Introduction

A landslide is the downslope movement of debris, rock, or earth material under the influence of gravity (Cruden 1991). Landslides are the most common geohazards occurring in the hilly and mountainous regions and occur when the slope becomes unstable (Chawla et al. 2018). A landslide disaster is a result of intrinsic factors and external (or triggering) factors (Raghuvanshi et al. 2015; Hamza and Raghuvanshi 2017). The intrinsic factors define the favorable or unfavorable stability conditions within the slope (Raghuvanshi et al. 2014). The most common intrinsic factors are slope geometry, slope material, land use and land cover, ground water, and structural discontinuities (Anbalagan 1992). The triggering factors include seismicity (Aimaiti et al. 2019; Nakamura et al. 2014; Sassa et al. 1996), rainfall (Cardinali et al. 2006; Lee et al. 2014; Senthilkumar et al. 2018), and the activities of humans. Excavation of a slope or its toe, loading of the slope or its crest, mining, deforestation, artificial vibration, irrigation, and water leakage from utilities are all examples of human-induced activities (United States Geological Survey 2004).

Landslide disasters lead to thousands of fatalities and cost billions of dollars in property damage worldwide annually (Hong et al. 2007). Landslides play a crucial role in landscape evolution (Guzzetti et al. 2012). It may also lead to water pollution that destroys fish habitat; alters soil texture, porosity, and density; and destroys farmland and forest cover (Geertsema et al. 2009). In India, about 12.6% of the land area is prone to landslides (Geological Survey of India: https://www.gsi.gov.in). The most landslide-prone areas in India are the Himalayan region (Sarkar et al. 1995; Kaur et al. 2017) and the Western Ghats and Nilgiri range (Kaur et al. 2017). Therefore, there is a need for mapping the landslide susceptible zones so that appropriate mitigation measures for effective disaster management can be implemented.

GIS techniques can be effectively used to delineate landslide susceptible zones. Various methods adopted for delineating landslide susceptible zones include neuro-fuzzy (Pradhan et al. 2010; Oh and Pradhan 2011), artificial neural networks (Lee 2007; Shahri et al. 2019), index of entropy (Pourghasemi et al. 2012a; Jaafari et al. 2014), decision tree models (Zhang et al. 2017; Park et al. 2018), fuzzy logic (Rostami et al. 2016; Aghda et al. 2018), weights of evidence (Kayastha et al. 2012; Elmoulat and Ait Brahim 2018), support vector machine (Pourghasemi et al. 2013; Kumar et al. 2017), and logistic regression (Kouhpeima et al. 2017; Hemasinghe et al. 2018).

The analytical hierarchy process (AHP) is a multi-criteria decision-making approach that allows the user to arrive at a preference scale drawn from a set of alternatives (Semlali et al. 2019). The AHP method enables opinions to be quantified and converted into a consistent decision model, thereby helping solve complex problems (Cancela et al. 2015). The AHP techniques have been effectively used to demarcate the landslide susceptible zones (El Jazouli et al. 2019; Semlali et al. 2019; Dahoua et al. 2018; Sharma and Mahajan 2018; Achour et al. 2017; Chen et al. 2016; Kumar and Anbalagan 2016; Myronidis et al. 2016; Wu et al. 2016; Althuwaynee et al. 2014).

The frequency ratio (FR) method has also been effectively used in demarcating landslide susceptible zones (Oh et al. 2017; Khan et al. 2019; Silalahi et al. 2019; Shano et al. 2021). The FR method is a simple method utilized to determine the correlation between landslide locations and each causative factor (Rasyid et al. 2016).

The objectives of this study are to prepare the landslide susceptible zone maps of Idukki district in Kerala using the AHP and the FR methods, to analyze the influence of landslide causative factors, and to compare the prediction capability of both AHP and FR methods. To prepare the susceptible zone maps, ten causative factors are selected, namely slope angle, elevation, lithology, land use/land cover types, normalized difference moisture index (NDMI), road buffer, normalized difference built-up index (NDBI), water ratio index (WRI), stream power index (SPI), and soil.

