic gradient, rock
strength,and the distribution,orientation,and strengthof poa portion of the hillslope.This resultedin a commonlyob- tentialfailureplanes.We againemploythe Culmanncriterion,
servedinner gorgethat wasremovedonlyby the largestslides. which predictsthat the most likely failure plane is one that
We thereforeselectpotentialsitesof landslideinitiation,or passesthroughthe toe of the slopeand dips at Oc.
targets,as the lowestpoints on each hillslopewhosetopoA potentialfailure plane, dippingat Oc,is assumedto daygraphicgradientexceedsa critical material friction angle 4) light at everypotentiallandslidetarget(Figure4). We project
(Figure 3). This ensuresthat landslidesbeginnear the toe of that failureplaneoutwardandupwardto all neighboringnodes
hillslopesandthat theyinitiateonlyon hillslopesthat are steep withina specifieddistancefrom the target.The lattercondition
enoughto promotefailure.
prevents,for example,nodes on the other side of a stream
Hillslope failure may be causedby a number of events, channelfrom failing. Those nodeswhosesurfaceelevationis
includingintenseprecipitationor coseismicshaking,weather- abovethe projectedfailureplane are consideredunstable,and
ing and subsequent
weakeningof planeswithin the rock mass, the volume of material between the surface and the failure
or a fall in localbaselevel.Here we simplyconsiderlandslides plane is recorded.The maximumpotential landslidesize at
causedby baselevel fall. We expectthat asbaselevel falls, the each target is the sum of the volumesat all unstablenodes
hillslopetoe will becomesteeperand lessbuttressed,and thus associatedwith that target.
more likely to fail. To assess
the localpotentialfor failure,we
During eachtime step,the failure probabilityat eachlandemploy the Culmann slope stabilitycriterion [Spantierand
Handy, 1982],whichholdsthat the maximumstableheightthat
a hillslopemay attainwill be reachedwhenthe shearstresson
a potentialfailure planewithin the hillslopeis balancedby the
shearstrengthon that plane. In terms of forces,the effective
weight of the hillslopematerial is
Feff= Fw sin 0
(10)
whereF,• is the weightof the hillslopematerialand 0 is the dip
of the potentialfailure plane.The balancingshearresistanceis
given by
F r '-- CL + Fw cos 0 tan qb
(11)
whereC is the effectivecohesionon the plane,L is the length
of the failure plane,and 4)is the effectivefrictionangleon the
plane [Spantierand Handy, 1982]. At the edge of stability,
Feff = Fr, and failure will occur at a critical angle Oc that
maximizesthe effectivecohesionon the failure plane, which
may be expressedas
1
sin (/3- 0) sin (0 -
C= •pgH sin(/3)cos
(qb)
(12)
Figure 4. Schematicdiagramof the bedrocklandslidingalgorithm.A landslidetarget (marked "T") is assignedas the
lowestpoint abovethe channel(marked"C") at which/3> 4).
The potentialfailure plane dips at 0 and is assumedto be
exposedat the target.The probabilityof failureis givenby the
ratio of the local hillslopeheight H to the maximumstable
hillslopeheight Hc, which in turn dependsupon the rock
strengthand the topographicgradient(inset).
DENSMORE
ET AL.: EVOLUTION
OF MOUNTAINOUS
TOPOGRAPHY
15,209
Elevation (m)
_
-500
-
- 1000
-
-5oo
Figure 5. Shadedrelief perspective
viewsof surfacetopographyfrom experiment1 after (a) 0, (b) 500, and
(c) 1000kyr. All plotsin this and subsequent
platesare 10 km by 10 km, and verticalexaggerationis 2x.
slidetargetis comparedwith a uniform deviate.If the uniform
deviate is smaller than the failure probability,a landslideinitiates at that node. The sizeof the landslideis directlyproportional
to the time since the last landslide
at that node. This is
spatial and temporal distributionof landslidespredicted by
ZSCAPE and comparethem with distributionsfrom real landscapes.
.
We compare our resultswith topographyfrom rangesthat
motivatedby the observationthat the sizeof slidesin a physical are boundedby active normal faults and that showclear signs
hillslopemodelis primarilya functionof the time sincethe last of tectonicactivity,suchas linear range fronts, triangular facevent [Densmoreet al., 1997].The size is limited by the maxi- ets,and piedmontfault scarps[Wallace,1978].On the basisof
mum potential size determinedabove.
our field observationsand the work of Stewart [1980] and
After failure, the depositionalpattern of the failed material Wallace[1978], amongothers,we identify five rangesin pardependsstronglyon both its rheologyand the topographyof ticular that meet our criteria: the Humboldt, Stillwater, Tobin,
the runout path. Thus a rockfall behavingas a Coulomb ma- and Toiyabe Rangesin Nevada, and SteensMountain in Orterial may form a steeptalus,while a more fluid, viscousdebris egon. We emphasizethat while our syntheticlandscapesare
flow may form a depositwith a much lower surfaceslopeand comparedbelow with specificranges,the visual and statistical
considerablylongerrunout. The presentalgorithmspreadsthe signaturesof theserangesare very similar despitetheir widely
resultingvolumeof material downthe path of steepestdescent disparatetectonic and lithologichistories.We draw compariasa depositthree nodeswide.We specifyboth the longitudinal sonswith a varietyof rangesin order to highlightthe consistent
mountains.
