Spatial prediction of landslide hazards in Hoa Binh province (Vietnam): A comparative assessment of the efficacy of evidential belief functions and fuzzy logic models

Catena 96 (2012) 28–40

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Spatial prediction of landslide hazards in Hoa Binh province (Vietnam): A comparative assessment of the efficacy of evidential belief functions and fuzzy logic models Dieu Tien Bui a, b,⁎, Biswajeet Pradhan c, Owe Lofman a, Inge Revhaug a, Oystein B. Dick a a b c

Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P.O. Box 5003IMT, N-1432, Aas, Norway Faculty of Surveying and Mapping, Hanoi University of Mining and Geology, Dong Ngac, Tu Liem, Hanoi, Vietnam Faculty of Engineering, Spatial and Numerical Modelling Research Group, University Putra Malaysia, Serdang, Selangor Darul Ehsan 43400, Malaysia

a r t i c l e

i n f o

Article history: Received 24 November 2011 Received in revised form 31 March 2012 Accepted 2 April 2012 Keywords: Landslide GIS Fuzzy operator Evidential belief functions Vietnam

a b s t r a c t The main objective of this study is to evaluate and compare the results of evidential belief functions and fuzzy logic models for spatial prediction of landslide hazards in the Hoa Binh province of Vietnam, using geographic information systems. First, a landslide inventory map showing the locations of 118 landslides that have occurred during the last ten years was constructed using data from various sources. Then, the landslide inventory was randomly partitioned into training and validation datasets (70% of the known landslide locations were used for training and building the landslide models and the remaining 30% for the model validation). Secondly, nine landslide conditioning factors were selected (i.e., slope, aspect, relief amplitude, lithology, landuse, soil type, distance to roads, distance to rivers and distance to faults). Using these factors, landslide susceptibility index values were calculated using evidential belief functions and fuzzy logic models. Finally, landslide susceptibility maps were validated and compared using the validation dataset that was not used in the model building. The prediction-rate curves and area under the curves were calculated to assess prediction capability. The results show that all the models have good prediction capabilities. The model derived using evidential belief functions has the highest prediction capability. The model derived using fuzzy SUM has the lowest prediction capability. The fuzzy PRODUCT and fuzzy GAMMA models have almost the same prediction capabilities. In general, all the models yield reasonable results that may be used for preliminary landuse planning purposes. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Vietnam is located in one of the storm centers in the world, in one of the region's most hit by natural disasters and in one of the most vulnerable regions for the impact of climate change (Alkema, 2010). Together with flooding, landslides are among the recurrent natural hazard problems that occur widespread and that have caused large losses of life and property in the mountainous region in northwestern of Vietnam (Lee and Dan, 2005). In particular, in the Hoa Binh area, many large landslides occurred during the heavy rainfalls of the tropical storm Lekima in October 2007. Those landslides mainly occurred on cut slopes in mountainous regions including residential areas. Therefore, understanding landslides and preventing them from occurring through suitable landuse planning and management, are one of the urgent tasks in Vietnam. However, only a few attempts have been carried out to assess and predict landslide prone so far. Through scientific analyses, geoscientists and civil engineers can ⁎ Corresponding author at: Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P.O. Box 5003IMT, N-1432, Aas, Norway. Tel.: + 47 64965424. E-mail addresses: [email protected], [email protected] (D. Tien Bui). 0341-8162/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.catena.2012.04.001

assess and predict landslide prone areas, offering potential measures to decrease landslide damages through proper slope management (Pradhan, 2011b). The susceptibility to landslide occurrence can be expressed as the probability of spatial occurrence of slope failures over a set of geoenvironmental conditions (Guzzetti et al., 2005). Landslide susceptibility can be estimated using a variety of methods and techniques, including heuristic methods, statistically based classification models and physical based models (Guzzetti et al., 2006). A brief review about the advantages and disadvantages of these techniques and methods are given by many researchers such as Varnes (1984), Aleotti and Chowdhury (1999), Guzzetti et al. (1999) and Chacon et al. (2006). In recent years, various modeling approaches using geographical information systems (GIS) have been widely used as the basic analysis tool for landslide studies and predictions worldwide. GIS has been considered to be effective for spatial data management and manipulation for the analysis of landslides (Lee and Sambath, 2006). The main advantage of the GIS-based approaches is that they can be successfully applied in multisource data analysis and especially with heterogenic and uncertain data (Binaghi et al., 1998; Chacon et al., 2006). Although many GISbased models have been proposed in the literature, it is still too early in

