3.1 Data Sources for Landslide Conditioning Factors
Various factors have been selected to investigate landslide susceptibility in the study area. Table 1 details the type and source of data used in the assessment of landslides susceptibility. Thematic maps were generated from these data in a GIS environment. Given the paucity of literature in the study area, the selection of factors was based on a review of literature that conducted comparable assessments of landslide susceptibility in areas with similar characteristics (Ayonghe et al. 1999; Ayonghe and Ntasin 2008; Ntasin et al. 2009; Ngatcha et al. 2011; Che et al. 2011, 2012).
Landsat 8 operational land imager (OLI) images were downloaded from the United States Geological Survey website (Table 1). These images were layer stacked in ERDAS Imagine 2018 employing contrast enhancement and feathering techniques (Kumar 2005).
3.2 Multicriteria Decision Analysis
Multicriteria decision analysis (MCDA) is a GIS-based method for decision making through the integration of geographic data and subjective judgements (Malczewski 1999).
3.2.1 Analytical Hierarchy Process
An analytic hierarchy process (AHP) is a form of MCDA quantitative method for decision making using factor weights through pairwise comparison (Saaty 1987). This method measures both tangible and intangible variables through relative weights given to each variable based on the preference of the researcher. It has been widely applied in MCDA, planning, natural and man-made resource allocation, and conflict resolution (Saaty 1986; Kamar and Anbalagan 2016; Jazouli et al. 2019; Nzotcha et al. 2019; Vargas and Zoffer 2019).
The AHP method has three distinct facets; decomposition, comparative judgment and synthesis of priorities. A complex problem is broken down into a hierarchy of variables or factors using a pairwise comparison matrix, factors are assigned weights on a nine-point scale see Table 2 (Eastman 2012). The factors are arranged in a matrix form with the same number of rows and columns with scores assigned to each factor in comparison to other factors (Saaty 1977). The scale of comparison of paired factors was determined from a careful literature review of landslide occurrences along the Cameroon Volcanic Line (Buh 2009; Diko 2012; Diko et al. 2012; Guedgjeo et al. 2013; Wotchoko et al. 2016; Ntchantcho et al. 2017). After generating the pairwise comparison matrix, weights of each factor were determined by calculating the principal Eigenvector of a square reciprocal of the metrics making sure they sum up to unity (Malczewski 1999; Ahmed 2015). The pairwise comparison is based on two intrinsic questions to determine criterion or factor more important than the others and the extent based on a ratio scale of 1/9 to 9 (Table 2). The AHP calculation was undertaken using Microsoft excel.
To validate the results of the pairwise comparison metrics and factor weights, the consistency index (CI) and the consistency ratio (CR) was determined (Eastman 2012). The consistency index is given by
$$CI= \frac{{\lambda }max-n}{n-1}\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \left(1\right)$$
Where CI = consistency index
λmax = normalized highest Eigenvalue of the pairwise matrix
n = number of factors (11 factors in this study)
The consistency ratio shows how random the matrix ratings were selected as given by Saaty (1980).
$$CR= \frac{CI}{RI}\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \left(2\right)$$
Where CR = consistency ratio
RI = Random Index
Random index (RI) has been proposed by Saaty (1987) and presented in Table 3
A consistency ratio of 0 implies perfect ratings of factors, CR of > 0.1 implies inconsistency of the ratings. Saaty (1980) suggested a re-evaluation of factor ratings for CR > 0.1.
The result of a pairwise comparison matrix gives rise to factor weight which is then aggregated to generate a landslide susceptibility map (Gorsevski et al. 2006; Jian & Eastman 2000; Boroumandi et al. 2015). Several methods have been employed to aggregate factor weights in generating susceptibility maps. These include; weighted linear combination, weighted sum, weighted overlay and ordered weighted average (Eastman and Jain 1995; Jain and Eastman 2000; Malczeswki 2004; Ahmed 2015; Vojtekova and Vojtek 2020).
3.3 Data Preparation
3.3.1 Landslide Inventory
The first step involved in producing a landslide susceptibility map is to generate an inventory of past landslides (Abedini and Tulabi 2018). Following the law of uniformitarianism, landslides are likely to occur in areas where past slope failures have been recorded (Guillard and Zezere 2012; Ge et al. 2018). Landslide inventory map can be used as a means for assigning weights to landslide triggering factors (Kumar et al. 2018). These maps can be generated from aerial photographs, field surveys, satellite images and existing landslides. Fourteen landslides were determined in the study area from the review of literature (Table 4) and the classification of satellite images (Fig. 1c).
3.3.2 Land use and Normalized Difference Vegetation Index
Land use map was generated from the Landsat 8 OLI satellite image through supervised classification using maximum likelihood (Lu and Weng 2007). False-colour composite images and Google Earth were used to obtain training data through the polygon method. Five landcover classes were identified; water body, agricultural land, built-up area, vegetation and bare soil (Fig. 2a).
