Shallow Landslides Stochastic Risk Modelling

EGU Journal Logos (RGB) Open Access Open Access Open Access Advances in Annales Nonlinear Processes Geosciences Geophysicae in Geophysics icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Open Access Open Access Nat. Hazards Earth Syst. Sci. Discuss.,Natural 1, 747–791, Hazards 2013 Natural Hazards www.nat-hazards-earth-syst-sci-discuss.net/1/747/2013/ and Earth System doi:10.5194/nhessd-1-747-2013and Earth System NHESSD Sciences Sciences © Author(s) 2013. CC Attribution 3.0 License. 1, 747–791, 2013 Discussions Open Access Open Access Atmospheric Atmospheric This discussion paper is/has been under review for the journal Natural Hazards and Earth Chemistry Chemistry Shallow landslides System Sciences (NHESS). Please refer to the corresponding ﬁnal paper in NHESS if available. and Physics and Physics stochastic risk Discussions modelling Open Access Open Access Atmospheric Atmospheric P. Nicolet et al. Shallow landslidesMeasurement stochastic riskMeasurement Techniques Techniques modelling based on the precipitationDiscussions Open Access Open Access Title Page Biogeosciences event of AugustBiogeosciences 2005 in Switzerland: Abstract Introduction Discussions results and implications Conclusions References Open Access Open Access Climate Tables Figures P. Nicolet1, L. Foresti1,2, O. CasparClimate1, and M. Jaboyedoﬀ1 of the Past of the Past 1 Discussions Center of Research on Terrestrial Environment, University of Lausanne, Lausanne, J I Open Access Switzerland Open Access 2 Centre for Australian WeatherEarth and ClimateSystem Research, Bureau of Meteorology,Earth System Melbourne, J I Australia Dynamics Dynamics Back Close Discussions Received: 28 February 2013 – Accepted: 12 March 2013 – Published: 28 March 2013 Full Screen / Esc Open Access Correspondence to: P. Nicolet ([email protected])Geoscientific Geoscientific Open Access Instrumentation Instrumentation Published by Copernicus PublicationsMethods on and behalf of the European GeosciencesMethods Union. and Printer-friendly Version Data Systems Data Systems Interactive Discussion Discussions Open Access Open Access Geoscientific Geoscientific Model Development Model Development747 Discussions Open Access Open Access Hydrology and Hydrology and Earth System Earth System Sciences Sciences Discussions Open Access Open Access Ocean Science Ocean Science Discussions Open Access Open Access Solid Earth Solid Earth Discussions Open Access Open Access

The Cryosphere The Cryosphere Discussions icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Abstract NHESSD Due to their relatively unpredictable characteristics, shallow-landslides represent a risk for human infrastructures. Multiple shallow-landslides can be triggered by large spread 1, 747–791, 2013 precipitation events. The event of August 2005 in Switzerland is used in order to pro- 5 pose a risk model to predict the expected number of landslides based on the precipi- Shallow landslides tation amounts and lithological units. The spatial distribution of rainfall is characterized stochastic risk by blending data coming from operational weather radars and a dense network of rain modelling gauges with an artiﬁcial neural network. Lithologies are grouped into four main units, with similar characteristics. Then, from a landslide inventory containing more than 5000 P. Nicolet et al. 10 landslides, a probabilistic relation linking the precipitation amount and the lithology to the number of landslides in a 1 km2 cell, is obtained. In a next step, this relation is used to randomly redistribute the landslides using Monte-Carlo simulations. The prob- Title Page

ability for a landslide to reach a building is assessed using stochastic geometry and Abstract Introduction the damage cost is assessed from the estimated mean damage cost using an expo- 15 nential distribution to account for the variability. Although the outputs reproduce well Conclusions References the number of landslides, the number of aﬀected buildings is not reproduced by the Tables Figures model. This seems to results from the human inﬂuence on landslide occurrence. Such a model might be useful to characterize the risk resulting from shallow-landslides and its variability. J I

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20 1 Introduction Back Close

Shallow landslides often represent a risk for housing, people and infrastructures. Com- Full Screen / Esc pared with deep-seated landslides, shallow landslides usually trigger spontaneously, flow at higher speed and are not likely to affect repeatedly the same location due to Printer-friendly Version the changes in soil stability conditions (e.g. van Westen et al., 2006; Corominas and Interactive Discussion 25 Moya, 2008). Consequently, most research efforts focus on the prediction of their exact location and, less frequently, their timing. Several methods for the mapping of landslide 748 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion susceptibility exist and are based on physical models (e.g. Pack et al., 1998; Mont- gomery and Dietrich, 1994; Godt et al., 2008) or statistical approaches (e.g. Carrara NHESSD et al., 1991). Since rainfall has been recognized as being a frequent triggering mech- 1, 747–791, 2013 anism (e.g. Wieczorek, 1996), many authors, following Campbell (1975) and Caine 5 (1980), proposed early-warning systems based upon criteria of precipitation intensity and duration (e.g. Guzzetti et al., 2008). Other studies also use the antecedent pre- Shallow landslides cipitation as a proxy for considering the groundwater level preceding the precipitation stochastic risk event (Crozier, 1999; Glade et al., 2000). More direct approaches are based upon the modelling real-time monitoring of soil moisture (Matsushi and Matsukura, 2007; Baum and Godt, P. Nicolet et al. 10 2010) or the use of transfer functions to estimate the soil water content from precipitation measurements (Cascini and Versace, 1988; Capparelli and Versace, 2011; Greco et al., 2013). Title Page 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; Abstract Introduction 15 Cardinali et al., 2006; Gulla` et al., 2008), Spain (Corominas and Moya, 1999), USA (Campbell, 1975; Whittaker and McShane, 2012), New Zealand (Crozier et al., 1980; Conclusions References

Glade, 1998; Crozier, 2005), Taiwan (Yu et al., 2006), the Portuguese island of Madeira Tables Figures (Nguyen et al., 2013) and in Switzerland (Bollinger et al., 2000). Despite the numerous contributions to the physical understanding of the phe- J I 20 nomenon itself (for a broad reference list, although not up to date, see De Vita et al., 1998), studies on the assessment of landslide risk are less commonly found in the lit- J I erature. Examples of quantitative risk analysis (QRA) at regional scale can be found in Back Close Cardinali et al. (2002), Remondo et al. (2005) or Catani et al. (2005). However, these studies provide a mean annual risk with no information on the expected distribution of Full Screen / Esc 25 annual costs. More recently, applications of regional scale QRA providing exceedance probabilities were presented in Jaiswal et al. (2011) and Ghosh et al. (2012). Although, Printer-friendly Version most of the QRA methodologies are developed for local or regional scales, some of them, as for example Catani et al. (2005), might be applied to a larger area. Interactive Discussion

749 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Switzerland was affected in August 2005 by a rainfall event with measured precipitation reaching 324 mm in 6 days. Although floods were the main damage cause, more NHESSD than 5000 landslides were reported (Raetzo and Rickli, 2007). Landslide-induced dam- 1, 747–791, 2013 age has been estimated by Hilker et al. (2007) at 92 million Swiss francs (USD 99 5 million; debris-flows not included) and represents 4.5 % of the total damage cost. As already mentioned by Jaboyedoff and Bonnard (2007) and by Rickli et al. (2008), Shallow landslides landslide density was highly correlated with the total precipitation amount. Following stochastic risk their ideas, this article proposes a risk model for shallow landslides based on the event modelling of August 2005. The input parameters of the model include a rainfall and a lithological P. Nicolet et al. 10 map. The map of 6 day rainfall accumulations is constructed by interpolating a high resolution rain gauge network using weather radar data as external drift. A geotechnical map is interpreted in order to group different units into 4 main lithological settings. The Title Page expected number of landslides is predicted as a function of rainfall level conditional to the lithological type. An intersection probability concept is then employed to predict the Abstract Introduction 15 potential number of landslides affecting buildings and the corresponding damage cost. The paper is structured as follows. Section 2 details the rainfall event of August Conclusions References

2005 in Switzerland both from a meteorological and lithological viewpoint. Section 3 Tables Figures explains the methodology to assess the landslide probability as a function of rainfall accumulation and lithological context. Section 4 presents the risk analysis results in J I 20 terms of expected number of landslides, number of aﬀected buildings and associated cost. Finally, Sects. 5 and 6 discuss and conclude the paper. J I

Back Close 2 The rainfall event of August 2005 in Switzerland Full Screen / Esc 2.1 Study area Printer-friendly Version The study area covers the entire Swiss territory (around 42 000 km2), which extends Interactive Discussion 25 from the Jura mountains in the North-West, to the Alps, in the South-East, through the Molassic Plateau, where most of the population is concentrated. Special attention is 750 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion given to the location where most of the landslides occurred, which is the central part of Switzerland, between the cities of Bern and Lucerne (Fig. 1). Landslides occurred NHESSD in the tectonic units described below (Trumpy¨ , 1980; University of Bern and FOWG, 1, 747–791, 2013 2005a,b), which are listed along a northwest-southeast direction (perpendicularly to 5 the geological structures): Shallow landslides – Upper Freshwater Molasse from Middle and early Upper Miocene (consisting of stochastic risk ﬂoodplains sediments including puddings, sandstones and silty shales). modelling – Other types of Molasse (narrower areas of Upper Marine Molasse, Lower Fresh- water Molasse and Lower Marine Molasse, the lower part of this series being in P. Nicolet et al. 10 Subalpine position).

– Subalpine Flysch. Title Page

– Upper Penninic Flysch (Schlieren Flysch). Abstract Introduction

– Ultrahelvetic and Helvetic Nappes (including tertiary shallow marine formation and Conclusions References Cretaceous Limestones from the Wildhorn nappe and Jurassic Limestones from Tables Figures 15 the Axen nappe). Soils (regolith) and loose materials cover most of the time the bedrock. Most of these J I shallow and superficial formations have not been mapped, except for the cases where the formation reaches a sufficient extension or thickness to be considered relevant J I at the map scale. This is for example the case of morainic material deposited by the Back Close 20 glaciations during the Quaternary, which is visible at several places, especially on the Plateau (Trumpy¨ , 1980). The properties of the local soils strongly depend on the un- Full Screen / Esc derlying bedrock. Printer-friendly Version 2.2 Description of the precipitation event Interactive Discussion The rainfall event of August 2005 in central and eastern Switzerland resulted in se- 25 vere damage due to flooding and induced slope instabilities (Rotach et al., 2006). The 751 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion presence of the Alps played a key role in controlling the spatial distribution of rainfall due to orographic precipitation enhancement processes. Persistent precipitation NHESSD patterns were mostly found on the exposed upwind slopes under northerly and north- 1, 747–791, 2013 easterly flow conditions as studied by Foresti and Pozdnoukhov (2011) and Foresti 5 et al. (2012). In particular, the stratiform precipitation was locally enhanced by smaller scale orographic features leading to persistent initiation and enhancement of the em- Shallow landslides bedded convection. stochastic risk The most intense period of the event was observed between 21 and 22 August. modelling Driven by cyclonic conditions during the first day, the moist air from the Mediterranean P. Nicolet et al. 10 sea circumvented the Austrian Alps and started approaching slightly crosswise the northern slopes of the Swiss Alps from the east. The mesoscale flows gradually turned from easterly to northerly conditions during the second day. The reduced supply of Title Page air moisture was compensated by a stronger upslope rainfall enhancement which extended the duration of precipitation. The return period for 48 h rainfall accumulations Abstract Introduction 15 largely exceeded 100 yr at several weather stations mostly located in the Berner Ober- land (Rotach et al., 2006). It is worth mentioning that the uncertainty of this estimation Conclusions References

is quite important as an event of such intensity was never observed in the past at the Tables Figures considered weather stations.

