A comparison between analytic approaches to model rainfall-induced development of shallow landslides in the central Apennine of Italy

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1 Landslides and Climate Change McInnes, Jakeways, Fairbank & Mathie (eds) 2007 Taylor & Francis Group, London, ISBN A comparison between analytic approaches to model rainfall-induced development of shallow landslides in the central Apennine of Italy D. Salciarini & P. Conversini Department of Civil and Environmental Engineering, University of Perugia, Italy ABSTRACT: Several predictive approaches have been proposed in the scientific literature to assess landslide susceptibility. To model the rainfall-induced development of shallow landslides in a study area in the eastern Umbria Region of central Italy, we compare the results from three different approaches. The TRIGRS (Transient Rainfall Infiltration and Grid-based Slope-stability) model couples an infinite-slope stability analysis with a onedimensional analytical solution for transient pore-pressure response to rainfall infiltration. The SHALSTAB code is a widely used model that couples an infinite-slope stability analysis with a steady-state hydrological model. The TM model is an approach based only on the topographic information. We show that the last two methods produce a greater over-prediction of the unstable hillslopes in the study area compared to TRIGRS results. Differences in the distribution of predicted slope failures between the models are primarily a function of the spatially varying soil depth and spatially distributed mechanical and hydrological properties that can be considered in TRIGRS simulations. Next, we show that TRIGRS is able to account for the influence of expected rainfall duration and depth on shallow landslides initiation. We model the climate-depending instabilities on a scenario basis, using precipitation-duration-frequency curves for the expected rainfalls. 1 INTRODUCTION Shallow landslides and debris flows are natural processes that have the potential to bring about damage, loss or other adverse effects to the built environment (Crozier & Glade 2005). Such phenomena are frequent on steep slopes mantled with loose soils. Typically, intense and prolonged rainfall is the major cause of the reduction of the soil strength and consequent slope failure. In the central Apennines of Italy, four surficial environments have been identified as prone to shallow landsliding: landslide deposits, highly fractured rocks, scree or talus deposits, and glacial deposits (Guzzetti & Cardinali 1991). Landslide susceptibility is defined as the propensity of a certain area to undergo landsliding (Crozier & Glade 2005). To assess landslide susceptibility, several predictive approaches have been proposed in the scientific literature, such as: statistical models based on logistic regression techniques; physically based, spatially distributed models that are based on the physics of landslide processes; and topographical models based on the definition of a topographic index that depends on the slope gradient. Statistical models rely on the correlation between landslide locations and various geological, gemorphological, and landuse characteristics to quantify landslide susceptibility (e.g. Coe et al. 2004). Coupled physical models can be used to examine shallow landslide and debris flow occurrence at the scale of a river basin or region and as a function of physical properties of the soil mantle and climate (i.e. rainfall) (e.g. Montgomery & Dietrich 1994, Iverson 2000, Baum et al. 2002, Savage et al. 2003). These models allow the quantification of the stability of each unit (grid cell or topographic element in which the study area is subdivided). Two important codes that implement physically based theories are SHALSTAB (Dietrich & Montgomery 1998) andtri- GRS (Baum et al. 2002). Topographical Models (TM) are subset of the statistical models and partition the landscape into susceptibility categories based only on topographic attributes (e.g. Salciarini et al. 2006b). In the first analysis, this paper discusses the results obtained from the SHALSTAB code, TRIGRS code andtm method for slope stability modelling, by applying each model to a study area in central Italy and comparing the results to the landslide data from the Landslide Inventory Map of Umbria Region (Guzzetti & Cardinali 1989, 1990). Because TRIGRS implements a transient hydrological solution, it is the only model suitable for evaluating stability conditions as function of time and depth. SHALSTAB (Montgomery & Dietrich 1994, Dietrich & Montgomery 1998) is a quantitative time-independent approach that has a strong dependence of shallow landslide and debris flow initiation on the topography. 185

