Shallow landslides pose a risk to infrastructure and residential areas. Therefore, we developed SlideforMAP, a probabilistic model that allows for a regional assessment of shallow-landslide probability while considering the effect of different scenarios of forest cover, forest management and rainfall intensity. SlideforMAP uses a probabilistic approach by distributing hypothetical landslides to uniformly randomized coordinates in a 2D space. The surface areas for these hypothetical landslides are derived from a distribution function calibrated on observed events. For each generated landslide, SlideforMAP calculates a factor of safety using the limit equilibrium approach. Relevant soil parameters are assigned to the generated landslides from log-normal distributions based on mean and standard deviation values representative of the study area. The computation of the degree of soil saturation is implemented using a stationary flow approach and the topographic wetness index. The root reinforcement is computed by root proximity and root strength derived from single-tree-detection data. The ratio of unstable landslides to the number of generated landslides, per raster cell, is calculated and used as an index for landslide probability. We performed a calibration of SlideforMAP for three test areas in Switzerland with a reliable landslide inventory by randomly generating 1000 combinations of model parameters and then maximizing the area under the curve (AUC) of the receiver operation curve. The test areas are located in mountainous areas ranging from 0.5–7.5 km

Landslides pose serious threats to inhabited areas worldwide. They were the cause of 17 % of the fatalities due to natural hazards in the period of 1994–2013

Modelling of shallow-landslide triggering has been an ongoing process. Shallow-landslide probability has been modelled mostly using a deterministic approach

Initiation of instability is a process that combines mechanical and hydrological processes on different spatial and temporal scales and can thereby be very localized, with successive movement increasing the magnitude of the event

The mechanical aspect of shallow-landslide initiation usually results from local instabilities that could extend indefinitely in an infinite constant slope if the shear resistance is low

Besides hydrology, slope and soil characteristics, vegetation plays a key role in landslide triggering

present the SlideforMAP model as a tool for shallow-landslide probability assessment,

show a calibration of SlideforMAP through a performance indicator over three study areas with 78 field-recorded shallow-landslide events in Switzerland,

analyse the expected improvement in the performance of SlideforMAP with a detailed inclusion of vegetation,

provide a qualitative sensitivity analysis and identify the parameters that are of greatest influence on the slope stability.

Strong emphasis within the SlideforMAP framework and this paper is put on the quantification of root reinforcement on a regional scale. We will show the effect of accurate, quantitative representation of root reinforcement has on slope stability over three study areas. Simplifications, lack of a temporal component and calibration constraints make it impossible to use SlideforMAP as an exact forecast tool. The main application for SlideforMAP is as a tool to quantify the effects of vegetation planting, growth and/or management for land managers in relation to shallow landslides.

SlideforMAP is a probabilistic model that generates a 2D raster of shallow-landslide probability (

Flow chart of the computational steps in SlideforMAP. Separate sections are outlined in colours. The central workflow is highlighted.

The estimate of the stability of each HL is calculated following the limit equilibrium approach (described well in the work of

Schematic overview of the forces acting upon a hypothetical landslide, as assumed in SlideforMAP. The blue arrow,

As seen in Fig.

The location of the centre of mass of the HLs is generated from two uniform distributions covering the latitudinal and longitudinal extent of the study area. HLs on the edge of the study area are taken into account as well, though cut to the extent of the study area in the later spatial processes of SlideforMAP. The total number of HLs is determined by multiplying the landslide density parameter (

Steeply sloped mountainous areas are prone to extreme and unpredictable heterogeneity in soil parameters

Three properties of vegetation are included in the model. These are vegetation weight, lateral root reinforcement and basal root reinforcement. SlideforMAP only incorporates trees and ignores possible effects by shrubs, grasses and other vegetation. This choice is due to the fact that trees are predominant in influencing slope stability

In Eq. (

In this equation

The hydrological module in SlideforMAP is based on the TOPOG model

The model has a total of 3 probabilistic parameters and 15 deterministic parameters (Table

An overview of all variable model parameters of SlideforMAP. The second-to-last column indicates the source of the default value. The last column indicates whether the default is global or specific for this research in Switzerland (CH).

After model initialization, the SF (Eq.

