modelling catchment-scale shallow landslide occurrence and ... · well-known example is caine’s...

HYDROLOGICAL PROCESSESHydrol. Process. (2011)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.8158

Modelling catchment-scale shallow landslide occurrence andsediment yield as a function of rainfall return period

C. I. Bovolo* and J. C. BathurstWater Resource Systems Research Laboratory, School of Civil Engineering and Geosciences, Newcastle University, Newcastle upon Tyne, NE1

7RU, UK

Abstract:

A model-based method is proposed for improving upon existing threshold relationships which define the rainfall conditions fortriggering shallow landslides but do not allow the magnitude of landsliding (i.e. the number of landslides) to be determined.The SHETRAN catchment-scale shallow landslide model is used to quantify the magnitude of landsliding as a function ofrainfall return period, for focus sites of 180 and 45 km2 in the Italian Southern Alps and the central Spanish Pyrenees. Rainfallevents with intensities of different return period are generated for a range of durations (1-day to 5-day) and applied to themodel to give the number of landslides triggered and the resulting sediment yield for each event. For a given event duration,simulated numbers of landslides become progressively less sensitive to return period as return period increases. Similarly,for an event of given return period, landslide magnitude becomes less sensitive to event duration as duration increases. Thetemporal distribution of rainfall within an event is shown to have a significant impact on the number of landslides andthe timing of their occurrence. The contribution of shallow landsliding to catchment sediment yield is similarly quantifiedas a function of the rainfall characteristics. Rainfall intensity–duration curves are presented which define different levelsof landsliding magnitude and which advance our predictive capability beyond, but are generally consistent with, publishedthreshold curves. The magnitude curves are relevant to the development of guidelines for landslide hazard assessment andforecasting. Copyright 2011 John Wiley & Sons, Ltd.

KEY WORDS catchment model; debris flow; landslide magnitude; rainfall intensity-duration; rainfall return period; sedimentyield; shallow landslide; SHETRAN

Received 7 June 2010; Accepted 18 April 2011

INTRODUCTION

An important component of landslide hazard assessmentis predicting landslide occurrence and impact. Much pastwork has been devoted to quantification of the conditionsunder which shallow landslides may be triggered (e.g. asa function of rainfall intensity and duration, Caine (1980))and to recording the nature of specific landslide events(e.g. Chen et al., 2005). Only relatively recently hasresearch started to quantify, not just the triggering condi-tions, but the extent of shallow landslide occurrence (i.e.spatial distribution and numbers of slides) as a functionof rainfall return period, raising the possibility of issuingwarnings of landslide severity on the basis of weatherforecasts (e.g. Crozier and Glade, 1999; Dhakal and Sidle,2004; Falorni et al., 2007; Schmidt et al., 2008). Further,very little of this work has considered the offsite impactof landslide events (such as downstream sediment yield),and much of the relevant modelling work has been limitedto areas of a few square kilometres or less. There are con-siderable practical difficulties in obtaining data on land-slide occurrence, sediment yield and rainfall frequencyfor events of different sizes at large catchment scales.As a result, for the time being, progress in the wider

* Correspondence to: C. I. Bovolo, Water Resource Systems ResearchLaboratory, School of Civil Engineering and Geosciences, NewcastleUniversity, Newcastle upon Tyne, NE1 7RU, UK.E-mail: [email protected]

topic is likely to depend on modelling studies rather thandata-based research. The aim of this paper is therefore topropose a model-based methodology for quantifying themagnitude of shallow landslide events and their sedimentyield as a function of rainfall return period, for rain-falls of different combinations of intensity and duration.Using a shallow landslide sediment yield model inte-grated with a distributed, physically based hydrological,erosion and sediment yield modelling system, simula-tions are carried out for focus catchments of area 180and 45 km2 in the Italian Southern Alps and the centralSpanish Pyrenees respectively. Rainfall events with inten-sities of different return period are generated for a rangeof durations (1-day to 5-day) and applied to the modelto give the number of landslides triggered and the result-ing sediment yield for each event. The results are thenused to develop a method for presenting landslide magni-tudes on rainfall intensity/duration graphs in a way whichcomplements but advances beyond the existing thresh-old curves for landslide occurrence. The work formed acomponent of the European Commission-funded LESS-LOSS project on Risk Mitigation for Earthquakes andLandslides (http://www.lessloss.org/) and builds on ear-lier work in the European Community-funded DAMO-CLES project on debris flow hazard assessment (Bathurstet al., 2003; http://damocles.irpi.cnr.it/).

Copyright 2011 John Wiley & Sons, Ltd.

C. I. BOVOLO AND J. C. BATHURST

LANDSLIDE INCIDENCE AND RAINFALLCHARACTERISTICS

There has been a recent trend in landslide researchtowards quantifying the temporal frequency and mag-nitude of landslides and debris flows (e.g. Crozier andGlade, 1999; D’Agostino and Marchi, 2001; Reid andPage, 2002; Jakob et al., 2005). A variety of approacheshave been followed, usually relating landslide magnitudeto storm rainfall. However, while the number of land-slides generally increases with rainfall magnitude, rainfallfrequency does not translate exactly into landslide fre-quency. Shallow landslides are generally considered tobe caused by high porewater pressures in the soil, butthe extent to which porewater conditions are related torainfall depends on soil properties, antecedent moistureconditions and other variables which exhibit consider-able spatial and temporal variability (Reichenbach et al.,1998). Account must therefore be taken of the interveningbehaviour and properties of the hillslope system (Crozierand Glade, 1999). This can be achieved by a variety ofmodelling approaches.

Crozier and Glade (1999) note that the frequency–magnitude characteristics of landslide activity can beinvestigated both empirically and deterministically. Theempirical approach depends on the availability of suffi-cient data and typically involves the quantification of arange of rainfall thresholds for triggering shallow land-slides. At the simplest level such thresholds separate theoccurrence and non-occurrence of shallow landslides. Awell-known example is Caine’s (1980) intensity-durationthreshold formula, based on data from 73 studies ofshallow landslides around the world and applicable forrainfall durations of between 10 min and 10 days:

I D 14Ð82 D�0Ð39 �1�

where I is the mean storm rainfall intensity (mm h�1)and D is the storm duration (h). More recently Crostaand Frattini (2001) have presented a threshold curve ofthe form

I D a��b/D� C c� �2�

where a, b and c are coefficients. For a curve whichencompasses almost all the data available to those authorson a global scale, a D 8, b D 0Ð9 and c D 0Ð06. For alocal curve relevant to the Italian Southern Alps, a D 12,b D 1 and c D 0Ð07. Most comprehensively, Guzzettiet al. (2008) analyse a large data base to present newglobal threshold curves varying with analytical methodand range of rainfall duration. Brunetti et al. (2010)subsequently use the data relevant to Italy to definenational and regional threshold curves. Any combinationof storm intensity and duration such that intensity exceedsthe threshold value given by such curves is likely to causewidespread shallow landslide activity. The approach canalso be refined to account for the moderating influenceof antecedent soil moisture (Crozier and Eyles, 1980;Sidle and Ochiai, 2006, 147–149). Sidle et al. (1985,90–93) indicate that such relationships can be of use

in identifying return periods for various combinations ofrainfall intensity and duration that will probably inducelandsliding. However, the approach refers only to whetheror not landslides will occur and not to the magnitude orseverity of an event, e.g. the number of landslides whichmay occur.

The deterministic approach to quantifying frequency–magnitude relationships involves the use of physicallybased, spatially distributed landslide models. These inte-grate hydrological models with geotechnical slope stabil-ity models and enable slope stability to be investigatedas a function of rainfall. Such models have been devel-oped both for detailed slope investigations (e.g. Wilkin-son et al., 2002) and for more general catchment-scalestudies (e.g. Montgomery and Dietrich, 1994; Wu andSidle, 1995; Burton and Bathurst, 1998; Gorsevski et al.,2006). In principle, they can be used to determine notonly rainfall thresholds for landslide occurrence but alsothe magnitude or extent of the landsliding. Applicationof different rainfalls then allows the simulated landslidemagnitude to be related to rainfall frequency. Difficultieswith the approach arise from the characteristic uncertain-ties of the modelling process: these include the extentto which the relevant physical processes are represented,the provision of the necessary topographic, soil and veg-etation data, the uncertainty inherent in parameterizingmodels with large numbers of parameters and the spatialresolution of the model. The literature contains only afew examples of this approach (e.g. Iida, 2004; Dhakaland Sidle, 2004; Frattini et al., 2009). Generally, they areconcerned only with landslide and debris flow occurrenceon hillslopes and in headwater streams and do not con-sider the off-site impacts of landsliding, such as sedimentdelivery into the downstream river-channel network.