Materials and Methods

Study Area

Idukki is the second largest district in Kerala and is situated in the southern Western Ghats (Abraham et al. 2019). The district lies between longitudes of 76˚ 35′ 0ʺ E and 77˚ 25′ 0ʺ E and latitudes of 9˚ 15′ 0ʺ N and 10˚ 25′ 0ʺ N and spans an area around 4358 km2. This district is bordered by the Tamilnadu state in the North and East, Ernakulam and Kottayam districts in the West, and Pathanamthitta district and Tamilnadu state in the South. The major rivers flowing through this district are Periyar, Thodupuzhayar, Muthirappuzhayar, and Thalayar. The district’s 14 mountain peaks exceed a height of 2000 m (Ramachandran and Reddy 2017). Anamudi, the highest peak in the Western Ghats, and the Idukki Dam, one of the highest arch dams in Asia, are in Idukki district (Abraham et al. 2021). The Western Ghats region of India is also prone to landslides and was severely affected by landslides during the 2018 southwest monsoon (Kanungo et al. 2020). A total of 47 landslide deaths were reported, and more than 1000 landslides have occurred in Idukki district during the 2018 southwest monsoon. The catastrophic Pettimudi landslide which resulted in the death of 66 residents is the major landslide reported (in number of deaths) in the Idukki district and in the state (Achu et al. 2021). The exact location of the study area is shown in Fig. 1.

Fig. 1
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Idukki district: the study area

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Data used

The study area falls over the Survey of India topographic maps numbered 58 B/16, 58 C/9, 58 C/13, 58 C/14, 58 C/15, 58 F/3, 58 F/4, 58 F/7, 58 F/8, 58 G/1, 58 G/2, 58 G/3, 58 G/5, 58 G/6, and 58 G/7 at 1:50,000 scale. The data used for this modelling includes Survey of India (SoI) topographic maps, Kerala State Land Use Board (KSLUB) soil data, Geological Survey of India (GSI) geological map of Kerala, Landsat 8 OLI (Operational land imager) satellite images, SRTM (Shuttle radar topography mission) DEM (Digital elevation model), and Google Earth Pro data. ERDAS Imagine 8.4 and ArcGIS 10.8 were used to create the thematic layers of the selected factors. The thematic layers of slope angle, elevation, NDMI, NDBI, WRI, and SPI were then classified using the ArcGIS natural breaks classification method. After assigning weights calculated by AHP and FR techniques, the thematic layers were then integrated with the map algebra tool of ArcGIS to derive the landslide susceptible zones. The prepared susceptible zone maps were validated using the landslide incidence data collected from the Bhukosh portal (https://bhukosh.gsi.gov.in/Bhukosh/Public) of GSI. The RStudio software package was used to plot the ROC curves and to estimate the AUC values for the susceptible zone maps prepared using the AHP and the FR models. The flowchart of landslide modelling is shown in Fig. 2.

Fig. 2
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The flowchart of the landslide modelling

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Causative Factors

Slope angle

In general, shear stress in soil generally increases with the angle of the slope (Lee et al. 2004). The shear stress results in the downslope movement of earth materials. Therefore, the chance of landslides is greater in areas with higher slope angles. The slope was generated from the DEM using ArcGIS spatial analyst (surface analysis) tools. The slope of the Idukki district is categorized into five classes: 0–8.90°, 8.90–16.89°, 16.89–25.18°, 25.18–35.93°, and 35.93–78.32° (Fig. 3).

Fig. 3
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Slope angle

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Elevation

Landslides generally occur at intermediate elevations, because slopes of that terrain usually contain thin layers of colluviums that are susceptible to landslides (Dai and Lee 2002). A DEM has been used to derive the elevation of the district using ArcGIS spatial analyst tools. The study area’s elevation is divided into five classes: 13–457 m, 457–904 m, 904–1306 m, 1306–1802 m, and 1802–2685 m (Fig. 4).

