Paper sobre mapa de susceptibilidad a inundaciones

1. Flood susceptibility mapping using a novel ensemble
weights-of-evidence and support vector machine models in GIS
Mahyat Shafapour Tehrany, Biswajeet Pradhan ⇑
, Mustafa Neamah Jebur
Department of Civil Engineering, Geospatial Information Science Research Center (GISRC), Faculty of Engineering, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia
a r t i c l e i n f o
Article history:
Received 24 October 2013
Received in revised form 27 February 2014
Accepted 2 March 2014
Available online 12 March 2014
This manuscript was handled by
Geoff Syme, Editor-in-Chief
Keywords:
Flood susceptibility
Weights-of-evidence (WoE)
Support vector machine (SVM)
GIS
Remote sensing
Malaysia
s u m m a r y
Flood is one of the most devastating natural disasters that occur frequently in Terengganu, Malaysia.
Recently, ensemble based techniques are getting extremely popular in flood modeling. In this paper,
weights-of-evidence (WoE) model was utilized first, to assess the impact of classes of each conditioning
factor on flooding through bivariate statistical analysis (BSA). Then, these factors were reclassified using
the acquired weights and entered into the support vector machine (SVM) model to evaluate the correla-
tion between flood occurrence and each conditioning factor. Through this integration, the weak point of
WoE can be solved and the performance of the SVM will be enhanced. The spatial database included flood
inventory, slope, stream power index (SPI), topographic wetness index (TWI), altitude, curvature, dis-
tance from the river, geology, rainfall, land use/cover (LULC), and soil type. Four kernel types of SVM (lin-
ear kernel (LN), polynomial kernel (PL), radial basis function kernel (RBF), and sigmoid kernel (SIG)) were
used to investigate the performance of each kernel type. The efficiency of the new ensemble WoE and
SVM method was tested using area under curve (AUC) which measured the prediction and success rates.
The validation results proved the strength and efficiency of the ensemble method over the individual
methods. The best results were obtained from RBF kernel when compared with the other kernel types.
Success rate and prediction rate for ensemble WoE and RBF-SVM method were 96.48% and 95.67%
respectively. The proposed ensemble flood susceptibility mapping method could assist researchers and
local governments in flood mitigation strategies.
Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction
Natural disasters are the main cause of irrecoverable damages
worldwide (Vorogushyn et al., 2012). Malaysia embraces flood
events annually mostly during the monsoon seasons (Kia et al.,
2012). These flooding have caused considerable damage to high-
ways, settlement, agriculture and livelihood (Pradhan and Youssef,
2011). These consequences can be decreased through an appropri-
ate and accurate susceptibility analysis. Therefore, generating
accurate flood modeling is one of the prime goals of scientists
and governments. Over the years, many hydrological approaches
have been used in the literature (Fenicia et al., 2013). Traditional
hydrological methods such as physical based rainfall–runoff
modeling techniques and data-driven techniques are not capable
for comprehensive analysis of rivers and inundation areas (Smith
and Ward, 1998). The reason being the hydrological methods
follow one-dimensional procedure while the morphology of the
river is not stable and it has dynamic characteristic due to the high
erosive potential (Chau and Lee, 1991; Refsgaard, 1997). Moreover,
these methods require fieldwork and huge budget for data collec-
tion (Fenicia et al., 2013).
Due to the aforementioned drawbacks, scientists started to use
the empirical and data driven methods such as artificial neural
networks (ANNs) (Kia et al., 2012; Oh and Pradhan, 2011), genetic
programming (GP) (Khu et al., 2001), evolutionary polynomial
regression (EPR) (Elshorbagy et al., 2010a), M5 model trees (M5)
(Elshorbagy et al., 2010b), and K-nearest neighbors (K-NN) (Toth
et al., 2000) techniques (Chau et al., 2005; Elshorbagy et al.,
2010b; Varoonchotikul, 2003). Remote sensing (RS) and geo-
graphic information system (GIS) techniques have made significant
contribution in flood modeling and prediction (Haq et al., 2012;
Pradhan et al., 2014; Pradhan and Shafiee, 2009). Variety of data
sources, high data quality, day and night data collection capabili-
ties, and rapid analysis were offered by RS and GIS techniques for
hydrological studies (Bates, 2004, 2012; Wanders et al., 2013).
2. Previous studies
The most popular methods in natural hazard modeling are ANN
(Pradhan and Buchroithner, 2010; Pradhan et al., 2010b), analytic
http://dx.doi.org/10.1016/j.jhydrol.2014.03.008
0022-1694/Ó 2014 Elsevier B.V. All rights reserved.
⇑ Corresponding author. Tel.: +60 3 89466383; fax: +60 3 89466459.
E-mail addresses: biswajeet24@gmail.com, biswajeet@lycos.com (B. Pradhan).
Journal of Hydrology 512 (2014) 332–343
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2. hierarchy process (AHP) (Yalcin, 2008), frequency ratio (FR) (Lee
et al., 2012; Pradhan et al., 2011), logistic regression (LR) (Pradhan,
2010) and fuzzy logic (Pradhan, 2011). In a recent paper, Zou et al.
(2013) described AHP as a cost-effective, understandable, and easy
to use method. The drawback of AHP is related to its dependency
on the expert’s knowledge which is the main source of uncertainty
(Chowdary et al., 2013). Statistical methods of LR and FR utilize
simple and understandable concepts which made them popular
(Liao and Carin, 2009). Some drawbacks can be seen in their perfor-
mance, although both have valuable advantages (Lee et al., 2012).
LR is capable to implement multivariate statistical analysis (MSA)
but it has some weak points to analyze the classes of each flood
conditioning factor. BSA can be done by FR which evaluates the
influence of classes of each conditioning factor on flooding (Lee
et al., 2012). The weak point of this method is the relationship
between the variables which is mostly neglected.
