1 Introduction

Natural disasters such as earthquakes, avalanches, landslides, and glacier lake outburst flood (GLOFs) represent a major threat to life and infrastructure damage in Himalayan terrain mainly (Chowdhuri et al. 2022a). Landslides have recently occurred in India's Himalayan hilly regions, causing destruction of infrastructure and cultural heritage (CH), loss of life, traffic challenges ranging from mildly inconvenient to catastrophic, and it impact on the economy's foundation (Kumar et al. 2018; Saha et al. 2021; Chakrabortty et al. 2022; Sonker et al. 2022). Because of intense tectonic movement, the Himalayan have terrain that is steep and a complex geological structure that causes avalanches, mass movements, and earthquakes. Among the many mountainous hazards that occur in the Himalayan region, landslides happen to be the most frequent and prominent occurrences. Overall, 80% of all landslides happen in India's Himalayan area, and particularly during the period with the most precipitation, the "Gharwal Himalaya, Himachal Himalaya, Kumaun Himalaya, Sikkim-Darjeeling, and middle Himalaya" have all seen several disastrous landslide incidents (Chowdhuri et al. 2022b; Islam et al. 2022).

In India, the Sikkim Himalaya of North-East Himalayan is one of the most susceptible regions for the landslide occurrence. This is because of transforming a forest area into cleared land, heavy rainfall, constructing more human settlement and industrialization, and changes in climate have all caused landslides here at all spatial scale (Bhattacharya 2013; Skilodimou et al. 2018; Tripathi et al. 2022). All of which have resulted in greater rock degradation and waterlogging of the soil that generates landslides on gentle to sharp and scraping gradients in the hilly terrain (Bhattacharya 2012, 2013; Chamling 2013; Mandal and Maiti 2013). Each year, hundreds of human lives are lost by landslides in the Sikkim Himalaya. More than 36,000 people have been killed in the year of 1968 due to the landslide (Bhasin et al. 2002; Kaur et al. 2019).

Therefore, the use of landslide susceptibility zonation (LSZ) is considered the initial stage in landslide risk zones preparation, analysis, and elimination. Due to this, numerous authors over the world have utilised these stages for identification of landslide susceptibility zonation (Gupta and Joshi 1990; Van Westen 1994; Binaghi et al. 1998; Gupta 2003; Sarkar et al. 2006; Lee 2005; Nefeslioglu et al. 2008, 2010; Pradhan et al. 2010; Pourghasemi et al. 2012a, b; Kayastha et al. 2013; Dou et al. 2015; Sangchini et al. 2016; Pal and Chowdhuri 2019; Basu and Pal 2020; Sonker et al. 2021, 2022). In recently, landslide susceptibility zonation (LSZ) map is a map that utilizes remotely sensed data and geographic information systems (GSI) to identify areas that are susceptible to landslides which produce better high precision outcomes. To make a landslide susceptibility zonation (LSZ) map, it is now necessary to make a factor/thematic layer of landslide causes and give each of them a calculated weight. Remote sensing is a useful tool because it works in space and time, as well as repeatedly collecting data, and it can also be used in inaccessible locations (Yalcin et al. 2011; Anbalagan et al. 2015; Zhao and Lu 2018; Mersha and Meten 2020; Gupta et al. 2022; Taloor et al. 2021a, b, c; 2022). Through the utilisation of GIS, we may collect geospatial data gathered from remote sensing and several different data products for use in assessment, modelling, simulations, and visual analytics, all of which help us arrive at more informed conclusions (Ilanloo 2011; Kannaujiya et al. 2019; Velayudham et al. 2021; Islam et al. 2022).

In this study, we utilise a frequency ratio (FR) method in remote sensing (RS) and a geographic information system (GIS) setting to determine potential landslide susceptibility zones by analysing a variety of morphometric and hydrological features. Morphometry is a term that is widely used to refer to the process of quantifying and performing statistical modelling on the arrangement of the surface of the earth, as well as the shape and size of the earth's landforms (Horton 1945; Miller 1953; Melton 1957; Clarke 1996; Agarwal 1998; Reddy et al. 2002; Yangchan et al. 2015; Farhan 2017; Bhatt et al. 2020; Sonker et al. 2023). The study of morphometric parameters measures the condition of the geo-hydrological phenomenon of a drainage basin of the study region, which also represents the predominant climate condition, lithology types, landforms, and other characteristics of the region (Horton 1932, 1945; Strahler 1952; Mueller 1968; Cox 1994; Oguchi 1997; Mishra and Rai 2020). Hydrological parameters represent sediment transportation during surface runoff and the region's moisture condition, which help understanding of the surface condition of the drainage basin (Rekha et al. 2011; Sreedevi et al.2013; Soni 2013). The goal of the research is to learn how the combination of morphometry and hydrological parameters can help us understand landslide susceptibility zonation mapping.