This paper follows the deterministic approach to inves-tigate the relationship between rainfall frequency and themagnitude of shallow landslide events, including eventimpact. The application highlights both the capabilitiesand the difficulties of the approach.

SHETRAN SHALLOW LANDSLIDE MODEL

Model background

The study uses the SHETRAN shallow landslide andsediment yield model; this is fully described by Bur-ton and Bathurst (1998), so only a summary is givenhere. The model is a component of the SHETRANphysically based, spatially distributed, catchment mod-elling system (described by Ewen et al., 2000), thatprovides the hydrological and sediment transport frame-work for simulating rain- and snowmelt-triggered land-sliding and its sediment yield. (Details are avail-able at http://research.ncl.ac.uk/shetran/) The hydrolog-ical model accounts in a fully integrated way for veg-etation interception and transpiration, snowmelt, over-land flow, subsurface unsaturated and saturated flow andriver/aquifer interaction. The version of SHETRAN usedin this application (v3.4) simulates an unconfined aquifer

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. (2011)

MODELLING SHALLOW LANDSLIDES AS A FUNCTION OF RAINFALL RETURN PERIOD

composed of a one-dimensional (vertical flow) unsatu-rated zone overlying a two-dimensional (horizontal flow)saturated zone, with a dynamic phreatic surface as theinterface between the two. Complementing the hydrolog-ical model is a conventional sediment transport model inwhich sediment yield is determined as a function of soilerosion by raindrop impact and overland flow and trans-port by overland and channel flow. The model requiresspatially variable data for topography and for vegetation,soil, sediment and geotechnical properties, and spatiallyvariable time-series of precipitation and evaporation todrive the model.

In the landslide model, the occurrence of shallowlandslides is determined as a function of the time- andspace-varying soil saturation conditions simulated by thehydrology model, using standard, geotechnical, infinite-slope, factor-of-safety analysis. This includes allowancefor the effect of vegetation root cohesion. However,in line with observation and theory (e.g. Sidle et al.,1985) shallow landslides are not simulated for slopes ofless than 25°. For each landslide, the volume of erodedmaterial is determined from the soil depth and the areaof the landslide. Eroded material is routed down thehillslope as an unconfined debris flow if the vegetation isforest or if the landslide occurs in a gully. However, if thelandslide occurs on a planar grass-covered slope, there isno onward transport and the landslide is assumed to be aslump. This rule-based approach was based on experiencein New Zealand (personal communication to Bathurst byNew Zealand researchers, 1990) but it is recognized thatit is not likely to be fully accurate in all cases. The roleof debris flows in transporting landslide material to thechannel network is highlighted by Johnson et al. (2000)and Acharya et al. (2009) among others. The model alsohas an option to allow the debris flow to collect additionalsediment by scouring along its track (although this wasnot applied in the cases described here). Deposition bythe debris flow starts to occur once the hillslope gradientfalls below a certain critical value (the default being10°) and takes place over the run-out distance, which iscalculated as a percentage of the difference in elevationbetween the landslide location and the critical slope(the default percentage being 40%). At slopes less than4° the debris flow halts unconditionally and depositsany remaining material. The proportion of the materialreaching the channel network is then calculated and fedto the SHETRAN sediment transport model for routingas conventional channel sediment load to the catchmentoutlet. Material deposited along the track of the debrisflow may subsequently be washed into the channel byoverland flow and will contribute to the sediment yieldtotals.

It is emphasized that the model simulates shallowlandslides and unconfined debris flows that develop onlyon hillslopes outside the channel network. Confineddebris flows along the channel network, including relatedchannel scour, are not simulated.

Within the main SHETRAN model, the spatial distri-bution of catchment properties, rainfall input and hydro-logical response is achieved in the horizontal directionthrough the representation of the catchment and its chan-nel system by an orthogonal grid network and in the verti-cal direction by a column of horizontal layers at each gridsquare. Grid resolution is typically large, however, (asmuch as 1 or 2 km) compared with the length dimensionsof shallow landslides (typically around 10–100 m). Thecentral feature of the landslide model, therefore, is the useof derived relationships (based on a topographic index)which link the larger SHETRAN grid resolution at whichthe basin hydrology and sediment yield are modelled, to asub-grid resolution at which landslide occurrence and ero-sion is modelled. That is, using the topographic index, theSHETRAN grid saturated zone thickness is distributedspatially at the sub-grid resolution. If the factor-of-safetyanalysis indicates slope failure at a sub-grid element, thatelement counts as one landslide; also the element can failonly once during the simulation, i.e. only one landslidecan be registered at the element. Through this dual reso-lution design, the model is able to represent landslidingat a physically realistic scale while remaining applica-ble at catchment scales (up to 500 km2) likely to beof interest, for example feeding a reservoir. The sub-grid discretization, landslide susceptibility and potentiallandslide impact (e.g. sediment delivered to the streamsystem) are determined in advance using a Geograph-ical Information System and this information is storedin a ‘look-up’ table. During the time-varying simula-tion, SHETRAN provides information on the temporalvariation in soil moisture content as input to the land-slide model. As landslides occur, their pre-determinedsediment impacts are passed to the SHETRAN sedimenttransport component from the look-up table and the sed-iment delivered to channels is routed along the channelsystem as conventional sediment load to the basin outlet.

Applications of the landslide model are describedby Bathurst et al. (2005, 2006, 2007). Some recentexamples of applications of the SHETRAN hydrologicaland sediment transport model are presented by Lukeyet al. (2000), Bathurst et al. (2002, 2004) and Adamset al. (2005).

FOCUS CATCHMENTS

The focus sites are the 180 km2 Valsassina-Esino catch-ment in the Italian Southern Alps and the 45 km2 Ijuezcatchment in the central Spanish Pyrenees (Figure 1).Both sites were originally selected for SHETRAN appli-cations in the DAMOCLES project (Bathurst et al.,2003). The Valsassina-Esino catchment was also selectedfor analysis by Frattini et al. (2009). The reader shouldnote that the SHETRAN models used here were origi-nally created, calibrated and applied in the DAMOCLESproject (Bathurst et al., 2005 and 2007) and that the workreported here builds upon those previous models andresults. As full details of the sites, the data collection



Figure 1. SHETRAN grid network, channel system (thick lines) and elevation distribution for the Valsassina (a) and Ijuez (b) catchments. The gridsquares have dimensions 500 m ð 500 m

to support the applications and the model parameters aregiven by Bathurst et al. (2005, 2007) respectively, theyare only summarized here.

The Valsassina catchment

Valsassina is a wide glaciated valley with a U-shapedprofile and hanging valleys. The main river (the Pioverna)discharges into Lake Como (also known as Lake Lario)near Bellano, where the catchment area is 160 km2.The total area modelled with SHETRAN was actually180 km2, incorporating the neighbouring 20 km2 Esinocatchment which also discharges directly into LakeComo. Elevation ranges from 197 m at Lake Comoto 2554 m. The valley corresponds to a fault line thatseparates two geological systems which are of a variednature but with notable occurrences of Permian andTriassic sedimentary rocks. There are four main landcovers: meadows and grass in the valley bottom; forest

on the valley sides up to around 1000 m; grass andmeadows at elevations up to about 1500 m; and barerock at higher elevations. From a field survey, three mainsoil textures (sandy, silt loam; sandy loam; and silt clay)were identified. Mean annual rainfall is around 1240 mmat Bellano and around 1540 mm at Barzio, towards thehead of Valsassina.

The original model parameterization and calibrationare described by Bathurst et al. (2005). Using a 20-m res-olution digital elevation model (DEM), the SHETRANgrid was discretized with a 500 m resolution and thelandslide-model sub-grid resolution was set at 20 m. Spa-tial variability was modelled in overland flow resistance,evapotranspiration and root cohesion as a function ofvegetation (three types) and in soil hydraulic and geotech-nical properties as a function of soil texture (three tex-tures). Soil depth varied according to soil texture andgeology (1Ð5–3 m). A nominal uniform soil depth of

2 10 50 100 T255

0

20

40

60

80

100

120

140

160

180

-2 -1 0 1 2 3 4 5 6

Standardised Gumbel Variate

Rai

nfal

l (m

m)

Bellagio (44 years of data)

GEV distribution

Return period (T years)

2 10 505 25 T100

0

20

40

60

80

100

120

140

160

180

-2 -1 0 1 2 3 4 5 6

Standardised Gumbel Variate

Bescos (23 years of data)

GEV distribution

Return period (T years)

IjuezValsassina(a) (b)

Figure 2. Gumbel plots for annual maximum rainfall of 1-day duration for the Valsassina catchment and 4-day duration for the Ijuez catchment



0Ð2 m was used to allow for hydrological response inlocal occurrences of soil, regolith and coarse debris inareas classified as bare rock. However, shallow landslideswere not allowed to occur in these areas. For a simula-tion period of 6 years and using data from six rain gaugesto represent spatial variability in input, the hydrologicalcomponent was calibrated against regionally derived dis-charge data (including normalized flow duration curves).In calibrating the hydrology model, adjustments weremade to several of the parameters to which the resultsare most sensitive: the overland flow resistance coeffi-cient, the ratio of actual to potential evapotranspirationat soil field capacity, the soil moisture content/tensionproperty curve and the soil saturated zone hydraulic con-ductivity (see Bathurst et al. (2005) for details). The land-slide component was tested against an inventory map oflandslide occurrence in Valsassina (compiled for a 50-year period from the 1950s to the present day), showinggood spatial representation of the observed pattern. Thesediment transport and yield component was calibratedagainst regional data.

