Landslide is one of the most complex movements of the earth. It’s very difficult to Identification and mapping of suitable landslide factors for the vulnerability modeling and assessment. The critical point was the selection of accurate pixel size for positional accuracy and precision of the landslide susceptibility levels in the study area (Sahabi et al., 2014). So we must be proper expertise knowledge for the identification of prime factors for the Landslide Susceptibility Index (LSI) and Landslide Risk (LR) modeling. Also, there are no standard guidance for selecting the parameters for slope instability modeling (Ayalew et al., 2005), the nature of the study area, the scale of the analysis, and data availability were taken into account (Yalcin 2008). In this respect, thirteen factors are considering for Landslide susceptibility Index (LSI) and Landslide risk (LR) modeling and analysis (Fig. 2). It is important to compile a digitized database for execution the landslide vulnerability modeling map using GIS. The spatial database has been design and execute for the landslide vulnerability modeling of this study area as shown in (Table 1) In this study, both categorical and continuous data were used for the landslide modeling and ArcGIS 10.2, SPSS 23 and R was applied for the entire analysis.
Table 1. Sources of data layers of various landslide causative factors
3.2 Selection of landslide conditioning factors
Although enormous studies have been contacted regarding landslide vulnerability analysis been done to develop landside susceptibility map of the Rorachu river basin. There are no such criteria for selecting factors for landslide vulnerability analysis (Ayalew and Yamagishi 2005). The factors controlling slope instability modeling considered in the present study are including Elevation, Geology, Slope, Soil, Drainage Density (DD), Road Density (RD), Rainfall, Normalize Difference Vegetation Index (NDVI), and Slope curvature, Topographic Position Index (TPI), Stream Power Index (SPI), Topographic Wetness Index (TWI) and Land Use Land Cover (LULC). A particular parameter may be important controlling factors for landslide occurrence in one area but not in another place. All the factors are applied by different researcher in across the globe (Wu et al., 2017).
Geology plays an important role in the occurrence of slope instability because the lithological and structural variations often leads to difference in strength of soil and rocks (Pradhan and Lee 2010a) of this Rorachu watershed. Geologically the study area is characterized by the process of five lithological units including 1.Basic Intrusive, 2. Chungthang Formation, 3.Gorubathan Formation, 4.Lingtse Gnesis, 5.Kanchenjunga Gnesis or Darjeeling Gnesis (undifferentiated) (Fig. 4. Table 2). The geology map of Rorachu watershed was prepared by district resource map of east Sikkim collected from geological survey of india (GSI), Kolkata. Large part of this watershed is covered by Kanchenjunga Gnesis or Darjeeling Gnesis. Lithological unit of basic Kanchenjunga gnesis cover large area (43.02%) ranked first and 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 are much more probable to slope instability.
Table 2. Description of geological parameters of Rorachu watershed
ERA
|
FORMATION
|
CHARACTERISTICS
|
LITHOLOGY
|
Meso-Proterozoic
|
Lingtse gneiss
|
The gneisses are sheet like bodies of coarse to medium grained, foliated to strongly lineated granite mylonite. These are streaky, banded, augen gneisses or porphyroblastic gneisses and are traversed by concordant and discordant pegmatite veins. Amphibolite intrusives with sharp contacts are also recorded within gneisses. The most characteristic feature of the Lingtse granite is the presence of a stretching lineation.
|
Granite gneiss (mylonite)
|
Proterozoic (Undifferentiated)
|
Basic intrusive
|
Basic Intrusive rocks are characterized by large crystal sizes, and as the individual crystals are visible, the rock is called phaneritic. This is formed as the magma cools underground and while cooling may be fast or slow; cooling is slower than on the surface, so larger crystals grow.
|
Tourmaline / biotite leuco granite, schroll rock/
pegmatite, aplite (Undifferentiated)
|
Gorubathan formation
|
The formation consists of mappable, monotonous sequence of inter banded chlorite sericite schist / phyllite,
quartzite, meta greywacke, pyritiferrous black slate/ carbon phylllite, basic meta volcanics. Chlorite phyllite is dark green to light green whereas the quartz chlorite
phyllite is only light green in color.
