Landslide distribution and size versus relative relief (Shaanxi Province, China)
Haijun Qiu, Peng Cui, Amar Deep Regmi, Sheng Hu, Yuzhu Zhang & Yi He
Bulletin of Engineering Geology and the Environment The official journal of the IAEG
ISSN 1435-9529
Bull Eng Geol Environ DOI 10.1007/s10064-017-1121-5
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Bull Eng Geol Environ DOI 10.1007/s10064-017-1121-5
ORIGINAL PAPER
Landslide distribution and size versus relative relief (Shaanxi Province, China)
1,2,3 3 3 1 1 Haijun Qiu • Peng Cui • Amar Deep Regmi • Sheng Hu • Yuzhu Zhang • Yi He1
Received: 12 April 2017 / Accepted: 4 July 2017 Ó Springer-Verlag GmbH Germany 2017
Abstract The present study aims to investigate the dis- certain size threshold. Below this value, it exhibited an tribution and size of landslides in relation to relative relief. obvious rollover effect. Further analysis has shown that For this, a landslide inventory map of the area was landslide cumulative frequency-area curve is strongly developed from the interpretation of satellite images and influenced by relative relief. The rollover effect is more detailed field survey. From this we could map 331 land- obvious with the increase of relative relief. The exponent slides in Ningqing County (Shaanxi Province). By using of power law correlation gradually increased from 0.993 to GIS and statistical approaches, we studied the coupling 1.872 with increasing relative relief. between landslide size distribution and relative relief. From this the control of relative relief on the rollover effect of the Keywords Landslides size and size distribution Á Satellite size distribution of landslides is obtained. The result shows imagery Á GIS Á Relative relief Á Rollover effect Á China that the landslide frequency-relative relief distribution is unimodal, with majority of landslides occurring in areas with relative reliefs in between 300 and 400. The relative Introduction number density of landslides decreased with the increase in the relative relief; on the contrary, the average area, aver- Landslide is one of the most widespread natural hazards age length and average width of landslide increased with responsible for many fatalities, as well as high levels of the increase in relative relief. The percentage of large-scale economic loss and social damage in many parts of the landslide increased with the increase of relative relief or world annually (Lee and Jones 2004; Mansour et al. 2011; vice versa. In addition, the cumulative frequency-area Massey et al. 2013). In many countries, landslides lead to distributions of these landslides empirically agree well with greater casualties and economic losses than other natural a power-law relation with an exponent of 1.776 above a hazards such as floods, earthquakes, volcanic eruptions, and severe storms (Schuster and Fleming 1986; Alexander 1989; Glade 1998; Guzzetti et al. 2002). Moreover, the occurrence of damaging landslides have substantially increased worldwide during recent decades in developing countries because of rapid population growth, uncontrolled urban sprawl, continued deforestation, and increased & Haijun Qiu regional precipitation in landslide prone areas due to cli- [email protected] mate change (Broothaerts et al. 2012; Conforti et al. 2014; 1 College of Urban and Environmental Science, Northwest Greco et al. 2013). University, Xi’an 710127, China It is extremely important to make clear the size dis- 2 Institute of Earth Surface System and Hazards, Northwest tribution of landslides in order to quantify the occurrence University, Xi’an 710127, China of landslides, as well as to understand correctly and 3 Institute of Mountain Hazards and Environment, Chinese characterize the hazard associated with the regional Academy of Sciences, Chengdu 610041, Sichuan, China landslide distribution and estimate the integrated effects 123 Author's personal copy
H. Qiu et al. of these hazards (Stark and Hovius 2001; Guthrie et al. Regional setting 2008). It is very widely accepted that a landslide of a given size cannot exceed the relief of the landscape in The Ningqiang County is bounded by longitudes which it occurs (Schmidt and Montgomery 1995; 105°2101000E to 106°3501800E and latitudes of 32°3700600N Guthrie et al. 2008). Relative relief, which is taken as and 33°1204200N extending for 3246.8 km2 in southwest the most basic natural geographical factor restricts the Shaanxi province of China (Fig. 1). The area is located in matter and energy of earth surface redistribution (Zhou the cross belt of Qin Mountain in the north and Daba et al. 2012). Numerous studies have taken relative relief Mountain in the south. Elevation in the area ranges from as an important causal factor to analysis the landslide 520 m to 2103.7 m above mean sea level (amsl). The area susceptibility and hazard (Dai et al. 2001;Confortietal. with slope gradients greater than 25° accounts for 58.85% 2014). However, less attention has been given to the of the total study area. The drainage network was generated comprehensive and systematic analysis of the quantita- from the digital elevation model (DEM) using hydrology tive relationship between relative relief and landslide tools of the ArcGIS software. The river network has a size, especially how relative relief can influence the dendritic pattern with 1.4 km-1 drainage density, which frequency-size distribution and its rollover effect. indicates that the area is structurally controlled by a dense Published literature has shown that frequency-size drainage network system (Fig. 1). Landslide occurrence is distribution of landslides generally exhibit power-law related to the drainage system of the area; with majority of scaling over a limited scale range because of the prop- landslides occurring in the proximity to drainage network erty of self-similarity. However, a large proportion of the (Fig. 1). The climate in the area is warm temperate and landslide data sets do not fit a simple power law rela- humid continental monsoon zone, with average annual tionship (Fuyii 1969; Stark and Hovius 2001;Daiand precipitation of 920.54 mm and average temperature of Lee 2001; Malamud et al. 2004a, b; Guthrie and Evans 12.9 °C (from the data of 1961 to 2012). Precipitation is 2004a, b, 2005). Landslide cumulative frequency size most abundant in the months of July–September; with a often departs from the power law relationship and mean annual rainfall of 581.76 mm at the Ningqiang rain exhibit a so-called rollover effect in the low size range gauge (Fig. 2). Concentrated rainfall patterns result in a (Hungr et al. 2008). Typical explanation for the rollover great number of landslides, mostly occurring during is data biasing which suggests that small landslides have intense, short-duration rainfall. Most of the landslides are been undercounted among other things, so artificially located at the southeast aspect, as major rainfall come from reducing the probability of small landslides (Hungr et al. the southeast. 1999;Brardinonietal.2003; Malamud et al. 2004a, b). Tectonically, the study area spans over the south Bashan For example, smaller landslides cannot be inventoried Fold Belt in the Yangtze plate and the north orogenic belt because identification by remote sensing is hampered by in Songpan-Ganzi. Based on the boundary of Jinshan the forest canopy in densely forested areas (Brardinoni Temple-Yangpingguan-Mianxian Great Fault (JYMF), the and Church 2004). But some authors proposed physical south of the county belongs to the Yangtze Plate, and the explanations for the rollover such as soil moisture vari- north belongs to the Songpan-Ganzi orogenic belt (Fig. 3). ability, interaction with topography, overall physio- Lithology in the area varies from south to north and the graphic variables of the landscape, and slope geometry area is demarcated by complex geological structures. The (Pelletier et al. 1997;Turcotteetal.2002; Guthrie and main stratigraphic units are Bikou Petrofabric, Dengying Evans 2004a, b; Guthrie et al. 2008; Hungr et al. 2008). Formation, Longmaxi Formation, Shipai Formation, However, the interaction between rollover effect and Luoreping Formation Maoxian Group Nantuo Formation, relative relief is poorly understood. and Chenjiaba Formation. Quaternary deposits consist of In this paper we have described the interdependent rela- river terraces. A majority of landslides were observed tionship on parameters of landslides based on an inventory within the Bikou Petrofabric. The main rock types are map of 331 landslides using statistical methods and geo- schist, slate, phyllite, shale, conglomerate, siltstone, and graphic information systems. We evaluated the role of rel- spilite. The study area lies within an active tectonic setting ative relief in determining landslide frequency and relative with many fault, thrust and folds. The main geological number density. We have also determined the relationship structures demarcating this area are JYMF, Kuanchuanpu between relative relief and landslide size. Furthermore, we fault and Dazhuba-Xinji fault (Fig. 3). The JYMF passes examined cumulative frequency-area distribution within through the northwestern part of the study area. This area different relative relief, discussed the rollover effect of fre- has also undergone local folding of different scales, dis- quency-area distribution, and elucidated how relative relief playing many synclines, anticlines and continuous folding. is related to the power law exponent. These tectonic features have created many deformation in
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Landslide distribution and size versus relative relief (Shaanxi Province, China)
Fig. 1 Map showing the location of the study area with digital elevation model (DEM) and drainage network. Dots show the locations of mapped landslides
Period, accompanied with the high intensity downward erosion by drainage, is responsible for the landscape of steep slopes, which are very prone to several geo-hazards, including landslides. Thus, landslides, triggered chiefly by prolonged rainfall, earthquakes, and human disturbances, are widespread in the study area and play an important role in the hillslope erosion process and modern geomorpho- logical evolution.
