Open Access Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 Natural Hazards www.nat-hazards-earth-syst-sci.net/13/3169/2013/ doi:10.5194/nhess-13-3169-2013 and Earth System © Author(s) 2013. CC Attribution 3.0 License. Sciences

Shallow landslide’s stochastic risk modelling based on the precipitation event of August 2005 in Switzerland: results and implications

P. Nicolet1, L. Foresti1,2, O. Caspar1, and M. Jaboyedoff1 1Center of Research on Terrestrial Environment, University of Lausanne, Lausanne, Switzerland 2Royal Meteorological Institute of Belgium, Brussels, Belgium

Correspondence to: P. Nicolet ([email protected])

Received: 28 February 2013 – Published in Nat. Hazards Earth Syst. Sci. Discuss.: 28 March 2013 Revised: 29 August 2013 – Accepted: 29 October 2013 – Published: 9 December 2013

Abstract. Due to their relatively unpredictable characteris- 1 Introduction tics, shallow landslides represent a risk for human infras- tructures. Multiple shallow landslides can be triggered by Shallow landslides often represent a risk for housing, peo- widespread intense precipitation events. The event of Au- ple and infrastructures. Compared with deep-seated land- gust 2005 in Switzerland is used in order to propose a risk slides, shallow landslides usually trigger spontaneously, flow model to predict the expected number of landslides based at higher speed and are not likely to affect repeatedly the on the precipitation amounts and lithological units. The spa- same location due to the changes in soil stability conditions tial distribution of rainfall is characterized by merging data (e.g. van Westen et al., 2006; Corominas and Moya, 2008). coming from operational weather radars and a dense network Consequently, most research efforts focus on the prediction of rain gauges with an artificial neural network. Lithologies of their exact location and, less frequently, their timing. Sev- are grouped into four main units, with similar characteris- eral methods for the mapping of landslide susceptibility ex- tics. Then, from a landslide inventory containing more than ist and are based on physical models (e.g. Pack et al., 1998; 5000 landslides, a probabilistic relation linking the precipita- Montgomery and Dietrich, 1994; Godt et al., 2008) or sta- tion amount and the lithology to the number of landslides in tistical approaches (e.g. Carrara et al., 1991). Since rainfall a 1 km2 cell, is derived. In a next step, this relation is used has been recognized as being a frequent triggering mecha- to randomly redistribute the landslides using Monte Carlo nism (e.g. Wieczorek, 1996), many authors, following Camp- simulations. The probability for a landslide to reach a build- bell (1975) and Caine (1980), proposed early-warning sys- ing is assessed using stochastic geometry and the damage tems based upon criteria of precipitation intensity and du- cost is assessed from the estimated mean damage cost us- ration (e.g. Guzzetti et al., 2008). Other studies also use ing an exponential distribution to account for the variabil- the antecedent precipitation as a proxy for considering the ity. Although the model reproduces well the number of land- groundwater level preceding the precipitation event (Crozier, slides, the number of affected buildings is underestimated. 1999; Glade et al., 2000). More direct approaches are based This seems to result from the human influence on landslide upon the real-time monitoring of soil moisture (Matsushi and occurrence. Such a model might be useful to characterize the Matsukura, 2007; Baum and Godt, 2010) or the use of trans- risk resulting from shallow landslides and its variability. fer functions to estimate the soil water content from precipi- tation measurements (Cascini and Versace, 1988; Capparelli and Versace, 2011; Greco et al., 2013). Many rainfall-induced large landslide events have been recognized worldwide, for example in Italy (Crosta, 1998; Crosta and Frattini, 2003; Crosta and Dal Negro, 2003; Cardinali et al., 2006; Gullà et al.,

Published by Copernicus Publications on behalf of the European Geosciences Union. 3170 P. Nicolet et al.: Shallow landslide’s stochastic risk modelling

2008), Spain (Corominas and Moya, 1999), the USA 2 The rainfall event of August 2005 in Switzerland (Campbell, 1975; Whittaker and McShane, 2012), New Zealand (Crozier et al., 1980; Glade, 1998; Crozier, 2005), 2.1 Study area Taiwan (Yu et al., 2006), the Portuguese island of Madeira (Nguyen et al., 2013) and in Switzerland (Bollinger et al., The study area covers the entire Swiss territory (around 2 2000). 42 000 km ), which extends from the Jura Mountains in the Despite the numerous contributions to the physical un- northwest, to the Alps, in the southeast, through the Molassic derstanding of the phenomenon itself (for a broad reference Plateau, where most of the population is concentrated. Spe- list, although not up to date, see De Vita et al., 1998), stud- cial attention is given to the location where most of the land- ies on the assessment of landslide risk are less commonly slides occurred, which is the central part of Switzerland, be- found in the literature. Examples of quantitative risk analy- tween the cities of Bern and Lucerne (Fig. 1). Landslides oc- sis (QRA) at regional scale can be found in Cardinali et al. curred in the tectonic units described below (Trümpy, 1980; (2002), Remondo et al. (2005) and Catani et al. (2005). How- University of Bern and FOWG, 2005a, b), which are listed ever, these studies provide a mean annual risk with no infor- along a northwest–southeast direction (perpendicularly to the mation on the expected distribution of annual costs. More geological structures). recently, applications of regional-scale QRA providing ex- ceedance probabilities were presented in Jaiswal et al. (2011) – Upper freshwater molasse from middle and early up- and Ghosh et al. (2012). Although most of the QRA method- per Miocene (consisting of floodplain sediments in- ologies are developed for local or regional scales, some of cluding puddings, sandstones and silty shales). them, for example Catani et al. (2005), might be generalized – Other types of molasse (narrower areas of upper ma- to a larger area. rine molasse, lower freshwater molasse and lower ma- Switzerland was affected in August 2005 by a rain- rine molasse, the lower part of this series being in sub- fall event with measured precipitation reaching 324 mm in Alpine position). 6 days. Although floods were the main cause of damage, more than 5000 landslides were reported (Raetzo and Rickli, – Sub-Alpine flysch. 2007). Landslide-induced damage has been estimated by Hilker et al. (2007) at CHF 92 million (USD 99 million; – Upper Penninic flysch (Schlieren flysch). debris-flows not included) and represents 4.5 % of the total damage cost. – Ultrahelvetic and Helvetic nappes (including Tertiary As already mentioned by Jaboyedoff and Bonnard (2007) shallow marine formations and Cretaceous limestones and by Rickli et al. (2008), landslide density was highly cor- from the Wildhorn nappe and Jurassic limestones from related with the total precipitation amount. Following their the Axen nappe). ideas, this article proposes a risk model for shallow land- slides based on the event of August 2005. The input pa- The bedrock is mostly covered by soil (regolith) and loose rameters of the model include a rainfall and a lithological materials. Most of these shallow and superficial formations map. The map of 6 day rainfall accumulations is constructed have not been mapped, except for the cases where the forma- by interpolating a high resolution rain gauge network using tion reaches a sufficient extension or thickness to be consid- weather radar data as external drift. A geotechnical map is ered relevant at the map scale. This is for example the case interpreted in order to group different units into 4 main litho- of morainic material deposited by the glaciations during the logical settings. The expected number of landslides is pre- Quaternary, which is visible at several places, especially on dicted as a function of rainfall level conditional to the litho- the plateau (Trümpy, 1980). The properties (e.g. mechanical, logical type. A geometrical probability concept is then em- hydrological) of the local soils strongly depend on the under- ployed to predict the potential number of landslides affecting lying bedrock. buildings and the corresponding damage cost. The paper is structured as follows. Section 2 details the 2.2 Description of the precipitation event rainfall event of August 2005 in Switzerland both from a meteorological and lithological viewpoint. Section 3 explains The rainfall event of August 2005 in central and eastern the methodology to assess the landslide probability as a func- Switzerland resulted in severe damage due to flooding and tion of rainfall accumulation and lithological context. Sec- induced slope instabilities (Rotach et al., 2006). The presence tion 4 presents the risk analysis results in terms of expected of the Alps played a key role in controlling the spatial number of landslides, number of affected buildings and asso- distribution of rainfall due to orographic precipitation en- ciated cost. Finally, Sects. 5 and 6 discuss and conclude the hancement processes. Persistent precipitation patterns were paper. mostly found on the exposed upwind slopes under northerly and northeasterly flow conditions as studied by Foresti and Pozdnoukhov (2012) and Foresti et al. (2012). In particular,

Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 www.nat-hazards-earth-syst-sci.net/13/3169/2013/ 2 P. NicoletP.P. Nicolet Nicolet et al.: et et al.: Shallow al.: Shallow Shallow landslides landslide’s landslides stochastic stochastic stochastic risk risk modelling modelling 3171 3 the assessment of landslide risk are less commonly found in 2.2 Description of the precipitation event 26 0.4 1 the literature. Examples of quantitative risk analysis (QRA) Basel 21 Entlebuch 16 at regional scale can be found in Cardinali et al. (2002), Re- The rainfall event of August 2005 in central and eastern 0.8 Zurich 11 0.3 y c y n mondo et al. (2005) or Catani et al. (2005). However, these Switzerland resulted in severe damage due to flooding and c 6 e n u Berner Oberland e q Lucerne 1 u 0.6 studies provide a mean annual risk with no information on induced slope instabilities (Rotach et al., 2006). The presence e q r f e

