1 Introduction

The most distressing environmental hazards in the Himalayan mountainous and adjacent foot-hill area are landslide. The landslide (LS) causes damage to human life, assets and infrastructure in the Himalayan mountain region [1, 2]. Landslide is a complex process, which is caused due to some internal and external factors. The inherent factors consist of the stability situation of the slope, geological factors, soil category, groundwater condition, geometry of slope (slope inclination, aspect, elevation and curvature) and land-use/land-cover changes [3,4,5,6]. Several researchers developed specific models or approaches to map the landslide susceptibility zone (LSZ) in numerous mountains areas around the world. Analysis of LSZ includes consideration of the physical factors that cause slope instability in an area, assessment of their contribution and appraisal of their aggregate influence. This is carried out using a variety of methodologies that can be widely categorized as qualitative and quantitative analyzes, considering the physical factors identified as variables causing landslides. Basharat and Saha offered a detailed description of the analysis of those techniques [4, 5]. The qualitative methodology uses specific parameters focused on subjective judgment rules taken by the geoscientist on the landslide-influencing physical factors [4, 7]. In addition to the recently introduced approaches, such as the fuzzy technique, they include statistical and geotechnical methods [7, 8].

The probability of LS was investigated in the mountainous area of several countries, like Japan, Korean, Bhutan, Malaysia, India, etc. [5, 9, 10]. Sakkas applied a generalized model of the linear combination process for analyzing LS susceptibility in Greece [11]. The slope failure probability models and logistic regression models were applied for LS risk assessment [12]. Raghuvanshi [13] described that the internal parameters handle the stable status of the shield, such as geological factors (lithological structure, soil type and underground conditions), shield geometry (shield aspect, curvature or height) and also land-use/land-cover. The machine language-based artificial neural network model for LSZ analysis was applied in the Cameron, Malaysia [14]. Saaty [15] initiated the analytical hierarchy process (AHP), the semiquantitative method based on comparative judgment. AHP method was subsequently applied in Taiwan and Nepal for LSZ map** [16, 17]. Soil characteristics were used for slope mass rating and modeling the landslide susceptibility in Himalayan mountainous area [18]. The LSZ map** was done in Inje area basin of Korea using logistic regression [19]. Saha et al. analysis [5] and Shit et al. analysis [20] applied the probabilistic approaches for the LSZ risk and hazard analysis. Ensemble model for LSZ map** using RS and GIS was applied by Basharat et al. [4], Park et al. [19] and Nithya et al. [21]. The risk of LS and its vulnerability in the European mountainous region were deliberated using various models used in different researcher’s work [9, 10]. Some notable LS modeling works have been done using the hybrid methods [22], explicit deep learning neural network model [23], artificial neural network model [4, 5, 20]. A large number of researchers produced LSZ maps using frequency ratio (FR) and binary logistic regression (BLR) models [5, 28,29,30]. The relationship between LS site and landslide-conditioning factors can be analyzed through the BLR model [30,31,32].

The Kurseong and its surrounding area are regularly hit by the landslides and trigger tremendous losses of life and property. Map** the landslide susceptibility zones is important for handling landslide problems in this area. The main objective of this paper is to prepare the LSZ maps of Kurseong municipal and it surrounding in Darjeeling Himalaya using individual AHP, FR, BLR methods and their ensemble models. The comparison of the efficiency of novel ensemble AHP–FR, AHP–BLR and FR–BLR methods with performance of individual AHP, FR and BLR models in landslide susceptibility assessment is the main novelty of this work. The ensemble technique of AHP–FR, AHP–BLR and FR–BLR methods is yet not implemented in landslide susceptibility studies in Darjeeling Himalayan, India. The key advantage of the study is that an accurate landslide susceptibility map (LSM) was being developed, which is a crucial asset for land and town planners in the mountainous area. These maps will assist the planner to adopt the mitigation strategies and to allocate suitable areas especially for the development of infrastructure activities.

2 Materials and methods

2.1 Study area

Kurseong municipality along with its neighboring downhill slope of Darjeeling Himalaya is extended between 26°46′30″ and 26°57′47″ North latitudes and 88°08′25′′ to 88°27′54′′ longitudes comprising an area of 380.33 km2 in the district of Darjeeling, WB, India (Fig. 1). Municipality of Kurseong is a subdivisional town and a hill station. The name ‘Kurseong’ is come from the word ‘Kharsang,’ originally a local word ‘Lepcha,’ connoting ‘the land of white orchids’ [33].

