Landslide Hazard Mapping of Penang Island using Probabilistic Methods and Logistic Regression

Lim Khai – Wern, Kevin * School of Electrical and Electronic Engineering

Universiti Sains Malaysia Engineering Campus 14300 Nibong Tebal

Penang, Malaysia *corresponding author

Lea Tien, Tay School of Electrical and Electronic Engineering

Universiti Sains Malaysia Engineering Campus 14300 Nibong Tebal

Penang, Malaysia

Habibah Lateh School of Distance Education

University Sains Malaysia 11800 USM

Pulau Pinang, Malaysia

Abstract—This paper summarizes landslide hazard mapping of Penang Island, Malaysia using probabilistic methods and logistic regression. Probabilistic methods such as frequency ratio, statistical index, certainty factor and landslide susceptibility analysis, and logistic regression were applied to produce landslide hazard maps. Correlations were used to determine effects and contributions of landslide-causative factor to landslide. Factors that show low correlations or proven to negatively contribute to the final results were ejected. Final results show logistic regression as the best method to predict landslide occurrences in Penang Island with an accuracy of 80.05%, followed by frequency ratio with 79.68%, landslide susceptibility analysis with 79.6%, statistical index with 79.38% and certainty factor with 79.37%.

I. INTRODUCTION Landslides are geological phenomenon that involves movement of ground, rock and soil due to soil erosion. Landslides have for decades pose to be hazardous as they destroy properties and even claim human lives. In Malaysia, landslides are normal occurrences and happen pretty frequently due to annual monsoons mainly known as Southwest Monsoon from late May to September, and Northeast Monsoon from November to March which tend to cause flash flood and landslide. These recent years from 2000 to 2009, damages due to landslides have been particularly high (Pradhan and Lee, 2009). In order to reduce damages caused by landslides, several attempts had been performed to try and predict risky areas so that it would serve as a warning. Among them are Pradhan and Lee (2006, 2009) and Lee and Talib (2005) which focused on Penang Island and Selangor. In this work, Penang Island is once again selected to be area of interest in landslide susceptibility and hazard analysis as it has suffered numerous damages due to landslide in recent years.

In recent years, there have been many studies on landslide hazard evaluation using GIS and various evaluation techniques. Probabilistic methods such as frequency ratio have been applied many times to achieve favorable result in landslide hazard evaluation (Pradhan and Lee, 2006, 2009, Lee and Talib, 2004). Logistic regression has also been

applied many times and has yielded good accuracy (Pradhan and Lee, 2009).

II. STUDY AREA The study area selected in this paper is Penang Island due to its heavy frequency of landslide over the years. Penang is one of the 13 states of Malaysia located on the North West of Malaysia peninsula. It is bounded to the north and east of the state of Kedah, to the south of the state of Perak and to the west of Strait of Malacca and Sumatra (Indonesia). Penang consists of both the island of Penang and a coastal strip on the mainland also known as Province Wellesley. In this paper, only the island of Penang is considered for landslide evaluation mapping. The island, separated from the mainland by a channel, covers an area of 285km2. It is located about 5o 15’N to 5o 30’N of latitudes and 100o 10’E to 100o 20’E of longitudes. Land use is consisted of mainly swamp, plantation, forest, grassland and urban area. Slope ranges from 0o to 87o and elevation of the terrain from 0 to 820 meters above sea level. Temperature of Penang Island ranges from between 29 to 32oC and the average amount of rainfall varies from 2254 to 2903mm annually. Vegetation cover in Penang Island consists mainly of forest and fruit plantation. Penang Island is also affected by fault lines that run from north to south mainly in the centre of the island.

III. DATA SET Data collection on geographical database of Penang Island is done through application of remote sensing methods and GIS. Topographical, geological and various images of Penang Island were obtained from various departments in Malaysia including Meteorological department, Jabatan Pengairan dan Saliran (JPS), Department of Agriculture (DOA), Minerals and Geoscience Department (JMG), Jabatan Ukur dan Pemetaan Malaysia (JUPEM) and Pusat PeGIS. Landslide occurrence points in Penang Island are also collected and

978-1-61284-896-9/11/$26.00 ©2011 IEEE

transformed into spatial database for probabilistic landslide susceptibility analysis. Data set available in this study consists of 12031193 pixels of Penang Island with resolution of 5 meters. Landslide occurrence points have been detected to be approximately 68786 pixels of the entire island. Most landslides happened at the mountainous terrain of the island which is situated in the middle of the island. These landslides consist of mainly shallow rotational debris slides, debris flows and rock falls.

