Predictive power of a shallow landslid model in a high resolution landscape : dissecting the e ff ects of forest roads

Introduction Conclusions References

in high risk where vulnerable targets are involved.The examination of a global data set of fatalities from non-seismically triggered landslides (Petley, 2012) showed that 2620 fatal landslides were recorded worldwide between 2004 and 2010, causing a total of 32 322 recorded fatalities.The analysis of landslides catalogues reported by Salvati et al. (2010) for Italy showed that for the 59-yr period 1950-2008, 2204 landslide events have caused at least 4077 casualties.Salvati et al. (2010) showed also that fatal events in Southern Italy are focused along the coast line, due to the combination of steep slopes, high rainfall rates and concentration of vulnerable communities.
Landslide susceptibility maps represent one of the key elements for landslide risk management.Landslide susceptibility is the probability that a landslide will occur in a specific area (van Westen, 2000).Quantitative susceptibility assessment is typically accomplished either through the use of empirical models (e.g., Baeza and Corominas, 2001;Lee et al., 2003;Fell et al., 2008), or spatially distributed process-based models of slope stability and hydrology (e.g., Montgomery and Dietrich, 1994;Casadei et al., 2003;Frattini et al., 2009).A number of recent process-based susceptibility models combine steady-state or quasi-steady state hydrology concepts with the infinite slope stability model to calculate the critical rainfall, i.e. the rainfall required to initiate a landslide (e.g.Montgomery et al., 1998;Burton and Bathurst, 1998;Borga et al., 2002;Claessens et al., 2005;Rosso et al., 2006).One of the most important factors controlling the landslide location is surface topography through slope and concentration of shallow subsurface flow (Borga et al., 2002;Freer et al., 2002;Penna et al., 2011).Other relevant factors are rainfall intensity and soil and vegetation properties.
Digital terrain model (DTM) resolution affects the calculation of critical rainfall (Zhang and Montgomery, 1994;Claessens et al., 2005;Tarolli and Tarboton, 2006;Santini et al., 2009).The last few years have been characterized by the development of new remotely sensed technologies for mapping and analysis of the surface topography (e.g.Terrestrial Laser Scanners and LiDAR) (Tarolli et al., 2009).Through high resolution topography is it possible to recognize in detail local variations in hillslope and valley morphology, and better detect the landslide locations (Tarolli and Dalla Fontana, 2009).Introduction

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Full However, Zhang and Montgomery (1994) suggested that a grid size of 10 m would be enough for DTM-based geomorphic and hydrological modelling.Similarly, Tarolli and Tarboton (2006) noticed that a very high resolution DTM may decrease the performance of a shallow landslide model.These findings suggest that such kind of processes are better represented by a smoother topography, which may provide a more realistic approximation of the water table configuration than very detailed ones (Freer et al., 2002;Lanni et al., 2013). However, De Sy et al. (2013) noted that for a smallscale catchment in New Zealand, landslide locations were better distinguished from stable areas by using the 1 m resolution topography than coarser resolutions.Contrary to earlier approaches, these authors calibrated the model for each of the DTM resolutions they tested.
Given the advances in high quality digital elevation data and the lack of guidance, it is desirable to investigate the effect of DTM resolution on the performances of landslide models.Tarolli and Tarboton (2006) reported that one of the reasons for the reduced discriminating capability at fine (< 10 m) DTM resolution was the excessive degree of detail in the surface features, leading to unrepresentative values of terrain slope.Other error sources may add to this one.For instance, a specific error source that arises when using LiDAR elevation data is related to the presence of small-scale artificial structures, such as road networks.Road networks, associated earthworks and drainage structures often result in significant changes to hydrologic and geomorphic responses at or near the earth's surface (Luce, 2002;Dutton et al., 2005).In steep terrain prone to landsliding, roads and the associated drainage structures may significantly impact on the surface/subsurface flow pathways, thus influencing the landsliding potential.For example, Miller and Burnett (2007) documented a density of road-related landslides double than the one of natural surface failures.Several road-related failures result from concentration in particular areas below fillslopes of runoff generated as intercepted subsurface flow by road cut slopes (Montgomery, 1994;Wemple et al., 2001;Borga et al., 2004).The effect of this concentration of flow will depend on the characteristics of the receiving areas.In several cases, road runoff will reinfiltrate into the unchanneled Introduction

