The infl uence of large landslides on river incision in a transient landscape: Eastern margin of the Tibetan Plateau (Sichuan, China)

William B. Ouimet† Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Kelin X. Whipple School of Earth and Space Exploration, Arizona State University, Tempe, Arizona 85287, USA Leigh H. Royden Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Zhiming Sun Zhiliang Chen Chengdu Institute of Geology and Mineral Resources, Chengdu, Sichuan Province, China

ABSTRACT along a river course, and thus the magnitude common, landslides dominate hillslope erosion of the landslide infl uence, is set by two funda- (Schmidt and Montgomery, 1995; Burbank et Deep landscape dissection by the Dadu mental timescales—the time it takes to erode al., 1996), and large landslides often fi ll river and Yalong rivers on the eastern margin of landslide deposits and erase individual dams valleys, forming landslide dams that inundate the Tibetan plateau has produced high-relief, and the recurrence interval of large landslides upstream channels with water and sediment narrow river gorges and threshold hillslopes that lead to stable dams. Stable, gradually (Costa and Schuster, 1988). The formation and that frequently experience large landslides. eroding landslide dams create mixed bedrock- failure of dams resulting from large mass wast- Large landslides inundate river valleys and alluvial channels with spatial and temporal ing events such as catastrophic landslides, rock- overwhelm channels with large volumes (>105 variations in incision, ultimately slowing long- falls, and rock avalanches are well-documented m3) of coarse material, commonly forming term rates of river incision, thereby reducing and have been studied extensively around the stable landslide dams that trigger extensive the total amount of incision occurring over world (Costa and Schuster, 1991). Landslide and prolonged aggradation upstream. These a given length of river. A stronger landslide dam stability and the style of dam failure (i.e., observations suggest that strong feedbacks effect implies that a higher percentage of catastrophic or gradual) depend on the size and among hillslope processes, channel morphol- channel length is buried by landslide-related geometry of the blockage and material char- ogy, and incision rate are prevalent through- sediment, leading to reduced river incision acteristics such as texture and sorting. Not all out this landscape and are likely characteris- effi ciency. The longer it takes a river channel landslide dams fail quickly and/or catastrophi- tic of transient landscapes experiencing large to incise into a landslide dam and remove all cally; many stabilize and block river valleys for increases in local relief, in general. Landslide landslide-related sediment, the more control hundreds to tens of thousands of years, with sig- effects are a by-product of rapid incision these events have on the evolution of the river nifi cant consequences for river morphology. initiated by regional uplift. However, over profi le and landscape evolution. This can be In this paper, we explore the infl uence of large timescales relevant to landscape evolution the result of slow erosion of stable dams, or a landslides and landslide dams in the context of (>104 yr), large landslides can also act as a higher frequency of large events. bedrock river incision and landscape evolution. primary control on channel morphology and Recent studies on this topic have emphasized longitudinal river profi les, inhibiting incision Keywords: Asia, Tibetan plateau, geomorphol- the enduring infl uence of large, catastrophic and further preventing the complete adjust- ogy, river incision, landslides, transient rivers, landslides on deposition and erosion in the Indus ment of rivers to regional tectonic, climatic, landscape evolution, Dadu River River within the northwest Himalaya (Hewitt, and lithologic forcing. 1998; 2006), and the effects of large landslides We explore a probabilistic, numerical INTRODUCTION and landslide dams on the channel morphology model to provide a quantitative framework and longitudinal profi les of rivers in southwest for evaluating how landslides infl uence bed- Landslides are an important erosional pro- New Zealand, the Swiss Alps, Tien Shan, and rock river incision and landscape evolution. cess in all landscapes with moderate to steep the Himalayas (Korup, 2005; 2006; Korup et al., The time-average number of landslide dams hillslopes. In rapidly uplifting and incising fl u- 2006). Both of these authors point out that land- vial landscapes, where high-relief, threshold slide effects are superimposed onto the other †[email protected] hillslopes, and relatively narrow river gorges are controls of river profi le and landscape evolution,

GSA Bulletin; November/December 2007; v. 119; no. 11/12; p. 1462–1476; doi: 10.1130/B26136.1; 10 fi gures; 1 table; Data Repository item 2007216.

1462 For permission to copy, contact [email protected] © 2007 Geological Society of America Infl uence of large landslides on river incision: Eastern Tibet

90°E 10 0°E A B M

i N 500 km n

llow R. ° R Ye 40 N 40°N Fig. 3 . Y a Qiadam l o Basin n a' g R D . a

Yellow R. d

u

Yangtze R. R

Mek . Tibetan ong R Y . D Plateau a 1B a a d Y n Salween R. al u o g

n R g t

R . M z . e Sichuan e Y ° a . k R n

30°N Tsangpo-Brahmaputra R. Basin 30 N R o . g ze t gt n z an a e Y g

y R. H i m a l a R .

. R y d Mongolia d a Low-relief relict topography dissected w 6 by major river gorges a earl R. r P

Ν aa' r R I ed

40∞ R China . 4

India 2 Mekong

Ν Yalong Elevation (km) Elevation Yangtze Dadu 20∞ South 0 Bay of China 0 200 400 600 20°N Bengal 90∞ Ε Sea C Distance (km) 90°E 100°E Figure 1. (A) Regional topography and rivers of the eastern margin of the Tibetan Plateau, a transient landscape characterized by deep river gorges cut into an uplifted, low-relief relict landscape. (B) Patches of low-relief, rel- ict landscape preserved at high elevations. For a detailed description of the criterion used to identify patches of relict landscape, see Clark et al., 2006. (C) Topographic cross-section (path a to a′ indicated in B), extracted from the ~1-km resolution GTOPO30 Digital Elevation Model (U.S. Geological Survey, 1993).

such as tectonics, climate, lithology, and base- Overview of Stable Landslide Dam river channels narrow. Upstream of landslide level fall, and that a better understanding of the Formation and Effects on Rivers dams, river gradients are low, and fi ne-grained infl uence of landslides is needed before valley lake sediments and alluvial gravels accumulate. landforms and channel morphology can be used A stable landslide dam is any landslide dam In conjunction with fi lling within the trunk river, to infer the effects of these external forcings. that stabilizes and blocks a river valley for hun- side tributaries may become fi lled with alluvial Deep landscape dissection on the eastern dreds to tens of thousands of years, either initially fans graded to the high fi ll level of the trunk margin of the Tibetan Plateau has produced or after some degree of catastrophic failure and stream. The abrupt change in slope associated high-relief, narrow river gorges and thresh- dam-outburst fl ood erosion. Landslide deposits with the transition from upstream, low-gradient old hillslopes that frequently experience large that fi ll river valleys and consist of a high per- fi lls to steep, dramatic rapids through the land- landslides, making the entire region highly centage of large (>2 m) boulders or defl ect rivers slide deposits creates signifi cant knickpoints susceptible to landslide dams. Here, we use over bedrock ridges often lead to the formation with a drop in elevation of up to 100- to 300-m key examples from the Dadu and Yalong river of stable landslide dams. Once upstream lake (Korup, 2006). gorges (Fig. 1) to highlight the infl uence of large levels reach the top of the landslide dam and The integrated effects of large landslides on landslides and the interaction between landslide streamfl ow over landslide deposits begins, ero- river channels completely prohibit rivers from dams, channel morphology, longitudinal river sion-resistant boulders armor the channel bed as eroding their bed and incising over the length of profi les, and river incision. We then develop a fi ner material is washed downstream. This pro- the landslide mass and associated fi ll deposits. numerical model to simulate the occurrence and cess condenses the original landslide material This period of local non-incision continues for erosion of landslide dams along a length of river, to a smaller mass composed of large boulders, the entire duration of a landslide dam event, from and examine long-term controls on the degree stabilizing the landslide dam, and protecting the emplacement of the dam, to complete inci- to which channels may be buried by landslide- the top of the initial deposit from further ero- sion through landslide deposits and some por- related sediment and inhibit river incision. Our sion. These large boulders are not easily moved tion of the associated upstream fi ll. During this model is an important step toward quantify- in even large fl oods, and serve to roughen the time, the long-term evolution of the river profi les ing the infl uence of large landslides in actively bottom of the channel. There is often evidence and landscape evolution are affected in two main incising landscapes and incorporating this infl u- of advanced fl uvial sculpting of boulders, which ways: (1) downstream reaches continue to incise, ence into models of bedrock river incision and attests to long periods of boulder stability. In while landslide reaches do not, and (2) fi lled landscape evolution. these steep reaches, dramatic rapids form and upstream reaches and the whole profi le upstream