Identification and mapping of a suitable set of instability and causative facts having relationship with the slope failures requires prior knowledge of the main causes of landslide (Guzzetti et al. 1999). To apply the probabilistic methods, data sets of landslide-causative factors were collected and constructed as spatial database. 12 landslide-causative factors were considered in calculating probability of landslides. From topographic database, digital elevation model (DEM) were constructed with a resolution of 5-meter. From DEM, elevation was extracted. Elevation was then used for calculation of slope angle, slope aspect and slope curvature. Distance from drainage and distance from road were calculated from drainage map and road map each available in digital map respectively. Van Westen et al. (2003) suggested that buffer zones for line features, such as, rivers and roads should be set to 50m. Similarly, distances from fault lines of Penang Island were calculated and segregated into 100m intervals. Soil texture database of the island which included sand, clay and urban land were obtained as well. Land use map were obtained from Pusat PeGIS and consisted of 17 classes of land usage. Vegetation cover map was also obtained from Pusat PeGIS and consisted of 14 classes. Geology map, tabling the types of rocks and granites of Penang Island were also used as landslide-causative factors. Rainfall or precipitation is one of the most efficient triggering factors of landslide as it dampens soils and washes away debris and rocks, creating landslides. There are only several rain gauge stations in Penang Island, therefore, interpolation method had to be used to prepare the precipitation map. Using 29 years of historical rainfall data (1980-2008), statistical distribution of the accumulated average precipitation was prepared using ArcGIS software’s inverse weight distance interpolation method.

IV. METHODOLOGY Probabilistic method or also known as statistical approach of landslide hazard analysis has been proven to be very successful in predicting landslides. The advantages of this method lie in its high efficiency, low cost, easy implementation and better understanding of the relationships between landslides and landslide-inducing factors. In probabilistic method, each factor’s data weights are calculated based on class distribution and its landslide density (Suzen and Doyuran, 2004). These weights represent the importance of each factor to landslide occurrence and are used to produce a landslide hazard index.

Frequency ratio (FR) approach is a type of probabilistic method that is based on the observed relationships between the distribution of landslides and landslide-causative factors. Frequency ratio or weight of each class is computed by dividing the landslide density of a class with the total landslide density. Therefore a value of 1 is the unity value and value higher than 1 shows higher correlation and vice versa. To calculate the landslide hazard index (LHI), each pixel’s frequency ratio of the map is summed up. It can then be inferred that areas with higher values of frequency ratio are areas that are more prone to landslide.

LHI (Landslide hazard index) = FR1 + FR2 + ...... + FRN. FR = Frequency ratio of each factor. Aab* = Area of observed landslide of class a of parameter b. Aab = Area of class a of parameter b. A = Total area of the map. A* = Total area of observed landslide of the map.

Statistical index (SI) is another approach of probabilistic method that is almost similar to frequency ratio. It was introduced by Van Westen (1997). In recent years, researchers have applied this method for landslide susceptibility analysis (Nguyen Thanh Long, 2008) and termed the method as statistical index. In this method, weight for every class of each parameter is defined as natural logarithm of the landslide density in the class divided by the total landslide density. Mathematical wise, it is the almost same as frequency ratio as the method simply takes natural logarithm of the frequency ratios. Van Westen (1997) gave us this formula: ln

LHI = SI1 + SI2 + ...... + SIN . SI = statistical index weight of each factor.

For ratio less than 1, weight will be negative and vice versa. Negative value shows decreasing correlation between the class with landslide and vice versa. In the case of no landslide occurrence, the weight of that particular class is assigned as 0. Thus, class that has weight of 0 shows no correlation with landslide and does not contribute to landslide hazard index.

