Landslide Susceptibility Mapping Using Statistical Methods along the Asian Highway, Bhutan

geosciences
Article
Landslide Susceptibility Mapping Using Statistical
Methods along the Asian Highway, Bhutan
Sangey Pasang *,† and Petr Kubíček *,†
Department of Geography, Masaryk University, Kotlářská 267/2, 611 37 Brno, Czech Republic
* Correspondence: sangey111@gmail.com (S.P.); kubicek@geogr.muni.cz (P.K.); Tel.: +975–7777-4567 (S.P.)
† These authors contributed equally to this work.
Received: 27 September 2020; Accepted: 26 October 2020; Published: 29 October 2020

Abstract: In areas prone to frequent landslides, the use of landslide susceptibility maps can greatly aid in
the decision-making process of the socio-economic development plans of the area. Landslide susceptibility
maps are generally developed using statistical methods and geographic information systems. In the
present study, landslide susceptibility along road corridors was considered, since the anthropogenic
impacts along a road in a mountainous country remain uniform and are mainly due to road construction.
Therefore, we generated landslide susceptibility maps along 80.9 km of the Asian Highway (AH48) in
Bhutan using the information value, weight of evidence, and logistic regression methods. These methods
have been used independently by some researchers to produce landslide susceptibility maps, but no
comparative analysis of these methods with a focus on road corridors is available. The factors contributing
to landslides considered in the study are land cover, lithology, elevation, proximity to roads, drainage,
and fault lines, aspect, and slope angle. The validation of the method performance was carried out by
using the area under the curve of the receiver operating characteristic on training and control samples.
The area under the curve values of the control samples were 0.883, 0.882, and 0.88 for the information
value, weight of evidence, and logistic regression models, respectively, which indicates that all models
were capable of producing reliable landslide susceptibility maps. In addition, when overlaid on the
generated landslide susceptibility maps, 89.3%, 85.6%, and 72.2% of the control landslide samples were
found to be in higher-susceptibility areas for the information value, weight of evidence, and logistic
regression methods, respectively. From these findings, we conclude that the information value method
has a better predictive performance than the other methods used in the present study. The landslide
susceptibility maps produced in the study could be useful to road engineers in planning landslide
prevention and mitigation works along the highway.
Keywords: landslide susceptibility mapping; road corridor; geographic information system; information
value model; weight of evidence model; logistic regression model
1. Introduction
A landslide is defined as “the movement of a mass of rock, earth, or debris down a slope”, and they
are classified according to the type of slope movement (fall, topple, spread, flow, slide), type of material
involved (rock, earth, debris), and the speed of movement [1,2]. Even though gravity is the essential
contributor to the occurrence of a landslide event, other triggering factors, such as an earthquake, rainfall,
flood, or human intervention [3], significantly increase the likelihood of landslide occurrence. Landslides
constitute a major geological hazard and pose considerable risks to the livelihood and lives of the
Geosciences 2020, 10, 430; doi:10.3390/geosciences10110430 www.mdpi.com/journal/geosciences

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population living in and around the affected area [4]. Prolonged disruption of transportation networks,
loss of fertile land, collapse and submergence of buildings, loss of life, etc. are some of the risks associated
with a landslide event that can translate into major social impacts and economic loss. Expansion of
human settlement into geologically sensitive areas, infrastructure development, and increased agricultural
practices result in land use changes that further aggravate the problem of landslides and associated
risks [5–7]. Cutting slopes for infrastructure development, particularly during road construction, is a
major triggering factor for most landslides. Conversely, landslides impede socio-economic activities,
such as the development of efficient transportation networks, reservoirs, settlement areas, and agricultural
fields, especially in mountainous regions [8]. Hence, to support sound decision-making in building up a
national socio-economic development plan that addresses the impact of landslides, information based on
risk analysis and landslide assessment concerning the likelihood of landslide occurrences are useful.
Risk analysis and landslide assessment are crucial in the development of mitigation and disaster
preparedness plans [8]. Landslide assessment is generally considered in terms of landslide susceptibility
(“the potential for a given slope to fail compared to others”), landslide hazard (“the potential posed by a
landslide to cause damage or loss”), and landslide risk (“the actual or potential damage or loss that may
occur as a result of a landslide”) [9,10]. To effectively mitigate landslide risk and prevent landslide hazards,
a dependable and detailed landslide susceptibility map (LSM) must be developed for the region [11–13]
to provide key information to a range of end users. An LSM may be developed for specific applications,
such as landfill zoning [14], road corridors [15–19], land use planning [20,21], and reservoir basins [22].
Landslide susceptibility mapping considers many causal factors, which are usually presented as
thematic layers in a geographic information system (GIS) platform. Various models and methodologies
have been utilized to decide the impact of causal factors on landslide occurrence, of which the multi-criteria
decision analysis (MCDA) method based on fuzzy logic [23], analytical hierarchy process (AHP) [24–26],
and weighted linear combination [27] are most commonly used. In terms of statistical methods,
the frequency ratio method is the simplest and easiest to perform, while the information value (IV) [28,29]
and weight of evidence (WOE) [30,31] methods are useful in determining the impact of causal factor class
on landslide occurrence. Logistic regression (LR) is also used by many researchers for determining the
weight of the causal factors [17,26,32,33]. The application of machine learning, such as artificial neural
networks (ANN) [34–36] and support vector machines (SVM) [37], has also been considered a promising
technique for LSMs. Various researchers have studied the comparative performance of these methods.
The LR model was found to be more suitable than the frequency ratio method in some studies [12,38],
whereas some studies found out that the frequency ratio method is better than the certainty factor [39]
and LR [40]. WOE was also established as comparatively less accurate than the fuzzy logic technique [41].
Some methods have been modified to enhance performance in predicting future landslides. Ba et al. [42]
improved the IV model by integrating it with an AHP and Gray clustering algorithms. The AHP technique
was modified by adopting an interval matrix in deriving the optimal decision matrix [43]. However,
only a few studies have developed LSMs for areas along road corridors, and no studies have carried out
comparative analysis using the information value (IV), weight of evidence (WOE), or logistic regression
(LR) model methods.
In Bhutan, the process of road building in the mountainous Bhutanese terrain has aggravated the
occurrence of landslides, affected economic growth, and caused loss of lives [44]. Furthermore, the road
corridors in Bhutan present a unique condition in that the anthropogenic impacts on the environment
are largely due to road construction and very rarely due to sparse human settlement. The objective of
this study, therefore, was to investigate the suitability of various methods for developing a landslide
susceptibility map in Bhutan along the highways. We derived the relative weights of different classes of
landslide causal factors using the IV, WOE, and LR methods, and compared the predictive performance of
the methods in generating an LSM.

