• capacità predittiva
• analisi multivariata
• Analisi della suscettività

University of Pisa - Department of Earth Sciences
Program of Earth Sciences, XXVI Cycle
2009 – 2011

Abstract
Doctor of Philosophy dissertation

“Predictive power analysis of the MSUE-Conditional-Method”

Marco Capitani

INTRODUCTION
Landslides are a major source of damage in economic terms and in human lives and represent the world's second natural hazard after earthquakes (Yalcin et al., 2011). In fact, since the beginning of the 21st century landslides have involved worldwide about 1.5 million of people and caused a total economic loss of more than $ 875 million (EM-DAT, 2010). The economic and human losses continue to grow steadily for the continue population growth and the resulting urban sprawl in unstable areas (Pasuto & Soldati, 1996; Schuster, 1996; Guzzetti et al., 1999; NRC, 2004). Even in Italy, landslides are an extremely frequent natural event (AVI data, project-GNDCI CNR) and a major cause of risk to the country socio-economic fabric. Only in the last century, in fact, landslides have caused 5,939 deaths and 1,860 injuries with an average of 60 deaths / year. This condition puts our country in the fourth place in the world, behind the Andean countries, China and Japan (Guzzetti, 2000). In 2010 88 major landslide occurred and caused 17 dead, 44 injured as well the evacuation of 4431 people. Ventotene, Meran and Maierato are just some of the serious events that have marked Italy, while Liguria, Campania, Tuscany, Sicily, Calabria and Lombardy are the regions mostly affected (data Ispra, 2011). For Italy, the estimated damage to public finance amounts to around 1-2 billion per year (Department of Civil Protection, 1992; Luino, 2005), placing our country second only to Japan. For Italy, the estimated damage grows up to about 3-4 billion per year if we also take into account indirect costs, such as the lost of productivity and the reducing of real estate value (Reed & Fanti, 2005).
To cope with this situation, the scientific community is increasingly interested in the development of methods for the landslides susceptibility zonation, able to constitute a valid basis for proper land management and adequate risk prevention. In particular, the need to properly assess the propensity to collapse of areas not yet affected by landslides has brought scientific research to develop increasingly complex systems of investigation.
Landslide Susceptibility (LS) is the spatial probability of landslide occurrence and differs from Landslides Hazard (LH), as it no provides information on the timing and magnitude of predicted landslide event (Carrara et al., 1995; Guzzetti et al., 2005). LS presents the first step in assessing Landslide risk (Clerici et al., 2010).
The methods currently used to LS zonation can be synthetically grouped into three main types (Carrara et al., 1992; Guzzetti et al., 1999):
a) Heuristic methods that are qualitative o semi quantitative methods in which the quality of the results is strictly depends on the knowledge and the experience of the operators.
b) Deterministic methods that base their prediction over the empirical geotechnical laws requiring a large amounts of data. For the latter reason they are generally used only for areas not very extended.
c) Statistical methods that analyze the historical link between landslide-controlling factors and landslide distribution.
To modeling the LS for large areas statistical methods are the common used technique (Carrara et al., 1995; Ayalew and Yamagishi, 2005). Many different methods of statistical analysis are applied to LS assessments. More information on the different methodologies and nomenclatures can be found in review papers (e.g., Soeters and van Westen, 1996; Aleotti and Chowdhury, 1999; Guzzetti et al., 1999; Dai et al., 2002; Chung and Fabbri, 2005; van Westen et al., 2006; and reference therein).
The main assumption on which are based all the statistical methods is that “the past and the present landslide locations are the key to the future” (Carrara et al., 1995; Hutchinson, 1995; Zêzere, 2002). Landslides will occur in the areas where the boundary conditions are the same of the areas where landslides have occurred in the past. In other words, the probability of landslide occurrence over landslide free areas is carried out by the study of the similarity geo-environmental conditions between these areas and those in which landslides have been occurred. Therefore, for all statistical methods the conceptual work behind to the LS zonation consists in (Carrara et al., 1995; Vijith and Madhu, 2008):
a) The knowledge of landslides distribution and their mapping.
b) The mapping of a set of factor that are supposed to be directly or indirectly predisposing the landslide occurrence.
c) The assessment of statistical relationships between predisposing factors and landslides.