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Full terrain, hence affecting the shallow landsliding potential in the receiving areas.Specific models have been developed to account for the potential of forest road to modify landsliding susceptibility (Borga et al., 2004;Dutton et al., 2005).However, we consider here generic models which are not extended to include road-related processes.This is often the case in practical situations of shallow landslide susceptibility assessment, given the data-intensive character of the road-related model applications (Borga et al., 2004).
The presence of a forest road network may impact on the predictive power of a shallow landslide model, depending on the DTM resolution.Firstly, a number of observed landslides, used for model assessment, may reflect road-related influences (e.g., drainage concentration, fill berm failures, etc.) (Montgomery et al., 1998).An error may occur when the model predicts that these landslides are not likely to occur.However, caution should be used when considering these errors to assess the model predictive power for road-free areas.Secondly, the high-resolution digital topography reflecting the existing road features may alter model predictions of landslide likelihood.
An error may occur when these predictions do not match the mapped failures.This error is mostly influenced by DTM resolution, since road-geometry features cannot be recognized in a coarse resolution DTM.Also in this case, this kind of error should not be used to assess model performances in road-free areas.
The objective of this work is to investigate the predictive power of a quasi-dynamic process-based landslide model (Borga et al., 2002) in a small-scale, high resolution landscape, as a function of the DTM resolution and by considering the specific impact of forest roads.Examination of the DTM resolution sensitivity of process-based shallow landsliding models has received considerable attention in the literature and the distribution of the landsliding susceptibility proved to be to some degree dependent on DTM resolution (Claessens et al., 2005;Tarolli and Tarboton, 2006;de Sy et al., 2013).However, to the best of our knowledge, this is the first time that the assessment is focused on a model which uses the quasi-dynamic wetness index to derive the groundwater forcing.The landslide susceptibility model is applied and validated by Introduction

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Full using LIDAR-derived DTM data at four different resolutions, ranging from 2 m to 20 m, on a small size catchment in Sicily (Italy) interested by a dense forest road network.For this area repeated field surveys made available an accurate inventory of landslide scars that were distinguished into road-related and natural slides.The model performances are quantified separately for the two types of landslides, to clarify the interplay existing between digital topography and process representation.

The shallow landslide model
The QD-SLaM model (Borga et al., 2002;Tarolli et al., 2008) is used in this work to predict the spatial distribution of shallow landslide susceptibility.The QD-SLaM model is based on the coupling of a topography-driven model of flow within the soil with an infinite slope, Mohr-Coulomb failure model to describe the shallow landsliding process.
The model may predict duration and intensity of the rainfall required for landslide initiation.The model uses a quasi-dynamic wetness index (QDWI) to predict the spatial distribution of soil saturation in response to a rainfall of specified duration.The QDWI is the ratio between the effective contributing area and the local slope (Borga et al., 2002).The effective contributing area a(d ) is the fraction of the total specific contributing area which contributes as subsurface flow to the contour segment within a specified drainage period d corresponding to a rainfall duration.This is based on the hypothesis that all precipitation infiltrates and that vertically infiltrating volumes quickly redistribute and produce lateral subsurface flow.The effective contributing area is computed under the hypothesis of kinematic lateral flow routing (Barling et al., 1994) as follows: where K s is the saturated hydraulic conductivity, θ is the local slope angle, and ε is the drainable porosity.Borga et al. (2002) assumed ε and K s vertically uniform, such that the celerity of the subsurface flow is independent from time and from the local Introduction

