the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Scale and spatial distribution assessment of rainfall-induced landslides in a catchment with mountain roads

### Chih-Ming Tseng

### Yie-Ruey Chen

### Szu-Mi Wu

This study focused on landslides in a catchment with mountain roads that were caused by Nanmadol (2011) and Kong-rey (2013) typhoons. Image interpretation techniques were employed to for satellite images captured before and after the typhoons to derive the surface changes. A multivariate hazard evaluation method was adopted to establish a landslide susceptibility assessment model. The evaluation of landslide locations and relationship between landslide and predisposing factors is preparatory for assessing and mapping landslide susceptibility. The results can serve as a reference for preventing and mitigating slope disasters on mountain roads.

Taiwan is an island with three quarters of its land area consisting of slope land that is 100 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$, or less but has an average gradient of 5 % above (SWCB, 2017). Much of this sloped land has a steep gradient and fragile geological formations. Taiwan is hit by an average of 3.4 typhoons every year during the years 1911 to 2016 (Central Weather Bureau, 2017). In addition, average annual rainfall reaches 2502 mm in the years 1949 to 2009 (Water Resources Agency, 2017). Typhoons usually occur between July and October, and 70–90 % of the annual rainfall is composed of heavy rain directly related to typhoons (SWCB, 2017). Concentrated rainfall causes heavy landslides and debris flows every year (Dadson et al., 2004). The threat of disaster currently influences industrial and economic development and the road networks in endangered areas, thus establishing disaster evaluation mechanisms is imperative.

Landslide susceptibility can be evaluated by analysing the relationships between landslides and various factors that are responsible for the occurrence of landslides (Brabb, 1984; Guzzetti et al., 1999, 2005). In general, the factors that affect landslides include predisposing factors (e.g. geology, topography, and hydrology) and triggering factors (e.g. rainfall, earthquakes, and anthropogenic factors) (Chen et al., 2013a, b; Chue et al., 2015). Geological factors include lithological factors, structural conditions, and soil thickness; topographical factors include slope, aspect, and elevation; and anthropogenic factors include deforestation, road construction, land development, mining, and alterations of surface vegetation (Chen et al., 2013a, b; Chue et al., 2015). The method used to assess landslide susceptibility can be divided into qualitative and quantitative. Qualitative methods are based completely on field observations and an expert's prior knowledge of the study area (Stevenson, 1977; Anbalagan, 1992; Gupta and Anbalagan, 1997). Some qualitative approaches incorporate ranking and weighting, and become semi-quantitative (Ayalew and Yamagishi, 2005). For example the analytic hierarchy process (AHP) (Saaty, 1980; Barredo et al., 2000; Yoshimatsu and Abe, 2006; Kamp et al., 2008; Yalcin, 2008; Kayastha et al., 2013; Zhang et al., 2016) and the weighted linear combination (WLC) (Jiang and Eastman, 2000; Ayalew et al., 2005; Akgün et al., 2008). Quantitative methods apply mathematical models to assess the probability of landslide occurrence, and thus define hazard zones on a continuous scale (Guzzetti et al., 1999). Quantitative methods developed to detect the areas prone to landslide can be divided mainly into two categories: deterministic approach and statistical approach. The deterministic approach is based on the physical laws driving landslides (Okimura and Kawatani, 1987; Hammond et al., 1992; Montgomery and Dietrich, 1994; Wu and Sidle, 1995; Gökceoglu and Aksoy, 1996; Pack et al., 1999; Iverson, 2000; Guimarães et al., 2003; Xie et al., 2004) and are generally more applicable when the underground conditions are relatively homogeneous and the landslides are mainly slope dominated. The statistical approach is based on the relationships between the affecting factors and past and present landslide distribution (Van Westen et al., 2008). Statistical methods analyse the relation between predisposing factors affecting the landslide which include bivariate statistical models (Van Westen et al., 2003; Süzen and Doyuran, 2004; Thiery et al., 2007; Bai et al., 2009; Constantin et al., 2011; Yilmaz et al., 2012), multivariate statistical approaches as discriminant analysis (Baeza and Corominas, 2001; Carrara et al., 2003, 2008; Pellicani et al., 2014), and linear and logistic regression (Dai and Lee, 2002; Ohlmacher and Davis, 2003; Ayalew and Yamagishi, 2005; Yesilnacar and Topal, 2005; Greco et al., 2007; Carrara et al., 2008; Lee et al., 2008; Pellicani et al., 2014), as well as non-linear methods such as artificial neural networks (ANN) (Lee et al., 2004; Yesilnacar and Topal, 2005; Kanungo et al., 2006; Wang and Sassa, 2006; Li et al., 2012) and multivariate hazard evaluation method (MHEM) (Su et al., 1998; Lin et al., 2009). The MHEM is a non-linear mathematical model that presents an instability index to indicate landslide susceptibility (Lin et al., 2009). In addition, in some studies, landslide susceptibility analyses have focused on man-made facilities such as roads and railroads and have examined the landslide susceptibility of the surrounding environments (Das et al., 2010, 2012; Pantelidis, 2011; Devkota et al., 2013; Martinović et al., 2016; Pellicani et al., 2016, 2017). The aforementioned studies on the landslide susceptibility of areas surrounding man-made facilities have not investigated characteristics such as the location and scale (area) of landslides occurring in upper or lower slopes, and these thus constitute one of the objectives of the present study.