(2ø) and the lateral (5ø) surfaceslopesof the deposit,which form taken by theseactive-fault-bounded
resultsin a debrisflowlike tongueof failed material. The maIt is worth noting that the few existingdata on landslide
terial is depositedas regolith,meaningit may subsequently
be occurrenceand magnitude-frequencydistributionscome from
high-relief regionswith high tectonic deformation rates, such
remobilizedby other geomorphicprocesses.
as the Andes [Blodgettet al., 1996] and the SouthernAlps of
New Zealand [Hoviuset al., 1997]. No such data have been
5. Experimental Results
collectedfor mountainsof the Basinand Range. We therefore
We first describe the synthetic landscapesgenerated by rely on the topographyof theseranges,which after all is due to
ZSCAPE, both with and without the bedrocklandslidingrule the integratedeffect of geomorphicand tectonicprocesses,to
enabled,and comparethoselandscapes
with selectedexamples constrainour presentset of experiments.
of mountainoustopographyfrom the Basin and Range province usingsimplestatisticalmeasures.We quantifythe role of 5.1. Synthetic and Real Landscapes
bedrocklandslidesby examiningthe model erosionrates due
In experiment1 we begin with a gently tilted (1ø) initial
to different geomorphicprocesses.We then explore the re- surfaceon which there is up to 5 m of randomly distributed
sponsesof both the hillslopeand fluvial systemsto changesin bedrock topography,and up to 1 m of randomly distributed
tectonic activity and precipitation. Finally, we examine the regolith (Figure 5a). We track the topographythrough1000
15,210
DENSMORE ET AL.: EVOLUTION
OF MOUNTAINOUS
TOPOGRAPHY
Elevation (m)
500 0
-500 -
- 1000 -1500
-
Elevation (m)
Figure 5. (continued)
kyr of model run time, with all tectonicand geomorphicprocessesactive. The resultinglandscape(Figures 5b and 5c)
appearsremarkablysimilarto topographyfrom manynormalfault-bounded mountain ranges, such as the Stillwater and
ToiyabeRangesin Nevada(Figure6). The landscapecontains
a number of characteristiclandformsthat are observedalong
active normal-fault-boundedranges [Wallace, 1978]. Catchmentswithin the mountainmassgenerallyare shortand steep
and trend normal
to the mountain
front. The catchments
are
shapedsomewhatlike a wineglass,
with a large collectionarea
DENSMORE ET AL.: EVOLUTION OF MOUNTAINOUb t OPOGRAPHY
15,211
Elevation (m)
2500 2000
-
1500 -
1000 -
Elevation (m)
3000
-
2500 -
1500 1000 -
Figure6. Shaded
reliefperspective
views
of (a)partoftheeastfaceoftheStillwater
Range,
Nevada,
and
(b)partoftheeastfaceoftheToiyabe
Range,
Nevada,
fromUSGS3-arcsec
DEM data.
basin.Thesedeposits,
anda narrowcanyonat the mountainfront [Wallace,1978]. mountainfront withina hanging-wall
which
are
fanlike
at
first,
eventually
coalesce
to form a bajada
Thespurs
between
thecatchments
aretruncated,
formingtriangular
facets[Davis,1903;Hamblin,1976].Finally,material on the hanging-wallblock.
The role of landsliding
in the evolutionof thesemountain
removedfrom the catchments
is depositedvery closeto the
-500
-
-lOOO ..•
-1500 -
•,
Figure 7. Shadedrelief perspectiveview of topographyafter 1000kyr from experiment2. In this experiment,
landslidingis disabled,and hillslope evolution occurssolelyby regolith productionand weathering-limited
diffusion.
Elevation (m)
.,,
-500
-1000
-15oo -
1000
2000
3000
Number of I andslides
Plate 1. Shadedperspectiveview of the topographyfrom experiment1. The shadingindicatesthe number
of landslidesthat have occurredat each node during the 1000-kyrmodel run.