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Full wetness conditions.Under these assumptions, the depth h of the topsoil affected by the subsurface flow (measured orthogonally to the slope angle) above an impending layer is computed as follows: where r is the constant rainfall rate and z is the soil depth measured perpendicular to the bed.The subsurface flow discharge per unit contour width q(d ) may be computed by using: This yields a simple model capable of incorporating the combined effect of storm duration and intensity in the dynamics of the groundwater flow.The methodology used for the computation of contributing area and local slope is based on a D8 single-flow direction algorithm.Thus, coupling the groundwater model and the infinite slope stability model provides the following relationship for the critical rainfall, i.e. the rainfall rate required to trigger slope failure for the specific topographic element: where C combines soil and root cohesion, W is vegetation surcharge, ϕ is the internal friction angle of the soil, ρ s is wet soil density, ρ w is the density of water, g is gravitational acceleration, T is the soil transmissivity, defined as the product of the saturated lateral hydraulic conductivity K s and soil thickness.Since root strength produces significant reinforcement in vegetation covered slopes, the formulation of QD-SLaM includes the effective soil cohesion due to vegetation.However to avoid making assumptions about landslide size we considered only basal cohesion and not cohesion around the perimeter of the slide.For a predefined storm duration d , Eq. ( 4) allows the determination of the minimum uniform rainfall r c needed to cause instability, which is the meaning Introduction

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Full of the critical rainfall.Equation ( 4) extends the definition of critical rainfall provided by Montgomery and Dietrich (1994) by removing the assumption of steady rainfall of infinite duration.In the Mediterranean climate, many slides are actually triggered by the transient response of pore pressures to bursts of intense rainfall, which may occur on short time scales of less than one day.By introducing a dynamic drainage area, the QD-SLaM may offer an efficient way to model the subsurface flow response at short temporal scales (Barling et al., 1994).Moreover, the model provides a framework to relate the characteristics of the critical rainfall (rate and duration) to their probability of exceedance.Application of Eq. ( 4) allows the definition of three slope stability conditions: unconditionally stable, unconditionally unstable and conditionally unstable.
A slope is defined as (a) unconditionally stable if it is stable even when it is saturated, (b) unconditionally unstable if it is unstable even when the soil is dry, and (c) conditionally unstable if the slope instability depends on rainfall conditions.One should note that the model, as applied here, does not include the description of the effects of road drainage on surface/subsurface flow.

Coupling the model with the GEV simple scaling model
Equation ( 4) provides the critical rainfall rate for a precipitation of a given duration, thus offering a way to quantify the return time of the critical rainfall.The variability of storm intensity with duration for a specified frequency level is often represented by the Intensity-Duration-Frequency (IDF) relationship.A power function is often used to model the IDF relationship (Koutsoyannis et al., 1998): where r F is the rainfall rate which can be exceeded with a probability of (1 − F ), and ς F and m F are model parameters.The scaling properties of the statistical moments of rainfall depths of different durations are used in this work to derive the IDF relationship (Ceresetti et al., 2010).Aronica et al. (2012) showed that a GEV simple scaling model Introduction

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Full described well the distribution of annual maximum series of rainfall for the study region.
The GEV simple scaling distribution the rainfall rate r F (d ) can be determined as: where u, α and k are the parameters of the GEV distribution, ζ 1 and m are scaling parameters, y T r is derived by the following relation: and T r corresponds to the exceedence probability (1−F ).The values of ζ 1 and m can be estimated by linear regression of mean values of annual maxima of precipitation depth against their durations, after log transformation.Combining Eqs. ( 4) and ( 6) yields the following equation for the critical value of y T r : Based on Eq. ( 7), the values of exp(y T r k) can be mapped over the landscape.Once the values of exp(y T r k) are known (represented here as Γ), then the value of return period T r may be computed as follows: Therefore, the critical duration d c r is the duration which minimizes the value of y T r accordingly with Eq. ( 7).After the computation of Γ, the value of return time can be 9769 Introduction

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Full determined by using Eq. ( 8).Equation ( 7) incorporates in a compact way both the topographic control (represented by the parameters of local slope and effective contributing area) and the climate control (represented by parameters ς 1 , u, αa, k, and m) on shallow landsliding.

