Performance assessment of the landslide susceptibility modelling using the support vector machine, radial basis function network, and weight of evidence models in the N'fis river basin, Morocco

Abstract

Landslides in mountainous areas are one of the most important natural hazards and potentially cause severe damage and loss of human life. In order to reduce this damage, it is essential to determine the potentially vulnerable sites. The objective of this study was to produce a landslide vulnerability map using the weight of evidence method (WoE), Radial Basis Function Network (RBFN), and Support Vector Machine (SVM) for the N'fis basin located on the northern border of the Marrakech High Atlas, a mountainous area prone to landslides. Firstly, an inventory of historical landslides was carried out based on the interpretation of satellite images and field surveys. A total of 156 historical landslide events were mapped in the study area. 70% of the data from this inventory (110 events) was used for model training and the remaining 30% (46 events) for model validation. Next, fourteen thematic maps of landslide causative factors, including lithology, slope, elevation, profile curvature, slope aspect, distance to rivers, topographic moisture index (TWI), topographic position index (TPI), distance to faults, distance to roads, normalized difference vegetation index (NDVI), precipitation, land use/land cover (LULC), and soil type, were determined and created using the available spatial database. Finally, landslide susceptibility maps of the N'fis basin were produced using the three models: WoE, RBFN, and SVM. The results were validated using several statistical indices and a receiver operating characteristic curve. The AUC values for the SVM, RBFN, and WoE models were 94.37%, 93.68%, and 83.72%, respectively. Hence, we can conclude that the SVM and RBFN models have better predictive capabilities than the WoE model. The obtained susceptibility maps could be helpful to the local decision-makers for LULC planning and risk mitigation.

Introduction

Landslides are considered one of the most significant geological and geomorphological events threatening the sustainability of environmental quality, especially in mountainous areas. Landslide events are accelerated as a result of the complex integration between physical factors and human activities (Zhang et al. 2022). Landslides are determined as an occurrence or sequence of occurrences where a rock mass and debris fall or flow down a slope (Silalahi et al. 2019). Landslides lead to life loss, the depletion of natural resources, and the destruction of infrastructure (Guzzetti 2005; Varnes 1978; Bourenane et al. 2016; Rahman et al. 2022). Compared to other physical disasters, like earthquakes, floods, and volcanoes, landslides are much more frequent and influential (Abdo HG 2022).

Recently, landslides have attracted attention since representing the most prevalent hazard worldwide related to damaging society and the economy (Nefeslioglu et al. 2008; Shahabi et al. 2014). Moreover, governments around the world are trying to find and develop safeguards to manage the landslides risk. The spatial prediction mapping of landslide susceptibility is one of the most effective methods for maintaining slope stability. Landslide susceptibility mapping is the spatial distribution of the possibilities of landslide occurrences in a specific location supported by statistical methods and local causative geo-environmental parameters (Wang et al. 2015). In this regard, landslide susceptibility evaluation and mapping are important tools in landslide risk management, assisting authorities, practitioners, and decision-makers in developing a more sustainable and appropriate land use and risk mitigation strategy, including the implementation of surveillance and warning systems (Roccati et al. 2021).

Many approaches have been globally developed to assess landslide susceptibility mapping. Recently, statistical methods based on the use of geographic information systems (GIS) and remote sensing (RS) data have become popular in the assessment of landslide susceptibility, such as fuzzy logic and the analytical hierarchical processes (FAHP) (Abdı et al. 2021); certainty factor (CF) (Soma and Kubota 2018); logistic regression (LR) (Aditian et al. 2018a); index of entropy (IoE) (Wang et al. 2016a, b); multi-criteria decision analysis (MCDA) (Nsengiyumva et al. 2018); statistical index (SI) (Zhang et al. 2016), frequency ratio (FR) (Chen et al. 2016; Abdo HG 2022), certainty factor (CF) (Kanungo et al. 2011), and the information value (IV) (Manchar et al. 2018).

Moreover, among probabilistic methods, machine learning techniques have become popular in recent years. Machine learning is an artificial intelligence discipline that effectively overcomes the constraints of data-dependent bivariate and multivariate statistical methods (Park et al. 2019). They are recommended because they do not require prior elimination of anomalies, data manipulation, or statistical assumptions. These algorithms automatically identify interactions between landslides and causal causes. Several studies have found that these strategies produce more accurate predictions than standard statistical methods (Pourghasemi and Rahmati 2018).

