Scale Effects of the Continental Coastline of China

Scale effects of the continental coastline of China

SU Fenzhen1, *GAO Yi1,2,3, ZHOU Chenghu1, YANG Xiaomei1, FEI Xianyun4,5

1. LREIS, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China; 2. Yantai Institute of Coastal Zone Research, CAS, Yantai 264003, Shandong, China; 3. Graduate University of Chinese Academy of Sciences, Beijing 100049, China; 4. School of Geodesy & Geomatics Engineering, Huaihai Institute of Technology, Lianyungang 222005, Jiangsu, China; 5. Jiangsu Marine Resources Development Research Institute, Lianyungang 222005, Jiangsu, China

Abstract: Spatial scale is a fundamental problem in Geography. Scale effect caused by fractal characteristic of coastline becomes a common focus of coastal zone managers and researchers. In this study, based on DEM and remote sensing images, multi-scale continental coastlines of China were extracted and the fractal characteristic was analyzed. The results are shown as follows. (1) The continental coastline of China fits the fractal model, and the fractal dimension is 1.195. (2) The scale effects with fractal dimensions of coastline have significant differences according to uplift and subsidence segments along the continental coastlines of China. (3) The fractal dimension of coastline has significant spatial heterogeneity according to the coastline types. The fractal dimension of sandy coastline located in Luanhe River plain is 1.109. The dimension of muddy coastline located in northern Jiangsu Plain is 1.059, while that of rocky coastline along southeastern Fujian is 1.293. (4) The length of rocky coastline is affected by scale more than that of muddy and sandy coastline. Since coastline is the conjunction of sea, land and air surface, the study of coastline scale effect is one of the scientific bases for the researches on air-sea-land interaction in multi-scales.

Keywords: scale effect; fractal dimension; coastline; uplift segment; subsidence segment; coastline type

1 Introduction Scale is a premise to understand characteristics of geo-objects and processes of geographical phenomena (Yang et al., 2009). Understanding-degree on Earth System depends on the ob- servation scale. Since coastline is the conjunction of sea, land and air interface, coastline spatial scale effect is one of the scientific bases for the research on air-sea-land interaction in multi-scales. Since various geo-objects in nature present fractal self-similarity, the building

Received: 2011-03-27 Accepted: 2011-05-31 Foundation: Chinese Academy of Sciences Program, No.KZCX1-YW-12-04; National Natural Science Foundation of China, No.40571129; Natural Science Foundation of Jiangsu Province, No.BK2009627; National High Technology Research and Development Program of China (863 Program), No.2011BAH23B04 Author: Su Fenzhen (1972–), Ph.D and Professor, specialized in coastal and marine geographical information system and spatial-temporal data mining. E-mail: [email protected] *Corresponding author: Gao Yi (1982–), Ph.D, specialized in the research on applications of remote sensing and geographical information system. E-mail: [email protected]