Technological progress has provided various advanced tools and techniques for land use monitoring. In recent years, aerial photos or satellite images have been commonly used in post-disaster interpretations and assessments of landslide damage on large-area slopes (Erbek et al., 2004; Lillesand et al., 2004; Nikolakopoulos et al., 2005; Lin et al., 2005; Chen et al., 2009; Otukei and Blaschke, 2010; Chen et al., 2013a). Satellite images offer the advantages of short data acquisition cycles, swift understanding of surface changes, large data ranges, and being low cost, particularly for mountainous and inaccessible areas. With the assistance of computer analysis and geographic information system (GIS) platforms, researchers can quickly determine land cover conditions. Thus, satellite images are suitable for investigating large areas and monitoring temporal changes in land use (Liu et al., 2001). Satellites can capture images of the same area multiple times within a short period. Studies have indicated that land surface change detection is the process of exploring the differences between images captured at different times (Liu et al., 2001; Chadwick et al., 2005; Chen et al., 2009; Chue et al., 2015). With multispectral satellite images, land surface interpretations involve comparisons of multitemporal images that are completely geometrically aligned.

We selected part of the catchment area of Laonung River which include Provincial Highway 20 in southern Taiwan as our study area. Regarding time, we focused on periods before and after landslides that occurred in the study area as a result of Typhoon Nanmadol (2011) and Typhoon Kong-rey (2013). We applied the maximum likelihood method to interpret and categorize high-resolution satellite images, thereby determining the land surface changes and landslides in the study area before and after the rainfall events. By using a GIS platform, we constructed a database of the rainfall and natural environment factors. Subsequently, we developed a landslide susceptibility assessment model by using the MHEM. The model performance was then verified by historical landslides. In addition, we extracted the locations of landslide areas to explore the relationship between the natural environment and the spatial distribution of the scale of these areas.

## 2.1 Maximum likelihood

The maximum likelihood classifier is a supervised classification method (SCM). SCMs include three processing stages: training data sampling, classification, and output. The underlying principle of supervised classification is the use of spectral pattern recognition and actual ground surface data to determine the types of data required and subsequently select a training site, which has a unique set of spectral patterns. To accurately estimate the various spectral conditions, the spectral patterns of the same type of feature are combined into a coincident spectral plot before the class of the training site is selected. Once training has been completed, the entire image is classified based on the spectral distribution characteristics of the training site by using statistical theory for automatic interpretation (Lillesand et al., 2004).

To facilitate the calculation of probability in the classification of unknown
pixels, the maximum likelihood method assumes a normal distribution in the
various classes of data. Under this assumption, the data distribution can be
expressed using covariance matrices and mean vectors, both of which are used
to calculate the probability of a pixel being assigned to a land cover class.
In other words, the probability of *X* appearing in class *i* is calculated
using Eq. (1), and the highest probability is used to determine the
feature of each pixel (Lillesand et al., 2004).

In this equation, *d* denotes the number of features, *X* denotes a sample
expressed using features and has *d* dimensions, *p*(*X*|*C*_{i}) denotes the
probability that *X* originates from class *i*, Σ_{i} denotes the
covariance matrix of class *i*, ${\mathrm{\Sigma}}_{i}^{-\mathrm{1}}$ denotes the inverse matrix
of Σ_{i}, $\left|{\mathrm{\Sigma}}_{i}\right|$ denotes the determinant of Σ_{i},
*μ*_{i} denotes the mean vector of classification *i*, (*X*−*μ*_{i})^{T}
denotes the transpose matrix of (*X*−*μ*_{i}), and *S*_{ij} denotes
the covariance of classes *i* and *j*.

During classification, the maximum value of the probability density functions
of sample *X* in each class is used to determine which class the sample
belongs to. The maximum likelihood classification decision is shown in
Eq. (2).

if

in which *k* denotes the number of classes. The question regarding classification
is how to effectively separate the classes in the feature space, or in other
words, how to divide the feature space. Maximum likelihood is a common
approach that offers fairly good classification accuracy (Bruzzone and
Prieto, 2001; Chen et al., 2004). Thus, we adopted maximum likelihood to
interpret and classify the satellite images.

## 2.2 Accuracy assessment

This study employed the aforementioned maximum likelihood method to classify satellite images. To determine whether the accuracy of image classification was acceptable, we adopted an error matrix to test for accuracy. An error matrix is a square matrix that presents error conditions in the relationship between ground surface classification results and reference data (Verbyla, 1995). It contains an equal number of columns and rows, and the number is determined by the number of classes. For example, Table 1 contains four classes. The columns show the reference data, and the rows show the classification results. The various elements in the table indicate the quantity of data corresponding to each combination of classes.

In the Table 1, *X*_{12} represents the amount of data that were interpreted
as Class A but actually belong to Class B, whereas *X*_{21} indicates the
amount of data that were interpreted as Class B but actually belong to Class
A. *X*_{11} and *X*_{22} represent the amount of data accurately classified
as Class A and Class B. An error matrix is generally used to
check the quality of classification results in statistics (Congalton, 1991;
Verbyla, 1995). In the present study, we evaluated the accuracy of the
classification results based on the overall accuracy and kappa value
(Cohen, 1960), which is the coefficient of agreement derived from the
relationship between the classification results and training data. These two
parameters are explained as follows.

### 2.2.1 Overall accuracy (OA)

OA is the simplest method of overall description. For all classes, OA represents the probability that any given point in the area will be classified correctly.

In Eq. (3), *N* denotes the total number of classifications, *n*
denotes the total number of rows in the matrix, and *X*_{ii} is the number
of correctly classified checkpoints.

### 2.2.2 Kappa coefficient

The kappa ($\widehat{K}$) coefficient indicates the degree of agreement between the classification results and reference values and shows the percentage reduction in the errors of a classification process compared with the errors of a completely random classification process. Generally, the kappa coefficient ranges from 0 to 1, and a greater value indicates a higher degree of agreement between the two sets of results, as shown in Eq. (4):

in which *X*_{i+} is the total number of pixels for a given class on the actual
ground surface and *X*_{+i} is the number of pixels in that class.
As reported by Landis and Koch (1977), a kappa coefficient greater
than 0.8 signifies a high degree of accuracy, whereas a coefficient between
0.4 and 0.8 or less than 0.4 indicates moderate or poor accuracy.