|
Interbanded chlorite-sericite schist / phyllite
and quartzite, meta-greywacke (quartzo
feldspathic greywacke), pyritiferous black slate,
biotite phyllite / mica schist, biotite quartzite,
mica schist with garnet, with / without staurolite,
chlorite quartzite
|
Kanchenjunga gneiss/Darjeeling gneiss
|
The gneisses, dominantly comprising quartz,
feldspar and biotite (with minor amounts of other
minerals) have been classified into three types, ie.1)
banded / streaky gneisses / migmatites, 2) augen bearing
biotite gneiss with/without garnet, kyanite, sillimanite and 3) sillimanite granite gneisses. Mapping of these rocks as individual units is very difficult because they are characterized by frequent interchanging and gradational features among themselves.
|
Banded / streaky migmatite, augen bearing (garnet) biotite gneiss with/ without kyanite,
sillimanlte with palaeosomes of staurolite,
kyanite, mica schist, biotite gneiss, sillimanite granite gneiss
|
Chungthang formation
|
The main rock types of this formation are quartzites, garnet-kyanite-staurolite bearing biotite schist, calc silicate rock, graphitic schist and amphibolite.
|
Quartzite 2. Garnet kyanite sillimanite
biotite schist / Garnetiferous mica schist Chungthang
3. Calc-silicate, carbonaceous schist Formation
|
Figure 4. Geology map of the study area
Table 2. Description of geological parameters of Rorachu watershed
Elevation or altitude is one of the significant parameter that has been frequently used for landslide conditioning parameters. It is controlled by different geological and geomorphological process (Ayalew et al., 2005; Pourghasemi, 2008). In the present study area, the elevation ranges between 816 m to 4100 m (Fig. 5. a). The elevation values were classified into 5 categories with 30 * 30 meter resolution. During the field visit we noticed that most of the landslides are seen in medium and high elevation of the Rorachu watershed area. Slope gradient is one of the most significant factors for 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 less probability for slope instability due to lower shear stress (Dai et al., 2001). In the current study slope map classified five categories using natural breaks method in ArcGIS 10.3. Slope angel ranges from 00 to 700 (Fig. 5. b) and there are more than 30% area under 35o to 70o slope angel in this Rorachu watershed. Soil is a very important factor for slope instability in mountain area due to soil saturation. In Rorachu watershed more than 90% becomes a hilly region. Soil of the Rorachu watershed was divided into six several categories (Fig. 5.c, Table 3) such as 1. Coarse loamy humic dystrudepts, 2. Coarse loamy humic lithic dystrudepts, 3. Coarse loamy typic hapludolls, 4. Fine loamy fluventic eutrudepts, 5. Fine skeletal cumuli hapludolls and 6. Loamy skeletal entic hapludolls. In Rorachu watershed, all soil categories are converted vector polygon to raster format into 30 *30 meter grids.
Table 3. Soil characteristics map of Rorachu watershed (According to Mandal S, Mandal K 2017a)
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 of that grid (Horton, 1932, 1945; Strahler, 1952). Drainage density (DD) indicates the measure of how well or how poorly a river watershed is drained by stream channels. Drainage density helps to determine the degree of reducing the shear strength of this slope which has affective for slope instability. In this study, drainage density was assessed by this formula (Eq. 1)
$$Dd=\left(Lt/Abasin\right)$$
1
Where, Dd represents drainage density, LT represents total length of the streams in that grid and Abasin represent total length of the grid area. Drainage density of the Rorachu river basin was prepared by the method of Euclidean distance in ArcGIS 10.3 into 30 * 30 meter grids (Fig. 5. d). It was classified into five classes by natural breaking method.