Materials and methods
In the present study we have used the following materials and methods.
Fig. 2 Mean monthly rainfall and temperature in Ningqiang County for the 52-year period from 1961 to 2012 Landslide data the rocks and soil. After the 2008 Wenchuan earthquake, It is recognized that landslide inventories are the simplest many aftershocks have struck the area. The rupture zone of form and most detailed data sets of landslide mapping the Wenchuan earthquake is one of the factors responsible (Wieczorek 1984; Guzzetti et al. 1999; Malamud et al. for the landslides. 2004b). A landslide inventory map of the study area was The area is very sensitive to erosion, with an annual developed through the interpretation of SPOT-5 satellite erosion modulus of 4642 t/km2. The rapid tectonic uplift imagery acquired on 2012 having a resolution of 2.5 m that took place starting from the Tertiary and Quaternary (Fig. 4) and Google Earth aerial imagery from 2014.
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Fig. 3 Geological map of the study area
information on individual landslide events and conducted an intensive field survey (from 2013 to 2014). Most of the inventoried landslides from the remote sensing method were verified from the field investigation, especially close to the road and adjacent areas. Further, we mapped land- slides boundaries in the field with a handheld GPS and added to the inventory with attributes in ArcGIS 9.3 run- ning on a Windows workstation. The length and width were measured using a handheld-laser. The landslide size representing the total disturbed area was measured directly from remote sensing image. In order to minimize errors, two geomorphologists independently identified and map- ped landslides. These two inventories were critically reviewed and merged together. After eliminating the Fig. 4 SPOT-5 satellite imagery acquired on 2012 with a resolution inconsistent records, a database of a total of 331 landslides of 2.5 m in the study area was compiled. In this paper, we have used the term ‘‘landslide’’ to encompass only slides according to Varnes However, in some cases it is hard to clearly identify (1954). The parameters of mapped landslides include area, landslides area and boundaries only through the visual length, width, slope gradient, location, etc. About 97% of interpretation of SPOT-5 satellite images because many the slides are soil landslide. All the slides are recent, active important features of landslides may be obscured partially or inactive. Most of the slides are shallow. The slides with or completely due to dense forest cover. In order to check thickness \10 m account for 98%. The overwhelming the results of interpretation and get more detailed charac- majority of landslides are of small-scale, which account for teristics of landslides that were not visible on SPOT-5 71% of the total number of landslides in this study area. satellite images, we tried to collect the historical They are observed in both natural and excavated slopes.
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Landslide distribution and size versus relative relief (Shaanxi Province, China)
Most of the slides were triggered by frequently severe 1) Where i = 2,….N, we divided the sample sequence rainfall and earthquake. From the collected data, it is seen into 2 section X1, X2,…. Xi-1 and Xi-?1,…. XN. Further- that landslides within the convex slope, linear slope and more, we calculated the average value (Xi1 and Xi2) and concave slope are 41.69, 39.88 and 18.43%, respectively. variance of every section, and then summed the variance of
every section (Si), Methods XiÀ1 XN 2 2 Si ¼ ðXt À Xi1Þ þ ðXt À Xi2Þ 2 i N: ð1Þ The relative relief extraction method i¼1 i¼1 2) We calculated the average value (X) and variance of Relative relief is defined as the difference between the sample (S), maximum and minimum altitudes within a certain cell (Oguchi 1997). In this paper, relative relief is derived from XN the digital elevation data. We extracted the relative relief X ¼ Xt=N; ð2Þ using window analysis method and Neighborhood and t¼1 XN Raster Calculator in the ArcGIS software. Elevation data 2 were derived from the DEM with a resolution of S ¼ ðXt À XÞ : ð3Þ t¼i 30 9 30 m obtained from the 1:25,000 scale digital topo- graphic map using a triangulated network (TIN) model. We 3) We also calculated the mathematical expectation of choose the rectangle window and calculated successively S - Si, i ¼ 2; 3; ...; N the relative relief within 3 9 3, 5 9 5, 7 9 7, 9 9 9, …, EðS À SiÞ¼E½N À 1ði À 1ÞðN À i þ 1ÞðXi1 À Xi2Þ: ð4Þ 61 9 61 grid units. We adopted logarithmic function to fit the relationship between the average relative relief and area According to the Eq. 3, S is 26.01. The best statistical in corresponding analysis window (Fig. 5). As shown in unit associated with the value is when the value of S - Si is Fig. 5, the average relative relief increases rapidly with the the highest. According to the Eq. 1, we calculated the value 5 increase of cell area when the area is less than 4.0 9 10 of Si and further obtained the value of S - Si (Fig. 6). As 2 m . However, the speed of growth becomes slow as the shown in Fig. 6, the maximum of S - Si is associated with area becomes greater than 5.0 9 105 m2. The inflection point number 10, i.e. the 23 9 23 grid. So the area of the point of the speed of growth is the optimal area of statis- best statistical unit is 4.761 9 105, i.e. a cell of tical unit. In this work, we adopted the change point 690 m 9 690 m. Figure 7 shows the relative relief map method to ascertain the inflection point. extracted using the Focal statistic module in ArcGIS soft- We assumed that there exists a sample sequence X, ware with the unit area 690 m 9 690 m. We then per- where X is logarithm (base 10) of average relative relief formed a statistics analysis on the landslide and GIS derived form 3 9 3, 5 9 5, 7 9 7, 9 9 9,…,61 9 61 grid database to explore the relationship between landslide size units, respectively. distributions with respect to relative relief.
Fig. 5 Plot of the average relative relief versus area in corresponding analysis window. Solid line is best-fit regression line, which has Fig. 6 Change curve for the difference value between S and Si. Si is logarithmic form the variance of every section of sample. S is variance of sample 123 Author's personal copy
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Results
Dependency relationship of the size parameters of landslides
In order to model the empirical correlation between the volume and area for multiple orders of magnitude, we adopt a power law equation of the form V = e 9 Aa to fit the empirical data in log–log coordinates. Figure 8a shows the empirical relationship between landslide volume (V) and area (A) of 331 landslides in this study area (V = 0.5448A1.2287)(R2 = 0.829, P value\0.01). The area and length (L) obey the power law relationship: (A = 4.167L1.6858)(R2 = 0.8626, P \ 0.05) (Fig. 8b), Fig. 7 Relative relief (m) and mapped landslides in the study area. while area and width (W) correlate with a power law The size of white circles represent the landslide area relation (A = 3.098 W1.7421)(R2 = 0.8505, P \ 0.05) (Fig. 8c). However, there is no liner or other power law relationship between area and Length/Width (L/W). It is Relative number density seen that L/W tends to decrease with an increase in the area from qualitative perspective (Fig. 8d). With the increase of The relative number density of landslides was calculated: area, L/W decreases and is limited to the curve L/ N =S N =N -6 RND ¼ i i ¼ i ; ð5Þ W =-9 9 10 A ? 4.7683. N=S Si=S where, RND is relative number density; S is the total area The landslide size distribution within the relative relief map; N is the total number of All the landslides area occurring within the study area landslides (within the relative relief map); Si is the area in ranges from 48 m2 to 0.3 km2, with an average size of each class of the relative relief map; Ni is the number of 2.31 9 104 m2 and a standard deviation of 3.93 9 104 m2. landslide in each class of relative relief map. 3 RND values of 1 indicates an average landslide number Landslides volumes range from as low as 120 m up to *1.4 9 107 m3, with a total volume for all landslides density for a relative relief class; if this value is less than 1, 7 3 then it implies that the relative landslide density is below equal to 5.37 9 10 m . Large and very large sized land- average, while if it is more than 1, it suggests that the slides play an important role in determining the total relative landslide density is higher than average for landslide area, and their length and width in Ningqinag respective relative relief class. County. Approximately 10% of the largest landslides cover 67.92% of the total landslide volume. Ten largest, longest, and widest landslides in the Ningqiang County (3.03% of Frequency-size statistics of landslides total number) account for 25.34, 11.88, and 13.87% of the total landslide area, length, and width, respectively. The 20 There is accumulating evidence showing that frequency largest, longest, and widest landslides in the Ningqiang sizes of landslides obey a power law function in a wide County (6.06% of total number) account for 38.00, 19.41, range of landslide areas (Guzzetti et al. 2002). In this and 22.47% of the total landslide area, length, and width, paper, we used power law correlation to fit cumulative respectively. frequency-area distribution for landslides that exceed a Figure 9 shows cumulative frequency-area distribution minimum area scale. This can be expressed as: of 331 landslides in the study area. The data describing the Àa landslide area demonstrate that there exists an obvious NCL ¼ CA ; ð6Þ L rollover effect at area larger than 4 9 104 m2. Moreover, where, NCL is the cumulative number of landslides with an we used Eq. 6 to fit the cumulative frequency-area distri- area larger than AL, C is constant depending on the local bution, and found that the landslide area larger than 4 2 conditions, AL is the landslides area, and a is a power law *4 9 10 m empirically correlate well with the power exponent. For a cumulative power law correlation, the law relation with an exponent of approximate 1.776. corresponding exponent of noncumulative distribution is Landslides with area lower than 4 9 104 m2 fall below a a ? 1 (Guzzetti et al. 2002). power law relation and flatten rapidly.
