In the present study, thirteen landslide causative factors i.e. Elevation, Geology, Slope, Soil, Drainage Density (DD), Road Density (RD), Rainfall, Normalize Difference Vegetation Index (NDVI), and Aspect, Topographic Position Index (TPI), Stream Power Index (SPI), Topographic Wetness Index (TWI) and Land Use Land Cover (LULC) were considered for performing landslide susceptibility Index (LSI) and landslide risk (LRA) modeling. Thus, this is important to compile a digitized database for executing the landslide susceptibility model and landslide risk model using geospatial techniques. The spatial databases have been designed and executed properly for the landslide vulnerability and landslide risk modeling (Table 2). In this study, both categorical and continuous data were used to perform landslide modeling with the help of ArcGIS 10.2, SPSS 23 and R software.
3.2 Selection of Landslide conditioning factors
There is no such criteria for selecting causative factors for landslide vulnerability analysis (Ayalew and Yamagishi 2005). The factors controlling slope instability modeling and risk modelling are elevation, geology, slope, soil, drainage density (DD), road density (RD), Rainfall, Normalize Difference Vegetation Index (NDVI), and slope aspect, topographic position index (TPI), stream power index (SPI), topographic wetness index (TWI) and land use land cover (LULC). All these landslide causative variables are being used by different researcher in across the globe (Wu et al. 2017).
3.2.1 Geology, elevation, slope, soil and drainage density
The geology plays a significant preface in the occurrence of the slope instability because of the lithological and structural variations often leads to difference in strength of soil and rocks (Pradhan and Lee 2010a) in Rorachu watershed. Rorachu watershed areas are characterized by the presence of five lithological units i.e. 1. Basic Intrusive, 2. Chungthang Formation, 3.Gorubathan Formation, 4. Lingtse Gnesis, 5. Kanchenjunga Gnesis or Darjeeling Gnesis (undifferentiated) (Fig. 4 and Table 2). The geology map of Rorachu watershed was made using district resource map of east Sikkim which was collected from geological survey of india (GSI), Kolkata. Major part of this watershed is encircled by Kanchenjunga Gnesis or Darjeeling Gnesis. Lithological unit of basic Kanchenjunga gnesis covering large area (43.02%) and ranked first which is followed by Basic intrusive (21.10%), Chungthang formation (18.48%), Gorubathan formation (12.12%) and Lingtse Gnesis (5.35%). Due to different sets of structural disturbance, numerous fractures, faults, cracks and joints landslide activities are common in Sikkim Himalaya. The lithological characteristics influence stability of rocks and occurrences of landslide.
Elevation or altitude is one of the significant parameter that has been frequently used for landslide susceptibility and landslide risk modelling. Elevation control the another landslide occurrences parameter in a geographical area. It is controlled by various geological and geomorphological process (Ayalew et al. 2005; Pourghasemi 2008). In this present study area, the elevation ranges between 816 m and 4100 m (Fig. 4a). The elevation map is classified into 5 categories with 30 * 30 meter resolution. It has been noticed that maximum landslides are being observed in the medium and high elevation zones of the Rorachu watershed.
Slope gradient is also another significant causative factors of slope stability assessment (Lee and Min 2001). Stability of the slope is the interaction between angel of the slope and materials properties of the slope (friction angel, cohesion, porosity, permeability and bonding). Gentle slopes have minor probability for slope instability due to lower shear stress (Dai et al. 2001). In contrast, higher the slope gradient higher the shear stresses and vice versa. In this present study slope map is classified into five categories using natural breaks method in ArcGIS 10.3. Slope angel ranges from 00 to 70o (Fig. 4b) and there are more than 30% areas under 35o to 70o slope angel in this Rorachu watershed.
The soil saturation depends on two factors i.e. intensity, duration and amount of precipitation of this area and soil physical characteristics like, soil texture, structure, porosity, permeability, compactness etc. In Rorachu watershed more than 90% area is under hilly region. Soil areas of the Rorachu watershed have been seprated into six categories (Fig. 5. c, Table 3) such as I. coarse loamy humic dystrudepts, II. Coarse loamy humic lithic dystrudepts, III. Coarse loamy typic hapludolls, IV. Fine loamy fluventic eutrudepts, V. Fine skeletal cumuli hapludolls and VI. Loamy skeletal entic hapludolls. In Rorachu watershed, all soil categories have been converted into vector polygon and then to raster format (30 *30 meter grid).
Table 3
Description of soil parameters in the Rorachu watershed
Mapping unit
|
Soil name
|
Soil code
|
characteristics
|
Inceptisols
|
Coarse loamy humic dystrudepts
|
S001
|
Very deep, well drained, moderately rapid permeable coarse loamy soil is found in structural benches and Foot slope of mountain associated with moderately shallow to deep, little stony, excessively drained coarse loamy soil with moderate erosion
|
Coarse loamy humic Pachic dystrudepts
|
S002
|
Moderately rapid permeability is occurred in upland slopes associated with moderately deep, well drained coarse loamy soil with medium run-off,, little stony, excessively drained fine loamy soils with moderate erosion
|
Coarse loamy typic hapludolls
|
S003
|
Excessively drained, deep coarse loamy soil having little stoniness and slight to moderate erosion is found mainly in the ridges associated with moderate deep to deep coarse loamy soil with little stoniness
and moderate erosion
|
Fine-loamy fluventic eutrudepts
|
S004
|
moderate permeability with Moderately shallow to deep, well drained fine loamy soil is found in steep slope, moderately high saturated hydraulic conductivity and moderate erosion associated with very deep, well drained fine loamy upland soils
|
Mollisols
|
Fine-skeletal cumilic hapludolls
|
S005
|
Moderately deep to very deep, excessively drained soils with gravelly surface, little stoniness and moderate erosion is found in very steep slope associated with moderately shallow to deep, slight stoniness, excessively drained, moderately erosion prone coarse loamy soil
|
Loamy skeletal entic hapludolls
|
S006
|
Excessively drained, gravelly loamy soil mainly found in very steep hill side with small stoniness and moderate erosion associated with moderately shallow to deep, slight stoniness, moderately deep to deep, excessively drained, moderately erosion prone gravelly loamy soil
|
Drainage density is the total length of all streams and rivers of that grid divided by the total area (Eq. 1) of that grid (Horton 1932, 1945; Strahler 1952). Drainage density (DD) indicates the measure of how enough or how unwell a river watershed is drained by the stream channels. Drainage density depends on both physical environment and climatic environments of an area. Drainage density helps to determine the degree of reducing the shear strength of mountain slope which has affective role in slope instability. Drainage density of Rorachu river basin has been made using Euclidean distance method in ArcGIS 10.3 into 30 * 30 meter grid (Fig. 4d) and classified into five by natural breaking method.