Fig. 1
figure 1

Location map of the study area: a India, b Northern part of West Bengal, c Kurseong and its surrounding area with landslide points

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It is one of the most ancient urban centers. Kurseong Town was founded back in 1835 when the British Government of India brought this region out of the kingship of Sikkim. The tiny hamlet eventually became a popular spot for the colonial government in 1880 and became a favored location for sanatoriums where the ill would heal. It has a nice year-round climate, and winters are not as extreme as they were in Darjeeling. The region's climate is aligned with climate-type CWA (subtropical humid) by Koppen. The average annual temperature is 23.69 °C, and the average annual rainfall is about 325 cm (weather record for the municipalities from 1991 to 2016). During the north-east monsoon, the marked rainy seasons are observed in the first week of June to the last week of September [5]. Through the northeast monsoon, it receives rainfall during both northeast monsoons. Every year, Monsoon (June–September) rainfall induces a number of landslides and destroys property and farmland. It is observed that the spatial distribution of landslides in the region is influenced by both morphological and hydrological characteristics of the slopes. The region portrays a heavily sculpted degraded environment in its youthful stage of turbulence cutting down by tumultuous streams and rivers coupled with preexisting geological deformities with rocks of Darjeeling gneiss and Daling sequence of Archaeans, Permian Gondwana rocks, Siwalik rocks and Pleistocene elevated terrace (Geological Survey of India) [34].

2.2 Database

The Landsat 8 OLI satellite imageries (30-m resolution) of 2018 were used to derive land-use data and Google Earth imageries were utilized to identify landslides in Kurseong and its surroundings. Nine contributing factors such as (a) altitude, (b) slope, (c) aspect, (d) rainfall map, (e) drainage system, (f) lithology, (g) land-use/land-cover (LULC), (h) lineament and (i) geology related to the occurrence of landslides were considered to prepare LSZ map in Kurseong and its nearby region of Darjeeling Himalaya. The aspect, slope and altitude map were derived from the Shuttle Rader Topography Mission (SRTM)-based DEM (created by NASA), using ArcGIS 10.3 platform (Table 1). In addition, these maps were classified using the quintile method [35, 36]. Geological map was derived from GSI, soil zonation map from NBSS and LUP Regional Centre, lineaments driven from bhuvan.nrsc.gov.in website and drainage system driven from Toposheet (Table 1). The LULC was generated from Landsat 8 OLI (Bands 2, 3 and 4; resolution 30 m) data using supervised classification technique and maximum likelihood algorithm through ERDAS 14.0 software. Field visits were carried out to realize the ground truth of landslide inventory. The process of preparing landslide susceptibility maps followed a number steps which are explained one by one (Fig. 2).

Table 1 Various data layer with source used in the study
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Fig. 2
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Flowchart of methodology

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2.3 Landslide inventory map**:

According to Balzano et al. [2], Roy et al. [28], Zhao et al. [31], the first and foremost move for the assessing of an area's landslide susceptibility is to examine, locate and map the landslides. This may be achieved by field surveys or via high-resolution aerial imagery. The LS occurrences were identified and mapped by field inspection and with the help of high-resolution imagery from Google Earth for the current study. The LS occurrences were identified and mapped by field inspection and with the help of high-resolution imagery from Google Earth for the current study. In general, spatial map** of landslides is required to assess the relationship between distributions of LS with the predisposing factors of the LS. At first, LS locations were recognized using the GPS coordination system, and later, the location of LS was drawn as a polygon using Google Earth images (Fig. 3). A total of 221 LSs locations are identified in this study area. Within 221 cases, 70% are being applied as training data to accumulate LSI, and the remaining 30% is applied to authenticate those models [37,38,39]. Hence, it was found out that LSs are most common in the middle and steep slope base upper altitude of this study area. In the lower part of the study area, the landslides were found along riverside, and they occur almost every year. Many landslides in the upper catchment are mainly restricted to under-gravity scrambling of rocks and rubble. The landslides are mostly debris, topsoil and mud flow in the middle catchment area, but in the western part of the middle catchment, rock falls sometimes happen as well.

