Introduction

Landslides are one of the damaging natural hazards occurring in many countries and lead to the loss of life and property. According to García-Rodríguez et al. (2008) and Dou et al. (2014), the annual loss of property caused by landslides is greater than other types of natural hazards, such as earthquakes and floods. Throughout the world, landslides cause hundreds of billions of dollars in damage and thousands of casualties and fatalities each year; additionally, they cause large environmental damages each year (Aleotti and Chowdhury 1999). In Shangnan County, China, landslides are occurring frequently mainly due to anthropogenic activities; thus, they have a great impact on the local economic and environmental developments. Currently, thousands of people are still threatened by landslides and live under the landslide-prone areas in the study area. Thus, it is essential to prepare landslide susceptibility maps for mitigating of landslide hazards in such areas.

Generally, landslide susceptibility mapping can be prepared as qualitative or quantitative methods, and direct or indirect techniques (Fell et al. 2008; Kayastha et al. 2013; Nourani et al. 2014). The reliability of landslide susceptibility maps depends on the quality and amount of available data, the selection of methodology of modeling, and the working scale (Baeza and Corominas 2001). The landslide susceptibility modeling methodology could be categorized into heuristic, deterministic, and statistical methods (Guillard and Zezere 2012; Regmi et al. 2014a). The heuristic method, which is established based on the assumption that the relationships between landslide susceptibility and the preparatory variables are known and are specified in the models, is a direct or semi-direct mapping methodology (Regmi et al. 2014a). This method was used in many landslide susceptibility researches (Ruff and Czurda 2008; Jaiswal et al. 2013).

In deterministic or physically based analysis, according to Regmi et al. (2014a), the landslide is determined employing slope stability methods in the form of calculating safety factors. These methods need a large number of detailed input factors to build the model; thus, these methods could be appropriate for small watersheds (Regmi et al. 2014b). Geotechnical and groundwater features are two main bases of the deterministic methods. Mathematical methods are employed to define the factor of safety of the unstable slopes (Gökceoglu and Aksoy 1996) and slope stability methods are employed for defining the landslide hazard (Clerici et al. 2006). The most important weakness of geotechnical and safety factor-based methods is that these methods are feasible only for areas where landslide types are simple and geomorphic and geologic features are relatively similar (Van Westen and Terlien 1996). Moreover, the mentioned approaches are difficult to do in regional landslide susceptibility investigations. These models were also used by many researchers (Gökceoglu and Aksoy 1996; Cervi et al. 2010; Jia et al. 2012; Armaş et al. 2014; Akgun and Erkan 2016). Considering the mentioned weak points of deterministic models, in this study, we employed data mining models for landslide susceptibility mapping.

Statistical models, which are the most commonly used approaches worldwide, have also been employed in landslide susceptibility evaluation using GIS, such as the logistic regression (Akgun 2012; Xu et al. 2012b; Devkota et al. 2013; Ozdemir and Altural 2013; Park et al. 2013; Grozavu et al. 2013; Talaei 2014; Chen et al. 2016a; Karimi Sangchini et al. 2016), frequency ratio (Vijith and Madhu 2008; Poudyal et al. 2010; Pourghasemi et al. 2014; Regmi et al. 2014a, b; Chen et al. 2015), certainty factor (Kanungo et al. 2011; Devkota et al. 2013; Pourghasemi et al. 2013d), weights of evidence (Dahal et al. 2008; Ozdemir and Altural 2013; Pourghasemi et al. 2013d; Regmi et al. 2014a), statistical index (Yilmaz et al. 2012; Regmi et al. 2014a), evidential belief function (Ding et al. 2016; Pourghasemi and Kerle 2016), and index of entropy models (Mihaela et al. 2011; Devkota et al. 2013; Jaafari et al. 2014; Pourghasemi et al. 2012c).