Fig. 4
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Elevation

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Lithology

Stronger rocks give the driving forces more resistance, which makes them less susceptible to landslides (Kanungo et al. 2006). Factors such as the genetic type of rock, the nature and existence of discontinuities such as joints or other fractures, and the degree of weathering influence the strength of a rock (Ajin et al. 2016). The lithology of this district was extracted from the geological map of Kerala at 1:50,000 scale using ArcGIS tools. The rock types present in the study area are charnockite, granite, pink granite gneiss, hornblende gneiss, and garnet-biotite gneiss (Fig. 5). Around 52.42% of the district is comprised of gneissic rock types.

Fig. 5
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Lithology

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Land use/land cover types

The land use/land cover of an area is one of the major factors responsible for slope instability. Forested areas are less prone to landslides compared to barren land. This is because vegetation with a strong root system stabilizes the slopes (García-Rodríguez et al. 2008) by binding the soil mass and thus increasing the shear strength of the soil (Turrini and Visintainer 1998). Areas with a high density of vegetation are able to sustain high water pressure during heavy precipitation (Oh et al. 2018), while barren and sparsely vegetated areas are vulnerable to weathering and instability in the slope (Anbalagan 1992). Land use plays a major role in the behavior of slopes by affecting the rate of infiltration of surface water during the rainy season (Ajin et al. 2016). Land cover change in the areas with higher slopes can result in landslides (Kanungo et al. 2009; Karsli et al. 2009).

Land use and land cover types were derived from the Landsat 8 OLI satellite image of 30-m spatial resolution. The supervised classification approach in the ERDAS Imagine software was used to classify the satellite image. The maximum likelihood (ML) classification method was applied to classify the land use/land cover types present in the district. The land use/land cover types present in the Idukki district are evergreen forest, deciduous forest, built-up area, water body, scrubland, cropland, plantation, and barren land (Fig. 6).

Fig. 6
figure 6

Land use/land cover types

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NDMI

NDMI was derived from the Landsat 8 OLI satellite image using Eq. (1) (Gao 1996). The NDMI value ranges between − 1 and + 1 (Zhang et al. 2016). The higher NDMI indicates higher soil moisture, and lower NDMI indicates lower soil moisture content (Sar et al. 2015). The NDMI of the study area ranges from − 0.38 to 0.37 (Fig. 7) and is grouped into five classes: − 0.38 to − 0.02, − 0.02–0.05, 0.05–0.12, 0.12–0.17, and 0.17–0.37.

Fig. 7
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Normalized difference moisture index

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$$\text{NDMI}=\frac{(\text{NIR }-\text{ SWIR})}{(\text{NIR }+\text{ SWIR})}$$
(1)

The chance of landslides is high in areas with higher NDMI. This is because moisture can increase the pressure of the pore water and thus reduce the strength of the soil (Ray and Jacobs 2007).

Road buffer

Roads are another important factor which causes instability on the slopes (Ortiz and Martínez-Graña 2018; Xie et al. 2018). The undercutting or excavation of slopes for road construction and the additional loads caused by the movement of vehicles can affect the slope equilibrium (Pourghasemi et al. 2012b). A road cutting can serve as a barrier, a net sink, a net source, or a water flow corridor (Pradhan and Lee 2010). This, in turn, may cause slope instability. The physiographic divisions of Kerala include the lowlands (< 7 m), the midlands (7–75 m), and the highlands (> 75 m) (Resmi et al. 2016). In this study, only the road networks within the highlands of Idukki district were selected. Road networks were digitized from the topographic maps and Google Earth Pro, and with ArcGIS Spatial Analyst (proximity) tools, the 100-m buffer distance was generated (Fig. 8). About 17% of the study area falls within the 100-m buffer distance from roads.

Fig. 8
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Road buffer

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NDBI

NDBI is used to extract impervious surface (Shahfahad et al. 2020). NDBI was extracted from the Landsat 8 OLI satellite image using ArcGIS tools and Eq. (2) (Zha et al. 2003). The NDBI ranges between − 1 and + 1 (Ibrahim 2017). The NDBI of the study area is grouped into five classes: − 0.37 to − 0.18, − 0.18 to − 0.12, − 0.12 to − 0.05, − 0.05–0.01, and 0.01–0.38 (Fig. 9).