These data-driven techniques are based on artificial intelligence algorithms (AIA) that use a high repetition rate of modelling processes, so allow analysis and predict information by learning from training datasets (Ghasemian et al. 2022). Various machine learning models were employed to map landslide susceptibility, such as artificial neuronal networks (ANNs) (Wang et al. 2016a, b; Pham et al. 2017a, b; Aditian et al. 2018a), fuzzy logic (FL) (Shahabi et al. 2015), neuro-fuzzy (NF) (Dehnavi et al. 2015; Chen et al. 2019), random forest (RF), decision tree (DT) (Tien Bui et al. 2016), maximum entropy (ME) (Park 2015), support vector machine (SVM) (Dou et al. 2019); general linear model (GLM) (Pourghasemi and Rahmati 2018), adaboost (AB) (Micheletti et al. 2014), multivariate adaptive regression splines (MARS) (Conoscenti et al. 2015), and the group method of data handling (GMDH) model (Jaafari et al. 2022a, b).

In Morocco, N'fis basin is considered one of the areas most exposed to natural hazards, as many studies indicated (Gourfi and Daoudi 2019; Meliho et al. 2020; Karmaoui et al. 2021). In this regard, the slopes of N'fis basin are exposed to severe geomorphological hazards due to the influence of a combination of physical and human geographical factors (Igmoulan et al. 2022). Landslide is one of the most frequent types of slope material movement in the study area. The spatial conducted investigations indicate the seriousness of the spatial consequences of the landslide events, especially on the lives and infrastructure. Thus, landslide susceptibility mapping is among the most important procedures for managing this acute spatial challenge.

Based on the issue discussed above, the principal goals of the present study are to produce landslide susceptibility maps using SVM, RBFN, and WoE models and to compare their performances for the N'fis basin in Morocco. The principal difference between the current assessment and the described techniques in the aforementioned publications is that three used models have never been explored for landslide modelling in the high Atlas region. Also, the performance comparison of these models is not found in the literature, thus enhancing the research values in this study. These contributions, however, provide a significant contribution to the scientific community. In addition, these landslide susceptibility maps delineate areas vulnerable to landslide phenomena, allowing planners to select appropriate locations for future development projects.

Literature review: Morocco context

In Morocco, several studies presented an assessment of the spatial susceptibility of landslides, which constituted a critical research advance in terms of data, tools, methods, and accuracy of results. In this regard, these studies have gained importance in landslide threat mitigation in mountainous areas. Field studies, including geological and topographical assessments, formed a solid basis for assessing the landslide risk in several regions in Morocco) Rouaia and Jaaidi 2003; El Khattabi and Carlier 2004). Similarly, Elmoulat et al. (2021) reported the effectiveness of a Mass movement susceptibility mapping method in landslide modelling on a large scale in the Tétouan province. Furthermore, El Jazouli et al. (2022) determined the liquid limit values (28% and 56%) and the mean plasticity index of the units (13%–24%) as a result of the significant effect of precipitation intensities and unconsolidated soil characteristics in increasing landslide events in the high basin of Oum Er Rbia in the Middle Atlas Mountain. The integration of bivariate statistical methods and geographic information system (GIS) has been used in many landslide vulnerability studies. Boualla et al. (2019) utilized GIS matrix method (GMM) to produce a spatial sensitivity map of landslides in the Safi region, West Morocco. Also, Bousta and Ait Brahim (2018) presented a spatial assessment of landslides using the Weights of evidence method in the Tangier area that witnesses a high intensity of landslide events. Elmoulat and Ait Brahim (2018) confirmed the high quality of a WoE method in mapping a landslide susceptibility map in the Tetouan-Ras-Mazari area (Northern Morocco). Es-Smairi et al. 2022 demonstrated that the information value (IV) method has achieved the highest accuracy compared to the statistical index (SI), weighting factors (WF), and evidential belief function (EBF) models in the spatial analysis of landslide hazard in the Rif chain (northernmost Morocco). The landslide susceptibility mapping of a physically based (PB) method has been improved in Al Hoceima, Northern Morocco using the Monte Carlo (MC) method backed with sensitivity analysis (SA) (Rahali 2019).

