Figure
1.
Landslide inventory map in Chenyulan Creek Basin. (a) Before and (b) after Typhoon Herb in 1996, (c) after Typhoon Mindulle in 2004.
| Citation: | Zon-Yee Yang, Hamid Reza Pourghasemi, Yen-Hung Lee. Fractal analysis of rainfall-induced landslide and debris flow spread distribution in the Chenyulan Creek Basin, Taiwan. Journal of Earth Science, 2016, 27(1): 151-159. doi: 10.1007/s12583-016-0633-4
|
Landslides are the most catastrophic natural hazards and the second most frequent natural catastrophic events, after hydro-meteorological events worldwide (Kouli et al., 2013). In recent years landslide hazard assessment has played an important role in developing land utilization regulations aimed at minimizing the loss of life and damage to property (Wang et al., 2005).
Quantitative estimates of the extent and intensity of triggered landslides might aid in improving our ability to assess landslide risk and mitigate disasters. Predicting the location and quantity of debris deposition is essential in protecting inhabitants in the alluvial fan. If landslide spatial distribution obeys a certain law, it would be very useful for disaster prevention administration, despite the prediction of each landslide is very difficult at present.
Landslide size and location distribution are complicated. The fractal theory was developed to describe the qualities of complex shapes or images in nature. Fractal theory was first introduced by Mandelbrot in 1967. It is a simple and generalmethod for solving complex problems and phenomena (Mandelbrot, 1967). Fractals are spatial objects whose geometric characteristics include scale dependence, irregularity, and self-similarity (Shen, 2002). The fractal theory is an alternative approach for studying the landslide problem. Rouai and Jaaidi (2003) presented landslide distribution in the Rif Mountains of Morocco. They found that the frequency of landslide occurrence as a function of their size can be described using a power law. Guzzetti et al. (2002) presented that the power-law distribution in a landslide area is valid over a wide range of landslides. This confirms that a landslide area may exhibit self-similar and fractal behavior. Moreover, Ueno et al. (1993) and Yokoi et al. (1996) indicated that the landslide block distribution inside a huge landslide has a self-similar geometry. That is, each small landslide within a huge landslide region (> 1 km2) can be considered a reduced-scale image of the entire landslide. The shapes of successive landslides on different scales for a region are similar and repetitive. This self- similarity can be expressed using a fractal dimension.
Tarutani et al. (2002) used fractal dimensions to identify the spatial distribution of rapid shallow landslides in the case study on the Amakusa Island (Japan). In their study the fractal dimension (D) values ranged between 0.81 to 1.16, which shows a linear pattern due to parallel strata distribution (sedimentary rocks and faults). Cello et al. (2006) assessed relationship between earthquake magnitude and the fractal dimension of seismic faults in the central Italy. The fractal dimension of different faults was obtained using the box-counting algorithm. According to this research, it is possible to obtain information on the seismogenic potential of a specific area using the fractal dimension of active faults.
Fan and Qiao (2006) evaluated equality, Poisson and fractal distributions to model the time distribution of recurrent landslides in the Three Gorges region of China. They indicated similarity and hierarchy in landslide occurrence in the fractal, as the scale spectrums for whole landslides were 2.4-4.2 and the size ranks were 1.98-5.84. Malamud and Turcotte (2006) have considered the frequency area statistics of three natural hazards such as wildfires, earthquakes, and landslides. In the mentioned research, they were used of robust power laws. The results showed that the power-low exponent of the frequency- area distribution of clusters is related to the fractal dimension of cluster shapes.
Wu et al. (2009) used fractal dimensions to assess slope instability for landslide boundary trace. Their results showed that landslides with larger fractal D did not have a stable state in view of the boundary trace. Sezer (2010) presented a computer program (FRACEK) to calculate the fractal dimension for various mass movement applications. According to the results of Sezer (2010), a clear difference exists between 116 mass movement events such as debris flow, rotational and translational failure. Li et al. (2012) used the spatial fractal clustering distribution of landslides and landslide susceptibility mapping implemented using fractal theory in Zhejiang Province, China. Pourghasemi et al. (2013) tried to assess the fractal dimension (D) and the geometric characteristics (length and width) of landslides identified in northern Tehran, Iran. The results showed that the fractal dimension for 528 landslides varied between 1.665 and 1.968. Also, in this research the relationship between the length/width ratios and their fractal D values of landslides were calculated. The results stated that correlation coefficients (R), for different regression models such as exponential, linear, logarithmic, polynomial, and power, were 0.75, 0.75, 0.76, 0.78, and 0.75, respectively.