The application of machine learning methods in flood studies is
proven by many researches (Chau et al., 2005; Kia et al., 2012; Ma-
ier et al., 2010). Machine learning is the main source of techniques
for the data-driven modeling problem (Jebur et al., 2013). The fun-
damental concepts of machine learning and its usages in spatially
distributed data are given in Kanevskij et al. (2009). The efficiency
of the machine learning methods in flooded area extraction has
been examined by Lamovec et al. (2013) and Tehrany et al.
(2013b). Lamovec et al. (2013) stated that, due to the need of prop-
er flood analysis, the tested machine learning methods such as
decision tree (DT) and random forest (RF) were capable to detect
the flooded locations with relatively higher accuracy. ANN which
is one of the machine learning methods has been used in many
hydrological and water resource engineering applications due to
its computational efficiency (Kia et al., 2012). ANN is very popular
for prediction analysis which tries to make correlation between
some input conditioning factors and an output (Pradhan and
Buchroithner, 2010; Wan et al., 2010a). In a recent paper, Tiwari
and Chatterjee (2010) stated that the length of the dataset can
cause error in the process of ANN modeling. Furthermore, poor
predictions can be achieved when the validation dataset contain
values outside of the range of those used for training. Although
the ANN has some drawbacks, many researchers utilized this
method in their hydrological analysis which is more robust that
other statistical and deterministic methods (Dawson et al., 2006;
Kim and Barros, 2001). The efficiency of DT has been assessed re-
cently by Tehrany et al. (2013b) to map the flood susceptible areas
in Kelantan, Malaysia. Their study indicated that while DT could
produce acceptable results, some difficulties were encountered
while defining the rules. Moreover, the accuracy of the DT method
needed to be enhanced. From the above literature review, it is evi-
dent that the precision of the machine learning algorithms can be
increased if they can be combined with BSA. This interest has been
stimulated by the complex nature of hydrological systems and the
capability of machine learning methods to model nonlinear corre-
lations (Maier et al., 2010).
As it has been explained above, some methods have few limita-
tions in flood susceptibility mapping. Therefore, the purpose is to
obtain more accurate results through ensemble methods. This
has been proven by the ensemble methods in the literature which
could enhance the analysis and overcome the weak points of the
standalone individual methods (Wan et al., 2012). For instance,
adaptive-network-based fuzzy inference system (ANFIS) which is
a combination of ANN and fuzzy interface system (FIS) is found
to be more efficient than using the individual ANN and FIS methods
(Chau et al., 2005; Pradhan, 2013; Tien Bui et al., 2012b). Another
example of ensemble modeling is genetic algorithm-based artifi-
cial neural network (ANN-GA) which is a hybrid integration of
ANN and genetic algorithm (GA) that took advantage of both
schemes. Chau et al. (2005) evaluated the robustness and strength
of ANFIS, ANN-GA and LR through comparison of their perfor-
mance. LR showed the highest uncertainty compared to the other
hybrid methods. Both ANFIS, ANN-GA methods due to their
nonlinear natures were capable to perform better than statistical
linear LR.
From the aforementioned literature review, it can be concluded
that nonlinear and complex problems can be handled using ensem-
ble methods. In recent years, Terengganu, Malaysia has been hit by
several floods (Arbain and Wibowo, 2012). The current research
deals with the 2009 flood event in Terengganu. This study aims
to generate an accurate flood susceptibility mapping method by
enhancing the machine learning procedure of support vector ma-
chine (SVM) through its integration with weights-of-evidence
(WoE) based statistical method. WoE is mostly used in landslide
mapping and it is relatively new in flood modeling (Dahal et al.,
2008; Regmi et al., 2013). WoE uses the Bayesian probabilistic
model for solving problems of decision-making under uncertain-
ties. This method is appropriate for hazard mapping because its
uncertainty is connected with hazard events and their associations
with the complex landscape (Pourghasemi et al., 2013c). WoE is
able to implement the BSA and extract the correlation between
classes of each conditioning factor and flooding. However it is
not capable to perform multivariate statistical analyses (MSA)
which leads to neglect the relationship between the conditioning
factors. Hence through its integration with SVM this drawback
can be solved and performance of SVM can be enhanced simulta-
neously. The output of WoE will be used as an input for MSA of
SVM which leads to find the relationship between all conditioning
factors and flood occurrence. This ensemble of WoE and SVM offers
the novelty in this study.
3. Study area
The study is carried out in Terengganu which is situated in the
north-eastern part of Peninsular Malaysia, and is bordered in the
Northwest by Kelantan, the southwest by Pahang, and the east
by the South China Sea (Zaleha et al., 2006). Following heavy rain-
fall in 27th November 2009 the Terengganu state faced destructive
flooding which was chosen as a suitable application site for flood
susceptibility mapping. The study area covers Kuala Terengganu
city and is located between the latitudes 5°000
N and 5°320
N, and
longitudes 102°400
E and 103°100
E. Since the flooding was most in-
tense in the North East part of Terengganu, the analysis focused on
the selected catchment (Fig. 1). The bedrock geology of the Tereng-
ganu is generally made by Phyllite, slate, shale and sandstone.
4. Data used
4.1. Flood inventory
In order to estimate the future flood event in an area, analyzing
the past records of its occurrence is essential (Manandhar, 2010).
Therefore, an inventory map is considered as the most important
factor for prediction of future disaster occurrence and it can repre-
sent single or multiple events in a specific area (Tien Bui et al.,
2012a). In the current research the inventory map is a collection
of single flood occurrence which took place in 27th November
2009. To begin, a flood inventory map was produced by mapping
the flood locations in the Terengganu using documentary sources
and field survey. A total of 180 flood locations and flood inventory
map was prepared using these locations.
