Arab J Geosci (2016) 9: 201 DOI 10.1007/s12517-015-2258-9
ORIGINAL PAPER
Assessment and comparison of combined bivariate and AHP models with logistic regression for landslide susceptibility mapping in the Chaharmahal-e-Bakhtiari Province, Iran Ebrahim Karimi Sangchini 1 & Seyed Naim Emami 2 & Naser Tahmasebipour 3 & Hamid Reza Pourghasemi 4 & Seyed Amir Naghibi 5 & Seyed Abdolhossein Arami 6 & Biswajeet Pradhan 7
Received: 3 August 2015 / Accepted: 18 November 2015 / Published online: 10 March 2016 # Saudi Society for Geosciences 2016
Abstract Landslide is one of the most important natural hazards that make numerous financial damages and life losses each year in the worldwide. Identifying the susceptible areas and prioritizing them in order to provide an efficient susceptibility management is very vital. In current study, a comparative analysis was made between combined bivariate and AHP models (bivariate-AHP) with a logistic regression. At first, landslide inventory map of the study area was prepared using extensive field surveys and aerial photographs interpretation. In the next step, nine landslide causative factors were selected including altitude, slope percentage, slope aspect, lithology, distance from faults, streams and roads, land use, and * Hamid Reza Pourghasemi
[email protected];
[email protected] 1
Department of Watershed Management Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran
2
Institute of Agriculture and Natural Resources, Shahrekord, Iran
3
Department of Watershed Management Engineering, College of Agriculture, Lorestan University, Khorramabad, Iran
4
Department of Natural Resources and Environmental Engineering, College of Agriculture, Shiraz University, Shiraz, Iran
5
Department of Watershed Management Engineering, College of Natural Resources, Tarbiat Modares University, Noor, Mazandaran, Iran
6
Combating Desertification, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran
7
Department of Civil Engineering, Faculty of Engineering, University Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia
precipitation which affect occurrence of the landslides in the study area. Subsequently, landslide susceptibility maps were produced using weighted (AHP) bivariate and logistic regression models. Finally, receiver operating characteristics (ROC) curve was used in order to evaluate the prediction capability of the mentioned models for landslide susceptibility mapping. According to the results, the combined bivariate and AHP models provided slightly higher prediction accuracy than logistic regression model. The combined bivariate and AHP, and logistic regression models had the area under the curve (AUCROC) values of 0.914, and 0.865, respectively. The resultant landslide susceptibility maps can be useful in appropriate watershed management practices and for sustainable development in the regions with similar conditions. Keywords Landslide susceptibility . Combined bivariate and AHP models . Logistic regression . GIS . Iran
Introduction Landslide is one of the most important natural hazards that cause numerous financial damages and life losses each year in the worldwide (Kelarestaghi and Ahmadi 2009). Landslides are amongst the most damaging natural hazards in the mountainous areas. The study of landslides has drawn worldwide attention mainly due to increasing awareness of the socioeconomic impacts of landslides, as well as, the increasing pressure of urbanization on the mountain environment (Aleotti and Chowdhury 1999). Landslide phenomenon annually occurs in many parts of the world including Iran. Losses that resulted from mass movements in Iran until the end of September 2007 have been estimated at 12.7 billion Iranian
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Rials were using the 4900 landslide database (Pourghasemi et al. 2013a). Burying of Abikar village of Charmahal-eBakhtiari Province in spring 1997 is one of the clear examples of landslide damages in the Iran. Therefore, landslide susceptibility mapping can be considered as one of the preliminary steps in mitigating these damages (Regmi et al. 2014a). Landslide susceptibility assessment also is an important process for prediction and management of natural disasters. It is also a necessary step for integrated watershed management, hazard mitigation, natural, and urban planning in government policies worldwide (Lekkas 2000; Carrara et al. 2003; Dahal et al. 2008; Bathrellos et al. 2009). Identification and classification of prone areas to landslide and its susceptibility mapping is a significant step in the evaluation of environmental hazards and plays a prominent role in the