Geomorphology 124 (2010) 137–149

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Geomorphology

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Contribution of dendrochronology to the determination of magnitude–frequencyrelationships for landslides

Jordi Corominas ⁎, Jose MoyaDepartment of Geotechnical Engineering and Geosciences, Technical University of Catalonia, UPC, Jordi Girona 1-3, D-2 Building, 08034 Barcelona, Spain

⁎ Corresponding author. Tel.: +34 93 401 68 61; fax:E-mail address: jordi.corominas@upc.edu (J. Coromi

0169-555X/$ – see front matter © 2010 Elsevier B.V. Adoi:10.1016/j.geomorph.2010.09.001

a b s t r a c t

a r t i c l e i n f o

Article history:Received 5 September 2009Received in revised form 7 July 2010Accepted 1 September 2010Available online 8 September 2010

Keywords:LandslidesRockfallsDebris flowsComplex slidesMagnitude–frequencyDendrogeomorphology

The determination of magnitude–frequency (M–F) relationships is necessary for landslide hazard assessment.Ideally, this is achieved by using inventories of past landslide events recorded by technical units or aerialphoto interpretation. However, direct sources of landslide data are often unavailable. Dendrogeomorpho-logical techniques allow us to determine the frequency of events, but few attempts have been made toestimate landslide magnitude by analysing the spatial distribution of disturbed trees. This paper addresses M–

F determination for rockfalls, debris flows and complex slides obtained by dendrogeomorphology. The casespresented require the appropriate understanding of both the geomorphological context and the disturbancecaused by landslide motion on trees. Both small and large rockfalls can be identified and dated byreconstructing the trajectories in the forest stand. The larger the rockfall size, the longer the path, the higherthe number of affected trees and the greater the area of deposition of rock fragments. The area of damagedtrees is proposed as an indicator of the rockfall magnitude. The frequency and extent of a series of debris flowswere reconstructed by mapping their deposits using relative dating criteria and by dating damaged trees.Local and global mudslide reactivations were deduced by sampling various tree generations and by analysingthe location of the disturbed trees in the landslide units. Magnitude–cumulative frequency curves weredetermined for the three cases.

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1. Introduction

The total risk at a given site results from exposure to small andfrequent landslide events and large and infrequent landslides. Areasthreatened by potential landslides with catastrophic consequencesmight be classed as low hazard areas if the probability of occurrence isvery low whereas areas with frequent landslides of low magnitudemay be considered as moderate or high hazard areas (Lateltin, 1997,2002). One of the main challenges faced by the authorities whenconsidering possible risk mitigation measures and allocating funds isto evaluate the risk level of a given area in terms of expected annuallosses. Quantitative risk analysis can play a role in this evaluation butdata on the magnitude and frequency distribution of the landslidesare indispensable (Hungr et al., 1999).

These two parameters are usually presented in plots of landslidemagnitude versus cumulative (or non-cumulative) frequency curves(Guzzetti et al., 2002). The construction of these curves is essential forhazard assessment.

The magnitude–frequency relationships for landslides havebeen discussed by a number of researchers (i.e. Hovius et al., 1997;Pelletier et al., 1997; Hungr et al., 1999; Guzzetti et al., 2002; Malamud

et al., 2004; Picarelli et al., 2005). These authors have consistently foundthat the M–F distribution of landslides appears to have a power-lawsimilar to that observed in seismology. The Gutenberg–Richter relation-ship between earthquake magnitude and cumulative frequency ofearthquakes is expressed as follows:

logN mð Þ = a−bM ð1Þ

where:N(m) is the cumulative number of earthquake events ofmagnitude equal or greater than M, and a and b are constants.

It can be shown that this equation is equivalent to a fractal (powerlaw) relationship between the number of earthquakes and thecharacteristic size of the rupture (Turcotte, 1997).

Themagnitude of landslides may be represented by either the area(Hovius et al., 1997; Pelletier et al., 1997; Guzzetti et al., 2002) or thevolume of the deposits (Hungr et al., 1999; Dai and Lee, 2001; Guzzettiet al., 2003). Magnitude–cumulative frequency (MCF) relationshipshave been developed for rockfalls (Bunce et al., 1997; Hungr et al.,1999; Dussauge-Peisser et al., 2002; Chau et al., 2003; Guzzetti et al.,2003), rock avalanches (Whitehouse and Griffiths, 1983), debris slidesand debris flows (Brardinoni and Church, 2004; Guthrie and Evans,2004; Hungr et al., 2008) and landslides (Guzzetti et al., 2002). Recentreviews of M–F relationships for landslides may be found in Guzzettiet al. (2002), Malamud et al. (2004) and Picarelli et al. (2005).

138 J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

Landslide inventories are used to prepare landslide M–F relation-ships. These inventories may be: a) a landslide set collected at a giventime (i.e. from aerial photointerpretation), b) a record of landslideoccurrence within a defined time interval, c) a continuous inventoryof landslide incidences, d) a set of landslides triggered by a singularevent (rainfall storm or earthquake) or e) a series composed of bothhistorical and dated prehistoric landslides (Picarelli et al., 2005;Corominas and Moya, 2008). The most reliable records of landslidesare those based on direct observations (Douglas, 1980; Gardner,1983), the systematic collection of landslide events by technical unitssuch as road maintenance or forest services (Hungr et al., 1999), andon the analysis and interpretation of multiple sets of aerial photo-graphs (Guzzetti et al., 2005). Landslides need to be recorded overmany decades to produce a representative estimate of landslidefrequency. As records on historical landslides are often unavailable orincomplete, they must be constructed by dating landslide deposits.The main advantage of inventories prepared with direct observationof recent landslide events is that the size can be easily determined.The determination of the magnitude of old landslide deposits is notstraightforward, especially in areas affected by repetitive landslides(rockfalls, debris flows) or by landslides showing local reactivations.This issue will be discussed in more detail in the later part.

Dendrogeomorphological techniques have proved to be effectivein the reconstruction of temporal series of landslide events. However,few attempts have so far been made to use the spatial distribution ofdisturbed trees to estimate landslide magnitude. Our paper addressesthe role of dendrogeomorphological techniques in (i) the analysis ofthe spatial and temporal distribution of the activity of landslides andin (ii) the determination of M–F relationships for different types oflandslide (rockfalls, debris flows and complex slides–mudslides). Tothis end, dendrochronological analyses were combined with detailedgeomorphological mapping and other relative dating techniques.