The Ijuez catchment

The Ijuez is a tributary of the Aragon river, 10 kmfrom the city of Jaca. Elevations in the catchment rangefrom 838 to 2173 m, the main lithology is calcareousflysch and the natural vegetation is mainly pines, shrubsand, in the highest parts, meadows. Part of the catchmentwas reforested in 1955–1956. From a field survey, twomain soil textures (silty clay and silty clay loam) wereidentified. Mean annual rainfall at Jaca is 874 mm. Aparticular reason for selecting the catchment was therelatively frequent occurrence of debris flows: 146 in theperiod 1956–2001 (Lorente et al., 2003; Beguerıa, 2006).

The original model parameterization and calibrationare described by Bathurst et al. (2007). Using a 10-m res-olution DEM, the SHETRAN grid was discretized witha 500-m resolution and the landslide-model sub-grid res-olution was set at 20 m. Spatial variability was modelledin overland flow resistance, evapotranspiration and rootcohesion as a function of vegetation (three types) and insoil hydraulic and geotechnical properties as a functionof soil texture (two textures). Soil depth was uniform at1Ð5 m, and parameters were adjusted during the calibra-tion process as in the Valsassina application. For a 4-yearsimulation period, using data from rain gauges at Bescosin the catchment and at Jaca, the hydrological componentwas calibrated against regionally derived discharge data(including normalized flow duration curves). The land-slide component was tested against an inventory mapof landslide occurrence in the catchment (compiled for1956–2001), showing an ability to represent the observedspatial pattern. The sediment transport and yield compo-nent were again calibrated against regional data.

Analysis of debris flow characteristics in the flyschsector of the Spanish Pyrenees quantified the meanvalue of the critical hillslope below which debris flowdeposition starts to occur as 18° and the run-out distance

as 60% of the difference in elevation between thelandslide location and the critical slope (Lorente et al.,2003). These values therefore replaced the SHETRANdefault values of 10° and 40% (Burton and Bathurst,1998) for the Ijuez application.

In both applications, the landslide-model sub-gridresolution of 20 m is potentially larger than typicalshallow landslide dimensions but is constrained by theavailable DEM resolution. In the area of the Ijuezcatchment, for example, landslide widths have beenmeasured in the range 7Ð4–30 m (mean about 15 m)(Lorente et al., 2003). It is acknowledged that the modelmay therefore not entirely represent local topographiccontrols on shallow landsliding. This, and other, scaleissues are a source of uncertainty in the simulations,discussed in some detail by Bathurst et al. (2006). Themeans of allowing for this uncertainty are explained inthe section on Uncertainty below.

METHODOLOGY

The following methodology was developed to relatethe magnitude of a landsliding event (quantified as thenumber of shallow landslides occurring) to the frequencyof occurrence represented by the rainfall-event returnperiod and to establish the magnitude of the impact interms of sediment yield at the catchment outlet:

1. Create SHETRAN models of each focus catchment, forhydrology, landslide occurrence and sediment yield.In this case the models were already created andcalibrated in the original applications to the Valsassina-Esino and Ijuez catchments (Bathurst et al., 2005,2007).

2. Generate rainfall events of different magnitude (i.e.intensities of different return period) for a range ofdurations (1-day to 5-day) for each focus area

3. Apply these events to the SHETRAN model to givenumbers of shallow landslides triggered and the result-ing sediment yield

4. Analyse the results graphically for relationshipsbetween rainfall intensity, rainfall duration and land-slide numbers and sediment yield.

Generation of rainfall events for different return periods

Using existing records, rainfall events were generatedfor 1-, 2-, 3-, 4- and 5-day durations, each for a rangeof return periods of 2 years and greater. This providedthe basis for exploring the relationship between landslidemagnitude and rainfall intensity and duration. The threemain steps in the procedure were the production of rain-fall frequency curves based on daily data, disaggregationof the daily rainfall into the hourly values required asinput to SHETRAN and representation of the appropriatespatial distribution in each catchment.

Daily rainfall data were available for five sites withinthe Valsassina catchment, for periods of 21, 29, 32, 34 and44 years respectively. Within the Ijuez catchment, daily



rainfall data were available at only one site (Bescos), fora total of 23 years. Additional data were available at twoneighbouring sites within 10 km of the catchment (forperiods of 20 and 31 years).

For the 1-day duration event, the annual maximum1-day rainfalls were extracted from each data set, thenranked and a generalized extreme value (GEV) distribu-tion was fitted using L-moments. The resulting frequencycurve gives the amount of rainfall expected in 1 dayat the gauge location as a function of return period.The procedure was repeated for the 2-, 3-, 4- and 5-day duration events and Figure 2 presents Gumbel plotswith examples of the goodness of fit achieved. Rain-fall events were generated for return periods of 2, 5, 10,25 and (for Valsassina only) 50 years. Given the maxi-mum lengths of the rainfall records, the frequency curvesfor return periods greater than about 20–25 years (Val-sassina) and 10–15 years (Ijuez) are likely to be moreuncertain because of the lack of data constraining thefit. The difficulties of defining return periods for highmagnitude rainfalls in mountain areas are highlighted byGarcıa-Ruiz et al. (2000). They include not only inad-equate record lengths but inadequate spatial density ofsampling, lack of sub-daily rainfall records, only partialdependency of rainfall on relief and large spatial variabil-ity in return periods of given rainfall.

SHETRAN requires precipitation input at the hourlytime scale, so the daily (or multiple day) rainfall totalswere disaggregated into hourly intervals. However, thetemporal distribution of rainfall within a day at the focussites is variable and cannot be characterized by a singlepattern. Crosta and Frattini (2001) identified two differ-ent rainfall patterns for northern Italy, each leading tosignificant landslide events: single burst events character-ized by short duration, high-intensity rainfall and multipleburst events of longer duration but lower intensity. If thestudy of the impacts of rainfall on shallow landslidingis to be representative, at least some of this variabilityshould be taken into account. Four different hourly rain-fall distribution patterns were therefore generated, havingdifferent hourly intensities but the same total precipita-tion in the same period (Tables I and II). Figure 3 showsan example of the patterns for the 1-day event for theValsassina catchment. The ‘central-peak’ hourly rainfalldistribution is a symmetrical variation rising from zeroat the start of the period to a maximum in the middle ofthe period and falling to zero at the end of the period.The ‘constant’ distribution is a steady low-intensity rain-fall throughout the period. The ‘early peak’ distributionhas its highest rainfall intensity at the start of the period,followed by a linear decrease in rainfall throughout therest of the period, whereas the ‘late peak’ distribution hasthe opposite pattern, with its highest rainfall intensity atthe end of the period. A Newcastle University rainfalldisaggregation code, Raindist (Kilsby, personal commu-nication), was modified and used to generate the chosendistributions. The distributions represent a compromisebetween simulating a wide range of single-peak rainfalldistributions and minimizing the number of simulations.

They contrast high-intensity rainfall of short duration andlow-intensity rainfall of long duration and they maximizethe differences due to timings of the peak rainfall (andthereby allow antecedent rainfall effects to be explored).The different rainfall patterns also enable the temporaloccurrence of landslides to be explored, an aspect whichhas received little attention in previous modelling studies.

For the Valsassina catchment, the preceding procedurewas followed for each of the five raingauges in the catch-ment and the spatial distribution of rainfall was calculatedusing Thiessen polygons. (An altitude dependency wasnot evident from the available data and was therefore notmodelled.) For the Ijuez catchment, only one raingaugelies within the catchment but spatial variation was rep-resented by three altitudinal bands, on the basis of analtitude dependency in annual rainfall determined fromlocal regional data (Bathurst et al., 2007).