The flood inventory map was partitioned into 70% and 30% to be
used for training and testing respectively (Ohlmacher and Davis,
2003; Tunusluoglu et al., 2008) (Fig. 1). The training flood locations
(126 points) were selected randomly and flood layer which is
M.S. Tehrany et al. / Journal of Hydrology 512 (2014) 332–343 333

3. considered as a dependent factor was made. Flood layer was made
up by 0 and 1 values, as the value of 1 showed the existence and
the value of 0 illustrated the absence of flooding over the area.
Similarly, equal number of points (126 points) was chosen as non-
flooded areas to give the value of 0. As the flooding cannot be oc-
curred in the high elevation regions such as high hills, non-flooded
areas were randomly selected form these locations. The rest of the
flood events (54 points) were utilized for the purpose of testing.
4.2. Flood conditioning factors
It is essential to determine the flood conditioning factors in or-
der to perform flood susceptibility mapping (Kia et al., 2012).
Therefore, in the first stage, a flood related spatial database should
be created. Through the knowledge attained from the literature
(Smith and Ward, 1998) and field investigation the conditioning
factors were chosen. Hence, ten flood conditioning factors were se-
lected for the susceptibility analysis and the spatial database of
these factors was compiled. Those factors are: slope, stream power
index (SPI), topographic wetness index (TWI), altitude, curvature,
distance form river, geology, rainfall, landuse/cover (LULC), and soil
type (Table 2). The conditioning factors were nominal, ordinal and
scale. All the scale conditioning factors were classified using popu-
lar method of quantile (Tehrany et al., 2013b) which is a require-
ment for WoE analysis (Fig. 2). Once the dataset was prepared,
each conditioning factor was transformed into a grid spatial data-
base by 15 Â 15 m size and the grid of the Terengganu region was
constructed by 3751 columns and 2138 rows (8,019,638 pixels;
1804 km2
).
The geomorphological information can be extracted through
the analysis of slope, SPI, TWI and curvature. The mentioned
geomorphological layers were derived from DEM using ArcGIS 10
software. Water-related factors of SPI and TWI were calculated
using following equations:
TWI ¼ lnðAs= tan bÞ ð1Þ
SPI ¼ As tan b ð2Þ
where As is the specific catchment area (m2
mÀ1
), and b (radian) is
the slope gradient (in degrees) (Regmi et al., 2010). All the derived
conditioning factors were initially continuous, but quantile method
was used to classify each conditioning factor into different catego-
ries. In the slope (0–62.9), SPI (0.00–23.12), TWI (0.30–34.13) and
altitude (0–1208) maps, ten categories were constructed for each
for the analysis (Fig. 2a–d respectively). Curvature was classified
into three classes of concave, convex and flat (Fig. 2e). The distance
from the river has significant impact on the spread and magnitude
of flooding in the study area (Glenn et al., 2012; Wan et al., 2010b).
This map was produced using the buffer tool in ArcGIS 10 software
and ten buffer categories were made (Fig. 2f). The geology was ex-
tracted from the geological database which differentiated into three
classes of (1) phyllite, slate, shale and sandstone, (2) intrusive rocks;
mainly granite with minor granodiorite and (3) clay, silt, sand, peat
with minor gravel (Fig. 2g). In Malaysia, the monsoon flooding takes
place after heavy rain, so this factor should be considered as one of
the main contributors in flood occurrence (Bajabaa et al., 2013).
Rainfall data was classified into six classes (2375, 2625, 2875,
3125, 3375 and 3625) using the data from the water gauge stations
Fig. 1. Flood location map with hill-shaded map of Kuala Terengganu, Terengganu, Malaysia.
334 M.S. Tehrany et al. / Journal of Hydrology 512 (2014) 332–343

4. (Fig. 2h). LULC is also one of the main conditioning factors that
strongly contribute in flooding. Vegetated areas are less prone to
flooding due to the negative relationship between flooding and
vegetation density (Tehrany et al., 2013b). On the other hand, urban
areas which are mostly made by impervious surfaces and bare lands
increase the storm runoff. LULC map consists of forest, built-up,
cropland, wetlands and paddy (Fig. 2i). The study area is mostly
covered by forest and cropland. Soil layer was produced using 14
Fig. 2. Input thematic layers: (a) slope, (b) SPI, (c) TWI, (d) altitude, (e) curvature, (f) distance form river, (g) geology, (h) rainfall, (i) LULC, and (j) soil type.
M.S. Tehrany et al. / Journal of Hydrology 512 (2014) 332–343 335

5. soil types as can be seen in Fig. 2j. The dominant soil type can be
seen around the river in which most of the flooding occurred in this
region.
5. Methodology
The flood susceptibility analysis is one of the important studies
of river hydrology which was conducted using the ensemble WoE
and SVM methods. The step-by-step procedures for the proposed
method are presented in Fig. 3.
5.1. Weights-of-evidence
The current research demonstrates the application of the
ensemble SVM and WoE (a Bayesian probability model) method
for flood susceptibility mapping using GIS in a tropical area of Ter-
engganu, Malaysia. Using flood layer and spatial database of condi-
tioning factors, the WoE was applied to measure each relevant
factor’s weight. These weights can be extracted using the analysis
of the spatial relationships between the flood location and each of
the conditioning factors. This method has many pros compared to
the other statistical methods as it is a data-driven method that is
basically uses the Bayesian probability model (Pradhan et al.,
2010). Many studies have used WoE for landslide mapping
(Mohammady et al., 2012; Pourghasemi et al., 2013a; Regmi
et al., 2013); however, this method is relatively new in flood sus-
ceptibility mapping.
