Combining release and runout in statistical landslide susceptibility modeling
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Abstract
We introduce and compare two approaches to consistently combine release and runout in GISbased landslide susceptibility modeling. The computational experiments are conducted on data from the Schnepfau investigation area in western Austria, which include a highquality landslide inventory and a landslide release susceptibility map. The two proposed methods use a constrained random walk approach for downslope routing of mass points and employ the probability density function (PDF) and the cumulative density function (CDF) of the angles of reach and the travel distances of the observed landslides. The bottomup approach (A) produces a quantitative spatial probability at the cost of losing the signal of the release susceptibility, whereas the topdown approach (B) retains the signal and performs better, but results in a semiquantitative score. Approach B also reproduces the observed impact area much better than a pure analysis of landslide release susceptibility. The levels of performance and conservativeness of the model results also strongly depend on the choice of the PDF and CDF (angle of reach, maximum travel distance, or a combination of both).
Keywords
GIS raster analysis Landslide susceptibility Landslide runout Statistical modelIntroduction
Overviews of spatial landslide probability (susceptibility) at local or regional scales are useful to support hazard indication zonation and for prioritizing target areas for risk mitigation. Computer models that utilize geographic information systems (GIS) are commonly employed to produce such overviews (Van Westen et al. 2006). With ever increasing computational power, physically based modeling of landslide susceptibility—also with reasonably complex modeling tools—is increasingly becoming not only technically feasible but also able to be conducted for large areas (Mergili et al. 2014a, b). However, slopes are often not uniform, but characterized by multiscale patterns in terms of the rock or soil characteristics governing their stability (De Lima Neves Seefelder et al. 2017). Since physically based models require this type of information, the parameterization of these models becomes a highly challenging task, leading to limitations of the quality of the results obtained. Heuristic models, based on the opinion of experts, are useful for larger areas, but they often provide qualitative results only. For these reasons, statistical methods—often coupled with stochastic concepts—are commonly employed to relate the spatial patterns of landslide occurrence to those of environmental variables such as slope, vegetation, or lithology, and applying these relationships to estimate landslide susceptibility (Guzzetti 2006). A broad array of statistical methods for landslide susceptibility analysis has been developed, documented by a large number of publications (e.g., Carrara et al. 1991; Baeza and Corominas 2001; Dai et al. 2001; Lee and Min 2001; Brenning 2005; Saha et al. 2005; Guzzetti 2006; Komac 2006; Lee and Sambath 2006; Lee and Pradhan 2007; Yalcin 2008; Yilmaz 2009; Schwarz et al. 2009; Nandi and Shakoor 2010; Yalcin et al. 2011; Tilch et al. 2011; De Graff et al. 2012; Petschko et al. 2014; Schwarz and Tilch 2017). Such methods only consider the release of landslides and not their further movement down slopes or channels.
The propagation of landslides often contributes substantially to the associated hazards and risks: the most severe landslide disasters in history occurred far away from the release areas. The 1962 and 1970 Huascarán events in Peru (Evans et al. 2009; Mergili et al. 2018) are only two examples of catastrophic longrunout landslides. Even though most cases are less extreme, particularly those which initiate at steeper slopes tend to evolve into flowlike movements with potentially long runout distances even on more gentle slopes. Therefore, simulations of such mass flows are important to anticipate their consequences. Advanced physically based models of landslide propagation (Christen et al. 2010a, b; Mergili et al. 2017) are usually employed for localscale studies. Conceptual approaches, in contrast, have been developed to analyze and to estimate travel distances and impact areas at broader scales. Some build upon the angle of reach or related parameters (e.g., Scheidegger 1973 for rock avalanches; Zimmermann et al. 1997 and Rickenmann 1999 for debris flows; Corominas et al. 2003 for various types of landslides; Noetzli et al. 2006 for rock/ice avalanches), and others consist of semideterministic models employing the concept of Voellmy (1955) (Perla et al. 1980; Gamma 2000; Wichmann and Becht 2005; Horton et al. 2013). Mergili et al. (2015) have introduced an automated approach to statistically derive cumulative density functions of the angle of reach from a given landslide inventory and to apply these functions to compute a spatially distributed impact probability. Modeling approaches considering both the release and the propagation of landslides do exist (Mergili et al. 2012 and Horton et al. 2013 for debris flows; Gruber and Mergili 2013 for various highmountain processes). However, they yield expected impact or deposition depths, binary results (impact/no impact expected), or semiquantitative scores.