Model runs

Each generated rainfall event was applied in turn tothe relevant catchment. A total run time of 3 monthswas simulated in each case, consisting of a ‘settlingdown’ period of 1 month before the actual event anda 2-month ‘follow-up’ period for simulating the impactof the event. No rain was applied during the settlingdown and follow-up periods. Both catchments were sim-ulated with minimum levels of evapotranspiration, set toaverage levels for January–March. The initial phreaticsurface level was set at a depth of 1 m but then allowedto adjust (improving consistency between grid squares)during the settling down period. The resulting river flowswere relatively high for the Valsassina catchment (cor-responding to discharges typical of autumn/winter) butrather lower for the Ijuez catchment (corresponding toconditions typical of a dry summer). These settings effec-tively defined the antecedent soil moisture conditions forthe event: the impact of different antecedent conditionson the simulation results was not investigated (exceptthrough the application of different rainfall events) but isrecognized as an important topic for any follow-up study,as highlighted by Frattini et al. (2009). Simulations (withthe hydrology, erosion and sediment yield components)were run both with and without the landslide component,in order to determine the sediment yield attributable tolandslides.

Simulation output for each event consisted of the num-ber of shallow landslides triggered (equal to the numberof model sub-grid elements in which a landslide is simu-lated), the time of occurrence and the spatial location ofeach landslide, identification of which landslides evolvedinto debris flows and the overall catchment-scale sedi-ment yield. The latter was determined for a period of1 month from the start of the rainfall, a duration whichwas chosen arbitrarily but which was considered longenough to account for the full event response.

Uncertainty

It is generally acknowledged that the parameterizationof physically based, spatially distributed models involves



Tabl

eI.

Eve

ntra

infa

ll(m

m)

for

the

Val

sass

ina

catc

hmen

t(r

ainf

all

for

Bel

lano

)

Cen

tral

-pea

kra

infa

llev

ent

Con

stan

tra

infa

llE

arly

/lat

epe

ak

Ret

urn

peri

od(y

ears

)R

etur

npe

riod

(yea

rs)

Ret

urn

peri

od(y

ears

)

25

1025

502

510

2550

25

1025

50

Tota

l(m

m)

1-da

yev

ent

77Ð5

108Ð9

130Ð9

160Ð1

182Ð9

77Ð5

108Ð9

130Ð9

160Ð1

182Ð9

77Ð5

108Ð9

130Ð9

160Ð1

182Ð9

2-da

yev

ent

109Ð1

143Ð3

163Ð0

185Ð1

199Ð6

109Ð1

143Ð3

163Ð0

185Ð1

199Ð6

109Ð1

143Ð3

163Ð0

185Ð1

199Ð6

3-da

yev

ent

123Ð9

158Ð9

179Ð2

201Ð9

217Ð0

123Ð9

158Ð9

179Ð2

201Ð9

217Ð0

123Ð9

158Ð9

179Ð2

201Ð9

217Ð0

4-da

yev

ent

135Ð3

171Ð9

192Ð9

216Ð3

231Ð7

135Ð3

171Ð9

192Ð9

216Ð3

231Ð7

135Ð3

171Ð9

192Ð9

216Ð3

231Ð7

5-da

yev

ent

141Ð4

177Ð3

198Ð5

222Ð8

239Ð1

141Ð4

177Ð3

198Ð5

222Ð8

239Ð1

141Ð4

177Ð3

198Ð5

222Ð8

239Ð1

Max

(mm

/h)

1-da

yev

ent

14Ð8

20Ð7

24Ð9

30Ð5

34Ð8

3Ð24Ð5

5Ð56Ð7

7Ð65Ð9

8Ð410

Ð012

Ð314

Ð02-

day

even

t10

Ð513

Ð815

Ð717

Ð824

Ð52Ð3

3Ð03Ð4

3Ð94Ð2

4Ð45Ð7

6Ð57Ð4

8Ð03-

day

even

t8Ð0

10Ð2

11Ð5

13Ð0

13Ð9

1Ð72Ð2

2Ð52Ð8

3Ð03Ð3

4Ð34Ð8

5Ð55Ð9

4-da

yev

ent

6Ð58Ð3

9Ð310

Ð411

Ð21Ð4

1Ð82Ð0

2Ð32Ð4

2Ð83Ð5

3Ð94Ð4

4Ð75-

day

even

t5Ð5

6Ð97Ð7

8Ð69Ð2

1Ð21Ð5

1Ð71Ð9

2Ð02Ð3

2Ð93Ð3

3Ð73Ð9

Mea

n(m

m/h

)1-

day

even

t3Ð2

4Ð55Ð5

6Ð77Ð6

3Ð24Ð5

5Ð56Ð7

7Ð63Ð2

4Ð55Ð5

6Ð77Ð6

2-da

yev

ent

2Ð33Ð0

3Ð43Ð9

4Ð22Ð3

3Ð03Ð4

3Ð94Ð2

2Ð33Ð0

3Ð43Ð9

4Ð23-

day

even

t1Ð7

2Ð22Ð5

2Ð83Ð0

1Ð72Ð2

2Ð52Ð8

3Ð01Ð7

2Ð22Ð5

2Ð83Ð0

4-da

yev

ent

1Ð41Ð8

2Ð02Ð3

2Ð41Ð4

1Ð82Ð0

2Ð32Ð4

1Ð41Ð8

2Ð02Ð3

2Ð45-

day

even

t1Ð2

1Ð51Ð7

1Ð92Ð0

1Ð21Ð5

1Ð71Ð9

2Ð01Ð2

1Ð51Ð7

1Ð92Ð0

Mea

n(m

m/d

ay)

1-da

yev

ent

77Ð5

108Ð9

130Ð9

160Ð1

182Ð9

77Ð5

108Ð9

130Ð9

160Ð1

182Ð9

77Ð5

108Ð9

130Ð9

160Ð1

182Ð9

2-da

yev

ent

54Ð6

71Ð6

81Ð5

92Ð5

99Ð8

54Ð6

71Ð6

81Ð5

92Ð5

99Ð8

54Ð6

71Ð6

81Ð5

92Ð5

99Ð8

3-da

yev

ent

41Ð3

53Ð0

59Ð7

67Ð3

72Ð3

41Ð3

53Ð0

59Ð7

67Ð3

72Ð3

41Ð3

53Ð0

59Ð7

67Ð3

72Ð3

4-da

yev

ent

33Ð8

43Ð0

48Ð2

54Ð1

57Ð9

33Ð8

43Ð0

48Ð2

54Ð1

57Ð9

33Ð8

43Ð0

48Ð2

54Ð1

57Ð9

5-da

yev

ent

28Ð3

35Ð5

39Ð7

44Ð6

47Ð8

28Ð3

35Ð5

39Ð7

44Ð6

47Ð8

28Ð3

35Ð5

39Ð7

44Ð6

47Ð8



Tabl

eII

.E

vent

rain

fall

(mm

)fo

rth

eIj

uez

catc

hmen

t(r

ainf

all

for

the

800

–12

00m

alti

tude

band

)

Cen

tral

-pea

kra

infa

llev

ent

Con

stan

tra

infa

llE

arly

/lat

epe

ak

Ret

urn

peri

od(y

ears

)R

etur

npe

riod

(yea

rs)

Ret

urn

peri

od(y

ears

)

25

1025

25

1025

25

1025

Tota

l(m

m)

1-da

yev

ent

57Ð2

69Ð7

76Ð7

84Ð3

57Ð2

69Ð7

76Ð7

84Ð3

57Ð2

69Ð7

76Ð7

84Ð3

2-da

yev

ent

69Ð6

86Ð4

98Ð2

113Ð9

69Ð6

86Ð4

98Ð2

113Ð9

69Ð6

86Ð4

98Ð2

113Ð9

3-da

yev

ent

84Ð1

105Ð2

118Ð3

133Ð9

84Ð1

105Ð2

118Ð3

133Ð9

84Ð1

105Ð2

118Ð3

133Ð9

4-da

yev

ent

91Ð0

114Ð3

129Ð7

148Ð9

91Ð0

114Ð3

129Ð7

148Ð9

91Ð0

114Ð3

129Ð7

148Ð9

5-da

yev

ent

99Ð1

122Ð9

136Ð7

152Ð1

99Ð1

122Ð9

136Ð7

152Ð1

99Ð1

122Ð9

136Ð7

152Ð1

Max

(mm

/h)