$$Dd=\left(Lt/Abasin\right)$$
1
Where, Dd represents drainage density, LT represents total length of the streams in that grid and Abasin represents total length of the grid area.
3.2.2 Road density, Normalized Difference vegetation Index (NDVI), Slope Aspect, Topographic position index (TPI)
The high road density reduces the strength of soil and slope which invites landslide. All the anthropogenic activities i.e. construction and extension of road networks are responsible for slope instability. Roads modify the inherent gradient of the slope and generate an obstacle for the surface water flow (Marcini 2010). Road map was made using Topographical map and Google Earth. In this Rorachu watershed area, road density was prepared by ArcGIS 10.3 into 30 * 30 meter grid cell (Fig. 5e) and then it has been classified into five groups.
Normalized difference vegetation index (NDVI) is a numerical indicator that uses for the vegetation conditions of the surface. NDVI has been estimated by the formula of NDVI = {(NIR – R) / (NIR + R)}, where NIR is the Near Infrared band and R is the Red band of satellite image. In Rorachu watershed, NDVI was assessed incorporating LANDSAT 8 OLI image in ERDAS 9.2 image processing software (Fig. 6. f) where NDVI value ranges from − 0.11 to 0.64. Positive value indicates the healthy vegetation cover which increase soil cohesion and slope stability. A negative NDVI value indicates no vegetation cover in Rorachu watershed areas which is more vulnerable for soil erosion and slope failure.
The Slope aspects are the compass direction of maximum slope faces of the terrain surface. The direction of the slope faces can affect physical and biological factors which are related to landslide hazards. Slope aspects are immensely influence on temperature and vegetation cover. The slope aspect map has been prepared from the DEM. The slope aspects are connected to the physiographic aptitude and the principle precipitation direction (Ercanoglu and Gokceoglu 2002). In this present study, the slope aspects are classified into ten categories (Flat, N, NE, E, SE, S, SW, W, NW, and N).
h. Topographic position index (TPI)
Topographic position index (TPI) is an algorithm which is immensely used to measure topographic slope positions and automated landform classifications. The topographic position index (TPI) refers to the topographic position classification identifying upper, middle and lower part of the landscape (Guisan et al. 1999). Positive TPI values have been representing the locations that are higher than the surroundings (ridges). Negative TPI values have been representing the locations that are lower than the surroundings (valleys). TPI values are close to zero have been representing either flat areas or a constant slope. In this study area, the TPI value was calculated by the SAGA GIS software, and the value of TPI ranges between the − 63.51 and 65.13. The Topographic position index is an important factor for the assessment of a landslide vulnerability and a landslide risk (Fig. 6. h).
3.2.3 Stream power index (SPI), Topographic Wetness Index (TWI), Land use Land cover (LULC) and rainfall
Stream power index (SPI) is quantifying the erosive power of the flowing water on a slope gradient. The stream power index (SPI) has been estimated based on the slope and specific catchment area (SCA). The stream power index (SPI) is defined after Moore and Grayson (1991) (Eq. 2).
$$\text{S}\text{P}\text{I}=(\text{A}\text{s} \times \text{t}\text{a}\text{n}{\beta })$$
2
Where, As is the specific catchment area (SCA) and β is the local slope gradient measured in degrees, respectively. In this Rorachu watershed, SPI values varies from 0 to 145.37 and the study area is classified into five classes (Fig. 7. i) after Hengl et al. (2003) (Eq. 3).
$$As=(Am \times {P}^{2} / \sum Li )$$
3
In the above equation, P is the pixel size, Am is the cumulative drainage fraction from m neighbors, and ∑Li is derived as the sum of lengths for drainage pixels.
Topographic wetness index (TWI) is another important factors for landslide susceptibility and a risk modeling. TWI refers to the accumulation of water in a particular point of time to any grid cell. For shallow landslide modeling, TWI has been used by various researchers (Gokceoglu et al. 2005; and Yilmaz 2009a 2009b). In this study, TWI map was prepared by SAGA GIS software after Beven and Kirkby (1979). TWI map was classified into five categories (Fig. 7j). TWI is defined as:
$$\text{T}\text{W}\text{I}=\text{l}\text{n}\left(\frac{\text{a}}{\text{t}\text{a}\text{n}{\beta }}\right)$$
4
Where, a is the cumulative upslope area draining through a point (per unit contour length) and tanβ is the slope angel at that point.
LULC map was prepared from the LANDSAT 8 OLI satellite image (2019) data, using supervised classification techniques in ERDAS 9.2 software. The forest area promotes infiltration and drainage which reduces the slope failure. The slope stability is affected by the cultivated lands (Devkota et al. 2012). The study area exhibits various types of land use land cover such as step cultivation, open forest, settlement, bare soil, landslide area, river and dense forest. In this Rorachu watershed most of the area covered by the forest (open and dense, 59%) which is followed by the settlement (3.47%) and bare land (3.23%) (Fig. 7. L, Table 4.).