2. Dating landslide events and defining landslide magnitude usingdendrogeomorphological techniques

Dendrogeomorphology, which is the application of tree-ringanalysis to the study of geomorphic processes, was first introducedby Alestalo (1971). This technique has been increasingly used todetermine the frequency of debris flows (Hupp et al., 1987;Osterkamp and Hupp, 1987; May and Gresswell, 2004; Stoffel et al.,2006, 2008; Bollschweiler et al., 2007, 2008; Pelfini and Santilli,2008); rockfalls (Schweingruber, 1996; Moya and Corominas, 2004;Stoffel et al., 2005; Perret et al., 2006; Stoffel, 2006; Schnewly andStoffel, 2008; Moya et al., 2010) and landslides showing repeatedreactivation events (Shroder, 1978; Braam et al., 1987; Corominas andMoya, 1999; Fantucci and Sorriso-Valvo, 1999; Stefanini, 2004; Guidaet al., 2008; Van den Eeckauht et al., 2009).

The reconstruction of the spatio-temporal pattern of landslideactivity with dendrogeomorphology is muchmore recent. Thismay beachieved by combining tree-ring datawith a geomorphic map. Severalworks have highlighted the importance of geo-referencing treedamage in order to understand the kinematics of the landslideprocess and its spatial evolution. Earlier studies have identified thepart of the landslides affected in different episodes of activity(Fantucci and McCord, 1995). Perret et al. (2006) showed that thespatial distribution of the annual rockfall rates of a test site atDiemtigtal in the Swiss Alps can be obtained by analysing injuriesrecorded on trunk discs. Bollschweiler et al. (2007, 2008) prepareddetailed geomorphic maps at 1:1000 scale of debris fans, showingformerly active flow paths, segments of levees, debris-flow lobes andthe position of the disturbed trees. More than forty event years (yearsin which a landslide event occurred) have been identified and thepath of several events has been reconstructed by considering theposition of trees that show growth disturbance in a given year.

Stoffel et al. (2008) have dated more than 200 debris-flow depositsand analysed their spatial pattern.

The determination of M–F relationships using dendrogeomorphol-ogy is not an easy task and has only been addressed recently(Jakob and Friele, 2010; Stoffel, 2010). The reason for this is that thespatial distribution of the disturbed trees is not directly related tolandslide magnitude. Under favourable conditions, dendrogeomor-phology provides the date and location of the tree disturbancewith anaccuracy of a season (Stoffel et al., 2005; Moya et al., 2010). However,neither the number of damaged trees nor their spatial extent isnecessarily indicative of the landslide magnitude. This can be easilyseen when considering that both the number of damaged trees andtheir distribution depend on the density of the forest stand. Thus, onsparsely forested slopes, few trees will be damaged while theirnumber will increase with the density of the forest stand. Thus, thelocation of the damaged trees by itself gives only a rough estimate ofthe landslide area (magnitude).

The size of recent landslides may be easily established by fieldreconnaissance and aerial photointerpretation of the landslidedeposits (Dikau et al., 1996; Soeters and VanWesten, 1996). However,the determination of the magnitude of old landslide deposits isusually a challenge. In debris fans subjected to frequent debris flows,the reconstruction of the area of old deposits is difficult or impossiblebecause these deposits may have been buried or eroded by youngerevents. Similarly, on talus slopes where rockfalls are frequent, blocksfrom consecutive falls may become indistinguishable. This may resultin an underestimation of the activity of older periods, whichconstitutes a major problem for M–F analysis.

Despite these drawbacks, landslide temporal series can beobtained in some locations and, under favourable conditions, as itwill be illustrated through the examples that we present, dendrogeo-morphology may play a useful role in the determination of landslidemagnitude.

3. General methods: tree damage sampling and dating

Each type of landslide exhibits a distinctive mechanism of motionthat entails a characteristic set of tree disturbances, demanding aspecific tree-sampling strategy (i.e. tree selection and sampleextraction and analysis). The description of tree damage and theprocedures for dating the disturbances caused by landslides havebeenwidely discussed in the literature (Alestalo, 1971; Shroder, 1978;Hupp et al., 1987; Braam et al., 1987; Lang et al., 1999; Stoffel et al.,2005; Stoffel, 2006; Stoffel and Bollschweiler, 2008; Moya et al.,2010). In this section, only the basic criteria for dating the types of treedamage in the study areas are summarized.

Wounds can be caused by rock impacts or by abrasion by debrisflows. The age of a wound is determined by the number of annualrings that cover the scar. Wedge-shaped samples were extracted witha small handsaw from the edge of the scar. In order to date thedisturbance, the sample had to include the end of the wound.

Tree beheadingmay result from the impact of a block. This causes asudden reduction of the growth rate, which is recognizable in samplesas a series of narrow rings. In beheaded trees, a cross-sectional discwas cut at the broken tip of the trunk or a core was taken along theslope direction.

Sudden growth reduction can also be a response to a severe tiltingor to a partial burial of the trunk by debris (Shroder, 1978; Osterkampand Hupp, 1987; Fantucci and McCord, 1995; Strunk, 1997). Inpartially buried trees, a core was bored as close as possible to theground surface. The occurrence of sudden growth reductions wasinterpreted with caution because variations of ring width may resultfrom other environmental factors (e.g.: climate, complex competitionbetween trees, and diseases). Sudden growth reduction data wereonly considered as landslide-induced if a strong replication wasobserved and if the other disturbing factors could be ruled out

139J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

(Shroder, 1978; Osterkamp and Hupp, 1987). In order to excludeother disturbing factors, a comparison with a reference tree-ringseries of trees undisturbed by the landslide is essential (Osterkampand Hupp, 1987). A reference tree-ring series was reconstructed fromten undisturbed trees for each of the three study areas.