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the evolution of GIS-based landslide modeling to identify which method or set of techniques is the best for prediction of landslide prone areas (Carrara and Pike, 2008). In the more recent years, some new approaches for landslide susceptibility assessment using soft computing techniques, such as knowledge-based systems using the fuzzy set theory (Akgun et al., 2012; Pradhan, 2011a, 2011b), neuro-fuzzy (Oh and Pradhan, 2011; Pradhan et al., 2010b; Sezer et al., 2011; Tien Bui et al., 2011b), artificial neural networks (Biswajeet and Saied, 2010; Caniani et al., 2007; Lee et al., 2007; Melchiorre et al., 2008; Pradhan and Lee, 2010b; Pradhan et al., 2010a; Yilmaz, 2009a, 2010a), support vector machines (Ballabio and Sterlacchini, 2012; Marjanović et al., 2011; Yao et al., 2008; Yilmaz, 2010a), and decision-tree model (Nefeslioglu et al., 2010; Saito et al., 2009; Yeon et al., 2010) have been proposed. Generally, these approaches give rise to qualitative and quantitative maps of landslide prone areas, and the results are appealing (Pradhan, 2010c). In general, the quality of landslide susceptibility models is influenced both by the methods used and the sampling strategies followed (Yilmaz, 2010b). Therefore, the comparative studies of using different methods are highly necessary. In the literature, there are some studies comparing the prediction and generalization capabilities of different methods and techniques for landslide susceptibility assessment (Akgun, 2012; Pradhan, 2011a; Pradhan and Lee, 2010a; Yilmaz, 2009b, 2010a). In the case of the evidential belief functions (EBF) model, the application to landslide mapping is still limited except a few case studies (Althuwaynee et al., 2012). The EBF model has been widely used in knowledge-driven approaches to mineral potential mapping (An et al., 1992; Carranza, 2009; Carranza and Hale, 2001; Carranza and Sadeghi, 2010; Carranza et al., 2005, 2008a, 2008b, 2009; Moon, 1989). Carranza and Hale (2002) proposed a data-driven mineral potential mapping method using the EBF model, in which ‘expert knowledge’ was used as a guide for classifying geological maps. To apply EBF models in mineral potential mapping, they used Dempster's rule of combination (Dempster, 1967, 1968) and a GIS (Carranza et al., 2008c). Tangestani (2009) compared the Dempster–Shafer with fuzzy models for landslide modeling of the Zagros Mountains in Iran, with the conclusion that the Dempster-Shafer model obtained less reliable results than the fuzzy logic model. It is clear that Tangestani (2009) determined the fuzzy membership function values based on expert opinions. This is different from our study where data-driven methods were used. Carranza and Castro (2006) showed that the data-driven EBF model can be used for prediction of areas that can be inundated by volcanic lahars in Mount Pinatubo (Philippines). Ghosh and Carranza (2010) have shown that the data-driven EBF model can be used for mapping of rockslide prone areas in Darjeeling Himalaya (India). In a different approach, Park (2011) applied the data-driven DempsterShafer model in the Jangheung area (Korea) and concluded that the data-driven Dempster-Shafer model shows better prediction capacity than logistic regression. Park (2011) also stated that more research should be done on application of EBF in extensive case studies. Fuzzy logic has been widely used in many fields (Carranza and Hale, 2001; Cheng and Agterberg, 1999; Porwal et al., 2003, 2006; Topcu and Sarıdemir, 2008). The advantage of fuzzy logic is that it is straightforward to apply, and the process of weighting landslide conditioning factors is totally controlled by the experts (Lee, 2007a). In addition, the fuzzy logic method provides a variety of fuzzy combination operators for generating landslide susceptibility index values. According to Gorsevski et al. (2003), integration of GIS and fuzzy logic showed to be very interesting, with high potential and robustness for landslide hazard predictions. In the present study, two data-driven models, EBF and fuzzy logic, were used to obtain more accurate and reliable landslide susceptibility maps. The main objective of this study is to evaluate the data-driven fuzzy logic and evidential belief functions in a GIS for

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spatial prediction of landslide hazards in the Hoa Binh province of Vietnam. 2. Study area and spatial database The Hoa Binh province is a hilly area situated between mountains and the Red River plain in the northwestern region of Vietnam. It covers an area of about 4660 km 2 between longitudes 104°48′E and 105°50′E, and latitudes 20°17′N and 21°08′N. The altitude varies from 0 to 1510 m, and it decreases from the northwest to the southeast. Approximately 42.5% of the study area has ground slopes greater than 15° and about 16% with slopes greater than 25°. The climate is characteristic of a monsoonal region, being hot, rainy, and with high humidity. According to statistics for the last decade, the coldest month was January with an average temperature of 14.9 °C while the warmest month was July with an average temperature of 26.7 °C. The rainy season falls within the period of May to October and accounts for 84–90% of the yearly rainfall. The study area receives the largest amount of rainfall with high frequency and intensity peaks in the months of August and September. In August and September, the rainfall varies between 300 and 400 mm per month. Regarding landuse, the study area is comprised of approximately 7.5% populated areas, 14.5% agricultural land, 52.6% forest land, 21% barren land and non-forest rocky mountain, 0.4% grass land and 4% water surface. The study area is geologically a part of the Paleozoic with different structures consisting of the Fansipan zone in the northwest, the Son La zone in the southwest, and the remaining in the Ninh Binh zone. There are five main fracture zones with a variety of active faults, passing through this region, causing rock mass weakness: the Hoa Binh, the Da Bac, the Muong La - Cho Bo, the Son La - Bim Son, and the Song Da fracture zones. Thirty nine lithologic formations outcrop in this region and their spatial distributions are different. Four lithologic formations (Dong Giao, Tan Lac, Vien An, and Song Boi) cover 62.3% of the study area where the main lithologies are limestone, conglomerate, sandstone, aphyric basalt, massive limestone, tuffaceous sandstone, silty sandstone, magnesium-high basalt and black clay shale. According to Varnes (1984), landslide occurrences in the past and present are keys to the spatial prediction of landslide hazard in the future. Hence, compiling the landslide inventory map, which is a dataset containing a single or multiple landslide events, is the first step in landslide modeling. In this study, the landslide inventory map prepared by Tien Bui et al. (2011a) was used to derive quantitative relationships between landslide occurrences and landslide conditioning factors. A total of 118 landslides during the last ten years were identified and registered in the map with 97 landslide-polygons and 21 rock fall locations. The size of the smallest landslide is about 380 m2. The largest landslide covers an area of 14,340 m 2 and the average landslide size is 3,440 m 2. The landslide inventory map was randomly partitioned into a training dataset with 70% (82 landslides) for building the landslide models and the remaining 30% (36 landslides locations) for the validation purpose. Fig. 1 shows the distribution of landslide locations in the study area. The next step is the construction of landslide conditioning factors. In our previous study (Tien Bui et al., 2011a), we investigated the relationship between landslide occurrences and landslide conditioning factors. Based on the findings, nine landslide conditioning factors were chosen for this study: slope, aspect, relief amplitude, lithology, landuse, soil type, distance to roads, distance to rivers and distance to faults. A digital elevation model (DEM) with a spatial resolution of 20×20 m was generated using 1:25,000 scale national topographic maps. Maps of three geomorphometric factors (slope, aspect and relief amplitude) were extracted from the DEM. In the slope map, six slope categories