Table 4
Landslide causative factors and their sub-class for landslide susceptibility and Landslide risk mapping
Factors
|
Sub-Class
|
Elevation
|
816–1495, 1495–1993, 1993–2516, 2516–3110, 3110–4100
|
Slope
|
0–15.37, 15.37–25.53, 25.53–35.14, 35.14–45.57, 45.57–70.01
|
Soil
|
S001, S002, S003, S004, S005, S006
|
Drainage Density (DD)
|
0.092–2.17, 2.17–3.62, 3.62–4.92, 4.92–6.25, 6.25–9.557
|
Geology
|
Basic intrusive, Chungthang formation, Gorubathan formation, Lingtse gnesis, Kanchenjunga gnesis/Darjeeling gnesis (undifferential)
|
Road Density (RD)
|
0–0.88, 0.88–2.55, 2.55–4.48, 4.48–6.86, 6.86–11.175
|
Normalize Difference Vegetation Index (NDVI)
|
-0.11–0.14, 0.14–0.24, 0.24–0.34, 0.34–0.43, 0.43–0.642
|
Aspect
|
Flat, North, Northeast, East, Southeast, South, Southwest, West, Northwest
|
Topographic Position Index (TPI)
|
-63.51 - -14.57, -14.57 - -4.48, -4.48–4.59, 4.59–15.18, 15.18–65.135
|
Stream Power Index (SPI)
|
0–2.85, 2.85–9.12, 9.12–20.52, 20.52–47.88, 47.88–145.37
|
Topographic Wetness Index (TWI)
|
5.83–8.31, 8.31–9.19, 9.19–10.15, 10.15–11.26, 11.26–15.25
|
Land Use Land Cover (LULC)
|
Step cultivation. Open forest, Settlement, Bare soil, Landslide area, River, Dense forest
|
Rainfall
|
1874.47–2386.86, 2386.86–2791.41, 2791.41–3096.59, 3096.59–3323.70, 3323.70–3657.28
|
Table 5
Monthly Rainfall distribution in the East Sikkim area (2009–2015).
Source: Indian Meteorological Department (IMD) Gangtok, Sikkim
Year
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
June
|
July
|
Aug
|
Sep
|
Oct
|
Nov
|
Dec
|
2009
|
5.7
|
4.2
|
87.3
|
251.7
|
335.4
|
355.4
|
408.6
|
454.1
|
180.1
|
201.6
|
1.7
|
5.4
|
2010
|
5.7
|
18
|
187
|
359.4
|
272.7
|
504.6
|
601
|
493.8
|
375.8
|
95.6
|
23.6
|
0.1
|
2011
|
21.6
|
40.5
|
68.5
|
14.7
|
278.8
|
515.9
|
587.3
|
459.1
|
376.7
|
44.9
|
60.8
|
2.3
|
2012
|
17.8
|
21.5
|
28.4
|
312.2
|
201.6
|
614.4
|
481.3
|
442.2
|
410.9
|
72.4
|
0.1
|
1
|
2013
|
4.3
|
32.1
|
128
|
256.1
|
409
|
382.6
|
412.1
|
325.1
|
195.5
|
191.8
|
40.7
|
7.9
|
2014
|
0
|
5.4
|
68.2
|
96.1
|
441.4
|
472.7
|
478.7
|
522.3
|
273
|
16.7
|
2.4
|
4.2
|
2015
|
7.4
|
17.4
|
73.3
|
270.3
|
387.8
|
603.1
|
561
|
284.7
|
316.1
|
99.6
|
55.8
|
1
|
Rainfall is one of the most significant triggering factors for landslides events in Rorachu watershed. The Rainfall map was prepared using world climatic data and applying inverse distance weighted (IDW) modeling and then classified into 5 categories. Rainfall in Rorachu watershed ranges between 1847 mm and 3657 mm. Maximum rainfall occurs between June and August (According to IMD data, Table 5. and Figure 7. m).
3.3 Modelling landslide susceptibility and Risk
3.3.1 Application of Bivariate Statistical index (BSI) model
The bivariate statistical index (BSI) model is used for the landslide susceptibility and landslide risk assessment modelling in Rorachu watershed (Table 6). The statistical index (SI) model is a bivariate statistical approach which has been used by van Westen (1997) for the landslide susceptibility modelling. In recent years the bivariate statistical index (BSI) model is widely used by different researcher for the landslide susceptibility and landslide risk modelling. In bivariate statistical index (BSI) model, a weighted value for every categorical units are defined as the natural logarithm of the landslide density in the categorical unit divided by the landslide density in the entire study area (van Westen 1997; Rautela and Lakhera 2000; Cevik and Topal 2003). This bivariate statistical index (SI) approach is based on this following equation (van Westen 1997).
Table 6
Spatial relationship between each landslide conditioning factors and observed landslides Using Bivariate Statistical Index (BSI) and Weight of Evidence (WOE) models.
