Abstract
The study area in northwestern Ethiopia is one of the most landslide-prone regions, which is characterized by frequent high landslide occurrences. To predict future landslide occurrence, preparing a landslide susceptibility mapping is imperative to manage the landslide hazard and reduce damages of properties and loss of lives. Geographic information system (GIS)-based frequency ratio (FR), information value (IV), certainty factor (CF), and logistic regression (LR) methods were applied. The landslide inventory map is prepared from historical records and Google Earth imagery interpretation. Thus, 717 landslides were mapped, of which 502 (70%) landslides were used to build landslide susceptibility models, and the remaining 215 (30%) landslides were used to model validation. Eleven factors such as lithology, land use/cover, distance to drainage, distance to lineament, normalized difference vegetation index, drainage density, rainfall, soil type, slope, aspect, and curvature were evaluated and their relationship with landslide occurrence was analyzed using the GIS tool. Then, landslide susceptibility maps of the study area are categorized into very low, low, moderate, high, and very high susceptibility classes. The four models were validated by the area under the curve (AUC) and landslide density. The results for the AUC are 93.9% for the CF model, which is better than 93.2% using IV, 92.7% using the FR model, and 87.9% using the LR model. Moreover, the statistical significance test between the models was performed using LR analysis by SPSS software. The result showed that the LR and CF models have higher statistical significance than the FR and IV methods. Although all statistical models indicated higher prediction accuracy, based on their statistical significance analysis result (Table 5), the LR model is relatively better followed by the CF model for regional land use planning, landslide hazard mitigation, and prevention purposes.
1 Introduction
As defined by Brunsden and Cruden [1,2], landslides are the downslope movements of debris, rocks, or earth material under the influence of the force of gravity [3]. Landslides are also defined as a large range of geotechnical phenomena under the influence of gravity. Although the cause of landslide incidence and its mechanisms are so complex, it is triggered by heavy rainfall, earthquake, and human interventions. It can occur when the driving force exceeds the resistance force because of the destabilization of natural soil or rock slopes [4,5]. Landslides can bury animals and humans in a short period as well as can destroy houses, farms, and infrastructures [6]. It is one of the most destructive and dangerous natural hazards that cause numerous fatality and economic losses worldwide [6,7,8,9]. Ethiopia is one of the countries affected by heavy rainfall, human intervention, and earthquake-triggered frequent landslide impacts yearly, resulting in loss of human and animal lives and damage of infrastructures and properties [5,10,11,12,13,14]. In the last 2 years, from 2018 to 2019, because of rainfall-triggered landslides 60 people died, 30 people injured, 5,091 households displaced, houses damaged, and a widely cultivated and non-cultivated land destructed in different parts of the country [5]. Besides, on 16 October 2019, 23 people died, and on 28 May, 22 people died and also there was a destruction of wide areas of farmlands by heavy rainfall-triggered landslide incidence. This shows that huge economic loss caused by landslide incidences retards the sustainable development of the economy of the country. Despite the landslide problem is critical in Ethiopia, still there is no adequate slope stability assessment applied in the different parts of the country [5]. The study area is one of the areas that were frequently affected by the rainfall-triggered landslide incidences, and so far, the area has not yet been studied. Landslide in this area resulted in the damage of three houses, farmlands, and loss of animal lives. From local people’s witness, rainfall and stream cut triggered deep-seated rotational landslides that occurred in 2018 and reactivated in 2019 in the Desa Enese village, which destroyed wide ranges of farmlands that covered by crops. Therefore, landslide susceptibility mapping and assessment in this area are very important to disaster loss reduction and serve as a guideline for sustainable land use planning in the study area.
The mitigation measures of landslide incidence in the area, which is already failing or susceptible to fall, require identification of existing landslide, determination of the contribution of prevailing causal factors, and generation of landslide susceptibility map [15]. Landslide susceptibility is the result of the relationship between past landslide and environmental factors [16]. It is an important basis and scientific support for the government’s response to landslide hazards management and land use practice [17,16]. The landslide susceptibility mapping is not only to ascertain the factors that are most influential to the landslides that occurred in the region but also to estimate the relative contribution of each factor for slope failures [16]. It is also important to inaugurate an association between the factors and landslides to foresee the landslide hazard in the future [16].
Several approaches are developed for landslide susceptibility mapping, which can be categorized into qualitative, semi-quantitative, and quantitative methods [19,20,21,22,23]. Qualitative methods are an expert-driven approach, which required field experience specialists [19,20,22,24,25,26,27]. It mainly includes field geomorphological analysis, parameter assignment superimposition, and landslide inventory analysis. Relying on the experience and professional background knowledge of experts and subjectivity is the drawback of these methods [19,20,22,23,24,25,26]. Semi-quantitative methods are the combination of qualitative and quantitative methods, which introduce grading and weighting of the effects of landslide factors on landslide incidence [23,28,29]. In this method, both qualitative and quantitative methods can be applied to evaluate the effects of landslide governing factors on landslide occurrence [30]. Analytical hierarchy process, weighted linear combination, and expert knowledge/heuristic [23,27,31,32] are examples of semi-quantitative methods. Although some statistical concepts are introduced in this method, it depends on the expert’s experience and the background of professional knowledge and some subjectivity remains [23,33]. The quantitative methods can be divided into three categories such as statistical, machine learning/data mining, and deterministic methods [34,35,36]. Statistical methods are indirect susceptibility mapping methods widely or routinely used to evaluate the correlation between landslide governing factors and landslides based on mathematical expression [16,19,20,21,22]. The statistical methods can be further divided into multivariate and bivariate statistical methods, which are widely used throughout the world and provide reliable results [5,14,23,37,38,39,40,41,42,43]. The bivariate statistical methods are used to evaluate the relationship between landslide governing factors and past landslides. Certainty factor (CF) [44,45,46,47,48], frequency ratio (FR) [14,49,50,51,52], information value (IV) [5,53,54,55], and weight of evidence [46,49,55,56,57,58] are examples of bivariate statistical methods, which are simple and easy and produce reliable models. It also helps to evaluate the effects of a landslide at a factor class level that is impossible in data mining or multivariate methods. However, it requires quality input data, past landslide data, and lacking to evaluate the relationship among landslide governing factors. Multivariate statistical methods are used to examine the relationship between three and above dependent and independent variables [39,40,43,59,60]. Although logistic regression (LR) and discriminant analysis are examples of multivariate statistical methods used frequently in landslide susceptibility modeling and provide reliable results [14,16,39,40,43,60], it is incapable to examine the contribution of each factor class for landslide probability like data mining, unlike bivariate methods. Deterministic methods are used to calculate the quantitative value of the inherent slope materials of the factor of safety over a defined area [61]. These methods can be applied when landslide types are simple (shallow landslides) and the intrinsic properties of slope material are homogeneous [61]. It requires detailed ground data such as soil strength, unit weight of soil, pore water pressure, soil layer thickness, slope angle, slope height, and depth below the terrain surface. Deterministic method has been employed over a small area, and oversimplification, data availability to acquire frequently is impossible are the drawback of these methods [61]. In recent times, advanced data mining methods have been widely used in landslide susceptibility modeling, including random forest [62], boosted regression tree [63], classification and regression tree [63], Naïve Bayes [29,64], support vector machines [31,65,66], kernel LR [67], logistic model tree [67,62], index of entropy [68], and artificial neural networks [69,70,71]. However, data mining methods are time-consuming, are incapable to determine the effects of each landslide factor class, and require high computing capacity, and the internal calculation process of these methods is intensive and cannot easily be understood. Although there is a bit little difference in the degree of predictive accuracy, both statistical and data mining methods provide reliable predictive accuracy [18,71,72]. In general, each of the methods has its merit and demerits. For example, the results of the qualitative methods highly depend on the expert of the researcher. In addition, the bivariate statistical method helps to evaluate the impact of each landslide governing factor classes on landslide occurrence, but excluded CF, and it does not consider the relationship between these factors and landslide occurrence [10], whereas multivariate statistical analysis (LR) can consider it.
Although CF, IV, FR, and LR methods are routinely used methods for landslide susceptibility mapping, they have some foreseeable limitations. For example, the LR model can perform multivariate statistical analysis between a dependent variable and a set of independent variables, but it is incapable to analyze the impacts of internal classes of landslide governing factors individually on landslide occurrence [61,73]. However, the CF can analyze both the impacts of individual factors and factor class on landslide occurrence. FR and IV are simple and effective statistical methods that can extract the influence of each landslide governing factor classes on landslide occurrence, but it cannot consider the relationship between these landslide governing factors and landslide occurrence [74]. Therefore, it is important to use both bivariate and multivariate statistical analyses to evaluate the impacts of landslide factors and landslide factor classes in prediction modeling of landslide susceptibility in the study area (in a part of Abay Basin).