## 2.3 Rainfall analysis method

In previous studies regarding the influence of rainfall on landslides, rainfall intensity and accumulated rainfall have been most commonly used as predisposing factors of landslides (Giannecchini, 2006; Chang et al., 2007; Giannecchini et al., 2012; Ali et al., 2014). Therefore, we adopted effective accumulated rainfall and intensity of rolling rainfall as rainfall indices and predisposing factors of landslides in the present study. These two indices are explained as follows.

### 2.3.1 Effective accumulated rainfall (EAR)

Generally, rainfall is considered the trigger of slope collapse, whereas previous rainfall can be regarded as a potential factor of a landslide. Previous rainfall influences the water content of the soil, which in turn affects the amount of rainfall required to trigger a landslide (Seo and Funasaki, 1973).

Figure 1 shows an illustration of rainfall events defined based on EAR (Seo and Funasaki, 1973). The diagram shows a concentrated rainfall event with no rainfall in the preceding or subsequent 24 h; thus it can be considered a continuous rainfall event. A continuous rainfall event that occurs simultaneously with a landslide is the main rainfall event. The beginning of the main rainfall event is defined as the time point when the rainfall first reaches 4 mm. The calculation of accumulated rainfall ends at the time when the landslide occurs. However, because the exact time of a landslide cannot be precisely determined, we regarded the hour with the maximum rainfall during the main rainfall event as the time at which the landslide occurred in this study.

In accordance with previous studies, we defined EAR as the sum of direct and previous indirect rainfall. Previous indirect rainfall is the rainfall accumulated during the 7 days prior to the main rainfall event and can be expressed as follows (Seo and Funasaki, 1973; Crozier and Eyles, 1980):

where *P*_{b} denotes the previous indirect rainfall, *P*_{n} denotes the
rainfall during the *n* days prior to the main rainfall event (mm), and *k*
denotes a diminishing coefficient set as 0.9 in this study (Chen et al.,
2005). Direct rainfall encompasses the continuous rainfall accumulated during
the rainfall events, starting from the first rainfall to the time of
landslide occurrence. Direct rainfall has a direct and effective impact on
landslide occurrence and is thus not diminished. Therefore, EAR could be
expressed as follows in this study:

where *P*_{r} (mm) represents the rainfall accumulated during the main
rainfall event from the first rainfall to the time of landslide occurrence,
and *P*_{b} (mm) represents the previous indirect rainfall.

### 2.3.2 Intensity of rolling rainfall (*I*_{R})

Rainfall intensity refers to the amount of rainfall within a unit of time. It
is considered a crucial index for evaluating disasters because greater
intensity or longer durations have considerable impacts on slope stability.
Furthermore, rainfall-induced landslides may be triggered by several hours of
continuous rainfall. The raw rainfall data in this study were hourly
precipitation; thus *I*_{R} (mm h^{−1}) can be expressed as
follows:

where *I* denotes rainfall intensity, *m* denotes the number of rolling hours
of rainfall (set as 3 h in this study), *I*_{mR} denotes the
*I*_{R} during *m* hours, and *I*_{t} denotes the rainfall intensity
during hour *t*.

## 2.4 MHEM

The MHEM is a diverse non-linear mathematical model. Based on relative
relationships, the MHEM presents an instability index (*D*_{t}) to indicate
susceptibility in different areas. The objective is to estimate the variance
of predisposing factors and then to determine the weight of each factor
according to the value of variance, finally to derive a suitable landslide
susceptibility assessment model (Su et al., 1998; Lin et al., 2009; Chue
et al., 2015).

The predisposing factors in the MHEM are rated based on the frequency of landslide occurrence, which is calculated as follows:

where *R*_{i} represents the landslide pixel ratio of the various factors in
class *i*, *r*_{i} represents the number of landslide pixels in class *i*,
and *r*_{T} represents the total number of pixels. Thus, landslide
percentage *X*_{i} is expressed as

where *X*_{i} denotes the landslide percentage of class *i* and Σ*R*_{i} denotes the sum of the landslide pixel ratios.

Based on the landslide percentages of the various classes for each
predisposing factor, the normalized score value of classes for each factor
(*d*_{n}) can be calculated using Eq. (10), and presented in relative
values ranging from 1 to 10.

In Eq. (10), *X*_{i} represents the causal rate of the sample region,
and *X*_{max} and *X*_{min} represent the maximum and minimum
landslide percentages of the factor in the various sample regions.

To estimate the weight of influence of each predisposing factor, the
coefficient of variation (*V*) of the landslide ratios derived from the class
of the predisposing factors is used to represent the sensitivity of landslide
ratios in different predisposing factor classes. A smaller coefficient of
variation denotes higher similarity among the landslide probabilities in the
various classes, which indicates that this factor grading method cannot
determine which areas have higher or lower landslide probabilities. By
contrast, a greater coefficient of variation denotes that this factor grading
method can be used to describe the influence of factor classes on landslides.
Thus, the coefficient of variation among the predisposing factors can
indicate the factor weights. The coefficient of variation is calculated as
shown in Eq. (11):

where *σ* is the standard deviation and *X* is the mean landslide
percentage of the various factor classes.

We divided the coefficient of variation of each individual factor by the
total coefficient of variation of all factors to derive the factor weight,
which represented the degree of influence of the factor on landslide
occurrence. The factor weight can be calculated as shown in Eq. (12),
where *W* is the factor weight and *V* is a coefficient of variation.