Study area and model application
The work is focused on the lower portion of the Giampilieri catchment (2.6 km 2 ), located on the Ionic sea in the north-eastern part of Sicily, south-east of the city of Messina (Fig. 1).The topography is very rugged: elevation ranges from 0 to 596 m a.s.l. with an average value of 236 m a.s.l. and an average slope of 28.5 • .The geology of the area is characterized by a meta-sedimentary terrain belonging to the Peloritani Belt that represents the westernmost part of the Calabria-Peloritani Arc and by alluvial deposits and pleistocenic conglomerates.Phyllites and metarenites develop a soil cover especially at medium/low elevations a.s.l., as the result of weathering; the thickness of colluvium is in the range 0.7-3.0m (Messina et al., 1996).The climate is typically Mediterranean, with rainfall events (mainly convective) characterized by short duration and high intensity during the wet season (October-April) and few events during the dry season (May-September).The mean annual rainfall is about 970 mm with 84 % in the wet season and about 16 % in the dry season.
The catchment is predominantly rural with grassland and crop cultivation (46 %) and shrubs and sparse forest (42.4 %) in the upper mountainous part.The floodplain is densely urbanized by the municipality of Giampilieri Superiore village (Aronica et al., 2012).A dense network of forest road is reported for the catchment (Fig. 1).The forest road system develops for a length of 19.2 km, with a density of 7.4 km km are not recognized because of coarse resolution, while at higher resolution the digital topography is affected by the road network.
In the last ten years, the study area has been impacted by several large storm events, triggering landslides and floods.On 25 October 2007 more than 120 mm of rain fell in less than three hours, with 50 % of the recorded rain concentrated in about 20 min (Aronica et al., 2008).A more extreme storm occurred on 1 October 2009, with high intensity rainfall (exceeding 230 mm in eight hours) on an area of about 60 km 2 around Giamplieri.The event caused more than 500 landslides (mainly soil slides and debris flows), widespread inundation associated with massive erosion and deposition of debris along the drainage network.Landslides and inundation caused 31 deaths, six missing persons, and an undetermined number of injured people.The evacuees and the homeless people exceeded 2500.Rainfall depths and corresponding durations and return periods for the rainfall data collected at the raingauges of S. Stefano Briga and Flumendisi are reported in Fig. 2, showing that the return period for durations of five and six hours ranges from 100 to 300 yr.These two raingauges are located within 6 km distance from the study basin.
For the study area, a detailed shallow landslide inventory is available (Fig. 1), which includes both landslides triggered by the 2009 event and previous events.The landslides have a rather high length/depth ratio, generally higher than 25.This condition ensures proper application of the infinite length assumption within the infinite slope stability model (Milledge et al., 2012).The landslides were subdivided into road-related and natural slides.Previous investigations (Miller and Burnett, 2007) used a fixed-width buffer on both sides of the road to identify road-related landslides from other slides.In our analysis we examined also the road drainage system features and the coupled hillslope-road topography in order to discriminate road-related landslides.Given the characteristics of the shallow landsliding model used here, which describes only the slope stability processes, just the initiation area is reported for the surveyed landslides.The total landslide initiation area amounts to 67 593 m 2 , with 9489 m 2 representing road-related slides.Counter to the conventional wisdom that roads cause the vast Introduction

