LANDSLIDE-DRIVEN EROSION AND TOPOGRAPHIC EVOLUTION OF
ACTIVE MOUNTAIN BELTS
N. HOVIUS*
Department of Earth Sciences, University of Cambridge
Downing Street, Cambridge CB2 3EQ, UK
C.P. STARK
Lamont-Doherty Earth Observatory of Columbia University
Route 9W, Palisades, NY 10964, USA
Abstract
Landslides play a crucial role in the erosion and topographic evolution of active
mountain belts. They drive the expansion of drainage networks in uplifting rock
mass, and counter the tectonic mass flux into orogenic systems. Moreover,
landslides are the source of most sediment eroded from the continents, and the
probability distributions of landslides and their triggers are a first-order control on
the variability of the sediment flux from active mountain belts. Here, we illustrate
these points with observations from the Southern Alps and other regions of New
Zealand, the Central Taiwan Mountains, the Finisterre Mountains of Papua New
Guinea and the eastern Greater Caucasus of Azerbaijan.
1. Introduction
The tectonic evolution of active plate boundaries is controlled not only by the
properties and deformation of the crust and mantle parts of the lithosphere, but
also by climate-driven erosion of the deforming pile [5, 31]. In turn, climate may
be moderated by the impact of topographic obstructions of atmospheric circulation
patterns, and the relationship between erosion rates and weatherability of the
silicate crust [7, 34]. Thus, erosion provides a first-order, two-way link between
lithospheric and atmospheric processes. The link is most effective in active,
compressional orogens that source most of the clastic sediment eroded from the
present-day continents [33].
Erosional landscape evolution and sediment flux to depositional basins are
driven by the incision of rivers into uplifting bedrock. However, river channels
occupy only a minor part of the resulting terrain: the bulk of their sediment load is
derived from interfluves. There, bedrock is exposed to physical and chemical
______________________
* E-mail of corresponding author: [email protected]
weathering processes, which are driven by climate and moderated by vegetation.
Given sufficient potential energy, the weathering products are eroded by hillslope
mass wasting and non-channelized wash processes, whose rates depend on the
local surface gradient as well as the probability of their triggers. Eventually, the
eroded material is transferred onto the valley floor, where its removal is a function
of the transport capacity of the fluvial system. An end-member scenario can be
formulated in which the rate of bedrock uplift is matched by the rate of valley
lowering, and in which both outpace the rate of weathering. In this case,
interfluves undergo relative uplift and steepen until topographic elements become
unstable and collapse, producing rock falls and landslides involving not only
regolith but also underlying bedrock [9]. Given sufficient sediment transport of the
rivers, such end-member landscapes yield sediment at a rate that is determined
principally by the rate of rock uplift. This is the erosion style characteristic of
active, compressional mountain belts [23, 25, 41].
Here we review the role of bedrock landslides in the erosion of active mountain
belts. This role is more substantial than the incidental mobilization and removal of
soil and rock mass from an unstable hillslope. Landslides govern the evolution of
drainage networks in young, growing mountain belts, limit mountain relief and
balance tectonic fluxes, and drive the sediment flux to adjacent basins.
2. Landslides drive drainage network evolution
First we consider the role of landslides in the evolution of montane topography
during early stages of mountain building. Using examples from the Finisterre
Mountains of Papua New Guinea, we will demonstrate that landsliding can drive
the formation of major valleys in uplifted terrain, and provide the nuclei for lowerorder tributary streams.
In areas of active tectonic compression, crustal shortening is achieved, in part,
through the vertical stacking of rock mass. This results in the progressive
construction of mountain ranges of increasing steepness and height. Winds across
such topographic barriers drive upward motion of air flow that leads, through
adiabatic decompression, to condensation of water vapour and to orographic
precipitation. Topographic steepness and orographic precipitation combine to help
denudational processes counteract the tectonic mass flux into a growing mountain
belt. Eventually a balance may be reached in which accretionary and erosional
fluxes are equal [51]. At this stage, and in the absence of a horizontal component
in the tectonic velocity field of a deforming mountain belt, rock mass is advected
upward through a topographic surface, the stability of which is subject only to
changes in tectonic, climatic and/or lithologic boundary conditions. It is during the
phase preceding balanced input and removal that the major drainage elements of a
mountain belt are established, principally through landsliding.
The early stage of mountain building and topographic evolution is manifest in
the Finisterre Mountains of Papua New Guinea [24]. Situated at the oblique
compressional boundary of the South Bismarck plate and the Australian plate, this
mountain range has propagated eastward since the onset of orogensis at around 3.5
Bismarck Sea
5
6
3
4
2
Ramu
1
6
N
50 km
Markham
Figure 1. Shaded relief image of a digital elevation model of the Finisterre Mountains, NE Papua
New Guinea, illustrating the sequence of catchment initiation, expansion, and entrenchment
along the range axis. (1) Uplifted and karstified limestone cap, with normal faults and internal
drainage. (2) Narrow gorge cut into the limestone substrate of the northern range flank. (3)
Nucleas of drainage network propagation, probably located where the contact between the
permeable carbonates and underlying volcaniclastic aquitard was first exposed in the narrow
flank gorge. (4) Amphitheatre-headed catchment swamped by debris generated by landslides at
the plateau edge. (5) Established catchments with a shared main divide. (6) Location of the
Kaiapit landslide.