Geological Society of America Bulletin, November/December 2007 1463 Ouimet et al. of the fi ll effectively have a new, unchanging Landslides, Bedrock River Incision, and The infl uence of large landslides is another base level that freezes all further adjustment Landscape Evolution way bedrock river incision and landscape evolu- (i.e., upstream migration of downstream inci- tion may be affected by tectonics and/or climate, sion signals). Therefore, within actively incising The persistence of landslide dams within which can vary across space and time throughout landscapes, large landslides establish spatial and actively incising river gorges such as those on a landscape. There are clear, well- documented temporal variations in incision rate, even if rock the eastern margin of the Tibetan Plateau is one relationships between earthquake size and the uplift is steady and uniform. aspect of the dynamic coupling between bed- probability of large landslides (Keefer, 1994). Whether or not large landslides have signifi - rock river incision and hillslope erosion that can In addition, changes in the intensity of precipi- cant long-term effects on river incision depends signifi cantly infl uence the evolution of fl uvial tation, such as increases in the monsoonal pre- on the longevity of individual landslide dams and landscapes. Hillslopes occupy a much higher cipitation on the Himalaya, have been directly their distribution in space and time. Landslide percentage of landscape area, therefore account- linked with increases in the occurrence of large occurrence and distribution depends on material ing for most of the denudation that occurs, but landslides, and subsequent periods of fl uvial properties, landslide triggers (i.e., heavy pre- bedrock river incision generates local relief and aggradation (Pratt et al., 2002; Trauth et al., cipitation and earthquakes), and the degree to ultimately controls regional erosion rates by set- 2003; Bookhagen et al., 2005). Tectonics also which hillslopes are over-steepened and primed ting the boundary condition for hillslope ero- infl uences the frequency and potential magni- for massive failure. Longevity of individual sion to occur (e.g., Whipple, 2004). However, to tude of landslide events more generally through landslide dams is a function of dam geotechni- incise, rivers must both erode bedrock and trans- increases in topographic relief and erosion rates cal stability and river incision into the landslide port all the sediment supplied to them from the driven by rock uplift. deposit. The stability of landslide dams depends entire upstream drainage basin and adjacent hill- By infl uencing river incision, landslides affect on a number of factors, most important of which slopes (e.g., Sklar and Dietrich, 1998). This sug- the form of river profi les and can signifi cantly are the size of the original landslide deposit, the gests that an important negative feedback may complicate their interpretation (Korup, 2006). percentage of large boulders within that deposit, exist within rapidly incising landscapes, where The shape and the slope-area relationships of and the geometry of the valley fi lled (Costa and hillslope erosion, following incision, slows and/ river profi les have been used by many research- Schuster, 1988). The percentage of boulders or stops river incision by covering the bed for an ers to infer patterns of rock uplift (Kirby et al., within the landslide deposit is a function of extended period of time with larger volumes of 2003; Lague et al., 2003; Kobor and Roering, bedrock strength, landslide process, and depth material or coarser grain sizes of sediment than 2004; Wobus et al., 2006). However, there is a of failure. Local bedrock lithology is important annual fl oods can easily transport downstream. strong link between profi le knickpoints, chan- here because it controls the cohesive strength of Aspects of this feedback are contained in sedi- nel steepness, and the occurrence of large hillslope material and determines the size of the ment fl ux–dependent river incision models that landslides. Some of the steepest channels and material within the landslide deposits, largely as emphasize the dual role of sediment as both a highest channel-steepness index values any- a function of how massive, fractured, or layered tool for erosion and an element inhibiting erosion where within a landscape may be associated is the bedrock in the area. by covering the channel bed (Sklar and Dietrich, with channel steepening through landslides The geometry of river valleys affects whether 1998, 2001; Whipple and Tucker, 2002). (Korup, 2006). River profi les are also used to or not stable landslide dams form and change in Large landslides can infl uence river profi les study the characteristics of transient landscapes response to large hillslope failures. Rapid depo- over timescales relevant to landscape evolu- (Gasparini, 2003; Crosby and Whipple, 2006; sition of landslide debris defl ects river channels tion (>104 yr), and as a result, there is a need to Gasparini et al., 2006; Wobus et al., 2006). Two within their valleys, and subsequent incision develop models that incorporate their effects on end-member models of bedrock river incision into landslide debris and upstream fi ll deposits bedrock river incision and landscape evolution are detachment-limited models (where incision may involve bedrock ridges of the former valley, (Hewitt, 1998; Korup, 2002). Localized, large, is regulated by the detachment and abrasion of enhancing the stability and duration of the land- hillslope-sediment input is seldom incorporated the bedrock channel bed) or transport-limited slide blockage. Narrow, bedrock-walled valleys into models and dynamics of long-term, longi- models (where incision is regulated by transport constrict landslide deposits and force rivers to tudinal river profi les and landscape evolution. of sediment) (Willgoose et al., 1991; Howard, incise directly into landslide deposits, limiting The landslide effect described here acts over 1994; Whipple and Tucker, 2002). These mod- lateral mobility in the valley. Narrow valleys are and above the more continuous sediment sup- els predict different forms for transient river pro- also, in general, more likely to concentrate large ply effects considered in recent modeling studies fi les. However, landslide effects may lead to the landslide deposits in the channel, leading to sta- (e.g., Sklar and Dietrich, 2004, 2006; Gasparini same transient morphologies as bedrock river ble dams. Big rivers characteristically have wide et al., 2006). Many models of hillslope evolution profi les evolving under detachment- and trans- valleys, therefore requiring bigger landslides, if have no expression for landslide erosion on hill- port-limited conditions—abrupt knickpoints as stable landslide dams are to form. Large land- slopes (e.g., Tucker et al., 2001). Densmore et al. in detachment-limited models and smooth, dif- slides change the geometry of river valleys by (1998) provide the most detailed landscape evolu- fuse, convexities as in transport-limited models. widening the valley fl oor and reducing hillslope tion model in terms of landslide erosion, empha- The two case studies we discuss in the next sec- relief, which can drive the lateral erosion of sizing the full range of landslide erosion and the tion are examples of both these situations. hillslopes and redefi ne drainage divides, such role of large landslides, but their approach does as has been recognized in physical experiments not allow for a dynamic coupling between bed- STUDY AREA of landscape evolution (Hasbargen and Paola, rock river incision and hillslope erosion. Instead, 2000). Most landscape evolution models do not all material that landslides deliver to the channel The eastern margin of the Tibetan Plateau is realistically treat large landslides. This omission in their model is regolith and transportable by one of the world’s broadest and most dramatic may, in part, explain the far greater stability of fl uvial processes, and signifi cant channel block- transient landscapes, characterized by a region- river networks in numerical simulations of land- ages with lakes and upstream sedimentation do ally persistent, elevated, low-relief relict land- scape evolution. not occur (Densmore et al., 1998). scape that has been deeply dissected by major

1464 Geological Society of America Bulletin, November/December 2007 Infl uence of large landslides on river incision: Eastern Tibet

Figure 2. Longitudinal river t landscap 4000 relic e A profi les of the Dadu River (A) and Yalong River (B), Knickpoints associated with 3000 large landslides extracted from ~90-m resolu- tion Shuttle Radar Topography 2000 Min River Mission (SRTM) data. In areas 4D Confluence where SRTM data are missing

Elevation (m) Elevation 1000 km 1000 within the river gorge, the pro- Dadu River fi le is inferred from adjacent 0 points. Solid-gray lines drawn 0 100 200 300 400 500 600 700 800 900 1000 above the profi les indicate where Distance (km) patches of relict landscape are 5000 well preserved within a distance relict landscape B of 20–30 km adjacent to the 4000 river gorges. Dashed lines indi- Knickpoints associated cate the relief bounds of the rel- 3000 with large landslides Yangtze Confluence ict landscape (Clark et al., 2006). 1570 km Each profi le has a diffusive, 2000

Elevation (m) Elevation smooth upper section rolling off the relict landscape, contrasted 1000 with a steep lower profi le that Yalong River Ertan Dam 0 has many knickpoints, some of 0 200 400 600 800 1000 1200 1400 which are associated with large Distance (km) landslides, as noted. rivers and their tributaries (Clark et al., 2006; these catchments is the Xianshuihe Fault, a river terraces, were determined to be fl uvially Fig. 1). Thermochronological data show that large-scale, strike-slip fault slipping at ~10 mm/ beveled landslide deposits, the tops of ancient rates of rock cooling on the eastern margin of yr (~60 km total offset) that has experienced landslide dams, or high levels of alluvial gravel the plateau increased dramatically between 9 four earthquakes greater than magnitude 7 in and lake sediment associated with landslide and 13 Ma, suggesting that uplift and major the last century (Allen et al., 1991). The Dadu deposits. Channel and valley widths vary greatly river incision began at that time (Kirby et al., and Yalong rivers have each experienced cata- as channels alternate between straight, narrow- 2002; Clark et al., 2005). Major rivers start at strophic landslide damming events within the walled, steep, incising bedrock reaches and high elevations over 4000 m, where they are past 250 yr that were triggered by large, >6.0- meandering, wide, gentle, depositional alluvial slightly incised into the relict landscape, and M earthquakes (Tianchi, 1990; Dai et al., 2005). reaches. Bedrock reaches generally have steep transition into rapidly incising, high-relief, Accounts from the example on the Dadu River bedrock hillslopes adjacent to channels. Hill- dissected gorges with steep hillslopes (Fig. 2). indicate as many as 100,000 deaths were caused slopes are also steep within alluvial reaches, but Estimates of long-term (106–107 yr) bedrock by the downstream fl ooding associated with ini- the large volume of sediment fi lling the valley river incision in these gorges are on the order of tial dam failure, making it one of the most disas- in these reaches and the meandering nature of 0.25–0.5 mm/yr (Clark et al., 2005). Longitudi- trous events ever resulting from a landslide dam the channel disconnects channels from adjacent nal river profi les exhibit transient morphologies, breach (Dai et al., 2005). Recent catastrophic hillslopes and suggests that the bedrock valley with large knickpoints, and convex to linear, events such as these have also been documented fl oor is far below the present channel bottom. rather than concave, profi le forms. Hillslopes, in the Min River gorge to the east of the Dadu Other than the occasional steep bedrock following incision, display zones of adjustment and in the main Yangtze River gorge to the west reaches, most steep reaches are boulder rapids, with steepest values in the lowermost reaches of of the Yalong, indicating that landslide dam- 10–1000 m long, that are found only in associa- individual basins. These observations highlight ming is a widespread and ongoing phenomenon tion with landslides, rockfalls, and debris fl ow the transient response of rivers to rapid incision in all river gorges on the eastern margin (Tian- deposits. Many of these rapids occur at the loca- on trunk streams as waves of landscape adjust- chi, 1990; Hejun et al., 2000). tion of well-defi ned, large, deep-seated land- ment propagate upstream and up hillslopes. slide events (>5 × 105 m3) that are easily iden- The Dadu River (Dadu He) and Yalong River River Morphology and Large Landslides tifi ed based on their morphology and textural (Yalong Jiang) are major tributaries of the Yang- characteristics (Fig. 3). These large landslides tze River (Jinsha Jiang), both over 1000 km in Fieldwork conducted during 2003–2006 appear, in many cases, to have led to exten- length (Fig. 2). Bedrock geology in these catch- along the trunk streams and major tributaries sive and prolonged river damming, as deposits ments consists mainly of the Songpan-Ganze of the Dadu and Yalong indicates that valleys from large landslides frequently coincide with fl ysch terrane, which is intruded by a series of contain a combination of fl uvial and landslide upstream sediment interpreted to be related to Jurassic age granitic plutons (Roger et al., 2004) deposits, tributary alluvial fans, lake sediments, and deformed Paleozoic rocks and crystalline debris-fl ow deposits, and bedrock (see Data 1 1 GSA Data Repository item 2007216, Fig- Precambrian basement that outcrop in the south- Repository for photos). Numerous low-gradi- ures DR1–DR7, is available at http://www.geoso- ern portions of each catchment (Burchfi el et al., ent topographic benches 50–1000 m above the ciety.org/pubs/ft2007.htm or by request to editing@ 1995). The most prominent active fault within modern river level, previously interpreted as geosociety.org.

