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Landslide susceptibility mapping at Zonouz Plain, Iran using genetic programming and comparison with... Article in Natural Hazards · November 2013 DOI: 10.1007/s11069-013-0932-3
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Nat Hazards (2014) 71:523–547 DOI 10.1007/s11069-013-0932-3 ORIGINAL PAPER
Landslide susceptibility mapping at Zonouz Plain, Iran using genetic programming and comparison with frequency ratio, logistic regression, and artificial neural network models Vahid Nourani • Biswajeet Pradhan • Hamid Ghaffari Seyed Saber Sharifi
•
Received: 13 July 2013 / Accepted: 26 October 2013 / Published online: 12 November 2013 Springer Science+Business Media Dordrecht 2013
Abstract Without a doubt, landslide is one of the most disastrous natural hazards and landslide susceptibility maps (LSMs) in regional scale are the useful guide to future development planning. Therefore, the importance of generating LSMs through different methods is popular in the international literature. The goal of this study was to evaluate the susceptibility of the occurrence of landslides in Zonouz Plain, located in North-West of Iran. For this purpose, a landslide inventory map was constructed using field survey, air photo/satellite image interpretation, and literature search for historical landslide records. Then, seven landslide-conditioning factors such as lithology, slope, aspect, elevation, land cover, distance to stream, and distance to road were utilized for generation LSMs by various models: frequency ratio (FR), logistic regression (LR), artificial neural network (ANN), and genetic programming (GP) methods in geographic information system (GIS). Finally, total four LSMs were obtained by using these four methods. For verification, the results of LSM analyses were confirmed using the landslide inventory map containing 190
V. Nourani (&) Department of Water Resources Engineering, Faculty of Civil Engineering, University of Tabriz, 29 Bahman Ave., Tabriz, Iran e-mail:
[email protected];
[email protected] B. Pradhan (&) Department of Civil Engineering, Faculty of Engineering, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia e-mail:
[email protected];
[email protected] H. Ghaffari Department of Water Resources Engineering, Faculty of Civil Engineering, Islamic Azad University, Mahabad Branch, Mahabad, Iran e-mail:
[email protected] S. S. Sharifi Department of Water Engineering, Faculty of Agriculture, University of Tabriz, 29 Bahman Ave., Tabriz, Iran e-mail:
[email protected]
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active landslide zones. The validation process showed that the prediction accuracy of LSMs, produced by the FR, LR, ANN, and GP, was 87.57, 89.42, 92.37, and 93.27 %, respectively. The obtained results indicated that the use of GP for generating LSMs provides more accurate prediction in comparison with FR, LR, and ANN. Furthermore; GP model is superior to the ANN model because it can present an explicit formulation instead of weights and biases matrices. Keywords Landslide GIS Genetic programming Remote sensing Artificial neural network Zonouz Plain
1 Introduction Landslide is a complex natural phenomenon that may lead to the loss of life and property. Annually, direct and indirect costs of slope failures exceed millions of dollars in all over the world. In last two decades, landslide susceptibility analyses have been widely reported that worldwide landslide susceptibility map (LSM) constitutes a valuable tool for allocating areas prone to landslide manifestation with graded risk levels in urban and rural areas. Therefore, the preparation of LSM is a major step in overall landslide hazard management. Landslide susceptibility mapping can be defined as qualitative or quantitative, and direct heuristic approaches or indirect heuristic approaches (Kayastha et al. 2013). These approaches can be classified under three main topics such as statistical, soft computing, and analytical methods. When study area is large, application of analytic methods is almost impossible. For this reason, the use of statistical and soft computing methods has increased gradually (Pradhan 2013). Moreover, the geographic information system (GIS) comprises the valuable tools for the compilation of LSMs (Sung et al. 2001; Saha et al. 2002; Lan et al. 2004; Ayalew and Yamagishi 2005; Ermini et al. 2005; Akgun et al. 2011). Application of GIS also gives the advantage of a quick analysis, processing, and correlation of large amounts of data. Recently, some studies applied probabilistic model such as frequency ratio (FR) and logistic regression (LR) methods to generate LSM (Dahal et al. 2008; Gorum et al. 2008; Lamelas et al. 2008; Pradhan et al. 2009; Tunusluoglu et al. 2008; Yilmaz 2009; Pradhan and Youssef 2010). Nowadays, artificial intelligence (AI) plays an important role in modeling and simulation of many complex phenomena. More recently, seven AI techniques have been applied for landslide susceptibility mapping. Those techniques that have been tried are neuro-fuzzy (Lee and Evangelista 2006; Vahidnia et al. 2010; Oh and Pradhan 2011; Sezer et al. 2011; Bui et al. 2012b; Pourghasemi et al. 2012c; Tien Bui et al. 2012b, c, d; Akgun et al. 2012; Pradhan 2013), support vector machine (SVM) (Yao et al. 2008; Yilmaz et al. 2011; Tien Bui et al. 2012a), decision tree method (Tien Bui et al. 2012a; Pradhan 2013), spatial multicriteria evaluation (Pourghasemi et al. 2012b), index of entropy (Bednarik et al. 2012; Pourghasemi et al. 2012a), and Dempster-Shafer (Mohammady et al. 2012; Althuwaynee et al. 2012), and their performances have been assessed. Among such AI-based approaches in landslide susceptibility evaluation, artificial neural network (ANN) model is quite popular (Lee and Evangelista 2006; Ermini et al. 2005; Caniani et al. 2008; Pradhan and Buchroithner 2010; Pradhan and Lee 2010a, b, c; Pradhan and Pirasteh 2010; Yilmaz 2010a, b; Pradhan et al. 2010c, d; Bui et al. 2012a; Zare et al. 2013). One of the advantages of using an ANN for modeling geoscience phenomena is that it can handle data at any