To perform WoE, positive weight (W+
) and negative weight
(WÀ
) should be calculated as the essential parameters. The method
measures the weight for each conditioning factor (B) based on the
presence or absence of the disaster (A) within the area (Bonham-
Carter, 1994) as follow:
Wþ
i ¼ ln
PfBjAg
PfBjAg
ð3Þ
WÀ
i ¼ ln
PfBjAg
PfBjAg
ð4Þ
where P is the probability and ln is the natural log. B and B are the
presence and absence of the conditioning factor respectively. Also A
and A represent the presence and absence of a disaster (Xu et al.,
2012). A positive weight (W+
) demonstrates the existence of the
conditioning factor at the disaster locations, and its magnitude
shows the positive relationship between the existence of the condi-
tioning factor and disaster occurrence respectively. A negative
weight (WÀ
) shows the absence of the conditioning factor and
indicates the level of negative relationship (Regmi et al., 2013).
The difference between the two weights of W+
and WÀ
is known
as the weight contrast which reveals the spatial association be-
tween the conditioning factor and the disaster occurrence (Dahal
et al., 2008). C is positive for a positive relationship and negative
for a negative spatial relationship. The studentized contrast which
is the final weight is a measure of confidence and is defined as
the ratio of the contrast divided by its standard deviation. The stu-
dentized contrast serves as an informal test that C is significantly
different from zero or if the contrast is likely to be ‘‘real’ (Regmi
et al., 2013). A detail explanation of the mathematical formulation
of this method can be seen in (Bonham-Carter, 1991, 1994, 2002;
Pradhan et al., 2010a; Regmi et al., 2013).
After applying the WoE model, the weights were normalized in
the range of 0 and 1. Conditioning factors were reclassified based
on these normalized values and consequently fed into SVM model.
The normalization should be done because the weights of condi-
tioning factors vary in dimensions and are not appropriate for di-
rect input for the SVM model.
5.2. Support vector machine
One of the popular machine learning algorithms is SVM which
is a supervised learning binary classifier and is based on the struc-
tural risk minimization principle (Wan and Lei, 2009; Yao et al.,
2008). Separating hyper-plane formation from training dataset is
the basis of this method. Separating hyper-plane is generated in
the original space of n coordinates (xi parameters in vector x) be-
tween the points of two distinct classes (Marjanovic´ et al., 2011).
Maximum margin of separation between the classes is discovered
by SVM and therefore, it builds a classification hyper-plane in the
central of the maximum margin (Pradhan, 2013; Tehrany et al.,
2013a). If the point is located over the hyper-plane it will be clas-
sified as +1, and if not, it will be classified as À1. The training points
Fig. 3. Methodological flow chart employed in this study.
336 M.S. Tehrany et al. / Journal of Hydrology 512 (2014) 332–343

6. that are closest to the optimal hyper-plane are called support vec-
tors. Once the decision surface is acquired, the classification of new
data can be done (Tien Bui et al., 2012a). Consider a training data-
set of instance-label pairs (xiyi) with xi 2 Rn
; yi 2 f1; À1g, and
i = 1, . . . , m. In the current situation of flood susceptibility, x is a
vector of input space that contains slope, SPI, TWI, altitude, curva-
ture, distance from the river, geology, rainfall, LULC, and soil type.
The two classes {1, À1} show flooded pixels and non-flooded
pixels. The goal of SVM is to recognize the optimal separating
hyper-plane, which can separate the two classes into flood and
non-flood {1, À1} from the training dataset. For the case of linear
separable data, a separating hyper-plane can be defined as:
yiðw Á xi þ bÞ P 1 À ni; ð5Þ
where w is a coefficient vector that defines the orientation of the
hyper-plane in the feature space, b is the offset of the hyper-plane
from the origin, and ni is the positive slack variables (Cortes and
Vapnik, 1995). The following optimization problem using Lagrang-
ian multipliers will be solved through the determination of an opti-
mal hyper-plane (Samui, 2008).
Minimize
Xn
i¼1
ai À
1
2
Xn
i¼1
Xn
j¼1
aiajyiyjðxixjÞ; ð6Þ
Subject to
Xn
i¼1
aiyj ¼ 0; 0 6 ai 6 C; ð7Þ
where ai are Lagrange multipliers, C is the penalty, and the slack
variables ni allows for penalized constraint violation. The decision
function, which will be used for the classification of new data, can
then be written as:
gðxÞ ¼ sign
Xn
i¼1
yiaixi þ b
!
ð8Þ
In the case where the hyper-plane cannot be separated by the
linear kernel function, the original input data may be shifted into
a high-dimension feature space through some nonlinear kernel
functions. The classification decision function is then written as:
gðxÞ ¼ sign
Xn
i¼1
yiajKðxi; xjÞ þ b
!
ð9Þ
where K(xi, xj) is the kernel function.
Precision of the results and successful classification are strongly
influenced by the choice of kernel type and its’ parameters
(Damaševicˇius, 2010). Linear kernel (LN), polynomial kernel (PL),
radial basis function kernel (RBF), and sigmoid kernel (SIG) are
the most demandable kernel types for SVM analysis (Pradhan,
2013). PL and RBF are called Gaussian kernels and they are the
most commonly used kernels in the literature (Marjanovic´ et al.,
2011). RBF is capable to produce efficient interpolation; however
it may have some weak points to give longer-range extrapolation.
PL compared to RBF has better extrapolation capabilities at lower-
order degrees but requires higher order degrees for good interpo-
lation (Zhu et al., 2011). The LN is considered to be a specific case
of RBF, and the SIG performs similar to the RBF for certain param-
eters (Song et al., 2011). In the case where RBF is used, LN is not
required, and also researchers believe that the precision of the
results acquired from SIG is less than using EBF (Keerthi and Lin,
2003; Lin and Lin, 2003). The LN is appropriate for linear separable
circumstances while the real world problems are not linearly
separable (Ali and Smith, 2003). Based on aforementioned litera-
ture, different kernels have different impacts on the results. Hence
current research aims to evaluate these impacts on the perfor-
mance of the proposed novel ensemble WoE and SVM method.