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of fractal model plays an important role in spatial recognition. Coastline has been the most traditional research topic in the fractal area. Mandelbrot published his paper “How long is the coast of Great Britain?” in Science in 1967, in which he made unique analysis on the features of coastline, elaborated the uncertainty of coastline length, and put forward con- cepts of fractal and fractal dimension. Then many scientists made further researches on fractal science and established two computation models of fractal numbers: divider method and box-counting method (Mandelbrot, 1982; Lievovich, 1989). The calculated results of different coastlines are as follows: the fractal dimension of Brit- ain coastline is 1.25, Australia 1.13, South Africa 1.02 (Mandelbrot, 1967); the number of fractal dimension of Delaware Bay coastline in US is 1.4(Philips,1986); the fractal dimensions of western coastline of Great Britain is 1.27 calculated by the divider method, Austra- lian southern coastline 1.13, Australian northern coastline 1.19, eastern coastline of Gulf of California 1.15 and western coastline of Gulf of California 1.19 (Carr et al., 1991); the fractal dimensions of coastline of western United States and coastline of eastern United States are 1.0–1.27 and 1.0–1.70 respectively (Jiang et al., 1998); when analyzing the impact of environmental changes on the erosion of Arctic coasts, Lantuit et al. (2009) calculated the fractal dimensions of different segments along the coasts and discussed the impact of scale effects on shoreline erosion and the estimation of organic carbon release; Feng et al. (1997) computed that the fractal dimension of Bohai Bay coastline is between 1.0199 and 1.1255 and studied the geological implication of coastline fractal dimension; Dai et al. (2006) re- searched on the stability and the fractal of arc-shaped coast in South China with the equilib- rium modes classified on the basis of dynamical geomorphology as well as sediment supply; Zhu et al. (2004) conducted systematical research on the spatial fractal characteristic of Ji- angsu coastline by different multi-fractal computational methods; Liu et al. (2004) analyzed the fractal dimensions of coastline by provinces; Zhang et al. (2006) analyzed the fractal dimensions of a certain island with the remote sensing images of different resolution ratios. These studies revealed the fractal characteristics of different segments along the coastline. However, the fractal differences of continental coastlines of China need to be studied in a comprehensive way while spatial variations and the reasons need further research. Mean- while, quantitative interpretations need to be given on some basic questions under the back- ground of great development of coastline in the new period. Such questions include: Impact of coastline fractal characteristics on coastline surveying; fractal influence of yardstick length on the lengths of different coastlines. Such questions constitute the essential basis for scientific management and sustainable use of coastline and its resources. Based on DEM and remote sensing images, multi-scale continental coastlines of China were extracted and the fractal characteristics of different coastline segments were analyzed in light of the distribution of geologic subsidence and uplift areas with the technology of GIS and RS; the fractal characteristics of typical coastlines with their reasons were analyzed through the comparison of sandy coastline, muddy coastline and rocky coastline.

2 Study area and data source

2.1 Study area

The continental coastline of China starts from the Yalu River Mouth in Liaoning Province

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Figure 1 Distribution of DEM and continental coastlines of China and extends to Beilun Estuary in Guangxi Zhuang Autonomous Region (Figure 1). Hang- zhou Bay divides the whole coastline as northern part and southern part. In the northern part, Jiangsu Plain is close to the Yellow Sea; Jiaodong Peninsula and Liaodong Peninsula stand facing each other in north-south contrast; Liaohe River Plain and North China Plain with Liaoxi Plain surround the Bohai Sea; as a result, mountain coasts and plain coasts are inter- laced. In the southern part, hills, mesas and low mountains scattered along the coasts of Zhejiang and Fujian provinces. Thus, the coastline fits the uplifted structures in Zhejiang, Fujian and Guangdong provinces. According to the spatial distribution of uplift and subsidence along the coastline, the continental coastline of China can be divided into five segments (ECCCZTWRI, 1991; Li et al., 2002): Liaodong Peninsula uplift segment, Liaohe River Plain–North China Plain subsidence segment, Shandong Peninsula uplift segment, northern Jiangsu–Hangzhou Bay subsidence segment and eastern Zhejiang–southern Guangxi uplift segment (Figure 1). There is no unified definition for coastline yet. According to the regulations of the Peo- ple’s Republic of China, coastline is defined as the boundary between sea and land at the perennial high spring tide level (GAQS, 2000).That means the 0 m contour line is next to the coastline and they overlap on maps of small and medium scales. Therefore, coastline can be replaced by the 0 m contour line when studying the scale effects of coastline at small and medium scales. 2.2 Data source

The 30-m resolution SRTM1-DEM (https://wist.echo.nasa.gov) is used as basic data (Figure

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1). SRTM is the acronym of Shuttle Radar Topography Mission. From February 11 to 22, 2000, after 222 hours and 23 minutes surveying and mapping of the earth surface by INSAR, Space shuttle Endeavour got 3D radar terrain data for 80% of the earth surface between 60°N–60°S. The data volume was 12TB (Rabus, 2003). Spatial resolutions of SRTM DEM are one second radian (30×30 m) and three seconds radian (90×90 m) with the number of SRTM1 and SRTM3 respectively. Its spatial reference is WGS1984, Volumetric positioning accuracy positioning is ±20 m, and vertical accuracy is ±16 m (Reuter, 2007). Besides, we also collected 33 Landsat TM remote sensing images (http://glovis.usgs.gov/). Imaging time was around the year of 2000, same with the acquisition time of SRTM1-DEM. As a base map for the revision of coastline, Landsat TM helps to ensure the positional preci- sion of coastline.