r f

Bern e the expected distribution of annual costs. More recently, ap- of the Alps played a key role in controlling the spatial 0.2 v e i t v i a t distribution of rainfall due to orographic precipitation en- 0.4 l plications of regional scale QRA providing exceedance prob- a u l e m u abilities were presented in Jaiswal et al. (2011) and Ghosh hancement processes. Persistent precipitation patterns were R Lausanne 0.1 C et al. (2012). Although most of the QRA methodologies are mostly found on the exposed upwind slopes under northerly 0.2 developed for local or regional scales, some of them, for ex- and north-easterly flow conditions as studied by Foresti and ample Catani et al. (2005), might be generalized to a larger Pozdnoukhov (2012a) and Foresti et al. (2012b). In partic- 0 0 Geneva 0 200 400 600 area. ular, the stratiform precipitation was locally enhanced by Distance [m] Switzerland was affected in August 2005 by a rain- smaller scale orographic features leading to persistent initia- 0 25 50 100 Fig. 2. Relative and cumulative frequency of the distance travelled fall event with measured precipitation reaching 324 mm tion and enhancementKilome ofters the embedded convection. Fig. 2. Relative and cumulative frequency of the distance travelled by 148 landslides (Raetzo and Rickli, 2007). in 6 days. Although floods were the main damage cause, The most intense period of the event was observed be- by 148 landslides (Raetzo and Rickli, 2007). Fig. 1. Number of landslides in 1 km2 cells2 (after Raetzo and Rickli, more than 5000 landslides were reported (Raetzo and Rickli, Fig.tween 1. Number 21 and of 22 landslides August. inDriven 1 km bycells cyclonic (after Raetzo conditions and 2007).Rickliduring, White2007 the). circles first White day, represents circles the moist represent the Berner air thefrom Oberland Berner the Mediterranean Oberlandand Entlebuch and 2007). Landslide-induced damage has been estimated by been analyzed for 148 cases and ranges from a few meters regionsEntlebuchsea circumvented (hillshade: regions (hillshade: © Swisstopo).the Austrian© Swisstopo). Alps and started approaching Hilker et al. (2007) at 92 million Swiss francs (USD 99 mil- up to 500 m (Raetzo and Rickli, 2007). Around 75 % of the slightly crosswise the northern slopes of the Swiss Alps from FOEN, but contains less landslides than the one built by lion; debris-flows not included) and represents 4.5 % of the landslides traveled less than 100 m and 90 % less than 200 m the east. The mesoscale flows gradually turned from east- Raetzo and Rickli (2007), since some of the cantons report total damage cost. (Fig. 2). landslideserly to northerly occurred, conditions which is the during central the partsecond of Switzerland, day. The re- every landslide, whereas others only report one point for each As already mentioned by Jaboyedoff and Bonnard (2007) the stratiform precipitation was locally enhanced by smaller- betweenduced supply the cities of air of moisture Bern and was Lucerne compensated (Fig. 1). by Landslides a stronger set of close landslides. The uncertainty about the location of and by Rickli et al. (2008), landslide density was highly cor- scale orographic features leading to persistent initiation and 2.4 Damage occurredupslope in rainfall the tectonic enhancement units which described extended below the (Tr durationumpy,¨ landslides complicates the analysis of their geological con- related with the total precipitation amount. Following their enhancement of the embedded convection. 1980;of precipitation. University of The Bern return and period FOWG, for 48 2005a,b),h rainfall which accumu- are text. ideas, this article proposes a risk model for shallow land- The most intense period of the event was observed be- According to the Swiss Federal Institute for Forest, Snow and listedlations along largely a northwest-southeast exceeded 100 yr at direction several (perpendicularly weather stations LandscapeStatistics Research on the landslides WSL, the 2005can be event found has inbeenRaetzo the most and slides based on the event of August 2005. The input pa- tween 21 and 22 August. Driven by cyclonic conditions tomostly the geological located in structures): the Berner Oberland (Rotach et al., 2006). Ricklicostly( since2007) the and beginning in Rickli of et the al. collection(2008) and of investigations damage data rameters of the model include a rainfall and a lithological during the first day, the moist air from the Mediterranean It is worth mentioning that the uncertainty of this estimation onin specific1972, with sites ain totalMueller damage and cost Loew estimated(2009) andat 1.83von billion Ruette map. The map of 6 day rainfall accumulations is constructed Sea circumvented the Austrian Alps and started approaching is– quiteUpper important Freshwater as an Molasse event of from such intensity Middle and was early never Up- ob- etSwiss al. (2011 francs). (around The travel USD distance 2 billion). of shallow On the other landslides hand, has in by interpolating a high resolution rain gauge network using slightly crosswise the northern slopes of the Swiss Alps from servedper in Miocene the past (consisting at the considered of floodplains weather stations. sediments in- beenspite analysedof being the for most 148 important cases and event ranges recorded, from a other few metres years weather radar data as external drift. A geotechnical map is the east. The atmospheric flow gradually turned from east- erly tocluding northerly puddings, conditions sandstones during and the silty second shales). day. The re- uphave to been 500 m equally (Raetzo or moreand Rickli damaging, 2007 regarding). Around landslides 75 % of the in interpreted in order to group different units into 4 main litho- duced2.3 supply Landslide of air inventory moisture was compensated by a stronger landslidesthe past 40 travelledyr (Hilker less et than al., 2009; 100 m WSL, and 90 2012). % less than 200 m logical settings. The expected number of landslides is pre- upslope– Other rainfall types enhancement of Molasse (narrower which extended areas of the Upper duration Ma- (Fig.Hilker2). et al. (2009) divided the damage values into three dicted as a function of rainfall level conditional to the litho- ofAs precipitation.rine a consequence Molasse, The Lowerof return this extreme Freshwater period for rainfall 48 Molasse h event, rainfall and many accumu- Lower shal- categories according to the cause, namely floods, debris logical type. A geometrical probability concept is then em- low landslides were triggered, mainly in the Entlebuch part lationsMarine largely Molasse, exceeded the 100 lower yr at part several of this weather series being stations in 2.4flows Damage and landslides (including mud-flows). Landslides rep- ployed to predict the potential number of landslides affecting of Lucerne canton and in the Bern canton. Some deep-seated mostlySubalpine located inposition). the Berner Oberland (Rotach et al., 2006). resent around 4.5 % of the total cost and affected private buildings and the corresponding damage cost. landslides were observed as well and are mainly located far- It is worth mentioning that the uncertainty of this estimation Accordingproperties to(22 the%, Swiss CHF Federal 16.3 million) Institute and for public Forest, infrastruc- Snow and The paper is structured as follows. Section 2 details the ther south-east. A landslide inventory has been collected by is quite important as an event of such intensity was never ob- Landscapetures (88 % Research, CHF 75.6 WSL, million) the 2005 (Hilker event et al., has 2007). been the Private most rainfall event of August 2005 in Switzerland both from a me- Raetzo– Subalpine and Rickli Flysch. (2007) from cantonal authorities informa- served in the past at the considered weather stations. costlydamage since includes the beginning damage to of buildings the collection as well of as damage furnitures, data teorological and lithological viewpoint. Section 3 explains tion and contains 5756 landslides. Although some additional invehicles, 1972, with other a property total damage damage cost and estimated loss of profits. at CHF Compar- 1.83 bil- the methodology to assess the landslide probability as a func- attributes– Upper suchPenninic as the Flysch exact (Schlieren timing have Flysch). been registered for 2.3 Landslide inventory lionatively, (around public USD damage 2 billion). includes On damage the other to waterways, hand, in spite roads of tion of rainfall accumulation and lithological context. Sec- some of the landslides, we only dispose of the version pro- being(except the small most ones), important railways, event farming recorded, andother forests. years In addi- have vided in the above publication and, as a result, we only know tion 4 presents the risk analysis results in terms of expected As– aUltrahelvetic consequence of and this Helvetic extreme Nappes rainfall (including event, many tertiary shal- beention to equally economic or more consequences, damaging six regarding casualties landslides are to be in de- the number of landslides, number of affected buildings and asso- theshallow approximate marine location. formations However, and theCretaceous Federal Office Limestones of the plored. lowEnvironment landslides (FOEN)were triggered, also provides mainly to in the the cantonal Entlebuch authori- part past 40 yr (Hilker et al., 2009; WSL, 2012). ciated cost. Finally, Sects. 5 and 6 discuss and conclude the of Lucernefrom the canton Wildhorn and in nappe the Bern and canton. Jurassic Some Limestones deep-seated from Hilker et al. (2009) divided the damage values into three paper. tiesthe a tool Axen to register nappe). the events (FOEN, 2012). An extract of landslidesthis database were has observed been provided as well and by the are FOEN, mainly butlocated contains far- categories3 Risk modelling according methodology to the cause, namely floods, debris ther southeast. A landslide inventory has been collected by flows and landslides (including mudflows). Landslides rep- Soilsless(regolith) landslides andthan loosethe one materials built by Raetzo cover andmost Rickli of the (2007), time Raetzosince someand Rickli of the(2007 cantons) from report cantonal every authorities’landslide, whereas infor- resent3.1 Introduction around 4.5 % of the total cost and affected private 2 The rainfall event of August 2005 in Switzerland the bedrock. Most of these shallow and superficial forma- mationothers and only contains report one 5756 point landslides. for each setAlthough of close some landslides. addi- properties (22 %, CHF 16.3 million) and public infrastruc- tions have not been mapped, except for the cases where the Risk is defined by Einstein (1988) as : tionalThe uncertainty attributes such about as the the location exact timing of landslides have beencomplicates regis- tures (88 %, CHF 75.6 million) (Hilker et al., 2007). Private 2.1 Study area formation reaches a sufficient extension or thickness to be teredthe analysis for some of theirof the geological landslides, context. we only dispose of the damage includes damage to buildings as well as furniture, considered relevant at the map scale. This is for example the versionStatistics provided on the in the landslides above publication can be found and, in as Raetzo a result, and vehicles, other property damage and loss of profits. Compar- The study area covers the entire Swiss territory (around case of morainic material deposited by the glaciations during Risk = hazard × potential worth of loss (1) weRickli only (2007) know the and approximate in Rickli et location. al. (2008) However, and investigations the Fed- atively, public damage includes damage to waterways, roads 42 000 km2), which extends from the Jura mountains in the the Quaternary, which is visible at several places, especially eralon specificOffice of sites the in Environment Mueller and Loew (FOEN) (2009) also and provides von Ruette to (exceptWhere small the hazard ones),is railways, the “probability farming that and a forests. particular In dan-addi- North-West, to the Alps, in the South-East, through the Mo- on the Plateau (Trumpy,¨ 1980). The properties (e.g. mechan- theet cantonal al. (2011). authorities The travel a tool distance to register of shallow the events landslides (FOEN has, tionger occurs to economic in a given consequences, period of time” six casualtiesand the potential are toworth be de- lassic Plateau, where most of the population is concentrated. ical,2012 hydrological)). An extract of of this the database local soils has strongly been provided depend by on the the plored. Special attention is given to the location where most of the underlying bedrock.

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3 Risk modelling methodology rain gauge adjustment, the interpolation from polar coordi- nates to a Cartesian grid, and the use of a fixed climatological 3.1 Introduction Z–R relationship (refer to Germann et al., 2006, for more de- tails). A geostatistical method for real-time adjustment with Risk is defined by Einstein (1988) as rain gauges was only recently implemented by Sideris et al. (2013). For long-term evaluation of the radar QPE accuracy Risk = hazard × potential worth of loss, (1) against rain gauges refer to Gabella et al. (2005). The radar × where the hazard is the “probability that a particular dan- QPE product used in this paper is a 1 km 1 km grid of the ger occurs in a given period of time” and the potential worth rainfall accumulation during the period 18–23 August 2005. of loss characterizes the estimated potential loss caused by Despite these corrections, the product still contains resid- an event of given intensity, which depends on the economic ual ground clutter and biases due to the blockage of low level value and vulnerability of the object. We prefer to define haz- radar beams, particularly in the inner Alpine valleys. To par- ard in terms of frequency, rather than in terms of probability tially account for these issues, an artificial neural network since we are dealing with events that can be considered as was applied to blend the radar-based QPE map with the rain repetitive over a large area (van Westen et al., 2006). Indeed, gauge rainfall accumulations. A 3-H-1 multiLayer percep- if the events are repetitive, Kaplan (1997) suggests to use tron (MLP) was trained to predict the rainfall amount ob- the frequency rather than the probability (or the frequency served at the rain gauges as a function of 3 variables: the expressed as a probability distribution), which is also more geographical location represented by the Swiss easting and rigorous since risk is expressed in terms of cost per year. northing coordinates and the radar QPE product which acts The methodology described hereafter is a partial risk cal- as an external drift. The geographical coordinates account culation. Indeed, a single precipitation event is used as an in- for the observed biases between rain gauges and radar-based put, which does not allow accounting for the temporal com- QPE, which show a significant spatial dependence. A con- ponent of the hazard. However, the hazard is considered by jugate gradient algorithm was employed to train the net- = its spatial aspect. In a first phase, the spatial distribution of work. A low number of hidden neurons H 6 was cho- the total rainfall accumulation is estimated using data from a sen to obtain a smooth representation of the spatial rain- dense network of rain gauges and 3 additional operational C- fall biases. The optimal model was selected by minimiz- band weather radars (Sect. 3.2). The second phase studies the ing the leave-one-out cross-validation root-mean-square er- statistical distribution of landslides as a function of precip- ror (RMSE). A randomly sampled test set of 137 stations itation accumulation and lithological type (Sect. 3.3) and is was kept to evaluate the expected prediction RMSE, which is used to estimate the probability of landsliding in 1 km × 1 km of 25.3 mm. No quantitative assessment of the performance cells given the occurrence of the precipitation event. These of the MLP model against geostatistical approaches (e.g. first steps do not however completely consider the spatial as- Sideris et al., 2013) was carried out. Some preliminary com- pects of the hazard. Indeed, the exact location as well as the parisons with kriging with external drift and additional de- propagation probability are virtually assessed using princi- tails on the MLP model are reported in Foresti et al. (2010). ples of stochastic geometry, and represent the probability of The regularized MLP solution is a smooth compromise be- buildings to be affected by circular landslides within a given tween the radar and rain gauge measurements. This allows cell. The potential worth of loss is then assessed by using being robust to local radar overestimations due to ground the estimation of the mean cost of the event and by artifi- clutter and the different sampling volume of radar and rain cially adding a variability accounting for the diversity of the gauge measurements. The Machine Learning Office software element at risk values and vulnerabilities, as well as the land- was used for the computations (Kanevski et al., 2009). slide intensities (see Sect. 3.4). Figure 3 illustrates the spatial analysis of the rainfall ac- cumulation from 18 to 23 August 2005. The highest accu- 3.2 Spatial analysis of rainfall mulations are observed on the northern slope of the Alps, in particular along a line from the Berner Oberland to the MeteoSwiss operates an automatic network of 76 weather mountain range of Saentis. The spatial distribution of land- stations and a dense network of additional 363 rain gauges. slides is strongly correlated to the spatial distribution of rain- The automatic network measures rainfall with a temporal res- fall amounts. The remaining unexplained spatial variability olution of 10 min while the second only reports daily accu- is due especially to the local geological and morphological mulations from 05:40 to 05:40 UTC of the next calendar day. settings, which control the sensitivity of the soil to the input An additional network of 3 C-band radars is used to mea- rainfall. sure precipitation with higher spatial resolution. The opera- tional radar data processing chain for quantitative precipita- 3.3 Landslide distribution tion estimation (QPE) at MeteoSwiss includes the removal of ground clutter, correction for the vertical profile of reflectiv- In order to improve the georeferencing of the landslide local- ity in connection with the bright band effect, climatological ization extracted from Raetzo and Rickli (2007), the StorMe

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Fig. 3. Total rainfall accumulation from 18 to 23 August 2005 [mm] estimated by MLP. Dots represent the stations used for the interpo- lation. The dashed area (Berner Oberland) and the triangle (Saentis) correspond to the end points of a line segment representing the re- gions with the highest rainfall accumulation.

Fig. 4. Probabilistic lithological maps showing the proportion of each lithological unit. Values range from green (lithological group database (FOEN, 2012) has been used as a reference. The slightly present) to blue, whereas white means that the lithologi- points known to correspond to multiple landslide events in cal group is non-existent in the cell; (A) limestone formations (LF); the latter database have been removed. The remaining points (B) crystalline formations (CF), (C) flysch, loose material (except are then supposed to correspond to a subset of the first land- moraine), marls and claystones (FLMC), (D) molasse and moraine slide map. As a result, each point of the StorMe database (MM) and (E) total. In map (E), white tones mark the absence should have its equivalent in the landslide map. The distance of lithological formations (i.e. lakes, glaciers) and other countries, while green tones depict their partial presence within the model cell, from each point of the StorMe database to its nearest neigh- which occurs when the cumulative proportion of the 4 units is be- bour in the landslide inventory has then been reduced by op- low 1. timizing 2 scale and 2 position factors affecting the coordi- nates of the points in the landslide inventory. For the opti- mization, the median distance was preferred to another pa- based on the 6 units used by Rickli et al. (2008) to assess the rameter, such as the RMSE, in order to ignore potentially landslide density distribution of the event: remaining points corresponding to multiple landslides. The – limestone formations (LF), median distance obtained after optimization is 104 m. To be consistent with the precipitation map, the landslide points – crystalline formations (CF), have been transformed into a raster grid with a resolution of 1 km ×1 km, by counting the number of landslides in each – flysch, loose material (except moraine), marls and cell (Fig. 1). claystones (FLMC), To establish a predictive relation linking the precipitation – molasse and moraine (MM). amounts and the lithological type to the landslide probability, a categorical lithological information should be coded into a The vector map is transformed into 4 raster maps display- set of variables describing the presence of a given litholog- ing the proportion covered by the lithological groups in each ical type into a cell. For this purpose, the geotechnical map cell (Fig. 4a–d). These products do not allow to relate di- of Switzerland has been used (SGTK, 2012). This map com- rectly each landslide to only one lithological unit. Therefore, bines the shape of the 1 : 500 000 geological map (Univer- in order to take into account the uncertainty on the lithology sity of Bern and FOWG, 2005b) with the attributes of the involved in each landslide, a stochastic strategy is employed. four 1 : 200 000 geotechnical maps (De Quervain and Frey, A lithology is randomly assigned to each cell according to 1963, 1965, 1967; De Quervain and Hofmänner, 1964). The the initial lithological proportions. This is achieved by sam- purpose of the latter maps is to transmit the geological in- pling a random variable 0 <= u <= 1 and comparing it to formation relevant for non-geologists involved in different the cumulative probability distribution of lithology classes activities dealing with the ground, especially for civil engi- (Fig. 5). This operation is performed several times to average neering. The map has been simplified into 4 units, loosely the results. www.nat-hazards-earth-syst-sci.net/13/3169/2013/ Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 6 P. Nicolet et al.: Shallow landslides stochastic risk modelling

RMSE between the observed and modelled distributions in order to model the number of landslides as a function of pre-

Vector map cipitation amount. The 2 parameter form of the gamma cu- mulative distribution function is given by (Johnson and Kotz, 1970) :