Integrated automated quantitative approaches to properly estimate the susceptibility of a given area to be affected by a landslide—considering both release and propagation—are still scarce. We postulate that such approaches would be highly important to better anticipate those areas most likely impacted by future landslides, compared to approaches covering either of the process components. The outcome of such a model would therefore represent an extremely valuable basis for hazard and risk management, particularly with regard to spatial planning and to the prioritization of areas requiring further research.
The present work attempts to elaborate on this gap by combining the two opensource software tools r.landslides.statistics and r.randomwalk. The combination of these tools is much more than just a technical issue: instead, we focus on strategies for the appropriate spatial combination of the impact probabilities or susceptibility indices related to different release areas or cells. Thereby, we partly build on an earlier attempt of Mergili and Chu (2015). When using the term “landslide” in the context of the present work, we mostly refer to shallow landslides developing into hillslope debris flows.
We will next introduce our computational framework and the Schnepfau investigation area in western Austria along with the data employed and the computational experiments performed on this area. After presenting and discussing the results, we will conclude with a set of takehome messages.
Methodical framework
General model layout
Definition of the susceptibilities and probabilities used in the context of the present work
Variable  Approach  Name  Description  Type, range 

P _{R}  A  Landslide release probability  Spatial probability of a raster cell to become a landslide release cell.  Float, 0–1 
P _{IS}  A  Specific impact probability  Spatial probability of a raster cell to be impacted by the propagation of a mass point starting from one specific point.  Float, 0–1 
P _{I}  A  Impact probability  Spatial probability of a raster cell to be impacted by the propagation of mass points starting in its upslope contributing area.  Float, 0–1 
P _{RZ}  A  Zonal release probability  Spatial probability that landslide release occurs at all (from at least one raster cell) in the upslope contributing area of a given cell.  Float, 0–1 
P _{L}  A  Integrated landslide probability  Spatial probability that a given raster cell is directly affected by at least one landslide either through release or through propagation.  Float, 0–1 
LRSI  B  Landslide release susceptibility index  Index denoting the likelihood of a raster cell to become a landslide release cell.  Float, 0–1 
ILSS  B  Integrated landslide susceptibility score  Semiquantitative score indicating the likelihood of a given raster cell to be directly affected by at least one landslide either through release or through propagation.  Integer, ≥ 0 
ILSI  B  Integrated landslide susceptibility index  Semiquantitative index derived by the normalization of ILSS to the range 0–1.  Float, 0–1 
 A.
Bottomup approach: for each raster cell (“impact cell”), the probability that landslide release is observed anywhere in its catchment is computed. This zonal release probability P_{RZ} is calculated from the landslide release susceptibility index at each of the GIS raster cells in the catchment of the impact cell in combination with the size of the catchment. P_{RZ} is then multiplied with the probability that the same impact cell is reached by a landslide released in its catchment (impact probability P_{I}) in order to derive the integrated landslide probability P_{L}. P_{I} is derived from the cumulative density function of the angles of reach and the travel distances of the past observed landslides in the study area.
 B.
Topdown approach: a set of random walks proportional to the landslide susceptibility index is started from each raster cell (“release cell”). Each random walk proceeds downslope until a threshold angle of reach or threshold travel distance is met. Individual thresholds for each random walk are probabilistically deduced from the angles of reach and the travel distances of the observed landslides in the study area. Each time a raster cell is impacted by a random walk, its integrated landslide susceptibility score ILSS is increased by 1.