Fig. 3
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Some landslide Google images collected through Google earth pro a 26°55′01′′N; 88°19′28′′E; b 26°52′23′′N; 88°21′01′′E; c 26°52′37′′N; 88°2′26′′E; d 26°55′42′′N; 88°26′31′′E; and e 26°53′09′′N; 88°27′07′′E in this study area

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2.4 Susceptibility modeling techniques

2.4.1 Analytic hierarchy process (AHP) analysis

AHP is an important multi-criteria decision approach (MCDA) which is used for assigning the weights. The AHP is a technique which calculates throughout pairwise comparisons of dissimilar factors. Based on expert decisions, the priority scales put on [39]. According Saaty, the comparison can be done using a nine-point scale or real data [39]. The 9-point weight extent includes: [9, 8, 7, 6, 5, …1/5, 1/6, 1/7, 1/8, 1/9], where 9 means extreme preference, 7 means very active preference, 5 means strong preference, and so on, low to 1, which means no preference (Table 2) [40, 41]. The procedure is to assign priority weights for every factor through computation of normalized eigenvector (EV) which is very popular method of measuring the preferences from inconsistent pairwise comparison matrices [40]. The weights were derived by summing up the values in each column of pairwise comparison matrix, and each cell value is divided by the summed values of the same factors column. The average value of each row is the primary eigenvector of the matrix. As this matrix was randomly prepared, for this reason, some degrees of inconsistency may occur [17, 41]. The calculation table arranges in the tabular format according to Saner technique [42].

Table 2 The comparison scale in AHP (Saaty 1990)
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2.4.2 Frequency ratio (FR) model

FR defines the proportion of landslide pixels for each input layer in the specific category [43,44,45]. FR assumes that future landslides will occur in conditions similar to the past. It may be defined as the ratio of landslide pixels in a category (a class of factor) to the relative frequency of all landslide pixels in an area. FR values for subclass of every factor were calculated using Eq. (1).

$$ {\text{FR}} = \frac{{{f \mathord{\left/ {\vphantom {f {tf}}} \right. \kern-\nulldelimiterspace} {tf}}}}{{{x \mathord{\left/ {\vphantom {x {tx}}} \right. \kern-\nulldelimiterspace} {tx}}}} $$
(1)

where ‘f’ is landslide pixels in the subclass of landslide conditioning; ‘tf’ is the total landslide pixels; ‘x’ is the total pixels in the subclass of landslide-conditioning factor; and ‘tx’ is the total pixels [43, 45, 46].

The FR value is indicating the association of landslide occurrence and landslide-conditioning variable. The landslide susceptibility index (LSI) was calculated by summing up of Fr values of every factor using the ArcGIS raster calculator in Eq. 2.

$$ {\text{LSI}} = \left( {\begin{array}{*{20}l} {{\text{slope}}{\kern 1pt} {\text{classes}}{\kern 1pt} {\text{fr}} + {\text{Altitude}}{\kern 1pt} {\text{fr}} + {\text{Geological}}{\kern 1pt} {\text{structure}}{\kern 1pt} {\text{fr}} + {\text{Distance}}} \hfill \\ {{\text{from}}{\kern 1pt} {\text{lineament}}{\kern 1pt} {\text{fr}} + {\text{Distance}}{\kern 1pt} {\text{from}}{\kern 1pt} {\text{river}}{\kern 1pt} {\text{fr}} + {\text{Soil}}{\kern 1pt} {\text{fr}} + {\text{LULC}}{\kern 1pt} {\text{fr}} + {\text{Aspect}}{\kern 1pt} {\text{fr}}} \hfill \\ \end{array} } \right) $$
(2)

(LSI: landslide susceptibility index; fr: the rating of each factor’s class). The landslide susceptibility map was prepared using the LSI values and is shown in Fig. 5b.

2.4.3 Binary logistic regression (BLR) model

Logistic regression (LR) is a statistical model that allows for the evaluation of multivariable regression between a dependent and a group of independent variables [9, 29, 31]. The major benefit of logistic regression is that it can perform with the help of an appropriate link function to the ordinary linear regression. In this case, if the data are either continuous or categorical, or both, there is no problem and the regression does not require the normal distribution of data. For this analysis, the binary number ‘0’ denotes non-landslide points and the binary number ‘1’ denotes landslide point. The logistic regression method means optimum likelihood calculation after the translation of the dependent variable into the logit component. Thus, logistic regression measures the probability of an event.