The coupling between the Analytic Hierarchy Process (AHP) method and GIS with diverse spatial data sources produced enhanced spatial outputs related to the landslide vulnerability in the mountainous regions of Morocco, such as the peninsula of Tangier, Rif-Northern Morocco (Brahim et al. 2018), Oum Er Rbia high basin (El Jazouli et al. 2019), Oued Laou watershed (Semlali et al. 2019), parts of the Rif chain, northernmost Morocco (Es-smairi et al. 2021), and the Province of Larache (El Hamdouni et al. 2022). Furthermore, Ozer et al. (2020) presented the first application of hierarchical fuzzy inference systems (HFIs) in expert-based landslide susceptibility mapping in a data-scarce region in the central part of the Rif Mountains (Morocco). Benchelha et al. (2019a, b) compared between logistic regression (LR) and multivariate adaptive regression spline (MarSpline) methods in landslide susceptibility mapping in Oudka, Northern Morocco, and the result indicated that the MarSpline model is a better model than the LR model.

Recently, a few studies have attempted to investigate landslide susceptibility using the integration between artificial intelligence algorithms (AIA) and GIS in response to global advances in this field. Machichi et al. (2020) demonstrated that the artificial neural network (ANN) method has achieved the best performance in assessing the landslide susceptibility in the Rif, North of Morocco compared to the logistic regression (LR). Similarly, landslide susceptibility maps were produced by using multilayer perceptron (MLP) and ANN methods in the Mediterranean Rif coastal zone of Morocco (Harmouzi et al. 2019). It can be noted, however, that there is a considerable research gap in assessing landslide susceptibility using the integration between AIS and GIS in Morocco. On the other hand, this study is the first comparative evaluation between SVM, RBFN, and WoE models at the national level, thus improving the quality of demarcation of potential landslide areas in an area scarce with geographical data like the study area. Moreover, addressing the landslide susceptibility mapping performance using SVM algorithm represents the first contribution to the Moroccan context.

Study area

The N'fis basin is located in the centre of the Western High Atlas of Morocco. It is a mountainous area characterized by slope instability due to climatic, geological, and geomorphological features. Landslide incidents are the most prominent patterns of slope instability in the study area, which cause a threat to the life of the population, infrastructure, and spatial development. Thus, it is important to construct a reliable spatial prediction of landslide susceptibility within the framework of a safe and sustainable spatial planning process. Geographically, the N'fis basin extends between 7°55' W and 8°40' W longitude, and 30°52' N and 31°25' N latitude, with an area of approximately 1712 km². Geologically, the N'fis watershed is part of the High Atlas of Marrakech. It includes several lithological facies that range from Palaeozoic to Quaternary (Michard et al. 2008). The southern margin is dominated by primary age rock, primarily shales linked with limestone bars, magmatic rock, Permo-Triassic sandstones, and clays (Hollard et al. 1985). The mechanical and chemical alteration of these hard formations relatively allows the development of very slim skeletal soils and zonal brown soils. The northern part of the study area is made up of limestone and marl from the Upper Cretaceous and Plio-Quaternary periods (Fig. 1). The N'fis river originates in the southwestern part of the Atlas Mountains and flows northward over a length of 80 km passing along several villages. The altitude ranges from 641 to 4164 m.a.s.l, with an average altitude and slope of 1860 m and 22 degrees, respectively. The climatic features in the study basin is arid to semi-arid, with an annual average temperature of roughly 18.6 °C, a maximum of 47.5 °C in July, and a minimum of 7.5 °C in January. However, the annual precipitation is 375 mm. March and April are the highest monthly rainfall, while July and August are the lowest.

Fig. 1

Geographical location of the N'fis basin

Material and methodology

The process of landslides susceptibility mapping in the study area included the following stages: (a) digitizing the current landslide events and division into training and test datasets, (b) mapping the causative factors layers, (c) mapping landslide susceptibility using spatial calibration between training dataset and driving factors using SVM, RBFN, and WoE models, and d) evaluation of accuracy mapping using the test dataset. However, Fig. 2 shows the flowchart implemented in this study.