Finally, the weight (*W*_{i}) of each factor is determined by the rank of its
variance (*V*), and each factor is assigned a different weight. Subsequently,
a non-linear mathematical model can be derived as follows:

where *D*_{t} is the instability index of the samples, expressed using
relative values ranging from 1 to 10. A cumulative value closer to 10
indicates greater landslide potential, whereas a cumulative value closer to 1
indicates lower landslide potential.

By using the concept of log-normal distribution in statistics, we converted the levels of instability index derived using the MHEM into probabilities of landslide occurrence. The calculation formula of the log-normal distribution is shown in Eq. (14):

where *x* denotes the level of the instability index and *μ* and *σ*
denote the mean and standard deviation of the level of the instability index.
After calculating the probabilities of landslide occurrence by
using the log-normal distribution, we normalized the probabilities to range
from 0 to 1 for convenience. The normalization formula is shown in
Eq. (15).

In Eq. (15), *X*_{i} represents the factor being normalized and
*X*_{max} and *X*_{min} represent the maximum and minimum
values of the factor, respectively.

We referred to the historical data on road disasters from the NCDR (National Science and Technology Center for Disaster Reduction, 2017) and considered road sections where rainfall-induced landslides occurred frequently in southern Taiwan. We focused on the periods before and after Typhoon Nanmadol (2011) and Typhoon Kong-rey (2013) hit southern Taiwan, and we selected part of the catchment area of Laonung River in southern Taiwan as our study area (Fig. 2), which includes areas from three districts in Kaohsiung city (Jiashian, Liouguei, and Taoyan). The Laonung River flows SW across the south of the study area and originates from the Jade Mountain. The study area is located in a tropical monsoon climate zone. According to the climate statistics (1983–2012) recorded by the Central Weather Bureau, the average annual rainfall is approximately 2758 mm. Provincial Highway 20 is in an east–west direction, the starting point of the highway is Tainan city in southern Taiwan, and the ending point is Degao Community in Guanshan town, Taitung County, with a total length of 203.982 km. Within the study area, Provincial Highway 20 starts from Liouguei District (76 K + 000) in the west and goes to Taoyan Village (87 K + 500) in the Taoyan District. According to the survey data from the Directorate General of Highways (2017), the road width of Provincial Highway 20 passing through the study area is about 8.8 m. The average traffic flow and the total number of vehicles carried per day for both directions are 2260 PCU (passenger car unit) and 1434. In the study area, most of the traffic vehicles are sedans, followed by trucks and buses.

## 4.1 Preprocessing of satellite images

This study employed and interpreted satellite images taken by FORMOSAT-2
(FM2). FM2 images have been extensively used to identify natural disasters
and land use (e.g. Lin et al., 2004, 2006, 2011; Liu et al., 2007; Chen
et al., 2009, 2013a). The FORMOSAT-2 satellite has a circular and sun
synchronous orbit. With its high torque reaction wheels for all axes, the
FORMOSAT-2 is able to point to a ±45^{∘} along track and
±45^{∘} across track and is thus able to capture any scene each day
in all of Taiwan if necessary (Liu et al., 2007). FORMOSAT-2 images are
available in 2 m resolution in panchromatic (pan) and 8 m in
multispectral (ms) from visible to near-infrared with a coverage of
24 km×24 km. In the present study, prior to
interpretation, the satellite images underwent spectral fusion, coordinate
positioning, cropping, and cloud removal. The images taken by FM2 are
multispectral with blue, green, red, and near-infrared (NIR) wavelengths
(Chen et al., 2013a; Chue et al., 2015). Image fusion and coordinate
positioning were conducted using the import data and coordinate positioning
tool of ERDAS IMAGINE (2013). Then, we used the image analysis tool of ArcGIS
to remove clouds from the images.

## 4.2 Training site selection and mapping

To map the sample areas required for image interpretation, we overlapped the high-resolution, preprocessed satellite images of the study area before and after the typhoons and mapped the training sites by using a GIS platform. Based on field investigations and relevant studies (Chen et al., 2009, 2013a; Chue et al., 2015), we selected areas with water, roads, buildings, crops, vegetation, river channels, and bare land within the study area as the sample area factors for interpretation training.

## 4.3 Image interpretation and accuracy assessment

Image interpretation and classification were conducted using the maximum likelihood module in ERDAS IMAGINE. The interpretation and classification results of the satellite images before and after Typhoon Nanmadol in 2011 and Typhoon Kong-rey in 2013 are shown in Fig. 3. The different colours in the images represent different interpretation factors.

To verify the accuracy of the results, we randomly extracted 25 points from the satellite images for each training factor as checkpoints and tested the accuracy by using the aforementioned error matrix approach. With the satellite images before and after Typhoon Kong-rey in 2013 as an example, Table 2 shows the error matrix and accuracy assessment results of the satellite image interpretation and classification processes. Table 3 presents the kappa values and OA results of the satellite images captured before and after the two typhoons. As mentioned, kappa values ranging from 0.4 to 0.8 indicate moderate accuracy, and thus the interpretation results had moderate to high accuracy.

Taking the landslide inventory after Typhoon Kong-rey in 2013 as an example, there were 291 landslides, which totaled a landslide area around 135 ha. This was equivalent to an average concentration of 5.1 % throughout the whole study area of 2659 ha. Among the 291 landslides, 256 landslides were recognized with an area smaller than 1 ha, the remaining 35 landslides were recognized in the range of 1 to 8 ha. The biggest landslide, with an area around 7 ha.

