基于Zipf尺度指数的城市化水平研究
Exploring the Level of Urbanization Based on Zipf's Scaling Exponent
摘要：
城市的等级规模分布遵循齐普夫定律，齐普夫标度指数往往趋于常数1。这似乎是一个普遍的规则。然而，最近的数值试验表明，在一个人口大国，齐夫指数1与高城市化水平之间存在着矛盾。本文采用数学建模、计算分析和反证的方法，揭示了城市化水平与Zipf标度指数之间的数值关系。主要调查结果如下。(1)如果齐普夫标度指数等于1，那么一个人口大国的城市化率很难超过50%。(2)如果齐普夫标度指数小于1，人口大国的城市化水平可以超过80%。结果表明，Zipf指数是城市化动力学的控制参数。为了提高人口大国的城市化水平，需要降低齐普夫标度指数。利用异速生长定律解释了Zipf指数的变化，并利用标度变换证明了不同的城市定义对上述分析结论没有本质影响。本研究为研究齐普夫城市规模分布规律和城市化动力学提供了一种新的视角。
英文摘要：
The rank-size distribution of cities follows Zipf's law, and the Zipf scaling exponent often tends to a constant 1. This seems to be a general rule. However, a recent numerical experiment shows that there exists a contradiction between the Zipf exponent 1 and high urbanization level in a large population country. In this paper, mathematical modeling, computational analysis, and the method of proof by contradiction are employed to reveal the numerical relationships between urbanization level and Zipf scaling exponent. The main findings are as follows. (1) If Zipf scaling exponent equals 1, the urbanization rate of a large populous country can hardly exceed 50%. (2) If Zipf scaling exponent is less than 1, the urbanization level of large populous countries can exceeds 80%. A conclusion can be drawn that the Zipf exponent is the control parameter for the urbanization dynamics. In order to improve the urbanization level of large population countries, it is necessary to reduce the Zipf scaling exponent. Allometric growth law is employed to interpret the change of Zipf exponent, and scaling transform is employed to prove that different definitions of cities do no influence the above analytical conclusion essentially. This study provides a new way of looking at Zipf's law of city-size distribution and urbanization dynamics.
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