Abbreviations used to describe the spatial subsets of the investigation area
Abbreviation  Name  Description 

TA  Training area  Subset of all raster cells within the study area used for the derivation of zonal statistics, CDFs, and PDFs 
VA  Validation area  Subset of all raster cells within the study area used for model validation 
OIA  Observed landslide impact area  Subset of all raster cells within the study area with observed landslides (including release, transit, and deposition areas) 
ORA  Observed landslide release area  Subset of all raster cells within the study area with observed landslide release 

r.landslides.statistics has been designed for the generation of the zonal probability function needed as part of the approach A.

r.randomwalk, introduced by Mergili et al. (2015), employs sets of constrained random walks to route hypothetic mass points—representing landslides—down through a DTM until a certain break criterion is met (approach B), optionally assigning an impact probability to each raster cell it hits (approach A). The probability density function (PDF) and the cumulative density function (CDF) used for this purpose are derived from the analysis of the observed landslides. Further, r.randomwalk includes an algorithm to combine release and impact probability, employing the zonal release probability function derived with r.landslides.statistics (approach A).
Approach A (bottomup): integrated landslide probability
Release susceptibility and probability
Statistical analyses of landslide release susceptibility have been treated exhaustively in previous studies (see “Introduction” for selected references) and are not the focus of the present work. Therefore, we use an existing map of the release susceptibility index LRSI (see Schwarz and Tilch 2018 for details). LRSI is an index within the range 0–1, where higher values stand for a higher susceptibility to landslide release, and lower values stand for a lower susceptibility to landslide release. For approach A, we have to convert the LRSI map into a spatial release probability P_{R} map. In contrast to LRSI, P_{R} has to be in line with the spatial probability of observed landslide release areas. Its average over the entire study area has to be identical to the “density” of observed landslides. For example, if, in a study area of 10 km^{2}, 0.1 km^{2} are classified as observed landslide areas, this would correspond to a “landslide density” of 0.01 (1%). The P_{R} map for the same area would have to show an average of 0.01 over all GIS raster cells, in order to be consistent with the observation.
In a case where the values of LRSI shown in the release susceptibility map are proportional to the spatial release probabilities, the map of P_{R} can be derived by linear scaling of the values of LRSI.
Zonal release probability
It is useful in many contexts to work with GIS raster cellbased spatial release probabilities P_{R}. They can be averaged in order to characterize the likelihood of landsliding in any type of landscape unit (such as slope units, catchment basins, or cells resampled to a coarser resolution). However, the average of P_{R} over a given landscape unit does not tell us how probable it is that landsliding occurs in that zone at all. Therefore, we take up the concept of the zonal release probability P_{RZ} first suggested by Mergili and Chu (2015), which increases with the size Z of the considered zone. P_{RZ}, which can take values in the range 0–1, represents the probability that at least one landslide initiates in a given zone and is based on the observed patterns of landslide release areas. When considering a zone size of one single GIS raster cell, P_{RZ} = P_{R}. For large areas such as mountainous catchments, P_{RZ} = 1 as there will always be at least one observed landslide release cell. We emphasize that P_{RZ} is always related to a zone of a given size rather than to a raster cell. In the present work, P_{RZ} assigned to each cell relates to its upslope contributing area, which is almost similar to its hydrological catchment area. This concept is needed for approach A as a basis to compute the integrated spatial landslide probability P_{L}. P_{RZ} cannot be computed in a fully analytic way. Consequently, we introduce an empirical approximation procedure described in detail in the Appendix.
CDFs of break criteria for landslide propagation
The values of ω_{OT} and L_{OT} are collected for all observed landslides and are employed to build CDFs for each of the two criteria (Fig. 2(b)). They describe the probability that a landslide has not yet stopped when a certain threshold of ω_{OT} or L_{OT} has been reached.
Impact probability
The tool r.randomwalk is applied for this step. Thereby, a set of constrained random walks is started from each raster cell and routed down through the terrain until it reaches the boundary of the investigation area. A specific impact probability P_{IS} is assigned to each cell impacted by a random walk. P_{IS} describes the probability of an arbitrary GIS raster cell (“impact cell”) to be hit by a mass point released from a defined cell (“release cell”). We define P_{IS} based on the angle of the path ω between the release cell and the impact cell, the distance along the same path L, or a combination of both. Thereby, the relevant CDFs are employed.