Each kernel requires different parameters as can be seen in
Table 1. Some researchers consider selecting the kernel parameters
as a difficult task of this method (Ali and Smith, 2003). Regulariza-
tion parameter or penalty (C) controls the tradeoff between
training errors and margin, which assists to prevent over-fitting
of the model (Marjanovic´ et al., 2011). Higher degree of training
errors can be expected in the case where value of C is small,
whereas, the precision of the results can be increased by increasing
the C value and subsequently generating a smaller margin. This
parameter needs to be defined for all the kernel types. Another
parameter which is involved in all the kernels except LN is the
kernel width or gamma (c) that controls the degree of nonlinearity
of the SVM model (Tien Bui et al., 2012a). Parameter d is the poly-
nomial degree in the kernel function for the PL kernel and r is the
bias term in the kernel function for the PL and SIG kernels.
The cross-validation was used to select the optimal kernel
parameters (Pradhan, 2013; Zhuang and Dai, 2006). To begin,
through the step size process, ranges of all parameters were de-
fined. For each set of parameters, the dataset was divided into n
folds: one fold was used for the purpose of validation and the com-
bination of the remaining n – 1-fold was considered as the training
dataset. After the cross validation method was performed using
SPSS Clementine V.14.2, n validation accuracies were attained
and the average of them was used to perform the final flood sus-
ceptibility model using each kernel type (Yao et al., 2008). In the
current study, the dataset was divided into five random groups
where every group had equal number of samples (Table 3). For
the first iteration (model 1), folds 2, 3, 4 and 5 were used as train-
ing and the fold 1, was used for validation. The same procedure
was repeated on the other four models. Finally, the area under
curve (AUC) was used to assess the performance of every combina-
tion in order to discover the best parameterization of SVM (Mu and
Nandi, 2007). The mentioned procedure was repeated for four
kernel types. A detailed cross-validation for RBF-SVM, SIG-SVM,
LN-SVM and PL-SVM is shown in Table 3.
6. Results and discussion
The basis of the WoE is constructed by W+
and WÀ
which the
weight contrast (C) can be measured by these two factors. Positive
correlation between the class of each conditioning factor and
flooding is shown by positive C, while the negative correlation is
shown by negative. The ratio of C to standard deviation is called
studentized value of C or C/S(C), which represents the final weight
for each class of conditioning factor. Standard deviation of the con-
trast is shown by S(C) and furthermore, two parameters of S2
W+
and S2
WÀ
are denoting the variances of W+
and WÀ
. As it has been
explained in the previous section all these parameters were calcu-
lated for each conditioning factor which are listed in Table 2. This
table represents the relationship between the classes of each con-
ditioning factors and flood occurrence.
Based on the value of C/S(C), it can be seen that the slope with the
range of 2.46–3.94 had a maximum weight among the other classes.
Therefore, the area which had the slope range of 2.46–3.94 repre-
sented maximum susceptibility with reference to flooding in the
Table 1
Kernel types and their required parameters. Source: Tien Bui et al. (2012a), Yao et al.
(2008).
Kernel Equation Kernel parameters
RBF Kðxi; xjÞ ¼ expðÀcxi À x2
j Þ c
LN Kðxi; xjÞ ¼ xT
i xj –
PL Kðxi; xjÞ ¼ ðÀcxT
i x þ 1Þ
d c, d
SIG Kðxi; xjÞ ¼ TanhðÀcxT
i x þ 1Þ
d c
M.S. Tehrany et al. / Journal of Hydrology 512 (2014) 332–343 337

7. Table 2
Spatial relationship between each conditioning factor and flooding extracted by WoE method.
Factor Class W+
WÀ
C S2
(W+
) S2
(WÀ
) S(C) C/S(C)
Slope 0–2.46 0.6010 À0.0911 0.6921 0.0526 0.0111 0.2525 2.7413
2.46–3.94 0.6425 À0.1132 0.7557 0.0455 0.0115 0.2386 3.1667
3.94–5.42 0.5942 À0.1073 0.7015 0.0455 0.0115 0.2386 2.9397
5.42–6.90 0.2020 À0.0266 0.2286 0.0714 0.0105 0.2863 0.7985
6.90–8.63 À0.1624 0.0180 À0.1803 0.1000 0.0101 0.3318 À0.5435
8.63–10.61 À0.2107 0.0213 À0.2320 0.1111 0.0100 0.3480 À0.6666
10.61–13.07 À0.2930 0.0273 À0.3203 0.1250 0.0099 0.3673 À0.8721
13.07–16.28 À1.1999 0.0679 À1.2678 0.3333 0.0094 0.5855 À2.1654
16.28–21.46 À1.6160 0.0784 À1.6944 0.5000 0.0093 0.7137 À2.3741
21.46–62.92 0 0.0943 0 0 0.0092 0 0
SPI 0.00–0.01 0.7058 À0.1078 0.8135 0.0500 0.0112 0.2475 3.2874
0.02–7.34 0.1590 À0.0214 0.1804 0.0714 0.0105 0.2863 0.6301
7.35–7.98 À0.2605 0.0271 À0.2877 0.1111 0.0100 0.3480 À0.8266
7.99–8.52 À0.0831 0.0088 À0.0919 0.1000 0.0101 0.3318 À0.2770
8.53–8.98 0.4119 À0.0525 0.4644 0.0667 0.0106 0.2780 1.6701
8.99–9.43 À0.1833 0.0205 À0.2038 0.1000 0.0101 0.3318 À0.6141
9.44–9.97 À0.0544 0.0063 À0.0607 0.0909 0.0102 0.3180 À0.1909
9.98–10.61 À0.9348 0.0607 À0.9955 0.2500 0.0095 0.5094 À1.9541
10.62–11.51 0.1041 À0.0122 0.1162 0.0833 0.0103 0.3060 0.3798