d) The classification of degree of LS on the basis of the observed statistical relationships.
The spatial analysis of the relationships between predisposing factors and landslides needs of the definition of the mapping unit on which the statistical observations are made and matching the observed data. Various methods have been proposed to partition the landscape for LS assessment and mapping (Meijerink, 1988; Carrara et al., 1995). Nowadays, the most used mapping units are the Grid Cells (Chung and Fabbri 1993), the Slope Units (Guzzetti et al., 1999) and the Unique Condition Units (UCUs) (Bonham-Carter, 1994; Chung and Fabbri, 1995; Carrara et al., 1995).
Over the last few decades, many researchers have produced landslide susceptibility maps using different methods of statistical analysis applied to the Unique Condition Units (UCUs) (Carrara et al., 1995; Chung et al., 1995; Guzzetti et al., 1999; Irigaray et al., 1999; Clerici et al., 2002; Falaschi et al., 2008). However, no one has emphasized how the choice of representing the dependent variable (which is defined into the landslides inventory) can lead to the construction of models with un-definable predictive power.
Theoretically, since susceptibility assessment tries to identify under what conditions landslides are generated, the dependent variable should be represented in the landslides inventory as the area where landslides originated, i.e., the detachment zones (Nefeslioglu et al., 2008). Moreover, if the landslides are also represented with their accumulation zone, the environmental factors so acquired are erroneously considered to be prone to landsliding (Clerici et al., 2006, 2010; Magliuolo et al., 2008).
Due to the fact that the detachment zones are only partially visible, their definition into an inventory map is highly subjective. Furthermore, without a geophysical prospecting, there is not the possibility to define how our representation differs from reality. This fact introduces unquantifiable errors in the dependent variable resolution that imply unquantifiable errors both in the definition of the UCU type involved in landslides and in the definition of the UCU instability extension (independent variables). Therefore, this way of variable dependent representation makes uncertain the results of the predictive power validation for the models so built. In fact, the dependent variable is used both in the construction of models and in their validation (Chung and Fabbri, 2003, 2008; Guzzetti et al., 2006; Guzzetti et al., 2009; Rossi et al., 2010). Basically, if the “undefined” detachment zone is considered as way to correlate the UCUs to the events of instability, the best predictive model, that is chosen from a validation process, could actually have a low predictive power for the future landslides occurrence. So, only a certain dependent variable should be used into landslides susceptibility analysis. Among the systems of representation of the landslide inventory that do not introduce large margins of subjectivity and therefore unquantifiable errors, the Main Scarp Upper Edge method (MSUE) (Clerici, 2002) is the only that could be better adapted to the purposes of the landslide susceptibility analysis. The applicability of statistical methods to the MSUE has been poorly studied in the past and only with a not rigorous way. In fact, the predictive ability of models was analyzed using a validation data set that was generated with a random split method of the occurred landslides, or regardless of the pre-landslide conditions in the relationship between predisposing factors and phenomena landslide. The random selection of a validation data set from the occurred landslides may lead us to the selection of the type and amount of the UCU involved in landslides not really representative of the landslide susceptibility image, that is the focus of the investigation. The statistical sample used for the analysis of the predictive ability of a forecasting model should be considered a part of all statistical units making up the population, chosen so as to give us a small but faithful image of the population characteristics (Bucciante et al., 2003). The forecasting model should be created using a dataset of landslides related to a period of time prior that to which belong the landslides used for its validation (Chung & Fabbri, 1999, 2008; Zêzere et al., 2005; Chung, 2006; Guzzetti et al., 2006b; Irigaray et al., 2007; Akgün et al., 2008; van Westen et al., 2008; Blahut et al., 2010; von Ruette et al., 2011 ).
On the other hand, among the methods of statistical analysis used to create landslide susceptibility maps, the conditional method appears to be one of the easiest to understand and to read for non-specialists.
Therefore, this study represents an attempt to assess the predictive capability of the MSUE Conditional Method and its advantages and limitations.