Geological Society of America Bulletin, November/December 2007 1465 Ouimet et al. impoundment and aggradation behind present and paleo-landslide dams (e.g., lake sediments and alluvial fi ll). Landslide deposits vary from 101°E 102°E large fragments of intact bedrock, variably 50 km 32°N 32°N brecciated and fractured, to a complete mix of DR-6 unconsolidated, poorly sorted material ranging in size from pulverized rock, dust, and sand to 10- to 30-m-diameter boulders. Depending on how recently the damming DADU event occurred and how large the event was, river channels are incised into landslide depos- RIVER its and upstream fi ll to varying degrees (Fig. 3). Some landslide dams still have lakes upstream, Xianshuihe Fau while others are completely fi lled in with allu- vium upstream, with large alluvial fans graded Fig. 4 to the height of the ancient landslide dam outlet level, some with picturesque villages built upon lt (XSHF) 31°N them indicating substantial antiquity. In other 31°N Dadu Star cases, preserved relics (lake sediments, alluvial Junction fi ll, and ancestral tributary fans) of much older landslide dams high up on valley walls suggest extremely large damming events have occurred, or that damming events occurred when the trunk level was higher than it is today. Throughout river gorges on the eastern mar- Fig. 6 gin of the Tibetan Plateau, we fi nd a range of landslide dam sizes with stable heights between DR-3 tens to hundreds of meters, affecting stretches of river ranging from hundreds of meters to over 20 km in length. The age of most of these land- YALONG slide events is unknown; known ages range from 30°N modern examples (as recently as 1933) to ones 30°N RIVER Li Qui River reaching as far back as >40,000 yr (14C age). We have dated three landslides with cosmogenic radionuclide (10Be) exposure ages to ~8800, ~6500, and ~57,000 years old. We have also used optically stimulated luminescence (OSL) to date lake sediments associated with one ancient dam to ~5,000 yr old. In some cases, landslides lin- Dadu Bend ger within river gorges, infl uencing incision for 105–106 yrs (as indicated by at least one location where recurrent landslides and local rock proper- Landslide dam sites ties appear to have effectively inhibited a major Active site (lake, LS deposits, rapids, knickpoint, etc.) tributary from keeping pace with trunk-stream Inferred site (LS deposits, incised lake sediments or aggraded fluvial sediments, no knickpoint, etc.)

incision in the past ~9–13 m.y.). In some regions 29°N 29°N Filled alluvial valleys behind active dams on the Dadu River, the integrated effect of many Active strands of the XSHF large landslides and dams appears to have effec- tively dammed stretches of river up to 100 km in 101°E 102°E length, forcing them to become alluviated. Figure 3. Landslide dam sites (active and inferred) within the Dadu and Yalong river gorges, Case Study 1: Dadu Gorge and Tributaries— superimposed on a shaded-relief rendering of the region. Identifi cation based on morphol- Danba Region ogy and characteristics of landslide deposits (typically >0.25 km3) and landslide dam depos- The Danba region in the Dadu catchment its (lake sediments, fi ll terraces, etc.). The main distinction between active and inferred sites hosts several excellent examples of the inter- is that active sites still defi ne signifi cant knickpoints on longitudinal profi les. Fieldwork was action between landslide dams, river profi les, restricted to the Dadu River gorge, major tributaries near Danba, and the Li Qui River. and channel morphology (Fig. 4). The bedrock Bold lines behind certain landslides indicate the degree to which river valleys are presently geology around Danba consists of a structural fi lled in with sediment behind large landslide dams. Note the location of Xianshuihe fault. antiform that exposes deeper, deformed levels Inset boxes refer to the locations of Figures 4, 6, DR-3, and DR-6. LS—landslides. of the Paleozoic sequence beneath the Triassic- Jurassic Songpan-Ganze fl ysch, notably a

1466 Geological Society of America Bulletin, November/December 2007 Infl uence of large landslides on river incision: Eastern Tibet

Figure 4. Danba region, Dadu River. 101 40' E 102 0' E A (A) Map of the Danba region indicat- 20 km ing the site of active landslide dams (gray N 2050m 4920m boxes), landslide scars (bold black lines with teeth), landslide boulder rapids (dark- gray shading), and currently dammed/fi lled in stretches of river (light-gray shading). 5050m n 4615m a (B) Lower 40 km of the Ge Sud Za He River

u h longitudinal profi le, with four active land-

C

n

i slide dams and associated upstream fi lling. j n

Fig. 5A a ua D G D iaojin Ch (C) Lower 40 km of the Xiaojin Chuan River e X S 4550m u longitudinal profi le, with two active land- d 31 0' N 4625m 31 0' N Z slide dams and associated upstream fi lling. a H e (D) Longitudinal profi le of the Dadu River through the Danba region, with two active 4750m landslide dams and associated upstream fi ll- 5155m ing. Dashed boxes denote landslide deposits, 1870m 4955m scaled by estimated landslide volumes. All Danba profi les extracted from ~90 m SRTM data. e H Inset boxes refer to location of Figures 5A 4938m u G g and 5B. The ages of all landslide dams are on D unknown except for one noted. 4530m D a d u H e 4466m Silurian mica-rich schist. This schist is prone to 4800m 5125m large landslides, and, consequently, hillslopes 1780m around Danba commonly have hummocky 30 40' N 101 50' E 102 10' E 30 40' N landslide morphology. At Danba, the Dadu trunk stream (named Dajin Chuan here) joins 2700 Age: 8,812 +/- three large tributaries, the Ge Sud Za He, Xiao- 590 yrs B 2500 jin Chuan, and Dong Gu He, in a star-shaped Fig. 5B pattern. Upstream from Danba, there are signifi - 2300 cant landslide-related knickpoints on the Dadu 2100 mainstem and on all three of these tributaries. The abrupt knickpoints in all these river profi les Elevation (m) Elevation 1900 are related to landslides, with the same mor- Ge Sud Za He 1700 phology as knickpoints created by rivers that 40 35 30 25 20 15 10 5 0 cross a sharp lithologic contrast (i.e., weak rock 2300 type to strong), or by transient river response C to upstream migration of incision in models 2100 of detachment-limited bedrock river incision (Whipple and Tucker, 2002). The Ge Sud Za He tributary, in particular, is 1900 dominated by landslide dams, boulder rapids, and Elevation (m) Elevation impounded alluvial fi lls for 40 km upstream of Xiaojin Chuan 1700 its confl uence with the Dadu mainstem (Fig. 4). 40 35 30 25 20 15 10 5 0 The most dramatic of these landslide dams 2150 occurs 15 km upstream from the confl uence D with the Dadu, with ~150 m of drop in the rapids 2050 caused by the landslide deposits. Field surveys show nicely the characteristic drop in channel 1950 width and increase in channel slope across the landslide mass where the channel is armored by Elevation (m) Elevation 1850 large boulders (Fig. 5). This particular example Dadu Trunk - Dajin Chuan 1750 shows a period of prolonged upstream fi lling, as 80 60 40 20 0 numerous large alluvial fans upstream are graded Distance (km) into the new base level set by the landslide dam. The age of the landslide is 8,812 ± 590 yr, based

Geological Society of America Bulletin, November/December 2007 1467 Ouimet et al.