The impact probability P_{I} results from the spatial overlay of all relevant values of P_{IS} at a given cell (Table 1, Fig. 2(c)). For reasons to be explained in the following section on the integrated landslide probability, for those cells with impacts from more than one release cell, P_{I} takes the average value of all relevant values of P_{IS}.
Integrated landslide probability
For illustration, let us consider a given impact cell characterized by a value of P_{RZ} = 0.5 for its upslope contributing area, depending on Z and on the separate values of P_{R} for each “release cell” (all cells in the upslope contributing area are considered as release cells). Let us further assume that the upslope contributing area consists of two release cells only, so that the impact cell is characterized by two values of P_{IS} (0.8 and 0.2), each relating to a possible landslide impact from one of the two release cells in the upslope contributing area (see description of the impact probability). Working with the concept of the zonal release probability, (i) we assume that the release of landslides is equally probable for each release cell in the upslope contributing area, whereas (ii) the probability that landsliding occurs in this area at all is given by P_{RZ}. It is important to note that P_{RZ} does not apply to each of the two release cells but represents an aggregated value also including the possibility of a release from both cells, or from none of the two cells. This means that the probability that a landslide reaches our impact cell can be approximated by the product of P_{RZ} and the average of P_{IS}. In our example, this results in P_{L} = 0.25.
We note that the described procedure is supposed to yield smoothed results due to averaging effects: on the one hand, Eq. 3 builds on the simplification of a uniformly distributed release probability over the possible release zone. On the other hand, as highlighted in the section on the impact probability, P_{I} represents the average of P_{IS} over all mass points impacting a cell. This type of averaging is necessary to ensure a consistent combination of P_{RZ} and P_{I}. We further note that also those cells with P_{R} = 0 are included as release cells. This means that Z and therefore also P_{RZ} are computed including those cells with P_{R} = 0. An alternative approach would consist in excluding those cells with P_{R} = 0 both from Z and from P_{I}. Preliminary tests, however, have shown that this would not change the results in a substantial way.
Approach B (topdown): integrated landslide susceptibility score
The integrated landslide susceptibility score ILSS (approach B) represents a more straightforward and intuitive, though semiquantitative alternative to P_{L} (approach A). The release susceptibility map is used as the basis for the procedure. It can be directly used as input, without the preprocessing required for approach A.
The entire procedure is performed with the tool r.randomwalk. In a way analogous to approach A, the values of ω_{OT} and L_{OT} are collected for all observed landslides. They are employed to build probability density functions (PDFs) instead of CDFs for each of the two criteria (Fig. 2(b)). They describe the probability that a landslide stops at a certain threshold of ω_{OT} or L_{OT}. A set of constrained random walks is started from each raster cell with LRSI > 0. Thereby, the number of random walks n_{W} is proportional to LRSI: n_{W} = int(100· LRSI + 0.5), meaning that 100 random walks start from cells with LRSI = 1.0, whereas 10 random walks start from cells with LRSI = 0.1, etc. The break criterion for each single random walk is randomly set according to the PDF of the angle of reach, the travel distance, or a combination of both. This means that more random walks use the more probable values of the break criteria, whereas fewer random walks use the less probable values.
Each time a random walk hits a raster cell (including the release cell), the landslide susceptibility score ILSS for this cell is increased by 1. At the end, those cells which are likely to be reached by landslides released from cells with high values of LRSI display high values of ILSS, whereas those cells less likely to be impacted by landslides released from cells with low values of LRSI show low values of ILSS (Fig. 2(c)). In order to facilitate the validation of the results by means of ROC plots, ILSS is converted to the index ILSI through normalization of its values to the range 0–1.
Investigation area and model parameterization
The Schnepfau investigation area
The Schnepfau investigation area covers an area of 58 km^{2} and is situated in the Bregenzerwald which is part of the federal state of Vorarlberg, western Austria. The area is located on the east bank of the Bregenzerach River and comprises parts of flat alluvial plains, mostly low mountain ranges, and partly also high mountains up to 1834 m. Hence, the morphology of the area is ranging from flat and hilly to steep and rocky parts.
