京津冀城镇用地空间结构的多分维谱分析

城市形态和城镇体系都具有分形性质,但简单分形模型不能有效揭示城市系统的复杂结构特征及其背后的问题。多分形模型及分析方法是研究城市空间复杂性和描述城市异质性的有效手段。利用城镇建设用地和总建设用地的多分维谱分析,可以发现京津冀城镇体系及主要城市的空间演化问题。主要结果如下：①京津冀总建设用地的全局谱线不正常,代表中心区的谱线收敛过快,而代表边缘区和乡村地区的谱线收敛位置严重越界;②局部谱线单峰左偏,左(趋向中心区)高密、右(趋向边缘区)低疏,且右边数值越界;③多分维增长曲线服从二次logistic函数,但不同区域和城市的增长曲线的拐点位置不同。深入分析谱线特征及其异常根源,得出如下结论：①京津冀主要城市的中心区填充过密,没有太多缓冲空间,而边缘区无序扩展,需要通过规划进行优化;②京津冀城市生长以外延扩展模式为主,但河北省总建设用地有中心集聚迹象;③京津冀地区特别是主要城市用地接近饱和,土地扩展速度高峰已经过去,只有河北省部分区域例外。

Multifractal spectral analysis of land use structure of the Beijing-Tianjin-Hebei urban system

Cities and urban systems both bear scale-free properties, from which no characteristic scales can be found for mathematical modeling and quantitative analysis. Therefore, fractal geometry is useful for making scaling analysis. Complex urban systems cannot be effectively described by simple fractal models, but can be characterized by multifractal theory. This paper is devoted to exploring the spatiotemporal features of urban change in the Beijing-Tianjin-Hebei region from 1995 to 2013. Using multifractal parameter spectrums, we can reveal the spatial dynamics of urbanization from the aspects of urban form and urban system. The main findings are as below: 1) The spectral curves of global fractal dimension are abnormal. If q>1 and q→∞, the spectral lines quickly converge to horizontal lines; when q<0 and q→-∞, the spectral lines quickly surpass the upper limit of fractal dimension, 2, which represents Euclidean dimension of embedding space. 2) The spectral curves of local fractal dimension are also not entirely normal. The peaks of the f(α) curves incline to the left, and the left ends of the curves are higher than the right ends. The problem lies in that the curves go beyond the maximum value of 2. 3) Fractal dimension growth curves can be described by the quadratic logistic function. Capacity parameters and inflection points of different fractal dimension growth curves are different. The main conclusions are as follows: 1) The urban fringes are disorderly developed, while the central areas of the main cities in the Beijing-Tianjin-Hebei region is overfilled with construction land, leaving little buffer space. 2) The main mode of urban growth is to expand to the outside region, but there are signs of central agglomeration in the total construction land of Hebei Province. 3) Land use of the main cities is close to saturation, and the speed of land expansion has peaked for Beijing and Tianjin, but not in Hebei Province yet. In short, it is necessary to optimize the land use structure in the Beijing-Tianjin-Hebei region by city planning.