Figure 5. Landslide conditioning factors a. elevation map, b. Slope, c. Soil map and d. Drainage density
Roads networks are major threat in slope instability in mountain areas. Roads modify the natural gradient of the slope and create an obstacle for surface water flow (Marcini, F., 2010). Road map was prepared by different source like, 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. 6. e). Normalize difference vegetation index (NDVI) is a numerical indicator that uses for the vegetation conditions of the surface. NDVI was calculating 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 this Rorachu watershed, calculated NDVI by the LANDSAT 8 OLI image in ERDAS 9.2 image processing software (Fig. 6. f) and ranges the NDVI value − 0.11 to 0.64. Positive value indicates the healthy vegetation cover in which useful for slope stability and also reduces soil erosion and slope failure. Negative NDVI values delimitate the no vegetation cover in Rorachu watershed areas which is more vulnerable for slop instability and excessive soil erosion and slope failure. Slope curvature is used to indicate the steepness of a curve at a particular point. Slope curvature is significant parameters for landslide susceptibility mapping (Lee and Sambath, 2006 and Greco et al., 2007). In this Rorachu watershed slope curvature was calculated by the ASTER GDEM data (Fig. 6. g). Slope curvature values illustrate the morphology of the topography (Lee and Min, 2001) that has described the surface condition of this Rorachu river basin. Positive curvature values represent a convex slope which is more probable to slope failure and less drainage concentration. Negative curvature values represent as concave slope which has more chance to drainage concentration and less landslide vulnerability. Zero curvature values represent the flat surface. Mathematically, it is the reciprocal of the radius of a circle that is tangent to a point on a curve (Roberts 2001). It helps us to identify the zones that exhibit instinct to landslide vulnerability. The curvature map of this Rorachu watershed was prepared with five classes. Topographic position index (TPI) is an algorithm in which increasingly used to measure topographic slope positions and automated landform classifications. Topographic position index (TPI) calculation as proposed by (Guisan et al., 1999).TPI is a topographic position classification identifying upper, middle and lower part of the landscape. Positive TPI values represent locations that are higher than the surroundings (ridges) .Negative TPI values represents locations that are lower than the surroundings (valleys).TPI values near zero are either flat areas or constant slope. In this study area TPI was calculated by SAGA GIS software, and the value of TPI ranges in between − 63.51 to 65.13 (Fig. 6. h).
Figure 6. Landslide conditioning factors e. Road density f. NDVI g. Curvature h. TPI
Stream power index (SPI) is a measured of the erosive power of the flowing water. Calculation of the stream power index (SPI) based on slope and Specific catchment area (SCA). The stream power index (SPI) can be defined as (Moore and Grayson1991):
$$\text{S}\text{P}\text{I}=\text{A}\text{s} \text{t}\text{a}\text{n}{\beta }$$
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 was represented in between 0 and 145.37 and classified into five classes (Fig. 7. i). Topographic wetness index (TWI) another important factors for landslide susceptibility modeling. It is commonly used for to quantify of the topographic control or hydrological process. TWI refers to the accumulation of water in a particular point at a time of any grid cell. For the shallow landslide modeling, using the TWI by different researcher (Gokceoglu et al. 2005; and Yilmaz, 2009). In this study area TWI map was prepared by SAGA GIS software using the following Eq. (3). TWI map was classified into five categories (Fig. 7. j). TWI model (Beven and Kirkby 1979) defined as
$$\text{T}\text{W}\text{I}=\text{l}\text{n}\left(\frac{\text{a}}{\text{t}\text{a}\text{n}{\beta }}\right)$$
3
Where, a is the cumulative upslope area draining through a point (per unit contour length) and tanβ is the slope angel at the point, which is used to replace approximately the hydraulic gradient under steady state conditions (Poudyal et al., 2010). In the present study, TWI classified into five classes (Fig. 6k), which ranges between 5.83 and 15.25. Land Use Land Cover (LULC) is one of the most important parameters and significant for the role of slope stability and instability. LULC map was derived LANDSAT 8 OLI satellite image (2019) data, and verified by Google earth image and field verification using supervised classification techniques by ERDAS 9.2 software. The study area is exhibit various types of land use land cover such as step cultivation, open forest, settlement, bare soil, landslide area, river and dense forest. In the Rorachu watershed most of the LULC covered by Forest (open and dense) 59% area followed by settlement 3.47% and bare land 3.23% (Fig. 7. k).
Figure 7. Landslide conditioning factors i. Stream power index (SPI), j. TWI, k. LULC and l. Rainfall (mm)
Rainfall is one of the most important factors for landslide in Rorachu watershed areas. In this mountain area abrupt rainfall causes shallow landslide. Rainfall map was prepared by world climatic data and applied Inverse distance weighted (IDW) modeling for the rainfall mapping and classified into 5 categories. Rorachu watersheds represent the ranges between 1847 mm to 3657 mm rainfall (according to http://www.geog.ucsb.edu/~bodo/TRMM/#tif). Maximum rainfall occurrence in between June and august (according to IMD data, Table 4. Figure 7. l).
Table 4
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
|
Table 4. Monthly Rainfall distribution in the East Sikkim area (2009–2015). Source: Indian Meteorological Department (IMD) Gangtok, Sikkim
3.3 Modelling landslide susceptibility and Risk
This study summarizes the outcomes of landslide susceptibility mapping in the Rorachu watershed, east Sikkim, through GIS techniques. Although there are several bivariate, multivariate statistical approach for landslide susceptibility or slope instability mapping. Due to their ease of implementation, we chose three alternative statistical models (FR, IV, and CF) for this landslide susceptibility analysis. Each statistical approach is described in detail in the subsections that follows.