Landslides commonly give rise to tree tilting. The externalresponse of the tree to tilting is to bend the trunk in order to recoverthe verticality of the tree apex. To this end, the tree forms new ringswith reaction wood (a denser wood that is easily identifiable inconifers) and with an eccentric pattern. Sampling of the tilted trees inthe study areas included an extraction of two cores per tree along thetilt direction. In slides or mudslides that have reactivated severaltimes, more than one tilt direction can be produced in trees, andseveral bends may develop in the trunk. In such a case, the analysis ofthe tree-ring eccentricity helps to unravel the history of landslidereactivations. Two cores must be taken from each trunk bend toanalyse tree-ring eccentricity. This was carried out by using an indexsimilar to that defined by Braam et al. (1987), but analysing two coresalong the tilt direction. To calculate the eccentricity index, tree-ringswere measured to the nearest 0.01 mm with WinDendro program incore images captured at 800 ppp resolution with a calibrated scanner.

Trees colonizing the landslide deposit but undisturbed by thelandslide motion were also sampled to obtain a minimum age ofdebris flows and mudslide reactivations. In such trees, a core samplewas bored as close as possible to the ground surface.

Wood samples were dried at room temperature and polished with aband sander until a flat and shinning wood surface was obtained.Thereafter, the sampleswere analysedunder abinocularmicroscope. Thedescription and synchronisation of the samples was carried out usingskeleton plots (Stokes and Smiley, 1968; Schweingruber et al., 1990).

Dating results were expressed in dendrological years. Onedendrological year includes a dormant season (the period withouttree-ring growth that usually extends from autumn to winter intemperate climates) and the following growing season (the period oftree-ring formation that takes place from spring to the end of thesummer in temperate climates) (Moya and Corominas, 1996;Corominas and Moya, 1999). Wounds can be dated with an accuracyof a dendrological season, which may correspond to the growingseason or to the dormant season.

Fig. 1. Location of the sampled

Details on the spatial distribution of the sampled trees and on themanner inwhich this distributionwas related to the landslidemagnitudein the three study areas are indicated in the following sections.

4. MCF curves for rockfalls: the caseofAlzina chute at Solàd'Andorra

4.1. The Alzina site

The Alzina chute and talus are located at Solà d'Andorra (Fig. 1). Solàis a long slope of the Enclar massif, which extends for more than 2 kmalong the north-western limit of the Santa Coloma–Andorra la Vellaconurbation (Andorra, Eastern Pyrenees). The highest point of theEnclar massif is the Carroi peak (2332 masl) while the valley bottom isaround 980 masl. Rockfall activity is frequent in the lower half of theslope where Pleistocene glaciers shaped steep walls 400 m high, withangles locally exceeding 60°. The bedrock consists of a massivegranodiorite showing up to five well-developed sets of joints. Freshscars are abundant in the rock outcrops providing evidence of intenserockfall activity. Solà d'Andorra is characterized by chute systems alongwhich most falling boulders reach the bottom of the slope, generatinglarge debris cones. The cones coalesce and form a continuous talus thatmerges with the alluvial plain of the Gran Valira River. A more detaileddescription of the geology of the sitemay be found inMoya et al. (2010).

Recent rockfalls at Solà commonly involved rock masses b100 m3

and up to a few tens of blocks. The volume of individual blocks usuallyranges between 0.5 and 25 m3. Less frequently, rockfalls maymobiliserock masses of a few hundred cubic metres. For instance, in February2003, a mass of 300 m3 was detached, consisting of blocks of up to70 m3 (Copons et al., 2004). In April 2008, a mass of 150 m3 wasreleased with blocks of up to 32 m3. The most damaging rockfalloccurred on January 21, 1997, during which a block of 25 m3 struck abuilding, causing injuries to one individual.

4.2. Assessment of the rockfall frequency

A dendrogeomorphological analysis was performed at the Alzinatalus where broad-leaved oak species Quercus robur and Quercus ilexaccount for 99% of the forest. Q. robur is the dominant species andaccounts for 75% of the forest stand. Forest density on the talus ranges

trees at the Alzina talus.

Fig. 2. Location of fallen blocks (solid circles) in two recent rockfall events at Solàd'Andorra. Both events consisted of several blocks but only the largest ones are shown.The volume of blocks in cubic metres is also indicated.From Moya et al. (2010).

100

s

140 J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

from 950 to 2700 trees/ha. The diameter of trees is usually small withan average of 10 cm at breast height (Moya et al., 2010). Beheadedtrees and wound scars were used to identify and date rock impacts.Further details of the approach adopted at Alzina may be found inMoya et al. (2010). In this paper, only the procedures relevant to theassessment of rockfall magnitude are described.

Reconstruction of the rockfall record demands an intensive treesampling in order to obtain a complete series of events and the spatialdistribution of the damaged trees. Tree sampling may vary dependingon the particularities of the study area. At the Schilt forest in the ValaisAlps, Schnewly and Stoffel (2008) carried out a regular scheme ofsampling of trees showing rockfall impact features (wound scars,broken crowns and branches, and tilted trunks) along horizontaltransects. In order to ensure an even distribution of trees throughoutthe study site, these authors chose transects every 15 m and selectedone tree every 10 m along each transect. This strategy was notconsidered at the Alzina talus because known historical rockfalls haveinvolved one or a few blocks and have damaged only a small number oftrees. Under these circumstances, the use of transects does notguarantee a rockfall record that is complete enough to reliably estimatethe frequency of events (Gsteiger, 1993; Schweingruber, 1996). AtAlzina, an exhaustive sampling of all the trees on the talus was carriedout. This enabled us to locate all the trees damaged by each rockfall.

A total of 254 trees were sampled at Alzina between 2002 and2004 (Fig. 1). In some cases, trees showed injuries inflicted during thesame dendrological season. One question is whether these injuries aredue to the impact of several rockfalls occurring during the season or toa single rockfall event involving several blocks travelling through theforest along different trajectories. In some cases (Perret et al., 2006) itwas assumed that each rock impact on trees represented one rockfallevent. This means that each rockfall consists of a single block. Thisassumption maximizes the estimated frequency of rockfalls andminimizes its estimated size. This is not applicable to the Alzina talus.