2.3 Landslide inventory J I

J I 20 As a consequence of this extreme rainfall event, many shallow landslides were triggered, mainly in the Entlebuch part of Lucerne canton and in the Bern canton. Some Back Close deep-seated landslides were observed as well and are mainly located farther south- Full Screen / Esc east. A landslide inventory has been collected by Raetzo and Rickli (2007) from cantonal authorities information and contains 5756 landslides (Fig. 1). Although some ad- Printer-friendly Version 25 ditional attributes such as the exact timing have been registered for some of the landslides, we only dispose of the version provided in the above publication and, as a result, Interactive Discussion we only know the approximate location. The uncertainty about the location of landslides complicates the analysis of geological context. 752 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Statistics on the landslides can be found in Raetzo and Rickli (2007) and in Rickli et al. (2008) and investigations on specific sites in Mueller and Loew (2009) and von NHESSD Ruette et al. (2011). The travel distance of shallow landslides has been analyzed for 1, 747–791, 2013 148 cases and ranges from a few meters up to 500 m (Raetzo and Rickli, 2007). Around 5 75 % of the landslides traveled less than 100 m and 90 % less than 200 m (Fig. 2). Shallow landslides 2.4 Damage stochastic risk modelling According to the Swiss Federal Institute for Forest, Snow and Landscape Research WSL, the 2005 event has been the most costly since the beginning of the collection of P. Nicolet et al. damage data in 1972, with a total damage cost estimated at 1.87 billion swiss francs 10 (around USD 2 billion). On the other hand, in spite of being the most important event recorded, other years have been equally or more damaging regarding landslides in the Title Page past 40 yr (Hilker et al., 2009; WSL, 2012). Abstract Introduction Hilker et al. (2009) divided the damage values into three categories according to the cause, namely floods, debris flows and landslides (including mud-flows). Land- Conclusions References 15 slides represent around 4.5 % of the total cost and affected private properties (22 %, CHF 16.3 million) and public infrastructures (88 %, CHF 75.6 million) (Hilker et al., Tables Figures 2007). Private damage includes damage to buildings as well as furnitures, vehicles, other property damage and loss of profits. Comparatively, public damage includes dam- J I age to waterways, roads (except small ones), rail, farming and forests. In addition to J I 20 economic consequences, six casualties are to be deplored. Back Close

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Interactive Discussion

753 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 3 Risk modeling methodology NHESSD 3.1 Introduction 1, 747–791, 2013 The annual risk to property is usually evaluated with the following equation (Dai et al., 2002; Fell et al., 2005): Shallow landslides stochastic risk 5 R(PD) = P (L) × P (S|L) × V (P |S) × E (1) modelling where L denotes the landslide, P the element at risk (property) and S the impact. P (L) P. Nicolet et al. represents the landslide frequency, P (S|L) the spatial probability of the landslide reaching the element at risk, V (P |S) the vulnerability of the element at risk to the landslide

10 impact and E the element at risk value. Title Page In the case studies considered in this article, this equation is not used directly since a single precipitation event is used as an input. However, since this event is used to Abstract Introduction redistribute the landslides according to the precipitation event, P (L) is not completely Conclusions References left out. In a ﬁrst phase, the spatial distribution of the event rainfall accumulation is es- 15 timated using data from a dense network of rain gauges and addional C-band weather Tables Figures radars (Sect. 3.2). The second phase studies the statistical distribution of landslides

as a function of precipitation intensity and lithological type (Sect. 3.3) and is used to J I estimate the probability of landsliding P (L). It must be mentioned that P (L) should also account for the climatological frequency, which is the probability of the precipitation J I

20 event to occur. As the analyses consider only one single event, this probability was set Back Close to 1 and the term P (L) is only estimated from the distribution of landslides conditional to the precipitation event. P (S|L) is assessed using principles of stochastic geometry, Full Screen / Esc and represents the probability of buildings to be affected by circular landslides within a given cell. This term partially accounts for P (L) since the exact location of the land- Printer-friendly Version 25 slides within the cell is randomly assigned at this step. The separate estimation of the terms V (P |S) and E is not possible as the cost of damages is assessed directly (see Interactive Discussion Sect. 3.4). 754 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 3.2 Spatial analysis of rainfall NHESSD MeteoSwiss operates an automatic network of 76 weather stations and a dense network of additional 363 rain gauges. The automatic network measures rainfall with 1, 747–791, 2013 a temporal resolution of 10 min while the second only reports daily accumulations from 5 05:40 to 05:40 UTC of the next calendar day. An additional network of 3 C-band radars Shallow landslides is used to measure precipitation with higher spatial resolution. The operational radar stochastic risk data processing chain for quantitative precipitation estimation (QPE) at MeteoSwiss modelling includes the removal of ground clutter, correction for the vertical profile of reflectivity in connection with the bright band effect, climatological rain gauge adjustment, the inter- P. Nicolet et al. 10 polation from polar coordinates to a Cartesian grid, and the use of a fixed climatological Z–R relationship (refer to Germann et al., 2006, for more details). A geostatistical method for real-time bias adjustment with rain gauges was only recently implemented Title Page

by Sideris et al. (2013). For long term evaluation of the radar QPE accuracy against Abstract Introduction rain gauges refer to Gabella et al. (2005). The radar QPE product used in this paper is 2 2 15 a 1 km ×1 km grid of the rainfall accumulation during the period 18–23 August 2005. Conclusions References Despite these corrections, the product still contains residual ground clutter and bi- Tables Figures ases due to the blockage of low level radar beams, in particular in the inner Alpine valleys. To partially account for these issues, an artiﬁcial neural network was applied to blend the radar-based QPE map with the rain gauge rainfall accumulations. A 3-H- J I

20 1 multiLayer perceptron (MLP) was trained to predict the rainfall amount observed at J I the rain gauges as a function of 3 variables: the geographical location represented by the Swiss Easting and Northing coordinates and the radar QPE product which acts Back Close

as an external drift. The geographical coordinates account for the observed biases be- Full Screen / Esc tween rain gauges and radar-based QPE, which show a signiﬁcant spatial dependence. 25 A conjugate gradient algorithm was employed to train the network. A low number of hid- Printer-friendly Version den neurons H was chosen to obtain a smooth representation of the spatial rainfall biases. The optimal model was selected by minimizing the leave-one-out cross-validation Interactive Discussion root-mean square error (RMSE). A randomly sampled test set was kept to evaluate the

755 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion expected prediction RMSE, which is of 25.28 mm. No quantitative assessment of the performance of the MLP model against geostatistical approaches (e.g. Sideris et al., NHESSD 2013) was carried out. The regularized MLP solution is a smooth compromise between 1, 747–791, 2013 the radar and rain gauge measurements. This allows being robust to local radar over- 5 estimations due to ground clutter and the different sampling volume of radar and rain gauge measurements. The Machine Learning Office software was used for the com- Shallow landslides putations (Kanevski et al., 2009). stochastic risk Figure 3 illustrates the spatial analysis of the rainfall accumulation from 18 to 23 Au- modelling gust 2005. The highest accumulations are observed on the northern slope of the Alps, P. Nicolet et al. 10 in particular along a line from the Berner Oberland to the mountain range of Saentis. The spatial distribution of landslides closely follows the regions with the highest rainfall totals with some spatial heterogeneity due to the different geological settings. Title Page

3.3 Landslide distribution Abstract Introduction

To be consistent with the precipitation map, the resolution of the landslide distribution Conclusions References 2 2 15 maps has also been set to 1 km ×1 km . For each grid cell, the probability to exceed a given number of landslides is computed based on the rainfall amount and the litho- Tables Figures logical type. Geology is extracted from the 1 : 200 000 geotechnical map of Switzerland (BFS J I GEOSTAT/BUWAL) and transformed from a vector map to a m×n×p cumulative matrix J I 20 which gives, for each cell, the proportion of each lithological unit (Figs. 4 and 5). The geotechnical types have been simpliﬁed into 4 diﬀerent units, loosely based on the Back Close 6 units used by Rickli et al. (2008) to assess the landslide density distribution of the Full Screen / Esc event:

– Limestone Formations (LF), Printer-friendly Version

25 – Cristalline Formations (CF), Interactive Discussion – Flysch, Loose material (except moraine), Marls and Claystones (FLMC), 756 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion – Molasse and Moraine (MM). NHESSD Cells that contain water (lake or glacier) or that are located on the Swiss border have a cumulative value below 1 (Fig. 4e). The model is run several times and assigns at 1, 747–791, 2013 each iteration a unique lithological unit following the probabilities given in the maps 5 shown in Fig. 4. Shallow landslides Landslides are transformed from point features to a raster displaying the landslide stochastic risk number in each cell (Fig. 1). This raster is then multiplied by the cumulative geological modelling raster (Fig. 4e) to take into account the smaller land surface inside the cell. Indeed, cells with a total value below one for the geology (borders of Switzerland, lakeshores, P. Nicolet et al. 10 etc.) are taken into account only at some iterations. Therefore, by dividing them with the geology allows to maintain a mean number of landslide consistent with the inventory. The precipitation field has been divided into 15 classes based on given quantiles and Title Page the statistical distribution is shown in Fig. 6. The histogram is highly skewed and only Abstract Introduction 10 % of the region exceeds 200 mm of rain. 15 Figure 7 summarizes the data processing workflow. The output of the model is a cu- Conclusions References mulative distribution of the landslide number given the geology and the precipitation amount. To allow a generalization of these results, gamma distributions were fitted to Tables Figures the data by minimizing the mean square error in order to model the number of landslides as a function of precipitation amount. Since the gamma distribution is a continu- J I 20 ous distribution whose domain is 0 → ∞, it this not exactly suitable to fit discrete data, J I especially as the highest frequency is obtained at a value of 0 (we can indeed expect that 0 landslides in a cell is always the most frequent, regardless of the precipitation Back Close amount). However, this problem has been solved by shifting the cumulative frequen- Full Screen / Esc cies to the upper number of landslides to fit the distributions, and by rounding down the 25 number of landslides obtained for a given quantile when using the inverse distribution function. Printer-friendly Version To estimate the models predictive ability, a second part consists in using the distri- Interactive Discussion bution previously assessed to simulate different potential consequences of the precipitation event using a Monte-Carlo approach. This step illustrate the uncertainty of the 757 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion model on the consequences of a given precipitation event. Indeed, since we consider that the landslides are controlled only by the precipitation and the lithology this step NHESSD gives the variability resulting from this simplification. The workflow of this step is given 1, 747–791, 2013 in Fig. 8.

5 3.4 Impact assessment Shallow landslides stochastic risk The impact assessment consists of two main steps, which are evaluating how many modelling buildings will be reached and estimating an associated cost. In order to asses the number of affected buildings, a concept of stochastic geometry is used. Assuming that P. Nicolet et al. the landslide has the same probability to occur anywhere within the cell, the conditional 10 probability that any building of the cell is reached if a dimension-less landslide occurs is given by the proportion of the cell covered by buildings. To take into account the Title Page landslides dimensions, a buffer is added to the buildings. Indeed, as shown in Fig. 9, Abstract Introduction if the landslide is considered to be circular, it will affect a house if its center is located inside the buffer area (buildings included). As a result, the conditional probability is Conclusions References 15 calculated considering the surface covered by the houses and their buffers. Since the buffers can overlap, the resulting probability considers the intersection with at least Tables Figures one building. Although landslides are usually not circular but have an elongated shape, a circle is used in order to simplify the model by avoiding the need to consider a real J I geometry. Indeed, for non-circular landslides, the intersection probability cannot be J I 20 simply reduced to a single number for each cell, since the intersection does not depend only on the position of the center, but also on the orientation of the considered shape. Back Close Since, for a given surface, an elongated shape is more likely to intersect a build- Full Screen / Esc ing than a round one, the circle diameter is set to 200 m in order to completely include 90 % of the landslides (Fig. 2). This diameter results in an overestimation of the Printer-friendly Version 25 landslide surface, but takes indirectly into account the landslide geometry and provide a slightly pessimistic risk estimation in terms of number of affected buildings. Thus Interactive Discussion a 100 m buffer has been added to the 1 814 667 buildings extracted from the vectorized landscape model of Switzerland (Vector25, © swisstopo). Then the total surface has 758 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion been compared with each cell surface to obtain the intersection probability (Fig. 10). It has to be mentioned that intersection is only considered with a boolean approach, NHESSD which means that a landslide can affect a building or not, but the potential for one land- 1, 747–791, 2013 slide to affect several buildings is not considered. It should also be noted that the buffers 5 are made before cutting shapes into cells in order to take into account the possibility for a landslide occurring in a given cell to reach a house located close to the border of Shallow landslides an adjacent cell. stochastic risk The estimation of the associated cost is more complicated as the value of the build- modelling ings is not known. This information could be obtained from the buildings insurance P. Nicolet et al. 10 for 19 over 26 cantons for which a public insurance exists and is mandatory. However, a suitable vulnerability curve linking the landslide intensity, characterized by parameters such as depth or area, to the damage rate, is difficult to assess. The lack of knowledge Title Page on the precise landslide characteristics and location as well as the inherent variability of the elements at risk complicates even more the assessment of the vulnerability (Galli Abstract Introduction 15 and Guzzetti, 2007). Therefore, in order to keep the models precision consistent with the previous step, we chose not to use a value and vulnerability curve to assess the Conclusions References

damage cost, but to assess it directly from the 2005 event mean damage cost. Tables Figures The expected damage cost for a given building x is assumed to follow an exponential distribution with probability density function: J I λexp(−λx), x ≥ 0 20 f (x) = . (2) J I 0, x < 0 Back Close The distribution is only defined in terms of its first moment λ, which is equal to x¯−1, x¯ Full Screen / Esc being the expected mean damage cost per building assumed for the 2005 event. This cost is estimated by dividing the total damage cost induced by landslides to private Printer-friendly Version 25 infrastructures (CHF 16.3 million) by the expected number of affected buildings. The latter is obtained by summing over all grid cells the product between the number of Interactive Discussion landslides (Fig. 1) and the intersection probability (Fig. 10). This approach results in

759 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2360 affected buildings, implying a mean cost x¯ of CHF 6907 per building. No uncertainty is considered on this parameter. NHESSD The generation of exponential variates is obtained by sampling from the quantile 1, 747–791, 2013 distribution, which is given by the inverse function of the exponential cumulative distri- 5 bution as: Shallow landslides ln(1 − u) F −1(u) = x = − (3) stochastic risk λ modelling where u is a uniformly distributed random number between 0 and 1. The exponentially P. Nicolet et al. distributed damage cost is sampled for each case of impact identified by the model. 10 The fat-tailed nature of the exponential distribution allows obtaining a more realistic estimate of the damage costs than a normal or triangular distribution and does not need Title Page the estimation of the second moment characterizing the variance of the distribution. The latter is a useful feature as the statistical distribution of the damage costs per Abstract Introduction building is not known in our particular case. The lognormal distribution also has heavy Conclusions References 15 tails and was successfully used to model the cost associated to floods (Merz et al., 2004). However, due to the larger number of degrees of freedom, it is also not suitable Tables Figures for our application.