3.3.1 Frequency Ratio (FR) Model
Various bivariate statistical methods were applied previously for landslide susceptibility analysis in different parts of the world where frequency ratio (FR) model is too much popular (Luzi et al. 2000; Lee and Choi 2003; Lee and Talib 2005; Porghasemi 2007; Lee and Pradhan 2007; Akgun et al. 2008; Jadda 2009; Pradhan and Lee 2009). Frequency ration (FR) model is a simple statistical method in which to calculate the probabilistic relationship between present landslide and landslide conditioning factors. This model based on the observed relationships between each factor and appeared landslides in this Rorachu watershed. Frequency ratio (FR) model is the ratio of the probabilities of landslide occurrence to a nonoccurrence for a given attribute (Bonhan – Carter, 1994; Pradhan and Lee 2009). The frequency ration (FR) model can be expressed as:
$$FR= \frac{\frac{Npix\left(SXi\right)}{\sum _{i=1}^{m}SXi}}{\frac{Npix\left(Xj\right)}{{\sum }_{j=1}^{n}Npix\left(Xj\right)}}$$
4
Where, Npix(SXi) is the number of pixel with landslides within class I of parameter variable X, Npix(Xj) is the number of pixel within parameter variable Xj, m is the number of classes in the parameter variable Xi. And N is the number of parameters in the study area (Regmi et al., 2014). The landslide susceptibility index (LSI) can be propagating by summation of each factors of FR value as:
$$LSI= \sum _{ij=1}^{N}FR$$
5
Where, LSI is the landslide susceptibility index, N is the total number of variables, ij is the frequency ratio value of each class and FR is the frequency ratio values. A FR value greater than 1 indicates the higher probability of landslide occurrence and less than the value 1 is indicating the lower probability of landslide occurrence or low correlation. To calculate the frequency ratio (FR) values in all factors are given (Table 5).
Table 5
Spatial relationship between each landslide conditioning factors and observed landslides
Factors
|
Class
|
Class pixel
|
Landslide pixel
|
Npix(Xj)
|
Npix(SXi)
|
FR
|
Si/Ni
|
S/N
|
IV
|
PPa
|
PPs
|
CF
|
Elevation (m)
|
4100–3110
|
6841
|
218
|
0.30
|
0.09
|
3.42
|
0.30
|
0.01
|
1.51
|
0.0319
|
0.0093
|
0.714
|
|
3110–2516
|
16104
|
338
|
0.47
|
0.21
|
2.25
|
0.47
|
0.01
|
1.70
|
0.0210
|
0.0093
|
0.561
|
|
2516–1993
|
20031
|
139
|
0.19
|
0.26
|
0.74
|
0.19
|
0.01
|
1.32
|
0.0069
|
0.0093
|
-0.257
|
|
1993–1495
|
19285
|
16
|
0.02
|
0.25
|
0.09
|
0.02
|
0.01
|
0.38
|
0.0008
|
0.0093
|
-0.912
|
|
1495 − 816
|
14545
|
5
|
0.01
|
0.19
|
0.04
|
0.01
|
0.01
|
-0.13
|
0.0003
|
0.0093
|
-0.963
|
Geology