The primary objective of this study is to determine landslide-prone areas using LR, FR, CF, and IV statistical methods in the study area. The second objective is to compare the application of FR, IV, LR, and CF methods for predictive modeling of landslide susceptibility in the study area. The study area is one of the areas characterized by populating settlements, intensive farming, and frequent landslide incidence, which destroyed widely cultivated land, and it is important to evaluate the factors that have more roles in causing slope failure and to minimize their socioeconomic impacts by generating a landslide susceptibility map. For this purpose, statistical methods including FR, LR, IV, and CF methods were applied. These methods are easy to apply and it gives a very well-meaning result. In the literature, various bivariate and multivariate approaches for landslide susceptibility mapping are available; however, a comparison among LR, CF, FR, and IV models has yet not been encountered. A comparison of the four models has been discussed in this study. The accuracy of the results of landslide susceptibility maps, which were generated using the statistical methods, was evaluated using the receiver operating characteristic curve (ROC) and landslide density. The resulted maps will be used for landslide mitigation purposes and regional land use planning.
2 Study area and geological setting
The study area is one part of the Abay basin (Gozamn, Baso Liben, and Awabel Districts), which is located in the northwestern highlands of Ethiopia. It lies within the latitude 10,90,000 mN to 11,40,000 mN and the longitude 3,30,000 mE to 4,00,000 mE. The minimum and maximum altitudes of the area are 902 m of the river gorge and 2,563 m in hills and plateau lands (Figure 1). Many tributaries are available in the entire study area, which drains into the Abay River. The various streams in the study area caused the removal of soil through stream bank erosion. The study area is characterized by variable topographic conditions, including ridge, cliff, hill, plateau, deep River gorge, and gentle slope. The fragile nature of topography has been in facilities the rate of soil erosion. Of this region, 50% is covered by agricultural lands, and rocky lands/bar lands, residential lands, and grazing lands cover the remaining lands. Tropical to subtropical climatic condition prevails in the study area. The main characteristic of the climates in the study area is the monsoon rainfall, which occurs between June and September and delivers an average of 90% of the total rainfall of the year. This resulted in landslide incidence in the study area. For example, reactivated landslides in the Desa Enese village occurred after heavy and prolonged rainfall in August 2019. The maximum annual rainfall is 1,394 mm, whereas 902 mm is the minimum annual rainfall.
Location map of the study area.
Geologically, Ethiopia comprised the Precambrian basement rock, Paleozoic sedimentary rock, Mesozoic marine sedimentary rock, and Cenozoic volcanic rocks. However, the study area comprised mainly two geological units besides recent soil sediments at the slope toe of the study area, which is grouped into early Mesozoic and Cenozoic Era of sedimentary (red sandstone, gypsum, and limestone) and volcanic rocks (flood basalt), respectively. The flood basalt rock units are grouped into four geological units, such as Ashengie formation (lower basalt), Aiba formation (middle basalt), Alaje formation (upper basalt), and Termaber formation. Nevertheless, the study area is comprised of only the lower basalt, middle basalt, the Mesozoic sedimentary rock (lower red sandstone, gypsum, and limestone), and the quaternary/recent soil deposit. This lithology is digitized from the existing 1:2,50,000 geological map of the Debre Maroks sheets. Figure 2 shows that the southern, southwestern, and southeastern parts of the study area are covered by the sedimentary rock (lower red sandstone, gypsum, and limestone, respectively). Lower sandstone is characterized by medium to thickly bedded thickness, fine to coarse texture, red-to-red-brown color, and strongly cross-bedded. The northern, northwestern, southeastern, and central parts of the study area are dominantly covered by the volcanic rock (lower basalt), which is underlined early to middle Mesozoic sedimentary rock (red sandstone unit and gypsum unit) and covered by thin dark color soil deposit (Figure 2). This unit is characterized by a high degree of weathering and fracturing. The northwestern, northeastern, and eastern parts of the study area are covered by a very loss/unconsolidated soil deposit. In this soil deposit, unplanned intensive agricultural activities are common.
Geological map of the study area.
3 Methodology
For this study, data collection, landslide inventory mapping, Google Earth imagery analysis, landslide factor evaluation, and mapping, geographic information system (GIS)-based FR, IV, LR, and CF landslide susceptibility modeling and model validation was applied. Furthermore, relevant data, including digital elevation model (DEM) with 30 m resolution, topographic map, borehole data, historical landslide events, geological map, and meteorological data were collected (Table 1). These data were collected from the geological survey of Ethiopia (GSE), the United States Geological Survey (USGS), Amhara water well drilling enterprise (AWWDE), field survey, Google Earth imagery from the NASA, and Ethiopian National Meteorological Agency (Table 1). The landslide location of the study area was identified using historical records and Google Earth imagery analysis. These are classified into training and testing landslide data sets. The training landslide data sets are used for model preparation, whereas the testing landslide data sets are used for model prediction accuracy evaluation. Based on the data availability, local environmental conditions, literature, data evaluation, and local people interview, 11 landslide-driving factors were determined. The landslide driving factor maps and landslide inventory maps were prepared using ArcGIS 10.1. Distance to stream, drainage density, slope angle, slope aspect, and curvature were extracted from 30 m resolution of DEM, which was downloaded from the USGS website. The lithological layer and lineament map are digitized from the existing geological map of the Debre Markos sheet at a scale of 1:2,50,000. The soil map was prepared from the FAO soil map and the rainfall map was prepared using 30 year rainfall data, which was gathered from the Ethiopian Meteorological Agency. The land use map was prepared using ArcGIS and Google Earth imagery analysis. Land use map digitized from Google Earth imagery interpretation, which can export to a GIS layer format (Kml) and verified by ground truth as well as by the experience of the users in the local area for the final map due to high spatial resolution, easiness as well as user friendly. The land use map is also prepared using the supervised classification of satellite images downloaded from the USGS website. The general procedure flow chart that was followed in this research work is summarized in Figure 3.
Information source for the various landslide factors used in the landslide susceptibility mapping
| Data | Map | Format | Source |
|---|---|---|---|
| Landslide inventory | Landslide inventory map | Vector (shapefile) | Google Earth imagery, field survey, and historical record |
| Geology | Lithology and lineament map | Vector (shapefile) | Digitized from geological map of Debre Markos Sheet provided by the GSE at 1:50,000 |
| DEM | Slope angle map | Raster (grid) | Derived from 30 m DEM, using ArcGIS 10.1, downloaded from USGS |
| Aspect map | |||
| Curvature map | |||
| Hydrology | Distance to stream and drainage density | Raster (grid) | Developed from DEM and buffering using distance to Euclidian |
| Topography | Topographic map | Vector (shapefile) | Ethiopian Mapping Agency at 1:50,000 |
| Meteorological data | Rainfall map | Vector (shapefile) | Ethiopian National Meteorological Agency |
| Land use | Land use and soil map | Vector (shapefile) | Sentinel 2 images in the USGS, Field Survey, FAO, and Google Earth imagery |
| Borehole data | ----- | Vector (shapefile) | Amhara Water Well Drilling Enterprise (AWWAE) |
General flow charts for the methodology of the study area.
Geodatabase building is one of the most fundamental elements in the landslide susceptibility mapping. Therefore, four databases were built for LR, FR, IV, and CF models. The FR, IV, and CF databases contain landslide inventory and landslide factors, whereas the LR database contains landslide and no landslide points with 11 weighted landslide factors. After the database was built, evaluation of the relationship between landslide and landslide factors and determination of the statistical significance of each landslide factor were the next steps in landslide susceptibility mapping. Therefore, 11 landslide factor maps were reclassified into subclass and overlaid with reclassified training landslide data sets. Weight ratings for all the landslide factor classes were assigned statistically using Excel as shown in equations (1), (3) and (5). These weighted maps were rasterized using lookup tool in spatial analysis. After rasterizing the factor maps, the landslide susceptibility index (LSI) maps were generated by the sum-up of all raster maps using a raster calculator in Map Algebra. These maps (LSI) are classified into a fivefold classification scheme: very low, low, moderate, high, and very high susceptibility classes using natural breaks (Figure 4b–d). In the case of the LR method, the study area was classified as training landslide and non-landslide points using GIS. Then, the weight of the 11 factors has been extracted to generate LR coefficients of each landslide factor in SPSS, and finally, the LSI of the area was generated using the logistic landslide probability equation (equation (8)) and GIS tools (Figure 4a). Finally, the accuracy of the four models was evaluated using the prediction rate curve and landslide density based on the observed testing landslide data sets (Figures 5 and 6).
(a) Landslide susceptibility map using LR method. (b) Landslide susceptibility map using the FR method. (c) Landslide susceptibility map using the CF method. (d) Landslide susceptibility map of IV method.
Landslide density in each susceptibility class.
Receiver operating characteristics curve (ROC).
