城市用地与人口的异速增长和相关经验研究

由于城市土地利用变化涉及的因素多，使获取动态研究研究所需的资料十分困难，所以，用少数几个主要因素定量地表达其变化就显得十分重要。从前人的成果，即以人口表示的城市位序-规模法则和建成区面积表示的位序-规模法则出发，绽绎出城市的用地规模和人口数量呈异速增长。这意味着，如果把整个城市看成是一个生命有机体，那么作为反映城市特征的城市用地规模和城市人口这两个重要变量，就是城市这个有机体的两个器官，他们的增长率是成比例的。还通过这个关系建立了城市建成区面积与市场人口和经济发展水平的数学模式。对我国部分城市的经验研究在一定程度上分别证明了这两经验关系。

The Allometric Growth of Urban Land Use and Population and Its Experiential Research

Urban land use dynamics has been an important issue for LUCC. But as many factors are involved, and for the lack of corresponding time-serial data, dynamic study of urban land use is a hard nut to crack. This article aims at obtaining a function that can describe the dynamic process of the change of urban land magnitude. We start at the rank-size rule by urban population and the rank-size rule by urban built-up area, and derive a mathematical relationship that the land use size of a city and its population observe the law of allo-metric growth, which is derived from biological studies. In other words, when we consider a city as an organism, at least it has two organs, the size of the built-up area and the population of such an area, where the growth rate of the former is in proportion to the growth rate of the latter.Because of the lack of time-serial data of urban built-up area-population, we substitute urban non-agricultural residents for built-up area population and do regression analysis for the allometric growth relationship. Forty cities in China are presented for the case study, and the results verify the theoretical relationship.Then we deduce a function consisted of the size of built-up area, the total population and the GDP (gross domestic product) per capita of the city. It is as follows:lgs = c(lgp + lglgy) + kwhere s represents urban built-up area, p is the total population of a city, y is the GDP per capita of the city, and c and k are parameters. We have presented many large cities including Beijing, Shanghai, and Tianjin etc. as experiential studies, and gained such a function by regression analysis of a time-serial data of those cities. Results show that the function is correctly derived.Our results can be used to predict the size change of built-up area of a city in China that is being in the rapid urbanization.