1-da

yev

ent

12Ð0

14Ð6

16Ð1

17Ð6

2Ð42Ð9

3Ð23Ð5

4Ð85Ð8

6Ð57Ð2

2-da

yev

ent

7Ð49Ð1

10Ð3

12Ð0

1Ð51Ð8

2Ð02Ð4

3Ð13Ð9

4Ð35Ð1

3-da

yev

ent

5Ð97Ð5

8Ð49Ð5

1Ð21Ð5

1Ð61Ð9

2Ð53Ð1

3Ð54Ð0

4-da

yev

ent

4Ð86Ð1

6Ð97Ð9

0Ð91Ð2

1Ð41Ð6

2Ð12Ð5

2Ð93Ð3

5-da

yev

ent

4Ð25Ð2

5Ð86Ð5

0Ð81Ð0

1Ð11Ð3

1Ð82Ð2

2Ð42Ð8

Mea

n(m

m/h

)1-

day

even

t2Ð4

2Ð93Ð2

3Ð52Ð4

2Ð93Ð2

3Ð52Ð4

2Ð93Ð2

3Ð52-

day

even

t1Ð5

1Ð82Ð0

2Ð41Ð5

1Ð82Ð0

2Ð41Ð5

1Ð82Ð0

2Ð43-

day

even

t1Ð2

1Ð51Ð6

1Ð91Ð2

1Ð51Ð6

1Ð91Ð2

1Ð51Ð6

1Ð94-

day

even

t0Ð9

1Ð21Ð4

1Ð60Ð9

1Ð21Ð4

1Ð60Ð9

1Ð21Ð4

1Ð65-

day

even

t0Ð8

1Ð01Ð1

1Ð30Ð8

1Ð01Ð1

1Ð30Ð8

1Ð01Ð1

1Ð3M

ean

(mm

/day

)1-

day

even

t57

Ð269

Ð776

Ð784

Ð357

Ð269

Ð776

Ð784

Ð357

Ð269

Ð776

Ð784

Ð32-

day

even

t34

Ð843

Ð249

Ð156

Ð934

Ð843

Ð249

Ð156

Ð934

Ð843

Ð249

Ð156

Ð93-

day

even

t28

Ð035

Ð139

Ð444

Ð628

Ð035

Ð139

Ð444

Ð628

Ð035

Ð139

Ð444

Ð64-

day

even

t22

Ð828

Ð632

Ð437

Ð222

Ð828

Ð632

Ð437

Ð222

Ð828

Ð632

Ð437

Ð25-

day

even

t19

Ð824

Ð627

Ð330

Ð419

Ð824

Ð627

Ð330

Ð419

Ð824

Ð627

Ð330

Ð4



0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14 16 18 20 22 24

Hours

2-year return period5-year return period10-year return period25-year return period50-year return period

"Early Peak"Rainfall

"Late Peak"Rainfall

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14 16 18 20 22 24

Hours

Pre

cipi

tatio

n (m

m)

"Central Peak"Rainfall

"Constant"Rainfall

Figure 3. Example of the simulated 1-day rainfall patterns for different return periods for the Bellano gauge, Valsassina catchment

uncertainty (e.g. Beven and Binley, 1992; Beven, 2001,19–23; Guimaraes et al., 2003), one potentially impor-tant source being inconsistencies between the model gridscale, the scale at which property measurements are madeand the scale relevant to each particular hydrologicalprocess (e.g. saturated conductivity is measured at thescale of an auger hole but the model grid scale maybe tens to hundreds of metres). This uncertainty createsthe potential for multiple parameterizations with possiblyquite different but apparently equally acceptable combi-nations of parameter values. It is therefore also acceptedthat the uncertainty and its implications for model outputshould be explicitly recognized in the modelling proce-dure (e.g. Beven and Binley, 1992; Ewen and Parkin,1996). Typically this is achieved by quantifying someform of uncertainty envelope. The original simulationstherefore established upper and lower uncertainty boundson the output as a function of uncertainty in key modelparameters. For example, bounds on landslide occurrencewere determined as a function of vegetation root cohe-sion. For the research reported here, though, (simplydeveloping and testing a hazard prediction method) itwas sufficient to use a single parameter set to charac-terize each catchment. The selected sets are those usedto produce the lower bounds for landslide occurrence inthe original simulations, which approximate the measuredannual rates of landsliding. The corresponding root cohe-sions were: for the Valsassina catchment, 7500 Pa forforest cover and 3500 Pa for pasture; and for the Ijuezcatchment, 1500 Pa for natural pine forest and 800 Pa forpine plantation, shrubs and meadows. These values arebased on such literature sources as Preston and Crozier(1999), Sidle et al. (1985, p62) and Sidle and Ochiai(2006, 103–104).

Because of the impracticality of measuring the requiredlandslide-model parameters (for the factor-of-safetyequation) at every model sub-grid square across the entire

catchment, there is a reliance on estimated values. A cer-tain proportion of squares is then characterized with unre-alistic combinations of parameter values and is simulatedto be unconditionally unstable, even in dry conditions.Eliminating these and taking into account also those land-slide squares which were determined to be stable for allconditions, the maximum numbers of squares at whichthe model could simulate landslides were 285 and 94 forthe Valsassina and Ijuez catchments respectively.

ANALYSIS AND DISCUSSION OF RESULTS

Comparison of observed and generated rainfall returnperiods for landsliding events

As noted earlier, the generated rainfall events have thesame total precipitation but different hourly intensitiesin the same period, depending on the sub-daily rain-fall distribution (Tables I and II). A distinction shouldtherefore be made between return periods based on dailyevents (as defined here) and the return period of hourlyevents which, in this study, are variable. The distinction isimportant since shallow landslides are typically triggeredby short intense bursts of rainfall of even less than hourlyduration within longer periods of rainfall (e.g. Dhakal andSidle, 2004; Sidle and Ochiai, 2006, p69). Therefore, itneeds to be shown that the generated daily (or longerperiod) rainfalls and their sub-daily distributions producelandsliding events in a manner comparable with observa-tion and that the return periods of the generated rainfallssimilarly match the observed return periods. The limitedavailability of data permits only one such comparison,for the 26 to 27 June 1997 storm event in the Esino-Valsassina area recorded by Frattini et al. (2009). In lessthan 2 h almost 100 mm of rain (i.e. an intensity of nearly50 mm h�1) triggered 147 shallow landslides within anarea of 40 km2 (i.e. 3Ð7 landslides per square kilometre).The associated 1-day rainfall was 168 mm. The return



period for the 2-h rainfall is 75 years, while the returnperiod for the daily rainfall, according to Figure 2, ismore than 50 years. (The uncertainty is too great in thisportion of the curve to determine an accurate value.) Forcomparison, Tables I and III present the necessary dataon the generated rainfall events and the numbers of land-slides for the central-peak rainfall distribution as a func-tion of rainfall return period and rainfall event duration.The 1-day rainfall for a 50-year return period is 183 mm,with a peak intensity of 35 mm h�1; this triggers 207landslides over the 180-km2 simulation area event (i.e.1 landslide per square kilometre). These figures showexcellent order of magnitude agreement with the obser-vations and suggest that it is possible to define rainfallreturn periods at the daily scale that, with the central-peakdistribution, can adequately represent the storm eventsthat generate landslides in the Valsassina region.

Nevertheless, the simulation data also show that a 1-day event with a 10-year return period is sufficient totrigger most of the above landslides, i.e. a 1-day rainfallof 131 mm with a peak intensity of 25 mm h�1 stillgenerates 196 landslides. Similarly, a 5-day event witha 10-year return period providing 199 mm of rainfall(i.e. a mean daily rainfall of 40 mm) with a peakintensity of 7Ð7 mm h�1 generates 226 landslides. Lackof observations means that it is not possible to confirm ifshorter return period events can, in reality, trigger suchsubstantial levels of landsliding. However, some supportis provided by Luino’s (2005) observation for the samearea that slope instabilities begin once the cumulativeevent rainfall exceeds approximately 10% of the localmean annual rainfall. On the basis of the Bellano annualtotal of 1240 mm noted earlier, an event total of 120 mmor more would therefore be expected to cause landslides.

Table III. Number of landslides simulated for the central-peakrainfall pattern for the Valsassina and Ijuez catchments

Valsassina

Number of landslidesfor events of duration (day)

Return period (year) 1 2 3 4 5

2 109 159 167 169 1755 147 204 208 210 21410 196 210 224 225 22625 207 218 231 237 23750 207 233 237 237 237

Ijuez

Number of landslidesfor events of duration (day)

Return period (year) 1 2 3 4 5

2 87 90 94 94 945 94 94 94 94 9410 94 94 94 94 9425 94 94 94 94 94

0

50

100

150

200

250

0 10 20 30 40 50

Rainfall Return Period (Years)

Num

ber

of L

ands

lides

1 day events2 day events3 day events4 day events5 day eventsValsassina

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25


Num

ber

of L

ands

lides

1 day events2 day events3 day events4 day events5 day eventsIjuez

Figure 4. Relationship between the number of landslides and rainfallreturn period for different event durations, for the central-peak rainfall

distribution, for the Valsassina and Ijuez catchments

Comparison of this threshold with the data in Table Isuggests, then, that 3-, 4- and 5-day events with a 2-yearreturn period and 1- and 2-day events with return periodsof less than 10 years should produce landslides. That is,it would seem that rainfalls with short return period canbe associated with landslides.

