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Effect of Landslide Factor Combinations on the Prediction Accuracy of Landslide Susceptibility Maps in the Blue Nile Gorge of Central Ethiopia

Effect of Landslide Factor Combinations on the Prediction Accuracy of Landslide Susceptibility... Database construction for landslide factors (slope, aspect, profile curvature, plan curvature, lithology, land use, distance from lineament & distance from river) and landslide inventory map is an important step in landslide susceptibility modelling. Using the frequency ratio model, the weights for each factor classes were calculated and assigned in GIS so as to add these factors and produce landslide susceptibility index maps based on mathematical combination theory. However, before combining them, their independence among each other should be ascertained. For this, the correlation matrix of logistic regression was applied and this showed that most of the correlations between factors were either absent or very insignificant suggesting that all landslide factors are independent. From a set of eight landslide factors, a total of 247 landslide susceptibility map combinations can be generated. However, for simplification, only 28 landslide susceptibility maps were chosen. Then the best landslide susceptibility map was selected based on high prediction accuracy. But, when there is similarity in the prediction accuracies of different combinations, the landslide susceptibility index difference values can be used as another selection criterion. Hence, the susceptibility map from a combination of all landslide factors except distance from river was found to be the best one. Among the 28 representative combinations, landslide susceptibility maps with the same prediction accuracy of 87.7% have been found in spite of their dissimilarity in their difference values. The combination, with a limited number of landslide factors and the highest prediction accuracy of 87.7%, was found from a combination of slope, lithology, land use and distance from lineament. In order to validate the prediction model, landslides were overlaid over the landslide susceptibility map and the number of landslides that fall into each susceptibility class was calculated. From this analysis 0.39%, 1.84%, 9.1%, 32.04% and 56.63% of the landslides fall in the very low, low, medium, high and very high landslide susceptibility classes respectively. Since 88.67% of the landslides fall in the high and very high susceptibility classes, the landslide susceptibility map can be considered reliable to predict future landslides. Keywords: Landslide susceptibility; GIS; Frequency ratio; Combination; Prediction accuracy; Ethiopia Background 2011), deterministic (Godt et al. 2008) and a combination Landslide is the movement of a mass of rock, debris or of statistical and deterministic (Terlien 1998) methods. earth (soil) down a slope and landslide susceptibility is a Susceptibility, hazard and risk maps are important tools quantitative or qualitative assessment of landslide about for engineers, earth scientists, planners and decision its classification, volume (or area) and spatial distribution makers select appropriate sites for agriculture, construc- (IUGS 1997, Fell et al. 2008). Landslide susceptibility tion and other development activities (Ercanoglu and mapping methods are classified into heuristic (Ruff and Gokceoglu 2002). They also play an important role in Czurda 2008), statistical (Lee et al. 2004; Pradhan et al. efforts to mitigate or prevent the disaster in landslide prone areas by providing important information to the concerned bodies. In heuristic methods, field observation and expert’s knowledge are used to identify landslides, * Correspondence: matebe21@gmail.com Geo-Disaster Research Laboratory, Graduate School of Science and Engineering, Ehime University, 3 Bunkyo, Matsuyama 790-8577, Japan © 2015 Meten et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 2 of 17 make a prior assumption about past and future landslide of its analysis potential and capability. A continuous and up movements on the site, assign weighted values for the clas- to date landslide susceptibility map is vital to planners, en- ses of index maps and overlay them to produce a landslide gineers and decision makers in order to devise appropriate susceptibility map. In deterministic method, data on slope landslide prevention and mitigation measures. In this re- geometry, shear strength (cohesion and angle of internal gard, a statistical (probabilistic) model known as frequency friction) and pore pressure are required (Regmi et al. 2010a). ratio has been applied in the current study area. This model A significant limitation of deterministic models is the need was chosen because it is easy to understand and simple to for geotechnical data (cohesion, internal angle of friction, implement. Data input, output and analysis processes are depth to groundwater table, degree of saturation etc.) which fast and a huge amount of data can be handled and run are difficult to obtain over large areas (Terlien et al. 1995). quickly (Lee and Pradhan 2007; Lee et al. 2007). Data from Ayalew (1999), Temesgen et al. (2001), Frequency ratio model avoids the lengthy procedures of Woldearegay (2008) and Ibrahim (Ibrahim J, 2011: raster to point data conversion in GIS, weight calculation in Landslide assessment and hazard zonation in Mersa and statistical software and switching from statistical software to Wurgessa, North Wollo, Ethiopia, unpublished Master GIS for the preparation of landslide susceptibility map un- Thesis) showed that landslide in Ethiopia has resulted loss like logistic regression and artificail neural network models. of human lives, properties and infrastructures particularly Besides this, it utilizes all the available data contrary to the in the last five decades. From 1960 to 2010 alone, about other two models, which may use a limited proportion of 388 people were dead, 24 people were injured and a great the data because of the low data processing capacity of the deal of agricultural lands, houses and infrastructures were statistical software. Using a frequency ratio model, Lee and affected. Landslide problem in the Abay (Blue Nile) Gorge Talib (2005) have found the prediction accuracy of 72.1% in is a serious challenge to the community residing in this area Penang, Malaysia and Lee and Sambath (2006) have found and to the road infrastructure that connects Addis Ababa a prediction accuracy of 86.97% in the Damrei Romel area to Bahir Dar. In 1960, a terrible landslide at Gembechi of Cambodia. Lee and Pradhan (2007) have shown that village within Bechet valley was responsible for the loss of the frequency ratio resulted a better prediction accuracy 45 people (Ayalew 1999). On September 2, 1993 a landslide than the logistic regression at Selangor area in Malaysia. incidence occurred in the Blue Nile Gorge, which killed an Similarly, Pradhan (2010a) showed that the validation result ox, damaged agricultural fields, destroyed crops and as a of the frequency ratio model in the Cameron catchment of result 700 households were stricken by food insecurity. Malaysia is slightly better than logistic regression and fuzzy Besides this the main road, which was 5 km south of Dejen logic models with a prediction accuracy of 89.25%. town has been damaged with a displacement of 1.5 meters Until now researchers, who were engaged in the this by the sliding mass (Tadesse T, Dessie T and Deresa K, model, were simply summing all the frequency ratio 1994: Landslideincidencein theBlueNileGorgeof East raster maps of landslide factors (Lee and Sambath 2006) Gojam, Ethiopia. Geological Survey of Ethiopia, 823 report, or exclude one factor and sum all the remaining ones 830-301-01, unpublished). The road damage is a common (Lee and Talib 2005). However, the previous works lack phenomenon of the mid to end of each rainy season (i.e. ways of systematic combination, identifying the number June 1 to September 30) due to the gradual weakening of of possible combinations, providing more than one the soft and weathered rocks by heavy rain and ground- selection criterion to select the best landslide suscepti- water percolation through big columnar joints of basalt to bility map and finding a combination with high predic- the underlying limestone formation bearing mudstone and tion accuracy from a limited number of factors. shale at its top and middle strata. For example, Asfaw The current study tries to prepare different landslide (2010) reported a road damage near Goha Tsiyon town on susceptibility maps from eight landslide factors and September 5, 2009. Such incidences happened due to the landslide inventory with different combinations using frequency ratio model and make a comparison on the progressive softening of weathered basalt and pyroclastic rocks by heavy rainfall, groundwater recharge through the prediction accuracies of these combinations in order to columnar joints of basalt and by a gushing stream that select the best landslide susceptibility map. This will help to suggest a limited number of landslide factors crosses a road. The Goha Tsion-Dejen transect is an important transport corridor connecting Addis Ababa with that can produce a susceptibility map with the highest the regions in the northwestern part of the country. How- prediction accuracy similar to a combination using all or most of the landslide factors. The main objectives of ever, it is affected by a complex landslide problem almost on a yearly basis. To overcome this problem, few re- this study are: (1) to apply the frequency ratio model searchers in the field of Geotechnics, Geoscience and slope using combination theory, (2) to identify the possible stability have been undertaking investigations in the Blue numbers of combinations, (3) to evaluate the effect of Nile Gorge. Recently, GIS is becoming a powerful tool to different combinations on the prediction accuracy of study landslide susceptibility and hazard worldwide because landslide susceptibility maps and (4) to select the best Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 3 of 17 landslide susceptibility map among different alternatives. and validation stages (Figure 3). During the data prepar- In light of this, the following questions will be addressed ation stage a database was constructed for landslide fac- in the subsequent chapters of this paper. (1) How many tor maps and landslide inventory map. The landslide combinations are possible in the frequency ratio model factor maps were derived from the geological map for with a certain number of landslide factors? (2) Which lithology and lineament, topographic maps for rivers, combination of landslide factors will give the best pre- Google earth images for land use, DEM (digital elevation diction accuracy? (3) How can we prioritize if the two model) for slope, aspect, profile curvature and plan landslide susceptibility maps have the same prediction curvature. The river and lineament data were changed accuracy? (4) How can we identify the best landslide into distance from river and lineament based on Arc GIS susceptibility map obtained from a limited number of multiple ring buffer analysis. The landslide inventory landslide factors? map, which contains 595 landslides, was also prepared from field observation and Google earth image analysis. Study area The continuous data like slope, aspect, profile curvature The study area is located in the Abay (Blue Nile) Gorge and plan curvature were reclassified into appropriate of Central Ethiopia and it is bounded by 38° 2' E to 38°15" number of classes. Then, all the eight landslide factors E longitudes and 10° 0′ N to 10° 15' N latitudes covering and landslide inventory map were organized in a raster an area of 391 sq. km (Figure 1). This area is found in the format with the same geographic projection and same highly dissected portion of the Blue Nile basin with a pixel size of 30 m. The frequency ratio model requires depth of 1.5 km from plateau top to the valley floor. The assigning the frequency ratio values (FRV) for each lowest elevation in the study area is 1000 m while the factor’s class by dividing landslide percentage to area per- highest is 2500 m. It contains the major Abay (Blue Nile) centage. Then the frequency ratio value maps of landslide River and its tributary rivers like Bechet, Muga and other factors were added based on the mathematical combin- unnamed small streams (Figure 2) with the level of ation rule in order to get the landslide susceptibility incision being higher in the three rivers. index maps for different combinations. A total of 247 combinations were possible but only 28 best combina- Methods tions were selected in order to simplify the data handling The methods applied in this paper include data prepar- and analysis process. For prediction purpose the landslide ation, data analysis through frequency ratio model, susceptibility index maps were extracted with landslide prediction, landslide susceptibility map preparation and non-landslide points and then analyzed using SPSS Figure 1 Location map of the study area showing the general landscape and elevation ranges in the Goha Tsiyon-Dejen transect of Abay (Blue Nile) gorge. