Introduction

Landslides are one of the most destructive natural hazards and very sensitive to climate change and urban expansion, particularly in mountainous terrain (Keefer and Larsen 2007). The Zhouqu to Wudu segment along Bailong River basin is located at the eastern edge of Tibetan Plateau, in Southern Gansu, China. In response to plateau uplift and river erosion, high mountains with steep slopes, active tectonics, weak rock types and intense rainfall, the Zhouqu to Wudu segment along Bailong River basin is one of the areas most severely affected by landslide and debris flow disasters in China (Derbyshire et al. 2000). As the increased extreme climate events, rapid expansion of urbanization and enhanced tectonic activity in recent years, several large landslide events have occurred in the region. The most recent destructive example was the Gansu mudslide, which took place on August 8, 2010. This rainfall-triggered fast-moving debris flow thrust through the urban area, destroying all building along the flow, then rushed into the Bailong River and formed a barrier lake. The debris flow destroyed a large area and claimed at least 1287 lives (Yu et al. 2010; Bai et al. 2013; Cui et al. 2013). Therefore, mapping areas susceptible to landslides is essential for effective land-use planning, disaster management and hazard mitigation in this area.

The landslide susceptibility (LS) mapping technique can be grouped into four categories: landslide inventories, heuristic, statistical and deterministic. Overviews of these categories and their advantages and disadvantages can be found in many publications (Carrara et al. 1995; Soeters and van Westen 1996; Guzzetti et al. 1999; Chacón et al. 2006; Bai et al. 2010; Yilmaz 2010). Within these techniques, statistical methods have been widely applied to determine the landslide susceptibility zones. The statistical methods relying on the basic assumption that environmental factors led to slope failure in the past are susceptible to landslides in the future (Varnes 1984) and are considered to be more suitable for LS mapping over large and complex terrains (Van Westen et al. 2006; Thiery et al. 2007). The bivariate weight of evidence (WoE) was the most favorable bivariate model that could be used to assess the relationship between different categories of each factor and landslide occurrence. This robust and flexible mapping approach has been adopted by numerous landslide studies (Van Westen et al. 2003; Süzen and Doyuran 2004; Thiery et al. 2007; Regmi et al. 2010; Kayastha et al. 2012; Ozdemir and Altural 2013). Among the most popular and widely used statistical method is the logistic regression (LR) as its simple form to solve the complex problem (e.g., landslide occurrence), this method has been applied for many LS zonation at local and regional scale (Dai and Lee 2002; Lee 2004; Ayalew and Yamagishi 2005; Greco et al. 2007; Bai et al. 2010; Kavzoglu et al. 2014). The LR determines the weight of landslide causal factors based on the relative contribution of each in the presence or absence of landslides within a defined land unit. More recent advances in knowledge-based techniques including fuzzy logic, artificial neural networks, decision trees, and support vector machines have been also applied for LS mapping. Specifically, support vector machine (SVM) was a recently developed machine learning (non-parametric technique) tool, which is based on statistical theory and has enhanced ability to solve the nonlinear problem. It is a particularly suitable means of solving the highly complicated relationship between a landslide and its conditioning factors and was preferred for landslide susceptibility mapping (Yao et al. 2008; Yilmaz 2010; Xu et al. 2012; Pourghasemi et al. 2013; Pradhan 2013; Peng et al. 2014).

Different statistical models provide various results because the predictions of the model are largely determined by the model applied even if the datasets are the same. In such a case, in order to obtain reliable result (for example, results with better prediction accuracy and more realistic which are more suitable for the practical application) in a given region, a comparative study of LS mapping using different methods is necessary and can be highly significant. In the scientific literature, some studies compare the prediction and interpretation capabilities of different methods and techniques for LS assessment (Yalcin 2008; Nandi and Shakoor 2010; Yalcin et al. 2011; Akgun 2012; Mohammady et al. 2012; Schicker and Moon 2012; Hong et al. 2016; Paulín et al. 2016; Youssef et al. 2016). However, LS models include uncertainties and limitations in determining the spatial and temporal risks inherit in areas sensitive to geohazards; in addition, the results of the LS models have seldom been compared with or evaluated by the regional surface deformation information which can be obtained by remote sensing technique such as Interferometric Synthetic Aperture Radar (InSAR) (Kincal et al. 2010). It is necessary to apply more efficient techniques to gain more accurate results to evaluate the model result; this will support a more effective management of geohazards and enable safer land planning.

