Introduction

Landslides account for considerable loss of life, damage to roads and human settlements in India. India suffers 20–30 million US dollars of monetary loss every year from landslides (Parkash 2011). Landslide susceptibility is defined as the occurrence of landslides in an area based on the landslide-controlling parameters. Researchers have developed different methods to assess landslide susceptibility and hazard using statistical techniques and GIS tools (Daneshvar and Bagherzadeh 2011; Ştefan et al. 2018; Arabameri et al. 2019; Chen et al. 2019; Zhang et al. 2020; Ozioko and Igwe 2020). Landslide susceptibility zonation (LSZ) mapping uses a landslide inventory and controlling parameters together with a prediction of the spatial areas with a likelihood of landslides in the future. LSZ is dependent on several controlling parameters, including topography, geology, tectonic feature, hydrology, vegetation cover, seismic and rainfall.

Two crucial phenomena take place after an earthquake. The first issue is that many landslides occur after an earthquake and these landslides remain active for some time. The second issue is related to the slopes where no co-seismic landslides have developed, but are still prone to landslide after intense rainfall periods following the earthquake. To explain these rationally well, there is a need to examine the effect of both triggering parameters on landslide susceptibility.

Rainfall- and earthquake-induced landslides are different in terms of mechanics and dynamics (Chang et al. 2007). Many researchers have emphasized the individual triggering parameter for producing LSZ maps (Glade et al. 2000; Yamagishi and Iwahashi 2007; Kamp et al. 2008; Peethambaran et al. 2019; Sangeeta and Maheshwari 2019; Sangeeta et al. 2020). Previously, earthquake-induced landslide (EIL) related studies were focused on the identification and description of co-seismic landslides (Keefer 2000; Qi et al. 2010; Ayalew et al. 2011). Moreover, only very limited research work has been reported to assess the susceptibility based on the collective effect of rainfall- and earthquake-triggered landslides (Lin et al. 2006; Li et al. 2012; Zhang et al. 2014, Martino et al. 2020).

Previously available literature was primarily focused on either rainfall- or earthquake-induced LSZ model. Single triggering-based modelling is found insufficient in places where both triggering parameters play a significant role in triggering landslides, such as the Indian Himalaya. Generally, this type of model provides only limited information about landslide spatial distribution and minimizes the probable combined effect of rainfall- and earthquake-induced landslides. The long-term impact of an earthquake on slope stability during the wet season is significant (Lin et al. 2006). It was reported that there was heavy rain before and after the Sikkim earthquake in 2011 and the region is mountainous. The quake triggered massive landslides (Maheshwari et al. 2013). Therefore, the proposed methodology would be very beneficial in the region where the combined triggering parameters are present.

Statistical techniques are widely used to assess landslide susceptibility. It is a quantitative approach for producing reliable outcomes. The frequency ratio (FR) method falls in the bivariate statistical analysis category, which is one of the popular techniques for LSZ assessment due to ease of implementation in a GIS environment (Lee and Pradhan 2006; Yilmaz 2009; Das and Lepcha 2019; Pal and Chowdhuri 2019). The FR method not only produces LSZ maps, but also encompasses the sensitivity of landslide failure to individual landslide-related parameters (Razavizadeh et al. 2017). Gholami et al. (2019) and Ding et al. (2017) performed a comparison and applicability of landslide susceptibility models and their results show that FR gives higher prediction rates and accuracy. Therefore, the FR model has been adopted in the study area.

Sangeeta et al. (2020) have developed a pre- and post-earthquake LSZ map with reference to the 1999 Chamoli earthquake for the same study area. In this work, the effect of rainfall parameter on LSZ mapping was not assessed. Thus, the combined effect of both rainfall and earthquake in triggering the landslides in the Himalaya region has not been considered, which is a primary novelty of the present work.

With this background, the primary aim of this study is to compare the variations in spatial distribution between rainfall-induced landslide (RIL) and earthquake-induced landslides (EIL) along with other controlling parameters in the same study area. The effects of rainfall-triggering parameter individually and along with seismic parameters have been examined. Furthermore, landslide susceptibility models for the different combinations of controlling and triggering parameters are generated and compared. Multi-triggering event-based LSZ maps developed in this study are of great importance for the planners, engineers and local government.

Study area

For the present study, a part of the Chamoli district of Uttarakhand state in India, with an extent of about 1015 km2 was selected. Chamoli and Joshimath are the two major towns falling in the study area (Fig. 1). The elevation varies from 787 to 5717 m above the mean sea level. The study area is drained by Alaknanda River, along with its tributaries. The study area is subjugated with landslide-prone parameters such as highly dissected steep hill slopes, barren land, rainfall and severe earthquake zone. The study area is seismically very active and falls in Seismic Zone V (BIS 2016). On 29th March 1999, an earthquake of magnitude 6.8 occurred in this area. The rescue and relief operations were hampered due to the steep mountainous terrain and landslides triggered by the earthquake, which blocked many travel routes. Many earthquake-induced landslides weren reported due to the 1999 Chamoli earthquake (Shrikhande et al. 2000, Barnard et al. 2001). Recently on 9th September 2020, two people died and five others awere suspected to be trapped in rubble after a cloudburst in Chamoli district led to a landslide.