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Fig. 1. Landslide inventory of the study area.

were constructed for the analysis (Fig. 2a). In the aspect map, nine aspect classes were determined (Fig. 2b). For the relief amplitude map, six classes (0–50 m, 50–100 m, 100–150 m, 150–200 m, 200–250 m, 250–532 m) were constructed using the Focal statistic module in ArcGIS 10.0 software with the unit area size of 20×20 pixels (Fig. 2c). The lithology and faults data were extracted from the 1:200,000 scale Geological and Mineral Resources Map of Vietnam. This is the only geological map available for the study area. In the lithological map, seven lithological groups were constructed based on the criteria of clay composition, degree of weathering and estimated strength and density (Arıkan et al., 2007; Van et al., 2006) (Fig. 2d). In the case of the distance-to-faults map, five buffer categories (0–200 m, 200–400 m, 400–700 m, 700–1000 m, and >1000 m) were compiled using the buffer tool in ArcGIS 10 software. The 1:50,000 scale landuse map, with 12 categories, was extracted from the National Status Landuse database (Fig. 2e). The soil type map with 13 soil groups (Fig. 2f) was extracted from the 1:100,000 scale National Pedology map. This is the only soil map available for the study area. The roads and rivers that undercut slopes were extracted from the 1:50,000 scale national topographic map, and used to construct the distance-to-roads map and the distance-to-rivers map. Five buffer categories (0–40 m, 40–80 m, 80–120 m and >120 m) were compiled for each of the two maps using the buffer tool of ArcGIS 10.0 software. 3. Landslide susceptibility mapping 3.1. Evidential belief functions The Dempster-Shafer theory of evidence, which was first developed by Dempster (1967; 1968) and then by Shafer (1976), is a generalization of the Bayesian theory of subjective probability. The main advantage of the Dempster-Shafer theory is that it has a relative flexibility to accept uncertainty and the ability to combine beliefs from multiple sources of evidence (Thiam, 2005). Rather than estimating probabilities that an hypothesis is true, the Dempster-Shafer theory

estimates how close the evidence proves the truth of that hypothesis (Pearl, 1989). The Dempster-Shafer theory has been successfully implemented using a GIS in many fields (Malpica et al., 2007). Suppose that we have a set of landslide conditioning factors C = (Ci, i = 1, 2, 3, …, n), consisting of mutually exclusive and exhaustive factors Ci. C is called the frame of discernment. A basic probability assignment is a function m : P(C) → [0, 1]. P(C) is the set of all subsets of C, including the empty set and C itself. This function is also called a mass function and satisfies m(Ф) = 0 and ∑A C mðAÞ ¼ 1, where Ф is an empty set, A is any subset of C. The m(A) measures the degree to which the evidence support A; it is denoted Bel(A), a belief function. There are four basic EBF used (Althuwaynee et al., 2012; Carranza et al., 2005): Bel (degree of belief), Dis (degree of disbelief), Unc (degree of uncertainty) and Pls (degree of plausibility). Bel and Pls present the lower and upper bounds of the probability, for the proposition (Awasthi and Chauhan, 2011). Unc is the difference between the belief and the plausibility. Unc presents the ignorance. Dis is the belief of the proposition being false on given evidence. Dis = 1 − Pls or 1 − Unc − Bel, and we always have: Bel + Unc + Dis = 1. For a case of Cij with no landslide occurrence indicating that Bel = 0, Dis is reset to zero, even if Dis is not (Carranza and Hale, 2002; Carranza et al., 2008a). The estimation of EBF can be based on subjective judgment or it can be data-driven (Carranza et al., 2005; Srivastava et al., 2011). By overlaying the landslide inventory map (L) on each of the nine maps of landslides conditioning factors, we determined the numbers of pixels with landslides and pixels with no-landslides for each factor class. Assuming that N(L) is the total number of landslide pixels and N(C) is the total number of pixels in the study area, Cij is the j-th class attribute of the landslide conditioning factors Ci(i = 1, 2, …, n), N(Cij) is the total number of pixels in the class Cij, and N(L ∩ Cij) is the number of landslide pixels in Cij. According to Carranza and Hale (2002), data-driven estimation of EBF may be done by:
 Bel C ij ¼

W C ij ðLandslideÞ ∑nj¼1 W C ij ðLandslideÞ

ð1Þ

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Fig. 2. Landslide conditioning factor maps (a) Slope ; (b) Aspect ; (c) Relief amplitude; (d) Lithology ; (e) Soil type ; (f) Landuse ; (g) Distance to roads; (h) Distance to rivers; and (i) Distance to faults.