STUDY AREAS
The MSUEs Conditional Method was applied to the Milia and Roglio basins, situated in the southern-central Tuscany, Italy. The Milia basin has an extension of 101 Km2 and an elevation ranging from 39 m to 913 m above sea level, with an average value of 336 m (standard deviation = 167.5 m). The basin is stretched out to SE direction and shows a prevalent hilly character. Hillslopes are generally not very steep. The highest value of the slope gradient is present in the eastern part of the Milia basin where the carbonatic formations outcrop. The physiographic structure of the area is typical of landscapes in which the zones between the valley floor and slopes have a significant extension (Fig. 8). In fact, approximately 50% of the study area is located between the altitude of 325 m and the minimum value of the basin that characterizes the corresponding closing section. Only near the eastern side of the study area, where we observe the presence of a high morpho-structural, the altitude value tends to increase until the maximum of 913 m. Areas characterized by altitudes above 550 m are mainly concentrated in this area of the basin and represent approximately the 9% of the total basin extension. The upward trend of the altitude from the eastern to the western sectors of the basin indicates that the basin physiographic evolution is strongly conditioned by the geological-structural situation. Most of the streams of higher order has a general anti-apenninic management type and shows a strong vertical erosion tendency at the far north-eastern areas of the basin while in western the river action evolves into a prevalent lateral erosion whose effects are manifested in a non-negligible way even along the T. Milia just before its merger into the Cornia River, one of the leading collectors of the central-southern Tuscany.
The catchment area of the T. Roglio is one of the major sub-basins of the Era valley. The area covers about 160 km2 and an elevation ranging from about 20 m to about 500 m above the sea level, with an average value of 130.9 m. The basin is elongated in the N-NW direction and shows a predominantly hilly morphology with not very steep slopes. The highest values of the steepness are found mainly in areas of the basin where Pliocene formations with clayey and sandy-clayey facies outcrop. About 80% of the basin surface shows a steepness value less than 20°, the 20% denotes a slope value less than 6° and only 5% of the basin surface is characterized by a steepness more than 29°. The physiographic structure of the basin is typical of landscapes in which areas of the valley floor and the connection between these and the slopes are a very dominant feature. In fact, about 87% of the surface of the study area is located between 175 m and the minimum value which characterizes the basin with the corresponding closing section.
The hypsometric curve indicates a situation more pronounced than that observed in the basin of the T. Milia, in which about 90% of the territory is confined within an interval of about 150 m elevation. Only near the eastern area of the basin, where the high morphological and structural of Iano occours, the value tends to increase until it reaches the maximum of 500 m. Areas characterized by altitudes above 375 m are mainly concentrated in this area of the basin and represent about 5% of the total. The concentration of the higher altitudes along the eastern sectors of this basin indicates that the physiographic evolution is strongly conditioned by the geological-structural situation. With the exception of the T. Roglio, which assumes a prevailing apenninic direction, most of the higher order streams generally presents an anti-apenninic direction and a strong tendency to vertical erosion. The erosive effects associated with the lateral rivers action occur in a non-negligible even along the T. Roglio, in the section between the central areas of the basin up to the confluence with the Era river, that is one of the main tributaries of the Arno river.