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Landslide distribution and size versus relative relief (Shaanxi Province, China)
Fig. 8 Interdependent relationship on parameters of 331 landslides. a Volume and area. The histograms show count of different landslides volume and area intervals, respectively. b Area and length. c Area and width. d Length/width and area
Size distribution of landslides in relation to relative relief
Relative relief restricts the magnitude of regional landslide distribution and is an important variable frequently used in landslide susceptibility analysis. As shown in Fig. 7, the relative relief varies from 0 to 688 m with a mean value of 313.63 m (standard deviation = 119.16 m). In order to get more insight into the relationship between size distribution of landslides and relative relief, the relative relief was divided into seven classes with 100 m size intervals:\100, 100–200, 200–300, 300–400, 400–500, 500–600, and [600 m. With the increase of relative relief, the number of landslides increases at first and then drops (white bars, Fig. 10). Abundant landslides corresponds to the class with relative relief ranging from 300–400 m, and it decreases in both the lower and higher relative relief. About 29.00% of Fig. 9 The cumulative frequency-area distribution for the landslides and its rollover effect in the study area. The landslide area greater the landslides occurred in slopes with relative relief in than approximate 4 9 104 m2 empirically agree with the power law between 300 and 400 m, while the 200–500 m relative correlation with a exponent of approximate 1.776 relief contained 67.98% of the total landslide. We used
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In order to quantify the size distribution of landslides in different relative relief, we grouped landslides into four size classes by area, they are:\103,103–104,104–105, and [105 m3. As there are few landslides in relative relief less than 100 m and more than 600 m (Fig. 10), we further divided the relative relief into 5 classes: \200, 200–300, 300–400, 400–500, and[500 m (Fig. 12a). The percentage of landslides with respect to relative relief whose area is \104 m2 decreases with the increase of relative relief; on the contrary, those whose area [10 m2 increases with the increase of relative relief. Similarly, based on the landslide length and width, the landslides were divided into two types: \100 and [100 m (Fig. 12b, c). With the increase of relative relief, the per- Fig. 10 Proportion of landslide number and relative number density centage of landslide with respect to relative relief whose at different relative relief intervals. Bar chart shows the percentage of landslide relative number within relative relief class. Solid line length and width is less than 100 m decreases while the indicates relative number density of landslides within various relative percentage of more than 100 m increases. Moreover, we reliefs classified the landslides into three classes according to length/width ratio:\0.5, 0.5–1.5, and[1.5. The percentage Eq. 5 to compute the relative number density of landslides of landslides with respect to relative relief whose length/ with respect to relative relief. The graph shows that the width \0.5 decreases with the increase of relative relief, relative number density of landslides reduces rapidly with and those whose length/width [1.5 increases with the increase of the relative relief (solid line, Fig. 10). Maxi- increase of relative relief. The percentage of landslides mum relative number density of landslides presented at with respect to relative relief whose length/width ranges relative relief less than 100 m is 9.24. The minimum rel- from 0.5 to1.5 exhibit an inconspicuous trend. ative number density of landslides presented at relative In addition, the relative relief significantly affects the relief more than 600 m is 0.07. The maximum relative landslide cumulative frequency-area distribution, and the number density of landslides is 141.05 times larger than the rollover effect increases with the increase of relative relief minimum one. However, average landslide length, width as shown in Fig. 13. The observed landslides area plotted and area increases with the increase in relative relief as a cumulative frequency on a log scale shows a very good (Fig. 11), with highest values occurring at a relative relief fit to power law relationship for larger landslide size. [600 m. The average of the largest landslides area, length However, they differ slightly in the exponent of power law and width within the relative relief greater than 600 m is correlation (Table 1). The exponent of power law corre- 7.09, 3.39, and 2.67 times larger than the smallest average lation gradually increased from 0.993 to 1.872 with landslide area, length and width within the relative relief increasing relative relief (see map in Fig. 13 inset). less than 100 m, respectively.