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Full majority of shallow slides in steep, soil mantled catchments, road-related slides account for just 14 % of the mapped slides.This may be due to the catastrophic nature of the event, which caused widespread slope instability in the catchment.Figure 3 provides pictures of two landslides (indicated as L1 and L2 in Fig. 1) just before and after the storm.The Figure clearly shows the initiation area as well as the depositional area that impacted the village.The debris flows generated by Landslide L1 destroyed or damaged several houses along the creek course, causing several victims.Landslide 2 severely impacted the primary school of the village (the school is the large building at the lower boundary of the deposition area).Examination of the picture taken before the storm shows that several scars could be identified, generated by the previous storm occurred on 2007.
Contrarily to earlier works on the topic (see Keijsers et al., 2011;De Sy et al., 2013), we decided not to calibrate the landslide model for each DTM resolution considered in the analysis.Recalibrating the model parameters would clearly partially compensate for the changing representation of the morphological attributes associated to each resolution.However, this would also cloud the comparison over the road-related and natural failures, making the examination of the results less straightforward.Owing to this reason, we decided to base the model parameterization on the geotechnical and hydraulic parameters obtained from in-situ analysis (Regional Department of Civil Protection for Sicily Region, personal communication, 2011).These parameters are reported in Table 1.The influence of vegetation surcharge and root strength on slope stability is confined to a limited portion of the area, where shrubs and forests are widespread.The remaining land is covered by grass which provides some root cohesion.Based on these observations, a value of 1000 Pa, averaged over the basin, was used as combined root and soil cohesion.An average value of soil depth was used, equal to 1 m.The vegetation surcharge was not considered in the analysis since the study area is not covered by forest stands, and the dominant component is grassland.Parameters of the GEV distribution (Table 2) were estimated by using the method of L-moments, as reported by Aronica et al. (2012).The LiDAR-derived DTM at 2 m was regridded on Introduction

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Full 4, 10 and 20 m grid cell resolution by using the mean aggregation function in order to obtain coarser digital terrain models.The mean aggregation function was found to ensure a high degree of consistency between surface flow paths extracted from gridded elevation data having different resolutions.

Influence of DTM resolution on slope, effective specific contributing area and QDWI
To investigate how different DTM resolutions (2 m, 4 m, 10 m and 20 m) affect the relative shallow landslide susceptibility distribution, the behaviour of three topographic indices derived from the DTM and used in the susceptibility assessment, i.e. local slope, effective contributing area and QDWI, was analyzed (Figs. 4 and 5).In the Figures we show the distribution of both the total (Fig. 4) and the effective (Fig. 5) contributing area, and the relevant wetness indexes.We term here wetness index (WI) the ratio between the total contributing area and the local slope.Although the total contributing area and WI are not used in QD-SLaM, these topographic attributes represent limiting conditions that help understanding the behaviour of their quasi-dynamic counterparts at very long precipitation durations.
Figure 4a shows the distribution of the slope values for the four DTM resolutions.Although the distributions are similar, it is clear that steep slopes are less represented at the coarser resolutions.The 90th and the 75th percentiles decrease from 0.91 to 0.79 and from 0.74 to 0.67, respectively, with increasing the DTM size from 2 to 20 m.The slope was calculated by a cell-to-cell computation.
The distribution of the total specific contributing area (contributing area per unit contour length) for the different grid cell sizes is shown in Fig. decreasing, were reported by several researchers for various landscapes (Zhang and Montgomery, 1994;Claessens et al., 2007;Keijsers et al., 2011).The distribution of the WI for the four resolutions is reported in Fig. 4c.The distribution reflects the behaviour of the specific contributing area and the slope, clearly showing a shift towards higher values with increasing resolution.The 90th and the 75th percentiles increase from 5.98 to 7.60 and from 4.54 to 6.05, respectively, with increasing the DTM size from 2 to 20 m.The distributions of the effective specific contributing area are reported in Fig. 5a-c for the three different durations of 1, 3 and 24 h, respectively, and for the four DTM resolutions.The distributions show that the influence of the resolution increases remarkably with the rainfall duration.The distribution of the 24 hspecific contributing area is similar to that reported for the total specific contributing area, for the four resolutions.It is interesting to note that, contrarily to the total case, the minimum specific contributing area values are not directly related to the grid size, since fractions of grid area are computed when the rainfall duration is less than the time taken by the subsurface flow to travel the grid.This is particularly evident for 1 h rainfall duration, where the four distributions exhibit the same behaviour for the left tail and are limited to a range of 1 to 5 m.The distributions of the QDWI are reported in Fig. 5d-f for the three different durations of 1, 3 and 24 h, respectively, and for the four resolutions.The distributions clearly display the smoothing effect related to the increasing grid size on both slope and effective specific contributing area.Two different patterns emerge.
At small rainfall duration (1 h), the distributions tend be more peaked with increasing grid size, showing the impact of slope smoothing.At longer rainfall duration (24 h), the distributions are shifted towards larger values with increasing grid size.However, while the left tail mimics the behaviour of the WI distributions, the right tail shows less sensitivity to DTM effect.For shallow landslide modelling, the left tail of the effective specific contributing areas and QDWI distributions is most interesting.Overall, this shows that increasing the grid size leads to an increase of the values at the left tail of the effective contributing areas and QDWI distributions.These effects are minimal at 1 h rainfall and increase with rainfall duration.Since different rainfall durations are used to generate the Introduction