4 Landslide inventory mapping
In landslide susceptibility mapping, landslide inventory mapping is one of the key elements, which can be prepared using various techniques such as the aerial photograph or Google Earth imagery interpretation, field investigation, and evaluation of archive data coupled with GIS tools [75]. Landslide inventory map is used as the base for future landslide prediction by evaluating the relationship between the existing landslide event and landslide driving factors [56,76,77]. A landslide inventory map was prepared using GIS from field investigation, historical landslide events, and satellite image analysis [75]. Landslide inventory maps can also be prepared using Google Earth imagery [5,14,54,78]. In the present research work, from the active and old landslide scarps, 717 landslides, which covered 7.8 km2, are identified using historical landslide record and time series Google Earth imagery analysis (Figure 7). It digitized into polygons using a GIS tool with the help of Google Earth imagery, and finally, a landslide inventory map was produced (Figure 7). From local people witness and time series Google Earth imagery analysis, the study area is affected by landslide incidence frequently because of heavy and prolonged rainfall and the presence of unconsolidated soil deposit as well as highly weathered basalt rock unit. Soil slide, weathered rockslide, debris flow, earth flow, and earth fall types of landslides are dominant in the study area. In the literature, some researchers classified landslides into 80% for training landslide data sets and 20% for testing landslide data sets. However, most of the researchers classified landslides into 70% for training data sets and 30% for testing landslide data sets [14,54,58,68,78,79]. Using ArcGIS 10.1, these landslides were classified randomly into 70% (502) for training landslide data sets and 30% (215) for validation data sets keeping their spatial distribution. The training landslide data sets observed landslides that were used to develop the model, whereas the validation landslide data sets observed landslides that were used to evaluate the performance and prediction accuracy of the model. As shown in Figures 8 and 9, the Desa Enese and Aba Libanos areas are affected by soil slides in 2019 because of heavy and prolonged rainfall. Rotational landslide in the Desa Enese area occurred because of the removal of the slope toe by a stream and resulted in damages in farmlands, which covered by crops, and two houses (Figure 8). As indicated in Figure 7, the spatial distribution of landslides concentrates dominantly on the ridge and along the stream bank.
Landslide inventory map of the study area.
![Figure 8 Time series Google Earth image showing failed slope at Desa Enese village in 2019 [80].](/document/doi/10.1515/geo-2020-0206/asset/graphic/j_geo-2020-0206_fig_008.jpg)
Time series Google Earth image showing failed slope at Desa Enese village in 2019 [80].
![Figure 9 Time series Google Earth image showing failed slope at Aba Libanos village in 2019 [80].](/document/doi/10.1515/geo-2020-0206/asset/graphic/j_geo-2020-0206_fig_009.jpg)
Time series Google Earth image showing failed slope at Aba Libanos village in 2019 [80].
5 Evaluation of landslide factors
In landslide susceptibility mapping, the selection of landslide factors is one of the most important elements. However, there are no well-defined standards to select the most significant landslide factors. The factors that initiate the landslide incidence in the study area are selected based on the data availability, local environmental conditions, literature review, local person interview, and data evaluation using LR analysis. These are slope angle, aspect, slope curvature, normalized difference vegetation index (NDVI), land use, lithology, distance to lineament, drainage density, rainfall, soil, and distance to stream/river considered into account to examine the spatial relationship between them and landslide occurrence in the study area. Distance to stream (five classes), drainage density (five classes), slope angle (five classes), aspect (ten classes), and slope curvature (three classes) map constructed from 30 m resolution DEM was downloaded from the USGS website (Figure 10). The lithological map and lineament map of the study area were prepared through digitization from 1:2,50,000 existing geological maps of Debre Markos sheet from the GSE, which has eight classes (lower basalt, middle basalt, fine to coarse sandstone, fine to medium sandstone, gypsum, limestone, and unconsolidated sediments [alluvium and eluvium]). Google Earth imagery and the supervised classification of Sentinel 2 images were used to prepare land use maps of the study area. From the results, the land use map, which was prepared from Google Earth imagery, is more reliable compared to the supervised classification of Sentinel 2 images. Preparation of land use map using the supervised classification of satellite images could be best when the study area is so large and the users are not familiar to the region. Nevertheless, from the resulting point of view, using a manual land use classification of the Google Earth imagery found to be effective as it has a high spatial resolution, and the expert who classifies this image has direct control to identify what stands for what. However, Google Earth imagery requires an advanced Internet condition, and it is so effective when the area is well known by the user. The land use map has seven classes such as grassland, cultivated/cropland, scatter forest, woodland, bare land, residential, and scatters bush (Figure 10). Earthquake was not considered in the present work because the study area is so far from the active earthquake sites. The source of various landslide factors used in landslide susceptibility mapping is summarized in Table 1. To determine the effects of each landslide factor class on landslide occurrence, the weight rate for each factor classes is very important. For this purpose, all landslide factor maps converted into raster and reclassified with the same pixel size (30 m) and the same projection using GIS tools under the Arc toolbox in conversion as well as a spatial analysis tool. Then, the landslide inventory raster map overlaid through the combination in spatial analysis tool under the local toolbox with the landslide factor raster class to extract landslide pixels for each landslide factor class. Then the effects of each factor class were determined using the equation of FR (equation (1)), IV (equation (3)), and CF (equation (5)) methods, and the results are summarized in Table 3.
Landslide governing factor maps.
6 Modeling approaches
6.1 FR model
The FR model is one of the bivariate probability methods, which is applicable to determine the correlation between landslide occurrence and landslide causative factor classes. The FR is the ratio of areas in which the landslide occurred to areas in which landslides not occurred. When the ratio value is greater than one, it indicates the strong correlation between factor class and landslide occurrence in a given terrain; however, the ratio value less than one indicated that weak coloration between landslide occurrence and landslide factors, which means a low probability of landslide occurrence [82,83]. It can be calculated using equation (1).
where FR is the frequency ratio, Nslpix is the landslide pixel/area in a landslide factor class, Ntslpix is the total area of a landslide in the entire study area (a), Ncpix is the area of the class in the study area, and Ntcpix is the total pixel area in the entire study area (b). In the present research work, the FR for each causative factor class is calculated using equation (1), and the results are summarized in Table 2.
Logistic regression coefficients and multicollinearity diagnosis of conditioning factors used in LR
| Collinearity statistics | |||
|---|---|---|---|
| Independent variables | Logistic coefficients (B) | Tolerance | VIF |
| Aspect | 0.648 | 0.937 | 1.068 |
| Curvature | 0.198 | 0.900 | 1.111 |
| Distance to lineament | 1.296 | 0.891 | 1.122 |
| Distance to drainage | 1.896 | 0.617 | 1.620 |
| Lithology | 1.012 | 0.782 | 1.279 |
| Land use | 0.184 | 0.964 | 1.038 |
| NDVI | 0.067 | 0.881 | 1.135 |
| Rainfall | 0.191 | 0.834 | 1.199 |
| Drainage density | 0.278 | 0.602 | 1.660 |
| SLOPE | 0.719 | 0.758 | 1.319 |
| Soil type | 1.235 | 0.762 | 1.312 |
| Constant | −8.905 | ||
After calculated the FR for each landslide factor class using Microsoft Excel and GIS, the FR value for each factor class assigned through the join in the ArcGIS tool. Then the weighted landslide factors were rasterized using the lookup tool in spatial analysis. The LSI indicated the degree of susceptibility of the area for landslide occurrence. The LSI of the study area was calculated by carefully summing up the weighted factor raster maps using equation (2) by the raster calculator in Map Algebra of the spatial analysis tool. To get the LSI, the FR of each factor type or class is summed as in equation (2).
where LSI is the landslide susceptibility index, n is the number of landslide factors, Xi is the landslide factor, and FRi is the FR of each landslide factor type or classes. After the LSI was calculated, the index values were classified into a different level of landslide susceptibility zones using natural breaks in the ArcGIS tool. The higher the value of the LSI, the higher the probability of landslide occurrence, but the lower the LSI, the lower the probability of landslide occurrence.
Based on the natural break classification, the landslide susceptibility map of the study area has five classes such as very low, low, moderate, high, and very high landslide susceptibility class (Figure 4b).
6.2 IV model
The IV method is one of the probabilistic methods of a bivariate statistical method, which is used to envisage the correlation between landslides and landslide factor classes [55]. The IVs for each factor class were determined through the combination of reclassified landslide raster to reclassified landslide factor raster based on the presence of landslide in a given map unit (Figure 4c). These values are important to define the role of each causal factor in classes for landslide occurrence. This can be calculated as in equation (4).
where conditional probability is the ratio of the pixel of a landslide in class to the pixel of a class and prior probability is the ratio of the total number of pixels of landslide to the total number of pixels of the study area. Nslpix is a landslide pixel/area in a landslide factor class. Ntslpix is the total area of a landslide in the entire study area. Ncpix is the area of the class in the study area and Ntcpix is the total pixel area in the entire study area. When IV > 0.1, the landslide occurrence with the factor classes has a high correlation, which means it will have a high probability of landslide occurrence; however, when the IV <0.1 or IV <0, it is a low correlation between landslide factors and landslide occurrence, which indicates a low probability of landslide occurrence. After calculated the IV for each landslide factor class using Microsoft excel and GIS, the IV for each factor class assigned through the join in the ArcGIS tool. Then, the weighted landslide factors were rasterized using the lookup tool in spatial analysis, and the LSI of the study area is calculated as in equation (3).
where LSI is the landslide susceptibility index and IV is the information value of each factor class. The higher value of LSI has indicated the higher probability of landslide occurrence.