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Fig. 2 (continued).

where

W C ij ðLandslideÞ
 Dis C ij ¼


 N L∩Cij =NðLÞ
i Þ ¼h
 N Cij −N L∩Cij =½NðCÞ−NðL W C ij ðNon−LandslideÞ

∑nj¼1 W C ij ðNon−LandslideÞ

ð2Þ

ð3Þ

where

W C ij ðNon−LandslideÞ

h

i N Cij −N L∩Cij =NðLÞ

i ð4Þ ¼h N ðCÞ−NðLÞ  N Cij þ N L∩Cij =½NðCÞ−NðLÞ

The numerator in Eq. (2) is the proportion of landslide pixels that occur in factor class Cij. The numerator in Eq. (4) is the proportion of landslide pixels that do not occur in factor class Cij. The denominator in Eq. (2) is the proportion of non-landslide pixels in factor class Cij. The denominator in Eq. (4) is the proportion of non-landslide pixels in other attributes outside factor class of Cij. Parameter WCij(Landslide) is the weight of Cij that supports the belief that landslides are more present than absent. Parameter WCij(Non − Landslide) is the weight of Cij that supports the belief that landslides are more absent than present.

Once the EBF function are calculated for all the landslide conditioning factors, the Dempster's rule of combination was used to obtain the four integrated EBF (Dempster, 1968). The formulae for combining of two landslide conditioning factors C1 and C2 are as follows (Carranza et al., 2005): BelC 1 C 2 ¼

DisC 1 C 2 ¼

BelC 1 BelC 2 þBelC 1 UncC 2 þ BelC 2 UncC 1 1−BelC 1 DisC 2 −DisC 1 BelC 2 DisC 1 DisC 2 þDisC 1 UncC 2 þ DisC 2 UncC 1

UncC 1 C 2 ¼

1−BelC 1 DisC 2 −DisC 1 BelC 2 UncC 1 UncC 2 1−BelC 1 DisC 2 −DisC 1 BelC 2

ð5Þ

ð6Þ

ð7Þ

Integrated EBF of the remaining landslide conditioning factors are implemented one after another by using Eqs. (5)–(7). Table 1 shows the estimated EBF for the nine landslide conditioning factors. In the slope map, slope angles in the range of 20°–30° have the highest Bel and low Dis values, indicating the highest probability of landslides, followed by slope ranges of 30°–40° and then of 10°–20°. For the remaining slope ranges, the Bel values are low, indicating low probability of landslide occurrence.

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Table 1 Values of fuzzy membership and evidential belief functions for classes of landslide conditioning factors. Data

Class

layers 0

Slope ( )

Aspect (0)

Relief Amplitude (m)

Lithology

Land use

Soil type

Distance to roads (m)

Distance to rivers (m)

Distance to faults (m)

0–10 10–20 20–30 30–40 40–50 >50 Flat (− 1) North (0–22.5; 337.5–360) Northeast (22.5–67.5) East (67.5–112.5) Southeast (112.5–157.5) South (157.5–202.5) Southwest (202.5–247.5) West (247.5–292.5) Northwest (292.5–337.5) 0–50 50–100 100–150 150–200 200–250 250–532 Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Populated Area Orchard Land Paddy Land Protective Forest Land Natural Forest Land Productive Forest Land Water Annual Crop land Non Forest Rocky Mountain Barren Land Specially Used Forest Land Grass Land Eutric Fluvisols Degraded soil Limestone Mountain Ferralic Acrisols Rhodic Ferralsols Humic Acrisols Dystric Fluvisols Dystric Gleysols Luvisols Humic Ferralsols Populated Area Water Gley Fluvisols 0–40 40–80 80–120 >120 0–40 40–80 80–120 >120 0–200 200–400 400–700 700–1000 >1000

Number of

Landslide

Frequency

Fuzzy

EBF

class pixels

pixels

ratio

value

Bel

Dis

Unc

4,919,804 3,346,950 2,326,636 785,451 106,715 4750 6556 1,380,854 1,672,941 1,385,498 1,383,072 1,482,483 1,677,042 1,299,469 1,202,391 3,101,843 2,753,898 2,640,812 1,694,502 811,634 487,617 468,851 4,552,855 3,740,521 1,338,571 135,801 645,785 607,922 864,840 426,524 1,053,442 985,889 3,666,190 1,347,068 455,666 184,205 468,692 1,947,114 41,129 49,547 400,659 3006 1,657,233 4,196,906 1,031,126 3,551,123 84,133 45,288 52,858 131,881 50,440 276,610 9043 160,806 193,382 215,495 10,920,623 443,909 519,168 553,405 9,973,824 2,078,812 1,832,167 2,285,798 1,644,799 3,648,730

2 222 368 92 0 0 0 27 82 44 106 138 174 65 48 6 228 235 126 53 36 36 264 183 131 0 59 11 109 3 27 120 119 158 1 2 42 103 0 0 45 0 104 294 30 199 6 6 0 0 0 0 0 306 126 33 219 79 74 64 467 179 106 86 192 121