0.1 0 0.3 x 0.6 1 Z t (α−1) − β

Grid mapsGrid F (x) = t e dt (2) βαΓ(α) 0 α β 0.7 1 Where is the shape parameter, is the scale parameter Cumulative 0.1 0.7 and Γ(x) is the generalized form of the factorial function, grid maps such as Γ(x) = (x−1)! if x is a positive integer. The gamma function is defined as: Fig. 5. Schematic transformation of the vector geotechnical map into 4 grids containing the proportion of each lithology individually ∞ and, then, into for grids which give, for each cell, the lithological Z Γ(x) = e−ttx−1dt (3) units cumulative distribution. A lithology is assigned at each model iteration by choosing a random number 0 ≤ u ≤ 1. In this example, 0 if u = 0.5, the second geology would be assigned, since 0.1 < u < Since the gamma distribution is a continuous distribution 3174 P. Nicolet et al.: Shallow landslide’s stochastic risk modelling 6 P. Nicolet0.7. et al.: Shallow landslides stochastic risk modelling whose domain is 0 → ∞, it is not exactly suitable to fit dis- crete data, especially as the most frequent number of land-

RMSE0 between50 the100 observed150 200 and modelled250 300 distributions350 in slide is expected to be x = 0 and as F (x = 0) is null, what- 1 6000 order to model the number of landslides as a function of pre- ever the values of α and β. As a workaround for these issues, cipitation0.9 amount. The 2 parameter form of the gamma cu- the distribution has been virtually modified as follows, to ex- Vector map 5000 mulative0.8 distribution function is given by (Johnson and Kotz, tend the definition domain from −1 → ∞:

1970)0.7 : 4000 x+1 0.6 Z 1 (α−1) − t x F (x) = t e β dt (4) 0.1 0.6 0 0.3 0.5 Z 3000 α 1 (α−1) − t β Γ(α) β 0 Grid mapsGrid F (x) = t e dt (2) 0.4 βαΓ(α) 0 of cells Number This modification is virtual since the distributions fitting is

Cumulative frequency 2000 0.3 1 Where α is the shape parameter, β is the scale parameter made by shifting the x values, i.e. by using the value F (x = 0.7 0.2 0) for x = 1, which is easier than modifying the function. Cumulative 0.7 and Γ(x) is the generalized form of the factorial function,1000 0.1 The consequences of this modification are discussed below. grid maps such0.1 as Γ(x) = (x−1)! if x is a positive integer. The gamma To estimate the models predictive ability, a second part function0 is defined as: 0 0 50 100 150 200 250 300 350 consists in using the distribution of the landslide number ac- Fig. 5. Schematic transformation of the vector geotechnical map Precipitation [mm] Fig. 5. Schematic transformation of the vector geotechnical map cording to the precipitation class and lithology previously into 4 grids containing the proportion of each lithology individually ∞ into 4 grids containing the proportion of each lithology individually Fig. 6. CumulativeZ distribution of the spatial precipitation amounts. assessed to simulate different potential consequences of the and, then, into for grids which give, for each cell, the lithological Fig. 6. Cumulative−t x distribution−1 of the spatial precipitation amounts. and, then, into 4 grids which give, for each cell, the lithological Γ(Dotsx) show = thee limitst ofdt the six classes and are rounded to the upper(3) precipitation event using a Monte-Carlo approach. This step units cumulative distribution. A lithology is assigned at each model Dots show the limits of the 6 classes and are rounded to the upper units’ cumulative distribution. A lithology is assigned at each model value. illustrates the uncertainty of the model on the consequences iteration by choosing a random number 0≤≤ u≤≤ 1. In this example, value. 0 iteration by choosing a random number 0 u 1. In this example, of a given precipitation event. Indeed, since we consider that ifif u =0 .5,5, the second geology geology would would be be assigned, assigned, since since 00.1.1<< u u < < Since the gamma distribution is a continuous distribution the landslides are controlled only by the precipitation and the 0..77.. whose domain is 0 → ∞, it is not exactly suitable to fit dis- map in terms of the number of landslides per km2, since the lithology, this step gives the variability resulting from this crete data, especially as the most frequent number of land- cumulated value of the lithological grids is the surface, in simplification. The workflow of this step is given in Fig. 8. 0 50 100 150 200 250 300 350 slide2 is expectedx to be x = 0 and as F (x = 0) is null, what- 1 6000 km , of land. Z Both the raw distributions and the gamma distributions are Cells that contain water (lakes or glaciers) or that are lo- 1 (α−1) − t Fever (x)The= the precipitation values of αt fieldand eβ has.β Asd beent, a workaround divided into for 6 theseclasses issues,(2) to used. cated0.9 on the Swiss border have a cumulative value below 1, βα0(α) thehave distribution a sufficient has number been virtually of landslides modified in each as follows, class while to ex- Since gamma parameters have been fitted with shifted val- since the lithology polygons only cover a fraction of the5000 sur- 0 0.8 tend the definition domain from −1 → ∞: face (Fig. 4e). As a result, if the random value u is above being enough discriminative in terms of precipitation levels. ues, the unmodified inverse distribution will overestimate the 0.7 whereAs visibleα is the onFig. shape 6, parameter,the histogramβ is is the highly scale skewed parameter and only and number of landslides. However, as the gamma distribution their total cumulated value, they are not taken into account4000 0(x)10 %isof the Switzerland generalizedx+1 exceeds form of 200 themm factorialof rain. function, such as is continuous and as we need to obtain the number of land- in the0.6 iteration. To build the probabilistic relation, the total Z 0(x)Figure= (x− 71 summarizes1)! if x is a positive(α the−1) data− integer.t processing The gamma workflow. function The slides in integers, the results of the inverse function for a number of landslides considered might then be lower than F (x) = t e β dt (4) 0.5 3000 isoutput defined ofβ as theαΓ( modelα) is a cumulative distribution of the ex- given quantile can be rounded down to be consistent with the actual number of landslides. To account for this effect, 0 ® 0.4 pected number∞ of landslide given the geology and the pre- the original data. Matlab was used to iteratively derive the the landslide map is divided by the cumulated value of the of cells Number ThisZ modification is virtual since the distributions fitting is Cumulative frequency 2000 cipitation amount.−t x−1 To allow a generalization of these results, Gamma cumulative distribution as there is not analytical so- lithological0.3 grids. This operation actually expresses the land- 0(x) = e t dt. x F(3)(x = 2 madegamma by distributions shifting the werevalues, fitted to i.e. the by data using by minimizing the value the lution (Johnson and Kotz, 1970). slide0.2 map in terms of the number of landslides per km , since 0 1000 0) for x = 1, which is easier than modifying the function. the cumulated value of the lithological grids is the surface of The consequences of this modification are discussed below. 0.1 2 Since the gamma distribution is a continuous distribution land (in km ). To estimate the models predictive ability, a second part The0 precipitation field has been divided into 6 classes0 to whose domain is 0 → ∞, it is not exactly suitable to fit dis- 0 50 100 150 200 250 300 350 consists in using the distribution of the landslide number ac- have a sufficient numberPrecipitation of landslides [mm] in each class while crete data, especially as the most frequent number of land- cording to the precipitation class and lithology previously being enough discriminative in terms of precipitation levels. slides is expected to be x = 0 and as F (x = 0) is null, what- Fig. 6. Cumulative distribution of the spatial precipitation amounts. assessed to simulate different potential consequences of the As visible in Fig. 6, the histogram is highly skewed and only ever the values of α and β. As a workaround for these issues, Dots show the limits of the six classes and are rounded to the upper precipitation event using a Monte-Carlo approach. This step 10 % of Switzerland exceeds 200 mm of rain. the distribution has been virtually modified to extend the def- value. illustrates the uncertainty of the model on the consequences Figure 7 summarizes the data processing workflow. The inition domain from −1 → ∞ as: of a given precipitation event. Indeed, since we consider that output of the model is a cumulative distribution of the ex- x+1 the landslides areZ controlled only by the precipitation and the pected number of landslide given the geology and the pre- 1 − − t map in terms of the number of landslides per km2, since the Flithology, (x) = this stept gives(α 1)e theβ d variabilityt. resulting from(4) this cipitation amount. To allow a generalization of these results, βα0(α) cumulated value of the lithological grids is the surface, in simplification. The0 workflow of this step is given in Fig. 8. gamma2 distributions were fitted to the data by minimizing the kmRMSE, of between land. the observed and modelled distributions in Both the raw distributions and the gamma distributions are This modification is virtual since the distributions’ fitting orderThe to precipitation model the number field has of landslides been divided as a intofunction 6 classes of pre- to used. is made by shifting the x values, i.e. by using the value havecipitation a sufficient amount. number The 2 parameter of landslides form in of each the gamma class while cu- Since gamma parameters have been fitted with shifted val- F (x = 0) for x = 1, which is easier than modifying the func- beingmulative enough distribution discriminative function in is giventerms by of (precipitationJohnson and Kotzlevels., ues, the unmodified inverse distribution will overestimate the tion. The consequences of this modification are discussed be- As1970 visible) on Fig. 6, the histogram is highly skewed and only number of landslides. However, as the gamma distribution 10 % of Switzerland exceeds 200 mm of rain. low.is continuous and as we need to obtain the number of land- Figure 7 summarizes the data processing workflow. The slidesTo estimate in integers, the predictive the results ability of the of theinverse model, function a second for a output of the model is a cumulative distribution of the ex- partgiven consists quantile in using can be the rounded distribution down of the to be number consistent of land- with pected number of landslide given the geology and the pre- slidesthe original according data. to Matlabthe precipitation® was used class to iteratively and lithology derive pre- the cipitation amount. To allow a generalization of these results, viouslyGamma assessed cumulative to simulate distribution different as therepotential is not consequences analytical so- gamma distributions were fitted to the data by minimizing the lution (Johnson and Kotz, 1970). Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 www.nat-hazards-earth-syst-sci.net/13/3169/2013/ P. Nicolet et al.: Shallow landslides stochastic risk modelling 7

d

a Start d d/2 Cumulative Precipitation Landslide Generate geological map Inventory map random matrix map A

Attribute each Divide into l l cell to one classes geological unit Fig. 9. Left: Buffon’s clean tile problem (modified from Mathai, 1999). The probability for the coin to touch the limit of the tile is no 2 i = iterations ? given by the ratio between the dashed square (area= (l − d) ) and 2 yes the plain square (area= l ). Right: The probability for a circular landslide of diameter d to reach a house is given by the ratio of the Probabilistic landslide distribution for each litho- buildings expanded with a d/2 buffer (a) with the total area (A). logical unit and precipita- tion class