DENSMORE
ET AL.: EVOLUTION
OF MOUNTAINOUS
frontsmay be judgedby comparingthe resultsof experiment1
(Figure 5c) with thoseof experiment2, in whichthe landslide
algorithmis turned off (Figure 6). In experiment2 the hillslopesevolveonly by regolithproductionand linear diffusion,
and the catchmentsare unable to widen significantly.This
resultsin considerablysteeperhillslopesand a much higher
drainagedensitythan in experiment1 (Figure 7). Drainage
density,relief, and mean slope along a representativecross
section acrossthe footwall block of the Humboldt Range,
Nevada, are far better reproducedby experiment 1 than by
experiment2 (Figure 8).
The probabilitydistributions
of elevationandof topographic
slopeindicatethat experiment1 is a better approximationof
real topographythan is experiment2 (Figure 9). Distributions
from the Tobin and Toiyabe Ranges,as well as from Steens
Mountain in Oregon, appear remarkablyconsistent,despite
wide variationsin lithologyand fault activity(Figure 9), indicating that the distributionsare relatively insensitiveto these
parameters.Experiment 1 yields probabilitydistributionsof
elevationand slopethat are similar to thoseof the ranges.In
contrast,experiment2 yieldsvery differentdistributions,which
implies that weathering-limiteddiffusion alone is unable to
statisticallyreproduceBasin and Range topography.As was
stated above,other workershave circumventedthis by folding
massmovementsinto a transport-limiteddiffusionlaw and by
resortingto artificiallyhigh valuesof diffusivity.We showbelow that by treatingbedrocklandslidingas a separateprocess,
we gain additional insightsinto the effects of landslidingon
topography.
TOPOGRAPHY
15,213
A
2
1 0
2
/•F•'•'•-•
.......
•_•
10
0
Steens-E
2.5
•
0
2
Tobin-E
Toiyabe-E2.s
0
•
•
1500
Elevation (m)
•
3000
•.•.
•.•.
B
]
25
0
2
o
Steens-E •2
0
-
Tobin-E
o
Toiyabe-E
•o•
o
Slope(degrees)
Figure 9. Probabilitydistributionsof (a) elevationand (b)
slope,derivedfrom the topographyof experiments1 and 2 and
from 3-arcsecDEM data from the Tobin and Toiyabe Range,
Nevada, and SteensMountain, Oregon. These three normalfault-boundedrangesyield compact,distinctlypeaked distributionsthat appearverysimilardespitedifferencesin lithology
and tectonichistory.Experiment 1 yields distributionsmuch
5.2. Role of Bedrock Landsliding in Landscape Evolution
like thoseof the three ranges.In contrast,experiment2 shows
The effectsof landslidingare highlydependenton the het- an excessof area at highelevations,aswell asan excessof high
erogeneityof slope distribution.As expected,the greatest slopes.Theseare due to an abundanceof high,slowlydiffusing
interfluvesand very steepcatchmentwalls,respectively.
A
•
0
Distance (km)
B
2200
16000'' ' k' ' '4
•
8
Distance (kin)
c
200
-60002 4 6 8
Distance(km)
Figure 8. Crosssections,parallel to the strike of the range
front, acrossthe footwallblock of (a) experiment1, (b) the
Humboldt Range, Nevada (taken from 3-arcsecDEM data),
and (c) experiment2. Vertical exaggerationis 5x for each
profile.
number of landslidesin experiment1 occur on the faceted
spursadjacentto the fault, and on the relatively long-lived
hillslopesadjacentto the major channels(Plate 1). Hillslopes
in the upper parts of the catchments,only recentlyexcavated
by channelincision,experiencecomparativelyfew landslides.
An important corollary of this observationis that triangular
facets are highly modified and shapedby geomorphicprocesses,and are therefore generallynot simplyexhumedremnants of the original fault surface.
In experiment1, bedrocklandslidingis the dominanterosionalprocesson the footwallblock,exceptwithin the bottoms
of streamvalleys(Figure10). Initial sculptingof the footwallis
by fluvial incision,which setsthe conditionsfor subsequent
hillslopedevelopmentby landsliding.The efficientdeliveryof
sedimentto the valleysby landslidingcausescontinualchange
in the channelnetwork,as channelsmigrate and adjustto the
changingsedimentload and slopedistribution.This migration
is manifestedas relatively broad zoneswithin the valleys in
whichfluvialerosionis the dominantprocess(Figure 10). Fluvial and bedrocklandslidingprocesses
yield long-term(1000
kyr), spatiallyandtemporallyaveragederosionratesof 0.8 and
0.5mmyr-•, respectively
(Figure11).In contrast,
the mean
rate of relief generationacrossthe fault, givenby the sum of
themeanratesofupliftandsubsidence,
is0.9mmyr-•. Fluvial
and landslidingprocesses
are by far the dominantgeomorphic
agents;the mean long-termregolithproductionrate duringthe
15,214
DENSMORE
ET AL.: EVOLUTION
OF MOUNTAINOUS
TOPOGRAPHY
Hevation (m)
0 •
-50O -
- lO00
-
- 1500 -
Landslides
..............................
::
.....................................
