Calibration scenarios for physically based rainfall-induced landslide modelling at regional scale. Application to Vall d’Aran (Central Pyrenees, Spain)

Open Access
01-01-2026
Original Paper

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Authors: Flavio Alexander Asurza; Clàudia Abancó; Marcel Hürlimann; Vicente Medina
Published in: Bulletin of Engineering Geology and the Environment | Issue 1/2026

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Abstract

This study delves into the calibration scenarios for physically based rainfall-induced landslide modeling, specifically in the Vall d’Aran region of the Central Pyrenees, Spain. The research compares single-objective and multi-objective calibration approaches to enhance the accuracy of landslide susceptibility predictions. Key topics include the evaluation of hydro-geotechnical parameters, the impact of antecedent and final landslide conditions, and the role of groundwater dynamics in landslide initiation. The study concludes that the multi-objective calibration approach offers superior performance, achieving high accuracy for both antecedent and final landslide conditions. By incorporating steady groundwater response time analysis, the model's predictive capabilities are further improved, providing valuable insights into slope stability dynamics during extreme rainfall events. The findings highlight the importance of accurate soil parameter estimation and the potential for coupled landslide-hydrological modeling to enhance shallow landslide hazard prediction in mountainous regions.

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Introduction

Predicting rainfall-induced landslides is a challenge for the scientific community and crucial for practical applications to mitigate potential impacts (Zhao et al. 2020). Rainfall-induced landslides and debris flows are among the most common geological hazards, capable of inflicting substantial economic losses and causing fatalities (Haque et al. 2016; Petley 2012). Susceptibility analysis is essential for identifying areas vulnerable to landslide initiation and propagation, forming the foundation for hazard and risk assessments (Corominas et al. 2014). A primary output of this analysis is the susceptibility map, which indicates the propensity of an area to undergo landsliding across different regions and serves as the initial step in every landslide hazard and risk assessment (Glade et al. 2005). Over the years, numerous physically based slope stability models have been developed for landslide susceptibility assessment (Baum et al. 2002; Medina et al. 2021; Rigon et al. 2006). Physically based slope stability models incorporate the geotechnical properties of soil materials, typically assessing slope stability by combining the infinite slope stability method with hydrological considerations (Medina et al. 2021). These models consider rainfall infiltration or snowmelt, and the resulting increase in pore water pressure, as the principal triggering mechanisms for landslides. (Iverson 2000), integrating both geotechnical and hydrological parameters to characterize soil conditions leading up to landslide events. In general, physically based slope-stability models share a common structure and failure-controlling variables (see Table 1).

Table 1

Hydro geotechnical parameters of selected physically based slope stability models. The key parameters that govern antecedent and final conditions leading to landslide initiation are summarised

Model	Hydro geotechnical parameters				Reference
Model	Antecedent conditions	Symbol^*	Final conditions	Symbol^*	Reference
GEOtop-FS	Water table position	-	Volumetric water content	θ	Rigon et al. (2006)
SINMAP	Hydrologic wetness parameter	-	Soil density ratio	r	Pack et al. (1998)
TRIGRS	Water table depth	-	Volumetric water content	θ	Baum et al. (2002)
SOIL SLIPS	Seepage force	F’	Soil saturation degree	S_r	Montrasio and Valentino (2008)
HIRESSS	Steady water table depth	dZ	Volumetric water content	θ	Rossi et al. (2013)
SHIA Landslide	Perched water table	Z_w	Soil water content (volume)	S	Aristizábal et al. (2016)
STEP-TRAMM	Initial soil water saturation	-	Soil water saturation	S	Lehmann and Or (2012)
SCOOPS 3D	Water table depth	-	Pore pressure ratio	r_u	Reid et al. (2000)
R.ROTSTAB	Seepage force	S	Weight of moist soil	G’	Mergili et al. (2014)
SLIDE	Initial soil water content	θ_o	Soil saturation degree	S_r	Liao et al. (2012)
FSLAM	Antecedent effective recharge	q_a	Fillable porosity	n_f	Medina et al. (2021), Durmaz et al. (2023)

^* Symbology used in the corresponding publication

Parameter values are often calibrated as a preliminary step before modelling. In principle, calibration might not be necessary if parameter values are obtained from an ample quantity of direct measurements or laboratory experiments. However, calibration is frequently recommended in cases where there is uncertainty regarding the spatial distribution and variance of parameter values (Simoni et al. 2008), when model efficiency needs to be optimized to reflect real-world physical phenomena, or when it is not possible to derive parameter values experimentally or through field measurements (Zieher et al. 2017). In addition, assessing parameter sensitivity prior to calibration is important to identify the most influential variables. Sensitivity analysis is often conducted to evaluate how model outputs respond to variations in input parameters. Local sensitivity methods, such as the One-at-a-Time approach, assess the influence of individual parameters by exploring small perturbations around a reference condition, whereas global sensitivity analysis investigates the entire parameter space, capturing nonlinear interactions and combined effects among variables (Yang 2011; Zieher et al. 2017).

Calibration is then achieved by adjusting input model parameters to identify optimal values or ranges that result in a more general agreement between observations and simulations satisfying a previously selected objective function (OF), with accuracy and area under the curve as the typically used OFs in slope stability modelling (Guo et al. 2022; Medina et al. 2021). This iterative procedure is often referred to as inverse modelling, which is more advantageous when it is automatically implemented (Calvello et al. 2017). Conventional calibration typically focuses on optimizing a single OF, which can enhance specific aspects of model performance but may overlook others. In contrast, multi-objective calibration involves using two or more OFs to simultaneously evaluate multiple objectives, resulting in a more balanced and comprehensive optimization. This practice is commonly encountered in hydrological modelling, particularly when addressing complex parameter spaces that require calibration across several objective, such as the Nash-Sutcliffe index or volume ratio (Asurza and Lavado 2020; Budhathoki et al. 2020; Dobler and Pappenberger 2013; Fernandez-Palomino et al. 2020). The fundamental principles of calibration are equally applicable in the domain of physically based slope stability models. Although some hydrological applications related to the ensembled prediction systems have already been adapted to the landslide forecasting field (Canli et al. 2018; Devoli et al. 2018; Ho et al. 2022; Khan et al. 2021), a promising area of research lies in the application of different calibration approaches which have not yet been comprehensively explored in physically based slope stability models.

Recently, several studies have introduced innovative calibration approaches for slope stability modelling. Initially, calibration was focused on parameter uncertainty and spatial variability by applying physically based slope stability models at catchment scale (e.g. Zieher et al. 2017). Further analyses were presented by Formetta et al. (2016), who emphasized the importance of reliable model applications through automatic parameter calibration by considering three simplified physically based models for landslide susceptibility. Furthermore, Calvello et al. (2017) emphasized the inverse analysis based on field observations and the evaluation of the numerical simulation’s reliability. In addition, Afterwards, computational challenges led to the emergence of probabilistic calibration. For instance, Zhao and Kowalski (2022), addressed the limitations of probabilistic parameter calibration for landslide runout models by integrating Bayesian inference and active learning to reduce computational costs. The integration of Bayesian frameworks was also applied by Depina et al. (2020), who proposed a novel Bayesian framework for statistical calibration in spatially distributed physically based slope stability models, addressing challenges related to high-dimensional likelihood functions. Similarly, Wang et al. (2019) applied Bayesian networks to update landslide susceptibility by incorporating spatial and cross-parameter correlations, while Aaron et al. (2019) performed repeatable calibration applying optimization theory and Bayesian statistics for semi-empirical numerical landslide runout models. More recently, Palazzolo et al. (2021) compared two physically based slope stability models, emphasizing the efficiency of a multi-objective calibration in balancing the trade-offs between the true positive rate (TPR) and the false positive rate (FPR). In addition, Durmaz et al. (2023) conducted a semi-automated calibration to compare different model’s performance focusing on landslide morphology’s influence. These previous studies have primarily focused on representing slope stability conditions after the triggering rainfall event (herein referred to as final landslide conditions) based on existing landslide inventories. However, the conditions prior to the rainfall event (herein referred to as antecedent landslide conditions) are generally not incorporated in the analysis.