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2. Study Area
For this paper, a road corridor of 80.9 km, averaging 5 km in width, along the Asian Highway-48
(AH-48) stretch from Phuentsholing to Chukha Thegchhen zam (bridge), covering an area of 237.28 km2,
was considered (Figure 1a).
Figure 1. (a) Location map of the study area with a 2.5 km buffer along the 80.9 km Asian Highway/
Phuentsholing-Thimphu Highway (AH48) superimposed on an elevation map (b) Elevation profile up to
2000 m over a road distance of 40 km with important settlements along the Asian Highway (AH48).
The AH-48 is a major trade route connecting the capital city of Thimphu and rest of Bhutan to India,
its main economic partner. The study area is located between 26◦5003400 N and 27◦502000 N latitude and
89◦2302900 E and 89◦3301200 E longitude. The highway ascends in altitude from 216 to 2159 m above Mean
Sea Level (MSL) over a distance of 40 km from Phuentsholing (Figure 1b) and runs through a geological
formation consisting of moderate to highly weathered phyllites [44,45]. During the monsoon season with
an average rainfall of 1663.4 mm per year [46], this section of road is subjected to frequent landslides of
varying magnitude at a number of locations (Figure 2).
Often, the landslides at a site along the road corridor are shallow in nature and occur mainly during
the monsoon season [47]. These landslides are caused due to deforestation and toe cutting on the fragile
slope during the road construction process. The landslides at Sorchen and Jumja [48] are most critical,
necessitating realignment of the road length as an avoidance strategy in 1992 [44,49]. In 2017, the highest
24-h rainfall of 285.4 mm in the study area [50] triggered a major landslide at three sites, leading to road
closure for many days. This affected the transport of goods and people between Phuentsholing and other
parts of Bhutan, causing major economic losses and disrupting everyday life.

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Figure 2. (a,b) Road and infrastructure affected by landslide at 5 km chainage, Rinchending and
(c) Landslides roadblock at 17 km chainage, Sorchen, in the study area (photo courtesy: College of Science
and Technology).
3. Data
3.1. Landslide Inventory
Landslide distribution—or inventory mapping—is the fundamental information required in
determining the size and features of a landslide [3,51]. Since a landslide inventory in Bhutan is not
available, the technical report of the Bhutan Land Cover Assessment 2010, National Soil Services Center
(NSSC), and Policy and Planning Division (PPD) [52] was used as the primary guide for field visits, as well
as digitized satellite imagery from the publicly available data source Google Earth. From this report,
in which a class of “degraded land” with subclass “landslide” showed landslide areas, and by interpreting
Google Earth images, 120 landslides totaling an area of 2.77 km2 were identified. This was obtained by
digitizing landslides ranging from 122 to 304,625 m2 area in the Google Earth environment and verified
with news reports and field visit. Sixty percent of landslides by area were aligned with the Ministry of
Agriculture and Forests, Royal Government of Bhutan (MoAF, RGoB) [52] report, while the rest were
obtained from Google Earth images, which were likely more recent and active landslides areas. Figure 3
shows the distribution of landslides in the study area.