The main objective of this study is to obtain a reliable LS map in Zhouqu to Wudu segment along Bailong River basin, a region that is seriously affected by landslides. For this purpose, landslide susceptibility maps were prepared by three different statistical methods including WoE, LR and SVM. The results of these models will then be evaluated by the deformation signals measured by the Small Baseline Subset InSAR (SBAS-InSAR) and Receiver Operating Characteristic curve (ROC).

Study area

The Bailong River catchment was the secondary tributary of the Yangtze River. The reach from Zhouqu to Wudu with an area of 5739 km2 in southern Gansu (Fig. 1), being the region most susceptible to landslide, was selected for analysis. The study area is located in the middle south of the west wing of Qinling orogeny. The dominant landform is alpine canyons, with elevation range from 835 to 4577 m asl. A wide variety of lithological strata with complex structure are present, including materials from the Silurian, Devonian, Carboniferous, Permian, Triassic, Mesozoic Era and Quaternary ages (Fig. 2). In particular, the Silurian phyllite, slate and schist are well known for their high susceptibility to landslide. The study area was strongly controlled by Qinghai–Tibet tectonic belt and Wudu arc-shaped structure and affected by the tectonic uplift of the Qinghai–Tibet plateau (Derbyshire et al. 2000). This segment lies within a seismically active belt, in which the historical Tianshui earthquake in 1654 (Ms = 8.0) and Wudu earthquake in 1879 (Ms = 8.0) were located and in addition, the 2008 Wenchuan earthquake that triggered a great number of landslides and caused movement of abundant loose debris as well as weakening the stability of the slopes in the study area (Xu et al. 2013). Study area receives average annual rainfall ranges from 500 to 900 mm, and 80% of the total rainfall concentrated in the period from June to September (Bai et al. 2013). Human activities are mainly concentrated along the banks of the Bailong River or valley floors, such as Tanchang, Zhouqu and Wudu (the county town). The main land cover types consist of cultivated land, grass and forest lands.

Fig. 1
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Location of the study area

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Fig. 2
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Geological map of the study area

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Data acquisition

Landslide inventory map

In this research, the landslides were detected in the study area by interpretation of SPOT 5 images (scanned on 24th March 2009 with 2.5-m resolution), analysis of available data and extensive field surveys (Chen et al. 2014). The locations of the individual landslides were drawn on at a scale of 1:50,000. Most of the landslides are deep-seated rotational or translational and are generally large scale [according to Varnes’ (1984) classification criteria; Fig. 3], with minimum and maximum areas of 0.12 and 1.75 km2, respectively. In the study area, 375 landslides were delineated in the inventory map (Fig. 1). The inventory map shows only deep-seated landslides and does not include small, shallow landslides, because the former exhibit high risk in the area and are therefore of major concerns. Shallow landslides are more frequent compared to the deep-seated and require high-resolution imagery to acquire their inventories.

Fig. 3
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Typical large deep-seated landslide with potential risk in the study area: a suoertou landslide, b nanshan landslide, c hongtupo landslide, d sanjiadi landslide

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Landslide conditioning factors

Seventeen conditioning factors related to landslide occurrence were considered: elevation, slope angle, slope aspect, slope curvature, roughness, lithology, distance from fault, fault density, peak ground acceleration—PGA, distance from drainage, drainage density, topographic wetness index—TWI, specific catchment area—SCA, rainfall, settlement density, land cover and normalized difference vegetation index—NDVI. These variables were selected based on the previous study of LS mapping in Bailong River Basin (Bai et al. 2012; Chen et al. 2014).

Topography

Topography controls the spatial variation of soil moisture and the groundwater flow, which plays a significant role in landslide occurrence. (Dai and Lee 2002).