Therefore, the main objective of this paper is to propose an original procedure to optimize the calibration of landslide susceptibility models by applying a multi-objective approach and to justify its suitability over the commonly used single-objective approach. Traditional calibration approaches often focus solely on final landslide conditions, yielding models with strong statistical performance but limited physical plausibility. Our proposed methodology addresses these limitations by incorporating both antecedent and final conditions of landslide events, ensuring a more comprehensive evaluation of model performance and a more physically accurate representation of the processes governing landslide initiation.

This approach aims to be model-independent and can therefore be applied to assess the performance of other physically based slope stability models, as summarised in Table 1. The proposed methodology is tested in the Vall d’Aran region, located in the Spanish Pyrenees, where shallow landslides triggered by rainfall are the predominant process. The present research: (i) compares two calibration approaches (single- and multi-objective) using a physically based slope stability model, (ii) analyses the most important hydrological–geotechnical parameters that influence the antecedent and final conditions of shallow landslide events, and (iii) highlights the improvements and challenges that the proposed calibration scenarios offer to the field of slope stability modelling.

Study area

The study area encompasses a large share of the Vall d’Aran district in the Central Pyrenees, Spain, covering 325.6 km². This region features elevations that range from approximately 1000 m in Vielha, the district’s capital, up to nearly 2750 m at surrounding peaks (Fig. 1). The area’s terrain has been significantly shaped by glacial and fluvial processes, resulting in steep valley slopes prone to landslides.

Fig. 1

The Vall d’Aran study area located in the Spanish Pyrenees, and the landslides triggered by the 2013 episode

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Vall d’Aran is part of the Axial Pyrenees and is geologically defined by Paleozoic bedrock, including Ordovician and Devonian formations, which were extensively folded during the Hercynian orogeny and later intruded by tardohercinian plutonic rocks (Beaumont et al. 2000; Muñoz 1992). In the course of glaciation cycles during the Upper Pleistocene, till material was deposited throughout the study area, which is now a predisposing factor for shallow slope failures (Fernandes et al. 2020; Serrat et al. 1994). Not only the glacial material but also the periglacial, fluvial and colluvial deposits shape the valleys of the region and play a critical role in landslide susceptibility. Despite the importance of these quaternary deposits, there are currently no regional data available that detail the soil depth and its hydro-geomechanically properties. This lack of information creates substantial uncertainty in modelling regional landslide susceptibility.

The Vall d’Aran district experiences an Alpine Atlantic climate, with average annual temperatures between 5 °C and 9 °C, and precipitation ranging from about 900 mm at valley floors to as much as 1200 mm in higher elevations (Victoriano et al. 2016). This significant precipitation, combined with seasonal snowmelt, exerts a destabilizing effect on the area’s already vulnerable slopes.

Land cover is primarily composed of forests (43%), grasslands (30%), and shrublands (17%), while scree and weathered bedrock collectively occupy less than 5% of the landscape. Urbanized areas cover less than 1% of the total area. Notably, land use patterns have shifted over time, with an expansion of forested zones since the 1940 s altering landslide susceptibility in some areas (Hürlimann et al. 2022).

The June 17–18, 2013, landslide-flood event has drawn significant attention from researchers due to the complex interactions between intense rainfall, snowmelt, and pre-existing geomorphological conditions. Most of the landslides triggered during this event were classified as shallow landslides, typically involving near-surface failures often on steep slopes (Shu et al. 2019). These failures are generally characterized by failure depths of less than 2–3 m and translational movement along planar slip surfaces (Hungr et al. 2014). In addition, this event caused widespread flooding, particularly in the Garona River basin, which has been subject to long-term entrenchment processes, exacerbating flood hazards (Victoriano et al. 2016). In the aftermath, a comprehensive landslide inventory with 393 recorded instances was compiled, providing crucial data for susceptibility mapping and modelling (Shu et al. 2019).

Materials and methods

This section specifies the overall methodology, the selected slope stability model and the calibration scenarios.

General framework

The overall modelling strategy begins with the slope stability model setup, which involves collecting input data from previous studies, including the landslide inventory of the 2013 event and soil-related data needed to represent the hydro-mechanical characteristics of the soil in the Vall d’Aran region.

The second stage involves calibrating the model and conducting a statistical evaluation in different scenarios. Two calibration approaches are applied: a conventional single-objective approach, which focuses on optimizing a single objective function (OF), and a multi-objective approach, which simultaneously considers multiple OFs (differences between them both are further explained in Sect. 3.3.). These methods are compared to assess their performance in reproducing antecedent and final landslide conditions. Different calibration scenarios were proposed by considering different set of parameters to be calibrated. These parameters, generally related to geotechnical and/or hydrological properties, are selected based on their model sensitivity. In depth description of calibration scenarios is provided in Sect. 3.4.

By evaluating antecedent and final slope stability and hydrological condition, we are providing a more comprehensive understanding of model performance, extending beyond the creation of optimized susceptibility maps. This evaluation is generally not considered when modelling, although most of the physically based slope stability models include both antecedent and final conditions in their modelling framework (see Table 1).

Finally, among all the proposed scenarios, the best one is selected for further analysis. This includes interpreting the optimal parameter set in terms of its physical plausibility. The corresponding susceptibility maps and soil condition maps (reflecting water table rise) are also presented to highlight the significant role of antecedent landslide conditions. Additionally, the impact of the optimal model parameters on slope stability is examined in relation to hydrological and soil characteristics.

Model description

General aspects

The Fast Shallow Landslide Assessment Model (FSLAM) is a physically based model designed to assess landslide susceptibility by rapidly computing slope stability at a regional scale Medina et al. (2021). It employs the infinite-slope theory, while the hydrological model integrates both lateral and vertical water movement to quantify the rise of the water table. The increase of the initial water table ($\:{h}_{a}$) is computed using the lateral flow method, which accounts for groundwater recharge from antecedent precipitation (herein called antecedent effective recharge $\:{q}_{a}$) and the corresponding contributing drainage area ($\:a$) (Montgomery and Dietrich 1994). The calculation of $\:{h}_{a}$ is carried out using the following equation:

$$\:\begin{array}{c}h_a=\left(\frac ab\right)\frac{q_a}{K_s\bullet\:sin\left(\theta\:\right)\bullet\:\text{c}\text{o}\text{s}\left(\theta\:\right)}\end{array}$$

(1)

Where $\:{K}_{s}$ is saturated hydraulic conductivity, $\:b$ is cell size, and $\:\theta\:$ is slope angle.

The FSLAM model estimates the rise of the water table ($\:{h}_{e}$) from the rainfall event using a vertical flow approach, ignoring recharge contributions from upstream areas. Surface runoff is calculated using the curve number (CN) method, a straightforward hydrological model that considers land use and soil type characteristics (USDA 1986). Rainfall infiltration ($\:{q}_{e}$) is quantified by subtracting runoff from total precipitation and finally water table rise $\:{h}_{e}$ is calculated.

$$\:\begin{array}{c}q_e=P_e-\frac{\left(P_e-\left(\frac{5080}{CN}-51\right)\right)^2}{P_e+4\ast\left(\frac{5080}{CN}-51\right)}\end{array}$$

