城市化Logistic过程的阶段划分及其空间解释--对Northam曲线的修正与发展

城市化过程在宏观意义上是一种Logistic过程,可以采用S形曲线描述。Northam注意到城市人口比重变化的Logistic曲线特征,并且将其分为三个演化阶段。Northam曲线在国内城市地理学研究中具有较大的影响,但其划分结果不尽准确,前因后果也未澄清。借助系统论的有关思想,从城市—乡村人口的异速生长关系出发,导出城市化水平的Logistic方程,揭示城市化过程的理论基础;进而运用导数原理、Logistic曲线的内禀特征尺度以及城市化水平与经济发展水平的关系模型修正并且改进了Northam曲线,得到一个四阶段的划分结果,最后对重新分段的结果进行了地理空间解释。

LOGISTIC PROCESS OF URBANIZATION FALLS INTO FOUR SUCCESSIVE PHASES: REVISING NORTHAM'S CURVE WITH NEW SPATIAL INTERPRETATION

A new pattern of Logistic process of urbanization is illustrated using mathematical transform and exponential laws in this paper.Urbanization course can be described by Logistic curve,which was divided into three stages by Northam(1979): initial stage,acceleration stage,and terminal stage.However,the Northam's is just a phenomenological theory with several defects,e.g.no theoretical basis,no critical scale,etc.The authors demonstrate that the Logistic process falls into four phases.Taking the 50% of urbanization ratio as a tipping point named "urban half",the Logistic curve is divided into two stages: acceleration stage(urban majority) and deceleration stage(urban minority).The tipping point is determined by differential coefficient of Logistic equation through mathematical transform.Then the two stages are respectively divided into two sub-stages by means of the exponential laws with a parameter as characteristic length.The first exponential law coming from Karmeshu's urban-rural population replacement model,which is in fact an equivalent of the Logistic function of urbanization level and can be expressed with an inverse function i.e.X(t)=Cexp(kt),where X(t) represents urban-rural population ratio,C and k are parameters 1/k is just the characteristic length of urbanization time t,which can be turn into an internal scale reflecting the local properties of urbanization course.In order to find an external scale reflecting the whole property of world urbanization in the sense of average,Zhou's model on the relationships between urbanization and economic development level is used as another exponential law,i.e.y=y_0exp(Z/Z_0)=85.6357exp(Z/19.0404),where y denotes the economic development level of a region,and the parameter Z_0=19.0404 is just the characteristic length of world urbanization that can act as an external scale.Taking Z_0/100=19.0404% as one dividing point,the acceleration stage is compartmentalized into two sub-stages: initial phase and acceleration phase;while taking 1-Z_0/100=80.9596% as another dividing point according to symmetry of Logistic curve,the deceleration stages is also curved up into two sub-stages: deceleration phase and terminal stage.Both the acceleration phase and deceleration one can combine to make a celerity phase corresponding to Northam's acceleration stage.The Logistic equation of urbanization is derived from the law of allometric growth of urban-rural population,which is associated with fractal relationships,and fractal dimension is employed to interpret the Logistic course of urbanization falling into four successive phases.Fractal dimension of urban population is a spatial parameter proportional to urbanization level.The higher the urban fractal dimension is,the shorter the internal scale of urbanization.However,the external scale seems to be out of touch with the dimension value of urban population.The idea from fractals provides us with a new insight into the Logistic process of urbanization,but many theoretical problems remain to be solved in the future.