Fig. 1
figure 1

Study area map. a Uttarakhand state in India. b Study area in Chamoli district, Uttarakhand. c Towns, drainage network and elevation classes of the study area

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Methodology

The present study targets at analyzing the variations of landslide spatial distribution due to rainfall and earthquake and to produce and compare LSZ maps for different combinations of controlling parameters and landslide inventories. In this study, a total of nine landslide-controlling parameters including slope angle, slope aspect, slope curvature, geology, NDVI, distance to drainage, distance to tectonic, seismic parameter (PGA) and rainfall were selected for the LSZ mapping. These landslide-controlling parameters were further divided into classes. Two types of landslide inventories awere included in this study, RIL and earthquake-induced landslide (EIL) (details are given in Rainfall- and earthquake-induced landslide inventories and Landslide-controlling parameters sections). This study utilized a GIS-based bivariate statistical approach, i.e. relative frequency ratio (RFR) method to generate LSZ maps.

Relative frequency ratio method

The frequency ratio (FR) is based on the correlation between the landslide incidences and controlling parameters of landslides. Equation 1 represents the formulation of the FR model.

$$FR_{{i,j}} = \frac{{{\raise0.7ex\hbox{${N_{{i,j}} }$} \!\mathord{\left/ {\vphantom {{N_{{i,j}} } {\mathop \sum \nolimits_{{j = 1}}^{{j = n}} N_{{i,j}} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\mathop \sum \nolimits_{{j = 1}}^{{j = n}} N_{{i,j}} }$}}}}{{{\raise0.7ex\hbox{${A_{{i,j}} }$} \!\mathord{\left/ {\vphantom {{A_{{i,j}} } {\mathop \sum \nolimits_{{j = 1}}^{{j = n}} A_{{i,j}} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\mathop \sum \nolimits_{{j = 1}}^{{j = n}} A_{{i,j}} }$}}}},$$
(1)

where FRi,j represents the frequency ratio of the jth parameter class of the ith controlling parameter. Ni,j is defined as the number of landslides in the jth parameter class of the ith parameter and Ai,j is an area of the jth parameter class of the ith parameter. n represents the total number of parameter classes in a particular parameter.

In the next step, FR values were normalized in the range of values (0, 1) as relative frequency ratio (RFR). The RFR is calculated using the following Eq. (2):

$${\mathrm{RFR}}_{i,j}=\frac{{\mathrm{FR}}_{i,j}}{ \sum_{j=1}^{j=n}{\mathrm{FR}}_{i,j}}.$$
(2)

LSI is defined as the landslide susceptibility index and calculated, adding values of RFR related to all the controlling parameters for a particular pixel. It shall be noted that for a particular pixel, the value of parameter class (j) for a particular controlling parameter (i) takes only one value depending on the location of the pixel. Thus, subscript (j) will get a particular number (j = 1, 2, 3…) and will be dropped before summing up the values of RFR for all controlling parameters (m) using Eq. 3.

$$\mathrm{LSI}= \sum_{i=1}^{i=m}{\mathrm{RFR}}_{i}.$$
(3)

All the landslide-controlling parameters are converted into equal cell (pixel) size, i.e. 30 m × 30 m. Therefore, the area of each cell (pixel) is 900 m2. The total study area of 1014.72 km2 accounts for 1.127 × 106 number of pixels. So, all the landslide-controlling parameter maps have the same area and number of pixels. Therefore, all the cells (pixel) are standardized in terms of size and area.

Different types of mapping units such as grid cell (pixels), slope unit, terrain units, unique condition units, geo-hydrological units, topographical units and political or administrative units may be adopted (Guzzetti et al. 1999). For statistical and physical-based approaches, grid cell or pixels mapping units in the raster datasets are most appropriate (Reichenbach et al. 2018). On a similar line, the present study has also adopted the grid cell (pixels) mapping unit. In previous studies, many researchers have adopted the same approach where controlling parameter maps have been classified into 30 m × 30 m (Mersha and Meten 2020).

Modelling strategy

To describe the influence of rainfall and earthquake parameters on LSZ mapping, five models based on five combinations of landslide-controlling parameters and landslide inventories were used in this study. The modelling strategy is summarized in Table 1 and encompasses five models. Model 1 excluded the rainfall and seismic parameter and incorporated only the RIL inventory, whereas Model 2 included rainfall parameter and only the RIL inventory. The third model utilized the seismic parameter and only the EIL inventory. The fourth model was prepared to utilize the seismic parameter and considered both the RIL and EIL inventory. Subsequently, the fifth model was developed by using both seismic and rainfall parameters along with the RIL and EIL inventory. From the 276 landslides, 196 (~70%) were selected as a training dataset for developing the LSZ model, and the remaining 80 (~30%) were used to test the model. This will be proportionally reduced when only RIL and EIL datasets are considered. In statistics in general, the more the data points used, the more accurate are the resulting estimates. From this viewpoint, 70% of data for training purposes were selected in this study. Degree of fit, success and prediction rate curves were adopted to validate the LSZ models.