J I 4 Results J I

The statistical distribution of landslides as a function of precipitation amount and litho- Back Close 20 logical group is given in Fig. 11. The probability to observe a given number of landslides in a given lithological group is a monotonically increasing function of the precip- Full Screen / Esc itation amount. CF show a very little susceptibility to landslides compared to the other groups as evidenced by the low number of observed landslides. With similar precipita- Printer-friendly Version

tion amount, MM formations tend to have a higher probability to contain at least one Interactive Discussion 25 landslide than FLMC or LF. However this relation is less evident for larger landslide numbers. 760 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Table 1 shows the fitted values of the gamma distribution for the highest five precipitation classes, whereas Fig. 12 display these values graphically. CF were not considered NHESSD due to the low number of samples. The α parameter (shape), characterizes the cen- 1, 747–791, 2013 tral location of the distribution, while the β parameter (inverse scale) characterizes its 5 dispersion. A general increase in both α and β parameters with precipitation amount can be observed, although some values are not following the general linear trend. This Shallow landslides is especially the case for α for the classes with precipitation lower than 184 mm for LF stochastic risk and lower than 158 mm for FLMC. modelling The general increase of both parameters is a desirable property and is in accordance P. Nicolet et al. 10 with our prior expectations. In fact, increasing precipitation amounts increase the expected number of landslides (represented by α) and the dispersion of the distribution (represented by β). Higher β values are representative of heavy-tails, which means Title Page that the probability of observing a high number of landslides rises with increasing precipitation amount. Abstract Introduction 15 The spatial distribution of the number of landslides was computed following the procedure described in Fig. 8 using both the raw data and the gamma fits. However, since Conclusions References

gamma distributions have been fitted only for the classes containing enough data sam- Tables Figures ples, raw data have been used instead of gamma distributions when not available. The mean modeled number of landslide with gamma fits is given in Fig. 13 and is very J I 20 similar to the mean number of landslides modeled with raw data. The spatial pattern is relatively similar to the spatial distribution of rainfall amounts, with two remarkable J I differences. First, the relation between precipitation amount and number of landslides Back Close is not linear, which implies that areas with low precipitation amounts show a null to very low number of landslides. The second difference is due to the sharp geograph- Full Screen / Esc 25 ical transitions between the lithological units, which lead to sharp transitions in the modeled number of landslides. An illustrative example occurs when moving from the Printer-friendly Version MM formations the CF, which strongly reduces the number of landslides (see Fig. 4). These results seems to be in good agreement with the observed distribution landslides Interactive Discussion (Fig. 1).

761 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion To evaluate the ability of the gamma fits to reproduce the raw data, maps for the 95th and 98th quantiles have been modeled, still using a Monte-Carlo simulation to NHESSD account for the probabilistic aspect of the lithology (Fig. 14). Although the results are 1, 747–791, 2013 relatively similar for the 95th quantile (with slightly lower values for the gamma fit), the 5 98th quantile shows more differences. Indeed, the gamma fit seems to underestimate the number of landslides observed in the raw data and indicates that the end of the tail Shallow landslides of the distribution is not adequately represented. stochastic risk modelling 4.1 Impact assessment P. Nicolet et al. Although the landslide number is reproduced, the expected number of hit buildings is 10 almost never reached in the simulations (Fig. 15). Indeed, the expected number of affected buildings for the event is 2360, whereas the simulations return a mean of around Title Page 1860. As a consequence, the damage amount is not reached either since it is derived Abstract Introduction from the latter. Tests have been made using a 20 m buffer for the houses and the same effect was observed. It is not yet clear why the observed total number of hit buildings Conclusions References 15 is underestimated by the model. One possible reason could be that the landslide localization is highly correlated with the buildings location. To test this hypothesis, we Tables Figures compared the intersection probability of cells within which landslides actually occurs to the intersection probability of cells in which the mean modeled number of landslides J I (Fig. 13) is above 0.5. Considering only these cells allows to keep the most suscepti- J I 20 ble cells according to the model. This comparison indicates that the modeled landslides tends to occur in cells with lower intersection probability than the actual landslides. This Back Close effect is not clearly visible with a 20 m buffer, but is more obvious with 100 m buffers Full Screen / Esc (Fig. 16).

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Interactive Discussion

762 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 5 Discussion NHESSD The landslide model presented in this paper only considers precipitation amounts and geology as input parameters. However, other variables such as terrain slope, soil thick- 1, 747–791, 2013 ness and permeability contrast, play a key role in shallow landslide generation. These 5 variables are either hard to measure over a large domain, e.g. the soil thickness, or Shallow landslides 2 2 show spatial variability at scales which are smaller than 1 km ×1 km resolution, e.g. stochastic risk the terrain slope. Additionally, the uncertainty of the landslide inventory does not allow modelling matching the location of the landslide with such high resolution variables. As a consequence, the 1 km2 ×1 km2 resolution model only gives information about the large scale P. Nicolet et al. 10 pre-conditioning factors for landslide generation. Smaller scale features may aﬀect the process of landslide triggering in a signiﬁcant way. Furthermore, this model is based only on one single event and should be compared with other similar rainfall events. In Title Page

particular, it should be compared with similar events producing landslides in different Abstract Introduction geological settings, to validate the aggregation of different lithology into four main units. 15 Indeed, landslides susceptibility might be different in Jura limestones than in Prealpine Conclusions References limestones, for example. Tables Figures The annual probability to overcome a given total damage cost could be assessed by analyzing different precipitation events, which are weighted based on their frequence of occurrence (return period). This step is essential in order to obtain a mean annual cost J I

20 as well as an exceedance probability curve. One possibility to generate a large number J I of rainfall ﬁelds to appropriately represent the full risk estimation could be based on design storms (Seed et al., 1999). Stochastic rainfall ﬁelds could be generated according Back Close

to a given return period and be used to simulate the spatial distribution of landslides Full Screen / Esc under extreme rainfall conditions. Attempts have been made to use a return period in 25 order to predict landslide triggering but, they were mainly performed at local scale (e.g. Printer-friendly Version Iida, 1999; D’Odorico et al., 2005; Iida, 2004; Tarolli et al., 2011) and would therefore not be suitable for a larger area, since the spatial variability is not taken into account. Interactive Discussion On the other hand, the spatial distribution of rainfall by means of radar data has been

763 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion used for early-warning (e.g. Apip et al., 2010), but as far as we know, is has not been used as in starting point to simulate potential future events. NHESSD Another issue concerns the landslide timing. We used the precipitation amount of the 1, 747–791, 2013 whole event (6 days) as a predictor for landslide occurrence. But, shallow-landslides 5 are known to be sensitive to the intensity and duration of the rainfall, as well as to the hyetograph shape (D’Odorico et al., 2005). There are two main reasons for this Shallow landslides simplification. The first is the lack of data on the exact timing of landslides, which does stochastic risk not allow analyzing the temporal precipitation pattern preceding their triggering. The modelling second reason is due to the uncertainty of the radar QPE product, which is higher P. Nicolet et al. 10 when used to analyze rainfall time series at high temporal resolutions, for instance hourly or 10 min accumulations. The spatial distribution of QPE accuracy can still be affected by some residual ground clutter, which overestimates the true rainfall amount, Title Page and by the blockage of low level beams, which leads to the underestimation of ground rainfall due to using only the beams aloft. Wuest¨ et al. (2010) present a method to Abstract Introduction 15 obtain hourly precipitation fields by disaggregating the daily rain gauge measurements with higher resolution radar fields. If the timing of landslide occurrence was known, Conclusions References

this dataset would be a valuable source of information. However, the product is not Tables Figures accompanied by uncertainty estimates. A possible solution could involve the generation of stochastic ensembles to represent the uncertainty of the radar QPE product with J I 20 respect to the automatic network of 76 meteorological stations. This approach was recently implemented at MeteoSwiss (Germann et al., 2009) and could be a smart J I alternative to integrate ensembles of precipitation fields together with ensembles of Back Close lithological types into the landslide model. When it comes to the damage cost assessment, due to the lack of information on Full Screen / Esc 25 the number of affected buildings and corresponding distribution of costs, a few important assumptions were made. The total number of affected buildings was estimated Printer-friendly Version by means of an intersection probability and this number was used to obtain a mean cost per hit building. The number of hit buildings is an uncertain estimation since it Interactive Discussion depends on the exact location of the landslides inside the cell. Indeed, we consider the

764 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion landslides to be uniformly distributed within a grid cell. This assumption is realistic at the model scale since every 1 km2 ×1 km2 cell contains slopes that might fail. However, NHESSD if susceptible slopes were located, inside of a cell, far from the houses, the modeled 1, 747–791, 2013 intersection probability would not be null, although it might be the case in reality. We 5 plan to overcome this issue in the future by using a susceptibility map to constrain the landslides location at the intersection probability step. Shallow landslides The distribution of costs was assumed to be exponential, which has a desirable long- stochastic risk tail property and is completely defined by its mean value. Despite being only defined in modelling terms of the average costs, the obtained variability is supposed to adequately represent P. Nicolet et al. 10 the reality. Nevertheless, with a mean cost of CHF 6907 per building, the probability to overcome CHF 500 000 is 5×10−36, i.e. one case over 1.8×1035. Since the mean price of a building is around CHF 1 million, this value is quite low as we know that at least one Title Page – but probably more – building has been destroyed. This could be the result of a too high number of affected buildings (since they have been estimated), which reduces the Abstract Introduction 15 mean damage cost, or an indication of the need for using a distribution of damages with a fatter tail. However, this confirms the fact that a distribution with a fat tail is suitable. Conclusions References

Nevertheless, since the damage cost varies independently for each affected house and Tables Figures since the number of affected houses is relatively high in the simulations, the effect of these parameters variability is attenuated when summing over all the damage costs. J I 20 Another problem concerns the absence of data about the type of damage. Therefore, we assumed that all of the private costs are related to buildings. This simplification is J I not an issue as long as the cost is related to objects located close to or inside the Back Close buildings (furnitures, parked cars), but is more problematic for costs related to loss of profits for example. However, we suppose that the vast majority is related to buildings. Full Screen / Esc 25 As a result, this model could be improved considerably if the type of damage was known. Thus, the damage assessment part has to be considered more as an example Printer-friendly Version than as a reference for further vulnerability assessment. Regarding the number of landslides, hit buildings and the amount of damage in Interactive Discussion each simulation, the variability of the results follows more or less a normal distribution

765 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion (Fig. 15). This distribution reflects the uncertainty induced by the lack of knowledge in the assessment of the consequences of a given precipitation event. Since the model is NHESSD based on the observed landslides to redistribute the landslides and assess the conse- 1, 747–791, 2013 quences, the number of modeled landslides using raw data is logically centered around 5 the observed value. Gamma fits results tend, on the other hand, to be lower than using raw data. This is due, in all likelihood, to the lack of ability of the gamma fits to repro- Shallow landslides duce the high observed numbers of landslides in some single cells. When it comes to stochastic risk the number of hit buildings, the expected value is hardly ever reproduced. Since the modelling same concept of intersection probability, with the same buffer value, is used to assess P. Nicolet et al. 10 the expected number of hit buildings of the 2005 event and of the simulation results, this should not be observed. Tests with a 20 m buffer gave similar results. By compar- ing the intersection probability of the cells in which landslides occurred with those of Title Page the cells in which the landslides were modeled, we can observe that the cells in which landslides occurred have higher intersection probability. Different hypotheses can be Abstract Introduction 15 made in order to explain this effect. First, we might have neglected an important parameter for the localization of landslides which would be correlated to the built areas, Conclusions References

redistributing then the landslides in less populated areas. A second option could be Tables Figures related to the quality of the inventory, which would be more complete in urbanized areas. Correcting this effect would imply a greater total number of landslides, with more J I 20 landslides on area with low intersection probability. The third one, which seems to us the most probable, would be that the urbanization tends to increase the susceptibility. J I Indeed, human activities can contribute to landslides, acting directly as a trigger or indi- Back Close rectly by destabilizing the slope, according to the classification of Michoud et al. (2011). Since, the trigger of the 2005 event is undeniably the rain, only the latter case can Full Screen / Esc 25 have played a role. Examples of landslides triggered by rain events on slopes destabi- lized by the modification of pore pressure induced by pipe leaks have been observed Printer-friendly Version in Switzerland, in Les Diablerets (Jaboyedoff and Bonnard, 2007) and in Lutzenberg (Valley et al., 2004). This second example is especially interesting since the landslide Interactive Discussion occurred within an event involving hundreds of landslides and debris-flows, and since

766 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion this particular landslide would not have occurred, thanks to the authors, without the pipe leak. Besides modifying pore pressure, pipe leaks can also destabilize slopes NHESSD by weakening clay minerals (Preuth et al., 2010). In addition, the degradation of old 1, 747–791, 2013 canalization network led to a landslide in 1930 in La Fouvriere` hill in Lyon (France), 5 killing 39 persons (Allix, 1930; Albenque, 1931). It would therefore be wise to include a parameter linked to the buildings to take account of this eﬀect. Shallow landslides All things considered, the model makes simpliﬁcations in order to assess risk for stochastic risk a large area rather than to be precise at local scale. Indeed, the lack of knowledge modelling and data at the sub-grid scale is balanced by the use of stochastic simulations, which P. Nicolet et al. 10 allows obtaining a probabilistic model for landslide occurrence and associated cost. Such kind of model might be useful to provide a rapid damage estimation following a precipitation event. Indeed, after a widespread event, the time needed by the Title Page insurance to process all claims is rather long and consequences might need several months, even years to be known. Applying this model quickly after the event could pro- Abstract Introduction 15 vide a rough estimation of the damage costs. In a second step, modeling precipitation events assigned to a frequency would make possible the calculation of exceedance Conclusions References

probability curves. Tables Figures

6 Conclusions J I

This article proposes a model to asses risk due to shallow landslides for a large region J I 20 using the data from 2005 event in Switzerland. Distribution of landslides with regard Back Close to precipitation and lithology is assessed in a first step, then the landslides are redis- tributed according to the relation obtained. Damage cost is obtained by the mean of an Full Screen / Esc intersection probability, which gives the probability, if a landslide occurs, that it reaches a building. Printer-friendly Version 25 Some improvements have to be made to the model, to corroborate the relation ob- Interactive Discussion tained, and to improve the assessment of the intersection probability, as well as the distribution of costs. Moreover, the human influence on landslide susceptibility has to 767 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion be evaluate carefully in a further step, since it appears that the landslides locations are highly correlated with the buildings. This observation tends to indicate that the human NHESSD influence on slope stability is substantial. Further developments are also conceivable 1, 747–791, 2013 to complete the risk analysis by simulating stochastic rainfall events characterized by 5 a frequency and to analyze the consequences. This would result in a complete risk analysis able to provide the temporal distribution of damage costs. Shallow landslides stochastic risk Acknowledgements. This study was partially supported by the Canton of Vaud Natural Hazard modelling Unit and by the the Swiss National Science Foundation project Data mining for precipitation nowcasting (PBLAP2-127713/1). We thank the Federal Office of Meteorology and Climatology P. Nicolet et al. 10 for providing the data for the rainfall event of August 2005.

