城市人口空间分布函数的理论基础与修正形式--利用最大熵方法推导关于城市人口密度衰减的Clark模型

基于理想地表形态和圆形城市假设,利用最大熵方法导出城市人口空间分布密度衰减的Clark模型(r)=瘢蔼玡xp(-r/r0);进而考虑现实地理条件,引入熵增受限思想,将模型推广为加幂指数形式,即(r)=瘢蔼玡xp(-r/髍0);最后借助北京市的人口资料验证了文中发展的模型.

Derivation and generalization of Clark's model on urban population density using entropy--Maximising methods and fractal ideas

The entropymaximization methodology is used to derive Clark's model which assumes that population density *(r) at distance r from the center of the city (r=0) declines monotonically according to the negative exponential (r)=exp(-r/r0), being based on the hypothesis of a circular city on ideal geosurface.By means of fractal ideas and comparison with Sherratt's model, (r)=exp(-r2/2r20), the exponential is transformed and improved and is expressed as follows,(r)=exp(-ro/ro), where rp is a constant of proportionality equal to the central density, na mely, r(0),r0 is the characteristic radius of a city, and * is a parameter of restriction. The new model is tested and verified by applying it to the s patial distribution of population of the city of Beijing.