Most of the recorded events at Solà d'Andorra mobilised severalblocks (Copons, 2004; Copons et al., 2004; Corominas et al., 2005).These rockfalls consisting of multiple blocks have a high probability ofproducing numerous impacts on trees on the talus, and theirtrajectories may be followed downslope (Fig. 2).

Consequently, we assume that all injuries produced in a givendendrological season at Alzina were caused by the same rockfallprovided that the spatial distribution of the impacts can be explainedby one or several divergent blocks. This implies that consecutiverockfalls occurring on the talus in the same season and following asimilar trajectory cannot be differentiated.

Fig. 3 shows the temporal distribution of tree damage observed atAlzina. Twelve rockfalls have been identified in the last 40 years. Thisnumber is a first estimation of the number of rockfall events. In standswith high forest density, such as Solà d'Andorra, the probability ofimpact on trees is high. However, the possibility that a rockfall couldtravel through the talus without damaging trees cannot be dis-regarded. To reliably estimate the frequency of rockfalls, it is thusnecessary to assess the probability of impact of falling blocks on thetrees located on the talus. This analysis is, however, outside the scopeof this study. Therefore, the frequency of rockfalls obtained in thiswork must be regarded as a minimum.

1959-60 1969-70

0

20

40

60

80

Num

ber

ofda

mag

ed tr

ee

1979-80 1989-90 1999-00

Dendrological year

Fig. 3. Temporal distribution of tree damage (impacts) in the forest stand at Alzina. Thevertical axis is the number of injured trees per dendrological season.

4.3. Estimate of rockfall magnitude from damaged forest

Rockfalls do not leave continuous deposits and, even in the case ofrecent rockfalls, it is not easy to determine the number and size ofblocks associated with each event given that the blocks are scatteredalong the talus. Commonly, blocks cannot be distinguished from thosefallen during other events in the same year or in a following year.Rockfall magnitude cannot therefore be determined by counting rockblocks.

Fig. 4 shows that a relationship between the number and the areaaffected by fallen blocks and the number and spatial distribution ofdamaged trees may be established. The runout distances of the twelvedated rockfall events at Alzina and the total number of damaged treesin each event are plotted in Fig. 5. The events may be grouped intoseveral classes ranging from events of short runout that damaged fewtrees (group A) to events of long runout that injured several tens oftrees (group D). The former group probably corresponds to smallrockfalls consisting of one single block of small size and the lattergroup to a “large” rockfall involving several tens of blocks. Theforegoing indicates that the path followed by each rockfall may bereconstructed by considering the age, number and location of treeimpacts. This suggests that the spatial distribution of damaged treescould be used to estimate rockfall magnitude.

The area enclosing the trees affected by each rockfall event istherefore proposed as a measure of the rockfall magnitude. This tree-damaged area (TDA) corresponds to the transit and depositionalzones of a given rockfall on the talus. TDA is an approximate andindirect measure of rockfall magnitude given that the larger therockfall size, the longer the runout (Corominas, 1996). The rationalefor this approach is that large fragmental rockfalls will mobilise manyblocks and, consequently, the area affected by fallen blocks as well asthe number of impacted trees will be large. Rockfalls involving eitherfew or small blocks will not travel long distances and will affect a

Fig. 4. Plot showing the location of fallen blocks in the 1999 rockfall event at Alzina (left) and the location of damaged trees in the dendrological year of 1998–1999 (right). The areacovered by the blocks and the area covered by the damaged trees have a high degree of coincidence. Notwithstanding, some trees are located further down slope than the mappedblocks, which was overlooked during the reconnaissance work. This illustrates the difficulty of recording data of recent rockfalls in forested slopes.

141J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

small area. Rockfalls involving one single large block (tens orhundreds of cubic metres) may travel long distances but in this casedamaged trees will define a linear path, and the area affected will besmall.

Another question is whether the area affected by the rockfall is ameasure of rockfall magnitude. The relationship between the rockfallvolume and the TDA has not yet been investigated in the literature. Anattempt to analyse such a relationship was made at Sola d'Andorra.Fig. 6 shows the relationship between rockfall volume and the areaaffected by fallen blocks for 10 rockfalls inventoried during the last tenyears at Sola d'Andorra. It is possible to trace a trend despite the smallnumber of events and high scattering for the smallest volumes. Eventhough this relationship needs to be corroborated by further data, itlends support to the use of TDA of rockfalls for M–F analysis.

TDA was traced on a map and calculated with Autocad 2004 foreach rockfall identified by dendrogeomorphology (Fig. 7).

Most of the tree damage at Alzina is wounds caused by the impactof blocks and, specifically, wounds that are visible on the surface of thetrunk. Although the rockfall record covered the last 40 years, it ispossible that the record is not complete for the period 1962–1978

0No. damaged trees per event

(wholetheAlzinatalus)

0

50

Run

out

(m

) (f

rom

the

talu

s ap

ex)

A

B

C D

150

100

10020 40 60 80

Fig. 5. Plot of the maximum runout distance covered by the identified rockfalls and thenumber of impacted trees at Alzina. Runout is measured from the talus apex to thefarthest damaged tree downslope (see explanation in the text).

since the disappearance of small wounds on tree trunks cannot beruled out (as discussed in Moya et al., 2010). The rockfall frequencywas assessed only for the period 1979–2002 (24 years). This timeinterval is similar to that used in other works for the construction ofMCF curves (Hungr et al., 1999; Guzzetti et al., 2003).

Fig. 8 shows the MCF curve obtained in the present study. Thiscurve cannot be compared with those of earlier studies, which usedrockfall volumes, because the relationship between the rockfallvolume and TDA (Fig. 6) must be confirmed by further data.Notwithstanding, the MCF curves obtained with dendrogeomorpho-logical analysis are useful for rockfall hazard assessment at Alzina. Thesmall number of inventoried rockfalls (two) does not facilitate thedetermination of hazard with historical data.

5. MCF for debris flows at the Tordó torrent

5.1. Measures of debris-flow magnitude

The parameter most frequently used to estimate the magnitude ofdebris flows is the volume of material deposited by an individualevent. Loss of debris material due to further transport or subsequenterosion is usually ignored with the result that the estimates are

0 50 100 150Rockfall volume at the source zone (m3)

0

5000

Ad = 2793* ln(Vs) - 3526R2 = 0.867

10000

Tra

nsit

and

depo

sitio

nal a

rea

of b

lock

s (m

2 )

Fig. 6. Areal extent of fallen blocks on the talus (transit and depositional area) versusrockfall volume for some recent historical events at Sola d'Andorra.