watershed management (Sakar et al. 1995). Using landslide susceptibility zonation, one can detect susceptible and high potential landslide susceptible areas. There are three main approaches in landslide susceptibility assessment such as qualitative, semi-quantitative, and quantitative (Lee and Jones 2004). Quantitative methods are based on mathematical logic, the correlation between factors and landslide occurrence that include bivariate regression analysis (Guzzetti 2002; Nandi and Shakoor 2009, Yalcin et al. 2011; Yilmaz et al. 2012, Bijukchhen et al. 2013a; Bijukchhen et al. 2013b, Kayastha et al. 2013a, b; Jaafari et al. 2014; Regmi et al. 2014b; Youssef 2015; Youssef et al. 2015a, b), logistic regression (Ayalew and Yamagishi 2005; Duman et al. 2006; Pradhan and Youssef 2010; Akgun 2012; Park et al. 2013; Pourghasemi et al. 2013b; Youssef 2015; Dou et al. 2015a, b), certainty factor model (Dou et al. 2014; Dou et al. 2015a), genetic algorithm (Dou et al. 2015c), fuzzy logic (Gupta et al. 2008; Tangestani 2009; Pradhan 2011; Pourghasemi et al. 2012), and artificial neural network model (Ermini et al. 2005; Melchiorre et al. 2008; Caniani et al. 2008; Pradhan et al. 2010; Zare et al. 2013; Polykretis et al. 2014; Dou et al. 2015b). Qualitative methods are based on expert opinions (Fall et al. 2006; Rahman and Saha 2008). Qualitative methods use weighting and rating approaches are known as semi-quantitative methods (Yalcin 2008). Examples of these methods are the analytic hierarchy process (AHP; Barredo et al. 2000; Yalcin 2008; Komac 2006; Rahman and Saha 2008; Ercanoglu et al. 2008; Akgun and Turk 2010; Yalcin et al. 2011; Hasekiogullari and Ercanoglu 2012; Pourghasemi et al. 2012), weighted linear combination (Ayalew et al. 2004; Gorsevski et al. 2006; Kouli et al. 2010; Nafooti and Chabok Boldaje 2011; Pourghasemi et al. 2014), and data mining techniques (Youssef et al. 2015c). The multivariate logistic regression approach has been used by various researchers in the literature (Yesilnacar and Topal 2005; Nandi and Shakoor 2009; Yilmaz 2010; Oh and Lee 2010; Felicisimo et al. 2013). In current study, a combined AHP and bivariate models was used for the landslide susceptibility assessment and the
Arab J Geosci (2016) 9: 201
results were compared with a logistic regression. According to the literature, in the previous studies, these two models had been used separately. The outcome of this method could be regarded quasi-quantitative. The proposed methodologies use both the expert choices and ground truth at the same time.
Materials and methods Study area Doab Samsami Watershed is located between 32° 5′ 12″ and 32° 15′ 21″ latitudes and 50° 10′ 1″ to 50° 26′ 16″ longitudes, covering an area of 276.3 km2 in the Chaharmahal-e-Bakhtiari Province, Iran (Fig. 1). This watershed is one of the major sub basins of the Karoon River. Elevation in the study area ranges from 1,775 to 3,825 m above sea level. Based on the Iranian meteorological organization report, the average annual rainfall in the study area is 970 mm. This watershed is located in the middle of Zagros Mountains. Subsequent erosion has removed softer rocks, such as mudstone (rock formed by consolidated mud) and siltstone (a slightly coarser-grained mudstone), leaving behind harder rocks exposed, such as limestone (calcium-rich rock consisting of the remains of marine organisms) and dolomite (rocks similar to limestone containing calcium and magnesium). This differential erosion formed the linear ridges of the Zagros Mountains. Sixty-six percent of this region is covered by rangelands and the rest of the area is covered by orchard, forest, agricultural, and rocky lands. Landslide inventory map In current study, a landslide inventory map was prepared using field surveys, local information, and aerial photographs interpretation (Fig. 1a, b, c; Dou et al. 2015d). The aerial photo belongs to the year 2002. Landslide inventory map showed that there are 37 landslides in the study area. According to landslide classification proposed by Varnes (1978), modes of failure in the study area were determined. Most of the landslides are shallow rotational with a few translational. Meanwhile, in this study, only rotational landslides are considered and translational slides were eliminated because its occurrence is rare. Affected total area by landslide is 635 ha (2.23 % of the watershed area). Landslide causative factors The main factors considered in current study and those influential in the occurrence of a landslide based on literature review are described as below. Nine landslide causative factors were considered in this investigation. These factors are altitude, slope percentage, slope aspect, lithology, distance from faults, streams and roads, land use, and precipitation amount