....
Fluvial Processes
,:.....,......:.:...
,. :
DiffusiveProcesses
Figure 10. Shadedperspectiveview of the topographyfrom experiment1. The shadingindicateswhich
geomorphicprocesshasresultedin the highesterosionrate at eachnode,averagedover the entire 1000-kyr
run. Fluvial processes
dominatethe erosionof streamchannelsand someof the lower hillslopes,while
landslidesdominate on the upper hillslopesof the catchmentsand on the interfluves.Diffusion is only
importanton the largelydepositionalhangingwall
block,and near the uppermostedgeof the modelspace,
where little streampower is availablefor channelincision.
runis 0.006mmyr-•, andthemeanerosionratedueto rego- ince have been publishedowingin part to the modernaridity
lith diffusion
on hillslopes
is 0.05mmyr- • (Figure11).
and paucity of active landslides.Available landslideerosion
Few dataexistwith whichto comparethesesyntheticerosion ratesand distributionsare primarilyfrom areaswith high rates
rates.No landslideerosionratesin the Basinand Rangeprov- of precipitationand tectonicuplift [Kelsey,1980;Pearceand
70
60
[ [[ ['R"esP"0
n'se
time
2•i00kYr,•:•
50
•!I[(time
tø
90%
øf
new
Ls
activit
'•
40
:30
20
i
-r
10
Weathering Diffusion
Channel
incision
Bedrock
Relief
landslides production
Figure 11. Long-term(averagedover 1000kyr) erosionrates
asa functionof processin experiment1. Vertical barsshowthe
spatial variability in the erosion rates: half-width horizontal
bars are the spatial mean rate. The rates are calculatedby
summingthe erosionor surfaceloweringdue to eachprocess
over the entire 1000-kyrmodel run. Note that weatheringresults in lowering of the bedrock elevation, rather than the
surfaceelevation;it is includedhere for comparison.
0
0.9 106
1.1 106
1.3 106
1.5 106
Time (yr)
Figure 12. Time seriesof the numberof landslidesper time
step,experiments3 and 4. In experiment3 (dashedline), fault
activityceasesat 1100kyr and precipitationis kept constantat
1.0 m yr-•. In experiment
4 (solidline), fault activityceases
andprecipitation
fallsfrom1.0myr-• to 0.1myr-1 at 1100kyr.
DENSMORE
ET AL.: EVOLUTION
OF MOUNTAINOUS
TOPOGRAPHY
15,215
Watson,1986;Blodgettet al., 1996;Hovius et al., 1997]. Kelsey
[1980] documentedsedimentfluxesconsistentwith a spatially
6 l0 s
averaged
erosion
rateof ---1mmyr-' in theVan DuzenRiver
basin of northern
California.
He also found that debris slides in
erosionratesof 10-14mmyr-• in theBolivianAndes,signif-
•, 510
5
'• 410
5
icantlyhigherthan long-termfissiontrack denudationrates of
'•
3 105
•
2 105
.1
1 105
competentbedrocksupplieda significantfraction of sediment
to the channelsystem.Blodgettet al. [1996] inferred landslide
0.7-2.8mmyr-•. Hoviusetal. [1997]calculated
landslide
erosionrates,averaged
over38 years,of 5-12 mmyr-1 in catchments on South Island, New Zealand; these are rates consistent with measured
5.3.
fluvial sediment
fluxes.
Landscape ResponseTime
0
0
Continuouslandscapeactivity requires that the local hillslope base level be consistentlylowered. In our experiments
this is accomplished
by (1) continuedactivityon the fault,
which lowersboth global baselevel for channelsdrainingthe
footwall and local baselevel for hillslopesalongthe mountain
front, and (2) continuedprecipitation,which providesthe
channelswith enough stream power to incise.We can assess
the importanceof these factors in landslide generation by
abruptlychangingone or both during a model run. In experi-
1 105
1.5 105
2 105
1.5 105
2 105
Time (yr)
6 105
C = 20000 kPa
5 105
phi = 40 ø
4 105
o
;>
ment
3,precipitation
isheld'constant
at1.0myr-1throughout
the run, but activityon the fault stopsat 1100kyr of model run
time (Figure 12). The number of landslidesper time step
decaysrapidly, reaching90% of the new mean in ---100 kyr
(Figure 12).
This 100-kyrresponsetime may be thought of as a convolution of two components:a fluvial component,duringwhich
channel incision is progressivelyreplaced by aggradation
throughoutthe network, and a hillslopecomponent,during
which landslidesoccur on unstablebut previouslyunfailed
hillslopes.The relative importanceof thesecomponentsmay
be estimatedby comparingexperiment3 with experiment4, in
which precipitationis lowered by an order of magnitudeto
5 104
3 105
2 105
1 105
0
0
5 104
1 105
Time (yr)
100
•
10
0.1 m yr-1, simultaneous
with the cessation
of fault activity.
