Landslides are an impacting natural hazard in alpine regions, calling for effective forecasting and warning systems. Here we compare two methods (physically based and probabilistic) for the prediction of shallow rainfall-induced landslides in an application to Switzerland, with a specific focus on the value of antecedent soil wetness. First, we show that landslide susceptibility predicted by the factor of safety in the infinite slope model is strongly dependent on soil data inputs, limiting the hydrologically active range where landslides can occur to only

Landslides are a natural hazard affecting alpine regions worldwide. They damage infrastructure and buildings, sometimes leading to loss of life

Several approaches exist for the prediction of landslides that focus on one or more predisposing and triggering factors, typically classified into three types: susceptibility mapping, probabilistic approaches, and physically based modelling

Susceptibility mapping assesses the vulnerability of a certain area to landsliding based on predisposing factors. In statistical susceptibility mapping, the different predisposing factors, geological, topographical, and climatological properties, are combined with landslide inventories and used as explanatory variables in a statistical model

Probabilistic approaches focus mainly on the temporal component of the landslide hazard (triggering factors) rather than the spatial susceptibility (predisposing factors). They are based on the assumption that rainfall is the main triggering factor and take advantage of historical records of rainfall and landslides. These databases are combined to learn which meteorological conditions have been associated with the triggering of landslides in the past. This allows us then to recognise critical conditions in weather forecasts of the coming days and estimate how likely the occurrence of landsliding is. The most common of these approaches is that of rainfall thresholds, and in particular intensity–duration or total rainfall–duration threshold curves

Finally, physically based modelling approaches are usually made up of two components to directly simulate slope stability in time and space: a hydrological and a geotechnical model. The hydrological model is used to estimate the condition of the soil, i.e. the pore water pressure and/or saturation, which are then used in the geotechnical model for the estimation of slope stability (e.g. by the infinite slope or other hydromechanical slope failure model). These approaches are theoretically the most sound and predict both when and where a landslide could occur, but they are computationally expensive and data demanding. For these reasons, they are typically applied on individual slopes in landslide-prone areas or small catchments only

In this work, we conduct a comparison of a probabilistic and physically based modelling approach to landslide prediction with the specific question of the value of the inclusion of antecedent soil wetness state in the prediction. Our scale of analysis is regional (Switzerland) instead of hillslope/catchment scale, because it is at this scale that landslide early warning systems need to be developed

A fully physically based approach that takes advantage of a state-of-the-art European simulation of hydrology

A probabilistic approach in which we develop rainfall threshold curves for landslide prediction based on a combination of historical databases of rainfall and landslides for Switzerland

For the stability assessment, we choose to follow the infinite slope approach, because this is one of the most widely used models for slope failure prediction

All calculations are done at the resolution of the DEM, i.e. a grid of cell size 25 m

To estimate the bulk soil density, cohesion, and friction angle, we used publicly available datasets in OpenLandMap

Maps of the distributed input used in the factor of safety calculations.

To assess the susceptibility to landsliding in Switzerland, we compute the factor of safety of the two endmember scenarios: completely wet soil (

We then compute the dynamic factor of safety in time and its statistics for all cells (25 m

Because soil depth is the most poorly known variable and uncertain parameter in the slope stability model in Eq. (

For the soil depth models (2)–(4), we fix the maximum soil depth

The water pressure head within the soil layer required for the calculation of the factor of safety (

We extract from the historical simulations the water pressure at the depth obtained by the soil depth model chosen and correct for the elevation difference between the centre of the corresponding TerrSysMP vertical layer and the estimated local depth and use it as the water pressure head term in Eq. (

We combine landslide inventory data in Switzerland and a daily gridded dataset of rainfall to develop rainfall threshold curves following the method by

For the definition of rainfall events, we follow the procedure introduced in

We then define a power-law total rainfall–duration (ED) threshold curve

We use the values of soil saturation estimated by the Swiss operational hydrological model PREVAH

For each susceptible cell defined in Sect.

We test the information content of soil saturation for the ED curves, i.e. analyse whether information on soil saturation could reduce some of the false positives and negatives generated by the ED threshold curve estimated in Sect.