6.3 CF model
The CF is one of the probabilistic methods that is widely used for landslide susceptibility mapping for different data [44,45,47,48]. Shortliffe and Buchanan [83] proposed the CF (the probability function) for landslide susceptibility mapping, and later Heckeman [84] improved it and it is expressed mathematically as:
where PPa is the conditional probability of landslide in the defined area a and PPb is the prior probability of landslide in the defined entire study area b. The CF value ranges from −1 to 1, a positive value indicates increasing certainty of landslide occurrence, and a negative value indicates decreasing certainty of landslide occurrence. If the certainty value is close to zero, it means there is no adequate information about the relation between landslide factor classes and landslide occurrence; therefore, it is difficult to give any certainty of landslide occurrence [48,85].
The CF values were calculated for all landslide factor classes through overlaying landslide factors with landslides using equations (5) and (6). After the calculation of CF for each landslide factor class, the LSI is determined as in equation (7).
where Z is the calculated CF value and X and Y are the two different layers of information.
where LSI is the landslide susceptibility index and CFi is the certainty factor.
6.4 LR model
The LR is one of the popular multivariate statistical analysis methods, which can be used to establish a multivariate regression relationship between dependent and independent variables [86]. Among other statistical methods, the LR model has been proven as one of the most reliable approaches for landslide susceptibility mapping to determine the most landslide influencing factors [87,88,89,90,91,92]. This model is advantageous, as it does not require normal distribution and it uses continuous or discrete variables. The difficulty in using the LR model lies in the sample size selection of dependent and independent variables for landslide susceptibility analysis. There are three ways of sampling landslide and non-landslide points [93]. The first way is using all data from all the study areas. However, this leads to an uneven proportion of non-landslide and landslide pixels, which incorporate a large volume of data in the analysis [94,95]. Using all landslide pixels with equal non-landslide pixels is the second method, which also results in a less reliable output, but it can reduce sample size and sampling bias. The third method uses an unequal or equal proportion of landslide and non-landslide pixels by classifying landslide into training and testing data sets [96,97].
In the present work, the landslides of the study area were classified into training landslides (70% with 502 landslides) and testing landslides (30% with 2,015 landslides). In this study, the dependent data are a binary variable and are made up of 0 and 1, which represent the absence and presence of landslides, respectively. Consequently, an equal number of non-landslide sample points (502), whose dependent variable value is 0 were randomly selected from landslide free areas to represent the absence of landslides using GIS. The 502 landslides and 502 non-landslides were merged. Moreover, all the values of independent variables containing landslides and non-landslides were extracted from the maps of each landslide-governing factors using ArcGIS. Then, the LR was conducted and coefficients were calculated in the SPSS program. It can be expressed mathematically [89,98] as:
where P is the probability of landslide occurrence that varies from zero to one and Z is the linear combination of the predictors and varies from −1 < z < 0 for higher odds of non-landslide occurrence to 0 < z < 1 for odds of higher landslide occurrence. Z can be defined as:
where x1, x2, x3, and xn are independent variables, β0 is the intercept of the slope of LR analysis, and β1, β2, β3, and βn are the coefficients of the LR analysis.
6.5 Model validation
Landslide susceptibility map without validation has no sense in the scientific world [5]. Therefore, validation of the landslide susceptibility model is very important to evaluate the degree of accuracy of modeling using different validation techniques [50,99]. For this purpose, the landslide area is classified based on time, space, and random partition [10,14,50]. In this case, the landslide in the study area was classified into 70% (502) training landslide data sets and 30% (215) validation landslide data sets randomly keeping their spatial distribution. As stated by ref. [100], the area under the curve (AUC) value is used to evaluate the performance of the model and its value range from 0.5 to 1. When the AUC value is in between the range of 0.9–1, the model has excellent performance; if in between the range of 0.8–0.9, the model has very good performance; if in between the range of 0.7–0.8, the model has good performance; and if in between the range of 0.6–0.7, the model has an average performance. However, if the AUC values are in between the range of 0.5–0.6 and equal to 0.5 or less than 0.5, the model has poor performance [100].
In the present work, the landslide area was randomly classified as 70% landslide for training and 30% landslide for model validation by keeping their spatial distribution using the random partition technique [14,50]. After the model is developed, its accuracy was validated by ROCs and landslide density.
7 Results and discussions
7.1 Results
In this section, the results of the four landslide susceptibility models generated using FR, LR, IV, and CF statistical methods are presented and compared. Table 3 shows the correlation between landslide locations and landslide driving factor classes, which was determined using FR (equation (1)), IV (equation (3)), and CF (equation (5)). The higher value of the FR, IV, and CF indicated the strong correlation between the landslide and landslide factor classes.
Spatial relationship between each landslide factors and landslide using FR, CF, and IV methods
| Factors | Class | Ncpix | Nspix | % Ncpix (b) | %Nspix (a) | FR = a/b | PPa | PPb | CF | IV | LR |
|---|---|---|---|---|---|---|---|---|---|---|---|
| LULC | Scatter forest | 1,20,151 | 591 | 4.139 | 8.290 | 2.003 | 0.005 | 0.002 | 0.502 | 0.695 | 0.184 |
| Woodland | 5,91,791 | 899 | 20.388 | 12.610 | 0.619 | 0.002 | 0.002 | −0.382 | −0.480 | ||
| Bush | 3,94,218 | 918 | 13.581 | 12.877 | 0.948 | 0.002 | 0.002 | −0.052 | −0.053 | ||
| Cropland | 11,46,131 | 2,412 | 39.485 | 33.834 | 0.857 | 0.002 | 0.002 | −0.143 | −0.154 | ||
| Grassland | 3,94,509 | 1,372 | 13.591 | 19.245 | 1.416 | 0.003 | 0.002 | 0.295 | 0.348 | ||
| Barre land | 2,54,507 | 921 | 8.768 | 12.919 | 1.473 | 0.004 | 0.002 | 0.322 | 0.388 | ||
| Settlement | 1,373 | 16 | 0.047 | 0.224 | 4.745 | 0.012 | 0.002 | 0.791 | 1.557 | ||
| NDVI | 0.1–0.4 | 3,20,744 | 225 | 11.050 | 3.156 | 0.286 | 0.001 | 0.002 | −0.715 | −1.253 | 0.067 |
| 0.4–0.45 | 7,32,428 | 1,483 | 25.232 | 20.802 | 0.824 | 0.002 | 0.002 | −0.176 | −0.193 | ||
| 0.45–0.5 | 8,59,086 | 2,541 | 29.596 | 35.643 | 1.204 | 0.003 | 0.002 | 0.170 | 0.186 | ||
| 0.5–0.6 | 6,27,764 | 2,051 | 21.627 | 28.770 | 1.330 | 0.003 | 0.002 | 0.249 | 0.285 | ||
| 0.6–0.8 | 3,62,729 | 829 | 12.496 | 11.629 | 0.931 | 0.002 | 0.002 | −0.070 | −0.072 | ||
| Lithology | Alluvium soil deposit | 5,05,536 | 0 | 17.416 | 0.000 | 0.000 | 0.000 | 0.002 | −1.000 | 0.000 | 1.012 |
| Eluvium soil deposit | 8,25,764 | 1,758 | 28.448 | 24.660 | 0.867 | 0.002 | 0.002 | −0.133 | −0.143 | ||
| Fine to coarse sandstone | 1,20,674 | 52 | 4.157 | 0.729 | 0.175 | 0.000 | 0.002 | −0.825 | −1.740 | ||
| Fine to medium sandstone | 1,30,651 | 134 | 4.501 | 1.880 | 0.418 | 0.001 | 0.002 | −0.583 | −0.873 | ||
| Gypsum | 8,46,403 | 5,145 | 29.159 | 72.170 | 2.475 | 0.006 | 0.002 | 0.597 | 0.906 | ||
| Limestone | 2,01,392 | 40 | 6.938 | 0.561 | 0.081 | 0.000 | 0.002 | −0.919 | −2.515 | ||