2 Figure 2. Perspective view showing the location of the rain gauges within the study area. Figure 1. Map showing the location of the study area. UnlikeTRIGRS (Baum et al. 2002, Savage et al. 2003), it cannot represent the spatial variation and distribution of the soil physical parameters. Both of the approaches assume an understanding of the physical processes that govern the phenomenon initiation. Finally, Topographical Models are very easy to use, but much less accurate and can be subject to bias in the interpretation of the results. In the second analysis, we show how TRIGRS may be used to assess regional shallow landslide instabilities that depend on climate. We derived the climatic factors for the study area from the probabilistic distribution of historic rainfalls and we used them for modelling the influence of different rainfall scenarios on shallow landslide initiation. 2 STUDY AREA The study area is located in the Apennine Mountains, in the eastern part of the Umbria region of central Italy (Fig. 1). Developed areas on alluvial fans and transportation corridors that cross the toes of unstable slopes have been periodically exposed to hazards from shallow landslides and debris flows. In the study area shallow landslides and debris flow events commonly occur in small basins (smaller than 3 km 2 ), in a hilly environment (with an average elevation of 800 m above sea level). Average slope gradient, within the watersheds varies between 25 and 30 and fan deposits of mobilized sediment can vary from 3,000 to 16,000 cubic meters (Conversini et al. 2005; Salciarini et al. 2006a). Shallow landslides that quickly develop into debris flows exclusively involve colluvium and talus underlain by calcareous or marl bedrock. The initiation is mostly due to the rapid infiltration through the permeable soil mantle. The rapid seepage is then detained from the lower less permeable substrate, and this causes a transient rising water table (Salciarini et al. 2006a). In the central Apennines the bedrock is a marl and limestone sequence characterized by an increasing marl fraction in the upper part of the series (Calamita & Deiana 1986). Erosion and weathering products from these sedimentary formations mantle slopes in the study area. These surficial deposits typically have varied sorting and thicknesses. Vegetation on the hillslopes is typically dense deciduous forest. The climate of the Umbria Region is typical of the central Apennine, characterized by hot dry summers and a mild winter. It is mainly derived from the interaction between the mountain chain and local atmospheric circulation (Corradini & Melone 1988). Within the study area there is one rain gauge at Forsivo, 818 m above sea level, that is managed by the Regional Hydrological Service and hourly rainfall information is available from 1992 to the present (Fig. 2). In addition, there are two rain gauges that belong to the local network: at Norcia (450 m above the sea level) and Poggiodomo (606 m above sea level) (Fig. 2). Average annual rainfall ranges from 830 mm to 944 mm. The heaviest rainfall, typically caused by frontal systems from the northwest, occurs in November and April, while the minimum is in July. The average monthly rainfall varies between about 70 and 80 mm and the average of the maximum daily rainfall varies between about 23 and 28 mm. The main triggering factors for shallow landslides and consequent debris-flow occurrence are short period storms (varying from less than an hour up to four hours) of very intense rainfall over limited areas (Salciarini et al. 2006a). Analyses of previous events reveals that daily cumulative rainfall that triggers shallow landslides and consequent debris flows frequently exceeds average peak daily values (>28 mm/day) (Salciarini et al. 2006b). A detailed historical record of 186