In this BLR model, the calculation was done applying Eqs. 3 and 4 and more detail can be found in some recently published articles [29, 30]. BLR model can be carried out using Eq. 3

$$ {\text{LS}}^{{\text{p}}} = \frac{1}{{(1 + {\text{Af}}^{ - z} )}} $$
(3)

where ‘LSp’ denotes the landslide probability. ‘Af’ denotes the affecting factors selected in this work. ‘LSI’ denotes the liner model combination, and it ranges between − ω and + ω (Eq. 4).

$$ {\text{LS}} = (a_{0} + a_{1} xv_{1} + a_{2} xv_{2} \ldots a_{n} xv_{n} ) $$
(4)

where ‘a0’ signifies models intercept. The ‘a1, a2…an’ signify the slope of coefficient. And the xv1, xv2, …, xvn denotes the independence factor number.

$$ \begin{aligned} {\text{LSI}} & = {\text{Intercept}} - ({\text{Slope}}*B) + ({\text{Altitude}}*B) + ({\text{Rainfall}}*B) + ({\text{Distance}}\;{\text{from}}\;{\text{lineament}}) \\ & \quad + ({\text{Distance}}\;{\text{from}}\;{\text{Drainage}}*B) + {\text{GeologyB}} + {\text{SoiltypeB}} + {\text{Land } - \text{ coverB}} + {\text{AspectB}} \\ \end{aligned} $$
(5)

where B is the logistic regression coefficient value, while land-use/land-use B, geology B, soil type B and aspect B are the logistic regression coefficient values.

Based on independent variables, the BLR model forecasts the existence or absence of LS. On the basis of pre-failure conditions (independent variables), the linear LR represents the existing conditions (presence or absence of landslide). For the landslide susceptibility map** by the BLR first, all the pixels of map were converted into points and then used these as input data layers in the SPSS software to calculate logistic regression values [47]. The logistic regression model is considered as quantitative method that finds out the effects of individual independent variable with the help of the coefficients and antilogarithm of the coefficients [9, 30]. Finally, the BLR model-based LSZ map was prepared using Eq. 5 [29, 30, 47, 48].

2.5 Process of models’ ensemble

The ensemble modeling is a technique of joining the effects of different models into an incorporated embedded model to develop predictive capability [35, 48,49,50]. This technique has risen in recent last few years of reducing gully erosion [35]; modeling flood probability [49]; landslides susceptibility [50]; and different purposes. In this work, the ensemble models can be generated using the weighted combination of an individual model. The ensemble technique of AHP–FR, AHP–BLR and FR–BLR has been followed by sequentially khosravi [49], althuwaynee [50] and Shafapour Tehrany [32, 38, 52, 53]. For this research, the slope map was prepared from DEM and classified into six groups (Fig. 4a).

Fig. 4
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Landslide-conditioning factors: a slope, b altitude, c rainfall, d geological structure, e distance from lineament, f distance from river, g soil map, h land-use/land-cover map and i aspect map

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2.6.2 Altitude

Altitude is a frequently used parameter for landslide susceptibility assessment [30, 48, 52]. In the study, the elevation ranges between 120 and 2440 m and is classified into 5 categories (Fig. 4b). To prepare this LSZ map, the elevation was divided into 5 groups and their weights were estimated according to matrix and consistency ratio for each class.

2.6.3 Rainfall

The role of antecedent rainfall in causing landslides is also investigated by considering daily rainfall during failure and the cumulative rainfall to discover at what point antecedent rainfall plays an important role in Himalayan landslide processes [43, 44]. Rainfall is an essential trigging factor in landslide occurrences [17]. In the Himalayan region, mean precipitation is very high compared to another part of India. The average is 525.5 cm in June, July, August and September month of the monsoon season (https://www.worldweatheronline.com/lang/en-in/west-bengal.aspx). In the study, the average monsoon rainfall map was generated and divided into three classes, i.e., 400 cm, 400–500 cm and more than 500 cm per monsoon season (Fig. 4c).