Factors
|
Class
|
Class pixel
|
Landslide pixel
|
W+
|
W-
|
C
|
BSI
|
Elevation (m)
|
4100–3110
|
6841
|
218
|
1.23
|
-0.27
|
1.50
|
1.23
|
|
3110–2516
|
16104
|
338
|
0.81
|
-0.40
|
1.22
|
0.81
|
|
2516–1993
|
20031
|
139
|
-0.30
|
0.09
|
-0.38
|
-0.30
|
|
1993–1495
|
19285
|
16
|
-2.42
|
0.27
|
-2.69
|
-2.42
|
|
1495 − 816
|
14545
|
5
|
-3.30
|
0.20
|
-3.50
|
-3.30
|
Geology
|
Gorubathan formation
|
9312
|
6
|
-2.67
|
0.12
|
-2.79
|
-2.67
|
|
Lingtse genesis
|
4112
|
0
|
0
|
0.06
|
-0.06
|
0
|
|
Basic intrusive
|
16210
|
54
|
-1.03
|
0.16
|
-1.19
|
-1.03
|
|
Chungthang formation
|
14123
|
255
|
0.66
|
-0.24
|
0.90
|
0.66
|
|
Kanchenjunga formation
|
33049
|
401
|
0.26
|
-0.26
|
0.52
|
0.26
|
Slope (o)
|
70.09–45.57
|
7799
|
114
|
0.45
|
-0.07
|
0.52
|
0.45
|
|
45.57–35.14
|
15677
|
210
|
0.36
|
-0.12
|
0.48
|
0.36
|
|
35.14–25.53
|
20253
|
218
|
0.14
|
-0.06
|
0.20
|
0.14
|
|
25.53–15.37
|
20229
|
126
|
-0.40
|
0.11
|
-0.52
|
-0.40
|
|
15.37–0
|
12848
|
48
|
-0.91
|
0.11
|
-1.03
|
-0.91
|
Soil
|
Fine skeletal
|
5224
|
1
|
-3.89
|
0.07
|
-3.95
|
-3.89
|
|
Coarse loamy distrudeptic
|
32878
|
127
|
-0.88
|
0.36
|
-1.24
|
-0.88
|
|
Coarse loamy holithic
|
11997
|
156
|
0.33
|
-0.08
|
0.41
|
0.33
|
|
Fine loamy
|
6534
|
0
|
0.00
|
0.09
|
-0.09
|
0
|
|
Loamy skeletal
|
3754
|
126
|
1.28
|
-0.14
|
1.42
|
1.28
|
|
Coarce loamy
|
16419
|
306
|
0.69
|
-0.32
|
1.01
|
0.69
|
Drainage Density
|
9.55–6.25
|
12033
|
62
|
-0.59
|
0.08
|
-0.67
|
-0.59
|
|
6.25–4.92
|
18190
|
73
|
-0.84
|
0.16
|
-1.01
|
-0.84
|
|
4.92–3.62
|
17869
|
140
|
-0.17
|
0.05
|
-0.22
|
-0.17
|
|
3.62–2.17
|
16626
|
312
|
0.70
|
-0.33
|
1.03
|
0.70
|
|
2.17–0.09
|
12088
|
129
|
0.14
|
-0.03
|
0.16
|
0.14
|
Road Density
|
11.17–6.86
|
2051
|
13
|
-0.39
|
0.01
|
-0.39
|
-0.39
|
|
6.86–4.48
|
4530
|
100
|
0.86
|
-0.09
|
0.95
|
0.86
|
|
4.48–2.55
|
8439
|
252
|
1.16
|
-0.32
|
1.48
|
1.16
|
|
2.55–0.88
|
14317
|
157
|
0.16
|
-0.04
|
0.20
|
0.16
|
|
0.88–0
|
47469
|
194
|
-0.82
|
0.65
|
-1.47
|
-0.82
|
Rainfall (mm)
|
1847–2386
|
6624
|
263
|
1.45
|
-0.37
|
1.82
|
1.45
|
|
2386–2791
|
5199
|
95
|
0.67
|
-0.07
|
0.75
|
0.67
|
|
2791–3096
|
12076
|
137
|
0.20
|
-0.04
|
0.24
|
0.20
|
|
3096–3323
|
31797
|
195
|
-0.42
|
0.22
|
-0.64
|
-0.42
|
|
3323–3657
|
21110
|
26
|
-2.02
|
0.28
|
-2.31
|
-2.02
|
TPI
|
15.25–11.26
|
6669
|
67
|
0.07
|
-0.01
|
0.08
|
0.07
|
|
11.26–10.15
|
18765
|
173
|
-0.01
|
0.00
|
-0.01
|
-0.01
|
|
10.15–9.19
|
25823
|
228
|
-0.05
|
0.03
|
-0.08
|
-0.05
|
|
9.19–8.31
|
18956
|
171
|
-0.03
|
0.01
|
-0.04
|
-0.03
|
|
8.31–5.83
|
6593
|
77
|
0.23
|
-0.02
|
0.25
|
0.23
|
SPI
|
145.37–47.88
|
133
|
0
|
0
|
0.00
|
0.00
|
0
|
|
47.88–20.52
|
1060
|
7
|
-0.34
|
0.00
|
-0.35
|
-0.34
|
|
20.52–9.12
|
4966
|
57
|
0.21
|
-0.02
|
0.22
|
0.21
|
|
9.12–2.85
|
21030
|
255
|
0.26
|
-0.12
|
0.38
|
0.26
|
|
2.85–0
|
49617
|
397
|
-0.15
|
0.23
|
-0.38
|
-0.15
|
TWI
|
65.13–15.18
|
5334
|
20
|
-0.91
|
0.04
|
-0.95
|
-0.91
|
|
15.18–4.59
|
13142
|
65
|
-0.63
|
0.09
|
-0.73
|
-0.63
|
|
4.59 - − 4.48
|
21264
|
206
|
0.04
|
-0.02
|
0.05
|
0.04
|
|
-4.48 - − 14.57
|
22952
|
263
|
0.21
|
-0.10
|
0.31
|
0.21
|
|
-14.57 - − 63.51
|
14114
|
162
|
0.21
|
-0.05
|
0.26
|
0.21
|
LULC
|
Step cultivation
|
1648
|
0
|
0
|
0.02
|
-0.02
|
0
|
|
dense forest
|
45962
|
309
|
-0.33
|
0.35
|
-0.67
|
-0.33
|
|
settlement
|
3865
|
7
|
-1.64
|
0.04
|
-1.68
|
-1.64
|
|
bare soil
|
3921
|
149
|
1.41
|
-0.18
|
1.59
|
1.41
|
|
river
|
1439
|
0
|
0
|
0.02
|
-0.02
|
0
|
|
open forest
|
19971
|
251
|
0.30
|
-0.13
|
0.43
|
0.30
|
Aspect
|
Flat
|
4
|
0
|
0
|
5E-05
|
-5E-05
|
0
|
|
North
|
2614
|
0
|
0
|
3E-02
|
-3E-02
|
0
|
|
Northeast
|
2042
|
5
|
-1.34
|
0.02
|
-1.36
|
-1.34
|
|
East
|
5587
|
52
|
0.00
|
0.00
|
0.00
|
0.00
|
|
Southeast
|
10496
|
137
|
0.34
|
-0.07
|
0.40
|
0.34
|
|
South
|
14015
|
174
|
0.29
|
-0.08
|
0.36
|
0.29
|
|
Southwest
|
10206
|
207
|
0.76
|
-0.19
|
0.96
|
0.76
|
|
West
|
12646
|
116
|
-0.02
|
0.00
|
-0.02
|
-0.02
|
|
Northwest
|
14206
|
28
|
-1.55
|
0.16
|
-1.72
|
-1.55
|
|
North
|
4990
|
0
|
0
|
0.07
|
-0.07
|
0
|
NDVI
|
0.64–0.43
|
9717
|
205
|
0.21
|
-0.06
|
0.26
|
0.82
|
|
0.43–0.33
|
13283
|
160
|
-0.78
|
0.19
|
-0.97
|
0.26
|
|
0.33–0.24
|
17463
|
90
|
-0.59
|
0.12
|
-0.72
|
-0.59
|
|
0.24–0.14
|
21584
|
92
|
0.26
|
-0.06
|
0.32
|
-0.78
|
|
0.14 − 0.11
|
14759
|
169
|
0.82
|
-0.20
|
1.02
|
0.21
|
(NDVI = Normalize Difference Vegetation Index, TWI = Topographic Wetness Index, SPI = Stream Power Index, TPI = Topographic Position Index and LULC = Land Use Land Cover) |