3 the relation between rainfall, shallow landslides, and debris flows is still not available for the study area. 2.1 Data collection The grid-based digital elevation model with a 5-m cell size used as input to SHALSTAB and TRIGRS was derived from digital topographic contour maps at scale 1:5000, using the Topogrid function in ArcGis. As rainfall test, we consider a real rainstorm recorded at the Forsivo rain gauge (the National Network rain gauge showed in Fig. 2) characterized by a significant concentration of rainfall over a small area (the Poggiodomo rain gauge, about 10 km away, recorded no rainfall). During this storm about 41 mm of rain fell in 16 hours and caused the initiation of both debris flows and shallow landslides. As test data set we use a landslide inventory map produced by the Italian National Research Council (CNR), based on aerial photo interpretation and field surveys. In this map, the source areas of shallow landslides and debris flows are displayed with a circle. 3 THEORETICAL BASIS OF THE MODELS 3.1 The SHALSTAB code The SHALSTAB approach (Dietrich & Montgomery 1998) combines an infinite slope stability model with a steady state hydrological model. The modelled basin is divided into topographic elements defined by the intersection of contours and flow tube boundaries, as sketched in Figure 3. The hydrological model reduces to a calculation of wetness W, expressed as: where I is the net rainfall rate, A the upslope drainage area, b the outflow boundary length, T is soil transmisivity which is depth integrated saturated hydraulic conductivity, and α the local slope. Combining this hydrological model with an infinite slope stability model for soil with cohesion, c, the stability equation implemented in the code is the following (Montgomery et al. 1998): where z is the soil depth, g is gravitational acceleration and γ w is the bulk density of water. The model has three topographic terms that are derived from the digital elevation model: drainage area, A, outflow boundary length, b, and hillslope angle, α. The material properties that need to be assigned to apply this Figure 3. Sketch of the catchments subdivision into topographic elements (after Montgomery & Dietrich 1994). model are: the soil bulk density, γ s, the angle of internal friction of the soil, φ, the effective soil cohesion, c, and the soil transmissivity, T (defined as K sat /soil-depth). SHALSTAB produces a stability index (SI) based on the safety factor calculations, ranging from 0 to 1.5. This stability index is defined as the probability that a location is stable assuming uniform distribution of the soil parameters over their range of values (Morissey et al. 2001). Based on the stability index value the territory is classified into 6 categories. The first three categories (1 3) are for regions that should not fail with the most conservative parameters within a specified range. For classes 4 and 5 the probability of failure is less than and greater than 50% respectively. The sixth class is for regions defined as unconditionally unstable that should fail even with the less conservative parameters in the specified range. SHALSTAB can be used in a deterministic manner assuming that the lower boundary and the upper boundary of the parameters variability range are identical. It s important to notice that a single set of parameters can only allow us to identify areas with equal topographic control on landslide initiation. 3.2 The TRIGRS code TRIGRS (Transient Rainfall Infiltration and Gridbased Regional Slope-stability) calculates transient pore pressure response and the attendant changes in the safety factor, due to rainfall infiltration over digital topography. The code extends Iverson s method (Iverson 2000, Baum et al. 2002) by implementing the solution for complex storms, a solution for an impervious lower boundary at finite depth, and a simple runoff-routing scheme. Infiltration, hydraulic properties, and slope stability input parameters are allowed 187

4 Table 1. Parameters used for SHALSTAB.CO application. c (Pa) φ ( ) γ s (N/m 3 ) K sat (m/s) 5, , Figure 4. Conceptual sketch of the hydrological model in TRIGRS (after Godt 2004). to vary over the grid areas thus making possible to analyse complex storm sequences over geologically complex terrain. Slope stability is calculated using an infinite-slope model. The factor of safety, FS, is defined as the ratio of the resisting and driving forces and is calculated at a depth Z by: where φ is the soil friction angle for effective stress, c is the effective cohesion, ψ is the pressure head as a function of depth, Z, and time, t, d lb is the depth of the impervious lower boundary, and γ w, and γ s are the unit weights of water and soil, respectively. The infinite slope is stable when FS > 1, in a state of limiting equilibrium when FS = 1 and FS < 1 denotes unstable conditions. Thus the