The investigation area is mostly composed of geological units of the Säntisdecke as part of the Helvetikum (Friebe 2007), consisting of a variety of rocks such as marl, sandstone, and limestone. The formations of the Säntisdecke generally show northwards overturned folding, whereby the fold axes indicate a stretching in WSW–ENE direction (Oberhauser 1951). Intersection with the surface can result in large, homogeneous or smaller, heterogeneous outcrops. Generally, large, homogeneous areas are found in the southern (Palfris Formation, Quintner Limestone) and central parts (Schratten Limestone) of the investigation area, whereas small heterogeneous areas exist in the central (e.g., Palfris Formation) and northern parts (e.g., Schratten Limestone, Drusberg Formation).
The competent, often karstified and bare carbonate rocks of Quintner Limestone and Schratten Limestone and their weathering products are the most widespread examples for geological formations hardly susceptible to shallow landslides and hillslope debris flows. In contrast, rocks such as the marl slates of the Palfris Formation and the marls of the Drusberg Formation weather to clayrich material highly susceptible to shallow landslides. Moreover, the Palfris and Drusberg Formations often show shallow embedded limestone layers inside the marls (Oberhauser et al. 1991), resulting in quite a heterogeneous landslide susceptibility. Further, wide areas are covered by glacial till (mostly on southfacing slopes) or debris, whereby both materials can be quite susceptible to landslides, depending on their often allochthonous or parautochthonous origin. Formations with an intermediate level of landslide susceptibility are less common in the investigation area.
Input data
For the runout map, we use a 5 × 5 m resolution DTM, deduced and resampled from an aerial LiDAR point cloud and provided by the Federal Government of Vorarlberg (Landesamt für Vermessung und Geoinformation). This DTM represents the situation before the occurrence of most landslides shown in the inventory. Those raster cells coinciding with stream lines at the bottom of valleys are set to no data, so that the runout simulations stop there and those cells are excluded from all analyses. This kind of preprocessing is necessary as the model approaches chosen and the data available do not support the analysis of landslides directly connected to the valley bottoms or even interacting with streams (such as channelized debris flows or river erosion) (see “Discussion”).
Key characteristics of the landslides observed in the Schnepfau investigation area
Parameter  ORA (n = 110)  OIA (n = 113)  

Minimum  Average  Maximum  Minimum  Average  Maximum  
Area (m^{2})  50  305  2450  100  1250  10,100 
Projected length (m)  0  24  101  0  83  336 
Average inclination (degree)  5.2  27.9  40.4  6.7  23.9  39.2 
Computational experiments
Summary of computational experiments conducted in the present study
Experiment  Approach  CDF (A) or PDF (B)  Remarks 

A1  Bottomup (A)  Observed angle of reach ω_{OT}  Conducted alternatively with spatially constant and spatially varied P_{R} 
A2  Bottomup (A)  Observed travel distance L_{OT}  
A3  Bottomup (A)  Combination of ω_{OT} and L_{OT}  
B1  Topdown (B)  Observed angle of reach ω_{OT}  Conducted alternatively with spatially constant and spatially varied LRSI 
B2  Topdown (B)  Observed travel distance L_{OT}  
B3  Topdown (B)  Combination of ω_{OT} and L_{OT} 
An issue of central importance consists in the strict separation of the data used for training of the model (in the present work, the derivation of the PDFs and CDFs) and the data used for the validation of the results. For each of the six experiments, the Schnepfau investigation area is divided into four subsets (W–Z in Fig. 4) in order to separate between a training area (TA) and a validation area (VA) (Table 2). The division lines between the subsets follow catchment boundaries in order to ensure that all landslides are clearly assigned to one of the four subsets and no landslide may impact more than one subset. Each computational experiment is repeated for four times, where three of the subsets are used as TA and one subset is used as VA. The resulting raster maps of P_{L} and ILSI are validated against the OIA by means of ROC plots. Thereby, only the VA is considered. The maps and the AUROC values derived for the four spatial subsets are averaged in order to derive the final result of each experiment. The relative level of conservativeness associated with each experiment is expressed by the averages of P_{L} and ILSS (μ_{PL} and μ_{ILSS}, respectively). For the experiments A1–A3, the factor of conservativeness (FOC) is computed as the ratio between μ_{PL} and the fraction of OIA compared to the total size of the investigation area (De Lima Neves Seefelder et al. 2017). Values of FOC > 1 indicate an overestimation of the landslide susceptibility, compared to the observation, whereas values of FOC < 1 indicate an underestimation.
