The weight of evidence statistical method in landslide susceptibility mapping of the Rio Pardu Valley (Sardinia, Italy)

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1 18 th World IMACS / MODSIM Congress, Cairns, Australia July The weight o eidence statistical method in landslide susceptibility mapping o the Rio Pardu Valley (Sardinia, Italy) Barbieri G. and P. Cambuli Dipartimento di Ingegneria del Territorio, Uniersità degli Studi di Cagliari, P.za D armi, Cagliari, Italia barbieri@unica.it Abstract: The landslide susceptibility o hillsides has been assessed using the statistical methodology known as weight o eidence, in order to estimate its potentiality, its diiculty o application and its suitability to speciic geomorphological settings. The Valley o the Rio Pardu Rier, eastern-central part o Sardinia, Italy, has been chosen or applying the method. On the basis o the IFFI Project (Inentory o Landslides Phenomena in Italy), the Rio Pardu Valley turns out to be one o more hazardous zone in Sardinia or the presence o ancient and current landslides, whose causes hae to be searched in the structural and lithological characteristics, the extreme meteorological conditions and the anthropic actors. The weight o eidence method has been implemented by means o the ArcView 3.2 sotware and the ArcSDM extension (Spatial Data Modeller). Like all the statistical methodologies, this method requires to identiy and to locate on a map all the instability phenomena which aected the studied area. On the basis o the territorial distribution o the past and present landslides the method calculates the weights to be assigned to the single classes o eery considered parameter. The landslide map o the Pardu Valley has been proided by the IFFI Project. The map has been digitized, georeerenced and supplemented by the obseration o the 2006 colour orthophotos. For ealuating the landslide hazard o the studied area, three basic parameters or landslide susceptibility hae been taken into consideration: the Lithology, the Land Use and the Slope. In order to check the reliability and the orecasting capability o the method, the inluence o each parameter on the instability phenomena has been calculated analyzing a sampled area, obtained by extracting at random a little percentage o the studied territory. In the sampled area the same proportion between the area aected by landslides and the total area calculated on the whole territory, equal to about the 0.063%, has been kept. Two subsets hae been so created: the Training set and the Validation set. In the extracting process, the morphometric, lithological and land use characteristics hae been considered, in order to obtain a sample which was actually representatie o the studied area, so that the distributions o the arious classes o eery single considered parameter were almost the same between the sampled area (training set) and the total area (alidation set). The Training set has been diided into two subgroups: the subgroup o the areas which do not present landslide phenomena, and the subgroup o the areas which present landslide phenomena. Then a statistical analysis o dierent parameters has been carried out, using the weight o eidence method, and the weights to be attributed to each class o eery single parameter hae been then obtained. Keywords: Landslide susceptibility zoning, Weight o eidence statistical method, Rio Pardu Italy. 2658

