Abstract: The model of allometric growth relationships between urban area and population, A=aP^b, can be rewrited as A(t)=a₁P(t)^b1 for cities as systems, or as A(k)=a₂P(k)^b2for systems of cities, where A is the land area, P is the population size, a is the proportionality coefficient, b is the scaling factor, t is the time (year), and k is the rank of city k. It was proved that the parameter b has fractal dimension nature and can be expressed as b=D_a/D_p, where D_a is the generalized dimension of urban area,and D_p，the dimension of urban population. With fractal theory related the hierarchical structure of urban systems and the dynamics of urbanization can be analysed. On the other hand，by defining A_s=∑A(k)，P_s=∑P(k), it is easy to have a new model A_s(t)=a₃P_s(t)^b3, so once obtaining RS data of A(k), the value of P_s in year t can be calculated. Going a step further, it is possible to analyse cities and systems of cities and predict the course of regional urbanization by means of integrating the allometric growth models and the RS data into geographical information systems. Allometric analyses of the urban system of Henan, China, are made as examples to show how to use the models advanced in the paper.

Key words: urban system, urbanization, allometric growth, fractal dimension, Henan cities of China

摘要： 将城市人口-城区面积异速生长模型由城市动态相似分析和城市体系的几何测度分析推广到城市体系(总量)的动态相似分析，并据此建立了城镇化水平预测模型，然后以河南省的城市为例说明了有关模型的应用方法，为实现基于RS数据的城市系统地理信息分析和区域城镇化进程的空间监测拓展了思路。

关键词: 城市体系, 城镇化, 异速生长, 分维, 河南城市