A i

i

ii Figure 5. Ge Sud Za River landslide dam close-up, photos, and data. (A) LANDSAT sat- ellite image, resolution 30 m; A-i and A-ii mark photo loca- ii tions. (A-i) Field photo of the fi lled valley upstream with large alluvial fans adjusted to the present river level. (A-ii) Field photo of the steep nar- row rapids through landslide Channel Width deposits. (A-iii) Field photo of B Channel Slope 70 0.15 the steep, narrow rapids that 60 Width (m) are composed of large boulders 50 0.10 of schist. (B) Profi le, slope, and 40 0.05 width data collected during a

Slope 30 fi eld survey; A-iii marks photo 20 0.00 location. Note the drop in width 10 and increase in channel slope at the top of the landslide dam.

iii 2250

2200

2150 iii

2100 Elevation (m) 2050 4 m

2000 012364 5 Distance (km)

on a cosmogenic radionuclide (10Be) exposure There is extensive evidence for the infl uence of and Yalong catchments, dropping at ~3.3% for age for a large, ~10-m-diameter boulder on top landslides on valley and river profi le geometry 40 km, and it coincides with where the Li Qui of the landslide deposit. (Fig. 6D). Well-preserved lake and alluvial fi ll River runs south of a granite intrusion. The large gravels record a period of prolonged river dam- boulders seen in the channel along this stretch Case Study 2: Li Qui River ming, but the river has subsequently incised into are granite, presumably delivered to the channel The Li Qui River is a 190-km-long tributary a portion of these sediments. The highest fi ll from rockfalls and landslides. of the Yalong River, with 1800 m of fl uvial level increases in height moving downstream, Barring the presence of an as-yet-unknown relief, and a total drainage area of 5,880 km2. and widespread landslide deposits indicate the localized tectonic uplift, we surmise that the The Li Qui drains off a low-relief landscape likely site of an ancestral landslide dam. All fi ll greater bed roughness created by these large, perched ~2–2.5 km above local base level and levels end at the site of the inferred landslide immobile unfractured boulders, together with transitions into a rapidly incising, dissected land- dam ~40 km upstream of the Yalong confl u- their intrinsic resistance to abrasion, have signif- scape in its lower reaches, where a pronounced ence. Farther downstream, within the last 20 km icantly impeded the incision of the Li Qui River, knickpoint on the longitudinal profi le accounts before its confl uence with the Yalong, the Li Qui leading to the formation of this ~1-km-high for most (~1 km) of the fl uvial relief (Fig. 6). River is extremely steep due to a combination of knickpoint. That channels are steeper crossing Landslides have fundamentally altered the mor- rapid base-level fall and large landslide debris stronger, more erosion-resistant lithologies is phologic expression of the transient response of within the present channel. This stretch of river to be expected, because rivers maintain steeper the Li Qui to mainstem incision on the Yalong. is one of the steepest reaches of river in the Dadu slopes and more erosive power to erode their bed

1468 Geological Society of America Bulletin, November/December 2007 Infl uence of large landslides on river incision: Eastern Tibet

in these areas to keep pace with areas upstream and downstream. However, landslide effects sug- A B gest that channels are steeper at stronger, more erosion-resistant lithologies because it is harder to erode bedrock in those areas, and the massive 4500 m N a nature of bedrock lithology in these areas yields

a Yal large, erosion-resistant boulders during mass o wasting events. The integrated effect of large n g landslides on the Li Qui is to prohibit bedrock incision and slow the upstream migration of

R incision on the Yalong trunk stream. This pro-

i

v b e motes the survival of large patches of relict land-

r 4300 m r e iv scape (see Figures 1 and 6A). Landslide dam- b R i u ming and subsequent re-incision give the Li Qui . Q R i L longitudinal profi le its smooth, convex shape,

g which otherwise might have been interpreted n

o as representing a diffuse, transport- limited tran-

al sient response to a base-level fall (e.g., Begin et Y c al., 1980). Transient river profi le form, there- fore, is not simply diagnostic of alternate forms 20 km of bedrock river incision models as suggested c by Whipple and Tucker (2002), but rather can Mesozoic Granitic Plutons Triassic Songpan-Ganze Flysch refl ect a complex combination of factors. 4.5 C Numerical Modeling 4.0 a The prevalence of landslide dams impacting 3.5 b Li Qui R. river-channel morphology on the eastern margin enters Yalong R. of the Tibetan Plateau, and elsewhere (Korup et 3.0 c al., 2006), motivates us to formulate a quantita-

Elevation (m) Elevation tive framework for how landslides infl uence river 2.5 6D incision, and, hence, landscapes in general. In this 2.0 section, we develop a numerical model to simu- 150 100 50 0 late the occurrence and erosion of stable landslide Distance from Yalong River / Li Qui River Confluence (km) dams along a length of river based on simple rules 3600 D for the timing and magnitude of landslide events 3400 and generalized models for the erosion of indi- Li Qu Landslide Scarps: i River vidual dams once they stabilize. We also derive Large Landslide Deposits 3200 in the river valley and channel basic analytical expressions for the long-term average number of landslide dams along a river 3000 and relate them to the burial of bedrock valley 2800 fl oors and reduced river-incision effi ciency. Elevation (m) 2600 Highest surveyed alluvial fill level Highest surveyed lake sediment level Overview Previous extrapolated river level Yal 2400 Steep rapids, large boulders in channel ong Trunk The schematic in Figure 7A represents a snap- 2200 shot in the evolution of rivers where landslide 90 70 50 30 10 0 10 30 dams occur and erode through time, such as on Distance from Yalong River / Li Qui River Confluence (km) the eastern margin. At any given time, there is a Figure 6. Li Qui River, tributary of Yalong River. (A) LANDSAT satellite image. (B) Simpli- distribution of landslide dams along a length of fi ed geologic map derived from “Geologic map of the Tibetan Plateau and adjacent areas,” river that may comprise all stages of erosional compiled by Chengdu Institute of Geology and Mineral Resources and Chinese Geologi- decay from fresh, uneroded dams to small rem- cal Survey (map scale 1:1,500,000). (C) Longitudinal river profi le extracted from 90-m- nants of previous dams. Each landslide dam is resolution Shuttle Radar Topography Mission data. (D) Lower Li Qui River longitudinal associated with a wedge of landslide deposits river profi le with mapping. Landslide damming and subsequent re-incision into the result- and aggraded material that buries bedrock val- ing fi ll deposit gives this profi le its smooth, convex shape, accentuated by the effects of a ley fl oors and inhibits incision. The percentage strong, more resistant bedrock lithology (granite) outcropping in the region and the tran- of channel buried, which we call the landslide sient response to rapid incision on the Yalong River. burial factor (Bf), is therefore a function of the number of landslide dams that exist and their heights above the bedrock fl oor (dam height

Geological Society of America Bulletin, November/December 2007 1469 Ouimet et al. sets the upstream extent of aggraded alluvium; A Fig. 7B). We can estimate Bf within river gorges on the eastern margin through a combination Total Profile Length (Lr) of fi eld mapping and analysis of river profi les (Fig. 4; Table 1). These modern estimates of ( b 1 + b 2 + b 3 ) Bf = Bf are appropriate for, at most, the past 8000– Lr 10,000 yr, but we take them as being indicative see detail of the long-term averages expected for these riv- below b1 ers. As we will show later in this section, Bf is roughly equivalent to the percentage of fl uvial b 2 relief on rapids and falls associated with land- slide knickpoints. b 3 Our modeling is aimed at understanding what B controls the average number and height of land- Sbr land slide dam slide dams along a river because these factors deposits Sf will directly, and signifi cantly, affect the effi - ΔS ciency of river incision. These long-term aver- lake sediments, alluvial gravels, etc. ages imply an average sum of landslide dam z heights and, therefore, a long-term average Bf. Bf is a direct measure of the infl uence of landslides on river-incision effi ciency, since the fraction of L the channel bottom not buried under deep fi lls, f and thus generally available for incision (Ba) is Figure 7. Landslide dams and river profi les. (A) To calculate the landslide burial factor (Bf), 1-Bf (i.e., 0–1). Low values of Ba imply a stron- we sum the individual channel lengths associated with landslide deposits and aggradational ger, more intense landslide effect with lower wedges behind stable landslide dams. (B) Vertically exaggerated close-up of a landslide dam river-incision effi ciency; values closer to one and the upstream aggradational wedge of sediment associated with it. Note the identifi ca- imply a weak, negligible landslide effect with tion of variables used in Equations 14 through 18. The wedge of sediment behind a landslide river-incision effi ciency close to what it should dam consists of alluvial gravels and lake sediments. As z0 decreases, wedge shape is assumed be in the absence of landslide dams. Ba can be to adjust in a similar manner. considered a rough scaling factor that should modulate the coeffi cient of river incision (K) in many models. Analysis of the controls on Ba is thus a key to gauging the long-term, integrated consider part of the background controls on river and may lead to stable dams (Ts). Our model infl uence of recurrent stable landslide dams. Our incision onto which the effect of river-damming simulates river systems experiencing frequent approach is to investigate the two fundamental landslides is superimposed. Incorporating the large landslides, where some subset of land- timescales that together govern the long-term role of outburst fl oods associated with full or slides that occur lead to stable landslide dams average number and heights of stable landslide partial failure of landslide dams is an interesting distributed randomly along a length of river. We dams, and, therefore, Bf and Ba. These are the problem that is beyond the scope of the current examine three model scenarios that draw from landslide recurrence interval and landslide dam analysis. We acknowledge that this phenomenon probability distributions of landslide recurrence survival time. is a mechanism by which large landslide block- intervals, Ts, and initial stable dam heights, z0. In this treatment we are only considering ages can act to enhance the effi ciency of river In the fi rst scenario, we explore the very sim- stable landslide dams that erode gradually after incision and may act to counteract the negative ple case in which one stable landslide of fi xed they form; this includes dams that stabilize ini- feedback addressed here. height, z0, occurs at constant recurrence interval tially or after some degree of catastrophic failure Ts. In the second scenario, we consider the case and dam-outburst fl ood erosion. We acknowl- Landslide Dam Occurrence in which z0 and Ts vary independently and are edge that many landslides will occur that do normally distributed around fi xed mean values. not form stable dams, but we do not consider The fi rst fundamental timescale that infl u- In the third scenario, we investigate the case in how these non-stable landslides might affect ences the average number of landslide dams which landslide area and resulting stable dam sediment dynamics and the modes by which along a river is the recurrence interval of large height are derived from a power-law, frequency- rivers erode existing landslide dams. These we landslides that occur randomly along a river magnitude distribution of landslides.