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 4 of 17 Figure 2 Landslide inventory map of the study area. statistical software so as to check the overall statistics, selected from a limited number of landslide factors. receiving operating characteristics (ROC) curves and area Finally, the two landslide susceptibility maps were reclassi- under the curve (AUC) values. The prediction accuracies fied into five susceptibility classes and the validation was of each combination of landslide factors can be found by done by overlaying the landslide inventory map over the multiplying AUC values by 100%. However, the prediction best landslide susceptibility map. accuracies of different combinations from the success-rate curve may not always be enough to discriminate which Landslide inventory landslide susceptibility map is best among many alterna- A landslide inventory map, consisting 595 landslides, tives. Hence, the difference between minimum and max- was prepared from field observations and Google earth imum landslide susceptibility index (LSI) difference values images of the study area (Figure 2). Landslides in the was also used as another distinguishing criterion. If the area include rock slides, rock falls, debris slide and mud- difference is higher, then it will be better as it contains a flow. According to Ayalew and Yamagishi (2004) rock broader range of values compared to the smaller differ- falls exist as discernible block topples and wedge failures ence values. Based on the highest prediction accuracy and along the mountains, valley walls and road cuts. Simi- LSI difference values, the best landslide susceptibility map larly, rock slides are also abundant on the ridge sides from each combination group or from all combinations and valley walls. The intensity of landslides is generally was selected. Another optimum landslide susceptibi- high in the upper catchments of Bechet and Muga lity map with the highest prediction accuracy was also valleys and on the road cut near GohaTsiyon town. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 5 of 17 Figure 3 Flow chart showing the whole process of the work. FR = Frequency ratio raster map for li = lithology, dl = distance from lineament, dr = distance from river, lu = land use, sl = slope, as = aspect, pr = profile curvature and pl = plan curvature. Landslide factors scenarios. The main effects of tectonics are localized The landslide factors used in this paper include lith- changes in the river course and changes in local topog- ology, distance from lineament, land use, distance from raphy (Pirasteh et al. 2009). river, slope, aspect, plan and profile curvatures (Figure 4). The landscapes are greatly influenced by tectonics, Lithology bedrock lithology and the courses of major rivers. The The lithology of the study area comprises seven litho- complex processes of tectonics, erosion and sedimen- logical units. These are (1) Paleozoic Sandstone (2) tation generates water gaps, knick points, meanders Mesozoic Lower Sandstone (3) Mesozoic Gypsum, shale and many other tectonic and geomorphic features (Pirasteh and mudstone (4) Mesozoic Limestone (5) Tertiary et al. 2009). Tectonics may probably promote river inci- Lower Basalt (6) Tertiary Upper Basalt and (7) Quater- sion in onesideand riveraggradation to theother side nary Soil in their chronological order from older to and rivers respond in different ways to similar tectonic younger units (Figures 5 4e). The Paleozoic Sandstone Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 6 of 17 Figure 4 Landslide influencing factors (a) slope (b) aspect (c) profile curvature (d) plan curvature (e) lithology (f) land use (g) distance from lineament (h) distance from river. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 7 of 17 Figure 5 Litho-stratigraphic sections along the GohaTsiyon – Dejen Road. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 8 of 17 consists of fine grained sandstone with whitish gray vegetation, particularly on the steep walled river banks and brown colors occupying the river course of Abay of Muga and Bechet rivers, is more highly susceptible to (Blue Nile) attaining a maximum vertical thickness of land sliding than the other land use types. 50 m. It is highly weathered, slightly friable forming mod- erately sloping morphology. Mesozoic Lower Sandstone is Distance from lineament reddish brown, light gray, medium to coarse grained, Lineaments, which are found along steep linear ridges in sometimes conglomeratic, medium to thickly bedded the Abay (Blue Nile) gorge, have a strong influence in and crossbedded sandstone forming steep to moderately conditioning landslide incidences provided that the other sloping cliffs on the river banks of the Abay (Blue Nile) favorable factors are also set in place. As can be seen in River overlying the Paleozoic Sandstone. This unit is Table 1, the frequency ratio values for the distance from found in elevation range between 1050 m and 1336 m lineament showed higher values in the distance range of 0 with a vertical thickness of 286 m. Mesozoic Gypsum, to 200 m. The other distance classes revealed a less Mudstone and Shale unit consists of the dominant gypsum number of landslides. The surface rupture intensity is also interbedded with minor mudstone and shale. This unit influenced by distance from lineament or fault and ground is exposed in the elevation range between 1336 m and conditions. As the distance from the lineaments becomes 1749 m in the GohaTsiyon – Abay River section with a smaller, the fracture of the rock masses and the degree vertical thickness of 413 m. Gypsum is whitish gray, gray of weathering increases resulting in greater chances of and sometimes banded, forming gentle morphology. landslide occurrence (Farrokhnia et al. 2010). Mudstone is yellowish gray, highly weathered and friable. Mesozoic Limestone is yellowish gray and light gray in Distance from river color, mostly fossiliferous, medium to thickly bedded Rivers usually play a significant role in modifying the and forms gentle to steep cliffs. The limestone forms a landscape by incising the different rocks. In the study bed thickness of 0.25 – 0.5 m and sometimes it may area, the Abay (Blue Nile), Bechet and Muga Rivers reach up to 1 m. The Tertiary Lower Basalt forms a steep and many other streams incised the Tertiary Volcanic morphology unconformably overlying the Mesozoic rocks and Paleozoic and Mesozoic sedimentary rocks Limestone. It is dark gray, fine to medium grained, to a maximum depth of 1.5 km. The role played by aphanitic basalt, plagioclase phyric and olivine - plagioclase rivers in creating a conducive environment for land- phyric basalts. The basalt in GohaTsiyon – Dejen Road slide occurrence has great significance. The maximum shows a spectacular columnar jointing and triggers a number of landslides in the close proximity of rivers, critical landslide problem. The Tertiary Upper Basalt is as can be seen in Table 1, shows how rivers are con- dark gray, fine to medium grained rock, consisting tributing to landsliding. In the steep-walled river banks plagioclasephyric, olivinephyricand aphaniticbasalts of Bechet and Muga, landslides are common, particu- overlying thin beds of pyroclastic rocks. Lastly, in-situ larly in fractured Tertiary Lower Basalt and the under- weathering of the Tertiary basalts has given rise to the lying Mesozoic Limestone units. development of Quaternarysoil on the Dejen plateau. Slope Land Use Slope is one of the most important topographic parame- The land use type in the area includes agricultural land, ters influencing the occurrence of landslides in the study barren land, bushes, dense forest, sparse forest, shrubs, area. The landslide frequency is higher in the slope grassland, rural settlement, urban settlement and river classes of 20 - 30°, 30 - 40° and 40 - 67° and the highest (Figure 4f; Table 1). The reason why dense forest, sparse one is recorded in the slope class of 30 - 40° (Table 1). forest and shrubs are susceptible to land sliding can be Generally speaking, as slope increases, the probability attributed to the existing steep slope morphology and of landslide occurrence also increases. the sallow rooted nature of different evergreen vegeta- tion types in the area. The presence of vegetation may Aspect increase the rate of infiltration. This in turn increases Aspect (slope orientation) affects the exposure to sun- the accumulation of water, thereby decreasing the stabil- light, wind and precipitation thereby indirectly affecting ity of the slope due to increased pore water pressure and other factors that contribute to landslides such as soil unit weight of the sliding mass (Farrokhnia et al., 2010). moisture, vegetation cover and soil thickness (Clerici This may be worsened if the vegetation types in the area et al. 2006). The aspect of the area is classified into flat, have a huge weight and are shallow rooted with the north, northeast, east, southeast, south, southwest, west roots found above the slip surface of the landslide mass. and northwest facing classes (Figure 4b). The number of It is obvious that the barren land comprising a degraded landslides is higher in the aspect classes of E, SE, S, SW portion of the study area which is devoid of any and W but the frequency ratio values of SE, S and SW Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 9 of 17 Table 1 Frequency ratio value calculation by rationing landslide percentage to area percentage Factor Class # landslide % landslide # area % area FRV = a b Pixels Pixels Pixels Pixels (a/b) Slope (°) 0 - 5 60 0.388 38089 8.770 0.04 5 - 10 333 2.151 87417 20.129 0.11 10 - 15 811 5.239 102933 23.702 0.22 15 - 20 1430 9.238 77279 17.794 0.52 20 - 30 4195 27.099 80829 18.612 1.46 30 - 40 4589 29.645 34095 7.851 3.78 40 - 67 4062 26.240 13645 3.142 8.35 Aspect Flat 5 0.03 1234 0.284 0.11 N 424 2.74 29729 6.845 0.40 NE 1013 6.54 44175 10.172 0.64 E 2127 13.74 64829 14.928 0.92 SE 3136 20.26 60584 13.950 1.45 S 2306 14.90 52443 12.076 1.23 SW 3144 20.31 73195 16.854 1.21 W 2366 15.28 67137 15.459 0.99 NW 959 6.20 40961 9.432 0.66 Plan curvature - 10.7829 - - 1.7917 620 4.005 2810 0.647 6.19 - 1.7917 - - 0.9103 1704 11.008 20924 4.818 2.28 - 0.9103 - - 0.1111 4986 32.209 154198 35.506 0.91 - 0.1111 - 0.1111 1724 11.137 78020 17.965 0.62 0.1111 - 0.5882 3117 20.136 121053 27.874 0.72 0.5882 - 1.3815 2315 14.955 49643 11.431 1.31 1.3815 - 11.7830 1014 6.550 7639 1.759 3.72 Profile curvature - 10.9947 - - 2.3629 767 4.955 3648 0.840 5.90 - 2.3629 - - 1.0810 1984 12.817 23076 5.314 2.41 - 1.0810 - - 0.1154 4045 26.130 151550 34.896 0.75 - 0.1154 - 0.1154 1332 8.605 74725 17.206 0.50 - 0.1154 - 0.7991 3358 21.693 134940 31.072 0.70 0.7991 - 1.9956 2737 17.681 40629 9.355 1.89 1.9956 - 10.8837 1257 8.120 5719 1.317 6.17 Distance from river 0 - 100 5975 38.60 173853 40.032 0.96 (m) 100 - 200 3728 24.08 116838 26.903 0.90 200 - 300 2305 14.89 63633 14.652 1.02 300 - 400 1323 8.55 34376 7.916 1.08 400 - 500 810 5.23 19283 4.440 1.18 500 - 600 480 3.10 11048 2.544 1.22 600 - 700 350 2.26 6352 1.463 1.55 700 - 800 223 1.44 3866 0.890 1.62 800 - 900 102 0.66 2253 0.519 1.27 900 - 1000 49 0.32 1351 0.311 1.02 1000 - 1100 74 0.48 748 0.172 2.78 1100 - 1200 47 0.30 485 0.112 2.72 1200 - 1300 14 0.09 150 0.035 2.62 Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 10 of 17 Table 1 Frequency ratio value calculation by rationing landslide percentage to area percentage (Continued) 1300 - 1400 0 0.00 46 0.011 0.00 1400 - 1500 0 0.00 5 0.001 0.00 Factor Class # landslide % landslide # area % area FRV = a b Pixels Pixels Pixels Pixels (a/b) Distance from 0 - 200 11297 72.978 108715 25.033 2.92 Lineament (m) 200 - 400 2017 13.030 84627 19.486 0.67 400 - 600 930 6.008 61629 14.191 0.42 600 - 800 487 3.146 47825 11.012 0.29 800 - 1000 236 1.525 36076 8.307 0.18 1000 - 1200 169 1.092 26915 6.198 0.18 1200 - 1400 175 1.130 23374 5.382 0.21 1400 - 1600 119 0.769 18887 4.349 0.18 1600 - 1800 42 0.271 12387 2.852 0.10 1800 - 2000 6 0.039 7334 1.689 0.02 2000 - 2200 2 0.013 3926 0.904 0.01 2200 - 2400 0 0.000 1634 0.376 0.00 2400 - 2600 0 0.000 576 0.133 0.00 2600 - 2800 0 0.000 281 0.065 0.00 2800 - 3000 0 0.000 101 0.023 0.00 Land use Agricultural land 7518 48.566 290914 66.987 0.725 Sparse forest 706 4.561 10747 2.475 1.843 Rural settlement 55 0.355 16384 3.773 0.094 Barren land 4085 26.389 12423 2.861 9.225 Bushes 2813 18.172 88635 20.409 0.890 River 0 0 10049 2.314 0 Dense forest 171 1.105 1347 0.310 3.562 Grass land 39 0.252 1357 0.312 0.806 Shrubs 93 0.601 999 0.230 2.612 Urban settlement 0 0 1432 0.330 0 Lithology Quaternary soil 184 1.189 6221 1.432 0.83 Tertiary lower basalt 7733 49.955 94821 21.834 2.29 Mesozoic limestone 4011 25.911 129156 29.740 0.87 Mesozoic gypsum, Mudstone and shale 1170 7.558 140797 32.420 0.23 Mesozoic lower sandstone 2086 13.475 46758 10.767 1.25 Paleozoic sandstone 55 0.355 12044 2.773 0.13 Tertiary upper basalt 241 1.557 4490 1.034 1.51 facing slopes were found to be significant in causing curvature of the topographic contours or the curvature landslides. of a line formed by the intersection of an imaginary horizontal plane with the ground surface. Hillsides can Profile and plan curvatures be concave outward plan curvatures called hollows, Profile and plan curvatures are used for hill-slope and land- convex outward plan curvatures called noses and slide analysis (Ayalew and Yamagishi 2004). (Ohlamacher straight contours called planar regions. In hollows land- 2007) presented a detailed account of plan curvature slide material converges into the narrow region at the and its effect on hill-slope stability in earth flow and base of the slope. Profile curvature is the curvature in earth slides dominated regions. Plan curvature is the the downslope direction along a line formed by the Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 11 of 17 intersection of an imaginary vertical plane with the the frequency ratio model. The eight landslide factors that ground surface (Ohlamacher 2007). Both profile and are used in this study include lithology, land use, distance plan curvatures affect the susceptibility to landslides. from lineament, distance from river, slope, aspect, profile Profile curvature affects the driving and resisting stresses and plan curvatures were used to establish this relation- within a landslide in the direction of motion. Plan ship with landslides (Table 1). curvature controls the convergence or divergence of The number of landslide pixels in each class has been landslide material and water in the direction of land- evaluated and the frequency ratio for each factor class is slide motion (Carson