2.6.4 Geological

The geomorphological element is the most notable phenomenon which plays an important role in landslides [55]. The high peak in the study area appears in the north-western part. This Himalayan part is regarded as the structural mountains, denudation plain and floodplain. Geological map of the study area was collected from the Geological Survey of India (GSI). The boundaries of geological segment and names of the geological unit were used in previous studies [34, 43, 55, 56]. This region is dissected into numerous small ridges, spurs, deep ‘V’-shaped valleys and other erosional features. The geological map was digitized using ArcGIS v10.3 software and was converted into a grid map with 30 m × 30 m resolution. Alluvium and limestone deposits have a high capability for water adsorption and influence the landslide occurrences. Gneiss and States-Schist are semipermeable and have a limited water adsorption potential, and this geological unit is moderately susceptible to the landslide.

2.6.5 Lineament

Faults form a weak line or zone well marked by broken rocks [28, 31, 34, 43]. The lineament map was derived from bhuvan.nrsc.gov.in with a 1:50,000 scale. The distance from lineaments was calculated by Euclidean distance buffer tool in GIS environment and classified into 5 categories considering an interval of 300 m (Fig. 4e).

2.6.6 Distance from the river

Another important, promising and functional variable is the distance from the river for landslide occurrences [43, 45, 47]. Howard (1997) notified that isolation is a limited model, which influences the dominant hills-shield transportation process in relation to distance from the river and mean decay rates, through a threshold presence or absence for landslides and climate corrosion [55, 56]. The distance from the river was divided into 5 categories where an interval of 500 m was taken into account [36, 55,56,57,58,59,60] (Fig. 4f).

2.6.7 Soil type

The soil of Eastern-Himalayan hill and foot-hill area depends upon the fundamental geological structure [14, 34]. But, in general, the soil has been formed in cooperation fluvial action with lithological disintegration (Fig. 4g). The soils formed in the Kurseong area are predominantly reddish in color. Occasional dark soil is found due to the extensive existence of Phyletic and schist. Soils in the highland stretching from the west to east of the district along most of the inter-fluvial areas are mainly a mixture of sandy loam and loamy, and southern slopes of Kurseong are mainly composed of clayey loam and reddish in color. The basic soil types of the study area are yellow soils, red-brown soils and forest soils. Main soil types of the study area are WOO2 (Course Loamy, Typic Udorthents, Loamy-skeletal, Typic Dystrochrepts), WOO4 (Loamy-skeletal, Typic Udorthents, Loamy-skeletal, Typic Haplumbbrepts), WOO6 (Course loamy, Umbric Dystrochrets) and WOO9 (Fine Loamy, Umbric Dystrochrepts, Course Loamy, Typic Udorthents). In the Kurseong, due to the presence of gneiss rock the red-brown soil and red soils are developed. In some parts of the study area, dark clayey soils are also present.

2.6.8 Land-use and land-cover

Rapid settlement expansion (building) takes place on mountain slopes where large landslides occurred historically that are not realistically sustainable in this area [34, 46, 60, 61]. This could result in major loss of property and human life at the time of future high magnitude landslide. In Kurseong hilly regions, land-use patterns are an important influencing factor for landslide occurrence [5]. Some restrictions should be imposed on building constructions for sustainable environmental management in Kurseong and its surrounding Darjeeling Himalaya [33, 34]. The forest and pasture areas should not be used for various purposes, which is announced by the Darjeeling hills area development program under the 8th 5-year plan. The major land-use is tea gardens where landslides are being observed noticeably. In addition, deep forest, plantation and riverside lands are also susceptible to landslides where the expansion of human settlement happened. The Sentinal-2 data were derived from glovis.usgs.gov satellite at 10 m scale (using band 2; band 3; and band 4). The West Bengal government blockwise LULC map, the topographical map from SOI no. 78B/5 and field verifications were incorporated and processed through ArcGIS v10.3 and ERDAS v14 software (Table 1) for preparing the LULC map of the study area. Thereafter, this LULC map was converted into a grid map with a resolution of 30 × 30 m (Fig. 4h). The accuracy of the LULC map was assessed by applying kappa statistics. Overall classification kappa statistics is 0.8727, which is desirable (Table 3).