(2)

$$\:\begin{array}{c}h_e=\frac{q_e}{n_f}\end{array}$$

(3)

where $\:{P}_{e}$ is the total rainfall event and $\:{n}_{f}\:$is the fillable porosity, which is a different parameter definition according to Medina et al. (2021) and first-time considered in Durmaz et al. (2023). The concept of fillable porosity has been extensively investigated in academic literature (Acharya et al. 2012; Park 2012; Xiao et al. 2022) to quantify groundwater variations in response to precipitation. It is defined as the quantity of water retained by an unconfined aquifer for each unit increase in the water table, per unit (Durmaz et al. 2023; Kayane 1983; Park and Parker 2008). The fillable porosity calculation depends on soil water content, water table depth and the type of soil; hence it is not easy to estimate. In simple terms, it can be expressed as:

$$\:\begin{array}{c}n_f=n\bullet\:\left(1-S_d\right)\end{array}$$

(4)

where $\:{S}_{d}$ is the soil saturation degree and $\:n$ the soil porosity. Equation 4 relies on several simplifications and assumptions, hence $\:{n}_{f}$ should be considered as a parameter to be calibrated (Durmaz et al. 2023). The final condition of slope stability is calculated based on the total water table rise (due to the combined effect of $\:{q}_{a}$ and $\:{q}_{e}$) by the sum of $\:{h}_{a}$ and $\:{h}_{e}$. Then, the factor of safety FS is computed as:

$$\:\begin{array}{c}FS=\:\frac{\text{tan}\left(\phi\right)}{\text{tan}\left(\theta\right)}+\frac{c-\left(h_a+h_e\right)\cdot\:{\rho_w\cdot}\text{t}\text{a}\text{n}\left(\phi\right)}{{\rho_s\:}\cdot Z\cdot g\cdot sin\left(\theta\right)\cdot\text{c}\text{o}\text{s}\left(\theta\right)}\end{array}$$

(5)

where $\:c$ represents the total soil cohesion for effective stress (hereafter referred only as cohesion) obtained by summing up the soil cohesion $\:\left({c}_{s}\right)$ and the root cohesion ($\:{c}_{r})$, $\:\theta\:$ is terrain slope angle, $\:Z$ is soil depth, $\:{\rho\:}_{w}$ is the water density, $\:{\rho\:}_{s}$ is the soil density, $\:g$ the constant of gravity, and $\:{\upvarphi\:}$ is the angle of internal friction for effective stress (hereafter referred as the internal friction angle). Furthermore, the stability model implements a stochastic methodology to address the variability in soil properties. Both cohesion and the internal friction angle are assumed to follow normal (Gaussian) probability distributions characterized by their mean and standard deviation (Medina et al. 2021). Therefore, the internal friction angle and cohesion parameters can be represented as stochastic variables within a specified range. As a result, the model facilitates the calculation of the probability of failure (PoF) by incorporating these stochastic parameters. In FSLAM, two key outputs based on PoF are produced, corresponding to the initial and final landslide conditions. The initial rise in the water table $\:{(h}_{a})$ is linked to the antecedent condition, while the total rise ($\:{h}_{a}+{h}_{e}$) represents the final condition. Only $\:{h}_{e}$ reflects the transient state, driven by the water table increase resulting from rainfall infiltration.

Input data

The main inputs of the stability model consist of five gridded files and two text files. Gridded data (Fig. 2) includes: (i) the antecedent effective recharge ($\:{q}_{a}$), (ii) the rainfall event that triggers landslides $\:{(P}_{e})$, (iii) the digital terrain model (DTM), (iv) the land use and land cover (LULC), and (v) the soil characteristics (SOIL). All the gridded data have a 5 m resolution and are summarised in Table 2. It is worth mentioning that $\:{P}_{e}$ and $\:{q}_{a}$ inputs already include the snow contribution, assuming that the snowfall and snowmelt processes add extra water into the soil (Hürlimann et al. 2022). On the other side, the two text files specify the soil properties of the LULC classes: root cohesion, hydrological soil group and curve number; and SOIL: soil cohesion, internal friction angle, density, hydraulic conductivity and soil depth. Both LUCL and SOIL have been reclassified from the official cartography and include 10 and 11 categories. More information of soil properties values and text file’s structure can be found inHürlimann et al. (2022) andMedina et al. (2021) respectively.

Table 2

Gridded input data

Input gridded data	Source	Access link
Rainfall event ($\:{\varvec{P}}_{\varvec{e}}$)	Hürlimann et al. (2022)	-
Antecedent effective recharge ($\:{\varvec{q}}_{\varvec{a}}$)	Hürlimann et al. (2022)	-
LULC	Center for Ecological Research and Forestry Applications (CREAF)	https://www.creaf.cat/land-cover-map-catalonia
SOIL	Cartographic and Geological Institute of Catalonia (ICGC)	https://www.icgc.cat/ca/Territori-sostenible/Sols/Mapa-de-sols-125000-continu
DTM	ICGC	https://www.icgc.cat/ca/Geoinformacio-i-mapes/Dades-i-productes/Geoinformacio-cartografica/Referencial-Topografic-Territorial

Fig. 2

(a) Reclassified Land use Land cover (LULC) map of 2009, (b) Reclassified lithological map, (c) the total rainfall event ($\:{P}_{e}$) and (d) the Antecedent effective recharge ($\:{q}_{a}$)

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Model calibration using single- and multi- objective approaches

To evaluate the model’s performance, an effective calibration process is crucial for identifying the input parameter values that best match observed and predicted landslide susceptibility maps. Specifically, in this research, the FSLAM model was selected to implement the proposed calibration approaches although it can be easily adapted to any slope stability model. FSLAM includes around 12 parameters requiring calibration, where cohesion $\:({c}_{s}$ and $\:{c}_{r})$, internal friction angle ($\:{\upvarphi\:}$), $\:{n}_{f}$ and $\:{q}_{a}\:$are the most sensitive parameters (Durmaz et al. 2023; Medina et al. 2021). Given the numerous possible parameter combinations, the development of a statistical tool is essential for effective calibration (Durmaz et al. 2023; Medina et al. 2021). Nowadays, programming languages have emerged as indispensable resources for creating software or plugins that facilitate user analysis. Among these languages, R stands out as a rapid tool for performing optimization, sensitivity, and uncertainty analyses (R Core Team 2024). Additionally, it provides a wealth of freely available libraries tailored for calibration purposes (Wu et al. 2014). Traditionally, the calibration of physically based models like FSLAM have relied on trial and error, demanding considerable time (Guo et al. 2022, 2023; Hürlimann et al. 2022; Medina et al. 2021). As a result, an automated calibration tool becomes essential to expedite the process.

The FSLAM model was originally created using the Fortran programming language (https://github.com/EnGeoModels/fslam). However, the automated calibration tool (herein referred as R-FSLAM) proposed in this study was coded in R, with additional functions incorporated to facilitate parameter optimization and output analysis.

The R-FSLAM module enables users to perform a single or multi-objective calibration to identify the optimal parameter set. The module incorporates metrics such as accuracy (ACC), true positive ratio (TPR), and true negative ratio (TNR) to evaluate the model’s performance (Eqs. 6, 7 and 8 respectively). These metrics are calculated based on the receiver operating characteristic (ROC) analysis, which is effective for comparing classifiers and illustrating their performance (Fawcett 2006).

$$\:\begin{array}{c}ACC=\frac{TP+TN}{TP+TN+FP+FN}\end{array}$$

(6)

$$\:\begin{array}{c}TPR=\frac{TP}{TP+FN}\end{array}$$

(7)

$$\:\begin{array}{c}TNR=\frac{TN}{TN+FP}\end{array}$$

(8)

Where $\:TP$, $\:FN$, $\:TN$ and $\:FP$ are the true positives, false negatives, true negatives and false positives respectively. In a slope stability modelling context, TP indicate correctly predicted slope failures, whereas TN refer to correctly predicted stable slopes. ACC indicates the general model’s performance.

The R-FSLAM module implements the single-objective calibration by the Dynamically Dimensioned Search (DDS) algorithm (Tolson and Shoemaker 2007) which optimizes model performance by aligning predictions with observed data based on a single OF. On the other hand, multi-objective calibration is conducted using the Elitist Non-dominated Sorting Genetic Algorithm II (NSGA-II) which involves adjusting model predictions to satisfy two or more OFs (Srinivas and Deb 1994). In contrast to the single-objective approach, multi-objective optimization aims to generate a range of solutions instead of focusing on a single near-optimal outcome. These solutions reflect the trade-offs between conflicting calibration objectives and are classified as Pareto-optimal or non-dominated solutions. A solution is considered Pareto-optimal when no other solution improves one OF without degrading another. Solutions that do not meet this criterion are classified as dominated, as they are inferior or equal across all objectives when compared to at least one non-dominated solution (Bomhof et al. 2019; Deb 2001). The Pareto curve, or Pareto front, visualizes these trade-offs, showing the boundary of optimal solutions and providing critical insights into balancing competing objectives, particularly in natural hazard modelling and mitigation strategies (Hodges 2015). The R-FSLAM workflow is displayed in Fig. 3.