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measurement scale ranging from nominal, ordinal to linear and ratio, and any form of data distribution (Nourani et al. 2013a). Niefeslioglu et al. (2008) indicated that the use of ANN for production of LSMs provide more accurate forecasts than the FR and LR models. Melchiorre et al. (2008) applied cluster analysis for production of LSM by use of ANN. Kawabata and Bandibas (2009) generated LSM using geological data, a DEM from advanced spaceborne thermal emission and reflection radiometer (ASTER) image and ANN. Pradhan et al. (2010a) applied an ANN model in landslide susceptibility mapping and validated the model using the existing landslide data. Although the ANNs are useful tools in geoscience computation modeling, the obvious disadvantage of the ANNs is that they represent their knowledge in terms of a weight matrix that is not accessible to human understanding at present (Savic et al. 1999). In addition, the number of inputs and hidden neurons are not clearly determined, and they should be obtained via a time-consuming trial and error process. Thus, it is still necessary to develop an explicit model to overcome this problem (Aytek and Kisi 2008). From this point of view, genetic programming (GP), which is an evolutionary computing method that provides transparent and structured system identification, has been developed (Nourani et al. 2012c; Hakimzadeh et al. 2013). The motivation behind this choice is that GP has advantages, which may allow the mitigation of some of the limitations of typical ANN models. These advantages can be summarized as follows: (1) generation of explicit model representations amenable to easy human comprehension, (2) automatic discovering of the model structure from the given data, (3) adaptive evolutionary search that allows to escape trapping in suboptimal, unsatisfactory local solutions, and (4) absence of specific knowledge (Nourani et al. 2013b). Genetic programming has been successfully applied to problems that are complex and nonlinear and where the size, shape, and overall form of the solutions are not explicitly known in advance (Nourani et al. 2012c). The state-of-the-art applications of the GP in the civil engineering have been listed by Shaw et al. (2004). However, there is an increasing trend toward opening up the black box and trying to understand how this model work, and more importantly, how it can be related to landslide susceptibility assessment and process the knowledge obtained from it. Furthermore, among artificial intelligence techniques, the GP method can present explicate and transparent formula for landslide susceptibility modeling. Moreover, another major advantage of artificial intelligence methods lies in their self-learning ability while dealing the data noise in comparison with other classic methods; the implication of intelligence methods using such data can led to appropriate outcomes while it is undeniable that the fine data lead to the better results. The main difference between the present study and the approaches described in the aforementioned publication is that a genetic programming method was developed and applied for landslide susceptibility analysis. Furthermore, this paper is to assess and compare the results of LSMs using frequency ratio, logistic regression, artificial neural network, and genetic programming models for the Zonouz Plain. Finally, the performances of the models are evaluated and compared.
2 Study area Zonouz Plain in East Azerbaijan province consists of approximately 260 km2 areas located between 38300 and 38390 north-south latitudes and 45460 and 45580 west-east longitudes in the North-West of Iran (Fig. 1). Altitudes reach 2,900 m in some parts of the region, and steep slopes are very common. This region contains a main channel and
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Fig. 1 Location map of the study area
sub-branches of the Zonouz river. This river drives from Soltan-Sanjar Mountain in the east and flows into the west in Cher-Cher area and joins to the Zilber river and finally discharges to the Caspian Sea. The climate of the study area is snowy and sub-humid having four welldefined seasons, e.g., spring, summer, autumn, and winter. The daily mean temperature varies from -30 C in January up to 42 C in July with a yearly average of 8 C. The annual precipitation is 325 mm, and dominant winds over the area blow from the Northeast and the Southwest whose variable conditions make this area prone to landslide.
3 Thematic map layer The first step for production of a LSM is gathering the available data in effort of the selection of the effective parameters for preparation of thematic digital maps. All such data maps used in this study are raster based on a cell size of 10 m 9 10 m. The preparation procedures for each data layer are summarized below. Also, an important step for production of a landslide susceptibility map is the construction of inventory map based on previously occurred landslides. More recently, many researchers have produced LSMs using several parameters such as lithology, slope, aspect, landcover, elevation, distance to stream, drainage density, distance to lineament, seismicity, and distance to road (e.g., Pradhan et al. 2010b; Yalcin et al. 2011; Bui et al. 2012a, b). In this study, seven possible landslide effective layers; lithology, slope, elevation, land cover, aspect, distance to stream, and distance to road were used to produce LSMs using the FR, LR, ANN, and GP methods. Eventually, the susceptibility maps were generated from these four methods, were compared and evaluated using validation data set.