3 Methodology

3.1 Computation model of fractal dimension

Fractal geometry proposes an invariant—fractal dimension according to the variation of scales, which provides a theoretical basis for quantitative description characteristics of physical geographic objects. Basic model for solution of fractal dimension in complex curves is as follows (Mandelbrot, 1967): 1−D LMGG =× (1) where LG refers to the coastline length measured by yardstick G; M is undetermined constant; G is the length of yardstick; D is the fractal dimension of the coastline to be measured. The following equation can be obtained when natural logarithms of the two sides of equation (1) are taken:

lnLDGCG = (1−+ )ln (2) where C is undetermined constant; slope k=1–D; and k can be calculated from array (LG, G); then the fractal dimension D can be obtained by D=1–k.

3.2 Map scale transformation model

According to regulations of map digitizing and aerosurveying as well as specifications for topographic maps, resolution for digitizing primary scale topographic maps is between 0.3–0.5 mm map units (GAQS, 1997, 1993). After converted into real distance, this value can be used as the yardstick to measure the coastline length. Based on the map unit of 0.3 mm in this study, it can be concluded that yardstick length in map digitizing is 30 m, 60 m and 150 m under the scale of 1:100,000, 1:200,000 and 1:500,000 respectively. Yardstick length G with different map scales Q can be computed similarly (Table 1). In conclusion, transformation model of length of coastline and scales according to different map scales can be established according to equation (2):

⎪⎧lnLDGCG =− (1 )ln + ⎨ (3) ⎩⎪GQQ =×0.3 /1000 where meanings of LG, D and G are the same as that in equation (1); GQ (unit: m) is the length of yardstick under scale denominator Q.

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3.3 Extracting of multi-scale coastlines based on DEM

Based on SRTM1 DEM with the spatial resolution of 30 m and ArcGIS software platform, DEM with different resolutions of G can be reestablished in light of yardstick G in Table 1. Then, 0 m contour line can be extracted under different scales according to different DEM resolutions. After that, coastline length measured by yardstick G can be got after revising the extracted data by superposition of remote sensing images. Lengths of continental coastlines of China as well as the subsidence and uplift segments measured by yardstick G according to different map scales are shown in Table 1.

Table 1 The length of coastline measured by yardstick G according to different map scales

Yardstick length: G(m) Scale denominator: Q L1(km) L2(km) L3(km) L4(km) L5(km) L6(km) 30 100000 1296.7 1625.9 1831.9 1965.9 8934.2 15654.7 60 200000 1214.7 1523.3 1745.4 1863.3 8205.5 14552.3 75 250000 1168.4 1470.0 1686.5 1799.0 7947.2 14071.2 150 500000 1009.2 1318.4 1486.4 1648.1 6776.8 12238.9 300 1000000 953.9 1192.1 1329.3 1480.1 5763.2 10718.5 600 2000000 846.7 1121.1 1202.8 1198.9 5005.4 9375.0 900 3000000 807.1 1048.0 1160.9 1156.2 4347.1 8519.3 1000 – 786.3 1033.6 1133.3 1144.3 4128.0 8225.4 1050 3500000 774.7 1031.4 1122.0 1136.4 4093.2 8157.7 1100 – 770.9 1029.5 1118.6 1123.1 4063.7 8105.8 1150 – 765.5 1028.8 1110.3 1097.7 3898.8 7901.1 1200 4000000 751.6 1023.3 1106.4 1091.6 3853.6 7826.5 1500 5000000 722.0 1003.0 1075.8 1083.0 3622.1 7505.8 1800 6000000 711.0 977.2 1024.1 1035.7 3516.4 7264.4 2500 – 687.6 959.6 952.2 1023.2 3245.1 6867.6 3000 10000000 674.7 947.1 931.9 1001.6 3209.6 6764.9 3500 – 643.3 926.3 917.4 919.9 3075.4 6482.3 4500 15000000 622.0 900.1 890.6 842.5 2986.3 6241.6 6000 20000000 591.8 888.0 841.9 802.1 2531.9 5655.6 7500 25000000 565.3 863.0 825.4 781.1 2508.7 5543.5 9000 30000000 544.7 834.8 816.7 751.5 2488.1 5435.9 15000 50000000 503.0 784.7 784.2 674.4 2300.0 5046.3