Fig. 3

General workflow of the calibration tool R-FSLAM. The user can calibrate up to nine parameters by the dynamically dimensioned search (DDS) or the elitist non-dominated sorting genetic algorithm (NSGA-II). Results can be visualized based on PoF and water table rise maps. See text for explanation of abbreviations

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Regardless the calibration approach, the R-FSLAM module requires the input data described in Sect. 3.2 for each point of analysis which comprises the landslide inventory and an equal set of a random non-landslide points (393 for each category in this study) generated uniformly at random across the study area. Hence, each point must contain data of water recharge ($\:{q}_{a}$, $\:{P}_{e}),\:\:$soil properties ($\:\theta\:$, $\:{c}_{s}$, $\:{c}_{r}$, $\:{\upvarphi\:}$, $\:Z$, $\:CN$), and the contributing area $\:a$. Furthermore, the module permits the calibration of up to nine FSLAM parameters which must be specified with their initial values and respective parameter boundaries. These boundaries establish the search space for calibration algorithms, ensuring that each parameter’s values are feasible and realistic for the model to be valid and practically applicable. Internally, the R-FSLAM module considers a threshold of 0.5 to categorise unstable (PoF > 0.5) and stable slope conditions (PoF < 0.5).

The model’s performance is evaluated using objective functions (OFs), which vary depending on the selected calibration approach. In the single-objective approach, accuracy (ACC) serves as the sole OF, focusing exclusively on the final landslide conditions. In this stage, both random and inventory points are treated according to their actual status (stable or unstable). Conversely, the multi-objective approach considers both antecedent and final conditions, utilizing two distinct OFs. For antecedent conditions, the goal is to predict stable conditions before any slope failure occurs. To achieve this, all points—both random and inventory—are treated as stable, and the true negative ratio (TNR) is employed as the OF to assess the model’s ability to correctly predict stable slope conditions. For final conditions, ACC is used again to evaluate model performance, with random and inventory points treated according to their actual status. This final step allows the visualization of the Pareto curve, which illustrates the trade-off between TNR and ACC. The entire process is managed internally by the R-FSLAM module and is only performed during calibration.

In general, model’s performance results shown in terms of the ACC, TPR and TNR indices, the receiver operating characteristic (ROC) curve and the area under the curve (AUC). The R-FSLAM module further supports interactive map visualizations based on the PoF for the antecedent and final landslide conditions, and water table rise relative to the soil depth ($\:{h}_{a}/z$ and $\:{h}_{e}/z$).

Calibration scenarios

The calibration scenarios were designed to evaluate the performance of the FSLAM model under the two different approaches described earlier: single-objective and multi-objective calibration (Fig. 4). The scenarios aimed to test the effectiveness of each approach in optimizing key parameters that influence landslide prediction. According to previous studies (Durmaz et al. 2023; Medina et al. 2021), the most sensitive parameters are the antecedent effective recharge ($\:{q}_{a})$ and the fillable porosity ($\:{n}_{f})$ which are significant for antecedent and final landslide conditions respectively. Moreover, the saturated hydraulic conductivity ($\:{K}_{s}$) parameter was also included in the calibration process. $\:{K}_{s}$ is considered equally important as $\:{q}_{a}$ for quantifying the initial water table height before the landslide-triggering rainfall event (see Equation 1). Initial FSLAM parameter values were adopted from Hürlimann et al. (2022).

Fig. 4

General flowchart of the modelling strategy for two different calibration approaches: the multi-objective, which includes 2 scenarios, and the single-objective, which encompasses 5 scenarios

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The novel approach is applied in the multi-objective calibration scenarios. In these scenarios, the parameter $\:{q}_{a}$ remains unchanged and retains its initial value. However, to obtain a good representation in antecedent landslide conditions, $\:{K}_{s}$ is optimised instead. In Scenario 1, the parameter $\:{n}_{f}$ is optimized due to its importance in representing final landslide conditions. In Scenario 2, $\:{n}_{f}$ is not optimized and is treated in line with its initial definition as soil porosity (Medina et al. 2021). This second scenario was included to highlight the significance of optimizing $\:{n}_{f}$ offering a more comprehensive analysis that had not been fully explored in previous studies (Abancó et al. 2024; Durmaz et al. 2023).

On the other hand, five different scenarios are suggested for the single-objective calibration. These scenarios are proposed to further analyse the approach applied in previous studies by using FSLAM. Parameter $\:{q}_{a}$ is fixed considering different percentages (5, 25, 50, 75 and 125%) of its initial value, while $\:{n}_{f}$ is calibrated simultaneously in each scenario. The adjustment of $\:{q}_{a}$ by different percentages aims to evaluate its impact on the antecedent landslide conditions while optimization only focus on the final conditions. This is proposed due to the high uncertainty related to this parameter (Durmaz et al. 2023; Medina et al. 2021). Other FSLAM parameters related to soil properties ($\:{C}_{s}$, $\:{C}_{r}$, $\:\varnothing\:$, $\:z$) were also optimised in both calibration approaches.

In the final phase of the analysis, the most suitable calibration scenario is evaluated based on the ability of the model to realistically represent both antecedent and final landslide conditions. This evaluation includes assessing the physical feasibility of key calibrated parameters and analysing the main hydrological factors influencing water table rise ($\:{h}_{a}$ and $\:{h}_{e}$). Additionally, Groundwater Response Time (GRT) is incorporated as a complementary indicator to characterize slope preconditioning and subsurface response times, enhancing the interpretation of landslide triggering mechanisms.

Results and discussion

Slope stability conditions are evaluated through the Probability of Failure (PoF) and the ratios of water table rise to soil depth ($\:{h}_{a}/z$ and $\:{h}_{e}/z$). These variables are preferred because they express changes as a percentage relative to the total soil depth, offering a more meaningful representation compared to using absolute values alone. The R-FSLAM module provides these values for each analysis point, comprising the landslide inventory and random points (hereafter referred to as ‘landslide’ and ‘non-landslide’ points, respectively). Although the non-landslide points were generated uniformly at random rather than stratified by terrain attributes, a minimum spacing was enforced to ensure spatially uniform distribution and avoid clustering. Evaluating alternative sampling schemes—such as terrain-stratified or attribute-matched selections—is outside the scope of this study. We acknowledge that this choice introduces some uncertainty, and stratified sampling could be explored in future work. Here, the focus remains on comparing calibration approaches under consistent input assumptions.

Multi-objective calibration of slope stability model

The slope stability based on water table rise is analysed for the two scenarios (Fig. 5a). In Scenario 1, the antecedent effective recharge ($\:{q}_{a}$) produces a median water table rise to 16% of the soil depth $\:({h}_{a}/z$=0.16). This contrasts with the rainfall infiltration contribution ($\:{q}_{e}$), where a median water table increase of 72% ($\:{h}_{e}/z$=0.72) is observed, culminating in an overall 88% rise relative to the soil depth. Meanwhile, Scenario 2 offers a different perspective presenting more initial water table rise reaching 38% of the soil depth ($\:{h}_{a}/z$=0.38). On the other hand, $\:{q}_{e}$ contribution only generates a median modest 15% increase due to the ($\:{h}_{e}/z$=0.15), resulting in a total rise of just 53% of the soil depth. Overall, Scenario 1 exhibits higher soil saturation levels, indicating increased slope failure. Furthermore, the results clearly show that in Scenario 1, the rainfall infiltration was sufficient to cause a significant rise in the water table ($\:72\%$), ultimately triggering the landslide event, an outcome that was much lower in Scenario 2 ($\:15\%$).