Arab J Geosci (2016) 9: 201 Fig. 1 Location map of the study area and two photos of landslides identified in the study area
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Arab J Geosci (2016) 9: 201
3552000
012
432000
6
8
Kilometers
440000
432000
448000
distance from fault(m) 1300-2300
500-1300
2300-3500 >3500
416000
424000
012 4 6 432000
8
Kilometers
440000
3568000 3560000
424000
424000
3552000 432000
Kilometers
440000
432000
440000
(d)
3560000
K
QR
K7
Qal
K8
Qt2
Pd
Qt1
EO
E
012 4
6
8
OM2 416000
416000
(e)
0-500
416000
3568000
440000
3568000
424000
4
012 4 6 8
424000
432000
424000
Kilometers
440000
432000
440000
(f)
3560000
>24.23
3560000
9.09-14.04
3552000
19.3-24.23
3568000
2.87-9.08
3700-3825
2700-2900
Lithology
3560000
14.05-19.29
3500-3700
2500-2700
416000
3552000
0-2.86
424000
3300-3500
3560000
3560000
3560000 3552000
Slope degree
3560000 3552000 3544000
3568000
448000
3552000
440000
(c)
416000
3100-3300
3568000
432000
3544000
440000
3544000
432000
Kilometers
3544000
4 6 8
3544000
424000
012
3568000
North
424000
416000
2900-3100
1900-2100
2300-2500
3568000
416000
1775-1900
2100-2300
West 416000
Elevation (m)
3544000
Northwest
(b)
3568000
Southwest
440000
3552000
Northeast
432000
3544000
Southeast
424000
3568000
East
416000
3552000
South
3552000
3552000
Slope aspect
3544000
3544000
3552000
3560000
(a)
3560000
440000 3568000
432000
3560000
424000
3568000
416000
the ArcGIS 9.3 (ESRI 2008). The resolutions or pixel size of the causative factors was 30 × 30 m.
distance from stream (m) 0-50
150-200
50-100
200-300
100-150
300-450
012 4
>450 416000
424000
432000
6
8
Kilometers
440000
3544000
(Fig. 2). Vector-type spatial data-base of the mentioned causative factors was extracted by transforming these factors using
Fig. 2 Landslide conditioning factors: a aspect, b elevation, c slope degree, d lithology, e distance from fault, f distance from stream, g distance from road, h land use, and i precipitation
75-150
300-500
150-225 416000
>500 424000
012 4 6 432000
8
Kilometers
440000
424000
3560000 3552000
3568000 3560000
Land use Rocky land
Irriged agricalture
Poor range
Rainfed agricalture
012 4
Medium range 416000
424000
432000
432000
440000
3568000
416000
6 8
Kilometers
440000
448000
3560000
(i)
3552000
3560000 3552000
440000
3544000
225-300
432000
3568000
0-75
3552000
distance from road (m)
424000
(h)
3544000
3544000
3552000
3560000
(g)
3568000
416000
3560000
440000
3552000
432000
3544000
424000
3568000
416000
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3568000
Arab J Geosci (2016) 9: 201
Precipitation (mm) 850-1000
1400-1600
1000-1200
>1820
012
4
6
8
1200-1400
416000
424000
432000
440000
Kilometers 448000
Fig. 2 (continued)
Topographical factors For the digital elevation model (DEM) creation, 20 m interval contours and survey base points showing the elevation values were extracted from the 1:50,000-scale topographic maps. Implementing this DEM, altitude, slope percentage, and slope aspect were prepared. Altitude was classified into 11 classes with 200 m intervals. Slope percentage was grouped in 6 classes of 0–5, 6–15, 16–25, 26–35, 36–45, and >45. Slope aspect was classified into eight classes of N, NE, E, SE, S, SW, W, and NW. Substantial attention was paid to the slope conditions because slope configuration and steepness plays an important role in landslide occurrence (Fig. 2a–c). Lithology The underlying geology is one of the most significant factors for landslides modeling. Different geology
formations have different compositions and structures which contribute to the strength of the material. In current study, using geology map in 1:100,000 scale, the lithology map was prepared and classified into 11 groups based on lithological units (type; Table 1 and Fig. 2d). Geology formations in this watershed including fossiliferous marly limestones with intercalations of marls and sandy limstones (OM2), white nummulitic limestones, marly limstones, and dolomitic limestones (EO), mainly orbitalina limstones, locally evaporitic in the lower part (K), shale and marls interbedded with marly limstones containing ammonites and Inceramuses (K8), marly fossiliferous limestones and thin sandly argillaceous limestones (K7), recent terraces and recent alloviumes (Qal), old terraces deposits (Qt and QR), carbonate-dominated sedimentary package with shale-marl intervals (Pd), and red conglomerates (mainly chert pebbles), sandstones (locally with volcanic intercalations), and silostone with evaporitic inercalations (E).