Fig. 2

Flowchart of the developed methodology

Landslide inventory map

Mapping the spatial distribution of historical landslide events is considered a critical step in forecasting landslide-prone zones (Carrara et al. 1995; Abdo et al., 2022). Many significant features, however, can be extracted from inventory map, like sites of current landslide events, landslides pattern, and motivations of landslides (Tien Bui et al. 2019). Inventorization of landslides is a systematic evaluation of the current distribution, extent, types, and patterns of landslides in the area under investigation using related methods (Tseng et al. 2015; Manchar et al. 2018). Based on fieldwork and interpretation of Google Earth satellite images, 156 landslide events were determined in order to construct the landslide inventory map in the N'fis basin. In this study, the landslide inventory map was constructed using the random sampling method (RSM) (Hong et al. 2018). A percentage of 70% of landslides were randomly determined as a training dataset, while the rest of the percentage (30%) were used for the model validation goals. These ratios are the most commonly used in the recent literature (Pourghasemi and Rahmati 2018; Wang et al. 2020a, b) (Fig. 3).

Fig. 3

Inventory map and examples of landslides in the N'fis basin

Predisposing factors

In this assessment, fourteen causative factors were selected to map the landslide susceptibility in the study area, including slope, aspect, elevation, topographic wetness index (TWI), topographic position index (TPI), curvature, distance to rivers, distance to roads, Normalized Difference Vegetation Index (NDVI), Land use/Land cover (LULC), soil type, lithology, and rainfall. The thematic maps of the different geomorphological factors were produced using several using a digital elevation model (DEM) with a spatial resolution of 12.5 m. This DEM is provided by ALOS PALSAR. The ALOS mission was initiated on January 24, 2006, and ended operations on April 22, 2011. The Japanese government approved the ALOS mission, with the overarching goal of ensuring the continuation of data utilized for regional observation and environmental monitoring. The PALSAR sensor is one of ALOS' three devices (Wang et al. 2020a, b; Jaafari et al. 2022a, b; Abdo HG 2020; Nasir et al. 2022). In addition, the geological map of Morocco has been used to construct the distance to fault and lithologic maps. NDVI and the LULC maps were produced based on multispectral images (sentinel 2). However, the soil map was obtained by referring to the works of Mtaiau (2002) (Table. 1). All of the aforementioned parameters were combined in a GIS-based system and saved in a raster grid format with a resolution of 12.5/12.5 m (Fig. 4).

Table 1 Data sources used in the current study

Fig. 4

Landslide conditioning factor A slope, B elevation, C aspect, D curvature, E distance to roads, F distance to rivers, G lithology, H rainfall, I NDVI, J land use, K distance to faults L TWI, M soil type, N TPI

Landslide causatives factors importance

The evaluation of the significance of the predisposing factors is one of the objective procedures in the studies of mapping landslides susceptibility as a result of the restriction of the mutual influence of those factors in creating the state of landslide (Pham et al. 2018; Hosseinalizadeh et al. 2019). In the present study, the Information gain ratio (IGR) method was adopted to assess the contribution of different factors to landslide occurrence. Increasing the IGR values indicates the significant influence of the factor for the landslide model, and vice versa.

Landslide susceptibility indicators

Weights of evidence (WoE)

The WoE technique is a bivariate method that takes many variables into consideration and is typically used to estimate the landslide event occurrence based on the training dataset (Song et al. 2008). Many landslide scholars have commonly devoted WoE method to landslide susceptibility mapping (Batar and Watanabe 2021; Kontoes et al. 2021). Moreover, it is a data-driven strategy that employs a log-linear variation of Bayesian analysis. The WoE technique is established on the basis that future landslide events will take place under impacts similar to those contributing to prior landslides.

When an adequate training dataset inventory is available, WoE uses prior and posterior (predicted) probability to evaluate the relative relevance of evidentiary elements. WoE method is applied by calculating two basic parameters: negative weight (W⁻) and positive weight (W⁺). Each landslide causative factor (B) is weighted according to the presence or absence of the landslide events locations (A) using Eqs. 1 and 2 (Bonham-Carter 1991):

$${W}^{+}=ln\frac{P\left\{B/A\right\}}{P\left\{B/\overline{A}\right\} },$$

(1)

$${W}^{-}=ln\frac{P\left\{\overline{B }/A\right\}}{P\left\{\overline{B }/\overline{A}\right\} },$$

(2)

where P is the probability of the percentage, ln is the natural logarithm, W- is the negative weight, and W + is the positive weight. ($\overline{B }$) is the absence of the landslide causative factor, (B) is the presence of the landslide causative factor, $\stackrel{-}{(A})$ is the absence of the landslide event location, and A is the presence of the landslide event location (Chen et al. 2016). In this sense, a positive weight indicates the presence of a landslide-causing factor, and its size indicates a favourable spatial correlation between these two inputs. However, a negative weight denotes a negative spatial association and the lack of the landslide causative factor at the landslide site.