In addition, some other widely accepted methods including an artificial neural network (ANN; Pradhan and Lee 2010; Yilmaz 2010a; Tsangaratos and Benardos 2014; Nourani et al. 2014; Tien Bui et al. 2015; Gorsevski et al. 2016), an analytical hierarchy process (Pourghasemi et al. 2013b; Park et al. 2013; Mandal and Maiti 2015; Chen et al. 2016b), fuzzy logic (Pourghasemi et al. 2012b; Guettouche 2013; Zhu et al. 2014; Kumar and Anbalagan 2015), support vector machine (Yilmaz 2010b; Marjanović et al. 2011; Xu et al. 2012a, b; Pradhan 2013; Peng et al. 2014; Tien Bui et al. 2015; Chen et al. 2016d), general additive model (Park and Chi 2008; Petschko et al. 2012), random forest (RF; Youssef et al. 2015b; Chen et al. 2017), and neuro-fuzzy methods (Pradhan 2013; Lee et al. 2015) have also been applied for landslide susceptibility evaluation.

In summary, in order to mitigate landslide hazards, all these models can be used to prepare landslide susceptibility maps. On the other hand, consideration of literature review on landslide susceptibility evaluation shows that there is no paper comparing the performance of multivariate adaptive regression spline (MARS) and RF models in landslide susceptibility mapping so far. Therefore, the main difference between the present study and the methods described in the aforementioned literature is that MARS and RF models were applied for landslide susceptibility mapping in the study area and their performances were compared together. Also, we tried to determine weight of each conditioning factor and its effect on landslide occurrence in the study area by an RF data-driven method.

Study area

The study area is located in Shangnan County, China, between latitudes 33°06′–33°44′N, and longitudes 110°24′–111°01′E (Fig. 1). It covers roughly a surface area of 2307 km2. The altitude of the area ranges from 189 to 2050 m a.s.l. The landform can be classified into mountain, hill, and plain. The slope angles of the area range from 0° to 65°. The rivers of the study area belong to the Yangtze River basin. The mean annual rainfall according to a local station in the past 40 years is around 829.8 mm. Also, based on the records from China’s meteorological department (C.H. of China Meteorological Administration), the minimum and maximum rainfall occurs in December and July, respectively. The average mean annual temperature is 14.6 °C.

Fig. 1
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Location map of the study area

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In terms of geological background, the geological structure system of the study area is located at the boundary of the North China and the Yangtze plates. Therefore, the geological structure is complex and the tectonic deformation is intense. The faults of the study area have mainly a NW–SE direction. These faults divide the study area into several structural zones that affect the distribution of landslides and geological formations in the study area. There are many geological formations with different ages in the study area, which vary from Archeozoic to Cenozoic. The lithological units are mainly slate, phyllite, schist, gneiss, limestone, dolomite, sandstone, and intrusive rocks. According to Table 1, the softer metamorphic rocks and hard carbonate rocks comprise the highest percentages of the area (29.72 and 28.31%, respectively).

Table 1 Spatial relationship between landslide conditioning factors and landslide by frequency ratio model
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Methodology

As it was mentioned, the main objective of this study was to prepare landslide susceptibility maps in Shangnan County, China, using MARS and RF models. For this purpose, a flowchart of the applied methodology including the following steps is presented in Fig. 2, including landslide inventory mapping, gathering of the landslide conditioning factors, preparation of thematic layers in the GIS, determination of relationships between each conditioning factor and landslide inventory maps using a frequency ratio (FR), application of MARS and RF models in R statistical packages and landslide susceptibility mapping, evaluation of the prediction accuracy of the above models using receiver operating characteristics (ROC) curves, and selection of the best model.

Fig. 2
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Flowchart of the used methodology

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Data production

Landslide inventory map

Landslide inventories include information related to topics of the regional landslide locations, activity, types, and physical properties that are usually mapped with an associated database (Fell et al. 2008; Demir et al. 2015). Accuracy of the data related to landslide occurrences is very important for landslide susceptibility analysis, hazard, and risk. So, the first step in these analyses is landslide inventory mapping. In the landslide inventory, some historic information about landslide occurrences including the frequency, volumes, damage, and types of the landslide phenomena is the backbone of landslide susceptibility studies (van Westen et al. 2006; Youssef et al. 2014). In the present study, landslides were collected from historical reports, interpretation of aerial photographs, and extensive field surveys using the global positioning system (GPS) to locate the position of landslides. A total of 348 landslides were identified and mapped (centroid) in Fig. 1. From these 348 landslides, 244 (70%) locations (grid cells) were randomly selected for training of the models, and 104 (30%) were used for validation of the built models (Maps). 348 non-landslide points (grid cells) were randomly selected from the landslide-free areas, and were also randomly divided into a ratio of 70/30 (244/104) to build training and validation datasets. In the present study, the presence of landslides was assigned a value of 1, while the absence of landslide was assigned a value of 0. Finally, the values of all the landslide conditioning factors were extracted to landslide and non-landslide grid cells to build training and validation datasets for running the mentioned data mining techniques in R statistical packages.