TABLE 1. LANDSLIDE BURIAL FOR CASE STUDIES (FIGURES 4 AND 6) L , channel length R , relief H, sum of dam Sum of channel r, f Number of active River name of interest over Lr heights lengths buried Bf Ba landslide dam sites † (km) (m) (m) (km) Dadu mainstem 90 260 2 100 65 0.72 0.28 Ge Sud Za He 40 760 4 350 30 0.75 0.25 Xiaojin Chuan 40 350 2 160 35 0.88 0.13 Li Qui 180 1800 2 400 70 0.39 0.61 †Burial associated with landslide deposits and upstream wedges of sediment behind dams.

1470 Geological Society of America Bulletin, November/December 2007 Infl uence of large landslides on river incision: Eastern Tibet

z0 lower probabilities of occurrence for the larg- A est landslide dams. Coeffi cient c represents not 3*z0 only the frequency of landslide events, but also 4 τ = 100 00 yrs the fraction of these events that ultimately form stable landslide dams, such that higher values of z0 2 m = 0.01 m/ c lead to higher probabilities of occurrence for

m = 0.1 m/yr all landslide dams.

τ yr z0 = 500 yrs

Landslide dam height, z 4 Landslide Dam Erosion τ = 5000 yr s 0 The second fundamental timescale that infl u- m = 0.5 m/yr Time (yrs) ences the average number and height of land- 100 slide dams along a river is the time it takes to Te = 5000 years for both erosion models B incise through landslide deposits, fully breach individual dams, and re-incise through the zavg over Te 75 associated sediment wedge (Te). Our model utilizes simple rules of erosion for individual 50 dams to calculate Te. Stable landslide dams m = 0.02 m/yr can act either as masses of tightly packed, large boulders that erode as a whole in essentially 25 the same manner as intact bedrock, or as more τ = 10 Landslide dam height, z [m] 00 yrs loosely packed, immobile boulders that armor 0 the bed, add roughness, dissipate stream energy, 0 1000 2000 3000 4000 5000 and inhibit erosion of the dam during even the Time (yrs) highest fl ows. In addition, landslide deposits may defl ect river channels within their valleys Figure 8. Landslide dam erosion. In our model, stable landslide dams decay and re-incision may incorporate bedrock spurs in one of two simplifi ed ways—exponentially (dashed lines) or linearly (solid of the former valley, enhancing the duration lines). (A) Plots tracking landslide height through time for both erosion sce- of the blockage. We do not attempt to model narios. We give three different curves for each erosion scenario to show the explicitly these complex processes. Rather we range we use in our model runs. We use values of m and τ to yield Te values seek only to highlight the fundamental role of on the order of 101 to 105 years. (B) Plot comparing the two erosional sce- the timescale of dam removal. narios using parameters such that Te is the same for both models; in this In our model, stable landslide dams decay case, z is 100 m and Te is 5000 yr. 0 either in a linear fashion or exponentially (Fig. 8). Linear erosion proceeds at a specifi ed, constant erosion rate (m). Exponential erosion

In this third model scenario, z0 and Ts are where Nlsd(A) is the number of landslide dams is based on the premise that incision rate scales related such that larger landslide dams have much that originate from a landslide of area A [m2], with dam height (i.e., downstream knickpoint lower recurrence intervals as a consequence c is the rate of landsliding per year [yr−1], and slope) and is parameterized by a decay times- of the properties of a power-law distribution. β is the dimensionless scaling exponent (e.g., cale (τ). We track landslide height through time,

A power-law distribution for medium to large Hovius et al., 1997). Our third model scenario z(t), based on an initial height, z0, where dz/dt is landslides (landslide area >104 m2) has been generates random landslide events that obey the the rate of change of landslide height. recognized by many authors (e.g., Hovius et power-law, frequency-magnitude distribution of Exponential erosion incorporates the follow- al., 1997; Stark and Hovius, 2001; Malamud Equation 1. As landslides happen, we also use a ing equations: et al., 2004a). This distribution holds for land- threshold landslide area (~0.1 km2, or 105 m2) to slides occurring in space and time throughout a set which landslides lead to landslide dams and a dz/dt = −Z/τ, (2) given landscape, and has been documented in conversion factor (20–150 m/km2) to determine −t/τ diverse landscapes around the world (Hovius et initial landslide dam height from landslide area. z(t) = z0e , (3) al., 2000; Malamud et al., 2004b). We assume Values of this conversion factor are constrained that a subset of all landslides occurring within by fi eld examples and published studies of land- Te = 5τ, (4) a landscape will reach the main channel, and slide sizes that have led to stable landslide dams furthermore, a subset of these landslides will (Hewitt, 1998). The resulting distribution of zavg = z0/5. (5) lead to stable landslide dams. Since this small initial landslide dam heights, z0, scales with the subset should have the same distribution as the power-law distribution of landslide events that Linear erosion, by comparison, incorporates: original, we argue that the distribution of stable occurred, governed by the scaling parameters landslide dams occurring along the length of a β and c, along with the threshold area size and dz/dt = −m, (6) river through time is reasonably modeled using landslide area to landslide dam height conver- β − a power-law distribution: sion factor. We use values of ranging from z(t) = z0 mt, (7) 0.7 to 1.4, where higher values of β lead to a β Nlsd(A) = cA , (1) steeper frequency magnitude distribution and Te = z0/m, (8)

Geological Society of America Bulletin, November/December 2007 1471 Ouimet et al.

zavg = z0/2. (9) long-term average number of landslide dams it, assuming that incision back into the sedi- can be combined with any mean property of ment wedge is simply limited by incision into In the exponential case, Te is 5τ, the time it takes the distribution to evaluate the integrated effect the dam blockage. If we consider a length of −5 to reduce z0 to ~1% of its original value (e = of all landslides through time. For instance, the a large river where drainage area varies mini- ~0.01). We adjust values of τ and m to produce product of mean landslide dam height and the mally along the section of interest such that Ts,

Te values between tens to ten thousands of years long-term average number of dams (Nd = Te/Ts) Te, and z0 are not functions of position along (i.e., faster or slower landslide dam erosion) gives the long-term average sum of dam heights, stream, then we can derive simple expressions

(Fig. 8A). For each model of erosion, we also denoted H. Using equations for Nd and zavg from for the length of upstream fi ll behind landslide calculate a mean landslide dam height over Te, Equations 5, 9, 10, and 11, this yields: dams. The difference between the bedrock denoted zavg. For cases with identical timescales channel slope (Sbr) and the transport slope of τ of erosion (Te), mean dam height over its life He = (z0 * /Ts), (12) alluvial material fi lling behind the dam (Sf), Δ time (zavg) is greatly reduced (by a factor of denoted S, sets the upstream length of fi ll 2 40%) in the exponential erosion case owing to Hl = z0 /(2 * m * Ts), (13) (Lf) behind a landslide dam from the spill point the very rapid initial incision (Fig. 8B). back (Fig. 7): where subscripts e and l refer to exponential and Δ Model Results linear erosion rules, respectively. Under sce- Lf = z0/ S. (14) narios 2 and 3, in which landslide occurrence

Model runs simulate the evolution of landslide and initial dam heights are not constant, fi xed The long-term average length of fi ll, (Lf)avg and dams as they occur and erode along a length of values of z0 and Ts are replaced by z0μ and Tsμ, landslide burial factor (Bf) follow: river. The sum of landslide dam heights refl ects mean values from the distribution of landslides Δ the total number and size of landslide dams used in the simulation. Analytically derived val- (Lf)avg = zavg/( S), (15) through time (Fig. 9). As erosion parameters ues for the long-term average sum of landslide are held constant, variability originates from the heights (dotted line) accurately approximate the Bf = (Lf)avg * (Te/Ts)/Lr, (16) variability in landslide occurrence (scenarios 1– numerical results (Fig. 9).

3). The constant nature of z0 and Ts in scenario The analytic long-term average describes where Lr is the channel length of interest and Te/ 1 leads to a simple, fi xed pattern of landslide the long-term mean of summed landslide Ts is the average number of landslide dams (i.e., heights though time, and the approach to long- heights, and should not be considered a static Nd in Equations 10 and 11). Combining Equa- term average conditions in ~2 ka in this simula- value that numeric simulations asymptotically tions (15) and (16) gives: tion is clear (Fig. 9A). In contrast, the variable approach. Model runs that employ linear ero- Δ − nature of landslide distributions used in scenarios sion show more deviation than exponential Bf = zavg* (Te/Ts)/( S * Lr) = H/(Rf Sf * Lr), (17) 2 and 3 leads to irregular variations in the sum erosion between analytic long-term average and of landslide heights though time. We directly numerical results, where the analytic long-term where H is the long-term average sum of heights set the variability in scenario 2 by setting the average is lower than the long-term mean of (i.e., Equations 12 and 13) and Rf is fl uvial relief standard deviation of the z0 and Ts distributions summed landslide heights from the simulation over the river length of interest (Sbr * Lr). Thus, (Fig. 9E). Model runs of scenario 2 using small under some conditions (Fig. 10). The explana- landslide burial Bf in the long term is directly standard deviation are very similar to scenario 1, tion for this is that exponential erosion is faster proportional to the fraction of fl uvial relief rep- but as the coeffi cient of variation increases (ratio than linear erosion in the early stages of land- resented by drops across landslide knickpoints. of standard deviation to mean), scenario 2 runs slide dam erosion, so landslide dam heights As suggested earlier, we can incorporate Bf deviate from scenario 1, eventually approaching are reduced to mean values more quickly. This and the negative feedback effects of large land- the variability inherent in scenario 3 (Fig. 9F). speaks to the signifi cance of large events driv- slides into models of generalized river incision, The long-term average number of landslide ing the system. In general, the process of add- following Whipple (2004): dams that exist at any time (distributed ran- ing landslide material (occurrence) affects the − M N domly along the length of the river) is set by Ts system more because the model adds material E = K(1 Bf) f(qs) A S , (18) and Te. Under the case where Ts and Te are con- very quickly, yet removes it (erosion) slowly; stants (i.e., scenario 1), the long-term average therefore, large landslides will linger in the sys- where E is erosion rate, f(qs) denotes the infl u- number of landslide dams is simply the ratio of tem longer and have a signifi cant impact on the ence of background sediment fl ux, A is area, S is these timescales (Te/Ts). Using Equations 4 and long-term average sum of heights. For scenario channel slope, exponents M and N are related to 8 for Te above, we may write: 3, high values of β decrease the occurrence of erosion process, and K is a coeffi cient of erosion the largest landslides, and thus lead to a history related to climate and lithology. This simply adds τ Nde = (5 )/Ts, (10) of summed landslide heights that more closely another dimension to K from the general form of agrees with analytic long-term average. the stream-power river incision model, such that