Building of the zonal statistics and the backcalculation of the PDFs and CDFs are conducted at a raster cell size of 5 m, whereas P_{I}, P_{L}, and ILSS are computed at a cell size of 10 m. The final results, however, are resampled to, and validated at, a cell size of 25 m which is in accordance with the cell size of the LRSI map. For backcalculating ω_{OT} and L_{OT}, we start a set of 10^{4} random walks from each cell in the ORA of the TA. For computing P_{I}, we start a set of 10^{2} random walks from each cell in the entire investigation area. We use Gaussian distributions to generate the PDFs and CDFs. The input parameters governing the behavior of the random walks consist of a weighting factor for the slope, a weighting factor and a control length for the perpetuation of the flow direction, the maximum runup height, and the segment length for computing the travel distance. Their values are chosen in accordance with the suggestions of Mergili et al. (2015) who also describe these parameters in more detail.
Results
PDFs and CDFs of angle of reach and travel distance
The validation of LRSI against the OIA results in an AUROC value of 0.700. This value is taken as a reference for the evaluation of the added value of the combined approach (signal of the runout component of the model).
Experiments A1–A3: bottomup approach
Key indicators describing the performance and conservativeness of the computational experiments introduced in Table 3. Note that the results obtained with spatially uniform values of P_{R} or LRSI only serve as a reference for the evaluation of the signal of the release component of the model. NA not available
Experiment  With spatially varied P_{R} or LRSI  With spatially uniform P_{R} or LRSI  

AUROC  μ _{PL}  FOC  μ _{ILSS}  AUROC  μ _{PL}  FOC  μ _{ILSS}  
A1  0.713  0.0130  1.75  NA  0.738  0.0139  1.87  NA 
A2  0.724  0.00440  0.59  NA  0.748  0.00485  0.65  NA 
A3  0.637  0.00306  0.41  NA  0.664  0.00347  0.47  NA 
B1  0.774  NA  NA  411  0.700  NA  NA  517 
B2  0.824  NA  NA  394  0.733  NA  NA  431 
B3  0.727  NA  NA  129  0.593  NA  NA  162 
Experiments B1–B3: topdown approach

The visual patterns of each ILSS map are largely similar to the P_{L} map derived with the corresponding experiment of approach A. Values of μ_{ILSS} decrease from 411 to 394, and then drastically to 129, from experiments B1–B3.

B2 clearly shows the best model performance (AUROC = 0.824) among the experiments B1–B3, whereas AUROC = 0.774 for B1 and AUROC = 0.727 for B3. This means that the general trend largely corresponds to the trends observed among the experiments A1–A3, with the more pronounced optimum obtained with the experiment B2 (Table 5).

The model performance associated with ILSS is always higher than the performance associated with the corresponding P_{L} maps.
There are two further important differences among the results obtained with the approaches A and B. First, the general performance in terms of AUROC is clearly higher than the performance of a pure analysis of release susceptibility in approach B. This is particularly true for the experiments B1 (difference of 0.074) and B2 (difference of 0.124).
Second, in approach B, the model performance in terms of AUROC is clearly weaker when using spatially uniform values of LRSI instead of the spatially varied maps (differences of 0.074, 0.091, and 0.134 for the experiments 1, 2, and 3). The corresponding experiments with the approach A are less sensitive to the P_{R} map (Table 5). This discrepancy indicates that the signal of the release component makes it all the way to the final result in approach B. This is not the case in approach A, where the noise even leads to slightly higher AUROC values with constant P_{R}. This may also explain the generally higher AUROC values obtained in the experiments B1–B3, compared to A1–A3: the signal of LRSI most likely improves the model performance in terms of empirical adequacy.
