Calculating factor weights has a crucial role in the production of landslide susceptibility maps by applying GIS-MCDA methods (Kavzoglu et al. 2013). The calculations of relative weights of the factors and order were based on the expert opinion surveying, analysing the landslide inventory map, and local knowledge obtained from field surveying.
LSM using AHP method
To apply the AHP method, first it is necessary to construct a pairwise matrix. Then, both the weight values of sub-criteria of the criterions and the datasets/factors were calculated (Tables 2 and 3). In the next step, the CR was calculated in order to determine whether the pairwise comparisons were consistent or not (Saaty 1977). In this research, the resulting CR for all the cases was found less than 0.10 (Tables 2 and 3). It means the relative weights were appropriate and the comparisons were consistent (Saaty 1977; Feizizadeh and Blaschke 2013).
It was found that the highest weight was assigned to soil permeability map. Slope, elevation, land cover, and NDVI factors were also found effective. The other layers (i.e., precipitation, distance to drain, road, and stream) were identified as less important (Table 3).
After applying the AHP generated weights in the data layers, the resulting map was reclassified into three meaningful levels as: low, medium, and high susceptibility zones (Fig. 14). This is helpful for presentation and evaluation purposes. An expert knowledge-based classification was used to define the class intervals. This technique of landslide susceptibility zoning was implemented for the rest two methods (WLC and OWA).
LSM using WLC method
Based on expert opinion surveying and using local knowledge, three different combinations of factor weights were generated (Table 4). At first, the factor maps multiplied the weights from the pairwise comparison matrix and all the weighted factor maps were then aggregated. Finally, the maps were reclassified to produce the WLC generated landslide susceptibility maps (Fig. 15).
LSM using OWA method
OWA method uses order weights in addition to criterion/factor weights. Order weights control the manner in which the weighted factors are aggregated (Eastman and Jiang 1996). In traditional WLC method, criteria weights determine how factors trade-off relative to each other (Jiang and Eastman 2000). Trade-off is the degree to which one factor can compensate for another; how they compensate is governed by a set of ‘factor weights’/‘trade-off weights’. A factor with a high factor/trade-off weight may compensate for low suitability in other factors that have lower factor/trade-off weights (Eastman 2012). However, the level of trade-off is not adjustable in WLC. But, in the case of OWA method, the criteria weights can be adjusted according to the level of trade-off by using the order weights (Jiang and Eastman 2000).
The factor with the lowest suitability score, after factor weights are applied, is given the first order weight. The factor with the next lowest suitability score is given the second order weight, and so on. Applying order weights has the effect of weighting factors based on their rank from minimum to maximum value for each location. When ordered weights are the same, OWA creates a result that is identical to WLC. This indicates that WLC is a special case of OWA (Eastman 2012). In this research, the factor and order weights (Tables 5 and 6) were obtained from the AHP and WLC methods, respectively, as described above. This is how, three different OWA generated landslide susceptibility maps were produced (Fig. 16).
Analysis of the results
At first, the landslide susceptibility maps were evaluated qualitatively. It helps to select the most appropriate method of LSM for a particular area (Feizizadeh and Blaschke 2013). In the case of the AHP method, high susceptibility zones cover about 23 % of the total area, while about 54 % area was classified as medium susceptible, and the remaining 24 % area was classified as low susceptible zone (Table 7). About 42, 20, and 2 % areas fall within the high susceptible zone for the WLC_1, WLC_2, and WLC_3, respectively. Similarly, about 20, 3, and 1 % areas were classified as high susceptible zones for the OWA_1, OWA_2, and OWA_3 methods, respectively (Table 7).