|
gorubathan formation
|
9312
|
6
|
0.01
|
0.12
|
0.07
|
0.01
|
0.01
|
-0.05
|
0.0006
|
0.0093
|
-0.931
|
|
lingtse genesis
|
4112
|
0
|
0
|
0.05
|
0
|
0
|
0.01
|
0
|
0.0000
|
0.0093
|
-1.000
|
|
basic intrusive
|
16210
|
54
|
0.08
|
0.21
|
0.36
|
0.08
|
0.01
|
0.91
|
0.0033
|
0.0093
|
-0.645
|
|
chungthang formation
|
14123
|
255
|
0.36
|
0.18
|
1.94
|
0.36
|
0.01
|
1.58
|
0.0181
|
0.0093
|
0.488
|
|
kanchanjangha formation
|
33049
|
401
|
0.56
|
0.43
|
1.30
|
0.56
|
0.01
|
1.78
|
0.0121
|
0.0093
|
0.234
|
Slope (in degree)
|
70.09–45.57
|
7799
|
114
|
0.16
|
0.10
|
1.57
|
0.16
|
0.01
|
1.23
|
0.0146
|
0.0093
|
0.366
|
|
45.57–35.14
|
15677
|
210
|
0.29
|
0.20
|
1.44
|
0.29
|
0.01
|
1.50
|
0.0134
|
0.0093
|
0.307
|
|
35.14–25.53
|
20253
|
218
|
0.30
|
0.26
|
1.15
|
0.30
|
0.01
|
1.51
|
0.0108
|
0.0093
|
0.135
|
|
25.53–15.37
|
20229
|
126
|
0.18
|
0.26
|
0.67
|
0.18
|
0.01
|
1.28
|
0.0062
|
0.0093
|
-0.334
|
|
15.37–0
|
12848
|
48
|
0.07
|
0.17
|
0.40
|
0.07
|
0.01
|
0.86
|
0.0037
|
0.0093
|
-0.601
|
Soil
|
fine skeletal
|
5224
|
1
|
0.00
|
0.07
|
0.02
|
0.00
|
0.01
|
-0.82
|
0.0002
|
0.0093
|
-0.980
|
|
coarse loamy distrudeptic
|
32878
|
127
|
0.18
|
0.43
|
0.41
|
0.18
|
0.01
|
1.28
|
0.0039
|
0.0093
|
-0.588
|
|
coarse loamy holithic
|
11997
|
156
|
0.22
|
0.16
|
1.39
|
0.22
|
0.01
|
1.37
|
0.0130
|
0.0093
|
0.286
|
|
fine loamy
|
6534
|
0
|
0
|
0.09
|
0
|
0
|
0.01
|
0
|
0.0000
|
0.0093
|
-1
|
|
loamy skeletal
|
3754
|
126
|
0.18
|
0.05
|
3.60
|
0.18
|
0.01
|
1.28
|
0.0336
|
0.0093
|
0.729
|
|
coarce loamy
|
16419
|
306
|
0.43
|
0.21
|
2.00
|
0.43
|
0.01
|
1.66
|
0.0186
|
0.0093
|
0.505
|
Drainage Density
|
9.55–6.25
|
12033
|
62
|
0.09
|
0.16
|
0.55
|
0.09
|
0.01
|
0.97
|
0.0052
|
0.0093
|
-0.450
|
|
6.25–4.92
|
18190
|
73
|
0.10
|
0.24
|
0.43
|
0.10
|
0.01
|
1.04
|
0.0040
|
0.0093
|
-0.572
|
|
4.92–3.62
|
17869
|
140
|
0.20
|
0.23
|
0.84
|
0.20
|
0.01
|
1.32
|
0.0078
|
0.0093
|
-0.161
|
|
3.62–2.17
|
16626
|
312
|
0.44
|
0.22
|
2.01
|
0.44
|
0.01
|
1.67
|
0.0188
|
0.0093
|
0.508
|
|
2.17–0.09
|
12088
|
129
|
0.18
|
0.16
|
1.14
|
0.18
|
0.01
|
1.29
|
0.0107
|
0.0093
|
0.128
|
Road Density
|
11.17–6.86
|
2051
|
13
|
0.02
|
0.03
|
0.68
|
0.02
|
0.01
|
0.29
|
0.0063
|
0.0093
|
-0.322
|
|
6.86–4.48
|
4530
|
100
|
0.14
|
0.06
|
2.37
|
0.14
|
0.01
|
1.18
|
0.0221
|
0.0093
|
0.583
|
|
4.48–2.55
|
8439
|
252
|
0.35
|
0.11
|
3.20
|
0.35
|
0.01
|
1.58
|
0.0299
|
0.0093
|
0.694
|
|
2.55–0.88
|
14317
|
157
|
0.22
|
0.19
|
1.18
|
0.22
|
0.01
|
1.37
|
0.0110
|
0.0093
|
0.151
|
|
0.88–0
|
47469
|
194
|
0.27
|
0.62
|
0.44
|
0.27
|
0.01
|
1.46
|
0.0041
|
0.0093