WBSI\(=\text{ln}\left(\frac{\text{E}\text{i}\text{j}}{\text{E}}\right)\) (5)
WBSI \(= ln\left[\frac{N\left(Si\right)}{N\left(Ni\right)}/\frac{?N\left(Si\right)}{?N\left(Ni\right)}\right]\)(6)
Where, WBSI, weight given to a certain class i of parameter j; Eij, landslide density within class i of parameter j; E, total landslide density within the entire study area. Here N (Si) is the number of landslide pixels in parameter class i, and N (Ni) is the total number of pixels in the same parameter class. In this current research every landslide causative factors were crossed checked with this landslide inventory map for determining the density of landslide for every class. The ultimate landslide susceptibility and risk map was produced in ArcGIS raster calculator tool. Positive WBSI values indicates the significant relationship within landslide causative variables and distribution of landslides. The negative WBSI values indicate the relationship between landslide causative factors and distribution of landslides are not relevant. In this study, the final landslide susceptibility index (LSI) map (Fig. 8) was prepared by bivariate statistical index (BSI) model (Eq. 7).
LSIBSI = ((WBSI * Elevation) + (WBSI * Slope) + (WBSI * Aspect) + (WBSI * Geology) +
(WBSI * Soil) + (WBSI * Drainage density) + (WBSI * Road density) + (7)
(WBSI * Rainfall) + (WBSI * TWI) + (WBSI * SPI) +
(WBSI * TPI) + (WBSI * NDVI) + (WBSI * LULC))
3.3.2 Weight of evidence (WOE) model
The WOE model is a bivariate statistical method based on the Bayesian approach and this was primary accomplish for non-spatial and quantitative imposition in the medical sciences (Lusted 1968). Thus, this success was extensively consecrated and acknowledgement on the geosciences for mineral potential mapping (Bonham-Carter et al., 1988), and ultimately applied in Slope instability and hazard mapping by different scholar (Lee et al. 2002a, b; van Westen et al. 2003; Mathew et al. 2007; Dahal et al. 2008a, b; Regmi et al. 2010). Weight of evidence (WOE) is a Bayesian approach with log-linear form which is uses preceding probability and subsequent probability (Regmi et al. 2010a). Previously, Van Western (2002) applied the method for landslide susceptibility assessment. This model is based on a log-linear form of Bayesian rule and can be written as:
$$P\left(A∣B\right)= \frac{P \left(B∣A\right) \times P\left(A\right)}{P \left(B\right)}$$
8
Thus, the probability of several events A occurring, given that event B has already occurred, P(A|B), is equal to the probability of event B taking place that event A has occurred, P(B|A), multiplied by the probability of event A occurring, P(A), and divided by the probability of event B occurring, P(B). WOE model calculates the weight of each landslide predictive factor (B) based on the degree of connection in the presence or absence of the landslide (L) within the area, (Bonham-Carter, 1994) as follows:
$${Wi}^{+}=\text{ln}\frac{P\left\{B|A\right\}}{P\left\{B|\stackrel{-}{A}\right\}}$$
9
$${Wi}^{+}=\text{ln}\left\{\frac{(Npix1 / (Npix1 + Npix2))}{(Npix3 / (Npix3 +Npix4))}\right\}$$
10
$${Wi}^{-}=\text{ln}\frac{P\left\{\stackrel{-}{B}|A\right\}}{P\left\{\stackrel{-}{B}|\stackrel{-}{A}\right\}}$$
11
$${Wi}^{-}=\text{ln}\left\{\frac{(Npix2 /(Npix1 + Npix2))}{(Npix4 /(Npix3 +Npix4))}\right\}$$
12
Where, P is the probability and ln is the natural log. Similarly, B is the availability of possible landslide predictive factor, \(\stackrel{-}{B}\) is the absence of a potential landslide predictive factor, A is the presence of landslide, and Ā is the absence of a landslide. The positive weight ( \({Wi}^{+}\) ) introduced that the predictable variable is present at the landslide locations in the sub-category factors and augmentation of this weight is an indication of positive correlation between predictable variables and landslides. The negative weight ( \({Wi}^{-}\) ) indicates the absence of the predictable variable and shows the level of negative correlation (Dahal et al. 2008a). The difference between two weights is called weighted contrast (C, EQ. 19). The final landslide susceptibility index (LSI) is produced by the combination of each landslide causative factors using overlay methods (Eq. 14).
$$C=({Wi}^{+}- {Wi}^{-})$$
13
$$LSI= \underset{i=1}{\overset{N}{?}}C$$
14
Applying bivariate WOE statistical model the landslide susceptibility index (LSI) map was made (Eq. 15).