2 Barbieri and Cambuli, The weight o eidence statistical method in landslide susceptibility mapping o the 1. INTRODUCTION The catchment basin o the Rio Pardu rier, in the Ogliastra region, eastern-central part o Sardinia (Italy), was sureyed or an area o about 29 km 2, including the little illage o Gairo S. Elena, which was reounded ater the old illage o Gairo was destroyed in 1952 by a landslide. The Rio Pardu alley is extensiely coered by Palaeozoic metasedimentary rocks, that are widely present in almost all the south-eastern part o Sardinia. The present geomorphological eatures deried rom the tectonic phases o Alpine Orogeny. The major tectonic rameworks are oriented NW-SE and NE-SW (Vardabasso, 1956; Cocozza, 1974). The Rio Pardu alley deeloped along one o these tectonic alignments, oriented NW-SE, that crosses the central part o Sardinia. To this main tectonic alignment more dierently oriented ault systems are associated. The geomorphological processes responsible or the present landorm started in Pliocene, at the end o the tectonic actiity. The rier erosion signiicantly deepened the alley, producing talus deposit, especially on the let side o the alley, at the toe o limestone reliees, in the orm o heterogeneous and chaotic blocks. This paper aims at assessing the landslide susceptibility o this area, using the statistical methodology known as Weight o Eidence (Bonham-Carter et al., 1988; 1989; Agterberg et al., 1990). 2. THE WEIGHT OF EVIDENCE STATISTICAL METHOD The weight o eidence method is based on a statistical bayesian biariate approach. Originally, this method was deeloped or gold mineralization researches. Ater seeral years, the interest or this method extended to seeral researchers working in the ield o landslide hazard assessment (Lee et al., 2004; Rezaei Moghaddam et al., 2007). The weight o eidence method was implemented using the ArcView 3.2 sotware and the ArcSDM extension (Spatial Data Modeller), deeloped by Kemp et al. (2001). This extension implements some o the most commonly used statistical spatial models. The weight o eidence method is based on the Bayes theorem and on the concepts o prior and posterior probability, or assessing the relations between the spatial distribution o the areas aected by landslides and the spatial distribution o the analyzed landslide susceptibility actors (or parameters). It is thereore possible to calculate the degree o inluence that each actor had, and will hae in the uture, on the deelopment o landslide eents. I a part A o the studied area is aected by landslide phenomena, the prior probability o inding a landslide within A t (total studied area) is: A P = 1 At This initial estimation can be then increased or decreased depending on the relations between analyzed actors and landslides. The probability o inding one o the actors examined in the study area is gien by: T P = 2 At where T = total area occupied by a certain class o a certain actor (e.g. slope class 20-35%). For the whole territory sureyed, the probability o inding a landslide in the areas occupied by the n class o the j parameter is the ratio between the probability o inding a landslide inside the territory occupied by the n class o the j parameter and the probability o inding an area occupied by the n class o the j parameter in the whole territory: P( T { } A ) P T A P { A T } = = P 3 P P Similarly, the posterior probability o inding a landslide in the areas not occupied by the n class o the j parameter is: P( T A ) P { } { T A } P A T = = P 4 P P For mathematical reasons, probabilities can be expressed more coneniently as odds: P O = 5 1 P Then, equations 3 and 4 can be expressed as: 2659

3 Barbieri and Cambuli, The weight o eidence statistical method in landslide susceptibility mapping o the { A T } { A } O T O 6 O = O O { } { T } A O A T = O O 7 In the weight o eidence method, the natural logarithms are applied to both equations 6 and 7 to obtain: T { A T } = W ln O ln O T { A T } = W ln O ln O where W is the positie weight to be assigned when the class n o the j parameter is present, and W- is the negatie weight to be assigned when the class n o the j parameter is absent. The weights are calculated by the ollowing equations: W T A Landslide area in the considered class P = ln Total lanslide area 10 P { T } { } A A = ln = ln T A T A Stable area in the considered class Total stab le area A T A Total lan slides are a in the o ther class es P{ T A } = { } A W = = Total lan slide area ln ln ln P T A T A Total sta ble area i n the othe r classes 11 Total sta ble area A The W positie weight is directly proportional to the inluence that the n class o the j parameter has on landslides deelopment. To analyze the inluence o seeral parameters on the distribution o landslides in the area, the weights o each parameter are summarized, as these parameters are mutually statistically independent: n k k k k K { A T T T... T } = Σ W ln O n i ln OT 12 i = 1 where k can take the sign or - depending on the presence or absence o this parameter. The dierence between the positie and negatie weights, as computed or each class o each parameter analyzed, is a good indicator o its relation with landslides: C = W W 13 The alue o C is typically between 0 and 2; when the alue o C tends to zero, the presence o the considered parameter does not aect the distribution o landslides in the area; conersely, when C is approximately 2 or more, the correlation is ery signiicant. T is the sum o the product between posterior probability and the area, extended to all elementary cells in which the territory was diided: ideally T should then be approximately equal to the total landslide area. In the practical applications, it requently happens that T is greater than the landslide area, because there are generally some conditional dependencies between the ariables; i T does not exceed landslide area or more than 15%, conditional independence between the considered ariables exists. This test is called omnibus test (Agterberg and Cheng, 2002). 3. ANALYSIS In order to construct a landslide susceptibility map, three basic susceptibility landslide parameters were utilized: Lithology, Land Use and Slope. In order to test the reliability and the predictie capabilities o the weight o eidence method, the inluence o each parameter on the landslide susceptibility is calculated in a data sub-set obtained randomly extracting around one percent o the whole study area (training set). These samples hae the same proportion between the landslide area and the total area than the whole studied area (alidation set), that is about 0,063%. The extraction process took into account the morphological, lithological and land use characteristics o the area, in order to obtain a sample that is truly representatie o the whole studied area