|
-0.564
|
Rainfall (mm)
|
1847–2386
|
6624
|
263
|
0.37
|
0.09
|
4.26
|
0.37
|
0.01
|
1.60
|
0.0397
|
0.0093
|
0.758
|
|
2386–2791
|
5199
|
95
|
0.13
|
0.07
|
1.96
|
0.13
|
0.01
|
1.15
|
0.0183
|
0.0093
|
0.485
|
|
2791–3096
|
12076
|
137
|
0.19
|
0.16
|
1.22
|
0.19
|
0.01
|
1.31
|
0.0113
|
0.0093
|
0.177
|
|
3096–3323
|
31797
|
195
|
0.27
|
0.41
|
0.66
|
0.27
|
0.01
|
1.47
|
0.0061
|
0.0093
|
-0.515
|
|
3323–3657
|
21110
|
26
|
0.04
|
0.27
|
0.13
|
0.04
|
0.01
|
0.59
|
0.0012
|
0.0093
|
-6.508
|
NDVI
|
0.64–0.43
|
9717
|
205
|
0.29
|
0.13
|
2.26
|
0.29
|
0.01
|
1.49
|
0.0211
|
0.0093
|
0.563
|
|
0.43–0.34
|
13283
|
160
|
0.22
|
0.17
|
1.29
|
0.22
|
0.01
|
1.38
|
0.0120
|
0.0093
|
0.228
|
|
0.34–0.24
|
17463
|
90
|
0.13
|
0.23
|
0.55
|
0.13
|
0.01
|
1.13
|
0.0052
|
0.0093
|
-0.816
|
|
0.24–0.14
|
21584
|
92
|
0.13
|
0.28
|
0.46
|
0.13
|
0.01
|
1.14
|
0.0043
|
0.0093
|
-1.198
|
|
0.14 - -0.11
|
14759
|
169
|
0.24
|
0.19
|
1.23
|
0.24
|
0.01
|
1.40
|
0.0115
|
0.0093
|
0.188
|
Curvature
|
CONCAVE
|
43887
|
375
|
0.52
|
0.57
|
0.92
|
0.52
|
0.01
|
1.75
|
0.0085
|
0.0093
|
-0.084
|
|
FLAT
|
14592
|
90
|
0.13
|
0.19
|
0.66
|
0.13
|
0.01
|
1.13
|
0.0062
|
0.0093
|
-0.516
|
|
CONVEX
|
18327
|
251
|
0.35
|
0.24
|
1.47
|
0.35
|
0.01
|
1.58
|
0.0137
|
0.0093
|
0.322
|
TPI
|
15.25–11.26
|
6669
|
67
|
0.09
|
0.09
|
1.08
|
0.09
|
0.01
|
1.00
|
0.0100
|
0.0093
|
0.073
|
|
11.26–10.15
|
18765
|
173
|
0.24
|
0.24
|
0.99
|
0.24
|
0.01
|
1.41
|
0.0092
|
0.0093
|
-0.011
|
|
10.15–9.19
|
25823
|
228
|
0.32
|
0.34
|
0.95
|
0.32
|
0.01
|
1.53
|
0.0088
|
0.0093
|
-0.053
|
|
9.19–8.31
|
18956
|
171
|
0.24
|
0.25
|
0.97
|
0.24
|
0.01
|
1.41
|
0.0090
|
0.0093
|
-0.033
|
|
8.31–5.83
|
6593
|
77
|
0.11
|
0.09
|
1.25
|
0.11
|
0.01
|
1.06
|
0.0117
|
0.0093
|
0.204
|
SPI
|
145.4–47.88
|
133
|
0
|
0
|
0.002
|
0
|
0
|
0.01
|
0
|
0
|
0.0093
|
-1
|
|
47.88–20.52
|
1060
|
7
|
0.01
|
0.01
|
0.71
|
0.01
|
0.01
|
0.02
|
0.0066
|
0.0093
|
-0.294
|
|
20.52–9.12
|
4966
|
57
|
0.08
|
0.06
|
1.23
|
0.08
|
0.01
|
0.93
|
0.0115
|
0.0093
|
0.190
|
|
9.12–2.85
|
21030
|
255
|
0.36
|
0.27
|
1.30
|
0.36
|
0.01
|
1.58
|
0.0121
|
0.0093
|
0.233
|
|
2.85–0
|
49617
|
397
|
0.55
|
0.65
|
0.86
|
0.55
|
0.01
|
1.77
|
0.0080
|
0.0093
|
-0.143
|
TWI
|
65.13–15.18
|
5334
|
20
|
0.03
|
0.07
|
0.40
|
0.03
|
0.01
|
0.48
|
0.0037
|
0.0093
|
-0.600
|
|
15.18–4.59
|
13142
|
65
|
0.09
|
0.17
|
0.53
|
0.09
|
0.01
|
0.99
|
0.0049
|
0.0093
|
-0.472
|
|
4.59 - − 4.48
|
21264
|
206
|
0.29
|
0.28
|
1.04
|
0.29
|
0.01
|
1.49
|
0.0097
|
0.0093
|
0.038
|
|
-4.5 - − 14.57
|
22952
|
263
|
0.37
|
0.30
|
1.23
|
0.37
|
0.01
|