11.52–23.12 À0.9238 0.0596 À0.9834 0.2500 0.0095 0.5094 À1.9303
TWI 0.30–2.55 À0.9371 0.0610 À0.9980 0.2500 0.0095 0.5094 À1.9591
2.56–3.09 0.0972 À0.0114 0.1086 0.0833 0.0103 0.3060 0.3548
3.10–3.48 0.3655 À0.0513 0.4169 0.0625 0.0108 0.2707 1.5402
3.49–3.88 0.1529 À0.0158 0.1687 0.0909 0.0102 0.3180 0.5304
3.89–4.41 À0.4635 0.0685 À0.5319 0.0909 0.0102 0.3180 À1.6728
4.42–5.21 À0.5127 0.0398 À0.5525 0.1667 0.0097 0.4200 À1.3155
5.22–7.07 0.1413 À0.0162 0.1575 0.0833 0.0103 0.3060 0.5145
7.08–19.14 0.0851 À0.0091 0.0942 0.0909 0.0102 0.3180 0.2962
19.15–21.79 0.1734 À0.0195 0.1930 0.0833 0.0103 0.3060 0.6305
21.80–34.13 0.4150 À0.0488 0.4639 0.0714 0.0105 0.2863 1.6203
DEM 0–9.61 1.3041 À0.2961 1.6002 0.0286 0.0135 0.2052 7.8002
9.61–14.35 1.1242 À0.3529 1.4771 0.0238 0.0149 0.1968 7.5050
14.35–19.08 0.6659 À0.1098 0.7757 0.0476 0.0114 0.2429 3.1939
19.08–23.82 À0.1073 0.0090 À0.1163 0.1250 0.0099 0.3673 À0.3166
23.82–28.56 0 0.0733 0 0 0.0092 0 0
28.56–38.04 À2.4797 0.1068 À2.5864 1.0000 0.0093 1.0046 À2.5745
38.04–57.00 À1.8284 0.1027 À1.9311 0.5000 0.0093 0.7137 À2.7058
57.00–94.91 0 0.1135 0 0 0.0092 0 0
94.91–175.47 0 0.0947 0 0 0.0092 0 0
175.47–1208.55 0 0.1220 0 0 0.0092 0 0
Curvature Concave À0.1323 0.02837 À0.1606 0.05556 0.01099 0.25797 À0.622756
Flat 0.06973 À0.128 0.19776 0.0137 0.02778 0.20366 0.971034855
Convex À0.1238 0.02641 À0.1502 0.05556 0.01099 0.25797 À0.58211988
Distance from river 0–277.73 0.6871 À0.1059 0.7929 0.0500 0.0112 0.2475 3.2042
277.73–634.82 0.1352 À0.0170 0.1522 0.0769 0.0104 0.2955 0.5149
634.82–991.91 0.4045 À0.0597 0.4641 0.0588 0.0109 0.2640 1.7580
991.91–1349.00 0.4349 À0.0631 0.4981 0.0588 0.0109 0.2640 1.8866
1349.00–1745.76 0.2513 À0.0348 0.2862 0.0667 0.0106 0.2780 1.0292
1745.76–2182.21 À0.2370 0.0244 À0.2614 0.1111 0.0100 0.3480 À0.7510
2182.2100–2698.00 À1.0103 0.0688 À1.0791 0.2500 0.0095 0.5094 À2.1183
2698.00–3451.85 À0.2969 0.0278 À0.3247 0.1250 0.0099 0.3673 À0.8841
3451.85–4919.89 À0.9431 0.0616 À1.0047 0.2500 0.0095 0.5094 À1.9722
4919.89–10117.51 À1.6230 0.0791 À1.7021 0.5000 0.0093 0.7137 À2.3850
Geology Phyllite, slate, shale and sandstone 0.0719 À0.0551 0.1270 0.0204 0.0167 0.1926 0.6593
Intrusive rocks, mainly granite with minor granodiorite À1.6350 0.3332 À1.9682 0.1429 0.0098 0.3907 À5.0373
Clay, silt, sand, peat with minor gravel 0.6564 À0.3753 1.0317 0.0189 0.0179 0.1916 5.3835
Rainfall 2375 0 0.0185 0 0 0.0092 0 0
2625 0 0.0415 0 0 0.0092 0 0
2875 0.3992 À0.2985 0.6977 0.0179 0.0189 0.1916 3.6405
3125 0.7383 À0.1659 0.9042 0.0357 0.0123 0.2192 4.1245
3375 À0.5291 0.2327 À0.7618 0.0400 0.0119 0.2278 À3.3436
3625 0 0.0880 0 0 0.0092 0 0
LULC Forest À0.4195 0.2696 À0.6891 0.0294 0.0133 0.2068 À3.3330
Built-up 0 0.0143 0 0 0.0092 0 0
Cropland 0.0823 À0.0502 0.1325 0.0233 0.0152 0.1960 0.6759
Wetlands 1.0588 À0.1215 1.1803 0.0556 0.0110 0.2580 4.5753
Paddy 0.3479 À0.0424 0.3903 0.0714 0.0105 0.2863 1.3634
Soil type Paleudults-Kandiudults 0 0.1979 0 0 0.0092 0 0
Palehumults 0 0.0042 0 0 0.0092 0 0
Hapludults-Paleudults 0 0.0515 0 0 0.0092 0 0
338 M.S. Tehrany et al. / Journal of Hydrology 512 (2014) 332–343

8. catchment. The first class of SPI (0.00–0.01) had the highest value of
C/S(C) which was 3.28 while the class 9.98–10.61 acquired lowest
weight of À1.95. In the case of TWI, the range in between 21.80
and 34.13 had the highest weight, demonstrating high flood suscep-
tibility at this range of TWI. In the case of altitude, the highest weight
(7.80) was for the range of 0–9.61 (m), and the lowest weight (À2.70)
was for the range of 38.04–57.00 (m). The flat curvature had the
highest value of C/S(C), indicating high flood susceptibility in flat
areas. This can be proven by the natural characteristic of the flood
that mostly happens in the flat areas. The distance from the river
from 0 to 1745.76 showed positive correlation with flood occur-
rence, while the areas more than 1745.76 m far from the river repre-
sented the negative influence in flooding. These results indicated
that the flooding mostly occurs near to the bank of the river and
occasionally far from the river. Among the different lithology types,
the class of clay, silt, sand, peat with minor gravel had the highest C/
S(C) value of 5.38. This lithology represented highest flood suscepti-
bility in the study area. In the case of rainfall, the highest C/S(C) val-
ues were for classes of 2875 and 3125 (mm). In the case of LULC,
wetlands followed by paddy field had the highest value of C/S(C),
showing maximum flood susceptibility. Forest acquired weight of
À3.33 which showed the negative correlation with flood occurrence,
as the vegetated areas can reduce the runoff and therefore decrease
the flooding. In soil type, the highest weight of 6.49 was achieved for
the Tropofibrists type and the least was acquired for the Haplorth-
ods-Endoaquods. Finally, the derived C/S(C) was normalized and
subsequently reclassified each conditioning factor in order to use
them as an input for SVM.