To evaluate the landslide susceptibility of slopes within the study area, we constructed 8 m×8 m grids by using the GIS platform along with the interpretation results of the two typhoons. We also constructed an 8 m×8 m digital elevation model (DEM) (SWCB, 2011) and input the classification results, thematic map of predisposing factors, and rainfall data into the pixel to aid subsequent landslide susceptibility assessments.

## 5.1 Predisposing factor selection and factor correlation test

### 5.1.1 Predisposing factor selection

Referring to Chen et al. (2009), we divided the predisposing factors of landslides into three categories: natural environment, land disturbance, and rainfall.

### Natural environment factors

*Elevation*

The influence
of elevation varies with the climate and thus affects the distribution of
vegetation on the slope and type of weathering. In addition, elevation
reflects the influence of geological structure, stress, and time. The highest
and lowest elevations in the study area were 1481 and 365 m,
respectively. Using the GIS platform, we extracted the elevation data from
the DEM of the study area to estimate the mean elevation of each grid. We
divided the elevation data into seven classes at intervals of 300 m.
*Slope gradient*

A slope's gradient
generally exerts significant impact on slope stability. By using the DEM and
gradient analysis of the GIS platform, we calculated the mean gradient of
each pixel in the study area; subsequently, we divided the gradient values in
the pixels within the study area into seven classes.
*Aspect*

Rainfall-induced
landslides are subject to the influence of seasonal changes such as those
related to rainfall and wind direction. Thus, the direction of the slope must
be considered. As described, we used the DEM and aspect analysis function of
the GIS platform to calculate the average aspect of the pixels in the study
area. According to their direction, we divided them into six classes from
windward to flat ground.

*Geology*

Referring
to the digital file of the Geologic Map of Taiwan, scale 1 : 50 000,
Chiahsien, which was compiled by the Central Geological Survey of the
Ministry of Economic Affairs in 2000, we determined that the geology of the
study area includes five types of rock: the upper part of Changshan
Formation, the Tangenshan Formation, the Changchihkeng Formation from the
Miocene period, and modern alluvium and terrace deposits from the Holocene
period. We divided geological strength into six classes (Chen et al., 2009).
*Terrain roughness*

Terrain roughness
refers to the degree of change in pixel height. Wilson and Gallant (2000)
proposed the use of the standard deviation of height within a radius to
measure the degree of change in height because of its indicative meaning in
relation to changes in regional height. Using the Neighborhood (focal
statistics) of the Spatial Analyst Toolbox in ArcGIS, we calculated the terrain
roughness of the DEM. Statistical cluster analysis was used to automatically
divide terrain roughness into six classes. *Slope roughness*

Slope roughness
refers to the fluctuations in slope gradient in the pixels. High slope
roughness means that the slope gradient varies considerably (Wilson and
Gallant, 2000). Slope roughness is calculated through the same method as
terrain roughness, except with the original elevation values being replaced
with the slope gradient values obtained using ArcGIS. Just as terrain
roughness was graded, we first used the Spatial Analyst Toolbox in ArcGIS to
estimate the slope roughness of each pixel, after which we used cluster
analysis to automatically divide slope roughness into six classes.
*Distance to water*

Streams will cause soil
erosion and riparian erosion, which directly or indirectly affect the
stability of the slope. We calculated the distances to water using the Buffer tool in ArcGIS and divided the distances into seven classes.
*Distance to road*

The construction of the
roads will also have an influence on the stability of the slope. Therefore,
we also calculated the distances to road using the Buffer tool in ArcGIS and
divided the distances into seven classes.

### Land disturbance factors

Land disturbance varies with space and time. Based on the tendency to promote
landslides, the index of land disturbance was developed, and we made some
revisions to the qualitative approach proposed by Chen et al. (2009, 2013b)
to calculate land disturbance and selected roads, buildings, crops, bare
land, and vegetation as the land disturbance factors of landslides in the
study area. We extracted the disaster and ground surface data from previous
satellite image interpretation and classification results and input the land
disturbance factors into the pixels by using the GIS platform. Referring to Chen
et al. (2009, 2013b), the scores of the index for the disturbance condition
(*I*_{DC}) in the pixels are assigned from five to one, corresponding to
bare land, roads, buildings, crops, and vegetation.

### Rainfall factors

We collected precipitation data from weather stations of the Central Weather
Bureau, including Guanshan, Biaohu, Hsiao Guanshan, Gaojhong, Sinfa,
Jiashian, and Xinan. We then calculated the EAR and 3 h *I*_{R}
(*I*_{3R}) levels observed at each station. The results from Typhoon Nanmadol in 2011 and Typhoon Kong-rey in 2013 are compiled in Table 4. By
using the inverse distance weighting (IDW) function of ArcGIS and the
EAR and maximum *I*_{3R} values of the weather stations, we
estimated the rainfall of each pixel throughout the study area and then used
cluster analysis to divide the results into six classes.

### 5.1.2 Factor correlation test

To establish a landslide susceptibility assessment model, we selected
elevation, slope gradient, aspect, geology, terrain roughness, slope
roughness, distance to water, distance to road, *I*_{DC}, and rainfall
as landslide-predisposing factors. Rainfall included EAR and maximum
*I*_{3R}.

We employed the Pearson correlation test tool in SPSS software (2005) to
examine the correlation among these factors. The correlation coefficients
ranged from −1 to +1, with +1, −1, and 0 indicating complete positive
correlation, complete negative correlation, and no correlation between two
variables, respectively. Factors with high correlation were then subjected to
a paired sample *t* test conducted using SPSS to examine the significance of
the correlation between them. Those with high correlation were eliminated.