and Kirkby 1972). The sign of the found by dividing the landslide ratio by the area ratio curvature value is important for determining concavity (Lee and Talib 2005). Frequency ratio shows the correlation or convexity of the curve. In both profile and plan between landslides and causative factors in a specific area. curvature maps, concave and convex surfaces are repre- If this ratio is greater than 1, then the relationship between sented by the respective negative and positive values a landslide and the factor’s class will be strong but if the ra- (Pradhan 2010a). Based on the plan curvature hill-slopes tio is less than 1, then the relationship will be weak and if can be subdivided into hollows, noses and relatively planar the value is 1, it means an average correlation (Lee and regions. Hollows are regions in which the plan curvature Sambath 2006; Pradhan 2010a). Once the frequency ratio of the contours is concave in the downslope direction of each landslide factor's class was found, the landslide sus- and where surface water would converge as it moves ceptibility index (LSI) can be calculated by summation of downslope (Reneau and Dietrich 1987). Noses or coves each factor’s frequency ratio values (Lee and Sambath are regions where the plan curvature of the contours is 2006). A higher LSI means a higher susceptibility to land- convex in the downslope direction and the surface slide while a lower LSI indicates a lower susceptibility to water will diverge (Hack and Goodlett 1960). Relatively landslides (Bui et al. 2012). planar regions have plan curvature values around zero. In the current study, landslide factors were converted Hollows concentrate groundwater and the concentra- into raster maps with a pixel size of 30 m, the spatial re- tion of groundwater probably leads to increased land- lationship between the landslide location and each land- slide activity. slide factor was analyzed and the ratings for each factor’s class were assigned to each class in a specific factor. Triggering factor Then the frequency ratio ratings of factors in the form The most important triggering factor for landslide of raster maps were summed to form the landslide sus- occurrence in the Blue Nile Gorge is heavy rainfall from ceptibility index (LSI) using equation (1). the beginning of June to the end of September. This season accounts for more than 75% of the annual rain- LSI ¼ Fr ð1Þ fall in the study area. Data from National Meteoro- i¼1 logical Agency of Ethiopia showed that the minimum, average and maximum annual rainfalls of the study area Where Fr is the raster map of each landslide factor in are 1100 mm, 1200 mm and 1400 mm respectively and which the frequency ratio values (FRV) are assigned to sometimes the peak annual rainfall reaches up to it. The current study tries to analyze the effect of differ- 1985 mm (Figure 6a). The peak monthly rainfall in four ent combinations of landslide factors on the perform- stations showed its maxima during the months of July ance of the frequency ratio model in order to get the and August (Figure 6b). Landslides usually occur at the minimum number of landslide factors which can pro- beginning or mid of September after the soil and rocks duce a susceptibility map with higher prediction accur- are saturated and the pore water pressure becomes acy similar to combining many landslide factors using high. In every rainy season landslide events are happen- the mathematical combination theory. ing along the main national road between Goha Tsiyon and Dejen and also at steeply sloping ridges and steep- Mathematical combination theory walled river banks. In mathematics, a combination is a way of selecting members from a grouping, such that the order of selec- Theory tion does not matter unlike permutations. In smaller Frequency ratio method cases it is possible to count the number of combinations. The assumption of conditions that are similar to the past For example, given three fruits, say an apple, an orange is very important for landslide susceptibility mapping (Lee and a pear, there are three combinations of two that can and Talib 2005). Probabilistic (statistical) approaches are be drawn from this set: an apple and a pear; an apple based on relationships between each landslide factor and and an orange; or a pear and an orange. More formally, the distribution of past landslides (Lee and Talib 2005) a k-combination of a set S is a subset of k distinct ele- and this relationship can be evaluated quantitatively using ments of S. If the set has n elements, the number of k- Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 12 of 17 Figure 6 Rainfall amount of (a) annual rainfall (b) average rainy season rainfall of the four stations in the study area. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 13 of 17 combinations is equal to the binomial coefficient (http:// approach in order to select and combine different num- en.wikipedia.org/wiki/Combination) as follows. ber of landslide factors among the eight landslide fac- tors. The possible numbers of combinations of 8, 7, 6, 5, nnðÞ −1 …ðÞ n−k þ 1 4, 3 and 2 landslide factors from a set of 8 landslide factors ¼ ; ð2Þ k kkðÞ −1 …1 are 1, 8, 28, 56, 70, 56 and 28 respectively totaling to 247 possible combinations (Table 2). This can be written using factorials as: Result and discussion n! ð3Þ In order to apply the frequency ratio model, the most k!ðÞ n−k ! important first step is to prepare a database of landslide Where k ≤ n, and which is zero when k > n. factors and a landslide inventory map. This involves Combinations refer to the combination of n things digitizing polygon features like lithology, land use and taken k at a time without repetition. landslide inventory; line feature like lineaments and riv- In combination, the ordering of selected objects is im- ers and preparing digital elevation model (DEM) deriva- material. The current study applies the combination tives such as slope, aspect, profile and profile and plan Table 2 Representative combinations of factors from each group giving the best landslide susceptibility maps using frequency ratio method No. Selected frequency Prediction # of landslide # of possible Min LSI (b) Max LSI (a) Difference ration maps accuracy (%) factors used combinations (a-b) 1 sl+as+pr+pl+li+lu+dl+dr 87.6 8 1 2.54 38.95 36.41 2 sl+as+pr+pl+li+dl+dr 86.2 7 8 2.46 29.73 27.27 3 sl+as+pr+pl+li+lu+dl 87.7* 1.58 36.59 35.01 4 sl+pr+pl+li+lu+dl+dr 87.6 2.37 37.74 35.37 5 sl+as+pr+pl+li+lu+dr 2.36 36.03 33.67 6 sl+as+pr+pl+lu+dl+dr 2.41 36.66 34.25 7 sl+as+pl+li+lu+dl+dr 87.7* 2.04 32.80 30.76 8 sl+as+pr+li+lu+dl+dr 87.7* 1.92 32.76 30.84 9 sl+as+pr+pl+li+lu 86.9 6 28 1.4 33.67 32.27 10 sl+pr+pl+li+dl+dr 86.1 2.29 28.70 26.41 11 sl+as+pr+pl+li+dr 84.9 2.36 26.81 24.45 12 sl+as+pr+li+dl+dr 86.3 1.79 23.90 22.11 13 sl+as+li+lu+dl+dr 87.6 14.42 26.61 25.19 14 sl+pr+pl+li+lu 86.8 5 56 1.29 32.20 30.91 15 sl+as+li+lu+dr 87.0 1.24 23.69 22.45 16 sl+as+li+dl+dr 86.2 1.28 17.79 16.51 17 li+sl+dl+dr 86.1 4 70 1.17 16.34 15.17 18 li+sl+lu+dr 86.8 1.07 22.46 21.39 19 li+sl+pr+lu 87.0 0.67 26.03 25.36 20 sl+as+pl+lu 86.4 0.77 25.21 24.44 21 sl+li+lu+dl 87.7* 0.27 22.78 22.51 22 sl+pl+li+lu 86.9 0.79 26.05 25.56 23 sl+as+li 85.3 3 56 0.28 12.09 11.81 24 sl+dl+li 86.3 0.27 13.57 13.30 25 sl+as+dr 84.7 1.07 13.42 12.35 26 Sl+li+lu 86.9 0.17 19.86 19.69 27 li+sl 85.0 2 28 0.17 10.64 10.47 28 sl+dr 84.3 0.04 11.13 11.09 Note: sl=slope, as=aspect, pr=profile curvature, pl=plan curvature, li=lithology, lu=land use, dl=distance from lineament, dr=distance from river, LSI=Landslide Susceptibility Index, *=Highest prediction accuracy. a = Max LSI = maximum landslide susceptibility index, b = Min LSI = minimum landslide susceptibility index. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 14 of 17 curvatures in Arc GIS 10. The distance from lineament many researchers (Dahal et al. 2008, Regmi et al. 2010a). and distance from rivers are obtained from multiple ring In this study, the raster maps of the frequency ratio buffering operation. Then all the data should be trans- values for the eight landslide factors were extracted with formed into a raster format with the same geographic landslide and non-landslide points. These are processed in projection and pixel size (30 m). The frequency ratio SPSS statistical software in such a way that landslide rep- model was applied to obtain a weight for each class in resents the presence (1) and non-landslide the absence (0) a certain factor. From the frequency ratio analysis, and each factor’s frequency ratio values were analyzed by slope classes ≥ 20° have shown a strong correlation binary logistic regression in order to check the degree of with landslides. In case of aspect, the southeast, south correlation among landslide factors. Based on this analysis, and southwest facing slopes showed a strong correl- all the correlations between two different landslide factors ation with landslides. For profile and plan curvatures, showed either no or very insignificant correlation i.e. < 0.1 the higher positive values and the lower negative values (Table 3). This suggests that all the factors are independ- showed a strong relationship with landslides. Distance ent from each other and can be used for the combination from lineament and landslides showed a strong relation- to prepare a landslide susceptibility map. ship. As the distance from lineament decreases, the fre- From the set of eight landslide factor maps, 8, 7, 6, 5, quency ratio values become higher. In a the distance class 4, 3 and 2 factor maps are combined to give 1, 8, 28, 56, of 0–200 m, the highest landslide frequency is recorded. 70, 56 and 28 landslide susceptibility maps respectively. From land use classes, barren land, sparse forest and For simplification, however, only a total of 28 landslide grassland classes showed a strong relation with landslides. susceptibility index maps have been selected. Then the Among lithologic units in the area, Mesozoic Lower best landslide susceptibility index map was selected from Sandstone, Tertiary Lower Basalt and Tertiary Upper groups with 8, 7, 6, 5, 4, 3 and 2 landslide factor combi- Basalt showed a strong relationship with landslides. The nations based on high prediction accuracies calculated frequency ratio values were assigned to each factor clas- from success-rate curves of areas under the curve ses and all these raster maps of landslide factors were (AUC). But when there is similarity in prediction accur- added to produce the landslide susceptibility index acy, the difference of maximum and minimum landslide maps based on the mathematical combination theory. susceptibility index values has been used (Table 2). Hence The frequency ratio model has some limitations des- the best landslide susceptibility map can be selected from pite its easiness and simplicity to understand and imple- a combination with the highest prediction accuracy and ment in a GIS environment. Higher frequency ratio the highest difference values and this map was found from values will be found if the area ratio (area percentage) a combination of all landslide factors except distance from is lower than the landslide ratio (landslide percentage) river (Figure 7a). Among the 28 representative combi- irrespective of higher number of landslides in a certain nations of different landslide factors, landslide suscepti- factor class. After the frequency ratio raster maps of all bility maps with the same prediction accuracy of 87.7% the landslide factors are prepared, the next step is to add have been found in spite of the dissimilarity in their dif- these raster maps based on the mathematical combin- ference values. The combination with a limited number ation theory. However, before combining the landslide of landslide factors but having the highest prediction factors it is important to ascertain their independence accuracy of 87.7% was also found from four landslide from each other (Van Westen et al. 2003, Dahal et al. factors, namely slope, lithology, land use and distance 2008). For this purpose logistic regression was applied, from lineament (Figure 7b). In order to show the predic- although the pairwise comparison was preferred by tion accuracy contrasts, seven success-rate curves from Table 3 Correlation matrix of landslide factors Distance from Land use Slope Lithology Aspect Plan Profile Distance lineament curvature curvature from river Distance from lineament 1 −0.085 −0.249 −0.39 −0.076 −0.005 −0.037 −0.062 Land use 1 −0.086 −0.07 −0.058 0.004 −0.008 0.055 Slope 1 −0.002 −0.01 −0.165 −0.294 0.011 Lithology 1 −0.077 −0.002 −0.043 −0.138 Aspect 1 0.015 −0.004 0.007 Plan curvature 1 −0.336 0.005 Profile curvature 1 −0.004 Distance from river 1 Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 15 of 17 Figure 7 Landslide susceptibility maps having the same prediction accuracy from (a) seven landslide factors excluding distance from river (FR_ wo_ dr) (b) four landslide factors including slope, lithology, land use and distance from lineament only (FR_ slliludl). ROC curves were constructed for each group’shigherpre- diction accuracy and difference values (Figure 8). For validation purpose of landslide susceptibility maps, many researchers divided the landslides in their respective study area into two parts based on time, space and ran- dom partitions (Chung and Fabbri 2003). These partitions fall into two categories: prediction (training) landslides and validation (testing) landslides. In time partition, past landslides are classified into landslides that occurred before a certain year X and those that occurred after a certain year X. In space partition, the entire study area is divided into two separate sub areas, A and B, one for prediction and the other for validation. By using the space-partition technique, the prediction model in the study area can be extended into the surrounding areas with similar geology, geomorphology and land use con- ditions. To know how much the prediction can be extended in space Chi et al. (2002) divided the entire study area into a northern and southern sub-areas because of the area's similarity in many aspects. Lee et al. (2007) divided into western and eastern areas for training Figure 8 Frequency ratio Success rate curves for different and validation purposes respectively. In random partition, combinations of landslide factors (FR_ wo_ dr includes all the past landslides are randomly divided into two groups factors except distance from river, FR_ slliludl includes slope, instead of two time periods. lithology, land use and distance from lineament, FR_ all data includes all factors, FR_ wo_prpl excludes profile and plan However, few researchers advocate for another valid- curvatures, FR_ wo_dlprp excludes distance from lineament, ation technique which is based on the comparison of profile and plan curvatures, FR_ sllilu includes slope, lithology existing landslides with the landslide susceptibility map and land use and FR_ lisl includes lithology and slope). and use the success-rate curve of area under the curve Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 16 of 17 (AUC) to assess the prediction accuracy qualitatively landslide factors. On the other hand, different combina- (Lee and Talib 2005; Lee and Sambath 2006; Pradhan tions may result the same and high prediction accuracy. 