Subsequently, cross validation was performed for four models
of RBF-SVM, SIG-SVM, LN-SVM and PL-SVM. Table 3 lists the
SVM Kernel types and their parameters acquired through cross
validation process. The efficiency and precision of each model
was assessed using AUC. Success rate and prediction rate were cal-
culated for each try of modeling and the parameters yielding the
highest accuracy for each model were then chosen as the optimal
parameters.
Table 2 (continued)
Factor Class W+
WÀ
C S2
(W+
) S2
(WÀ
) S(C) C/S(C)
Kandiudults-Hapludults À0.1373 0.0316 À0.1689 0.0526 0.0111 0.2525 À0.6688
Tropofibrists 1.1828 À0.2243 1.4071 0.0345 0.0125 0.2168 6.4914
Haplorthods-Endoaquods À0.6840 0.0282 À0.7122 0.3333 0.0094 0.5855 À1.2165
Tropohemists-Troposaprist 1.1226 À0.0730 1.1956 0.0909 0.0102 0.3180 3.7599
Paleudults-Hapludults 0 0.1521 0 0 0.0092 0 0
Paleudults-Paleudalfs 0.7052 À0.2572 0.9624 0.0250 0.0145 0.1987 4.8427
Urban land 0 0.0115 0 0 0.0092 0 0
Tropopsamments-Fluvaquents 0.0126 À0.0009 0.0134 0.1429 0.0098 0.3907 0.0343
Table 3
The optimal RBF-SVM, SIG-SVM, LN-SVM and PL-SVM parameters for each testing model and their accuracies.
WoE & RBF-SVM Model Training fold Testing fold c C Success rate% Prediction rate%
1 2, 3, 4, 5 1 0.1 10 95 94
2 1, 3, 4, 5 2 0.1 15 95.40 95.02
3 1, 2, 4, 5 3 0.3 10 95.95 95.52
4 1, 2, 3, 5 4 0.2 10 95.57 95.68
5 1, 2, 3, 4 5 0.3 20 96.23 95.45
0.2 13
WoE & SIG-SVM Model Training fold Testing fold c C Success rate% Prediction rate%
1 2, 3, 4, 5 1 1 10 80.57 82.67
2 1, 3, 4, 5 2 1 20 80.57 82.67
3 1, 2, 4, 5 3 2.5 20 85.30 84.80
4 1, 2, 3, 5 4 1.5 10 83.91 80.83
5 1, 2, 3, 4 5 3 10 85.36 85.72
1.8 14
WoE & LN-SVM Model Training fold Testing fold C Success rate% Prediction rate%
1 2, 3, 4, 5 1 10 95.22 93.76
2 1, 3, 4, 5 2 11 94.27 93.73
3 1, 2, 4, 5 3 14 94.13 93.70
4 1, 2, 3, 5 4 15 94.09 93.71
5 1, 2, 3, 4 5 15 94.02 93.66
13
WoE & PL-SVM Model Training fold Testing fold c d C Success rate% Prediction rate%
1 2, 3, 4, 5 1 1 3 10 95.42 90.88
2 1, 3, 4, 5 2 1 3 20 95.86 87.20
3 1, 2, 4, 5 3 5 5 20 91.64 86.86
4 1, 2, 3, 5 4 5 1 10 93.66 94.02
5 1, 2, 3, 4 5 10 7 10 92.58 93.25
4.4 3.8 14
The bold texts show the mean values.
Table 4
The results of ROC for each derived model.
Method c C d Success rate Prediction rate
WoE & RBF-SVM 0.2 13 – 96.48 95.67
WoE & SIG-SVM 2 14 – 84.67 84.28
WoE & LN-SVM – 13 – 93.65 94.18
WoE & PL-SVM 4.5 14 4 93.77 94.17
Standalone RBF-SVM 0.2 13 – 86.47 81.27
WoE – – – 71.91 66.09
M.S. Tehrany et al. / Journal of Hydrology 512 (2014) 332–343 339

9. Average of optimal parameters resulted from each kernel type
was used to perform final RBF-SVM, SIG-SVM, LN-SVM and
PL-SVM modeling. Table 4 shows the parameters which were used
to perform final modeling. In order to assess the efficiency of the
novel ensemble WoE and SVM method, each method was applied
individually for comparison purpose. RBF was selected to be used
in the individual SVM modeling as it is the most popular SVM
kernel type (Pourghasemi et al., 2013b). The results were then
converted into a GIS and probability index was measured. Fig. 4
shows the probability maps derived from each WoE and SVM
ensemble method.