Table 5 presents the test results regarding the correlation between the
predisposing factors. As shown, the degree of correlation between most
factors was moderate to low. A high degree of correlation was found only
between elevation and terrain roughness and between slope gradient and slope
roughness. Thus, we administered paired sample *t* tests to these two factor
pairs to test the significance of the correlation. The results in Table 6
show that the significance was 0 (<0.05) for the correlation between both
pairs, indicating no correlation; thus these factors were not eliminated.

## 5.2 Landslide susceptibility assessment and hazard map

To apply the MHEM in order to establish a landslide susceptibility assessment model, we input the natural environment, land disturbance, and rainfall factors into the pixels by using the GIS platform. By using the changes in bare land between the images before and after the typhoons and applying image subtraction aided by manual checking, we obtained the pixel data of the rainfall-induced landslide locations in the study area. With the study area after Typhoon Nanmadol in 2011 as an example, we examined EAR during the rainfall period and rated the classes by using the factor weights derived using the MHEM, as shown in Table A1 of Appendix A.

The calculation process is explained in this paper using elevation as an
example. In accordance with factor selection, the elevation factor was
divided into seven classes. Aided by the GIS platform, we calculated the
total number of pixels, total number of landslides, and landslide percentage
within each elevation level in the study area by using Eqs. (8)
and (9). Based on the landslide percentages of the elevation factor
and the minimum and maximum landslide percentages, we subsequently obtained
the scores of the factors by using Eq. (10). We then calculated the
standard deviation, coefficient of variation, and weight values by using
Eqs. (11) and (12); the results are listed in Table A1 of
Appendix A. The presented results show that the standard deviation
(*σ*), coefficient of variation (*V*), and factor weight (*W*) of the
landslide percentage were 0.021, 0.764, and 0.087, respectively. Finally, we
calculated the instability indices by using the weight values and scores of
the factors through Eq. (13). Furthermore, the results in Table A1 of
Appendix A indicate that the degrees of land disturbance (*I*_{DC}),
geology (*G*_{s}), slope gradient (*S*_{s}), and slope roughness had the
greatest influence on landslides in the study area, followed by distance to
water (*D*_{s}), EAR, and elevation (*E*_{l}).

For EAR and *I*_{3R} we used an instability index to
determine the level of landslide susceptibility of slopes throughout the
study area. The derived instability index intervals (Table 7) for EAR
and *I*_{3R} ranged from 2.05 to 9.59 and 2.02 to 9.96. By using Eqs. (14) and (15), the landslide
probability intervals calculated based on EAR and *I*_{3R} are
presented in Table 7.

We employed the mean probability of landslide occurrence to differentiate
between high and low landslide susceptibility. Landslides were considered
more likely to occur in areas where the probability of landslide occurrence
was greater than the mean. By contrast, landslides were considered less
likely to occur in areas where the probability of landslide occurrence was
lower than the mean. With rainfall factor EAR as an example, we
determined the mean probability of landslide occurrence to be 0.46. We
further divided landslide susceptibility into four levels: high (0.731–1),
medium high (0.461–0.73), medium low (0.23–0.46), and low (0–0.23). The
results showed that the mean probability of landslide occurrence varied
little, regardless of whether it was calculated using EAR or
*I*_{3R}.

By using the GIS platform, we considered the landslide susceptibility calculated using EAR for Typhoon Nanmadol in 2011 as an example. As illustrated in Fig. 4, we included an overlay created by the NCDR showing the locations of historical disasters within the study area. The results revealed a total of 24 historical disasters, 17 of which were situated in areas of medium high or high landslide susceptibility. Therefore, the estimation accuracy in this study was approximately 71 %. Regarding Typhoon Kong-rey in 2013, 18 historical disasters occurred within areas of medium high or high landslide susceptibility, thereby yielding 75 % accuracy. Table 8 presents the accuracy levels associated with using different rainfall factors to calculate landslide susceptibility for different typhoons.

## 5.3 Investigation of rainfall factors and instability index

To understand the relationship between the rainfall factors and the degree of
instability on the slopes in the study area after the typhoons, we first removed
the cloud cover grids from post typhoon images and subsequently employed
cluster analysis to divide the instability indices of the pixels into three
levels: high, medium, and low. We then collected random samples based on the
proportions of landslide and non-slide pixels at each level (50 landslide and
50 non-landslide pixel points) and plotted their relationship. Table 9 and
Fig. 5a–d present the relationships between the rainfall factors (EAR
and *I*_{3R}), instability index, and landslide occurrence in the
pixels following Typhoon Nanmadol in 2011 and Typhoon Kong-rey in 2013.
Figure 5a and b show EAR, whereas Fig. 5c and d show
*I*_{3R}. The presented results indicate that the typhoon events
increased the degree of slope instability (*D*_{t}) and landslide occurrence,
regardless of whether EAR or *I*_{3R} was considered.
Furthermore, significantly more landslide points were situated in areas of
high instability than in areas of other levels of instability, and landslides
rarely occurred in areas of low instability. Moreover, areas of high slope
instability were prone to landslides even if their EAR or
*I*_{3R} was low. By contrast, areas of low instability required more
rainfall for the occurrence of landslides. The results (Table 9) further showed
that the EAR and *I*_{3R} levels of Typhoon Kong-rey in 2013
were greater than those of Typhoon Nanmadol in 2011. Thus, at any *D*_{t}
level, the proportion of landslides that occurred in the study area after
Typhoon Kong-rey was higher than that after Typhoon Nanmadol. Figure 5e and f
present the relationships between EAR×*I*_{3R}, the
instability index, and landslide occurrence; EAR×*I*_{3R} is the index of rainfall-induced landslide (ILR), with
a higher value indicating higher susceptibility to a landslide. The figures
show that for a high instability index, even a small rainfall event could
trigger a landslide (lower-right corners of the figures). By contrast, for
a low instability index, a larger rainfall event could not easily trigger
a landslide (upper-left corners of the figures).