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Full critical rainfall return time map, the differential sensitivity of the QDWI to the DTM resolution directly translates into a complex pattern of critical rainfall frequency sensitivity to DTM resolution.

Distribution of the critical rainfall values
The spatial distributions of the critical rainfall frequency are reported in Fig. 6 for the four different DTM resolutions.The Figures show that the main characteristics of the mapped landslides are well represented at the four resolutions, with the observed failures characterized either as unconditionally unstable or with low critical rainfall return period.More specifically, this is the case of the steep valley above the village of Giampilieri, on the left side of the creek, where most of the mapped failures are concentrated.
Tables 3 and 4 summarise some key characteristics of the critical rainfall distributions.Table 3 provides the percentages of catchment area considered unconditionally unstable and unconditionally stable with the QD-SLaM application for the four DTM resolutions, whereas Table 4 provides the same percentages for two main ranges of critical rainfall frequency.Table 3 shows that more unconditionally unstable cells are reported over the study basin with decreasing grid size, ranging from 13.8 % at 2 m to 6.3 % at 20 m.On the other hand, the percentage of the unconditionally stable cells behaves in a similar way albeit in a much reduced range of values, comprised between 30 % at 2 m and 29 % at 20 m.In our application the distribution of unconditionally stable and unstable states is mainly influenced by local slope.Thus, these effects are related to the distribution of local slope as reported in Fig. 4a, showing a marked impact of the DTM resolution on the right tail of the distribution, which controls the unconditionally unstable condition, and much less on the central values, which control the unconditionally stable condition.
Table 4 shows that the relative frequency of the two main classes of critical rainfall frequency changes in negligible way by varying the DTM resolution from 2 m to 10 m.Only for the 20 m grid size large values of return time increase noticeably.According to 9775 Introduction

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Full Eq. ( 4), the critical rainfall depends on both the local slope and the QDWI.The effect of the coarse resolution DTM having larger QDWI values at the left tail and smaller local slope values at the right tail produce opposite impacts on the critical rainfall computation.The results reported in Table 4 imply that the two effects of DTM size on slope and QDWI compensate each other effectively, at least between 2 m and 10 m.For a grid size of 20 m the smoothing effect on slope is stronger, thus leading to larger values of critical rain rate and hence of return period.

Performance assessment methodology
The quality of the model representation of landsliding susceptibility was first assessed by comparing the locations of the observed landslide with those predicted by the model.
Better model performance is achieved when a larger difference between fractions of catchment and landslide area corresponding to short recurrence interval of critical rainfall is observed.Tables 5 and 6 report these comparison for all landslides, without distinction between road-related slides and natural scars.
For a more complete model verification over the three landslide groups (road-related landslides, natural landslides, all landslides), we adopted the assessment methodology developed by Tarolli et al. ( 2011), which is an extension of the method described above.The methodology can be summarized in a plot where fraction of basin T r area F B (T r ) is reported on the x axis and fraction of landslide T r area F L (T r ) on the y axis.The steeper the curve of the plot, the better the performance of the model, because a higher fraction of low T r area is reported over the observed landslides.The 1 : 1 line represents the "naive" model, i.e. a model without predictive power.The measure of the area below the empirical function is selected here to provide a measure of the model performance.We term this statistic as "Efficiency Index" (EI).The statistic ranges between 0 and 1, with 1 representing perfect model performance, and 0.5 representing naïve model performance.We examine the model performance for three different set of landslides: (i) road-related slides; (ii) natural slides, and (iii) all landslides, including both roadrelated and natural slides.