Researchers have used morphometric parameters to learn more about areas of the Himalayas that are prone to landslides (Ghosh 2015; Das and Lepcha et al., 2019). Therefore, the researcher has used morphometric parameters such as drainage density, drainage frequency, junction frequency, relative relief, relief ratio, altitude, texture, slope, and other responsible factors for landslides to generate the landslide susceptibility zonation map (Devkota et al. 2013; Anbalagan et al. 2015; Ghosh 2015; Rawat et al. 2017; Das and Lepcha et al. 2019; Saha et al. 2022). The hydrological parameters TWI (topographic witness index), SPI (stream power index), STI (stream transportation index), and rainfall have also been used by several researchers to generate the LSZ map (Rożycka et al. 2017; Kalantar et al. 2018; Das and Lepcha et al. 2019; Moazzam et al. 2020, Sur et al. 2020; Sonker et al. 2022). The major causes of landslide in the Sikkim Himalaya are the rainfall in rainy season, so this factor plays major role for help to understand the morphometric and hydrological analysis for the LSZ mapping in this region.

The objectives of this study are: (1) the integration of the morphometric and hydrological parameters for the mapping of the landslide susceptibility zonation with the help of remote sensing data and GIS, (2) this map of landslide susceptibility zonation is validated and calculated with accuracy using the landslide inventory location for predicting the possibility of landslide susceptibility in interior regions of the state of Sikkim.

2 Materials and methods

2.1 Study area

The Sikkim Himalaya (Fig. 1) lies mostly in the Lesser and Greater Himalaya of the North-Eastern Himalayan, and is made up of a younger mountain structure with faulting and folding. The topography of the region is entirely hilly, with less flat areas, and the elevation varies from 240 to above 8000 m, above mean sea level (msl). The area's latitude and longitude are 27° 5′ to 28° 10′ and 88° 01′ to 88° 58′. The length of the state from north to south is 113 kms, while the width of the region from east to west is 65 kms. The total land area of the region is 7096 square kilometres. Nepal, Bhutan, Tibet, the state of West Bengal surrounds it on the west, east, north, and south, respectively. The state of Sikkim has four districts: North, East, South, and West Sikkim. Sikkim's largest district is North Sikkim, which has a land area of 4226 km2 and contributes for almost 60% of the surface area of the state. The remaining three districts have included East, West, and South Sikkim, each of which covers around 13%, 16%, and 11% of the total surface area, respectively. Gangtok, the state capital and most important city, is located in North Sikkim district. The region contains two rivers such as the Teesta River and Rangit River. The landforms and river systems of the Teesta River are primarily distinguished by the presence of four-tiered terraces, canyons or gorge-valleys at various elevations, asymmetric valleys, polyprofilic U-shaped valleys and steps or troughs, lakes, alluvial cones, truncated ridge-spurs, and terracettes (soil landscape systems). The river exhibits many different types of river systems, ranging from straight to meandering and braided channels, including rectangular-barbed-parallel-trellis-radial to sub dendritic river systems. Each of the above physical characteristics shows that degradation, erosion, and deposition are still happening in the region, which makes it very fragile. The climate of the area can be generally classified as tropical, temperate, or alpine zone. Humidity and cold dominate the weather pattern for the majority of season. The majority of the region has consistently high rates of rainfall from May to October.

Fig. 1
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Study map of the Sikkim Himalaya with location of the landslide inventory and drainage order of the region

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2.2 Landslide inventory data

The concept of "landslide inventory location" refers to the historical data on landslides that have happened in various locations and at different periods. It is used for the forecasting of the LSZ mapping and evaluations of risk (Wu et al. 2016; Sonker et al. 2021). Landslide’s locations for the inventory (Number of landslides are 688 and locations show in Fig. 1) were gathered from the Bhukosh portal (Geological Survey of India) and utilized to assessment and validity of the present research. These inventory locations are separated among two separate categories as random, such as training data, which is utilized 70% (479) to generate the FR model, and validation and result verification, utilizing 30% (209) of the data. The aim of the current inventory was to forecast and minimize the potential of future landslides.