The landscaperesponsetime shouldthus reflect only the influenceof the hillslopecomponent,sinceall channelincision
effectivelyceasesimmediately.In fact, the number of landslidesimmediatelydecreases
to ---0per time step(Figure 12),
indicatingthat the hillsloperesponsetime is extremelyrapid
comparedwith the fluvial responsetime. Thus, relativeto the
channels,the hillslopesrapidly achievea steadystate, as was
assumedbyAnderson[1994].
5.4.
Landslide
Statistics
Landslidesin our experimentsshowsignificantvariation in
size with time (Figure 13a). The probabilitydistributionof
landslidesizemaybe approximatedby a powerlaw, a behavior
that is observedin laboratory landslide experiments[e.g.,
Grumbacheret al., 1993;Fretteet al., 1996]aswell asin natural
settings[Noever,1993;Blodgettet al., 1996;Hoviuset al., 1997].
For experiment1 we calculatea power law exponentof -2.2,
very similar to the exponentsoften observedin laboratory
experiments(Figure 13c) [Fretteet al., 1996].In contrast,the
few measured natural landslide distributionshave yielded
power law exponentsof approximately-1.3 (Figure 13c)
[Blodgettet al., 1996;Hoviuset al., 1997].One possiblereason
for thisdiscrepancy
liesin the differingspatialresolutionof the
methodsusedto observelandslidedistributions.For example,
Hoviuset al. [1997]userepeat aerialphotographsto assess
the
extentof landslides,and claim an areal resolutionof 102-106
;E
0.1
O.Ol
0.001
1000
Landslide
volume(m3)
Figure 13. Time seriesand probabilitydistributionsof landslidesizes.(a) Time seriesof individuallandslidevolumesfrom
experiment1. Rock strengthparametersare set to landscapescalevalues derived by Schmidtand Montgomery[1995] for
sedimentary
rocksin the SantaCruz Mountains,California.(b)
SameasFigure 13a exceptthat the strengthparametersare set
to laboratory-measuredvalues presented by Schmidt and
Montgomery[1995]. The high rock strengthsuppresses
the
number and volume of individual landslides.(c) Probability
distributions
of landslide volumes derived from the time series
shownin Figures 13a and 13b. The low-strengthdistribution
may be fit by a power law with exponent -2.2, while the
high-strengthdistributionis better fit by a powerlaw exponent
of -1.8. The thin solidlinesshowschematicallythe exponents
derived from natural (-1.3 [Blodgettet al., 1996] and -1.2
[Hoviuset al., 1997]) and laboratory(-2.0 [Fretteet al., 1996])
landslide
distributions.
15,216
DENSMORE
ET AL.: EVOLUTION
OF MOUNTAINOUS
TOPOGRAPHY
m2. Our algorithm
is limitedto resolving
landslides
between longtimeperiods(>--10
3 years).Innergorgesare commonly
104 and2.5 x 105m2 in area,whichmeansthatwe maybe observedin activelyerodinglandscapes
and may be misinterunable to accuratelyreproduceportionsof the landslidesize
spectrumin particular regions.Another potential reasonfor
the difference in power law exponentsis that the remotesensingstudiesof Blodgettet al. [1996]andHoviuset al. [1997]
computelandslidemagnitude-frequency
relationson the basis
preted as an indication of a recent increasein incisionrate
causedby regional base level lowering or climate change
[Densmore
et al., 1997].
Weissel
and Seidl[1997]haveshownthat hillslopeprocesses,
particularlybedrockmasswasting,limit the headwardpropaof landslide area, whereas we use landslide volume. Hovius et gationrate of drainageson the passiveeasternmargin of Ausal. [1997] relate area to volumevia an empiricalfunctionthat tralia. Their findingsdo not contradictour conclusionsin this
maywell be location-specific
andmay accountfor the variation paper, as they deal with different stagesof drainage basin
in exponents.
evolution.Weisseland Seidl [1997] were concernedwith the
The bedrocklandslidingalgorithmis primarilycontrolledby initial incisionof a drainagenetworkinto low-relief topograthe rock cohesionand friction angle,which are complex,often phy, while our resultsapply to portionsof the drainagenettime-dependentpropertiesof the rockmass[Selby,1993].Val- work that haveevolvedto a steadystateform and relief.
ues of theseparametersfor variousrock types,measuredboth
in the field and in the laboratory,rangeover severalordersof 6.2. SystemResponseas a Measure of LandscapeEvolution
magnitude[Schmidtand Montgomery,1995]. Severalworkers
Kooi and Beaumont[1996] presentedan analysisof land[Selby,1980;SchmidtandMontgomery,
1995]havepointedout
scaperesponsetimesand the effectsof the interactionbetween
that rockmassstrengthdecreases
with increasingspatiallength
responsetime and timescalesof tectonicforcing.They demscale.The appropriaterockstrengthvaluesin ZSCAPE should
onstratedquasi-linearbehaviorof their LEM, as evidencedby
therefore reflect the influence of discontinuities within the
the exponential response of particular variables to step
rockmass,rather than laboratorystrengthmeasurements.