2010a; Pradhan 2011). The success rate curve explains For instance, the combination from seven landslide factors how well the model and the factor predict landslides (except distance from river) and the combination from (Chung and Fabbri 2003) and it was constructed for the four landslide factors (slope, lithology, land use and representative combinations of seven groups in the study distance from lineament) showed the same prediction area (Table 2). After an overlay analysis of landslides accuracy of 87.7%. This showed that these four landslide with the best landslide susceptibility map, the number factors should have a greater degree of influence in of landslides that fall into each susceptibility class was causing landslides. A prediction accuracy as high as 85% calculated. If the number of landslides is very significant was also possible from a combination of slope & lithology in the high and very high susceptibility classes, then the only. This demonstrates how these two factors are very landslide susceptibility map can be considered accurate much important in causing landslide occurrence. High and reliable to predict future landslides. The prediction prediction accuracy & LSI difference values are used to accuracy that is used for selection of best susceptibility select the best landslide susceptibility map. By selecting map was derived from the success - rate curves. In this 2 to 8 numbers of landslide factors from a set of 8 land- study, the percentage of landslides in each susceptibility slide factors, a total of 247 landslide susceptibility map class were calculated to check the validity of the final combinations are possible. However 28 combinations susceptibility map. For this, all the landslides have been were selected based on higher prediction accuracy from overlaid over the final landslide susceptibility map. In success rate curves, higher LSI difference values and doing so, 0.39%, 1.84%, 9.1%, 32.04% and 56.63% of the through visual inspection of output susceptibility maps. landslides fall in the very low, low, medium, high and very An optimum landslide susceptibility map was prepared high landslide susceptibility classes respectively (Figure 9). from four landslide factors (lithology, slope, land use and distance from lineament) while the best landslide Conclusion susceptibility map was obtained from the combination From this study, we have found that the mathematical of 7 landslide factors excluding distance from river combination theory is an important technique to identify (Figure 7a, b). Both maps have the prediction accuracy the possible number of combinations in the frequency of 87.7% but with different LSI difference values of ratio model. This paper showed that using all landslide 35.01 and 25.51 respectively. In order to highlight the factors in the frequency ratio model may not always prediction accuracy contrasts of landslide susceptibility result in higher prediction accuracy even though the maps from success-rate curves were chosen from the 28 range of values in the susceptibility index map is higher. combinations as shown in Table 2. For example, the combination of 8 landslide factors results Once the most important landslide factors are deter- a prediction accuracy of 87.6%, while the combinations of mined in a certain area, then these can be used to scale all landslide factors except distance from the river pro- up the investigation at the regional level using these vided an accuracy 87.7%. This shows that distance from causative landslide factors. When landslide inventory river is less important as compared to other factors. But map is overlaid over the best landslide susceptibility the landslide susceptibility index (LSI) difference value map, most of the landslides fall in the high and very high always higher in the combination with higher number of susceptibility classes accounting for 88.67% of the Figure 9 Percentage of lndslides in each landslide susceptibility class for FR_ wo_ dr. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 17 of 17 landslides. Besides this the success-rate of this map is Ercanoglu M, Gokceoglu C (2002) Assessment of landslide susceptibility for a landslide-prone area (north of Yenice, NW Turkey) by fuzzy approach. Environ being 87.7%, proving that the landslide susceptibility Geol 41:720–730, doi:10.1007/s00254-001-0454-2 map from the frequency ratio model in the study area is Farrokhnia A, Pirasteh S, Pradhan B, Pourkermani M and Arian M (2010) A recent quite acceptable. After the best and optimal landslide scenario of mass wasting and its impact on the transportation on Albroz mountains, Iran using geo-information technology. Arab J Geosci. susceptibility maps (Figure 7 a, b) are selected these doi:10.1007/s 12517-010-0238-7 maps are divided into five categories and are expressed Fell R, Corominas J, Bonnard C, Cascini L, Leroi E, Savage WZ (2008) Guidelines as probabilities in qualitative terms of very low, low, for landslide susceptibility, hazard and risk zoning for land use planning. Eng Geol 102(2008):85–98 medium, high and very high susceptibility classes. Using Godt JW, Baum RL, Savage WZ, Salciarini D, Schulz WH, Harp EL (2008) Transient this output, proper planning can be made to prevent, deterministic shallow landslide modeling, Requirements for susceptibility and reduce or mitigate the possibility of future landslide di- hazard assessments in a GIS framework. Eng Geol 102:214–226 Hack JT, Goodlett JC (1960) Geomorphology and forest ecology of a mountain sasters in this area. Creating awareness about the risk of region in the central Appalachians. United States Geological Survey, high and very high susceptible zones to the general pub- Professional Paper 347:66 lic will help to save the lives and properties of the IUGS (1997) Quantitative risk assessment for slopes and landslides- the state of the art. In: Cruden D, Fell R (eds) Landslide risk assessment. Balkema, people. Susceptibility, hazard and risk maps are the Rotterdam, pp 3–12 basis for decision making usually in the form of tech- Lee S, Pradhan B (2007) Landslide Hazard mapping at Selangor, Malaysia using nical countermeasures, regulatory measures or combi- frequency ratio and logistic regression model. Landslides 4:33–41, doi:10.1007/s10346-006-0047-y nations of the two (Pradhan et al. 2011). Lee S, Sambath T (2006) Landslide susceptibility mapping in the Damrei Romel area, Cambodia using frequency ratio and logistic regression models. Environ Competing interests Geol 50:847–855, doi:10.1007/s00254-006-0256-7 The authors declare that we do not have any financial or non-financial Lee S, Talib JA (2005) Probabilistic landslide susceptibility and factor effect competing interests with any individual or institution. analysis. Environ Geol 47:982–990, doi:10.1007/s00254-005-1228-z Lee S, Choi J, Woo I (2004) The effect of spatial resolution on the accuracy of Authors’ contributions landslide susceptibility mapping: a case study in Boun, Korea. MM as a first author, has mostly participated in the whole process including Geosci J 8(No. 1):51–60 field work, data collection, database preparation,compiling the results from Lee S, Ryu JH, Kim LS (2007) Landslide susceptibility analysis and its verification using himself and from PB, taking comments from RY, address the comments and likelihood ratio, logistic regression, and artificial neural network models: case finalize the draft for journal submission after a consensus is reached with RY study of Youngin, Korea. Landslides 4:327–338, doi:10.1007/s10346-007-0088-x and PB. PB has participated from the inception and design of this paper and Ohlamacher GC (2007) Plan curvature and landslide probability in regions helped greatly in data preparation and analysis. RY has also involved in a dominated by earth flows and earth slides. Eng Geol 91(2007):117–134 detailed review of the manuscript before submission. Both authors have Pirasteh S, Woodbridge K, Rizvis SMA (2009) Geo-information technology (GiT) given the final approval of the version to be published. and tectonic signatures: the River Karun and Dez, Zagros Orogen in south-west Iran. Int J Remote Sens 30(No. 2):389–403 Pradhan B (2010a) Landslide susceptibility mapping of a catchment area using Acknowledgements frequency ratio, fuzzy logic and multiple logistic regression approaches. The first author would like to thank Japan’s Ministry of Education, Culture, J Indian Soc Remote Sens 38:301–320, Springer Science and Technology (MEXT) for the scholarship grant to pursue the PhD Pradhan B (2011) Manifestations of an advanced fuzzy logic model coupled with study. Geo-information techniques to landlside susceptibility mapping and their comparison. Environ Ecol Stat. 18-471-493 doi:10. 1007/s10651-010-0147-7. Received: 26 November 2014 Accepted: 10 February 2015 Pradhan B, Mansor S, Pirasteh S, Buchroithner MF (2011) Landslide hazard and risk analyses at a landslide prone catchment area using statistical based geospatial model. Int J Remote Sens 32(No. 14):4075–4087 References Regmi NR, Giardino JR, Vitek JD (2010a) Modeling susceptibility to landslides Asfaw YE (2010) Landslide assessment in the Blue Nile Gorge. University Ghent, using the weights of evidence approach: Western Colorado, USA. Master Thesis, September, Central Ethiopia, 2010 Geomorphology 115:172–187 Ayalew L (1999) The effect of seasonal rainfall on landslides in the highlands of Reneau SL, Dietrich WE (1987) The importance of hollows in debris flow studies; Ethiopia. Bull Eng Geol Env 58:9–19, 7 Q Springer-Verlag examples from Marin County, California. In: Costa, J.E., Wieczorek, G.F. (Eds.), Ayalew L, Yamagishi H (2004) Slope failures in the Blue Nile basin, as seen from Debris Flows/Avalanches: Process, Recognition, and Mitigation. Geological landscape evolution perspective. Geomorphology 57(2004):95–116 Society of America, Boulder, Colorado. Rev Eng Geol VII:165–180 Bui DT, Pradhan B, Lofman O, Revhaug I, Dick OB (2012) Landslide Susceptibility Ruff M, Czurda K (2008) Landslide susceptibility analysis with a heuristic approach Assessment at Hoa Binh Province of Vietnam Using Frequency Ratio Model. in the Eastern Alps (Vorarlberg, Austria). Geomorphology 94(2008):314–324 2012 Asia Pacific Conference on Environmental Science and Technology. Temesgen B, Mohammed U, Korme T (2001) Natural Hazard Assessment Using GIS Advances in Biomedical Engineering 6:476 and Remote Sensing Methods, with Particular Reference to the Landslides in Carson MA, Kirkby MJ (1972) Hillslope Form and Process. Cambridge University the Wondogenet Area, Ethiopia, Pergamon. Phys Chem Earth 26(No. 9):665–e Press, London, 475 pp Terlien MTJ (1998) The determination of statistical and deterministic hydrological Chi KH, Park NW, Chang CJ (2002) Fuzzylogic integration for landslide hazard landslide-triggering thresholds. Environ Geol 35(2–3):124–130 mapping using spatial data from Boeun, Korea. Symposium on Geospatial Terlien MTJ, Van Westen CJ, Van Asch TWJ (1995) Deterministic modelling in GIS Theory, processing and applications, Ottawa based landslide hazard assessment. In: Carrara A, Guzzetti F (eds) Chung CJF, Fabbri AG (2003) Validation of Spatial Prediction Models for Landslide Geographical Information System in Assessing Natural Hazard. Kluwer Hazard Mapping. Nat Hazards 30(451–472):2003 Academic Publishers, Dordrecht pp 57–77 Clerici A, Perego S, Tellini C, Vescovi P (2006) A GIS-based automated procedure Van Westen CJ, Rengers N, Soeters R (2003) Use of geomorphological information for landslide susceptibility mapping by the Conditional Analysis method: the inindirect landslide susceptibility assessment. Nat Hazards 30:399–419 Baganza valley case study (Italian Northern Apennines). Environ Geol Woldearegay K (2008) Characteristics of large-scale landslide triggered by heavy 50:941–961, doi:10.1007/s00254-006-0264-7 rainfall in Tarmaber area, Central Highlands of Ethiopia. Geophysical Research Dahal RK, Hasegawa S, Nonomura A, Yamanaka M, Dhakal S, Paudyal P (2008) 10: , EGU2008-A-04506,2008, SRef – ID:1607-7962/gra/EGU2008-A-04506 EGU Predictive modelling of rainfall-induced landslide hazard in the Lesser Himalaya General Assembly 2008 ofNepal based on weights-of-evidence. Geomorphology 102:496–510 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geoenvironmental Disasters Springer Journals

Effect of Landslide Factor Combinations on the Prediction Accuracy of Landslide Susceptibility Maps in the Blue Nile Gorge of Central Ethiopia

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Copyright © 2015 by Meten et al.; licensee Springer.