Table 1 Details of modelling strategy for LSZ maps
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Landslide inventories and controlling parameters

The landslide inventory is utilized to assess the influence of nine controlling parameters on landslide occurrence. So, this is the essential requirement for landslide susceptibility studies. The reliability and accuracy of the landslide inventory affect the success rate of LSZ mapping.

Rainfall- and earthquake-induced landslide inventories

For this study, a GIS-based map of landslide inventory was collected from Barnard et al. (2001), which is a methodical mapping of existing landslides in the study area at the time of 1999 Chamoli earthquake. According to the landslide inventory, 220 landslides that occurred before the Chamoli earthquake were rainfall induced and 56 were earthquake induced. The details are given in Fig. 2. Figure 2a illustrates the locations of RIL and EIL in the area, while Fig. 2b groups RIL and EIL in terms of types of the landslide; it can be observed that for both cases, about 50% of the landslides are debris avalanches. The seismicity of the area was studied, and the earthquakes recorded before 1999 were with a magnitude less than 5 and were expected not to trigger landslides. Therefore, the landslides that occurred before the 1999 Chamoli earthquake were verified to be rainfall induced. Both landslide inventories were incorporated individually and in a combination to produce susceptibility models using a GIS-based bivariate statistical method.

Fig. 2
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Landslide inventory. a Spatial distribution of RIL and EIL. b Statistical details of type of landslides

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Landslide-controlling parameters

Landslide incidences and frequency of the landslides are considerably controlled by the topography, geology, tectonic feature, hydrology, vegetation cover, rainfall and seismic conditions.

Nine landslide-controlling parameters, including slope angle, slope aspect, slope curvature, geology, NDVI, distance to drainage, distance to tectonic, seismic parameter (PGA) and rainfall were considered using the RFR method. Details of all nine landslide-controlling parameters and their respective classes are presented in Table 2. Data of four parameters, namely slope angle, slope aspect, slope curvature and distance to drainage were produced from the digital elevation model. For this, CartoDEM data was used and is freely available at BHUVAN (http://bhuvan.nrsc.gov.in (accessed July 2017)). Data for developing distance to tectonic map were collected from the Geological Survey of India (GSI). Geology map was collected from published literature (Valdiya 1980). Normalized difference vegetation index (NDVI) was prepared by Landsat 4–5 Thematic Mapper (TM) data. Landsat 4–5 Thematic Mapper (TM) data were obtained from the United States Geological Survey (USGC) (https://www.usgs.gov/ assessed July 2017)). Seismic parameter, i.e. PGA map was derived from Shrikhande et al. (2000). The rainfall map was prepared by 0.25 m × 0.25 m grid data assessed from the Indian Meteorological Department (https://mausam.imd.gov.in (Assessed on 2015). All the landslide-controlling parameters were converted into a raster of 30 m × 30 m (part a of Figs. 3, 4, 5, 6, 7, 8, 9, 10 and 11). The details of each controlling parameter preparation are presented in the following section. A comparison between spatial distributions of RIL and EIL with controlling parameters was calculated from landslide frequency analysis and shown in part b of Figs. 3, 4, 5, 6, 7, 8, 9, 10 and 11. For estimation of topographical parameters, spatial analyst tool (surface) available in ArcGIS software was used to calculate slope angle, slope aspect and slope curvature.

Table 2 Details of all nine landslide-controlling parameters along with respective classes
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Fig. 3
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Slope angle: spatial distribution, a different parameter class, b landslide incidences

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Fig. 4
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Slope aspect: spatial distribution, a different parameter class, b landslide incidences

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Fig. 5
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Slope curvature: spatial distribution, a different parameter class, b landslide incidences

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Fig. 6
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Distance to drainage: spatial distribution, a different parameter class, b landslide incidences

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Fig. 7
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Distance to tectonic: spatial distribution, a different parameter class, b landslide incidences

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Fig. 8
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NDVI: spatial distribution, a different parameter class, b landslide incidences

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Fig. 9
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Geology: spatial distribution, a different parameter class, b landslide incidences

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Fig. 10
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PGA: spatial distribution, a different parameter class, b landslide incidences

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Fig. 11
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Rainfall: spatial distribution, a different parameter class, b landslide incidences

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Slope angle

Slope angle is a critical parameter for landslide analysis and used in preparing landslide susceptibility maps (Saha et al. 2005; Gorsevski et al. 2012). In this study, the slope angle map (Fig. 3a) was prepared from the 30 × 30 m2 DEM using ArcGIS spatial analyst tool. DEM is classified in pixels. For each pixel, the slope tool calculates the maximum rate of change in value from that cell to its neighbours. Basically, the maximum change in elevation over the distance between the cell and its eight neighbours identifies the steepest downward slope from the cell (ESRI 2016). Figure 3b shows the RIL and EIL spatial distribution in each parameter class. The result shows that about 33% of the landslides occurred on slope angle from 25° to 35° for RIL case and about 36% landslides occurred on slopes angle from 15° to 25° for EIL case (Fig. 3b). For both cases, landslides incidence increases with the increase of slope angle either up to 15°–25°or up to 25°–35°, where the maximum frequency of landslide is reached. Then follow a decreasing trend. Dai and Lee (2002) have reported similar observations.