Discussion
We have presented and compared two innovative approaches to approximate the susceptibility of any point in a landscape—represented by a GIS raster cell—to be affected by shallow landslide processes or the resulting hillslope debris flows, be it through release or through runout.
Approach A employs a bottomup method and, from a technical point of view, yields a “true” integrated landslide probability P_{L}, whereas the approach B uses a more intuitive and straightforward topdown method in order to yield a semiquantitative landslide susceptibility score ILSS. Within the bottomup approach, the concept of the zonal release probability P_{RZ} is employed. The purpose of P_{RZ} consists in the appropriate consideration of the probability of landslide release within the upslope contributing area of a given cell (Fig. 3, Appendix Fig. 9). This is necessary to make the result a “true” probability, where FOC ≈ 1, but is done at the cost of smoothing of the spatial patterns of the cellbased release probability P_{R}. No such smoothing is required within the approach B. As a consequence, the signal of P_{R} does not survive the routing procedure in the approach A, whereas it does in the approach B (Table 5, Fig. 6). Model performance in terms of empirical adequacy is therefore better in approach B. We conclude that approach B is certainly most suitable in cases where a semiquantitative spatial overview of landslide susceptibility is required, whereas approach A is better suitable in cases where “true” probabilities are needed, e.g., as part of quantitative risk analyses. However, in doing so, it also has to be kept in mind that even comprehensive landslide inventories are never complete but just represent a snapshot, e.g., depicting only those landslides associated with one or more rainstorm events. Converting spatial probabilities in spatiotemporal probabilities therefore remains a challenge.
Whereas traditional statistically based landslide susceptibility studies (e.g., Carrara et al. 1991; Baeza and Corominas 2001; Dai et al. 2001; Lee and Min 2001; Saha et al. 2005; Guzzetti 2006; Komac 2006; Lee and Sambath 2006; Lee and Pradhan 2007; Yalcin 2008; Yilmaz 2009; Nandi and Shakoor 2010; Yalcin et al. 2011; Schwarz et al. 2009; Tilch et al. 2011; De Graff et al. 2012; Petschko et al. 2014; Schwarz and Tilch 2017, 2018) are useful to identify likely release areas at the level of GIS raster cells, their results to play a limited role when considering integrated landslide probability (approach A). This is—as it was already discussed—most probably a result of the strong correlation between zone size and P_{RZ}—and, consequently, the nonexistent reflection of P_{R} in P_{L} (Fig. 7). However, the results summarized in Table 5 reveal a decreasing signal of LRSI with increasing travel distance in approach B, where no smoothing is applied. The difference in AUROC between the spatially varied and the spatially uniform input of LRSI is smallest in the experiment B1 (longest travel distances due to the effects discussed above) and largest in the experiment B3 (shortest travel distance). Hence, the longer the travel distance becomes, the more dominant are the effects of propagation, as the signal of LRSI gets lost in superimposing random walks originating from many release cells. The poor signal of the release component in approach A leads to a performance level comparable to a pure release susceptibility analysis, where runout is neglected. Only in approach B, where the signals of release and runout are both reflected in the results, the AUROC values clearly exceed a “base level” of approx. 0.7.
As a consequence of what was said above, the suggested methods are considered particularly useful for those situations where landslides are highly mobile, e.g., where shallow landslides convert into hillslope debris flows, as it is reflected in the inventory used for the present study. The methods have to be used with care where landslides are less mobile. In these cases, the PDF and CDF of the angle of reach or of the travel distance would reflect the length distribution of the observed release areas rather than the mobility of the landslides. In general, we note that the angles of reach used in the present study rely on another concept than those included in published relationships (e.g., Scheidegger 1973; Zimmermann et al. 1997; Rickenmann 1999; Corominas et al. 2003; Noetzli et al. 2006). Whereas these and other authors refer to the angle between the highest and the terminal point of the landslide, we consider the angles between any release cell of an observed or hypothetic landslide and its terminal point (Fig. 2). This applies to the travel distance in an analogous way and is required as the random walks are started from all raster cells, which may coincide with any random position within landslide release areas, but not necessarily with the highest point of a landslide. Further, it is not possible to make runout dependent on landslide volumes in a straightforward way as it was done, e.g., by Scheidegger (1973), Rickenmann (1999), or Noetzli et al. (2006). Such approaches are useful for single events with known volumes. As the volumes of possible future landslides are not a priori known at the scale relevant for the present study, we rely on the plain PDFs and CDFs.