The
changesin tectonicforcing.We observesimilar quasi-linear
majority of our experimentsuselandscape-scale
valuesof co- behavior in the evolution of our channel network. For examhesionand friction angle,C = 60 kPa and 4>= 20ø(Santa
ple, the meandenudationrate on the footwallincreases
as[1 Cruz Mountain sedimentaryrock of Schmidtand Montgomery
exp (-t/t,)]
after a step increasein tectonicactivity,where
[1995]). The effect of rock strengthon experimentallandthe timescalet, •- 200 kyr.
scapesis illustratedby experiment5, in which we use values
The bedrocklandslidingalgorithmalsoexhibitsa charactermore typicalof thosemeasuredin the laboratory,C - 20,000
isticresponsetime after changesin tectonicactivity,although
kPa and (k = 40ø (hard sedimentaryrock of Schmidtand
the responseis highlynonlinear.This is not surprising,given
Montgomery[1995]).The higherstrengthleadsto steepercritthe nonlinearrelationshipbetweenfailureprobabilityand hillical hillslopeheights(equation(14)) andthusresultsin fewer
slopegradient(equations(14) and(15)). Recallthat an abrupt
and smallerlandslides(Figure 13b). In addition,the smaller
cessationof tectonicactivity,and thusbaselevel fall, causesa
exponent implies that large landslidesare relatively more
decreasein the number of landslidesper time step, with a
abundantthan in the low-strengthexperiments.However, we
response
timeof the orderof 100kyr (Figure12).We interpret
stressthat experimentswith nearly any degreeof landsliding
this responsetime as reflectingthe progressivecessationof
result in topographythat is fundamentallydifferent from that
channelincisionand the onsetof aggradationthroughoutthe
generatedby weathering-limiteddiffusionalone.
network.An initial waveof aggradationpassesvery rapidlyup
the network(on a timescaleof <10 kyr,whichagreeswith the
6.
Discussion
observationof Wallace[1978] in the Basin and Range) and
resultsin the precipitousinitial drop in the number of land6.1. Fluvial Incision as a Rate-Limiting Process
slides.Aggradationlowershillslopeheights,essentiallyfreezThe similarity between rates of erosion from fluvial and
ing the failure probabilityat any particulartarget.Those hilllandslideprocesses
impliesthat they are tightlycoupled.This
slopesthat are alreadysteepenoughto fail, do so eventually,
couplingis a natural consequence
of their relative efficiency and the lack of continued base level fall means that few new
and responsetimesand is not explicitlyspecifiedin the model.
landslide-pronehillslopesare created.
If landslidesin a particularlandscapeare causedprimarilyby
fluvial channel incision,as is modeled here, the degree of
couplingwill be quite high. However,if other mechanismsof 6.3. Assumptions and Improvements
destabilizingslopes,suchas groundwatersappingor seismic
Our approachto modelingmassmovementsvia landslides
accelerations,are present,we expectthe couplingto be much involvestwo algorithms,one for determiningthe locationand
lesspronounced,as landslidingwill occurin responseto those size of a landslide and a secondfor distributingthe failed
other mechanisms as well.
material downslope.The first of theseis motivatedstronglyby
In our experimentsthe rate of fluvial channelincisionde- the physicsand observationsof slopefailure both in the real
terminesthe rate at whichthe landscapeevolves;the channel workedand in controlledexperiments,althoughat presentwe
networksetsthe lengthsand distributionof hillslopesandthus ignoremost of the range of landsliderheologies[e.g., Varnes,
is primarilyresponsible
for the grossmorphologyof the land- 1978]. The means of distributingfailed material, however,is
scape.We arguethereforethat field measurementsof ratesof tied less to physicsthan to basic field observations.This is
landscapeevolution in setting similar to our experiments partly becausethe physicsof slidematerial is stronglydepenshouldfocus on rates of fluvial processes.Nevertheless,the dent on the rheologyof the material.Our simplealgorithmto
stochasticnature of the landslidingprocessand its intrinsic distributeslide material can be tuned by adjustinga limited
responsetime can yield hillslopesthat in essencelag behind numberof parameters,but we hastento point out that these
the processof localbaselevellowering.This lag time mayyield parametersare simpleproxiesfor a complicatedphysicalprounstablehillslopessuchasinner gorgesthat existfor relatively cess.Particularapplicationsof the modelmustat leastinvolve
DENSMORE
a landslide
rule set that is modified
ET AL.: EVOLUTION
to fit the dominant
OF MOUNTAINOUS
land-
slidetype observedin the region.