| Lower basalt | 86,341 | 0 | 2.974 | 0.000 | 0.000 | 0.000 | 0.002 | −1.000 | 0.000 | ||
| Middle basalt | 1,85,973 | 0 | 6.407 | 0.000 | 0.000 | 0.000 | 0.002 | −1.000 | 0.000 | ||
| Distance to lineament | 0–1,000 | 3,87,844 | 1,991 | 13.362 | 27.928 | 2.090 | 0.005 | 0.002 | 0.523 | 0.737 | 1.296 |
| 1,000–2,000 | 4,37,943 | 972 | 15.089 | 13.634 | 0.904 | 0.002 | 0.002 | −0.097 | −0.101 | ||
| 2,000–3,000 | 4,59,530 | 1,181 | 15.832 | 16.566 | 1.046 | 0.003 | 0.002 | 0.044 | 0.045 | ||
| 3,000–4,000 | 3,94,585 | 1,072 | 13.595 | 15.037 | 1.106 | 0.003 | 0.002 | 0.096 | 0.101 | ||
| 4,000–5,000 | 2,88,500 | 869 | 9.940 | 12.190 | 1.226 | 0.003 | 0.002 | 0.185 | 0.204 | ||
| 5,000–6,000 | 2,28,501 | 609 | 7.873 | 8.543 | 1.085 | 0.003 | 0.002 | 0.079 | 0.082 | ||
| 6,000–7,000 | 1,74,276 | 212 | 6.004 | 2.974 | 0.495 | 0.001 | 0.002 | −0.505 | −0.703 | ||
| 7,000–16,827 | 5,31,312 | 223 | 18.305 | 3.128 | 0.171 | 0.000 | 0.002 | −0.829 | −1.767 | ||
| Drainage density | 0–0.3 | 16,27,264 | 3,260 | 56.064 | 45.729 | 0.816 | 0.002 | 0.002 | −0.226 | −0.204 | 0.278 |
| 0.3–0.6 | 9,22,131 | 2,701 | 31.770 | 37.888 | 1.193 | 0.003 | 0.002 | 0.162 | 0.176 | ||
| 0.6–0.9 | 3,22,233 | 1,166 | 11.102 | 16.356 | 1.473 | 0.004 | 0.002 | 0.322 | 0.387 | ||
| 0.9–1.3 | 25,892 | 2 | 0.892 | 0.028 | 0.031 | 0.000 | 0.002 | −30.800 | −3.459 | ||
| 1.3–1.6 | 4,986 | 0 | 0.172 | 0.000 | 0.000 | 0.000 | 0.002 | 0.000 | 0.000 | ||
| Distance to drainage | |||||||||||
| Curvature | 0–200 | 3,35,052 | 1,158 | 11.544 | 16.244 | 1.407 | 0.003 | 0.002 | 0.290 | 0.342 | 1.846 |
| 200–400 | 3,15,809 | 980 | 10.881 | 13.747 | 1.263 | 0.003 | 0.002 | 0.209 | 0.234 | ||
| 400–800 | 5,93,467 | 1,607 | 20.447 | 22.542 | 1.102 | 0.003 | 0.002 | 0.093 | 0.098 | ||
| 800–1,200 | 5,36,717 | 1,459 | 18.492 | 20.466 | 1.107 | 0.003 | 0.002 | 0.097 | 0.101 | ||
| 1,200–4,137 | 11,21,461 | 1,925 | 38.638 | 27.002 | 0.699 | 0.002 | 0.002 | −0.302 | −0.358 | ||
| −6.7 to −0.6 | 1,55,774 | 697 | 5.367 | 9.777 | 1.822 | 0.004 | 0.002 | 0.452 | 0.600 | 0.198 | |
| −0.4 to 0.3 | 25,46,217 | 5,442 | 87.725 | 76.336 | 0.870 | 0.002 | 0.002 | −0.130 | −0.139 | ||
| 0.3 to 8 | 2,00,515 | 990 | 6.908 | 13.887 | 2.010 | 0.005 | 0.002 | 0.504 | 0.698 | ||
| Aspect | Flat | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.002 | −1.000 | 0.000 | 0.645 |
| N | 90,209 | 67 | 3.108 | 0.940 | 0.302 | 0.001 | 0.002 | −0.698 | −1.196 | ||
| NE | 2,15,295 | 110 | 7.418 | 1.543 | 0.208 | 0.001 | 0.002 | −0.792 | −1.570 | ||
| E | 3,99,044 | 385 | 13.748 | 5.400 | 0.393 | 0.001 | 0.002 | −0.608 | −0.934 | ||
| SE | 5,05,127 | 995 | 17.403 | 13.957 | 0.802 | 0.002 | 0.002 | −0.198 | −0.221 | ||
| S | 4,22,902 | 1,543 | 14.570 | 21.644 | 1.485 | 0.004 | 0.002 | 0.328 | 0.396 | ||
| SW | 4,02,422 | 1,353 | 13.865 | 18.979 | 1.369 | 0.003 | 0.002 | 0.270 | 0.314 | ||
| W | 4,23,429 | 1,952 | 14.588 | 27.381 | 1.877 | 0.005 | 0.002 | 0.468 | 0.630 | ||
| NW | 3,35,102 | 628 | 11.545 | 8.809 | 0.763 | 0.002 | 0.002 | −0.237 | −0.270 | ||
| N | 1,08,976 | 96 | 3.755 | 1.347 | 0.359 | 0.001 | 0.002 | −0.642 | −1.025 | ||
| Slope | <5° | 12,85,973 | 999 | 44.306 | 14.013 | 0.316 | 0.001 | 0.002 | −0.684 | −1.151 | 0.719 |
| 5–12° | 7,25,015 | 1,581 | 24.979 | 22.177 | 0.888 | 0.002 | 0.002 | −0.112 | −0.119 | ||
| 12–19° | 4,81,190 | 1,776 | 16.578 | 24.912 | 1.503 | 0.004 | 0.002 | 0.335 | 0.407 | ||
| 19–29° | 2,81,637 | 1,461 | 9.703 | 20.494 | 2.112 | 0.005 | 0.002 | 0.528 | 0.748 | ||
| 29–62° | 1,28,691 | 1,312 | 4.434 | 18.404 | 4.151 | 0.010 | 0.002 | 0.761 | 1.423 | ||
| Soil type | Eutric vertisols | 1,58,642 | 135 | 5.466 | 1.894 | 0.346 | 0.001 | 0.002 | −0.653 | −1.060 | 1.235 |
| Humic nitisols | 14,61,188 | 2,805 | 50.344 | 39.346 | 0.782 | 0.002 | 0.002 | −0.218 | −0.246 | ||
| Rendzic leptosols | 11,57,550 | 4,082 | 39.882 | 57.259 | 1.436 | 0.004 | 0.002 | 0.303 | 0.362 | ||
| Hapzic paeozems | 1,25,040 | 107 | 4.308 | 1.501 | 0.348 | 0.001 | 0.002 | −0.651 | −1.054 | ||
| Rainfall | 968–1,117 | 3,10,624 | 84 | 10.701 | 1.178 | 0.110 | 0.000 | 0.002 | −0.890 | −2.206 | 0.719 |
| 1,117–1,213 | 5,38,921 | 413 | 18.566 | 5.793 | 0.312 | 0.001 | 0.002 | −0.687 | −1.165 | ||
| 1,213–1,289 | 7,70,880 | 1,836 | 26.557 | 25.754 | 0.970 | 0.002 | 0.002 | −0.030 | −0.031 | ||
| 1,289–1,344 | 5,15,393 | 1,851 | 17.755 | 25.964 | 1.462 | 0.004 | 0.002 | 0.315 | 0.380 | ||
| 1,344–1,394 | 7,66,946 | 2,945 | 26.421 | 41.310 | 1.564 | 0.004 | 0.002 | 0.360 | 0.447 | ||
Note: Nspix is landslide pixel/area in a landslide factor class; Ncpix is the area of the class in the study area.
7.2 FR
To understand the significance of landslide factor classes for landslide occurrence, weight value was computed using FR methods as shown in equation (1) (Table 3). The FR for all landslide factor classes was rating and showed the statistical significance of each factor class on slope instability (Table 3). As it can be observed from Table 3, the lithology class gypsum produced a higher value of the FR (2.475) which is >1, indicating a high landslide probability occurrence, but the remaining lithological classes indicated weak statistical correlation and its FR value is <1, indicating a low probability of landslide occurrence. As presented in Table 3, the slope classes <5° and 5–12° have low FR value (0.316 and 0.888, respectively) and the slope classes 12–19°, 19–29°, and 29–62° have high FR value (1.503, 3.112, and 4.151, respectively). This correlation indicated that landslide probability increased as the slope gradient increased [5,10]. This is because of the presence of shallow loose soil deposit, highly weathered rock, active soil erosion, and improper land use practice. However, it may not be always true when the steep slope comprises massive and strong slope material. In the case of the aspect factor class, the FR value is >1 for south facing (1.485), southwest facing (1.369), and west facing (1.877), indicating high landslide probability. However, the remaining slope aspect classes have FR value <1, indicating a low probability of landslide occurrence. The FR value of the slope curvature classes of −6.7 to −0.6 (1.822) and 0.3–8 (2.01) is >1, indicating high landslide probability occurrence. This is because of the effects of slope shape for rainwater impounding and gravity effect. However, the FR value of the slope curvature class of −0.4 to 0.3 (0.87) is <1, indicating a low probability of landslide occurrence. As presented in Table 3, as the distance to stream increased, the probability of landslide occurrence decreased. At a distance of 0–200, 200–400, 400–800, and 800–1,200 m, the value of the FR (1.407, 1.263, 1.102, and 1.107) is >1, indicating high landslide probability; however, at a distance >1,200 m, the value of the FR is <1, indicating low landslide probability. This is because of the effects of slope modification, gully erosion, riverbank erosion, and river undercutting. As noticed in Table 3, the value of the FR for land use/cover class of grassland (1.416), settlement (4.745), bar land (1.473), and scatter forest (2) is >1, indicating high landslide probability. This is because of the scatter forest, grassland can increase soil moisture. As the soil moisture increased in slope material, the weight of slope material as well as the pore water pressure in slope material increased in parallel [5]. This can result in a reduction in the normal force in the soil mass. This leads to slope failure when the driving force exceeds a resisting force. In the case of bare land class, FR value showed a higher correlation with the probability of landslide occurrence. Therefore, bare land in the study area was highly affected by gully erosion, which caused a reduction in shear strength of soil material. The remaining classes have FR value <1, indicating a low probability of landslide occurrence.