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Sci., 4, 153–163, doi:10.5194/nhess-4-153-2004, 2004. 760 Michoud, C., Derron, M.-H., Jaboyedoff, M., Nadim, F., and Leroi, E.: Classification of landslide- J I inducing anthropogenic activities, in: 5th Canadian Conference on Geotechnique and Natural Hazards, 15–17 May 2011, Kelowna, BC, Canada, 10 pp., 2011. 766 J I 25 Montgomery, D. and Dietrich, W.: A physically based model for the topographic control on shal- Back Close low landsliding, Water Resour. Res., 30, 1153–1171, 1994. 749 Mueller, R. and Loew, S.: Predisposition and cause of the catastrophic landslides of August Full Screen / Esc 2005 in Brienz (Switzerland), Swiss J. Geosci., 102, 331–344, doi:10.1007/s00015-009- 1315-3, 2009. 753 Printer-friendly Version 30 Nguyen, H., Wiatr, T., Fernandez-Steeger,´ T., Reicherter, K., Rodrigues, D., and Azzam, R.: Landslide hazard and cascading effects following the extreme rainfall event on Madeira Island Interactive Discussion (February 2010), Nat. Hazards, 65, 635–652, 2013. 749

772 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Pack, R., Tarboton, D. G., and Goodwin, C. N.: The SINMAP approach to terrain stability mapping, in: 8th Congress of the International Association of Engineering Geology, 21–25 NHESSD September 1998, Vancouver, British Columbia, Canada, 8 pp., 1998. 749 Preuth, T., Glade, T., and Demoulin, A.: Stability analysis of a human-inﬂuenced landslide in 1, 747–791, 2013 5 eastern Belgium, Geomorphology, 120, 38–47, doi:10.1016/j.geomorph.2009.09.013, 2010. 767 Raetzo, H. and Rickli, C.: Ereignisanalyse Hochwasser 2005: Teil 1 – Prozesse, Schaden¨ und Shallow landslides erste Einordnung, chap. Rutschungen, edited by: Bezzola, G. R. and Hegg, C., Bundesamt stochastic risk fur¨ Umwelt BAFU, Eidg. Forschungsanstalt WSL, Bern and Birmensdorf, Switzerland, 195– modelling 10 210, 2007 (in German). 750, 752, 753, 776, 777 Remondo, J., Bonachea, J., and Cendrero, A.: A statistical approach to landslide risk modelling P. Nicolet et al. at basin scale: from landslide susceptibility to quantitative risk assessment, Landslides, 2, 321–328, doi:10.1007/s10346-005-0016-x, 2005. 749 Rickli, C., Raetzo, H., McArdell, B., and Presler, J.: Ereignisanalyse Hochwasser 2005: Title Page 15 Teil 2 – Analyse von Prozessen, Massnahmen und Gefahrengrundlagen, chap. Hangin- stabilitaten,¨ edited by: Bezzola, G. R. and Hegg, C., Bundesamt fur¨ Umwelt BAFU, Eidg. Abstract Introduction Forschungsanstalt WSL, Bern and Birmensdorf, Switzerland, 97–116, 2008 (in German). 750, 753, 756 Conclusions References Rotach, M., Appenzeller, C., and Albisser, P. E.: Starkniederschlagsereignis August 2005, Ar- Tables Figures 20 beitsberichte 211, MeteoSchweiz, Zurich,¨ Switzerland, 2006 (in German). 751, 752 Seed, A. W., Srikanthan, R., and Menabde, M.: A space and time model for design storm rainfall, J. Geophys. Res.-Atmos., 104, 31623–31630, doi:10.1029/1999JD900767, 1999. 763 J I Sideris, I., Gabella, M., Erdin, R., and Germann, U.: Real-time radar-raingauge merging using spatiotemporal co-kriging with external drift in the alpine terrain of Switzerland, Q. J. Roy. J I 25 Meteor. Soc., in review, 2013. 755, 756 Back Close Tarolli, P., Borga, M., Chang, K.-T., and Chiang, S.-H.: Modeling shallow landsliding susceptibility by incorporating heavy rainfall statistical properties, Geomorphology, 133, 199–211, Full Screen / Esc doi:10.1016/j.geomorph.2011.02.033, 2011. 763 Trumpy,¨ R.: Geology of Switzerland, Part A: An outline of the Geology of Switzerland, Wepf & Printer-friendly Version 30 Co. Verlag, Basel, Switzerland, 1980. 751 University of Bern and FOWG: Geological Map of Switzerland 1 : 500 000, Swisstopo, Bern, Interactive Discussion Switzerland, ISBN 3-906723-39-9, 2005a. 751

773 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion University of Bern and FOWG: Tectonic Map of Switzerland 1 : 500 000, Swisstopo, Bern, Switzerland, ISBN 3-906723-56-9, 2005b. 751 NHESSD Valley, B., Thuro, K., Eberhardt, E., and Raetzo, H.: Geological and geotechnical investigation of a shallow translational slide along a weathered rock/soil contact for the purpose of model 1, 747–791, 2013 5 development and hazard assessment, in: Proceedings of the 9th International Symposium on Landslides, Rio de Janeiro, 28 June–2 July 2004, edited by: Lacerda, W. A., Ehrlich, M., Fontoura, S. A. B., and Sayao,˜ A. S. F., A. A. Balkema, 385–391, 2004. 766 Shallow landslides van Westen, C., van Asch, T., and Soeters, R.: Landslide hazard and risk zonation – why is stochastic risk it still so difficult?, B. Eng. Geol. Environ., 65, 167–184, doi:10.1007/s10064-005-0023-0, modelling 10 2006. 748 von Ruette, J., Papritz, A., Lehmann, P., Rickli, C., and Or, D.: Spatial statistical modeling P. Nicolet et al. of shallow landslides – validating predictions for different landslide inventories and rainfall events, Geomorphology, 133, 11–22, doi:10.1016/j.geomorph.2011.06.010, 2011. 753 Whittaker, K. A. and McShane, D.: Comparison of slope instability screening tools following a Title Page 15 large storm event and application to forest management and policy, Geomorphology, 145– 146, 115–122, doi:10.1016/j.geomorph.2012.01.001, 2012. 749 Abstract Introduction Wieczorek, G. F.: Landslide triggering mechanisms, in: Landslides Investigation and Mitigation, edited by: Turner, A. K. and Schuster, R. L., Special Report 247, Transportation Research Conclusions References Board, National Research Council, National Academy Press, Washington, DC, 76–90, 1996. Tables Figures 20 749 WSL: Swiss flood and landslide damage database, http://www.wsl.ch/fe/gebirgshydrologie/ HEX/projekte/schadendatenbank/index EN, last access: 26.02.2013, 2012. 753 J I Wuest,¨ M., Frei, C., Altenhoff, A., Hagen, M., Litschi, M., and Schar,¨ C.: A gridded hourly precipitation dataset for Switzerland using rain-gauge analysis and radar-based disaggregation, J I 25 Int. J. Climatol., 30, 1764–1775, 2010. 764 Back Close Yu, F.-C., Chen, T.-C., Lin, M.-L., Chen, C.-Y., and Yu, W.-H.: Landslides and rainfall characteristics analysis in Taipei City during the Typhoon Nari event, Nat. Hazards, 37, 153–167, Full Screen / Esc doi:10.1007/s11069-005-4661-0, 2006. 749

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Table 1. Fitted parameters of the gamma distribution.

Title Page Precipitation LF FLMC MM [mm] α β α β α β Abstract Introduction 114–134 0.0323 1.4438 0.1347 0.7346 0.0683 1.0392 134–158 0.3604 0.5403 0.2241 0.9303 0.0801 2.6114 Conclusions References 158–184 0.1927 0.9673 0.1288 2.1937 0.1531 4.3495 Tables Figures 184–219 0.0839 3.7578 0.2026 2.7379 0.2265 6.0948 219–321 0.1214 7.0373 0.2457 5.4336 0.4966 4.4464 J I

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70 the expected distribution of annual costs. More recently, ap- 30 Shallow landslides plications of regional scale QRA providing exceedance prob- Basel stochastic risk abilities were presented in Jaiswal et al. (2011) and Ghosh modelling 1 Zurich et al. (2012). Although, most of the QRA methodologies are P. Nicolet et al. developed for local or regional scales, some of them, as for Lucerne 75 Bern example Catani et al. (2005), might be applied to a larger Title Page area. Abstract Introduction Switzerland was affected in August 2005 by a rain- Lausanne fall event with measured precipitation reaching 324 mm in Conclusions References 6 days. Although floods were the main damage cause, Tables Figures 80 more than 5000 landslides were reported (Raetzo and Rickli, Geneva 2007). Landslide-induced damage has been estimated by J I J I Hilker et al. (2007) at 92 million Swiss francs (99 million $; 025 50 100 Kilometers debris-flows not included) and represents 4.5 % of the total Back Close 2 damage cost. Fig. 1. Number of landslides in 1 km cells (after Raetzo and Rickli, 2007, hillshade: © Swis- Full Screen / Esc stopo). 85 As already mentioned by Jaboyedoff and Bonnard (2007) Fig. 1. Number of landslides in 1 km2 cells (after Raetzo and Rickli, Printer-friendly Version and by Rickli et al. (2008), landslide density was highly cor- 2007, hillshade: © Swisstopo) related with the total precipitation amount. Following their Interactive Discussion ideas, this article proposes a risk model for shallow landslides based on the event of August 2005. The input pa- 120 listed along a northwest-southeast776 direction (perpendicularly 90 rameters of the model include a rainfall and a lithological to the geological structures) : map. The map of 6-day rainfall accumulations is constructed – Upper Freshwater Molasse from Middle and early Up- by interpolating a high resolution rain gauge network using per Miocene (consisting of floodplains sediments in- weather radar data as external drift. A geotechnical map is cluding puddings, sandstones and silty shales) interpreted in order to group different units into 4 main litho- 95 logical settings. The expected number of landslides is pre- 125 – Other types of Molasse (narrower areas of Upper Ma- dicted as a function of rainfall level conditional to the litho- rine Molasse, Lower Freshwater Molasse and Lower logical type. An intersection probability concept is then em- Marine Molasse, the lower part of this series being in ployed to predict the potential number of landslides affecting Subalpine position) buildings and the corresponding damage cost. 100 The paper is structured as follows. Section 2 details the – Subalpine Flysch rainfall event of August 2005 in Switzerland both from a me- 130 – Upper Penninic Flysch (Schlieren Flysch) teorological and lithological viewpoint. Section 3 explains the methodology to assess the landslide probability as a func- – Ultrahelvetic and Helvetic Nappes (including tertiary tion of rainfall accumulation and lithological context. Sec- shallow marine formation and Cretaceous Limestones 105 tion 4 presents the risk analysis results in terms of expected from the Wildhorn nappe and Jurassic Limestones from number of landslides, number of affected buildings and as- the Axen nappe) sociated cost. Finally, Section 5 and Section 6 discuss and conclude the paper. 135 Soils (regolith) and loose materials were deposited on top of the geological formations during the Quaternary. Most of these shallow and superficial formations have not been mapped, except for the cases where the formation reaches 2 The rainfall event of August 2005 in Switzerland a sufficient extension or thickness to be considered relevant 140 at the map scale. This is for example the case of morainic 110 2.1 Study area material deposited by the glaciations during the Quaternary, which is visible at several places, especially on the Plateau The study area covers the entire Swiss territory (around (Trumpy,¨ 1980). The properties of the local soils strongly 2 42 000 km ), which extends from the Jura mountains in the depend on the underlying bedrock. North-West, to the Alps, in the South-East, through the Mo- lassic Plateau, where most of the population is concentrated. 145 2.2 Description of the precipitation event 115 Special attention is given to the location where most of the landslides occurred, which is the central part of Switzerland, The rainfall event of August 2005 in central and eastern between the cities of Bern and Lucerne (Fig. 1). Landslides Switzerland resulted in severe damage due to flooding and occurred in the tectonic units described below (Trumpy,¨ induced slope instabilities (Rotach et al., 2006). The pres- 1980; University of Bern and FOWG, 2005a,b), which are ence of the Alps played a key role in controlling the spa- icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