Fig. 7. Flow diagram showing the assessment methodology used to obtain the cumulative frequency of the number of landslides per 3.4 Impact assessment lithological unit and precipitation class. The impact assessment consists of two main steps, which are evaluating how many buildings will be reached and estimat- P. Nicolet et al.: Shallow landslides stochastic risk modelling 7 ing an associated cost. In order to assess the number of affected buildings, ge- ometrical probabilities are used. The concept used in this d model is inspired from Buffon’s clean tile problem, which P. Nicolet et al.: Shallow landslide’s stochastic risk modelling 3175 consists of calculating the probability for a coin to fall on the crack separating two tiles of a paved ground (Mathai, 1999; a Weisstein, 2013). For square tiles, the probability that a cir- Start d Start cular coin of diameter d falls completely inside a square of d/2 side l (with l > d), is given by the ratio of a square of side Cumulative Precipitation Landslide Generate Precipitation- Cumulative geological Precipitation Generate map Inventory map random matrix landslide relation geological l−d with the tile of side l. The smaller square corresponds to map map random matrix (for each geology) map the tile eroded by a buffer of size d/2 (Fig. 9, left). Therefore, A the probability for the coin to fall on the crack is the ratio of Attribute each Attribute each 2 2 Divide into Divide into l l the area between the two squares (l −(l−d) ) and the bigger cell to one cell to one classes classes geological unit geological unit square. Buffon also investigated the ”needle problem”, which Fig. 9. Left: Buffon’s clean tile problem (modified from Mathai, consists of calculating the probability that a needle falling on 1999). The probability for the coin to touch the limit of the tile is Assess the a ground made of infinite parallel strips of equal width falls no Generate 2 i = iterations ? given by the ratio between the dashed squarenumber of (area= (l − d) ) and random matrix landslides on one of the lines (Mathai, 1999). In contrast, the falling the plain square (area= l2). Right: The probability for a circular yes object is, in the needle problem, not only characterized by d landslide of diameter to reach a houseAssess is given the by the ratio of the Probabilistic landslide Generate the position of its center, but also by its orientation. As a re- number of distribution for each litho- buildings expanded withrandom a d/ matrix2 buffer (a) with the total area (A). logical unit and precipita- intersections sult, dilating the lines by a buffer is not suitable to solve the tion class problem and Buffon’s solution cannot be straightforwardly no Fig. 7. Flow diagram showing the assessment methodology used i = iterations ? extended to other objects than the straight lines. Fig. 7. Flow diagram showing the assessment methodology used yes to obtain the cumulative frequency of the number of landslides per 3.4 Impact assessment To assess the conditional probability for a landslide to to obtain the cumulative frequency of the number of landslides per lithological unit and precipitation class. Number of reach a building, the coin of Buffon’s problem is replaced lithological unit and precipitation class. affected buildings The impact assessment consists of two(distribution) main steps, which are with circular landslides of diameter d, and the cracks be- evaluating how many buildings will be reached and estimat- tween the tiles are replaced with the actual buildings (Fig. 9, ingFig.Fig. an 8. 8.associatedFlowFlow diagram diagram cost. showing showing the assessment methodology methodology used used to to right). Therefore, adding a buffer of a distance d/2 to the of the precipitation event using a Monte Carlo approach. This obtainInobtain order the the number tonumber assess of of affected affected the number buildings. buildings. of affected buildings, ge- buildings allows to compare the area covered by the ex- step illustrates the uncertainty of the model on the conse- ometrical probabilities are used. The concept used in this panded buildings with the total area, which corresponds to quences of a given precipitation event. Indeed, since we con- model is inspired from Buffon’s clean tile problem, which the conditional probability for a landslide to reach a building. sider that the landslides are controlled only by the precipita- consistsand the ofarea calculating of the bigger the probability square. Buffon for a also coin investigated to fall on the the At this step, it is considered that the landslide has the same probability to occur anywhere inside the considered area. tion and the lithology, this step gives the variability resulting crack“needle separating problem”, two which tiles ofconsists a paved of groundcalculating (Mathai, the probabil- 1999; from this simplification. The workflow of this step is given Weisstein,ity that a needle 2013). falling For square on a tiles, ground the made probability of infinite that parallel a cir- in Fig. 8. Both the raw distributions and the gammaStart distribu- cularstrips coin of equal of diameter width fallsd falls on onecompletely of the lines inside (Mathai a square, 1999 of ). tions are used. sideIn contrast,l (with l the > d falling), is given object by is, the in ratio the of needle a square problem, of side not Precipitation- Cumulative Precipitation Generate Since gamma parameterslandslide relation have beengeological fitted with shifted val- lonly−d with characterized the tile of side by thel. The position smaller of square its centre, corresponds but also to by map random matrix ues, the unmodified(for each inverse geology) distributionmap will overestimate the theits tile orientation. eroded by As a buffer a result, of dilating size d/2 the(Fig. lines 9, left). by a Therefore, buffer is not number of landslides. However, as the gamma distribution thesuitable probability to solve for the the problem coin to falland on Buffon’s the crack solution is the cannot ratio of be Attribute each 2 2 Divide into thestraightforwardly area between the extended two squares to other(l −( objectsl−d) ) thanand the the bigger straight is continuous and as we need to obtain thecell to number one of land- classes slides in integers, the results of the inversegeological functionunit for a square.lines. Buffon also investigated the ”needle problem”, which given quantile can be rounded down to be consistent with consistsTo assess of calculating the conditional the probability probability that a forneedle a landslide falling on to ® the original data. Matlab was usedAssess to theiteratively derive the areach ground a building, made of infinite the coin parallel of Buffon’s strips of problem equal width is replaced falls Generate number of gamma cumulativerandom distribution matrix aslandslides there is not analytical so- onwith one circular of the lines landslides (Mathai, of diameter 1999). Ind contrast,, and the the cracks falling be- lution (Johnson and Kotz, 1970). objecttween is, the in tiles the are needle replaced problem, withnot the actualonly characterized buildings (Fig. by9, Assess the Generate the position of its center, but also by its orientation. As a re- number of right). Therefore, adding a buffer of a distance d/2 to the random matrix 3.4 Impact assessment intersections sult,buildings dilating allows the lines one byto compare a buffer is the not area suitable covered to solve by the the ex- problempanded buildingsand Buffon’s with solution the total cannot area, be which straightforwardly corresponds to no The impact assessment consists ofi =two iterations main ? steps, which are extendedthe conditional to other probability objects than for the a landslide straight lines. to reach a building. evaluating how many buildings will beyes reached and estimat- AtTo this assess step, the it is conditional considered probability that the landslide for a landslide has the same to ing an associated cost. Number of reachprobability a building, to occur the anywhere coin of Buffon’s inside the problem considered is replaced area. affected buildings In order to assess the number(distribution) of affected buildings, ge- withAssuming circular landslides circular landslides of diameter isd a,simplification and the cracks which be- ometrical probabilities are used. The concept used in this tweenmight the have tiles consequences are replaced onwith the the model, actual since, buildings as illustrated (Fig. 9, modelFig. 8. Flow is inspired diagram from showing Buffon’s the assessment clean tile methodology problem, used which to right).by the Therefore, needle problem, adding an a elongatedbuffer of a shape distance is mored/2 likelyto the to consistsobtain the of number calculating of affected the probability buildings. for a coin to fall on the buildingsaffect the allows buildings. to compare Moreover, the the area shape covered of the by landslides the ex- is crack separating two tiles of a paved ground (Mathai, 1999; pandedexpected buildings to be elongated. with the total As a area, consequence, which corresponds the circle to di- Weisstein, 2013). For square tiles, the probability that a cir- theameter conditional is set to probability 200 m in for order a landslide to completely to reach include a building. 90 % cular coin of diameter d falls completely inside a square of Atof this the landslides,step, it is considered since the distancethat the landslide measure hascorresponds the same to side l (with l > d), is given by the ratio of a square of side probabilitythe largest to dimension occur anywhere (Fig. 2), inside i.e. the the length considered of thearea. landslide. l−d with the tile of side l. The smaller square corresponds to This diameter results in an overestimation of the landslide the tile eroded by a buffer of size d/2 (Fig. 9, left). Therefore, surface, but it takes indirectly into account the landslide ge- the probability for the coin to fall on the crack is the ratio of ometry and provides a slightly pessimistic risk estimation in the area between the plain and the dashed lines (l2 −(l−d)2) terms of the number of affected buildings. Thus, a 100 m www.nat-hazards-earth-syst-sci.net/13/3169/2013/ Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 83176 P. P. Nicolet Nicolet et et al.: al.: Shallow Shallow landslide’s landslides stochastic risk risk modelling modelling P. Nicolet et al.: Shallow landslides stochastic risk modelling 7 Assuming circular landslides is a simplification which

might have consequencesd on the model, since, as illustrated 1 by the needle problem, an elongated shape is more likely to 0.75 0.5 affect the buildings. Moreover, the shape of the landslides is 0.25 a expected to be elongated. As a consequence, the circle di- 0 Start ameter is set to 200 m in order to completelyd include 90 % d/2 Cumulative of the landslides, since the distance measure correspond to Precipitation Landslide Generate geological map Inventory map random matrix map the largest dimension (Fig. 2), i.e. the length of the landslide. This diameter results in an overestimation of the landslideA

Attribute each surface, but it takes indirectly into account the landslide ge- Divide into l l cell to one classes geological unit ometry and provides a slightly pessimistic risk estimation in termsFig.Fig. 9. 9. ofLeft:Left: the Buffon’s Buffon’snumber clean clean of affected tile problem buildings. (modified (modified Thus, from from a Mathai,Mathai 100 m, buffer19991999).). has The The been probability probability added for for to the the coin 1 814 to to touch touch 667 thebuildings the limit limit of of theextracted the tile tile is is no 2 0 25 50 100 i = iterations ? given by the ratio between the dashed square (area= (l − d) ) and fromgiven the by the vectorized ratio between landscape the dashed model square of (area Switzerland= (l − d) (Vec-2) and Kilometers the plain square (area= l2). Right: The probability for a circular yes tor25,the plain © swisstopo). square (area = Then,l2). Right: the total The surface probability has for been a circular com- landslide of diameter d to reach a house is given by the ratio of the Fig. 10. Impact probability map displaying the conditional proba- Probabilistic landslide paredlandslide with of each diameter celld surfaceto reach to a obtain house is the given impact by the probability. ratio of the Fig. 10. Impact probability map displaying the conditional proba- distribution for each litho- buildings expanded with a d/2 buffer (a) with the total area (A). bility for a 100 m radius circular landslide to affect a house for each logical unit and precipita- Itbuildings has to be expanded mentioned with a thatd/2 impactbuffer (a is) with only the considered total area (A with). bility for a 100 m radius circular landslide to affect a house for each tion class cell of of the the model. model. Dots Dots corresponds correspond to to the the cities cities visible visible in in Fig. Fig.1 1 a boolean approach, which means that a landslide can affect (hillshade: © Swisstopo). Fig. 7. Flow diagram showing the assessment methodology used a building or not, but the potential for one landslide to affect (hillshade: Swisstopo). 3.4 Impact assessment to obtain the cumulative frequency of the number of landslides per severalbuffer hasbuildings been added is not toconsidered. the 1 814 It667 should buildings also extractedbe noted lithological unit and precipitation class. thatfrom the the buffers vectorized are made landscape before model cutting of shapes Switzerland into cells (Vec- in The impact assessment consists of two main steps, which are tory. However, a suitable vulnerability curve linking the land- ordertor25, to© takeswisstopo). into account Then, the the possibility total surface for ahas landslide been com- oc- there is an uncertainty on the landslide locations, an in depth evaluating how many buildings will be reached and estimat- slide intensity, characterized by parameters such as depth or curringpared with in a each given cell cell surface to reach to obtain a house the located impact close probability. to the analysis of the landslide locations with regard to the hazard ing an associated cost. area, to the damage rate, is difficult to assess. The lack of borderIt has toof bean mentionedadjacent cell. that impact is only considered with a map cannot be made. In order to assess the number of affected buildings, ge- knowledgeThe estimation on the of precise the associated landslide cost characteristics is more complicated and lo- BooleanHowever, approach, a shallow which landslide means preliminary that a landslide hazard can map affect ex- a ometrical probabilities are used. The concept used in this cationas the value as well of as the the buildings inherent is variability not known. of This the information elements at istsbuilding at Switzerland or not, but scale the potential(Geotest etfor al., one 2006) landslide and provides to affect model is inspired from Buffon’s clean tile problem, which riskcould complicates be obtained even from more the buildings’ the assessment insurances of the for vulnera- 19 of aseveral global buildings area where is shallow not considered. landslides It shouldcan occur, also including be noted consists of calculating the probability for a coin to fall on the bility26 cantons, (Galli for and which Guzzetti, a public 2007). insurance Therefore, exists in and order is manda- to keep boththatcrack the the separating initiation buffers are two and made tiles propagation before of a paved cutting zones. ground shapes This (Mathai, map into is cells 1999; based in thetory. precision However, of a the suitable model vulnerability consistent with curve the linking previous the land- step, onorderWeisstein, a global to take analysis 2013). into account For in two square steps: the tiles, possibility first the the probability stability for a landslide is that assessed a cir- oc- weslide chose intensity, not to characterized use a value and by parameters a vulnerability such curve as depth to as- or Start usingcurringcular a coininfinite in a of given diameterslope cell analysis tod falls reach (model completely a house SLIDISP, located inside Liener a close square toet ofal., the sessarea, the to damagethe damage cost, rate, but to is assessdifficult it todirectly assess. from The the lack 2005 of 1996),borderside l then of(with an propagation adjacentl > d), is cell. given prone by the areas ratio are of aassessed square of with side a Precipitation- Cumulative Precipitation Generate eventknowledge mean on damage the precise cost. This landslide cost characteristics is estimated by and divid- lo- landslide relation geological l−However,d with the a tile shallow of side landslidel. The smaller preliminary square hazardcorresponds map toex- map random matrix model adapted from debris-flow (model SLIDESIM, based (for each geology) map ingcation the as total well damage as the inherent cost induced variability by landslides of the elements to private at oniststhe Gamma, at tile Switzerland eroded 2000). by aThescale buffer final ( ofGeotest size versiond/ et2 (Fig. al. of, this2006 9, left). map) and Therefore, combines provides infrastructuresrisk complicates (CHF even 16.3 more million) the assessment by the expected of the vulnera- number bothathe globalareas probability area without where for thefurther shallow coin attributes. to landslides fall on the Thanks can crack occur, isto the this including ratio map of a Attribute each 2 2 ofbility affected (Galli buildings. and Guzzetti The, latter2007). is Therefore, obtained by in summing order to keep over Divide into the area between the two squares (l −(l−d) ) and the bigger cell to one both the initiation and propagation zones. This map is based classes small modification is made to the impact probability. If a geological unit allthe grid precision cells ofthe the product model between consistent the with number the previous of landslides step, landslideonsquare. a global Buffon occurs analysis also in a investigatedin cell two where steps: the the first ”needle hazard the stability problem”, map exists, is assessed which it is (Fig.we chose 1) and not the to impactuse a value probability and a vulnerability (Fig. 10). This curve approach to as- consideredusingconsists an of infinite that calculating the slope landslide the analysis probability will occur(model that inside a SLIDISP, needle the falling areaLiener cov- on Assess the eta al. ground, 1996 made), then of propagation infinite parallel prone strips areas of equal are assessed width falls with resultssess the in damage 2260 affected cost, but buildings, to assess implying it directly a meanfrom the cost 2005x¯ of Generate number of ered by the hazard map. Therefore, the ratio a/A described random matrix landslides on one of the lines (Mathai, 1999). In contrast, the falling CHFevent 7211 mean per damage building. cost. No This uncertainty cost is isestimated considered by on divid- this ina Fig.model 9 becomes adapted from(a ∈ debrisS)/S,flow where (modelS is the SLIDESIM, surface covered based object is, in the needle problem, not only characterized by parameter.ing the total damage cost induced by landslides to private byon theGamma hazard, 2000 map.). The The impact final versionprobability of this map map including combines this Assess the Generate the position of its center, but also by its orientation. As a re- infrastructures (CHF 16.3 million) by the expected number number of both areas without further attributes. Thanks to this map a It is apparent that damage costs are varying. Therefore, to random matrix modification is given in Fig. 10. The hazard map has however intersections sult, dilating the lines by a buffer is not suitable to solve the reproduceof affected a buildings. possible The distribution latter is obtained of costs, by a summing statistical over dis- notsmall been modification used yet toassess is made the to location the impact of the probability. landslides, If but a landslideproblem occursand Buffon’s in a cell solution where cannot the hazard be straightforwardly map exists, it is tributionall grid cells is chosen. the product Thus, between the expected the number damage of costlandslidesx for no a usage of this map for the landslide distribution has to be i = iterations ? extended to other objects than the straight lines. a(Fig. given1) building and the impact is assumed probability to follow (Fig. an10 exponential). This approach distri- considered.considered Indeed,that the onlylandslide 8 landslides will occur (0.14%) inside werethe area located cov- yes To assess the conditional probability for a landslide to butionresults with in 2260 probability affecteddensity buildings, function implying (e.g. a meanRoss, cost 2010):x of inered cells by with the no hazard hazard map. according Therefore, to the the map ratio anda/A 133described (2.31%) Number of reach a building, the coin of Buffon’s problem is replaced CHF 7211 per building. No uncertainty is considered for this affected buildings in Fig. 9 becomes (a ∈ S)/S, where S is the surface covered werewith located circular within landslides cells where of diameter less thand, and 10% the of cracks the surface be- (distribution) by the hazard map. The impact probability map including parameter. istween covered the by tiles the are hazard replaced map. with This the tends actual to buildings indicate (Fig.that this 9, λexp(−λx), x ≥ 0 this modification is given in Fig. 10. The hazard map has f(xIt) is = apparent that damage costs. are varying. Therefore,(5) to Fig. 8. Flow diagram showing the assessment methodology used to preliminaryright). Therefore, hazard addingmap is arealistic, buffer of but a since distance thered/2 isto an the un- 0, x < 0 however not been used yet to assess the location of the land- reproduce a possible distribution of costs, a statistical dis- obtain the number of affected buildings. certaintybuildings on allows the landslide to compare locations, the area an coveredin depth by analysis the ex- of tribution is chosen. Thus, the expected damage cost x for a theslides,panded landslide but buildings a locations usage with of this with the map totalregard for area, to the the which landslide hazard corresponds map distribution cannot to The distribution is only defined in terms of its first moment has to be considered. Indeed, only 8 landslides (0.14 %) were given building is assumed to follow an exponential distribu- bethe made. conditional probability for a landslide to reach a building. 1/λ, which is equal to x¯, namely the expected mean damage located in cells with no hazard according to the map and 133 tion with probability density function (e.g. Ross, 2010) as AtThe this estimation step, it is of considered the associated that the cost landslide is more has complicated the same cost per building assumed for the 2005 event. (2.31 %) were located within cells where less than 10 % of asprobability the value of to theoccur buildings anywhere is inside not known. the considered This information area. The generation of exponential variates is obtained by sam- the surface is covered by the hazard map. This tends to in- λexp(−λx), x ≥ 0 could be obtained from the buildings insurance for 19 over plingf (x) = from the quantile distribution,. which is given by(5) the dicate that this preliminary hazard map is realistic, but since 0, x < 0 26 cantons for which a public insurance exists and is manda- inverse function of the exponential cumulative distribution

Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 www.nat-hazards-earth-syst-sci.net/13/3169/2013/ P.10 Nicolet et al.: Shallow landslide’s stochastic risk modelling P. Nicolet et al.: Shallow landslides stochastic risk modelling 3177

LF CF FLMC MM 1 1 1 1

0.98 0.99 0.95 0.9 0.96 0.98 0.9 0.94 0.97 0.8 0.85 0.92 0.96

0.9 0.95 0.8 0.7

0.88 0.94 Cumulative frequency

Cumulative frequency Cumulative frequency 0.75 Cumulative frequency 0.6 0.86 0.93 0.7 0−100 mm (6/5749) 0−100 mm (3/6130) 0−100 mm (8/8746) 0−100 mm (2/2737) 0.84 0.92 100−130 mm (21/998) 100−130 mm (4/1226) 100−130 mm (27/1901) 100−130 mm (12/755) 0.5 130−160 mm (34/780) 130−160 mm (0/425) 130−160 mm (101/1318) 130−160 mm (112/757) 0.65 0.82 160−190 mm (76/798) 0.91 160−190 mm (7/339) 160−190 mm (278/1126) 160−190 mm (527/603) 190−220 mm (251/806) 190−220 mm (7/120) 190−220 mm (447/811) 190−220 mm (600/387) 220−321 mm (860/1069) 220−321 mm (0/12) 220−321 mm (1049/853) 220−321 mm (1323/599) 0.8 0.9 0.6 0.4 0 5 10 15 0 1 2 3 4 5 0 5 10 15 0 5 10 15 Number of landslides Number of landslides Number of landslides Number of landslides

Fig. 11. Landslide relation with precipitation and lithological group. The curves for small precipitation amounts are not always visible Fig. 11. Landslide relation with precipitation and lithological group. The curves for small precipitation amounts are not always visible because of the low number of landslides. Note that scales are different. Numbers between brackets are respectively the number of landslides because of the low number of landslides. Note that scales are different. Numbers between brackets are respectively the number of landslides in the cells and the number of cells in the class, averaged over the iterations. in the cells and the number of cells in the class, averaged over the iterations.

Table 1. Fitted parameters of the gamma distribution. The distribution is only defined in terms of its first moment lithological group is a monotonically increasing function of 1/λ,Precipitation which is equal to x, namely LF the expected mean damage CFthe precipitation FLMC amount. CF show a very little MM susceptibility cost per building[mm] assumedα for β the 2005RMSE event. α β RMSEto landslidesα compared β RMSE to the otherα groups β as evidencedRMSE by The generation0–100 of – exponential – variates – is obtained – by – sam- –the low number – of– observed – landslides. – With – similar – precip- pling from100–130 the quantile 0.149 distribution, 0.666 1.77E-05 which is – given by – the –itation 0.112 amount, 0.643 MM formations 9.56E-05 tend 0.042 to have 1.148 a higher 1.94E-04 prob- inverse130–160 function of 0.255 the exponential 0.685 6.28E-05 cumulative 0.118 distribution 0.012 0.00E+00ability 0.144 to contain 1.245 at least 7.19E-04 one landslide 0.059 than3.632 FLMC 1.72E-03 or LF. as 160–190 0.127 1.570 2.44E-04 0.052 1.195 3.54E-04However 0.159 this relation 2.421 1.26E-03is less evident 0.193 for 5.798a larger 2.14E-03 number of 190–220 0.139 2.962 3.28E-03 0.279 0.775 4.60E-04landslides. 0.242 3.077 2.45E-03 0.282 6.835 6.65E-03 220–321ln 0.108(1 − u) 8.846 3.57E-03 0.118 0.012 0.00E+00 0.290 5.133 3.18E-03 0.566 4.653 3.71E-03 F −1(u) = x = − , (6) Table 1 shows the fitted values of the gamma distribu- λ tion (missing data denotes that the fitting did not converge in where u is a uniformly distributed random number between 0 the allowed number of iterations), whereas Fig. 12 displays and 1. The exponentially distributed damage cost is sampled these values graphically. CF have to be considered with cau- for each0.8 case of impact identified by the model. tion because of the low number of samples. The α parameter2.4 LF (shape), characterizes the central location of the distribution,2 The fat-tailedCF nature of the exponential distribution allows 0.6 while the β parameter (scale) characterizes its dispersion.1.6 obtaining a moreFLMC realistic estimate of the damage costs than 1.2 MM a normalα 0.4 or triangular distribution and does not need the esti- A general increase in both α and β parameters with0 precipi-.8 tation amount can be observed, although some values0.4 are not mation0.2 of the second moment characterizing the variance of 0 the distribution. The latter is a useful feature as the statistical following the general linear trend. This is especially the case 0 distribution100 of the damage150 costs200 per building250 is not known300 for α for LF and for β for the highest precipitation class. in our particular case. ThePrecipitation log-normal amount [mm] distribution also has The general increase of both parameters is a desirable heavy10 tails and was successfully used to model the cost as- property and is in accordance with our prior expectations. In LF sociated8 to floodsCF (Merz et al., 2004). However, due to the fact, increasing precipitation amounts increase the expected FLMC larger number6 of degrees of freedom, it is also not suitable number of landslides (represented by α) and the dispersion of MM β the distribution (represented by β). Higher β values are rep- for our4 application. resentative of heavy tails, which means that the probability of 2 0 25 50 100 observing a high numberKilometers of landslides rises with increasing 0 4 Results100 150 200 250 300 precipitation amount. Precipitation amount [mm] Fig.The 13. spatialMean modelled distribution number of of the landslides number with of the landslides gamma func- was tions. No color is displayed on the cells that never contain land- The statistical distribution of landslides as a function of pre- computed following the procedure described in Fig. 8 using Fig. 12. Fitted parameters for α and β of the gamma distribution. slides. cipitation amount and lithological group is given in Fig. 11 both the raw data and the gamma fits and performing 10 000 and results from 10 000 iterations of the model. The prob- iterations for each. However, since gamma distributions have ability to observe a given number of landslides in a given www.nat-hazards-earth-syst-sci.net/13/3169/2013/ Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 10 P. Nicolet et al.: Shallow landslides stochastic risk modelling

10 P. Nicolet et al.: Shallow landslides stochastic risk modelling LF CF FLMC MM 1 1 1 1

LF CF FLMC MM 0.98 1 0.99 1 1 1 0.95 0.9 0.960.98 0.980.99 0.95 0.9 0.9 0.940.96 0.970.98 0.9 0.8 0.85 0.920.94 0.960.97 0.8 0.85 0.90.92 0.950.96 0.8 0.7

0.9 0.95 0.8 0.7 0.88 0.94 Cumulative frequency

Cumulative frequency Cumulative frequency 0.75 Cumulative frequency 0.88 0.94 0.6 0.86 0.93 Cumulative frequency

Cumulative frequency Cumulative frequency 0.75 Cumulative frequency 0.7 0.6 0.86 0−100 mm (6/5749) 0.93 0−100 mm (3/6130) 0−100 mm (8/8746) 0−100 mm (2/2737) 0.84 0.92 100−130 mm (21/998) 100−130 mm (4/1226) 100−130 mm (27/1901) 100−130 mm (12/755) 0.7 0.5 130−1600−100 mm (6/5749)(34/780) 130−1600−100 mm mm (3/6130) (0/425) 0−100130−160 mm mm(8/8746) (101/1318) 0−100130−160 mm (2/2737) mm (112/757) 0.84 0.92 100−130 mm (21/998) 100−130 mm (4/1226) 0.65 100−130 mm (27/1901) 100−130 mm (12/755) 0.82 160−190 mm (76/798) 0.91 160−190 mm (7/339) 160−190 mm (278/1126) 0.5 160−190 mm (527/603) 130−160 mm (34/780) 130−160 mm (0/425) 130−160 mm (101/1318) 130−160 mm (112/757) 190−220 mm (251/806) 190−220 mm (7/120) 0.65 190−220 mm (447/811) 190−220 mm (600/387) 0.82 220−321160−190 mm mm (860/1069) (76/798) 0.91 220−321160−190 mm (0/12)(7/339) 160−190220−321 mm mm (278/1126) (1049/853) 160−190220−321 mm mm(527/603) (1323/599) 0.8 190−220 mm (251/806) 0.9 190−220 mm (7/120) 0.6 190−220 mm (447/811) 0.4 190−220 mm (600/387) 0 5220−321 mm10 (860/1069) 15 0 1 220−3212 3mm (0/12)4 5 0 220−3215 mm (1049/853)10 15 0 220−3215 mm (1323/599)10 15 0.8 Number of landslides 0.9 Number of landslides 0.6 Number of landslides 0.4 Number of landslides 0 5 10 15 0 1 2 3 4 5 0 5 10 15 0 5 10 15 Number of landslides Number of landslides Number of landslides Number of landslides Fig. 11. Landslide relation with precipitation and lithological group. The curves for small precipitation amounts are not always visible becauseFig. 11. of theLandslide low number relation of with landslides. precipitation Note that and scales lithological are different. group. NumbersThe curves between for small brackets precipitation are respectively amounts are the notnumber always of landslides visible in thebecause cells of and the the low number number of of cells landslides. in the class, Note that averaged scales over are different. the iterations. Numbers between brackets are respectively the number of landslides in the cells and the number of cells in the class, averaged over the iterations. Table3178 1. Fitted parameters of the gamma distribution. P. Nicolet et al.: Shallow landslide’s stochastic risk modelling Table 1. Fitted parameters of the gamma distribution. PrecipitationTable 1. Fitted parameters of LF the gamma distribution. CF FLMC MM Precipitation[mm] α β LFRMSE α β CFRMSE α FLMC β RMSE α MM β RMSE Precipitation[mm] α βLFRMSE α β CFRMSE α βFLMCRMSE α β MM RMSE 0–100 – – – – – – – – – – – – 0–100[mm] α – β –RMSE – –α β –RMSE – –α β –RMSE – –α – β RMSE – 100–130 0.149 0.666 1.77E-05 – – – 0.112 0.643 9.56E-05 0.042 1.148 1.94E-04 100–130 0.149 0.666 1.77E-05 – – – 0.112 0.643 9.56E-05 0.042 1.148 1.94E-04 130–1600–100 0.255 – 0.685 – 6.28E-05 – 0.118 – 0.012 – 0.00E+00 – 0.144 – 1.245 – 7.19E-04 – 0.059 – 3.632 – 1.72E-03 – 130–160 0.255 0.685 6.28E-05× −5 0.118 0.012 0.00E+00 0.144 1.245 7.19E-04× −5 0.059 3.632 1.72E-03× −4 160–190100–130 0.127 0.149 0.666 1.570 1.77 2.44E-0410 0.052– 1.195 – 3.54E-04 – 0.159 0.112 0.643 2.421 9.56 1.26E-0310 0.1930.042 1.148 5.798 1.94 2.14E-0310 160–190130–160 0.255 0.127 0.685 1.570 6.28 2.44E-04×10−5 0.0520.118 0.012 1.195 3.54E-04 0.00 0.159 0.144 1.2452.421 7.19 1.26E-03×10−4 0.1930.059 5.798 3.632 1.722.14E-03×10−3 190–220190–220160–190 0.139 0.127 0.139 1.570 2.962 2.962 2.44 3.28E-03 3.28E-03×10−4 0.279 0.2790.052 1.195 0.775 3.54 4.60E-04×10−4 0.242 0.2420.159 2.4213.077 3.077 1.26 2.45E-03 2.45E-03×10−3 0.282 0.2820.193 6.835 5.798 6.835 2.146.65E-03 6.65E-03×10−3 220–321220–321190–220 0.108 0.139 0.108 2.962 8.846 8.846 3.28 3.57E-03 3.57E-03×10−3 0.118 0.1180.279 0.775 0.012 4.60 0.00E+00×10−4 0.290 0.2900.242 3.0775.133 5.133 2.45 3.18E-03 3.18E-03×10−3 0.566 0.5660.282 4.653 6.835 4.653 6.653.71E-03 3.71E-03×10−3 220–321 0.108 8.846 3.57 ×10−3 0.118 0.012 0.00 0.290 5.133 3.18 ×10−3 0.566 4.653 3.71 ×10−3

0.8 0.8 2.4 2.4 LF LF 2 2 0.6 0.6 CF CF 1.6 1.6 FLMCFLMC 1.2 1.2 MM MM α α 0.4 0.4 0.8 0.8 0.4 0.4 0.2 0.2 0 0

0 0 100100 150150 200200 250250 300 PrecipitationPrecipitation amount amount [mm] [mm]

10 10 LF LF 8 CF 8 CF FLMC 6 FLMC 6 MM β MM β 4 4 2 0 25 50 100 2 0 25 50 1K0i0lometers 0 Kilometers 0 100 150 200 250 300 100 150 Precipitation200 amount [mm] 250 300 Fig. 13. Mean modelled number of landslides with the gamma func- Precipitation amount [mm] tions.Fig.Fig. 13. 13. NoMeanMean color modelled is displayed number on the of landslides landslidescells that neverwith with the the contain gamma gamma land- func- func- Fig. 12. Fitted parameters for forαα andandββofof the the gamma gamma distribution. distribution. slides.tions.tions. No No color colour is is displayed displayed on on the the cells that that never never contain contain land- land- α β Fig. 12. Fitted parameters for and of the gamma distribution. slides.slides.