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Environment; Environment, general; Earth Sciences, general; Geography (general); Geoecology/Natural Processes; Natural Hazards; Environmental Science and Engineering
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Abstract

Database construction for landslide factors (slope, aspect, profile curvature, plan curvature, lithology, land use, distance from lineament & distance from river) and landslide inventory map is an important step in landslide susceptibility modelling. Using the frequency ratio model, the weights for each factor classes were calculated and assigned in GIS so as to add these factors and produce landslide susceptibility index maps based on mathematical combination theory. However, before combining them, their independence among each other should be ascertained. For this, the correlation matrix of logistic regression was applied and this showed that most of the correlations between factors were either absent or very insignificant suggesting that all landslide factors are independent. From a set of eight landslide factors, a total of 247 landslide susceptibility map combinations can be generated. However, for simplification, only 28 landslide susceptibility maps were chosen. Then the best landslide susceptibility map was selected based on high prediction accuracy. But, when there is similarity in the prediction accuracies of different combinations, the landslide susceptibility index difference values can be used as another selection criterion. Hence, the susceptibility map from a combination of all landslide factors except distance from river was found to be the best one. Among the 28 representative combinations, landslide susceptibility maps with the same prediction accuracy of 87.7% have been found in spite of their dissimilarity in their difference values. The combination, with a limited number of landslide factors and the highest prediction accuracy of 87.7%, was found from a combination of slope, lithology, land use and distance from lineament. In order to validate the prediction model, landslides were overlaid over the landslide susceptibility map and the number of landslides that fall into each susceptibility class was calculated. From this analysis 0.39%, 1.84%, 9.1%, 32.04% and 56.63% of the landslides fall in the very low, low, medium, high and very high landslide susceptibility classes respectively. Since 88.67% of the landslides fall in the high and very high susceptibility classes, the landslide susceptibility map can be considered reliable to predict future landslides. Keywords: Landslide susceptibility; GIS; Frequency ratio; Combination; Prediction accuracy; Ethiopia Background 2011), deterministic (Godt et al. 2008) and a combination Landslide is the movement of a mass of rock, debris or of statistical and deterministic (Terlien 1998) methods. earth (soil) down a slope and landslide susceptibility is a Susceptibility, hazard and risk maps are important tools quantitative or qualitative assessment of landslide about for engineers, earth scientists, planners and decision its classification, volume (or area) and spatial distribution makers select appropriate sites for agriculture, construc- (IUGS 1997, Fell et al. 2008). Landslide susceptibility tion and other development activities (Ercanoglu and mapping methods are classified into heuristic (Ruff and Gokceoglu 2002). They also play an important role in Czurda 2008), statistical (Lee et al. 2004; Pradhan et al. efforts to mitigate or prevent the disaster in landslide prone areas by providing important information to the concerned bodies. In heuristic methods, field observation and expert’s knowledge are used to identify landslides, * Correspondence: matebe21@gmail.com Geo-Disaster Research Laboratory, Graduate School of Science and Engineering, Ehime University, 3 Bunkyo, Matsuyama 790-8577, Japan © 2015 Meten et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 2 of 17 make a prior assumption about past and future landslide of its analysis potential and capability. A continuous and up movements on the site, assign weighted values for the clas- to date landslide susceptibility map is vital to planners, en- ses of index maps and overlay them to produce a landslide gineers and decision makers in order to devise appropriate susceptibility map. In deterministic method, data on slope landslide prevention and mitigation measures. In this re- geometry, shear strength (cohesion and angle of internal gard, a statistical (probabilistic) model known as frequency friction) and pore pressure are required (Regmi et al. 2010a). ratio has been applied in the current study area. This model A significant limitation of deterministic models is the need was chosen because it is easy to understand and simple to for geotechnical data (cohesion, internal angle of friction, implement. Data input, output and analysis processes are depth to groundwater table, degree of saturation etc.) which fast and a huge amount of data can be handled and run are difficult to obtain over large areas (Terlien et al. 1995). quickly (Lee and Pradhan 2007; Lee et al. 2007). Data from Ayalew (1999), Temesgen et al. (2001), Frequency ratio model avoids the lengthy procedures of Woldearegay (2008) and Ibrahim (Ibrahim J, 2011: raster to point data conversion in GIS, weight calculation in Landslide assessment and hazard zonation in Mersa and statistical software and switching from statistical software to Wurgessa, North Wollo, Ethiopia, unpublished Master GIS for the preparation of landslide susceptibility map un- Thesis) showed that landslide in Ethiopia has resulted loss like logistic regression and artificail neural network models. of human lives, properties and infrastructures particularly Besides this, it utilizes all the available data contrary to the in the last five decades. From 1960 to 2010 alone, about other two models, which may use a limited proportion of 388 people were dead, 24 people were injured and a great the data because of the low data processing capacity of the deal of agricultural lands, houses and infrastructures were statistical software. Using a frequency ratio model, Lee and affected. Landslide problem in the Abay (Blue Nile) Gorge Talib (2005) have found the prediction accuracy of 72.1% in is a serious challenge to the community residing in this area Penang, Malaysia and Lee and Sambath (2006) have found and to the road infrastructure that connects Addis Ababa a prediction accuracy of 86.97% in the Damrei Romel area to Bahir Dar. In 1960, a terrible landslide at Gembechi of Cambodia. Lee and Pradhan (2007) have shown that village within Bechet valley was responsible for the loss of the frequency ratio resulted a better prediction accuracy 45 people (Ayalew 1999). On September 2, 1993 a landslide than the logistic regression at Selangor area in Malaysia. incidence occurred in the Blue Nile Gorge, which killed an Similarly, Pradhan (2010a) showed that the validation result ox, damaged agricultural fields, destroyed crops and as a of the frequency ratio model in the Cameron catchment of result 700 households were stricken by food insecurity. Malaysia is slightly better than logistic regression and fuzzy Besides this the main road, which was 5 km south of Dejen logic models with a prediction accuracy of 89.25%. town has been damaged with a displacement of 1.5 meters Until now researchers, who were engaged in the this by the sliding mass (Tadesse T, Dessie T and Deresa K, model, were simply summing all the frequency ratio 1994: Landslideincidencein theBlueNileGorgeof East raster maps of landslide factors (Lee and Sambath 2006) Gojam, Ethiopia. Geological Survey of Ethiopia, 823 report, or exclude one factor and sum all the remaining ones 830-301-01, unpublished). The road damage is a common (Lee and Talib 2005). However, the previous works lack phenomenon of the mid to end of each rainy season (i.e. ways of systematic combination, identifying the number June 1 to September 30) due to the gradual weakening of of possible combinations, providing more than one the soft and weathered rocks by heavy rain and ground- selection criterion to select the best landslide suscepti- water percolation through big columnar joints of basalt to bility map and finding a combination with high predic- the underlying limestone formation bearing mudstone and tion accuracy from a limited number of factors. shale at its top and middle strata. For example, Asfaw The current study tries to prepare different landslide (2010) reported a road damage near Goha Tsiyon town on susceptibility maps from eight landslide factors and September 5, 2009. Such incidences happened due to the landslide inventory with different combinations using frequency ratio model and make a comparison on the progressive softening of weathered basalt and pyroclastic rocks by heavy rainfall, groundwater recharge through the prediction accuracies of these combinations in order to columnar joints of basalt and by a gushing stream that select the best landslide susceptibility map. This will help to suggest a limited number of landslide factors crosses a road. The Goha Tsion-Dejen transect is an important transport corridor connecting Addis Ababa with that can produce a susceptibility map with the highest the regions in the northwestern part of the country. How- prediction accuracy similar to a combination using all or most of the landslide factors. The main objectives of ever, it is affected by a complex landslide problem almost on a yearly basis. To overcome this problem, few re- this study are: (1) to apply the frequency ratio model searchers in the field of Geotechnics, Geoscience and slope using combination theory, (2) to identify the possible stability have been undertaking investigations in the Blue numbers of combinations, (3) to evaluate the effect of Nile Gorge. Recently, GIS is becoming a powerful tool to different combinations on the prediction accuracy of study landslide susceptibility and hazard worldwide because landslide susceptibility maps and (4) to select the best Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 3 of 17 landslide susceptibility map among different alternatives. and validation stages (Figure 3). During the data prepar- In light of this, the following questions will be addressed ation stage a database was constructed for landslide fac- in the subsequent chapters of this paper. (1) How many tor maps and landslide inventory map. The landslide combinations are possible in the frequency ratio model factor maps were derived from the geological map for with a certain number of landslide factors? (2) Which lithology and lineament, topographic maps for rivers, combination of landslide factors will give the best pre- Google earth images for land use, DEM (digital elevation diction accuracy? (3) How can we prioritize if the two model) for slope, aspect, profile curvature and plan landslide susceptibility maps have the same prediction curvature. The river and lineament data were changed accuracy? (4) How can we identify the best landslide into distance from river and lineament based on Arc GIS susceptibility map obtained from a limited number of multiple ring buffer analysis. The landslide inventory landslide factors? map, which contains 595 landslides, was also prepared from field observation and Google earth image analysis. Study area The continuous data like slope, aspect, profile curvature The study area is located in the Abay (Blue Nile) Gorge and plan curvature were reclassified into appropriate of Central Ethiopia and it is bounded by 38° 2' E to 38°15" number of classes. Then, all the eight landslide factors E longitudes and 10° 0′ N to 10° 15' N latitudes covering and landslide inventory map were organized in a raster an area of 391 sq. km (Figure 1). This area is found in the format with the same geographic projection and same highly dissected portion of the Blue Nile basin with a pixel size of 30 m. The frequency ratio model requires depth of 1.5 km from plateau top to the valley floor. The assigning the frequency ratio values (FRV) for each lowest elevation in the study area is 1000 m while the factor’s class by dividing landslide percentage to area per- highest is 2500 m. It contains the major Abay (Blue Nile) centage. Then the frequency ratio value maps of landslide River and its tributary rivers like Bechet, Muga and other factors were added based on the mathematical combin- unnamed small streams (Figure 2) with the level of ation rule in order to get the landslide susceptibility incision being higher in the three rivers. index maps for different combinations. A total of 247 combinations were possible but only 28 best combina- Methods tions were selected in order to simplify the data handling The methods applied in this paper include data prepar- and analysis process. For prediction purpose the landslide ation, data analysis through frequency ratio model, susceptibility index maps were extracted with landslide prediction, landslide susceptibility map preparation and non-landslide points and then analyzed using SPSS Figure 1 Location map of the study area showing the general landscape and elevation ranges in the Goha Tsiyon-Dejen transect of Abay (Blue Nile) gorge. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 4 of 17 Figure 2 Landslide inventory map of the study area. statistical software so as to check the overall statistics, selected from a limited number of landslide factors. receiving operating characteristics (ROC) curves and area Finally, the two landslide susceptibility maps were reclassi- under the curve (AUC) values. The prediction accuracies fied into five susceptibility classes and the validation was of each combination of landslide factors can be found by done by overlaying the landslide inventory map over the multiplying AUC values by 100%. However, the prediction best landslide susceptibility map. accuracies of different combinations from the success-rate curve may not always be enough to discriminate which Landslide inventory landslide susceptibility map is best among many alterna- A landslide inventory map, consisting 595 landslides, tives. Hence, the difference between minimum and max- was prepared from field observations and Google earth imum landslide susceptibility index (LSI) difference values images of the study area (Figure 2). Landslides in the was also used as another distinguishing criterion. If the area include rock slides, rock falls, debris slide and mud- difference is higher, then it will be better as it contains a flow. According to Ayalew and Yamagishi (2004) rock broader range of values compared to the smaller differ- falls exist as discernible block topples and wedge failures ence values. Based on the highest prediction accuracy and along the mountains, valley walls and road cuts. Simi- LSI difference values, the best landslide susceptibility map larly, rock slides are also abundant on the ridge sides from each combination group or from all combinations and valley walls. The intensity of landslides is generally was selected. Another optimum landslide susceptibi- high in the upper catchments of Bechet and Muga lity map with the highest prediction accuracy was also valleys and on the road cut near GohaTsiyon town. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 5 of 17 Figure 3 Flow chart showing the whole process of the work. FR = Frequency ratio raster map for li = lithology, dl = distance from lineament, dr = distance from river, lu = land use, sl = slope, as = aspect, pr = profile curvature and pl = plan curvature. Landslide factors scenarios. The main effects of tectonics are localized The landslide factors used in this paper include lith- changes in the river course and changes in local topog- ology, distance from lineament, land use, distance from raphy (Pirasteh et al. 2009). river, slope, aspect, plan and profile curvatures (Figure 4). The landscapes are greatly influenced by tectonics, Lithology bedrock lithology and the courses of major rivers. The The lithology of the study area comprises seven litho- complex processes of tectonics, erosion and sedimen- logical units. These are (1) Paleozoic Sandstone (2) tation generates water gaps, knick points, meanders Mesozoic Lower Sandstone (3) Mesozoic Gypsum, shale and many other tectonic and geomorphic features (Pirasteh and mudstone (4) Mesozoic Limestone (5) Tertiary et al. 2009). Tectonics may probably promote river inci- Lower Basalt (6) Tertiary Upper Basalt and (7) Quater- sion in onesideand riveraggradation to theother side nary Soil in their chronological order from older to and rivers respond in different ways to similar tectonic younger units (Figures 5 4e). The Paleozoic Sandstone Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 6 of 17 Figure 4 Landslide influencing factors (a) slope (b) aspect (c) profile curvature (d) plan curvature (e) lithology (f) land use (g) distance from lineament (h) distance from river. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 7 of 17 Figure 5 Litho-stratigraphic sections along the GohaTsiyon – Dejen Road. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 8 of 17 consists of fine grained sandstone with whitish gray vegetation, particularly on the steep walled river banks and brown colors occupying the river course of Abay of Muga and Bechet rivers, is more highly susceptible to (Blue Nile) attaining a maximum vertical thickness of land sliding than the other land use types. 50 m. It is highly weathered, slightly friable forming mod- erately sloping morphology. Mesozoic Lower Sandstone is Distance from lineament reddish brown, light gray, medium to coarse grained, Lineaments, which are found along steep linear ridges in sometimes conglomeratic, medium to thickly bedded the Abay (Blue Nile) gorge, have a strong influence in and crossbedded sandstone forming steep to moderately conditioning landslide incidences provided that the other sloping cliffs on the river banks of the Abay (Blue Nile) favorable factors are also set in place. As can be seen in River overlying the Paleozoic Sandstone. This unit is Table 1, the frequency ratio values for the distance from found in elevation range between 1050 m and 1336 m lineament showed higher values in the distance range of 0 with a vertical thickness of 286 m. Mesozoic Gypsum, to 200 m. The other distance classes revealed a less Mudstone and Shale unit consists of the dominant gypsum number of landslides. The surface rupture intensity is also interbedded with minor mudstone and shale. This unit influenced by distance from lineament or fault and ground is exposed in the elevation range between 1336 m and conditions. As the distance from the lineaments becomes 1749 m in the GohaTsiyon – Abay River section with a smaller, the fracture of the rock masses and the degree vertical thickness of 413 m. Gypsum is whitish gray, gray of weathering increases resulting in greater chances of and sometimes banded, forming gentle morphology. landslide occurrence (Farrokhnia et al. 2010). Mudstone is yellowish gray, highly weathered and friable. Mesozoic Limestone is yellowish gray and light gray in Distance from river color, mostly fossiliferous, medium to thickly bedded Rivers usually play a significant role in modifying the and forms gentle to steep cliffs. The limestone forms a landscape by incising the different rocks. In the study bed thickness of 0.25 – 0.5 m and sometimes it may area, the Abay (Blue Nile), Bechet and Muga Rivers reach up to 1 m. The Tertiary Lower Basalt forms a steep and many other streams incised the Tertiary Volcanic morphology unconformably overlying the Mesozoic rocks and Paleozoic and Mesozoic sedimentary rocks Limestone. It is dark gray, fine to medium grained, to a maximum depth of 1.5 km. The role played by aphanitic basalt, plagioclase phyric and olivine - plagioclase rivers in creating a conducive environment for land- phyric basalts. The basalt in GohaTsiyon – Dejen Road slide occurrence has great significance. The maximum shows a spectacular columnar jointing and triggers a number of landslides in the close proximity of rivers, critical landslide problem. The Tertiary Upper Basalt is as can be seen in Table 1, shows how rivers are con- dark gray, fine to medium grained rock, consisting tributing to landsliding. In the steep-walled river banks plagioclasephyric, olivinephyricand aphaniticbasalts of Bechet and Muga, landslides are common, particu- overlying thin beds of pyroclastic rocks. Lastly, in-situ larly in fractured Tertiary Lower Basalt and the under- weathering of the Tertiary basalts has given rise to the lying Mesozoic Limestone units. development of Quaternarysoil on the Dejen plateau. Slope Land Use Slope is one of the most important topographic parame- The land use type in the area includes agricultural land, ters influencing the occurrence of landslides in the study barren land, bushes, dense forest, sparse forest, shrubs, area. The landslide frequency is higher in the slope grassland, rural settlement, urban settlement and river classes of 20 - 30°, 30 - 40° and 40 - 67° and the highest (Figure 4f; Table 1). The reason why dense forest, sparse one is recorded in the slope class of 30 - 40° (Table 1). forest and shrubs are susceptible to land sliding can be Generally speaking, as slope increases, the probability attributed to the existing steep slope morphology and of landslide occurrence also increases. the sallow rooted nature of different evergreen vegeta- tion types in the area. The presence of vegetation may Aspect increase the rate of infiltration. This in turn increases Aspect (slope orientation) affects the exposure to sun- the accumulation of water, thereby decreasing the stabil- light, wind and precipitation thereby indirectly affecting ity of the slope due to increased pore water pressure and other factors that contribute to landslides such as soil unit weight of the sliding mass (Farrokhnia et al., 2010). moisture, vegetation cover and soil thickness (Clerici This may be worsened if the vegetation types in the area et al. 2006). The aspect of the area is classified into flat, have a huge weight and are shallow rooted with the north, northeast, east, southeast, south, southwest, west roots found above the slip surface of the landslide mass. and northwest facing classes (Figure 4b). The number of It is obvious that the barren land comprising a degraded landslides is higher in the aspect classes of E, SE, S, SW portion of the study area which is devoid of any and W but the frequency ratio values of SE, S and SW Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 9 of 17 Table 1 Frequency ratio value calculation by rationing landslide percentage to area percentage Factor Class # landslide % landslide # area % area FRV = a b Pixels Pixels Pixels Pixels (a/b) Slope (°) 0 - 5 60 0.388 38089 8.770 0.04 5 - 10 333 2.151 87417 20.129 0.11 10 - 15 811 5.239 102933 23.702 0.22 15 - 20 1430 9.238 77279 17.794 0.52 20 - 30 4195 27.099 80829 18.612 1.46 30 - 40 4589 29.645 34095 7.851 3.78 40 - 67 4062 26.240 13645 3.142 8.35 Aspect Flat 5 0.03 1234 0.284 0.11 N 424 2.74 29729 6.845 0.40 NE 1013 6.54 44175 10.172 0.64 E 2127 13.74 64829 14.928 0.92 SE 3136 20.26 60584 13.950 1.45 S 2306 14.90 52443 12.076 1.23 SW 3144 20.31 73195 16.854 1.21 W 2366 15.28 67137 15.459 0.99 NW 959 6.20 40961 9.432 0.66 Plan curvature - 10.7829 - - 1.7917 620 4.005 2810 0.647 6.19 - 1.7917 - - 0.9103 1704 11.008 20924 4.818 2.28 - 0.9103 - - 0.1111 4986 32.209 154198 35.506 0.91 - 0.1111 - 0.1111 1724 11.137 78020 17.965 0.62 0.1111 - 0.5882 3117 20.136 121053 27.874 0.72 0.5882 - 1.3815 2315 14.955 49643 11.431 1.31 1.3815 - 11.7830 1014 6.550 7639 1.759 3.72 Profile curvature - 10.9947 - - 2.3629 767 4.955 3648 0.840 5.90 - 2.3629 - - 1.0810 1984 12.817 23076 5.314 2.41 - 1.0810 - - 0.1154 4045 26.130 151550 34.896 0.75 - 0.1154 - 0.1154 1332 8.605 74725 17.206 0.50 - 0.1154 - 0.7991 3358 21.693 134940 31.072 0.70 0.7991 - 1.9956 2737 17.681 40629 9.355 1.89 1.9956 - 10.8837 1257 8.120 5719 1.317 6.17 Distance from river 0 - 100 5975 38.60 173853 40.032 0.96 (m) 100 - 200 3728 24.08 116838 26.903 0.90 200 - 300 2305 14.89 63633 14.652 1.02 300 - 400 1323 8.55 34376 7.916 1.08 400 - 500 810 5.23 19283 4.440 1.18 500 - 600 480 3.10 11048 2.544 1.22 600 - 700 350 2.26 6352 1.463 1.55 700 - 800 223 1.44 3866 0.890 1.62 800 - 900 102 0.66 2253 0.519 1.27 900 - 1000 49 0.32 1351 0.311 1.02 1000 - 1100 74 0.48 748 0.172 2.78 1100 - 1200 47 0.30 485 0.112 2.72 1200 - 1300 14 0.09 150 0.035 2.62 Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 10 of 17 Table 1 Frequency ratio value calculation by rationing landslide percentage to area percentage (Continued) 1300 - 1400 0 0.00 46 0.011 0.00 1400 - 1500 0 0.00 5 0.001 0.00 Factor Class # landslide % landslide # area % area FRV = a b Pixels Pixels Pixels Pixels (a/b) Distance from 0 - 200 11297 72.978 108715 25.033 2.92 Lineament (m) 200 - 400 2017 13.030 84627 19.486 0.67 400 - 600 930 6.008 61629 14.191 0.42 600 - 800 487 3.146 47825 11.012 0.29 800 - 1000 236 1.525 36076 8.307 0.18 1000 - 1200 169 1.092 26915 6.198 0.18 1200 - 1400 175 1.130 23374 5.382 0.21 1400 - 1600 119 0.769 18887 4.349 0.18 1600 - 1800 42 0.271 12387 2.852 0.10 1800 - 2000 6 0.039 7334 1.689 0.02 2000 - 2200 2 0.013 3926 0.904 0.01 2200 - 2400 0 0.000 1634 0.376 0.00 2400 - 2600 0 0.000 576 0.133 0.00 2600 - 2800 0 0.000 281 0.065 0.00 2800 - 3000 0 0.000 101 0.023 0.00 Land use Agricultural land 7518 48.566 290914 66.987 0.725 Sparse forest 706 4.561 10747 2.475 1.843 Rural settlement 55 0.355 16384 3.773 0.094 Barren land 4085 26.389 12423 2.861 9.225 Bushes 2813 18.172 88635 20.409 0.890 River 0 0 10049 2.314 0 Dense forest 171 1.105 1347 0.310 3.562 Grass land 39 0.252 1357 0.312 0.806 Shrubs 93 0.601 999 0.230 2.612 Urban settlement 0 0 1432 0.330 0 Lithology Quaternary soil 184 1.189 6221 1.432 0.83 Tertiary lower basalt 7733 49.955 94821 21.834 2.29 Mesozoic limestone 4011 25.911 129156 29.740 0.87 Mesozoic gypsum, Mudstone and