2.3 Steps for identification of landslides susceptibility mapping

The Sikkim Himalaya regions that are susceptible to landslides prone are identified using a frequency ratio and geospatial tools method based on the assessment of morphometric and hydrological parameters. Frequency ratio model is used to analyse the landslide susceptibility map in this area with the help of the Arc GIS tools. In this model, weights of the factors are calculated on the basis of landslide inventory location and factors classes of the morphometry and hydrological parameters. Therefore, each step of the methodology for the LSZ mapping are given below:

2.3.1 Generating thematic layers

The drainage order of the study area was extracted using Alos Palsar (spatial resolution of 12.5 m) DEM (Digital Elevation Model) data and the order is seven which is validated with toposheet of Sikkim (Survey of India) (Because they belong to a border state, not all toposheets are available.). The Alos Palsar-DEM data was downloaded from Earth Data (https://asf.alaska.edu/data-sets/sar-data-sets/alos-palsar/). The drainage system and DEM data of the study area used to generate different raster maps of morphometric parameters (factors of drainages and relief) with the help of different formula given in Table 1 and the class of the factor in Table 2, such as absolute relief (Ar), relative relief (R), relief ratio (Rh), dissection index (Di), hypsometric integral (HI), slope index (Sl), drainage density (Dd), drainage frequency (Fs), drainage intensity (Di), drainage texture (Dt), infiltration number (If), junction frequency (Jf), length of overland flow (Lg), ruggedness index (Rn), with the help of the Arc GIS Software, as shown in Fig. 2a–n. The hydrological parameters such as stream transport index (STI), topographic wetness index (TWI), stream power index (SPI), were generated using DEM data with the help of the Arc GIS, as shown in Fig. 2o–q. Rainfall (Rf) map was generated using rainfall data using Arc GIS, as shown in Fig. 2r. Daily rainfall data from 1988 to 2018 was collected by IMD, Pune (Indian Metrological Department, Pune (https://www.imdpune.gov.in/).

Table 1 The process of determining various morphometric (drainage and relief factors) and hydrological parameters
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Table 2 Range values of the classes of various morphometric (drainage and relief factors) and hydrological parameters
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Fig. 2
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Factor/thematic layer for different morphological and hydrological parameters: a absolute relief, b relative relief, c relief ratio, d dissection index, e hypsometric integral, f slope index, g drainage density, h drainage frequency, i drainage intensity, j drainage texture, k infiltration number, l junction frequency, m length of overland flow, n ruggedness index, o SPI, p STI, q TWI, and r rainfall for the landslide susceptibility zonation mapping in Sikkim Himalaya

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2.3.2 The logic that involved into choosing of the different factor/thematic layers

Landslides typically happen owing to a range of variables, such as high precipitation and subsoil wetness, gradient variability, landscape degradation, forest degradation, subsurface composition, etc. in different areas of the study region. The morphometric and hydrological parameters are preferred based on this above condition. Landslide-causing circumstances can be assessed with the use of these variables. Explanation of the logic involved into choosing of such factor/thematic layers are shown in Table 3.

Table 3 The logic for choosing the factors of morphometry and hydrological parameters
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2.3.3 The scale/weight procedure as well as its justification of the factors in FR model

All the thematic layers are classified into 10 classes. The scale/weight has been classified into a 10 ranked scale where 0 is the lowest and 1 is the highest effect of the landslide occurrence with respect to the factors which are selected for landslide phenomenon occurrences. Table 4 below illustrates the weight procedure and the logic for the scale/weight.

Table 4 The scale/weight process for factors as well as its justification of the factors for morphometry and hydrological parameters
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2.3.4 Frequency ratio (FR) Model

The Frequency ratio (FR) model is utilized in this study. The FR model is the statistical method that is currently being utilized to evaluate landslide susceptibility zonation (LSZ). This model is used to figure out the relationship between the reported geographical distribution of prior landslides and all of the factors that are considered to be the primary contributors to the occurrence of landslides. Many researchers have utilized this model for LSZ mapping ( Yilmaz 2009; Mezughi et al. 2011; Choi et al. 2012; Mohammady et al. 2012; Yalcin et al. 2011; Lee 2014; Anbalagan et al. 2015; Das and Lepcha 2019; Mirdda et al. 2020; Sonker et al. 2022).