Fig. 7. Plan of the tree-damaged area (TDA) for some of the dated rockfalls at Alzina.

142 J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

approximate (Innes, 1983). The volume of mobilised debris iscommonly estimated by (i) measuring length, width and depth ofthe initiation and transportation zones (Hungr et al., 1984; Brardinoniand Church, 2004) or by (ii) measuring the area and depth of thedebris deposits in the deposition area (Van Steijn, 1996).

In regional studiesbasedonaerial photo interpretation, theareaof thewhole debris-flow source and track is alternatively used (Hungr et al.,2008). Innes (1985) found a strong correlation between planimetric areaand volume for debris flows.

Volumes of recent debris flows may be easily estimated when thedeposits accumulate in different zones. Nevertheless, at sites whererepeated activity occurs (i.e. a debris cone) new debris-flow eventsmay remove the evidence of earlier ones by eroding or overlappingthem. This is the case of the Tordó torrent, where several generationsof debris-flow deposits have been identified.

5.2. The Tordò torrent

The basin of the Tordó torrent extends over an area of 2.11 km2

and is located in the Port de Comte massif, Eastern Pyrenees(García, 2004). The Tordó torrent is a tributary of the La Vansatorrent which drains into the River Segre. The upper reaches of the

Tree-damaged area (TDA)(ha)

1

Cum

ulat

ive

freq

uenc

y (e

vent

s/ye

ar)

F = 0.046 * A-0.649

R2 = 0.934

0.1

0.01

0.0001 0.001 0.01 0.1 1

Fig. 8. Tree-damaged area (TDA) versus cumulative frequency of rockfalls at Alzina.

basin attain a height of 2278 masl and the lower reaches are located ata height of 1100 masl. The basin has a Mediterranean climate with amean annual precipitation of 1080 mm. High-intensity rainstorms insummer and autumn that may exceed 200 mm in 24 h seem toaccount for the debris-flow activity in the region. The Tordó torrentbasin is composed of limestone outcrops that form steep slopes withaverage angles exceeding 35°. Scree deposits have accumulated at thebottom of the slopes. There is a translational slide in the upper part ofthe basin. This slide involves a surficial formation of old scree depositsseveral metres thick. This can be observed at the foot of the slide. Thisfoot constitutes themajor source of debris flows in the basin. Here, theavailability of debris does not seem to be a limiting factor for theformation of debris flows. The valley bottom is filled with a thickaccumulation of debris-flow deposits.

5.3. Identification of event deposits

At the Tordó torrent, the magnitude of debris-flow events wasdetermined by considering the area of their deposits. Sedimentsdeposited by debris-flow events were differentiated using stratigra-phical and degradation criteria, and were grouped into relative-ageclasses. Relative dating is a well known technique by which the datesof landforms and deposits are expressed in relation to one another onthe basis of a set of parameters that evolve with time (Burke andBirkeland, 1979; Dawson et al., 1986). Relative-age classes can bedefined by landforms displaying similar degradation characteristics(i.e. degree of preservation, stream dissection or soil profiledevelopment). Relative dating has been used to obtain landsliderelative-age classes by means of detailed geomorphic observations(Wieczorek, 1984; McCalpin, 1984; Crozier, 1992). The analysis of thedegree of degradation of landslide features such as scarps, ridges, sags,and toes, clast weathering, stratigraphic relationships, and otherfeatures found in pits and outcrops allows us to assign relative ages tovarious landslide deposits. In this paper, the term depositional unit isused for a set of deposits included in a relative-age class and can beregarded as accumulated by a debris-flow event. The definition of thedepositional units is indispensable for estimating debris-flow volumeand age. The main criteria employed for establishing the relative ageof the debris-flow depositional units at the Tordó torrent were(García, 2004) (Fig. 9) (a) morphostratigraphic relationships;(b) presence and size of lichens colonizing rock blocks; (c) presenceof vegetation cover and age of new trees growing on the deposits;(d) clast weathering features; and (e) presence and/or absence ofdeposits in the aerial photograph sequences.

A detailed geomorphological map of the upper basin of the Tordótorrent was prepared at a scale of 1:1000 by interpreting two series of

Fig. 9. Partial view of two debris-flow deposits of different ages at the Tordó torrent. Allclasts have the same lithological composition. (a) New trees grow on the deposit, clastsare dark grey with 20% of lichen cover (evolutionary stage IV). (b) No new trees arepresent, clasts are brown-yellowish with no lichen cover (evolutionary stage I).

Table 1Summary of morphostratigraphic relationships between different depositional unitsidentified with aerial photo interpretation and field work.

Unit Weatheringdegree

Morphostratigraphic relationship Aerial photo (year)

D1 I It overlies units D3 and D4 Post July 1993D2 II It overlies and erodes units D4,

D7, D8 and D9Prior to July 1993

D3 III It overlies unit D4 Prior to July 1993D4 III It overlies and erodes units D5,

D7, D8 and D9Prior to July 1993

D5 III It overlies units D8 and D9 andthe scar of D6

Prior to July 1993

D6 III It overlies unit D9 Prior to July 1993D7 IV It overlies units D8 and D9 Prior to June 1982D8 IV It overlies unit D9 Prior to June 1982D9 V – Prior to June 1982

143J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

aerial photographs (June 1982 and July 1993), and field work (Fig. 10).The aim of the geomorphological reconnaissance was to map theboundary of the debris-flow depositional units and to determine therelative age of the units. The interpretation of the depositional units

Fig. 10. Map of the debris-flow depositional un

must take into account that a debris-flow event may produce differenttypes of deposits (i.e. channel deposits, lateral levees, frontal lobes) thathave to be related to one another. All the depositional featureswerefirstmapped and then grouped into depositional units.