Table 3 Classification accuracies of LULC
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2.6.9 Aspect

The slope aspect was recognized as a driving factor for a landslide [17, 34, 59]. The aspect map was derived from the digital elevation model (Fig. 4i). Due to an increase in moisture during the rainy season (July–September), some parts in the south-east and the south-western part of this Himalayan range become much more vulnerable to landslide occurrences.

3 Results

3.1 Multi collinearity test

Before preparing the landslide susceptibility models by the AHP, FR and BLR testing of multi-collinearity among the independent variables is essential [36, 56, 60, 61]. A tolerance of less than 0.10 and/or a VIF of 5 and above indicates a multi-collinearity problem [62,63,64]. In this study, both indices were calculated (Table 4). The values of tolerances and VIF of all the selected parameters are more than 0.2 and < 10% [62, 64]. So, there is no collinearity problem among the selected landslide determining factors. Among these selected factors rainfall factor has the highest VIF (2.648) and the slope aspect has the lowest VIF value (1.146).

Table 4 Result of multi-collinearity diagnosis of landslide conditioning factors
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3.2 Landslide susceptibility maps

In the calculation of AHP highest consistency ratio (CR) is achieved by slope (0.137) and lowest by aspect (0.033). Rainfall (0.092), altitude (0.112), distance from river (0.059) and geological structure (0.076) are also have high CR value (Table 5). In FR model the weight of soil type w-004 (16.22) is the highest and 83% of landslides are found in this soil segment. FR model also depicting that soil type w-006 (3.57) settlement (1.25) and fellow land (0.95) are highly influencing factors for LS and the opposite situation found in slope 0 to 5° (0.19), dense forest (0.63); open forest (0.79); soil w-002 (0.061); sandbank (0.18); distance from lineament subclass 600–900 m (0.17); 900–1200 m (0.21); and more than 1200 m (0.18) (Table 6). BLR model shows that the all the factors have not equal role in making the area susceptible to landslide in Kurseong and its surrounding. Slope (0.028); altitude (0.338); rainfall (1.476); geological structure (0.119); settlement; fellow land; and cultivation land in LULC have a positive role in causing the LS as the coefficient value which has found in the BLRM is positive. On the other hand, FCFs like distance from the river (− 0.005) and w-006 (soil type) distance from the lineaments have a negative relationship with the LS. According to the BLR, rainfall (4.37) is the most important determining factor for the landslide in this region (Table 7).

Table 5 Pairwise comparisons, factors priority and consistency ratio by AHP
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Table 6 Pairwise comparison matrix for consistency ratio; weights of each sub layer by AHP method and frequency ratio (FR) values of the landslide-conditioning factors
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Table 7 Coefficient of logistic regression model of landslide conditioning factors
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Applying the AHP method (Table 5), LSZ map was obtained. The higher value of the LSI indicates the higher probability of landslide and vice versa. The LSI has a minimum value of 1.08 and the highest value of 2.85. The Kurseong range and its surrounding areas were divided into major 5 susceptibility regions according to the quintile method [57]: very low 16.63% of total area 63.25 km2, low 21.43% of total area 81.19 km2, moderate 88.65 km2, high 20.88% of total area 99.91 km2 and very high 17.75% of total area 71.08 km2 (Fig. 5a; Table 8).

Fig. 5
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Landslide susceptibility maps prepared by a AHP method and statistical prediction techniques, b FR model, c BLR model, d AHP–FR model, e AHP–BLR model and f FR–BLR model

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Table 8 Area under the landslide susceptibility classes
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Applying the FR model, an LSZ map was obtained. If the LSI value is very higher, it means a high probability of landslide; lower value means lower probability to the landslide. The LSI has a minimum value of 10.48, and the highest value of 42.85 came in probability assessment. The Kurseong range and its surrounding were divided into major 5 susceptibility regions according to the quintile method [57]: very low, low, moderate, high and very high susceptibility classes cover 24.63% (93.63 km2); 17.72% (71.19 km2); (33.09 km2), 11.70% (44.50 km2); 26.27% (99.91 km2) and 19.69% (71.08 km2) areas of the study area, respectively (Fig. 5b; Table 8). Another single model BLR (Fig. 5c) was very high 13.23% (50.23 km2); low 20.67% (78.61 km2); and very low 30.48% (113.58 km2) LS suspect region.