201 Page 6 of 15 Table 1 Calculation of the final susceptibility value of each identified land unit
Arab J Geosci (2016) 9: 201
Data layers
Aspect N
Total area (ha)
% of total area (A)
Area of Landslide (ha)
% of area landslide (B)
Area density value
1,719.99
6.23
30.38
4.79
−5.32
NE
7,715.25
27.93
262.21
41.30
11.01
E SE
2,518.976 2,455.739
9.12 8.89
125.04 49.94
19.70 7.87
26.66 −2.64
S SW
4,798.129 4,676.126
17.37 16.93
85.43 59.57
13.46 9.38
−5.17 −10.24
W
1,370.671
4.96
0.00
0.00
−22.98
2,372.664
8.59
22.29
3.51
−13.58
1,775–1,900
4,61.9037
1.67
57.97
9.13
102.53
1,900–2,100
2,932.099
10.61
289.84
45.65
75.87
2,100–2,300 2,300–2,500 2,500–2,700 2,700–2,900
5,057.21 4,882.323 4,593.758 3,952.74
18.30 17.67 16.63 14.31
172.11 25.45 53.76 35.73
27.11 4.01 8.47 5.63
11.05 −17.77 −11.28 −13.94
2,900–3,100 3,100–3,300 3,300–3,500
2,929.929 860.752 1,532.477
10.61 3.12 5.55
0.00 0.00 0.00
0.00 0.00 0.00
−22.98 −22.98 −22.98
3,500–3,700 3,700–3,825 Slope (degree) 0–5
382.009 43.83642
1.38 0.16
0.00 0.00
0.00 0.00
−22.98 −22.98
201.0076
0.73
21.17
3.33
82.34
2,119.803 4,522.01 2,157.286 492.5005
7.67 16.37 7.81 1.78
59.33 244.67 112.02 7.39
9.35 38.54 17.65 1.16
5.01 31.13 28.95 −7.97
18,136.12
65.65
190.28
29.97
−12.49
449.9949 190.4042
1.63 0.69
3.30 0.18
0.52 0.03
−15.63 −22.04
11,334.27 1,297.833 5,018.204 201.7005 898.8312 542.9987 399.7744 2,948.512 3,555.478
41.03 4.70 18.16 0.73 3.25 1.97 1.45 10.67 12.87
27.59 179.93 10.84 46.45 114.50 85.34 14.76 150.77 1.21
4.35 28.34 1.71 7.32 18.03 13.44 2.33 23.75 0.19
−20.54 115.66 −20.82 207.33 104.41 134.18 13.95 28.16 −22.64
2,463.077 3,740.476 4,152.376 6,133.214 1,1139.89
8.92 13.54 15.03 22.20 40.32
94.81 192.53 141.37 114.22 91.94
14.93 30.33 22.27 17.99 14.48
15.51 28.49 11.07 −4.35 −14.72
2,092.495 2,011.261
7.57 7.28
51.84 52.52
8.17 8.27
1.80 3.14
NW Elevation (m)
6–15 16–25 26–35 36–45 > 45 Geology units OM2 E EO QR K Qal Pd Qt1 Qt2 K8 K7 Distance from fault (m) 0–500 500–1,300 1,300–2,300 2,300–3,500 >3,500 Distance from stream (m) 0–50 50–100
Arab J Geosci (2016) 9: 201
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Table 1 (continued) Data layers
Total area (ha)
% of total area (A)
Area of Landslide (ha)
% of area landslide (B)
Area density value
100–150
1,942.973
7.03
51.18
8.06
3.36
150–200 200–300
1,882.406 3,563.991
6.81 12.90
47.21 84.96
7.44 13.38
2.10 0.86
4,803.816
17.39
106.37
16.76
−0.83
11,331.47
41.02
240.77
37.92
−1.73
0–75
1,583.822
5.73
140.51
22.13
65.74
75–150 150–225
1,372.74 1,234.877
4.97 4.47
125.47 109.28
19.76 17.21
68.42 65.52
225–300 300–500
1,134.911 2,622.979
4.11 9.49
92.53 121.87
14.57 19.20
58.55 23.49
> 500
1,9679.09
71.23
45.20
7.12
−20.68
5,512.351
19.95
0.59
0.09
−22.87
1,645.76 2,214.199 12,072.93 6,183.487
5.96 8.01 43.70 22.38
10.04 155.03 391.81 77.39
1.58 24.42 61.72 12.19
−16.88 47.04 9.48 −10.46
10,589.69 7,996.283
38.33 28.94
539.27 69.14
84.94 10.89
27.95 −14.33
300–450 > 450 Distance from road (m)
Land use Rocky land Rain-fed agriculture Irrigated agriculture Poor range Medium range Precipitation (mm) 780–900 900–1,000 1,000–1,100
6,078.483
22.00
26.45
4.17
−18.63
1,100–1,200 1,200–1,260
2,292.567 671.9949
8.30 2.43
0.00 0.00
0.00 0.00
−22.98 −22.98
Distance from faults, streams, and road
Precipitation