*L1: length of Liaodong Peninsula uplift coastline; L2: length of Liaohe River Plain–North China Plain subsidence coastline; L3: length of Shandong Peninsula uplift coastline; L4: length of northern Jiangsu–Hangzhou Bay subsidence coastline; L5: length of Zhejiang–southern Guangxi uplift coastline; L6: length of continental coastlines of China

4 Results analysis

4.1 Analysis on the scale effects of continental coastlines of China

A function graph of L-G (Figure 2) can be obtained from yardstick G and coastline length L in Table 1. The array of continental coastline of China length L and yardstick G fits the curve’s fractal dimension model (1) with a high correlation coefficient of 0.996 (Figure 2a). The coastline length L of continental China decreases with the increasing of yardstick G, but such decrease slows down gradually. The length of continental coastline of China can be calculated in any map scales by using Scale Conversion Model (3). Based on formula (2), a functional equation (Figure 2b) can be obtained by the logarithm of array L-G. If slope of

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curve k = –0.195, then the fractal dimension of continental coastlines of China can be calculated as D = 1–k = 1.195.

Figure 2 Function graph of coastline length L and yardstick length G

The fractal dimension of continental coastlines of China is lower than that of western coastline of Great Britain, but equals to that of Australian northern coastline and western coastline of Gulf of California. The continental coastline of China passes through five segments of uplift and subsidence areas with sub-subsidence areas among uplift areas. In this sense, the integrated fractal dimension of continental coastlines of China proves to be a comprehensive mathematical expression of the coastline’s spatial form. Since the coastline is so long, the composition and form of substances along it have significant spatial heterogeneity.

4.2 Analysis on the scale effects of coastline in subsidence and uplift segments

Functions of L-G (Figures 3a, c, e, g and i) can be obtained from yardstick G according to different map scales and the coastline length L of subsidence and uplifts segments (see Table 1); the function graph of coastline length of the uplift and subsidence segments and yardstick length is ln(L)-ln(G), as shown in Figures 3b, d, f, h and k. The array of L-G of the uplift and subsidence segments also fits the curve’s fractal dimension model (1). The coastline length L of each segment decreases with the increasing of yardstick G, and such decrease slows down gradually (Figures 3a, c, e, g and i). This is similar to that between length L and yardstick G of the continental coastlines of China. Some results are shown as follows: the fractal dimension of continental coastlines along Liaodong Peninsula uplift area is 1.153; the fractal dimension of coastline located in Liaohe River Plain-North China Plain subsidence area is 1.116; Shandong Peninsula uplift segment 1.148; northern Jiangsu–Hangzhou Bay subsidence segment 1.177; eastern Zheji- ang–southern Guangxi uplift segment 1.239 (Figures 3b, d, f, h and k). It can be concluded from the above data that: the fractal dimension of Liaohe River Plain-North China Plain subsidence area coastline is the lowest while that of eastern Zhejiang–southern Guangxi uplift area is the highest; fractal dimensions of the three uplifts areas are higher than that of Liaohe River Plain–North China Plain subsidence segment; fractal dimensions of northern Jiangsu–Hangzhou Bay subsidence segment is significantly higher than that of Liaohe River Plain–North China Plain subsidence area; of the three uplift areas, the fractal dimension of eastern Zhejiang–southern Guangxi uplift segment is significantly higher than those of the other two.