7.3 IV
The IV rating for different landslide factor classes was calculated by overlaid landslide raster with landslide factor, and it showed the significant effect of each factor class on slope instability (Table 3). When the IV value is >0.1, the given factor class will have a positive correlation for landslide occurrence, but the IV <0.1 indicates a low probability of landslide occurrence. As presented in Table 3, the IV >0.1 for lithology class such as gypsum (0.906) indicated high landslide probability, but the IV <0.1 for the remaining lithology class indicated a low probability of landslide occurrence. As observed in Table 3, the IV <0.1 for slope classes <5° and 5–12° (IV = −1.151 and −0.119, respectively) indicated low landslide probability, and the IV >0.1 for slope classes 12–19°, 19–29°, and 29–62°, respectively (IV = 0.407, 0.748, and 1.423), indicated high landslide probability. In the case of slope aspect factor class, the IV >0.1 for south facing (IV = 0.396), southwest facing (IV = 0.314), and west facing (IV = 0.630) indicated high landslide probability. However, IV <0.1 for the remaining slope aspect classes indicated a low probability of landslide occurrence. The IV >0.1 for the slope curvature class of −6.7 to −0.6 (IV = 0.6) and 0.3–8 (IV = 0.698) indicated high landslide probability. However, the IV <0.1 for the slope curvature class −4 to 0.3 (IV = −0.139) indicated low probability of landslide occurrence. At a distance of 0–200, 200–400, 400–800, and 800–1,200 m, the value of the IV >0.1, which is 0.342, 0.234, 0.095, and 0.101, indicated high landslide probability; however, at a distance of 1,200 m, the IV <0.1 indicated low landslide probability. As noticed in Table 3, the value of IV for land use/cover class of grassland (0.348), settlement (1.557), bar land (0.388), and scatter forest (0.6) is >0.1, indicating high landslide probability. The IV for the remaining factor classes is <0.1, indicating a low probability of landslide occurrence.
7.4 CF
The CF rating for different landslide factor classes was calculated by overlaid landslide raster with landslide factor using equations (5) and (6), and it showed a significant effect of each factor class on slope instability. As presented in Table 3, the lithology class such as gypsum has a positive and high value of CF (0.597), indicating high landslide probability, but the remaining lithology class has a negative CF value and indicated low probability of landslide occurrence. As observed in Table 3, the slope classes <5° and 5–12° produced negative CF value (CF = −0.684 and −0.112, respectively), indicating low landslide probability. For slope classes 12–19°, 19–29°, and 29–62°, the CF value is positive and relatively higher (CF = 0.335, 0.528, and 0.761, respectively), indicating high landslide occurrence probability. In the case of aspect factor class, the CF value is positive for south facing (0.328), southwest facing (0.27), and west facing (0.468), indicating high landslide occurrence probability. However, the remaining slope aspect classes have negative CF value, indicating a low probability of landslide occurrence. The CF value of the slope curvature class of −6.7 to −0.6 (0.452) and 0.3–8 (0.504) is positive, indicating high landslide occurrence probability. However, the slope curvature class −0.4 to 0.3 has a negative CF value (−0.130), indicating a low probability of landslide occurrence. At a distance of 0–200, 200–400, 400–800, and 800–1,200, the value of CF (0.29, 0.209, 0.093, and 0.097) is positive, indicating high landslide occurrence probability; however, a distance >1,200 m produced negative CF value, indicating low landslide probability. As noticed in Table 3, the value of CF for land use/cover class of grassland (0.295), settlement (0.791), bar land (0.322), and scatter forest (0.5) is positive, indicating high landslide probability. The remaining factor classes produced negative CF value, indicating a low probability of landslide occurrence.
7.5 LR
The LR was used for the modeling of landslide susceptibility in the study area. Before the LR analysis, it is essential to perform collinearity analysis to evade possible multicollinearity among the independent variables. For these purposes, two main indexes of Tolerance (TOL) and the variance inflation factor (VIF) were applied to measure the multicollinearity [67]. When the TOL is less than 0.1 or the VIF greater than 10, it indicates that a multicollinearity problem exists. As shown in Table 2, the TOL and VIF values of all independent variables have no multicollinearity problem among all independent variables. After collinearity analysis, the relationship between the dependent and independent variables was evaluated using SPSS software to obtain the logistic coefficients of landslide governing factors under forwarding stepwise. Then, the value of Z was calculated by entering the LR coefficients of landslide governing factors in equation (10).
The calculated Z values of the study area range from −5.8 to 5.4. After calculating the values of Z, the probability landslide occurrence P of the study area was calculated by entering the values of Z to equation (8), which range from 0.0021 to 0.996. Finally, the landslide susceptibility map of the study area was classified into five classes by classifying the P values using the natural break classification method in ArcGIS: very low, low, moderate, high, and very high landslide susceptibility (Figure 4a). As shown in Table 2, all landslide factors indicated a positive relationship for landslide occurrence. For example, distance to drainage, distance to lineament, soil type, and lithology have higher LR coefficients compared to others, which indicates a strong statistical correlation between landslide factors and landslide occurrence. Based on the sample data, the goodness of fit model was evaluated through Nagelkerke’s R-square, Homer–Lemeshow test, and the percentage rate of classifications with a cutoff of 0.5. From the analysis, the Nagelkerke’s R-square value is 0.487 and the model correctly classifies 76.7% of the landslides and 76.1% of the non-landslides when a cutoff of 0.5 is considered. All these results indicate that the present study model performed reasonably well.
7.6 Landslide susceptibility mapping
All weighted landslide-governing factors were summed using a raster calculator in ArcGIS in terms of equations (2), (4), (7) and (8) to obtain LSI. After calculating the LSI, it is important to classify the LSI into different susceptibility classes based on the LSI value. The LSI map of the study area, which was generated using LR method, IV method, CF method, and FR method, was classified into five levels of susceptibility classes (very low, low, moderate, high, and very high) using the natural break method (Figure 4a–d). From the results of the IV analysis (Table 4), 6.6 and 17.7% of the study area fell in very low and low susceptibility classes, respectively. Moderate, high, and very high landslide susceptibility classes comprised 31.7, 29.4, and 14.6% of the study area, respectively. As presented in Table 4, 0.1 and 0.6% of the validation landslides fell in very low and low susceptibility classes of the study area, respectively. The remaining 2.9, 17.2, and 79.3% of validation landslides fell into moderate, high, and very high landslide susceptibility classes, respectively. From the results of landslide susceptibility map produced using CF model (Table 4), very low and low susceptibility classes cover 13.4 and 26.7% of the total study area, however, 29, 22, and 9% of the total area fell into moderate, high and very high landslide susceptibility classes, respectively. As indicated in Table 4, 0 and 0.7% of the validation landslides fell in very low and low susceptibility classes of the study area, respectively. The remaining 5.8, 27.5, and 66% of validation landslides fell into moderate, high, and very high landslide susceptibility classes, respectively. As it observed from Table 4, the landslide susceptibility map produced using the FR model, very low and low landslide susceptibility classes covered 18.9 and 28.9% of the total area; however, 25.6, 20, and 6.5% of the total area fell into moderate, high, and very high landslide susceptibility classes, respectively. As presented in Table 4, 0 and 1.5% of the landslide fell in very low and low susceptibility classes of the study area, respectively. The remaining 11.7, 32.2, and 54.5% of validation landslides fell into moderate, high, and very high landslide susceptibility classes, respectively. The landslide susceptibility map, which produced using the LR method, covered 41.9% of a region by very low susceptibility class, 21.1% by low susceptibility class, 16% by moderate susceptibility class, 12.6% by high susceptibility class, and 8.4% by very high susceptibility class (Table 4). Besides, 0.6 and 3.4% of the landslide fell in very low and low susceptibility classes in the study area, respectively. The remaining 15.8, 19, and 61.2% of validation landslides fell into moderate, high, and very high landslide susceptibility classes, respectively (Table 4).