Fig. 9
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Normalized difference built-up index

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$$\text{NDBI}=\frac{(\text{SWIR }-\text{ NIR})}{(\text{SWIR }+\text{ NIR})}$$
(2)

NDBI represents impervious surfaces such as roads and settlements, influencing water runoff (Pham et al. 2020) and these structures can decrease the stability of slopes. Hence, the chance of landslides is high in areas with high NDBI.

WRI

WRI was derived from the Landsat 8 OLI satellite images using ArcGIS tools and Eq. (3) (Shen and Li 2010). The WRI of this district ranges from 0.07 to 1.33 (Fig. 10) and is grouped into five classes (0.07–0.60, 0.60–0.64, 0.64–0.69, 0.69–0.86, and 0.86–1.33).

Fig. 10
figure 10

Water ratio index

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$$\text{WRI }=\frac{(\text{Green }+\text{ Red})}{(\text{NIR }+\text{ SWIR})}$$
(3)

The WRI above 1 represents water (Shen and Li 2010). Hence, the likelihood of landslides is more on slopes with WRI below 1, as these slopes will be more saturated.

SPI

SPI is an erosive water flow power measurement and was calculated using Eq. (4) (Moore et al. 1991). The SPI of this area has been generated from the DEM using spatial analyst tools, and the value ranges between − 31.32 and 14.84 (Fig. 11):

$$\text{SPI }=\alpha \tan\beta$$
(4)

where α is the specific catchment area (A = A/L, catchment area (A) divided by contour length (L)] and β is the local slope.

Fig. 11
figure 11

Stream power index

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The probability of landslides is high in areas with higher SPI. This is because streams can negatively affect the stability of the slope (Ortiz and Martínez-Graña 2018) by undercutting and eroding the slopes (Chen et al. 2018; Elmoulat and Ait Brahim 2018; Sifa et al. 2019) or saturating the lower part of slopes (Chen et al. 2018). The increase in the pore water pressure due to water infiltration reduces the soil’s shear strength and leads to slope failure (Chawla et al. 2018; Sifa et al. 2019).

Soil

Clay is the soil type with high porosity and low permeability and hence holds more water. The increase in pore water pressure decreases the soil’s shear strength and results in a slope failure (Chawla et al. 2018). Thus, clay acts as the potential slip zone causing landslides (Sartohadi et al. 2018). The shape file of soil data at 1:250,000 scale was collected from the KSLUB. The soil types present in the study area are clay, gravelly clay, loam, and gravelly loam (Fig. 12). Clayey soil makes up approximately 88% of the study area.

Fig. 12
figure 12

Soil texture

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AHP Modelling

The AHP method (Saaty 1980) is a decision-making tool developed to evaluate complex multi-criteria alternatives (Emrouznejad and Marra 2017). AHP can hierarchically calculate and synthesize a variety of factors of a complex decision and making it simple and easy to integrate (Russo and Camanho 2015). This method assigns reasonable weights to variables under consideration owing to its unique consistency test (Devara et al. 2021).

The processes involved in the AHP modelling include construction of a pair-wise comparison matrix, calculation of eigen vector, and weighting coefficient (Table 1), and calculation of eigen value, consistency index, and consistency ratio (Table 2). Equations (5) and (6) determined eigen vector (Vp) and weighting coefficient (Cp) (Danumah et al. 2016). Equations (7), (8), and (9) were used to determine the eigen value (λmax), consistency index (CI), and consistency ratio (CR) (Danumah et al. 2016). The major steps involved in AHP modelling are included in Fig. 13.

Table 1 Pairwise comparison matrix
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Table 2 Normalized matrix
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Fig. 13
figure 13

Flowchart of the AHP modelling

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where Slp. = slope angle; Ele. = elevation, Litho. = lithology, and RB = road buffer.

$$\text{Vp}=\sqrt[k]{W1\mathrm{x}\dots Wk}$$
(5)

where k = number of factors and W = ratings of the factors.

$$\text{Cp }=\frac{Vp}{Vp1+\dots Vpk}$$
(6)
$${\lambda max}=\frac{[E]}{k}$$
(7)
$$\text{CI}=({\lambda max}-k)/(k-1)$$
(8)
$$\text{CR}=\frac{CI}{RI}$$
(9)

where RI is the random index (Table 3).