Relationship between central-peak daily rainfall returnperiod and landsliding magnitude

Figure 4 complements Table III in showing numbersof landslides for the central-peak rainfall distribution asa function of rainfall return period and rainfall eventduration. A striking feature, for a given event duration,is the insensitivity of simulated landslide magnitudeto return period for return periods greater than about10 years for the Valsassina catchment and 5 years forthe Ijuez catchment. In the latter case the number oflandslides quickly reaches 94, the maximum possible,while in the Valsassina catchment the number asymptotesto 237, which is less than the maximum possible (285).Similarly, for an event of given return period, landslidemagnitude becomes less sensitive to event duration asduration increases. The results may be interpreted interms of the model design as follows.

For the Valsassina catchment a similar pattern has beenobtained by Frattini et al. (2009) using a different but



still physically based model. Those authors suggest anexplanation whereby, as rainfall intensity increases, land-sliding in effect becomes limited by the rate at which raincan infiltrate into the soil. For the SHETRAN simula-tions, though, apart from a few cases, rainfall intensitiesare generally less than the soil saturated conductivity.A more likely explanation for the simulated pattern inthis case, is that, for each rainfall duration, the soil inthe critical areas is already simulated to be saturatedby the events with approximately 10-year return peri-ods, thus producing the maximum number of landslidesfrom those areas. Within the model, the additional rain-fall from larger events generates surface runoff and doesnot affect the porewater pressures responsible for land-sliding. It may be queried, though, why the maximumnumber of simulated landslides asymptotes to a value(237) which is less than the maximum possible num-ber (285), i.e. Why does the additional rainfall of thehigher return period events not cause any of the remain-ing squares to fail? The answer appears to be that thenon-failing landslide squares are concentrated in just sixSHETRAN grid squares (with the majority in only threesquares). These squares are all on the edge of the sim-ulation area or at a catchment watershed (or divide)with no uphill contributing area. It is likely, therefore,that, within the simulations, these few squares have justthe necessary characteristics to allow rapid drainage ofthe soil column for the applied rainfalls, thus prevent-ing the occurrence of the necessary porewater condi-tions to trigger slope failure, i.e. it is the result ofthe way in which the catchment is represented in themodel.

For the Ijuez catchment, rainfalls with relatively lowrecurrence intervals are sufficient, in the simulation, totrigger the maximum possible number of landslides;larger rainfalls can then have no additional effect. Thispattern is consistent with the observation of Lorente et al.(2003) that the triggering of shallow landslides and thesubsequent formation of debris flows in the Ijuez catch-ment is related to relatively frequent intense rainfallswith recurrence intervals of no more than 2–5 years.However, it may be queried if the maximum number oflandslides possible (94) is realistic. Within the model,this maximum is a function of the selected root cohesionvalues and the number of unconditionally unstable sub-grid elements (which are eliminated from consideration).Root cohesion varies spatially with vegetation type but,within the model, is constant for each individual type,thereby reducing the scope for representing local varia-tion in landslide susceptibility. Likewise, limited abilityto represent local variations in soil depth, elevation andother characteristics may result in too many sub-gridelements being designated as unconditionally unstable.Further research into sensitivity to parameter evaluationand into model refinement is necessary to address thispoint.

It is likely that the pattern of landslide numbersshowing progressive insensitivity as the rainfall eventincreases to extreme levels has been exaggerated in

the simulations as a result of the model characteristics.Nevertheless, such behaviour is not physically unrealistic,although not necessarily typical of all catchments. Theonly example found in the literature is from NorthIsland, New Zealand, which is admittedly a differentphysical context from the mountain chains of the Alpsand Pyrenees: Reid and Page (2002), in their Figure 6,present data-based convex-upwards curves relating areallandslide frequency (i.e. number of slides per squarekilometre per year) to storm recurrence interval forthe Waipaoa catchment. Their observation that 50% oflandslides occur in storms with return periods of less than8 years, while raising the occurrence to 75% requiresstorms with return periods of up to 27 years, fits thepattern of decreasing sensitivity.

Effect of temporal distribution of rainfall

The simulation results for the four within-event rain-fall distributions are compared in Figures 5–7. Figure 5repeats Figure 4 but shows the effects of the differentdistributions. For reasons of clarity, results are shown foronly the 1-day duration events but the general patternis the same for all the durations. For a given event, therainfall total is the same but the temporal distributionvaries as shown in Figure 3. Figure 6 provides hydro-logical context by comparing the catchment outlet dis-charges associated with the different patterns for a 1-dayrainfall event with a 2-year return period. For the sameevent, Figure 7 shows the numbers of landslides occur-ring as a function of time through the event and relativeto the outlet discharge hydrograph. For both catchments,the ‘central-peak’ and ‘constant’ rainfall patterns producealmost the same numbers of landslides and thus similarcurves in Figure 5. However, the hydrological responseand the incidence of landsliding differ between the pat-terns and between the catchments. For the Valsassinacatchment, the central-peak rainfall pattern produces aflashy, high peak discharge response, while the constantrainfall pattern produces a more moderate, lower dis-charge response (Figure 6). More landslides tend to occurearlier with the central-peak rainfall and later with theconstant rainfall (following a build-up of critical condi-tions) (Figure 7). For the Ijuez catchment, the constantrainfall pattern produces a higher peak discharge thanthe central-peak rainfall pattern but with a greater delay(Figure 6). In both cases, the occurrence of landslides isdelayed relative to the timings for the Valsassina catch-ment (Figure 7). The differences between the catchmentsmay be explained by the drier soil conditions in the Ijuezcatchment absorbing more of the rainfall and delayingboth landslide occurrence and stormflow response.

The ‘early peak’ and ‘late peak’ rainfall patterns pro-duce somewhat similar curves in Figure 5 but dissim-ilar responses in Figures 6 and 7. Both produce lowernumbers of landslides than the central-peak and constantpatterns. It is perhaps not surprising that the central-peakpattern produces more landslides as its peak rainfall inten-sity is significantly higher than those of the other two.



0

50

100

150

200

250

0 10 20 30 40 50


Num

ber

of L

ands

lides

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25


IjuezValsassina

Figure 5. Relationship between the number of landslides and rainfall return period for the 1-day duration events, for the four rainfall patterns (showndiagrammatically), for the Valsassina and Ijuez catchments

That the constant pattern should also produce more land-slides, though, suggests that the effects of the higher peakintensities of the early and late peak patterns are morethan compensated for by the constant rainfall intensityexceeding the other two intensities for half the period(Figure 3). In the case of the early peak, much of the ini-tial higher rainfall is likely to have been absorbed in therelatively dry soil. Landslides are triggered in some quan-tity after the rainfall peak and continue at a lesser rateas rainfall (and soil moisture) declines. In the case of theIjuez, the peak discharge is not generated until after thepeak discharge for the central-peak case, again indicatingvariations in the interaction between time-varying rainfallintensity and soil moisture conditions. In the case of thelate peak pattern, the steady build-up of rainfall start-ing from zero allows the early moisture to drain without

causing significant landsliding, thus blunting the impactof later increases in soil moisture. However, landslidingbegins before the peak rainfall occurs and continues forsome time later. In the Ijuez, these variations are againdelayed because of the drier soil conditions and are moremuted since, once the maximum number of landslideshas occurred, there can be no further time variation oflandslide numbers.