We analysed the spatial characteristics of landslides by using landslide locations collected from before and after the two typhoons and the land surface interpretation results of the study area.

## 6.1 Investigation of landslide predisposing factors and landslide area

The influence of predisposing factors on landslides varies. In this study, we examined the relationships between landslide area and various predisposing factors. By using the area of landslides (i.e. the number of landslide pixels) induced by Typhoon Nanmadol in 2011 as an example, we investigated the influences of the predisposing factors (elevation, slope gradient, aspect, geology, slope roughness, terrain roughness, distance to water, distance to road, and degree of land disturbance) on landslides. The various factor classes and corresponding numbers of landslide pixels are shown in Fig. 6a–i.

Figure 6a presents the relationship between different classes of elevation
and the number of landslide pixels (landslide area). As shown in the figure,
the number of landslide pixels in the study area peaked at elevations between
450 and 750 m and then declined as the elevation increased. Figure 6b
displays the relationship between different classes of slope gradient and the
number of landslide pixels (landslide area). As shown in the figure, the
number of landslide pixels in the study area increased with the slope gradient
and peaked between 30 and 55^{∘}. Landslides rarely occurred on slopes
steeper than 55^{∘}. Figure 6c illustrates the relationship between
aspect and the number of landslide pixels, with aspect divided into eight
categories: north, north-east, east, south-east, south, south-west, west, and
north-west. As shown in the figure, the number of landslide pixels was highest
on slopes facing south, followed by those on slopes facing east and
south-east. We speculate that this is because rainfall during the typhoon
season in Taiwan promotes poor cementation and high weathering on slopes
along rivers, which consequently prompts these slopes to develop toward
low-lying rivers (which run from the north-east to the south-west) after
rainfall events.

Figure 6d shows the relationship between geology and the number of landslide pixels. As shown in the figure, the Sanhsia Group and its stratigraphic equivalence lead to landslides more easily than the Lushan Formation in the study area. The Sanhsia Group and its stratigraphic equivalence mainly comprise sandstone, shale, and interbedded sandstone and shale. Shale has weaker cementation, lower strength, and a greater tendency to weather and fracture. By contrast, the Lushan Formation consists of argillite, slate, and interbedded argillite and sandstone, and its strength is controlled by cleaving; some areas are prone to weathering and fracturing. Thus, both rock types are more likely to collapse, but on the whole, the Sanhsia Group and its stratigraphic equivalence collapse more easily than the Lushan Formation. Furthermore, this result indicates that the locations of landslide areas within the study area are associated with geology. Figure 6e presents the relationship between slope roughness and the number of landslide pixels. The number of landslide pixels within a level of slope roughness first increased with the slope roughness and then began to decline once a certain level of slope roughness (35–40) was reached. This result is similar to that of the influence of the slope gradient on the number of landslide pixels. Figure 6f displays the relationship between terrain roughness and the number of landslide pixels. As shown in this figure, the results are similar to those regarding the influence of elevation on the number of landslide pixels: the number of pixels declined when the terrain roughness was greater than 500 and was very small when the terrain roughness was greater than 1200.

Figure 6g illustrates the relationship between distance to water and the number of landslide pixels. The presented results show a significantly greater number of landslide pixels within 300 m of water. The width of the river channel within the study area was determined to range from 100 to 200 m, revealing that the development of landslide areas near water in the study area is caused by rainfall significantly raising the water level in the river, which scours the slope toe, affects slope stability, and triggers landslides. Figure 6h presents the relationship between distance to road and the number of landslide pixels. The presented results reveal that areas between 100 and 300 m from roads had the greatest number of landslide pixels. Further examination of the relationship between distance to road and the area and number of landslides revealed that most landslides between 0 and 100 m from roads were small collapses, whereas those between 100 and 300 m from roads were larger in area. The number of landslides 0–100 m from roads was greater than that 100–300 m from roads.

The degree of land disturbance can represent the changes in surface conditions including roads, buildings, crops, bare land, and vegetation. A greater degree of land disturbance likely indicates a greater degree of surface changes, which can yield a greater number of landslide pixels. Figure 6i shows the relationship between the degree of land disturbance and the number of landslide pixels. The presented results indicate that the number of landslide pixels increased with the degree of land disturbance.

## 6.2 Landslide scale and spatial distribution

We employed the terrain tool in ERDAS IMAGINE and the DEM to identify the
ridges and valleys in the study area. Following the methods in previous
studies (Meunier et al., 2008; Chue et al., 2015), we extracted the distances
between the highest point of a landslide area and the nearest ridge
(*d*_{r}), between the lowest point of the landslide area and the
nearest stream (*d*_{s}), and between the ridge and the stream
(*d*_{t}) (Fig. 7). Furthermore, in Taiwan, many slopes are visible on
developed mountain roads built between ridges and streams. Therefore, we
explored the spatial distribution of landslides above and below mountain
roads. Similarly to Fig. 7a, to explore the spatial distribution of
landslides, we extracted the distances between the highest point of
a landslide area on a slope above a road and the nearest ridge
(*d*_{r}), between the lowest point of the landslide area and the
nearest mountain road (*d*_{mu}), and between the ridge and the mountain
road (*d*_{tu}) (Fig. 7b). We also investigated this distribution by
extracting the distances between the highest point of a landslide area on
a slope below a road and the nearest mountain road (*d*_{md}) between
the lowest point of the landslide area and the nearest stream (*d*_{s})
and between the mountain road and the stream (*d*_{td}) (Fig. 7c).