Visually all the probability maps appeared similar except
ensemble WoE and SIG-SVM. This can be due to the less efficiency
of the SIG kernel to detect the flood probable areas precisely.
However the comparison and judgment cannot be done through
the visual assessment for which a proper validation method is
needed. For validation, the resultant probability maps were evalu-
ated using the AUC method and both success rate and prediction
rate curves were measured (Table 4). The AUC is considered as
one of the most popular methods to assess the efficiency of the
generated method which produce both success and prediction
rates (Pradhan and Lee, 2010). To calculate the relative ranks for
each prediction pattern, the measured probability index was sorted
in descending order. Consequently, the cell values were partitioned
into 100 classes on the vertical axis (y), with accumulated 1% inter-
vals in the horizontal axis (x). The existence of the flood locations
(training and testing) in each interval was assessed and the resul-
tant success and prediction rates were measured.
For visual interpretation of flood susceptible locations, the
probability map was needed to be classified into different zones.
For classification, various methods exist in the literature such as
equal interval, quantile, standard deviation, and natural break
Fig. 4. Flood probability maps derived from ensemble: (a) WoE and RBF-SVM, (b) WoE and SIG-SVM, (c) WoE and LN-SVM, and (d) WoE and PL-SVM.
Fig. 5. Flood susceptibility maps derived from ensemble: (a) WoE and RBF-SVM, (b) WoE and SIG-SVM, (c) WoE and LN-SVM, and (d) WoE and PL-SVM.
340 M.S. Tehrany et al. / Journal of Hydrology 512 (2014) 332–343

10. (Tehrany et al., 2013b). All these classification methods were ap-
plied and the results of all methods were examined. The best out-
put was achieved using quantile method, while other methods
classified the large part of the area as a highly susceptible zone
with high degree of exaggeration. Finally, flood susceptibility maps
were obtained and the study area was divided into five classes of
flood susceptibility using quantile classification scheme: very
low, low, moderate, high and very high (Pradhan, 2010). The flood
susceptibility maps are shown in Fig. 5.
It can be seen that the high susceptible zones are mostly located
in the East and South-East part of the catchment. A large part of the
catchment was classified as susceptible zone using the ensemble
WoE and SIG-SVM method. Based on the validation results that
can be seen in Table 4, ensemble WoE and RBF-SVM method
achieved 96.48% and 95.67% for success and prediction rate respec-
tively. The efficiency of the proposed ensemble method was proven
by the higher prediction accuracy than the individual WoE and
SVM methods. Results indicated a significant difference of around
29% can be seen between the derived prediction accuracies from
ensemble WoE and RBF-SVM method and individual WoE method.
Also the amount of difference between the measured prediction
accuracies from ensemble WoE and RBF-SVM method and individ-
ual RBF-SVM was 14%. The success rate and prediction rate of WoE
were 71.91% and 66.09% respectively, and success rate and predic-
tion rate of RBF-SVM were 86.47% and 81.27% respectively. The
achievement of this research can assist the hydrological studies
to detect the flood prone areas more accurately. The success rate
and prediction rate results were produced using the training and
testing flood locations respectively which can be seen in Fig. 6.
The highest accuracies achieved by the RBF and PL kernel types,
while the lowest accuracy was acquired using SIG kernel. Results
proved how the choice of kernel type could produce different out-
comes for the similar dataset. Through this analysis the efficiency
of each kernel type was measured and the strength of one model
over another was evaluated.
7. Conclusions
Flood is one of the most damaging catastrophic phenomena in
the tropical environments. Therefore flood susceptibility mapping
is vital for catchment management in order to have proper and
sustainable development. Over the last decades, the flood
susceptibility evaluation has been one of the hot topics in the
literature, because this evaluation is a tough and nonlinear prob-
lem. Various methods were proposed and examined by many
researchers in the literature; however each method has some weak
points which are required to be solved. The need of having accurate
and reliable method to detect the flood prone areas prompted the
authors to examine the integration of individual methods in order
to enhance the capability of the individual methods. The flooding
event which occurred on 27th November 2009 caused serious
damages in the state of Terengganu, Malaysia. Therefore Tereng-
ganu has been selected as study area for flood susceptibility map-
ping using the proposed novel ensemble method. In the current
research WoE was integrated with SVM in order to enhance the
performance of each individual method. Furthermore, the goal of
this study was to increase the accuracy of the flood susceptibility
mapping to assist having proper management over the prone
areas. Various SVM kernel types were utilized to map the flood
susceptible areas from a number of conditioning factors. An
ensemble WoE and SVM model was applied by using four kernel
types of RBF, SIG, LN and PL. The results were compared with the
flood susceptibility maps derived from individual WoE and SVM
methods. Comparison of the proposed methods gave the advanta-
ges of ensemble WoE and RBF-SVM which produced 96.48% and
95.67% for success and prediction rate respectively. The current
research showed the advantage in terms of selection of proper ker-
nel type and introduction of the novel ensemble WoE and SVM
method. RBF showed higher accuracy compared to other kernels
types. The information derived from current research can assist
governments, planners, and researchers to perform proper actions
in order to prevent and mitigate this disaster in future. Further-
more, suitable and safe locations can be detected to carry out
development. As a conclusion, the outputs attained from the pro-
posed ensemble method should be evaluated attentively by
hydrologists. Due to its high prediction power, it is possible to
acquire some misleading results. Furthermore, the precision of
the results could be enhanced if the quality of the data increases.
Acknowledgements
Thanks to two anonymous reviewers and editorial comment by
Professor Geoff Syme for their valuable comments in the earlier
version which helped us to improve the quality of the manuscript.
Fig. 6. Illustration of cumulative frequency diagram showing cumulative flood occurrence (%; y-axis) occurring in flood probability index rank (%; x-axis); (a) success rate and
(b) prediction rate.
M.S. Tehrany et al. / Journal of Hydrology 512 (2014) 332–343 341

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