Distance from streams was created by using a topographical map, whereas, distance from faults map was calculated using a geological map of the study area. On the other hand, distance from roads map was prepared using a road map of the study area. Distance from faults was classified into 5 classes of 0– 500, 500–1,300, 1,300–2,300, 2,300–3,500, and >3,500. In the case of distance from streams, there are 7 classes with 50 m intervals. For distance from roads, there are 6 classes of 0–75, 75–150, 150–225, 225–300, 300–500, and >500 (Fig. 2e–g).
There is no doubt that rainfall is the most important triggering factor in landslide occurrences. This factor was mapped and classified into 5 classes of 850–1,000, 1,000–1,200, 1,200–1,400, 1,400–1,600, and >1,600 in the study area (Fig. 2i).
Land use The land use map was created using Landsat images by Iranian forest, range land, and watershed management organization (http://www.frw.org.ir/pageid/34/ language/ en-US/Default.aspx). Five classes of rocky land, poor range, medium range, irrigated agriculture, and rain fed agriculture were detected in the study area (Fig. 2h).
Landslide susceptibility mapping with bivariate statistical model weighted with AHP (combined AHP-bivariate models) The analytic hierarchical process is based on the simplification of complex problems into simple ranks and orders, being the center, the main objective of the task of interest. In the following step, stand the criteria. The sub-criteria and the alternative options are placed inferior to the superior levels of division. Being divided into different hierarchies, the elements of each level are compared in a pair-wise manner and based on the importance of each element compared to other, scoring is made (Pourghasemi et al. 2012). This approach could be briefed in four steps as follow:
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Creation of hierarchical tree Selection of the criteria and the influence factors determining the objective of the decision maker. Pair-wise comparison Pair-wise comparison being carried out by informed expert groups and Expert Choice software package. In this step, regarding the influential elements, comparison matrices were created and the elements were compared pair-wised. Generally, the AHP method regards all comparison to be pair-wise. The experts state all the comparisons verbally. These kinds of comparison were converted into quantitative values ranged between zero and nine according to Saaty (1997; Tables 2 and 3). Standardization and prioritization The standardization and weighted average concepts were used in order to establish the level of importance of each element, which is, given the values obtained from the relative criteria, all the alternative options were compared and standardized using the concept of normal weighted average. In this manner, the priority of each option was extracted. Determination of weight or the level of influence for each element Various methods have been devised for this type of problems such as the minimum of squares, the logarithmic minimum of squares, the special vector, and the approximation methods including the sum of rows and columns, the geometric mean method. The bivariate method is on the basis of the areal cover of each level of elements proportioned to the areal cover of landslides occurred in each level. In calculating the ratio of each level, the landslide density of the level of interest was deducted from the total land-slide density in the whole area.