Ndl = (z0/m)/Ts, (11) our new K, denoted Keff, is K(1-Bf). Both steady- Discussion state channel slope and transient response time where Nde is the long-term average number of will be functions of Keff (Whipple, 2001; 2004). landslide dams for the exponential erosion rule, The long-term average sum of landslide Higher values of the average sum of dam heights and Ndl is the same for the linear erosion rule. dam heights (H) directly implies an aver- (H) produce higher Bf (i.e., a stronger landslide Note that the long-term average number of age sum of channel lengths buried (i.e., Bf) effect), and thus lead to slower river incision landslide dams using an exponential model of (Fig. 7). Through time, landslide dams erode (i.e., reduced river effi ciency), increases in dam erosion (Nde) does not depend on the ini- and their height decreases, changing the length steady-state river gradients, and slower response tial height of dams. These expressions for the scale of the remaining sediment wedge behind times to perturbations in tectonic, climatic, or

1472 Geological Society of America Bulletin, November/December 2007 Infl uence of large landslides on river incision: Eastern Tibet

800

[m] A C F H 600

400

200 Sum of landslide dam heights, Sum of landslide dam heights, 0 150 B D G [m]

0 z 100

50 Landslide dam events, Landslide dam events,

0 0 2 4 6 81002468100246810 Years (ka) Years (ka) Years (ka)

100 E H Landslide Events z0 Landslide Events Ts 10-1

8 z0μ = 52.5 +/- 24 m Tsμ = 200 +/- 92 yr 10-2

6 p(x) # 4 10-3

2 10-4 0 0 50 100 0 200 400 z0 [m] Ts [yr] 104 105 106 107 Landslide Area (m2)

Figure 9. Model runs for each scenario of landslide occurrence using linear erosion for individual landslide dams. Model outputs are plots of the sum of landslide dam height, H, through time. In each scenario, the distribution of landslide dams is such that the mean initial stable landslide dam height, z0, is ~50 m, and the mean recurrence interval of that dam, Ts, is ~200 yr. (A) Sum of landslide dam heights through time for a fi xed landslide dam height, z0, occurring at constant recurrence interval, Ts. (B) Landslide dam events for (9A) (z0 = 50 m, Ts =

200 yr, m = 0.02 m/yr). (C) Sum of landslide dam heights through time, where z0 and Ts vary independently and are normally distributed

around fi xed mean values. (D) Landslide dam events for (9C) (z0μ = 52 ± 24 m, Tsμ = 200 ± 92 yr, m = 0.02 m/yr). (E) Distribution of z0 and Ts from (9D). (F) Sum of landslide dam heights through time, where landslide area and resulting stable dam height are derived from a power- law, frequency-magnitude distribution of landslides. (G) Landslide dam events for (9F) (z0μ = 44 ± 23 m, Tsμ = 200 ± 279 yr, m = 0.02 m/yr). (H) Plot showing the power-law relationship between landslide size and probability, p(x), for the landslide dam events depicted in (9G) (β = 1.5; c = 6400 yr−1; landslide area to dam height conversion = 125 m/m2). Landslides smaller than 0.1 km2 did not make a stable landslide dam. Dashed lines in (9A), (9C), and (9F) are analytically derived long-term average sum of landslide dam heights for the three scenarios (312 m for scenario 1,337 m for scenario 2, and 242 m for scenario 3) (Equations 12 and 13). Note that these averages are not derived from the entire probability distribution function; they are the averages from the landslide dams that happened randomly in the simulation.

Geological Society of America Bulletin, November/December 2007 1473 Ouimet et al.

1000 imply longer Te (lower m or higher τ), leading

[m] Linear Erosion H A to higher Te/Ts. 800 Te >> Ts Limitations and Guidelines for Further Work 600 We have intentionally kept our quantita- 400 tive framework simple enough to highlight the most important aspects of this problem. Many 200 aspects of river profi les must be accounted for Te < Ts to estimate a long-term average Bf. Our model

Sum of landslide dam heights, Sum of landslide dam heights, 0 considers only the situation in which Ts, Te, and

1000 z0 are not functions of position along the stream.

[m] Exponential Erosion Along concave-up river profi les, even under

H B 800 steady-state conditions, discharge, channel slope, river and valley widths, hillslope relief, 600 and grain size all vary along stream, and all of these factors might affect the shape and volume

400 Te >> Ts of aggradation wedges behind stable landslide dams. Drainage area may affect maximum slide size (local relief), initial landslide dam height 200 (valley width), and the effi ciency of landslide dam incision (discharge). In terms of the geom- Sum of landslide dam heights, Sum of landslide dam heights, 0 01020304050etry of the sediment wedge behind landslide Years (ka) dams, drainage area affects the bedrock channel slope, S , and the transport slope of sediment Figure 10. Comparison of model runs that employ linear versus exponential erosion using br fi lling behind the dam, S (grain size). There the same scenario for landslide occurrence (scenario 3) (i.e., Fig. 9F). Each model simula- f would also need to be rules for overlapping sedi- tion is 50,000 yr long and the distribution of landslide dams is such that the mean initial ment wedges, rules limiting the occurrence of stable landslide dam height, z , is ~50 m, and the mean recurrence interval of that dam, 0 landslides in proximity to recently failed areas, Ts, is ~200 yr. Parameters and thresholds governing the power-law, frequency-size distri- and rules for how landslide distributions link to bution of landslides that occur are the same as shown in Figure 9H. Dashed lines are the background incision/erosion rates. analytically derived long-term average sum of landslide dam heights for the two model In the short term, landslide dams also greatly runs. (A) Te >> Ts: Linear erosion (m = 0.02 m/yr). Landslide dam events distribution: z 0μ impact sediment fl ux along the river as sedi- = 48.8 m ± 34.6 m; Ts = 192.9 ± 200.1 yr; analytical long-term average = ~310 m. Te < Ts: μ ment delivered from upstream is trapped in Linear erosion (m = 0.5 m/yr). Landslide dam events distribution: z = 53.2 m ± 36.1 m; 0μ natural reservoirs, with potentially important Ts = 197.0 ± 202.9 yr; analytical long-term average = ~14 m. (B) Te >> Ts: Exponential μ consequences for the effi ciency of river incision erosion (τ = 500 yr-1). Landslide dam events distribution: z = 49.5 m ± 34.3 m; Ts = 198.5 0μ μ downstream of the dam (e.g., Sklar and Diet- ± 198.8 yr; analytical long-term average = ~127 m. Initially rapid erosion explains the lower rich, 1998; 2004). Once the upstream sediment long-term average in the case with exponential erosion. wedge has aggraded to the spillway height and reestablished the transport slope, however, sedi- ment fl ux both upstream and downstream of the dam will return to the background rate. This cir- base-level conditions. The high values of Bf for 5 * τ >> Ts (19) cumstance may prevail for much of the life of a select Dadu River channels (Table 1), therefore, stable landslide dam; our simple model focused suggest slower long-term river incision rates, under the exponential erosion model, and on the effect of landslide dam blockages during higher steady-state channel gradients, and more this phase. Thus we have assumed that away prolonged transient response to regional uplift. z0/m >> Ts (20) from landslide dams and the associated upstream Stable landslide dam size, occurrence, and sediment wedge, the effi ciency of bedrock chan- erosion parameters ultimately dictate the infl u- under the linear erosion model. Landscapes nel incision processes is not perturbed by the ence of landslides on river incision through their prone to a higher density of large landslides, such presence of upstream landslide dams (i.e., f(qs) control on Nd and H, and therefore Bf. If Te << as those that experience many large earthquakes is set by the background sediment fl ux). A more

Ts (low Nd), landslide dams are eroding more and/or those experiencing a rapid increase in complete model would account for the transient quickly than they are occurring, and the long- local relief, will have higher mean values of z0 perturbations associated with the initial aggra- term average sum of landslide heights is close to and lower mean values of Ts, resulting in higher dation of sediment wedges behind dams. 0, leading to low Bf values (Fig. 10). Conversely, Te/Ts. Lithology, meanwhile, affects the size of Future modeling will address these complexi- if Te >> Ts (high Nd), the long-term average sum material comprising dam deposits and the ero- ties and explore simulations where landslides of landslide heights is much greater than zero, sivity of landslide boulders, both of which can erode and occur along fully evolving concave- and there is a stronger landslide effect (i.e., ultimately control z0. We parameterize the affect up river profi les. This will allow us to address higher Bf). For Te >> Ts, values of z0 (or z0μ), Ts of lithology within our model through both z0 the direct effects of transient river profi le evo- τ τ (or Tsμ), m, and must be such that and erosion parameters m and ; stronger rocks lution, and how the landslide infl uence would