Finally we explore two different approaches to combine rainfall characteristics and antecedent saturation. On the one hand, a hydrometeorological threshold separating the antecedent

Distributed inputs (Fig. 1) are used to compute the FoS across Switzerland as a function of the hydrological term

From top to bottom: digital elevation model (DEM, Swisstopo 25 m) and four soil depth distributions: constant (

These result in quite different spatial soil depth distributions, with the elevation-dependent soil depth mirroring the DEM, the slope-dependent soil depth showing low variability in depth in valleys and lowlands where slope is constant, and the linear diffusion model soil depth showing the highest spatial heterogeneity, with large differences in soil depth over short distances. This is due to the dependence on the second derivative of elevation (curvature) and results in low soil depth on mountain ridges but sometimes larger values in convergent topography right next to them.

We then compute the minimum (assuming soil completely wet,

Maps of (un)conditionally (un)stable regions of Switzerland obtained from the two factor of safety limiting cases (soil completely wet or dry) and the different soil depth models. Panel in the bottom row is the reference case obtained with the linear diffusion model neglecting cohesion (

Percentage of unconditionally stable (US), conditionally (un)stable (CUS), and unconditionally unstable (UU) cells in Switzerland according to the FoS calculations for each soil depth model and percentage of landslides in each condition from the landslide inventory. For the linear diffusion model, the results are also shown when cohesion is neglected (

Under the conditions studied here, only 22 %–25 % of the area of Switzerland is conditionally unstable, i.e. area where hydrology matters for landslide occurrence according to the infinite slope model. The presence of so many landslides in unconditionally stable areas (65 %–66 % of the total number of landslides) and the existence of some unconditionally unstable cells (10 %–13 % of the country) are undesirable outcomes. While some inaccuracy in the location of the landslides (which might not refer to the detachment zone) could play a role, these results also suggest that either the infinite slope model is inadequate or that the input parameters are inaccurate. In fact, the sensitivity of the FoS to cohesion makes the point (Fig.

To address the temporal dynamics of FoS in the susceptible areas (25 m

The expectation is that landslides should occur when and where FoS

Histograms of the departures of the minimum factor of safety from its grid-based long-term mean during landslide triggering (T) and non-triggering (NT) rainfall events, combining spatial (i.e. differences between landslide locations) and temporal (i.e. differences between events in the cells) variability.

In addition to soil pore water pressure and the FoS, we also consider the mean saturation over the top two model layers estimated by TerrSysMP and compare the departure of it from its long-term local temporal mean (Fig.

Histograms of the departure of the maximum event saturation from its long-term local temporal mean for landslide triggering and non-triggering events, considering

The role of antecedent wetness and the information content of the saturation estimates provided by the hydrological model PREVAH

Plots of mean antecedent soil saturation averaged over 5, 10, 20, 30, and 60 d prior to the beginning of the corresponding rainfall event for durations of 1–6 d. Events are divided into four groups: true positive (TP, triggering events above the threshold), false positive (FP, non-triggering events above the threshold, also called false alarms), false negative (FN, triggering events below the threshold, also called misses), and true negative (TN, non-triggering events below the threshold). The plot in the lower right shows the number of events in each group of events for each duration, to check the robustness of the mean estimates.

Based on these results, we consider two alternative approaches to combine antecedent saturation and rainfall characteristics for a landslide warning system. First we optimised thresholds by combining

Relative frequency plot of triggering

While these results show clearly the usefulness of antecedent soil saturation (i.e. smaller amounts of rainfall being necessary to trigger a landslide in wetter conditions), the performances are not superior to that of a standard rainfall threshold, which does not account for saturation. In fact, the total rainfall–duration (ED) threshold obtained, considering the same rainfall events, results in a maximum TSS of 0.68.

We therefore explored an alternative approach, where pure rainfall thresholds are defined but for different levels of antecedent soil saturation conditions, similarly to what

True skill statistic values associated with the dual total rainfall–duration (ED) thresholds for high/low antecedent saturation conditions separated by thresholds of mean antecedent saturation (

Relative frequency plot of triggering

The results presented here suggest that the probabilistic approach with rainfall and soil saturation thresholds is superior to the physically based approach with the factor of safety calculation. It is important to stress that this is not a general statement but rather a conclusion drawn from the specific models and data which we compared. In fact, if a physically based approach would accurately capture the pore water pressure variations at the required high-resolution scales and therefore reproduce and predict slope failure with the FoS (or another geotechnical) model, we maintain that it would be superior to a probabilistic approach. It is therefore worthwhile to discuss the limitations of the tested physically based approach and the results obtained with regards to the geotechnical component (i.e. the infinite slope approach and FoS calculations) and those related to the hydrological component.