0.007 1.114 2.657 1.968 0.000 0.000 0.000 0.328 0.823 0.533 1.287 1.564 1.743 0.840 0.671 0.032 1.391 1.495 1.249 1.097 1.240 1.290 0.974 0.822 1.644 0.000 1.535 0.304 2.117 0.118 0.431 2.045 0.545 1.970 0.037 0.182 1.505 0.889 0.000 0.000 1.887 0.000 1.054 1.177 0.489 0.941 1.198 2.226 0.000 0.000 0.000 0.000 0.000 31.966 10.945 2.572 0.337 2.990 2.394 1.943 0.787 1.446 0.972 0.632 1.961 0.557

0.102 0.435 0.900 0.692 0.100 0.100 0.100 0.251 0.478 0.345 0.691 0.818 0.900 0.486 0.408 0.100 0.843 0.900 0.766 0.682 0.761 0.728 0.574 0.500 0.900 0.100 0.847 0.248 0.900 0.145 0.263 0.873 0.306 0.845 0.114 0.169 0.669 0.436 0.100 0.100 0.778 0.100 0.479 0.523 0.276 0.438 0.531 0.900 0.100 0.100 0.100 0.100 0.100 0.900 0.368 0.157 0.100 0.900 0.684 0.520 0.100 0.607 0.336 0.143 0.900 0.100

0.001 0.194 0.462 0.342 0.000 0.000 0.000 0.042 0.106 0.068 0.165 0.201 0.224 0.108 0.086 0.005 0.214 0.230 0.192 0.169 0.191 0.196 0.148 0.125 0.250 0.000 0.234 0.046 0.215 0.012 0.044 0.208 0.055 0.200 0.004 0.019 0.153 0.090 0.000 0.000 0.210 0.000 0.118 0.131 0.054 0.105 0.134 0.248 0.000 0.000 0.000 0.000 0.000 0.698 0.239 0.056 0.007 0.368 0.295 0.239 0.097 0.260 0.175 0.113 0.352 0.100

0.281 0.153 0.093 0.149 0.000 0.000 0.000 0.121 0.115 0.118 0.107 0.102 0.097 0.113 0.115 0.225 0.146 0.141 0.159 0.165 0.164 0.141 0.145 0.155 0.130 0.000 0.138 0.148 0.075 0.086 0.088 0.075 0.101 0.072 0.086 0.084 0.081 0.085 0.000 0.000 0.075 0.077 0.076 0.069 0.081 0.079 0.077 0.077 0.000 0.000 0.000 0.000 0.000 0.035 0.052 0.060 0.853 0.177 0.179 0.183 0.461 0.179 0.199 0.216 0.166 0.239

0.718 0.653 0.444 0.508 1.000 1.000 1.000 0.836 0.780 0.813 0.728 0.697 0.679 0.779 0.798 0.770 0.641 0.629 0.649 0.667 0.645 0.663 0.707 0.720 0.619 1.000 0.629 0.806 0.709 0.902 0.868 0.717 0.844 0.727 0.910 0.897 0.766 0.825 1.000 1.000 0.715 0.923 0.806 0.800 0.865 0.816 0.790 0.675 1.000 1.000 1.000 1.000 1.000 0.267 0.710 0.884 0.139 0.455 0.526 0.578 0.442 0.562 0.626 0.670 0.481 0.661

In the aspect map, high Bel and low Dis values for south and southwest facing slopes indicate that these categories have positive spatial associations with landslides. They are followed by the southeast, west and northeast categories. In the case of the relief amplitude factor, the classes 50–100 m, 100–150 m, and 200–250 m have high

Bel and low Dis values, indicating high probability of landslide occurrence. Values of Bel for the remaining categories are relatively low and indicate low probability of landslides. For lithology, there are high Bel and low Dis values for group 4 (mafic–ultramafic magma rocks), group 6 (metamorphic rock with

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Fig. 3. Integrated EBF map: (a) Belief; (b) Disbelief; (c) Uncertainty; and (d) Plausibility.

rich aluminosilicate component) and group 1 (quaternary deposit). This suggests a higher probability of landslide occurrence than in other lithologies. Based on the interpretation of Bel and Dis values for the landuse factor, there is high probability of landslides for populated areas (PO), protective forest land (PT), productive forest land (PD), and non-forest rocky mountains (RM). High probability of landslides in these landuse categories is due to very high activity of clearcut logging and the increase in inappropriate new highland settlements because of population growth during the last 15 years. For the soil type factor, the highest Bel value with low Dis value is for the dystric glaysols (DG), followed by eutric fluvisols (EF), dystric fluvisols (DF), ferralic acrisols (FA), limestone mountain (LM), and humic acrysols (HA), indicating high probability of landslide. The low Bel and high Dis values for the remaining classes indicate that the probability of landslides is low. For distance to roads and distance to rivers, the Bel and Dis values show that when the distance from roads increases, the probability of landslides decreases. The highest probability for landslide occurrence is within distances less than 40 m. There is very low probability of landslide occurrence at distances >120 m. For distance to faults, the Bel and Dis values show that as the distance to faults decreases, the probability of landslide occurrence increases. The integrated results are shown in Fig. 3. Comparison between the belief map (Fig. 3a) and the disbelief map (Fig. 3b) shows that belief values are high for areas where disbelief values are low and vice