4 Barbieri and Cambuli, The weight o eidence statistical method in landslide susceptibility mapping o the The arious thematic maps o the training set were oerlapped with the landslides map. On the basis o these intersections, by using ArcView 3.2 sotware and its extension ArcSDM (Spatial Data Modeller) positie and negatie weights or each class o each parameter were calculated (Table 1): Table 1. The weights calculated or the Lithology parameter Classes Areas (km 2 ) Landslides (n.) Weight Alluial deposits Limestones and dolomites Metasandstones Limestones talus Poriric dikes Argillaceous talus A quick analysis o these results highlighted some aspects o this methodology: the absence o landslide areas in the training set occupied by Alluial deposits makes impossible to calculate their weight; the presence o a single landslide in the training set occupied by Poriric dikes means that the weight assigned to them is too high, because there are some statistical problems due to the ery small area occupied by this ormation. These two anomalies are attributable to the act that these two lithologies occupy a ery small area, compared to the extension o the basin. Looking at the weights assigned to other ormations, the best correlation between the Argillaceous talus and the landslides may be obsered. Limestones and dolomites receied the lowest weights, and this was expected as these rocks hae excellent mechanical properties. Metasandstones obtained only a slightly higher weight than limestones and dolomites: they hae ery dierent geomechanical eatures rom the point o iew o racturing and alteration, that are certainly greater in the metasandstones than in limestones and dolomites. Statistical analyses do not highlight these patterns and underestimate the weight assigned to metasandstones. The Table 2 sets out the main results o the analysis with regard to the Land Use parameter. Table 2. The weights calculated or the Land Use parameter Classes Areas (km 2 ) Landslides (n.) Weight Shrubby areas Crops areas Heterogeneous agricultural areas Areas with rock outcrop Forest Urbanization The calculation o the weights or the "Slope" parameter presents more diiculties than the other actors, since the continuous nature o this parameter does not allow an immediate processing. To sole this problem, the discreetization in a inite number o classes is necessary; the inal classes were ound ater numerous attempts, when the best correlation between the parameter "Slope" and landslides were ound (Table 3). Table 3. The weights calculated or the Slope parameter Classes Areas (km 2 ) Landslides (n.) Weight THE LANDSLIDE SUSCEPTIBILITY MAP The weight calculated or each class o each parameter is assigned to each elementary grid cell. For each cell the inal probability is the sum o the weights o each parameter and the prior probability. The inal probability was obtained using the expression 12: ln P. Finale= W lno P. Finale= Exp( W lno ) = Exp(2.012 ln(0.052)) =

5 Barbieri and Cambuli, The weight o eidence statistical method in landslide susceptibility mapping o the In the Table 4 an example o how to calculate the weights or the cells is shown. Table 4. Weights assigned to the cells 1 and 2 Id Slope Slope W Land use Land use W Lithology Lithology W Sum o Weights Prior probability Final probability Forest Metasandstones Areas with rock outcrop Limestones talus Ater the calculation, the weights are applied to the alidation set to obtain the landslide susceptibility map. The probability was split in our classes: the range o each class was not chosen arbitrarily, but on the basis o the graph shown in Figure 1. Figure 1. Ranges o the probability classes 120% Real landslide areas 100% Cumulated landslide areas Calculated landslide areas 80% 60% 40% 20% Probability Looking at this graph, two main obserations can be made: the two cures, related to calculated and real landslide areas, seem to be ery similar; in both cures, some abrupt changes o the slope may be obsered, where the limits o the probability classes were placed. On the ground o these obserations, our classes o landslide susceptibility were singled out (Table 5). Table 5. Classes o landslide susceptibility Classes Value Hg Hg Hg Hg % 2662