Topographic factors including elevation, slope, aspect, slope curvature and roughness were extracted or calculated based on a digital elevation model (DEM) with 30 m × 30 m resolution. The DEM was created using 1:50,000 scale topographic maps (Fig. 4a–c).

Fig. 4
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Landslide and PCA selected factors applying zonal statistics in ArcGIS a elevation, b slope, c aspect, d distance from fault, e lithology group, f precipitation, g distance from drainage, h land-use type, i settlement density

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Geology

Tectonic structure influences the spatial distribution of landslide in this area (Chen et al. 2014). The distance from faults was calculated based on the 1:200,000 geological map, which is the Euclidean distance from the fault (Fig. 4d). The fault density was also calculated in ArcGIS. PGA map derived from the National Seismological Bureau (Lu et al. 2010; Bai et al. 2012) was applied to assess the correlation between landslide and earthquake acceleration on the ground.

Lithology plays a significant role in the distribution of landslides and is associated with the properties of slope-forming materials such as rock mass strength and structure. Geological map of scale 1:200,000 has been divided into five categories (Fig. 4e) according to different lithologies present in the study area (Chen et al. 2006).

Hydrology

Rainfall data from 224 rainfall gauges surrounding the study area were available in this research (Fig. 4f). The rain gauge in the higher elevation are lacked as the stations are mainly concentrated in the river valley. Multi-temporal rainfall data at interval of 6 h were interpolated using spatial Kriging within ArcGIS.

Distance from drainage is the Euclidean distance from the stream network; drainage line density was calculated using ArcGIS 9.3 (Fig. 4g). The TWI and SCA were also calculated based on the topographic data.

Human activities

Land cover is widely considered as an important factor for landslides because it is correlated with their hydrological and mechanical effects. Land-use-type data were processed with supervised classification in ENVI software from Landsat TM5 imagery with a 30-m resolution, which was then verified by field survey (Fig. 4h).

Human activities concentrated in or nearby the towns such as excavation and ramp loading can cause slope instability. Settlement density was considered as another indicator of human activities. Based on the residential data, the settlement density was then computed using ArcGIS (Fig. 4i).

Ecological

The NDVI is a measure of surface reflectance and gives a quantitative estimate of the vegetation growth and biomass and was calculated based on Landsat TM5 image data, which reflects the relation between the vegetation condition and landslides.

Modeling strategy

In this study, LS maps were generated using GIS-based WoE, LR and SVM methods. In order to obtain reliable results, 80% of the landslides were randomly selected to train the model, and an equivalent number of slope units situated outside of the landslides were randomly selected in the areas without landslides.

Selection of major and independent parameters

In order to select the significant and independent factors, principal component analysis (PCA) in combination with Chi-square test was adopted. As a consequence, 17 conditioning factors related to landslide occurrence were applied for PCA analysis. Before the Chi-square test was conducted, the major factors contribute to landslide occurrence had to be classified into different classes, and the maximum likelihood ratio method proposed by Chung and Fabbri (2003) and Chung (2006) was used.

LS mapping using three models

Weight of evidence (WoE)

WoE is a bivariate method using the statistical approach, known as log-linear form of the Bayesian probability model, to estimate the relative importance of evidence (Bonham-Carter 1994).

The WoE approach was employed to calculate the weight of a certain category of a factor map related to the landslide occurrence, expressed as follows:

$$W_{i}^{ + } = \log_{e} \left( {\frac{{P\left\{ {F\left| L \right.} \right\}}}{{P\left\{ {F\left| {\overline{L} } \right.} \right\}}}} \right)$$
(1)
$$W_{i}^{ - } = \log_{e} \left( {\frac{{P\left\{ {\overline{F} \left| L \right.} \right\}}}{{P\left\{ {\overline{F} \left| {\overline{L} } \right.} \right\}}}} \right)$$
(2)
$$W_{i} \, = \, W_{i}^{ + } - \, W_{i}^{ - }$$
(3)

where P is the landslide probability, F is the presence of landslide conditioning factor, \(\overline{F}\) is the absence of landslide conditioning factor, L is the presence of landslide and \(\overline{L}\) is the absence of landslide. W + i and W − i indicate that the causative factor is present (positive correlation) and absent (negative correlation), respectively. C (contrast, W i ) is determined by the difference between W + i and W − i .