MAIN GEOLOGICAL AND GEOMORPHOLOGICAL FEATURES
In the T. Milia basin the compressional events occurring before and during the collisional apenninic episode originated the complex sheet stack where three allochthonous units are emplaced above the Tuscan Unit. The two units at the top of this complex are derived from the Ligurian Domain and are, from top to bottom, the Palombini Shale Ophiolitic Unit and the Monteverdi-Lanciaia Ophiolitic Unit, respectively. Between these units and the Tuscany Unit there is the Argille and Calcari Unit that belongs to the Sub-Ligurian Domain (Costantini et al., 1991). All the allochthonous units are characteristic of distal turbiditic and hemipelagic environments and are composed by altering siltitic, argillitic, and fine arenitic formations and by argillitic with inter-bedded limestone formations. The ophiolitic units also contain remains of the basalt, gabbros and serpentinites complex disseminate as blocks in their sediments.
The Tuscan Unit is represented prevalently by the Mesozoic carbonatic succession, associated to very few outcrops of the middle and upper turbiditic and hemipelagic sequence.
Ligurian units show a complex, pre-upper Oligocene deformation history related to subduction, accretion and later exhumation events. The deformation history includes almost two deformation phases of veining, folding and thrusting. (Marroni et al., 2004). These deformative structures are successively superimposed by the deformative structures due to collisional and post collisional events. In the collisional event the Ligurian and Sub-Ligurian Units overthrusted the Tuscan Domain and have been deformed, with the units belonging to this later domain, by a kilometric folds that in the Milia basin have a WNW-ESE axial general direction.
Post collisional deformations are strictly related to the extensional tectonic, which began at the end of the Early Miocene and caused the collapse of a large part of the Apennines chain. This extensional event started with low and high angle normal faults as result of thinning of the upper crust. Then differential uplift, lowering and tilting phenomena have occurred since the middle Pleistocene (Bossio et al., 1993). The deposition of the Neogene-Quaternary successions has been largely controlled by vertical crustal movements. These successions are representative of coastal-marine and continental environments and are generally characterized by sandy clays and sandy conglomerates deposits.
In the Roglio basin the Apennine compressional phase has originated a complex of thrust between the formations belonging to the Succession Liguride and Tuscany (Costantini et al., 2002; Costantini et al., In press). In particular, in the eastern areas formations belonging to the Ofiolitifera Montaione Unit outcrop (Flysch of Montaione, a complex of M. Carulli) above those of the no-metamorphic Tuscan Succession, which in turn are over-thrusting above the Tuscan Metamorphic Unit. The units belonging to the Ligurian Domain are representative both of distal turbiditic and pelagic environments and of the oceanic crust that formed the ancient Ligurian-Piedmont Basin. These units are composed mainly by formations characterized by alternating shales, limestone and shales interspersed with basalts, gabbros, and serpentinites. The Tuscan Nappe is mainly composed by non-metamorphic mesozoic carbonate formations and with limited outcrops of paleocenic-miocenic turbidite formations. All pre-Neogene formations emerge only on the east of the basin, at the high morphological of Iano, while over the 80% of the area studied is formed by outcrops of Plio-Pleistocene deposits, mainly characterized by marine facies.
The extensional phase conditioned the hydrographic evolution of each basin. In particular, from the Pleistocene the tectonic evolution was followed by a rapid sinking of the hydrographic network, with the development of considerable level difference. The lowering of the network base level is suggested by numerous erosive terraces that are located at different altitudes along the basins. The lateral erosion action of the Milia and the Roglio river is an important still-active morphogenetic process.
The morphology of the study areas is also strongly conditioned by the numerous mass movements related to a prevalent rotational slide, translational slide and flow types (Cruden and Varnes, 1996). Moreover, in the Milia basin many phenomena of Deep-seated Gravitational Slope Deformation (DGSDs) are present and their evolution appears strictly related to the Pleistocenic tectonic evolution and the base level fluvial lowering. From a classification point of view, the type of movement of these DGSDs could be considered similar to Block-slide and Sackung (Zischinsky, 1969; Sorriso-Valvo, 1988; Dramis and Sorriso-Valvo, 1994; Cruden and Varnes, 1996). Most of these DGDSs are involved in landsliding processes.