Another probabilistic method is called certainty factor (CF). It was first introduced in MYCIN, a rule-based expert system for the diagnosis and therapy of blood infections and meningitis (Shortliffe and Buchanan, 1975). The idea of certainty factor is to describe weight as a degree of confirmation based on available evidence and expert’s opinion. CF has been used before by authors such as Chung and Fabbri (1998) and Nguyen Thanh Long (2008) to compute landslide hazard index. CF formula is given as follows:

1 1

fab = Aab*/ Aab = Landslide density of class a of parameter b f = A*/A = Total landslide density

Range of value for CF is between -1 and +1. A value of -1 means strong negative correlation of the class with landslide occurrence and vice versa. In expert term, it means -1 is definitely false and +1 is definitely true (Nguyen Thanh Long, 2008). Value of 0 means a certain class is difficult to be given a degree of confirmation because of lack of evidence. Landslide hazard index for CF is computed by using the formula (Nguyen Thanh Long, 2008):

, 0 1 min | | , | | , , 0

f = output data sets combined pair-wise from data sets a and b. a, b = CF values of causative factors.

This pair-wise combination is repeated until all landslide-causative factors are combined to produce landslide hazard index. Landslide susceptibility analysis (LSA) is a simple method to determine weights of landslide-causative factors. It is very similar to frequency ratio. Weights of classes are determined by comparing classes’ landslide densities with overall density in the area (Suzen and Doyuran, 2004): 1000

LHI = LSA1 + LSA2 + ...... + LSAN LSA = landslide susceptibility analysis weight of each factor

Logistic regression (LR) is a multivariate analysis model which is used for prediction of probability of occurrence of an event given set of values of predictor variables. Logistic regression allows forming of a multivariate regression relation between a dependent variable with multiple independent variables. According to Atkinson and Massari (1998), if the searched variable is dichotomous outcome, LR has been known to give the best prediction accuracy.

In this study, LR is used to predict the absence or presence of landslide occurrence in each mapping unit given the independent variables which are the landslide-causative factors. Therefore, the dependent variable is an input of binary number consisting of 1 for presence of landslide and 0 for absence of landslide. LR analysis involves fitting data to the equation: ln 1 0 1 1 2 2 Where, p is the probability of an event occurring, xi is the data of each factor and an is the corresponding regression coefficients. The regression coefficients show the importance of each factor to landslide occurrence, similar to weights of probabilistic methods.

According to Lulseged Ayalew and Hiromitsu Yamagishi (2004), it does little good to combine data with different measuring scales. In order to avoid wrong interpretation of final results, normalization of data is usually needed. One of the common solutions of normalization is by creating dummy variables for each class of independent variable (Dai and Lee, 2002, Lee and Min, 2001). Some

studies used only dummy variables for nominal data such as land use and vegetation while retaining the numerical values of factors such as slope and elevation. Dai and Lee (2002) and Lee and Min (2001) both used this method for logistic regression. In this study, however, all landslide-causative factors are normalized to their landslide densities. Landslide densities are used as a normalization parameter as it allows the independent variables to be expressed in the same scale. Therefore, if a class of a factor has a large landslide density, it can be expected that its regression coefficient will be large as well to reflect its importance to landslide occurrence (Lulseged Ayalew and Hiromitsu Yamagishi, 2004).

The sample size of data for logistic regression also differs from authors to authors. Some prefer to use a fixed percentage of area while others prefer to use equal areas of landslides and non-landslides. For example, Atkinson and Massari (1998) used training data from 1.2% of total area which would result in an unequal proportion of 1 and 0 pixels. It has been known and recommended that sample size should be taken with an equal proportion of 1 and 0 pixels and this method has been used by Dai and Lee (2002). In this study, an equal proportion of 1 and 0 pixels of the map are used as data for LR. Hence, data for each factor is represented by their dummy variables and are treated as continuous data. These data are imported to statistical package SPSS (Statistical Package for the Social Sciences) for LR analysis.

V. LANDSLIDE SUSCEPTIBILITY VERIFICATION AND ANALYSIS

Landslide susceptibility index (LSI) for each method was computed first by not adding precipitation to the calculations. To verify the efficiency and accuracy of each method, ROC (Rate of Curve) method was employed. Two assumptions are needed in order to verify the maps. One is that landslides are related to spatial information such as slope and aspect, and the other is that the future landslides will be affected by triggering factor such as rainfall. (Chung and Fabbri, 1999). Both assumptions are satisfied in this study.