1474 Geological Society of America Bulletin, November/December 2007 Infl uence of large landslides on river incision: Eastern Tibet interact with transient evolution. We argue, of river per unit time. A stronger landslide effect LIST OF VARIABLES however, that the probabilistic, long-term analy- implies that a higher percentage of channel is A [m2] area sis employed here would hold for such evolving buried by landslide-related sediment, leading to β [-] dimensionless scaling exponent profi les with similar controls and that the same reduced river incision effi ciency. The longer it (power-law distribution of land- key variables would drive the system and scale takes a river channel to incise into a landslide slides) of infl uence. In the end, the controls on Te and dam and cut through all landslide-related sedi- Ba [-] % river channel not buried, able Ts, landslide dam longevity and occurrence, will ment, the more control these events have on the to incise still dictate the system response. evolution of the river profi le and landscape evo- Bf [-] landslide burial factor (i.e., % river Our treatment of the effects of landslide dams lution. This can be the result of slow erosion of channel buried, not able to incise) on river incision excludes the role of outburst dams, a higher frequency of large events, or a c [yr-1] rate of landsliding (power-law fl oods associated with full or partial failure of denser concentration of landslide dams along a distribution of landslides) landslide dams that occurs before dams stabi- specifi c river segment. dz/dt [m/yr] rate of change of landslide height lize and in cases where no stable dam forms. Our results speak to the dynamic coupling E [m/yr] erosion rate These fl oods may act to enhance the effi ciency that exists between hillslope erosion by mass f(qs) [-] infl uence of sediment fl ux of river incision and potentially counteract the movements and river incision. Incision creates He [-] long-term sum of landslide dam negative feedback we have addressed in this the necessary conditions for large landslides to heights for the exponential ero- paper. At present, though, it is not clear on occur (relief and steep hillslopes), but they in sion rule theoretical grounds whether the fl ood enhance- turn slow and/or stop river incision by covering Hl [-] long-term sum of landslide dam ment or the burial effect will be more important the bed for an extended period of time. In such heights for the linear erosion rule in the long term. Our fi eld observations tend to situations, long-term bedrock river incision may K [-] coeffi cient of erosion related to indicate that the integrated effect is one of an proceed through pulses of river incision into climate and lithology inhibition of incision, rather than the reverse. bedrock, followed by large landslides, valley fi ll- Keff [-] coeffi cient of erosion incorporat- A full model of the problem would incorpo- ing, and subsequent incision into fi ll sediments ing the effects of landslides rate the details of dam outburst fl oods and the and landslide debris, before river incision into Lf [m] upstream length of fi ll behind complexities of burial on real river profi les. A bedrock can continue. The feedback between a landslide dam from the spill- model like this would probably not be mean- landslides and river incision is both autogenic point back ingful in the predictive sense, but it could be (originating from the internal dynamics of long- Lr [m] channel length of interest used to explore the evolution of a river system term river incision) and allogenic (driven by m [m/yr] erosion rate for linear erosion of where we can estimate Bf or Ba from river pro- transient adjustment to external, outside forc- landslide dams fi le analysis, satellite image interpretation, and ings such as changes in base-level fall, uplift, or M, N [-] exponents related to erosion pro- fi eld observations, and where we can constrain climate). Landslides are a fundamental aspect of cess the frequency of outburst fl oods from historic the transient response to the upstream migration Nde [-] long-term average number of accounts, as we can on the eastern margin on of incision signals, but they also slow it down by landslide dams; exponential ero- the Tibetan Plateau. reducing river incision effi ciency. sion rule The landslide-dominated character of many Ndl [-] long-term average number of land- CONCLUSIONS deep river gorges around the world warrants slide dams; linear erosion rule investigation into how large landslides infl u- N [-] number of landslide dams The illustrative examples from within the ence river channels, bedrock river incision, and lsd R [m] fl uvial relief over the river length Dadu and Yalong river catchments that we have potentially, landscape evolution. River profi les f of interest discussed highlight the landslide-dominated are often used to make inferences about the tec- S [-] channel slope character of these rivers and the interaction tonic, climatic, base level, and lithologic controls S [-] bedrock channel slope between incision, landslides, river profi les, and on landscape evolution and the characteristics br S [-] transport slope of alluvial mate- channel morphology typical of rivers through- of transient adjustment to changes in these forc- f rial fi lling behind the dam out the region. As we attempt to understand how ings. However, on spatial and temporal scales [-] difference between S and S river profi les can be used to highlight important relevant to landscape evolution, landslides have ΔS br f aspects of the tectonic and geomorphic evolution effects on channel morphology and river profi le τ [yr] decay timescale for exponential of this landscape, mainly as they relate to uplift form that may be superimposed onto, or directly erosion of landslide dams and transient river adjustment, the effects of coupled with, these other controls. By simulat- Te [yr] timescale of erosion for stable large landslides must be addressed. Using sim- ing landslide dams occurring and eroding along landslide dams ple erosion rules for individual landslide dams a length of river and examining controls on the Ts [yr] timescale of recurrence for stable and realistic statistical models of how often they long-term average number and average height landslide dams occur, we have shown how, and under what cir- of landslide dams, we have begun to quantify [yr] mean Ts from the distribution of Tsμ cumstances, landslides may signifi cantly impact the infl uence of large landslides in actively landslides that occur river incision by regulating where and when incising landscapes. Within models of bedrock z [m] landslide height channels can and cannot incise. Stable, gradually river incision and landscape evolution, there- z(t) [m] landslide height through time eroding landslide dams create mixed bedrock- fore, it is necessary, at a minimum, to include a zavg [m] mean landslide dam height over Te alluvial channels with spatial and temporal vari- coeffi cient of river incision effi ciency [Keff = (1 − ations in incision, ultimately slowing long-term Bf)], which speaks to the spatial and temporal z0 [m] initial height of the dam rates of river incision, thereby reducing the total intermittency of incision due to the effects of [m] mean z from the distribution of z μ 0 amount of incision occurring over a given length stable landslide dams. 0 landslides that occur

Geological Society of America Bulletin, November/December 2007 1475 Ouimet et al.