Support vector machine (SVM)

The support vector machine (SVM) is considered among the novel machine learning algorithms (MLA) proposed by Vapnik (1995). SVM relies on non-linear transformations of variables in higher dimensional feature space (Oh and Pradhan 2011; Tien Bui et al. 2018; Yousefi et al. 2022). SVM is an accurate simulation method used for classification and regression based on statistical learning theory (Hong et al. 2017). In the first step of application, like most MLAT models, SVM must be learned by a training dataset, then the trained model will be used to assess the issue of the test dataset (Brenning 2005). Two key concepts perform as the foundation of the SVM approach, which handles discriminative issues. The first one is a hyperplane for optimum linear separation that divides the data models. The second one involves transforming the original non-linear data models using kernel functions into the most suitable data model (Yao et al. 2008). The set of separable linear training vectors xi (i = 1, 2,…, n) with two classes, represented by yi =  ± 1, is needed for the two-class SVM model. The SVM goal is to find an n-dimensional hyperplane that discriminates between the two classes. The two classes are separated in n dimensions by the largest deviation that can be mathematically reduced using Eq. 3 (Yilmaz 2009):

$$\frac{1}{2}{\Vert w\Vert }^{2}$$

(3)

with the following condition:

$${y}_{i}(\left(w.{x}_{i}\right)+b)\ge 1,$$

(4)

where w is the normal separator hyperplane, b is a scalable datum, and (.) signifies a multiplication operation. The following is obtained using Lagrangian coefficients of cost:

$$L=\frac{1}{2}{\Vert W\Vert }^{2}- \sum_{i=1}^{n}{\lambda }_{i}\left({y}_{i}\left(\left(w{x}_{i}\right)+b\right)-1\right),$$

(5)

where ${\lambda }_{i}$ is the Lagrangian multiplier. Equation 6 can be minimized by using the w and b ratios as a standard. A variable ${\xi }_{i}$ can be used as a weak meaning (slack variables ${\xi }_{i}$), in which case Eq. 7 becomes

$${y}_{i}\left(\left(w.{x}_{i}\right)+b\right)\ge 1-{\xi }_{i},$$

(5)

$$L=\frac{1}{2}{\Vert W\Vert }^{2}-\frac{1}{\upsilon n} \sum_{i=1}^{n}{\xi }_{i}.$$

(6)

Radial basis function network (RBF)

The radial basis function (RBF) is a receptive-field neural network model that is applied to deal with multivariate interpolation problems (He et al. 2019). Subsequently, RBF technique has been used in landslide detection over many areas (Powell 1992; Zeybek and Şanlıoğlu 2020). A K-means clustering algorithm is the basis of the RBF network model. It is efficient in solving non-linear problems (Rumellhart 1986). The principle of RBF model is relatively simple, fundamentally based on a radial function. Initially, it imports the data into the input layer without any computation. Then, it processes the non-linear problem of the hidden layer neuron, and finally, it sends the results to the linear output layer. The RBF network is characterized by a single hidden layer, but there is no hidden layer in the model. The activation function in the hidden layer can be as follows: f: Rn → R, if the model is well trained. The basic function commonly used by researchers in RBF networks is the Gaussian one, which can be written as (Lei et al. 2020)

$$fi\left(\mathrm{x}\right)=fi\left({e}^{\frac{-\Vert xp-ci\Vert }{di}}\right), i=1, 2, \dots .,n,$$

(7)

$$Y={W}^{t}{f}_{p},$$

(8)

where C_i $\in$ Rn indicates the centre of the basis function. f_i d_i $\in$ R is the radius of the first hidden layer node. f_p is the hidden node vector.