shale 1170 7.558 140797 32.420 0.23 Mesozoic lower sandstone 2086 13.475 46758 10.767 1.25 Paleozoic sandstone 55 0.355 12044 2.773 0.13 Tertiary upper basalt 241 1.557 4490 1.034 1.51 facing slopes were found to be significant in causing curvature of the topographic contours or the curvature landslides. of a line formed by the intersection of an imaginary horizontal plane with the ground surface. Hillsides can Profile and plan curvatures be concave outward plan curvatures called hollows, Profile and plan curvatures are used for hill-slope and land- convex outward plan curvatures called noses and slide analysis (Ayalew and Yamagishi 2004). (Ohlamacher straight contours called planar regions. In hollows land- 2007) presented a detailed account of plan curvature slide material converges into the narrow region at the and its effect on hill-slope stability in earth flow and base of the slope. Profile curvature is the curvature in earth slides dominated regions. Plan curvature is the the downslope direction along a line formed by the Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 11 of 17 intersection of an imaginary vertical plane with the the frequency ratio model. The eight landslide factors that ground surface (Ohlamacher 2007). Both profile and are used in this study include lithology, land use, distance plan curvatures affect the susceptibility to landslides. from lineament, distance from river, slope, aspect, profile Profile curvature affects the driving and resisting stresses and plan curvatures were used to establish this relation- within a landslide in the direction of motion. Plan ship with landslides (Table 1). curvature controls the convergence or divergence of The number of landslide pixels in each class has been landslide material and water in the direction of land- evaluated and the frequency ratio for each factor class is slide motion (Carson and Kirkby 1972). The sign of the found by dividing the landslide ratio by the area ratio curvature value is important for determining concavity (Lee and Talib 2005). Frequency ratio shows the correlation or convexity of the curve. In both profile and plan between landslides and causative factors in a specific area. curvature maps, concave and convex surfaces are repre- If this ratio is greater than 1, then the relationship between sented by the respective negative and positive values a landslide and the factor’s class will be strong but if the ra- (Pradhan 2010a). Based on the plan curvature hill-slopes tio is less than 1, then the relationship will be weak and if can be subdivided into hollows, noses and relatively planar the value is 1, it means an average correlation (Lee and regions. Hollows are regions in which the plan curvature Sambath 2006; Pradhan 2010a). Once the frequency ratio of the contours is concave in the downslope direction of each landslide factor's class was found, the landslide sus- and where surface water would converge as it moves ceptibility index (LSI) can be calculated by summation of downslope (Reneau and Dietrich 1987). Noses or coves each factor’s frequency ratio values (Lee and Sambath are regions where the plan curvature of the contours is 2006). A higher LSI means a higher susceptibility to land- convex in the downslope direction and the surface slide while a lower LSI indicates a lower susceptibility to water will diverge (Hack and Goodlett 1960). Relatively landslides (Bui et al. 2012). planar regions have plan curvature values around zero. In the current study, landslide factors were converted Hollows concentrate groundwater and the concentra- into raster maps with a pixel size of 30 m, the spatial re- tion of groundwater probably leads to increased land- lationship between the landslide location and each land- slide activity. slide factor was analyzed and the ratings for each factor’s class were assigned to each class in a specific factor. Triggering factor Then the frequency ratio ratings of factors in the form The most important triggering factor for landslide of raster maps were summed to form the landslide sus- occurrence in the Blue Nile Gorge is heavy rainfall from ceptibility index (LSI) using equation (1). the beginning of June to the end of September. This season accounts for more than 75% of the annual rain- LSI ¼ Fr ð1Þ fall in the study area. Data from National Meteoro- i¼1 logical Agency of Ethiopia showed that the minimum, average and maximum annual rainfalls of the study area Where Fr is the raster map of each landslide factor in are 1100 mm, 1200 mm and 1400 mm respectively and which the frequency ratio values (FRV) are assigned to sometimes the peak annual rainfall reaches up to it. The current study tries to analyze the effect of differ- 1985 mm (Figure 6a). The peak monthly rainfall in four ent combinations of landslide factors on the perform- stations showed its maxima during the months of July ance of the frequency ratio model in order to get the and August (Figure 6b). Landslides usually occur at the minimum number of landslide factors which can pro- beginning or mid of September after the soil and rocks duce a susceptibility map with higher prediction accur- are saturated and the pore water pressure becomes acy similar to combining many landslide factors using high. In every rainy season landslide events are happen- the mathematical combination theory. ing along the main national road between Goha Tsiyon and Dejen and also at steeply sloping ridges and steep- Mathematical combination theory walled river banks. In mathematics, a combination is a way of selecting members from a grouping, such that the order of selec- Theory tion does not matter unlike permutations. In smaller Frequency ratio method cases it is possible to count the number of combinations. The assumption of conditions that are similar to the past For example, given three fruits, say an apple, an orange is very important for landslide susceptibility mapping (Lee and a pear, there are three combinations of two that can and Talib 2005). Probabilistic (statistical) approaches are be drawn from this set: an apple and a pear; an apple based on relationships between each landslide factor and and an orange; or a pear and an orange. More formally, the distribution of past landslides (Lee and Talib 2005) a k-combination of a set S is a subset of k distinct ele- and this relationship can be evaluated quantitatively using ments of S. If the set has n elements, the number of k- Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 12 of 17 Figure 6 Rainfall amount of (a) annual rainfall (b) average rainy season rainfall of the four stations in the study area. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 13 of 17 combinations is equal to the binomial coefficient (http:// approach in order to select and combine different num- en.wikipedia.org/wiki/Combination) as follows. ber of landslide factors among the eight landslide fac- tors. The possible numbers of combinations of 8, 7, 6, 5, nnðÞ −1 …ðÞ n−k þ 1 4, 3 and 2 landslide factors from a set of 8 landslide factors ¼ ; ð2Þ k kkðÞ −1 …1 are 1, 8, 28, 56, 70, 56 and 28 respectively totaling to 247 possible combinations (Table 2). This can be written using factorials as: Result and discussion n! ð3Þ In order to apply the frequency ratio model, the most k!ðÞ n−k ! important first step is to prepare a database of landslide Where k ≤ n, and which is zero when k > n. factors and a landslide inventory map. This involves Combinations refer to the combination of n things digitizing polygon features like lithology, land use and taken k at a time without repetition. landslide inventory; line feature like lineaments and riv- In combination, the ordering of selected objects is im- ers and preparing digital elevation model (DEM) deriva- material. The current study applies the combination tives such as slope, aspect, profile and profile and plan Table 2 Representative combinations of factors from each group giving the best landslide susceptibility maps using frequency ratio method No. Selected frequency Prediction # of landslide # of possible Min LSI (b) Max LSI (a) Difference ration maps accuracy (%) factors used combinations (a-b) 1 sl+as+pr+pl+li+lu+dl+dr 87.6 8 1 2.54 38.95 36.41 2 sl+as+pr+pl+li+dl+dr 86.2 7 8 2.46 29.73 27.27 3 sl+as+pr+pl+li+lu+dl 87.7* 1.58 36.59 35.01 4 sl+pr+pl+li+lu+dl+dr 87.6 2.37 37.74 35.37 5 sl+as+pr+pl+li+lu+dr 2.36 36.03 33.67 6 sl+as+pr+pl+lu+dl+dr 2.41 36.66 34.25 7 sl+as+pl+li+lu+dl+dr 87.7* 2.04 32.80 30.76 8 sl+as+pr+li+lu+dl+dr 87.7* 1.92 32.76 30.84 9 sl+as+pr+pl+li+lu 86.9 6 28 1.4 33.67 32.27 10 sl+pr+pl+li+dl+dr 86.1 2.29 28.70 26.41 11 sl+as+pr+pl+li+dr 84.9 2.36 26.81 24.45 12 sl+as+pr+li+dl+dr 86.3 1.79 23.90 22.11 13 sl+as+li+lu+dl+dr 87.6 14.42 26.61 25.19 14 sl+pr+pl+li+lu 86.8 5 56 1.29 32.20 30.91 15 sl+as+li+lu+dr 87.0 1.24 23.69 22.45 16 sl+as+li+dl+dr 86.2 1.28 17.79 16.51 17 li+sl+dl+dr 86.1 4 70 1.17 16.34 15.17 18 li+sl+lu+dr 86.8 1.07 22.46 21.39 19 li+sl+pr+lu 87.0 0.67 26.03 25.36 20 sl+as+pl+lu 86.4 0.77 25.21 24.44 21 sl+li+lu+dl 87.7* 0.27 22.78 22.51 22 sl+pl+li+lu 86.9 0.79 26.05 25.56 23 sl+as+li 85.3 3 56 0.28 12.09 11.81 24 sl+dl+li 86.3 0.27 13.57 13.30 25 sl+as+dr 84.7 1.07 13.42 12.35 26 Sl+li+lu 86.9 0.17 19.86 19.69 27 li+sl 85.0 2 28 0.17 10.64 10.47 28 sl+dr 84.3 0.04 11.13 11.09 Note: sl=slope, as=aspect, pr=profile curvature, pl=plan curvature, li=lithology, lu=land use, dl=distance from lineament, dr=distance from river, LSI=Landslide Susceptibility Index, *=Highest prediction accuracy. a = Max LSI = maximum landslide susceptibility index, b = Min LSI = minimum landslide susceptibility index. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 14 of 17 curvatures in Arc GIS 10. The distance from lineament many researchers (Dahal et al. 2008, Regmi et al. 2010a). and distance from rivers are obtained from multiple ring In this study, the raster maps of the frequency ratio buffering operation. Then all the data should be trans- values for the eight landslide factors were extracted with formed into a raster format with the same geographic landslide and non-landslide points. These are processed in projection and pixel size (30 m). The frequency ratio SPSS statistical software in such a way that landslide rep- model was applied to obtain a weight for each class in resents the presence (1) and non-landslide the absence (0) a certain factor. From the frequency ratio analysis, and each factor’s frequency ratio values were analyzed by slope classes ≥ 20° have shown a strong correlation binary logistic regression in order to check the degree of with landslides. In case of aspect, the southeast, south correlation among landslide factors. Based on this analysis, and southwest facing slopes showed a strong correl- all the correlations between two different landslide factors ation with landslides. For profile and plan curvatures, showed either no or very insignificant correlation i.e. < 0.1 the higher positive values and the lower negative values (Table 3). This suggests that all the factors are independ- showed a strong relationship with landslides. Distance ent from each other and can be used for the combination from lineament and landslides showed a strong relation- to prepare a landslide susceptibility map. ship. As the distance from lineament decreases, the fre- From the set of eight landslide factor maps, 8, 7, 6, 5, quency ratio values become higher. In a the distance class 4, 3 and 2 factor maps are combined to give 1, 8, 28, 56, of 0–200 m, the highest landslide frequency is recorded. 