Multi-scaling allometric analysis for urban and regional development

The concept of allometric growth is based on scaling relations, and it has been applied to urban and regional analysis for a long time. However, most allometric analyses were devoted to the single proportional relation between two elements of a geographical system. Few researches focus on the allometric scaling of multielements. In this paper, a process of multiscaling allometric analysis is developed for the studies on spatio-temporal evolution of complex systems. By means of linear algebra, general system theory, and by analogy with the analytical hierarchy process, the concepts of allometric growth can be integrated with the ideas from fractal dimension. Thus a new methodology of geo-spatial analysis and the related theoretical models emerge. Based on the least squares regression and matrix operations, a simple algorithm is proposed to solve the multiscaling allometric equation. Applying the analytical method of multielement allometry to Chinese cities and regions yields satisfying results. A conclusion is reached that the multiscaling allometric analysis can be employed to make a comprehensive evaluation for the relative levels of urban and regional development, and explain spatial heterogeneity. The notion of multiscaling allometry may enrich the current theory and methodology of spatial analyses of urban and regional evolution.