Discussion
Dependency relationship of the landslide size parameters and landslide size distribution
It is seen that there exists dependency relationships among parameters of landslides in the above section. Previous studies mostly focused on the power law relationship between volume and area of landslide (Korup 2005a, b; Guzzetti et al. 2008), but in this paper we found that there also exist relationships between area and both the length and width of the landslide. This suggests that the empirical relationships for landslide size parameters are substantially independent of the local topographic setting. We can use Fig. 11 Average length, width and area of landslides at different the empirical relationship to estimate the volume and area relative relief of individual landslides when the length and width of the 123 Author's personal copy
Landslide distribution and size versus relative relief (Shaanxi Province, China)
Fig. 12 Number percentage distribution of different landslide types on area (a), length (b), width (c), and length/width (d) at different relative relief
Table 1 Exponent of power law correlation for larger landslide size within different relative relief class Exponent R2 P value Relative relief (m)
1 0.993 0.9609 0.01 \200 2 1.122 0.9633 0.01 200–300 3 1.263 0.9751 0.01 300–400 4 1.65 0.9608 0.01 400–500 5 1.872 0.9589 0.01 [500
play an important role in determining the total landslide size.
Fig. 13 Cumulative frequency-area distribution of landslides at Landslide size in response to relative relief different relative reliefs. The inset map shows the slope of power law relation within relative relief class Relief is a significant landscape attribute reflecting the result of uplift and erosion (Schmidt and Montgomery landslide is known. This is very important for regional 1995). Landslides limit and feedback to mountain relief landslide investigation and assessment. Secondly, the and the relief is important geometric conditions that favor results suggest that length/width of landslide tend to the formation of landslides (Bui et al. 2012; Roering 2012; decrease with the increase of landslide area. It is possible Bucci et al. 2016). Relative relief play a significant control that landslide length is restricted by topography but width on the frequency of landslides, and more landslides are is not obvious. Our results also imply that the over- observed in higher relative relief (Pareek et al. 2010). We whelming majority of landslides are of small–scale in the investigated the landslide relative relief-frequency distri- study area; however, the large and very large landslides bution and observed that the majority of landslides occur in
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H. Qiu et al. areas with relative reliefs in between 300 and 400. The exponent depends on local geological and geomorphic landslide frequency-relative relief distribution is unimodal conditions (Van Den Eeckhaut et al. 2007). So further and is similar to one obtained by Bui et al. (2012), but analysis on frequency-size distribution curve shows that the differ from Pareek et al. (2010), who found that landslide relative relief significantly affects the landslide cumulative frequency decreases as relative relief increases for both frequency-area curve, the exponent of power law correla- pre- and post-Chamoli earthquake. We further analyzed the tion gradually increased from 0.993 to 1.872 with coupling between relative number density of landslide and increasing relative relief, and the rollover effect is more relative reliefs, and found the relative number density of and more obvious with the increase of relative relief, which landslides decreases with increasing relative relief. is in accordance with the published literatures (Fuyii 1969; It is well known that landslide occurrence is the result of Guzzetti et al. 2002; Malamud et al. 2004b). The exponent geomorphic evolution process (Stark and Hovius 2001). A of the power law, considered as a general characteristic of landslide in size cannot exceed the relief of the landform landslides, varies generally between 0.96 and 2 (Guzzetti on which it occurs, and larger landslides are certainly et al. 2002). In this article, an exponent of power law inclined to be limited by constrains of slope geometry dependence on area, which ranges between 0.993 and (Schmidt and Montgomery 1995; Brardinoni and Church 1.872, are within the range of earlier published results. 