The continuous variables were classified into different categories using the maximum likelihood ratio method proposed by Chung and Fabbri (2003). W + i , W − i and C for each class of the factors were calculated based on Eqs. (1)–(3) (Table 1).

Table 1 Likelihood ratio classified factor categorical and WoE calculated weight for each class
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As the WoE method is restricted by the independence of the input variables, the conditional independence of the major influence factors that contribute to landslide was further examined through pair-wise comparison using Chi-square statistics. Two steps, including conversion of all factors causing landslides into binary mode and preparation of the 2 × 2 contingency table for all possible pairs of the primary causative factors, should be conducted when the Chi-square test is executed at the 99% significance level and 1 degree of freedom. If the χ 2 value in the contingency table is below 6.63, the pair of dichotomous predictor patterns is independent (Oh and Lee 2010). The studentized value of C referred as the ratio of C to its standard deviation S(C) need to be computed before dichotomous transform (Bonham-Carter 1994). On the basis of the inflection point in the C/S(C) graph, classes which are more susceptibility to landslide were assigned to the class given the value W + with the sort have maximum C/S(C). Conversely, W − with the same rating was assigned to the class less sensitive to landslide occurrence.

Logistic regression model (LR)

The LR is one of the most widely applied multivariate methods in LS mapping as it involves a multivariate regression between a dependent variable and several independent variables, and can yield less biased results (Hosmer and Lemeshow 1989; Atkinson and Massari 1998). In the case of LS mapping, logistic regression can determine the best-fit model to describe the relation between the dependent variable (presence or absence of a landslide) and a set of independent parameters, such as slope angle, lithology and distance to drainage (Ayalew and Yamagishi 2005). Furthermore, the regression coefficient determined in the logistic regression can be interpreted as a measure of the relative importance of the independent variables. The logistic model representing the maximum likelihood regression model can be expressed in its simplest form as:

$$P = \frac{1}{{1 + e^{ - z} }}$$
(4)

where P is the probability of an occurrence (landslide) that varies from 0 to 1; z is defined as the following equation:

$$z = b_{0} + b_{1} x_{1} + b_{2} x_{2} + \cdots + b_{n} x_{n}$$
(5)

where b 0 is a constant, n is the number of independent variables, x i (i = 1, 2, 3, …, n) represents the value of the independent variable, and b i (i = 1, 2, 3, …, n) is the slope coefficient of the model.

Support machine learning (SVM)

The SVM is a machine learning method which was firstly proposed by Vapink (1995). It is based on the statistical approach in order to find an optimal hyper-plane for separating two classes (Kavzoglu et al. 2014). A more detailed SVM algorithm for landslide assessment has recently been depicted (Yao et al. 2008; Marjanović et al. 2011; Xu et al. 2012); it can be summarized as follows:

Consider a set of linear separable training vectors x i (i = 1, 2,…,n) consisting of two classes, denoted as y i  = ± 1. The goal of the SVM is to search for an n-dimensional hyper-plane differentiating the two classes by the maximum gap. Mathematically, it is expressed as:

$$\frac{1}{2}\left\| {\left. w \right\|} \right.^{2}$$
(6)

subject to the following constraints:

$$y_{i} ((w \cdot x_{i} ) + b) \ge 1$$
(7)

where ‖w‖ is the norm of the normal of the hyper-plane, b is a scalar base, and (·) denotes the scalar product operation. Introducing the Lagrangian multiplier, the cost function can be defined as:

$$L = \frac{1}{2}\left\| {\left. w \right\|} \right.^{2} - \sum\limits_{i = 1}^{n} {\lambda_{i} } (y_{i} ((w \cdot x_{i} ) + b) - 1)$$
(8)

where λ i is the Lagrangian multiplier. The solution can be achieved by dual minimizing of Eq. (8) with respect to w and b through the standard procedures; the detailed discussions can be found in Vapink (1995) and Tax and Duin (2002).