Fig. 5

Multi-objective approach scenarios based on (a) water table rise ($\:{h}_{a}$ and $\:{h}_{e}$) relative to soil depth ($\:z$), and (b) Probability of Failure (PoF). Vertical dashed lines represent the median of the water table rise ratio and the threshold for stable (PoF < 0.5) and unstable (PoF > 0.5) soil conditions respectively. Scenario 1 optimizes $\:{k}_{s}$ and $\:{n}_{f}$, while Scenario 2 only optimizes $\:{k}_{s}$. Initial values of $\:{q}_{a}$ are not calibrated here

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Slope stability based on the Probability of Failure (PoF) is indicated in Fig. 5b. During antecedent landslide conditions in Scenario 1, about 95% of both non-landslide and landslide points, are stable (PoF < 0.5), with only a minimal 5% falling into the unstable category (PoF > 0.5). Similar antecedent conditions are presented in Scenario 2, where 83% and 17% of points are categorised as stable and unstable respectively. During final landslide conditions, a significant redistribution of points is evident in Scenario (1) Here, approximately 70% of the points become unstable, with many reaching a PoF of 1, predominantly within the landslide inventory. In contrast, Scenario 2 shows a different trend, with 85% of points being stable and only 15% unstable. Notably, more presence of landslide inventory points in stable conditions (PoF < 0.5) is observed in Scenario 2 (23%) compared to Scenario 1 (10%), which indicates a smaller number of landslides inventory points classified as unstable (PoF > 0.5), leading to a low accuracy representation of landslide events during final conditions in Scenario (2) Generally, the landslide inventory is more effectively categorized in Scenario 1, indicating a more accurate representation of landslide susceptibility.

Final landslide conditions representation is also explained based on the ROC curves and the corresponding AUC (Fig. 6a). For both Scenarios, AUC values are rather similar (~ 0.77) although ACC is different which suggests that Scenario 2 is better at ranking or ordering predictions (ACC = 0.65), and Scenario 1 is more accurate (ACC = 0.72) when it comes to making a definitive classification decision at a particular threshold (PoF = 0.5 in this research). Additionally, the Pareto curve (Fig. 6b) indicates the trade-offs between TNR and ACC for antecedent and final landslide conditions respectively. For Scenario 1, a relatively high TNR is maintained without a significant sacrifice in ACC, indicating a balanced and consistent model performance across the two evaluated OFs. In contrast, Scenario 2 displays a broader dispersion of points, suggesting that high TNR may lead to lower ACC. The spread of points indicates variability in performance, with no single solution achieving high marks in both TNR and ACC. Specifically in this case, values of TNR greater than 0.9 are recommended for the optimal representation of antecedent landslide conditions. This was concluded after visual inspection of the corresponding PoF maps for TNR < 0.9, where slope failures appeared over large areas similar to those observed under final landslide conditions. Hence, considering the highest levels of ACC and TNR > 0.9, the most suitable set of model parameters was identified. Complete statistical indices are summarized in Table 3.

Table 3

Calibrated parameters and statistical performance based on true negative (TNR), positive (TPR) Ratio, and the accuracy for the multi-objective approach. Values of $\:{n}_{f}$ are the average for the 11 SOIL categories presented in the study area

Scenario	Performance					Calibrated parameters
	Antecedent conditions		Final conditions			n_f average	ΔK_s (%)
	TNR	TPR	Final TNR	ACC	AUC	n_f average	ΔK_s (%)
1	0.91	0.66	0.78	0.72	0.77	0.1	+ 350
2	0.87	0.34	0.94	0.65	0.78	0.35	+ 190

Fig. 6

The model performance of multi objective approach for Scenario 1 (optimizes $\:{k}_{s}$ and $\:{n}_{f}$) and Scenario 2 (only optimizes $\:{k}_{s}$): (a) The ROC-analysis based on the True Positive Ratio (TPR) and False Positive Ratio (FPR). PoF = 0.5 are indicated by dots in their corresponding curves (b) The Pareto curves composed by the non-dominated solutions. The horizontal axis represents the True Negative Ratio (TNR), which evaluates the performance of the antecedent conditions, while the vertical axis represents the Accuracy (ACC), assessing the performance of the final conditions

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Regardless the calibration procedure, one of the main differences between Scenarios 1 and 2 performance was the inclusion of $\:{n}_{f}$ for calibration. This is demonstrated when final conditions in Scenario 2 do not lead to landslide events because of the less impact of $\:{h}_{e}$ as $\:{n}_{f}$ is taken as the soil porosity. Therefore, slope failure is more presented in the antecedent conditions causing more $\:{h}_{a}/z$ rise. In contrast, Scenario 1 performance is higher as $\:{n}_{f}$ is less (due to soil saturation after the rainfall event), hence there is more water table rise ($\:{h}_{e}$) leading to more unstable conditions. The importance of calibrating $\:{n}_{f}$ is also highlighted in Durmaz et al. (2023) and Abancó et al. (2024). However, this parameter has not been included for optimization in previous studies where FSLAM model was applied (Guo et al. 2023; Hürlimann et al. 2022; Medina et al. 2021). Finally, in both scenarios, the optimal values of $\:{K}_{s}$ were raised. In this case, optimization aimed to prevent an excessive initial water table rise to maintain stable slope conditions, hence $\:{K}_{s}$ tend to be higher due to the lack of calibration for $\:{q}_{a}$ (see Equation 1).

Single-objective calibration of slope stability model

Five different scenarios associated with different percentage of the initial value of $\:{q}_{a}$ are presented and discussed in this section. The lowest percentage scenario (5%$\:{q}_{a}$) indicates a median initial water table rise of 5% ($\:{h}_{a}/z$=0.05) relative to soil depth, with a subsequent 68% increase ($\:{h}_{e}/z$=0.68) in response to rainfall infiltration, ending in a 73% total rise. Figure 7a additionally shows the high sensitivity of the $\:{q}_{a}$ parameter. Increasing $\:{q}_{a}$ by 25% markedly affects the water table, causing the median rise to escalate from 20% to 100% soil depth across the 25%$\:{q}_{a}$ to 125%$\:{q}_{a}$ scenarios. Correspondingly, the final conditions vary significantly, with the median rise due to rainfall infiltration ($\:{h}_{e}/z$) shifting from 68% to 0%. Figure 7b further analyses slope stability conditions using the Probability of Failure (PoF). Among the scenarios, the 5%$\:{q}_{a}$ scenario stands out, demonstrating optimal performance with a TNR of 0.94 in antecedent landslide conditions, where most points are classified as stable (PoF < 0.5). The final landslide conditions are also acceptably represented, with an ACC of 0.72. In contrast, the remaining scenarios show diminished performance in representing antecedent conditions, a trend linked to the increase in $\:{q}_{a}$. With higher values of $\:{q}_{a}$, the model is predicting slope failures without needing a tigger- rainfall event. In summary, the sensitivity of the $\:{q}_{a}$ parameter plays a significant role in slope stability, with lower $\:{q}_{a}$ percentages yielding optimal performance in representing antecedent hydrological conditions.

Fig. 7

Scenarios comparison among different $\:{q}_{a}$ percentages variation based on (a) water table rise ($\:{h}_{a}$ and $\:{h}_{e}$) relative to soil depth ($\:z$), and (b) based on the Probability of Failure (PoF). Vertical dashed lines represent the median of the water table rise ratio and the threshold for stable (PoF < 0.5) and unstable (PoF > 0.5) soil conditions respectively

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Additionally, the ROC curve (Fig. 8a) reveals a trend where model discrimination improves as $\:{q}_{a}$ increases. Notably, the 150%$\:{q}_{a}$ scenario achieves the highest level of performance (AUC = 0.80). This highlights the enhancement of model’s performance in distinguishing between stable and unstable cases at higher $\:{q}_{a}$ values.