Validation of landslide susceptibility maps

Statistical validation is employed to assess and compare the implementation and quality of performance of machine learning algorithms in mapping landslide susceptibility. In the current evaluation, the receiver operating characteristics (ROC) curve with the area under curve (AUC) was developed to assess the performance of the three models used and to validate the generated landslide susceptibility maps. On the x-axis is the false-positive rate (specificity), while on the y-axis is the real positive rate (sensitivity). Furthermore, the performance of the modelling techniques used was evaluated using some statistical measures. Each model probability was compared to historical landslide locations to create a confusion matrix that yields true negative (TN), true positive (TP), false negative (FN), and false positive (FP) (Park et al. 2019):

$$Specifity=\frac{TN}{FP+TN},$$

(9)

$$Sensitivity=\frac{TP}{FN+TP},$$

(10)

$$Accuracy=\frac{TN+TP}{FP+TP+FN+TN},$$

(11)

$$Precision=\frac{TP}{FP+TP}.$$

(12)

Results and analysis

Assessment of landslide causatives factors importance

The IG approach was employed to assess the quantitative impact of each landslide conditioning factor in the creation of landslide events. However, the removal of conditioning factors with zero predictive value is recommended by Chen et al. (2017). All fourteen landslide factors showed positive predictive capacity ratings, as illustrated in Fig. 5. The slope has the highest predictive capability with average merit (AM) value of 0.098. However, the rest of conditioning factors have less predictive capabilities i.e. distance to roads (0.07), distance to rivers (0.069), lithology (0.054), altitude (0.051), precipitation (0.048), soil type (0.046), TWI (0.032), NDVI (0.029), aspect (0.018), TPI (0.016), curvature (0.009), LULC (0.005), and distance to faults (0.004). Additionally, AG analysis indicated that all motivation factors have a positive contribution, therefore can be included in the implemented landslide modelling.

Fig. 5

Predictive capabilities of the fourteen landslide conditioning factors

Application of landslide susceptibility models

In the present study, two machine learning models (SVM and RBFN) and one bivariate statistical model (WoE) were applied to assess the landslide susceptibility at the N'fis watershed. After testing the importance of the variables by the IG method, fourteen causative factors were used as inputs to the landslide modelling process. The outcomes of the WoE analysis, however, are shown in Table 2. The spatial correlation between landslide events and each class of causative factors was measured using the contrast values (C). High values of C indicate a positive effect between the class of each factor and the occurrence of landslides. The landslide susceptibility value obtained using the WoE model ranges from 0.014 to 0.978, which was reclassified into five classes using the Natural Breaks method in ArcGIS 10.4: very low (0.014–0.195), low (0.195–0.334), moderate (0.334–0.516), high (0.516–0.679), and very high (0.679–0.978) as shown in Fig. 6.

Table 2 WoE weights for the different classes of each parameter based on landslide occurrences

Fig. 6

Landslide susceptibility map using WoE model

TensorFlow was used in this assessment to build the SVM model. SVM ideal parameters were determined through a number of trial and error procedures. However, the degree is 3, the gamma is the reciprocal of the number of features, the kernel function coefficient is 0.5, and the polynomial kernel function was chosen as the kernel function. The computed LSI values using the SVM model ranged from 0.013 to 0.987. The landslide susceptibility map was created by converting these values into a raster format in the GIS environment as Fig. 7 shows. The landslide susceptibility map was categorized into five categories of SVM model ranging: very high (0.755–0.987), high (0.630–0.755), moderate (0.378–0.630), low (0.235–0.378), and very low (0.013–0.235). Using the Natural Break method in GIS, the spatial zone of very high, high, medium, low, and very low susceptibility assigned as 7.69%, 17.18%, 29.48%, 25.75%, and 19.9%, respectively.

Fig. 7

Landslide susceptibility map using SVM model

The RBFN model was built using the landslide training dataset. The Weka software ten− fold cross− validation procedure not only decreases model variability but also eliminates the problem of overfitting throughout the modelling process as suggested by several studies (Wang et al. 2020a, b). The parameters used in the RBFN model are as follows: the clustering seed is 1, the maximum number of iterations is − 1, the number of clusters is 2, the minimum standard deviation is 0.1, and the ridge is 1.0E− 8. The landslide susceptibility index values calculated by the RBFN model ranged from 0.015 to 0.971. These values were reclassified into five classes: very high (0.638–0.932), high (0.434–0.638), moderate (0.252–0.434), low (0.110–0.252), and very low (0.005–0.110) based on the Natural Breaks method. The very low class has the largest area (11.58%), followed by low (24.36%), moderate (31.14%), high (22.87%), and very high (10.05%) as Fig. 8 depicts. Figure 9, in this context, shows graphically the proportional distribution of the susceptibility classes obtained by the three models applied in this assessment.