MATERIALS AND METHODS
MSUE-Conditional Method
The Conditional Method is based on Bayes Theorem (Morgan, 1968) where the probability of the future occurrence of an event with determinate boundary conditions is determinated by the same type of events that occurred in the past with the same boundary conditions (conditional probability). In particular, for the landslide susceptibility (LS) assessment the conditional probability of landslide occurrence at specific UCU (boundary conditions) is assumed equivalent to the currently landslide density in that UCU (Carrara et al., 1995).
Considering the problems for the use of the detachment zones as dependent variable representation, in this study the landslides have been identified by their MSUEs (Clerici, 2002; Clerici et al., 2006, 2010). Furthermore, an upstream buffer of 10 m is used for each MSUEs, in order to consider the UCUs involved in the landslide process as potential representative of the boundary conditions existing before the landslides development (Clerici, 2002; Süzen and Doyuran, 2004a,b; Clerici et al., 2006; Nefeslioglu et al., 2008; Clerici et al., 2010).
Therefore, in the method applied to the LS zonation of the Milia and Roglio basins the conditional probability of landslide occurrence for a given UCU is assumed as the ratio of the sum of the areas of each UCU that fall within the MSUEs buffer and the total area for each specific UCU.
Considering the different orders of magnitude between the areas of the UCU inside the MSUE buffer and the total of the specific UCU, the landslide density has been expressed in m2/km2.

Landslides mapping
The landslide map is the result of a two-year detailed geological and geomorphological field survey. The landslides were mapped on a 1:10,000 Tuscany Region topographic map. This process has been carried out also with the aid of the aerial photographs taken in 1975 at the scale 1:13,000 (flight EIRA75). The use of these aerial photographs was necessary to split landslides into two temporal groups. The landslides occurred before the 1975 have been used to create the models, while the landslides occurred after the 1975 have been used to validate their predictive capability.
Following the division proposed by Keefer (1984), only 2039 deep-seated (≥ 3m) landslides were considered for the Milia basin. They occupy a surface of about 22.66 Km2, representing the 22.43% of the whole study area.
In accord to Guzzetti (1999), LS analysis should be carried out for different landslide types. For this reason, the landslides have been mapped into separate datasets on the base of their prevalent movement typology. Because in this study the MSUE is considered as the dependent variable, the landslides belonging to the complex typology have been classified on the base of their initial prevalent movement. So, in the Milia basin 2,039 landslides have been divided into three typologies: translational slide (1,577), flow type (155), and rotational type (307). Among these, 128 translational landslides, 31 flow landslides and 46 rotational landslides have been occurred after the 1975.
In the Roglio basin, only the 4.137 deep-seated landslides were considered. They occupy a surface of about 20.7 Km2, representing the 12.5% of the whole basin area. The landslides have been classified into three typologies: translational slide (3,174), flow type (873), and rotational type (90). Among these, 233 translational landslides, 109 flow landslides and 19 rotational landslides have been occurred after the 1975.
For the correct mapping of the MSUEs into a ArcGIS (ESRI) feature-class the landslides occurred before the 1975 have been mapped directly on the orthophotos (at the scale 1:10,000), with the aid of the aerial photograph inspection. The orthophotos have been successively scanned, imported into ArcGIS, rectified, geo-referenced, assembled and digitized into a feature-class. For the landslides occurred after the 1975, a GPS (Garmin 60CSx) field survey was necessary to delimit their MSUEs, where almost 7 points for a single main scarp have been marked. Within these 7 points, the landslide main scarp-body contacts are also taken. The MSUEs points have been successively imported into a ArcGIS and digitized as lines.

Instability factors
In the LS assessment of the study areas old landslides have been also introduced into the statistical analysis. This fact has made necessary to consider only time-invariant (or quasi-static) environmental factors that can be supposed to change over geomorphological time scale, as geological or morphometric characteristics (Clerici et al., 2010). In fact, if time-variant factors – i.e. human activity, land-use and climatic conditions - are introduced into LS analysis, the resulting role of these factors can be completely misunderstood (Atkinson and Massari, 1998). Moreover, applying the Conditional Method to LS zonation, it is necessary to limit the number of factors that have to be introduced into the analysis, in order to limit the presence of small UCU of little statistical significance (Carrara et al., 1995). As consequence, only the following time-invariant factors are considered.