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Figure 3. Landslide distribution along the Asian Highway (AH48).
3.2. Causative Factor Selection
In the study, the slope failure susceptibility due to underlying causative factors [8] was considered.
Land cover, lithology, elevation, proximity to roads, drainage, fault lines, slope aspect, and slope angle
were considered as causal factors based on literature [53] and the availability of data for the study area.
Each causal factor was mapped and divided into the several equal interval classes described in the legend
in Figure 4.
The percentage of landslides against each class of causal factor is illustrated in Figure 5.
The geomorphic factors of elevation, slope aspect, and slope angle were derived from corrected DEM
of 30 m resolution obtained from the Ministry of Work and Human Settlement, Bhutan. The highway
altitude climbs from 216 to 2159 m above MSL over a distance of 40 km (Figure 1b) with diverse climatic
conditions, hydrology, and geology. Hence, an elevation map with eight classes of 300 m intervals was
produced. The slope aspect indicates the saturation of the slope with water and heat, which affects soil,
rock, and vegetation types [11]. The south-facing aspect has a higher frequency (30%) of landslides in the
nine proposed classes. The angle of slope in degrees was divided into six classes of equal intervals of 10◦,
with 26.59% of landslides falling in the slope angle class of 30◦–40◦. The lithological and fault details were
digitized from a 1:50,000 geological map of Bhutan from Long et al. [45].
The study area includes eleven classes of lithology under the three main zones of the greater
Himalayan zone, lesser Himalayan zone, and Paro formation, and seven classes of distance to faults.
The lithology consists mainly of amphibolite, quartzite, schist, slate, phyllite, marble, paragneiss, limestone,
dolostone, and granite dating to the Paleoproterozoic to Ordovician Era [45]. The details of the lithology
and the ages of geological formations are given in Table 1. The number of landslides is relatively higher in
the Phuentsholing formation (Pzph) region, where the more commonly found lithologies are slate and
phyllite. The AH-48 highway is routed over three active main faults: Shumar thrust (ST), Main Central
thrust (MCT), and the Southern Tibetan Detachment (STD), plus a few other minor fault lines and

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folds [45,54]. Landslide density is significantly higher closer to fault lines, with 35% of overall landslides
being within 0–500 m of them. Furthermore, one of the major contributors to landslides is land cover [55,56].
Vegetation aids in protecting a slope whereas bare soil or sparse vegetation agitates the occurrence of a
landslide [57,58]. Land cover maps from the MoAF/RGoB [52] report were used to derive seven simplified
broad land cover categories to meet the aim of the study. Traffic intensity and the cutting of steep slopes
during road construction are another factor influencing landslide occurrence [59–61]. The proximity of
drainage streams also results in saturating the area and causing landslides [62]. Drainage and road maps
were acquired from the Bhutan Geospatial portal website [63], and thematic layers were created with six
equidistant buffers of 100 m each.
Figure 4. Cont.

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Figure 4. Landslide causal factor maps showing the different classes: (a) slope angle, (b) slope aspect,
(c) elevation, (d) distance to road, (e) distance to drainage, (f) distance to fault, (g) lithology as described in
Table 1, and (h) land cover.

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Figure 5. Percentage of landslides in each class of the causal factors of landslide occurrence: (a) slope angle,
(b) slope aspect, (c) elevation, (d) distance to road, (e) distance to drainage, (f) distance to fault, (g) lithology,
and (h) land cover.

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Table 1. Lithology and age of geological formations in the study area [45].
Formation and Unit Age Lithology
GHIo Greater Himalayan Zone: Orthogenesis unit Cambrian– Ordovician Granite, Paragneiss, Schist, quartzite
GHImu Greater Himalayan Zone: Upper metasedimentary unit Neoproterozoic–Ordovician Amphibolite, Paragneiss, Quartzite, Schist
Pzpm Paro Formation: Middle unit Cambrian–Ordovician Quartzite, Marble 10 m thick
Pzpm2 Paro Formation: Middle unit (100–200 m thick) Cambrian–Ordovician Quartzite, Marble 100–200 m thick
GHIml Greater Himalayan Zone: Lower metasedimentary unit Neoproterozoi–Cambrian Amphibolite, Quartzite, Schist, Paragneiss
Pzph Lesser Himalayan Zone: Phuentsholing Formation (Baxa Group) Age range uncertain: Neoproterozoic or younger Slate, Phyllite, Limestone
pCp Lesser Himalayan Zone: Pangsari Formation (Baxa Group) Age range uncertain: Mesoproterozoic–Cambrian Phyllite, Dolostone, Marble
pCo Lesser Himalayan Zone: Orthogneiss (Daling-Shumar Group) Paleoproterozoic Granite
pCs Lesser Himalayan Zone: Shumar Formation (Daling- Shumar Group) Paleoproterozoic Quartzite, Schist, Phyllite
pCd Lesser Himalayan Zone: Daling Formation (Daling-Shumar Group) Paleoproterozoic Schist, Phyllite
pZj Lesser Himalayan Zone: Jaishidanda Formation Neoproterozoic–Ordovician Schist, Quartzite

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4. Methodology
An inventory of 120 landslide areas and various factors, such as land cover, lithology, elevation,
proximity to roads, drainage, and fault lines, slope aspect, and slope angle, was created and converted
into 30 × 30 m grid cells in ArcGIS 10.6 to suit the DEM resolution. An 80% training sample equally
proportioned between the landslide and non-landslide pixels was generated randomly and was used
to create the spatial associations between occurrences of landslides and the causal factors [64–66].
The control sample of 20% was used to validate and verify (Table 2) the accuracy of the models. The three
methodological approaches of IV, WOE, and LR were used to derive the relationship between causal factors
and landslide occurrence. The landslide susceptibility indices (LSIs) were generated to produce an LSM.
LSIs were divided into the five classes of very low, low, moderate, high, and very high susceptibility using
the Jenks natural break classification method [24,53,67]. The Jenks natural break classification method is
used to determine the arrangement of values into different classes by minimizing and maximizing each
class’s deviation from the class mean and other groups’ means, respectively [12,42,68]. To validate the
performance of the methods, the area under the curve (AUC) of the receiver operating characteristic (ROC)
was calculated. The control sample was overlaid on the LSM to examine the predictive capability for
future landslides. Additionally, a correlation test was performed to assess the level of similarity between
LSMs produced using the models. IBM Statistical Product and Service Solutions 25 (SPSS 25) was used
for data management and validation. The flowchart in Figure 6 shows the data sources, thematic layers,
and methodology applied in the study.
Figure 6. Flowchart showing the methodology of the study.