Table 3 Random index (Saaty 1980)
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According to Saaty (1980), the CR should not exceed 10% (0.1). If the CR exceeds 10%, the judgments are inconsistent and the subjective judgments need to be revised.

The landslide susceptible zones were derived using Eq. (10).

$$\text{LSZ }=\left(0.291\times \text{Slp}.\right)+\left(0.216\times \text{Ele}.\right)+\left(0.155\times \text{Litho}.\right)+\left(0.110\times \text{LULC}\right)+\left(0.077\times \text{NDMI}\right)+\left(0.054\times \text{RB}\right)+\left(0.038\times \text{NDBI}\right)+\left(0.027\times \text{WRI}\right)+(0.019\times \text{SPI})+(0.014\times \text{Soil})$$
(10)

FR Modelling

The FR model shows the correlation between the landslide locations and the factors, based on the relationship found between landslide distribution and each causative factors (Lee and Pradhan 2006). To calculate the frequency ratio for each class of the causative factors, the following equation (Ehret et al. 2010) was used:

$$\text{FR}=(\frac{Mi}{M})/ (\frac{Ni}{N})$$
(11)

where Mi is the number of landslide pixels for each factor class, M is the number of landslides within the study area, Ni is the number of pixels for each factor class, and N is the number of pixels in total for the study area. (Ehret et al. 2010). When the FR value is more than 1, a high likelihood of landslides and higher correlations is inferred, whereas values less than 1 imply a lower correlation (Lee and Talib 2005). The frequency ratio of each class is shown in Table 4.

Table 4 The frequency ratio of each classes
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The landslide susceptible zones were derived using Eq. (12).

$$\text{LSZ }=Fr\left(Slp.\right)+Fr\left(Ele.\right)+Fr\left(Litho.\right)+Fr\left(LULC\right)+Fr\left(NDMI\right)+Fr\left(RB\right)+Fr\left(NDBI\right)+ Fr\left(WRI\right)+Fr\left(SPI\right)+Fr\left(Soil\right)$$
(12)

Validation Using the ROC Curve Method

The ROC curve method was used to validate the landslide susceptibility maps created using the AHP and FR methods. For validating the maps, the landslide incidence data collected from the Bhukosh portal of GSI was used. A total of 1304 landslide incidences have been recorded in this district. These incidences have been randomly split into a training dataset with 913 landslides (70% of the incidences) and a validation dataset consists of 391 landslides (30% of the incidences). The validation dataset was used to validate the results using the ROC curve method. RStudio was used to plot the ROC curves and to estimate the AUC values. The value of the AUC varies from 0.5 to 1.0, where the lowest value indicates random classification, while the highest value represents an excellent classification (Melo 2013). The AUC value ranges and corresponding discriminations are included in Table 5.

Table 5 AUC values and discrimination (
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Results and Discussion

This study demarcated landslide susceptible zones in the Idukki district using the AHP and FR methods. The very high susceptible zone covers 11.14% of the study area using the AHP model, and 6.57% using the FR model. The area of the district is grouped into five susceptible zones, and the area of each susceptible zone is mentioned in Table 6. The number and percentage of landslide incidences in each susceptible zone are shown in Table 7.

Table 6 Area and percentage of landslide susceptible zones
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Table 7 Number and percentage of landslide incidences in each susceptible zone
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About 71% of the landslides occurred in the high and very high susceptible zones for the AHP method, whereas 77.75% occurred in those zones for the FR method. The prepared landslide susceptibility maps are depicted in Figs. 14 and 15. This study confirmed that gravelly loam soil, followed by NDBI ranging between 0.01 and 0.38, elevation ranging between 457 and 904 m, hornblende gneiss rock type, built-up and plantation areas, slope ranging between 16.89 and 35.93°, road cuttings, and WRI ranging between 0.69 and 0.86 are the major landslide-inducing factors in Idukki district. The study area’s middle portion shows very high susceptibility to landslides due to steeper slopes, proximity to streams, and the presence of roads with vertical cuts. Most of the landslides occurred on this portion of the district.