The use of historical landslide inventories that summarize past multiple landslide events may enable a robust landslide susceptibility mapping because it reflects various environmental conditions, and the number of available data tends to be large (Malamud et al. 2004; Paudel et al. 2016). In the present study, detailed landslide data for more than 10 rainfall events occurred in years of 1998, 2000, and 2003–2015 have been used, which crossed a time span of more than 20 years. Besides, with highly developed remote sensing technology, multi-temporal aerial photographs have been used to map landslides after each rainfall event which were verified by field surveys. All these data sources ensure a reliable landslide susceptibility mapping for the study area.

According to our analyses in a GIS environment, the size of the smallest landslide is nearly 15 m2, whereas, the largest is more than 30,000 m2, while the average is 9600 m2. For the volume of the landslides, more than 90% of landslides are less than 100,000 m3, and more than 85% of the landslides are shallow-seated landslides (<6 m). The landslide area percentage (LAP), which is expressed as a percentage of the area affected by landslide activity, is LAP = (3.34 km2/2307 km2) × 100% = 0.145% (Xu et al. 2012b).

The quality of a landslide inventory is affected by its accuracy; however, determining the accuracy of the inventory does not have a specific standard (Galli et al. 2008). Some methods have been suggested in order to increase the accuracy of spatial inventories such as: (1) employing very high-resolution digital elevation models (DEMs) for analyzing surface morphology, (2) interpretation of satellite images, and (3) application of new tools for facilitation of field mapping.

Landslide conditioning factors

The selection of landslide conditioning factors depends on the characteristics of the study area, the landslide type, the scale of the analysis, etc. (Tseng et al. 2015). However, there is no agreement on the universal guidelines for selecting landslide conditioning factors (Xu et al. 2013). In the present study, the landslide conditioning factors were selected from those most commonly used in the literature to evaluate landslide susceptibility (Lee and Talib 2005; Xu et al. 2012a, b; Pradhan 2013; Pourghasemi et al. 2013b; Tien Bui et al. 2015; Hong et al. 2015, 2016; Chen et al. 2014, 2015, 2016c). Particularly, the results of satellite image interpretation and field surveys suggest the following 12 parameters: slope aspect, altitude, distance to faults, lithology, normalized difference vegetation index (NDVI), plan curvature, profile curvature, distance to rivers, distance to roads, slope angle, stream power index (SPI), and topographic wetness index (TWI). Therefore, these 12 landslide conditioning factors were selected in the present study and were standardized to the same size (30 × 30 m) for further analyses.