Slope aspect

Slope aspect is a derivative of slope angle and defines the direction of the slope. Slope aspect map for the study area is shown in Fig. 4a. Slope aspect influences the other landslide controlling parameters such as lineaments, rainfalls, wind effects and exposure to sunshine is controlled by the slope aspect (Yalcin and Bulut 2007). Slope aspect was categorized into eight directional classes, namely (i) north, (ii) northeast, (iii) east, (iv) southeast, (v) south, (vi) southwest, (vii) west and (viii) northwest. Figure 4b shows the distribution of RIL and EIL in the slope aspect map. Figure 4b depicts that south-facing slopes have more landslide incidence as compared to others for both cases, i.e. RIL and EIL.

Slope curvature

Slope curvature signifies the rate of change of slope angle and helps to analyse the flow and slope morphology (Nefeslioglu et al. 2008). The slope curvature affects erosion and deposition (Kritikos and Davies 2015). In this study, profile curvature was extracted from the DEM and categorized into five classes, namely, (I) −20 to −2.2 (highly convex) (II) −2.2 to −0.6 (convex) (III) −0.6 to 0.6 (flatter) (IV) 0.6 to 2.2 (concave) and (V) 2.2 to 20 (highly concave). The spatial distribution of slope failure is shown in Fig. 5a. Figure 5b shows that the maximum landslide incidence is in class 3 (flatter class) using RIL and EIL. Thus, the effect of slope curvature appears not to be significant.

Distance to drainage

Distance to drainage is a hydrological parameter that controls the degree of saturation in slopes. Six buffer categories of 500 m, namely, (I) <500, (II) 500–1000, (III) 1000–1500, (IV) 1500–2000, (V) 2000–2500 and (VI) >2500 were created to calculate distance from drainage. Figure 6a shows the distance to the drainage map. Details of the buffer class are presented in Table 2. Figure 6b shows that 45% of landslides occurred for class < 500 m for the RIL case, whereas only 30% of landslides occurred in this range for the EIL case.

Distance to tectonic

The study area is characterized by several thrusts, folds, lineaments and faults, which greatly influence the occurrence of landslides. The structural features are zones or planes of weakness characterized by shearing and tectonic activities along the weak places that make them more vulnerable for occurrence of landslides. Landslide frequency decreases with increasing distance from tectonic features (Saha et al. 2002). In the present study, structural features (thrusts, folds, faults and lineaments) were merged together for distance buffering. In Garhwal Himalayas, the effect of structural features over the landslide incidences varies from 250 to 500 m (Saha et al. 2002). A buffer map was derived for the structural features and categorized into five equal distance classes at 500 m intervals. It can be observed from Fig. 7a that the distance to tectonic map is classified in five groups: (I) <500, (II) 500–1000, (III) 1000–1500, (IV) 1500–2000 and (V) >2000. It can be observed from Fig. 7b that for both RIL and EIL landslide incidences are highest in class 1, i.e. >500 m.

Vegetation index: NDVI

The vegetation cover represents the anthropogenic interference on hill slopes, which is related to landslide occurrences (Pradhan 2010). Equation 4 shows the mathematical formula to calculate NDVI.

$$\mathrm{NDVI}= \frac{\left(\mathrm{NIR}-\mathrm{RED}\right)}{\left(\mathrm{NIR}+\mathrm{RED}\right)},$$
(4)

where NIR and RED represent the spectral reflectance of near-infrared and red bands of the electromagnetic spectrum, respectively. NDVI map is classified into five categories, namely, (I) −0.1 to 0.1 (water), (II) 0.1 to 0.2 (no vegetation), (III) 0.2 to 0.3 (very less vegetation), (IV) 0.3 to 0.4 (less vegetation) and (V) 0.4 to 0.55 (high vegetation). NDVI map for the study area is given in Fig. 8a. Mostly landslides were found either in very less vegetation or no vegetation class for both RIL and EIL cases (Fig. 8b).

Geology: lithology

Different rock types show different resistance against weathering and erosion processes due to their varied inherent characteristics, such as composition, structure, and compactness. For example, quartzite, limestone and igneous rocks are generally hard, massive and resistant to erosion, forming steep slopes. In comparison, terrigenous sedimentary rocks are vulnerable to erosion and form more easily landslides. Phyllites and schists are characterized by flaky minerals which weather quickly and promote instability (Anbalagan 1992). Thus, lithology is an important parameter for landslide susceptibility zonation mapping.