In ensemble AHP–FR, AHP–BLR and FR–BLR models, very low, high and very high susceptibility classes cover 18.92% (71.59 km2), 20.68% (78.63 km2) and 18.64% (71.31 km2); 23.22% (88.31 km2), 16.36% (62.21 km2) and 17.43% (66.29 km2); and 22.72% (86.40 km2), 21.47% (81.64 km2) and 18.29% (69.56 km2) of the study area, respectively (Fig. 5d–f).

3.3 Models validation and comparison

For measuring the prediction accuracy of landslide susceptibility maps induced by different methods, application of suitable methods is necessary. Among the different validation approaches, area under curve (AUC) of receiver operating characteristic (ROC) curve has been widely used in geographical community [28, 47]. The ROC has been prepared by plotting the true positive (TP) against the false positive (FP) values at different threshold settings. ROC represents the true positive rate (TPR) and the false positive rate (FPR). The true positive rate (TPR) is called as the sensitivity, and false positive rate (FPR) is termed as specificity. The higher TPR denotes more accuracy, and higher FPR reflects error prediction of the models. ROC curves were used to decide the threshold value for the LSZ map [17, 19, 56]. The area under the curve (AUC) reflects the accuracy of the model [19, 46, 59, 66]. The area under curve (AUC) values can be classified into five categories such as poor (0.5–0.6), average (0.6–0.7), good (0.7–0.8), very good (0.8–0.9) and excellent (0.9–1) [2, 64, 65]. The intensity of the accuracy of the model has been categorized after Pradhan et al. [14].

The perfect model demonstrates a curve that has the largest area under curve (AUC). A perfect model concludes an AUC value nearest to 1.0, whereas a value close to 0.5 indicates the erroneousness of the model [13, 45, 65, 66]. In the study, the ROC curve was produced by imprint y-axis TPR against FPR at the x-axis with a fixed threshold or cutoff value (Fig. 6). The constructed LSZ map was matched up to recognize landslide locations through ROC curve. To verify the accuracy rate of LSZ maps, 66 of the 221 landslide points were used (Table 8). The diagram (Fig. 6) is showing the AUC values are 78.86% in AHP, 80.22% in FR, 80.67% in BLRM, 83.44% in AHP–FR, 84.39% in AHP–BLR and 84.73% in FR–BLR models. All the models revealed a very good accuracy in map** the landslide susceptibility (Fig. 6). Another accuracy process, kappa statistics, showed that overall accuracy is 0.789 in AHP, 0.842 in FR, 0.799 in the BLR, AHP–FR 0.837, AHP–BLR 0.856 and 0.868 in FR–BLR models for the final output maps (Table 9). The ROC and kappa statistics both results were showed FR–BLR ensemble model giving better output and AHP model giving comparatively low accuracy in map** the susceptibility to landslide in Kurseong of Darjeeling Himalaya.

Fig. 6
figure 6

ROC curve for the assessment of susceptibility maps prepared for a AHP (83.58%), FR (86.82%), BLRM (85.17%); b AHP–FR (85.34%), AHP–BLR (87.32%) and FR–BLR (88.73%) models

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Table 9 Applied kappa statistics for accuracy assessment of landslide susceptibility maps with field data
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4 Discussion

Landslide is a complex phenomenon on account of multiple variables influence in its occurrence. Improving the performance of models of LS susceptibility has still drawn enormous attention from the research community for proper map**. The application of remote sensing and GIS can be useful in the study of hazard management due to their high accuracy and speed where accuracy and time are two vital aspects of landslide modeling [1, 34, 67, 68]. Factor selection is also a significant concern for making the model more effective and precise. Different causes lead to the occurrence of landslides where some are significant and others are minor contributory factors [34, 61].

Different methodologies were examined from the viewpoints of effectiveness and reliability to prepare LS susceptibility maps. This present study attempted to assess the proficiency of various methods such as knowledge-driven AHP, probabilistic FR and BLR models and ensemble models AHP–FR, AHP–BLR and FR–BLR to assess the LS susceptibility of Kurseong region of the Himalaya, India. The employ of ensemble methods to generate high accuracy map** [68, 69] is considered an important step in this regard. This Kurseong is chosen as a case study because of the high frequency of LS in eastern Himalaya and high sensitivity of this area in terms of population, concentration, tea garden and agricultural land.