Slope aspect was selected as a landslide conditioning factor which represents the direction of slope (Ercanoglu et al. 2004; Pourghasemi et al. 2012a, b). The slope aspect of the study area was classified into nine directional classes as flat, north, northeast, east, southeast, south, west, southwest, and northwest (Fig. 3a). Altitude/elevation is another frequently used conditioning factor for landslide susceptibility analysis. Ercanoglu and Gokceoglu (2002) mentioned that altitude influences earth surface and topographic attributes which account for spatial variability of erosion, precipitation, soil thickness, and vegetation. In the present study, the elevation of the study area ranges from 189 to 2050 m (Fig. 3b). The faults are responsible for triggering a huge number of landslides due to the tectonic breaks that usually decrease the rock strength. In the study area, the distance to faults was prepared using the geological map and ranges from 0 to 17,526 m (Fig. 3c). Lithology is one of the most common influence factors in most landslide susceptibility studies. Since different lithological units have various landslide susceptibility values, they are very important in the landslide occurrences. The lithology map of the study area was extracted from existing geological maps. The study area is covered with several lithological units, and classified into five groups of harder metamorphic rocks, softer metamorphic rocks, hard carbonate rocks, hard intrusive rocks, and soft gravelly soils (Fig. 3d). The NDVI, as a conditioning factor, could be considered as a measure of surface reflectance and gives a quantitative estimate  of biomass and the vegetation growth (Yilmaz 2009a, b; Pourghasemi et al. 2013a). In this research, an NDVI map was derived from the Landsat 7/ETM+ images of Nov 4, 2014. The NDVI values vary from −0.23 to 0.71 in the present study area (Fig. 3e). Plan curvature is the curvature of a contour line which is formed by intersecting a horizontal plane with the surface (Conforti et al. 2014). Plan curvature influences the divergence or convergence of water during downhill flow (Yilmaz et al. 2012). In this study, the plan curvature was extracted from the DEM with a spatial resolution of 30 m in ArcGIS 10.0. The values of plan curvature range from −9.57 to 11.42 (Fig. 3f). Profile curvature depicts the curvature in the vertical plane parallel to the slope direction. This factor measures the rate of change of slope (Kritikos and Davies 2014). Therefore, it influences the flow velocity of water draining the surface and thus erosion and the resulting down-slope movement of sediment (Yilmaz et al. 2012). In this study, the profile curvature values vary from −11.93 to 11.43 and were also derived from the DEM in ArcGIS 10.0 (Fig. 3g). Runoff plays an important role as a triggering factor for landslides due to rivers being the main mechanisms that contribute to the occurrence of landslides in mountainous regions (Park et al. 2013). For the current study, buffer zones were created to determine the degree to which the streams affected the slopes and range from 0 to 4401 m (Fig. 3h). The distance to roads has been considered as one of the major anthropogenic factors influencing landslides occurrences (Demir et al. 2015). The creation of cut slopes during road construction disturbs the natural topology and affects the stability of the slope. In the study area, buffer zones were used to designate the influence of the road on slope stability and range from 0 to 9281 m (Fig. 3i). Slope angle is an important factor in assessment of slope instability, and it is frequently used in landslide susceptibility mapping (Lee and Min 2001; Saha et al. 2005; Althuwaynee et al. 2014; Guo et al. 2015). The slope angle map of the study area was prepared from the DEM and ranges from 0° to 65° (Fig. 3j). The SPI, a measure of the erosive power of water flow, assuming that discharge is proportional to the specific catchment area, is a compound topographic attribute (Conforti et al. 2011). The SPI values of the study area range from 0 to 28,323 (Fig. 3k). The TWI is another secondary topographic factor in the runoff model (Beven and Kirkby 1979; Moore et al. 1991). The TWI values were extracted from the DEM and vary from 2.69 to 30.31 (Fig. 3l).

Fig. 3
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Thematic maps of the study area: a slope aspect; b altitude; c distance to faults; d lithology; e NDVI; f plan curvature; g profile curvature; h distance to rivers; i distance to roads; j slope angle; k SPI; l TWI

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Fig. 4
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The error rate of the overall RF model [OOB: out of bag (black line), 0: absent landslide (red line) and 1: present landslide (green line)]

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Fig. 5
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The error rate of the overall RF model (OOB: out of bag, 0: absent landslide and 1: present landslide)

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Models

Frequency ratio (FR)

FR is based on the observed relationships between the distribution of the landslides and each landslide conditioning factor (Tay et al. 2014). The frequency ratios for the class or type of each conditioning factor were calculated by dividing the landslide occurrence ratio by the area ratio (Demir et al. 2013). Each factor’s ratio value was calculated using Eq. (1):

$${\text{FR}} = \frac{\text{Percentage of landslide }}{\text{Percentage of domain }}.$$
(1)

In this study, frequency ratio model was used to show the relationship between each factor’s subclasses and landslide occurrences. A higher FR value shows that the probability of landslide occurrence is higher in the class.