For application to a complicated non-separable problem, the Slack variable ξ i can be introduced to modify the following limitation:

$$y_{i} ((w \cdot x_{i} ) + b) \ge 1 - \xi_{i}$$
(9)

And modification of Eq. (6) is as follows:

$$L = \frac{1}{2}\left\| {\left. w \right\|} \right.^{2} - \frac{1}{vn}\sum\limits_{i = 1}^{n} {\xi_{i} }$$
(10)

where v(0, 1) is introduced to account for misclassification. In addition, Vapink (1995) brought in a kernel function K(x i , x j ) to account for a nonlinear decision boundary (Yao et al. 2008).

LS class rating

In this study, we applied the maximum likelihood ratio classification method (Chung and Fabbri 2003) to divide the LS values. The likelihood ratio classification method was then compared with the automated “natural break” methods in order to verify the robustness of this method. The latter method is conventional and widely used for classification of the susceptibility map (Schicker and Moon 2012). Relative landslide density (RLD) is derived from the ratio of percentages of total landslide area in each susceptibility category to the total area in the class and gives an indication of the goodness of fit. (Santacana et al. 2003; Arora et al. 2004)

$${\text{RLD}} = (n_{i} /N_{i} )/\sum ( n_{i} /N_{i} )$$
(11)

where n i is the sum of the landslide area with susceptibility level i, and N i is the total area of the susceptibility class i. By deriving RLD for each class, comparative charts for the two classifications method can be plotted.

Accuracy assessment

Future landslides provide a much better means of assessing the performance of the models. As there was no temporal information on the landslide dataset in this research, the spatiotemporal surface deformation which could reflect the activity of landslide to a certain extent was firstly applied to validate the three models. InSAR can be used to detect ground deformation by calculating the phase differences in complex SAR images acquired in similar geometric conditions, but at two different epochs. The SBAS-InSAR allows reliable deformation measurements to be obtained by implementing an easy combination of the SAR interferograms generated from an appropriate selection of SAR data pairs characterized by a small spatial and temporal baseline (Tizzani et al. 2007). The StaMPS (Stanford Method for Persistent Scatterers) package has proven its ability to study landslide dynamics even in a densely vegetated environment. In this study, the Delft Object-Oriented Radar Interferometric Software (DORIS) and StaMPS package were used to process 55 ENVISAT images from descending track 018 and 290 collected between November 2003 and September 2010, and the detailed data processing of SBAS-InSAR in the study area could be found at Zhang et al. (2016). Due to the decorrelation caused by layover and shadows in mountainous regions, we only selected areas of less rugged terrain in populated valleys as our SBAS-InSAR calculated areas (Zhang et al. 2016). The SBAS-derived mean velocity map of the Bailong River Basin is used for further model validation.

In order to access the models in a more quantitative way, landslides, other than those from the calibrating dataset with a total of 75 landslides and equivalent slope units, were randomly selected from the non-landslide locations and prepared for model verification. The receiver operating characteristic (ROC) curve which shows goodness of fit was also applied to assess the performance of the three LS methods.

Results

Principal and conditional independent factors

As shown in Table 2, nine factors including elevation, slope gradient, aspect, lithology, distance from fault, rainfall, distance from drainage, land-use and settlement density were identified as the main factors contributing to landslide occurrence and accounting for 79.3% of the total variance (Fig. 4). A multicollinearity diagnosis was further implemented to test the correlation for each of the major factors; the variance inflation factors (VIF) and tolerance (TOL) are two important indexes for multicollinearity diagnosis. According to Allison (2001), the variables with VIF > 2 and TOL < 0.4 were identified as multicollinearity with other factors; as a result (Table 3), nine major factors were found to be “independent” of each other.