Fig. 8

(a) Results of the ROC-analysis based on the True Positive Ratio (TPR) and False Positive Ratio (FPR) for the single-objective calibration scenarios. Each scenario is related to a pre-defined percentage variation of $\:{q}_{a}$. Dots represent PoF = 0.5 values in their corresponding curves. b Fillable porosity ($\:{n}_{f}$), True Negative ratio (TNR) and True Positive ratio (TPR) variation according to different values of the antecedent effective recharge ($\:{q}_{a}$)

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The relationship between parameter $\:{q}_{a}$ and$\:\:{n}_{f}$ is clearly established within this calibration scenarios. Based on the statistical performance (Table 4), it is observed that when less contribution of $\:{q}_{a}$, specifically at 5%, there is a corresponding decrease in $\:{n}_{f}$. This is due to the optimization performed by the single-objective algorithm, which aims to obtain the best possible accuracy for the final landslide conditions only. Therefore, as $\:{q}_{a}$ is not enough to generate unstable conditions, $\:{n}_{f}$ tends to be lower leading to more water table rise due to rainfall infiltration (see Equation 3). However, when $\:{q}_{a}$ is increased, the impact of rainfall infiltration diminishes ($\:{n}_{f}$ adjusts upwards) as unstable conditions are already occurring. This adjustment, however, can lead to an incorrect representation of the antecedent landslide conditions, with TNR decreasing as $\:{q}_{a}$ values rise. A more graphical explanation of $\:{q}_{a}$-$\:\:{n}_{f}$ relationship is presented in Fig. 8b. Variation of indices to indicate soil unstable conditions (TPR) or stable conditions (TNR) are varying according to different values of $\:{q}_{a}$. At higher values of $\:{q}_{a}$ (> 3 mm/d), no variation of TNR or TPR are observed, suggesting that $\:{n}_{f}$ remains at its initial value when calibration is performed. On the other side, at lower $\:{q}_{a}$ (< 1 mm/d), $\:{n}_{f}$ exhibits considerable variability, becoming a critical parameter to obtain the best possible accuracy during final landslide condition. This interlinking among physically based parameters model is common and supports the idea of calibrating the model with a smaller number of parameters to avoid equifinality, which is not usually considered in slope stability modelling, but it is broader applied in the hydrological field (Asurza and Lavado 2020; Foulon and Rousseau 2018; Nemri and Kinnard 2020). Due to the importance in slope stability conditions, $\:{q}_{a}$ and $\:\:{n}_{f}$ parameters must be estimated as accurate as possible. A more precise estimation can potentially be achieved through hydrological modelling, which has demonstrated its effectiveness in improving the representation of landslide conditions when coupled modelling approaches are applied (He et al. 2016; Zhang et al. 2016).

Table 4

Calibrated parameters and statistical performance based on true negative (TNR), true positive ratio (TPR), and the accuracy (ACC) for the single-objective approach. Values of $\:{n}_{f}$ are the average for the 11 SOIL categories presented in the study area

q_a [%]	Performance					Calibrated parameter
	Antecedent conditions		Final conditions			n_f
	TNR	TPR	Final TNR	ACC	AUC
5	0.94	0.66	0.77	0.72	0.76	0.12
25	0.59	0.71	0.7	0.71	0.78	0.31
50	0.79	0.58	0.85	0.71	0.79	0.2
75	0.69	0.6	0.87	0.73	0.80	0.4
125	0.64	0.64	0.84	0.74	0.80	0.34

Best performance scenario

Within the statistical analysis, two scenarios stand out for their performance: Scenario 1 from the multi-objective calibration and Scenario 5%$\:{q}_{a}$ from the single-objective calibration. Scenario 1 considers calibration of $\:{K}_{s}$ and $\:{n}_{f}$ to provide a good representation of antecedent and final landslide conditions while maintaining the initial $\:{q}_{a}$ value (~ 1 mm/day). On the other hand, Scenario 5%$\:{q}_{a}$ optimised $\:{q}_{a}$ to improve antecedent condition modelling, however the $\:{q}_{a}$ reduction to an approximate 0.05 mm/d may not be hydrologically plausible when accounting for the additional soil water infiltration from rainfall and snowmelt occurred in the June 2013 event. Although this scenario also provides good statistical results in modelling final landslide conditions, Scenario 1 applying the multi-objective calibration is preferred.

The stability conditions of the soil are illustrated by Probability of Failure (PoF) maps (Fig. 9). Figure 9b uniquely illustrates the antecedent conditions of landslides, as determined in the previous study by Hürlimann et al. (2022). Improved performance is clearly visible by the proposed calibration approach where stable conditions (PoF < 0.5) are predominant before the triggering rainfall (Fig. 9a), while most of the slope failure (PoF > 0.5) occurs afterward (Fig. 9c). The calibrated soil properties in Table 5 reveal significant differences in $\:{n}_{f}$ and $\:{K}_{s}$ compared to the previous results. The near-zero $\:{n}_{f}$ values indicate a range of soil saturation between 66% and 88% (derived from Equation 4) prior to the triggering rainfall event. It is worth highlighting that the findings ofHürlimann et al. (2022) were derived using a trial-and-error approach, focusing on only the final landslide conditions—a widely accepted practice in many studies employing physically-based slope stability models (e.g. Formetta et al. 2016; Guo et al. 2023; Palazzolo et al. 2021). Unlike the multi-objective calibration module (R-FSLAM) applied in this study, their methodology did not involve further refinement of parameters related to antecedent conditions. Instead, their focus was on assessing the impacts of climate change scenarios.

Table 5

Best-fit values of soil properties obtained from the multi-objective calibration in scenario 1. Additional variable $\:{S}_{d}$ is obtained from $\:{n}_{f}$ based on Eq. 4, which represents the soil saturation degree before the rainfall triggering event

Classification	Lithological class	Cs average (KPa)	φ average (°)	K_s (m/s)	n (-)	n_f (-)	S_d (%)
Mapped soils	Alluvial	1	43	4.5 × 10^− 3	0.3	0.036	88
	Colluvium	1.5	33	4.5 × 10^− 6	0.3	0.036	88
	Scree	1	48	4.5 × 10^− 2	0.4	0.136	66
	Till	1.7	38	4.5 × 10^− 5	0.3	0.036	88
Fine-grained bedrock	Mudstone	2.2	28	4.5 × 10^− 6	0.3	0.036	88
	Limestone	1.5	31	4.5 × 10^− 6	0.3	0.036	88
	Phyllite-slate	1.7	31	4.5 × 10^− 6	0.3	0.036	88
	Hornfels-marble	1.5	38	4.5 × 10^− 5	0.3	0.036	88
Coarse-grained bedrock	Conglomerate	2.2	43	4.5 × 10^− 5	0.35	0.086	75
	Sandstone	2.2	43	4.5 × 10^− 4	0.35	0.086	75
	Granitic rock + quartzite	1.4	43	4.5 × 10^− 5	0.3	0.036	88

Fig. 9

Landslide susceptibility maps indicating Probability of Failure. a and c are the antecedent and final conditions (respectively) of slope stability obtained from the Scenario 1 through the multi-objective calibration. b Antecedent slope stability conditions obtained from previous study using a trial-and-error calibration

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PoF map comparison is complemented by Fig. 10 where the water table rise in terms of $\:{h}_{a}/z$ and $\:{h}_{e}/z$ is indicated. In the multi-objective calibration approach, the initial water table rise conditions (Fig. 10a) show relatively small increases compared to those caused by rainfall infiltration (Fig. 10b), indicating that the rainfall event is the primary landslide-triggering factor. Conversely, previous results from Hürlimann et al. (2022) showed that the initial water table rise (Fig. 10c) already induces slope failure (with higher $\:{h}_{a}/z$ values), while rainfall infiltration has a minimal effect (with lower $\:{h}_{e}/z$ values) on further water table rise (Fig. 10d).

Fig. 10

Comparison of water table rise ($\:{h}_{a}$ and $\:{h}_{e})$ relative to the total soil depth ($\:z$) obtained from the multi-objective calibration (a and b) and from previous study by using trial and error calibration (c and d)

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The calibrated parameters of the best scenario align with expected soil characteristics for each lithological unit (see Fig. 11; Table 5). Comparison of these values’ suitability are discussed based on the literature (FAO 2023; Geotechdata 2024) and expert criteria. In addition, three groups of soils have been defined to facilitate further discussion of the results by grouping soils with similar characteristics: soils, which are explicitly indicated in the geological map (“mapped soils”) and include alluvial, colluvium, scree, and till; soils formed on fine-grained bedrock (soils on FGB) such as mudstone, limestone, phyllite-slate, and hornfels-marble; and soils formed on coarse-grained bedrock (soils on CGB), including conglomerate, sandstone, and granitic rock with quartzite. This classification is intentionally simplified and subject to some uncertainty.