not been fitted for some of the precipitation classes, raw the simulations (Fig. 14). Indeed, the expected number of data have been used instead of gamma distributions when affected buildings for the event is 2260, whereas the simu- not available. The mean modelled number of landslides with lations return a mean of 1689.5 for raw data and 1665.8 for gamma fits is given in Fig. 13 and is very similar to the mean gamma fits. As a consequence, the damage amount is not number of landslides modelled with raw data (not shown). reached either since it is derived from the latter. It is not yet The spatial pattern is relatively similar to the spatial distri- clear why the observed total number of hit buildings is under- bution of rainfall amounts, with two remarkable differences. estimated by the model. One possible reason could be that the First, the relation between precipitation amount and num- landslide localization is highly correlated with the location of ber of landslides is not linear, which implies that areas with the buildings. To test this hypothesis, we compared the im- low precipitation amounts show a null to very low number pact probability of cells within which landslides actually oc- of landslides. The second difference is due to the sharp ge- curred to the impact probability of cells in which landslides ographical transitions between the lithological units, which were modelled (the impact probability is taken into account lead to sharp transitions in the modelled number of land- n times if the number of landslides n in the cell is greater slides. An illustrative example occurs when moving from the than 1, for both curves). This comparison indicates that the MM formations to the CF, which strongly reduces the num- modelled landslides tend to occur in cells with lower impact ber of landslides (see Fig. 4). These results seem to be in probability than the actual landslides (Fig. 15). good agreement with the observed distribution of landslides (Fig. 1). 5 Discussion 4.1 Impact assessment The landslide model presented in this paper only consid- Although the number of landslides is reproduced, the ex- ers precipitation amounts and geology as input parameters. pected number of hit buildings is almost never reached in However, other variables such as terrain slope, soil thickness

Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 www.nat-hazards-earth-syst-sci.net/13/3169/2013/ P. Nicolet et al.: Shallow landslides stochastic risk modelling 11

lution variables. As a consequence, the 1 km ×1 km resolu-

1 tion model only gives information about the large scale pre- 0.8 conditioning factors for landslide generation. Smaller scale

0.6 features may affect the process of landslide triggering in a significant way and should be taken into account if this 0.4 kind of model was used at a higher resolution. Furthermore, 0.2 Raw data: x¯ =5752.5 this model is based only on one single event and should be Cumulative frequency Gamma fit: x¯ =5646.2 0 compared with other similar rainfall events. In particular, it 5000 5200 5400 5600 5800 6000 6200 6400 6600 should be compared with similar events producing landslides Number of modeled landslides in iteration in different geological settings, to validate the aggregation of 1 the different lithologies into four main units. Indeed, land- 0.8 slides susceptibility might be different in Jura limestones than in Prealpine limestones, for example. Lithological in- 0.6 formation is also very coarse at the working scale and local 0.4 variations could affect the susceptibility. Furthermore, shal- low landslides are sensitive to the properties of the soil layer, 0.2 Raw data: x¯ =1689.5 Cumulative frequency Gamma fit: x¯ =1665.8 for which generally no map exists. 0 1200 1400 1600 1800 2000 2200 2400 The annual probability to overcome a given total damage Number of hit buildings cost could be assessed by analysing different precipitation 1 events, which are weighted based on their frequency of oc- currence (return period). This step is essential in order to ob- 0.8 tain a mean annual cost as well as an exceedance probability 0.6 curve. One possibility to generate a large number of rainfall

0.4 fields to appropriately represent the full risk estimation could be based on design storms (Seed et al., 1999). Stochastic 0.2 Raw data: x¯ =12.2 Cumulative frequency Gamma fit: x¯ =12 rainfall fields could be generated according to a given return 0 9 10 11 12 13 14 15 16 17 period and be used to simulate the spatial distribution of land- Damage amount [million CHF] slides under extreme rainfall conditions. Attempts have been made to use a return period in order to predict landslide trig- Fig. 14. Number of landslides, number of hit buildings and damage gering but, they were mainly performed at local scale (e.g. amount calculated from raw data and gamma fits. Mean value x¯ for Iida, 1999; D’Odorico et al., 2005; Iida, 2004; Tarolli et al., each line is displayed on the graph, whereas black lines correspond to the data of the event or the expected number of affected buildings. 2011) and would therefore not be suitable for a larger area, 10 000 iterations have been computed. since the spatial variability is not taken into account. On the P.P. Nicolet Nicolet et et al.: al.: Shallow Shallow landslide’s landslides stochastic risk modelling modelling 3179 11 other hand, the spatial distribution of rainfall by means of data with a smaller time step (in this case satellite data) has lution1 variables. As a consequence, the 1 km ×1 km resolu- been used for early-warning (e.g. Apip et al., 2010), but as far 1 tion0.9 model only gives information about the large scale pre- as we know, is has not been used as a starting point to simu- 0.8 conditioning0.8 factors for landslide generation. Smaller scale late potential future events. However, for precipitation events 0.6 features0.7 may affect the process of landslide triggering in with long return periods, the uncertainty on the frequency is a significant0.6 way and should be taken into account if this rather high, as mentioned in section 2.3 for this event. This 0.4 kind0.5 of model was used at a higher resolution. Furthermore, would add an uncertainty on the risk analysis. 0.2 Raw data: x¯ =5752.5 this0.4 model is based only on one single event and should be Another issue concerns the landslide timing. We used the Cumulative frequency Gamma fit: x¯ =5646.2 0 compared0.3 with other similar rainfall events.Modeled In particular, landslides it precipitation amount of the whole event (6 days) as a pre- 5000 5200 5400 5600 5800 6000 6200 6400 6600 occurence Cumulative should0.2 be compared with similar events producingObserved landslides dictor for landslide occurrence. But, shallow-landslides are Number of modeled landslides in iteration All Switzerland 0.1 known to be sensitive to the intensity and duration of the in different geological settings, to validate theHazard aggregation map of 1 the different0 lithologies into four main units. Indeed, land- rainfall, as well as to the hyetograph shape (D’Odorico et al., 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 slides susceptibility mightImpact be differentprobability in Jura limestones 2005). There are two main reasons for this simplification. than in Prealpine limestones, for example. Lithological in- The first is the lack of data on the exact timing of land- 0.6 Fig.formationFig. 15. 15.ComparisonComparison is also very of thecoarse impact at the probability working of of scale the the cells cells and where local where slides, which does not allow analyzing the temporal precip- 0.4 landslidesvariationslandslides occurred occurredcould affect and and where wherethe susceptibility. landslides have have Furthermore, been been modelled modelled shal- (if (if itation pattern preceding their triggering. The second reason n > 1 nlow > 1 landslides landslideslandslide are occurs occur sensitive in in a a cell, cell, to the the properties impact probability of the soil of of the the layer, cell cell is due to the uncertainty of the radar QPE product, which is 0.2 Raw data: x¯ =1689.5 is considered n times). As a comparison, the distribution over all Cumulative frequency is considered n times). As a comparison, the distribution over all Gamma fit: x¯ =1665.8 for which generally no map exists. higher when used to analyze rainfall time series at high tem- 0 ofSwitzerland Switzerland is is shown, shown, as as well well as as the the results results for for the the existing existing haz- haz- 1200 1400 1600 1800 2000 2200 2400 The annual probability to overcome a given total damage poral resolutions, for instance hourly or 10 min accumula- ardard map map (weighted (weighted by by the the surface of the cell included included in in the the hazard hazard Number of hit buildings cost could be assessed by analysing different precipitation tions. The spatial distribution of QPE accuracy can still be af- map).map). 1 events, which are weighted based on their frequency of oc- fected by some residual ground clutter, which overestimates currence (return period). This step is essential in order to ob- 0.8 tain a mean annual cost as well as an exceedance probability 0.6 Lithologicalcurve. One possibility information to generate is also very a large coarse number at the ofworking rainfall 0.4 scalefields and to appropriately local variations represent could the affect full the risk susceptibility. estimation could Fur- thermore,be based onshallow design landslides storms (Seed are sensitive et al., to1999). the properties Stochastic of 0.2 Raw data: x¯ =12.2 Cumulative frequency rainfall fields could be generated according to a given return Gamma fit: x¯ =12 the soil layer, for which generally no map exists. 0 period and be used to simulate the spatial distribution of land- 9 10 11 12 13 14 15 16 17 The annual probability to exceed a given total damage cost Damage amount [million CHF] couldslides beunder assessed extreme by rainfallanalysing conditions. different Attempts precipitation have events, been whichmade to are use weighted a return periodbased on in order their tofrequency predict landslide of occurrence trig- Fig.Fig. 14. 14.NumberNumber of of landslides, landslides, number number of of hit hit buildings buildings and and damage damage gering but, they were mainly performed at local scale (e.g. amount calculated from raw data and gamma fits. Mean value x¯ for (return period). This step is essential in order to obtain a amount calculated from raw data and gamma fits. Mean value x for Iida, 1999; D’Odorico et al., 2005; Iida, 2004; Tarolli et al., each line is displayed on the graph, whereas black lines correspond mean annual cost as well as an exceedance probability curve. each line is displayed on the graph, whereas black lines correspond 2011) and would therefore not be suitable for a larger area, to the data of the event or the expected number of affected buildings. One possibility to generate a large number of rainfall fields to the data of the event or the expected number of affected buildings. since the spatial variability is not taken into account. On the 1010 000 000 iterations iterations have have been been computed. computed. to appropriately represent the full risk estimation could be other hand, the spatial distribution of rainfall by means of based on design storms (Seed et al., 1999). Stochastic rainfall data with a smaller time step (in this case satellite data) has fields could be generated according to a given return period been used for early-warning (e.g. Apip et al., 2010), but as far and permeability1 contrast, for example, play a key role in and be used to simulate the spatial distribution of landslides as we know, is has not been used as a starting point to simu- shallow0.9 landslide generation. These variables are either hard under extreme rainfall conditions. Attempts have been made late potential future events. However, for precipitation events to measure0.8 over a large domain, e.g. the soil thickness, or to use a return period in order to predict landslide trigger- with long return periods, the uncertainty on the frequency is show0.7 spatial variability at extents which are smaller than ing, but they were mainly performed at local scale (e.g. Iida, 0.6 rather high, as mentioned in section 2.3 for this event. This 1 km ×1 km resolution, e.g. the terrain slope. Additionally, 1999; D’Odorico et al., 2005; Iida, 2004; Tarolli et al., 2011) 0.5 would add an uncertainty on the risk analysis. the uncertainty of the landslide inventory does not allow and would therefore not be suitable for a larger area, since 0.4 Another issue concerns the landslide timing. We used the matching the location of the landslide with such high res- the spatial variability is not taken into account. However, the 0.3 Modeled landslides precipitation amount of the whole event (6 days) as a pre- olution occurence Cumulative variables. As a consequence, the 1 km ×1 km reso- spatial distribution of rainfall by means of data with a smaller 0.2 Observed landslides dictor for landslide occurrence. But, shallow-landslides are lution model only gives information aboutAll Switzerland the large-scale time step (in this case satellite data) has been used for early 0.1 known to be sensitive to the intensity and duration of the pre-conditioning factors for landslide generation.Hazard map Smaller- warning (e.g. Apip et al., 2010), but as far as we know, it has 0 rainfall, as well as to the hyetograph shape (D’Odorico et al., scale features0 0.1 may0.2 affect0.3 0.4 the process0.5 0.6 of0.7 landslide0.8 trigger-0.9 1 not been used as a starting point to simulate potential future Impact probability 2005). There are two main reasons for this simplification. ing in a significant way and should be taken into account events.The first Furthermore, is the lackof for data precipitation on the exact events timing with of long land- re- toFig. extend 15. Comparison this kind of of the model impact to probability a higherof resolution. the cells where Fur- turnslides, periods, which the does uncertainty not allow onanalyzing the frequency the temporal is rather precip- high, thermore,landslides this occurred model and is where based landslides only on onehave single been modelled event and (if asitation mentioned pattern in preceding Sect. 2.3 theirfor this triggering. event. This The second would add reason un- shouldn > 1 landslide be compared occurs with in a cell, other the similar impact probability rainfall events. of the cell In certaintyis due to theto the uncertainty risk analysis. of the radar QPE product, which is n particular,is considered it shouldtimes). be As compared a comparison, with the similar distribution events over pro- all higherAnother when issue used concerns to analyze the rainfall landslide time timing. series at We high used tem- the Switzerland is shown, as well as the results for the existing haz- ducing landslides in different geological settings, to validate precipitationporal resolutions, amount for ofinstance the whole hourly event or 10 (6min days)accumula- as a pre- theard aggregation map (weighted of by the the different surface of lithologies the cell included into in four the hazard main dictor for landslide occurrence. But, shallow landslides are map). tions. The spatial distribution of QPE accuracy can still be af- units. Indeed, landslide susceptibility might be different in knownfected by to some be sensitive residual to ground the intensity clutter, which and duration overestimates of the Jura limestones than in pre-Alpine limestones, for example. rainfall, as well as to the hyetograph shape (D’Odorico et al., www.nat-hazards-earth-syst-sci.net/13/3169/2013/ Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 3180 P. Nicolet et al.: Shallow landslide’s stochastic risk modelling