Table 2 Total variance explained of the nine selected variables
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Table 3 Multicollinearity diagnosis indexes for principle variables
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Table 4 summarizes the result of the Chi-square test, the χ 2 values higher than 6.64 reflecting a stronger association with other factors. Of the 9 key influencing factors, only six factors (consisting of elevation, slope, aspect, distance from fault, lithology and settlement density) were found to be extremely independent of each other; these six factors were utilized to construct the three LS mapping models in this research. The outcome shows that the influencing factors including elevation, rainfall and land-use that were identified as independent of each other based on the VIF and TOL judgment criteria when linear regression was undertaken; in contrast, the three factors are closely correlated within the Chi-square test. It could be concluded that when the conditional independent of the factors was required, the Chi-square test was more effective to detect the correlation of the input factors in this research.

Table 4 Pairwise Chi-square statistics of the nine principal factors
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LS class rating and LS maps

Figure 5 shows the likelihood ratio curve of landslide probability with uptrend across the whole range; this is consistent with the real condition that higher probability corresponds to larger likelihood ratio. Their cutoff points were determined according to their characteristic inflection point (Table 5). Susceptibility maps can be classified into the following categories: very low susceptibility, low susceptibility, moderate susceptibility, high susceptibility and very high susceptibility. On the basis of the charts shown in Fig. 6, it is clear that in both the likelihood ratio and natural breaks classifications considered here, the likelihood ratios are apparently superior for the LR as this method produces the highest densities in both the high and very high classes and the lower densities from the very low to the moderate class. In the case of the WoE and SVM, the likelihood ratios and the natural breaks are very similar relative for these two models. Both classified methods in the WoE and SVM show low density in the very low and low susceptibility classes, and peak relative density in the very high class in both likelihood ratio and natural breaks. These results indicate that the likelihood ratio method can also result in robust classification in all three models, providing a categorization that most sensitively reflects the true distribution of landslides in the region.

Fig. 5
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Empirical likelihood ratio classification of the three models a WoE, b LR and c SVM, (VL very low, L low, M moderate, H high, VH very high)

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Table 5 Landslide probability range of different LS class for the three models
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Fig. 6
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Comparison of the relative density for the three models applied using likelihood ratio and natural breaks classified methods a WoE, b LR and c SVM

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The LS maps produced by the three models (WoE, LR and SVM) are presented in Fig. 7a–c, while Table 6 presents the numeric results.

Fig. 7
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Landslide susceptibility mapping generated by a WoE, b LR and c SVM

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Table 6 LS class distribution of the three models
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Accuracy evaluation

To evaluate the three LS models, the deformation information derived from SBAS-InSAR was overlaid onto the susceptibility maps. Since the majority of the basin has been a rural environment with its consequent vegetation cover, high slope inclination, and unsuitable orientation, most of the region has no radar coverage (Colombo et al. 2006) and single descending acquisition data therefore lead to an absence of information on movement on NE-facing slopes (Meisina et al. 2008; Zhang et al. 2016). The mean velocity maps of the Bailong River Basin were constructed (Fig. 8a–c). The velocity was extracted along the line of sight (LOS) of the satellite, which is 23° on average from the vertical. Reliability of the high precise deformation derived from the SBAS-InSAR in this study area has been proved by field survey (Zhang et al. 2016). In Fig. 8a–c, red (−25 to −8 mm/year) and orange (−8 to −2 mm/year) points indicate subsidence, green points (−2 to 2 mm/year) represent stable, and light blue (2–7 mm/year) and blue (7–22 mm/year) points imply uplift. It should be noted that the density of SBAS-InSAR points does not indicate the magnitude of deformation. The substantial clusters of SBAS-InSAR points mostly correspond to more populated areas in the river valley (e.g. towns of Zhouqu, Wudu) which possibly exhibit high radar backscatters from man-made buildings, and also the slowly decorrelating filtered phase (SDFP) points were not evenly distributed. It can be seen in Fig. 8a–c and Table 7 that there is a good correspondence of SDFP points to the LS models, 63.31, 60.71 and 65.16% of the deformation points (both subsidence and uplift) are located in areas classified by the LS models as high and very high susceptibility to landslide, for the WoE, LR and SVM, respectively, and the stable points correspond to the low and very low LS, for the WoE, LR and SVM were 0.49, 0.76 and 1.13%, respectively. It could be concluded that the SVM classified more instability slope as high LS level, and also more stable slope as low LS level. As a consequence, it indicates that the result of SVM is more reasonable and has a good engineering application value. Nevertheless, we also should believe that it is not appropriate to consider each deformation point in Fig. 8a–c to be a landslide or mass movement.