At the first and second steps, LS inventory map (221 LS locations) was made and randomly divided into two subsets for testing and training (70:30), respectively, and after that, LS-conditioning factors were prepared after multi-collinearity test. Afterward, these factors were used to correlate LS with the each class of conditioning factors and then evaluated the susceptibility to LS by AHP, FR, BLR, AHP–FR, AHP–BLR and FR–BLR models. The LSMs were constructed and classified into five categories in order to produce the susceptibility map. The success rate and prediction rate curves were used to determine efficiencies and compare the results of LSMs. The landslide susceptible maps both single model and ensemble model have provided better result than the previous works done by the different researchers in the Himalayan region [5, 8, 17, 27, 29, 33, 46]. In addition, validation results indicated the better performance of FR–BLR ensemble model with a prediction rate of 84.76% compared with AHP, FR, BLR, the ensemble of AHP–FR and AHP–BLR models having the AUC values of 78.86%, 80.67%, 83.44% and 84.39% respectively. A different accuracy process, kappa statistics, confirmed that overall accuracy is 0.789 in AHP, 0.842 in FR, 0.799 in the BLR, AHP–FR 0.837, AHP–BLR 0.856 and 0.868 in FR–BLR models for the final output maps.

It is shown in Tables 5 and 8 that the Damuda, limestone geological structure with slope above 15° and altitude above 1500 m are extremely vulnerable to landslides. Areas closer to the lineament and river are highly susceptible to landslides. Soil type w-004 (Loamy-skeletal, Typic Udorthents and Loamy-skeletal, Typical Haplumbbrepts) also plays a crucial role in triggering landslides. Sandy clay with the largest frequency ratio was identified as the most susceptible type. Intense commercial agriculture is done in this particular soil type by small terraces. Most of the settlements are located in the moderately susceptible areas. Site-specific slope control is necessary to check and mitigate landslide phenomena in the Kurseong range and its surrounding region. The LS maintenance could involve armoring the drain along the junction between the road and the hill slope, building a retaining wall, wall and trap water drain, controlling subsurface water, installation of fern vegetation, strict and constant surveillance along NH 55 and road diversion to prevent high landslide occurrence. The failure of unstable slopes in hazardous areas, in addition to fatalities and economic damage, has devastating social and environmental effects. Identification of vulnerable landslide areas is an important source for local authorities and decision makers.

5 Conclusion

The LSZ maps of Kurseong subdivision of Himalaya were produced using one knowledge-driven method, i.e., AHP method, two probabilistic methods, i.e., FR and BLR and their ensemble, i.e., AHP–FR, AHP–BLR and FR–BLR. Major 9 landslide-conditioning factors have been considered for the generation of landslide susceptibility maps using GIS. The numerical weights have been assigned by AHP, FR and BLR to each subclass of every factor, after ensemble approach applied for AHP–FR, AHP–BLR and FR–BLR modeling landslide susceptibility. LSZ maps study areas have been classified into five zones, such as very high, high, medium, low and very low. The AHP-based LSZ map shows that large portion of the study area (38.63%) falls in high and very high LS susceptibility due to the prevalence of very steep slopes, high altitude, rainfall and distance from the river. On the other hand, FR model-based map showed 45.96% and BLRM showed 26.69% of the total areas fall in high and very high LSZ. But their ensembles AHP–FR map showed 39.32%, AHP–BLR map showed 32.79%, and FR–BLR showed 37.76% of total area under very high and high LSZ. The low LSZ is safe for construction and needs some geotechnical investigation before any construction. The outcome of the LSZ map** was verified applying the ROC curve and kappa statistics. The ROC curves are showing 78.86% (AHP), 80.22% (FR), 80.67% (BLR), 83.44% (AHP–FR), 84.39% (AHP–BLR) and 84.76% (FR–BLR) accuracy of models, respectively. Similarly, kappa coefficient values also show the accurateness of the produced landslide susceptible maps. Therefore, the LSZ maps can be used for LULC planning and future construction in this mountain region. The LSZ map can be efficiently used for ensuring further developmental activities. In addition, the probability map of the region will provide enough information about current and future possibility of landslides to common people, engineers and planners.