Figure 9a shows the lithological map of the study area, which is classified into nine classes based on formation. Their group and formation are provided in Table 3. From Fig. 9b, it can be observed that the maximum landslides are in Class 3 (Nagthat–Berinag Formations) for both RIL and EIL cases.

Table 3 Litho-stratigraphic detail of the study area (after Valdiya 1980)
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Seismic parameter: PGA

Many studies show that there is a positive correlation between PGA and earthquake-induced landslides. Higher PGA led to more serious earthquake-induced landslide hazards (Keefer 1984; Carlton et al. 2016). Results achieved from other researchers give a good consistency when an earthquake-induced landslide is measured by ground motion parameters (Umar et al. 2014; Tanoli et al. 2017). The relationship between PGA and earthquake-induced landslides can be used to evaluate earthquake-induced landslide hazards quickly.

Peak ground acceleration (PGA) is equal to the maximum ground acceleration that occurred during earthquake shaking at a location. PGA is equal to the amplitude of the largest absolute acceleration recorded on an accelerogram at a site during a particular earthquake (Douglas 2003). In the present study, the 1999 Chamoli earthquake has been considered to assess the earthquake-induced landslides. The PGA map of Chamoli earthquake was derived from Shrikhande et al. (2000). Shrikhande et al. (2000) used several strong motion data recorded at 11 accelerograph stations, including 1 in the epicentral region (Gopeshwar).

The PGA map of the 1999 Chamoli earthquake is shown in Fig. 10a. PGA is classified into four classes based on PGA values, i.e. (I) >0.13 g, (II) 0.11 g, (III) 0.09 g and (IV) <0.09 g. Hill slopes become unstable due to strong ground motion and induce several landslides. Thus, earthquake-induced landslides are directly predisposed by the PGA (Keefer 1984). Figure 10b shows that EIL follows an increasing trend with the increasing PGA of the class. As expected, maximum landslides are in Class I (PGA 0.13g) for both RIL and EIL cases.

Rainfall

The large part of the Chamoli district is situated on the southern slopes of the outer Himalayas; monsoon currents can penetrate through trenched valleys, and the rainfall reaches its maximum value in the monsoon season that spans between June to September. Beside this, the considered study area consists of fractured and weathered rocks which are very weak. These rocks lose their strength due to saturation in rainy season. Therefore, the study area is prone to rainfall-induced landslides. So, rainfall was taken as a triggering parameter for LSZ mapping. A rainfall map was produced for the monsoon period (June to September) before the 1999 Chamoli earthquake, using the rainfall precipitation data collected from IMD. Inverse distance weighted (IDW) interpolation method was utilized to produce a rainfall map. A rainfall map is given in Fig. 11a, which indicates classification into five groups based on precipitation (in mm), i.e. (I) 867–901, (II) 901–935, (III) 935–969, (IV) 969–1003 and (IV) 1003–1037. Figure 11b shows that rainfall-induced landslides are maximum in the highest range of precipitation (class 5) for RIL, while it is for Class 2 for EIL, where the effect of rainfall is not significant.

Multicollinearity analysis for selection of landslide-controlling parameters

Multicollinearity analysis is a vital way of identifying and selecting appropriate landslide-controlling parameter (Roy and Saha 2019). It is essential to select influencing parameters using multicollinearity analysis, as the LSZ model may be sensitive to collinearities. Moreover, parameters that present multicollinearity may cause disturbances during the modelling process and consequently decrease the predictive capacity (Chen et al. 2018). In this study, multicollinearity was evaluated through the tolerance value (TOL) and variance inflation parameter (VIF). In normal conditions, tolerance values less than 0.10 or VIF values equal to or greater than 10 indicate multicollinearity (Bui et al. 2011). The outcomes of the multicollinearity analysis in this study (Table 4) show that there are no multicollinearities among the landslide-controlling parameters, because all the landslide-controlling parameters have values of TOL greater than the threshold value and values of VIF less than the threshold value.

Table 4 Multicollinearity analysis among landslide-controlling parameters
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Landslide susceptibility index analysis

This study incorporated an RFR method to evaluate the LSI from which the LSZ models were produced. The advantage of the RFR method is that this objectively assigns weights to different controlling parameters. The distribution of the training dataset in all-controlling parameters is shown in Table 5. Description of the class area is given in “Landslide‑controlling parameters”. Based on the training dataset, FR and RFR values were calculated as per Eqs. (1) and (2) separately for three cases, namely: only for RIL, only for EIL and combined RIL and EIL. The landslide-controlling parameters were combined to calculate LSI according to the integration rules given in Eq. (3). Higher LSI values indicate higher susceptibility class, whereas a lower range of LSI values implies a lower susceptibility class.