Ma [1]. As a result, the evolution of its montane topography can be observed from
drainage initiation on the Huon Peninsula in the east, through catchment expansion
and stream entrenchment, to a ridge-and-valley landscape in which fluvial incision
and hillslope mass wasting effectively counter rock uplift in the west (Figure 1).
The pattern of evolution is strongly influenced by the geology of the mountain belt
[12, 14] which consists of a volcaniclastic core conformably overlain by a
kilometre-thick sequence of marine carbonates. This sequence of pre-orogenic
sediments has been folded and thrust southward over foreland deposits, and
subsequently eroded into high plateaus, separated by deep, steep-sided valleys.
Catchments in the western sections of the opposing range flanks share a ridgeshaped divide, leaving only small plateau remnants, but further east they are
separated by >10 km of undissected plateau. The least developed montane
topography is found in the northeastern range flank where large tracts of gently
arched carbonates are separated by deep slot canyons in limestone. Further west,
several such catchments have developed dendritic drainage networks in which
volcaniclastic rocks are exposed.
In order to understand this topographic evolution, we briefly consider fluvial
incision of bedrock. Streams erode bedrock through abrasion by bedload and
suspended load, and joint block plucking [15, 20, 22, 49]. The efficacy of these
processes is a function of water discharge and channel bed slope [26] and sediment
flux [27]. If a stream is under capacity, its sediment load is limited by supply from
its valley sides. Thus, there is a feedback between fluvial incision and hillslope
erosion. An evolving mountain belt may initially have modest local relief, and thus
small sediment loads derived from shallow valley sides. These sustain only low
fluvial incision rates, which in turn do not promote effective catchment expansion
and hillslope mass wasting. Erosion is thus outpaced by tectonic uplift resulting in
growth of a regional topographic high. This is the state of the easternmost
Finisterre Mountains whose form is broadly that of a large growth anticline, the
crest and north flank of which have a contiguous limestone envelope. Subdued
local relief is associated with internal, karstic drainage, while shallow, elongate
catchments drain with the regional topographic dip to the north.
As regional topography steepens because of continued rock uplift, rates of mass
wasting increase. Debris is supplied faster to fluvial systems of increasing stream
power, accelerating valley lowering. However, it is generally by hillslope mass
wasting alone that catchment expansion may occur. In the Finisterre Mountains,
this phase of landscape evolution is represented along the edges of the limestone
plateau of the Huon Peninsula. On the plateau, limestones have become
progressively karstified, with high rates of infiltration and subsurface flow.
Seepage concentrates along subsurface permeability contrasts and emerges where
such interfaces are exposed. Sapping [4] then results in undercutting of valley
heads and side walls, and slope failure may ensue. On the north flank of the
eastern Finisterre Mountains, several drainage networks branch out from single
points along canyon-like valleys. Upstream of these points, low-permeability
volcaniclastic rocks are exposed below steep headwalls, suggesting that catchment
expansion initiated when their contact with the overlying limestones was exhumed.
In this area, headwaters consist of large (some >5 km), amphitheatre-shaped
concavities, filled with debris lobes. These deposits have a chaotic topography,
sometimes with pressure ridges and ponded drainage, implying catastrophic failure
of the plateau edge. Analogous features have been described for historic failures of
the limestone cap of the nearby island of New Britain.
In the eastern Finisterre Mountains, valley-head landslide scars form
semicircular clusters. Large transverse catchments have several such aggregates.
Some are located on major, active faults, and downstream of such clusters, river
valleys follow the same structures. Evidently, large faults have guided and
facilitated drainage propagation, possibly by focusing seepage. More generally, we
conclude that the pattern of landslide-driven drainage network expansion in the
Finisterre Mountains reflects the organization of seepage in the antecedent,
undissected topography.
Downstream of headwalls, valley widths are constant and equal to the diameter
of the corresponding landslide clusters. Valley sides are poorly dissected, and mass
wasting occurs principally through slope-clearing landslides. Away from the
plateau margin, most mountain ridges and peaks are defined by coalescing,
multiple-kilometre scale landslide scars, whose pattern responds to the local
gradients associated with the established valley network. Generally, headscarps are
steep and arcuate; hummocky debris deposits fill the lower parts of scars and spill
into adjacent valleys. The 1988 Kaiapit landslide [40] is a recent example of such a
failure. Without obvious trigger, this landslide collapsed the entire south face of a
spur descending from the main divide of the Finisterre Mountains, involving
displacement of ~1.5 km3 rock mass. The failure had a height of 1.5 km, a base
width of 2.5 km, and a concave shape with slope gradients as steep as 60°.