70, 56 and 28 landslide susceptibility maps respectively. From land use classes, barren land, sparse forest and For simplification, however, only a total of 28 landslide grassland classes showed a strong relation with landslides. susceptibility index maps have been selected. Then the Among lithologic units in the area, Mesozoic Lower best landslide susceptibility index map was selected from Sandstone, Tertiary Lower Basalt and Tertiary Upper groups with 8, 7, 6, 5, 4, 3 and 2 landslide factor combi- Basalt showed a strong relationship with landslides. The nations based on high prediction accuracies calculated frequency ratio values were assigned to each factor clas- from success-rate curves of areas under the curve ses and all these raster maps of landslide factors were (AUC). But when there is similarity in prediction accur- added to produce the landslide susceptibility index acy, the difference of maximum and minimum landslide maps based on the mathematical combination theory. susceptibility index values has been used (Table 2). Hence The frequency ratio model has some limitations des- the best landslide susceptibility map can be selected from pite its easiness and simplicity to understand and imple- a combination with the highest prediction accuracy and ment in a GIS environment. Higher frequency ratio the highest difference values and this map was found from values will be found if the area ratio (area percentage) a combination of all landslide factors except distance from is lower than the landslide ratio (landslide percentage) river (Figure 7a). Among the 28 representative combi- irrespective of higher number of landslides in a certain nations of different landslide factors, landslide suscepti- factor class. After the frequency ratio raster maps of all bility maps with the same prediction accuracy of 87.7% the landslide factors are prepared, the next step is to add have been found in spite of the dissimilarity in their dif- these raster maps based on the mathematical combin- ference values. The combination with a limited number ation theory. However, before combining the landslide of landslide factors but having the highest prediction factors it is important to ascertain their independence accuracy of 87.7% was also found from four landslide from each other (Van Westen et al. 2003, Dahal et al. factors, namely slope, lithology, land use and distance 2008). For this purpose logistic regression was applied, from lineament (Figure 7b). In order to show the predic- although the pairwise comparison was preferred by tion accuracy contrasts, seven success-rate curves from Table 3 Correlation matrix of landslide factors Distance from Land use Slope Lithology Aspect Plan Profile Distance lineament curvature curvature from river Distance from lineament 1 −0.085 −0.249 −0.39 −0.076 −0.005 −0.037 −0.062 Land use 1 −0.086 −0.07 −0.058 0.004 −0.008 0.055 Slope 1 −0.002 −0.01 −0.165 −0.294 0.011 Lithology 1 −0.077 −0.002 −0.043 −0.138 Aspect 1 0.015 −0.004 0.007 Plan curvature 1 −0.336 0.005 Profile curvature 1 −0.004 Distance from river 1 Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 15 of 17 Figure 7 Landslide susceptibility maps having the same prediction accuracy from (a) seven landslide factors excluding distance from river (FR_ wo_ dr) (b) four landslide factors including slope, lithology, land use and distance from lineament only (FR_ slliludl). ROC curves were constructed for each group’shigherpre- diction accuracy and difference values (Figure 8). For validation purpose of landslide susceptibility maps, many researchers divided the landslides in their respective study area into two parts based on time, space and ran- dom partitions (Chung and Fabbri 2003). These partitions fall into two categories: prediction (training) landslides and validation (testing) landslides. In time partition, past landslides are classified into landslides that occurred before a certain year X and those that occurred after a certain year X. In space partition, the entire study area is divided into two separate sub areas, A and B, one for prediction and the other for validation. By using the space-partition technique, the prediction model in the study area can be extended into the surrounding areas with similar geology, geomorphology and land use con- ditions. To know how much the prediction can be extended in space Chi et al. (2002) divided the entire study area into a northern and southern sub-areas because of the area's similarity in many aspects. Lee et al. (2007) divided into western and eastern areas for training Figure 8 Frequency ratio Success rate curves for different and validation purposes respectively. In random partition, combinations of landslide factors (FR_ wo_ dr includes all the past landslides are randomly divided into two groups factors except distance from river, FR_ slliludl includes slope, instead of two time periods. lithology, land use and distance from lineament, FR_ all data includes all factors, FR_ wo_prpl excludes profile and plan However, few researchers advocate for another valid- curvatures, FR_ wo_dlprp excludes distance from lineament, ation technique which is based on the comparison of profile and plan curvatures, FR_ sllilu includes slope, lithology existing landslides with the landslide susceptibility map and land use and FR_ lisl includes lithology and slope). and use the success-rate curve of area under the curve Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 16 of 17 (AUC) to assess the prediction accuracy qualitatively landslide factors. On the other hand, different combina- (Lee and Talib 2005; Lee and Sambath 2006; Pradhan tions may result the same and high prediction accuracy. 2010a; Pradhan 2011). The success rate curve explains For instance, the combination from seven landslide factors how well the model and the factor predict landslides (except distance from river) and the combination from (Chung and Fabbri 2003) and it was constructed for the four landslide factors (slope, lithology, land use and representative combinations of seven groups in the study distance from lineament) showed the same prediction area (Table 2). After an overlay analysis of landslides accuracy of 87.7%. This showed that these four landslide with the best landslide susceptibility map, the number factors should have a greater degree of influence in of landslides that fall into each susceptibility class was causing landslides. A prediction accuracy as high as 85% calculated. If the number of landslides is very significant was also possible from a combination of slope & lithology in the high and very high susceptibility classes, then the only. This demonstrates how these two factors are very landslide susceptibility map can be considered accurate much important in causing landslide occurrence. High and reliable to predict future landslides. The prediction prediction accuracy & LSI difference values are used to accuracy that is used for selection of best susceptibility select the best landslide susceptibility map. By selecting map was derived from the success - rate curves. In this 2 to 8 numbers of landslide factors from a set of 8 land- study, the percentage of landslides in each susceptibility slide factors, a total of 247 landslide susceptibility map class were calculated to check the validity of the final combinations are possible. However 28 combinations susceptibility map. For this, all the landslides have been were selected based on higher prediction accuracy from overlaid over the final landslide susceptibility map. In success rate curves, higher LSI difference values and doing so, 0.39%, 1.84%, 9.1%, 32.04% and 56.63% of the through visual inspection of output susceptibility maps. landslides fall in the very low, low, medium, high and very An optimum landslide susceptibility map was prepared high landslide susceptibility classes respectively (Figure 9). from four landslide factors (lithology, slope, land use and distance from lineament) while the best landslide Conclusion susceptibility map was obtained from the combination From this study, we have found that the mathematical of 7 landslide factors excluding distance from river combination theory is an important technique to identify (Figure 7a, b). Both maps have the prediction accuracy the possible number of combinations in the frequency of 87.7% but with different LSI difference values of ratio model. This paper showed that using all landslide 35.01 and 25.51 respectively. In order to highlight the factors in the frequency ratio model may not always prediction accuracy contrasts of landslide susceptibility result in higher prediction accuracy even though the maps from success-rate curves were chosen from the 28 range of values in the susceptibility index map is higher. combinations as shown in Table 2. For example, the combination of 8 landslide factors results Once the most important landslide factors are deter- a prediction accuracy of 87.6%, while the combinations of mined in a certain area, then these can be used to scale all landslide factors except distance from the river pro- up the investigation at the regional level using these vided an accuracy 87.7%. This shows that distance from causative landslide factors. When landslide inventory river is less important as compared to other factors. But map is overlaid over the best landslide susceptibility the landslide susceptibility index (LSI) difference value map, most of the landslides fall in the high and very high always higher in the combination with higher number of susceptibility classes accounting for 88.67% of the Figure 9 Percentage of lndslides in each landslide susceptibility class for FR_ wo_ dr. Meten et al. Geoenvironmental Disasters (2015) 2:9 Page 17 of 17 landslides. Besides this the success-rate of this map is Ercanoglu M, Gokceoglu C (2002) Assessment of landslide susceptibility for a landslide-prone area (north of Yenice, NW Turkey) by fuzzy approach. Environ being 87.7%, proving that the landslide susceptibility Geol 41:720–730, doi:10.1007/s00254-001-0454-2 map from the frequency ratio model in the study area is Farrokhnia A, Pirasteh S, Pradhan B, Pourkermani M and Arian M (2010) A recent quite acceptable. After the best and optimal landslide scenario of mass wasting and its impact on the transportation on Albroz mountains, Iran using geo-information technology. Arab J Geosci. susceptibility maps (Figure 7 a, b) are selected these doi:10.1007/s 12517-010-0238-7 maps are divided into five categories and are expressed Fell R, Corominas J, Bonnard C, Cascini L, Leroi E, Savage WZ (2008) Guidelines as probabilities in qualitative terms of very low, low, for landslide susceptibility, hazard and risk zoning for land use planning. Eng Geol 102(2008):85–98 medium, high and very high susceptibility classes. Using Godt JW, Baum RL, Savage WZ, Salciarini D, Schulz WH, Harp EL (2008) Transient this output, proper planning can be made to prevent, deterministic shallow landslide modeling, Requirements for susceptibility and reduce or mitigate the possibility of future landslide di- hazard assessments in a GIS framework. Eng Geol 102:214–226 Hack JT, Goodlett JC (1960) Geomorphology and forest ecology of a mountain sasters in this area. Creating awareness about the risk of region in the central Appalachians. United States Geological Survey, high and very high susceptible zones to the general pub- Professional Paper 347:66 lic will help to save the lives and properties of the IUGS (1997) Quantitative risk assessment for slopes and landslides- the state of the art. In: Cruden D, Fell R (eds) Landslide risk assessment. Balkema, people. Susceptibility, hazard and risk maps are the Rotterdam, pp 3–12 basis for decision making usually in the form of tech- Lee S, Pradhan B (2007) Landslide Hazard mapping at Selangor, Malaysia using nical countermeasures, regulatory measures or combi- frequency ratio and logistic regression model. Landslides 4:33–41, doi:10.1007/s10346-006-0047-y nations of the two (Pradhan et al. 2011). Lee S, Sambath T (2006) Landslide susceptibility mapping in the Damrei Romel area, Cambodia using frequency ratio and logistic regression models. Environ Competing interests Geol 50:847–855, doi:10.1007/s00254-006-0256-7 The authors declare that we do not have any financial or non-financial Lee S, Talib JA (2005) Probabilistic landslide susceptibility and factor effect competing interests with any individual or institution. analysis. Environ Geol 47:982–990, doi:10.1007/s00254-005-1228-z Lee S, Choi J, Woo I (2004) The effect of spatial resolution on the accuracy of Authors’ contributions landslide susceptibility mapping: a case study in Boun, Korea. MM as a first author, has mostly participated in the whole process including Geosci J 8(No. 1):51–60 field work, data collection, database preparation,compiling the results from Lee S, Ryu JH, Kim LS (2007) Landslide susceptibility analysis and its verification using himself and from PB, taking comments from RY, address the comments and likelihood ratio, logistic regression, and artificial neural network models: case finalize the draft for journal submission after a consensus is reached with RY study of Youngin, Korea. Landslides 4:327–338, doi:10.1007/s10346-007-0088-x and PB. PB has participated from the inception and design of this paper and Ohlamacher GC (2007) Plan curvature and landslide probability in regions helped greatly in data preparation and analysis. RY has also involved in a dominated by earth flows and earth slides. Eng Geol 91(2007):117–134 detailed review of the manuscript before submission. Both authors have Pirasteh S, Woodbridge K, Rizvis SMA (2009) Geo-information technology (GiT) given the final approval of the version to be published. and tectonic signatures: the River Karun and Dez, Zagros Orogen in south-west Iran. Int J Remote Sens 30(No. 2):389–403 Pradhan B (2010a) Landslide susceptibility mapping of a catchment area using Acknowledgements frequency ratio, fuzzy logic and multiple logistic regression approaches. The first author would like to thank Japan’s Ministry of Education, Culture, J Indian Soc Remote Sens 38:301–320, Springer Science and Technology (MEXT) for the scholarship grant to pursue the PhD Pradhan B (2011) Manifestations of an advanced fuzzy logic model coupled with study. Geo-information techniques to landlside susceptibility mapping and their comparison. Environ Ecol Stat. 18-471-493 doi:10. 1007/s10651-010-0147-7. 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