Multivariate adaptive regression splines (MARS)

MARS could be implemented in order to fit the relationship between output and input variables (Friedman 1991; Naghibi and Moradi Dashtpagerdi 2016). The MARS model applies a non-parametric modeling approach that does not need assumptions about the relationship’s form between the independent and dependent factors (Friedman 1991; Balshi et al. 2009). A MARS algorithm operates by splitting the ranges of the interpretive variables into regions and by generating a linear regression equation for each of the mentioned regions. Knots are the break values between regions, while the term bases function (BF) represents each distinct interval of the predictors. BFs are functions of the following form:

$${ \hbox{max} }\left( {0,x{-}k} \right){\text{ or max }}\left( {0,k{-}x} \right),$$
(2)

in which x is an independent variable and k shows a constant corresponding to a knot. The general phrase of MARS can be obtained as follows:

$$\hat{y} = \hat{f}\left( x \right) = \beta + \mathop \sum \limits_{m = 1}^{M} \alpha_{m} H_{m} (x),$$
(3)

where \(\hat{y}\) represents the dependent variable predicted by the function f(x), β is a constant, M shows the number of terms, and each of them formed by a coefficient α m , and H m (x) is an individual basis function or a product of two or more BFs (Conoscenti et al. 2015).

MARS models were developed in two steps. In the first step, the forward algorithm and basis functions are introduced to introduce Eq. 3. Many basis functions are incorporated in Eq. 3 to get better performance. The developed MARS can indicate an over-fitting problem due to a large number of basic functions. Then, in the next step, a backward algorithm, for hindering over-fitting, redundant basis functions are omitted from Eq. 3. MARS uses generalized cross-validation (GCV) to remove the redundant basis functions (Craven and Wahba 1979). The expression of GCV is calculated as Eq. 4:

$${\text{GCV}} = \frac{{\frac{1}{N}\mathop \sum \nolimits_{i = 1}^{N} \left[ {y_{i} - \hat{f}(x_{i} )} \right]^{2} }}{{\left[ {1 - \frac{C(H)}{N}} \right]^{2} }},$$
(4)

where N is the number of data points and C(K) corresponds to a complexity penalty that goes up with the number of BFs in the model and which is introduced as:

$$C\left( H \right) = \left( {H + 1} \right) + {\text{d}}H,$$
(5)

where d is a penalty for each BF covered in the model and H corresponds to the number of BFs in Eq. 2 (Friedman 1991).

Random forest (RF)

Classification trees are a non-linear technique for predicting a response by a set of binary decision rules that establish class assignment based on the predictors (Breiman et al. 1984). The RF multivariate statistical technique is a variation of the Bayesian tree or binary classification tree, because it considers a group (forest) of n trees to multiply the efficiency and predictive capability (Breiman 2001; Cutler et al. 2007; Trigila et al. 2015). The model was performed with the R statistical package (randomForest) which is suitable to cope with mixed variables, both categorical and numerical. Bootstrapping is a way of assessing the accuracy of a parameter estimate or a prediction. The RF uses the bagging technique (bootstrap aggregation) to choose, at each node of the tree, random samples of variables and observations as the training dataset for model training (Trigila et al. 2015). The random selection of the training dataset in an RF model may have effects on the results of the model; so, a set of numerous trees are used to guarantee the stability of the model. Unselected cases [out of the bag (OOB)] are used to compute the error of the model (OOB error), equal to the standard deviation error between predicted and observed values, and to establish a ranking of importance of the variables. Also, RF calculates two specific importance measures including mean decrease accuracy and mean decrease Gini to show the importance and contribution of different factors in the modeling process. Because of the randomness of the RF technique at the extraction of independent variables and observations in each node, it is appropriate to preliminarily validate the effect of the number of trees and the number of runs on the stability of the model (Catani et al. 2013; Trigila et al. 2015).

