中国城市规模分布实证研究————基于微观空间数据和城市聚类算法的探索

齐普夫定律反映了城市规模与其位序之间简单而准确的关系，也是研究判别城市集聚和城市体系合理性的重要原则。关于齐普夫定律中城市的定义一直颇有争议，由于传统的空间研究尺度过于宏观，不能反映出真实的城市规模，学术界逐渐开始将眼光转向微观空间尺度，突破传统的行政区划界限，研究真正起到城市功能的微观城市组团。引入国外研究用于划分城市界限的新方法--城市聚类算法，对中国微观空间数据进行处理，以得到的功能性城市组团作为研究对象，根据齐普夫定律对中国城市规模分布进行分析，结果表明中国城市规模分布基本上服从齐普夫定律。此外，将基于城市聚类算法的城市规模分布研究结果与中国地级、区县级和乡镇街道级空间层面的研究结果进行比较，证实了城市聚类算法是研究城市规模分布的一种较好的新方法，它成功架设了宏观层面和微观层面研究之间的桥梁。

The Empirical Research on China's City Size Distribution :An Exploration Based on the Micro Spatial Data and City Clustering Algorithm

Zipf's Law is an important principle to determine city agglomeration and urban system rationality,which reflects the simple and accurate relationship between city size and its rank . Since the definition of cities in Zipf's Law has roused much controversy due to the too macro spatial scale that cannot exactly reflect the actual city size,scholars have moved on to the functional urban areas (city clusters) at the micro level,which breaks down the traditional administrative boundaries . To solve this problem,this article introduces a new method of defining city boundaries from abroad-City Clustering Algorithm to analyze China's city size distribution,that is,a″city″is defined as a maximally connected cluster of contiguous populated sites within a prescribed distance l and above a population density cutoff threshold D .These established city clusters are used to analyze China's city size distribution,with the sum of population of all populated sites within each city cluster as its population .The main findings of this article are shown as follows :First,China's city size distribution basically obeys Zipf's Law,indicating that the urban system based on employed population has a rank-size distribution,namely,a relatively balanced development of cities with different ranks .Second,by comparing the results of the city size distribution based on City Clustering Algorithm and the results at different scales of prefecture-level cities,counties,townships and streets,it has been proved that City Clustering Algorithm is an effective method to study the city size distribution,which breaks down the traditional administrative boundaries and makes up for deficiencies at both the macro (underestimating the number of small city clusters with a small sample of cities) and the micro (overestimating the number of small city clusters with data errors) level .Third,this method can reflect actual city sizes,making the results more scientific and reasonable;the effectiveness and robustness of this method have been verified by the related analysis of US,Great Britain and China (this article) .Last but not least,with regard to China's current new era of the urban and rural dual structure in transition and the abolishment of the boundaries between urban and rural areas,it is of great significance to define the urban functional areas (or city clusters) according to certain rules (just like the combination of the distance threshold and the population density threshold in this paper) and to set up China's cities based on the urban functional areas . However,there are two main deficiencies in this study :One is the lack of data accuracy at the micro level,which is obtained by matching the employment data of the second (2008) economic census data and the spatial map at the level of townships and streets in 2000 after data correction;the other one is lack of population data at the micro level,making it impossible to be compared with the result of employment data at the micro level .