LSIWOE = ((WWOE * Elevation) + (WWOE * Slope) + (WWOE * Aspect) +
(WWOE * Geology) + (WWOE * Soil) + (WWOE * Drainage density) + (15)
(WWOE * Road density) + (WWOE * Rainfall) + (WWOE * TWI) +
(WWOE * SPI) + (WWOE * TPI) + (WWOE * NDVI) + (WWOE * LULC))
3.3.3 Application of Index of Entropy (IOE) model
The index of entropy (IOE) model computes the weight of all landslides causative factors based by the bivariate analysis approach and used for determine the landslide susceptibility and landslide risk. The entropy by Shannon (1948) which is based on measured of uncertainty amalgamated with a random variable, imitating the system information content. Imbalance, disorder, uncertainty and instability of a systems are determined based on entropy (Yufeng and Fengxiang 2009). In this IOE model, the weighting process is based on this methodology which is proposed by Vlcko et al. (1980). The index of entropy (IOE) is widely used model and that determine the weight index of natural hazards and has been used various environmental impact assessment modelling, such as sand storms, droughts, debris flows and landslides (Li et al., 2002; Mon et al. 1994; Ren, 2000; Yi and Shi, 1994; Yang and Qiao 2009; Devkota et al. 2013; Jaafari et al. 2014; Youssef et al., 2014a, b). In the present study, the weighted parameter was obtained from the defined level of entropy representing the boundary where various factors influence the development of a landslide susceptibility and landslide risk. The information coefficient Wj representing the weight value for the causative factors and, it was calculated after Bednarik et al. (2010) and Constantin et al. (2011) which are as follows.
$$Pij= \frac{b}{a} ,$$
16
$$\left(Pij\right)= \frac{Pij}{{?}_{j=1}^{Sj}Pij} ,$$
17
Here, Hj and Hjmax are the entropy values (Eq. 16, 17) and they are written as;
$$Hj= -\underset{i=1}{\overset{Sj}{?}}\left(Pij\right) log2 \left(Pij\right) , j=1, 2, . . . , n ,$$
18
\(Hj max=log2 Sj ,\) Sj is the number of classes (19)
Ij is the information coefficient (Eq. 20) and Wj narrate the resultant weight value for the landslide causative parameter as a whole (Eq. 21).
\(Ij= \frac{Hj\text{max}- Hj}{Hj max}\) I = (0, 1) j = 1, 2.. . n, (20)
Where a and b are the domain and landslide percentages, respectively (Pij) is the probability density. The result ranges from 0 to 1. The closer the value of 1, the greater the slope instability and vice versa. The complete calculation of weight determination for the individual landslide causative parameters is presented in Table 7. The ultimate landslide susceptibility map was prepared by the summation of all individual landslide causative parameter classes. The final landslide susceptibility map was prepared using by this following equation as follows:
Table 7
The spatial relationship between every landslide conditioning factors and observed landslides Using Index of Entropy (IOE) models for all landslide causative factors classes.
Factors
|
Class
|
Class pixel
|
Landslide pixel
|
PIJ
|
(PIJ)
|
HJ
|
HJ max
|
IJ
|
PJ
|
WIJ
|
Elevation (m)
|
4100–3110
|
6841
|
218
|
3.42
|
0.52
|
1.502
|
2.32
|
0.353
|
1.308
|
0.4617
|
|
3110–2516
|
16104
|
338
|
2.25
|
0.34
|
|
|
|
|
|
|
2516–1993
|
20031
|
139
|
0.74
|
0.11
|
|
|
|
|
|
|
1993–1495
|
19285
|
16
|
0.09
|
0.01
|
|
|
|
|
|
|
1495 − 816
|
14545
|
5
|
0.04
|
0.01
|
|
|
|
|
|
Geology
|
gorubathan formation
|
9312
|
6
|
0.07
|
0.02
|
1.45
|
2.32
|
0.375
|
0.773
|
0.2898
|
|
lingtse genesis
|
4112
|
0
|
0
|
0.00
|
|
|
|
|
|
|
basic intrusive
|
16210
|
54
|
0.36
|
0.10
|
|
|
|
|
|
|
chungthang formation
|
14123
|
255
|
1.94
|
0.53
|
|
|
|
|
|
|
kanchanjangha formation
|
33049
|
401
|
1.30
|
0.36
|
|
|
|
|
|
Slope (o)
|
70.09–45.57
|
7799
|
114
|
1.57
|
0.30
|
2.18
|
2.32
|
0.064
|
1.046
|
0.068
|
|
45.57–35.14
|
15677
|
210
|
1.44
|
0.27
|
|
|
|
|
|
|
35.14–25.53
|
20253
|
218
|
1.15
|
0.22
|
|
|
|
|
|
|
25.53–15.37
|
20229
|
126
|
0.67
|
0.13
|
|
|
|
|
|
|
15.37–0
|
12848
|
48
|
0.40
|
0.08
|
|
|
|
|
|
Soil
|
fine skeletal
|
5224
|
1
|
0.02
|