Due to the influence of vegetation coverage on slope stability, normalized difference vegetation index (NDVI) was carried out to characterize vegetation extent in the study area Eq. 4
$$NDVI= \frac{IR-R}{IR+R}\dots \dots \dots \dots \dots \dots . \dots \dots \dots \dots \dots \dots ..\left(4\right)$$
Where NDVI = normalized difference vegetation index
IR = Infrared (band 5)
R = Red (band 4)
NDVI analysis results in an output of values ranging from − 1 to 1 where the negative values represent clouds, water and snow (Zaitunah et al. 2018). NDVI values of 0–0.1 represent barren land, rocks and soils while values of 0.6–1 represent dense vegetation (Fig. 2b).
3.3.3 Elevation
A 30m resolution shuttle radar topography mission (SRTM) digital elevation model (DEM) was downloaded from the USGS website. The average elevation of the study area is 155m, the lowest point is 224m and the highest point is 2744m (Fig. 2c). Generally, areas with higher elevations are more susceptible to landslides. The elevation generated was reclassified into five classes to determine the level of contribution of each category to landslides.
3.3.4 Slope
The digital elevation model (DEM) was used to generate a slope map, the slope in the study area ranges from 3.64o to 77.33o with an average of 40.49o (Fig. 2d). Areas with steep slopes are often more prone to landslides (Kavzoglu et al. 2014). The Slope was reclassified into five classes following the recommendation of Kumar et al. (2018). The categories are; flat to gentle, moderate, fairly moderate, steep and very steep slopes (Fig. 2d).
3.3.5 Aspect
Aspect refers to the orientation of a slope from 0o to 360o. Sunlight exposure, drying winds, rainfall and discontinuities are factors associated with slope aspect which influences the degree of susceptibility to landslides (Dai et al. 2001). Nine slope directions were generated and reclassified according to their contribution to landslide susceptibility (Fig. 2e).
3.3.6 Geology
A scanned geologic map of Cameroon was georeferenced, the geology of the study area was digitised into polygons that were converted to raster format. Four lithologies were identified; pre-syn tectonic granitoids, syn-post tectonic granitoids, orthogneiss, and volcanic rocks (Fig. 2f). The area has highly weathered volcanic rocks which have been identified in some studies as landslide-prone lithologies (Che et al. 2011).
3.3.7 Soils
The stability of slopes depends on the soils they contain (Sartohadi et al. 2018; Schiliro et al. 2019). The soil map was digitized from the African groundwater Atlas map. The soil atlas was converted from shapefile to a 30 m raster file in Arcmap. Five soil types of varying permeability and susceptibility to landslides were derived; andosols, loxisols, luvisols, stagnosols, and vertisols (Fig. 2g). luvisols are the dominant soil type in the study area. Soils capable of holding water have a higher level of susceptibility (Nandi and Shakoor 2009).
3.3.8 Rainfall
The average monthly rainfall data of the study area from the year 2000 to 2020 were downloaded from the NASA Earth Data website, this data was interpolated to generate the rainfall map (Fig. 2h). The average monthly rainfall ranges from 97 to 171mm/month. The rainfall data were reclassified into five classes representing susceptibility levels.
3.3.9 Distance to Road and River
Road cut and drainage density have been shown to influence slope stability (Van Buskirk et al. 2005; Yalcin et al. 2011). Road and river network data was downloaded from the OpenStreetMap data repository as shapefiles. The shapefiles were converted to raster data with a resolution of 30m. The Euclidean distance function in ArcMap was used to derive the distance to roads and rivers. Five classes were generated for both distances to road and distance to rivers (Fig. 2i and j).
Construction of roads along steep slopes leads to slope instability which is exacerbated by vehicle movement and high-water retention capacity in cracks that result (Yalcin et al. 2011; Awahdeh et al. 2018).
3.3.10 Distance to Fault
From the georeferenced geologic map of Cameroon, faults were digitised into line features (Fig. 2k). The multiple ring buffer function was used to generate a distance to faults. Five classes were derived with intervals of 5km.
3.4 Aggregation of Factor weights
In this study, the weighted linear combination (WLC) method was used (Appendix). This method is customized in many GIS platforms and it is flexible in combining thematic maps of conditioning factors to generate landslide susceptibility maps (Feizizadeh and Blaschke 2013). It requires the standardization of classes within each factor to a common numeric scale. The factor classes are multiplied by the weights obtained from the comparison matrix and their results summed to obtain the landslide susceptibility index (Eq. 3).
$$LSI=\sum _{j=1}^{n}Wj X Zij\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots .\left(3\right)$$
Where LSI = Landslide Susceptibility Index
Wj = Weight value of causative factor j
Zij = Weight value of class i of causative factor j
The landslide susceptibility indices generated was reclassified to derive the landslide susceptibility map using the Jenk classification method. The map was reclassified into five classes; very high, high, moderate, low and very low susceptibilities (Fig. 3).