Fig. 8

Landslide susceptibility map using RBFN model

Fig. 9

Distribution of landslides in each landslide susceptibility category

Further, the visual analysis revealed similar spatial distributions of landslide susceptibility classes in the three maps produced in this evaluation. The southeastern part of the study area shows a very high susceptibility to landslides. The areas along with the rivers in most parts of the N'fis basin are also vulnerable to landslides. These maps also show a low to very low susceptibility to landslides in the northern part of the basin featured by gentle slopes. These results highlight the importance of the slope and distance to the river factors in the creation of landslide events which corresponds to the GI method outcome.

Validation and comparison of the models

The quantitative measurement of the accuracy of landslide susceptibility maps produced by the different classification models is a fundamental step (Luo et al. 2018). Moreover, the resulting landslide susceptibility maps will have no practical significance without validation of a landslide susceptibility model (Pham et al. 2017a, b). For this reason, the ROC and other statistical indices were used to evaluate the predictive performance of the models applied in this study. Using the training dataset, the AUC values for the WoE, SVM, and RBFN models were 83.72%, 94.37%, and 93.68%, respectively. The same ranking was obtained using the validation data with a little increase in the AUC values. In fact, the SVM model still has the best performance (94.60%), followed by RBFN (93.30%), and finally WoE (87.68%) (Fig. 10). However, the landslide susceptibility map developed with the SVM model is the best performing one followed by the map produced by the RBF model, while the WoE model is the least performing.

Fig. 10

Analysis of the ROC curve of different landslide models using training and validation dataset

The performance of the three models was also evaluated using several statistical indices (Table 3). The SVM model has the best performance, with the highest values of sensitivity (0.999), specificity (0.990), precision (0.997), and accuracy (0.987). With the RBFN model, we obtained a slightly lower performance than the SVM model. In this assessment, the WoE model is the least performing model with the lowest values of statistical performance indices.

Table 3 Statistical indices of different prediction models

Discussion

In Morocco, the landslides incidence is accelerating in mountainous areas due to the complex spatial integration of climate change, LULC change, and the pressure of human activities (El Hamdouni et al. 2022). Hence, there is an urgent need to conduct more accurate studies assessing landslide susceptibility with enhanced spatial outcomes. This accuracy is based on criteria of adequate data quality, appropriate modelling methods, and effective causative factors (Ayalew et al., 2005). In this study, a comparison performance of the WoE, RBFN, and SVM models was constructed in delineating the spatial susceptibility of landslides in N'fis basin with a total of 156 landslide events.

Evaluation of the correlation between historical landslide events and causal factors is a crucial step in landslide susceptibility modelling. This procedure is used to select the appropriate factors, thus improving the performance of the models used. In the current study, IG analysis was used to enhance the modelling process. With fourteen factors considered as motivating factors for landslides, the results of the IG analysis indicated that the slope, distance to road, and distance to river factors were the most important in creating landslide status with AM values of 0.098, 0.07, and 0.069, respectively. These results are consistent with the studies of Yu et al. (2019), Zhang et al. (2019), and Abedini et al., (2018). This can be justified by the intense mountainous geomorphological characteristics of the study area with an elevation of more than 4000 m.a.s.l. Steep slopes, which reach many locations more than 40 degrees, increase the potential landslide occurrences. Despite the importance of physical factors in creating the current stability of slope materials, landslide events are closely linked with human and economic factors that are very important in mountain watersheds (Lei et al. 2020; Saha et al. 2021).

One of the bivariate model merits is its flexible application because there is no need for training and parameter modification (Magliulo et al. 2009; Chen et al. 2020). In this evaluation, the SVM model achieved the best performance in producing a spatial susceptibility landslide map. In this regard, despite the flexibility of using bivariate statistics models, the machine learning algorithms provide the best performance due to the possibility of determining the best parameters involved in the modelling process, analysing the relationship between the driving factors and removing variance from the training dataset (Abedini et al. 2019a, b). Thus, the SVM model provided a reliable performance with a high accuracy rate that allowed us to reduce the limitations of this study. These investigations reveal that the occurrence of landslides is closely associated with geo− ecological factors (Huang et al. 2022). Moreover, the application of machine learning models, such as SVM and RBFN in this study, is relatively complex and requires data transformation. Despite this complexity, these models are recommended for assessing landslide susceptibility due to their high accuracy compared to the bivariate statistical model (Chen et al. 2020).