Five relative-age classes of deposits were identified using suchweathering degree and botanical criteria (classes I to V of Table 1). Insome of these classes, overlapping and cross-cutting of deposits wereobserved (Table 1), indicating the existence of deposits of severaldebris-flow events. A total of eight depositional units were differen-tiated. A set of old debris-flow deposits was grouped into another unit(unit D9). These deposits were probably formed by various events andcannot therefore be differentiated using the aforementioned criteria.

Themain difficulty in preparing theM–F relationship was to definethe original extent of each depositional unit. This extent was obtainedfrom geomorphological reconnaissance and relative dating. Erosionand partial burying by younger events leave isolated patches of olderdebris-flow deposits. The original boundary of each depositional unitwas then reconstructed by a) classifying the deposits according to theirrelative ages, b) correlating the deposits belonging to a same relative-ageclass and grouping them into a depositional unit, and by c) linking theouter edges of the mapped units (Fig. 10). The reconstruction is lessreliable in the highest part of each unit close to the debris source becausethe deposits are easily eroded by subsequent debris-flow events. Theextent obtained must therefore be regarded as a minimum. Thereconstruction of the boundaries of some units was defined moreaccurately by analysing aerial photographs, particularly those of 1982,which were taken before the occurrence of three major debris-flowevents. Earlier deposits were partially eroded and buried by these events.

its identified with relative dating criteria.

Dendrological year

Vol

ume

of d

epos

ition

al u

nit (

m3 )

1949/50 1959/60 1969/70 1979/80 1989/90 1999/00

Post-July 1993

0

10000

20000

Fig. 12. Age of debris-flow depositional units and associated volume at the Tordótorrent.

100 100000Area of depositional unit (m2)

0.01

Cum

ulat

ive

freq

uenc

y (e

vent

s / y

ear)

F = 152*A-0.95

R2= 0.988

0.3

0.1

1000 10000

a)

144 J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

The volume of the debris-flow events was calculated bymeasuringthe area of the debris depositional units and an average depth fromseveral cross-sections. It is not easy to apply this procedure to theoldest depositional units since they are partially buried by youngerunits and since their outcrops display a minimum thickness. For theolder depositional units (D7 and D9), the volume was estimated bycorrelating the volume with the area of the other debris flows at thesite in line with other authors (i.e. Innes, 1983; Helsen et al., 2002;Guthrie and Evans, 2004) (Fig. 11).

5.4. Dating of depositional units and M–F calculation

Tree-ring dating of the depositional units was made considering(a) presence of new trees colonizing the debris-flow deposits thatgives a minimum age; (b) presence of abrasion wounds (OsterkampandHupp, 1987); (c) reactionwood associatedwith the tilting of treesand (d) partial burial of the tree trunk by accumulated debris. A totalof 196 Pinus sylvestriswere sampled (97 disturbed by debris flows andshowing growth disturbances and 99 trees unaffected by the flowsand colonizing the deposits).

The eight depositional debris-flow units identified and dated at theTordó torrent cover a period of 47 years. The age and volume of thedebris-flow depositional units are shown in Fig. 12. Both frequencyand volume of the dated debris-flow events must be regarded asminimum values. Small debris-flow events could have remained inthe incised channels before being eroded by younger flows. Themagnitude–cumulative frequency plot obtained with these data isshown in Fig. 13.

The proposed approach suffers from a number of limitations. First,this approach may not work in locations where debris flows are veryfrequent given that the parameters measuring relative-age features(i.e. weathering degree or lichen cover) will probably show acontinuous range of values rather than a discrete set of classes,which does not facilitate differentiation of the depositional units.Second, the occurrence of a large event may bury most of the earlierdeposits. The approach used at the Tordó torrent seems therefore tobe applicable to catchment areas where the frequency and magnitudeof debris flows are moderate. Third, in the absence of damaged trees,tree-ring dating gives only a minimum age for the debris-flowdeposits that are older than the trees (Osterkamp and Hupp, 1987;Bollschweiler et al., 2008).

0 5000 10000Area of depositional unit (m2)

0

V = 0.026* A1.44

R2 = 0.917

20000

10000

15000

Vol

ume

ofde

posi

tiona

luni

t(m

3 )

Fig. 11. Relationship between the area and volume of the six younger debris-flowdepositional units at the Tordó torrent (D1 to D6). This relationship was used toestimate the volume of the two older units (D7 and D8) from their area.

b)

0.01

Cum

ulat

ive

freq

uenc

y (e

vent

s / y

ear)

0.3

0.1

Volume of depositional unit (m3)100 1000001000 10000

F = 31.46*V-0.75

R2= 0.965

Fig. 13. Magnitude (area and volume) of the debris-flow depositional units versuscumulative frequency of the events at the Tordó torrent.

No. sampled trees= 49

0

50

100

I (%)

1919/20 29/30 39/404 9/50 59/606 9/70 79/80 89/90

Dendrological year

Fig. 15. Tree landslide-related responses at the Clot d'Esquers mudslide. The response ofthe year 1982–83 corresponds to the reactivation event of November 1982.

145J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

6. M–F relationship of reactivation events at the Clotd'Esquers landslide

6.1. Temporal and spatial analysis of dormant landslides

Dendrochronology has also been applied to the assessment of thefrequency of reactivation of dormant landslides (Shroder, 1978;Fantucci and McCord, 1995; Corominas and Moya, 1999; Stefanini,2004). Typical landslide types showing episodic activity are rotationalslides, mudslides and large landslides. A reactivation episode maytake place after resting periods of a few, several tens or even hundredsof years (Bonnard et al., 1995).

Analysis of the spatial evolution of landslide activity is possible bycarefully mapping every tree or group of trees on the landslide.Fantucci and McCord (1995) identified several reactivation events ofthe landslide at the Fossatello creek between 1880 and 1994. Theseauthors produced maps showing the part of the landslide that wasreactivated in 10-year periods. Stefanini (2004), following a similarprocedure, determined the spatio-temporal evolution of the Secchiolandslide and the relationship with triggering factors. The authorprepared event-response maps with the location of trees showing anabrupt growth reduction for the years in which the landslideunderwent a reactivation event.