Table 5 Calculation for FR and RFR
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Results and discussion

Classification of spatial susceptibility by success rate curve

For the demarking of LSI boundaries, a method proposed by Saha et al. (2005) is adopted. To quantify the susceptibility class, the data is categorized into five LSZ classes, namely very low (VLS), low (LS), moderate (MS), high (HS), and very high (VHS). The mean (\(\mu\)) and standard deviation (\(\sigma\)) of the LSI range were calculated by the best-fit probability distribution curve. LSI values were classified into five susceptibility classes with boundaries at (\(\mu -1.5 m\sigma\)), \((\mu -0.5 m\sigma\)), (\(\mu +0.5 m\sigma\)) and (\(\mu +1.5 m\sigma\)). Here, m is defined as a number greater than zero (Saha et al. 2005; Kanungo et al. 2006). The m value rules the most rational boundaries within the LSI. Different m values, i.e. 0.7, 0.8, 1.0 and 1.1 were used to check the most appropriate LSZ map.

Based on a given LSZ map, cumulative percentages of the area of the susceptibility class can be plotted against the cumulative percentages of landslide incidences in five susceptibility zones ordered from very high to very low. This curve is referred to as the success rate curve in the literature (Chung and Fabbri 1999). In this work, the success rate curve was used for two purposes, first is to select the appropriate value of m to decide the suitability of a particular LSZ map and the second is to determine how well the resulting landslide susceptibility maps have classified the areas of existing landslides. The success rate curve was plotted with landslide training data (70%) and susceptibility class area data, which are given in Table 5 for all LSZ models.

LSZ map, which contains more landslides in the VHS class, is considered most suitable. Figure 12 shows the plot between cumulative percentages of landslide incidences and cumulative percentages of the area of the susceptibility class. This analysis indicates that m = 0.8 gives the most suitable LSZ map. So, for all models, the success rate curve at m = 0.8 is presented in Fig. 12. It can be noted that for 10% area of VHS class, the curves respective to Model 1, 2, 3, 4 and 5 show the landslide incidences of 36, 38, 42, 44 and 55%, respectively. LSZ Model 5 shows the highest success rate.

Fig. 12
figure 12

Success rate curves of the LSZ map

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Landslide susceptibility zonation mapping

In this section, LSZ maps are presented for all five models discussed in Table 1 (part a of Figs. 13, 14, 15, 16 and 17). The percentage area of different classes is presented in the form of bar charts (part b of Figs. 13, 14, 15, 16 and 17), where landslide incidences for five susceptibility classes are also presented. However, a comparative analysis between training and testing datasets of landslides are presented in the validation section.

Fig. 13
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For Model 1. a LSZ map. b Area and landslide incidences in susceptibility class

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Fig. 14
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For Model 2. a Rainfall-induced LSZ map. b Area and landslide incidences in susceptibility class

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Fig. 15
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For Model 3. a Earthquake-induced LSZ map. b Area and landslide incidences in susceptibility class

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Fig. 16
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For Model 4. a LSZ map. b Area and landslide incidences in susceptibility class

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Fig. 17
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For Model 5. a Rainfall- and earthquake-induced LSZ map. b Area and landslide incidences in susceptibility class

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LSZ Model 1

Firstly, a landslide susceptibility zonation map (Fig. 13a) is reported here as Model 1, which excludes seismic and rainfall parameters and consider only RIL inventory. Details of different susceptibility classes are given in Fig. 13b. Figure 13b shows that 12.43% of the study area was located in the VLS class. LS, MS and HS classes comprised 25.01, 28.45 and 21.48% of the study area, respectively. In all, 12.64% of the region was placed in the VHS class. Figure 13b depicts that for the training dataset, 3.21 and 6.41% of the total landslide incidences are in the VLS and LS classes, respectively. MS, HS, and VHS classes represent 17.95, 28.21, and 44.23% of the landslides, respectively. Thus, the maximum landslide incidence is in VHS class, though the class area is lowest in this category.

LSZ Model 2

In LSZ Model 1, the rainfall parameter is considered as an additional landslide-controlling parameter to assess the impact of rainfall and, thus, a new LSZ map for Model 2 is produced. LSZ Model 2 may be reported as “Rainfall-Induced LSZ Map.” Similar to the previous case, LSI values are calculated. LSZ map for Model 2 is presented in Fig. 14a. Details of different susceptibility classes are given in Fig. 14b.

In LSZ Model 2, which is produced by including the rainfall controlling parameter, the VLS and LS classes cover 37.33% of the study area. In contrast, MS, HS, and VHS classes cover 28.72, 22.13 and 11.81% of the study area, respectively. Figure 14b shows that the percentages of the total landslides in VLS, LS and MS class are 26%, whereas the rest of the class contains 74% of total landslides. Thus, VHS class has the highest number of landslides with the lowest % of the area.