Landslide debris traveled 6.5 km down two adjoining valleys, leaving 150-200-mthick deposits, and killing 75 people. Slope clearing landslides such as the Kaiapit
example generate concavities that concentrate runoff on a scale sufficient to
initiate watersheds. On the south flank of the Finisterre Mountains, most lowerorder catchments were apparently created by this mechanism.
Once the sub-escarpment drainage pattern is established, development of a
complex ridge-and-peak topography proceeds rapidly. Runoff concentration
causes fluvial incision of landslide scars and deposits, resulting in the formation of
steep inner valleys, bounded by debris terraces. Such terraces are found throughout
the southern and western Finisterre Mountains. In most valleys, fluvial incision has
progressed beyond the base of landslide deposits into bedrock. Thus, the drainage
network is entrenched in the uplifting rock mass, consolidating runoff into trunk
streams. Continued fluvial incision reduces the upper length scale of the local
topography, replacing the initial landslide-induced concavities with entire drainage
networks. Consequently, the potential for slope failure on a multiple-kilometre
scale, which currently dominates erosion of the eastern Finisterre Mountains, is
eventually removed from the landscape. In the ensuing phase of orogenic
evolution, erosion occurs primarily through local slope failure in response to
fluvial incision. The upper length scale of such landslides is constrained by the
local drainage density. In this scenario, large, drainage altering landslides are
extremely rare and the topographic template is essentially fixed. Major
rearrangements of this mature montane landscape can only be caused by
progressive, lateral motion of channels, for example as a result of anisotropic
substrate resistance or structural entrainment of drainage, renewal of large-scale
landsliding due to changes in tectonic and/or climatic boundary conditions, or
horizontal advection of topographic elements through an orogenic system.
This last point should be amplified. In our discussion of the topographic
evolution of the Finisterre Mountains we have assumed that surface motion was
approximately vertically upward. This may be appropriate in the case of the
Finisterre Mountains, especially if we consider the establishment of drainage
networks in a passively advecting limestone cap. However, in many orogens,
horizontal rock displacement rates are an order of magnitude greater than tectonic
uplift rates [53]. This implies that rock displacement paths are largely horizontal
through active orogens [50], and that topographic elements are carried into zones
of enhanced denudation where the deformation field has a larger vertical
component. Thus, major drainage elements can be added to a catchment by
horizontal advection across the crest line of a mountain belt. One example of this
is the Landsborough River in the western Southern Alps of New Zealand. Other
possible examples have been identified in this and other mountain belts. Moreover,
horizontal advection of rock mass makes range divides prone to frequent, large
landslides of the ‘Kaiapit’ type, especially in headwaters of relatively wet
catchments facing with the direction of rock advection. Preliminary observations
in the Central Mountains of Taiwan indicate that kilometre-scale landslides cluster
along the east side of the main divide, as predicted from the eastward motion of
rock mass through the orogen and toward its typhoon-prone east flank. We
anticipate a similar prevalence of very large landslides in the headwaters of westdraining catchments in the Southern Alps of New Zealand.
To conclude this section we ask whether the key geomorphic features of the
Finisterre Mountains, including the prominence of very large landslides, are shared
with other pre-steady-state orogens. It would be easy to attribute these features to
the special geology of the Finisterres, notably their thick limestone cap and strong
permeability contrast with underlying rocks. However, we have observed similar
geomorphic trends in the eastern Greater Caucasus of Azerbaijan, where very large
landslides dominate the headwaters of catchments propagating into a thick pile of
muddy, clastic and calcareous sediments. The eastern tip of this mountain belt is
arid and in the absence of considerable erosion, weak rocks have built several
kilometers of relief. Fluvial dissection of this topography commences where
orographically-forced precipitation first generates significant runoff. In this
transitional area rapid catchment expansion occurs, as in the eastern Finisterre
Mountains, by the propagation of large, deep-seated landslides into elevated
topography with low, undulating relief. However, great escarpments are absent, as
a result of the lesser competence of the sedimentary rocks constituting the tip of
the Azeri Caucasus. Both the eastern Greater Caucasus and the eastern Finisterre
Mountains contrast with the emerging, southern tip of the Taiwan mountain belt
where rapid orogen growth occurs from below sea level to elevations of up to 4 km.
In south Taiwan, structurally controlled drainage rapidly makes way for regularly
spaced streams traversing the structural and topographic grain of the mountain belt.
These catchments appear to grow self-similarly, with the expanding mountain belt,
and without known evidence of catastrophic, landslide-induced changes.
In summary, we have found that drainage initiation in growing mountain belts is
commonly retarded due to lack of orographic forcing of precipitation, high
infiltration rates in sedimentary and possibly karstified cover rocks, and low
sediment yields from subdued relief. However, once fluvial incision has started,
rapid drainage network propagation may be driven by multiple-kilometer-scale
landslides, the location of which is strongly linked with upslope seepage patterns.