To consider the infinite slope approach independently from the hydrology, we can focus on the analysis of conditionally and unconditionally stable/unstable areas of Switzerland and their validation against the location of historical landslides. There are two concerning aspects in these results: the presence of many historical landslides (65 %–66 %) in unconditionally stable areas and the existence of unconditionally unstable areas. The uncertainty in the location of the landslides could explain some of the slope failures in unconditionally stable areas. Out of the 1354 landslides in unconditionally stable (US) areas, for 937 there are no US cells in the 24 neighbouring cells (area of 125 m

Another important aspect to consider for the FoS calculation is the spatial resolution. Higher resolutions allow models to better capture the local heterogeneities (if data are available), most importantly the topography (i.e. slope). On the other hand, at high resolutions, the assumption of slope length much greater than soil depth becomes invalid, and if the cell size becomes much smaller than the typical detachment area of landslides, the interactions between neighbouring cells become even more critical. For this reason, geotechnical models have been developed that explicitly model progressive failure, lateral interactions, and stress redistribution

The limitations of the hydrological component in the coarse-resolution TerrSysMP model, regardless of the geotechnical model, are evident from the very weak separation between triggering and non-triggering events in the FoS but even more in the soil saturation values themselves. In our analysis we focused on the temporal variability (i.e. departure from the local mean, for triggering and non-triggering events), and the only variable in the FoS calculation which can vary in time is the soil pore water pressure. This means that the lack of temporal variability in the FoS is a direct consequence of the lack of temporal variability in the water pressure head. While combining the hydrological estimates with the infinite slope approach does improve the separation compared to using saturation only, it is still insufficient to establish a threshold. The separation is instead mush stronger when considering soil saturation obtained from PREVAH.

Theoretically, a physically based model like TerrSysMP should be better capable of simulating the movement of water in the soil and therefore predicting the saturation or pressure more accurately. The lack of temporal variability in soil water distribution in TerrSysMP is evident in the large number of both triggering and non-triggering events for which the departure of maximum event saturation from the local mean saturation is 0 (bars for

For the specific cases presented here, having a higher spatial resolution (500 m

We explore two approaches for the prediction of landslides and the value of soil wetness in these predictions applied to a regional-scale study in Switzerland. In the first approach we use the soil water pressure estimates from a coarse-resolution physically based model (TerrSysMP) and slope stability assessment using the infinite slope approach. In the second approach we use rainfall–duration threshold curves informed by soil saturation obtained by a high-resolution conceptual hydrological model (PREVAH).

Our main findings are the following:

The infinite slope approach for quantifying slope instability is largely affected by the accuracy of input soil parameters, in particular cohesion in our case (removing cohesion doubled the area where hydrology mattered in FoS prediction), but the FoS can discern landslide triggering events better than soil moisture only by accounting for local topography and stress/strength balance.

According to the infinite slope approach and without considering parameter uncertainty, hydrology can play a role in the initiation of landslides over only ca. 20 % of Switzerland (the conditionally (un)stable area, where about 30 % of all observed landslides have occurred). Soil depth does not seem to affect the estimate of (un)conditionally (un)stable areas, although it is an essential parameter for the estimate of local wetness and determines the landslide volume.

Soil saturation estimates from a high-resolution conceptual hydrological model (PREVAH) are more useful in improving landslide predictions than those from a coarse-resolution physically based modelling framework (TerrSysMP), mainly due to effects related to the coarse spatial resolution of the latter model.

We suggest the use of sequential rainfall ED thresholds that first consider antecedent soil saturation conditions (with a optimal threshold of 10 d mean antecedent saturation of 0.45) and then different rainfall ED curves for wet and dry conditions.

The friction angle data were obtained from Geotechdata.info (Angle of Friction,

EL conducted the analysis. EL and PM conceived the research. All authors contributed to writing the paper.

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors thank Adrin Tohari and two anonymous referees, whose comments and suggestions in the revision helped improve and clarify this paper.

This research has been supported by the Swiss National Science Foundation (grant no. 165979).

This paper was edited by Carlo De Michele and reviewed by Adrin Tohari and two anonymous referees.