NHESSD P. Nicolet et al.: Shallow landslides stochastic risk modeling1, 747–791, 2013 3

Shallow landslides 0.4 1 185 the locationstochastic of landslides risk complicates the analysis of geological context. modelling 0.8 0.3 StatisticsP. on Nicolet the et landslides al. can be found in Raetzo and Rickli (2007) and in Rickli et al. (2008) and investigations 0.6 on speciﬁc sites in Mueller and Loew (2009) and von Ruette Title Page 0.2 190 et al. (2011). The travel distance of shallow landslides has 0.4 been analyzedAbstract for 148Introduction cases and ranges from a few meters

Relative frequency Conclusions References 0.1 up to 500 m (Raetzo and Rickli, 2007). Around 75% of the 0.2 Cumulative frequency landslides traveledTables lessFigures than 100 m and 90% less than 200 m (Fig. 2). 0 0 J I 0 200 400 600 195 Distance [m] 2.4 DamageJ I

Back Close Fig. 2. Relative and cumulative frequency of the distance traveled by 148 landslides (Raetzo and Rickli, 2007). According to the Swiss Federal Institute for Forest, Snow and Fig. 2. Relative and cumulative frequency of the distance traveled Landscape ResearchFull Screen / Esc WSL, the 2005 event has been the most by 148 landslides (Raetzo and Rickli, 2007). costly sincePrinter-friendly the beginning Version of the collection of damage data in 1972, with a total damage cost estimated at 1.87 billion Interactive Discussion 200 swiss francs (around 2 billion US$). On the other hand, in 150 tial distribution of rainfall due to orographic precipitation en- spite of being the most important event recorded, other years hancement processes. Persistent777 precipitation patterns were have been equally or more damaging regarding landslides in mostly found on the exposed upwind slopes under northerly the past 40 years (Hilker et al., 2009; WSL, 2012). and north-easterly flow conditions as studied by Foresti and Hilker et al. (2009) divided the damage values into three Pozdnoukhov (2011) and Foresti et al. (2012). In particular, 205 categories according to the cause, namely floods, debris 155 the stratiform precipitation was locally enhanced by smaller flows and landslides (including mud-flows). Landslides rep- scale orographic features leading to persistent initiation and resent around 4.5 % of the total cost and affected private enhancement of the embedded convection. properties (22 %, 16.3 million CHF) and public infrastruc- The most intense period of the event was observed be- tures (88 %, 75.6 million CHF) (Hilker et al., 2007). Private tween the 21 and 22 August. Driven by cyclonic conditions 210 damage includes damage to buildings as well as furnitures, 160 during the first day, the moist air from the Mediterranean vehicles, other property damage and loss of profits. Compar- sea circumvented the Austrian Alps and started approaching atively, public damage includes damage to waterways, roads slightly crosswise the northern slopes of the Swiss Alps from (except small ones), rail, farming and forests. In addition to the east. The mesoscale flows gradually turned from easterly economic consequences, six casualties are to be deplored. to northerly conditions during the second day. The reduced 165 supply of air moisture was compensated by a stronger upslope rainfall enhancement which extended the duration of 215 3 Risk modeling methodology precipitation. The return period for 48h rainfall accumulations largely exceeded 100 years at several weather stations 3.1 Introduction mostly located in the Berner Oberland (Rotach et al., 2006). 170 It is worth mentioning that the uncertainty of this estimation The annual risk to property is usually evaluated with the fol- is quite important as an event of such intensity was never ob- lowing equation (Dai et al., 2002; Fell et al., 2005) : served in the past at the considered weather stations. R(PD)=P (L)×P (S|L)×V (P |S)×E (1) 2.3 Landslide inventory 220 where L denotes the landslide, P the element at risk (prop- As a consequence of this extreme rainfall event, many shal- erty) and S the impact. P (L) represents the landslide fre- 175 low landslides were triggered, mainly in the Entlebuch part quency, P (S|L) the spatial probability of the landslide reach- of Lucerne canton and in the Bern canton. Some deep-seated ing the element at risk, V (P |S) the vulnerability of the ele- landslides were observed as well and are mainly located far- ment at risk to the landslide impact and E the element at risk ther south-east. A landslide inventory has been collected by 225 value. Raetzo and Rickli (2007) from cantonal authorities informa- In the case studies considered in this article, this equation 180 tion and contains 5’756 landslides (Fig. 1). Although some is not used directly since a single precipitation event is used additional attributes such as the exact timing have been reg- as an input. However, since this event is used to redistribute istered for some of the landslides, we only dispose of the the landslides according to the precipitation event, P (L) is version provided in the above publication and, as a result, we 230 not completely left out. In a first phase, the spatial distri- only know the approximate location. The uncertainty about bution of the event rainfall accumulation is estimated using icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

NHESSD 4 P. Nicolet et al.: Shallow landslides stochastic risk modeling 1, 747–791, 2013

50 100 150 200 250 300 data from a dense network of rain gauges and addional C- Shallow landslides band weather radars (Section 3.2). The second phase studies stochastic risk the statistical distribution of landslides as a function of pre- modelling 235 cipitation intensity and lithological type (Section 3.3) and is P. Nicolet et al. P (L) used to estimate the probability of landsliding . It must 250’000 be mentioned that P (L) should also account for the clima- Title Page tological frequency, which is the probability of the precipitation event to occur. As the analyses consider only one sin- 200’000 Abstract Introduction 240 gle event, this probability was set to 1 and the term P (L) is Conclusions References only estimated from the distribution of landslides conditional Tables Figures to the precipitation event. P (S|L) is assessed using princi- 150’000 ples of stochastic geometry, and represents the probability of J I buildings to be affected by circular landslides within a given

100’000 J I 245 cell. This term partially accounts for P (L) since the exact lo- 500’000 550’000 600’000 650’000 700’000 750’000 800’000 Back Close cation of the landslides within the cell is randomly assigned at this step. The separate estimation of the terms V (P |S) andFig. 3. Total rainfall accumulation from 18 to 23 August 2005 [mm] estimated by MLP. Dots Full Screen / Esc E represent the stations used for the interpolation. is not possible as the cost of damages is assessed directly Fig. 3. Total rainfall accumulation from 18 to 23 August 2005 [mm] Printer-friendly Version (see Section 3.4). estimated by MLP. Dots represent the stations used for the interpo- Interactive Discussion lation 250 3.2 Spatial analysis of rainfall 778 MeteoSwiss operates an automatic network of 76 weather 285 gate gradient algorithm was employed to train the network. stations and a dense network of additional 363 rain gauges. A low number of hidden neurons H was chosen to obtain The automatic network measures rainfall with a temporal res- a smooth representation of the spatial rainfall biases. The olution of 10 minutes while the second only reports daily optimal model was selected by minimizing the leave-one- 255 accumulations from 05:40 to 05:40 UTC of the next calen- out cross-validation root-mean square error (RMSE). A ran- dar day. An additional network of 3 C-band radars is used 290 domly sampled test set was kept to evaluate the expected pre- to measure precipitation with higher spatial resolution. The diction RMSE, which is of 25.28 mm. No quantitative as- operational radar data processing chain for quantitative pre- sessment of the performance of the MLP model against geo- cipitation estimation (QPE) at MeteoSwiss includes the re- statistical approaches (e.g., Sideris et al. (2013)) was carried 260 moval of ground clutter, correction for the vertical profile of out. The regularized MLP solution is a smooth compromise reflectivity in connection with the bright band effect, clima- 295 between the radar and rain gauge measurements. This allows tological rain gauge adjustment, the interpolation from polar being robust to local radar over-estimations due to ground coordinates to a Cartesian grid, and the use of a fixed cli- clutter and the different sampling volume of radar and rain matological Z-R relationship (refer to Germann et al., 2006, gauge measurements. The Machine Learning Office software 265 for more details). A geostatistical method for real-time bias was used for the computations (Kanevski et al., 2009). adjustment with rain gauges was only recently implemented 300 Fig. 3 illustrates the spatial analysis of the rainfall accu- by Sideris et al. (2013). For long term evaluation of the mulation from the 18 to the 23 August 2005. The highest ac- radar QPE accuracy against rain gauges refer to Gabella et al. cumulations are observed on the northern slope of the Alps, (2005). The radar QPE product used in this paper is a 1x1 in particular along a line from the Berner Oberland to the 2 270 km grid of the rainfall accumulation during the period 18– mountain range of Saentis. The spatial distribution of land- 23 of August 2005. 305 slides closely follows the regions with the highest rainfall Despite these corrections, the product still contains resid- totals with some spatial heterogeneity due to the different ge- ual ground clutter and biases due to the blockage of low level ological settings. radar beams, in particular in the inner Alpine valleys. To 275 partially account for these issues, an artificial neural network 3.3 Landslide distribution was applied to blend the radar-based QPE map with the rain gauge rainfall accumulations. A 3-H-1 multiLayer percep- To be consistent with the precipitation map, the resolution of 2 tron (MLP) was trained to predict the rainfall amount ob- 310 the landslide distribution maps has also been set to 1x1 km . served at the rain gauges as a function of 3 variables: the For each grid cell, the probability to exceed a given number 280 geographical location represented by the Swiss Easting and of landslides is computed based on the rainfall amount and Northing coordinates and the radar QPE product which acts the lithological type. as an external drift. The geographical coordinates account Geology is extracted from the 1:200 000 geotechnical map for the observed biases between rain gauges and radar-based 315 of Switzerland (BFS GEOSTAT/BUWAL) and transformed QPE, which show a significant spatial dependence. A conju- from a vector map to a m × n × p cumulative matrix which P. Nicolet et al.: Shallow landslides stochastic risk modeling 5 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

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Back Close Fig. 4. Fig.Probabilistic 4. Probabilistic lithological lithological maps showing maps the proportion showing of each thelithological proportion unit. Values range of fromeach green lithological (lithological group unit. sligthly Values present) to blue, whereas white means that the lithological group is non-existent in the cell; A: Limestone formations (LF); B: Cristalline Full Screen / Esc range fromformations green (CF), C: (lithological Flysch, Loose material group (except moraine), sligthly marls present) and claystones to (FLMC), blue, D: whereas Molasse and Moraine white (MM) means and E: total. that the lithologicalIn map E, group white tones is mark non-existent the absence of lithological in the formations cell; (i.e.(A) lakes,Limestone glaciers) and other Formations countries, while green (LF); tones(B) depictCristalline their partial presence within the model cell, which occurs when the cumulative proportion of the 4 units is below 1. Formations (CF), (C) Flysch, Loose material (except moraine), Marls and Claystones (FLMC), Printer-friendly Version (D) Molasse and Moraine (MM) and (E) total. In map (E), white tones mark the absence of gives, for each cell, the proportion of each lithological unit Cells that contain water (lake or glacier) or that are located lithological(Fig. 4 formations and 5). The geotechnical (i.e. lakes, types have glaciers) been simpliﬁed and otheron the Swiss countries, border have while a cumulative green value tones below 1 depict(Fig. 4 their Interactive Discussion partialinto presence 4 different units,within loosely the based model on the cell,6 units whichused by occursE). The model when is run the several cumulative times and assigns proportion at each it- of the 320 Rickli et al. (2008) to assess the landslide density distribution 330 eration a unique lithological unit following the probabilities 4 unitsof is the below event : 1. given in the maps shown in Fig. 4.