This study examined the spatial distribution of landslides in the region
along Provincial Highway 20 before and after Typhoon Nanmadol in 2011 and
Typhoon Kong-rey in 2013. Using the approach shown in Fig. 7a, we mapped the
bare land in the study area, as shown in Fig. 8a–d. Of these figures,
Fig. 8a and c show the conditions before the typhoons, whereas Fig. 8b and d
present the conditions after the typhoons. The presence of bare locations
near the *Y* axis (${d}_{\text{r}}/{d}_{\text{t}}\approx \mathrm{0}$) denotes that the bare
land originated near the ridge. By contrast, the presence of bare locations
near the *X* axis (${d}_{\text{s}}/{d}_{\text{t}}\approx \mathrm{0}$) denotes that the bare
land progressed toward the stream. Thus, the presence of bare locations near
the origin denotes that the bare land originated near the ridge and
progressed toward the stream.

The results in Fig. 8a–d show more bare locations in the lower-right halves of the graphs, some of which are larger in area. The figures indicate fewer bare locations in the upper-left halves of the graphs, and the ones that are present are smaller in area. These spatial distribution characteristics are similar to those derived by Meunier et al. (2008). We speculate that this is because the frequency of rainfall-induced landslides increases significantly because of bank erosion, which is shown in the lower-right half of Fig. 8 (${d}_{\text{r}}/{d}_{\text{t}}\ge \mathrm{0.5}$ and ${d}_{\text{s}}/{d}_{\text{t}}\le \mathrm{0.5}$). Furthermore, the bare locations before and after typhoons Nanmadol and Kong-rey show that the bare land does not increase in number but increases significantly in area, implying that old landslides may result in more collapses or expansions of the affected area. In addition, the number of old landslides is greater than that of new landslides.

We explored the spatial distribution of landslides on slopes above (Fig. 9) and below (Fig. 10) mountain roads in the study area before and after Typhoon Kong-rey in 2013. Figures 9a and 10a present the spatial distribution of bare land before the typhoon, whereas Figs. 9b and 10b present the spatial distribution of bare land after the typhoon.

As shown in Fig. 9, most landslides on the slopes above the mountain roads occurred close to the roads, most likely because road construction involves cutting the slope toe and increasing the gradient. After the typhoon, the bare locations on the slopes above the roads in the study area did not increase in number significantly; thus rainfall did not exert a substantial impact on the slopes above the roads. The results in Fig. 10 show bare locations on the slopes below the mountain roads developing from near the roads to the streams. The bare locations near the streams may also have been affected by rainfall-induced bank erosion. However, the bare land near the roads may have been a result of roads being constructed in the study area, which affects slope stability and increases the probability of landslides. Furthermore, the bare locations near the roads slightly increased in number after the typhoon, likely because the roads changed the routes of surface run-off. The area of bare land near the streams also increased, possibly because the water flow scours the slope toe and causes continual bank collapses. Thus, typhoons have a significant impact on the stability of slopes below mountain roads.

This study applied the maximum likelihood method to interpret and classify
satellite images before and after two typhoons in 2011 and 2013. We extracted
landslide and land use information from the areas surrounding roads and then
compiled the rainfall and DEM data from the typhoon events. By using the
MHEM, we established a landslide susceptibility assessment model and examined
the relationships between predisposing factors and the area and number of
landslides within the study area, as well as the relationships between roads
and the spatial distribution of landslides. The results show that the kappa
coefficients associated with the use of the maximum likelihood method to
interpret and classify satellite images before and after Typhoon Nanmadol in
2011 and Typhoon Kong-rey in 2013 ranged from 0.53 to 0.66, whereas the OA
ranged from 61 to 71 %, indicating moderately high accuracy. According to
the results of the instability index-based landslide susceptibility
assessment model, the degree of land disturbance, geology, slope gradient,
and slope roughness had the greatest impacts on landslides. A comparison of
historical landslides triggered by the typhoons and the results of the hazard
map revealed 71 % accuracy for Typhoon Nanmadol in 2011 and 75 %
accuracy for Typhoon Kong-rey in 2013. Regarding the influence of the
predisposing factors, an elevation of 450–750 m, a slope gradient of
30–55^{∘}, and distances within 300 m of water or roads were
associated with a larger scale of landslides. The scale of landslides also
increased with the degree of land disturbance. The relationships between the
ILR, instability index, and landslide occurrence indicate that for a high
instability index, even a smaller rainfall event could trigger a landslide.
By contrast, for a low instability index, a larger rainfall event could not
easily trigger a landslide. Thus, the instability index can effectively
reflect landslide susceptibility. Comparisons of the distribution of bare
land before and after typhoon events showed that most landslides in the study
area were caused by stream water scouring away the
toes of bank slopes. Although bare locations did not significantly increase
in number after the typhoon events, they increased significantly in area,
implying that the number of old landslide areas holding more collapses or
expansions was greater than that of new landslide areas developing. In
addition, the results obtained from observing changes on slopes above and
below mountain roads after the typhoon events indicate that the number of
bare locations on the slopes above the roads in the study area did not
increase significantly, whereas the bare locations near the roads on the
slopes below the roads slightly increased in number after the typhoon events,
likely because of the roads changing the routes of surface run-off. The
amount of bare land near streams also increased, possibly because the water
flow scours the slope toe.

The data sets of geology data, rainfall data, satellite images, and topography data can be provided on request from the institutions and projects mentioned in the acknowledgements.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Landslide–road network interactions”. It is not associated with a conference.

This work is funded by the Soil and Water Conservation Bureau, Taiwan,
Republic of China and
by the grant MOST 105-2625-M-309-002, MOST 105-2625-M-309-003 from the
Ministry of Science and Technology, Taiwan,
Republic of China

Edited by: Faith Taylor

Reviewed by: two anonymous referees

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