2005). There are two main reasons for this simplification. destroyed. This could be the result of a too high number of The first is the lack of data on the exact timing of landslides, affected buildings (since they have been estimated), which which does not allow the analysis of the temporal precipi- reduces the mean damage cost, or an indication of the need tation pattern preceding their triggering. The second reason for using a distribution of damages with a fatter tail. How- is due to the uncertainty of the radar QPE product, which is ever, this confirms the fact that a distribution with a fat tail is higher when used to analyse rainfall time series at high tem- suitable. Nevertheless, since the damage cost varies indepen- poral resolutions, for instance hourly or 10 min accumula- dently for each affected house and since the number of af- tions. The spatial distribution of QPE accuracy can still be af- fected houses is relatively high in the simulations, the effect fected by some residual ground clutter, which overestimates of varying the individual damage costs is attenuated when the true rainfall amount, and by the blockage of low level summing over all of Switzerland. Another problem concerns beams, which leads to the underestimation of ground rainfall the absence of data about the type of damage. Therefore, we due to using only the beams aloft. Wüest et al. (2010) present assumed that all of the private costs are related to buildings. a method to obtain hourly precipitation fields by disaggre- This simplification is not an issue as long as the cost is re- gating the daily rain gauge measurements with higher reso- lated to objects located close to or inside the buildings (e.g. lution radar fields. If the timing of landslide occurrence was furniture, parked cars), but is more problematic, for exam- known, this dataset would be a valuable source of informa- ple, for costs related to loss of profits. However, we suppose tion. However, the product is not accompanied by uncertainty that the vast majority is related to buildings. As a result, this estimates. A possible solution could involve the generation model could be improved considerably if the type of damage of stochastic ensembles to represent the uncertainty of the was known. Thus, the damage assessment part has to be con- radar QPE product with respect to the automatic network of sidered more as an example than as a reference for further 76 meteorological stations. This approach was recently im- vulnerability assessment. plemented at MeteoSwiss (Germann et al., 2009) and could Regarding the total number of landslides, hit buildings and be a smart alternative to integrate ensembles of precipitation the amount of damage in each simulation, the variability of fields together with ensembles of lithological types into the the results follows more or less a normal or a log-normal landslide model. distribution (Fig. 14). This distribution reflects the uncer- When it comes to the damage cost assessment, due to the tainty induced by the lack of knowledge in the assessment lack of information on the number of affected buildings and of the consequences of a given precipitation event. Since the corresponding distribution of costs, a few important assump- model is based on the observed landslides, to redistribute the tions were made. The total number of affected buildings was landslides and assess the consequences, the number of mod- estimated by means of an impact probability and this number elled landslides using raw data is logically centred around was used to obtain a mean cost per hit building. The number the observed value. Gamma fit results tend, however, to be of hit buildings is an uncertain estimation since it depends on slightly lower than using raw data. When it comes to the the exact location of the landslides inside the cell. Indeed, we number of hit buildings, the expected value is hardly ever consider the probability of landsliding to be uniform within reproduced. Since the same concept of impact probability, a grid cell, or within the hazard zone if it exists in the cell with the same buffer value, is used to assess the expected (which is the case in most of the cells in which landslides number of hit buildings of the 2005 event and of the simula- actually occurred). For the latter case, it takes partly into ac- tion results, this should not be observed. By comparing the count the position of each element inside the cell, in particu- impact probability of the cells in which landslides occurred lar the position of the slopes that might fail relatively to the with those of the cells in which the landslides were mod- buildings. However, since the hazard map is only indicative, elled, we can observe that the cells in which landslides oc- no distinction is made between low hazard area and high haz- curred have higher impact probability. Different hypotheses ard area. As a result, if buildings are located relatively more can be made in order to explain this effect. First, we might on low hazard area, our estimation of the number of affected have neglected an important parameter for the localization of buildings would be too high and, as a consequence, the mean landslides which would be correlated to the built areas such price would be too low. as the repartition of the forested and non-forested areas, re- The distribution of costs was assumed to be exponential, distributing then the landslides in less populated areas. This which has a desirable long-tail property and is completely seems however to be in contradiction with the fact the grid defined by its mean value. Despite being only defined in cells covered by the preliminary hazard map have a lower terms of the average costs, the obtained variability is sup- impact probability than the ones where landslides occurred posed to adequately represent the reality. Nevertheless, with or than the cells of the entire Swiss territory (Fig. 15). A a mean cost of CHF 7211 per building, the probability to second interpretation could be related to the quality of the overcome CHF 500 000 is almost null (8 × 10−31, i.e. one inventory, which would be more complete in urbanized ar- case over 1 × 1030). Since the mean price of a building is eas. Correcting for this effect would imply a greater total around CHF 1 million, this value is quite low as we know number of landslides, with more landslides on areas with that at least one – but probably more – building has been low impact probability. The third one, which seems to us

Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 www.nat-hazards-earth-syst-sci.net/13/3169/2013/ P. Nicolet et al.: Shallow landslide’s stochastic risk modelling 3181 the most probable, would be that the urbanization tends to Moreover, the human influence on landslide susceptibility increase the susceptibility. Indeed, human activities can con- has to be evaluated carefully in a further step, since it ap- tribute to landslides, acting directly as a trigger or indirectly pears that the landslide locations are highly correlated with by destabilizing the slope, according to the classification of the buildings. This observation tends to indicate that the hu- Michoud et al. (2011). Since, the trigger of the 2005 event man influence on slope stability is substantial. Further devel- is undeniably the rain, human activities could have played opments are also conceivable to complete the risk analysis by a role only as destabilizing factors. Examples of landslides simulating stochastic rainfall events characterized by a given triggered by rain events on slopes destabilized by the mod- frequency and to analyse the consequences. This would re- ification of pore pressure induced by pipe leaks have been sult in a complete risk analysis able to provide the temporal observed in Switzerland, in Les Diablerets (Jaboyedoff and distribution of damage costs. Bonnard, 2007) and in Lutzenberg (Valley et al., 2004). This second example is especially interesting since the landslide occurred within an event involving hundreds of landslides Acknowledgements. This study was partially supported by the and debris flows, and since this particular landslide would Canton of Vaud Natural Hazard Unit and by the the Swiss Na- not have occurred, thanks to the authors, without the pipe tional Science Foundation project: Data mining for precipitation leak. Besides modifying pore pressure, pipe leaks can also nowcasting (PBLAP2-127713/1). We thank the Federal Office of destabilize slopes by weakening clay minerals (Preuth et al., Meteorology and Climatology for providing the data for the rainfall 2010). In addition, the degradation of an old canalization net- event of August 2005. Stéphane Losey, from the Federal Office work led to a landslide in 1930 in La Fouvrière hill in Lyon of the Environment, prepared and provided the Silvaprotect data, (France), killing 39 persons (Allix, 1930; Albenque, 1931). whereas Bernard Loup, from the same Office, provided the StorMe database extract. Both are also thanked for fruitful discussions. It would therefore be wise to include a parameter linked to Finally, we are grateful to the two anonymous referees that helped the buildings to take account of this effect. to improve the manuscript. All things considered, the model makes simplifications in order to assess the risk for a large area rather than to be pre- Edited by: P. Reichenbach cise at local scale. Indeed, the lack of knowledge and data at Reviewed by: two anonymous referees the sub-grid scale is balanced by the use of stochastic simu- lations, which allows one to obtain a probabilistic model for landslide occurrence and associated cost. References Such kind of model might be useful to provide a rapid damage estimation following a precipitation event. Indeed, Albenque, A.: L’éboulement de Lyon, Ann. Geogr., 40, 105–106, after a widespread event, the time needed by the insurance to 1931 (in French). process all claims is rather long and the exact consequences Allix, A.: L’éboulement de Fourvière (note préliminaire), Les might need several months, even years to be known. Apply- Études rhodaniennes, 6, 454–455, 1930 (in French). ing this model quickly after the event could provide a rough Apip, Takara, K., Yamashiki, Y., Sassa, K., Ibrahim, A., and estimation of the damage costs. In a second step, modelling Fukuoka, H.: A distributed hydrological–geotechnical model us- precipitation events assigned to a frequency could make pos- ing satellite-derived rainfall estimates for shallow landslide pre- sible the calculation of exceedance probability curves. De- diction system at a catchment scale, Landslides, 7, 237–258, velopments are also ongoing to assess the consequences of a doi:10.1007/s10346-010-0214-z, 2010. Baum, R. and Godt, J.: Early warning of rainfall-induced shallow landslide event for a road network with comparable models landslides and debris flows in the USA, Landslides, 7, 259–272, (Taylor et al., 2013). doi:10.1007/s10346-009-0177-0, 2010. Bollinger, D., Hegg, C., Keusen, H., and Lateltin, O.: Ursachenanal- yse der Hanginstabilitäten 1999, Bulletin für angewandte Geolo- 6 Conclusions gie, 5, 5–38, 2000 (in German). Caine, N.: The rainfall intensity – duration control of shallow land- This article proposes a model to assess the risk due to shallow slides and debris flows, Geogr. Ann. A, 62, 23–27, 1980. landslides for a large region using the data from the rainfall Campbell, R. H.: Soil Slips, Debris Flows, and Rainstorms in the event of 2005 in Switzerland. The first step assesses the dis- Santa Monica Mountains and Vicinity, Southern California, Pro- tribution of landslides with regard to precipitation and lithol- fessional paper 851, US Geological Survey, Washington, 1975. ogy. Then the landslides are redistributed in a second step Capparelli, G. and Versace, P.: FLaIR and SUSHI: two mathemat- ical models for early warning of landslides induced by rainfall, according to the relation obtained. Damage cost is obtained Landslides, 8, 67–79, doi:10.1007/s10346-010-0228-6, 2011. by means of an impact probability, which gives the probabil- Cardinali, M., Reichenbach, P., Guzzetti, F., Ardizzone, F., An- ity, if a landslide occurs, that it reaches a building. tonini, G., Galli, M., Cacciano, M., Castellani, M., and Sal- Some improvements have to be made to the model, to cor- vati, P.: A geomorphological approach to the estimation of land- roborate the relation obtained, and to improve the assessment slide hazards and risks in Umbria, Central Italy, Nat. Hazards of the impact probability, as well as the distribution of costs. Earth Syst. Sci., 2, 57–72, doi:10.5194/nhess-2-57-2002, 2002. www.nat-hazards-earth-syst-sci.net/13/3169/2013/ Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 3182 P. Nicolet et al.: Shallow landslide’s stochastic risk modelling

Cardinali, M., Galli, M., Guzzetti, F., Ardizzone, F., Reichen- De Quervain, F. and Frey, D.: Carta Geotecnica della Svizzera bach, P., and Bartoccini, P.: Rainfall induced landslides in De- 1 : 200 000: Foglio no 4 Bellinzona–St. Mortiz: Note esplicative, cember 2004 in south-western Umbria, central Italy: types, ex- Commissione Geotecnica Svizzera, 2nd Edn., 1967 (in Italian tent, damage and risk assessment, Nat. Hazards Earth Syst. Sci., and German). 6, 237–260, doi:10.5194/nhess-6-237-2006, 2006. De Quervain, F. and Hofmänner, F.: Carte Géotechnique de la Su- Carrara, A., Cardinali, M., Detti, R., Guzzetti, F., Pasqui, V., and isse 1 : 200 000: Feuille no 1 Neuchâtel–Bern–Basel: Texte ex- Reichenbach, P.: GIS techniques and statistical models in eval- plicatif, Commission Géotechnique Suisse, 2nd Edn., 1964 (in uating landslide hazard, Earth Surf. Processes, 16, 427–445, French and German). doi:10.1002/esp.3290160505, 1991. De Vita, P., Reichenbach, P., Bathurst, J. C., Borga, M., Crosta, G., Cascini, L. and Versace, P.: Relationship between rainfall and land- Crozier, M., Glade, T., Guzzetti, F., Hansen, A., and Wa- slide in a gneissic cover, in: Proceedings of the 5th International sowski, J.: Rainfall-triggered landslides: a reference list, Environ. Symposium on Landslides, Lausanne, Switzerland, 10–15 July Geol., 35, 219–233, doi:10.1007/s002540050308, 1998. 1988, vol. 1, edited by: Bonnard, C., 565–570, 1988. D’Odorico, P., Fagherazzi, S., and Rigon, R.: Potential for land- Catani, F., Casagli, N., Ermini, L., Righini, G., and Menduni, G.: sliding: dependence on hyetograph characteristics, J. Geophys. Landslide hazard and risk mapping at catchment scale in the Res.-Earth, 110, nF01007, doi:10.1029/2004JF000127, 2005. Arno River basin, Landslides, 2, 329–342, doi:10.1007/s10346- Einstein, H. H.: Special lecture: Landslide risk assessment proce- 005-0021-0, 2005. dure, in: Proceedings of the 5th International Symposium on Corominas, J. and Moya, J.: Reconstructing recent landslide Landslides, edited by: Bonnard, C., Lausanne, Switzerland, 2, activity in relation to rainfall in the Llobregat River basin, 1075–1090, 1988. Eastern Pyrenees, Spain, Geomorphology, 30, 79–93, FOEN: Naturereigniskataster – StorMe, available at: http://www. available at: http://www.sciencedirect.com/science/article/ bafu.admin.ch/naturgefahren/11421/11426/index.html, last up- B6V93-3YS8JHH-8/2/58792b4a7097ce611f0586788e2c2a9f, date: 21.08.2012, last access: 15.08.2013 (in German). 1999. Foresti, L. and Pozdnoukhov, A.: Exploration of alpine orographic Corominas, J. and Moya, J.: A review of assessing landslide fre- precipitation patterns with radar image processing and clustering quency for hazard zoning purposes, Eng. Geol., 102, 193– techniques, Meteorol. Appl., 19, 407–419, doi:10.1002/met.272, 213, doi:10.1016/j.enggeo.2008.03.018, special issue: Landslide 2012. Susceptibility, Hazard and Risk Zoning for Land Use Plan- Foresti, L., Pozdnoukhov, A., Tuia, D., and Kanevski, M.: Extreme ning, available at: http://www.sciencedirect.com/science/article/ precipitation modelling using geostatistics and machine learning pii/S0013795208001841, last access: 21 March 2013, 2008. algorithms, in: geoENV VII – Geostatistics for Environmental Crosta, G.: Regionalization of rainfall thresholds: an aid to Applications, Quant. Geol. Geostat. 16, 41–52, 2010. landslide hazard evaluation, Environ. Geol., 35, 131–145, Foresti, L., Kanevski, M., and Pozdnoukhov, A.: Kernel-based map- doi:10.1007/s002540050300, 1998. ping of orographic rainfall enhancement in the Swiss Alps as Crosta, G. B. and Dal Negro, P.: Observations and modelling of detected by weather radar, IEEE T. Geosci. Remote, 50, 2954– soil slip-debris flow initiation processes in pyroclastic deposits: 2967, 2012. the Sarno 1998 event, Nat. Hazards Earth Syst. Sci., 3, 53–69, Gabella, M., Bolliger, M., Germann, U., and Perona, G.: Large sam- doi:10.5194/nhess-3-53-2003, 2003. ple evaluation of cumulative rainfall amounts in the Alps using a Crosta, G. B. and Frattini, P.: Distributed modelling of shallow land- network of three radars, Atmos. Res., 77, 256–268, 2005. slides triggered by intense rainfall, Nat. Hazards Earth Syst. Sci., Galli, M. and Guzzetti, F.: Landslide vulnerability criteria: a case 3, 81–93, doi:10.5194/nhess-3-81-2003, 2003. study from umbria, central Italy, Environ. Manage., 40, 649–665, Crozier, M. J.: Prediction of rainfall-triggered landslides: doi:10.1007/s00267-006-0325-4, 2007. a test of the Antecedent Water Status Model, Earth Gamma, P.: dfwalk — Ein Murgang-Simulationsprogramm zur Surf. Processes, 24, 825–833, doi:10.1002/(SICI)1096- Gefahrenzonierung, Ph.D. thesis, University of Bern, Switzer- 9837(199908)24:9<825::AID-ESP14>3.0.CO;2-M, 1999. land, 2000 (in German). Crozier, M. J.: Multiple-occurrence regional landslide events in Geotest, Geo7 and Oeko-B: SilvaProtect-CH: Schutzwaldhin- New Zealand: hazard management issues, Landslides, 2, 247– weiskarte der Schweiz: Modul EVENT (Los 1: Prozess Stein- 256, doi:10.1007/s10346-005-0019-7, 2005. schlag/Blockschlag und Los 2: Prozesse Hangmure/Rutschung, Crozier, M. J., Eyles, R. J., Marx, S. L., McConchie, J. A., Murgang), Zollikofen, Switzerland, 2006. and Owen, R. C.: Distribution of landslips in the Wairarapa Germann, U., Galli, G., Boscacci, M., and Bolliger, M.: Radar pre- hill country, New Zeal. J. Geol. Geop., 23, 575–586, cipitation measurement in mountainous region, Q. J. Roy. Me- doi:10.1080/00288306.1980.10424129, 1980. teor. Soc., 132, 1669–1692, 2006. De Quervain, F. and Frey, D.: Geotechnische Karte der Schweiz Germann, U., Berenguer, M., Sempere-Torres, D., and Zappa, M.: 1 : 200 000: Blatt Nr. 2 Luzern–Zürich–St. Gallen–Chur: Er- REAL – ensemble radar precipitation estimation for hydrology läuterungen, Schweizerischen Geotechnischen Kommission, 2nd in mountainous region, Q. J. Roy. Meteor. Soc., 135, 445–456, edition, 1963 (in German). 2009. De Quervain, F. and Frey, D.: Carte Géotechnique de la Suisse 1 : Ghosh, S., van Westen, C. J., Carranza, E. J. M., and Jetten, V. G.: 200 000: Feuille no 3 Genève–Lausanne–Sion: Texte explicatif, Integrating spatial, temporal, and magnitude probabilities for Commission Géotechnique Suisse, 2nd Edn., 1965 (in French medium-scale landslide risk analysis in Darjeeling Himalayas, and German). India, Landslides, 9, 371–384, doi:10.1007/s10346-011-0304-6, 2012.

Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 www.nat-hazards-earth-syst-sci.net/13/3169/2013/ P. Nicolet et al.: Shallow landslide’s stochastic risk modelling 3183

Glade, T.: Establishing the frequency and magnitude of landslide- slides – Glissements de terrain, Proceedings of the seventh inter- triggering rainstorm events in New Zealand, Environ. Geol., 35, national symposium on landslides, 17–21 June 1996, Trondheim, 160–174, doi:10.1007/s002540050302, 1998. Norway, edited by: Senneset, K., Balkema, Rotterdam, 1996. Glade, T., Crozier, M., and Smith, P.: Applying probability determi- Mathai, A. M.: An Introduction to Geometrical Probability: Dis- nation to refine landslide-triggering rainfall thresholds using an tributional Aspects with Applications, Gordon and Breach, empirical “Antecedent Daily Rainfall Model”, Pure Appl. Geo- Newark, USA, 1999. phys., 157, 1059–1079, doi:10.1007/s000240050017, 2000. Matsushi, Y. and Matsukura, Y.: Rainfall thresholds for shallow Godt, J., Baum, R., Savage, W., Salciarini, D., Schulz, W., landsliding derived from pressure-head monitoring: cases with and Harp, E.: Transient deterministic shallow landslide mod- permeable and impermeable bedrocks in Boso Peninsula, Japan, eling: Requirements for susceptibility and hazard assess- Earth Surf. Processes, 32, 1308–1322, doi:10.1002/esp.1491, ments in a GIS framework, Eng. Geol., 102, 214–226, 2007. doi:10.1016/j.enggeo.2008.03.019, 2008. Merz, B., Kreibich, H., Thieken, A., and Schmidtke, R.: Estimation Greco, R., Giorgio, M., Capparelli, G., and Versace, P.: uncertainty of direct monetary flood damage to buildings, Nat. Early warning of rainfall-induced landslides based on em- Hazards Earth Syst. Sci., 4, 153–163, doi:10.5194/nhess-4-153- pirical mobility function predictor, Eng. Geol., 153, 67–79, 2004, 2004. doi:10.1016/j.enggeo.2012.11.009, 2013. Michoud, C., Derron, M.-H., Jaboyedoff, M., Nadim, F., and Gullà, G., Antronico, L., Iaquinta, P., and Terranova, O.: Leroi, E.: Classification of landslide-inducing anthropogenic ac- Susceptibility and triggering scenarios at a regional tivities, in: 5th Canadian Conference on Geotechnique and Nat- scale for shallow landslides, Geomorphology, 99, 39–58, ural Hazards, 15–17 May 2011, Kelowna, BC, Canada, 10 pp., doi:10.1016/j.geomorph.2007.10.005, 2008. 2011. Guzzetti, F., Peruccacci, S., Rossi, M., and Stark, C.: The rainfall Montgomery, D. and Dietrich, W.: A physically based model for the intensity–duration control of shallow landslides and debris flows: topographic control on shallow landsliding, Water Resour. Res., an update, Landslides, 5, 3–17, doi:10.1007/s10346-007-0112-1, 30, 1153–1171, 1994. 2008. Mueller, R. and Loew, S.: Predisposition and cause of the catas- Hilker, N., Aller, D., and Hegg, C.: Ereignisanalyse Hochwasser trophic landslides of August 2005 in Brienz (Switzerland), 2005: Teil 1 – Prozesse, Schäden und erste Einordnung, chap. Swiss J. Geosci., 102, 331–344, doi:10.1007/s00015-009-1315- Schäden, Bundesamt für Umwelt BAFU, edited by: Bezzola, G. 3, 2009. R. and Hegg, C., Eidg. Forschungsanstalt WSL, Bern and Bir- Nguyen, H., Wiatr, T., Fernández-Steeger, T., Reicherter, K., Ro- mensdorf, Switzerland, 127–148, 2007 (in German). drigues, D., and Azzam, R.: Landslide hazard and cascading Hilker, N., Badoux, A., and Hegg, C.: The Swiss flood and landslide effects following the extreme rainfall event on Madeira Island damage database 1972–2007, Nat. Hazards Earth Syst. Sci., 9, (February 2010), Nat. Hazards, 65, 635–652, 2013. 913–925, doi:10.5194/nhess-9-913-2009, 2009. Pack, R., Tarboton, D. G., and Goodwin, C. N.: The SINMAP ap- Iida, T.: A stochastic hydro-geomorphological model for shal- proach to terrain stability mapping, in: 8th Congress of the Inter- low landsliding due to rainstorm, Catena, 34, 293–313, national Association of Engineering Geology, 21–25 September available at: http://www.sciencedirect.com/science/article/ 1998, Vancouver, British Columbia, Canada, 8 pp., 1998. B6VCG-3VTYVWW-5/1/272affa188fa14bbfd4d7290700da4c3 Preuth, T., Glade, T., and Demoulin, A.: Stability analysis of a (last access: 21 March 2013), 1999. human-influenced landslide in eastern Belgium, Geomorphol- Iida, T.: Theoretical research on the relationship between return pe- ogy, 120, 38–47, doi:10.1016/j.geomorph.2009.09.013, 2010. riod of rainfall and shallow landslides, Hydrol. Process., 18, 739– Raetzo, H. and Rickli, C.: Ereignisanalyse Hochwasser 2005: Teil 1 756, doi:10.1002/hyp.1264, 2004. – Prozesse, Schäden und erste Einordnung, chap. Rutschungen, Jaboyedoff, M. and Bonnard, C.: Report on landslide impacts and edited by: Bezzola, G. R. and Hegg, C., Bundesamt für Umwelt practices in Switzerland: Need for new risk assessment strate- BAFU, Eidg. Forschungsanstalt WSL, Bern and Birmensdorf, gies, in: The 2007 International Forum on Landslide Disaster Switzerland, 195–210, 2007 (in German). Management, edited by: Ho, K. and Li, V., Geotechnical Divi- Remondo, J., Bonachea, J., and Cendrero, A.: A statistical approach sion, The Hong Kong Institution of Engineers, Hong Kong, 79– to landslide risk modelling at basin scale: from landslide suscep- 97, 2007. tibility to quantitative risk assessment, Landslides, 2, 321–328, Jaiswal, P., van Westen, C. J., and Jetten, V.: Quantitative estimation doi:10.1007/s10346-005-0016-x, 2005. of landslide risk from rapid debris slides on natural slopes in the Rickli, C., Raetzo, H., McArdell, B., and Presler, J.: Ereignisanal- Nilgiri hills, India, Nat. Hazards Earth Syst. Sci., 11, 1723–1743, yse Hochwasser 2005: Teil 2 – Analyse von Prozessen, Massnah- doi:10.5194/nhess-11-1723-2011, 2011. men und Gefahrengrundlagen, chap. Hanginstabilitäten, edited Johnson, N. L., and Kotz, S.: Continuous univariate distributions-1, by: Bezzola, G. R. and Hegg, C., Bundesamt für Umwelt BAFU, John Wiley & Sons, 1970. Eidg. Forschungsanstalt WSL, Bern and Birmensdorf, Switzer- Kanevski, M., Pozdnoukhov, A., and Timonin, V.: Machine Learn- land, 97–116, 2008 (in German). ing for Spatial Environmental Data: Theory, Applications and Ross, S. M.: A first course in probability, 8th Edn., Pearson Educa- Software, EPFL Press, Lausanne, Switzerland, 2009. tion, Upper Saddle River, USA, 2010. Kaplan, S.: The Words of Risk Analysis, Risk Anal, 17, 407–417, Rotach, M., Appenzeller, C., and Albisser, P. E.: Starknieder- doi:10.1111/j.1539-6924.1997.tb00881.x, 1997. schlagsereignis August 2005, Arbeitsberichte 211, Me- Liener, S., Kienholz, H., Liniger, M., and Krummenacher, B.: teoSchweiz, Zürich, Switzerland, 2006 (in German). SLIDISP - A procedure to locate landslide prone areas, in: Land-

www.nat-hazards-earth-syst-sci.net/13/3169/2013/ Nat. Hazards Earth Syst. Sci., 13, 3169–3184, 2013 3184 P. Nicolet et al.: Shallow landslide’s stochastic risk modelling

Seed, A. W., Srikanthan, R., and Menabde, M.: A space and time van Westen, C., van Asch, T., and Soeters, R.: Landslide hazard and model for design storm rainfall, J. Geophys. Res.-Atmos., 104, risk zonation – why is it still so difficult?, B. Eng. Geol. Environ., 31623–31630, doi:10.1029/1999JD900767, 1999. 65, 167–184, doi:10.1007/s10064-005-0023-0, 2006. SGTK: Datenbeschreibung der geotechnischen, lithologisch- von Ruette, J., Papritz, A., Lehmann, P., Rickli, C., and Or, D.: Spa- petrographischen Polygone, Schweizerische Geotechnische tial statistical modeling of shallow landslides – validating predic- Kommission, Zürich, Switzerland, 2012 (in German). tions for different landslide inventories and rainfall events, Geo- Sideris, I. V., Gabella, M., Erdin, R., and Germann, U.: Real-time morphology, 133, 11–22, doi:10.1016/j.geomorph.2011.06.010, radar-raingauge merging using spatiotemporal co-kriging with 2011. external drift in the alpine terrain of Switzerland, Q. J. Roy. Me- Weisstein, E. W.: Clean Tile Problem, MathWorld – A Wol- teor. Soc., doi10.1002/qj.2188, in press, 2013. fram Web Resource, available at: http://mathworld.wolfram. Tarolli, P., Borga, M., Chang, K.-T., and Chiang, S.-H.: Model- com/CleanTileProblem.html (last access: 15 August 2013), ing shallow landsliding susceptibility by incorporating heavy 2013. rainfall statistical properties, Geomorphology, 133, 199–211, Whittaker, K. A. and McShane, D.: Comparison of slope instability doi:10.1016/j.geomorph.2011.02.033, 2011. screening tools following a large storm event and application to Taylor, F. E., Santangelo, M., Marchesini, I. and Malamud,B. D.: forest management and policy, Geomorphology, 145–146, 115– A GRASS GIS Semi-Stochastic Model for Evaluating the Prob- 122, doi:10.1016/j.geomorph.2012.01.001, 2012. ability of Landslides Impacting Road Networks in Collazzone, Wieczorek, G. F.: Landslide triggering mechanisms, in: Landslides Central Italy, Abstr., EGU2013-7624, EGU General Assembly Investigation and Mitigation, edited by: Turner, A. K. and Schus- 2013, Vienna, Austria, 2013. ter, R. L., Special Report 247, Transportation Research Board, Trümpy, R.: Geology of Switzerland, Part A: An outline of the Ge- National Research Council, National Academy Press, Washing- ology of Switzerland, Wepf & Co. Verlag, Basel, Switzerland, ton, DC, 76–90, 1996. 1980. WSL: Swiss flood and landslide damage database, avail- University of Bern and FOWG: Geological Map of Switzerland able at: http://www.wsl.ch/fe/gebirgshydrologie/HEX/projekte/ 1 : 500 000, Swisstopo, Bern, Switzerland, ISBN 3-906723-39- schadendatenbank/index_EN (last access: 26 February 2013), 9, 2005a. 2012. University of Bern and FOWG: Tectonic Map of Switzerland 1 : Wüest, M., Frei, C., Altenhoff, A., Hagen, M., Litschi, M., and 500 000, Swisstopo, Bern, Switzerland, ISBN 3-906723-56-9, Schär, C.: A gridded hourly precipitation dataset for Switzerland 2005b. using rain-gauge analysis and radar-based disaggregation, Int. J. Valley, B., Thuro, K., Eberhardt, E., and Raetzo, H.: Geological and Climatol., 30, 1764–1775, 2010. geotechnical investigation of a shallow translational slide along Yu, F.-C., Chen, T.-C., Lin, M.-L., Chen, C.-Y., and Yu, W.-H.: a weathered rock/soil contact for the purpose of model develop- Landslides and rainfall characteristics analysis in Taipei City ment and hazard assessment, in: Proceedings of the 9th Interna- during the Typhoon Nari event, Nat. Hazards, 37, 153–167, tional Symposium on Landslides, Rio de Janeiro, 28 June–2 July doi:10.1007/s11069-005-4661-0, 2006. 2004, edited by: Lacerda, W. A., Ehrlich, M., Fontoura, S. A. B., and Sayão, A. S. F., A. A. Balkema, 385–391, 2004.

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