The FR method can be utilized for figure out how much that every component has an impact in zonation mapping of landslides. The FR model is calculated (Table 5), given below:

$${\text{FR}} = \frac{a/b}{{c/d}}$$

where frequency of landslides for each factor class (a), sum of all landslides that are present in the factor (b), frequency of pixels of each class of factor having landslides happen (c), and the sum of all number of the pixels that are present in the factor (d).

Table 5 Calculations of the FR and FRn values for different factor classes for landslide susceptibility zonation mapping in the Sikkim Himalaya
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Greater correlations between landslide phenomena and influencing factors are shown by FR values greater than one, whereas lower correlations are indicated by FR values less than one (Fig. 3).

Fig. 3
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a Figure of the FR values of different relief factor with class of the factors, b figure of the FR values of different drainage factor vrs class of the factors c figure of the FR values of different hydrological factor vrs class of the factors

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The calculated FR values, it’s are normalized and the normalized FR is calculated (Table 5) as given below:

$$\mathrm{FRn }= \frac{{\text{FR}}}{\mathrm{\Sigma Class FR}}$$

Therefore, the landslide susceptibility index (LSI) map is generated by adding all values of normalised FR with their factor. This is a quantity that has no dimensions and is utilised for the categorization of landslide susceptibility zonation:

$${\text{LSI }} = \, \Sigma {\text{ FR}}\neg {\text{n}}$$

where FRn represents the normalization of FR for each factor class.

There are different ways to categorize the landslide susceptibility index, but in this study, the natural break is used.