– Limestone formations (LF) 779 Landslides are transformed from point features to a raster displaying the landslide number in each cell (Fig. 1). This – Cristalline formations (CF) raster is then multiplied by the cumulative geological raster – Flysch, Loose material (except moraine), marls and 335 (Fig. 4 E) to take into account the smaller land surface inside 325 claystones (FLMC) the cell. Indeed, cells with a total value below one for the geology (borders of Switzerland, lakeshores, etc) are taken – Molasse and Moraine (MM) into account only at some iterations. Therefore, by dividing 6 | Paper Discussion | Paper Discussion | Paper P. Discussion | Nicolet Paper Discussion et al.: Shallow landslides stochastic risk modeling NHESSD 1, 747–791, 2013 0.5 0.2 Start

Shallow landslides Cumulative Vector map Precipitation Landslide Generate geological 0.3 map Invetory map random matrix stochastic risk map modelling

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Tables ProbabilisticFigures landslide distribution for each litho- 0.4 logical unit and precipita- J tion classI

0.2 J I 0 Fig. 7. Flow diagramBack showingClose the assessment methodology used to obtain the cumulative frequency of landslide number per lithologi- Fig. 5. Schematic transformation of the geotechnical map into a m × n × p matrix which gives Full Screen / Esc for each cell the lithological units cumulative distribution. A lithology is assigned at each modelcal unit and precipitation class. iterationFig. by choosing 5. Schematic a random transformation number u. For example, of the geotechnical if u = 0.6 in the map lower into left cell,a since Printer-friendly Version 0.5 < u

1 6000 exactly suitable to ﬁt discrete data, especially as the highest frequency is obtained at a value of 0 (we can indeed expect 0.9 355 5000 that 0 landslides in a cell is always the most frequent, re- 0.8 gardless of the precipitation amount). However, this problem 0.7 has been solved by shifting the cumulative frequencies to the 4000 0.6 upper number of landslides to ﬁt the distributions, and by rounding down the number of landslides obtained for a given 0.5 3000 360 quantile when using the inverse distribution function. 0.4

Number of cells To estimate the models predictive ability, a second part

Cumulative frequency 2000 0.3 consists in using the distribution previously assessed to sim-

0.2 ulate different potential consequences of the precipitation 1000 event using a Monte-Carlo approach. This step illustrate the 0.1 365 uncertainty of the model on the consequences of a given pre- 0 0 0 50 100 150 200 250 300 350 cipitation event. Indeed, since we consider that the landslides Precipitations [mm] are controlled only by the precipitation and the lithology this step gives the variability resulting from this simpliﬁcation. The workﬂow of this step is given in Fig. 8. Fig. 6. Cumulative distribution of the spatial precipitation amounts. Dots show the class limits and are rounded to the upper value. 370 3.4 Impact assessment

The impact assessment consists of two main steps, which are them with the geology allows to maintain a mean number of evaluating how many buildings will be reached and estimat- 340 landslide consistent with the inventory. ing an associated cost. In order to asses the number of af- The precipitation ﬁeld has been divided into 15 classes fected buildings, a concept of stochastic geometry is used. based on given quantiles and the statistical distribution is 375 Assuming that the landslide has the same probability to oc- shown in Fig. 6. The histogram is highly skewed and only cur anywhere within the cell, the conditional probability that 10 % of the region exceeds 200 mm of rain. any building of the cell is reached if a dimension-less land- 345 Fig. 7 summarizes the data processing workﬂow. The out- slide occurs is given by the proportion of the cell covered by put of the model is a cumulative distribution of the landslide buildings. To take into account the landslides dimensions, a number given the geology and the precipitation amount. To 380 buffer is added to the buildings. Indeed, as shown in Fig. 9, 6 P. Nicolet et al.: Shallow landslides stochastic risk modeling

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0.8 no i = iterations ? 0.6 yes

Probabilistic landslide distribution for each litho- 0.4 logical unit and precipitation class 0.2

0 Fig. 7. Flow diagram showing the assessment methodology used to obtain the cumulative frequency of landslide number per lithological unit and precipitation class. Fig. 5. Schematic transformation of the geotechnical map into a m × n × p matrix which gives for each cell the lithological units cumulative distribution. A lithology is assigned at each model it- allow a generalization of these results, gamma distributions eration by choosing a random number u. For example, if u =0.6 were ﬁtted to the data by minimizing the mean square er- icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion in the lower left cell, since 0.5

1 6000 exactly suitable to ﬁt discrete data, especially as the highest frequencyShallow is obtained landslides at a value of 0 (we can indeed expect 0.9 stochastic risk 355 that 0 landslides in a cell is always the most frequent, re- 5000 modelling 0.8 gardless of the precipitation amount). However, this problem P. Nicolet et al. 0.7 has been solved by shifting the cumulative frequencies to the 4000 0.6 upper number of landslides to ﬁt the distributions, and by rounding downTitle the Page number of landslides obtained for a given 0.5 3000 360 quantile whenAbstract usingIntroduction the inverse distribution function. 0.4

Number of cells To estimate the models predictive ability, a second part Conclusions References

Cumulative frequency 2000 0.3 consists in using the distribution previously assessed to sim- Tables Figures 0.2 ulate different potential consequences of the precipitation 1000 event using a Monte-Carlo approach. This step illustrate the 0.1 J I 365 uncertainty of the model on the consequences of a given pre- J I 0 0 0 50 100 150 200 250 300 350 cipitation event. Indeed, since we consider that the landslides Precipitations [mm] are controlledBack only byClose the precipitation and the lithology this Fig. 6. Cumulative distribution of the spatial precipitation amounts. Dots show the class limitsstep gives theFull Screen variability / Esc resulting from this simpliﬁcation. and are rounded to the upper value. The workﬂow of this step is given in Fig. 8. Fig. 6. Cumulative distribution of the spatial precipitation amounts. Printer-friendly Version Dots show the class limits and are rounded to the upper value. 370 3.4 ImpactInteractive assessment Discussion

781 The impact assessment consists of two main steps, which are them with the geology allows to maintain a mean number of evaluating how many buildings will be reached and estimat- 340 landslide consistent with the inventory. ing an associated cost. In order to asses the number of af- The precipitation ﬁeld has been divided into 15 classes fected buildings, a concept of stochastic geometry is used. based on given quantiles and the statistical distribution is 375 Assuming that the landslide has the same probability to oc- shown in Fig. 6. The histogram is highly skewed and only cur anywhere within the cell, the conditional probability that 10 % of the region exceeds 200 mm of rain. any building of the cell is reached if a dimension-less land- 345 Fig. 7 summarizes the data processing workﬂow. The out- slide occurs is given by the proportion of the cell covered by put of the model is a cumulative distribution of the landslide buildings. To take into account the landslides dimensions, a number given the geology and the precipitation amount. To 380 buffer is added to the buildings. Indeed, as shown in Fig. 9, icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

NHESSD 6 P. Nicolet et al.: Shallow landslides stochastic risk modeling 1, 747–791, 2013

Start Shallow landslides 0.5 0.2 stochastic risk modelling Cumulative Vector map Precipitation Landslide Generate geological 0.3 map Invetory map random matrix map P. Nicolet et al.

m x n x p matrix Attribute each Title Page divide into celle to one classes 1 geological unit Abstract Introduction Conclusions References

0.8 no i = iterations ? Tables Figures 0.6 yes J I Probabilistic landslide distribution for each litho- J I 0.4 logical unit and precipitation class Back Close 0.2 Fig. 7. Flow diagram showing the assessment methodology used to obtain the cumulative Full Screen / Esc frequency of landslide number per lithological unit and precipitation class. 0 Fig. 7. Flow diagram showing the assessment methodology used to Printer-friendly Version obtain the cumulative frequency of landslide number per lithological unit and precipitation class. Interactive Discussion Fig. 5. Schematic transformation of the geotechnical map into a m × n × p matrix which gives for each cell the lithological units 782 cumulative distribution. A lithology is assigned at each model it- allow a generalization of these results, gamma distributions eration by choosing a random number u. For example, if u =0.6 were ﬁtted to the data by minimizing the mean square er- in the lower left cell, since 0.5

Number of cells To estimate the models predictive ability, a second part

Cumulative frequency 2000 0.3 consists in using the distribution previously assessed to sim-

The impact assessment consists of two main steps, which are them with the geology allows to maintain a mean number of evaluating how many buildings will be reached and estimat- 340 landslide consistent with the inventory. ing an associated cost. In order to asses the number of af- The precipitation ﬁeld has been divided into 15 classes fected buildings, a concept of stochastic geometry is used. based on given quantiles and the statistical distribution is 375 Assuming that the landslide has the same probability to oc- shown in Fig. 6. The histogram is highly skewed and only cur anywhere within the cell, the conditional probability that 10 % of the region exceeds 200 mm of rain. any building of the cell is reached if a dimension-less land- 345 Fig. 7 summarizes the data processing workﬂow. The out- slide occurs is given by the proportion of the cell covered by put of the model is a cumulative distribution of the landslide buildings. To take into account the landslides dimensions, a number given the geology and the precipitation amount. To 380 buffer is added to the buildings. Indeed, as shown in Fig. 9, P. Nicolet et al.: Shallow landslides stochastic risk modeling | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 7 NHESSD Start High 1, 747–791, 2013

Precipitation- Cumulative Precipitation Generate landslide relation geological LowShallow landslides map random matrix (for each geology) map stochastic risk modelling

Attribute each divide into P. Nicolet et al. celle to one classes geological unit

Title Page

Assess the Generate number of Abstract Introduction random matrix landslides Conclusions References

Assess the Tables Figures Generate number of random matrix intersections 05010025 Kilometers J I

no i = iterations ? J I

yes Fig. 10. IntersectionBack probabilityClose map displaying the conditional probability for a 100 m radius circular landslide to affect a house Number of Full Screen / Esc affected buildings for each cell of the model. High means that the probability is equal (distribution) or close to one,Printer-friendly yellow Version that it is close to 0, whereas white indicate a Fig. 8. Flow diagram showing the assessment methodology used to obtain the number of af-null probability (hillshade: © Swisstopo) fected buildings. Interactive Discussion Fig. 8. Flow diagram showing the assessment methodology used to obtain the number of affected buildings. 783 385 buffers. Since the buffers can overlap, the resulting probability considers the intersection with at least one building. Al- though landslides are usually not circular but have an elongated shape, a circle is used in order to simplify the model by avoiding the need to consider a real geometry. Indeed, 390 for non-circular landslides, the intersection probability cannot be simply reduced to a single number for each cell, since the intersection does not depend only on the position of the center, but also on the orientation of the considered shape. Since, for a given surface, an elongated shape is more 395 likely to intersect a building than a round one, the circle diameter is set to 200 m in order to completely include 90% of the landslides (Fig. 2). This diameter results in an overestimation of the landslide surface, but takes indirectly into account the landslide geometry and provide a slightly pes- 400 simistic risk estimation in terms of number of affected build- Fig. 9. Schematic example of intersection probability. The houses ings. Thus a 100 m buffer has been added to the 1 814 667 (in grey) are expanded with a buffer (in green). Thus, if the center buildings extracted from the vectorized landscape model of of a circular landslide (in brown), with a radius equal to the buffer Switzerland (Vector25, © swisstopo). Then the total surface distance, occurs inside of the buildings + buffer area , the land- has been compared with each cell surface to obtain the inter- slide is assumed to reach a house. The probability of intersection 405 section probability (Fig. 10). It has to be mentioned that in- is then given by the ratio of the buildings + buffer area with the total area. In this example, the probability that a landslide, knowing tersection is only considered with a boolean approach, which it occurs, reaches a house is 0.158. The buffer permits to simplify means that a landslide can affect a building or not, but the po- the intersection probability calculation since landslides can then be tential for one landslide to affect several buildings is not con- considered as points, without however neglecting their surface. The sidered. It should also be noted that the buffers are made be- intersection probability of a point and a surface is indeed easier to 410 fore cutting shapes into cells in order to take into account the calculate than the intersection probability of two shapes. possibility for a landslide occurring in a given cell to reach a house located close to the border of an adjacent cell. The estimation of the associated cost is more complicated if the landslide is considered to be circular, it will affect a as the value of the buildings is not known. This information house if its center is located inside the buffer area (buildings 415 could be obtained from the buildings insurance for 19 over 26 included). As a result, the conditional probability is calcu- cantons for which a public insurance exists and is mandatory. lated considering the surface covered by the houses and their However, a suitable vulnerability curve linking the landslide P. Nicolet et al.: Shallow landslides stochastic risk modeling 7

Start High

Precipitation- Cumulative Precipitation Generate landslide relation geological Low map random matrix (for each geology) map

Attribute each divide into celle to one classes geological unit

Assess the Generate number of random matrix landslides

Assess the Generate number of random matrix intersections 05010025 Kilometers

no i = iterations ?

yes Fig. 10. Intersection probability map displaying the conditional probability for a 100 m radius circular landslide to affect a house Number of affected buildings for each cell of the model. High means that the probability is equal (distribution) or close to one, yellow that it is close to 0, whereas white indicate a null probability (hillshade: © Swisstopo)

Fig. 8. Flow diagram showing the assessment methodology used to obtain the number of affected buildings. 385 buffers. Since the buffers can overlap, the resulting probabil-

icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion ity considers the intersection with at least one building. Al- NHESSD though landslides are usually not circular but have an elon- 1, 747–791, 2013 gated shape, a circle is used in order to simplify the model Shallow landslides stochastic risk by avoiding the need to consider a real geometry. Indeed, modelling P. Nicolet390 et al. for non-circular landslides, the intersection probability cannot be simply reduced to a single number for each cell, since Title Page

Abstract Introductionthe intersection does not depend only on the position of the Conclusions Referencescenter, but also on the orientation of the considered shape. Tables Figures Since, for a given surface, an elongated shape is more J I Fig. 9. Schematic example of intersection probability. The houses (in grey) are expanded with 395 a buffer (in green). Thus, if the center of a circular landslide (in brown), with a radius equal to J I likely to intersect a building than a round one, the circle di- the buffer distance, occurs inside of the buildings + buffer area, the landslide is assumed to reach a house. The probability of intersection is then given by the ratio of the buildings + buffer Back Close area with the total area. In this example, the probability that a landslide, knowing it occurs, ameter is set to 200 m in order to completely include 90% reaches a house is 0.158. The buffer permits to simplify the intersection probability calculation Full Screen / Esc since landslides can then be considered as points, without however neglecting their surface. of the landslides (Fig. 2). This diameter results in an over- The intersection probability of a point and a surface is indeed easier to calculate than the Printer-friendly Version intersection probability of two shapes. Interactive Discussion estimation of the landslide surface, but takes indirectly into account the landslide geometry and provide a slightly pes- 784 400 simistic risk estimation in terms of number of affected build- Fig. 9. Schematic example of intersection probability. The houses ings. Thus a 100 m buffer has been added to the 1 814 667 (in grey) are expanded with a buffer (in green). Thus, if the center buildings extracted from the vectorized landscape model of of a circular landslide (in brown), with a radius equal to the buffer Switzerland (Vector25, © swisstopo). Then the total surface distance, occurs inside of the buildings + buffer area , the land- has been compared with each cell surface to obtain the inter- slide is assumed to reach a house. The probability of intersection 405 section probability (Fig. 10). It has to be mentioned that in- is then given by the ratio of the buildings + buffer area with the total area. In this example, the probability that a landslide, knowing tersection is only considered with a boolean approach, which it occurs, reaches a house is 0.158. The buffer permits to simplify means that a landslide can affect a building or not, but the po- the intersection probability calculation since landslides can then be tential for one landslide to affect several buildings is not con- considered as points, without however neglecting their surface. The sidered. It should also be noted that the buffers are made be- intersection probability of a point and a surface is indeed easier to 410 fore cutting shapes into cells in order to take into account the calculate than the intersection probability of two shapes. possibility for a landslide occurring in a given cell to reach a house located close to the border of an adjacent cell. The estimation of the associated cost is more complicated if the landslide is considered to be circular, it will affect a as the value of the buildings is not known. This information house if its center is located inside the buffer area (buildings 415 could be obtained from the buildings insurance for 19 over 26 included). As a result, the conditional probability is calcu- cantons for which a public insurance exists and is mandatory. lated considering the surface covered by the houses and their However, a suitable vulnerability curve linking the landslide icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

P. Nicolet et al.: Shallow landslides stochastic risk modeling 7 NHESSD 1, 747–791, 2013

Start High Shallow landslides stochastic risk Precipitation- Cumulative Precipitation Generate landslide relation geological Low modelling map random matrix (for each geology) map P. Nicolet et al.