Statistical results of landslide susceptibility map produced by FR, IV, and CF methods
| LSI value | LSI | Susceptibility class area (%) | Validation data set (a) (%) | Landslide density (a) | Training data set (%) | Landslide density (b) | AUC for validation landslide | AUC for training landslide | |
|---|---|---|---|---|---|---|---|---|---|
| Information value method | −12 to −5 | VLS | 6.6 | 0.1 | 0.0 | 0.4 | 0.0 | 0.932 | 0.902 |
| −5 to −3 | LS | 17.7 | 0.6 | 0.0 | 2.5 | 0.1 | |||
| −3 to −0.9 | MS | 31.7 | 2.9 | 0.1 | 14.7 | 0.6 | |||
| −0.9 to 0.9 | HS | 29.4 | 17.2 | 0.6 | 34.7 | 1.7 | |||
| 0.9 to 6.2 | VHS | 14.6 | 79.3 | 5.4 | 47.7 | 7.3 | |||
| CF | −6 to −3 | VLS | 13.4 | 0.0 | 0.0 | 0.3 | 0.0 | 0.939 | 0.905 |
| −3 to −1.4 | LS | 26.7 | 0.7 | 0.0 | 1.2 | 0.0 | |||
| −1.4 to −0.3 | MS | 29.0 | 5.8 | 0.2 | 12.6 | 0.4 | |||
| −0.3 to 0.9 | HS | 22.0 | 27.5 | 1.3 | 28.1 | 1.3 | |||
| 0.9 to 4.3 | VHS | 9.0 | 66.0 | 7.4 | 57.8 | 6.4 | |||
| FR | 5 to 9 | VLS | 18.9 | 0.0 | 0.0 | 0.41 | 0.1 | 0.927 | 0.916 |
| 9 to 11 | LS | 28.9 | 1.5 | 0.1 | 1.05 | 0.1 | |||
| 11 to 12.3 | MS | 25.6 | 11.7 | 0.5 | 6.54 | 0.2 | |||
| 12.3 to 14.3 | HS | 20.0 | 32.2 | 1.6 | 21.08 | 0.7 | |||
| 14.3 to 20.7 | VHS | 6.5 | 54.5 | 8.3 | 70.92 | 4.9 | |||
| LR | 0 to 0.2 | VLS | 41.9 | 0.6 | 0.0 | 1.89 | 0.0 | 0.879 | 0.844 |
| 0.2 to 0.3 | LS | 21.1 | 3.4 | 0.2 | 7.01 | 0.3 | |||
| 0.3 to 0.5 | MS | 16.0 | 15.8 | 1.0 | 18.01 | 1.1 | |||
| 0.5 to 0.7 | HS | 12.6 | 19.0 | 1.5 | 21.60 | 1.7 | |||
| 0.7 to 0.996 | VHS | 8.4 | 61.2 | 7.3 | 51.48 | 6.1 |
LSI is landslide susceptibility index, VLS is very low susceptibility, LS is low susceptibility, MS is moderate susceptibility, HS is high susceptibility, VHS is very high susceptibility, and AUC is the area under the curve
7.7 Model validation and sensitivity analysis
In this research, the ROC, the AUC, and landslide density were used to evaluate the accuracy of the landslide susceptibility model generated by LR, FR, IV, and CF methods. The four models were validated by the researcher experience in the area and comparing the existing training and validation landslide data sets with the produced landslide susceptibility maps. Both the success rate and prediction rate curves were calculated using training landslide data sets and validation/testing landslide data sets, respectively. The success rate curve can show how well the models classified the region based on the existing landslide events [14,102]. The prediction rate curve can show how well the models can predict the unknown forthcoming landslide events [101,102]. In this study, the success rate and prediction rate curves were calculated by reclassifying the LSI values into 100 for all cells and sorting in descending order and compared with both training and validation landslide data sets. Finally, the AUC and ROC curves for the four models were calculated using Real Statistics software. As the results of the analysis showed in Figure 6 and Table 4, the closer the ROC curve to the left of the top of the curve indicated the higher the accuracy of the model. As indicated in Table 4, the AUC value is closer to one, indicating the higher accuracy of the model. The training landslide data set was used to calculate the success rate (Figure 6b), which showed a success rate of 91.6% using the FR model that is better than the success rate of 90.5% using the CF model, 90.2% using the IV model, and 84.4% using the LR model. The validation landslide data set was used to measure or evaluate the prediction rate of the models (Figure 6a), which showed a prediction rate of 93.9% using the CF model that is better than the prediction rate of 93.2% using the IV model, 92.7% using FR model, and 87.9% using LR model. Although all methods showed little difference in AUC values, it is evident that the four methods can serve as an effective method to perform landslide susceptibility assessment. Moreover, the AUC values of all methods except LR (very good) fell in the same range of excellent performance. These results indicated that the FR, CF, IV, and LR models have successfully estimated the landslide susceptibility classes of the region, and these models, which were used in this study, have reasonable accuracy in predicting the landslide susceptibility classes of the study area. For the four models, greater than 80% of validation landslides fell in high and very high susceptibility classes (Figure 11), and the landslide density increased as the landslide susceptibility increased (Figure 5) which again confirms that the models have higher accuracy. However, based on AUC values, CF, IV, and FR models revealed a little better result than the LR model for landslide susceptibility mapping in the study area (Figures 6 and 11). As shown in Table 4 and Figure 11, the areas with high and very high landslide susceptibility cover 21, 26.5, 31, and 44% of the study area by LR, FR, CF, and IV models, respectively, and 96.5% for IV, 93.5% for CF, 86.7% for FR, and 80.2% of LR models of validation landslides occurred in these areas, whereas <5% of the validation landslides falls in the areas with very low and low landslide susceptibility class. From these, the IV model has overestimated the high and very high landslide susceptibility of a region followed by CF models. For the training landslide data set, a higher percentage that ranges from 73 to 93.9% is correctly distributed in the areas with high and very high landslide susceptibility, and a lower percentage of <14% of the training landslide data set falls in the areas with very low and low landslide susceptibility. Thus, it can be concluded that the proposed models produced an accurate prediction of the spatial probabilities of landslide occurrence in the study area.
Spatial distribution of predicted and observed landslides.
![Figure 12 Time series Google Earth image showing unfailed slope at Desa Enese village in 2018 [80].](/document/doi/10.1515/geo-2020-0206/asset/graphic/j_geo-2020-0206_fig_012.jpg)
Time series Google Earth image showing unfailed slope at Desa Enese village in 2018 [80].
![Figure 13 Time series Google Earth image showing unfailed slope at Aba Libanos village in 2018 [80].](/document/doi/10.1515/geo-2020-0206/asset/graphic/j_geo-2020-0206_fig_013.jpg)
Time series Google Earth image showing unfailed slope at Aba Libanos village in 2018 [80].
Time series Google Earth image showing unfailed slope at Gobetima village in 2014 and failed slope in 2016.
Time series Google Earth image showing unfailed slope at Gobetima village in 2014 and failed slope in 2016.
To determine the statistical significance of the models, a statistical significance test between the models was performed (Table 5) using LR analysis by SPSS software, for both training and testing landslide data sets with an equal number of pixels of non-landslides. The results presented in Table 5 show that the LR and CF models have indicated higher statistical significance than the FR and IV methods. In this study, a factor sensitivity analysis was performed to determine the sensitivity of the landslide governing factors for landslide susceptibility mapping. It was conducted by (1) removing each landslide factor during the summation stage using FR under raster calculator and (2) validating the resulted map using success rate curves, and the success rate value was obtained by subtracting from the success rate value of the map, which produced using all landslide-governing factors. From the results of sensitivity analysis (Table 5), soil type, slope, land use land cover (LULC), curvature, distance to drainage, drainage density, aspect, and distance to lineament indicated a positive effect on landslide susceptibility mapping with the decrease of 1.3, 1.26, 1.1, 0.9, 0.7, 0.3, 0.1, and 0.1%. However, lithology, NDVI, and rainfall with −0.2, −0.5, and −0.85% of increments of success rate value from the model, which produced using all landslide-governing factors when they remove from modeling so they have a negative effect on landslide susceptibility mapping in the study area. The sensitivity analyses showed how a solution changes as the input landslide governing factors are changed (Table 5). The higher the values of decrease of success rate, the higher sensitivity of landslide factors to landslide susceptibility mapping. From the results, it can be concluded that the performance of landslide susceptibility mapping is affected not only by landslide susceptibility mapping methods but also by incorporated landslide governing factors.