3 Result and discussion

3.1 Frequency ratio model for landslide susceptibility mapping

The frequency ratio model was utilised to categorize the susceptibility map into the following five categories: “very high,” “high,” “moderate,” “low,” and “very low” (Fig. 4). These categories, when applied to the region as a whole, represent, respectively, 13.20%, 19.75%, 30.81%, 27.14%, and 9.09% of the total area as shown in Fig. 5a. The lower side of the study region, mainly West, South, and East Sikkim, may have higher chances of the occurrence of a landslide with very high to high susceptibility (about 32.95% of the total study area) (Fig. 5a). These regions represent about 86.78% of the total number of prior landslides that are shown in Fig. 5b. It contains the highest density of landslide inventory locations (Fig. 6). The FR model indicates how probable or essential each class is to trigger a landslide based on our variables for multiple classes of each factor. In the case of the relief parameters (Fig. 2), landslide susceptibility zones vary from different relief classes. Low class (1 to 3) of the absolute index (Fig. 2a), the FR value greater than 1 is most effective (very high to high zones, FRn values vary from 0.6 to 1), but FR values less than 1 (in the high absolute index class) are least affective (moderate to low zones, FRn values varies from 0 to 0.6) for the landslide susceptibility, as shown in Fig. 3a and Table 5. Landslides are most common in low-absolute-index (low-altitude) areas. This region is mostly found along the drainage valleys (Teesta and Rangit Rivers) and moderate hill areas of Sikkim's southern region (West, South, and East Sikkim), as shown in Fig. 1. This factor is most responsible for landslide occurrence in the study region. The relative relief and relief ratio (Fig. 2b, c) is very high from classes 4 to 6, indicating moderate relief in Sikkim's southern region, but the graph shows the same variation in FR values, shown in Fig. 3a. The FR values of these classes are greater than 1, which indicates higher chance of the landslide’s occurrence because that indicates the effects of erosion or uplift and also indicates the tectonics of the area. FRn values of these classes vary from 0.6 to 1, which is a higher correlation for very high to high susceptibility for landslide occurrences. Classes 1, 2, 3, 7, 8, 9, and 10 of the factors occur in the moderate to low region of the susceptibility for landslides because the FR values are less than 1 and the FRn values lie from 0 to 0.6 (Table 5). This region is shown in the northern region of the study area, which has shown moderate-to-low chances of landslides occurrence. The dissection index (Fig. 2d) of the area is very high, as are the valleys of the region, particularly the Teesta and Rangit River basins, where FR values are greater than 1, indicating the possibility of landslides due to slope degradation or separation degree of landscape changes, as shown in Fig. 3a and Table 5. The FRn of the dissection class such as classes 9 and 10 varies from 0.6 to 1, which indicates a very high to high susceptibility for landslides. The classes 1, 2, 3, 4, 5, 6, 7 and 8 of the dissection occurred in the moderate to low susceptibility region for landslides because the FRn values lie from 0 to 0.6 (Table 5). The hypsometric integral (Fig. 2e) of the area is very high along the valley (Teesta and Rangit River) and on moderate terrain in the region where FR values are greater than 1 (Fig. 3a and Table 5) because it generates a significant amount of surface runoff, which caused sediment erosion and also indicates the tectonic evolution of the region. The tectonic evolution of the rocks indicates a decrease in rigidity, which causes landslides. The FRn value for the classes of the hypsometric integral, such as classes 6 and 10, varies from 0.6 to 1, which indicates a very high to high susceptibility for landslides, and the FRn value for the classes 1–5 of the hypsometric integral varies from 0 to 0.6, which indicates a moderate to low susceptibility. The slope (Fig. 2f) of the area is varying from 0 to 84 degrees, in which the moderate to high gradient is more prone to landslides occurrences where the FR values are greater than 1, as shown in Fig. 3a and Table 5. The very high to high susceptibility zones occur in class 4 to 8 of the slope gradient where the FRn values from 0.6 to 1 and the FRn value for class 1, 2, 3, 9, and 10 of the slopes varies from 0 to 0.6 (Table 5), which indicates a moderate to low susceptibility. The drainage density (Fig. 2g) of the area ranges from 0.71 to 4.24 km/km2, and drainage density classes 1, 5, and 9 are more vulnerable to landslides due to FR values larger than 1. As indicated in Fig. 3b and Table 5, the very high, high, and moderate susceptibility zones occur in this class 1,4, 5, 6, and 9 of drainage density where the FRn is more than 0.4 and FRn value less than 0.4 indicating low to very low susceptibility of landslide occurrence. The drainage frequency (Fig. 2h) of the area ranges from 0 to 9.57 (number of drainages/km2), and the drainage frequency of classes 4, 7, 8, 9, and 10 are more susceptible to landslides due to FR values greater than 1. The very high, high, moderate susceptibility zones occur in the class from 2 to 10 of the drainage frequency where the FRn is more than 0.4, this mainly occurs along the valley slope of the southern region of the drainages in the area. FRn value of class 1 is less than 0.4 indicating low to very low susceptibility to landslide occurrence mostly occurs in the northern region of the area as shown in Fig. 3b and Table 5. The drainage intensity (Fig. 2i) of the region ranges from 0 to 4.76, and classes 6, 7, 8, and 9 are more prone to landslides due to FR values greater than 1. The very high, high, and moderate susceptibility zones occur in the class from 6 to 10 of the drainage intensity where FRn is more than 0.4. The drainage texture (Fig. 2j) of the region ranges from 0 to 2.13 (No. of drainages/km), and classes 4, 7, 8, and 9 are more prone to landslides due to FR values greater than 1 (Fig. 3b and Table 5). The very high, high, and moderate susceptibility zones occur in the class from 2 to 10 of the drainage texture where FRn is more than 0.4 and the class 1 of the drainage texture is very low to low susceptibility zones because the FRn value is less than 0.4 (Table 5). The drainage texture and frequency of the region show the same FRn value shown in the graph (Fig. 3b). Infiltration number (Fig. 2k) of the area varies from 0 to 37, and classes 3, 4, 5, 6, 8, and 9 are more prone to landslides due to FR values greater than 1 (Fig. 3b, Table 5). Class 9 of the infiltration number is higher infiltration numbers indicating lower infiltration and higher run-off, which lead to higher occurrences of landslides. The junction frequency (Fig. 2l) of the area varies from 0 to 9, and classes 6 to 10 are more prone to landslides due to FR values greater than 1 (Fig. 3b, Table 5). The very high, high, and moderate susceptibility zones occur in the class from 4 to 10 of the junction frequency where FRn is more than 0.4 and the class 1 to 3 of the junction frequency is very low to low susceptibility zones because FRn value is less than 0.4 (Table 5). Length overland flow (Fig. 2m) varies from 0 to 2.12, and very high, high, and moderate susceptibility zones occur in classes 1, 4, 5, 6, and 9 because FRn values are greater than 0.4. Roughness index (Fig. 2n) varies from 0.0098 to 0.9902, and very high, high, and moderate susceptibility zones occur in classes 1 to 8 because FRn values are greater than 0.4 (Table 5). Low to higher roughness area is highly susceptible to landslides in this area which lies on the river valley side of the region. The SPI (Fig. 2o) of the region varies from − 3.51 to 13.30, and classes 3, 4, 5, 6, and 8 are more prone to landslides due to FR values greater than 1 as shown in Fig. 3c and Table 5. Class 3–10 of SPI has zones of very high, high, and moderate susceptibility for the occurrence of the landslide because FRn values are more than 0.4 (Table 5). The SPI of the region increases whenever there is an increased risk of landslides occurring in the region. The STI (Fig. 2p) of the region varies from 0 to 409.92 and classes from 2 to 6 are more prone to landslides due to FR values greater than 1 as shown in Fig. 3c and Table 5. Class 1–6 of STI factor has zones of very high to moderate susceptibility for the landslide because FRn values are more than 0.4 (Table 5). The region’s TWI (Fig. 2q) ranges from 1.11 to 18.81, and classes 1 through 9 have zones of very high, high, and moderate sensitivity because FRn values are larger than 0.4 (Table 5). This region has a low to higher TWI, which implies a high susceptibility to landslides. Class of Rainfall 1, 3 to 6 and 10 shows the very high to moderate risk zones of landslide and second most responsible parameter for landslide occurrences as shown in Fig. 2r, 3c and Table 5.