ACKNOWLEDGMENTS model, in Willett, S.D., Hovius, N., Brandon, M.T., strengthened monsoons, central Nepal Himalaya: and Fisher, D., eds., Tectonics, climate, and landscape Geology, v. 30, no. 10, p. 911–914, doi: 10.1130/0091- This work was supported by the National Science evolution: Geological Society of America Special 7613(2002)030<0911:IADEHS>2.0.CO;2. Paper 398, p. 127–142. Roger, F., Malavieille, J., Leloup, H., Calassou, S., and Foundation Continental Dynamics program (EAR- Hasbargen, L., and Paola, C., 2000, Landscape instability in Xu, Z., 2004, Timing of granite emplacement and cool- 0003571), in collaboration with the Chengdu Insti- an experimental drainage basin: Geology, v. 28, no. 12, ing in the Songpan–Garze Fold Belt (eastern Tibetan tute of Geology and Mineral Resources. We wish to p. 1067–1070, doi: 10.1130/0091-7613(2000)28<1067: Plateau) with tectonic implications: Journal of Asian thank Joel Johnson, Jamon Frostenson, Tang Fawei, LIIAED>2.0.CO;2. Earth Sciences, v. 22, p. 465–481, doi: 10.1016/S1367- and Miu Guoxia for assistance in the fi eld; Ken Hewitt Hejun, C., Hanchao, L., Zhuoyuan, Z., and Zhiwen, X., 9120(03)00089-0. and Oliver Korup for stimulating discussion; Shannon 2000, The distribution, causes and effects of damming Schmidt, K.M., and Montgomery, D.R., 1995, Limits to Mahon for help with preliminary OSL dates; and Dar- landslides in China: Journal of the Chengdu University relief: Science, v. 270, p. 617–620, doi: 10.1126/sci- of Technology, v. 27, no. 3, p. 302–307. ence.270.5236.617. ryl Granger, Tom Clifton, Andy Cyr, Marc Caffee, Hewitt, K., 1998, Catastrophic landslides and their effects Sklar, L., and Dietrich, W.E., 1998, River longitudinal pro- and the Purdue PRIME Lab for help with cosmogenic on the Upper Indus streams, Karakorum Himalaya, fi les and bedrock incision models: Stream power and analysis. We also thank Lewis Owen, Robert Ander- northern Pakistan: Geomorphology, v. 26, p. 47–80, the infl uence of sediment supply, in Tinkler, K.J., and son, David Keefer, and an anonymous reviewer for doi: 10.1016/S0169-555X(98)00051-8. Wohl, E.E., eds., Rivers over rock: Fluvial processes constructive and helpful reviews. Hewitt, K., 2006, Disturbance regime landscapes: Mountain in bedrock channels: Geophysical Monograph Series, drainage systems interrupted by large rockslides: Prog- v. 107, p. 237–260. ress in Physical Geography, v. 30, no. 3, p. 365–393, Sklar, L., and Dietrich, W.E., 2001, Sediment supply, grain REFERENCES CITED doi: 10.1191/0309133306pp486ra. size and rock strength controls on rates of river incision Hovius, N., Stark, C.P., and Allen, P.A., 1997, Sediment into bedrock: Geology, v. 29, no. 12, p. 1087–1090, Allen, C.R., Zhuoli, L., Hong, Q., Xueze, W., Huawei, Z., fl ux from a mountain belt derived by landslide map- doi: 10.1130/0091-7613(2001)029<1087:SARSCO and Weishi, H., 1991, Field study of a highly active ping: Geology, v. 25, p. 231–234, doi: 10.1130/0091- >2.0.CO;2. fault zone: The Xianshuihe fault of southwestern 7613(1997)025<0231:SFFAMB>2.3.CO;2. Sklar, L., and Dietrich, W.E., 2004, A mechanistic China: Geological Society of America Bulletin, Hovius, N., Stark, C.P., Chu, H.-T., and Lin, J.C., 2000, Sup- model for river incision into bedrock by saltat- v. 103, p. 1178–1199, doi: 10.1130/0016-7606(1991) ply and removal of sediment in a landslide-dominated ing bed load: Water Resources Research, v. 40, doi: 103<1178:FSOAHA>2.3.CO;2. mountain belt: Central Range, Taiwan: The Journal of 10.1029/2003WR002496. Begin, Z.B., Meyer, D.F., and Schumm, S.A., 1980, Knick- Geology, v. 108, no. 1, p. 73–89, doi: 10.1086/314387. Sklar, L., and Dietrich, W.E., 2006, The role of sediment in point migration due to base level lowering: American Howard, A.D., 1994, A detachment-limited model of drain- controlling steady-state bedrock channel slope: Impli- Society of Civil Engineers Journal of the Waterway, age basin evolution: Water Resources Research, v. 30, cations of the saltation-abrasion incision model: Geo- Port: Coastal and Ocean Division, v. 106, p. 369–388. p. 2261–2285, doi: 10.1029/94WR00757. morphology, v. 82, p. 58–83. Bookhagen, B., Thiede, R., and Strecker, M., 2005, Late Keefer, D.K., 1994, The importance of earthquake-induced Stark, C., and Hovius, N., 2001, The characterization of land- Quaternary intensifi ed monsoon phases control land- landslides to long-term slope erosion and slope-failure slide size distributions: Geophysical Research Letters, scape evolution in the northwest Himalaya: Geology, hazards in seismically active regions: Geomorphology, v. 28, p. 1091–1094, doi: 10.1029/2000GL008527. v. 33, no. 2, p. 149–152, doi: 10.1130/G20982.1. v. 10, p. 265–284, doi: 10.1016/0169-555X(94)90021-3. Tianchi, L., 1990, Landslide management in the mountain Burbank, D.W., Leland, J., Fielding, E., Anderson, R.S., Kirby, E., Reiners, P.W., Krol, M.A., Whipple, K.X., areas of China: ICIMOD Occasional Paper No. 15, Brozovic, N., Reid, M.R., and Duncan, C., 1996, Bed- Hodges, K.V., Farley, K.A., Tang, W., and Chen, Z., Kathmandu, Nepal. rock incision, rock uplift and threshold hillslopes in the 2002, Late Cenozoic evolution of the eastern margin Trauth, M.H., Bookhagen, B., Marwan, N., and Strecker, M.R., northwestern Himalayas: Nature, v. 379, p. 505–510, of the Tibetan Plateau: Inferences from 40Ar/39Ar 2003, Multiple landslide clusters record Quaternary doi: 10.1038/379505a0. and (U-Th)/He thermochronology: Tectonics, v. 21, climate changes in the NW Argentine Andes: Palaeo- Burchfi el, B.C., Chen, Zhiliang, Liu, Yuping, and Royden, no. 1, p. 1001, doi: 10.1029/2000TC001246, doi: geography, Palaeoclimatology, Palaeoecology, v. 194, L.H., 1995, Tectonics of the Longmen Shan and adja- 10.1029/2000TC001246. p. 109–121, doi: 10.1016/S0031-0182(03)00273-6. cent regions, Central China: International Geology Kirby, E., Whipple, K.X., Tang, W., and Chen, Z., 2003, Dis- Tucker, G.E., Catani, F., Rinaldo, A., and Bras, R.L., 2001, Review, v. 37, no. 8, p. 661–735. tribution of active rock uplift along the eastern margin Statistical analysis of drainage density from digital Clark, M.K., House, M.A., Royden, L.H., Whipple, K.X., of the Tibetan Plateau: Inferences from bedrock channel terrain data: Geomorphology, v. 36, p. 187–202, doi: Burchfi el, B.C., Zhang, X., and Tang, W., 2005, Late longitudinal profi les: Journal of Geophysical Research, 10.1016/S0169-555X(00)00056-8. Cenozoic uplift of southeastern Tibet: Geology, v. 33, v. 108, B4, p. 2217, doi: 10.1029/2001JB000861. U.S. Geological Survey, 1993, Digital elevation models– no. 6, p. 525–528, doi: 10.1130/G21265.1. Kobor, J.S., and Roering, J.J., 2004, Systematic variation Data user guide 5: Reston, Virginia, U.S. Geological Clark, M.K., Royden, L.H., Whipple, K.X., Burchfi el, B.C., of bedrock channel gradients in the central Oregon Survey, p. 48. Zhang, X., and Tang, W., 2006, Use of a regional, relict Coast Range: Implications for rock uplift and shallow Whipple, K.X., 2001, Fluvial landscape response time: landscape to measure vertical deformation of the east- landsliding: Geomorphology, v. 62, p. 239–256, doi: How plausible is steady-state denudation?: American ern Tibetan Plateau: Journal of Geophysical Research, 10.1016/j.geomorph.2004.02.013. Journal of Science, v. 301, p. 313–325, doi: 10.2475/ v. 111, p. F03002, doi: 10.1029/2005JF000294. Korup, O., 2002, Recent research on landslide dams—A lit- ajs.301.4-5.313. Costa, J.E., and Schuster, R.L., 1988, The formation and erature review with special attention to New Zealand: Whipple, K.X., 2004, Bedrock rivers and the geomorphol- failure of natural dams: Geological Society of America Progress in Physical Geography, v. 26, no. 2, p. 206– ogy of active orogens: Annual Review of Earth and Bulletin, v. 100, p. 1054–1068, doi: 10.1130/0016- 235, doi: 10.1191/0309133302pp333ra. Planetary Sciences, v. 32, p. 151–185, doi: 10.1146/ 7606(1988)100<1054:TFAFON>2.3.CO;2. Korup, O., 2005, Geomorphic imprint of landslides on alpine annurev.earth.32.101802.120356. Costa, J.E., and Schuster, R.L., 1991, Documented historical river systems, southwest New Zealand: Earth Surface Whipple, K.X., and Tucker, G.E., 2002, Implications of landslide dams from around the world: U.S. Geological Processes and Landforms, v. 30, no. 7, p. 783–800, sediment-fl ux dependent river incision models for Survey Open-File Report 91-239, 486 p. doi: 10.1002/esp.1171. landscape evolution: Journal of Geophysical Research, Crosby, B.T., and Whipple, K.X., 2006, Knickpoint initiation Korup, O., 2006, Rock-slope failure and the river long profi le: v. 107, no. B2, doi: 10.1029/2000JB000044. and distribution within fl uvial networks: 236 waterfalls Geology, v. 34, no. 1, p. 45–48, doi: 10.1130/G21959.1. Willgoose, G., Bras, R.L., and Rodriguez-Iturbe, I., 1991, in the Waipaoa River, North Island, New Zealand: Geo- Korup, O., Strom, A., and Weidinger, J., 2006, Fluvial A coupled channel network growth and hillslope evo- morphology, v. 82, p. 16–38. response to large rock-slope failures: Examples from the lution model, 1. Theory: Water Resources Research, Dai, F.C., Lee, C.F., Deng, J.H., and Tham, L.G., 2005, The Himalayas, the Tien shan, and the southern Alps in New v. 27, p. 1671–1684, doi: 10.1029/91WR00935. 1786 earthquake-triggered landslide dam and subse- Zealand: Geomorphology, v. 78, no. 1–2, p. 3–21. Wobus, C.W., Whipple, K.X., Kirby, E., Snyder, N.P., John- quent dam-break fl ood on the Dadu River, southwest- Lague, D., Crave, A., and Davy, P., 2003, Laboratory experi- son, J., Spyropolou, K., Crosby, B.T., and Sheehan, D., ern China: Geomorphology, v. 65, p. 205–221, doi: ments simulating the geomorphic response to tectonic 2006, Tectonics from topography: Procedures, prom- 10.1016/j.geomorph.2004.08.011. uplift: Journal of Geophysical Research, v. 108, B1, ise, and pitfalls, in Willett, S.D., Hovius, N., Brandon, Densmore, A., Ellis, M., and Anderson, R., 1998, Land- p. 2008, doi: 10.1029/2002JB001785. M.T., and Fisher, D., eds., Tectonics, climate, and land- sliding and the evolution of normal-fault-bounded Malamud, B.D., Turcotte, D.L., Guzzetti, F., and Reichen- scape evolution: Geological Society of America Spe- mountains: Journal of Geophysical Research, v. 103, bach, P., 2004a, Landslide inventories and their statisti- cial Paper 398, p. 55–74. p. 15203–15219, doi: 10.1029/98JB00510. cal properties: Earth Surface Processes and Landforms, Gasparini, N.M., 2003, Long-term average and transient v. 29, no. 6, p. 687–711, doi: 10.1002/esp.1064. morphologies of river networks: Discriminating among Malamud, B.D., Turcotte, D.L., Guzzetti, F., and Reichen- fl uvial erosion models [Ph.D. thesis]: Cambridge, Mas- bach, P., 2004b, Landslides, earthquakes and erosion: sachusetts Institute of Technology. Earth and Planetary Science Letters, v. 229, no. 1-2, MANUSCRIPT RECEIVED 4 NOVEMBER 2006 REVISED MANUSCRIPT RECEIVED 30 MAY 2007 Gasparini, N.M., Bras, R.L., and Whipple, K.X., 2006, p. 45–59, doi: 10.1016/j.epsl.2004.10.018. MANUSCRIPT ACCEPTED 7 JUNE 2007 Numerical modeling of non-steady-state river profi le Pratt, B., Burbank, D., Heimsath, A., and Ojha, T., evolution using a sediment-fl ux-dependent incision 2002, Impulsive alluviation during early Holocene Printed in the USA

1476 Geological Society of America Bulletin, November/December 2007