Verification by ROC is done by first sorting the landslide susceptibility indexes in a descending order. The ordered indexes are then divided into 100 classes and set on y-axis, with accumulated 1% intervals on x-axis (Pradhan and Lee, 2009). The resulting graph shows a line curve that explains how well the model and factors predict future landslide (Chung and Fabbri, 1999). The area under the curves constitutes the accuracies of the prediction models and is one of the commonly used accuracy statistics in natural hazard assessments (Beguria, 2006). TABLE I shows the accuracies for each method and it can be seen that LR exhibits the highest accuracy with 80.03%, followed by FR 78.18%, LSA, 78.16%, SI 77.66% and CF 77.65%.

TABLE I. Area under curve (AUC) in percentages

FR SI CF LSA LR 78.18% 77.66% 77.65% 78.16% 80.03%

Certain factors such as land use and vegetation cover consist of a lot of classes and this various segregation of classes might affect the credibility of landslide prediction method as data are spread all over the classes. It is also observed that certain factors might correlate with each another and this might induce redundancy which will affect the landslide prediction accuracy. To study the effects of landslide-causative factors with landslide, correlation analysis is performed. Pearson correlations are used to determine how correlated each factors are to each another. The formula is given: , , 1 1 ∑

Where cov(x,y) is the covariance between x and y, σ is standard deviation, μ is the mean and n is the number of pixels in the map. TABLE II shows the correlations of each factor. From TABLE II, it can be observed that elevation, distance from fault lines, geology and land use are among the factors showing the lowest correlations with landslides. Hence, it can be expected that by removing these factors from the landslide susceptibility maps, accuracy of the prediction models should increase. To verify these findings, ROC analysis is used. Each factor is removed one at a time from the landslide susceptibility map of each method and area under the curve is recalculated. TABLE III shows the accuracy for the prediction models after every factor is removed one at a time from the model.

From TABLE III, elevation, distance from road, land use and vegetation cover are identified to be negatively contributing to the prediction models. It can be seen that by removing these factors one at a time, accuracies increase by around 0.1-0.3%. Therefore, these 4 factors were chosen to be removed from the landslide susceptibility mapping. Elevation was chosen to be removed as well because prior experimentations on the factor show that although accuracy did not increase when it was removed just by itself, accuracy improved when it was removed together with distance from road, land use and vegetation cover. It is also important to note that the reason these factors improve the accuracies of the models might be due to redundancies in data sets. For example, elevation shows high correlation with slope while land use with distance from drainage. FR shows an accuracy of 79.59%, an increase of 1.41% from its original model, SI 79.14% with an increase of 1.48%, CF 79.14% with an increase of 1.47% and LSA 79.56% with an increase of 1.4%.

In the case of logistic regression, landslide-causative factors were not removed as per the analysis in TABLE III. This is because LR has already assigned regression coefficient to each factor to fit the prediction model and this coefficient already reflects the importance of each factor. In LR, multicollinearity is used to determine if two independent variables are related to each other. If tolerance is smaller than 0.2, multicollinearity exists and if it is smaller than 0.1, serious multicollinearity exists (Menard, 1995). From TABLE IV, all factors passed multicollinearity diagnosis as the lowest

tolerance is 0.231. Therefore, all factors are included into LR model.

VI. LANDSLIDE HAZARD MAPPING

With all results finalized for each method, precipitation map is added to the prediction models to produce landslide hazard index. Then, landslide hazard mapping is done by segregating LHI (Landslide hazard index) into several categories of risks. In this study, the indexes are categorized into 4 groups: Highly hazardous for the highest 10% of the indexes (90-100%), Hazardous for the next 10% (80-90%), Moderately hazardous for the next 20% (60-80%) and Not hazardous for the remaining 60% (0-60%). TABLE V shows accuracy of each method with precipitation added in.

ROC line curves explain how well the prediction models fit the data of landslide-causative factors with landslide occurrences to predict future landslides. Line curves for all method exhibit similar pattern, which is why their accuracies are so similar to each another. At the first 10% of highest landslide hazard indexes, the models managed to predict about 34% of the total landslides of Penang Island. Areas with these indexes are classified as highly hazardous and immediate attention needed to be taken to warn people of landslide risks. At 20%, 56% of total landslides are predicted and areas with these indexes are classified as hazardous. Then, at 40%, the graphs shows prediction of 78% and areas of these indexes are considered to be moderately hazardous. Finally, the rest of the indexes from 40% to 100% are considered to be not hazardous. FIGURE I shows the final landslide hazard maps for all methods.