versa. It indicates high susceptibility of landslides for areas where there are high degrees of belief and low degree of disbelief for the occurrence. The pixel values in the integrated belief function map are used as the landslide susceptibility index values in this study. The uncertainty map (Fig. 3c) shows lack of information support uncertainty for landslide occurrences. The uncertainty is the difference between plausibility and support. The high uncertainty values are in areas where belief values are low. The plausibility map (Fig. 3d) shows high values for areas where both belief and uncertainty values are high. 3.2. Fuzzy logic model Fuzzy logic, which was introduced by Zadeh (1965), is a way of mapping an input space to an output space by using a list of if-then rules. A fuzzy logic system provides a systematic calculation for processing knowledge that is uncertain, imprecise or with incomplete information. The difference between classical logic and fuzzy logic is that classical logic gives an output only either as 1 or 0, while fuzzy logic allows objects to be partially true or partially false corresponding to membership function values that can fall within any value between 0 and 1 (Gottwald, 1995). A fuzzy set contains elements that have no crisp membership values and where there is no clearly defined boundary (Uzkent et

D. Tien Bui et al. / Catena 96 (2012) 28–40

al., 2011). Fuzzy set theory allows an element to be a member in a fuzzy set and also member in other fuzzy sets with different degrees of membership values (Ross, 2004). Assume that Ci (i = 1, 2, 3, …, n) is a set of landslide conditioning factors and Cij represents the value of the j-th factor class of Ci, then μ(Cij) ∈ [0, 1] is the corresponding membership value in a landslide conditioning factor. The value 0 indicates non-membership and 1 indicates full membership. Fuzzy set theory does not tell us how to specify fuzzy membership functions and it does not require that the sum of all fuzzy membership values in a set equal 1 (Singpurwalla and Booker, 2004). A fuzzy membership function can provide a vehicle for developing operations with fuzzy sets in landslide modeling. Therefore, determination of fuzzy membership values is considered to be the most important task. Various methods have been proposed for assigning fuzzy membership values to elements and they can be classified into four groups: standard membership functions, problem-specific membership functions, specification of standard membership functions, and fuzzy clustering (Robinson, 2003). In general, these methods are either knowledge-based approaches or data-driven approaches or a combination of both. In knowledge-based approaches for landslide studies, fuzzy membership values are assigned to each factor class mainly based on experts knowledge, whereas in data-driven approaches fuzzy membership values are determined according to correlations between landslide locations and landslide conditioning factors (Champati ray et al., 2007). Many data-driven methods have been developed for determining fuzzy membership values, however, the cosine amplitude (Ercanoglu and Gokceoglu, 2004; Kanungo et al., 2008, 2009; Shujun et al., 2006) and the frequency ratio methods (Lee, 2007a; Pradhan, 2010a, 2010b, 2011b) are the most widely used in landslide modeling. In the cosine amplitude method, the fuzzy membership value, rij, for each factor class can be estimated as the ratio of the total number of landslide grid cells over the square root of the product of the total number of pixels in that factor class and the total number landslide grid cells in the study area (Kanungo et al., 2009). Values of rij closer to 1 indicate a strong relationship between landslide occurrence and the factor class. The cosine amplitude method, however, is not suitable for this study area because the ratio of the number of landslide grid cells to the number of pixels in the factor class is too small. In the frequency ratio method, the frequency ratio for each factor class is calculated first using Eq. (8).
 N L∩Cij =NðLÞ
 FRij ¼ N Cij =NðCÞ

ð8Þ

Fig. 4. Success-rate curves of the EBF and fuzzy logic prediction models.

fuzzy membership values by using the Max-Min normalization procedure as:


 μ Cij ¼


 h



i FRij −Min FRij

 Max μ Cij −Min μ Cij Max FRij −Min FRij

 þ Min μ Cij


 n μ PRODUCT ¼ ∏ μ Cij

Ratio greater than 1 indicates high probability for landslides in the factor class, while ratio less than 1 indicates low probability. Since fuzzy membership values are in the range from 0 to 1, the next step is the normalization process to transform the frequency ratio into

Table 2 Statistics of landslide susceptibility index values in each of the ten landslide prediction models. Landslide susceptibility Model

LSI statistics Min

Max

Mean

StD

1 2 3 4 5 6 7 8 9 10

Evidential Belief Functions Fuzzy SUM Fuzzy PRODUCT Fuzzy GAMMA (λ = 0.1) Fuzzy GAMMA (λ = 0.3) Fuzzy GAMMA (λ = 0.5) Fuzzy GAMMA (λ = 0.7) Fuzzy GAMMA (λ = 0.9) Fuzzy GAMMA (λ = 0.95) Fuzzy GAMMA (λ = 0.975)

0.285 0.735 0.000 0.000 0.000 0.000 0.003 0.113 0.288 0.460

3.238 1.000 0.188 0.222 0.310 0.443 0.606 0.846 0.920 0.959

1.100 0.990 0.001 0.002 0.006 0.021 0.085 0.418 0.641 0.798

0.330 0.014 0.005 0.007 0.013 0.028 0.062 0.099 0.077 0.051

ð9Þ

where μ(Cij) is the fuzzy membership value; Max(μ(Cij)) and Min(μ(Cij)) are the upper and lower normalization bounds. In this study, the frequency ratio was calculated for each class of the landslide conditioning factors using the landslide grid cells in the training dataset. Then, the fuzzy membership values were calculated by normalizing the ratio values into the range of 0.1 to 0.9 (Pradhan, 2011a). The results are shown in Table 1. In order to calculate landslide susceptibility index values, membership values of the factor classes were combined using the fuzzy operator method. This method provide various tools to combine different datasets (Champati ray et al., 2007). Three fuzzy operators (An et al., 1991; Bonham-Carter, 1994; Robinson, 2003; Zimmermann, 1991) were used in this study: fuzzy PRODUCT, fuzzy SUM, and fuzzy GAMMA. Fuzzy PRODUCT is defined as:

i¼1

No

35

Fig. 5. Prediction-rate curves of the EBF and fuzzy logic prediction models.