0.00
|
1.73
|
2.58
|
0.331
|
1.238
|
0.4097
|
|
coarse loamy distrudeptic
|
32878
|
127
|
0.41
|
0.06
|
|
|
|
|
|
|
coarse loamy holithic
|
11997
|
156
|
1.39
|
0.19
|
|
|
|
|
|
|
fine loamy
|
6534
|
0
|
0
|
0.00
|
|
|
|
|
|
|
loamy skeletal
|
3754
|
126
|
3.60
|
0.48
|
|
|
|
|
|
|
coarce loamy
|
16419
|
306
|
2.00
|
0.27
|
|
|
|
|
|
Drainage Density
|
9.55–6.25
|
12033
|
62
|
0.55
|
0.11
|
2.11
|
2.32
|
0.09
|
0.996
|
0.08964
|
|
6.25–4.92
|
18190
|
73
|
0.43
|
0.09
|
|
|
|
|
|
|
4.92–3.62
|
17869
|
140
|
0.84
|
0.17
|
|
|
|
|
|
|
3.62–2.17
|
16626
|
312
|
2.01
|
0.40
|
|
|
|
|
|
|
2.17–0.09
|
12088
|
129
|
1.14
|
0.23
|
|
|
|
|
|
Road Density
|
11.17–6.86
|
2051
|
13
|
0.67
|
0.09
|
2.0
|
2.32
|
0.142
|
1.553
|
0.2204
|
|
6.86–4.48
|
4530
|
100
|
2.33
|
0.30
|
|
|
|
|
|
|
4.48–2.55
|
8439
|
252
|
3.16
|
0.41
|
|
|
|
|
|
|
2.55–0.88
|
14317
|
157
|
1.16
|
0.15
|
|
|
|
|
|
|
0.88–0
|
47469
|
194
|
0.43
|
0.06
|
|
|
|
|
|
Rainfall (mm)
|
1847–2386
|
6624
|
263
|
4.26
|
0.52
|
1.8
|
2.32
|
0.224
|
1.653
|
0.37054
|
|
2386–2791
|
5199
|
95
|
1.96
|
0.24
|
|
|
|
|
|
|
2791–3096
|
12076
|
137
|
1.22
|
0.15
|
|
|
|
|
|
|
3096–3323
|
31797
|
195
|
0.66
|
0.08
|
|
|
|
|
|
|
3323–3657
|
21110
|
26
|
0.13
|
0.02
|
|
|
|
|
|
TPI
|
15.25–11.26
|
6669
|
67
|
1.08
|
0.21
|
2.31
|
2.32
|
0.004
|
1.047
|
0.00418
|
|
11.26–10.15
|
18765
|
173
|
0.99
|
0.19
|
|
|
|
|
|
|
10.15–9.19
|
25823
|
228
|
0.95
|
0.18
|
|
|
|
|
|
|
9.19–8.31
|
18956
|
171
|
0.97
|
0.18
|
|
|
|
|
|
|
8.31–5.83
|
6593
|
77
|
1.25
|
0.24
|
|
|
|
|
|
SPI
|
145.37–47.88
|
133
|
0
|
0
|
0
|
1.96
|
2.32
|
0.159
|
0.819
|
0.1303
|
|
47.88–20.52
|
1060
|
7
|
0.71
|
0.17
|
|
|
|
|
|
|
20.52–9.12
|
4966
|
57
|
1.23
|
0.30
|
|
|
|
|
|
|
9.12–2.85
|
21030
|
255
|
1.30
|
0.32
|
|
|
|
|
|
|
2.85–0
|
49617
|
397
|
0.86
|
0.21
|
|
|
|
|
|
TWI
|
65.13–15.18
|
5334
|
20
|
0.40
|
0.09
|
2.20
|
2.32
|
0.056
|
0.884
|
0.0495
|
|
15.18–4.59
|
13142
|
65
|
0.53
|
0.12
|
|
|
|
|
|
|
4.59 - − 4.48
|
21264
|
206
|
1.04
|
0.23
|
|
|
|
|
|
|
-4.48 - − 14.57
|
22952
|
263
|
1.23
|
0.28
|
|
|
|
|
|
|
-14.57 - − 63.51
|
14114
|
162
|
1.23
|
0.28
|
|
|
|
|
|
LULC
|
Step cultivation
|
1648
|
0
|
0
|
0
|
1.40
|
2.81
|
0.504
|
1.056
|
0.53206
|
|
dense forest
|
45962
|
309
|
0.72
|
0.11
|
|
|
|
|
|
|
settlement
|
3865
|
7
|
0.19
|
0.03
|
|
|
|
|
|
|
bare soil
|
3921
|
149
|
4.08
|
0.64
|
|
|
|
|
|
|
river
|
1439
|
0
|
0
|
0.00
|
|
|
|
|
|
|
open forest
|
19971
|
251
|
1.35
|
0.21
|
|
|
|
|
|
Aspect
|
Flat
|
4
|
0
|
0
|
0
|
2.54
|
3.32
|
0.235
|
0.733
|
0.17221
|
|
North
|
2614
|
0
|
0
|
0
|
|
|
|
|
|
|
Northeast
|
2042
|
5
|
0.26
|
0.04
|
|
|
|
|
|
|
East
|
5587
|
52
|
1.00
|
0.14
|
|
|
|
|
|
|
Southeast
|
10496
|
137
|
1.40
|
0.19
|
|
|
|
|
|
|
South
|
14015
|
174
|
1.33
|
0.18
|
|
|
|
|
|
|
Southwest
|
10206
|
207
|
2.14
|
0.29
|
|
|
|
|
|
|
West
|
12646
|
116
|
0.98
|
0.13
|
|
|
|
|
|
|
Northwest
|
14206
|
28
|
0.21
|
0.03
|
|
|
|
|
|
|
North
|
4990
|
0
|
0
|
0
|
|
|
|
|
|
NDVI
|
0.64–0.43
|
9717
|
205
|
2.26
|
0.39
|
2.11
|
2.32
|
0.091
|
1.158
|
0.1048
|
|
0.43–0.33
|
13283
|
160
|
1.29
|
0.22
|
|
|
|
|
|
|
0.33–0.24
|
17463
|
90
|
0.55
|
0.10
|
|
|
|
|
|
|
0.24–0.14
|
21584
|
92
|
0.46
|
0.08
|
|
|
|
|
|
|
0.14 - − 0.11
|
14759
|
169
|
1.23
|
0.21
|
|
|
|
|
|
(NDVI = Normalize Difference Vegetation Index, TWI = Topographic Wetness Index, SPI = Stream Power Index, TPI = Topographic Position Index and LULC = Land Use Land Cover) |
$$YIOE= \sum _{i}^{n}\frac{z}{mi} \times C \times Wj ,$$
22
Where YIOE is the aggregate of all the factors classes; i is the number of particular parametric map (1, 2,. . ., n); z is the number of classes within landslide parametric map with the greatest number of classes; mi is the number of classes within particular landslide parametric map; C is the value of the class after secondary classification and Wj is the weight of a parameter (Bednarik et al.2010; Devkota et al.2013; Jaafari et al.2014). Applying IOE approach, the landslide susceptibility index (LSI) map was made for the Rorachu Watershed using Eq. 23.