1.60
|
0.0115
|
0.0093
|
0.188
|
|
-14.6 - − 63.5
|
14114
|
162
|
0.23
|
0.18
|
1.23
|
0.23
|
0.01
|
1.39
|
0.0115
|
0.0093
|
0.190
|
LULC
|
Step cultivation
|
1648
|
0
|
0
|
0.02
|
0
|
0
|
0.01
|
0
|
0
|
0.0093
|
-1
|
|
dense forest
|
45962
|
309
|
0.43
|
0.60
|
0.72
|
0.43
|
0.01
|
1.67
|
0.0067
|
0.0093
|
-0.281
|
|
settlement
|
3865
|
7
|
0.01
|
0.05
|
0.19
|
0.01
|
0.01
|
0.02
|
0.0018
|
0.0093
|
-0.807
|
|
bare soil
|
3921
|
149
|
0.21
|
0.05
|
4.08
|
0.21
|
0.01
|
1.35
|
0.0380
|
0.0093
|
0.762
|
|
river
|
1439
|
0
|
0
|
0.02
|
0
|
0
|
0.01
|
0
|
0
|
0.0093
|
-1
|
|
open forest
|
19971
|
251
|
0.35
|
0.26
|
1.35
|
0.35
|
0.01
|
1.58
|
0.0126
|
0.0093
|
0.261
|
Using Frequency Ratio (FR), Information Value (IV) and Certainty Factor (CF) models for all landslide causative factors classes. |
3.3.2 Information Value (IV) model
The information value (IV) is a bivariate statistical method that was develops from information theory. Information model employed for the spatial prediction on an event based on the parameter and event relationships. It has been very useful method for landslide susceptibility modeling by determining the influence of parameter. This information value (IV) model was originally introduced by Yin and Yan (1988) and modified slightly by Van Westen (1993). This model was first applied for geological hazard and disaster risk assessment. The information value (IV) can be expressed by:
$$Ii= \text{log}\frac{Si/Ni}{S/N}$$
6
Where, Ii is the information value (IV), N = total number of data points (Grid cells), S = number of grid cells with landslides, Si = number of grid cells involving the parameter and containing landslide, Ni = number of grid cells involving the parameter. The landslide susceptibility index (LSI) can be represented by the summation of total information value (IV) in a grid cell j is:
$$LSI \left(Ij\right)= \sum _{i=1}^{M}Xji \times Ii$$
7
$$LSI \left(Ij\right)= \sum _{i=1}^{M}Xji \times log\frac{Si/Ni}{S/N}$$
8
Where, Xji is the value parameter I, j = 1, 2, 3……..M: = 1, if parameter i exists in grid cell j and = 0, if parameter does not exist in grid cell j; M = number of parameter considered. The above model was prepared for each class of parameter variables for landslide susceptibility analysis and total calculate total information value (IV) of grid cell of this Rorachu watershed. More the information value (IV) high probability of landslide susceptibility and less the information value (IV) lowers the probability of landslide susceptibility. To calculate the information value (IV) in all variables in (Table 5).