ð10Þ

36

D. Tien Bui et al. / Catena 96 (2012) 28–40

Fuzzy SUM is defined as:
i n h μ SUM ¼ 1− ∏ 1−μ Cij

ð11Þ

i¼1

Fuzzy GAMMA is defined as: λ

1−λ

μ GAMMA ¼ ðFuzzy SUMÞ :ðFuzzy PRODUCT Þ

ð12Þ

Using the three fuzzy operators (Eqs. (10)–(12)), the landslide susceptibility index values were calculated by combining fuzzy membership values of all factor classes. In the case of fuzzy GAMMA, values of lambda (λ) are chosen in the range of [0, 1]. The gamma operator enables a compromise between the increasing tendencies of fuzzy SUM and the decreasing effect of the fuzzy PRODUCT (Malins and Metternicht, 2006). In this study, the fuzzy GAMMA with seven values of λ (0.1, 0.3, 0.5, 0.7, 0.9, 0.95, and 0.975), the fuzzy PRODUCT, and the fuzzy SUM were used to generate landslide susceptibility index values (i.e., nine susceptibility cases). The statistics of the landslide susceptibility index values for all landslide models are shown in Table 2. 4. Validation and comparison of landslide susceptibility models Validation of predictive landslide susceptibility maps is an absolutely essential component in landslide modeling. Without a validation, prediction models are totally useless and have no scientific significance (Chung and Fabbri, 2003). Using the success-rate and prediction-rate methods, the ten landslide susceptibility maps were validated by comparing them with known landslide locations. The success-rate results were obtained based on a comparison of the landslide grid cells in the training dataset (684 landslide grid cells) with each of the ten landslide susceptibility maps that were obtained from the fuzzy logic and EBF models. The success-rate curve for each case was obtained by varying the decision threshold and plotting the respective sensitivities against the total proportions of the classified data set (Brenning, 2005). Subsequently, the areas under the success- rate curves (AUC) were calculated for all cases. The result shows that all the models have a good fit (Fig. 4). The validation results showed that the EBF model had the highest AUC (0.9350) and the fuzzy SUM model (0.8965) showed the lowest AUC. The remaining models have almost equal values of AUC (Fig. 4). It indicates that the capability for correctly classifying the areas with existing landslides is highest for the EBF model, lowest for the fuzzy SUM model, and almost equal for the remaining models. Since the success-rate measures the goodness of fit for the landslide models to the training data, the success rate is not a suitable

Fig. 6. Cumulative percentages of observed landslide occurrence according to landslide susceptibility index values.

Fig. 7. Frequency ratio plots of five landslide susceptibility classes of the ten prediction models.

method for measuring the prediction capability of the landslide models. The prediction-rate can provide the validation and explains how well the model and landslide conditioning factors predicts the existing landslides (Chung and Fabbri, 2003; Lee, 2007b; Lee et al., 2003; Pradhan and Lee, 2010c). In this study, the prediction capabilities of the ten landslide models were assessed by comparing the landslide grid cells in the validation dataset (315 landslide grid cells) with the landslide susceptibility maps using the prediction-rate method. Fig. 5 shows ten prediction-rate curves for the ten landslide susceptibility models. In order to compare the accuracy of the ten landslide models quantitatively, the areas under the prediction-rate curves (AUC) were calculated. When the AUC is equal to 1, it indicates a perfect prediction accuracy (Lee and Dan, 2005). The results show that values of AUC for the ten models vary from 0.9185 to 0.9370, indicating that all the models have a reasonable good prediction capability. The EBF model has the highest prediction capability. The fuzzy SUM model has lowest prediction capability. The remaining models with almost equal prediction capabilities are intermediate between the EBF and fuzzy SUM models. Landslide susceptibility index values were visualized by means of five susceptibility levels (very high, high, moderate, low, very low). There are many methods for classifying susceptibility index values such as the equal interval method, the natural break method and the standard deviation method. In this study, the equal area classification method (Pradhan and Lee, 2010a, 2010b, 2010c) was used. By overlaying all landslide grid cells with ten landslide susceptibility maps, cumulative percentages of observed landslide occurrence against landslide susceptibility index values were calculated and shown in Fig. 6. Then, based on percentage of area, five susceptibility classes were determined as very high (10%), high (10%), moderate (20%), low (20%) and very low (40%). The relative frequency ratio analysis was performed on the classification results and landslide location data (Sarkar and Kanungo, 2004) by overlaying the five landslide susceptibility zones with the landslide inventory map. Ideally, the frequency ratio value should increase from very low to very high susceptibility zones, since the high and very high zones are generally more prone to landslides than other zones (Pradhan and Lee, 2010b, 2010c; Pradhan et al., 2010b; Sarkar and Kanungo, 2004). The graph of the relative frequencies of areas with the five landslide susceptibility zones for the ten landslide models (Fig. 7) shows that there is a gradual increase in landslide frequency from the very low susceptible zone to the very high susceptible zone. In general, the EBF model performs better than the other models. For visualization purpose, only two landslide susceptibility maps the EBF and fuzzy GAMMA (λ = 0.975) models are shown (Fig. 8). Characteristics of the five susceptibility zones for the two landslide models are shown in Table 3. The percentage of existing landslide pixels that fell into the high and very high susceptibility classes is lowest with the fuzzy SUM model (81.7%) and highest with the EBF model (88.49%).