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3.1 Inventory map Landslide inventory map contains the location of landslide, which has occurred previously. These landslides were related to geological, topographical, and climate conditions. Therefore, they may facilitate the prediction of landslides locations in the future. In this study, the archived 1:50,000 aerial photographs from Natural Cartographic Center of Iran (NCC) during the past 15 years were used to detect landslide locations. Furthermore, field work was carried out at randomly selected landslide sites to verify the landslide locations. Eventually, a total of 190 landslides were identified in the landslide inventory map. Figure 2a shows the distribution of landslide location in the Zonouz Plain. 3.2 Causative data layers Lithology is one of the most decisive parameters regarding the landslide manifestation (Sarkar et al. 1995; Dai et al. 2001; Slide and Ochiai 2006). For the study area, the lithology map was prepared using available geological map based on NCC map and field work. Three major soil types are presented as: inceptisols (Typic Haploxerepts, Litihic Haploxerepts, hilly), rock out corps/entisols (Litihic Haploxerepts, medium Type, hilly), and rock out corps/ inceptisols (Litihic Xerothents, Typic Haploxerepts, steep), which are shown in Fig. 2b. Slope is a principal causative factor because the steeper slopes have direct influence due to higher shear forces (Dai et al. 2001; Niefeslioglu et al. 2008). In this study, digital elevation model (DEM) was prepared by digitizing a detailed topographical map of the area at 1/25,000 scale and a contour intervals of 25 m. Further, slope, aspect, and elevation maps were derived from the DEM. Finally, according to the importance of slope conditions and configurations in landslide occurring, the study area was divided into five slope categories as: (0–15), (15–30), (30–45), (45–60), and ([60), which are shown in Fig. 2c. For the classification of the slope aspect, the grid maps of the parameter were from the DEM. As shown in Fig. 2d, aspect regions were classified into nine categories according to the aspect class as: 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), and northwest (292.5–337.5). Elevation is also considered as another important factor in LSMs. Usually, elevation is associated with landslides as a result of other factors such as slope, erosion, precipitation, soil thickness, and land use. It is useful to classify the local relief and location points of maximum and minimum heights within terrains. In addition, a slope consists of soil or soft rocky formations, which has high angle, fails almost immediately, and gives a lower slope angle. According to the obtained map of the NCC, the elevation of the study area was classified into five classes using 400 m intervals: (\1,300), (1,300–1,700), (1,700–2,100), (2,100, 2,500), and (2,500–2,900) m and is shown in Fig. 2e. Land cover is one of the main factors for slope stability analysis. Land cover performs as a shelter and reduces the susceptibility of soil erosion. The variation in the vegetation in an area is a dominant factor that seriously affects the slope failure while slope stability is very sensitive to changes in vegetation. Vegetation leads to increase in soil strength by root reinforcement, which has great potential to reduce the rate of landslide occurrence (Begueria 2006). In this study, a single date image of Landsat ETM? using a supervised classification scheme on October 19, 2005, with multispectral bands with 28 m resolution, one thermal band with a 60 m resolution, and panchromatic band with 15 m resolution, was used to derive the land cover types. Then, the land cover was classified into five categories as: uncultivated, garden or forest, grassland, residential, and agriculture (Fig. 2f).
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Fig. 2 The inventory map and thematic layers of the seven principal parameters involved: a Inventory map, b lithology, c slope, d aspect, e land cover, f elevation, g distance to stream, and h distance to road
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The closeness of the slope to stream is another important factor in terms of stability. Streams may adversely affect stability by eroding the slope or by saturating the lower part of material until resulting in the water level increase (Cevik and Topal 2003; Yalcin 2008). With this regard, six classes were created using intervals of 25, 50, and 100 m as: (0–25), (25–100), (50–100), (100–200), (200–300), and ([300) m, which are shown in Fig. 2g. From the analysis, it is obvious that distance to road is one of the causal factors for landslide manifestation. A road or highway in mountain area, constructed alongside slopes, causes a decrease in the load on both the topography and on the toe of slope. Thus, the road network can be chosen as a principal parameter for generation of the LSM (Yalcin 2008). For designating the influence of the road on the slope stability, the study area was divided into six different buffer categorizes: (0–25), (25–50), (50–100), (100–200), (200–300), and ([300) m and is shown in Fig. 2h. The precipitation intensity affects the occurrence of landslide, but in the study area, rainfall was assumed to be relatively uniform, and for that reason is neglected from the calculation.
4 Landslide susceptibility mapping This study demonstrates the implementation of the FR, LR, ANN, and GP methods for generation of LSM at the Zonouz Plain, which are presented below. The FR model is one of the common methods in landslide susceptibility assessments. The key advantage of FR method is that it is easy to apply, and obtained results are readily intelligible. Also LR is one of the most well-known linear methods to predict the presence or absence of a characteristics or outcomes based on values of a set of predictor variables. More recently, ANNs as black-box models have been widely used for modeling complex problems. ANNs are effective tools for handling highdimensional data sets with nonlinear characteristics, especially in cases where the underlying physical relationships are not clear. On the other hand, GP is considered as a new generation of AI approaches and gives insight into the relationship between input and output data. Furthermore, the GP method can present formula for modeling the complex process. 4.1 Results of frequency ratio (FR) method FR allows one to derive spatial relationship between all landslides and each related factor, which have occurred previously (Lee and Pradhan 2007). The FR ratio is the ratio between the landslides in the class as a percentage of all landslides and the area of the class as a percentage of the entire map. The landslide susceptibility index (LSI), Eq. (1), is calculated by a summation of each factor ratio value as (Lee and Min 2001): LSI ¼ Fr1 þ Fr2 þ Fr3 þ þ Frn
ð1Þ