Then the accuracies of the landslide susceptibility maps were determined quantitatively. To do this, the landslide inventory map with the 20 known landslide events was compared with the respective susceptibility maps derived from the AHP, WLC, and OWA methods (Table 7). For the AHP method, the comparison shows that 100 % of the known landslides fall into the high susceptibility zone. No known landslide event was observed in the remaining categories (Table 7). The comparisons showed that the high susceptibility zones covered exactly 100, 100, and 90 % of the known landslides for the WLC_1, WLC_2, and WLC_3, respectively. Lastly, the high susceptible zones covered 100, 90, and 45 % of the known landslides for the OWA_1, OWA_2, and OWA_3 methods, respectively. In all the cases, no landslide was observed in the low susceptibility zones (Table 7).
High susceptibility zone covering 100 % of known landslides does not always mean that the results are accurate. In some cases, high susceptibility zone occurred in the flat areas with moderate or mixed moderate soil permeability indicates that the results obtained using the MCDA methods also have some errors. MCDA methods are generally based on weighting the factor maps and finally overlaying those layers. As a result, any incorrect perception on the role of the different slope-failure criteria can be easily conveyed from the expert’s opinion into the weight assignment (Kritikos and Davies 2011). This can cause errors in the final outputs. In this research, a total of 9 factor maps each with 5 classes were considered. It is difficult to assign criteria weights for all these sub-factors and develop a proper combination. Therefore, it is important to keep the factor map layers and their classes into reasonable numbers for getting better results. Errors can also occur due to incorrect pairwise comparisons between the criteria, classifying the factor maps and defining the susceptibility zones qualitatively. Moreover, there might be errors in the GIS/remotely sensed datasets, problems while conducting questionnaire surveying for defining the weights, and taking the GPS values, etc. The main challenge of this kind of GIS-MCDA analyses is to keep the errors as less as possible. This can be achieved by defining the best combination of criteria weights.
AHP method uses pairwise comparison of each criterion, while WLC directly assigns the weights of relative importance to each attribute map layer and OWA involves two-step weighting (criterion and order weights). Each method follows its own way of assigning weights to factors or orders. Therefore, it is not possible to declare that one method is superior to other. As it is a trial and error/iterative process, the final output maps may give some errors as well. Still the MCDA methods give better accuracies, which are acceptable for producing real-world LSM in terms of landslide disaster risk reduction. Moreover, each MCDA method can produce different types of landslide susceptibility maps based on assigning different weights for the instability factors. The weights can be obtained through expert opinion surveying, or even it can be achieved from the participatory-based community surveying, or it can be a combination of both. Finally, it is the researcher's or policy makers’ decision to choose the appropriate weighting combination and the output maps, as per the local context and research/project objectives.
Validation of the methods
In order to determine the statistical reliability of the results, it is important to perform validation of spatial results in a structured manner (Ahmed et al. 2013b). To do this validation, Relative Operating Characteristic (ROC) method was used in this research. The ROC analysis is useful for cases in which the scientist wants to see how well the suitability map portrays the location of a particular category, but does not have an estimate of the quantity of the category. For example, the ROC could be used to compare an image of modelled probability for landslides against an image of actual observed landslides (Eastman 2012). The area under ROC curves (AUC) constitutes one of the most common used accuracy statistics for the prediction models in natural hazard assessments (Ahmed and Rubel 2013). The minimum value of AUC is 0.5, which means no improvement over random assignment. The maximum value of AUC is 1 that denotes perfect discrimination (Nefeslioglu et al. 2008).
The comparison results are shown in Fig. 17 as a line graph (threshold type is equal interval and number of thresholds is 25 %). The AUC values are indicating the accuracies of the methods used for LSM. The AUC values of the AHP, WLC_1, WLC_2, WLC_3, OWA_1, OWA_2, and OWA_3 methods were calculated as 0.898, 0.839, 0.911, 0.885, 0.904, 0.951, and 0.871, respectively (Fig. 17). In general, the verification results showed satisfactory agreement between the susceptibility map produced and the observed landslide location map (AUC values ranged from 0.871 to 0.951). Finally, it can be stated that higher accuracy was found for all the MCDA methods applied. But the landslide susceptibility map produced by the OWA_2 method appeared to be slightly more accurate than those generated by applying the other methods (Fig. 17).