3.3.3 Certainty Factor (CF) model
Certainty factor (CF) is one of the most probabilistic models in used for landslide susceptibility analysis. Certainty Factor (CF) is a probabilistic model that has been applied by different researchers in landslide susceptibility mapping in different parts of the world (Kanungo et al. 2011; Gokceolu et al. 2005). The certainty factor (CF) model is one of the most possible proposed functions that handle and combine different type of data and heterogeneity and uncertainty of the input data. Higher the percentages of landslides correctly predicted, greater the validity of the CF model which is based on the assumptions. Certainty factor (CF) is calculated on the basis of landslide inventory and landslide frequency occurrence probability of each class in thematic layers. The certainty factor as a function of probability was originally proposed by Shortliffe and Buchanan (1975) and modified by Heckerman (1986). The certainty factor (CF) was calculated in the following equations:
$$CF=\left\{\begin{array}{c}\frac{PPa-PPs}{PPa(1-PPs)} if PPa \ge PPs\\ \frac{PPa-PPs}{PPs(1-PPa)} if PPa < PPs \end{array}\right.$$
9
Where, CF is the certainty factor, PPa is the conditional probability of having a number of landslides in the class ‘a’ (e.g., forest in land use land cover layer, concave curvature in curvature layer, etc.) and PPs is the prior probability of having the total number of landslides in the study area ‘A’. The certainty factor (CF) value ranges between + 1 to -1. Positive values intimate an increase of certainty whereas negative value corresponding decrease the certainty. A value close to 0 indicates that the prior probability is very similar to conditional probability. The layers are combined brace wise according to the integration rules (Chung and Fabbri 1993; Binaghi et al.1998). The combination of CF values of two thematic layers ‘z’ is revealed in the following equation as given by Binaghi et al. (1998):
$$Z= \left\{\begin{array}{c}x+y-xy , x,y >=0 \\ \frac{x+y}{1-min(x , y )} x,y opposite sign \\ x+y+xy x , y <0 \end{array}\right.$$
10
The certainty factor (CF) values were calculated in Rorachu watershed by overlaying each factor with the landslide map and computed the landslide frequencies. Every thematic layer reclassified according to their certainty factor (CF) values and amalgamated pairwise to propagate the landslide susceptibility map of Rorachu watershed area using the integrating rule of Eq. (9). Calculations of certainty factor (CF) in each landslide factors are representing in (Table 5).
Table 5. Spatial relationship between each landslide conditioning factors and observed landslides
Using Frequency Ratio (FR), Information Value (IV) and Certainty Factor (CF) models for all landslide causative factors classes.
3.4 Multicollinearity test
Multicollinearity is a statistical testing phenomenon in which one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy (Fig. 8). Multicollinearity does not reduce the predictive power or reliability of the model as a whole; it only effects calculations regarding individual predictors. Before using the landslide causative factors for the landslide susceptibility index (LSI) and landslide risk modeling, it is necessary 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 simply 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 6, the smallest tolerance (TOL) of different models (FR, IV and CF) were 0.20, 0.33 and 0.176 showing the elevation parameter respectively. The variance influencing factors (VIF) of these models (FR, IV and CF) are 1.11, 1.16 and 1.109 values showing Road density parameter respectively. So there is no multicollinearity between independent landslide causative factors and current research. The variance influencing factors (VIF) and the tolerance (TOL) as calculated following equations which is as follows
Table 6
Multicollinearity analysis of FR, IV and CF approach.
Variable
|
FR
|
IV
|
CF
|
TOL
|
VIF
|
TOL
|
VIF
|
TOL
|
VIF
|
TPI
|
0.29
|
3.42
|
0.30
|
3.39
|
0.315
|
3.177
|
NDVI
|
0.53
|
1.88
|
0.51
|
1.98
|
0.536
|
1.865
|
SPI
|
0.69
|
1.45
|
0.69
|
1.45
|
0.818
|
1.222
|
WI
|
0.52
|
1.92
|
0.52
|
1.92
|
0.675
|
1.481
|
slope
|
0.59
|
1.69
|
0.59
|
1.70
|
0.573
|
1.744
|
RD
|
0.90
|
1.11
|
0.86
|
1.16
|
0.902
|
1.109
|
Curvature
|
0.38
|
2.66
|
0.37
|
2.67
|
0.376
|
2.658
|
DD
|
0.50
|
1.99
|
0.59
|
1.69
|
0.509
|
1.963
|
Lulc Class
|
0.87
|
1.15
|
0.87
|
1.15
|
0.857
|
1.166
|
Geology
|
0.38
|
2.63
|
0.39
|
2.58
|
0.38
|
2.628
|
Soil
|
0.65
|
1.54
|
0.56
|
1.78
|
0.656
|
1.524
|
Rainfall
|
0.25
|
4.02
|
0.39
|
2.57
|
0.249
|
4.023
|
Elevation
|
0.20
|
4.96
|
0.33
|
3.00
|
0.176
|
5.677
|
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 (FR, IV and CF) are shows in Table 6.
Table 6. Multicollinearity analysis of FR, IV and CF approach.
Figure 8. The conceptual framework of multicollinearity testing phenomenon showing 1. No relationship between variables, 2. Showing moderate relationship and 3. Showing very high collinearity