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The scale effect of coastline of uplift and subsidence areas and the difference of fractal dimensions are intensely connected and affected by geographic environments. For the coastline form, geological structure is the inner stress, interaction between land and water is the shaping force, and human development is an important influencing factor. One of the three

Figure 3 Function graph of coastline length L and yardstick length G

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factors will play a dominating role which varies according to geographical positions. Dif- ferent types of rivers flowing into the sea results in distribution variance of sediments, which in turn causes different coastline forms. In subsidence segments, rivers flowing into the sea are far and long while in uplift areas rivers are near and short. As a result, coastlines located in Liaodong Peninsula, Shandong Peninsula and eastern Zhejiang–southern Guangxi uplift areas are winding and the fractal dimensions are high. In subsidence segments, the coastline fractal dimension in Liaohe River Plain–North China Plain is much lower than that in northern Jiangsu–Hangzhou Bay subsidence area due to differences in geologic structures, land features and hydrodynamic forces along the coast. For Liaohe River Plain subsidence area to North China Plain subsidence area: The coastline is located in a transitional zone of hills and sea; the hydrodynamic force and the corresponding transporting capacity of water environment are comparatively strong due to steep slope; since strong transporting capacity of water plays a dominating role in shaping coastline forms, the coastline is relatively flat. For northern Jiangsu–Hangzhou Bay subsidence segment: Since the coastline is located in vast plain, the hydrodynamic force is comparatively weak due to small slope; the coastline is seg- mented severely due to numerous rivers flowing into the sea and various tidal creeks formed as a result of sediment accumulation; so the form of coastline is irregular, indented and fragmentary. For eastern Zhejiang–southern Guangxi uplift segment: Under the cathaysoid tectonic system, coastline is winding and complex due to the combination of NE-SW oriented and NW-SE oriented hills as well as river valleys (Wang, 2007). So the fractal dimension of coastline in this segment is relatively high.

4.3 Analysis on the scale effects of typical continental coastline

Sandy, muddy and rocky coastlines are basic types of continental coastlines of China. So the analysis on scale effects of the typical continental coastline plays an important role for understanding the scale effect of China coastline and helps to study the special heterogeneity of scale effect of continental coastlines of China. In this study, we have chosen three segments of sandy coastline, muddy coastline and rocky coastline with an average straight-line distance of 200 km (Figure 4).

Figure 4 Distribution of typical continental coastlines of China

The segment from the Yantai estuary to Daqing river estuary, located in the transitional area of northern Hebei hills to northern Hebei plain and Luanhe Delta plain, is mainly sandy coast; the segment from Jiangsu Xinyang port to Tongqi canal, located in northern Jiangsu plain, is muddy coast; and the segment from Fujian Niutou Bay to Xinglin reservoir, located

SU Fenzhen et al.: Scale effects of the continental coastline of China 1109 in mountainous area of southeast Fujian province, is mainly rocky coast. The straight line distance of the three segments of sandy, muddy and rocky coastlines are 206.1 km, 216.3 km and 203.5 km respectively. And the coastline lengths of the three segments, measured by yardstick of 30 m on a map at the 1:100,000 scale, are 422.9 km, 302.2 km and 1122.2 km respectively. Therefore, the curve and straight rate of sandy, muddy and rocky coastlines are 2.05, 1.40 and 5.51 separately. It can be concluded that rocky coastline is much tortuous than sandy and muddy coastline. Based on the map scale transformation model (3), coastline length of the three segments measured by yardstick G according to different map scales are shown in Table 2. From the comparison of measured coastline lengths, the function graph of L-G can be obtained as Figure 5.