Fig. 11

Dumbbell plot comparison of calibrated and recommended literature values for cohesion ($\:{C}_{s}$), saturated hydraulic conductivity ($\:{K}_{s}$) and internal frictional angle (φ) for the lithological units grouped as mapped soils, fine-grained bedrock (FGB) and coarse-grained bedrock (CGB). For each group and parameter, the horizontal connector links the group medians of literature and calibrated values; shorter segments indicate closer agreement, longer segments indicate larger discrepancies

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In general, the calibration reflects low cohesion and high internal friction angles for the mapped soils, aligning with the looser, unconsolidated structure typical of these deposits. For example, calibrated cohesion for alluvial soils is 1 kPa with a high internal friction angle of 43°, which is suitable for loose, granular soil, although cohesion seems to be overestimated. Scree, with calibrated values of low cohesion (1 KPa), a high internal friction angle (48°), and high $\:{K}_{s}$ (4.5 × 10^− 2 m/s), matches expectations for this deposit type, which is typically loose and well-draining, even if cohesion again looks overestimated. Similarly, till shows some cohesion (1.7 KPa) and an internal friction angle of 38°, consistent with the mixed, often compacted composition of these glacial deposits. However, $\:{K}_{s}$ values for these soils, especially scree, are higher than in the literature.

In the case of soils on FGB, the calibration shows generally higher cohesion and lower internal friction angles, with relatively low $\:{K}_{s}$ values suitable for fine-grained soils. Mudstone-derived soil, for instance, has a calibrated cohesion of 2.2 KPa and a low internal friction angle of 28°, reflecting the cohesive, low-permeability characteristics expected of fine-grained materials, with a calibrated $\:{K}_{s}$ value of 4.5 × 10^− 6 m/s. Soils formed over limestone and hornfels-marble, similarly, show generally lower internal friction angles (31° and 38°, respectively) and some cohesion values (1.5 KPa each), capturing the stable but less-draining nature of soils above these rocks.

In contrast, soils on CGB show generally lower cohesion, high internal friction angles, and higher $\:{K}_{s}$, capturing the coarser and better-draining nature of these soils. For instance, soils derived from sandstone exhibit a cohesion of 2.2 KPa and a high internal friction angle of 43°, with a $\:{K}_{s}$ of 4.5 × 10^− 4 m/s, reflecting good drainage expected in sandy soils. Similarly, soils formed on conglomerate exhibit a calibrated cohesion of 2.2 KPa and high $\:{K}_{s}$ (4.5 × 10^− 5 m/s), aligning with the stable nature of conglomerate soils. Soils formed over granitic rock and quartzite show slightly lower cohesion (1.4 KPa) but a high internal friction angle (43°) and moderate $\:{K}_{s}$ (4.5 × 10^− 5 m/s), reflecting a stable, well-draining structure typical of coarse soils.

In conclusion, the general variability in the soil parameters ($\:{c}_{s}$, $\:{K}_{s}$, φ, $\:{n}_{f}$) highlights the critical importance of understanding the uncertainties associated with their spatial distribution. The relatively high effective friction angles (> 40°) obtained for some type of soils likely reflect parameter equifinality between φ and c in the infinite-slope stability formulation (Eq. 5). Because both parameters contribute positively to the factor of safety, similar stability conditions can result from increasing cohesion while decreasing internal friction angle, or vice versa. This trade-off indicates that the calibrated values should be interpreted as effective representations of overall shear resistance rather than as strictly physical soil properties. Improved quantification through detailed fieldwork in smaller areas can significantly enhance the accuracy of models and predictions when applied to larger regions (Li et al. 2020; Zhao et al. 2013). Such efforts would also help to refine the statistical distribution assumptions for key parameters such as cohesion and friction angle, thereby improving the physical realism of the PoF estimates. Additionally, the values of soil depth and cohesion in the study area directly influence the validity of the infinite length assumption in slope stability modelling. Milledge et al. (2012) show that landslides occurring in soils with low cohesion or shallow failure planes are less affected by edge effects and can be reliably assessed using the infinite slope model, even at relatively fine spatial scales. In our case, the combination of shallow soil depths in our study area (1.5–4 m, see Hürlimann et al. 2022) and the lateral flow formulation in FSLAM, which generates spatially coherent water table patterns, reduces the likelihood of short, isolated failures and supports the validity of applying the infinite slope model at 5 m resolution. While coarser grids tend to smooth slope variability, working at 5 m resolution enables better capture of terrain features relevant to slope failure initiation.

Analysis of governing factors

In the following, the analysis and discussion are focused on the main governing factors to predispose landslides for the best performance scenario explained in the previous section.

The relationship between terrain slope and contributing drainage area ($\:a$) indicates that during antecedent landslide conditions (Fig. 12a), while all points should ideally remain stable (PoF < 0.5), slope failure is notable on slopes ranging between 20° and 40°, with contributing areas greater than 10² m². This suggests that even before rainfall-triggered failures, $\:a$>10² m² can accumulate sufficient groundwater to increase susceptibility to landslides, especially at moderate slope angles. The clustering of landslide points at higher contributing areas further indicates the importance of antecedent water saturation in predisposing the soil to failure, despite the expectation of stability during these conditions. In contrast, under final landslide conditions (Fig. 12b), slope failure is evident in slopes less than 40°, including most of the landslide inventory points. Despite this, stability is retained in areas with slopes lower than 20°, suggesting that these areas remained stable throughout the landslide-triggering rainfall event. The presence of slope failures in several random points that were expected to remain stable under final conditions introduces uncertainty, which could be attributed to spatial variability in soil properties or the limitations inherent in the infinite slope model. Figure 12c emphasizes the role of antecedent saturation, showing that high initial water table rise relative to soil depth ($\:{h}_{a}/z$) occurs in areas with $\:a$ >10³ m², with values ranging between 0.5 and 1. This underscores the critical influence of larger drainage areas in raising the initial water table, increasing the PoF. On the other hand, Fig. 12d highlights that the water table rise due to rainfall infiltration ($\:{h}_{e}/z$) is more pronounced in areas with $\:a$ <10³ m², particularly in smaller drainage areas where rapid infiltration leads to significant rises in the water table.

Fig. 12

Landslide and non-landslide points distribution based on the Probability of Failure (PoF) and water table rise relative to the soil depth ($\:h/z$) considering the contributing drainage area and the soil slope for the antecedent (a, c) and final landslide (b, d) conditions

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Overall, this analysis emphasizes that slope angle does influence soil failure as much as the size of the contributing area. Larger contributing areas, typically found in valley regions, contribute to higher water table rises, particularly during antecedent landslide conditions. Conversely, smaller contributing areas, often located in steep mountainous regions, are more affected by heavy rainfall, making them highly susceptible to rapid slope failure.

Further analysis based on Fig. 13a reveals that water table rise due to rainfall infiltration ($\:{h}_{e}/z$) is generally higher across all soil classes than the initial water table rise ($\:{h}_{a}/z$). By focusing solely on saturated hydraulic conductivity ($\:{K}_{s}$), soils with higher $\:{h}_{a}/z$ values are generally associated with higher $\:{K}_{s}$ (e.g., sandstone, granitic rock) due to their ability to allow water to infiltrate deeper into the soil, rather than retaining it in the upper layers. This characteristic often facilitates aquifer recharge, which contributes to a higher initial water table level. In contrast, soils with lower $\:{h}_{a}/z$ values (e.g., colluvium, mudstone) are associated with lower $\:{K}_{s}$, causing water to be retained longer in the upper soil layers, potentially increasing soil saturation and pore pressure buildup. However, some low $\:{K}_{s}$ soils, such as colluvium and mudstone, exhibit relatively high $\:{h}_{a}/z$ values, highlighting the complexity of soil-water interactions. These apparent inconsistencies are due to the use of a simplified approach for estimating $\:{h}_{a}$ (Equation 1). The estimation of $\:{h}_{a}$ relies on several factors, including antecedent effective recharge, which was estimated with certain limitations that could affect the accuracy of the results.