Past studies refer to landslides occurring during a rain-fall event but the simulations show also a significantnumber of landslides occurring after the rain has stopped(Figure 7). These are considered to be the result, withinthe model, of subsurface downslope transfers of watercreating the critical saturation (or porewater pressure)conditions in the soil column. Field data on the temporaloccurrence of landslides through an event are rare and at

0

10

20

30

40

50

60

70

80

90

100

110

120

740 750 760 770 780 790 800

Time (hours)

Dis

char

ge (

m3 s

-1)

0

1

2

3

4

5

6

740 750 760 770 780 790 800

Time (hours)

Central Peak RainfallConstant RainfallLate Peak RainfallEarly Peak Rainfall

IjuezValsassina

Figure 6. Comparison of discharges simulated at the outlets of the Valsassina and Ijuez catchments for the four rainfall patterns. The examples arefor a 1-day rainfall event with a 2-year return period



0

20

40

60

80

100

120

740

750

760

770

780

790

800

810

820

830

840

Time (hours)

Dis

char

ge (

m3

s-1)

Num

ber

of L

ands

lides

02468101214161820

0

20

40

60

80

100

120

740

750

760

770

780

790

800

810

820

830

840Time (hours)

Dis

char

ge (

m3 s

-1)

Num

ber

of L

ands

lides

02468101214161820

0

20

40

60

80

100

120

740

750

760

770

780

790

800

810

820

830

840

Time (hours)

02468101214161820

Pre

cipi

tatio

n (m

m)

0

20

40

60

80

100

120

740

750

760

770

780

790

800

810

820

830

840

Time (hours)

02468101214161820

Pre

cipi

tatio

n (m

m)

Discharge for Pioverna outlet

Number of landslides

Precipitation-Bellano

(a)

0

5

10

15

20

25

740

750

760

770

780

790

800

810

820

830

840

Time (hours)

02468101214161820

Pre

cipi

tatio

n (m

m)

Discharge for Ijuez outlet

Number of landslides

Precipitation-Bescos

0

5

10

15

20

25

740

750

760

770

780

790

800

810

820

830

840

Time (hours)

Dis

char

ge (

m3 s

-1)

Num

ber

of L

ands

lides

/ 10

02468101214161820

0

5

10

15

20

25

740

750

760

770

780

790

800

810

820

830

840

Time (hours)

Dis

char

ge (

m3 s

-1)

Num

ber

of L

ands

lides

/ 10

02468101214161820

0

5

10

15

20

25

740

750

760

770

780

790

800

810

820

830

840

Time (hours)

02468101214161820

Pre

cipi

tatio

n (m

m)

(b)

Figure 7. Outlet discharge hydrographs and time variation of landslide occurrence for the four rainfall patterns. Results are shown for the Valsassina(a) and Ijuez (b) catchments for a 1-day event with a 2-year return period. Each cross indicates the number of landslides occurring at a specific

simulation time

present it is not clear whether such post-rain failures arelikely to occur in practice or whether the model has high-lighted an interesting but not very typical phenomenon.However, Chen et al. (2005) report the temporal occur-rence of 39 debris flows caused by typhoons and othermajor rainfall events hitting Taiwan. In 16 cases, debrisflows occurred prior to the peak hourly rainfall; 10 casesoccurred at the time of peak hourly rainfall and 13 casesoccurred after the peak rainfall.

The simulation results described above show that thetemporal distribution of rainfall in an event can have

a significant effect on the potential number of land-slides. For an event of given duration and return period,high-intensity central-peak rainfalls and constant low-intensity rainfalls seem to cause the maximum numberof landslides, despite variations in catchment hydrologi-cal response and in the timing of landslide occurrence.

Cumulative and antecedent precipitation has a largeinfluence on soil moisture conditions and affects thetype and timing of landslide occurrence. Although theValsassina and Ijuez hydrological responses to the variousrainfall events differ (Figure 6) and their initial soil



moisture conditions also differ (dry summer conditionsfor Ijuez and autumn conditions for Valsassina), thesimulations show that, for events of a given return period,the majority of landslides occur at timings related more tothe rainfall distribution pattern than to other factors suchas catchment characteristics. A similar time distributionof landslides occurs in both catchments as a function ofthe rainfall distribution pattern.

Volume of sediment reaching the river network

The volume of landslide material delivered to the chan-nel network depends on the number of landslides whichevolve into hillslope debris flows, the number of thosedebris flows which connect directly with the channelsystem and the amount of material which is either lostfrom the debris flow through deposition in the run-outzone before the debris flow reaches the river or addedthrough scour along the debris flow path. (The modelallows for a part of the deposited material to be sub-sequently washed into the channel by overland flow. Asnoted earlier, though, the option to allow additional scourwas not exercised at the focus sites.) Its contribution tothe sediment yield at the catchment outlet then dependson the routing of the material along the channel network(as a conventional sediment load) as a function of timingof the sediment injection and the discharge hydrograph.Total sediment yield also depends on material from othersources, limited in the model to soil eroded by raindropimpact and overland flow and to sediment already inthe channel bed. For the Valsassina catchment only onedebris flow from the 285 maximum possible landslidescould potentially reach the channel network. This meansthat 0Ð35% of landslides have the potential for some partof their material to be deposited into the channel network.For a 5-day, 50-year return period event, the simulatedevent sediment yield without any landslide contribution(i.e. from erosion by raindrop impact and overland flowplus transport of sediment already in the channel bed)is 31 960 t, while the total event sediment yield includ-ing the landslide contribution is 32 202 t. The landslidesediment yield at the catchment outlet is therefore 242 tor 0Ð75% of the total event sediment yield. A possibleexplanation for this seemingly rather low figure is thatthe channel network is represented with too coarse a res-olution to include the low-order streams which, in reality,may be adjacent to landslide sites and thus allow moredebris flows to reach the channel network. It should beremembered also that the debris flows referred to hereare hillslope flows; the model does not represent debrisflows which develop within the channels.

Similarly, for the Ijuez catchment, 13 debris flows fromthe 94 maximum possible landslides could potentiallyreach the channel network, meaning that 13Ð8% oflandslides have the potential for some part of theirmaterial to be deposited into the channel. For a 5-day,25-year return period event, the simulated event sedimentyield without any landslide contribution is 3520 t, whilethe total event sediment yield including the landslide

contribution is 5050 t. The landslide sediment yield at thecatchment outlet is therefore 1530 t or 30% of the totalevent sediment yield. The greater contribution in the Ijuezcatchment relative to the Valsassina catchment is likely tobe the result of a greater presence of steep slopes near thechannel network and thus a greater potential for debrisflows to reach the network. That is, the Ijuez is more of aheadwater catchment with greater landslide connectivity.

The few available field surveys show similarly that thecapacity of hillslope debris flows to deliver material tothe channel network varies widely. Reid and Page (2002)found that, for debris flows generated during a majorcyclone in an unspecified sub-catchment of the Waipaoacatchment in New Zealand, 35% of debris flows did notreach the channel network, 40% of debris flows travelleddown a hillslope before depositing some sediment ina channel and 25% of landslides abutted a channeland delivered all their sediment. The overall sedimentdelivery ratio from shallow landslides was estimated tobe 45%. Page et al. (2004) similarly calculated that thelong-term (114 years) delivery ratio for landslide-derivedsediment in the Tutira catchment was 43%. Imaizumiand Sidle (2007), for the Miyagawa Dam catchment inJapan, found that the percentages of landslides deliveringsome part of their material to channels varied from 56 to75% in a 35-year period and that they were correlatedwith maximum hourly rainfall. They suggest that debrisflow mobility varies as a function of water content inboth initially failed material and transported sediment.At a smaller scale of landslide, Johnson et al. (2000) ina survey in southeastern Alaska found many examples oflandslides or debris flows contributing sediment directlyto channels (especially first and second-order streams),including one that deposited over 100 m3 of sedimentand woody debris.

Figure 8 shows the total event sediment yield simu-lated at both catchment outlets as a function of rain-fall event, event duration and event return period forthe central-peak rainfall distribution. For comparison, theyield simulated without landslides is also shown (labelled‘no landslides’ in the figure). For the Valsassina catch-ment, only one debris flow can reach the channel andlandslides add little to the overall sediment yield; the twosets of curves therefore more or less coincide. For theIjuez catchment, the landslides increase sediment yieldby 0–71%.

There are few data in the literature with which thesimulated sediment yield data and the relationships ofFigure 8 can be compared. It is evident, though, that thecontribution of landslides to total sediment yield can varywidely even in the same catchment. From two studiesin New Zealand, Hicks et al. (2000) found that shallowlandslides generated most of the sediment supply to thestream network in the 83 km2 Te Arai catchment (lowertributary to the Waipaoa), while Reid and Page (2002)calculated that shallow landslides contribute about 15%of the annual suspended sediment yield exported by theupper Waipaoa river catchment (1580 km2). A diagram inthe field notes for the 6th Gravel-bed Rivers Conference



Figure 8. Relationship between total event sediment yield (with and without the landslide contribution) and rainfall event intensity for different eventdurations and return periods, for the central-peak rainfall pattern, for the Valsassina and Ijuez catchments

in 2005 (Dieter Rickenmann, personal communication)shows debris flow volume varying as a function of rainfallintensity for the 2Ð6-km2 Wartschenbach catchment inEastern Tyrol with a convex-upwards relationship. (Inthis case, the source of the sediment is not limited toshallow failures.) An event with a rainfall intensity ofabout 55 mm h�1 lasting approximately 30 min producedabout 45 000 m3 of debris flow material whilst an eventof 6 mm h�1 lasting 6Ð5 h produced about 10 000 m3 ofmaterial. Similarly, Figure 5 of Mao et al. (2006) showsevent sediment yield as a function of return period fortwo mountain streams subject to debris flows and largebed load movements. In their published form, plotted onlogarithmic axes, the relationships of Mao et al. have aconvex-upwards nature but on linear axes they rather

more resemble those curves of Figure 8 which have alinear form.