We also ignore tectonicand climaticvariationsas potential
landslidetriggers.Seismictriggeringof landslidesis well documented[Keefer,1984, 1994],and attemptshavebeen made to
relate earthquakemagnitudeto landslidelikelihood [Wilson
and Keefer,1985;Jibsonand Keefer,1993]. There is disagreement, however,betweentheoreticaland measuredgroundaccelerationsduring earthquakes,primarily due to topographic
effects[e.g.,Geli et al., 1988], and no general,physicallybased
model of seismicallytriggered landslidinghas yet been proposed.
Variations in climate should affect the bedrock landsliding
algorithmin both direct and indirectways,althoughwe have
not yet explored the effect of climate changeon landscape
development.In particular,we expectthat increasedprecipitation should increase the channel incision rate and thus more
rapidly lower the local base level seen by the hillslopes.In
addition, higher precipitationwill increasethe rate at which
informationon ultimatebaselevel(asdictated,for example,by
tectonicactivity)is transmittedupstream.More rainfall should
alsoincreasethe regolithproductionrate and shouldresult in
saturationof the hillsloperegolith,whichwould be reflectedin
a higherdiffusivityand increasedmassfluxesby regolith mass
movement.Finally, increasedprecipitationwill hastenweatheringof the bedrockalongjoint planes,therebydecreasingthe
bulk cohesionand enablingbedrock landslides.
We approximatethe accumulatingtectonic displacement
field by superposingdisplacementfields calculatedfrom the
initial flat surfacerather than from the incrementallydeform-
ingsurface.
Thisleads
to/aprogressively
largermismatch
betweenthe theoreticaland applieddisplacementfields.This is a
small sourceof error, however,sincevertical gradientsin the
relief acrossthe displacementfield are of the order of 2.5% per
kilometerof fault displacement.In experiment1, for instance,
total fault displacementis 3.3 km, implying an error of less
TOPOGRAPHY
15,217
are at presentignoredby the bedrocklandslidingalgorithmin
ZSCAPE, being folded into the rock strength parameters.
However, any analysisof the spatially distributed effects of
fractureson hillslopemorphologyand landslideoccurrence,as
well as explicit comparisonsbetween observedand synthetic
landslidemorphologies,will require an algorithmcapableof
resolvingsuchvariables.
As such issuesare resolved, we believe that models such as
ZSCAPE may eventuallybe useful in predictingthe geomorphic evolutionof specificsites.Accurate,high-resolutionDEM
data will serveas the template on which geomorphicand tectonic processesact; ZSCAPE is then ideally suitedto monitor
the evolutionof topography,as well as landslidelocation and
size, erosion rates, and sediment fluxes. Such simulations will
providean independent,long-termcheckon historicallymeasuredparameterssuchas catchmentsedimentfluxes,and may
help to determinewhethermodernprocessrate measurements
agreewith long-term equilibria.
7.
Conclusions
We have demonstratedthe first quantitativemodel of landscapeevolutionthat includesa realistictectonicdeformation
input and erosionby bedrocklandslides,and have shownthat
it produceslandscapesthat are consistentwith laboratoryand
field observations.In particular,we draw the followingconclusions:
1. Our experimentssupport the hypothesisthat bedrock
landslidingis an important processin the evolutionof realistic
mountainoustopography.A weathering-limiteddiffusionrule,
althoughappropriatefor modelingregolith transportin many
environments, cannot remove sufficient material from the
modelspaceusingfield-measuredvaluesof topographicdiffusivity.While previousstudieshavesimulatedbedrocklandsliding by using artificiallyhigh diffusivities,we argue that such
approachesobscurethe contribution of discrete,large landthan 10%.
slide eventsto landscapedevelopment.
ZSCAPE does not yet accountfor the flexural effects of
2. Experimental rates of erosiondue to bedrock landsliddifferentialloadingand unloading,which have been shownto ing are comparableto thosedue to fluvial channelincision.In
be significantin generatingfootwall uplift in an extensional addition,the responsetime of individualhillslopesto changes
setting[Weissel
andKarner,1989;KingandEllis, 1990].We may in local baselevelis very rapid comparedwith the response
obtain a crude estimate of the magnitudeof the elevation time of the channel network as a whole. These lines of evichangesdue to flexure by calculatingthe displacementin re- dence argue that fluvial and landslidingprocessesare tightly
sponseto the total load accumulatedduring an experiment. coupled. In steady state, and in the absenceof alternative
The negativeload due to erosionis representedby the differ- meansof generatinglandslides(suchas groundwatersapping
encebetweenthe summedtectonicdisplacementenvelopeand or seismicaccelerations),
fluvial channelincisionis the ratethe final bedrock topography,while the positiveload due to limiting processof landscapeevolution. Bedrock landslides
depositionis simply the accumulatedregolith thickness.As- allow the hillslopesto keep pace with channelincision.