depth Z where FS first reaches one will be the depth of landslide triggering at time t. The hydrological model implemented in TRIGRS is based on solutions to a linearised form of the Richards equation (Iverson 2000, Baum et al. 2002, Savage et al. 2003;). This solution is appropriate for initial conditions where the hillslope is saturated, tension saturated, or nearly saturated. Figure 4 is a conceptual sketch showing a hillslope inclined at an angle α subject to time-varying surface infiltration, I, with a tensionsaturated zone above a water table at a depth, d wt, vertically below the ground surface. The water table overlies an impermeable boundary at a depth, d lb, below the ground surface. Figure 4 also shows the slope-normal coordinate z, and Z = z/cosa is defined as the vertical coordinate. 3.3 The topographical model To apply the topographic model and obtain slope categories for the study area, the topographic slope at each inventoried shallow landslide location is determined using the digital elevation model. Next, a cumulative distribution of slope angles at these locations is constructed. Finally, we determine the range of slope angles that include a given percentage of shallow landslides in the inventory (i.e. 40%, 50%, 60%, etc.). In this way, it is possible to compute the percentage of the map area that falls within those ranges of slope angles. 4 APPLICATION OF THE MODELS 4.1 Application of SHALSTAB The study area was divided into topographical elements based on the 5-m digital elevation model. We used an extended version of SHALSTAB, called SHALSTAB.CO, which takes into account the effects of soil and root cohesion on the soil strength (Montgomery et al. 1998). Therefore, besides the digital surface information, the other data required for the calculation are: soil cohesion, internal friction angle, transmissivity and soil weight. For the purpose of the comparison between deterministic approaches, we elect to use the parameters with their exact value, shown in Table 1, rather than with their probabilistic variability. The soil thickness is assumed to be uniform with a value of 2 m. In Figure 5 the result provided by SHALSTAB.CO is shown. The response of the hillslope to the test rainfall, recorded at the Forsivo rain gauge, is a widespread failure for a large part of the region. Note that, being SHALSTAB.CO a steady-state model, the rainfall is fed into the code as a steady-state rainfall of mean intensity equal to 2.64 mm/h. 4.2 Application of TRIGRS The study area was divided into a regular 5-m grid based on the digital elevation model. The parameters used for the analysis are shown in Table 2 and are the same of the SHALSTAB.CO simulation. In addition, for the TRIGRS analysis we assumed that the soil thickness, d lb, varies exponentially as function of the slope angle α by the following relation (Salciarini et al. 2006b): 188

5 Figure 5. Failure prediction provided by SHALSTAB.CO application. White circles indicate the location of shallow landslides (Guzzetti & Cardinali, 1989). Table 2. Parameters used for TRIGRS application. 3 Table 3. Parameters used for TRIGRS application, subdividing the study area into 5 zones. 2 c (Pa) φ( ) γs (N/m ) Ksat (m/s) D0 (m /s) 5, , Figure 6. Potential instability prediction from TRIGRS, assuming a uniform distribution of the soil physical parameters for the entire study area. White circles indicate the location of shallow landslides (Guzzetti & Cardinali, 1989). ZONE c (Pa) Figure 6 shows the results provided by TRIGRS at the end of the rainfall input. The red areas display where the safety factor is less than 1, denoting instability. According to the TRIGRS prediction, 11.7% of the study area is potentially unstable. Thus, the area that TRIGRS predicts to be potentially unstable is about 1/3 less than SHALSTAB.CO. The difference in these results can be attributed to the spatially varying soil thickness in the TRIGRS application. The assumption of uniformity for the physical parameters over the entire study area can be further improved using TRIGRS if we subdivide the study area into 5 zones, based on surficial geology. These zones are: Soils (surficial, loose, coarse grained, variably sorted materials of varying thickness) that are primarily products of erosion and weathering of bedrock. Well-consolidated ancient landslide deposits (inactive) within the marl-clay formations. Layered rocks dominated by marl-clay formations (Scaglia Cinerea Formation, Marne a Fucoidi Formation