D. Tien Bui et al. / Catena 96 (2012) 28–40

37

Fig. 8. Landslide susceptibility zonation maps: (a) EBF model and (b) fuzzy GAMMA (0.975) model.

5. Discussions and conclusion In this study, fuzzy logic and evidential belief functions were used for landslide susceptibility mapping in the Hoa Binh province of Vietnam. The resulting maps represent spatial predictions of landslide hazards; they do not forecast “when” and “how frequently” a landslide will occur. Ten landslide susceptibility maps were prepared. The validation shows that both the EBF model and the nine fuzzy logic models have high prediction capabilities with the best being the EBF model. Among the fuzzy logic models, the fuzzy SUM model has the lowest prediction capacity (AUC

equal to 0.9185); the remaining fuzzy logic models have almost equal prediction capacity (AUC around 0.9265). Many methods and techniques for landslide susceptibility assessment have been proposed so far. However, it is important to note that simpler procedures and techniques with high accuracy give better landslide models. The results of this study showed that both EBF and fuzzy logic models are simple, cost-effective. They are easy to apply with high prediction capability. For the EBF model, four maps (belief map, disbelief map, uncertainty map, and plausibility map) are presented. These maps can

38

D. Tien Bui et al. / Catena 96 (2012) 28–40

Table 3 Characteristics of the five susceptibility classes in each of the ten landslide prediction models. LSZ

PA

Frequency ratio Fuzzy

VL L M H VH

40.0 20.0 20.0 10.0 10.0

Fuzzy

Fuzzy

Fuzzy

Fuzzy

Fuzzy

Fuzzy

Fuzzy

Fuzzy

GAMMA

GAMMA

GAMMA

GAMMA

GAMMA

(0.975)

(0.950)

(0.900)

(0.700)

(0.500)

GAMMA

GAMMA

PRODUCT

SUM

(0.300)

(0.100)

0.018 0.135 0.511 1.101 7.538

0.004 0.117 0.585 1.462 7.120

0.004 0.117 0.585 1.461 7.120

0.004 0.117 0.592 1.447 7.120

0.004 0.117 0.592 1.447 7.120

0.004 0.117 0.592 1.447 7.120

0.004 0.117 0.592 1.447 7.120

0.004 0.117 0.592 1.447 7.120

0.004 0.204 0.702 1.623 6.550

EBF

0.015 0.135 0.361 0.851 8.098

LSZ: Landslide susceptibility zonation; PA: Percentage of area.

give meaningful interpretations for landslide susceptibility. Landslides in the study area are strongly correlated with many factors. Using the EBF model, the quantitative relationships between landslide occurrence and the nine landslide conditioning factors (slope, aspect, relief amplitude, lithology, landuse, soil types, distance to roads, distance to rivers and distance to faults) were assessed. The results show that slope angles between 10° and 40° provide the highest susceptibility for landslides. In the case of the aspect factor, three facing slopes (southeast, south and southwest) have high susceptibility for landslides. In the relief amplitude factor, areas with relief amplitudes from 50 to 150 m have high susceptibility for landslides. In the lithology, mafic–ultramafic rocks and metamorphic rocks with rich aluminosilicate component yield high susceptibility for landslides. Landuse with populated areas and soil type with ferralic acrysols showed high susceptibility for landslides. In the distance-to-roads and distance-to-rivers maps, the range of 0–40 m has the highest susceptibility for landslides. High susceptibility for landslides also exists for to the class 0–200 m of distance to faults. In the case of the fuzzy logic modeling, the selection of method for determining fuzzy membership function values, plays an important role and influences the final result. In this study, the frequency ratio method was used to derive fuzzy membership values to eliminate the subjectivity of assigning such values. Three fuzzy operators (fuzzy SUM, fuzzy PRODUCT, and fuzzy GAMMA with different lambda values) were used to generate nine landslide susceptibility models. The validation result shows that the selection of fuzzy operator affects the quality of the resulting landslide model. In the case of the fuzzy GAMMA, AUC values in the success-rate and prediction-rate curves show that there are no significant differences between landslide models with different lambda values in this case study. The fuzzy logic and the evidential belief functions are generally considered useful for regional-scale landslide susceptibility mapping, such as the present study. The results and findings of this study can help developers, planners, and engineers in slope management and landuse planning. Since the output maps are regional-scale, they may be less useful for a site-specific development that requires large-scale maps.

Acknowledgements The authors would like to thank Dr. Emmanuel John M. Carranza, Prof. Isik Yilmaz and two anonymous reviewers for their valuable and constructive comments on the earlier version of the manuscript. This research was funded by the Norwegian Quota scholarship. The data analysis and write-up were carried out as a part of the first author's PhD studies at the Geomatics Section, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Norway.

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