In such cases, the mode and rate of drainage network expansion are governed not
by fluvial incision but by hillslope mass wasting at valley heads. Slope-clearing
landslides initiate the formation of tributary catchments in the wake of retreating
headwaters. Stream entrenchment then follows from runoff concentration in trunk
streams and tributaries, promoting valley floor lowering through landslide debris
and into bedrock. With increasing dissection of the landscape, the potential for
catchment altering landslides is reduced, although it remains high around the main
divide of orogens with strong, but opposing tectonic and climatic asymmetries.
This course of events is shared by some, but apparently not all pre-steady-state
mountain belts. It is likely that in mountain belts where significant surface runoff
occurs in newly emerging topography, for example due to location within the
monsoon belt (e.g., Taiwan), drainage networks are established before topographic
growth permits multiple-kilometre-scale slope failure. In such cases, the maximum
length scale of hillslopes is limited throughout the orogen by effective fluvial
dissection. We attribute the fact that the Finisterre Mountains do not appear to
follow this evolutionary path despite their position in the humid tropics to an
inferred high seepage loss and subdued surface runoff over the limestone cap.
3. Landslides limit relief and balance tectonic fluxes
Having addressed the role of landslides in pre-steady-state mountain belts, we now
turn to mass wasting in common, ridge-and-valley topography. The aim of this
section is to demonstrate that landsliding is the dominant mode of hillslope mass
wasting where creation of relief, by the combined effects of rock uplift and fluvial
and/or glacial valley lowering, occurs faster than regolith production by
weathering of newly exhumed rocks. Landslides effectively limit relief in such
landscapes; and, as a consequence, landslides balance the tectonic rock mass flux
where valley floor long profiles are in steady state.
Hillslope erosion is often represented as a diffusion process, in which the
hillslope sediment transport rate Qs is proportional to the local topographic slope,
and its spatial variation is proportional to the vertical erosion or aggradation rate of
the substrate such that
∂2z
∂z
=κ 2 ,
∂t
∂x
(1)
where x is distance from the divide, z is elevation, t is time, and κ is a diffusion
coefficient. This expression implies that the steady-state profile of hillslopes
dominated by diffusion processes, and underlain by a homogeneous substrate, is
parabolic. Thus, the topographic fingerprint of diffusion is a unique, positive
correlation of local topographic gradient and upslope area. Convex-up hillslopes
are common in upland landscapes with low erosion rates, where erosion occurs by
splash, wash, and creep. In tectonically active mountain belts, they tend to be
limited to sections of drainage divides not recently affected by slope failure.
Splash, wash and creep are limited by the rate of production of regolith by
weathering of intact rock mass. This is a slow process, limited by the kinetics of
the chemical reactions involved. Where the rate of valley floor lowering is greater
than the rate of regolith production, weathering-limited mass wasting cannot keep
pace with local base level lowering, and valley sides become progressively
undercut. Eventually, this will give rise to landslides involving not only weathered
material, but also unweathered rock mass. In active mountain belts, rates of rock
uplift and fluvial incision are commonly greater than 1 mm yr-1, and significantly
faster than most weathering processes [18]. Therefore, bedrock landslides
dominate hillslope mass wasting in tectonically active mountain belts. This is
supported by several lines of evidence.
A power law relation exists between the rates of erosion and silicate weathering
across a range of climates and catchment sizes [34], implying that the two are
intimately linked, through weathering-limited mass wasting, and the associated
refreshing of the weathering front. But, in a number of active mountain belts,
erosion rates are up to an order of magnitude higher than would be expected from
measured silicate weathering rates (J. West, Personal Communication, 2003). In
such areas, weathering rates may be at the kinetic limit for a given substrate and
climate, a limit that is subdued by the absence of continuous, organic-rich soils,
due to relentless mass wasting: active orogens have bedrock landscapes.
Fundamentally, the stability of a hillslope is determined by its surface geometry,
the density, cohesion and frictional properties of its substrate, the depth of
potential failure plains, and the gravitational acceleration. A change in any of these
parameters might cause the destabilization and failure of a slope. For example, the
topographic gradient may increase due to undercutting by river erosion at the base
of the slope. Similarly, the frictional or cohesive strengths may decrease by
weathering of material, seismic shaking, or wetting of the rock mass, which also
increases the weight of the slide block. In the absence of any external landslide
triggers, substrate properties determine the maximum stabile gradient of a hillslope.
Rock mass strength decreases with increasing spatial scale because of the
influence of spatially distributed discontinuities. The mountain-scale strength of
the rock mass therefore limits the steepness of bedrock landscapes [43]. In such
landscapes the maximum hillslope height is determined by the spacing between
higher-order streams and the bulk mass strength of the interfluves. Given effective
fluvial bedrock incision, it may therefore be expected that dry mountain belts have
greater relief than their wetter equivalents.