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Table 2. Number of pixel cell samples for the study area.
Training Sample (80%) Validation Sample (20%) Total
Pixels with Landslide 2159 522 2681
Pixels without Landslide 208,524 52,360 260,884
Total 210,683 52,882 263,565
4.1. Information Value Method
The IV model, a simple statistical method for mapping areas vulnerable to landslides by determining
the influence of each class of causal factors on landslide occurrence, was found suitable in a number of
studies and has been implemented in numerous landslide hazard assessment studies [28,29,42,69]. In this
model, the information value Ii for a class i in a thematic layer considering 80% as the training sample is
given by:
Ii = log
Si/Ni
S/N
, (1)
where Si represents the number of pixels of the class containing a landslide, Ni represents the total number
of pixels in the class, S is the total number of pixels with a landslide in the layer, and N is the total number
of pixels in the layer.
After deriving the information values for each class of causal factor, raster maps were overlaid in a
GIS environment. The LSIs were determined by averaging the information value of the causal factors as:
LSI =
1
M
M
∑
n=1
Ii, (2)
where M is the number of factors considered. The total information value of factors contributing to
landslide occurrence is obtained from Equation (2). The influence of these factors on landslide occurrence
is lesser if the LSI value is lower, and vice versa.
4.2. Weights of Evidence Model
The WOE method based on Bayes’ theorem was used to find the spatial association between the
location of a landslide and a set of contributing factors. Numerous studies have been conducted using
WOE, emphasizing its theoretical background and application. A detailed mathematical description and
formulation can be found in the literature [61,70,71]. The weights of the causal factor for the presence and
absence of a landslide are determined by:
W+
= ln
P(B|D)
P(B|D)
(3)
W−
= ln
P(B|D)
P(B|D)
, (4)
where W+ and W− are the WOE when a binary predictor factor is present or absent, respectively, P is the
probability, B is the presence of the desired class of landslide causal factor, B is the absence of the desired
class of landslide causal factor, D is the presence of a landslide, and D is the absence of a landslide.
A simplified form of Equation (3) above can be expressed as [41]:
W+
= ln
LSin%
nonLSin%
(5)

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W−
= ln
LSout%
nonLSout%
, (6)
where LSin% and nonLSin% are the proportions of landslide pixels and non-landslide pixels in the class,
respectively. LSout% and nonLSout% are the proportions of landslide pixels and non-landslide pixels
outside the same class, respectively. W+ implies a positive correlation and W− indicates a negative
correlation between the causal factor and the occurrence of a landslide [40,41,70]. The weight contrast is
given by C = (W+ − W−), and its magnitude represents the measure of spatial association between the
class of the causal factor and the occurrence of a landslide [72–74]. The LSI is derived by aggregating the
contrasts of all the factors, with higher values of LSI indicating a higher likelihood of landslide occurrence.
4.3. Logistic Regression Model
An LR model is a regression analysis technique used to determine the likelihood of a binary dependent
variable from several independent variables. It is used to predict the presence of an outcome based on the
values of predictor variables. The method does not require normally distributed data, and the variable can
be continuous, discrete, or any combination of both types [75].
In order to perform the LR method on a sample, it is necessary to check for collinearity between
the variables [40,76]. If the tolerance (TOL) 0.1 and variance inflation factor (VIF) 10, this indicates
multicollinearity between independent variables [77]. The dependent variable (landslide variable) and the
independent variable (causal factor) were modeled using the LR application in SPSS 25 to determine the
coefficient of each factor. The 80% training sample consisting of an equal proportion of landslide pixels
and causal factor pixels was imported into SPSS. The frequency ratio of each class of causal factor was
derived as the percentage of landslides against the percentage of the area of the class. The logistic function
was applied to causal factors to constrain the values between 0 and 1, where zero indicates the probability
of 0% landslide occurrence and one indicates the probability of 100%, according to the equation:
P =
1
(1 + exp−z)
, (7)
where P is the probability of landslide occurrence, and z is the landslide causal factors assumed to be a
linear combination of the causal factors Xi(i = 1, 2, 3, . . . , n), where
Z = B0 + B1X1 + B2X2 + B3X3 . . . + BnXn, (8)
and Bi is the regression coefficient of landslide causal factors.
4.4. Validation of the Models
The AUC-ROC graphically illustrates the performance of a binary classifier for the false positive
rate (1-specificity) against the true positive rate (sensitivity). The AUC represents the performance of the
success rate and prediction of the model against the occurrence of a landslide [78]. A landslide predicted
in an existing landslide area is a true positive outcome, whereas a landslide predicted in a non-existing
landslide area is a false positive [79]. Rasyid et al. [12] defined the diagnostic values as “0.5–0.6 (fail),
0.6–0.7 (poor), 0.7–0.8 (fair), 0.8–0.9 (good), and 0.9–1.0 (excellent)” in the AUC curve. The AUC success
rate of each model was derived for the LSI computed for each model and the training samples, while the
rate of prediction was verified using a control sample. In addition, the training and control samples were
overlaid on the LSMs to assess predictive performance. The training sample covered a small area of
higher susceptibility classes, whereas the landslide data would lie in higher classes when overlaid on the

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LSM [12,66]. Correlation coefficients ranging from 0 (no correlation) to 1 (strong relationship) were derived
from the correlation analyses between a pair of LSMs developed from the IV, WOE, and LR models.
5. Results
Three LSMs were produced using the IV, WOE, and LR models with 80% training samples.
The detailed calculations and values of each class of causal factors derived using the three methods
are given in Table A1. In each of the models, the LSIs of the classes under different causal factors
corresponding to each pixel in the map were divided into five susceptibility levels and mapped as shown
in Figure 7.
Figure 7. Landslide susceptibility maps produced for the 80.9 km Asian Highway (AH48) using:
(a) information value, (b) weight of evidence, and (c) logistic regression.