Fig. 4
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Landslide Susceptibility map of Sikkim Himalaya

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Fig. 5
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a Landslide susceptibility zones in area (%) of the Sikkim Himalaya, b Landslide susceptibility zones in area (%) with respect to number of past landslides in (%) of the Sikkim Himalaya

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Fig. 6
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a. The successive rate curve for FR model for LSZ mapping of Sikkim Himalaya, b. validation rate curve for FR model for LSZ mapping of Sikkim Himalaya

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3.2 Importance check of the thematic layers using sensitivity of map removal analysis

The purpose of this method is to explore the consequences of eliminating any of the thematic layers used to estimate the landslide risk zones (LSZ). After deleting each thematic layer, a new LSZ map with the remaining layers overlay is generated. Now, the sensitivity index is estimated using equation () every time.

$${\text{SI}}=\frac{\left|\left(\frac{{\text{LSZ}}}{N}\right)-\left(\frac{{\text{LSZ}}{\prime}}{n}\right)\right|}{{\text{LSZ}}} \times 100$$

where SI represents the sensitivity index linked including an omitted thematic layer, LSZ represents landslide susceptibility zones mapping using each the thematic factors, LSZ′ represents landslide susceptibility zones mapping by eliminating one thematic layer at once, N represents the number of factors utilized in the production of the LSZ map, while n represents the number of factors evaluated in the creation of the LSZ map. The estimated values of all factors, such as Min, Max, Mean and Standard deviation (Table 6). The absolute index and rainfall are the two most sensitive parameters, with standard deviations of 0.44 and 0.42 (Table 6) for thematic layers when mapping landslide susceptibility zones, respectively. The relative relief, relief ratio, dissection index and hypsometric integral are moderately sensitive parameters because the standard deviations of the thematic layers are 0.32, 0.33, 0.31 and 0.30 (Table 6). However, slope index, drainage density, drainage frequency, drainage intensity, drainage texture, infiltration number, junction frequency, length of overland flow, ruggedness index, SPI, and TWI are showing equal importance according to the standard deviation, shows the almost same value, which varies from 0.28 to 0.29 (Table 6) for the sensitivity analysis for the landslide susceptibility zones mapping.

Table 6 Statistical analysis of map removal sensitivity analysis for the Landslide susceptibility zonation mapping
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3.3 Validation of landslide susceptible model using ROC

The validation of the landslide susceptible zones created by the FR model and previous landslide location can be assessed using the receiver operating characteristic (ROC) curve, which is a commonly used statistical tool. The ROC curve was prepared with the use of the Arc SDM tool, which can be add within the Arc GIS software. For this work, the total number of previous landslide locations is 688 and these landslides were randomly divided into two distinct types of data sets: 70% for training data (479 landslides) and 30% for validation data (209 landslides). The area under the curve (AUC) was utilised to execute an analysis of the efficiency of this model (AUC). This curve represents an approximation of the proportion of the method's successive rate as well as its prediction rate. Training and validation data sets are used to execute the model's successive and predication rate. The FR model performs well when the AUC value is closer to 1. The AUC successive rate and validation rate are approximately 82.00% and 84.6%, respectively, as shown in Fig. 6a, b.