In this regard, the indicators of evaluating accuracy and performance proved the high potential of the three methods in mapping the landslide susceptibility in the study area. Despite this, those indicators reported that the SVM model was the most high quality in comparison to the WOE and RBFN model. Furthermore, many landslide susceptibility scholars have confirmed the high efficiency of the SVM model in evaluating landslides. Abedini et al. (2019a, b) reported that the SVM was more precise than the other models. Similarly, Tien Bui et al. (2012) stated that the SVM model outperformed landslide risk assessment compared to decision tree (DT) and Naïve Bayes (NB) algorithms. The same result was found in a study conducted by Ballabio and Sterlacchini (2012).

SVM has the merit of having non-linear kernel functions which deal with the non-linear association between landslide events and causative factors (Zhao and Zhao 2021). Furthermore, the SVM model application provided an optimal level of landslide vulnerability classification due to the ability to accurately separate the training dataset points of landslides and non-landslides (Kong et al., 2021). The RBFN has the features of unique global approximation, linear association of output significances in the network structure, reasonable classification capacity, and quick training rate (Kim et al. 2019). However, WoE provided an acceptable performance in mapping landslide susceptibility despite the collinearity between motivating factors and landslide events that affected the model performance. However, the three models showed remarkable consistency in the predictive ability of the training dataset and that of the verification dataset, which indicates that these models have achieved practical and reliable spatial results in mapping landslide susceptibility in the study area.

The three models applied confirmed that the eastern and southeastern regions were the most vulnerable to landslide events. However, this result is consistent with the observations of the extensive fieldwork carried out in the study area. In this respect, these areas are characterized by extreme elevation (< 4000 m), steep slopes (< 40°), intense rainfall storms, low vegetation density, fragile rock formations, dense fissures and faults, and rapidly topsoil eroding. These characteristics make these areas highly prone to landslides, therefore should be included in mitigation and maintenance priorities (Mohammed et al. 2020).

In this regard, the diversity of data sources and the spatial resolution of the variables are the main certain uncertainty and limitations of this study. For example, the data resolution of DEM, LULC, lithology, and soil types was not consistent (Table. 1). Several studies indicate that choosing the appropriate spatial resolution remains a challenge in the context of advances in landslide modelling studies (Wang and Brenning 2021; Huang et al. 2022). However, these limitations are common in areas with scarce geographical data, such as the study area. All the thematic layers were resampled at a 12.5 m resolution in order to conduct this study. The absence of data of some important parameters, such as soil texture, soil depth, and water table depth, remains also among the main limitations of the current study. Despite these limitations and in light of the results of performance evaluation, the results of this study can be considered objectively efficient in improving the quality of spatial outputs related to landslide prediction at the national level.

Finally, the three implemented methods demonstrated sufficient performance for landslide susceptibility mapping. Nevertheless, the SVM model achieved suitable performance. Hence, it can be utilized to evaluate and create more reliable landslide susceptibility maps for appropriate landslide risk management. Overall, the outcomes of this study can introduce very valuable and critical knowledge for local decision-makers and LULC planners to mitigate and manage the high and very landslide susceptibility areas in the N'fis basin.

Conclusion

The identification of landslide-prone areas is an important procedure for LULC planning and developing landslide mitigation techniques. The aim of this study is to conduct a comparative evaluation of landslide susceptibility mapping using SVM, RBFN, and WoE models in the N'fis river basin, Morocco. An inventory map of 156 landslide events was produced and divided into 70% as a training dataset and 30% as a test dataset. Moreover, 14 causative factors, i.e. slope angle, elevation, slope aspect, LULC, TWI, curvature, lithology, distance to faults, distance to roads, TPI, rainfall, distance to rivers, NDVI, and soil type, were mapped using a different source database. These factors were spatially calibrated with the training dataset using the three models in order to map the landslide susceptibility in the study area.

The three maps produced were reclassified into five classes, i.e. very low, low, moderate, high, and very high. The high and very high areas are located in the eastern and southeastern parts of the basin, characterized by high altitudes and steep slopes. The maps obtained were validated by ROC and statistical indices, which showed that the SVM method is the most suitable performing (AUC = 94.60%), followed by RBFN (AUC = 93.30%), while the WoE model remains the least performing (AUC = 87.68%). The findings of this study showed that machine learning methods, such as SVM and RBFN, have improved the simulation maps of landslide susceptibility at the national level.