LSZ Model 3

In LSZ Model 1 and 2, only RIL inventory was used for the calculation of RFR values. Now LSZ map, which utilizes only EIL dataset along with the seismic controlling parameter, has been produced. This LSZ map is reported here as LSZ Model 3. LSZ Model 3 could be reported as “Earthquake-Induced LSZ Map” (Fig. 15a). LSZ Model 3 is produced by the seismic controlling parameter, where the VLS, LS and MS classes cover 79% of the total study area. In contrast, the remaining classes, i.e. HS and VHS, cover 21% of the total area. Figure 15b shows that more than 30% of the total landslides occurred in the VHS class. In LSZ Model 3, a VHS class is clustered around the high PGA values.

Though Model 2 is based on RIL inventory, it can be used to predict the spatial location of EIL (Fig. 14b). It can be observed that the difference between EIL and the testing dataset is not significant. Similarly, Model 3 is solely based on EIL inventory, but used to predict the location of RIL in Fig. 15b, where the difference with the training dataset is significant.

Thus LSZ Model 2 produced with the RIL inventory is useful to predict the location of EIL, which constitutes an event-based inventory. In contrary, the LSZ Model 3, which is built with EIL, did not predict well the location of RIL (Fig. 15b). These outcomes could be attributed to the enormous inequality in the number of landslides (220 RIL and 56 EIL). Further, EIL inventory landslides are clustered in a small area. Thus, it is demonstrated that consideration of rainfall-induced landslide inventories is essential.

LSZ Model 4

LSZ Model 1, 2 and 3 are single event-based susceptibility maps. These susceptibility maps are usually insufficient for the areas which are prone to multi-hazards like the Himalayan region. Considering the presence of a multi-hazard scenario in the study area, both RIL and EIL inventories were been used in LSZ Model 4 and 5. LSZ Model 4 includes seismic parameters and combines landslide inventory to develop the LSZ Model (Fig. 16a).

The LSZ Model 4 map determined 15.54% of the total area as VLS class, 30.83% of the area as LS class, 26.89% as MS class, 19.37% as HS class, and 7.37% of the area as VHS class. Figure 16b shows that 3.06% and 7.14% landslides occurred in the VLS and LS classes, respectively. MS, HS, and VHS classes represent 20.92, 34.69, and 34.18% of the landslides, respectively.

LSZ Model 5

Rainfall parameter was added to LSZ Model 4 to assess the effect of rainfall parameter on previous LSZ Model 4. Considering the multi-hazard nature of the study area, LSZ map Model 5 presents the potential impact of combined triggering parameters (Fig. 17a).

In the case of LSZ Model 5, 70% of the total area is enclosed by VLS, LS and MS classes. Figure 17b shows that 84% of the total landslides incidences are in HS and VHS classes, which have only 30% of the total area.

Table 6 shows the statistical data corresponding to LSZ Model 1 to 5. All 5 LSZ Models follow an almost similar trend, i.e. susceptibility class area increases with the increase of susceptibility level (primarily up to LS or MS class) and then follows a decreasing trend. LSZ Model 1 shows the minimum mean value, whereas LSZ Model 5 has significantly highest as compared to other models. Model 5, which gives the highest success rate curve, shows that the VHS class contains a minimum % of the class area, whereas LS and MS have almost the same % class area, which is maximum. VHS class of LSZ Model 5 contains more than 50% landslide incidences, which is the highest among all the LSZ models.

Table 6 Statistical data corresponding to LSZ Models 1–5
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The success rate based on Model 5 is the highest. Model 5 includes both rainfall and seismic controlling parameter along with EIL andsceptibility situation in the Indian Himalayan region is dominated by both rainfall- and earthquake-triggering parameters. Therefore, including both rainfall and earthquake should give more accurate predictions of landslide susceptible zone.

LSZ maps show a drastic change in the spatial distribution of susceptible locations after the inclusion of both seismic and rainfall parameters. Focusing on Gopeshwar township (30°24′34.2″N, 79°19′11.28″E) in the Garhwal hills, 48% area falls in VHS class under LSZ Model 1, while applying LSZ Model 5 it increases to 85%. This comparison shows the importance of an integrated LSZ model which accommodates both triggering parameters for the area that is susceptible to both earthquake- and rainfall-induced landslides.

Validation

In this study, the testing dataset (30% of landslide inventory) was used. In this study, the degree of fit and prediction rate curve were used to validate LSZ models.

Degree of fit

Landslide density was calculated to assess the degree of fit between the landslide inventory and the landslide susceptibility class. The landslide incidences using training and testing datasets are compared for LSZ models in part b of Figs. 13, 14, 15, 16 and 17. It can be observed that there is an excellent agreement for Models 4 and 5 where both RIL and EIL are considered. However, this agreement is not so good for Models 1–3. Further, landslide density is calculated using Eqs. 5(a), 5(b).

$$\mathrm{Training\, density }= \frac{{\mathrm{btr}}_{i}}{{\mathrm{a}}_{i}},$$
(5a)
$$\mathrm{Training\, density }= \frac{{\mathrm{btr}}_{i}}{{\mathrm{a}}_{i}},$$
(5b)

where \({\mathrm{btr}}_{i}\) and \({\mathrm{bts}}_{i}\) are the landslide incidences in training and testing datasets, respectively, and \({\mathrm{a}}_{i}\) is susceptibility class area for the ith LSZ Model (where i = 1 to 5).