and Bisciaro Formation). Layered calcareous rocks (Calcare Massiccio, Maiolica, Calcari Diasprigni and the older rocks of the Scaglia Series). Competent and massive rocks ,000 5,000 30,000 50, ,000 φ( ) γs (N/m3 ) Ksat (m/s) D0 (m/s2 ) ,000 18,000 20,000 21,000 21, The range of variability of the physical parameters for each surficial material has been evaluated, and parametric studies were carried out to assess the strength and hydraulic parameters for each zone in a previous paper (Salciarini et al. 2006b). Values based on this work are shown in Table 3. The results provided by TRIGRS when the study area is subdivided into five zones are shown in Figure 7. The code predicts only about 4.5% of territory as potentially unstable. The area predicted to be unstable is about 2 times smaller than the predicted unstable area in the previous simulation with spatially uniform physical parameters. We see that the grid cells characterized by high strengths that were predicted as unstable in the previous simulation (where the topographic control prevailed) are now predicted to be stable, owing to the subdivision of the study area into 5 different soil property zones. 4.3 Application of the TM model Performing the slope classification, as described in section 3.3, we obtain the result shown in Table

6 Figure 7. Failure prediction provided by TRIGRS assuming a different distribution of the physical parameter, depending on the surficial geology. White circles indicate the location of shallow landslides (Guzzetti & Cardinali, 1989). Table 4. model. Creation of the slope categories, using the TM Percentage of agreement Percentage of between the the study area model predictions Slope predicted to be and the inventoried Category range unstable (%) landslides (%) I II III IV V Figure 8. Spatial distribution of the V slope-categories shown in Table 4. White circles indicate the location of shallow landslides (Guzzetti & Cardinali, 1989). Table 5. Summary of the area predicted to be unstable and the agreement between the prediction and the landslide inventory. Percentage of agreement btween Percentage of the model predicted instability predictions and the over the inventoried shallow territory (%) landslides (%) TM method SHALSTAB.CO TRIGRS 1 zone TRIGRS 5 zones Increasing the range of slope angles beyond that for category V improves the percentage of agreement between the model prediction and landslide inventory only slightly. The spatial distribution of slopes that fall in the Category V range is shown in Figure 8. 5 COMPARISON OF THE RESULTS AND DISCUSSION To quantify the agreement of the different methods results with the inventoried location of shallow landslides by CNR, we conducted an analysis of the total area predicted to be unstable encompassed within the white circles which represent landslide source areas. We assume that the model prediction agrees with the landslide inventory when at least 6 predicted unstable cells (each cell is 5 m 5 m) or topographical elements lie within the land-slide source circle. Table 5 lists the total area predicted to be unstable (first column) and the percentage of agreement between the prediction and the landslide inventory (second column) for each model. An ideal landslide susceptibility map should maximize the agreement between known and predicted landslide locations and minimize the over-predictions. There are two distinct types of prediction errors: prediction of a landslide where none has occurred ( false positives ) and no prediction of a landslide where one has occurred ( false negatives ). To evaluate the total error in the prediction we compute the sum of these two errors for each of the model results (Table 6). The optimal map will have the lowest value of the total error since it both maximizes the agreement of the landslide inventory with the area predicted to be unstable and minimizes the over-predictions. We can state that false positive and false negative represent the over-prediction and the under-prediction, 190