Table 2
Thus, supposing the landslide density of a level is greater than the total value obtained for the whole area, the rate established for this level would be positive and this would cause some degrees of instability. On the contrary, if the landslide density of a level is below the total value obtained for the whole area, this would result in a stable condition with a negative rate. The area and landslide percentages on each category of map of causative factors were calculated and then the rate of each category was calculated using the surface density equation (Feiznia et al. 2004; Kelarestaghi and Ahmadi 2009). The rate of each class was obtained using Eq. (1) as follows: A C −1000 ð1Þ Ra ¼ 1000 B D where A is the landslide area per unit, B represents the area of each unit, C is the total landslide area in each watershed, D represents the total area of watershed, and Ra is surface area rate (Table 1). The weight of nine factors was calculated by AHP model and using Expert Choice-11 software. Finally, landslide susceptibility map was produced by multiplying the weight of each factor to rate (Table 1). Then, landslide susceptibility map was classified into four classes based on the natural break scheme (Fig 3). Y ¼ ð0:053Þ*Aspect þ ð0:098Þ*Precipitation þ ð0:193Þ*Slope þ ð0:029Þ*Elevation þ ð0:243Þ*Geologyþð0:064Þ*Fault þ ð0:162Þ*Land Use þ ð0:035Þ*Stram þ ð0:121Þ*Road
ð2Þ
Landslide susceptibility mapping using logistic regression model At first, the landslide density in each class of the nine landslide causative factors was calculated for landslide susceptibility
Scale of relative importance suggested by Saaty (1997)
Intensity of importance
Definition
Explanation
1 3 5 7 9
Equal importance Weak importance of one over another Essential or strong importance Demonstrated importance Absolute importance
2, 4, 6, and 8
Intermediate values between the two adjacent judgments
Two activities contribute equally to objective Experience and judgment slightly favor one activity over another Experience and judgment strongly favor one activity over another An activity is strongly favored and its dominance demonstrated in practice The evidence favoring one activity over another is the highest possible order of affirmation When compromise is needed
Arab J Geosci (2016) 9: 201 Table 3
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AHP paired comparisons and determining final weight factors of landslide
Factors
Aspect
Elevation
Slope degree
Lithology
Distance from faults
Distance from stream
Distance from road
Land use
Precipitation
Aspect
1
2
0.25
0.2
0.33
2
0.33
0.33
0.5
Elevation Slope degree
0.5 4
1 6
0.16 1
0.14 0.5
0.33 3
1 5
0.25 2
0.2 1
0.25 3
Lithology
5
7
2
1
4
5
2
1
3
Distance from faults
1
3
0.33
0.25
1
2
0.5
0.5
0.5
Distance from stream Distance from road
0.5 3
1 4
0.2 0.5
0.2 0.5
0.5 2
1 3
0.33 1
0.25 1
0.33 1
Land use Precipitation
3 2
5 4
1 0.33
1 0.33
2 2
4 3
1 1
1 0.5
2 1
Final weight
0.053
0.029
0.193
0.243
0.064
0.035
0.121
0.162
0.098
Consistency ratio = 0.02
mapping using logistic statistical regression. For this purpose, homogeneous unit’s map was prepared by integrating maps of the mentioned factors. After matching the map of homogeneous units up with landslide distribution map, the units of the landslide were determined and to all homogeneous landslide units, the code (1) and to all homogeneous with no landslide units, the code (0) were given. The absence or presence of landslide in homogeneous units, as dependent variable and landslide density percent in each class of nine landslide causative factors in units, as independent variable were entered in the R statistical package (R Development Core Team 2006). Logistic regression equation is as follows (Ayalew and Yamagishi 2005): p Y ¼ Logit ðpÞ ¼ ln ¼ C 0 þ C 1 X 1 þ C 2 X 2 þ ⋅⋅⋅ þ C n X n ð3Þ 1−p
where p is the probability of independent variable(Y), p/(1 − p) is the so-called odds or the likelihood ratio, C0 is the intercept, and C1, C2,….Cn represent coefficients (which measure the size and the contribution of independent factors (X1, X2, … and Xn) in a dependent variable). Using the density of factors as independent variables and the presence or absence of landslides as the dependent variable, an attempt to determine the best equation that is meaningful at 0.01 % error level was made as follows: 1 −1:838 þ ð0:00059Þ*Aspect þ ð0:00344Þ*Precipitation C B C B þ ð0:00178Þ*Elevation C B Y ¼B C C B þð0:00318Þ*Geology−ð0:000077Þ*Fault A @ þð0:00167Þ*Land Use−ð0:000163Þ*Stream−ð0:000415Þ*Road 0
ð4Þ Using the mentioned model, the landslide susceptibility map was produced and then classified in low, medium, high, and very high classes.
Pseudo-R2 index The Pseudo-R2 index was used in order to evaluate the efficiency of logistic regression model. This index, based on the likelihood ratio principle, tests the goodness of fitting and is calculated using following equation: logðliklihood Þ 2 ð5Þ Pseudo R ¼ 1− logðl 0 Þ where likelihood is the likelihood function amount in a case that the model is fully fitted, L0 is the likelihood function amount in a case that all coefficients except for the intercept are zero. Unlike R2 in ordinary regression, Pseudo-R2 does not indicate the proportion of variance explained by the model, but this indicates the dependency rate of the empirical and output data of the regression model; thus, its value is generally much lower than R2. The Pseudo-R2 equivalent to one indicates perfect fit and the Pseudo-R2 equivalent to zero means that there is no significant relationship between independent and dependent variables. In spatial studies, Pseudo-R2 more than 0.2 can be considered as a relatively good fit (Clark & Hosking 1986).