Fig. 8
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Landslide susceptibility maps overlaid with SBAS-InSAR derived deformation. a WoE, b LR, c SVM

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Table 7 Percentages of SDFP points versus landslide susceptibility classes for WoE, LR and SVM models
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Determination of the accuracy of different models applied in this study was also achieved by plotting ROC curves. The area under the ROC curve (AUC) can be used to assess the quantitative prediction accuracy. For the calibration set, the AUC values for the WoE, LR and SVM were found to be 0.797, 0.840 and 0.844, respectively (Fig. 9a), which indicates that the LR and SVM are models with a better training capability. With respect to the prediction skill, the three models show a similar tendency with regard to the calibration set. The AUC of the WoE is 0.777, while the AUCs of the LR and SVM methods are 0.812 and 0.830, respectively (Fig. 9b). Inspection of Fig. 9 clearly shows the similar performance of the LR and SVM. On this basis, it can be concluded that estimations drawn from the LR and SVM are relatively good in determining LS in the study area, whereas the WoE model is a relative poor estimator. The SVM model is with better prediction ability and is much more robust statistically. And this is consistent with the result evaluated by high precise deformation derived from SBAS-InSAR.

Fig. 9
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ROC curve evaluation of the model fit and predictive capability of the three models. a Calibration set, b validation set

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Discussion

The reliability of LS maps depends mostly on the quality of available data and on the model applied (Ayalew and Yamagishi 2005; Yilmaz 2010; Pourghasemi et al. 2013). As can be seen in Fig. 7, several landslides in Northwestern Zhouqu were classified into low to moderate LS level, and these landslides were not highlighted by an apparently increased LS level in any of the three models. This may be caused by the limited quality of input data: as shown in Fig. 4d, most of the landslides in Northwestern Zhouqu are located in limestone areas, and this stratum was classified as relative hard rock; however, the detailed rock property such as weathering rate and joint distribution could not be referenced in the current applied geological map. In addition, rain gauges in the Northwestern Zhouqu are mainly concentrated in the river valley, with no rain gauges emplaced at higher elevation areas (Fig. 4f). This may also influence the LS result to some extent. Therefore, better quality input data would be needed to solve this problem.

Model evaluation is a significant process for LS mapping, which determines whether the LS map could be applied for land planning and hazard mitigation; in addition, it could provide reliable basis on model comparison. Traditional evaluation mostly used the contemporaneous landslide or “future” landslide which were not applied for calibration to test the model performance; besides, these dataset could not reveal the real activity state of landslide. In this study, the surface deformation derived from the SBAS-InSAR was applied to evaluate the three LS models. The surface deformation can also reveal the dynamic deformation processes of landslides, and these activity states of landslides are with more concern to the decision maker. As seen from Fig. 8a–c and Table 7, for the three LS models, most of the deformation points correspond well to the high and very high LS levels. And it could also challenge the traditional view that the knowledge-based SVM was prone to overfitting (Brenning 2005; Pradhan 2013), however, in this study, more stable points (1.13%) corresponding to low and very low LS levels for the SVM when compared with the WoE and LR. This could provide significant support that the SVM is effective in predicting the slope units with deformation as high or very high LS level and also classifying the stable slope units as low and very low LS level.