7 Table 6. Summary of the errors produced by the codes. False False Total Positives Negatives error (%) (%) (%) TM method SHALSTAB.CO TRIGRS 1 zone TRIGRS 5 zone respectively. They have different implications for practical applications. Decision makers might give a different importance to each of them in terms of land management. The error that we have defined false negatives is crucial, because it indicates that the model is not able to accurately reproduce the actual triggering condition. The error defined as false positives could instead associate to the degree of caution that we need to have in the land management. Decision makers might decide to prefer a conservative model, that is over-predictive, rather than a model that misses the prediction of the effective landslides, or vice versa, anyway this is an administrative decision. From a scientific point of view, each of these types of error represents an inaccuracy of the model in landslide prediction. For this reason we compared the different models results in terms of the minimization of the sum of these two errors, without giving different weights to each of them. The comparison show that results from the TM and SHALSTAB.CO models capture the greatest percentage of landslides in the inventory, however, as shown in Figures 5 and 8 these two methods also predict that a large part of the study area is potentially unstable. The two TRIGRS results produce much smaller total errors, particularly the simulation that accounts for the subdivision of the physical properties into 5 zones. Predictive models like SHALSTAB are very efficient in numerous study cases (Montgomery et al. 1997, Guimaraes et al. 2003, Dietrich et al. 1998) but some assumptions on the morphologic and geologic conditions have to be verified for their application. For instance, the lithological characters and the spatial distribution of the soil mantle should be homogenous over the study area to obtain a good agreement with the real cases. In the central Apennine, this hypothesis is not always valid, because the outcropping formations are very variable and we can find the rapid alternation of cliffs and loose soil in the same hillslope. The possibility of considering the study area subdivided into zones with different hydraulic and mechanical properties make a significant improvement in the results because local variation in geology and soils strongly influence patterns of landsliding. However, as noted by (Morissey et al. 2001) the choice of a model depends, primarily, on the available data for the study area. For instance, most of the successful TRIGRS applications are for cases with abundant input data. In the central Italy applications, the TRIGRS code gives correct prevision only after an accurate calibration of the model (Salciarini et al. 2006b). 6 INSTABILITY PREDICTIONS THAT DEPEND ON CLIMATIC FACTORS Climate-landslide models are used to model the landslide movements, in different climate scenarios. We introduce the climate information (rainfall) in TRIGRS model using the historical climate data as input. Therefore, TRIGRS is able to simulate the occurrence of shallow landslides as function of different climatic scenarios, using a probabilistic distribution for the expected rainfalls. The climatic factors for the study area were developed by the Hydrological Service of Umbria Region, using 50 years of rainfall histories recorded at the national network rain gauges. Since both rainfall intensity and duration play a key role in hillslope hydrology and lead to the conditions for slope failure, we perform a series of analyses considering the extreme expected rainfalls provided by the PDF (Precipitation Duration Frequency) curves, varying the recurrence time, and assuming a uniform distribution of rainfall during the event. The PDF curves for the study area are estimated from the regional rainfall climatic factors provided by the Pluviometric Atlas of the Umbria Region (Regione Umbria, 1991). The PDF curve is described by the following general law: where the rainfall climatic factors given by the atlas are: n = 0.37, m 1 = 26.08, V = In Figure 9 we display the PDF curves, calculated from equation (5), for six recurrence periods (T =2, 5, 10, 25, 50, and 100 years) and for five rainfall durations (d = 1, 3, 6, 12, and 24 hours). Using the hydraulic and geotechnical parameters shown in the previous section, we ran TRIGRS simulations using rainfall from the PDF curves for various return periods (Salciarini et al., submitted). Table 7 shows the percentage of predicted unstable territory (where FS < 1) by TRIGRS for different rainfall duration and depth. For each recurrence interval and for each rainfall duration, TRIGRS predicts different failure scenarios. The results show the rainfall-duration robust control on hillslope stability. For prolonged rainfall the predicted unstable territory increases significantly. This is due to the effect of the progressive water table increase 191