The rock mass control on topographic development was illustrated in a terrain
analysis of the northwestern Himalaya [9]. There, the frequency distributions of
slopes were found to be essentially indistinguishable among different mountain
regions, despite differences in denudation rates of up to an order of magnitude
(Figure 2). In each region, most slopes fell between 20° and 45°, the mean slope
was 32° ± 2°, and the modal slope was only marginally steeper. This similarity of
slope distributions suggests homogenous topographic characteristics, largely
independent of denudation variations, and set by rock mass strength. The rapid
decrease in the frequency of slopes steeper than 35° implies that such slopes are
prone to collapse. They do not, in general, survive for geomorphologically
significant amounts of time. Interestingly, this cut off value is only slightly higher
than the maximum stable slope in loose, dry sand, implying that the rock mass
strength in the northwest Himalayas, and probably most other mountain belts, is
determined by through-going discontinuities rather than the properties of the intact
rocks: to first order, mountains are built of low-cohesion material.
Another, frequently used method of terrain analysis considers the relation of
local slope and upslope (drainage) area across a landscape [36]. It has been
demonstrated that the principal upland erosion processes have significantly
different area-slope fingerprints. We have mentioned the positive correlation of
area and slope for ‘diffusion’-dominated topography. Similarly, bedrock rivers
have a power-law relation between area and slope with a negative scaling
exponent whose normal value is between -0.3 and -0.6 [44, 49]. Bedrock
landslides commonly have straight failure plains and are therefore characterized by
a constant local slope for a range of upslope areas. Although they exist, it is rare to
find examples of the flat area-slope relation associated with this geometry in large
Fraction of area
0.05
0.04
1
3
0.03
5
4
0.02
2
0.01
0
0
20
40
60
Slope (degrees)
Figure 2. Slope distributions from subregions in the northwestern Himalaya. Slopes were
calculated as best-fit planes to a 4 × 4 grid cell matrix in a ~90 m DEM. Areas 1-3 have apatite
fission track ages of 0-1 my; Areas 4 and 5 have apatite fission track ages of 1-6 my. Regardless
of the ten-fold contrast in denudation rates, implied by these fission track ages, there are few
significant differences in slope statistics among them. After: Burbank et al. [9].
topographic data sets of active mountain belts, probably due to the mixing with
other process signals over the characteristic length scale range of bedrock
landslides (101 m – 103 m). For example, debris flows typically dominate channels
with upstream drainage areas of less than 1 km2, or 103 m equivalent length scale.
Such ‘colluvial’ channels have a power law relation between area and slope with a
small, negative scaling exponent [35]. This mixing detracts from the
overwhelming importance of bedrock landslides in many active mountain belts.
A scenario for the erosion of mountain belts has now emerged in which the rate
of bedrock uplift is matched by the rate of valley lowering (steady state
longitudinal river profiles) but surpasses the rate of weathering. Then interfluves
grow until topographic elements become unstable and collapse, producing bedrock
landslides. Given sufficient transport capacity of the rivers, this type of landscape
yields sediment, principally by landsliding, at a rate that is solely determined by
the rate of rock uplift, and independent of local relief. Confirmation comes from a
study of local relief and erosion rates by Montgomery and Brandon [37]. They
found that a well defined, linear relation exists between erosion rates and local
relief, calculated over 10 km, for catchments outside areas of active mountain
building [3]. However, erosion rates in active orogens vary by an order of
magnitude whereas mean local relief over 10 km is fairly constant, between 1.0 km
and 1.5 km (Figure 3). This implies that topographic relief is not a first order
control on the rate of hillslope mass wasting in active mountain belts, that erosion
rates are set, instead, by external, tectonic forcing, and that there is a limit to local
relief, imposed by bedrock landslides.
4. Landslide magnitude and frequency
If landslides dominate the erosion of active mountain belts, it is important to
quantify their long-term impact. Extrapolating short-term geomorphic observations
10
9
NZw
Erosion Rate (mm y-1 )
8
7
Np2
6
Np1
5
T
4
3
H
2
NZe
1
BC
A
D
0
0
500
1000
1500
Mean Local Relief (m)
Figure 3. Plot of erosion rate versus mean local relief (measured over 10 km) from mostly
tectonically inactive areas (open circles) and tectonically active, convergent areas (solid squares).
NZ is Southern Alps, New Zealand, NP is Nanga Parbat region, western Himalaya, T is Taiwan,
H is central Himalaya, D is Denali portion of the Alaska Range, A is European Alps, BC is
British Columbia. After: Montgomery and Brandon [37].
to time scales pertinent to landscape evolution and orogen dynamics requires an
understanding of the scaling behaviour of the processes involved, in particular the
magnitude and frequency with which they occur [52]. The magnitude-frequency
distribution of landslides is characterized by a maximum at small to intermediate
size events (103 m2) and a broad, negative power law tail for larger landslides
(Figure 4). This power law scaling holds true whether the landslide size is defined
as the scar area [25], or the total area disturbed [41], and whether landslides are
triggered over a long period of time [19, 23], or almost instantaneously [19, 21]; it
also holds true if landslide volume is considered instead of area [8], although
volume is typically much more difficult to measure (both in the field and in air
photographs). For an idealized landslide size distribution to be power-law
distributed across the size range x ∈ [c, ∞) , the size probability density is defined
as
(2)
p( x) ≡ αcα x −α −1 , c>0, α>0
where α is the power law scaling exponent [45], and x is usually defined as
planform area. The scaling exponent explicitly determines the impact of large
versus small landslides on integrated measures such as the total area disturbed, or
the volume of material yielded. Power law scaling is typically observed for areas
greater than 1000-5000 m2 up to the largest landslide areas for which a distribution
can be reliably estimated (of the order of 105 m2).