6 Barbieri and Cambuli, The weight o eidence statistical method in landslide susceptibility mapping o the On the basis o all these data, the landslide susceptibility map o the studied area was drawn (Figure 2). Figure 2. Landslide susceptibility map o the Rio Pardu Valley near Gairo S. Elena Checking this map, the stable areas appear those with a slope less than 20 and, partly, the areas where the metasandstones, limestones and dolomites outcrop. The areas classiied as Hg2 are occupied by orests and are concentrated in the north-east part o the Pardu Valley and partly at north o the Gairo illage. Finally the areas classiied as Hg3 and Hg4 are concentrated where the Limestone and Argillaceous talus outcrop and the slope is greater then CONCLUSIONS The analysis perormed using the weight o eidence method showed the ollowing adantages: - it is an objectie system that can discriminate between the arious parameters, in order to understand which are the most important parameters in the deelopment o landslide phenomena; - the weights are calculated separately or each study area, allowing the method to choose dierent weights, or the same parameters, or dierent geomorphological settings; - the process o assigning weights is objectie and almost independent by choices o the obserer. The analysis showed also the ollowing disadantages: - the results o dierent analyzed areas are comparable only i the classiication ranking is standardized; - the method is not suitable or areas where dierent types o landslide moements occur; - the method need accurate and reliable inormation on past landslide moements; - the method either oeralues or underalues the weights o the parameters related to ery small portions o the study area. 2663

7 Barbieri and Cambuli, The weight o eidence statistical method in landslide susceptibility mapping o the REFERENCES Agterberg, F.P., G.F. Bonham-Carter, and D.F. Wright, (1990), Statistical Pattern Integration or Mineral Exploration. Geological Surey o Canada Contribution, Agterberg, F. P. and Q. Cheng, (2002), Conditional Independence Test or Weights-o-Eidence Modeling. Natural Resources Research, 11(4), Bonham-Carter, G.F., F.P. Agterberg, and D.F. Wright, (1988), Integration o Geological Datasets or Gold Exploration in Noa Scotia. American Society or Photogrammetry and Remote Sensing. Bonham-Carter, G.F., F.P. Agterberg, and D.F. Wright, (1989), Weights o eidence modelling: a new approach to mapping mineral potential. Statistical Application in the Earth Sciences, Agterberg, F.P. and Bonham-Carter, G.F. (Eds.), Geological Surey o Canada, 89(9), Cocozza, T. (1974), Schema stratigraico-strutturale del massiccio sardo-corso e minerogenesi della Sardegna. Memorie della società geologica italiana, 13. Kemp, L.D., G.F. Bonham-Carter, G.L. Raines, and C.G. Looney, (2001), Arc-SDM: Arciew extension or spatial data modelling using weights o eidence, logistic regression, uzzy logic and neural network analysis. Lee, S., J. Choi, and K. Min, (2004), Probabilistic landslide hazard mapping using GIS and remote sensing data at Boun, Korea. International Journal o Remote Sensing, 25(11), Rezaei Moghaddam, M.H., M. Khayyam, M. Ahmadi, and M. Farajzadeh, (2007), Mapping susceptibility landslide by using the weight-o-eidence model: a case study in Merek Valley, Iran. Journal o Applied Science, 7(22), Vardabasso, S. (1956), La ase Sarda dell'orogenesi Caledonica in Sardegna. Zeitschrit der Deutschen Geologischen Gesellschat, Band Symp,