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5.1. Information Value Method
The information values of each class under causal factors were determined using Equation (1) and by
overlaying the causal factor map on the landslide distribution map. As indicated in Table A1, the IV is
directly proportional to the slope angle. A slope angle of 50 degrees had the highest IV value of 0.483
in the class. All southern exposure aspects had higher IV in classes, with a maximum IV of 0.267 on the
southern aspect. The 300–600 m elevation class had the highest IV, followed by the 0–300 m and 600–900 m
elevation classes. The least IV value was at a higher altitude of 2100 m. The highest IV for the distance to
road factor was 0.141 in the 200–300 m class, with classes over 300 m having lower IV values. In contrast
to distance to road, the distance to drainage factor showed no specific relationship of its proximity with
the occurrence of a landslide. However, the IV value for the closest distance class, 0–100 m, was 0.071,
which indicates a higher likelihood of occurrence of landslides within the class, but all other classes had
insignificant IVs. As shown in Table A1, the proximity to a fault line suggests a greater likelihood of
landslide occurrence. The 0–500 m class had the highest IV of 0.285, whereas the 3000 m class had the
lowest value of −0.657. For lithology factors, Pzph had the highest IV of 0.515, followed by PCs with 0.382
and pCp with 0.314, suggesting a greater probability of landslide occurrence in these classes. Among all
factor classes, the land cover bare area class had the highest IV of 1.562, and, as expected, the forest and
built-up area class had the minimum IV. To create the LSI, the IV of the classes under different causal
factors corresponding to each pixel in the map was derived using Equation (2).
5.2. Weights of Evidence Model
In this model, the weights and contrast were determined using Equations (5) and (6) and are shown
in Table A1. Similarly to the findings with IV, the highest contributors to landslides are the degree of slope
of 50 degree (WOE = 1.162), south exposure aspect (WOE = 0.797), 300–600 m elevation (WOE = 1.444),
200–300 m distance to road (WOE = 0.363), 0–100 m distance to drainage (WOE = 0.312), 0–500 m distance to
fault lines (WOE = 0.890), lithology group Pzph (WOE = 1.364), and bare area in land cover (WOE = 3.988).
The LSI was computed by totaling the WOE contrasts.
5.3. Logistic Regression Model
The TOL and VIF calculated for this study (Table 3) were more than 0.39 and less than 2.6, respectively,
indicating that there was no multicollinearity between variables. We could, therefore, use all the variables
for LR analysis. The forward step-wise LR analysis shows that all factors with an estimated logistic
coefficient have a significance value of less than 0.05. This indicates that all the independent variables
have an influence on the landslide occurrence variable (Table 4), and, therefore, all causal factors were
considered for analysis.
Table 3. Multicollinearity indices for causal factors.
Collinearity Statistics
Tolerance VIF
Slope angle 0.953 1.050
Aspect 0.980 1.021
Elevation 0.414 2.413
Distance to road 0.966 1.035
Distance to drainage 0.990 1.010
Distance to fault lines 0.856 1.168
Lithology 0.396 2.527
Land cover 0.982 1.018
Dependent variable: landslide.

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Table 4. Coefficients of each factor derived from logistic regression.
B S.E. Wald df Sig. Exp (B)
95% C.I. for EXP(B)
Lower Upper
Slope angle 1.419 0.092 239.425 1 0.000 4.131 3.452 4.944
Aspect 1.518 0.083 337.914 1 0.000 4.564 3.882 5.366
Elevation 0.487 0.115 18.005 1 0.000 1.628 1.300 2.039
Distance to road 0.483 0.066 54.081 1 0.000 1.622 1.426 1.845
Distance to drainage 0.467 0.056 69.624 1 0.000 1.596 1.430 1.781
Distance to fault lines 1.137 0.074 237.883 1 0.000 3.118 2.698 3.602
Lithology 1.435 0.112 163.460 1 0.000 4.200 3.371 5.234
Land cover 3.882 0.059 4268.221 1 0.000 48.522 43.188 54.515
Constant −7.896 0.097 6693.400 1 0.000 0.000
B = logistic coefficient; S.E. = standard error of estimate; Wald = Wald chi-square; df = degree of freedom;
Sig. = significance; EXP(B) = exponentiated coefficient; 95% C.I. for EXP(B) = 95% confidence interval for EXP(B).
The highest regression coefficient was computed for land cover at 3.882, followed by aspect, lithology,
slope angle, distance to fault lines, elevation, distance to road, and distance to drainage. The Z value or
LSI was computed in a GIS environment using Equation (8), as follows:
Z = −7.896 + 1.419×slopeangle + 1.528×aspect + 0.487×elevation + 0.483×distancetoroad+
0.467×distancetodrainage + 1.137×distanceto f ault + 1.435×litology + 3.882×landcover. (9)
5.4. Validation
For the IV, WOE, and LR models, the AUC-success rates were 0.873, 0.872, and 0.866, while the
prediction rates were 0.883, 0.882, and 0.880, respectively. From this, we conclude that all the models
are suitable methods for generating LSMs (Figure 8), although the IV model shows a slightly better
predictive performance.
Figure 8. Receiver operating characteristic (ROC) area under the curve (AUC) for (a) success rate of the
sample and (b) prediction rate of the control sample.
Figure 9 shows that the overlaid training sample covered 33.2%, 27%, and 16.2% of the study region
for IV, WOE, and LR, respectively, in the higher susceptibility classes. When overlaying the training