Fig. 13

(a) Average water table rise relative to the soil depth ($\:h/z$) of the landslide inventory for the SOIL categories. b Probability of Failure (PoF) points distribution based on the steady groundwater response time ($\:GRT=\sqrt{A}/K$) and the initial water table rise ($\:{h}_{a}$) for the antecedent landslide conditions

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Results related to $\:{h}_{e}/z$ are directly connected to fillable porosity values ($\:{n}_{f}$) and so the soil saturation ($\:{S}_{d}$) (see Equation $\:3$). The high $\:{S}_{d}$ values observed across most soil and bedrock classes (88%) is attributed to a combination of low $\:{K}_{s}$, limited $\:{n}_{f}$, and fine-grained structure, which collectively enhance soil moisture retention. These factors, combined with the impact of a recent high rainfall event, contributed to maintain high $\:{S}_{d}$ values and become prone to failure during prolonged rainfall (Huang et al. 2018; Zhang et al. 2021). This saturation plays a significant role in the observed landslides, as soils like alluvial, colluvium, and fine-grained bedrocks tend to retain water in the upper layers, increasing pore pressure and PoF. Coarse-grained materials like conglomerate and sandstone, with lower $\:{S}_{d}$ (75%), presented less saturation levels due to better drainage.

In general, the analysis underscores rainfall infiltration as the primary trigger for landslide events across various soil classes. The higher water table rise ($\:{h}_{e}/z$) observed during rainfall events, combined with high soil saturation levels ($\:{S}_{d}$), points to the critical role of prolonged or intense rainfall in reducing slope stability. Soils with lower $\:{K}_{s}$ which retain water in the upper layers, are particularly prone to pore pressure buildup, increasing the landslide susceptibility. Therefore, the findings strongly indicate that rainfall infiltration is a dominant factor in landslide susceptibility in the study area.

Finally, we analyse the steady groundwater response time (GRT), which is a useful component, but usually not evaluated. The GRT is a critical factor in evaluating landslide susceptibility, as it reflects the duration required for groundwater pressure to stabilize following rainfall events, and defined as the square root of the drainage area divided by the saturated hydraulic conductivity ($\:\sqrt{A}/K$) (Iverson 2000). Although the primary trigger for landslides in the study area is assumed to be the rainfall event itself, our analysis (Fig. 13b) highlights that some areas with elevated GRT values—particularly those exceeding 100 days—are already unstable (PoF > 0.5), especially when the initial water table rise ($\:{h}_{a}$) exceeds 2 m. However, the remaining stable areas ($\:{h}_{a}$ < 2 m) suggest that the rinfall event serves as the immediate trigger for failure, as groundwater levels have already been elevated for a long period preconditioning slopes for failure. Interestingly, some regions with high GRT values remain stable when observing the non-landslide points set, reinforcing the idea of GRT alone does not determine soil failure. Incorporating GRT analysis offers a better understanding of landslide triggers, particularly under conditions of prolonged rainfall or pre-saturated soil conditions. The importance of knowing such GRT-values is significant to understand the role of groundwater dynamics in slope stability and landslide initiation. By incorporating GRT to monitor rainfall thresholds, researchers and practitioners can improve prediction of landslide occurrences in a context of early warning systems (Liu et al. 2021; Xu et al. 2016).

Conclusions

This study introduces a novel approach for assessing landslide susceptibility by comparing single-objective and multi-objective calibration approaches. A physically based slope stability model was applied in the Vall d’Aran region to analyse shallow landslides triggered by a regional rainfall event in 2013. This marks the first use of a multi-objective calibration to improve slope stability representation during both antecedent and final landslide conditions. This advancement surpasses traditional single-objective methods, offering a more comprehensive evaluation of landslide dynamics and improving model accuracy for susceptibility predictions.

An adaptable calibration framework was introduced along with an open-source calibration module, well-suited for data-scarce regions and applicable to other physically based slope stability models (see Table 1). The best-performing single-objective calibration scenario achieved 94% accuracy for antecedent conditions and 72% for final landslide conditions. However, this approach struggled to represent soil water conditions dynamics under the assumption that rainfall infiltration is the main landslide trigger. The best results were obtained through the multi-objective calibration approach, achieving also a good performance with accuracies of 91% for antecedent and 72% for final conditions. Findings based on this approach indicate that antecedent effective recharge rises soil saturation and susceptibility to landslides, without necessarily acting as the direct trigger for slope failure. Additionally, results indicated that the size of the contributing drainage area plays as critical role as the slope angle in predisposing areas to failure.

Incorporating steady groundwater response time analysis further enhanced the model’s predictive capabilities, particularly in understanding groundwater’s role in shallow landslide initiation. In practice, a groundwater response time of ~ 100 days means that the effect of a single large rainfall event can persist for months, acting similarly to long periods of antecedent precipitation. This connection highlights how groundwater dynamics control the effective duration of rainfall influence, thereby improving early warning systems and rainfall-induced shallow landslide prediction accuracy.

In general, optimal parameter values for each soil class in the region aligned well with soil properties reported in the literature, which supports the physical representativeness of the slope stability model under extreme rainfall conditions. Further refinement of parameter estimation through hydrological modelling would improve model accuracy and support a coupled landslide-hydrological approach. Although, challenges such as landslide inventory quality and spatial uncertainty in soil properties remain, this study provides valuable insights into slope stability dynamics during extreme rainfall and emphasizes the importance of estimating accurate soil parameters for enhancing shallow landslide hazard prediction in mountainous regions.

Acknowledgements

This work was supported by the European Commission’s Horizon Europe Framework Programme with the project The Hut (The Human-Tech Nexus – Building a Safe Haven to cope with Climate Extremes) under Grant Agreement 101073957.

Declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Title: Calibration scenarios for physically based rainfall-induced landslide modelling at regional scale. Application to Vall d’Aran (Central Pyrenees, Spain)
Authors: Flavio Alexander Asurza
Clàudia Abancó
Marcel Hürlimann
Vicente Medina
Publication date: 01-01-2026
Publisher: Springer Berlin Heidelberg
Published in: Bulletin of Engineering Geology and the Environment / Issue 1/2026
Print ISSN: 1435-9529
Electronic ISSN: 1435-9537
DOI: https://doi.org/10.1007/s10064-025-04697-y

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Calibration scenarios for physically based rainfall-induced landslide modelling at regional scale. Application to Vall d’Aran (Central Pyrenees, Spain)

Abstract

Abstract

Publisher’s note

Introduction

Study area

Materials and methods

General framework

Model description

General aspects

Input data

Model calibration using single- and multi- objective approaches

Calibration scenarios

Results and discussion

Multi-objective calibration of slope stability model

Single-objective calibration of slope stability model

Best performance scenario

Analysis of governing factors

Conclusions

Acknowledgements

Declarations

Conflict of interest

Publisher’s note

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Input gridded data	Source	Access link
Rainfall event (\(\:{\varvec{P}}_{\varvec{e}}\))	Hürlimann et al. (2022)	-
Antecedent effective recharge (\(\:{\varvec{q}}_{\varvec{a}}\))	Hürlimann et al. (2022)	-
LULC	Center for Ecological Research and Forestry Applications (CREAF)	https://www.creaf.cat/land-cover-map-catalonia
SOIL	Cartographic and Geological Institute of Catalonia (ICGC)	https://www.icgc.cat/ca/Territori-sostenible/Sols/Mapa-de-sols-125000-continu
DTM	ICGC	https://www.icgc.cat/ca/Geoinformacio-i-mapes/Dades-i-productes/Geoinformacio-cartografica/Referencial-Topografic-Territorial