城市人口分布空间自相关的功率谱分析

doi:10.11867/j.issn.1001-8166.2006.01.0001

地球科学进展 ›› 2006, Vol. 21 ›› Issue (1): 1 -9. doi: 10.11867/j.issn.1001-8166.2006.01.0001

研究论文下一篇

城市人口分布空间自相关的功率谱分析

陈彦光 ¹,刘继生 ²

1.北京大学地理科学研究中心，北京 100871；2.东北师范大学城市与环境科学学院,吉林长春 130024

收稿日期:2004-10-18 修回日期:2005-09-28 出版日期:2006-01-15
通讯作者: 陈彦光 E-mail:chenyg@pku.edu.cn
基金资助:
国家自然科学基金项目“城市结构的的空间复杂性研究”(编号:40371039) 资助.

Power Spectra Analyses of Spatial Auto-Correlations of Urban Density: An Application to the Hangzhou Metropolis

Chen Yanguang ¹, Liu Jisheng ²

1.Department of Geography, Peking University, Beijing 100871,China;2.College of Urban and Environment Science, Northeast Normal University, Changchun 130024,China

Received:2004-10-18 Revised:2005-09-28 Online:2006-01-15 Published:2006-01-15

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从理论上可以证明标准的城市人口密度负指数距离衰减模型本质上是一种空间相关函数，基于这种思想对Clark模型进行Fourier变换，可以导出城市人口密度的幂次频谱分布，且功率谱指数理应为β=2^±。负指数与幂指数的这种变换关系暗示了城市地理系统简单与复杂的辩证关系。借助中国杭州市4年的人口普查资料转换的平均人口密度分布数据对上述推论进行检验，发现β渐进式趋近于2但并不约等于2。将β值进一步换算为人口过程的分维D和Hurst指数H，结果表明：城市人口具有长程负相关作用，但这种空间作用显示明确的局域化倾向。目前的城市形态演化模拟几乎无一例外地引入了长程作用，根据杭州人口分布的局域化特征，有关地理长程作用的假设和应用有必要重新探讨。

关键词: 杭州, 城市密度, 城市分形, 局域化, 长程作用, 空间复杂性, 自组织临界性

The standard negative exponential distance-decay relationship of urban population density, namely the Clark empirical law, ρ(r)=ρ₀exp(-br), is proved to be a correlation function reflecting the relation between the center of the city and the point at a given distance. Therefore the Fourier transformation of the urban density should give an index/exponent of power spectra such as β≈2 theoretically. However, when the fast Fourier transformation (FFT) is applied to the urban densities of the Hangzhou metropolis in 1964, 1982, 1990 and 2000 (according to Census time), it turns out to be that the β values vary from 1.44 to 1.80, not often approximating to 2. If the exponential function with power,ρ(r)=ρ₀exp(-br^σ), is employed to fit the urban density data of Hangzhou instead of Clark’s model, the results are the restraint parameter σ values vary from 0.45 to 0.78, not often approximating to 1. A semi-log relation between σ and β values can be expressed as β≈2+0.7 lnσ . Going a further step, the fractal dimension of self-similar curves, D, and Hurst exponent, H, can be given by means of the formulae β=5-2D and D=2-H. The conclusions can be drawn from the mathematical transformations and computations as follows: First, Urban density has a long-distance dependence, but it is passive/negative and tends to become weak with the lapse of time; Second, the action of urban population in space is localized as a city grows. Third, since the Clark model can be derived using entropy-maximizing method, the calculated results imply that the so-called entropy-maximization is only a developing tendency instead of a realistic state. Last but not least, the idea of action-at-a-distance has been introduced into the various urban simulations based on cellular automata (CA) and all that, but the localization of urban population activity means that the long-range effect should be reflected and revised in the light of amplitude-spectra analyses of urban density equation as an auto-correlation function.

Key words: City fractals, Localization, Action-at-a-distance, Spatial complexity, Self-organized criticality, Hangzhou city., Urban density

中图分类号:

F224

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