Three study areas were chosen to test SlideforMAP based on the availability of elevation data and detailed records of historical shallow-landslide events (Fig.

Locations of the study areas in Switzerland with observed shallow-landslide occurrence over the period 1997–2012 (blue dots); the case study names are given according to nearby villages: Trub, St. Antönien and Eriz. Forest-covered area is presented in green. Source of forest cover: Federal Office of Topography swisstopo

The geological formations in the Eriz study area vary with Oligocene freshwater molasse in the lower northern part, morainic material in the central part and Cretaceous limestone in the highest parts. Forests are dominated by spruce (

Study area characteristics. Meteorological data are from the HADES yearly average precipitation for the time period 1981–2010

To accurately measure

a digital surface model (DSM) and digital elevation model (DEM);

average and standard deviation values for soil cohesion, thickness and the friction angle;

a representative landslide inventory containing at least

average landslide soil thickness,

landslide surface area.

In addition to the DEM, the DSM is applied in the vegetation module of SlideforMAP. The DEM and the DSM are both acquired from the swissALTI3D database

Overview of landslide properties for the studied regions. Top row: mean soil thickness

Vegetation parameters in the study areas. Source of forest cover: Federal Office of Topography swisstopo

The lateral root reinforcement and the basal root reinforcement (Eqs.

A landslide inventory is required to quantify a distribution for slope, surface area and soil thickness for the HLs. This inventory does not necessarily have to be well distributed in the study area or even be present in the area. However, it should be representative of the conditions in the area of interest as much as possible. A dataset of 668 shallow landslides that occurred between 1997 and 2012 in Switzerland has been created by the Swiss Federal Office for the Environment (BAFU;

The inventory is used to estimate the parameters for the surface area distribution used in SlideforMAP (Eq.

The model has a total of 21 parameters that are derived from observed data, derived from the literature or set to default values; their values, given in Table

The basis of the application of the AUC method is a spatial representation of the landslide inventory in a Boolean raster (

The confusion matrix, resulting from the comparison of a reference Boolean raster and a raster corresponding to a simulation.

A so-called receiver operator curve (ROC) can be obtained by computing the values of the confusion matrix for all unique values in the simulated raster as threshold values and for each plotting the sensitivity, TP

The parameter samples for the Monte Carlo-based model calibration and the subsequent sensitivity analysis are generated using the Latin hypercube sampling (LHS) technique

Rainfall intensity [mm h

The R script implementing the sampling methodology and a description are included in the Supplement. The minimum and maximum values from Table

Parameters used in the SlideforMAP qualitative sensitivity analysis and corresponding ranges for parameter sampling via LHS.

For the model calibration and qualitative sensitivity analysis, 1000 LHS parameter sets were generated per study area by drawing samples from the ranges in Table

SlideforMAP has potential in testing the effect of different vegetation scenarios on the landslide probability. For this research, besides the reference scenario for model calibration and sensitivity analysis (global uniform vegetation), three additional scenarios are tested: (i) without vegetation, (ii) with uniform vegetation in forested areas and (iii) with a fully diverse vegetation based on single-tree detection. The single-tree version uses the input data as mentioned in Sect.

We use the 1000 model simulations corresponding to the 1000 generated parameter sets per study area for a sensitivity analysis of the model. The objective of this analysis is to quantify how the distribution of AUC values and of the landslide probability vary as a function of the parameters. Applying the parameter subsampling technique (see Sect.

Histograms of different subsamples of the LHS parameter sets for the Trub study area. The shading (from light to dark) corresponds to subsamples retaining only the

Histograms of different subsamples of the LHS parameter sets for the Trub study area. The shading (from light to dark) corresponds to subsamples retaining only the

Based on the generated 1000 parameter sets, we identified the parameter set that resulted in the highest AUC value and assumed this to be an optimal calibration of the model. These calibrated parameter sets for each study area and their AUC values are shown in Table

Outcome of the Monte Carlo-based calibration: the parameter sets per study area resulting in the highest AUC value. The last row shows the ratio of unstable HLs resulting from these parameter sets.

Parameter consistency between the study areas appears to be visible in

Overview of the landslide probability of the study areas simulated with the calibrated parameter sets of Table

In general, the model represents well the spatial distribution of the shallow landslides from the inventory. A cumulative plot of the shallow-landslide probability for the study areas based on Fig.