Results

Application of the FR model

The results of spatial relationship between landslide locations and landslide conditioning factors using the FR model are shown in Table 1. From the FR values, it is seen that east-facing slopes followed by south-facing, northeast-facing, west-facing, and northeast-facing slopes are more susceptible to landsliding. In the case of altitude, results showed that there was no trend between landslide occurrence and altitude increase. The class of 500–800 m had the highest FR value of 1.46, followed by the classes of 189–500 m (1.29), and 800–1100 m (0.49). In the case of distance to faults, it can be seen that there is a reverse relationship between this factor and landslide occurrence. The distance from faults of 0–1000 m and 1000–2000 m had the highest FR values of 1.33 and 0.98, respectively. For the lithology, it is seen that most landslides occurred in lithological units of softer metamorphic rocks with an FR value of 1.94, followed by the lithological unit of soft gravelly soils with an FR value of 1.43. In the case of NDVI, the class −0.23 to 0.17 had the highest FR value of 1.31, indicating that this class is the most susceptible to landsliding. In the case of plan curvature, classes of −0.11 to 0.88 and −1.09 to −0.11 had the highest FR values of 1.02 and 1.01, respectively. For the profile curvature, the classes of 1.26–11.43 had the highest FR value (1.08), followed by the classes of −0.02 to 1.26 (1.04) and −1.30 to −0.02 (0.98). From the analysis of distance to rivers, it can be seen that there is a reverse relationship between this factor and landslide occurrence. In the case of distance to roads, distance to roads of 0–500 had the highest FR value of 1.72, indicating that the roads have a high influence on landslide occurrence. In the case of slope angle, the classes of 0–10 and 10–20 had the highest FR values of 1.22, and 1.18, respectively. While other slope classes have FR values lower than 1. For the SPI, the results showed that the class of 0–30 had the highest FR value (1.08), followed by 60–90 (1.00), 30–60 (0.93), and >90 (0.87). In the case of TWI, the results showed that the class of 7–9 had the highest FR value (1.15), followed by 5–7 (1.09), <5 (0.88), and >9 (0.77), which indicates that there is no clear relationship between this factor and landslide occurrence.

Application of the MARS model

The optimal model presents 18 terms and includes 18 BF (the terms created during the forward pass were 86), with a GCV of 0.19. Only 12 of the 17 independent variables were used in the optimal model (Table 2), because MARS only uses the essential independent variables (Gutiérrez et al. 2009). Table 2 presents the nsubset is the index vector specifying which cases to implement, i.e., which rows in x to implement (default is NULL, meaning all), the GCV of the model (summed over all responses; the GCV is calculated using the penalty argument) and the residual sum-of-squares (RSS) of the model (summed over all responses if y has multiple columns). So, based on Table 2, regarding the importance of independent variables to support the model, the most significant are altitude and distance to faults. Other important factors to describe the spatial distribution of landslides in the study area are lithology, SPI, and NDVI. In this kind of model, the importance of the independent variables should be perceived with caution (Donati and Turrini 2002; Gutiérrez et al. 2009). Finally, the landslide potential map produced by the MARS model is presented in Fig. 6.

Table 2 The distribution of the landslide values and areas with respect to the landslide occurrence potential zones
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Fig. 6
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Landslide potential map produced by multivariate adaptive regression spline (MARS) model

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Application of the RF model

Aggregation of the OOB prediction is presented in Table 3 (confusion matrix). The OOB represents that when the resulting model is applied to new data, the answer will be in error 25% of the time. A 75% accuracy is indicated, which is a reasonably good model. The overall measure of accuracy is then followed by a confusion matrix that records the conflict between that final model’s predictions and the present outcomes of the training observations. The present observations are the rows of Table 3, whereas the columns corresponded to what the model predicts for an observations and the cell count the number of observations in each variable (Williams 2011). The results of the confusion matrix showed that the model predicted 143 non-landslides as non-landslides and 101 non-landslides as landslides. On the other hand, RF models predicted 177 landslides as landslide and 67 landslides as non-landslides. Moreover, the OOB estimate of the error rate for this model was 34.43% which indicates that the model is 65.57% accurate, which is a reasonably good model (Fig. 4). Results from variable selection in the RF model are represented in Table 4 and Fig. 5. The higher values show that the variable is relatively more important (Williams 2011). The accuracy measure (mean decrease) then lists lithology (23.47), distance to faults (22.21), altitude (19.58) as next most important. We also notice that altitude (19.04), distance to faults (18.83), and distance to roads (15.29) have higher importance according to the Gini  measure than with the accuracy measure (Fig. 6).