3. Rates of bedrock landsliding respond nonlinearly to
sumingan effectiveelasticthicknessof 2 km [Kingand Ellis,
1990], differential elevation changesdue to the flexural re- temporalchangesin tectonicactivity.On the basisof the rapid
sponseto this load are ---80m acrossthe 10-km-widespaceof hillsloperesponse,we attributethe bedrocklandslideresponse
experiment1. In contrast,the cumulativetectonicrelief across time to progressiveaggradationand adjustmentof the channel
this samedistancein experiment1 is 620 m. This analysisis of network.
4. A simple, stochasticbedrock landslidingalgorithm is
courseapproximate,as it ignoresthe feedbackbetween the
flexuralresponseandgeomorphicactivity[KingandEllis, 1990; sufficient to generate landslide size distributionsthat show
power law behavior, consistentwith laboratoryexperiments.
SmallandAnderson,1995].
A final issueconcernsthe spatialresolutionof the geomor- There is some discrepancybetween numerically derived and
phicrule set,particularlyof the bedrocklandslidingalgorithm. field-measuredexponentvalues,which may be due to differSelby[1980],amongothers,helpedto quantifythe role played encesin spatial resolutionbetween the numericalmodel and
by joints and fractures in dictating rock strength and slope remote-sensingmeasurementtechniques,or to differencesbestability.Recent work by Weisseland Seidl [1997] has high- tweenvolume-frequencyand area-frequencyrelationships.
Finally, we wish to point out the need for additionaldata on
lighted the dramatic effect that fracture densityand orientation have on hillslope morphology.Such fine-scalevariables landslide size distributionsand temporal sequencesfrom a
15,218
DENSMORE ET AL.: EVOLUTION
OF MOUNTAINOUS
TOPOGRAPHY
varietyof geologicenvironments.In particular,we stressthat Anderson, R. S., Evolution of the Santa Cruz Mountains, California,
throughtectonicgrowthandgeomorphicdecay,J. Geophys.
Res.,99,
future field investigations
shouldfocuson fluvial and bedrock
20,161-20,179, 1994.
landslidingprocesses,as our experimentsdemonstratethat Anderson,R. S., and N. F. Humphrey,Interactionof weatheringand
these are responsiblefor the bulk of the geomorphicwork
transportprocesses
in the evolutionof arid landscapes,
in Quantidone on the landscape.
tativeDynamicStratigraphy,
edited by T. A. Cross,pp. 349-361,
Prentice Hall, EnglewoodCliffs, N.J., 1989.
Anderson,R. S., and K. M. Menking, The Quaternarymarineterraces
of Santa Cruz, California: Evidence for coseismicuplift on two
Notation
,4 drainage
area,m2.
/3 topographicslope,rad.
/3crit criticaltopographicslopefor shallowlandsliding,
rad.
C cohesion,
kg m-1 s-2.
Cr
At
Ax
Feff
Fw
Fr
!7
3'
runoff coefficient,dimensionless.
timestep,years.
grid spacing,m.
componentof weightof hillslopematerial along
failureplane,kg m s-2.
weightof hillslope
material,kgm s-2.
resisting
forcealongfailureplane,kgm s-2.
gravitational
acceleration,
m s-2.
unitweight,kg m-2 s-2.
H hillslopeheight,m.
Hc maximumhillslopeheight,m.
k
•(
ka
kt,
diffusion
coefficient,
kgm-• s-•.
diffusivity,
m2 s- 1.
alluvial
sediment
transport
coefficient,
m2 s2 kg-1.
bedrockincision
coefficient,
m s2 kg-1.
kw channelwidth coefficient,dimensionless.
L hillslopelength, m.
11 streampowerperunitbedwidth,kg s-3.
110 threshold
stream
powerperunitbedwidth,kgs-3.
Ilextessexcess
streampowerperunitbedwidth,kgs-3.
P fail probabilityof failure, dimensionless.
P precipitation
rate,m s-1.
p bulkdensity,kg m-3.
q5 material friction angle,rad.
qs masstransport
perunitwidth,kgm-• s-•.
Qs volumetric
transport
rateperunitwidth,m2 s-•.
R regolith thickness,m.
R. depth of maximumregolithproduction,m.
Rs•ale regolithproductionlengthscale,m.
OR/Ot regolithproduction
rate,m yr-•.
(OR/Ot)o surface
regolithproduction
rate,m yr-•.
(OR/Ot). maximum
regolithproduction
rate,m yr-•.
S
•-•
0
Oc
channelbed slope,rad.
earthquakerecurrenceinterval,years.
failure plane dip, rad.
critical angle of failure, deg.
w
z
channel width, m.
surface elevation, m.
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