Attribute each divide into celle to one classes Title Page geological unit

Abstract Introduction

Assess the Conclusions References Generate number of random matrix landslides Tables Figures

Assess the J I Generate number of random matrix intersections 05010025 Kilometers J I

Back Close no Fig. 10. Intersection probability map displaying the conditional probability for a 100 m radius i = iterations ? circular landslide to aﬀect a house for each cell of the model. High means that the probability Full Screen / Esc yes is equalFig. or close 10. toIntersection one, yellow that probability it is close to map 0, whereas displaying white theindicate conditional a null probability (hillshade:probability © Swisstopo). for a 100 m radius circular landslide to affect a house Number of Printer-friendly Version affected buildings for each cell of the model. High means that the probability is equal (distribution) or close to one, yellow that it is close to 0, whereas white indicate a Interactive Discussion null probability (hillshade: © Swisstopo) 785 Fig. 8. Flow diagram showing the assessment methodology used to obtain the number of affected buildings. 385 buffers. Since the buffers can overlap, the resulting probability considers the intersection with at least one building. Al- though landslides are usually not circular but have an elongated shape, a circle is used in order to simplify the model by avoiding the need to consider a real geometry. Indeed, 390 for non-circular landslides, the intersection probability cannot be simply reduced to a single number for each cell, since the intersection does not depend only on the position of the center, but also on the orientation of the considered shape. Since, for a given surface, an elongated shape is more 395 likely to intersect a building than a round one, the circle diameter is set to 200 m in order to completely include 90% of the landslides (Fig. 2). This diameter results in an overestimation of the landslide surface, but takes indirectly into account the landslide geometry and provide a slightly pes- 400 simistic risk estimation in terms of number of affected build- Fig. 9. Schematic example of intersection probability. The houses ings. Thus a 100 m buffer has been added to the 1 814 667 (in grey) are expanded with a buffer (in green). Thus, if the center buildings extracted from the vectorized landscape model of of a circular landslide (in brown), with a radius equal to the buffer Switzerland (Vector25, © swisstopo). Then the total surface distance, occurs inside of the buildings + buffer area , the land- has been compared with each cell surface to obtain the inter- slide is assumed to reach a house. The probability of intersection 405 section probability (Fig. 10). It has to be mentioned that in- is then given by the ratio of the buildings + buffer area with the total area. In this example, the probability that a landslide, knowing tersection is only considered with a boolean approach, which it occurs, reaches a house is 0.158. The buffer permits to simplify means that a landslide can affect a building or not, but the po- the intersection probability calculation since landslides can then be tential for one landslide to affect several buildings is not con- considered as points, without however neglecting their surface. The sidered. It should also be noted that the buffers are made be- intersection probability of a point and a surface is indeed easier to 410 fore cutting shapes into cells in order to take into account the calculate than the intersection probability of two shapes. possibility for a landslide occurring in a given cell to reach a house located close to the border of an adjacent cell. The estimation of the associated cost is more complicated if the landslide is considered to be circular, it will affect a as the value of the buildings is not known. This information house if its center is located inside the buffer area (buildings 415 could be obtained from the buildings insurance for 19 over 26 included). As a result, the conditional probability is calcu- cantons for which a public insurance exists and is mandatory. lated considering the surface covered by the houses and their However, a suitable vulnerability curve linking the landslide icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

NHESSD 1, 747–791, 2013 8 P. Nicolet et al.: Shallow landslides stochastic risk modeling

LF CF FLMC MM 1 1 1 1 Shallow landslides stochastic risk 0.99 0.95 0.95 0.9 modelling 0.98 0.9 P. Nicolet et al. 0.97 0.9 0.8 0.85 0.96 Title Page 0.85 0.95 0.8 0.7

0.94 Abstract Introduction 0−41 mm (688/0) 0−41 mm (6/0) 0−41 mm (196/0) 0−41 mm (1499/1)

Cumulative frequency Cumulative frequency Cumulative frequency 0.75 Cumulative frequency 41−47 mm (835/1) 41−47 mm (431/0) 41−47 mm (600/0) 41−47 mm (1101/0) 0.8 47−52 mm (501/0) 47−52 mm (644/0) 47−52 mm (593/0) 0.6 47−52 mm (1051/0) 52−56 mm (299/0) 0.93 52−56 mm (673/0) 52−56 mm (367/0) 52−56 mm (862/0) Conclusions References 56−62 mm (390/1) 56−62 mm (795/0) 56−62 mm (301/0) 56−62 mm (1193/0) 62−71 mm (429/2) 62−71 mm (689/1) 0.7 62−71 mm (390/0) 62−71 mm (1185/0) 71−81 mm (482/0) 71−81 mm (610/0) 71−81 mm (447/0) 71−81 mm (1004/1) 81−91 mm (453/1) 0.92 81−91 mm (654/0) 81−91 mm (499/2) 81−91 mm (958/1) Tables Figures 0.75 91−101 mm (386/1) 91−101 mm (635/2) 91−101 mm (533/2) 0.5 91−101 mm (864/2) 101−114 mm (367/7) 101−114 mm (635/2) 101−114 mm (529/6) 101−114 mm (1040/14) 114−134 mm (328/6) 114−134 mm (335/1) 0.65 114−134 mm (661/16) 114−134 mm (1134/27) 134−158 mm (393/15) 0.91 134−158 mm (266/1) 134−158 mm (745/59) 134−158 mm (1127/151) 158−184 mm (431/26) 158−184 mm (254/1) 158−184 mm (804/149) 158−184 mm (1029/512) 184−219 mm (642/159) 184−219 mm (140/9) 184−219 mm (861/328) 184−219 mm (921/1008) 219−321 mm (793/566) 219−321 mm (13/1) 219−321 mm (832/932) 219−321 mm (939/1727) J I 0.7 0.9 0.6 0.4 0 10 20 0 1 2 3 0 10 20 0 10 20 Number of landslides Number of landslides Number of landslides Number of landslides J I

Fig. 11.Fig. 11.LandslideLandslide relation relation with precipitation with precipitation and lithological group. and The lithological curves for small group. precipitation The amounts curves are not visiblefor small because precip- of Back Close itationthe amounts low number of are landslides. not Note visible that scales because are not similar. of the Numbers low between number brackets of are landslides. respectively the number Note of cells that in scalesthe class are and the number of landslides in the cells, averaged over the iterations. not similar. Numbers between brackets are respectively the number of cells in the class and the Full Screen / Esc number of landslides in the cells, averaged over the iterations. intensity, characterized by parameters such as depth or area, 440 (Fig. 10). This approach results in 2 360 affected buildings, to the damage rate, is difficult to assess. The lack of knowl- implying a mean cost x¯ of 6 907 CHF per building. No un- Printer-friendly Version 420 edge on the precise landslide characteristics and location as certainty is considered on this parameter. well as the inherent variability of the elements at risk com- The generation of exponential variates is obtained by sam- plicates even more the assessment of the vulnerability (Galli pling from the quantile distribution, which is given by the Interactive Discussion and Guzzetti, 2007). Therefore, in order to keep the mod- 445 inverse function of the exponential cumulative distribution els precision consistent with the previous step, we chose not as: 425 to use a value and vulnerability curve to assess the damage ln(1−u) cost, but to assess it directly from the 2005 event mean dam- F −1(u)=x = − 786 λ (3) age cost. The expected damage cost for a given building x is as- where u is a uniformly distributed random number between 0 sumed to follow an exponential distribution with probability and 1. The exponentially distributed damage cost is sampled 430 density function: 450 for each case of impact identified by the model. λexp(−λx),x≥ 0 The fat-tailed nature of the exponential distribution allows f(x)= 0,x<0 (2) obtaining a more realistic estimate of the damage costs than a normal or triangular distribution and does not need the esti- The distribution is only defined in terms of its first mo- mation of the second moment characterizing the variance of −1 ment λ, which is equal to x¯ , x¯ being the expected mean 455 the distribution. The latter is a useful feature as the statistical damage cost per building assumed for the 2005 event. This distribution of the damage costs per building is not known 435 cost is estimated by dividing the total damage cost induced in our particular case. The lognormal distribution also has by landslides to private infrastructures (16.3 million CHF) by heavy tails and was successfully used to model the cost as- the expected number of affected buildings. The latter is ob- sociated to floods (Merz et al., 2004). However, due to the tained by summing over all grid cells the product between the 460 larger number of degrees of freedom, it is also not suitable number of landslides (Fig. 1) and the intersection probability for our application. icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion P. Nicolet et al.: Shallow landslides stochastic risk modeling 9 NHESSD 0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 α 1, 747–791, 2013 0.4

0.3 Shallow landslides stochastic risk 0.2 250’000 modelling

0.1

200’000 P. Nicolet et al.

0 120 160 200 240 280 150’000 Precipitation amount [mm] Title Page

Limestones FLMC MM Abstract Introduction 100’000

500’000 550’000 600’000 650’000 700’000 750’000 800’000 8 Conclusions References β Fig. 13. Mean modeled number of landslidesTables with the gammaFigures func- 6 tions. X et Y labels are the Swiss Easting and Swiss Northing coordinates [km].) J I 4

for α for the classes with precipitationJ lower thanI 184 mm 2 for LF and lower than 158 mm forBack FLMC. Close 485 The general increase of both parameters is a desirable 0 property and is in accordance with ourFull prior Screen expectations. / Esc In 120 160 200 240 280 fact, increasing precipitation amounts increase the expected Precipitation amount [mm] number of landslides (represented by α) and the dispersion of Printer-friendly Version the distribution (represented by β). Higher β values are rep- Fig. 12. Fitted parameters for α and β of the gamma distribution. 490 resentative of heavy-tails, which means that the probability Fig. 12. Fitted parameters for α and β of the gamma distribution Interactive Discussion of observing a high number of landslides rises with increasing precipitation amount. The spatial distribution of the number of landslides was 4 Results 787 computed following the procedure described in Fig. 8 using 495 both the raw data and the gamma fits. However, since gamma The statistical distribution of landslides as a function of pre- distributions have been fitted only for the classes contain- cipitation amount and lithological group is given in Fig. 11. ing enough data samples, raw data have been used instead of 465 The probability to observe a given number of landslides in a gamma distributions when not available. The mean modeled given lithological group is a monotonically increasing func- number of landslide with gamma fits is given in Fig. 13 and tion of the precipitation amount. CF show a very little sus- 500 is very similar to the mean number of landslides modeled ceptibility to landslides compared to the other groups as ev- with raw data. The spatial pattern is relatively similar to the idenced by the low number of observed landslides. With spatial distribution of rainfall amounts, with two remarkable 470 similar precipitation amount, MM formations tend to have differences. First, the relation between precipitation amount a higher probability to contain at least one landslide than and number of landslides is not linear, which implies that FLMC or LF. However this relation is less evident for larger 505 areas with low precipitation amounts show a null to very landslide numbers. low number of landslides. The second difference is due to Table 1 shows the fitted values of the gamma distribution the sharp geographical transitions between the lithological 475 for the highest five precipitation classes, whereas Fig. 12 dis- units, which lead to sharp transitions in the modeled number play these values graphically. CF were not considered due to of landslides. An illustrative example occurs when moving the low number of samples. The α parameter (shape), char- 510 from the MM formations the CF, which strongly reduces the acterizes the central location of the distribution, while the β number of landslides (see Fig. 4). These results seems to be parameter (inverse scale) characterizes its dispersion. A gen- in good agreement with the observed distribution landslides 480 eral increase in both α and β parameters with precipitation (Fig. 1). amount can be observed, although some values are not fol- To evaluate the ability of the gamma fits to reproduce the th th lowing the general linear trend. This is especially the case 515 raw data, maps for the 95 and 98 quantiles have been icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

P. Nicolet et al.: Shallow landslides stochastic risk modeling 9 NHESSD 1, 747–791, 2013 0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Shallow landslides α stochastic risk 0.4 modelling

0.3 P. Nicolet et al.

0.2 250’000 Title Page

0.1 Abstract Introduction 200’000 Conclusions References 0 Tables Figures 120 160 200 240 280 150’000 Precipitation amount [mm] J I

J I Limestones FLMC MM 100’000 Back Close 500’000 550’000 600’000 650’000 700’000 750’000 800’000 Full Screen / Esc 8 Fig. 13. Mean modeled number of landslides with the gamma functions. X- and Y-labels are β the Swiss Easting and Swiss Northing coordinates [km]. Fig. 13. Mean modeled number of landslides with the gamma func- Printer-friendly Version 6 tions. X et Y labels are the Swiss Easting and Swiss Northing coor- Interactive Discussion dinates [km].)