where Fr is rating of each factor’s type or range. In relationship analysis, the ratio is that of the area where landslides occurred to the total area, so that a value of one is an average value. If the value is[1, it means a high correlation, and a value lower than 1 means lower correlation. Therefore, the frequency rations of each factor’s type or range were calculated from their relationship with landslide events as shown in Table 1. Finally, the frequency ratio of each layer classes was determined, and landslide susceptibility map (Fig. 3) was produced using the LSI map using Eq. (1). In FR model, the lithological characteristic of study area is an important factor in landslide occurrence. There are three types of lithological units within the study area, inceptisols, rock out corp/entisols, and rock out corps/inceptisols which include 12.39,
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Table 1 Frequency ratio values of the landslide-conditioning parameters Factors
Lithology (d1)
Slope (d2)
Aspect (d3)
Land cover (d4)
Elevation (d5)
Dist. to stream (d6)
Dist. to road (d7)
Classes
% of total area (a)
% of landslide area (b)
Inc
11.88
12.39
1.04
Ren
75.63
74.54
0.99
Rin
12.49
13.07
1.04
0–15
21.32
4.71
0.22
15–30
12.15
11.73
0.97
30–45
34.04
41.93
1.23
45–60
19.26
30.13
1.56
[60
13.23
11.50
0.87
Flat
10.54
0
0
North
12.39
8.93
0.72
Northeast
12.90
8.82
0.68
East
11.86
8.79
0.74
Southeast
9.24
13.77
1.49
South
8.68
12.31
1.41
Southwest
10.54
16.17
1.53
West
11.73
16.87
1.44
Northwest
12.12
14.34
1.18
Uncultivated
37.95
47.52
1.25
Garden
8.42
2.43
0.29
Grassland
7.58
2.25
0.30
Residential
40.10
45.37
1.31
Agriculture
5.95
2.43
0.41
\1,300 (m)
13.01
10.31
0.79
1,300–1,700
27.03
32.53
1.20
1,700–2,100
10.01
15.33
1.53
2,100–2,500
28.13
30.42
1.08
2,500–2,900
21.82
11.41
0.52
0–25 (m)
25.96
33.41
1.29
25–50
10.65
15.02
1.41
50–100
15.05
13.11
0.87
100–200
15.72
13.16
0.84
200–300
18.41
14.85
0.80
[300
14.21
10.45
0.74
0–25 (m)
29.97
41.02
1.37
25–50
41.95
45.84
1.10
50–100
7.23
5.30
1.73
100–200
12.40
5.66
0.46
200–300
3.88
1.05
0.27
[300
4.57
1.13
0.25
Inc, inceptisols; Ren, rock outcrops/entisols; Rin, rock outcrops/inceptisols
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Frequency ratio (b/a)
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Fig. 3 Landslide susceptibility map produced using FR method
74.54, and 13.07 % of the frequency ratio, respectively. The slope angle is easily relatable to the slope movement, because it is strongly linked to the forces involved. In this study, most landslides occur at slope angle above 45. Also, the slope class between 0 and 15 contains \5 % landslide coverage. The aspect is very important for landslide studies. According to Table 1, most of the landslides occurred at the west (16.87 %), southwest (16.17 %), southeast (13.77 %), and south (12.31 %) directions showing that most landslides occurred on slopes facing west and southwest. The variation in the vegetation in an area is a parameter that seriously affects the slope failures, as slope stability is very sensitive in changes on vegetation. In this study, landcover analysis showed that landslide commonly occurred in the uncultivated and residential areas, the FR being 1.25 and 1.13, respectively (Table 1). FR analysis showed that elevation in a range of 1,700–2,500 m shows high probabilities of landslide occurrence while the relatively flat and gentle areas like areas with altitudes lower than 1,300 m present low probability of landslide occurrence. Additionally, the area with elevation of higher than 2,500 m with rocky characteristic indicates lower FR value. A close relationship has been found between the distance to stream and location of the slope failures. Assessment of distance from stream showed that 48.43 % of the landslides occurred in the area within the range of 0–50 m from the stream (Table 1). Distance to road is usually taken into account in landslide susceptibility assessments and is parallel to the influence of the distance to streams. Normally, the connection between landslides and proximity to roads, gives reverse value 1.37 and 1.10, was found for distance between 0 and 25 and 25 and 50 m, respectively.
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4.2 Results of logistic regression (LR) method One of the most common statistical methods used in geosciences especially in landslide assessment is the logistic regression model. Logistic multiple regression allows one to evaluate a multivariate regression relationship between a dependent and independent variables. As stated by Lee and Sambath (2006), logistic regression is useful for predicting the presence or absence of a characteristic or outcome based on value of a sat of predictor variables. One of the important advantages of logistic regression is that, through addition of an appropriate link function to the usual linear regression model, the variables may be either continuous or discrete, or any combination of both types, and they do not necessarily have normal distributions (Lee and Sambath 2006). In the present study, the dependent variable is a binary variable representing presence (1) or absence (0) of a landslide, where the dependent variable is binary, and the logistic link is applicable. The logistic regression model is expressed as a linear equation (Atkinson and Massari 1998): z ¼ b0 þ b1 d1 þ b2 d2 þ þ bn dn
ð2Þ
where z is linear combination, b0 is the intercept of the model, the bi (i = 0, 1, 2, …, n) are the slope coefficients of the logistic regression model, and di (i = 0, 1, 2, …, n) are the independent variables. Using the logistic regression model, the spatial relationship between landslide occurrence and factors affecting landslides could be assessed. For this purpose, a map showing the area affected by landslides and factor maps (lithology, slope, aspect, elevation, land cover, distance to streams, and distance to road) in a raster format was first converted in to ASCII format. Then, the correlation between landslide event and landslide affecting factors was estimated. The equation predicting the landslide occurrence was obtained as: z ¼ 4:7485 þ 0:000929d1 þ 0:050838d2 þ 0:000503d3 0:052129d4 0:0239024d5 0:098631d6 0:006434d7
ð3Þ
In order to predict the possibility of landslide occurrence in each grid, probability (p) was calculated using: p¼
1 1 ez
ð4Þ
Eventually, a susceptibility map was obtained by converting the file into the raster format (Fig. 4). According to Eq. (3), the lithology, slope, and aspect coefficients are positive; the land use, elevation, distance to road, and distance to stream coefficients are negative. This means that lithology, slope, and aspect are positively related to the occurrence of a landslide, whereas land use, elevation, distance to stream, and distance to road indicate a negative relation with the landslide occurrence in the study area. In addition, slope coefficient shows that among the effective parameters in landslide occurrence, ‘‘slope’’ parameter has more crucial effect than any other parameters. 4.3 Results of artificial neural network (ANN) method The artificial neural network (ANN) has been widely applied in geoscience studies as a powerful estimation tool. It has already been demonstrated that a feed-forward neural network (FFNN) model trained by the back-propagation (BP) algorithm with three layers is satisfactory for forecasting and simulating engineering problems (Hornik et al. 1989).