2004; Guthrie et al. 2008). Therefore, we further tentatively We can partly attribute the rollover effect for small put forward that the landslide size may be restricted by landslides to incompleteness of the landslides record due to relative relief. Thus, it can be said that the larger the the fact that small landslides are difficult to recognize in landslide area, the more limited the landform conditions the remote sensing images. However, in this work, it seems (Guthrie and Evans 2004b). There are fewer locations that that the rollover effect in frequency-size distributions are can support the landslide area larger than 4 9 104 m2 in not merely data biasing due to artificially undercounting the study area. As a result, large-size landslide occurs more the small landslides, but represent a physical reflect of the rarely in the low relative relief and the power law portion natural conditions under which the landslides occur demonstrate its inherent landscape limitations. (Guthrie and Evans 2004b). Malamud et al. (2004a, b) We addressed the relationship between the size of examined three well-documented landslide events with a landslide and relative relief in this study area, and found different triggering mechanism, from Italy, Guatemala, and that the average area, length and width of landslide all the USA. They found that the rollover effect also exists. increases with the increasing relative relief. These results Previous studies have also indicated that rollover effect are similar to findings from Bucci et al. (2016), who found of frequency-size distribution may be influenced by that the landslide size increases with increasing relative numerous conditioning factors such as soil moisture vari- relief. In addition, the statistical analysis revealed that the ability, triggering mechanism, material properties, inter- relative percentage of large-size landslides increase with action with topography, etc. (Pelletier et al. 1997; Turcotte the increase of relative relief; however, the relative per- et al. 2002; Hungr et al. 2008), so it should be noted that centage of small-size landslides show a converse trend this study has examined only relative relief. Although the (Fig. 12). This indicated that the landslide size is strongly cause of rollover effect on frequency-size distribution was influenced by the relative relief, and the higher relief will not made totally clear so far, this study does suggest that produce larger landslides on average. relative relief is an important impact factor of rollover effect. Thus, there remains much work to be done in future Relative relief controls on the rollover effect that can provide a comprehensive explanation for under- lying physical basis of the rollover effect, which is Many authors have pointed out that several systems (e.g., described in this paper. sand piles, earthquakes, and landslides) tend to a critical state and exhibits scale invariant and a power law distri- bution of event size stems from self-organized criticality Conclusions (Bak et al. 1988). However, many empirical observations have shown that the rollover of the landslides data depar- The study area within Ningqiang County is intensively ture from the power law relationship for small landslides. affected by landslides. In the present paper, we examine In this research we found that the cumulative frequency- relative relief controls to landslide size and distribution area distribution of landslides empirically agree with the based on 331 landslides gathered through remote sensing power law relationship with exponent 1.776, over the range analysis and field observations. We concluded that the 4 9 104 to 3 9 105 m2. This exponent is close to the range overwhelming majority of landslides are of small-scale; of values published in previous literature, i.e. between 0.96 however, the large and very large size landslides play an and 2 (Guzzetti et al. 2002). It is well known that the important role in determining the total landslide size. We 123 Author's personal copy
Landslide distribution and size versus relative relief (Shaanxi Province, China) showed that landslide distribution and size are significantly activity: the Peloritani Range, NE Sicily, Italy. Earth Surf Proc correlated with the relative relief. Our analysis revealed Land 41(5):711–720 Bui DT, Pradhan B, Lofman O, Revhaug I, Dick OB (2012) Spatial that the landslides are more abundant in the areas with prediction of landslide hazards in Hoa Binh province (Vietnam): relative reliefs between 300 and 400 m. We further noted a comparative assessment of the efficacy of evidential belief that the relative number density of the landslide decreased functions and fuzzy logic models. CATENA 96:28–40 with the increase in relative relief. However, the landslide Conforti M, Pascale S, Robustelli G, Sdao F (2014) Evaluation of prediction capability of the artificial neural networks for size increased with increasing relative relief. 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