Many severe landslides (including slides, slumps, avalanches and debris flows) have been reported in Taiwan (Chang and Slaymaker, 2002; Lin and Jeng, 2000; Wu et al., 1989). The frequency of landslides (number of landslides per unit area) is 0.27 /km2 and the intensity of landslides (area of landslide per unit area) is 0.84 ha/km2 (Wu et al., 1989). Slope failure associated with annual high intensity precipitation from typhoons occurs on structurally weak rocks. Chang and Slaymaker (2002) showed that the heavy rainfall accompanied with extreme typhoons in Taiwan is responsible for landslide activity acceleration. In recent years, many destructive landslides have occurred in the Chenyulan Creek Basin after heavy rainfall from several strong typhoons.
In 31 July and 1 August 1996, Typhoon Herb caused to intense rainfall almost 780 mm/hr, and subsequently 1 094 mm fall in 24 h in Taiwan (Lin and Jeng, 2000). Herb caused 1 315 landslides in central Taiwan. There were 73 deaths, 463 wounded and 1 383 houses destroyed. The heaviest rainfall occurred in the Chenyulan Creek Basin with a maximum 1 day rainfall intensity of 610 mm and a maximum 1 hour intensity of 74 mm recorded. The Chenyulan creek drainage basin suffered the most severe hazards including landslides and debris flows (Lin and Jeng, 2000). This creek basin was selected as the study area in this paper. Lee (1996) had determined two figures of landslides in Chenyulan Creek Basin from SPOT images before Typhoon Herb (see Fig. 1a) and after typhoon Herb (see Fig. 1b) in 1996. The number of landslides is about 51 before Herb and 251 after Herb.
Typhoon Mindulle on June 29, 2004 introduced a high-intensity, high-accumulation storm that dumped more than 1 600 mm of rain in central and southern Taiwan from 2-4 July. The most severe rainfall event with a maximum 1 day rainfall intensity of 416 mm and a maximum 1 hour intensity of 68 mm occurred in the Chenyulan Creek Basin. The rainfall intensity was less than that of Typhoon Herb. It caused flooding and triggered more than 14 800 landslides and 130 debris flows in Central Taiwan (Chen and Petley, 2005). This paper determined the landslides from SPOT image for Chenyulan Creek Basin after Typhoon Mindulle as shown in Fig. 1c.
The current research studies the landslide distribution advancement expressed by landslide area size and the distance between every two landslides in 1996 and 2004 for the Chenyulan Creek Basin.
Taiwan is geologically very active, formed on a complex convergent boundary between the Yangtze subplate of the Eurasian Plate to the west and north, the Okinawa Plate to the north-east, the Philippine Plate to the east and south, and the Sunda Plate to the southwest. The study area is located in the central part of Taiwan between longitudes 120°48′08″E and 121°00′10″E, and latitudes 23°27′44″N and 23°45′59″N (Fig. 2). It covers an area of about 450 km2. The altitude of the area ranges from 308.6 to 3 816 m a.s.l.. While the slope varies from 0° to as much as 69°. This study area is generally hill slope or mountainous and its lithological units are sandstone or shale alternative. The sandstone has different ages and strengths. The altitude of hill slope is less than 1 000 m. Meanwhile in the central mountains, it ranges of 1 000-3 000 m with lithological units, mainly cover of sedimentary and metamorphic rocks.
The Chenyulan Stream originates from the north peak of the Yu Mountain, with an elevation ranging from 310 to 3 952 m a.s.l., with an average slope of 5% from the riverhead to the debouchure. The river is 42.4 km long and its drainage basin area is about 450 km2 with a mean annual rainfall of about 3 000 mm.
The Chenyulan River in central Taiwan closely follows the Chenyulan fault line. The Chenyulan fault is a major boundary fault in Taiwan. The Chenyulan fault separates the Neogene sedimentary rocks of the western foothills from the Paleogene metamorphic rocks of the Hsuehshan Range (Lin and Jeng, 2000). Differential uplifting along this fault has generated abundant fractures that result in frequent landslides (Lin et al., 2003).
Figure 3 shows the methodology used in this study, as a flowchart. Before performing the image analysis by eVision software (eVision 2.1 software, 2011, www.euresys.com), the aerial photography of landslides is edited by PhotoImapct software. The regions of landslides are first painted in black and the outside regions of each landslide are removed and painted in white. Then, adjust the landslide to its real size according to the scale of the photo. The photo in white/black color is saved in a TIF format that is available to eVison software. Using these sizes of landslide areas and centroid coordinates of landslides, a FORTRAN program is adopted to count the number within each specified scan distance and to calculate the distances between each two landslides.