The runout is modeled only for hillslope debris flows, whereas flow channels have to be excluded from all the analyses. At such a slopechannel interface, we have no empirical evidence for the change of landslide behavior. For instance, landslides may stop due to the sudden drop in slope angle, or the material deposited may be mobilized by flowing water. This means that the methods, as applied in the present study, are not suitable to predict the possible impacts of extreme events and process chains at the outlet of flow channels. More data and some adaptations would be necessary to do so: a future direction could be to include the conditions along the landslide path (distinction between slopes and channels, type of basal material, vegetation) in the parameterization of the random walks.
Conclusions
We have presented and compared two approaches for integrated statistical modeling of landslide susceptibility at catchment or even broader scales. These methods were applied to shallow landslides developing into hillslope debris flows in the Schnepfau investigation area in western Austria. A map showing the spatial patterns of the landslide release susceptibility index was used as the basis. Approach A—characterized as bottomup approach—employs the concept of the zonal release probability (Mergili and Chu 2015), approximating the probability that landslide release occurs from at least one place in the upslope contributing area of a given raster cell, whereas the approach B—characterized as topdown approach—works directly with the cellbased release susceptibility index and is therefore more straightforward and intuitive at the cost of providing only semiquantitative results. Both methods impose a constrained random walk approach onto the release in order to compute landslide propagation (Mergili et al. 2015) and thereby rely on the density functions of the angles of reach and/or travel distances of the observed landslides.

Most computational experiments have performed well or fair in terms of empirical adequacy (AUROC), possibly indicating a certain degree of validity of both approaches. The visual appearance of the final maps is largely similar among the two approaches. The approach B generally performs better than the approach A. This observation is most likely associated with the better representation of the release susceptibility in the approach B, whereas the release probability is smoothed out in the approach A, so that the result is dominated by landslide propagation. We therefore recommend using the approach B for semiquantitative spatial overviews, whereas the approach A is still needed as the basis of quantitative risk analyses. We conclude that there is a profit of combining release and propagation models. This profit is clearly reflected in those AUROC values obtained with the approach B (Table 5). However, we still need a better way to consider the release probability in a fully quantitative way without losing too much of its signal (approach A).

We further conclude that employing the travel distance as break criterion yields the best overall performance particularly in approach B, even though the angle of reach appears most suitable from a physical point of view. Using a combination of angle of reach and travel distance leads to an underestimate of landslide susceptibility. However, the influence of the type of probability functions used remains a question of future research.

In approach B, the signal of the spatial differentiation of the release component weakens with increasing travel distance. Whereas the results of the integrated analyses are particularly useful for situations with highly mobile events, the propagation of landslides through flow channels as channelized debris flows is excluded due to lacking empirical evidence and missing computational implementation. This, besides the loss of the signal of P_{R} with approach A, remains one of the major limitations of the approaches and means that analyzing the possible impact of extreme events and complex process chains is out of scope of the present study.
As a consequence thereof, future enhancements could go in the direction of including the conditions along the landslide path in the parameterization of the random walks, in order to be able to consider also more complex situations at the small catchment scale. The spatial diversity of geological or if possible rheological conditions should be included into the modeling process.
Notes
Acknowledgments
Part of this work was conducted within the international cooperation project “A GIS simulation model for avalanche and debris flows (avaflow)” supported by the German Research Foundation (DFG, project number PU 386/31) and the Austrian Science Fund (FWF, project number I 1600N30). We further acknowledge the support of Matthias Benedikt, William Ries, and Edmund Winkler.
Funding Information
Open access funding provided by Austrian Science Fund (FWF).
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