8 Rainfall depth (mm) T = 50 years T = 25 years T = 10 years T = 5 years T = 2 years Figure 9. Rainfall duration (hours) PDF curves for the study area. Table 7. Results provided by TRIGRS simulations using different rainfall duration and depth. Rainfall duration T (years) 1 hour 3 hours 6 hours 12 hours 24 hours % % 1.91% % 2.11% % 2.30% % 1.80% 2.44% and consequent increase of pore pressure. The recurrence interval of rainfall of a given duration also has an effect on the total area predicted to be unstable. For example, the area predicted to be unstable by TRIGRS for rainfall of 12 hours duration increases by about a factor of 2.4 when the return period is increased from 5 to 50 years. The model results were compared with the observations in the study area, that reveal that the main triggering factors for debris flow and shallow landslides occurrence are prolonged rainstorms (varying from 12 up to 24 hours) with a short peak of very intense rainfalls (varying from less than 1 hour up to 4 hours), which impact a very localized area (Salciarini et al. 2006a). We find that the model results are able to correctly identify the rainfall pattern (prolonged, high-frequency rainfalls) that induces slope failure. However, the model predictions generally overestimated the total triggering rainfall, and consequently under-predict the recurrence time of failures. We attribute this to the assumption of a constant rainfall rate for a storm (Salciarini et al., submitted). This paper addresses the possibility of the TRIGRS model to simulate different climate scenarios. The model can be coupled with a historical variations of historic climate and can be used to assess the effects on slope stability for different hillslopes. For each recurrence interval and for each rainfall duration TRIGRS predicts different failure scenarios. The results show the rainfall-duration robust control on hillslope stability. For prolonged rainfall the predicted unstable territory increases significantly. This is due to the effect of the progressive water table increase and consequent increase of pore pressure. The recurrence interval of rainfall of a given duration also has an effect on the total area predicted to be unstable. For example, the area predicted to be unstable by TRIGRS for rainfall of 12 hours duration increases by about a factor of 2.4 when the return period is increased from 5 to 50 years. The model results were compared with the observations in the study area, that reveal that the main triggering factors for debris flow and shallow landslides occurrence are prolonged rainstorms (varying from 12 up to 24 hours) with a short peak of very intense rainfalls (varying from less than 1 hour up to 4 hours), which impact a very localized area (Salciarini et al. 2006a). We find that the model results are able to correctly identify the rainfall pattern (prolonged, high-frequency rainfalls) that induces slope failure. However, the model predictions generally overestimated the total triggering rainfall, and consequently under-predicted the recurrence time of failures. We attribute this to the assumption of a constant rainfall rate for a storm (Salciarini et al., submitted). This paper addresses the possibility of the TRIGRS model to simulate different climate scenarios. The model can be coupled with historical variations of historic climate and can be used to assess the effects on slope stability for different hillslopes. 7 CONCLUDING DISCUSSION We have presented a comparison between two analytic approaches and a method based on slope angle, to estimate the potential susceptibility to shallow landslides and consequent debris flows in a study area in the Umbria Region of central Italy. The physicallybased models (TRIGRS and SHALTAB.CO) couple solutions for groundwater flow with infinite slopestability models. The TM model only considers the effect of topographic slope on the location of shallow landslides and debris flows initiation. Assuming that a certain amount of uncertainty will always remain in hazard and susceptibility analysis, the performance of a model can be assessed by estimating the error that is produced in a prediction. Results from each of these models were evaluated in terms of agreement with the landslide inventory data for the study area. The analysis has revealed that the minimum error in the prediction has been provided by the TRIGRS approach when the study area is subdivided into different zones characterized by differing values for the soil properties. Thus, the accuracy improves when variable 192