Geosciences 2020, 10, 430 16 of 26
landslide and control landslide samples on the LSM, the area coverage above high susceptibility was 87.4%
and 89.3% in the IV model, 84.1% and 85.6% in the WOE model, and 69.6% and 72.2% in the LR model.
The IV and WOE models appear to be more reliable, since their values have lesser disparity. From the
correlation analysis, the correlation coefficients at a significance level of 0.01 (two-tailed) were 0.699 or
greater, with the highest coefficient of 0.845 between WOE and LR (Table 5).
Figure 9. Density of landslides in each susceptibility class for the IV, WOE, and LR models using the
(a) training sample, (b) training landslide sample, and (c) control landslide sample.

Geosciences 2020, 10, 430 17 of 26
Table 5. Correlation between the methods.
Methods Information Value Weight of Evidence Logistic Regression
Information Value 1 0.755 ** 0.699 **
Weight of Evidence 0.755 ** 1 0.845 **
Logistic Regression 0.699 ** 0.845 ** 1
** Correlation is significant at the 0.01 level (two-tailed).
6. Discussion
LSMs were generated from the IV, WOE, and LR models considering the relationship between
causal factors and landslides. The LSMs were compared for predictive performance using AUC-ROC
by overlaying the training and control samples on LSMs and performing correlation coefficient tests.
Higher susceptibility was observed in the extreme southern and northern parts of the focus area,
where human settlements, steeper slopes, and more fault lines can be found. Factors such as roads
and landcover were found to have a high correlation with the occurrence of landslides, as found by [80].
From the LR model, it was found that the land cover contributes the most to landslide occurrence out
of all the factors, followed by aspect, lithology, slope angle, distance to fault lines, elevation, distance
to road, and distance to drainage. As shown in Table A1, the most significant contributors to landslide
occurrence from each factor were slope angle of 50, southern exposure aspect, 300–600 m elevation,
200–300 m distance to road, 0–100 m distance to drainage, 0–500 m distance to fault lines, lithology group
Pzph (Phuentsholing formation), and bare land cover.
The northern region of the study area had the greatest slope angle, and the lowest slope angle was
in the south (Figure 4). Landslide occurrence was directly proportional to the slope angle, which agrees
with the general conclusion of expecting fewer landslides on gentler slopes because of lower associated
shear stresses [11]. This also conforms to the findings of other research [81]. The south, southeast,
and southwest had the highest LSIs in aspect classes in the present study. This may be due to the high
humidity in the south-facing aspect [11]. Field knowledge also dictates that south-facing slopes are warm,
wet, and forested. Most of the study area falls within the elevation class of 2100 m above mean sea
level, which is less susceptible to landslide occurrence. In our study, we observed that elevation classes
300–600 m and 0–300 m had a higher influence on landslide occurrence, which gradually decreased
as elevation increased. Other studies have also demonstrated similar findings [82]. The stability and
resistance to weathering processes of rocky cliffs at higher altitudes may explain this phenomenon [60].
All classes with a distance less than 300 m from the road had a higher influence on landslide occurrence
than distances over 300 m. However, the highest LSI was in the 200–300 m class rather than a distance
closer to a road. This causal factor contributes to landslides when the slope is eroded from the bottom
of the slope [83]. Various studies have shown different patterns depending on the interval of the class.
Some studies have shown higher susceptibility closer to roads [81,84,85], while others presented similar
findings to the current study [78,86,87]. The results for the occurrence of landslide and distance to drainage
suggest that the 0–100 m class is the main contributor. The influencing factor here could be the degree
of saturation of material in the area and streams eroding the slopes [25]. The study area has three main
fault lines in the south and one fault line in the north. Under the distance to faults factor, the 0–500 m class
has the most impact on the probability of landslides, while other classes contribute comparatively less.
A landslide occurs closer to a fault because of fractures in the rock masses [36,88], as concluded in other
studies [69,89]. The influence of lithology on landslide occurrence is highest where the class consists of
phyllite, slate, and schist, with the highest value of LSI [40]. From the results, the bare area land cover
class has the highest influence on the occurrence of landslides in the classes considered. Bare areas lacking

Geosciences 2020, 10, 430 18 of 26
vegetation are more prone to landslides because vegetation helps prevent erosion through an anchoring
effect [90].
The AUC of 0.8 and higher suggests that all three models performed well and produced reliable LSMs.
The IV model had the highest AUC, while the WOE and LR models had slightly lower values. An LSM
developed for the Zigui–Badong area near the Three Gorges Reservoir in China found that the IV model
performs better than the LR model, although the deviation was small [91]. Ozdemir and Altural [40] have
also reported that the WOE model has a higher AUC than the LR model. By contrast, a study conducted in
the city of Mizunami, Japan found that the LR model has a better predictive performance than the WOE
model [84]. The correlation analysis indicated that the LSM generated from the WOE and LR models
had similar distribution patterns, whereas the LSM by the IV method was less similar to other methods
(Table 5). When landslide pixels were overlaid onto the LSM, it showed that the LSM produced with the
IV model was better, since it predicted a higher percentage of landslides of higher susceptibility in both
the training and control groups (Figure 9). Figure 10 shows some of the existing landslide photographs
overlaid onto the LSM produced with the IV method, with most of the landslides lying in areas with high
landslide susceptibility.
Figure 10. Landslides along the AH48 superimposed on the landslide susceptibility map (LSM) produced
with the IV model.