YIOE = ((Elevation * 0.4617) + (Slope * 0.068) + (Aspect * 0.1722) +
(Geology * 0.2898) + (Soil * 0.4097) + (Drainage density * 0.0896) + (23)
(Road density * 0.2204) + (Rainfall * 0.3705) + (TWI * 0.0495) +
(SPI * 0.1303) + (TPI * 0.0041) + (NDVI * 0.1048) + (LULC * 0.532))
3.4 Multicollinearity test
Multicollinearity is a statistical testing phenomenon in which is tested the occurrences of intercorrelations among two or multiple independent variables with an earmarked degree of accuracy. Multicollinearity does not reduce the predictive power or reliability of the model as a whole; it only effects calculations regarding individual predictors (Fig. 9). previously using the landslide causative variables for the landslide susceptibility index (LSI) and landslide risk modeling, it is indispensable to test the multicollinearity of all the landslide causative factors (Zhou et al. 2018; Arabameri et al. 2019; Chen et al. 2018). Tolerance (TOL) and the Variance influencing factors (VIF) are both important indexes for multicollinearity diagnostic. VIF is just the reciprocal of tolerance (TOL). A tolerance (TOL) of less than 0.20 or 0.10 and/or a VIF of 5 or 10 and above implies a multicollinearity problem (O’Brien 2007). According to the Table 8, the smallest tolerance (TOL) of different models (BSI, IOE and WOE) were 0.321, 0.383 and 0.386 showing the rainfall parameter respectively. The variance influencing factors (VIF) of these models (BSI, IOE and WOE) are 3.115, 2.610 and 2.590 values showing rainfall parameter respectively. So there is no multicollinearity between independent landslide causative factors in this current research. The variance influencing factors (VIF) and the tolerance (TOL) as calculated following equations which is as follows
Table 8
Multicollinearity analysis of BSI, IOE and WOE approach
Factors
|
BSI
|
WOE
|
IOE
|
TOL
|
VIF
|
TOL
|
VIF
|
TOL
|
VIF
|
Elevation
|
0.634
|
1.577
|
0.589
|
1.697
|
0.524
|
1.908
|
Slope
|
0.568
|
1.760
|
0.598
|
1.672
|
0.592
|
1.688
|
Aspect
|
0.821
|
1.218
|
0.825
|
1.213
|
0.818
|
1.223
|
Geology
|
0.571
|
1.753
|
0.579
|
1.728
|
0.567
|
1.763
|
Soil
|
0.661
|
1.513
|
0.663
|
1.509
|
0.656
|
1.523
|
Drainage Density
|
0.559
|
1.789
|
0.772
|
1.296
|
0.552
|
1.811
|
Road density
|
0.847
|
1.181
|
0.845
|
1.183
|
0.844
|
1.185
|
TPI
|
0.705
|
1.418
|
0.626
|
1.598
|
0.621
|
1.611
|
TWI
|
0.686
|
1.459
|
0.527
|
1.898
|
0.524
|
1.910
|
SPI
|
0.863
|
1.158
|
0.715
|
1.399
|
0.714
|
1.400
|
NDVI
|
0.504
|
1.986
|
0.505
|
1.981
|
0.499
|
2.003
|
Rainfall
|
0.321
|
3.115
|
0.386
|
2.590
|
0.383
|
2.610
|
LULC
|
0.979
|
1.021
|
0.969
|
1.031
|
0.979
|
1.022
|
TOL is the tolerance; VIF is the variance influencing factors and \({Ri}^{2}\) is the coefficient of determination of landslide conditioning factors i. The multicollinearity statistics of all the models (BSI, IOE and WOE) are shows in Table 8.
3.6 Landslide risk mapping
The risk is the maximum prospective dimension of loss due to particular landslide events in a particular area and during certain time of period. Landslide hazard risk resolution aims to determine the probability of element-at-risk by the specific hazard will cause harm, and it inquire into the relevance between the instance of damaging events and the predominance of the consequences (Guzzetti et al. 2009). The risk analysis is very much significant for establishment of settlements in mountain areas, construction of roads, and land use practices. Varnes DJ. (1984), Fell (1994), Leroi (1996), and Xu et al. (2012) have successfully assessed landslide risk in different areas. According to the Xu et al. (2012), the risk is defined as the probability of damage caused by a particular hazard to a specific element is followed by this equation as
Here, H denotes the Hazard expressed as probability of occurrence within a reference period and V define the Physical vulnerability of a particular type of element-at-risk (from 0 = not vulnerable and 1 = vulnerable) for a specific type of hazard and for a specific element-at-risk.