A picture of the landslides interpreted in a photo (Fig. 1c) for the landslide after Typhoon Mindulle is first transformed into a white and black picture using PhotoImpact software. The eVision image processing software was used to obtain the landslide geometrical data, such as the area, size and landslide center (Fig. 4). eVision is (data system imaging Co., Ltd, DSI) agents Euresys set of image analysis software for measurement, identification, marking detection, gray-scale and color image analysis (eVision 1.2, 2011, www.euresys.com).
The black region in this picture is the landside area. For each landslide, the landslide area is calculated based on the pixel percentage of individual black regions in a specified scale. The central coordinates of each landslide area are determined to represent the location of the landslide using eVision. Fractal dimensions of the landslide area in different sizes and distance distribution were calculated from these data (landslide area distribution) and the central coordinates.
In fractal theory the box-counting method is used to estimate the fractal dimensions of a planar set. This method uses squares or boxes (grids) of various sizes, placed over a figure to compute the box dimension in two-dimensional space. The equal sized boxes required to cover the picture are numbered (Fig. 5a). The number of boxes required to cover every portion of the fractal object is dependent upon the box width. As the box size (d) decreases, the number of boxes (N) grows according to a power law
|
N∝d−Db |
(1) |
The exponent (Db) in this power law is the box dimension, a real number that characterizes the level of complexity of the fractal shape. This fractal dimension reflects how rapidly the complexity develops as the box size decreases. The greater the fractal complexity of a figure, the higher is its fractal dimension. The box dimension value for a grain in a two-dimensional space is less than 2. Very roughly, the box dimension provides a description of how much space the set fills.
This box covering and counting concept is very similar to the sieve analysis procedure in soil mechanics (Yang and Juo, 2001). In sieve analysis a series of sieves with different sized openings are used (Fig. 5b) to determine the particle size distribution. The particle size data are presented in a semi- logarithmic plot to obtain the particle-size distribution curve. If the data shown in a classic particle-size distribution curve form are re-plotted on a double-logarithmic scale, a good linear relationship between the cumulative passing percentage and the particle sizes can be achieved. The fractal dimensions (box dimension) of this particle collection can be calculated from this log-log plot. The fractal dimension (Db) of the gradation is calculated from the slope of the linear regression, Db=3-slope in three dimensional space. In two-dimensional space the fractal dimension is subtracted one, i.e., Db=2-slope.
The relative complexity of the particle size distribution is described in addition to the gradation. A grain collection with a larger fractal dimension value implies that the grain size distribution is more complicated. This box dimension is used to study the complexity of the landslide area distribution.
One way to demonstrate spatial fractal is to examine the distance distribution between a pair of points, i.e., the center of the landslide area using a two-point correlation function (Coughlin and Kranz, 1991; Kagan and Knopoff, 1980), in a data set over a range of distances. The two-point correlation function C(R) is expressed as
|
C(R)=2×N(r<R)n(n−1) |
(2) |
where, R is the distance that landslide points to be considered in this region (we counted those landslides within the R distance (distance < R) for each time or period). N(r < R) is the number of point-pairs with a distance r less than R. The total number of points in this region is n. If N(r < R) is proportional to a power function to R in a power-law, function, then a regression relationship of logC(R) versus logR should be linear. For the range of R over which it is linear, the point pattern (landslide distribution) can be considered self-similar or fractal. The slope of this regression line is called the two-point correlation dimension of the point distribution. For a random distribution of points, the fractal dimension is 2 in a two-dimensional space (Coughlin and Kranz, 1991). Fractal point patterns with slopes less than 2 display clustering (landslides concentrate within a small region, not distributed over a large region), and the degree of clustering increases with the decrease in the two-point correlation dimension.
Three examples of different artificial landslide distribution types are displayed in Fig. 6. In case (a), the landslides are clustered in some limited region. In case (b) the landslides are distributed everywhere. The two-point correlation dimension (Dcorr) is calculated using Eq. (2). It demonstrates that the landslides with a lower correlation dimension value (Dcorr=1.57) are more clustered than that with a higher value (Dcorr=1.81). The distribution in case c has a higher correlation dimension and it is close to the random distribution type.