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Fig. 4 Landslide susceptibility map produced using LR method
Three-layered FFNNs, which have usually been used in generating LSMs, provide general framework for representing nonlinear functional mapping between a set of input and output variables (Fig. 5). They are based on a linear combination of the input variables, which are transformed by a nonlinear activation function. The term ‘‘feed forward’’ means that a neuron connection only exists from a neuron in the input layer to other neurons in the hidden layer or from a neuron in the hidden layer to neuron in the output layer. The neurons within a layer are not interconnected. In Fig. 5, i, j, and k denote input layer, hidden layer, and output layer neurons, respectively, and w is the applied weight by the neurons. The explicit formula for an output value of a three-layered FFNN is given as (Nourani et al. 2012a): " ! # MN NN X X ð5Þ wkj :fh wji xi þ wjo þ wko y^k ¼ f0 j¼1
i¼1
where wji is a weight in the hidden layer connecting the ith neuron in the input layer and the jth neuron in the hidden layer, wjo is the bias for the jth hidden neuron, fh is the activation function of the hidden neuron, wkj is a weight in the output layer connecting the jth neuron in the hidden layer and the kth neuron in the output layer, wko is the bias for the kth output neuron, f0 is the activation function for the output neuron, xi is ith input variable for input layer, and yˆk, y are computed and observed output variables, respectively. NN and MN are the number of the neurons in the input and hidden layers, respectively. The weights
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Fig. 5 A three-layered feed-forward neural network with back-propagation training algorithm
are different in the hidden and output layers, and their values can be changed during the process of the network training. In any ANN modeling, appropriate selection of the architecture, i.e., the number of neurons in hidden layers and the training iteration (epoch) number improves model efficiency in both the training and testing steps. Furthermore, a high epoch number and poor quality of data could cause the network to over-fit during the training step. If this occurs, the model cannot adequately generalize new data outside of the training set. It is important to normalize the data in a suitable form before they are applied to the ANN; for this purpose, input and output variables are usually normalized by scaling between zero and one, to ensure that all variables receive equal attention during the training step of the model as (Nourani et al. 2012b): xi xmin ð6Þ x0i ¼ xmax xmin where xi is the actual value and xi0 is the respective normalized value. xmin and xmax are the minimum and maximum of the values, respectively. Two different criteria were used to measure the efficiency of the ANN method: the root mean square error (RMSE) and the determination coefficient (DC). The RMSE and DC are used to demonstrate discrepancies between forecasts and observations by following equations (Nourani et al. 2013a): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 2 1X di d^i ð7Þ RMSE ¼ n i¼1 2 Pn di d^i DC ¼ 1 Pi¼1 n ^ 2 i¼1 d i d i
ð8Þ
In Eqs. (7) and (8), n is the date number, di and d^i are the observed data and the calculated values, respectively, and di is the averaged value of the observed data. High value for DC and small values for RMSE indicate that the model is highly efficient (for the best model, the values of DC and RMSE would be one and zero, respectively).
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For application of ANN to the study area, the maps of the seven effective factors in landslide occurring were converted into appropriate input data. Then, the FFNN model trained by the BP algorithm was implemented to generate the LSM of the study area. Afterward, for training ANN model, the data set was divided into two parts as training and verification data. Therefore, the randomly selected landslide database was separated into two parts: the first part, which accounted for 70 % (133 landslide area containing 1,027 landslide grid cells), was used in the training phase of the ANN model, and the rest 30 % (57 landslide areas containing 438 landslide grid cells) was used for the validation of the models. Also during the training phase, areas where landslides were not occurred and where the values of the slopes were zero were classified as ‘‘areas not prone to landslide,’’ while areas affected by the landslide were assigned to the ‘‘areas prone to landslide.’’ In this way, training data set consists of the equal number of landslide occurrence and nonoccurrence data. For producing the best LSM in the study area by ANN model, sensitivity analysis was also implemented. In this way, various combinations of the seven causative factors were examined using the FFNN model as: Comb. (1): Lithology, Slope. Comb. (2): Lithology, Slope, aspect. Comb. (3): Lithology, Slope, aspect, land cover. Comb. (4): Lithology, Slope, aspect, land cover, elevation. Comb. (5): Lithology, Slope, aspect, land cover, elevation, distance to stream. Comb. (6): Lithology, Slope, aspect, land cover, elevation, distance to stream, distance to road. Each FFNN was trained by examining 3–25 hidden neurons in a single hidden layer using the Levenberg–Marquardt training scheme (Hagen and Menhaj 1994) via up to 200 training epochs, with 10-4 as the goal performance. The training was terminated at the point where the error in the validation data set began to rise to ensure that neural network did not over-fit the training data and then fail to generalize the unseen test data set. The results of ANN-based modeling for different input variables and structures are provided in Table 2. By comparing the obtained results, the best architecture for the prediction of landslide susceptibility map was obtained by ANN (7, 23, 2) where 7, 23, and 2 are the numbers of neurons in input, hidden, and output layers, respectively, whereas DC and RMSE values in verification phase are 0.901, and 0.0142, respectively. Finally, after network goal was reached, the seven effective factors of landslide in the study area were fed into the network. Then, a set of susceptibility value obtained in each grid was converted to raster file in the GIS. Subsequently, the landslide susceptibility map was produced by ANN model as shown in Fig. 6. 4.4 Results of genetic programming (GP) method GP is an evolutionary computing method that generates a transparent and structured representation of the system being studied (Koza 1992). The nature of GP allows the user to gain additional information on how the system performs, i.e., gives insight into the relationship between input and output data. The GP is similar to genetic algorithm (GA), but unlike the latter, its solution is a computer program or an equation as against a set of numbers in the genetic algorithm. So, GP is more attractive than traditional GA for problems that require the