Table 3 Confusion matrix from the RF model (0 = no landslide, 1 = landslide)
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Table 4 Relative influence of effective conditioning factors in the RF model (0 = no landslide, 1 = landslide)
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Finally, landslide susceptibility mapping by the RF model was prepared in ArcGIS 10.0 and  grouped using a natural break classification (Pourghasemi et al. 2013c; Zare et al. 2013; Naghibi et al. 2015, 2016) into low, moderate, high, and very high potential groups (Fig. 7).

Fig. 7
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Landslide potential map produced by the random forest (RF) model

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Validation of the landslide susceptibility maps

A proper method is required to verify the landslide susceptibility maps. In the present study, the produced landslide susceptibility maps were validated using the ROC curve. This method has been widely used in landslide susceptibility mapping to compare the different models (Guo et al. 2015; Youssef et al. 2015a). In the ROC curve, the true positive rate of the model (the percentage of existing landslides correctly predicted by the model) is plotted against the false positive rate (the percentage of predicted landslides out of the total actual negatives). The area under the curve (AUC) reflects the predictive ability of the models. The AUC values range from 0.5 to 1. The ideal model has an AUC value close to 1.0 (perfect fit), while a value close to 0.5 indicates a random fit.

Generally, there are two methods used for evaluating a model, such as success rate and prediction rate curves. Pourghasemi et al. (2012a, b) depicted that the success rate method used the training landslide points that have been used for building the landslide models, so it is not a proper method for assessing the prediction capability of the models. Thus, in the present study, the validation analysis was performed using the remaining 104 landslide data points (validation dataset). Figure 8 shows the ROC curves of the MARS and RF models for the validation data set. The ROC plot showed that in the landslide susceptibility map prepared using the MARS method, the AUC value is 87.51%, while in the RF model, the AUC value is 77.31%. So, the results indicate that the landslide susceptibility map obtained by the MARS model has higher prediction capability than the RF model.

Fig. 8
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Prediction rate curves for the landslide potential maps produced by a RF and b MARS models

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Discussion

In the current study, the results are represented and discussed in two important sections, including the performance of the models and the importance of the conditioning factors in landslide susceptibility mapping.

The performance of the models

Application and comparison of the MARS and RF models is relatively new in landslide susceptibility mapping studies. The results of the current study showed that the MARS model had a relatively higher prediction performance than the RF model. According to the literature review, these models had acceptable performance in different fields of study, including landslide, gully, and groundwater studies. In research, Conoscenti et al. (2015) determined terrain susceptibility to earth-flow using logistic regression and MARS models. They found that the MARS model performed better than logistic regression considering both the goodness-of-fit and the predictive power according to ROC values. They also indicated that MARS reproduces non-linear relationships using several linear regressions, which allows MARS to create models with a better fit to the training data while maintaining high predictive power. In other research, Adoko et al. (2013) concluded that MARS can constitute a reliable alternative to an ANN in modeling geo-engineering problems such as tunnel convergence. Also, Gutiérrez et al. (2009) compared classification and regression tree (CART) and MARS models, non-parametric models, to map the potential distribution of gullies. They found that MARS exhibit a better performance for predicting gullying with areas under the ROC curve values of 0.98 and 0.97 for the validation datasets, while CART presented values of 0.96 and 0.66. Trigila et al. (2015) carried out a comparison study of shallow landslide susceptibility mapping using LR and RF models. They concluded that the LR and RF methods are fully comparable in terms of identification of the most significant variables and predictive capabilities, and the RF technique is better for the minimization of false positives. Youssef et al. (2015b) produced landslide susceptibility maps using four data mining models, namely RF, CART, a boosted regression tree (BRT), and a general linear model (GLM). The success and prediction rate curves showed that the RF model had satisfactory performance. Goetz et al. (2015) applied logistic regression, generalized additive models, weights-of-evidence, support vector machine, RF, and bootstrap aggregated classification trees with penalized discriminant analysis in landslide susceptibility modeling for three areas in the Province of Lower Austria, Austria. They concluded that in terms of pure prediction performance, the RF and bootstrap aggregated classification trees with penalized discriminant analysis modeling techniques were the best.