The power law property of the landslide size distribution introduces several
complications. First, the disturbance area and eroded volume of a landslide are
highly variable. Second, there is no characteristic landslide scale that dominates
the erosion budget: a power-law distribution indicates that events at many scales
play an important role. This makes it hard to quantify the pattern and rate at which
a mountain landscape evolves by landsliding. At present there exists no
mathematical means of assessing the flux of sediment from a zone dominated by
landslide mass-wasting. In other words, no differential operator or partial
differential equation (analogous to the diffusion equation) yet exists to formalize
the relationship between mountain relief and landslide sediment flux (quite apart
from the difficulty in calibrating such an equation were it to exist).
10
Probability density, p(x)
10
-3
-4
10
Southern Alps
West Flank
-5
10
-6
10
-7
Whataroa
10
-8
10
-9
Αα
10
2
10
3
10
4
10
5
2
Area, x [m ]
Figure 4. Examples of landslide size distributions, from the western Southern Alps, of New
Zealand, plotted as a probability density function p(x) plotted in log [p(x)] versus log(x) form.
Solid squares show the probability density of landslides in the Whataroa catchment, mapped at
1:25,000, N = 3986; open circles show the probability-density of landslides in a larger part of the
western Southern Alps, mapped at 1:50,000, N = 5086. The data sets show similar scaling of
landslide magnitude and frequency. Above a cut-off size, related to the resolution of the mapping
and/or a break in the failure mechanism, the data scale as a power-law. This portion of the data
is the tail end of the distribution and represents about a quarter of the observed landslides. α is
the slope of the best fit power-law, and values are almost identical at α = 1.45 for both data sets.
After: Stark and Hovius [45].
Power laws pose further technical problems that have impeded conceptual
progress in several respects. It is well known in the statistics community that
heavy-tailed distributions are difficult to characterize reliably [2]. The steepness of
a negative power-law tail, which represents the relative frequency of small versus
large events, cannot be estimated with confidence unless the sample size (the
number of landslides) is very large. If the underlying distribution is only
asymptotically a power law, as is probably the case with landslides, then the
frequency of small to medium events can strongly distort any estimate of the
power-law scaling [45]. The practical consequence of erroneous inference is a
faulty emphasis on either small or large events. In several recent studies [23, 25,
41], the steepness of the power-law scaling was underestimated, largely as a result
of unsophisticated statistical analysis. This has resulted in the inference that large
landslides dominate the erosion budget, since integration of the power-law
magnitude-frequency distribution indicated a strong dependence on the largest
events. Recent work [19, 45] has shown that the power-law distribution of
landslide size-frequency is steep, and reasonably consistently so for a variety of
data sets (with some exceptions). The scaling exponent α expresses this steepness
and generally varies between 1.3 and 1.5.
In light of these recent studies it is clear that the area disturbed by landslides,
over the long term, is dominated by small to medium scale failures (up to an area
of around 103-104 m2). Most of the landslide data sets assembled over the years are
unreliable in their representation of the magnitude-frequency distribution of small
to medium scale failures. Only those data sets acquired with great care, high
quality air photography, and detailed field verification can be regarded as having
counted accurately the smaller landslides [8, 19, 21]. For these very rare data sets,
there is convincing evidence for a rollover, or break in scaling, typically at around
1000-5000 m2. The mean and most common (modal) size landslides are
approximately of this scale, but the strong asymmetry of the landslide sizefrequency distribution means that these averages are not equal.
Some major challenges remain. First, most data sets undercount the smaller
failures and misrepresent the frequency of the dominant events. The rollover in the
magnitude-frequency distribution in these cases is unreliable, and the estimate of
the power-law component of the distribution is distorted. Fortunately, this
distortion is quantifiable [45], and a more reliable value of α can be elicited if a
censoring model is applied. However, no reliable estimate can be made of the area
disturbed for such data sets. Given the importance of such estimates, for example
in the evaluation of soil loss and mobilization of particulate organic matter, there is
a clear need for high fidelity, regional landslide maps. Second, the volume eroded
by landsliding also remains difficult to quantify, particularly where the power-law
scaling is steeper than previously thought, since the smaller, poorly enumerated
failures are now seen to play a stronger role. This is due, in part, to the fact that the
scaling relationship between landslide thickness and landslide planform area
remains unclear. This scaling is important because it sets the transformation
between the area-frequency and the volume-frequency distributions. For strictly
soil/regolith failures, it could be argued that the depth of landslide failure is
approximately constant. For failures that involve bedrock, however, it has been
argued that the depth of failure likely correlates with landslide length scale, giving
a volume to area relation of V ~ A3/2 [23]. At present, neither model has been
vindicated with field data, but must be so before any reliable estimate of total
landslide sediment flux can be made. If the constant thickness model applies, then
the volume eroded by landslides is set by the frequency of the average area
landslide and is weakly dependent on the power-law scaling. In contrast, if the
scaling thickness model applies, then the total erosion volume is a more equal
function of small and large landslides, with a weighting that is a sensitive function
of the power-law scaling exponent α.
