What on earth is the size of China’s land area in total? No person can answer this question.Indeed,this paper tries to discuss the scale dependency of geographical area measurement rather than the total area of Chinese land.In theory,a country bordering on oceans can be divided into two parts.The main land can be modeled with Koch’s island,and the islands and islets in the marginal seas can be described with the Pareto distribution.The Koch island model suggests that the boundary line of the land area is a fractal line,while Pareto’s law suggests that the size distribution of islands and islets in an ocean is of scaling invariance.A coastline,consisting of bays and headlands,has irregularity at a certain degree,which was discussed by B.B.Mandelbrot in his fractal works.On the other hand,an archipelago is made up of many islands and islets.Zoom in on a smaller portion and it,in turn,will be composed of smaller islands and islets.The distribution of islands and islets does not change with distance.In technical terms,the archipelago is said to be of self-similarity at different scales,that is,it is a fractal set of random phenomena.
A fractal is based on a form of symmetry with scale invariance under contraction or dilation.The scale invariance is known as dilation symmetry or scaling symmetry.Symmetry implies some kind of immeasurable quantity.Because of scaling symmetry,the length of coastline,the area of a country’s land,and so on,cannot be well and truly measured.Measuring the area of a country from space will give a lower total than measuring it from 100 meters away,because of the extra detail at a larger scale.As the scale gets finer,more details(smaller islands or islets) can be picked up.The inevitable conclusion is that the total area of the country appears to increase indefinitely.This is just the scale-dependency of geographical measurements.The essence of land area is similar to that of the coastline length.The result(area or length) depends on the scale at which you make the measurement.Therefore,the land area data of different sources is not always comparable due to different sizes of yard measure,different scales of digital maps and different resolutions of geographical images.
CHEN Yan-guang
. How large is the total land area of China?[J]. GEOGRAPHICAL RESEARCH, 2012
, 31(1)
: 178
-186
.
DOI: 10.11821/yj2012010017
[1] Mandelbrot B B.How long is the coast of Britain?:Statistical self-similarity and fractional dimension.Science, 1967,156:636～638.
[2] 陈彦光。中国的城市化水平有多高？-城市地理研究为什么要借助分形几何学？ 城市规划,2003,27(7):12 ～17
[3] 吴传钧。保土求存。见:吴传钧。重负的大地。北京:人民教育出版社,1994.54～56
[4] 靳尔刚。记写方域。北京:中国社会出版社,2002
[5] 刘宏煊。中国疆域史。武汉:武汉出版社,1995
[6] Batty M.The fractal nature of geography.Geographical Magazine,1992,64(5):33～36
[7] Goodchild M F,Mark DM.The fractal nature of geographical phenomena.Annals of Association of American Geographers, 1987,77(2):265～278
[8] Mandelbrot B B.The Fractal Geometry of Nature.New York:W.H.Freeman and Company,1983
[9] Zhu X H,Cai Y L,Yang X C.On fractal dimensions of China's coastlines.Mathematical Geology,2004,36(4):447～461
[10] 艾南山,陈嵘,李后强。走向分形地貌学。地理学与国土研究,1999,15(2):92～96
[11] Batty M.Cities as fractals:Simulating growth and form.In:Earnshaw R A,Jones H.Fractals and Chaos.Crilly A J.New York:Springer– Verlag,1991.43～69
[12] 朱晓华,曹云刚,杨秀春。中国长江、黄河水系长度的分形标定。人民长江,2006,37(4):75～76
[13] Richardson L F.The problem of contiguity:An appendix of'Statistics of deadly quarrels'.General Systems Yearbook, 1961,6:139～187
[14] 陈彦光。分形城市系统:标度、对称和空间复杂性。北京:科学出版社,2008
[15] Barrow J D.The Artful Universe.New York:Oxford University Press,1995
[16] Takayasu H.Fractals in the Physical Sciences.Manchester:Manchester University Press,1990
[17] Turcotte D L.Fractals and Chaos in Geology and Geophysics(2nd).Cambridge,UK:Cambridge University Press,1997
[18] Lee T D.Symmetries,Asymmetries,and the World of Particles.Seattle and London:University of Washington Press,1988
[19] Mandelbrot B B.Fractal geometry:What is it,and what does it do?Proceedings of the Royal Society of London A:Mathematical and Physical Sciences,1989,423(1864):3～16
[20] Batty M,Longley P A.Fractal Cities:A Geometry of Form and Function.London:Academic Press,1994
[21] 陈彦光,李后强。城市空间体系的Koch(分形)模式-对中心地学说的一种可能的修正。经济地理,1994,14(3):10～14
[22] 叶大年。地理与对称。上海:上海科技教育出版社,2000
[23] 叶大年,赫伟,李哲,等。城市对称分布与中国城市化趋势。合肥:安徽教育出版社,2011