Statistics of the sensitivity analysis of landslide governing factors and statistical test results between landslide susceptibility models
| Expected factors | Success rate value (%) | Decreased success rate value (%) | Landslide susceptibility models | Significant coefficients for training landslide data sets | Significant coefficients for testing landslide data sets |
|---|---|---|---|---|---|
| Aspect | 91.5 | 0.1 | Certainty factor | 1.003 | 0.601 |
| Curvature | 90.7 | 0.9 | Frequency ratio | −0.188 | 0.126 |
| Distance to lineament | 91.5 | 0.1 | Information value | −0.178 | −0.06 |
| Distance to drainage | 90.9 | 0.7 | Logistic regression | 3.75 | 0.698 |
| Lithology | 91.8 | −0.2 | |||
| Land use | 90.5 | 1.1 | |||
| NDVI | 92.1 | −0.5 | |||
| Rainfall | 92.45 | −0.85 | |||
| Drainage density | 91.3 | 0.3 | |||
| SLOPE | 90.34 | 1.26 | |||
| Soil type | 90.3 | 1.3 |
7.8 Discussion
Landslide susceptibility maps can forecast/provide important information about the occurrence of landslides in a region. This is a function of the relationship between preexisting landslide and the environmental condition of the area. These maps also show the spatial distribution of predicted landslides where it will occur. However, the maps cannot forecast the volume of material to displace, time, and return period of the landslides. Nevertheless, the predictive models can be important for the regional land use planning of landslide hazard mitigation and prevention relief [60,61,101,102,103,104,105]. The landslide susceptibility maps of the study area are classified into fivefold classification schemes of very low, low, moderate, high, and very high susceptibility classes using the natural break method, which is applicable to classify unevenly distributed data, and it is capable of classifying LSI map into different categories considering the inherent data value similarity. The resulted map’s accuracy was validated using training and testing/validation landslide data sets through the success rate curve and predictive rate curve. The success rate curves for the three models were generated from the training landslide data sets through combining tools with landslide susceptibility classes, which was used to evaluate how well the models classified the region based on the existing landslide events [14,105]. The prediction rate curve for the four models was generated from the validation landslide data sets through combining tools with landslide susceptibility classes used to evaluate how well the models can predict the unknown forthcoming landslide events [101,105]. High and very high susceptibility classes in the region are fell in a steep slope, which covered with very lose shallow soil deposit, closer to the stream, agricultural land on a steep slope, active gully erosion, and concave slope shapes while the moderate susceptibility class fell in the area of highland landscapes. Low and very low susceptibility of a region fell in the area of low plain landscapes and areas, which are covered by massive weathering resistant rock masses.
Although FR and IV methods can quantitatively reflect the influence of numerous landslide governing factor classes to landslide occurrence probability, it does not consider the important degree of the factors to landslide occurrence [112]. However, LR and CF methods help to describe the relationship between a landslide occurrence and the landslide-governing factors [59]. Nevertheless, except for the CF, it does not analyze the influence of classes of each landslide-governing factor on landslide occurrence [61,73,81,108], and the process of input data, calculation, and output is time consuming [111,112]. Therefore, in landslide susceptibility mapping, using integrated methods are very important to solve the limitation among the statistical methods. For example, the FR and IV methods are incapable to determine the effects of landslide factor on landslide occurrence probability rather than evaluating the effects of landslide factor class, which can be solved using LR methods that are incapable to determine the effects of landslide factor classes. There is some literature regarding the comparison of the FR method with the IV method, LR method with IV and frequency methods, the CF method with the IV method, and the CF method with the FR method. Reference [78] states that the prediction rate of 89.05% using the IV is better than the prediction rate of 85.57% using the FR method. However, in this study, the FR method showed better performance for both success rates (AUC = 91.6%) and predictive rate curve (AUC = 92.7%) than the IV method with success rate curve (AUC = 90.2%) and predictive rate curve (AUC = 93.2%). Even though the FR model showed a little bit difference in AUC value in general, the accuracy of the two models fell in the same ranges, which is a very good performance. As shown from the work of ref. [58], the CF model showed a high predictive accuracy of AUC value of 75% compared to the IV model with prediction rate curve value (AUC = 64.08%), but their accuracy value fell in the same ranges, which is an excellent performance. Nevertheless, in the present model, the CF model showed a relatively few difference in prediction rate value (AUC = 93.9%) than the IV model with prediction rate value (AUC = 93.2%), but they have the same accuracy range, which is an excellent performance. From the work of ref. [68], based on the predictive rate value of the area under the receiver operating characteristic curve (AUC), the FR and CF models showed more or less similar predictive capacity, which is 81.18% for the CF model and 80.14% for the FR model. However, CF showed a bit of little performance than the FR model. In the present work, the prediction rate of 92.7% using the FR model is better performance than the prediction rate curve (93.9% for the CF model). Refs. [110,111] found that the IV method gave a more realistic landslide susceptibility map than the LR model. This result is the same as the work of ref. [5,106], which stated that the IV method has higher prediction accuracy than the LR. Similarly, in this study, the IV method has higher prediction accuracy (Figure 6. From the work of ref. [14], the prediction accuracy is a little better in the LR method (AUC = 74.5%) than the FR method (AUC = 73.7%). However, ref. [109] found that the FR (AUC = 79.48%) has a higher prediction accuracy than the LR (AUC = 77.4%). This result is similar to the work of ref. [107], which stated that the prediction accuracy of FR (AUC = 81.4%) is better than the LR (75.1%). This result is the same, as the prediction rate of FR is better than the LR in the present study. Generally, the three bivariate statistical and multivariate statistical methods in the literature and this study showed the closer prediction capacity with AUC > 64% and AUC > 80%, respectively, which fell in the range of good and very good/excellent performance [100]. The landslide validation results for three models (FR, IV, and CF) are closer to each other, it fell in the same range of excellent performance, and LR produced a very good performance. Besides this, the percent of landslides that fell in the high and very susceptibility classes are more than 80% validation landslides. Therefore, from these results, the research work finds out that in landslide susceptibility mapping, the four models have equal potential to generate landslide-prone areas but factor selection should be playing a more important role than the methods. Nevertheless, in a specific case, the high and very high susceptibility area coverage of the IV model showed high differences compared to the CF, FR, and LR methods. This is because of the problems ascertained in IV during weight rating for each factor class, i.e., when no landslide exists in a certain factor class, the results of IV becoming zero. This brings an impact on the overall accuracy of the model. Although all statistical models indicated higher prediction accuracy, based on their statistical significance analysis result (Table 5), the LR model is relatively better followed by the CF model for regional land use planning, landslide hazard mitigation, and prevention purposes.
8 Conclusion
The study area is characterized by recent unconsolidated soil deposits, rugged topography, active gulley, and riverbank erosion, and improper land use practice that makes it very prone to different landslides, including soil slide, weathered rockslide, debris flow, earth flow, earthfall, and soil creep. Based on the LR coefficients, the impacts of 11 landslide factors (distance to drainage, distance to lineament, soil type, lithology, slope, aspect, drainage density, curvature, rainfall, land use, and NDVI with decreased order of coefficients) on landslide occurrence are determined. A landslide is the most serious natural hazard in the study area. To determine the landslide susceptibility–prone areas, FR (FR), CF, LR, and IV models were applied. The landslide susceptibility maps of the study area are categorized into very low, low, moderate, high, and very high susceptibility classes. The high and very high susceptibility classes are high in the villages including Tedem, Dendo, Anjimo, Dinguabe, Denba, Kok, Desa Enese, Moching, Yewebi Enefoch, Aratu Amba, Aba Libanos, Denba, and Kebi in order of decreasing the risk of landslide incidence because of the presence of active riverbank erosion, lose soil deposit, high concentration of stream density, and undulating topography. Therefore, these areas need to slope vegetation and water management tasks. The accuracy of the landslide susceptibility models was evaluated using the ROCs curve and landslide density through comparison of training and validation landslide raster with the models. The prediction rate curve value of AUC for the four models is closing in 1, indicating very good accuracy of the models. Based on the AUC value of the results and >80% of observed validation landslides which fell in high and very high susceptibility classes, the statistical methods can prove as the most economical and effective methods in landslide susceptibility mapping in the similar regions to the study area. The models, which were generated using the four statistical models, can help to understand the landslide hazard problems in the study area. Although the resulting maps cannot forecast the time, and how often it can occur, it has provided the spatial distribution of landslide probability. These models can also provide important information to the researchers, local people, government, and planners to reduce the landslide hazard problems in the study area. Therefore, the concerned bodies may at the Wereda/District, Zone, Region, and Federal levels take tangible activities to mitigate the landslide problem by afforestation of the high and very high regions with the integration of terracing and construction of check dams for streams, gabion, and retaining walls along the riverbanks.
Acknowledgments
First, the author would like to thank the almighty God who allowed him to accomplish this research work. Next, the author would like to give his gratitude to his lovely wife Ms. Seble Asmare and his brother Mr. Zemene Wubalem for their valuable support and advice during this research work. The author would like to give his special thanks to Dr. Veera and his friends for their continuous support during the research work. Finally, the author would like to thank the University of Gondar for geological equipment, the National Meteorological Agency staffs, the GSE, the disaster head office, natural resource management head office, and the rural community, for their valuable data.
Author contributions: Starting from the conception and design of the work, modeling, as well as the statistical analysis and interpretations of the results were done by the author.
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