Landslide magnitude relationships

Figure 9 shows the number of landslides simulated asa function of rainfall event duration and intensity for thecentral-peak rainfall distribution for the Valsassina andIjuez catchments. Log scales are used in conformancewith practice in the literature but the results are alsoshown with linear scales as the wider spread of the datapoints allows easier visual interpretation. On this basis,it is possible to plot rainfall intensity–duration curves(grey lines in the diagram) which define different levels oflandslide magnitude as quantified by the number of land-slides. Also shown are the global threshold relationships



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Figure 9. Relationship between the number of landslides and rainfall event intensity and duration for the central-peak rainfall pattern, in comparisonwith published threshold curves. Lines of equal numbers of landslides are fitted by eye. Results are shown for the Valsassina and Ijuez catchments,

with linear and logarithmic scales

of Caine (1980) (Equation (1)), Innes (1983) and Crostaand Frattini (2001) (Equation (2)) and (on the Valsassinaplots) the local threshold for the Southern Italian Alpsof Crosta and Frattini (2001) (Equation (2)) (black linesin the diagram). Since, in this study, all the simulationrainfall events generated landslides, it was not possi-ble to define a simulation threshold curve for landslideoccurrence which could be compared directly with the lit-erature curves. However, the landslide magnitude curves(grey lines) have the same general form as the literaturecurves, i.e. the intensity required to generate a given mag-nitude declines as duration increases. It should also beexpected that the simulation points at least lie above theliterature curves. This is the case for the global thresholdcurves of Innes (1983) and Crosta and Frattini (2001),and the Valsassina data are similarly in good correspon-dence with Crosta and Frattini’s (2001) local thresholdfor the Southern Italian Alps. The Caine threshold onthe other hand exceeds most of the simulation data butthis is in agreement with Rossi et al. (2006) and Guzzettiet al. (2008) who also found the Caine threshold to bean overestimate. The reasons may lie in the data usedby Caine, which were from a range of environments andantecedent moisture conditions, with precipitation fromhourly, daily and monthly records. Intensities were cal-culated from averaging the durations and rainfall recordedfor the events.

A feature of the logarithmic plots in Figure 9 is thatthe simulation data curves are steeper than the literaturethreshold curves. Thus, for long duration, low-intensityrainfall events, landslides could potentially be simulated

at conditions below the literature threshold curves. Thismay be an artefact of the SHETRAN model as thetrend is evident for both the Valsassina and the Ijuezcatchments. However, Rossi et al. (2006) also found that,on a log–log intensity–duration plot, local thresholdswere steeper than regional and global thresholds, a patternwhich they attributed to differences in rainfall samplingresolution. In general, incompleteness of rainfall data(lack of short or long duration values) will cause thethreshold curves to rotate preferentially in a clockwiseor anticlockwise direction (Crosta and Frattini, 2001).Further, Rossi et al. (2006) found that, except for Caine’s(1980) threshold, global thresholds were generally thelowest thresholds in the literature. Regional thresholdswere higher than global thresholds and local thresholdswere in turn higher than regional thresholds. The relativeposition of the curves can also be affected by theway in which rainfall intensity is calculated (Crostaand Frattini, 2001). Thus, downward shifting of thethreshold curves can result from using total rainfall eventintensity (the total event rainfall divided by the eventduration, as in Figure 9), rather than maximum eventintensity (determined for a limited time interval usually,but not necessarily, close to the time when landslidesoccurred) (Crosta and Frattini, 2001). Thresholds basedon maximum intensity take no account of total eventduration, antecedent rainfall or rainfall pattern and tendto underestimate the amount of rainfall needed to triggerlandslides. Total event intensity, on the other hand,does not take short duration–high-intensity storms intoaccount and thresholds based on total event intensity



therefore tend to underestimate the rainfall intensityrequired to trigger landslides. It is important, therefore,when developing or applying threshold or magnituderelationships, to define their applicability (global, regionalor local), the rainfall intensity (maximum or total eventintensity) and the rainfall sampling resolution.

The landslide magnitude curves in Figure 9 advanceour predictive capability beyond the existing thresholdcurves (which indicate only whether or not landslidesshould occur) and show how model simulations can beused to relate landslide magnitude to rainfall frequency.Not only numbers of landslides but location within acatchment, proportion of the catchment affected, likelytiming of occurrence and impact in terms of sedimentyield can be determined for given rainfall conditions.This type of information could be a helpful contributionto the wider process of landslide hazard assessment andforecasting.

CONCLUSIONS

Determining the extent of shallow landslide occurrence asa function of rainfall return period improves our abilityto assess landslide hazard for specified conditions andraises the possibility of issuing warnings of landslidemagnitude on the basis of weather forecasts. This studyhas investigated the use of a shallow landslide sedimentyield model to quantify the magnitude of landslide eventsand their sediment yield as a function of rainfall returnperiod, for rainfalls of different combinations of intensityand duration. The model transfers landslide material tothe channel system via hillslope or unconfined debrisflows but does not account for debris flows whichmay develop within the channel system. The principalconclusions are:

1. For a given event duration, simulated landslide mag-nitude becomes progressively less sensitive to returnperiod as return period increases. Similarly, for anevent of given return period, landslide magnitudebecomes less sensitive to event duration as durationincreases. These are not unrealistic patterns, althoughthey may not be typical of all catchments. Neverthe-less, it is likely that the patterns have been exaggeratedby the model limitations and parameter evaluation.

2. As modelled, the temporal distribution of rainfallwithin an event (central peak, constant, early peak, latepeak) has a significant effect on the simulated numberof landslides and on the timing of their occurrence.Although the precise effects remain to be confirmedby field study, the result suggests that it is importantto base the overall method on the characteristic rainfallpattern of events likely to trigger landslides in a region.

3. The contribution of shallow landsliding to catchmentsediment yield can be quantified as a function of therainfall characteristics. Downstream impacts of land-slides can thus be determined for specified conditionsas part of hazard assessment. For the two test sites,

the contribution is likely to be small for the Valsassinacatchment and moderate for the Ijuez catchment.

4. Rainfall intensity–duration curves can be determinedwhich define different levels of landslide magnitude: aswith threshold curves, the intensity required to generatea given magnitude declines as duration increases. Thedata are generally consistent with published thresholdcurves but it is important to define applicability (global,regional or local), rainfall intensity and rainfall sam-pling resolution.

The study has established and demonstrated a method-ology by which a physically based, spatially distributedmodel can be used to relate landslide magnitude torainfall frequency, thereby advancing our predictivecapability beyond the threshold curves and providinginformation for use in landslide hazard assessment andforecasting. However, there remain a number of uncer-tainties in the procedure. These include uncertainty inquantifying rainfall of given return periods (especiallylarge-return periods) from limited data records, uncer-tainty in generating the landslide response (as a functionof model and parameter uncertainty) and uncertainty aris-ing from processes and conditions not fully consideredhere, such as antecedent soil moisture content. Furtherapplications and developments to reduce this uncertaintyare needed to refine the approach. Given the significantcontrol on landslide occurrence exercised by antecedentsoil moisture content, a particularly useful developmentwould be a set of simulations relating landslide magni-tude to, for example, the duration of the rain-free periodpreceding a rainfall event. Similarly, considerably morefield data on landslide occurrence and its relationship torainfall return period are required so that simulations suchas those reported here can be checked and calibrated.

ACKNOWLEDGEMENTS

The authors thank Professor Giovanni Crosta and DrPaolo Frattini (University of Milan-Bicocca) for theiradvice and interest in the simulation results. The LESS-LOSS (Risk Mitigation for Earthquakes and Landslides)project was funded by the Framework Programme 6 The-matic Sub-priority “Global Change and Ecosystems” ofthe European Commission Research Directorate Gen-eral, under Contract Number GOCE-CT-2003-505448,and this support is gratefully acknowledged. ProfessorRoy Sidle and an anonymous referee are thanked fortheir comments, which have greatly helped to improvethe paper.

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