Evaluation of landslide susceptibility models Finally, the receiver operating characteristic (ROC) curve (Pontius and Schneider 2001; Mohammady et al. 2012; Pourghasemi et al. 2012; Jaafari et al. 2015; Naghibi et al. 2015; Naghibi and Pourghasemi 2015) was employed to determine the accuracy of landslide susceptibility and groundwater potential maps produced in this research. The ROC curve is a diagram in which the pixels ratio that is correctly predicted the occurrence or nonoccurrence of landslides (true positive) is plotted against the supplement amount that is the pixels ratio that is wrongly predicted.
201 Page 10 of 15
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Fig. 3 Landslide susceptibility maps produced by a logistic regression model and b combined bivariate and AHP models
Results and discussion
The performance of the models
The results are represented and then discussed by three parts: (1) the performance of the models, (2) the landslide susceptibility maps, and (3) the importance of causative factors.
In current study, accuracy of logistic regression model was evaluated using Pseudo-R2 index. The Pseudo-R2 amount was calculated to be equal to 0.5217, which depicts that
Arab J Geosci (2016) 9: 201
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model’s fitting is relatively good. According to the results, two implemented models had high and relatively close performance. However, weighted (AHP) bivariate (AUC = 0.914) had better performance than logistic multivariate regression (AUC = 0.865; Fig. 4). The main advantage of logistic regression over simple multiple regressions is that LR allows the use of binary dependent variable types in landslide susceptibility mapping. Although logistic regression is a commonly applied quantitative susceptibility mapping method, it has a major limitation of yielding average parameters for the study area (Fotheringham et al. 2001; Erner et al. 2010), which may differ locally in different parts of the study area. According to the results of Esmali Ouri and Amirian (2009), AHP model had better performance than logistic regression in Iran. Also, Pourghasemi et al. (2013a, b) mentioned that logistic regression model had reasonably good performance in landslide susceptibility mapping. In another papers of Akgun (2012) and Pradhan (2010), LR model had good performance in landslide susceptibility mapping. Devkota et al. (2013) evaluated the performance of LR model in landslide mapping. Their results showed that LR had ROC value of 83.57 % which shows its good performance. Also, Lee and Sambath (2006) investigated the performance of LR model in landslide susceptibility mapping and their results showed high-prediction accuracy for LR model. In another study, Mathew et al. (2008) investigated the performance of LR in landslide susceptibility mapping in India. Their results showed good performance of LR model. Also, Nandi and Shakoor (2009) evaluated the performance of LR in landslide susceptibility mapping in the Cuyahoga River watershed, northeastern Ohio, USA. Their results showed good performance of the LR model. Yalcin (2008) reported AHP method gave a more realistic landslide susceptibility map than the bivariate statistical models (Wi and Wf). On the other hand, area density method, one of the bivariate approaches, is based on the
observed relationship between distribution of landslides and each landslide causative factor to determine correlation between landslide locations and the factors (Cevik and Topal 2003; Yalcin 2008; Kelarestaghi and Ahmadi 2009). AHP is a multi-objective, multi-criteria decisionmaking approach which enables the user to arrive at a scale of preference drawn from a set of alternatives. AHP-gained wide application in site selection, suitability analysis, regional planning, and landslide susceptibility analysis (Yalcin 2008). So, in current study, these two models were combined and a semi-quantitative model was developed. This model had high capability in landslide susceptibility mapping and better results than logistic regression model. The landslide susceptibility maps Landslide susceptibility maps produced by logistic multivariate regression and weighted (AHP) bivariate models are represented in Fig. 3a, b. The mentioned susceptibility maps were classified into low, moderate, high, and very high classes based on natural break scheme. The moderate land slide susceptibility map class derived using the logistic regression model covers 25.06 % of the total area; 24.98, 24.98, and 24.98 % of the total area are related to low, high, and very high SPM zones, respectively (Fig. 3a and Table 4). In the case of weighted (AHP) bivariate model, low, moderate, high, and very high landslide susceptibility map classes cover 25.28, 24.35, 25.62, and 24.75 % of the total area, respectively. The importance of landslide causative factors Determining importance of different landslide causative factors is a necessary step in landslide susceptibility mapping. In several studies, logistic regression model has been used in order to determine the importance of causative