VII. CONCLUSION AND SUMMARY

Landslide has for years causes damages and casualties. As development progresses, more hill areas are being explored for housing and development. This creates a scenario where landslide alert system are needed to warn people of impending landslides on risky area much like how tsunami alert is to people living near the sea. Prediction models such as statistical or probabilistic methods are simple methods which have been proven to yield good results in landslide prediction. Logistic regression has also been used by many researchers and is among one of the best methods for landslide prediction.

Landslide causative factors depends on the availability of GIS images in the research area. In this paper, 11 images have been identified as landslide-causative factors but not all factors have huge impact on landslide occurrences. Slope angle, distance to fault lines and distance to drainage are generally the more important factors in landslide causation. Factors such as land use, vegetation cover and elevation are not very effective as landslide-causative factors. Correlations of factors are important to determine how closely related the factors are to each another as closely related factors induce redundancy and affect landslide prediction accuracy. Correlation analysis is one of the simplest methods to observe

TABLE II. Correlations of landslide-causative factors with landslide occurrences Landslide-causative

factors

Correlations of landslide-causative factors Elevation

(E) Slope (S) Aspect (A)

Curvature (C)

Drainage (D) Road (R) Fault

Lines (F) Geology

(G) Soil types

(T) Vegetation cover (V)

Land use (L)

Landslide (LS)

E 100.00% S 94.67% 100.00% A 59.14% 54.86% 100.00% C 52.99% 47.62% 94.79% 100.00% D 70.21% 60.71% 74.80% 75.40% 100.00% R 82.11% 88.69% 65.75% 55.33% 53.55% 100.00% F 65.97% 64.70% 93.94% 84.40% 61.14% 78.17% 100.00% G 67.82% 62.19% 93.94% 88.39% 78.00% 70.29% 91.13% 100.00% T 44.97% 40.23% 63.86% 64.53% 85.63% 45.95% 48.64% 67.42% 100.00% V 59.19% 54.13% 79.42% 82.51% 87.11% 55.84% 63.05% 77.95% 80.58% 100.00% L 63.98% 54.72% 56.18% 58.23% 92.51% 41.25% 42.83% 59.56% 78.21% 73.85% 100.00%

LS 30.01% 41.86% -35.54% -41.12% -32.38% 32.77% -13.07% -26.00% -40.53% -34.94% -27.87% 100.00%

TABLE III. Accuracy for FR, SI, CF and LSA prediction models

TABLE IV. Multicollinearity diagnosis Independent variables Tolerance

Elevation 0.414 Slope 0.409

Aspect 0.231 Curvature 0.346 Drainage 0.789

Road 0.516 Fault Lines 0.828

Geology 0.524 Soil texture 0.235

Vegetation cover 0.288 Land cover 0.368

Precipitation 0.822

TABLE V. Area under curve (AUC) in percentages

FR SI CF LSA LR 79.68% 79.38% 79.37% 79.6% 80.05%

the relationships between variables. There are other more comprehensive but complex methods such as principal component analysis and discriminant analysis which are not discussed in this paper. For example, principal component analysis converts a set of possibly correlated variables into a set of values of uncorrelated variables. This could possibly improve the accuracy of landslide prediction model.

FIGURE I. Landslide Hazard Maps

Prediction models

Accuracy of landslide susceptibility maps (%)

All Without A Without C

Without E

Without S

Without D

Without L

Without R

Without V

Without F Without G Without

T Highest

accuracy FR 78.18% 78.04% 77.86% 78.17% 77.39% 77.28% 78.31% 78.8% 78.5% 77.91% 78.14% 78.1% 79.59%

SI 77.66% 77.56% 77.49% 77.65% 77.00% 76.79% 77.79% 78.22% 78.11% 77.34% 77.58% 77.54% 79.14%

CF 77.65% 77.61% 77.52% 77.66% 77.04% 76.83% 77.77% 78.21% 78.17% 77.37% 77.59% 77.54% 79.12%

LSA 78.16% 77.94% 77.83% 78.11% 77.32% 77.26% 78.25% 78.77% 78.54% 77.88% 78.08% 78.07% 79.56%

(A)

(B) (C)

(D)

(E)

(A) Frequency ratio (B) Statistical Index (C) Certainty Factor (D) Landslide Susceptibility Analysis (E) Logistic Regression

Highly hazardous Hazardous Moderately hazardous Not hazardous Historical landslide a occurrences

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