However, there still are some limitations by applying the SBAS-InSAR for evaluating the model accuracy in this research. Firstly, most of the SDFP points were concentrated in the populated valley; in addition, these SDFP points also cover other deformation types including potential landslides, the movement of debris and subsidence (Zhang et al. 2016). Although some researches have made use of SAR interferometry for LS assessment or updating the risk map (Singh et al. 2005; Lu et al. 2014), how to efficiently integrate LS models and InSAR technique to obtain more reliable LS maps is still a problem. A potential solution might be to seek a strategy that could demonstrate the temporal deformation information, either with highly deformed history or with long-term stability, of landslides in the LS map. This could possibly be achieved by analyzing the relationship between the ground deformation which is obtained by time series analysis of PS-InSAR and SBAS-InSAR, and environmental factors with statistical models.

The lack of interpretability regarding the contribution of individual variables when applied to statistical methods for LS mapping has always been criticized. In the case of the three models used here, the importance of the different classes of the influencing factors related to slope instability could be highlighted in the WoE model (Table 1), as this method using an categorization to transform the nominal variables to numeric variable, the weighted value of each class could be obtained; the spatial distribution of LS obtained by the WoE models was mainly influenced by elevations from 835 to 1150 m, slope ranges between 9° and 20°, aspect between 270° and 315°, the 0–800 m class of proximity to faults, lithology with phyllite, slate, mudstone, thin limestone and siltstone groups, and settlement more than 0.3, as relatively high weights assigned to these classes. In addition, the most important contributing factors could also be identified from the WoE model; for example, the settlement density, elevation and lithology were found to be having the higher maximum contrast weight (Table 1). With regard to the LR, each factor can be assigned a weight; there is an element which cannot be attributed to any one factor but to the group as a whole which is represented by the model intercept in LR (Schicker and Moon 2012). Therefore, relative weights of the each influence factor can be derived from the model (Table 3). The coefficient for the elevation, settlement density and distance from faults was relatively higher in the LR model, indicating that these three factors dominated the results issued by the LR model. For the SVM, it is not an interpret model just like a black box which cannot provide relative weights for the variables.

Conclusion

In this study, three statistical models, including the WoE, LR and SVM pertain to the bivariate statistical, multivariate statistical and knowledge-based statistical methods, respectively, are compared on LS mapping in a study of the Zhouqu to Wudu segment in Bailong River Basin, China. Six major independent explanatory variables, i.e., elevation, slope, aspect, distance from fault, lithology and settlement density, related to landslide occurrence were selected after implementation of the PCA and Chi-square test. The accuracy of the models was evaluated by the SBAS-InSAR derived high precise deformation and ROC. Results show that the three LS maps agree well with our SBAS-InSAR-derived deformation maps, most of the deformation points (subsidence or uplift) are correspond to the high and very high LS level, which are 63.31, 60.71 and 65.16% for the WoE, LR and SVM, respectively, particularly more points of stable correspond to the low and very low LS level for the SVM. The AUCs values for the prediction of the WoE, LR and SVM are 0.777, 0.812 and 0.830, respectively. The accuracy evaluation provides a strong support of SVM with better performance on LS mapping in the study area.

With regard to their operational and interpretation capability, the WoE is a simple bivariate model, whereas the LR and SVM are much more complicated when applied to LS mapping. The WoE is effective in determining the contribution of different class rates in the controlling factors, which derives the class of factors consisting of the elevation from 835 to 1150 m, slope range from 9° to 20°, aspect between 270° and 315°, the class 0–800 m of proximity to fault, lithology with phyllite, slate, mudstone, thin limestone and siltstone group, and settlement density more than 0.3 most contributed to landsliding in the study area; with regard to the LR, the relative weights in each factor as a group can be derived reveal that factors including elevation, settlement density and distance from fault played major roles in landslide occurrence and distribution. Finally, the SVM is not an interpretable model; rather, it is like a black box in which the internal processing steps are difficult to follow.

To sum up, the SVM with better prediction ability was the most reasonable model for LS mapping of the study area, whereas the WoE and LR have better interpretation capability could be applied to enhance our understanding between the landslide occurrence and the landslide conditioning factors. Thus, the SVM LS maps could be used as the preliminary basis by decision makers, planners, and engineers to avoid and/or minimize the damage and losses caused by existing and future landslides. However, site-specific studies need to be undertaken so as to complement the assessment and when the results of these models are taken into practical engineering applications.