Lithology
The lithology map has been derived from the geological field survey. The map was scanned, imported into ArcGIS, rectified, geo-referenced, assembled and digitized into a feature-class. The process of geologic map digitalization is resolved by the topologic method of ArcGIS. Even though this method is a very complex way to create a polygonal feature class, it can resolve the problem of the sliver polygons.
For lithology, different classes have been extracted from the geological map on the basis of their lithological and structural analogies. Moreover, considering that in the study areas many landslides have been occurred from the body of other landslides and from the DGSDs, it was also necessary to insert these elements into a specific class. On the whole, 11 different classes have been introduced into the analysis for each basin.

Morphometric factors DEM-derived
Among the morphometric factors usually used in the LS assessment, slope angle and slope aspect are the most commons. While the slope angle is accepted as one of the most landslide-influencing factor, the importance of the slope aspect as landslide-controlling factor is nowadays still debated.
In the study areas the slope angle and the slope aspect are derived from the 10×10 pixel resolution DEM, obtained by transforming a TIN in GRID. The TIN was generated by interpolation of digital contour lines and elevation points, extracted from a topographic map at scale 1:10,000 (Shape Files of the Region Tuscany, CTR). These morphometric factors, expressed in a raster form, have been reclassified and transformed in a vector format (polygonal feature class).
According to Clerici (2010), in order to create classes statistically significant, i.e., classes with great areas, the reclassification of the slope angle has been made into six classes with similar areas (percentile criteria), while slope aspect has been reclassified into the eight classes corresponding to the classic angular sectors, 45° wide and clockwise from north (equal interval criteria). During the transformation of the factors maps from raster to vector format the classes so identified have been codified with a respective unique value. For all of these classes MSUEs density has been performed.

Distance from hydrographic, morphologic and tectonic elements
Considering that the evolution of the study basin is strictly connected to the neogenic tectonic activity and to the fluvial erosion phases, it was also necessary to consider these thematic elements as probable landslide-inducing factors. For the Roglio basin also distance from morphological elements has been considered. Distance from hydrographic, morphologic and tectonic elements maps are derived in a vector format directly from the geological and geomorphological maps. The procedure consists of extracting the thematic linear elements and buffering these in a relative polygonal feature class. The relative maps have been then reclassified in their attribute tables. The maps of the distance from hydrographic and tectonic elements have been made by four similar area classes.
PROCEDURE TO LS ZONATION
A preliminary univariate analysis was performed by crossed tabulation (contingency tables) to understand the possible relations between each factor (predictor variable) and the landslides occurrence. This analysis was made for each basin and for each single landslide typology. Then, Cramer’s Ѵ coefficient was derived from Chi2 (χ2) to tests the strength of factors-landslides association. From this first analysis it was possible to ascertain how for each basin the selected factors have usually a high degree of association with the landslides inventories. Only the slope aspect shows a low Cramer’s Ѵ to flow type for the Milia basin. Among the factors, lithology and slope angle show the highest degree of association with the MSUEs distribution.
A conditional analysis was performed to evaluate the relationship between landslides and the factors considered simultaneously. Though the conditional method is conceptually very simple to understand, it is operationally very complicated because it needs to be applied many times for the same study area and for different landslide types. So a Model-Builder (scripts) in ArcGis (ESRI) has been created in which all geoprocessing steps have been automatized.
In the Model-Builder, for each basin and for each landslides type, all of possible factors combinations (UCUs feature class) are overlaid (intersect) with the buffer feature class of the MSUE belonging to pre-1975 landslides. For each UCU the ratio of the sum of the UCU area that fall within the MSUEs buffer and the total area for that UCU is calculated. Successively, the UCUs are grouped into five density classes (LS classes) on the basis of their ratio value. For the class definition it is used a similar method already used by Clerici (2010). The classes are defined on the basis of the MSUEs mean density, carried out by dividing the sum of the MSUEs buffer area and that of the study area. This value (Md) represents the middle point of the middle class. More precisely, the class interval on which LS maps are created is Ci= (Md/5)×2 and the susceptibility class intervals are: 0-Ci (Very Low), Ci-2Ci (Low), 2Ci-3Ci (Medium), 3Ci-4Ci (High) and 4Ci-5Ci (Very High).
For each of the three landslide type, LS zonation has been so built. A validation procedure has been performed into Model-Builder to choose the best model. The validation procedure is based on the “wait and see” concept, that is the only rigorous way to evaluate the LS map reliability. In this method the distribution into the LS classes of pre-1975 MSUEs (training set) is compared with that of the post-1975 MSUEs (validation set). For each of the five susceptibility class the absolute value of the difference between the pre-1975 and post-1975 MSUEs percentage is computed. The sum of these latter values, Validation Error (VE), is reported for each LS Models. The VE assesses the predictive power of each model built and its value ranging from 0 (the best predictive power) to 200 (the worst predictive power).
In according with Clerici (2010), a good validation is a necessary but not a sufficient prerequisite for assessing the model efficiency. A good model should have a great dispersion around the main density value to distinguish between significantly different landslides density distributions. Therefore, a MSUE mean deviation (MD) was computed for each model and the ratio VE/MD (Best Model Index, BMI) was utilized to choose the best LS model, that should have the highest MD/VE value (Clerici et al., 2010).