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Evaluation of the model performances at different DTM resolutions
A first assessment is based on results reported in Tables 5 and 6 and concerns all landslides, without distinction between road-related slides and natural failures.Similar to the results already reported for the basin area (Sect.4.2), Table 5 shows that more unconditionally unstable cells are predicted over the landslide area with decreasing grid size, ranging from 56.2 % at 2 m to 42.9 % at 20 m.This shows again the effect of decreasing slope with coarsening the DTM resolution.Interestingly, the percentage of landslide area corresponding to unconditionally stable cells is always zero.
The occurrence of mapped landslide in areas predicted to be unconditionally stable is generally considered an indication about the occurrence of processes external to the model framework (Tarolli et al., 2011).So, these results show that the processes which are external to the model representation, such as road-related processes, are not emerging over areas considered as unconditionally stable.
Results reported in Table 6, which are weighted on the percentage of area considered as conditionally unstable, offer a first assessment of the DTM resolution impact on the model prediction accuracy.Examination of the results shows that even though the catchment percentages falling into the two main critical rainfall frequencies are roughly similar with coarsening the DTM resolution (Table 4), the corresponding spatial organizations of the critical rainfall frequency with respect to the mapped scars are markedly different.Indeed, more landslides are reported in the first range of critical T r (< 10 yr) for the DTM resolution corresponding to 4 m and 10 m, whereas DTMs of 2 m and 20 m provide less accurate results, with less landslides reported in the first range of critical T r .This shows that the 2 m and 20 m resolution appear to be of similar poorer quality compared to intermediate resolutions.
Overall, Tables 5 and 6 show that many more cells are predicted to be unconditionally 2.7 % of the study area.Indeed, this result is consistent with the general tendency of several process-based models to overestimate the areas predicted as unconditionally unstable or failing with low critical rainfall.Lanni et al. (2012) showed that the main reasons for this tendency are the uncertainty in the soil depth distribution and the limits of any survey which can only capture and map the most recent landslide evidences.
We consider this prediction as an indication for likely failing sites in future storms rather than areas proved stable during previous storms (Borga et al., 2002).Table 7 reports results in terms of EI for road-related, natural and all landslides and allows for a more complete examination of the interplay between digital topography features and forest roads.Figure 7 provides an example of the intercomparison when considering all landslides and 10 m DTM resolution.Confirming the results shown in Table 6, the statistics reported in Table 7 for all landslides indicate better landslide capability recognition for DTM resolutions corresponding to 4 m and 10 m, with relatively high values of EI around 0.83.EI is lower and ranges between 0.67 and 0.71 when considering a grid size of 2 m and 2 m, respectively.
The same ranking arises for the natural landslides, with slightly better results.Even in this case, the worst predictions are obtained by using a 20 m DTM (EI = 0.67), whereas predictions with 4 m DTM and 10 m DTMs are marked with EI ranging around 0.87.
Model performances over road-related failures are, as expected, lower than for the other cases.This is not surprising, given that the QD-SLaM model does not incorporate the description required to predict road-related failures.The model is only able to show better performances than the naïve model (characterized by EI = 0.5) due to the overestimation of the low critical rainfall frequency area which characterizes QD-SLaM as well as other similar models.The performances over the road-related failures show a well-defined ranking, with EI decreasing correspondingly to the grid size.This result is likely associated to the increasing impact of the road system on the drainage patterns, thanks to the finer digital topography.At 10 m and 20 m grid size, the features related to the roads network are not recognized because of coarse resolution, whereas at higher resolution the digital topography is affected by the road network with a considerable impact on the computation of the contributing area.
Overall, these results show that caution should be used when assessing the impact of DTM resolution on shallow landslide model predictive power, particularly when the effects of external processes may be themselves dependent on the resolution of the digital topography.