5. Landslide-driven sediment flux
Finally, we shift our focus to the output of sediment from active mountain belts.
This output is set to first order by the tectonic mass flux. Systematic, long-lived
trends in sediment delivery to the mountain front may result from changes in
tectonic and/or climatic boundary conditions [10, 32, 54]. Superimposed on these
long-term trends are shorter term (<103 - 104 y) variations in sediment yield that
control the stratigraphic detail of adjacent basins [17, 42]. These variations arise
from the stochastic nature of upland erosion. The production of sediment on
hillslopes, its transfer into the channel network and downstream projection are
driven by concatenations of seismic and/or climatic events. These stochasts, each
with their characteristic event probability distributions operate on landscapes with
variable topography, and colluvial and alluvial cover, resulting in an enormous
spatial and temporal variation of sediment movement within and out of mountain
belts [6, 25, 47]. The complex nature of montane sediment flux originates in the
pattern of landsliding, which is the primary means of sediment production in active
orogens. The aim of this final section is to illustrate the controls on sediment
production by landsliding and its subsequent routing.
Progressive incision of uplifting bedrock is a necessary and sufficient condition
for the destabilization and failure of hillslopes [13, 30]. In most mountain belts,
fluvial wear is the dominant incision process. It occurs over a range of flow
conditions. Detailed observations in the Liwu River of Taiwan [22] have revealed
that steady incision during low and intermediate flow conditions leads to thalweg
lowering while significant channel widening occurs during big floods. Crucially,
such floods help transmit the effect of accumulated thalweg lowering to adjacent
hillslopes (Figure 5). It is therefore expected that the propensity to slope failure is
subdued during prolonged episodes of moderate river discharge, and enhanced
throughout the affected drainage network during and after major floods. Thus,
spatial and temporal variability of hillslope mass wastage is imposed by the
process driving base level lowering in montane landscapes. However, this
variability is strongly enhanced by the probability distributions of landslide size
and common triggers of slope failure such as rainstorms and earthquakes.
Landslide magnitude and frequency have already been discussed. Below we
briefly explore landslide triggers.
The effect of rainstorms is perhaps best illustrated by the example of Lake
Tutira in the northern Hawke’s Bay area of New Zealand. This landslide-dammed
lake has received sediment from a 32 km2, hilly catchment. It is estimated that for
natural catchment conditions, all rainstorms generating >300 mm precipitation
have triggered significant numbers of landslides [39]. During the largest storm on
record, in March 1988, landslides accounted for 89% of the sediment mobilized
and 87% of the sediment delivered to Lake Tutira [38], suggesting that a
relationship exists between landslide intensity in the catchment and sedimentation
in the lake (Figure 6). This, together with the observation that the sediment
delivery ratio of the catchment scales linearly with storm magnitude, has provided
a context for the interpretation of the stratigraphic record of the lake. Using
historic data only, Trustrum et al. [47] have shown that above the precipitation
A
B
C
Figure 5. Schematic showing changing relationship between channel erosion and hillslope
response. In (A), frequent low to moderate discharge/wear events mainly lower the central
channel thalweg, cutting through the parabolic channel shape, and leaving hillslopes untouched.
A rare, intense flood fills the channel (B), and high sediment flux and water levels work to widen
the channel out, restoring a wider parabolic shape consistent with the previous lowering. This
wider parabola undercuts and oversteepens adjacent hillslopes, and landslides result (C),
restoring stability in the hillslope-channel relationship.
threshold for landsliding, the impact of storm events increases, seemingly in
exponential fashion, with their size (Figure 6), such that the two largest storms
have generated about half the sediment supplied to Lake Tutira between 1895 and
1988. From longer (2 kyr) lake records, it appears that the magnitude-frequency
distribution of sediment layers attributed to storm-triggered landsliding, and the
duration of time intervals between landslide episodes can be described by power
laws, with scaling exponents of approximately -2.1 and -1.4, respectively [17]
(Figure 6). Thus, the Lake Tutira record suggests that landslide intensity closely
tracks local, meteorological conditions. This applies globally, although the relation
between landsliding and storm size is likely to be obscured by other local factors
such as geology, vegetation, land use, and the history of landscape perturbation.
Similar observations have been made for earthquake-triggered landslides. Notably,
the area affected by slope failure, the epicentral landslide intensity, and the total
mobilized sediment volume scale with earthquake magnitude [29]. Such
observations provide a semi-quantitative basis for natural hazard risk prediction,
and modelling of erosional landscape evolution and the associated sediment flux
[6].