Fig. 14
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Landslide susceptible zones: AHP method

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Fig. 15
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Landslide susceptible zones: FR method

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The FR of 1.79 and 1.62 confirmed that the probability of landslide occurrences is high in areas with moderate slopes ranging between 16.89–25.18° and 25.18–35.93°. The lower FR (0.39) indicates lower landslide probability in areas with slopes above 35°. In their study, Nakileza and Nedala (2020) also found slopes ranging between 15 and 25° as the most influencing factor in landslide occurrence. Huang et al. (2018) found that the high and very high landslide susceptible zones in the Nantian area of China are mainly distributed in areas with slopes ranging from 7.68 to 34.70°. Most of the landslides (627) occurred in areas with an elevation ranging from 457 to 904 m with a FR of 2.36. Also, the number of landslides significantly decreases as the elevation increases above 904 m. This was confirmed after analyzing the number of landslides recorded within higher elevation classes (904–1306 m, 1306–1802 m, and 1802–2685 m).

Nakileza and Nedala (2020) found that most of the landslides occurred between elevations ranging from 1500 to 1800 m. Around 70% of the landslides occurred in areas with hornblende gneiss rock type. More than 500 landslides have been recorded in plantation areas. Among the land use land cover types, the built-up area (with a FR of 1.87) followed by plantation area (FR = 1.59) has a high correlation with landslide occurrences. The hill-toe modified for infrastructure development without any lateral support and slopes modified for monoculture plantations without proper drainage provisions are the causes of landslides in the Idukki district (Abraham et al. 2019).

Road cuttings with a FR of 1.59 indicate a higher probability of landslides. The vertical cuts along the hilly roads in Idukki district make these roads susceptible to cut slope failures (Abraham et al. 2019). Sujatha and Sridhar (2021) found that around 74% of the landslides occurred in Coonoor due to road cuttings. The areas with positive NDBI (0.01–0.38) have the highest correlation with the landslide occurrence (FR = 4.3). Like this study, Huang et al. (2018) also found that landslide occurrence is high in areas with high NDBI.

Landslide occurrence in this district is highly correlated with the soil saturation. The FR (1.31) of the WRI class ranging between 0.69 and 0.86 confirmed this correlation. Though the number of landslides occurred in areas with clayey soil is 834 (91.34%), the FR (1.03) is much less than that of gravelly loam with a FR of 4.62. This is due to the fact that clayey soil accounts for approximately 88% of the district’s land area. In their study, Roy and Saha (2019) found 15.79% of landslide areas in gravelly loam soil.

The AUC values estimated through the ROC curve method (Fig. 16) confirmed that the FR method is more effective in identifying landslide susceptible zones than the AHP method (Li and He 2018). The AUC value for the FR method is 0.81, which is considered good, while the AUC value for the AHP method (0.69) is considered poor. Thus, it is confirmed that the FR method is more suitable for landslide susceptibility modelling in the Idukki district and has thus been chosen as the best method. In their study, Kumar and Annadurai (2015), and Demir et al. (2013) also found the FR method as more effective than the AHP method in landslide susceptibility modelling. The geological structures (joints, faults, and shear zones) were not considered in this study due to the non-availability of data. This is a limitation of this study.

Fig. 16
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The ROC curves

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Conclusions

In this study, landslide susceptible zones in the Idukki district, the most landslide-prone district in Kerala, were delineated using the AHP and FR methods. The factors used to model landslide susceptibility were slope angle, elevation, lithology, LULC, NDMI, road buffer, NDBI, WRI, SPI, and soil.

It was found that the gravelly loam soil, higher NDBI, elevation ranges between 457 and 904 m, hornblende gneiss rock types, built up areas, moderate slopes, road cuttings, and higher WRI were most strongly associated with landslides in this district. This study found that the FR model has greater prediction capability than the AHP model. According to the FR model, 6.57% area of Idukki district is very highly susceptible to landslides.

The landslide susceptibility maps will be extremely useful to researchers and to the agencies/departments dealing with landslides for implementing suitable mitigation strategies and to develop projects with the objective of landslide risk reduction. The result of this study will help policy makers, planners, and local government to identify the settlements and roads in the high and very high susceptible zones, thereby reducing the risk of landslides in the future.