6.2. Identification of landslide units

The Clot d'Esquers landslide offers the possibility of dendrogeomor-phology to determine M–F relationships for landslide reactivation. Tothis end, it is necessary to define the magnitude of the reactivationevent. Both large and complex landslides undergo episodic reactivationevents. Some of these reactivations only affect a small part of thelandslide and may be regarded as local reactivations whereas othersinvolve the whole landslide mass and may be considered as globalreactivations. The approach adopted at Clot d'Esquers was to produce ageomorphological map of the landslide (Fig. 14) showing the differentparts that are susceptible tomove independently and to locate the treessampled on them. The landslideunitswere characterized by a slidemassthat is bounded by distinct scarps, lateral shear surfaces or tensioncracks. These units could have been generated simultaneously or afterthe occurrence of the main failure. Even though most of the units mayshare a common failure surface, they are able to produce independent

Fig. 14. Geomorphological sketch o

responses to the triggers. A number of large landslides have displayedboth local and global reactivation events (Clerici and Perego, 2000;Bertolini et al., 2005; Borgatti et al., 2005). Local reactivation events aremore likely to occur than global ones. Bearing this in mind, themagnitude of the reactivation event was defined by the size of thelandslide area affected.

6.3. The Clot d'Esquers landslide

Clot d'Esquers is a complex landslide–mudslide located in theEastern Pyrenees (see Fig. 14). It occupies an area of 0.12 km2. Duringthe intense rainfall episode of 7 and 8 November 1982, this landslideunderwent a general destabilisation with displacements exceedinglocally several metres, causing the disruption of the road connectingGuardiola de Berguedà to Vallcebre, Saldes and Gòsol.

This landslide developed in claystones and shales of LowerPalaeocene age (Garumnian facies). This lithological formation isaffected by many slope failures in the region. Field reconnaissanceafter the 1982 event indicated that the Clot d'Esquers landslide wasnot a first-time failure. This landslide showed old scarps and scars,hummocky ground and water ponding. Many trees standing on themudslide displayed tilting prior to the 1982 event. The local archivescontained no information about other reactivation events.

6.4. Dating of reactivation events and determination of their extent

A systematic dendrogeomorphological sampling was carried out in1994 on coniferous trees (P. sylvestris) on the mudslide (Moya, 2002).Forty nine trees were sampled. The aim of the dendrogeomorphological

f the Clot d'Esquers mudslide.

146 J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

analysis was to identify and date the disturbances on trees caused byground displacement. These disturbances consisted of tree tilting,resulting in growth anomalies such as reaction wood and eccentricgrowth. Undisturbed young trees were also sampled because theyprovide a minimum age of reactivation. The survey provided acontinuous record of reactivation events for a period of more than60 years (Fig. 15).

Fig. 16. Reactivation events identified at the Clot d'Esquers mudsl

Fig. 15 shows the landslide reactivations expressed as the activityindex (I) plotted against the dendrological year. The activity index, ina given year, is defined by the ratio between the number of sampledtrees showing anomalies related to landsliding and the total numberof sampled trees alive that year (Shroder, 1978). The larger theactivity index, the more reliable the identification of the reactivationepisode. The results show, that although themudslide was reactivated

ide. Shaded area depicts the area associated with each event.

147J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

by a very intense and short rainfall event in 1982, it underwent otherreactivations related to persistent above-average precipitation epi-sodes. These rainfalls caused a high stream discharge that eroded thelandslide toe (Corominas and Moya, 1999). A more detailed analysisof the reactivation episodes revealed that the individual episodes haddifferent magnitudes in terms of activity index (see Fig. 16).

The analysis of reactivation events at the Clot d'Esquers landslidewas carried out by using the spatial location of the disturbed trees andtheir relationship with the landslide units. The geomorphological mapshows that the landslide is composed of several units (Fig. 14). Most ofthe landslide units contain trees. Fig. 16 shows the part of themudslide affected during several reactivation events. It was assumedthat a reactivation revealed by the trees in a given unit affected thewhole unit. Consequently, a MCF curve may be plotted using theidentified reactivation events, where magnitude is expressed as thearea affected by the reactivation (Fig. 17).

In the case of frequent reactivations occurring in successive years,tree responses could overlap with the result that some landslideepisodes could be overlooked (Lang et al., 1999; Corominas andMoya,2008).

7. Discussion

The straight line of the MCF plots for rockfalls at the Alzina talus,debris flows at the Tordó torrent and mudslide reactivation at Clotd'Esquers (Figs. 8, 13 and 17) can be represented by a power-lawrelationship. The slopes of these relationships were determined byregression. The form of the equations is that of the Gutenberg–Richterrelationship (Eq. (1)):

F = A*M−b ð2Þ

where F is the cumulative frequency of events expressed as events peryear,M is themagnitude expressed as area of the deposits, and A and bare constants. Hungr et al. (1999) stated that constant A depends onthe relative propensity of various locations to produce landslideswhile slope b characterizes the distribution of rockfall frequencies inthe study areas and in its subdomains, and reflects the geologicalconditions of the sites. The slopes of the power relationship of thestraight line determined by regression in the cases presented in thisstudy are listed in Table 2.

0.0001 0.001 0.01 0.1

Cum

ulat

ive

freq

uenc

y (e

vent

s/ye

ar)

0.3

0.1

0.01

F = 2.2* 10-2 A-0.9

R2 = 0.936

Area affected by the mudslide event (km2)

Fig. 17. Magnitude (area) of the reactivated part the Clot d'Esquers mudslide versuscumulative frequency of the events.

The results obtained with our dendrogeomorphological approachfor rockfalls cannot be directly compared with those obtained inearlier works since the manner in which rockfall magnitude wasdefined is different. Notwithstanding, the b value obtained at Alzinausing the correlation of Fig. 6 is in the range found at other rockfallsites (Table 3).

Exponent b of the Clot d'Esquers mudslide is higher than thoseobtained for the rockfalls at Alzina and debris flows at the TordóTorrent. This has also been observed by Brunetti et al. (2009), whoattributed it to different landslide mechanisms.