DISCUSSION AND CONCLUSIONS
For both the studied basins, the MSUE Conditional Method shows a good predictive power only for the translational landslides. In the Milia area the combination of the Lithology-Slope angle (LS) factors represents the best model with a BMI = 2,522.1. For rotational and flow types the best model is represented by the Slope Angle-Distance from Tectonics elements (SDF) and Lithology-Distance from Hydrographics elements (LDI) factors combinations respectively. Considering the results of the univariate analysis, the Conditional Method seems to confirm the same important factors in the prediction of the translational and the flow landslides occurrence. For the rotational type, the conditional method reveals the landslide-influencing factors different to the factors that have a highest Cramer’s Ѵ coefficient. This fact confirms that the conditional analysis has a greater capacity to extract the landslide-influencing factors compared to the univariate analysis.
For the Roglio basin, the combination of the Aspect-Distance from Hydrographics elements and Distance from Tectonics element (ADIDF) factors represents the best model with a BMI = 576.0. For rotational and flow types the best model is represented by the SDIDF and LSDFDS factors combinations respectively.
For each landslide type, the VE value tends generally to increase as the number of factors introduced into the analysis increases. The VE increment is strictly related with the introduction of a large number of small UCUs that have a littler statistical significance (Clerici et al., 2010). Furthermore, the presence of small UCUs makes the choose of the MSUE as detachment zone representation more unsuitable. In fact, the UCUs individuated by the MSUEs are less representative than those belonging to the detachment zones as much as the UCUs are small.
The predictive power of the Milia best models moves from a 3.4 VE for the translational landslides to a 19.5 VE for the rotational landslides. In the Roglio basin the predictive power of the best models moves from a 6.3 VE for the translational landslides to a 10.1 VE for the rotational landslides. The VE value for flow and rotational types is not completely acceptable. This discrepancy can reflect the presence of landslides belonging to these later typologies with MSUEs buffer extension statistically higher than that of the translational type. In fact, in the Milia basin, MSUEs buffer of the translational landslides has a mean extension of 837.2 m2 (standard deviation = 352.2 m2) against those of the flow and rotational types that have mean of 995.3 m2 and 1293.5 m2 (standard deviation = 350, 537 m2) respectively. In the Roglio basin also the MSUEs buffer has a mean extension that increase from translational type to flow and rotational types. The lowering of the predictive power, connected to the increasing of the mean MSUEs extension, can be associated to the MSUEs degradation processes that involve the main scarps, causing a withdrawal effect. The MSUEs withdrawal implies the buffering of the UCUs that are not strictly connected to those present before the landslides occurrence and so a lowering of the predictive power of the MSUE Conditional Method. This problem is particularly accentuated in the MSUEs with greater original extension (i.e. large landslides), in the MSUEs originated in more degradable lithotypes and in the MSUEs related to the oldest landslides. Therefore, the introduction of the big and old landslides into the MSUE Conditional Method can provide a LS models with a low predictive power. Even if the old landslides are not introduced into the statistical analysis, the MSUE Conditional Method applied for LS assessment in areas where very degradable lithotypes outcrop can also show a lower predictive power.