中国大陆海岸线随机前分形分维及其长度不确定性探讨

Random prefractal dimension and length uncertainty of the continental coastline of China

一个国家或地区海岸线长度的确定,应首先计算其标度区和分维,然后选用标度区下限附近的量测尺度进行量算。以1∶50万电子地图为基础,在Arc GIS技术支持下选用33种尺度研究中国大陆海岸线的标度区及其盒计维,用手工作业法量测海岸线的量规维,并对中国现行大陆海岸线长度的可靠性进行讨论。结果表明:中国大陆海岸线的标度区在400~0.1 km之间。海岸线量规维和盒计维分别是1.2004和1.0929,量规维比盒计维更能精确表征海岸线不规则程度。杭州湾以南和以北海岸线的量规维分别是1.2565和1.1204。当量测尺度为0.1 km时,中国大陆海岸线的长度约21900 km;当尺度为0.25 km时,长度为18214 km,接近现行海岸线长度。

Coastline can be treated as a random prefractal object whose length is uncertain. Different lengths of the continental coastline of China were promulgated in the last century: 8000 km in 1914, 10537 km in 1935, 14000 km in the 1950 s, and 18400.5 km in 1975, which has been used till now. How long is the continental coastline of China? To determine the coastline length of a country, we should calculate the scaling range and fractal dimension of the coastline first, and then measure the coastline length with the measurement scale at the lower or near the limit of the scaling range. Although many scholars investigated the fractal dimension and the length of the continental coastline of China, yet none of them identified the scale range of the coastline, which led to the results slightly inaccurate. The scaling range of the continental coastline of China on 1:500,000 map from the Google Earth Website was determined with 33 measurement scales, and the box-counting dimension was calculated automatically with the aid of Arc GIS software, while the divider dimension was calculated manually. Reliability of the length of Chinese coastline using popularly today was discussed in this paper. The results show that the scaling range of the continental coastline of China is from 400 km to 0.1 km. Within the scaling range, the box-counting dimension and the divider dimension of the coastline are1.2004 and 1.0929, respectively. Divider dimension represents the irregularity of coastline more accurately than the box-counting dimension because the divider method is the most accurate method to measure the fractal dimension for linear geometric object. The divider dimension of the coastline south of the Hangzhou Bay is 1.2565, and that of north of the bay is1.1204. The length of the continental coastline of China is about 21900 km when the measurement scale is 0.1 km, and 18214 km when the measurement scale is 0.25 km, which is close to the continental length of China(18400 km) used widely today. The measurement scale of 0.25 km is within the scaling range and in the vicinity of the lower scaling range limit, consequently,the current coastline length of China is accurate and acceptable. Our recommendation is that the fractal dimension of 1.2004 and measurement scale of 0.25 km should be annotated when the current coastline length of China is cited.