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Table 2 Results of ANN modeling for the different input variables Input variables
Epoch
Network structurea
RMSE (normalized)
DC
Calibration
Verification
Calibration
Verification
Comb. (1)
74
(2-17-2)b
0.0184
0.0210
0.723
0.719
Comb. (2)
87
(3-13-2)
0.0172
0.0191
0.818
0.805
Comb. (3)
92
(4-19-2)
0.0164
0.0183
0.844
0.823
Comb. (4)
77
(5-19-2)
0.0152
0.0163
0.890
0.868
Comb. (5)
77
(6-21-2)
0.0138
0.0150
0.903
0.872
Comb. (6)
77
(7-23-2)
0.0121
0.0142
0.916
0.901
a
The results have been presented for the best structure
b
First number from left represents number of the input neurons, second one is the number of the hidden neurons, and third shows the number of output neuron
Fig. 6 Landslide susceptibility map produced using ANN method
construction of explicit models (Savic et al. 1999). The GA and GP deal with two different structures, but the solution procedure of both algorithms is similar. Genetic programming is based on a tree structure. For example, the outline of simple genetic programming structure for a sample mathematical expression is illustrated in Fig. 7.
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Fig. 7 Tree structure of genetic programming for a mathematical expression (modified after, Koza 1992)
In GP, a random population of individuals is created; the fitness of the individuals is evaluated, and then, the parents are selected out of these individuals. The parents are then made to yield offspring by following the process of reproduction, mutation, and crossover (Sivanandam and Deepa 2008). The creation of offspring continues (in an iterative manner) until a specified number of offspring in a generation is produced and further until another specified number of generations are created. The resulting offspring at the end of this entire process (an equation or a computer program) is the solution of the problem. The GP thus transforms one population of individuals into another one in an iterative manner by applying operators. In evolutionary computation, it can distinguish between three different types of operators which are named crossover, reproduction, and mutation (Sivanandam and Deepa 2008). These operators are briefly described below. 4.4.1 Crossover operator Two parent individuals are selected, and a subtree is picked on each one. Then, crossover swaps the nodes and their relative subtrees from one parent to the other (Fig. 8). 4.4.2 Mutation operator The mutation operator can be applied to either a function (arithmetic operations) node or a terminal (variables and constants) node. A node in the tree is randomly selected. If the chosen node is a terminal, it is simply replaced by another terminal. If it is a function and a point mutation is to be performed, it is replaced by a new function with the same linearity (Fig. 9). 4.4.3 Reproduction operator The reproduction operator simply chooses an individual in the current population and copies it without changes into the new population. For application of GP to the study area, the classic GP model was employed for generation of LSM. The data sets considered exactly the same as those data sets that used to train the ANN to predict LSI of each grid. The mathematical relationship could be expressed as a function of f: LSI ¼ f ðd1 ; d2 ; d3 ; d4 ; d5 ; d6 ; d7 Þ
ð9Þ
In an evolutionary model such as GP, the model output depends not only on the input variables but also initial population size, and sampling method which must be calibrated by sensitivity analysis, correctly. Since the evolution process is a nondeterministic process, it does not end with a successful solution in each program run. So, these parameters must be
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Fig. 8 Crossover operator (modified after, Koza 1992)
Fig. 9 Mutation operator (modified after, Koza 1992)
set by a trial and error method. For this purpose, the program must be processed in several independent runs to obtain a successful solution for the problem. The number of required program runs for the satisfactory solution depends on the difficulty of the problem or model. In the current research, different sets of evolutionary parameters were examined for the GP model. And the best combination of the value/method for evolutionary parameters is listed in Table 3. The arithmetical functions such as four basic operators (?, -, 9 , 7) and two basic mathematical functions (H, power) can be used to create the initial population. Also, genetic operators (crossover, mutation, and reproduction) can be used to create a new generation in the GP process. In addition to parameter selection, the main concern in using a GP model is the training process. When a GP model is trained iteratively in order to improve its performance on the training data, it is possible that the GP formulation finally ‘‘memorizes’’ the training samples and does not ‘‘learn’’ the underlying pattern. This is called an over-fitting (overtraining) problem in the AI models. This is more likely to happen in the GP model with a large number of generations. For this reason, the GP model with suitable generations is preferred just enough to provide an adequate fit to avoid over-training. Also, the GP formulation should adjust only on the account of the training (calibration) set, but the error should be monitored on the validation data set, simultaneously. The error on the validation data will normally decrease during the initial iterations together with the error on the training set, and when the GP formulation begins to over-fit the training data, the error on