Geosciences 2020, 10, 430 19 of 26
7. Conclusions
This paper presents a comparative performance of the IV, WOE, and LR models in developing
landslide susceptibility maps along a road corridor in Bhutan. The LSM assessment on the studied road
corridor showed that the probability of landslide occurrence is greater in the southern area, with the
mid-region being more stable. The influence of each class of causal factor is evident from the IV and
WOE models. The highest contributors to landslide occurrence from each factor were slope angle of 50,
southern exposure aspect, 300–600 m elevation, 200–300 m distance to road, 0–100 m distance to drainage,
0–500 m distance to fault lines, lithology group Pzph (Phuentsholing formation), and bare area in land
cover. As a whole, the LR model has greater advantage in identifying the influence of causal factors on
the probability of a landslide. In order from most to least influential, the factors were: land cover, aspect,
lithology, slope angle, distance to fault lines, elevation, distance to road, and distance to drainage.
The LSMs generated by the three methods were evaluated for suitability by deriving the AUC and
overlaying the actual landslide map on the LSM. The correlation coefficients for all the models were greater
than 0.699, indicating strong correlation. The WOE and LR models were determined to be similar with a
correlation coefficient of 0.85. The validation showed the success rate and prediction rate of all the models
to be suitable. The comparative test of the models showed that the IV model was better than the WOE
and LR models. We therefore recommend the IV as the most suitable method to predict future landslides.
However, its performance can be improved by using higher-resolution images and large-scale maps.
We conclude that the methods considered in the present study can be suitably performed to study
areas in Bhutan to develop an accurate and reliable LSM. The LSM thus developed may be used to support
planning and decision-making for landslide prevention and mitigation activities during the construction,
operation, and maintenance of the road network in Bhutan.
Author Contributions: Conceptualization, S.P. and P.K.; methodology, S.P. and P.K.; formal analysis, S.P. and P.K.;
investigation, S.P.; data curation, S.P. and P.K.; writing—original draft preparation, S.P.; writing—review and editing,
S.P. and P.K.; visualization, S.P.; supervision and project administration, P.K.; funding acquisition, P.K. All authors
have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Acknowledgments: The study was supported by Erasmus Mundus Experts Sustain and MUNI/A/1251/2017
Integrated Research of Environmental Changes in the Landscape Sphere III projects. The College of Science and
Technology in Phuentsholing is duly thanked for aiding with field work and supporting photographs.
Conflicts of Interest: The authors declare no conflict of interest.

Geosciences 2020, 10, 430 20 of 26
Appendix A
Table A1. Information value, weight of evidence, and logistic regression indices for landslide causal factors.
No. of Landslide
Pixels in Class (Si)
Total No. of Pixels
in Class (Ni)
Landslide
Ratio Area
Total Ratio
Area
Information
Value
Frequency
Ratio (FR)
Standar-
Dized FR
W+ W− Weight of
Evidence (C)
Slope angle (degree) 0–10 96 10,750 4.447 5.102 −0.060 0.871 0.071 −0.138 0.007 −0.144
10–20 405 44,423 18.759 21.085 −0.051 0.890 0.079 −0.117 0.029 −0.146
20–30 556 76,822 25.753 36.463 −0.151 0.706 0.000 −0.348 0.156 −0.504
30–40 574 54,488 26.586 25.863 0.012 1.028 0.138 0.028 −0.010 0.037
40–50 374 19,257 17.323 9.140 0.278 1.895 0.509 0.639 −0.094 0.734
50 154 4943 7.133 2.346 0.483 3.040 1.000 1.112 −0.050 1.162
Aspect Flat 2 294 0.093 0.140 0.000 0.664 0.355 −0.410 0.000 −0.410
North 2 17,654 0.093 8.379 −1.956 0.011 0.000 −4.505 0.087 −4.591
North East 88 27,963 4.076 13.273 −0.513 0.307 0.161 −1.181 0.101 −1.281
East 168 30,236 7.781 14.351 −0.266 0.542 0.289 −0.612 0.074 −0.686
South East 450 31,550 20.843 14.975 0.144 1.392 0.751 0.331 −0.072 0.402
South 655 34,561 30.338 16.404 0.267 1.849 1.000 0.615 −0.182 0.797
South West 494 30,132 22.881 14.302 0.204 1.600 0.864 0.470 −0.105 0.575
West 238 21,278 11.024 10.100 0.038 1.091 0.588 0.088 −0.010 0.098
North West 62 17,015 2.872 8.076 −0.449 0.356 0.187 −1.034 0.055 −1.089
Elevation (m) 0–300 108 4796 5.002 2.276 0.342 2.197 0.610 0.787 −0.028 0.816
300–600 554 15,863 25.660 7.529 0.533 3.408 1.000 1.226 −0.218 1.444
600–900 254 12,265 11.765 5.822 0.306 2.021 0.553 0.704 −0.065 0.769
900–1200 166 17,450 7.689 8.283 −0.032 0.928 0.201 −0.074 0.006 −0.081
1200–1500 260 33,634 12.043 15.964 −0.122 0.754 0.145 −0.282 0.046 −0.328
1500–1800 316 39,074 14.636 18.546 −0.103 0.789 0.156 −0.237 0.047 −0.284
1800–2100 338 35,574 15.655 16.885 −0.033 0.927 0.200 −0.076 0.015 −0.090
2100 163 52,027 7.550 24.694 −0.515 0.306 0.000 −1.185 0.205 −1.390
Distance to road (m) 0–100 368 31,726 17.045 15.059 0.054 1.132 0.536 0.124 −0.024 0.148
100–200 300 23,159 13.895 10.992 0.102 1.264 0.780 0.234 −0.033 0.268
200–300 265 18,694 12.274 8.873 0.141 1.383 1.000 0.324 −0.038 0.363
300–400 158 16,087 7.318 7.636 −0.018 0.958 0.216 −0.042 0.003 −0.046
400–500 147 14,199 6.809 6.740 0.004 1.010 0.312 0.010 −0.001 0.011
500 921 106,818 42.659 50.701 −0.075 0.841 0.000 −0.173 0.151 −0.324