Cumulative plots for shallow-landslide probability in the study areas, derived from the results in Fig.

To test the impact of vegetation on the model behaviour, we compare the different vegetation scenarios. The spatial distribution of lateral root reinforcement, resulting from single-tree detection and SlideforMAP, is given in Fig.

The spatial distribution of maximum root reinforcement (Eq.

The selected vegetation scenarios (no vegetation, global uniform vegetation, forest area uniform vegetation, single-tree detection) affect the computation of the vegetation weight, the lateral root reinforcement and the basal root reinforcement. The latter is due to its dependence on lateral root reinforcement (Eq.

The AUC and unstable ratio under different vegetation scenarios with the optimal parameter sets of Table

Significance of the difference in distribution between results of vegetation scenarios at a 90 % and 99 % confidence level. Scenario names are shortened. Significance measured by Welch's

ROCs corresponding to the scenarios with repetitions as presented in Table

ROCs of the 10 runs per vegetation scenario from Table

It is important to point out that the inventory to which the model performance is calibrated plays a key role in all the results discussed below. The inventory was obtained after triggering rainfall events, for which the precipitation intensity, duration and the spatial distribution are not known precisely. Despite this shortcoming, the inventory represents a unique source of information, and the spatial localization of the landslides can be assumed to be of high quality. Below, we discuss the model behaviour as a function of the different model parameter groups and the performance of the model and give directions for future research.

The best-performing parameter sets show high values for the soil thickness for all study areas (by comparing the values of Tables

Soil transmissivity showed considerable sensitivity to the AUC (Fig.

A key aspect of the model is the use of single-tree detection to parametrize vegetation, a method that was previously found by

In Table

In both Eriz and Trub, the single-tree detection is the best-performing scenario. Our overall finding that the model output is sensitive to the vegetation scenario and gives the second-lowest values in the unstable ratio and highest values in the AUC for single-tree detection. We argue that even though the model is calibrated on a global uniform-vegetation scenario (Table

As pointed out by

A comparison between the shallow-landslide density (Table

The main advantage of SlideforMAP compared to other models is the more realistic approach to implementing root reinforcement. This includes a spatial distribution in both the basal and the lateral root reinforcement and a focus on the second stage of the activation phase in accordance with the Root Bundle Model as described in

A hydrological and slope stability model identical to SlideforMAP is applied in

SlideforMAP uses a relatively simple hydrological module to estimate soil saturation. The TOPOG approach used could be improved, and multiple papers have presented simple to more advanced rewriting of formulas

In this paper, we present a probabilistic model to assess shallow-landslide (landslides with a scar thickness

Plot of the probability density of the soil thickness data from the BAFU dataset as used in this paper. The best fit is given of a normal and a log-normal distribution. The mean square errors are 0.096 and 0.053 for the normal and log-normal fit respectively.

Shallow-landslide slope–soil thickness relationship as used in this research. Box plots are classes with a width of 2.5 slope units. The red dots are the 95th percentile per class. The red line is the fit of Eq. (

The hybrid table for the soil cohesion and angle of internal friction for the relevant set of USCS soil classes. Values are derived from laboratory experiments

All data used in this research are open data. The topographical data and the landslide inventory as used in this research are published on Zenodo:

The supplement related to this article is available online at:

AA collected the landslide inventory and made it ready for use. DC and MS developed the basic concept of SlideforMAP. LD contributed to further development. FBvZ executed further development, the sensitivity analysis and testing. FBvZ is the main writer. BS, LD, CP, AA and MS revised the text. CP and MS organized funds.

The contact author has declared that none of the authors has any competing interests.

The shallow-landslide probability maps generated by SlideforMAP are a guideline and should be interpreted by an expert before application.Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank the STEC (Smarter Targeting of Erosion Control) project by the Ministry of Business, Innovation and Employment of New Zealand for financial support. In addition we would like to thank the two anonymous reviewers and David Milledge, who contributed a community review. Their contribution greatly improved the quality of this paper.

This research has been supported by the Ministry of Business, Innovation and Employment, New Zealand (grant no. C09X1804).

This paper was edited by David J. Peres and reviewed by Dave Milledge and two anonymous referees.