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Nat Hazards (2014) 71:523–547 Table 3 GP control parameters in analysis
539
Item
Value/method
Number of initial population
500
Number of generation
300
Sampling method
Tournament
Crossover probability
0.5
Mutation probability
0.5
Fitness function
RMSE
Elitism
Yes
the validation data will begin to rise. For this reason, the calibration and verification errors must be considered in the training process simultaneously. This technique was applied in the modeling process of this paper, and it was found that 300 generations is a good choice to prevent the over-fitting issue. The results of GP model for different input variables are presented in Table 4. By considering the factors in the GP modeling, various runs were conducted and the optimum formulations were selected according to the obtained evaluation criteria in terms of DC and RMSE. The highest accuracy could be obtained by comb. 4, which was attained using the largest data set. It was apparent from the success of the larger data set that more rather than fewer variables were needed to compute the variability inherent in the landslide in order to generate LSM. The GP model provides different answers for the problem. Therefore, the user may select one of them considering both accuracy and simplicity issue. According to Table 4, the best GP formulations for comb.4 are presented as Eqs. (9)–(12), respectively. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi LSI ¼ d6 þ d1 d4 ðd7 d3 Þ þ ððd4 d2 Þ d2 2:97d3 Þ 2:53d1 ð10Þ pffiffiffiffiffi d5 þ ðd5 ðd3 d6 ÞÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi LSI ¼ d1 þ d4 ðd4 þ d7 Þ ðd3 d6 Þ þ ðd4 d2 Þ d5 1:21d1 ð11Þ pffiffiffiffiffi d3 þ ðd2 Þ2 þ 1:37 d2 pffiffiffiffiffi ð12Þ LSI ¼ d1 þ ð0:61d6 þ ðd2 d4 d3 ÞÞ 0:027d5 þ ðd7 Þ2 d4 d6 þ d4 þ ð0:61Þ2 LSI ¼ ðd5 ðd3 d6 ÞÞ2 þ ððd2 þ 0:078Þ d4 Þ þ 3:44 ð13Þ þ ð0:61d4 þ d7 Þ d3 As shown in Eq. (12), the complex relationship between seven effective factors in landslide occurring in the study area can be simply presented by a few variables with arithmetical and mathematical operators. The best GP formulation (Eq. 12) was implemented to produce LSM of the study area, shown in Fig. 10.
5 Discussion and comparative analysis In this study, the landslide susceptibility analyses were implemented using the FR, LR, ANN, and GP methods for Zonouz district, East Azerbaijan, Iran. For this aim, the LSMs were firstly generated using four different weighting procedures in a GIS-based approach.
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Table 4 Results of GP modeling for different input variables Input variables
RMSE (normalized)
DC
Calibration
Verification
Calibration
Verification
Comb. (1)
0.0174
0.0202
0.749
0.771
Comb. (2)
0.0164
0.0187
0.831
0.819
Comb. (3)
0.0157
0.0179
0.850
0.833
Comb. (4)
0.0145
0.0164
0.887
0.882
Comb. (5)
0.0130
0.0155
0.905
0.886
Comb. (6)
0.0117
0.0140
0.920
0.907
Fig. 10 Landslide susceptibility map produced from GP method
Then, the area and percentage distribution of the susceptibility classes in the study area were determined as a result of the four different methods. Subsequently, the receiver operating characteristics (ROC) curves for all landslide susceptibility models were drawn, and the area under curves was calculated. For investigating the effect of each input parameters on the output, sensitivity analysis was implemented to produce the best LSM. The comparison of sensitivity analyses using different methods indicates that ANNs are powerful tools for sensitivity analysis of input
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541
Table 5 Relative distribution of susceptibility classes of the models used Model FR (%)
LR (%)
ANN (%)
GP (%)
18.85
15.75
14.60
17.50
34.60
28.50
26.95
28.75
27.70
35
34.60
32.25
18.85
20.75
23.85
21.50
parameters. But the major shortcoming of ANNs is the difficulty of interpreting the knowledge gained by such a black-box-type models. Because of credibility of an AI program frequently depends on its ability to explain, it is may be an essential and instructive mater to perform sensitivity analysis in the GP. The GP model may even provide additional insights into the problem at hand, and a user can find straight mathematical or logical relationships between some input and output. Sensitivity analysis results using ANN, and GP methods showed that slope and lithology have maximum effect on landslide occurrence. Also, obtained results using FR, and LR showed that slope and aspect have more effective than other parameters. The LSM has a continuous scale of numerical values, and there is a need to separate these values into possible classes. Various classifier systems exist for the conversion of the maps into one or more categories with the continuous data technique such as natural break, equal interval, standard deviation (Ayalew and Yamagishi 2005). The standard deviation classifier is proposed when the histogram of data values exhibits a normal distribution (Suzen and Doyuran 2004; Yalcin et al. 2011). As a result, the standard deviation classifier was used since the data values in the LSMs obtained using the FR, LR, ANN, and GP models show a normal distribution (Table 5). The landslide susceptibility map generated with FR model, which included 18.85 % of total area, is determined to be of low landslide susceptibility. Moderate, high, and very high susceptibility zones represent 34.60, 27.70, and 18.85 % of the total area, respectively. The landslide susceptibility map generated in LR model, which 14.60 % of total area, is determined to be of low landslide susceptibility. Moderate, high, and very high susceptibility zones make up 26.95, 34.60, and 23.85 % of the total area, respectively. The landslide susceptibility map created by ANN model contains 15.75 % of the total area, which is considered to be of low landslide susceptibility. Moderate and high susceptibility zones constitute 28.5 %, and 35 % of the total area, respectively. The landslide susceptibility map generated with GP model, which included 17.50 % of total area, is determined to be low landslide susceptibility. The moderate and high susceptible zones values are close to each other, 28.75 % and 32.50 %, respectively. The very high landslide susceptibility area is 21.50 % of the total study area.