Table 7 shows the degree of fit of landslide occurrences, including training and testing dataset of landslide inventory. Firstly, training landslides were used to check the degree of fit. The training landslide's occurrence value was mostly concentrated in the VHS class. Next, the degree of fit for the testing landslide data was calculated. The results showed that the landslides were again concentrated in the VHS class. In this study, a large number of landslides were clearly evident in the HS and VHS classes. It can be observed that the density of landslides for both training and testing data are comparable and maximum in VHS class, validating developed maps.

Table 7 Landslide density for different LSZ maps
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Area under curve (AUC): success and prediction rate curves

The area under the curve (success rate curve and prediction curve) analysis was used to evaluate model compatibility and predictability. The AUC computed from the success and prediction rate curves validates the accuracy of a landslide model in two aspects: prediction skill and model fitting (Ozdemir and Altural 2013). When we exploit an inventory that was unknown in the model calibration, a predictive value is expected. When, instead of an independent population, the same landslide set is used, what is determined is how well the model fits the data. Similarly, the success rate curve uses the training landslide dataset that has already been used for building the landslide models; thus, it is not suitable for assessing the prediction capacity of the models. The prediction rate curve uses the testing landslide dataset. This is suitable for the predictive value of the model.

The success rate method can help determine how well the resulting landslide susceptibility maps have classified the areas of existing landslides (Bui et al. 2012). The area under the success rate curve represents the quality of landslide models to reliably classify the occurrence of existing landslides (training dataset). In contrast, the area under the predicted rate curve explains the capacity of the proposed landslide model for predicting landslide susceptibility. The AUC value ranges from 0.5 to 1.0 (50–100%), and an ideal model has an AUC value close to 1.0 or (100%) (Perfect fit/prediction). In this study, 5 subdivisions of LSI values of all cells in the study area are used. Where the cumulative percentage of landslide occurrence for training and testing dataset was calculated in all classes and curves were then drawn to calculate their AUCs.

The predictive capacity of the susceptibility maps has been examined by the prediction rate curve. It was determined using the testing dataset (Fig. 18). This is produced on similar lines as done for success rate curves using a training dataset (Fig. 12). Table 8 shows the calculation data for success and prediction rate curves. Table 9 shows that area under curve (AUC) for both success and prediction rates are highest for Model 5. Respective AUC values of training and testing dataset for Model 5 showed that the map obtained from Model 5 gives higher accuracy and predictive capacity.

Fig. 18
figure 18

Predictive rate curves of the LSZ maps

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Table 8 Calculation for success and prediction rate curves
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Table 9 AUC values for training and testing datasets
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Conclusions

In this study, the effect of rainfall- and earthquake-triggering parameters on landslide susceptibility zonation was assessed employing GIS-based bivariate statistical relative frequency ratio method. The variation between landslide incidences and controlling parameters were analysed from landslide frequency analysis. The following major conclusions are drawn from this study:

  1. 1.

    LSZ Model 2 represents rainfall-induced landslide (RIL) susceptibility zonation map, whereas Model 3 represents earthquake-induced landslide (EIL) susceptibility zonation map for the same study area. It was verified that LSZ Model 2 produced with RIL is very effective in predicting the spatial location of EIL. However, Model 3 is not well predicting the location of RIL. Thus, a model that includes rainfall inventory performed better.

  2. 2.

    LSZ Model 2 reflects the effect of rainfall on LSZ mapping, whereas LSZ Model 5 represents the combined effect of rainfall and earthquake triggering parameter. The success rate and prediction rate, both increased after the addition of the rainfall parameter. Thus it is essential to include RIL inventory.

  3. 3.

    Validation results revealed that LSZ Model 5, which includes all-controlling parameters and both EIL and RIL inventories, had the highest success and prediction rates than that for the other models. The area under curve (AUC) for both success and prediction rates are highest for Model 5.

  4. 4.

    This study recommends considering both rainfall and seismic parameters while developing LSZ map for an area like Chamoli, which is vulnerable to rainfall as well as earthquake-induced landslides.

Limitation

The major limitation of this study is that the statistically-based susceptibility models are functional i.e., they depend entirely on the type, abundance, quality and relevance of the available landslide and the geo-environmental information. A consequence is that the results of the susceptibility models are much dependent on the accuracy of input data including landslide inventories and controlling parameters.

A major limitation of the present study is that the conclusions are based only on the spatial distribution and the temporal distribution is not considered. However, the title of the manuscript acknowledges this fact.

Practical application

Landslide susceptibility zonation maps presented in the manuscript can be used at the preliminary stage, i.e. at an early stage of planning and these maps can be further developed for a particular location as the study progresses and more data are available. The maps presented can be used as a tool to help identify and avoid the areas having the potential risk of landslides.