Research On The Key Issues And Applications Of Urban Scaling Laws From The Perspective Of Complex Theory

Sustainable development of urbanization presents an increasing need for a quantitative and predictive theory of urban organization,and complex theory brings new paradigm for urban science.One of macro emergence behavior of urban complex system,urban scaling law is an accurate mathematical equation reflecting the power law relationship between urban attributes and population,furthermore,mechanisms behind urban scaling law reveal how cities function and evolve.Theoretical and empirical research of urban scaling law receive much attention from different fields.Introducing complex theory as the paradigm,this dissertation is devoted to key factors(urban boundary and urban scaling estimation method)and quantitative application analysis model of urban scaling law.The main contributions of this study can be described as follows.Firstly,a Zipf's law-based method is proposed to define urban boundary of natural cities.Previous methods have utilized visual particularities of cities with ancillary data to obtain the optimal thresholds.How cities behave differently from rural areas should be considered.A Zipf's law-based method is proposed to bootstrap the optimal threshold based on the statistical properties of a Zipf's law model on continuous thresholds at the country scale.In our method,the Zipf's law model is utilized to quantify fractal,self-organized,and agglomeration behaviors of cities.The three-phase cluster dynamics are discovered,and the abrupt transition denotes the rural-urban demarcation point.Validation results based on accuracy assessment,point of interest(POI)data and method comparison verify that the proposed method provide effective and efficient method to define urban boundaries,and the derived urban areas can be a proxy for human activities and behaviors of complex systems.Secondly,aiming at the problem that the heterogeneous variance influences the accuracy of urban scaling estimation,a statistical regression method based on the maximum likelihood estimation considering the lower bound constraints and the heterogeneous variance of error structure is proposed.The heterogeneous properties of variance are explored and modeled in the form of a power-of-the-mean variance model.The maximum likelihood fitting method is supplemented to satisfy the lower bound constraints in empirical data.Method evaluations based on three different criteria validate that compared with classical methods,the proposed method is more effective and robust.Moreover,a statistical test and long-term variations of the parameter in the variance function demonstrate that the proposed heterogeneous variance function can provide more meaningful urban information.Thirdly,aiming at the problem that it is difficult to quantitatively analyze urban efficiency based on the mechanism of urban scale law,the quantitative model and analytical framework for urban goodness value based on the mechanism of urban scale law are studied,while the urban system in China is quantitatively analyzed.This study is based on the social interactive model and transforms the absolute urban efficiency to the ratio with the optimal urban efficiency,which is then defined as the urban goodness value.Therefore,the quantitative model and analytical framework are proposed.The goodness value in both administrative and natural boundaries in China are studied and the interfering factor and the improvement measures are analysed from both internal and external perspectives according to the proposed spatial hierarchical clustering method.