9 soil thicknesses and soil parameters are considered over the study area. Then, different rainfalls are used as input into the model to examine the variation of the hillslope response to rainfall return period and duration. The input rainfalls are obtained by a statistical analysis of historical climate information.to effectively assess the effects of climate variability on landslide occurrence the TRIGRS code can be coupled with a model for estimating future rainfall patterns. Indeed, the results show that the model can be successfully combined with the climate information to produce forecasting of the hillslope stability. REFERENCES Baum, R.L., Savage, W.Z. & Godt, J.W TRIGRS A Fortran Program for Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Analysis. U.S. Geological Survey Open-File Report 02- York, 764 p. Calamita, F. & Deiana, G Geodinamica dell Appennino umbro-marchigiano (In italian): Memorie della Società Geologica Italiana. v. 35, p Carslaw, & Jaeger Conduction of heat in solids. Oxford University Press, Oxford, 510 p. Coe, J.A., Michael, J.A., Crovelli, R.A., Savage, W.Z., Laprade, W.T. & Nashem, W.D Probabilistic assessment of precipitation-triggered landslides using historical records of landslide occurrence, Seattle, Washington. Environmental Engineering and Geoscience, v. 10, no. 2, p Conversini, P., Salciarini, D., Felicioni, G. & Boscherini, A The debris flow hazard in the Lagarelle Creek in the eastern Umbria region, central Italy. NHESS, v. 5, p Corradini, C. & Melone, F Spatial distribution of prewarm front rainfall in the Mediterranean area. Nordic Hydrology, v. 19, p Crozier, M.J. & Glade, T Landslide hazard and risk: issues, concepts and approach. In: Landslide hazard and risk. Glade, Anderson and Crozier Eds. Wiley, 824 p. Dietrich, W.E. & Montgomery, D.R SHALSTAB A digital terrain model for mapping shallow landslide potential. Technical report by NCASI. Godt, J.W Observed and modeled conditions for shallow landsliding in the Seattle, Washington, area. Boulder, University of Colorado, Ph.D. dissertation, 151 p., 1 pl., 32 figs. Guimaraes, R.F., Montgomery, D.R., Greenberg, H.M., Fernandes, N.F., Trancoso Gomes, R.A. & Carvalho, O.A Parametrization of soil properties for a model of topographic controls on shallow landsliding: application to Rio de Janeiro. Engineerin Geology, v. 69, p Guzzetti, F. & Cardinali, M Carta inventario dei fenomeni franosi della regione Umbria e aree limitrofe. G.N.D.C.I., pub. n. 204, map at 1: scale. Guzzetti, F. & Cardinali, M Landslide inventory map of the Umbria region, Central Italy. 6th ICFL-ALPS 90, Milan, Italy, p Guzzetti, F. & Cardinali, M Debris-flow phenomena in the Central Appenines of Italy. Terra Nova, v. 3, p Iverson, R Landslide triggering by rain infiltration. Water Resources Research, v. 36, p Morissey, M.M., Wieczorek, G.F. & Morgan, B.A A comparative analysis of hazard models for predicting debris flow in Madison County, Virginia. USGS OFR Montgomery, D.R. & Dietrich, W.E A physically-based model for the topographic control on shallow landsliding. Water Resources Research, v. 30, p Montgomery, D.R., Sullivan, K. & Greenberg, H.M Regional test of a model for shallow landsliding. Hydrological Processes, v. 12, p Reid EM Slope instability caused by small variations in hydraulic conductivity. Journal of Geotechnical and Geoenvironmental Engineering 123 (8): Salciarini, D., Conversini, P., & Godt, J.W. 2006a. Characteristics of debris flow events in eastern Umbria, central Italy. In: Proceeding of IAEG2006, London, UK. Salciarini, D., Godt, J.W., Savage, W.Z., Conversini, P., Baum, R.L. & Michael, J.A. 2006b. Modeling regional initiation of rainfall-induced shallow landslides in the eastern Umbria region of central Italy. Landslide, v. 3 n. 3. Salciarini, D., Godt, J.W., Savage, W.Z., Conversini, P., Baum, R.L Modeling land-slides recurrence in Seattle, Washington (submitted). Savage, W.Z., Godt, J.W. & Baum, R.L A model for spatially and temporally distributed shallow landslide initiation by rainfall infiltration. Proceedings, 3rd International Conference on Debris Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, September 10 12, 2003, Davos, Switzerland, p Savage, W.Z., Godt, J.W. & Baum, R.L Modeling timedependent slope stability. Proceedings 9th International Symposium on Landslides, Rio de Janeiro, Brazil, June 27 July 2, 2004, p

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