4 788 for α for the classes with precipitation lower than 184 mm 2 for LF and lower than 158 mm for FLMC. 485 The general increase of both parameters is a desirable 0 property and is in accordance with our prior expectations. In 120 160 200 240 280 fact, increasing precipitation amounts increase the expected Precipitation amount [mm] number of landslides (represented by α) and the dispersion of the distribution (represented by β). Higher β values are rep- 490 resentative of heavy-tails, which means that the probability Fig. 12. Fitted parameters for α and β of the gamma distribution of observing a high number of landslides rises with increasing precipitation amount. The spatial distribution of the number of landslides was 4 Results computed following the procedure described in Fig. 8 using 495 both the raw data and the gamma fits. However, since gamma The statistical distribution of landslides as a function of pre- distributions have been fitted only for the classes contain- cipitation amount and lithological group is given in Fig. 11. ing enough data samples, raw data have been used instead of 465 The probability to observe a given number of landslides in a gamma distributions when not available. The mean modeled given lithological group is a monotonically increasing func- number of landslide with gamma fits is given in Fig. 13 and tion of the precipitation amount. CF show a very little sus- 500 is very similar to the mean number of landslides modeled ceptibility to landslides compared to the other groups as ev- with raw data. The spatial pattern is relatively similar to the idenced by the low number of observed landslides. With spatial distribution of rainfall amounts, with two remarkable 470 similar precipitation amount, MM formations tend to have differences. First, the relation between precipitation amount a higher probability to contain at least one landslide than and number of landslides is not linear, which implies that FLMC or LF. However this relation is less evident for larger 505 areas with low precipitation amounts show a null to very landslide numbers. low number of landslides. The second difference is due to Table 1 shows the fitted values of the gamma distribution the sharp geographical transitions between the lithological 475 for the highest five precipitation classes, whereas Fig. 12 dis- units, which lead to sharp transitions in the modeled number play these values graphically. CF were not considered due to of landslides. An illustrative example occurs when moving the low number of samples. The α parameter (shape), char- 510 from the MM formations the CF, which strongly reduces the acterizes the central location of the distribution, while the β number of landslides (see Fig. 4). These results seems to be parameter (inverse scale) characterizes its dispersion. A gen- in good agreement with the observed distribution landslides 480 eral increase in both α and β parameters with precipitation (Fig. 1). amount can be observed, although some values are not fol- To evaluate the ability of the gamma fits to reproduce the th th lowing the general linear trend. This is especially the case 515 raw data, maps for the 95 and 98 quantiles have been 10 P. Nicolet et al.: Shallow landslides stochastic risk modeling

Table 1. Fitted parameters of the gamma distribution.

Precipitation LF FLMC MM [mm] αβαβαβ

114–134 0.0323 1.4438 0.1347 0.7346 0.0683 1.0392 134–158 0.3604 0.5403 0.2241 0.9303 0.0801 2.6114 158–184 0.1927 0.9673 0.1288 2.1937 0.1531 4.3495 184–219 0.0839 3.7578 0.2026 2.7379 0.2265 6.0948

219–321 0.1214 7.0373 0.2457 5.4336 0.4966 4.4464 | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

95th percentile 98th percentile NHESSD

8 16 1, 747–791, 2013 7 14 6 12 5 10 Shallow landslides 4 8 stochastic risk 3 6 Raw data 2 4 modelling 1 2

0 0 P. Nicolet et al.

8 16 7 14 6 12 Title Page 5 10 4 8 Abstract Introduction 3 6 Gamma fit 2 4 Conclusions References 1 2

0 0 Tables Figures

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Printer-friendly Version Fig.Fig. 14. 14.95th95th and and 98th percentiles 98th percentiles of the number of landslidesof the using number raw data of (first landslides row) and gamma using fits (second raw row). data The third (first presents row) the and difference between the raw and gamma fits of both percentiles gamma fits (second row). The third presents the difference between the raw and gamma fits of Interactive Discussion both percentiles. modeled, still using a Monte-Carlo simulation to account for the results are relatively similar for the 95th quantile (with the probabilistic aspect of the lithology (Fig. 14). Although slightly lower values for the gamma fit), the 98th quantile 789 P. Nicolet et al.: Shallow landslides stochastic risk modeling 11 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

520 shows more differences. Indeed, the gamma ﬁt seems to un- 1 derestimate the number of landslides observed in the raw data Raw data: x¯ =5738 NHESSD 0.8 and indicates that the end of the tail of the distribution is not Gamma ﬁt: x¯ =5600.1 adequately represented. 1, 747–791, 2013 0.6

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0.2 Shallow landslides 525 Although the landslide number is reproduced, the expected Cumulative frequency stochastic risk number of hit buildings is almost never reached in the sim- 0 ulations (Fig 15). Indeed, the expected number of affected 4500 5000 5500 6000 6500 7000 modelling Number of modeled landslides buildings for the event is 2 360, whereas the simulations return a mean of around 1 860. As a consequence, the damage 1 P. Nicolet et al. 530 amount is not reached either since it is derived from the lat- Raw data: x¯ =1880.6 0.8 ter. Tests have been made using a 20 m buffer for the houses Gamma ﬁt: x¯ =1844.6 and the same effect was observed. It is not yet clear why the 0.6 observed total number of hit buildings is underestimated by Title Page 0.4 the model. One possible reason could be that the landslide 535 localization is highly correlated with the buildings location. 0.2 Abstract Introduction

To test this hypothesis, we compared the intersection proba- Cumulative frequency 0 bility of cells within which landslides actually occurs to the 1400 1600 1800 2000 2200 2400 Conclusions References intersection probability of cells in which the mean modeled Number of hit building number of landslides (Fig. 13) is above 0.5. Considering only Tables Figures 1 540 these cells allows to keep the most susceptible cells accord- Raw data: x¯ =13 ing to the model. This comparison indicates that the mod- 0.8 Gamma fit: x¯ =12.7 eled landslides tends to occur in cells with lower intersec- J I 0.6 tion probability than the actual landslides. This effect is not clearly visible with a 20 m buffer, but is more obvious with 0.4 J I 545 100 m buffers (Fig. 16). 0.2 Back Close Cumulative frequency 0 10 11 12 13 14 15 16 17 Full Screen / Esc 5 Discussion Damage amount [million CHF] The landslide model presented in this paper only considers precipitation amounts and geologyFig. as 15. inputNumber parameters. of landslides, number of hit buildings and damage amount calculated from raw Printer-friendly Version However, other variables such as terraindata slope, (blue soil solid thickness line) andFig. gamma 15. Number fits of (red landslides, dashed number line). of hit Mean buildings value and damagex¯ for each line is displayed amount calculated from raw data (blue solid line) and gamma fits 550 and permeability contrast, play a key role in shallow land- Interactive Discussion on the graph, whereas black(red dashed dots line). correspond Mean value x¯ tofor the each data line is of displayed the event on the or the expected number slide generation. These variables areof either affected hard tobuildings. measure graph, whereas black dots correspond to the data of the event or the over a large domain, e.g. the soil thickness, or show spatial expected number of affected buildings. variability at scales which are smaller than 1x1 km2 resolution, e.g. the terrain slope. Additionally, the uncertainty of 790 555 the landslide inventory does not allow matching the location of the landslide with such high resolution variables. As a 570 events, which are weighted based on their frequence of oc- consequence, the 1x1 km2 resolution model only gives in- currence (return period). This step is essential in order to ob- formation about the large scale pre-conditioning factors for tain a mean annual cost as well as an exceedance probability landslide generation. Smaller scale features may affect the curve. One possibility to generate a large number of rainfall 560 process of landslide triggering in a significant way. Further- fields to appropriately represent the full risk estimation could more, this model is based only on one single event and should 575 be based on design storms (Seed et al., 1999). Stochastic be compared with other similar rainfall events. In particular, rainfall fields could be generated according to a given return it should be compared with similar events producing land- period and be used to simulate the spatial distribution of landslides in different geological settings, to validate the aggre- slides under extreme rainfall conditions. Attempts have been 565 gation of different lithology into four main units. Indeed, made to use a return period in order to predict landslide trig- landslides susceptibility might be different in Jura limestones 580 gering but, they were mainly performed at local scale (e. g., than in Prelpine limestones, for example. Iida, 1999; D’Odorico et al., 2005; Iida, 2004; Tarolli et al., The annual probability to overcome a given total damage 2011) and would therefore not be suitable for a larger area, cost could be assessed by analyzing different precipitation since the spatial variability is not taken into account. On the icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

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Cumulative occurence 0.3 Cumulative occurence 0.3 Conclusions References 0.2 0.2 All Switzerland All Switzerland 0.1 Observed landslides 0.1 Observed landslides Tables Figures Modeled landslides Modeled landslides 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Intersection probability (with 20m buffer) Intersection probability (with 100m buffer) J I Fig. 16. Comparison of the intersection probability for the cells in which landslides occurred Fig. 16. Comparison of the intersection probability for the cells in which landslides occurred and in which landslides have been modeled J I (cellsand with in a which mean above landslides 0.5 have been have kept). been As a comparison, modeled the (cells distribution with over a mean all Switzerland above is shown0.5 have been kept). As a comparison, the distribution over all Switzerland is shown. Back Close

other hand, the spatial distribution of rainfall by means of types into the landslide model. Full Screen / Esc 585 radar data has been used for early-warning (e. g., Apip et al., When it comes to the damage cost assessment, due to the 2010), but as far as we know, is has not been used as in start- lack of information on the number of affected buildings and ing point to simulate potential future events. 620 corresponding distribution of costs, a few important assump- Printer-friendly Version Another issue concerns the landslide timing. We used the tions were made. The total number of affected buildings precipitation amount of the whole event (6 days) as a pre- was estimated by means of an intersection probability and Interactive Discussion 590 dictor for landslide occurrence. But, shallow-landslides are this number was used to obtain a mean cost per hit build- known to be sensitive to the intensity and duration of the rain- ing. The number of hit buildings is an uncertain estimation fall, as well as to the hyetograph shape (D’Odorico et al., 625 since it depends on the exact location of the landslides inside 2005). There are two main reasons for this simplification.791the cell. Indeed, we consider the landslides to be uniformly The first is the lack of data on the exact timing of landslides, distributed within a grid cell. This assumption is realistic at 2 595 which does not allow analysing the temporal precipitation the model scale since every 1x1 km cell contains slopes that pattern preceding their triggering. The second reason is due might fail. However, if susceptible slopes were located, in- to the uncertainty of the radar QPE product, which is higher 630 side of a cell, far from the houses, the modeled intersection when used to analyse rainfall time series at high temporal probability would not be null, although it might be the case resolutions, for instance hourly or 10 minute accumulations. in reality. We plan to overcome this issue in the future by us- 600 The spatial distribution of QPE accuracy can still be affected ing a susceptibility map to constrain the landslides location by some residual ground clutter, which overestimates the true at the intersection probability step. rainfall amount, and by the blockage of low level beams, 635 The distribution of costs was assumed to be exponential, which leads to the underestimation of ground rainfall due to which has a desirable long-tail property and is completely de- using only the beams aloft. Wuest¨ et al. (2010) present a fined by its mean value. Despite being only defined in terms 605 method to obtain hourly precipitation fields by disaggregat- of the average costs, the obtained variability is supposed to ing the daily rain gauge measurements with higher resolu- adequately represent the reality. Nevertheless, with a mean tion radar fields. If the timing of landslide occurrence was 640 cost of CHF 6 907 per building, the probability to overcome known, this dataset would be a valuable source of informa- 500 000 CHF is 5 × 10−36, i. e. one case over 1.8 × 1035. tion. However, the product is not accompanied by uncer- Since the mean price of a building is around one million CHF, 610 tainty estimates. A possible solution could involve the gen- this value is quite low as we know that at least one – but prob- eration of stochastic ensembles to represent the uncertainty ably more – building has been destroyed. This could be the of the radar QPE product with respect to the automatic net- 645 result of a too high number of affected buildings (since they work of 76 meteorological stations. This approach was re- have been estimated), which reduces the mean damage cost, cently implemented at MeteoSwiss (Germann et al., 2009) or an indication of the need for using a distribution of dam- 615 and could be a smart alternative to integrate ensembles of ages with a fatter tail. However, this confirms the fact that precipitation fields together with ensembles of lithological a distribution with a fat tail is suitable. Nevertheless, since