Also, other researchers used RF in the field of groundwater potential mapping and got acceptable results. Rahmati et al. (2016) applied maximum entropy (ME) and RF models for groundwater potential mapping in the Mehran Region, Iran. They found that the AUC for prediction performance of the RF and ME methods was calculated as 83.1 and 87.7%, respectively. In other research, Naghibi and Pourghasemi (2015) evaluated the capability of three machine learning models such as BRT, CART, and RF, and comparison of their performance by multivariate GLM, and bivariate [evidential belief function (EBF)] statistical methods in the groundwater potential mapping. They concluded that CART, BRT, and RF machine learning techniques showed acceptable performance in mapping groundwater potential with the AUC values of 86.39, 86.12, and 86.05%, respectively. Rahmati et al. (2016) applied RF and maximum entropy (ME) models for groundwater potential mapping in the Mehran Region, Iran. Their results depicted that RF and ME models had AUC for success rates of 86.5 and 91%, respectively, while the AUC for prediction rates of RF and ME methods were 83.1 and 87.7%, respectively. Comparing the results of this study and other studies showed that RF and MARS with AUC values of 77.32 and 87.51%, respectively, have outperformed other models such as EBF (AUC = 0.73) and FR (AUC = 0.77) models in Hong et al. (2016), weights of evidence (AUC = 0.74) in Mohammady et al. (2012), logistic regression in Chen et al. (2016c), naïve Bayes (AUC = 0.81 which is lower than RF in the current study) in Tien Bui et al. (2012), and Dempster Shafer (AUC = 0.72) in Pourghasemi et al. (2013a). In Naghibi et al. (2016), RF (AUC = 0.71) showed weak performance in the modeling process as well as the results of the current study depicted. Although RF performed weaker than MARS in this study, it can be concluded that RF and MARS models could provide better landslide susceptibility maps than the mentioned models.

In the case of landslide inventory accuracy, two methods were considered to increase the accuracy of the inventory, field work and using satellite images. It is mentioned by Malamud et al. (2004) that determining the level of completeness of an inventory map is not a simple task. Therefore, work on this subject could be suggested for future works as inventory accuracy highly affects the results of the models and landslide susceptibility maps.

The importance of the conditioning factors in landslide susceptibility mapping

Determining the importance of conditioning factors in landslide susceptibility mapping is important in landslide studies. The study revealed that the most important conditioning factors according to the accuracy measure (mean decrease) of an RF model are lithology (23.47%), distance to faults (22.21%), and altitude (19.58%). We also notice that altitude (19.04%), distance to faults (18.83%), and distance to roads (15.29%) have higher importance according to the Gini measure than with the accuracy measure. Also, Kawabata and Bandibas (2009) introduced geology as the most important factor in landslide susceptibility mapping. In other research, Youssef et al. (2015a) concluded that slope angle, land use, and altitude have higher importance in landslide occurrence, which is consistent with the results of current study. In other research, lithology and altitude were the most important factors in landslide susceptibility mapping (Devkota et al. 2013).

Conclusions

Landslide spatial modeling with more advanced models such as MARS and RF can give handy landslide susceptibility maps, and consideration of these maps by different organizations can lessen severe damages caused by landslides. This study was conducted to compare the spatial capability of the MARS and RF models to produce landslide susceptibility maps and determine areas prone to landslide occurrence in Shangnan County, Shangluo City, China. For this purpose, 12 landslide effective factors were selected to be used as model inputs: slope aspect, altitude, distance to faults, lithology, NDVI, plan curvature, TWI, SPI, profile curvature, distance to rivers, distance to roads, and slope angle. The location of the landslides was detected from historical reports, interpretation of aerial photographs, and extensive field surveys by GPS. From  these locations, 70% (244) and 30% (104) of the landslides were used for training and validation of the MARS and RF models, respectively. Finally, the ROC curve was used to validate these results. The AUC results showed that the prediction rate of the MARS model is higher than the RF model. Further, it was inferred that the most important conditioning factors according to the accuracy measure (mean decrease) of the RF model are lithology, distance to faults, and altitude. We also noticed that altitude, distance to faults, and distance to roads have higher importance according to the Gini measure than with the accuracy measure. The produced landslide susceptibility maps could be appreciated as a useful tool for local authorities and government agencies in choosing suitable locations for future land-use planning. As a final conclusion, MARS was applied successfully and its application in landslide-prone areas could be proposed in other areas and regional scale.