6 Validation of the susceptibility maps For the verification procedure, LSMs produced by FR, LR, ANN, and GP methods were evaluated by comparing them separately with landslide testing data. Then, all the landslides that were not used in the training phase were selected as testing sites. Of the 190 landslides identified, 133 (70 %) cases were used for the model validation. There are
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Fig. 11 AUC representing quality of the models used Table 6 Comparison of different landslide susceptibility modeling Model
Model type
Input variables
RMSE (normalized)
DC
Calibration
Verification
Calibration
Verification
FR
Linear
d1, d2, d3, d4, d5, d6, d7
0.0133
0.0153
0.826
0.874
LR
Linear
d1, d2, d3, d4, d5, d6, d7
0.0141
0.0159
0.803
0.858
ANN
Nonlinear
d1, d2, d3, d4, d5, d6, d7
0.0121
0.0142
0.916
0.901
GP
Nonlinear
d1, d2, d3, d4, d5, d6, d7
0.0117
0.0140
0.920
0.907
different ways to validate LSM with mathematical and statistical tools. One of the useful methods for representing the quality of deterministic and probabilistic detection, especially for landslide susceptibility assessment, is receiver operating characteristics (ROC). The area under ROC curve (AUC) characterizes the quality of a forecast system by describing the system’s ability to anticipate correctly the occurrence or nonoccurrence of predefined ‘‘event’’ (Yesilnacar and Topal 2005). The ROC curve plots the false positive rate on X-axis and 1-the false negative rate on the Y-axis. It shows the trade-off between the two rates (Biggerstaff 2000). To obtain the relative ranks for each prediction pattern, the calculated index values of all the pixels in the study area were sorted in descending order. If the AUC is close to 1, the result of the test is excellent. On the contrary, the closer the AUC to 0.5, the fairer the result of the test is. The results of the ROC curve test are illustrated in Fig. 11 for the implemented methods. These curves indicate that the map obtained by GP model has relatively higher prediction performance than the other methods. ROC plot assessment results show that in the susceptibility map using GP method, the AUC is 0.9327. Also, in the susceptibility maps using ANN, FR, and LR methods, the AUCs are 0.9327, 0.8942, and 0.8757, respectively. Table 6 indicates the comparison of the best obtained results using FR, LR, ANN, and GP methods using seven effective factors in the study area. It can be concluded that the selection of the accumulation effective parameters in GP and ANN models has an important role on the accuracy of the final results. Furthermore,
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results indicate that nonlinear-based models (e.g., GP, ANN) are more suitable than those of linear models (e.g., FR, LR), which cannot cope with nonlinear characteristics of the landslides occurring. Also, GP model gives better results than ANN, FR, and LR models regarding the spatial distribution of the susceptibility areas. It is reasonable that the data processing via GP method, beside the capability of GP in giving insight into the relationship between input and output data, leads to a more realistic landslide susceptibility modeling. Since the GP method, as an adaptive evolutionary method, allows escaping to trap in suboptimal, unsatisfactory local solutions, its results are more accurate than those of the FR, LR, and ANN models.
7 Conclusions There are various possible causes for landslide occurrence, with complex inter-relations. Hence, it is a difficult task to produce LSMs on regional scale, and the degree of experience of the person and the efficiency of the work are very important. The object of this study was the comparison of four conventional methods, namely FR, LR, ANN, and GP used for landslide susceptibility mapping for the Zonouz Plain, East Azerbaijan, Iran. These methods pose some distinct advances for analyzing complex geoscience problems and have proven to be applicable and accurate for landslide susceptibility assessment. For generating LSMs in the study region, seven effective factors were considered as lithology, slope, elevation, land cover, aspect, distance to stream, and distance to road, for which maps were derived using various GIS tools. According to the GP method, the slope and lithology parameters scored higher than the aspect, landcover, elevation, distance to stream, and distance to road were implicated in the occurrence of landslide phenomena in the study area. Therefore, we believe that the GP can be used to generate landslide susceptibility map, to gain insight about the dominant processes in geoscience systems, and it may even be used as a creative tool to help formulating more practical and parsimonious on geoscience models. In this study, four landslide susceptibility classes, i.e., low, moderate, high, and very high susceptibility for land sliding, were derived using the standard deviation classifier. Then, LSM was generated by FR, LR, ANN, and GP methods. As a result, the LSMs produced by FR, LR, ANN, and GP methods included 18.85, 23.85, 20.75, and 21.50 % of total area are found to have very high landslide susceptibility, respectively. Also, the LSM produced by GP method, including 53.75 % of total area, was determined to be of high and very high landslide susceptibility with GP method. Finally, all of the LSMs were verified by comparing with known landslide locations not used for training the models. The assessment of AUCs indicated that the prediction accuracy of LSMs produced by FR, LR, ANN, and GP methods were 0.8942, 0.8757, 0.9237, and 0.9327 %, respectively. It is obvious that FR and LR methods are basically linear, and they have a limited ability to capture nonlinearity and complexity of landslide phenomenon. On the other hand, GP model led to better result than those of ANN, FR, and LR models and it can easily handle qualitative variables making it widely used in integrated analysis of spatial data from multiple sources for generating LSMs. Furthermore, in the field of searching for suitable formula for quantitative description of physical phenomena, GP with inherent evolutionary rules can play an important role. This type of modeling prepares a proper area for finding touch-based and descriptive mathematical formula for complex data set. Moreover, due to the uncertainty of the landslide susceptibility assessment, the conjunction of the GP and ANN models could provide useful results for landslide susceptibility assessment.
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Acknowledgments Authors would like to thank two anonymous reviewers for their constructive comments, which helped to improve the quality of the manuscript.
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