4 Conclusion

In this study, morphological and hydrological parameters were considered to generate the landslide susceptibility zonation in Sikkim Himalaya using frequency ratio model and geospatial technologies. The LSZ map has been classified into five different categories such as ‘very high (13.20%)’, ‘high (19.75%)’, ‘moderate (30.81%)’, ‘low (27.14%)’, and ‘very low (9.09%)’. According to this research, the most risky zones for the landslide-prone area are located in the southern region of Sikkim (the South, West, and East Districts of Sikkim). These prone areas of landslides mostly occur in the river valley (mostly in the southern region of the Upper Teesta and Rangit river valleys) and due to deforestation, complex geological and tectonic settings, farming, and other human activities. These most sensitive areas of the relief parameters indicate less than 2500 m of absolute index, classes 5 and 6 (800–960, 960–1100) of relative relief, classes 4 and 5 (0.0060–0.0074, 0.0074–0.0088) of relief ratio, classes 6 to 10 (0.39–0.46, 0.46–0.53, 0.53–0.61, 0.61–0.68, > 0.68) of the dissection index, classes 6, 7, 9 (0.44–0.47, 0.47–0.50, 0.53–0.56) of hypsometric integral, classes 4 to 8 (23–28, 28–33, 33–38, 38–43, 43–49) of slope index in which the FR values greater than 1. However, most sensitive areas of the drainage parameters indicate classes 1, 5, 9 (< 1.28, 1.88–2.06, 2.72–3.14) of drainage density, classes 4,7 to 10 (3.38–3.94, 4.92–5.44, 5.44–6.04, 6.04–6.87, > 6.87) of the drainage frequency, classes 6 to 9 (2.33–2.54, 2.54–2.74, 2.74–2.99, 2.99–3.30) of drainage intensity, classes 4, 7 to 10 (0.75–0.88, 1.10–1.21, 1.21–1.35, 1.35–1.53, > 1.53) of drainage texture, classes 3 to 6 ( 6.32–8.04, 8.04–9.77, 9.77–11.64, 11.64–13.65) and 8 to 9 (15.95–18.96, 18.96–23.42) of infiltration number, classes 6 to 10 (4.90–5.40, 5.40–5.91, 5.91–6.42, 6.42–7.06, > 7.06) of junction frequency, classes 1, 5, 9 (< 0.64, 0.94–1.03, 1.36–1.57) of the length of overland flow, and classes 1 to 3 (< 0.2597, 0.2597–0.3443, 0.3443–0.402) and 5 to 6 (0.4481–0.4865, 0.4865–0.5250) in which classes the FR values is greater than 1. Other most sensitive areas of the drainage parameters indicate classes 3 to 6 (2.29–3.15, 3.15- 3.94, 3.94- 4.80, 4.80–5.65) and 9 (7.63–8.88) of SPI, classes of 2 to 6 (1.61–8.04, 8.04–17.68, 17.68–28.94, 28.94–43.40, 43.40–61.09) of STI, classes 1, 2, 7, 8 (< 4.23, 4.23–5.00, 8.61–9.72, 9.72–11.04) of TWI, and classes 1 (< 2473), 4 to 8 (2685–2819, 2819–2959, 2959–3088, 3088–3223, 3223–3363), 10 (> 3492) of rainfall in which the FR values is higher than 1. Single thematic layer removal analysis is used for thematic layer sensitivity for landslide susceptibility zonation mapping. The absolute index and rainfall are highly influential factors for landslides. This finding is validated by using the ROC curve, which provides an accuracy assessment of around 84.6% for the model. The future scope of the landslide susceptibility zonation mapping of this study may indicate advanced predictive modelling and early warning systems, integrating with remote sensing, GIS, and FR model technologies. Additionally, this research may focus on sustainable mitigation strategies and policy frameworks to minimize the impact of landslides in vulnerable regions, fostering a safer environment for communities in this region.