All the relationships obtained in this study showpronounced curves,suggesting some censoring effect. Hungr et al. (1999) found thatcensoring for rockfalls occurred at volumes smaller than 1 m3. Dai andLee (2001) analysed a variety of landslide types (most of them cut slopefailures and rockfalls) and found that censoring occurred at volumessmaller than 4 m3.This threshold rises up to 50 m3 in the data set usedbyDussauge-Peisser et al. (2002) for a rockfall set of 87 events recordedover 60 years for a cliff length of 120 km. The magnitude at whichcensoring occurs varies from one study to another, ranging from lessthan 1 m3 for rockfalls to 10,000 m3 for debris slides and avalanches(Pelletier et al., 1997; Guzzetti et al., 2002).

The sample interval at the study sites consists of several decades.This temporal window is short and hencemight not adequately reflectthe natural fluctuations and trends. However, it is similar to that usedin other studies. Based on a 60-year record of landslides, Hovius et al.(1997) prepared a M–F plot where the magnitude–frequencydistribution could be described as a power law over two orders ofarea magnitude. Hungr et al. (1999) provided a constant sampleinterval of 22 years for rockfalls and rockslides.

Our results must be viewed with caution. The MCF relationshipswere obtained using a small number of landslide events. Although theexponents of such relationships are similar to those published inearlier studies, they must be corroborated by further observations.

8. Final remarks

The present study addresses the reconstruction of rockfalls, debrisflows and complex landslide reactivations on selected forested slopesin the Eastern Pyrenees (Spain and Andorra). The approach used isbased on tree-ring analysis and detailed geomorphic mapping.Dendrochronology yields the date of the tree disturbance caused bya landslide. Landslide frequency can be calculated using the dates oftree disturbances. However, the frequency obtained should beregarded as a minimum value. The determination of the M–Frelationships requires expert judgement and further reconnaissancework since the results of the tree-ring analysis do not provideinformation directly associated with landslide size. Our approachdemands a sound grasp of both the geomorphic context and thelandslide mechanism.

Nevertheless, it is possible to estimate the magnitude of thelandslide event by interpreting the spatial distribution of damagedtrees. The geomorphological analysis of the landslide, which includesthe source, the track and the deposits, is indispensable.

Table 2Characteristics of the studied landslide data sets from which the M–F relationship wasdetermined.

Landslide type Site Number ofevents

Fit range(km2)

Time window(years)

Exponent b

Rockfall Alzina chute 11 5×10−4−1×10−2

24 0.65

Debris flow Tordó torrent 8 1×10−3−1×10−2

50 0.95

Complex slide Clot d'Esquers 6 1×10−2−5×10−2

55 0.90

Table 3Characteristics of M–F relations for rockfalls determined at different locations, including the Alzina study site.

Reference Site Number of events Fit range (m3) Time window (years) Exponent b

Hungr et al. (1999) Highway 99, British Columbia 390 1×10−2–1×104 30 0.43Hungr et al. (1999) BCR line, British Columbia 403 1×100–1×104 50 0.40Hungr et al. (1999) Highway 1, British Columbia 226 1×100–1×104 0.70Hungr et al. (1999) CP line, British Columbia 918 1×100–1×104 0.65Dai and Lee (2001) Hong Kong 2811 3×100–5×105 6 0.79Dussauge-Peisser et al. (2002) Upper Arly gorges, French Alps 59 2×101–3×103 22 0.45Dussauge-Peisser et al., (2002) Grenoble, French Alps 87 5×101–1×106 60 0.41Dussauge-Peisser et al. (2002) Yosemite, California 101 5×101–1×106 78 0.46Corominas and Moya, this study Alzina chute 10 5×100–1.5×102 24 0.65

148 J. Corominas, J. Moya / Geomorphology 124 (2010) 137–149

Our approach provides a relationship between the area where thedisturbed trees are located and the frequency of the landslide events.In the case of rockfalls, the greater the affected area, the larger therockfall event. The analysis of the available historical rockfall recordsat Solà d'Andorra suggests that such a relationship exists (Fig. 6).However, it is necessary to confirm the aforementioned relationshipusing more rockfall cases.

The regression lines obtained should be regarded as preliminarygiven the lack of data. The temporal window used is short (severaldecades) and might not adequately reflect the natural fluctuationsand trends. Nevertheless, it should be noted that the exponents “b”obtained are similar to those in other studies.

Determination of M–F relationships using dendrogeomorphologi-cal techniques is feasible only under favourable conditions. Theseconditions may be summarized as follows:

(a) Landslide events should occur episodically so that the responseof the disturbed trees may be identified without difficulty. Itmay be possible that events occurring in the same dendrolog-ical season are not differentiated unless additional informationis provided (i.e. rockfall paths).

(b) The number of available trees for sampling must be large enoughto detect the maximum number of events and must besatisfactorily distributed throughout the landslide. Large cata-strophic landslide events may kill or remove large numbers oftrees. This could result in gaps in the dendrochronological recordor could hinder the reconstruction of earlier events. Very frequentrockfallsmayprevent trees fromcolonizing themost active chuteswith the result that many events might have been unrecorded.

(c) The extent of the landslide event, which is related to itsmagnitude, should be clearly associated with the number andlocation of the damaged trees. The magnitude of the landslideevent is usually obtained by means of field reconnaissance andphoto interpretation. However, dendrogeomorphology canplay a useful role when inventoried data on landslides areunavailable or scarce.

(d) Trees must be evenly distributed throughout the landslideotherwise some events may not be recorded and the comple-tion of the event series may result in failure.

(e) The landslide series obtained should be complete. At Alzina, itwas observed that impact scars (in Q. robur) vanished after40 years. This shortened the temporal window for which theM–F relationship was determined.

A satisfactory tree-sampling strategy must be adopted for eachlandslide mechanism. In order to interpret the dendrochronologicalresults, it is necessary to thoroughly understand the nature of thelandslide process, especially its dynamics and spatial evolution.

Acknowledgements

The collaboration of Joan Pérez Arcas and Raquel García in both fieldwork and tree-sampling campaigns is gratefully acknowledged.We alsoexpress our gratitude to Dr. Markus Stoffel for his careful review.

This research work received partial support from the Safelandproject funded by the Commission of the European Communities(grant agreement 226479) and from the Big Risk (contract numberBIA2008-06614) and Debriscatch (contract number CGL2008-00299/BTE) projects funded by the Spanish Ministry of Science.

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