There are some important differences between storm-triggered landslides and
earthquake triggered landslides. First, storm-triggered landslides result primarily
from local pore water pressure gradients and changes of pore water pressure that
are likely to be most pronounced in the shallow subsurface. Storm-triggered slope
failure is therefore likely to be located at the soil/regolith-rock interface or above it,
although deeper, bedrock failures may occur. In contrast, seismic ground motion
affects local stress fields well below the topographic surface and may trigger a
relatively large number of deep-seated, bedrock-involved landslides. Such
landslides are likely to produce coarser debris than their shallow counterparts, and
onward transport may be more difficult as a result. Second, storm-triggered
landslides occur at a time when the transport capacity of rivers is enhanced, and
surface runoff on hillslopes ensures effective downslope translation of debris. This
Sediment Thickness (mm)
Layer Thickness (mm)
A
60
40
20
0
100
200
500
3
10
B
2
10
10
Cumulative
Average
1
150- 200- 250- 300- 400- >500
200 250 300 400 500
1000
Storm Rainfall (mm)
Storm Rainfall (mm)
C
6
2
-2
-6
-10
0
2
4
6
8
Log2 Layer Thickness (mm)
Log2 Number of Intervals
Log2 Number of Layers
10
6
D
2
-2
-6
0
2
4
6
Log2 Time Interval (yr)
8
Figure 6. Statistics of landslide-driven sediment supply from a 32 km2, rainfall-dominated
catchment to landslide-dammed Lake Tutira, North Island, New Zealand. (A) Relation of sediment
layer thickness in Lake Tutira to storm rainfall in the catchment. (B) Average and cumulative
sediment layer thickness in Lake Tutira for specified storm magnitudes. (C) Frequency
distribution of 316 storm-related sediment layers that accumulated in Lake Tutira over a 2250 yr
period. The best-fit regression line computed from all points has a slope of -2.06. (D) Distribution
of intervals between storm-related sediment layers (≥3 mm) in Lake Tutira. The slope of the
regression line is -1.4. After: Trustrum et al. [47] and Gomez et al. [17].
reduces the potential residence time of sediment in the montane catchment.
Earthquakes, on the other hand, do not appear to correlate with specific
meteorological conditions. They can generate very large volumes of landslide
debris when the potential for onward transport is low. Third, storm-triggered slope
failure appears to affect all steep locations in ridge-and-valley landscapes, possibly
with a bias towards slope toes [28] where onward transport is guaranteed. Seismic
strong ground motion is strongest at ridge crests [16]. As a result, co-seismic
landslides often cluster around high points and deposit debris on hillslopes rather
than on channel floors. The combined effect of these differences is a potentially
very significant difference in the residence times of storm-generated and coseismic landslide debris in montane catchments.
We reinforce this point, briefly, with an example from Taiwan, using data
assembled by the Taiwan Water Resources Agency [48]. In 1999, central west
Taiwan was struck by a Mw 7.6 earthquake (return time 50-70 yr) that triggered
more than 22,000 landslides in the epicentral area. The year following the
earthquake was relatively dry and without major storms. Although the sediment
concentration in rivers draining the epicentral area was elevated, the sediment
loads of most Taiwanese rivers remained below the 30-yr average [11]. However,
when several big typhoons hit Taiwan in 2001, a disproportionately large number
of landslides occurred throughout the central Taiwan mountains, and the average
sediment concentration in affected rivers increased by up to 8,000 ppm. As a result
the sediment yield of epicentral catchments increased by a factor 3-11, potentially
making the Choshui river (drainage area 3,000 km2), albeit temporarily, the third
most important river (globally) in terms of suspended sediment supply to the ocean.
This was primarily due to the remobilization of the debris of co-seismic landslides
that remained in the landscape, and the preparation of other slopes, by seismic
cracking and shattering of the substrate, for failure during subsequent storms. This
example indicates that the sediment cascade from valley side to mountain front
may have many steps, and that sediment production and transfer together
determine the supply to nearby basins [6, 25]. Importantly, it implies that the
distant sedimentary record of mountain belt erosion is likely to be dominated by
storm-driven input, even though most sediment may have a co-seismic origin.
Moreover, the recent events in Taiwan have shown that the probability of slope
failure remains elevated in epicentral areas for years, and possibly decades, after a
major earthquake. Taiwan offers a unique opportunity to study the geomorphic
response to a large, seismic perturbation in full.
In closing we reemphasize the crucial role of landslides in the erosion and
topographic evolution of active mountain belts. Landslides drive the expansion of
drainage networks in uplifting rock mass, and counter the tectonic mass flux into
orogenic systems. Moreover, they are the source of most sediment eroded from the
continents, and the probability distributions of landslides and their triggers are a
first-order control on the variability of the sediment flux from active mountain
belts. Finally, landslides are the primary cause of material damage and loss of life
associated with earthquakes and rainstorms in upland areas [46]. This is, without
doubt, the strongest motivation for further investigations into the mechanisms,
patterns and rates of landsliding.
6. Acknowledgements
We thank the many organizations and people who have supported our work on
landslides by providing access to imagery and data, assistance in the field, and
help with data processing. Supported by EC Framework 5 grant EVG1-2001-0003.
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