Geosciences 2020, 10, 430 21 of 26
Table A1. Cont.
No. of Landslide
Pixels in Class (Si)
Total No. of Pixels
in Class (Ni)
Landslide
Ratio Area
Total Ratio
Area
Information
Value
Frequency
Ratio (FR)
Standar-
Dized FR
W+ W− Weight of
Evidence (C)
Distance to drainage (m) 0–100 1107 91,695 51.274 43.523 0.071 1.178 1.000 0.164 −0.148 0.312
100–200 502 60,914 23.252 28.913 −0.095 0.804 0.027 −0.218 0.077 −0.295
200–300 281 29,545 13.015 14.023 −0.032 0.928 0.350 −0.075 0.012 −0.086
300–400 135 14,204 6.253 6.742 −0.033 0.927 0.348 −0.075 0.005 −0.081
400–500 78 7440 3.613 3.531 0.010 1.023 0.597 0.023 −0.001 0.024
500 56 6885 2.594 3.268 −0.100 0.794 0.000 −0.231 0.007 −0.238
Distance to fault lines (m) 0–500 773 39,183 35.804 18.639 0.285 1.921 1.000 0.653 −0.237 0.890
500–1000 443 37,506 20.519 17.842 0.062 1.150 0.547 0.140 −0.033 0.173
1000–1500 160 26,458 7.411 12.586 −0.228 0.589 0.217 −0.530 0.058 −0.587
1500–2000 289 20,786 13.386 9.888 0.133 1.354 0.667 0.303 −0.040 0.342
2000–2500 257 18,081 11.904 8.601 0.143 1.384 0.684 0.325 −0.037 0.362
2500–3000 103 12,317 4.771 5.859 −0.088 0.814 0.350 −0.206 0.011 −0.217
3000 126 55,885 5.836 26.585 −0.657 0.220 0.000 −1.516 0.249 −1.765
Lithology GHIo 43 16,863 1.996 8.012 −0.604 0.249 0.000 −1.390 0.063 −1.453
GHImu 231 13,688 10.724 6.503 0.217 1.649 0.462 0.500 −0.046 0.546
Pzpm 172 12,505 7.985 5.941 0.128 1.344 0.362 0.296 −0.022 0.318
Pzpm2 46 4079 2.136 1.938 0.042 1.102 0.282 0.097 −0.002 0.099
GHIml 429 93,368 19.916 44.360 −0.348 0.449 0.066 −0.801 0.364 −1.165
Pzph 471 14,049 21.866 6.675 0.515 3.276 1.000 1.187 −0.178 1.364
pCp 277 13,127 12.860 6.237 0.314 2.062 0.599 0.724 −0.073 0.797
pCo 36 3247 1.671 1.543 0.035 1.083 0.276 0.080 −0.001 0.081
pCs 215 8727 9.981 4.146 0.382 2.407 0.713 0.879 −0.063 0.941
pCd 150 22,637 6.964 10.755 −0.189 0.647 0.132 −0.435 0.042 −0.476
pZj 84 8189 3.900 3.891 0.001 1.002 0.249 0.002 0.000 0.002
Land cover Forests 895 172,299 41.454 81.781 −0.295 0.507 0.000 −0.679 1.167 −1.847
Meadows 33 4416 1.528 2.096 −0.137 0.729 0.006 −0.316 0.006 −0.322
Cultivated
agricultural
land
68 10,104 3.150 4.796 −0.183 0.657 0.004 −0.420 0.017 −0.438
Bare areas 711 1900 32.932 0.902 1.562 36.517 1.000 3.598 −0.390 3.988
Shrubs 365 14,685 16.906 6.970 0.385 2.425 0.053 0.886 −0.113 0.999
Water
bodies
57 2366 2.640 1.123 0.371 2.351 0.051 0.855 −0.015 0.870
Built-up
areas
30 4913 1.390 2.332 −0.225 0.596 0.002 −0.518 0.010 −0.527
* S/N = 2159/210,683 = 0.0102.

Geosciences 2020, 10, 430 22 of 26
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