100
Fig. 4 ROC curves for logistic regression (LR) and combined bivariate and AHP models
90
True Positive %
80 70 60
Combined Bivariate and AHP model Logistic regrression model
50 40 30 20 10 0
0
68
91
91
91
91
91
92
False Positive %
97
99
100
201 Page 12 of 15 Table 4 classes
Arab J Geosci (2016) 9: 201
The distribution of area in different landslide susceptibility
Bivariate statistical model weighted Logistic regression model with AHP Susceptibility Area (ha) % Area Susceptibility Area (ha) % Area class class Low
6,983.17
25.28
Low
6,900.07
24.98
Medium
6,727.62
24.35
Medium
6,922.40
25.06
High Very high
7,078.07 6,838.33
25.62 24.75
High Very high
6,902.15 6,902.58
24.98 24.98
Total
27,627.19 100
Total
27,627.19 100
factors on landslide occurrence (Yesilnacar and Topal 2005; Ayalew and Yamagishi 2005; Lee and Pradhan 2007; Nandi and Shakoor 2009). According to the results, the causative factors such as slope aspect, precipitation, elevation, geology, and land use affect the multivariate logistic regression model function positively (Eq. 4). The highest positive β coefficient is allocated to the precipitation which is 0.003. On the other hand, distance from faults, distance from stream, and distance from roads had negative effect on landslide occurrence with β coefficients of −0.000077, −0.000163, and −0.000415, respectively, which is consistent with the results of Devkota et al. (2013). Also, it can be seen that distance from roads had the highest negative affect on logistic regression. BVariance inflation factor^ (VIF) and the BTolerance^ (TOL) are two important indices for multi-collinearity diagnosis (O’Brien 2007). The tolerance and variance inflation factors were computed for this study, and variables with VIF > 5 and TOL < 0.1 should be excluded from the LR analysis, but there was not any multi-collinearity problem in used landslide causative factors in this study. The weight of nine factors was calculated by AHP using Expert Choice-11 software (Table 2). According to the results of weighted (AHP) bivariate model, slope percentage, land use, and distance from road had highest weights in landslide susceptibility mapping with values of 0.243, 0.193, 0.162, and 0.121, respectively. On the other hand, elevation and distance from stream had the lowest weights with values of 0.029 and 0.035, respectively (Table. 2) In another research, Youssef et al. (2015a) used different probabilistic and bivariate statistical models including frequency ratio, weight of evidence, index of entropy, and Dempster–Shafer models in landslide susceptibility mapping. According to the results, slope length, altitude, distance from roads, and slope angle had the highest weights based on produced landslide susceptibility maps by index of entropy model.
Conclusion The Doab Samsami watershed’s conditions such as geology, roughness, geomorphology, and tectonic conditions as well as human pressure factors such as land use and rural roads’ changes have created a proper background for the landslide that its occurrence is about 37 cases with approximate extent of 635 ha in watershed basin. Converting the rangeland to rain-fed farming and road construction is performed sharply in Doab Samsami watershed during recent years and led to presenting high role of human factors on landslide occurrences. Therefore, in current study weighted (AHP), bivariate and logistic regression models were used for landslide susceptibility mapping in the Doab Samsami watershed, Chaharmahal-e-Bakhtiari Province, Iran. A landslide inventory map and nine landslide causative factors were prepared for this investigation. Then, landslide susceptibility maps were produced using two mentioned models and then evaluated using area under curve of ROC. According to the results, two implemented models had high and relatively close performance. However, weighted (AHP) bivariate (AUC = 0.914) had better performance than logistic multivariate regression (AUC = 0.865). Considering the better results of weighted (AHP) bivariate in landslide susceptibility mapping in the study area, it is important to consider the very high susceptible class of landslide susceptibility produced by this model which covered 24.75 % of the study area. This shows high susceptibility to landslide for watershed basin that should be considered in susceptibility management, landslide losses, and land use planning. Finally, the methodology produced in current study can be applied in other areas with similar climatic, geological, and topographical conditions in order to facilitate land use planning and hazard management. Acknowledgments The authors would like to thank two anonymous reviewers for their helpful comments on the primary version of the manuscript.
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