Three landslide examples identified from aerial photography in 1996 and 2004, as shown in Fig. 1, are analyzed in this study. These three examples occurred in the same landslide system and geological circumstance of the Chenyulan Creek Basin. It was found that using eVision the total number of landslides was about 40 before Herb and increased to 189 after Herb in 1996 (Fig. 7).
The distance in between two landslides (a pair of landslides) is calculated using central coordinates of their landslide area. The distribution of a pair-landslide distance is plotted in Fig. 7. It shows that the mean distance between two landslides in the Chenyulan Creek Basin is 10.9 km before Typhoon Herb in 1996 and 11.7 km after Typhoon Herb. In 2004, after Typhoon Mindulle, the mean distance increased to 12.23 km. Before Typhoon Herb in 1996, the landslides were limited within a special region. However, prior to 2004, the distance in between two landslides increased. This means that the landslide distribution scope tended to expand. For each example the relationship between a two-point correlation function C(R) and scan distance R is plotted in Fig. 8. It shows that the linearity of the fit line is very good. This indicates that the distance distribution in between landslides exhibits fractal behavior. The slope value of the best fit line is its two-point correlation dimension (Dcorr). The correlation dimension (Dcorr) is used to describe the relative distribution behavior between landslides. The correlation dimension (fractal dimension) is 1.15 before Typhoon Herb in 1996 and 1.28 after Typhoon Herb. From 1996 to 2004, after Typhoon Mindulle the correlation dimension was 1.32. As shown in Fig. 9, this correlation dimension increased gradually from 1996 to 2004. This implies that the landslide distribution of the Chenyulan Creek Basin in 1996 was clustered within limited regions and in 2004 became distributed arbitrarily.
The area of each landslide in the previous three examples (Fig. 1) was obtained using eVision software. The landslide area size distribution is plotted in Fig. 10 in the form of a particle size distribution curve, as used in soil mechanics.
From this landslide area size distribution curve, the mean size (%finer equals 50%) is obtained as a percent of finer equaling to 50%. The mean landslide area was about 80 000 m2 before Typhoon Herb and 60 000 m2 after Typhoon Herb. Moreover, the mean size decreased to 12 000 m2 in 2004 with Typhoon Mindulle. This indicates that from 1996 to 2004, although the number of landslides increased, the mean size of the landslide area decreased in the Chenyulan Creek Basin. This implies that new and smaller landslides developed gradually in this basin.
In order to explain this landslide size distribution behavior using the fractal concept, each the landslide area size distribution curve in Fig. 10 is drawn in a double logarithmic plot (Fig. 11). In these three plots the high root-square (R2) value reveals that the linearity of the fit line is very good. This implies that the landslide area distribution exhibits fractal behavior. That is, the relationship between the landslide size and number of landslides distributes according to a power law. The box dimension (Db) is thus obtained using the slope linear fit line value (i.e., Db=2-slope). The box dimension value responds to landslide density occupied in a two-dimensional space was 0.3 before Typhoon Herb in 1996 and was 0.53 after Typhoon Herb. Five years later, in 2004, Typhoon Mindulle showed an increased box dimension of 0.69. This increasing box dimension behavior (a fractal dimension) means that the landslide area occupied in this creek basin gradually increased (Fig. 12) from 1996 to 2004. This implies that the unstable slopes became more diffuse and extensive after every successive typhoon during this period.
This research used Fractal dimension to describe the rainfall-induced landslide and debris flow distribution spread in the Chenyulan Creek Basin, Taiwan. Three landslide distribution examples in the Chenyulan Creek Basin before and after the 1996 Typhoon Herb, and after 2004 Typhoon Mindulle were analyzed. In general, the mean landslide area size decreased, which implies a great number of small landslides were generated.
According to the fractal analysis, it showed that both the landslide area size distributions and distance in between landslides were fractal in this region followed the power-law distribution, indicating a fractal behavior. The increase of landslide area distribution described by box dimension means the landslide occurrence gradually increased and the landslides became more active from 1996 to 2004. The increase in correlation dimension between every two landslides indicates that this landslide site distribution became successively more diffuse and extensive. Usually, the larger box dimension implies that there are various sizes of landslides in a single event. In conclusion, the fractal dimension is a useful alternative index to describe the complexity of the two-dimensional landslide spatial distribution.
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Zon-Yee Yang, Hamid Reza Pourghasemi, Yen-Hung Lee. Fractal analysis of rainfall-induced landslide and debris flow spread distribution in the Chenyulan Creek Basin, Taiwan. Journal of Earth Science, 2016, 27(1): 151-159. doi: 10.1007/s12583-016-0633-4
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