Conclusions
In this work a quasi-dynamic shallow landslide model has been applied to the 2.6 km 2 Giampilieri catchment, with the main goal to examine the model predictive power as a function of the DTM resolution and by considering the specific impact of forest roads.
Five main remarks arise from our work.
1. Use of coarser resolution has a smoothing effect on terrain attributes, with local slope angles decreasing and contributing areas becoming larger.However, the effect on the effective contributing areas is shown to be dependent on the precipitation duration, with DTM effects which are negligible for 1 h precipitation and which are increasing with the duration.This pattern of sensitivity is transmitted to the QDWI.Since the critical rainfall spatial pattern is composed by several precipitation durations, depending on local topography and climate, a complex pattern of model sensitivity to the DTM resolution results.
2. The DTM resolution has a remarkable impact on the area percentage considered as unconditionally unstable, which decreases with increasing the DTM size.
An almost negligible impact is reported for the unconditionally stable areas.The distribution of the critical rainfall frequency is also weakly influenced by DTM resolution.This result is due to compensating effect of QDWI and local slope.considering both fine and coarse resolutions, the corresponding spatial organizations of the critical rainfall frequency over the mapped scars are markedly different.In simple terms, the model predictive power is shown to be DTM-resolution dependent.When assessed over the sample of mapped natural landslides (i.e., landslides that are not road-influenced), better model performances are reported for 4 m and 10 m DTM resolution.This agrees with earlier findings (Tarolli and Tarboton, 2006;Keijsers et al., 2011) and highlightes the fact that higher DTM resolution does not necessarily mean better model performance.
4. Model results over the mapped road-related failures outline a specific prediction and DTM-sensitivity patterns.Model performances are remarkably lower than those obtained when considering natural landslides.This is not surprising, given that road-related processes are external to the model structure.Nevertheless, the model performances are still higher than those corresponding to the naïve model, due to the general tendency of the model to overestimate areas characterized by low critical rainfall.
5. The model predictive power decreases with increasing the DTM resolution, when assessed over the road-related landslides.This is due to the interaction of the model structure (which does not describe the road-related processes) and the impact of road geometry on the digital topography.Model structural error is DTMresolution neutral and as such it is expected to affect model outcomes independently on DTM resolution.The road impact on digital topography increases with DTM resolution and adds to the error, as shown by the pattern of EI.
Overall, these findings show that shallow landslide predictive power can benefit from increasing DTM resolution only when the model is able to describe the physical processes emerging at the smaller spatial scales resolved by the digital topography.When this is not the case, it seems that better DTM resolution does not necessarily translate in better model performances.For the specific case of forest road impact, it is expected Introduction

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Full that the combined use of high DTM resolution and a model capable to deal with roadrelated processes may lead to substantially better performances in landscapes where forest roads play a significant role in slope stability.This combination of susceptibility modelling and digital topography may have limitations in the description of natural slides, but nonetheless it has strong potential to better identify road-related failures.Introduction

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Full  Full precipitation-triggered shallow landslides is of concern in hydrogeomorphic and natural hazards science due to the high ranking of such events among natural disasters in terms of both the number of people affected globally and the proportion of individual fatalities.Shallow landsliding can evolve in debris flows, resulting Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | −2 .Roads are unpaved; road cuts truncate colluvial fills in topographic hollows and weathered bedrock in noses and divert both surface and subsurface flow into an in-board ditch system that drains through culvers into valley bottom.The road width is ranging between 4 and 6 m.At 10 m and 20 m DTM the features related to the roads network Introduction Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 4b.It is possible to observe larger values of specific catchment area for coarser DTM.Similar smoothing effects of coarser resolutions, with contributing areas becoming larger and the local slope angles Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | unstable or to fail with moderate rainfall (T r < 10 yr) than are mapped as landslides.This percentage of catchment area ranges between 19.5 % at 20 m DTM and 29.5 % at 2 m DTM, and should be compared with the landslide percentage which amounts to HESSD Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 3. Comparison with mapped landslides shows that, even though the catchment percentages falling into the main critical rainfall frequencies are similar when Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .Fig. 3 .Fig. 5 .
Fig. 1.Location map of the study area.Road-related landslides are highlighted in red, while the others are reported in black.The landslides L1 and L2, described as example in Fig.4, are also reported.

Table 2 .
Parameters estimated for application of GEV model.