Table 2 Coastline length of the three segments measured by yardstick G according to different map scales

Yardstick Scale LSandy LMuddy LRock Yardstick Scale denomina- LSandy LMuddy LRock Length: G(m) denominator: Q (km) (km) (km) Length: G(m) tor: Q (km) (km) (km) 30 100000 422.9 302.2 1122.0 1500 5000000 253.0 250.3 439.1 60 200000 375.0 296.7 1021.9 1800 6000000 248.8 244.9 392.1 75 250000 357.2 295.5 996.6 3000 10000000 243.3 235.3 335.1 150 500000 325.6 290.8 858.5 4500 15000000 230.8 229.5 286.5 300 1000000 309.0 278.3 736.8 6000 20000000 228.0 228.4 261.5 600 2000000 289.5 271.0 625.1 7500 25000000 221.0 224.8 241.1 900 3000000 273.8 260.5 530.3 9000 30000000 219.7 221.1 229.1 1200 4000000 263.5 254.8 469.6 15000 50000000 215.5 220.1 227.5

Figure 5 Function graph of L-G of typical continental coastlines of China

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The lengths of the chosen sandy, muddy and rocky coastlines decrease when yardstick increasing, but such decrease slows down gradually. Among the three types of coastlines, length of winding rocky coastline changes fastest. When yardstick reaches a certain value (in this paper yardstick length exceeds 6000 m), coastline lengths of the three segments are al- most the same. As yardstick increases, the coastline length gradually comes to the straight- line distance between its two ends (Table 2 and Figure 5). The fractal dimension of sandy coastline from Yantai estuary to Daqing river estuary is 1.109; muddy coastline between Jiangsu Xinyang port and Tongqi canal 1.059; and rocky coastline from Fujian Niutou Bay to Xinglin reservoir 1.293 (Figures 5b, d, f). From the results, the fractal dimension of rocky coastline is the highest, followed by that of sandy coastline and muddy coastline. Reasons for the differences of fractal dimension among sandy, muddy and rocky coastlines are similar to those between coastlines in uplift areas and subsidence areas. Sandy coastline and muddy coastline are mainly located in subsidence areas or secondary fault ba- sins of uplift areas. With the continuous supply of sediments from rivers along the coastline, and the sediments are transported and scoured by coastal current, the sandy and muddy shorelines tend to smooth. Thus, the fractal dimensions of sandy and muddy coastline are smaller than that of rocky coastline. The causes of the fractal dimension differences between muddy and sandy coastline are closely connected to differences in geological environment, geomorphologic environment, longshore hydrodynamic force, material composition and human development. Since the sample sandy coastline is located in the transitional zone of marine plain and hills, there are many capes and rocks along the coast which affects greatly the coastline form and makes the fractal dimension high. The muddy coastline is located in the vast northern Jiangsu plain. Topography and material composition of plain coastline are comparatively simple and the factor of human development is dominant. So the coastline is straight and the fractal dimension is lower. Besides, fractal dimensions vary significantly due to variations in types of coastline and geographic conditions. To sum up, the form of coastline is influenced by many integrated factors, such as geologic structure, geomorphologic environments, hydrodynamic force, material composition and human development.

5 Conclusions Based on SRTM1 DEM with the spatial resolution of 30 m, multi-scale continental coastlines of China were extracted in this study. And the scale effects of coastlines were further analyzed based on the calculation of the fractal dimension of continental coastlines of China, the uplift and subsidence segments and three typical types of coastlines. The results are shown as follows. The fractal dimension of continental China is 1.195, so the continental coastline of China is of significant scale effects. The fractal dimensions have significant differences among the uplift and subsidence segments. The fractal dimension of coastline in eastern Zhejiang– southern Guangxi uplift area is the highest; while that of Liaohe River Plain–North China Plain subsidence area is the smallest; the fractal dimensions of uplift segments are all bigger than that of Liaohe River Plain–North China Plain subsidence segment; though also located in subsidence area, the northern Jiangsu–Hangzhou Bay subsidence segment is intensely affected by geomorphologic environments and hydrologic factors and accordingly its fractal dimension is higher than that of Liaohe River Plain–North China Plain subsidence area. The

SU Fenzhen et al.: Scale effects of the continental coastline of China 1111 scale effect of coastline has significant differences in light of different types of coastlines. As the conjunction of sea, land and air interface, coastline has significant scale effect and significant spatial heterogeneity according to geographic environments, coastline types and materials supply. In this sense, scale effects cannot be neglected in the research of quantitative description of coastline length, simulation analysis of continental China as well as the study of coastline response to global changes.

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